LMFDB - Embedded newform 177.8.a.d.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,8,Mod(1,177)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	177.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$55.2921495107$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 1798 x^{16} + 11087 x^{15} + 1326765 x^{14} - 8403720 x^{13} - 518334228 x^{12} + \cdots + 51\!\cdots\!48 $ x^18 - 6x^17 - 1798x^16 + 11087x^15 + 1326765x^14 - 8403720x^13 - 518334228x^12 + 3375594921x^11 + 115310342333x^10 - 774932111214x^9 - 14600047830166x^8 + 102185027148481x^7 + 988557475638619x^6 - 7379206238519716x^5 - 30152342836849520x^4 + 260578770749067175x^3 + 182609347488069978x^2 - 3481290425710753600*x + 5164646074739714048
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{5} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-6.28523$ 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)

$f(q)$	$=$	$q-5.28523 q^{2} +27.0000 q^{3} -100.066 q^{4} +498.961 q^{5} -142.701 q^{6} +341.176 q^{7} +1205.38 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-5.28523 q^{2} +27.0000 q^{3} -100.066 q^{4} +498.961 q^{5} -142.701 q^{6} +341.176 q^{7} +1205.38 q^{8} +729.000 q^{9} -2637.13 q^{10} +2091.72 q^{11} -2701.79 q^{12} +4481.72 q^{13} -1803.19 q^{14} +13472.0 q^{15} +6437.77 q^{16} +22387.5 q^{17} -3852.93 q^{18} +6302.72 q^{19} -49929.3 q^{20} +9211.75 q^{21} -11055.2 q^{22} +8949.56 q^{23} +32545.3 q^{24} +170838. q^{25} -23686.9 q^{26} +19683.0 q^{27} -34140.2 q^{28} -232539. q^{29} -71202.4 q^{30} -109526. q^{31} -188314. q^{32} +56476.3 q^{33} -118323. q^{34} +170234. q^{35} -72948.4 q^{36} +123858. q^{37} -33311.3 q^{38} +121006. q^{39} +601440. q^{40} +133392. q^{41} -48686.2 q^{42} +326147. q^{43} -209310. q^{44} +363743. q^{45} -47300.5 q^{46} -479181. q^{47} +173820. q^{48} -707142. q^{49} -902916. q^{50} +604464. q^{51} -448469. q^{52} -906342. q^{53} -104029. q^{54} +1.04369e6 q^{55} +411248. q^{56} +170173. q^{57} +1.22902e6 q^{58} +205379. q^{59} -1.34809e6 q^{60} +3.23653e6 q^{61} +578868. q^{62} +248717. q^{63} +171249. q^{64} +2.23620e6 q^{65} -298490. q^{66} +1.18481e6 q^{67} -2.24024e6 q^{68} +241638. q^{69} -899724. q^{70} +1.35464e6 q^{71} +878724. q^{72} -5.84208e6 q^{73} -654616. q^{74} +4.61261e6 q^{75} -630690. q^{76} +713643. q^{77} -639546. q^{78} +4.69904e6 q^{79} +3.21220e6 q^{80} +531441. q^{81} -705006. q^{82} +1.26796e6 q^{83} -921786. q^{84} +1.11705e7 q^{85} -1.72376e6 q^{86} -6.27856e6 q^{87} +2.52132e6 q^{88} +2.48381e6 q^{89} -1.92246e6 q^{90} +1.52905e6 q^{91} -895550. q^{92} -2.95719e6 q^{93} +2.53258e6 q^{94} +3.14481e6 q^{95} -5.08448e6 q^{96} +4.51095e6 q^{97} +3.73741e6 q^{98} +1.52486e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 24 q^{2} + 486 q^{3} + 1358 q^{4} + 678 q^{5} + 648 q^{6} + 3081 q^{7} + 4107 q^{8} + 13122 q^{9}+O(q^{10}) $ 18 * q + 24 * q^2 + 486 * q^3 + 1358 * q^4 + 678 * q^5 + 648 * q^6 + 3081 * q^7 + 4107 * q^8 + 13122 * q^9	\( 18 q + 24 q^{2} + 486 q^{3} + 1358 q^{4} + 678 q^{5} + 648 q^{6} + 3081 q^{7} + 4107 q^{8} + 13122 q^{9} + 3609 q^{10} + 15070 q^{11} + 36666 q^{12} + 13662 q^{13} + 20861 q^{14} + 18306 q^{15} + 60482 q^{16} + 71919 q^{17} + 17496 q^{18} + 56231 q^{19} + 143053 q^{20} + 83187 q^{21} + 274198 q^{22} + 150029 q^{23} + 110889 q^{24} + 399672 q^{25} + 182846 q^{26} + 354294 q^{27} + 434150 q^{28} + 591285 q^{29} + 97443 q^{30} + 426733 q^{31} + 1205630 q^{32} + 406890 q^{33} + 403548 q^{34} + 912879 q^{35} + 989982 q^{36} + 7703 q^{37} - 417859 q^{38} + 368874 q^{39} + 618020 q^{40} + 770959 q^{41} + 563247 q^{42} + 793050 q^{43} + 2591274 q^{44} + 494262 q^{45} - 4068019 q^{46} + 1410373 q^{47} + 1633014 q^{48} + 1637427 q^{49} + 1021549 q^{50} + 1941813 q^{51} - 3749190 q^{52} + 1037934 q^{53} + 472392 q^{54} + 331974 q^{55} - 391748 q^{56} + 1518237 q^{57} + 653724 q^{58} + 3696822 q^{59} + 3862431 q^{60} - 1374623 q^{61} + 5251718 q^{62} + 2246049 q^{63} + 5077197 q^{64} + 3257170 q^{65} + 7403346 q^{66} - 2436904 q^{67} + 14119909 q^{68} + 4050783 q^{69} + 5185580 q^{70} + 14289172 q^{71} + 2994003 q^{72} + 5482515 q^{73} + 14934154 q^{74} + 10791144 q^{75} + 3822912 q^{76} + 23157109 q^{77} + 4936842 q^{78} + 19786414 q^{79} + 31978143 q^{80} + 9565938 q^{81} + 9749509 q^{82} + 30227337 q^{83} + 11722050 q^{84} + 9946981 q^{85} + 44295864 q^{86} + 15964695 q^{87} + 39970897 q^{88} + 31061677 q^{89} + 2630961 q^{90} + 26377785 q^{91} + 4719698 q^{92} + 11521791 q^{93} + 44488296 q^{94} + 15534599 q^{95} + 32552010 q^{96} + 12084118 q^{97} + 42274744 q^{98} + 10986030 q^{99}+O(q^{100}) \) 18 * q + 24 * q^2 + 486 * q^3 + 1358 * q^4 + 678 * q^5 + 648 * q^6 + 3081 * q^7 + 4107 * q^8 + 13122 * q^9 + 3609 * q^10 + 15070 * q^11 + 36666 * q^12 + 13662 * q^13 + 20861 * q^14 + 18306 * q^15 + 60482 * q^16 + 71919 * q^17 + 17496 * q^18 + 56231 * q^19 + 143053 * q^20 + 83187 * q^21 + 274198 * q^22 + 150029 * q^23 + 110889 * q^24 + 399672 * q^25 + 182846 * q^26 + 354294 * q^27 + 434150 * q^28 + 591285 * q^29 + 97443 * q^30 + 426733 * q^31 + 1205630 * q^32 + 406890 * q^33 + 403548 * q^34 + 912879 * q^35 + 989982 * q^36 + 7703 * q^37 - 417859 * q^38 + 368874 * q^39 + 618020 * q^40 + 770959 * q^41 + 563247 * q^42 + 793050 * q^43 + 2591274 * q^44 + 494262 * q^45 - 4068019 * q^46 + 1410373 * q^47 + 1633014 * q^48 + 1637427 * q^49 + 1021549 * q^50 + 1941813 * q^51 - 3749190 * q^52 + 1037934 * q^53 + 472392 * q^54 + 331974 * q^55 - 391748 * q^56 + 1518237 * q^57 + 653724 * q^58 + 3696822 * q^59 + 3862431 * q^60 - 1374623 * q^61 + 5251718 * q^62 + 2246049 * q^63 + 5077197 * q^64 + 3257170 * q^65 + 7403346 * q^66 - 2436904 * q^67 + 14119909 * q^68 + 4050783 * q^69 + 5185580 * q^70 + 14289172 * q^71 + 2994003 * q^72 + 5482515 * q^73 + 14934154 * q^74 + 10791144 * q^75 + 3822912 * q^76 + 23157109 * q^77 + 4936842 * q^78 + 19786414 * q^79 + 31978143 * q^80 + 9565938 * q^81 + 9749509 * q^82 + 30227337 * q^83 + 11722050 * q^84 + 9946981 * q^85 + 44295864 * q^86 + 15964695 * q^87 + 39970897 * q^88 + 31061677 * q^89 + 2630961 * q^90 + 26377785 * q^91 + 4719698 * q^92 + 11521791 * q^93 + 44488296 * q^94 + 15534599 * q^95 + 32552010 * q^96 + 12084118 * q^97 + 42274744 * q^98 + 10986030 * 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 $

$2$	−5.28523	−0.467153	−0.233576	−	0.972338i	$-0.575043\pi$
$2$	−5.28523	−0.467153	−0.233576	+	0.972338i	$0.575043\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	−100.066	−0.781768
$5$	498.961	1.78514	0.892569	−	0.450910i	$-0.148900\pi$
$5$	498.961	1.78514	0.892569	+	0.450910i	$0.148900\pi$
$6$	−142.701	−0.269711
$7$	341.176	0.375954	0.187977	−	0.982173i	$-0.439807\pi$
$7$	341.176	0.375954	0.187977	+	0.982173i	$0.439807\pi$
$8$	1205.38	0.832358
$9$	729.000	0.333333
$10$	−2637.13	−0.833932
