LMFDB - Embedded newform 4011.2.a.j.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.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:	$32.0279962507$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.272327 q^{2} -1.00000 q^{3} -1.92584 q^{4} -2.12381 q^{5} -0.272327 q^{6} -1.00000 q^{7} -1.06911 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.272327 q^{2} -1.00000 q^{3} -1.92584 q^{4} -2.12381 q^{5} -0.272327 q^{6} -1.00000 q^{7} -1.06911 q^{8} +1.00000 q^{9} -0.578372 q^{10} +3.95929 q^{11} +1.92584 q^{12} -6.83710 q^{13} -0.272327 q^{14} +2.12381 q^{15} +3.56053 q^{16} -3.01361 q^{17} +0.272327 q^{18} -4.39515 q^{19} +4.09012 q^{20} +1.00000 q^{21} +1.07822 q^{22} -0.487418 q^{23} +1.06911 q^{24} -0.489426 q^{25} -1.86193 q^{26} -1.00000 q^{27} +1.92584 q^{28} +4.16162 q^{29} +0.578372 q^{30} -6.39176 q^{31} +3.10786 q^{32} -3.95929 q^{33} -0.820689 q^{34} +2.12381 q^{35} -1.92584 q^{36} -4.80152 q^{37} -1.19692 q^{38} +6.83710 q^{39} +2.27059 q^{40} -10.9800 q^{41} +0.272327 q^{42} -8.26929 q^{43} -7.62496 q^{44} -2.12381 q^{45} -0.132737 q^{46} -4.00681 q^{47} -3.56053 q^{48} +1.00000 q^{49} -0.133284 q^{50} +3.01361 q^{51} +13.1672 q^{52} -2.58889 q^{53} -0.272327 q^{54} -8.40879 q^{55} +1.06911 q^{56} +4.39515 q^{57} +1.13332 q^{58} +6.83089 q^{59} -4.09012 q^{60} -9.24318 q^{61} -1.74065 q^{62} -1.00000 q^{63} -6.27470 q^{64} +14.5207 q^{65} -1.07822 q^{66} +9.95956 q^{67} +5.80373 q^{68} +0.487418 q^{69} +0.578372 q^{70} -0.904685 q^{71} -1.06911 q^{72} -16.9543 q^{73} -1.30759 q^{74} +0.489426 q^{75} +8.46434 q^{76} -3.95929 q^{77} +1.86193 q^{78} +14.4473 q^{79} -7.56189 q^{80} +1.00000 q^{81} -2.99016 q^{82} +1.48631 q^{83} -1.92584 q^{84} +6.40034 q^{85} -2.25196 q^{86} -4.16162 q^{87} -4.23293 q^{88} +0.491165 q^{89} -0.578372 q^{90} +6.83710 q^{91} +0.938689 q^{92} +6.39176 q^{93} -1.09116 q^{94} +9.33447 q^{95} -3.10786 q^{96} +4.97786 q^{97} +0.272327 q^{98} +3.95929 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9}+O(q^{10}) $ 26 * q - 26 * q^3 + 34 * q^4 + 2 * q^5 - 26 * q^7 + 26 * q^9	$ 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9} - q^{10} + 13 q^{11} - 34 q^{12} - q^{13} - 2 q^{15} + 54 q^{16} + q^{19} - 22 q^{20} + 26 q^{21} + 17 q^{22} - 3 q^{23} + 48 q^{25} + 6 q^{26} - 26 q^{27} - 34 q^{28} + 23 q^{29} + q^{30} + 18 q^{31} + 10 q^{32} - 13 q^{33} - 19 q^{34} - 2 q^{35} + 34 q^{36} + 23 q^{37} - 15 q^{38} + q^{39} + 14 q^{40} - 4 q^{41} + 5 q^{43} + 60 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{47} - 54 q^{48} + 26 q^{49} + 26 q^{50} + 19 q^{52} + 31 q^{53} + 41 q^{55} - q^{57} + 19 q^{58} - 2 q^{59} + 22 q^{60} - 2 q^{61} - 35 q^{62} - 26 q^{63} + 132 q^{64} + 40 q^{65} - 17 q^{66} + 47 q^{67} - 60 q^{68} + 3 q^{69} + q^{70} + 16 q^{71} - 23 q^{73} + 34 q^{74} - 48 q^{75} + 72 q^{76} - 13 q^{77} - 6 q^{78} + 14 q^{79} - 21 q^{80} + 26 q^{81} + 60 q^{82} - 4 q^{83} + 34 q^{84} + 36 q^{85} + 21 q^{86} - 23 q^{87} + 67 q^{88} + 14 q^{89} - q^{90} + q^{91} + 20 q^{92} - 18 q^{93} + 58 q^{94} - 4 q^{95} - 10 q^{96} + 48 q^{97} + 13 q^{99}+O(q^{100}) $ 26 * q - 26 * q^3 + 34 * q^4 + 2 * q^5 - 26 * q^7 + 26 * q^9 - q^10 + 13 * q^11 - 34 * q^12 - q^13 - 2 * q^15 + 54 * q^16 + q^19 - 22 * q^20 + 26 * q^21 + 17 * q^22 - 3 * q^23 + 48 * q^25 + 6 * q^26 - 26 * q^27 - 34 * q^28 + 23 * q^29 + q^30 + 18 * q^31 + 10 * q^32 - 13 * q^33 - 19 * q^34 - 2 * q^35 + 34 * q^36 + 23 * q^37 - 15 * q^38 + q^39 + 14 * q^40 - 4 * q^41 + 5 * q^43 + 60 * q^44 + 2 * q^45 + 8 * q^46 - 20 * q^47 - 54 * q^48 + 26 * q^49 + 26 * q^50 + 19 * q^52 + 31 * q^53 + 41 * q^55 - q^57 + 19 * q^58 - 2 * q^59 + 22 * q^60 - 2 * q^61 - 35 * q^62 - 26 * q^63 + 132 * q^64 + 40 * q^65 - 17 * q^66 + 47 * q^67 - 60 * q^68 + 3 * q^69 + q^70 + 16 * q^71 - 23 * q^73 + 34 * q^74 - 48 * q^75 + 72 * q^76 - 13 * q^77 - 6 * q^78 + 14 * q^79 - 21 * q^80 + 26 * q^81 + 60 * q^82 - 4 * q^83 + 34 * q^84 + 36 * q^85 + 21 * q^86 - 23 * q^87 + 67 * q^88 + 14 * q^89 - q^90 + q^91 + 20 * q^92 - 18 * q^93 + 58 * q^94 - 4 * q^95 - 10 * q^96 + 48 * q^97 + 13 * 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 $

$2$	0.272327	0.192565	0.0962823	−	0.995354i	$-0.469305\pi$
$2$	0.272327	0.192565	0.0962823	+	0.995354i	$0.469305\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.92584	−0.962919
$5$	−2.12381	−0.949797	−0.474899	−	0.880041i	$-0.657515\pi$
$5$	−2.12381	−0.949797	−0.474899	+	0.880041i	$0.657515\pi$
$6$	−0.272327	−0.111177
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.06911	−0.377989
$9$	1.00000	0.333333
$10$	−0.578372	−0.182897
$11$	3.95929	1.19377	0.596886	−	0.802326i	$-0.296404\pi$
$11$	3.95929	1.19377	0.596886	+	0.802326i	$0.296404\pi$
$12$	1.92584	0.555941
$13$	−6.83710	−1.89627	−0.948136	−	0.317866i	$-0.897034\pi$
$13$	−6.83710	−1.89627	−0.948136	+	0.317866i	$0.897034\pi$
$14$	−0.272327	−0.0727826
$15$	2.12381	0.548366
$16$	3.56053	0.890132
$17$	−3.01361	−0.730908	−0.365454	−	0.930829i	$-0.619086\pi$
$17$	−3.01361	−0.730908	−0.365454	+	0.930829i	$0.619086\pi$
$18$	0.272327	0.0641882
$19$	−4.39515	−1.00832	−0.504158	−	0.863611i	$-0.668197\pi$
$19$	−4.39515	−1.00832	−0.504158	+	0.863611i	$0.668197\pi$
$20$	4.09012	0.914578
$21$	1.00000	0.218218
$22$	1.07822	0.229878
$23$	−0.487418	−0.101634	−0.0508169	−	0.998708i	$-0.516182\pi$
$23$	−0.487418	−0.101634	−0.0508169	+	0.998708i	$0.516182\pi$
$24$	1.06911	0.218232
$25$	−0.489426	−0.0978851
$26$	−1.86193	−0.365155
$27$	−1.00000	−0.192450
$28$	1.92584	0.363949
$29$	4.16162	0.772793	0.386396	−	0.922333i	$-0.373720\pi$
