LMFDB - Embedded newform 121.14.a.i.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [121,14,Mod(1,121)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(121, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("121.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	121.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:	$129.749424032$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 11)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	121.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+94.5345 q^{2} +1957.79 q^{3} +744.772 q^{4} -61885.3 q^{5} +185079. q^{6} +147705. q^{7} -704020. q^{8} +2.23863e6 q^{9} +O(q^{10})$	\(q+94.5345 q^{2} +1957.79 q^{3} +744.772 q^{4} -61885.3 q^{5} +185079. q^{6} +147705. q^{7} -704020. q^{8} +2.23863e6 q^{9} -5.85030e6 q^{10} +1.45811e6 q^{12} -9.91266e6 q^{13} +1.39632e7 q^{14} -1.21159e8 q^{15} -7.26553e7 q^{16} -3.90786e7 q^{17} +2.11627e8 q^{18} +3.14209e8 q^{19} -4.60904e7 q^{20} +2.89176e8 q^{21} +2.30121e8 q^{23} -1.37832e9 q^{24} +2.60909e9 q^{25} -9.37088e8 q^{26} +1.26141e9 q^{27} +1.10006e8 q^{28} +1.33491e9 q^{29} -1.14537e10 q^{30} +8.94860e9 q^{31} -1.10111e9 q^{32} -3.69428e9 q^{34} -9.14076e9 q^{35} +1.66727e9 q^{36} +6.44096e9 q^{37} +2.97036e10 q^{38} -1.94069e10 q^{39} +4.35685e10 q^{40} +2.63864e10 q^{41} +2.73371e10 q^{42} -6.09429e10 q^{43} -1.38538e11 q^{45} +2.17544e10 q^{46} +5.32995e10 q^{47} -1.42244e11 q^{48} -7.50723e10 q^{49} +2.46649e11 q^{50} -7.65078e10 q^{51} -7.38267e9 q^{52} +1.80727e9 q^{53} +1.19247e11 q^{54} -1.03987e11 q^{56} +6.15157e11 q^{57} +1.26195e11 q^{58} +6.03549e11 q^{59} -9.02355e10 q^{60} +3.16702e11 q^{61} +8.45952e11 q^{62} +3.30656e11 q^{63} +4.91100e11 q^{64} +6.13448e11 q^{65} +2.23523e11 q^{67} -2.91046e10 q^{68} +4.50529e11 q^{69} -8.64117e11 q^{70} +1.90484e11 q^{71} -1.57604e12 q^{72} -8.60942e11 q^{73} +6.08893e11 q^{74} +5.10805e12 q^{75} +2.34014e11 q^{76} -1.83462e12 q^{78} +1.81039e12 q^{79} +4.49630e12 q^{80} -1.09951e12 q^{81} +2.49442e12 q^{82} +2.05984e12 q^{83} +2.15370e11 q^{84} +2.41839e12 q^{85} -5.76121e12 q^{86} +2.61348e12 q^{87} -9.81139e11 q^{89} -1.30966e13 q^{90} -1.46415e12 q^{91} +1.71387e11 q^{92} +1.75195e13 q^{93} +5.03864e12 q^{94} -1.94449e13 q^{95} -2.15573e12 q^{96} -2.23486e12 q^{97} -7.09692e12 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 128 q^{2} + 1068 q^{3} + 90294 q^{4} + 26080 q^{5} + 98495 q^{6} + 386592 q^{7} + 1548294 q^{8} + 7656268 q^{9}+O(q^{10}) $ 24 * q + 128 * q^2 + 1068 * q^3 + 90294 * q^4 + 26080 * q^5 + 98495 * q^6 + 386592 * q^7 + 1548294 * q^8 + 7656268 * q^9	\( 24 q + 128 q^{2} + 1068 q^{3} + 90294 q^{4} + 26080 q^{5} + 98495 q^{6} + 386592 q^{7} + 1548294 q^{8} + 7656268 q^{9} + 8146536 q^{10} + 31486019 q^{12} + 17561904 q^{13} - 16549212 q^{14} - 47315512 q^{15} + 189327378 q^{16} + 161930636 q^{17} + 442641953 q^{18} + 647216196 q^{19} + 443499298 q^{20} + 217276816 q^{21} + 2094437136 q^{23} + 1627544589 q^{24} + 2084691168 q^{25} + 2355630004 q^{26} + 742899600 q^{27} + 3032872896 q^{28} + 8699178576 q^{29} + 1243218300 q^{30} - 9494900112 q^{31} + 18962452446 q^{32} - 21315904743 q^{34} + 19181301256 q^{35} - 39894746479 q^{36} + 3089149344 q^{37} + 129844728457 q^{38} + 49031676912 q^{39} + 194691582558 q^{40} + 83280861028 q^{41} - 124381258176 q^{42} + 161991034068 q^{43} + 50827898320 q^{45} + 437334676134 q^{46} - 143404218008 q^{47} - 20850971437 q^{48} + 306774688344 q^{49} + 321735931268 q^{50} + 545715464528 q^{51} + 612093584562 q^{52} - 392354896952 q^{53} + 85719376742 q^{54} - 27658271244 q^{56} + 275972269320 q^{57} - 34679215332 q^{58} + 276513783196 q^{59} + 718672116538 q^{60} + 230121481992 q^{61} - 302794066266 q^{62} - 643203605848 q^{63} + 2023123568130 q^{64} + 957140617352 q^{65} - 692937587460 q^{67} - 1735237886973 q^{68} + 1117466070944 q^{69} - 307144167534 q^{70} - 4277414185816 q^{71} - 3242879740353 q^{72} - 4979010172020 q^{73} - 2672607341782 q^{74} + 3983565507508 q^{75} - 3691319323131 q^{76} + 242673994778 q^{78} - 2105593756968 q^{79} + 8461209269858 q^{80} + 887412594856 q^{81} - 8574013790565 q^{82} + 6824767308444 q^{83} - 8438329587858 q^{84} + 3374484393528 q^{85} + 18312276652385 q^{86} + 11079389891856 q^{87} - 6018805846820 q^{89} - 4577924266292 q^{90} - 10934505244368 q^{91} + 4722880465206 q^{92} + 5494546269696 q^{93} + 22894507263180 q^{94} + 17781364000928 q^{95} + 35355473398269 q^{96} + 11153302493028 q^{97} + 26143145346994 q^{98}+O(q^{100}) \) 24 * q + 128 * q^2 + 1068 * q^3 + 90294 * q^4 + 26080 * q^5 + 98495 * q^6 + 386592 * q^7 + 1548294 * q^8 + 7656268 * q^9 + 8146536 * q^10 + 31486019 * q^12 + 17561904 * q^13 - 16549212 * q^14 - 47315512 * q^15 + 189327378 * q^16 + 161930636 * q^17 + 442641953 * q^18 + 647216196 * q^19 + 443499298 * q^20 + 217276816 * q^21 + 2094437136 * q^23 + 1627544589 * q^24 + 2084691168 * q^25 + 2355630004 * q^26 + 742899600 * q^27 + 3032872896 * q^28 + 8699178576 * q^29 + 1243218300 * q^30 - 9494900112 * q^31 + 18962452446 * q^32 - 21315904743 * q^34 + 19181301256 * q^35 - 39894746479 * q^36 + 3089149344 * q^37 + 129844728457 * q^38 + 49031676912 * q^39 + 194691582558 * q^40 + 83280861028 * q^41 - 124381258176 * q^42 + 161991034068 * q^43 + 50827898320 * q^45 + 437334676134 * q^46 - 143404218008 * q^47 - 20850971437 * q^48 + 306774688344 * q^49 + 321735931268 * q^50 + 545715464528 * q^51 + 612093584562 * q^52 - 392354896952 * q^53 + 85719376742 * q^54 - 27658271244 * q^56 + 275972269320 * q^57 - 34679215332 * q^58 + 276513783196 * q^59 + 718672116538 * q^60 + 230121481992 * q^61 - 302794066266 * q^62 - 643203605848 * q^63 + 2023123568130 * q^64 + 957140617352 * q^65 - 692937587460 * q^67 - 1735237886973 * q^68 + 1117466070944 * q^69 - 307144167534 * q^70 - 4277414185816 * q^71 - 3242879740353 * q^72 - 4979010172020 * q^73 - 2672607341782 * q^74 + 3983565507508 * q^75 - 3691319323131 * q^76 + 242673994778 * q^78 - 2105593756968 * q^79 + 8461209269858 * q^80 + 887412594856 * q^81 - 8574013790565 * q^82 + 6824767308444 * q^83 - 8438329587858 * q^84 + 3374484393528 * q^85 + 18312276652385 * q^86 + 11079389891856 * q^87 - 6018805846820 * q^89 - 4577924266292 * q^90 - 10934505244368 * q^91 + 4722880465206 * q^92 + 5494546269696 * q^93 + 22894507263180 * q^94 + 17781364000928 * q^95 + 35355473398269 * q^96 + 11153302493028 * q^97 + 26143145346994 * q^98

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 $

$2$	94.5345	1.04447	0.522234	−	0.852802i	$-0.325099\pi$
$2$	94.5345	1.04447	0.522234	+	0.852802i	$0.325099\pi$
$3$	1957.79	1.55052	0.775262	−	0.631640i	$-0.217618\pi$
$3$	1957.79	1.55052	0.775262	+	0.631640i	$0.217618\pi$
$4$	744.772	0.0909145
$5$	−61885.3	−1.77126	−0.885630	−	0.464391i	$-0.846273\pi$
$5$	−61885.3	−1.77126	−0.885630	+	0.464391i	$0.846273\pi$
$6$	185079.	1.61947
