LMFDB - Embedded newform 177.14.a.a.1.8

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			1.8
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)

$f(q)$	$=$	$q-108.701 q^{2} +729.000 q^{3} +3623.83 q^{4} -15679.8 q^{5} -79242.8 q^{6} -222995. q^{7} +496563. q^{8} +531441. q^{9} +O(q^{10})$	\(q-108.701 q^{2} +729.000 q^{3} +3623.83 q^{4} -15679.8 q^{5} -79242.8 q^{6} -222995. q^{7} +496563. q^{8} +531441. q^{9} +1.70441e6 q^{10} +5.89635e6 q^{11} +2.64177e6 q^{12} +5.02542e6 q^{13} +2.42398e7 q^{14} -1.14306e7 q^{15} -8.36631e7 q^{16} +1.53014e8 q^{17} -5.77680e7 q^{18} -3.69560e8 q^{19} -5.68211e7 q^{20} -1.62564e8 q^{21} -6.40937e8 q^{22} -5.84237e8 q^{23} +3.61994e8 q^{24} -9.74846e8 q^{25} -5.46266e8 q^{26} +3.87420e8 q^{27} -8.08098e8 q^{28} +4.10315e9 q^{29} +1.24251e9 q^{30} -3.52084e9 q^{31} +5.02640e9 q^{32} +4.29844e9 q^{33} -1.66327e10 q^{34} +3.49653e9 q^{35} +1.92585e9 q^{36} +1.57485e10 q^{37} +4.01714e10 q^{38} +3.66353e9 q^{39} -7.78601e9 q^{40} -4.03243e10 q^{41} +1.76708e10 q^{42} -2.10059e10 q^{43} +2.13674e10 q^{44} -8.33290e9 q^{45} +6.35070e10 q^{46} +6.19726e10 q^{47} -6.09904e10 q^{48} -4.71620e10 q^{49} +1.05966e11 q^{50} +1.11547e11 q^{51} +1.82113e10 q^{52} +2.85355e11 q^{53} -4.21129e10 q^{54} -9.24537e10 q^{55} -1.10731e11 q^{56} -2.69409e11 q^{57} -4.46015e11 q^{58} +4.21805e10 q^{59} -4.14226e10 q^{60} -1.72604e11 q^{61} +3.82718e11 q^{62} -1.18509e11 q^{63} +1.38996e11 q^{64} -7.87977e10 q^{65} -4.67243e11 q^{66} +4.13709e10 q^{67} +5.54497e11 q^{68} -4.25909e11 q^{69} -3.80075e11 q^{70} -6.91656e11 q^{71} +2.63894e11 q^{72} +1.67509e12 q^{73} -1.71188e12 q^{74} -7.10663e11 q^{75} -1.33922e12 q^{76} -1.31486e12 q^{77} -3.98228e11 q^{78} -9.79322e11 q^{79} +1.31182e12 q^{80} +2.82430e11 q^{81} +4.38328e12 q^{82} -4.95100e12 q^{83} -5.89104e11 q^{84} -2.39923e12 q^{85} +2.28336e12 q^{86} +2.99120e12 q^{87} +2.92791e12 q^{88} +1.48553e11 q^{89} +9.05792e11 q^{90} -1.12065e12 q^{91} -2.11718e12 q^{92} -2.56669e12 q^{93} -6.73647e12 q^{94} +5.79463e12 q^{95} +3.66424e12 q^{96} +7.18251e11 q^{97} +5.12655e12 q^{98} +3.13356e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−108.701	−1.20098	−0.600492	−	0.799631i	$-0.705029\pi$
$2$	−108.701	−1.20098	−0.600492	+	0.799631i	$0.705029\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	3623.83	0.442363
$5$	−15679.8	−0.448783	−0.224391	−	0.974499i	$-0.572039\pi$
$5$	−15679.8	−0.448783	−0.224391	+	0.974499i	$0.572039\pi$
$6$	−79242.8	−0.693388
$7$	−222995.	−0.716405	−0.358203	−	0.933644i	$-0.616610\pi$
$7$	−222995.	−0.716405	−0.358203	+	0.933644i	$0.616610\pi$
$8$	496563.	0.669714
$9$	531441.	0.333333
$10$	1.70441e6	0.538981
$11$	5.89635e6	1.00353	0.501766	−	0.865004i	$-0.332684\pi$
$11$	5.89635e6	1.00353	0.501766	+	0.865004i	$0.332684\pi$
$12$	2.64177e6	0.255398
$13$	5.02542e6	0.288762	0.144381	−	0.989522i	$-0.453881\pi$
$13$	5.02542e6	0.288762	0.144381	+	0.989522i	$0.453881\pi$
$14$	2.42398e7	0.860391
$15$	−1.14306e7	−0.259105
$16$	−8.36631e7	−1.24668
$17$	1.53014e8	1.53749	0.768746	−	0.639554i	$-0.220881\pi$
$17$	1.53014e8	1.53749	0.768746	+	0.639554i	$0.220881\pi$
$18$	−5.77680e7	−0.400328
$19$	−3.69560e8	−1.80213	−0.901065	−	0.433683i	$-0.857214\pi$
$19$	−3.69560e8	−1.80213	−0.901065	+	0.433683i	$0.857214\pi$
$20$	−5.68211e7	−0.198525
$21$	−1.62564e8	−0.413617
$22$	−6.40937e8	−1.20522
$23$	−5.84237e8	−0.822921	−0.411461	−	0.911428i	$-0.634981\pi$
$23$	−5.84237e8	−0.822921	−0.411461	+	0.911428i	$0.634981\pi$
$24$	3.61994e8	0.386659
$25$	−9.74846e8	−0.798594
$26$	−5.46266e8	−0.346799
$27$	3.87420e8	0.192450
$28$	−8.08098e8	−0.316911
$29$	4.10315e9	1.28095	0.640473	−	0.767981i	$-0.278738\pi$
$29$	4.10315e9	1.28095	0.640473	+	0.767981i	$0.278738\pi$
$30$	1.24251e9	0.311181
$31$	−3.52084e9	−0.712517	−0.356259	−	0.934387i	$-0.615948\pi$
$31$	−3.52084e9	−0.712517	−0.356259	+	0.934387i	$0.615948\pi$
$32$	5.02640e9	0.827527
$33$	4.29844e9	0.579389
$34$	−1.66327e10	−1.84650
$35$	3.49653e9	0.321510
$36$	1.92585e9	0.147454
$37$	1.57485e10	1.00909	0.504544	−	0.863386i	$-0.331661\pi$
$37$	1.57485e10	1.00909	0.504544	+	0.863386i	$0.331661\pi$
$38$	4.01714e10	2.16433
$39$	3.66353e9	0.166717
$40$	−7.78601e9	−0.300556
$41$	−4.03243e10	−1.32578	−0.662890	−	0.748717i	$-0.730670\pi$
$41$	−4.03243e10	−1.32578	−0.662890	+	0.748717i	$0.730670\pi$
$42$	1.76708e10	0.496747
$43$	−2.10059e10	−0.506754	−0.253377	−	0.967368i	$-0.581541\pi$
$43$	−2.10059e10	−0.506754	−0.253377	+	0.967368i	$0.581541\pi$
$44$	2.13674e10	0.443925
$45$	−8.33290e9	−0.149594
$46$	6.35070e10	0.988315
$47$	6.19726e10	0.838617	0.419309	−	0.907844i	$-0.362273\pi$
$47$	6.19726e10	0.838617	0.419309	+	0.907844i	$0.362273\pi$
$48$	−6.09904e10	−0.719770
$49$	−4.71620e10	−0.486764
$50$	1.05966e11	0.959099
$51$	1.11547e11	0.887672
$52$	1.82113e10	0.127738
$53$	2.85355e11	1.76845	0.884224	−	0.467062i	$-0.154688\pi$
$53$	2.85355e11	1.76845	0.884224	+	0.467062i	$0.154688\pi$
$54$	−4.21129e10	−0.231129
$55$	−9.24537e10	−0.450367
$56$	−1.10731e11	−0.479786
$57$	−2.69409e11	−1.04046
$58$	−4.46015e11	−1.53839
$59$	4.21805e10	0.130189
$59$	4.21805e10	0.130189
$60$	−4.14226e10	−0.114618
$61$	−1.72604e11	−0.428951	−0.214476	−	0.976729i	$-0.568804\pi$
$61$	−1.72604e11	−0.428951	−0.214476	+	0.976729i	$0.568804\pi$
$62$	3.82718e11	0.855722
$63$	−1.18509e11	−0.238802
$64$	1.38996e11	0.252832
$65$	−7.87977e10	−0.129591
$66$	−4.67243e11	−0.695837
$67$	4.13709e10	0.0558739	0.0279369	−	0.999610i	$-0.491106\pi$
$67$	4.13709e10	0.0558739	0.0279369	+	0.999610i	$0.491106\pi$
$68$	5.54497e11	0.680129
$69$	−4.25909e11	−0.475114
$70$	−3.80075e11	−0.386129
$71$	−6.91656e11	−0.640783	−0.320391	−	0.947285i	$-0.603814\pi$
$71$	−6.91656e11	−0.640783	−0.320391	+	0.947285i	$0.603814\pi$
$72$	2.63894e11	0.223238
$73$	1.67509e12	1.29551	0.647754	−	0.761849i	$-0.275708\pi$
$73$	1.67509e12	1.29551	0.647754	+	0.761849i	$0.275708\pi$
$74$	−1.71188e12	−1.21190
$75$	−7.10663e11	−0.461069
$76$	−1.33922e12	−0.797195
$77$	−1.31486e12	−0.718935
$78$	−3.98228e11	−0.200224
