LMFDB - Embedded newform 177.10.a.b.1.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,10,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, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 10 $
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:	$91.1613430010$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.21
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)

$f(q)$	$=$	$q+42.7873 q^{2} -81.0000 q^{3} +1318.75 q^{4} -657.216 q^{5} -3465.77 q^{6} +2359.02 q^{7} +34518.6 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+42.7873 q^{2} -81.0000 q^{3} +1318.75 q^{4} -657.216 q^{5} -3465.77 q^{6} +2359.02 q^{7} +34518.6 q^{8} +6561.00 q^{9} -28120.5 q^{10} -48603.9 q^{11} -106819. q^{12} -181586. q^{13} +100936. q^{14} +53234.5 q^{15} +801757. q^{16} -33203.5 q^{17} +280727. q^{18} -533100. q^{19} -866703. q^{20} -191081. q^{21} -2.07963e6 q^{22} +711338. q^{23} -2.79601e6 q^{24} -1.52119e6 q^{25} -7.76959e6 q^{26} -531441. q^{27} +3.11096e6 q^{28} +351893. q^{29} +2.27776e6 q^{30} -1.44240e6 q^{31} +1.66314e7 q^{32} +3.93692e6 q^{33} -1.42069e6 q^{34} -1.55039e6 q^{35} +8.65232e6 q^{36} +1.69246e7 q^{37} -2.28099e7 q^{38} +1.47085e7 q^{39} -2.26862e7 q^{40} -2.49969e7 q^{41} -8.17583e6 q^{42} +1.83565e7 q^{43} -6.40964e7 q^{44} -4.31199e6 q^{45} +3.04362e7 q^{46} -1.25038e7 q^{47} -6.49423e7 q^{48} -3.47886e7 q^{49} -6.50877e7 q^{50} +2.68949e6 q^{51} -2.39467e8 q^{52} -7.15319e7 q^{53} -2.27389e7 q^{54} +3.19433e7 q^{55} +8.14302e7 q^{56} +4.31811e7 q^{57} +1.50565e7 q^{58} -1.21174e7 q^{59} +7.02029e7 q^{60} -4.58629e7 q^{61} -6.17163e7 q^{62} +1.54775e7 q^{63} +3.01114e8 q^{64} +1.19341e8 q^{65} +1.68450e8 q^{66} +1.49604e8 q^{67} -4.37871e7 q^{68} -5.76184e7 q^{69} -6.63368e7 q^{70} -3.47372e8 q^{71} +2.26477e8 q^{72} -8.25280e7 q^{73} +7.24159e8 q^{74} +1.23217e8 q^{75} -7.03026e8 q^{76} -1.14658e8 q^{77} +6.29337e8 q^{78} -5.99311e8 q^{79} -5.26927e8 q^{80} +4.30467e7 q^{81} -1.06955e9 q^{82} -2.20456e7 q^{83} -2.51988e8 q^{84} +2.18219e7 q^{85} +7.85423e8 q^{86} -2.85033e7 q^{87} -1.67774e9 q^{88} +1.41941e8 q^{89} -1.84498e8 q^{90} -4.28367e8 q^{91} +9.38077e8 q^{92} +1.16834e8 q^{93} -5.35003e8 q^{94} +3.50362e8 q^{95} -1.34715e9 q^{96} +5.95410e8 q^{97} -1.48851e9 q^{98} -3.18890e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9}+O(q^{10}) $ 21 * q + 20 * q^2 - 1701 * q^3 + 4950 * q^4 + 2058 * q^5 - 1620 * q^6 - 17167 * q^7 - 2853 * q^8 + 137781 * q^9	\( 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9} - 31559 q^{10} - 38751 q^{11} - 400950 q^{12} - 58915 q^{13} + 3453 q^{14} - 166698 q^{15} + 1655714 q^{16} - 64233 q^{17} + 131220 q^{18} - 1937236 q^{19} - 1065507 q^{20} + 1390527 q^{21} - 5386882 q^{22} - 1838574 q^{23} + 231093 q^{24} + 4565755 q^{25} - 839702 q^{26} - 11160261 q^{27} - 4471034 q^{28} + 15658544 q^{29} + 2556279 q^{30} - 14282802 q^{31} - 2205286 q^{32} + 3138831 q^{33} + 19005532 q^{34} - 8633300 q^{35} + 32476950 q^{36} + 7531195 q^{37} + 26649773 q^{38} + 4772115 q^{39} + 17775672 q^{40} + 18338245 q^{41} - 279693 q^{42} - 22480305 q^{43} - 80230922 q^{44} + 13502538 q^{45} - 83894107 q^{46} - 110397260 q^{47} - 134112834 q^{48} + 130653638 q^{49} + 65575693 q^{50} + 5202873 q^{51} + 177908014 q^{52} + 145498338 q^{53} - 10628820 q^{54} + 86448944 q^{55} + 354387888 q^{56} + 156916116 q^{57} + 115508368 q^{58} - 254464581 q^{59} + 86306067 q^{60} + 287595506 q^{61} + 819899030 q^{62} - 112632687 q^{63} + 822446413 q^{64} + 77238206 q^{65} + 436337442 q^{66} - 392860610 q^{67} + 167325073 q^{68} + 148924494 q^{69} - 424902116 q^{70} - 248960491 q^{71} - 18718533 q^{72} - 758406074 q^{73} - 923266846 q^{74} - 369826155 q^{75} - 2312747568 q^{76} - 878126795 q^{77} + 68015862 q^{78} - 1925801029 q^{79} - 1898919861 q^{80} + 903981141 q^{81} - 3249102191 q^{82} - 1650336307 q^{83} + 362153754 q^{84} - 2342480762 q^{85} - 3609864952 q^{86} - 1268342064 q^{87} - 5987792887 q^{88} - 574997526 q^{89} - 207058599 q^{90} - 4481387117 q^{91} - 5317166770 q^{92} + 1156906962 q^{93} - 5360726568 q^{94} - 2789231462 q^{95} + 178628166 q^{96} - 4651540898 q^{97} - 5566652976 q^{98} - 254245311 q^{99}+O(q^{100}) \) 21 * q + 20 * q^2 - 1701 * q^3 + 4950 * q^4 + 2058 * q^5 - 1620 * q^6 - 17167 * q^7 - 2853 * q^8 + 137781 * q^9 - 31559 * q^10 - 38751 * q^11 - 400950 * q^12 - 58915 * q^13 + 3453 * q^14 - 166698 * q^15 + 1655714 * q^16 - 64233 * q^17 + 131220 * q^18 - 1937236 * q^19 - 1065507 * q^20 + 1390527 * q^21 - 5386882 * q^22 - 1838574 * q^23 + 231093 * q^24 + 4565755 * q^25 - 839702 * q^26 - 11160261 * q^27 - 4471034 * q^28 + 15658544 * q^29 + 2556279 * q^30 - 14282802 * q^31 - 2205286 * q^32 + 3138831 * q^33 + 19005532 * q^34 - 8633300 * q^35 + 32476950 * q^36 + 7531195 * q^37 + 26649773 * q^38 + 4772115 * q^39 + 17775672 * q^40 + 18338245 * q^41 - 279693 * q^42 - 22480305 * q^43 - 80230922 * q^44 + 13502538 * q^45 - 83894107 * q^46 - 110397260 * q^47 - 134112834 * q^48 + 130653638 * q^49 + 65575693 * q^50 + 5202873 * q^51 + 177908014 * q^52 + 145498338 * q^53 - 10628820 * q^54 + 86448944 * q^55 + 354387888 * q^56 + 156916116 * q^57 + 115508368 * q^58 - 254464581 * q^59 + 86306067 * q^60 + 287595506 * q^61 + 819899030 * q^62 - 112632687 * q^63 + 822446413 * q^64 + 77238206 * q^65 + 436337442 * q^66 - 392860610 * q^67 + 167325073 * q^68 + 148924494 * q^69 - 424902116 * q^70 - 248960491 * q^71 - 18718533 * q^72 - 758406074 * q^73 - 923266846 * q^74 - 369826155 * q^75 - 2312747568 * q^76 - 878126795 * q^77 + 68015862 * q^78 - 1925801029 * q^79 - 1898919861 * q^80 + 903981141 * q^81 - 3249102191 * q^82 - 1650336307 * q^83 + 362153754 * q^84 - 2342480762 * q^85 - 3609864952 * q^86 - 1268342064 * q^87 - 5987792887 * q^88 - 574997526 * q^89 - 207058599 * q^90 - 4481387117 * q^91 - 5317166770 * q^92 + 1156906962 * q^93 - 5360726568 * q^94 - 2789231462 * q^95 + 178628166 * q^96 - 4651540898 * q^97 - 5566652976 * q^98 - 254245311 * 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 $

$2$	42.7873	1.89095	0.945474	−	0.325698i	$-0.105599\pi$
$2$	42.7873	1.89095	0.945474	+	0.325698i	$0.105599\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	1318.75	2.57568
$5$	−657.216	−0.470265	−0.235133	−	0.971963i	$-0.575552\pi$
$5$	−657.216	−0.470265	−0.235133	+	0.971963i	$0.575552\pi$
$6$	−3465.77	−1.09174
$7$	2359.02	0.371356	0.185678	−	0.982611i	$-0.440552\pi$
$7$	2359.02	0.371356	0.185678	+	0.982611i	$0.440552\pi$
$8$	34518.6	2.97953
$9$	6561.00	0.333333
$10$	−28120.5	−0.889247
$11$	−48603.9	−1.00093	−0.500466	−	0.865756i	$-0.666838\pi$
$11$	−48603.9	−1.00093	−0.500466	+	0.865756i	$0.666838\pi$
$12$	−106819.	−1.48707
$13$	−181586.	−1.76335	−0.881675	−	0.471858i	$-0.843584\pi$
$13$	−181586.	−1.76335	−0.881675	+	0.471858i	$0.843584\pi$
$14$	100936.	0.702216
$15$	53234.5	0.271508
$16$	801757.	3.05846
$17$	−33203.5	−0.0964193	−0.0482097	−	0.998837i	$-0.515352\pi$
