LMFDB - Embedded newform 177.8.a.b.1.10

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			1.10
Root			$2.41303$ 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)

$f(q)$	$=$	$q+0.413031 q^{2} +27.0000 q^{3} -127.829 q^{4} +231.152 q^{5} +11.1518 q^{6} +302.150 q^{7} -105.665 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+0.413031 q^{2} +27.0000 q^{3} -127.829 q^{4} +231.152 q^{5} +11.1518 q^{6} +302.150 q^{7} -105.665 q^{8} +729.000 q^{9} +95.4729 q^{10} +1281.53 q^{11} -3451.39 q^{12} -14851.9 q^{13} +124.797 q^{14} +6241.10 q^{15} +16318.5 q^{16} -21166.2 q^{17} +301.100 q^{18} -1755.31 q^{19} -29548.0 q^{20} +8158.05 q^{21} +529.311 q^{22} +91962.2 q^{23} -2852.97 q^{24} -24693.8 q^{25} -6134.31 q^{26} +19683.0 q^{27} -38623.7 q^{28} +62655.4 q^{29} +2577.77 q^{30} -103275. q^{31} +20265.2 q^{32} +34601.2 q^{33} -8742.32 q^{34} +69842.6 q^{35} -93187.6 q^{36} -37921.6 q^{37} -724.998 q^{38} -401003. q^{39} -24424.8 q^{40} -45664.2 q^{41} +3369.53 q^{42} -637229. q^{43} -163817. q^{44} +168510. q^{45} +37983.3 q^{46} +229428. q^{47} +440600. q^{48} -732248. q^{49} -10199.3 q^{50} -571488. q^{51} +1.89852e6 q^{52} -1.07832e6 q^{53} +8129.69 q^{54} +296227. q^{55} -31926.8 q^{56} -47393.4 q^{57} +25878.6 q^{58} -205379. q^{59} -797796. q^{60} -2.75987e6 q^{61} -42655.6 q^{62} +220267. q^{63} -2.08040e6 q^{64} -3.43305e6 q^{65} +14291.4 q^{66} -3.11037e6 q^{67} +2.70567e6 q^{68} +2.48298e6 q^{69} +28847.1 q^{70} +4.01814e6 q^{71} -77030.1 q^{72} -5.86422e6 q^{73} -15662.8 q^{74} -666733. q^{75} +224380. q^{76} +387214. q^{77} -165627. q^{78} +4.62456e6 q^{79} +3.77206e6 q^{80} +531441. q^{81} -18860.7 q^{82} +9.51599e6 q^{83} -1.04284e6 q^{84} -4.89262e6 q^{85} -263195. q^{86} +1.69170e6 q^{87} -135413. q^{88} -6.95658e6 q^{89} +69599.7 q^{90} -4.48752e6 q^{91} -1.17555e7 q^{92} -2.78841e6 q^{93} +94760.7 q^{94} -405743. q^{95} +547161. q^{96} -9.56241e6 q^{97} -302441. q^{98} +934234. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.413031	0.0365071	0.0182536	−	0.999833i	$-0.494189\pi$
$2$	0.413031	0.0365071	0.0182536	+	0.999833i	$0.494189\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	−127.829	−0.998667
$5$	231.152	0.826994	0.413497	−	0.910505i	$-0.364307\pi$
$5$	231.152	0.826994	0.413497	+	0.910505i	$0.364307\pi$
$6$	11.1518	0.0210774
$7$	302.150	0.332950	0.166475	−	0.986046i	$-0.446761\pi$
$7$	302.150	0.332950	0.166475	+	0.986046i	$0.446761\pi$
$8$	−105.665	−0.0729656
$9$	729.000	0.333333
$10$	95.4729	0.0301912
$11$	1281.53	0.290304	0.145152	−	0.989409i	$-0.453633\pi$
$11$	1281.53	0.290304	0.145152	+	0.989409i	$0.453633\pi$
$12$	−3451.39	−0.576581
$13$	−14851.9	−1.87491	−0.937457	−	0.348100i	$-0.886827\pi$
$13$	−14851.9	−1.87491	−0.937457	+	0.348100i	$0.886827\pi$
$14$	124.797	0.0121551
$15$	6241.10	0.477465
$16$	16318.5	0.996003
$17$	−21166.2	−1.04489	−0.522447	−	0.852672i	$-0.674981\pi$
$17$	−21166.2	−1.04489	−0.522447	+	0.852672i	$0.674981\pi$
$18$	301.100	0.0121690
$19$	−1755.31	−0.0587106	−0.0293553	−	0.999569i	$-0.509345\pi$
$19$	−1755.31	−0.0587106	−0.0293553	+	0.999569i	$0.509345\pi$
$20$	−29548.0	−0.825892
$21$	8158.05	0.192229
$22$	529.311	0.0105982
$23$	91962.2	1.57602	0.788011	−	0.615662i	$-0.211111\pi$
$23$	91962.2	1.57602	0.788011	+	0.615662i	$0.211111\pi$
$24$	−2852.97	−0.0421267
$25$	−24693.8	−0.316081
$26$	−6134.31	−0.0684478
$27$	19683.0	0.192450
$28$	−38623.7	−0.332507
$29$	62655.4	0.477052	0.238526	−	0.971136i	$-0.423336\pi$
$29$	62655.4	0.477052	0.238526	+	0.971136i	$0.423336\pi$
$30$	2577.77	0.0174309
$31$	−103275.	−0.622626	−0.311313	−	0.950307i	$-0.600769\pi$
$31$	−103275.	−0.622626	−0.311313	+	0.950307i	$0.600769\pi$
$32$	20265.2	0.109327
$33$	34601.2	0.167607
$34$	−8742.32	−0.0381461
$35$	69842.6	0.275348
$36$	−93187.6	−0.332889
$37$	−37921.6	−0.123078	−0.0615390	−	0.998105i	$-0.519601\pi$
$37$	−37921.6	−0.123078	−0.0615390	+	0.998105i	$0.519601\pi$
$38$	−724.998	−0.00214335
$39$	−401003.	−1.08248
$40$	−24424.8	−0.0603421
$41$	−45664.2	−0.103474	−0.0517371	−	0.998661i	$-0.516476\pi$
$41$	−45664.2	−0.103474	−0.0517371	+	0.998661i	$0.516476\pi$
$42$	3369.53	0.00701773
$43$	−637229.	−1.22224	−0.611119	−	0.791539i	$-0.709280\pi$
$43$	−637229.	−1.22224	−0.611119	+	0.791539i	$0.709280\pi$
$44$	−163817.	−0.289917
$45$	168510.	0.275665
$46$	37983.3	0.0575360
$47$	229428.	0.322332	0.161166	−	0.986927i	$-0.448475\pi$
$47$	229428.	0.322332	0.161166	+	0.986927i	$0.448475\pi$
$48$	440600.	0.575043
$49$	−732248.	−0.889144
$50$	−10199.3	−0.0115392
$51$	−571488.	−0.603270
$52$	1.89852e6	1.87242
$53$	−1.07832e6	−0.994906	−0.497453	−	0.867491i	$-0.665731\pi$
$53$	−1.07832e6	−0.994906	−0.497453	+	0.867491i	$0.665731\pi$
$54$	8129.69	0.00702580
$55$	296227.	0.240080
$56$	−31926.8	−0.0242939
$57$	−47393.4	−0.0338966
$58$	25878.6	0.0174158
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	−797796.	−0.476829
$61$	−2.75987e6	−1.55680	−0.778402	−	0.627767i	$-0.783969\pi$
$61$	−2.75987e6	−1.55680	−0.778402	+	0.627767i	$0.783969\pi$
$62$	−42655.6	−0.0227303
$63$	220267.	0.110983
$64$	−2.08040e6	−0.992012
$65$	−3.43305e6	−1.55054
$66$	14291.4	0.00611886
$67$	−3.11037e6	−1.26343	−0.631715	−	0.775201i	$-0.717649\pi$
$67$	−3.11037e6	−1.26343	−0.631715	+	0.775201i	$0.717649\pi$
$68$	2.70567e6	1.04350
$69$	2.48298e6	0.909916
$70$	28847.1	0.0100522
$71$	4.01814e6	1.33236	0.666179	−	0.745792i	$-0.267929\pi$
$71$	4.01814e6	1.33236	0.666179	+	0.745792i	$0.267929\pi$
$72$	−77030.1	−0.0243219
$73$	−5.86422e6	−1.76433	−0.882165	−	0.470940i	$-0.843915\pi$
$73$	−5.86422e6	−1.76433	−0.882165	+	0.470940i	$0.843915\pi$
$74$	−15662.8	−0.00449322
$75$	−666733.	−0.182489
$76$	224380.	0.0586323
$77$	387214.	0.0966570
$78$	−165627.	−0.0395183
$79$	4.62456e6	1.05530	0.527649	−	0.849462i	$-0.323074\pi$
$79$	4.62456e6	1.05530	0.527649	+	0.849462i	$0.323074\pi$
$80$	3.77206e6	0.823689
$81$	531441.	0.111111
