LMFDB - Embedded newform 177.14.a.a.1.4

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			1.4
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)

$f(q)$	$=$	$q-152.210 q^{2} +729.000 q^{3} +14976.0 q^{4} -42581.4 q^{5} -110961. q^{6} -571520. q^{7} -1.03259e6 q^{8} +531441. q^{9} +O(q^{10})$	\(q-152.210 q^{2} +729.000 q^{3} +14976.0 q^{4} -42581.4 q^{5} -110961. q^{6} -571520. q^{7} -1.03259e6 q^{8} +531441. q^{9} +6.48132e6 q^{10} -6.58581e6 q^{11} +1.09175e7 q^{12} +4.28374e6 q^{13} +8.69912e7 q^{14} -3.10418e7 q^{15} +3.44876e7 q^{16} -1.87480e8 q^{17} -8.08908e7 q^{18} -2.31872e8 q^{19} -6.37697e8 q^{20} -4.16638e8 q^{21} +1.00243e9 q^{22} +1.28925e9 q^{23} -7.52758e8 q^{24} +5.92471e8 q^{25} -6.52029e8 q^{26} +3.87420e8 q^{27} -8.55907e9 q^{28} +2.90122e9 q^{29} +4.72489e9 q^{30} -1.60330e9 q^{31} +3.20961e9 q^{32} -4.80106e9 q^{33} +2.85364e10 q^{34} +2.43361e10 q^{35} +7.95884e9 q^{36} +2.91197e10 q^{37} +3.52933e10 q^{38} +3.12285e9 q^{39} +4.39691e10 q^{40} -3.68274e10 q^{41} +6.34166e10 q^{42} +2.91441e10 q^{43} -9.86289e10 q^{44} -2.26295e10 q^{45} -1.96237e11 q^{46} -2.29465e10 q^{47} +2.51415e10 q^{48} +2.29746e11 q^{49} -9.01802e10 q^{50} -1.36673e11 q^{51} +6.41532e10 q^{52} -1.99989e11 q^{53} -5.89694e10 q^{54} +2.80433e11 q^{55} +5.90146e11 q^{56} -1.69035e11 q^{57} -4.41595e11 q^{58} +4.21805e10 q^{59} -4.64881e11 q^{60} +4.98973e11 q^{61} +2.44039e11 q^{62} -3.03729e11 q^{63} -7.71057e11 q^{64} -1.82408e11 q^{65} +7.30770e11 q^{66} +3.43120e11 q^{67} -2.80770e12 q^{68} +9.39864e11 q^{69} -3.70421e12 q^{70} +1.13561e12 q^{71} -5.48760e11 q^{72} -1.48911e12 q^{73} -4.43232e12 q^{74} +4.31911e11 q^{75} -3.47250e12 q^{76} +3.76393e12 q^{77} -4.75330e11 q^{78} +2.64540e12 q^{79} -1.46853e12 q^{80} +2.82430e11 q^{81} +5.60551e12 q^{82} -3.22063e12 q^{83} -6.23956e12 q^{84} +7.98316e12 q^{85} -4.43604e12 q^{86} +2.11499e12 q^{87} +6.80044e12 q^{88} -6.12635e12 q^{89} +3.44444e12 q^{90} -2.44824e12 q^{91} +1.93078e13 q^{92} -1.16881e12 q^{93} +3.49270e12 q^{94} +9.87342e12 q^{95} +2.33980e12 q^{96} +7.26379e11 q^{97} -3.49697e13 q^{98} -3.49997e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−152.210	−1.68170	−0.840851	−	0.541267i	$-0.817945\pi$
$2$	−152.210	−1.68170	−0.840851	+	0.541267i	$0.817945\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	14976.0	1.82812
$5$	−42581.4	−1.21875	−0.609375	−	0.792882i	$-0.708580\pi$
$5$	−42581.4	−1.21875	−0.609375	+	0.792882i	$0.708580\pi$
$6$	−110961.	−0.970931
$7$	−571520.	−1.83609	−0.918046	−	0.396475i	$-0.870233\pi$
$7$	−571520.	−1.83609	−0.918046	+	0.396475i	$0.870233\pi$
$8$	−1.03259e6	−1.39265
$9$	531441.	0.333333
$10$	6.48132e6	2.04957
$11$	−6.58581e6	−1.12087	−0.560437	−	0.828197i	$-0.689367\pi$
$11$	−6.58581e6	−1.12087	−0.560437	+	0.828197i	$0.689367\pi$
$12$	1.09175e7	1.05547
$13$	4.28374e6	0.246145	0.123073	−	0.992398i	$-0.460725\pi$
$13$	4.28374e6	0.246145	0.123073	+	0.992398i	$0.460725\pi$
$14$	8.69912e7	3.08776
$15$	−3.10418e7	−0.703646
$16$	3.44876e7	0.513905
$17$	−1.87480e8	−1.88381	−0.941905	−	0.335879i	$-0.890967\pi$
$17$	−1.87480e8	−1.88381	−0.941905	+	0.335879i	$0.890967\pi$
$18$	−8.08908e7	−0.560567
$19$	−2.31872e8	−1.13071	−0.565353	−	0.824849i	$-0.691260\pi$
$19$	−2.31872e8	−1.13071	−0.565353	+	0.824849i	$0.691260\pi$
$20$	−6.37697e8	−2.22802
$21$	−4.16638e8	−1.06007
$22$	1.00243e9	1.88498
$23$	1.28925e9	1.81596	0.907981	−	0.419012i	$-0.137624\pi$
$23$	1.28925e9	1.81596	0.907981	+	0.419012i	$0.137624\pi$
$24$	−7.52758e8	−0.804048
$25$	5.92471e8	0.485352
$26$	−6.52029e8	−0.413943
$27$	3.87420e8	0.192450
$28$	−8.55907e9	−3.35660
$29$	2.90122e9	0.905719	0.452860	−	0.891582i	$-0.350404\pi$
$29$	2.90122e9	0.905719	0.452860	+	0.891582i	$0.350404\pi$
$30$	4.72489e9	1.18332
$31$	−1.60330e9	−0.324463	−0.162231	−	0.986753i	$-0.551869\pi$
$31$	−1.60330e9	−0.324463	−0.162231	+	0.986753i	$0.551869\pi$
$32$	3.20961e9	0.528417
$33$	−4.80106e9	−0.647137
$34$	2.85364e10	3.16801
$35$	2.43361e10	2.23774
$36$	7.95884e9	0.609374
$37$	2.91197e10	1.86585	0.932924	−	0.360073i	$-0.117248\pi$
$37$	2.91197e10	1.86585	0.932924	+	0.360073i	$0.117248\pi$
$38$	3.52933e10	1.90151
$39$	3.12285e9	0.142112
$40$	4.39691e10	1.69730
$41$	−3.68274e10	−1.21081	−0.605405	−	0.795917i	$-0.706989\pi$
$41$	−3.68274e10	−1.21081	−0.605405	+	0.795917i	$0.706989\pi$
$42$	6.34166e10	1.78272
$43$	2.91441e10	0.703082	0.351541	−	0.936172i	$-0.385658\pi$
$43$	2.91441e10	0.703082	0.351541	+	0.936172i	$0.385658\pi$
$44$	−9.86289e10	−2.04909
$45$	−2.26295e10	−0.406250
$46$	−1.96237e11	−3.05391
$47$	−2.29465e10	−0.310514	−0.155257	−	0.987874i	$-0.549621\pi$
$47$	−2.29465e10	−0.310514	−0.155257	+	0.987874i	$0.549621\pi$
$48$	2.51415e10	0.296703
$49$	2.29746e11	2.37123
$50$	−9.01802e10	−0.816218
$51$	−1.36673e11	−1.08762
$52$	6.41532e10	0.449983
$53$	−1.99989e11	−1.23941	−0.619703	−	0.784836i	$-0.712747\pi$
$53$	−1.99989e11	−1.23941	−0.619703	+	0.784836i	$0.712747\pi$
$54$	−5.89694e10	−0.323644
$55$	2.80433e11	1.36607
$56$	5.90146e11	2.55704
$57$	−1.69035e11	−0.652813
$58$	−4.41595e11	−1.52315
$59$	4.21805e10	0.130189
$59$	4.21805e10	0.130189
$60$	−4.64881e11	−1.28635
$61$	4.98973e11	1.24003	0.620016	−	0.784589i	$-0.287126\pi$
$61$	4.98973e11	1.24003	0.620016	+	0.784589i	$0.287126\pi$
$62$	2.44039e11	0.545650
$63$	−3.03729e11	−0.612030
$64$	−7.71057e11	−1.40255
$65$	−1.82408e11	−0.299990
$66$	7.30770e11	1.08829
$67$	3.43120e11	0.463404	0.231702	−	0.972787i	$-0.425571\pi$
$67$	3.43120e11	0.463404	0.231702	+	0.972787i	$0.425571\pi$
$68$	−2.80770e12	−3.44383
$69$	9.39864e11	1.04845
$70$	−3.70421e12	−3.76321
$71$	1.13561e12	1.05208	0.526041	−	0.850459i	$-0.323676\pi$
$71$	1.13561e12	1.05208	0.526041	+	0.850459i	$0.323676\pi$
$72$	−5.48760e11	−0.464218
$73$	−1.48911e12	−1.15167	−0.575834	−	0.817567i	$-0.695322\pi$
$73$	−1.48911e12	−1.15167	−0.575834	+	0.817567i	$0.695322\pi$
$74$	−4.43232e12	−3.13780
$75$	4.31911e11	0.280218
$76$	−3.47250e12	−2.06707
$77$	3.76393e12	2.05803