$17$	−33203.5	−0.0964193	−0.0482097	+	0.998837i	$0.515352\pi$
$18$	280727.	0.630316
$19$	−533100.	−0.938465	−0.469232	−	0.883075i	$-0.655469\pi$
$19$	−533100.	−0.938465	−0.469232	+	0.883075i	$0.655469\pi$
$20$	−866703.	−1.21125
$21$	−191081.	−0.214403
$22$	−2.07963e6	−1.89271
$23$	711338.	0.530030	0.265015	−	0.964244i	$-0.414623\pi$
$23$	711338.	0.530030	0.265015	+	0.964244i	$0.414623\pi$
$24$	−2.79601e6	−1.72023
$25$	−1.52119e6	−0.778851
$26$	−7.76959e6	−3.33440
$27$	−531441.	−0.192450
$28$	3.11096e6	0.956496
$29$	351893.	0.0923888	0.0461944	−	0.998932i	$-0.485291\pi$
$29$	351893.	0.0923888	0.0461944	+	0.998932i	$0.485291\pi$
$30$	2.27776e6	0.513407
$31$	−1.44240e6	−0.280516	−0.140258	−	0.990115i	$-0.544793\pi$
$31$	−1.44240e6	−0.280516	−0.140258	+	0.990115i	$0.544793\pi$
$32$	1.66314e7	2.80385
$33$	3.93692e6	0.577888
$34$	−1.42069e6	−0.182324
$35$	−1.55039e6	−0.174636
$36$	8.65232e6	0.858561
$37$	1.69246e7	1.48461	0.742304	−	0.670063i	$-0.233733\pi$
$37$	1.69246e7	1.48461	0.742304	+	0.670063i	$0.233733\pi$
$38$	−2.28099e7	−1.77459
$39$	1.47085e7	1.01807
$40$	−2.26862e7	−1.40117
$41$	−2.49969e7	−1.38152	−0.690761	−	0.723083i	$-0.742724\pi$
$41$	−2.49969e7	−1.38152	−0.690761	+	0.723083i	$0.742724\pi$
$42$	−8.17583e6	−0.405424
$43$	1.83565e7	0.818806	0.409403	−	0.912354i	$-0.365737\pi$
$43$	1.83565e7	0.818806	0.409403	+	0.912354i	$0.365737\pi$
$44$	−6.40964e7	−2.57808
$45$	−4.31199e6	−0.156755
$46$	3.04362e7	1.00226
$47$	−1.25038e7	−0.373767	−0.186884	−	0.982382i	$-0.559839\pi$
$47$	−1.25038e7	−0.373767	−0.186884	+	0.982382i	$0.559839\pi$
$48$	−6.49423e7	−1.76580
$49$	−3.47886e7	−0.862094
$50$	−6.50877e7	−1.47277
$51$	2.68949e6	0.0556677
$52$	−2.39467e8	−4.54183
$53$	−7.15319e7	−1.24525	−0.622627	−	0.782519i	$-0.713935\pi$
$53$	−7.15319e7	−1.24525	−0.622627	+	0.782519i	$0.713935\pi$
$54$	−2.27389e7	−0.363913
$55$	3.19433e7	0.470703
$56$	8.14302e7	1.10647
$57$	4.31811e7	0.541823
$58$	1.50565e7	0.174702
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	7.02029e7	0.699318
$61$	−4.58629e7	−0.424109	−0.212054	−	0.977258i	$-0.568015\pi$
$61$	−4.58629e7	−0.424109	−0.212054	+	0.977258i	$0.568015\pi$
$62$	−6.17163e7	−0.530441
$63$	1.54775e7	0.123785
$64$	3.01114e8	2.24348
$65$	1.19341e8	0.829242
$66$	1.68450e8	1.09276
$67$	1.49604e8	0.906996	0.453498	−	0.891257i	$-0.350176\pi$
$67$	1.49604e8	0.906996	0.453498	+	0.891257i	$0.350176\pi$
$68$	−4.37871e7	−0.248346
$69$	−5.76184e7	−0.306013
$70$	−6.63368e7	−0.330228
$71$	−3.47372e8	−1.62231	−0.811153	−	0.584834i	$-0.801160\pi$
$71$	−3.47372e8	−1.62231	−0.811153	+	0.584834i	$0.801160\pi$
$72$	2.26477e8	0.993178
$73$	−8.25280e7	−0.340133	−0.170066	−	0.985433i	$-0.554398\pi$
$73$	−8.25280e7	−0.340133	−0.170066	+	0.985433i	$0.554398\pi$
$74$	7.24159e8	2.80732
$75$	1.23217e8	0.449670
$76$	−7.03026e8	−2.41719
$77$	−1.14658e8	−0.371702
$78$	6.29337e8	1.92512
$79$	−5.99311e8	−1.73113	−0.865566	−	0.500796i	$-0.833041\pi$
$79$	−5.99311e8	−1.73113	−0.865566	+	0.500796i	$0.833041\pi$
$80$	−5.26927e8	−1.43829
$81$	4.30467e7	0.111111
$82$	−1.06955e9	−2.61239
$83$	−2.20456e7	−0.0509883	−0.0254942	−	0.999675i	$-0.508116\pi$
$83$	−2.20456e7	−0.0509883	−0.0254942	+	0.999675i	$0.508116\pi$
$84$	−2.51988e8	−0.552233
$85$	2.18219e7	0.0453426
$86$	7.85423e8	1.54832
$87$	−2.85033e7	−0.0533407
$88$	−1.67774e9	−2.98231
$89$	1.41941e8	0.239802	0.119901	−	0.992786i	$-0.461742\pi$
$89$	1.41941e8	0.239802	0.119901	+	0.992786i	$0.461742\pi$
$90$	−1.84498e8	−0.296416
$91$	−4.28367e8	−0.654831
$92$	9.38077e8	1.36519
$93$	1.16834e8	0.161956
$94$	−5.35003e8	−0.706775
$95$	3.50362e8	0.441327
$96$	−1.34715e9	−1.61880
$97$	5.95410e8	0.682878	0.341439	−	0.939904i	$-0.389086\pi$
$97$	5.95410e8	0.682878	0.341439	+	0.939904i	$0.389086\pi$
$98$	−1.48851e9	−1.63018
$99$	−3.18890e8	−0.333644
$100$	−2.00607e9	−2.00607
$101$	−1.08108e9	−1.03374	−0.516872	−	0.856063i	$-0.672904\pi$
$101$	−1.08108e9	−1.03374	−0.516872	+	0.856063i	$0.672904\pi$
$102$	1.15076e8	0.105265
$103$	4.54417e8	0.397820	0.198910	−	0.980018i	$-0.436260\pi$
$103$	4.54417e8	0.397820	0.198910	+	0.980018i	$0.436260\pi$
$104$	−6.26811e9	−5.25396
$105$	1.25581e8	0.100826
$106$	−3.06065e9	−2.35471
$107$	2.27530e9	1.67807	0.839037	−	0.544074i	$-0.183119\pi$
$107$	2.27530e9	1.67807	0.839037	+	0.544074i	$0.183119\pi$
$108$	−7.00838e8	−0.495690
$109$	−7.26827e8	−0.493187	−0.246594	−	0.969119i	$-0.579311\pi$
$109$	−7.26827e8	−0.493187	−0.246594	+	0.969119i	$0.579311\pi$
$110$	1.36676e9	0.890075
$111$	−1.37090e9	−0.857139
$112$	1.89136e9	1.13578
$113$	1.98208e9	1.14358	0.571791	−	0.820399i	$-0.306249\pi$
$113$	1.98208e9	1.14358	0.571791	+	0.820399i	$0.306249\pi$
$114$	1.84760e9	1.02456
$115$	−4.67502e8	−0.249255
$116$	4.64059e8	0.237964
$117$	−1.19139e9	−0.587783
$118$	−5.18469e8	−0.246180
$119$	−7.83279e7	−0.0358059
$120$	1.83758e9	0.808966
$121$	4.39429e6	0.00186361
$122$	−1.96235e9	−0.801968
$123$	2.02475e9	0.797622
$124$	−1.90216e9	−0.722520
$125$	2.28338e9	0.836532
$126$	6.62242e8	0.234072
$127$	2.85044e9	0.972289	0.486145	−	0.873878i	$-0.338403\pi$
$127$	2.85044e9	0.972289	0.486145	+	0.873878i	$0.338403\pi$
$128$	4.36856e9	1.43845
$129$	−1.48687e9	−0.472738
$130$	5.10629e9	1.56805
$131$	2.79973e9	0.830605	0.415303	−	0.909683i	$-0.363676\pi$
$131$	2.79973e9	0.830605	0.415303	+	0.909683i	$0.363676\pi$
$132$	5.19181e9	1.48846
$133$	−1.25760e9	−0.348505
$134$	6.40113e9	1.71508
$135$	3.49271e8	0.0905026
$136$	−1.14614e9	−0.287285
$137$	4.85275e8	0.117692	0.0588458	−	0.998267i	$-0.481258\pi$
$137$	4.85275e8	0.117692	0.0588458	+	0.998267i	$0.481258\pi$
$138$	−2.46533e9	−0.578655
$139$	−2.60875e9	−0.592741	−0.296371	−	0.955073i	$-0.595776\pi$
$139$	−2.60875e9	−0.592741	−0.296371	+	0.955073i	$0.595776\pi$
$140$	−2.04457e9	−0.449807
$141$	1.01281e9	0.215795
$142$	−1.48631e10	−3.06770
$143$	8.82582e9	1.76499
$144$	5.26032e9	1.01949
$145$	−2.31269e8	−0.0434473
$146$	−3.53114e9	−0.643173
$147$	2.81788e9	0.497730
$148$	2.23194e10	3.82388
$149$	−2.02379e9	−0.336378	−0.168189	−	0.985755i	$-0.553792\pi$
$149$	−2.02379e9	−0.336378	−0.168189	+	0.985755i	$0.553792\pi$
$150$	5.27210e9	0.850302
$151$	1.20168e9	0.188101	0.0940507	−	0.995567i	$-0.470018\pi$
$151$	1.20168e9	0.188101	0.0940507	+	0.995567i	$0.470018\pi$
$152$	−1.84019e10	−2.79619
$153$	−2.17848e8	−0.0321398
$154$	−4.90589e9	−0.702870
$155$	9.47967e8	0.131917
$156$	1.93968e10	2.62223
$157$	5.66519e9	0.744160	0.372080	−	0.928201i	$-0.378645\pi$
$157$	5.66519e9	0.744160	0.372080	+	0.928201i	$0.378645\pi$
$158$	−2.56429e10	−3.27348
$159$	5.79408e9	0.718948
$160$	−1.09304e10	−1.31855
$161$	1.67806e9	0.196830
$162$	1.84185e9	0.210105
$163$	1.49740e10	1.66147	0.830736	−	0.556666i	$-0.187920\pi$
$163$	1.49740e10	1.66147	0.830736	+	0.556666i	$0.187920\pi$
$164$	−3.29646e10	−3.55836
$165$	−2.58740e9	−0.271761
$166$	−9.43271e8	−0.0964163
$167$	−1.24471e10	−1.23836	−0.619178	−	0.785251i	$-0.712534\pi$
