LMFDB - Embedded newform 177.8.a.b.1.5

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			1.5
Root			$-11.3335$ 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)

$f(q)$	$=$	$q-13.3335 q^{2} +27.0000 q^{3} +49.7814 q^{4} +152.093 q^{5} -360.004 q^{6} -1328.47 q^{7} +1042.93 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-13.3335 q^{2} +27.0000 q^{3} +49.7814 q^{4} +152.093 q^{5} -360.004 q^{6} -1328.47 q^{7} +1042.93 q^{8} +729.000 q^{9} -2027.93 q^{10} +5132.02 q^{11} +1344.10 q^{12} -12251.2 q^{13} +17713.2 q^{14} +4106.51 q^{15} -20277.8 q^{16} +26601.9 q^{17} -9720.10 q^{18} +33197.2 q^{19} +7571.39 q^{20} -35868.8 q^{21} -68427.7 q^{22} -97057.0 q^{23} +28159.0 q^{24} -54992.8 q^{25} +163351. q^{26} +19683.0 q^{27} -66133.3 q^{28} +209269. q^{29} -54754.0 q^{30} -308874. q^{31} +136879. q^{32} +138565. q^{33} -354695. q^{34} -202052. q^{35} +36290.6 q^{36} +287842. q^{37} -442634. q^{38} -330783. q^{39} +158622. q^{40} +581611. q^{41} +478256. q^{42} +540792. q^{43} +255479. q^{44} +110876. q^{45} +1.29411e6 q^{46} -650609. q^{47} -547501. q^{48} +941302. q^{49} +733244. q^{50} +718250. q^{51} -609883. q^{52} -49948.0 q^{53} -262443. q^{54} +780544. q^{55} -1.38550e6 q^{56} +896326. q^{57} -2.79028e6 q^{58} -205379. q^{59} +204428. q^{60} -20025.0 q^{61} +4.11836e6 q^{62} -968458. q^{63} +770486. q^{64} -1.86332e6 q^{65} -1.84755e6 q^{66} -1.38680e6 q^{67} +1.32428e6 q^{68} -2.62054e6 q^{69} +2.69405e6 q^{70} +1.24373e6 q^{71} +760293. q^{72} -4.83751e6 q^{73} -3.83794e6 q^{74} -1.48480e6 q^{75} +1.65260e6 q^{76} -6.81777e6 q^{77} +4.41048e6 q^{78} -2.94089e6 q^{79} -3.08411e6 q^{80} +531441. q^{81} -7.75490e6 q^{82} -8.62802e6 q^{83} -1.78560e6 q^{84} +4.04595e6 q^{85} -7.21064e6 q^{86} +5.65025e6 q^{87} +5.35232e6 q^{88} -879309. q^{89} -1.47836e6 q^{90} +1.62754e7 q^{91} -4.83163e6 q^{92} -8.33960e6 q^{93} +8.67488e6 q^{94} +5.04907e6 q^{95} +3.69574e6 q^{96} -1.62017e7 q^{97} -1.25508e7 q^{98} +3.74125e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−13.3335	−1.17852	−0.589262	−	0.807942i	$-0.700581\pi$
$2$	−13.3335	−1.17852	−0.589262	+	0.807942i	$0.700581\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	49.7814	0.388917
$5$	152.093	0.544144	0.272072	−	0.962277i	$-0.412291\pi$
$5$	152.093	0.544144	0.272072	+	0.962277i	$0.412291\pi$
$6$	−360.004	−0.680421
$7$	−1328.47	−1.46390	−0.731948	−	0.681361i	$-0.761389\pi$
$7$	−1328.47	−1.46390	−0.731948	+	0.681361i	$0.761389\pi$
$8$	1042.93	0.720176
$9$	729.000	0.333333
$10$	−2027.93	−0.641286
$11$	5132.02	1.16256	0.581279	−	0.813705i	$-0.302553\pi$
$11$	5132.02	1.16256	0.581279	+	0.813705i	$0.302553\pi$
$12$	1344.10	0.224541
$13$	−12251.2	−1.54660	−0.773299	−	0.634041i	$-0.781395\pi$
$13$	−12251.2	−1.54660	−0.773299	+	0.634041i	$0.781395\pi$
$14$	17713.2	1.72524
$15$	4106.51	0.314162
$16$	−20277.8	−1.23766
$17$	26601.9	1.31323	0.656615	−	0.754226i	$-0.271988\pi$
$17$	26601.9	1.31323	0.656615	+	0.754226i	$0.271988\pi$
$18$	−9720.10	−0.392841
$19$	33197.2	1.11036	0.555181	−	0.831730i	$-0.312649\pi$
$19$	33197.2	1.11036	0.555181	+	0.831730i	$0.312649\pi$
$20$	7571.39	0.211627
$21$	−35868.8	−0.845181
$22$	−68427.7	−1.37010
$23$	−97057.0	−1.66333	−0.831667	−	0.555274i	$-0.812613\pi$
$23$	−97057.0	−1.66333	−0.831667	+	0.555274i	$0.812613\pi$
$24$	28159.0	0.415794
$25$	−54992.8	−0.703907
$26$	163351.	1.82270
$27$	19683.0	0.192450
$28$	−66133.3	−0.569334
$29$	209269.	1.59335	0.796675	−	0.604408i	$-0.206590\pi$
$29$	209269.	1.59335	0.796675	+	0.604408i	$0.206590\pi$
$30$	−54754.0	−0.370247
$31$	−308874.	−1.86215	−0.931077	−	0.364823i	$-0.881129\pi$
$31$	−308874.	−1.86215	−0.931077	+	0.364823i	$0.881129\pi$
$32$	136879.	0.738436
$33$	138565.	0.671203
$34$	−354695.	−1.54767
$35$	−202052.	−0.796570
$36$	36290.6	0.129639
$37$	287842.	0.934219	0.467110	−	0.884199i	$-0.345295\pi$
$37$	287842.	0.934219	0.467110	+	0.884199i	$0.345295\pi$
$38$	−442634.	−1.30859
$39$	−330783.	−0.892929
$40$	158622.	0.391879
$41$	581611.	1.31792	0.658960	−	0.752178i	$-0.270996\pi$
$41$	581611.	1.31792	0.658960	+	0.752178i	$0.270996\pi$
$42$	478256.	0.996065
$43$	540792.	1.03727	0.518634	−	0.854996i	$-0.326441\pi$
$43$	540792.	1.03727	0.518634	+	0.854996i	$0.326441\pi$
$44$	255479.	0.452138
$45$	110876.	0.181381
$46$	1.29411e6	1.96028
$47$	−650609.	−0.914066	−0.457033	−	0.889450i	$-0.651088\pi$
$47$	−650609.	−0.914066	−0.457033	+	0.889450i	$0.651088\pi$
$48$	−547501.	−0.714564
$49$	941302.	1.14299
$50$	733244.	0.829571
$51$	718250.	0.758194
$52$	−609883.	−0.601499
$53$	−49948.0	−0.0460843	−0.0230421	−	0.999734i	$-0.507335\pi$
$53$	−49948.0	−0.0460843	−0.0230421	+	0.999734i	$0.507335\pi$
$54$	−262443.	−0.226807
$55$	780544.	0.632599
$56$	−1.38550e6	−1.05426
$57$	896326.	0.641068
$58$	−2.79028e6	−1.87780
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	204428.	0.122183
$61$	−20025.0	−0.0112958	−0.00564791	−	0.999984i	$-0.501798\pi$
$61$	−20025.0	−0.0112958	−0.00564791	+	0.999984i	$0.501798\pi$
$62$	4.11836e6	2.19459
$63$	−968458.	−0.487965
$64$	770486.	0.367396
$65$	−1.86332e6	−0.841573
$66$	−1.84755e6	−0.791028
$67$	−1.38680e6	−0.563314	−0.281657	−	0.959515i	$-0.590884\pi$
$67$	−1.38680e6	−0.563314	−0.281657	+	0.959515i	$0.590884\pi$
$68$	1.32428e6	0.510738
$69$	−2.62054e6	−0.960327
$70$	2.69405e6	0.938776
$71$	1.24373e6	0.412403	0.206201	−	0.978510i	$-0.433890\pi$
$71$	1.24373e6	0.412403	0.206201	+	0.978510i	$0.433890\pi$
$72$	760293.	0.240059
$73$	−4.83751e6	−1.45543	−0.727716	−	0.685879i	$-0.759418\pi$
$73$	−4.83751e6	−1.45543	−0.727716	+	0.685879i	$0.759418\pi$
$74$	−3.83794e6	−1.10100
$75$	−1.48480e6	−0.406401
$76$	1.65260e6	0.431839
$77$	−6.81777e6	−1.70186
$78$	4.41048e6	1.05234
$79$	−2.94089e6	−0.671095	−0.335547	−	0.942023i	$-0.608921\pi$
$79$	−2.94089e6	−0.671095	−0.335547	+	0.942023i	$0.608921\pi$
$80$	−3.08411e6	−0.673466
$81$	531441.	0.111111
$82$	−7.75490e6	−1.55320
$83$	−8.62802e6	−1.65630	−0.828148	−	0.560510i	$-0.810605\pi$
$83$	−8.62802e6	−1.65630	−0.828148	+	0.560510i	$0.810605\pi$
$84$	−1.78560e6	−0.328705
$85$	4.04595e6	0.714586
$86$	−7.21064e6	−1.22244
$87$	5.65025e6	0.919921
$88$	5.35232e6	0.837245
$89$	−879309.	−0.132214	−0.0661069	−	0.997813i	$-0.521058\pi$
$89$	−879309.	−0.132214	−0.0661069	+	0.997813i	$0.521058\pi$