$29$	4.16162	0.772793	0.386396	+	0.922333i	$0.373720\pi$
$30$	0.578372	0.105596
$31$	−6.39176	−1.14799	−0.573997	−	0.818857i	$-0.694608\pi$
$31$	−6.39176	−1.14799	−0.573997	+	0.818857i	$0.694608\pi$
$32$	3.10786	0.549396
$33$	−3.95929	−0.689225
$34$	−0.820689	−0.140747
$35$	2.12381	0.358990
$36$	−1.92584	−0.320973
$37$	−4.80152	−0.789365	−0.394683	−	0.918817i	$-0.629145\pi$
$37$	−4.80152	−0.789365	−0.394683	+	0.918817i	$0.629145\pi$
$38$	−1.19692	−0.194166
$39$	6.83710	1.09481
$40$	2.27059	0.359013
$41$	−10.9800	−1.71479	−0.857396	−	0.514657i	$-0.827919\pi$
$41$	−10.9800	−1.71479	−0.857396	+	0.514657i	$0.827919\pi$
$42$	0.272327	0.0420210
$43$	−8.26929	−1.26106	−0.630528	−	0.776167i	$-0.717162\pi$
$43$	−8.26929	−1.26106	−0.630528	+	0.776167i	$0.717162\pi$
$44$	−7.62496	−1.14951
$45$	−2.12381	−0.316599
$46$	−0.132737	−0.0195711
$47$	−4.00681	−0.584453	−0.292227	−	0.956349i	$-0.594396\pi$
$47$	−4.00681	−0.584453	−0.292227	+	0.956349i	$0.594396\pi$
$48$	−3.56053	−0.513918
$49$	1.00000	0.142857
$50$	−0.133284	−0.0188492
$51$	3.01361	0.421990
$52$	13.1672	1.82596
$53$	−2.58889	−0.355611	−0.177806	−	0.984066i	$-0.556900\pi$
$53$	−2.58889	−0.355611	−0.177806	+	0.984066i	$0.556900\pi$
$54$	−0.272327	−0.0370591
$55$	−8.40879	−1.13384
$56$	1.06911	0.142866
$57$	4.39515	0.582152
$58$	1.13332	0.148813
$59$	6.83089	0.889307	0.444653	−	0.895703i	$-0.353327\pi$
$59$	6.83089	0.889307	0.444653	+	0.895703i	$0.353327\pi$
$60$	−4.09012	−0.528032
$61$	−9.24318	−1.18347	−0.591734	−	0.806133i	$-0.701556\pi$
$61$	−9.24318	−1.18347	−0.591734	+	0.806133i	$0.701556\pi$
$62$	−1.74065	−0.221063
$63$	−1.00000	−0.125988
$64$	−6.27470	−0.784337
$65$	14.5207	1.80107
$66$	−1.07822	−0.132720
$67$	9.95956	1.21675	0.608377	−	0.793648i	$-0.291821\pi$
$67$	9.95956	1.21675	0.608377	+	0.793648i	$0.291821\pi$
$68$	5.80373	0.703805
$69$	0.487418	0.0586783
$70$	0.578372	0.0691287
$71$	−0.904685	−0.107366	−0.0536832	−	0.998558i	$-0.517096\pi$
$71$	−0.904685	−0.107366	−0.0536832	+	0.998558i	$0.517096\pi$
$72$	−1.06911	−0.125996
$73$	−16.9543	−1.98435	−0.992176	−	0.124848i	$-0.960156\pi$
$73$	−16.9543	−1.98435	−0.992176	+	0.124848i	$0.960156\pi$
$74$	−1.30759	−0.152004
$75$	0.489426	0.0565140
$76$	8.46434	0.970927
$77$	−3.95929	−0.451203
$78$	1.86193	0.210822
$79$	14.4473	1.62545	0.812725	−	0.582647i	$-0.197983\pi$
$79$	14.4473	1.62545	0.812725	+	0.582647i	$0.197983\pi$
$80$	−7.56189	−0.845445
$81$	1.00000	0.111111
$82$	−2.99016	−0.330208
$83$	1.48631	0.163143	0.0815717	−	0.996667i	$-0.474006\pi$
$83$	1.48631	0.163143	0.0815717	+	0.996667i	$0.474006\pi$
$84$	−1.92584	−0.210126
$85$	6.40034	0.694215
$86$	−2.25196	−0.242835
$87$	−4.16162	−0.446172
$88$	−4.23293	−0.451232
$89$	0.491165	0.0520634	0.0260317	−	0.999661i	$-0.491713\pi$
$89$	0.491165	0.0520634	0.0260317	+	0.999661i	$0.491713\pi$
$90$	−0.578372	−0.0609658
$91$	6.83710	0.716723
$92$	0.938689	0.0978651
$93$	6.39176	0.662795
$94$	−1.09116	−0.112545
$95$	9.33447	0.957696
$96$	−3.10786	−0.317194
$97$	4.97786	0.505425	0.252712	−	0.967541i	$-0.418677\pi$
$97$	4.97786	0.505425	0.252712	+	0.967541i	$0.418677\pi$
$98$	0.272327	0.0275092
$99$	3.95929	0.397924
$100$	0.942555	0.0942555
$101$	2.17949	0.216868	0.108434	−	0.994104i	$-0.465416\pi$
$101$	2.17949	0.216868	0.108434	+	0.994104i	$0.465416\pi$
$102$	0.820689	0.0812604
$103$	12.0641	1.18871	0.594357	−	0.804201i	$-0.297407\pi$
$103$	12.0641	1.18871	0.594357	+	0.804201i	$0.297407\pi$
$104$	7.30964	0.716769
$105$	−2.12381	−0.207263
$106$	−0.705025	−0.0684781
$107$	4.34031	0.419593	0.209797	−	0.977745i	$-0.432720\pi$
$107$	4.34031	0.419593	0.209797	+	0.977745i	$0.432720\pi$
$108$	1.92584	0.185314
$109$	−9.84454	−0.942936	−0.471468	−	0.881883i	$-0.656276\pi$
$109$	−9.84454	−0.942936	−0.471468	+	0.881883i	$0.656276\pi$
$110$	−2.28994	−0.218338
$111$	4.80152	0.455740
$112$	−3.56053	−0.336438
$113$	16.7455	1.57529	0.787643	−	0.616132i	$-0.211301\pi$
$113$	16.7455	1.57529	0.787643	+	0.616132i	$0.211301\pi$
$114$	1.19692	0.112102
$115$	1.03518	0.0965315
$116$	−8.01460	−0.744137
$117$	−6.83710	−0.632090
$118$	1.86024	0.171249
$119$	3.01361	0.276257
$120$	−2.27059	−0.207276
$121$	4.67600	0.425091
$122$	−2.51717	−0.227894
$123$	10.9800	0.990036
$124$	12.3095	1.10543
$125$	11.6585	1.04277
$126$	−0.272327	−0.0242609
$127$	0.0454229	0.00403063	0.00201531	−	0.999998i	$-0.499359\pi$
$127$	0.0454229	0.00403063	0.00201531	+	0.999998i	$0.499359\pi$
$128$	−7.92448	−0.700432
$129$	8.26929	0.728071
$130$	3.95439	0.346823
$131$	−9.53817	−0.833354	−0.416677	−	0.909055i	$-0.636805\pi$
$131$	−9.53817	−0.833354	−0.416677	+	0.909055i	$0.636805\pi$
$132$	7.62496	0.663667
$133$	4.39515	0.381108
$134$	2.71226	0.234304
$135$	2.12381	0.182789
$136$	3.22189	0.276275
$137$	−22.6534	−1.93541	−0.967705	−	0.252084i	$-0.918884\pi$
$137$	−22.6534	−1.93541	−0.967705	+	0.252084i	$0.918884\pi$
$138$	0.132737	0.0112994
$139$	2.65501	0.225195	0.112598	−	0.993641i	$-0.464083\pi$
$139$	2.65501	0.225195	0.112598	+	0.993641i	$0.464083\pi$
$140$	−4.09012	−0.345678
$141$	4.00681	0.337434
$142$	−0.246370	−0.0206749
$143$	−27.0701	−2.26372
$144$	3.56053	0.296711
$145$	−8.83849	−0.733996
$146$	−4.61712	−0.382116
$147$	−1.00000	−0.0824786
$148$	9.24695	0.760095
$149$	−15.0882	−1.23607	−0.618037	−	0.786149i	$-0.712072\pi$
$149$	−15.0882	−1.23607	−0.618037	+	0.786149i	$0.712072\pi$
$150$	0.133284	0.0108826
$151$	1.04394	0.0849544	0.0424772	−	0.999097i	$-0.486475\pi$
$151$	1.04394	0.0849544	0.0424772	+	0.999097i	$0.486475\pi$
$152$	4.69891	0.381132
