LMFDB - Embedded newform 177.14.a.a.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,14,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, 14, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 14 $
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:	$189.798744245$
Analytic rank:	$1$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
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)

$f(q)$	$=$	$q-17.8149 q^{2} +729.000 q^{3} -7874.63 q^{4} +5823.96 q^{5} -12987.1 q^{6} -495710. q^{7} +286225. q^{8} +531441. q^{9} +O(q^{10})$	\(q-17.8149 q^{2} +729.000 q^{3} -7874.63 q^{4} +5823.96 q^{5} -12987.1 q^{6} -495710. q^{7} +286225. q^{8} +531441. q^{9} -103753. q^{10} +4.50618e6 q^{11} -5.74060e6 q^{12} +2.28397e7 q^{13} +8.83102e6 q^{14} +4.24566e6 q^{15} +5.94099e7 q^{16} -1.25892e8 q^{17} -9.46757e6 q^{18} -1.03025e8 q^{19} -4.58615e7 q^{20} -3.61372e8 q^{21} -8.02772e7 q^{22} -1.20045e9 q^{23} +2.08658e8 q^{24} -1.18678e9 q^{25} -4.06886e8 q^{26} +3.87420e8 q^{27} +3.90353e9 q^{28} +4.62707e9 q^{29} -7.56361e7 q^{30} +8.13029e9 q^{31} -3.40314e9 q^{32} +3.28500e9 q^{33} +2.24275e9 q^{34} -2.88699e9 q^{35} -4.18490e9 q^{36} -7.22768e9 q^{37} +1.83538e9 q^{38} +1.66501e10 q^{39} +1.66696e9 q^{40} +9.28321e9 q^{41} +6.43781e9 q^{42} +3.44773e10 q^{43} -3.54845e10 q^{44} +3.09509e9 q^{45} +2.13859e10 q^{46} +3.11971e10 q^{47} +4.33098e10 q^{48} +1.48839e11 q^{49} +2.11425e10 q^{50} -9.17753e10 q^{51} -1.79854e11 q^{52} +6.65705e10 q^{53} -6.90186e9 q^{54} +2.62438e10 q^{55} -1.41885e11 q^{56} -7.51053e10 q^{57} -8.24309e10 q^{58} +4.21805e10 q^{59} -3.34330e10 q^{60} +6.87416e11 q^{61} -1.44840e11 q^{62} -2.63440e11 q^{63} -4.26059e11 q^{64} +1.33017e11 q^{65} -5.85220e10 q^{66} +5.94901e11 q^{67} +9.91353e11 q^{68} -8.75129e11 q^{69} +5.14315e10 q^{70} +6.97722e11 q^{71} +1.52112e11 q^{72} -1.61175e12 q^{73} +1.28760e11 q^{74} -8.65166e11 q^{75} +8.11284e11 q^{76} -2.23376e12 q^{77} -2.96620e11 q^{78} -3.41655e12 q^{79} +3.46001e11 q^{80} +2.82430e11 q^{81} -1.65380e11 q^{82} +2.41715e12 q^{83} +2.84567e12 q^{84} -7.33189e11 q^{85} -6.14210e11 q^{86} +3.37314e12 q^{87} +1.28978e12 q^{88} +3.97254e12 q^{89} -5.51387e10 q^{90} -1.13218e13 q^{91} +9.45311e12 q^{92} +5.92698e12 q^{93} -5.55774e11 q^{94} -6.00014e11 q^{95} -2.48089e12 q^{96} -7.61457e12 q^{97} -2.65155e12 q^{98} +2.39477e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 138 q^{2} + 21870 q^{3} + 114598 q^{4} - 137742 q^{5} - 100602 q^{6} - 879443 q^{7} - 872301 q^{8} + 15943230 q^{9}+O(q^{10}) $ 30 * q - 138 * q^2 + 21870 * q^3 + 114598 * q^4 - 137742 * q^5 - 100602 * q^6 - 879443 * q^7 - 872301 * q^8 + 15943230 * q^9	\( 30 q - 138 q^{2} + 21870 q^{3} + 114598 q^{4} - 137742 q^{5} - 100602 q^{6} - 879443 q^{7} - 872301 q^{8} + 15943230 q^{9} - 5352519 q^{10} - 13950782 q^{11} + 83541942 q^{12} - 17256988 q^{13} + 33780109 q^{14} - 100413918 q^{15} + 499996762 q^{16} - 317583695 q^{17} - 73338858 q^{18} - 863401469 q^{19} - 1841280623 q^{20} - 641113947 q^{21} - 2723764842 q^{22} - 3142075981 q^{23} - 635907429 q^{24} + 5435751692 q^{25} - 6441414040 q^{26} + 11622614670 q^{27} - 7538400046 q^{28} - 4604589283 q^{29} - 3901986351 q^{30} + 4308675373 q^{31} + 6094556360 q^{32} - 10170120078 q^{33} + 38097713432 q^{34} - 15447827315 q^{35} + 60902075718 q^{36} - 19633376949 q^{37} - 18152222923 q^{38} - 12580344252 q^{39} + 14680384170 q^{40} - 103644439493 q^{41} + 24625699461 q^{42} - 64494894924 q^{43} - 199714496208 q^{44} - 73201746222 q^{45} - 265425792847 q^{46} - 293365585139 q^{47} + 364497639498 q^{48} + 414396765797 q^{49} - 126058522207 q^{50} - 231518513655 q^{51} + 156029960316 q^{52} - 76747013118 q^{53} - 53464027482 q^{54} - 433465885754 q^{55} - 502955241518 q^{56} - 629419670901 q^{57} - 1755031845830 q^{58} + 1265416009230 q^{59} - 1342293574167 q^{60} - 2022612531219 q^{61} - 3816005187046 q^{62} - 467372067363 q^{63} - 3570205594131 q^{64} - 3889749040576 q^{65} - 1985624569818 q^{66} - 502618987776 q^{67} - 8953998390517 q^{68} - 2290573390149 q^{69} - 6805178272420 q^{70} - 1599540605456 q^{71} - 463576515741 q^{72} - 3826795087235 q^{73} - 7573387813210 q^{74} + 3962662983468 q^{75} - 19498723328388 q^{76} - 9088623115219 q^{77} - 4695790835160 q^{78} - 8595482172338 q^{79} - 17452527463963 q^{80} + 8472886094430 q^{81} - 11181116792901 q^{82} - 13548556984389 q^{83} - 5495493633534 q^{84} - 12851795888367 q^{85} + 8539949468848 q^{86} - 3356745587307 q^{87} - 25134826741387 q^{88} - 21826401667403 q^{89} - 2844548049879 q^{90} - 26577050621355 q^{91} - 34908210763168 q^{92} + 3141024346917 q^{93} - 26426808959500 q^{94} - 29105233533993 q^{95} + 4442931586440 q^{96} + 417815797414 q^{97} + 29159956938360 q^{98} - 7414017536862 q^{99}+O(q^{100}) \) 30 * q - 138 * q^2 + 21870 * q^3 + 114598 * q^4 - 137742 * q^5 - 100602 * q^6 - 879443 * q^7 - 872301 * q^8 + 15943230 * q^9 - 5352519 * q^10 - 13950782 * q^11 + 83541942 * q^12 - 17256988 * q^13 + 33780109 * q^14 - 100413918 * q^15 + 499996762 * q^16 - 317583695 * q^17 - 73338858 * q^18 - 863401469 * q^19 - 1841280623 * q^20 - 641113947 * q^21 - 2723764842 * q^22 - 3142075981 * q^23 - 635907429 * q^24 + 5435751692 * q^25 - 6441414040 * q^26 + 11622614670 * q^27 - 7538400046 * q^28 - 4604589283 * q^29 - 3901986351 * q^30 + 4308675373 * q^31 + 6094556360 * q^32 - 10170120078 * q^33 + 38097713432 * q^34 - 15447827315 * q^35 + 60902075718 * q^36 - 19633376949 * q^37 - 18152222923 * q^38 - 12580344252 * q^39 + 14680384170 * q^40 - 103644439493 * q^41 + 24625699461 * q^42 - 64494894924 * q^43 - 199714496208 * q^44 - 73201746222 * q^45 - 265425792847 * q^46 - 293365585139 * q^47 + 364497639498 * q^48 + 414396765797 * q^49 - 126058522207 * q^50 - 231518513655 * q^51 + 156029960316 * q^52 - 76747013118 * q^53 - 53464027482 * q^54 - 433465885754 * q^55 - 502955241518 * q^56 - 629419670901 * q^57 - 1755031845830 * q^58 + 1265416009230 * q^59 - 1342293574167 * q^60 - 2022612531219 * q^61 - 3816005187046 * q^62 - 467372067363 * q^63 - 3570205594131 * q^64 - 3889749040576 * q^65 - 1985624569818 * q^66 - 502618987776 * q^67 - 8953998390517 * q^68 - 2290573390149 * q^69 - 6805178272420 * q^70 - 1599540605456 * q^71 - 463576515741 * q^72 - 3826795087235 * q^73 - 7573387813210 * q^74 + 3962662983468 * q^75 - 19498723328388 * q^76 - 9088623115219 * q^77 - 4695790835160 * q^78 - 8595482172338 * q^79 - 17452527463963 * q^80 + 8472886094430 * q^81 - 11181116792901 * q^82 - 13548556984389 * q^83 - 5495493633534 * q^84 - 12851795888367 * q^85 + 8539949468848 * q^86 - 3356745587307 * q^87 - 25134826741387 * q^88 - 21826401667403 * q^89 - 2844548049879 * q^90 - 26577050621355 * q^91 - 34908210763168 * q^92 + 3141024346917 * q^93 - 26426808959500 * q^94 - 29105233533993 * q^95 + 4442931586440 * q^96 + 417815797414 * q^97 + 29159956938360 * q^98 - 7414017536862 * 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 $

$2$	−17.8149	−0.196829	−0.0984144	−	0.995146i	$-0.531377\pi$
$2$	−17.8149	−0.196829	−0.0984144	+	0.995146i	$0.531377\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	−7874.63	−0.961258
$5$	5823.96	0.166691	0.0833457	−	0.996521i	$-0.473439\pi$
