LMFDB - Embedded newform 177.12.a.a.1.5

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			1.5
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)

$f(q)$	$=$	$q-66.9000 q^{2} -243.000 q^{3} +2427.61 q^{4} -5686.53 q^{5} +16256.7 q^{6} +26687.5 q^{7} -25395.7 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-66.9000 q^{2} -243.000 q^{3} +2427.61 q^{4} -5686.53 q^{5} +16256.7 q^{6} +26687.5 q^{7} -25395.7 q^{8} +59049.0 q^{9} +380429. q^{10} +282948. q^{11} -589908. q^{12} +1.28590e6 q^{13} -1.78539e6 q^{14} +1.38183e6 q^{15} -3.27277e6 q^{16} -4.91113e6 q^{17} -3.95038e6 q^{18} -4.23666e6 q^{19} -1.38047e7 q^{20} -6.48505e6 q^{21} -1.89292e7 q^{22} +3.04935e7 q^{23} +6.17115e6 q^{24} -1.64915e7 q^{25} -8.60268e7 q^{26} -1.43489e7 q^{27} +6.47867e7 q^{28} +1.00209e8 q^{29} -9.24442e7 q^{30} -1.83681e8 q^{31} +2.70958e8 q^{32} -6.87563e7 q^{33} +3.28555e8 q^{34} -1.51759e8 q^{35} +1.43348e8 q^{36} -4.83150e8 q^{37} +2.83432e8 q^{38} -3.12474e8 q^{39} +1.44413e8 q^{40} -4.31814e8 q^{41} +4.33850e8 q^{42} -3.19027e8 q^{43} +6.86886e8 q^{44} -3.35784e8 q^{45} -2.04002e9 q^{46} +1.15008e9 q^{47} +7.95283e8 q^{48} -1.26511e9 q^{49} +1.10328e9 q^{50} +1.19341e9 q^{51} +3.12167e9 q^{52} -1.32282e9 q^{53} +9.59942e8 q^{54} -1.60899e9 q^{55} -6.77747e8 q^{56} +1.02951e9 q^{57} -6.70395e9 q^{58} +7.14924e8 q^{59} +3.35453e9 q^{60} +4.52154e9 q^{61} +1.22882e10 q^{62} +1.57587e9 q^{63} -1.14245e10 q^{64} -7.31233e9 q^{65} +4.59980e9 q^{66} +1.21583e10 q^{67} -1.19223e10 q^{68} -7.40993e9 q^{69} +1.01527e10 q^{70} +2.63791e10 q^{71} -1.49959e9 q^{72} -1.30795e9 q^{73} +3.23227e10 q^{74} +4.00743e9 q^{75} -1.02849e10 q^{76} +7.55116e9 q^{77} +2.09045e10 q^{78} -1.29817e10 q^{79} +1.86107e10 q^{80} +3.48678e9 q^{81} +2.88883e10 q^{82} -6.28207e10 q^{83} -1.57432e10 q^{84} +2.79273e10 q^{85} +2.13429e10 q^{86} -2.43507e10 q^{87} -7.18566e9 q^{88} +4.23991e10 q^{89} +2.24639e10 q^{90} +3.43175e10 q^{91} +7.40263e10 q^{92} +4.46344e10 q^{93} -7.69402e10 q^{94} +2.40919e10 q^{95} -6.58429e10 q^{96} +5.43637e10 q^{97} +8.46356e10 q^{98} +1.67078e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−66.9000	−1.47829	−0.739147	−	0.673544i	$-0.764771\pi$
$2$	−66.9000	−1.47829	−0.739147	+	0.673544i	$0.764771\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	2427.61	1.18535
$5$	−5686.53	−0.813790	−0.406895	−	0.913475i	$-0.633389\pi$
$5$	−5686.53	−0.813790	−0.406895	+	0.913475i	$0.633389\pi$
$6$	16256.7	0.853494
$7$	26687.5	0.600162	0.300081	−	0.953914i	$-0.402986\pi$
$7$	26687.5	0.600162	0.300081	+	0.953914i	$0.402986\pi$
$8$	−25395.7	−0.274009
$9$	59049.0	0.333333
$10$	380429.	1.20302
$11$	282948.	0.529720	0.264860	−	0.964287i	$-0.414674\pi$
$11$	282948.	0.529720	0.264860	+	0.964287i	$0.414674\pi$
$12$	−589908.	−0.684365
$13$	1.28590e6	0.960549	0.480275	−	0.877118i	$-0.340537\pi$
$13$	1.28590e6	0.960549	0.480275	+	0.877118i	$0.340537\pi$
$14$	−1.78539e6	−0.887216
$15$	1.38183e6	0.469842
$16$	−3.27277e6	−0.780289
$17$	−4.91113e6	−0.838905	−0.419452	−	0.907777i	$-0.637778\pi$
$17$	−4.91113e6	−0.838905	−0.419452	+	0.907777i	$0.637778\pi$
$18$	−3.95038e6	−0.492765
$19$	−4.23666e6	−0.392535	−0.196268	−	0.980550i	$-0.562882\pi$
$19$	−4.23666e6	−0.392535	−0.196268	+	0.980550i	$0.562882\pi$
$20$	−1.38047e7	−0.964630
$21$	−6.48505e6	−0.346503
$22$	−1.89292e7	−0.783083
$23$	3.04935e7	0.987881	0.493941	−	0.869496i	$-0.335556\pi$
$23$	3.04935e7	0.987881	0.493941	+	0.869496i	$0.335556\pi$
$24$	6.17115e6	0.158199
$25$	−1.64915e7	−0.337745
$26$	−8.60268e7	−1.41997
$27$	−1.43489e7	−0.192450
$28$	6.47867e7	0.711404
$29$	1.00209e8	0.907227	0.453614	−	0.891198i	$-0.350135\pi$
$29$	1.00209e8	0.907227	0.453614	+	0.891198i	$0.350135\pi$
$30$	−9.24442e7	−0.694565
$31$	−1.83681e8	−1.15232	−0.576161	−	0.817336i	$-0.695450\pi$
$31$	−1.83681e8	−1.15232	−0.576161	+	0.817336i	$0.695450\pi$
$32$	2.70958e8	1.42751
$33$	−6.87563e7	−0.305834
$34$	3.28555e8	1.24015
$35$	−1.51759e8	−0.488406
$36$	1.43348e8	0.395118
$37$	−4.83150e8	−1.14544	−0.572720	−	0.819751i	$-0.694112\pi$
$37$	−4.83150e8	−1.14544	−0.572720	+	0.819751i	$0.694112\pi$
$38$	2.83432e8	0.580283
$39$	−3.12474e8	−0.554573
$40$	1.44413e8	0.222986
$41$	−4.31814e8	−0.582084	−0.291042	−	0.956710i	$-0.594002\pi$
$41$	−4.31814e8	−0.582084	−0.291042	+	0.956710i	$0.594002\pi$
$42$	4.33850e8	0.512234
$43$	−3.19027e8	−0.330941	−0.165470	−	0.986215i	$-0.552914\pi$
$43$	−3.19027e8	−0.330941	−0.165470	+	0.986215i	$0.552914\pi$
$44$	6.86886e8	0.627907
$45$	−3.35784e8	−0.271263
$46$	−2.04002e9	−1.46038
$47$	1.15008e9	0.731457	0.365729	−	0.930721i	$-0.380820\pi$
$47$	1.15008e9	0.731457	0.365729	+	0.930721i	$0.380820\pi$
$48$	7.95283e8	0.450500
$49$	−1.26511e9	−0.639806
$50$	1.10328e9	0.499287
$51$	1.19341e9	0.484342
$52$	3.12167e9	1.13859
$53$	−1.32282e9	−0.434495	−0.217247	−	0.976117i	$-0.569708\pi$
$53$	−1.32282e9	−0.434495	−0.217247	+	0.976117i	$0.569708\pi$
$54$	9.59942e8	0.284498
$55$	−1.60899e9	−0.431081
$56$	−6.77747e8	−0.164450
$57$	1.02951e9	0.226630
$58$	−6.70395e9	−1.34115
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	3.35453e9	0.556930
$61$	4.52154e9	0.685444	0.342722	−	0.939437i	$-0.388651\pi$
$61$	4.52154e9	0.685444	0.342722	+	0.939437i	$0.388651\pi$
$62$	1.22882e10	1.70347
$63$	1.57587e9	0.200054
$64$	−1.14245e10	−1.32999
$65$	−7.31233e9	−0.781686
$66$	4.59980e9	0.452113
$67$	1.21583e10	1.10017	0.550087	−	0.835107i	$-0.314594\pi$
$67$	1.21583e10	1.10017	0.550087	+	0.835107i	$0.314594\pi$
$68$	−1.19223e10	−0.994400
$69$	−7.40993e9	−0.570353
$70$	1.01527e10	0.722007
$71$	2.63791e10	1.73516	0.867580	−	0.497298i	$-0.165675\pi$
$71$	2.63791e10	1.73516	0.867580	+	0.497298i	$0.165675\pi$
$72$	−1.49959e9	−0.0913364
$73$	−1.30795e9	−0.0738438	−0.0369219	−	0.999318i	$-0.511755\pi$
$73$	−1.30795e9	−0.0738438	−0.0369219	+	0.999318i	$0.511755\pi$
$74$	3.23227e10	1.69330
$75$	4.00743e9	0.194997
$76$	−1.02849e10	−0.465294
$77$	7.55116e9	0.317918
$78$	2.09045e10	0.819823
$79$	−1.29817e10	−0.474662	−0.237331	−	0.971429i	$-0.576273\pi$
