LMFDB - Embedded newform 177.14.a.d.1.25

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:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.25
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)

$f(q)$	$=$	$q+113.354 q^{2} -729.000 q^{3} +4657.03 q^{4} -13656.9 q^{5} -82634.7 q^{6} -32606.1 q^{7} -400702. q^{8} +531441. q^{9} +O(q^{10})$	\(q+113.354 q^{2} -729.000 q^{3} +4657.03 q^{4} -13656.9 q^{5} -82634.7 q^{6} -32606.1 q^{7} -400702. q^{8} +531441. q^{9} -1.54806e6 q^{10} -9.33487e6 q^{11} -3.39497e6 q^{12} +2.15491e7 q^{13} -3.69601e6 q^{14} +9.95589e6 q^{15} -8.35713e7 q^{16} -8.77038e6 q^{17} +6.02407e7 q^{18} +8.65329e7 q^{19} -6.36006e7 q^{20} +2.37698e7 q^{21} -1.05814e9 q^{22} -1.33436e8 q^{23} +2.92112e8 q^{24} -1.03419e9 q^{25} +2.44267e9 q^{26} -3.87420e8 q^{27} -1.51847e8 q^{28} -3.35684e9 q^{29} +1.12854e9 q^{30} -7.90937e9 q^{31} -6.19056e9 q^{32} +6.80512e9 q^{33} -9.94153e8 q^{34} +4.45298e8 q^{35} +2.47494e9 q^{36} -2.32875e10 q^{37} +9.80881e9 q^{38} -1.57093e10 q^{39} +5.47235e9 q^{40} +3.73107e10 q^{41} +2.69439e9 q^{42} +7.82609e10 q^{43} -4.34727e10 q^{44} -7.25785e9 q^{45} -1.51255e10 q^{46} -9.20948e10 q^{47} +6.09235e10 q^{48} -9.58259e10 q^{49} -1.17229e11 q^{50} +6.39360e9 q^{51} +1.00355e11 q^{52} +1.70526e11 q^{53} -4.39155e10 q^{54} +1.27486e11 q^{55} +1.30653e10 q^{56} -6.30825e10 q^{57} -3.80510e11 q^{58} +4.21805e10 q^{59} +4.63649e10 q^{60} +6.91961e11 q^{61} -8.96555e11 q^{62} -1.73282e10 q^{63} -1.71054e10 q^{64} -2.94294e11 q^{65} +7.71384e11 q^{66} +2.36934e11 q^{67} -4.08439e10 q^{68} +9.72751e10 q^{69} +5.04761e10 q^{70} +4.03073e11 q^{71} -2.12949e11 q^{72} +6.40096e11 q^{73} -2.63972e12 q^{74} +7.53926e11 q^{75} +4.02986e11 q^{76} +3.04373e11 q^{77} -1.78070e12 q^{78} -9.80499e9 q^{79} +1.14133e12 q^{80} +2.82430e11 q^{81} +4.22930e12 q^{82} +2.21182e12 q^{83} +1.10697e11 q^{84} +1.19776e11 q^{85} +8.87115e12 q^{86} +2.44714e12 q^{87} +3.74050e12 q^{88} -1.78470e12 q^{89} -8.22703e11 q^{90} -7.02632e11 q^{91} -6.21417e11 q^{92} +5.76593e12 q^{93} -1.04393e13 q^{94} -1.18177e12 q^{95} +4.51292e12 q^{96} -8.80654e12 q^{97} -1.08622e13 q^{98} -4.96093e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 12 q^{2} - 23328 q^{3} + 139174 q^{4} + 2236 q^{5} - 8748 q^{6} + 746845 q^{7} - 733317 q^{8} + 17006112 q^{9}+O(q^{10}) $ 32 * q + 12 * q^2 - 23328 * q^3 + 139174 * q^4 + 2236 * q^5 - 8748 * q^6 + 746845 * q^7 - 733317 * q^8 + 17006112 * q^9	\( 32 q + 12 q^{2} - 23328 q^{3} + 139174 q^{4} + 2236 q^{5} - 8748 q^{6} + 746845 q^{7} - 733317 q^{8} + 17006112 q^{9} + 6145337 q^{10} + 400846 q^{11} - 101457846 q^{12} + 9411686 q^{13} - 36368387 q^{14} - 1630044 q^{15} + 734877786 q^{16} + 228113833 q^{17} + 6377292 q^{18} + 524233755 q^{19} - 420745331 q^{20} - 544450005 q^{21} - 1844479318 q^{22} - 399937087 q^{23} + 534588093 q^{24} + 8617402914 q^{25} - 499433574 q^{26} - 12397455648 q^{27} + 12648993070 q^{28} - 225284149 q^{29} - 4479950673 q^{30} + 9454638761 q^{31} + 11648295118 q^{32} - 292216734 q^{33} + 39279537096 q^{34} + 17608963479 q^{35} + 73962769734 q^{36} + 37463929597 q^{37} + 65554547351 q^{38} - 6861119094 q^{39} + 144414252742 q^{40} + 22650227173 q^{41} + 26512554123 q^{42} + 96253617602 q^{43} - 132186868002 q^{44} + 1188302076 q^{45} + 327853892309 q^{46} + 239981844027 q^{47} - 535725905994 q^{48} + 286262776863 q^{49} - 671840368399 q^{50} - 166294984257 q^{51} - 952971648498 q^{52} - 47446514136 q^{53} - 4649045868 q^{54} - 474454082548 q^{55} - 1167728875984 q^{56} - 382166407395 q^{57} + 547596592762 q^{58} + 1349777076512 q^{59} + 306723346299 q^{60} + 661498471821 q^{61} + 555821093242 q^{62} + 396904053645 q^{63} + 3522679273173 q^{64} + 1269187682756 q^{65} + 1344625422822 q^{66} + 2838711491386 q^{67} + 1395029358261 q^{68} + 291554136423 q^{69} + 5677102514386 q^{70} + 1912914480734 q^{71} - 389714719797 q^{72} + 2403595726697 q^{73} - 742136417562 q^{74} - 6282086724306 q^{75} - 4020161987188 q^{76} - 4878303804101 q^{77} + 364087075446 q^{78} - 1705546365970 q^{79} - 4347383766449 q^{80} + 9037745167392 q^{81} - 6943720239935 q^{82} - 2549647313691 q^{83} - 9221115948030 q^{84} - 8455706309615 q^{85} - 33993832711012 q^{86} + 164232144621 q^{87} - 42970239360587 q^{88} - 17356719361241 q^{89} + 3265884040617 q^{90} - 30776775043291 q^{91} - 13184590997480 q^{92} - 6892431656769 q^{93} - 35604563339520 q^{94} + 219501126195 q^{95} - 8491607141022 q^{96} - 4427131429152 q^{97} - 32707332037060 q^{98} + 213025999086 q^{99}+O(q^{100}) \) 32 * q + 12 * q^2 - 23328 * q^3 + 139174 * q^4 + 2236 * q^5 - 8748 * q^6 + 746845 * q^7 - 733317 * q^8 + 17006112 * q^9 + 6145337 * q^10 + 400846 * q^11 - 101457846 * q^12 + 9411686 * q^13 - 36368387 * q^14 - 1630044 * q^15 + 734877786 * q^16 + 228113833 * q^17 + 6377292 * q^18 + 524233755 * q^19 - 420745331 * q^20 - 544450005 * q^21 - 1844479318 * q^22 - 399937087 * q^23 + 534588093 * q^24 + 8617402914 * q^25 - 499433574 * q^26 - 12397455648 * q^27 + 12648993070 * q^28 - 225284149 * q^29 - 4479950673 * q^30 + 9454638761 * q^31 + 11648295118 * q^32 - 292216734 * q^33 + 39279537096 * q^34 + 17608963479 * q^35 + 73962769734 * q^36 + 37463929597 * q^37 + 65554547351 * q^38 - 6861119094 * q^39 + 144414252742 * q^40 + 22650227173 * q^41 + 26512554123 * q^42 + 96253617602 * q^43 - 132186868002 * q^44 + 1188302076 * q^45 + 327853892309 * q^46 + 239981844027 * q^47 - 535725905994 * q^48 + 286262776863 * q^49 - 671840368399 * q^50 - 166294984257 * q^51 - 952971648498 * q^52 - 47446514136 * q^53 - 4649045868 * q^54 - 474454082548 * q^55 - 1167728875984 * q^56 - 382166407395 * q^57 + 547596592762 * q^58 + 1349777076512 * q^59 + 306723346299 * q^60 + 661498471821 * q^61 + 555821093242 * q^62 + 396904053645 * q^63 + 3522679273173 * q^64 + 1269187682756 * q^65 + 1344625422822 * q^66 + 2838711491386 * q^67 + 1395029358261 * q^68 + 291554136423 * q^69 + 5677102514386 * q^70 + 1912914480734 * q^71 - 389714719797 * q^72 + 2403595726697 * q^73 - 742136417562 * q^74 - 6282086724306 * q^75 - 4020161987188 * q^76 - 4878303804101 * q^77 + 364087075446 * q^78 - 1705546365970 * q^79 - 4347383766449 * q^80 + 9037745167392 * q^81 - 6943720239935 * q^82 - 2549647313691 * q^83 - 9221115948030 * q^84 - 8455706309615 * q^85 - 33993832711012 * q^86 + 164232144621 * q^87 - 42970239360587 * q^88 - 17356719361241 * q^89 + 3265884040617 * q^90 - 30776775043291 * q^91 - 13184590997480 * q^92 - 6892431656769 * q^93 - 35604563339520 * q^94 + 219501126195 * q^95 - 8491607141022 * q^96 - 4427131429152 * q^97 - 32707332037060 * q^98 + 213025999086 * 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 $

$2$	113.354	1.25239	0.626196	−	0.779666i	$-0.284611\pi$
$2$	113.354	1.25239	0.626196	+	0.779666i	$0.284611\pi$
$3$	−729.000	−0.577350
$3$	−729.000	−0.577350
$4$	4657.03	0.568485
$5$	−13656.9	−0.390884	−0.195442	−	0.980715i	$-0.562614\pi$
$5$	−13656.9	−0.390884	−0.195442	+	0.980715i	$0.562614\pi$
$6$	−82634.7	−0.723069
$7$	−32606.1	−0.104752	−0.0523759	−	0.998627i	$-0.516679\pi$
$7$	−32606.1	−0.104752	−0.0523759	+	0.998627i	$0.516679\pi$