$79$	−9.79322e11	−0.453262	−0.226631	−	0.973981i	$-0.572771\pi$
$79$	−9.79322e11	−0.453262	−0.226631	+	0.973981i	$0.572771\pi$
$80$	1.31182e12	0.559487
$81$	2.82430e11	0.111111
$82$	4.38328e12	1.59224
$83$	−4.95100e12	−1.66221	−0.831104	−	0.556117i	$-0.812291\pi$
$83$	−4.95100e12	−1.66221	−0.831104	+	0.556117i	$0.812291\pi$
$84$	−5.89104e11	−0.182969
$85$	−2.39923e12	−0.690000
$86$	2.28336e12	0.608603
$87$	2.99120e12	0.739554
$88$	2.92791e12	0.672078
$89$	1.48553e11	0.0316845	0.0158422	−	0.999875i	$-0.494957\pi$
$89$	1.48553e11	0.0316845	0.0158422	+	0.999875i	$0.494957\pi$
$90$	9.05792e11	0.179660
$91$	−1.12065e12	−0.206871
$92$	−2.11718e12	−0.364030
$93$	−2.56669e12	−0.411372
$94$	−6.73647e12	−1.00717
$95$	5.79463e12	0.808765
$96$	3.66424e12	0.477773
$97$	7.18251e11	0.0875508	0.0437754	−	0.999041i	$-0.486061\pi$
$97$	7.18251e11	0.0875508	0.0437754	+	0.999041i	$0.486061\pi$
$98$	5.12655e12	0.584595
$99$	3.13356e12	0.334510
$100$	−3.53268e12	−0.353268
$101$	−4.51100e11	−0.0422847	−0.0211424	−	0.999776i	$-0.506730\pi$
$101$	−4.51100e11	−0.0422847	−0.0211424	+	0.999776i	$0.506730\pi$
$102$	−1.21252e13	−1.06608
$103$	1.45809e13	1.20321	0.601605	−	0.798794i	$-0.294528\pi$
$103$	1.45809e13	1.20321	0.601605	+	0.798794i	$0.294528\pi$
$104$	2.49544e12	0.193388
$105$	2.54897e12	0.185624
$106$	−3.10183e13	−2.12388
$107$	1.93892e13	1.24901	0.624503	−	0.781023i	$-0.285302\pi$
$107$	1.93892e13	1.24901	0.624503	+	0.781023i	$0.285302\pi$
$108$	1.40395e12	0.0851327
$109$	1.35000e13	0.771015	0.385507	−	0.922705i	$-0.374026\pi$
$109$	1.35000e13	0.771015	0.385507	+	0.922705i	$0.374026\pi$
$110$	1.00498e13	0.540884
$111$	1.14807e13	0.582598
$112$	1.86565e13	0.893127
$113$	2.23948e13	1.01190	0.505950	−	0.862563i	$-0.331142\pi$
$113$	2.23948e13	1.01190	0.505950	+	0.862563i	$0.331142\pi$
$114$	2.92849e13	1.24958
$115$	9.16074e12	0.369313
$116$	1.48691e13	0.566642
$117$	2.67071e12	0.0962541
$118$	−4.58505e12	−0.156355
$119$	−3.41214e13	−1.10147
$120$	−5.67600e12	−0.173526
$121$	2.44235e11	0.00707461
$122$	1.87622e13	0.515164
$123$	−2.93964e13	−0.765440
$124$	−1.27589e13	−0.315191
$125$	3.44258e13	0.807178
$126$	1.28820e13	0.286797
$127$	−2.82759e13	−0.597989	−0.298994	−	0.954255i	$-0.596651\pi$
$127$	−2.82759e13	−0.597989	−0.298994	+	0.954255i	$0.596651\pi$
$128$	−5.62852e13	−1.13117
$129$	−1.53133e13	−0.292574
$130$	8.56536e12	0.155637
$131$	1.00006e13	0.172887	0.0864437	−	0.996257i	$-0.472450\pi$
$131$	1.00006e13	0.172887	0.0864437	+	0.996257i	$0.472450\pi$
$132$	1.55768e13	0.256300
$133$	8.24101e13	1.29106
$134$	−4.49704e12	−0.0671036
$135$	−6.07468e12	−0.0863683
$136$	7.59810e13	1.02968
$137$	1.21278e14	1.56711	0.783553	−	0.621325i	$-0.213405\pi$
$137$	1.21278e14	1.56711	0.783553	+	0.621325i	$0.213405\pi$
$138$	4.62966e13	0.570604
$139$	−2.91391e13	−0.342673	−0.171337	−	0.985213i	$-0.554809\pi$
$139$	−2.91391e13	−0.342673	−0.171337	+	0.985213i	$0.554809\pi$
$140$	1.26708e13	0.142224
$141$	4.51780e13	0.484176
$142$	7.51835e13	0.769570
$143$	2.96316e13	0.289782
$144$	−4.44620e13	−0.415559
$145$	−6.43367e13	−0.574866
$146$	−1.82084e14	−1.55589
$147$	−3.43811e13	−0.281033
$148$	5.70701e13	0.446383
$149$	−7.22942e11	−0.00541243	−0.00270622	−	0.999996i	$-0.500861\pi$
$149$	−7.22942e11	−0.00541243	−0.00270622	+	0.999996i	$0.500861\pi$
$150$	7.72495e13	0.553736
$151$	−1.45349e14	−0.997844	−0.498922	−	0.866647i	$-0.666271\pi$
$151$	−1.45349e14	−0.997844	−0.498922	+	0.866647i	$0.666271\pi$
$152$	−1.83510e14	−1.20691
$153$	8.13179e13	0.512497
$154$	1.42926e14	0.863429
$155$	5.52062e13	0.319765
$156$	1.32760e13	0.0737493
$157$	3.36777e14	1.79471	0.897356	−	0.441308i	$-0.145485\pi$
$157$	3.36777e14	1.79471	0.897356	+	0.441308i	$0.145485\pi$
$158$	1.06453e14	0.544360
$159$	2.08024e14	1.02101
$160$	−7.88130e13	−0.371380
$161$	1.30282e14	0.589545
$162$	−3.07003e13	−0.133443
$163$	−1.95831e14	−0.817827	−0.408913	−	0.912573i	$-0.634092\pi$
$163$	−1.95831e14	−0.817827	−0.408913	+	0.912573i	$0.634092\pi$
$164$	−1.46128e14	−0.586476
$165$	−6.73988e13	−0.260020
$166$	5.38177e14	1.99629
$167$	−4.48292e14	−1.59920	−0.799602	−	0.600530i	$-0.794956\pi$
$167$	−4.48292e14	−1.59920	−0.799602	+	0.600530i	$0.794956\pi$
$168$	−8.07231e13	−0.277005
$169$	−2.77620e14	−0.916616
$170$	2.60798e14	0.828679
$171$	−1.96399e14	−0.600710
$172$	−7.61220e13	−0.224169
$173$	5.90983e13	0.167601	0.0838003	−	0.996483i	$-0.473294\pi$
$173$	5.90983e13	0.167601	0.0838003	+	0.996483i	$0.473294\pi$
$174$	−3.25145e14	−0.888193
$175$	2.17386e14	0.572117
$176$	−4.93307e14	−1.25108
$177$	3.07496e13	0.0751646
$178$	−1.61478e13	−0.0380525
$179$	2.93637e14	0.667215	0.333608	−	0.942712i	$-0.391734\pi$
$179$	2.93637e14	0.667215	0.333608	+	0.942712i	$0.391734\pi$
$180$	−3.01970e13	−0.0661749
$181$	−1.37598e14	−0.290871	−0.145435	−	0.989368i	$-0.546458\pi$
$181$	−1.37598e14	−0.290871	−0.145435	+	0.989368i	$0.546458\pi$
$182$	1.21815e14	0.248448
$183$	−1.25829e14	−0.247655
$184$	−2.90110e14	−0.551122
$185$	−2.46934e14	−0.452861
$186$	2.79001e14	0.494051
$187$	9.02224e14	1.54292
$188$	2.24578e14	0.370973
$189$	−8.63930e13	−0.137872
$190$	−6.29880e14	−0.971314
$191$	−6.54949e14	−0.976091	−0.488046	−	0.872818i	$-0.662290\pi$
$191$	−6.54949e14	−0.976091	−0.488046	+	0.872818i	$0.662290\pi$
$192$	1.01328e14	0.145972
$193$	9.63404e14	1.34179	0.670897	−	0.741550i	$-0.265909\pi$
$193$	9.63404e14	1.34179	0.670897	+	0.741550i	$0.265909\pi$
$194$	−7.80744e13	−0.105147
$195$	−5.74435e13	−0.0748197
$196$	−1.70907e14	−0.215326
$197$	1.25137e14	0.152530	0.0762652	−	0.997088i	$-0.475700\pi$
$197$	1.25137e14	0.152530	0.0762652	+	0.997088i	$0.475700\pi$
$198$	−3.40620e14	−0.401742
$199$	−1.21862e15	−1.39099	−0.695494	−	0.718532i	$-0.744815\pi$
$199$	−1.21862e15	−1.39099	−0.695494	+	0.718532i	$0.744815\pi$
$200$	−4.84072e14	−0.534829
$201$	3.01594e13	0.0322588
$202$	4.90348e13	0.0507833
$203$	−9.14984e14	−0.917676
$204$	4.04228e14	0.392673
$205$	6.32277e14	0.594987
$206$	−1.58495e15	−1.44504
$207$	−3.10488e14	−0.274307
$208$	−4.20442e14	−0.359994