$79$	−1.29817e10	−0.474662	−0.237331	+	0.971429i	$0.576273\pi$
$80$	1.86107e10	0.634991
$81$	3.48678e9	0.111111
$82$	2.88883e10	0.860491
$83$	−6.28207e10	−1.75055	−0.875273	−	0.483630i	$-0.839318\pi$
$83$	−6.28207e10	−1.75055	−0.875273	+	0.483630i	$0.839318\pi$
$84$	−1.57432e10	−0.410730
$85$	2.79273e10	0.682693
$86$	2.13429e10	0.489228
$87$	−2.43507e10	−0.523788
$88$	−7.18566e9	−0.145148
$89$	4.23991e10	0.804845	0.402422	−	0.915454i	$-0.368168\pi$
$89$	4.23991e10	0.804845	0.402422	+	0.915454i	$0.368168\pi$
$90$	2.24639e10	0.401007
$91$	3.43175e10	0.576485
$92$	7.40263e10	1.17099
$93$	4.46344e10	0.665294
$94$	−7.69402e10	−1.08131
$95$	2.40919e10	0.319441
$96$	−6.58429e10	−0.824171
$97$	5.43637e10	0.642783	0.321391	−	0.946946i	$-0.395850\pi$
$97$	5.43637e10	0.642783	0.321391	+	0.946946i	$0.395850\pi$
$98$	8.46356e10	0.945822
$99$	1.67078e10	0.176573
$100$	−4.00348e10	−0.400348
$101$	2.15225e10	0.203763	0.101881	−	0.994797i	$-0.467514\pi$
$101$	2.15225e10	0.203763	0.101881	+	0.994797i	$0.467514\pi$
$102$	−7.98388e10	−0.716000
$103$	1.12937e11	0.959911	0.479956	−	0.877293i	$-0.340653\pi$
$103$	1.12937e11	0.959911	0.479956	+	0.877293i	$0.340653\pi$
$104$	−3.26564e10	−0.263199
$105$	3.68775e10	0.281981
$106$	8.84968e10	0.642311
$107$	2.55906e11	1.76388	0.881942	−	0.471357i	$-0.156236\pi$
$107$	2.55906e11	1.76388	0.881942	+	0.471357i	$0.156236\pi$
$108$	−3.48335e10	−0.228122
$109$	2.26916e10	0.141260	0.0706300	−	0.997503i	$-0.477499\pi$
$109$	2.26916e10	0.141260	0.0706300	+	0.997503i	$0.477499\pi$
$110$	1.07642e11	0.637265
$111$	1.17405e11	0.661320
$112$	−8.73419e10	−0.468299
$113$	2.38933e11	1.21996	0.609979	−	0.792417i	$-0.291178\pi$
$113$	2.38933e11	1.21996	0.609979	+	0.792417i	$0.291178\pi$
$114$	−6.88741e10	−0.335026
$115$	−1.73402e11	−0.803928
$116$	2.43267e11	1.07539
$117$	7.59313e10	0.320183
$118$	−4.78284e10	−0.192458
$119$	−1.31066e11	−0.503478
$120$	−3.50925e10	−0.128741
$121$	−2.05252e11	−0.719396
$122$	−3.02491e11	−1.01329
$123$	1.04931e11	0.336066
$124$	−4.45904e11	−1.36591
$125$	3.71442e11	1.08864
$126$	−1.05426e11	−0.295739
$127$	2.39317e11	0.642767	0.321384	−	0.946949i	$-0.395852\pi$
$127$	2.39317e11	0.642767	0.321384	+	0.946949i	$0.395852\pi$
$128$	2.09375e11	0.538604
$129$	7.75235e10	0.191069
$130$	4.89194e11	1.15556
$131$	−3.16017e11	−0.715679	−0.357840	−	0.933783i	$-0.616487\pi$
$131$	−3.16017e11	−0.715679	−0.357840	+	0.933783i	$0.616487\pi$
$132$	−1.66913e11	−0.362522
$133$	−1.13066e11	−0.235585
$134$	−8.13391e11	−1.62638
$135$	8.15955e10	0.156614
$136$	1.24722e11	0.229868
$137$	−9.07763e11	−1.60698	−0.803488	−	0.595322i	$-0.797025\pi$
$137$	−9.07763e11	−1.60698	−0.803488	+	0.595322i	$0.797025\pi$
$138$	4.95724e11	0.843150
$139$	−6.26986e11	−1.02489	−0.512444	−	0.858721i	$-0.671260\pi$
$139$	−6.26986e11	−1.02489	−0.512444	+	0.858721i	$0.671260\pi$
$140$	−3.68412e11	−0.578934
$141$	−2.79469e11	−0.422307
$142$	−1.76476e12	−2.56508
$143$	3.63843e11	0.508823
$144$	−1.93254e11	−0.260096
$145$	−5.69840e11	−0.738293
$146$	8.75015e10	0.109163
$147$	3.07421e11	0.369392
$148$	−1.17290e12	−1.35775
$149$	−6.38390e11	−0.712134	−0.356067	−	0.934460i	$-0.615882\pi$
$149$	−6.38390e11	−0.712134	−0.356067	+	0.934460i	$0.615882\pi$
$150$	−2.68097e11	−0.288263
$151$	−1.10415e12	−1.14460	−0.572302	−	0.820043i	$-0.693950\pi$
$151$	−1.10415e12	−1.14460	−0.572302	+	0.820043i	$0.693950\pi$
$152$	1.07593e11	0.107558
$153$	−2.89998e11	−0.279635
$154$	−5.05173e11	−0.469976
$155$	1.04451e12	0.937749
$156$	−7.58565e11	−0.657366
$157$	−1.69080e12	−1.41463	−0.707316	−	0.706898i	$-0.750094\pi$
$157$	−1.69080e12	−1.41463	−0.707316	+	0.706898i	$0.750094\pi$
$158$	8.68479e11	0.701690
$159$	3.21446e11	0.250856
$160$	−1.54081e12	−1.16169
$161$	8.13795e11	0.592888
$162$	−2.33266e11	−0.164255
$163$	1.43370e12	0.975948	0.487974	−	0.872858i	$-0.337736\pi$
$163$	1.43370e12	0.975948	0.487974	+	0.872858i	$0.337736\pi$
$164$	−1.04827e12	−0.689976
$165$	3.90985e11	0.248885
$166$	4.20270e12	2.58782
$167$	−5.68321e11	−0.338574	−0.169287	−	0.985567i	$-0.554146\pi$
$167$	−5.68321e11	−0.338574	−0.169287	+	0.985567i	$0.554146\pi$
$168$	1.64692e11	0.0949451
$169$	−1.38615e11	−0.0773454
$170$	−1.86834e12	−1.00922
$171$	−2.50170e11	−0.130845
$172$	−7.74471e11	−0.392282
$173$	3.65112e12	1.79132	0.895659	−	0.444741i	$-0.146704\pi$
$173$	3.65112e12	1.79132	0.895659	+	0.444741i	$0.146704\pi$
$174$	1.62906e12	0.774313
$175$	−4.40115e11	−0.202702
$176$	−9.26023e11	−0.413335
$177$	−1.73727e11	−0.0751646
$178$	−2.83650e12	−1.18980
$179$	−2.92612e12	−1.19015	−0.595074	−	0.803671i	$-0.702877\pi$
$179$	−2.92612e12	−1.19015	−0.595074	+	0.803671i	$0.702877\pi$
$180$	−8.15152e11	−0.321543
$181$	−8.42623e11	−0.322404	−0.161202	−	0.986921i	$-0.551537\pi$
$181$	−8.42623e11	−0.322404	−0.161202	+	0.986921i	$0.551537\pi$
$182$	−2.29584e12	−0.852214
$183$	−1.09873e12	−0.395742
$184$	−7.74405e11	−0.270689
$185$	2.74745e12	0.932149
$186$	−2.98604e12	−0.983500
$187$	−1.38960e12	−0.444385
$188$	2.79194e12	0.867037
$189$	−3.82936e11	−0.115501
$190$	−1.61175e12	−0.472229
$191$	3.36937e12	0.959102	0.479551	−	0.877514i	$-0.340800\pi$
$191$	3.36937e12	0.959102	0.479551	+	0.877514i	$0.340800\pi$
$192$	2.77615e12	0.767867
$193$	−2.62087e12	−0.704498	−0.352249	−	0.935906i	$-0.614583\pi$
$193$	−2.62087e12	−0.704498	−0.352249	+	0.935906i	$0.614583\pi$
$194$	−3.63693e12	−0.950222
$195$	1.77690e12	0.451306
$196$	−3.07118e12	−0.758397
$197$	−3.85437e12	−0.925528	−0.462764	−	0.886481i	$-0.653142\pi$
$197$	−3.85437e12	−0.925528	−0.462764	+	0.886481i	$0.653142\pi$
$198$	−1.11775e12	−0.261028
$199$	6.03566e12	1.37099	0.685493	−	0.728080i	$-0.259587\pi$
$199$	6.03566e12	1.37099	0.685493	+	0.728080i	$0.259587\pi$
$200$	4.18812e11	0.0925453
$201$	−2.95447e12	−0.635186
$202$	−1.43985e12	−0.301222
$203$	2.67431e12	0.544483
$204$	2.89712e12	0.574117
$205$	2.45552e12	0.473694
$206$	−7.55548e12	−1.41903
$207$	1.80061e12	0.329294
$208$	−4.20846e12	−0.749506
$209$	−1.19875e12	−0.207934
