LMFDB - Embedded newform 177.12.a.a.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,12,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, 12, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 12 $
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:	$135.996742959$
Analytic rank:	$1$
Dimension:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
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)

$f(q)$	$=$	$q-16.5456 q^{2} -243.000 q^{3} -1774.24 q^{4} +2844.36 q^{5} +4020.58 q^{6} +41460.7 q^{7} +63241.3 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-16.5456 q^{2} -243.000 q^{3} -1774.24 q^{4} +2844.36 q^{5} +4020.58 q^{6} +41460.7 q^{7} +63241.3 q^{8} +59049.0 q^{9} -47061.6 q^{10} +49404.8 q^{11} +431141. q^{12} -2.15805e6 q^{13} -685992. q^{14} -691179. q^{15} +2.58728e6 q^{16} +2.16906e6 q^{17} -977001. q^{18} +7.65694e6 q^{19} -5.04658e6 q^{20} -1.00749e7 q^{21} -817432. q^{22} -2.58011e7 q^{23} -1.53676e7 q^{24} -4.07377e7 q^{25} +3.57062e7 q^{26} -1.43489e7 q^{27} -7.35613e7 q^{28} -5.29779e7 q^{29} +1.14360e7 q^{30} -7.09513e6 q^{31} -1.72326e8 q^{32} -1.20054e7 q^{33} -3.58884e7 q^{34} +1.17929e8 q^{35} -1.04767e8 q^{36} +1.02432e7 q^{37} -1.26689e8 q^{38} +5.24405e8 q^{39} +1.79881e8 q^{40} +1.31085e9 q^{41} +1.66696e8 q^{42} +1.41318e9 q^{43} -8.76561e7 q^{44} +1.67957e8 q^{45} +4.26895e8 q^{46} -9.75486e8 q^{47} -6.28710e8 q^{48} -2.58341e8 q^{49} +6.74031e8 q^{50} -5.27081e8 q^{51} +3.82890e9 q^{52} -9.42664e8 q^{53} +2.37411e8 q^{54} +1.40525e8 q^{55} +2.62203e9 q^{56} -1.86064e9 q^{57} +8.76551e8 q^{58} +7.14924e8 q^{59} +1.22632e9 q^{60} +7.22349e9 q^{61} +1.17393e8 q^{62} +2.44821e9 q^{63} -2.44751e9 q^{64} -6.13826e9 q^{65} +1.98636e8 q^{66} +1.55270e10 q^{67} -3.84844e9 q^{68} +6.26966e9 q^{69} -1.95121e9 q^{70} +1.91439e10 q^{71} +3.73434e9 q^{72} -1.37117e10 q^{73} -1.69481e8 q^{74} +9.89927e9 q^{75} -1.35853e10 q^{76} +2.04835e9 q^{77} -8.67660e9 q^{78} -3.29619e9 q^{79} +7.35916e9 q^{80} +3.48678e9 q^{81} -2.16889e10 q^{82} -6.18447e10 q^{83} +1.78754e10 q^{84} +6.16958e9 q^{85} -2.33819e10 q^{86} +1.28736e10 q^{87} +3.12442e9 q^{88} +7.94446e10 q^{89} -2.77894e9 q^{90} -8.94740e10 q^{91} +4.57774e10 q^{92} +1.72412e9 q^{93} +1.61400e10 q^{94} +2.17791e10 q^{95} +4.18753e10 q^{96} -1.08245e11 q^{97} +4.27441e9 q^{98} +2.91730e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9}+O(q^{10}) $ 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9} - 859751 q^{10} + 579094 q^{11} - 5606010 q^{12} - 2018538 q^{13} + 4157413 q^{14} - 925344 q^{15} + 20190274 q^{16} - 13084493 q^{17} - 4605822 q^{18} + 9917231 q^{19} + 10165633 q^{20} + 24013017 q^{21} - 89820518 q^{22} - 63513223 q^{23} + 28587735 q^{24} + 218986852 q^{25} - 77999532 q^{26} - 373071582 q^{27} - 444601862 q^{28} + 81530981 q^{29} + 208919493 q^{30} - 408861231 q^{31} - 26253128 q^{32} - 140719842 q^{33} - 508910076 q^{34} - 75731421 q^{35} + 1362260430 q^{36} - 802381301 q^{37} + 732704675 q^{38} + 490504734 q^{39} - 646130800 q^{40} - 1354472849 q^{41} - 1010251359 q^{42} + 282952194 q^{43} + 1846047996 q^{44} + 224858592 q^{45} + 9629305849 q^{46} - 1196794197 q^{47} - 4906236582 q^{48} + 10889725683 q^{49} - 6236232091 q^{50} + 3179531799 q^{51} - 1968200812 q^{52} - 8276044236 q^{53} + 1119214746 q^{54} - 6672895076 q^{55} + 2579741342 q^{56} - 2409887133 q^{57} - 9401656060 q^{58} + 18588031774 q^{59} - 2470248819 q^{60} - 21181559029 q^{61} - 6117706514 q^{62} - 5835163131 q^{63} + 42975855037 q^{64} + 25680681860 q^{65} + 21826385874 q^{66} + 26234163394 q^{67} + 19707344091 q^{68} + 15433713189 q^{69} + 129203099090 q^{70} + 52088830406 q^{71} - 6946819605 q^{72} + 20943384867 q^{73} + 41969200146 q^{74} - 53213805036 q^{75} + 223987219368 q^{76} + 94604773153 q^{77} + 18953886276 q^{78} + 68965662774 q^{79} + 218947784293 q^{80} + 90656394426 q^{81} + 11938614923 q^{82} + 17947446393 q^{83} + 108038252466 q^{84} - 52849386709 q^{85} + 384986147852 q^{86} - 19812028383 q^{87} - 49061112607 q^{88} + 38570593981 q^{89} - 50767436799 q^{90} - 226268806999 q^{91} - 79559686310 q^{92} + 99353279133 q^{93} - 16709400108 q^{94} - 252795831501 q^{95} + 6379510104 q^{96} - 186894587836 q^{97} - 252443311612 q^{98} + 34194921606 q^{99}+O(q^{100}) \) 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9 - 859751 * q^10 + 579094 * q^11 - 5606010 * q^12 - 2018538 * q^13 + 4157413 * q^14 - 925344 * q^15 + 20190274 * q^16 - 13084493 * q^17 - 4605822 * q^18 + 9917231 * q^19 + 10165633 * q^20 + 24013017 * q^21 - 89820518 * q^22 - 63513223 * q^23 + 28587735 * q^24 + 218986852 * q^25 - 77999532 * q^26 - 373071582 * q^27 - 444601862 * q^28 + 81530981 * q^29 + 208919493 * q^30 - 408861231 * q^31 - 26253128 * q^32 - 140719842 * q^33 - 508910076 * q^34 - 75731421 * q^35 + 1362260430 * q^36 - 802381301 * q^37 + 732704675 * q^38 + 490504734 * q^39 - 646130800 * q^40 - 1354472849 * q^41 - 1010251359 * q^42 + 282952194 * q^43 + 1846047996 * q^44 + 224858592 * q^45 + 9629305849 * q^46 - 1196794197 * q^47 - 4906236582 * q^48 + 10889725683 * q^49 - 6236232091 * q^50 + 3179531799 * q^51 - 1968200812 * q^52 - 8276044236 * q^53 + 1119214746 * q^54 - 6672895076 * q^55 + 2579741342 * q^56 - 2409887133 * q^57 - 9401656060 * q^58 + 18588031774 * q^59 - 2470248819 * q^60 - 21181559029 * q^61 - 6117706514 * q^62 - 5835163131 * q^63 + 42975855037 * q^64 + 25680681860 * q^65 + 21826385874 * q^66 + 26234163394 * q^67 + 19707344091 * q^68 + 15433713189 * q^69 + 129203099090 * q^70 + 52088830406 * q^71 - 6946819605 * q^72 + 20943384867 * q^73 + 41969200146 * q^74 - 53213805036 * q^75 + 223987219368 * q^76 + 94604773153 * q^77 + 18953886276 * q^78 + 68965662774 * q^79 + 218947784293 * q^80 + 90656394426 * q^81 + 11938614923 * q^82 + 17947446393 * q^83 + 108038252466 * q^84 - 52849386709 * q^85 + 384986147852 * q^86 - 19812028383 * q^87 - 49061112607 * q^88 + 38570593981 * q^89 - 50767436799 * q^90 - 226268806999 * q^91 - 79559686310 * q^92 + 99353279133 * q^93 - 16709400108 * q^94 - 252795831501 * q^95 + 6379510104 * q^96 - 186894587836 * q^97 - 252443311612 * q^98 + 34194921606 * 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 $

$2$	−16.5456	−0.365610	−0.182805	−	0.983149i	$-0.558518\pi$
$2$	−16.5456	−0.365610	−0.182805	+	0.983149i	$0.558518\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	−1774.24	−0.866330
$5$	2844.36	0.407051	0.203526	−	0.979070i	$-0.434760\pi$
$5$	2844.36	0.407051	0.203526	+	0.979070i	$0.434760\pi$
$6$	4020.58	0.211085
$7$	41460.7	0.932388	0.466194	−	0.884682i	$-0.345625\pi$
$7$	41460.7	0.932388	0.466194	+	0.884682i	$0.345625\pi$
$8$	63241.3	0.682348
$9$	59049.0	0.333333
$10$	−47061.6	−0.148822
$11$	49404.8	0.0924931	0.0462465	−	0.998930i	$-0.485274\pi$
$11$	49404.8	0.0924931	0.0462465	+	0.998930i	$0.485274\pi$
$12$	431141.	0.500176
$13$	−2.15805e6	−1.61203	−0.806013	−	0.591898i	$-0.798379\pi$
$13$	−2.15805e6	−1.61203	−0.806013	+	0.591898i	$0.798379\pi$
$14$	−685992.	−0.340890