$8$	−400702.	−0.540426
$9$	531441.	0.333333
$10$	−1.54806e6	−0.489540
$11$	−9.33487e6	−1.58875	−0.794375	−	0.607427i	$-0.792202\pi$
$11$	−9.33487e6	−1.58875	−0.794375	+	0.607427i	$0.792202\pi$
$12$	−3.39497e6	−0.328215
$13$	2.15491e7	1.23822	0.619110	−	0.785305i	$-0.287494\pi$
$13$	2.15491e7	1.23822	0.619110	+	0.785305i	$0.287494\pi$
$14$	−3.69601e6	−0.131190
$15$	9.95589e6	0.225677
$16$	−8.35713e7	−1.24531
$17$	−8.77038e6	−0.0881252	−0.0440626	−	0.999029i	$-0.514030\pi$
$17$	−8.77038e6	−0.0881252	−0.0440626	+	0.999029i	$0.514030\pi$
$18$	6.02407e7	0.417464
$19$	8.65329e7	0.421971	0.210986	−	0.977489i	$-0.432333\pi$
$19$	8.65329e7	0.421971	0.210986	+	0.977489i	$0.432333\pi$
$20$	−6.36006e7	−0.222211
$21$	2.37698e7	0.0604784
$22$	−1.05814e9	−1.98974
$23$	−1.33436e8	−0.187950	−0.0939752	−	0.995575i	$-0.529957\pi$
$23$	−1.33436e8	−0.187950	−0.0939752	+	0.995575i	$0.529957\pi$
$24$	2.92112e8	0.312015
$25$	−1.03419e9	−0.847210
$26$	2.44267e9	1.55074
$27$	−3.87420e8	−0.192450
$28$	−1.51847e8	−0.0595497
$29$	−3.35684e9	−1.04796	−0.523979	−	0.851731i	$-0.675553\pi$
$29$	−3.35684e9	−1.04796	−0.523979	+	0.851731i	$0.675553\pi$
$30$	1.12854e9	0.282636
$31$	−7.90937e9	−1.60063	−0.800315	−	0.599580i	$-0.795334\pi$
$31$	−7.90937e9	−1.60063	−0.800315	+	0.599580i	$0.795334\pi$
$32$	−6.19056e9	−1.01919
$33$	6.80512e9	0.917266
$34$	−9.94153e8	−0.110367
$35$	4.45298e8	0.0409457
$36$	2.47494e9	0.189495
$37$	−2.32875e10	−1.49215	−0.746073	−	0.665865i	$-0.768063\pi$
$37$	−2.32875e10	−1.49215	−0.746073	+	0.665865i	$0.768063\pi$
$38$	9.80881e9	0.528473
$39$	−1.57093e10	−0.714886
$40$	5.47235e9	0.211244
$41$	3.73107e10	1.22670	0.613350	−	0.789811i	$-0.289822\pi$
$41$	3.73107e10	1.22670	0.613350	+	0.789811i	$0.289822\pi$
$42$	2.69439e9	0.0757427
$43$	7.82609e10	1.88799	0.943996	−	0.329958i	$-0.107035\pi$
$43$	7.82609e10	1.88799	0.943996	+	0.329958i	$0.107035\pi$
$44$	−4.34727e10	−0.903181
$45$	−7.25785e9	−0.130295
$46$	−1.51255e10	−0.235387
$47$	−9.20948e10	−1.24623	−0.623116	−	0.782130i	$-0.714134\pi$
$47$	−9.20948e10	−1.24623	−0.623116	+	0.782130i	$0.714134\pi$
$48$	6.09235e10	0.718980
$49$	−9.58259e10	−0.989027
$50$	−1.17229e11	−1.06104
$51$	6.39360e9	0.0508791
$52$	1.00355e11	0.703909
$53$	1.70526e11	1.05681	0.528406	−	0.848992i	$-0.322790\pi$
$53$	1.70526e11	1.05681	0.528406	+	0.848992i	$0.322790\pi$
$54$	−4.39155e10	−0.241023
$55$	1.27486e11	0.621017
$56$	1.30653e10	0.0566106
$57$	−6.30825e10	−0.243625
$58$	−3.80510e11	−1.31245
$59$	4.21805e10	0.130189
$59$	4.21805e10	0.130189
$60$	4.63649e10	0.128294
$61$	6.91961e11	1.71964	0.859820	−	0.510597i	$-0.170576\pi$
$61$	6.91961e11	1.71964	0.859820	+	0.510597i	$0.170576\pi$
$62$	−8.96555e11	−2.00461
$63$	−1.73282e10	−0.0349172
$64$	−1.71054e10	−0.0311145
$65$	−2.94294e11	−0.484000
$66$	7.71384e11	1.14878
$67$	2.36934e11	0.319993	0.159996	−	0.987118i	$-0.448852\pi$
$67$	2.36934e11	0.319993	0.159996	+	0.987118i	$0.448852\pi$
$68$	−4.08439e10	−0.0500978
$69$	9.72751e10	0.108513
$70$	5.04761e10	0.0512801
$71$	4.03073e11	0.373426	0.186713	−	0.982415i	$-0.440217\pi$
$71$	4.03073e11	0.373426	0.186713	+	0.982415i	$0.440217\pi$
$72$	−2.12949e11	−0.180142
$73$	6.40096e11	0.495047	0.247524	−	0.968882i	$-0.420383\pi$
$73$	6.40096e11	0.495047	0.247524	+	0.968882i	$0.420383\pi$
$74$	−2.63972e12	−1.86875
$75$	7.53926e11	0.489137
$76$	4.02986e11	0.239884
$77$	3.04373e11	0.166424
$78$	−1.78070e12	−0.895317
$79$	−9.80499e9	−0.00453807	−0.00226903	−	0.999997i	$-0.500722\pi$
$79$	−9.80499e9	−0.00453807	−0.00226903	+	0.999997i	$0.500722\pi$
$80$	1.14133e12	0.486771
$81$	2.82430e11	0.111111
$82$	4.22930e12	1.53631
$83$	2.21182e12	0.742578	0.371289	−	0.928517i	$-0.378916\pi$
$83$	2.21182e12	0.742578	0.371289	+	0.928517i	$0.378916\pi$
$84$	1.10697e11	0.0343811
$85$	1.19776e11	0.0344467
$86$	8.87115e12	2.36450
$87$	2.44714e12	0.605039
$88$	3.74050e12	0.858602
$89$	−1.78470e12	−0.380655	−0.190327	−	0.981721i	$-0.560955\pi$
$89$	−1.78470e12	−0.380655	−0.190327	+	0.981721i	$0.560955\pi$
$90$	−8.22703e11	−0.163180
$91$	−7.02632e11	−0.129706
$92$	−6.21417e11	−0.106847
$93$	5.76593e12	0.924124
$94$	−1.04393e13	−1.56077
$95$	−1.18177e12	−0.164942
$96$	4.51292e12	0.588429
$97$	−8.80654e12	−1.07347	−0.536734	−	0.843751i	$-0.680342\pi$
$97$	−8.80654e12	−1.07347	−0.536734	+	0.843751i	$0.680342\pi$
$98$	−1.08622e13	−1.23865
$99$	−4.96093e12	−0.529584
$100$	−4.81626e12	−0.481626
$101$	−1.79445e13	−1.68207	−0.841033	−	0.540983i	$-0.818052\pi$
$101$	−1.79445e13	−1.68207	−0.841033	+	0.540983i	$0.818052\pi$
$102$	7.24738e11	0.0637206
$103$	−5.37717e12	−0.443723	−0.221862	−	0.975078i	$-0.571213\pi$
$103$	−5.37717e12	−0.443723	−0.221862	+	0.975078i	$0.571213\pi$
$104$	−8.63476e12	−0.669166
$105$	−3.24623e11	−0.0236400
$106$	1.93297e13	1.32354
$107$	−3.77400e12	−0.243113	−0.121556	−	0.992585i	$-0.538789\pi$
$107$	−3.77400e12	−0.243113	−0.121556	+	0.992585i	$0.538789\pi$
$108$	−1.80423e12	−0.109405
$109$	1.43335e13	0.818617	0.409308	−	0.912396i	$-0.365770\pi$
$109$	1.43335e13	0.818617	0.409308	+	0.912396i	$0.365770\pi$
$110$	1.44509e13	0.777756
$111$	1.69766e13	0.861490
$112$	2.72493e12	0.130448
$113$	1.73125e13	0.782257	0.391128	−	0.920336i	$-0.372085\pi$
$113$	1.73125e13	0.782257	0.391128	+	0.920336i	$0.372085\pi$
$114$	−7.15062e12	−0.305114
$115$	1.82233e12	0.0734668
$116$	−1.56329e13	−0.595748
$117$	1.14521e13	0.412740
$118$	4.78131e12	0.163047
$119$	2.85967e11	0.00923127
$120$	−3.98934e12	−0.121962
$121$	5.26171e13	1.52413
$122$	7.84362e13	2.15366
$123$	−2.71995e13	−0.708236
$124$	−3.68341e13	−0.909933
$125$	3.07949e13	0.722044
$126$	−1.96421e12	−0.0437301
$127$	2.35800e13	0.498678	0.249339	−	0.968416i	$-0.419787\pi$
$127$	2.35800e13	0.498678	0.249339	+	0.968416i	$0.419787\pi$
$128$	4.87741e13	0.980222
$129$	−5.70522e13	−1.09003
$130$	−3.33593e13	−0.606157
$131$	9.37069e13	1.61997	0.809987	−	0.586448i	$-0.199474\pi$
$131$	9.37069e13	1.61997	0.809987	+	0.586448i	$0.199474\pi$
$132$	3.16916e13	0.521452
$133$	−2.82150e12	−0.0442022
$134$	2.68573e13	0.400756
$135$	5.29097e12	0.0752256
$136$	3.51430e12	0.0476252
$137$	−3.17883e13	−0.410755	−0.205378	−	0.978683i	$-0.565842\pi$
$137$	−3.17883e13	−0.410755	−0.205378	+	0.978683i	$0.565842\pi$
$138$	1.10265e13	0.135901
$139$	6.28162e13	0.738712	0.369356	−	0.929288i	$-0.379578\pi$
$139$	6.28162e13	0.738712	0.369356	+	0.929288i	$0.379578\pi$
$140$	2.07377e12	0.0232770
$141$	6.71371e13	0.719512
$142$	4.56897e13	0.467675
$143$	−2.01158e14	−1.96722
$144$	−4.44132e13	−0.415103
$145$	4.58441e13	0.409630
$146$	7.25572e13	0.619993
$147$	6.98570e13	0.571015
$148$	−1.08450e14	−0.848262
$149$	−1.00420e13	−0.0751815	−0.0375907	−	0.999293i	$-0.511968\pi$
$149$	−1.00420e13	−0.0751815	−0.0375907	+	0.999293i	$0.511968\pi$
$150$	8.54602e13	0.612591
$151$	2.05370e14	1.40989	0.704946	−	0.709261i	$-0.250971\pi$
$151$	2.05370e14	1.40989	0.704946	+	0.709261i	$0.250971\pi$
$152$	−3.46739e13	−0.228044
$153$	−4.66094e12	−0.0293751
$154$	3.45018e13	0.208428
$155$	1.08018e14	0.625660
$156$	−7.31586e13	−0.406402
$157$	3.29345e14	1.75511	0.877554	−	0.479477i	$-0.159174\pi$
$157$	3.29345e14	1.75511	0.877554	+	0.479477i	$0.159174\pi$