$78$	−4.75330e11	−0.238990
$79$	2.64540e12	1.22438	0.612188	−	0.790712i	$-0.290289\pi$
$79$	2.64540e12	1.22438	0.612188	+	0.790712i	$0.290289\pi$
$80$	−1.46853e12	−0.626322
$81$	2.82430e11	0.111111
$82$	5.60551e12	2.03622
$83$	−3.22063e12	−1.08127	−0.540633	−	0.841258i	$-0.681815\pi$
$83$	−3.22063e12	−1.08127	−0.540633	+	0.841258i	$0.681815\pi$
$84$	−6.23956e12	−1.93793
$85$	7.98316e12	2.29589
$86$	−4.43604e12	−1.18237
$87$	2.11499e12	0.522917
$88$	6.80044e12	1.56099
$89$	−6.12635e12	−1.30667	−0.653336	−	0.757068i	$-0.726631\pi$
$89$	−6.12635e12	−1.30667	−0.653336	+	0.757068i	$0.726631\pi$
$90$	3.44444e12	0.683192
$91$	−2.44824e12	−0.451945
$92$	1.93078e13	3.31980
$93$	−1.16881e12	−0.187329
$94$	3.49270e12	0.522192
$95$	9.87342e12	1.37805
$96$	2.33980e12	0.305082
$97$	7.26379e11	0.0885416	0.0442708	−	0.999020i	$-0.485904\pi$
$97$	7.26379e11	0.0885416	0.0442708	+	0.999020i	$0.485904\pi$
$98$	−3.49697e13	−3.98770
$99$	−3.49997e12	−0.373625
$100$	8.87283e12	0.887283
$101$	−1.29660e13	−1.21539	−0.607697	−	0.794169i	$-0.707906\pi$
$101$	−1.29660e13	−1.21539	−0.607697	+	0.794169i	$0.707906\pi$
$102$	2.08030e13	1.82905
$103$	1.56871e13	1.29450	0.647249	−	0.762279i	$-0.275920\pi$
$103$	1.56871e13	1.29450	0.647249	+	0.762279i	$0.275920\pi$
$104$	−4.42335e12	−0.342795
$105$	1.77410e13	1.29196
$106$	3.04404e13	2.08431
$107$	2.39164e13	1.54064	0.770322	−	0.637656i	$-0.220096\pi$
$107$	2.39164e13	1.54064	0.770322	+	0.637656i	$0.220096\pi$
$108$	5.80200e12	0.351822
$109$	−1.28871e13	−0.736008	−0.368004	−	0.929824i	$-0.619959\pi$
$109$	−1.28871e13	−0.736008	−0.368004	+	0.929824i	$0.619959\pi$
$110$	−4.26848e13	−2.29732
$111$	2.12283e13	1.07725
$112$	−1.97104e13	−0.943577
$113$	−6.32178e12	−0.285647	−0.142823	−	0.989748i	$-0.545618\pi$
$113$	−6.32178e12	−0.285647	−0.142823	+	0.989748i	$0.545618\pi$
$114$	2.57288e13	1.09784
$115$	−5.48981e13	−2.21320
$116$	4.34486e13	1.65576
$117$	2.27656e12	0.0820484
$118$	−6.42031e12	−0.218939
$119$	1.07149e14	3.45885
$120$	3.20535e13	0.979934
$121$	8.85024e12	0.256360
$122$	−7.59488e13	−2.08536
$123$	−2.68472e13	−0.699062
$124$	−2.40110e13	−0.593157
$125$	2.67510e13	0.627227
$126$	4.62307e13	1.02925
$127$	−3.67988e13	−0.778234	−0.389117	−	0.921188i	$-0.627220\pi$
$127$	−3.67988e13	−0.778234	−0.389117	+	0.921188i	$0.627220\pi$
$128$	9.10698e13	1.83025
$129$	2.12461e13	0.405925
$130$	2.77643e13	0.504493
$131$	−4.29974e13	−0.743326	−0.371663	−	0.928368i	$-0.621212\pi$
$131$	−4.29974e13	−0.743326	−0.371663	+	0.928368i	$0.621212\pi$
$132$	−7.19005e13	−1.18305
$133$	1.32519e14	2.07608
$134$	−5.22264e13	−0.779307
$135$	−1.64969e13	−0.234549
$136$	1.93590e14	2.62349
$137$	5.42287e13	0.700722	0.350361	−	0.936615i	$-0.386059\pi$
$137$	5.42287e13	0.700722	0.350361	+	0.936615i	$0.386059\pi$
$138$	−1.43057e14	−1.76317
$139$	1.53326e14	1.80310	0.901548	−	0.432679i	$-0.142432\pi$
$139$	1.53326e14	1.80310	0.901548	+	0.432679i	$0.142432\pi$
$140$	3.64457e14	4.09085
$141$	−1.67280e13	−0.179275
$142$	−1.72852e14	−1.76929
$143$	−2.82119e13	−0.275898
$144$	1.83281e13	0.171302
$145$	−1.23538e14	−1.10385
$146$	2.26657e14	1.93676
$147$	1.67485e14	1.36903
$148$	4.36096e14	3.41100
$149$	9.07270e13	0.679244	0.339622	−	0.940562i	$-0.389701\pi$
$149$	9.07270e13	0.679244	0.339622	+	0.940562i	$0.389701\pi$
$150$	−6.57414e13	−0.471244
$151$	1.05410e14	0.723658	0.361829	−	0.932244i	$-0.382152\pi$
$151$	1.05410e14	0.723658	0.361829	+	0.932244i	$0.382152\pi$
$152$	2.39428e14	1.57468
$153$	−9.96346e13	−0.627937
$154$	−5.72908e14	−3.46099
$155$	6.82709e13	0.395439
$156$	4.67677e13	0.259798
$157$	5.16344e13	0.275164	0.137582	−	0.990490i	$-0.456067\pi$
$157$	5.16344e13	0.275164	0.137582	+	0.990490i	$0.456067\pi$
$158$	−4.02657e14	−2.05904
$159$	−1.45792e14	−0.715572
$160$	−1.36669e14	−0.644008
$161$	−7.36833e14	−3.33427
$162$	−4.29887e13	−0.186856
$163$	−3.75621e13	−0.156867	−0.0784334	−	0.996919i	$-0.524992\pi$
$163$	−3.75621e13	−0.156867	−0.0784334	+	0.996919i	$0.524992\pi$
$164$	−5.51526e14	−2.21351
$165$	2.04436e14	0.788699
$166$	4.90213e14	1.81837
$167$	2.16665e14	0.772916	0.386458	−	0.922307i	$-0.373698\pi$
$167$	2.16665e14	0.772916	0.386458	+	0.922307i	$0.373698\pi$
$168$	4.30216e14	1.47631
$169$	−2.84525e14	−0.939413
$170$	−1.21512e15	−3.86101
$171$	−1.23226e14	−0.376902
$172$	4.36462e14	1.28532
$173$	4.17054e14	1.18275	0.591374	−	0.806397i	$-0.298586\pi$
$173$	4.17054e14	1.18275	0.591374	+	0.806397i	$0.298586\pi$
$174$	−3.21923e14	−0.879391
$175$	−3.38609e14	−0.891151
$176$	−2.27129e14	−0.576023
$177$	3.07496e13	0.0751646
$178$	9.32493e14	2.19743
$179$	−4.23921e14	−0.963254	−0.481627	−	0.876376i	$-0.659954\pi$
$179$	−4.23921e14	−0.963254	−0.481627	+	0.876376i	$0.659954\pi$
$180$	−3.38899e14	−0.742674
$181$	3.73841e14	0.790271	0.395136	−	0.918623i	$-0.370698\pi$
$181$	3.73841e14	0.790271	0.395136	+	0.918623i	$0.370698\pi$
$182$	3.72648e14	0.760037
$183$	3.63751e14	0.715933
$184$	−1.33127e15	−2.52900
$185$	−1.23996e15	−2.27400
$186$	1.77905e14	0.315031
$187$	1.23471e15	2.11152
$188$	−3.43646e14	−0.567657
$189$	−2.21419e14	−0.353356
$190$	−1.50284e15	−2.31746
$191$	−1.83012e14	−0.272749	−0.136375	−	0.990657i	$-0.543545\pi$
$191$	−1.83012e14	−0.272749	−0.136375	+	0.990657i	$0.543545\pi$
$192$	−5.62101e14	−0.809760
$193$	1.82454e14	0.254115	0.127058	−	0.991895i	$-0.459447\pi$
$193$	1.82454e14	0.254115	0.127058	+	0.991895i	$0.459447\pi$
$194$	−1.10562e14	−0.148901
$195$	−1.32975e14	−0.173199
$196$	3.44067e15	4.33490
$197$	−3.29248e14	−0.401321	−0.200661	−	0.979661i	$-0.564309\pi$
$197$	−3.29248e14	−0.401321	−0.200661	+	0.979661i	$0.564309\pi$
$198$	5.32732e14	0.628326
$199$	1.39933e15	1.59726	0.798628	−	0.601825i	$-0.205559\pi$
$199$	1.39933e15	1.59726	0.798628	+	0.601825i	$0.205559\pi$
$200$	−6.11779e14	−0.675927
$201$	2.50134e14	0.267546
$202$	1.97356e15	2.04393
$203$	−1.65811e15	−1.66298
$204$	−2.04681e15	−1.98830
$205$	1.56816e15	1.47568
$206$	−2.38774e15	−2.17696
$207$	6.85161e14	0.605320
$208$	1.47736e14	0.126495