$153$	−3.01361	−0.243636
$154$	−1.07822	−0.0868858
$155$	13.5749	1.09036
$156$	−13.1672	−1.05422
$157$	10.2110	0.814923	0.407462	−	0.913222i	$-0.366414\pi$
$157$	10.2110	0.814923	0.407462	+	0.913222i	$0.366414\pi$
$158$	3.93440	0.313004
$159$	2.58889	0.205312
$160$	−6.60050	−0.521815
$161$	0.487418	0.0384140
$162$	0.272327	0.0213961
$163$	−4.66398	−0.365311	−0.182656	−	0.983177i	$-0.558469\pi$
$163$	−4.66398	−0.365311	−0.182656	+	0.983177i	$0.558469\pi$
$164$	21.1457	1.65121
$165$	8.40879	0.654624
$166$	0.404762	0.0314156
$167$	1.63671	0.126652	0.0633261	−	0.997993i	$-0.479829\pi$
$167$	1.63671	0.126652	0.0633261	+	0.997993i	$0.479829\pi$
$168$	−1.06911	−0.0824839
$169$	33.7460	2.59585
$170$	1.74299	0.133681
$171$	−4.39515	−0.336105
$172$	15.9253	1.21429
$173$	10.0749	0.765984	0.382992	−	0.923752i	$-0.374894\pi$
$173$	10.0749	0.765984	0.382992	+	0.923752i	$0.374894\pi$
$174$	−1.13332	−0.0859169
$175$	0.489426	0.0369971
$176$	14.0972	1.06261
$177$	−6.83089	−0.513441
$178$	0.133758	0.0100256
$179$	−0.142282	−0.0106347	−0.00531734	−	0.999986i	$-0.501693\pi$
$179$	−0.142282	−0.0106347	−0.00531734	+	0.999986i	$0.501693\pi$
$180$	4.09012	0.304859
$181$	8.22225	0.611155	0.305577	−	0.952167i	$-0.401151\pi$
$181$	8.22225	0.611155	0.305577	+	0.952167i	$0.401151\pi$
$182$	1.86193	0.138016
$183$	9.24318	0.683275
$184$	0.521106	0.0384164
$185$	10.1975	0.749737
$186$	1.74065	0.127631
$187$	−11.9318	−0.872538
$188$	7.71646	0.562781
$189$	1.00000	0.0727393
$190$	2.54203	0.184418
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	6.27470	0.452837
$193$	3.96525	0.285425	0.142712	−	0.989764i	$-0.454418\pi$
$193$	3.96525	0.285425	0.142712	+	0.989764i	$0.454418\pi$
$194$	1.35561	0.0973269
$195$	−14.5207	−1.03985
$196$	−1.92584	−0.137560
$197$	15.5079	1.10489	0.552447	−	0.833548i	$-0.313694\pi$
$197$	15.5079	1.10489	0.552447	+	0.833548i	$0.313694\pi$
$198$	1.07822	0.0766261
$199$	13.4720	0.955008	0.477504	−	0.878630i	$-0.341542\pi$
$199$	13.4720	0.955008	0.477504	+	0.878630i	$0.341542\pi$
$200$	0.523252	0.0369995
$201$	−9.95956	−0.702493
$202$	0.593536	0.0417610
$203$	−4.16162	−0.292088
$204$	−5.80373	−0.406342
$205$	23.3195	1.62870
$206$	3.28539	0.228904
$207$	−0.487418	−0.0338779
$208$	−24.3437	−1.68793
$209$	−17.4017	−1.20370
$210$	−0.578372	−0.0399115
$211$	−27.1468	−1.86886	−0.934432	−	0.356141i	$-0.884092\pi$
$211$	−27.1468	−1.86886	−0.934432	+	0.356141i	$0.884092\pi$
$212$	4.98578	0.342425
$213$	0.904685	0.0619880
$214$	1.18198	0.0807988
$215$	17.5624	1.19775
$216$	1.06911	0.0727439
$217$	6.39176	0.433901
$218$	−2.68094	−0.181576
$219$	16.9543	1.14567
$220$	16.1940	1.09180
$221$	20.6044	1.38600
$222$	1.30759	0.0877594
$223$	21.1643	1.41727	0.708633	−	0.705578i	$-0.249312\pi$
$223$	21.1643	1.41727	0.708633	+	0.705578i	$0.249312\pi$
$224$	−3.10786	−0.207652
$225$	−0.489426	−0.0326284
$226$	4.56026	0.303344
$227$	−11.5895	−0.769222	−0.384611	−	0.923079i	$-0.625664\pi$
$227$	−11.5895	−0.769222	−0.384611	+	0.923079i	$0.625664\pi$
$228$	−8.46434	−0.560565
$229$	18.3041	1.20957	0.604785	−	0.796389i	$-0.293259\pi$
$229$	18.3041	1.20957	0.604785	+	0.796389i	$0.293259\pi$
$230$	0.281909	0.0185885
$231$	3.95929	0.260502
$232$	−4.44924	−0.292107
$233$	−1.82546	−0.119590	−0.0597949	−	0.998211i	$-0.519045\pi$
$233$	−1.82546	−0.119590	−0.0597949	+	0.998211i	$0.519045\pi$
$234$	−1.86193	−0.121718
$235$	8.50971	0.555112
$236$	−13.1552	−0.856330
$237$	−14.4473	−0.938454
$238$	0.820689	0.0531974
$239$	28.2378	1.82655	0.913275	−	0.407344i	$-0.133545\pi$
$239$	28.2378	1.82655	0.913275	+	0.407344i	$0.133545\pi$
$240$	7.56189	0.488118
$241$	1.61677	0.104146	0.0520728	−	0.998643i	$-0.483417\pi$
$241$	1.61677	0.104146	0.0520728	+	0.998643i	$0.483417\pi$
$242$	1.27340	0.0818575
$243$	−1.00000	−0.0641500
$244$	17.8009	1.13958
$245$	−2.12381	−0.135685
$246$	2.99016	0.190646
$247$	30.0501	1.91204
$248$	6.83352	0.433929
$249$	−1.48631	−0.0941908
$250$	3.17493	0.200800
$251$	4.11324	0.259626	0.129813	−	0.991539i	$-0.458562\pi$
$251$	4.11324	0.259626	0.129813	+	0.991539i	$0.458562\pi$
$252$	1.92584	0.121316
$253$	−1.92983	−0.121328
$254$	0.0123699	0.000776156 0
$255$	−6.40034	−0.400805
$256$	10.3913	0.649459
$257$	−18.0988	−1.12897	−0.564485	−	0.825443i	$-0.690925\pi$
$257$	−18.0988	−1.12897	−0.564485	+	0.825443i	$0.690925\pi$
$258$	2.25196	0.140201
$259$	4.80152	0.298352
$260$	−27.9645	−1.73429
$261$	4.16162	0.257598
$262$	−2.59751	−0.160474
$263$	−26.4387	−1.63028	−0.815142	−	0.579262i	$-0.803341\pi$
$263$	−26.4387	−1.63028	−0.815142	+	0.579262i	$0.803341\pi$
$264$	4.23293	0.260519
$265$	5.49831	0.337759
$266$	1.19692	0.0733878
$267$	−0.491165	−0.0300588
$268$	−19.1805	−1.17163
$269$	22.9612	1.39997	0.699985	−	0.714158i	$-0.253190\pi$
$269$	22.9612	1.39997	0.699985	+	0.714158i	$0.253190\pi$
$270$	0.578372	0.0351986
$271$	−7.65566	−0.465048	−0.232524	−	0.972591i	$-0.574698\pi$
$271$	−7.65566	−0.465048	−0.232524	+	0.972591i	$0.574698\pi$
$272$	−10.7300	−0.650605
$273$	−6.83710	−0.413800
$274$	−6.16914	−0.372691
$275$	−1.93778	−0.116853
$276$	−0.938689	−0.0565024
$277$	−28.3774	−1.70504	−0.852518	−	0.522698i	$-0.824925\pi$
$277$	−28.3774	−1.70504	−0.852518	+	0.522698i	$0.824925\pi$
$278$	0.723033	0.0433647
$279$	−6.39176	−0.382665
$280$	−2.27059	−0.135694
$281$	−2.30931	−0.137762	−0.0688808	−	0.997625i	$-0.521943\pi$
$281$	−2.30931	−0.137762	−0.0688808	+	0.997625i	$0.521943\pi$
$282$	1.09116	0.0649779
$283$	4.31325	0.256396	0.128198	−	0.991749i	$-0.459081\pi$
$283$	4.31325	0.256396	0.128198	+	0.991749i	$0.459081\pi$