$5$	5823.96	0.166691	0.0833457	+	0.996521i	$0.473439\pi$
$6$	−12987.1	−0.113639
$7$	−495710.	−1.59254	−0.796269	−	0.604942i	$-0.793196\pi$
$7$	−495710.	−1.59254	−0.796269	+	0.604942i	$0.793196\pi$
$8$	286225.	0.386032
$9$	531441.	0.333333
$10$	−103753.	−0.0328097
$11$	4.50618e6	0.766930	0.383465	−	0.923555i	$-0.374731\pi$
$11$	4.50618e6	0.766930	0.383465	+	0.923555i	$0.374731\pi$
$12$	−5.74060e6	−0.554983
$13$	2.28397e7	1.31237	0.656187	−	0.754598i	$-0.272168\pi$
$13$	2.28397e7	1.31237	0.656187	+	0.754598i	$0.272168\pi$
$14$	8.83102e6	0.313457
$15$	4.24566e6	0.0962393
$16$	5.94099e7	0.885276
$17$	−1.25892e8	−1.26497	−0.632485	−	0.774573i	$-0.717965\pi$
$17$	−1.25892e8	−1.26497	−0.632485	+	0.774573i	$0.717965\pi$
$18$	−9.46757e6	−0.0656096
$19$	−1.03025e8	−0.502394	−0.251197	−	0.967936i	$-0.580824\pi$
$19$	−1.03025e8	−0.502394	−0.251197	+	0.967936i	$0.580824\pi$
$20$	−4.58615e7	−0.160233
$21$	−3.61372e8	−0.919453
$22$	−8.02772e7	−0.150954
$23$	−1.20045e9	−1.69088	−0.845442	−	0.534067i	$-0.820663\pi$
$23$	−1.20045e9	−1.69088	−0.845442	+	0.534067i	$0.820663\pi$
$24$	2.08658e8	0.222876
$25$	−1.18678e9	−0.972214
$26$	−4.06886e8	−0.258313
$27$	3.87420e8	0.192450
$28$	3.90353e9	1.53084
$29$	4.62707e9	1.44451	0.722253	−	0.691629i	$-0.243107\pi$
$29$	4.62707e9	1.44451	0.722253	+	0.691629i	$0.243107\pi$
$30$	−7.56361e7	−0.0189427
$31$	8.13029e9	1.64534	0.822669	−	0.568521i	$-0.192484\pi$
$31$	8.13029e9	1.64534	0.822669	+	0.568521i	$0.192484\pi$
$32$	−3.40314e9	−0.560280
$33$	3.28500e9	0.442788
$34$	2.24275e9	0.248982
$35$	−2.88699e9	−0.265462
$36$	−4.18490e9	−0.320419
$37$	−7.22768e9	−0.463114	−0.231557	−	0.972821i	$-0.574382\pi$
$37$	−7.22768e9	−0.463114	−0.231557	+	0.972821i	$0.574382\pi$
$38$	1.83538e9	0.0988856
$39$	1.66501e10	0.757700
$40$	1.66696e9	0.0643482
$41$	9.28321e9	0.305213	0.152607	−	0.988287i	$-0.451233\pi$
$41$	9.28321e9	0.305213	0.152607	+	0.988287i	$0.451233\pi$
$42$	6.43781e9	0.180975
$43$	3.44773e10	0.831742	0.415871	−	0.909424i	$-0.363477\pi$
$43$	3.44773e10	0.831742	0.415871	+	0.909424i	$0.363477\pi$
$44$	−3.54845e10	−0.737218
$45$	3.09509e9	0.0555638
$46$	2.13859e10	0.332815
$47$	3.11971e10	0.422161	0.211081	−	0.977469i	$-0.432302\pi$
$47$	3.11971e10	0.422161	0.211081	+	0.977469i	$0.432302\pi$
$48$	4.33098e10	0.511114
$49$	1.48839e11	1.53618
$50$	2.11425e10	0.191360
$51$	−9.17753e10	−0.730331
$52$	−1.79854e11	−1.26153
$53$	6.65705e10	0.412561	0.206281	−	0.978493i	$-0.433864\pi$
$53$	6.65705e10	0.412561	0.206281	+	0.978493i	$0.433864\pi$
$54$	−6.90186e9	−0.0378797
$55$	2.62438e10	0.127841
$56$	−1.41885e11	−0.614771
$57$	−7.51053e10	−0.290057
$58$	−8.24309e10	−0.284320
$59$	4.21805e10	0.130189
$59$	4.21805e10	0.130189
$60$	−3.34330e10	−0.0925108
$61$	6.87416e11	1.70835	0.854173	−	0.519989i	$-0.174064\pi$
$61$	6.87416e11	1.70835	0.854173	+	0.519989i	$0.174064\pi$
$62$	−1.44840e11	−0.323850
$63$	−2.63440e11	−0.530846
$64$	−4.26059e11	−0.774997
$65$	1.33017e11	0.218761
$66$	−5.85220e10	−0.0871533
$67$	5.94901e11	0.803449	0.401724	−	0.915761i	$-0.368411\pi$
$67$	5.94901e11	0.803449	0.401724	+	0.915761i	$0.368411\pi$
$68$	9.91353e11	1.21596
$69$	−8.75129e11	−0.976232
$70$	5.14315e10	0.0522506
$71$	6.97722e11	0.646403	0.323201	−	0.946330i	$-0.395241\pi$
$71$	6.97722e11	0.646403	0.323201	+	0.946330i	$0.395241\pi$
$72$	1.52112e11	0.128677
$73$	−1.61175e12	−1.24652	−0.623258	−	0.782016i	$-0.714191\pi$
$73$	−1.61175e12	−1.24652	−0.623258	+	0.782016i	$0.714191\pi$
$74$	1.28760e11	0.0911541
$75$	−8.65166e11	−0.561308
$76$	8.11284e11	0.482931
$77$	−2.23376e12	−1.22137
$78$	−2.96620e11	−0.149137
$79$	−3.41655e12	−1.58129	−0.790645	−	0.612275i	$-0.790254\pi$
$79$	−3.41655e12	−1.58129	−0.790645	+	0.612275i	$0.790254\pi$
$80$	3.46001e11	0.147568
$81$	2.82430e11	0.111111
$82$	−1.65380e11	−0.0600747
$83$	2.41715e12	0.811513	0.405757	−	0.913981i	$-0.367008\pi$
$83$	2.41715e12	0.811513	0.405757	+	0.913981i	$0.367008\pi$
$84$	2.84567e12	0.883832
$85$	−7.33189e11	−0.210860
$86$	−6.14210e11	−0.163711
$87$	3.37314e12	0.833986
$88$	1.28978e12	0.296060
$89$	3.97254e12	0.847292	0.423646	−	0.905828i	$-0.360750\pi$
$89$	3.97254e12	0.847292	0.423646	+	0.905828i	$0.360750\pi$
$90$	−5.51387e10	−0.0109366
$91$	−1.13218e13	−2.09001
$92$	9.45311e12	1.62538
$93$	5.92698e12	0.949936
$94$	−5.55774e11	−0.0830935
$95$	−6.00014e11	−0.0837448
$96$	−2.48089e12	−0.323478
$97$	−7.61457e12	−0.928174	−0.464087	−	0.885790i	$-0.653617\pi$
$97$	−7.61457e12	−0.928174	−0.464087	+	0.885790i	$0.653617\pi$
$98$	−2.65155e12	−0.302364
$99$	2.39477e12	0.255643
$100$	9.34549e12	0.934549
$101$	2.64783e12	0.248200	0.124100	−	0.992270i	$-0.460396\pi$
$101$	2.64783e12	0.248200	0.124100	+	0.992270i	$0.460396\pi$
$102$	1.63497e12	0.143750
$103$	−1.04265e13	−0.860394	−0.430197	−	0.902735i	$-0.641556\pi$
$103$	−1.04265e13	−0.860394	−0.430197	+	0.902735i	$0.641556\pi$
$104$	6.53729e12	0.506619
$105$	−2.10462e12	−0.153265
$106$	−1.18595e12	−0.0812039
$107$	−6.83692e10	−0.00440419	−0.00220209	−	0.999998i	$-0.500701\pi$
$107$	−6.83692e10	−0.00440419	−0.00220209	+	0.999998i	$0.500701\pi$
$108$	−3.05079e12	−0.184994
$109$	1.22444e13	0.699301	0.349651	−	0.936880i	$-0.386300\pi$
$109$	1.22444e13	0.699301	0.349651	+	0.936880i	$0.386300\pi$
$110$	−4.67531e11	−0.0251627
$111$	−5.26898e12	−0.267379
$112$	−2.94500e13	−1.40984
$113$	−3.21032e13	−1.45057	−0.725286	−	0.688448i	$-0.758292\pi$
$113$	−3.21032e13	−1.45057	−0.725286	+	0.688448i	$0.758292\pi$
$114$	1.33799e12	0.0570916
$115$	−6.99138e12	−0.281856
$116$	−3.64365e13	−1.38854
$117$	1.21379e13	0.437458
$118$	−7.51442e11	−0.0256249
$119$	6.24059e13	2.01451
$120$	1.21522e12	0.0371515
$121$	−1.42171e13	−0.411818
$122$	−1.22463e13	−0.336252
$123$	6.76746e12	0.176215
$124$	−6.40230e13	−1.58159
$125$	−1.40211e13	−0.328751
$126$	4.69317e12	0.104486
$127$	−5.98520e13	−1.26577	−0.632884	−	0.774246i	$-0.718129\pi$
$127$	−5.98520e13	−1.26577	−0.632884	+	0.774246i	$0.718129\pi$
$128$	3.54687e13	0.712822
$129$	2.51340e13	0.480207
$130$	−2.36969e12	−0.0430585
$131$	3.92221e13	0.678059	0.339029	−	0.940776i	$-0.389901\pi$
$131$	3.92221e13	0.678059	0.339029	+	0.940776i	$0.389901\pi$
$132$	−2.58682e13	−0.425633
$133$	5.10705e13	0.800082
$134$	−1.05981e13	−0.158142
$135$	2.25632e12	0.0320798
$136$	−3.60335e13	−0.488319
$137$	−1.30617e14	−1.68778	−0.843888	−	0.536520i	$-0.819739\pi$
$137$	−1.30617e14	−1.68778	−0.843888	+	0.536520i	$0.819739\pi$
$138$	1.55903e13	0.192151
$139$	−3.81902e13	−0.449113	−0.224556	−	0.974461i	$-0.572093\pi$
$139$	−3.81902e13	−0.449113	−0.224556	+	0.974461i	$0.572093\pi$
$140$	2.27340e13	0.255178
$141$	2.27427e13	0.243735
$142$	−1.24299e13	−0.127231
$143$	1.02920e14	1.00650
$144$	3.15728e13	0.295092
$145$	2.69479e13	0.240787
$146$	2.87131e13	0.245350
$147$	1.08504e14	0.886914
$148$	5.69153e13	0.445172
$149$	−1.06117e14	−0.794464	−0.397232	−	0.917718i	$-0.630029\pi$
$149$	−1.06117e14	−0.794464	−0.397232	+	0.917718i	$0.630029\pi$
$150$	1.54129e13	0.110482
$151$	2.68008e14	1.83992	0.919958	−	0.392018i	$-0.128223\pi$
$151$	2.68008e14	1.83992	0.919958	+	0.392018i	$0.128223\pi$
$152$	−2.94884e13	−0.193940
$153$	−6.69042e13	−0.421657
$154$	3.97941e13	0.240400
$155$	4.73505e13	0.274264