$15$	−691179.	−0.235011
$16$	2.58728e6	0.616856
$17$	2.16906e6	0.370512	0.185256	−	0.982690i	$-0.440689\pi$
$17$	2.16906e6	0.370512	0.185256	+	0.982690i	$0.440689\pi$
$18$	−977001.	−0.121870
$19$	7.65694e6	0.709431	0.354716	−	0.934974i	$-0.384578\pi$
$19$	7.65694e6	0.709431	0.354716	+	0.934974i	$0.384578\pi$
$20$	−5.04658e6	−0.352641
$21$	−1.00749e7	−0.538315
$22$	−817432.	−0.0338164
$23$	−2.58011e7	−0.835863	−0.417931	−	0.908479i	$-0.637245\pi$
$23$	−2.58011e7	−0.835863	−0.417931	+	0.908479i	$0.637245\pi$
$24$	−1.53676e7	−0.393954
$25$	−4.07377e7	−0.834309
$26$	3.57062e7	0.589372
$27$	−1.43489e7	−0.192450
$28$	−7.35613e7	−0.807756
$29$	−5.29779e7	−0.479629	−0.239814	−	0.970819i	$-0.577087\pi$
$29$	−5.29779e7	−0.479629	−0.239814	+	0.970819i	$0.577087\pi$
$30$	1.14360e7	0.0859224
$31$	−7.09513e6	−0.0445114	−0.0222557	−	0.999752i	$-0.507085\pi$
$31$	−7.09513e6	−0.0445114	−0.0222557	+	0.999752i	$0.507085\pi$
$32$	−1.72326e8	−0.907877
$33$	−1.20054e7	−0.0534009
$34$	−3.58884e7	−0.135463
$35$	1.17929e8	0.379530
$36$	−1.04767e8	−0.288777
$37$	1.02432e7	0.0242844	0.0121422	−	0.999926i	$-0.496135\pi$
$37$	1.02432e7	0.0242844	0.0121422	+	0.999926i	$0.496135\pi$
$38$	−1.26689e8	−0.259375
$39$	5.24405e8	0.930704
$40$	1.79881e8	0.277751
$41$	1.31085e9	1.76703	0.883514	−	0.468405i	$-0.155171\pi$
$41$	1.31085e9	1.76703	0.883514	+	0.468405i	$0.155171\pi$
$42$	1.66696e8	0.196813
$43$	1.41318e9	1.46595	0.732977	−	0.680253i	$-0.238130\pi$
$43$	1.41318e9	1.46595	0.732977	+	0.680253i	$0.238130\pi$
$44$	−8.76561e7	−0.0801295
$45$	1.67957e8	0.135684
$46$	4.26895e8	0.305599
$47$	−9.75486e8	−0.620416	−0.310208	−	0.950669i	$-0.600399\pi$
$47$	−9.75486e8	−0.620416	−0.310208	+	0.950669i	$0.600399\pi$
$48$	−6.28710e8	−0.356142
$49$	−2.58341e8	−0.130652
$50$	6.74031e8	0.305031
$51$	−5.27081e8	−0.213915
$52$	3.82890e9	1.39655
$53$	−9.42664e8	−0.309628	−0.154814	−	0.987944i	$-0.549478\pi$
$53$	−9.42664e8	−0.309628	−0.154814	+	0.987944i	$0.549478\pi$
$54$	2.37411e8	0.0703616
$55$	1.40525e8	0.0376494
$56$	2.62203e9	0.636214
$57$	−1.86064e9	−0.409590
$58$	8.76551e8	0.175357
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	1.22632e9	0.203597
$61$	7.22349e9	1.09505	0.547524	−	0.836790i	$-0.315571\pi$
$61$	7.22349e9	1.09505	0.547524	+	0.836790i	$0.315571\pi$
$62$	1.17393e8	0.0162738
$63$	2.44821e9	0.310796
$64$	−2.44751e9	−0.284928
$65$	−6.13826e9	−0.656178
$66$	1.98636e8	0.0195239
$67$	1.55270e10	1.40500	0.702500	−	0.711684i	$-0.252067\pi$
$67$	1.55270e10	1.40500	0.702500	+	0.711684i	$0.252067\pi$
$68$	−3.84844e9	−0.320985
$69$	6.26966e9	0.482585
$70$	−1.95121e9	−0.138760
$71$	1.91439e10	1.25924	0.629621	−	0.776902i	$-0.283210\pi$
$71$	1.91439e10	1.25924	0.629621	+	0.776902i	$0.283210\pi$
$72$	3.73434e9	0.227449
$73$	−1.37117e10	−0.774134	−0.387067	−	0.922052i	$-0.626512\pi$
$73$	−1.37117e10	−0.774134	−0.387067	+	0.922052i	$0.626512\pi$
$74$	−1.69481e8	−0.00887863
$75$	9.89927e9	0.481689
$76$	−1.35853e10	−0.614601
$77$	2.04835e9	0.0862395
$78$	−8.67660e9	−0.340274
$79$	−3.29619e9	−0.120521	−0.0602605	−	0.998183i	$-0.519193\pi$
$79$	−3.29619e9	−0.120521	−0.0602605	+	0.998183i	$0.519193\pi$
$80$	7.35916e9	0.251092
$81$	3.48678e9	0.111111
$82$	−2.16889e10	−0.646043
$83$	−6.18447e10	−1.72335	−0.861674	−	0.507462i	$-0.830584\pi$
$83$	−6.18447e10	−1.72335	−0.861674	+	0.507462i	$0.830584\pi$
$84$	1.78754e10	0.466358
$85$	6.16958e9	0.150817
$86$	−2.33819e10	−0.535967
$87$	1.28736e10	0.276914
$88$	3.12442e9	0.0631125
$89$	7.94446e10	1.50806	0.754032	−	0.656838i	$-0.228107\pi$
$89$	7.94446e10	1.50806	0.754032	+	0.656838i	$0.228107\pi$
$90$	−2.77894e9	−0.0496073
$91$	−8.94740e10	−1.50303
$92$	4.57774e10	0.724132
$93$	1.72412e9	0.0256987
$94$	1.61400e10	0.226830
$95$	2.17791e10	0.288775
$96$	4.18753e10	0.524163
$97$	−1.08245e11	−1.27987	−0.639933	−	0.768431i	$-0.721038\pi$
$97$	−1.08245e11	−1.27987	−0.639933	+	0.768431i	$0.721038\pi$
$98$	4.27441e9	0.0477675
$99$	2.91730e9	0.0308310
$100$	7.22787e10	0.722787
$101$	−1.15397e11	−1.09252	−0.546259	−	0.837616i	$-0.683949\pi$
$101$	−1.15397e11	−1.09252	−0.546259	+	0.837616i	$0.683949\pi$
$102$	8.72088e9	0.0782094
$103$	8.55381e10	0.727034	0.363517	−	0.931588i	$-0.381576\pi$
$103$	8.55381e10	0.727034	0.363517	+	0.931588i	$0.381576\pi$
$104$	−1.36478e11	−1.09996
$105$	−2.86567e10	−0.219122
$106$	1.55970e10	0.113203
$107$	−1.05757e10	−0.0728949	−0.0364475	−	0.999336i	$-0.511604\pi$
$107$	−1.05757e10	−0.0728949	−0.0364475	+	0.999336i	$0.511604\pi$
$108$	2.54584e10	0.166725
$109$	2.13576e11	1.32956	0.664779	−	0.747040i	$-0.268526\pi$
$109$	2.13576e11	1.32956	0.664779	+	0.747040i	$0.268526\pi$
$110$	−2.32507e9	−0.0137650
$111$	−2.48911e9	−0.0140206
$112$	1.07270e11	0.575150
$113$	−2.24026e11	−1.14385	−0.571923	−	0.820307i	$-0.693803\pi$
$113$	−2.24026e11	−1.14385	−0.571923	+	0.820307i	$0.693803\pi$
$114$	3.07854e10	0.149750
$115$	−7.33875e10	−0.340239
$116$	9.39956e10	0.415517
$117$	−1.27430e11	−0.537342
$118$	−1.18289e10	−0.0475983
$119$	8.99306e10	0.345461
$120$	−4.37111e10	−0.160360
$121$	−2.82871e11	−0.991445
$122$	−1.19517e11	−0.400360
$123$	−3.18538e11	−1.02019
$124$	1.25885e10	0.0385615
$125$	−2.54757e11	−0.746658
$126$	−4.05071e10	−0.113630
$127$	−8.92835e10	−0.239801	−0.119900	−	0.992786i	$-0.538258\pi$
$127$	−8.92835e10	−0.239801	−0.119900	+	0.992786i	$0.538258\pi$
$128$	3.93420e11	1.01205
$129$	−3.43402e11	−0.846369
$130$	1.01561e11	0.239905
$131$	1.39957e11	0.316958	0.158479	−	0.987362i	$-0.449341\pi$
$131$	1.39957e11	0.316958	0.158479	+	0.987362i	$0.449341\pi$
$132$	2.13004e10	0.0462628
$133$	3.17462e11	0.661466
$134$	−2.56904e11	−0.513682
$135$	−4.08134e10	−0.0783371
$136$	1.37174e11	0.252818
$137$	−5.16655e11	−0.914613	−0.457306	−	0.889309i	$-0.651186\pi$
$137$	−5.16655e11	−0.914613	−0.457306	+	0.889309i	$0.651186\pi$
$138$	−1.03735e11	−0.176438
$139$	6.30410e11	1.03049	0.515243	−	0.857044i	$-0.327702\pi$
$139$	6.30410e11	1.03049	0.515243	+	0.857044i	$0.327702\pi$
$140$	−2.09235e11	−0.328798
$141$	2.37043e11	0.358197
$142$	−3.16747e11	−0.460391
$143$	−1.06618e11	−0.149101
$144$	1.52777e11	0.205619
$145$	−1.50688e11	−0.195234
$146$	2.26869e11	0.283031
$147$	6.27769e10	0.0754318
$148$	−1.81740e10	−0.0210383
$149$	−9.13502e10	−0.101903	−0.0509513	−	0.998701i	$-0.516225\pi$
$149$	−9.13502e10	−0.101903	−0.0509513	+	0.998701i	$0.516225\pi$
$150$	−1.63789e11	−0.176110
$151$	9.49321e11	0.984102	0.492051	−	0.870566i	$-0.336247\pi$
$151$	9.49321e11	0.984102	0.492051	+	0.870566i	$0.336247\pi$
$152$	4.84235e11	0.484079
$153$	1.28081e11	0.123504
$154$	−3.38913e10	−0.0315300
$155$	−2.01811e10	−0.0181184
$156$	−9.30422e11	−0.806296
$157$	1.26333e11	0.105698	0.0528491	−	0.998603i	$-0.483170\pi$
$157$	1.26333e11	0.105698	0.0528491	+	0.998603i	$0.483170\pi$
$158$	5.45374e10	0.0440636
$159$	2.29067e11	0.178764
$160$	−4.90158e11	−0.369553
$161$	−1.06973e12	−0.779349
$162$	−5.76910e10	−0.0406233
$163$	−1.75646e12	−1.19566	−0.597828	−	0.801625i	$-0.703969\pi$
$163$	−1.75646e12	−1.19566	−0.597828	+	0.801625i	$0.703969\pi$