$209$	−2.17905e15	−1.80849
$210$	−2.77075e14	−0.222931
$211$	−1.39131e15	−1.08539	−0.542697	−	0.839929i	$-0.682597\pi$
$211$	−1.39131e15	−1.08539	−0.542697	+	0.839929i	$0.682597\pi$
$212$	1.03408e15	0.782295
$213$	−5.04217e14	−0.369956
$214$	−2.10761e15	−1.50004
$215$	3.29369e14	0.227422
$216$	1.92379e14	0.128886
$217$	7.85132e14	0.510451
$218$	−1.46746e15	−0.925976
$219$	1.22114e15	0.747962
$220$	−3.35037e14	−0.199226
$221$	7.68959e14	0.443970
$222$	−1.24796e15	−0.699690
$223$	1.05743e14	0.0575796	0.0287898	−	0.999585i	$-0.490835\pi$
$223$	1.05743e14	0.0575796	0.0287898	+	0.999585i	$0.490835\pi$
$224$	−1.12086e15	−0.592844
$225$	−5.18073e14	−0.266198
$226$	−2.43433e15	−1.21528
$227$	−3.35126e15	−1.62570	−0.812850	−	0.582473i	$-0.802085\pi$
$227$	−3.35126e15	−1.62570	−0.812850	+	0.582473i	$0.802085\pi$
$228$	−9.76294e14	−0.460261
$229$	7.61807e13	0.0349071	0.0174536	−	0.999848i	$-0.494444\pi$
$229$	7.61807e13	0.0349071	0.0174536	+	0.999848i	$0.494444\pi$
$230$	−9.95778e14	−0.443539
$231$	−9.58532e14	−0.415077
$232$	2.03747e15	0.857867
$233$	9.95149e14	0.407450	0.203725	−	0.979028i	$-0.434695\pi$
$233$	9.95149e14	0.407450	0.203725	+	0.979028i	$0.434695\pi$
$234$	−2.90308e14	−0.115600
$235$	−9.71720e14	−0.376357
$236$	1.52855e14	0.0575907
$237$	−7.13926e14	−0.261691
$238$	3.70902e15	1.32284
$239$	−2.71528e15	−0.942386	−0.471193	−	0.882030i	$-0.656176\pi$
$239$	−2.71528e15	−0.942386	−0.471193	+	0.882030i	$0.656176\pi$
$240$	9.56319e14	0.323020
$241$	3.45190e14	0.113487	0.0567437	−	0.998389i	$-0.481928\pi$
$241$	3.45190e14	0.113487	0.0567437	+	0.998389i	$0.481928\pi$
$242$	−2.65485e13	−0.00849650
$243$	2.05891e14	0.0641500
$244$	−6.25490e14	−0.189752
$245$	7.39492e14	0.218451
$246$	3.19541e15	0.919281
$247$	−1.85719e15	−0.520387
$248$	−1.74832e15	−0.477183
$249$	−3.60928e15	−0.959676
$250$	−3.74211e15	−0.969408
$251$	1.14308e15	0.288534	0.144267	−	0.989539i	$-0.453918\pi$
$251$	1.14308e15	0.288534	0.144267	+	0.989539i	$0.453918\pi$
$252$	−4.29457e14	−0.105637
$253$	−3.44487e15	−0.825827
$254$	3.07361e15	0.718175
$255$	−1.74904e15	−0.398372
$256$	4.97958e15	1.10569
$257$	−3.33503e15	−0.721995	−0.360997	−	0.932567i	$-0.617564\pi$
$257$	−3.33503e15	−0.721995	−0.360997	+	0.932567i	$0.617564\pi$
$258$	1.66457e15	0.351377
$259$	−3.51185e15	−0.722916
$260$	−2.85550e14	−0.0573264
$261$	2.18058e15	0.426982
$262$	−1.08707e15	−0.207635
$263$	7.95745e14	0.148273	0.0741364	−	0.997248i	$-0.476380\pi$
$263$	7.95745e14	0.148273	0.0741364	+	0.997248i	$0.476380\pi$
$264$	2.13444e15	0.388025
$265$	−4.47432e15	−0.793649
$266$	−8.95804e15	−1.55054
$267$	1.08295e14	0.0182930
$268$	1.49921e14	0.0247165
$269$	−8.89539e15	−1.43145	−0.715723	−	0.698384i	$-0.753903\pi$
$269$	−8.89539e15	−1.43145	−0.715723	+	0.698384i	$0.753903\pi$
$270$	6.60322e14	0.103727
$271$	−5.35745e15	−0.821596	−0.410798	−	0.911726i	$-0.634750\pi$
$271$	−5.35745e15	−0.821596	−0.410798	+	0.911726i	$0.634750\pi$
$272$	−1.28016e16	−1.91676
$273$	−8.16950e14	−0.119437
$274$	−1.31830e16	−1.88207
$275$	−5.74804e15	−0.801414
$276$	−1.54342e15	−0.210173
$277$	−6.20275e15	−0.825022	−0.412511	−	0.910953i	$-0.635348\pi$
$277$	−6.20275e15	−0.825022	−0.412511	+	0.910953i	$0.635348\pi$
$278$	3.16744e15	0.411545
$279$	−1.87112e15	−0.237506
$280$	1.73625e15	0.215320
$281$	1.00835e16	1.22186	0.610930	−	0.791685i	$-0.290796\pi$
$281$	1.00835e16	1.22186	0.610930	+	0.791685i	$0.290796\pi$
$282$	−4.91088e15	−0.581488
$283$	−8.89753e15	−1.02957	−0.514787	−	0.857318i	$-0.672129\pi$
$283$	−8.89753e15	−1.02957	−0.514787	+	0.857318i	$0.672129\pi$
$284$	−2.50645e15	−0.283458
$285$	4.22429e15	0.466941
$286$	−3.22098e15	−0.348023
$287$	8.99213e15	0.949796
$288$	2.67123e15	0.275842
$289$	1.35087e16	1.36388
$290$	6.99344e15	0.690405
$291$	5.23605e14	0.0505475
$292$	6.07026e15	0.573085
$293$	−3.28434e15	−0.303255	−0.151628	−	0.988438i	$-0.548451\pi$
$293$	−3.28434e15	−0.303255	−0.151628	+	0.988438i	$0.548451\pi$
$294$	3.73725e15	0.337516
$295$	−6.61383e14	−0.0584265
$296$	7.82014e15	0.675800
$297$	2.28437e15	0.193130
$298$	7.85842e13	0.00650025
$299$	−2.93604e15	−0.237629
$300$	−2.57532e15	−0.203959
$301$	4.68423e15	0.363041
$302$	1.57996e16	1.19839
$303$	−3.28852e14	−0.0244131
$304$	3.09185e16	2.24668
$305$	2.70641e15	0.192506
$306$	−8.83931e15	−0.615501
$307$	−9.09345e15	−0.619911	−0.309955	−	0.950751i	$-0.600314\pi$
$307$	−9.09345e15	−0.619911	−0.309955	+	0.950751i	$0.600314\pi$
$308$	−4.76483e15	−0.318030
$309$	1.06295e16	0.694674
$310$	−6.00095e15	−0.384033
$311$	1.40180e16	0.878503	0.439252	−	0.898364i	$-0.355244\pi$
$311$	1.40180e16	0.878503	0.439252	+	0.898364i	$0.355244\pi$
$312$	1.81917e15	0.111653
$313$	−2.17374e15	−0.130668	−0.0653340	−	0.997863i	$-0.520811\pi$
$313$	−2.17374e15	−0.130668	−0.0653340	+	0.997863i	$0.520811\pi$
$314$	−3.66079e16	−2.15542
$315$	1.85820e15	0.107170
$316$	−3.54890e15	−0.200506
$317$	1.68840e16	0.934522	0.467261	−	0.884120i	$-0.345241\pi$
$317$	1.68840e16	0.934522	0.467261	+	0.884120i	$0.345241\pi$
$318$	−2.26123e16	−1.22622
$319$	2.41936e16	1.28547
$320$	−2.17943e15	−0.113467
$321$	1.41347e16	0.721114
$322$	−1.41618e16	−0.708034
$323$	−5.65478e16	−2.77076
$324$	1.02348e15	0.0491514
$325$	−4.89901e15	−0.230604
$326$	2.12869e16	0.982197
$327$	9.84153e15	0.445146
$328$	−2.00235e16	−0.887893
$329$	−1.38196e16	−0.600790
$330$	7.32629e15	0.312279
$331$	−2.34060e16	−0.978241	−0.489121	−	0.872216i	$-0.662682\pi$
$331$	−2.34060e16	−0.978241	−0.489121	+	0.872216i	$0.662682\pi$
$332$	−1.79416e16	−0.735299
$333$	8.36942e15	0.336363
$334$	4.87296e16	1.92062
$335$	−6.48688e14	−0.0250752
$336$	1.36006e16	0.515647
$337$	1.19509e16	0.444432	0.222216	−	0.974997i	$-0.428671\pi$
$337$	1.19509e16	0.444432	0.222216	+	0.974997i	$0.428671\pi$
$338$	3.01775e16	1.10084
$339$	1.63258e16	0.584221
$340$	−8.69441e15	−0.305230
$341$	−2.07601e16	−0.715033
$342$	2.13487e16	0.721443
$343$	3.21227e16	1.06513
$344$	−1.04308e16	−0.339380
$345$	6.67818e15	0.213223
$346$	−6.42403e15	−0.201286
$347$	1.62883e16	0.500881	0.250440	−	0.968132i	$-0.419425\pi$