$90$	−1.47836e6	−0.213762
$91$	1.62754e7	2.26406
$92$	−4.83163e6	−0.646899
$93$	−8.33960e6	−1.07511
$94$	8.67488e6	1.07725
$95$	5.04907e6	0.604197
$96$	3.69574e6	0.426336
$97$	−1.62017e7	−1.80244	−0.901220	−	0.433362i	$-0.857327\pi$
$97$	−1.62017e7	−1.80244	−0.901220	+	0.433362i	$0.857327\pi$
$98$	−1.25508e7	−1.34704
$99$	3.74125e6	0.387519
$100$	−2.73761e6	−0.273761
$101$	617795.	0.0596650	0.0298325	−	0.999555i	$-0.490503\pi$
$101$	617795.	0.0596650	0.0298325	+	0.999555i	$0.490503\pi$
$102$	−9.57677e6	−0.893549
$103$	−6.98654e6	−0.629988	−0.314994	−	0.949094i	$-0.602002\pi$
$103$	−6.98654e6	−0.629988	−0.314994	+	0.949094i	$0.602002\pi$
$104$	−1.27771e7	−1.11382
$105$	−5.45539e6	−0.459900
$106$	665980.	0.0543114
$107$	−7.47019e6	−0.589506	−0.294753	−	0.955573i	$-0.595237\pi$
$107$	−7.47019e6	−0.589506	−0.294753	+	0.955573i	$0.595237\pi$
$108$	979847.	0.0748471
$109$	−2.25015e7	−1.66425	−0.832125	−	0.554588i	$-0.812876\pi$
$109$	−2.25015e7	−1.66425	−0.832125	+	0.554588i	$0.812876\pi$
$110$	−1.04074e7	−0.745532
$111$	7.77175e6	0.539372
$112$	2.69386e7	1.81181
$113$	7.33737e6	0.478372	0.239186	−	0.970974i	$-0.423119\pi$
$113$	7.33737e6	0.478372	0.239186	+	0.970974i	$0.423119\pi$
$114$	−1.19511e7	−0.755513
$115$	−1.47617e7	−0.905094
$116$	1.04177e7	0.619681
$117$	−8.93114e6	−0.515533
$118$	2.73841e6	0.153431
$119$	−3.53399e7	−1.92243
$120$	4.28278e6	0.226252
$121$	6.85051e6	0.351539
$122$	267002.	0.0133124
$123$	1.57035e7	0.760902
$124$	−1.53762e7	−0.724223
$125$	−2.02463e7	−0.927171
$126$	1.29129e7	0.575078
$127$	−1.12559e7	−0.487605	−0.243803	−	0.969825i	$-0.578395\pi$
$127$	−1.12559e7	−0.487605	−0.243803	+	0.969825i	$0.578395\pi$
$128$	−2.77938e7	−1.17142
$129$	1.46014e7	0.598867
$130$	2.48446e7	0.991813
$131$	4.30156e6	0.167177	0.0835885	−	0.996500i	$-0.473362\pi$
$131$	4.30156e6	0.167177	0.0835885	+	0.996500i	$0.473362\pi$
$132$	6.89794e6	0.261042
$133$	−4.41017e7	−1.62545
$134$	1.84908e7	0.663879
$135$	2.99364e6	0.104721
$136$	2.77438e7	0.945756
$137$	−1.85481e7	−0.616281	−0.308140	−	0.951341i	$-0.599707\pi$
$137$	−1.85481e7	−0.616281	−0.308140	+	0.951341i	$0.599707\pi$
$138$	3.49409e7	1.13177
$139$	−4.12956e7	−1.30422	−0.652112	−	0.758123i	$-0.726117\pi$
$139$	−4.12956e7	−1.30422	−0.652112	+	0.758123i	$0.726117\pi$
$140$	−1.00584e7	−0.309800
$141$	−1.75664e7	−0.527736
$142$	−1.65832e7	−0.486026
$143$	−6.28736e7	−1.79801
$144$	−1.47825e7	−0.412554
$145$	3.18283e7	0.867012
$146$	6.45008e7	1.71526
$147$	2.54152e7	0.659906
$148$	1.43292e7	0.363334
$149$	2.77964e7	0.688394	0.344197	−	0.938897i	$-0.388151\pi$
$149$	2.77964e7	0.688394	0.344197	+	0.938897i	$0.388151\pi$
$150$	1.97976e7	0.478953
$151$	5.05159e7	1.19401	0.597006	−	0.802236i	$-0.296357\pi$
$151$	5.05159e7	1.19401	0.597006	+	0.802236i	$0.296357\pi$
$152$	3.46223e7	0.799655
$153$	1.93928e7	0.437743
$154$	9.09045e7	2.00568
$155$	−4.69775e7	−1.01328
$156$	−1.64668e7	−0.347275
$157$	−3.27653e7	−0.675717	−0.337858	−	0.941197i	$-0.609703\pi$
$157$	−3.27653e7	−0.675717	−0.337858	+	0.941197i	$0.609703\pi$
$158$	3.92122e7	0.790901
$159$	−1.34860e6	−0.0266068
$160$	2.08184e7	0.401816
$161$	1.28938e8	2.43495
$162$	−7.08595e6	−0.130947
$163$	3.27745e7	0.592761	0.296381	−	0.955070i	$-0.404220\pi$
$163$	3.27745e7	0.592761	0.296381	+	0.955070i	$0.404220\pi$
$164$	2.89534e7	0.512562
$165$	2.10747e7	0.365231
$166$	1.15041e8	1.95198
$167$	−4.91242e7	−0.816183	−0.408092	−	0.912941i	$-0.633806\pi$
$167$	−4.91242e7	−0.816183	−0.408092	+	0.912941i	$0.633806\pi$
$168$	−3.74085e7	−0.608678
$169$	8.73439e7	1.39197
$170$	−5.39466e7	−0.842157
$171$	2.42008e7	0.370121
$172$	2.69214e7	0.403411
$173$	2.08181e7	0.305688	0.152844	−	0.988250i	$-0.451157\pi$
$173$	2.08181e7	0.305688	0.152844	+	0.988250i	$0.451157\pi$
$174$	−7.53375e7	−1.08415
$175$	7.30565e7	1.03045
$176$	−1.04066e8	−1.43885
$177$	−5.54523e6	−0.0751646
$178$	1.17242e7	0.155817
$179$	8.64093e7	1.12609	0.563047	−	0.826425i	$-0.309629\pi$
$179$	8.64093e7	1.12609	0.563047	+	0.826425i	$0.309629\pi$
$180$	5.51954e6	0.0705423
$181$	−6.54723e7	−0.820696	−0.410348	−	0.911929i	$-0.634593\pi$
$181$	−6.54723e7	−0.820696	−0.410348	+	0.911929i	$0.634593\pi$
$182$	−2.17008e8	−2.66825
$183$	−540674.	−0.00652164
$184$	−1.01223e8	−1.19789
$185$	4.37788e7	0.508350
$186$	1.11196e8	1.26705
$187$	1.36521e8	1.52671
$188$	−3.23882e7	−0.355496
$189$	−2.61484e7	−0.281727
$190$	−6.73215e7	−0.712060
$191$	−8.45503e7	−0.878007	−0.439004	−	0.898485i	$-0.644669\pi$
$191$	−8.45503e7	−0.878007	−0.439004	+	0.898485i	$0.644669\pi$
$192$	2.08031e7	0.212116
$193$	−2.04209e7	−0.204467	−0.102234	−	0.994760i	$-0.532599\pi$
$193$	−2.04209e7	−0.204467	−0.102234	+	0.994760i	$0.532599\pi$
$194$	2.16026e8	2.12422
$195$	−5.03097e7	−0.485882
$196$	4.68593e7	0.444529
$197$	3.23191e7	0.301181	0.150591	−	0.988596i	$-0.451882\pi$
$197$	3.23191e7	0.301181	0.150591	+	0.988596i	$0.451882\pi$
$198$	−4.98838e7	−0.456700
$199$	−7.22071e7	−0.649522	−0.324761	−	0.945796i	$-0.605284\pi$
$199$	−7.22071e7	−0.649522	−0.324761	+	0.945796i	$0.605284\pi$
$200$	−5.73534e7	−0.506937
$201$	−3.74435e7	−0.325229
$202$	−8.23736e6	−0.0703166
$203$	−2.78008e8	−2.33250
$204$	3.57555e7	0.294874
$205$	8.84589e7	0.717139
$206$	9.31549e7	0.742455
$207$	−7.07546e7	−0.554445
$208$	2.48428e8	1.91416
$209$	1.70369e8	1.29086
$210$	7.27393e7	0.542003
$211$	−1.90681e8	−1.39739	−0.698696	−	0.715419i	$-0.746236\pi$
$211$	−1.90681e8	−1.39739	−0.698696	+	0.715419i	$0.746236\pi$
$212$	−2.48648e6	−0.0179230
$213$	3.35807e7	0.238101
$214$	9.96036e7	0.694747
$215$	8.22507e7	0.564423
$216$	2.05279e7	0.138598
$217$	4.10331e8	2.72600
$218$	3.00023e8	1.96136
$219$	−1.30613e8	−0.840294
$220$	3.88566e7	0.246028
$221$	−3.25905e8	−2.03104
$222$	−1.03624e8	−0.635662
$223$	2.03359e8	1.22800	0.613998	−	0.789307i	$-0.289560\pi$
$223$	2.03359e8	1.22800	0.613998	+	0.789307i	$0.289560\pi$
$224$	−1.81841e8	−1.08099
$225$	−4.00897e7	−0.234636
$226$	−9.78326e7	−0.563773
$227$	3.52165e7	0.199828	0.0999139	−	0.994996i	$-0.468143\pi$
$227$	3.52165e7	0.199828	0.0999139	+	0.994996i	$0.468143\pi$
$228$	4.46203e7	0.249322
$229$	−3.50737e8	−1.93000	−0.965000	−	0.262249i	$-0.915536\pi$
$229$	−3.50737e8	−1.93000	−0.965000	+	0.262249i	$0.915536\pi$
$230$	1.96824e8	1.06667
$231$	−1.84080e8	−0.982571
$232$	2.18252e8	1.14749