$158$	−1.11143e12	−0.00568344
$159$	−1.24314e14	−0.610151
$160$	8.45439e13	0.398385
$161$	4.35083e12	0.0196881
$162$	3.20144e13	0.139155
$163$	3.20070e14	1.33668	0.668338	−	0.743858i	$-0.267006\pi$
$163$	3.20070e14	1.33668	0.668338	+	0.743858i	$0.267006\pi$
$164$	1.73757e14	0.697360
$165$	−9.29370e13	−0.358544
$166$	2.50717e14	0.929998
$167$	2.54317e14	0.907232	0.453616	−	0.891197i	$-0.350134\pi$
$167$	2.54317e14	0.907232	0.453616	+	0.891197i	$0.350134\pi$
$168$	−9.52461e12	−0.0326841
$169$	1.61489e14	0.533186
$170$	1.35771e13	0.0431408
$171$	4.59871e13	0.140657
$172$	3.64463e14	1.07329
$173$	−4.91536e14	−1.39398	−0.696988	−	0.717083i	$-0.745477\pi$
$173$	−4.91536e14	−1.39398	−0.696988	+	0.717083i	$0.745477\pi$
$174$	2.77392e14	0.757745
$175$	3.37209e13	0.0887467
$176$	7.80127e14	1.97849
$177$	−3.07496e13	−0.0751646
$178$	−2.02303e14	−0.476729
$179$	−4.20620e14	−0.955752	−0.477876	−	0.878427i	$-0.658593\pi$
$179$	−4.20620e14	−0.955752	−0.477876	+	0.878427i	$0.658593\pi$
$180$	−3.38000e13	−0.0740705
$181$	3.59657e13	0.0760287	0.0380144	−	0.999277i	$-0.487897\pi$
$181$	3.59657e13	0.0760287	0.0380144	+	0.999277i	$0.487897\pi$
$182$	−7.96458e13	−0.162442
$183$	−5.04439e14	−0.992835
$184$	5.34682e13	0.101573
$185$	3.18035e14	0.583255
$186$	6.53589e14	1.15736
$187$	8.18703e13	0.140009
$188$	−4.28888e14	−0.708464
$189$	1.26323e13	0.0201595
$190$	−1.33958e14	−0.206572
$191$	2.42915e14	0.362025	0.181012	−	0.983481i	$-0.442063\pi$
$191$	2.42915e14	0.362025	0.181012	+	0.983481i	$0.442063\pi$
$192$	1.24698e13	0.0179640
$193$	6.18413e14	0.861303	0.430652	−	0.902518i	$-0.358284\pi$
$193$	6.18413e14	0.861303	0.430652	+	0.902518i	$0.358284\pi$
$194$	−9.98253e14	−1.34440
$195$	2.14541e14	0.279437
$196$	−4.46264e14	−0.562247
$197$	8.55087e14	1.04227	0.521135	−	0.853474i	$-0.325509\pi$
$197$	8.55087e14	1.04227	0.521135	+	0.853474i	$0.325509\pi$
$198$	−5.62339e14	−0.663246
$199$	4.51893e14	0.515811	0.257906	−	0.966170i	$-0.416968\pi$
$199$	4.51893e14	0.515811	0.257906	+	0.966170i	$0.416968\pi$
$200$	4.14402e14	0.457854
$201$	−1.72725e14	−0.184748
$202$	−2.03408e15	−2.10661
$203$	1.09453e14	0.109775
$204$	2.97752e13	0.0289240
$205$	−5.09549e14	−0.479497
$206$	−6.09522e14	−0.555715
$207$	−7.09135e13	−0.0626501
$208$	−1.80089e15	−1.54197
$209$	−8.07773e14	−0.670407
$210$	−3.67971e13	−0.0296066
$211$	4.71461e14	0.367798	0.183899	−	0.982945i	$-0.441128\pi$
$211$	4.71461e14	0.367798	0.183899	+	0.982945i	$0.441128\pi$
$212$	7.94145e14	0.600782
$213$	−2.93840e14	−0.215597
$214$	−4.27796e14	−0.304472
$215$	−1.06880e15	−0.737985
$216$	1.55240e14	0.104005
$217$	2.57893e14	0.167669
$218$	1.62476e15	1.02523
$219$	−4.66630e14	−0.285816
$220$	5.93704e14	0.353039
$221$	−1.88994e14	−0.109118
$222$	1.92435e15	1.07892
$223$	−5.75767e14	−0.313520	−0.156760	−	0.987637i	$-0.550105\pi$
$223$	−5.75767e14	−0.313520	−0.156760	+	0.987637i	$0.550105\pi$
$224$	2.01850e14	0.106762
$225$	−5.49612e14	−0.282403
$226$	1.96243e15	0.979692
$227$	−3.05455e15	−1.48176	−0.740882	−	0.671636i	$-0.765592\pi$
$227$	−3.05455e15	−1.48176	−0.740882	+	0.671636i	$0.765592\pi$
$228$	−2.93777e14	−0.138497
$229$	−2.59764e15	−1.19028	−0.595138	−	0.803623i	$-0.702903\pi$
$229$	−2.59764e15	−1.19028	−0.595138	+	0.803623i	$0.702903\pi$
$230$	2.06567e14	0.0920092
$231$	−2.21888e14	−0.0960851
$232$	1.34509e15	0.566344
$233$	3.00137e15	1.22887	0.614436	−	0.788967i	$-0.289384\pi$
$233$	3.00137e15	1.22887	0.614436	+	0.788967i	$0.289384\pi$
$234$	1.29813e15	0.516912
$235$	1.25773e15	0.487132
$236$	1.96436e14	0.0740104
$237$	7.14784e12	0.00262005
$238$	3.24154e13	0.0115612
$239$	−2.74697e15	−0.953383	−0.476692	−	0.879071i	$-0.658164\pi$
$239$	−2.74697e15	−0.953383	−0.476692	+	0.879071i	$0.658164\pi$
$240$	−8.32027e14	−0.281038
$241$	−5.81460e15	−1.91165	−0.955826	−	0.293933i	$-0.905036\pi$
$241$	−5.81460e15	−1.91165	−0.955826	+	0.293933i	$0.905036\pi$
$242$	5.96433e15	1.90881
$243$	−2.05891e14	−0.0641500
$244$	3.22248e15	0.977589
$245$	1.30869e15	0.386595
$246$	−3.08316e15	−0.886988
$247$	1.86471e15	0.522493
$248$	3.16930e15	0.865022
$249$	−1.61242e15	−0.428727
$250$	3.49071e15	0.904282
$251$	−1.41612e14	−0.0357454	−0.0178727	−	0.999840i	$-0.505689\pi$
$251$	−1.41612e14	−0.0357454	−0.0178727	+	0.999840i	$0.505689\pi$
$252$	−8.06979e13	−0.0198499
$253$	1.24561e15	0.298606
$254$	2.67288e15	0.624540
$255$	−8.73169e13	−0.0198878
$256$	5.66884e15	1.25874
$257$	−5.15394e15	−1.11577	−0.557884	−	0.829919i	$-0.688387\pi$
$257$	−5.15394e15	−1.11577	−0.557884	+	0.829919i	$0.688387\pi$
$258$	−6.46707e15	−1.36515
$259$	7.59313e14	0.156305
$260$	−1.37054e15	−0.275146
$261$	−1.78396e15	−0.349319
$262$	1.06220e16	2.02884
$263$	−4.75462e15	−0.885938	−0.442969	−	0.896537i	$-0.646075\pi$
$263$	−4.75462e15	−0.885938	−0.442969	+	0.896537i	$0.646075\pi$
$264$	−2.72682e15	−0.495714
$265$	−2.32886e15	−0.413091
$266$	−3.19827e14	−0.0553585
$267$	1.30105e15	0.219771
$268$	1.10341e15	0.181911
$269$	5.78267e15	0.930548	0.465274	−	0.885167i	$-0.345956\pi$
$269$	5.78267e15	0.930548	0.465274	+	0.885167i	$0.345956\pi$
$270$	5.99750e14	0.0942119
$271$	2.80289e14	0.0429840	0.0214920	−	0.999769i	$-0.493158\pi$
$271$	2.80289e14	0.0429840	0.0214920	+	0.999769i	$0.493158\pi$
$272$	7.32952e14	0.109743
$273$	5.12218e14	0.0748855
$274$	−3.60331e15	−0.514426
$275$	9.65404e15	1.34601
$276$	4.53013e14	0.0616881
$277$	8.48029e15	1.12796	0.563978	−	0.825790i	$-0.309270\pi$
$277$	8.48029e15	1.12796	0.563978	+	0.825790i	$0.309270\pi$
$278$	7.12044e15	0.925157
$279$	−4.20336e15	−0.533543
$280$	−1.78432e14	−0.0221282
$281$	−2.14388e15	−0.259782	−0.129891	−	0.991528i	$-0.541463\pi$
$281$	−2.14388e15	−0.259782	−0.129891	+	0.991528i	$0.541463\pi$
$282$	7.61023e15	0.901111
$283$	1.43691e16	1.66272	0.831360	−	0.555735i	$-0.187563\pi$
$283$	1.43691e16	1.66272	0.831360	+	0.555735i	$0.187563\pi$
$284$	1.87712e15	0.212287
$285$	8.61512e14	0.0952292
$286$	−2.28020e16	−2.46373
$287$	−1.21656e15	−0.128499
$288$	−3.28992e15	−0.339730
$289$	−9.82766e15	−0.992234
$290$	5.19659e15	0.513017
$291$	6.41997e15	0.619767
$292$	2.98094e15	0.281427
$293$	1.70021e16	1.56987	0.784933	−	0.619581i	$-0.212697\pi$
$293$	1.70021e16	1.56987	0.784933	+	0.619581i	$0.212697\pi$
$294$	7.91854e15	0.715134
$295$	−5.76056e14	−0.0508887
$296$	9.33133e15	0.806394
$297$	3.61652e15	0.305755
$298$	−1.13830e15	−0.0941566
$299$	−2.87543e15	−0.232724
$300$	3.51105e15	0.278067
$301$	−2.55178e15	−0.197770
$302$	2.32794e16	1.76574
$303$	1.30816e16	0.971142
$304$	−7.23167e15	−0.525485
$305$	−9.45005e15	−0.672179
$306$	−5.28334e14	−0.0367891
$307$	1.71673e16	1.17031	0.585157	−	0.810920i	$-0.301033\pi$
$307$	1.71673e16	1.17031	0.585157	+	0.810920i	$0.301033\pi$
$308$	1.41747e15	0.0946097
$309$	3.91996e15	0.256184
$310$	1.22442e16	0.783572
$311$	2.08815e16	1.30864	0.654318	−	0.756219i	$-0.272956\pi$
$311$	2.08815e16	1.30864	0.654318	+	0.756219i	$0.272956\pi$
$312$	6.29474e15	0.386343
$313$	−1.20830e16	−0.726337	−0.363168	−	0.931724i	$-0.618305\pi$
$313$	−1.20830e16	−0.726337	−0.363168	+	0.931724i	$0.618305\pi$
$314$	3.73325e16	2.19808
$315$	2.36650e14	0.0136486
$316$	−4.56621e13	−0.00257982