$167$	−1.24471e10	−1.23836	−0.619178	+	0.785251i	$0.712534\pi$
$168$	−6.59584e9	−0.638820
$169$	2.23691e10	2.10940
$170$	9.33698e8	0.0857406
$171$	−3.49767e9	−0.312822
$172$	2.42076e10	2.10898
$173$	1.72619e10	1.46514	0.732571	−	0.680690i	$-0.238320\pi$
$173$	1.72619e10	1.46514	0.732571	+	0.680690i	$0.238320\pi$
$174$	−1.21958e9	−0.100865
$175$	−3.58853e9	−0.289231
$176$	−3.89685e10	−3.06131
$177$	9.81506e8	0.0751646
$178$	6.07328e9	0.453454
$179$	−1.00563e10	−0.732149	−0.366074	−	0.930586i	$-0.619298\pi$
$179$	−1.00563e10	−0.732149	−0.366074	+	0.930586i	$0.619298\pi$
$180$	−5.68644e9	−0.403751
$181$	−2.26777e10	−1.57053	−0.785263	−	0.619162i	$-0.787472\pi$
$181$	−2.26777e10	−1.57053	−0.785263	+	0.619162i	$0.787472\pi$
$182$	−1.83286e10	−1.23825
$183$	3.71490e9	0.244859
$184$	2.45544e10	1.57924
$185$	−1.11231e10	−0.698159
$186$	4.99902e9	0.306250
$187$	1.61382e9	0.0965091
$188$	−1.64894e10	−0.962706
$189$	−1.25368e9	−0.0714676
$190$	1.49910e10	0.834527
$191$	6.57044e9	0.357227	0.178614	−	0.983919i	$-0.442839\pi$
$191$	6.57044e9	0.357227	0.178614	+	0.983919i	$0.442839\pi$
$192$	−2.43903e10	−1.29527
$193$	−1.29375e10	−0.671185	−0.335592	−	0.942007i	$-0.608936\pi$
$193$	−1.29375e10	−0.671185	−0.335592	+	0.942007i	$0.608936\pi$
$194$	2.54760e10	1.29129
$195$	−9.66666e9	−0.478763
$196$	−4.58775e10	−2.22048
$197$	−2.00782e9	−0.0949788	−0.0474894	−	0.998872i	$-0.515122\pi$
$197$	−2.00782e9	−0.0949788	−0.0474894	+	0.998872i	$0.515122\pi$
$198$	−1.36444e10	−0.630903
$199$	3.70480e10	1.67466	0.837329	−	0.546700i	$-0.184116\pi$
$199$	3.70480e10	1.67466	0.837329	+	0.546700i	$0.184116\pi$
$200$	−5.25094e10	−2.32061
$201$	−1.21179e10	−0.523654
$202$	−4.62566e10	−1.95476
$203$	8.30123e8	0.0343092
$204$	3.54676e9	0.143382
$205$	1.64283e10	0.649682
$206$	1.94433e10	0.752257
$207$	4.66709e9	0.176677
$208$	−1.45588e11	−5.39313
$209$	2.59108e10	0.939339
$210$	5.37328e9	0.190657
$211$	−3.63173e10	−1.26137	−0.630685	−	0.776039i	$-0.717226\pi$
$211$	−3.63173e10	−1.26137	−0.630685	+	0.776039i	$0.717226\pi$
$212$	−9.43326e10	−3.20738
$213$	2.81372e10	0.936639
$214$	9.73538e10	3.17315
$215$	−1.20642e10	−0.385056
$216$	−1.83446e10	−0.573411
$217$	−3.40265e9	−0.104171
$218$	−3.10989e10	−0.932591
$219$	6.68476e9	0.196376
$220$	4.21252e10	1.21238
$221$	6.02931e9	0.170021
$222$	−5.86569e10	−1.62080
$223$	2.81624e8	0.00762603	0.00381301	−	0.999993i	$-0.498786\pi$
$223$	2.81624e8	0.00762603	0.00381301	+	0.999993i	$0.498786\pi$
$224$	3.92340e10	1.04123
$225$	−9.98055e9	−0.259617
$226$	8.48076e10	2.16245
$227$	−5.77345e10	−1.44318	−0.721588	−	0.692323i	$-0.756588\pi$
$227$	−5.77345e10	−1.44318	−0.721588	+	0.692323i	$0.756588\pi$
$228$	5.69451e10	1.39556
$229$	4.27956e10	1.02835	0.514173	−	0.857686i	$-0.328099\pi$
$229$	4.27956e10	1.02835	0.514173	+	0.857686i	$0.328099\pi$
$230$	−2.00031e10	−0.471328
$231$	9.28728e9	0.214602
$232$	1.21469e10	0.275276
$233$	4.80875e10	1.06888	0.534442	−	0.845205i	$-0.320522\pi$
$233$	4.80875e10	1.06888	0.534442	+	0.845205i	$0.320522\pi$
$234$	−5.09763e10	−1.11147
$235$	8.21769e9	0.175770
$236$	−1.59798e10	−0.335325
$237$	4.85442e10	0.999469
$238$	−3.35143e9	−0.0677071
$239$	2.30840e10	0.457636	0.228818	−	0.973469i	$-0.426514\pi$
$239$	2.30840e10	0.457636	0.228818	+	0.973469i	$0.426514\pi$
$240$	4.26811e10	0.830395
$241$	−9.44907e10	−1.80432	−0.902158	−	0.431406i	$-0.858017\pi$
$241$	−9.44907e10	−1.80432	−0.902158	+	0.431406i	$0.858017\pi$
$242$	1.88019e8	0.00352398
$243$	−3.48678e9	−0.0641500
$244$	−6.04817e10	−1.09237
$245$	2.28636e10	0.405413
$246$	8.66333e10	1.50826
$247$	9.68038e10	1.65484
$248$	−4.97896e10	−0.835807
$249$	1.78569e9	0.0294381
$250$	9.76994e10	1.58184
$251$	1.11571e11	1.77428	0.887138	−	0.461505i	$-0.152690\pi$
$251$	1.11571e11	1.77428	0.887138	+	0.461505i	$0.152690\pi$
$252$	2.04110e10	0.318832
$253$	−3.45738e10	−0.530524
$254$	1.21963e11	1.83855
$255$	−1.76757e9	−0.0261786
$256$	3.27483e10	0.476550
$257$	−6.39601e10	−0.914555	−0.457278	−	0.889324i	$-0.651175\pi$
$257$	−6.39601e10	−0.914555	−0.457278	+	0.889324i	$0.651175\pi$
$258$	−6.36193e10	−0.893923
$259$	3.99256e10	0.551319
$260$	1.57381e11	2.13586
$261$	2.30877e9	0.0307963
$262$	1.19793e11	1.57063
$263$	4.45994e10	0.574816	0.287408	−	0.957808i	$-0.407207\pi$
$263$	4.45994e10	0.574816	0.287408	+	0.957808i	$0.407207\pi$
$264$	1.35897e11	1.72184
$265$	4.70119e10	0.585600
$266$	−5.38091e10	−0.659004
$267$	−1.14972e10	−0.138450
$268$	1.97290e11	2.33613
$269$	8.21991e10	0.957154	0.478577	−	0.878046i	$-0.341153\pi$
$269$	8.21991e10	0.957154	0.478577	+	0.878046i	$0.341153\pi$
$270$	1.49444e10	0.171136
$271$	−6.98071e10	−0.786209	−0.393105	−	0.919494i	$-0.628599\pi$
$271$	−6.98071e10	−0.786209	−0.393105	+	0.919494i	$0.628599\pi$
$272$	−2.66211e10	−0.294894
$273$	3.46977e10	0.378067
$274$	2.07636e10	0.222549
$275$	7.39359e10	0.779576
$276$	−7.59842e10	−0.788193
$277$	5.80623e10	0.592564	0.296282	−	0.955100i	$-0.404253\pi$
$277$	5.80623e10	0.592564	0.296282	+	0.955100i	$0.404253\pi$
$278$	−1.11621e11	−1.12084
$279$	−9.46358e9	−0.0935053
$280$	−5.35172e10	−0.520334
$281$	−1.50634e10	−0.144127	−0.0720636	−	0.997400i	$-0.522958\pi$
$281$	−1.50634e10	−0.144127	−0.0720636	+	0.997400i	$0.522958\pi$
$282$	4.33352e10	0.408057
$283$	−3.90859e10	−0.362227	−0.181114	−	0.983462i	$-0.557970\pi$
$283$	−3.90859e10	−0.362227	−0.181114	+	0.983462i	$0.557970\pi$
$284$	−4.58097e11	−4.17855
$285$	−2.83793e10	−0.254800
$286$	3.77632e11	3.33751
$287$	−5.89681e10	−0.513037
$288$	1.09119e11	0.934617
$289$	−1.17485e11	−0.990703
$290$	−9.89539e9	−0.0821565
$291$	−4.82282e10	−0.394260
$292$	−1.08834e11	−0.876074
$293$	−2.26031e11	−1.79169	−0.895847	−	0.444363i	$-0.853430\pi$
$293$	−2.26031e11	−1.79169	−0.895847	+	0.444363i	$0.853430\pi$
$294$	1.20569e11	0.941182
$295$	7.96372e9	0.0612233
$296$	5.84215e11	4.42344
$297$	2.58301e10	0.192629
$298$	−8.65924e10	−0.636073
$299$	−1.29169e11	−0.934629
$300$	1.62492e11	1.15821
$301$	4.33033e10	0.304069
$302$	5.14165e10	0.355690
$303$	8.75678e10	0.596833
$304$	−4.27417e11	−2.87025
$305$	3.01418e10	0.199444
$306$	−9.32113e9	−0.0607746
$307$	−3.39886e10	−0.218379	−0.109189	−	0.994021i	$-0.534826\pi$
$307$	−3.39886e10	−0.218379	−0.109189	+	0.994021i	$0.534826\pi$
$308$	−1.51205e11	−0.957387
$309$	−3.68078e10	−0.229682
$310$	4.05609e10	0.249448
$311$	2.43508e11	1.47602	0.738008	−	0.674792i	$-0.235767\pi$
$311$	2.43508e11	1.47602	0.738008	+	0.674792i	$0.235767\pi$
$312$	5.07717e11	3.03337
$313$	2.06485e11	1.21602	0.608009	−	0.793930i	$-0.291968\pi$
$313$	2.06485e11	1.21602	0.608009	+	0.793930i	$0.291968\pi$
$314$	2.42398e11	1.40717
$315$	−1.01721e10	−0.0582120
$316$	−7.90340e11	−4.45884
$317$	−1.16249e11	−0.646581	−0.323291	−	0.946300i	$-0.604789\pi$
$317$	−1.16249e11	−0.646581	−0.323291	+	0.946300i	$0.604789\pi$
$318$	2.47913e11	1.35949
$319$	−1.71034e10	−0.0924749
$320$	−1.97897e11	−1.05503