$164$	−2.32577e12	−1.53083
$165$	−3.41475e10	−0.0217369
$166$	1.02326e12	0.630073
$167$	−8.26293e11	−0.492259	−0.246129	−	0.969237i	$-0.579159\pi$
$167$	−8.26293e11	−0.492259	−0.246129	+	0.969237i	$0.579159\pi$
$168$	−6.37152e11	−0.367318
$169$	2.86500e12	1.59863
$170$	−1.02079e11	−0.0551403
$171$	4.52135e11	0.236477
$172$	−2.50732e12	−1.27000
$173$	−1.77758e12	−0.872118	−0.436059	−	0.899918i	$-0.643626\pi$
$173$	−1.77758e12	−0.872118	−0.436059	+	0.899918i	$0.643626\pi$
$174$	−2.13002e11	−0.101242
$175$	−1.68901e12	−0.777900
$176$	1.27824e11	0.0570549
$177$	−1.73727e11	−0.0751646
$178$	−1.31446e12	−0.551363
$179$	−3.18380e12	−1.29495	−0.647477	−	0.762085i	$-0.724176\pi$
$179$	−3.18380e12	−1.29495	−0.647477	+	0.762085i	$0.724176\pi$
$180$	−2.97996e11	−0.117547
$181$	−6.48052e11	−0.247958	−0.123979	−	0.992285i	$-0.539565\pi$
$181$	−6.48052e11	−0.247958	−0.123979	+	0.992285i	$0.539565\pi$
$182$	1.48040e12	0.549524
$183$	−1.75531e12	−0.632226
$184$	−1.63169e12	−0.570349
$185$	2.91355e10	0.00988502
$186$	−2.85266e10	−0.00939568
$187$	1.07162e11	0.0342698
$188$	1.73075e12	0.537484
$189$	−5.94915e11	−0.179438
$190$	−3.60348e11	−0.105579
$191$	6.04436e11	0.172055	0.0860274	−	0.996293i	$-0.472583\pi$
$191$	6.04436e11	0.172055	0.0860274	+	0.996293i	$0.472583\pi$
$192$	5.94745e11	0.164503
$193$	−6.09808e12	−1.63919	−0.819593	−	0.572947i	$-0.805800\pi$
$193$	−6.09808e12	−1.63919	−0.819593	+	0.572947i	$0.805800\pi$
$194$	1.79098e12	0.467931
$195$	1.49160e12	0.378844
$196$	4.58360e11	0.113187
$197$	−3.12704e12	−0.750878	−0.375439	−	0.926847i	$-0.622508\pi$
$197$	−3.12704e12	−0.750878	−0.375439	+	0.926847i	$0.622508\pi$
$198$	−4.82685e10	−0.0112721
$199$	7.35466e11	0.167059	0.0835297	−	0.996505i	$-0.473381\pi$
$199$	7.35466e11	0.167059	0.0835297	+	0.996505i	$0.473381\pi$
$200$	−2.57631e12	−0.569289
$201$	−3.77306e12	−0.811177
$202$	1.90932e12	0.399435
$203$	−2.19650e12	−0.447201
$204$	9.35170e11	0.185321
$205$	3.72854e12	0.719271
$206$	−1.41528e12	−0.265811
$207$	−1.52353e12	−0.278621
$208$	−5.58348e12	−0.994389
$209$	3.78289e11	0.0656175
$210$	4.74143e11	0.0801131
$211$	−3.01668e12	−0.496564	−0.248282	−	0.968688i	$-0.579866\pi$
$211$	−3.01668e12	−0.496564	−0.248282	+	0.968688i	$0.579866\pi$
$212$	1.67252e12	0.268240
$213$	−4.65196e12	−0.727024
$214$	1.74981e11	0.0266511
$215$	4.01959e12	0.596719
$216$	−9.07444e11	−0.131318
$217$	−2.94169e11	−0.0415019
$218$	−3.53375e12	−0.486099
$219$	3.33195e12	0.446947
$220$	−2.49325e11	−0.0326168
$221$	−4.68093e12	−0.597275
$222$	4.11838e10	0.00512608
$223$	2.13109e12	0.258776	0.129388	−	0.991594i	$-0.458699\pi$
$223$	2.13109e12	0.258776	0.129388	+	0.991594i	$0.458699\pi$
$224$	−7.14477e12	−0.846494
$225$	−2.40552e12	−0.278103
$226$	3.70665e12	0.418201
$227$	1.14890e13	1.26515	0.632573	−	0.774501i	$-0.281999\pi$
$227$	1.14890e13	1.26515	0.632573	+	0.774501i	$0.281999\pi$
$228$	3.30122e12	0.354840
$229$	−1.83816e13	−1.92881	−0.964404	−	0.264432i	$-0.914816\pi$
$229$	−1.83816e13	−1.92881	−0.964404	+	0.264432i	$0.914816\pi$
$230$	1.21424e12	0.124395
$231$	−4.97750e11	−0.0497904
$232$	−3.35039e12	−0.327274
$233$	−7.86981e12	−0.750769	−0.375385	−	0.926869i	$-0.622489\pi$
$233$	−7.86981e12	−0.750769	−0.375385	+	0.926869i	$0.622489\pi$
$234$	2.10841e12	0.196457
$235$	−2.77463e12	−0.252541
$236$	−1.26845e12	−0.112787
$237$	8.00973e11	0.0695828
$238$	−1.48796e12	−0.126304
$239$	1.67805e12	0.139193	0.0695964	−	0.997575i	$-0.477829\pi$
$239$	1.67805e12	0.139193	0.0695964	+	0.997575i	$0.477829\pi$
$240$	−1.78828e12	−0.144968
$241$	9.79471e12	0.776064	0.388032	−	0.921646i	$-0.373155\pi$
$241$	9.79471e12	0.776064	0.388032	+	0.921646i	$0.373155\pi$
$242$	4.68027e12	0.362482
$243$	−8.47289e11	−0.0641500
$244$	−1.28162e13	−0.948672
$245$	−7.34815e11	−0.0531820
$246$	5.27040e12	0.372993
$247$	−1.65240e13	−1.14362
$248$	−4.48705e11	−0.0303723
$249$	1.50283e13	0.994975
$250$	4.21512e12	0.272985
$251$	7.32224e12	0.463915	0.231957	−	0.972726i	$-0.425487\pi$
$251$	7.32224e12	0.463915	0.231957	+	0.972726i	$0.425487\pi$
$252$	−4.34372e12	−0.269252
$253$	−1.27470e12	−0.0773115
$254$	1.47725e12	0.0876735
$255$	−1.49921e12	−0.0870745
$256$	−1.49687e12	−0.0850872
$257$	2.22220e13	1.23637	0.618187	−	0.786031i	$-0.287867\pi$
$257$	2.22220e13	1.23637	0.618187	+	0.786031i	$0.287867\pi$
$258$	5.68180e12	0.309441
$259$	4.24692e11	0.0226425
$260$	1.08908e13	0.568466
$261$	−3.12829e12	−0.159876
$262$	−2.31567e12	−0.115883
$263$	1.95089e13	0.956039	0.478020	−	0.878349i	$-0.341355\pi$
$263$	1.95089e13	0.956039	0.478020	+	0.878349i	$0.341355\pi$
$264$	−7.59235e11	−0.0364380
$265$	−2.68128e12	−0.126034
$266$	−5.25260e12	−0.241838
$267$	−1.93050e13	−0.870681
$268$	−2.75487e13	−1.21719
$269$	−9.39033e12	−0.406484	−0.203242	−	0.979129i	$-0.565148\pi$
$269$	−9.39033e12	−0.406484	−0.203242	+	0.979129i	$0.565148\pi$
$270$	6.75283e11	0.0286408
$271$	−9.28184e12	−0.385747	−0.192874	−	0.981224i	$-0.561781\pi$
$271$	−9.28184e12	−0.385747	−0.192874	+	0.981224i	$0.561781\pi$
$272$	5.61197e12	0.228553
$273$	2.17422e13	0.867778
$274$	8.54836e12	0.334391
$275$	−2.01264e12	−0.0771678
$276$	−1.11239e13	−0.418078
$277$	−2.18617e13	−0.805463	−0.402731	−	0.915318i	$-0.631939\pi$
$277$	−2.18617e13	−0.805463	−0.402731	+	0.915318i	$0.631939\pi$
$278$	−1.04305e13	−0.376755
$279$	−4.18960e11	−0.0148371
$280$	7.45798e12	0.258972
$281$	1.68565e13	0.573962	0.286981	−	0.957936i	$-0.407348\pi$
$281$	1.68565e13	0.573962	0.286981	+	0.957936i	$0.407348\pi$
$282$	−3.92202e12	−0.130960
$283$	−5.37145e13	−1.75900	−0.879500	−	0.475899i	$-0.842123\pi$
$283$	−5.37145e13	−1.75900	−0.879500	+	0.475899i	$0.842123\pi$
$284$	−3.39659e13	−1.09092
$285$	−5.29232e12	−0.166724
$286$	1.76406e12	0.0545129
$287$	5.43489e13	1.64756
$288$	−1.01757e13	−0.302626
$289$	−2.95671e13	−0.862721
$290$	2.49322e12	0.0713793
$291$	2.63036e13	0.738931
$292$	2.43279e13	0.670655
$293$	−4.19452e13	−1.13478	−0.567388	−	0.823451i	$-0.692046\pi$
$293$	−4.19452e13	−1.13478	−0.567388	+	0.823451i	$0.692046\pi$
$294$	−1.03868e12	−0.0275786
$295$	2.03350e12	0.0529936
$296$	6.47797e11	0.0165704
$297$	−7.08905e11	−0.0178003
$298$	1.51144e12	0.0372565
$299$	5.56799e13	1.34743
$300$	−1.75637e13	−0.417301
$301$	5.85913e13	1.36684
$302$	−1.57071e13	−0.359797
$303$	2.80416e13	0.630766
$304$	1.98107e13	0.437617
$305$	2.05462e13	0.445741
$306$	−2.11917e12	−0.0451542
$307$	1.16139e13	0.243063	0.121531	−	0.992588i	$-0.461220\pi$
$307$	1.16139e13	0.243063	0.121531	+	0.992588i	$0.461220\pi$
$308$	−3.63428e12	−0.0747118
$309$	−2.07858e13	−0.419753
$310$	3.33908e11	0.00662427
$311$	−2.32744e13	−0.453624	−0.226812	−	0.973939i	$-0.572830\pi$
$311$	−2.32744e13	−0.453624	−0.226812	+	0.973939i	$0.572830\pi$
$312$	3.31641e13	0.635064
$313$	−3.25730e13	−0.612863	−0.306432	−	0.951893i	$-0.599135\pi$
$313$	−3.25730e13	−0.612863	−0.306432	+	0.951893i	$0.599135\pi$
$314$	−2.09025e12	−0.0386443
$315$	6.96359e12	0.126510
$316$	5.84823e12	0.104411
$317$	−1.66067e13	−0.291378	−0.145689	−	0.989330i	$-0.546540\pi$