$233$	−2.71870e8	−1.40804	−0.704020	−	0.710180i	$-0.748613\pi$
$233$	−2.71870e8	−1.40804	−0.704020	+	0.710180i	$0.748613\pi$
$234$	1.19083e8	0.607568
$235$	−9.89530e7	−0.497384
$236$	−1.02240e7	−0.0506327
$237$	−7.94040e7	−0.387457
$238$	4.71203e8	2.26563
$239$	−7.12076e7	−0.337391	−0.168696	−	0.985668i	$-0.553955\pi$
$239$	−7.12076e7	−0.337391	−0.168696	+	0.985668i	$0.553955\pi$
$240$	−8.32711e7	−0.388826
$241$	−2.36356e8	−1.08770	−0.543848	−	0.839184i	$-0.683033\pi$
$241$	−2.36356e8	−1.08770	−0.543848	+	0.839184i	$0.683033\pi$
$242$	−9.13410e7	−0.414297
$243$	1.43489e7	0.0641500
$244$	−996870.	−0.00439313
$245$	1.43165e8	0.621952
$246$	−2.09382e8	−0.896741
$247$	−4.06707e8	−1.71728
$248$	−3.22133e8	−1.34108
$249$	−2.32957e8	−0.956263
$250$	2.69953e8	1.09269
$251$	3.04691e7	0.121619	0.0608094	−	0.998149i	$-0.480632\pi$
$251$	3.04691e7	0.121619	0.0608094	+	0.998149i	$0.480632\pi$
$252$	−4.82112e7	−0.189778
$253$	−4.98099e8	−1.93372
$254$	1.50081e8	0.574654
$255$	1.09241e8	0.412567
$256$	2.71966e8	1.01315
$257$	2.69817e8	0.991524	0.495762	−	0.868458i	$-0.334889\pi$
$257$	2.69817e8	0.991524	0.495762	+	0.868458i	$0.334889\pi$
$258$	−1.94687e8	−0.705779
$259$	−3.82391e8	−1.36760
$260$	−9.27588e7	−0.327302
$261$	1.52557e8	0.531117
$262$	−5.73548e7	−0.197022
$263$	−3.30750e8	−1.12113	−0.560564	−	0.828111i	$-0.689415\pi$
$263$	−3.30750e8	−1.12113	−0.560564	+	0.828111i	$0.689415\pi$
$264$	1.44513e8	0.483384
$265$	−7.59674e6	−0.0250765
$266$	5.88029e8	1.91564
$267$	−2.37413e7	−0.0763336
$268$	−6.90366e7	−0.219082
$269$	3.87843e8	1.21485	0.607426	−	0.794377i	$-0.292202\pi$
$269$	3.87843e8	1.21485	0.607426	+	0.794377i	$0.292202\pi$
$270$	−3.99157e7	−0.123416
$271$	3.62357e8	1.10597	0.552986	−	0.833191i	$-0.313488\pi$
$271$	3.62357e8	1.10597	0.552986	+	0.833191i	$0.313488\pi$
$272$	−5.39428e8	−1.62533
$273$	4.39437e8	1.30716
$274$	2.47311e8	0.726301
$275$	−2.82224e8	−0.818333
$276$	−1.30454e8	−0.373487
$277$	3.92785e8	1.11039	0.555195	−	0.831721i	$-0.312644\pi$
$277$	3.92785e8	1.11039	0.555195	+	0.831721i	$0.312644\pi$
$278$	5.50614e8	1.53706
$279$	−2.25169e8	−0.620718
$280$	−2.10725e8	−0.573670
$281$	2.62473e7	0.0705686	0.0352843	−	0.999377i	$-0.488766\pi$
$281$	2.62473e7	0.0705686	0.0352843	+	0.999377i	$0.488766\pi$
$282$	2.34222e8	0.621950
$283$	3.02721e8	0.793945	0.396972	−	0.917831i	$-0.370061\pi$
$283$	3.02721e8	0.793945	0.396972	+	0.917831i	$0.370061\pi$
$284$	6.19146e7	0.160390
$285$	1.36325e8	0.348833
$286$	8.38323e8	2.11900
$287$	−7.72656e8	−1.92930
$288$	9.97850e7	0.246145
$289$	2.97321e8	0.724574
$290$	−4.24381e8	−1.02179
$291$	−4.37447e8	−1.04064
$292$	−2.40818e8	−0.566042
$293$	4.44159e8	1.03158	0.515789	−	0.856716i	$-0.327499\pi$
$293$	4.44159e8	1.03158	0.515789	+	0.856716i	$0.327499\pi$
$294$	−3.38872e8	−0.777715
$295$	−3.12367e7	−0.0708415
$296$	3.00198e8	0.672802
$297$	1.01014e8	0.223734
$298$	−3.70623e8	−0.811288
$299$	1.18907e9	2.57251
$300$	−7.39156e7	−0.158056
$301$	−7.18429e8	−1.51845
$302$	−6.73552e8	−1.40717
$303$	1.66805e7	0.0344476
$304$	−6.73168e8	−1.37425
$305$	−3.04566e6	−0.00614655
$306$	−2.58573e8	−0.515891
$307$	−7.17875e8	−1.41600	−0.708002	−	0.706211i	$-0.750403\pi$
$307$	−7.17875e8	−1.41600	−0.708002	+	0.706211i	$0.750403\pi$
$308$	−3.39398e8	−0.661883
$309$	−1.88637e8	−0.363724
$310$	6.26374e8	1.19417
$311$	−9.91134e8	−1.86841	−0.934203	−	0.356743i	$-0.883887\pi$
$311$	−9.91134e8	−1.86841	−0.934203	+	0.356743i	$0.883887\pi$
$312$	−3.44982e8	−0.643066
$313$	−1.77188e7	−0.0326610	−0.0163305	−	0.999867i	$-0.505198\pi$
$313$	−1.77188e7	−0.0326610	−0.0163305	+	0.999867i	$0.505198\pi$
$314$	4.36875e8	0.796348
$315$	−1.47296e8	−0.265523
$316$	−1.46401e8	−0.261000
$317$	6.67310e8	1.17658	0.588289	−	0.808651i	$-0.299802\pi$
$317$	6.67310e8	1.17658	0.588289	+	0.808651i	$0.299802\pi$
$318$	1.79815e7	0.0313567
$319$	1.07397e9	1.85236
$320$	1.17185e8	0.199917
$321$	−2.01695e8	−0.340352
$322$	−1.71919e9	−2.86964
$323$	8.83109e8	1.45816
$324$	2.64559e7	0.0432130
$325$	6.73728e8	1.08866
$326$	−4.36998e8	−0.698583
$327$	−6.07540e8	−0.960855
$328$	6.06577e8	0.949134
$329$	8.64318e8	1.33810
$330$	−2.80999e8	−0.430433
$331$	1.21309e9	1.83863	0.919313	−	0.393526i	$-0.128745\pi$
$331$	1.21309e9	1.83863	0.919313	+	0.393526i	$0.128745\pi$
$332$	−4.29515e8	−0.644161
$333$	2.09837e8	0.311406
$334$	6.54996e8	0.961891
$335$	−2.10922e8	−0.306524
$336$	7.27342e8	1.04605
$337$	4.03850e8	0.574799	0.287399	−	0.957811i	$-0.407209\pi$
$337$	4.03850e8	0.574799	0.287399	+	0.957811i	$0.407209\pi$
$338$	−1.16460e9	−1.64047
$339$	1.98109e8	0.276188
$340$	2.01413e8	0.277915
$341$	−1.58515e9	−2.16486
$342$	−3.22681e8	−0.436196
$343$	−1.56440e8	−0.209324
$344$	5.64006e8	0.747015
$345$	−3.98565e8	−0.522556
$346$	−2.77577e8	−0.360261
$347$	−5.73452e8	−0.736791	−0.368395	−	0.929669i	$-0.620093\pi$
$347$	−5.73452e8	−0.736791	−0.368395	+	0.929669i	$0.620093\pi$
$348$	2.81277e8	0.357773
$349$	−3.21244e8	−0.404525	−0.202263	−	0.979331i	$-0.564829\pi$
$349$	−3.21244e8	−0.404525	−0.202263	+	0.979331i	$0.564829\pi$
$350$	−9.74096e8	−1.21441
$351$	−2.41141e8	−0.297643
$352$	7.02468e8	0.858474
$353$	3.98442e8	0.482118	0.241059	−	0.970510i	$-0.422505\pi$
$353$	3.98442e8	0.482118	0.241059	+	0.970510i	$0.422505\pi$
$354$	7.39372e7	0.0885832
$355$	1.89162e8	0.224407
$356$	−4.37732e7	−0.0514202
$357$	−9.54177e8	−1.10992
$358$	−1.15214e9	−1.32713
$359$	1.40704e9	1.60500	0.802501	−	0.596651i	$-0.203502\pi$
$359$	1.40704e9	1.60500	0.802501	+	0.596651i	$0.203502\pi$
$360$	1.15635e8	0.130626
$361$	2.08186e8	0.232903
$362$	8.72973e8	0.967210
$363$	1.84964e8	0.202961
$364$	8.10214e8	0.880531
$365$	−7.35751e8	−0.791965
$366$	7.20906e6	0.00768590
$367$	−9.65705e8	−1.01980	−0.509898	−	0.860235i	$-0.670317\pi$
$367$	−9.65705e8	−1.01980	−0.509898	+	0.860235i	$0.670317\pi$
$368$	1.96811e9	2.05864
$369$	4.23995e8	0.439307
$370$	−5.83723e8	−0.599102
$371$	6.63547e7	0.0674626
$372$	−4.15157e8	−0.418130
$373$	−6.50998e8	−0.649529	−0.324765	−	0.945795i	$-0.605285\pi$
$373$	−6.50998e8	−0.649529	−0.324765	+	0.945795i	$0.605285\pi$
$374$	−1.82030e9	−1.79926
$375$	−5.46649e8	−0.535302
$376$	−6.78537e8	−0.658288
$377$	−2.56380e9	−2.46427
$378$	3.48648e8	0.332022
$379$	−3.97991e7	−0.0375522	−0.0187761	−	0.999824i	$-0.505977\pi$