$347$	1.62883e16	0.500881	0.250440	+	0.968132i	$0.419425\pi$
$348$	1.08396e16	0.327151
$349$	2.82702e15	0.0837460	0.0418730	−	0.999123i	$-0.486668\pi$
$349$	2.82702e15	0.0837460	0.0418730	+	0.999123i	$0.486668\pi$
$350$	−2.36300e16	−0.687103
$351$	1.94695e15	0.0555723
$352$	2.96374e16	0.830449
$353$	−5.21024e16	−1.43325	−0.716625	−	0.697458i	$-0.754314\pi$
$353$	−5.21024e16	−1.43325	−0.716625	+	0.697458i	$0.754314\pi$
$354$	−3.34250e15	−0.0902715
$355$	1.08450e16	0.287572
$356$	5.38331e14	0.0140160
$357$	−2.48745e16	−0.635932
$358$	−3.19185e16	−0.801315
$359$	1.76819e16	0.435928	0.217964	−	0.975957i	$-0.430059\pi$
$359$	1.76819e16	0.435928	0.217964	+	0.975957i	$0.430059\pi$
$360$	−4.13781e15	−0.100185
$361$	9.45214e16	2.24767
$362$	1.49570e16	0.349331
$363$	1.78047e14	0.00408453
$364$	−4.06103e15	−0.0915119
$365$	−2.62652e16	−0.581402
$366$	1.36777e16	0.297430
$367$	−9.04870e15	−0.193311	−0.0966556	−	0.995318i	$-0.530815\pi$
$367$	−9.04870e15	−0.193311	−0.0966556	+	0.995318i	$0.530815\pi$
$368$	4.88791e16	1.02592
$369$	−2.14300e16	−0.441927
$370$	2.68419e16	0.543879
$371$	−6.36329e16	−1.26693
$372$	−9.30127e15	−0.181976
$373$	7.31250e14	0.0140591	0.00702957	−	0.999975i	$-0.497762\pi$
$373$	7.31250e14	0.0140591	0.00702957	+	0.999975i	$0.497762\pi$
$374$	−9.80723e16	−1.85302
$375$	2.50964e16	0.466024
$376$	3.07733e16	0.561633
$377$	2.06201e16	0.369889
$378$	9.39098e15	0.165582
$379$	−5.04940e16	−0.875154	−0.437577	−	0.899181i	$-0.644163\pi$
$379$	−5.04940e16	−0.875154	−0.437577	+	0.899181i	$0.644163\pi$
$380$	2.09988e16	0.357767
$381$	−2.06132e16	−0.345249
$382$	7.11934e16	1.17227
$383$	2.01642e16	0.326430	0.163215	−	0.986591i	$-0.447814\pi$
$383$	2.01642e16	0.326430	0.163215	+	0.986591i	$0.447814\pi$
$384$	−4.10319e16	−0.653083
$385$	2.06168e16	0.322645
$386$	−1.04723e17	−1.61147
$387$	−1.11634e16	−0.168918
$388$	2.60282e15	0.0387292
$389$	−8.84541e16	−1.29433	−0.647166	−	0.762349i	$-0.724046\pi$
$389$	−8.84541e16	−1.29433	−0.647166	+	0.762349i	$0.724046\pi$
$390$	6.24415e15	0.0898572
$391$	−8.93964e16	−1.26524
$392$	−2.34189e16	−0.325992
$393$	7.29045e15	0.0998166
$394$	−1.36025e16	−0.183187
$395$	1.53556e16	0.203416
$396$	1.13555e16	0.147975
$397$	−1.49539e17	−1.91697	−0.958484	−	0.285145i	$-0.907958\pi$
$397$	−1.49539e17	−1.91697	−0.958484	+	0.285145i	$0.907958\pi$
$398$	1.32465e17	1.67056
$399$	6.00770e16	0.745391
$400$	8.15587e16	0.995590
$401$	−1.50861e17	−1.81192	−0.905959	−	0.423365i	$-0.860849\pi$
$401$	−1.50861e17	−1.81192	−0.905959	+	0.423365i	$0.860849\pi$
$402$	−3.27835e15	−0.0387423
$403$	−1.76937e16	−0.205748
$404$	−1.63471e15	−0.0187052
$405$	−4.42844e15	−0.0498647
$406$	9.94594e16	1.10211
$407$	9.28590e16	1.01265
$408$	5.53901e16	0.594486
$409$	−1.27486e17	−1.34667	−0.673336	−	0.739336i	$-0.735139\pi$
$409$	−1.27486e17	−1.34667	−0.673336	+	0.739336i	$0.735139\pi$
$410$	−6.87290e16	−0.714570
$411$	8.84116e16	0.904769
$412$	5.28387e16	0.532255
$413$	−9.40607e15	−0.0932680
$414$	3.37502e16	0.329438
$415$	7.76308e16	0.745970
$416$	2.52597e16	0.238958
$417$	−2.12424e16	−0.197842
$418$	2.36865e17	2.17197
$419$	−1.56729e17	−1.41501	−0.707504	−	0.706710i	$-0.750179\pi$
$419$	−1.56729e17	−1.41501	−0.707504	+	0.706710i	$0.750179\pi$
$420$	9.23704e15	0.0821131
$421$	−1.86804e17	−1.63513	−0.817565	−	0.575836i	$-0.804677\pi$
$421$	−1.86804e17	−1.63513	−0.817565	+	0.575836i	$0.804677\pi$
$422$	1.51236e17	1.30354
$423$	3.29348e16	0.279539
$424$	1.41697e17	1.18435
$425$	−1.49165e17	−1.22783
$426$	5.48088e16	0.444312
$427$	3.84900e16	0.307303
$428$	7.02631e16	0.552513
$429$	2.16015e16	0.167306
$430$	−3.58026e16	−0.273130
$431$	2.66341e16	0.200141	0.100070	−	0.994980i	$-0.468093\pi$
$431$	2.66341e16	0.200141	0.100070	+	0.994980i	$0.468093\pi$
$432$	−3.24128e16	−0.239923
$433$	−3.73070e16	−0.272031	−0.136016	−	0.990707i	$-0.543430\pi$
$433$	−3.73070e16	−0.272031	−0.136016	+	0.990707i	$0.543430\pi$
$434$	−8.53443e16	−0.613044
$435$	−4.69014e16	−0.331899
$436$	4.89219e16	0.341068
$437$	2.15911e17	1.48301
$438$	−1.32739e17	−0.898291
$439$	1.67544e17	1.11715	0.558574	−	0.829455i	$-0.311349\pi$
$439$	1.67544e17	1.11715	0.558574	+	0.829455i	$0.311349\pi$
$440$	−4.59091e16	−0.301617
$441$	−2.50638e16	−0.162255
$442$	−8.35863e16	−0.533201
$443$	−1.61581e17	−1.01570	−0.507851	−	0.861445i	$-0.669560\pi$
$443$	−1.61581e17	−1.01570	−0.507851	+	0.861445i	$0.669560\pi$
$444$	4.16041e16	0.257719
$445$	−2.32928e15	−0.0142194
$446$	−1.14943e16	−0.0691522
$447$	−5.27025e14	−0.00312487
$448$	−3.09954e16	−0.181130
$449$	−6.95012e16	−0.400305	−0.200153	−	0.979765i	$-0.564144\pi$
$449$	−6.95012e16	−0.400305	−0.200153	+	0.979765i	$0.564144\pi$
$450$	5.63149e16	0.319700
$451$	−2.37766e17	−1.33046
$452$	8.11551e16	0.447627
$453$	−1.05960e17	−0.576105
$454$	3.64284e17	1.95244
$455$	1.75715e16	0.0928400
$456$	−1.33778e17	−0.696811
$457$	−8.78228e16	−0.450974	−0.225487	−	0.974246i	$-0.572397\pi$
$457$	−8.78228e16	−0.450974	−0.225487	+	0.974246i	$0.572397\pi$
$458$	−8.28089e15	−0.0419229
$459$	5.92807e16	0.295891
$460$	3.31970e16	0.163370
$461$	3.70986e17	1.80012	0.900059	−	0.435768i	$-0.143523\pi$
$461$	3.70986e17	1.80012	0.900059	+	0.435768i	$0.143523\pi$
$462$	1.04193e17	0.498501
$463$	−1.05637e17	−0.498358	−0.249179	−	0.968458i	$-0.580161\pi$
$463$	−1.05637e17	−0.498358	−0.249179	+	0.968458i	$0.580161\pi$
$464$	−3.43283e17	−1.59693
$465$	4.02453e16	0.184617
$466$	−1.08173e17	−0.489341
$467$	1.34010e17	0.597829	0.298914	−	0.954280i	$-0.403375\pi$
$467$	1.34010e17	0.597829	0.298914	+	0.954280i	$0.403375\pi$
$468$	9.67822e15	0.0425792
$469$	−9.22552e15	−0.0400283
$470$	1.05627e17	0.451999
$471$	2.45510e17	1.03618
$472$	2.09453e16	0.0871893
$473$	−1.23858e17	−0.508543
$474$	7.76042e16	0.314287
$475$	3.60264e17	1.43917
$476$	−1.23650e17	−0.487248
$477$	1.51649e17	0.589483
$478$	2.95153e17	1.13179
$479$	−2.99679e17	−1.13364	−0.566820	−	0.823842i	$-0.691826\pi$
$479$	−2.99679e17	−1.13364	−0.566820	+	0.823842i	$0.691826\pi$
$480$	−5.74547e16	−0.214416
$481$	7.91430e16	0.291387