$156$	−1.31113e14	−0.728345
$157$	−5.26124e13	−0.280376	−0.140188	−	0.990125i	$-0.544771\pi$
$157$	−5.26124e13	−0.280376	−0.140188	+	0.990125i	$0.544771\pi$
$158$	6.08655e13	0.311243
$159$	4.85299e13	0.238192
$160$	−1.98197e13	−0.0933938
$161$	5.95075e14	2.69280
$162$	−5.03146e12	−0.0218699
$163$	−2.09132e14	−0.873375	−0.436687	−	0.899613i	$-0.643848\pi$
$163$	−2.09132e14	−0.873375	−0.436687	+	0.899613i	$0.643848\pi$
$164$	−7.31018e13	−0.293389
$165$	1.91317e13	0.0738088
$166$	−4.30613e13	−0.159729
$167$	−6.41900e13	−0.228987	−0.114493	−	0.993424i	$-0.536524\pi$
$167$	−6.41900e13	−0.228987	−0.114493	+	0.993424i	$0.536524\pi$
$168$	−1.03434e14	−0.354938
$169$	2.18775e14	0.722326
$170$	1.30617e13	0.0415032
$171$	−5.47518e13	−0.167465
$172$	−2.71496e14	−0.799519
$173$	3.25761e14	0.923846	0.461923	−	0.886920i	$-0.347160\pi$
$173$	3.25761e14	0.923846	0.461923	+	0.886920i	$0.347160\pi$
$174$	−6.00921e13	−0.164152
$175$	5.88300e14	1.54829
$176$	2.67712e14	0.678945
$177$	3.07496e13	0.0751646
$178$	−7.07704e13	−0.166772
$179$	−3.21077e14	−0.729565	−0.364783	−	0.931093i	$-0.618857\pi$
$179$	−3.21077e14	−0.729565	−0.364783	+	0.931093i	$0.618857\pi$
$180$	−2.43727e13	−0.0534112
$181$	−4.10482e14	−0.867727	−0.433864	−	0.900979i	$-0.642850\pi$
$181$	−4.10482e14	−0.867727	−0.433864	+	0.900979i	$0.642850\pi$
$182$	2.01697e14	0.411373
$183$	5.01126e14	0.986314
$184$	−3.43600e14	−0.652735
$185$	−4.20937e13	−0.0771971
$186$	−1.05589e14	−0.186975
$187$	−5.67292e14	−0.970144
$188$	−2.45666e14	−0.405806
$189$	−1.92048e14	−0.306484
$190$	1.06892e13	0.0164834
$191$	−1.00717e15	−1.50102	−0.750510	−	0.660859i	$-0.770192\pi$
$191$	−1.00717e15	−1.50102	−0.750510	+	0.660859i	$0.770192\pi$
$192$	−3.10597e14	−0.447445
$193$	4.24901e14	0.591787	0.295893	−	0.955221i	$-0.404383\pi$
$193$	4.24901e14	0.591787	0.295893	+	0.955221i	$0.404383\pi$
$194$	1.35653e14	0.182691
$195$	9.69695e13	0.126302
$196$	−1.17205e15	−1.47667
$197$	−5.01772e14	−0.611612	−0.305806	−	0.952094i	$-0.598926\pi$
$197$	−5.01772e14	−0.611612	−0.305806	+	0.952094i	$0.598926\pi$
$198$	−4.26626e13	−0.0503180
$199$	−9.86515e14	−1.12605	−0.563026	−	0.826439i	$-0.690363\pi$
$199$	−9.86515e14	−1.12605	−0.563026	+	0.826439i	$0.690363\pi$
$200$	−3.39688e14	−0.375306
$201$	4.33683e14	0.463871
$202$	−4.71708e13	−0.0488528
$203$	−2.29368e15	−2.30043
$204$	7.22696e14	0.702036
$205$	5.40650e13	0.0508764
$206$	1.85748e14	0.169350
$207$	−6.37969e14	−0.563628
$208$	1.35690e15	1.16181
$209$	−4.64249e14	−0.385301
$210$	3.74935e13	0.0301669
$211$	−2.84359e13	−0.0221835	−0.0110918	−	0.999938i	$-0.503531\pi$
$211$	−2.84359e13	−0.0221835	−0.0110918	+	0.999938i	$0.503531\pi$
$212$	−5.24218e14	−0.396578
$213$	5.08640e14	0.373201
$214$	1.21799e12	0.000866870 0
$215$	2.00794e14	0.138644
$216$	1.10890e14	0.0742919
$217$	−4.03026e15	−2.62026
$218$	−2.18132e14	−0.137643
$219$	−1.17496e15	−0.719677
$220$	−2.06660e14	−0.122888
$221$	−2.87533e15	−1.66011
$222$	9.38663e13	0.0526278
$223$	−2.22345e15	−1.21073	−0.605364	−	0.795949i	$-0.706972\pi$
$223$	−2.22345e15	−1.21073	−0.605364	+	0.795949i	$0.706972\pi$
$224$	1.68697e15	0.892267
$225$	−6.30706e14	−0.324071
$226$	5.71916e14	0.285514
$227$	2.23256e15	1.08301	0.541507	−	0.840696i	$-0.317854\pi$
$227$	2.23256e15	1.08301	0.541507	+	0.840696i	$0.317854\pi$
$228$	5.91426e14	0.278820
$229$	3.04475e15	1.39515	0.697575	−	0.716512i	$-0.254263\pi$
$229$	3.04475e15	1.39515	0.697575	+	0.716512i	$0.254263\pi$
$230$	1.24551e14	0.0554773
$231$	−1.62841e15	−0.705156
$232$	1.32439e15	0.557626
$233$	−4.29493e15	−1.75850	−0.879251	−	0.476359i	$-0.841956\pi$
$233$	−4.29493e15	−1.75850	−0.879251	+	0.476359i	$0.841956\pi$
$234$	−2.16236e14	−0.0861043
$235$	1.81691e14	0.0703707
$236$	−3.32156e14	−0.125145
$237$	−2.49066e15	−0.912958
$238$	−1.11175e15	−0.396514
$239$	−5.94158e14	−0.206213	−0.103106	−	0.994670i	$-0.532878\pi$
$239$	−5.94158e14	−0.206213	−0.103106	+	0.994670i	$0.532878\pi$
$240$	2.52234e14	0.0851984
$241$	−1.69537e15	−0.557384	−0.278692	−	0.960380i	$-0.589901\pi$
$241$	−1.69537e15	−0.557384	−0.278692	+	0.960380i	$0.589901\pi$
$242$	2.53276e14	0.0810576
$243$	2.05891e14	0.0641500
$244$	−5.41315e15	−1.64216
$245$	8.66831e14	0.256068
$246$	−1.20562e14	−0.0346842
$247$	−2.35306e15	−0.659329
$248$	2.32710e15	0.635153
$249$	1.76210e15	0.468528
$250$	2.49785e14	0.0647077
$251$	6.00464e15	1.51568	0.757841	−	0.652439i	$-0.226254\pi$
$251$	6.00464e15	1.51568	0.757841	+	0.652439i	$0.226254\pi$
$252$	2.07450e15	0.510280
$253$	−5.40945e15	−1.29679
$254$	1.06626e15	0.249140
$255$	−5.34495e14	−0.121740
$256$	2.85840e15	0.634693
$257$	−1.37803e15	−0.298326	−0.149163	−	0.988813i	$-0.547658\pi$
$257$	−1.37803e15	−0.298326	−0.149163	+	0.988813i	$0.547658\pi$
$258$	−4.47759e14	−0.0945185
$259$	3.58283e15	0.737527
$260$	−1.04746e15	−0.210286
$261$	2.45902e15	0.481502
$262$	−6.98738e14	−0.133461
$263$	−4.10341e15	−0.764597	−0.382299	−	0.924039i	$-0.624867\pi$
$263$	−4.10341e15	−0.764597	−0.382299	+	0.924039i	$0.624867\pi$
$264$	9.40252e14	0.170930
$265$	3.87703e14	0.0687704
$266$	−9.09816e14	−0.157479
$267$	2.89598e15	0.489185
$268$	−4.68462e15	−0.772322
$269$	−2.14891e15	−0.345802	−0.172901	−	0.984939i	$-0.555314\pi$
$269$	−2.14891e15	−0.345802	−0.172901	+	0.984939i	$0.555314\pi$
$270$	−4.01961e13	−0.00631422
$271$	−6.32922e15	−0.970622	−0.485311	−	0.874342i	$-0.661294\pi$
$271$	−6.32922e15	−0.970622	−0.485311	+	0.874342i	$0.661294\pi$
$272$	−7.47923e15	−1.11985
$273$	−8.25362e15	−1.20667
$274$	2.32692e15	0.332203
$275$	−5.34786e15	−0.745621
$276$	6.89132e15	0.938411
$277$	−1.08935e16	−1.44893	−0.724464	−	0.689312i	$-0.757913\pi$
$277$	−1.08935e16	−1.44893	−0.724464	+	0.689312i	$0.757913\pi$
$278$	6.80355e14	0.0883984
$279$	4.32077e15	0.548446
$280$	−8.26330e14	−0.102477
$281$	2.55877e15	0.310056	0.155028	−	0.987910i	$-0.450453\pi$
$281$	2.55877e15	0.310056	0.155028	+	0.987910i	$0.450453\pi$
$282$	−4.05159e14	−0.0479741
$283$	−1.77363e15	−0.205235	−0.102618	−	0.994721i	$-0.532722\pi$
$283$	−1.77363e15	−0.205235	−0.102618	+	0.994721i	$0.532722\pi$
$284$	−5.49430e15	−0.621360
$285$	−4.37410e14	−0.0483501
$286$	−1.83350e15	−0.198108
$287$	−4.60178e15	−0.486064
$288$	−1.80857e15	−0.186760
$289$	5.94422e15	0.600148
$290$	−4.80074e14	−0.0473937
$291$	−5.55102e15	−0.535881
$292$	1.26919e16	1.19822
$293$	2.09932e16	1.93838	0.969192	−	0.246307i	$-0.0792171\pi$
$293$	2.09932e16	1.93838	0.969192	+	0.246307i	$0.0792171\pi$
$294$	−1.93298e15	−0.174570
$295$	2.45658e14	0.0217014
$296$	−2.06875e15	−0.178777
$297$	1.74579e15	0.147596
$298$	1.89046e15	0.156373
$299$	−2.74179e16	−2.21907
$300$	6.81286e15	0.539562
$301$	−1.70907e16	−1.32458
$302$	−4.77454e15	−0.362148
$303$	1.93027e15	0.143298
$304$	−6.12071e15	−0.444758
$305$	4.00348e15	0.284766
$306$	1.19189e15	0.0829941
$307$	−3.18012e15	−0.216792	−0.108396	−	0.994108i	$-0.534571\pi$
$307$	−3.18012e15	−0.216792	−0.108396	+	0.994108i	$0.534571\pi$
$308$	1.75900e16	1.17405
$309$	−7.60094e15	−0.496749
$310$	−8.43544e14	−0.0539830
$311$	−3.43922e15	−0.215535	−0.107767	−	0.994176i	$-0.534370\pi$
$311$	−3.43922e15	−0.215535	−0.107767	+	0.994176i	$0.534370\pi$
$312$	4.76569e15	0.292496
