LMFDB - Embedded newform 177.14.a.a.1.10

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			1.10
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)

$f(q)$	$=$	$q-73.9227 q^{2} +729.000 q^{3} -2727.43 q^{4} -22721.6 q^{5} -53889.7 q^{6} +405591. q^{7} +807194. q^{8} +531441. q^{9} +O(q^{10})$	\(q-73.9227 q^{2} +729.000 q^{3} -2727.43 q^{4} -22721.6 q^{5} -53889.7 q^{6} +405591. q^{7} +807194. q^{8} +531441. q^{9} +1.67964e6 q^{10} -6.65185e6 q^{11} -1.98830e6 q^{12} +2.06527e7 q^{13} -2.99824e7 q^{14} -1.65640e7 q^{15} -3.73269e7 q^{16} +2.16354e7 q^{17} -3.92856e7 q^{18} +1.30507e8 q^{19} +6.19715e7 q^{20} +2.95676e8 q^{21} +4.91723e8 q^{22} -7.96941e8 q^{23} +5.88444e8 q^{24} -7.04433e8 q^{25} -1.52670e9 q^{26} +3.87420e8 q^{27} -1.10622e9 q^{28} -3.04026e9 q^{29} +1.22446e9 q^{30} -2.02696e9 q^{31} -3.85323e9 q^{32} -4.84920e9 q^{33} -1.59935e9 q^{34} -9.21566e9 q^{35} -1.44947e9 q^{36} +5.59860e9 q^{37} -9.64743e9 q^{38} +1.50558e10 q^{39} -1.83407e10 q^{40} +3.73394e9 q^{41} -2.18572e10 q^{42} +6.33576e10 q^{43} +1.81425e10 q^{44} -1.20752e10 q^{45} +5.89121e10 q^{46} -2.15292e10 q^{47} -2.72113e10 q^{48} +6.76148e10 q^{49} +5.20736e10 q^{50} +1.57722e10 q^{51} -5.63287e10 q^{52} -2.07104e11 q^{53} -2.86392e10 q^{54} +1.51141e11 q^{55} +3.27390e11 q^{56} +9.51395e10 q^{57} +2.24744e11 q^{58} +4.21805e10 q^{59} +4.51772e10 q^{60} -1.72658e11 q^{61} +1.49838e11 q^{62} +2.15548e11 q^{63} +5.90623e11 q^{64} -4.69261e11 q^{65} +3.58466e11 q^{66} +6.74693e11 q^{67} -5.90090e10 q^{68} -5.80970e11 q^{69} +6.81247e11 q^{70} +3.55112e10 q^{71} +4.28976e11 q^{72} +2.22111e11 q^{73} -4.13864e11 q^{74} -5.13532e11 q^{75} -3.55948e11 q^{76} -2.69793e12 q^{77} -1.11297e12 q^{78} -5.78321e11 q^{79} +8.48126e11 q^{80} +2.82430e11 q^{81} -2.76023e11 q^{82} -3.89792e12 q^{83} -8.06434e11 q^{84} -4.91590e11 q^{85} -4.68357e12 q^{86} -2.21635e12 q^{87} -5.36934e12 q^{88} +5.37443e12 q^{89} +8.92630e11 q^{90} +8.37654e12 q^{91} +2.17360e12 q^{92} -1.47765e12 q^{93} +1.59150e12 q^{94} -2.96532e12 q^{95} -2.80900e12 q^{96} -7.20961e12 q^{97} -4.99827e12 q^{98} -3.53507e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−73.9227	−0.816739	−0.408369	−	0.912817i	$-0.633902\pi$
$2$	−73.9227	−0.816739	−0.408369	+	0.912817i	$0.633902\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	−2727.43	−0.332938
$5$	−22721.6	−0.650329	−0.325165	−	0.945657i	$-0.605420\pi$
$5$	−22721.6	−0.650329	−0.325165	+	0.945657i	$0.605420\pi$
$6$	−53889.7	−0.471544
$7$	405591.	1.30302	0.651509	−	0.758640i	$-0.274136\pi$
$7$	405591.	1.30302	0.651509	+	0.758640i	$0.274136\pi$
$8$	807194.	1.08866
$9$	531441.	0.333333
$10$	1.67964e6	0.531149
$11$	−6.65185e6	−1.13211	−0.566057	−	0.824366i	$-0.691532\pi$
$11$	−6.65185e6	−1.13211	−0.566057	+	0.824366i	$0.691532\pi$
$12$	−1.98830e6	−0.192222
$13$	2.06527e7	1.18671	0.593355	−	0.804941i	$-0.297803\pi$
$13$	2.06527e7	1.18671	0.593355	+	0.804941i	$0.297803\pi$
$14$	−2.99824e7	−1.06423
$15$	−1.65640e7	−0.375468
$16$	−3.73269e7	−0.556214
$17$	2.16354e7	0.217394	0.108697	−	0.994075i	$-0.465332\pi$
$17$	2.16354e7	0.217394	0.108697	+	0.994075i	$0.465332\pi$
$18$	−3.92856e7	−0.272246
$19$	1.30507e8	0.636407	0.318204	−	0.948022i	$-0.396920\pi$
$19$	1.30507e8	0.636407	0.318204	+	0.948022i	$0.396920\pi$
$20$	6.19715e7	0.216519
$21$	2.95676e8	0.752298
$22$	4.91723e8	0.924641
$23$	−7.96941e8	−1.12252	−0.561262	−	0.827638i	$-0.689684\pi$
$23$	−7.96941e8	−1.12252	−0.561262	+	0.827638i	$0.689684\pi$
$24$	5.88444e8	0.628539
$25$	−7.04433e8	−0.577072
$26$	−1.52670e9	−0.969232
$27$	3.87420e8	0.192450
$28$	−1.10622e9	−0.433825
$29$	−3.04026e9	−0.949125	−0.474563	−	0.880222i	$-0.657394\pi$
$29$	−3.04026e9	−0.949125	−0.474563	+	0.880222i	$0.657394\pi$
$30$	1.22446e9	0.306659
$31$	−2.02696e9	−0.410198	−0.205099	−	0.978741i	$-0.565752\pi$
$31$	−2.02696e9	−0.410198	−0.205099	+	0.978741i	$0.565752\pi$
$32$	−3.85323e9	−0.634380
$33$	−4.84920e9	−0.653626
$34$	−1.59935e9	−0.177554
$35$	−9.21566e9	−0.847392
$36$	−1.44947e9	−0.110979
$37$	5.59860e9	0.358730	0.179365	−	0.983783i	$-0.442596\pi$
$37$	5.59860e9	0.358730	0.179365	+	0.983783i	$0.442596\pi$
$38$	−9.64743e9	−0.519778
$39$	1.50558e10	0.685148
$40$	−1.83407e10	−0.707989
$41$	3.73394e9	0.122764	0.0613822	−	0.998114i	$-0.480449\pi$
$41$	3.73394e9	0.122764	0.0613822	+	0.998114i	$0.480449\pi$
$42$	−2.18572e10	−0.614431
$43$	6.33576e10	1.52846	0.764229	−	0.644945i	$-0.223120\pi$
$43$	6.33576e10	1.52846	0.764229	+	0.644945i	$0.223120\pi$
$44$	1.81425e10	0.376924
$45$	−1.20752e10	−0.216776
$46$	5.89121e10	0.916808
$47$	−2.15292e10	−0.291334	−0.145667	−	0.989334i	$-0.546533\pi$
$47$	−2.15292e10	−0.291334	−0.145667	+	0.989334i	$0.546533\pi$
$48$	−2.72113e10	−0.321130
$49$	6.76148e10	0.697858
$50$	5.20736e10	0.471317
$51$	1.57722e10	0.125512
$52$	−5.63287e10	−0.395101
$53$	−2.07104e11	−1.28350	−0.641748	−	0.766916i	$-0.721790\pi$
$53$	−2.07104e11	−1.28350	−0.641748	+	0.766916i	$0.721790\pi$
$54$	−2.86392e10	−0.157181
$55$	1.51141e11	0.736247
$56$	3.27390e11	1.41855
$57$	9.51395e10	0.367430
$58$	2.24744e11	0.775187
$59$	4.21805e10	0.130189
$59$	4.21805e10	0.130189
$60$	4.51772e10	0.125008
$61$	−1.72658e11	−0.429084	−0.214542	−	0.976715i	$-0.568826\pi$
$61$	−1.72658e11	−0.429084	−0.214542	+	0.976715i	$0.568826\pi$
$62$	1.49838e11	0.335025
$63$	2.15548e11	0.434340
$64$	5.90623e11	1.07434
$65$	−4.69261e11	−0.771753
$66$	3.58466e11	0.533842
$67$	6.74693e11	0.911214	0.455607	−	0.890181i	$-0.349422\pi$
$67$	6.74693e11	0.911214	0.455607	+	0.890181i	$0.349422\pi$
$68$	−5.90090e10	−0.0723787
$69$	−5.80970e11	−0.648089
$70$	6.81247e11	0.692097
$71$	3.55112e10	0.0328993	0.0164496	−	0.999865i	$-0.494764\pi$
$71$	3.55112e10	0.0328993	0.0164496	+	0.999865i	$0.494764\pi$
$72$	4.28976e11	0.362887
$73$	2.22111e11	0.171779	0.0858896	−	0.996305i	$-0.472627\pi$
$73$	2.22111e11	0.171779	0.0858896	+	0.996305i	$0.472627\pi$
$74$	−4.13864e11	−0.292989
$75$	−5.13532e11	−0.333173
$76$	−3.55948e11	−0.211884
$77$	−2.69793e12	−1.47517
$78$	−1.11297e12	−0.559586