$7$	147705.	0.474523	0.237262	−	0.971446i	$-0.423750\pi$
$7$	147705.	0.474523	0.237262	+	0.971446i	$0.423750\pi$
$8$	−704020.	−0.949511
$9$	2.23863e6	1.40412
$10$	−5.85030e6	−1.85003
$11$	0	0
$11$	0	0
$12$	1.45811e6	0.140965
$13$	−9.91266e6	−0.569585	−0.284792	−	0.958589i	$-0.591925\pi$
$13$	−9.91266e6	−0.569585	−0.284792	+	0.958589i	$0.591925\pi$
$14$	1.39632e7	0.495625
$15$	−1.21159e8	−2.74638
$16$	−7.26553e7	−1.08265
$17$	−3.90786e7	−0.392664	−0.196332	−	0.980537i	$-0.562903\pi$
$17$	−3.90786e7	−0.392664	−0.196332	+	0.980537i	$0.562903\pi$
$18$	2.11627e8	1.46656
$19$	3.14209e8	1.53222	0.766110	−	0.642710i	$-0.222190\pi$
$19$	3.14209e8	1.53222	0.766110	+	0.642710i	$0.222190\pi$
$20$	−4.60904e7	−0.161033
$21$	2.89176e8	0.735760
$22$	0	0
$23$	2.30121e8	0.324134	0.162067	−	0.986780i	$-0.448184\pi$
$23$	2.30121e8	0.324134	0.162067	+	0.986780i	$0.448184\pi$
$24$	−1.37832e9	−1.47224
$25$	2.60909e9	2.13736
$26$	−9.37088e8	−0.594913
$27$	1.26141e9	0.626604
$28$	1.10006e8	0.0431411
$29$	1.33491e9	0.416740	0.208370	−	0.978050i	$-0.433184\pi$
$29$	1.33491e9	0.416740	0.208370	+	0.978050i	$0.433184\pi$
$30$	−1.14537e10	−2.86851
$31$	8.94860e9	1.81094	0.905471	−	0.424409i	$-0.139518\pi$
$31$	8.94860e9	1.81094	0.905471	+	0.424409i	$0.139518\pi$
$32$	−1.10111e9	−0.181282
$33$	0	0
$34$	−3.69428e9	−0.410125
$35$	−9.14076e9	−0.840505
$36$	1.66727e9	0.127655
$37$	6.44096e9	0.412705	0.206352	−	0.978478i	$-0.433841\pi$
$37$	6.44096e9	0.412705	0.206352	+	0.978478i	$0.433841\pi$
$38$	2.97036e10	1.60035
$39$	−1.94069e10	−0.883155
$40$	4.35685e10	1.68183
$41$	2.63864e10	0.867531	0.433765	−	0.901026i	$-0.357185\pi$
$41$	2.63864e10	0.867531	0.433765	+	0.901026i	$0.357185\pi$
$42$	2.73371e10	0.768478
$43$	−6.09429e10	−1.47021	−0.735103	−	0.677955i	$-0.762866\pi$
$43$	−6.09429e10	−1.47021	−0.735103	+	0.677955i	$0.762866\pi$
$44$	0	0
$45$	−1.38538e11	−2.48707
$46$	2.17544e10	0.338548
$47$	5.32995e10	0.721252	0.360626	−	0.932710i	$-0.382563\pi$
$47$	5.32995e10	0.721252	0.360626	+	0.932710i	$0.382563\pi$
$48$	−1.42244e11	−1.67867
$49$	−7.50723e10	−0.774828
$50$	2.46649e11	2.23241
$51$	−7.65078e10	−0.608835
$52$	−7.38267e9	−0.0517835
$53$	1.80727e9	0.0112003	0.00560014	−	0.999984i	$-0.498217\pi$
$53$	1.80727e9	0.0112003	0.00560014	+	0.999984i	$0.498217\pi$
$54$	1.19247e11	0.654468
$55$	0	0
$56$	−1.03987e11	−0.450565
$57$	6.15157e11	2.37574
$58$	1.26195e11	0.435271
$59$	6.03549e11	1.86283	0.931417	−	0.363954i	$-0.118573\pi$
$59$	6.03549e11	1.86283	0.931417	+	0.363954i	$0.118573\pi$
$60$	−9.02355e10	−0.249686
$61$	3.16702e11	0.787059	0.393529	−	0.919312i	$-0.371254\pi$
$61$	3.16702e11	0.787059	0.393529	+	0.919312i	$0.371254\pi$
$62$	8.45952e11	1.89147
$63$	3.30656e11	0.666290
$64$	4.91100e11	0.893306
$65$	6.13448e11	1.00888
$66$	0	0
$67$	2.23523e11	0.301882	0.150941	−	0.988543i	$-0.451770\pi$
$67$	2.23523e11	0.301882	0.150941	+	0.988543i	$0.451770\pi$
$68$	−2.91046e10	−0.0356989
$69$	4.50529e11	0.502578
$70$	−8.64117e11	−0.877881
$71$	1.90484e11	0.176473	0.0882365	−	0.996100i	$-0.471877\pi$
$71$	1.90484e11	0.176473	0.0882365	+	0.996100i	$0.471877\pi$
$72$	−1.57604e12	−1.33323
$73$	−8.60942e11	−0.665848	−0.332924	−	0.942954i	$-0.608035\pi$
$73$	−8.60942e11	−0.665848	−0.332924	+	0.942954i	$0.608035\pi$
$74$	6.08893e11	0.431057
$75$	5.10805e12	3.31404
$76$	2.34014e11	0.139301
$77$	0	0
$78$	−1.83462e12	−0.922427
$79$	1.81039e12	0.837908	0.418954	−	0.908007i	$-0.362397\pi$
$79$	1.81039e12	0.837908	0.418954	+	0.908007i	$0.362397\pi$
$80$	4.49630e12	1.91765
$81$	−1.09951e12	−0.432560
$82$	2.49442e12	0.906109
$83$	2.05984e12	0.691553	0.345776	−	0.938317i	$-0.387616\pi$
$83$	2.05984e12	0.691553	0.345776	+	0.938317i	$0.387616\pi$
$84$	2.15370e11	0.0668912
$85$	2.41839e12	0.695510
$86$	−5.76121e12	−1.53558
$87$	2.61348e12	0.646165
$88$	0	0
$89$	−9.81139e11	−0.209264	−0.104632	−	0.994511i	$-0.533367\pi$
$89$	−9.81139e11	−0.209264	−0.104632	+	0.994511i	$0.533367\pi$
$90$	−1.30966e13	−2.59767
$91$	−1.46415e12	−0.270281
$92$	1.71387e11	0.0294685
$93$	1.75195e13	2.80791
$94$	5.03864e12	0.753325
$95$	−1.94449e13	−2.71396
$96$	−2.15573e12	−0.281082
$97$	−2.23486e12	−0.272416	−0.136208	−	0.990680i	$-0.543492\pi$
$97$	−2.23486e12	−0.272416	−0.136208	+	0.990680i	$0.543492\pi$
$98$	−7.09692e12	−0.809283
$99$	0	0
$100$	1.94317e12	0.194317
$101$	−7.83983e12	−0.734882	−0.367441	−	0.930047i	$-0.619766\pi$
$101$	−7.83983e12	−0.734882	−0.367441	+	0.930047i	$0.619766\pi$
$102$	−7.23263e12	−0.635909
$103$	−1.33798e13	−1.10410	−0.552050	−	0.833811i	$-0.686154\pi$
$103$	−1.33798e13	−1.10410	−0.552050	+	0.833811i	$0.686154\pi$
$104$	6.97871e12	0.540827
$105$	−1.78957e13	−1.30322
$106$	1.70849e11	0.0116983
$107$	1.57602e13	1.01524	0.507620	−	0.861581i	$-0.330525\pi$
$107$	1.57602e13	1.01524	0.507620	+	0.861581i	$0.330525\pi$
$108$	9.39465e11	0.0569674
$109$	1.41059e13	0.805617	0.402808	−	0.915284i	$-0.368034\pi$
$109$	1.41059e13	0.805617	0.402808	+	0.915284i	$0.368034\pi$
$110$	0	0
$111$	1.26101e13	0.639908
$112$	−1.07316e13	−0.513742
$113$	−3.56576e12	−0.161117	−0.0805586	−	0.996750i	$-0.525670\pi$
$113$	−3.56576e12	−0.161117	−0.0805586	+	0.996750i	$0.525670\pi$
$114$	5.81535e13	2.48139
$115$	−1.42411e13	−0.574126
$116$	9.94203e11	0.0378877
$117$	−2.21907e13	−0.799768
$118$	5.70562e13	1.94567
$119$	−5.77210e12	−0.186328
$120$	8.52981e13	2.60772
$121$	0	0
$122$	2.99393e13	0.822058
$123$	5.16591e13	1.34513
$124$	6.66467e12	0.164641
$125$	−8.59206e13	−2.01457
$126$	3.12584e13	0.695919
$127$	3.66678e13	0.775463	0.387732	−	0.921772i	$-0.373259\pi$
$127$	3.66678e13	0.775463	0.387732	+	0.921772i	$0.373259\pi$
$128$	5.54462e13	1.11431
$129$	−1.19314e14	−2.27959
$130$	5.79920e13	1.05375
$131$	−1.81000e13	−0.312908	−0.156454	−	0.987685i	$-0.550006\pi$
$131$	−1.81000e13	−0.312908	−0.156454	+	0.987685i	$0.550006\pi$
$132$	0	0
$133$	4.64103e13	0.727074
$134$	2.11307e13	0.315306
$135$	−7.80630e13	−1.10988
$136$	2.75121e13	0.372839
$137$	9.27093e11	0.0119795	0.00598976	−	0.999982i	$-0.498093\pi$
$137$	9.27093e11	0.0119795	0.00598976	+	0.999982i	$0.498093\pi$
$138$	4.25905e13	0.524927
$139$	5.07664e13	0.597008	0.298504	−	0.954408i	$-0.403512\pi$
$139$	5.07664e13	0.597008	0.298504	+	0.954408i	$0.403512\pi$
$140$	−6.80778e12	−0.0764141
$141$	1.04349e14	1.11832
$142$	1.80073e13	0.184321
$143$	0	0
$144$	−1.62648e14	−1.52017
$145$	−8.26113e13	−0.738155
$146$	−8.13887e13	−0.695458
$147$	−1.46976e14	−1.20139
$148$	4.79704e12	0.0375208
$149$	2.43009e14	1.81933	0.909664	−	0.415345i	$-0.136339\pi$
$149$	2.43009e14	1.81933	0.909664	+	0.415345i	$0.136339\pi$
$150$	4.82887e14	3.46141
$151$	−1.62073e14	−1.11265	−0.556326	−	0.830964i	$-0.687789\pi$
$151$	−1.62073e14	−1.11265	−0.556326	+	0.830964i	$0.687789\pi$
$152$	−2.21210e14	−1.45486
$153$	−8.74824e13	−0.551349
$154$	0	0
$155$	−5.53787e14	−3.20765
$156$	−1.44537e13	−0.0802916