$313$	1.43474e16	0.862453	0.431227	−	0.902244i	$-0.358081\pi$
$313$	1.43474e16	0.862453	0.431227	+	0.902244i	$0.358081\pi$
$314$	9.37286e14	0.0551860
$315$	−1.53427e15	−0.0884875
$316$	2.69040e16	1.52003
$317$	−1.44462e15	−0.0799594	−0.0399797	−	0.999200i	$-0.512729\pi$
$317$	−1.44462e15	−0.0799594	−0.0399797	+	0.999200i	$0.512729\pi$
$318$	−8.64555e14	−0.0468831
$319$	2.08504e16	1.10784
$320$	−2.48135e15	−0.129185
$321$	−4.98411e13	−0.00254276
$322$	−1.06012e16	−0.530020
$323$	1.29700e16	0.635513
$324$	−2.22403e15	−0.106806
$325$	−2.71058e16	−1.27591
$326$	3.72566e15	0.171905
$327$	8.92615e15	0.403742
$328$	2.65709e15	0.117822
$329$	−1.54647e16	−0.672308
$330$	−3.40830e14	−0.0145277
$331$	1.70816e16	0.713914	0.356957	−	0.934121i	$-0.383814\pi$
$331$	1.70816e16	0.713914	0.356957	+	0.934121i	$0.383814\pi$
$332$	−1.90341e16	−0.780074
$333$	−3.84109e15	−0.154371
$334$	1.14354e15	0.0450712
$335$	3.46468e15	0.133928
$336$	−2.14691e16	−0.813970
$337$	−2.15042e16	−0.799705	−0.399852	−	0.916580i	$-0.630939\pi$
$337$	−2.15042e16	−0.799705	−0.399852	+	0.916580i	$0.630939\pi$
$338$	−3.89745e15	−0.142175
$339$	−2.34033e16	−0.837488
$340$	5.77360e15	0.202690
$341$	3.66365e16	1.26186
$342$	9.75397e14	0.0329619
$343$	−2.57521e16	−0.853886
$344$	9.86829e15	0.321079
$345$	−5.09671e15	−0.162729
$346$	−5.80341e15	−0.181840
$347$	−5.59137e16	−1.71940	−0.859699	−	0.510801i	$-0.829349\pi$
$347$	−5.59137e16	−1.71940	−0.859699	+	0.510801i	$0.829349\pi$
$348$	−2.65622e16	−0.801676
$349$	1.77625e16	0.526184	0.263092	−	0.964771i	$-0.415258\pi$
$349$	1.77625e16	0.526184	0.263092	+	0.964771i	$0.415258\pi$
$350$	−1.04805e16	−0.304748
$351$	8.84855e15	0.252567
$352$	−1.53352e16	−0.429696
$353$	−3.20503e16	−0.881651	−0.440825	−	0.897593i	$-0.645314\pi$
$353$	−3.20503e16	−0.881651	−0.440825	+	0.897593i	$0.645314\pi$
$354$	−5.47801e14	−0.0147946
$355$	4.06350e15	0.107750
$356$	−3.12823e16	−0.814467
$357$	4.54939e16	1.16308
$358$	5.71995e15	0.143599
$359$	−5.13535e16	−1.26606	−0.633032	−	0.774125i	$-0.718190\pi$
$359$	−5.13535e16	−1.26606	−0.633032	+	0.774125i	$0.718190\pi$
$360$	8.85893e14	0.0214494
$361$	−3.14388e16	−0.747600
$362$	7.31270e15	0.170794
$363$	−1.03642e16	−0.237763
$364$	8.91552e16	2.00904
$365$	−9.38674e15	−0.207783
$366$	−8.92752e15	−0.194135
$367$	−4.56541e16	−0.975327	−0.487663	−	0.873032i	$-0.662151\pi$
$367$	−4.56541e16	−0.975327	−0.487663	+	0.873032i	$0.662151\pi$
$368$	−7.13187e16	−1.49690
$369$	4.93348e15	0.101738
$370$	7.49895e14	0.0151946
$371$	−3.29996e16	−0.657020
$372$	−4.66728e16	−0.913134
$373$	2.56728e16	0.493589	0.246795	−	0.969068i	$-0.420623\pi$
$373$	2.56728e16	0.493589	0.246795	+	0.969068i	$0.420623\pi$
$374$	1.01063e16	0.190952
$375$	−1.02214e16	−0.189804
$376$	8.92941e15	0.162968
$377$	1.05681e17	1.89573
$378$	3.42132e15	0.0603249
$379$	2.01093e16	0.348532	0.174266	−	0.984699i	$-0.444245\pi$
$379$	2.01093e16	0.348532	0.174266	+	0.984699i	$0.444245\pi$
$380$	4.72488e15	0.0805004
$381$	−4.36321e16	−0.730792
$382$	1.79427e16	0.295444
$383$	−1.79861e16	−0.291170	−0.145585	−	0.989346i	$-0.546506\pi$
$383$	−1.79861e16	−0.291170	−0.145585	+	0.989346i	$0.546506\pi$
$384$	2.58567e16	0.411548
$385$	−1.30093e16	−0.203591
$386$	−7.56957e15	−0.116481
$387$	1.83227e16	0.277247
$388$	5.99619e16	0.892215
$389$	2.11128e16	0.308940	0.154470	−	0.987998i	$-0.450633\pi$
$389$	2.11128e16	0.308940	0.154470	+	0.987998i	$0.450633\pi$
$390$	−1.72750e15	−0.0248599
$391$	1.51127e17	2.13892
$392$	4.26015e16	0.593015
$393$	2.85929e16	0.391477
$394$	8.93902e15	0.120383
$395$	−1.98978e16	−0.263587
$396$	−1.88579e16	−0.245739
$397$	1.03371e17	1.32514	0.662569	−	0.749001i	$-0.269466\pi$
$397$	1.03371e17	1.32514	0.662569	+	0.749001i	$0.269466\pi$
$398$	1.75747e16	0.221639
$399$	3.72304e16	0.461928
$400$	−7.05067e16	−0.860678
$401$	−5.08166e16	−0.610334	−0.305167	−	0.952299i	$-0.598712\pi$
$401$	−5.08166e16	−0.610334	−0.305167	+	0.952299i	$0.598712\pi$
$402$	−7.72601e15	−0.0913032
$403$	1.85693e17	2.15930
$404$	−2.08507e16	−0.238584
$405$	1.64486e15	0.0185213
$406$	4.08618e16	0.452791
$407$	−3.25692e16	−0.355176
$408$	−2.62684e16	−0.281931
$409$	1.31002e16	0.138381	0.0691903	−	0.997603i	$-0.477958\pi$
$409$	1.31002e16	0.138381	0.0691903	+	0.997603i	$0.477958\pi$
$410$	−9.63163e14	−0.0100139
$411$	−9.52195e16	−0.974438
$412$	8.21050e16	0.827061
$413$	−2.09093e16	−0.207331
$414$	1.13654e16	0.110938
$415$	1.40774e16	0.135272
$416$	−7.77266e16	−0.735297
$417$	−2.78406e16	−0.259296
$418$	8.27056e15	0.0758384
$419$	2.02887e17	1.83174	0.915868	−	0.401480i	$-0.131504\pi$
$419$	2.02887e17	1.83174	0.915868	+	0.401480i	$0.131504\pi$
$420$	1.65731e16	0.147327
$421$	6.73135e16	0.589208	0.294604	−	0.955619i	$-0.404812\pi$
$421$	6.73135e16	0.589208	0.294604	+	0.955619i	$0.404812\pi$
$422$	5.06582e14	0.00436636
$423$	1.65794e16	0.140720
$424$	1.90542e16	0.159262
$425$	1.49407e17	1.22982
$426$	−9.06137e15	−0.0734567
$427$	−3.40759e17	−2.72061
$428$	5.38382e14	0.00423356
$429$	7.50284e16	0.581103
$430$	−3.57713e15	−0.0272892
$431$	−1.62884e17	−1.22399	−0.611993	−	0.790863i	$-0.709632\pi$
$431$	−1.62884e17	−1.22399	−0.611993	+	0.790863i	$0.709632\pi$
$432$	2.30166e16	0.170371
$433$	−1.79440e17	−1.30842	−0.654210	−	0.756313i	$-0.726999\pi$
$433$	−1.79440e17	−1.30842	−0.654210	+	0.756313i	$0.726999\pi$
$434$	7.17988e16	0.515743
$435$	1.96450e16	0.139018
$436$	−9.64199e16	−0.672209
$437$	1.23677e17	0.849490
$438$	2.09319e16	0.141653
$439$	7.31787e16	0.487939	0.243969	−	0.969783i	$-0.421550\pi$
$439$	7.31787e16	0.487939	0.243969	+	0.969783i	$0.421550\pi$
$440$	7.51164e15	0.0493506
$441$	7.90991e16	0.512060
$442$	5.12237e16	0.326758
$443$	1.60047e17	1.00606	0.503030	−	0.864269i	$-0.332219\pi$
$443$	1.60047e17	1.00606	0.503030	+	0.864269i	$0.332219\pi$
$444$	4.14912e16	0.257020
$445$	2.31359e16	0.141236
$446$	3.96106e16	0.238306
$447$	−7.73593e16	−0.458684
$448$	2.11202e17	1.23421
$449$	1.47310e17	0.848458	0.424229	−	0.905555i	$-0.360545\pi$
$449$	1.47310e17	0.848458	0.424229	+	0.905555i	$0.360545\pi$
$450$	1.12360e16	0.0637866
$451$	4.18318e16	0.234077
$452$	2.52801e17	1.39437
$453$	1.95378e17	1.06228
$454$	−3.97728e16	−0.213168
$455$	−6.59379e16	−0.348386
$456$	−2.14970e16	−0.111971
$457$	−1.44949e17	−0.744321	−0.372161	−	0.928168i	$-0.621383\pi$
$457$	−1.44949e17	−0.744321	−0.372161	+	0.928168i	$0.621383\pi$
$458$	−5.42419e16	−0.274606
$459$	−4.87731e16	−0.243444
$460$	5.50545e16	0.270936
$461$	3.92089e17	1.90252	0.951258	−	0.308395i	$-0.0997918\pi$
$461$	3.92089e17	1.90252	0.951258	+	0.308395i	$0.0997918\pi$
$462$	2.90099e16	0.138795
$463$	−1.53392e17	−0.723648	−0.361824	−	0.932246i	$-0.617846\pi$
$463$	−1.53392e17	−0.723648	−0.361824	+	0.932246i	$0.617846\pi$
$464$	2.74894e17	1.27879
$465$	3.45185e16	0.158346
$466$	7.65138e16	0.346124
$467$	−3.07378e17	−1.37124	−0.685620	−	0.727959i	$-0.740469\pi$
$467$	−3.07378e17	−1.37124	−0.685620	+	0.727959i	$0.740469\pi$
$468$	−9.55817e16	−0.420510
$469$	−2.94898e17	−1.27952
$470$	−3.23680e15	−0.0138510
$471$	−3.83545e16	−0.161875
$472$	1.20731e16	0.0502571
$473$	1.55361e17	0.637888
$474$	4.43709e16	0.179696
$475$	1.22269e17	0.488435
$476$	−4.91423e17	−1.93647
$477$	3.53783e16	0.137520
$478$	1.05849e16	0.0405886
