LMFDB - Embedded newform 121.18.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [121,18,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, 18, names="a")

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

chi := DirichletCharacter("121.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 18 $
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:	$221.698725687$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 142182x^{4} - 2828860x^{3} + 4365765216x^{2} - 37243791360x - 26396402886656 $ x^6 - 142182x^4 - 2828860x^3 + 4365765216x^2 - 37243791360x - 26396402886656
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{6}\cdot 11 $
Twist minimal:	no (minimal twist has level 11)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-225.978$ of defining polynomial
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)

$f(q)$	$=$	$q-451.956 q^{2} +8582.51 q^{3} +73191.9 q^{4} -1.00486e6 q^{5} -3.87891e6 q^{6} +1.88093e7 q^{7} +2.61592e7 q^{8} -5.54807e7 q^{9} +O(q^{10})$	\(q-451.956 q^{2} +8582.51 q^{3} +73191.9 q^{4} -1.00486e6 q^{5} -3.87891e6 q^{6} +1.88093e7 q^{7} +2.61592e7 q^{8} -5.54807e7 q^{9} +4.54152e8 q^{10} +6.28170e8 q^{12} -7.84654e8 q^{13} -8.50098e9 q^{14} -8.62421e9 q^{15} -2.14162e10 q^{16} -3.52778e10 q^{17} +2.50748e10 q^{18} -1.01332e11 q^{19} -7.35475e10 q^{20} +1.61431e11 q^{21} -9.68328e9 q^{23} +2.24512e11 q^{24} +2.46801e11 q^{25} +3.54629e11 q^{26} -1.58451e12 q^{27} +1.37669e12 q^{28} +5.24329e12 q^{29} +3.89776e12 q^{30} -2.88452e11 q^{31} +6.25044e12 q^{32} +1.59440e13 q^{34} -1.89007e13 q^{35} -4.06074e12 q^{36} -1.56299e13 q^{37} +4.57977e13 q^{38} -6.73430e12 q^{39} -2.62863e13 q^{40} -8.27593e13 q^{41} -7.29598e13 q^{42} +5.50702e13 q^{43} +5.57502e13 q^{45} +4.37641e12 q^{46} +8.65871e12 q^{47} -1.83805e14 q^{48} +1.21161e14 q^{49} -1.11543e14 q^{50} -3.02772e14 q^{51} -5.74303e13 q^{52} -2.29179e14 q^{53} +7.16128e14 q^{54} +4.92038e14 q^{56} -8.69685e14 q^{57} -2.36973e15 q^{58} +7.57251e14 q^{59} -6.31222e14 q^{60} +2.29409e15 q^{61} +1.30367e14 q^{62} -1.04355e15 q^{63} -1.78544e13 q^{64} +7.88466e14 q^{65} -1.57751e15 q^{67} -2.58205e15 q^{68} -8.31068e13 q^{69} +8.54229e15 q^{70} -6.00695e15 q^{71} -1.45133e15 q^{72} -1.02546e16 q^{73} +7.06400e15 q^{74} +2.11818e15 q^{75} -7.41670e15 q^{76} +3.04360e15 q^{78} +1.74050e15 q^{79} +2.15203e16 q^{80} -6.43429e15 q^{81} +3.74035e16 q^{82} +2.13414e16 q^{83} +1.18155e16 q^{84} +3.54492e16 q^{85} -2.48893e16 q^{86} +4.50006e16 q^{87} -1.90853e16 q^{89} -2.51966e16 q^{90} -1.47588e16 q^{91} -7.08737e14 q^{92} -2.47564e15 q^{93} -3.91335e15 q^{94} +1.01825e17 q^{95} +5.36445e16 q^{96} +1.03763e17 q^{97} -5.47592e16 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 11865 q^{3} + 351024 q^{4} + 347991 q^{5} + 16302972 q^{6} + 31314630 q^{7} + 67892640 q^{8} + 377752851 q^{9}+O(q^{10}) $ 6 * q + 11865 * q^3 + 351024 * q^4 + 347991 * q^5 + 16302972 * q^6 + 31314630 * q^7 + 67892640 * q^8 + 377752851 * q^9	\( 6 q + 11865 q^{3} + 351024 q^{4} + 347991 q^{5} + 16302972 q^{6} + 31314630 q^{7} + 67892640 q^{8} + 377752851 q^{9} + 144090324 q^{10} + 4513961760 q^{12} + 7119892710 q^{13} - 1766662392 q^{14} - 19550343855 q^{15} + 23307418752 q^{16} - 14847960120 q^{17} + 207033381900 q^{18} + 96642651252 q^{19} - 175684379136 q^{20} + 541163623038 q^{21} - 836632018455 q^{23} + 3775860484704 q^{24} - 2511064443309 q^{25} - 61179995016 q^{26} - 2108694116025 q^{27} + 7550013575040 q^{28} + 6178015368186 q^{29} + 4599681241020 q^{30} + 636857332041 q^{31} + 34717785780480 q^{32} - 22577342383344 q^{34} - 7652188071450 q^{35} + 92057284438416 q^{36} - 1233417487215 q^{37} + 99623910494640 q^{38} - 22828491583500 q^{39} - 139157596758432 q^{40} + 43234265835054 q^{41} + 244981786044840 q^{42} - 145352338376130 q^{43} + 63552616359372 q^{45} + 18844814685660 q^{46} + 432778220316120 q^{47} + 832919384734080 q^{48} - 55920612074934 q^{49} - 368804230203396 q^{50} - 562418817395262 q^{51} + 26\!\cdots\!80 q^{52}+ \cdots - 65\!\cdots\!00 q^{98}+O(q^{100}) \) 6 * q + 11865 * q^3 + 351024 * q^4 + 347991 * q^5 + 16302972 * q^6 + 31314630 * q^7 + 67892640 * q^8 + 377752851 * q^9 + 144090324 * q^10 + 4513961760 * q^12 + 7119892710 * q^13 - 1766662392 * q^14 - 19550343855 * q^15 + 23307418752 * q^16 - 14847960120 * q^17 + 207033381900 * q^18 + 96642651252 * q^19 - 175684379136 * q^20 + 541163623038 * q^21 - 836632018455 * q^23 + 3775860484704 * q^24 - 2511064443309 * q^25 - 61179995016 * q^26 - 2108694116025 * q^27 + 7550013575040 * q^28 + 6178015368186 * q^29 + 4599681241020 * q^30 + 636857332041 * q^31 + 34717785780480 * q^32 - 22577342383344 * q^34 - 7652188071450 * q^35 + 92057284438416 * q^36 - 1233417487215 * q^37 + 99623910494640 * q^38 - 22828491583500 * q^39 - 139157596758432 * q^40 + 43234265835054 * q^41 + 244981786044840 * q^42 - 145352338376130 * q^43 + 63552616359372 * q^45 + 18844814685660 * q^46 + 432778220316120 * q^47 + 832919384734080 * q^48 - 55920612074934 * q^49 - 368804230203396 * q^50 - 562418817395262 * q^51 + 2663217125395680 * q^52 - 1098463886245560 * q^53 + 1564527203783460 * q^54 + 164642910803520 * q^56 + 2438041510213920 * q^57 - 688806293721720 * q^58 - 1354427895404325 * q^59 - 4634689473664800 * q^60 + 4680147076091550 * q^61 - 327068618103780 * q^62 + 2437011498083580 * q^63 + 4119359220996096 * q^64 - 1694576167351992 * q^65 - 1422221695594785 * q^67 - 13013443225631520 * q^68 + 4340393479871841 * q^69 + 7242718895843400 * q^70 - 241024392605325 * q^71 + 15782344028415360 * q^72 - 16535978199148590 * q^73 - 35346993162556884 * q^74 + 2786718509400840 * q^75 - 874633109814912 * q^76 + 96469292799543120 * q^78 + 11287689680330886 * q^79 - 2948966505238656 * q^80 - 27976963515226290 * q^81 + 57330488162524920 * q^82 + 38342699617260150 * q^83 + 22250959697175168 * q^84 + 78911850100793814 * q^85 - 100218510690927384 * q^86 + 83644469453943720 * q^87 - 72526069382037411 * q^89 - 96101996279722272 * q^90 - 57857689770132840 * q^91 + 21581518865280480 * q^92 - 233344518597393495 * q^93 - 27995732830541280 * q^94 + 146785535344378824 * q^95 + 167024768158235904 * q^96 - 3850252891123905 * q^97 - 65640418784062800 * 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 $

$2$	−451.956	−1.24836	−0.624181	−	0.781279i	$-0.714567\pi$
$2$	−451.956	−1.24836	−0.624181	+	0.781279i	$0.714567\pi$
$3$	8582.51	0.755238	0.377619	−	0.925961i	$-0.376743\pi$
$3$	8582.51	0.755238	0.377619	+	0.925961i	$0.376743\pi$
$4$	73191.9	0.558410
$5$	−1.00486e6	−1.15043	−0.575215	−	0.818003i	$-0.695081\pi$
$5$	−1.00486e6	−1.15043	−0.575215	+	0.818003i	$0.695081\pi$
$6$	−3.87891e6	−0.942811
$7$	1.88093e7	1.23322	0.616609	−	0.787269i	$-0.288506\pi$
$7$	1.88093e7	1.23322	0.616609	+	0.787269i	$0.288506\pi$
