LMFDB - Embedded newform 177.14.a.a.1.22

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			1.22
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)

$f(q)$	$=$	$q+76.7885 q^{2} +729.000 q^{3} -2295.53 q^{4} +8611.65 q^{5} +55978.8 q^{6} +343688. q^{7} -805321. q^{8} +531441. q^{9} +O(q^{10})$	\(q+76.7885 q^{2} +729.000 q^{3} -2295.53 q^{4} +8611.65 q^{5} +55978.8 q^{6} +343688. q^{7} -805321. q^{8} +531441. q^{9} +661275. q^{10} +2.10913e6 q^{11} -1.67344e6 q^{12} +1.64154e7 q^{13} +2.63913e7 q^{14} +6.27789e6 q^{15} -4.30344e7 q^{16} -1.54112e8 q^{17} +4.08085e7 q^{18} -1.40672e8 q^{19} -1.97683e7 q^{20} +2.50549e8 q^{21} +1.61957e8 q^{22} -7.50683e8 q^{23} -5.87079e8 q^{24} -1.14654e9 q^{25} +1.26052e9 q^{26} +3.87420e8 q^{27} -7.88948e8 q^{28} -5.30324e9 q^{29} +4.82070e8 q^{30} +6.09654e9 q^{31} +3.29265e9 q^{32} +1.53755e9 q^{33} -1.18340e10 q^{34} +2.95972e9 q^{35} -1.21994e9 q^{36} +1.01295e10 q^{37} -1.08020e10 q^{38} +1.19668e10 q^{39} -6.93514e9 q^{40} -2.18330e8 q^{41} +1.92392e10 q^{42} +6.90652e9 q^{43} -4.84157e9 q^{44} +4.57658e9 q^{45} -5.76438e10 q^{46} -7.05108e10 q^{47} -3.13721e10 q^{48} +2.12325e10 q^{49} -8.80412e10 q^{50} -1.12347e11 q^{51} -3.76822e10 q^{52} +1.26195e11 q^{53} +2.97494e10 q^{54} +1.81631e10 q^{55} -2.76779e11 q^{56} -1.02550e11 q^{57} -4.07227e11 q^{58} +4.21805e10 q^{59} -1.44111e10 q^{60} +3.47997e11 q^{61} +4.68144e11 q^{62} +1.82650e11 q^{63} +6.05375e11 q^{64} +1.41364e11 q^{65} +1.18066e11 q^{66} +7.19021e11 q^{67} +3.53768e11 q^{68} -5.47248e11 q^{69} +2.27272e11 q^{70} -1.79801e12 q^{71} -4.27981e11 q^{72} -6.59872e11 q^{73} +7.77831e11 q^{74} -8.35830e11 q^{75} +3.22916e11 q^{76} +7.24882e11 q^{77} +9.18915e11 q^{78} +6.24170e11 q^{79} -3.70597e11 q^{80} +2.82430e11 q^{81} -1.67652e10 q^{82} -3.14870e12 q^{83} -5.75143e11 q^{84} -1.32715e12 q^{85} +5.30341e11 q^{86} -3.86606e12 q^{87} -1.69852e12 q^{88} -5.10394e12 q^{89} +3.51429e11 q^{90} +5.64179e12 q^{91} +1.72322e12 q^{92} +4.44438e12 q^{93} -5.41441e12 q^{94} -1.21141e12 q^{95} +2.40034e12 q^{96} +2.84901e12 q^{97} +1.63041e12 q^{98} +1.12088e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	76.7885	0.848401	0.424200	−	0.905568i	$-0.360555\pi$
$2$	76.7885	0.848401	0.424200	+	0.905568i	$0.360555\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	−2295.53	−0.280217
$5$	8611.65	0.246480	0.123240	−	0.992377i	$-0.460672\pi$
$5$	8611.65	0.246480	0.123240	+	0.992377i	$0.460672\pi$
$6$	55978.8	0.489824
$7$	343688.	1.10415	0.552074	−	0.833795i	$-0.313837\pi$
$7$	343688.	1.10415	0.552074	+	0.833795i	$0.313837\pi$
$8$	−805321.	−1.08614
$9$	531441.	0.333333
$10$	661275.	0.209114
$11$	2.10913e6	0.358963	0.179482	−	0.983761i	$-0.442558\pi$
$11$	2.10913e6	0.358963	0.179482	+	0.983761i	$0.442558\pi$
$12$	−1.67344e6	−0.161783
$13$	1.64154e7	0.943236	0.471618	−	0.881803i	$-0.343670\pi$
$13$	1.64154e7	0.943236	0.471618	+	0.881803i	$0.343670\pi$
$14$	2.63913e7	0.936760
$15$	6.27789e6	0.142305
$16$	−4.30344e7	−0.641262
$17$	−1.54112e8	−1.54852	−0.774261	−	0.632867i	$-0.781878\pi$
$17$	−1.54112e8	−1.54852	−0.774261	+	0.632867i	$0.781878\pi$
$18$	4.08085e7	0.282800
$19$	−1.40672e8	−0.685975	−0.342987	−	0.939340i	$-0.611439\pi$
$19$	−1.40672e8	−0.685975	−0.342987	+	0.939340i	$0.611439\pi$
$20$	−1.97683e7	−0.0690677
$21$	2.50549e8	0.637480
$22$	1.61957e8	0.304545
$23$	−7.50683e8	−1.05737	−0.528683	−	0.848819i	$-0.677314\pi$
$23$	−7.50683e8	−1.05737	−0.528683	+	0.848819i	$0.677314\pi$
$24$	−5.87079e8	−0.627081
$25$	−1.14654e9	−0.939248
$26$	1.26052e9	0.800242
$27$	3.87420e8	0.192450
$28$	−7.88948e8	−0.309400
$29$	−5.30324e9	−1.65560	−0.827798	−	0.561027i	$-0.810406\pi$
$29$	−5.30324e9	−1.65560	−0.827798	+	0.561027i	$0.810406\pi$
$30$	4.82070e8	0.120732
$31$	6.09654e9	1.23376	0.616882	−	0.787055i	$-0.288395\pi$
$31$	6.09654e9	1.23376	0.616882	+	0.787055i	$0.288395\pi$
$32$	3.29265e9	0.542089
$33$	1.53755e9	0.207248
$34$	−1.18340e10	−1.31377
$35$	2.95972e9	0.272150
$36$	−1.21994e9	−0.0934055
$37$	1.01295e10	0.649050	0.324525	−	0.945877i	$-0.394796\pi$
$37$	1.01295e10	0.649050	0.324525	+	0.945877i	$0.394796\pi$
$38$	−1.08020e10	−0.581981
$39$	1.19668e10	0.544578
$40$	−6.93514e9	−0.267711
$41$	−2.18330e8	−0.00717824	−0.00358912	−	0.999994i	$-0.501142\pi$
$41$	−2.18330e8	−0.00717824	−0.00358912	+	0.999994i	$0.501142\pi$
$42$	1.92392e10	0.540838
$43$	6.90652e9	0.166615	0.0833075	−	0.996524i	$-0.473452\pi$
$43$	6.90652e9	0.166615	0.0833075	+	0.996524i	$0.473452\pi$
$44$	−4.84157e9	−0.100587
$45$	4.57658e9	0.0821599
$46$	−5.76438e10	−0.897070
$47$	−7.05108e10	−0.954156	−0.477078	−	0.878861i	$-0.658304\pi$
$47$	−7.05108e10	−0.954156	−0.477078	+	0.878861i	$0.658304\pi$
$48$	−3.13721e10	−0.370233
$49$	2.12325e10	0.219142
$50$	−8.80412e10	−0.796858
$51$	−1.12347e11	−0.894039
$52$	−3.76822e10	−0.264310
$53$	1.26195e11	0.782079	0.391039	−	0.920374i	$-0.372116\pi$
$53$	1.26195e11	0.782079	0.391039	+	0.920374i	$0.372116\pi$
$54$	2.97494e10	0.163275
$55$	1.81631e10	0.0884772
$56$	−2.76779e11	−1.19926
$57$	−1.02550e11	−0.396048
$58$	−4.07227e11	−1.40461
$59$	4.21805e10	0.130189
$59$	4.21805e10	0.130189
$60$	−1.44111e10	−0.0398763
$61$	3.47997e11	0.864831	0.432416	−	0.901674i	$-0.357661\pi$
$61$	3.47997e11	0.864831	0.432416	+	0.901674i	$0.357661\pi$
$62$	4.68144e11	1.04673
$63$	1.82650e11	0.368049
$64$	6.05375e11	1.10117
$65$	1.41364e11	0.232489
$66$	1.18066e11	0.175829
$67$	7.19021e11	0.971081	0.485541	−	0.874214i	$-0.338623\pi$
$67$	7.19021e11	0.971081	0.485541	+	0.874214i	$0.338623\pi$
$68$	3.53768e11	0.433921
$69$	−5.47248e11	−0.610471
$70$	2.27272e11	0.230892
$71$	−1.79801e12	−1.66576	−0.832879	−	0.553455i	$-0.813309\pi$
$71$	−1.79801e12	−1.66576	−0.832879	+	0.553455i	$0.813309\pi$
$72$	−4.27981e11	−0.362045
$73$	−6.59872e11	−0.510342	−0.255171	−	0.966896i	$-0.582132\pi$
$73$	−6.59872e11	−0.510342	−0.255171	+	0.966896i	$0.582132\pi$
$74$	7.77831e11	0.550654
$75$	−8.35830e11	−0.542275
$76$	3.22916e11	0.192221
$77$	7.24882e11	0.396349
$78$	9.18915e11	0.462020