$11$	2091.72	0.473836	0.236918	−	0.971530i	$-0.423863\pi$
$11$	2091.72	0.473836	0.236918	+	0.971530i	$0.423863\pi$
$12$	−2701.79	−0.451354
$13$	4481.72	0.565774	0.282887	−	0.959153i	$-0.408708\pi$
$13$	4481.72	0.565774	0.282887	+	0.959153i	$0.408708\pi$
$14$	−1803.19	−0.175628
$15$	13472.0	1.03065
$16$	6437.77	0.392930
$17$	22387.5	1.10519	0.552593	−	0.833451i	$-0.313639\pi$
$17$	22387.5	1.10519	0.552593	+	0.833451i	$0.313639\pi$
$18$	−3852.93	−0.155718
$19$	6302.72	0.210809	0.105405	−	0.994429i	$-0.466386\pi$
$19$	6302.72	0.210809	0.105405	+	0.994429i	$0.466386\pi$
$20$	−49929.3	−1.39557
$21$	9211.75	0.217057
$22$	−11055.2	−0.221354
$23$	8949.56	0.153375	0.0766875	−	0.997055i	$-0.475566\pi$
$23$	8949.56	0.153375	0.0766875	+	0.997055i	$0.475566\pi$
$24$	32545.3	0.480562
$25$	170838.	2.18672
$26$	−23686.9	−0.264303
$27$	19683.0	0.192450
$28$	−34140.2	−0.293909
$29$	−232539.	−1.77053	−0.885265	−	0.465087i	$-0.846023\pi$
$29$	−232539.	−1.77053	−0.885265	+	0.465087i	$0.846023\pi$
$30$	−71202.4	−0.481471
$31$	−109526.	−0.660312	−0.330156	−	0.943926i	$-0.607101\pi$
$31$	−109526.	−0.660312	−0.330156	+	0.943926i	$0.607101\pi$
$32$	−188314.	−1.01592
$33$	56476.3	0.273569
$34$	−118323.	−0.516290
$35$	170234.	0.671131
$36$	−72948.4	−0.260589
$37$	123858.	0.401992	0.200996	−	0.979592i	$-0.435582\pi$
$37$	123858.	0.401992	0.200996	+	0.979592i	$0.435582\pi$
$38$	−33311.3	−0.0984802
$39$	121006.	0.326650
$40$	601440.	1.48587
$41$	133392.	0.302263	0.151132	−	0.988514i	$-0.451708\pi$
$41$	133392.	0.302263	0.151132	+	0.988514i	$0.451708\pi$
$42$	−48686.2	−0.101399
$43$	326147.	0.625567	0.312784	−	0.949824i	$-0.398739\pi$
$43$	326147.	0.625567	0.312784	+	0.949824i	$0.398739\pi$
$44$	−209310.	−0.370430
$45$	363743.	0.595046
$46$	−47300.5	−0.0716495
$47$	−479181.	−0.673221	−0.336610	−	0.941644i	$-0.609280\pi$
$47$	−479181.	−0.673221	−0.336610	+	0.941644i	$0.609280\pi$
$48$	173820.	0.226858
$49$	−707142.	−0.858658
$50$	−902916.	−1.02153
$51$	604464.	0.638079
$52$	−448469.	−0.442304
$53$	−906342.	−0.836231	−0.418116	−	0.908394i	$-0.637309\pi$
$53$	−906342.	−0.836231	−0.418116	+	0.908394i	$0.637309\pi$
$54$	−104029.	−0.0899036
$55$	1.04369e6	0.845863
$56$	411248.	0.312929
$57$	170173.	0.121711
$58$	1.22902e6	0.827108
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	−1.34809e6	−0.805730
$61$	3.23653e6	1.82568	0.912842	−	0.408312i	$-0.133883\pi$
$61$	3.23653e6	1.82568	0.912842	+	0.408312i	$0.133883\pi$
$62$	578868.	0.308467
$63$	248717.	0.125318
$64$	171249.	0.0816578
$65$	2.23620e6	1.00998
$66$	−298490.	−0.127799
$67$	1.18481e6	0.481267	0.240633	−	0.970616i	$-0.422645\pi$
$67$	1.18481e6	0.481267	0.240633	+	0.970616i	$0.422645\pi$
$68$	−2.24024e6	−0.863999
$69$	241638.	0.0885511
$70$	−899724.	−0.313521
$71$	1.35464e6	0.449181	0.224590	−	0.974453i	$-0.427896\pi$
$71$	1.35464e6	0.449181	0.224590	+	0.974453i	$0.427896\pi$
$72$	878724.	0.277453
$73$	−5.84208e6	−1.75767	−0.878836	−	0.477125i	$-0.841679\pi$
$73$	−5.84208e6	−1.75767	−0.878836	+	0.477125i	$0.841679\pi$
$74$	−654616.	−0.187791
$75$	4.61261e6	1.26250
$76$	−630690.	−0.164804
$77$	713643.	0.178141
$78$	−639546.	−0.152595
$79$	4.69904e6	1.07230	0.536148	−	0.844124i	$-0.319879\pi$
$79$	4.69904e6	1.07230	0.536148	+	0.844124i	$0.319879\pi$
$80$	3.21220e6	0.701435
$81$	531441.	0.111111
$82$	−705006.	−0.141203
$83$	1.26796e6	0.243406	0.121703	−	0.992567i	$-0.461165\pi$
$83$	1.26796e6	0.243406	0.121703	+	0.992567i	$0.461165\pi$
$84$	−921786.	−0.169689
$85$	1.11705e7	1.97291
$86$	−1.72376e6	−0.292235
$87$	−6.27856e6	−1.02222
$88$	2.52132e6	0.394401
$89$	2.48381e6	0.373468	0.186734	−	0.982411i	$-0.440210\pi$
$89$	2.48381e6	0.373468	0.186734	+	0.982411i	$0.440210\pi$
$90$	−1.92246e6	−0.277977
$91$	1.52905e6	0.212705
$92$	−895550.	−0.119904
$93$	−2.95719e6	−0.381232
$94$	2.53258e6	0.314497
$95$	3.14481e6	0.376324
$96$	−5.08448e6	−0.586540
$97$	4.51095e6	0.501841	0.250921	−	0.968008i	$-0.419267\pi$
$97$	4.51095e6	0.501841	0.250921	+	0.968008i	$0.419267\pi$
$98$	3.73741e6	0.401125
$99$	1.52486e6	0.157945
$100$	−1.70951e7	−1.70951
$101$	−812528.	−0.0784718	−0.0392359	−	0.999230i	$-0.512492\pi$
$101$	−812528.	−0.0784718	−0.0392359	+	0.999230i	$0.512492\pi$
$102$	−3.19473e6	−0.298080
$103$	1.18581e7	1.06926	0.534630	−	0.845086i	$-0.320451\pi$
$103$	1.18581e7	1.06926	0.534630	+	0.845086i	$0.320451\pi$
$104$	5.40219e6	0.470926
$105$	4.59631e6	0.387478
$106$	4.79022e6	0.390648
$107$	1.53725e7	1.21311	0.606555	−	0.795041i	$-0.292551\pi$
$107$	1.53725e7	1.21311	0.606555	+	0.795041i	$0.292551\pi$
$108$	−1.96961e6	−0.150451
$109$	68968.8	0.00510106	0.00255053	−	0.999997i	$-0.499188\pi$
$109$	68968.8	0.00510106	0.00255053	+	0.999997i	$0.499188\pi$
$110$	−5.51612e6	−0.395147
$111$	3.34416e6	0.232090
$112$	2.19641e6	0.147724
$113$	2.00851e7	1.30948	0.654740	−	0.755854i	$-0.272778\pi$
$113$	2.00851e7	1.30948	0.654740	+	0.755854i	$0.272778\pi$
$114$	−899405.	−0.0568576
$115$	4.46549e6	0.273796
$116$	2.32694e7	1.38414
$117$	3.26717e6	0.188591
$118$	−1.08548e6	−0.0608181
$119$	7.63809e6	0.415499
$120$	1.62389e7	0.857870
$121$	−1.51119e7	−0.775479
$122$	−1.71058e7	−0.852873
$123$	3.60158e6	0.174512
$124$	1.09598e7	0.516211
$125$	4.62600e7	2.11846
$126$	−1.31453e6	−0.0585427
$127$	2.70641e6	0.117241	0.0586207	−	0.998280i	$-0.481330\pi$
$127$	2.70641e6	0.117241	0.0586207	+	0.998280i	$0.481330\pi$
$128$	2.31991e7	0.977770
$129$	8.80597e6	0.361171
$130$	−1.18189e7	−0.471817
$131$	2.11862e6	0.0823386	0.0411693	−	0.999152i	$-0.486892\pi$
$131$	2.11862e6	0.0823386	0.0411693	+	0.999152i	$0.486892\pi$
$132$	−5.65138e6	−0.213868
$133$	2.15033e6	0.0792547
$134$	−6.26198e6	−0.224825
$135$	9.82106e6	0.343550
$136$	2.69856e7	0.919910
$137$	3.48905e7	1.15927	0.579636	−	0.814875i	$-0.303195\pi$
$137$	3.48905e7	1.15927	0.579636	+	0.814875i	$0.303195\pi$
$138$	−1.27711e6	−0.0413669
$139$	−3.13281e7	−0.989422	−0.494711	−	0.869058i	$-0.664726\pi$
$139$	−3.13281e7	−0.989422	−0.494711	+	0.869058i	$0.664726\pi$
$140$	−1.70347e7	−0.524669
$141$	−1.29379e7	−0.388684
$142$	−7.15960e6	−0.209836
$143$	9.37448e6	0.268084
$144$	4.69313e6	0.130977
$145$	−1.16028e8	−3.16064
$146$	3.08767e7	0.821101
$147$	−1.90928e7	−0.495747
$148$	−1.23940e7	−0.314264
$149$	−1.74202e6	−0.0431421	−0.0215710	−	0.999767i	$-0.506867\pi$
$149$	−1.74202e6	−0.0431421	−0.0215710	+	0.999767i	$0.506867\pi$
$150$	−2.43787e7	−0.589782
$151$	−2.12520e7	−0.502321	−0.251160	−	0.967945i	$-0.580812\pi$
$151$	−2.12520e7	−0.502321	−0.251160	+	0.967945i	$0.580812\pi$
$152$	7.59719e6	0.175469
$153$	1.63205e7	0.368395
$154$	−3.77177e6	−0.0832189
$155$	−5.46490e7	−1.17875
$156$	−1.21087e7	−0.255364
$157$	−2.17178e7	−0.447886	−0.223943	−	0.974602i	$-0.571893\pi$
$157$	−2.17178e7	−0.447886	−0.223943	+	0.974602i	$0.571893\pi$
$158$	−2.48355e7	−0.500926
$159$	−2.44712e7	−0.482798
$160$	−9.39615e7	−1.81355