$8$	2.61592e7	0.551265
$9$	−5.54807e7	−0.429616
$10$	4.54152e8	1.43615
$11$	0	0
$11$	0	0
$12$	6.28170e8	0.421732
$13$	−7.84654e8	−0.266784	−0.133392	−	0.991063i	$-0.542587\pi$
$13$	−7.84654e8	−0.266784	−0.133392	+	0.991063i	$0.542587\pi$
$14$	−8.50098e9	−1.53950
$15$	−8.62421e9	−0.868848
$16$	−2.14162e10	−1.24659
$17$	−3.52778e10	−1.22655	−0.613275	−	0.789870i	$-0.710148\pi$
$17$	−3.52778e10	−1.22655	−0.613275	+	0.789870i	$0.710148\pi$
$18$	2.50748e10	0.536317
$19$	−1.01332e11	−1.36881	−0.684403	−	0.729103i	$-0.739937\pi$
$19$	−1.01332e11	−1.36881	−0.684403	+	0.729103i	$0.739937\pi$
$20$	−7.35475e10	−0.642411
$21$	1.61431e11	0.931373
$22$	0	0
$23$	−9.68328e9	−0.0257831	−0.0128916	−	0.999917i	$-0.504104\pi$
$23$	−9.68328e9	−0.0257831	−0.0128916	+	0.999917i	$0.504104\pi$
$24$	2.24512e11	0.416336
$25$	2.46801e11	0.323488
$26$	3.54629e11	0.333043
$27$	−1.58451e12	−1.07970
$28$	1.37669e12	0.688642
$29$	5.24329e12	1.94635	0.973174	−	0.230069i	$-0.0738951\pi$
$29$	5.24329e12	1.94635	0.973174	+	0.230069i	$0.0738951\pi$
$30$	3.89776e12	1.08464
$31$	−2.88452e11	−0.0607433	−0.0303717	−	0.999539i	$-0.509669\pi$
$31$	−2.88452e11	−0.0607433	−0.0303717	+	0.999539i	$0.509669\pi$
$32$	6.25044e12	1.00493
$33$	0	0
$34$	1.59440e13	1.53118
$35$	−1.89007e13	−1.41873
$36$	−4.06074e12	−0.239902
$37$	−1.56299e13	−0.731544	−0.365772	−	0.930705i	$-0.619195\pi$
$37$	−1.56299e13	−0.731544	−0.365772	+	0.930705i	$0.619195\pi$
$38$	4.57977e13	1.70877
$39$	−6.73430e12	−0.201485
$40$	−2.62863e13	−0.634191
$41$	−8.27593e13	−1.61865	−0.809327	−	0.587358i	$-0.800168\pi$
$41$	−8.27593e13	−1.61865	−0.809327	+	0.587358i	$0.800168\pi$
$42$	−7.29598e13	−1.16269
$43$	5.50702e13	0.718514	0.359257	−	0.933239i	$-0.383030\pi$
$43$	5.50702e13	0.718514	0.359257	+	0.933239i	$0.383030\pi$
$44$	0	0
$45$	5.57502e13	0.494243
$46$	4.37641e12	0.0321867
$47$	8.65871e12	0.0530422	0.0265211	−	0.999648i	$-0.491557\pi$
$47$	8.65871e12	0.0530422	0.0265211	+	0.999648i	$0.491557\pi$
$48$	−1.83805e14	−0.941470
$49$	1.21161e14	0.520828
$50$	−1.11543e14	−0.403830
$51$	−3.02772e14	−0.926337
$52$	−5.74303e13	−0.148975
$53$	−2.29179e14	−0.505627	−0.252814	−	0.967515i	$-0.581356\pi$
$53$	−2.29179e14	−0.505627	−0.252814	+	0.967515i	$0.581356\pi$
$54$	7.16128e14	1.34786
$55$	0	0
$56$	4.92038e14	0.679830
$57$	−8.69685e14	−1.03377
$58$	−2.36973e15	−2.42975
$59$	7.57251e14	0.671426	0.335713	−	0.941964i	$-0.391023\pi$
$59$	7.57251e14	0.671426	0.335713	+	0.941964i	$0.391023\pi$
$60$	−6.31222e14	−0.485173
$61$	2.29409e15	1.53217	0.766084	−	0.642740i	$-0.222202\pi$
$61$	2.29409e15	1.53217	0.766084	+	0.642740i	$0.222202\pi$
$62$	1.30367e14	0.0758297
$63$	−1.04355e15	−0.529810
$64$	−1.78544e13	−0.00792894
$65$	7.88466e14	0.306916
$66$	0	0
$67$	−1.57751e15	−0.474608	−0.237304	−	0.971435i	$-0.576264\pi$
$67$	−1.57751e15	−0.474608	−0.237304	+	0.971435i	$0.576264\pi$
$68$	−2.58205e15	−0.684918
$69$	−8.31068e13	−0.0194724
$70$	8.54229e15	1.77109
$71$	−6.00695e15	−1.10397	−0.551986	−	0.833853i	$-0.686130\pi$
$71$	−6.00695e15	−1.10397	−0.551986	+	0.833853i	$0.686130\pi$
$72$	−1.45133e15	−0.236832
$73$	−1.02546e16	−1.48824	−0.744121	−	0.668045i	$-0.767131\pi$
$73$	−1.02546e16	−1.48824	−0.744121	+	0.668045i	$0.767131\pi$
$74$	7.06400e15	0.913232
$75$	2.11818e15	0.244310
$76$	−7.41670e15	−0.764355
$77$	0	0
$78$	3.04360e15	0.251527
$79$	1.74050e15	0.129075	0.0645376	−	0.997915i	$-0.479443\pi$
$79$	1.74050e15	0.129075	0.0645376	+	0.997915i	$0.479443\pi$
$80$	2.15203e16	1.43411
$81$	−6.43429e15	−0.385814
$82$	3.74035e16	2.02067
$83$	2.13414e16	1.04006	0.520032	−	0.854147i	$-0.325920\pi$
$83$	2.13414e16	1.04006	0.520032	+	0.854147i	$0.325920\pi$
$84$	1.18155e16	0.520088
$85$	3.54492e16	1.41106
$86$	−2.48893e16	−0.896966
$87$	4.50006e16	1.46996
$88$	0	0
$89$	−1.90853e16	−0.513906	−0.256953	−	0.966424i	$-0.582719\pi$
$89$	−1.90853e16	−0.513906	−0.256953	+	0.966424i	$0.582719\pi$
$90$	−2.51966e16	−0.616994
$91$	−1.47588e16	−0.329003
$92$	−7.08737e14	−0.0143976
$93$	−2.47564e15	−0.0458756
$94$	−3.91335e15	−0.0662159
$95$	1.01825e17	1.57472
$96$	5.36445e16	0.758961
$97$	1.03763e17	1.34426	0.672130	−	0.740433i	$-0.265379\pi$
$97$	1.03763e17	1.34426	0.672130	+	0.740433i	$0.265379\pi$
$98$	−5.47592e16	−0.650183
$99$	0	0
$100$	1.80639e16	0.180639
$101$	−9.97565e16	−0.916662	−0.458331	−	0.888781i	$-0.651553\pi$
$101$	−9.97565e16	−0.916662	−0.458331	+	0.888781i	$0.651553\pi$
$102$	1.36839e17	1.15640
$103$	−1.39113e17	−1.08206	−0.541029	−	0.841004i	$-0.681965\pi$
$103$	−1.39113e17	−1.08206	−0.541029	+	0.841004i	$0.681965\pi$
$104$	−2.05259e16	−0.147068
$105$	−1.62216e17	−1.07148
$106$	1.03579e17	0.631206
$107$	−7.93012e16	−0.446188	−0.223094	−	0.974797i	$-0.571616\pi$
$107$	−7.93012e16	−0.446188	−0.223094	+	0.974797i	$0.571616\pi$
$108$	−1.15973e17	−0.602915
$109$	3.86848e16	0.185958	0.0929790	−	0.995668i	$-0.470361\pi$
$109$	3.86848e16	0.185958	0.0929790	+	0.995668i	$0.470361\pi$
$110$	0	0
$111$	−1.34143e17	−0.552489
$112$	−4.02825e17	−1.53732
$113$	−2.75861e17	−0.976165	−0.488083	−	0.872797i	$-0.662303\pi$
$113$	−2.75861e17	−0.976165	−0.488083	+	0.872797i	$0.662303\pi$
$114$	3.93059e17	1.29053
$115$	9.73032e15	0.0296617
$116$	3.83766e17	1.08686
$117$	4.35331e16	0.114615
$118$	−3.42244e17	−0.838183
$119$	−6.63551e17	−1.51260
$120$	−2.25603e17	−0.478965
$121$	0	0
$122$	−1.03683e18	−1.91270
$123$	−7.10283e17	−1.22247
$124$	−2.11123e16	−0.0339197
$125$	5.18646e17	0.778280
$126$	4.71640e17	0.661396
$127$	−1.20013e18	−1.57361	−0.786804	−	0.617203i	$-0.788266\pi$
$127$	−1.20013e18	−1.57361	−0.786804	+	0.617203i	$0.788266\pi$
$128$	−8.11188e17	−0.995032
$129$	4.72641e17	0.542648
$130$	−3.56352e17	−0.383142
$131$	1.76565e18	1.77868	0.889342	−	0.457242i	$-0.151163\pi$
$131$	1.76565e18	1.77868	0.889342	+	0.457242i	$0.151163\pi$
$132$	0	0
$133$	−1.90599e18	−1.68804
$134$	7.12963e17	0.592484
$135$	1.59221e18	1.24212
$136$	−9.22839e17	−0.676154
$137$	−2.84167e18	−1.95636	−0.978179	−	0.207765i	$-0.933381\pi$
$137$	−2.84167e18	−1.95636	−0.978179	+	0.207765i	$0.933381\pi$
$138$	3.75606e16	0.0243086
$139$	1.12722e18	0.686095	0.343047	−	0.939318i	$-0.388541\pi$
$139$	1.12722e18	0.686095	0.343047	+	0.939318i	$0.388541\pi$
$140$	−1.38338e18	−0.792233
$141$	7.43134e16	0.0400594
$142$	2.71488e18	1.37816
$143$	0	0
$144$	1.18819e18	0.535554
$145$	−5.26876e18	−2.23914
$146$	4.63461e18	1.85787
$147$	1.03986e18	0.393349
$148$	−1.14398e18	−0.408501
$149$	−3.19677e18	−1.07802	−0.539011	−	0.842299i	$-0.681202\pi$
$149$	−3.19677e18	−1.07802	−0.539011	+	0.842299i	$0.681202\pi$
$150$	−9.57322e17	−0.304988
$151$	3.97621e16	0.0119720	0.00598598	−	0.999982i	$-0.498095\pi$
$151$	3.97621e16	0.0119720	0.00598598	+	0.999982i	$0.498095\pi$
$152$	−2.65077e18	−0.754575
$153$	1.95723e18	0.526945
$154$	0	0
$155$	2.89853e17	0.0698809