$79$	6.24170e11	0.288886	0.144443	−	0.989513i	$-0.453861\pi$
$79$	6.24170e11	0.288886	0.144443	+	0.989513i	$0.453861\pi$
$80$	−3.70597e11	−0.158058
$81$	2.82430e11	0.111111
$82$	−1.67652e10	−0.00609003
$83$	−3.14870e12	−1.05712	−0.528560	−	0.848896i	$-0.677268\pi$
$83$	−3.14870e12	−1.05712	−0.528560	+	0.848896i	$0.677268\pi$
$84$	−5.75143e11	−0.178632
$85$	−1.32715e12	−0.381679
$86$	5.30341e11	0.141356
$87$	−3.86606e12	−0.955858
$88$	−1.69852e12	−0.389883
$89$	−5.10394e12	−1.08861	−0.544303	−	0.838889i	$-0.683206\pi$
$89$	−5.10394e12	−1.08861	−0.544303	+	0.838889i	$0.683206\pi$
$90$	3.51429e11	0.0697045
$91$	5.64179e12	1.04147
$92$	1.72322e12	0.296292
$93$	4.44438e12	0.712314
$94$	−5.41441e12	−0.809507
$95$	−1.21141e12	−0.169079
$96$	2.40034e12	0.312975
$97$	2.84901e12	0.347278	0.173639	−	0.984809i	$-0.444447\pi$
$97$	2.84901e12	0.347278	0.173639	+	0.984809i	$0.444447\pi$
$98$	1.63041e12	0.185920
$99$	1.12088e12	0.119654
$100$	2.63193e12	0.263193
$101$	−1.38799e13	−1.30106	−0.650529	−	0.759481i	$-0.725453\pi$
$101$	−1.38799e13	−1.30106	−0.650529	+	0.759481i	$0.725453\pi$
$102$	−8.62698e12	−0.758504
$103$	4.18122e12	0.345033	0.172517	−	0.985007i	$-0.444810\pi$
$103$	4.18122e12	0.345033	0.172517	+	0.985007i	$0.444810\pi$
$104$	−1.32197e13	−1.02448
$105$	2.15764e12	0.157126
$106$	9.69035e12	0.663516
$107$	−2.51194e13	−1.61813	−0.809067	−	0.587717i	$-0.800027\pi$
$107$	−2.51194e13	−1.61813	−0.809067	+	0.587717i	$0.800027\pi$
$108$	−8.89337e11	−0.0539277
$109$	−2.51900e13	−1.43865	−0.719327	−	0.694672i	$-0.755550\pi$
$109$	−2.51900e13	−1.43865	−0.719327	+	0.694672i	$0.755550\pi$
$110$	1.39471e12	0.0750641
$111$	7.38443e12	0.374729
$112$	−1.47904e13	−0.708048
$113$	−3.23342e13	−1.46101	−0.730504	−	0.682909i	$-0.760715\pi$
$113$	−3.23342e13	−1.46101	−0.730504	+	0.682909i	$0.760715\pi$
$114$	−7.87463e12	−0.336007
$115$	−6.46462e12	−0.260619
$116$	1.21738e13	0.463925
$117$	8.72383e12	0.314412
$118$	3.23898e12	0.110452
$119$	−5.29663e13	−1.70980
$120$	−5.05572e12	−0.154563
$121$	−3.00743e13	−0.871145
$122$	2.67221e13	0.733723
$123$	−1.59163e11	−0.00414436
$124$	−1.39948e13	−0.345721
$125$	−2.03859e13	−0.477985
$126$	1.40254e13	0.312253
$127$	6.21896e13	1.31521	0.657603	−	0.753364i	$-0.271570\pi$
$127$	6.21896e13	1.31521	0.657603	+	0.753364i	$0.271570\pi$
$128$	1.95124e13	0.392145
$129$	5.03485e12	0.0961953
$130$	1.08551e13	0.197243
$131$	−2.18425e13	−0.377606	−0.188803	−	0.982015i	$-0.560461\pi$
$131$	−2.18425e13	−0.377606	−0.188803	+	0.982015i	$0.560461\pi$
$132$	−3.52951e12	−0.0580742
$133$	−4.83472e13	−0.757417
$134$	5.52125e13	0.823866
$135$	3.33633e12	0.0474350
$136$	1.24109e14	1.68191
$137$	6.08541e13	0.786332	0.393166	−	0.919467i	$-0.371380\pi$
$137$	6.08541e13	0.786332	0.393166	+	0.919467i	$0.371380\pi$
$138$	−4.20223e13	−0.517924
$139$	3.74691e13	0.440633	0.220317	−	0.975428i	$-0.429291\pi$
$139$	3.74691e13	0.440633	0.220317	+	0.975428i	$0.429291\pi$
$140$	−6.79414e12	−0.0762609
$141$	−5.14024e13	−0.550882
$142$	−1.38066e14	−1.41323
$143$	3.46222e13	0.338587
$144$	−2.28702e13	−0.213754
$145$	−4.56696e13	−0.408071
$146$	−5.06706e13	−0.432974
$147$	1.54785e13	0.126522
$148$	−2.32527e13	−0.181875
$149$	−1.78413e13	−0.133572	−0.0667861	−	0.997767i	$-0.521275\pi$
$149$	−1.78413e13	−0.133572	−0.0667861	+	0.997767i	$0.521275\pi$
$150$	−6.41821e13	−0.460066
$151$	−1.23097e14	−0.845080	−0.422540	−	0.906344i	$-0.638861\pi$
$151$	−1.23097e14	−0.845080	−0.422540	+	0.906344i	$0.638861\pi$
$152$	1.13286e14	0.745062
$153$	−8.19012e13	−0.516174
$154$	5.56625e13	0.336262
$155$	5.25012e13	0.304098
$156$	−2.74703e13	−0.152600
$157$	−8.41553e13	−0.448470	−0.224235	−	0.974535i	$-0.571988\pi$
$157$	−8.41553e13	−0.448470	−0.224235	+	0.974535i	$0.571988\pi$
$158$	4.79290e13	0.245091
$159$	9.19965e13	0.451533
$160$	2.83551e13	0.133614
$161$	−2.58001e14	−1.16749
$162$	2.16873e13	0.0942667
$163$	2.96776e14	1.23939	0.619697	−	0.784841i	$-0.287256\pi$
$163$	2.96776e14	1.23939	0.619697	+	0.784841i	$0.287256\pi$
$164$	5.01184e11	0.00201146
$165$	1.32409e13	0.0510823
$166$	−2.41784e14	−0.896861
$167$	−7.20047e13	−0.256864	−0.128432	−	0.991718i	$-0.540994\pi$
$167$	−7.20047e13	−0.256864	−0.128432	+	0.991718i	$0.540994\pi$
$168$	−2.01772e14	−0.692390
$169$	−3.34089e13	−0.110306
$170$	−1.01910e14	−0.323817
$171$	−7.47587e13	−0.228658
$172$	−1.58541e13	−0.0466883
$173$	4.81605e12	0.0136581	0.00682907	−	0.999977i	$-0.497826\pi$
$173$	4.81605e12	0.0136581	0.00682907	+	0.999977i	$0.497826\pi$
$174$	−2.96869e14	−0.810951
$175$	−3.94053e14	−1.03707
$176$	−9.07649e13	−0.230190
$177$	3.07496e13	0.0751646
$178$	−3.91924e14	−0.923574
$179$	7.75206e13	0.176146	0.0880729	−	0.996114i	$-0.471929\pi$
$179$	7.75206e13	0.176146	0.0880729	+	0.996114i	$0.471929\pi$
$180$	−1.05057e13	−0.0230226
$181$	−6.20019e14	−1.31067	−0.655336	−	0.755337i	$-0.727473\pi$
$181$	−6.20019e14	−1.31067	−0.655336	+	0.755337i	$0.727473\pi$
$182$	4.33224e14	0.883585
$183$	2.53690e14	0.499311
$184$	6.04541e14	1.14844
$185$	8.72320e13	0.159978
$186$	3.41277e14	0.604328
$187$	−3.25041e14	−0.555863
$188$	1.61860e14	0.267370
$189$	1.33152e14	0.212493
$190$	−9.30226e13	−0.143447
$191$	−1.03485e14	−0.154228	−0.0771139	−	0.997022i	$-0.524571\pi$
$191$	−1.03485e14	−0.154228	−0.0771139	+	0.997022i	$0.524571\pi$
$192$	4.41318e14	0.635761
$193$	−7.29182e14	−1.01558	−0.507789	−	0.861481i	$-0.669537\pi$
$193$	−7.29182e14	−1.01558	−0.507789	+	0.861481i	$0.669537\pi$
$194$	2.18771e14	0.294631
$195$	1.03054e14	0.134227
$196$	−4.87399e13	−0.0614073
$197$	1.49693e15	1.82462	0.912308	−	0.409504i	$-0.134298\pi$
$197$	1.49693e15	1.82462	0.912308	+	0.409504i	$0.134298\pi$
$198$	8.60704e13	0.101515
$199$	8.30367e14	0.947819	0.473909	−	0.880574i	$-0.342842\pi$
$199$	8.30367e14	0.947819	0.473909	+	0.880574i	$0.342842\pi$
$200$	9.23335e14	1.02015
$201$	5.24167e14	0.560654
$202$	−1.06581e15	−1.10382
$203$	−1.82266e15	−1.82802
$204$	2.57897e14	0.250525
$205$	−1.88018e12	−0.00176929
$206$	3.21069e14	0.292727
$207$	−3.98944e14	−0.352455
$208$	−7.06428e14	−0.604862
$209$	−2.96694e14	−0.246240
