LMFDB - Embedded newform 2366.2.a.bh.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2366,2,Mod(1,2366)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2366, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("2366.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2366 = 2 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2366.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:	$18.8926051182$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.285686784.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 10x^{4} + 12x^{3} + 21x^{2} + 2x - 2 $ x^6 - 2x^5 - 10x^4 + 12x^3 + 21x^2 + 2*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.55629$ of defining polynomial
Character	$\chi$	$=$	2366.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.55629 q^{3} +1.00000 q^{4} -3.48754 q^{5} -2.55629 q^{6} +1.00000 q^{7} +1.00000 q^{8} +3.53463 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.55629 q^{3} +1.00000 q^{4} -3.48754 q^{5} -2.55629 q^{6} +1.00000 q^{7} +1.00000 q^{8} +3.53463 q^{9} -3.48754 q^{10} +2.68172 q^{11} -2.55629 q^{12} +1.00000 q^{14} +8.91517 q^{15} +1.00000 q^{16} -5.91517 q^{17} +3.53463 q^{18} -5.19793 q^{19} -3.48754 q^{20} -2.55629 q^{21} +2.68172 q^{22} -7.05268 q^{23} -2.55629 q^{24} +7.16292 q^{25} -1.36668 q^{27} +1.00000 q^{28} +7.13278 q^{29} +8.91517 q^{30} +0.782383 q^{31} +1.00000 q^{32} -6.85526 q^{33} -5.91517 q^{34} -3.48754 q^{35} +3.53463 q^{36} -7.81450 q^{37} -5.19793 q^{38} -3.48754 q^{40} +0.157708 q^{41} -2.55629 q^{42} -0.330202 q^{43} +2.68172 q^{44} -12.3272 q^{45} -7.05268 q^{46} +1.60161 q^{47} -2.55629 q^{48} +1.00000 q^{49} +7.16292 q^{50} +15.1209 q^{51} +3.92601 q^{53} -1.36668 q^{54} -9.35259 q^{55} +1.00000 q^{56} +13.2874 q^{57} +7.13278 q^{58} +9.54021 q^{59} +8.91517 q^{60} +15.4105 q^{61} +0.782383 q^{62} +3.53463 q^{63} +1.00000 q^{64} -6.85526 q^{66} +0.966765 q^{67} -5.91517 q^{68} +18.0287 q^{69} -3.48754 q^{70} -4.18658 q^{71} +3.53463 q^{72} +15.0361 q^{73} -7.81450 q^{74} -18.3105 q^{75} -5.19793 q^{76} +2.68172 q^{77} -0.293356 q^{79} -3.48754 q^{80} -7.11027 q^{81} +0.157708 q^{82} -2.87495 q^{83} -2.55629 q^{84} +20.6294 q^{85} -0.330202 q^{86} -18.2335 q^{87} +2.68172 q^{88} -5.21325 q^{89} -12.3272 q^{90} -7.05268 q^{92} -2.00000 q^{93} +1.60161 q^{94} +18.1280 q^{95} -2.55629 q^{96} +3.15946 q^{97} +1.00000 q^{98} +9.47889 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 2 q^{3} + 6 q^{4} - 2 q^{5} + 2 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 - 2 * q^5 + 2 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9	$ 6 q + 6 q^{2} + 2 q^{3} + 6 q^{4} - 2 q^{5} + 2 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9} - 2 q^{10} + 2 q^{11} + 2 q^{12} + 6 q^{14} + 14 q^{15} + 6 q^{16} + 4 q^{17} + 6 q^{18} - 4 q^{19} - 2 q^{20} + 2 q^{21} + 2 q^{22} - 6 q^{23} + 2 q^{24} + 12 q^{25} + 20 q^{27} + 6 q^{28} + 10 q^{29} + 14 q^{30} - 2 q^{31} + 6 q^{32} + 4 q^{34} - 2 q^{35} + 6 q^{36} - 4 q^{38} - 2 q^{40} + 6 q^{41} + 2 q^{42} + 26 q^{43} + 2 q^{44} - 6 q^{45} - 6 q^{46} - 8 q^{47} + 2 q^{48} + 6 q^{49} + 12 q^{50} + 18 q^{51} + 18 q^{53} + 20 q^{54} + 6 q^{55} + 6 q^{56} - 28 q^{57} + 10 q^{58} + 2 q^{59} + 14 q^{60} + 28 q^{61} - 2 q^{62} + 6 q^{63} + 6 q^{64} + 6 q^{67} + 4 q^{68} + 32 q^{69} - 2 q^{70} + 4 q^{71} + 6 q^{72} - 22 q^{73} - 48 q^{75} - 4 q^{76} + 2 q^{77} + 22 q^{79} - 2 q^{80} + 34 q^{81} + 6 q^{82} - 10 q^{83} + 2 q^{84} + 32 q^{85} + 26 q^{86} - 2 q^{87} + 2 q^{88} - 4 q^{89} - 6 q^{90} - 6 q^{92} - 12 q^{93} - 8 q^{94} + 32 q^{95} + 2 q^{96} - 12 q^{97} + 6 q^{98} - 2 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 - 2 * q^5 + 2 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9 - 2 * q^10 + 2 * q^11 + 2 * q^12 + 6 * q^14 + 14 * q^15 + 6 * q^16 + 4 * q^17 + 6 * q^18 - 4 * q^19 - 2 * q^20 + 2 * q^21 + 2 * q^22 - 6 * q^23 + 2 * q^24 + 12 * q^25 + 20 * q^27 + 6 * q^28 + 10 * q^29 + 14 * q^30 - 2 * q^31 + 6 * q^32 + 4 * q^34 - 2 * q^35 + 6 * q^36 - 4 * q^38 - 2 * q^40 + 6 * q^41 + 2 * q^42 + 26 * q^43 + 2 * q^44 - 6 * q^45 - 6 * q^46 - 8 * q^47 + 2 * q^48 + 6 * q^49 + 12 * q^50 + 18 * q^51 + 18 * q^53 + 20 * q^54 + 6 * q^55 + 6 * q^56 - 28 * q^57 + 10 * q^58 + 2 * q^59 + 14 * q^60 + 28 * q^61 - 2 * q^62 + 6 * q^63 + 6 * q^64 + 6 * q^67 + 4 * q^68 + 32 * q^69 - 2 * q^70 + 4 * q^71 + 6 * q^72 - 22 * q^73 - 48 * q^75 - 4 * q^76 + 2 * q^77 + 22 * q^79 - 2 * q^80 + 34 * q^81 + 6 * q^82 - 10 * q^83 + 2 * q^84 + 32 * q^85 + 26 * q^86 - 2 * q^87 + 2 * q^88 - 4 * q^89 - 6 * q^90 - 6 * q^92 - 12 * q^93 - 8 * q^94 + 32 * q^95 + 2 * q^96 - 12 * q^97 + 6 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.55629	−1.47588	−0.737938	−	0.674868i	$-0.764200\pi$
$3$	−2.55629	−1.47588	−0.737938	+	0.674868i	$0.764200\pi$
$4$	1.00000	0.500000
$5$	−3.48754	−1.55967	−0.779837	−	0.625983i	$-0.784698\pi$
$5$	−3.48754	−1.55967	−0.779837	+	0.625983i	$0.784698\pi$
$6$	−2.55629	−1.04360
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	3.53463	1.17821
$10$	−3.48754	−1.10286
$11$	2.68172	0.808569	0.404284	−	0.914633i	$-0.367521\pi$
$11$	2.68172	0.808569	0.404284	+	0.914633i	$0.367521\pi$
$12$	−2.55629	−0.737938
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	8.91517	2.30189
$16$	1.00000	0.250000
$17$	−5.91517	−1.43464	−0.717319	−	0.696745i	$-0.754631\pi$
$17$	−5.91517	−1.43464	−0.717319	+	0.696745i	$0.754631\pi$
$18$	3.53463	0.833121
$19$	−5.19793	−1.19249	−0.596243	−	0.802804i	$-0.703341\pi$
$19$	−5.19793	−1.19249	−0.596243	+	0.802804i	$0.703341\pi$
$20$	−3.48754	−0.779837
$21$	−2.55629	−0.557829
$22$	2.68172	0.571744
$23$	−7.05268	−1.47058	−0.735292	−	0.677750i	$-0.762955\pi$
$23$	−7.05268	−1.47058	−0.735292	+	0.677750i	$0.762955\pi$
$24$	−2.55629	−0.521801
$25$	7.16292	1.43258
$26$	0	0
$27$	−1.36668	−0.263017
$28$	1.00000	0.188982
$29$	7.13278	1.32452	0.662262	−	0.749272i	$-0.269596\pi$
$29$	7.13278	1.32452	0.662262	+	0.749272i	$0.269596\pi$
$30$	8.91517	1.62768
$31$	0.782383	0.140520	0.0702601	−	0.997529i	$-0.477617\pi$
$31$	0.782383	0.140520	0.0702601	+	0.997529i	$0.477617\pi$
$32$	1.00000	0.176777
$33$	−6.85526	−1.19335
$34$	−5.91517	−1.01444