$82$	−18860.7	−0.00377755
$83$	9.51599e6	1.82676	0.913378	−	0.407113i	$-0.133465\pi$
$83$	9.51599e6	1.82676	0.913378	+	0.407113i	$0.133465\pi$
$84$	−1.04284e6	−0.191973
$85$	−4.89262e6	−0.864122
$86$	−263195.	−0.0446204
$87$	1.69170e6	0.275426
$88$	−135413.	−0.0211822
$89$	−6.95658e6	−1.04600	−0.522999	−	0.852333i	$-0.675187\pi$
$89$	−6.95658e6	−1.04600	−0.522999	+	0.852333i	$0.675187\pi$
$90$	69599.7	0.0100637
$91$	−4.48752e6	−0.624254
$92$	−1.17555e7	−1.57392
$93$	−2.78841e6	−0.359473
$94$	94760.7	0.0117674
$95$	−405743.	−0.0485533
$96$	547161.	0.0631199
$97$	−9.56241e6	−1.06382	−0.531908	−	0.846802i	$-0.678525\pi$
$97$	−9.56241e6	−1.06382	−0.531908	+	0.846802i	$0.678525\pi$
$98$	−302441.	−0.0324601
$99$	934234.	0.0967681
$100$	3.15660e6	0.315660
$101$	−9.74084e6	−0.940744	−0.470372	−	0.882468i	$-0.655880\pi$
$101$	−9.74084e6	−0.940744	−0.470372	+	0.882468i	$0.655880\pi$
$102$	−236043.	−0.0220237
$103$	−1.17131e7	−1.05619	−0.528093	−	0.849186i	$-0.677093\pi$
$103$	−1.17131e7	−1.05619	−0.528093	+	0.849186i	$0.677093\pi$
$104$	1.56934e6	0.136804
$105$	1.88575e6	0.158972
$106$	−445380.	−0.0363212
$107$	−2.32996e7	−1.83867	−0.919337	−	0.393471i	$-0.871274\pi$
$107$	−2.32996e7	−1.83867	−0.919337	+	0.393471i	$0.871274\pi$
$108$	−2.51607e6	−0.192194
$109$	1.84368e7	1.36362	0.681808	−	0.731531i	$-0.261194\pi$
$109$	1.84368e7	1.36362	0.681808	+	0.731531i	$0.261194\pi$
$110$	122351.	0.00876463
$111$	−1.02388e6	−0.0710591
$112$	4.93064e6	0.331620
$113$	−1.69409e7	−1.10449	−0.552247	−	0.833681i	$-0.686229\pi$
$113$	−1.69409e7	−1.10449	−0.552247	+	0.833681i	$0.686229\pi$
$114$	−19574.9	−0.00123747
$115$	2.12572e7	1.30336
$116$	−8.00921e6	−0.476416
$117$	−1.08271e7	−0.624972
$118$	−84827.9	−0.00475282
$119$	−6.39538e6	−0.347898
$120$	−659469.	−0.0348385
$121$	−1.78449e7	−0.915723
$122$	−1.13991e6	−0.0568344
$123$	−1.23293e6	−0.0597409
$124$	1.32015e7	0.621796
$125$	−2.37668e7	−1.08839
$126$	90977.3	0.00405169
$127$	−1.02426e7	−0.443708	−0.221854	−	0.975080i	$-0.571211\pi$
$127$	−1.02426e7	−0.443708	−0.221854	+	0.975080i	$0.571211\pi$
$128$	−3.45322e6	−0.145542
$129$	−1.72052e7	−0.705660
$130$	−1.41796e6	−0.0566059
$131$	2.19669e7	0.853728	0.426864	−	0.904316i	$-0.359618\pi$
$131$	2.19669e7	0.853728	0.426864	+	0.904316i	$0.359618\pi$
$132$	−4.42306e6	−0.167384
$133$	−530367.	−0.0195477
$134$	−1.28468e6	−0.0461242
$135$	4.54976e6	0.159155
$136$	2.23654e6	0.0762414
$137$	1.76506e6	0.0586459	0.0293229	−	0.999570i	$-0.490665\pi$
$137$	1.76506e6	0.0586459	0.0293229	+	0.999570i	$0.490665\pi$
$138$	1.02555e6	0.0332184
$139$	−2.43007e7	−0.767481	−0.383740	−	0.923441i	$-0.625364\pi$
$139$	−2.43007e7	−0.767481	−0.383740	+	0.923441i	$0.625364\pi$
$140$	−8.92793e6	−0.274981
$141$	6.19454e6	0.186098
$142$	1.65962e6	0.0486406
$143$	−1.90332e7	−0.544296
$144$	1.18962e7	0.332001
$145$	1.44829e7	0.394519
$146$	−2.42210e6	−0.0644107
$147$	−1.97707e7	−0.513348
$148$	4.84749e6	0.122914
$149$	7.68149e7	1.90236	0.951181	−	0.308633i	$-0.0998715\pi$
$149$	7.68149e7	1.90236	0.951181	+	0.308633i	$0.0998715\pi$
$150$	−275382.	−0.00666217
$151$	4.28340e7	1.01244	0.506220	−	0.862404i	$-0.331042\pi$
$151$	4.28340e7	1.01244	0.506220	+	0.862404i	$0.331042\pi$
$152$	185476.	0.00428385
$153$	−1.54302e7	−0.348298
$154$	159931.	0.00352867
$155$	−2.38721e7	−0.514908
$156$	5.12599e7	1.08104
$157$	5.51222e7	1.13678	0.568392	−	0.822758i	$-0.307566\pi$
$157$	5.51222e7	1.13678	0.568392	+	0.822758i	$0.307566\pi$
$158$	1.91009e6	0.0385259
$159$	−2.91146e7	−0.574409
$160$	4.68435e6	0.0904126
$161$	2.77864e7	0.524737
$162$	219502.	0.00405635
$163$	3.76340e7	0.680650	0.340325	−	0.940308i	$-0.389463\pi$
$163$	3.76340e7	0.680650	0.340325	+	0.940308i	$0.389463\pi$
$164$	5.83723e6	0.103336
$165$	7.99814e6	0.138610
$166$	3.93040e6	0.0666896
$167$	9.25680e7	1.53799	0.768995	−	0.639255i	$-0.220757\pi$
$167$	9.25680e7	1.53799	0.768995	+	0.639255i	$0.220757\pi$
$168$	−862025.	−0.0140261
$169$	1.57832e8	2.51531
$170$	−2.02080e6	−0.0315466
$171$	−1.27962e6	−0.0195702
$172$	8.14566e7	1.22061
$173$	−1.09599e8	−1.60933	−0.804665	−	0.593729i	$-0.797655\pi$
$173$	−1.09599e8	−1.60933	−0.804665	+	0.593729i	$0.797655\pi$
$174$	698723.	0.0100550
$175$	−7.46124e6	−0.105239
$176$	2.09126e7	0.289144
$177$	−5.54523e6	−0.0751646
$178$	−2.87328e6	−0.0381864
$179$	4.35682e7	0.567786	0.283893	−	0.958856i	$-0.408374\pi$
$179$	4.35682e7	0.567786	0.283893	+	0.958856i	$0.408374\pi$
$180$	−2.15405e7	−0.275297
$181$	−1.29762e8	−1.62656	−0.813282	−	0.581870i	$-0.802321\pi$
$181$	−1.29762e8	−1.62656	−0.813282	+	0.581870i	$0.802321\pi$
$182$	−1.85348e6	−0.0227897
$183$	−7.45164e7	−0.898821
$184$	−9.71724e6	−0.114995
$185$	−8.76564e6	−0.101785
$186$	−1.15170e6	−0.0131233
$187$	−2.71251e7	−0.303337
$188$	−2.93276e7	−0.321902
$189$	5.94722e6	0.0640763
$190$	−167585.	−0.00177254
$191$	3.07331e7	0.319146	0.159573	−	0.987186i	$-0.448988\pi$
$191$	3.07331e7	0.319146	0.159573	+	0.987186i	$0.448988\pi$
$192$	−5.61708e7	−0.572739
$193$	1.24448e8	1.24606	0.623029	−	0.782199i	$-0.285902\pi$
$193$	1.24448e8	1.24606	0.623029	+	0.782199i	$0.285902\pi$
$194$	−3.94957e6	−0.0388369
$195$	−9.26925e7	−0.895207
$196$	9.36029e7	0.887959
$197$	−5.43655e7	−0.506630	−0.253315	−	0.967384i	$-0.581521\pi$
$197$	−5.43655e7	−0.506630	−0.253315	+	0.967384i	$0.581521\pi$
$198$	385868.	0.00353273
$199$	1.40875e8	1.26721	0.633606	−	0.773656i	$-0.281574\pi$
$199$	1.40875e8	1.26721	0.633606	+	0.773656i	$0.281574\pi$
$200$	2.60929e6	0.0230630
$201$	−8.39801e7	−0.729441
$202$	−4.02327e6	−0.0343439
$203$	1.89313e7	0.158835
$204$	7.30530e7	0.602466
$205$	−1.05554e7	−0.0855726
$206$	−4.83786e6	−0.0385584
$207$	6.70405e7	0.525340
$208$	−2.42362e8	−1.86742
$209$	−2.24948e6	−0.0170439
$210$	778873.	0.00580362
$211$	2.07381e8	1.51978	0.759891	−	0.650051i	$-0.225252\pi$
$211$	2.07381e8	1.51978	0.759891	+	0.650051i	$0.225252\pi$
$212$	1.37841e8	0.993580