$210$	1.65682e14	0.133306
$211$	−1.71589e15	−1.33861	−0.669306	−	0.742987i	$-0.733408\pi$
$211$	−1.71589e15	−1.33861	−0.669306	+	0.742987i	$0.733408\pi$
$212$	−2.89686e14	−0.219151
$213$	−1.31075e15	−0.961726
$214$	−1.92888e15	−1.37283
$215$	5.94765e13	0.0410672
$216$	−3.11998e14	−0.209027
$217$	2.09531e15	1.36226
$218$	−1.93430e15	−1.22055
$219$	−4.81047e14	−0.294646
$220$	−4.16939e13	−0.0247928
$221$	−2.52981e15	−1.46062
$222$	5.67039e14	0.317921
$223$	4.75904e14	0.259142	0.129571	−	0.991570i	$-0.458640\pi$
$223$	4.75904e14	0.259142	0.129571	+	0.991570i	$0.458640\pi$
$224$	1.13164e15	0.598547
$225$	−6.09320e14	−0.313083
$226$	−2.48289e15	−1.23952
$227$	2.78931e14	0.135310	0.0676548	−	0.997709i	$-0.478448\pi$
$227$	2.78931e14	0.135310	0.0676548	+	0.997709i	$0.478448\pi$
$228$	2.35406e14	0.110979
$229$	3.77467e15	1.72961	0.864805	−	0.502107i	$-0.167442\pi$
$229$	3.77467e15	1.72961	0.864805	+	0.502107i	$0.167442\pi$
$230$	−4.96408e14	−0.221110
$231$	5.28439e14	0.228832
$232$	4.27081e15	1.79820
$233$	2.36280e15	0.967418	0.483709	−	0.875229i	$-0.339289\pi$
$233$	2.36280e15	0.967418	0.483709	+	0.875229i	$0.339289\pi$
$234$	6.69889e14	0.266747
$235$	−6.07214e14	−0.235180
$236$	−9.68268e13	−0.0364811
$237$	4.55020e14	0.166788
$238$	−4.06720e15	−1.45059
$239$	−3.91248e15	−1.35789	−0.678947	−	0.734187i	$-0.737564\pi$
$239$	−3.91248e15	−1.35789	−0.678947	+	0.734187i	$0.737564\pi$
$240$	−2.70165e14	−0.0912549
$241$	−1.97175e15	−0.648248	−0.324124	−	0.946015i	$-0.605070\pi$
$241$	−1.97175e15	−0.648248	−0.324124	+	0.946015i	$0.605070\pi$
$242$	−2.30936e15	−0.739080
$243$	2.05891e14	0.0641500
$244$	−7.98839e14	−0.242340
$245$	1.82847e14	0.0540141
$246$	−1.22218e13	−0.00351608
$247$	−2.30918e15	−0.647036
$248$	−4.90967e15	−1.34004
$249$	−2.29541e15	−0.610328
$250$	−1.56540e15	−0.405523
$251$	−1.67742e15	−0.423412	−0.211706	−	0.977333i	$-0.567902\pi$
$251$	−1.67742e15	−0.423412	−0.211706	+	0.977333i	$0.567902\pi$
$252$	−4.19279e14	−0.103133
$253$	−1.58328e15	−0.379556
$254$	4.77545e15	1.11582
$255$	−9.67496e14	−0.220363
$256$	−3.46090e15	−0.768475
$257$	6.30357e15	1.36465	0.682325	−	0.731049i	$-0.260969\pi$
$257$	6.30357e15	1.36465	0.682325	+	0.731049i	$0.260969\pi$
$258$	3.86619e14	0.0816121
$259$	3.48140e15	0.716647
$260$	−3.24506e14	−0.0651471
$261$	−2.81836e15	−0.551865
$262$	−1.67725e15	−0.320361
$263$	2.60734e15	0.485832	0.242916	−	0.970047i	$-0.421896\pi$
$263$	2.60734e15	0.485832	0.242916	+	0.970047i	$0.421896\pi$
$264$	−1.23822e15	−0.225099
$265$	1.08675e15	0.192767
$266$	−3.71250e15	−0.642593
$267$	−3.72077e15	−0.628507
$268$	−1.65054e15	−0.272113
$269$	−1.09355e15	−0.175974	−0.0879868	−	0.996122i	$-0.528043\pi$
$269$	−1.09355e15	−0.175974	−0.0879868	+	0.996122i	$0.528043\pi$
$270$	2.56192e14	0.0402439
$271$	8.18155e15	1.25469	0.627343	−	0.778743i	$-0.284142\pi$
$271$	8.18155e15	1.25469	0.627343	+	0.778743i	$0.284142\pi$
$272$	6.63210e15	0.993008
$273$	4.11286e15	0.601294
$274$	4.67289e15	0.667125
$275$	−2.41820e15	−0.337156
$276$	1.25623e15	0.171064
$277$	−6.43750e15	−0.856247	−0.428123	−	0.903720i	$-0.640825\pi$
$277$	−6.43750e15	−0.856247	−0.428123	+	0.903720i	$0.640825\pi$
$278$	2.87720e15	0.373834
$279$	3.23995e15	0.411255
$280$	−2.38353e15	−0.295592
$281$	−9.95467e15	−1.20625	−0.603123	−	0.797648i	$-0.706077\pi$
$281$	−9.95467e15	−1.20625	−0.603123	+	0.797648i	$0.706077\pi$
$282$	−3.94711e15	−0.467369
$283$	3.16274e14	0.0365976	0.0182988	−	0.999833i	$-0.494175\pi$
$283$	3.16274e14	0.0365976	0.0182988	+	0.999833i	$0.494175\pi$
$284$	4.12739e15	0.466773
$285$	−8.83121e14	−0.0976177
$286$	2.65859e15	0.287258
$287$	−7.50374e13	−0.00792584
$288$	1.74985e15	0.180696
$289$	1.38458e16	1.39792
$290$	−3.50690e15	−0.346207
$291$	2.07693e15	0.200501
$292$	1.51476e15	0.143006
$293$	−1.80488e16	−1.66652	−0.833258	−	0.552885i	$-0.813527\pi$
$293$	−1.80488e16	−1.66652	−0.833258	+	0.552885i	$0.813527\pi$
$294$	1.18857e15	0.107341
$295$	3.63244e14	0.0320889
$296$	−8.15753e15	−0.704957
$297$	8.17119e14	0.0690825
$298$	−1.37001e15	−0.113323
$299$	−1.23228e16	−0.997346
$300$	1.91868e15	0.151954
$301$	2.37369e15	0.183968
$302$	−9.45244e15	−0.716966
$303$	−1.01184e16	−0.751166
$304$	6.05372e15	0.439890
$305$	2.99683e15	0.213163
$306$	−6.28907e15	−0.437922
$307$	−9.77787e15	−0.666568	−0.333284	−	0.942826i	$-0.608157\pi$
$307$	−9.77787e15	−0.666568	−0.333284	+	0.942826i	$0.608157\pi$
$308$	−1.66399e15	−0.111063
$309$	3.04811e15	0.199205
$310$	4.03149e15	0.257997
$311$	9.68949e15	0.607237	0.303618	−	0.952794i	$-0.401805\pi$
$311$	9.68949e15	0.607237	0.303618	+	0.952794i	$0.401805\pi$
$312$	−9.63716e15	−0.591485
$313$	−2.56809e16	−1.54373	−0.771867	−	0.635785i	$-0.780677\pi$
$313$	−2.56809e16	−1.54373	−0.771867	+	0.635785i	$0.780677\pi$
$314$	−6.46215e15	−0.380482
$315$	1.57292e15	0.0907167
$316$	−1.43280e15	−0.0809506
$317$	2.06363e15	0.114221	0.0571105	−	0.998368i	$-0.481811\pi$
$317$	2.06363e15	0.114221	0.0571105	+	0.998368i	$0.481811\pi$
$318$	7.06427e15	0.383081
$319$	−1.11852e16	−0.594298
$320$	5.21328e15	0.271416
$321$	−1.83120e16	−0.934230
$322$	−1.98115e16	−0.990498
$323$	2.16791e16	1.06225
$324$	−6.48327e14	−0.0311352
$325$	−1.88210e16	−0.885932
$326$	2.27890e16	1.05150
$327$	−1.83635e16	−0.830607
$328$	1.75826e14	0.00779655
$329$	−2.42337e16	−1.05353
$330$	1.01675e15	0.0433383
$331$	−3.78462e16	−1.58176	−0.790879	−	0.611972i	$-0.790376\pi$
$331$	−3.78462e16	−1.58176	−0.790879	+	0.611972i	$0.790376\pi$
$332$	7.22796e15	0.296222
$333$	5.38325e15	0.216350
$334$	−5.52913e15	−0.217924
$335$	6.19196e15	0.239352
$336$	−1.07822e16	−0.408792
$337$	−4.52293e16	−1.68200	−0.840999	−	0.541037i	$-0.818032\pi$
$337$	−4.52293e16	−1.68200	−0.840999	+	0.541037i	$0.818032\pi$
$338$	−2.56542e15	−0.0935837
$339$	−2.35716e16	−0.843513
$340$	3.04653e15	0.106953
$341$	1.28584e16	0.442876
$342$	−5.74060e15	−0.193994
$343$	−2.60022e16	−0.862182
$344$	−5.56197e15	−0.180967
$345$	−4.71270e15	−0.150469
$346$	3.69817e14	0.0115876
$347$	4.54759e16	1.39843	0.699213	−	0.714914i	$-0.253534\pi$