$35$	−3.48754	−0.589501
$36$	3.53463	0.589105
$37$	−7.81450	−1.28470	−0.642348	−	0.766413i	$-0.722040\pi$
$37$	−7.81450	−1.28470	−0.642348	+	0.766413i	$0.722040\pi$
$38$	−5.19793	−0.843215
$39$	0	0
$40$	−3.48754	−0.551428
$41$	0.157708	0.0246299	0.0123149	−	0.999924i	$-0.496080\pi$
$41$	0.157708	0.0246299	0.0123149	+	0.999924i	$0.496080\pi$
$42$	−2.55629	−0.394445
$43$	−0.330202	−0.0503553	−0.0251777	−	0.999683i	$-0.508015\pi$
$43$	−0.330202	−0.0503553	−0.0251777	+	0.999683i	$0.508015\pi$
$44$	2.68172	0.404284
$45$	−12.3272	−1.83762
$46$	−7.05268	−1.03986
$47$	1.60161	0.233619	0.116810	−	0.993154i	$-0.462733\pi$
$47$	1.60161	0.233619	0.116810	+	0.993154i	$0.462733\pi$
$48$	−2.55629	−0.368969
$49$	1.00000	0.142857
$50$	7.16292	1.01299
$51$	15.1209	2.11735
$52$	0	0
$53$	3.92601	0.539279	0.269639	−	0.962961i	$-0.413095\pi$
$53$	3.92601	0.539279	0.269639	+	0.962961i	$0.413095\pi$
$54$	−1.36668	−0.185981
$55$	−9.35259	−1.26110
$56$	1.00000	0.133631
$57$	13.2874	1.75996
$58$	7.13278	0.936580
$59$	9.54021	1.24203	0.621015	−	0.783799i	$-0.286721\pi$
$59$	9.54021	1.24203	0.621015	+	0.783799i	$0.286721\pi$
$60$	8.91517	1.15094
$61$	15.4105	1.97311	0.986556	−	0.163421i	$-0.0522527\pi$
$61$	15.4105	1.97311	0.986556	+	0.163421i	$0.0522527\pi$
$62$	0.782383	0.0993627
$63$	3.53463	0.445322
$64$	1.00000	0.125000
$65$	0	0
$66$	−6.85526	−0.843824
$67$	0.966765	0.118109	0.0590546	−	0.998255i	$-0.481191\pi$
$67$	0.966765	0.118109	0.0590546	+	0.998255i	$0.481191\pi$
$68$	−5.91517	−0.717319
$69$	18.0287	2.17040
$70$	−3.48754	−0.416840
$71$	−4.18658	−0.496855	−0.248428	−	0.968650i	$-0.579914\pi$
$71$	−4.18658	−0.496855	−0.248428	+	0.968650i	$0.579914\pi$
$72$	3.53463	0.416560
$73$	15.0361	1.75984	0.879919	−	0.475124i	$-0.157597\pi$
$73$	15.0361	1.75984	0.879919	+	0.475124i	$0.157597\pi$
$74$	−7.81450	−0.908417
$75$	−18.3105	−2.11432
$76$	−5.19793	−0.596243
$77$	2.68172	0.305610
$78$	0	0
$79$	−0.293356	−0.0330052	−0.0165026	−	0.999864i	$-0.505253\pi$
$79$	−0.293356	−0.0330052	−0.0165026	+	0.999864i	$0.505253\pi$
$80$	−3.48754	−0.389919
$81$	−7.11027	−0.790030
$82$	0.157708	0.0174159
$83$	−2.87495	−0.315566	−0.157783	−	0.987474i	$-0.550435\pi$
$83$	−2.87495	−0.315566	−0.157783	+	0.987474i	$0.550435\pi$
$84$	−2.55629	−0.278914
$85$	20.6294	2.23757
$86$	−0.330202	−0.0356066
$87$	−18.2335	−1.95483
$88$	2.68172	0.285872
$89$	−5.21325	−0.552603	−0.276302	−	0.961071i	$-0.589109\pi$
$89$	−5.21325	−0.552603	−0.276302	+	0.961071i	$0.589109\pi$
$90$	−12.3272	−1.29940
$91$	0	0
$92$	−7.05268	−0.735292
$93$	−2.00000	−0.207390
$94$	1.60161	0.165194
$95$	18.1280	1.85989
$96$	−2.55629	−0.260901
$97$	3.15946	0.320794	0.160397	−	0.987053i	$-0.448723\pi$
$97$	3.15946	0.320794	0.160397	+	0.987053i	$0.448723\pi$
$98$	1.00000	0.101015
$99$	9.47889	0.952664
$100$	7.16292	0.716292
$101$	3.78650	0.376771	0.188386	−	0.982095i	$-0.439675\pi$
$101$	3.78650	0.376771	0.188386	+	0.982095i	$0.439675\pi$
$102$	15.1209	1.49719
$103$	6.80839	0.670850	0.335425	−	0.942067i	$-0.391120\pi$
$103$	6.80839	0.670850	0.335425	+	0.942067i	$0.391120\pi$
$104$	0	0
$105$	8.91517	0.870031
$106$	3.92601	0.381328
$107$	14.3017	1.38259	0.691297	−	0.722571i	$-0.257040\pi$
$107$	14.3017	1.38259	0.691297	+	0.722571i	$0.257040\pi$
$108$	−1.36668	−0.131508
$109$	4.57669	0.438367	0.219184	−	0.975684i	$-0.429661\pi$
$109$	4.57669	0.438367	0.219184	+	0.975684i	$0.429661\pi$
$110$	−9.35259	−0.891735
$111$	19.9762	1.89605
$112$	1.00000	0.0944911
$113$	−3.01297	−0.283436	−0.141718	−	0.989907i	$-0.545263\pi$
$113$	−3.01297	−0.283436	−0.141718	+	0.989907i	$0.545263\pi$
$114$	13.2874	1.24448
$115$	24.5965	2.29363
$116$	7.13278	0.662262
$117$	0	0
$118$	9.54021	0.878248
$119$	−5.91517	−0.542242
$120$	8.91517	0.813840
$121$	−3.80839	−0.346217
$122$	15.4105	1.39520
$123$	−0.403148	−0.0363506
$124$	0.782383	0.0702601
$125$	−7.54326	−0.674689
$126$	3.53463	0.314890
$127$	11.1256	0.987233	0.493616	−	0.869680i	$-0.335675\pi$
$127$	11.1256	0.987233	0.493616	+	0.869680i	$0.335675\pi$
$128$	1.00000	0.0883883
$129$	0.844093	0.0743183
$130$	0	0
$131$	14.9117	1.30284	0.651420	−	0.758718i	$-0.274174\pi$
$131$	14.9117	1.30284	0.651420	+	0.758718i	$0.274174\pi$
$132$	−6.85526	−0.596674
$133$	−5.19793	−0.450717
$134$	0.966765	0.0835158
$135$	4.76633	0.410220
$136$	−5.91517	−0.507221
$137$	−15.4617	−1.32098	−0.660492	−	0.750833i	$-0.729652\pi$
$137$	−15.4617	−1.32098	−0.660492	+	0.750833i	$0.729652\pi$
$138$	18.0287	1.53471
$139$	14.3022	1.21310	0.606548	−	0.795046i	$-0.292554\pi$
$139$	14.3022	1.21310	0.606548	+	0.795046i	$0.292554\pi$
$140$	−3.48754	−0.294751
$141$	−4.09419	−0.344793
$142$	−4.18658	−0.351330
$143$	0	0
$144$	3.53463	0.294553
$145$	−24.8758	−2.06583
$146$	15.0361	1.24439
$147$	−2.55629	−0.210839
$148$	−7.81450	−0.642348
$149$	3.55717	0.291415	0.145708	−	0.989328i	$-0.453454\pi$
$149$	3.55717	0.291415	0.145708	+	0.989328i	$0.453454\pi$
$150$	−18.3105	−1.49505
$151$	9.52740	0.775329	0.387664	−	0.921801i	$-0.373282\pi$
$151$	9.52740	0.775329	0.387664	+	0.921801i	$0.373282\pi$
$152$	−5.19793	−0.421608
$153$	−20.9079	−1.69031
$154$	2.68172	0.216099
$155$	−2.72859	−0.219166
$156$	0	0
$157$	20.8345	1.66278	0.831388	−	0.555692i	$-0.187547\pi$
$157$	20.8345	1.66278	0.831388	+	0.555692i	$0.187547\pi$
$158$	−0.293356	−0.0233382
$159$	−10.0360	−0.795909
$160$	−3.48754	−0.275714
$161$	−7.05268	−0.555829
$162$	−7.11027	−0.558636
$163$	6.30603	0.493927	0.246963	−	0.969025i	$-0.420567\pi$
$163$	6.30603	0.493927	0.246963	+	0.969025i	$0.420567\pi$
$164$	0.157708	0.0123149
$165$	23.9080	1.86123
$166$	−2.87495	−0.223139
$167$	−6.66871	−0.516041	−0.258020	−	0.966139i	$-0.583070\pi$
$167$	−6.66871	−0.516041	−0.258020	+	0.966139i	$0.583070\pi$
$168$	−2.55629	−0.197222
$169$	0	0
$170$	20.6294	1.58220
$171$	−18.3728	−1.40500
$172$	−0.330202	−0.0251777
$173$	−21.3192	−1.62087	−0.810434	−	0.585830i	$-0.800769\pi$
$173$	−21.3192	−1.62087	−0.810434	+	0.585830i	$0.800769\pi$
$174$	−18.2335	−1.38228
$175$	7.16292	0.541466
$176$	2.68172	0.202142
$177$	−24.3876	−1.83308
$178$	−5.21325	−0.390750
$179$	15.4384	1.15392	0.576961	−	0.816772i	$-0.304239\pi$
$179$	15.4384	1.15392	0.576961	+	0.816772i	$0.304239\pi$