$379$	−3.97991e7	−0.0375522	−0.0187761	+	0.999824i	$0.505977\pi$
$380$	2.51349e8	0.234982
$381$	−3.03910e8	−0.281519
$382$	1.12735e9	1.03475
$383$	6.27745e7	0.0570936	0.0285468	−	0.999592i	$-0.490912\pi$
$383$	6.27745e7	0.0570936	0.0285468	+	0.999592i	$0.490912\pi$
$384$	−7.50433e8	−0.676320
$385$	−1.03693e9	−0.926058
$386$	2.72281e8	0.240970
$387$	3.94238e8	0.345756
$388$	−8.06545e8	−0.701000
$389$	−4.14596e8	−0.357109	−0.178555	−	0.983930i	$-0.557142\pi$
$389$	−4.14596e8	−0.357109	−0.178555	+	0.983930i	$0.557142\pi$
$390$	6.70803e8	0.572623
$391$	−2.58190e9	−2.18434
$392$	9.81708e8	0.823154
$393$	1.16142e8	0.0965197
$394$	−4.30926e8	−0.354949
$395$	−4.47288e8	−0.365172
$396$	1.86244e8	0.150713
$397$	−5.40817e8	−0.433794	−0.216897	−	0.976194i	$-0.569594\pi$
$397$	−5.40817e8	−0.433794	−0.216897	+	0.976194i	$0.569594\pi$
$398$	9.62771e8	0.765477
$399$	−1.19075e9	−0.938456
$400$	1.11513e9	0.871198
$401$	1.82362e9	1.41231	0.706153	−	0.708059i	$-0.250429\pi$
$401$	1.82362e9	1.41231	0.706153	+	0.708059i	$0.250429\pi$
$402$	4.99251e8	0.383290
$403$	3.78408e9	2.88000
$404$	3.07547e7	0.0232047
$405$	8.08284e7	0.0604604
$406$	3.70681e9	2.74890
$407$	1.47721e9	1.08608
$408$	7.49082e8	0.546033
$409$	1.97200e9	1.42520	0.712599	−	0.701571i	$-0.247518\pi$
$409$	1.97200e9	1.42520	0.712599	+	0.701571i	$0.247518\pi$
$410$	−1.17946e9	−0.845165
$411$	−5.00800e8	−0.355810
$412$	−3.47800e8	−0.245013
$413$	2.72841e8	0.190583
$414$	9.43404e8	0.653426
$415$	−1.31226e9	−0.901263
$416$	−1.67694e9	−1.14206
$417$	−1.11498e9	−0.752994
$418$	−2.27161e9	−1.52131
$419$	4.90370e8	0.325668	0.162834	−	0.986653i	$-0.447936\pi$
$419$	4.90370e8	0.325668	0.162834	+	0.986653i	$0.447936\pi$
$420$	−2.71577e8	−0.178863
$421$	−1.72536e8	−0.112692	−0.0563459	−	0.998411i	$-0.517945\pi$
$421$	−1.72536e8	−0.112692	−0.0563459	+	0.998411i	$0.517945\pi$
$422$	2.54244e9	1.64686
$423$	−4.74294e8	−0.304689
$424$	−5.20921e7	−0.0331888
$425$	−1.46291e9	−0.924392
$426$	−4.47747e8	−0.280607
$427$	2.66027e7	0.0165359
$428$	−3.71876e8	−0.229269
$429$	−1.69759e9	−1.03808
$430$	−1.09669e9	−0.665186
$431$	1.99685e9	1.20136	0.600681	−	0.799489i	$-0.294896\pi$
$431$	1.99685e9	1.20136	0.600681	+	0.799489i	$0.294896\pi$
$432$	−3.99129e8	−0.238188
$433$	−6.53171e8	−0.386651	−0.193326	−	0.981135i	$-0.561927\pi$
$433$	−6.53171e8	−0.386651	−0.193326	+	0.981135i	$0.561927\pi$
$434$	−5.47114e9	−3.21265
$435$	8.59364e8	0.500570
$436$	−1.12015e9	−0.647255
$437$	−3.22203e9	−1.84690
$438$	1.74152e9	0.990306
$439$	−2.18962e9	−1.23521	−0.617607	−	0.786487i	$-0.711898\pi$
$439$	−2.18962e9	−1.23521	−0.617607	+	0.786487i	$0.711898\pi$
$440$	8.14050e8	0.455582
$441$	6.86209e8	0.380997
$442$	4.34545e9	2.39363
$443$	2.98274e9	1.63006	0.815028	−	0.579422i	$-0.196722\pi$
$443$	2.98274e9	1.63006	0.815028	+	0.579422i	$0.196722\pi$
$444$	3.86888e8	0.209771
$445$	−1.33737e8	−0.0719433
$446$	−2.71149e9	−1.44722
$447$	7.50504e8	0.397444
$448$	−1.02357e9	−0.537830
$449$	−1.54617e9	−0.806111	−0.403055	−	0.915176i	$-0.632052\pi$
$449$	−1.54617e9	−0.806111	−0.403055	+	0.915176i	$0.632052\pi$
$450$	5.34535e8	0.276524
$451$	2.98484e9	1.53216
$452$	3.65264e8	0.186047
$453$	1.36393e9	0.689364
$454$	−4.69558e8	−0.235502
$455$	2.47538e9	1.23197
$456$	9.34801e8	0.461681
$457$	−7.00396e8	−0.343271	−0.171635	−	0.985161i	$-0.554905\pi$
$457$	−7.00396e8	−0.343271	−0.171635	+	0.985161i	$0.554905\pi$
$458$	4.67654e9	2.27455
$459$	5.23605e8	0.252731
$460$	−7.34857e8	−0.352006
$461$	−2.39080e9	−1.13655	−0.568277	−	0.822838i	$-0.692390\pi$
$461$	−2.39080e9	−1.13655	−0.568277	+	0.822838i	$0.692390\pi$
$462$	2.45442e9	1.15798
$463$	2.71887e9	1.27308	0.636539	−	0.771244i	$-0.280365\pi$
$463$	2.71887e9	1.27308	0.636539	+	0.771244i	$0.280365\pi$
$464$	−4.24352e9	−1.97203
$465$	−1.26839e9	−0.585017
$466$	3.62496e9	1.65941
$467$	3.63245e9	1.65041	0.825203	−	0.564836i	$-0.191061\pi$
$467$	3.63245e9	1.65041	0.825203	+	0.564836i	$0.191061\pi$
$468$	−4.44604e8	−0.200500
$469$	1.84232e9	0.824633
$470$	1.31939e9	0.586178
$471$	−8.84662e8	−0.390125
$472$	−2.14195e8	−0.0937589
$473$	2.77536e9	1.20588
$474$	1.05873e9	0.456627
$475$	−1.82561e9	−0.781592
$476$	−1.75927e9	−0.747666
$477$	−3.64121e7	−0.0153614
$478$	9.49444e8	0.397623
$479$	−7.60336e8	−0.316105	−0.158053	−	0.987431i	$-0.550522\pi$
$479$	−7.60336e8	−0.316105	−0.158053	+	0.987431i	$0.550522\pi$
$480$	5.62096e8	0.231988
$481$	−3.52642e9	−1.44486
$482$	3.15145e9	1.28188
$483$	3.48132e9	1.40582
$484$	3.41028e8	0.136720
$485$	−2.46417e9	−0.980787
$486$	−1.91321e8	−0.0756023
$487$	−3.11666e9	−1.22275	−0.611375	−	0.791341i	$-0.709383\pi$
$487$	−3.11666e9	−1.22275	−0.611375	+	0.791341i	$0.709383\pi$
$488$	−2.08846e7	−0.00813497
$489$	8.84912e8	0.342231
$490$	−1.90889e9	−0.732984
$491$	−2.02161e9	−0.770749	−0.385374	−	0.922760i	$-0.625928\pi$
$491$	−2.02161e9	−0.770749	−0.385374	+	0.922760i	$0.625928\pi$
$492$	7.81742e8	0.295928
$493$	5.56694e9	2.09244
$494$	5.42281e9	2.02386
$495$	5.69017e8	0.210866
$496$	6.26330e9	2.30471
$497$	−1.65226e9	−0.603715
$498$	3.10612e9	1.12698
$499$	−3.90803e9	−1.40801	−0.704006	−	0.710194i	$-0.748607\pi$
$499$	−3.90803e9	−1.40801	−0.704006	+	0.710194i	$0.748607\pi$
$500$	−1.00789e9	−0.360593
$501$	−1.32635e9	−0.471224
$502$	−4.06258e8	−0.143331
$503$	−5.07994e9	−1.77980	−0.889899	−	0.456158i	$-0.849225\pi$
$503$	−5.07994e9	−1.77980	−0.889899	+	0.456158i	$0.849225\pi$
$504$	−1.01003e9	−0.351421
$505$	9.39623e7	0.0324664
$506$	6.64139e9	2.27894
$507$	2.35829e9	0.803653
$508$	−5.60336e8	−0.189638
$509$	−2.67138e9	−0.897892	−0.448946	−	0.893559i	$-0.648200\pi$
$509$	−2.67138e9	−0.897892	−0.448946	+	0.893559i	$0.648200\pi$
$510$	−1.45656e9	−0.486219
$511$	6.42651e9	2.13060
$512$	−6.86375e7	−0.0226004
$513$	6.53421e8	0.213689
$514$	−3.59760e9	−1.16853
$515$	−1.06260e9	−0.342804
$516$	7.26878e8	0.232910
$517$	−3.33894e9	−1.06265
$518$	5.09860e9	1.61175
$519$	5.62088e8	0.176489
$520$	−1.94331e9	−0.606080
$521$	1.52466e9	0.472326	0.236163	−	0.971713i	$-0.424110\pi$
$521$	1.52466e9	0.472326	0.236163	+	0.971713i	$0.424110\pi$
$522$	−2.03411e9	−0.625933
$523$	9.55727e8	0.292131	0.146066	−	0.989275i	$-0.453339\pi$
$523$	9.55727e8	0.292131	0.146066	+	0.989275i	$0.453339\pi$
$524$	2.14138e8	0.0650180
$525$	1.97253e9	0.594929
$526$	4.41005e9	1.32127
$527$	−8.21663e9	−2.44544