$317$	−1.66067e13	−0.291378	−0.145689	+	0.989330i	$0.546540\pi$
$318$	−3.79006e12	−0.0653577
$319$	−2.61736e12	−0.0443624
$320$	−6.96160e12	−0.115980
$321$	2.56989e12	0.0420859
$322$	1.76993e13	0.284937
$323$	1.66083e13	0.262853
$324$	−6.18640e12	−0.0962588
$325$	8.79139e13	1.34493
$326$	2.90617e13	0.437143
$327$	−5.18990e13	−0.767621
$328$	8.29002e13	1.20573
$329$	−4.04443e13	−0.578468
$330$	5.64992e11	0.00794723
$331$	8.26670e13	1.14361	0.571805	−	0.820389i	$-0.306243\pi$
$331$	8.26670e13	1.14361	0.571805	+	0.820389i	$0.306243\pi$
$332$	1.09728e14	1.49299
$333$	6.04854e11	0.00809482
$334$	1.36715e13	0.179975
$335$	4.41644e13	0.571907
$336$	−2.60667e13	−0.332063
$337$	−4.67427e13	−0.585800	−0.292900	−	0.956143i	$-0.594620\pi$
$337$	−4.67427e13	−0.585800	−0.292900	+	0.956143i	$0.594620\pi$
$338$	−4.74032e13	−0.584474
$339$	5.44384e13	0.660400
$340$	−1.09463e13	−0.130658
$341$	−3.50533e11	−0.00411699
$342$	−7.48084e12	−0.0864583
$343$	−9.26922e13	−1.05421
$344$	8.93713e13	1.00029
$345$	1.78332e13	0.196437
$346$	2.94111e13	0.318855
$347$	1.56968e14	1.67494	0.837469	−	0.546485i	$-0.184034\pi$
$347$	1.56968e14	1.67494	0.837469	+	0.546485i	$0.184034\pi$
$348$	−2.28409e13	−0.239899
$349$	7.50899e13	0.776322	0.388161	−	0.921592i	$-0.373110\pi$
$349$	7.50899e13	0.776322	0.388161	+	0.921592i	$0.373110\pi$
$350$	2.79458e13	0.284408
$351$	3.09656e13	0.310235
$352$	−8.51375e12	−0.0839723
$353$	1.15618e14	1.12270	0.561350	−	0.827579i	$-0.310282\pi$
$353$	1.15618e14	1.12270	0.561350	+	0.827579i	$0.310282\pi$
$354$	2.87441e12	0.0274809
$355$	5.44521e13	0.512576
$356$	−1.40954e14	−1.30648
$357$	−2.18531e13	−0.199452
$358$	5.26779e13	0.473448
$359$	−1.55424e14	−1.37562	−0.687811	−	0.725890i	$-0.741428\pi$
$359$	−1.55424e14	−1.37562	−0.687811	+	0.725890i	$0.741428\pi$
$360$	1.06218e13	0.0925836
$361$	−5.78615e13	−0.496707
$362$	1.07224e13	0.0906557
$363$	6.87376e13	0.572411
$364$	1.58749e14	1.30212
$365$	−3.90011e13	−0.315112
$366$	2.90426e13	0.231148
$367$	−1.54518e14	−1.21148	−0.605739	−	0.795663i	$-0.707123\pi$
$367$	−1.54518e14	−1.21148	−0.605739	+	0.795663i	$0.707123\pi$
$368$	−6.67547e13	−0.515607
$369$	7.74047e13	0.589009
$370$	−4.82064e11	−0.00361406
$371$	−3.90835e13	−0.288693
$372$	−3.05900e12	−0.0222635
$373$	−1.43977e14	−1.03251	−0.516256	−	0.856434i	$-0.672675\pi$
$373$	−1.43977e14	−1.03251	−0.516256	+	0.856434i	$0.672675\pi$
$374$	−1.77306e12	−0.0125294
$375$	6.19061e13	0.431083
$376$	−6.16910e13	−0.423340
$377$	1.14329e14	0.773175
$378$	9.84323e12	0.0656044
$379$	−1.71279e14	−1.12509	−0.562547	−	0.826765i	$-0.690179\pi$
$379$	−1.71279e14	−1.12509	−0.562547	+	0.826765i	$0.690179\pi$
$380$	−3.86414e13	−0.250174
$381$	2.16959e13	0.138449
$382$	−1.00008e13	−0.0629049
$383$	−5.17030e13	−0.320570	−0.160285	−	0.987071i	$-0.551241\pi$
$383$	−5.17030e13	−0.320570	−0.160285	+	0.987071i	$0.551241\pi$
$384$	−9.56011e13	−0.584307
$385$	5.82625e12	0.0351039
$386$	1.00896e14	0.599302
$387$	8.34468e13	0.488651
$388$	1.92053e14	1.10879
$389$	1.07061e14	0.609407	0.304704	−	0.952447i	$-0.401443\pi$
$389$	1.07061e14	0.609407	0.304704	+	0.952447i	$0.401443\pi$
$390$	−2.46794e13	−0.138509
$391$	−5.59640e13	−0.309697
$392$	−1.63378e13	−0.0891499
$393$	−3.40095e13	−0.182996
$394$	5.17388e13	0.274528
$395$	−9.37553e12	−0.0490582
$396$	−5.17600e12	−0.0267098
$397$	1.22203e14	0.621919	0.310959	−	0.950423i	$-0.399350\pi$
$397$	1.22203e14	0.621919	0.310959	+	0.950423i	$0.399350\pi$
$398$	−1.21687e13	−0.0610785
$399$	−7.71432e13	−0.381897
$400$	−1.05400e14	−0.514649
$401$	2.29196e14	1.10386	0.551928	−	0.833892i	$-0.313892\pi$
$401$	2.29196e14	1.10386	0.551928	+	0.833892i	$0.313892\pi$
$402$	6.24276e13	0.296574
$403$	1.53116e13	0.0717535
$404$	2.04743e14	0.946481
$405$	9.91766e12	0.0452279
$406$	3.63424e13	0.163501
$407$	5.06065e11	0.00224614
$408$	−3.33333e13	−0.145965
$409$	−2.66904e14	−1.15313	−0.576563	−	0.817053i	$-0.695606\pi$
$409$	−2.66904e14	−1.15313	−0.576563	+	0.817053i	$0.695606\pi$
$410$	−6.16910e13	−0.262973
$411$	1.25547e14	0.528052
$412$	−1.51765e14	−0.629851
$413$	2.96412e13	0.121387
$414$	2.52077e13	0.101866
$415$	−1.75908e14	−0.701491
$416$	3.71888e14	1.46352
$417$	−1.53190e14	−0.594951
$418$	−6.25903e12	−0.0239904
$419$	−2.26201e14	−0.855693	−0.427846	−	0.903852i	$-0.640728\pi$
$419$	−2.26201e14	−0.855693	−0.427846	+	0.903852i	$0.640728\pi$
$420$	5.08440e13	0.189832
$421$	−2.91017e14	−1.07243	−0.536213	−	0.844083i	$-0.680146\pi$
$421$	−2.91017e14	−1.07243	−0.536213	+	0.844083i	$0.680146\pi$
$422$	4.99128e13	0.181549
$423$	−5.76015e13	−0.206805
$424$	−5.96154e13	−0.211274
$425$	−8.83625e13	−0.309121
$426$	7.69696e13	0.265807
$427$	2.99491e14	1.02101
$428$	1.87638e13	0.0631510
$429$	2.59081e13	0.0860837
$430$	−6.65065e13	−0.218166
$431$	5.44197e14	1.76251	0.881254	−	0.472644i	$-0.156700\pi$
$431$	5.44197e14	1.76251	0.881254	+	0.472644i	$0.156700\pi$
$432$	−3.71247e13	−0.118714
$433$	−2.85221e14	−0.900531	−0.450265	−	0.892895i	$-0.648671\pi$
$433$	−2.85221e14	−0.900531	−0.450265	+	0.892895i	$0.648671\pi$
$434$	4.86720e12	0.0151735
$435$	3.66172e13	0.112718
$436$	−3.78936e14	−1.15184
$437$	−1.97557e14	−0.592987
$438$	−5.51291e13	−0.163408
$439$	3.89958e14	1.14147	0.570733	−	0.821135i	$-0.306659\pi$
$439$	3.89958e14	1.14147	0.570733	+	0.821135i	$0.306659\pi$
$440$	8.88698e12	0.0256900
$441$	−1.52548e13	−0.0435506
$442$	7.74488e13	0.218369
$443$	−4.51653e14	−1.25772	−0.628861	−	0.777518i	$-0.716479\pi$
$443$	−4.51653e14	−1.25772	−0.628861	+	0.777518i	$0.716479\pi$
$444$	4.41628e12	0.0121465
$445$	2.25969e14	0.613859
$446$	−3.52601e13	−0.0946110
$447$	2.21981e13	0.0588334
$448$	−1.01475e14	−0.265663
$449$	−1.64956e14	−0.426592	−0.213296	−	0.976988i	$-0.568420\pi$
$449$	−1.64956e14	−0.426592	−0.213296	+	0.976988i	$0.568420\pi$
$450$	3.98008e13	0.101677
$451$	6.47625e13	0.163438
$452$	3.97477e14	0.990948
$453$	−2.30685e14	−0.568172
$454$	−1.90093e14	−0.462549
$455$	−2.54496e14	−0.611813
$456$	−1.17669e14	−0.279483
$457$	6.44813e14	1.51319	0.756597	−	0.653882i	$-0.226861\pi$
$457$	6.44813e14	1.51319	0.756597	+	0.653882i	$0.226861\pi$
$458$	3.04135e14	0.705191
$459$	−3.11236e13	−0.0713050
$460$	1.30207e14	0.294759
$461$	−2.06718e14	−0.462405	−0.231202	−	0.972906i	$-0.574266\pi$
$461$	−2.06718e14	−0.462405	−0.231202	+	0.972906i	$0.574266\pi$
$462$	8.23558e12	0.0182038
$463$	−3.31636e14	−0.724380	−0.362190	−	0.932104i	$-0.617971\pi$
$463$	−3.31636e14	−0.724380	−0.362190	+	0.932104i	$0.617971\pi$
$464$	−1.37069e14	−0.295862
$465$	4.90401e12	0.0104607
$466$	1.30211e14	0.274489
$467$	6.31321e14	1.31525	0.657623	−	0.753347i	$-0.271562\pi$
$467$	6.31321e14	1.31525	0.657623	+	0.753347i	$0.271562\pi$
$468$	2.26093e14	0.465515
$469$	6.43760e14	1.31001
$470$	4.59080e13	0.0923315
$471$	−3.06988e13	−0.0610249
$472$	4.52128e13	0.0888342
$473$	6.98177e13	0.135591
$474$	−1.32526e13	−0.0254402
$475$	−3.11926e14	−0.591885
$476$	−1.59559e14	−0.299283
$477$	−5.56634e13	−0.103209
$478$	−2.77644e13	−0.0508902