$209$	1.52706e15	1.26738
$210$	−2.70037e15	−2.17269
$211$	−1.16737e15	−0.910691	−0.455346	−	0.890315i	$-0.650484\pi$
$211$	−1.16737e15	−0.910691	−0.455346	+	0.890315i	$0.650484\pi$
$212$	−2.99503e15	−2.26579
$213$	8.27860e14	0.607420
$214$	−3.64033e15	−2.59090
$215$	−1.24100e15	−0.856882
$216$	−4.00046e14	−0.268016
$217$	9.16321e14	0.595743
$218$	1.96155e15	1.23775
$219$	−1.08556e15	−0.664915
$220$	4.19976e15	2.49733
$221$	−8.03116e14	−0.463691
$222$	−3.23116e15	−1.81161
$223$	3.86468e14	0.210442	0.105221	−	0.994449i	$-0.466445\pi$
$223$	3.86468e14	0.210442	0.105221	+	0.994449i	$0.466445\pi$
$224$	−1.83435e15	−0.970222
$225$	3.14863e14	0.161784
$226$	9.62240e14	0.480373
$227$	−1.09793e15	−0.532607	−0.266303	−	0.963889i	$-0.585802\pi$
$227$	−1.09793e15	−0.532607	−0.266303	+	0.963889i	$0.585802\pi$
$228$	−2.53146e15	−1.19342
$229$	1.86090e15	0.852694	0.426347	−	0.904560i	$-0.359800\pi$
$229$	1.86090e15	0.852694	0.426347	+	0.904560i	$0.359800\pi$
$230$	8.35605e15	3.72195
$231$	2.74390e15	1.18820
$232$	−2.99577e15	−1.26135
$233$	−3.86130e15	−1.58096	−0.790479	−	0.612489i	$-0.790168\pi$
$233$	−3.86130e15	−1.58096	−0.790479	+	0.612489i	$0.790168\pi$
$234$	−3.46515e14	−0.137981
$235$	9.77095e14	0.378439
$236$	6.31694e14	0.238001
$237$	1.92850e15	0.706894
$238$	−1.63091e16	−5.81675
$239$	1.74556e15	0.605826	0.302913	−	0.953018i	$-0.402041\pi$
$239$	1.74556e15	0.605826	0.302913	+	0.953018i	$0.402041\pi$
$240$	−1.07056e15	−0.361607
$241$	−3.64739e15	−1.19914	−0.599572	−	0.800321i	$-0.704663\pi$
$241$	−3.64739e15	−1.19914	−0.599572	+	0.800321i	$0.704663\pi$
$242$	−1.34710e15	−0.431121
$243$	2.05891e14	0.0641500
$244$	7.47260e15	2.26693
$245$	−9.78291e15	−2.88994
$246$	4.08642e15	1.17561
$247$	−9.93279e14	−0.278318
$248$	1.65556e15	0.451864
$249$	−2.34784e15	−0.624270
$250$	−4.07178e15	−1.05481
$251$	3.03593e15	0.766325	0.383163	−	0.923681i	$-0.374835\pi$
$251$	3.03593e15	0.766325	0.383163	+	0.923681i	$0.374835\pi$
$252$	−4.54864e15	−1.11887
$253$	−8.49077e15	−2.03546
$254$	5.60116e15	1.30876
$255$	5.81973e15	1.32554
$256$	−7.54525e15	−1.67538
$257$	−2.33106e15	−0.504648	−0.252324	−	0.967643i	$-0.581195\pi$
$257$	−2.33106e15	−0.504648	−0.252324	+	0.967643i	$0.581195\pi$
$258$	−3.23387e15	−0.682644
$259$	−1.66425e16	−3.42587
$260$	−2.73173e15	−0.548417
$261$	1.54183e15	0.301906
$262$	6.54465e15	1.25005
$263$	−4.83143e15	−0.900250	−0.450125	−	0.892966i	$-0.648621\pi$
$263$	−4.83143e15	−0.900250	−0.450125	+	0.892966i	$0.648621\pi$
$264$	4.95752e15	0.901237
$265$	8.51582e15	1.51053
$266$	−2.01708e16	−3.49134
$267$	−4.46611e15	−0.754407
$268$	5.13855e15	0.847158
$269$	−6.27431e14	−0.100966	−0.0504831	−	0.998725i	$-0.516076\pi$
$269$	−6.27431e14	−0.100966	−0.0504831	+	0.998725i	$0.516076\pi$
$270$	2.51100e15	0.394441
$271$	1.05451e16	1.61715	0.808576	−	0.588392i	$-0.200239\pi$
$271$	1.05451e16	1.61715	0.808576	+	0.588392i	$0.200239\pi$
$272$	−6.46574e15	−0.968100
$273$	−1.78477e15	−0.260931
$274$	−8.25416e15	−1.17840
$275$	−3.90190e15	−0.544019
$276$	1.40754e16	1.91669
$277$	1.23864e16	1.64750	0.823750	−	0.566954i	$-0.191878\pi$
$277$	1.23864e16	1.64750	0.823750	+	0.566954i	$0.191878\pi$
$278$	−2.33378e16	−3.03227
$279$	−8.52062e14	−0.108154
$280$	−2.51292e16	−3.11639
$281$	6.73357e15	0.815933	0.407966	−	0.912997i	$-0.366238\pi$
$281$	6.73357e15	0.815933	0.407966	+	0.912997i	$0.366238\pi$
$282$	2.54618e15	0.301487
$283$	−6.19163e15	−0.716462	−0.358231	−	0.933633i	$-0.616620\pi$
$283$	−6.19163e15	−0.716462	−0.358231	+	0.933633i	$0.616620\pi$
$284$	1.70069e16	1.92333
$285$	7.19772e15	0.795616
$286$	4.29415e15	0.463978
$287$	2.10476e16	2.22316
$288$	1.70572e15	0.176139
$289$	2.52442e16	2.54874
$290$	1.88037e16	1.85634
$291$	5.29531e14	0.0511195
$292$	−2.23008e16	−2.10539
$293$	−1.57340e16	−1.45278	−0.726390	−	0.687283i	$-0.758803\pi$
$293$	−1.57340e16	−1.45278	−0.726390	+	0.687283i	$0.758803\pi$
$294$	−2.54929e16	−2.30230
$295$	−1.79611e15	−0.158668
$296$	−3.00687e16	−2.59848
$297$	−2.55148e15	−0.215712
$298$	−1.38096e16	−1.14229
$299$	5.52282e15	0.446990
$300$	6.46829e15	0.512273
$301$	−1.66565e16	−1.29092
$302$	−1.60446e16	−1.21698
$303$	−9.45221e15	−0.701708
$304$	−7.99670e15	−0.581076
$305$	−2.12470e16	−1.51129
$306$	1.51654e16	1.05600
$307$	−2.54581e16	−1.73551	−0.867753	−	0.496996i	$-0.834436\pi$
$307$	−2.54581e16	−1.73551	−0.867753	+	0.496996i	$0.834436\pi$
$308$	5.63684e16	3.76232
$309$	1.14359e16	0.747378
$310$	−1.03915e16	−0.665011
$311$	−1.31612e16	−0.824806	−0.412403	−	0.911002i	$-0.635310\pi$
$311$	−1.31612e16	−0.824806	−0.412403	+	0.911002i	$0.635310\pi$
$312$	−3.22462e15	−0.197913
$313$	8.71316e15	0.523766	0.261883	−	0.965100i	$-0.415656\pi$
$313$	8.71316e15	0.523766	0.261883	+	0.965100i	$0.415656\pi$
$314$	−7.85929e15	−0.462744
$315$	1.29332e16	0.745912
$316$	3.96174e16	2.23831
$317$	−2.88553e16	−1.59713	−0.798564	−	0.601910i	$-0.794407\pi$
$317$	−2.88553e16	−1.59713	−0.798564	+	0.601910i	$0.794407\pi$
$318$	2.21911e16	1.20338
$319$	−1.91069e16	−1.01520
$320$	3.28327e16	1.70935
$321$	1.74351e16	0.889491
$322$	1.12154e17	5.60725
$323$	4.34713e16	2.13003
$324$	4.22966e15	0.203125
$325$	2.53799e15	0.119467
$326$	5.71734e15	0.263803
$327$	−9.39469e15	−0.424935
$328$	3.80276e16	1.68624
$329$	1.31144e16	0.570132
$330$	−3.11172e16	−1.32636
$331$	−1.40302e15	−0.0586385	−0.0293193	−	0.999570i	$-0.509334\pi$
$331$	−1.40302e15	−0.0586385	−0.0293193	+	0.999570i	$0.509334\pi$
$332$	−4.82320e16	−1.97669
$333$	1.54754e16	0.621949
$334$	−3.29787e16	−1.29981
$335$	−1.46105e16	−0.564773
$336$	−1.43689e16	−0.544774
$337$	1.32900e16	0.494233	0.247117	−	0.968986i	$-0.420517\pi$
$337$	1.32900e16	0.494233	0.247117	+	0.968986i	$0.420517\pi$
$338$	4.33076e16	1.57981
$339$	−4.60858e15	−0.164918
$340$	1.19556e17	4.19717
$341$	1.05591e16	0.363682
$342$	1.87563e16	0.633836
$343$	−7.59306e16	−2.51771
$344$	−3.00939e16	−0.979149
$345$	−4.00207e16	−1.27779
$346$	−6.34799e16	−1.98903
$347$	−1.46139e16	−0.449391	−0.224696	−	0.974429i	$-0.572139\pi$