$210$	−2.46710e12	−0.416851
$211$	2.87168e12	0.472696	0.236348	−	0.971668i	$-0.424049\pi$
$211$	2.87168e12	0.472696	0.236348	+	0.971668i	$0.424049\pi$
$212$	−3.21129e12	−0.515030
$213$	−6.41013e12	−1.00179
$214$	−1.71201e13	−2.60754
$215$	1.81416e12	0.269317
$216$	3.64400e11	0.0527331
$217$	−4.90197e12	−0.691580
$218$	−1.51807e12	−0.208824
$219$	3.17831e11	0.0426337
$220$	−3.90600e12	−0.510985
$221$	−6.31524e12	−0.805809
$222$	−7.85442e12	−0.977626
$223$	−2.02890e11	−0.0246368	−0.0123184	−	0.999924i	$-0.503921\pi$
$223$	−2.02890e11	−0.0246368	−0.0123184	+	0.999924i	$0.503921\pi$
$224$	7.23120e12	0.856734
$225$	−9.73805e11	−0.112582
$226$	−1.59846e13	−1.80346
$227$	6.43975e10	0.00709132	0.00354566	−	0.999994i	$-0.498871\pi$
$227$	6.43975e10	0.00709132	0.00354566	+	0.999994i	$0.498871\pi$
$228$	2.49924e12	0.268637
$229$	−5.01326e12	−0.526047	−0.263024	−	0.964789i	$-0.584720\pi$
$229$	−5.01326e12	−0.526047	−0.263024	+	0.964789i	$0.584720\pi$
$230$	1.16006e13	1.18844
$231$	−1.83493e12	−0.183550
$232$	−2.54487e12	−0.248589
$233$	−1.08417e12	−0.103428	−0.0517142	−	0.998662i	$-0.516468\pi$
$233$	−1.08417e12	−0.103428	−0.0517142	+	0.998662i	$0.516468\pi$
$234$	−5.07980e12	−0.473325
$235$	−6.53996e12	−0.595253
$236$	1.73556e12	0.154320
$237$	3.15457e12	0.274046
$238$	8.76829e12	0.744289
$239$	−1.15366e13	−0.956950	−0.478475	−	0.878101i	$-0.658810\pi$
$239$	−1.15366e13	−0.956950	−0.478475	+	0.878101i	$0.658810\pi$
$240$	−4.52240e12	−0.366612
$241$	1.51057e13	1.19687	0.598434	−	0.801172i	$-0.295790\pi$
$241$	1.51057e13	1.19687	0.598434	+	0.801172i	$0.295790\pi$
$242$	1.37314e13	1.06348
$243$	−8.47289e11	−0.0641500
$244$	1.09765e13	0.812495
$245$	7.19407e12	0.520668
$246$	−7.01987e12	−0.496805
$247$	−5.44793e12	−0.377049
$248$	4.66470e12	0.315747
$249$	1.52654e13	1.01068
$250$	−2.48495e13	−1.60934
$251$	−1.46102e13	−0.925658	−0.462829	−	0.886448i	$-0.653166\pi$
$251$	−1.46102e13	−0.925658	−0.462829	+	0.886448i	$0.653166\pi$
$252$	3.82559e12	0.237135
$253$	8.62808e12	0.523301
$254$	−1.60103e13	−0.950199
$255$	−6.78634e12	−0.394153
$256$	9.39017e12	0.533769
$257$	−2.37008e13	−1.31865	−0.659327	−	0.751856i	$-0.729159\pi$
$257$	−2.37008e13	−1.31865	−0.659327	+	0.751856i	$0.729159\pi$
$258$	−5.18632e12	−0.282456
$259$	−1.28941e13	−0.687449
$260$	−1.77515e13	−0.926575
$261$	5.91722e12	0.302409
$262$	2.11415e13	1.05798
$263$	1.05117e13	0.515129	0.257564	−	0.966261i	$-0.417080\pi$
$263$	1.05117e13	0.515129	0.257564	+	0.966261i	$0.417080\pi$
$264$	1.74612e12	0.0838014
$265$	7.52227e12	0.353587
$266$	7.56409e12	0.348263
$267$	−1.03030e13	−0.464677
$268$	2.95156e13	1.30410
$269$	−1.72454e12	−0.0746510	−0.0373255	−	0.999303i	$-0.511884\pi$
$269$	−1.72454e12	−0.0746510	−0.0373255	+	0.999303i	$0.511884\pi$
$270$	−5.45874e12	−0.231522
$271$	−4.51661e12	−0.187707	−0.0938537	−	0.995586i	$-0.529919\pi$
$271$	−4.51661e12	−0.187707	−0.0938537	+	0.995586i	$0.529919\pi$
$272$	1.60730e13	0.654588
$273$	−8.33915e12	−0.332834
$274$	6.07293e13	2.37558
$275$	−4.66623e12	−0.178911
$276$	−1.79884e13	−0.676071
$277$	7.49024e12	0.275967	0.137983	−	0.990435i	$-0.455938\pi$
$277$	7.49024e12	0.275967	0.137983	+	0.990435i	$0.455938\pi$
$278$	4.19453e13	1.51509
$279$	−1.08462e13	−0.384108
$280$	3.85403e12	0.133828
$281$	5.21166e13	1.77456	0.887281	−	0.461230i	$-0.152592\pi$
$281$	5.21166e13	1.77456	0.887281	+	0.461230i	$0.152592\pi$
$282$	1.86965e13	0.624294
$283$	−1.20033e13	−0.393073	−0.196537	−	0.980496i	$-0.562969\pi$
$283$	−1.20033e13	−0.393073	−0.196537	+	0.980496i	$0.562969\pi$
$284$	6.40381e13	2.05678
$285$	−5.85433e12	−0.184430
$286$	−2.43411e13	−0.752190
$287$	−1.15240e13	−0.349344
$288$	1.59998e13	0.475835
$289$	−1.01527e13	−0.296239
$290$	3.81223e13	1.09141
$291$	−1.32104e13	−0.371111
$292$	−3.17518e12	−0.0875311
$293$	3.11650e13	0.843131	0.421565	−	0.906798i	$-0.361481\pi$
$293$	3.11650e13	0.843131	0.421565	+	0.906798i	$0.361481\pi$
$294$	−2.05664e13	−0.546071
$295$	−4.06544e12	−0.105946
$296$	1.22699e13	0.313861
$297$	−4.05999e12	−0.101945
$298$	4.27083e13	1.05274
$299$	3.92117e13	0.948908
$300$	9.72846e12	0.231141
$301$	−8.51401e12	−0.198618
$302$	7.38677e13	1.69206
$303$	−5.22997e12	−0.117643
$304$	1.38656e13	0.306291
$305$	−2.57119e13	−0.557808
$306$	1.94008e13	0.413383
$307$	−2.42596e13	−0.507718	−0.253859	−	0.967241i	$-0.581700\pi$
$307$	−2.42596e13	−0.507718	−0.253859	+	0.967241i	$0.581700\pi$
$308$	1.83313e13	0.376845
$309$	−2.74437e13	−0.554205
$310$	−6.98774e13	−1.38627
$311$	7.39191e13	1.44070	0.720351	−	0.693609i	$-0.243981\pi$
$311$	7.39191e13	1.44070	0.720351	+	0.693609i	$0.243981\pi$
$312$	7.93550e12	0.151958
$313$	−3.42215e13	−0.643881	−0.321940	−	0.946760i	$-0.604335\pi$
$313$	−3.42215e13	−0.643881	−0.321940	+	0.946760i	$0.604335\pi$
$314$	1.13114e14	2.09124
$315$	−8.96123e12	−0.162802
$316$	−3.15146e13	−0.562643
$317$	1.74596e13	0.306344	0.153172	−	0.988200i	$-0.451051\pi$
$317$	1.74596e13	0.306344	0.153172	+	0.988200i	$0.451051\pi$
$318$	−2.15047e13	−0.370838
$319$	2.83538e13	0.480577
$320$	6.49657e13	1.08233
$321$	−6.21852e13	−1.01838
$322$	−5.44429e13	−0.876463
$323$	2.08068e13	0.329300
$324$	8.46454e12	0.131706
$325$	−2.12064e13	−0.324421
$326$	−9.59145e13	−1.44274
$327$	−5.51406e12	−0.0815566
$328$	1.09662e13	0.159496
$329$	3.06927e13	0.438993
$330$	−2.61569e13	−0.367925
$331$	1.41060e14	1.95141	0.975706	−	0.219084i	$-0.0703068\pi$
$331$	1.41060e14	1.95141	0.975706	+	0.219084i	$0.0703068\pi$
$332$	−1.52504e14	−2.07502
$333$	−2.85295e13	−0.381814
$334$	3.80207e13	0.500512
$335$	−6.91386e13	−0.895312
$336$	2.12241e13	0.270373
$337$	−3.86749e12	−0.0484690	−0.0242345	−	0.999706i	$-0.507715\pi$
$337$	−3.86749e12	−0.0484690	−0.0242345	+	0.999706i	$0.507715\pi$
$338$	9.27336e12	0.114339
$339$	−5.80608e13	−0.704343
$340$	6.77966e13	0.809233
$341$	−5.19721e13	−0.610409
$342$	1.67364e13	0.193428
$343$	−8.65323e13	−0.984149
$344$	8.10190e12	0.0906809
$345$	4.21368e13	0.464148
$346$	−2.44260e14	−2.64810
$347$	−4.70102e12	−0.0501626	−0.0250813	−	0.999685i	$-0.507984\pi$
