LMFDB - Embedded newform 177.12.a.a.1.18

Newspace parameters

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	177.a (trivial)

Newform invariants

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			1.18
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q+27.2209 q^{2} -243.000 q^{3} -1307.02 q^{4} -8750.00 q^{5} -6614.68 q^{6} -68225.0 q^{7} -91326.7 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+27.2209 q^{2} -243.000 q^{3} -1307.02 q^{4} -8750.00 q^{5} -6614.68 q^{6} -68225.0 q^{7} -91326.7 q^{8} +59049.0 q^{9} -238183. q^{10} +664138. q^{11} +317607. q^{12} -1.65425e6 q^{13} -1.85715e6 q^{14} +2.12625e6 q^{15} +190787. q^{16} +1.11788e7 q^{17} +1.60737e6 q^{18} -829403. q^{19} +1.14365e7 q^{20} +1.65787e7 q^{21} +1.80784e7 q^{22} +1.30559e6 q^{23} +2.21924e7 q^{24} +2.77345e7 q^{25} -4.50302e7 q^{26} -1.43489e7 q^{27} +8.91717e7 q^{28} -4.39688e7 q^{29} +5.78785e7 q^{30} +1.84585e8 q^{31} +1.92231e8 q^{32} -1.61385e8 q^{33} +3.04296e8 q^{34} +5.96969e8 q^{35} -7.71784e7 q^{36} +7.52080e7 q^{37} -2.25771e7 q^{38} +4.01983e8 q^{39} +7.99109e8 q^{40} -5.89404e8 q^{41} +4.51287e8 q^{42} +1.11165e9 q^{43} -8.68043e8 q^{44} -5.16679e8 q^{45} +3.55392e7 q^{46} -2.06811e9 q^{47} -4.63613e7 q^{48} +2.67733e9 q^{49} +7.54957e8 q^{50} -2.71644e9 q^{51} +2.16215e9 q^{52} -3.47306e9 q^{53} -3.90590e8 q^{54} -5.81121e9 q^{55} +6.23077e9 q^{56} +2.01545e8 q^{57} -1.19687e9 q^{58} +7.14924e8 q^{59} -2.77906e9 q^{60} -2.03845e9 q^{61} +5.02457e9 q^{62} -4.02862e9 q^{63} +4.84195e9 q^{64} +1.44747e10 q^{65} -4.39306e9 q^{66} -3.18226e9 q^{67} -1.46109e10 q^{68} -3.17258e8 q^{69} +1.62500e10 q^{70} +1.90460e10 q^{71} -5.39275e9 q^{72} +2.41193e10 q^{73} +2.04723e9 q^{74} -6.73947e9 q^{75} +1.08405e9 q^{76} -4.53108e10 q^{77} +1.09423e10 q^{78} +1.77091e10 q^{79} -1.66939e9 q^{80} +3.48678e9 q^{81} -1.60441e10 q^{82} -3.46150e10 q^{83} -2.16687e10 q^{84} -9.78144e10 q^{85} +3.02602e10 q^{86} +1.06844e10 q^{87} -6.06535e10 q^{88} -6.60387e10 q^{89} -1.40645e10 q^{90} +1.12861e11 q^{91} -1.70643e9 q^{92} -4.48541e10 q^{93} -5.62957e10 q^{94} +7.25728e9 q^{95} -4.67120e10 q^{96} +4.44981e10 q^{97} +7.28793e10 q^{98} +3.92167e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} + O(q^{10}) $	\( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} - 859751q^{10} + 579094q^{11} - 5606010q^{12} - 2018538q^{13} + 4157413q^{14} - 925344q^{15} + 20190274q^{16} - 13084493q^{17} - 4605822q^{18} + 9917231q^{19} + 10165633q^{20} + 24013017q^{21} - 89820518q^{22} - 63513223q^{23} + 28587735q^{24} + 218986852q^{25} - 77999532q^{26} - 373071582q^{27} - 444601862q^{28} + 81530981q^{29} + 208919493q^{30} - 408861231q^{31} - 26253128q^{32} - 140719842q^{33} - 508910076q^{34} - 75731421q^{35} + 1362260430q^{36} - 802381301q^{37} + 732704675q^{38} + 490504734q^{39} - 646130800q^{40} - 1354472849q^{41} - 1010251359q^{42} + 282952194q^{43} + 1846047996q^{44} + 224858592q^{45} + 9629305849q^{46} - 1196794197q^{47} - 4906236582q^{48} + 10889725683q^{49} - 6236232091q^{50} + 3179531799q^{51} - 1968200812q^{52} - 8276044236q^{53} + 1119214746q^{54} - 6672895076q^{55} + 2579741342q^{56} - 2409887133q^{57} - 9401656060q^{58} + 18588031774q^{59} - 2470248819q^{60} - 21181559029q^{61} - 6117706514q^{62} - 5835163131q^{63} + 42975855037q^{64} + 25680681860q^{65} + 21826385874q^{66} + 26234163394q^{67} + 19707344091q^{68} + 15433713189q^{69} + 129203099090q^{70} + 52088830406q^{71} - 6946819605q^{72} + 20943384867q^{73} + 41969200146q^{74} - 53213805036q^{75} + 223987219368q^{76} + 94604773153q^{77} + 18953886276q^{78} + 68965662774q^{79} + 218947784293q^{80} + 90656394426q^{81} + 11938614923q^{82} + 17947446393q^{83} + 108038252466q^{84} - 52849386709q^{85} + 384986147852q^{86} - 19812028383q^{87} - 49061112607q^{88} + 38570593981q^{89} - 50767436799q^{90} - 226268806999q^{91} - 79559686310q^{92} + 99353279133q^{93} - 16709400108q^{94} - 252795831501q^{95} + 6379510104q^{96} - 186894587836q^{97} - 252443311612q^{98} + 34194921606q^{99} + O(q^{100}) \)

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 $

$2$	27.2209	0.601503	0.300751	−	0.953703i	$-0.402763\pi$
$2$	27.2209	0.601503	0.300751	+	0.953703i	$0.402763\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	−1307.02	−0.638195
$5$	−8750.00	−1.25220	−0.626099	−	0.779743i	$-0.715350\pi$
$5$	−8750.00	−1.25220	−0.626099	+	0.779743i	$0.715350\pi$
$6$	−6614.68	−0.347278
$7$	−68225.0	−1.53428	−0.767140	−	0.641480i	$-0.778321\pi$
$7$	−68225.0	−1.53428	−0.767140	+	0.641480i	$0.778321\pi$
$8$	−91326.7	−0.985378
$9$	59049.0	0.333333
$10$	−238183.	−0.753201
$11$	664138.	1.24336	0.621682	−	0.783270i	$-0.286450\pi$
$11$	664138.	1.24336	0.621682	+	0.783270i	$0.286450\pi$
$12$	317607.	0.368462
$13$	−1.65425e6	−1.23570	−0.617850	−	0.786296i	$-0.711996\pi$
$13$	−1.65425e6	−1.23570	−0.617850	+	0.786296i	$0.711996\pi$
$14$	−1.85715e6	−0.922873
$15$	2.12625e6	0.722957
$16$	190787.	0.0454873
$17$	1.11788e7	1.90952	0.954762	−	0.297370i	$-0.0961096\pi$
$17$	1.11788e7	1.90952	0.954762	+	0.297370i	$0.0961096\pi$
$18$	1.60737e6	0.200501
$19$	−829403.	−0.0768459	−0.0384229	−	0.999262i	$-0.512233\pi$
$19$	−829403.	−0.0768459	−0.0384229	+	0.999262i	$0.512233\pi$
$20$	1.14365e7	0.799147
$21$	1.65787e7	0.885817
$22$	1.80784e7	0.747887
$23$	1.30559e6	0.0422963	0.0211482	−	0.999776i	$-0.493268\pi$
$23$	1.30559e6	0.0422963	0.0211482	+	0.999776i	$0.493268\pi$
$24$	2.21924e7	0.568908
$25$	2.77345e7	0.568002
$26$	−4.50302e7	−0.743277
$27$	−1.43489e7	−0.192450
$28$	8.91717e7	0.979169
$29$	−4.39688e7	−0.398067	−0.199033	−	0.979993i	$-0.563780\pi$
$29$	−4.39688e7	−0.398067	−0.199033	+	0.979993i	$0.563780\pi$
$30$	5.78785e7	0.434861
$31$	1.84585e8	1.15800	0.578998	−	0.815329i	$-0.303444\pi$
$31$	1.84585e8	1.15800	0.578998	+	0.815329i	$0.303444\pi$
$32$	1.92231e8	1.01274
$33$	−1.61385e8	−0.717857
$34$	3.04296e8	1.14858
$35$	5.96969e8	1.92122
$36$	−7.71784e7	−0.212732
$37$	7.52080e7	0.178301	0.0891506	−	0.996018i	$-0.471585\pi$
$37$	7.52080e7	0.178301	0.0891506	+	0.996018i	$0.471585\pi$
$38$	−2.25771e7	−0.0462230
$39$	4.01983e8	0.713432
$40$	7.99109e8	1.23389
$41$	−5.89404e8	−0.794515	−0.397258	−	0.917707i	$-0.630038\pi$
$41$	−5.89404e8	−0.794515	−0.397258	+	0.917707i	$0.630038\pi$
$42$	4.51287e8	0.532821
$43$	1.11165e9	1.15317	0.576585	−	0.817037i	$-0.304385\pi$
$43$	1.11165e9	1.15317	0.576585	+	0.817037i	$0.304385\pi$
$44$	−8.68043e8	−0.793509
$45$	−5.16679e8	−0.417400
$46$	3.55392e7	0.0254413