$479$	2.58208e14	0.467869	0.233935	−	0.972252i	$-0.424840\pi$
$479$	2.58208e14	0.467869	0.233935	+	0.972252i	$0.424840\pi$
$480$	1.19108e14	0.213361
$481$	−2.21054e13	−0.0391472
$482$	−1.62059e14	−0.283737
$483$	2.59944e14	0.449957
$484$	5.01882e14	0.858918
$485$	−3.07888e14	−0.520971
$486$	1.40189e13	0.0234539
$487$	−7.53305e14	−1.24613	−0.623063	−	0.782172i	$-0.714112\pi$
$487$	−7.53305e14	−1.24613	−0.623063	+	0.782172i	$0.714112\pi$
$488$	4.56823e14	0.747204
$489$	4.26819e14	0.690312
$490$	1.21580e13	0.0194438
$491$	−8.96454e14	−1.41769	−0.708843	−	0.705367i	$-0.750782\pi$
$491$	−8.96454e14	−1.41769	−0.708843	+	0.705367i	$0.750782\pi$
$492$	5.65163e14	0.883824
$493$	−1.14912e14	−0.177708
$494$	2.73400e14	0.418119
$495$	8.29785e12	0.0125498
$496$	−1.83571e13	−0.0274571
$497$	7.93718e14	1.17410
$498$	−2.48652e14	−0.363773
$499$	−1.31048e15	−1.89617	−0.948086	−	0.318014i	$-0.896984\pi$
$499$	−1.31048e15	−1.89617	−0.948086	+	0.318014i	$0.896984\pi$
$500$	4.52002e14	0.646852
$501$	2.00789e14	0.284206
$502$	−1.21151e14	−0.169612
$503$	5.74181e14	0.795106	0.397553	−	0.917579i	$-0.369859\pi$
$503$	5.74181e14	0.795106	0.397553	+	0.917579i	$0.369859\pi$
$504$	1.54828e14	0.212071
$505$	−3.28232e14	−0.444711
$506$	2.10906e13	0.0282658
$507$	−6.96195e14	−0.922969
$508$	1.58411e14	0.207746
$509$	−9.19197e14	−1.19251	−0.596254	−	0.802796i	$-0.703345\pi$
$509$	−9.19197e14	−1.19251	−0.596254	+	0.802796i	$0.703345\pi$
$510$	2.48053e13	0.0318353
$511$	−5.68497e14	−0.721794
$512$	−7.80958e14	−0.980941
$513$	−1.09869e14	−0.136530
$514$	−3.67676e14	−0.452031
$515$	2.43301e14	0.295940
$516$	6.09279e14	0.733234
$517$	−4.81937e13	−0.0573841
$518$	−7.02678e12	−0.00827833
$519$	4.31952e14	0.503518
$520$	−3.88191e14	−0.447742
$521$	−1.39135e15	−1.58792	−0.793958	−	0.607973i	$-0.791983\pi$
$521$	−1.39135e15	−1.58792	−0.793958	+	0.607973i	$0.791983\pi$
$522$	5.17594e13	0.0584523
$523$	−3.26568e14	−0.364933	−0.182467	−	0.983212i	$-0.558408\pi$
$523$	−3.26568e14	−0.364933	−0.182467	+	0.983212i	$0.558408\pi$
$524$	−2.48317e14	−0.274590
$525$	4.10430e14	0.449121
$526$	−3.22786e14	−0.349537
$527$	−1.53897e13	−0.0164920
$528$	−3.10613e13	−0.0329407
$529$	−2.87114e14	−0.301334
$530$	4.43633e13	0.0460794
$531$	4.22156e13	0.0433963
$532$	−5.63254e14	−0.573047
$533$	−2.82888e15	−2.84850
$534$	3.19414e14	0.318329
$535$	−3.00810e13	−0.0296720
$536$	9.81949e14	0.958700
$537$	7.73664e14	0.747642
$538$	1.55369e14	0.148614
$539$	−1.27633e13	−0.0120844
$540$	7.24129e13	0.0678657
$541$	−5.99446e14	−0.556115	−0.278058	−	0.960564i	$-0.589691\pi$
$541$	−5.99446e14	−0.556115	−0.278058	+	0.960564i	$0.589691\pi$
$542$	1.53574e14	0.141033
$543$	1.57477e14	0.143158
$544$	−3.73786e14	−0.336379
$545$	6.07488e14	0.541199
$546$	−3.59737e14	−0.317268
$547$	−7.46132e14	−0.651456	−0.325728	−	0.945463i	$-0.605609\pi$
$547$	−7.46132e14	−0.651456	−0.325728	+	0.945463i	$0.605609\pi$
$548$	9.16671e14	0.792356
$549$	4.26540e14	0.365016
$550$	3.33003e13	0.0282133
$551$	−4.05648e14	−0.340264
$552$	3.96502e14	0.329291
$553$	−1.36662e14	−0.112372
$554$	3.61715e14	0.294485
$555$	−7.07992e12	−0.00570712
$556$	−1.11850e15	−0.892740
$557$	1.38536e15	1.09486	0.547432	−	0.836850i	$-0.315605\pi$
$557$	1.38536e15	1.09486	0.547432	+	0.836850i	$0.315605\pi$
$558$	6.93195e12	0.00542460
$559$	−3.04970e15	−2.36316
$560$	3.05116e14	0.234116
$561$	−2.60403e13	−0.0197857
$562$	−2.78901e14	−0.209846
$563$	−7.17447e14	−0.534557	−0.267278	−	0.963619i	$-0.586124\pi$
$563$	−7.17447e14	−0.534557	−0.267278	+	0.963619i	$0.586124\pi$
$564$	−4.20572e14	−0.310317
$565$	−6.37211e14	−0.465604
$566$	8.88738e14	0.643107
$567$	1.44564e14	0.103599
$568$	1.21068e15	0.859241
$569$	−3.65447e14	−0.256866	−0.128433	−	0.991718i	$-0.540995\pi$
$569$	−3.65447e14	−0.256866	−0.128433	+	0.991718i	$0.540995\pi$
$570$	8.75646e13	0.0609560
$571$	−8.60431e14	−0.593222	−0.296611	−	0.954998i	$-0.595857\pi$
$571$	−8.60431e14	−0.593222	−0.296611	+	0.954998i	$0.595857\pi$
$572$	1.89166e14	0.129171
$573$	−1.46878e14	−0.0993359
$574$	−8.99235e14	−0.602363
$575$	1.05108e15	0.697368
$576$	−1.44523e14	−0.0949760
$577$	−2.43951e15	−1.58795	−0.793974	−	0.607952i	$-0.791991\pi$
$577$	−2.43951e15	−1.58795	−0.793974	+	0.607952i	$0.791991\pi$
$578$	4.89205e14	0.315419
$579$	1.48183e15	0.946384
$580$	2.67357e14	0.169137
$581$	−2.56412e15	−1.60683
$582$	−4.35209e14	−0.270160
$583$	−4.65721e13	−0.0286384
$584$	−8.67148e14	−0.528229
$585$	−3.62458e14	−0.218726
$586$	6.94008e14	0.414885
$587$	−2.16572e15	−1.28261	−0.641303	−	0.767288i	$-0.721606\pi$
$587$	−2.16572e15	−1.28261	−0.641303	+	0.767288i	$0.721606\pi$
$588$	−1.11381e14	−0.0653488
$589$	−5.43270e13	−0.0315778
$590$	−3.36455e13	−0.0193750
$591$	7.59871e14	0.433520
$592$	2.65022e13	0.0149800
$593$	−2.96460e15	−1.66022	−0.830110	−	0.557599i	$-0.811723\pi$
$593$	−2.96460e15	−1.66022	−0.830110	+	0.557599i	$0.811723\pi$
$594$	1.17293e13	0.00650796
$595$	2.55795e14	0.140620
$596$	1.62077e14	0.0882812
$597$	−1.78718e14	−0.0964518
$598$	−9.21258e14	−0.492634
$599$	−1.93205e14	−0.102369	−0.0511847	−	0.998689i	$-0.516300\pi$
$599$	−1.93205e14	−0.102369	−0.0511847	+	0.998689i	$0.516300\pi$
$600$	6.26043e14	0.328679
$601$	1.00117e15	0.520835	0.260418	−	0.965496i	$-0.416140\pi$
$601$	1.00117e15	0.520835	0.260418	+	0.965496i	$0.416140\pi$
$602$	−9.69428e14	−0.499729
$603$	9.16855e14	0.468333
$604$	−1.68433e15	−0.852557
$605$	−8.04586e14	−0.403569
$606$	−4.63965e14	−0.230614
$607$	−1.85054e15	−0.911509	−0.455754	−	0.890106i	$-0.650630\pi$
$607$	−1.85054e15	−0.911509	−0.455754	+	0.890106i	$0.650630\pi$
$608$	−1.31949e15	−0.644076
$609$	5.33749e14	0.258191
$610$	−3.39949e14	−0.162967
$611$	2.10514e15	1.00013
$612$	−2.27246e14	−0.106995
$613$	1.13216e15	0.528292	0.264146	−	0.964483i	$-0.414910\pi$
$613$	1.13216e15	0.528292	0.264146	+	0.964483i	$0.414910\pi$
$614$	−1.92159e14	−0.0888660
$615$	−9.06036e14	−0.415271
$616$	1.29541e14	0.0588453
$617$	2.96469e15	1.33478	0.667392	−	0.744707i	$-0.267411\pi$
$617$	2.96469e15	1.33478	0.667392	+	0.744707i	$0.267411\pi$
$618$	3.43913e14	0.153466
$619$	−1.13102e15	−0.500234	−0.250117	−	0.968216i	$-0.580469\pi$
$619$	−1.13102e15	−0.500234	−0.250117	+	0.968216i	$0.580469\pi$
$620$	3.58062e13	0.0156965
$621$	3.70217e14	0.160862
$622$	3.85089e14	0.165849
$623$	3.29383e15	1.40610
$624$	1.35678e15	0.574111
$625$	1.26453e15	0.530381
$626$	5.38940e14	0.224069
$627$	−9.19243e13	−0.0378843
$628$	−2.24145e14	−0.0915695
$629$	2.22182e13	0.00899767
$630$	−1.15217e14	−0.0462533
$631$	−2.46195e15	−0.979755	−0.489878	−	0.871791i	$-0.662959\pi$
$631$	−2.46195e15	−0.979755	−0.489878	+	0.871791i	$0.662959\pi$
$632$	−2.08455e14	−0.0822373
$633$	7.33053e14	0.286691
$634$	2.74768e14	0.106531
$635$	−2.53954e14	−0.0976112
$636$	−4.06421e14	−0.154868
$637$	5.57512e14	0.210614
$638$	4.33058e13	0.0162193
$639$	1.13043e15	0.419747
$640$	1.11903e15	0.411956
$641$	1.10162e15	0.402082	0.201041	−	0.979583i	$-0.435568\pi$
$641$	1.10162e15	0.402082	0.201041	+	0.979583i	$0.435568\pi$
$642$	−4.25204e13	−0.0153870