$347$	−4.70102e12	−0.0501626	−0.0250813	+	0.999685i	$0.507984\pi$
$348$	−5.91139e13	−0.620875
$349$	−1.29440e14	−1.33822	−0.669112	−	0.743162i	$-0.733325\pi$
$349$	−1.29440e14	−1.33822	−0.669112	+	0.743162i	$0.733325\pi$
$350$	2.94437e13	0.299653
$351$	−1.84513e13	−0.184858
$352$	7.66671e13	0.756179
$353$	−5.55019e13	−0.538948	−0.269474	−	0.963008i	$-0.586850\pi$
$353$	−5.55019e13	−0.538948	−0.269474	+	0.963008i	$0.586850\pi$
$354$	1.16223e13	0.111115
$355$	−1.50006e14	−1.41206
$356$	1.02928e14	0.954027
$357$	3.18490e13	0.290683
$358$	1.95758e14	1.75939
$359$	1.26971e14	1.12379	0.561893	−	0.827210i	$-0.310073\pi$
$359$	1.26971e14	1.12379	0.561893	+	0.827210i	$0.310073\pi$
$360$	8.52747e12	0.0743287
$361$	−9.85410e13	−0.845916
$362$	5.63714e13	0.476609
$363$	4.98763e13	0.415344
$364$	8.33094e13	0.683339
$365$	7.43768e12	0.0600934
$366$	7.35053e13	0.585023
$367$	−5.95911e13	−0.467216	−0.233608	−	0.972331i	$-0.575053\pi$
$367$	−5.95911e13	−0.467216	−0.233608	+	0.972331i	$0.575053\pi$
$368$	−9.97982e13	−0.770832
$369$	−2.54982e13	−0.194028
$370$	−1.83804e14	−1.37799
$371$	−3.53028e13	−0.260767
$372$	1.08355e14	0.788609
$373$	−4.28866e13	−0.307555	−0.153778	−	0.988105i	$-0.549144\pi$
$373$	−4.28866e13	−0.307555	−0.153778	+	0.988105i	$0.549144\pi$
$374$	9.29639e13	0.656932
$375$	−9.02604e13	−0.628529
$376$	−2.92070e13	−0.200426
$377$	1.28859e14	0.871436
$378$	2.56184e13	0.170745
$379$	2.27560e13	0.149479	0.0747395	−	0.997203i	$-0.476187\pi$
$379$	2.27560e13	0.149479	0.0747395	+	0.997203i	$0.476187\pi$
$380$	5.84857e13	0.378652
$381$	−5.81541e13	−0.371102
$382$	−2.25410e14	−1.41783
$383$	9.29424e13	0.576263	0.288131	−	0.957591i	$-0.406966\pi$
$383$	9.29424e13	0.576263	0.288131	+	0.957591i	$0.406966\pi$
$384$	−5.08781e13	−0.310963
$385$	−4.29399e13	−0.258718
$386$	1.75336e14	1.04146
$387$	−1.88382e13	−0.110314
$388$	1.31974e14	0.761926
$389$	1.07869e14	0.614006	0.307003	−	0.951709i	$-0.400674\pi$
$389$	1.07869e14	0.614006	0.307003	+	0.951709i	$0.400674\pi$
$390$	−1.18874e14	−0.667164
$391$	−1.49758e14	−0.828738
$392$	3.21282e13	0.175313
$393$	7.67922e13	0.413198
$394$	2.57858e14	1.36820
$395$	7.38212e13	0.386275
$396$	4.05600e13	0.209302
$397$	−2.79738e13	−0.142365	−0.0711826	−	0.997463i	$-0.522677\pi$
$397$	−2.79738e13	−0.142365	−0.0711826	+	0.997463i	$0.522677\pi$
$398$	−4.03785e14	−2.02672
$399$	2.74750e13	0.136015
$400$	5.39727e13	0.263539
$401$	2.90854e13	0.140082	0.0700409	−	0.997544i	$-0.477687\pi$
$401$	2.90854e13	0.140082	0.0700409	+	0.997544i	$0.477687\pi$
$402$	1.97654e14	0.938993
$403$	−2.36195e14	−1.10686
$404$	5.22482e13	0.241531
$405$	−1.98277e13	−0.0904212
$406$	−1.78912e14	−0.804906
$407$	−1.36706e14	−0.606763
$408$	−3.03074e13	−0.132714
$409$	−2.71616e14	−1.17348	−0.586742	−	0.809774i	$-0.699590\pi$
$409$	−2.71616e14	−1.17348	−0.586742	+	0.809774i	$0.699590\pi$
$410$	−1.64274e14	−0.700259
$411$	2.20586e14	0.927787
$412$	2.74166e14	1.13784
$413$	1.90795e13	0.0781344
$414$	−1.20461e14	−0.486793
$415$	3.57232e14	1.42458
$416$	3.48426e14	1.37119
$417$	1.52358e14	0.591719
$418$	8.01966e13	0.307388
$419$	1.26526e14	0.478635	0.239317	−	0.970941i	$-0.423076\pi$
$419$	1.26526e14	0.478635	0.239317	+	0.970941i	$0.423076\pi$
$420$	8.95240e13	0.334248
$421$	−1.78571e14	−0.658051	−0.329025	−	0.944321i	$-0.606720\pi$
$421$	−1.78571e14	−0.658051	−0.329025	+	0.944321i	$0.606720\pi$
$422$	−1.92115e14	−0.698784
$423$	6.79110e13	0.243819
$424$	3.35940e13	0.119056
$425$	8.09918e13	0.283336
$426$	4.28837e14	1.48095
$427$	1.20668e14	0.411377
$428$	6.21240e14	2.09083
$429$	−8.84140e13	−0.293769
$430$	−1.21367e14	−0.398129
$431$	2.71648e14	0.879795	0.439898	−	0.898048i	$-0.355015\pi$
$431$	2.71648e14	0.879795	0.439898	+	0.898048i	$0.355015\pi$
$432$	4.69606e13	0.150167
$433$	−3.49275e14	−1.10277	−0.551384	−	0.834252i	$-0.685900\pi$
$433$	−3.49275e14	−1.10277	−0.551384	+	0.834252i	$0.685900\pi$
$434$	3.27942e14	1.02236
$435$	1.38471e14	0.426254
$436$	5.50863e13	0.167443
$437$	−1.29191e14	−0.387778
$438$	−2.12629e13	−0.0630252
$439$	6.49482e13	0.190113	0.0950566	−	0.995472i	$-0.469697\pi$
$439$	6.49482e13	0.190113	0.0950566	+	0.995472i	$0.469697\pi$
$440$	4.08615e13	0.118120
$441$	−7.47032e13	−0.213269
$442$	4.22489e14	1.19122
$443$	−2.80298e14	−0.780547	−0.390273	−	0.920699i	$-0.627620\pi$
$443$	−2.80298e14	−0.780547	−0.390273	+	0.920699i	$0.627620\pi$
$444$	2.85014e14	0.783899
$445$	−2.41104e14	−0.654975
$446$	1.35733e13	0.0364204
$447$	1.55129e14	0.411151
$448$	−3.04891e14	−0.798206
$449$	−4.83240e14	−1.24971	−0.624853	−	0.780743i	$-0.714841\pi$
$449$	−4.83240e14	−1.24971	−0.624853	+	0.780743i	$0.714841\pi$
$450$	6.51475e13	0.166429
$451$	−1.22181e14	−0.308342
$452$	5.80036e14	1.44608
$453$	2.68309e14	0.660838
$454$	−4.30819e12	−0.0104831
$455$	−1.95147e14	−0.469138
$456$	−2.61451e13	−0.0620988
$457$	−4.72542e14	−1.10892	−0.554461	−	0.832210i	$-0.687076\pi$
$457$	−4.72542e14	−1.10892	−0.554461	+	0.832210i	$0.687076\pi$
$458$	3.35387e14	0.777653
$459$	7.04694e13	0.161447
$460$	−4.20953e14	−0.952940
$461$	7.26202e14	1.62444	0.812218	−	0.583354i	$-0.198260\pi$
$461$	7.26202e14	1.62444	0.812218	+	0.583354i	$0.198260\pi$
$462$	1.22757e14	0.271341
$463$	2.66401e14	0.581890	0.290945	−	0.956740i	$-0.406030\pi$
$463$	2.66401e14	0.581890	0.290945	+	0.956740i	$0.406030\pi$
$464$	−3.27960e14	−0.707899
$465$	−2.53815e14	−0.541410
$466$	7.25309e13	0.152898
$467$	−8.75398e14	−1.82374	−0.911870	−	0.410479i	$-0.865361\pi$
$467$	−8.75398e14	−1.82374	−0.911870	+	0.410479i	$0.865361\pi$
$468$	1.84331e14	0.379531
$469$	3.24474e14	0.660283
$470$	4.37523e14	0.879959
$471$	4.10864e14	0.816738
$472$	−1.81560e13	−0.0356730
$473$	−9.02679e13	−0.175306
$474$	−2.11040e14	−0.405121
$475$	6.98687e13	0.132577
$476$	−3.18176e14	−0.596801
$477$	−7.81113e13	−0.144832
$478$	7.71798e14	1.41465
$479$	−3.50732e14	−0.635521	−0.317761	−	0.948171i	$-0.602931\pi$
$479$	−3.50732e14	−0.635521	−0.317761	+	0.948171i	$0.602931\pi$
$480$	3.74418e14	0.670702