$284$	1.74228	0.103385
$285$	−9.33447	−0.552926
$286$	−7.37193	−0.435911
$287$	10.9800	0.648130
$288$	3.10786	0.183132
$289$	−7.91814	−0.465773
$290$	−2.40696	−0.141342
$291$	−4.97786	−0.291807
$292$	32.6513	1.91077
$293$	20.4818	1.19656	0.598280	−	0.801287i	$-0.295851\pi$
$293$	20.4818	1.19656	0.598280	+	0.801287i	$0.295851\pi$
$294$	−0.272327	−0.0158825
$295$	−14.5075	−0.844661
$296$	5.13337	0.298371
$297$	−3.95929	−0.229742
$298$	−4.10893	−0.238024
$299$	3.33253	0.192725
$300$	−0.942555	−0.0544184
$301$	8.26929	0.476634
$302$	0.284293	0.0163592
$303$	−2.17949	−0.125209
$304$	−15.6490	−0.897534
$305$	19.6308	1.12405
$306$	−0.820689	−0.0469157
$307$	14.1964	0.810232	0.405116	−	0.914265i	$-0.367231\pi$
$307$	14.1964	0.810232	0.405116	+	0.914265i	$0.367231\pi$
$308$	7.62496	0.434472
$309$	−12.0641	−0.686304
$310$	3.69682	0.209965
$311$	22.9030	1.29871	0.649355	−	0.760485i	$-0.275039\pi$
$311$	22.9030	1.29871	0.649355	+	0.760485i	$0.275039\pi$
$312$	−7.30964	−0.413827
$313$	−12.2798	−0.694096	−0.347048	−	0.937847i	$-0.612816\pi$
$313$	−12.2798	−0.694096	−0.347048	+	0.937847i	$0.612816\pi$
$314$	2.78072	0.156925
$315$	2.12381	0.119663
$316$	−27.8232	−1.56518
$317$	−16.9663	−0.952923	−0.476462	−	0.879195i	$-0.658081\pi$
$317$	−16.9663	−0.952923	−0.476462	+	0.879195i	$0.658081\pi$
$318$	0.705025	0.0395359
$319$	16.4771	0.922538
$320$	13.3263	0.744961
$321$	−4.34031	−0.242252
$322$	0.132737	0.00739717
$323$	13.2453	0.736987
$324$	−1.92584	−0.106991
$325$	3.34625	0.185617
$326$	−1.27013	−0.0703460
$327$	9.84454	0.544404
$328$	11.7389	0.648172
$329$	4.00681	0.220903
$330$	2.28994	0.126057
$331$	30.0894	1.65386	0.826931	−	0.562304i	$-0.190085\pi$
$331$	30.0894	1.65386	0.826931	+	0.562304i	$0.190085\pi$
$332$	−2.86238	−0.157094
$333$	−4.80152	−0.263122
$334$	0.445720	0.0243887
$335$	−21.1522	−1.15567
$336$	3.56053	0.194243
$337$	−21.8207	−1.18865	−0.594325	−	0.804225i	$-0.702581\pi$
$337$	−21.8207	−1.18865	−0.594325	+	0.804225i	$0.702581\pi$
$338$	9.18996	0.499868
$339$	−16.7455	−0.909492
$340$	−12.3260	−0.668473
$341$	−25.3069	−1.37044
$342$	−1.19692	−0.0647220
$343$	−1.00000	−0.0539949
$344$	8.84081	0.476665
$345$	−1.03518	−0.0557325
$346$	2.74369	0.147501
$347$	−34.5827	−1.85650	−0.928248	−	0.371963i	$-0.878685\pi$
$347$	−34.5827	−1.85650	−0.928248	+	0.371963i	$0.878685\pi$
$348$	8.01460	0.429628
$349$	17.7732	0.951377	0.475689	−	0.879614i	$-0.342199\pi$
$349$	17.7732	0.951377	0.475689	+	0.879614i	$0.342199\pi$
$350$	0.133284	0.00712433
$351$	6.83710	0.364938
$352$	12.3049	0.655854
$353$	−0.629592	−0.0335098	−0.0167549	−	0.999860i	$-0.505334\pi$
$353$	−0.629592	−0.0335098	−0.0167549	+	0.999860i	$0.505334\pi$
$354$	−1.86024	−0.0988706
$355$	1.92138	0.101976
$356$	−0.945904	−0.0501328
$357$	−3.01361	−0.159497
$358$	−0.0387474	−0.00204786
$359$	−17.7943	−0.939148	−0.469574	−	0.882893i	$-0.655592\pi$
$359$	−17.7943	−0.939148	−0.469574	+	0.882893i	$0.655592\pi$
$360$	2.27059	0.119671
$361$	0.317328	0.0167015
$362$	2.23914	0.117687
$363$	−4.67600	−0.245427
$364$	−13.1672	−0.690146
$365$	36.0078	1.88473
$366$	2.51717	0.131575
$367$	25.6301	1.33788	0.668939	−	0.743317i	$-0.266749\pi$
$367$	25.6301	1.33788	0.668939	+	0.743317i	$0.266749\pi$
$368$	−1.73547	−0.0904674
$369$	−10.9800	−0.571597
$370$	2.77707	0.144373
$371$	2.58889	0.134408
$372$	−12.3095	−0.638218
$373$	−11.5188	−0.596421	−0.298210	−	0.954500i	$-0.596390\pi$
$373$	−11.5188	−0.596421	−0.298210	+	0.954500i	$0.596390\pi$
$374$	−3.24935	−0.168020
$375$	−11.6585	−0.602043
$376$	4.28373	0.220917
$377$	−28.4534	−1.46542
$378$	0.272327	0.0140070
$379$	7.69580	0.395307	0.197653	−	0.980272i	$-0.436668\pi$
$379$	7.69580	0.395307	0.197653	+	0.980272i	$0.436668\pi$
$380$	−17.9767	−0.922184
$381$	−0.0454229	−0.00232708
$382$	0.272327	0.0139335
$383$	18.4958	0.945089	0.472544	−	0.881307i	$-0.343336\pi$
$383$	18.4958	0.945089	0.472544	+	0.881307i	$0.343336\pi$
$384$	7.92448	0.404395
$385$	8.40879	0.428552
$386$	1.07985	0.0549627
$387$	−8.26929	−0.420352
$388$	−9.58654	−0.486683
$389$	−34.9410	−1.77158	−0.885790	−	0.464087i	$-0.846383\pi$
$389$	−34.9410	−1.77158	−0.885790	+	0.464087i	$0.846383\pi$
$390$	−3.95439	−0.200238
$391$	1.46889	0.0742850
$392$	−1.06911	−0.0539984
$393$	9.53817	0.481137
$394$	4.22324	0.212764
$395$	−30.6834	−1.54385
$396$	−7.62496	−0.383168
$397$	−32.0503	−1.60856	−0.804279	−	0.594252i	$-0.797448\pi$
$397$	−32.0503	−1.60856	−0.804279	+	0.594252i	$0.797448\pi$
$398$	3.66881	0.183901
$399$	−4.39515	−0.220033
$400$	−1.74261	−0.0871307
$401$	5.15336	0.257346	0.128673	−	0.991687i	$-0.458928\pi$
$401$	5.15336	0.257346	0.128673	+	0.991687i	$0.458928\pi$
$402$	−2.71226	−0.135275
$403$	43.7012	2.17691
$404$	−4.19735	−0.208826
$405$	−2.12381	−0.105533
$406$	−1.13332	−0.0562458
$407$	−19.0106	−0.942322
$408$	−3.22189	−0.159507
$409$	17.1776	0.849379	0.424689	−	0.905339i	$-0.360383\pi$
$409$	17.1776	0.849379	0.424689	+	0.905339i	$0.360383\pi$
$410$	6.35054	0.313631
$411$	22.6534	1.11741
$412$	−23.2336	−1.14464
$413$	−6.83089	−0.336126
$414$	−0.132737	−0.00652369
$415$	−3.15663	−0.154953
$416$	−21.2487	−1.04180
$417$	−2.65501	−0.130017
$418$	−4.73896	−0.231790
$419$	11.8104	0.576977	0.288488	−	0.957483i	$-0.406847\pi$
$419$	11.8104	0.576977	0.288488	+	0.957483i	$0.406847\pi$
$420$	4.09012	0.199577
$421$	3.93850	0.191951	0.0959753	−	0.995384i	$-0.469403\pi$
$421$	3.93850	0.191951	0.0959753	+	0.995384i	$0.469403\pi$
$422$	−7.39283	−0.359877
$423$	−4.00681	−0.194818
$424$	2.76782	0.134417
$425$	1.47494	0.0715451