$347$	−1.46139e16	−0.449391	−0.224696	+	0.974429i	$0.572139\pi$
$348$	3.16740e16	0.955956
$349$	2.46782e16	0.731053	0.365526	−	0.930801i	$-0.380889\pi$
$349$	2.46782e16	0.731053	0.365526	+	0.930801i	$0.380889\pi$
$350$	5.15398e16	1.49865
$351$	1.65961e15	0.0473707
$352$	−2.11379e16	−0.592289
$353$	6.52067e16	1.79373	0.896864	−	0.442307i	$-0.145840\pi$
$353$	6.52067e16	1.79373	0.896864	+	0.442307i	$0.145840\pi$
$354$	−4.68041e15	−0.126404
$355$	−4.83559e16	−1.28223
$356$	−9.17480e16	−2.38875
$357$	7.81114e16	1.99697
$358$	6.45252e16	1.61991
$359$	−2.21586e16	−0.546296	−0.273148	−	0.961972i	$-0.588065\pi$
$359$	−2.21586e16	−0.546296	−0.273148	+	0.961972i	$0.588065\pi$
$360$	2.33670e16	0.565765
$361$	1.17115e16	0.278495
$362$	−5.69024e16	−1.32900
$363$	6.45183e15	0.148010
$364$	−3.66648e16	−0.826210
$365$	6.34082e16	1.40359
$366$	−5.53667e16	−1.20399
$367$	−2.84583e16	−0.607967	−0.303983	−	0.952677i	$-0.598317\pi$
$367$	−2.84583e16	−0.607967	−0.303983	+	0.952677i	$0.598317\pi$
$368$	4.44632e16	0.933232
$369$	−1.95716e16	−0.403604
$370$	1.88735e17	3.82420
$371$	1.14298e17	2.27566
$372$	−1.75040e16	−0.342460
$373$	−7.18716e16	−1.38181	−0.690907	−	0.722943i	$-0.742789\pi$
$373$	−7.18716e16	−1.38181	−0.690907	+	0.722943i	$0.742789\pi$
$374$	−1.87935e17	−3.55094
$375$	1.95015e16	0.362130
$376$	2.36943e16	0.432438
$377$	1.24281e16	0.222938
$378$	3.37022e16	0.594239
$379$	−4.67445e16	−0.810170	−0.405085	−	0.914279i	$-0.632758\pi$
$379$	−4.67445e16	−0.810170	−0.405085	+	0.914279i	$0.632758\pi$
$380$	1.47864e17	2.51924
$381$	−2.68264e16	−0.449313
$382$	2.78564e16	0.458683
$383$	−7.65345e16	−1.23898	−0.619491	−	0.785004i	$-0.712661\pi$
$383$	−7.65345e16	−1.23898	−0.619491	+	0.785004i	$0.712661\pi$
$384$	6.63899e16	1.05669
$385$	−1.60273e17	−2.50822
$386$	−2.77713e16	−0.427346
$387$	1.54884e16	0.234361
$388$	1.08782e16	0.161865
$389$	2.48310e16	0.363347	0.181674	−	0.983359i	$-0.441849\pi$
$389$	2.48310e16	0.363347	0.181674	+	0.983359i	$0.441849\pi$
$390$	2.02402e16	0.291269
$391$	−2.41709e17	−3.42093
$392$	−2.37234e17	−3.30230
$393$	−3.13451e16	−0.429159
$394$	5.01149e16	0.674903
$395$	−1.12645e17	−1.49221
$396$	−5.24155e16	−0.683032
$397$	3.49176e16	0.447617	0.223808	−	0.974633i	$-0.428151\pi$
$397$	3.49176e16	0.447617	0.223808	+	0.974633i	$0.428151\pi$
$398$	−2.12992e17	−2.68611
$399$	9.66066e16	1.19862
$400$	2.04329e16	0.249425
$401$	7.57544e15	0.0909849	0.0454925	−	0.998965i	$-0.485514\pi$
$401$	7.57544e15	0.0909849	0.0454925	+	0.998965i	$0.485514\pi$
$402$	−3.80730e16	−0.449933
$403$	−6.86814e15	−0.0798650
$404$	−1.94178e17	−2.22189
$405$	−1.20262e16	−0.135417
$406$	2.52381e17	2.79664
$407$	−1.91777e17	−2.09138
$408$	1.41127e17	1.51467
$409$	1.08789e17	1.14917	0.574583	−	0.818446i	$-0.305164\pi$
$409$	1.08789e17	1.14917	0.574583	+	0.818446i	$0.305164\pi$
$410$	−2.38690e17	−2.48165
$411$	3.95327e16	0.404562
$412$	2.34930e17	2.36650
$413$	−2.41070e16	−0.239039
$414$	−1.04289e17	−1.01797
$415$	1.37139e17	1.31779
$416$	1.37491e16	0.130067
$417$	1.11774e17	1.04102
$418$	−2.32435e17	−2.13135
$419$	−1.04836e17	−0.946496	−0.473248	−	0.880929i	$-0.656919\pi$
$419$	−1.04836e17	−0.946496	−0.473248	+	0.880929i	$0.656919\pi$
$420$	2.65689e17	2.36186
$421$	−4.22342e16	−0.369684	−0.184842	−	0.982768i	$-0.559177\pi$
$421$	−4.22342e16	−0.369684	−0.184842	+	0.982768i	$0.559177\pi$
$422$	1.77685e17	1.53151
$423$	−1.21947e16	−0.103505
$424$	2.06507e17	1.72606
$425$	−1.11077e17	−0.914312
$426$	−1.26009e17	−1.02150
$427$	−2.85173e17	−2.27681
$428$	3.58172e17	2.81648
$429$	−2.05665e16	−0.159290
$430$	1.88893e17	1.44102
$431$	2.02917e15	0.0152481	0.00762406	−	0.999971i	$-0.497573\pi$
$431$	2.02917e15	0.0152481	0.00762406	+	0.999971i	$0.497573\pi$
$432$	1.33612e16	0.0989011
$433$	7.28398e16	0.531126	0.265563	−	0.964094i	$-0.414442\pi$
$433$	7.28398e16	0.531126	0.265563	+	0.964094i	$0.414442\pi$
$434$	−1.39473e17	−1.00186
$435$	−9.00591e16	−0.637306
$436$	−1.92997e17	−1.34551
$437$	−2.98941e17	−2.05332
$438$	1.65233e17	1.11819
$439$	1.64714e16	0.109827	0.0549136	−	0.998491i	$-0.482512\pi$
$439$	1.64714e16	0.109827	0.0549136	+	0.998491i	$0.482512\pi$
$440$	−2.89572e17	−1.90246
$441$	1.22097e17	0.790410
$442$	1.22243e17	0.779790
$443$	1.07069e17	0.673039	0.336520	−	0.941676i	$-0.390750\pi$
$443$	1.07069e17	0.673039	0.336520	+	0.941676i	$0.390750\pi$
$444$	3.17914e17	1.96934
$445$	2.60868e17	1.59251
$446$	−5.88244e16	−0.353900
$447$	6.61400e16	0.392162
$448$	4.40675e17	2.57520
$449$	1.87302e17	1.07880	0.539399	−	0.842050i	$-0.318651\pi$
$449$	1.87302e17	1.07880	0.539399	+	0.842050i	$0.318651\pi$
$450$	−4.79254e16	−0.272073
$451$	2.42539e17	1.35717
$452$	−9.46748e16	−0.522197
$453$	7.68442e16	0.417804
$454$	1.67116e17	0.895686
$455$	1.04250e17	0.550808
$456$	1.74543e17	0.909142
$457$	2.59517e16	0.133263	0.0666315	−	0.997778i	$-0.478775\pi$
$457$	2.59517e16	0.133263	0.0666315	+	0.997778i	$0.478775\pi$
$458$	−2.83249e17	−1.43398
$459$	−7.26336e16	−0.362540
$460$	−8.22152e17	−4.04600
$461$	−3.19776e17	−1.55164	−0.775819	−	0.630956i	$-0.782663\pi$
$461$	−3.19776e17	−1.55164	−0.775819	+	0.630956i	$0.782663\pi$
$462$	−4.17650e17	−1.99820
$463$	−1.91330e17	−0.902622	−0.451311	−	0.892367i	$-0.649044\pi$
$463$	−1.91330e17	−0.902622	−0.451311	+	0.892367i	$0.649044\pi$
$464$	1.00056e17	0.465454
$465$	4.97695e16	0.228307
$466$	5.87730e17	2.65870
$467$	−1.59663e16	−0.0712271	−0.0356136	−	0.999366i	$-0.511339\pi$
$467$	−1.59663e16	−0.0712271	−0.0356136	+	0.999366i	$0.511339\pi$
$468$	3.40936e16	0.149994
$469$	−1.96100e17	−0.850852
$470$	−1.48724e17	−0.636421
$471$	3.76415e16	0.158866
$472$	−4.35552e16	−0.181308
$473$	−1.91938e17	−0.788067
$474$	−2.93537e17	−1.18879
$475$	−1.37377e17	−0.548790
$476$	1.60465e18	6.32319
$477$	−1.06283e17	−0.413136
$478$	−2.65692e17	−1.01882
$479$	3.47734e17	1.31542	0.657712	−	0.753269i	$-0.271524\pi$
$479$	3.47734e17	1.31542	0.657712	+	0.753269i	$0.271524\pi$
$480$	−9.96320e16	−0.371818
$481$	1.24741e17	0.459270