$481$	−6.21284e14	−1.10025
$482$	−1.01057e15	−1.76932
$483$	−1.97752e14	−0.342304
$484$	−4.98272e14	−0.852740
$485$	−3.09141e14	−0.523090
$486$	5.66836e13	0.0948326
$487$	−3.92805e14	−0.649782	−0.324891	−	0.945752i	$-0.605328\pi$
$487$	−3.92805e14	−0.649782	−0.324891	+	0.945752i	$0.605328\pi$
$488$	−1.14828e14	−0.187818
$489$	−3.48389e14	−0.563464
$490$	−4.81283e14	−0.769701
$491$	−1.10794e15	−1.75213	−0.876066	−	0.482192i	$-0.839841\pi$
$491$	−1.10794e15	−1.75213	−0.876066	+	0.482192i	$0.839841\pi$
$492$	2.54731e14	0.398358
$493$	−4.92138e14	−0.761077
$494$	3.64466e14	0.557390
$495$	−9.50094e13	−0.143694
$496$	6.01144e14	0.899144
$497$	7.03992e14	1.04138
$498$	−1.02126e15	−1.49408
$499$	7.31455e14	1.05836	0.529182	−	0.848509i	$-0.322499\pi$
$499$	7.31455e14	1.05836	0.529182	+	0.848509i	$0.322499\pi$
$500$	9.01715e14	1.29043
$501$	1.38102e14	0.195476
$502$	9.77422e14	1.36840
$503$	9.77802e14	1.35403	0.677013	−	0.735971i	$-0.263274\pi$
$503$	9.77802e14	1.35403	0.677013	+	0.735971i	$0.263274\pi$
$504$	−4.00203e13	−0.0548166
$505$	−1.22388e14	−0.165820
$506$	−5.77219e14	−0.773593
$507$	3.36835e13	0.0446554
$508$	5.80969e14	0.761907
$509$	−7.70280e14	−0.999311	−0.499655	−	0.866224i	$-0.666540\pi$
$509$	−7.70280e14	−0.999311	−0.499655	+	0.866224i	$0.666540\pi$
$510$	4.54006e14	0.582674
$511$	−3.49058e13	−0.0443182
$512$	−1.05700e15	−1.32767
$513$	6.07914e13	0.0755435
$514$	1.58558e15	1.94936
$515$	−6.42219e14	−0.781167
$516$	1.88197e14	0.226484
$517$	3.25412e14	0.387468
$518$	8.62612e14	1.01625
$519$	−8.87223e14	−1.03422
$520$	1.85702e14	0.214189
$521$	−5.29303e14	−0.604083	−0.302041	−	0.953295i	$-0.597668\pi$
$521$	−5.29303e14	−0.604083	−0.302041	+	0.953295i	$0.597668\pi$
$522$	−3.95862e14	−0.447050
$523$	2.66049e14	0.297305	0.148653	−	0.988889i	$-0.452506\pi$
$523$	2.66049e14	0.297305	0.148653	+	0.988889i	$0.452506\pi$
$524$	−7.67165e14	−0.848334
$525$	1.06948e14	0.117030
$526$	−7.03231e14	−0.761512
$527$	9.02080e14	0.966689
$528$	2.25024e14	0.238639
$529$	−2.29541e13	−0.0240910
$530$	−5.03240e14	−0.522706
$531$	4.22156e13	0.0433963
$532$	−2.74479e14	−0.279251
$533$	−5.55271e14	−0.559120
$534$	6.89270e14	0.686930
$535$	−1.45522e15	−1.43543
$536$	−3.08769e14	−0.301458
$537$	7.11048e14	0.687132
$538$	1.15372e14	0.110356
$539$	−3.57959e14	−0.338918
$540$	1.98082e14	0.185643
$541$	5.18467e14	0.480991	0.240495	−	0.970650i	$-0.422690\pi$
$541$	5.18467e14	0.480991	0.240495	+	0.970650i	$0.422690\pi$
$542$	3.02161e14	0.277487
$543$	2.04757e14	0.186140
$544$	−1.33071e15	−1.19754
$545$	−1.29037e14	−0.114956
$546$	5.57889e14	0.492026
$547$	−3.81590e14	−0.333171	−0.166585	−	0.986027i	$-0.553274\pi$
$547$	−3.81590e14	−0.333171	−0.166585	+	0.986027i	$0.553274\pi$
$548$	−2.20369e15	−1.90484
$549$	2.66992e14	0.228481
$550$	3.12170e14	0.264483
$551$	−4.24550e14	−0.356119
$552$	1.88180e14	0.156282
$553$	−3.46450e14	−0.284874
$554$	−5.01097e14	−0.407960
$555$	−6.67630e14	−0.538176
$556$	−1.52207e15	−1.21486
$557$	−5.81758e14	−0.459768	−0.229884	−	0.973218i	$-0.573835\pi$
$557$	−5.81758e14	−0.459768	−0.229884	+	0.973218i	$0.573835\pi$
$558$	7.25608e14	0.567824
$559$	−4.10237e14	−0.317885
$560$	4.96672e14	0.381097
$561$	3.37672e14	0.256566
$562$	−3.48660e15	−2.62333
$563$	−1.95441e15	−1.45619	−0.728097	−	0.685474i	$-0.759595\pi$
$563$	−1.95441e15	−1.45619	−0.728097	+	0.685474i	$0.759595\pi$
$564$	−6.78441e14	−0.500584
$565$	−1.35870e15	−0.992790
$566$	8.03017e14	0.581078
$567$	9.30534e13	0.0666846
$568$	−6.69916e14	−0.475450
$569$	4.68451e14	0.329266	0.164633	−	0.986355i	$-0.447356\pi$
$569$	4.68451e14	0.329266	0.164633	+	0.986355i	$0.447356\pi$
$570$	3.91655e14	0.272641
$571$	1.80483e15	1.24434	0.622169	−	0.782883i	$-0.286252\pi$
$571$	1.80483e15	1.24434	0.622169	+	0.782883i	$0.286252\pi$
$572$	8.83269e14	0.603135
$573$	−8.18756e14	−0.553738
$574$	7.70957e14	0.516434
$575$	−5.02883e14	−0.333652
$576$	−6.74605e14	−0.443328
$577$	1.86255e14	0.121239	0.0606195	−	0.998161i	$-0.480692\pi$
$577$	1.86255e14	0.121239	0.0606195	+	0.998161i	$0.480692\pi$
$578$	6.79213e14	0.437928
$579$	6.36870e14	0.406742
$580$	−1.38335e15	−0.875139
$581$	−1.67653e15	−1.05061
$582$	8.83773e14	0.548611
$583$	−3.74290e14	−0.230161
$584$	3.32162e13	0.0202339
$585$	−4.31786e14	−0.260562
$586$	−2.08494e15	−1.24640
$587$	−1.85232e15	−1.09700	−0.548501	−	0.836150i	$-0.684801\pi$
$587$	−1.85232e15	−1.09700	−0.548501	+	0.836150i	$0.684801\pi$
$588$	7.46297e14	0.437861
$589$	7.78192e14	0.452327
$590$	2.71978e14	0.156620
$591$	9.36613e14	0.534354
$592$	1.58124e15	0.893774
$593$	−2.53968e15	−1.42226	−0.711129	−	0.703062i	$-0.751816\pi$
$593$	−2.53968e15	−1.42226	−0.711129	+	0.703062i	$0.751816\pi$
$594$	2.71613e14	0.150704
$595$	7.45310e14	0.409726
$596$	−1.54976e15	−0.844131
$597$	−1.46667e15	−0.791539
$598$	−2.62326e15	−1.40277
$599$	2.39471e15	1.26884	0.634418	−	0.772990i	$-0.281240\pi$
$599$	2.39471e15	1.26884	0.634418	+	0.772990i	$0.281240\pi$
$600$	−1.01771e14	−0.0534311
$601$	−5.26533e14	−0.273915	−0.136958	−	0.990577i	$-0.543732\pi$
$601$	−5.26533e14	−0.273915	−0.136958	+	0.990577i	$0.543732\pi$
$602$	5.69587e14	0.293616
$603$	7.17936e14	0.366725
$604$	−2.68045e15	−1.35676
$605$	1.16717e15	0.585438
$606$	3.49885e14	0.173910
$607$	5.86876e14	0.289074	0.144537	−	0.989499i	$-0.453831\pi$
$607$	5.86876e14	0.289074	0.144537	+	0.989499i	$0.453831\pi$
$608$	−1.14796e15	−0.560346
$609$	−6.49858e14	−0.314357
$610$	1.72012e15	0.824605
$611$	1.47889e15	0.702601
$612$	−7.04000e14	−0.331467
$613$	−2.13130e15	−0.994515	−0.497258	−	0.867603i	$-0.665660\pi$
$613$	−2.13130e15	−0.994515	−0.497258	+	0.867603i	$0.665660\pi$
$614$	1.62297e15	0.750556
$615$	−5.96692e14	−0.273487
$616$	−1.91767e14	−0.0871124
$617$	−4.23326e14	−0.190593	−0.0952964	−	0.995449i	$-0.530380\pi$
$617$	−4.23326e14	−0.190593	−0.0952964	+	0.995449i	$0.530380\pi$
$618$	1.83598e15	0.819278
$619$	6.04776e14	0.267483	0.133741	−	0.991016i	$-0.457301\pi$
$619$	6.04776e14	0.267483	0.133741	+	0.991016i	$0.457301\pi$
$620$	2.53565e15	1.11157