$79$	−5.78321e11	−0.267666	−0.133833	−	0.991004i	$-0.542729\pi$
$79$	−5.78321e11	−0.267666	−0.133833	+	0.991004i	$0.542729\pi$
$80$	8.48126e11	0.361722
$81$	2.82430e11	0.111111
$82$	−2.76023e11	−0.100266
$83$	−3.89792e12	−1.30865	−0.654327	−	0.756211i	$-0.727048\pi$
$83$	−3.89792e12	−1.30865	−0.654327	+	0.756211i	$0.727048\pi$
$84$	−8.06434e11	−0.250469
$85$	−4.91590e11	−0.141378
$86$	−4.68357e12	−1.24835
$87$	−2.21635e12	−0.547978
$88$	−5.36934e12	−1.23249
$89$	5.37443e12	1.14630	0.573149	−	0.819451i	$-0.305722\pi$
$89$	5.37443e12	1.14630	0.573149	+	0.819451i	$0.305722\pi$
$90$	8.92630e11	0.177050
$91$	8.37654e12	1.54631
$92$	2.17360e12	0.373731
$93$	−1.47765e12	−0.236828
$94$	1.59150e12	0.237944
$95$	−2.96532e12	−0.413874
$96$	−2.80900e12	−0.366260
$97$	−7.20961e12	−0.878811	−0.439405	−	0.898289i	$-0.644811\pi$
$97$	−7.20961e12	−0.878811	−0.439405	+	0.898289i	$0.644811\pi$
$98$	−4.99827e12	−0.569968
$99$	−3.53507e12	−0.377371
$100$	1.92129e12	0.192129
$101$	−1.99582e12	−0.187082	−0.0935412	−	0.995615i	$-0.529819\pi$
$101$	−1.99582e12	−0.187082	−0.0935412	+	0.995615i	$0.529819\pi$
$102$	−1.16592e12	−0.102511
$103$	9.85943e12	0.813598	0.406799	−	0.913518i	$-0.366645\pi$
$103$	9.85943e12	0.813598	0.406799	+	0.913518i	$0.366645\pi$
$104$	1.66707e13	1.29193
$105$	−6.71822e12	−0.489242
$106$	1.53097e13	1.04828
$107$	2.52989e13	1.62970	0.814848	−	0.579675i	$-0.196820\pi$
$107$	2.52989e13	1.62970	0.814848	+	0.579675i	$0.196820\pi$
$108$	−1.05666e12	−0.0640740
$109$	−1.25521e13	−0.716877	−0.358438	−	0.933553i	$-0.616691\pi$
$109$	−1.25521e13	−0.716877	−0.358438	+	0.933553i	$0.616691\pi$
$110$	−1.11727e13	−0.601321
$111$	4.08138e12	0.207113
$112$	−1.51394e13	−0.724757
$113$	2.02967e13	0.917097	0.458549	−	0.888669i	$-0.348369\pi$
$113$	2.02967e13	0.917097	0.458549	+	0.888669i	$0.348369\pi$
$114$	−7.03298e12	−0.300094
$115$	1.81078e13	0.730010
$116$	8.29209e12	0.316000
$117$	1.09757e13	0.395570
$118$	−3.11810e12	−0.106330
$119$	8.77512e12	0.283268
$120$	−1.33704e13	−0.408758
$121$	9.72444e12	0.281682
$122$	1.27633e13	0.350449
$123$	2.72204e12	0.0708780
$124$	5.52839e12	0.136571
$125$	4.37421e13	1.02562
$126$	−1.59339e13	−0.354742
$127$	−7.48199e13	−1.58232	−0.791158	−	0.611612i	$-0.790521\pi$
$127$	−7.48199e13	−1.58232	−0.791158	+	0.611612i	$0.790521\pi$
$128$	−1.20948e13	−0.243072
$129$	4.61877e13	0.882456
$130$	3.46891e13	0.630320
$131$	−5.97698e13	−1.03328	−0.516641	−	0.856202i	$-0.672818\pi$
$131$	−5.97698e13	−1.03328	−0.516641	+	0.856202i	$0.672818\pi$
$132$	1.32259e13	0.217617
$133$	5.29324e13	0.829251
$134$	−4.98752e13	−0.744223
$135$	−8.80280e12	−0.125156
$136$	1.74640e13	0.236668
$137$	6.52191e13	0.842735	0.421367	−	0.906890i	$-0.361550\pi$
$137$	6.52191e13	0.842735	0.421367	+	0.906890i	$0.361550\pi$
$138$	4.29469e13	0.529319
$139$	7.83997e13	0.921973	0.460987	−	0.887407i	$-0.347496\pi$
$139$	7.83997e13	0.921973	0.460987	+	0.887407i	$0.347496\pi$
$140$	2.51351e13	0.282129
$141$	−1.56948e13	−0.168202
$142$	−2.62509e12	−0.0268701
$143$	−1.37379e14	−1.34349
$144$	−1.98370e13	−0.185405
$145$	6.90795e13	0.617244
$146$	−1.64190e13	−0.140299
$147$	4.92912e13	0.402909
$148$	−1.52698e13	−0.119435
$149$	−5.43424e13	−0.406844	−0.203422	−	0.979091i	$-0.565206\pi$
$149$	−5.43424e13	−0.406844	−0.203422	+	0.979091i	$0.565206\pi$
$150$	3.79617e13	0.272115
$151$	2.63424e14	1.80844	0.904222	−	0.427064i	$-0.140452\pi$
$151$	2.63424e14	1.80844	0.904222	+	0.427064i	$0.140452\pi$
$152$	1.05344e14	0.692832
$153$	1.14979e13	0.0724646
$154$	1.99438e14	1.20483
$155$	4.60557e13	0.266764
$156$	−4.10636e13	−0.228112
$157$	−3.57640e14	−1.90589	−0.952947	−	0.303136i	$-0.901966\pi$
$157$	−3.57640e14	−1.90589	−0.952947	+	0.303136i	$0.901966\pi$
$158$	4.27511e13	0.218613
$159$	−1.50978e14	−0.741027
$160$	8.75514e13	0.412556
$161$	−3.23232e14	−1.46267
$162$	−2.08780e13	−0.0907487
$163$	−6.38714e12	−0.0266739	−0.0133370	−	0.999911i	$-0.504245\pi$
$163$	−6.38714e12	−0.0266739	−0.0133370	+	0.999911i	$0.504245\pi$
$164$	−1.01841e13	−0.0408729
$165$	1.10181e14	0.425072
$166$	2.88145e14	1.06883
$167$	−9.22707e13	−0.329160	−0.164580	−	0.986364i	$-0.552627\pi$
$167$	−9.22707e13	−0.329160	−0.164580	+	0.986364i	$0.552627\pi$
$168$	2.38668e14	0.818999
$169$	1.23658e14	0.408281
$170$	3.63397e13	0.115468
$171$	6.93567e13	0.212136
$172$	−1.72803e14	−0.508882
$173$	−6.02265e14	−1.70800	−0.854000	−	0.520272i	$-0.825830\pi$
$173$	−6.02265e14	−1.70800	−0.854000	+	0.520272i	$0.825830\pi$
$174$	1.63839e14	0.447555
$175$	−2.85712e14	−0.751935
$176$	2.48293e14	0.629698
$177$	3.07496e13	0.0751646
$178$	−3.97293e14	−0.936226
$179$	1.25780e13	0.0285803	0.0142902	−	0.999898i	$-0.495451\pi$
$179$	1.25780e13	0.0285803	0.0142902	+	0.999898i	$0.495451\pi$
$180$	3.29342e13	0.0721731
$181$	−5.90066e13	−0.124735	−0.0623677	−	0.998053i	$-0.519865\pi$
$181$	−5.90066e13	−0.124735	−0.0623677	+	0.998053i	$0.519865\pi$
$182$	−6.19217e14	−1.26293
$183$	−1.25867e14	−0.247732
$184$	−6.43286e14	−1.22205
$185$	−1.27209e14	−0.233293
$186$	1.09232e14	0.193427
$187$	−1.43916e14	−0.246114
$188$	5.87194e13	0.0969963
$189$	1.57134e14	0.250766
$190$	2.19205e14	0.338027
$191$	4.09226e14	0.609882	0.304941	−	0.952371i	$-0.401363\pi$
$191$	4.09226e14	0.609882	0.304941	+	0.952371i	$0.401363\pi$
$192$	4.30564e14	0.620269
$193$	6.63173e14	0.923644	0.461822	−	0.886973i	$-0.347196\pi$
$193$	6.63173e14	0.923644	0.461822	+	0.886973i	$0.347196\pi$
$194$	5.32954e14	0.717759
$195$	−3.42092e14	−0.445572
$196$	−1.84415e14	−0.232344
$197$	1.17801e15	1.43588	0.717942	−	0.696103i	$-0.245084\pi$
$197$	1.17801e15	1.43588	0.717942	+	0.696103i	$0.245084\pi$
$198$	2.61322e14	0.308214
$199$	−9.99388e14	−1.14075	−0.570373	−	0.821386i	$-0.693201\pi$
$199$	−9.99388e14	−1.14075	−0.570373	+	0.821386i	$0.693201\pi$
$200$	−5.68614e14	−0.628236
$201$	4.91851e14	0.526089
$202$	1.47537e14	0.152797
$203$	−1.23310e15	−1.23673
$204$	−4.30176e13	−0.0417878
$205$	−8.48410e13	−0.0798373
$206$	−7.28836e14	−0.664497
$207$	−4.23527e14	−0.374175
$208$	−7.70901e14	−0.660065
$209$	−8.68113e14	−0.720486