$321$	−1.84299e11	−0.968837
$322$	7.17997e10	0.372196
$323$	1.77008e10	0.0904861
$324$	5.67678e10	0.286187
$325$	2.76228e11	1.37339
$326$	6.40696e11	3.14176
$327$	5.88730e10	0.284742
$328$	−8.62856e11	−4.11629
$329$	−2.94967e10	−0.138801
$330$	−1.10708e11	−0.513885
$331$	−3.14065e11	−1.43811	−0.719057	−	0.694951i	$-0.755426\pi$
$331$	−3.14065e11	−1.43811	−0.719057	+	0.694951i	$0.755426\pi$
$332$	−2.90726e10	−0.131330
$333$	1.11043e11	0.494869
$334$	−5.32579e11	−2.34167
$335$	−9.83218e10	−0.426529
$336$	−1.53200e11	−0.655742
$337$	−9.81657e10	−0.414596	−0.207298	−	0.978278i	$-0.566467\pi$
$337$	−9.81657e10	−0.414596	−0.207298	+	0.978278i	$0.566467\pi$
$338$	9.57114e11	3.98877
$339$	−1.60548e11	−0.660247
$340$	2.87776e10	0.116788
$341$	7.01062e10	0.280777
$342$	−1.49656e11	−0.591529
$343$	−1.77262e11	−0.691501
$344$	6.33640e11	2.43966
$345$	3.78677e10	0.143907
$346$	7.38587e11	2.77051
$347$	2.39488e11	0.886749	0.443374	−	0.896337i	$-0.353781\pi$
$347$	2.39488e11	0.886749	0.443374	+	0.896337i	$0.353781\pi$
$348$	−3.75887e10	−0.137389
$349$	3.28600e11	1.18564	0.592821	−	0.805334i	$-0.298014\pi$
$349$	3.28600e11	1.18564	0.592821	+	0.805334i	$0.298014\pi$
$350$	−1.53543e11	−0.546921
$351$	9.65025e10	0.339357
$352$	−8.08353e11	−2.80646
$353$	2.60516e11	0.892993	0.446497	−	0.894785i	$-0.352672\pi$
$353$	2.60516e11	0.892993	0.446497	+	0.894785i	$0.352672\pi$
$354$	4.19960e10	0.142132
$355$	2.28299e11	0.762914
$356$	1.87185e11	0.617655
$357$	6.34456e9	0.0206726
$358$	−4.30281e11	−1.38445
$359$	−9.74143e10	−0.309527	−0.154763	−	0.987952i	$-0.549461\pi$
$359$	−9.74143e10	−0.309527	−0.154763	+	0.987952i	$0.549461\pi$
$360$	−1.48844e11	−0.467057
$361$	−3.84916e10	−0.119284
$362$	−9.70316e11	−2.96978
$363$	−3.55937e8	−0.00107595
$364$	−5.64908e11	−1.68664
$365$	5.42387e10	0.159952
$366$	1.58950e11	0.463016
$367$	1.15391e11	0.332029	0.166014	−	0.986123i	$-0.446910\pi$
$367$	1.15391e11	0.332029	0.166014	+	0.986123i	$0.446910\pi$
$368$	5.70320e11	1.62108
$369$	−1.64004e11	−0.460508
$370$	−4.75929e11	−1.32018
$371$	−1.68745e11	−0.462433
$372$	1.54075e11	0.417147
$373$	3.61024e11	0.965709	0.482854	−	0.875701i	$-0.339600\pi$
$373$	3.61024e11	0.965709	0.482854	+	0.875701i	$0.339600\pi$
$374$	6.90510e10	0.182494
$375$	−1.84953e11	−0.482972
$376$	−4.31613e11	−1.11365
$377$	−6.38990e10	−0.162914
$378$	−5.36416e10	−0.135141
$379$	−5.42298e10	−0.135009	−0.0675044	−	0.997719i	$-0.521504\pi$
$379$	−5.42298e10	−0.135009	−0.0675044	+	0.997719i	$0.521504\pi$
$380$	4.62040e11	1.13672
$381$	−2.30886e11	−0.561352
$382$	2.81131e11	0.675498
$383$	3.26277e11	0.774805	0.387403	−	0.921911i	$-0.373372\pi$
$383$	3.26277e11	0.774805	0.387403	+	0.921911i	$0.373372\pi$
$384$	−3.53854e11	−0.830488
$385$	7.53549e10	0.174799
$386$	−5.53560e11	−1.26917
$387$	1.20437e11	0.272935
$388$	7.85197e11	1.75888
$389$	2.61998e11	0.580129	0.290065	−	0.957007i	$-0.406323\pi$
$389$	2.61998e11	0.580129	0.290065	+	0.957007i	$0.406323\pi$
$390$	−4.13610e11	−0.905316
$391$	−2.36189e10	−0.0511052
$392$	−1.20085e12	−2.56864
$393$	−2.26778e11	−0.479550
$394$	−8.59091e10	−0.179600
$395$	3.93876e11	0.814091
$396$	−4.20537e11	−0.859361
$397$	9.35404e10	0.188991	0.0944956	−	0.995525i	$-0.469876\pi$
$397$	9.35404e10	0.188991	0.0944956	+	0.995525i	$0.469876\pi$
$398$	1.58518e12	3.16669
$399$	1.01865e11	0.201209
$400$	−1.21963e12	−2.38208
$401$	5.87576e11	1.13479	0.567394	−	0.823447i	$-0.307952\pi$
$401$	5.87576e11	1.13479	0.567394	+	0.823447i	$0.307952\pi$
$402$	−5.18491e11	−0.990203
$403$	2.61920e11	0.494648
$404$	−1.42568e12	−2.66260
$405$	−2.82910e10	−0.0522517
$406$	3.55187e10	0.0648769
$407$	−8.22604e11	−1.48599
$408$	9.28373e10	0.165864
$409$	−5.70374e11	−1.00787	−0.503935	−	0.863742i	$-0.668115\pi$
$409$	−5.70374e11	−1.00787	−0.503935	+	0.863742i	$0.668115\pi$
$410$	7.02923e11	1.22851
$411$	−3.93073e10	−0.0679493
$412$	5.99262e11	1.02466
$413$	−2.85851e10	−0.0483465
$414$	1.99692e11	0.334087
$415$	1.44887e10	0.0239780
$416$	−3.02004e12	−4.94417
$417$	2.11308e11	0.342219
$418$	1.10865e12	1.77624
$419$	1.04647e11	0.165868	0.0829338	−	0.996555i	$-0.473571\pi$
$419$	1.04647e11	0.165868	0.0829338	+	0.996555i	$0.473571\pi$
$420$	1.65610e11	0.259696
$421$	−6.55144e11	−1.01641	−0.508203	−	0.861237i	$-0.669690\pi$
$421$	−6.55144e11	−1.01641	−0.508203	+	0.861237i	$0.669690\pi$
$422$	−1.55392e12	−2.38518
$423$	−8.20374e10	−0.124589
$424$	−2.46918e12	−3.71028
$425$	5.05090e10	0.0750962
$426$	1.20391e12	1.77114
$427$	−1.08192e11	−0.157496
$428$	3.00055e12	4.32219
$429$	−7.14891e11	−1.01902
$430$	−5.16192e11	−0.728121
$431$	−4.83798e11	−0.675331	−0.337666	−	0.941266i	$-0.609637\pi$
$431$	−4.83798e11	−0.675331	−0.337666	+	0.941266i	$0.609637\pi$
$432$	−4.26086e11	−0.588601
$433$	1.32672e11	0.181378	0.0906888	−	0.995879i	$-0.471093\pi$
$433$	1.32672e11	0.181378	0.0906888	+	0.995879i	$0.471093\pi$
$434$	−1.45590e11	−0.196983
$435$	1.87328e10	0.0250843
$436$	−9.58503e11	−1.27029
$437$	−3.79215e11	−0.497415
$438$	2.86023e11	0.371336
$439$	−1.12774e12	−1.44917	−0.724583	−	0.689188i	$-0.757968\pi$
$439$	−1.12774e12	−1.44917	−0.724583	+	0.689188i	$0.757968\pi$
$440$	1.10264e12	1.40248
$441$	−2.28248e11	−0.287365
$442$	2.57978e11	0.321501
$443$	8.14597e10	0.100491	0.0502454	−	0.998737i	$-0.484000\pi$
$443$	8.14597e10	0.100491	0.0502454	+	0.998737i	$0.484000\pi$
$444$	−1.80787e12	−2.20772
$445$	−9.32860e10	−0.112771
$446$	1.20499e10	0.0144204
$447$	1.63927e11	0.194208
$448$	7.10336e11	0.833130
$449$	−1.45273e12	−1.68685	−0.843427	−	0.537244i	$-0.819465\pi$
$449$	−1.45273e12	−1.68685	−0.843427	+	0.537244i	$0.819465\pi$
$450$	−4.27040e11	−0.490922
$451$	1.21495e12	1.38281
$452$	2.61386e12	2.94550
$453$	−9.73360e10	−0.108600
$454$	−2.47030e12	−2.72897
$455$	2.81529e11	0.307944
$456$	1.49055e12	1.61438
$457$	2.42592e11	0.260168	0.130084	−	0.991503i	$-0.458475\pi$
$457$	2.42592e11	0.260168	0.130084	+	0.991503i	$0.458475\pi$
$458$	1.83111e12	1.94455
$459$	1.76457e10	0.0185559
$460$	−6.16519e11	−0.642001
$461$	−4.62835e11	−0.477278	−0.238639	−	0.971108i	$-0.576701\pi$
$461$	−4.62835e11	−0.477278	−0.238639	+	0.971108i	$0.576701\pi$
$462$	3.97377e11	0.405802
$463$	−1.32143e12	−1.33638	−0.668190	−	0.743991i	$-0.732930\pi$
$463$	−1.32143e12	−1.33638	−0.668190	+	0.743991i	$0.732930\pi$
$464$	2.82132e11	0.282567
$465$	−7.67853e10	−0.0761622
$466$	2.05753e12	2.02120
$467$	2.80898e11	0.273290	0.136645	−	0.990620i	$-0.456368\pi$
$467$	2.80898e11	0.273290	0.136645	+	0.990620i	$0.456368\pi$
$468$	−1.57114e12	−1.51394
$469$	3.52918e11	0.336819
$470$	3.51612e11	0.332371
$471$	−4.58881e11	−0.429641
$472$	−4.18274e11	−0.387902
$473$	−8.92197e11	−0.819569
$474$	2.07707e12	1.88994
$475$	8.10949e11	0.730924
$476$	−1.03295e11	−0.0922247
$477$	−4.69321e11	−0.415085
$478$	9.87701e11	0.865366
$479$	1.53003e12	1.32797	0.663987	−	0.747744i	$-0.268863\pi$
$479$	1.53003e12	1.32797	0.663987	+	0.747744i	$0.268863\pi$