$479$	3.09329e17	1.17015	0.585073	−	0.810981i	$-0.301066\pi$
$479$	3.09329e17	1.17015	0.585073	+	0.810981i	$0.301066\pi$
$480$	−1.44486e16	−0.0539209
$481$	−1.65078e17	−0.607779
$482$	3.02029e16	0.109709
$483$	4.33810e17	1.55469
$484$	1.11954e17	0.395863
$485$	−4.43469e16	−0.154719
$486$	−3.66793e15	−0.0126266
$487$	−4.72135e17	−1.60372	−0.801858	−	0.597514i	$-0.796155\pi$
$487$	−4.72135e17	−1.60372	−0.801858	+	0.597514i	$0.796155\pi$
$488$	1.96756e17	0.659476
$489$	−1.52457e17	−0.504243
$490$	−1.54425e16	−0.0504015
$491$	−4.75203e17	−1.53056	−0.765278	−	0.643700i	$-0.777398\pi$
$491$	−4.75203e17	−1.53056	−0.765278	+	0.643700i	$0.777398\pi$
$492$	−5.32912e16	−0.169388
$493$	−5.82511e17	−1.82726
$494$	4.19195e16	0.129775
$495$	1.39470e16	0.0426136
$496$	4.83020e17	1.45658
$497$	−3.45868e17	−1.02942
$498$	−3.13917e16	−0.0922197
$499$	−9.98967e16	−0.289666	−0.144833	−	0.989456i	$-0.546264\pi$
$499$	−9.98967e16	−0.289666	−0.144833	+	0.989456i	$0.546264\pi$
$500$	1.10411e17	0.316015
$501$	−4.67945e16	−0.132206
$502$	−1.06972e17	−0.298330
$503$	−1.48123e17	−0.407786	−0.203893	−	0.978993i	$-0.565359\pi$
$503$	−1.48123e17	−0.407786	−0.203893	+	0.978993i	$0.565359\pi$
$504$	−7.54033e16	−0.204924
$505$	1.54208e16	0.0413727
$506$	9.63688e16	0.255246
$507$	1.59487e17	0.417035
$508$	4.71312e17	1.21673
$509$	4.66800e17	1.18978	0.594888	−	0.803809i	$-0.297196\pi$
$509$	4.66800e17	1.18978	0.594888	+	0.803809i	$0.297196\pi$
$510$	9.52198e15	0.0239619
$511$	7.98958e17	1.98513
$512$	−3.41482e17	−0.837747
$513$	−3.99140e16	−0.0966858
$514$	2.45494e16	0.0587192
$515$	−6.07236e16	−0.143420
$516$	−1.97921e17	−0.461603
$517$	1.40580e17	0.323768
$518$	−6.38278e16	−0.145166
$519$	2.37480e17	0.533383
$520$	3.80729e16	0.0844489
$521$	−2.93718e17	−0.643406	−0.321703	−	0.946841i	$-0.604255\pi$
$521$	−2.93718e17	−0.643406	−0.321703	+	0.946841i	$0.604255\pi$
$522$	−4.38071e16	−0.0947734
$523$	2.20371e17	0.470861	0.235431	−	0.971891i	$-0.424350\pi$
$523$	2.20371e17	0.470861	0.235431	+	0.971891i	$0.424350\pi$
$524$	−3.08859e17	−0.651790
$525$	4.28871e17	0.893905
$526$	7.31019e16	0.150495
$527$	−1.02354e18	−2.08130
$528$	1.95162e17	0.391989
$529$	9.37048e17	1.85909
$530$	−6.90690e15	−0.0135360
$531$	2.24165e16	0.0433963
$532$	−4.02161e17	−0.769086
$533$	2.12025e17	0.400554
$534$	−5.15917e16	−0.0962856
$535$	−3.98179e14	−0.000734140 0
$536$	1.70276e17	0.310157
$537$	−2.34065e17	−0.421215
$538$	3.82826e16	0.0680639
$539$	6.70695e17	1.17814
$540$	−1.77677e16	−0.0308369
$541$	−1.02405e17	−0.175606	−0.0878029	−	0.996138i	$-0.527985\pi$
$541$	−1.02405e17	−0.175606	−0.0878029	+	0.996138i	$0.527985\pi$
$542$	1.12755e17	0.191046
$543$	−2.99241e17	−0.500983
$544$	4.28428e17	0.708737
$545$	7.13107e16	0.116567
$546$	1.47037e17	0.237507
$547$	−4.00721e17	−0.639624	−0.319812	−	0.947481i	$-0.603620\pi$
$547$	−4.00721e17	−0.639624	−0.319812	+	0.947481i	$0.603620\pi$
$548$	1.02856e18	1.62239
$549$	3.65321e17	0.569449
$550$	9.52717e16	0.146760
$551$	−4.76705e17	−0.725711
$552$	−2.50484e17	−0.376857
$553$	1.69361e18	2.51826
$554$	1.94066e17	0.285191
$555$	−3.06863e16	−0.0445697
$556$	3.00734e17	0.431714
$557$	4.72473e17	0.670376	0.335188	−	0.942151i	$-0.391200\pi$
$557$	4.72473e17	0.670376	0.335188	+	0.942151i	$0.391200\pi$
$558$	−7.69741e16	−0.107950
$559$	7.87450e17	1.09156
$560$	−1.71516e17	−0.235008
$561$	−4.13556e17	−0.560113
$562$	−4.55842e16	−0.0610278
$563$	−1.37459e18	−1.81915	−0.909574	−	0.415542i	$-0.863592\pi$
$563$	−1.37459e18	−1.81915	−0.909574	+	0.415542i	$0.863592\pi$
$564$	−1.79090e17	−0.234292
$565$	−1.86968e17	−0.241798
$566$	3.15971e16	0.0403962
$567$	−1.40003e17	−0.176949
$568$	1.99706e17	0.249532
$569$	5.06442e17	0.625605	0.312802	−	0.949818i	$-0.398732\pi$
$569$	5.06442e17	0.625605	0.312802	+	0.949818i	$0.398732\pi$
$570$	7.79242e15	0.00951668
$571$	−1.25224e18	−1.51200	−0.756002	−	0.654569i	$-0.772850\pi$
$571$	−1.25224e18	−1.51200	−0.756002	+	0.654569i	$0.772850\pi$
$572$	−8.10453e17	−0.967506
$573$	−7.34228e17	−0.866614
$574$	8.19802e16	0.0956713
$575$	1.42468e18	1.64390
$576$	−2.26425e17	−0.258332
$577$	3.91117e17	0.441229	0.220615	−	0.975361i	$-0.429194\pi$
$577$	3.91117e17	0.441229	0.220615	+	0.975361i	$0.429194\pi$
$578$	−1.05896e17	−0.118126
$579$	3.09753e17	0.341668
$580$	−2.12204e17	−0.231458
$581$	−1.19820e18	−1.29237
$582$	9.88910e16	0.105477
$583$	2.99978e17	0.316406
$584$	−4.61323e17	−0.481195
$585$	7.06908e16	0.0729205
$586$	−3.73992e17	−0.381530
$587$	−1.38275e17	−0.139507	−0.0697537	−	0.997564i	$-0.522221\pi$
$587$	−1.38275e17	−0.139507	−0.0697537	+	0.997564i	$0.522221\pi$
$588$	−8.54425e17	−0.852553
$589$	−8.37624e17	−0.826608
$590$	−4.37637e15	−0.00427145
$591$	−3.65792e17	−0.353114
$592$	−4.29396e17	−0.409984
$593$	−7.41382e17	−0.700143	−0.350072	−	0.936723i	$-0.613843\pi$
$593$	−7.41382e17	−0.700143	−0.350072	+	0.936723i	$0.613843\pi$
$594$	−3.11010e16	−0.0290511
$595$	3.63449e17	0.335802
$596$	8.35632e17	0.763685
$597$	−7.19169e17	−0.650127
$598$	4.88447e17	0.436777
$599$	−5.07866e17	−0.449236	−0.224618	−	0.974447i	$-0.572113\pi$
$599$	−5.07866e17	−0.449236	−0.224618	+	0.974447i	$0.572113\pi$
$600$	−2.47633e17	−0.216683
$601$	4.57309e17	0.395845	0.197923	−	0.980218i	$-0.436580\pi$
$601$	4.57309e17	0.395845	0.197923	+	0.980218i	$0.436580\pi$
$602$	3.04470e17	0.260716
$603$	3.16155e17	0.267816
$604$	−2.11046e18	−1.76863
$605$	−8.27995e16	−0.0686464
$606$	−3.43875e16	−0.0282052
$607$	1.23098e17	0.0998904	0.0499452	−	0.998752i	$-0.484095\pi$
$607$	1.23098e17	0.0998904	0.0499452	+	0.998752i	$0.484095\pi$
$608$	3.50609e17	0.281481
$609$	−1.67210e18	−1.32815
$610$	−7.13216e16	−0.0560502
$611$	7.12532e17	0.554034
$612$	5.26846e17	0.405321
$613$	1.47113e18	1.11985	0.559923	−	0.828545i	$-0.310831\pi$
$613$	1.47113e18	1.11985	0.559923	+	0.828545i	$0.310831\pi$
$614$	5.66535e16	0.0426709
$615$	3.94134e16	0.0293735
$616$	−6.39358e17	−0.471487
$617$	−2.51258e18	−1.83344	−0.916719	−	0.399532i	$-0.869172\pi$
$617$	−2.51258e18	−1.83344	−0.916719	+	0.399532i	$0.869172\pi$
$618$	1.35410e17	0.0977745
$619$	−2.12558e18	−1.51876	−0.759379	−	0.650649i	$-0.774497\pi$
$619$	−2.12558e18	−1.51876	−0.759379	+	0.650649i	$0.774497\pi$
$620$	−3.72867e17	−0.263638
$621$	−4.65080e17	−0.325411
$622$	6.12694e16	0.0424235
$623$	−1.96923e18	−1.34935
$624$	9.89181e17	0.670774
$625$	1.36705e18	0.917414
$626$	−2.55598e17	−0.169756
$627$	−3.38438e17	−0.222454
$628$	4.14303e17	0.269514
$629$	9.09907e17	0.585825
$630$	2.73328e16	0.0174169
$631$	−5.79679e16	−0.0365592	−0.0182796	−	0.999833i	$-0.505819\pi$
$631$	−5.79679e16	−0.0365592	−0.0182796	+	0.999833i	$0.505819\pi$
$632$	−9.77903e17	−0.610428
$633$	−2.07297e16	−0.0128077
$634$	2.57358e16	0.0157383
$635$	−3.48575e17	−0.210993
$636$	−3.82155e17	−0.228964
$637$	3.39943e18	2.01604
$638$	−3.71448e17	−0.218054
$639$	3.70798e17	0.215468
$640$	2.06568e17	0.118821
$641$	8.34332e17	0.475075	0.237537	−	0.971378i	$-0.423660\pi$
$641$	8.34332e17	0.475075	0.237537	+	0.971378i	$0.423660\pi$
$642$	8.87915e14	0.000500488 0
$643$	2.66018e18	1.48436	0.742180	−	0.670201i	$-0.233792\pi$
$643$	2.66018e18	1.48436	0.742180	+	0.670201i	$0.233792\pi$
$644$	−4.68600e18	−2.58847