$482$	5.55170e17	2.01660
$483$	−5.37151e17	−1.92504
$484$	1.32541e17	0.468657
$485$	−3.09302e16	−0.107910
$486$	−3.13387e16	−0.107881
$487$	−2.06116e17	−0.700120	−0.350060	−	0.936727i	$-0.613839\pi$
$487$	−2.06116e17	−0.700120	−0.350060	+	0.936727i	$0.613839\pi$
$488$	−5.15234e17	−1.72693
$489$	−2.73828e16	−0.0905671
$490$	1.48906e18	4.86001
$491$	−1.42640e17	−0.459423	−0.229712	−	0.973259i	$-0.573778\pi$
$491$	−1.42640e17	−0.459423	−0.229712	+	0.973259i	$0.573778\pi$
$492$	−4.02063e17	−1.27797
$493$	−5.43921e17	−1.70620
$494$	1.51187e17	0.468047
$495$	1.49034e17	0.455355
$496$	−5.52941e16	−0.166743
$497$	−6.49024e17	−1.93172
$498$	3.57365e17	1.04984
$499$	3.53103e17	1.02388	0.511939	−	0.859022i	$-0.328927\pi$
$499$	3.53103e17	1.02388	0.511939	+	0.859022i	$0.328927\pi$
$500$	4.00622e17	1.14665
$501$	1.57949e17	0.446243
$502$	−4.62100e17	−1.28873
$503$	4.75636e16	0.130943	0.0654716	−	0.997854i	$-0.479145\pi$
$503$	4.75636e16	0.130943	0.0654716	+	0.997854i	$0.479145\pi$
$504$	3.13628e17	0.852346
$505$	5.52110e17	1.48126
$506$	1.29238e18	3.42305
$507$	−2.07418e17	−0.542370
$508$	−5.51098e17	−1.42271
$509$	7.86117e15	0.0200365	0.0100182	−	0.999950i	$-0.496811\pi$
$509$	7.86117e15	0.0200365	0.0100182	+	0.999950i	$0.496811\pi$
$510$	−8.85822e17	−2.22916
$511$	8.51054e17	2.11457
$512$	4.02421e17	0.987248
$513$	−8.98319e16	−0.217604
$514$	3.54811e17	0.848667
$515$	−6.67979e17	−1.57767
$516$	3.18181e17	0.742080
$517$	1.51122e17	0.348047
$518$	2.53316e18	5.76129
$519$	3.04032e17	0.682860
$520$	1.88352e17	0.417781
$521$	−5.55593e17	−1.21706	−0.608530	−	0.793531i	$-0.708240\pi$
$521$	−5.55593e17	−1.21706	−0.608530	+	0.793531i	$0.708240\pi$
$522$	−2.34682e17	−0.507717
$523$	−2.93225e17	−0.626528	−0.313264	−	0.949666i	$-0.601422\pi$
$523$	−2.93225e17	−0.626528	−0.313264	+	0.949666i	$0.601422\pi$
$524$	−6.43928e17	−1.35889
$525$	−2.46846e17	−0.514506
$526$	7.35393e17	1.51395
$527$	3.00588e17	0.611227
$528$	−1.65577e17	−0.332567
$529$	1.15813e18	2.29772
$530$	−1.29620e18	−2.54026
$531$	2.24165e16	0.0433963
$532$	1.98461e18	3.79532
$533$	−1.57759e17	−0.298035
$534$	6.79787e17	1.26869
$535$	−1.01840e18	−1.87766
$536$	−3.54302e17	−0.645360
$537$	−3.09039e17	−0.556135
$538$	9.55014e16	0.169795
$539$	−1.51307e18	−2.65785
$540$	−2.47057e17	−0.428783
$541$	1.44892e16	0.0248463	0.0124231	−	0.999923i	$-0.496045\pi$
$541$	1.44892e16	0.0248463	0.0124231	+	0.999923i	$0.496045\pi$
$542$	−1.60507e18	−2.71957
$543$	2.72530e17	0.456263
$544$	−6.01737e17	−0.995438
$545$	5.48750e17	0.897011
$546$	2.71660e17	0.438808
$547$	−7.50787e17	−1.19839	−0.599196	−	0.800602i	$-0.704513\pi$
$547$	−7.50787e17	−1.19839	−0.599196	+	0.800602i	$0.704513\pi$
$548$	8.12127e17	1.28100
$549$	2.65175e17	0.413344
$550$	5.93910e17	0.914878
$551$	−6.72711e17	−1.02410
$552$	−9.70494e17	−1.46012
$553$	−1.51190e18	−2.24807
$554$	−1.88533e18	−2.77060
$555$	−9.03930e17	−1.31290
$556$	2.29620e18	3.29628
$557$	−1.31115e17	−0.186034	−0.0930172	−	0.995665i	$-0.529651\pi$
$557$	−1.31115e17	−0.186034	−0.0930172	+	0.995665i	$0.529651\pi$
$558$	1.29693e17	0.181883
$559$	1.24846e17	0.173060
$560$	8.39294e17	1.14998
$561$	9.00103e17	1.21908
$562$	−1.02492e18	−1.37216
$563$	2.43724e17	0.322548	0.161274	−	0.986910i	$-0.448440\pi$
$563$	2.43724e17	0.322548	0.161274	+	0.986910i	$0.448440\pi$
$564$	−2.50518e17	−0.327737
$565$	2.69190e17	0.348132
$566$	9.42430e17	1.20488
$567$	−1.61414e17	−0.204010
$568$	−1.17262e18	−1.46519
$569$	−6.65466e17	−0.822046	−0.411023	−	0.911625i	$-0.634828\pi$
$569$	−6.65466e17	−0.822046	−0.411023	+	0.911625i	$0.634828\pi$
$570$	−1.09557e18	−1.33799
$571$	1.37419e18	1.65925	0.829626	−	0.558320i	$-0.188554\pi$
$571$	1.37419e18	1.65925	0.829626	+	0.558320i	$0.188554\pi$
$572$	−4.22501e17	−0.504375
$573$	−1.33416e17	−0.157472
$574$	−3.20366e18	−3.73869
$575$	7.63844e17	0.881381
$576$	−4.09771e17	−0.467515
$577$	8.93806e17	1.00833	0.504163	−	0.863609i	$-0.331801\pi$
$577$	8.93806e17	1.00833	0.504163	+	0.863609i	$0.331801\pi$
$578$	−3.84243e18	−4.28622
$579$	1.33009e17	0.146713
$580$	−1.85010e18	−2.01796
$581$	1.84065e18	1.98530
$582$	−8.06000e16	−0.0859678
$583$	1.31709e18	1.38922
$584$	1.53764e18	1.60387
$585$	−9.69389e16	−0.0999965
$586$	2.39488e18	2.44314
$587$	4.31503e17	0.435347	0.217674	−	0.976022i	$-0.430153\pi$
$587$	4.31503e17	0.435347	0.217674	+	0.976022i	$0.430153\pi$
$588$	2.50825e18	2.50275
$589$	3.71761e17	0.366872
$590$	2.73386e17	0.266832
$591$	−2.40022e17	−0.231703
$592$	1.00427e18	0.958869
$593$	−1.47166e17	−0.138980	−0.0694902	−	0.997583i	$-0.522137\pi$
$593$	−1.47166e17	−0.138980	−0.0694902	+	0.997583i	$0.522137\pi$
$594$	3.88361e17	0.362764
$595$	−4.56254e18	−4.21547
$596$	1.35873e18	1.24174
$597$	1.02011e18	0.922176
$598$	−8.40630e17	−0.751704
$599$	1.90569e17	0.168569	0.0842847	−	0.996442i	$-0.473139\pi$
$599$	1.90569e17	0.168569	0.0842847	+	0.996442i	$0.473139\pi$
$600$	−4.45987e17	−0.390247
$601$	1.95341e18	1.69087	0.845435	−	0.534078i	$-0.179341\pi$
$601$	1.95341e18	1.69087	0.845435	+	0.534078i	$0.179341\pi$
$602$	2.53528e18	2.17095
$603$	1.82348e17	0.154468
$604$	1.57862e18	1.32293
$605$	−3.76856e17	−0.312439
$606$	1.43872e18	1.18006
$607$	−4.76753e17	−0.386872	−0.193436	−	0.981113i	$-0.561963\pi$
$607$	−4.76753e17	−0.386872	−0.193436	+	0.981113i	$0.561963\pi$
$608$	−7.44217e17	−0.597484
$609$	−1.20876e18	−0.960124
$610$	3.23400e18	2.54154
$611$	−9.82970e16	−0.0764315
$612$	−1.49212e18	−1.14794
$613$	−5.08493e17	−0.387072	−0.193536	−	0.981093i	$-0.561996\pi$
$613$	−5.08493e17	−0.387072	−0.193536	+	0.981093i	$0.561996\pi$
$614$	3.87498e18	2.91860
$615$	1.14319e18	0.851982
$616$	−3.88659e18	−2.86612
$617$	1.48244e18	1.08174	0.540870	−	0.841106i	$-0.318095\pi$
$617$	1.48244e18	1.08174	0.540870	+	0.841106i	$0.318095\pi$
$618$	−1.74066e18	−1.25687
$619$	−1.06056e18	−0.757783	−0.378891	−	0.925441i	$-0.623695\pi$
$619$	−1.06056e18	−0.757783	−0.378891	+	0.925441i	$0.623695\pi$
$620$	1.02242e18	0.722911
$621$	4.99482e17	0.349482