$317$	−3.13899e16	−1.73742	−0.868709	−	0.495322i	$-0.835050\pi$
$317$	−3.13899e16	−1.73742	−0.868709	+	0.495322i	$0.835050\pi$
$318$	−1.40914e16	−0.764148
$319$	3.13357e16	1.66494
$320$	2.33607e14	0.0121622
$321$	2.75125e15	0.140361
$322$	4.93182e14	0.0246572
$323$	−7.58926e14	−0.0371863
$324$	1.31528e15	0.0631650
$325$	−2.22859e16	−1.04903
$326$	3.62811e16	1.67404
$327$	−1.04491e16	−0.472629
$328$	−1.49505e16	−0.662941
$329$	3.00285e15	0.130545
$330$	−1.05347e16	−0.449038
$331$	2.05723e16	0.859808	0.429904	−	0.902875i	$-0.358547\pi$
$331$	2.05723e16	0.859808	0.429904	+	0.902875i	$0.358547\pi$
$332$	1.03005e16	0.422144
$333$	−1.23759e16	−0.497382
$334$	2.88277e16	1.13621
$335$	−3.23578e15	−0.125080
$336$	−1.98648e15	−0.0753144
$337$	−3.66340e16	−1.36235	−0.681177	−	0.732118i	$-0.738532\pi$
$337$	−3.66340e16	−1.36235	−0.681177	+	0.732118i	$0.738532\pi$
$338$	1.83053e16	0.667758
$339$	−1.26208e16	−0.451636
$340$	5.57801e14	0.0195824
$341$	7.38329e16	2.54300
$342$	5.21281e15	0.176158
$343$	6.28367e15	0.208354
$344$	−3.13593e16	−1.02032
$345$	−1.32848e15	−0.0424161
$346$	−5.57173e16	−1.74580
$347$	2.38124e15	0.0732253	0.0366127	−	0.999330i	$-0.488343\pi$
$347$	2.38124e15	0.0732253	0.0366127	+	0.999330i	$0.488343\pi$
$348$	1.13964e16	0.343955
$349$	−8.08305e15	−0.239447	−0.119724	−	0.992807i	$-0.538201\pi$
$349$	−8.08305e15	−0.239447	−0.119724	+	0.992807i	$0.538201\pi$
$350$	3.82239e15	0.111146
$351$	−8.34857e15	−0.238295
$352$	5.77880e16	1.61924
$353$	−6.31989e15	−0.173850	−0.0869249	−	0.996215i	$-0.527704\pi$
$353$	−6.31989e15	−0.173850	−0.0869249	+	0.996215i	$0.527704\pi$
$354$	−3.48558e15	−0.0941355
$355$	−5.50473e15	−0.145966
$356$	−8.31142e15	−0.216396
$357$	−2.08470e14	−0.00532967
$358$	−4.76788e16	−1.19698
$359$	6.10031e16	1.50397	0.751983	−	0.659182i	$-0.229097\pi$
$359$	6.10031e16	1.50397	0.751983	+	0.659182i	$0.229097\pi$
$360$	2.90823e15	0.0704146
$361$	−3.45650e16	−0.821940
$362$	4.07684e15	0.0952178
$363$	−3.83578e16	−0.879956
$364$	−3.27217e15	−0.0737356
$365$	−8.74174e15	−0.193506
$366$	−5.71800e16	−1.24342
$367$	−1.78750e16	−0.381870	−0.190935	−	0.981603i	$-0.561152\pi$
$367$	−1.78750e16	−0.381870	−0.190935	+	0.981603i	$0.561152\pi$
$368$	1.11515e16	0.234056
$369$	1.98284e16	0.408900
$370$	3.60504e16	0.730464
$371$	−5.56019e15	−0.110703
$372$	2.68521e16	0.525350
$373$	−9.12373e15	−0.175414	−0.0877072	−	0.996146i	$-0.527954\pi$
$373$	−9.12373e15	−0.175414	−0.0877072	+	0.996146i	$0.527954\pi$
$374$	9.28029e15	0.175346
$375$	−2.24495e16	−0.416873
$376$	3.69025e16	0.673496
$377$	−7.23369e16	−1.29760
$378$	1.43191e15	0.0252476
$379$	2.59261e16	0.449347	0.224673	−	0.974434i	$-0.427868\pi$
$379$	2.59261e16	0.449347	0.224673	+	0.974434i	$0.427868\pi$
$380$	−5.50355e15	−0.0937669
$381$	−1.71898e16	−0.287912
$382$	2.75353e16	0.453397
$383$	−5.37785e16	−0.870597	−0.435298	−	0.900286i	$-0.643357\pi$
$383$	−5.37785e16	−0.870597	−0.435298	+	0.900286i	$0.643357\pi$
$384$	−3.55563e16	−0.565931
$385$	−4.15680e15	−0.0650526
$386$	7.00993e16	1.07869
$387$	4.15911e16	0.629330
$388$	−4.10123e16	−0.610250
$389$	−1.93067e16	−0.282511	−0.141255	−	0.989973i	$-0.545114\pi$
$389$	−1.93067e16	−0.282511	−0.141255	+	0.989973i	$0.545114\pi$
$390$	2.43189e16	0.349965
$391$	1.17029e15	0.0165632
$392$	3.83976e16	0.534496
$393$	−6.83123e16	−0.935293
$394$	9.69272e16	1.30533
$395$	1.33906e14	0.00177386
$396$	−2.31032e16	−0.301060
$397$	−9.30650e16	−1.19302	−0.596510	−	0.802605i	$-0.703447\pi$
$397$	−9.30650e16	−1.19302	−0.596510	+	0.802605i	$0.703447\pi$
$398$	5.12237e16	0.645998
$399$	2.05687e15	0.0255202
$400$	8.64288e16	1.05504
$401$	−6.84199e16	−0.821758	−0.410879	−	0.911690i	$-0.634778\pi$
$401$	−6.84199e16	−0.821758	−0.410879	+	0.911690i	$0.634778\pi$
$402$	−1.95789e16	−0.231377
$403$	−1.70440e17	−1.98193
$404$	−8.35682e16	−0.956229
$405$	−3.85712e15	−0.0434315
$406$	1.24069e16	0.137482
$407$	2.17385e17	2.37065
$408$	−2.56193e15	−0.0274964
$409$	−1.84727e17	−1.95132	−0.975661	−	0.219283i	$-0.929628\pi$
$409$	−1.84727e17	−1.95132	−0.975661	+	0.219283i	$0.929628\pi$
$410$	−5.77592e16	−0.600518
$411$	2.31736e16	0.237150
$412$	−2.50416e16	−0.252250
$413$	−1.37534e15	−0.0136375
$414$	−8.03830e15	−0.0784625
$415$	−3.02066e16	−0.290262
$416$	−1.33401e17	−1.26198
$417$	−4.57930e16	−0.426496
$418$	−9.15640e16	−0.839612
$419$	−9.11101e16	−0.822575	−0.411288	−	0.911506i	$-0.634921\pi$
$419$	−9.11101e16	−0.822575	−0.411288	+	0.911506i	$0.634921\pi$
$420$	−1.51178e15	−0.0134390
$421$	3.75497e16	0.328680	0.164340	−	0.986404i	$-0.447451\pi$
$421$	3.75497e16	0.328680	0.164340	+	0.986404i	$0.447451\pi$
$422$	5.34418e16	0.460628
$423$	−4.89429e16	−0.415411
$424$	−6.83301e16	−0.571129
$425$	9.07025e15	0.0746606
$426$	−3.33078e16	−0.270012
$427$	−2.25621e16	−0.180135
$428$	−1.75756e16	−0.138206
$429$	1.46644e17	1.13578
$430$	−1.21153e17	−0.924247
$431$	1.33483e17	1.00305	0.501526	−	0.865143i	$-0.332772\pi$
$431$	1.33483e17	1.00305	0.501526	+	0.865143i	$0.332772\pi$
$432$	3.23772e16	0.239660
$433$	1.49890e17	1.09295	0.546476	−	0.837475i	$-0.315969\pi$
$433$	1.49890e17	1.09295	0.546476	+	0.837475i	$0.315969\pi$
$434$	2.92331e16	0.209987
$435$	−3.34204e16	−0.236500
$436$	6.67516e16	0.465371
$437$	−1.15466e16	−0.0793097
$438$	−5.28942e16	−0.357953
$439$	1.73853e17	1.15921	0.579606	−	0.814897i	$-0.303206\pi$
$439$	1.73853e17	1.15921	0.579606	+	0.814897i	$0.303206\pi$
$440$	−5.10837e16	−0.335614
$441$	−5.09258e16	−0.329676
$442$	−2.14231e16	−0.136659
$443$	7.04888e16	0.443094	0.221547	−	0.975150i	$-0.428889\pi$
$443$	7.04888e16	0.443094	0.221547	+	0.975150i	$0.428889\pi$
$444$	7.90603e16	0.489744
$445$	2.43736e16	0.148792
$446$	−6.52652e16	−0.392650
$447$	7.32064e15	0.0434060
$448$	5.57740e14	0.00325930
$449$	−6.53293e15	−0.0376276	−0.0188138	−	0.999823i	$-0.505989\pi$
$449$	−6.53293e15	−0.0376276	−0.0188138	+	0.999823i	$0.505989\pi$
$450$	−6.23005e16	−0.353679
$451$	−3.48291e17	−1.94892
$452$	8.06247e16	0.444701
$453$	−1.49714e17	−0.814002
$454$	−3.46244e17	−1.85575
$455$	9.59578e15	0.0506998
$456$	2.52773e16	0.131661
$457$	1.89446e17	0.972816	0.486408	−	0.873732i	$-0.338307\pi$
$457$	1.89446e17	0.972816	0.486408	+	0.873732i	$0.338307\pi$
$458$	−2.94451e17	−1.49069
$459$	3.39782e15	0.0169597
$460$	8.48664e15	0.0417647
$461$	−8.04558e16	−0.390392	−0.195196	−	0.980764i	$-0.562534\pi$
$461$	−8.04558e16	−0.390392	−0.195196	+	0.980764i	$0.562534\pi$
$462$	−2.51518e16	−0.120336
$463$	−1.97040e17	−0.929560	−0.464780	−	0.885426i	$-0.653867\pi$
$463$	−1.97040e17	−0.929560	−0.464780	+	0.885426i	$0.653867\pi$
$464$	2.80536e17	1.30503
$465$	−7.87448e16	−0.361225
$466$	3.40216e17	1.53903
$467$	−3.44766e17	−1.53803	−0.769016	−	0.639230i	$-0.779253\pi$
$467$	−3.44766e17	−1.53803	−0.769016	+	0.639230i	$0.779253\pi$
$468$	5.33326e16	0.234636
$469$	−7.72547e15	−0.0335198
$470$	1.42568e17	0.610080
$471$	−2.40093e17	−1.01331
$472$	−1.69018e16	−0.0703575
$473$	−7.30555e17	−2.99955
$474$	8.10233e14	0.00328133
$475$	−8.94916e16	−0.357498
$476$	1.33176e15	0.00524783
$477$	9.06246e16	0.352271
$478$	−3.11379e17	−1.19401
$479$	3.69786e17	1.39884	0.699422	−	0.714709i	$-0.253441\pi$