$347$	4.54759e16	1.39843	0.699213	+	0.714914i	$0.253534\pi$
$348$	8.87467e15	0.267847
$349$	1.79338e16	0.531259	0.265629	−	0.964075i	$-0.414420\pi$
$349$	1.79338e16	0.531259	0.265629	+	0.964075i	$0.414420\pi$
$350$	−3.02587e16	−0.879849
$351$	6.35967e15	0.181526
$352$	6.94462e15	0.194590
$353$	5.08417e16	1.39857	0.699285	−	0.714843i	$-0.253502\pi$
$353$	5.08417e16	1.39857	0.699285	+	0.714843i	$0.253502\pi$
$354$	2.36121e15	0.0637697
$355$	−1.54838e16	−0.410576
$356$	1.17163e16	0.305045
$357$	−3.86124e16	−0.987152
$358$	5.95268e15	0.149442
$359$	3.52166e16	0.868227	0.434113	−	0.900858i	$-0.357062\pi$
$359$	3.52166e16	0.868227	0.434113	+	0.900858i	$0.357062\pi$
$360$	−3.68562e15	−0.0892369
$361$	−2.22645e16	−0.529439
$362$	−4.76103e16	−1.11197
$363$	−2.19242e16	−0.502956
$364$	−1.29509e16	−0.291838
$365$	−5.68259e15	−0.125789
$366$	1.94804e16	0.423615
$367$	−2.18731e15	−0.0467283	−0.0233642	−	0.999727i	$-0.507438\pi$
$367$	−2.18731e15	−0.0467283	−0.0233642	+	0.999727i	$0.507438\pi$
$368$	3.23052e16	0.678049
$369$	−1.16029e14	−0.00239275
$370$	6.69841e15	0.135725
$371$	4.33719e16	0.863530
$372$	−1.02022e16	−0.199602
$373$	3.93006e16	0.755600	0.377800	−	0.925887i	$-0.376681\pi$
$373$	3.93006e16	0.755600	0.377800	+	0.925887i	$0.376681\pi$
$374$	−2.49594e16	−0.471594
$375$	−1.48613e16	−0.275965
$376$	5.67839e16	1.03634
$377$	−8.70549e16	−1.56162
$378$	1.02245e16	0.180279
$379$	−1.24895e15	−0.0216467	−0.0108234	−	0.999941i	$-0.503445\pi$
$379$	−1.24895e15	−0.0216467	−0.0108234	+	0.999941i	$0.503445\pi$
$380$	2.78084e15	0.0473787
$381$	4.53363e16	0.759335
$382$	−7.94649e15	−0.130847
$383$	1.51746e15	0.0245655	0.0122827	−	0.999925i	$-0.496090\pi$
$383$	1.51746e15	0.0245655	0.0122827	+	0.999925i	$0.496090\pi$
$384$	1.42246e16	0.226405
$385$	6.24243e15	0.0976919
$386$	−5.59928e16	−0.861617
$387$	3.67041e15	0.0555384
$388$	−6.54000e15	−0.0973132
$389$	2.38298e16	0.348697	0.174349	−	0.984684i	$-0.444218\pi$
$389$	2.38298e16	0.348697	0.174349	+	0.984684i	$0.444218\pi$
$390$	7.91338e15	0.113879
$391$	1.15689e17	1.63735
$392$	−1.70990e16	−0.238018
$393$	−1.59232e16	−0.218011
$394$	1.14947e17	1.54801
$395$	5.37513e15	0.0712046
$396$	−2.57301e15	−0.0335292
$397$	−3.87404e16	−0.496622	−0.248311	−	0.968680i	$-0.579876\pi$
$397$	−3.87404e16	−0.496622	−0.248311	+	0.968680i	$0.579876\pi$
$398$	6.37626e16	0.804130
$399$	−3.52451e16	−0.437295
$400$	4.93407e16	0.602304
$401$	7.83431e16	0.940941	0.470470	−	0.882416i	$-0.344084\pi$
$401$	7.83431e16	0.940941	0.470470	+	0.882416i	$0.344084\pi$
$402$	4.02499e16	0.475659
$403$	1.00077e17	1.16373
$404$	3.18617e16	0.364578
$405$	2.43218e15	0.0273866
$406$	−1.39959e17	−1.55089
$407$	2.13645e16	0.232985
$408$	9.04757e16	0.971049
$409$	−1.07399e17	−1.13448	−0.567241	−	0.823552i	$-0.691989\pi$
$409$	−1.07399e17	−1.13448	−0.567241	+	0.823552i	$0.691989\pi$
$410$	−1.44376e14	−0.00150107
$411$	4.43626e16	0.453989
$412$	−9.59813e15	−0.0966841
$413$	1.44969e16	0.143748
$414$	−3.06343e16	−0.299023
$415$	−2.71155e16	−0.260559
$416$	5.40503e16	0.511318
$417$	2.73150e16	0.254400
$418$	−2.27827e16	−0.208910
$419$	−1.78230e17	−1.60912	−0.804562	−	0.593869i	$-0.797600\pi$
$419$	−1.78230e17	−1.60912	−0.804562	+	0.593869i	$0.797600\pi$
$420$	−4.95293e15	−0.0440293
$421$	1.71934e16	0.150497	0.0752484	−	0.997165i	$-0.476025\pi$
$421$	1.71934e16	0.150497	0.0752484	+	0.997165i	$0.476025\pi$
$422$	−1.31761e17	−1.13568
$423$	−3.74723e16	−0.318052
$424$	−1.01628e17	−0.849444
$425$	1.76696e17	1.45445
$426$	−1.00650e17	−0.815929
$427$	1.19602e17	0.954902
$428$	5.76624e16	0.453428
$429$	2.52396e16	0.195483
$430$	4.56711e15	0.0348415
$431$	1.08757e17	0.817248	0.408624	−	0.912703i	$-0.366009\pi$
$431$	1.08757e17	0.817248	0.408624	+	0.912703i	$0.366009\pi$
$432$	−1.66724e16	−0.123411
$433$	7.20835e16	0.525611	0.262805	−	0.964849i	$-0.415352\pi$
$433$	7.20835e16	0.525611	0.262805	+	0.964849i	$0.415352\pi$
$434$	1.60895e17	1.15574
$435$	−3.32932e16	−0.235600
$436$	5.78245e16	0.403135
$437$	1.05600e17	0.725326
$438$	−3.69388e16	−0.249978
$439$	9.77140e16	0.651534	0.325767	−	0.945450i	$-0.394377\pi$
$439$	9.77140e16	0.651534	0.325767	+	0.945450i	$0.394377\pi$
$440$	−1.46271e16	−0.0960983
$441$	1.12838e16	0.0730474
$442$	−1.94260e17	−1.23919
$443$	3.97269e16	0.249724	0.124862	−	0.992174i	$-0.460151\pi$
$443$	3.97269e16	0.249724	0.124862	+	0.992174i	$0.460151\pi$
$444$	−1.69512e16	−0.105005
$445$	−4.39533e16	−0.268319
$446$	3.65440e16	0.219856
$447$	−1.30063e16	−0.0771179
$448$	2.08060e17	1.21586
$449$	1.91140e17	1.10091	0.550453	−	0.834866i	$-0.314455\pi$
$449$	1.91140e17	1.10091	0.550453	+	0.834866i	$0.314455\pi$
$450$	−4.67887e16	−0.265619
$451$	−4.60485e14	−0.00257673
$452$	7.42243e16	0.409399
$453$	−8.97378e16	−0.487907
$454$	2.14187e16	0.114797
$455$	4.85851e16	0.256702
$456$	8.25854e16	0.430162
$457$	2.69665e17	1.38474	0.692372	−	0.721540i	$-0.256566\pi$
$457$	2.69665e17	1.38474	0.692372	+	0.721540i	$0.256566\pi$
$458$	2.89851e17	1.46740
$459$	−5.97060e16	−0.298013
$460$	1.48397e16	0.0730299
$461$	−8.41504e15	−0.0408320	−0.0204160	−	0.999792i	$-0.506499\pi$
$461$	−8.41504e15	−0.0408320	−0.0204160	+	0.999792i	$0.506499\pi$
$462$	4.05780e16	0.194141
$463$	5.63024e16	0.265614	0.132807	−	0.991142i	$-0.457601\pi$
$463$	5.63024e16	0.265614	0.132807	+	0.991142i	$0.457601\pi$
$464$	2.28222e17	1.06167
$465$	3.82734e16	0.175571
$466$	1.81436e17	0.820758
$467$	3.93932e17	1.75736	0.878681	−	0.477410i	$-0.158424\pi$
$467$	3.93932e17	1.75736	0.878681	+	0.477410i	$0.158424\pi$
$468$	−2.00258e16	−0.0881034
$469$	2.47119e17	1.07222
$470$	−4.66270e16	−0.199527
$471$	−6.13492e16	−0.258924
$472$	−3.39689e16	−0.141403
$473$	1.45667e16	0.0598087
$474$	3.49403e16	0.141503
$475$	1.61286e17	0.644300
$476$	1.21586e17	0.479113
$477$	6.70654e16	0.260693
$478$	−3.00433e17	−1.15204
$479$	−1.30163e17	−0.492387	−0.246193	−	0.969221i	$-0.579180\pi$
$479$	−1.30163e17	−0.492387	−0.246193	+	0.969221i	$0.579180\pi$
$480$	2.06709e16	0.0771421
$481$	1.66281e17	0.612207
$482$	−1.51408e17	−0.549974
$483$	−1.88083e17	−0.674050