$213$	1.08490e8	0.769237
$214$	−9.62345e6	−0.0671247
$215$	−1.47297e8	−1.01078
$216$	−2.07981e6	−0.0140422
$217$	−3.12044e7	−0.207304
$218$	7.61496e6	0.0497817
$219$	−1.58334e8	−1.01864
$220$	−3.78666e7	−0.239760
$221$	3.14360e8	1.95909
$222$	−422895.	−0.00259416
$223$	−2.57344e8	−1.55398	−0.776992	−	0.629511i	$-0.783255\pi$
$223$	−2.57344e8	−1.55398	−0.776992	+	0.629511i	$0.783255\pi$
$224$	6.12314e6	0.0364004
$225$	−1.80018e7	−0.105360
$226$	−6.99714e6	−0.0403219
$227$	−1.28065e8	−0.726676	−0.363338	−	0.931657i	$-0.618363\pi$
$227$	−1.28065e8	−0.726676	−0.363338	+	0.931657i	$0.618363\pi$
$228$	6.05827e6	0.0338514
$229$	9.10898e7	0.501240	0.250620	−	0.968086i	$-0.419366\pi$
$229$	9.10898e7	0.501240	0.250620	+	0.968086i	$0.419366\pi$
$230$	8.77990e6	0.0475819
$231$	1.04548e7	0.0558049
$232$	−6.62052e6	−0.0348084
$233$	−6.28725e7	−0.325623	−0.162812	−	0.986657i	$-0.552056\pi$
$233$	−6.28725e7	−0.325623	−0.162812	+	0.986657i	$0.552056\pi$
$234$	−4.47192e6	−0.0228159
$235$	5.30326e7	0.266566
$236$	2.62535e7	0.130015
$237$	1.24863e8	0.609277
$238$	−2.64149e6	−0.0127008
$239$	−2.11572e8	−1.00246	−0.501229	−	0.865315i	$-0.667119\pi$
$239$	−2.11572e8	−1.00246	−0.501229	+	0.865315i	$0.667119\pi$
$240$	1.01846e8	0.475557
$241$	1.41219e7	0.0649882	0.0324941	−	0.999472i	$-0.489655\pi$
$241$	1.41219e7	0.0649882	0.0324941	+	0.999472i	$0.489655\pi$
$242$	−7.37048e6	−0.0334304
$243$	1.43489e7	0.0641500
$244$	3.52792e8	1.55473
$245$	−1.69261e8	−0.735317
$246$	−509240.	−0.00218097
$247$	2.60698e7	0.110077
$248$	1.09126e7	0.0454303
$249$	2.56932e8	1.05468
$250$	−9.81641e6	−0.0397340
$251$	8.14251e7	0.325013	0.162506	−	0.986707i	$-0.448042\pi$
$251$	8.14251e7	0.325013	0.162506	+	0.986707i	$0.448042\pi$
$252$	−2.81567e7	−0.110836
$253$	1.17852e8	0.457526
$254$	−4.23051e6	−0.0161985
$255$	−1.32101e8	−0.498901
$256$	2.64865e8	0.986699
$257$	2.21346e8	0.813402	0.406701	−	0.913561i	$-0.366679\pi$
$257$	2.21346e8	0.813402	0.406701	+	0.913561i	$0.366679\pi$
$258$	−7.10628e6	−0.0257616
$259$	−1.14580e7	−0.0409789
$260$	4.38845e8	1.54848
$261$	4.56758e7	0.159017
$262$	9.07301e6	0.0311672
$263$	4.49267e8	1.52286	0.761429	−	0.648249i	$-0.224498\pi$
$263$	4.49267e8	1.52286	0.761429	+	0.648249i	$0.224498\pi$
$264$	−3.65616e6	−0.0122296
$265$	−2.49256e8	−0.822781
$266$	−219058.	−0.000713631 0
$267$	−1.87828e8	−0.603907
$268$	3.97597e8	1.26175
$269$	−4.00214e8	−1.25360	−0.626801	−	0.779180i	$-0.715636\pi$
$269$	−4.00214e8	−1.25360	−0.626801	+	0.779180i	$0.715636\pi$
$270$	1.87919e6	0.00581030
$271$	2.23102e8	0.680944	0.340472	−	0.940255i	$-0.389413\pi$
$271$	2.23102e8	0.680944	0.340472	+	0.940255i	$0.389413\pi$
$272$	−3.45402e8	−1.04072
$273$	−1.21163e8	−0.360413
$274$	729025.	0.00214099
$275$	−3.16458e7	−0.0917597
$276$	−3.17398e8	−0.908704
$277$	2.84338e8	0.803815	0.401907	−	0.915680i	$-0.368347\pi$
$277$	2.84338e8	0.803815	0.401907	+	0.915680i	$0.368347\pi$
$278$	−1.00370e7	−0.0280185
$279$	−7.52871e7	−0.207542
$280$	−7.37995e6	−0.0200909
$281$	−3.25571e8	−0.875332	−0.437666	−	0.899138i	$-0.644195\pi$
$281$	−3.25571e8	−0.875332	−0.437666	+	0.899138i	$0.644195\pi$
$282$	2.55854e6	0.00679392
$283$	−4.66681e7	−0.122396	−0.0611980	−	0.998126i	$-0.519492\pi$
$283$	−4.66681e7	−0.122396	−0.0611980	+	0.998126i	$0.519492\pi$
$284$	−5.13636e8	−1.33058
$285$	−1.09551e7	−0.0280323
$286$	−7.86129e6	−0.0198707
$287$	−1.37974e7	−0.0344518
$288$	1.47734e7	0.0364423
$289$	3.76710e7	0.0918048
$290$	5.98190e6	0.0144028
$291$	−2.58185e8	−0.614194
$292$	7.49619e8	1.76198
$293$	−7.70273e7	−0.178899	−0.0894495	−	0.995991i	$-0.528511\pi$
$293$	−7.70273e7	−0.178899	−0.0894495	+	0.995991i	$0.528511\pi$
$294$	−8.16592e6	−0.0187408
$295$	−4.74737e7	−0.107665
$296$	4.00700e6	0.00898046
$297$	2.52243e7	0.0558691
$298$	3.17269e7	0.0694498
$299$	−1.36582e9	−2.95491
$300$	8.52281e7	0.182246
$301$	−1.92539e8	−0.406945
$302$	1.76918e7	0.0369613
$303$	−2.63003e8	−0.543139
$304$	−2.86441e7	−0.0584759
$305$	−6.37948e8	−1.28747
$306$	−6.37315e6	−0.0127154
$307$	−1.67909e8	−0.331200	−0.165600	−	0.986193i	$-0.552956\pi$
$307$	−1.67909e8	−0.331200	−0.165600	+	0.986193i	$0.552956\pi$
$308$	−4.94973e7	−0.0965281
$309$	−3.16253e8	−0.609790
$310$	−9.85992e6	−0.0187978
$311$	−2.22728e8	−0.419868	−0.209934	−	0.977716i	$-0.567325\pi$
$311$	−2.22728e8	−0.419868	−0.209934	+	0.977716i	$0.567325\pi$
$312$	4.23721e7	0.0789840
$313$	−2.23952e8	−0.412809	−0.206404	−	0.978467i	$-0.566176\pi$
$313$	−2.23952e8	−0.412809	−0.206404	+	0.978467i	$0.566176\pi$
$314$	2.27672e7	0.0415007
$315$	5.09152e7	0.0917827
$316$	−5.91154e8	−1.05389
$317$	7.57737e8	1.33601	0.668007	−	0.744155i	$-0.267147\pi$
$317$	7.57737e8	1.33601	0.668007	+	0.744155i	$0.267147\pi$
$318$	−1.20252e7	−0.0209700
$319$	8.02947e7	0.138490
$320$	−4.80888e8	−0.820388
$321$	−6.29089e8	−1.06156
$322$	1.14766e7	0.0191566
$323$	3.71533e7	0.0613464
$324$	−6.79338e7	−0.110963
$325$	3.66751e8	0.592625
$326$	1.55440e7	0.0248486
$327$	4.97793e8	0.787284
$328$	4.82513e6	0.00755006
$329$	6.93215e7	0.107320
$330$	3.30348e6	0.00506026
$331$	2.98249e8	0.452044	0.226022	−	0.974122i	$-0.427428\pi$
$331$	2.98249e8	0.452044	0.226022	+	0.974122i	$0.427428\pi$
$332$	−1.21642e9	−1.82432
$333$	−2.76448e7	−0.0410260
$334$	3.82335e7	0.0561476
$335$	−7.18969e8	−1.04485
$336$	1.33127e8	0.191461
$337$	−1.29895e9	−1.84879	−0.924393	−	0.381442i	$-0.875428\pi$
$337$	−1.29895e9	−1.84879	−0.924393	+	0.381442i	$0.875428\pi$
$338$	6.51894e7	0.0918266
$339$	−4.57406e8	−0.637680
$340$	6.25420e8	0.862970
$341$	−1.32349e8	−0.180751
$342$	−528523.	−0.000714452 0
$343$	−4.70083e8	−0.628991
$344$	6.73331e7	0.0891814
$345$	5.73945e8	0.752495
$346$	−4.52678e7	−0.0587521
$347$	1.13535e9	1.45874	0.729369	−	0.684120i	$-0.239814\pi$
$347$	1.13535e9	1.45874	0.729369	+	0.684120i	$0.239814\pi$
$348$	−2.16249e8	−0.275059
$349$	2.24671e8	0.282916	0.141458	−	0.989944i	$-0.454821\pi$