$643$	−5.45536e14	−0.195733	−0.0978664	−	0.995200i	$-0.531202\pi$
$643$	−5.45536e14	−0.195733	−0.0978664	+	0.995200i	$0.531202\pi$
$644$	1.89796e15	0.675173
$645$	−9.76759e14	−0.344516
$646$	−2.74795e14	−0.0961015
$647$	6.85317e14	0.237639	0.118820	−	0.992916i	$-0.462089\pi$
$647$	6.85317e14	0.237639	0.118820	+	0.992916i	$0.462089\pi$
$648$	2.20509e14	0.0758165
$649$	3.53207e13	0.0120416
$650$	−1.45459e15	−0.491719
$651$	7.14830e13	0.0239611
$652$	3.11638e15	1.03583
$653$	4.88769e15	1.61095	0.805473	−	0.592633i	$-0.201912\pi$
$653$	4.88769e15	1.61095	0.805473	+	0.592633i	$0.201912\pi$
$654$	8.58701e14	0.280650
$655$	3.98087e14	0.129018
$656$	3.39155e15	1.09000
$657$	−8.09664e14	−0.258045
$658$	6.69175e14	0.211494
$659$	2.33955e15	0.733268	0.366634	−	0.930365i	$-0.380510\pi$
$659$	2.33955e15	0.733268	0.366634	+	0.930365i	$0.380510\pi$
$660$	6.05860e13	0.0188313
$661$	9.05484e14	0.279108	0.139554	−	0.990214i	$-0.455433\pi$
$661$	9.05484e14	0.279108	0.139554	+	0.990214i	$0.455433\pi$
$662$	−1.36778e15	−0.418115
$663$	1.13746e15	0.344837
$664$	−3.91114e15	−1.17592
$665$	9.02975e14	0.269251
$666$	−1.00077e13	−0.00295954
$667$	1.36689e15	0.400904
$668$	1.46604e15	0.426458
$669$	−5.17854e14	−0.149404
$670$	−7.30727e14	−0.209095
$671$	3.56875e14	0.101284
$672$	1.73618e15	0.488724
$673$	4.27924e15	1.19477	0.597384	−	0.801956i	$-0.296207\pi$
$673$	4.27924e15	1.19477	0.597384	+	0.801956i	$0.296207\pi$
$674$	7.73387e14	0.214174
$675$	5.84542e14	0.160563
$676$	−5.08321e15	−1.38494
$677$	1.05288e14	0.0284537	0.0142269	−	0.999899i	$-0.495471\pi$
$677$	1.05288e14	0.0284537	0.0142269	+	0.999899i	$0.495471\pi$
$678$	−9.00717e14	−0.241449
$679$	−4.48792e15	−1.19333
$680$	3.90172e14	0.102910
$681$	−2.79183e15	−0.730432
$682$	5.79979e12	0.00150521
$683$	7.50102e15	1.93111	0.965554	−	0.260202i	$-0.0837891\pi$
$683$	7.50102e15	1.93111	0.965554	+	0.260202i	$0.0837891\pi$
$684$	−8.02197e14	−0.204867
$685$	−1.46955e15	−0.372294
$686$	1.53365e15	0.385428
$687$	4.46674e15	1.11360
$688$	3.65629e15	0.904283
$689$	2.03431e15	0.499128
$690$	−2.95061e14	−0.0718193
$691$	3.16800e15	0.764990	0.382495	−	0.923957i	$-0.375065\pi$
$691$	3.16800e15	0.764990	0.382495	+	0.923957i	$0.375065\pi$
$692$	3.15386e15	0.755542
$693$	1.20953e14	0.0287465
$694$	−2.59713e15	−0.612374
$695$	1.79311e15	0.419461
$696$	8.14145e14	0.188952
$697$	2.84332e15	0.654705
$698$	−1.24241e15	−0.283831
$699$	1.91236e15	0.433457
$700$	2.99672e15	0.673918
$701$	−3.78543e15	−0.844628	−0.422314	−	0.906449i	$-0.638782\pi$
$701$	−3.78543e15	−0.844628	−0.422314	+	0.906449i	$0.638782\pi$
$702$	−5.12345e14	−0.113425
$703$	7.84319e13	0.0172281
$704$	−1.20919e14	−0.0263539
$705$	6.74235e14	0.145805
$706$	−1.91296e15	−0.410470
$707$	−4.78445e15	−1.01865
$708$	3.08233e14	0.0651173
$709$	−8.63490e15	−1.81010	−0.905051	−	0.425303i	$-0.860167\pi$
$709$	−8.63490e15	−1.81010	−0.905051	+	0.425303i	$0.860167\pi$
$710$	−9.00943e14	−0.187403
$711$	−1.94636e14	−0.0401737
$712$	5.02418e15	1.02902
$713$	1.83062e14	0.0372054
$714$	3.61573e14	0.0729216
$715$	−3.03259e14	−0.0606919
$716$	5.64884e15	1.12186
$717$	−4.07767e14	−0.0803630
$718$	2.57159e15	0.502941
$719$	−7.12634e15	−1.38311	−0.691557	−	0.722322i	$-0.743075\pi$
$719$	−7.12634e15	−1.38311	−0.691557	+	0.722322i	$0.743075\pi$
$720$	4.34551e14	0.0836974
$721$	3.54646e15	0.677878
$722$	9.57354e14	0.181601
$723$	−2.38011e15	−0.448061
$724$	1.14980e15	0.214813
$725$	2.15820e15	0.400159
$726$	−1.13731e15	−0.209279
$727$	−4.80671e15	−0.877826	−0.438913	−	0.898529i	$-0.644636\pi$
$727$	−4.80671e15	−0.877826	−0.438913	+	0.898529i	$0.644636\pi$
$728$	−5.65845e15	−1.02559
$729$	2.05891e14	0.0370370
$730$	6.45296e14	0.115208
$731$	3.06526e15	0.543153
$732$	3.11434e15	0.547716
$733$	4.93840e15	0.862015	0.431007	−	0.902348i	$-0.358158\pi$
$733$	4.93840e15	0.862015	0.431007	+	0.902348i	$0.358158\pi$
$734$	2.55659e15	0.442928
$735$	1.78560e14	0.0307046
$736$	4.44621e15	0.758860
$737$	7.67109e14	0.129953
$738$	−1.28071e15	−0.215348
$739$	1.12139e16	1.87160	0.935798	−	0.352536i	$-0.114680\pi$
$739$	1.12139e16	1.87160	0.935798	+	0.352536i	$0.114680\pi$
$740$	−5.16934e13	−0.00856368
$741$	4.01534e15	0.660271
$742$	6.46660e14	0.105549
$743$	−9.98430e15	−1.61763	−0.808815	−	0.588064i	$-0.799890\pi$
$743$	−9.98430e15	−1.61763	−0.808815	+	0.588064i	$0.799890\pi$
$744$	1.09035e14	0.0175354
$745$	−2.59833e14	−0.0414796
$746$	2.38219e15	0.377497
$747$	−3.65187e15	−0.574449
$748$	−1.90131e14	−0.0296889
$749$	−4.38474e14	−0.0679664
$750$	−1.02427e15	−0.157608
$751$	−9.54628e15	−1.45819	−0.729096	−	0.684412i	$-0.760059\pi$
$751$	−9.54628e15	−1.45819	−0.729096	+	0.684412i	$0.760059\pi$
$752$	−2.52386e15	−0.382707
$753$	−1.77930e15	−0.267841
$754$	−1.89164e15	−0.282680
$755$	2.70021e15	0.400580
$756$	1.05552e15	0.155453
$757$	−5.84451e15	−0.854517	−0.427258	−	0.904130i	$-0.640520\pi$
$757$	−5.84451e15	−0.854517	−0.427258	+	0.904130i	$0.640520\pi$
$758$	2.83392e15	0.411345
$759$	3.09751e14	0.0446358
$760$	1.37734e15	0.197045
$761$	−3.51497e14	−0.0499236	−0.0249618	−	0.999688i	$-0.507946\pi$
$761$	−3.51497e14	−0.0499236	−0.0249618	+	0.999688i	$0.507946\pi$
$762$	−3.58971e14	−0.0506183
$763$	8.85501e15	1.23966
$764$	−1.07242e15	−0.149056
$765$	3.64307e14	0.0502725
$766$	8.55458e14	0.117203
$767$	−1.54284e15	−0.209868
$768$	3.63739e14	0.0491251
$769$	−2.12882e15	−0.285459	−0.142730	−	0.989762i	$-0.545588\pi$
$769$	−2.12882e15	−0.285459	−0.142730	+	0.989762i	$0.545588\pi$
$770$	−9.63989e13	−0.0128343
$771$	−5.39994e15	−0.713821
$772$	1.08195e16	1.42007
$773$	1.51816e16	1.97848	0.989240	−	0.146303i	$-0.0467374\pi$
$773$	1.51816e16	1.97848	0.989240	+	0.146303i	$0.0467374\pi$
$774$	−1.38068e15	−0.178656
$775$	2.89040e14	0.0371362
$776$	−6.84557e15	−0.873314
$777$	−1.03200e14	−0.0130727
$778$	−1.77139e15	−0.222805
$779$	1.00371e16	1.25359
$780$	−2.64645e15	−0.328204
$781$	9.45799e14	0.116471
$782$	9.25959e14	0.113228
$783$	7.60174e14	0.0923046
$784$	−6.68402e14	−0.0805933
$785$	3.59335e14	0.0430246
$786$	5.62708e14	0.0669051
$787$	−2.45701e15	−0.290099	−0.145050	−	0.989424i	$-0.546334\pi$
$787$	−2.45701e15	−0.290099	−0.145050	+	0.989424i	$0.546334\pi$
$788$	5.54813e15	0.650508
$789$	−4.74066e15	−0.551969
$790$	1.55124e14	0.0179362
$791$	−9.28828e15	−1.06651
$792$	1.84494e14	0.0210375
$793$	−1.55886e16	−1.76525
$794$	−2.02192e15	−0.227380
$795$	6.51550e14	0.0727660
$796$	−1.30490e15	−0.144728
$797$	−8.50843e15	−0.937192	−0.468596	−	0.883413i	$-0.655240\pi$
$797$	−8.50843e15	−0.937192	−0.468596	+	0.883413i	$0.655240\pi$
$798$	1.27638e15	0.139625
$799$	−2.11589e15	−0.229871
$800$	7.02019e15	0.757450
$801$	4.69113e15	0.502688
$802$	−3.79218e15	−0.403580
$803$	−6.77425e14	−0.0716021
$804$	6.69433e15	0.702747
$805$	−3.04270e15	−0.317235
$806$	−2.53340e14	−0.0262338
$807$	2.28185e15	0.234684
$808$	−7.29789e15	−0.745478
$809$	7.02046e15	0.712276	0.356138	−	0.934433i	$-0.384093\pi$
$809$	7.02046e15	0.712276	0.356138	+	0.934433i	$0.384093\pi$
$810$	−1.64094e14	−0.0165358