$484$	6.90366e16	0.244109
$485$	2.45347e16	0.0855971
$486$	1.58101e16	0.0544249
$487$	1.78044e17	0.604768	0.302384	−	0.953186i	$-0.402218\pi$
$487$	1.78044e17	0.604768	0.302384	+	0.953186i	$0.402218\pi$
$488$	−2.80249e17	−0.939325
$489$	2.16350e17	0.715564
$490$	1.40405e16	0.0458256
$491$	2.01033e17	0.647498	0.323749	−	0.946143i	$-0.395057\pi$
$491$	2.01033e17	0.647498	0.323749	+	0.946143i	$0.395057\pi$
$492$	3.65363e14	0.00116132
$493$	8.17290e17	2.56373
$494$	−1.77319e17	−0.548946
$495$	9.65259e15	0.0294924
$496$	−2.62361e17	−0.791166
$497$	−6.17954e17	−1.83924
$498$	−1.76261e17	−0.517803
$499$	−6.38814e17	−1.85234	−0.926170	−	0.377105i	$-0.876920\pi$
$499$	−6.38814e17	−1.85234	−0.926170	+	0.377105i	$0.876920\pi$
$500$	4.67965e16	0.133939
$501$	−5.24915e16	−0.148301
$502$	−1.28807e17	−0.359223
$503$	2.91620e17	0.802832	0.401416	−	0.915896i	$-0.368518\pi$
$503$	2.91620e17	0.802832	0.401416	+	0.915896i	$0.368518\pi$
$504$	−1.47092e17	−0.399752
$505$	−1.19529e17	−0.320684
$506$	−1.21578e17	−0.322015
$507$	−2.43551e16	−0.0636852
$508$	−1.42758e17	−0.368543
$509$	5.67017e17	1.44521	0.722604	−	0.691262i	$-0.242945\pi$
$509$	5.67017e17	1.44521	0.722604	+	0.691262i	$0.242945\pi$
$510$	−7.42925e16	−0.186956
$511$	−2.26790e17	−0.563493
$512$	−4.25603e17	−1.04412
$513$	−5.44991e16	−0.132016
$514$	4.84041e17	1.15777
$515$	3.60072e16	0.0850437
$516$	−1.15577e16	−0.0269555
$517$	−1.48716e17	−0.342507
$518$	2.67331e17	0.608004
$519$	3.51090e15	0.00788553
$520$	−1.13843e17	−0.252514
$521$	−1.79693e16	−0.0393629	−0.0196814	−	0.999806i	$-0.506265\pi$
$521$	−1.79693e16	−0.0393629	−0.0196814	+	0.999806i	$0.506265\pi$
$522$	−2.16417e17	−0.468203
$523$	4.87927e17	1.04254	0.521271	−	0.853391i	$-0.325458\pi$
$523$	4.87927e17	1.04254	0.521271	+	0.853391i	$0.325458\pi$
$524$	5.01402e16	0.105812
$525$	−2.87265e17	−0.598752
$526$	2.00214e17	0.412180
$527$	−9.39547e17	−1.91051
$528$	−6.61676e16	−0.132900
$529$	5.94882e16	0.118024
$530$	8.34499e16	0.163543
$531$	2.24165e16	0.0433963
$532$	1.10983e17	0.212241
$533$	−3.58398e15	−0.00677078
$534$	−2.85712e17	−0.533225
$535$	−2.16319e17	−0.398837
$536$	−5.79043e17	−1.05473
$537$	5.65125e16	0.101698
$538$	−8.39718e16	−0.149296
$539$	4.47820e16	0.0786641
$540$	−7.65866e15	−0.0132921
$541$	−2.65595e17	−0.455448	−0.227724	−	0.973726i	$-0.573128\pi$
$541$	−2.65595e17	−0.455448	−0.227724	+	0.973726i	$0.573128\pi$
$542$	6.28249e17	1.06448
$543$	−4.51994e17	−0.756717
$544$	−5.07436e17	−0.839437
$545$	−2.16928e17	−0.354599
$546$	3.15820e17	0.510138
$547$	9.23920e17	1.47474	0.737372	−	0.675486i	$-0.236066\pi$
$547$	9.23920e17	1.47474	0.737372	+	0.675486i	$0.236066\pi$
$548$	−1.39693e17	−0.220343
$549$	1.84940e17	0.288277
$550$	−1.85690e17	−0.286043
$551$	7.46015e17	1.13570
$552$	4.40710e17	0.663054
$553$	2.14520e17	0.318973
$554$	−4.94326e17	−0.726440
$555$	6.35921e16	0.0923632
$556$	−8.60117e16	−0.123473
$557$	−9.57495e17	−1.35856	−0.679278	−	0.733881i	$-0.737707\pi$
$557$	−9.57495e17	−1.35856	−0.679278	+	0.733881i	$0.737707\pi$
$558$	2.48791e17	0.348909
$559$	1.13373e17	0.157157
$560$	−1.27370e17	−0.174520
$561$	−2.36955e17	−0.320927
$562$	−7.64404e17	−1.02338
$563$	−1.06753e18	−1.41278	−0.706388	−	0.707824i	$-0.749677\pi$
$563$	−1.06753e18	−1.41278	−0.706388	+	0.707824i	$0.749677\pi$
$564$	1.17996e17	0.154366
$565$	−2.78451e17	−0.360109
$566$	2.42862e16	0.0310494
$567$	9.70677e16	0.122683
$568$	1.44797e18	1.80924
$569$	−3.70781e17	−0.458023	−0.229011	−	0.973424i	$-0.573549\pi$
$569$	−3.70781e17	−0.458023	−0.229011	+	0.973424i	$0.573549\pi$
$570$	−6.78135e16	−0.0828189
$571$	2.25137e17	0.271839	0.135919	−	0.990720i	$-0.456601\pi$
$571$	2.25137e17	0.271839	0.135919	+	0.990720i	$0.456601\pi$
$572$	−7.94764e16	−0.0948777
$573$	−7.54409e16	−0.0890434
$574$	−5.76201e15	−0.00672429
$575$	8.60690e17	0.993129
$576$	3.21721e17	0.367057
$577$	−1.24891e18	−1.40893	−0.704464	−	0.709740i	$-0.748813\pi$
$577$	−1.24891e18	−1.40893	−0.704464	+	0.709740i	$0.748813\pi$
$578$	1.06320e18	1.18600
$579$	−5.31574e17	−0.586344
$580$	1.04836e17	0.114348
$581$	−1.08217e18	−1.16722
$582$	1.59484e17	0.170105
$583$	2.66162e17	0.280738
$584$	5.31409e17	0.554301
$585$	7.51265e16	0.0774962
$586$	−1.38594e18	−1.41387
$587$	6.44717e17	0.650461	0.325231	−	0.945635i	$-0.394558\pi$
$587$	6.44717e17	0.650461	0.325231	+	0.945635i	$0.394558\pi$
$588$	−3.55314e16	−0.0354535
$589$	−8.57610e17	−0.846331
$590$	2.78929e16	0.0272243
$591$	1.09126e18	1.05344
$592$	−4.35918e17	−0.416211
$593$	−8.38047e17	−0.791430	−0.395715	−	0.918373i	$-0.629503\pi$
$593$	−8.38047e17	−0.791430	−0.395715	+	0.918373i	$0.629503\pi$
$594$	6.27453e16	0.0586097
$595$	−4.56127e17	−0.421430
$596$	4.09553e16	0.0374291
$597$	6.05338e17	0.547223
$598$	−9.46247e17	−0.846149
$599$	6.02182e17	0.532664	0.266332	−	0.963881i	$-0.414188\pi$
$599$	6.02182e17	0.532664	0.266332	+	0.963881i	$0.414188\pi$
$600$	6.73112e17	0.588985
$601$	1.32927e18	1.15061	0.575305	−	0.817939i	$-0.304884\pi$
$601$	1.32927e18	1.15061	0.575305	+	0.817939i	$0.304884\pi$
$602$	1.82272e17	0.156078
$603$	3.82117e17	0.323694
$604$	2.82574e17	0.236805
$605$	−2.58989e17	−0.214720
$606$	−7.76979e17	−0.637290
$607$	1.14934e18	0.932658	0.466329	−	0.884611i	$-0.345576\pi$
$607$	1.14934e18	0.932658	0.466329	+	0.884611i	$0.345576\pi$
$608$	−4.63182e17	−0.371859
$609$	−1.32872e18	−1.05541
$610$	2.30122e17	0.180848
$611$	−1.15746e18	−0.899995
$612$	1.88007e17	0.144640
$613$	−2.29915e17	−0.175015	−0.0875073	−	0.996164i	$-0.527890\pi$
$613$	−2.29915e17	−0.175015	−0.0875073	+	0.996164i	$0.527890\pi$
$614$	−7.50827e17	−0.565517
$615$	−1.37065e15	−0.00102150
$616$	−5.83763e17	−0.430489
$617$	7.07545e17	0.516298	0.258149	−	0.966105i	$-0.416887\pi$
$617$	7.07545e17	0.516298	0.258149	+	0.966105i	$0.416887\pi$
$618$	2.34060e17	0.169006
$619$	3.24098e17	0.231573	0.115786	−	0.993274i	$-0.463061\pi$
$619$	3.24098e17	0.231573	0.115786	+	0.993274i	$0.463061\pi$
$620$	−1.20518e17	−0.0852133
$621$	−2.90830e17	−0.203490
$622$	7.44041e17	0.515180
$623$	−1.75416e18	−1.20198
$624$	−5.14986e17	−0.349217