$156$	−4.92896e17	−0.112511
$157$	3.38286e18	0.731371	0.365685	−	0.930739i	$-0.380835\pi$
$157$	3.38286e18	0.731371	0.365685	+	0.930739i	$0.380835\pi$
$158$	−7.86627e17	−0.161133
$159$	−1.96693e18	−0.381869
$160$	−6.28081e18	−1.15610
$161$	−1.82136e17	−0.0317962
$162$	2.90801e18	0.481636
$163$	−1.72544e18	−0.271209	−0.135604	−	0.990763i	$-0.543298\pi$
$163$	−1.72544e18	−0.271209	−0.135604	+	0.990763i	$0.543298\pi$
$164$	−6.05731e18	−0.903873
$165$	0	0
$166$	−9.64538e18	−1.29838
$167$	3.12295e18	0.399461	0.199731	−	0.979851i	$-0.435993\pi$
$167$	3.12295e18	0.399461	0.199731	+	0.979851i	$0.435993\pi$
$168$	4.22292e18	0.513433
$169$	−8.03473e18	−0.928826
$170$	−1.60214e19	−1.76151
$171$	5.62198e18	0.588061
$172$	4.03069e18	0.401225
$173$	−1.60722e19	−1.52294	−0.761470	−	0.648200i	$-0.775522\pi$
$173$	−1.60722e19	−1.52294	−0.761470	+	0.648200i	$0.775522\pi$
$174$	−2.03383e19	−1.83504
$175$	4.64217e18	0.398931
$176$	0	0
$177$	6.49912e18	0.507086
$178$	8.62571e18	0.641542
$179$	2.09463e19	1.48544	0.742722	−	0.669600i	$-0.233534\pi$
$179$	2.09463e19	1.48544	0.742722	+	0.669600i	$0.233534\pi$
$180$	4.08047e18	0.275990
$181$	2.74622e18	0.177201	0.0886007	−	0.996067i	$-0.471761\pi$
$181$	2.74622e18	0.177201	0.0886007	+	0.996067i	$0.471761\pi$
$182$	6.67033e18	0.410715
$183$	1.96890e19	1.15715
$184$	−2.53307e17	−0.0142133
$185$	1.57058e19	0.841589
$186$	1.11888e18	0.0572695
$187$	0	0
$188$	6.33747e17	0.0296193
$189$	−2.98036e19	−1.33151
$190$	−4.60202e19	−1.96582
$191$	4.10590e19	1.67735	0.838677	−	0.544629i	$-0.183329\pi$
$191$	4.10590e19	1.67735	0.838677	+	0.544629i	$0.183329\pi$
$192$	−1.53236e17	−0.00598824
$193$	−2.74114e19	−1.02493	−0.512465	−	0.858708i	$-0.671267\pi$
$193$	−2.74114e19	−1.02493	−0.512465	+	0.858708i	$0.671267\pi$
$194$	−4.68964e19	−1.67813
$195$	6.76702e18	0.231794
$196$	8.86797e18	0.290836
$197$	3.97528e19	1.24855	0.624273	−	0.781206i	$-0.285395\pi$
$197$	3.97528e19	1.24855	0.624273	+	0.781206i	$0.285395\pi$
$198$	0	0
$199$	−2.90850e19	−0.838336	−0.419168	−	0.907909i	$-0.637678\pi$
$199$	−2.90850e19	−0.838336	−0.419168	+	0.907909i	$0.637678\pi$
$200$	6.45614e18	0.178327
$201$	−1.35390e19	−0.358442
$202$	4.50855e19	1.14433
$203$	9.86227e19	2.40027
$204$	−2.21604e19	−0.517276
$205$	8.31614e19	1.86215
$206$	6.28728e19	1.35080
$207$	5.37235e17	0.0110768
$208$	1.68043e19	0.332570
$209$	0	0
$210$	7.33143e19	1.33759
$211$	9.39405e19	1.64608	0.823042	−	0.567980i	$-0.192275\pi$
$211$	9.39405e19	1.64608	0.823042	+	0.567980i	$0.192275\pi$
$212$	−1.67741e19	−0.282347
$213$	−5.15547e19	−0.833762
$214$	3.58406e19	0.557004
$215$	−5.53378e19	−0.826599
$216$	−4.14496e19	−0.595200
$217$	−5.42558e18	−0.0749098
$218$	−1.74838e19	−0.232143
$219$	−8.80100e19	−1.12398
$220$	0	0
$221$	2.76808e19	0.327224
$222$	6.06268e19	0.689707
$223$	−1.58383e20	−1.73427	−0.867137	−	0.498069i	$-0.834042\pi$
$223$	−1.58383e20	−1.73427	−0.867137	+	0.498069i	$0.834042\pi$
$224$	1.17567e20	1.23930
$225$	−1.36927e19	−0.138975
$226$	1.24677e20	1.21861
$227$	−3.23522e19	−0.304568	−0.152284	−	0.988337i	$-0.548663\pi$
$227$	−3.23522e19	−0.304568	−0.152284	+	0.988337i	$0.548663\pi$
$228$	−6.36539e19	−0.577270
$229$	−1.05060e20	−0.917989	−0.458994	−	0.888439i	$-0.651790\pi$
$229$	−1.05060e20	−0.917989	−0.458994	+	0.888439i	$0.651790\pi$
$230$	−4.39767e18	−0.0370285
$231$	0	0
$232$	1.37160e20	1.07295
$233$	2.12356e20	1.60154	0.800771	−	0.598971i	$-0.204424\pi$
$233$	2.12356e20	1.60154	0.800771	+	0.598971i	$0.204424\pi$
$234$	−1.96750e19	−0.143081
$235$	−8.70078e18	−0.0610213
$236$	5.54247e19	0.374931
$237$	1.49378e19	0.0974824
$238$	2.99896e20	1.88828
$239$	1.92754e20	1.17118	0.585588	−	0.810609i	$-0.300864\pi$
$239$	1.92754e20	1.17118	0.585588	+	0.810609i	$0.300864\pi$
$240$	1.84698e20	1.08310
$241$	−6.22852e19	−0.352566	−0.176283	−	0.984340i	$-0.556407\pi$
$241$	−6.22852e19	−0.352566	−0.176283	+	0.984340i	$0.556407\pi$
$242$	0	0
$243$	1.49402e20	0.788319
$244$	1.67909e20	0.855578
$245$	−1.21749e20	−0.599176
$246$	3.21016e20	1.52608
$247$	7.95107e19	0.365176
$248$	−7.54567e18	−0.0334856
$249$	1.83163e20	0.785495
$250$	−2.34405e20	−0.971575
$251$	2.96523e20	1.18804	0.594020	−	0.804450i	$-0.297540\pi$
$251$	2.96523e20	1.18804	0.594020	+	0.804450i	$0.297540\pi$
$252$	−7.63798e19	−0.295851
$253$	0	0
$254$	5.42405e20	1.96443
$255$	3.04243e20	1.06568
$256$	3.68961e20	1.25009
$257$	2.36864e20	0.776367	0.388184	−	0.921582i	$-0.373103\pi$
$257$	2.36864e20	0.776367	0.388184	+	0.921582i	$0.373103\pi$
$258$	−2.13613e20	−0.677422
$259$	−2.93987e20	−0.902153
$260$	5.77093e19	0.171385
$261$	−2.90901e20	−0.836183
$262$	−7.97996e20	−2.22044
$263$	−7.13390e19	−0.192178	−0.0960889	−	0.995373i	$-0.530633\pi$
$263$	−7.13390e19	−0.192178	−0.0960889	+	0.995373i	$0.530633\pi$
$264$	0	0
$265$	2.30293e20	0.581688
$266$	8.61424e20	2.10728
$267$	−1.63800e20	−0.388121
$268$	−1.15461e20	−0.265026
$269$	1.55200e20	0.345141	0.172570	−	0.984997i	$-0.444793\pi$
$269$	1.55200e20	0.345141	0.172570	+	0.984997i	$0.444793\pi$
$270$	−7.19608e20	−1.55061
$271$	−7.51664e20	−1.56959	−0.784793	−	0.619758i	$-0.787231\pi$
$271$	−7.51664e20	−1.56959	−0.784793	+	0.619758i	$0.787231\pi$
$272$	7.55516e20	1.52900
$273$	−1.26668e20	−0.248475
$274$	1.28431e21	2.44224
$275$	0	0
$276$	−6.08275e18	−0.0108736
$277$	3.88953e20	0.674247	0.337124	−	0.941460i	$-0.390546\pi$
$277$	3.88953e20	0.674247	0.337124	+	0.941460i	$0.390546\pi$
$278$	−5.09455e20	−0.856495
$279$	1.60035e19	0.0260963
$280$	−4.94428e20	−0.782096
$281$	−5.61082e20	−0.861039	−0.430519	−	0.902581i	$-0.641670\pi$
$281$	−5.61082e20	−0.861039	−0.430519	+	0.902581i	$0.641670\pi$
$282$	−3.35864e19	−0.0500087
$283$	−9.58929e19	−0.138548	−0.0692742	−	0.997598i	$-0.522068\pi$
$283$	−9.58929e19	−0.138548	−0.0692742	+	0.997598i	$0.522068\pi$
$284$	−4.39660e20	−0.616469
$285$	8.73911e20	1.18928
$286$	0	0
$287$	−1.55665e21	−1.99615
$288$	−3.46779e20	−0.431734
$289$	4.17280e20	0.504424
$290$	2.38125e21	2.79526
$291$	8.90549e20	1.01524
$292$	−7.50552e20	−0.831049
$293$	8.64067e20	0.929336	0.464668	−	0.885485i	$-0.346174\pi$
$293$	8.64067e20	0.929336	0.464668	+	0.885485i	$0.346174\pi$
$294$	−4.69971e20	−0.491042
$295$	−7.60931e20	−0.772428
$296$	−4.08865e20	−0.403274
$297$	0	0
$298$	1.44480e21	1.34576
$299$	7.59802e18	0.00687852
$300$	1.55033e20	0.136425
$301$	1.03583e21	0.886084
$302$	−1.79707e19	−0.0149453
$303$	−8.56161e20	−0.692298
$304$	2.17015e21	1.70634
$305$	−2.30523e21	−1.76265
$306$	−8.84583e20	−0.657819
$307$	5.03598e20	0.364257	0.182129	−	0.983275i	$-0.441701\pi$
$307$	5.03598e20	0.364257	0.182129	+	0.983275i	$0.441701\pi$
$308$	0	0
$309$	−1.19394e21	−0.817211
$310$	−1.31001e20	−0.0872367
$311$	6.03318e20	0.390915	0.195458	−	0.980712i	$-0.437381\pi$
$311$	6.03318e20	0.390915	0.195458	+	0.980712i	$0.437381\pi$