$811$	−1.72598e16	−1.72752	−0.863758	−	0.503907i	$-0.831895\pi$
$811$	−1.72598e16	−1.72752	−0.863758	+	0.503907i	$0.831895\pi$
$812$	3.89712e15	0.387423
$813$	2.25549e15	0.222711
$814$	−8.37316e12	−0.000821212 0
$815$	−4.99600e15	−0.486693
$816$	−1.36371e15	−0.131955
$817$	1.08206e16	1.03999
$818$	4.41609e15	0.421594
$819$	−5.28335e15	−0.501012
$820$	−6.61534e15	−0.623126
$821$	−1.53967e16	−1.44059	−0.720295	−	0.693668i	$-0.755993\pi$
$821$	−1.53967e16	−1.44059	−0.720295	+	0.693668i	$0.755993\pi$
$822$	−2.07725e15	−0.193061
$823$	8.63994e15	0.797649	0.398824	−	0.917027i	$-0.369418\pi$
$823$	8.63994e15	0.797649	0.398824	+	0.917027i	$0.369418\pi$
$824$	5.40954e15	0.496090
$825$	4.89071e14	0.0445529
$826$	−4.90432e14	−0.0443801
$827$	2.35190e15	0.211416	0.105708	−	0.994397i	$-0.466289\pi$
$827$	2.35190e15	0.211416	0.105708	+	0.994397i	$0.466289\pi$
$828$	2.70311e15	0.241377
$829$	1.30697e16	1.15935	0.579677	−	0.814847i	$-0.303179\pi$
$829$	1.30697e16	1.15935	0.579677	+	0.814847i	$0.303179\pi$
$830$	2.91051e15	0.256472
$831$	5.31240e15	0.465034
$832$	5.28184e15	0.459311
$833$	−5.60357e14	−0.0484080
$834$	2.53462e15	0.217520
$835$	−2.35027e15	−0.200375
$836$	−6.71177e14	−0.0568464
$837$	1.01807e14	0.00856622
$838$	3.74264e15	0.312850
$839$	−2.20551e15	−0.183155	−0.0915776	−	0.995798i	$-0.529191\pi$
$839$	−2.20551e15	−0.183155	−0.0915776	+	0.995798i	$0.529191\pi$
$840$	−1.81229e15	−0.149517
$841$	−9.39386e15	−0.769956
$842$	4.81506e15	0.392089
$843$	−4.09613e15	−0.331377
$844$	5.35232e15	0.430188
$845$	8.14909e15	0.650724
$846$	9.53051e14	0.0756100
$847$	−1.17280e16	−0.924412
$848$	−2.43894e15	−0.190996
$849$	1.30526e16	1.01556
$850$	1.46201e15	0.113018
$851$	−2.64287e14	−0.0202985
$852$	8.25371e15	0.629842
$853$	−4.82327e15	−0.365697	−0.182849	−	0.983141i	$-0.558532\pi$
$853$	−4.82327e15	−0.365697	−0.182849	+	0.983141i	$0.558532\pi$
$854$	−4.95525e15	−0.373291
$855$	1.28603e15	0.0962584
$856$	−6.68820e14	−0.0497397
$857$	1.82356e16	1.34749	0.673743	−	0.738965i	$-0.264685\pi$
$857$	1.82356e16	1.34749	0.673743	+	0.738965i	$0.264685\pi$
$858$	−4.28665e14	−0.0314730
$859$	1.35505e16	0.988538	0.494269	−	0.869309i	$-0.335436\pi$
$859$	1.35505e16	0.988538	0.494269	+	0.869309i	$0.335436\pi$
$860$	−7.13172e15	−0.516955
$861$	−1.32068e16	−0.951217
$862$	−9.00406e15	−0.644390
$863$	3.58064e15	0.254625	0.127313	−	0.991863i	$-0.459365\pi$
$863$	3.58064e15	0.254625	0.127313	+	0.991863i	$0.459365\pi$
$864$	2.47270e15	0.174721
$865$	−5.05607e15	−0.354997
$866$	4.71916e15	0.329243
$867$	7.18480e15	0.498092
$868$	5.21927e14	0.0359543
$869$	−1.62847e14	−0.0111474
$870$	−6.05854e14	−0.0412109
$871$	−3.35080e16	−2.26490
$872$	1.35068e16	0.907222
$873$	−6.39177e15	−0.426622
$874$	3.26871e15	0.216802
$875$	−1.05624e16	−0.696176
$876$	−5.91169e15	−0.387203
$877$	1.08631e16	0.707060	0.353530	−	0.935423i	$-0.384981\pi$
$877$	1.08631e16	0.707060	0.353530	+	0.935423i	$0.384981\pi$
$878$	−6.45210e15	−0.417331
$879$	1.01927e16	0.655163
$880$	3.63578e14	0.0232243
$881$	1.47375e16	0.935524	0.467762	−	0.883854i	$-0.345060\pi$
$881$	1.47375e16	0.935524	0.467762	+	0.883854i	$0.345060\pi$
$882$	2.52400e14	0.0159225
$883$	−1.93222e16	−1.21136	−0.605680	−	0.795709i	$-0.707099\pi$
$883$	−1.93222e16	−1.21136	−0.605680	+	0.795709i	$0.707099\pi$
$884$	8.30510e15	0.517437
$885$	−4.94141e14	−0.0305959
$886$	7.47288e15	0.459836
$887$	−2.98238e16	−1.82383	−0.911913	−	0.410384i	$-0.865395\pi$
$887$	−2.98238e16	−1.82383	−0.911913	+	0.410384i	$0.865395\pi$
$888$	−1.57415e14	−0.00956695
$889$	−3.70175e15	−0.223587
$890$	−3.73879e15	−0.224433
$891$	1.72264e14	0.0102770
$892$	−3.78106e15	−0.224185
$893$	−7.46924e15	−0.440142
$894$	−3.67281e14	−0.0215101
$895$	−9.05588e15	−0.527113
$896$	1.63115e16	0.943623
$897$	−1.35302e16	−0.777941
$898$	2.72929e15	0.155966
$899$	3.75885e14	0.0213489
$900$	4.26798e15	0.240929
$901$	−2.04469e15	−0.114721
$902$	−1.07153e15	−0.0597545
$903$	−1.42377e16	−0.789145
$904$	−1.41677e16	−0.780502
$905$	−1.84329e15	−0.100931
$906$	3.81683e15	0.207729
$907$	−2.12927e16	−1.15183	−0.575917	−	0.817508i	$-0.695355\pi$
$907$	−2.12927e16	−1.15183	−0.575917	+	0.817508i	$0.695355\pi$
$908$	−2.03843e16	−1.09603
$909$	−6.81411e15	−0.364173
$910$	4.21079e15	0.223685
$911$	3.26708e14	0.0172508	0.00862540	−	0.999963i	$-0.497254\pi$
$911$	3.26708e14	0.0172508	0.00862540	+	0.999963i	$0.497254\pi$
$912$	−4.81399e15	−0.252658
$913$	−3.05542e15	−0.159398
$914$	−1.06688e16	−0.553238
$915$	−4.99272e15	−0.257348
$916$	3.26135e16	1.67098
$917$	5.80270e15	0.295528
$918$	5.14959e14	0.0260698
$919$	−1.89702e16	−0.954633	−0.477316	−	0.878732i	$-0.658390\pi$
$919$	−1.89702e16	−0.954633	−0.477316	+	0.878732i	$0.658390\pi$
$920$	−4.64113e15	−0.232162
$921$	−2.82218e15	−0.140332
$922$	3.42027e15	0.169060
$923$	−4.13134e16	−2.02993
$924$	8.83130e14	0.0431349
$925$	−4.17287e14	−0.0202607
$926$	5.48712e15	0.264840
$927$	5.05094e15	0.242345
$928$	9.12948e15	0.435444
$929$	4.78262e15	0.226767	0.113383	−	0.993551i	$-0.463831\pi$
$929$	4.78262e15	0.226767	0.113383	+	0.993551i	$0.463831\pi$
$930$	−8.11397e13	−0.00382452
$931$	−1.97810e15	−0.0926884
$932$	1.39629e16	0.650414
$933$	5.65568e15	0.261900
$934$	−1.04456e16	−0.480867
$935$	3.04807e14	0.0139496
$936$	−8.05887e15	−0.366654
$937$	3.44010e16	1.55598	0.777989	−	0.628277i	$-0.216240\pi$
$937$	3.44010e16	1.55598	0.777989	+	0.628277i	$0.216240\pi$
$938$	−1.06514e16	−0.478951
$939$	7.91523e15	0.353837
$940$	4.92287e15	0.218784
$941$	−2.78341e16	−1.22980	−0.614901	−	0.788605i	$-0.710804\pi$
$941$	−2.78341e16	−1.22980	−0.614901	+	0.788605i	$0.710804\pi$
$942$	5.07931e14	0.0223113
$943$	−3.38215e16	−1.47699
$944$	1.84971e15	0.0803079
$945$	−1.69215e15	−0.0730406
$946$	−1.15518e15	−0.0495732
$947$	2.68749e16	1.14663	0.573314	−	0.819336i	$-0.305657\pi$
$947$	2.68749e16	1.14663	0.573314	+	0.819336i	$0.305657\pi$
$948$	−1.42112e15	−0.0602817
$949$	2.95905e16	1.24792
$950$	5.16101e15	0.216399
$951$	4.03542e15	0.168227
$952$	5.68733e15	0.235725
$953$	1.03588e16	0.426873	0.213437	−	0.976957i	$-0.431534\pi$
$953$	1.03588e16	0.426873	0.213437	+	0.976957i	$0.431534\pi$
$954$	9.20985e14	0.0377343
$955$	1.71923e15	0.0700352
$956$	−2.97727e15	−0.120587
$957$	6.36018e14	0.0256126
$958$	−4.27221e15	−0.171058
$959$	−2.14208e16	−0.852774
$960$	1.69167e15	0.0669613
$961$	−2.53581e16	−0.998019
$962$	3.65747e14	0.0143126
$963$	−6.24483e14	−0.0242983
$964$	−1.73782e16	−0.672327
$965$	−1.73451e16	−0.667233
$966$	−4.30094e15	−0.164509
$967$	1.97119e16	0.749692	0.374846	−	0.927087i	$-0.377696\pi$
$967$	1.97119e16	0.749692	0.374846	+	0.927087i	$0.377696\pi$
$968$	−1.78891e16	−0.676511
$969$	−4.03583e15	−0.151758
$970$	5.09420e15	0.190472
$971$	1.13357e16	0.421445	0.210722	−	0.977546i	$-0.432418\pi$
$971$	1.13357e16	0.421445	0.210722	+	0.977546i	$0.432418\pi$
$972$	1.50330e15	0.0555751
$973$	2.61372e16	0.960813
$974$	1.24639e16	0.455596
$975$	−2.13631e16	−0.776495
$976$	1.86892e16	0.675487
$977$	1.73424e16	0.623288	0.311644	−	0.950199i	$-0.399120\pi$