$480$	8.85366e11	0.761267
$481$	−3.07329e12	−2.61788
$482$	−4.04300e12	−3.41187
$483$	−1.35923e11	−0.113640
$484$	5.79496e9	0.00480006
$485$	−3.91313e11	−0.321134
$486$	−1.49190e11	−0.121304
$487$	−1.70582e12	−1.37421	−0.687106	−	0.726558i	$-0.741119\pi$
$487$	−1.70582e12	−1.37421	−0.687106	+	0.726558i	$0.741119\pi$
$488$	−1.58312e12	−1.26365
$489$	−1.21289e12	−0.959252
$490$	9.78272e11	0.766615
$491$	2.21766e12	1.72198	0.860991	−	0.508621i	$-0.169845\pi$
$491$	2.21766e12	1.72198	0.860991	+	0.508621i	$0.169845\pi$
$492$	2.67013e12	2.05442
$493$	−1.16841e10	−0.00890807
$494$	4.14197e12	3.12922
$495$	2.09580e11	0.156901
$496$	−1.15645e12	−0.857946
$497$	−8.19460e11	−0.602454
$498$	7.64050e10	0.0556660
$499$	1.86226e12	1.34458	0.672291	−	0.740287i	$-0.265310\pi$
$499$	1.86226e12	1.34458	0.672291	+	0.740287i	$0.265310\pi$
$500$	3.01120e12	2.15464
$501$	1.00822e12	0.714965
$502$	4.77383e12	3.35506
$503$	1.07591e11	0.0749408	0.0374704	−	0.999298i	$-0.488070\pi$
$503$	1.07591e11	0.0749408	0.0374704	+	0.999298i	$0.488070\pi$
$504$	5.34263e11	0.368823
$505$	7.10505e11	0.486134
$506$	−1.47932e12	−1.00319
$507$	−1.81190e12	−1.21786
$508$	3.75902e12	2.50431
$509$	−1.93516e12	−1.27787	−0.638934	−	0.769262i	$-0.720624\pi$
$509$	−1.93516e12	−1.27787	−0.638934	+	0.769262i	$0.720624\pi$
$510$	−7.56295e10	−0.0495023
$511$	−1.94685e11	−0.126310
$512$	−8.35496e11	−0.537316
$513$	2.83311e11	0.180608
$514$	−2.73668e12	−1.72938
$515$	−2.98650e11	−0.187081
$516$	−1.96081e12	−1.21762
$517$	6.07734e11	0.374116
$518$	1.70831e12	1.04251
$519$	−1.39821e12	−0.845900
$520$	4.11950e12	2.47075
$521$	−2.42521e12	−1.44205	−0.721024	−	0.692910i	$-0.756328\pi$
$521$	−2.42521e12	−1.44205	−0.721024	+	0.692910i	$0.756328\pi$
$522$	9.87859e10	0.0582342
$523$	5.59223e11	0.326834	0.163417	−	0.986557i	$-0.447748\pi$
$523$	5.59223e11	0.326834	0.163417	+	0.986557i	$0.447748\pi$
$524$	3.69214e12	2.13938
$525$	2.90671e11	0.166988
$526$	1.90829e12	1.08695
$527$	4.78927e10	0.0270472
$528$	3.15645e12	1.76745
$529$	−1.29515e12	−0.719068
$530$	2.01151e12	1.10734
$531$	−7.95020e10	−0.0433963
$532$	−1.65845e12	−0.897638
$533$	4.53909e12	2.43611
$534$	−4.91935e11	−0.261802
$535$	−1.49536e12	−0.789140
$536$	5.16411e12	2.70242
$537$	8.14560e11	0.422706
$538$	3.51707e12	1.80993
$539$	1.69086e12	0.862897
$540$	4.60601e11	0.233106
$541$	1.46118e12	0.733360	0.366680	−	0.930347i	$-0.380494\pi$
$541$	1.46118e12	0.733360	0.366680	+	0.930347i	$0.380494\pi$
$542$	−2.98686e12	−1.48668
$543$	1.83689e12	0.906744
$544$	−5.52222e11	−0.270345
$545$	4.77682e11	0.231929
$546$	1.48462e12	0.714905
$547$	−2.60707e12	−1.24512	−0.622559	−	0.782573i	$-0.713907\pi$
$547$	−2.60707e12	−1.24512	−0.622559	+	0.782573i	$0.713907\pi$
$548$	6.39957e11	0.303136
$549$	−3.00907e11	−0.141370
$550$	3.16352e12	1.47414
$551$	−1.87594e11	−0.0867037
$552$	−1.98891e12	−0.911776
$553$	−1.41379e12	−0.642867
$554$	2.48433e12	1.12051
$555$	9.00974e11	0.403082
$556$	−3.44028e12	−1.52671
$557$	−5.27218e11	−0.232082	−0.116041	−	0.993244i	$-0.537020\pi$
$557$	−5.27218e11	−0.232082	−0.116041	+	0.993244i	$0.537020\pi$
$558$	−4.04920e11	−0.176814
$559$	−3.33329e12	−1.44384
$560$	−1.24303e12	−0.534117
$561$	−1.30720e11	−0.0557196
$562$	−6.44524e11	−0.272537
$563$	−3.32450e12	−1.39457	−0.697283	−	0.716796i	$-0.745608\pi$
$563$	−3.32450e12	−1.39457	−0.697283	+	0.716796i	$0.745608\pi$
$564$	1.33564e12	0.555819
$565$	−1.30265e12	−0.537787
$566$	−1.67238e12	−0.684953
$567$	1.01548e11	0.0412618
$568$	−1.19908e13	−4.83372
$569$	−3.99544e12	−1.59794	−0.798969	−	0.601373i	$-0.794621\pi$
$569$	−3.99544e12	−1.59794	−0.798969	+	0.601373i	$0.794621\pi$
$570$	−1.21427e12	−0.481814
$571$	−4.25250e12	−1.67410	−0.837052	−	0.547124i	$-0.815723\pi$
$571$	−4.25250e12	−1.67410	−0.837052	+	0.547124i	$0.815723\pi$
$572$	1.16390e13	4.54606
$573$	−5.32206e11	−0.206245
$574$	−2.52309e12	−0.970127
$575$	−1.08208e12	−0.412814
$576$	1.97561e12	0.747826
$577$	−4.65488e12	−1.74831	−0.874153	−	0.485651i	$-0.838582\pi$
$577$	−4.65488e12	−1.74831	−0.874153	+	0.485651i	$0.838582\pi$
$578$	−5.02688e12	−1.87337
$579$	1.04794e12	0.387509
$580$	−3.04987e11	−0.111906
$581$	−5.20061e10	−0.0189348
$582$	−2.06355e12	−0.745525
$583$	3.47673e12	1.24641
$584$	−2.84875e12	−1.01344
$585$	7.82999e11	0.276414
$586$	−9.67125e12	−3.38800
$587$	−2.61501e12	−0.909079	−0.454539	−	0.890727i	$-0.650196\pi$
$587$	−2.61501e12	−0.909079	−0.454539	+	0.890727i	$0.650196\pi$
$588$	3.71608e12	1.28200
$589$	7.68943e11	0.263254
$590$	3.40746e11	0.115770
$591$	1.62633e11	0.0548360
$592$	1.35694e13	4.54061
$593$	−3.34176e10	−0.0110976	−0.00554881	−	0.999985i	$-0.501766\pi$
$593$	−3.34176e10	−0.0110976	−0.00554881	+	0.999985i	$0.501766\pi$
$594$	1.10520e12	0.364252
$595$	5.14783e10	0.0168383
$596$	−2.66887e12	−0.866402
$597$	−3.00089e12	−0.966864
$598$	−5.52680e12	−1.76733
$599$	−4.55497e12	−1.44566	−0.722828	−	0.691028i	$-0.757158\pi$
$599$	−4.55497e12	−1.44566	−0.722828	+	0.691028i	$0.757158\pi$
$600$	4.25327e12	1.33981
$601$	2.89301e12	0.904512	0.452256	−	0.891888i	$-0.350619\pi$
$601$	2.89301e12	0.904512	0.452256	+	0.891888i	$0.350619\pi$
$602$	1.85283e12	0.574978
$603$	9.81549e11	0.302332
$604$	1.58471e12	0.484490
$605$	−2.88799e9	−0.000876389 0
$606$	3.74679e12	1.12858
$607$	−4.67485e12	−1.39771	−0.698857	−	0.715262i	$-0.746308\pi$
$607$	−4.67485e12	−1.39771	−0.698857	+	0.715262i	$0.746308\pi$
$608$	−8.86623e12	−2.63132
$609$	−6.72400e10	−0.0198084
$610$	1.28969e12	0.377137
$611$	2.27052e12	0.659083
$612$	−2.87287e11	−0.0827818
$613$	1.39611e12	0.399344	0.199672	−	0.979863i	$-0.436012\pi$
$613$	1.39611e12	0.399344	0.199672	+	0.979863i	$0.436012\pi$
$614$	−1.45428e12	−0.412943
$615$	−1.33069e12	−0.375094
$616$	−3.95783e12	−1.10750
$617$	−8.49636e11	−0.236020	−0.118010	−	0.993012i	$-0.537652\pi$
$617$	−8.49636e11	−0.236020	−0.118010	+	0.993012i	$0.537652\pi$
$618$	−1.57490e12	−0.434316
$619$	−6.22814e12	−1.70510	−0.852551	−	0.522644i	$-0.824946\pi$
$619$	−6.22814e12	−1.70510	−0.852551	+	0.522644i	$0.824946\pi$
$620$	1.25013e12	0.339776
$621$	−3.78034e11	−0.102004
$622$	1.04190e13	2.79107
$623$	3.34843e11	0.0890522
$624$	1.17926e13	3.11373
$625$	1.47041e12	0.385459
$626$	8.83495e12	2.29943
$627$	−2.09877e12	−0.542327
$628$	7.47097e12	1.91672
$629$	−5.61958e11	−0.143145
$630$	−4.35236e11	−0.110076
$631$	−6.02955e11	−0.151409	−0.0757047	−	0.997130i	$-0.524121\pi$
$631$	−6.02955e11	−0.151409	−0.0757047	+	0.997130i	$0.524121\pi$
$632$	−2.06874e13	−5.15796
$633$	2.94170e12	0.728252
$634$	−4.97398e12	−1.22265
$635$	−1.87336e12	−0.457234
$636$	7.64094e12	1.85178
$637$	6.31714e12	1.52017
$638$	−7.31807e11	−0.174865
$639$	−2.27911e12	−0.540769
$640$	−2.87109e12	−0.676452
$641$	6.15869e12	1.44088	0.720439	−	0.693518i	$-0.243940\pi$
$641$	6.15869e12	1.44088	0.720439	+	0.693518i	$0.243940\pi$
$642$	−7.88566e12	−1.83202
$643$	−3.26746e12	−0.753808	−0.376904	−	0.926252i	$-0.623011\pi$