$312$	−1.76164e20	−0.111072
$313$	−2.14351e21	−1.31522	−0.657612	−	0.753357i	$-0.728433\pi$
$313$	−2.14351e21	−1.31522	−0.657612	+	0.753357i	$0.728433\pi$
$314$	−1.52890e21	−0.913016
$315$	1.04862e21	0.609509
$316$	1.27390e20	0.0720768
$317$	−5.39361e20	−0.297082	−0.148541	−	0.988906i	$-0.547458\pi$
$317$	−5.39361e20	−0.297082	−0.148541	+	0.988906i	$0.547458\pi$
$318$	8.88967e20	0.476711
$319$	0	0
$320$	1.79411e19	0.00912169
$321$	−6.80603e20	−0.336978
$322$	8.23174e19	0.0396932
$323$	3.57478e21	1.67891
$324$	−4.70938e20	−0.215442
$325$	−1.93654e20	−0.0863013
$326$	7.79820e20	0.338567
$327$	3.32013e20	0.140443
$328$	−2.16492e21	−0.892307
$329$	1.62865e20	0.0654126
$330$	0	0
$331$	−2.99010e20	−0.114064	−0.0570318	−	0.998372i	$-0.518164\pi$
$331$	−2.99010e20	−0.114064	−0.0570318	+	0.998372i	$0.518164\pi$
$332$	1.56202e21	0.580782
$333$	8.67155e20	0.314283
$334$	−1.41143e21	−0.498673
$335$	1.58517e21	0.546003
$336$	−3.45725e21	−1.16104
$337$	1.38778e21	0.454431	0.227215	−	0.973845i	$-0.427038\pi$
$337$	1.38778e21	0.454431	0.227215	+	0.973845i	$0.427038\pi$
$338$	3.63134e21	1.15951
$339$	−2.36758e21	−0.737237
$340$	2.59459e21	0.787949
$341$	0	0
$342$	−2.54089e21	−0.734114
$343$	−2.09668e21	−0.590924
$344$	1.44059e21	0.396091
$345$	8.35106e19	0.0224016
$346$	7.26391e21	1.90118
$347$	3.98529e21	1.01779	0.508896	−	0.860828i	$-0.330054\pi$
$347$	3.98529e21	1.01779	0.508896	+	0.860828i	$0.330054\pi$
$348$	3.29368e21	0.820838
$349$	5.59640e21	1.36111	0.680554	−	0.732698i	$-0.261739\pi$
$349$	5.59640e21	1.36111	0.680554	+	0.732698i	$0.261739\pi$
$350$	−2.09806e21	−0.498011
$351$	1.24329e21	0.288046
$352$	0	0
$353$	5.12985e21	1.13245	0.566225	−	0.824250i	$-0.308403\pi$
$353$	5.12985e21	1.13245	0.566225	+	0.824250i	$0.308403\pi$
$354$	−2.93731e21	−0.633027
$355$	6.03614e21	1.27004
$356$	−1.39689e21	−0.286970
$357$	−5.69493e21	−1.14238
$358$	−9.46679e21	−1.85437
$359$	1.04724e21	0.200328	0.100164	−	0.994971i	$-0.468063\pi$
$359$	1.04724e21	0.200328	0.100164	+	0.994971i	$0.468063\pi$
$360$	1.45838e21	0.272459
$361$	4.78784e21	0.873633
$362$	−1.24117e21	−0.221212
$363$	0	0
$364$	−1.08023e21	−0.183718
$365$	1.03044e22	1.71212
$366$	−8.89857e21	−1.44454
$367$	8.20181e21	1.30091	0.650456	−	0.759544i	$-0.274578\pi$
$367$	8.20181e21	1.30091	0.650456	+	0.759544i	$0.274578\pi$
$368$	2.07379e20	0.0321410
$369$	4.59154e21	0.695400
$370$	−7.09832e21	−1.05061
$371$	−4.31071e21	−0.623549
$372$	−1.81197e20	−0.0256174
$373$	1.19732e22	1.65458	0.827288	−	0.561778i	$-0.189883\pi$
$373$	1.19732e22	1.65458	0.827288	+	0.561778i	$0.189883\pi$
$374$	0	0
$375$	4.45128e21	0.587786
$376$	2.26505e20	0.0292403
$377$	−4.11416e21	−0.519254
$378$	1.34699e22	1.66220
$379$	−3.28643e21	−0.396544	−0.198272	−	0.980147i	$-0.563533\pi$
$379$	−3.28643e21	−0.396544	−0.198272	+	0.980147i	$0.563533\pi$
$380$	7.45274e21	0.879337
$381$	−1.03001e22	−1.18845
$382$	−1.85569e22	−2.09395
$383$	1.28496e22	1.41808	0.709040	−	0.705169i	$-0.249129\pi$
$383$	1.28496e22	1.41808	0.709040	+	0.705169i	$0.249129\pi$
$384$	−6.96203e21	−0.751485
$385$	0	0
$386$	1.23887e22	1.27948
$387$	−3.05533e21	−0.308685
$388$	7.59462e21	0.750649
$389$	−8.91336e21	−0.861926	−0.430963	−	0.902370i	$-0.641826\pi$
$389$	−8.91336e21	−0.861926	−0.430963	+	0.902370i	$0.641826\pi$
$390$	−3.05839e21	−0.289364
$391$	3.41604e20	0.0316243
$392$	3.16947e21	0.287114
$393$	1.51537e22	1.34333
$394$	−1.79665e22	−1.55864
$395$	−1.74895e21	−0.148492
$396$	0	0
$397$	−1.48314e22	−1.20632	−0.603159	−	0.797621i	$-0.706092\pi$
$397$	−1.48314e22	−1.20632	−0.603159	+	0.797621i	$0.706092\pi$
$398$	1.31451e22	1.04655
$399$	−1.63582e22	−1.27487
$400$	−5.28556e21	−0.403256
$401$	1.53764e22	1.14849	0.574245	−	0.818684i	$-0.305296\pi$
$401$	1.53764e22	1.14849	0.574245	+	0.818684i	$0.305296\pi$
$402$	6.11901e21	0.447466
$403$	2.26335e20	0.0162053
$404$	−7.30137e21	−0.511873
$405$	6.46555e21	0.443852
$406$	−4.45731e22	−2.99641
$407$	0	0
$408$	−7.92028e21	−0.510657
$409$	1.79961e22	1.13640	0.568200	−	0.822890i	$-0.307640\pi$
$409$	1.79961e22	1.13640	0.568200	+	0.822890i	$0.307640\pi$
$410$	−3.75853e22	−2.32464
$411$	−2.43886e22	−1.47752
$412$	−1.01819e22	−0.604232
$413$	1.42434e22	0.828015
$414$	−2.42806e20	−0.0138279
$415$	−2.14451e22	−1.19652
$416$	−4.90443e21	−0.268099
$417$	9.67440e21	0.518164
$418$	0	0
$419$	2.45038e22	1.26013	0.630063	−	0.776544i	$-0.283029\pi$
$419$	2.45038e22	1.26013	0.630063	+	0.776544i	$0.283029\pi$
$420$	−1.18729e22	−0.598325
$421$	1.71489e22	0.846910	0.423455	−	0.905917i	$-0.360817\pi$
$421$	1.71489e22	0.846910	0.423455	+	0.905917i	$0.360817\pi$
$422$	−4.24569e22	−2.05491
$423$	−4.80391e20	−0.0227878
$424$	−5.99516e21	−0.278734
$425$	−8.70660e21	−0.396774
$426$	2.33005e22	1.04084
$427$	4.31503e22	1.88950
$428$	−5.80421e21	−0.249156
$429$	0	0
$430$	2.50102e22	1.03190
$431$	8.10910e21	0.328032	0.164016	−	0.986458i	$-0.447555\pi$
$431$	8.10910e21	0.328032	0.164016	+	0.986458i	$0.447555\pi$
$432$	3.39342e22	1.34594
$433$	9.62215e21	0.374218	0.187109	−	0.982339i	$-0.440088\pi$
$433$	9.62215e21	0.374218	0.187109	+	0.982339i	$0.440088\pi$
$434$	2.45212e21	0.0935146
$435$	−4.52192e22	−1.69108
$436$	2.83141e21	0.103841
$437$	9.81228e20	0.0352921
$438$	3.97766e22	1.40313
$439$	−1.06429e22	−0.368225	−0.184112	−	0.982905i	$-0.558941\pi$
$439$	−1.06429e22	−0.368225	−0.184112	+	0.982905i	$0.558941\pi$
$440$	0	0
$441$	−6.72207e21	−0.223756
$442$	−1.25105e22	−0.408494
$443$	1.01228e22	0.324241	0.162121	−	0.986771i	$-0.448167\pi$
$443$	1.01228e22	0.324241	0.162121	+	0.986771i	$0.448167\pi$
$444$	−9.81821e21	−0.308516
$445$	1.91780e22	0.591213
$446$	7.15822e22	2.16500
$447$	−2.74363e22	−0.814163
$448$	−3.35829e20	−0.00977812
$449$	−7.84026e21	−0.223994	−0.111997	−	0.993709i	$-0.535725\pi$
$449$	−7.84026e21	−0.223994	−0.111997	+	0.993709i	$0.535725\pi$
$450$	6.18850e21	0.173492
$451$	0	0
$452$	−2.01908e22	−0.545100
$453$	3.41259e20	0.00904167
$454$	1.46218e22	0.380212
$455$	1.48305e22	0.378494
$456$	−2.27503e22	−0.569883
$457$	5.69492e22	1.40023	0.700116	−	0.714029i	$-0.253131\pi$
$457$	5.69492e22	1.40023	0.700116	+	0.714029i	$0.253131\pi$
$458$	4.74826e22	1.14598
$459$	5.58980e22	1.32431
$460$	7.12181e20	0.0165634
$461$	−3.51246e22	−0.801961	−0.400980	−	0.916087i	$-0.631330\pi$
$461$	−3.51246e22	−0.801961	−0.400980	+	0.916087i	$0.631330\pi$
$462$	0	0
$463$	−6.52096e22	−1.43507	−0.717535	−	0.696522i	$-0.754730\pi$
$463$	−6.52096e22	−1.43507	−0.717535	+	0.696522i	$0.754730\pi$
$464$	−1.12291e23	−2.42630
$465$	2.48767e21	0.0527767
$466$	−9.59753e22	−1.99931
$467$	6.05067e22	1.23768	0.618842	−	0.785516i	$-0.287602\pi$
$467$	6.05067e22	1.23768	0.618842	+	0.785516i	$0.287602\pi$
$468$	3.18627e21	0.0640019
$469$	−2.96719e22	−0.585296
$470$	3.93237e21	0.0761767
$471$	2.90335e22	0.552359