$210$	4.96629e14	0.399583
$211$	−6.25962e14	−0.488329	−0.244164	−	0.969734i	$-0.578514\pi$
$211$	−6.25962e14	−0.488329	−0.244164	+	0.969734i	$0.578514\pi$
$212$	5.64860e14	0.427325
$213$	2.58877e13	0.0189944
$214$	−1.87016e15	−1.33104
$215$	−1.43958e15	−0.994001
$216$	3.12724e14	0.209513
$217$	−8.22116e14	−0.534496
$218$	9.27886e14	0.585501
$219$	1.61919e14	0.0991768
$220$	−4.12225e14	−0.245125
$221$	4.46829e14	0.257983
$222$	−3.01707e14	−0.169157
$223$	−1.95755e15	−1.06594	−0.532968	−	0.846136i	$-0.678923\pi$
$223$	−1.95755e15	−1.06594	−0.532968	+	0.846136i	$0.678923\pi$
$224$	−1.56283e15	−0.826610
$225$	−3.74365e14	−0.192357
$226$	−1.50039e15	−0.749029
$227$	−6.83556e14	−0.331594	−0.165797	−	0.986160i	$-0.553020\pi$
$227$	−6.83556e14	−0.331594	−0.165797	+	0.986160i	$0.553020\pi$
$228$	−2.59486e14	−0.122331
$229$	−1.85010e15	−0.847744	−0.423872	−	0.905722i	$-0.639329\pi$
$229$	−1.85010e15	−0.847744	−0.423872	+	0.905722i	$0.639329\pi$
$230$	−1.33858e15	−0.596227
$231$	−1.96679e15	−0.851688
$232$	−2.45408e15	−1.03328
$233$	−1.56061e15	−0.638971	−0.319486	−	0.947591i	$-0.603510\pi$
$233$	−1.56061e15	−0.638971	−0.319486	+	0.947591i	$0.603510\pi$
$234$	−8.11353e14	−0.323077
$235$	4.89177e14	0.189463
$236$	−1.15044e14	−0.0433449
$237$	−4.21596e14	−0.154537
$238$	−6.48681e14	−0.231356
$239$	−3.48409e15	−1.20921	−0.604606	−	0.796524i	$-0.706670\pi$
$239$	−3.48409e15	−1.20921	−0.604606	+	0.796524i	$0.706670\pi$
$240$	6.18284e14	0.208840
$241$	−1.87385e15	−0.616061	−0.308031	−	0.951376i	$-0.599670\pi$
$241$	−1.87385e15	−0.616061	−0.308031	+	0.951376i	$0.599670\pi$
$242$	−7.18857e14	−0.230061
$243$	2.05891e14	0.0641500
$244$	4.70912e14	0.142858
$245$	−1.53631e15	−0.453838
$246$	−2.01221e14	−0.0578888
$247$	2.69532e15	0.755231
$248$	−1.63615e15	−0.446567
$249$	−2.84158e15	−0.755552
$250$	−3.23354e15	−0.837660
$251$	3.05131e15	0.770207	0.385104	−	0.922873i	$-0.374166\pi$
$251$	3.05131e15	0.770207	0.385104	+	0.922873i	$0.374166\pi$
$252$	−5.87891e14	−0.144608
$253$	5.30114e15	1.27082
$254$	5.53090e15	1.29234
$255$	−3.58369e14	−0.0816243
$256$	−3.94430e15	−0.875811
$257$	2.01896e15	0.437082	0.218541	−	0.975828i	$-0.429870\pi$
$257$	2.01896e15	0.437082	0.218541	+	0.975828i	$0.429870\pi$
$258$	−3.41432e15	−0.720736
$259$	2.27074e15	0.467432
$260$	1.27988e15	0.256946
$261$	−1.61572e15	−0.316375
$262$	4.41835e15	0.843921
$263$	−5.63699e15	−1.05035	−0.525176	−	0.850994i	$-0.676000\pi$
$263$	−5.63699e15	−1.05035	−0.525176	+	0.850994i	$0.676000\pi$
$264$	−3.91425e15	−0.711578
$265$	4.70572e15	0.834695
$266$	−3.91291e15	−0.677281
$267$	3.91796e15	0.661816
$268$	−1.84018e15	−0.303378
$269$	−3.56599e15	−0.573839	−0.286920	−	0.957955i	$-0.592631\pi$
$269$	−3.56599e15	−0.573839	−0.286920	+	0.957955i	$0.592631\pi$
$270$	6.50727e14	0.102220
$271$	−7.85140e15	−1.20406	−0.602028	−	0.798475i	$-0.705640\pi$
$271$	−7.85140e15	−1.20406	−0.602028	+	0.798475i	$0.705640\pi$
$272$	−8.07582e14	−0.120917
$273$	6.10650e15	0.892760
$274$	−4.82117e15	−0.688294
$275$	4.68579e15	0.653311
$276$	1.58456e15	0.215774
$277$	8.54872e15	1.13706	0.568529	−	0.822663i	$-0.307513\pi$
$277$	8.54872e15	1.13706	0.568529	+	0.822663i	$0.307513\pi$
$278$	−5.79552e15	−0.753011
$279$	−1.07721e15	−0.136733
$280$	−7.43883e15	−0.922523
$281$	1.27072e16	1.53978	0.769892	−	0.638174i	$-0.220310\pi$
$281$	1.27072e16	1.53978	0.769892	+	0.638174i	$0.220310\pi$
$282$	1.16020e15	0.137377
$283$	−5.88727e15	−0.681244	−0.340622	−	0.940200i	$-0.610638\pi$
$283$	−5.88727e15	−0.681244	−0.340622	+	0.940200i	$0.610638\pi$
$284$	−9.68543e13	−0.0109534
$285$	−2.16172e15	−0.238950
$286$	1.01554e16	1.09728
$287$	1.51445e15	0.159964
$288$	−2.04776e15	−0.211460
$289$	−9.43649e15	−0.952740
$290$	−5.10654e15	−0.504127
$291$	−5.25580e15	−0.507382
$292$	−6.05791e14	−0.0571918
$293$	−1.39837e16	−1.29117	−0.645585	−	0.763688i	$-0.723386\pi$
$293$	−1.39837e16	−1.29117	−0.645585	+	0.763688i	$0.723386\pi$
$294$	−3.64374e15	−0.329071
$295$	−9.58408e14	−0.0846657
$296$	4.51916e15	0.390536
$297$	−2.57706e15	−0.217875
$298$	4.01714e15	0.332285
$299$	−1.64590e16	−1.33211
$300$	1.40062e15	0.110926
$301$	2.56972e16	1.99161
$302$	−1.94730e16	−1.47703
$303$	−1.45495e15	−0.108012
$304$	−4.87142e15	−0.353979
$305$	3.92306e15	0.279046
$306$	−8.49959e14	−0.0591846
$307$	1.64488e14	0.0112133	0.00560667	−	0.999984i	$-0.498215\pi$
$307$	1.64488e14	0.0112133	0.00560667	+	0.999984i	$0.498215\pi$
$308$	7.35841e15	0.491139
$309$	7.18753e15	0.469731
$310$	−3.40456e15	−0.217877
$311$	−2.72673e16	−1.70884	−0.854418	−	0.519586i	$-0.826086\pi$
$311$	−2.72673e16	−1.70884	−0.854418	+	0.519586i	$0.826086\pi$
$312$	1.21530e16	0.745894
$313$	−1.85330e16	−1.11406	−0.557028	−	0.830494i	$-0.688058\pi$
$313$	−1.85330e16	−1.11406	−0.557028	+	0.830494i	$0.688058\pi$
$314$	2.64378e16	1.55662
$315$	−4.89758e15	−0.282464
$316$	1.57733e15	0.0891161
$317$	−1.76561e16	−0.977260	−0.488630	−	0.872491i	$-0.662503\pi$
$317$	−1.76561e16	−0.977260	−0.488630	+	0.872491i	$0.662503\pi$
$318$	1.11607e16	0.605225
$319$	2.02234e16	1.07452
$320$	−1.34199e16	−0.698673
$321$	1.84429e16	0.940905
$322$	2.38942e16	1.19462
$323$	2.82357e15	0.138351
$324$	−7.70307e14	−0.0369931
$325$	−1.45484e16	−0.684817
$326$	4.72155e14	0.0217856
$327$	−9.15049e15	−0.413889
$328$	3.01402e15	0.133649
$329$	−8.73204e15	−0.379614
$330$	−8.14492e15	−0.347173
$331$	5.12050e15	0.214008	0.107004	−	0.994259i	$-0.465874\pi$
$331$	5.12050e15	0.214008	0.107004	+	0.994259i	$0.465874\pi$
$332$	1.06313e16	0.435701
$333$	2.97532e15	0.119577
$334$	6.82091e15	0.268838
$335$	−1.53301e16	−0.592589
$336$	−1.10367e16	−0.418439
$337$	8.62510e15	0.320752	0.160376	−	0.987056i	$-0.448729\pi$
$337$	8.62510e15	0.320752	0.160376	+	0.987056i	$0.448729\pi$
$338$	−9.14116e15	−0.333459
$339$	1.47963e16	0.529486
$340$	1.34078e15	0.0470700
$341$	1.34830e16	0.464391
$342$	−5.12704e15	−0.173259
$343$	−1.18733e16	−0.393696
$344$	5.11419e16	1.66397
$345$	1.32006e16	0.421471
$346$	4.45211e16	1.39499
$347$	−5.69006e16	−1.74975	−0.874874	−	0.484351i	$-0.839056\pi$