$426$	0.246370	0.0119367
$427$	9.24318	0.447309
$428$	−8.35872	−0.404034
$429$	27.0701	1.30696
$430$	4.78273	0.230644
$431$	−17.2825	−0.832467	−0.416233	−	0.909258i	$-0.636650\pi$
$431$	−17.2825	−0.832467	−0.416233	+	0.909258i	$0.636650\pi$
$432$	−3.56053	−0.171306
$433$	15.0902	0.725187	0.362594	−	0.931947i	$-0.381891\pi$
$433$	15.0902	0.725187	0.362594	+	0.931947i	$0.381891\pi$
$434$	1.74065	0.0835540
$435$	8.83849	0.423773
$436$	18.9590	0.907971
$437$	2.14228	0.102479
$438$	4.61712	0.220615
$439$	−0.347293	−0.0165754	−0.00828769	−	0.999966i	$-0.502638\pi$
$439$	−0.347293	−0.0165754	−0.00828769	+	0.999966i	$0.502638\pi$
$440$	8.98995	0.428579
$441$	1.00000	0.0476190
$442$	5.61114	0.266895
$443$	−5.36598	−0.254946	−0.127473	−	0.991842i	$-0.540687\pi$
$443$	−5.36598	−0.254946	−0.127473	+	0.991842i	$0.540687\pi$
$444$	−9.24695	−0.438841
$445$	−1.04314	−0.0494496
$446$	5.76362	0.272915
$447$	15.0882	0.713647
$448$	6.27470	0.296452
$449$	5.91315	0.279059	0.139530	−	0.990218i	$-0.455441\pi$
$449$	5.91315	0.279059	0.139530	+	0.990218i	$0.455441\pi$
$450$	−0.133284	−0.00628307
$451$	−43.4731	−2.04707
$452$	−32.2492	−1.51687
$453$	−1.04394	−0.0490484
$454$	−3.15614	−0.148125
$455$	−14.5207	−0.680742
$456$	−4.69891	−0.220047
$457$	−31.6566	−1.48084	−0.740418	−	0.672147i	$-0.765372\pi$
$457$	−31.6566	−1.48084	−0.740418	+	0.672147i	$0.765372\pi$
$458$	4.98471	0.232920
$459$	3.01361	0.140663
$460$	−1.99360	−0.0929520
$461$	4.35496	0.202831	0.101415	−	0.994844i	$-0.467663\pi$
$461$	4.35496	0.202831	0.101415	+	0.994844i	$0.467663\pi$
$462$	1.07822	0.0501635
$463$	−21.6922	−1.00812	−0.504061	−	0.863668i	$-0.668161\pi$
$463$	−21.6922	−1.00812	−0.504061	+	0.863668i	$0.668161\pi$
$464$	14.8175	0.687887
$465$	−13.5749	−0.629521
$466$	−0.497123	−0.0230288
$467$	−17.7221	−0.820080	−0.410040	−	0.912067i	$-0.634485\pi$
$467$	−17.7221	−0.820080	−0.410040	+	0.912067i	$0.634485\pi$
$468$	13.1672	0.608652
$469$	−9.95956	−0.459890
$470$	2.31743	0.106895
$471$	−10.2110	−0.470496
$472$	−7.30300	−0.336148
$473$	−32.7406	−1.50541
$474$	−3.93440	−0.180713
$475$	2.15110	0.0986992
$476$	−5.80373	−0.266013
$477$	−2.58889	−0.118537
$478$	7.68992	0.351729
$479$	−10.3411	−0.472496	−0.236248	−	0.971693i	$-0.575918\pi$
$479$	−10.3411	−0.472496	−0.236248	+	0.971693i	$0.575918\pi$
$480$	6.60050	0.301270
$481$	32.8285	1.49685
$482$	0.440292	0.0200548
$483$	−0.487418	−0.0221783
$484$	−9.00523	−0.409328
$485$	−10.5720	−0.480051
$486$	−0.272327	−0.0123530
$487$	4.85306	0.219913	0.109957	−	0.993936i	$-0.464929\pi$
$487$	4.85306	0.219913	0.109957	+	0.993936i	$0.464929\pi$
$488$	9.88200	0.447337
$489$	4.66398	0.210913
$490$	−0.578372	−0.0261282
$491$	23.7114	1.07008	0.535041	−	0.844826i	$-0.320296\pi$
$491$	23.7114	1.07008	0.535041	+	0.844826i	$0.320296\pi$
$492$	−21.1457	−0.953324
$493$	−12.5415	−0.564841
$494$	8.18346	0.368191
$495$	−8.40879	−0.377947
$496$	−22.7580	−1.02187
$497$	0.904685	0.0405806
$498$	−0.404762	−0.0181378
$499$	18.0556	0.808280	0.404140	−	0.914697i	$-0.367571\pi$
$499$	18.0556	0.808280	0.404140	+	0.914697i	$0.367571\pi$
$500$	−22.4524	−1.00410
$501$	−1.63671	−0.0731227
$502$	1.12015	0.0499947
$503$	6.77887	0.302255	0.151127	−	0.988514i	$-0.451710\pi$
$503$	6.77887	0.302255	0.151127	+	0.988514i	$0.451710\pi$
$504$	1.06911	0.0476221
$505$	−4.62883	−0.205980
$506$	−0.525546	−0.0233634
$507$	−33.7460	−1.49871
$508$	−0.0874771	−0.00388117
$509$	0.0202055	0.000895592 0	0.000447796	−	1.00000i	$-0.499857\pi$
$509$	0.0202055	0.000895592 0	0.000447796		1.00000i	$0.499857\pi$
$510$	−1.74299	−0.0771809
$511$	16.9543	0.750015
$512$	18.6788	0.825495
$513$	4.39515	0.194051
$514$	−4.92879	−0.217400
$515$	−25.6219	−1.12904
$516$	−15.9253	−0.701073
$517$	−15.8641	−0.697704
$518$	1.30759	0.0574520
$519$	−10.0749	−0.442241
$520$	−15.5243	−0.680785
$521$	4.35593	0.190837	0.0954183	−	0.995437i	$-0.469581\pi$
$521$	4.35593	0.190837	0.0954183	+	0.995437i	$0.469581\pi$
$522$	1.13332	0.0496042
$523$	−3.85713	−0.168661	−0.0843304	−	0.996438i	$-0.526875\pi$
$523$	−3.85713	−0.168661	−0.0843304	+	0.996438i	$0.526875\pi$
$524$	18.3690	0.802452
$525$	−0.489426	−0.0213603
$526$	−7.20000	−0.313935
$527$	19.2623	0.839079
$528$	−14.0972	−0.613501
$529$	−22.7624	−0.989671
$530$	1.49734	0.0650403
$531$	6.83089	0.296436
$532$	−8.46434	−0.366976
$533$	75.0716	3.25171
$534$	−0.133758	−0.00578826
$535$	−9.21799	−0.398528
$536$	−10.6479	−0.459919
$537$	0.142282	0.00613994
$538$	6.25297	0.269585
$539$	3.95929	0.170539
$540$	−4.09012	−0.176011
$541$	10.5065	0.451709	0.225855	−	0.974161i	$-0.427483\pi$
$541$	10.5065	0.451709	0.225855	+	0.974161i	$0.427483\pi$
$542$	−2.08485	−0.0895518
$543$	−8.22225	−0.352850
$544$	−9.36587	−0.401558
$545$	20.9079	0.895598
$546$	−1.86193	−0.0796833
$547$	19.6347	0.839518	0.419759	−	0.907635i	$-0.362115\pi$
$547$	19.6347	0.839518	0.419759	+	0.907635i	$0.362115\pi$
$548$	43.6268	1.86364
$549$	−9.24318	−0.394489
$550$	−0.527711	−0.0225017
$551$	−18.2909	−0.779219
$552$	−0.521106	−0.0221797
$553$	−14.4473	−0.614362
$554$	−7.72796	−0.328329
$555$	−10.1975	−0.432861
$556$	−5.11313	−0.216845
$557$	40.5094	1.71644	0.858219	−	0.513283i	$-0.171571\pi$
$557$	40.5094	1.71644	0.858219	+	0.513283i	$0.171571\pi$
$558$	−1.74065	−0.0736877
$559$	56.5380	2.39130
$560$	7.56189	0.319548
$561$	11.9318	0.503760
$562$	−0.628888	−0.0265280
$563$	−7.50322	−0.316223	−0.158111	−	0.987421i	$-0.550541\pi$
$563$	−7.50322	−0.316223	−0.158111	+	0.987421i	$0.550541\pi$
$564$	−7.71646	−0.324922
$565$	−35.5643	−1.49620
$566$	1.17462	0.0493728