$161$	3.05338e6	0.0576620
$162$	−2.80879e6	−0.0519059
$163$	−5.00693e7	−0.905556	−0.452778	−	0.891623i	$-0.649567\pi$
$163$	−5.00693e7	−0.905556	−0.452778	+	0.891623i	$0.649567\pi$
$164$	−1.33480e7	−0.236300
$165$	2.81795e7	0.488359
$166$	−6.70143e6	−0.113708
$167$	3.77408e7	0.627052	0.313526	−	0.949580i	$-0.398490\pi$
$167$	3.77408e7	0.627052	0.313526	+	0.949580i	$0.398490\pi$
$168$	1.11037e7	0.180669
$169$	−4.26627e7	−0.679900
$170$	−5.90388e7	−0.921650
$171$	4.59468e6	0.0702698
$172$	−3.26364e7	−0.489049
$173$	−1.26205e8	−1.85317	−0.926584	−	0.376087i	$-0.877269\pi$
$173$	−1.26205e8	−1.85317	−0.926584	+	0.376087i	$0.877269\pi$
$174$	3.31836e7	0.477531
$175$	5.82857e7	0.822107
$176$	1.34660e7	0.186184
$177$	5.54523e6	0.0751646
$178$	−1.31275e7	−0.174467
$179$	−8.64515e7	−1.12664	−0.563322	−	0.826237i	$-0.690477\pi$
$179$	−8.64515e7	−1.12664	−0.563322	+	0.826237i	$0.690477\pi$
$180$	−3.63984e7	−0.465188
$181$	1.43002e7	0.179254	0.0896268	−	0.995975i	$-0.471433\pi$
$181$	1.43002e7	0.179254	0.0896268	+	0.995975i	$0.471433\pi$
$182$	−8.08140e6	−0.0993658
$183$	8.73864e7	1.05406
$184$	1.07877e7	0.127663
$185$	6.18002e7	0.717611
$186$	1.56294e7	0.178093
$187$	4.68284e7	0.523677
$188$	4.79499e7	0.526303
$189$	6.71536e6	0.0723525
$190$	−1.66211e7	−0.175801
$191$	−1.45821e8	−1.51427	−0.757136	−	0.653257i	$-0.773402\pi$
$191$	−1.45821e8	−1.51427	−0.757136	+	0.653257i	$0.773402\pi$
$192$	4.62372e6	0.0471452
$193$	−1.60189e8	−1.60391	−0.801957	−	0.597381i	$-0.796208\pi$
$193$	−1.60189e8	−1.60391	−0.801957	+	0.597381i	$0.796208\pi$
$194$	−2.38414e7	−0.234437
$195$	6.03775e7	0.583115
$196$	7.07611e7	0.671272
$197$	−1.81066e7	−0.168735	−0.0843677	−	0.996435i	$-0.526887\pi$
$197$	−1.81066e7	−0.168735	−0.0843677	+	0.996435i	$0.526887\pi$
$198$	−8.05924e6	−0.0737846
$199$	2.17069e8	1.95260	0.976298	−	0.216430i	$-0.0694412\pi$
$199$	2.17069e8	1.95260	0.976298	+	0.216430i	$0.0694412\pi$
$200$	2.05925e8	1.82013
$201$	3.19898e7	0.277859
$202$	4.29440e6	0.0366583
$203$	−7.93368e7	−0.665638
$204$	−6.04865e7	−0.498830
$205$	6.65573e7	0.539582
$206$	−6.26726e7	−0.499508
$207$	6.52423e6	0.0511250
$208$	2.88523e7	0.222310
$209$	1.31835e7	0.0998891
$210$	−2.42925e7	−0.181011
$211$	−1.96840e7	−0.144253	−0.0721266	−	0.997395i	$-0.522979\pi$
$211$	−1.96840e7	−0.144253	−0.0721266	+	0.997395i	$0.522979\pi$
$212$	9.06943e7	0.653739
$213$	3.65754e7	0.259335
$214$	−8.12470e7	−0.566708
$215$	1.62735e8	1.11672
$216$	2.37256e7	0.160187
$217$	−3.73675e7	−0.248247
$218$	−364516.	−0.00238297
$219$	−1.57736e8	−1.01479
$220$	−1.04438e8	−0.661269
$221$	1.00335e8	0.625285
$222$	−1.76746e7	−0.108421
$223$	1.80353e8	1.08907	0.544536	−	0.838738i	$-0.316706\pi$
$223$	1.80353e8	1.08907	0.544536	+	0.838738i	$0.316706\pi$
$224$	−6.42482e7	−0.381938
$225$	1.24541e8	0.728907
$226$	−1.06154e8	−0.611727
$227$	−1.17899e8	−0.668993	−0.334496	−	0.942397i	$-0.608566\pi$
$227$	−1.17899e8	−0.668993	−0.334496	+	0.942397i	$0.608566\pi$
$228$	−1.70286e7	−0.0951497
$229$	7.05269e7	0.388089	0.194044	−	0.980993i	$-0.437839\pi$
$229$	7.05269e7	0.388089	0.194044	+	0.980993i	$0.437839\pi$
$230$	−2.36011e7	−0.127904
$231$	1.92684e7	0.102850
$232$	−2.80299e8	−1.47371
$233$	−2.32980e8	−1.20663	−0.603313	−	0.797505i	$-0.706153\pi$
$233$	−2.32980e8	−1.20663	−0.603313	+	0.797505i	$0.706153\pi$
$234$	−1.72678e7	−0.0881009
$235$	−2.39093e8	−1.20179
$236$	−2.05515e7	−0.101778
$237$	1.26874e8	0.619090
$238$	−4.03690e7	−0.194102
$239$	4.21184e8	1.99562	0.997812	−	0.0661120i	$-0.0210595\pi$
$239$	4.21184e8	1.99562	0.997812	+	0.0661120i	$0.0210595\pi$
$240$	8.67294e7	0.404974
$241$	1.65428e8	0.761291	0.380645	−	0.924721i	$-0.375702\pi$
$241$	1.65428e8	0.761291	0.380645	+	0.924721i	$0.375702\pi$
$242$	7.98699e7	0.362267
$243$	1.43489e7	0.0641500
$244$	−3.23868e8	−1.42726
$245$	−3.52837e8	−1.53282
$246$	−1.90352e7	−0.0815237
$247$	2.82470e7	0.119270
$248$	−1.32020e8	−0.549616
$249$	3.42348e7	0.140530
$250$	−2.44495e8	−0.989645
$251$	4.33192e8	1.72911	0.864554	−	0.502540i	$-0.167601\pi$
$251$	4.33192e8	1.72911	0.864554	+	0.502540i	$0.167601\pi$
$252$	−2.48882e7	−0.0979698
$253$	1.87199e7	0.0726746
$254$	−1.43040e7	−0.0547696
$255$	3.01604e8	1.13906
$256$	−1.44533e8	−0.538426
$257$	−1.31387e8	−0.482821	−0.241411	−	0.970423i	$-0.577610\pi$
$257$	−1.31387e8	−0.482821	−0.241411	+	0.970423i	$0.577610\pi$
$258$	−4.65416e7	−0.168722
$259$	4.22573e7	0.151131
$260$	−2.23769e8	−0.789574
$261$	−1.69521e8	−0.590177
$262$	−1.11974e7	−0.0384647
$263$	−2.55280e8	−0.865311	−0.432655	−	0.901559i	$-0.642423\pi$
$263$	−2.55280e8	−0.865311	−0.432655	+	0.901559i	$0.642423\pi$
$264$	6.80756e7	0.227708
$265$	−4.52230e8	−1.49279
$266$	−1.13650e7	−0.0370241
$267$	6.70629e7	0.215622
$268$	−1.18559e8	−0.376239
$269$	−1.16484e8	−0.364867	−0.182434	−	0.983218i	$-0.558397\pi$
$269$	−1.16484e8	−0.364867	−0.182434	+	0.983218i	$0.558397\pi$
$270$	−5.19065e7	−0.160490
$271$	2.19711e8	0.670593	0.335297	−	0.942113i	$-0.391164\pi$
$271$	2.19711e8	0.670593	0.335297	+	0.942113i	$0.391164\pi$
$272$	1.44126e8	0.434261
$273$	4.12845e7	0.122805
$274$	−1.84404e8	−0.541557
$275$	3.57344e8	1.03615
$276$	−2.41799e7	−0.0692264
$277$	−2.25909e8	−0.638638	−0.319319	−	0.947647i	$-0.603454\pi$
$277$	−2.25909e8	−0.638638	−0.319319	+	0.947647i	$0.603454\pi$
$278$	1.65576e8	0.462211
$279$	−7.98441e7	−0.220104
$280$	2.05197e8	0.558621
$281$	2.43072e8	0.653527	0.326763	−	0.945106i	$-0.394042\pi$
$281$	2.43072e8	0.653527	0.326763	+	0.945106i	$0.394042\pi$
$282$	6.83797e7	0.181575
$283$	2.39190e6	0.00627323	0.00313662	−	0.999995i	$-0.499002\pi$
$283$	2.39190e6	0.00627323	0.00313662	+	0.999995i	$0.499002\pi$
$284$	−1.35554e8	−0.351155
$285$	8.49099e7	0.217271
$286$	−4.95463e7	−0.125236
$287$	4.55100e7	0.113637
$288$	−1.37281e8	−0.338639
$289$	9.08632e7	0.221435
$290$	6.13235e8	1.47650
$291$	1.21796e8	0.289738
$292$	5.84596e8	1.37409
$293$	−5.43356e8	−1.26197	−0.630984	−	0.775796i	$-0.717349\pi$
$293$	−5.43356e8	−1.26197	−0.630984	+	0.775796i	$0.717349\pi$
$294$	1.00910e8	0.231589
$295$	1.02476e8	0.232405
$296$	1.49296e8	0.334601
$297$	4.11712e7	0.0911898
$298$	9.20697e6	0.0201539
$299$	4.01094e7	0.0867755
$300$	−4.61568e8	−0.986986
$301$	1.11274e8	0.235185
$302$	1.12322e8	0.234661
$303$	−2.19383e7	−0.0453057
$304$	4.05754e7	0.0828334
$305$	1.61491e9	3.25910
$306$	−8.62577e7	−0.172097
$307$	−2.04302e8	−0.402985	−0.201492	−	0.979490i	$-0.564579\pi$
$307$	−2.04302e8	−0.402985	−0.201492	+	0.979490i	$0.564579\pi$
$308$	−7.14116e7	−0.139265
$309$	3.20168e8	0.617338
$310$	2.88833e8	0.550656
$311$	4.81659e8	0.907984	0.453992	−	0.891006i	$-0.349999\pi$
$311$	4.81659e8	0.907984	0.453992	+	0.891006i	$0.349999\pi$
$312$	1.45859e8	0.271889
$313$	−1.77600e8	−0.327369	−0.163684	−	0.986513i	$-0.552338\pi$
$313$	−1.77600e8	−0.327369	−0.163684	+	0.986513i	$0.552338\pi$