$349$	2.24671e8	0.282916	0.141458	+	0.989944i	$0.454821\pi$
$350$	−3.08172e6	−0.00384199
$351$	−2.92331e8	−0.360828
$352$	2.59705e7	0.0317381
$353$	1.00698e9	1.21846	0.609228	−	0.792995i	$-0.291480\pi$
$353$	1.00698e9	1.21846	0.609228	+	0.792995i	$0.291480\pi$
$354$	−2.29035e6	−0.00274404
$355$	9.28800e8	1.10185
$356$	8.89256e8	1.04460
$357$	−1.72675e8	−0.200859
$358$	1.79950e7	0.0207282
$359$	−5.34366e7	−0.0609548	−0.0304774	−	0.999535i	$-0.509703\pi$
$359$	−5.34366e7	−0.0609548	−0.0304774	+	0.999535i	$0.509703\pi$
$360$	−1.78057e7	−0.0201140
$361$	−8.90791e8	−0.996553
$362$	−5.35956e7	−0.0593812
$363$	−4.81811e8	−0.528693
$364$	5.73637e8	0.623422
$365$	−1.35552e9	−1.45909
$366$	−3.07776e7	−0.0328134
$367$	1.32145e8	0.139547	0.0697733	−	0.997563i	$-0.477772\pi$
$367$	1.32145e8	0.139547	0.0697733	+	0.997563i	$0.477772\pi$
$368$	1.50069e9	1.56972
$369$	−3.32892e7	−0.0344914
$370$	−3.62048e6	−0.00371587
$371$	−3.25814e8	−0.331254
$372$	3.56441e8	0.358994
$373$	1.16722e8	0.116458	0.0582292	−	0.998303i	$-0.481455\pi$
$373$	1.16722e8	0.116458	0.0582292	+	0.998303i	$0.481455\pi$
$374$	−1.12035e7	−0.0110740
$375$	−6.41703e8	−0.628383
$376$	−2.42426e7	−0.0235191
$377$	−9.30555e8	−0.894432
$378$	2.45639e6	0.00233924
$379$	1.54193e9	1.45488	0.727440	−	0.686172i	$-0.240710\pi$
$379$	1.54193e9	1.45488	0.727440	+	0.686172i	$0.240710\pi$
$380$	5.18659e7	0.0484886
$381$	−2.76550e8	−0.256175
$382$	1.26937e7	0.0116511
$383$	−1.11000e9	−1.00955	−0.504774	−	0.863252i	$-0.668424\pi$
$383$	−1.11000e9	−1.00955	−0.504774	+	0.863252i	$0.668424\pi$
$384$	−9.32370e7	−0.0840289
$385$	8.95052e7	0.0799347
$386$	5.14010e7	0.0454900
$387$	−4.64540e8	−0.407413
$388$	1.22236e9	1.06240
$389$	3.52125e8	0.303301	0.151650	−	0.988434i	$-0.451541\pi$
$389$	3.52125e8	0.303301	0.151650	+	0.988434i	$0.451541\pi$
$390$	−3.82849e7	−0.0326814
$391$	−1.94649e9	−1.64678
$392$	7.73734e7	0.0648769
$393$	5.93106e8	0.492900
$394$	−2.24546e7	−0.0184956
$395$	1.06897e9	0.872725
$396$	−1.19423e8	−0.0966392
$397$	1.23251e9	0.988611	0.494305	−	0.869288i	$-0.335422\pi$
$397$	1.23251e9	0.988611	0.494305	+	0.869288i	$0.335422\pi$
$398$	5.81859e7	0.0462623
$399$	−1.43199e7	−0.0112859
$400$	−4.02967e8	−0.314818
$401$	−1.95405e9	−1.51332	−0.756661	−	0.653808i	$-0.773171\pi$
$401$	−1.95405e9	−1.51332	−0.756661	+	0.653808i	$0.773171\pi$
$402$	−3.46864e7	−0.0266298
$403$	1.53383e9	1.16737
$404$	1.24517e9	0.939491
$405$	1.22844e8	0.0918882
$406$	7.81924e6	0.00579860
$407$	−4.85975e7	−0.0357301
$408$	6.03866e7	0.0440180
$409$	−8.06706e8	−0.583020	−0.291510	−	0.956568i	$-0.594158\pi$
$409$	−8.06706e8	−0.583020	−0.291510	+	0.956568i	$0.594158\pi$
$410$	−4.35969e6	−0.00312401
$411$	4.76566e7	0.0338592
$412$	1.49728e9	1.05478
$413$	−6.20553e7	−0.0433465
$414$	2.76898e7	0.0191787
$415$	2.19964e9	1.51072
$416$	−3.00978e8	−0.204979
$417$	−6.56120e8	−0.443105
$418$	−929105.	−0.000622225 0
$419$	−1.37468e9	−0.912960	−0.456480	−	0.889734i	$-0.650890\pi$
$419$	−1.37468e9	−0.912960	−0.456480	+	0.889734i	$0.650890\pi$
$420$	−2.41054e8	−0.158760
$421$	−8.51303e8	−0.556028	−0.278014	−	0.960577i	$-0.589676\pi$
$421$	−8.51303e8	−0.556028	−0.278014	+	0.960577i	$0.589676\pi$
$422$	8.56549e7	0.0554829
$423$	1.67253e8	0.107444
$424$	1.13941e8	0.0725939
$425$	5.22675e8	0.330271
$426$	4.48096e7	0.0280826
$427$	−8.33894e8	−0.518338
$428$	2.97837e9	1.83622
$429$	−5.13896e8	−0.314249
$430$	−6.08381e7	−0.0369008
$431$	3.76775e8	0.226679	0.113339	−	0.993556i	$-0.463845\pi$
$431$	3.76775e8	0.226679	0.113339	+	0.993556i	$0.463845\pi$
$432$	3.21197e8	0.191681
$433$	1.14074e9	0.675270	0.337635	−	0.941277i	$-0.390373\pi$
$433$	1.14074e9	0.675270	0.337635	+	0.941277i	$0.390373\pi$
$434$	−1.28884e7	−0.00756806
$435$	3.91039e8	0.227776
$436$	−2.35676e9	−1.36180
$437$	−1.61422e8	−0.0925291
$438$	−6.53968e7	−0.0371875
$439$	1.15020e9	0.648854	0.324427	−	0.945911i	$-0.394829\pi$
$439$	1.15020e9	0.648854	0.324427	+	0.945911i	$0.394829\pi$
$440$	−3.13010e7	−0.0175176
$441$	−5.33809e8	−0.296381
$442$	1.29840e8	0.0715207
$443$	4.99658e8	0.273061	0.136531	−	0.990636i	$-0.456405\pi$
$443$	4.99658e8	0.273061	0.136531	+	0.990636i	$0.456405\pi$
$444$	1.30882e8	0.0709644
$445$	−1.60803e9	−0.865034
$446$	−1.06291e8	−0.0567315
$447$	2.07400e9	1.09833
$448$	−6.28593e8	−0.330291
$449$	1.70526e9	0.889054	0.444527	−	0.895766i	$-0.353372\pi$
$449$	1.70526e9	0.889054	0.444527	+	0.895766i	$0.353372\pi$
$450$	−7.43530e6	−0.00384640
$451$	−5.85199e7	−0.0300390
$452$	2.16555e9	1.10302
$453$	1.15652e9	0.584533
$454$	−5.28949e7	−0.0265289
$455$	−1.03730e9	−0.516254
$456$	5.00785e6	0.00247328
$457$	−6.10097e8	−0.299015	−0.149507	−	0.988761i	$-0.547769\pi$
$457$	−6.10097e8	−0.299015	−0.149507	+	0.988761i	$0.547769\pi$
$458$	3.76229e7	0.0182988
$459$	−4.16615e8	−0.201090
$460$	−2.71730e9	−1.30162
$461$	2.09113e9	0.994093	0.497046	−	0.867724i	$-0.334418\pi$
$461$	2.09113e9	0.994093	0.497046	+	0.867724i	$0.334418\pi$
$462$	4.31815e6	0.00203728
$463$	−3.87258e8	−0.181329	−0.0906643	−	0.995882i	$-0.528899\pi$
$463$	−3.87258e8	−0.181329	−0.0906643	+	0.995882i	$0.528899\pi$
$464$	1.02244e9	0.475146
$465$	−6.44547e8	−0.297282
$466$	−2.59683e7	−0.0118876
$467$	2.46901e8	0.112180	0.0560898	−	0.998426i	$-0.482137\pi$
$467$	2.46901e8	0.112180	0.0560898	+	0.998426i	$0.482137\pi$
$468$	1.38402e9	0.624139
$469$	−9.39800e8	−0.420659
$470$	2.19041e7	0.00973157
$471$	1.48830e9	0.656322
$472$	2.17015e7	0.00949931
$473$	−8.16627e8	−0.354821
$474$	5.15723e7	0.0222429
$475$	4.33453e7	0.0185573
$476$	8.17518e8	0.347434
$477$	−7.86095e8	−0.331635
$478$	−8.73860e7	−0.0365969
$479$	−3.29359e9	−1.36929	−0.684645	−	0.728877i	$-0.740043\pi$
$479$	−3.29359e9	−1.36929	−0.684645	+	0.728877i	$0.740043\pi$
$480$	1.26477e8	0.0521998
$481$	5.63209e8	0.230761
$482$	5.83280e6	0.00237253
$483$	7.50233e8	0.302957
$484$	2.28110e9	0.914503
$485$	−2.21037e9	−0.879769
$486$	5.92654e6	0.00234193