$47$	−2.06811e9	−1.31533	−0.657665	−	0.753310i	$-0.728456\pi$
$47$	−2.06811e9	−1.31533	−0.657665	+	0.753310i	$0.728456\pi$
$48$	−4.63613e7	−0.0262621
$49$	2.67733e9	1.35401
$50$	7.54957e8	0.341654
$51$	−2.71644e9	−1.10246
$52$	2.16215e9	0.788618
$53$	−3.47306e9	−1.14076	−0.570381	−	0.821380i	$-0.693204\pi$
$53$	−3.47306e9	−1.14076	−0.570381	+	0.821380i	$0.693204\pi$
$54$	−3.90590e8	−0.115759
$55$	−5.81121e9	−1.55694
$56$	6.23077e9	1.51185
$57$	2.01545e8	0.0443670
$58$	−1.19687e9	−0.239438
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	−2.77906e9	−0.461388
$61$	−2.03845e9	−0.309019	−0.154510	−	0.987991i	$-0.549380\pi$
$61$	−2.03845e9	−0.309019	−0.154510	+	0.987991i	$0.549380\pi$
$62$	5.02457e9	0.696537
$63$	−4.02862e9	−0.511427
$64$	4.84195e9	0.563678
$65$	1.44747e10	1.54734
$66$	−4.39306e9	−0.431793
$67$	−3.18226e9	−0.287954	−0.143977	−	0.989581i	$-0.545989\pi$
$67$	−3.18226e9	−0.287954	−0.143977	+	0.989581i	$0.545989\pi$
$68$	−1.46109e10	−1.21865
$69$	−3.17258e8	−0.0244198
$70$	1.62500e10	1.15562
$71$	1.90460e10	1.25281	0.626403	−	0.779500i	$-0.284527\pi$
$71$	1.90460e10	1.25281	0.626403	+	0.779500i	$0.284527\pi$
$72$	−5.39275e9	−0.328459
$73$	2.41193e10	1.36173	0.680863	−	0.732411i	$-0.261605\pi$
$73$	2.41193e10	1.36173	0.680863	+	0.732411i	$0.261605\pi$
$74$	2.04723e9	0.107249
$75$	−6.73947e9	−0.327936
$76$	1.08405e9	0.0490426
$77$	−4.53108e10	−1.90767
$78$	1.09423e10	0.429131
$79$	1.77091e10	0.647513	0.323756	−	0.946140i	$-0.395054\pi$
$79$	1.77091e10	0.647513	0.323756	+	0.946140i	$0.395054\pi$
$80$	−1.66939e9	−0.0569591
$81$	3.48678e9	0.111111
$82$	−1.60441e10	−0.477903
$83$	−3.46150e10	−0.964572	−0.482286	−	0.876014i	$-0.660193\pi$
$83$	−3.46150e10	−0.964572	−0.482286	+	0.876014i	$0.660193\pi$
$84$	−2.16687e10	−0.565324
$85$	−9.78144e10	−2.39110
$86$	3.02602e10	0.693634
$87$	1.06844e10	0.229824
$88$	−6.06535e10	−1.22518
$89$	−6.60387e10	−1.25358	−0.626792	−	0.779187i	$-0.715632\pi$
$89$	−6.60387e10	−1.25358	−0.626792	+	0.779187i	$0.715632\pi$
$90$	−1.40645e10	−0.251067
$91$	1.12861e11	1.89591
$92$	−1.70643e9	−0.0269933
$93$	−4.48541e10	−0.668569
$94$	−5.62957e10	−0.791175
$95$	7.25728e9	0.0962263
$96$	−4.67120e10	−0.584705
$97$	4.44981e10	0.526135	0.263067	−	0.964777i	$-0.415266\pi$
$97$	4.44981e10	0.526135	0.263067	+	0.964777i	$0.415266\pi$
$98$	7.28793e10	0.814443
$99$	3.92167e10	0.414455
$100$	−3.62496e10	−0.362496
$101$	−6.89078e10	−0.652380	−0.326190	−	0.945304i	$-0.605765\pi$
$101$	−6.89078e10	−0.652380	−0.326190	+	0.945304i	$0.605765\pi$
$102$	−7.39440e10	−0.663135
$103$	8.40518e9	0.0714401	0.0357201	−	0.999362i	$-0.488628\pi$
$103$	8.40518e9	0.0714401	0.0357201	+	0.999362i	$0.488628\pi$
$104$	1.51077e11	1.21763
$105$	−1.45064e11	−1.10922
$106$	−9.45398e10	−0.686171
$107$	2.85129e11	1.96531	0.982655	−	0.185444i	$-0.0593722\pi$
$107$	2.85129e11	1.96531	0.982655	+	0.185444i	$0.0593722\pi$
$108$	1.87543e10	0.122821
$109$	−6.32925e10	−0.394010	−0.197005	−	0.980403i	$-0.563121\pi$
$109$	−6.32925e10	−0.394010	−0.197005	+	0.980403i	$0.563121\pi$
$110$	−1.58186e11	−0.936503
$111$	−1.82755e10	−0.102942
$112$	−1.30165e10	−0.0697902
$113$	2.13515e11	1.09017	0.545087	−	0.838379i	$-0.316496\pi$
$113$	2.13515e11	1.09017	0.545087	+	0.838379i	$0.316496\pi$
$114$	5.48623e9	0.0266869
$115$	−1.14239e10	−0.0529634
$116$	5.74683e10	0.254044
$117$	−9.76820e10	−0.411900
$118$	1.94609e10	0.0783090
$119$	−7.62672e11	−2.92974
$120$	−1.94184e11	−0.712386
$121$	1.55767e11	0.545955
$122$	−5.54883e10	−0.185876
$123$	1.43225e11	0.458714
$124$	−2.41257e11	−0.739027
$125$	1.84570e11	0.540948
$126$	−1.09663e11	−0.307624
$127$	−5.37182e11	−1.44278	−0.721391	−	0.692528i	$-0.756497\pi$
$127$	−5.37182e11	−1.44278	−0.721391	+	0.692528i	$0.756497\pi$
$128$	−2.61886e11	−0.673685
$129$	−2.70132e11	−0.665783
$130$	3.94015e11	0.930731
$131$	3.30858e11	0.749290	0.374645	−	0.927168i	$-0.377765\pi$
$131$	3.30858e11	0.749290	0.374645	+	0.927168i	$0.377765\pi$
$132$	2.10935e11	0.458132
$133$	5.65860e10	0.117903
$134$	−8.66238e10	−0.173205
$135$	1.25553e11	0.240986
$136$	−1.02092e12	−1.88160
$137$	6.30957e11	1.11696	0.558479	−	0.829519i	$-0.311385\pi$
$137$	6.30957e11	1.11696	0.558479	+	0.829519i	$0.311385\pi$
$138$	−8.63603e9	−0.0146886
$139$	8.10012e11	1.32407	0.662033	−	0.749474i	$-0.269694\pi$
$139$	8.10012e11	1.32407	0.662033	+	0.749474i	$0.269694\pi$
$140$	−7.80253e11	−1.22611
$141$	5.02550e11	0.759407
$142$	5.18450e11	0.753565
$143$	−1.09865e12	−1.53643
$144$	1.12658e10	0.0151624
$145$	3.84728e11	0.498459
$146$	6.56550e11	0.819081
$147$	−6.50591e11	−0.781740
$148$	−9.82986e10	−0.113791
$149$	−2.38458e11	−0.266004	−0.133002	−	0.991116i	$-0.542462\pi$
$149$	−2.38458e11	−0.266004	−0.133002	+	0.991116i	$0.542462\pi$
$150$	−1.83455e11	−0.197254
$151$	−2.44355e11	−0.253307	−0.126653	−	0.991947i	$-0.540424\pi$
$151$	−2.44355e11	−0.253307	−0.126653	+	0.991947i	$0.540424\pi$
$152$	7.57466e10	0.0757223
$153$	6.60096e11	0.636508
$154$	−1.23340e12	−1.14747
$155$	−1.61512e12	−1.45004
$156$	−5.25401e11	−0.455309
$157$	3.50711e11	0.293428	0.146714	−	0.989179i	$-0.453130\pi$
$157$	3.50711e11	0.293428	0.146714	+	0.989179i	$0.453130\pi$
$158$	4.82058e11	0.389481
$159$	8.43954e11	0.658619
$160$	−1.68202e12	−1.26815
$161$	−8.90737e10	−0.0648944
$162$	9.49134e10	0.0668336
$163$	1.30317e12	0.887094	0.443547	−	0.896251i	$-0.353720\pi$
$163$	1.30317e12	0.887094	0.443547	+	0.896251i	$0.353720\pi$
$164$	7.70365e11	0.507055
$165$	1.41212e12	0.898899
$166$	−9.42251e11	−0.580193
$167$	−2.42144e12	−1.44256	−0.721278	−	0.692646i	$-0.756445\pi$
$167$	−2.42144e12	−1.44256	−0.721278	+	0.692646i	$0.756445\pi$
$168$	−1.51408e12	−0.872865
$169$	9.44391e11	0.526957
$170$	−2.66259e12	−1.43826
$171$	−4.89754e10	−0.0256153
$172$	−1.45296e12	−0.735947
$173$	−1.37292e12	−0.673584	−0.336792	−	0.941579i	$-0.609342\pi$
$173$	−1.37292e12	−0.673584	−0.336792	+	0.941579i	$0.609342\pi$
$174$	2.90840e11	0.138240
$175$	−1.89218e12	−0.871474
$176$	1.26709e11	0.0565573
$177$	−1.73727e11	−0.0751646
$178$	−1.79763e12	−0.754034
$179$	3.97937e11	0.161854	0.0809269	−	0.996720i	$-0.474212\pi$
$179$	3.97937e11	0.161854	0.0809269	+	0.996720i	$0.474212\pi$
$180$	6.75311e11	0.266382
$181$	2.56106e12	0.979913	0.489957	−	0.871747i	$-0.337013\pi$
$181$	2.56106e12	0.979913	0.489957	+	0.871747i	$0.337013\pi$
$182$	3.07219e12	1.14040
$183$	4.95342e11	0.178412
$184$	−1.19235e11	−0.0416779
$185$	−6.58070e11	−0.223269
$186$	−1.22097e12	−0.402146
$187$	7.42425e12	2.37423