$622$	2.00326e18	1.38708
$623$	3.50133e18	2.39917
$624$	1.07700e17	0.0730321
$625$	−1.86233e18	−1.24979
$626$	−1.32623e18	−0.880819
$627$	1.11323e18	0.731722
$628$	7.73275e17	0.503033
$629$	−5.45937e18	−3.51491
$630$	−1.96857e18	−1.25440
$631$	−1.24574e18	−0.785664	−0.392832	−	0.919610i	$-0.628505\pi$
$631$	−1.24574e18	−0.785664	−0.392832	+	0.919610i	$0.628505\pi$
$632$	−2.73161e18	−1.70513
$633$	−8.51010e17	−0.525788
$634$	4.39207e18	2.68589
$635$	1.56695e18	0.948472
$636$	−2.18338e18	−1.30815
$637$	9.84174e17	0.583667
$638$	2.90827e18	1.70726
$639$	6.03510e17	0.350694
$640$	−3.87788e18	−2.23061
$641$	1.82273e18	1.03788	0.518938	−	0.854812i	$-0.326328\pi$
$641$	1.82273e18	1.03788	0.518938	+	0.854812i	$0.326328\pi$
$642$	−2.65380e18	−1.49586
$643$	7.68443e17	0.428786	0.214393	−	0.976748i	$-0.431223\pi$
$643$	7.68443e17	0.428786	0.214393	+	0.976748i	$0.431223\pi$
$644$	−1.10348e19	−6.09545
$645$	−9.04687e17	−0.494721
$646$	−6.61679e18	−3.58208
$647$	7.15651e17	0.383551	0.191776	−	0.981439i	$-0.438575\pi$
$647$	7.15651e17	0.383551	0.191776	+	0.981439i	$0.438575\pi$
$648$	−2.91634e17	−0.154739
$649$	−2.77793e17	−0.145925
$650$	−3.86309e17	−0.200908
$651$	6.67998e17	0.343953
$652$	−5.62529e17	−0.286771
$653$	3.77084e18	1.90328	0.951640	−	0.307214i	$-0.0993968\pi$
$653$	3.77084e18	1.90328	0.951640	+	0.307214i	$0.0993968\pi$
$654$	1.42997e18	0.714613
$655$	1.83089e18	0.905928
$656$	−1.27009e18	−0.622242
$657$	−7.91372e17	−0.383889
$658$	−1.99615e18	−0.958791
$659$	−2.72591e18	−1.29645	−0.648227	−	0.761447i	$-0.724489\pi$
$659$	−2.72591e18	−1.29645	−0.648227	+	0.761447i	$0.724489\pi$
$660$	3.06162e18	1.44184
$661$	2.79637e18	1.30402	0.652012	−	0.758209i	$-0.273925\pi$
$661$	2.79637e18	1.30402	0.652012	+	0.758209i	$0.273925\pi$
$662$	2.13555e17	0.0986125
$663$	−5.85472e17	−0.267712
$664$	3.32559e18	1.50583
$665$	−5.64286e18	−2.53022
$666$	−2.35552e18	−1.04593
$667$	3.74040e18	1.64475
$668$	3.24477e18	1.41298
$669$	2.81735e17	0.121499
$670$	2.22387e18	0.949781
$671$	−3.28614e18	−1.38992
$672$	−1.33724e18	−0.560158
$673$	−2.50350e18	−1.03860	−0.519302	−	0.854591i	$-0.673808\pi$
$673$	−2.50350e18	−1.03860	−0.519302	+	0.854591i	$0.673808\pi$
$674$	−2.02288e18	−0.831153
$675$	2.29535e17	0.0934061
$676$	−4.26103e18	−1.71736
$677$	−3.17013e18	−1.26547	−0.632733	−	0.774370i	$-0.718067\pi$
$677$	−3.17013e18	−1.26547	−0.632733	+	0.774370i	$0.718067\pi$
$678$	7.01473e17	0.277343
$679$	−4.15140e17	−0.162570
$680$	−8.24333e18	−3.19738
$681$	−8.00391e17	−0.307501
$682$	−1.60720e18	−0.611605
$683$	2.34851e18	0.885233	0.442617	−	0.896711i	$-0.354050\pi$
$683$	2.34851e18	0.885233	0.442617	+	0.896711i	$0.354050\pi$
$684$	−1.84543e18	−0.689022
$685$	−2.30913e18	−0.854005
$686$	1.15574e19	4.23403
$687$	1.35660e18	0.492303
$688$	1.00511e18	0.361318
$689$	−8.56703e17	−0.305074
$690$	6.09156e18	2.14887
$691$	−3.90699e18	−1.36532	−0.682661	−	0.730735i	$-0.739177\pi$
$691$	−3.90699e18	−1.36532	−0.682661	+	0.730735i	$0.739177\pi$
$692$	6.24578e18	2.16221
$693$	2.00030e18	0.686009
$694$	2.22439e18	0.755742
$695$	−6.52882e18	−2.19752
$696$	−2.18392e18	−0.728242
$697$	6.90441e18	2.28094
$698$	−3.75628e18	−1.22941
$699$	−2.81489e18	−0.912767
$700$	−5.07100e18	−1.62913
$701$	4.66427e18	1.48462	0.742312	−	0.670054i	$-0.233729\pi$
$701$	4.66427e18	1.48462	0.742312	+	0.670054i	$0.233729\pi$
$702$	−2.52610e17	−0.0796634
$703$	−6.75205e18	−2.10972
$704$	5.07804e18	1.57208
$705$	7.12302e17	0.218492
$706$	−9.92513e18	−3.01652
$707$	7.41032e18	2.23157
$708$	4.60505e17	0.137410
$709$	3.06020e18	0.904792	0.452396	−	0.891817i	$-0.350569\pi$
$709$	3.06020e18	0.904792	0.452396	+	0.891817i	$0.350569\pi$
$710$	7.36026e18	2.15632
$711$	1.40587e18	0.408126
$712$	6.32600e18	1.81974
$713$	−2.06706e18	−0.589212
$714$	−1.18894e19	−3.35830
$715$	1.20130e18	0.336251
$716$	−6.34863e18	−1.76094
$717$	1.27251e18	0.349774
$718$	3.37276e18	0.918707
$719$	2.03325e18	0.548848	0.274424	−	0.961609i	$-0.411513\pi$
$719$	2.03325e18	0.548848	0.274424	+	0.961609i	$0.411513\pi$
$720$	−7.80437e17	−0.208774
$721$	−8.96550e18	−2.37681
$722$	−1.78261e18	−0.468345
$723$	−2.65895e18	−0.692327
$724$	5.59863e18	1.44471
$725$	1.71889e18	0.439593
$726$	−9.82035e17	−0.248908
$727$	−2.88259e18	−0.724118	−0.362059	−	0.932155i	$-0.617926\pi$
$727$	−2.88259e18	−0.724118	−0.362059	+	0.932155i	$0.617926\pi$
$728$	2.52803e18	0.629403
$729$	1.50095e17	0.0370370
$730$	−9.65138e18	−2.36043
$731$	−5.46395e18	−1.32447
$732$	5.44753e18	1.30881
$733$	−5.56719e18	−1.32575	−0.662873	−	0.748732i	$-0.730663\pi$
$733$	−5.56719e18	−1.32575	−0.662873	+	0.748732i	$0.730663\pi$
$734$	4.33165e18	1.02242
$735$	−7.13174e18	−1.66851
$736$	4.13799e18	0.959585
$737$	−2.25972e18	−0.519418
$738$	2.97900e18	0.678741
$739$	2.39026e18	0.539829	0.269915	−	0.962884i	$-0.413004\pi$
$739$	2.39026e18	0.539829	0.269915	+	0.962884i	$0.413004\pi$
$740$	−1.85696e19	−4.15715
$741$	−7.24100e17	−0.160687
$742$	−1.73973e19	−3.82699
$743$	−2.73176e18	−0.595683	−0.297841	−	0.954615i	$-0.596267\pi$
$743$	−2.73176e18	−0.595683	−0.297841	+	0.954615i	$0.596267\pi$
$744$	1.20690e18	0.260884
$745$	−3.86328e18	−0.827829
$746$	1.09396e19	2.32380
$747$	−1.71157e18	−0.360422
$748$	1.84910e19	3.86011
$749$	−1.36687e19	−2.82876
$750$	−2.96832e18	−0.608994
$751$	−5.28293e18	−1.07452	−0.537261	−	0.843416i	$-0.680541\pi$
$751$	−5.28293e18	−1.07452	−0.537261	+	0.843416i	$0.680541\pi$
$752$	−7.91371e17	−0.159575
$753$	2.21320e18	0.442438
$754$	−1.89168e18	−0.374916
$755$	−4.48852e18	−0.881959
$756$	−3.31596e18	−0.645977
$757$	−3.79811e18	−0.733575	−0.366788	−	0.930305i	$-0.619542\pi$
$757$	−3.79811e18	−0.733575	−0.366788	+	0.930305i	$0.619542\pi$
$758$	7.11500e18	1.36246
$759$	−6.18977e18	−1.17518
$760$	−1.01952e19	−1.91914
$761$	3.86359e18	0.721092	0.360546	−	0.932741i	$-0.382590\pi$
$761$	3.86359e18	0.721092	0.360546	+	0.932741i	$0.382590\pi$
$762$	4.08325e18	0.755611
$763$	7.36523e18	1.35138
$764$	−2.74079e18	−0.498618
$765$	4.24258e18	0.765298