$625$	1.22403e18	0.821434
$626$	−1.97200e18	−1.30970
$627$	−2.16290e17	−0.142167
$628$	1.93181e17	0.125669
$629$	−1.56108e18	−1.00507
$630$	1.20782e17	0.0769641
$631$	1.56666e18	0.988059	0.494029	−	0.869445i	$-0.335524\pi$
$631$	1.56666e18	0.988059	0.494029	+	0.869445i	$0.335524\pi$
$632$	−5.02657e17	−0.313770
$633$	−1.25089e18	−0.772848
$634$	1.58463e17	0.0969051
$635$	5.35555e17	0.324172
$636$	−2.11181e17	−0.126527
$637$	3.48540e17	0.206703
$638$	−8.58894e17	−0.504203
$639$	−9.55535e17	−0.555253
$640$	1.68034e17	0.0966558
$641$	−8.52146e17	−0.485218	−0.242609	−	0.970124i	$-0.578003\pi$
$641$	−8.52146e17	−0.485218	−0.242609	+	0.970124i	$0.578003\pi$
$642$	−1.40615e18	−0.792601
$643$	2.59198e17	0.144630	0.0723152	−	0.997382i	$-0.476961\pi$
$643$	2.59198e17	0.144630	0.0723152	+	0.997382i	$0.476961\pi$
$644$	5.92249e17	0.327150
$645$	4.33584e16	0.0237102
$646$	1.66471e18	0.901211
$647$	2.06094e18	1.10456	0.552278	−	0.833660i	$-0.313759\pi$
$647$	2.06094e18	1.10456	0.552278	+	0.833660i	$0.313759\pi$
$648$	−2.27447e17	−0.120682
$649$	8.89641e16	0.0467331
$650$	−1.44523e18	−0.751625
$651$	1.52748e18	0.786500
$652$	−6.81259e17	−0.347299
$653$	−3.70684e18	−1.87098	−0.935488	−	0.353358i	$-0.885040\pi$
$653$	−3.70684e18	−1.87098	−0.935488	+	0.353358i	$0.885040\pi$
$654$	−1.41011e18	−0.704688
$655$	−1.88100e17	−0.0930723
$656$	9.39569e15	0.00460314
$657$	−3.50683e17	−0.170114
$658$	−1.86087e18	−0.893815
$659$	4.20177e18	1.99838	0.999189	−	0.0402739i	$-0.0128230\pi$
$659$	4.20177e18	1.99838	0.999189	+	0.0402739i	$0.0128230\pi$
$660$	−3.03949e16	−0.0143141
$661$	1.35612e18	0.632395	0.316197	−	0.948693i	$-0.397594\pi$
$661$	1.35612e18	0.632395	0.316197	+	0.948693i	$0.397594\pi$
$662$	−2.90615e18	−1.34196
$663$	−1.84423e18	−0.843290
$664$	2.53572e18	1.14818
$665$	−4.16349e17	−0.186688
$666$	4.13371e17	0.183551
$667$	3.98105e18	1.75057
$668$	1.65289e17	0.0719777
$669$	3.46934e17	0.149616
$670$	4.75471e17	0.203066
$671$	7.33969e17	0.310443
$672$	8.24969e17	0.345571
$673$	−2.87276e18	−1.19179	−0.595897	−	0.803061i	$-0.703203\pi$
$673$	−2.87276e18	−1.19179	−0.595897	+	0.803061i	$0.703203\pi$
$674$	−3.47309e18	−1.42701
$675$	−4.44194e17	−0.180758
$676$	7.66913e16	0.0309096
$677$	−1.07415e18	−0.428783	−0.214391	−	0.976748i	$-0.568777\pi$
$677$	−1.07415e18	−0.428783	−0.214391	+	0.976748i	$0.568777\pi$
$678$	−1.81003e18	−0.715637
$679$	9.79171e17	0.383447
$680$	1.06879e18	0.414556
$681$	2.03341e17	0.0781211
$682$	9.87374e17	0.375736
$683$	−3.44874e18	−1.29995	−0.649973	−	0.759957i	$-0.725220\pi$
$683$	−3.44874e18	−1.29995	−0.649973	+	0.759957i	$0.725220\pi$
$684$	1.71611e17	0.0640738
$685$	5.24054e17	0.193815
$686$	−1.99667e18	−0.731476
$687$	2.75173e18	0.998591
$688$	−2.97218e17	−0.106844
$689$	2.07155e18	0.737685
$690$	−3.61881e17	−0.127658
$691$	−7.16038e17	−0.250224	−0.125112	−	0.992143i	$-0.539929\pi$
$691$	−7.16038e17	−0.250224	−0.125112	+	0.992143i	$0.539929\pi$
$692$	−1.10554e16	−0.00382724
$693$	3.85232e17	0.132116
$694$	3.49202e18	1.18642
$695$	3.22671e17	0.108607
$696$	3.11342e18	1.03819
$697$	3.36472e16	0.0111157
$698$	1.37711e18	0.450720
$699$	1.72248e18	0.558539
$700$	9.04562e17	0.290604
$701$	4.24864e18	1.35233	0.676165	−	0.736750i	$-0.263641\pi$
$701$	4.24864e18	1.35233	0.676165	+	0.736750i	$0.263641\pi$
$702$	4.88349e17	0.154007
$703$	−1.42494e18	−0.445232
$704$	1.27681e18	0.395280
$705$	−4.42659e17	−0.135781
$706$	3.90406e18	1.18655
$707$	−4.77035e18	−1.43656
$708$	−7.05868e16	−0.0210624
$709$	−1.51425e16	−0.00447709	−0.00223855	−	0.999997i	$-0.500713\pi$
$709$	−1.51425e16	−0.00447709	−0.00223855	+	0.999997i	$0.500713\pi$
$710$	−1.18898e18	−0.348333
$711$	3.31709e17	0.0962954
$712$	4.11031e18	1.18237
$713$	−4.57657e18	−1.30454
$714$	−2.96499e18	−0.837500
$715$	2.98154e17	0.0834549
$716$	−1.77951e17	−0.0493590
$717$	−2.85220e18	−0.783981
$718$	2.70423e18	0.736604
$719$	−5.69358e18	−1.53691	−0.768453	−	0.639906i	$-0.778973\pi$
$719$	−5.69358e18	−1.53691	−0.768453	+	0.639906i	$0.778973\pi$
$720$	−1.96950e17	−0.0526860
$721$	1.43704e18	0.380968
$722$	−1.70966e18	−0.449176
$723$	−1.43741e18	−0.374266
$724$	1.42327e18	0.367272
$725$	6.08039e18	1.55501
$726$	−1.68352e18	−0.426708
$727$	3.11211e18	0.781773	0.390887	−	0.920439i	$-0.372168\pi$
$727$	3.11211e18	0.781773	0.390887	+	0.920439i	$0.372168\pi$
$728$	−4.54345e18	−1.13118
$729$	1.50095e17	0.0370370
$730$	−4.36357e17	−0.106719
$731$	−1.06437e18	−0.258007
$732$	−5.82353e17	−0.139915
$733$	4.51504e18	1.07519	0.537596	−	0.843203i	$-0.319333\pi$
$733$	4.51504e18	1.07519	0.537596	+	0.843203i	$0.319333\pi$
$734$	−1.67960e17	−0.0396443
$735$	1.33295e17	0.0311851
$736$	−2.47174e18	−0.573187
$737$	1.51651e18	0.348583
$738$	−8.90972e15	−0.00203001
$739$	−7.27367e18	−1.64272	−0.821362	−	0.570408i	$-0.806785\pi$
$739$	−7.27367e18	−1.64272	−0.821362	+	0.570408i	$0.806785\pi$
$740$	−2.00244e17	−0.0448284
$741$	−1.68340e18	−0.373566
$742$	3.33046e18	0.732620
$743$	4.41522e18	0.962775	0.481388	−	0.876508i	$-0.340133\pi$
$743$	4.41522e18	0.962775	0.481388	+	0.876508i	$0.340133\pi$
$744$	−3.57915e18	−0.773670
$745$	−1.53643e17	−0.0329228
$746$	3.01783e18	0.641052
$747$	−1.67335e18	−0.352373
$748$	7.46142e17	0.155762
$749$	−8.63323e18	−1.78666
$750$	−1.14118e18	−0.234129
$751$	4.39874e18	0.894683	0.447341	−	0.894363i	$-0.352371\pi$
$751$	4.39874e18	0.894683	0.447341	+	0.894363i	$0.352371\pi$
$752$	3.03439e18	0.611864
$753$	−1.22284e18	−0.244457
$754$	−6.68481e18	−1.32488
$755$	−1.06007e18	−0.208295
$756$	−3.05654e17	−0.0595441
$757$	4.09692e18	0.791288	0.395644	−	0.918404i	$-0.370521\pi$
$757$	4.09692e18	0.791288	0.395644	+	0.918404i	$0.370521\pi$
$758$	−9.59053e16	−0.0183651
$759$	−1.15421e18	−0.219137
$760$	9.75578e17	0.183643
$761$	2.07652e18	0.387556	0.193778	−	0.981045i	$-0.437926\pi$
$761$	2.07652e18	0.387556	0.193778	+	0.981045i	$0.437926\pi$
$762$	3.48130e18	0.644220
$763$	−8.65751e18	−1.58849
$764$	2.37554e17	0.0432172
$765$	−7.05304e17	−0.127226
$766$	1.16523e17	0.0208414
$767$	6.92411e17	0.122799
$768$	−2.52300e18	−0.443679