$479$	3.69786e17	1.39884	0.699422	+	0.714709i	$0.253441\pi$
$480$	−6.16325e16	−0.230008
$481$	−5.01824e17	−1.84760
$482$	−6.59105e17	−2.39414
$483$	−3.17176e15	−0.0113669
$484$	2.45039e17	0.866444
$485$	1.20270e17	0.419601
$486$	−2.33385e16	−0.0803410
$487$	−3.20166e17	−1.08752	−0.543760	−	0.839241i	$-0.683000\pi$
$487$	−3.20166e17	−1.08752	−0.543760	+	0.839241i	$0.683000\pi$
$488$	−2.77270e17	−0.929338
$489$	−2.33331e17	−0.771730
$490$	1.48344e17	0.484168
$491$	−8.58817e16	−0.276612	−0.138306	−	0.990390i	$-0.544166\pi$
$491$	−8.58817e16	−0.276612	−0.138306	+	0.990390i	$0.544166\pi$
$492$	−1.26669e17	−0.402621
$493$	2.94408e16	0.0923515
$494$	2.11371e17	0.654366
$495$	6.77510e16	0.207006
$496$	6.60996e17	1.99328
$497$	−1.31426e16	−0.0391170
$498$	−1.82773e17	−0.536935
$499$	4.18832e17	1.21447	0.607234	−	0.794523i	$-0.292279\pi$
$499$	4.18832e17	1.21447	0.607234	+	0.794523i	$0.292279\pi$
$500$	1.43413e17	0.410471
$501$	−1.85397e17	−0.523790
$502$	−1.60522e16	−0.0447672
$503$	5.90088e17	1.62452	0.812260	−	0.583295i	$-0.198237\pi$
$503$	5.90088e17	1.62452	0.812260	+	0.583295i	$0.198237\pi$
$504$	6.94344e15	0.0188702
$505$	2.45067e17	0.657493
$506$	1.41194e17	0.373972
$507$	−1.17725e17	−0.307835
$508$	1.09813e17	0.283491
$509$	2.07985e17	0.530110	0.265055	−	0.964233i	$-0.414610\pi$
$509$	2.07985e17	0.530110	0.265055	+	0.964233i	$0.414610\pi$
$510$	−9.89768e15	−0.0249073
$511$	−2.08710e16	−0.0518570
$512$	2.43026e17	0.596209
$513$	−3.35246e16	−0.0812084
$514$	−5.84217e17	−1.39738
$515$	7.34356e16	0.173444
$516$	−2.65694e17	−0.619667
$517$	8.59692e17	1.97995
$518$	8.60708e16	0.195755
$519$	3.58329e17	0.804812
$520$	1.17924e17	0.261566
$521$	−4.08519e17	−0.894884	−0.447442	−	0.894313i	$-0.647665\pi$
$521$	−4.08519e17	−0.894884	−0.447442	+	0.894313i	$0.647665\pi$
$522$	−2.02219e17	−0.437484
$523$	−7.96818e17	−1.70254	−0.851271	−	0.524726i	$-0.824168\pi$
$523$	−7.96818e17	−1.70254	−0.851271	+	0.524726i	$0.824168\pi$
$524$	4.36396e17	0.920931
$525$	−2.45826e16	−0.0512379
$526$	−5.38953e17	−1.10954
$527$	6.93681e16	0.141056
$528$	−5.68713e17	−1.14228
$529$	−4.86231e17	−0.964675
$530$	−2.63985e17	−0.517351
$531$	2.24165e16	0.0433963
$532$	−1.31398e16	−0.0251283
$533$	8.04012e17	1.51892
$534$	1.47479e17	0.275239
$535$	5.15412e16	0.0950288
$536$	−9.49397e16	−0.172933
$537$	3.06632e17	0.551804
$538$	6.55487e17	1.16541
$539$	8.94522e17	1.57132
$540$	2.46402e16	0.0427646
$541$	−4.03610e16	−0.0692117	−0.0346059	−	0.999401i	$-0.511018\pi$
$541$	−4.03610e16	−0.0692117	−0.0346059	+	0.999401i	$0.511018\pi$
$542$	3.17718e16	0.0538327
$543$	−2.62190e16	−0.0438952
$544$	5.42935e16	0.0898163
$545$	−1.95752e17	−0.319984
$546$	5.80618e16	0.0937860
$547$	−9.25350e17	−1.47703	−0.738514	−	0.674239i	$-0.764472\pi$
$547$	−9.25350e17	−1.47703	−0.738514	+	0.674239i	$0.764472\pi$
$548$	−1.48039e17	−0.233508
$549$	3.67736e17	0.573213
$550$	1.09432e18	1.68573
$551$	−2.90477e17	−0.442208
$552$	−3.89783e16	−0.0586434
$553$	3.19702e14	0.000475370 0
$554$	9.61271e17	1.41264
$555$	−2.31848e17	−0.336743
$556$	2.92537e17	0.419947
$557$	−8.40666e17	−1.19279	−0.596396	−	0.802690i	$-0.703401\pi$
$557$	−8.40666e17	−1.19279	−0.596396	+	0.802690i	$0.703401\pi$
$558$	−4.76466e17	−0.668205
$559$	1.68645e18	2.33775
$560$	−3.72142e16	−0.0509901
$561$	−5.96835e16	−0.0808342
$562$	−2.43016e17	−0.325349
$563$	−9.91311e17	−1.31191	−0.655957	−	0.754798i	$-0.727735\pi$
$563$	−9.91311e17	−1.31191	−0.655957	+	0.754798i	$0.727735\pi$
$564$	3.12659e17	0.409032
$565$	−2.36435e17	−0.305772
$566$	1.62879e18	2.08238
$567$	−9.20892e15	−0.0116391
$568$	−1.61512e17	−0.201809
$569$	1.03565e18	1.27933	0.639667	−	0.768652i	$-0.279072\pi$
$569$	1.03565e18	1.27933	0.639667	+	0.768652i	$0.279072\pi$
$570$	9.76555e16	0.119264
$571$	1.26671e18	1.52947	0.764735	−	0.644345i	$-0.222870\pi$
$571$	1.26671e18	1.52947	0.764735	+	0.644345i	$0.222870\pi$
$572$	−9.36799e17	−1.11834
$573$	−1.77085e17	−0.209015
$574$	−1.37901e17	−0.160931
$575$	1.37999e17	0.159233
$576$	−9.09051e15	−0.0103715
$577$	8.18402e17	0.923260	0.461630	−	0.887073i	$-0.347265\pi$
$577$	8.18402e17	0.923260	0.461630	+	0.887073i	$0.347265\pi$
$578$	−1.11400e18	−1.24267
$579$	−4.50823e17	−0.497274
$580$	2.13497e17	0.232868
$581$	−7.21187e16	−0.0777863
$582$	7.27726e17	0.776191
$583$	−1.59184e18	−1.67901
$584$	−2.56488e17	−0.267536
$585$	−1.56400e17	−0.161333
$586$	1.92725e18	1.96609
$587$	−1.10069e18	−1.11050	−0.555248	−	0.831685i	$-0.687377\pi$
$587$	−1.10069e18	−1.11050	−0.555248	+	0.831685i	$0.687377\pi$
$588$	3.25326e17	0.324613
$589$	−6.84421e17	−0.675420
$590$	−6.52980e16	−0.0637326
$591$	−6.23359e17	−0.601755
$592$	1.94616e18	1.85818
$593$	3.06592e17	0.289538	0.144769	−	0.989465i	$-0.453756\pi$
$593$	3.06592e17	0.289538	0.144769	+	0.989465i	$0.453756\pi$
$594$	4.09945e17	0.382925
$595$	−3.90543e15	−0.00360835
$596$	−4.67660e16	−0.0427395
$597$	−3.29430e17	−0.297804
$598$	−3.25941e17	−0.291461
$599$	−5.29606e17	−0.468467	−0.234233	−	0.972180i	$-0.575258\pi$
$599$	−5.29606e17	−0.468467	−0.234233	+	0.972180i	$0.575258\pi$
$600$	−3.02099e17	−0.264342
$601$	8.61630e17	0.745824	0.372912	−	0.927867i	$-0.378359\pi$
$601$	8.61630e17	0.745824	0.372912	+	0.927867i	$0.378359\pi$
$602$	−2.89253e17	−0.247686
$603$	1.25916e17	0.106664
$604$	9.56412e17	0.801502
$605$	−7.18587e17	−0.595757
$606$	1.48284e18	1.21625
$607$	1.62580e18	1.31930	0.659648	−	0.751575i	$-0.270706\pi$
$607$	1.62580e18	1.31930	0.659648	+	0.751575i	$0.270706\pi$
$608$	−5.35687e17	−0.430069
$609$	−7.97915e16	−0.0633788
$610$	−1.07120e18	−0.841832
$611$	−1.98456e18	−1.54311
$612$	−2.17061e16	−0.0166993
$613$	1.39515e18	1.06201	0.531005	−	0.847369i	$-0.321815\pi$
$613$	1.39515e18	1.06201	0.531005	+	0.847369i	$0.321815\pi$
$614$	1.94597e18	1.46569
$615$	3.71461e17	0.276838
$616$	−1.21963e17	−0.0899401
$617$	−2.56881e18	−1.87447	−0.937234	−	0.348702i	$-0.886623\pi$
$617$	−2.56881e18	−1.87447	−0.937234	+	0.348702i	$0.886623\pi$
$618$	4.44341e17	0.320842
$619$	−2.28518e18	−1.63279	−0.816396	−	0.577492i	$-0.804031\pi$
$619$	−2.28518e18	−1.63279	−0.816396	+	0.577492i	$0.804031\pi$
$620$	5.03041e17	0.355678
$621$	5.16960e16	0.0361711
$622$	2.36699e18	1.63893
$623$	5.81922e16	0.0398742
$624$	1.31285e18	0.890255
$625$	8.41877e17	0.564974
$626$	−1.36966e18	−0.909658
$627$	5.88867e17	0.387060
$628$	1.53377e18	0.997752
$629$	2.04240e17	0.131496
$630$	2.68251e16	0.0170934
$631$	3.08947e18	1.94847	0.974235	−	0.225536i	$-0.0724133\pi$
$631$	3.08947e18	1.94847	0.974235	+	0.225536i	$0.0724133\pi$
$632$	3.92888e15	0.00245249
$633$	−3.43695e17	−0.212348
$634$	−3.55815e18	−2.17593
$635$	−3.22031e17	−0.194925
$636$	−5.78931e17	−0.346861
$637$	−2.06496e18	−1.22463
$638$	3.55201e18	2.08516
$639$	2.14209e17	0.124475
$640$	−6.66104e17	−0.383153
$641$	2.63976e18	1.50310	0.751549	−	0.659677i	$-0.229307\pi$
$641$	2.63976e18	1.50310	0.751549	+	0.659677i	$0.229307\pi$
$642$	3.11864e17	0.175787
$643$	8.76260e17	0.488947	0.244473	−	0.969656i	$-0.421385\pi$
$643$	8.76260e17	0.488947	0.244473	+	0.969656i	$0.421385\pi$
$644$	2.02619e16	0.0111924
$645$	7.79157e17	0.426076
$646$	−8.60270e16	−0.0465718
$647$	−2.39802e18	−1.28521	−0.642607	−	0.766196i	$-0.722147\pi$