$314$	1.14784e8	0.209231
$315$	1.24100e8	0.223710
$316$	−4.70216e8	−0.838287
$317$	4.19257e8	0.739218	0.369609	−	0.929187i	$-0.379492\pi$
$317$	4.19257e8	0.739218	0.369609	+	0.929187i	$0.379492\pi$
$318$	1.29336e8	0.225541
$319$	−4.86406e8	−0.838941
$320$	8.54466e7	0.145771
$321$	4.15057e8	0.700390
$322$	−1.61378e7	−0.0269370
$323$	1.41102e8	0.232984
$324$	−5.31794e7	−0.0868632
$325$	7.65646e8	1.23719
$326$	2.64628e8	0.423033
$327$	1.86216e6	0.00294510
$328$	1.60788e8	0.251591
$329$	−1.63485e8	−0.253100
$330$	−1.48935e8	−0.228138
$331$	−6.53330e8	−0.990226	−0.495113	−	0.868829i	$-0.664873\pi$
$331$	−6.53330e8	−0.990226	−0.495113	+	0.868829i	$0.664873\pi$
$332$	−1.26880e8	−0.190287
$333$	9.02923e7	0.133997
$334$	−1.99469e8	−0.292929
$335$	5.91173e8	0.859128
$336$	5.93031e7	0.0852884
$337$	2.22015e8	0.315993	0.157997	−	0.987440i	$-0.449497\pi$
$337$	2.22015e8	0.315993	0.157997	+	0.987440i	$0.449497\pi$
$338$	2.25482e8	0.317617
$339$	5.42297e8	0.756029
$340$	−1.11779e9	−1.54236
$341$	−2.29096e8	−0.312880
$342$	−2.42839e7	−0.0328267
$343$	−5.22233e8	−0.698771
$344$	3.93132e8	0.520696
$345$	1.20568e8	0.158076
$346$	6.67022e8	0.865713
$347$	−7.82082e8	−1.00485	−0.502423	−	0.864622i	$-0.667558\pi$
$347$	−7.82082e8	−1.00485	−0.502423	+	0.864622i	$0.667558\pi$
$348$	6.28273e8	0.799136
$349$	2.24931e8	0.283243	0.141622	−	0.989921i	$-0.454768\pi$
$349$	2.24931e8	0.283243	0.141622	+	0.989921i	$0.454768\pi$
$350$	−3.08053e8	−0.384050
$351$	8.82136e7	0.108883
$352$	−3.93899e8	−0.481378
$353$	−9.53452e8	−1.15368	−0.576842	−	0.816855i	$-0.695715\pi$
$353$	−9.53452e8	−1.15368	−0.576842	+	0.816855i	$0.695715\pi$
$354$	−2.93078e7	−0.0351133
$355$	6.75915e8	0.801850
$356$	−2.48546e8	−0.291965
$357$	2.06228e8	0.239889
$358$	4.56916e8	0.526315
$359$	8.80036e8	1.00385	0.501926	−	0.864910i	$-0.332625\pi$
$359$	8.80036e8	1.00385	0.501926	+	0.864910i	$0.332625\pi$
$360$	4.38450e8	0.495291
$361$	−8.54148e8	−0.955559
$362$	−7.55800e7	−0.0837388
$363$	−4.08021e8	−0.447723
$364$	−1.53007e8	−0.166286
$365$	−2.91497e9	−3.13769
$366$	−4.61857e8	−0.492407
$367$	−4.42919e8	−0.467727	−0.233864	−	0.972269i	$-0.575137\pi$
$367$	−4.42919e8	−0.467727	−0.233864	+	0.972269i	$0.575137\pi$
$368$	5.76152e7	0.0602656
$369$	9.72426e7	0.100754
$370$	−3.26628e8	−0.335234
$371$	−3.09222e8	−0.314385
$372$	2.95915e8	0.298035
$373$	6.56422e8	0.654942	0.327471	−	0.944861i	$-0.393804\pi$
$373$	6.56422e8	0.654942	0.327471	+	0.944861i	$0.393804\pi$
$374$	−2.47499e8	−0.244637
$375$	1.24902e9	1.22309
$376$	−5.77597e8	−0.560360
$377$	−1.04218e9	−1.00172
$378$	−3.54922e7	−0.0337996
$379$	4.00683e7	0.0378062	0.0189031	−	0.999821i	$-0.493983\pi$
$379$	4.00683e7	0.0378062	0.0189031	+	0.999821i	$0.493983\pi$
$380$	−3.14690e8	−0.294198
$381$	7.30731e7	0.0676893
$382$	7.70699e8	0.707397
$383$	4.34731e8	0.395389	0.197694	−	0.980264i	$-0.436655\pi$
$383$	4.34731e8	0.395389	0.197694	+	0.980264i	$0.436655\pi$
$384$	6.26376e8	0.564516
$385$	3.56080e8	0.318006
$386$	8.46634e8	0.749273
$387$	2.37761e8	0.208522
$388$	−4.51394e8	−0.392324
$389$	−7.97933e8	−0.687294	−0.343647	−	0.939099i	$-0.611662\pi$
$389$	−7.97933e8	−0.687294	−0.343647	+	0.939099i	$0.611662\pi$
$390$	−3.19109e8	−0.272404
$391$	2.00359e8	0.169508
$392$	−8.52377e8	−0.714711
$393$	5.72027e7	0.0475382
$394$	9.56977e7	0.0788252
$395$	2.34464e9	1.91420
$396$	−1.52587e8	−0.123477
$397$	2.94069e8	0.235875	0.117938	−	0.993021i	$-0.462372\pi$
$397$	2.94069e8	0.235875	0.117938	+	0.993021i	$0.462372\pi$
$398$	−1.14726e9	−0.912161
$399$	5.80590e7	0.0457577
$400$	1.09981e9	0.859229
$401$	1.98521e9	1.53745	0.768724	−	0.639580i	$-0.220892\pi$
$401$	1.98521e9	1.53745	0.768724	+	0.639580i	$0.220892\pi$
$402$	−1.69073e8	−0.129803
$403$	−4.90863e8	−0.373587
$404$	8.13067e7	0.0613468
$405$	2.65169e8	0.198349
$406$	4.19313e8	0.310955
$407$	2.59075e8	0.190478
$408$	7.28610e8	0.531110
$409$	8.07703e8	0.583741	0.291871	−	0.956458i	$-0.405722\pi$
$409$	8.07703e8	0.583741	0.291871	+	0.956458i	$0.405722\pi$
$410$	−3.51771e8	−0.252067
$411$	9.42044e8	0.669306
$412$	−1.18659e9	−0.835914
$413$	7.00704e7	0.0489451
$414$	−3.44821e7	−0.0238832
$415$	6.32661e8	0.434513
$416$	−8.43971e8	−0.574779
$417$	−8.45857e8	−0.571243
$418$	−6.96777e7	−0.0466635
$419$	1.07006e9	0.710653	0.355326	−	0.934742i	$-0.384370\pi$
$419$	1.07006e9	0.710653	0.355326	+	0.934742i	$0.384370\pi$
$420$	−4.59936e8	−0.302918
$421$	−1.95522e9	−1.27705	−0.638526	−	0.769600i	$-0.720456\pi$
$421$	−1.95522e9	−1.27705	−0.638526	+	0.769600i	$0.720456\pi$
$422$	1.04035e8	0.0673882
$423$	−3.49323e8	−0.224407
$424$	−1.09249e9	−0.696044
$425$	3.82463e9	2.41673
$426$	−1.93309e8	−0.121149
$427$	1.10423e9	0.686374
$428$	−1.53827e9	−0.948371
$429$	2.53111e8	0.154778
$430$	−8.60091e8	−0.521681
$431$	−2.40194e9	−1.44508	−0.722540	−	0.691329i	$-0.757025\pi$
$431$	−2.40194e9	−1.44508	−0.722540	+	0.691329i	$0.757025\pi$
$432$	1.26715e8	0.0756194
$433$	−1.31134e9	−0.776259	−0.388129	−	0.921605i	$-0.626879\pi$
$433$	−1.31134e9	−0.776259	−0.388129	+	0.921605i	$0.626879\pi$
$434$	1.97496e8	0.115969
$435$	−3.13276e9	−1.82480
$436$	−6.90146e6	−0.00398785
$437$	5.64066e7	0.0323329
$438$	8.33672e8	0.474063
$439$	−2.63455e8	−0.148621	−0.0743105	−	0.997235i	$-0.523676\pi$
$439$	−2.63455e8	−0.148621	−0.0743105	+	0.997235i	$0.523676\pi$
$440$	1.25804e9	0.704061
$441$	−5.15507e8	−0.286219
$442$	−5.30291e8	−0.292103
$443$	1.46341e9	0.799748	0.399874	−	0.916570i	$-0.369054\pi$
$443$	1.46341e9	0.799748	0.399874	+	0.916570i	$0.369054\pi$
$444$	−3.34638e8	−0.181441
$445$	1.23933e9	0.666692
$446$	−9.53207e8	−0.508763
$447$	−4.70345e7	−0.0249081
$448$	5.84260e7	0.0306996
$449$	−2.17952e9	−1.13631	−0.568157	−	0.822920i	$-0.692343\pi$
$449$	−2.17952e9	−1.13631	−0.568157	+	0.822920i	$0.692343\pi$
$450$	−6.58226e8	−0.340511
$451$	2.79018e8	0.143223
$452$	−2.00984e9	−1.02371
$453$	−5.73805e8	−0.290015
$454$	6.23126e8	0.312522
$455$	7.62939e8	0.379708
$456$	2.05124e8	0.101307
$457$	2.47142e9	1.21127	0.605634	−	0.795743i	$-0.292920\pi$
$457$	2.47142e9	1.21127	0.605634	+	0.795743i	$0.292920\pi$
$458$	−3.72751e8	−0.181297
$459$	4.40654e8	0.212693
$460$	−4.46845e8	−0.214045
$461$	2.72822e9	1.29696	0.648479	−	0.761232i	$-0.275405\pi$
$461$	2.72822e9	1.29696	0.648479	+	0.761232i	$0.275405\pi$
$462$	−1.01838e8	−0.0480465
$463$	−2.36027e9	−1.10517	−0.552583	−	0.833458i	$-0.686358\pi$
$463$	−2.36027e9	−1.10517	−0.552583	+	0.833458i	$0.686358\pi$
$464$	−1.49703e9	−0.695695
$465$	−1.47552e9	−0.680551
$466$	1.23135e9	0.563678
$467$	−3.71806e9	−1.68930	−0.844650	−	0.535318i	$-0.820192\pi$
$467$	−3.71806e9	−1.68930	−0.844650	+	0.535318i	$0.820192\pi$
$468$	−3.26934e8	−0.147435
$469$	4.04228e8	0.180934
$470$	1.26366e9	0.561420
$471$	−5.86381e8	−0.258587
$472$	2.47560e8	0.108364
$473$	6.82207e8	0.296416
$474$	−6.70559e8	−0.289210