$769$	4.09552e18	0.714147	0.357074	−	0.934076i	$-0.383774\pi$
$769$	4.09552e18	0.714147	0.357074	+	0.934076i	$0.383774\pi$
$770$	4.79346e17	0.0828819
$771$	4.59530e18	0.787881
$772$	1.67386e18	0.284582
$773$	−6.34771e18	−1.07016	−0.535082	−	0.844800i	$-0.679719\pi$
$773$	−6.34771e18	−1.07016	−0.535082	+	0.844800i	$0.679719\pi$
$774$	2.81845e17	0.0471188
$775$	−6.98994e18	−1.15881
$776$	−2.29437e18	−0.377192
$777$	2.53794e18	0.413756
$778$	1.82986e18	0.295835
$779$	3.07128e16	0.00492409
$780$	−2.36565e17	−0.0376127
$781$	−3.79222e18	−0.597946
$782$	8.88357e18	1.38913
$783$	−2.05458e18	−0.318619
$784$	−9.13726e17	−0.140528
$785$	−7.24716e17	−0.110539
$786$	−1.22272e18	−0.184961
$787$	−9.40418e18	−1.41086	−0.705432	−	0.708778i	$-0.749247\pi$
$787$	−9.40418e18	−1.41086	−0.705432	+	0.708778i	$0.749247\pi$
$788$	−3.43626e18	−0.511288
$789$	1.90075e18	0.280495
$790$	4.12748e17	0.0604100
$791$	−1.11129e19	−1.61317
$792$	−9.02666e17	−0.129961
$793$	5.71252e18	0.815740
$794$	−2.97482e18	−0.421335
$795$	7.92241e17	0.111294
$796$	−1.90614e18	−0.265594
$797$	−1.07134e17	−0.0148064	−0.00740320	−	0.999973i	$-0.502357\pi$
$797$	−1.07134e17	−0.0148064	−0.00740320	+	0.999973i	$0.502357\pi$
$798$	−2.70641e18	−0.371001
$799$	1.08665e19	1.47753
$800$	−3.77516e18	−0.509156
$801$	−2.71244e18	−0.362869
$802$	6.01585e18	0.798295
$803$	−1.39175e18	−0.183194
$804$	−1.20324e18	−0.157105
$805$	−2.22181e18	−0.287762
$806$	7.68478e18	0.987310
$807$	−7.97196e17	−0.101598
$808$	1.11778e19	1.41313
$809$	−2.53947e18	−0.318477	−0.159238	−	0.987240i	$-0.550904\pi$
$809$	−2.53947e18	−0.318477	−0.159238	+	0.987240i	$0.550904\pi$
$810$	1.86764e17	0.0232348
$811$	−1.10168e19	−1.35963	−0.679813	−	0.733385i	$-0.737939\pi$
$811$	−1.10168e19	−1.35963	−0.679813	+	0.733385i	$0.737939\pi$
$812$	4.18398e18	0.512242
$813$	5.96435e18	0.724394
$814$	1.64054e18	0.197665
$815$	2.55573e18	0.305485
$816$	4.83480e18	0.573314
$817$	−9.71551e17	−0.114294
$818$	−8.24698e18	−0.962495
$819$	2.99828e18	0.347157
$820$	4.31602e15	0.000495785 0
$821$	−9.54149e18	−1.08739	−0.543695	−	0.839283i	$-0.682975\pi$
$821$	−9.54149e18	−1.08739	−0.543695	+	0.839283i	$0.682975\pi$
$822$	3.40654e18	0.385165
$823$	9.44397e16	0.0105939	0.00529695	−	0.999986i	$-0.498314\pi$
$823$	9.44397e16	0.0105939	0.00529695	+	0.999986i	$0.498314\pi$
$824$	−3.36723e18	−0.374753
$825$	−1.76287e18	−0.194657
$826$	1.11320e18	0.121956
$827$	1.47888e18	0.160749	0.0803744	−	0.996765i	$-0.474388\pi$
$827$	1.47888e18	0.160749	0.0803744	+	0.996765i	$0.474388\pi$
$828$	9.15788e17	0.0987638
$829$	8.97164e18	0.959992	0.479996	−	0.877271i	$-0.340638\pi$
$829$	8.97164e18	0.959992	0.479996	+	0.877271i	$0.340638\pi$
$830$	−2.08216e18	−0.221058
$831$	−4.69294e18	−0.494354
$832$	9.93749e18	1.03866
$833$	−3.27217e18	−0.339347
$834$	2.09748e18	0.215833
$835$	−6.20079e17	−0.0633119
$836$	6.81072e17	0.0690005
$837$	2.36192e18	0.237438
$838$	−1.36860e19	−1.36518
$839$	1.97263e19	1.95251	0.976255	−	0.216623i	$-0.0695041\pi$
$839$	1.97263e19	1.95251	0.976255	+	0.216623i	$0.0695041\pi$
$840$	−1.73759e18	−0.170660
$841$	1.78637e19	1.74100
$842$	1.32025e18	0.127682
$843$	−7.25695e18	−0.696426
$844$	3.93889e18	0.375101
$845$	−2.87706e17	−0.0271882
$846$	−2.87744e18	−0.269836
$847$	−1.03362e19	−0.961873
$848$	−5.43074e18	−0.501517
$849$	2.30564e17	0.0211296
$850$	1.35682e19	1.23395
$851$	−7.60407e18	−0.686284
$852$	3.00886e18	0.269492
$853$	−3.16030e18	−0.280905	−0.140453	−	0.990087i	$-0.544856\pi$
$853$	−3.16030e18	−0.280905	−0.140453	+	0.990087i	$0.544856\pi$
$854$	9.18408e18	0.810139
$855$	−6.43795e17	−0.0563596
$856$	2.02292e19	1.75751
$857$	−1.46970e19	−1.26722	−0.633612	−	0.773651i	$-0.718429\pi$
$857$	−1.46970e19	−1.26722	−0.633612	+	0.773651i	$0.718429\pi$
$858$	1.93811e18	0.165848
$859$	−7.87423e17	−0.0668732	−0.0334366	−	0.999441i	$-0.510645\pi$
$859$	−7.87423e17	−0.0668732	−0.0334366	+	0.999441i	$0.510645\pi$
$860$	−1.36530e17	−0.0115077
$861$	−5.47023e16	−0.00457599
$862$	8.35126e18	0.693354
$863$	1.47985e19	1.21940	0.609701	−	0.792632i	$-0.291290\pi$
$863$	1.47985e19	1.21940	0.609701	+	0.792632i	$0.291290\pi$
$864$	1.27564e18	0.104325
$865$	4.14742e16	0.00336646
$866$	5.53518e18	0.445929
$867$	1.00936e19	0.807089
$868$	−4.80985e18	−0.381727
$869$	1.31645e18	0.103700
$870$	−2.55653e18	−0.199883
$871$	1.18030e19	0.915959
$872$	2.02861e19	1.56257
$873$	1.51408e18	0.115759
$874$	8.10884e18	0.615367
$875$	−7.00639e18	−0.527766
$876$	1.10426e18	0.0825647
$877$	8.02347e18	0.595476	0.297738	−	0.954648i	$-0.403768\pi$
$877$	8.02347e18	0.595476	0.297738	+	0.954648i	$0.403768\pi$
$878$	7.50330e18	0.552762
$879$	−1.31576e19	−0.962163
$880$	−7.81636e17	−0.0567371
$881$	−1.25518e19	−0.904401	−0.452201	−	0.891916i	$-0.649361\pi$
$881$	−1.25518e19	−0.904401	−0.452201	+	0.891916i	$0.649361\pi$
$882$	8.66466e17	0.0619735
$883$	−2.91253e17	−0.0206788	−0.0103394	−	0.999947i	$-0.503291\pi$
$883$	−2.91253e17	−0.0206788	−0.0103394	+	0.999947i	$0.503291\pi$
$884$	5.80726e18	0.409290
$885$	2.64805e17	0.0185266
$886$	3.05056e18	0.211866
$887$	1.57640e19	1.08684	0.543418	−	0.839462i	$-0.317130\pi$
$887$	1.57640e19	1.08684	0.543418	+	0.839462i	$0.317130\pi$
$888$	−5.94684e18	−0.407007
$889$	2.13738e19	1.45218
$890$	−3.37511e18	−0.227642
$891$	5.95680e17	0.0398848
$892$	−1.09245e18	−0.0726159
$893$	9.91887e18	0.654527
$894$	−9.98735e17	−0.0654269
$895$	6.67580e17	0.0434164
$896$	6.70619e18	0.432986
$897$	−8.98330e18	−0.575818
$898$	1.46773e19	0.934010
$899$	−3.23314e19	−2.04261
$900$	1.39871e18	0.0877309
$901$	−1.94482e19	−1.21107
$902$	−3.53600e16	−0.00218610
$903$	1.73042e18	0.106214
$904$	2.60394e19	1.58685
$905$	−5.33938e18	−0.323054
$906$	−6.89083e18	−0.413941
$907$	−1.46154e18	−0.0871691	−0.0435846	−	0.999050i	$-0.513878\pi$
$907$	−1.46154e18	−0.0871691	−0.0435846	+	0.999050i	$0.513878\pi$
$908$	−6.40296e17	−0.0379160
$909$	−7.37634e18	−0.433686
$910$	3.73077e18	0.217786
$911$	2.82120e19	1.63517	0.817587	−	0.575805i	$-0.195311\pi$
$911$	2.82120e19	1.63517	0.817587	+	0.575805i	$0.195311\pi$