$472$	1.98091e22	0.370133
$473$	0	0
$474$	−6.75123e21	−0.121693
$475$	−2.50090e22	−0.442792
$476$	−4.85666e22	−0.844653
$477$	1.27150e22	0.217226
$478$	−8.71164e22	−1.46205
$479$	4.91851e22	0.810927	0.405464	−	0.914111i	$-0.367110\pi$
$479$	4.91851e22	0.810927	0.405464	+	0.914111i	$0.367110\pi$
$480$	−5.39051e22	−0.873131
$481$	1.22640e22	0.195164
$482$	2.81501e22	0.440130
$483$	−1.56318e21	−0.0240137
$484$	0	0
$485$	−1.04267e23	−1.54648
$486$	−6.75229e22	−0.984108
$487$	6.39329e22	0.915647	0.457824	−	0.889043i	$-0.348629\pi$
$487$	6.39329e22	0.915647	0.457824	+	0.889043i	$0.348629\pi$
$488$	6.00116e22	0.844630
$489$	−1.48086e22	−0.204827
$490$	5.50252e22	0.747989
$491$	−9.66330e22	−1.29102	−0.645509	−	0.763752i	$-0.723355\pi$
$491$	−9.66330e22	−1.29102	−0.645509	+	0.763752i	$0.723355\pi$
$492$	−5.19870e22	−0.682639
$493$	−1.84971e23	−2.38729
$494$	−3.59353e22	−0.455872
$495$	0	0
$496$	6.17754e21	0.0757219
$497$	−1.12987e23	−1.36144
$498$	−8.27816e22	−0.980583
$499$	−2.04716e22	−0.238395	−0.119198	−	0.992871i	$-0.538032\pi$
$499$	−2.04716e22	−0.238395	−0.119198	+	0.992871i	$0.538032\pi$
$500$	3.79607e22	0.434599
$501$	2.68027e22	0.301688
$502$	−1.34015e23	−1.48311
$503$	−2.05666e21	−0.0223787	−0.0111894	−	0.999937i	$-0.503562\pi$
$503$	−2.05666e21	−0.0223787	−0.0111894	+	0.999937i	$0.503562\pi$
$504$	−2.72986e22	−0.292066
$505$	1.00241e23	1.05456
$506$	0	0
$507$	−6.89582e22	−0.701485
$508$	−8.78397e22	−0.878718
$509$	1.08907e23	1.07141	0.535706	−	0.844405i	$-0.320046\pi$
$509$	1.08907e23	1.07141	0.535706	+	0.844405i	$0.320046\pi$
$510$	−1.37504e23	−1.33036
$511$	−1.92882e23	−1.83533
$512$	−6.04301e22	−0.565534
$513$	1.60562e23	1.47790
$514$	−1.07052e23	−0.969188
$515$	1.39789e23	1.24483
$516$	3.45935e22	0.303020
$517$	0	0
$518$	1.32869e23	1.12621
$519$	−1.37940e23	−1.15018
$520$	2.06257e22	0.169192
$521$	−1.20681e22	−0.0973910	−0.0486955	−	0.998814i	$-0.515506\pi$
$521$	−1.20681e22	−0.0973910	−0.0486955	+	0.998814i	$0.515506\pi$
$522$	1.31474e23	1.04386
$523$	−1.79015e23	−1.39838	−0.699190	−	0.714936i	$-0.746456\pi$
$523$	−1.79015e23	−1.39838	−0.699190	+	0.714936i	$0.746456\pi$
$524$	1.29231e23	0.993235
$525$	3.98415e22	0.301288
$526$	3.22421e22	0.239908
$527$	1.01759e22	0.0745047
$528$	0	0
$529$	−1.40956e23	−0.999335
$530$	−1.04082e23	−0.726158
$531$	−4.20128e22	−0.288455
$532$	−1.39503e23	−0.942617
$533$	6.49374e22	0.431831
$534$	7.40302e22	0.484516
$535$	7.96865e22	0.513307
$536$	−4.12664e22	−0.261635
$537$	1.79772e23	1.12186
$538$	−7.01433e22	−0.430861
$539$	0	0
$540$	1.16537e23	0.693611
$541$	1.79586e23	1.05220	0.526098	−	0.850424i	$-0.323655\pi$
$541$	1.79586e23	1.05220	0.526098	+	0.850424i	$0.323655\pi$
$542$	3.39719e23	1.95941
$543$	2.35694e22	0.133829
$544$	−2.20502e23	−1.23260
$545$	−3.88727e22	−0.213932
$546$	5.72482e22	0.310187
$547$	8.49721e22	0.453298	0.226649	−	0.973976i	$-0.427223\pi$
$547$	8.49721e22	0.453298	0.226649	+	0.973976i	$0.427223\pi$
$548$	−2.07987e23	−1.09245
$549$	−1.27278e23	−0.658244
$550$	0	0
$551$	−5.31314e23	−2.66418
$552$	−2.17401e21	−0.0107344
$553$	3.27376e22	0.159178
$554$	−1.75790e23	−0.841705
$555$	1.34795e23	0.635600
$556$	8.25036e22	0.383122
$557$	−1.42949e23	−0.653749	−0.326874	−	0.945068i	$-0.605995\pi$
$557$	−1.42949e23	−0.653749	−0.326874	+	0.945068i	$0.605995\pi$
$558$	−7.23287e21	−0.0325777
$559$	−4.32110e22	−0.191688
$560$	4.04782e23	1.76857
$561$	0	0
$562$	2.53584e23	1.07489
$563$	4.45167e23	1.85867	0.929333	−	0.369242i	$-0.120383\pi$
$563$	4.45167e23	1.85867	0.929333	+	0.369242i	$0.120383\pi$
$564$	5.43914e21	0.0223696
$565$	2.77201e23	1.12301
$566$	4.33393e22	0.172959
$567$	−1.21025e23	−0.475793
$568$	−1.57137e23	−0.608581
$569$	1.61119e23	0.614743	0.307371	−	0.951590i	$-0.400551\pi$
$569$	1.61119e23	0.614743	0.307371	+	0.951590i	$0.400551\pi$
$570$	−3.94969e23	−1.48466
$571$	−4.24902e23	−1.57355	−0.786776	−	0.617238i	$-0.788252\pi$
$571$	−4.24902e23	−1.57355	−0.786776	+	0.617238i	$0.788252\pi$
$572$	0	0
$573$	3.52389e23	1.26680
$574$	7.03536e23	2.49193
$575$	−2.38985e21	−0.00834052
$576$	9.90574e20	0.00340640
$577$	−2.84147e23	−0.962830	−0.481415	−	0.876493i	$-0.659877\pi$
$577$	−2.84147e23	−0.962830	−0.481415	+	0.876493i	$0.659877\pi$
$578$	−1.88592e23	−0.629705
$579$	−2.35258e23	−0.774065
$580$	−3.85631e23	−1.25036
$581$	4.01418e23	1.28263
$582$	−4.02488e23	−1.26738
$583$	0	0
$584$	−2.68252e23	−0.820415
$585$	−4.37446e22	−0.131856
$586$	−3.90520e23	−1.16015
$587$	5.25165e23	1.53770	0.768850	−	0.639429i	$-0.220829\pi$
$587$	5.25165e23	1.53770	0.768850	+	0.639429i	$0.220829\pi$
$588$	7.61094e22	0.219650
$589$	2.92295e22	0.0831459
$590$	3.43907e23	0.964270
$591$	3.41179e23	0.942949
$592$	3.34732e23	0.911934
$593$	6.89753e22	0.185237	0.0926186	−	0.995702i	$-0.470476\pi$
$593$	6.89753e22	0.185237	0.0926186	+	0.995702i	$0.470476\pi$
$594$	0	0
$595$	6.66775e23	1.74014
$596$	−2.33977e23	−0.601978
$597$	−2.49623e23	−0.633143
$598$	−3.43397e21	−0.00858689
$599$	−1.88793e23	−0.465434	−0.232717	−	0.972544i	$-0.574762\pi$
$599$	−1.88793e23	−0.465434	−0.232717	+	0.972544i	$0.574762\pi$
$600$	5.54099e22	0.134679
$601$	2.93390e23	0.703093	0.351547	−	0.936170i	$-0.385656\pi$
$601$	2.93390e23	0.703093	0.351547	+	0.936170i	$0.385656\pi$
$602$	−4.68151e23	−1.10615
$603$	8.75212e22	0.203899
$604$	2.91026e21	0.00668526
$605$	0	0
$606$	3.86947e23	0.864239
$607$	−4.91665e22	−0.108284	−0.0541421	−	0.998533i	$-0.517242\pi$
$607$	−4.91665e22	−0.108284	−0.0541421	+	0.998533i	$0.517242\pi$
$608$	−6.33371e23	−1.37556
$609$	8.46431e23	1.81278
$610$	1.04186e24	2.20043
$611$	−6.79409e21	−0.0141508
$612$	1.43254e23	0.294252
$613$	1.34480e23	0.272422	0.136211	−	0.990680i	$-0.456507\pi$
$613$	1.34480e23	0.272422	0.136211	+	0.990680i	$0.456507\pi$
$614$	−2.27604e23	−0.454725
$615$	7.13734e23	1.40636
$616$	0	0
$617$	6.25333e23	1.19864	0.599319	−	0.800511i	$-0.295438\pi$
$617$	6.25333e23	1.19864	0.599319	+	0.800511i	$0.295438\pi$
$618$	5.39606e23	1.02018
$619$	−5.25817e23	−0.980537	−0.490268	−	0.871572i	$-0.663101\pi$
$619$	−5.25817e23	−0.980537	−0.490268	+	0.871572i	$0.663101\pi$
$620$	2.12149e22	0.0390222
$621$	1.53433e22	0.0278380
$622$	−2.72673e23	−0.488004
$623$	−3.58982e23	−0.633759
$624$	1.44223e23	0.251169
$625$	−7.09460e23	−1.21884
$626$	9.68773e23	1.64188
$627$	0	0
$628$	2.47598e23	0.408405
$629$	5.51386e23	0.897275
$630$	−4.73932e23	−0.760889
$631$	−5.22448e23	−0.827548	−0.413774	−	0.910380i	$-0.635790\pi$
$631$	−5.22448e23	−0.827548	−0.413774	+	0.910380i	$0.635790\pi$
$632$	4.55300e22	0.0711546
$633$	8.06245e23	1.24318
$634$	2.43767e23	0.370866
$635$	1.20596e24	1.81032
$636$	−1.43964e23	−0.213239
$637$	−9.50690e22	−0.138949
$638$	0	0
$639$	3.33270e23	0.474284
$640$	8.15130e23	1.14471
$641$	7.43357e23	1.03016	0.515079	−	0.857143i	$-0.327762\pi$