$188$	2.70306e12	0.839437
$189$	9.78955e11	0.295272
$190$	1.97550e11	0.0578804
$191$	2.33603e10	0.00664958	0.00332479	−	0.999994i	$-0.498942\pi$
$191$	2.33603e10	0.00664958	0.00332479	+	0.999994i	$0.498942\pi$
$192$	−1.17660e12	−0.325439
$193$	−2.98688e12	−0.802883	−0.401441	−	0.915885i	$-0.631491\pi$
$193$	−2.98688e12	−0.802883	−0.401441	+	0.915885i	$0.631491\pi$
$194$	1.21128e12	0.316471
$195$	−3.51736e12	−0.893359
$196$	−3.49933e12	−0.864125
$197$	4.89501e12	1.17541	0.587705	−	0.809075i	$-0.300032\pi$
$197$	4.89501e12	1.17541	0.587705	+	0.809075i	$0.300032\pi$
$198$	1.06751e12	0.249296
$199$	−5.23981e12	−1.19021	−0.595106	−	0.803648i	$-0.702890\pi$
$199$	−5.23981e12	−1.19021	−0.595106	+	0.803648i	$0.702890\pi$
$200$	−2.53290e12	−0.559697
$201$	7.73288e11	0.166250
$202$	−1.87573e12	−0.392408
$203$	2.99978e12	0.610746
$204$	3.55045e12	0.703587
$205$	5.15729e12	0.994891
$206$	2.28796e11	0.0429714
$207$	7.70936e10	0.0140988
$208$	−3.15611e11	−0.0562087
$209$	−5.50838e11	−0.0955474
$210$	−3.94876e12	−0.667198
$211$	1.28415e12	0.211380	0.105690	−	0.994399i	$-0.466295\pi$
$211$	1.28415e12	0.211380	0.105690	+	0.994399i	$0.466295\pi$
$212$	4.53937e12	0.728028
$213$	−4.62818e12	−0.723307
$214$	7.76147e12	1.18214
$215$	−9.72698e12	−1.44400
$216$	1.31044e12	0.189636
$217$	−1.25933e13	−1.77669
$218$	−1.72288e12	−0.236998
$219$	−5.86100e12	−0.786192
$220$	7.59538e12	0.993631
$221$	−1.84925e13	−2.35960
$222$	−4.97477e11	−0.0619201
$223$	−7.57568e11	−0.0919909	−0.0459955	−	0.998942i	$-0.514646\pi$
$223$	−7.57568e11	−0.0919909	−0.0459955	+	0.998942i	$0.514646\pi$
$224$	−1.31149e13	−1.55382
$225$	1.63769e12	0.189334
$226$	5.81206e12	0.655743
$227$	2.35281e12	0.259087	0.129543	−	0.991574i	$-0.458649\pi$
$227$	2.35281e12	0.259087	0.129543	+	0.991574i	$0.458649\pi$
$228$	−2.63424e11	−0.0283148
$229$	−9.82529e12	−1.03098	−0.515490	−	0.856896i	$-0.672390\pi$
$229$	−9.82529e12	−1.03098	−0.515490	+	0.856896i	$0.672390\pi$
$230$	−3.10969e11	−0.0318576
$231$	1.10105e13	1.10139
$232$	4.01553e12	0.392246
$233$	−1.72545e13	−1.64606	−0.823028	−	0.568000i	$-0.807717\pi$
$233$	−1.72545e13	−1.64606	−0.823028	+	0.568000i	$0.807717\pi$
$234$	−2.65899e12	−0.247759
$235$	1.80960e13	1.64706
$236$	−9.34422e11	−0.0830859
$237$	−4.30332e12	−0.373842
$238$	−2.07606e13	−1.76225
$239$	−2.07219e13	−1.71887	−0.859433	−	0.511249i	$-0.829183\pi$
$239$	−2.07219e13	−1.71887	−0.859433	+	0.511249i	$0.829183\pi$
$240$	4.05662e11	0.0328854
$241$	−2.16204e13	−1.71305	−0.856524	−	0.516107i	$-0.827381\pi$
$241$	−2.16204e13	−1.71305	−0.856524	+	0.516107i	$0.827381\pi$
$242$	4.24013e12	0.328393
$243$	−8.47289e11	−0.0641500
$244$	2.66430e12	0.197214
$245$	−2.34266e13	−1.69549
$246$	3.89872e12	0.275917
$247$	1.37204e12	0.0949585
$248$	−1.68575e13	−1.14106
$249$	8.41144e12	0.556896
$250$	5.02415e12	0.325381
$251$	2.18129e12	0.138200	0.0691001	−	0.997610i	$-0.477987\pi$
$251$	2.18129e12	0.138200	0.0691001	+	0.997610i	$0.477987\pi$
$252$	5.26550e12	0.326390
$253$	8.67089e11	0.0525897
$254$	−1.46226e13	−0.867837
$255$	2.37689e13	1.38050
$256$	−1.70451e13	−0.968901
$257$	2.66641e13	1.48352	0.741761	−	0.670664i	$-0.233991\pi$
$257$	2.66641e13	1.48352	0.741761	+	0.670664i	$0.233991\pi$
$258$	−7.35323e12	−0.400470
$259$	−5.13107e12	−0.273564
$260$	−1.89188e13	−0.987506
$261$	−2.59632e12	−0.132689
$262$	9.00626e12	0.450700
$263$	−7.43238e12	−0.364226	−0.182113	−	0.983278i	$-0.558294\pi$
$263$	−7.43238e12	−0.364226	−0.182113	+	0.983278i	$0.558294\pi$
$264$	1.47388e13	0.707360
$265$	3.03893e13	1.42846
$266$	1.54032e12	0.0709190
$267$	1.60474e13	0.723757
$268$	4.15928e12	0.183771
$269$	−6.93975e11	−0.0300404	−0.0150202	−	0.999887i	$-0.504781\pi$
$269$	−6.93975e11	−0.0300404	−0.0150202	+	0.999887i	$0.504781\pi$
$270$	3.41767e12	0.144954
$271$	2.12225e13	0.881993	0.440997	−	0.897509i	$-0.354625\pi$
$271$	2.12225e13	0.881993	0.440997	+	0.897509i	$0.354625\pi$
$272$	2.13277e12	0.0868591
$273$	−2.74253e13	−1.09460
$274$	1.71752e13	0.671853
$275$	1.84195e13	0.706233
$276$	4.14663e11	0.0155846
$277$	−2.67735e13	−0.986430	−0.493215	−	0.869907i	$-0.664178\pi$
$277$	−2.67735e13	−0.986430	−0.493215	+	0.869907i	$0.664178\pi$
$278$	2.20492e13	0.796429
$279$	1.08996e13	0.385999
$280$	−5.45193e13	−1.89313
$281$	−3.05388e12	−0.103984	−0.0519921	−	0.998647i	$-0.516557\pi$
$281$	−3.05388e12	−0.103984	−0.0519921	+	0.998647i	$0.516557\pi$
$282$	1.36799e13	0.456785
$283$	−1.73422e13	−0.567908	−0.283954	−	0.958838i	$-0.591646\pi$
$283$	−1.73422e13	−0.567908	−0.283954	+	0.958838i	$0.591646\pi$
$284$	−2.48936e13	−0.799534
$285$	−1.76352e12	−0.0555563
$286$	−2.99063e13	−0.924164
$287$	4.02121e13	1.21901
$288$	1.13510e13	0.337580
$289$	9.06932e13	2.64628
$290$	1.04726e13	0.299824
$291$	−1.08130e13	−0.303764
$292$	−3.15245e13	−0.869046
$293$	−2.92304e13	−0.790792	−0.395396	−	0.918511i	$-0.629393\pi$
$293$	−2.92304e13	−0.790792	−0.395396	+	0.918511i	$0.629393\pi$
$294$	−1.77097e13	−0.470219
$295$	−6.25559e12	−0.163022
$296$	−6.86850e12	−0.175694
$297$	−9.52965e12	−0.239286
$298$	−6.49105e12	−0.160002
$299$	−2.15977e12	−0.0522656
$300$	8.80865e12	0.209287
$301$	−7.58426e13	−1.76928
$302$	−6.65155e12	−0.152365
$303$	1.67446e13	0.376652
$304$	−1.58240e11	−0.00349551
$305$	1.78364e13	0.386953
$306$	1.79684e13	0.382861
$307$	−2.63689e13	−0.551862	−0.275931	−	0.961177i	$-0.588986\pi$
$307$	−2.63689e13	−0.551862	−0.275931	+	0.961177i	$0.588986\pi$
$308$	5.92223e13	1.21746
$309$	−2.04246e12	−0.0412460
$310$	−4.39650e13	−0.872203
$311$	7.04786e13	1.37365	0.686823	−	0.726824i	$-0.259005\pi$
$311$	7.04786e13	1.37365	0.686823	+	0.726824i	$0.259005\pi$
$312$	−3.67118e13	−0.703001
$313$	4.84770e13	0.912099	0.456049	−	0.889954i	$-0.349264\pi$
$313$	4.84770e13	0.912099	0.456049	+	0.889954i	$0.349264\pi$
$314$	9.54667e12	0.176498
$315$	3.52504e13	0.640408
$316$	−2.31462e13	−0.413239
$317$	5.95063e13	1.04409	0.522044	−	0.852919i	$-0.325170\pi$
$317$	5.95063e13	1.04409	0.522044	+	0.852919i	$0.325170\pi$
$318$	2.29732e13	0.396161
$319$	−2.92014e13	−0.494942
$320$	−4.23671e13	−0.705837
$321$	−6.92864e13	−1.13467
$322$	−2.42467e12	−0.0390341
$323$	−9.27171e12	−0.146739
$324$	−4.55731e12	−0.0709105
$325$	−4.58798e13	−0.701880
$326$	3.54735e13	0.533589
$327$	1.53801e13	0.227482
$328$	5.38284e13	0.782898
$329$	1.41097e14	2.01809
$330$	3.84393e13	0.540690
$331$	1.15288e14	1.59489	0.797443	−	0.603395i	$-0.206186\pi$
$331$	1.15288e14	1.59489	0.797443	+	0.603395i	$0.206186\pi$
$332$	4.52426e13	0.615585