$647$	−2.39802e18	−1.28521	−0.642607	+	0.766196i	$0.722147\pi$
$648$	−1.13170e17	−0.0600473
$649$	−3.93750e17	−0.206838
$650$	−2.52619e18	−1.31380
$651$	−1.88004e17	−0.0968036
$652$	1.49058e18	0.759880
$653$	8.01370e17	0.404480	0.202240	−	0.979336i	$-0.435178\pi$
$653$	8.01370e17	0.404480	0.202240	+	0.979336i	$0.435178\pi$
$654$	−1.18445e18	−0.591916
$655$	−1.27975e18	−0.633222
$656$	−3.11811e18	−1.52762
$657$	3.40173e17	0.165016
$658$	3.40383e17	0.163493
$659$	−7.29518e17	−0.346961	−0.173481	−	0.984837i	$-0.555501\pi$
$659$	−7.29518e17	−0.346961	−0.173481	+	0.984837i	$0.555501\pi$
$660$	−4.32810e17	−0.203827
$661$	4.25095e17	0.198233	0.0991166	−	0.995076i	$-0.468398\pi$
$661$	4.25095e17	0.198233	0.0991166	+	0.995076i	$0.468398\pi$
$662$	2.33195e18	1.07682
$663$	1.37776e17	0.0629995
$664$	−8.86280e17	−0.401308
$665$	3.85330e16	0.0172779
$666$	−1.40285e18	−0.622917
$667$	4.47925e17	0.196964
$668$	1.18436e18	0.515747
$669$	4.19734e17	0.181011
$670$	−3.66787e17	−0.156649
$671$	−6.45936e18	−2.73208
$672$	−1.47148e17	−0.0616390
$673$	3.76325e18	1.56122	0.780612	−	0.625016i	$-0.214908\pi$
$673$	3.76325e18	1.56122	0.780612	+	0.625016i	$0.214908\pi$
$674$	−4.15260e18	−1.70620
$675$	4.00667e17	0.163046
$676$	7.52058e17	0.303108
$677$	2.73534e18	1.09191	0.545953	−	0.837816i	$-0.316168\pi$
$677$	2.73534e18	1.09191	0.545953	+	0.837816i	$0.316168\pi$
$678$	−1.43061e18	−0.565625
$679$	2.87147e17	0.112448
$680$	−4.79946e16	−0.0186159
$681$	2.22677e18	0.855497
$682$	8.36922e18	3.18483
$683$	4.26204e18	1.60651	0.803255	−	0.595635i	$-0.203100\pi$
$683$	4.26204e18	1.60651	0.803255	+	0.595635i	$0.203100\pi$
$684$	2.14163e17	0.0799614
$685$	4.34130e17	0.160558
$686$	7.12277e17	0.260941
$687$	1.89368e18	0.687206
$688$	−6.54037e18	−2.35113
$689$	3.67469e18	1.30856
$690$	−1.50588e17	−0.0531215
$691$	2.27874e18	0.796321	0.398161	−	0.917316i	$-0.369649\pi$
$691$	2.27874e18	0.796321	0.398161	+	0.917316i	$0.369649\pi$
$692$	−2.28909e18	−0.792454
$693$	1.61756e17	0.0554748
$694$	2.69922e17	0.0917068
$695$	−8.57875e17	−0.288751
$696$	−9.80572e17	−0.326979
$697$	−3.27229e17	−0.108103
$698$	−9.16242e17	−0.299882
$699$	−2.18800e18	−0.709489
$700$	1.57039e17	0.0504511
$701$	−4.05425e18	−1.29046	−0.645228	−	0.763990i	$-0.723238\pi$
$701$	−4.05425e18	−1.29046	−0.645228	+	0.763990i	$0.723238\pi$
$702$	−9.46340e17	−0.298439
$703$	−2.01513e18	−0.629642
$704$	1.59677e17	0.0494332
$705$	−9.16886e17	−0.281246
$706$	−7.16382e17	−0.217728
$707$	5.85101e17	0.176199
$708$	−1.43202e17	−0.0427299
$709$	6.03796e18	1.78521	0.892606	−	0.450838i	$-0.148875\pi$
$709$	6.03796e18	1.78521	0.892606	+	0.450838i	$0.148875\pi$
$710$	−6.23981e17	−0.182807
$711$	−5.21077e15	−0.00151269
$712$	7.15134e17	0.205716
$713$	1.05540e18	0.300839
$714$	−2.36308e16	−0.00667484
$715$	2.74720e18	0.768955
$716$	−1.95884e18	−0.543330
$717$	2.00254e18	0.550436
$718$	6.91492e18	1.88356
$719$	−5.16281e18	−1.39363	−0.696817	−	0.717249i	$-0.745401\pi$
$719$	−5.16281e18	−1.39363	−0.696817	+	0.717249i	$0.745401\pi$
$720$	6.06548e17	0.162257
$721$	1.75328e17	0.0464808
$722$	−3.91807e18	−1.02939
$723$	4.23884e18	1.10369
$724$	1.67493e17	0.0432212
$725$	3.47162e18	0.887840
$726$	−4.34800e18	−1.10205
$727$	−2.91401e18	−0.732010	−0.366005	−	0.930613i	$-0.619275\pi$
$727$	−2.91401e18	−0.732010	−0.366005	+	0.930613i	$0.619275\pi$
$728$	2.81546e17	0.0700963
$729$	1.50095e17	0.0370370
$730$	−9.90907e17	−0.242345
$731$	−6.86378e17	−0.166380
$732$	−2.34919e18	−0.564411
$733$	−2.85832e18	−0.680668	−0.340334	−	0.940305i	$-0.610540\pi$
$733$	−2.85832e18	−0.680668	−0.340334	+	0.940305i	$0.610540\pi$
$734$	−2.02619e18	−0.478251
$735$	−9.54032e17	−0.223201
$736$	8.26045e17	0.191557
$737$	−2.21174e18	−0.508389
$738$	2.24762e18	0.512103
$739$	7.64367e18	1.72629	0.863144	−	0.504959i	$-0.168492\pi$
$739$	7.64367e18	1.72629	0.863144	+	0.504959i	$0.168492\pi$
$740$	1.48110e18	0.331572
$741$	−1.35937e18	−0.301661
$742$	−6.30267e17	−0.138643
$743$	−7.66120e18	−1.67059	−0.835294	−	0.549803i	$-0.814703\pi$
$743$	−7.66120e18	−1.67059	−0.835294	+	0.549803i	$0.814703\pi$
$744$	−2.31042e18	−0.499421
$745$	1.37143e17	0.0293872
$746$	−1.03421e18	−0.219687
$747$	1.17545e18	0.247526
$748$	3.81272e17	0.0795930
$749$	1.23055e17	0.0254665
$750$	−2.54473e18	−0.522088
$751$	3.41386e18	0.694362	0.347181	−	0.937798i	$-0.387139\pi$
$751$	3.41386e18	0.694362	0.347181	+	0.937798i	$0.387139\pi$
$752$	7.69648e18	1.55194
$753$	1.03235e17	0.0206376
$754$	−8.19965e18	−1.62510
$755$	−2.80472e18	−0.551104
$756$	5.88288e16	0.0114604
$757$	−7.12369e18	−1.37588	−0.687942	−	0.725766i	$-0.741485\pi$
$757$	−7.12369e18	−1.37588	−0.687942	+	0.725766i	$0.741485\pi$
$758$	2.93881e18	0.562758
$759$	−9.08050e17	−0.172400
$760$	4.73538e17	0.0891388
$761$	4.50157e18	0.840163	0.420081	−	0.907486i	$-0.362002\pi$
$761$	4.50157e18	0.840163	0.420081	+	0.907486i	$0.362002\pi$
$762$	−1.94853e18	−0.360578
$763$	−4.67360e17	−0.0857515
$764$	1.13126e18	0.205806
$765$	6.36540e16	0.0114822
$766$	−6.09599e18	−1.09033
$767$	9.08953e17	0.161202
$768$	−4.13259e18	−0.726732
$769$	−1.83062e18	−0.319210	−0.159605	−	0.987181i	$-0.551022\pi$
$769$	−1.83062e18	−0.319210	−0.159605	+	0.987181i	$0.551022\pi$
$770$	−4.71188e17	−0.0814713
$771$	3.75722e18	0.644189
$772$	2.87997e18	0.489638
$773$	1.85723e18	0.313111	0.156556	−	0.987669i	$-0.449961\pi$
$773$	1.85723e18	0.313111	0.156556	+	0.987669i	$0.449961\pi$
$774$	4.71449e18	0.788168
$775$	8.17980e18	1.35607
$776$	3.52880e18	0.580130
$777$	−5.53539e17	−0.0902426
$778$	−2.18848e18	−0.353814
$779$	3.22860e18	0.517632
$780$	9.99121e17	0.158856
$781$	−3.76263e18	−0.593280
$782$	1.32656e17	0.0207436
$783$	1.30051e18	0.201680
$784$	8.00829e18	1.23165
$785$	−4.49784e18	−0.686043
$786$	−7.74345e18	−1.17135
$787$	1.24951e19	1.87458	0.937289	−	0.348552i	$-0.113327\pi$
$787$	1.24951e19	1.87458	0.937289	+	0.348552i	$0.113327\pi$
$788$	3.98217e18	0.592514
$789$	3.46612e18	0.511497
$790$	1.51787e16	0.00222156
$791$	−5.64492e17	−0.0819427
$792$	1.98785e18	0.286201
$793$	1.49111e19	2.12929
$794$	−1.05492e19	−1.49413
$795$	1.69774e18	0.238498
$796$	2.10448e18	0.293231
$797$	−3.39172e18	−0.468749	−0.234375	−	0.972146i	$-0.575304\pi$
$797$	−3.39172e18	−0.468749	−0.234375	+	0.972146i	$0.575304\pi$
$798$	2.33154e17	0.0319612
$799$	8.07706e17	0.109824
$800$	6.40222e18	0.863467
$801$	−9.48465e17	−0.126885
$802$	−7.75563e18	−1.02916
$803$	−5.97521e18	−0.786507
$804$	−8.04383e17	−0.105026
$805$	−5.94190e16	−0.00769577
$806$	−1.93200e19	−2.48215
$807$	−4.21557e18	−0.537252
$808$	7.19041e18	0.909033
$809$	−8.37465e18	−1.05027	−0.525135	−	0.851019i	$-0.675985\pi$
$809$	−8.37465e18	−1.05027	−0.525135	+	0.851019i	$0.675985\pi$
$810$	−4.37218e17	−0.0543933
$811$	1.21843e19	1.50372	0.751859	−	0.659323i	$-0.229157\pi$
$811$	1.21843e19	1.50372	0.751859	+	0.659323i	$0.229157\pi$
$812$	5.09727e17	0.0624056
$813$	−2.04331e17	−0.0248168
$814$	2.46414e19	2.96898
$815$	−4.37117e18	−0.522485
$816$	−5.34322e17	−0.0633603
$817$	6.77215e18	0.796678
$818$	−2.09395e19	−2.44382
$819$	−3.73407e17	−0.0432352
$820$	−2.37298e18	−0.272587
$821$	−1.03438e19	−1.17883	−0.589414	−	0.807831i	$-0.700641\pi$