$641$	7.43357e23	1.03016	0.515079	+	0.857143i	$0.327762\pi$
$642$	3.07603e23	0.420671
$643$	4.40297e23	0.594226	0.297113	−	0.954842i	$-0.403976\pi$
$643$	4.40297e23	0.594226	0.297113	+	0.954842i	$0.403976\pi$
$644$	−1.33309e22	−0.0177553
$645$	−4.74937e23	−0.624279
$646$	−1.61564e24	−2.09589
$647$	2.04079e23	0.261283	0.130642	−	0.991430i	$-0.458296\pi$
$647$	2.04079e23	0.261283	0.130642	+	0.991430i	$0.458296\pi$
$648$	−1.68316e23	−0.212686
$649$	0	0
$650$	8.75229e22	0.107735
$651$	−4.65651e22	−0.0565747
$652$	−1.26288e23	−0.151446
$653$	9.18378e23	1.08707	0.543537	−	0.839385i	$-0.317085\pi$
$653$	9.18378e23	1.08707	0.543537	+	0.839385i	$0.317085\pi$
$654$	−1.50055e23	−0.175323
$655$	−1.77423e24	−2.04625
$656$	1.77239e24	2.01780
$657$	5.68931e23	0.639372
$658$	−7.36075e22	−0.0816586
$659$	−2.77502e22	−0.0303907	−0.0151954	−	0.999885i	$-0.504837\pi$
$659$	−2.77502e22	−0.0303907	−0.0151954	+	0.999885i	$0.504837\pi$
$660$	0	0
$661$	−3.93902e23	−0.420413	−0.210206	−	0.977657i	$-0.567414\pi$
$661$	−3.93902e23	−0.420413	−0.210206	+	0.977657i	$0.567414\pi$
$662$	1.35139e23	0.142393
$663$	2.37571e23	0.247132
$664$	5.58276e23	0.573350
$665$	1.91525e24	1.94197
$666$	−3.91915e23	−0.392339
$667$	−5.07722e22	−0.0501830
$668$	2.28575e23	0.223063
$669$	−1.35933e24	−1.30979
$670$	−7.16427e23	−0.681610
$671$	0	0
$672$	1.00902e24	0.935965
$673$	3.74408e23	0.342939	0.171470	−	0.985189i	$-0.445148\pi$
$673$	3.74408e23	0.342939	0.171470	+	0.985189i	$0.445148\pi$
$674$	−6.27217e23	−0.567295
$675$	−3.91059e23	−0.349270
$676$	−5.88078e23	−0.518666
$677$	5.82502e22	0.0507334	0.0253667	−	0.999678i	$-0.491925\pi$
$677$	5.82502e22	0.0507334	0.0253667	+	0.999678i	$0.491925\pi$
$678$	1.07004e24	0.920339
$679$	1.95172e24	1.65777
$680$	9.27323e23	0.777867
$681$	−2.77664e23	−0.230021
$682$	0	0
$683$	−2.45830e24	−1.98636	−0.993181	−	0.116578i	$-0.962807\pi$
$683$	−2.45830e24	−1.98636	−0.993181	+	0.116578i	$0.962807\pi$
$684$	4.11484e23	0.328379
$685$	2.85547e24	2.25065
$686$	9.47605e23	0.737687
$687$	−9.01682e23	−0.693300
$688$	−1.17940e24	−0.895691
$689$	1.79826e23	0.134893
$690$	−3.77431e22	−0.0279653
$691$	2.35805e23	0.172580	0.0862899	−	0.996270i	$-0.472499\pi$
$691$	2.35805e23	0.172580	0.0862899	+	0.996270i	$0.472499\pi$
$692$	−1.17635e24	−0.850425
$693$	0	0
$694$	−1.80117e24	−1.27057
$695$	−1.13270e24	−0.789303
$696$	1.17718e24	0.810335
$697$	2.91956e24	1.98536
$698$	−2.52932e24	−1.69916
$699$	1.82254e24	1.20954
$700$	3.39769e23	0.222767
$701$	−2.44501e24	−1.58371	−0.791857	−	0.610706i	$-0.790886\pi$
$701$	−2.44501e24	−1.58371	−0.791857	+	0.610706i	$0.790886\pi$
$702$	−5.61913e23	−0.359587
$703$	1.58381e24	1.00134
$704$	0	0
$705$	−7.46745e22	−0.0460856
$706$	−2.31846e24	−1.41371
$707$	−1.87635e24	−1.13045
$708$	4.75683e23	0.283162
$709$	−8.28516e23	−0.487313	−0.243656	−	0.969862i	$-0.578347\pi$
$709$	−8.28516e23	−0.487313	−0.243656	+	0.969862i	$0.578347\pi$
$710$	−2.72807e24	−1.58547
$711$	−9.65639e22	−0.0554527
$712$	−4.99257e23	−0.283298
$713$	2.79316e21	0.00156615
$714$	2.57386e24	1.42610
$715$	0	0
$716$	1.53310e24	0.829487
$717$	1.65432e24	0.884516
$718$	−4.73304e23	−0.250082
$719$	−3.49365e24	−1.82425	−0.912124	−	0.409915i	$-0.865558\pi$
$719$	−3.49365e24	−1.82425	−0.912124	+	0.409915i	$0.865558\pi$
$720$	−1.19396e24	−0.616117
$721$	−2.61662e24	−1.33441
$722$	−2.16389e24	−1.09061
$723$	−5.34563e23	−0.266271
$724$	2.01001e23	0.0989510
$725$	1.29405e24	0.629620
$726$	0	0
$727$	−6.22179e23	−0.295715	−0.147857	−	0.989009i	$-0.547238\pi$
$727$	−6.22179e23	−0.295715	−0.147857	+	0.989009i	$0.547238\pi$
$728$	−3.86079e23	−0.181368
$729$	2.11317e24	0.981182
$730$	−4.65713e24	−2.13734
$731$	−1.94275e24	−0.881293
$732$	1.44108e24	0.646165
$733$	5.00592e23	0.221871	0.110935	−	0.993828i	$-0.464615\pi$
$733$	5.00592e23	0.221871	0.110935	+	0.993828i	$0.464615\pi$
$734$	−3.70685e24	−1.62401
$735$	−1.04491e24	−0.452520
$736$	−6.05247e22	−0.0259102
$737$	0	0
$738$	−2.07517e24	−0.868111
$739$	−7.37050e23	−0.304803	−0.152402	−	0.988319i	$-0.548701\pi$
$739$	−7.37050e23	−0.304803	−0.152402	+	0.988319i	$0.548701\pi$
$740$	1.14954e24	0.469952
$741$	6.82402e23	0.275794
$742$	1.94825e24	0.778415
$743$	1.44368e24	0.570251	0.285126	−	0.958490i	$-0.407965\pi$
$743$	1.44368e24	0.570251	0.285126	+	0.958490i	$0.407965\pi$
$744$	−6.47608e22	−0.0252896
$745$	3.21230e24	1.24019
$746$	−5.41137e24	−2.06551
$747$	−1.18404e24	−0.446828
$748$	0	0
$749$	−1.49160e24	−0.550247
$750$	−2.01178e24	−0.733770
$751$	−2.37610e24	−0.856891	−0.428446	−	0.903568i	$-0.640939\pi$
$751$	−2.37610e24	−0.856891	−0.428446	+	0.903568i	$0.640939\pi$
$752$	−1.85437e23	−0.0661217
$753$	2.54491e24	0.897253
$754$	1.85942e24	0.648218
$755$	−3.99553e22	−0.0137729
$756$	−2.18138e24	−0.743526
$757$	−2.22594e24	−0.750238	−0.375119	−	0.926977i	$-0.622398\pi$
$757$	−2.22594e24	−0.750238	−0.375119	+	0.926977i	$0.622398\pi$
$758$	1.48532e24	0.495030
$759$	0	0
$760$	2.66365e24	0.868085
$761$	−1.81359e24	−0.584479	−0.292239	−	0.956345i	$-0.594400\pi$
$761$	−1.81359e24	−0.584479	−0.292239	+	0.956345i	$0.594400\pi$
$762$	4.65520e24	1.48361
$763$	7.27635e23	0.229327
$764$	3.00519e24	0.936651
$765$	−1.96674e24	−0.606213
$766$	−5.80746e24	−1.77028
$767$	−5.94180e23	−0.179126
$768$	3.16661e24	0.944115
$769$	1.69098e24	0.498613	0.249307	−	0.968425i	$-0.419797\pi$
$769$	1.69098e24	0.498613	0.249307	+	0.968425i	$0.419797\pi$
$770$	0	0
$771$	2.03289e24	0.586342
$772$	−2.00629e24	−0.572331
$773$	−1.64676e24	−0.464628	−0.232314	−	0.972641i	$-0.574630\pi$
$773$	−1.64676e24	−0.464628	−0.232314	+	0.972641i	$0.574630\pi$
$774$	1.38088e24	0.385351
$775$	−7.11903e22	−0.0196497
$776$	2.71437e24	0.741043
$777$	−2.52315e24	−0.681340
$778$	4.02844e24	1.07600
$779$	8.38619e24	2.21563
$780$	4.95291e23	0.129436
$781$	0	0
$782$	−1.54390e23	−0.0394786
$783$	−8.30804e24	−2.10147
$784$	−2.59480e24	−0.649258
$785$	−3.39930e24	−0.841390
$786$	−6.84881e24	−1.67696
$787$	2.06465e24	0.500106	0.250053	−	0.968232i	$-0.419552\pi$
$787$	2.06465e24	0.500106	0.250053	+	0.968232i	$0.419552\pi$
$788$	2.90958e24	0.697200
$789$	−6.12268e23	−0.145140
$790$	7.90449e23	0.185372
$791$	−5.18876e24	−1.20382
$792$	0	0
$793$	−1.80006e24	−0.408758
$794$	6.70312e24	1.50592
$795$	1.97649e24	0.439313
$796$	−2.12879e24	−0.468135
$797$	−2.33751e24	−0.508577	−0.254289	−	0.967128i	$-0.581841\pi$
$797$	−2.33751e24	−0.508577	−0.254289	+	0.967128i	$0.581841\pi$
$798$	7.39318e24	1.59150
$799$	−3.05460e23	−0.0650589
$800$	1.54262e24	0.325082
$801$	1.05887e24	0.220782
$802$	−6.94945e24	−1.43373
$803$	0	0
$804$	−9.90943e23	−0.200158
$805$	1.83021e23	0.0365793
$806$	−1.02293e23	−0.0202301
$807$	1.33200e24	0.260663
$808$	−2.60955e24	−0.505324
$809$	1.76086e24	0.337414	0.168707	−	0.985666i	$-0.446041\pi$
$809$	1.76086e24	0.337414	0.168707	+	0.985666i	$0.446041\pi$