$347$	−5.69006e16	−1.74975	−0.874874	+	0.484351i	$0.839056\pi$
$348$	6.04493e15	0.182443
$349$	−4.99645e16	−1.48012	−0.740058	−	0.672543i	$-0.765202\pi$
$349$	−4.99645e16	−1.48012	−0.740058	+	0.672543i	$0.765202\pi$
$350$	2.11206e16	0.614135
$351$	8.00127e15	0.228383
$352$	2.56311e16	0.718191
$353$	−1.03749e16	−0.285395	−0.142698	−	0.989766i	$-0.545578\pi$
$353$	−1.03749e16	−0.285395	−0.142698	+	0.989766i	$0.545578\pi$
$354$	−2.27310e15	−0.0613898
$355$	−8.06871e14	−0.0213954
$356$	−1.46584e16	−0.381646
$357$	6.39706e15	0.163545
$358$	−9.29800e14	−0.0233426
$359$	−6.87515e16	−1.69500	−0.847498	−	0.530799i	$-0.821892\pi$
$359$	−6.87515e16	−1.69500	−0.847498	+	0.530799i	$0.821892\pi$
$360$	−9.74701e15	−0.235996
$361$	−2.50209e16	−0.594986
$362$	4.36193e15	0.101876
$363$	7.08912e15	0.162629
$364$	−2.28464e16	−0.514824
$365$	−5.04670e15	−0.111713
$366$	9.30447e15	0.202332
$367$	1.71367e16	0.366099	0.183050	−	0.983104i	$-0.441403\pi$
$367$	1.71367e16	0.366099	0.183050	+	0.983104i	$0.441403\pi$
$368$	2.97473e16	0.624363
$369$	1.98437e15	0.0409215
$370$	9.40363e15	0.190539
$371$	−8.39993e16	−1.67242
$372$	4.03020e15	0.0788491
$373$	5.47060e16	1.05179	0.525893	−	0.850550i	$-0.323731\pi$
$373$	5.47060e16	1.05179	0.525893	+	0.850550i	$0.323731\pi$
$374$	1.06386e16	0.201011
$375$	3.18880e16	0.592140
$376$	−1.73782e16	−0.317165
$377$	−6.27895e16	−1.12634
$378$	−1.16158e16	−0.204810
$379$	2.25107e16	0.390152	0.195076	−	0.980788i	$-0.437505\pi$
$379$	2.25107e16	0.390152	0.195076	+	0.980788i	$0.437505\pi$
$380$	8.08771e15	0.137795
$381$	−5.45437e16	−0.913551
$382$	−3.02511e16	−0.498114
$383$	1.35313e16	0.219052	0.109526	−	0.993984i	$-0.465067\pi$
$383$	1.35313e16	0.219052	0.109526	+	0.993984i	$0.465067\pi$
$384$	−8.81713e15	−0.140338
$385$	6.13012e16	0.959344
$386$	−4.90236e16	−0.754376
$387$	3.36708e16	0.509486
$388$	1.96637e16	0.292590
$389$	3.04140e16	0.445043	0.222521	−	0.974928i	$-0.428571\pi$
$389$	3.04140e16	0.445043	0.222521	+	0.974928i	$0.428571\pi$
$390$	2.52883e16	0.363915
$391$	−1.72421e16	−0.244030
$392$	5.45783e16	0.759732
$393$	−4.35722e16	−0.596565
$394$	−8.70818e16	−1.17274
$395$	1.31404e16	0.174071
$396$	9.64165e15	0.125641
$397$	4.37303e16	0.560588	0.280294	−	0.959914i	$-0.409568\pi$
$397$	4.37303e16	0.560588	0.280294	+	0.959914i	$0.409568\pi$
$398$	7.38775e16	0.931691
$399$	3.85877e16	0.478768
$400$	2.62943e16	0.320975
$401$	2.43011e16	0.291869	0.145934	−	0.989294i	$-0.453381\pi$
$401$	2.43011e16	0.291869	0.145934	+	0.989294i	$0.453381\pi$
$402$	−3.63590e16	−0.429677
$403$	−4.18622e16	−0.486787
$404$	5.44346e15	0.0622868
$405$	−6.41724e15	−0.0722588
$406$	9.11542e16	1.01008
$407$	−3.72411e16	−0.406124
$408$	1.27312e16	0.136640
$409$	2.90956e16	0.307345	0.153673	−	0.988122i	$-0.450890\pi$
$409$	2.90956e16	0.307345	0.153673	+	0.988122i	$0.450890\pi$
$410$	6.27168e15	0.0652062
$411$	4.75447e16	0.486553
$412$	−2.68909e16	−0.270878
$413$	1.71080e16	0.169639
$414$	3.13083e16	0.305603
$415$	8.85668e16	0.851057
$416$	−7.95795e16	−0.752826
$417$	5.71534e16	0.532301
$418$	6.41733e16	0.588448
$419$	2.68455e16	0.242371	0.121185	−	0.992630i	$-0.461330\pi$
$419$	2.68455e16	0.242371	0.121185	+	0.992630i	$0.461330\pi$
$420$	1.83235e16	0.162887
$421$	−1.46995e17	−1.28668	−0.643338	−	0.765582i	$-0.722451\pi$
$421$	−1.46995e17	−1.28668	−0.643338	+	0.765582i	$0.722451\pi$
$422$	4.62728e16	0.398837
$423$	−1.14415e16	−0.0971115
$424$	−1.67173e17	−1.39729
$425$	−1.52407e16	−0.125452
$426$	−1.91369e15	−0.0155135
$427$	−7.00284e16	−0.559104
$428$	−6.90009e16	−0.542588
$429$	−1.00149e17	−0.775665
$430$	1.06418e17	0.811839
$431$	−4.04267e16	−0.303785	−0.151892	−	0.988397i	$-0.548537\pi$
$431$	−4.04267e16	−0.303785	−0.151892	+	0.988397i	$0.548537\pi$
$432$	−1.44612e16	−0.107043
$433$	1.95272e17	1.42386	0.711931	−	0.702250i	$-0.247821\pi$
$433$	1.95272e17	1.42386	0.711931	+	0.702250i	$0.247821\pi$
$434$	6.07731e16	0.436544
$435$	5.03589e16	0.356366
$436$	3.42350e16	0.238676
$437$	−1.04006e17	−0.714382
$438$	−1.19695e16	−0.0810015
$439$	−1.80564e17	−1.20396	−0.601981	−	0.798510i	$-0.705622\pi$
$439$	−1.80564e17	−1.20396	−0.601981	+	0.798510i	$0.705622\pi$
$440$	1.22000e17	0.801524
$441$	3.59333e16	0.232619
$442$	−3.30308e16	−0.210705
$443$	2.79182e16	0.175494	0.0877472	−	0.996143i	$-0.472033\pi$
$443$	2.79182e16	0.175494	0.0877472	+	0.996143i	$0.472033\pi$
$444$	−1.11317e16	−0.0689558
$445$	−1.22116e17	−0.745471
$446$	1.44707e17	0.870591
$447$	−3.96156e16	−0.234892
$448$	2.39551e17	1.39988
$449$	−1.61837e17	−0.932131	−0.466066	−	0.884750i	$-0.654329\pi$
$449$	−1.61837e17	−0.932131	−0.466066	+	0.884750i	$0.654329\pi$
$450$	2.76741e16	0.157106
$451$	−2.48376e16	−0.138983
$452$	−5.53578e16	−0.305337
$453$	1.92036e17	1.04411
$454$	5.05303e16	0.270825
$455$	−1.90328e17	−1.00561
$456$	7.67961e16	0.400007
$457$	2.19082e17	1.12500	0.562500	−	0.826797i	$-0.309840\pi$
$457$	2.19082e17	1.12500	0.562500	+	0.826797i	$0.309840\pi$
$458$	1.36765e17	0.692385
$459$	8.38200e15	0.0418374
$460$	−4.93876e16	−0.243048
$461$	−2.60837e16	−0.126565	−0.0632823	−	0.997996i	$-0.520157\pi$
$461$	−2.60837e16	−0.126565	−0.0632823	+	0.997996i	$0.520157\pi$
$462$	1.45391e17	0.695606
$463$	3.11269e17	1.46845	0.734225	−	0.678906i	$-0.237546\pi$
$463$	3.11269e17	1.46845	0.734225	+	0.678906i	$0.237546\pi$
$464$	1.13483e17	0.527917
$465$	3.35746e16	0.154016
$466$	1.15365e17	0.521872
$467$	−6.18115e16	−0.275746	−0.137873	−	0.990450i	$-0.544027\pi$
$467$	−6.18115e16	−0.275746	−0.137873	+	0.990450i	$0.544027\pi$
$468$	−2.99354e16	−0.131700
$469$	2.73649e17	1.18733
$470$	−3.61613e16	−0.154742
$471$	−2.60720e17	−1.10037
$472$	3.40479e16	0.141732
$473$	−4.21445e17	−1.73039
$474$	3.11655e16	0.126216
$475$	−9.19334e16	−0.367253
$476$	−2.39335e16	−0.0943108
$477$	−1.10063e17	−0.427832
$478$	2.57553e17	0.987610
$479$	8.98587e16	0.339922	0.169961	−	0.985451i	$-0.445636\pi$
$479$	8.98587e16	0.339922	0.169961	+	0.985451i	$0.445636\pi$
$480$	6.38250e16	0.238189
$481$	1.15626e17	0.425709
$482$	1.38520e17	0.503161
$483$	−2.35636e17	−0.844473