$180$	−12.3272	−0.918812
$181$	13.2818	0.987231	0.493616	−	0.869680i	$-0.335675\pi$
$181$	13.2818	0.987231	0.493616	+	0.869680i	$0.335675\pi$
$182$	0	0
$183$	−39.3938	−2.91207
$184$	−7.05268	−0.519930
$185$	27.2534	2.00371
$186$	−2.00000	−0.146647
$187$	−15.8628	−1.16000
$188$	1.60161	0.116810
$189$	−1.36668	−0.0994110
$190$	18.1280	1.31514
$191$	−11.9246	−0.862833	−0.431417	−	0.902153i	$-0.641986\pi$
$191$	−11.9246	−0.862833	−0.431417	+	0.902153i	$0.641986\pi$
$192$	−2.55629	−0.184485
$193$	−5.34936	−0.385055	−0.192528	−	0.981292i	$-0.561668\pi$
$193$	−5.34936	−0.385055	−0.192528	+	0.981292i	$0.561668\pi$
$194$	3.15946	0.226836
$195$	0	0
$196$	1.00000	0.0714286
$197$	−13.1938	−0.940017	−0.470009	−	0.882662i	$-0.655749\pi$
$197$	−13.1938	−0.940017	−0.470009	+	0.882662i	$0.655749\pi$
$198$	9.47889	0.673635
$199$	20.0516	1.42142	0.710709	−	0.703486i	$-0.248374\pi$
$199$	20.0516	1.42142	0.710709	+	0.703486i	$0.248374\pi$
$200$	7.16292	0.506495
$201$	−2.47133	−0.174314
$202$	3.78650	0.266417
$203$	7.13278	0.500623
$204$	15.1209	1.05867
$205$	−0.550013	−0.0384146
$206$	6.80839	0.474363
$207$	−24.9286	−1.73266
$208$	0	0
$209$	−13.9394	−0.964207
$210$	8.91517	0.615205
$211$	−7.96144	−0.548088	−0.274044	−	0.961717i	$-0.588361\pi$
$211$	−7.96144	−0.548088	−0.274044	+	0.961717i	$0.588361\pi$
$212$	3.92601	0.269639
$213$	10.7021	0.733297
$214$	14.3017	0.977642
$215$	1.15159	0.0785379
$216$	−1.36668	−0.0929905
$217$	0.782383	0.0531116
$218$	4.57669	0.309972
$219$	−38.4366	−2.59730
$220$	−9.35259	−0.630552
$221$	0	0
$222$	19.9762	1.34071
$223$	−21.5417	−1.44254	−0.721271	−	0.692653i	$-0.756442\pi$
$223$	−21.5417	−1.44254	−0.721271	+	0.692653i	$0.756442\pi$
$224$	1.00000	0.0668153
$225$	25.3183	1.68789
$226$	−3.01297	−0.200419
$227$	−3.65771	−0.242771	−0.121385	−	0.992605i	$-0.538734\pi$
$227$	−3.65771	−0.242771	−0.121385	+	0.992605i	$0.538734\pi$
$228$	13.2874	0.879981
$229$	−9.74752	−0.644134	−0.322067	−	0.946717i	$-0.604378\pi$
$229$	−9.74752	−0.644134	−0.322067	+	0.946717i	$0.604378\pi$
$230$	24.5965	1.62184
$231$	−6.85526	−0.451043
$232$	7.13278	0.468290
$233$	2.72895	0.178779	0.0893897	−	0.995997i	$-0.471508\pi$
$233$	2.72895	0.178779	0.0893897	+	0.995997i	$0.471508\pi$
$234$	0	0
$235$	−5.58568	−0.364370
$236$	9.54021	0.621015
$237$	0.749905	0.0487115
$238$	−5.91517	−0.383423
$239$	12.2347	0.791400	0.395700	−	0.918380i	$-0.370502\pi$
$239$	12.2347	0.791400	0.395700	+	0.918380i	$0.370502\pi$
$240$	8.91517	0.575471
$241$	−24.2176	−1.56000	−0.779998	−	0.625782i	$-0.784780\pi$
$241$	−24.2176	−1.56000	−0.779998	+	0.625782i	$0.784780\pi$
$242$	−3.80839	−0.244812
$243$	22.2760	1.42900
$244$	15.4105	0.986556
$245$	−3.48754	−0.222811
$246$	−0.403148	−0.0257038
$247$	0	0
$248$	0.782383	0.0496814
$249$	7.34921	0.465737
$250$	−7.54326	−0.477077
$251$	2.01371	0.127104	0.0635521	−	0.997979i	$-0.479757\pi$
$251$	2.01371	0.127104	0.0635521	+	0.997979i	$0.479757\pi$
$252$	3.53463	0.222661
$253$	−18.9133	−1.18907
$254$	11.1256	0.698079
$255$	−52.7347	−3.30237
$256$	1.00000	0.0625000
$257$	−2.14218	−0.133625	−0.0668127	−	0.997766i	$-0.521283\pi$
$257$	−2.14218	−0.133625	−0.0668127	+	0.997766i	$0.521283\pi$
$258$	0.844093	0.0525509
$259$	−7.81450	−0.485570
$260$	0	0
$261$	25.2118	1.56057
$262$	14.9117	0.921247
$263$	−10.8626	−0.669818	−0.334909	−	0.942250i	$-0.608706\pi$
$263$	−10.8626	−0.669818	−0.334909	+	0.942250i	$0.608706\pi$
$264$	−6.85526	−0.421912
$265$	−13.6921	−0.841099
$266$	−5.19793	−0.318705
$267$	13.3266	0.815574
$268$	0.966765	0.0590546
$269$	−14.8051	−0.902686	−0.451343	−	0.892351i	$-0.649055\pi$
$269$	−14.8051	−0.902686	−0.451343	+	0.892351i	$0.649055\pi$
$270$	4.76633	0.290070
$271$	−0.0646361	−0.00392636	−0.00196318	−	0.999998i	$-0.500625\pi$
$271$	−0.0646361	−0.00392636	−0.00196318	+	0.999998i	$0.500625\pi$
$272$	−5.91517	−0.358660
$273$	0	0
$274$	−15.4617	−0.934077
$275$	19.2089	1.15834
$276$	18.0287	1.08520
$277$	4.25115	0.255427	0.127713	−	0.991811i	$-0.459236\pi$
$277$	4.25115	0.255427	0.127713	+	0.991811i	$0.459236\pi$
$278$	14.3022	0.857789
$279$	2.76544	0.165562
$280$	−3.48754	−0.208420
$281$	11.0454	0.658916	0.329458	−	0.944170i	$-0.393134\pi$
$281$	11.0454	0.658916	0.329458	+	0.944170i	$0.393134\pi$
$282$	−4.09419	−0.243805
$283$	11.2854	0.670849	0.335424	−	0.942067i	$-0.391120\pi$
$283$	11.2854	0.670849	0.335424	+	0.942067i	$0.391120\pi$
$284$	−4.18658	−0.248428
$285$	−46.3404	−2.74497
$286$	0	0
$287$	0.157708	0.00930922
$288$	3.53463	0.208280
$289$	17.9892	1.05819
$290$	−24.8758	−1.46076
$291$	−8.07650	−0.473453
$292$	15.0361	0.879919
$293$	−26.0442	−1.52152	−0.760758	−	0.649036i	$-0.775172\pi$
$293$	−26.0442	−1.52152	−0.760758	+	0.649036i	$0.775172\pi$
$294$	−2.55629	−0.149086
$295$	−33.2719	−1.93716
$296$	−7.81450	−0.454209
$297$	−3.66504	−0.212667
$298$	3.55717	0.206062
$299$	0	0
$300$	−18.3105	−1.05716
$301$	−0.330202	−0.0190325
$302$	9.52740	0.548240
$303$	−9.67941	−0.556067
$304$	−5.19793	−0.298122
$305$	−53.7447	−3.07741
$306$	−20.9079	−1.19523
$307$	25.0551	1.42997	0.714986	−	0.699139i	$-0.246433\pi$
$307$	25.0551	1.42997	0.714986	+	0.699139i	$0.246433\pi$
$308$	2.68172	0.152805
$309$	−17.4042	−0.990092
$310$	−2.72859	−0.154974
$311$	32.4330	1.83911	0.919554	−	0.392964i	$-0.128550\pi$
$311$	32.4330	1.83911	0.919554	+	0.392964i	$0.128550\pi$
$312$	0	0
$313$	2.22517	0.125774	0.0628870	−	0.998021i	$-0.479969\pi$
$313$	2.22517	0.125774	0.0628870	+	0.998021i	$0.479969\pi$
$314$	20.8345	1.17576
$315$	−12.3272	−0.694557
$316$	−0.293356	−0.0165026
$317$	3.83753	0.215537	0.107769	−	0.994176i	$-0.465629\pi$
$317$	3.83753	0.215537	0.107769	+	0.994176i	$0.465629\pi$
$318$	−10.0360	−0.562793
$319$	19.1281	1.07097
$320$	−3.48754	−0.194959
$321$	−36.5592	−2.04054
$322$	−7.05268	−0.393030
$323$	30.7466	1.71079
$324$	−7.11027	−0.395015
$325$	0	0
$326$	6.30603	0.349259
$327$	−11.6994	−0.646976
$328$	0.157708	0.00870797
$329$	1.60161	0.0882997
$330$	23.9080	1.31609
$331$	−6.08365	−0.334387	−0.167194	−	0.985924i	$-0.553471\pi$
$331$	−6.08365	−0.334387	−0.167194	+	0.985924i	$0.553471\pi$
$332$	−2.87495	−0.157783
$333$	−27.6214	−1.51364
$334$	−6.66871	−0.364896