$643$	−3.26746e12	−0.753808	−0.376904	+	0.926252i	$0.623011\pi$
$644$	2.21294e12	0.506972
$645$	9.77197e11	0.222312
$646$	7.57369e11	0.171104
$647$	3.35452e12	0.752595	0.376298	−	0.926499i	$-0.377197\pi$
$647$	3.35452e12	0.752595	0.376298	+	0.926499i	$0.377197\pi$
$648$	1.48591e12	0.331059
$649$	5.88951e11	0.130310
$650$	1.18190e13	2.59700
$651$	2.75615e11	0.0601434
$652$	1.97469e13	4.27943
$653$	1.38240e12	0.297526	0.148763	−	0.988873i	$-0.452471\pi$
$653$	1.38240e12	0.297526	0.148763	+	0.988873i	$0.452471\pi$
$654$	2.51901e12	0.538432
$655$	−1.84002e12	−0.390605
$656$	−2.00414e13	−4.22533
$657$	−5.41466e11	−0.113378
$658$	−1.26208e12	−0.262465
$659$	7.62869e12	1.57567	0.787835	−	0.615886i	$-0.211202\pi$
$659$	7.62869e12	1.57567	0.787835	+	0.615886i	$0.211202\pi$
$660$	−3.41214e12	−0.699969
$661$	5.38101e12	1.09637	0.548185	−	0.836357i	$-0.315319\pi$
$661$	5.38101e12	1.09637	0.548185	+	0.836357i	$0.315319\pi$
$662$	−1.34380e13	−2.71940
$663$	−4.88374e11	−0.0981616
$664$	−7.60984e11	−0.151921
$665$	8.26512e11	0.163890
$666$	4.75121e12	0.935772
$667$	2.50315e11	0.0489689
$668$	−1.64147e13	−3.18961
$669$	−2.28116e10	−0.00440289
$670$	−4.20692e12	−0.806543
$671$	2.22912e12	0.424504
$672$	−3.17795e12	−0.601153
$673$	−2.15151e12	−0.404275	−0.202137	−	0.979357i	$-0.564789\pi$
$673$	−2.15151e12	−0.404275	−0.202137	+	0.979357i	$0.564789\pi$
$674$	−4.20024e12	−0.783980
$675$	8.08424e11	0.149890
$676$	2.94993e13	5.43315
$677$	−7.41756e12	−1.35710	−0.678550	−	0.734554i	$-0.737391\pi$
$677$	−7.41756e12	−1.35710	−0.678550	+	0.734554i	$0.737391\pi$
$678$	−6.86941e12	−1.24849
$679$	1.40459e12	0.253591
$680$	7.53260e11	0.135100
$681$	4.67650e12	0.833218
$682$	2.99965e12	0.530935
$683$	1.05646e12	0.185763	0.0928817	−	0.995677i	$-0.470392\pi$
$683$	1.05646e12	0.185763	0.0928817	+	0.995677i	$0.470392\pi$
$684$	−4.61255e12	−0.805729
$685$	−3.18930e11	−0.0553463
$686$	−7.58456e12	−1.30759
$687$	−3.46644e12	−0.593716
$688$	1.47174e13	2.50428
$689$	1.29892e13	2.19582
$690$	1.62025e12	0.272121
$691$	1.62209e12	0.270660	0.135330	−	0.990801i	$-0.456791\pi$
$691$	1.62209e12	0.270660	0.135330	+	0.990801i	$0.456791\pi$
$692$	2.27641e13	3.77374
$693$	−7.52270e11	−0.123901
$694$	1.02470e13	1.67680
$695$	1.71451e12	0.278746
$696$	−9.83895e11	−0.158930
$697$	8.29984e11	0.133205
$698$	1.40599e13	2.24199
$699$	−3.89509e12	−0.617121
$700$	−4.73237e12	−0.744968
$701$	−3.66991e12	−0.574016	−0.287008	−	0.957928i	$-0.592661\pi$
$701$	−3.66991e12	−0.574016	−0.287008	+	0.957928i	$0.592661\pi$
$702$	4.12908e12	0.641706
$703$	−9.02253e12	−1.39325
$704$	−1.46353e13	−2.24557
$705$	−6.65633e11	−0.101481
$706$	1.11468e13	1.68860
$707$	−2.55030e12	−0.383888
$708$	1.29436e12	0.193600
$709$	−5.84825e12	−0.869196	−0.434598	−	0.900625i	$-0.643109\pi$
$709$	−5.84825e12	−0.869196	−0.434598	+	0.900625i	$0.643109\pi$
$710$	9.76827e12	1.44263
$711$	−3.93208e12	−0.577044
$712$	4.89961e12	0.714499
$713$	−1.02603e12	−0.148682
$714$	2.71466e11	0.0390907
$715$	−5.80046e12	−0.830014
$716$	−1.32617e13	−1.88578
$717$	−1.86980e12	−0.264216
$718$	−4.16809e12	−0.585298
$719$	−9.33619e12	−1.30284	−0.651418	−	0.758719i	$-0.725826\pi$
$719$	−9.33619e12	−1.30284	−0.651418	+	0.758719i	$0.725826\pi$
$720$	−3.45717e12	−0.479429
$721$	1.07198e12	0.147733
$722$	−1.64695e12	−0.225560
$723$	7.65375e12	1.04172
$724$	−2.99062e13	−4.04518
$725$	−5.35297e11	−0.0719571
$726$	−1.52296e10	−0.00203457
$727$	−4.94586e12	−0.656655	−0.328328	−	0.944564i	$-0.606485\pi$
$727$	−4.94586e12	−0.656655	−0.328328	+	0.944564i	$0.606485\pi$
$728$	−1.47866e13	−1.95109
$729$	2.82430e11	0.0370370
$730$	2.32072e12	0.302462
$731$	−6.09499e11	−0.0789487
$732$	4.89902e12	0.630680
$733$	−1.46192e10	−0.00187049	−0.000935244	−	1.00000i	$-0.500298\pi$
$733$	−1.46192e10	−0.00187049	−0.000935244		1.00000i	$0.500298\pi$
$734$	4.93728e12	0.627849
$735$	−1.85195e12	−0.234065
$736$	1.18306e13	1.48613
$737$	−7.27132e12	−0.907841
$738$	−7.01730e12	−0.870796
$739$	2.91723e12	0.359808	0.179904	−	0.983684i	$-0.442421\pi$
$739$	2.91723e12	0.359808	0.179904	+	0.983684i	$0.442421\pi$
$740$	−1.46686e13	−1.79824
$741$	−7.84111e12	−0.955423
$742$	−7.22015e12	−0.874437
$743$	−3.54178e12	−0.426356	−0.213178	−	0.977013i	$-0.568381\pi$
$743$	−3.54178e12	−0.426356	−0.213178	+	0.977013i	$0.568381\pi$
$744$	4.03296e12	0.482553
$745$	1.33007e12	0.158187
$746$	1.54472e13	1.82610
$747$	−1.44641e11	−0.0169961
$748$	2.12823e12	0.248577
$749$	5.36748e12	0.623164
$750$	−7.91365e12	−0.913274
$751$	7.51614e11	0.0862214	0.0431107	−	0.999070i	$-0.486273\pi$
$751$	7.51614e11	0.0862214	0.0431107	+	0.999070i	$0.486273\pi$
$752$	−1.00250e13	−1.14315
$753$	−9.03728e12	−1.02438
$754$	−2.73406e12	−0.308061
$755$	−7.89762e11	−0.0884575
$756$	−1.65329e12	−0.184078
$757$	1.78036e13	1.97050	0.985250	−	0.171123i	$-0.0547394\pi$
$757$	1.78036e13	1.97050	0.985250	+	0.171123i	$0.0547394\pi$
$758$	−2.32035e12	−0.255294
$759$	2.80048e12	0.306298
$760$	1.20940e13	1.31495
$761$	−1.69702e12	−0.183424	−0.0917120	−	0.995786i	$-0.529234\pi$
$761$	−1.69702e12	−0.183424	−0.0917120	+	0.995786i	$0.529234\pi$
$762$	−9.87897e12	−1.06149
$763$	−1.71460e12	−0.183148
$764$	8.66477e12	0.920104
$765$	1.43173e11	0.0151142
$766$	1.39605e13	1.46512
$767$	2.20035e12	0.229569
$768$	−2.65261e12	−0.275136
$769$	6.68588e12	0.689430	0.344715	−	0.938707i	$-0.387976\pi$
$769$	6.68588e12	0.689430	0.344715	+	0.938707i	$0.387976\pi$
$770$	3.22423e12	0.330535
$771$	5.18077e12	0.528019
$772$	−1.70613e13	−1.72876
$773$	1.82641e13	1.83989	0.919944	−	0.392051i	$-0.128234\pi$
$773$	1.82641e13	1.83989	0.919944	+	0.392051i	$0.128234\pi$
$774$	5.15316e12	0.516106
$775$	2.19417e12	0.218480
$776$	2.05527e13	2.03466
$777$	−3.23397e12	−0.318304
$778$	1.12102e13	1.09699
$779$	1.33258e13	1.29651
$780$	−1.27479e13	−1.23314
$781$	1.68837e13	1.62382
$782$	−1.01059e12	−0.0966372
$783$	−1.87010e11	−0.0177802
$784$	−2.78920e13	−2.63668
$785$	−3.72325e12	−0.349953
$786$	−9.70320e12	−0.906804
$787$	−1.99057e13	−1.84965	−0.924827	−	0.380388i	$-0.875790\pi$
$787$	−1.99057e13	−1.84965	−0.924827	+	0.380388i	$0.875790\pi$
$788$	−2.64781e12	−0.244635
$789$	−3.61255e12	−0.331870
$790$	1.68529e13	1.53940
$791$	4.67576e12	0.424676
$792$	−1.10076e13	−0.994103
$793$	8.32808e12	0.747852
$794$	4.00234e12	0.357373
$795$	−3.80796e12	−0.338096
$796$	4.88570e13	4.31339
$797$	1.37013e13	1.20282	0.601408	−	0.798942i	$-0.294607\pi$
$797$	1.37013e13	1.20282	0.601408	+	0.798942i	$0.294607\pi$
$798$	4.35854e12	0.380476
$799$	4.15170e11	0.0360384
$800$	−2.52996e13	−2.18378
$801$	9.31277e11	0.0799342
$802$	2.51408e13	2.14582
$803$	4.01118e12	0.340449
$804$	−1.59805e13	−1.34877
$805$	−1.10285e12	−0.0925624
$806$	1.12068e13	0.935353
$807$	−6.65813e12	−0.552613
$808$	−3.73175e13	−3.08008
$809$	−6.34089e12	−0.520453	−0.260227	−	0.965548i	$-0.583797\pi$
$809$	−6.34089e12	−0.520453	−0.260227	+	0.965548i	$0.583797\pi$