$487$	1.64421e9	0.645070	0.322535	−	0.946558i	$-0.395465\pi$
$487$	1.64421e9	0.645070	0.322535	+	0.946558i	$0.395465\pi$
$488$	2.91623e8	0.113593
$489$	1.01612e9	0.392974
$490$	−6.99099e7	−0.0268443
$491$	2.85157e9	1.08717	0.543587	−	0.839353i	$-0.317066\pi$
$491$	2.85157e9	1.08717	0.543587	+	0.839353i	$0.317066\pi$
$492$	1.57605e8	0.0596613
$493$	−1.32618e9	−0.498469
$494$	1.07676e7	0.00401861
$495$	2.15950e8	0.0800267
$496$	−1.68529e9	−0.620138
$497$	1.21408e9	0.443609
$498$	1.06121e8	0.0385033
$499$	3.73412e9	1.34535	0.672676	−	0.739937i	$-0.265145\pi$
$499$	3.73412e9	1.34535	0.672676	+	0.739937i	$0.265145\pi$
$500$	3.03809e9	1.08694
$501$	2.49934e9	0.887958
$502$	3.36311e7	0.0118653
$503$	−4.65904e9	−1.63233	−0.816166	−	0.577817i	$-0.803905\pi$
$503$	−4.65904e9	−1.63233	−0.816166	+	0.577817i	$0.803905\pi$
$504$	−2.32747e7	−0.00809798
$505$	−2.25161e9	−0.777990
$506$	4.86766e7	0.0167030
$507$	4.26146e9	1.45221
$508$	1.30931e9	0.443117
$509$	4.17061e9	1.40180	0.700902	−	0.713258i	$-0.252781\pi$
$509$	4.17061e9	1.40180	0.700902	+	0.713258i	$0.252781\pi$
$510$	−5.45617e7	−0.0182134
$511$	−1.77187e9	−0.587435
$512$	5.51410e8	0.181564
$513$	−3.45498e7	−0.0112989
$514$	9.14226e7	0.0296950
$515$	−2.70750e9	−0.873460
$516$	2.19933e9	0.704719
$517$	2.94018e8	0.0935743
$518$	−4.73251e6	−0.00149602
$519$	−2.95917e9	−0.929148
$520$	3.62755e8	0.113136
$521$	−1.08528e9	−0.336209	−0.168104	−	0.985769i	$-0.553765\pi$
$521$	−1.08528e9	−0.336209	−0.168104	+	0.985769i	$0.553765\pi$
$522$	1.88655e7	0.00580527
$523$	−4.07601e9	−1.24589	−0.622945	−	0.782266i	$-0.714064\pi$
$523$	−4.07601e9	−1.24589	−0.622945	+	0.782266i	$0.714064\pi$
$524$	−2.80802e9	−0.852590
$525$	−2.01454e8	−0.0607599
$526$	1.85561e8	0.0555952
$527$	2.18593e9	0.650579
$528$	5.64641e8	0.166937
$529$	5.05223e9	1.48384
$530$	−1.02950e8	−0.0300374
$531$	−1.49721e8	−0.0433963
$532$	6.77965e7	0.0195217
$533$	6.78202e8	0.194005
$534$	−7.75787e7	−0.0220469
$535$	−5.38574e9	−1.52057
$536$	3.28659e8	0.0921869
$537$	1.17634e9	0.327811
$538$	−1.65301e8	−0.0457654
$539$	−9.38396e8	−0.258122
$540$	−5.81593e8	−0.158943
$541$	−4.61079e9	−1.25194	−0.625972	−	0.779846i	$-0.715297\pi$
$541$	−4.61079e9	−1.25194	−0.625972	+	0.779846i	$0.715297\pi$
$542$	9.21481e7	0.0248593
$543$	−3.50356e9	−0.939097
$544$	−4.28939e8	−0.114235
$545$	4.26169e9	1.12770
$546$	−5.00441e7	−0.0131577
$547$	−3.70849e9	−0.968817	−0.484409	−	0.874842i	$-0.660965\pi$
$547$	−3.70849e9	−0.968817	−0.484409	+	0.874842i	$0.660965\pi$
$548$	−2.25627e8	−0.0585677
$549$	−2.01194e9	−0.518934
$550$	−1.30707e7	−0.00334988
$551$	−1.09980e8	−0.0280080
$552$	−2.62365e8	−0.0663926
$553$	1.39731e9	0.351362
$554$	1.17441e8	0.0293450
$555$	−2.36672e8	−0.0587654
$556$	3.10635e9	0.766458
$557$	−4.17975e9	−1.02484	−0.512421	−	0.858734i	$-0.671251\pi$
$557$	−4.17975e9	−1.02484	−0.512421	+	0.858734i	$0.671251\pi$
$558$	−3.10959e7	−0.00757676
$559$	9.46409e9	2.29159
$560$	1.13973e9	0.274248
$561$	−7.32378e8	−0.175132
$562$	−1.34471e8	−0.0319559
$563$	5.00396e9	1.18178	0.590888	−	0.806754i	$-0.298778\pi$
$563$	5.00396e9	1.18178	0.590888	+	0.806754i	$0.298778\pi$
$564$	−7.91845e8	−0.185850
$565$	−3.91593e9	−0.913410
$566$	−1.92754e7	−0.00446833
$567$	1.60575e8	0.0369945
$568$	−4.24579e8	−0.0972163
$569$	5.07854e8	0.115570	0.0577851	−	0.998329i	$-0.481596\pi$
$569$	5.07854e8	0.115570	0.0577851	+	0.998329i	$0.481596\pi$
$570$	−4.52478e6	−0.00102338
$571$	−5.27683e9	−1.18617	−0.593085	−	0.805140i	$-0.702090\pi$
$571$	−5.27683e9	−1.18617	−0.593085	+	0.805140i	$0.702090\pi$
$572$	2.43300e9	0.543571
$573$	8.29792e8	0.184259
$574$	−5.69877e6	−0.00125774
$575$	−2.27090e9	−0.498150
$576$	−1.51661e9	−0.330671
$577$	−1.54218e9	−0.334209	−0.167105	−	0.985939i	$-0.553442\pi$
$577$	−1.54218e9	−0.334209	−0.167105	+	0.985939i	$0.553442\pi$
$578$	1.55593e7	0.00335153
$579$	3.36010e9	0.719411
$580$	−1.85134e9	−0.393993
$581$	2.87526e9	0.608219
$582$	−1.06638e8	−0.0224225
$583$	−1.38190e9	−0.288826
$584$	6.19645e8	0.128735
$585$	−2.50270e9	−0.516848
$586$	−3.18147e7	−0.00653109
$587$	9.40246e8	0.191870	0.0959352	−	0.995388i	$-0.469416\pi$
$587$	9.40246e8	0.191870	0.0959352	+	0.995388i	$0.469416\pi$
$588$	2.52728e9	0.512663
$589$	1.81279e8	0.0365547
$590$	−1.96081e7	−0.00393056
$591$	−1.46787e9	−0.292503
$592$	−6.18824e8	−0.122586
$593$	3.28316e9	0.646547	0.323274	−	0.946306i	$-0.395217\pi$
$593$	3.28316e9	0.646547	0.323274	+	0.946306i	$0.395217\pi$
$594$	1.04184e7	0.00203962
$595$	−1.47830e9	−0.287710
$596$	−9.81920e9	−1.89983
$597$	3.80363e9	0.731625
$598$	−5.64125e8	−0.107875
$599$	7.40433e8	0.140764	0.0703820	−	0.997520i	$-0.477578\pi$
$599$	7.40433e8	0.140764	0.0703820	+	0.997520i	$0.477578\pi$
$600$	7.04507e7	0.0133155
$601$	−2.01096e9	−0.377870	−0.188935	−	0.981990i	$-0.560504\pi$
$601$	−2.01096e9	−0.377870	−0.188935	+	0.981990i	$0.560504\pi$
$602$	−7.95245e7	−0.0148564
$603$	−2.26746e9	−0.421143
$604$	−5.47545e9	−1.01109
$605$	−4.12487e9	−0.757298
$606$	−1.08628e8	−0.0198285
$607$	−4.88190e9	−0.885990	−0.442995	−	0.896524i	$-0.646084\pi$
$607$	−4.88190e9	−0.885990	−0.442995	+	0.896524i	$0.646084\pi$
$608$	−3.55718e7	−0.00641864
$609$	5.11146e8	0.0917033
$610$	−2.63493e8	−0.0470017
$611$	−3.40744e9	−0.604344
$612$	1.97243e9	0.347834
$613$	−6.53926e9	−1.14661	−0.573306	−	0.819341i	$-0.694339\pi$
$613$	−6.53926e9	−1.14661	−0.573306	+	0.819341i	$0.694339\pi$
$614$	−6.93517e7	−0.0120912
$615$	−2.84995e8	−0.0494054
$616$	−4.09151e7	−0.00705264
$617$	1.08583e9	0.186108	0.0930541	−	0.995661i	$-0.470337\pi$
$617$	1.08583e9	0.186108	0.0930541	+	0.995661i	$0.470337\pi$
$618$	−1.30622e8	−0.0222617
$619$	−1.46677e9	−0.248568	−0.124284	−	0.992247i	$-0.539663\pi$
$619$	−1.46677e9	−0.248568	−0.124284	+	0.992247i	$0.539663\pi$
$620$	3.05156e9	0.514222
$621$	1.81009e9	0.303305
$622$	−9.19935e7	−0.0153282
$623$	−2.10193e9	−0.348266
$624$	−6.54377e9	−1.07816