$333$	4.44096e12	0.0594338
$334$	−6.59137e13	−0.867701
$335$	2.78447e13	0.360576
$336$	3.16300e12	0.0402934
$337$	1.33412e14	1.67198	0.835990	−	0.548745i	$-0.184894\pi$
$337$	1.33412e14	1.67198	0.835990	+	0.548745i	$0.184894\pi$
$338$	2.57072e13	0.316966
$339$	−5.18840e13	−0.629413
$340$	1.27846e14	1.52599
$341$	1.22590e14	1.43981
$342$	−1.33315e12	−0.0154077
$343$	−4.77577e13	−0.543157
$344$	−1.01524e14	−1.13631
$345$	2.77601e12	0.0305784
$346$	−3.73721e13	−0.405162
$347$	−9.01792e13	−0.962264	−0.481132	−	0.876648i	$-0.659774\pi$
$347$	−9.01792e13	−0.962264	−0.481132	+	0.876648i	$0.659774\pi$
$348$	−1.39648e13	−0.146672
$349$	2.10940e13	0.218082	0.109041	−	0.994037i	$-0.465222\pi$
$349$	2.10940e13	0.218082	0.109041	+	0.994037i	$0.465222\pi$
$350$	−5.15070e13	−0.524194
$351$	2.37367e13	0.237811
$352$	1.27668e14	1.25920
$353$	−1.47536e14	−1.43264	−0.716322	−	0.697769i	$-0.754176\pi$
$353$	−1.47536e14	−1.43264	−0.716322	+	0.697769i	$0.754176\pi$
$354$	−4.72899e12	−0.0452117
$355$	−1.66653e14	−1.56876
$356$	8.63141e13	0.800031
$357$	1.85329e14	1.69149
$358$	1.08322e13	0.0973555
$359$	6.40285e13	0.566701	0.283350	−	0.959016i	$-0.408554\pi$
$359$	6.40285e13	0.566701	0.283350	+	0.959016i	$0.408554\pi$
$360$	4.71866e13	0.411296
$361$	−1.15802e14	−0.994095
$362$	6.97143e13	0.589420
$363$	−3.78515e13	−0.315207
$364$	−1.47512e14	−1.20996
$365$	−2.11044e14	−1.70515
$366$	1.34837e13	0.107315
$367$	1.63466e14	1.28164	0.640818	−	0.767693i	$-0.278595\pi$
$367$	1.63466e14	1.28164	0.640818	+	0.767693i	$0.278595\pi$
$368$	2.49090e11	0.00192394
$369$	−3.48037e13	−0.264838
$370$	−1.79133e13	−0.134297
$371$	2.36950e14	1.75025
$372$	5.86254e13	0.426677
$373$	−1.66447e14	−1.19365	−0.596827	−	0.802370i	$-0.703572\pi$
$373$	−1.66447e14	−1.19365	−0.596827	+	0.802370i	$0.703572\pi$
$374$	2.02095e14	1.42811
$375$	−4.48504e13	−0.312316
$376$	1.88874e14	1.29610
$377$	7.27356e13	0.491892
$378$	2.66480e13	0.177607
$379$	1.95984e14	1.28737	0.643687	−	0.765289i	$-0.277404\pi$
$379$	1.95984e14	1.28737	0.643687	+	0.765289i	$0.277404\pi$
$380$	−9.48543e12	−0.0614111
$381$	1.30535e14	0.832991
$382$	6.35888e11	0.00399974
$383$	−1.90371e14	−1.18034	−0.590172	−	0.807278i	$-0.700940\pi$
$383$	−1.90371e14	−1.18034	−0.590172	+	0.807278i	$0.700940\pi$
$384$	6.36382e13	0.388952
$385$	3.96470e14	2.38878
$386$	−8.13055e13	−0.482936
$387$	6.56420e13	0.384390
$388$	−5.81600e13	−0.335776
$389$	2.88431e14	1.64180	0.820899	−	0.571073i	$-0.193473\pi$
$389$	2.88431e14	1.64180	0.820899	+	0.571073i	$0.193473\pi$
$390$	−9.57456e13	−0.537358
$391$	1.45949e13	0.0807659
$392$	−2.44512e14	−1.33422
$393$	−8.03986e13	−0.432603
$394$	1.33247e14	0.707012
$395$	−1.54955e14	−0.810815
$396$	−5.12571e13	−0.264503
$397$	2.38162e14	1.21206	0.606030	−	0.795441i	$-0.292761\pi$
$397$	2.38162e14	1.21206	0.606030	+	0.795441i	$0.292761\pi$
$398$	−1.42632e14	−0.715915
$399$	−1.37504e13	−0.0680714
$400$	5.29139e12	0.0258368
$401$	−8.38112e13	−0.403653	−0.201826	−	0.979421i	$-0.564688\pi$
$401$	−8.38112e13	−0.403653	−0.201826	+	0.979421i	$0.564688\pi$
$402$	2.10496e13	0.100000
$403$	−3.05350e14	−1.43094
$404$	9.00640e13	0.416346
$405$	−3.05094e13	−0.139133
$406$	8.16566e13	0.367365
$407$	4.99485e13	0.221693
$408$	2.48084e14	1.08634
$409$	−4.14093e14	−1.78904	−0.894520	−	0.447028i	$-0.852483\pi$
$409$	−4.14093e14	−1.78904	−0.894520	+	0.447028i	$0.852483\pi$
$410$	1.40386e14	0.598429
$411$	−1.53323e14	−0.644876
$412$	−1.09858e13	−0.0455927
$413$	−4.87757e13	−0.199746
$414$	2.09856e12	0.00848045
$415$	3.02881e14	1.20784
$416$	−3.17998e14	−1.25144
$417$	−1.96833e14	−0.764450
$418$	−1.49943e13	−0.0574720
$419$	4.99942e14	1.89122	0.945610	−	0.325301i	$-0.105466\pi$
$419$	4.99942e14	1.89122	0.945610	+	0.325301i	$0.105466\pi$
$420$	1.89601e14	0.707898
$421$	1.98871e14	0.732857	0.366428	−	0.930446i	$-0.380580\pi$
$421$	1.98871e14	0.732857	0.366428	+	0.930446i	$0.380580\pi$
$422$	3.49558e13	0.127146
$423$	−1.22120e14	−0.438444
$424$	3.17183e14	1.12408
$425$	3.10037e14	1.08461
$426$	−1.25983e14	−0.435071
$427$	1.39073e14	0.474122
$428$	−3.72670e14	−1.25425
$429$	2.66972e14	0.887056
$430$	−2.64777e14	−0.868568
$431$	−2.31495e14	−0.749749	−0.374874	−	0.927076i	$-0.622314\pi$
$431$	−2.31495e14	−0.749749	−0.374874	+	0.927076i	$0.622314\pi$
$432$	−2.73759e12	−0.00875403
$433$	−1.23881e13	−0.0391131	−0.0195565	−	0.999809i	$-0.506225\pi$
$433$	−1.23881e13	−0.0391131	−0.0195565	+	0.999809i	$0.506225\pi$
$434$	−3.42801e14	−1.06868
$435$	−9.34888e13	−0.287785
$436$	8.27248e13	0.251455
$437$	−1.08286e12	−0.00325030
$438$	−1.59542e14	−0.472897
$439$	−2.24804e14	−0.658036	−0.329018	−	0.944324i	$-0.606718\pi$
$439$	−2.24804e14	−0.658036	−0.329018	+	0.944324i	$0.606718\pi$
$440$	5.30719e14	1.53417
$441$	1.58094e14	0.451338
$442$	−5.03383e14	−1.41931
$443$	−1.11592e14	−0.310750	−0.155375	−	0.987856i	$-0.549659\pi$
$443$	−1.11592e14	−0.310750	−0.155375	+	0.987856i	$0.549659\pi$
$444$	2.38866e13	0.0656972
$445$	5.77839e14	1.56974
$446$	−2.06217e13	−0.0553328
$447$	5.79453e13	0.153577
$448$	−3.30343e14	−0.864839
$449$	−3.55719e14	−0.919924	−0.459962	−	0.887939i	$-0.652137\pi$
$449$	−3.55719e14	−0.919924	−0.459962	+	0.887939i	$0.652137\pi$
$450$	4.45794e13	0.113885
$451$	−3.91446e14	−0.987872
$452$	−2.79068e14	−0.695744
$453$	5.93781e13	0.146247
$454$	6.40457e13	0.155841
$455$	−9.87538e14	−2.37406
$456$	−1.84064e13	−0.0437183
$457$	−1.75577e13	−0.0412030	−0.0206015	−	0.999788i	$-0.506558\pi$
$457$	−1.75577e13	−0.0412030	−0.0206015	+	0.999788i	$0.506558\pi$
$458$	−2.67453e14	−0.620137
$459$	−1.60403e14	−0.367488
$460$	1.49313e13	0.0338010
$461$	3.32355e14	0.743441	0.371720	−	0.928345i	$-0.378768\pi$
$461$	3.32355e14	0.743441	0.371720	+	0.928345i	$0.378768\pi$
$462$	2.99717e14	0.662491
$463$	−3.59705e14	−0.785689	−0.392845	−	0.919605i	$-0.628509\pi$
$463$	−3.59705e14	−0.785689	−0.392845	+	0.919605i	$0.628509\pi$
$464$	−8.38870e12	−0.0181070
$465$	3.92474e14	0.837182
$466$	−4.69683e14	−0.990107
$467$	−7.51804e14	−1.56625	−0.783126	−	0.621863i	$-0.786376\pi$
$467$	−7.51804e14	−1.56625	−0.783126	+	0.621863i	$0.786376\pi$
$468$	1.27673e14	0.262873
$469$	2.17109e14	0.441802
$470$	4.92588e14	0.990708
$471$	−8.52228e13	−0.169411
$472$	−6.52917e13	−0.128285
$473$	7.38291e14	1.43381
$474$	−1.17140e14	−0.224867
$475$	−2.30030e13	−0.0436486
$476$	9.96830e14	1.86975
$477$	−2.05081e14	−0.380254
$478$	−5.64070e14	−1.03390
$479$	9.00575e14	1.63183	0.815914	−	0.578173i	$-0.196234\pi$