$645$	1.46379e17	0.0800463
$646$	−2.31060e17	−0.125087
$647$	3.58040e18	1.91891	0.959453	−	0.281869i	$-0.0909544\pi$
$647$	3.58040e18	1.91891	0.959453	+	0.281869i	$0.0909544\pi$
$648$	8.08385e16	0.0428925
$649$	1.90073e17	0.0998458
$650$	4.82886e17	0.251136
$651$	−2.93806e18	−1.51281
$652$	1.64684e18	0.839539
$653$	−1.59955e18	−0.807352	−0.403676	−	0.914902i	$-0.632268\pi$
$653$	−1.59955e18	−0.807352	−0.403676	+	0.914902i	$0.632268\pi$
$654$	−1.59019e17	−0.0794680
$655$	2.28428e17	0.113027
$656$	5.51514e17	0.270198
$657$	−8.56548e17	−0.415505
$658$	2.75502e17	0.132330
$659$	1.68722e18	0.802447	0.401223	−	0.915980i	$-0.368585\pi$
$659$	1.68722e18	0.802447	0.401223	+	0.915980i	$0.368585\pi$
$660$	−1.50655e17	−0.0709494
$661$	−2.36990e18	−1.10515	−0.552575	−	0.833463i	$-0.686355\pi$
$661$	−2.36990e18	−1.10515	−0.552575	+	0.833463i	$0.686355\pi$
$662$	−3.04307e17	−0.140519
$663$	−2.09612e18	−0.958467
$664$	6.91850e17	0.313270
$665$	2.97432e17	0.133367
$666$	6.84286e16	0.0303847
$667$	−5.55458e18	−2.44249
$668$	5.05473e17	0.220115
$669$	−1.62090e18	−0.699014
$670$	−6.17229e16	−0.0263609
$671$	3.09762e18	1.31018
$672$	1.22980e18	0.515151
$673$	2.89363e18	1.20045	0.600226	−	0.799831i	$-0.295077\pi$
$673$	2.89363e18	1.20045	0.600226	+	0.799831i	$0.295077\pi$
$674$	3.83096e17	0.157405
$675$	−4.59785e17	−0.187103
$676$	−1.72277e18	−0.694342
$677$	−2.12791e18	−0.849428	−0.424714	−	0.905328i	$-0.639625\pi$
$677$	−2.12791e18	−0.849428	−0.424714	+	0.905328i	$0.639625\pi$
$678$	4.16927e17	0.164842
$679$	3.77462e18	1.47815
$680$	−2.09858e17	−0.0813985
$681$	1.62753e18	0.625279
$682$	−6.52677e17	−0.248370
$683$	−5.01423e18	−1.89004	−0.945018	−	0.327019i	$-0.893956\pi$
$683$	−5.01423e18	−1.89004	−0.945018	+	0.327019i	$0.893956\pi$
$684$	4.31150e17	0.160977
$685$	−7.60705e17	−0.281338
$686$	4.58770e17	0.168069
$687$	2.21962e18	0.805490
$688$	2.04829e18	0.736322
$689$	1.52045e18	0.541435
$690$	9.07975e16	0.0320298
$691$	−2.64832e18	−0.925473	−0.462736	−	0.886496i	$-0.653132\pi$
$691$	−2.64832e18	−0.925473	−0.462736	+	0.886496i	$0.653132\pi$
$692$	−2.56525e18	−0.888055
$693$	−1.18711e18	−0.407122
$694$	9.96097e17	0.338427
$695$	−2.22418e17	−0.0748632
$696$	9.65478e17	0.321945
$697$	−1.16868e18	−0.386085
$698$	−3.16437e17	−0.103568
$699$	−3.13101e18	−1.01527
$700$	−4.63265e18	−1.48831
$701$	3.12315e18	0.994090	0.497045	−	0.867725i	$-0.334418\pi$
$701$	3.12315e18	0.994090	0.497045	+	0.867725i	$0.334418\pi$
$702$	−1.57636e17	−0.0497124
$703$	7.44632e17	0.232666
$704$	−1.91990e18	−0.594369
$705$	1.32453e17	0.0406285
$706$	5.70973e17	0.173534
$707$	−1.31255e18	−0.395268
$708$	−2.42142e17	−0.0722526
$709$	3.53911e18	1.04639	0.523195	−	0.852213i	$-0.324740\pi$
$709$	3.53911e18	1.04639	0.523195	+	0.852213i	$0.324740\pi$
$710$	−7.23909e16	−0.0212083
$711$	−1.81569e18	−0.527096
$712$	1.13704e18	0.327082
$713$	−9.76002e18	−2.78208
$714$	−8.10469e17	−0.228928
$715$	5.99399e17	0.167775
$716$	2.52836e18	0.701301
$717$	−4.33141e17	−0.119057
$718$	9.14857e17	0.249198
$719$	−3.87900e18	−1.04708	−0.523542	−	0.852000i	$-0.675390\pi$
$719$	−3.87900e18	−1.04708	−0.523542	+	0.852000i	$0.675390\pi$
$720$	1.83879e17	0.0491893
$721$	5.16853e18	1.37021
$722$	5.60080e17	0.147149
$723$	−1.23593e18	−0.321806
$724$	3.23239e18	0.834110
$725$	−5.49134e18	−1.40437
$726$	1.84638e17	0.0467986
$727$	−5.85872e18	−1.47173	−0.735866	−	0.677127i	$-0.763225\pi$
$727$	−5.85872e18	−1.47173	−0.735866	+	0.677127i	$0.763225\pi$
$728$	−3.24060e18	−0.806810
$729$	1.50095e17	0.0370370
$730$	1.67224e17	0.0408978
$731$	−4.34042e18	−1.05213
$732$	−3.94618e18	−0.948103
$733$	−2.14921e17	−0.0511804	−0.0255902	−	0.999673i	$-0.508146\pi$
$733$	−2.14921e17	−0.0511804	−0.0255902	+	0.999673i	$0.508146\pi$
$734$	8.13323e17	0.191972
$735$	6.31920e17	0.147841
$736$	4.08531e18	0.947368
$737$	2.68073e18	0.616189
$738$	−8.78895e16	−0.0200249
$739$	−4.67683e17	−0.105624	−0.0528121	−	0.998604i	$-0.516818\pi$
$739$	−4.67683e17	−0.105624	−0.0528121	+	0.998604i	$0.516818\pi$
$740$	3.31472e17	0.0742063
$741$	−1.71538e18	−0.380664
$742$	5.87885e17	0.129320
$743$	2.89660e18	0.631629	0.315814	−	0.948821i	$-0.397722\pi$
$743$	2.89660e18	0.631629	0.315814	+	0.948821i	$0.397722\pi$
$744$	1.69645e18	0.366706
$745$	−6.18021e17	−0.132430
$746$	−4.57358e17	−0.0971526
$747$	1.28457e18	0.270504
$748$	4.46721e18	0.932559
$749$	3.38912e16	0.00701384
$750$	1.82093e17	0.0373590
$751$	−2.86710e18	−0.583154	−0.291577	−	0.956547i	$-0.594180\pi$
$751$	−2.86710e18	−0.583154	−0.291577	+	0.956547i	$0.594180\pi$
$752$	1.85342e18	0.373729
$753$	4.37739e18	0.875079
$754$	−1.88269e18	−0.373135
$755$	1.56087e18	0.306698
$756$	1.51231e18	0.294611
$757$	3.95257e18	0.763407	0.381703	−	0.924285i	$-0.375338\pi$
$757$	3.95257e18	0.763407	0.381703	+	0.924285i	$0.375338\pi$
$758$	−3.58245e17	−0.0686011
$759$	−3.94349e18	−0.748702
$760$	−1.71739e17	−0.0323282
$761$	1.05752e18	0.197373	0.0986866	−	0.995119i	$-0.468536\pi$
$761$	1.05752e18	0.197373	0.0986866	+	0.995119i	$0.468536\pi$
$762$	7.77301e17	0.143841
$763$	−6.06965e18	−1.11366
$764$	7.93110e18	1.44287
$765$	−3.89647e17	−0.0702865
$766$	3.20421e17	0.0573106
$767$	9.63389e17	0.170857
$768$	2.08378e18	0.366440
$769$	−2.34180e18	−0.408346	−0.204173	−	0.978935i	$-0.565450\pi$
$769$	−2.34180e18	−0.408346	−0.204173	+	0.978935i	$0.565450\pi$
$770$	2.31759e17	0.0400726
$771$	−1.00458e18	−0.172239
$772$	−3.34594e18	−0.568860
$773$	6.14843e18	1.03657	0.518284	−	0.855209i	$-0.326571\pi$
$773$	6.14843e18	1.03657	0.518284	+	0.855209i	$0.326571\pi$
$774$	−3.26417e17	−0.0545703
$775$	−9.64891e18	−1.59962
$776$	−2.17948e18	−0.358305
$777$	2.61188e18	0.425811
$778$	−3.76123e17	−0.0608082
$779$	−9.56404e17	−0.153337
$780$	−7.63599e17	−0.121409
$781$	3.14406e18	0.495746
$782$	−2.69232e18	−0.421000
$783$	1.79262e18	0.277995
$784$	8.84250e18	1.35994
$785$	−3.06412e17	−0.0467362
$786$	−5.09380e17	−0.0770540
$787$	1.71869e18	0.257847	0.128924	−	0.991655i	$-0.458848\pi$
$787$	1.71869e18	0.257847	0.128924	+	0.991655i	$0.458848\pi$
$788$	3.95127e18	0.587917
$789$	−2.99139e18	−0.441440
$790$	3.54478e17	0.0518815
$791$	1.59139e19	2.31009
$792$	6.85444e17	0.0986866
$793$	1.57003e19	2.24199
$794$	−1.84155e18	−0.260825
$795$	2.82636e17	0.0397046
$796$	7.76844e18	1.08243
$797$	−5.26477e18	−0.727613	−0.363806	−	0.931475i	$-0.618523\pi$
$797$	−5.26477e18	−0.727613	−0.363806	+	0.931475i	$0.618523\pi$
$798$	−6.63256e17	−0.0909206
$799$	−3.92747e18	−0.534021
$800$	4.03880e18	0.544712
$801$	2.11117e18	0.282431
$802$	9.05293e17	0.120131
$803$	−7.26282e18	−0.955991
$804$	−3.41509e18	−0.445900
$805$	3.46569e18	0.448866
$806$	−3.30810e18	−0.425012
$807$	−1.56655e18	−0.199649
$808$	7.57877e17	0.0958130
$809$	3.65111e18	0.457888	0.228944	−	0.973440i	$-0.426473\pi$
$809$	3.65111e18	0.457888	0.228944	+	0.973440i	$0.426473\pi$
$810$	−2.93030e16	−0.00364552
$811$	3.66951e18	0.452869	0.226434	−	0.974026i	$-0.427293\pi$
$811$	3.66951e18	0.452869	0.226434	+	0.974026i	$0.427293\pi$
$812$	1.80619e19	2.21131
$813$	−4.61400e18	−0.560389
$814$	5.80218e17	0.0699089
$815$	−1.21797e18	−0.145584
$816$	−5.45236e18	−0.646544
$817$	−3.55203e18	−0.417862
$818$	−2.33378e17	−0.0272373
$819$	−6.01689e18	−0.696669