$621$	−4.37549e14	−0.190118
$622$	−4.94518e15	−2.12978
$623$	1.13153e15	0.483037
$624$	1.02266e15	0.432727
$625$	−1.30697e15	−0.548183
$626$	2.28942e15	0.951846
$627$	2.91297e14	0.120051
$628$	−4.10459e15	−1.67684
$629$	2.37281e15	0.960916
$630$	5.99506e14	0.240669
$631$	7.18347e14	0.285873	0.142936	−	0.989732i	$-0.454346\pi$
$631$	7.18347e14	0.285873	0.142936	+	0.989732i	$0.454346\pi$
$632$	3.29681e14	0.130062
$633$	−6.97817e14	−0.272911
$634$	−1.16805e15	−0.452866
$635$	−1.36089e15	−0.523078
$636$	7.80344e14	0.297353
$637$	−1.62680e15	−0.614565
$638$	−1.89687e15	−0.710434
$639$	1.55766e15	0.578386
$640$	−1.19062e15	−0.438311
$641$	1.07268e15	0.391519	0.195759	−	0.980652i	$-0.437283\pi$
$641$	1.07268e15	0.391519	0.195759	+	0.980652i	$0.437283\pi$
$642$	4.16019e15	1.50546
$643$	2.66156e15	0.954939	0.477470	−	0.878648i	$-0.341554\pi$
$643$	2.66156e15	0.954939	0.477470	+	0.878648i	$0.341554\pi$
$644$	1.97557e15	0.702783
$645$	−4.40840e14	−0.155490
$646$	−1.39197e15	−0.486802
$647$	−3.31850e15	−1.15071	−0.575357	−	0.817902i	$-0.695137\pi$
$647$	−3.31850e15	−1.15071	−0.575357	+	0.817902i	$0.695137\pi$
$648$	−8.85493e13	−0.0304455
$649$	2.02286e14	0.0689637
$650$	1.41871e15	0.479590
$651$	1.19118e15	0.399284
$652$	3.48046e15	1.15684
$653$	3.50654e15	1.15573	0.577865	−	0.816132i	$-0.303886\pi$
$653$	3.50654e15	1.15573	0.577865	+	0.816132i	$0.303886\pi$
$654$	3.68891e14	0.120565
$655$	1.79704e15	0.582413
$656$	1.41323e15	0.454193
$657$	−7.72329e13	−0.0246146
$658$	−2.05334e15	−0.648960
$659$	−3.21725e15	−1.00836	−0.504180	−	0.863599i	$-0.668205\pi$
$659$	−3.21725e15	−1.00836	−0.504180	+	0.863599i	$0.668205\pi$
$660$	9.49159e14	0.295017
$661$	−1.56999e14	−0.0483938	−0.0241969	−	0.999707i	$-0.507703\pi$
$661$	−1.56999e14	−0.0483938	−0.0241969	+	0.999707i	$0.507703\pi$
$662$	−9.43689e15	−2.88476
$663$	1.53460e15	0.465234
$664$	1.59538e15	0.479666
$665$	6.42952e14	0.191716
$666$	1.90862e15	0.564433
$667$	3.05571e15	0.896233
$668$	−1.37966e15	−0.401330
$669$	4.93023e13	0.0142241
$670$	4.62537e15	1.32353
$671$	1.27936e15	0.363094
$672$	−1.75718e15	−0.494636
$673$	−4.28054e15	−1.19513	−0.597566	−	0.801820i	$-0.703865\pi$
$673$	−4.28054e15	−1.19513	−0.597566	+	0.801820i	$0.703865\pi$
$674$	2.58735e14	0.0716515
$675$	2.36635e14	0.0649991
$676$	−3.36504e14	−0.0916817
$677$	2.31899e15	0.626701	0.313351	−	0.949637i	$-0.398548\pi$
$677$	2.31899e15	0.626701	0.313351	+	0.949637i	$0.398548\pi$
$678$	3.88426e15	1.04123
$679$	1.45083e15	0.385773
$680$	−7.09234e14	−0.187064
$681$	−1.56486e13	−0.00409417
$682$	3.47693e15	0.902364
$683$	−6.35794e15	−1.63683	−0.818413	−	0.574630i	$-0.805146\pi$
$683$	−6.35794e15	−1.63683	−0.818413	+	0.574630i	$0.805146\pi$
$684$	−6.07316e14	−0.155098
$685$	5.16202e15	1.30774
$686$	5.78901e15	1.45486
$687$	1.21822e15	0.303714
$688$	1.04410e15	0.258229
$689$	−1.70102e15	−0.417353
$690$	−2.81895e15	−0.686148
$691$	6.58604e14	0.159036	0.0795179	−	0.996833i	$-0.474662\pi$
$691$	6.58604e14	0.159036	0.0795179	+	0.996833i	$0.474662\pi$
$692$	8.86349e15	2.12335
$693$	4.45889e14	0.105973
$694$	3.14498e14	0.0741551
$695$	3.56537e15	0.834044
$696$	6.18403e14	0.143523
$697$	2.12070e15	0.488313
$698$	8.65953e15	1.97829
$699$	2.63453e14	0.0597144
$700$	−1.06843e15	−0.240273
$701$	6.66341e15	1.48678	0.743391	−	0.668857i	$-0.233216\pi$
$701$	6.66341e15	1.48678	0.743391	+	0.668857i	$0.233216\pi$
$702$	1.23439e15	0.273274
$703$	2.04694e15	0.449626
$704$	−3.23253e15	−0.704520
$705$	1.58921e15	0.343670
$706$	3.71308e15	0.796724
$707$	5.74381e14	0.122291
$708$	−4.21740e14	−0.0890967
$709$	4.88271e15	1.02354	0.511772	−	0.859121i	$-0.328989\pi$
$709$	4.88271e15	1.02354	0.511772	+	0.859121i	$0.328989\pi$
$710$	1.00354e16	2.08743
$711$	−7.66559e14	−0.158221
$712$	−1.07676e15	−0.220535
$713$	−5.60107e15	−1.13836
$714$	−2.13070e15	−0.429716
$715$	−2.06901e15	−0.414075
$716$	−7.10348e15	−1.41075
$717$	2.80339e15	0.552495
$718$	−8.49433e15	−1.66129
$719$	6.15063e15	1.19374	0.596872	−	0.802337i	$-0.296410\pi$
$719$	6.15063e15	1.19374	0.596872	+	0.802337i	$0.296410\pi$
$720$	1.09894e15	0.211664
$721$	3.01400e15	0.576102
$722$	6.59239e15	1.25051
$723$	−3.67068e15	−0.691012
$724$	−2.04556e15	−0.382164
$725$	−1.65259e15	−0.306412
$726$	−3.33672e15	−0.614000
$727$	−6.39610e15	−1.16809	−0.584045	−	0.811721i	$-0.698531\pi$
$727$	−6.39610e15	−1.16809	−0.584045	+	0.811721i	$0.698531\pi$
$728$	−8.71516e14	−0.157962
$729$	2.05891e14	0.0370370
$730$	−4.97580e14	−0.0888357
$731$	1.56678e15	0.277628
$732$	−2.66729e15	−0.469094
$733$	−5.15349e15	−0.899558	−0.449779	−	0.893140i	$-0.648497\pi$
$733$	−5.15349e15	−0.899558	−0.449779	+	0.893140i	$0.648497\pi$
$734$	3.98664e15	0.690684
$735$	−1.74816e15	−0.300608
$736$	8.26248e15	1.41021
$737$	3.44017e15	0.582785
$738$	1.70583e15	0.286830
$739$	−8.68311e15	−1.44921	−0.724604	−	0.689165i	$-0.757977\pi$
$739$	−8.68311e15	−1.44921	−0.724604	+	0.689165i	$0.757977\pi$
$740$	6.66973e15	1.10493
$741$	1.32385e15	0.217690
$742$	2.36176e15	0.385490
$743$	−5.07891e14	−0.0822872	−0.0411436	−	0.999153i	$-0.513100\pi$
$743$	−5.07891e14	−0.0822872	−0.0411436	+	0.999153i	$0.513100\pi$
$744$	−1.13352e15	−0.182297
$745$	3.63023e15	0.579528
$746$	2.86912e15	0.454658
$747$	−3.70950e15	−0.583515
$748$	−3.37339e15	−0.526754
$749$	6.82949e15	1.05862
$750$	6.03842e15	0.929151
$751$	−2.30518e15	−0.352116	−0.176058	−	0.984380i	$-0.556335\pi$
$751$	−2.30518e15	−0.352116	−0.176058	+	0.984380i	$0.556335\pi$
$752$	−3.76394e15	−0.570748
$753$	3.55028e15	0.534429
$754$	−8.62063e15	−1.28824
$755$	6.27879e15	0.931468
$756$	−9.29618e14	−0.136910
$757$	1.28362e15	0.187676	0.0938382	−	0.995587i	$-0.470086\pi$
$757$	1.28362e15	0.187676	0.0938382	+	0.995587i	$0.470086\pi$
$758$	−1.52238e15	−0.220974
$759$	−2.09662e15	−0.302128
$760$	−6.11831e14	−0.0875299
$761$	−4.41140e15	−0.626557	−0.313278	−	0.949661i	$-0.601427\pi$
$761$	−4.41140e15	−0.626557	−0.313278	+	0.949661i	$0.601427\pi$
$762$	3.89051e15	0.548598
$763$	6.05582e14	0.0847789
$764$	8.17950e15	1.13688