$475$	1.07674e9	0.460981
$476$	−7.64316e8	−0.324824
$477$	−6.60723e8	−0.278744
$478$	−2.22605e9	−0.932261
$479$	−3.64251e9	−1.51435	−0.757175	−	0.653212i	$-0.773421\pi$
$479$	−3.64251e9	−1.51435	−0.757175	+	0.653212i	$0.773421\pi$
$480$	−2.53696e9	−1.04705
$481$	5.55095e8	0.227436
$482$	−8.74327e8	−0.355639
$483$	8.24411e7	0.0332912
$484$	1.51219e9	0.606245
$485$	2.25079e9	0.895857
$486$	−7.58373e7	−0.0299679
$487$	−4.68073e9	−1.83638	−0.918190	−	0.396140i	$-0.870350\pi$
$487$	−4.68073e9	−1.83638	−0.918190	+	0.396140i	$0.870350\pi$
$488$	3.90126e9	1.51962
$489$	−1.35187e9	−0.522823
$490$	1.86482e9	0.716063
$491$	4.42989e9	1.68892	0.844458	−	0.535622i	$-0.179923\pi$
$491$	4.42989e9	1.68892	0.844458	+	0.535622i	$0.179923\pi$
$492$	−3.60397e8	−0.136428
$493$	−5.20598e9	−1.95676
$494$	−1.49292e8	−0.0557175
$495$	7.60847e8	0.281954
$496$	−7.05100e8	−0.259457
$497$	4.62172e8	0.168871
$498$	−1.80939e8	−0.0656491
$499$	2.99262e9	1.07820	0.539100	−	0.842242i	$-0.318765\pi$
$499$	2.99262e9	1.07820	0.539100	+	0.842242i	$0.318765\pi$
$500$	−4.62907e9	−1.65615
$501$	1.01900e9	0.362029
$502$	−2.28952e9	−0.807757
$503$	−6.91728e8	−0.242353	−0.121176	−	0.992631i	$-0.538667\pi$
$503$	−6.91728e8	−0.242353	−0.121176	+	0.992631i	$0.538667\pi$
$504$	2.99799e8	0.104310
$505$	−4.05420e8	−0.140083
$506$	−9.89392e7	−0.0339501
$507$	−1.15189e9	−0.392541
$508$	−2.70821e8	−0.0916556
$509$	1.02248e9	0.343671	0.171835	−	0.985126i	$-0.445030\pi$
$509$	1.02248e9	0.343671	0.171835	+	0.985126i	$0.445030\pi$
$510$	−1.59405e9	−0.532115
$511$	−1.99318e9	−0.660804
$512$	−2.20560e9	−0.726243
$513$	1.24056e8	0.0405703
$514$	6.94411e8	0.225551
$515$	5.91671e9	1.90878
$516$	−8.81182e8	−0.282352
$517$	−1.00231e9	−0.318996
$518$	−2.23339e8	−0.0706010
$519$	−3.40753e9	−1.06993
$520$	2.69548e9	0.840669
$521$	−1.33952e9	−0.414970	−0.207485	−	0.978238i	$-0.566528\pi$
$521$	−1.33952e9	−0.414970	−0.207485	+	0.978238i	$0.566528\pi$
$522$	8.95958e8	0.275703
$523$	2.03575e9	0.622255	0.311127	−	0.950368i	$-0.399293\pi$
$523$	2.03575e9	0.622255	0.311127	+	0.950368i	$0.399293\pi$
$524$	−2.12002e8	−0.0643697
$525$	1.57371e9	0.474644
$526$	1.34921e9	0.404232
$527$	−2.45201e9	−0.729768
$528$	3.63581e8	0.107494
$529$	−3.32473e9	−0.976476
$530$	2.39014e9	0.697361
$531$	1.49721e8	0.0433963
$532$	−2.15176e8	−0.0619589
$533$	5.97824e8	0.171013
$534$	−3.54443e8	−0.100728
$535$	7.67027e9	2.16557
$536$	1.42815e9	0.400586
$537$	−2.33419e9	−0.650468
$538$	6.15647e8	0.170449
$539$	−1.47914e9	−0.406863
$540$	−9.82758e8	−0.268577
$541$	−3.66614e9	−0.995449	−0.497724	−	0.867335i	$-0.665831\pi$
$541$	−3.66614e9	−0.995449	−0.497724	+	0.867335i	$0.665831\pi$
$542$	−1.16122e9	−0.313269
$543$	3.86106e8	0.103492
$544$	−4.21589e9	−1.12278
$545$	3.44128e7	0.00910610
$546$	−2.18198e8	−0.0573688
$547$	−1.78158e9	−0.465426	−0.232713	−	0.972545i	$-0.574760\pi$
$547$	−1.78158e9	−0.465426	−0.232713	+	0.972545i	$0.574760\pi$
$548$	−3.49137e9	−0.906282
$549$	2.35943e9	0.608561
$550$	−1.88864e9	−0.484039
$551$	−1.46563e9	−0.373244
$552$	2.91267e8	0.0737062
$553$	1.60320e9	0.403134
$554$	1.19398e9	0.298341
$555$	1.66861e9	0.414313
$556$	3.13488e9	0.773499
$557$	5.09999e9	1.25048	0.625239	−	0.780434i	$-0.285002\pi$
$557$	5.09999e9	1.25048	0.625239	+	0.780434i	$0.285002\pi$
$558$	4.21994e8	0.102822
$559$	1.46170e9	0.353930
$560$	1.09592e9	0.263708
$561$	1.26437e9	0.302345
$562$	−1.28469e9	−0.305297
$563$	−5.89137e9	−1.39135	−0.695676	−	0.718356i	$-0.744895\pi$
$563$	−5.89137e9	−1.39135	−0.695676	+	0.718356i	$0.744895\pi$
$564$	1.29465e9	0.303861
$565$	1.00217e10	2.33760
$566$	−1.26418e7	−0.00293056
$567$	1.81315e8	0.0417727
$568$	1.63286e9	0.373879
$569$	8.17341e9	1.85999	0.929994	−	0.367574i	$-0.119812\pi$
$569$	8.17341e9	1.85999	0.929994	+	0.367574i	$0.119812\pi$
$570$	−4.48768e8	−0.101499
$571$	5.67551e9	1.27579	0.637894	−	0.770124i	$-0.279806\pi$
$571$	5.67551e9	1.27579	0.637894	+	0.770124i	$0.279806\pi$
$572$	−9.38070e8	−0.209580
$573$	−3.93717e9	−0.874266
$574$	−2.40531e8	−0.0530859
$575$	1.52892e9	0.335388
$576$	1.24840e8	0.0272193
$577$	7.16256e9	1.55222	0.776109	−	0.630598i	$-0.217190\pi$
$577$	7.16256e9	1.55222	0.776109	+	0.630598i	$0.217190\pi$
$578$	−4.80233e8	−0.103444
$579$	−4.32509e9	−0.926021
$580$	1.16105e10	2.47089
$581$	4.32596e8	0.0915094
$582$	−6.43717e8	−0.135352
$583$	−1.89581e9	−0.396237
$584$	−7.04195e9	−1.46301
$585$	1.63019e9	0.336662
$586$	2.87176e9	0.589531
$587$	−2.83241e9	−0.577993	−0.288997	−	0.957330i	$-0.593322\pi$
$587$	−2.83241e9	−0.577993	−0.288997	+	0.957330i	$0.593322\pi$
$588$	1.91055e9	0.387559
$589$	−6.90308e8	−0.139200
$590$	−5.41610e8	−0.108569
$591$	−4.88879e8	−0.0974194
$592$	7.97367e8	0.157955
$593$	−3.85485e9	−0.759130	−0.379565	−	0.925165i	$-0.623926\pi$
$593$	−3.85485e9	−0.759130	−0.379565	+	0.925165i	$0.623926\pi$
$594$	−2.17599e8	−0.0425996
$595$	3.81111e9	0.741724
$596$	1.74318e8	0.0337271
$597$	5.86087e9	1.12733
$598$	−2.11987e8	−0.0405374
$599$	−9.88088e9	−1.87846	−0.939229	−	0.343290i	$-0.888459\pi$
$599$	−9.88088e9	−1.87846	−0.939229	+	0.343290i	$0.888459\pi$
$600$	5.55997e9	1.05086
$601$	7.33104e9	1.37754	0.688771	−	0.724979i	$-0.258150\pi$
$601$	7.33104e9	1.37754	0.688771	+	0.724979i	$0.258150\pi$
$602$	−5.88106e8	−0.109867
$603$	8.63724e8	0.160422
$604$	2.12661e9	0.392699
$605$	−7.54026e9	−1.38434
$606$	1.15949e8	0.0211647
$607$	−6.93033e9	−1.25775	−0.628873	−	0.777508i	$-0.716484\pi$
$607$	−6.93033e9	−1.25775	−0.628873	+	0.777508i	$0.716484\pi$
$608$	−1.18689e9	−0.214165
$609$	−2.14209e9	−0.384307
$610$	−8.53515e9	−1.52250
$611$	−2.14756e9	−0.380890
$612$	−1.63313e9	−0.288000
$613$	−5.61223e9	−0.984065	−0.492033	−	0.870577i	$-0.663746\pi$
$613$	−5.61223e9	−0.984065	−0.492033	+	0.870577i	$0.663746\pi$
$614$	1.07978e9	0.188255
$615$	1.79705e9	0.311528
$616$	8.60213e8	0.148277
$617$	−5.35454e9	−0.917750	−0.458875	−	0.888501i	$-0.651747\pi$
$617$	−5.35454e9	−0.917750	−0.458875	+	0.888501i	$0.651747\pi$
$618$	−1.69216e9	−0.288391
$619$	−1.02326e10	−1.73408	−0.867038	−	0.498242i	$-0.833979\pi$
$619$	−1.02326e10	−1.73408	−0.867038	+	0.498242i	$0.833979\pi$
$620$	5.46853e9	0.921509
$621$	1.76154e8	0.0295170
$622$	−2.54568e9	−0.424167
$623$	8.47416e8	0.140407
$624$	7.79011e8	0.128350
$625$	9.73528e9	1.59503
$626$	9.38656e8	0.152931
$627$	3.55954e8	0.0576710
$628$	2.17322e9	0.350143
$629$	2.77287e9	0.444275
$630$	−6.55899e8	−0.104507
$631$	−2.22654e9	−0.352800	−0.176400	−	0.984319i	$-0.556445\pi$
$631$	−2.22654e9	−0.352800	−0.176400	+	0.984319i	$0.556445\pi$
$632$	5.66415e9	0.892534
$633$	−5.31469e8	−0.0832846
$634$	−2.21587e9	−0.345328
$635$	1.35040e9	0.209292
$636$	2.44875e9	0.377437
$637$	−3.16921e9	−0.485806
$638$	2.57077e9	0.391913
$639$	9.87536e8	0.149727
$640$	1.15755e10	1.74545
$641$	−4.46510e9	−0.669620	−0.334810	−	0.942286i	$-0.608672\pi$