$335$	−3.37163	−0.184212
$336$	−2.55629	−0.139457
$337$	19.3746	1.05540	0.527700	−	0.849431i	$-0.323054\pi$
$337$	19.3746	1.05540	0.527700	+	0.849431i	$0.323054\pi$
$338$	0	0
$339$	7.70202	0.418316
$340$	20.6294	1.11878
$341$	2.09813	0.113620
$342$	−18.3728	−0.993485
$343$	1.00000	0.0539949
$344$	−0.330202	−0.0178033
$345$	−62.8758	−3.38512
$346$	−21.3192	−1.14613
$347$	−9.02056	−0.484249	−0.242124	−	0.970245i	$-0.577844\pi$
$347$	−9.02056	−0.484249	−0.242124	+	0.970245i	$0.577844\pi$
$348$	−18.2335	−0.977417
$349$	−6.97685	−0.373462	−0.186731	−	0.982411i	$-0.559789\pi$
$349$	−6.97685	−0.373462	−0.186731	+	0.982411i	$0.559789\pi$
$350$	7.16292	0.382874
$351$	0	0
$352$	2.68172	0.142936
$353$	−25.0386	−1.33267	−0.666335	−	0.745653i	$-0.732138\pi$
$353$	−25.0386	−1.33267	−0.666335	+	0.745653i	$0.732138\pi$
$354$	−24.3876	−1.29619
$355$	14.6008	0.774932
$356$	−5.21325	−0.276302
$357$	15.1209	0.800283
$358$	15.4384	0.815946
$359$	−37.6090	−1.98493	−0.992463	−	0.122545i	$-0.960894\pi$
$359$	−37.6090	−1.98493	−0.992463	+	0.122545i	$0.960894\pi$
$360$	−12.3272	−0.649698
$361$	8.01845	0.422024
$362$	13.2818	0.698078
$363$	9.73535	0.510973
$364$	0	0
$365$	−52.4388	−2.74477
$366$	−39.3938	−2.05914
$367$	21.0910	1.10094	0.550470	−	0.834855i	$-0.314449\pi$
$367$	21.0910	1.10094	0.550470	+	0.834855i	$0.314449\pi$
$368$	−7.05268	−0.367646
$369$	0.557440	0.0290192
$370$	27.2534	1.41684
$371$	3.92601	0.203828
$372$	−2.00000	−0.103695
$373$	14.0942	0.729768	0.364884	−	0.931053i	$-0.381109\pi$
$373$	14.0942	0.729768	0.364884	+	0.931053i	$0.381109\pi$
$374$	−15.8628	−0.820246
$375$	19.2828	0.995758
$376$	1.60161	0.0825968
$377$	0	0
$378$	−1.36668	−0.0702942
$379$	33.1137	1.70093	0.850467	−	0.526028i	$-0.176319\pi$
$379$	33.1137	1.70093	0.850467	+	0.526028i	$0.176319\pi$
$380$	18.1280	0.929945
$381$	−28.4402	−1.45703
$382$	−11.9246	−0.610115
$383$	25.9321	1.32507	0.662534	−	0.749032i	$-0.269481\pi$
$383$	25.9321	1.32507	0.662534	+	0.749032i	$0.269481\pi$
$384$	−2.55629	−0.130450
$385$	−9.35259	−0.476652
$386$	−5.34936	−0.272275
$387$	−1.16714	−0.0593292
$388$	3.15946	0.160397
$389$	30.5647	1.54969	0.774847	−	0.632149i	$-0.217827\pi$
$389$	30.5647	1.54969	0.774847	+	0.632149i	$0.217827\pi$
$390$	0	0
$391$	41.7178	2.10976
$392$	1.00000	0.0505076
$393$	−38.1186	−1.92283
$394$	−13.1938	−0.664692
$395$	1.02309	0.0514773
$396$	9.47889	0.476332
$397$	22.4614	1.12731	0.563653	−	0.826012i	$-0.309396\pi$
$397$	22.4614	1.12731	0.563653	+	0.826012i	$0.309396\pi$
$398$	20.0516	1.00509
$399$	13.2874	0.665203
$400$	7.16292	0.358146
$401$	17.0288	0.850376	0.425188	−	0.905105i	$-0.360208\pi$
$401$	17.0288	0.850376	0.425188	+	0.905105i	$0.360208\pi$
$402$	−2.47133	−0.123259
$403$	0	0
$404$	3.78650	0.188386
$405$	24.7973	1.23219
$406$	7.13278	0.353994
$407$	−20.9563	−1.03876
$408$	15.1209	0.748596
$409$	−5.13532	−0.253925	−0.126963	−	0.991908i	$-0.540523\pi$
$409$	−5.13532	−0.253925	−0.126963	+	0.991908i	$0.540523\pi$
$410$	−0.550013	−0.0271632
$411$	39.5247	1.94961
$412$	6.80839	0.335425
$413$	9.54021	0.469443
$414$	−24.9286	−1.22517
$415$	10.0265	0.492181
$416$	0	0
$417$	−36.5606	−1.79038
$418$	−13.9394	−0.681797
$419$	−31.8836	−1.55762	−0.778808	−	0.627263i	$-0.784175\pi$
$419$	−31.8836	−1.55762	−0.778808	+	0.627263i	$0.784175\pi$
$420$	8.91517	0.435016
$421$	−14.7648	−0.719594	−0.359797	−	0.933031i	$-0.617154\pi$
$421$	−14.7648	−0.719594	−0.359797	+	0.933031i	$0.617154\pi$
$422$	−7.96144	−0.387557
$423$	5.66111	0.275252
$424$	3.92601	0.190664
$425$	−42.3698	−2.05524
$426$	10.7021	0.518519
$427$	15.4105	0.745767
$428$	14.3017	0.691297
$429$	0	0
$430$	1.15159	0.0555347
$431$	35.1088	1.69113	0.845565	−	0.533872i	$-0.179264\pi$
$431$	35.1088	1.69113	0.845565	+	0.533872i	$0.179264\pi$
$432$	−1.36668	−0.0657542
$433$	−3.97251	−0.190907	−0.0954533	−	0.995434i	$-0.530430\pi$
$433$	−3.97251	−0.190907	−0.0954533	+	0.995434i	$0.530430\pi$
$434$	0.782383	0.0375556
$435$	63.5899	3.04890
$436$	4.57669	0.219184
$437$	36.6593	1.75365
$438$	−38.4366	−1.83657
$439$	5.75277	0.274565	0.137282	−	0.990532i	$-0.456163\pi$
$439$	5.75277	0.274565	0.137282	+	0.990532i	$0.456163\pi$
$440$	−9.35259	−0.445867
$441$	3.53463	0.168316
$442$	0	0
$443$	−27.0804	−1.28663	−0.643315	−	0.765602i	$-0.722441\pi$
$443$	−27.0804	−1.28663	−0.643315	+	0.765602i	$0.722441\pi$
$444$	19.9762	0.948026
$445$	18.1814	0.861881
$446$	−21.5417	−1.02003
$447$	−9.09318	−0.430092
$448$	1.00000	0.0472456
$449$	8.24914	0.389301	0.194650	−	0.980873i	$-0.437643\pi$
$449$	8.24914	0.389301	0.194650	+	0.980873i	$0.437643\pi$
$450$	25.3183	1.19351
$451$	0.422929	0.0199149
$452$	−3.01297	−0.141718
$453$	−24.3548	−1.14429
$454$	−3.65771	−0.171665
$455$	0	0
$456$	13.2874	0.622241
$457$	38.6967	1.81015	0.905077	−	0.425247i	$-0.139813\pi$
$457$	38.6967	1.81015	0.905077	+	0.425247i	$0.139813\pi$
$458$	−9.74752	−0.455472
$459$	8.08411	0.377334
$460$	24.5965	1.14682
$461$	−13.1348	−0.611751	−0.305875	−	0.952072i	$-0.598949\pi$
$461$	−13.1348	−0.611751	−0.305875	+	0.952072i	$0.598949\pi$
$462$	−6.85526	−0.318935
$463$	6.98417	0.324582	0.162291	−	0.986743i	$-0.448112\pi$
$463$	6.98417	0.324582	0.162291	+	0.986743i	$0.448112\pi$
$464$	7.13278	0.331131
$465$	6.97507	0.323461
$466$	2.72895	0.126416
$467$	−5.62691	−0.260382	−0.130191	−	0.991489i	$-0.541559\pi$
$467$	−5.62691	−0.260382	−0.130191	+	0.991489i	$0.541559\pi$
$468$	0	0
$469$	0.966765	0.0446411
$470$	−5.58568	−0.257648
$471$	−53.2591	−2.45405
$472$	9.54021	0.439124
$473$	−0.885509	−0.0407158
$474$	0.749905	0.0344443
$475$	−37.2323	−1.70834
$476$	−5.91517	−0.271121
$477$	13.8770	0.635384
$478$	12.2347	0.559604
$479$	−25.1191	−1.14772	−0.573861	−	0.818953i	$-0.694555\pi$
$479$	−25.1191	−1.14772	−0.573861	+	0.818953i	$0.694555\pi$
$480$	8.91517	0.406920
$481$	0	0
$482$	−24.2176	−1.10308
$483$	18.0287	0.820334
$484$	−3.80839	−0.173108
$485$	−11.0187	−0.500334
$486$	22.2760	1.01046
$487$	17.6758	0.800968	0.400484	−	0.916304i	$-0.368842\pi$
$487$	17.6758	0.800968	0.400484	+	0.916304i	$0.368842\pi$
$488$	15.4105	0.697601
$489$	−16.1201	−0.728975
$490$	−3.48754	−0.157551
$491$	31.9949	1.44391	0.721956	−	0.691939i	$-0.243243\pi$