$484$	−2.65227e16	−0.0937828
$485$	1.63814e17	0.571516
$486$	−1.52200e16	−0.0523938
$487$	4.61636e17	1.56806	0.784028	−	0.620725i	$-0.213162\pi$
$487$	4.61636e17	1.56806	0.784028	+	0.620725i	$0.213162\pi$
$488$	−1.39368e17	−0.467127
$489$	−4.65623e15	−0.0154002
$490$	1.13569e17	0.370667
$491$	−2.59579e17	−0.836066	−0.418033	−	0.908432i	$-0.637280\pi$
$491$	−2.59579e17	−0.836066	−0.418033	+	0.908432i	$0.637280\pi$
$492$	−7.42418e15	−0.0235980
$493$	−6.57772e16	−0.206334
$494$	−1.99245e17	−0.616826
$495$	8.03223e16	0.245416
$496$	7.56601e16	0.228158
$497$	1.44030e16	0.0428684
$498$	2.10058e17	0.617089
$499$	4.39408e17	1.27413	0.637066	−	0.770809i	$-0.280148\pi$
$499$	4.39408e17	1.27413	0.637066	+	0.770809i	$0.280148\pi$
$500$	−1.19304e17	−0.341467
$501$	−6.72654e16	−0.190041
$502$	−2.25561e17	−0.629058
$503$	6.89573e17	1.89840	0.949202	−	0.314668i	$-0.101893\pi$
$503$	6.89573e17	1.89840	0.949202	+	0.314668i	$0.101893\pi$
$504$	1.73989e17	0.472849
$505$	4.53482e16	0.121665
$506$	−3.91875e17	−1.03793
$507$	9.01469e16	0.235721
$508$	2.04066e17	0.526813
$509$	1.60134e17	0.408147	0.204074	−	0.978956i	$-0.434582\pi$
$509$	1.60134e17	0.408147	0.204074	+	0.978956i	$0.434582\pi$
$510$	2.64916e16	0.0666658
$511$	9.00860e16	0.223832
$512$	3.90654e17	0.958380
$513$	5.05611e16	0.122477
$514$	−1.49247e17	−0.356982
$515$	−2.24022e17	−0.529107
$516$	−1.25974e17	−0.293803
$517$	1.43209e17	0.329824
$518$	−1.67859e17	−0.381770
$519$	−4.39051e17	−0.986115
$520$	−3.78785e17	−0.840178
$521$	−1.08470e17	−0.237611	−0.118805	−	0.992918i	$-0.537906\pi$
$521$	−1.08470e17	−0.237611	−0.118805	+	0.992918i	$0.537906\pi$
$522$	1.19438e17	0.258396
$523$	6.19612e17	1.32391	0.661955	−	0.749543i	$-0.269727\pi$
$523$	6.19612e17	1.32391	0.661955	+	0.749543i	$0.269727\pi$
$524$	1.63018e17	0.344019
$525$	−2.08284e17	−0.434130
$526$	4.16702e17	0.857863
$527$	−4.38541e16	−0.0891746
$528$	1.81006e17	0.363556
$529$	1.31079e17	0.260059
$530$	−3.47860e17	−0.681727
$531$	2.24165e16	0.0433963
$532$	−1.44369e17	−0.276089
$533$	7.71159e16	0.145686
$534$	−2.89626e17	−0.540530
$535$	−5.74830e17	−1.05984
$536$	5.44608e17	0.992004
$537$	9.16936e15	0.0165009
$538$	2.63608e17	0.468677
$539$	−4.49764e17	−0.790055
$540$	2.40090e16	0.0416692
$541$	−8.20789e17	−1.40750	−0.703752	−	0.710446i	$-0.748493\pi$
$541$	−8.20789e17	−1.40750	−0.703752	+	0.710446i	$0.748493\pi$
$542$	5.80397e17	0.983399
$543$	−4.30158e16	−0.0720160
$544$	−8.33661e16	−0.137910
$545$	2.85204e17	0.466206
$546$	−4.51409e17	−0.729152
$547$	−2.43277e16	−0.0388314	−0.0194157	−	0.999811i	$-0.506181\pi$
$547$	−2.43277e16	−0.0388314	−0.0194157	+	0.999811i	$0.506181\pi$
$548$	−1.77880e17	−0.280579
$549$	−9.17574e16	−0.143028
$550$	−3.46386e17	−0.533584
$551$	−3.96775e17	−0.604030
$552$	−4.68956e17	−0.705550
$553$	−2.34562e17	−0.348773
$554$	−6.31945e17	−0.928679
$555$	−9.27353e16	−0.134692
$556$	−2.13830e17	−0.306960
$557$	4.44633e17	0.630875	0.315437	−	0.948946i	$-0.397849\pi$
$557$	4.44633e17	0.630875	0.315437	+	0.948946i	$0.397849\pi$
$558$	7.96303e16	0.111675
$559$	1.30850e18	1.81384
$560$	3.43992e17	0.471331
$561$	−1.04914e17	−0.142094
$562$	−9.39353e17	−1.25760
$563$	1.40313e18	1.85693	0.928463	−	0.371424i	$-0.121130\pi$
$563$	1.40313e18	1.85693	0.928463	+	0.371424i	$0.121130\pi$
$564$	4.28064e16	0.0560009
$565$	−4.61173e17	−0.596415
$566$	4.35203e17	0.556398
$567$	1.14551e17	0.144780
$568$	2.86644e16	0.0358162
$569$	3.41246e16	0.0421539	0.0210770	−	0.999778i	$-0.493290\pi$
$569$	3.41246e16	0.0421539	0.0210770	+	0.999778i	$0.493290\pi$
$570$	1.59800e17	0.195160
$571$	−7.95222e17	−0.960182	−0.480091	−	0.877219i	$-0.659396\pi$
$571$	−7.95222e17	−0.960182	−0.480091	+	0.877219i	$0.659396\pi$
$572$	3.74690e17	0.447300
$573$	2.98326e17	0.352116
$574$	−1.11952e17	−0.130649
$575$	5.61392e17	0.647777
$576$	3.13881e17	0.358112
$577$	−5.90770e17	−0.666462	−0.333231	−	0.942845i	$-0.608139\pi$
$577$	−5.90770e17	−0.666462	−0.333231	+	0.942845i	$0.608139\pi$
$578$	6.97571e17	0.778139
$579$	4.83453e17	0.533266
$580$	−1.88409e17	−0.205504
$581$	−1.58096e18	−1.70520
$582$	3.88523e17	0.414398
$583$	1.37762e18	1.45306
$584$	1.79286e17	0.187009
$585$	−2.49385e17	−0.257251
$586$	1.03372e18	1.05455
$587$	9.85934e17	0.994718	0.497359	−	0.867545i	$-0.334303\pi$
$587$	9.85934e17	0.994718	0.497359	+	0.867545i	$0.334303\pi$
$588$	−1.34438e17	−0.134144
$589$	−2.64532e17	−0.261053
$590$	7.08481e16	0.0691497
$591$	8.58770e17	0.829008
$592$	−2.08978e17	−0.199531
$593$	6.26668e17	0.591809	0.295905	−	0.955218i	$-0.404379\pi$
$593$	6.26668e17	0.591809	0.295905	+	0.955218i	$0.404379\pi$
$594$	1.90504e17	0.177947
$595$	−1.99384e17	−0.184218
$596$	1.48215e17	0.135454
$597$	−7.28554e17	−0.658610
$598$	1.21669e18	1.08799
$599$	−1.83224e18	−1.62072	−0.810359	−	0.585934i	$-0.800728\pi$
$599$	−1.83224e18	−1.62072	−0.810359	+	0.585934i	$0.800728\pi$
$600$	−4.14520e17	−0.362712
$601$	−7.92129e17	−0.685665	−0.342832	−	0.939397i	$-0.611386\pi$
$601$	−7.92129e17	−0.685665	−0.342832	+	0.939397i	$0.611386\pi$
$602$	−1.89961e18	−1.62663
$603$	3.58560e17	0.303738
$604$	−7.18470e17	−0.602100
$605$	−2.20955e17	−0.183186
$606$	1.07554e17	0.0882176
$607$	1.53324e18	1.24418	0.622092	−	0.782944i	$-0.286283\pi$
$607$	1.53324e18	1.24418	0.622092	+	0.782944i	$0.286283\pi$
$608$	−5.02873e17	−0.403724
$609$	−8.98930e17	−0.714025
$610$	−2.90003e17	−0.227907
$611$	−4.44636e17	−0.345730
$612$	−3.13598e16	−0.0241262
$613$	−3.11862e17	−0.237394	−0.118697	−	0.992931i	$-0.537872\pi$
$613$	−3.11862e17	−0.237394	−0.118697	+	0.992931i	$0.537872\pi$
$614$	−1.21594e16	−0.00915836
$615$	−6.18491e16	−0.0460941
$616$	−2.17775e18	−1.60596
$617$	−9.04006e17	−0.659656	−0.329828	−	0.944041i	$-0.606991\pi$
$617$	−9.04006e17	−0.659656	−0.329828	+	0.944041i	$0.606991\pi$
$618$	−5.31322e17	−0.383648
$619$	−1.66469e18	−1.18945	−0.594724	−	0.803930i	$-0.702739\pi$
$619$	−1.66469e18	−1.18945	−0.594724	+	0.803930i	$0.702739\pi$
$620$	−1.25614e17	−0.0888159
$621$	−3.08751e17	−0.216030
$622$	2.01568e18	1.39567
$623$	2.17982e18	1.49365