$641$	−4.46510e9	−0.669620	−0.334810	+	0.942286i	$0.608672\pi$
$642$	−2.19367e9	−0.327189
$643$	8.21135e9	1.21808	0.609041	−	0.793139i	$-0.291555\pi$
$643$	8.21135e9	1.21808	0.609041	+	0.793139i	$0.291555\pi$
$644$	−3.05540e8	−0.0450783
$645$	4.39384e9	0.644741
$646$	−7.45758e8	−0.108839
$647$	1.31007e10	1.90164	0.950820	−	0.309745i	$-0.100244\pi$
$647$	1.31007e10	1.90164	0.950820	+	0.309745i	$0.100244\pi$
$648$	6.40590e8	0.0924842
$649$	4.29594e8	0.0616882
$650$	−4.04661e9	−0.577956
$651$	−1.00892e9	−0.143326
$652$	5.01025e9	0.707935
$653$	−4.31273e9	−0.606116	−0.303058	−	0.952972i	$-0.598008\pi$
$653$	−4.31273e9	−0.606116	−0.303058	+	0.952972i	$0.598008\pi$
$654$	−9.84194e6	−0.00137581
$655$	1.05711e9	0.146986
$656$	8.58745e8	0.118768
$657$	−4.25888e9	−0.585890
$658$	8.64056e8	0.118236
$659$	3.34441e9	0.455219	0.227610	−	0.973752i	$-0.426909\pi$
$659$	3.34441e9	0.455219	0.227610	+	0.973752i	$0.426909\pi$
$660$	−2.81982e9	−0.381784
$661$	7.28830e9	0.981570	0.490785	−	0.871281i	$-0.336710\pi$
$661$	7.28830e9	0.981570	0.490785	+	0.871281i	$0.336710\pi$
$662$	3.45300e9	0.462587
$663$	2.70903e9	0.361008
$664$	1.52837e9	0.202601
$665$	1.07293e9	0.141481
$666$	−4.77215e8	−0.0625971
$667$	−2.08112e9	−0.271555
$668$	−3.77659e9	−0.490210
$669$	4.86953e9	0.628776
$670$	−3.12449e9	−0.401344
$671$	6.76991e9	0.865075
$672$	−1.73470e9	−0.220512
$673$	−2.74970e9	−0.347723	−0.173861	−	0.984770i	$-0.555624\pi$
$673$	−2.74970e9	−0.347723	−0.173861	+	0.984770i	$0.555624\pi$
$674$	−1.17340e9	−0.147617
$675$	3.36260e9	0.420835
$676$	4.26910e9	0.531524
$677$	7.33717e9	0.908800	0.454400	−	0.890798i	$-0.349854\pi$
$677$	7.33717e9	0.908800	0.454400	+	0.890798i	$0.349854\pi$
$678$	−2.86616e9	−0.353181
$679$	1.53903e9	0.188670
$680$	1.34648e10	1.64217
$681$	−3.18329e9	−0.386243
$682$	1.21083e9	0.146163
$683$	5.10390e9	0.612956	0.306478	−	0.951878i	$-0.400849\pi$
$683$	5.10390e9	0.612956	0.306478	+	0.951878i	$0.400849\pi$
$684$	−4.59773e8	−0.0549347
$685$	1.74090e10	2.06946
$686$	2.76012e9	0.326433
$687$	1.90423e9	0.224063
$688$	2.09966e9	0.245804
$689$	−4.06197e9	−0.473118
$690$	−6.37230e8	−0.0738456
$691$	−1.60504e10	−1.85061	−0.925303	−	0.379229i	$-0.876189\pi$
$691$	−1.60504e10	−1.85061	−0.925303	+	0.379229i	$0.876189\pi$
$692$	1.26289e10	1.44875
$693$	5.20246e8	0.0593803
$694$	4.13348e9	0.469416
$695$	−1.56315e10	−1.76626
$696$	−7.56807e9	−0.850849
$697$	2.98631e9	0.334057
$698$	−1.18881e9	−0.132318
$699$	−6.29046e9	−0.696646
$700$	−5.83243e9	−0.642698
$701$	−1.74438e10	−1.91261	−0.956307	−	0.292366i	$-0.905558\pi$
$701$	−1.74438e10	−1.91261	−0.956307	+	0.292366i	$0.905558\pi$
$702$	−4.66229e8	−0.0508651
$703$	7.80640e8	0.0847436
$704$	3.58204e8	0.0386924
$705$	−6.45551e9	−0.693855
$706$	5.03921e9	0.538947
$707$	−2.77215e8	−0.0295018
$708$	−5.54891e8	−0.0587613
$709$	1.51506e9	0.159650	0.0798250	−	0.996809i	$-0.474564\pi$
$709$	1.51506e9	0.159650	0.0798250	+	0.996809i	$0.474564\pi$
$710$	−3.57237e9	−0.374586
$711$	3.42560e9	0.357432
$712$	2.99394e9	0.310859
$713$	−9.80206e8	−0.101275
$714$	−1.08996e9	−0.112065
$715$	4.67750e9	0.478567
$716$	8.65089e9	0.880775
$717$	1.13720e10	1.15217
$718$	−4.65119e9	−0.468952
$719$	−7.46523e9	−0.749018	−0.374509	−	0.927223i	$-0.622189\pi$
$719$	−7.46523e9	−0.749018	−0.374509	+	0.927223i	$0.622189\pi$
$720$	2.34169e9	0.233812
$721$	4.04568e9	0.401993
$722$	4.51437e9	0.446392
$723$	4.46657e9	0.439531
$724$	−1.43097e9	−0.140135
$725$	−3.97264e10	−3.87165
$726$	2.15649e9	0.209155
$727$	−9.95066e9	−0.960465	−0.480233	−	0.877141i	$-0.659448\pi$
$727$	−9.95066e9	−0.960465	−0.480233	+	0.877141i	$0.659448\pi$
$728$	1.84310e9	0.177047
$729$	3.87420e8	0.0370370
$730$	1.54063e10	1.46578
$731$	7.30163e9	0.691368
$732$	−8.74444e9	−0.824030
$733$	−1.32840e10	−1.24585	−0.622926	−	0.782281i	$-0.714056\pi$
$733$	−1.32840e10	−1.24585	−0.622926	+	0.782281i	$0.714056\pi$
$734$	2.34093e9	0.218500
$735$	−9.52659e9	−0.884977
$736$	−1.68533e9	−0.155816
$737$	2.47828e9	0.228042
$738$	−5.13949e8	−0.0470677
$739$	−1.90326e10	−1.73477	−0.867386	−	0.497637i	$-0.834201\pi$
$739$	−1.90326e10	−1.73477	−0.867386	+	0.497637i	$0.834201\pi$
$740$	−6.18412e9	−0.561005
$741$	7.62669e8	0.0688608
$742$	1.63431e9	0.146866
$743$	1.49051e10	1.33313	0.666567	−	0.745445i	$-0.267763\pi$
$743$	1.49051e10	1.33313	0.666567	+	0.745445i	$0.267763\pi$
$744$	−3.56455e9	−0.317321
$745$	−8.69201e8	−0.0770146
$746$	−3.46934e9	−0.305958
$747$	9.24339e8	0.0811352
$748$	−4.68594e9	−0.409394
$749$	5.24472e9	0.456074
$750$	−6.60136e9	−0.571372
$751$	1.38756e10	1.19540	0.597699	−	0.801721i	$-0.296082\pi$
$751$	1.38756e10	1.19540	0.597699	+	0.801721i	$0.296082\pi$
$752$	−3.08486e9	−0.264529
$753$	1.16962e10	0.998301
$754$	5.50813e9	0.467956
$755$	−1.06039e10	−0.896713
$756$	−6.71982e8	−0.0565629
$757$	2.56500e9	0.214907	0.107454	−	0.994210i	$-0.465730\pi$
$757$	2.56500e9	0.214907	0.107454	+	0.994210i	$0.465730\pi$
$758$	−2.11770e8	−0.0176613
$759$	5.05438e8	0.0419587
$760$	3.79070e9	0.313236
$761$	6.51304e8	0.0535720	0.0267860	−	0.999641i	$-0.491473\pi$
$761$	6.51304e8	0.0535720	0.0267860	+	0.999641i	$0.491473\pi$
$762$	−3.86208e8	−0.0316213
$763$	2.35305e7	0.00191776
$764$	1.45918e10	1.18381
$765$	8.14331e9	0.657636
$766$	−2.29765e9	−0.184707
$767$	9.20451e8	0.0736575
$768$	−3.90238e9	−0.310860
$769$	−2.24597e10	−1.78099	−0.890496	−	0.454991i	$-0.849643\pi$
$769$	−2.24597e10	−1.78099	−0.890496	+	0.454991i	$0.849643\pi$
$770$	−1.88197e9	−0.148557
$771$	−3.54745e9	−0.278757
$772$	1.60295e10	1.25389
$773$	−1.23734e9	−0.0963518	−0.0481759	−	0.998839i	$-0.515341\pi$
$773$	−1.23734e9	−0.0963518	−0.0481759	+	0.998839i	$0.515341\pi$
$774$	−1.25662e9	−0.0974118
$775$	−1.87111e10	−1.44392
$776$	5.43742e9	0.417712
$777$	1.14095e9	0.0872552
$778$	4.21726e9	0.321071
$779$	8.40730e8	0.0637200
$780$	−6.04176e9	−0.455861
$781$	2.83353e9	0.212838
$782$	−1.05894e9	−0.0791860
$783$	−4.57707e9	−0.340739
$784$	−4.55242e9	−0.337393
$785$	−1.08364e10	−0.799538
$786$	−3.02329e8	−0.0222076
$787$	−2.95191e9	−0.215870	−0.107935	−	0.994158i	$-0.534424\pi$
$787$	−2.95191e9	−0.215870	−0.107935	+	0.994158i	$0.534424\pi$
$788$	1.81187e9	0.131912
$789$	−6.89257e9	−0.499587
$790$	−1.23920e10	−0.894222
$791$	6.85254e9	0.492305
$792$	1.83804e9	0.131467
$793$	1.45052e10	1.03292
$794$	−1.55422e9	−0.110190
$795$	−1.22102e10	−0.861862
$796$	−2.17213e10	−1.52648
$797$	1.12703e10	0.788553	0.394276	−	0.918992i	$-0.370995\pi$
$797$	1.12703e10	0.788553	0.394276	+	0.918992i	$0.370995\pi$
$798$	−3.06855e8	−0.0213759
$799$	−1.07277e10	−0.744034
$800$	−3.21711e10	−2.22153
$801$	1.81070e9	0.124489
$802$	−1.04923e10	−0.718223
$803$	−1.22200e10	−0.832848
$804$	−3.20110e9	−0.217222
$805$	1.52352e9	0.102935
$806$	2.59432e9	0.174522
$807$	−3.14508e9	−0.210656
$808$	−9.79407e8	−0.0653166