$766$	1.16493e19	2.08360
$767$	1.80691e17	0.0320454
$768$	−5.50049e18	−0.967283
$769$	−3.11599e18	−0.543345	−0.271672	−	0.962390i	$-0.587577\pi$
$769$	−3.11599e18	−0.543345	−0.271672	+	0.962390i	$0.587577\pi$
$770$	2.43952e19	4.21808
$771$	−1.69934e18	−0.291359
$772$	2.73242e18	0.464553
$773$	−4.00105e18	−0.674540	−0.337270	−	0.941408i	$-0.609503\pi$
$773$	−4.00105e18	−0.674540	−0.337270	+	0.941408i	$0.609503\pi$
$774$	−2.35749e18	−0.394125
$775$	−9.49911e17	−0.157479
$776$	−7.50052e17	−0.123308
$777$	−1.21324e19	−1.97793
$778$	−3.77953e18	−0.611042
$779$	8.53924e18	1.36907
$780$	−1.99143e18	−0.316629
$781$	−7.47892e18	−1.17925
$782$	3.67906e19	5.75298
$783$	1.12399e18	0.174306
$784$	7.92340e18	1.21859
$785$	−2.19866e18	−0.335356
$786$	4.77105e18	0.721718
$787$	1.67609e18	0.251456	0.125728	−	0.992065i	$-0.459873\pi$
$787$	1.67609e18	0.251456	0.125728	+	0.992065i	$0.459873\pi$
$788$	−4.93080e18	−0.733664
$789$	−3.52211e18	−0.519759
$790$	1.71457e19	2.50945
$791$	3.61302e18	0.524474
$792$	3.61403e18	0.520330
$793$	2.13747e18	0.305228
$794$	−5.31482e18	−0.752758
$795$	6.20804e18	0.872103
$796$	2.09563e19	2.91998
$797$	−5.73881e18	−0.793127	−0.396563	−	0.918007i	$-0.629797\pi$
$797$	−5.73881e18	−0.793127	−0.396563	+	0.918007i	$0.629797\pi$
$798$	−1.47045e19	−2.01573
$799$	4.30202e18	0.584949
$800$	1.90160e18	0.256468
$801$	−3.25579e18	−0.435557
$802$	−1.15306e18	−0.153010
$803$	9.80698e18	1.29087
$804$	3.74600e18	0.489107
$805$	3.13754e19	4.06364
$806$	1.04540e18	0.134309
$807$	−4.57397e17	−0.0582929
$808$	1.33885e19	1.69262
$809$	1.49923e19	1.88020	0.940100	−	0.340900i	$-0.110732\pi$
$809$	1.49923e19	1.88020	0.940100	+	0.340900i	$0.110732\pi$
$810$	1.83052e18	0.227731
$811$	1.98826e18	0.245379	0.122690	−	0.992445i	$-0.460848\pi$
$811$	1.98826e18	0.245379	0.122690	+	0.992445i	$0.460848\pi$
$812$	−2.48317e19	−3.04013
$813$	7.68739e18	0.933663
$814$	2.91905e19	3.51708
$815$	1.59945e18	0.191181
$816$	−4.71352e18	−0.558933
$817$	−6.75770e18	−0.794979
$818$	−1.65588e19	−1.93255
$819$	−1.30110e18	−0.150648
$820$	2.34847e19	2.69771
$821$	1.39607e19	1.59103	0.795514	−	0.605936i	$-0.207201\pi$
$821$	1.39607e19	1.59103	0.795514	+	0.605936i	$0.207201\pi$
$822$	−6.01729e18	−0.680352
$823$	9.75233e18	1.09398	0.546990	−	0.837139i	$-0.315773\pi$
$823$	9.75233e18	1.09398	0.546990	+	0.837139i	$0.315773\pi$
$824$	−1.61983e19	−1.80278
$825$	−2.84449e18	−0.314090
$826$	3.66934e18	0.401992
$827$	−7.70194e18	−0.837171	−0.418585	−	0.908177i	$-0.637474\pi$
$827$	−7.70194e18	−0.837171	−0.418585	+	0.908177i	$0.637474\pi$
$828$	1.02609e19	1.10660
$829$	2.84102e18	0.303997	0.151999	−	0.988381i	$-0.451429\pi$
$829$	2.84102e18	0.303997	0.151999	+	0.988381i	$0.451429\pi$
$830$	−2.08739e19	−2.21614
$831$	9.02966e18	0.951184
$832$	−3.30301e18	−0.345230
$833$	−4.30729e19	−4.46695
$834$	−1.70132e19	−1.75068
$835$	−9.22590e18	−0.941991
$836$	2.28693e19	2.31692
$837$	−6.21153e17	−0.0624429
$838$	1.59571e19	1.59172
$839$	1.30494e19	1.29163	0.645817	−	0.763493i	$-0.276517\pi$
$839$	1.30494e19	1.29163	0.645817	+	0.763493i	$0.276517\pi$
$840$	−1.83192e19	−1.79925
$841$	−1.84356e18	−0.179673
$842$	6.42848e18	0.621698
$843$	4.90877e18	0.471079
$844$	−1.74824e19	−1.66485
$845$	1.21155e19	1.14491
$846$	1.85616e18	0.174064
$847$	−5.05809e18	−0.470700
$848$	−6.89715e18	−0.636938
$849$	−4.51370e18	−0.413650
$850$	1.69070e19	1.53760
$851$	3.75427e19	3.38831
$852$	1.23980e19	1.11044
$853$	1.54188e19	1.37051	0.685254	−	0.728304i	$-0.259691\pi$
$853$	1.54188e19	1.37051	0.685254	+	0.728304i	$0.259691\pi$
$854$	4.34063e19	3.82892
$855$	5.24714e18	0.459349
$856$	−2.46959e19	−2.14558
$857$	−7.58947e18	−0.654389	−0.327195	−	0.944957i	$-0.606103\pi$
$857$	−7.58947e18	−0.654389	−0.327195	+	0.944957i	$0.606103\pi$
$858$	3.13043e18	0.267878
$859$	2.10137e18	0.178463	0.0892313	−	0.996011i	$-0.471559\pi$
$859$	2.10137e18	0.178463	0.0892313	+	0.996011i	$0.471559\pi$
$860$	−1.85851e19	−1.56648
$861$	1.53437e19	1.28354
$862$	−3.08860e17	−0.0256428
$863$	1.95772e19	1.61317	0.806584	−	0.591119i	$-0.201314\pi$
$863$	1.95772e19	1.61317	0.806584	+	0.591119i	$0.201314\pi$
$864$	1.24347e18	0.101694
$865$	−1.77587e19	−1.44148
$866$	−1.10870e19	−0.893195
$867$	1.84030e19	1.47152
$868$	1.37228e19	1.08909
$869$	−1.74221e19	−1.37237
$870$	1.37079e19	1.07176
$871$	1.46984e18	0.114065
$872$	1.33071e19	1.02500
$873$	3.86028e17	0.0295139
$874$	4.55019e19	3.45307
$875$	−1.52887e19	−1.15165
$876$	−1.62573e19	−1.21555
$877$	−1.64212e18	−0.121873	−0.0609367	−	0.998142i	$-0.519409\pi$
$877$	−1.64212e18	−0.121873	−0.0609367	+	0.998142i	$0.519409\pi$
$878$	−2.50711e18	−0.184697
$879$	−1.14701e19	−0.838762
$880$	9.67147e18	0.702029
$881$	−1.55048e19	−1.11718	−0.558590	−	0.829444i	$-0.688657\pi$
$881$	−1.55048e19	−1.11718	−0.558590	+	0.829444i	$0.688657\pi$
$882$	−1.85844e19	−1.32923
$883$	1.93639e19	1.37483	0.687414	−	0.726266i	$-0.258746\pi$
$883$	1.93639e19	1.37483	0.687414	+	0.726266i	$0.258746\pi$
$884$	−1.20274e19	−0.847683
$885$	−1.30936e18	−0.0916069
$886$	−1.62970e19	−1.13185
$887$	−3.71331e18	−0.256011	−0.128005	−	0.991773i	$-0.540857\pi$
$887$	−3.71331e18	−0.256011	−0.128005	+	0.991773i	$0.540857\pi$
$888$	−2.19201e19	−1.50023
$889$	2.10313e19	1.42891
$890$	−3.97068e19	−2.67812
$891$	−1.86003e18	−0.124542
$892$	5.78773e18	0.384713
$893$	5.32065e18	0.351100
$894$	−1.00672e19	−0.659499
$895$	1.80512e19	1.17397
$896$	−5.20482e19	−3.36050
$897$	4.02613e18	0.258070
$898$	−2.85092e19	−1.81422
$899$	−4.65154e18	−0.293872
$900$	4.71538e18	0.295761
$901$	3.74940e19	2.33481
$902$	−3.69169e19	−2.28235
$903$	−1.21426e19	−0.745315
$904$	6.52780e18	0.397807
$905$	−1.59187e19	−0.963143
$906$	−1.16965e19	−0.702622
$907$	4.46231e18	0.266142	0.133071	−	0.991107i	$-0.457516\pi$
$907$	4.46231e18	0.266142	0.133071	+	0.991107i	$0.457516\pi$
$908$	−1.64426e19	−0.973670
$909$	−6.89066e18	−0.405131
$910$	−1.58679e19	−0.926295
$911$	2.68282e19	1.55497	0.777486	−	0.628900i	$-0.216495\pi$