$157$	−2.18485e14	−1.16432	−0.582162	−	0.813073i	$-0.697793\pi$
$157$	−2.18485e14	−1.16432	−0.582162	+	0.813073i	$0.697793\pi$
$158$	1.71144e14	0.875168
$159$	3.53825e12	0.0173663
$160$	6.81422e13	0.321097
$161$	3.39900e13	0.153809
$162$	−1.03942e14	−0.451795
$163$	2.84574e14	1.18843	0.594217	−	0.804305i	$-0.297462\pi$
$163$	2.84574e14	1.18843	0.594217	+	0.804305i	$0.297462\pi$
$164$	1.96518e13	0.0788711
$165$	0	0
$166$	1.94726e14	0.722305
$167$	3.46035e14	1.23442	0.617210	−	0.786798i	$-0.288263\pi$
$167$	3.46035e14	1.23442	0.617210	+	0.786798i	$0.288263\pi$
$168$	−2.03585e14	−0.698612
$169$	−2.04614e14	−0.675573
$170$	2.28621e14	0.726439
$171$	7.03398e14	2.15143
$172$	−4.53886e13	−0.133663
$173$	−1.23096e13	−0.0349096	−0.0174548	−	0.999848i	$-0.505556\pi$
$173$	−1.23096e13	−0.0349096	−0.0174548	+	0.999848i	$0.505556\pi$
$174$	2.47064e14	0.674899
$175$	3.85375e14	1.01423
$176$	0	0
$177$	1.18162e15	2.88837
$178$	−9.27515e13	−0.218570
$179$	−3.97438e13	−0.0903078	−0.0451539	−	0.998980i	$-0.514378\pi$
$179$	−3.97438e13	−0.0903078	−0.0451539	+	0.998980i	$0.514378\pi$
$180$	−1.03179e14	−0.226111
$181$	−2.00792e14	−0.424458	−0.212229	−	0.977220i	$-0.568072\pi$
$181$	−2.00792e14	−0.424458	−0.212229	+	0.977220i	$0.568072\pi$
$182$	−1.38413e14	−0.282300
$183$	6.20037e14	1.22035
$184$	−1.62010e14	−0.307769
$185$	−3.98601e14	−0.731007
$186$	1.65620e15	2.93277
$187$	0	0
$188$	3.96960e13	0.0655723
$189$	1.86317e14	0.297338
$190$	−1.83822e15	−2.83465
$191$	2.00162e14	0.298308	0.149154	−	0.988814i	$-0.452345\pi$
$191$	2.00162e14	0.298308	0.149154	+	0.988814i	$0.452345\pi$
$192$	9.61472e14	1.38509
$193$	−1.07064e15	−1.49115	−0.745576	−	0.666421i	$-0.767825\pi$
$193$	−1.07064e15	−1.49115	−0.745576	+	0.666421i	$0.767825\pi$
$194$	−2.11271e14	−0.284530
$195$	1.20100e15	1.56430
$196$	−5.59117e13	−0.0704431
$197$	6.29297e14	0.767052	0.383526	−	0.923530i	$-0.374710\pi$
$197$	6.29297e14	0.767052	0.383526	+	0.923530i	$0.374710\pi$
$198$	0	0
$199$	2.79107e14	0.318585	0.159292	−	0.987231i	$-0.449079\pi$
$199$	2.79107e14	0.318585	0.159292	+	0.987231i	$0.449079\pi$
$200$	−1.83685e15	−2.02945
$201$	4.37612e14	0.468075
$202$	−7.41134e14	−0.767561
$203$	1.97173e14	0.197753
$204$	−5.69808e13	−0.0553519
$205$	−1.63293e15	−1.53662
$206$	−1.26486e15	−1.15320
$207$	5.15155e14	0.455125
$208$	7.20208e14	0.616660
$209$	0	0
$210$	−1.69176e15	−1.36117
$211$	−1.26652e15	−0.988043	−0.494022	−	0.869450i	$-0.664474\pi$
$211$	−1.26652e15	−0.988043	−0.494022	+	0.869450i	$0.664474\pi$
$212$	1.34600e12	0.00101827
$213$	3.72927e14	0.273626
$214$	1.48989e15	1.06039
$215$	3.77147e15	2.60412
$216$	−8.88060e14	−0.594967
$217$	1.32175e15	0.859334
$218$	1.33349e15	0.841441
$219$	−1.68555e15	−1.03241
$220$	0	0
$221$	3.87373e14	0.223655
$222$	1.19209e15	0.668364
$223$	1.57138e15	0.855656	0.427828	−	0.903860i	$-0.359279\pi$
$223$	1.57138e15	0.855656	0.427828	+	0.903860i	$0.359279\pi$
$224$	−1.62639e14	−0.0860224
$225$	5.84078e15	3.00113
$226$	−3.37087e14	−0.168282
$227$	2.15331e15	1.04457	0.522287	−	0.852770i	$-0.325079\pi$
$227$	2.15331e15	1.04457	0.522287	+	0.852770i	$0.325079\pi$
$228$	4.58151e14	0.215989
$229$	−4.15194e15	−1.90248	−0.951241	−	0.308449i	$-0.900190\pi$
$229$	−4.15194e15	−1.90248	−0.951241	+	0.308449i	$0.900190\pi$
$230$	−1.34627e15	−0.599657
$231$	0	0
$232$	−9.39803e14	−0.395699
$233$	−8.92633e14	−0.365477	−0.182738	−	0.983162i	$-0.558496\pi$
$233$	−8.92633e14	−0.365477	−0.182738	+	0.983162i	$0.558496\pi$
$234$	−2.09779e15	−0.835332
$235$	−3.29846e15	−1.27753
$236$	4.49506e14	0.169359
$237$	3.54437e15	1.29920
$238$	−5.45663e14	−0.194614
$239$	3.25538e15	1.12984	0.564918	−	0.825147i	$-0.308908\pi$
$239$	3.25538e15	1.12984	0.564918	+	0.825147i	$0.308908\pi$
$240$	8.80282e15	2.97337
$241$	3.30867e15	1.08778	0.543891	−	0.839156i	$-0.316950\pi$
$241$	3.30867e15	1.08778	0.543891	+	0.839156i	$0.316950\pi$
$242$	0	0
$243$	−4.16371e15	−1.29730
$244$	2.35871e14	0.0715550
$245$	4.64587e15	1.37242
$246$	4.88356e15	1.40494
$247$	−3.11465e15	−0.872729
$248$	−6.30000e15	−1.71951
$249$	4.03273e15	1.07227
$250$	−8.12246e15	−2.10415
$251$	2.99007e15	0.754749	0.377375	−	0.926061i	$-0.376827\pi$
$251$	2.99007e15	0.754749	0.377375	+	0.926061i	$0.376827\pi$
$252$	2.46263e14	0.0605754
$253$	0	0
$254$	3.46638e15	0.809947
$255$	4.73471e15	1.07841
$256$	1.21848e15	0.270557
$257$	−6.03624e15	−1.30678	−0.653388	−	0.757023i	$-0.726653\pi$
$257$	−6.03624e15	−1.30678	−0.653388	+	0.757023i	$0.726653\pi$
$258$	−1.12792e16	−2.38096
$259$	9.51361e14	0.195838
$260$	4.56879e14	0.0917221
$261$	2.98836e15	0.585154
$262$	−1.71108e15	−0.326822
$263$	9.67660e15	1.80306	0.901531	−	0.432715i	$-0.142444\pi$
$263$	9.67660e15	1.80306	0.901531	+	0.432715i	$0.142444\pi$
$264$	0	0
$265$	−1.11843e14	−0.0198386
$266$	4.38737e15	0.759406
$267$	−1.92087e15	−0.324470
$268$	1.66474e14	0.0274454
$269$	−4.48980e15	−0.722500	−0.361250	−	0.932469i	$-0.617650\pi$
$269$	−4.48980e15	−0.722500	−0.361250	+	0.932469i	$0.617650\pi$
$270$	−7.37964e15	−1.15923
$271$	−4.31399e15	−0.661574	−0.330787	−	0.943705i	$-0.607314\pi$
$271$	−4.31399e15	−0.661574	−0.330787	+	0.943705i	$0.607314\pi$
$272$	2.83927e15	0.425117
$273$	−2.86650e15	−0.419078
$274$	8.76423e13	0.0125122
$275$	0	0
$276$	3.35541e14	0.0456916
$277$	6.94161e15	0.923298	0.461649	−	0.887063i	$-0.347258\pi$
$277$	6.94161e15	0.923298	0.461649	+	0.887063i	$0.347258\pi$
$278$	4.79918e15	0.623557
$279$	2.00326e16	2.54279
$280$	6.43528e15	0.798069
$281$	1.02298e16	1.23958	0.619790	−	0.784767i	$-0.287218\pi$
$281$	1.02298e16	1.23958	0.619790	+	0.784767i	$0.287218\pi$
$282$	9.86461e15	1.16805
$283$	7.97149e15	0.922417	0.461209	−	0.887292i	$-0.347416\pi$
$283$	7.97149e15	0.922417	0.461209	+	0.887292i	$0.347416\pi$
$284$	1.41867e14	0.0160440
$285$	−3.80692e16	−4.20806
$286$	0	0
$287$	3.89740e15	0.411664
$288$	−2.46496e15	−0.254542
$289$	−8.37744e15	−0.845815
$290$	−7.80962e15	−0.770979
$291$	−4.37538e15	−0.422388
$292$	−6.41205e14	−0.0605353
$293$	−5.25225e15	−0.484960	−0.242480	−	0.970156i	$-0.577961\pi$
$293$	−5.25225e15	−0.484960	−0.242480	+	0.970156i	$0.577961\pi$
$294$	−1.38943e16	−1.25481
$295$	−3.73508e16	−3.29957
$296$	−4.53456e15	−0.391868
$297$	0	0
$298$	2.29727e16	1.90023
$299$	−2.28111e15	−0.184622
$300$	3.80433e15	0.301294
$301$	−9.00157e15	−0.697647
$302$	−1.53215e16	−1.16213
$303$	−1.53488e16	−1.13945
$304$	−2.28290e16	−1.65886
$305$	−1.95992e16	−1.39409
$306$	−8.27011e15	−0.575867
$307$	−1.66059e16	−1.13205	−0.566023	−	0.824390i	$-0.691519\pi$
$307$	−1.66059e16	−1.13205	−0.566023	+	0.824390i	$0.691519\pi$
$308$	0	0
$309$	−2.61949e16	−1.71193
$310$	−5.23520e16	−3.35029
$311$	−2.88877e15	−0.181038	−0.0905191	−	0.995895i	$-0.528853\pi$
$311$	−2.88877e15	−0.181038	−0.0905191	+	0.995895i	$0.528853\pi$
$312$	1.36629e16	0.838565
$313$	−1.08402e16	−0.651628	−0.325814	−	0.945434i	$-0.605638\pi$