$820$	−4.25742e17	−0.0489054
$821$	−5.29791e18	−0.603774	−0.301887	−	0.953344i	$-0.597616\pi$
$821$	−5.29791e18	−0.603774	−0.301887	+	0.953344i	$0.597616\pi$
$822$	1.69633e18	0.191797
$823$	1.46955e19	1.64848	0.824241	−	0.566239i	$-0.191602\pi$
$823$	1.46955e19	1.64848	0.824241	+	0.566239i	$0.191602\pi$
$824$	−2.98434e18	−0.332140
$825$	−3.89859e18	−0.430484
$826$	3.72497e17	0.0408087
$827$	−1.44513e19	−1.57081	−0.785403	−	0.618985i	$-0.787544\pi$
$827$	−1.44513e19	−1.57081	−0.785403	+	0.618985i	$0.787544\pi$
$828$	5.02377e18	0.541792
$829$	3.73464e18	0.399618	0.199809	−	0.979835i	$-0.435968\pi$
$829$	3.73464e18	0.399618	0.199809	+	0.979835i	$0.435968\pi$
$830$	−2.50787e17	−0.0266255
$831$	−7.94133e18	−0.836539
$832$	−9.73104e18	−1.01709
$833$	−1.87376e19	−1.94322
$834$	4.95979e17	0.0510368
$835$	−3.73840e17	−0.0381701
$836$	3.65579e18	0.370374
$837$	3.14984e18	0.316645
$838$	−3.61441e18	−0.360538
$839$	−1.12147e18	−0.111003	−0.0555016	−	0.998459i	$-0.517676\pi$
$839$	−1.12147e18	−0.111003	−0.0555016	+	0.998459i	$0.517676\pi$
$840$	−6.02395e17	−0.0591651
$841$	1.11492e19	1.08660
$842$	−1.19918e18	−0.115973
$843$	1.86534e18	0.179011
$844$	2.23922e17	0.0213241
$845$	1.27413e18	0.120406
$846$	−2.95361e17	−0.0276978
$847$	7.04753e18	0.655836
$848$	3.95494e18	0.365231
$849$	−1.29298e18	−0.118493
$850$	−2.66167e18	−0.242064
$851$	8.67648e18	0.783071
$852$	−4.00535e18	−0.358743
$853$	2.67783e18	0.238020	0.119010	−	0.992893i	$-0.462028\pi$
$853$	2.67783e18	0.238020	0.119010	+	0.992893i	$0.462028\pi$
$854$	6.07058e18	0.535494
$855$	−3.18872e17	−0.0279149
$856$	−1.95690e16	−0.00170016
$857$	−6.61516e18	−0.570381	−0.285191	−	0.958471i	$-0.592057\pi$
$857$	−6.61516e18	−0.570381	−0.285191	+	0.958471i	$0.592057\pi$
$858$	−1.33662e18	−0.114378
$859$	2.83552e18	0.240811	0.120406	−	0.992725i	$-0.461580\pi$
$859$	2.83552e18	0.240811	0.120406	+	0.992725i	$0.461580\pi$
$860$	−1.58118e18	−0.133273
$861$	−3.35469e18	−0.280629
$862$	2.90176e18	0.240916
$863$	−8.70517e18	−0.717311	−0.358655	−	0.933470i	$-0.616765\pi$
$863$	−8.70517e18	−0.717311	−0.358655	+	0.933470i	$0.616765\pi$
$864$	−1.31845e18	−0.107826
$865$	1.89722e18	0.153997
$866$	3.19670e18	0.257535
$867$	4.33333e18	0.346496
$868$	3.17368e19	2.51875
$869$	−1.53956e19	−1.21274
$870$	−3.49974e17	−0.0273628
$871$	1.35873e19	1.05443
$872$	3.50465e18	0.269953
$873$	−4.04670e18	−0.309391
$874$	−2.20329e18	−0.167204
$875$	6.95039e18	0.523549
$876$	9.25240e18	0.691795
$877$	1.21686e19	0.903114	0.451557	−	0.892242i	$-0.350869\pi$
$877$	1.21686e19	0.903114	0.451557	+	0.892242i	$0.350869\pi$
$878$	−1.30367e18	−0.0960404
$879$	1.53041e19	1.11913
$880$	1.55914e18	0.113174
$881$	−4.97522e18	−0.358483	−0.179242	−	0.983805i	$-0.557364\pi$
$881$	−4.97522e18	−0.358483	−0.179242	+	0.983805i	$0.557364\pi$
$882$	−1.40914e18	−0.100788
$883$	1.82648e19	1.29679	0.648396	−	0.761303i	$-0.275440\pi$
$883$	1.82648e19	1.29679	0.648396	+	0.761303i	$0.275440\pi$
$884$	2.26422e19	1.59580
$885$	1.79084e17	0.0125293
$886$	−2.85122e18	−0.198021
$887$	−4.48217e18	−0.309018	−0.154509	−	0.987991i	$-0.549380\pi$
$887$	−4.48217e18	−0.309018	−0.154509	+	0.987991i	$0.549380\pi$
$888$	−1.50812e18	−0.103217
$889$	2.96692e19	2.01578
$890$	−4.12164e17	−0.0277994
$891$	1.27268e18	0.0852145
$892$	1.75089e19	1.16382
$893$	−3.21409e18	−0.212091
$894$	1.37815e18	0.0902822
$895$	−1.86994e18	−0.121612
$896$	−1.75822e19	−1.13520
$897$	−1.99876e19	−1.28118
$898$	−2.62431e18	−0.167001
$899$	3.76195e19	2.37670
$900$	4.96658e18	0.311516
$901$	−8.38069e18	−0.521877
$902$	−7.45230e17	−0.0460731
$903$	−1.24592e19	−0.764748
$904$	−9.18877e18	−0.559967
$905$	−2.39063e18	−0.144643
$906$	−3.48064e18	−0.209086
$907$	−2.93556e19	−1.75083	−0.875414	−	0.483374i	$-0.839411\pi$
$907$	−2.93556e19	−1.75083	−0.875414	+	0.483374i	$0.839411\pi$
$908$	−1.75806e19	−1.04106
$909$	1.40717e18	0.0827332
$910$	1.17468e18	0.0685724
$911$	−2.54876e19	−1.47727	−0.738635	−	0.674105i	$-0.764529\pi$
$911$	−2.54876e19	−1.47727	−0.738635	+	0.674105i	$0.764529\pi$
$912$	−4.46200e18	−0.256781
$913$	1.08921e19	0.622374
$914$	2.58226e18	0.146504
$915$	2.91854e18	0.164410
$916$	−2.39763e19	−1.34110
$917$	−1.94428e19	−1.07983
$918$	8.68889e17	0.0479167
$919$	2.13951e19	1.17156	0.585779	−	0.810471i	$-0.300789\pi$
$919$	2.13951e19	1.17156	0.585779	+	0.810471i	$0.300789\pi$
$920$	−2.00111e18	−0.108805
$921$	−2.31830e18	−0.125165
$922$	−6.98503e18	−0.374470
$923$	1.59357e19	0.848323
$924$	1.28231e19	0.677837
$925$	8.57770e18	0.450246
$926$	2.73267e18	0.142435
$927$	−5.54108e18	−0.286798
$928$	−1.57466e19	−0.809328
$929$	1.54861e19	0.790388	0.395194	−	0.918598i	$-0.370677\pi$
$929$	1.54861e19	0.790388	0.395194	+	0.918598i	$0.370677\pi$
$930$	−6.14944e17	−0.0311671
$931$	−1.53341e19	−0.771768
$932$	3.38210e19	1.69037
$933$	−2.50719e18	−0.124439
$934$	5.47592e18	0.269900
$935$	−3.30388e18	−0.161715
$936$	3.47418e18	0.168873
$937$	−1.07879e18	−0.0520752	−0.0260376	−	0.999661i	$-0.508289\pi$
$937$	−1.07879e18	−0.0520752	−0.0260376	+	0.999661i	$0.508289\pi$
$938$	5.25358e18	0.251847
$939$	1.04593e19	0.497938
$940$	−1.43075e18	−0.0676444
$941$	−1.61059e19	−0.756226	−0.378113	−	0.925759i	$-0.623427\pi$
$941$	−1.61059e19	−0.756226	−0.378113	+	0.925759i	$0.623427\pi$
$942$	6.83281e17	0.0318617
$943$	−1.11440e19	−0.516080
$944$	2.50594e18	0.115253
$945$	−1.11848e18	−0.0510883
$946$	−2.76774e18	−0.125555
$947$	1.64926e19	0.743042	0.371521	−	0.928425i	$-0.378836\pi$
$947$	1.64926e19	0.743042	0.371521	+	0.928425i	$0.378836\pi$
$948$	1.96130e19	0.877588
$949$	−3.68117e19	−1.63590
$950$	−2.17820e18	−0.0961380
$951$	−1.05313e18	−0.0461646
$952$	1.78621e19	0.777667
$953$	3.53366e19	1.52799	0.763995	−	0.645222i	$-0.223235\pi$
$953$	3.53366e19	1.52799	0.763995	+	0.645222i	$0.223235\pi$
$954$	−6.30261e17	−0.0270680
$955$	−5.86572e18	−0.250207
$956$	4.67877e18	0.198224
$957$	1.52000e19	0.639609
$958$	−5.51067e18	−0.230318
$959$	6.47479e19	2.68785
$960$	−1.80890e18	−0.0745852
$961$	4.16841e19	1.70714
$962$	2.94084e18	0.119628
$963$	−3.63342e16	−0.00146806
$964$	1.33504e19	0.535790
$965$	2.47461e18	0.0986458
$966$	−7.72828e18	−0.306007
$967$	−1.56512e19	−0.615566	−0.307783	−	0.951457i	$-0.599587\pi$
$967$	−1.56512e19	−0.615566	−0.307783	+	0.951457i	$0.599587\pi$
$968$	−4.06929e18	−0.158975
$969$	9.45515e18	0.366914
$970$	7.90036e17	0.0304531
$971$	1.94259e19	0.743801	0.371901	−	0.928273i	$-0.378706\pi$
$971$	1.94259e19	0.743801	0.371901	+	0.928273i	$0.378706\pi$
$972$	−1.62132e18	−0.0616648
$973$	1.89312e19	0.715230
$974$	8.41104e18	0.315658
$975$	−1.97601e19	−0.736646
$976$	4.08393e19	1.51236
$977$	−5.14788e19	−1.89371	−0.946855	−	0.321660i	$-0.895759\pi$
$977$	−5.14788e19	−1.89371	−0.946855	+	0.321660i	$0.895759\pi$
$978$	2.71601e18	0.0992496
$979$	1.79010e19	0.649814
$980$	−6.82597e18	−0.246147
$981$	6.50716e18	0.233100
$982$	8.46569e18	0.301257
$983$	−4.53291e19	−1.60243	−0.801216	−	0.598376i	$-0.795813\pi$
$983$	−4.53291e19	−1.60243	−0.801216	+	0.598376i	$0.795813\pi$
$984$	1.93702e18	0.0680246
$985$	−2.92230e18	−0.101950
$986$	1.03774e19	0.359657
$987$	−1.12738e19	−0.388157
$988$	1.85295e19	0.633786
$989$	−4.13884e19	−1.40638
$990$	−2.48465e17	−0.00838757