$491$	31.9949	1.44391	0.721956	+	0.691939i	$0.243243\pi$
$492$	−0.403148	−0.0181753
$493$	−42.1916	−1.90021
$494$	0	0
$495$	−33.0580	−1.48585
$496$	0.782383	0.0351300
$497$	−4.18658	−0.187794
$498$	7.34921	0.329326
$499$	−11.6416	−0.521149	−0.260574	−	0.965454i	$-0.583912\pi$
$499$	−11.6416	−0.521149	−0.260574	+	0.965454i	$0.583912\pi$
$500$	−7.54326	−0.337345
$501$	17.0472	0.761612
$502$	2.01371	0.0898762
$503$	15.0353	0.670390	0.335195	−	0.942149i	$-0.391198\pi$
$503$	15.0353	0.670390	0.335195	+	0.942149i	$0.391198\pi$
$504$	3.53463	0.157445
$505$	−13.2056	−0.587640
$506$	−18.9133	−0.840798
$507$	0	0
$508$	11.1256	0.493616
$509$	2.56096	0.113513	0.0567563	−	0.998388i	$-0.481924\pi$
$509$	2.56096	0.113513	0.0567563	+	0.998388i	$0.481924\pi$
$510$	−52.7347	−2.33513
$511$	15.0361	0.665156
$512$	1.00000	0.0441942
$513$	7.10388	0.313644
$514$	−2.14218	−0.0944874
$515$	−23.7445	−1.04631
$516$	0.844093	0.0371591
$517$	4.29507	0.188897
$518$	−7.81450	−0.343349
$519$	54.4981	2.39220
$520$	0	0
$521$	−31.0544	−1.36052	−0.680259	−	0.732972i	$-0.738133\pi$
$521$	−31.0544	−1.36052	−0.680259	+	0.732972i	$0.738133\pi$
$522$	25.2118	1.10349
$523$	−4.36360	−0.190807	−0.0954035	−	0.995439i	$-0.530414\pi$
$523$	−4.36360	−0.190807	−0.0954035	+	0.995439i	$0.530414\pi$
$524$	14.9117	0.651420
$525$	−18.3105	−0.799136
$526$	−10.8626	−0.473633
$527$	−4.62793	−0.201596
$528$	−6.85526	−0.298337
$529$	26.7402	1.16262
$530$	−13.6921	−0.594747
$531$	33.7211	1.46337
$532$	−5.19793	−0.225359
$533$	0	0
$534$	13.3266	0.576698
$535$	−49.8776	−2.15640
$536$	0.966765	0.0417579
$537$	−39.4651	−1.70305
$538$	−14.8051	−0.638295
$539$	2.68172	0.115510
$540$	4.76633	0.205110
$541$	−17.2191	−0.740305	−0.370152	−	0.928971i	$-0.620695\pi$
$541$	−17.2191	−0.740305	−0.370152	+	0.928971i	$0.620695\pi$
$542$	−0.0646361	−0.00277636
$543$	−33.9523	−1.45703
$544$	−5.91517	−0.253611
$545$	−15.9614	−0.683710
$546$	0	0
$547$	42.8331	1.83141	0.915706	−	0.401849i	$-0.131632\pi$
$547$	42.8331	1.83141	0.915706	+	0.401849i	$0.131632\pi$
$548$	−15.4617	−0.660492
$549$	54.4705	2.32474
$550$	19.2089	0.819071
$551$	−37.0757	−1.57948
$552$	18.0287	0.767353
$553$	−0.293356	−0.0124748
$554$	4.25115	0.180614
$555$	−69.6676	−2.95722
$556$	14.3022	0.606548
$557$	24.2206	1.02626	0.513129	−	0.858312i	$-0.328486\pi$
$557$	24.2206	1.02626	0.513129	+	0.858312i	$0.328486\pi$
$558$	2.76544	0.117070
$559$	0	0
$560$	−3.48754	−0.147375
$561$	40.5500	1.71202
$562$	11.0454	0.465924
$563$	−13.2481	−0.558341	−0.279170	−	0.960242i	$-0.590059\pi$
$563$	−13.2481	−0.558341	−0.279170	+	0.960242i	$0.590059\pi$
$564$	−4.09419	−0.172396
$565$	10.5078	0.442068
$566$	11.2854	0.474362
$567$	−7.11027	−0.298603
$568$	−4.18658	−0.175665
$569$	−24.9921	−1.04772	−0.523861	−	0.851804i	$-0.675509\pi$
$569$	−24.9921	−1.04772	−0.523861	+	0.851804i	$0.675509\pi$
$570$	−46.3404	−1.94099
$571$	−22.5276	−0.942750	−0.471375	−	0.881933i	$-0.656242\pi$
$571$	−22.5276	−0.942750	−0.471375	+	0.881933i	$0.656242\pi$
$572$	0	0
$573$	30.4827	1.27344
$574$	0.157708	0.00658261
$575$	−50.5177	−2.10674
$576$	3.53463	0.147276
$577$	12.9848	0.540564	0.270282	−	0.962781i	$-0.412883\pi$
$577$	12.9848	0.540564	0.270282	+	0.962781i	$0.412883\pi$
$578$	17.9892	0.748252
$579$	13.6745	0.568294
$580$	−24.8758	−1.03291
$581$	−2.87495	−0.119273
$582$	−8.07650	−0.334782
$583$	10.5285	0.436044
$584$	15.0361	0.622197
$585$	0	0
$586$	−26.0442	−1.07587
$587$	3.49432	0.144226	0.0721131	−	0.997396i	$-0.477026\pi$
$587$	3.49432	0.144226	0.0721131	+	0.997396i	$0.477026\pi$
$588$	−2.55629	−0.105420
$589$	−4.06677	−0.167568
$590$	−33.2719	−1.36978
$591$	33.7271	1.38735
$592$	−7.81450	−0.321174
$593$	−23.2140	−0.953283	−0.476642	−	0.879098i	$-0.658146\pi$
$593$	−23.2140	−0.953283	−0.476642	+	0.879098i	$0.658146\pi$
$594$	−3.66504	−0.150378
$595$	20.6294	0.845721
$596$	3.55717	0.145708
$597$	−51.2577	−2.09784
$598$	0	0
$599$	18.3645	0.750354	0.375177	−	0.926953i	$-0.377582\pi$
$599$	18.3645	0.750354	0.375177	+	0.926953i	$0.377582\pi$
$600$	−18.3105	−0.747524
$601$	−4.75965	−0.194150	−0.0970751	−	0.995277i	$-0.530949\pi$
$601$	−4.75965	−0.194150	−0.0970751	+	0.995277i	$0.530949\pi$
$602$	−0.330202	−0.0134580
$603$	3.41716	0.139157
$604$	9.52740	0.387664
$605$	13.2819	0.539986
$606$	−9.67941	−0.393199
$607$	20.9656	0.850968	0.425484	−	0.904966i	$-0.360104\pi$
$607$	20.9656	0.850968	0.425484	+	0.904966i	$0.360104\pi$
$608$	−5.19793	−0.210804
$609$	−18.2335	−0.738858
$610$	−53.7447	−2.17606
$611$	0	0
$612$	−20.9079	−0.845153
$613$	−29.3124	−1.18392	−0.591959	−	0.805968i	$-0.701645\pi$
$613$	−29.3124	−1.18392	−0.591959	+	0.805968i	$0.701645\pi$
$614$	25.0551	1.01114
$615$	1.40599	0.0566952
$616$	2.68172	0.108050
$617$	5.26343	0.211898	0.105949	−	0.994372i	$-0.466212\pi$
$617$	5.26343	0.211898	0.105949	+	0.994372i	$0.466212\pi$
$618$	−17.4042	−0.700101
$619$	−10.9663	−0.440774	−0.220387	−	0.975413i	$-0.570732\pi$
$619$	−10.9663	−0.440774	−0.220387	+	0.975413i	$0.570732\pi$
$620$	−2.72859	−0.109583
$621$	9.63872	0.386788
$622$	32.4330	1.30045
$623$	−5.21325	−0.208864
$624$	0	0
$625$	−9.50720	−0.380288
$626$	2.22517	0.0889357
$627$	35.6331	1.42305
$628$	20.8345	0.831388
$629$	46.2241	1.84307
$630$	−12.3272	−0.491126
$631$	−24.3229	−0.968278	−0.484139	−	0.874991i	$-0.660867\pi$
$631$	−24.3229	−0.968278	−0.484139	+	0.874991i	$0.660867\pi$
$632$	−0.293356	−0.0116691
$633$	20.3518	0.808910
$634$	3.83753	0.152408
$635$	−38.8008	−1.53976
$636$	−10.0360	−0.397954
$637$	0	0
$638$	19.1281	0.757289
$639$	−14.7980	−0.585400
$640$	−3.48754	−0.137857
$641$	1.30118	0.0513937	0.0256968	−	0.999670i	$-0.491820\pi$
$641$	1.30118	0.0513937	0.0256968	+	0.999670i	$0.491820\pi$
$642$	−36.5592	−1.44288
$643$	−5.62971	−0.222014	−0.111007	−	0.993820i	$-0.535408\pi$
$643$	−5.62971	−0.222014	−0.111007	+	0.993820i	$0.535408\pi$
$644$	−7.05268	−0.277914
$645$	−2.94381	−0.115912
$646$	30.7466	1.20971
$647$	−11.8127	−0.464405	−0.232202	−	0.972667i	$-0.574593\pi$
$647$	−11.8127	−0.464405	−0.232202	+	0.972667i	$0.574593\pi$
$648$	−7.11027	−0.279318
$649$	25.5842	1.00427
$650$	0	0
$651$	−2.00000	−0.0783862
$652$	6.30603	0.246963