$313$	−1.08402e16	−0.651628	−0.325814	+	0.945434i	$0.605638\pi$
$314$	−2.06544e16	−1.21610
$315$	−2.04628e16	−1.18017
$316$	1.34833e15	0.0761780
$317$	1.36697e16	0.756613	0.378307	−	0.925680i	$-0.376507\pi$
$317$	1.36697e16	0.756613	0.378307	+	0.925680i	$0.376507\pi$
$318$	3.34487e14	0.0181385
$319$	0	0
$320$	−3.03919e16	−1.58228
$321$	3.08553e16	1.57415
$322$	3.21322e15	0.160649
$323$	−1.22789e16	−0.601647
$324$	−8.18883e14	−0.0393260
$325$	−2.58630e16	−1.21741
$326$	2.69020e16	1.24128
$327$	2.76164e16	1.24913
$328$	−1.85765e16	−0.823730
$329$	7.87260e15	0.342251
$330$	0	0
$331$	3.73471e16	1.56090	0.780450	−	0.625218i	$-0.214990\pi$
$331$	3.73471e16	1.56090	0.780450	+	0.625218i	$0.214990\pi$
$332$	1.53411e15	0.0628722
$333$	1.44189e16	0.579488
$334$	3.27122e16	1.28931
$335$	−1.38328e16	−0.534711
$336$	−2.10101e16	−0.796570
$337$	−1.98238e16	−0.737213	−0.368606	−	0.929586i	$-0.620165\pi$
$337$	−1.98238e16	−0.737213	−0.368606	+	0.929586i	$0.620165\pi$
$338$	−1.93431e16	−0.705615
$339$	−6.98101e15	−0.249816
$340$	1.80115e15	0.0632320
$341$	0	0
$342$	6.64954e16	2.24710
$343$	−2.53995e16	−0.842197
$344$	4.29050e16	1.39598
$345$	−2.78811e16	−0.890196
$346$	−1.16368e15	−0.0364619
$347$	2.80836e16	0.863596	0.431798	−	0.901970i	$-0.357879\pi$
$347$	2.80836e16	0.863596	0.431798	+	0.901970i	$0.357879\pi$
$348$	1.94644e15	0.0587458
$349$	−1.83610e16	−0.543915	−0.271957	−	0.962309i	$-0.587671\pi$
$349$	−1.83610e16	−0.543915	−0.271957	+	0.962309i	$0.587671\pi$
$350$	3.64312e16	1.05933
$351$	−1.25040e16	−0.356904
$352$	0	0
$353$	5.11605e15	0.140734	0.0703670	−	0.997521i	$-0.477583\pi$
$353$	5.11605e15	0.140734	0.0703670	+	0.997521i	$0.477583\pi$
$354$	1.11704e17	3.01681
$355$	−1.17881e16	−0.312580
$356$	−7.30725e14	−0.0190252
$357$	−1.13006e16	−0.288906
$358$	−3.75716e15	−0.0943236
$359$	−9.03330e15	−0.222706	−0.111353	−	0.993781i	$-0.535518\pi$
$359$	−9.03330e15	−0.222706	−0.111353	+	0.993781i	$0.535518\pi$
$360$	9.75336e16	2.36150
$361$	5.66746e16	1.34770
$362$	−1.89817e16	−0.443333
$363$	0	0
$364$	−1.09046e15	−0.0245725
$365$	5.32797e16	1.17939
$366$	5.86149e16	1.27462
$367$	3.74088e16	0.799180	0.399590	−	0.916694i	$-0.369152\pi$
$367$	3.74088e16	0.799180	0.399590	+	0.916694i	$0.369152\pi$
$368$	−1.67195e16	−0.350924
$369$	5.90693e16	1.21812
$370$	−3.76815e16	−0.763514
$371$	2.66942e14	0.00531479
$372$	1.30480e16	0.255279
$373$	8.19671e15	0.157591	0.0787956	−	0.996891i	$-0.474893\pi$
$373$	8.19671e15	0.157591	0.0787956	+	0.996891i	$0.474893\pi$
$374$	0	0
$375$	−1.68215e17	−3.12364
$376$	−3.75239e16	−0.684837
$377$	−1.32325e16	−0.237369
$378$	1.76134e16	0.310560
$379$	1.68353e16	0.291787	0.145893	−	0.989300i	$-0.453394\pi$
$379$	1.68353e16	0.291787	0.145893	+	0.989300i	$0.453394\pi$
$380$	−1.44820e16	−0.246738
$381$	7.17880e16	1.20237
$382$	1.89222e16	0.311574
$383$	−8.15550e16	−1.32026	−0.660128	−	0.751153i	$-0.729498\pi$
$383$	−8.15550e16	−1.32026	−0.660128	+	0.751153i	$0.729498\pi$
$384$	1.08552e17	1.72777
$385$	0	0
$386$	−1.01213e17	−1.55746
$387$	−1.36428e17	−2.06435
$388$	−1.66446e15	−0.0247666
$389$	3.34351e16	0.489249	0.244624	−	0.969618i	$-0.421335\pi$
$389$	3.34351e16	0.489249	0.244624	+	0.969618i	$0.421335\pi$
$390$	1.13536e17	1.63386
$391$	−8.99280e15	−0.127276
$392$	5.28524e16	0.735707
$393$	−3.54361e16	−0.485171
$394$	5.94902e16	0.801162
$395$	−1.12037e17	−1.48415
$396$	0	0
$397$	1.16561e16	0.149422	0.0747110	−	0.997205i	$-0.476197\pi$
$397$	1.16561e16	0.149422	0.0747110	+	0.997205i	$0.476197\pi$
$398$	2.63852e16	0.332752
$399$	9.08617e16	1.12735
$400$	−1.89564e17	−2.31402
$401$	5.49190e16	0.659605	0.329803	−	0.944050i	$-0.393018\pi$
$401$	5.49190e16	0.659605	0.329803	+	0.944050i	$0.393018\pi$
$402$	4.13695e16	0.488889
$403$	−8.87045e16	−1.03148
$404$	−5.83888e15	−0.0668114
$405$	6.80435e16	0.766176
$406$	1.86396e16	0.206547
$407$	0	0
$408$	5.38630e16	0.578096
$409$	−7.44180e16	−0.786097	−0.393049	−	0.919518i	$-0.628580\pi$
$409$	−7.44180e16	−0.786097	−0.393049	+	0.919518i	$0.628580\pi$
$410$	−1.54368e17	−1.60495
$411$	1.81505e15	0.0185745
$412$	−9.96492e15	−0.100379
$413$	8.91471e16	0.883958
$414$	4.86999e16	0.475363
$415$	−1.27474e17	−1.22492
$416$	1.09149e16	0.103255
$417$	9.93901e16	0.925676
$418$	0	0
$419$	8.97643e16	0.810425	0.405212	−	0.914223i	$-0.367198\pi$
$419$	8.97643e16	0.810425	0.405212	+	0.914223i	$0.367198\pi$
$420$	−1.33282e16	−0.118482
$421$	−6.45308e16	−0.564850	−0.282425	−	0.959289i	$-0.591139\pi$
$421$	−6.45308e16	−0.564850	−0.282425	+	0.959289i	$0.591139\pi$
$422$	−1.19730e17	−1.03198
$423$	1.19318e17	1.01273
$424$	−1.27235e15	−0.0106348
$425$	−1.01960e17	−0.839266
$426$	3.52545e16	0.285793
$427$	4.67785e16	0.373478
$428$	1.17378e16	0.0923000
$429$	0	0
$430$	3.56534e17	2.71992
$431$	7.91963e16	0.595117	0.297559	−	0.954704i	$-0.403828\pi$
$431$	7.91963e16	0.595117	0.297559	+	0.954704i	$0.403828\pi$
$432$	−9.16484e16	−0.678392
$433$	2.11285e17	1.54063	0.770314	−	0.637665i	$-0.220100\pi$
$433$	2.11285e17	1.54063	0.770314	+	0.637665i	$0.220100\pi$
$434$	1.24951e17	0.897547
$435$	−1.61736e17	−1.14453
$436$	1.05057e16	0.0732422
$437$	7.23061e16	0.496645
$438$	−1.59342e17	−1.07832
$439$	1.87313e16	0.124896	0.0624479	−	0.998048i	$-0.480109\pi$
$439$	1.87313e16	0.124896	0.0624479	+	0.998048i	$0.480109\pi$
$440$	0	0
$441$	−1.68059e17	−1.08795
$442$	3.66201e16	0.233601
$443$	−4.59694e16	−0.288965	−0.144482	−	0.989507i	$-0.546152\pi$
$443$	−4.59694e16	−0.288965	−0.144482	+	0.989507i	$0.546152\pi$
$444$	9.39161e15	0.0581769
$445$	6.07181e16	0.370662
$446$	1.48550e17	0.893706
$447$	4.75760e17	2.82091
$448$	7.25379e16	0.423895
$449$	3.29008e16	0.189498	0.0947490	−	0.995501i	$-0.469795\pi$
$449$	3.29008e16	0.189498	0.0947490	+	0.995501i	$0.469795\pi$
$450$	5.52155e17	3.13458
$451$	0	0
$452$	−2.65568e15	−0.0146479
$453$	−3.17304e17	−1.72519
$454$	2.03563e17	1.09103
$455$	9.06093e16	0.478739
$456$	−4.33083e17	−2.25579
$457$	5.33525e16	0.273968	0.136984	−	0.990573i	$-0.456259\pi$
$457$	5.33525e16	0.273968	0.136984	+	0.990573i	$0.456259\pi$
$458$	−3.92502e17	−1.98708
$459$	−4.92943e16	−0.246045
$460$	−1.06064e16	−0.0521964
$461$	5.22483e16	0.253522	0.126761	−	0.991933i	$-0.459542\pi$
$461$	5.22483e16	0.253522	0.126761	+	0.991933i	$0.459542\pi$
$462$	0	0
$463$	−1.52045e17	−0.717292	−0.358646	−	0.933474i	$-0.616761\pi$
$463$	−1.52045e17	−0.717292	−0.358646	+	0.933474i	$0.616761\pi$
$464$	−9.69883e16	−0.451183
$465$	−1.08420e18	−4.97354
$466$	−8.43847e16	−0.381729
$467$	−3.81255e17	−1.70081	−0.850404	−	0.526130i	$-0.823643\pi$
$467$	−3.81255e17	−1.70081	−0.850404	+	0.526130i	$0.823643\pi$
$468$	−1.65270e16	−0.0727105
$469$	3.30155e16	0.143250
$470$	−3.11818e17	−1.33434
$471$	−4.27748e17	−1.80531
$472$	−4.24910e17	−1.76878
$473$	0	0
$474$	3.35065e17	1.35697
$475$	8.19800e17	3.27491
$476$	−4.29890e15	−0.0169399
$477$	4.04579e15	0.0157266
$478$	3.07746e17	1.18008