$482$	−3.75224e16	−0.136296
$483$	9.49758e16	0.340374
$484$	8.85066e14	0.00312954
$485$	−1.12620e16	−0.0392913
$486$	−2.23805e16	−0.0770432
$487$	4.24453e17	1.44176	0.720878	−	0.693062i	$-0.243739\pi$
$487$	4.24453e17	1.44176	0.720878	+	0.693062i	$0.243739\pi$
$488$	−8.57089e16	−0.287275
$489$	−1.42761e17	−0.472173
$490$	−8.03833e16	−0.262356
$491$	2.82075e16	0.0908519	0.0454260	−	0.998968i	$-0.485535\pi$
$491$	2.82075e16	0.0908519	0.0454260	+	0.998968i	$0.485535\pi$
$492$	−1.06528e17	−0.338602
$493$	6.27839e17	1.96944
$494$	2.01878e17	0.624977
$495$	−4.91337e16	−0.150122
$496$	2.94565e17	0.888280
$497$	1.54236e17	0.459060
$498$	3.92331e17	1.15256
$499$	−9.74998e16	−0.282716	−0.141358	−	0.989959i	$-0.545147\pi$
$499$	−9.74998e16	−0.282716	−0.141358	+	0.989959i	$0.545147\pi$
$500$	1.24753e17	0.357065
$501$	−3.26805e17	−0.923301
$502$	−1.24253e17	−0.346525
$503$	−4.98003e16	−0.137101	−0.0685504	−	0.997648i	$-0.521837\pi$
$503$	−4.98003e16	−0.137101	−0.0685504	+	0.997648i	$0.521837\pi$
$504$	−5.88471e16	−0.159929
$505$	7.07316e15	0.0189767
$506$	3.74459e17	0.991805
$507$	−2.02385e17	−0.529209
$508$	−1.02467e17	−0.264528
$509$	−4.57244e17	−1.16542	−0.582710	−	0.812680i	$-0.698008\pi$
$509$	−4.57244e17	−1.16542	−0.582710	+	0.812680i	$0.698008\pi$
$510$	1.90122e17	0.478438
$511$	−3.73538e17	−0.928109
$512$	−8.01958e16	−0.196742
$513$	−1.43175e17	−0.346820
$514$	3.62520e17	0.867104
$515$	−2.28626e17	−0.539980
$516$	−5.54929e16	−0.129424
$517$	3.65412e17	0.841578
$518$	3.81741e17	0.868211
$519$	4.30827e16	0.0967643
$520$	−3.91280e16	−0.0867892
$521$	4.43418e17	0.971332	0.485666	−	0.874144i	$-0.338577\pi$
$521$	4.43418e17	0.971332	0.485666	+	0.874144i	$0.338577\pi$
$522$	−2.37031e17	−0.512798
$523$	−1.27369e17	−0.272146	−0.136073	−	0.990699i	$-0.543448\pi$
$523$	−1.27369e17	−0.272146	−0.136073	+	0.990699i	$0.543448\pi$
$524$	3.62406e16	0.0764789
$525$	1.58475e17	0.330312
$526$	−8.64980e16	−0.178073
$527$	−5.38738e17	−1.09549
$528$	−3.59621e17	−0.722311
$529$	−1.62703e17	−0.322800
$530$	4.86361e17	0.953160
$531$	2.24165e16	0.0433963
$532$	2.98641e17	0.571115
$533$	−2.02646e17	−0.382835
$534$	−1.17718e16	−0.0219696
$535$	−3.04018e17	−0.560532
$536$	2.05432e16	0.0374195
$537$	2.14061e17	0.385217
$538$	9.66934e17	1.71914
$539$	−2.78084e17	−0.488482
$540$	−2.20136e16	−0.0382061
$541$	2.09010e17	0.358413	0.179207	−	0.983811i	$-0.442647\pi$
$541$	2.09010e17	0.358413	0.179207	+	0.983811i	$0.442647\pi$
$542$	5.82359e17	0.986723
$543$	−1.00309e17	−0.167934
$544$	7.69109e17	1.27232
$545$	−2.11678e17	−0.346018
$546$	8.88031e16	0.143442
$547$	9.22458e17	1.47241	0.736206	−	0.676758i	$-0.236616\pi$
$547$	9.22458e17	1.47241	0.736206	+	0.676758i	$0.236616\pi$
$548$	4.39491e17	0.693229
$549$	−9.17291e16	−0.142984
$550$	6.24815e17	0.962485
$551$	−1.51636e18	−2.30843
$552$	−2.11491e17	−0.318190
$553$	2.18384e17	0.324719
$554$	6.74243e17	0.990838
$555$	−1.80015e17	−0.261460
$556$	−1.05595e17	−0.151586
$557$	−1.22276e18	−1.73493	−0.867466	−	0.497497i	$-0.834253\pi$
$557$	−1.22276e18	−1.73493	−0.867466	+	0.497497i	$0.834253\pi$
$558$	2.03392e17	0.285241
$559$	−1.05564e17	−0.146331
$560$	−2.92531e17	−0.400820
$561$	6.57721e17	0.890806
$562$	−1.09609e18	−1.46743
$563$	−1.25872e18	−1.66580	−0.832902	−	0.553421i	$-0.813322\pi$
$563$	−1.25872e18	−1.66580	−0.832902	+	0.553421i	$0.813322\pi$
$564$	1.63718e17	0.214181
$565$	−3.51147e17	−0.454123
$566$	9.67167e17	1.23650
$567$	−6.29805e16	−0.0796006
$568$	−3.43451e17	−0.429141
$569$	9.77509e17	1.20751	0.603756	−	0.797170i	$-0.293670\pi$
$569$	9.77509e17	1.20751	0.603756	+	0.797170i	$0.293670\pi$
$570$	−4.59183e17	−0.560788
$571$	−8.17555e17	−0.987147	−0.493574	−	0.869704i	$-0.664310\pi$
$571$	−8.17555e17	−0.987147	−0.493574	+	0.869704i	$0.664310\pi$
$572$	1.07380e17	0.128189
$573$	−4.77458e17	−0.563547
$574$	−9.77450e17	−1.14069
$575$	5.69542e17	0.657180
$576$	7.38680e16	0.0842773
$577$	−8.66108e17	−0.977078	−0.488539	−	0.872542i	$-0.662470\pi$
$577$	−8.66108e17	−0.977078	−0.488539	+	0.872542i	$0.662470\pi$
$578$	−1.46840e18	−1.63800
$579$	7.02322e17	0.774686
$580$	−2.33145e17	−0.254299
$581$	1.10405e18	1.19081
$582$	−5.69162e16	−0.0607067
$583$	1.68255e18	1.77469
$584$	8.31789e17	0.867620
$585$	−4.18763e16	−0.0431972
$586$	3.57010e17	0.364205
$587$	1.48954e17	0.150281	0.0751407	−	0.997173i	$-0.476059\pi$
$587$	1.48954e17	0.150281	0.0751407	+	0.997173i	$0.476059\pi$
$588$	−1.24592e17	−0.124319
$589$	1.30116e18	1.28405
$590$	7.18928e16	0.0701693
$591$	9.12251e16	0.0880635
$592$	−1.31757e18	−1.25801
$593$	1.21099e18	1.14363	0.571813	−	0.820384i	$-0.306240\pi$
$593$	1.21099e18	1.14363	0.571813	+	0.820384i	$0.306240\pi$
$594$	−2.48312e17	−0.231946
$595$	5.35017e17	0.494319
$596$	−2.61982e15	−0.00239426
$597$	−8.88375e17	−0.803088
$598$	3.19149e17	0.285388
$599$	−1.99866e18	−1.76793	−0.883963	−	0.467556i	$-0.845134\pi$
$599$	−1.99866e18	−1.76793	−0.883963	+	0.467556i	$0.845134\pi$
$600$	−3.52889e17	−0.308784
$601$	7.84877e17	0.679388	0.339694	−	0.940536i	$-0.389677\pi$
$601$	7.84877e17	0.679388	0.339694	+	0.940536i	$0.389677\pi$
$602$	−5.09178e17	−0.436006
$603$	2.19862e16	0.0186246
$604$	−5.26721e17	−0.441409
$605$	−3.82956e15	−0.00317496
$606$	3.57464e16	0.0293197
$607$	1.47836e17	0.119965	0.0599823	−	0.998199i	$-0.480896\pi$
$607$	1.47836e17	0.119965	0.0599823	+	0.998199i	$0.480896\pi$
$608$	−1.85755e18	−1.49131
$609$	−6.67023e17	−0.529820
$610$	−2.94188e17	−0.231197
$611$	3.11438e17	0.242161
$612$	2.94682e17	0.226710
$613$	−7.80291e17	−0.593969	−0.296984	−	0.954882i	$-0.595981\pi$
$613$	−7.80291e17	−0.593969	−0.296984	+	0.954882i	$0.595981\pi$
$614$	9.88464e17	0.744503
$615$	4.60930e17	0.343516
$616$	−6.52910e17	−0.481480
$617$	1.41434e18	1.03205	0.516024	−	0.856574i	$-0.327411\pi$
$617$	1.41434e18	1.03205	0.516024	+	0.856574i	$0.327411\pi$
$618$	−1.15543e18	−0.834292
$619$	−2.15988e17	−0.154326	−0.0771632	−	0.997018i	$-0.524586\pi$
$619$	−2.15988e17	−0.154326	−0.0771632	+	0.997018i	$0.524586\pi$
$620$	2.00058e17	0.141452
$621$	−2.26345e17	−0.158371