$479$	9.00575e14	1.63183	0.815914	+	0.578173i	$0.196234\pi$
$480$	4.08730e14	0.732167
$481$	−1.24413e14	−0.220327
$482$	−5.88526e14	−1.03040
$483$	2.16449e13	0.0374668
$484$	−2.03592e14	−0.348426
$485$	−3.89359e14	−0.658825
$486$	−2.30640e13	−0.0385864
$487$	−6.74263e14	−1.11537	−0.557686	−	0.830052i	$-0.688311\pi$
$487$	−6.74263e14	−1.11537	−0.557686	+	0.830052i	$0.688311\pi$
$488$	1.86165e14	0.304501
$489$	−3.16671e14	−0.512164
$490$	−6.37694e14	−1.01984
$491$	6.05535e14	0.957615	0.478808	−	0.877920i	$-0.341069\pi$
$491$	6.05535e14	0.957615	0.478808	+	0.877920i	$0.341069\pi$
$492$	−1.87199e14	−0.292749
$493$	−4.91518e14	−0.760118
$494$	3.73482e13	0.0571178
$495$	−3.43146e14	−0.518980
$496$	3.52165e13	0.0526741
$497$	−1.29942e15	−1.92215
$498$	2.28967e14	0.334974
$499$	−9.33233e14	−1.35032	−0.675161	−	0.737671i	$-0.735926\pi$
$499$	−9.33233e14	−1.35032	−0.675161	+	0.737671i	$0.735926\pi$
$500$	−2.41237e14	−0.345230
$501$	5.88409e14	0.832860
$502$	5.93768e13	0.0831278
$503$	8.39570e14	1.16261	0.581303	−	0.813687i	$-0.302543\pi$
$503$	8.39570e14	1.16261	0.581303	+	0.813687i	$0.302543\pi$
$504$	3.67921e14	0.503949
$505$	6.02943e14	0.816910
$506$	2.36030e13	0.0316329
$507$	−2.29487e14	−0.304239
$508$	7.02109e14	0.920776
$509$	7.03132e14	0.912198	0.456099	−	0.889929i	$-0.349246\pi$
$509$	7.03132e14	0.912198	0.456099	+	0.889929i	$0.349246\pi$
$510$	6.47010e14	0.830377
$511$	−1.64554e15	−2.08927
$512$	7.23595e13	0.0908889
$513$	1.19010e13	0.0147890
$514$	7.25819e14	0.892342
$515$	−7.35453e13	−0.0894572
$516$	3.53069e14	0.424899
$517$	−1.37351e15	−1.63544
$518$	−1.39672e14	−0.164549
$519$	3.33620e14	0.388894
$520$	−1.32193e15	−1.52472
$521$	7.78604e14	0.888606	0.444303	−	0.895877i	$-0.353451\pi$
$521$	7.78604e14	0.888606	0.444303	+	0.895877i	$0.353451\pi$
$522$	−7.06741e13	−0.0798127
$523$	1.20304e15	1.34438	0.672189	−	0.740379i	$-0.265354\pi$
$523$	1.20304e15	1.34438	0.672189	+	0.740379i	$0.265354\pi$
$524$	−4.32440e14	−0.478193
$525$	4.59801e14	0.503145
$526$	−2.02316e14	−0.219083
$527$	2.06343e15	2.21122
$528$	−3.07903e13	−0.0326533
$529$	−9.51105e14	−0.998211
$530$	8.27224e14	0.859223
$531$	4.22156e13	0.0433963
$532$	−7.39592e13	−0.0752451
$533$	9.75024e14	0.981783
$534$	4.36825e14	0.435342
$535$	−2.49488e15	−2.46096
$536$	2.90625e14	0.283744
$537$	−9.66988e13	−0.0934464
$538$	−1.88906e13	−0.0180694
$539$	1.77812e15	1.68353
$540$	−1.64101e14	−0.153796
$541$	−5.14851e14	−0.477635	−0.238818	−	0.971064i	$-0.576760\pi$
$541$	−5.14851e14	−0.477635	−0.238818	+	0.971064i	$0.576760\pi$
$542$	5.77695e14	0.530521
$543$	−6.22338e14	−0.565753
$544$	2.14890e15	1.93385
$545$	5.53810e14	0.493378
$546$	−7.46542e14	−0.658407
$547$	−1.50647e15	−1.31531	−0.657657	−	0.753317i	$-0.728452\pi$
$547$	−1.50647e15	−1.31531	−0.657657	+	0.753317i	$0.728452\pi$
$548$	−8.24675e14	−0.712837
$549$	−1.20368e14	−0.103006
$550$	5.01395e14	0.424801
$551$	3.64679e13	0.0305898
$552$	2.89741e13	0.0240627
$553$	−1.20821e15	−0.993466
$554$	−7.28799e14	−0.593340
$555$	1.59911e14	0.128904
$556$	−1.05870e15	−0.845012
$557$	−1.78211e15	−1.40841	−0.704206	−	0.709995i	$-0.748697\pi$
$557$	−1.78211e15	−1.40841	−0.704206	+	0.709995i	$0.748697\pi$
$558$	2.96696e14	0.232179
$559$	−1.83896e15	−1.42497
$560$	1.13894e14	0.0873912
$561$	−1.80409e15	−1.37077
$562$	−8.31294e13	−0.0625468
$563$	−1.93847e15	−1.44432	−0.722158	−	0.691728i	$-0.756850\pi$
$563$	−1.93847e15	−1.44432	−0.722158	+	0.691728i	$0.756850\pi$
$564$	−6.56845e14	−0.484649
$565$	−1.86825e15	−1.36512
$566$	−4.72069e14	−0.341598
$567$	−2.37886e14	−0.170476
$568$	−1.73941e15	−1.23449
$569$	1.21352e15	0.852964	0.426482	−	0.904496i	$-0.359753\pi$
$569$	1.21352e15	0.852964	0.426482	+	0.904496i	$0.359753\pi$
$570$	−4.80045e13	−0.0334172
$571$	−1.68489e15	−1.16164	−0.580820	−	0.814032i	$-0.697268\pi$
$571$	−1.68489e15	−1.16164	−0.580820	+	0.814032i	$0.697268\pi$
$572$	1.43596e15	0.980539
$573$	−5.67655e12	−0.00383914
$574$	1.09461e15	0.733237
$575$	3.62097e13	0.0240244
$576$	2.85913e14	0.187893
$577$	−5.11907e14	−0.333215	−0.166607	−	0.986023i	$-0.553281\pi$
$577$	−5.11907e14	−0.333215	−0.166607	+	0.986023i	$0.553281\pi$
$578$	2.46875e15	1.59175
$579$	7.25811e14	0.463545
$580$	−5.02848e14	−0.318114
$581$	2.36161e15	1.47992
$582$	−2.94341e14	−0.182715
$583$	−2.30659e15	−1.41838
$584$	−2.20274e15	−1.34181
$585$	8.54718e14	0.515781
$586$	−7.95677e14	−0.475664
$587$	−1.36053e15	−0.805745	−0.402873	−	0.915256i	$-0.631988\pi$
$587$	−1.36053e15	−0.805745	−0.402873	+	0.915256i	$0.631988\pi$
$588$	8.50337e14	0.498903
$589$	−1.53095e14	−0.0889872
$590$	−1.70283e14	−0.0980584
$591$	−1.18949e15	−0.678623
$592$	1.43487e13	0.00811044
$593$	−2.90584e15	−1.62731	−0.813656	−	0.581346i	$-0.802526\pi$
$593$	−2.90584e15	−1.62731	−0.813656	+	0.581346i	$0.802526\pi$
$594$	−2.59406e14	−0.143931
$595$	6.67339e15	3.66862
$596$	3.11670e14	0.169762
$597$	1.27328e15	0.687169
$598$	−5.87909e13	−0.0314379
$599$	3.99294e14	0.211566	0.105783	−	0.994389i	$-0.466265\pi$
$599$	3.99294e14	0.211566	0.105783	+	0.994389i	$0.466265\pi$
$600$	6.15494e14	0.323141
$601$	1.25221e15	0.651431	0.325716	−	0.945468i	$-0.394395\pi$
$601$	1.25221e15	0.651431	0.325716	+	0.945468i	$0.394395\pi$
$602$	−2.06450e15	−1.06423
$603$	−1.87909e14	−0.0959848
$604$	3.19377e14	0.161659
$605$	−1.36297e15	−0.683644
$606$	4.55803e14	0.226557
$607$	−3.11779e14	−0.153571	−0.0767856	−	0.997048i	$-0.524466\pi$
$607$	−3.11779e14	−0.153571	−0.0767856	+	0.997048i	$0.524466\pi$
$608$	−1.59437e14	−0.0778248
$609$	−7.28946e14	−0.352614
$610$	4.85523e14	0.232753
$611$	3.42117e15	1.62536
$612$	−8.62760e14	−0.406216
$613$	4.85794e14	0.226683	0.113342	−	0.993556i	$-0.463845\pi$
$613$	4.85794e14	0.226683	0.113342	+	0.993556i	$0.463845\pi$
$614$	−7.17785e14	−0.331947
$615$	−1.25322e15	−0.574401
$616$	4.13809e15	1.87978
$617$	−2.01403e15	−0.906769	−0.453385	−	0.891315i	$-0.649784\pi$
$617$	−2.01403e15	−0.906769	−0.453385	+	0.891315i	$0.649784\pi$
$618$	−5.55975e13	−0.0248096
$619$	−2.87650e15	−1.27223	−0.636114	−	0.771595i	$-0.719459\pi$
$619$	−2.87650e15	−1.27223	−0.636114	+	0.771595i	$0.719459\pi$
$620$	2.11100e15	0.925408
$621$	−1.87337e13	−0.00813993
$622$	1.91849e15	0.826252
$623$	4.50549e15	1.92335
$624$	7.66934e13	0.0324521
$625$	−2.96921e15	−1.24538
$626$	1.31959e15	0.548630
$627$	1.33854e14	0.0551643
$628$	−4.58387e14	−0.187264
$629$	8.40733e14	0.340471
$630$	9.59549e14	0.385207
$631$	3.57834e15	1.42403	0.712017	−	0.702162i	$-0.247782\pi$
$631$	3.57834e15	1.42403	0.712017	+	0.702162i	$0.247782\pi$