$479$	6.28655e16	0.237811	0.118905	−	0.992906i	$-0.462061\pi$
$479$	6.28655e16	0.237811	0.118905	+	0.992906i	$0.462061\pi$
$480$	1.33408e17	0.497869
$481$	−6.38470e16	−0.235070
$482$	3.12783e17	1.13615
$483$	6.65453e16	0.238485
$484$	0	0
$485$	1.38305e17	0.482520
$486$	−3.93614e17	−1.35499
$487$	−7.13749e16	−0.242442	−0.121221	−	0.992626i	$-0.538681\pi$
$487$	−7.13749e16	−0.242442	−0.121221	+	0.992626i	$0.538681\pi$
$488$	−2.22965e17	−0.747321
$489$	5.57136e17	1.84270
$490$	4.39195e17	1.43345
$491$	4.05499e17	1.30605	0.653026	−	0.757336i	$-0.273499\pi$
$491$	4.05499e17	1.30605	0.653026	+	0.757336i	$0.273499\pi$
$492$	3.84742e16	0.122292
$493$	−5.21664e16	−0.163639
$494$	−2.94442e17	−0.911538
$495$	0	0
$496$	−6.50164e17	−1.96061
$497$	2.81354e16	0.0837406
$498$	3.81232e17	1.11995
$499$	−2.83717e17	−0.822680	−0.411340	−	0.911482i	$-0.634939\pi$
$499$	−2.83717e17	−0.822680	−0.411340	+	0.911482i	$0.634939\pi$
$500$	−6.39912e16	−0.183154
$501$	6.77465e17	1.91400
$502$	2.82665e17	0.788312
$503$	1.52010e17	0.418484	0.209242	−	0.977864i	$-0.432900\pi$
$503$	1.52010e17	0.418484	0.209242	+	0.977864i	$0.432900\pi$
$504$	−2.32789e17	−0.632650
$505$	4.85170e17	1.30167
$506$	0	0
$507$	−4.00592e17	−1.04749
$508$	2.73092e16	0.0705009
$509$	6.68784e17	1.70459	0.852296	−	0.523060i	$-0.175210\pi$
$509$	6.68784e17	1.70459	0.852296	+	0.523060i	$0.175210\pi$
$510$	4.47593e17	1.12636
$511$	−1.27165e17	−0.315961
$512$	−3.39026e17	−0.831723
$513$	3.96348e17	0.960094
$514$	−5.70633e17	−1.36489
$515$	8.28015e17	1.95565
$516$	−8.88614e16	−0.207248
$517$	0	0
$518$	8.99364e16	0.204547
$519$	−2.40996e16	−0.0541281
$520$	−4.31880e17	−0.957946
$521$	−2.30495e17	−0.504912	−0.252456	−	0.967608i	$-0.581238\pi$
$521$	−2.30495e17	−0.504912	−0.252456	+	0.967608i	$0.581238\pi$
$522$	2.82504e17	0.611175
$523$	−4.44469e17	−0.949687	−0.474843	−	0.880070i	$-0.657495\pi$
$523$	−4.44469e17	−0.949687	−0.474843	+	0.880070i	$0.657495\pi$
$524$	−1.34804e16	−0.0284478
$525$	7.54484e17	1.57259
$526$	9.14773e17	1.88324
$527$	−3.49699e17	−0.711091
$528$	0	0
$529$	−4.51081e17	−0.894937
$530$	−1.05730e16	−0.0207208
$531$	1.35112e18	2.61565
$532$	3.45651e16	0.0661016
$533$	−2.61559e17	−0.494132
$534$	−1.81588e17	−0.338898
$535$	−9.75328e17	−1.79825
$536$	−1.57365e17	−0.286640
$537$	−7.78102e16	−0.140024
$538$	−4.24441e17	−0.754628
$539$	0	0
$540$	−5.81391e16	−0.100904
$541$	6.00227e17	1.02928	0.514640	−	0.857407i	$-0.327926\pi$
$541$	6.00227e17	1.02928	0.514640	+	0.857407i	$0.327926\pi$
$542$	−4.07821e17	−0.690993
$543$	−3.93108e17	−0.658132
$544$	4.30297e16	0.0711828
$545$	−8.72948e17	−1.42696
$546$	−2.70983e17	−0.437713
$547$	−1.06676e18	−1.70275	−0.851374	−	0.524559i	$-0.824230\pi$
$547$	−1.06676e18	−1.70275	−0.851374	+	0.524559i	$0.824230\pi$
$548$	6.90472e14	0.00108911
$549$	7.08978e17	1.10513
$550$	0	0
$551$	4.19441e17	0.638536
$552$	−3.17181e17	−0.477203
$553$	2.67404e17	0.397607
$554$	6.56222e17	0.964355
$555$	−7.80377e17	−1.13344
$556$	3.78094e16	0.0542767
$557$	5.24722e17	0.744510	0.372255	−	0.928131i	$-0.378585\pi$
$557$	5.24722e17	0.744510	0.372255	+	0.928131i	$0.378585\pi$
$558$	1.89377e18	2.65586
$559$	6.04106e17	0.837407
$560$	6.64125e17	0.909972
$561$	0	0
$562$	9.67066e17	1.29470
$563$	−1.38227e18	−1.82932	−0.914660	−	0.404225i	$-0.867541\pi$
$563$	−1.38227e18	−1.82932	−0.914660	+	0.404225i	$0.867541\pi$
$564$	7.77164e16	0.101671
$565$	2.20668e17	0.285381
$566$	7.53580e17	0.963436
$567$	−1.62403e17	−0.205260
$568$	−1.34104e17	−0.167563
$569$	6.26888e17	0.774390	0.387195	−	0.921998i	$-0.373444\pi$
$569$	6.26888e17	0.774390	0.387195	+	0.921998i	$0.373444\pi$
$570$	−3.59885e18	−4.39519
$571$	−1.54502e18	−1.86552	−0.932758	−	0.360504i	$-0.882605\pi$
$571$	−1.54502e18	−1.86552	−0.932758	+	0.360504i	$0.882605\pi$
$572$	0	0
$573$	3.91876e17	0.462534
$574$	3.68439e17	0.429970
$575$	6.00405e17	0.692793
$576$	1.09939e18	1.25431
$577$	−1.45158e17	−0.163757	−0.0818784	−	0.996642i	$-0.526092\pi$
$577$	−1.45158e17	−0.163757	−0.0818784	+	0.996642i	$0.526092\pi$
$578$	−7.91957e17	−0.883427
$579$	−2.09609e18	−2.31207
$580$	−6.15265e16	−0.0671090
$581$	3.04248e17	0.328158
$582$	−4.13625e17	−0.441171
$583$	0	0
$584$	6.06120e17	0.632230
$585$	1.37328e18	1.41660
$586$	−4.96519e17	−0.506526
$587$	−8.57720e17	−0.865362	−0.432681	−	0.901547i	$-0.642432\pi$
$587$	−8.57720e17	−0.865362	−0.432681	+	0.901547i	$0.642432\pi$
$588$	−1.09463e17	−0.109224
$589$	2.81174e18	2.77476
$590$	−3.53094e18	−3.44629
$591$	1.23203e18	1.18933
$592$	−4.67970e17	−0.446814
$593$	8.25981e17	0.780035	0.390018	−	0.920807i	$-0.372469\pi$
$593$	8.25981e17	0.780035	0.390018	+	0.920807i	$0.372469\pi$
$594$	0	0
$595$	3.57208e17	0.330036
$596$	1.80986e17	0.165403
$597$	5.46433e17	0.493974
$598$	−2.15643e17	−0.192832
$599$	4.43343e16	0.0392162	0.0196081	−	0.999808i	$-0.493758\pi$
$599$	4.43343e16	0.0392162	0.0196081	+	0.999808i	$0.493758\pi$
$600$	−3.59617e18	−3.14671
$601$	8.49363e17	0.735206	0.367603	−	0.929983i	$-0.380179\pi$
$601$	8.49363e17	0.735206	0.367603	+	0.929983i	$0.380179\pi$
$602$	−8.50959e17	−0.728671
$603$	5.00386e17	0.423879
$604$	−1.20707e17	−0.101156
$605$	0	0
$606$	−1.45099e18	−1.19012
$607$	3.72751e17	0.302477	0.151238	−	0.988497i	$-0.451674\pi$
$607$	3.72751e17	0.302477	0.151238	+	0.988497i	$0.451674\pi$
$608$	−3.45978e17	−0.277763
$609$	3.86023e17	0.306620
$610$	−1.85280e18	−1.45608
$611$	−5.28340e17	−0.410814
$612$	−6.51544e16	−0.0501256
$613$	−1.02909e18	−0.783359	−0.391680	−	0.920102i	$-0.628106\pi$
$613$	−1.02909e18	−0.783359	−0.391680	+	0.920102i	$0.628106\pi$
$614$	−1.56983e18	−1.18239
$615$	−3.19694e18	−2.38257
$616$	0	0
$617$	2.83422e17	0.206814	0.103407	−	0.994639i	$-0.467026\pi$
$617$	2.83422e17	0.206814	0.103407	+	0.994639i	$0.467026\pi$
$618$	−2.47632e18	−1.78806
$619$	2.64400e18	1.88918	0.944588	−	0.328259i	$-0.106462\pi$
$619$	2.64400e18	1.88918	0.944588	+	0.328259i	$0.106462\pi$
$620$	−4.12445e17	−0.291622
$621$	2.90277e17	0.203104
$622$	−2.73088e17	−0.189089
$623$	−1.44919e17	−0.0993009
$624$	1.41002e18	0.956147
$625$	2.13230e18	1.43096
$626$	−1.02477e18	−0.680605
$627$	0	0
$628$	−1.62721e17	−0.105854
$629$	−2.51704e17	−0.162054
$630$	−1.93444e18	−1.23265
$631$	1.24287e17	0.0783853	0.0391927	−	0.999232i	$-0.487521\pi$
$631$	1.24287e17	0.0783853	0.0391927	+	0.999232i	$0.487521\pi$
$632$	−1.27455e18	−0.795603
$633$	−2.47958e18	−1.53198
$634$	1.29226e18	0.790259
$635$	−2.26920e18	−1.37355
$636$	2.63519e15	0.00157885
$637$	7.44166e17	0.441330
$638$	0	0
$639$	4.26422e17	0.247790
$640$	−3.43130e18	−1.97374
$641$	4.86719e17	0.277141	0.138571	−	0.990353i	$-0.455749\pi$
$641$	4.86719e17	0.277141	0.138571	+	0.990353i	$0.455749\pi$
$642$	2.91689e18	1.64415
$643$	3.06008e17	0.170750	0.0853750	−	0.996349i	$-0.472791\pi$
$643$	3.06008e17	0.170750	0.0853750	+	0.996349i	$0.472791\pi$
$644$	2.53148e16	0.0139835
$645$	7.38376e18	4.03775