$765$	1.64908e15	0.227564
$766$	−6.21784e15	−0.851886
$767$	9.19323e14	0.125053
$768$	−2.28181e15	−0.308172
$769$	−1.01419e16	−1.35995	−0.679977	−	0.733233i	$-0.738010\pi$
$769$	−1.01419e16	−1.35995	−0.679977	+	0.733233i	$0.738010\pi$
$770$	2.87268e15	0.382462
$771$	5.75929e15	0.761325
$772$	−6.36243e15	−0.835080
$773$	−4.95978e15	−0.646361	−0.323181	−	0.946337i	$-0.604752\pi$
$773$	−4.95978e15	−0.646361	−0.323181	+	0.946337i	$0.604752\pi$
$774$	1.26028e15	0.163076
$775$	3.02916e15	0.389192
$776$	−1.38060e15	−0.176128
$777$	3.13325e15	0.396899
$778$	−7.21641e15	−0.907681
$779$	1.82945e15	0.228488
$780$	4.31360e15	0.534958
$781$	7.46392e15	0.919149
$782$	1.00188e16	1.22512
$783$	−1.43788e15	−0.174596
$784$	4.14040e15	0.499233
$785$	9.61478e15	1.15121
$786$	−5.13739e15	−0.610828
$787$	9.30653e15	1.09882	0.549410	−	0.835553i	$-0.314852\pi$
$787$	9.30653e15	1.09882	0.549410	+	0.835553i	$0.314852\pi$
$788$	−9.35691e15	−1.09708
$789$	−2.55434e15	−0.297410
$790$	−4.93863e15	−0.571028
$791$	6.37652e15	0.732172
$792$	−4.24306e14	−0.0483828
$793$	5.81426e15	0.658403
$794$	1.87145e15	0.210458
$795$	−1.82791e15	−0.204144
$796$	1.46522e16	1.62510
$797$	1.45081e16	1.59804	0.799021	−	0.601303i	$-0.205351\pi$
$797$	1.45081e16	1.59804	0.799021	+	0.601303i	$0.205351\pi$
$798$	−1.83807e15	−0.201070
$799$	−5.64819e15	−0.613623
$800$	−4.46850e15	−0.482133
$801$	2.50363e15	0.268282
$802$	−1.94581e15	−0.207082
$803$	−3.70081e14	−0.0391166
$804$	−7.17229e15	−0.752921
$805$	−4.62767e15	−0.482487
$806$	1.58015e16	1.63627
$807$	4.19063e14	0.0430998
$808$	−5.46579e14	−0.0558329
$809$	−1.65147e16	−1.67554	−0.837768	−	0.546027i	$-0.816140\pi$
$809$	−1.65147e16	−1.67554	−0.837768	+	0.546027i	$0.816140\pi$
$810$	1.32647e15	0.133669
$811$	−8.53438e15	−0.854196	−0.427098	−	0.904205i	$-0.640464\pi$
$811$	−8.53438e15	−0.854196	−0.427098	+	0.904205i	$0.640464\pi$
$812$	6.49218e15	0.645405
$813$	1.09754e15	0.108373
$814$	9.14565e15	0.896975
$815$	−8.15279e15	−0.794217
$816$	−3.90574e15	−0.377926
$817$	1.35161e15	0.129906
$818$	1.81711e16	1.73475
$819$	2.02641e15	0.192162
$820$	5.96105e15	0.561496
$821$	−1.65806e16	−1.55137	−0.775683	−	0.631123i	$-0.782594\pi$
$821$	−1.65806e16	−1.55137	−0.775683	+	0.631123i	$0.782594\pi$
$822$	−1.47572e16	−1.37154
$823$	−1.86136e15	−0.171843	−0.0859216	−	0.996302i	$-0.527383\pi$
$823$	−1.86136e15	−0.171843	−0.0859216	+	0.996302i	$0.527383\pi$
$824$	−2.86811e15	−0.263025
$825$	1.13389e15	0.103294
$826$	−1.27642e15	−0.115506
$827$	3.16390e15	0.284408	0.142204	−	0.989837i	$-0.454581\pi$
$827$	3.16390e15	0.284408	0.142204	+	0.989837i	$0.454581\pi$
$828$	4.37118e15	0.390330
$829$	−1.59763e16	−1.41718	−0.708591	−	0.705620i	$-0.750669\pi$
$829$	−1.59763e16	−1.41718	−0.708591	+	0.705620i	$0.750669\pi$
$830$	−2.38988e16	−2.10594
$831$	−1.82013e15	−0.159330
$832$	−1.46908e16	−1.27752
$833$	6.21310e15	0.536736
$834$	−1.01927e16	−0.874735
$835$	3.23178e15	0.275528
$836$	−2.91010e15	−0.246476
$837$	2.63562e15	0.221765
$838$	−8.46462e15	−0.707563
$839$	−1.01739e16	−0.844885	−0.422442	−	0.906390i	$-0.638827\pi$
$839$	−1.01739e16	−0.844885	−0.422442	+	0.906390i	$0.638827\pi$
$840$	−9.36529e14	−0.0772654
$841$	−2.15874e15	−0.176939
$842$	1.19464e16	0.972793
$843$	−1.26643e16	−1.02454
$844$	6.97130e15	0.560313
$845$	7.88241e14	0.0629429
$846$	−4.54324e15	−0.360437
$847$	−5.47766e15	−0.431754
$848$	4.32929e15	0.339031
$849$	2.91679e15	0.226941
$850$	−5.41835e15	−0.418854
$851$	−1.47330e16	−1.13156
$852$	−1.55613e16	−1.18748
$853$	−8.79916e15	−0.667147	−0.333573	−	0.942724i	$-0.608255\pi$
$853$	−8.79916e15	−0.667147	−0.333573	+	0.942724i	$0.608255\pi$
$854$	−8.07272e15	−0.608137
$855$	1.42260e15	0.106480
$856$	−6.49892e15	−0.483321
$857$	−1.52913e16	−1.12993	−0.564963	−	0.825116i	$-0.691110\pi$
$857$	−1.52913e16	−1.12993	−0.564963	+	0.825116i	$0.691110\pi$
$858$	5.91489e15	0.434277
$859$	−1.76287e16	−1.28605	−0.643025	−	0.765845i	$-0.722321\pi$
$859$	−1.76287e16	−1.28605	−0.643025	+	0.765845i	$0.722321\pi$
$860$	4.40406e15	0.319236
$861$	2.80034e15	0.201694
$862$	−1.81732e16	−1.30060
$863$	−1.29163e16	−0.918496	−0.459248	−	0.888308i	$-0.651881\pi$
$863$	−1.29163e16	−0.918496	−0.459248	+	0.888308i	$0.651881\pi$
$864$	−3.88796e15	−0.274724
$865$	−2.07622e16	−1.45776
$866$	2.33665e16	1.63022
$867$	2.46710e15	0.171033
$868$	−1.19001e16	−0.819768
$869$	−3.67316e15	−0.251438
$870$	−9.26371e15	−0.630128
$871$	1.56344e16	1.05677
$872$	−5.76269e14	−0.0387066
$873$	3.21012e15	0.214261
$874$	8.64286e15	0.573250
$875$	9.91285e15	0.653362
$876$	7.71568e14	0.0505361
$877$	9.20752e15	0.599301	0.299650	−	0.954049i	$-0.403130\pi$
$877$	9.20752e15	0.599301	0.299650	+	0.954049i	$0.403130\pi$
$878$	−4.34503e15	−0.281043
$879$	−7.57309e15	−0.486782
$880$	5.26586e15	0.336368
$881$	−1.38703e16	−0.880480	−0.440240	−	0.897880i	$-0.645107\pi$
$881$	−1.38703e16	−0.880480	−0.440240	+	0.897880i	$0.645107\pi$
$882$	4.99764e15	0.315274
$883$	2.21230e15	0.138695	0.0693473	−	0.997593i	$-0.477908\pi$
$883$	2.21230e15	0.138695	0.0693473	+	0.997593i	$0.477908\pi$
$884$	−1.53309e16	−0.955170
$885$	9.87902e14	0.0611682
$886$	1.87519e16	1.15388
$887$	−3.40669e15	−0.208331	−0.104165	−	0.994560i	$-0.533217\pi$
$887$	−3.40669e15	−0.208331	−0.104165	+	0.994560i	$0.533217\pi$
$888$	−2.98159e15	−0.181208
$889$	6.38678e15	0.385764
$890$	1.61299e16	0.968246
$891$	9.86578e14	0.0588578
$892$	−4.92537e14	−0.0292033
$893$	−4.87249e15	−0.287123
$894$	−1.03781e16	−0.607802
$895$	1.66395e16	0.968531
$896$	5.58769e15	0.323250
$897$	−9.52845e15	−0.547852
$898$	3.23287e16	1.84743
$899$	−1.84064e16	−1.04542
$900$	−2.36401e15	−0.133449
$901$	6.49656e15	0.364500
$902$	8.17390e15	0.455820
$903$	2.06891e15	0.114672
$904$	−6.06787e15	−0.334280
$905$	4.79160e15	0.262370
$906$	−1.79499e16	−0.976913
$907$	−2.12226e16	−1.14805	−0.574023	−	0.818839i	$-0.694618\pi$
$907$	−2.12226e16	−1.14805	−0.574023	+	0.818839i	$0.694618\pi$
$908$	1.56332e14	0.00840573
$909$	1.27088e15	0.0679210
$910$	1.30554e16	0.693524