$632$	−1.61732e15	−0.638045
$633$	−3.12050e14	−0.122040
$634$	1.61981e15	0.628021
$635$	4.70034e15	1.80665
$636$	−1.10307e15	−0.420327
$637$	−4.42898e15	−1.67316
$638$	−7.94888e14	−0.297709
$639$	1.12465e15	0.417602
$640$	2.29150e15	0.843588
$641$	1.79966e15	0.656856	0.328428	−	0.944529i	$-0.393481\pi$
$641$	1.79966e15	0.656856	0.328428	+	0.944529i	$0.393481\pi$
$642$	−1.88604e15	−0.682508
$643$	−2.88174e15	−1.03394	−0.516970	−	0.856004i	$-0.672940\pi$
$643$	−2.88174e15	−1.03394	−0.516970	+	0.856004i	$0.672940\pi$
$644$	1.16421e14	0.0414153
$645$	2.36366e15	0.833692
$646$	−2.52384e14	−0.0882639
$647$	−3.67263e15	−1.27351	−0.636756	−	0.771065i	$-0.719724\pi$
$647$	−3.67263e15	−1.27351	−0.636756	+	0.771065i	$0.719724\pi$
$648$	−3.18437e14	−0.109486
$649$	4.74808e14	0.161872
$650$	−1.24889e15	−0.422183
$651$	3.06018e15	1.02577
$652$	−1.70328e15	−0.566139
$653$	−4.94676e15	−1.63041	−0.815207	−	0.579170i	$-0.803377\pi$
$653$	−4.94676e15	−1.63041	−0.815207	+	0.579170i	$0.803377\pi$
$654$	4.18660e14	0.136831
$655$	−2.89501e15	−0.938260
$656$	−1.12451e14	−0.0361403
$657$	1.42422e15	0.453908
$658$	3.84078e15	1.21388
$659$	−5.20368e15	−1.63095	−0.815475	−	0.578793i	$-0.803524\pi$
$659$	−5.20368e15	−1.63095	−0.815475	+	0.578793i	$0.803524\pi$
$660$	−1.84568e15	−0.573673
$661$	7.86702e14	0.242495	0.121247	−	0.992622i	$-0.461311\pi$
$661$	7.86702e14	0.242495	0.121247	+	0.992622i	$0.461311\pi$
$662$	3.13824e15	0.959327
$663$	4.49368e15	1.36232
$664$	3.16127e15	0.950468
$665$	−4.95128e14	−0.147638
$666$	1.20887e14	0.0357496
$667$	−5.74051e13	−0.0168368
$668$	3.16487e15	0.920631
$669$	1.84089e14	0.0531110
$670$	7.57959e14	0.216887
$671$	−1.35381e15	−0.384223
$672$	3.18693e15	0.897101
$673$	1.34979e15	0.376863	0.188432	−	0.982086i	$-0.439660\pi$
$673$	1.34979e15	0.376863	0.188432	+	0.982086i	$0.439660\pi$
$674$	3.63160e15	1.00570
$675$	−3.97959e14	−0.109312
$676$	−1.23434e15	−0.336301
$677$	−5.70336e15	−1.54132	−0.770661	−	0.637245i	$-0.780074\pi$
$677$	−5.70336e15	−1.54132	−0.770661	+	0.637245i	$0.780074\pi$
$678$	−1.41233e15	−0.378593
$679$	−3.03589e15	−0.807238
$680$	8.93306e15	2.35614
$681$	−5.71734e14	−0.149584
$682$	3.33701e15	0.866050
$683$	2.68427e15	0.691054	0.345527	−	0.938409i	$-0.387700\pi$
$683$	2.68427e15	0.691054	0.345527	+	0.938409i	$0.387700\pi$
$684$	6.40120e13	0.0163475
$685$	−5.52088e15	−1.39865
$686$	−1.30001e15	−0.326710
$687$	2.38755e15	0.595237
$688$	2.12090e14	0.0524545
$689$	5.74532e15	1.40964
$690$	7.55653e13	0.0183930
$691$	−2.29109e15	−0.553240	−0.276620	−	0.960979i	$-0.589214\pi$
$691$	−2.29109e15	−0.553240	−0.276620	+	0.960979i	$0.589214\pi$
$692$	1.79444e15	0.429878
$693$	−2.67556e15	−0.635890
$694$	−2.45476e15	−0.578804
$695$	−7.08760e15	−1.65799
$696$	−9.75774e14	−0.226464
$697$	−6.58882e15	−1.51715
$698$	5.74199e14	0.131177
$699$	4.19284e15	0.950351
$700$	2.47313e15	0.556170
$701$	6.08661e15	1.35808	0.679041	−	0.734100i	$-0.262396\pi$
$701$	6.08661e15	1.35808	0.679041	+	0.734100i	$0.262396\pi$
$702$	6.46135e14	0.143044
$703$	−6.23777e13	−0.0137017
$704$	3.21573e15	0.700857
$705$	−4.39732e15	−0.950928
$706$	−4.01608e15	−0.861740
$707$	4.70124e15	1.00093
$708$	2.27065e14	0.0479697
$709$	2.23119e15	0.467716	0.233858	−	0.972271i	$-0.424865\pi$
$709$	2.23119e15	0.467716	0.233858	+	0.972271i	$0.424865\pi$
$710$	−4.53644e15	−0.943614
$711$	1.04571e15	0.215838
$712$	6.03110e15	1.23525
$713$	2.40992e14	0.0489790
$714$	5.04483e15	1.01743
$715$	9.61321e15	1.92391
$716$	−5.20113e14	−0.103294
$717$	5.03543e15	0.992388
$718$	1.74291e15	0.340872
$719$	2.77472e15	0.538530	0.269265	−	0.963066i	$-0.413219\pi$
$719$	2.77472e15	0.538530	0.269265	+	0.963066i	$0.413219\pi$
$720$	−9.85759e13	−0.0189864
$721$	−5.73444e14	−0.109609
$722$	−3.15224e15	−0.597950
$723$	5.25375e15	0.989029
$724$	−3.34736e15	−0.625375
$725$	−1.21945e15	−0.226103
$726$	−1.03035e15	−0.189598
$727$	−8.74528e15	−1.59711	−0.798554	−	0.601923i	$-0.794402\pi$
$727$	−8.74528e15	−1.59711	−0.798554	+	0.601923i	$0.794402\pi$
$728$	−1.03073e16	−1.86819
$729$	2.05891e14	0.0370370
$730$	−5.74481e15	−1.02565
$731$	1.24269e16	2.20200
$732$	−6.47424e14	−0.113862
$733$	−7.84581e15	−1.36951	−0.684756	−	0.728772i	$-0.740091\pi$
$733$	−7.84581e15	−1.36951	−0.684756	+	0.728772i	$0.740091\pi$
$734$	4.44970e15	0.770907
$735$	5.69267e15	0.978894
$736$	2.50974e14	0.0428351
$737$	−2.11346e15	−0.358032
$738$	−9.47389e14	−0.159301
$739$	5.26678e15	0.879024	0.439512	−	0.898237i	$-0.355151\pi$
$739$	5.26678e15	0.879024	0.439512	+	0.898237i	$0.355151\pi$
$740$	8.60113e14	0.142489
$741$	−3.33406e14	−0.0548243
$742$	6.44998e15	1.05278
$743$	8.32342e13	0.0134854	0.00674269	−	0.999977i	$-0.497854\pi$
$743$	8.32342e13	0.0134854	0.00674269	+	0.999977i	$0.497854\pi$
$744$	4.09638e15	0.658794
$745$	2.08651e15	0.333090
$746$	−4.53085e15	−0.717986
$747$	−2.04398e15	−0.321524
$748$	−9.70366e15	−1.51522
$749$	−1.94530e16	−3.01534
$750$	−1.22087e15	−0.187859
$751$	1.04791e16	1.60069	0.800343	−	0.599542i	$-0.204651\pi$
$751$	1.04791e16	1.60069	0.800343	+	0.599542i	$0.204651\pi$
$752$	−3.94569e14	−0.0598308
$753$	−5.30055e14	−0.0797900
$754$	1.97993e15	0.295874
$755$	2.13810e15	0.317191
$756$	−1.27952e15	−0.188441
$757$	−4.74174e15	−0.693282	−0.346641	−	0.937998i	$-0.612678\pi$
$757$	−4.74174e15	−0.693282	−0.346641	+	0.937998i	$0.612678\pi$
$758$	5.33486e15	0.774359
$759$	−2.10703e14	−0.0303627
$760$	−6.62783e14	−0.0948193
$761$	−3.54806e15	−0.503935	−0.251968	−	0.967736i	$-0.581078\pi$
$761$	−3.54806e15	−0.503935	−0.251968	+	0.967736i	$0.581078\pi$
$762$	3.55328e15	0.501046
$763$	4.31814e15	0.604521
$764$	−3.05324e13	−0.00424373
$765$	−5.77584e15	−0.797035
$766$	−5.18208e15	−0.709980
$767$	−1.18267e15	−0.160875
$768$	4.14196e15	0.559395
$769$	−1.03550e16	−1.38853	−0.694263	−	0.719721i	$-0.744270\pi$
$769$	−1.03550e16	−1.38853	−0.694263	+	0.719721i	$0.744270\pi$
$770$	1.07923e16	1.43686
$771$	−6.47937e15	−0.856512
$772$	3.90392e15	0.512396
$773$	−4.02175e15	−0.524116	−0.262058	−	0.965052i	$-0.584401\pi$
$773$	−4.02175e15	−0.524116	−0.262058	+	0.965052i	$0.584401\pi$
$774$	1.78684e15	0.231211
$775$	5.11936e15	0.657744
$776$	−4.06387e15	−0.518442
$777$	1.24685e15	0.157942
$778$	7.85136e15	0.987546
$779$	4.88854e14	0.0610552
$780$	4.59727e15	0.570137
$781$	1.26492e16	1.55769
$782$	3.97285e14	0.0485809
$783$	6.30905e14	0.0766080
$784$	5.10801e14	0.0615904
$785$	−3.06872e15	−0.367430
$786$	−2.18852e15	−0.260212