$646$	−1.16078e18	−0.628402
$647$	−1.29027e18	−0.691517	−0.345758	−	0.938324i	$-0.612378\pi$
$647$	−1.29027e18	−0.691517	−0.345758	+	0.938324i	$0.612378\pi$
$648$	7.74076e17	0.410720
$649$	0	0
$650$	−2.44495e18	−1.27155
$651$	2.58772e18	1.33242
$652$	2.11942e17	0.108046
$653$	−2.74176e18	−1.38386	−0.691932	−	0.721962i	$-0.743240\pi$
$653$	−2.74176e18	−1.38386	−0.691932	+	0.721962i	$0.743240\pi$
$654$	2.61070e18	1.30467
$655$	1.12013e18	0.554241
$656$	−1.91711e18	−0.939231
$657$	−1.92733e18	−0.934933
$658$	7.44232e17	0.357470
$659$	−2.16326e18	−1.02885	−0.514426	−	0.857535i	$-0.671995\pi$
$659$	−2.16326e18	−1.02885	−0.514426	+	0.857535i	$0.671995\pi$
$660$	0	0
$661$	3.09700e18	1.44421	0.722106	−	0.691782i	$-0.243174\pi$
$661$	3.09700e18	1.44421	0.722106	+	0.691782i	$0.243174\pi$
$662$	3.53059e18	1.63031
$663$	7.58396e17	0.346783
$664$	−1.45017e18	−0.656637
$665$	−2.87211e18	−1.28784
$666$	1.36308e18	0.605257
$667$	3.07190e17	0.135080
$668$	2.57717e17	0.112227
$669$	3.07643e18	1.32672
$670$	−1.30768e18	−0.558489
$671$	0	0
$672$	−3.18413e17	−0.133380
$673$	4.44155e18	1.84263	0.921313	−	0.388823i	$-0.127118\pi$
$673$	4.44155e18	1.84263	0.921313	+	0.388823i	$0.127118\pi$
$674$	−1.87403e18	−0.769996
$675$	3.29114e18	1.33928
$676$	−1.52391e17	−0.0614194
$677$	4.72047e18	1.88434	0.942169	−	0.335137i	$-0.108783\pi$
$677$	4.72047e18	1.88434	0.942169	+	0.335137i	$0.108783\pi$
$678$	−6.59947e17	−0.260925
$679$	−3.30099e17	−0.129268
$680$	−1.70260e18	−0.660395
$681$	4.21574e18	1.61964
$682$	0	0
$683$	−2.65750e18	−1.00170	−0.500852	−	0.865533i	$-0.666980\pi$
$683$	−2.65750e18	−1.00170	−0.500852	+	0.865533i	$0.666980\pi$
$684$	5.23871e17	0.195596
$685$	−5.73734e16	−0.0212189
$686$	−2.40113e18	−0.879649
$687$	−8.12864e18	−2.94984
$688$	4.42783e18	1.59172
$689$	−1.79148e16	−0.00637951
$690$	−2.63573e18	−0.929782
$691$	−2.77225e18	−0.968778	−0.484389	−	0.874853i	$-0.660958\pi$
$691$	−2.77225e18	−0.968778	−0.484389	+	0.874853i	$0.660958\pi$
$692$	−9.16784e15	−0.00317379
$693$	0	0
$694$	2.65486e18	0.901999
$695$	−3.14170e18	−1.05746
$696$	−1.83994e18	−0.613541
$697$	−1.03114e18	−0.340648
$698$	−1.73575e18	−0.568102
$699$	−1.74759e18	−0.566680
$700$	2.87016e17	0.0922082
$701$	5.30913e18	1.68988	0.844941	−	0.534860i	$-0.179636\pi$
$701$	5.30913e18	1.68988	0.844941	+	0.534860i	$0.179636\pi$
$702$	−1.18206e18	−0.372775
$703$	2.02381e18	0.632354
$704$	0	0
$705$	−6.45769e18	−1.98083
$706$	4.83643e17	0.146992
$707$	−1.15798e18	−0.348719
$708$	8.80039e17	0.262595
$709$	3.68053e18	1.08820	0.544102	−	0.839019i	$-0.316871\pi$
$709$	3.68053e18	1.08820	0.544102	+	0.839019i	$0.316871\pi$
$710$	−1.11439e18	−0.326480
$711$	4.05279e18	1.17653
$712$	6.90742e17	0.198699
$713$	2.05926e18	0.586988
$714$	−1.06829e18	−0.301754
$715$	0	0
$716$	−2.96001e16	−0.00821029
$717$	6.37336e18	1.75184
$718$	−8.53958e17	−0.232610
$719$	8.96742e17	0.242064	0.121032	−	0.992649i	$-0.461380\pi$
$719$	8.96742e17	0.242064	0.121032	+	0.992649i	$0.461380\pi$
$720$	1.00655e19	2.69262
$721$	−1.97627e18	−0.523922
$722$	5.35771e18	1.40763
$723$	6.47768e18	1.68663
$724$	−1.49544e17	−0.0385894
$725$	3.48290e18	0.890725
$726$	0	0
$727$	−2.97724e17	−0.0747893	−0.0373947	−	0.999301i	$-0.511906\pi$
$727$	−2.97724e17	−0.0747893	−0.0373947	+	0.999301i	$0.511906\pi$
$728$	1.03079e18	0.256635
$729$	−6.39871e18	−1.57893
$730$	5.03677e18	1.23184
$731$	2.38156e18	0.577297
$732$	4.61786e17	0.110948
$733$	−6.49787e18	−1.54737	−0.773687	−	0.633568i	$-0.781590\pi$
$733$	−6.49787e18	−1.54737	−0.773687	+	0.633568i	$0.781590\pi$
$734$	3.53643e18	0.834719
$735$	9.09565e18	2.12797
$736$	−2.53387e17	−0.0587596
$737$	0	0
$738$	5.58409e18	1.27229
$739$	−5.11359e18	−1.15488	−0.577441	−	0.816433i	$-0.695949\pi$
$739$	−5.11359e18	−1.15488	−0.577441	+	0.816433i	$0.695949\pi$
$740$	−2.96866e17	−0.0664592
$741$	−6.09784e18	−1.35319
$742$	2.52352e16	0.00555113
$743$	−6.11449e17	−0.133332	−0.0666658	−	0.997775i	$-0.521236\pi$
$743$	−6.11449e17	−0.133332	−0.0666658	+	0.997775i	$0.521236\pi$
$744$	−1.23341e19	−2.66614
$745$	−1.50387e19	−3.22250
$746$	7.74872e17	0.164599
$747$	4.61121e18	0.971025
$748$	0	0
$749$	2.32787e18	0.481755
$750$	−1.59021e19	−3.26254
$751$	−8.09947e17	−0.164739	−0.0823696	−	0.996602i	$-0.526249\pi$
$751$	−8.09947e17	−0.164739	−0.0823696	+	0.996602i	$0.526249\pi$
$752$	−3.87249e18	−0.780863
$753$	5.85394e18	1.17026
$754$	−1.25093e18	−0.247924
$755$	1.00299e19	1.97080
$756$	1.38764e17	0.0270324
$757$	−6.16285e18	−1.19031	−0.595153	−	0.803613i	$-0.702908\pi$
$757$	−6.16285e18	−1.19031	−0.595153	+	0.803613i	$0.702908\pi$
$758$	1.59151e18	0.304762
$759$	0	0
$760$	1.36896e19	2.57693
$761$	−7.31471e18	−1.36520	−0.682601	−	0.730792i	$-0.739151\pi$
$761$	−7.31471e18	−1.36520	−0.682601	+	0.730792i	$0.739151\pi$
$762$	6.78644e18	1.25584
$763$	2.08351e18	0.382284
$764$	1.49075e17	0.0271206
$765$	5.41388e18	0.976583
$766$	−7.70976e18	−1.37897
$767$	−5.98277e18	−1.06104
$768$	2.38554e18	0.419506
$769$	8.58515e18	1.49702	0.748508	−	0.663125i	$-0.230770\pi$
$769$	8.58515e18	1.49702	0.748508	+	0.663125i	$0.230770\pi$
$770$	0	0
$771$	−1.18177e19	−2.02619
$772$	−7.97384e17	−0.135567
$773$	2.38163e18	0.401520	0.200760	−	0.979640i	$-0.435659\pi$
$773$	2.38163e18	0.401520	0.200760	+	0.979640i	$0.435659\pi$
$774$	−1.28972e19	−2.15615
$775$	2.33477e19	3.87064
$776$	1.57338e18	0.258662
$777$	1.86257e18	0.303651
$778$	3.16077e18	0.511005
$779$	8.29085e18	1.32925
$780$	8.94473e17	0.142217
$781$	0	0
$782$	−8.50130e17	−0.132936
$783$	1.68387e18	0.261131
$784$	5.45440e18	0.838866
$785$	1.35210e19	2.06232
$786$	−3.34993e18	−0.506745
$787$	−4.85310e17	−0.0728088	−0.0364044	−	0.999337i	$-0.511590\pi$
$787$	−4.85310e17	−0.0728088	−0.0364044	+	0.999337i	$0.511590\pi$
$788$	4.68682e17	0.0697362
$789$	1.89448e19	2.79569
$790$	−1.05913e19	−1.55015
$791$	−5.26680e17	−0.0764539
$792$	0	0
$793$	−3.13936e18	−0.448297
$794$	1.10190e18	0.156067
$795$	−2.18966e17	−0.0307602
$796$	2.07871e17	0.0289640
$797$	−8.92197e18	−1.23305	−0.616526	−	0.787334i	$-0.711461\pi$
$797$	−8.92197e18	−1.23305	−0.616526	+	0.787334i	$0.711461\pi$
$798$	8.58956e18	1.17748
$799$	−2.08287e18	−0.283210
$800$	−2.87288e18	−0.387465
$801$	−2.19640e18	−0.293833
$802$	5.19174e18	0.688937
$803$	0	0
$804$	3.25921e17	0.0425548
$805$	−2.10348e18	−0.272436
$806$	−8.38563e18	−1.07735
$807$	−8.79010e18	−1.12025
$808$	5.51940e18	0.697779
$809$	−1.09787e19	−1.37685	−0.688423	−	0.725310i	$-0.741697\pi$
$809$	−1.09787e19	−1.37685	−0.688423	+	0.725310i	$0.741697\pi$
$810$	6.43245e18	0.800247
$811$	6.07390e18	0.749605	0.374802	−	0.927105i	$-0.377711\pi$
$811$	6.07390e18	0.749605	0.374802	+	0.927105i	$0.377711\pi$
$812$	1.46849e17	0.0179786
$813$	−8.44589e18	−1.02579
$814$	0	0
$815$	−1.76109e19	−2.10503
$816$	5.55870e18	0.659155
$817$	−1.91488e19	−2.25268
$818$	−7.03506e18	−0.821054
$819$	−3.27768e18	−0.379508