$911$	−3.16343e16	−1.67035	−0.835176	−	0.549983i	$-0.814634\pi$
$911$	−3.16343e16	−1.67035	−0.835176	+	0.549983i	$0.814634\pi$
$912$	−3.36934e15	−0.176837
$913$	−1.77750e16	−0.927300
$914$	3.16130e16	1.63931
$915$	6.24799e15	0.322051
$916$	−1.21702e16	−0.623553
$917$	−8.43370e15	−0.429523
$918$	−4.71440e15	−0.238667
$919$	3.53008e16	1.77643	0.888216	−	0.459425i	$-0.151945\pi$
$919$	3.53008e16	1.77643	0.888216	+	0.459425i	$0.151945\pi$
$920$	4.40368e15	0.220284
$921$	5.89508e15	0.293131
$922$	−4.85829e16	−2.40140
$923$	3.39210e16	1.66671
$924$	−4.45450e15	−0.217572
$925$	7.96785e15	0.386867
$926$	−1.78222e16	−0.860205
$927$	6.66881e15	0.319970
$928$	2.71524e16	1.29507
$929$	2.83247e16	1.34301	0.671505	−	0.741000i	$-0.265648\pi$
$929$	2.83247e16	1.34301	0.671505	+	0.741000i	$0.265648\pi$
$930$	1.69802e16	0.800363
$931$	5.35982e15	0.251147
$932$	−2.63194e15	−0.122599
$933$	−1.79623e16	−0.831790
$934$	5.85641e16	2.69603
$935$	7.90198e15	0.361636
$936$	−1.92833e15	−0.0877331
$937$	−6.67418e15	−0.301877	−0.150939	−	0.988543i	$-0.548230\pi$
$937$	−6.67418e15	−0.301877	−0.150939	+	0.988543i	$0.548230\pi$
$938$	−2.17073e16	−0.976092
$939$	8.31583e15	0.371745
$940$	−1.58764e16	−0.705586
$941$	−2.20696e16	−0.975106	−0.487553	−	0.873093i	$-0.662110\pi$
$941$	−2.20696e16	−0.975106	−0.487553	+	0.873093i	$0.662110\pi$
$942$	−2.74868e16	−1.20738
$943$	−1.31675e16	−0.575029
$944$	−2.33978e15	−0.101585
$945$	2.17758e15	0.0939937
$946$	6.03892e15	0.259154
$947$	−2.03690e16	−0.869049	−0.434525	−	0.900660i	$-0.643084\pi$
$947$	−2.03690e16	−0.869049	−0.434525	+	0.900660i	$0.643084\pi$
$948$	7.65804e15	0.324842
$949$	−1.68189e15	−0.0709306
$950$	−4.67422e15	−0.195988
$951$	−4.24269e15	−0.176868
$952$	3.32851e15	0.137958
$953$	−2.99023e16	−1.23224	−0.616118	−	0.787654i	$-0.711296\pi$
$953$	−2.99023e16	−1.23224	−0.616118	+	0.787654i	$0.711296\pi$
$954$	5.22565e15	0.214104
$955$	−1.91600e16	−0.780508
$956$	−2.80063e16	−1.13433
$957$	−6.88998e15	−0.277461
$958$	2.34640e16	0.939487
$959$	−2.42259e16	−0.964445
$960$	−1.57867e16	−0.624883
$961$	8.33011e15	0.327848
$962$	4.15639e16	1.62650
$963$	1.51110e16	0.587961
$964$	3.66706e16	1.41871
$965$	1.49036e16	0.573314
$966$	1.32296e16	0.506026
$967$	−1.85775e16	−0.706550	−0.353275	−	0.935520i	$-0.614932\pi$
$967$	−1.85775e16	−0.706550	−0.353275	+	0.935520i	$0.614932\pi$
$968$	5.21252e15	0.197121
$969$	−5.05605e15	−0.190121
$970$	2.06815e16	0.773282
$971$	−1.34524e16	−0.500143	−0.250071	−	0.968227i	$-0.580454\pi$
$971$	−1.34524e16	−0.500143	−0.250071	+	0.968227i	$0.580454\pi$
$972$	−2.05688e15	−0.0760406
$973$	−1.67327e16	−0.615098
$974$	2.62786e16	0.960569
$975$	5.15316e15	0.187304
$976$	−1.47979e16	−0.534844
$977$	1.65741e16	0.595674	0.297837	−	0.954617i	$-0.403735\pi$
$977$	1.65741e16	0.595674	0.297837	+	0.954617i	$0.403735\pi$
$978$	2.33072e16	0.832966
$979$	1.19968e16	0.426343
$980$	1.74644e16	0.617177
$981$	1.33992e15	0.0470867
$982$	7.41209e16	2.59017
$983$	−6.50952e15	−0.226206	−0.113103	−	0.993583i	$-0.536079\pi$
$983$	−6.50952e15	−0.226206	−0.113103	+	0.993583i	$0.536079\pi$
$984$	−2.66479e15	−0.0920852
$985$	2.19180e16	0.753186
$986$	3.29240e16	1.12510
$987$	−7.45832e15	−0.253453
$988$	−1.32254e16	−0.446937
$989$	−9.72825e15	−0.326930
$990$	6.35613e15	0.212422
$991$	4.78987e14	0.0159191	0.00795955	−	0.999968i	$-0.497466\pi$
$991$	4.78987e14	0.0159191	0.00795955	+	0.999968i	$0.497466\pi$
$992$	−4.97698e16	−1.64495
$993$	−3.42775e16	−1.12665
$994$	−4.70970e16	−1.53946
$995$	−3.43220e16	−1.11569
$996$	3.70585e16	1.19801
$997$	−5.55846e15	−0.178703	−0.0893513	−	0.996000i	$-0.528479\pi$
$997$	−5.55846e15	−0.178703	−0.0893513	+	0.996000i	$0.528479\pi$
$998$	−4.89343e16	−1.56457
$999$	6.93268e15	0.220440

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.a.1.5	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.a.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-66.9000 q^{2} -243.000 q^{3} +2427.61 q^{4} -5686.53 q^{5} +16256.7 q^{6} +26687.5 q^{7} -25395.7 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-66.9000 q^{2} -243.000 q^{3} +2427.61 q^{4} -5686.53 q^{5} +16256.7 q^{6} +26687.5 q^{7} -25395.7 q^{8} +59049.0 q^{9} +380429. q^{10} +282948. q^{11} -589908. q^{12} +1.28590e6 q^{13} -1.78539e6 q^{14} +1.38183e6 q^{15} -3.27277e6 q^{16} -4.91113e6 q^{17} -3.95038e6 q^{18} -4.23666e6 q^{19} -1.38047e7 q^{20} -6.48505e6 q^{21} -1.89292e7 q^{22} +3.04935e7 q^{23} +6.17115e6 q^{24} -1.64915e7 q^{25} -8.60268e7 q^{26} -1.43489e7 q^{27} +6.47867e7 q^{28} +1.00209e8 q^{29} -9.24442e7 q^{30} -1.83681e8 q^{31} +2.70958e8 q^{32} -6.87563e7 q^{33} +3.28555e8 q^{34} -1.51759e8 q^{35} +1.43348e8 q^{36} -4.83150e8 q^{37} +2.83432e8 q^{38} -3.12474e8 q^{39} +1.44413e8 q^{40} -4.31814e8 q^{41} +4.33850e8 q^{42} -3.19027e8 q^{43} +6.86886e8 q^{44} -3.35784e8 q^{45} -2.04002e9 q^{46} +1.15008e9 q^{47} +7.95283e8 q^{48} -1.26511e9 q^{49} +1.10328e9 q^{50} +1.19341e9 q^{51} +3.12167e9 q^{52} -1.32282e9 q^{53} +9.59942e8 q^{54} -1.60899e9 q^{55} -6.77747e8 q^{56} +1.02951e9 q^{57} -6.70395e9 q^{58} +7.14924e8 q^{59} +3.35453e9 q^{60} +4.52154e9 q^{61} +1.22882e10 q^{62} +1.57587e9 q^{63} -1.14245e10 q^{64} -7.31233e9 q^{65} +4.59980e9 q^{66} +1.21583e10 q^{67} -1.19223e10 q^{68} -7.40993e9 q^{69} +1.01527e10 q^{70} +2.63791e10 q^{71} -1.49959e9 q^{72} -1.30795e9 q^{73} +3.23227e10 q^{74} +4.00743e9 q^{75} -1.02849e10 q^{76} +7.55116e9 q^{77} +2.09045e10 q^{78} -1.29817e10 q^{79} +1.86107e10 q^{80} +3.48678e9 q^{81} +2.88883e10 q^{82} -6.28207e10 q^{83} -1.57432e10 q^{84} +2.79273e10 q^{85} +2.13429e10 q^{86} -2.43507e10 q^{87} -7.18566e9 q^{88} +4.23991e10 q^{89} +2.24639e10 q^{90} +3.43175e10 q^{91} +7.40263e10 q^{92} +4.46344e10 q^{93} -7.69402e10 q^{94} +2.40919e10 q^{95} -6.58429e10 q^{96} +5.43637e10 q^{97} +8.46356e10 q^{98} +1.67078e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9}+O(q^{10}) \) 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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