$787$	−5.58523e15	−0.659447	−0.329724	−	0.944077i	$-0.606956\pi$
$787$	−5.58523e15	−0.659447	−0.329724	+	0.944077i	$0.606956\pi$
$788$	−6.39789e15	−0.750140
$789$	1.80607e15	0.210286
$790$	−4.21801e15	−0.487707
$791$	−1.45670e16	−1.67263
$792$	−3.58153e15	−0.408395
$793$	3.37211e15	0.381855
$794$	6.48298e15	0.729058
$795$	−7.38460e15	−0.824722
$796$	6.84856e15	0.759587
$797$	1.12022e16	1.23390	0.616952	−	0.787000i	$-0.288367\pi$
$797$	1.12022e16	1.23390	0.616952	+	0.787000i	$0.288367\pi$
$798$	−3.74298e14	−0.0409451
$799$	−2.31189e16	−2.51166
$800$	5.33141e15	0.575237
$801$	−3.89952e15	−0.417861
$802$	−2.28141e15	−0.242798
$803$	1.60186e16	1.69312
$804$	−1.01071e15	−0.106100
$805$	7.79395e14	0.0812607
$806$	−8.31190e15	−0.860712
$807$	1.68636e14	0.0173439
$808$	6.29312e15	0.642841
$809$	−1.42853e16	−1.44935	−0.724675	−	0.689091i	$-0.758010\pi$
$809$	−1.42853e16	−1.44935	−0.724675	+	0.689091i	$0.758010\pi$
$810$	−8.30493e14	−0.0836890
$811$	−9.38781e15	−0.939614	−0.469807	−	0.882769i	$-0.655677\pi$
$811$	−9.38781e15	−0.939614	−0.469807	+	0.882769i	$0.655677\pi$
$812$	−3.92078e15	−0.389775
$813$	−5.15706e15	−0.509219
$814$	1.35964e15	0.133349
$815$	−1.14028e16	−1.11082
$816$	−5.18263e14	−0.0501481
$817$	−9.22009e14	−0.0886163
$818$	−1.12720e16	−1.07611
$819$	6.66436e15	0.631970
$820$	−6.74070e15	−0.634934
$821$	1.93523e16	1.81069	0.905347	−	0.424672i	$-0.139611\pi$
$821$	1.93523e16	1.81069	0.905347	+	0.424672i	$0.139611\pi$
$822$	−4.17358e15	−0.387894
$823$	1.83381e16	1.69299	0.846495	−	0.532397i	$-0.178708\pi$
$823$	1.83381e16	1.69299	0.846495	+	0.532397i	$0.178708\pi$
$824$	−7.67617e14	−0.0703955
$825$	−4.47594e15	−0.407744
$826$	−1.32772e15	−0.120148
$827$	6.01570e15	0.540761	0.270381	−	0.962754i	$-0.412850\pi$
$827$	6.01570e15	0.540761	0.270381	+	0.962754i	$0.412850\pi$
$828$	−1.00763e14	−0.00899776
$829$	1.05787e16	0.938384	0.469192	−	0.883096i	$-0.344545\pi$
$829$	1.05787e16	0.938384	0.469192	+	0.883096i	$0.344545\pi$
$830$	8.24470e15	0.726516
$831$	6.50596e15	0.569516
$832$	−8.00982e15	−0.696537
$833$	2.99293e16	2.58552
$834$	−5.35797e15	−0.459819
$835$	2.11876e16	1.80637
$836$	7.19957e14	0.0609779
$837$	−2.64859e15	−0.222856
$838$	1.36089e16	1.13757
$839$	−1.18712e16	−0.985837	−0.492919	−	0.870075i	$-0.664070\pi$
$839$	−1.18712e16	−0.985837	−0.492919	+	0.870075i	$0.664070\pi$
$840$	1.32482e16	1.09300
$841$	−1.02673e16	−0.841543
$842$	5.41344e15	0.440815
$843$	7.42093e14	0.0600353
$844$	−1.67842e15	−0.134902
$845$	−8.26343e15	−0.659855
$846$	−3.32421e15	−0.263725
$847$	−1.06272e16	−0.837648
$848$	−6.62616e14	−0.0518902
$849$	4.21414e15	0.327882
$850$	8.43949e15	0.652398
$851$	9.81905e13	0.00754149
$852$	6.04914e15	0.461611
$853$	5.71978e15	0.433670	0.216835	−	0.976208i	$-0.430427\pi$
$853$	5.71978e15	0.433670	0.216835	+	0.976208i	$0.430427\pi$
$854$	3.78569e15	0.285185
$855$	4.28535e14	0.0320754
$856$	−2.60399e16	−1.93657
$857$	1.98359e16	1.46574	0.732870	−	0.680368i	$-0.238180\pi$
$857$	1.98359e16	1.46574	0.732870	+	0.680368i	$0.238180\pi$
$858$	7.26723e15	0.533567
$859$	−1.28081e16	−0.934380	−0.467190	−	0.884157i	$-0.654734\pi$
$859$	−1.28081e16	−0.934380	−0.467190	+	0.884157i	$0.654734\pi$
$860$	1.27134e16	0.921551
$861$	−9.77155e15	−0.703795
$862$	−6.30149e15	−0.450976
$863$	−1.09758e16	−0.780506	−0.390253	−	0.920708i	$-0.627612\pi$
$863$	−1.09758e16	−0.780506	−0.390253	+	0.920708i	$0.627612\pi$
$864$	−2.75830e15	−0.194902
$865$	1.20131e16	0.843461
$866$	−3.37216e14	−0.0235266
$867$	−2.20384e16	−1.52783
$868$	1.64597e16	1.13387
$869$	1.17613e16	0.805094
$870$	−2.54485e15	−0.173104
$871$	5.26425e15	0.355825
$872$	5.78030e15	0.388248
$873$	2.62757e15	0.175378
$874$	−2.94763e13	−0.00195506
$875$	−1.25923e16	−0.829965
$876$	7.66046e15	0.501744
$877$	1.89070e16	1.23062	0.615312	−	0.788284i	$-0.289030\pi$
$877$	1.89070e16	1.23062	0.615312	+	0.788284i	$0.289030\pi$
$878$	−6.11938e15	−0.395811
$879$	7.10298e15	0.456564
$880$	−1.10871e15	−0.0708209
$881$	2.73060e15	0.173337	0.0866684	−	0.996237i	$-0.472378\pi$
$881$	2.73060e15	0.173337	0.0866684	+	0.996237i	$0.472378\pi$
$882$	4.30345e15	0.271481
$883$	1.90415e16	1.19376	0.596881	−	0.802330i	$-0.296407\pi$
$883$	1.90415e16	1.19376	0.596881	+	0.802330i	$0.296407\pi$
$884$	2.41701e16	1.50589
$885$	1.52011e15	0.0941210
$886$	−3.03763e15	−0.186917
$887$	−7.35165e15	−0.449578	−0.224789	−	0.974407i	$-0.572169\pi$
$887$	−7.35165e15	−0.449578	−0.224789	+	0.974407i	$0.572169\pi$
$888$	1.66905e15	0.101437
$889$	3.66492e16	2.21363
$890$	1.57293e16	0.944200
$891$	2.31571e15	0.138152
$892$	9.90159e14	0.0587081
$893$	1.71529e15	0.101078
$894$	1.57732e15	0.0923772
$895$	−3.48195e15	−0.202673
$896$	1.78672e16	1.03362
$897$	5.24824e14	0.0301756
$898$	−9.68299e15	−0.553337
$899$	−8.11599e15	−0.460960
$900$	−2.14050e15	−0.120832
$901$	−3.88246e16	−2.17831
$902$	−1.06555e16	−0.594207
$903$	1.84298e16	1.02150
$904$	−1.94996e16	−1.07423
$905$	−2.24093e16	−1.22705
$906$	1.61633e15	0.0879678
$907$	−2.98228e15	−0.161327	−0.0806637	−	0.996741i	$-0.525704\pi$
$907$	−2.98228e15	−0.161327	−0.0806637	+	0.996741i	$0.525704\pi$
$908$	−3.07518e15	−0.165348
$909$	−4.06894e15	−0.217460
$910$	−2.68817e16	−1.42800
$911$	−2.38748e16	−1.26063	−0.630317	−	0.776338i	$-0.717075\pi$
$911$	−2.38748e16	−1.26063	−0.630317	+	0.776338i	$0.717075\pi$
$912$	3.84522e13	0.00201813
$913$	−2.29891e16	−1.19931
$914$	−4.77937e14	−0.0247837
$915$	−4.33425e15	−0.223408
$916$	1.28419e16	0.657966
$917$	−2.25728e16	−1.14962
$918$	−4.36632e15	−0.221045
$919$	3.24634e16	1.63365	0.816826	−	0.576885i	$-0.195732\pi$
$919$	3.24634e16	1.63365	0.816826	+	0.576885i	$0.195732\pi$
$920$	1.04331e15	0.0521890
$921$	6.40764e15	0.318618
$922$	9.04699e15	0.447182
$923$	−3.15069e16	−1.54809
$924$	−1.43910e16	−0.702903
$925$	2.08585e15	0.101275
$926$	−9.79149e15	−0.472594
$927$	4.96317e14	0.0238134
$928$	−8.45215e15	−0.403138
$929$	−2.26731e16	−1.07504	−0.537521	−	0.843250i	$-0.680639\pi$
$929$	−2.26731e16	−1.07504	−0.537521	+	0.843250i	$0.680639\pi$
$930$	1.06835e16	0.503567
$931$	−2.22058e15	−0.104050
$932$	2.25520e16	1.05050
$933$	−1.71263e16	−0.793075
$934$	−2.04648e16	−0.942104
$935$	−6.49622e16	−2.97301
$936$	8.92097e15	0.405878
$937$	−2.84366e16	−1.28621	−0.643103	−	0.765780i	$-0.722353\pi$
$937$	−2.84366e16	−1.28621	−0.643103	+	0.765780i	$0.722353\pi$
$938$	5.90991e15	0.265745
$939$	−1.17799e16	−0.526601
$940$	−2.36518e16	−1.05114
$941$	−3.16014e16	−1.39625	−0.698124	−	0.715977i	$-0.745982\pi$