$625$	−3.56453e9	−0.584012
$626$	−9.24990e7	−0.0150705
$627$	−6.07359e7	−0.00984032
$628$	−7.04624e9	−1.13527
$629$	8.02657e8	0.128603
$630$	2.10296e7	0.00335072
$631$	5.56162e9	0.881248	0.440624	−	0.897692i	$-0.354757\pi$
$631$	5.56162e9	0.881248	0.440624	+	0.897692i	$0.354757\pi$
$632$	−4.88656e8	−0.0770005
$633$	5.59930e9	0.877446
$634$	3.12969e8	0.0487741
$635$	−2.36760e9	−0.366944
$636$	3.72171e9	0.573644
$637$	1.08753e10	1.66707
$638$	3.31642e7	0.00505588
$639$	2.92922e9	0.444119
$640$	−7.98218e8	−0.120363
$641$	−8.98365e8	−0.134726	−0.0673628	−	0.997729i	$-0.521458\pi$
$641$	−8.98365e8	−0.134726	−0.0673628	+	0.997729i	$0.521458\pi$
$642$	−2.59833e8	−0.0387545
$643$	6.66060e9	0.988042	0.494021	−	0.869450i	$-0.335527\pi$
$643$	6.66060e9	0.988042	0.494021	+	0.869450i	$0.335527\pi$
$644$	−3.55192e9	−0.524038
$645$	−3.97701e9	−0.583576
$646$	1.53455e7	0.00223958
$647$	2.89308e9	0.419948	0.209974	−	0.977707i	$-0.432662\pi$
$647$	2.89308e9	0.419948	0.209974	+	0.977707i	$0.432662\pi$
$648$	−5.61550e7	−0.00810729
$649$	−2.63199e8	−0.0377944
$650$	1.51480e8	0.0216350
$651$	−8.42519e8	−0.119687
$652$	−4.81074e9	−0.679743
$653$	5.97319e9	0.839480	0.419740	−	0.907644i	$-0.362121\pi$
$653$	5.97319e9	0.839480	0.419740	+	0.907644i	$0.362121\pi$
$654$	2.05604e8	0.0287415
$655$	5.07769e9	0.706028
$656$	−7.45172e8	−0.103061
$657$	−4.27501e9	−0.588110
$658$	2.86320e7	0.00391796
$659$	8.14255e9	1.10831	0.554155	−	0.832414i	$-0.313041\pi$
$659$	8.14255e9	1.10831	0.554155	+	0.832414i	$0.313041\pi$
$660$	−1.02240e9	−0.138425
$661$	3.91035e9	0.526635	0.263318	−	0.964709i	$-0.415183\pi$
$661$	3.91035e9	0.526635	0.263318	+	0.964709i	$0.415183\pi$
$662$	1.23186e8	0.0165028
$663$	8.48772e9	1.13108
$664$	−1.00551e9	−0.133290
$665$	−1.22595e8	−0.0161658
$666$	−1.14182e7	−0.00149774
$667$	5.76193e9	0.751844
$668$	−1.18329e10	−1.53594
$669$	−6.94828e9	−0.897193
$670$	−2.96956e8	−0.0381444
$671$	−3.53685e9	−0.451947
$672$	1.65325e8	0.0210158
$673$	−8.56370e9	−1.08295	−0.541475	−	0.840717i	$-0.682134\pi$
$673$	−8.56370e9	−1.08295	−0.541475	+	0.840717i	$0.682134\pi$
$674$	−5.36505e8	−0.0674939
$675$	−4.86049e8	−0.0608298
$676$	−2.01755e10	−2.51195
$677$	−1.32503e10	−1.64122	−0.820608	−	0.571492i	$-0.806365\pi$
$677$	−1.32503e10	−1.64122	−0.820608	+	0.571492i	$0.806365\pi$
$678$	−1.88923e8	−0.0232799
$679$	−2.88928e9	−0.354198
$680$	5.16981e8	0.0630512
$681$	−3.45776e9	−0.419546
$682$	−5.46643e7	−0.00659870
$683$	1.52557e10	1.83214	0.916070	−	0.401018i	$-0.131344\pi$
$683$	1.52557e10	1.83214	0.916070	+	0.401018i	$0.131344\pi$
$684$	1.63573e8	0.0195441
$685$	4.07997e8	0.0484998
$686$	−1.94159e8	−0.0229627
$687$	2.45942e9	0.289391
$688$	−1.03986e10	−1.21735
$689$	1.60151e10	1.86536
$690$	2.37057e8	0.0274714
$691$	2.37047e9	0.273314	0.136657	−	0.990618i	$-0.456364\pi$
$691$	2.37047e9	0.273314	0.136657	+	0.990618i	$0.456364\pi$
$692$	1.40100e10	1.60719
$693$	2.82279e8	0.0322190
$694$	4.68936e8	0.0532544
$695$	−5.61716e9	−0.634702
$696$	−1.78754e8	−0.0200966
$697$	9.66540e8	0.108120
$698$	9.27960e7	0.0103285
$699$	−1.69756e9	−0.187999
$700$	9.53766e8	0.105099
$701$	−8.71012e9	−0.955017	−0.477508	−	0.878627i	$-0.658460\pi$
$701$	−8.71012e9	−0.955017	−0.477508	+	0.878627i	$0.658460\pi$
$702$	−1.20742e8	−0.0131728
$703$	6.65641e7	0.00722598
$704$	−2.66609e9	−0.287985
$705$	1.43188e9	0.153902
$706$	4.15914e8	0.0444823
$707$	−2.94320e9	−0.313221
$708$	7.08844e8	0.0750644
$709$	−8.22562e9	−0.866775	−0.433388	−	0.901208i	$-0.642682\pi$
$709$	−8.22562e9	−0.866775	−0.433388	+	0.901208i	$0.642682\pi$
$710$	3.83623e8	0.0402254
$711$	3.37130e9	0.351766
$712$	7.35071e8	0.0763219
$713$	−9.49736e9	−0.981272
$714$	−7.13203e7	−0.00733279
$715$	−4.39955e9	−0.450130
$716$	−5.56930e9	−0.567029
$717$	−5.71245e9	−0.578770
$718$	−2.20710e7	−0.00222529
$719$	−5.78538e9	−0.580471	−0.290236	−	0.956955i	$-0.593734\pi$
$719$	−5.78538e9	−0.580471	−0.290236	+	0.956955i	$0.593734\pi$
$720$	2.74983e9	0.274563
$721$	−3.53911e9	−0.351658
$722$	−3.67924e8	−0.0363813
$723$	3.81292e8	0.0375210
$724$	1.65873e10	1.62440
$725$	−1.54720e9	−0.150787
$726$	−1.99003e8	−0.0193011
$727$	−1.00474e10	−0.969798	−0.484899	−	0.874570i	$-0.661144\pi$
$727$	−1.00474e10	−0.969798	−0.484899	+	0.874570i	$0.661144\pi$
$728$	4.74176e8	0.0455491
$729$	3.87420e8	0.0370370
$730$	−5.59874e8	−0.0532672
$731$	1.34877e10	1.27711
$732$	9.52539e9	0.897623
$733$	7.89455e9	0.740395	0.370198	−	0.928953i	$-0.379290\pi$
$733$	7.89455e9	0.740395	0.370198	+	0.928953i	$0.379290\pi$
$734$	5.45800e7	0.00509445
$735$	−4.57003e9	−0.424535
$736$	1.86364e9	0.172301
$737$	−3.98603e9	−0.366779
$738$	−1.37495e7	−0.00125918
$739$	8.45416e9	0.770575	0.385288	−	0.922797i	$-0.374102\pi$
$739$	8.45416e9	0.770575	0.385288	+	0.922797i	$0.374102\pi$
$740$	1.12051e9	0.101649
$741$	7.03884e8	0.0635532
$742$	−1.34571e8	−0.0120931
$743$	5.05511e9	0.452137	0.226068	−	0.974111i	$-0.427413\pi$
$743$	5.05511e9	0.452137	0.226068	+	0.974111i	$0.427413\pi$
$744$	2.94639e8	0.0262292
$745$	1.77559e10	1.57324
$746$	4.82097e7	0.00425156
$747$	6.93715e9	0.608919
$748$	3.46739e9	0.302933
$749$	−7.03997e9	−0.612187
$750$	−2.65043e8	−0.0229405
$751$	−1.42778e10	−1.23005	−0.615023	−	0.788509i	$-0.710853\pi$
$751$	−1.42778e10	−1.23005	−0.615023	+	0.788509i	$0.710853\pi$
$752$	3.74392e9	0.321043
$753$	2.19848e9	0.187646
$754$	−3.84348e8	−0.0326532
$755$	9.90116e9	0.837282
$756$	−7.60230e8	−0.0639909
$757$	1.01019e10	0.846388	0.423194	−	0.906039i	$-0.360909\pi$
$757$	1.01019e10	0.846388	0.423194	+	0.906039i	$0.360909\pi$
$758$	6.36864e8	0.0531135
$759$	3.18201e9	0.264153
$760$	4.28731e7	0.00354272
$761$	−3.03041e9	−0.249261	−0.124631	−	0.992203i	$-0.539775\pi$
$761$	−3.03041e9	−0.249261	−0.124631	+	0.992203i	$0.539775\pi$
$762$	−1.14224e8	−0.00935222
$763$	5.57067e9	0.454016
$764$	−3.92859e9	−0.318720
$765$	−3.56672e9	−0.288041
$766$	−4.58464e8	−0.0368557
$767$	3.05028e9	0.244093