$810$	−1.21049e12	−0.0988052
$811$	1.11051e13	0.901424	0.450712	−	0.892669i	$-0.351170\pi$
$811$	1.11051e13	0.901424	0.450712	+	0.892669i	$0.351170\pi$
$812$	1.09472e12	0.0883696
$813$	5.65438e12	0.453918
$814$	−3.51970e13	−2.80993
$815$	−9.84114e12	−0.781333
$816$	2.15631e12	0.170257
$817$	−9.78584e12	−0.768421
$818$	−2.44047e13	−1.90583
$819$	−2.81051e12	−0.218277
$820$	2.16648e13	1.67337
$821$	1.75847e13	1.35080	0.675399	−	0.737452i	$-0.263971\pi$
$821$	1.75847e13	1.35080	0.675399	+	0.737452i	$0.263971\pi$
$822$	−1.68185e12	−0.128489
$823$	−2.42604e13	−1.84331	−0.921657	−	0.388006i	$-0.873164\pi$
$823$	−2.42604e13	−1.84331	−0.921657	+	0.388006i	$0.873164\pi$
$824$	1.56858e13	1.18532
$825$	−5.98881e12	−0.450088
$826$	−1.22308e12	−0.0914207
$827$	4.94281e12	0.367450	0.183725	−	0.982978i	$-0.441184\pi$
$827$	4.94281e12	0.367450	0.183725	+	0.982978i	$0.441184\pi$
$828$	6.15472e12	0.455063
$829$	−1.61075e13	−1.18450	−0.592248	−	0.805756i	$-0.701760\pi$
$829$	−1.61075e13	−1.18450	−0.592248	+	0.805756i	$0.701760\pi$
$830$	6.19933e11	0.0453412
$831$	−4.70305e12	−0.342117
$832$	−5.46783e13	−3.95603
$833$	1.15510e12	0.0831225
$834$	9.04131e12	0.647119
$835$	8.18045e12	0.582355
$836$	3.41698e13	2.41944
$837$	7.66550e11	0.0539853
$838$	4.47754e12	0.313647
$839$	−1.48792e13	−1.03669	−0.518347	−	0.855170i	$-0.673452\pi$
$839$	−1.48792e13	−1.03669	−0.518347	+	0.855170i	$0.673452\pi$
$840$	4.33489e12	0.300415
$841$	−1.43833e13	−0.991464
$842$	−2.80318e13	−1.92197
$843$	1.22014e12	0.0832119
$844$	−4.78934e13	−3.24889
$845$	−1.47013e13	−0.991978
$846$	−3.51016e12	−0.235592
$847$	1.03662e10	0.000692062 0
$848$	−5.73511e13	−3.80856
$849$	3.16596e12	0.209132
$850$	2.16114e12	0.142003
$851$	1.20391e13	0.786887
$852$	3.71059e13	2.41248
$853$	8.77378e12	0.567435	0.283717	−	0.958908i	$-0.408432\pi$
$853$	8.77378e12	0.567435	0.283717	+	0.958908i	$0.408432\pi$
$854$	−4.62922e12	−0.297816
$855$	2.29872e12	0.147109
$856$	7.85401e13	4.99988
$857$	−1.82612e13	−1.15642	−0.578211	−	0.815887i	$-0.696249\pi$
$857$	−1.82612e13	−1.15642	−0.578211	+	0.815887i	$0.696249\pi$
$858$	−3.05882e13	−1.92691
$859$	2.07770e13	1.30201	0.651003	−	0.759076i	$-0.274349\pi$
$859$	2.07770e13	1.30201	0.651003	+	0.759076i	$0.274349\pi$
$860$	−1.59096e13	−0.991782
$861$	4.77642e12	0.296202
$862$	−2.07004e13	−1.27702
$863$	2.60244e13	1.59710	0.798551	−	0.601927i	$-0.205600\pi$
$863$	2.60244e13	1.59710	0.798551	+	0.601927i	$0.205600\pi$
$864$	−8.83863e12	−0.539601
$865$	−1.13448e13	−0.689006
$866$	5.67667e12	0.342976
$867$	9.51632e12	0.571983
$868$	−4.48724e12	−0.268312
$869$	2.91288e13	1.73274
$870$	8.01526e11	0.0474331
$871$	−2.71660e13	−1.59935
$872$	−2.50891e13	−1.46947
$873$	3.90649e12	0.227626
$874$	−1.62256e13	−0.940585
$875$	5.38654e12	0.310651
$876$	8.81553e12	0.505801
$877$	−2.19715e13	−1.25419	−0.627093	−	0.778944i	$-0.715755\pi$
$877$	−2.19715e13	−1.25419	−0.627093	+	0.778944i	$0.715755\pi$
$878$	−4.82528e13	−2.74030
$879$	1.83085e13	1.03443
$880$	2.56107e13	1.43963
$881$	1.06893e13	0.597800	0.298900	−	0.954284i	$-0.403380\pi$
$881$	1.06893e13	0.597800	0.298900	+	0.954284i	$0.403380\pi$
$882$	−9.76611e12	−0.543392
$883$	−1.78787e12	−0.0989721	−0.0494861	−	0.998775i	$-0.515758\pi$
$883$	−1.78787e12	−0.0989721	−0.0494861	+	0.998775i	$0.515758\pi$
$884$	7.95115e12	0.437920
$885$	−6.45061e11	−0.0353473
$886$	3.48544e12	0.190023
$887$	2.56732e13	1.39259	0.696295	−	0.717756i	$-0.254831\pi$
$887$	2.56732e13	1.39259	0.696295	+	0.717756i	$0.254831\pi$
$888$	−4.73214e13	−2.55387
$889$	6.72426e12	0.361066
$890$	−3.99145e12	−0.213244
$891$	−2.09224e12	−0.111215
$892$	3.71392e11	0.0196422
$893$	6.66578e12	0.350767
$894$	7.01399e12	0.367237
$895$	6.60915e12	0.344304
$896$	1.03055e13	0.534177
$897$	1.04627e13	0.539608
$898$	−6.21585e13	−3.18975
$899$	−5.07570e11	−0.0259165
$900$	−1.31618e13	−0.668691
$901$	2.37511e12	0.120067
$902$	5.19842e13	2.61482
$903$	−3.50757e12	−0.175554
$904$	6.84185e13	3.40734
$905$	1.49041e13	0.738564
$906$	−4.16474e12	−0.205358
$907$	3.31074e12	0.162440	0.0812199	−	0.996696i	$-0.474118\pi$
$907$	3.31074e12	0.162440	0.0812199	+	0.996696i	$0.474118\pi$
$908$	−7.61374e13	−3.71716
$909$	−7.09299e12	−0.344581
$910$	1.20459e13	0.582306
$911$	2.51156e13	1.20812	0.604061	−	0.796938i	$-0.293548\pi$
$911$	2.51156e13	1.20812	0.604061	+	0.796938i	$0.293548\pi$
$912$	3.46208e13	1.65714
$913$	1.07150e12	0.0510358
$914$	1.03798e13	0.491963
$915$	−2.44149e12	−0.115149
$916$	5.64367e13	2.64869
$917$	6.60462e12	0.308451
$918$	7.55012e11	0.0350882
$919$	−7.48231e12	−0.346031	−0.173016	−	0.984919i	$-0.555351\pi$
$919$	−7.48231e12	−0.346031	−0.173016	+	0.984919i	$0.555351\pi$
$920$	−1.61375e13	−0.742663
$921$	2.75308e12	0.126081
$922$	−1.98034e13	−0.902508
$923$	6.30781e13	2.86069
$924$	1.22476e13	0.552748
$925$	−2.57456e13	−1.15629
$926$	−5.65404e13	−2.52702
$927$	2.98143e12	0.132607
$928$	5.85249e12	0.259045
$929$	1.67063e13	0.735884	0.367942	−	0.929849i	$-0.380062\pi$
$929$	1.67063e13	0.735884	0.367942	+	0.929849i	$0.380062\pi$
$930$	−3.28543e12	−0.144019
$931$	1.85458e13	0.809045
$932$	6.34154e13	2.75311
$933$	−1.97241e13	−0.852178
$934$	1.20189e13	0.516777
$935$	−1.06063e12	−0.0453849
$936$	−4.11251e13	−1.75132
$937$	−7.82086e12	−0.331457	−0.165728	−	0.986171i	$-0.552997\pi$
$937$	−7.82086e12	−0.331457	−0.165728	+	0.986171i	$0.552997\pi$
$938$	1.51004e13	0.636907
$939$	−1.67253e13	−0.702068
$940$	1.08371e13	0.452727
$941$	1.49201e13	0.620325	0.310163	−	0.950684i	$-0.399617\pi$
$941$	1.49201e13	0.620325	0.310163	+	0.950684i	$0.399617\pi$
$942$	−1.96342e13	−0.812429
$943$	−1.77812e13	−0.732249
$944$	−9.71517e12	−0.398177
$945$	8.23939e11	0.0336087
$946$	−3.81746e13	−1.54976
$947$	−9.39893e12	−0.379755	−0.189877	−	0.981808i	$-0.560809\pi$
$947$	−9.39893e12	−0.379755	−0.189877	+	0.981808i	$0.560809\pi$
$948$	6.40176e13	2.57432
$949$	1.49860e13	0.599773
$950$	3.46983e13	1.38214
$951$	9.41618e12	0.373304
$952$	−2.70377e12	−0.106685
$953$	9.28381e12	0.364593	0.182296	−	0.983244i	$-0.441647\pi$
$953$	9.28381e12	0.364593	0.182296	+	0.983244i	$0.441647\pi$
$954$	−2.00809e13	−0.784904
$955$	−4.31820e12	−0.167991
$956$	3.04420e13	1.17873
$957$	1.38537e12	0.0533904
$958$	6.54657e13	2.51113
$959$	1.14478e12	0.0437055
$960$	1.60297e13	0.609121
$961$	−2.43591e13	−0.921311
$962$	−1.31497e14	−4.95028
$963$	1.49282e13	0.559358
$964$	−1.24610e14	−4.64734
$965$	8.50272e12	0.315635
$966$	−5.81578e12	−0.214887
$967$	−2.25073e13	−0.827758	−0.413879	−	0.910332i	$-0.635826\pi$
$967$	−2.25073e13	−0.827758	−0.413879	+	0.910332i	$0.635826\pi$
$968$	1.51685e11	0.00555268
$969$	−1.43377e12	−0.0522422
$970$	−1.67432e13	−0.607247
$971$	−2.75257e12	−0.0993693	−0.0496847	−	0.998765i	$-0.515822\pi$
$971$	−2.75257e12	−0.0993693	−0.0496847	+	0.998765i	$0.515822\pi$
$972$	−4.59820e12	−0.165230
$973$	−6.15409e12	−0.220118
$974$	−7.29875e13	−2.59856
$975$	−2.23745e13	−0.792925