$653$	−3.12013	−0.122100	−0.0610500	−	0.998135i	$-0.519445\pi$
$653$	−3.12013	−0.122100	−0.0610500	+	0.998135i	$0.519445\pi$
$654$	−11.6994	−0.457481
$655$	−52.0050	−2.03201
$656$	0.157708	0.00615747
$657$	53.1469	2.07346
$658$	1.60161	0.0624373
$659$	37.5067	1.46105	0.730526	−	0.682885i	$-0.239275\pi$
$659$	37.5067	1.46105	0.730526	+	0.682885i	$0.239275\pi$
$660$	23.9080	0.930616
$661$	−35.7746	−1.39147	−0.695735	−	0.718299i	$-0.744921\pi$
$661$	−35.7746	−1.39147	−0.695735	+	0.718299i	$0.744921\pi$
$662$	−6.08365	−0.236448
$663$	0	0
$664$	−2.87495	−0.111570
$665$	18.1280	0.702972
$666$	−27.6214	−1.07031
$667$	−50.3052	−1.94783
$668$	−6.66871	−0.258020
$669$	55.0670	2.12901
$670$	−3.37163	−0.130257
$671$	41.3266	1.59540
$672$	−2.55629	−0.0986111
$673$	−8.62162	−0.332339	−0.166170	−	0.986097i	$-0.553140\pi$
$673$	−8.62162	−0.332339	−0.166170	+	0.986097i	$0.553140\pi$
$674$	19.3746	0.746281
$675$	−9.78938	−0.376793
$676$	0	0
$677$	−15.5551	−0.597829	−0.298915	−	0.954280i	$-0.596625\pi$
$677$	−15.5551	−0.597829	−0.298915	+	0.954280i	$0.596625\pi$
$678$	7.70202	0.295794
$679$	3.15946	0.121249
$680$	20.6294	0.791100
$681$	9.35019	0.358300
$682$	2.09813	0.0803416
$683$	−8.89795	−0.340471	−0.170235	−	0.985403i	$-0.554453\pi$
$683$	−8.89795	−0.340471	−0.170235	+	0.985403i	$0.554453\pi$
$684$	−18.3728	−0.702500
$685$	53.9233	2.06030
$686$	1.00000	0.0381802
$687$	24.9175	0.950663
$688$	−0.330202	−0.0125888
$689$	0	0
$690$	−62.8758	−2.39364
$691$	−38.1797	−1.45243	−0.726213	−	0.687470i	$-0.758721\pi$
$691$	−38.1797	−1.45243	−0.726213	+	0.687470i	$0.758721\pi$
$692$	−21.3192	−0.810434
$693$	9.47889	0.360073
$694$	−9.02056	−0.342416
$695$	−49.8795	−1.89204
$696$	−18.2335	−0.691138
$697$	−0.932870	−0.0353350
$698$	−6.97685	−0.264078
$699$	−6.97600	−0.263856
$700$	7.16292	0.270733
$701$	−44.0952	−1.66545	−0.832727	−	0.553684i	$-0.813221\pi$
$701$	−44.0952	−1.66545	−0.832727	+	0.553684i	$0.813221\pi$
$702$	0	0
$703$	40.6192	1.53198
$704$	2.68172	0.101071
$705$	14.2786	0.537765
$706$	−25.0386	−0.942340
$707$	3.78650	0.142406
$708$	−24.3876	−0.916541
$709$	12.2637	0.460573	0.230287	−	0.973123i	$-0.426034\pi$
$709$	12.2637	0.460573	0.230287	+	0.973123i	$0.426034\pi$
$710$	14.6008	0.547960
$711$	−1.03691	−0.0388870
$712$	−5.21325	−0.195375
$713$	−5.51789	−0.206647
$714$	15.1209	0.565885
$715$	0	0
$716$	15.4384	0.576961
$717$	−31.2756	−1.16801
$718$	−37.6090	−1.40355
$719$	27.1933	1.01414	0.507070	−	0.861905i	$-0.330728\pi$
$719$	27.1933	1.01414	0.507070	+	0.861905i	$0.330728\pi$
$720$	−12.3272	−0.459406
$721$	6.80839	0.253558
$722$	8.01845	0.298416
$723$	61.9074	2.30236
$724$	13.2818	0.493616
$725$	51.0915	1.89749
$726$	9.73535	0.361313
$727$	18.5289	0.687200	0.343600	−	0.939116i	$-0.388354\pi$
$727$	18.5289	0.687200	0.343600	+	0.939116i	$0.388354\pi$
$728$	0	0
$729$	−35.6131	−1.31900
$730$	−52.4388	−1.94085
$731$	1.95320	0.0722417
$732$	−39.3938	−1.45604
$733$	−50.8986	−1.87998	−0.939992	−	0.341196i	$-0.889168\pi$
$733$	−50.8986	−1.87998	−0.939992	+	0.341196i	$0.889168\pi$
$734$	21.0910	0.778482
$735$	8.91517	0.328841
$736$	−7.05268	−0.259965
$737$	2.59259	0.0954993
$738$	0.557440	0.0205197
$739$	8.58969	0.315977	0.157988	−	0.987441i	$-0.449499\pi$
$739$	8.58969	0.315977	0.157988	+	0.987441i	$0.449499\pi$
$740$	27.2534	1.00185
$741$	0	0
$742$	3.92601	0.144128
$743$	38.1873	1.40095	0.700477	−	0.713675i	$-0.252971\pi$
$743$	38.1873	1.40095	0.700477	+	0.713675i	$0.252971\pi$
$744$	−2.00000	−0.0733236
$745$	−12.4058	−0.454512
$746$	14.0942	0.516024
$747$	−10.1619	−0.371804
$748$	−15.8628	−0.580002
$749$	14.3017	0.522572
$750$	19.2828	0.704107
$751$	−2.84971	−0.103987	−0.0519937	−	0.998647i	$-0.516558\pi$
$751$	−2.84971	−0.103987	−0.0519937	+	0.998647i	$0.516558\pi$
$752$	1.60161	0.0584048
$753$	−5.14763	−0.187590
$754$	0	0
$755$	−33.2272	−1.20926
$756$	−1.36668	−0.0497055
$757$	19.2790	0.700707	0.350354	−	0.936618i	$-0.386061\pi$
$757$	19.2790	0.700707	0.350354	+	0.936618i	$0.386061\pi$
$758$	33.1137	1.20274
$759$	48.3479	1.75492
$760$	18.1280	0.657570
$761$	−11.5840	−0.419919	−0.209959	−	0.977710i	$-0.567333\pi$
$761$	−11.5840	−0.419919	−0.209959	+	0.977710i	$0.567333\pi$
$762$	−28.4402	−1.03028
$763$	4.57669	0.165687
$764$	−11.9246	−0.431417
$765$	72.9172	2.63633
$766$	25.9321	0.936964
$767$	0	0
$768$	−2.55629	−0.0922423
$769$	24.4203	0.880619	0.440310	−	0.897846i	$-0.354869\pi$
$769$	24.4203	0.880619	0.440310	+	0.897846i	$0.354869\pi$
$770$	−9.35259	−0.337044
$771$	5.47603	0.197214
$772$	−5.34936	−0.192528
$773$	−6.98615	−0.251275	−0.125637	−	0.992076i	$-0.540098\pi$
$773$	−6.98615	−0.251275	−0.125637	+	0.992076i	$0.540098\pi$
$774$	−1.16714	−0.0419521
$775$	5.60415	0.201307
$776$	3.15946	0.113418
$777$	19.9762	0.716640
$778$	30.5647	1.09580
$779$	−0.819755	−0.0293708
$780$	0	0
$781$	−11.2272	−0.401741
$782$	41.7178	1.49182
$783$	−9.74820	−0.348372
$784$	1.00000	0.0357143
$785$	−72.6612	−2.59339
$786$	−38.1186	−1.35965
$787$	−17.3473	−0.618364	−0.309182	−	0.951003i	$-0.600055\pi$
$787$	−17.3473	−0.618364	−0.309182	+	0.951003i	$0.600055\pi$
$788$	−13.1938	−0.470009
$789$	27.7681	0.988569
$790$	1.02309	0.0363999
$791$	−3.01297	−0.107129
$792$	9.47889	0.336818
$793$	0	0
$794$	22.4614	0.797125
$795$	35.0010	1.24136
$796$	20.0516	0.710709
$797$	40.3340	1.42871	0.714353	−	0.699786i	$-0.246721\pi$
$797$	40.3340	1.42871	0.714353	+	0.699786i	$0.246721\pi$
$798$	13.2874	0.470370
$799$	−9.47380	−0.335159
$800$	7.16292	0.253247
$801$	−18.4269	−0.651083
$802$	17.0288	0.601307
$803$	40.3225	1.42295
$804$	−2.47133	−0.0871572
$805$	24.5965	0.866912
$806$	0	0
$807$	37.8463	1.33225
$808$	3.78650	0.133209
$809$	2.71050	0.0952961	0.0476481	−	0.998864i	$-0.484827\pi$
$809$	2.71050	0.0952961	0.0476481	+	0.998864i	$0.484827\pi$
$810$	24.7973	0.871290
$811$	29.7449	1.04448	0.522242	−	0.852797i	$-0.325096\pi$
$811$	29.7449	1.04448	0.522242	+	0.852797i	$0.325096\pi$
$812$	7.13278	0.250312
$813$	0.165229	0.00579483
$814$	−20.9563	−0.734518
$815$	−21.9925	−0.770365
$816$	15.1209	0.529337
$817$	1.71637	0.0600481
$818$	−5.13532	−0.179552
$819$	0	0
$820$	−0.550013	−0.0192073
$821$	17.3317	0.604880	0.302440	−	0.953168i	$-0.402199\pi$