$768$	7.15135e9	0.569671
$769$	−1.80433e10	−1.43078	−0.715392	−	0.698723i	$-0.753752\pi$
$769$	−1.80433e10	−1.43078	−0.715392	+	0.698723i	$0.753752\pi$
$770$	3.69684e7	0.00291819
$771$	5.97633e9	0.469618
$772$	−1.59081e10	−1.24440
$773$	−1.03732e10	−0.807766	−0.403883	−	0.914811i	$-0.632340\pi$
$773$	−1.03732e10	−0.807766	−0.403883	+	0.914811i	$0.632340\pi$
$774$	−1.91869e8	−0.0148735
$775$	2.55024e9	0.196800
$776$	1.01042e9	0.0776220
$777$	−3.09366e8	−0.0236592
$778$	1.45439e8	0.0110726
$779$	8.01549e7	0.00607503
$780$	1.18488e10	0.894014
$781$	5.14936e9	0.386789
$782$	−8.03963e8	−0.0601191
$783$	1.23325e9	0.0918087
$784$	−1.19492e10	−0.885590
$785$	1.27416e10	0.940113
$786$	2.44971e8	0.0179944
$787$	−1.10014e10	−0.804518	−0.402259	−	0.915526i	$-0.631775\pi$
$787$	−1.10014e10	−0.804518	−0.402259	+	0.915526i	$0.631775\pi$
$788$	6.94950e9	0.505955
$789$	1.21302e10	0.879222
$790$	4.41520e8	0.0318607
$791$	−5.11871e9	−0.367742
$792$	−9.87163e7	−0.00706075
$793$	4.09894e10	2.91887
$794$	5.09067e8	0.0360913
$795$	−6.72990e9	−0.475033
$796$	−1.80080e10	−1.26552
$797$	1.83467e10	1.28367	0.641834	−	0.766843i	$-0.278174\pi$
$797$	1.83467e10	1.28367	0.641834	+	0.766843i	$0.278174\pi$
$798$	−5.91457e6	−0.000412015 0
$799$	−4.85612e9	−0.336803
$800$	−5.00426e8	−0.0345561
$801$	−5.07135e9	−0.348666
$802$	−8.07085e8	−0.0552470
$803$	−7.51515e9	−0.512193
$804$	1.07351e10	0.728469
$805$	6.42288e9	0.433954
$806$	6.33518e8	0.0426174
$807$	−1.08058e10	−0.723767
$808$	1.02927e9	0.0686420
$809$	1.83197e10	1.21646	0.608231	−	0.793760i	$-0.291879\pi$
$809$	1.83197e10	1.21646	0.608231	+	0.793760i	$0.291879\pi$
$810$	5.07382e7	0.00335458
$811$	−8.15379e9	−0.536768	−0.268384	−	0.963312i	$-0.586490\pi$
$811$	−8.15379e9	−0.536768	−0.268384	+	0.963312i	$0.586490\pi$
$812$	−2.41998e9	−0.158623
$813$	6.02376e9	0.393143
$814$	−2.00723e7	−0.00130440
$815$	8.69918e9	0.562894
$816$	−9.32585e9	−0.600859
$817$	1.11853e9	0.0717583
$818$	−3.33195e8	−0.0212844
$819$	−3.27140e9	−0.208085
$820$	1.34929e9	0.0854586
$821$	−1.71557e10	−1.08195	−0.540977	−	0.841038i	$-0.681945\pi$
$821$	−1.71557e10	−1.08195	−0.540977	+	0.841038i	$0.681945\pi$
$822$	1.96837e7	0.00123610
$823$	3.13687e10	1.96154	0.980771	−	0.195160i	$-0.0625227\pi$
$823$	3.13687e10	1.96154	0.980771	+	0.195160i	$0.0625227\pi$
$824$	1.23767e9	0.0770653
$825$	−8.54437e8	−0.0529775
$826$	−2.56308e7	−0.00158246
$827$	−3.08831e10	−1.89868	−0.949338	−	0.314256i	$-0.898245\pi$
$827$	−3.08831e10	−1.89868	−0.949338	+	0.314256i	$0.898245\pi$
$828$	−8.56974e9	−0.524640
$829$	2.08621e10	1.27180	0.635899	−	0.771773i	$-0.280630\pi$
$829$	2.08621e10	1.27180	0.635899	+	0.771773i	$0.280630\pi$
$830$	9.08519e8	0.0551519
$831$	7.67713e9	0.464083
$832$	3.08980e10	1.85994
$833$	1.54989e10	0.929062
$834$	−2.70998e8	−0.0161765
$835$	2.13973e10	1.27191
$836$	2.87550e8	0.0170212
$837$	−2.03275e9	−0.119824
$838$	−5.67784e8	−0.0333295
$839$	3.33343e10	1.94861	0.974303	−	0.225241i	$-0.0723169\pi$
$839$	3.33343e10	1.94861	0.974303	+	0.225241i	$0.0723169\pi$
$840$	−1.99259e8	−0.0115995
$841$	−1.33242e10	−0.772421
$842$	−3.51615e8	−0.0202990
$843$	−8.79040e9	−0.505373
$844$	−2.65094e10	−1.51776
$845$	3.64831e10	2.08014
$846$	6.90805e7	0.00392247
$847$	−5.39183e9	−0.304891
$848$	−1.75966e10	−0.990930
$849$	−1.26004e9	−0.0706654
$850$	2.15881e8	0.0120573
$851$	−3.48735e9	−0.193973
$852$	−1.38682e10	−0.768212
$853$	−5.30610e9	−0.292721	−0.146360	−	0.989231i	$-0.546756\pi$
$853$	−5.30610e9	−0.292721	−0.146360	+	0.989231i	$0.546756\pi$
$854$	−3.44424e8	−0.0189231
$855$	−2.95787e8	−0.0161844
$856$	2.46196e9	0.134160
$857$	−3.22916e9	−0.175250	−0.0876248	−	0.996154i	$-0.527928\pi$
$857$	−3.22916e9	−0.175250	−0.0876248	+	0.996154i	$0.527928\pi$
$858$	−2.12255e8	−0.0114723
$859$	−1.09723e10	−0.590637	−0.295318	−	0.955399i	$-0.595426\pi$
$859$	−1.09723e10	−0.590637	−0.295318	+	0.955399i	$0.595426\pi$
$860$	1.88288e10	1.00944
$861$	−3.72531e8	−0.0198908
$862$	1.55620e8	0.00827540
$863$	1.83908e10	0.974009	0.487005	−	0.873399i	$-0.338090\pi$
$863$	1.83908e10	0.974009	0.487005	+	0.873399i	$0.338090\pi$
$864$	3.98881e8	0.0210400
$865$	−2.53340e10	−1.33091
$866$	4.71159e8	0.0246522
$867$	1.01712e9	0.0530035
$868$	3.98884e9	0.207027
$869$	5.92650e9	0.306358
$870$	1.61511e8	0.00831544
$871$	4.61951e10	2.36882
$872$	−1.94813e9	−0.0994970
$873$	−6.97100e9	−0.354605
$874$	−6.66724e7	−0.00337797
$875$	−7.18113e9	−0.362380
$876$	2.02397e10	1.01728
$877$	2.93823e10	1.47091	0.735456	−	0.677572i	$-0.236968\pi$
$877$	2.93823e10	1.47091	0.735456	+	0.677572i	$0.236968\pi$
$878$	4.75068e8	0.0236878
$879$	−2.07974e9	−0.103287
$880$	4.83399e9	0.239120
$881$	7.96639e9	0.392506	0.196253	−	0.980553i	$-0.437123\pi$
$881$	7.96639e9	0.392506	0.196253	+	0.980553i	$0.437123\pi$
$882$	−2.20480e8	−0.0108200
$883$	−2.11047e10	−1.03161	−0.515806	−	0.856706i	$-0.672507\pi$
$883$	−2.11047e10	−1.03161	−0.515806	+	0.856706i	$0.672507\pi$
$884$	−4.01844e10	−1.95648
$885$	−1.28179e9	−0.0621607
$886$	2.06374e8	0.00996868
$887$	−3.91929e10	−1.88571	−0.942854	−	0.333206i	$-0.891870\pi$
$887$	−3.91929e10	−1.88571	−0.942854	+	0.333206i	$0.891870\pi$
$888$	1.08189e8	0.00518487
$889$	−3.09480e9	−0.147733
$890$	−6.64165e8	−0.0315799
$891$	6.81056e8	0.0322560
$892$	3.28961e10	1.55191
$893$	−4.02717e8	−0.0189243
$894$	8.56627e8	0.0400969
$895$	1.00709e10	0.469555
$896$	−1.04339e9	−0.0484584
$897$	−3.68771e10	−1.70602
$898$	7.04325e8	0.0324568
$899$	−6.47071e9	−0.297025
$900$	2.30116e9	0.105220
$901$	2.28240e10	1.03957
$902$	−2.41706e7	−0.00109664
$903$	−5.19855e9	−0.234950
$904$	1.79007e9	0.0805901
$905$	−2.99946e10	−1.34516
$906$	4.77678e8	0.0213396
$907$	7.45412e9	0.331719	0.165860	−	0.986149i	$-0.446960\pi$
$907$	7.45412e9	0.331719	0.165860	+	0.986149i	$0.446960\pi$
$908$	1.63705e10	0.725707
$909$	−7.10107e9	−0.313581
$910$	−4.28436e8	−0.0188470