$820$	−1.21616e18	−0.139701
$821$	−7.02431e18	−0.800521	−0.400261	−	0.916401i	$-0.631080\pi$
$821$	−7.02431e18	−0.800521	−0.400261	+	0.916401i	$0.631080\pi$
$822$	1.71585e17	0.0194005
$823$	3.26014e18	0.365710	0.182855	−	0.983140i	$-0.441466\pi$
$823$	3.26014e18	0.365710	0.182855	+	0.983140i	$0.441466\pi$
$824$	9.41967e18	1.04836
$825$	0	0
$826$	8.42748e18	0.923267
$827$	1.14381e19	1.24327	0.621636	−	0.783306i	$-0.286468\pi$
$827$	1.14381e19	1.24327	0.621636	+	0.783306i	$0.286468\pi$
$828$	3.83673e17	0.0413774
$829$	8.80866e18	0.942552	0.471276	−	0.881986i	$-0.343794\pi$
$829$	8.80866e18	0.942552	0.471276	+	0.881986i	$0.343794\pi$
$830$	−1.20507e19	−1.27939
$831$	1.35902e19	1.43159
$832$	−4.86811e18	−0.508814
$833$	2.93372e18	0.304247
$834$	9.39580e18	0.966839
$835$	−2.14145e19	−2.18648
$836$	0	0
$837$	1.12879e19	1.13474
$838$	8.48583e18	0.846463
$839$	1.78648e19	1.76825	0.884127	−	0.467247i	$-0.154754\pi$
$839$	1.78648e19	1.76825	0.884127	+	0.467247i	$0.154754\pi$
$840$	1.25989e19	1.23742
$841$	−8.47865e18	−0.826328
$842$	−6.10038e18	−0.589968
$843$	2.00278e19	1.92200
$844$	−9.43268e17	−0.0898275
$845$	1.26626e19	1.19662
$846$	1.12796e19	1.05776
$847$	0	0
$848$	−1.31307e17	−0.0121260
$849$	1.56065e19	1.43023
$850$	−9.63869e18	−0.876587
$851$	1.48220e18	0.133772
$852$	2.77746e17	0.0248765
$853$	1.24103e19	1.10309	0.551547	−	0.834144i	$-0.314038\pi$
$853$	1.24103e19	1.10309	0.551547	+	0.834144i	$0.314038\pi$
$854$	4.42218e18	0.390086
$855$	−4.35300e19	−3.81074
$856$	−1.10955e19	−0.963981
$857$	−3.47670e18	−0.299773	−0.149886	−	0.988703i	$-0.547891\pi$
$857$	−3.47670e18	−0.299773	−0.149886	+	0.988703i	$0.547891\pi$
$858$	0	0
$859$	−1.92533e18	−0.163512	−0.0817562	−	0.996652i	$-0.526053\pi$
$859$	−1.92533e18	−0.163512	−0.0817562	+	0.996652i	$0.526053\pi$
$860$	2.80888e18	0.236752
$861$	7.63030e18	0.638294
$862$	7.48678e18	0.621581
$863$	6.33551e18	0.522050	0.261025	−	0.965332i	$-0.415940\pi$
$863$	6.33551e18	0.522050	0.261025	+	0.965332i	$0.415940\pi$
$864$	−1.38895e18	−0.113592
$865$	7.61784e17	0.0618339
$866$	1.99737e19	1.60914
$867$	−1.64013e19	−1.31146
$868$	9.84404e17	0.0781259
$869$	0	0
$870$	−1.52896e19	−1.19542
$871$	−2.21571e18	−0.171947
$872$	−9.93083e18	−0.764942
$873$	−5.00301e18	−0.382506
$874$	6.83542e18	0.518730
$875$	−1.26909e19	−0.955961
$876$	−1.25535e18	−0.0938614
$877$	−5.43721e18	−0.403533	−0.201766	−	0.979434i	$-0.564668\pi$
$877$	−5.43721e18	−0.403533	−0.201766	+	0.979434i	$0.564668\pi$
$878$	1.77075e18	0.130450
$879$	−1.02828e19	−0.751942
$880$	0	0
$881$	1.37299e19	0.989291	0.494645	−	0.869095i	$-0.335298\pi$
$881$	1.37299e19	0.989291	0.494645	+	0.869095i	$0.335298\pi$
$882$	−1.58874e19	−1.13633
$883$	1.70583e17	0.0121113	0.00605565	−	0.999982i	$-0.498072\pi$
$883$	1.70583e17	0.0121113	0.00605565	+	0.999982i	$0.498072\pi$
$884$	2.88504e17	0.0203335
$885$	−7.31251e19	−5.11605
$886$	−4.34570e18	−0.301815
$887$	2.40922e19	1.66102	0.830508	−	0.557007i	$-0.188050\pi$
$887$	2.40922e19	1.66102	0.830508	+	0.557007i	$0.188050\pi$
$888$	−8.87773e18	−0.607600
$889$	5.41602e18	0.367975
$890$	5.73995e18	0.387145
$891$	0	0
$892$	1.17032e18	0.0777916
$893$	1.67472e19	1.10512
$894$	4.49758e19	2.94635
$895$	2.45956e18	0.159959
$896$	8.18967e18	0.528767
$897$	−4.46594e18	−0.286261
$898$	3.11026e18	0.197925
$899$	1.19456e19	0.754691
$900$	4.35004e18	0.272846
$901$	−7.06254e16	−0.00439795
$902$	0	0
$903$	−1.76232e19	−1.08172
$904$	2.51037e18	0.152983
$905$	1.24260e19	0.751826
$906$	−2.99962e19	−1.80191
$907$	1.35984e19	0.811039	0.405519	−	0.914086i	$-0.367091\pi$
$907$	1.35984e19	0.811039	0.405519	+	0.914086i	$0.367091\pi$
$908$	1.60373e18	0.0949670
$909$	−1.75505e19	−1.03187
$910$	8.56570e18	0.500028
$911$	−1.22478e19	−0.709887	−0.354943	−	0.934888i	$-0.615500\pi$
$911$	−1.22478e19	−0.709887	−0.354943	+	0.934888i	$0.615500\pi$
$912$	−4.46944e19	−2.57209
$913$	0	0
$914$	5.04365e18	0.286151
$915$	−3.83712e19	−2.16156
$916$	−3.09225e18	−0.172963
$917$	−2.67346e18	−0.148482
$918$	−4.66001e18	−0.256986
$919$	1.99043e19	1.08992	0.544961	−	0.838462i	$-0.316545\pi$
$919$	1.99043e19	1.08992	0.544961	+	0.838462i	$0.316545\pi$
$920$	1.00260e19	0.545139
$921$	−3.25110e19	−1.75526
$922$	4.93927e18	0.264796
$923$	−1.88820e18	−0.100516
$924$	0	0
$925$	1.68050e19	0.882100
$926$	−1.43735e19	−0.749189
$927$	−2.99524e19	−1.55029
$928$	−1.46988e18	−0.0755473
$929$	5.01946e18	0.256186	0.128093	−	0.991762i	$-0.459114\pi$
$929$	5.01946e18	0.256186	0.128093	+	0.991762i	$0.459114\pi$
$930$	−1.02494e20	−5.19470
$931$	−2.35884e19	−1.18721
$932$	−6.64808e17	−0.0332271
$933$	−5.65561e18	−0.280704
$934$	−3.60417e19	−1.77644
$935$	0	0
$936$	1.56227e19	0.759388
$937$	7.65729e18	0.369630	0.184815	−	0.982773i	$-0.440831\pi$
$937$	7.65729e18	0.369630	0.184815	+	0.982773i	$0.440831\pi$
$938$	3.12110e18	0.149620
$939$	−2.12229e19	−1.01036
$940$	−2.45660e18	−0.116146
$941$	1.78887e19	0.839938	0.419969	−	0.907538i	$-0.362041\pi$
$941$	1.78887e19	0.839938	0.419969	+	0.907538i	$0.362041\pi$
$942$	−4.04370e19	−1.88559
$943$	6.07206e18	0.281196
$944$	−4.38510e19	−2.01680
$945$	−1.15303e19	−0.526663
$946$	0	0
$947$	−1.02681e19	−0.462608	−0.231304	−	0.972881i	$-0.574299\pi$
$947$	−1.02681e19	−0.462608	−0.231304	+	0.972881i	$0.574299\pi$
$948$	2.63975e18	0.118116
$949$	8.53422e18	0.379257
$950$	7.74994e19	3.42054
$951$	2.67624e19	1.17315
$952$	4.06368e18	0.176921
$953$	−1.65179e19	−0.714252	−0.357126	−	0.934056i	$-0.616243\pi$
$953$	−1.65179e19	−0.714252	−0.357126	+	0.934056i	$0.616243\pi$
$954$	3.82467e17	0.0164259
$955$	−1.23871e19	−0.528382
$956$	2.42452e18	0.102718
$957$	0	0
$958$	5.94296e18	0.248386
$959$	1.36936e17	0.00568456
$960$	−5.95010e19	−2.45336
$961$	5.56600e19	2.27951
$962$	−6.03575e18	−0.245523
$963$	3.52813e19	1.42552
$964$	2.46420e18	0.0988952
$965$	6.62570e19	2.64122
$966$	6.29083e18	0.249090
$967$	7.40680e18	0.291312	0.145656	−	0.989335i	$-0.453471\pi$
$967$	7.40680e18	0.291312	0.145656	+	0.989335i	$0.453471\pi$
$968$	0	0
$969$	−2.40395e19	−0.932869
$970$	1.30746e19	0.503977
$971$	6.06699e18	0.232299	0.116150	−	0.993232i	$-0.462945\pi$
$971$	6.06699e18	0.232299	0.116150	+	0.993232i	$0.462945\pi$
$972$	−3.10101e18	−0.117943
$973$	7.49845e18	0.283295
$974$	−6.74739e18	−0.253223
$975$	−5.06344e19	−1.88762
$976$	−2.30101e19	−0.852108
$977$	−3.72500e19	−1.37029	−0.685144	−	0.728408i	$-0.740261\pi$
$977$	−3.72500e19	−1.37029	−0.685144	+	0.728408i	$0.740261\pi$
$978$	5.26686e19	1.92464
$979$	0	0
$980$	3.46011e18	0.124773
$981$	3.15778e19	1.13119
$982$	3.83337e19	1.36413
$983$	−4.85322e19	−1.71566	−0.857831	−	0.513932i	$-0.828188\pi$
$983$	−4.85322e19	−1.71566	−0.857831	+	0.513932i	$0.828188\pi$
$984$	−3.63690e19	−1.27721
$985$	−3.89442e19	−1.35865
$986$	−4.93153e18	−0.170915
$987$	1.54129e19	0.530668
$988$	−2.31970e18	−0.0793437
$989$	−1.40242e19	−0.476544
$990$	0	0