$567$	−1.00000	−0.0419961
$568$	0.967210	0.0405832
$569$	5.24705	0.219968	0.109984	−	0.993933i	$-0.464920\pi$
$569$	5.24705	0.219968	0.109984	+	0.993933i	$0.464920\pi$
$570$	−2.54203	−0.106474
$571$	−20.2419	−0.847099	−0.423549	−	0.905873i	$-0.639216\pi$
$571$	−20.2419	−0.847099	−0.423549	+	0.905873i	$0.639216\pi$
$572$	52.1326	2.17977
$573$	−1.00000	−0.0417756
$574$	2.99016	0.124807
$575$	0.238555	0.00994844
$576$	−6.27470	−0.261446
$577$	−30.4427	−1.26735	−0.633673	−	0.773601i	$-0.718453\pi$
$577$	−30.4427	−1.26735	−0.633673	+	0.773601i	$0.718453\pi$
$578$	−2.15633	−0.0896914
$579$	−3.96525	−0.164790
$580$	17.0215	0.706779
$581$	−1.48631	−0.0616624
$582$	−1.35561	−0.0561917
$583$	−10.2502	−0.424519
$584$	18.1261	0.750062
$585$	14.5207	0.600358
$586$	5.57776	0.230415
$587$	−31.3813	−1.29524	−0.647622	−	0.761962i	$-0.724236\pi$
$587$	−31.3813	−1.29524	−0.647622	+	0.761962i	$0.724236\pi$
$588$	1.92584	0.0794202
$589$	28.0928	1.15754
$590$	−3.95080	−0.162652
$591$	−15.5079	−0.637911
$592$	−17.0959	−0.702639
$593$	24.6295	1.01141	0.505707	−	0.862705i	$-0.331232\pi$
$593$	24.6295	1.01141	0.505707	+	0.862705i	$0.331232\pi$
$594$	−1.07822	−0.0442401
$595$	−6.40034	−0.262389
$596$	29.0574	1.19024
$597$	−13.4720	−0.551374
$598$	0.907539	0.0371120
$599$	−12.8355	−0.524444	−0.262222	−	0.965008i	$-0.584455\pi$
$599$	−12.8355	−0.524444	−0.262222	+	0.965008i	$0.584455\pi$
$600$	−0.523252	−0.0213617
$601$	−2.86313	−0.116789	−0.0583947	−	0.998294i	$-0.518598\pi$
$601$	−2.86313	−0.116789	−0.0583947	+	0.998294i	$0.518598\pi$
$602$	2.25196	0.0917829
$603$	9.95956	0.405584
$604$	−2.01045	−0.0818042
$605$	−9.93095	−0.403751
$606$	−0.593536	−0.0241107
$607$	−27.9874	−1.13597	−0.567987	−	0.823037i	$-0.692278\pi$
$607$	−27.9874	−1.13597	−0.567987	+	0.823037i	$0.692278\pi$
$608$	−13.6595	−0.553965
$609$	4.16162	0.168637
$610$	5.34600	0.216453
$611$	27.3950	1.10828
$612$	5.80373	0.234602
$613$	−23.4681	−0.947869	−0.473935	−	0.880560i	$-0.657167\pi$
$613$	−23.4681	−0.947869	−0.473935	+	0.880560i	$0.657167\pi$
$614$	3.86607	0.156022
$615$	−23.3195	−0.940333
$616$	4.23293	0.170550
$617$	−22.4670	−0.904488	−0.452244	−	0.891894i	$-0.649376\pi$
$617$	−22.4670	−0.904488	−0.452244	+	0.891894i	$0.649376\pi$
$618$	−3.28539	−0.132158
$619$	8.23120	0.330840	0.165420	−	0.986223i	$-0.447102\pi$
$619$	8.23120	0.330840	0.165420	+	0.986223i	$0.447102\pi$
$620$	−26.1431	−1.04993
$621$	0.487418	0.0195594
$622$	6.23712	0.250086
$623$	−0.491165	−0.0196781
$624$	24.3437	0.974528
$625$	−22.3133	−0.892533
$626$	−3.34413	−0.133658
$627$	17.4017	0.694956
$628$	−19.6647	−0.784705
$629$	14.4699	0.576954
$630$	0.578372	0.0230429
$631$	30.3855	1.20963	0.604813	−	0.796367i	$-0.293248\pi$
$631$	30.3855	1.20963	0.604813	+	0.796367i	$0.293248\pi$
$632$	−15.4458	−0.614402
$633$	27.1468	1.07899
$634$	−4.62039	−0.183499
$635$	−0.0964696	−0.00382828
$636$	−4.98578	−0.197699
$637$	−6.83710	−0.270896
$638$	4.48716	0.177648
$639$	−0.904685	−0.0357888
$640$	16.8301	0.665268
$641$	−20.9380	−0.827002	−0.413501	−	0.910504i	$-0.635694\pi$
$641$	−20.9380	−0.827002	−0.413501	+	0.910504i	$0.635694\pi$
$642$	−1.18198	−0.0466492
$643$	−5.08664	−0.200597	−0.100299	−	0.994957i	$-0.531980\pi$
$643$	−5.08664	−0.200597	−0.100299	+	0.994957i	$0.531980\pi$
$644$	−0.938689	−0.0369895
$645$	−17.5624	−0.691520
$646$	3.60705	0.141918
$647$	−49.7585	−1.95621	−0.978105	−	0.208114i	$-0.933267\pi$
$647$	−49.7585	−1.95621	−0.978105	+	0.208114i	$0.933267\pi$
$648$	−1.06911	−0.0419987
$649$	27.0455	1.06163
$650$	0.911277	0.0357432
$651$	−6.39176	−0.250513
$652$	8.98208	0.351765
$653$	−25.7446	−1.00746	−0.503731	−	0.863860i	$-0.668040\pi$
$653$	−25.7446	−1.00746	−0.503731	+	0.863860i	$0.668040\pi$
$654$	2.68094	0.104833
$655$	20.2573	0.791517
$656$	−39.0947	−1.52639
$657$	−16.9543	−0.661451
$658$	1.09116	0.0425380
$659$	21.5695	0.840227	0.420113	−	0.907472i	$-0.361990\pi$
$659$	21.5695	0.840227	0.420113	+	0.907472i	$0.361990\pi$
$660$	−16.1940	−0.630349
$661$	36.8565	1.43355	0.716775	−	0.697304i	$-0.245617\pi$
$661$	36.8565	1.43355	0.716775	+	0.697304i	$0.245617\pi$
$662$	8.19416	0.318475
$663$	−20.6044	−0.800208
$664$	−1.58903	−0.0616663
$665$	−9.33447	−0.361975
$666$	−1.30759	−0.0506679
$667$	−2.02845	−0.0785418
$668$	−3.15203	−0.121956
$669$	−21.1643	−0.818259
$670$	−5.76033	−0.222541
$671$	−36.5964	−1.41279
$672$	3.10786	0.119888
$673$	34.0816	1.31375	0.656874	−	0.754000i	$-0.271878\pi$
$673$	34.0816	1.31375	0.656874	+	0.754000i	$0.271878\pi$
$674$	−5.94238	−0.228892
$675$	0.489426	0.0188380
$676$	−64.9893	−2.49959
$677$	24.9293	0.958111	0.479055	−	0.877785i	$-0.340979\pi$
$677$	24.9293	0.958111	0.479055	+	0.877785i	$0.340979\pi$
$678$	−4.56026	−0.175136
$679$	−4.97786	−0.191033
$680$	−6.84269	−0.262405
$681$	11.5895	0.444111
$682$	−6.89176	−0.263899
$683$	10.2886	0.393681	0.196840	−	0.980436i	$-0.436932\pi$
$683$	10.2886	0.393681	0.196840	+	0.980436i	$0.436932\pi$
$684$	8.46434	0.323642
$685$	48.1115	1.83825
$686$	−0.272327	−0.0103975
$687$	−18.3041	−0.698345
$688$	−29.4430	−1.12251
$689$	17.7005	0.674335
$690$	−0.281909	−0.0107321
$691$	5.72155	0.217658	0.108829	−	0.994060i	$-0.465290\pi$
$691$	5.72155	0.217658	0.108829	+	0.994060i	$0.465290\pi$
$692$	−19.4027	−0.737581
$693$	−3.95929	−0.150401
$694$	−9.41781	−0.357495
$695$	−5.63875	−0.213890
$696$	4.44924	0.168648
$697$	33.0895	1.25336
$698$	4.84013	0.183202
$699$	1.82546	0.0690452
$700$	−0.942555	−0.0356252
$701$	−40.1902	−1.51796	−0.758981	−	0.651113i	$-0.774302\pi$