$991$	−1.51168e19	−0.506970	−0.253485	−	0.967339i	$-0.581577\pi$
$991$	−1.51168e19	−0.506970	−0.253485	+	0.967339i	$0.581577\pi$
$992$	−2.76685e19	−0.921850
$993$	1.24525e19	0.412178
$994$	6.16160e18	0.202620
$995$	−5.74542e18	−0.187703
$996$	−1.38759e19	−0.450376
$997$	3.60190e18	0.116148	0.0580742	−	0.998312i	$-0.481504\pi$
$997$	3.60190e18	0.116148	0.0580742	+	0.998312i	$0.481504\pi$
$998$	1.77965e18	0.0570146
$999$	−2.80015e18	−0.0891263

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.a.1.15	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.a.1.15	✓	30	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-17.8149 q^{2} +729.000 q^{3} -7874.63 q^{4} +5823.96 q^{5} -12987.1 q^{6} -495710. q^{7} +286225. q^{8} +531441. q^{9} +O(q^{10})\)	\(q-17.8149 q^{2} +729.000 q^{3} -7874.63 q^{4} +5823.96 q^{5} -12987.1 q^{6} -495710. q^{7} +286225. q^{8} +531441. q^{9} -103753. q^{10} +4.50618e6 q^{11} -5.74060e6 q^{12} +2.28397e7 q^{13} +8.83102e6 q^{14} +4.24566e6 q^{15} +5.94099e7 q^{16} -1.25892e8 q^{17} -9.46757e6 q^{18} -1.03025e8 q^{19} -4.58615e7 q^{20} -3.61372e8 q^{21} -8.02772e7 q^{22} -1.20045e9 q^{23} +2.08658e8 q^{24} -1.18678e9 q^{25} -4.06886e8 q^{26} +3.87420e8 q^{27} +3.90353e9 q^{28} +4.62707e9 q^{29} -7.56361e7 q^{30} +8.13029e9 q^{31} -3.40314e9 q^{32} +3.28500e9 q^{33} +2.24275e9 q^{34} -2.88699e9 q^{35} -4.18490e9 q^{36} -7.22768e9 q^{37} +1.83538e9 q^{38} +1.66501e10 q^{39} +1.66696e9 q^{40} +9.28321e9 q^{41} +6.43781e9 q^{42} +3.44773e10 q^{43} -3.54845e10 q^{44} +3.09509e9 q^{45} +2.13859e10 q^{46} +3.11971e10 q^{47} +4.33098e10 q^{48} +1.48839e11 q^{49} +2.11425e10 q^{50} -9.17753e10 q^{51} -1.79854e11 q^{52} +6.65705e10 q^{53} -6.90186e9 q^{54} +2.62438e10 q^{55} -1.41885e11 q^{56} -7.51053e10 q^{57} -8.24309e10 q^{58} +4.21805e10 q^{59} -3.34330e10 q^{60} +6.87416e11 q^{61} -1.44840e11 q^{62} -2.63440e11 q^{63} -4.26059e11 q^{64} +1.33017e11 q^{65} -5.85220e10 q^{66} +5.94901e11 q^{67} +9.91353e11 q^{68} -8.75129e11 q^{69} +5.14315e10 q^{70} +6.97722e11 q^{71} +1.52112e11 q^{72} -1.61175e12 q^{73} +1.28760e11 q^{74} -8.65166e11 q^{75} +8.11284e11 q^{76} -2.23376e12 q^{77} -2.96620e11 q^{78} -3.41655e12 q^{79} +3.46001e11 q^{80} +2.82430e11 q^{81} -1.65380e11 q^{82} +2.41715e12 q^{83} +2.84567e12 q^{84} -7.33189e11 q^{85} -6.14210e11 q^{86} +3.37314e12 q^{87} +1.28978e12 q^{88} +3.97254e12 q^{89} -5.51387e10 q^{90} -1.13218e13 q^{91} +9.45311e12 q^{92} +5.92698e12 q^{93} -5.55774e11 q^{94} -6.00014e11 q^{95} -2.48089e12 q^{96} -7.61457e12 q^{97} -2.65155e12 q^{98} +2.39477e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 138 q^{2} + 21870 q^{3} + 114598 q^{4} - 137742 q^{5} - 100602 q^{6} - 879443 q^{7} - 872301 q^{8} + 15943230 q^{9}+O(q^{10}) \) 30 * q - 138 * q^2 + 21870 * q^3 + 114598 * q^4 - 137742 * q^5 - 100602 * q^6 - 879443 * q^7 - 872301 * q^8 + 15943230 * q^9	\( 30 q - 138 q^{2} + 21870 q^{3} + 114598 q^{4} - 137742 q^{5} - 100602 q^{6} - 879443 q^{7} - 872301 q^{8} + 15943230 q^{9} - 5352519 q^{10} - 13950782 q^{11} + 83541942 q^{12} - 17256988 q^{13} + 33780109 q^{14} - 100413918 q^{15} + 499996762 q^{16} - 317583695 q^{17} - 73338858 q^{18} - 863401469 q^{19} - 1841280623 q^{20} - 641113947 q^{21} - 2723764842 q^{22} - 3142075981 q^{23} - 635907429 q^{24} + 5435751692 q^{25} - 6441414040 q^{26} + 11622614670 q^{27} - 7538400046 q^{28} - 4604589283 q^{29} - 3901986351 q^{30} + 4308675373 q^{31} + 6094556360 q^{32} - 10170120078 q^{33} + 38097713432 q^{34} - 15447827315 q^{35} + 60902075718 q^{36} - 19633376949 q^{37} - 18152222923 q^{38} - 12580344252 q^{39} + 14680384170 q^{40} - 103644439493 q^{41} + 24625699461 q^{42} - 64494894924 q^{43} - 199714496208 q^{44} - 73201746222 q^{45} - 265425792847 q^{46} - 293365585139 q^{47} + 364497639498 q^{48} + 414396765797 q^{49} - 126058522207 q^{50} - 231518513655 q^{51} + 156029960316 q^{52} - 76747013118 q^{53} - 53464027482 q^{54} - 433465885754 q^{55} - 502955241518 q^{56} - 629419670901 q^{57} - 1755031845830 q^{58} + 1265416009230 q^{59} - 1342293574167 q^{60} - 2022612531219 q^{61} - 3816005187046 q^{62} - 467372067363 q^{63} - 3570205594131 q^{64} - 3889749040576 q^{65} - 1985624569818 q^{66} - 502618987776 q^{67} - 8953998390517 q^{68} - 2290573390149 q^{69} - 6805178272420 q^{70} - 1599540605456 q^{71} - 463576515741 q^{72} - 3826795087235 q^{73} - 7573387813210 q^{74} + 3962662983468 q^{75} - 19498723328388 q^{76} - 9088623115219 q^{77} - 4695790835160 q^{78} - 8595482172338 q^{79} - 17452527463963 q^{80} + 8472886094430 q^{81} - 11181116792901 q^{82} - 13548556984389 q^{83} - 5495493633534 q^{84} - 12851795888367 q^{85} + 8539949468848 q^{86} - 3356745587307 q^{87} - 25134826741387 q^{88} - 21826401667403 q^{89} - 2844548049879 q^{90} - 26577050621355 q^{91} - 34908210763168 q^{92} + 3141024346917 q^{93} - 26426808959500 q^{94} - 29105233533993 q^{95} + 4442931586440 q^{96} + 417815797414 q^{97} + 29159956938360 q^{98} - 7414017536862 q^{99}+O(q^{100}) \) 30 * q - 138 * q^2 + 21870 * q^3 + 114598 * q^4 - 137742 * q^5 - 100602 * q^6 - 879443 * q^7 - 872301 * q^8 + 15943230 * q^9 - 5352519 * q^10 - 13950782 * q^11 + 83541942 * q^12 - 17256988 * q^13 + 33780109 * q^14 - 100413918 * q^15 + 499996762 * q^16 - 317583695 * q^17 - 73338858 * q^18 - 863401469 * q^19 - 1841280623 * q^20 - 641113947 * q^21 - 2723764842 * q^22 - 3142075981 * q^23 - 635907429 * q^24 + 5435751692 * q^25 - 6441414040 * q^26 + 11622614670 * q^27 - 7538400046 * q^28 - 4604589283 * q^29 - 3901986351 * q^30 + 4308675373 * q^31 + 6094556360 * q^32 - 10170120078 * q^33 + 38097713432 * q^34 - 15447827315 * q^35 + 60902075718 * q^36 - 19633376949 * q^37 - 18152222923 * q^38 - 12580344252 * q^39 + 14680384170 * q^40 - 103644439493 * q^41 + 24625699461 * q^42 - 64494894924 * q^43 - 199714496208 * q^44 - 73201746222 * q^45 - 265425792847 * q^46 - 293365585139 * q^47 + 364497639498 * q^48 + 414396765797 * q^49 - 126058522207 * q^50 - 231518513655 * q^51 + 156029960316 * q^52 - 76747013118 * q^53 - 53464027482 * q^54 - 433465885754 * q^55 - 502955241518 * q^56 - 629419670901 * q^57 - 1755031845830 * q^58 + 1265416009230 * q^59 - 1342293574167 * q^60 - 2022612531219 * q^61 - 3816005187046 * q^62 - 467372067363 * q^63 - 3570205594131 * q^64 - 3889749040576 * q^65 - 1985624569818 * q^66 - 502618987776 * q^67 - 8953998390517 * q^68 - 2290573390149 * q^69 - 6805178272420 * q^70 - 1599540605456 * q^71 - 463576515741 * q^72 - 3826795087235 * q^73 - 7573387813210 * q^74 + 3962662983468 * q^75 - 19498723328388 * q^76 - 9088623115219 * q^77 - 4695790835160 * q^78 - 8595482172338 * q^79 - 17452527463963 * q^80 + 8472886094430 * q^81 - 11181116792901 * q^82 - 13548556984389 * q^83 - 5495493633534 * q^84 - 12851795888367 * q^85 + 8539949468848 * q^86 - 3356745587307 * q^87 - 25134826741387 * q^88 - 21826401667403 * q^89 - 2844548049879 * q^90 - 26577050621355 * q^91 - 34908210763168 * q^92 + 3141024346917 * q^93 - 26426808959500 * q^94 - 29105233533993 * q^95 + 4442931586440 * q^96 + 417815797414 * q^97 + 29159956938360 * q^98 - 7414017536862 * q^99

Introduction

L-functions

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