$528$	−2.80979e9	−0.830721
$529$	6.01524e9	1.76668
$530$	1.01291e8	0.0295532
$531$	−1.49721e8	−0.0433963
$532$	−2.19544e9	−0.632167
$533$	−7.12545e9	−2.03829
$534$	3.16554e8	0.0899610
$535$	−1.13616e9	−0.320776
$536$	−1.44632e9	−0.405685
$537$	2.33305e9	0.650151
$538$	−5.17129e9	−1.43173
$539$	4.83079e9	1.32879
$540$	1.49028e8	0.0407276
$541$	1.12167e9	0.304561	0.152280	−	0.988337i	$-0.451338\pi$
$541$	1.12167e9	0.304561	0.152280	+	0.988337i	$0.451338\pi$
$542$	−4.83147e9	−1.30341
$543$	−1.76775e9	−0.473829
$544$	3.64125e9	0.969737
$545$	−3.42232e9	−0.905591
$546$	−5.85922e9	−1.54051
$547$	5.80841e8	0.151740	0.0758702	−	0.997118i	$-0.475827\pi$
$547$	5.80841e8	0.151740	0.0758702	+	0.997118i	$0.475827\pi$
$548$	−9.23352e8	−0.239682
$549$	−1.45982e7	−0.00376527
$550$	3.76303e9	0.964424
$551$	6.94715e9	1.76920
$552$	−2.73303e9	−0.691604
$553$	3.90690e9	0.982413
$554$	−5.23718e9	−1.30862
$555$	1.18203e9	0.293496
$556$	−2.05575e9	−0.507235
$557$	3.50741e9	0.859989	0.429994	−	0.902832i	$-0.358516\pi$
$557$	3.50741e9	0.859989	0.429994	+	0.902832i	$0.358516\pi$
$558$	3.00229e9	0.731530
$559$	−6.62537e9	−1.60424
$560$	4.09717e9	0.985883
$561$	3.68608e9	0.881444
$562$	−3.49967e8	−0.0831668
$563$	1.57440e9	0.371822	0.185911	−	0.982567i	$-0.440476\pi$
$563$	1.57440e9	0.371822	0.185911	+	0.982567i	$0.440476\pi$
$564$	−8.74482e8	−0.205246
$565$	1.11596e9	0.260303
$566$	−4.03632e9	−0.935682
$567$	−7.06006e8	−0.162655
$568$	1.29712e9	0.297003
$569$	−2.71007e7	−0.00616719	−0.00308360	−	0.999995i	$-0.500982\pi$
$569$	−2.71007e7	−0.00616719	−0.00308360	+	0.999995i	$0.500982\pi$
$570$	−1.81768e9	−0.411108
$571$	−8.12943e9	−1.82740	−0.913700	−	0.406390i	$-0.866787\pi$
$571$	−8.12943e9	−1.82740	−0.913700	+	0.406390i	$0.866787\pi$
$572$	−3.12993e9	−0.699276
$573$	−2.28286e9	−0.506918
$574$	1.03022e10	2.27372
$575$	5.33743e9	1.17083
$576$	5.61684e8	0.122465
$577$	−8.89512e8	−0.192769	−0.0963844	−	0.995344i	$-0.530728\pi$
$577$	−8.89512e8	−0.192769	−0.0963844	+	0.995344i	$0.530728\pi$
$578$	−3.96431e9	−0.853927
$579$	−5.51364e8	−0.118049
$580$	1.58446e9	0.337196
$581$	1.14621e10	2.42464
$582$	5.83269e9	1.22642
$583$	−2.56334e8	−0.0535756
$584$	−5.04516e9	−1.04817
$585$	−1.35836e9	−0.280524
$586$	−5.92218e9	−1.21574
$587$	8.09762e8	0.165243	0.0826217	−	0.996581i	$-0.473671\pi$
$587$	8.09762e8	0.165243	0.0826217	+	0.996581i	$0.473671\pi$
$588$	1.26520e9	0.256649
$589$	−1.02538e10	−2.06766
$590$	4.16493e8	0.0834884
$591$	8.72617e8	0.173887
$592$	−5.83682e9	−1.15625
$593$	−6.48925e9	−1.27792	−0.638959	−	0.769241i	$-0.720635\pi$
$593$	−6.48925e9	−1.27792	−0.638959	+	0.769241i	$0.720635\pi$
$594$	−1.34686e9	−0.263676
$595$	−5.37495e9	−1.04608
$596$	1.38374e9	0.267728
$597$	−1.94959e9	−0.375002
$598$	−1.58544e10	−3.03176
$599$	6.51857e8	0.123925	0.0619624	−	0.998078i	$-0.480264\pi$
$599$	6.51857e8	0.123925	0.0619624	+	0.998078i	$0.480264\pi$
$600$	−1.54854e9	−0.292680
$601$	−2.97476e9	−0.558974	−0.279487	−	0.960150i	$-0.590164\pi$
$601$	−2.97476e9	−0.558974	−0.279487	+	0.960150i	$0.590164\pi$
$602$	9.57915e9	1.78953
$603$	−1.01097e9	−0.187771
$604$	2.51475e9	0.464372
$605$	1.04191e9	0.191288
$606$	−2.22409e8	−0.0405973
$607$	−4.76572e9	−0.864905	−0.432452	−	0.901657i	$-0.642352\pi$
$607$	−4.76572e9	−0.864905	−0.432452	+	0.901657i	$0.642352\pi$
$608$	4.54402e9	0.819931
$609$	−7.50622e9	−1.34667
$610$	4.06091e7	0.00724385
$611$	7.97076e9	1.41369
$612$	9.65398e8	0.170246
$613$	4.10844e9	0.720385	0.360193	−	0.932878i	$-0.382711\pi$
$613$	4.10844e9	0.720385	0.360193	+	0.932878i	$0.382711\pi$
$614$	9.57176e9	1.66879
$615$	2.38839e9	0.414040
$616$	−7.11042e9	−1.22564
$617$	8.36433e9	1.43362	0.716809	−	0.697270i	$-0.245602\pi$
$617$	8.36433e9	1.43362	0.716809	+	0.697270i	$0.245602\pi$
$618$	2.51518e9	0.428657
$619$	−1.37677e8	−0.0233315	−0.0116658	−	0.999932i	$-0.503713\pi$
$619$	−1.37677e8	−0.0233315	−0.0116658	+	0.999932i	$0.503713\pi$
$620$	−2.33861e9	−0.394082
$621$	−1.91037e9	−0.320109
$622$	1.32153e10	2.20196
$623$	1.16814e9	0.193547
$624$	6.70756e9	1.10514
$625$	1.21700e9	0.199393
$626$	2.36253e8	0.0384917
$627$	4.59997e9	0.745278
$628$	−1.63110e9	−0.262798
$629$	7.65715e9	1.22685
$630$	1.96396e9	0.312925
$631$	−1.86229e9	−0.295083	−0.147542	−	0.989056i	$-0.547136\pi$
$631$	−1.86229e9	−0.295083	−0.147542	+	0.989056i	$0.547136\pi$
$632$	−3.06713e9	−0.483306
$633$	−5.14838e9	−0.806784
$634$	−8.89756e9	−1.38662
$635$	−1.71195e9	−0.265328
$636$	−6.71350e7	−0.0103478
$637$	−1.15321e10	−1.76775
$638$	−1.43198e10	−2.18305
$639$	9.06679e8	0.137468
$640$	−4.22724e9	−0.637422
$641$	1.04508e10	1.56727	0.783637	−	0.621219i	$-0.213362\pi$
$641$	1.04508e10	1.56727	0.783637	+	0.621219i	$0.213362\pi$
$642$	2.68930e9	0.401112
$643$	−1.17114e10	−1.73728	−0.868642	−	0.495440i	$-0.835007\pi$
$643$	−1.17114e10	−1.73728	−0.868642	+	0.495440i	$0.835007\pi$
$644$	6.41870e9	0.946993
$645$	2.22077e9	0.325870
$646$	−1.17749e10	−1.71848
$647$	−2.82698e7	−0.00410353	−0.00205176	−	0.999998i	$-0.500653\pi$
$647$	−2.82698e7	−0.00410353	−0.00205176	+	0.999998i	$0.500653\pi$
$648$	5.54253e8	0.0800195
$649$	−1.05401e9	−0.151352
$650$	−8.98314e9	−1.28301
$651$	1.10789e10	1.57386
$652$	1.63156e9	0.230535
$653$	1.03288e10	1.45163	0.725813	−	0.687892i	$-0.241464\pi$
$653$	1.03288e10	1.45163	0.725813	+	0.687892i	$0.241464\pi$
$654$	8.10062e9	1.13239
$655$	6.54237e8	0.0909684
$656$	−1.17938e10	−1.63114
$657$	−3.52654e9	−0.485144
$658$	−1.15244e10	−1.57698
$659$	−8.85377e9	−1.20512	−0.602558	−	0.798075i	$-0.705852\pi$
$659$	−8.85377e9	−1.20512	−0.602558	+	0.798075i	$0.705852\pi$
$660$	1.04913e9	0.142045
$661$	3.94438e8	0.0531219	0.0265610	−	0.999647i	$-0.491544\pi$
$661$	3.94438e8	0.0531219	0.0265610	+	0.999647i	$0.491544\pi$
$662$	−1.61746e10	−2.16686
$663$	−8.79944e9	−1.17262
$664$	−8.99838e9	−1.19282
$665$	−6.70756e9	−0.884481
$666$	−2.79786e9	−0.367000
$667$	−2.03110e10	−2.65027
$668$	−2.44547e9	−0.317427
$669$	5.49070e9	0.708984
$670$	2.81232e9	0.361246
$671$	−1.02769e8	−0.0131320
$672$	−4.90970e9	−0.624112
$673$	−3.32239e8	−0.0420144	−0.0210072	−	0.999779i	$-0.506687\pi$
$673$	−3.32239e8	−0.0420144	−0.0210072	+	0.999779i	$0.506687\pi$
$674$	−5.38472e9	−0.677413
$675$	−1.08242e9	−0.135467
$676$	4.34810e9	0.541360
$677$	−7.35957e9	−0.911574	−0.455787	−	0.890089i	$-0.650642\pi$