$976$	−3.67709e13	−1.29712
$977$	8.23553e12	0.289179	0.144589	−	0.989492i	$-0.453814\pi$
$977$	8.23553e12	0.289179	0.144589	+	0.989492i	$0.453814\pi$
$978$	−5.18964e13	−1.81389
$979$	−6.89890e12	−0.240026
$980$	3.01514e13	1.04422
$981$	−4.76871e12	−0.164396
$982$	9.48876e13	3.25618
$983$	−4.25116e13	−1.45217	−0.726083	−	0.687607i	$-0.758661\pi$
$983$	−4.25116e13	−1.45217	−0.726083	+	0.687607i	$0.758661\pi$
$984$	6.98914e13	2.37654
$985$	1.31957e12	0.0446652
$986$	−4.99930e11	−0.0168447
$987$	2.38924e12	0.0801368
$988$	1.27660e14	4.26234
$989$	1.30577e13	0.433992
$990$	8.96734e12	0.296692
$991$	3.56476e13	1.17408	0.587041	−	0.809557i	$-0.300293\pi$
$991$	3.56476e13	1.17408	0.587041	+	0.809557i	$0.300293\pi$
$992$	−2.39892e13	−0.786525
$993$	2.54393e13	0.830296
$994$	−3.50624e13	−1.13921
$995$	−2.43485e13	−0.787533
$996$	2.35488e12	0.0758233
$997$	−3.66768e13	−1.17561	−0.587804	−	0.809003i	$-0.700008\pi$
$997$	−3.66768e13	−1.17561	−0.587804	+	0.809003i	$0.700008\pi$
$998$	7.96809e13	2.54254
$999$	−8.99445e12	−0.285713

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.b.1.21	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.b.1.21	✓	21	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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+42.7873 q^{2} -81.0000 q^{3} +1318.75 q^{4} -657.216 q^{5} -3465.77 q^{6} +2359.02 q^{7} +34518.6 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+42.7873 q^{2} -81.0000 q^{3} +1318.75 q^{4} -657.216 q^{5} -3465.77 q^{6} +2359.02 q^{7} +34518.6 q^{8} +6561.00 q^{9} -28120.5 q^{10} -48603.9 q^{11} -106819. q^{12} -181586. q^{13} +100936. q^{14} +53234.5 q^{15} +801757. q^{16} -33203.5 q^{17} +280727. q^{18} -533100. q^{19} -866703. q^{20} -191081. q^{21} -2.07963e6 q^{22} +711338. q^{23} -2.79601e6 q^{24} -1.52119e6 q^{25} -7.76959e6 q^{26} -531441. q^{27} +3.11096e6 q^{28} +351893. q^{29} +2.27776e6 q^{30} -1.44240e6 q^{31} +1.66314e7 q^{32} +3.93692e6 q^{33} -1.42069e6 q^{34} -1.55039e6 q^{35} +8.65232e6 q^{36} +1.69246e7 q^{37} -2.28099e7 q^{38} +1.47085e7 q^{39} -2.26862e7 q^{40} -2.49969e7 q^{41} -8.17583e6 q^{42} +1.83565e7 q^{43} -6.40964e7 q^{44} -4.31199e6 q^{45} +3.04362e7 q^{46} -1.25038e7 q^{47} -6.49423e7 q^{48} -3.47886e7 q^{49} -6.50877e7 q^{50} +2.68949e6 q^{51} -2.39467e8 q^{52} -7.15319e7 q^{53} -2.27389e7 q^{54} +3.19433e7 q^{55} +8.14302e7 q^{56} +4.31811e7 q^{57} +1.50565e7 q^{58} -1.21174e7 q^{59} +7.02029e7 q^{60} -4.58629e7 q^{61} -6.17163e7 q^{62} +1.54775e7 q^{63} +3.01114e8 q^{64} +1.19341e8 q^{65} +1.68450e8 q^{66} +1.49604e8 q^{67} -4.37871e7 q^{68} -5.76184e7 q^{69} -6.63368e7 q^{70} -3.47372e8 q^{71} +2.26477e8 q^{72} -8.25280e7 q^{73} +7.24159e8 q^{74} +1.23217e8 q^{75} -7.03026e8 q^{76} -1.14658e8 q^{77} +6.29337e8 q^{78} -5.99311e8 q^{79} -5.26927e8 q^{80} +4.30467e7 q^{81} -1.06955e9 q^{82} -2.20456e7 q^{83} -2.51988e8 q^{84} +2.18219e7 q^{85} +7.85423e8 q^{86} -2.85033e7 q^{87} -1.67774e9 q^{88} +1.41941e8 q^{89} -1.84498e8 q^{90} -4.28367e8 q^{91} +9.38077e8 q^{92} +1.16834e8 q^{93} -5.35003e8 q^{94} +3.50362e8 q^{95} -1.34715e9 q^{96} +5.95410e8 q^{97} -1.48851e9 q^{98} -3.18890e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9}+O(q^{10}) \) 21 * q + 20 * q^2 - 1701 * q^3 + 4950 * q^4 + 2058 * q^5 - 1620 * q^6 - 17167 * q^7 - 2853 * q^8 + 137781 * q^9	\( 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9} - 31559 q^{10} - 38751 q^{11} - 400950 q^{12} - 58915 q^{13} + 3453 q^{14} - 166698 q^{15} + 1655714 q^{16} - 64233 q^{17} + 131220 q^{18} - 1937236 q^{19} - 1065507 q^{20} + 1390527 q^{21} - 5386882 q^{22} - 1838574 q^{23} + 231093 q^{24} + 4565755 q^{25} - 839702 q^{26} - 11160261 q^{27} - 4471034 q^{28} + 15658544 q^{29} + 2556279 q^{30} - 14282802 q^{31} - 2205286 q^{32} + 3138831 q^{33} + 19005532 q^{34} - 8633300 q^{35} + 32476950 q^{36} + 7531195 q^{37} + 26649773 q^{38} + 4772115 q^{39} + 17775672 q^{40} + 18338245 q^{41} - 279693 q^{42} - 22480305 q^{43} - 80230922 q^{44} + 13502538 q^{45} - 83894107 q^{46} - 110397260 q^{47} - 134112834 q^{48} + 130653638 q^{49} + 65575693 q^{50} + 5202873 q^{51} + 177908014 q^{52} + 145498338 q^{53} - 10628820 q^{54} + 86448944 q^{55} + 354387888 q^{56} + 156916116 q^{57} + 115508368 q^{58} - 254464581 q^{59} + 86306067 q^{60} + 287595506 q^{61} + 819899030 q^{62} - 112632687 q^{63} + 822446413 q^{64} + 77238206 q^{65} + 436337442 q^{66} - 392860610 q^{67} + 167325073 q^{68} + 148924494 q^{69} - 424902116 q^{70} - 248960491 q^{71} - 18718533 q^{72} - 758406074 q^{73} - 923266846 q^{74} - 369826155 q^{75} - 2312747568 q^{76} - 878126795 q^{77} + 68015862 q^{78} - 1925801029 q^{79} - 1898919861 q^{80} + 903981141 q^{81} - 3249102191 q^{82} - 1650336307 q^{83} + 362153754 q^{84} - 2342480762 q^{85} - 3609864952 q^{86} - 1268342064 q^{87} - 5987792887 q^{88} - 574997526 q^{89} - 207058599 q^{90} - 4481387117 q^{91} - 5317166770 q^{92} + 1156906962 q^{93} - 5360726568 q^{94} - 2789231462 q^{95} + 178628166 q^{96} - 4651540898 q^{97} - 5566652976 q^{98} - 254245311 q^{99}+O(q^{100}) \) 21 * q + 20 * q^2 - 1701 * q^3 + 4950 * q^4 + 2058 * q^5 - 1620 * q^6 - 17167 * q^7 - 2853 * q^8 + 137781 * q^9 - 31559 * q^10 - 38751 * q^11 - 400950 * q^12 - 58915 * q^13 + 3453 * q^14 - 166698 * q^15 + 1655714 * q^16 - 64233 * q^17 + 131220 * q^18 - 1937236 * q^19 - 1065507 * q^20 + 1390527 * q^21 - 5386882 * q^22 - 1838574 * q^23 + 231093 * q^24 + 4565755 * q^25 - 839702 * q^26 - 11160261 * q^27 - 4471034 * q^28 + 15658544 * q^29 + 2556279 * q^30 - 14282802 * q^31 - 2205286 * q^32 + 3138831 * q^33 + 19005532 * q^34 - 8633300 * q^35 + 32476950 * q^36 + 7531195 * q^37 + 26649773 * q^38 + 4772115 * q^39 + 17775672 * q^40 + 18338245 * q^41 - 279693 * q^42 - 22480305 * q^43 - 80230922 * q^44 + 13502538 * q^45 - 83894107 * q^46 - 110397260 * q^47 - 134112834 * q^48 + 130653638 * q^49 + 65575693 * q^50 + 5202873 * q^51 + 177908014 * q^52 + 145498338 * q^53 - 10628820 * q^54 + 86448944 * q^55 + 354387888 * q^56 + 156916116 * q^57 + 115508368 * q^58 - 254464581 * q^59 + 86306067 * q^60 + 287595506 * q^61 + 819899030 * q^62 - 112632687 * q^63 + 822446413 * q^64 + 77238206 * q^65 + 436337442 * q^66 - 392860610 * q^67 + 167325073 * q^68 + 148924494 * q^69 - 424902116 * q^70 - 248960491 * q^71 - 18718533 * q^72 - 758406074 * q^73 - 923266846 * q^74 - 369826155 * q^75 - 2312747568 * q^76 - 878126795 * q^77 + 68015862 * q^78 - 1925801029 * q^79 - 1898919861 * q^80 + 903981141 * q^81 - 3249102191 * q^82 - 1650336307 * q^83 + 362153754 * q^84 - 2342480762 * q^85 - 3609864952 * q^86 - 1268342064 * q^87 - 5987792887 * q^88 - 574997526 * q^89 - 207058599 * q^90 - 4481387117 * q^91 - 5317166770 * q^92 + 1156906962 * q^93 - 5360726568 * q^94 - 2789231462 * q^95 + 178628166 * q^96 - 4651540898 * q^97 - 5566652976 * q^98 - 254245311 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more