$701$	−40.1902	−1.51796	−0.758981	+	0.651113i	$0.774302\pi$
$702$	1.86193	0.0702741
$703$	21.1034	0.795930
$704$	−24.8434	−0.936320
$705$	−8.50971	−0.320494
$706$	−0.171455	−0.00645280
$707$	−2.17949	−0.0819682
$708$	13.1552	0.494402
$709$	43.8236	1.64583	0.822914	−	0.568166i	$-0.192347\pi$
$709$	43.8236	1.64583	0.822914	+	0.568166i	$0.192347\pi$
$710$	0.523244	0.0196370
$711$	14.4473	0.541817
$712$	−0.525111	−0.0196794
$713$	3.11546	0.116675
$714$	−0.820689	−0.0307135
$715$	57.4918	2.15007
$716$	0.274013	0.0102403
$717$	−28.2378	−1.05456
$718$	−4.84588	−0.180847
$719$	11.3970	0.425037	0.212518	−	0.977157i	$-0.431833\pi$
$719$	11.3970	0.425037	0.212518	+	0.977157i	$0.431833\pi$
$720$	−7.56189	−0.281815
$721$	−12.0641	−0.449292
$722$	0.0864171	0.00321611
$723$	−1.61677	−0.0601285
$724$	−15.8347	−0.588493
$725$	−2.03680	−0.0756449
$726$	−1.27340	−0.0472605
$727$	−7.10666	−0.263572	−0.131786	−	0.991278i	$-0.542071\pi$
$727$	−7.10666	−0.263572	−0.131786	+	0.991278i	$0.542071\pi$
$728$	−7.30964	−0.270913
$729$	1.00000	0.0370370
$730$	9.80590	0.362933
$731$	24.9204	0.921716
$732$	−17.8009	−0.657939
$733$	−23.4749	−0.867065	−0.433533	−	0.901138i	$-0.642733\pi$
$733$	−23.4749	−0.867065	−0.433533	+	0.901138i	$0.642733\pi$
$734$	6.97977	0.257628
$735$	2.12381	0.0783380
$736$	−1.51483	−0.0558372
$737$	39.4328	1.45253
$738$	−2.99016	−0.110069
$739$	−18.9068	−0.695499	−0.347749	−	0.937587i	$-0.613054\pi$
$739$	−18.9068	−0.695499	−0.347749	+	0.937587i	$0.613054\pi$
$740$	−19.6388	−0.721936
$741$	−30.0501	−1.10392
$742$	0.705025	0.0258823
$743$	−33.3631	−1.22397	−0.611987	−	0.790868i	$-0.709630\pi$
$743$	−33.3631	−1.22397	−0.611987	+	0.790868i	$0.709630\pi$
$744$	−6.83352	−0.250529
$745$	32.0445	1.17402
$746$	−3.13688	−0.114849
$747$	1.48631	0.0543811
$748$	22.9787	0.840183
$749$	−4.34031	−0.158591
$750$	−3.17493	−0.115932
$751$	24.8167	0.905574	0.452787	−	0.891619i	$-0.350430\pi$
$751$	24.8167	0.905574	0.452787	+	0.891619i	$0.350430\pi$
$752$	−14.2664	−0.520240
$753$	−4.11324	−0.149895
$754$	−7.74864	−0.282189
$755$	−2.21712	−0.0806894
$756$	−1.92584	−0.0700420
$757$	−30.4490	−1.10669	−0.553344	−	0.832953i	$-0.686649\pi$
$757$	−30.4490	−1.10669	−0.553344	+	0.832953i	$0.686649\pi$
$758$	2.09578	0.0761221
$759$	1.92983	0.0700485
$760$	−9.97960	−0.361998
$761$	−0.614897	−0.0222900	−0.0111450	−	0.999938i	$-0.503548\pi$
$761$	−0.614897	−0.0222900	−0.0111450	+	0.999938i	$0.503548\pi$
$762$	−0.0123699	−0.000448114 0
$763$	9.84454	0.356396
$764$	−1.92584	−0.0696744
$765$	6.40034	0.231405
$766$	5.03690	0.181991
$767$	−46.7035	−1.68637
$768$	−10.3913	−0.374965
$769$	−6.82358	−0.246065	−0.123032	−	0.992403i	$-0.539262\pi$
$769$	−6.82358	−0.246065	−0.123032	+	0.992403i	$0.539262\pi$
$770$	2.28994	0.0825239
$771$	18.0988	0.651811
$772$	−7.63643	−0.274841
$773$	−18.7826	−0.675564	−0.337782	−	0.941224i	$-0.609677\pi$
$773$	−18.7826	−0.675564	−0.337782	+	0.941224i	$0.609677\pi$
$774$	−2.25196	−0.0809449
$775$	3.12829	0.112372
$776$	−5.32189	−0.191045
$777$	−4.80152	−0.172254
$778$	−9.51540	−0.341143
$779$	48.2588	1.72905
$780$	27.9645	1.00129
$781$	−3.58191	−0.128171
$782$	0.400019	0.0143047
$783$	−4.16162	−0.148724
$784$	3.56053	0.127162
$785$	−21.6862	−0.774012
$786$	2.59751	0.0926500
$787$	16.9209	0.603166	0.301583	−	0.953440i	$-0.402485\pi$
$787$	16.9209	0.603166	0.301583	+	0.953440i	$0.402485\pi$
$788$	−29.8658	−1.06392
$789$	26.4387	0.941244
$790$	−8.35592	−0.297290
$791$	−16.7455	−0.595402
$792$	−4.23293	−0.150411
$793$	63.1966	2.24418
$794$	−8.72817	−0.309751
$795$	−5.49831	−0.195005
$796$	−25.9450	−0.919595
$797$	52.1788	1.84827	0.924134	−	0.382068i	$-0.124788\pi$
$797$	52.1788	1.84827	0.924134	+	0.382068i	$0.124788\pi$
$798$	−1.19692	−0.0423705
$799$	12.0750	0.427182
$800$	−1.52106	−0.0537778
$801$	0.491165	0.0173545
$802$	1.40340	0.0495558
$803$	−67.1271	−2.36886
$804$	19.1805	0.676444
$805$	−1.03518	−0.0364855
$806$	11.9010	0.419196
$807$	−22.9612	−0.808273
$808$	−2.33012	−0.0819735
$809$	−49.0254	−1.72364	−0.861820	−	0.507214i	$-0.830676\pi$
$809$	−49.0254	−1.72364	−0.861820	+	0.507214i	$0.830676\pi$
$810$	−0.578372	−0.0203219
$811$	−23.3777	−0.820902	−0.410451	−	0.911883i	$-0.634629\pi$
$811$	−23.3777	−0.820902	−0.410451	+	0.911883i	$0.634629\pi$
$812$	8.01460	0.281257
$813$	7.65566	0.268496
$814$	−5.17712	−0.181458
$815$	9.90542	0.346972
$816$	10.7300	0.375627
$817$	36.3448	1.27154
$818$	4.67794	0.163560
$819$	6.83710	0.238908
$820$	−44.9096	−1.56831
$821$	32.7593	1.14331	0.571654	−	0.820494i	$-0.306302\pi$
$821$	32.7593	1.14331	0.571654	+	0.820494i	$0.306302\pi$
$822$	6.16914	0.215174
$823$	35.1363	1.22477	0.612387	−	0.790558i	$-0.290209\pi$
$823$	35.1363	1.22477	0.612387	+	0.790558i	$0.290209\pi$
$824$	−12.8979	−0.449320
$825$	1.93778	0.0674648
$826$	−1.86024	−0.0647260
$827$	−35.7409	−1.24283	−0.621417	−	0.783480i	$-0.713443\pi$
$827$	−35.7409	−1.24283	−0.621417	+	0.783480i	$0.713443\pi$
$828$	0.938689	0.0326217
$829$	−12.5519	−0.435944	−0.217972	−	0.975955i	$-0.569944\pi$
$829$	−12.5519	−0.435944	−0.217972	+	0.975955i	$0.569944\pi$
$830$	−0.859638	−0.0298385
$831$	28.3774	0.984403
$832$	42.9008	1.48732
$833$	−3.01361	−0.104415
$834$	−0.723033	−0.0250366
$835$	−3.47606	−0.120294
$836$	33.5128	1.15906
$837$	6.39176	0.220932
$838$	3.21630	0.111105
$839$	34.6322	1.19564	0.597818	−	0.801632i	$-0.296034\pi$
$839$	34.6322	1.19564	0.597818	+	0.801632i	$0.296034\pi$
$840$	2.27059	0.0783430
$841$	−11.6810	−0.402791
$842$	1.07256	0.0369629
$843$	2.30931	0.0795367
$844$	52.2804	1.79957
$845$	−71.6701	−2.46553