$810$	−2.92214e24	−0.554088
$811$	1.30791e24	0.245416	0.122708	−	0.992443i	$-0.460842\pi$
$811$	1.30791e24	0.245416	0.122708	+	0.992443i	$0.460842\pi$
$812$	7.21839e24	1.34034
$813$	−6.45117e24	−1.18541
$814$	0	0
$815$	1.73382e24	0.312007
$816$	6.48423e24	1.15476
$817$	−5.58039e24	−0.983506
$818$	−8.13346e24	−1.41864
$819$	8.18829e23	0.141345
$820$	6.08674e24	1.03984
$821$	1.01811e25	1.72139	0.860696	−	0.509119i	$-0.170029\pi$
$821$	1.01811e25	1.72139	0.860696	+	0.509119i	$0.170029\pi$
$822$	1.10226e25	1.84448
$823$	6.32769e24	1.04796	0.523982	−	0.851729i	$-0.324446\pi$
$823$	6.32769e24	1.04796	0.523982	+	0.851729i	$0.324446\pi$
$824$	−3.63908e24	−0.596500
$825$	0	0
$826$	−6.43738e24	−1.03366
$827$	5.69500e24	0.905101	0.452551	−	0.891739i	$-0.350514\pi$
$827$	5.69500e24	0.905101	0.452551	+	0.891739i	$0.350514\pi$
$828$	3.93212e22	0.00618542
$829$	−9.90078e23	−0.154154	−0.0770772	−	0.997025i	$-0.524559\pi$
$829$	−9.90078e23	−0.154154	−0.0770772	+	0.997025i	$0.524559\pi$
$830$	9.69224e24	1.49369
$831$	3.33819e24	0.509217
$832$	1.40095e22	0.00211531
$833$	−4.27427e24	−0.638822
$834$	−4.37240e24	−0.646857
$835$	−3.13812e24	−0.459552
$836$	0	0
$837$	4.57054e23	0.0655846
$838$	−1.10746e25	−1.57309
$839$	−4.31983e24	−0.607422	−0.303711	−	0.952764i	$-0.598226\pi$
$839$	−4.31983e24	−0.607422	−0.303711	+	0.952764i	$0.598226\pi$
$840$	−4.24344e24	−0.590669
$841$	2.02349e25	2.78827
$842$	−7.75052e24	−1.05725
$843$	−4.81549e24	−0.650289
$844$	6.87569e24	0.919190
$845$	8.07377e24	1.06855
$846$	2.17115e23	0.0284474
$847$	0	0
$848$	4.90816e24	0.630309
$849$	−8.23001e23	−0.104637
$850$	3.93500e24	0.495318
$851$	1.51348e23	0.0188615
$852$	−3.77339e24	−0.465581
$853$	1.39240e25	1.70097	0.850484	−	0.526001i	$-0.176309\pi$
$853$	1.39240e25	1.70097	0.850484	+	0.526001i	$0.176309\pi$
$854$	−1.95020e25	−2.35878
$855$	−5.64930e24	−0.676523
$856$	−2.07446e24	−0.245968
$857$	−1.84076e24	−0.216103	−0.108052	−	0.994145i	$-0.534461\pi$
$857$	−1.84076e24	−0.216103	−0.108052	+	0.994145i	$0.534461\pi$
$858$	0	0
$859$	−1.00691e25	−1.15891	−0.579453	−	0.815006i	$-0.696734\pi$
$859$	−1.00691e25	−1.15891	−0.579453	+	0.815006i	$0.696734\pi$
$860$	−4.05028e24	−0.461581
$861$	−1.33599e25	−1.50757
$862$	−3.66495e24	−0.409503
$863$	7.52680e23	0.0832758	0.0416379	−	0.999133i	$-0.486742\pi$
$863$	7.52680e23	0.0832758	0.0416379	+	0.999133i	$0.486742\pi$
$864$	−9.90389e24	−1.08502
$865$	1.61503e25	1.75203
$866$	−4.34878e24	−0.467160
$867$	3.58131e24	0.380960
$868$	−3.97109e23	−0.0418304
$869$	0	0
$870$	2.04371e25	2.11108
$871$	1.23780e24	0.126618
$872$	1.01196e24	0.102512
$873$	−5.75685e24	−0.577516
$874$	−4.43472e23	−0.0440574
$875$	9.75538e24	0.959789
$876$	−6.44162e24	−0.627639
$877$	−1.10696e25	−1.06816	−0.534079	−	0.845435i	$-0.679342\pi$
$877$	−1.10696e25	−1.06816	−0.534079	+	0.845435i	$0.679342\pi$
$878$	4.81013e24	0.459678
$879$	7.41587e24	0.701870
$880$	0	0
$881$	1.17642e25	1.09211	0.546056	−	0.837749i	$-0.316128\pi$
$881$	1.17642e25	1.09211	0.546056	+	0.837749i	$0.316128\pi$
$882$	3.03808e24	0.279329
$883$	−1.56790e24	−0.142775	−0.0713875	−	0.997449i	$-0.522743\pi$
$883$	−1.56790e24	−0.142775	−0.0713875	+	0.997449i	$0.522743\pi$
$884$	2.02601e24	0.182725
$885$	−6.53069e24	−0.583367
$886$	−4.57505e24	−0.404771
$887$	−4.73712e24	−0.415110	−0.207555	−	0.978223i	$-0.566551\pi$
$887$	−4.73712e24	−0.415110	−0.207555	+	0.978223i	$0.566551\pi$
$888$	−3.50909e24	−0.304568
$889$	−2.25736e25	−1.94060
$890$	−8.66762e24	−0.738048
$891$	0	0
$892$	−1.15924e25	−0.968436
$893$	−8.77407e23	−0.0726045
$894$	1.24000e25	1.01637
$895$	−2.10481e25	−1.70890
$896$	−1.52579e25	−1.22709
$897$	6.52101e22	0.00519492
$898$	3.54345e24	0.279626
$899$	−1.51243e24	−0.118228
$900$	−1.00220e24	−0.0776053
$901$	8.08493e24	0.620177
$902$	0	0
$903$	8.89006e24	0.669204
$904$	−7.21631e24	−0.538125
$905$	−2.75956e24	−0.203858
$906$	−1.54234e23	−0.0112873
$907$	1.30274e25	0.944484	0.472242	−	0.881469i	$-0.343445\pi$
$907$	1.30274e25	0.944484	0.472242	+	0.881469i	$0.343445\pi$
$908$	−2.36792e24	−0.170074
$909$	5.53456e24	0.393813
$910$	−6.70274e24	−0.472498
$911$	3.20840e23	0.0224069	0.0112034	−	0.999937i	$-0.496434\pi$
$911$	3.20840e23	0.0224069	0.0112034	+	0.999937i	$0.496434\pi$
$912$	1.86254e25	1.28869
$913$	0	0
$914$	−2.57385e25	−1.74800
$915$	−1.97847e25	−1.33122
$916$	−7.68957e24	−0.512614
$917$	3.32107e25	2.19351
$918$	−2.52634e25	−1.65321
$919$	−2.83206e24	−0.183621	−0.0918103	−	0.995777i	$-0.529265\pi$
$919$	−2.83206e24	−0.183621	−0.0918103	+	0.995777i	$0.529265\pi$
$920$	2.54538e23	0.0163514
$921$	4.32214e24	0.275101
$922$	1.58747e25	1.00114
$923$	4.71338e24	0.294522
$924$	0	0
$925$	−3.85747e24	−0.236645
$926$	2.94718e25	1.79149
$927$	7.71807e24	0.464869
$928$	3.27729e25	1.95594
$929$	−1.33754e25	−0.790995	−0.395498	−	0.918467i	$-0.629428\pi$
$929$	−1.33754e25	−0.790995	−0.395498	+	0.918467i	$0.629428\pi$
$930$	−1.12432e24	−0.0658845
$931$	−1.22775e25	−0.712913
$932$	1.55427e25	0.894317
$933$	5.17798e24	0.295234
$934$	−2.73463e25	−1.54508
$935$	0	0
$936$	1.13879e24	0.0631830
$937$	1.81588e25	0.998393	0.499196	−	0.866489i	$-0.333629\pi$
$937$	1.81588e25	0.998393	0.499196	+	0.866489i	$0.333629\pi$
$938$	1.34104e25	0.730662
$939$	−1.83967e25	−0.993306
$940$	−6.36826e23	−0.0340749
$941$	−9.10446e24	−0.482772	−0.241386	−	0.970429i	$-0.577602\pi$
$941$	−9.10446e24	−0.482772	−0.241386	+	0.970429i	$0.577602\pi$
$942$	−1.31218e25	−0.689544
$943$	8.01381e23	0.0417340
$944$	−1.62175e25	−0.836991
$945$	2.99484e25	1.53180
$946$	0	0
$947$	−1.41617e25	−0.711445	−0.355723	−	0.934592i	$-0.615765\pi$
$947$	−1.41617e25	−0.711445	−0.355723	+	0.934592i	$0.615765\pi$
$948$	1.09333e24	0.0544352
$949$	8.04629e24	0.397039
$950$	1.13029e25	0.552765
$951$	−4.62908e24	−0.224367
$952$	−1.73580e25	−0.833845
$953$	6.54898e24	0.311806	0.155903	−	0.987772i	$-0.450171\pi$
$953$	6.54898e24	0.311806	0.155903	+	0.987772i	$0.450171\pi$
$954$	−5.74663e24	−0.271176
$955$	−4.12585e25	−1.92968
$956$	1.41081e25	0.653996
$957$	0	0
$958$	−2.22295e25	−1.01233
$959$	−5.34499e25	−2.41262
$960$	1.53980e23	0.00688904
$961$	−2.24669e25	−0.996310
$962$	−5.54279e24	−0.243635
$963$	4.39968e24	0.191689
$964$	−4.55877e24	−0.196876
$965$	2.75446e25	1.17911
$966$	7.06490e23	0.0299778
$967$	−1.88201e25	−0.791586	−0.395793	−	0.918340i	$-0.629530\pi$
$967$	−1.88201e25	−0.791586	−0.395793	+	0.918340i	$0.629530\pi$
$968$	0	0
$969$	3.06806e25	1.26798
$970$	4.71242e25	1.93056
$971$	4.20550e25	1.70787	0.853933	−	0.520383i	$-0.174211\pi$
$971$	4.20550e25	1.70787	0.853933	+	0.520383i	$0.174211\pi$
$972$	1.09350e25	0.440205
$973$	2.12023e25	0.846105
$974$	−2.88948e25	−1.14306
$975$	−1.66203e24	−0.0651780
$976$	−4.91307e25	−1.90998
$977$	−1.23297e25	−0.475169	−0.237584	−	0.971367i	$-0.576356\pi$