$977$	1.73424e16	0.623288	0.311644	+	0.950199i	$0.399120\pi$
$978$	−7.06198e15	−0.252385
$979$	3.92494e15	0.139485
$980$	1.30374e15	0.0460731
$981$	1.26115e16	0.443186
$982$	1.48324e16	0.518320
$983$	−5.57930e16	−1.93881	−0.969406	−	0.245464i	$-0.921060\pi$
$983$	−5.57930e16	−1.93881	−0.969406	+	0.245464i	$0.921060\pi$
$984$	−2.01447e16	−0.696128
$985$	−8.89443e15	−0.305646
$986$	1.90129e15	0.0649718
$987$	9.82796e15	0.333979
$988$	2.93176e16	0.990754
$989$	−3.64615e16	−1.22534
$990$	−1.37293e14	−0.00458833
$991$	4.68425e16	1.55681	0.778404	−	0.627764i	$-0.216030\pi$
$991$	4.68425e16	1.55681	0.778404	+	0.627764i	$0.216030\pi$
$992$	1.22268e15	0.0404108
$993$	−2.00881e16	−0.660264
$994$	−1.31325e16	−0.429263
$995$	2.09193e15	0.0680018
$996$	−2.66638e16	−0.861976
$997$	4.70992e16	1.51422	0.757112	−	0.653285i	$-0.226610\pi$
$997$	4.70992e16	1.51422	0.757112	+	0.653285i	$0.226610\pi$
$998$	2.16827e16	0.693259
$999$	−1.46979e14	−0.00467354

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.a.1.12	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.a.1.12	✓	26	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:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-16.5456 q^{2} -243.000 q^{3} -1774.24 q^{4} +2844.36 q^{5} +4020.58 q^{6} +41460.7 q^{7} +63241.3 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-16.5456 q^{2} -243.000 q^{3} -1774.24 q^{4} +2844.36 q^{5} +4020.58 q^{6} +41460.7 q^{7} +63241.3 q^{8} +59049.0 q^{9} -47061.6 q^{10} +49404.8 q^{11} +431141. q^{12} -2.15805e6 q^{13} -685992. q^{14} -691179. q^{15} +2.58728e6 q^{16} +2.16906e6 q^{17} -977001. q^{18} +7.65694e6 q^{19} -5.04658e6 q^{20} -1.00749e7 q^{21} -817432. q^{22} -2.58011e7 q^{23} -1.53676e7 q^{24} -4.07377e7 q^{25} +3.57062e7 q^{26} -1.43489e7 q^{27} -7.35613e7 q^{28} -5.29779e7 q^{29} +1.14360e7 q^{30} -7.09513e6 q^{31} -1.72326e8 q^{32} -1.20054e7 q^{33} -3.58884e7 q^{34} +1.17929e8 q^{35} -1.04767e8 q^{36} +1.02432e7 q^{37} -1.26689e8 q^{38} +5.24405e8 q^{39} +1.79881e8 q^{40} +1.31085e9 q^{41} +1.66696e8 q^{42} +1.41318e9 q^{43} -8.76561e7 q^{44} +1.67957e8 q^{45} +4.26895e8 q^{46} -9.75486e8 q^{47} -6.28710e8 q^{48} -2.58341e8 q^{49} +6.74031e8 q^{50} -5.27081e8 q^{51} +3.82890e9 q^{52} -9.42664e8 q^{53} +2.37411e8 q^{54} +1.40525e8 q^{55} +2.62203e9 q^{56} -1.86064e9 q^{57} +8.76551e8 q^{58} +7.14924e8 q^{59} +1.22632e9 q^{60} +7.22349e9 q^{61} +1.17393e8 q^{62} +2.44821e9 q^{63} -2.44751e9 q^{64} -6.13826e9 q^{65} +1.98636e8 q^{66} +1.55270e10 q^{67} -3.84844e9 q^{68} +6.26966e9 q^{69} -1.95121e9 q^{70} +1.91439e10 q^{71} +3.73434e9 q^{72} -1.37117e10 q^{73} -1.69481e8 q^{74} +9.89927e9 q^{75} -1.35853e10 q^{76} +2.04835e9 q^{77} -8.67660e9 q^{78} -3.29619e9 q^{79} +7.35916e9 q^{80} +3.48678e9 q^{81} -2.16889e10 q^{82} -6.18447e10 q^{83} +1.78754e10 q^{84} +6.16958e9 q^{85} -2.33819e10 q^{86} +1.28736e10 q^{87} +3.12442e9 q^{88} +7.94446e10 q^{89} -2.77894e9 q^{90} -8.94740e10 q^{91} +4.57774e10 q^{92} +1.72412e9 q^{93} +1.61400e10 q^{94} +2.17791e10 q^{95} +4.18753e10 q^{96} -1.08245e11 q^{97} +4.27441e9 q^{98} +2.91730e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9}+O(q^{10}) \) 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9} - 859751 q^{10} + 579094 q^{11} - 5606010 q^{12} - 2018538 q^{13} + 4157413 q^{14} - 925344 q^{15} + 20190274 q^{16} - 13084493 q^{17} - 4605822 q^{18} + 9917231 q^{19} + 10165633 q^{20} + 24013017 q^{21} - 89820518 q^{22} - 63513223 q^{23} + 28587735 q^{24} + 218986852 q^{25} - 77999532 q^{26} - 373071582 q^{27} - 444601862 q^{28} + 81530981 q^{29} + 208919493 q^{30} - 408861231 q^{31} - 26253128 q^{32} - 140719842 q^{33} - 508910076 q^{34} - 75731421 q^{35} + 1362260430 q^{36} - 802381301 q^{37} + 732704675 q^{38} + 490504734 q^{39} - 646130800 q^{40} - 1354472849 q^{41} - 1010251359 q^{42} + 282952194 q^{43} + 1846047996 q^{44} + 224858592 q^{45} + 9629305849 q^{46} - 1196794197 q^{47} - 4906236582 q^{48} + 10889725683 q^{49} - 6236232091 q^{50} + 3179531799 q^{51} - 1968200812 q^{52} - 8276044236 q^{53} + 1119214746 q^{54} - 6672895076 q^{55} + 2579741342 q^{56} - 2409887133 q^{57} - 9401656060 q^{58} + 18588031774 q^{59} - 2470248819 q^{60} - 21181559029 q^{61} - 6117706514 q^{62} - 5835163131 q^{63} + 42975855037 q^{64} + 25680681860 q^{65} + 21826385874 q^{66} + 26234163394 q^{67} + 19707344091 q^{68} + 15433713189 q^{69} + 129203099090 q^{70} + 52088830406 q^{71} - 6946819605 q^{72} + 20943384867 q^{73} + 41969200146 q^{74} - 53213805036 q^{75} + 223987219368 q^{76} + 94604773153 q^{77} + 18953886276 q^{78} + 68965662774 q^{79} + 218947784293 q^{80} + 90656394426 q^{81} + 11938614923 q^{82} + 17947446393 q^{83} + 108038252466 q^{84} - 52849386709 q^{85} + 384986147852 q^{86} - 19812028383 q^{87} - 49061112607 q^{88} + 38570593981 q^{89} - 50767436799 q^{90} - 226268806999 q^{91} - 79559686310 q^{92} + 99353279133 q^{93} - 16709400108 q^{94} - 252795831501 q^{95} + 6379510104 q^{96} - 186894587836 q^{97} - 252443311612 q^{98} + 34194921606 q^{99}+O(q^{100}) \) 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9 - 859751 * q^10 + 579094 * q^11 - 5606010 * q^12 - 2018538 * q^13 + 4157413 * q^14 - 925344 * q^15 + 20190274 * q^16 - 13084493 * q^17 - 4605822 * q^18 + 9917231 * q^19 + 10165633 * q^20 + 24013017 * q^21 - 89820518 * q^22 - 63513223 * q^23 + 28587735 * q^24 + 218986852 * q^25 - 77999532 * q^26 - 373071582 * q^27 - 444601862 * q^28 + 81530981 * q^29 + 208919493 * q^30 - 408861231 * q^31 - 26253128 * q^32 - 140719842 * q^33 - 508910076 * q^34 - 75731421 * q^35 + 1362260430 * q^36 - 802381301 * q^37 + 732704675 * q^38 + 490504734 * q^39 - 646130800 * q^40 - 1354472849 * q^41 - 1010251359 * q^42 + 282952194 * q^43 + 1846047996 * q^44 + 224858592 * q^45 + 9629305849 * q^46 - 1196794197 * q^47 - 4906236582 * q^48 + 10889725683 * q^49 - 6236232091 * q^50 + 3179531799 * q^51 - 1968200812 * q^52 - 8276044236 * q^53 + 1119214746 * q^54 - 6672895076 * q^55 + 2579741342 * q^56 - 2409887133 * q^57 - 9401656060 * q^58 + 18588031774 * q^59 - 2470248819 * q^60 - 21181559029 * q^61 - 6117706514 * q^62 - 5835163131 * q^63 + 42975855037 * q^64 + 25680681860 * q^65 + 21826385874 * q^66 + 26234163394 * q^67 + 19707344091 * q^68 + 15433713189 * q^69 + 129203099090 * q^70 + 52088830406 * q^71 - 6946819605 * q^72 + 20943384867 * q^73 + 41969200146 * q^74 - 53213805036 * q^75 + 223987219368 * q^76 + 94604773153 * q^77 + 18953886276 * q^78 + 68965662774 * q^79 + 218947784293 * q^80 + 90656394426 * q^81 + 11938614923 * q^82 + 17947446393 * q^83 + 108038252466 * q^84 - 52849386709 * q^85 + 384986147852 * q^86 - 19812028383 * q^87 - 49061112607 * q^88 + 38570593981 * q^89 - 50767436799 * q^90 - 226268806999 * q^91 - 79559686310 * q^92 + 99353279133 * q^93 - 16709400108 * q^94 - 252795831501 * q^95 + 6379510104 * q^96 - 186894587836 * q^97 - 252443311612 * q^98 + 34194921606 * q^99

Introduction

L-functions

Modular forms

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