$809$	−2.44387e10	−1.62277	−0.811386	−	0.584511i	$-0.801286\pi$
$809$	−2.44387e10	−1.62277	−0.811386	+	0.584511i	$0.801286\pi$
$810$	−1.40148e9	−0.0926592
$811$	1.77574e10	1.16898	0.584488	−	0.811402i	$-0.301295\pi$
$811$	1.77574e10	1.16898	0.584488	+	0.811402i	$0.301295\pi$
$812$	7.93894e9	0.520375
$813$	5.93219e9	0.387167
$814$	−1.36927e9	−0.0889824
$815$	−2.49827e10	−1.61654
$816$	3.89140e9	0.250721
$817$	2.05561e9	0.131876
$818$	−4.26890e9	−0.272696
$819$	1.11468e9	0.0709017
$820$	−6.66015e9	−0.421828
$821$	1.19253e10	0.752090	0.376045	−	0.926601i	$-0.377284\pi$
$821$	1.19253e10	0.752090	0.376045	+	0.926601i	$0.377284\pi$
$822$	−4.97892e9	−0.312668
$823$	−2.32580e10	−1.45436	−0.727182	−	0.686445i	$-0.759170\pi$
$823$	−2.32580e10	−1.45436	−0.727182	+	0.686445i	$0.759170\pi$
$824$	1.42935e10	0.890007
$825$	9.64828e9	0.598220
$826$	−3.70338e8	−0.0228648
$827$	6.50185e9	0.399731	0.199866	−	0.979823i	$-0.435949\pi$
$827$	6.50185e9	0.399731	0.199866	+	0.979823i	$0.435949\pi$
$828$	−6.52856e8	−0.0399679
$829$	1.11632e10	0.680529	0.340265	−	0.940330i	$-0.389483\pi$
$829$	1.11632e10	0.680529	0.340265	+	0.940330i	$0.389483\pi$
$830$	−3.34376e9	−0.202984
$831$	−6.09955e9	−0.368718
$832$	7.67489e8	0.0461999
$833$	−1.58312e10	−0.948977
$834$	4.47055e9	0.266858
$835$	1.88312e10	1.11938
$836$	−1.31922e9	−0.0780902
$837$	−2.15579e9	−0.127077
$838$	−5.65549e9	−0.331983
$839$	2.99442e10	1.75043	0.875217	−	0.483731i	$-0.160719\pi$
$839$	2.99442e10	1.75043	0.875217	+	0.483731i	$0.160719\pi$
$840$	5.54031e9	0.322520
$841$	3.68246e10	2.13478
$842$	1.03338e10	0.596578
$843$	6.56295e9	0.377314
$844$	1.96971e9	0.112773
$845$	−2.12871e10	−1.21372
$846$	1.84625e9	0.104832
$847$	−5.15582e9	−0.291545
$848$	−5.83482e9	−0.328581
$849$	6.45814e7	0.00362185
$850$	−2.02141e10	−1.12898
$851$	1.10847e9	0.0616554
$852$	−3.65997e9	−0.202740
$853$	−2.44170e10	−1.34701	−0.673504	−	0.739184i	$-0.735212\pi$
$853$	−2.44170e10	−1.34701	−0.673504	+	0.739184i	$0.735212\pi$
$854$	−5.83609e9	−0.320641
$855$	2.29257e9	0.125441
$856$	1.85297e10	1.00974
$857$	6.74647e9	0.366137	0.183069	−	0.983100i	$-0.441397\pi$
$857$	6.74647e9	0.366137	0.183069	+	0.983100i	$0.441397\pi$
$858$	−1.33775e9	−0.0723051
$859$	−1.73978e10	−0.936520	−0.468260	−	0.883591i	$-0.655119\pi$
$859$	−1.73978e10	−0.936520	−0.468260	+	0.883591i	$0.655119\pi$
$860$	−1.62843e10	−0.873020
$861$	1.22877e9	0.0656085
$862$	1.26948e10	0.675073
$863$	3.06467e10	1.62310	0.811551	−	0.584282i	$-0.198624\pi$
$863$	3.06467e10	1.62310	0.811551	+	0.584282i	$0.198624\pi$
$864$	−3.70659e9	−0.195513
$865$	−6.29714e10	−3.30816
$866$	6.93072e9	0.362631
$867$	2.45331e9	0.127845
$868$	3.73923e9	0.194072
$869$	9.82906e9	0.508092
$870$	1.65574e10	0.852459
$871$	5.30997e9	0.272288
$872$	8.31339e7	0.00424590
$873$	3.28848e9	0.167280
$874$	−2.98122e8	−0.0151044
$875$	1.57828e10	0.796445
$876$	1.57841e10	0.793332
$877$	1.20979e10	0.605634	0.302817	−	0.953049i	$-0.402073\pi$
$877$	1.20979e10	0.605634	0.302817	+	0.953049i	$0.402073\pi$
$878$	1.39242e9	0.0694287
$879$	−1.46706e10	−0.728597
$880$	6.71900e9	0.332365
$881$	−2.44049e10	−1.20243	−0.601217	−	0.799086i	$-0.705317\pi$
$881$	−2.44049e10	−1.20243	−0.601217	+	0.799086i	$0.705317\pi$
$882$	2.72457e9	0.133708
$883$	−4.56189e9	−0.222989	−0.111494	−	0.993765i	$-0.535564\pi$
$883$	−4.56189e9	−0.222989	−0.111494	+	0.993765i	$0.535564\pi$
$884$	−1.00401e10	−0.488828
$885$	2.76686e9	0.134179
$886$	−7.73446e9	−0.373604
$887$	2.10603e9	0.101328	0.0506642	−	0.998716i	$-0.483866\pi$
$887$	2.10603e9	0.101328	0.0506642	+	0.998716i	$0.483866\pi$
$888$	4.03099e9	0.193182
$889$	9.23363e8	0.0440774
$890$	−6.55012e9	−0.311447
$891$	1.11162e9	0.0526485
$892$	−1.80473e10	−0.851402
$893$	−3.02014e9	−0.141921
$894$	2.48588e8	0.0116359
$895$	−4.31360e10	−2.01122
$896$	7.91498e9	0.367597
$897$	1.08295e9	0.0500999
$898$	1.15193e10	0.530832
$899$	2.54690e10	1.16910
$900$	−1.24623e10	−0.569836
$901$	−2.02908e10	−0.924191
$902$	−1.47467e9	−0.0669071
$903$	3.00439e9	0.135784
$904$	2.42102e10	1.08996
$905$	7.13526e9	0.319992
$906$	3.03269e9	0.135481
$907$	1.54356e10	0.686906	0.343453	−	0.939170i	$-0.388403\pi$
$907$	1.54356e10	0.686906	0.343453	+	0.939170i	$0.388403\pi$
$908$	1.17978e10	0.522997
$909$	−5.92333e8	−0.0261573
$910$	−4.03231e9	−0.177382
$911$	1.76826e10	0.774874	0.387437	−	0.921896i	$-0.373360\pi$
$911$	1.76826e10	0.774874	0.387437	+	0.921896i	$0.373360\pi$
$912$	1.09554e9	0.0478239
$913$	2.65220e9	0.115334
$914$	−1.30620e10	−0.565847
$915$	4.36025e10	1.88164
$916$	−7.05737e9	−0.303395
$917$	7.22822e8	0.0309555
$918$	−2.32896e9	−0.0993601
$919$	7.03662e9	0.299061	0.149531	−	0.988757i	$-0.452224\pi$
$919$	7.03662e9	0.299061	0.149531	+	0.988757i	$0.452224\pi$
$920$	5.38262e9	0.227896
$921$	−5.51616e9	−0.232663
$922$	−1.44193e10	−0.605878
$923$	6.07113e9	0.254135
$924$	−1.92811e9	−0.0804046
$925$	2.11595e10	0.879043
$926$	1.24745e10	0.516281
$927$	8.64453e9	0.356420
$928$	4.37904e10	1.79871
$929$	1.13152e10	0.463028	0.231514	−	0.972832i	$-0.425632\pi$
$929$	1.13152e10	0.463028	0.231514	+	0.972832i	$0.425632\pi$
$930$	7.79848e9	0.317921
$931$	−4.45692e9	−0.181013
$932$	2.33134e10	0.943302
$933$	1.30048e10	0.524225
$934$	1.96508e10	0.789161
$935$	2.33655e10	0.934836
$936$	3.93819e9	0.156975
$937$	−4.20315e10	−1.66911	−0.834557	−	0.550921i	$-0.814276\pi$
$937$	−4.20315e10	−1.66911	−0.834557	+	0.550921i	$0.814276\pi$
$938$	−2.13644e9	−0.0845240
$939$	−4.79520e9	−0.189007
$940$	2.39252e10	0.939523
$941$	−1.96707e10	−0.769585	−0.384792	−	0.923003i	$-0.625727\pi$
$941$	−1.96707e10	−0.769585	−0.384792	+	0.923003i	$0.625727\pi$
$942$	3.09916e9	0.120800
$943$	1.19380e9	0.0463596
$944$	1.32218e9	0.0511551
$945$	3.35071e9	0.129159
$946$	−3.60562e9	−0.138472
$947$	1.69371e10	0.648058	0.324029	−	0.946047i	$-0.394962\pi$
$947$	1.69371e10	0.648058	0.324029	+	0.946047i	$0.394962\pi$
$948$	−1.26958e10	−0.483985
$949$	−2.61826e10	−0.994444
$950$	−5.69082e9	−0.215349
$951$	1.13199e10	0.426788
$952$	9.20682e9	0.345844
$953$	1.91845e10	0.718002	0.359001	−	0.933337i	$-0.383117\pi$
$953$	1.91845e10	0.718002	0.359001	+	0.933337i	$0.383117\pi$
$954$	3.49207e9	0.130216
$955$	−7.27592e10	−2.70319
$956$	−4.21463e10	−1.56012
$957$	−1.31330e10	−0.484363
$958$	1.92515e10	0.707433
$959$	1.19038e10	0.435833
$960$	2.30706e9	0.0841607
$961$	−1.55168e10	−0.563987
$962$	−2.93381e9	−0.106247
$963$	1.12065e10	0.404370
$964$	−1.65538e10	−0.595153
$965$	−7.99280e10	−2.86321
$966$	−4.35720e8	−0.0155521
$967$	−8.35028e9	−0.296967	−0.148484	−	0.988915i	$-0.547439\pi$
$967$	−8.35028e9	−0.296967	−0.148484	+	0.988915i	$0.547439\pi$
$968$	−1.82156e10	−0.645476
$969$	3.80976e9	0.134513
$970$	−1.18959e10	−0.418502
$971$	1.35240e10	0.474064	0.237032	−	0.971502i	$-0.423825\pi$
$971$	1.35240e10	0.474064	0.237032	+	0.971502i	$0.423825\pi$
$972$	−1.43584e9	−0.0501505