$821$	−1.03438e19	−1.17883	−0.589414	+	0.807831i	$0.700641\pi$
$822$	2.62681e18	0.297004
$823$	−1.54641e19	−1.73471	−0.867355	−	0.497691i	$-0.834181\pi$
$823$	−1.54641e19	−1.73471	−0.867355	+	0.497691i	$0.834181\pi$
$824$	2.15464e18	0.239800
$825$	−7.03780e18	−0.777116
$826$	−1.55900e17	−0.0170795
$827$	5.24394e18	0.569996	0.284998	−	0.958528i	$-0.408007\pi$
$827$	5.24394e18	0.569996	0.284998	+	0.958528i	$0.408007\pi$
$828$	−3.30246e17	−0.0356156
$829$	4.59297e18	0.491461	0.245730	−	0.969338i	$-0.420972\pi$
$829$	4.59297e18	0.491461	0.245730	+	0.969338i	$0.420972\pi$
$830$	−3.42403e18	−0.363521
$831$	−6.18213e18	−0.651226
$832$	−3.68606e17	−0.0385266
$833$	8.40429e17	0.0871582
$834$	−5.19080e18	−0.534140
$835$	−3.47319e18	−0.354622
$836$	−3.76182e18	−0.381116
$837$	3.06425e18	0.308041
$838$	−1.03277e19	−1.03019
$839$	1.39587e19	1.38163	0.690813	−	0.723033i	$-0.257253\pi$
$839$	1.39587e19	1.38163	0.690813	+	0.723033i	$0.257253\pi$
$840$	1.30077e17	0.0127757
$841$	1.00775e18	0.0982154
$842$	4.25639e18	0.411636
$843$	1.56289e18	0.149985
$844$	2.19561e18	0.209088
$845$	−2.20544e18	−0.208414
$846$	−5.54785e18	−0.520257
$847$	−1.71564e18	−0.159655
$848$	−1.42511e19	−1.31606
$849$	−1.04751e19	−0.959971
$850$	1.02814e18	0.0935042
$851$	3.10739e18	0.280449
$852$	−1.36842e18	−0.122564
$853$	−5.79828e17	−0.0515384	−0.0257692	−	0.999668i	$-0.508203\pi$
$853$	−5.79828e17	−0.0515384	−0.0257692	+	0.999668i	$0.508203\pi$
$854$	−2.55750e18	−0.225600
$855$	−6.28043e17	−0.0549806
$856$	1.51225e18	0.131384
$857$	9.99908e18	0.862154	0.431077	−	0.902315i	$-0.358134\pi$
$857$	9.99908e18	0.862154	0.431077	+	0.902315i	$0.358134\pi$
$858$	1.66226e19	1.42244
$859$	3.96762e18	0.336957	0.168479	−	0.985705i	$-0.446115\pi$
$859$	3.96762e18	0.336957	0.168479	+	0.985705i	$0.446115\pi$
$860$	−4.97744e18	−0.419533
$861$	8.86869e17	0.0741889
$862$	1.51308e19	1.25621
$863$	1.59481e19	1.31413	0.657066	−	0.753833i	$-0.271797\pi$
$863$	1.59481e19	1.31413	0.657066	+	0.753833i	$0.271797\pi$
$864$	2.39835e18	0.196143
$865$	6.71286e18	0.544883
$866$	1.69906e19	1.36880
$867$	7.16436e18	0.572867
$868$	1.20102e18	0.0953171
$869$	9.15283e16	0.00720986
$870$	−3.78832e18	−0.296190
$871$	5.10571e18	0.396221
$872$	−5.74347e18	−0.442402
$873$	−4.68016e18	−0.357823
$874$	−1.30885e18	−0.0993268
$875$	−1.00410e18	−0.0756354
$876$	−2.17311e18	−0.162482
$877$	6.94364e18	0.515335	0.257668	−	0.966234i	$-0.417046\pi$
$877$	6.94364e18	0.515335	0.257668	+	0.966234i	$0.417046\pi$
$878$	1.97069e19	1.45179
$879$	−1.23945e19	−0.906362
$880$	−1.06541e19	−0.773359
$881$	−2.08214e18	−0.150026	−0.0750129	−	0.997183i	$-0.523900\pi$
$881$	−2.08214e18	−0.150026	−0.0750129	+	0.997183i	$0.523900\pi$
$882$	−5.77262e18	−0.412883
$883$	−6.29301e17	−0.0446800	−0.0223400	−	0.999750i	$-0.507112\pi$
$883$	−6.29301e17	−0.0446800	−0.0223400	+	0.999750i	$0.507112\pi$
$884$	−8.80149e17	−0.0620321
$885$	4.19945e17	0.0293806
$886$	7.99015e18	0.554927
$887$	5.08893e18	0.350851	0.175425	−	0.984493i	$-0.443870\pi$
$887$	5.08893e18	0.350851	0.175425	+	0.984493i	$0.443870\pi$
$888$	−6.80254e18	−0.465572
$889$	−7.68852e17	−0.0522374
$890$	2.76283e18	0.186346
$891$	−2.63644e18	−0.176528
$892$	−2.68136e18	−0.178231
$893$	−7.96923e18	−0.525874
$894$	8.29821e17	0.0543614
$895$	5.74437e18	0.373588
$896$	−1.59033e18	−0.102680
$897$	2.09619e18	0.134363
$898$	−7.40531e17	−0.0471245
$899$	2.65505e19	1.67739
$900$	−2.55956e18	−0.160542
$901$	−1.49558e18	−0.0931318
$902$	−3.94800e19	−2.44081
$903$	1.86025e18	0.114183
$904$	−6.93714e18	−0.422752
$905$	−4.91181e17	−0.0297184
$906$	−1.69707e19	−1.01945
$907$	−1.41366e19	−0.843135	−0.421567	−	0.906797i	$-0.638520\pi$
$907$	−1.41366e19	−0.843135	−0.421567	+	0.906797i	$0.638520\pi$
$908$	−1.42251e19	−0.842360
$909$	−9.53646e18	−0.560689
$910$	1.08772e18	0.0634960
$911$	−7.79326e18	−0.451699	−0.225850	−	0.974162i	$-0.572516\pi$
$911$	−7.79326e18	−0.451699	−0.225850	+	0.974162i	$0.572516\pi$
$912$	5.27189e18	0.303389
$913$	−2.06470e19	−1.17977
$914$	2.14744e19	1.21835
$915$	6.88909e18	0.388083
$916$	−1.20973e19	−0.676654
$917$	−3.05541e18	−0.169695
$918$	3.85155e17	0.0212402
$919$	−1.39931e19	−0.766237	−0.383118	−	0.923699i	$-0.625150\pi$
$919$	−1.39931e19	−0.766237	−0.383118	+	0.923699i	$0.625150\pi$
$920$	−7.30210e17	−0.0397034
$921$	−1.25150e19	−0.675682
$922$	−9.11995e18	−0.488924
$923$	8.68586e18	0.462383
$924$	−1.03334e18	−0.0546229
$925$	2.40837e19	1.26416
$926$	−2.23351e19	−1.16417
$927$	−2.85765e18	−0.147908
$928$	2.07807e19	1.06807
$929$	2.29359e19	1.17061	0.585306	−	0.810812i	$-0.300974\pi$
$929$	2.29359e19	1.17061	0.585306	+	0.810812i	$0.300974\pi$
$930$	−8.92601e18	−0.452395
$931$	−8.29209e18	−0.417341
$932$	1.39775e19	0.698594
$933$	−1.52226e19	−0.755542
$934$	−3.90805e19	−1.92622
$935$	−1.11810e18	−0.0547273
$936$	−4.58887e18	−0.223055
$937$	−9.39414e18	−0.453471	−0.226736	−	0.973956i	$-0.572805\pi$
$937$	−9.39414e18	−0.453471	−0.226736	+	0.973956i	$0.572805\pi$
$938$	−8.75710e17	−0.0419799
$939$	8.80853e18	0.419351
$940$	5.85729e18	0.276927
$941$	3.08608e19	1.44902	0.724510	−	0.689265i	$-0.242066\pi$
$941$	3.08608e19	1.44902	0.724510	+	0.689265i	$0.242066\pi$
$942$	−2.72154e19	−1.26906
$943$	−4.97860e18	−0.230559
$944$	−3.52508e18	−0.162126
$945$	−1.72518e17	−0.00788001
$946$	−8.28111e19	−3.75661
$947$	−1.75870e19	−0.792351	−0.396176	−	0.918175i	$-0.629663\pi$
$947$	−1.75870e19	−0.792351	−0.396176	+	0.918175i	$0.629663\pi$
$948$	3.32877e16	0.00148946
$949$	1.37935e19	0.612977
$950$	−1.01442e19	−0.447728
$951$	2.28832e19	1.00310
$952$	−1.14588e17	−0.00498882
$953$	3.37204e19	1.45811	0.729053	−	0.684457i	$-0.239961\pi$
$953$	3.37204e19	1.45811	0.729053	+	0.684457i	$0.239961\pi$
$954$	1.02726e19	0.441181
$955$	−3.31748e18	−0.141510
$956$	−1.27927e19	−0.541984
$957$	−2.28437e19	−0.961256
$958$	4.19165e19	1.75190
$959$	1.03649e18	0.0430273
$960$	−1.70299e17	−0.00702183
$961$	3.81406e19	1.56201
$962$	−5.68835e19	−2.31392
$963$	−2.00566e18	−0.0810375
$964$	−2.70787e19	−1.08674
$965$	−8.44562e18	−0.336670
$966$	−3.59530e17	−0.0142359
$967$	3.04184e18	0.119637	0.0598183	−	0.998209i	$-0.480948\pi$
$967$	3.04184e18	0.119637	0.0598183	+	0.998209i	$0.480948\pi$
$968$	−2.10837e19	−0.823679
$969$	5.53257e17	0.0214695
$970$	1.36331e19	0.525505
$971$	−1.65309e19	−0.632953	−0.316477	−	0.948600i	$-0.602500\pi$
$971$	−1.65309e19	−0.632953	−0.316477	+	0.948600i	$0.602500\pi$
$972$	−9.58841e17	−0.0364683
$973$	−2.04819e18	−0.0773814
$974$	−3.62920e19	−1.36200
$975$	1.62464e19	0.605659
$976$	−5.78281e19	−2.14148
$977$	−3.29887e19	−1.21353	−0.606766	−	0.794881i	$-0.707533\pi$
$977$	−3.29887e19	−1.21353	−0.606766	+	0.794881i	$0.707533\pi$
$978$	−2.64489e19	−0.966508
$979$	1.66600e19	0.604765
$980$	6.09459e18	0.219773
$981$	7.61742e18	0.272872
$982$	−9.73499e18	−0.346426
$983$	3.60033e18	0.127275	0.0636377	−	0.997973i	$-0.479730\pi$
$983$	3.60033e18	0.127275	0.0636377	+	0.997973i	$0.479730\pi$
$984$	1.08989e19	0.382749
$985$	−1.16779e19	−0.407406
$986$	3.33721e18	0.115660
$987$	−2.18908e18	−0.0753701
$988$	8.68399e18	0.297029
$989$	−1.04429e19	−0.354849
$990$	7.67982e18	0.259252