$991$	3.45741e19	1.15950	0.579752	−	0.814793i	$-0.303149\pi$
$991$	3.45741e19	1.15950	0.579752	+	0.814793i	$0.303149\pi$
$992$	−9.85335e18	−0.328290
$993$	7.31179e19	2.42021
$994$	2.65976e18	0.0874644
$995$	−1.72726e19	−0.564297
$996$	3.00346e18	0.0974848
$997$	3.27147e19	1.05493	0.527466	−	0.849576i	$-0.323142\pi$
$997$	3.27147e19	1.05493	0.527466	+	0.849576i	$0.323142\pi$
$998$	−2.68210e19	−0.859264
$999$	8.12471e18	0.258602

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.14.a.i.1.17		24
11.7	odd	10		11.14.c.a.5.4	✓	48
11.8	odd	10		11.14.c.a.9.4	yes	48
11.10	odd	2		121.14.a.h.1.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.14.c.a.5.4	✓	48	11.7	odd	10
11.14.c.a.9.4	yes	48	11.8	odd	10
121.14.a.h.1.8		24	11.10	odd	2
121.14.a.i.1.17		24	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:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	121.a (trivial)

\(f(q)\)	\(=\)	\(q+94.5345 q^{2} +1957.79 q^{3} +744.772 q^{4} -61885.3 q^{5} +185079. q^{6} +147705. q^{7} -704020. q^{8} +2.23863e6 q^{9} +O(q^{10})\)	\(q+94.5345 q^{2} +1957.79 q^{3} +744.772 q^{4} -61885.3 q^{5} +185079. q^{6} +147705. q^{7} -704020. q^{8} +2.23863e6 q^{9} -5.85030e6 q^{10} +1.45811e6 q^{12} -9.91266e6 q^{13} +1.39632e7 q^{14} -1.21159e8 q^{15} -7.26553e7 q^{16} -3.90786e7 q^{17} +2.11627e8 q^{18} +3.14209e8 q^{19} -4.60904e7 q^{20} +2.89176e8 q^{21} +2.30121e8 q^{23} -1.37832e9 q^{24} +2.60909e9 q^{25} -9.37088e8 q^{26} +1.26141e9 q^{27} +1.10006e8 q^{28} +1.33491e9 q^{29} -1.14537e10 q^{30} +8.94860e9 q^{31} -1.10111e9 q^{32} -3.69428e9 q^{34} -9.14076e9 q^{35} +1.66727e9 q^{36} +6.44096e9 q^{37} +2.97036e10 q^{38} -1.94069e10 q^{39} +4.35685e10 q^{40} +2.63864e10 q^{41} +2.73371e10 q^{42} -6.09429e10 q^{43} -1.38538e11 q^{45} +2.17544e10 q^{46} +5.32995e10 q^{47} -1.42244e11 q^{48} -7.50723e10 q^{49} +2.46649e11 q^{50} -7.65078e10 q^{51} -7.38267e9 q^{52} +1.80727e9 q^{53} +1.19247e11 q^{54} -1.03987e11 q^{56} +6.15157e11 q^{57} +1.26195e11 q^{58} +6.03549e11 q^{59} -9.02355e10 q^{60} +3.16702e11 q^{61} +8.45952e11 q^{62} +3.30656e11 q^{63} +4.91100e11 q^{64} +6.13448e11 q^{65} +2.23523e11 q^{67} -2.91046e10 q^{68} +4.50529e11 q^{69} -8.64117e11 q^{70} +1.90484e11 q^{71} -1.57604e12 q^{72} -8.60942e11 q^{73} +6.08893e11 q^{74} +5.10805e12 q^{75} +2.34014e11 q^{76} -1.83462e12 q^{78} +1.81039e12 q^{79} +4.49630e12 q^{80} -1.09951e12 q^{81} +2.49442e12 q^{82} +2.05984e12 q^{83} +2.15370e11 q^{84} +2.41839e12 q^{85} -5.76121e12 q^{86} +2.61348e12 q^{87} -9.81139e11 q^{89} -1.30966e13 q^{90} -1.46415e12 q^{91} +1.71387e11 q^{92} +1.75195e13 q^{93} +5.03864e12 q^{94} -1.94449e13 q^{95} -2.15573e12 q^{96} -2.23486e12 q^{97} -7.09692e12 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 128 q^{2} + 1068 q^{3} + 90294 q^{4} + 26080 q^{5} + 98495 q^{6} + 386592 q^{7} + 1548294 q^{8} + 7656268 q^{9}+O(q^{10}) \) 24 * q + 128 * q^2 + 1068 * q^3 + 90294 * q^4 + 26080 * q^5 + 98495 * q^6 + 386592 * q^7 + 1548294 * q^8 + 7656268 * q^9	\( 24 q + 128 q^{2} + 1068 q^{3} + 90294 q^{4} + 26080 q^{5} + 98495 q^{6} + 386592 q^{7} + 1548294 q^{8} + 7656268 q^{9} + 8146536 q^{10} + 31486019 q^{12} + 17561904 q^{13} - 16549212 q^{14} - 47315512 q^{15} + 189327378 q^{16} + 161930636 q^{17} + 442641953 q^{18} + 647216196 q^{19} + 443499298 q^{20} + 217276816 q^{21} + 2094437136 q^{23} + 1627544589 q^{24} + 2084691168 q^{25} + 2355630004 q^{26} + 742899600 q^{27} + 3032872896 q^{28} + 8699178576 q^{29} + 1243218300 q^{30} - 9494900112 q^{31} + 18962452446 q^{32} - 21315904743 q^{34} + 19181301256 q^{35} - 39894746479 q^{36} + 3089149344 q^{37} + 129844728457 q^{38} + 49031676912 q^{39} + 194691582558 q^{40} + 83280861028 q^{41} - 124381258176 q^{42} + 161991034068 q^{43} + 50827898320 q^{45} + 437334676134 q^{46} - 143404218008 q^{47} - 20850971437 q^{48} + 306774688344 q^{49} + 321735931268 q^{50} + 545715464528 q^{51} + 612093584562 q^{52} - 392354896952 q^{53} + 85719376742 q^{54} - 27658271244 q^{56} + 275972269320 q^{57} - 34679215332 q^{58} + 276513783196 q^{59} + 718672116538 q^{60} + 230121481992 q^{61} - 302794066266 q^{62} - 643203605848 q^{63} + 2023123568130 q^{64} + 957140617352 q^{65} - 692937587460 q^{67} - 1735237886973 q^{68} + 1117466070944 q^{69} - 307144167534 q^{70} - 4277414185816 q^{71} - 3242879740353 q^{72} - 4979010172020 q^{73} - 2672607341782 q^{74} + 3983565507508 q^{75} - 3691319323131 q^{76} + 242673994778 q^{78} - 2105593756968 q^{79} + 8461209269858 q^{80} + 887412594856 q^{81} - 8574013790565 q^{82} + 6824767308444 q^{83} - 8438329587858 q^{84} + 3374484393528 q^{85} + 18312276652385 q^{86} + 11079389891856 q^{87} - 6018805846820 q^{89} - 4577924266292 q^{90} - 10934505244368 q^{91} + 4722880465206 q^{92} + 5494546269696 q^{93} + 22894507263180 q^{94} + 17781364000928 q^{95} + 35355473398269 q^{96} + 11153302493028 q^{97} + 26143145346994 q^{98}+O(q^{100}) \) 24 * q + 128 * q^2 + 1068 * q^3 + 90294 * q^4 + 26080 * q^5 + 98495 * q^6 + 386592 * q^7 + 1548294 * q^8 + 7656268 * q^9 + 8146536 * q^10 + 31486019 * q^12 + 17561904 * q^13 - 16549212 * q^14 - 47315512 * q^15 + 189327378 * q^16 + 161930636 * q^17 + 442641953 * q^18 + 647216196 * q^19 + 443499298 * q^20 + 217276816 * q^21 + 2094437136 * q^23 + 1627544589 * q^24 + 2084691168 * q^25 + 2355630004 * q^26 + 742899600 * q^27 + 3032872896 * q^28 + 8699178576 * q^29 + 1243218300 * q^30 - 9494900112 * q^31 + 18962452446 * q^32 - 21315904743 * q^34 + 19181301256 * q^35 - 39894746479 * q^36 + 3089149344 * q^37 + 129844728457 * q^38 + 49031676912 * q^39 + 194691582558 * q^40 + 83280861028 * q^41 - 124381258176 * q^42 + 161991034068 * q^43 + 50827898320 * q^45 + 437334676134 * q^46 - 143404218008 * q^47 - 20850971437 * q^48 + 306774688344 * q^49 + 321735931268 * q^50 + 545715464528 * q^51 + 612093584562 * q^52 - 392354896952 * q^53 + 85719376742 * q^54 - 27658271244 * q^56 + 275972269320 * q^57 - 34679215332 * q^58 + 276513783196 * q^59 + 718672116538 * q^60 + 230121481992 * q^61 - 302794066266 * q^62 - 643203605848 * q^63 + 2023123568130 * q^64 + 957140617352 * q^65 - 692937587460 * q^67 - 1735237886973 * q^68 + 1117466070944 * q^69 - 307144167534 * q^70 - 4277414185816 * q^71 - 3242879740353 * q^72 - 4979010172020 * q^73 - 2672607341782 * q^74 + 3983565507508 * q^75 - 3691319323131 * q^76 + 242673994778 * q^78 - 2105593756968 * q^79 + 8461209269858 * q^80 + 887412594856 * q^81 - 8574013790565 * q^82 + 6824767308444 * q^83 - 8438329587858 * q^84 + 3374484393528 * q^85 + 18312276652385 * q^86 + 11079389891856 * q^87 - 6018805846820 * q^89 - 4577924266292 * q^90 - 10934505244368 * q^91 + 4722880465206 * q^92 + 5494546269696 * q^93 + 22894507263180 * q^94 + 17781364000928 * q^95 + 35355473398269 * q^96 + 11153302493028 * q^97 + 26143145346994 * q^98

Introduction

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