$624$	−5.61987e17	−0.381089
$625$	−1.33986e17	−0.0899165
$626$	1.37001e18	0.909892
$627$	−6.32854e17	−0.415973
$628$	9.75439e17	0.634545
$629$	1.21128e17	0.0779857
$630$	3.62042e17	0.230699
$631$	2.29635e18	1.44826	0.724132	−	0.689661i	$-0.242241\pi$
$631$	2.29635e18	1.44826	0.724132	+	0.689661i	$0.242241\pi$
$632$	−4.66817e17	−0.291397
$633$	−4.56326e17	−0.281937
$634$	1.30519e18	0.798166
$635$	1.70003e18	1.02903
$636$	4.11783e17	0.246716
$637$	1.39643e18	0.828156
$638$	−1.49497e18	−0.877600
$639$	1.88721e16	0.0109664
$640$	2.74814e17	0.158077
$641$	−2.04247e18	−1.16300	−0.581498	−	0.813548i	$-0.697533\pi$
$641$	−2.04247e18	−1.16300	−0.581498	+	0.813548i	$0.697533\pi$
$642$	−1.36335e18	−0.768474
$643$	1.39038e18	0.775825	0.387912	−	0.921696i	$-0.373196\pi$
$643$	1.39038e18	0.775825	0.387912	+	0.921696i	$0.373196\pi$
$644$	8.81592e17	0.486978
$645$	−1.04946e18	−0.573887
$646$	−2.08726e17	−0.112997
$647$	−2.12148e18	−1.13700	−0.568501	−	0.822683i	$-0.692476\pi$
$647$	−2.12148e18	−1.13700	−0.568501	+	0.822683i	$0.692476\pi$
$648$	2.27975e17	0.120962
$649$	−2.80579e17	−0.147389
$650$	1.07546e18	0.559316
$651$	−5.99322e17	−0.308592
$652$	1.74205e16	0.00888077
$653$	−3.44621e18	−1.73943	−0.869713	−	0.493558i	$-0.835696\pi$
$653$	−3.44621e18	−1.73943	−0.869713	+	0.493558i	$0.835696\pi$
$654$	6.76429e17	0.338039
$655$	1.35806e18	0.671973
$656$	−1.39376e17	−0.0682833
$657$	1.18039e17	0.0572597
$658$	6.45497e17	0.310046
$659$	−3.67266e18	−1.74673	−0.873364	−	0.487067i	$-0.838067\pi$
$659$	−3.67266e18	−1.74673	−0.873364	+	0.487067i	$0.838067\pi$
$660$	−3.00512e17	−0.141523
$661$	−3.05397e18	−1.42415	−0.712075	−	0.702103i	$-0.752245\pi$
$661$	−3.05397e18	−1.42415	−0.712075	+	0.702103i	$0.752245\pi$
$662$	−3.78521e17	−0.174789
$663$	3.25738e17	0.148947
$664$	−3.14638e18	−1.42468
$665$	−1.20271e18	−0.539286
$666$	−2.19944e17	−0.0976630
$667$	2.42291e18	1.06542
$668$	2.51662e17	0.109590
$669$	−1.42705e18	−0.615418
$670$	1.13324e18	0.483990
$671$	1.14849e18	0.485772
$672$	−1.13931e18	−0.477243
$673$	−2.24216e18	−0.930182	−0.465091	−	0.885263i	$-0.653978\pi$
$673$	−2.24216e18	−0.930182	−0.465091	+	0.885263i	$0.653978\pi$
$674$	−6.37591e17	−0.261971
$675$	−2.72912e17	−0.111058
$676$	−3.37269e17	−0.135932
$677$	−3.35268e18	−1.33834	−0.669169	−	0.743110i	$-0.733350\pi$
$677$	−3.35268e18	−1.33834	−0.669169	+	0.743110i	$0.733350\pi$
$678$	−1.09378e18	−0.432452
$679$	−2.92415e18	−1.14511
$680$	−3.96809e17	−0.153912
$681$	−4.98312e17	−0.191446
$682$	−9.96703e17	−0.379286
$683$	−5.18072e17	−0.195279	−0.0976395	−	0.995222i	$-0.531129\pi$
$683$	−5.18072e17	−0.195279	−0.0976395	+	0.995222i	$0.531129\pi$
$684$	−1.89166e17	−0.0706281
$685$	−1.48188e18	−0.548055
$686$	8.77710e17	0.321547
$687$	−1.34872e18	−0.489445
$688$	−2.36494e18	−0.850150
$689$	−4.27724e18	−1.52314
$690$	−9.75821e17	−0.344232
$691$	−3.30114e18	−1.15360	−0.576801	−	0.816884i	$-0.695699\pi$
$691$	−3.30114e18	−1.15360	−0.576801	+	0.816884i	$0.695699\pi$
$692$	1.64264e18	0.568659
$693$	−1.43379e18	−0.491722
$694$	4.20625e18	1.42909
$695$	−1.78136e18	−0.599586
$696$	−1.78902e18	−0.596563
$697$	8.07853e16	0.0266882
$698$	3.69351e18	1.20887
$699$	−1.13769e18	−0.368910
$700$	7.79258e17	0.250348
$701$	−1.46369e17	−0.0465889	−0.0232944	−	0.999729i	$-0.507416\pi$
$701$	−1.46369e17	−0.0465889	−0.0232944	+	0.999729i	$0.507416\pi$
$702$	−5.91476e17	−0.186529
$703$	7.30656e17	0.228299
$704$	−3.92874e18	−1.21627
$705$	3.56610e17	0.109387
$706$	7.66939e17	0.233093
$707$	−8.09487e17	−0.243772
$708$	−8.38674e16	−0.0250252
$709$	−1.86794e18	−0.552284	−0.276142	−	0.961117i	$-0.589056\pi$
$709$	−1.86794e18	−0.552284	−0.276142	+	0.961117i	$0.589056\pi$
$710$	5.96461e16	0.0174744
$711$	−3.07343e17	−0.0892219
$712$	4.33821e18	1.24793
$713$	1.61537e18	0.460457
$714$	−4.72888e17	−0.133573
$715$	3.12146e18	0.873712
$716$	−3.43056e16	−0.00951548
$717$	−2.53990e18	−0.698139
$718$	5.08230e18	1.38437
$719$	−4.52864e18	−1.22245	−0.611224	−	0.791458i	$-0.709323\pi$
$719$	−4.52864e18	−1.22245	−0.611224	+	0.791458i	$0.709323\pi$
$720$	4.50729e17	0.120574
$721$	3.99889e18	1.06013
$722$	1.84962e18	0.485948
$723$	−1.36604e18	−0.355683
$724$	1.60936e17	0.0415292
$725$	2.14166e18	0.547713
$726$	−5.24047e17	−0.132826
$727$	−3.33011e18	−0.836537	−0.418269	−	0.908323i	$-0.637363\pi$
$727$	−3.33011e18	−0.836537	−0.418269	+	0.908323i	$0.637363\pi$
$728$	6.76149e18	1.68340
$729$	1.50095e17	0.0370370
$730$	3.73066e17	0.0912404
$731$	1.37077e18	0.332277
$732$	3.43295e17	0.0824793
$733$	−4.12137e18	−0.981446	−0.490723	−	0.871316i	$-0.663267\pi$
$733$	−4.12137e18	−0.981446	−0.490723	+	0.871316i	$0.663267\pi$
$734$	−1.26680e18	−0.299007
$735$	−1.11997e18	−0.262023
$736$	3.07080e18	0.712107
$737$	−4.48796e18	−1.03160
$738$	−1.46690e17	−0.0334221
$739$	3.01257e18	0.680374	0.340187	−	0.940358i	$-0.389510\pi$
$739$	3.01257e18	0.680374	0.340187	+	0.940358i	$0.389510\pi$
$740$	3.46953e17	0.0776721
$741$	1.96489e18	0.436033
$742$	6.20946e18	1.36593
$743$	2.14100e18	0.466864	0.233432	−	0.972373i	$-0.425004\pi$
$743$	2.14100e18	0.466864	0.233432	+	0.972373i	$0.425004\pi$
$744$	−1.19275e18	−0.257826
$745$	1.23475e18	0.264583
$746$	−4.04402e18	−0.859035
$747$	−2.07151e18	−0.436218
$748$	3.92519e17	0.0819409
$749$	1.02610e19	2.12352
$750$	−2.35725e18	−0.483623
$751$	6.79051e18	1.38116	0.690578	−	0.723258i	$-0.257356\pi$
$751$	6.79051e18	1.38116	0.690578	+	0.723258i	$0.257356\pi$
$752$	8.03618e17	0.162044
$753$	2.22441e18	0.444679
$754$	4.64157e18	0.919923
$755$	−5.98540e18	−1.17608
$756$	−4.28572e17	−0.0834896
$757$	7.85706e17	0.151753	0.0758765	−	0.997117i	$-0.475825\pi$
$757$	7.85706e17	0.151753	0.0758765	+	0.997117i	$0.475825\pi$
$758$	−1.66405e18	−0.318652
$759$	3.86453e18	0.733711
$760$	−2.39359e18	−0.450569
$761$	4.22023e18	0.787655	0.393828	−	0.919184i	$-0.371151\pi$
$761$	4.22023e18	0.787655	0.393828	+	0.919184i	$0.371151\pi$
$762$	4.03202e18	0.746132
$763$	−5.09102e18	−0.934104
$764$	−1.11613e18	−0.203053
$765$	−2.61251e17	−0.0471258
$766$	−1.00027e18	−0.178908