$677$	−7.35957e9	−0.911574	−0.455787	+	0.890089i	$0.650642\pi$
$678$	−2.64148e9	−0.325494
$679$	2.15236e10	2.63858
$680$	4.21963e9	0.514628
$681$	9.50846e8	0.115371
$682$	2.11355e10	2.55134
$683$	−1.53063e10	−1.83822	−0.919111	−	0.393999i	$-0.871091\pi$
$683$	−1.53063e10	−1.83822	−0.919111	+	0.393999i	$0.871091\pi$
$684$	1.20475e9	0.143946
$685$	−2.82104e9	−0.335345
$686$	2.08589e9	0.246693
$687$	−9.46990e9	−1.11429
$688$	−1.09661e10	−1.28379
$689$	6.11924e8	0.0712739
$690$	5.31426e9	0.615844
$691$	−1.49200e10	−1.72026	−0.860132	−	0.510072i	$-0.829619\pi$
$691$	−1.49200e10	−1.72026	−0.860132	+	0.510072i	$0.829619\pi$
$692$	1.03635e9	0.118887
$693$	−4.97015e9	−0.567288
$694$	7.64611e9	0.868325
$695$	−6.28077e9	−0.709686
$696$	5.89280e9	0.662505
$697$	1.54719e10	1.73073
$698$	4.28329e9	0.476742
$699$	−7.34048e9	−0.812932
$700$	3.63685e9	0.400758
$701$	−6.52424e9	−0.715347	−0.357673	−	0.933847i	$-0.616430\pi$
$701$	−6.52424e9	−0.715347	−0.357673	+	0.933847i	$0.616430\pi$
$702$	3.21524e9	0.350779
$703$	9.55558e9	1.03732
$704$	3.95415e9	0.427119
$705$	−2.67173e9	−0.287165
$706$	−5.31262e9	−0.568188
$707$	−8.20726e8	−0.0873434
$708$	−2.76049e8	−0.0292328
$709$	4.55527e9	0.480012	0.240006	−	0.970771i	$-0.422851\pi$
$709$	4.55527e9	0.480012	0.240006	+	0.970771i	$0.422851\pi$
$710$	−2.52219e9	−0.264468
$711$	−2.14391e9	−0.223698
$712$	−9.17054e8	−0.0952171
$713$	2.99784e10	3.09738
$714$	1.27225e10	1.30806
$715$	−9.56262e9	−0.978376
$716$	4.30157e9	0.437957
$717$	−1.92260e9	−0.194793
$718$	−1.87607e10	−1.89153
$719$	6.09158e9	0.611194	0.305597	−	0.952161i	$-0.401144\pi$
$719$	6.09158e9	0.611194	0.305597	+	0.952161i	$0.401144\pi$
$720$	−2.24832e9	−0.224489
$721$	9.28145e9	0.922236
$722$	−2.77584e9	−0.274482
$723$	−6.38162e9	−0.627982
$724$	−3.25930e9	−0.319183
$725$	−1.15083e10	−1.12157
$726$	−2.46621e9	−0.239195
$727$	1.68599e10	1.62737	0.813684	−	0.581308i	$-0.197459\pi$
$727$	1.68599e10	1.62737	0.813684	+	0.581308i	$0.197459\pi$
$728$	1.69741e10	1.63052
$729$	3.87420e8	0.0370370
$730$	9.81011e9	0.933349
$731$	1.43861e10	1.36217
$732$	−2.69155e7	−0.00253638
$733$	−1.44578e9	−0.135593	−0.0677966	−	0.997699i	$-0.521597\pi$
$733$	−1.44578e9	−0.135593	−0.0677966	+	0.997699i	$0.521597\pi$
$734$	1.28762e10	1.20185
$735$	3.86546e9	0.359084
$736$	−1.32851e10	−1.22827
$737$	−7.11707e9	−0.654885
$738$	−5.65332e9	−0.517733
$739$	8.56684e8	0.0780845	0.0390423	−	0.999238i	$-0.487569\pi$
$739$	8.56684e8	0.0780845	0.0390423	+	0.999238i	$0.487569\pi$
$740$	2.17937e9	0.197706
$741$	−1.09811e10	−0.991475
$742$	−8.84738e8	−0.0795062
$743$	1.09080e10	0.975630	0.487815	−	0.872947i	$-0.337794\pi$
$743$	1.09080e10	0.975630	0.487815	+	0.872947i	$0.337794\pi$
$744$	−8.69758e9	−0.774271
$745$	4.22764e9	0.374585
$746$	8.68006e9	0.765485
$747$	−6.28983e9	−0.552098
$748$	6.79622e9	0.593762
$749$	9.92396e9	0.862976
$750$	7.28873e9	0.630866
$751$	−5.27485e9	−0.454433	−0.227217	−	0.973844i	$-0.572963\pi$
$751$	−5.27485e9	−0.454433	−0.227217	+	0.973844i	$0.572963\pi$
$752$	1.31929e10	1.13130
$753$	8.22665e8	0.0702167
$754$	3.41843e10	2.90420
$755$	7.68311e9	0.649715
$756$	−1.30170e9	−0.109568
$757$	−2.07054e10	−1.73479	−0.867395	−	0.497620i	$-0.834208\pi$
$757$	−2.07054e10	−1.73479	−0.867395	+	0.497620i	$0.834208\pi$
$758$	5.30659e8	0.0442562
$759$	−1.34487e10	−1.11643
$760$	5.26580e9	0.435128
$761$	1.35780e10	1.11683	0.558417	−	0.829561i	$-0.311409\pi$
$761$	1.35780e10	1.11683	0.558417	+	0.829561i	$0.311409\pi$
$762$	4.05218e9	0.331777
$763$	2.98927e10	2.43629
$764$	−4.20903e9	−0.341472
$765$	2.94950e9	0.238195
$766$	−8.37001e8	−0.0672861
$767$	2.51614e9	0.201350
$768$	7.34307e9	0.584943
$769$	1.62978e10	1.29237	0.646184	−	0.763182i	$-0.276364\pi$
$769$	1.62978e10	1.29237	0.646184	+	0.763182i	$0.276364\pi$
$770$	1.38259e10	1.09138
$771$	7.28506e9	0.572457
$772$	−1.01658e9	−0.0795208
$773$	−2.64697e9	−0.206120	−0.103060	−	0.994675i	$-0.532863\pi$
$773$	−2.64697e9	−0.206120	−0.103060	+	0.994675i	$0.532863\pi$
$774$	−5.25656e9	−0.407482
$775$	1.69858e10	1.31078
$776$	−1.68972e10	−1.29807
$777$	−1.03246e10	−0.789584
$778$	5.52800e9	0.420862
$779$	1.93079e10	1.46337
$780$	−2.50449e9	−0.188968
$781$	6.38285e9	0.479442
$782$	3.44257e10	2.57430
$783$	4.11904e9	0.306640
$784$	−1.90876e10	−1.41463
$785$	−4.98336e9	−0.367687
$786$	−1.54858e9	−0.113751
$787$	−7.25919e9	−0.530856	−0.265428	−	0.964131i	$-0.585513\pi$
$787$	−7.25919e9	−0.530856	−0.265428	+	0.964131i	$0.585513\pi$
$788$	1.60889e9	0.117134
$789$	−8.93025e9	−0.647283
$790$	5.96390e9	0.430364
$791$	−9.74751e9	−0.700287
$792$	3.90184e9	0.279082
$793$	2.45330e8	0.0174701
$794$	7.21097e9	0.511237
$795$	−2.05112e8	−0.0144779
$796$	−3.59457e9	−0.252610
$797$	−3.67130e9	−0.256871	−0.128436	−	0.991718i	$-0.540996\pi$
$797$	−3.67130e9	−0.256871	−0.128436	+	0.991718i	$0.540996\pi$
$798$	1.58768e10	1.10599
$799$	−1.73074e10	−1.20038
$800$	−7.52737e9	−0.519791
$801$	−6.41016e8	−0.0440712
$802$	−2.43152e10	−1.66444
$803$	−2.48262e10	−1.69202
$804$	−1.86399e9	−0.126487
$805$	1.96105e10	1.32496
$806$	−5.04550e10	−3.39415
$807$	1.04718e10	0.701395
$808$	6.44315e8	0.0429693
$809$	−5.97080e9	−0.396472	−0.198236	−	0.980154i	$-0.563521\pi$
$809$	−5.97080e9	−0.396472	−0.198236	+	0.980154i	$0.563521\pi$
$810$	−1.07772e9	−0.0712540
$811$	2.51680e10	1.65682	0.828409	−	0.560123i	$-0.189246\pi$
$811$	2.51680e10	1.65682	0.828409	+	0.560123i	$0.189246\pi$
$812$	−1.38396e10	−0.907148
$813$	9.78363e9	0.638533
$814$	−1.96964e10	−1.27997
$815$	4.98477e9	0.322548
$816$	−1.45646e10	−0.938387
$817$	1.79528e10	1.15174
$818$	−2.62936e10	−1.67963
$819$	1.18648e10	0.754686
$820$	4.40361e9	0.278907
$821$	1.74411e10	1.09995	0.549975	−	0.835181i	$-0.314637\pi$
$821$	1.74411e10	1.09995	0.549975	+	0.835181i	$0.314637\pi$
$822$	6.67740e9	0.419330
$823$	1.10753e10	0.692557	0.346278	−	0.938132i	$-0.387445\pi$
$823$	1.10753e10	0.692557	0.346278	+	0.938132i	$0.387445\pi$
$824$	−7.28644e9	−0.453702
$825$	−7.62005e9	−0.472464
$826$	−3.63791e9	−0.224606
$827$	−7.16696e9	−0.440622	−0.220311	−	0.975430i	$-0.570707\pi$
$827$	−7.16696e9	−0.440622	−0.220311	+	0.975430i	$0.570707\pi$
$828$	−3.52226e9	−0.215633
$829$	1.09285e9	0.0666224	0.0333112	−	0.999445i	$-0.489395\pi$
$829$	1.09285e9	0.0666224	0.0333112	+	0.999445i	$0.489395\pi$