$977$	−1.23297e25	−0.475169	−0.237584	+	0.971367i	$0.576356\pi$
$978$	6.69282e24	0.255699
$979$	0	0
$980$	−8.91106e24	−0.334586
$981$	−2.14626e24	−0.0798905
$982$	4.36738e25	1.61166
$983$	2.01765e24	0.0738144	0.0369072	−	0.999319i	$-0.488249\pi$
$983$	2.01765e24	0.0738144	0.0369072	+	0.999319i	$0.488249\pi$
$984$	−1.85805e25	−0.673904
$985$	−3.99459e25	−1.43636
$986$	8.35989e25	2.98021
$987$	1.39779e24	0.0494021
$988$	5.81954e24	0.203918
$989$	−5.33260e23	−0.0185255
$990$	0	0
$991$	4.24997e25	1.45131	0.725654	−	0.688060i	$-0.241538\pi$
$991$	4.24997e25	1.45131	0.725654	+	0.688060i	$0.241538\pi$
$992$	−1.80295e24	−0.0610428
$993$	−2.56625e24	−0.0861452
$994$	5.10650e25	1.69957
$995$	2.92263e25	0.964447
$996$	1.34061e25	0.438628
$997$	2.27800e25	0.739002	0.369501	−	0.929230i	$-0.379529\pi$
$997$	2.27800e25	0.739002	0.369501	+	0.929230i	$0.379529\pi$
$998$	9.25227e24	0.297604
$999$	2.47657e25	0.789848

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.18.a.c.1.2		6
11.10	odd	2		11.18.a.a.1.5	✓	6
33.32	even	2		99.18.a.a.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.18.a.a.1.5	✓	6	11.10	odd	2
99.18.a.a.1.2		6	33.32	even	2
121.18.a.c.1.2		6	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:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	121.a (trivial)

\(f(q)\)	\(=\)	\(q-451.956 q^{2} +8582.51 q^{3} +73191.9 q^{4} -1.00486e6 q^{5} -3.87891e6 q^{6} +1.88093e7 q^{7} +2.61592e7 q^{8} -5.54807e7 q^{9} +O(q^{10})\)	\(q-451.956 q^{2} +8582.51 q^{3} +73191.9 q^{4} -1.00486e6 q^{5} -3.87891e6 q^{6} +1.88093e7 q^{7} +2.61592e7 q^{8} -5.54807e7 q^{9} +4.54152e8 q^{10} +6.28170e8 q^{12} -7.84654e8 q^{13} -8.50098e9 q^{14} -8.62421e9 q^{15} -2.14162e10 q^{16} -3.52778e10 q^{17} +2.50748e10 q^{18} -1.01332e11 q^{19} -7.35475e10 q^{20} +1.61431e11 q^{21} -9.68328e9 q^{23} +2.24512e11 q^{24} +2.46801e11 q^{25} +3.54629e11 q^{26} -1.58451e12 q^{27} +1.37669e12 q^{28} +5.24329e12 q^{29} +3.89776e12 q^{30} -2.88452e11 q^{31} +6.25044e12 q^{32} +1.59440e13 q^{34} -1.89007e13 q^{35} -4.06074e12 q^{36} -1.56299e13 q^{37} +4.57977e13 q^{38} -6.73430e12 q^{39} -2.62863e13 q^{40} -8.27593e13 q^{41} -7.29598e13 q^{42} +5.50702e13 q^{43} +5.57502e13 q^{45} +4.37641e12 q^{46} +8.65871e12 q^{47} -1.83805e14 q^{48} +1.21161e14 q^{49} -1.11543e14 q^{50} -3.02772e14 q^{51} -5.74303e13 q^{52} -2.29179e14 q^{53} +7.16128e14 q^{54} +4.92038e14 q^{56} -8.69685e14 q^{57} -2.36973e15 q^{58} +7.57251e14 q^{59} -6.31222e14 q^{60} +2.29409e15 q^{61} +1.30367e14 q^{62} -1.04355e15 q^{63} -1.78544e13 q^{64} +7.88466e14 q^{65} -1.57751e15 q^{67} -2.58205e15 q^{68} -8.31068e13 q^{69} +8.54229e15 q^{70} -6.00695e15 q^{71} -1.45133e15 q^{72} -1.02546e16 q^{73} +7.06400e15 q^{74} +2.11818e15 q^{75} -7.41670e15 q^{76} +3.04360e15 q^{78} +1.74050e15 q^{79} +2.15203e16 q^{80} -6.43429e15 q^{81} +3.74035e16 q^{82} +2.13414e16 q^{83} +1.18155e16 q^{84} +3.54492e16 q^{85} -2.48893e16 q^{86} +4.50006e16 q^{87} -1.90853e16 q^{89} -2.51966e16 q^{90} -1.47588e16 q^{91} -7.08737e14 q^{92} -2.47564e15 q^{93} -3.91335e15 q^{94} +1.01825e17 q^{95} +5.36445e16 q^{96} +1.03763e17 q^{97} -5.47592e16 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 11865 q^{3} + 351024 q^{4} + 347991 q^{5} + 16302972 q^{6} + 31314630 q^{7} + 67892640 q^{8} + 377752851 q^{9}+O(q^{10}) \) 6 * q + 11865 * q^3 + 351024 * q^4 + 347991 * q^5 + 16302972 * q^6 + 31314630 * q^7 + 67892640 * q^8 + 377752851 * q^9	\( 6 q + 11865 q^{3} + 351024 q^{4} + 347991 q^{5} + 16302972 q^{6} + 31314630 q^{7} + 67892640 q^{8} + 377752851 q^{9} + 144090324 q^{10} + 4513961760 q^{12} + 7119892710 q^{13} - 1766662392 q^{14} - 19550343855 q^{15} + 23307418752 q^{16} - 14847960120 q^{17} + 207033381900 q^{18} + 96642651252 q^{19} - 175684379136 q^{20} + 541163623038 q^{21} - 836632018455 q^{23} + 3775860484704 q^{24} - 2511064443309 q^{25} - 61179995016 q^{26} - 2108694116025 q^{27} + 7550013575040 q^{28} + 6178015368186 q^{29} + 4599681241020 q^{30} + 636857332041 q^{31} + 34717785780480 q^{32} - 22577342383344 q^{34} - 7652188071450 q^{35} + 92057284438416 q^{36} - 1233417487215 q^{37} + 99623910494640 q^{38} - 22828491583500 q^{39} - 139157596758432 q^{40} + 43234265835054 q^{41} + 244981786044840 q^{42} - 145352338376130 q^{43} + 63552616359372 q^{45} + 18844814685660 q^{46} + 432778220316120 q^{47} + 832919384734080 q^{48} - 55920612074934 q^{49} - 368804230203396 q^{50} - 562418817395262 q^{51} + 26\!\cdots\!80 q^{52}+ \cdots - 65\!\cdots\!00 q^{98}+O(q^{100}) \) 6 * q + 11865 * q^3 + 351024 * q^4 + 347991 * q^5 + 16302972 * q^6 + 31314630 * q^7 + 67892640 * q^8 + 377752851 * q^9 + 144090324 * q^10 + 4513961760 * q^12 + 7119892710 * q^13 - 1766662392 * q^14 - 19550343855 * q^15 + 23307418752 * q^16 - 14847960120 * q^17 + 207033381900 * q^18 + 96642651252 * q^19 - 175684379136 * q^20 + 541163623038 * q^21 - 836632018455 * q^23 + 3775860484704 * q^24 - 2511064443309 * q^25 - 61179995016 * q^26 - 2108694116025 * q^27 + 7550013575040 * q^28 + 6178015368186 * q^29 + 4599681241020 * q^30 + 636857332041 * q^31 + 34717785780480 * q^32 - 22577342383344 * q^34 - 7652188071450 * q^35 + 92057284438416 * q^36 - 1233417487215 * q^37 + 99623910494640 * q^38 - 22828491583500 * q^39 - 139157596758432 * q^40 + 43234265835054 * q^41 + 244981786044840 * q^42 - 145352338376130 * q^43 + 63552616359372 * q^45 + 18844814685660 * q^46 + 432778220316120 * q^47 + 832919384734080 * q^48 - 55920612074934 * q^49 - 368804230203396 * q^50 - 562418817395262 * q^51 + 2663217125395680 * q^52 - 1098463886245560 * q^53 + 1564527203783460 * q^54 + 164642910803520 * q^56 + 2438041510213920 * q^57 - 688806293721720 * q^58 - 1354427895404325 * q^59 - 4634689473664800 * q^60 + 4680147076091550 * q^61 - 327068618103780 * q^62 + 2437011498083580 * q^63 + 4119359220996096 * q^64 - 1694576167351992 * q^65 - 1422221695594785 * q^67 - 13013443225631520 * q^68 + 4340393479871841 * q^69 + 7242718895843400 * q^70 - 241024392605325 * q^71 + 15782344028415360 * q^72 - 16535978199148590 * q^73 - 35346993162556884 * q^74 + 2786718509400840 * q^75 - 874633109814912 * q^76 + 96469292799543120 * q^78 + 11287689680330886 * q^79 - 2948966505238656 * q^80 - 27976963515226290 * q^81 + 57330488162524920 * q^82 + 38342699617260150 * q^83 + 22250959697175168 * q^84 + 78911850100793814 * q^85 - 100218510690927384 * q^86 + 83644469453943720 * q^87 - 72526069382037411 * q^89 - 96101996279722272 * q^90 - 57857689770132840 * q^91 + 21581518865280480 * q^92 - 233344518597393495 * q^93 - 27995732830541280 * q^94 + 146785535344378824 * q^95 + 167024768158235904 * q^96 - 3850252891123905 * q^97 - 65640418784062800 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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