$622$	−1.52377e18	−1.05507
$623$	−3.31266e16	−0.0226989
$624$	−3.06502e17	−0.207842
$625$	6.50207e17	0.436347
$626$	2.36287e17	0.156930
$627$	−1.58853e18	−1.04413
$628$	1.22042e18	0.793913
$629$	2.40975e18	1.55147
$630$	−2.01987e17	−0.128710
$631$	−1.79839e18	−1.13421	−0.567106	−	0.823645i	$-0.691937\pi$
$631$	−1.79839e18	−1.13421	−0.567106	+	0.823645i	$0.691937\pi$
$632$	−4.86295e17	−0.303556
$633$	−1.01426e18	−0.626652
$634$	−1.83530e18	−1.12235
$635$	4.43362e17	0.268367
$636$	7.53844e17	0.451658
$637$	−2.37009e17	−0.140559
$638$	−2.62986e18	−1.54383
$639$	−3.67574e17	−0.213594
$640$	8.82541e17	0.507651
$641$	2.38786e18	1.35966	0.679831	−	0.733369i	$-0.262053\pi$
$641$	2.38786e18	1.35966	0.679831	+	0.733369i	$0.262053\pi$
$642$	−1.53645e18	−0.866046
$643$	5.98871e17	0.334166	0.167083	−	0.985943i	$-0.446565\pi$
$643$	5.98871e17	0.334166	0.167083	+	0.985943i	$0.446565\pi$
$644$	4.72121e17	0.260793
$645$	2.40110e17	0.131302
$646$	6.14678e18	3.32764
$647$	−2.24528e18	−1.20335	−0.601677	−	0.798740i	$-0.705500\pi$
$647$	−2.24528e18	−1.20335	−0.601677	+	0.798740i	$0.705500\pi$
$648$	1.40244e17	0.0744126
$649$	2.48711e17	0.130649
$650$	5.32526e17	0.276952
$651$	5.72361e17	0.294709
$652$	−7.09658e17	−0.361776
$653$	−1.57701e18	−0.795972	−0.397986	−	0.917392i	$-0.630291\pi$
$653$	−1.57701e18	−0.795972	−0.397986	+	0.917392i	$0.630291\pi$
$654$	−1.06978e18	−0.534613
$655$	−1.56808e17	−0.0775889
$656$	3.37366e18	1.65282
$657$	8.90213e17	0.431836
$658$	1.50220e18	0.721539
$659$	−3.46469e17	−0.164782	−0.0823908	−	0.996600i	$-0.526256\pi$
$659$	−3.46469e17	−0.164782	−0.0823908	+	0.996600i	$0.526256\pi$
$660$	−2.44242e17	−0.115023
$661$	7.70176e17	0.359154	0.179577	−	0.983744i	$-0.442527\pi$
$661$	7.70176e17	0.359154	0.179577	+	0.983744i	$0.442527\pi$
$662$	2.54425e18	1.17485
$663$	5.60571e17	0.256326
$664$	−2.45848e18	−1.11320
$665$	−1.29218e18	−0.579403
$666$	−9.09762e17	−0.403966
$667$	−2.39721e18	−1.05412
$668$	−1.62454e18	−0.707428
$669$	7.70864e16	0.0332436
$670$	7.05129e16	0.0301149
$671$	−1.01774e18	−0.430466
$672$	−8.17110e17	−0.342279
$673$	−9.65115e17	−0.400388	−0.200194	−	0.979756i	$-0.564157\pi$
$673$	−9.65115e17	−0.400388	−0.200194	+	0.979756i	$0.564157\pi$
$674$	−1.29907e18	−0.533756
$675$	−3.77675e17	−0.153690
$676$	−1.00605e18	−0.405477
$677$	−3.92149e18	−1.56540	−0.782699	−	0.622400i	$-0.786158\pi$
$677$	−3.92149e18	−1.56540	−0.782699	+	0.622400i	$0.786158\pi$
$678$	−1.77463e18	−0.701640
$679$	−1.60167e17	−0.0627218
$680$	−1.19137e18	−0.462102
$681$	−2.44307e18	−0.938598
$682$	2.25664e18	0.858744
$683$	6.77789e16	0.0255482	0.0127741	−	0.999918i	$-0.495934\pi$
$683$	6.77789e16	0.0255482	0.0127741	+	0.999918i	$0.495934\pi$
$684$	−7.11718e17	−0.265732
$685$	−1.90162e18	−0.703290
$686$	−3.49176e18	−1.27920
$687$	5.55357e16	0.0201536
$688$	1.75742e18	0.631759
$689$	1.43403e18	0.510661
$690$	−7.25922e17	−0.256077
$691$	−4.59196e18	−1.60469	−0.802344	−	0.596862i	$-0.796414\pi$
$691$	−4.59196e18	−1.60469	−0.802344	+	0.596862i	$0.796414\pi$
$692$	2.14163e17	0.0741402
$693$	−6.98770e17	−0.239645
$694$	−1.77055e18	−0.601550
$695$	4.56896e17	0.153786
$696$	1.48532e18	0.495289
$697$	−6.17018e18	−2.03838
$698$	−3.07299e17	−0.100578
$699$	7.25464e17	0.235242
$700$	7.87772e17	0.253083
$701$	−3.91029e18	−1.24463	−0.622317	−	0.782765i	$-0.713808\pi$
$701$	−3.91029e18	−1.24463	−0.622317	+	0.782765i	$0.713808\pi$
$702$	−2.11635e17	−0.0667415
$703$	−5.82003e18	−1.81851
$704$	8.19568e17	0.253725
$705$	−7.08384e17	−0.217290
$706$	5.66357e18	1.72131
$707$	1.00593e17	0.0302930
$708$	1.11431e17	0.0332500
$709$	3.21057e18	0.949252	0.474626	−	0.880188i	$-0.342583\pi$
$709$	3.21057e18	0.949252	0.474626	+	0.880188i	$0.342583\pi$
$710$	−1.17886e18	−0.345370
$711$	−5.20452e17	−0.151087
$712$	7.37659e16	0.0212195
$713$	2.05701e18	0.586346
$714$	2.70387e18	0.763745
$715$	−4.64619e17	−0.130049
$716$	1.06409e18	0.295151
$717$	−1.97944e18	−0.544087
$718$	−1.92203e18	−0.523542
$719$	6.18425e18	1.66936	0.834679	−	0.550737i	$-0.185653\pi$
$719$	6.18425e18	1.66936	0.834679	+	0.550737i	$0.185653\pi$
$720$	6.97157e17	0.186496
$721$	−3.25147e18	−0.861986
$722$	−1.02745e19	−2.69942
$723$	2.51644e17	0.0655220
$724$	−4.98631e17	−0.128670
$725$	−3.99994e18	−1.02296
$726$	−1.93538e16	−0.00490545
$727$	−3.41497e18	−0.857855	−0.428927	−	0.903339i	$-0.641108\pi$
$727$	−3.41497e18	−0.857855	−0.428927	+	0.903339i	$0.641108\pi$
$728$	−5.56471e17	−0.138544
$729$	1.50095e17	0.0370370
$730$	2.85504e18	0.698254
$731$	−3.21420e18	−0.779130
$732$	−4.55982e17	−0.109553
$733$	7.38761e18	1.75925	0.879626	−	0.475667i	$-0.157793\pi$
$733$	7.38761e18	1.75925	0.879626	+	0.475667i	$0.157793\pi$
$734$	9.83600e17	0.232164
$735$	5.39090e17	0.126123
$736$	−2.93661e18	−0.680989
$737$	2.43937e17	0.0560712
$738$	2.32945e18	0.530747
$739$	1.68606e18	0.380790	0.190395	−	0.981708i	$-0.439023\pi$
$739$	1.68606e18	0.380790	0.190395	+	0.981708i	$0.439023\pi$
$740$	−8.94849e17	−0.200329
$741$	−1.35389e18	−0.300446
$742$	6.91694e18	1.52156
$743$	4.13569e18	0.901821	0.450910	−	0.892569i	$-0.351099\pi$
$743$	4.13569e18	0.901821	0.450910	+	0.892569i	$0.351099\pi$
$744$	−1.27452e18	−0.275502
$745$	1.13356e16	0.00242901
$746$	−7.94874e16	−0.0168848
$747$	−2.63116e18	−0.554069
$748$	3.26951e18	0.682531
$749$	−4.32369e18	−0.894794
$750$	−2.72800e18	−0.559688
$751$	2.78525e18	0.566507	0.283253	−	0.959045i	$-0.408586\pi$
$751$	2.78525e18	0.566507	0.283253	+	0.959045i	$0.408586\pi$
$752$	−5.18482e18	−1.04549
$753$	8.33305e17	0.166585
$754$	−2.24141e18	−0.444230
$755$	2.27905e18	0.447815
$756$	−3.13074e17	−0.0609895
$757$	−6.22247e18	−1.20182	−0.600911	−	0.799316i	$-0.705195\pi$
$757$	−6.22247e18	−1.20182	−0.600911	+	0.799316i	$0.705195\pi$
$758$	5.48873e18	1.05105
$759$	−2.51131e18	−0.476792
$760$	2.87740e18	0.541641
$761$	−6.95135e18	−1.29738	−0.648692	−	0.761051i	$-0.724684\pi$
$761$	−6.95135e18	−1.29738	−0.648692	+	0.761051i	$0.724684\pi$
$762$	2.24066e18	0.414638
$763$	−3.01045e18	−0.552359
$764$	−2.37343e18	−0.431786
$765$	−1.27505e18	−0.230000