$830$	1.74970e10	1.06216
$831$	1.06052e10	0.641083
$832$	−9.43940e9	−0.568215
$833$	2.50404e10	1.50101
$834$	1.48666e10	0.887421
$835$	−7.47144e9	−0.444121
$836$	8.48121e9	0.502037
$837$	−6.07957e9	−0.358372
$838$	−6.53834e9	−0.383807
$839$	−2.38628e10	−1.39494	−0.697469	−	0.716615i	$-0.745691\pi$
$839$	−2.38628e10	−1.39494	−0.697469	+	0.716615i	$0.745691\pi$
$840$	−5.68957e9	−0.331209
$841$	2.65435e10	1.53877
$842$	2.30050e9	0.132810
$843$	7.08676e8	0.0407428
$844$	−9.49235e9	−0.543469
$845$	1.32844e10	0.757431
$846$	6.32398e9	0.359083
$847$	−9.10073e9	−0.514617
$848$	1.01284e9	0.0570367
$849$	8.17347e9	0.458384
$850$	1.95057e10	1.08942
$851$	−2.79371e10	−1.55392
$852$	1.67169e9	0.0926015
$853$	1.71276e10	0.944878	0.472439	−	0.881363i	$-0.343374\pi$
$853$	1.71276e10	0.944878	0.472439	+	0.881363i	$0.343374\pi$
$854$	−3.54706e8	−0.0194879
$855$	3.68077e9	0.201399
$856$	−7.79086e9	−0.424548
$857$	3.37860e8	0.0183360	0.00916798	−	0.999958i	$-0.497082\pi$
$857$	3.37860e8	0.0183360	0.00916798	+	0.999958i	$0.497082\pi$
$858$	2.26347e10	1.22340
$859$	3.39086e9	0.182530	0.0912649	−	0.995827i	$-0.470909\pi$
$859$	3.39086e9	0.182530	0.0912649	+	0.995827i	$0.470909\pi$
$860$	4.09455e9	0.219514
$861$	−2.08617e10	−1.11388
$862$	−2.66249e10	−1.41583
$863$	9.19359e9	0.486909	0.243454	−	0.969912i	$-0.421719\pi$
$863$	9.19359e9	0.486909	0.243454	+	0.969912i	$0.421719\pi$
$864$	2.69420e9	0.142112
$865$	3.16628e9	0.166339
$866$	8.70904e9	0.455678
$867$	8.02766e9	0.418333
$868$	2.04269e10	1.06019
$869$	−1.50927e10	−0.780186
$870$	−1.14583e10	−0.589933
$871$	1.69899e10	0.871221
$872$	−2.34674e10	−1.19855
$873$	−1.18111e10	−0.600813
$874$	4.29608e10	2.17662
$875$	2.68966e10	1.35728
$876$	−6.50208e9	−0.326805
$877$	−1.78531e10	−0.893747	−0.446874	−	0.894597i	$-0.647463\pi$
$877$	−1.78531e10	−0.893747	−0.446874	+	0.894597i	$0.647463\pi$
$878$	2.91952e10	1.45573
$879$	1.19923e10	0.595582
$880$	−1.58277e10	−0.782942
$881$	−1.00212e10	−0.493746	−0.246873	−	0.969048i	$-0.579403\pi$
$881$	−1.00212e10	−0.493746	−0.246873	+	0.969048i	$0.579403\pi$
$882$	−9.14955e9	−0.449014
$883$	4.80376e8	0.0234811	0.0117406	−	0.999931i	$-0.496263\pi$
$883$	4.80376e8	0.0234811	0.0117406	+	0.999931i	$0.496263\pi$
$884$	−1.62240e10	−0.789906
$885$	−8.43390e8	−0.0409004
$886$	−3.97703e10	−1.92106
$887$	−2.86366e9	−0.137781	−0.0688903	−	0.997624i	$-0.521946\pi$
$887$	−2.86366e9	−0.137781	−0.0688903	+	0.997624i	$0.521946\pi$
$888$	8.10535e9	0.388442
$889$	1.49532e10	0.713804
$890$	1.78317e9	0.0847869
$891$	2.72737e9	0.129173
$892$	1.01235e10	0.477589
$893$	−2.15984e10	−1.01494
$894$	−1.00068e10	−0.468398
$895$	1.31422e10	0.612758
$896$	3.69234e10	1.71484
$897$	3.21048e10	1.48524
$898$	2.06158e10	0.950020
$899$	−6.46377e10	−2.96706
$900$	−1.99572e9	−0.0912538
$901$	−1.32871e9	−0.0605193
$902$	−3.97983e10	−1.80568
$903$	−1.93976e10	−0.876679
$904$	7.65233e9	0.344512
$905$	−9.95787e9	−0.446577
$906$	−1.81859e10	−0.812431
$907$	−5.67695e9	−0.252633	−0.126316	−	0.991990i	$-0.540315\pi$
$907$	−5.67695e9	−0.252633	−0.126316	+	0.991990i	$0.540315\pi$
$908$	1.75313e9	0.0777164
$909$	4.50373e8	0.0198883
$910$	−3.30054e10	−1.45191
$911$	2.67566e10	1.17251	0.586256	−	0.810126i	$-0.300601\pi$
$911$	2.67566e10	1.17251	0.586256	+	0.810126i	$0.300601\pi$
$912$	−1.81755e10	−0.793424
$913$	−4.42792e10	−1.92554
$914$	9.33871e9	0.404553
$915$	−8.22327e7	−0.00354871
$916$	−1.74602e10	−0.750610
$917$	−5.71452e9	−0.244730
$918$	−6.98146e9	−0.297850
$919$	2.00200e10	0.850862	0.425431	−	0.904991i	$-0.360122\pi$
$919$	2.00200e10	0.850862	0.425431	+	0.904991i	$0.360122\pi$
$920$	−1.53953e10	−0.651826
$921$	−1.93826e10	−0.817530
$922$	3.18776e10	1.33945
$923$	−1.52372e10	−0.637822
$924$	−9.16374e9	−0.382138
$925$	−1.58293e10	−0.657604
$926$	−3.62520e10	−1.50035
$927$	−5.09319e9	−0.209996
$928$	2.86446e10	1.17659
$929$	2.42743e10	0.993326	0.496663	−	0.867943i	$-0.334559\pi$
$929$	2.42743e10	0.993326	0.496663	+	0.867943i	$0.334559\pi$
$930$	1.69121e10	0.689457
$931$	3.12486e10	1.26913
$932$	−1.35340e10	−0.547611
$933$	−2.67606e10	−1.07872
$934$	−4.84332e10	−1.94504
$935$	2.07639e10	0.830748
$936$	−9.31452e9	−0.371274
$937$	2.31846e10	0.920683	0.460342	−	0.887742i	$-0.347727\pi$
$937$	2.31846e10	0.920683	0.460342	+	0.887742i	$0.347727\pi$
$938$	−2.45645e10	−0.971849
$939$	−4.78408e8	−0.0188568
$940$	−4.92602e9	−0.193441
$941$	−4.82845e10	−1.88905	−0.944527	−	0.328434i	$-0.893479\pi$
$941$	−4.82845e10	−1.88905	−0.944527	+	0.328434i	$0.893479\pi$
$942$	1.17956e10	0.459772
$943$	−5.64495e10	−2.19214
$944$	4.16464e9	0.161130
$945$	−3.97698e9	−0.153300
$946$	−3.70052e10	−1.42116
$947$	−9.48483e9	−0.362915	−0.181457	−	0.983399i	$-0.558081\pi$
$947$	−9.48483e9	−0.362915	−0.181457	+	0.983399i	$0.558081\pi$
$948$	−3.95284e9	−0.150688
$949$	5.92654e10	2.25097
$950$	2.43417e10	0.921124
$951$	1.80174e10	0.679297
$952$	−3.68569e10	−1.38449
$953$	3.13620e10	1.17376	0.586880	−	0.809674i	$-0.300356\pi$
$953$	3.13620e10	1.17376	0.586880	+	0.809674i	$0.300356\pi$
$954$	4.85500e8	0.0181038
$955$	−1.28595e10	−0.477762
$956$	−3.54481e9	−0.131217
$957$	2.89972e10	1.06946
$958$	1.01379e10	0.372537
$959$	2.46407e10	0.902171
$960$	3.16401e9	0.115422
$961$	6.78906e10	2.46762
$962$	4.70194e10	1.70280
$963$	−5.44577e9	−0.196502
$964$	−1.17661e10	−0.423024
$965$	−3.10587e9	−0.111260
$966$	−4.64181e10	−1.65679
$967$	−4.56505e10	−1.62350	−0.811752	−	0.584003i	$-0.801486\pi$
$967$	−4.56505e10	−1.62350	−0.811752	+	0.584003i	$0.801486\pi$
$968$	7.14457e9	0.253170
$969$	2.38439e10	0.841869
$970$	3.28559e10	1.15588
$971$	−4.75876e10	−1.66812	−0.834059	−	0.551675i	$-0.813989\pi$
$971$	−4.75876e10	−1.66812	−0.834059	+	0.551675i	$0.813989\pi$
$972$	7.14308e8	0.0249490
$973$	5.48602e10	1.90925
$974$	4.15558e10	1.44104
$975$	1.81907e10	0.628539
$976$	4.06063e8	0.0139804
$977$	−3.64883e10	−1.25176	−0.625882	−	0.779918i	$-0.715261\pi$
$977$	−3.64883e10	−1.25176	−0.625882	+	0.779918i	$0.715261\pi$
$978$	−1.17990e10	−0.403327
$979$	−4.51264e9	−0.153706
$980$	7.12697e9	0.241888
$981$	−1.64036e10	−0.554750
$982$	2.69551e10	0.908346
$983$	−2.58715e10	−0.868729	−0.434365	−	0.900737i	$-0.643027\pi$
$983$	−2.58715e10	−0.868729	−0.434365	+	0.900737i	$0.643027\pi$
$984$	1.63776e10	0.547983
$985$	4.91551e9	0.163886