$991$	1.08430e19	0.363640	0.181820	−	0.983332i	$-0.441801\pi$
$991$	1.08430e19	0.363640	0.181820	+	0.983332i	$0.441801\pi$
$992$	4.89634e19	1.63134
$993$	−1.49972e19	−0.496411
$994$	−1.48976e18	−0.0489898
$995$	−6.17147e18	−0.201622
$996$	−7.50906e18	−0.243725
$997$	1.32138e19	0.426097	0.213049	−	0.977042i	$-0.431661\pi$
$997$	1.32138e19	0.426097	0.213049	+	0.977042i	$0.431661\pi$
$998$	4.74760e19	1.52099
$999$	9.02204e18	0.287163

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.d.1.25	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.d.1.25	✓	32	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)

\(f(q)\)	\(=\)	\(q+113.354 q^{2} -729.000 q^{3} +4657.03 q^{4} -13656.9 q^{5} -82634.7 q^{6} -32606.1 q^{7} -400702. q^{8} +531441. q^{9} +O(q^{10})\)	\(q+113.354 q^{2} -729.000 q^{3} +4657.03 q^{4} -13656.9 q^{5} -82634.7 q^{6} -32606.1 q^{7} -400702. q^{8} +531441. q^{9} -1.54806e6 q^{10} -9.33487e6 q^{11} -3.39497e6 q^{12} +2.15491e7 q^{13} -3.69601e6 q^{14} +9.95589e6 q^{15} -8.35713e7 q^{16} -8.77038e6 q^{17} +6.02407e7 q^{18} +8.65329e7 q^{19} -6.36006e7 q^{20} +2.37698e7 q^{21} -1.05814e9 q^{22} -1.33436e8 q^{23} +2.92112e8 q^{24} -1.03419e9 q^{25} +2.44267e9 q^{26} -3.87420e8 q^{27} -1.51847e8 q^{28} -3.35684e9 q^{29} +1.12854e9 q^{30} -7.90937e9 q^{31} -6.19056e9 q^{32} +6.80512e9 q^{33} -9.94153e8 q^{34} +4.45298e8 q^{35} +2.47494e9 q^{36} -2.32875e10 q^{37} +9.80881e9 q^{38} -1.57093e10 q^{39} +5.47235e9 q^{40} +3.73107e10 q^{41} +2.69439e9 q^{42} +7.82609e10 q^{43} -4.34727e10 q^{44} -7.25785e9 q^{45} -1.51255e10 q^{46} -9.20948e10 q^{47} +6.09235e10 q^{48} -9.58259e10 q^{49} -1.17229e11 q^{50} +6.39360e9 q^{51} +1.00355e11 q^{52} +1.70526e11 q^{53} -4.39155e10 q^{54} +1.27486e11 q^{55} +1.30653e10 q^{56} -6.30825e10 q^{57} -3.80510e11 q^{58} +4.21805e10 q^{59} +4.63649e10 q^{60} +6.91961e11 q^{61} -8.96555e11 q^{62} -1.73282e10 q^{63} -1.71054e10 q^{64} -2.94294e11 q^{65} +7.71384e11 q^{66} +2.36934e11 q^{67} -4.08439e10 q^{68} +9.72751e10 q^{69} +5.04761e10 q^{70} +4.03073e11 q^{71} -2.12949e11 q^{72} +6.40096e11 q^{73} -2.63972e12 q^{74} +7.53926e11 q^{75} +4.02986e11 q^{76} +3.04373e11 q^{77} -1.78070e12 q^{78} -9.80499e9 q^{79} +1.14133e12 q^{80} +2.82430e11 q^{81} +4.22930e12 q^{82} +2.21182e12 q^{83} +1.10697e11 q^{84} +1.19776e11 q^{85} +8.87115e12 q^{86} +2.44714e12 q^{87} +3.74050e12 q^{88} -1.78470e12 q^{89} -8.22703e11 q^{90} -7.02632e11 q^{91} -6.21417e11 q^{92} +5.76593e12 q^{93} -1.04393e13 q^{94} -1.18177e12 q^{95} +4.51292e12 q^{96} -8.80654e12 q^{97} -1.08622e13 q^{98} -4.96093e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{2} - 23328 q^{3} + 139174 q^{4} + 2236 q^{5} - 8748 q^{6} + 746845 q^{7} - 733317 q^{8} + 17006112 q^{9}+O(q^{10}) \) 32 * q + 12 * q^2 - 23328 * q^3 + 139174 * q^4 + 2236 * q^5 - 8748 * q^6 + 746845 * q^7 - 733317 * q^8 + 17006112 * q^9	\( 32 q + 12 q^{2} - 23328 q^{3} + 139174 q^{4} + 2236 q^{5} - 8748 q^{6} + 746845 q^{7} - 733317 q^{8} + 17006112 q^{9} + 6145337 q^{10} + 400846 q^{11} - 101457846 q^{12} + 9411686 q^{13} - 36368387 q^{14} - 1630044 q^{15} + 734877786 q^{16} + 228113833 q^{17} + 6377292 q^{18} + 524233755 q^{19} - 420745331 q^{20} - 544450005 q^{21} - 1844479318 q^{22} - 399937087 q^{23} + 534588093 q^{24} + 8617402914 q^{25} - 499433574 q^{26} - 12397455648 q^{27} + 12648993070 q^{28} - 225284149 q^{29} - 4479950673 q^{30} + 9454638761 q^{31} + 11648295118 q^{32} - 292216734 q^{33} + 39279537096 q^{34} + 17608963479 q^{35} + 73962769734 q^{36} + 37463929597 q^{37} + 65554547351 q^{38} - 6861119094 q^{39} + 144414252742 q^{40} + 22650227173 q^{41} + 26512554123 q^{42} + 96253617602 q^{43} - 132186868002 q^{44} + 1188302076 q^{45} + 327853892309 q^{46} + 239981844027 q^{47} - 535725905994 q^{48} + 286262776863 q^{49} - 671840368399 q^{50} - 166294984257 q^{51} - 952971648498 q^{52} - 47446514136 q^{53} - 4649045868 q^{54} - 474454082548 q^{55} - 1167728875984 q^{56} - 382166407395 q^{57} + 547596592762 q^{58} + 1349777076512 q^{59} + 306723346299 q^{60} + 661498471821 q^{61} + 555821093242 q^{62} + 396904053645 q^{63} + 3522679273173 q^{64} + 1269187682756 q^{65} + 1344625422822 q^{66} + 2838711491386 q^{67} + 1395029358261 q^{68} + 291554136423 q^{69} + 5677102514386 q^{70} + 1912914480734 q^{71} - 389714719797 q^{72} + 2403595726697 q^{73} - 742136417562 q^{74} - 6282086724306 q^{75} - 4020161987188 q^{76} - 4878303804101 q^{77} + 364087075446 q^{78} - 1705546365970 q^{79} - 4347383766449 q^{80} + 9037745167392 q^{81} - 6943720239935 q^{82} - 2549647313691 q^{83} - 9221115948030 q^{84} - 8455706309615 q^{85} - 33993832711012 q^{86} + 164232144621 q^{87} - 42970239360587 q^{88} - 17356719361241 q^{89} + 3265884040617 q^{90} - 30776775043291 q^{91} - 13184590997480 q^{92} - 6892431656769 q^{93} - 35604563339520 q^{94} + 219501126195 q^{95} - 8491607141022 q^{96} - 4427131429152 q^{97} - 32707332037060 q^{98} + 213025999086 q^{99}+O(q^{100}) \) 32 * q + 12 * q^2 - 23328 * q^3 + 139174 * q^4 + 2236 * q^5 - 8748 * q^6 + 746845 * q^7 - 733317 * q^8 + 17006112 * q^9 + 6145337 * q^10 + 400846 * q^11 - 101457846 * q^12 + 9411686 * q^13 - 36368387 * q^14 - 1630044 * q^15 + 734877786 * q^16 + 228113833 * q^17 + 6377292 * q^18 + 524233755 * q^19 - 420745331 * q^20 - 544450005 * q^21 - 1844479318 * q^22 - 399937087 * q^23 + 534588093 * q^24 + 8617402914 * q^25 - 499433574 * q^26 - 12397455648 * q^27 + 12648993070 * q^28 - 225284149 * q^29 - 4479950673 * q^30 + 9454638761 * q^31 + 11648295118 * q^32 - 292216734 * q^33 + 39279537096 * q^34 + 17608963479 * q^35 + 73962769734 * q^36 + 37463929597 * q^37 + 65554547351 * q^38 - 6861119094 * q^39 + 144414252742 * q^40 + 22650227173 * q^41 + 26512554123 * q^42 + 96253617602 * q^43 - 132186868002 * q^44 + 1188302076 * q^45 + 327853892309 * q^46 + 239981844027 * q^47 - 535725905994 * q^48 + 286262776863 * q^49 - 671840368399 * q^50 - 166294984257 * q^51 - 952971648498 * q^52 - 47446514136 * q^53 - 4649045868 * q^54 - 474454082548 * q^55 - 1167728875984 * q^56 - 382166407395 * q^57 + 547596592762 * q^58 + 1349777076512 * q^59 + 306723346299 * q^60 + 661498471821 * q^61 + 555821093242 * q^62 + 396904053645 * q^63 + 3522679273173 * q^64 + 1269187682756 * q^65 + 1344625422822 * q^66 + 2838711491386 * q^67 + 1395029358261 * q^68 + 291554136423 * q^69 + 5677102514386 * q^70 + 1912914480734 * q^71 - 389714719797 * q^72 + 2403595726697 * q^73 - 742136417562 * q^74 - 6282086724306 * q^75 - 4020161987188 * q^76 - 4878303804101 * q^77 + 364087075446 * q^78 - 1705546365970 * q^79 - 4347383766449 * q^80 + 9037745167392 * q^81 - 6943720239935 * q^82 - 2549647313691 * q^83 - 9221115948030 * q^84 - 8455706309615 * q^85 - 33993832711012 * q^86 + 164232144621 * q^87 - 42970239360587 * q^88 - 17356719361241 * q^89 + 3265884040617 * q^90 - 30776775043291 * q^91 - 13184590997480 * q^92 - 6892431656769 * q^93 - 35604563339520 * q^94 + 219501126195 * q^95 - 8491607141022 * q^96 - 4427131429152 * q^97 - 32707332037060 * q^98 + 213025999086 * q^99

Introduction

L-functions

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