$766$	−2.19186e18	−0.392037
$767$	2.11975e17	0.0375936
$768$	3.63012e18	0.638370
$769$	9.83745e18	1.71538	0.857692	−	0.514164i	$-0.171898\pi$
$769$	9.83745e18	1.71538	0.857692	+	0.514164i	$0.171898\pi$
$770$	−2.24105e18	−0.387492
$771$	−2.43123e18	−0.416844
$772$	3.49122e18	0.593560
$773$	3.78743e18	0.638525	0.319262	−	0.947666i	$-0.396565\pi$
$773$	3.78743e18	0.638525	0.319262	+	0.947666i	$0.396565\pi$
$774$	1.21347e18	0.202868
$775$	3.43228e18	0.569012
$776$	3.56657e17	0.0586339
$777$	−2.56014e18	−0.417376
$778$	9.61502e18	1.55447
$779$	1.49022e19	2.38923
$780$	−2.08166e17	−0.0330974
$781$	−4.07825e18	−0.643046
$782$	9.71745e18	1.51953
$783$	1.58964e18	0.246518
$784$	3.94572e18	0.606837
$785$	−5.28060e18	−0.805435
$786$	−7.92477e17	−0.119878
$787$	1.63498e18	0.245288	0.122644	−	0.992451i	$-0.460863\pi$
$787$	1.63498e18	0.245288	0.122644	+	0.992451i	$0.460863\pi$
$788$	4.53477e17	0.0674737
$789$	5.80098e17	0.0856053
$790$	−1.66916e18	−0.244300
$791$	−4.99394e18	−0.724931
$792$	1.55601e18	0.224026
$793$	−8.67409e17	−0.123865
$794$	1.62549e19	2.30225
$795$	−3.26178e18	−0.458213
$796$	−4.41608e18	−0.615321
$797$	7.73550e18	1.06908	0.534539	−	0.845144i	$-0.320485\pi$
$797$	7.73550e18	1.06908	0.534539	+	0.845144i	$0.320485\pi$
$798$	−6.53041e18	−0.895203
$799$	9.48267e18	1.28937
$800$	−4.89997e18	−0.660858
$801$	7.89471e16	0.0105615
$802$	1.63987e19	2.17608
$803$	9.87694e18	1.30008
$804$	1.09293e17	0.0142701
$805$	−2.04280e18	−0.264578
$806$	1.92332e18	0.247100
$807$	−6.48474e18	−0.826446
$808$	−2.23999e17	−0.0283187
$809$	−1.10550e18	−0.138642	−0.0693210	−	0.997594i	$-0.522083\pi$
$809$	−1.10550e18	−0.138642	−0.0693210	+	0.997594i	$0.522083\pi$
$810$	4.81375e17	0.0598868
$811$	−7.65197e18	−0.944360	−0.472180	−	0.881502i	$-0.656533\pi$
$811$	−7.65197e18	−0.944360	−0.472180	+	0.881502i	$0.656533\pi$
$812$	−3.31575e18	−0.405945
$813$	−3.90558e18	−0.474348
$814$	−1.00938e19	−1.21618
$815$	3.07059e18	0.367027
$816$	−9.33238e18	−1.10664
$817$	7.76295e18	0.913236
$818$	1.38578e19	1.61733
$819$	−5.95557e17	−0.0689569
$820$	2.29127e18	0.263200
$821$	4.27254e18	0.486918	0.243459	−	0.969911i	$-0.421718\pi$
$821$	4.27254e18	0.486918	0.243459	+	0.969911i	$0.421718\pi$
$822$	−9.61040e18	−1.08661
$823$	5.01299e18	0.562339	0.281169	−	0.959658i	$-0.409278\pi$
$823$	5.01299e18	0.562339	0.281169	+	0.959658i	$0.409278\pi$
$824$	7.24032e18	0.805807
$825$	−4.19032e18	−0.462697
$826$	1.02245e18	0.112013
$827$	8.17322e18	0.888397	0.444199	−	0.895928i	$-0.353488\pi$
$827$	8.17322e18	0.888397	0.444199	+	0.895928i	$0.353488\pi$
$828$	−1.12516e18	−0.121343
$829$	1.32811e19	1.42112	0.710559	−	0.703637i	$-0.248442\pi$
$829$	1.32811e19	1.42112	0.710559	+	0.703637i	$0.248442\pi$
$830$	−8.43852e18	−0.895898
$831$	−4.52180e18	−0.476327
$832$	6.98512e17	0.0730083
$833$	−7.21645e18	−0.748395
$834$	2.30906e18	0.237606
$835$	7.02914e18	0.717695
$836$	−7.89653e18	−0.800010
$837$	−1.36405e18	−0.137124
$838$	1.70366e19	1.69940
$839$	6.20921e18	0.614587	0.307293	−	0.951615i	$-0.400577\pi$
$839$	6.20921e18	0.614587	0.307293	+	0.951615i	$0.400577\pi$
$840$	1.26572e18	0.124315
$841$	6.57522e18	0.640821
$842$	2.03057e19	1.96376
$843$	7.35089e18	0.705441
$844$	−5.04187e18	−0.480138
$845$	4.35304e18	0.411362
$846$	−3.58003e18	−0.335722
$847$	−5.44633e16	−0.00506829
$848$	−2.38737e19	−2.20469
$849$	−6.48630e18	−0.594425
$850$	1.62143e19	1.47461
$851$	−9.20089e18	−0.830401
$852$	−1.82720e18	−0.163655
$853$	8.60050e18	0.764460	0.382230	−	0.924067i	$-0.375156\pi$
$853$	8.60050e18	0.764460	0.382230	+	0.924067i	$0.375156\pi$
$854$	−4.18389e18	−0.369066
$855$	3.07950e18	0.269588
$856$	9.62793e18	0.836476
$857$	1.07445e18	0.0926426	0.0463213	−	0.998927i	$-0.485250\pi$
$857$	1.07445e18	0.0926426	0.0463213	+	0.998927i	$0.485250\pi$
$858$	−2.34809e18	−0.200931
$859$	4.33075e18	0.367797	0.183898	−	0.982945i	$-0.441128\pi$
$859$	4.33075e18	0.367797	0.183898	+	0.982945i	$0.441128\pi$
$860$	1.19358e18	0.100603
$861$	6.55526e18	0.548365
$862$	−2.89515e18	−0.240366
$863$	3.00588e17	0.0247686	0.0123843	−	0.999923i	$-0.496058\pi$
$863$	3.00588e17	0.0247686	0.0123843	+	0.999923i	$0.496058\pi$
$864$	1.94733e18	0.159258
$865$	−9.26651e17	−0.0752163
$866$	4.05530e18	0.326705
$867$	9.84783e18	0.787438
$868$	2.84519e18	0.225804
$869$	−5.77442e18	−0.454863
$870$	5.09822e18	0.398605
$871$	2.07906e17	0.0161343
$872$	6.70361e18	0.516359
$873$	3.81708e17	0.0291836
$874$	−2.34696e19	−1.78107
$875$	−7.67680e18	−0.578266
$876$	4.42522e18	0.330871
$877$	5.68672e18	0.422051	0.211025	−	0.977481i	$-0.432320\pi$
$877$	5.68672e18	0.422051	0.211025	+	0.977481i	$0.432320\pi$
$878$	−1.82122e19	−1.34168
$879$	−2.39428e18	−0.175085
$880$	7.73497e18	0.561463
$881$	−2.30035e19	−1.65749	−0.828744	−	0.559628i	$-0.810944\pi$
$881$	−2.30035e19	−1.65749	−0.828744	+	0.559628i	$0.810944\pi$
$882$	2.72446e18	0.194865
$883$	1.11208e19	0.789571	0.394786	−	0.918773i	$-0.370819\pi$
$883$	1.11208e19	0.789571	0.394786	+	0.918773i	$0.370819\pi$
$884$	2.78658e18	0.196396
$885$	−4.82148e17	−0.0337326
$886$	1.75640e19	1.21984
$887$	−1.02391e19	−0.705923	−0.352962	−	0.935638i	$-0.614825\pi$
$887$	−1.02391e19	−0.705923	−0.352962	+	0.935638i	$0.614825\pi$
$888$	5.70088e18	0.390174
$889$	6.30541e18	0.428402
$890$	2.53195e17	0.0170773
$891$	1.66530e18	0.111503
$892$	3.83194e17	0.0254711
$893$	−2.29026e19	−1.51130
$894$	5.72879e16	0.00375292
$895$	−4.60417e18	−0.299435
$896$	1.25513e19	0.810379
$897$	−2.14037e18	−0.137195
$898$	7.55483e18	0.480760
$899$	−1.44465e19	−0.912696
$900$	−1.87741e18	−0.117756
$901$	4.36633e19	2.71898
$902$	2.58453e19	1.59786
$903$	3.41480e18	0.209602
$904$	1.11204e19	0.677684
$905$	2.15751e18	0.130538
$906$	1.15179e19	0.691893
$907$	1.48848e19	0.887761	0.443881	−	0.896086i	$-0.353601\pi$
$907$	1.48848e19	0.887761	0.443881	+	0.896086i	$0.353601\pi$
$908$	−1.21444e19	−0.719149
$909$	−2.39733e17	−0.0140949
$910$	−1.91004e18	−0.111499
$911$	1.33460e19	0.773540	0.386770	−	0.922176i	$-0.373591\pi$
$911$	1.33460e19	0.773540	0.386770	+	0.922176i	$0.373591\pi$