$767$	8.71141e17	0.154497
$768$	−2.87540e18	−0.505650
$769$	−4.73172e17	−0.0825084	−0.0412542	−	0.999149i	$-0.513135\pi$
$769$	−4.73172e17	−0.0825084	−0.0412542	+	0.999149i	$0.513135\pi$
$770$	−4.53155e18	−0.783533
$771$	1.47182e18	0.252349
$772$	−1.80876e18	−0.307516
$773$	−5.60410e18	−0.944799	−0.472400	−	0.881384i	$-0.656612\pi$
$773$	−5.60410e18	−0.944799	−0.472400	+	0.881384i	$0.656612\pi$
$774$	−2.48904e18	−0.416117
$775$	1.42786e18	0.236714
$776$	−5.81955e18	−0.956728
$777$	1.65537e18	0.269872
$778$	−2.24829e18	−0.363484
$779$	4.87305e17	0.0781281
$780$	9.33031e17	0.148348
$781$	−2.36215e17	−0.0372457
$782$	1.27459e18	0.199308
$783$	−1.17786e18	−0.182659
$784$	−2.52385e18	−0.388159
$785$	8.12615e18	1.23946
$786$	3.22098e18	0.487238
$787$	8.83339e17	0.132523	0.0662616	−	0.997802i	$-0.478893\pi$
$787$	8.83339e17	0.132523	0.0662616	+	0.997802i	$0.478893\pi$
$788$	−3.21294e18	−0.478060
$789$	−4.10936e18	−0.606421
$790$	−9.71371e17	−0.142170
$791$	8.23215e18	1.19500
$792$	−2.85349e18	−0.410830
$793$	−3.56585e18	−0.509198
$794$	−3.23266e18	−0.457854
$795$	3.43047e18	0.481911
$796$	2.72576e18	0.379798
$797$	5.83844e18	0.806897	0.403448	−	0.915002i	$-0.367812\pi$
$797$	5.83844e18	0.806897	0.403448	+	0.915002i	$0.367812\pi$
$798$	−2.85251e18	−0.391028
$799$	−4.65793e17	−0.0633343
$800$	2.71434e18	0.366083
$801$	2.85619e18	0.382099
$802$	−1.79640e18	−0.238381
$803$	−1.47745e18	−0.194474
$804$	−1.34149e18	−0.175155
$805$	7.34434e18	0.951217
$806$	3.09456e18	0.397578
$807$	−2.59961e18	−0.331306
$808$	−1.61102e18	−0.203669
$809$	3.17753e18	0.398496	0.199248	−	0.979949i	$-0.436150\pi$
$809$	3.17753e18	0.398496	0.199248	+	0.979949i	$0.436150\pi$
$810$	4.74380e17	0.0590166
$811$	1.45204e18	0.179202	0.0896008	−	0.995978i	$-0.471441\pi$
$811$	1.45204e18	0.179202	0.0896008	+	0.995978i	$0.471441\pi$
$812$	3.36320e18	0.411754
$813$	−5.72367e18	−0.695162
$814$	2.75296e18	0.331697
$815$	1.45126e17	0.0173468
$816$	−5.88728e17	−0.0698117
$817$	8.26860e18	0.972722
$818$	−2.15083e18	−0.251021
$819$	4.45164e18	0.515435
$820$	2.31398e17	0.0265809
$821$	−4.77895e18	−0.544630	−0.272315	−	0.962208i	$-0.587789\pi$
$821$	−4.77895e18	−0.544630	−0.272315	+	0.962208i	$0.587789\pi$
$822$	−3.51463e18	−0.397387
$823$	−6.12708e18	−0.687314	−0.343657	−	0.939095i	$-0.611666\pi$
$823$	−6.12708e18	−0.687314	−0.343657	+	0.939095i	$0.611666\pi$
$824$	7.95848e18	0.885733
$825$	3.41594e18	0.377189
$826$	−1.26467e18	−0.138550
$827$	8.31290e18	0.903581	0.451790	−	0.892124i	$-0.350785\pi$
$827$	8.31290e18	0.903581	0.451790	+	0.892124i	$0.350785\pi$
$828$	1.15514e18	0.124577
$829$	−1.14288e19	−1.22292	−0.611459	−	0.791276i	$-0.709417\pi$
$829$	−1.14288e19	−1.22292	−0.611459	+	0.791276i	$0.709417\pi$
$830$	−6.54710e18	−0.695091
$831$	6.23202e18	0.656481
$832$	1.21980e19	1.27493
$833$	1.46287e18	0.151710
$834$	−4.22493e18	−0.434751
$835$	2.09654e18	0.214062
$836$	2.36772e18	0.239877
$837$	−7.85286e17	−0.0789427
$838$	−1.98449e18	−0.197954
$839$	−6.25053e18	−0.618677	−0.309338	−	0.950952i	$-0.600108\pi$
$839$	−6.25053e18	−0.618677	−0.309338	+	0.950952i	$0.600108\pi$
$840$	−5.42290e18	−0.532619
$841$	−1.01745e18	−0.0991610
$842$	1.08663e19	1.05088
$843$	9.26357e18	0.888995
$844$	1.70727e18	0.162583
$845$	−2.80971e18	−0.265517
$846$	8.45787e17	0.0793147
$847$	3.94414e18	0.367037
$848$	7.73053e18	0.713898
$849$	−4.29182e18	−0.393316
$850$	1.12663e18	0.102461
$851$	−4.46175e18	−0.402683
$852$	−7.06068e16	−0.00632396
$853$	1.41877e19	1.26108	0.630541	−	0.776156i	$-0.282833\pi$
$853$	1.41877e19	1.26108	0.630541	+	0.776156i	$0.282833\pi$
$854$	5.17669e18	0.456642
$855$	−1.57589e18	−0.137958
$856$	2.04211e19	1.77419
$857$	3.03510e18	0.261696	0.130848	−	0.991402i	$-0.458230\pi$
$857$	3.03510e18	0.261696	0.130848	+	0.991402i	$0.458230\pi$
$858$	7.40329e18	0.633516
$859$	3.39531e18	0.288353	0.144176	−	0.989552i	$-0.453947\pi$
$859$	3.39531e18	0.288353	0.144176	+	0.989552i	$0.453947\pi$
$860$	3.92636e18	0.330941
$861$	1.10404e18	0.0923554
$862$	2.98845e18	0.248113
$863$	−1.00010e19	−0.824087	−0.412043	−	0.911164i	$-0.635185\pi$
$863$	−1.00010e19	−0.824087	−0.412043	+	0.911164i	$0.635185\pi$
$864$	−1.49282e18	−0.122087
$865$	1.36844e19	1.11076
$866$	−1.44350e19	−1.16292
$867$	−6.87920e18	−0.550065
$868$	2.24226e18	0.177954
$869$	3.84690e18	0.303028
$870$	−3.72267e18	−0.291058
$871$	1.39342e19	1.08135
$872$	−1.01320e19	−0.780437
$873$	−3.83148e18	−0.292937
$874$	7.68843e18	0.583463
$875$	1.77414e19	1.33640
$876$	−4.41621e17	−0.0330197
$877$	−7.20095e18	−0.534432	−0.267216	−	0.963637i	$-0.586104\pi$
$877$	−7.20095e18	−0.534432	−0.267216	+	0.963637i	$0.586104\pi$
$878$	1.33478e19	0.983322
$879$	−1.01941e19	−0.745457
$880$	−5.64161e18	−0.409511
$881$	1.65348e19	1.19140	0.595698	−	0.803208i	$-0.296875\pi$
$881$	1.65348e19	1.19140	0.595698	+	0.803208i	$0.296875\pi$
$882$	−2.65629e18	−0.189989
$883$	−6.17888e18	−0.438697	−0.219349	−	0.975647i	$-0.570393\pi$
$883$	−6.17888e18	−0.438697	−0.219349	+	0.975647i	$0.570393\pi$
$884$	−1.21869e18	−0.0858925
$885$	−6.98679e17	−0.0488817
$886$	−2.06379e18	−0.143333
$887$	4.08100e18	0.281361	0.140680	−	0.990055i	$-0.455071\pi$
$887$	4.08100e18	0.281361	0.140680	+	0.990055i	$0.455071\pi$
$888$	3.29446e18	0.225476
$889$	−3.03463e19	−2.06179
$890$	9.02712e18	0.608855
$891$	−1.87868e18	−0.125790
$892$	5.33907e18	0.354891
$893$	−2.80971e18	−0.185407
$894$	2.92850e18	0.191845
$895$	−2.85792e17	−0.0185866
$896$	−4.90555e18	−0.316727
$897$	−1.19986e19	−0.769094
$898$	1.19634e19	0.761307
$899$	6.16248e18	0.389330
$900$	1.02105e18	0.0640431
$901$	−4.48077e18	−0.279024
$902$	1.83607e18	0.113513
$903$	1.87333e19	1.14986
$904$	1.63834e19	0.998409
$905$	1.34072e18	0.0811191
$906$	−1.41958e19	−0.852761
$907$	1.35829e19	0.810112	0.405056	−	0.914292i	$-0.367252\pi$
$907$	1.35829e19	0.810112	0.405056	+	0.914292i	$0.367252\pi$
$908$	1.86435e18	0.110400
$909$	−1.06066e18	−0.0623608
$910$	1.40696e19	0.821319
$911$	−1.54250e19	−0.894038	−0.447019	−	0.894525i	$-0.647514\pi$
$911$	−1.54250e19	−0.894038	−0.447019	+	0.894525i	$0.647514\pi$