$821$	17.3317	0.604880	0.302440	+	0.953168i	$0.402199\pi$
$822$	39.5247	1.37858
$823$	11.4589	0.399432	0.199716	−	0.979854i	$-0.435998\pi$
$823$	11.4589	0.399432	0.199716	+	0.979854i	$0.435998\pi$
$824$	6.80839	0.237181
$825$	−49.1036	−1.70957
$826$	9.54021	0.331946
$827$	5.41259	0.188214	0.0941070	−	0.995562i	$-0.470000\pi$
$827$	5.41259	0.188214	0.0941070	+	0.995562i	$0.470000\pi$
$828$	−24.9286	−0.866329
$829$	34.8694	1.21107	0.605533	−	0.795820i	$-0.292960\pi$
$829$	34.8694	1.21107	0.605533	+	0.795820i	$0.292960\pi$
$830$	10.0265	0.348024
$831$	−10.8672	−0.376979
$832$	0	0
$833$	−5.91517	−0.204948
$834$	−36.5606	−1.26599
$835$	23.2574	0.804855
$836$	−13.9394	−0.482103
$837$	−1.06926	−0.0369592
$838$	−31.8836	−1.10140
$839$	24.7350	0.853947	0.426973	−	0.904264i	$-0.359580\pi$
$839$	24.7350	0.853947	0.426973	+	0.904264i	$0.359580\pi$
$840$	8.91517	0.307602
$841$	21.8766	0.754365
$842$	−14.7648	−0.508830
$843$	−28.2354	−0.972478
$844$	−7.96144	−0.274044
$845$	0	0
$846$	5.66111	0.194633
$847$	−3.80839	−0.130858
$848$	3.92601	0.134820
$849$	−28.8488	−0.990089
$850$	−42.3698	−1.45327
$851$	55.1132	1.88925
$852$	10.7021	0.366648
$853$	6.14219	0.210304	0.105152	−	0.994456i	$-0.466467\pi$
$853$	6.14219	0.210304	0.105152	+	0.994456i	$0.466467\pi$
$854$	15.4105	0.527337
$855$	64.0757	2.19134
$856$	14.3017	0.488821
$857$	−32.2072	−1.10018	−0.550088	−	0.835106i	$-0.685406\pi$
$857$	−32.2072	−1.10018	−0.550088	+	0.835106i	$0.685406\pi$
$858$	0	0
$859$	−17.3714	−0.592705	−0.296352	−	0.955079i	$-0.595770\pi$
$859$	−17.3714	−0.592705	−0.296352	+	0.955079i	$0.595770\pi$
$860$	1.15159	0.0392690
$861$	−0.403148	−0.0137393
$862$	35.1088	1.19581
$863$	0.309300	0.0105287	0.00526435	−	0.999986i	$-0.498324\pi$
$863$	0.309300	0.0105287	0.00526435	+	0.999986i	$0.498324\pi$
$864$	−1.36668	−0.0464952
$865$	74.3515	2.52803
$866$	−3.97251	−0.134991
$867$	−45.9856	−1.56175
$868$	0.782383	0.0265558
$869$	−0.786699	−0.0266869
$870$	63.5899	2.15590
$871$	0	0
$872$	4.57669	0.154986
$873$	11.1675	0.377963
$874$	36.6593	1.24002
$875$	−7.54326	−0.255009
$876$	−38.4366	−1.29865
$877$	21.8148	0.736633	0.368316	−	0.929701i	$-0.379934\pi$
$877$	21.8148	0.736633	0.368316	+	0.929701i	$0.379934\pi$
$878$	5.75277	0.194147
$879$	66.5765	2.24557
$880$	−9.35259	−0.315276
$881$	−10.3626	−0.349126	−0.174563	−	0.984646i	$-0.555851\pi$
$881$	−10.3626	−0.349126	−0.174563	+	0.984646i	$0.555851\pi$
$882$	3.53463	0.119017
$883$	−47.4366	−1.59637	−0.798184	−	0.602414i	$-0.794206\pi$
$883$	−47.4366	−1.59637	−0.798184	+	0.602414i	$0.794206\pi$
$884$	0	0
$885$	85.0526	2.85901
$886$	−27.0804	−0.909785
$887$	20.3479	0.683216	0.341608	−	0.939843i	$-0.389028\pi$
$887$	20.3479	0.683216	0.341608	+	0.939843i	$0.389028\pi$
$888$	19.9762	0.670356
$889$	11.1256	0.373139
$890$	18.1814	0.609442
$891$	−19.0678	−0.638794
$892$	−21.5417	−0.721271
$893$	−8.32506	−0.278588
$894$	−9.09318	−0.304121
$895$	−53.8421	−1.79974
$896$	1.00000	0.0334077
$897$	0	0
$898$	8.24914	0.275277
$899$	5.58057	0.186122
$900$	25.3183	0.843943
$901$	−23.2230	−0.773670
$902$	0.422929	0.0140820
$903$	0.844093	0.0280897
$904$	−3.01297	−0.100210
$905$	−46.3209	−1.53976
$906$	−24.3548	−0.809135
$907$	−17.0130	−0.564908	−0.282454	−	0.959281i	$-0.591148\pi$
$907$	−17.0130	−0.564908	−0.282454	+	0.959281i	$0.591148\pi$
$908$	−3.65771	−0.121385
$909$	13.3839	0.443916
$910$	0	0
$911$	12.8289	0.425040	0.212520	−	0.977157i	$-0.431833\pi$
$911$	12.8289	0.425040	0.212520	+	0.977157i	$0.431833\pi$
$912$	13.2874	0.439991
$913$	−7.70980	−0.255157
$914$	38.6967	1.27997
$915$	137.387	4.54188
$916$	−9.74752	−0.322067
$917$	14.9117	0.492427
$918$	8.08411	0.266815
$919$	−38.5765	−1.27252	−0.636261	−	0.771474i	$-0.719520\pi$
$919$	−38.5765	−1.27252	−0.636261	+	0.771474i	$0.719520\pi$
$920$	24.5965	0.810922
$921$	−64.0482	−2.11046
$922$	−13.1348	−0.432573
$923$	0	0
$924$	−6.85526	−0.225521
$925$	−55.9746	−1.84043
$926$	6.98417	0.229514
$927$	24.0651	0.790403
$928$	7.13278	0.234145
$929$	4.34958	0.142705	0.0713526	−	0.997451i	$-0.477268\pi$
$929$	4.34958	0.142705	0.0713526	+	0.997451i	$0.477268\pi$
$930$	6.97507	0.228722
$931$	−5.19793	−0.170355
$932$	2.72895	0.0893897
$933$	−82.9083	−2.71430
$934$	−5.62691	−0.184118
$935$	55.3221	1.80923
$936$	0	0
$937$	−13.5931	−0.444068	−0.222034	−	0.975039i	$-0.571270\pi$
$937$	−13.5931	−0.444068	−0.222034	+	0.975039i	$0.571270\pi$
$938$	0.966765	0.0315660
$939$	−5.68819	−0.185627
$940$	−5.58568	−0.182185
$941$	24.5649	0.800792	0.400396	−	0.916342i	$-0.368873\pi$
$941$	24.5649	0.800792	0.400396	+	0.916342i	$0.368873\pi$
$942$	−53.2591	−1.73528
$943$	−1.11226	−0.0362203
$944$	9.54021	0.310508
$945$	4.76633	0.155049
$946$	−0.885509	−0.0287904
$947$	2.09781	0.0681697	0.0340848	−	0.999419i	$-0.489148\pi$
$947$	2.09781	0.0681697	0.0340848	+	0.999419i	$0.489148\pi$
$948$	0.749905	0.0243558
$949$	0	0
$950$	−37.2323	−1.20798
$951$	−9.80985	−0.318106
$952$	−5.91517	−0.191712
$953$	−40.3398	−1.30673	−0.653367	−	0.757042i	$-0.726644\pi$
$953$	−40.3398	−1.30673	−0.653367	+	0.757042i	$0.726644\pi$
$954$	13.8770	0.449284
$955$	41.5875	1.34574
$956$	12.2347	0.395700
$957$	−48.8971	−1.58062
$958$	−25.1191	−0.811562
$959$	−15.4617	−0.499285
$960$	8.91517	0.287736
$961$	−30.3879	−0.980254
$962$	0	0
$963$	50.5511	1.62899
$964$	−24.2176	−0.779998
$965$	18.6561	0.600560
$966$	18.0287	0.580064
$967$	2.90536	0.0934300	0.0467150	−	0.998908i	$-0.485125\pi$
$967$	2.90536	0.0934300	0.0467150	+	0.998908i	$0.485125\pi$
$968$	−3.80839	−0.122406
$969$	−78.5973	−2.52491
$970$	−11.0187	−0.353790
$971$	−11.7552	−0.377242	−0.188621	−	0.982050i	$-0.560402\pi$
$971$	−11.7552	−0.377242	−0.188621	+	0.982050i	$0.560402\pi$
$972$	22.2760	0.714502
$973$	14.3022	0.458508
$974$	17.6758	0.566370
$975$	0	0
$976$	15.4105	0.493278
$977$	20.0905	0.642751	0.321375	−	0.946952i	$-0.395855\pi$
$977$	20.0905	0.642751	0.321375	+	0.946952i	$0.395855\pi$
$978$	−16.1201	−0.515463
$979$	−13.9805	−0.446818
$980$	−3.48754	−0.111405
$981$	16.1769	0.516489
$982$	31.9949	1.02100
$983$	−30.8037	−0.982487	−0.491243	−	0.871022i	$-0.663457\pi$
$983$	−30.8037	−0.982487	−0.491243	+	0.871022i	$0.663457\pi$