$911$	2.68282e19	1.55497	0.777486	+	0.628900i	$0.216495\pi$
$912$	−5.82960e18	−0.335484
$913$	2.12105e19	1.21196
$914$	−3.95011e18	−0.224109
$915$	−1.54890e19	−0.872544
$916$	2.78688e19	1.55883
$917$	2.45739e19	1.36481
$918$	1.10556e19	0.609683
$919$	−3.80892e17	−0.0208570	−0.0104285	−	0.999946i	$-0.503320\pi$
$919$	−3.80892e17	−0.0208570	−0.0104285	+	0.999946i	$0.503320\pi$
$920$	5.66872e19	3.08222
$921$	−1.85589e19	−1.00199
$922$	4.86732e19	2.60939
$923$	4.86466e18	0.258965
$924$	4.10926e19	2.17218
$925$	1.72526e19	0.905594
$926$	2.91223e19	1.51794
$927$	8.33678e18	0.431499
$928$	9.31177e18	0.478597
$929$	−1.39725e19	−0.713133	−0.356567	−	0.934270i	$-0.616053\pi$
$929$	−1.39725e19	−0.713133	−0.356567	+	0.934270i	$0.616053\pi$
$930$	−7.57543e18	−0.383944
$931$	−5.32717e19	−2.68116
$932$	−5.78267e19	−2.89018
$933$	−9.59449e18	−0.476202
$934$	2.43024e18	0.119783
$935$	−5.25756e19	−2.57341
$936$	−2.35075e18	−0.114265
$937$	5.23457e18	0.252682	0.126341	−	0.991987i	$-0.459677\pi$
$937$	5.23457e18	0.252682	0.126341	+	0.991987i	$0.459677\pi$
$938$	2.98484e19	1.43088
$939$	6.35190e18	0.302397
$940$	1.46329e19	0.691832
$941$	3.00658e19	1.41169	0.705845	−	0.708366i	$-0.250567\pi$
$941$	3.00658e19	1.41169	0.705845	+	0.708366i	$0.250567\pi$
$942$	−5.72942e18	−0.267165
$943$	−4.74798e19	−2.19878
$944$	1.45471e18	0.0669048
$945$	9.42831e18	0.430653
$946$	2.92149e19	1.32529
$947$	1.61344e19	0.726906	0.363453	−	0.931613i	$-0.381598\pi$
$947$	1.61344e19	0.726906	0.363453	+	0.931613i	$0.381598\pi$
$948$	2.88811e19	1.29229
$949$	−6.37895e18	−0.283477
$950$	2.09102e19	0.922902
$951$	−2.10355e19	−0.922102
$952$	−1.10641e20	−4.81697
$953$	−7.86102e17	−0.0339919	−0.0169959	−	0.999856i	$-0.505410\pi$
$953$	−7.86102e17	−0.0339919	−0.0169959	+	0.999856i	$0.505410\pi$
$954$	1.61773e19	0.694771
$955$	7.79292e18	0.332413
$956$	2.61414e19	1.10752
$957$	−1.39289e19	−0.586125
$958$	−5.29286e19	−2.21215
$959$	−3.09928e19	−1.28659
$960$	2.39350e19	0.986895
$961$	−2.18470e19	−0.894724
$962$	−1.89869e19	−0.772355
$963$	1.27102e19	0.513548
$964$	−5.46232e19	−2.19218
$965$	−7.76914e18	−0.309703
$966$	8.17599e19	3.23735
$967$	3.74423e17	0.0147262	0.00736309	−	0.999973i	$-0.497656\pi$
$967$	3.74423e17	0.0147262	0.00736309	+	0.999973i	$0.497656\pi$
$968$	−9.13867e18	−0.357020
$969$	3.16906e19	1.22978
$970$	4.70790e18	0.181473
$971$	−2.13260e19	−0.816553	−0.408277	−	0.912858i	$-0.633870\pi$
$971$	−2.13260e19	−0.816553	−0.408277	+	0.912858i	$0.633870\pi$
$972$	3.08342e18	0.117274
$973$	−8.76287e19	−3.31065
$974$	3.13729e19	1.17739
$975$	1.85020e18	0.0689744
$976$	1.72084e19	0.637259
$977$	1.93222e19	0.710789	0.355395	−	0.934716i	$-0.384346\pi$
$977$	1.93222e19	0.710789	0.355395	+	0.934716i	$0.384346\pi$
$978$	4.16794e18	0.152307
$979$	4.03470e19	1.46462
$980$	−1.46509e20	−5.28316
$981$	−6.84873e18	−0.245336
$982$	2.17113e19	0.772613
$983$	3.48169e18	0.123081	0.0615407	−	0.998105i	$-0.480399\pi$
$983$	3.48169e18	0.123081	0.0615407	+	0.998105i	$0.480399\pi$
$984$	2.77221e19	0.973550
$985$	1.40198e19	0.489111
$986$	8.27904e19	2.86933
$987$	9.56040e18	0.329166
$988$	−1.48753e19	−0.508799
$989$	3.75741e19	1.27677
$990$	−2.26845e19	−0.765772
$991$	9.31452e18	0.312379	0.156189	−	0.987727i	$-0.450079\pi$
$991$	9.31452e18	0.312379	0.156189	+	0.987727i	$0.450079\pi$
$992$	−5.14597e18	−0.171452
$993$	−1.02280e18	−0.0338550
$994$	9.87881e19	3.24858
$995$	−5.95853e19	−1.94666
$996$	−3.51611e19	−1.14124
$997$	−6.79851e18	−0.219227	−0.109614	−	0.993974i	$-0.534961\pi$
$997$	−6.79851e18	−0.219227	−0.109614	+	0.993974i	$0.534961\pi$
$998$	−5.37459e19	−1.72186
$999$	1.12816e19	0.359083

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.a.1.4	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.a.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-152.210 q^{2} +729.000 q^{3} +14976.0 q^{4} -42581.4 q^{5} -110961. q^{6} -571520. q^{7} -1.03259e6 q^{8} +531441. q^{9} +O(q^{10})\)	\(q-152.210 q^{2} +729.000 q^{3} +14976.0 q^{4} -42581.4 q^{5} -110961. q^{6} -571520. q^{7} -1.03259e6 q^{8} +531441. q^{9} +6.48132e6 q^{10} -6.58581e6 q^{11} +1.09175e7 q^{12} +4.28374e6 q^{13} +8.69912e7 q^{14} -3.10418e7 q^{15} +3.44876e7 q^{16} -1.87480e8 q^{17} -8.08908e7 q^{18} -2.31872e8 q^{19} -6.37697e8 q^{20} -4.16638e8 q^{21} +1.00243e9 q^{22} +1.28925e9 q^{23} -7.52758e8 q^{24} +5.92471e8 q^{25} -6.52029e8 q^{26} +3.87420e8 q^{27} -8.55907e9 q^{28} +2.90122e9 q^{29} +4.72489e9 q^{30} -1.60330e9 q^{31} +3.20961e9 q^{32} -4.80106e9 q^{33} +2.85364e10 q^{34} +2.43361e10 q^{35} +7.95884e9 q^{36} +2.91197e10 q^{37} +3.52933e10 q^{38} +3.12285e9 q^{39} +4.39691e10 q^{40} -3.68274e10 q^{41} +6.34166e10 q^{42} +2.91441e10 q^{43} -9.86289e10 q^{44} -2.26295e10 q^{45} -1.96237e11 q^{46} -2.29465e10 q^{47} +2.51415e10 q^{48} +2.29746e11 q^{49} -9.01802e10 q^{50} -1.36673e11 q^{51} +6.41532e10 q^{52} -1.99989e11 q^{53} -5.89694e10 q^{54} +2.80433e11 q^{55} +5.90146e11 q^{56} -1.69035e11 q^{57} -4.41595e11 q^{58} +4.21805e10 q^{59} -4.64881e11 q^{60} +4.98973e11 q^{61} +2.44039e11 q^{62} -3.03729e11 q^{63} -7.71057e11 q^{64} -1.82408e11 q^{65} +7.30770e11 q^{66} +3.43120e11 q^{67} -2.80770e12 q^{68} +9.39864e11 q^{69} -3.70421e12 q^{70} +1.13561e12 q^{71} -5.48760e11 q^{72} -1.48911e12 q^{73} -4.43232e12 q^{74} +4.31911e11 q^{75} -3.47250e12 q^{76} +3.76393e12 q^{77} -4.75330e11 q^{78} +2.64540e12 q^{79} -1.46853e12 q^{80} +2.82430e11 q^{81} +5.60551e12 q^{82} -3.22063e12 q^{83} -6.23956e12 q^{84} +7.98316e12 q^{85} -4.43604e12 q^{86} +2.11499e12 q^{87} +6.80044e12 q^{88} -6.12635e12 q^{89} +3.44444e12 q^{90} -2.44824e12 q^{91} +1.93078e13 q^{92} -1.16881e12 q^{93} +3.49270e12 q^{94} +9.87342e12 q^{95} +2.33980e12 q^{96} +7.26379e11 q^{97} -3.49697e13 q^{98} -3.49997e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 138 q^{2} + 21870 q^{3} + 114598 q^{4} - 137742 q^{5} - 100602 q^{6} - 879443 q^{7} - 872301 q^{8} + 15943230 q^{9}+O(q^{10}) \) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more