$911$	3.46618e9	0.151893	0.0759463	−	0.997112i	$-0.475802\pi$
$911$	3.46618e9	0.151893	0.0759463	+	0.997112i	$0.475802\pi$
$912$	−7.73390e8	−0.0337611
$913$	1.21950e10	0.530315
$914$	−2.51989e8	−0.0109162
$915$	−1.72246e10	−0.743319
$916$	−1.16440e10	−0.500572
$917$	6.63730e9	0.284249
$918$	−1.72075e8	−0.00734122
$919$	−1.94364e9	−0.0826060	−0.0413030	−	0.999147i	$-0.513151\pi$
$919$	−1.94364e9	−0.0826060	−0.0413030	+	0.999147i	$0.513151\pi$
$920$	−2.24616e9	−0.0951005
$921$	−4.53355e9	−0.191218
$922$	8.63700e8	0.0362915
$923$	−5.96772e10	−2.49806
$924$	−1.33643e9	−0.0557306
$925$	9.36428e8	0.0389026
$926$	−1.59949e8	−0.00661979
$927$	−8.53883e9	−0.352062
$928$	1.26973e9	0.0521546
$929$	3.65536e10	1.49581	0.747904	−	0.663807i	$-0.231061\pi$
$929$	3.65536e10	1.49581	0.747904	+	0.663807i	$0.231061\pi$
$930$	−2.66218e8	−0.0108529
$931$	1.28532e9	0.0522022
$932$	8.03696e9	0.325189
$933$	−6.01365e9	−0.242411
$934$	1.01978e8	0.00409536
$935$	−6.27002e9	−0.250858
$936$	1.14405e9	0.0456014
$937$	−2.70613e10	−1.07463	−0.537317	−	0.843380i	$-0.680562\pi$
$937$	−2.70613e10	−1.07463	−0.537317	+	0.843380i	$0.680562\pi$
$938$	−3.88167e8	−0.0153571
$939$	−6.04669e9	−0.238335
$940$	−6.77912e9	−0.266211
$941$	−3.52735e10	−1.38002	−0.690010	−	0.723800i	$-0.742394\pi$
$941$	−3.52735e10	−1.38002	−0.690010	+	0.723800i	$0.742394\pi$
$942$	6.14714e8	0.0239604
$943$	−4.19938e9	−0.163078
$944$	−3.35148e9	−0.129669
$945$	1.37471e9	0.0529908
$946$	−3.37292e8	−0.0129535
$947$	−1.60900e10	−0.615648	−0.307824	−	0.951443i	$-0.599601\pi$
$947$	−1.60900e10	−0.615648	−0.307824	+	0.951443i	$0.599601\pi$
$948$	−1.59612e10	−0.608465
$949$	8.70950e10	3.30797
$950$	1.79030e7	0.000677474 0
$951$	2.04589e10	0.771349
$952$	6.75771e8	0.0253846
$953$	2.34617e10	0.878081	0.439040	−	0.898467i	$-0.355319\pi$
$953$	2.34617e10	0.878081	0.439040	+	0.898467i	$0.355319\pi$
$954$	−3.24682e8	−0.0121071
$955$	7.10400e9	0.263932
$956$	2.70452e10	1.00112
$957$	2.16796e9	0.0799574
$958$	−1.36035e9	−0.0499888
$959$	5.33313e8	0.0195262
$960$	−1.29840e10	−0.473651
$961$	−1.68470e10	−0.612337
$962$	2.32623e8	0.00842441
$963$	−1.69854e10	−0.612891
$964$	−1.80520e9	−0.0649016
$965$	2.87664e10	1.03048
$966$	3.09869e8	0.0110601
$967$	2.75570e10	0.980029	0.490014	−	0.871714i	$-0.336992\pi$
$967$	2.75570e10	0.980029	0.490014	+	0.871714i	$0.336992\pi$
$968$	1.88559e9	0.0668163
$969$	1.00314e9	0.0354183
$970$	−9.12951e8	−0.0321179
$971$	−3.36601e10	−1.17991	−0.589954	−	0.807437i	$-0.700854\pi$
$971$	−3.36601e10	−1.17991	−0.589954	+	0.807437i	$0.700854\pi$
$972$	−1.83421e9	−0.0640645
$973$	−7.34247e9	−0.255533
$974$	6.79111e8	0.0235496
$975$	9.90228e9	0.342152
$976$	−4.50370e10	−1.55058
$977$	−3.08878e9	−0.105963	−0.0529817	−	0.998595i	$-0.516872\pi$
$977$	−3.08878e9	−0.105963	−0.0529817	+	0.998595i	$0.516872\pi$
$978$	4.19689e8	0.0143463
$979$	−8.91505e9	−0.303658
$980$	2.16365e10	0.734337
$981$	1.34404e10	0.454538
$982$	1.17779e9	0.0396896
$983$	−4.00750e10	−1.34566	−0.672832	−	0.739796i	$-0.734922\pi$
$983$	−4.00750e10	−1.34566	−0.672832	+	0.739796i	$0.734922\pi$
$984$	1.30279e8	0.00435903
$985$	−1.25667e10	−0.418980
$986$	−5.47754e8	−0.0181977
$987$	1.87168e9	0.0619615
$988$	−3.33248e9	−0.109931
$989$	−5.86010e10	−1.92627
$990$	8.91940e7	0.00292154
$991$	−3.18674e9	−0.104013	−0.0520066	−	0.998647i	$-0.516562\pi$
$991$	−3.18674e9	−0.104013	−0.0520066	+	0.998647i	$0.516562\pi$
$992$	−2.09288e9	−0.0680697
$993$	8.05272e9	0.260988
$994$	5.01453e8	0.0161949
$995$	3.25636e10	1.04798
$996$	−3.28434e10	−1.05327
$997$	−4.16475e8	−0.0133093	−0.00665465	−	0.999978i	$-0.502118\pi$
$997$	−4.16475e8	−0.0133093	−0.00665465	+	0.999978i	$0.502118\pi$
$998$	1.54231e9	0.0491150
$999$	−7.46410e8	−0.0236864

Twists

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

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

\(f(q)\)	\(=\)	\(q+0.413031 q^{2} +27.0000 q^{3} -127.829 q^{4} +231.152 q^{5} +11.1518 q^{6} +302.150 q^{7} -105.665 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+0.413031 q^{2} +27.0000 q^{3} -127.829 q^{4} +231.152 q^{5} +11.1518 q^{6} +302.150 q^{7} -105.665 q^{8} +729.000 q^{9} +95.4729 q^{10} +1281.53 q^{11} -3451.39 q^{12} -14851.9 q^{13} +124.797 q^{14} +6241.10 q^{15} +16318.5 q^{16} -21166.2 q^{17} +301.100 q^{18} -1755.31 q^{19} -29548.0 q^{20} +8158.05 q^{21} +529.311 q^{22} +91962.2 q^{23} -2852.97 q^{24} -24693.8 q^{25} -6134.31 q^{26} +19683.0 q^{27} -38623.7 q^{28} +62655.4 q^{29} +2577.77 q^{30} -103275. q^{31} +20265.2 q^{32} +34601.2 q^{33} -8742.32 q^{34} +69842.6 q^{35} -93187.6 q^{36} -37921.6 q^{37} -724.998 q^{38} -401003. q^{39} -24424.8 q^{40} -45664.2 q^{41} +3369.53 q^{42} -637229. q^{43} -163817. q^{44} +168510. q^{45} +37983.3 q^{46} +229428. q^{47} +440600. q^{48} -732248. q^{49} -10199.3 q^{50} -571488. q^{51} +1.89852e6 q^{52} -1.07832e6 q^{53} +8129.69 q^{54} +296227. q^{55} -31926.8 q^{56} -47393.4 q^{57} +25878.6 q^{58} -205379. q^{59} -797796. q^{60} -2.75987e6 q^{61} -42655.6 q^{62} +220267. q^{63} -2.08040e6 q^{64} -3.43305e6 q^{65} +14291.4 q^{66} -3.11037e6 q^{67} +2.70567e6 q^{68} +2.48298e6 q^{69} +28847.1 q^{70} +4.01814e6 q^{71} -77030.1 q^{72} -5.86422e6 q^{73} -15662.8 q^{74} -666733. q^{75} +224380. q^{76} +387214. q^{77} -165627. q^{78} +4.62456e6 q^{79} +3.77206e6 q^{80} +531441. q^{81} -18860.7 q^{82} +9.51599e6 q^{83} -1.04284e6 q^{84} -4.89262e6 q^{85} -263195. q^{86} +1.69170e6 q^{87} -135413. q^{88} -6.95658e6 q^{89} +69599.7 q^{90} -4.48752e6 q^{91} -1.17555e7 q^{92} -2.78841e6 q^{93} +94760.7 q^{94} -405743. q^{95} +547161. q^{96} -9.56241e6 q^{97} -302441. q^{98} +934234. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 32 q^{2} + 459 q^{3} + 1166 q^{4} - 1072 q^{5} - 864 q^{6} - 2407 q^{7} - 6645 q^{8} + 12393 q^{9}+O(q^{10}) \) 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

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