$912$	−3.55126e18	−0.204370
$913$	2.59284e19	1.48155
$914$	−1.61952e19	−0.918830
$915$	2.85991e18	0.161107
$916$	5.04602e18	0.282246
$917$	−2.42421e19	−1.34639
$918$	−6.19620e17	−0.0341703
$919$	2.04618e19	1.12045	0.560226	−	0.828340i	$-0.310714\pi$
$919$	2.04618e19	1.12045	0.560226	+	0.828340i	$0.310714\pi$
$920$	1.46165e19	0.794734
$921$	1.19912e17	0.00647402
$922$	1.92818e18	0.103370
$923$	7.33402e17	0.0390419
$924$	5.36428e18	0.283559
$925$	−3.94384e18	−0.207013
$926$	−2.30099e19	−1.19934
$927$	5.23971e18	0.271199
$928$	1.17148e19	0.602107
$929$	−3.95502e18	−0.201858	−0.100929	−	0.994894i	$-0.532182\pi$
$929$	−3.95502e18	−0.201858	−0.100929	+	0.994894i	$0.532182\pi$
$930$	−2.48193e18	−0.125791
$931$	8.82420e18	0.444122
$932$	4.25646e18	0.212738
$933$	−1.98779e19	−0.986597
$934$	4.56927e18	0.225212
$935$	3.26999e18	0.160055
$936$	8.85951e18	0.430642
$937$	2.30300e19	1.11170	0.555848	−	0.831284i	$-0.312394\pi$
$937$	2.30300e19	1.11170	0.555848	+	0.831284i	$0.312394\pi$
$938$	−2.02289e19	−0.969737
$939$	−1.35105e19	−0.643200
$940$	−1.33420e18	−0.0630796
$941$	3.96413e18	0.186130	0.0930648	−	0.995660i	$-0.470334\pi$
$941$	3.96413e18	0.186130	0.0930648	+	0.995660i	$0.470334\pi$
$942$	1.92731e19	0.898714
$943$	−2.97573e18	−0.137806
$944$	−1.57447e18	−0.0724129
$945$	−3.57034e18	−0.163081
$946$	3.11544e19	1.41328
$947$	−2.82175e19	−1.27129	−0.635644	−	0.771982i	$-0.719265\pi$
$947$	−2.82175e19	−1.27129	−0.635644	+	0.771982i	$0.719265\pi$
$948$	1.14987e18	0.0514512
$949$	4.58718e18	0.203852
$950$	6.79597e18	0.299949
$951$	−1.28713e19	−0.564221
$952$	7.08322e18	0.308383
$953$	−1.14223e19	−0.493914	−0.246957	−	0.969026i	$-0.579431\pi$
$953$	−1.14223e19	−0.493914	−0.246957	+	0.969026i	$0.579431\pi$
$954$	8.13618e18	0.349427
$955$	−9.29825e18	−0.396624
$956$	9.50260e18	0.402593
$957$	1.47428e19	0.620373
$958$	−6.64260e18	−0.277627
$959$	2.64522e19	1.09810
$960$	−9.78310e18	−0.403379
$961$	−2.03090e19	−0.831737
$962$	−8.54740e18	−0.347693
$963$	1.34449e19	0.543232
$964$	5.11079e18	0.205110
$965$	−1.50683e19	−0.600673
$966$	1.74189e19	0.689713
$967$	−2.70774e19	−1.06496	−0.532482	−	0.846441i	$-0.678741\pi$
$967$	−2.70774e19	−1.06496	−0.532482	+	0.846441i	$0.678741\pi$
$968$	7.84951e18	0.306657
$969$	2.05838e18	0.0798769
$970$	−1.21096e19	−0.466779
$971$	−4.38871e19	−1.68040	−0.840198	−	0.542280i	$-0.817561\pi$
$971$	−4.38871e19	−1.68040	−0.840198	+	0.542280i	$0.817561\pi$
$972$	−5.61553e17	−0.0213580
$973$	3.17982e19	1.20135
$974$	−3.41254e19	−1.28069
$975$	−1.06058e19	−0.395379
$976$	6.44478e18	0.238662
$977$	−3.09328e18	−0.113790	−0.0568950	−	0.998380i	$-0.518120\pi$
$977$	−3.09328e18	−0.113790	−0.0568950	+	0.998380i	$0.518120\pi$
$978$	3.44201e17	0.0125779
$979$	−3.57499e19	−1.29774
$980$	4.19019e18	0.151100
$981$	−6.67071e18	−0.238959
$982$	1.91888e19	0.682847
$983$	1.53172e19	0.541480	0.270740	−	0.962653i	$-0.412732\pi$
$983$	1.53172e19	0.541480	0.270740	+	0.962653i	$0.412732\pi$
$984$	2.19722e18	0.0771622
$985$	−2.67663e19	−0.933797
$986$	4.86243e18	0.168521
$987$	−6.36566e18	−0.219170
$988$	−7.35129e18	−0.251445
$989$	−5.04923e19	−1.71573
$990$	−5.93764e18	−0.200440
$991$	−4.12391e19	−1.38303	−0.691514	−	0.722363i	$-0.743056\pi$
$991$	−4.12391e19	−1.38303	−0.691514	+	0.722363i	$0.743056\pi$
$992$	7.81034e18	0.260222
$993$	3.73284e18	0.123558
$994$	−1.06471e18	−0.0350123
$995$	2.27077e19	0.741861
$996$	7.75021e18	0.251552
$997$	5.20025e18	0.167689	0.0838447	−	0.996479i	$-0.473280\pi$
$997$	5.20025e18	0.167689	0.0838447	+	0.996479i	$0.473280\pi$
$998$	−3.24823e19	−1.04063
$999$	2.16901e18	0.0690377

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.a.1.10	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.a.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-73.9227 q^{2} +729.000 q^{3} -2727.43 q^{4} -22721.6 q^{5} -53889.7 q^{6} +405591. q^{7} +807194. q^{8} +531441. q^{9} +O(q^{10})\)	\(q-73.9227 q^{2} +729.000 q^{3} -2727.43 q^{4} -22721.6 q^{5} -53889.7 q^{6} +405591. q^{7} +807194. q^{8} +531441. q^{9} +1.67964e6 q^{10} -6.65185e6 q^{11} -1.98830e6 q^{12} +2.06527e7 q^{13} -2.99824e7 q^{14} -1.65640e7 q^{15} -3.73269e7 q^{16} +2.16354e7 q^{17} -3.92856e7 q^{18} +1.30507e8 q^{19} +6.19715e7 q^{20} +2.95676e8 q^{21} +4.91723e8 q^{22} -7.96941e8 q^{23} +5.88444e8 q^{24} -7.04433e8 q^{25} -1.52670e9 q^{26} +3.87420e8 q^{27} -1.10622e9 q^{28} -3.04026e9 q^{29} +1.22446e9 q^{30} -2.02696e9 q^{31} -3.85323e9 q^{32} -4.84920e9 q^{33} -1.59935e9 q^{34} -9.21566e9 q^{35} -1.44947e9 q^{36} +5.59860e9 q^{37} -9.64743e9 q^{38} +1.50558e10 q^{39} -1.83407e10 q^{40} +3.73394e9 q^{41} -2.18572e10 q^{42} +6.33576e10 q^{43} +1.81425e10 q^{44} -1.20752e10 q^{45} +5.89121e10 q^{46} -2.15292e10 q^{47} -2.72113e10 q^{48} +6.76148e10 q^{49} +5.20736e10 q^{50} +1.57722e10 q^{51} -5.63287e10 q^{52} -2.07104e11 q^{53} -2.86392e10 q^{54} +1.51141e11 q^{55} +3.27390e11 q^{56} +9.51395e10 q^{57} +2.24744e11 q^{58} +4.21805e10 q^{59} +4.51772e10 q^{60} -1.72658e11 q^{61} +1.49838e11 q^{62} +2.15548e11 q^{63} +5.90623e11 q^{64} -4.69261e11 q^{65} +3.58466e11 q^{66} +6.74693e11 q^{67} -5.90090e10 q^{68} -5.80970e11 q^{69} +6.81247e11 q^{70} +3.55112e10 q^{71} +4.28976e11 q^{72} +2.22111e11 q^{73} -4.13864e11 q^{74} -5.13532e11 q^{75} -3.55948e11 q^{76} -2.69793e12 q^{77} -1.11297e12 q^{78} -5.78321e11 q^{79} +8.48126e11 q^{80} +2.82430e11 q^{81} -2.76023e11 q^{82} -3.89792e12 q^{83} -8.06434e11 q^{84} -4.91590e11 q^{85} -4.68357e12 q^{86} -2.21635e12 q^{87} -5.36934e12 q^{88} +5.37443e12 q^{89} +8.92630e11 q^{90} +8.37654e12 q^{91} +2.17360e12 q^{92} -1.47765e12 q^{93} +1.59150e12 q^{94} -2.96532e12 q^{95} -2.80900e12 q^{96} -7.20961e12 q^{97} -4.99827e12 q^{98} -3.53507e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 138 q^{2} + 21870 q^{3} + 114598 q^{4} - 137742 q^{5} - 100602 q^{6} - 879443 q^{7} - 872301 q^{8} + 15943230 q^{9}+O(q^{10}) \) 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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