$912$	2.25396e19	1.29712
$913$	−2.91928e19	−1.66808
$914$	9.54639e18	0.541613
$915$	1.97297e18	0.111143
$916$	2.76066e17	0.0154416
$917$	−2.23009e18	−0.123857
$918$	−6.44385e18	−0.355360
$919$	−2.89001e19	−1.58252	−0.791260	−	0.611480i	$-0.790575\pi$
$919$	−2.89001e19	−1.58252	−0.791260	+	0.611480i	$0.790575\pi$
$920$	4.54888e18	0.247334
$921$	−6.62912e18	−0.357906
$922$	−4.03264e19	−2.16191
$923$	−3.47586e18	−0.185034
$924$	−3.47356e18	−0.183615
$925$	−1.53524e19	−0.805852
$926$	1.14828e19	0.598519
$927$	7.74888e18	0.401070
$928$	2.06241e19	1.06002
$929$	1.62264e19	0.828169	0.414085	−	0.910238i	$-0.364102\pi$
$929$	1.62264e19	0.828169	0.414085	+	0.910238i	$0.364102\pi$
$930$	−4.37469e18	−0.221722
$931$	1.74292e19	0.877212
$932$	3.60626e18	0.180241
$933$	1.02191e19	0.507204
$934$	−1.45670e19	−0.717983
$935$	−1.41467e19	−0.692436
$936$	1.32618e18	0.0644627
$937$	2.81456e19	1.35864	0.679318	−	0.733844i	$-0.262276\pi$
$937$	2.81456e19	1.35864	0.679318	+	0.733844i	$0.262276\pi$
$938$	1.00282e18	0.0480734
$939$	−1.58466e18	−0.0754412
$940$	−3.52135e18	−0.166486
$941$	−2.97283e19	−1.39585	−0.697923	−	0.716172i	$-0.745892\pi$
$941$	−2.97283e19	−1.39585	−0.697923	+	0.716172i	$0.745892\pi$
$942$	−2.66871e19	−1.24443
$943$	2.35589e19	1.09101
$944$	−3.52896e18	−0.162304
$945$	1.35463e18	0.0618747
$946$	1.34635e19	0.610752
$947$	−1.34786e19	−0.607253	−0.303626	−	0.952791i	$-0.598197\pi$
$947$	−1.34786e19	−0.607253	−0.303626	+	0.952791i	$0.598197\pi$
$948$	−2.58715e18	−0.115762
$949$	8.41804e18	0.374094
$950$	−3.91609e19	−1.72842
$951$	1.23084e19	0.539546
$952$	−1.69434e19	−0.737668
$953$	8.08120e18	0.349440	0.174720	−	0.984618i	$-0.444098\pi$
$953$	8.08120e18	0.349440	0.174720	+	0.984618i	$0.444098\pi$
$954$	−1.64844e19	−0.707960
$955$	1.02695e19	0.438053
$956$	−9.83973e18	−0.416876
$957$	1.76371e19	0.742166
$958$	3.25753e19	1.36148
$959$	−2.70444e19	−1.12268
$960$	−1.58880e18	−0.0655099
$961$	−1.20212e19	−0.492319
$962$	−8.60290e18	−0.349951
$963$	1.03042e19	0.416335
$964$	1.25091e18	0.0502026
$965$	−1.51060e19	−0.602174
$966$	−1.03239e19	−0.408784
$967$	1.29236e19	0.508290	0.254145	−	0.967166i	$-0.418206\pi$
$967$	1.29236e19	0.508290	0.254145	+	0.967166i	$0.418206\pi$
$968$	1.21278e17	0.00473797
$969$	−4.12233e19	−1.59970
$970$	1.22419e18	0.0471882
$971$	4.54011e19	1.73837	0.869184	−	0.494489i	$-0.164645\pi$
$971$	4.54011e19	1.73837	0.869184	+	0.494489i	$0.164645\pi$
$972$	7.46115e17	0.0283776
$973$	6.49789e18	0.245493
$974$	−4.61384e19	−1.73153
$975$	−3.57138e18	−0.133139
$976$	1.44406e19	0.534764
$977$	−1.55782e19	−0.573062	−0.286531	−	0.958071i	$-0.592502\pi$
$977$	−1.55782e19	−0.573062	−0.286531	+	0.958071i	$0.592502\pi$
$978$	1.55182e19	0.567072
$979$	8.75920e17	0.0317963
$980$	2.67980e18	0.0966346
$981$	7.17447e18	0.257005
$982$	−3.06617e18	−0.109112
$983$	−8.04089e18	−0.284254	−0.142127	−	0.989848i	$-0.545394\pi$
$983$	−8.04089e18	−0.284254	−0.142127	+	0.989848i	$0.545394\pi$
$984$	−1.45972e19	−0.512625
$985$	−1.96213e18	−0.0684530
$986$	−6.82465e19	−2.36527
$987$	−1.00745e19	−0.346866
$988$	−6.73016e18	−0.230200
$989$	1.22724e19	0.417018
$990$	5.34086e18	0.180295
$991$	−4.02795e18	−0.135085	−0.0675423	−	0.997716i	$-0.521516\pi$
$991$	−4.02795e18	−0.135085	−0.0675423	+	0.997716i	$0.521516\pi$
$992$	−1.76971e19	−0.589627
$993$	−1.70630e19	−0.564788
$994$	−1.67656e19	−0.551324
$995$	1.91078e19	0.624252
$996$	−1.30794e19	−0.424525
$997$	−6.13845e19	−1.97943	−0.989715	−	0.143052i	$-0.954308\pi$
$997$	−6.13845e19	−1.97943	−0.989715	+	0.143052i	$0.954308\pi$
$998$	1.05983e19	0.339537
$999$	6.10131e18	0.194199

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.a.1.8	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.a.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-108.701 q^{2} +729.000 q^{3} +3623.83 q^{4} -15679.8 q^{5} -79242.8 q^{6} -222995. q^{7} +496563. q^{8} +531441. q^{9} +O(q^{10})\)	\(q-108.701 q^{2} +729.000 q^{3} +3623.83 q^{4} -15679.8 q^{5} -79242.8 q^{6} -222995. q^{7} +496563. q^{8} +531441. q^{9} +1.70441e6 q^{10} +5.89635e6 q^{11} +2.64177e6 q^{12} +5.02542e6 q^{13} +2.42398e7 q^{14} -1.14306e7 q^{15} -8.36631e7 q^{16} +1.53014e8 q^{17} -5.77680e7 q^{18} -3.69560e8 q^{19} -5.68211e7 q^{20} -1.62564e8 q^{21} -6.40937e8 q^{22} -5.84237e8 q^{23} +3.61994e8 q^{24} -9.74846e8 q^{25} -5.46266e8 q^{26} +3.87420e8 q^{27} -8.08098e8 q^{28} +4.10315e9 q^{29} +1.24251e9 q^{30} -3.52084e9 q^{31} +5.02640e9 q^{32} +4.29844e9 q^{33} -1.66327e10 q^{34} +3.49653e9 q^{35} +1.92585e9 q^{36} +1.57485e10 q^{37} +4.01714e10 q^{38} +3.66353e9 q^{39} -7.78601e9 q^{40} -4.03243e10 q^{41} +1.76708e10 q^{42} -2.10059e10 q^{43} +2.13674e10 q^{44} -8.33290e9 q^{45} +6.35070e10 q^{46} +6.19726e10 q^{47} -6.09904e10 q^{48} -4.71620e10 q^{49} +1.05966e11 q^{50} +1.11547e11 q^{51} +1.82113e10 q^{52} +2.85355e11 q^{53} -4.21129e10 q^{54} -9.24537e10 q^{55} -1.10731e11 q^{56} -2.69409e11 q^{57} -4.46015e11 q^{58} +4.21805e10 q^{59} -4.14226e10 q^{60} -1.72604e11 q^{61} +3.82718e11 q^{62} -1.18509e11 q^{63} +1.38996e11 q^{64} -7.87977e10 q^{65} -4.67243e11 q^{66} +4.13709e10 q^{67} +5.54497e11 q^{68} -4.25909e11 q^{69} -3.80075e11 q^{70} -6.91656e11 q^{71} +2.63894e11 q^{72} +1.67509e12 q^{73} -1.71188e12 q^{74} -7.10663e11 q^{75} -1.33922e12 q^{76} -1.31486e12 q^{77} -3.98228e11 q^{78} -9.79322e11 q^{79} +1.31182e12 q^{80} +2.82430e11 q^{81} +4.38328e12 q^{82} -4.95100e12 q^{83} -5.89104e11 q^{84} -2.39923e12 q^{85} +2.28336e12 q^{86} +2.99120e12 q^{87} +2.92791e12 q^{88} +1.48553e11 q^{89} +9.05792e11 q^{90} -1.12065e12 q^{91} -2.11718e12 q^{92} -2.56669e12 q^{93} -6.73647e12 q^{94} +5.79463e12 q^{95} +3.66424e12 q^{96} +7.18251e11 q^{97} +5.12655e12 q^{98} +3.13356e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 138 q^{2} + 21870 q^{3} + 114598 q^{4} - 137742 q^{5} - 100602 q^{6} - 879443 q^{7} - 872301 q^{8} + 15943230 q^{9}+O(q^{10}) \) 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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