$986$	−7.42266e10	−2.46598
$987$	2.33366e10	0.772551
$988$	−2.02464e10	−0.667881
$989$	−5.24877e10	−1.72532
$990$	−7.58697e9	−0.248511
$991$	5.08417e10	1.65944	0.829722	−	0.558177i	$-0.188499\pi$
$991$	5.08417e10	1.65944	0.829722	+	0.558177i	$0.188499\pi$
$992$	−4.22785e10	−1.37508
$993$	3.27533e10	1.06153
$994$	2.20304e10	0.711492
$995$	−1.09822e10	−0.353434
$996$	−1.15969e10	−0.371907
$997$	−7.59411e9	−0.242686	−0.121343	−	0.992611i	$-0.538720\pi$
$997$	−7.59411e9	−0.242686	−0.121343	+	0.992611i	$0.538720\pi$
$998$	5.21076e10	1.65937
$999$	5.66560e9	0.179791

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.b.1.5	✓	17
3.2	odd	2		531.8.a.d.1.13		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.b.1.5	✓	17	1.1	even	1	trivial
531.8.a.d.1.13		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)

\(f(q)\)	\(=\)	\(q-13.3335 q^{2} +27.0000 q^{3} +49.7814 q^{4} +152.093 q^{5} -360.004 q^{6} -1328.47 q^{7} +1042.93 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-13.3335 q^{2} +27.0000 q^{3} +49.7814 q^{4} +152.093 q^{5} -360.004 q^{6} -1328.47 q^{7} +1042.93 q^{8} +729.000 q^{9} -2027.93 q^{10} +5132.02 q^{11} +1344.10 q^{12} -12251.2 q^{13} +17713.2 q^{14} +4106.51 q^{15} -20277.8 q^{16} +26601.9 q^{17} -9720.10 q^{18} +33197.2 q^{19} +7571.39 q^{20} -35868.8 q^{21} -68427.7 q^{22} -97057.0 q^{23} +28159.0 q^{24} -54992.8 q^{25} +163351. q^{26} +19683.0 q^{27} -66133.3 q^{28} +209269. q^{29} -54754.0 q^{30} -308874. q^{31} +136879. q^{32} +138565. q^{33} -354695. q^{34} -202052. q^{35} +36290.6 q^{36} +287842. q^{37} -442634. q^{38} -330783. q^{39} +158622. q^{40} +581611. q^{41} +478256. q^{42} +540792. q^{43} +255479. q^{44} +110876. q^{45} +1.29411e6 q^{46} -650609. q^{47} -547501. q^{48} +941302. q^{49} +733244. q^{50} +718250. q^{51} -609883. q^{52} -49948.0 q^{53} -262443. q^{54} +780544. q^{55} -1.38550e6 q^{56} +896326. q^{57} -2.79028e6 q^{58} -205379. q^{59} +204428. q^{60} -20025.0 q^{61} +4.11836e6 q^{62} -968458. q^{63} +770486. q^{64} -1.86332e6 q^{65} -1.84755e6 q^{66} -1.38680e6 q^{67} +1.32428e6 q^{68} -2.62054e6 q^{69} +2.69405e6 q^{70} +1.24373e6 q^{71} +760293. q^{72} -4.83751e6 q^{73} -3.83794e6 q^{74} -1.48480e6 q^{75} +1.65260e6 q^{76} -6.81777e6 q^{77} +4.41048e6 q^{78} -2.94089e6 q^{79} -3.08411e6 q^{80} +531441. q^{81} -7.75490e6 q^{82} -8.62802e6 q^{83} -1.78560e6 q^{84} +4.04595e6 q^{85} -7.21064e6 q^{86} +5.65025e6 q^{87} +5.35232e6 q^{88} -879309. q^{89} -1.47836e6 q^{90} +1.62754e7 q^{91} -4.83163e6 q^{92} -8.33960e6 q^{93} +8.67488e6 q^{94} +5.04907e6 q^{95} +3.69574e6 q^{96} -1.62017e7 q^{97} -1.25508e7 q^{98} +3.74125e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 32 q^{2} + 459 q^{3} + 1166 q^{4} - 1072 q^{5} - 864 q^{6} - 2407 q^{7} - 6645 q^{8} + 12393 q^{9}+O(q^{10}) \) 17 * q - 32 * q^2 + 459 * q^3 + 1166 * q^4 - 1072 * q^5 - 864 * q^6 - 2407 * q^7 - 6645 * q^8 + 12393 * q^9	\( 17 q - 32 q^{2} + 459 q^{3} + 1166 q^{4} - 1072 q^{5} - 864 q^{6} - 2407 q^{7} - 6645 q^{8} + 12393 q^{9} - 6391 q^{10} - 8888 q^{11} + 31482 q^{12} - 12702 q^{13} - 17555 q^{14} - 28944 q^{15} + 139226 q^{16} - 36167 q^{17} - 23328 q^{18} - 71037 q^{19} - 274883 q^{20} - 64989 q^{21} - 325182 q^{22} - 269995 q^{23} - 179415 q^{24} + 97329 q^{25} - 336906 q^{26} + 334611 q^{27} - 901362 q^{28} - 543825 q^{29} - 172557 q^{30} - 633109 q^{31} - 837062 q^{32} - 239976 q^{33} - 529288 q^{34} - 287621 q^{35} + 850014 q^{36} - 867607 q^{37} - 1727169 q^{38} - 342954 q^{39} - 815662 q^{40} - 1428939 q^{41} - 473985 q^{42} - 477060 q^{43} - 1667926 q^{44} - 781488 q^{45} + 5305549 q^{46} - 1217849 q^{47} + 3759102 q^{48} + 4350738 q^{49} + 4561369 q^{50} - 976509 q^{51} + 4175994 q^{52} - 3487068 q^{53} - 629856 q^{54} - 960484 q^{55} - 5363196 q^{56} - 1917999 q^{57} - 3082906 q^{58} - 3491443 q^{59} - 7421841 q^{60} + 998917 q^{61} - 5742614 q^{62} - 1754703 q^{63} + 17531621 q^{64} - 6075816 q^{65} - 8779914 q^{66} - 356026 q^{67} - 16149231 q^{68} - 7289865 q^{69} - 548798 q^{70} - 12879428 q^{71} - 4844205 q^{72} - 6176157 q^{73} - 5971906 q^{74} + 2627883 q^{75} - 17624580 q^{76} + 239687 q^{77} - 9096462 q^{78} - 18886490 q^{79} - 70463349 q^{80} + 9034497 q^{81} - 19351611 q^{82} - 22824893 q^{83} - 24336774 q^{84} - 7973079 q^{85} - 27502196 q^{86} - 14683275 q^{87} - 62527651 q^{88} - 30609647 q^{89} - 4659039 q^{90} - 36301521 q^{91} - 41388548 q^{92} - 17093943 q^{93} + 1010176 q^{94} - 29303629 q^{95} - 22600674 q^{96} - 26249806 q^{97} - 93110852 q^{98} - 6479352 q^{99}+O(q^{100}) \) 17 * q - 32 * q^2 + 459 * q^3 + 1166 * q^4 - 1072 * q^5 - 864 * q^6 - 2407 * q^7 - 6645 * q^8 + 12393 * q^9 - 6391 * q^10 - 8888 * q^11 + 31482 * q^12 - 12702 * q^13 - 17555 * q^14 - 28944 * q^15 + 139226 * q^16 - 36167 * q^17 - 23328 * q^18 - 71037 * q^19 - 274883 * q^20 - 64989 * q^21 - 325182 * q^22 - 269995 * q^23 - 179415 * q^24 + 97329 * q^25 - 336906 * q^26 + 334611 * q^27 - 901362 * q^28 - 543825 * q^29 - 172557 * q^30 - 633109 * q^31 - 837062 * q^32 - 239976 * q^33 - 529288 * q^34 - 287621 * q^35 + 850014 * q^36 - 867607 * q^37 - 1727169 * q^38 - 342954 * q^39 - 815662 * q^40 - 1428939 * q^41 - 473985 * q^42 - 477060 * q^43 - 1667926 * q^44 - 781488 * q^45 + 5305549 * q^46 - 1217849 * q^47 + 3759102 * q^48 + 4350738 * q^49 + 4561369 * q^50 - 976509 * q^51 + 4175994 * q^52 - 3487068 * q^53 - 629856 * q^54 - 960484 * q^55 - 5363196 * q^56 - 1917999 * q^57 - 3082906 * q^58 - 3491443 * q^59 - 7421841 * q^60 + 998917 * q^61 - 5742614 * q^62 - 1754703 * q^63 + 17531621 * q^64 - 6075816 * q^65 - 8779914 * q^66 - 356026 * q^67 - 16149231 * q^68 - 7289865 * q^69 - 548798 * q^70 - 12879428 * q^71 - 4844205 * q^72 - 6176157 * q^73 - 5971906 * q^74 + 2627883 * q^75 - 17624580 * q^76 + 239687 * q^77 - 9096462 * q^78 - 18886490 * q^79 - 70463349 * q^80 + 9034497 * q^81 - 19351611 * q^82 - 22824893 * q^83 - 24336774 * q^84 - 7973079 * q^85 - 27502196 * q^86 - 14683275 * q^87 - 62527651 * q^88 - 30609647 * q^89 - 4659039 * q^90 - 36301521 * q^91 - 41388548 * q^92 - 17093943 * q^93 + 1010176 * q^94 - 29303629 * q^95 - 22600674 * q^96 - 26249806 * q^97 - 93110852 * q^98 - 6479352 * q^99

Introduction

L-functions

Modular forms

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