$912$	4.41316e18	0.253970
$913$	−6.64101e18	−0.379467
$914$	2.07072e19	1.17482
$915$	2.18469e18	0.123070
$916$	−8.66488e18	−0.484666
$917$	−7.50701e18	−0.416933
$918$	−4.58473e18	−0.252835
$919$	−3.13383e19	−1.71603	−0.858014	−	0.513626i	$-0.828302\pi$
$919$	−3.13383e19	−1.71603	−0.858014	+	0.513626i	$0.828302\pi$
$920$	5.20609e18	0.283068
$921$	−7.12806e18	−0.384843
$922$	−6.46178e17	−0.0346419
$923$	−2.95150e19	−1.57120
$924$	−1.21305e18	−0.0641225
$925$	−1.16139e19	−0.609619
$926$	4.32337e18	0.225347
$927$	2.22207e18	0.115011
$928$	−1.74617e19	−0.897480
$929$	−8.09784e18	−0.413301	−0.206651	−	0.978415i	$-0.566256\pi$
$929$	−8.09784e18	−0.413301	−0.206651	+	0.978415i	$0.566256\pi$
$930$	2.93896e18	0.148955
$931$	−2.98681e18	−0.150326
$932$	−5.42390e18	−0.271087
$933$	7.06363e18	0.350588
$934$	3.02494e19	1.49095
$935$	−2.79914e18	−0.137009
$936$	−7.02549e18	−0.341494
$937$	1.90542e19	0.919779	0.459890	−	0.887976i	$-0.347889\pi$
$937$	1.90542e19	0.919779	0.459890	+	0.887976i	$0.347889\pi$
$938$	1.89759e19	0.909670
$939$	−1.87214e19	−0.891275
$940$	1.39388e18	0.0659014
$941$	−2.66077e18	−0.124932	−0.0624662	−	0.998047i	$-0.519897\pi$
$941$	−2.66077e18	−0.124932	−0.0624662	+	0.998047i	$0.519897\pi$
$942$	−4.71091e18	−0.219672
$943$	1.63897e17	0.00759003
$944$	−1.81521e18	−0.0834852
$945$	1.14666e18	0.0523753
$946$	1.11856e18	0.0507418
$947$	−9.21560e18	−0.415192	−0.207596	−	0.978215i	$-0.566564\pi$
$947$	−9.21560e18	−0.415192	−0.207596	+	0.978215i	$0.566564\pi$
$948$	−1.04451e18	−0.0467369
$949$	−1.08321e19	−0.481373
$950$	1.23849e19	0.546625
$951$	1.50438e18	0.0659455
$952$	4.26549e19	1.85707
$953$	−1.78222e19	−0.770652	−0.385326	−	0.922780i	$-0.625911\pi$
$953$	−1.78222e19	−0.770652	−0.385326	+	0.922780i	$0.625911\pi$
$954$	5.14985e18	0.221172
$955$	−8.91181e17	−0.0380140
$956$	8.98123e18	0.380504
$957$	−8.15401e18	−0.343118
$958$	−9.99500e18	−0.417741
$959$	2.09148e19	0.868227
$960$	3.80048e18	0.156702
$961$	1.27502e19	0.522175
$962$	1.27684e19	0.519397
$963$	−1.33495e19	−0.539378
$964$	4.52622e18	0.181650
$965$	−6.27946e18	−0.250319
$966$	−1.44426e19	−0.571864
$967$	1.99762e19	0.785670	0.392835	−	0.919609i	$-0.371494\pi$
$967$	1.99762e19	0.785670	0.392835	+	0.919609i	$0.371494\pi$
$968$	2.42195e19	0.946183
$969$	1.58041e19	0.613288
$970$	1.88398e18	0.0726206
$971$	2.21119e19	0.846645	0.423322	−	0.905979i	$-0.360864\pi$
$971$	2.21119e19	0.846645	0.423322	+	0.905979i	$0.360864\pi$
$972$	−4.72630e17	−0.0179759
$973$	1.28777e19	0.486524
$974$	1.36717e19	0.513085
$975$	−1.37205e19	−0.511493
$976$	−1.49758e19	−0.554584
$977$	−3.48798e19	−1.28310	−0.641548	−	0.767083i	$-0.721707\pi$
$977$	−3.48798e19	−1.28310	−0.641548	+	0.767083i	$0.721707\pi$
$978$	1.66132e19	0.607085
$979$	−1.07649e19	−0.390770
$980$	−4.19731e17	−0.0151357
$981$	−1.33870e19	−0.479551
$982$	1.54370e19	0.549337
$983$	1.62288e19	0.573703	0.286852	−	0.957975i	$-0.407391\pi$
$983$	1.62288e19	0.573703	0.286852	+	0.957975i	$0.407391\pi$
$984$	1.28177e17	0.00450134
$985$	1.28910e19	0.449731
$986$	6.27585e19	2.17507
$987$	−1.76664e19	−0.608256
$988$	5.30081e18	0.181310
$989$	−5.18461e18	−0.176173
$990$	7.41208e17	0.0250214
$991$	1.89013e18	0.0633889	0.0316945	−	0.999498i	$-0.489910\pi$
$991$	1.89013e18	0.0633889	0.0316945	+	0.999498i	$0.489910\pi$
$992$	2.00738e19	0.668810
$993$	−2.75899e19	−0.913229
$994$	−4.74517e19	−1.56042
$995$	7.15083e18	0.233618
$996$	5.26918e18	0.171024
$997$	4.69666e19	1.51450	0.757252	−	0.653123i	$-0.226541\pi$
$997$	4.69666e19	1.51450	0.757252	+	0.653123i	$0.226541\pi$
$998$	−4.90535e19	−1.57153
$999$	3.92439e18	0.124910

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.a.1.22	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.a.1.22	✓	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)

\(f(q)\)	\(=\)	\(q+76.7885 q^{2} +729.000 q^{3} -2295.53 q^{4} +8611.65 q^{5} +55978.8 q^{6} +343688. q^{7} -805321. q^{8} +531441. q^{9} +O(q^{10})\)	\(q+76.7885 q^{2} +729.000 q^{3} -2295.53 q^{4} +8611.65 q^{5} +55978.8 q^{6} +343688. q^{7} -805321. q^{8} +531441. q^{9} +661275. q^{10} +2.10913e6 q^{11} -1.67344e6 q^{12} +1.64154e7 q^{13} +2.63913e7 q^{14} +6.27789e6 q^{15} -4.30344e7 q^{16} -1.54112e8 q^{17} +4.08085e7 q^{18} -1.40672e8 q^{19} -1.97683e7 q^{20} +2.50549e8 q^{21} +1.61957e8 q^{22} -7.50683e8 q^{23} -5.87079e8 q^{24} -1.14654e9 q^{25} +1.26052e9 q^{26} +3.87420e8 q^{27} -7.88948e8 q^{28} -5.30324e9 q^{29} +4.82070e8 q^{30} +6.09654e9 q^{31} +3.29265e9 q^{32} +1.53755e9 q^{33} -1.18340e10 q^{34} +2.95972e9 q^{35} -1.21994e9 q^{36} +1.01295e10 q^{37} -1.08020e10 q^{38} +1.19668e10 q^{39} -6.93514e9 q^{40} -2.18330e8 q^{41} +1.92392e10 q^{42} +6.90652e9 q^{43} -4.84157e9 q^{44} +4.57658e9 q^{45} -5.76438e10 q^{46} -7.05108e10 q^{47} -3.13721e10 q^{48} +2.12325e10 q^{49} -8.80412e10 q^{50} -1.12347e11 q^{51} -3.76822e10 q^{52} +1.26195e11 q^{53} +2.97494e10 q^{54} +1.81631e10 q^{55} -2.76779e11 q^{56} -1.02550e11 q^{57} -4.07227e11 q^{58} +4.21805e10 q^{59} -1.44111e10 q^{60} +3.47997e11 q^{61} +4.68144e11 q^{62} +1.82650e11 q^{63} +6.05375e11 q^{64} +1.41364e11 q^{65} +1.18066e11 q^{66} +7.19021e11 q^{67} +3.53768e11 q^{68} -5.47248e11 q^{69} +2.27272e11 q^{70} -1.79801e12 q^{71} -4.27981e11 q^{72} -6.59872e11 q^{73} +7.77831e11 q^{74} -8.35830e11 q^{75} +3.22916e11 q^{76} +7.24882e11 q^{77} +9.18915e11 q^{78} +6.24170e11 q^{79} -3.70597e11 q^{80} +2.82430e11 q^{81} -1.67652e10 q^{82} -3.14870e12 q^{83} -5.75143e11 q^{84} -1.32715e12 q^{85} +5.30341e11 q^{86} -3.86606e12 q^{87} -1.69852e12 q^{88} -5.10394e12 q^{89} +3.51429e11 q^{90} +5.64179e12 q^{91} +1.72322e12 q^{92} +4.44438e12 q^{93} -5.41441e12 q^{94} -1.21141e12 q^{95} +2.40034e12 q^{96} +2.84901e12 q^{97} +1.63041e12 q^{98} +1.12088e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 138 q^{2} + 21870 q^{3} + 114598 q^{4} - 137742 q^{5} - 100602 q^{6} - 879443 q^{7} - 872301 q^{8} + 15943230 q^{9}+O(q^{10}) \) 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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