$941$	−3.16014e16	−1.39625	−0.698124	+	0.715977i	$0.745982\pi$
$942$	−2.31984e15	−0.101901
$943$	−7.69519e14	−0.0336051
$944$	1.36399e14	0.00592194
$945$	−8.56586e15	−0.369740
$946$	2.00970e16	0.862440
$947$	−1.87145e16	−0.798460	−0.399230	−	0.916851i	$-0.630723\pi$
$947$	−1.87145e16	−0.798460	−0.399230	+	0.916851i	$0.630723\pi$
$948$	5.62454e15	0.238584
$949$	−3.98995e16	−1.68268
$950$	−6.26163e14	−0.0262547
$951$	−1.44600e16	−0.602804
$952$	6.96524e16	2.88691
$953$	3.18697e15	0.131331	0.0656654	−	0.997842i	$-0.479083\pi$
$953$	3.18697e15	0.131331	0.0656654	+	0.997842i	$0.479083\pi$
$954$	−5.58248e15	−0.228724
$955$	−2.04403e14	−0.00832660
$956$	2.70840e16	1.09697
$957$	7.09593e15	0.285755
$958$	2.45144e16	0.981548
$959$	−4.30471e16	−1.71373
$960$	1.02952e16	0.407515
$961$	8.66313e15	0.340954
$962$	−3.38663e15	−0.132527
$963$	1.68366e16	0.655103
$964$	2.82583e16	1.09326
$965$	2.61352e16	1.00537
$966$	5.89194e14	0.0225364
$967$	−2.85691e16	−1.08655	−0.543277	−	0.839553i	$-0.682817\pi$
$967$	−2.85691e16	−1.08655	−0.543277	+	0.839553i	$0.682817\pi$
$968$	−1.42257e16	−0.537972
$969$	2.25302e15	0.0847199
$970$	−1.05987e16	−0.396285
$971$	−2.35784e16	−0.876615	−0.438307	−	0.898825i	$-0.644422\pi$
$971$	−2.35784e16	−0.876615	−0.438307	+	0.898825i	$0.644422\pi$
$972$	1.10743e15	0.0409402
$973$	−5.52631e16	−2.03149
$974$	−1.83540e16	−0.670899
$975$	1.11488e16	0.405231
$976$	−3.88910e14	−0.0140564
$977$	−1.01719e16	−0.365581	−0.182790	−	0.983152i	$-0.558513\pi$
$977$	−1.01719e16	−0.365581	−0.182790	+	0.983152i	$0.558513\pi$
$978$	−8.62006e15	−0.308068
$979$	−4.38588e16	−1.55866
$980$	3.06192e16	1.08206
$981$	−3.73736e15	−0.131337
$982$	1.64832e16	0.576008
$983$	−1.37295e16	−0.477101	−0.238551	−	0.971130i	$-0.576672\pi$
$983$	−1.37295e16	−0.477101	−0.238551	+	0.971130i	$0.576672\pi$
$984$	−1.30803e16	−0.452006
$985$	−4.28314e16	−1.47185
$986$	−1.33796e16	−0.457213
$987$	−3.42865e16	−1.16514
$988$	−1.79329e15	−0.0606020
$989$	1.45136e15	0.0487748
$990$	−9.34074e15	−0.312168
$991$	3.58942e16	1.19294	0.596471	−	0.802635i	$-0.296569\pi$
$991$	3.58942e16	1.19294	0.596471	+	0.802635i	$0.296569\pi$
$992$	3.54829e16	1.17275
$993$	−2.80149e16	−0.920807
$994$	−3.53713e16	−1.15618
$995$	4.58484e16	1.49038
$996$	−1.09939e16	−0.355408
$997$	−1.47560e16	−0.474402	−0.237201	−	0.971461i	$-0.576230\pi$
$997$	−1.47560e16	−0.474402	−0.237201	+	0.971461i	$0.576230\pi$
$998$	−2.54034e16	−0.812222
$999$	−1.07915e15	−0.0343141

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.a.1.18	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.a.1.18	✓	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)

\(f(q)\)	\(=\)	\(q+27.2209 q^{2} -243.000 q^{3} -1307.02 q^{4} -8750.00 q^{5} -6614.68 q^{6} -68225.0 q^{7} -91326.7 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+27.2209 q^{2} -243.000 q^{3} -1307.02 q^{4} -8750.00 q^{5} -6614.68 q^{6} -68225.0 q^{7} -91326.7 q^{8} +59049.0 q^{9} -238183. q^{10} +664138. q^{11} +317607. q^{12} -1.65425e6 q^{13} -1.85715e6 q^{14} +2.12625e6 q^{15} +190787. q^{16} +1.11788e7 q^{17} +1.60737e6 q^{18} -829403. q^{19} +1.14365e7 q^{20} +1.65787e7 q^{21} +1.80784e7 q^{22} +1.30559e6 q^{23} +2.21924e7 q^{24} +2.77345e7 q^{25} -4.50302e7 q^{26} -1.43489e7 q^{27} +8.91717e7 q^{28} -4.39688e7 q^{29} +5.78785e7 q^{30} +1.84585e8 q^{31} +1.92231e8 q^{32} -1.61385e8 q^{33} +3.04296e8 q^{34} +5.96969e8 q^{35} -7.71784e7 q^{36} +7.52080e7 q^{37} -2.25771e7 q^{38} +4.01983e8 q^{39} +7.99109e8 q^{40} -5.89404e8 q^{41} +4.51287e8 q^{42} +1.11165e9 q^{43} -8.68043e8 q^{44} -5.16679e8 q^{45} +3.55392e7 q^{46} -2.06811e9 q^{47} -4.63613e7 q^{48} +2.67733e9 q^{49} +7.54957e8 q^{50} -2.71644e9 q^{51} +2.16215e9 q^{52} -3.47306e9 q^{53} -3.90590e8 q^{54} -5.81121e9 q^{55} +6.23077e9 q^{56} +2.01545e8 q^{57} -1.19687e9 q^{58} +7.14924e8 q^{59} -2.77906e9 q^{60} -2.03845e9 q^{61} +5.02457e9 q^{62} -4.02862e9 q^{63} +4.84195e9 q^{64} +1.44747e10 q^{65} -4.39306e9 q^{66} -3.18226e9 q^{67} -1.46109e10 q^{68} -3.17258e8 q^{69} +1.62500e10 q^{70} +1.90460e10 q^{71} -5.39275e9 q^{72} +2.41193e10 q^{73} +2.04723e9 q^{74} -6.73947e9 q^{75} +1.08405e9 q^{76} -4.53108e10 q^{77} +1.09423e10 q^{78} +1.77091e10 q^{79} -1.66939e9 q^{80} +3.48678e9 q^{81} -1.60441e10 q^{82} -3.46150e10 q^{83} -2.16687e10 q^{84} -9.78144e10 q^{85} +3.02602e10 q^{86} +1.06844e10 q^{87} -6.06535e10 q^{88} -6.60387e10 q^{89} -1.40645e10 q^{90} +1.12861e11 q^{91} -1.70643e9 q^{92} -4.48541e10 q^{93} -5.62957e10 q^{94} +7.25728e9 q^{95} -4.67120e10 q^{96} +4.44981e10 q^{97} +7.28793e10 q^{98} +3.92167e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} + O(q^{10}) \)	\( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} - 859751q^{10} + 579094q^{11} - 5606010q^{12} - 2018538q^{13} + 4157413q^{14} - 925344q^{15} + 20190274q^{16} - 13084493q^{17} - 4605822q^{18} + 9917231q^{19} + 10165633q^{20} + 24013017q^{21} - 89820518q^{22} - 63513223q^{23} + 28587735q^{24} + 218986852q^{25} - 77999532q^{26} - 373071582q^{27} - 444601862q^{28} + 81530981q^{29} + 208919493q^{30} - 408861231q^{31} - 26253128q^{32} - 140719842q^{33} - 508910076q^{34} - 75731421q^{35} + 1362260430q^{36} - 802381301q^{37} + 732704675q^{38} + 490504734q^{39} - 646130800q^{40} - 1354472849q^{41} - 1010251359q^{42} + 282952194q^{43} + 1846047996q^{44} + 224858592q^{45} + 9629305849q^{46} - 1196794197q^{47} - 4906236582q^{48} + 10889725683q^{49} - 6236232091q^{50} + 3179531799q^{51} - 1968200812q^{52} - 8276044236q^{53} + 1119214746q^{54} - 6672895076q^{55} + 2579741342q^{56} - 2409887133q^{57} - 9401656060q^{58} + 18588031774q^{59} - 2470248819q^{60} - 21181559029q^{61} - 6117706514q^{62} - 5835163131q^{63} + 42975855037q^{64} + 25680681860q^{65} + 21826385874q^{66} + 26234163394q^{67} + 19707344091q^{68} + 15433713189q^{69} + 129203099090q^{70} + 52088830406q^{71} - 6946819605q^{72} + 20943384867q^{73} + 41969200146q^{74} - 53213805036q^{75} + 223987219368q^{76} + 94604773153q^{77} + 18953886276q^{78} + 68965662774q^{79} + 218947784293q^{80} + 90656394426q^{81} + 11938614923q^{82} + 17947446393q^{83} + 108038252466q^{84} - 52849386709q^{85} + 384986147852q^{86} - 19812028383q^{87} - 49061112607q^{88} + 38570593981q^{89} - 50767436799q^{90} - 226268806999q^{91} - 79559686310q^{92} + 99353279133q^{93} - 16709400108q^{94} - 252795831501q^{95} + 6379510104q^{96} - 186894587836q^{97} - 252443311612q^{98} + 34194921606q^{99} + O(q^{100}) \)

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