$984$	−0.403148	−0.0128519
$985$	46.0138	1.46612
$986$	−42.1916	−1.34365
$987$	−4.09419	−0.130319
$988$	0	0
$989$	2.32881	0.0740518
$990$	−33.0580	−1.05065
$991$	−42.6457	−1.35469	−0.677343	−	0.735668i	$-0.736869\pi$
$991$	−42.6457	−1.35469	−0.677343	+	0.735668i	$0.736869\pi$
$992$	0.782383	0.0248407
$993$	15.5516	0.493514
$994$	−4.18658	−0.132790
$995$	−69.9306	−2.21695
$996$	7.34921	0.232868
$997$	−31.5540	−0.999326	−0.499663	−	0.866220i	$-0.666543\pi$
$997$	−31.5540	−0.999326	−0.499663	+	0.866220i	$0.666543\pi$
$998$	−11.6416	−0.368508
$999$	10.6799	0.337897

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2366.2.a.bh.1.1		6
13.2	odd	12		182.2.m.b.43.6	✓	12
13.5	odd	4		2366.2.d.r.337.1		12
13.7	odd	12		182.2.m.b.127.6	yes	12
13.8	odd	4		2366.2.d.r.337.7		12
13.12	even	2		2366.2.a.bf.1.1		6
39.2	even	12		1638.2.bj.g.1135.1		12
39.20	even	12		1638.2.bj.g.127.3		12
52.7	even	12		1456.2.cc.d.673.1		12
52.15	even	12		1456.2.cc.d.225.1		12
91.2	odd	12		1274.2.o.d.459.3		12
91.20	even	12		1274.2.m.c.491.4		12
91.33	even	12		1274.2.v.d.361.3		12
91.41	even	12		1274.2.m.c.589.4		12
91.46	odd	12		1274.2.o.d.569.6		12
91.54	even	12		1274.2.o.e.459.1		12
91.59	even	12		1274.2.o.e.569.4		12
91.67	odd	12		1274.2.v.e.667.1		12
91.72	odd	12		1274.2.v.e.361.1		12
91.80	even	12		1274.2.v.d.667.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.m.b.43.6	✓	12	13.2	odd	12
182.2.m.b.127.6	yes	12	13.7	odd	12
1274.2.m.c.491.4		12	91.20	even	12
1274.2.m.c.589.4		12	91.41	even	12
1274.2.o.d.459.3		12	91.2	odd	12
1274.2.o.d.569.6		12	91.46	odd	12
1274.2.o.e.459.1		12	91.54	even	12
1274.2.o.e.569.4		12	91.59	even	12
1274.2.v.d.361.3		12	91.33	even	12
1274.2.v.d.667.3		12	91.80	even	12
1274.2.v.e.361.1		12	91.72	odd	12
1274.2.v.e.667.1		12	91.67	odd	12
1456.2.cc.d.225.1		12	52.15	even	12
1456.2.cc.d.673.1		12	52.7	even	12
1638.2.bj.g.127.3		12	39.20	even	12
1638.2.bj.g.1135.1		12	39.2	even	12
2366.2.a.bf.1.1		6	13.12	even	2
2366.2.a.bh.1.1		6	1.1	even	1	trivial
2366.2.d.r.337.1		12	13.5	odd	4
2366.2.d.r.337.7		12	13.8	odd	4

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:	\( N \)	\(=\)	\( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2366.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.55629 q^{3} +1.00000 q^{4} -3.48754 q^{5} -2.55629 q^{6} +1.00000 q^{7} +1.00000 q^{8} +3.53463 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.55629 q^{3} +1.00000 q^{4} -3.48754 q^{5} -2.55629 q^{6} +1.00000 q^{7} +1.00000 q^{8} +3.53463 q^{9} -3.48754 q^{10} +2.68172 q^{11} -2.55629 q^{12} +1.00000 q^{14} +8.91517 q^{15} +1.00000 q^{16} -5.91517 q^{17} +3.53463 q^{18} -5.19793 q^{19} -3.48754 q^{20} -2.55629 q^{21} +2.68172 q^{22} -7.05268 q^{23} -2.55629 q^{24} +7.16292 q^{25} -1.36668 q^{27} +1.00000 q^{28} +7.13278 q^{29} +8.91517 q^{30} +0.782383 q^{31} +1.00000 q^{32} -6.85526 q^{33} -5.91517 q^{34} -3.48754 q^{35} +3.53463 q^{36} -7.81450 q^{37} -5.19793 q^{38} -3.48754 q^{40} +0.157708 q^{41} -2.55629 q^{42} -0.330202 q^{43} +2.68172 q^{44} -12.3272 q^{45} -7.05268 q^{46} +1.60161 q^{47} -2.55629 q^{48} +1.00000 q^{49} +7.16292 q^{50} +15.1209 q^{51} +3.92601 q^{53} -1.36668 q^{54} -9.35259 q^{55} +1.00000 q^{56} +13.2874 q^{57} +7.13278 q^{58} +9.54021 q^{59} +8.91517 q^{60} +15.4105 q^{61} +0.782383 q^{62} +3.53463 q^{63} +1.00000 q^{64} -6.85526 q^{66} +0.966765 q^{67} -5.91517 q^{68} +18.0287 q^{69} -3.48754 q^{70} -4.18658 q^{71} +3.53463 q^{72} +15.0361 q^{73} -7.81450 q^{74} -18.3105 q^{75} -5.19793 q^{76} +2.68172 q^{77} -0.293356 q^{79} -3.48754 q^{80} -7.11027 q^{81} +0.157708 q^{82} -2.87495 q^{83} -2.55629 q^{84} +20.6294 q^{85} -0.330202 q^{86} -18.2335 q^{87} +2.68172 q^{88} -5.21325 q^{89} -12.3272 q^{90} -7.05268 q^{92} -2.00000 q^{93} +1.60161 q^{94} +18.1280 q^{95} -2.55629 q^{96} +3.15946 q^{97} +1.00000 q^{98} +9.47889 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 2 q^{3} + 6 q^{4} - 2 q^{5} + 2 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 - 2 * q^5 + 2 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} + 2 q^{3} + 6 q^{4} - 2 q^{5} + 2 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9} - 2 q^{10} + 2 q^{11} + 2 q^{12} + 6 q^{14} + 14 q^{15} + 6 q^{16} + 4 q^{17} + 6 q^{18} - 4 q^{19} - 2 q^{20} + 2 q^{21} + 2 q^{22} - 6 q^{23} + 2 q^{24} + 12 q^{25} + 20 q^{27} + 6 q^{28} + 10 q^{29} + 14 q^{30} - 2 q^{31} + 6 q^{32} + 4 q^{34} - 2 q^{35} + 6 q^{36} - 4 q^{38} - 2 q^{40} + 6 q^{41} + 2 q^{42} + 26 q^{43} + 2 q^{44} - 6 q^{45} - 6 q^{46} - 8 q^{47} + 2 q^{48} + 6 q^{49} + 12 q^{50} + 18 q^{51} + 18 q^{53} + 20 q^{54} + 6 q^{55} + 6 q^{56} - 28 q^{57} + 10 q^{58} + 2 q^{59} + 14 q^{60} + 28 q^{61} - 2 q^{62} + 6 q^{63} + 6 q^{64} + 6 q^{67} + 4 q^{68} + 32 q^{69} - 2 q^{70} + 4 q^{71} + 6 q^{72} - 22 q^{73} - 48 q^{75} - 4 q^{76} + 2 q^{77} + 22 q^{79} - 2 q^{80} + 34 q^{81} + 6 q^{82} - 10 q^{83} + 2 q^{84} + 32 q^{85} + 26 q^{86} - 2 q^{87} + 2 q^{88} - 4 q^{89} - 6 q^{90} - 6 q^{92} - 12 q^{93} - 8 q^{94} + 32 q^{95} + 2 q^{96} - 12 q^{97} + 6 q^{98} - 2 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 - 2 * q^5 + 2 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9 - 2 * q^10 + 2 * q^11 + 2 * q^12 + 6 * q^14 + 14 * q^15 + 6 * q^16 + 4 * q^17 + 6 * q^18 - 4 * q^19 - 2 * q^20 + 2 * q^21 + 2 * q^22 - 6 * q^23 + 2 * q^24 + 12 * q^25 + 20 * q^27 + 6 * q^28 + 10 * q^29 + 14 * q^30 - 2 * q^31 + 6 * q^32 + 4 * q^34 - 2 * q^35 + 6 * q^36 - 4 * q^38 - 2 * q^40 + 6 * q^41 + 2 * q^42 + 26 * q^43 + 2 * q^44 - 6 * q^45 - 6 * q^46 - 8 * q^47 + 2 * q^48 + 6 * q^49 + 12 * q^50 + 18 * q^51 + 18 * q^53 + 20 * q^54 + 6 * q^55 + 6 * q^56 - 28 * q^57 + 10 * q^58 + 2 * q^59 + 14 * q^60 + 28 * q^61 - 2 * q^62 + 6 * q^63 + 6 * q^64 + 6 * q^67 + 4 * q^68 + 32 * q^69 - 2 * q^70 + 4 * q^71 + 6 * q^72 - 22 * q^73 - 48 * q^75 - 4 * q^76 + 2 * q^77 + 22 * q^79 - 2 * q^80 + 34 * q^81 + 6 * q^82 - 10 * q^83 + 2 * q^84 + 32 * q^85 + 26 * q^86 - 2 * q^87 + 2 * q^88 - 4 * q^89 - 6 * q^90 - 6 * q^92 - 12 * q^93 - 8 * q^94 + 32 * q^95 + 2 * q^96 - 12 * q^97 + 6 * q^98 - 2 * q^99

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