$973$	−1.06884e10	−0.371978
$974$	2.47388e10	0.857870
$975$	2.06724e10	0.714291
$976$	2.08361e10	0.717366
$977$	−4.40527e10	−1.51127	−0.755633	−	0.654995i	$-0.772671\pi$
$977$	−4.40527e10	−1.51127	−0.755633	+	0.654995i	$0.772671\pi$
$978$	7.14495e9	0.244238
$979$	5.19542e9	0.176963
$980$	3.53071e10	1.19831
$981$	5.02783e7	0.00170035
$982$	−2.34130e10	−0.788981
$983$	−9.32750e9	−0.313204	−0.156602	−	0.987662i	$-0.550054\pi$
$983$	−9.32750e9	−0.313204	−0.156602	+	0.987662i	$0.550054\pi$
$984$	4.34128e9	0.145256
$985$	−9.03452e9	−0.301216
$986$	2.75148e10	0.914107
$987$	−4.41410e9	−0.146127
$988$	−2.82657e9	−0.0932419
$989$	2.91888e9	0.0959464
$990$	−4.02125e9	−0.131716
$991$	4.28591e10	1.39890	0.699448	−	0.714683i	$-0.253429\pi$
$991$	4.28591e10	1.39890	0.699448	+	0.714683i	$0.253429\pi$
$992$	2.06252e10	0.670822
$993$	−1.76399e10	−0.571707
$994$	−2.44268e9	−0.0788887
$995$	1.08309e11	3.48566
$996$	−3.42575e9	−0.109862
$997$	−1.75144e10	−0.559709	−0.279855	−	0.960042i	$-0.590286\pi$
$997$	−1.75144e10	−0.559709	−0.279855	+	0.960042i	$0.590286\pi$
$998$	−1.58167e10	−0.503684
$999$	2.43789e9	0.0773633

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.d.1.8	✓	18
3.2	odd	2		531.8.a.e.1.11		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.d.1.8	✓	18	1.1	even	1	trivial
531.8.a.e.1.11		18	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)

\(f(q)\)	\(=\)	\(q-5.28523 q^{2} +27.0000 q^{3} -100.066 q^{4} +498.961 q^{5} -142.701 q^{6} +341.176 q^{7} +1205.38 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-5.28523 q^{2} +27.0000 q^{3} -100.066 q^{4} +498.961 q^{5} -142.701 q^{6} +341.176 q^{7} +1205.38 q^{8} +729.000 q^{9} -2637.13 q^{10} +2091.72 q^{11} -2701.79 q^{12} +4481.72 q^{13} -1803.19 q^{14} +13472.0 q^{15} +6437.77 q^{16} +22387.5 q^{17} -3852.93 q^{18} +6302.72 q^{19} -49929.3 q^{20} +9211.75 q^{21} -11055.2 q^{22} +8949.56 q^{23} +32545.3 q^{24} +170838. q^{25} -23686.9 q^{26} +19683.0 q^{27} -34140.2 q^{28} -232539. q^{29} -71202.4 q^{30} -109526. q^{31} -188314. q^{32} +56476.3 q^{33} -118323. q^{34} +170234. q^{35} -72948.4 q^{36} +123858. q^{37} -33311.3 q^{38} +121006. q^{39} +601440. q^{40} +133392. q^{41} -48686.2 q^{42} +326147. q^{43} -209310. q^{44} +363743. q^{45} -47300.5 q^{46} -479181. q^{47} +173820. q^{48} -707142. q^{49} -902916. q^{50} +604464. q^{51} -448469. q^{52} -906342. q^{53} -104029. q^{54} +1.04369e6 q^{55} +411248. q^{56} +170173. q^{57} +1.22902e6 q^{58} +205379. q^{59} -1.34809e6 q^{60} +3.23653e6 q^{61} +578868. q^{62} +248717. q^{63} +171249. q^{64} +2.23620e6 q^{65} -298490. q^{66} +1.18481e6 q^{67} -2.24024e6 q^{68} +241638. q^{69} -899724. q^{70} +1.35464e6 q^{71} +878724. q^{72} -5.84208e6 q^{73} -654616. q^{74} +4.61261e6 q^{75} -630690. q^{76} +713643. q^{77} -639546. q^{78} +4.69904e6 q^{79} +3.21220e6 q^{80} +531441. q^{81} -705006. q^{82} +1.26796e6 q^{83} -921786. q^{84} +1.11705e7 q^{85} -1.72376e6 q^{86} -6.27856e6 q^{87} +2.52132e6 q^{88} +2.48381e6 q^{89} -1.92246e6 q^{90} +1.52905e6 q^{91} -895550. q^{92} -2.95719e6 q^{93} +2.53258e6 q^{94} +3.14481e6 q^{95} -5.08448e6 q^{96} +4.51095e6 q^{97} +3.73741e6 q^{98} +1.52486e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 24 q^{2} + 486 q^{3} + 1358 q^{4} + 678 q^{5} + 648 q^{6} + 3081 q^{7} + 4107 q^{8} + 13122 q^{9}+O(q^{10}) \) 18 * q + 24 * q^2 + 486 * q^3 + 1358 * q^4 + 678 * q^5 + 648 * q^6 + 3081 * q^7 + 4107 * q^8 + 13122 * q^9	\( 18 q + 24 q^{2} + 486 q^{3} + 1358 q^{4} + 678 q^{5} + 648 q^{6} + 3081 q^{7} + 4107 q^{8} + 13122 q^{9} + 3609 q^{10} + 15070 q^{11} + 36666 q^{12} + 13662 q^{13} + 20861 q^{14} + 18306 q^{15} + 60482 q^{16} + 71919 q^{17} + 17496 q^{18} + 56231 q^{19} + 143053 q^{20} + 83187 q^{21} + 274198 q^{22} + 150029 q^{23} + 110889 q^{24} + 399672 q^{25} + 182846 q^{26} + 354294 q^{27} + 434150 q^{28} + 591285 q^{29} + 97443 q^{30} + 426733 q^{31} + 1205630 q^{32} + 406890 q^{33} + 403548 q^{34} + 912879 q^{35} + 989982 q^{36} + 7703 q^{37} - 417859 q^{38} + 368874 q^{39} + 618020 q^{40} + 770959 q^{41} + 563247 q^{42} + 793050 q^{43} + 2591274 q^{44} + 494262 q^{45} - 4068019 q^{46} + 1410373 q^{47} + 1633014 q^{48} + 1637427 q^{49} + 1021549 q^{50} + 1941813 q^{51} - 3749190 q^{52} + 1037934 q^{53} + 472392 q^{54} + 331974 q^{55} - 391748 q^{56} + 1518237 q^{57} + 653724 q^{58} + 3696822 q^{59} + 3862431 q^{60} - 1374623 q^{61} + 5251718 q^{62} + 2246049 q^{63} + 5077197 q^{64} + 3257170 q^{65} + 7403346 q^{66} - 2436904 q^{67} + 14119909 q^{68} + 4050783 q^{69} + 5185580 q^{70} + 14289172 q^{71} + 2994003 q^{72} + 5482515 q^{73} + 14934154 q^{74} + 10791144 q^{75} + 3822912 q^{76} + 23157109 q^{77} + 4936842 q^{78} + 19786414 q^{79} + 31978143 q^{80} + 9565938 q^{81} + 9749509 q^{82} + 30227337 q^{83} + 11722050 q^{84} + 9946981 q^{85} + 44295864 q^{86} + 15964695 q^{87} + 39970897 q^{88} + 31061677 q^{89} + 2630961 q^{90} + 26377785 q^{91} + 4719698 q^{92} + 11521791 q^{93} + 44488296 q^{94} + 15534599 q^{95} + 32552010 q^{96} + 12084118 q^{97} + 42274744 q^{98} + 10986030 q^{99}+O(q^{100}) \) 18 * q + 24 * q^2 + 486 * q^3 + 1358 * q^4 + 678 * q^5 + 648 * q^6 + 3081 * q^7 + 4107 * q^8 + 13122 * q^9 + 3609 * q^10 + 15070 * q^11 + 36666 * q^12 + 13662 * q^13 + 20861 * q^14 + 18306 * q^15 + 60482 * q^16 + 71919 * q^17 + 17496 * q^18 + 56231 * q^19 + 143053 * q^20 + 83187 * q^21 + 274198 * q^22 + 150029 * q^23 + 110889 * q^24 + 399672 * q^25 + 182846 * q^26 + 354294 * q^27 + 434150 * q^28 + 591285 * q^29 + 97443 * q^30 + 426733 * q^31 + 1205630 * q^32 + 406890 * q^33 + 403548 * q^34 + 912879 * q^35 + 989982 * q^36 + 7703 * q^37 - 417859 * q^38 + 368874 * q^39 + 618020 * q^40 + 770959 * q^41 + 563247 * q^42 + 793050 * q^43 + 2591274 * q^44 + 494262 * q^45 - 4068019 * q^46 + 1410373 * q^47 + 1633014 * q^48 + 1637427 * q^49 + 1021549 * q^50 + 1941813 * q^51 - 3749190 * q^52 + 1037934 * q^53 + 472392 * q^54 + 331974 * q^55 - 391748 * q^56 + 1518237 * q^57 + 653724 * q^58 + 3696822 * q^59 + 3862431 * q^60 - 1374623 * q^61 + 5251718 * q^62 + 2246049 * q^63 + 5077197 * q^64 + 3257170 * q^65 + 7403346 * q^66 - 2436904 * q^67 + 14119909 * q^68 + 4050783 * q^69 + 5185580 * q^70 + 14289172 * q^71 + 2994003 * q^72 + 5482515 * q^73 + 14934154 * q^74 + 10791144 * q^75 + 3822912 * q^76 + 23157109 * q^77 + 4936842 * q^78 + 19786414 * q^79 + 31978143 * q^80 + 9565938 * q^81 + 9749509 * q^82 + 30227337 * q^83 + 11722050 * q^84 + 9946981 * q^85 + 44295864 * q^86 + 15964695 * q^87 + 39970897 * q^88 + 31061677 * q^89 + 2630961 * q^90 + 26377785 * q^91 + 4719698 * q^92 + 11521791 * q^93 + 44488296 * q^94 + 15534599 * q^95 + 32552010 * q^96 + 12084118 * q^97 + 42274744 * q^98 + 10986030 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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