$846$	−1.09116	−0.0375150
$847$	−4.67600	−0.160669
$848$	−9.21781	−0.316541
$849$	−4.31325	−0.148030
$850$	0.401666	0.0137770
$851$	2.34035	0.0802262
$852$	−1.74228	−0.0596894
$853$	35.6492	1.22061	0.610303	−	0.792168i	$-0.291048\pi$
$853$	35.6492	1.22061	0.610303	+	0.792168i	$0.291048\pi$
$854$	2.51717	0.0861358
$855$	9.33447	0.319232
$856$	−4.64028	−0.158601
$857$	16.0359	0.547776	0.273888	−	0.961762i	$-0.411690\pi$
$857$	16.0359	0.547776	0.273888	+	0.961762i	$0.411690\pi$
$858$	7.37193	0.251674
$859$	−11.1827	−0.381548	−0.190774	−	0.981634i	$-0.561100\pi$
$859$	−11.1827	−0.381548	−0.190774	+	0.981634i	$0.561100\pi$
$860$	−33.8224	−1.15333
$861$	−10.9800	−0.374198
$862$	−4.70649	−0.160304
$863$	40.1402	1.36639	0.683194	−	0.730237i	$-0.260591\pi$
$863$	40.1402	1.36639	0.683194	+	0.730237i	$0.260591\pi$
$864$	−3.10786	−0.105731
$865$	−21.3973	−0.727530
$866$	4.10947	0.139645
$867$	7.91814	0.268914
$868$	−12.3095	−0.417812
$869$	57.2012	1.94042
$870$	2.40696	0.0816037
$871$	−68.0945	−2.30729
$872$	10.5249	0.356419
$873$	4.97786	0.168475
$874$	0.583401	0.0197338
$875$	−11.6585	−0.394129
$876$	−32.6513	−1.10318
$877$	46.1801	1.55939	0.779695	−	0.626160i	$-0.215374\pi$
$877$	46.1801	1.55939	0.779695	+	0.626160i	$0.215374\pi$
$878$	−0.0945774	−0.00319183
$879$	−20.4818	−0.690834
$880$	−29.9397	−1.00927
$881$	−46.9543	−1.58193	−0.790965	−	0.611862i	$-0.790421\pi$
$881$	−46.9543	−1.58193	−0.790965	+	0.611862i	$0.790421\pi$
$882$	0.272327	0.00916974
$883$	41.2635	1.38863	0.694314	−	0.719672i	$-0.255708\pi$
$883$	41.2635	1.38863	0.694314	+	0.719672i	$0.255708\pi$
$884$	−39.6807	−1.33461
$885$	14.5075	0.487665
$886$	−1.46130	−0.0490935
$887$	−25.6052	−0.859738	−0.429869	−	0.902891i	$-0.641440\pi$
$887$	−25.6052	−0.859738	−0.429869	+	0.902891i	$0.641440\pi$
$888$	−5.13337	−0.172265
$889$	−0.0454229	−0.00152343
$890$	−0.284076	−0.00952225
$891$	3.95929	0.132641
$892$	−40.7590	−1.36471
$893$	17.6105	0.589314
$894$	4.10893	0.137423
$895$	0.302181	0.0101008
$896$	7.92448	0.264738
$897$	−3.33253	−0.111270
$898$	1.61031	0.0537369
$899$	−26.6001	−0.887162
$900$	0.942555	0.0314185
$901$	7.80191	0.259919
$902$	−11.8389	−0.394193
$903$	−8.26929	−0.275185
$904$	−17.9029	−0.595440
$905$	−17.4625	−0.580473
$906$	−0.284293	−0.00944499
$907$	20.1729	0.669830	0.334915	−	0.942248i	$-0.391292\pi$
$907$	20.1729	0.669830	0.334915	+	0.942248i	$0.391292\pi$
$908$	22.3195	0.740699
$909$	2.17949	0.0722892
$910$	−3.95439	−0.131087
$911$	−33.1733	−1.09908	−0.549540	−	0.835467i	$-0.685197\pi$
$911$	−33.1733	−1.09908	−0.549540	+	0.835467i	$0.685197\pi$
$912$	15.6490	0.518192
$913$	5.88472	0.194756
$914$	−8.62097	−0.285156
$915$	−19.6308	−0.648973
$916$	−35.2507	−1.16472
$917$	9.53817	0.314978
$918$	0.820689	0.0270868
$919$	−21.3669	−0.704830	−0.352415	−	0.935844i	$-0.614639\pi$
$919$	−21.3669	−0.704830	−0.352415	+	0.935844i	$0.614639\pi$
$920$	−1.10673	−0.0364878
$921$	−14.1964	−0.467788
$922$	1.18598	0.0390580
$923$	6.18542	0.203596
$924$	−7.62496	−0.250843
$925$	2.34999	0.0772672
$926$	−5.90738	−0.194128
$927$	12.0641	0.396238
$928$	12.9337	0.424570
$929$	14.9463	0.490371	0.245185	−	0.969476i	$-0.421151\pi$
$929$	14.9463	0.490371	0.245185	+	0.969476i	$0.421151\pi$
$930$	−3.69682	−0.121223
$931$	−4.39515	−0.144045
$932$	3.51554	0.115155
$933$	−22.9030	−0.749811
$934$	−4.82621	−0.157918
$935$	25.3408	0.828734
$936$	7.30964	0.238923
$937$	−5.59849	−0.182895	−0.0914474	−	0.995810i	$-0.529149\pi$
$937$	−5.59849	−0.182895	−0.0914474	+	0.995810i	$0.529149\pi$
$938$	−2.71226	−0.0885584
$939$	12.2798	0.400737
$940$	−16.3883	−0.534528
$941$	−33.6085	−1.09560	−0.547802	−	0.836608i	$-0.684535\pi$
$941$	−33.6085	−1.09560	−0.547802	+	0.836608i	$0.684535\pi$
$942$	−2.78072	−0.0906009
$943$	5.35187	0.174281
$944$	24.3216	0.791600
$945$	−2.12381	−0.0690876
$946$	−8.91615	−0.289889
$947$	−12.0116	−0.390325	−0.195162	−	0.980771i	$-0.562523\pi$
$947$	−12.0116	−0.390325	−0.195162	+	0.980771i	$0.562523\pi$
$948$	27.8232	0.903655
$949$	115.918	3.76287
$950$	0.585803	0.0190060
$951$	16.9663	0.550171
$952$	−3.22189	−0.104422
$953$	−47.5300	−1.53965	−0.769824	−	0.638256i	$-0.779656\pi$
$953$	−47.5300	−1.53965	−0.769824	+	0.638256i	$0.779656\pi$
$954$	−0.705025	−0.0228260
$955$	−2.12381	−0.0687249
$956$	−54.3814	−1.75882
$957$	−16.4771	−0.532628
$958$	−2.81616	−0.0909860
$959$	22.6534	0.731516
$960$	−13.3263	−0.430104
$961$	9.85465	0.317892
$962$	8.94010	0.288240
$963$	4.34031	0.139864
$964$	−3.11365	−0.100284
$965$	−8.42144	−0.271096
$966$	−0.132737	−0.00427076
$967$	1.24431	0.0400144	0.0200072	−	0.999800i	$-0.493631\pi$
$967$	1.24431	0.0400144	0.0200072	+	0.999800i	$0.493631\pi$
$968$	−4.99918	−0.160680
$969$	−13.2453	−0.425499
$970$	−2.87905	−0.0924408
$971$	10.1499	0.325724	0.162862	−	0.986649i	$-0.447927\pi$
$971$	10.1499	0.325724	0.162862	+	0.986649i	$0.447927\pi$
$972$	1.92584	0.0617713
$973$	−2.65501	−0.0851159
$974$	1.32162	0.0423475
$975$	−3.34625	−0.107166
$976$	−32.9106	−1.05344
$977$	42.0890	1.34655	0.673273	−	0.739394i	$-0.264888\pi$
$977$	42.0890	1.34655	0.673273	+	0.739394i	$0.264888\pi$
$978$	1.27013	0.0406143
$979$	1.94467	0.0621518
$980$	4.09012	0.130654
$981$	−9.84454	−0.314312
$982$	6.45727	0.206060
$983$	−28.3686	−0.904819	−0.452409	−	0.891810i	$-0.649435\pi$
$983$	−28.3686	−0.904819	−0.452409	+	0.891810i	$0.649435\pi$
$984$	−11.7389	−0.374222
$985$	−32.9359	−1.04943
$986$	−3.41539	−0.108768
$987$	−4.00681	−0.127538
$988$	−57.8716	−1.84114
$989$	4.03061	0.128166
$990$	−2.28994	−0.0727792
$991$	17.9108	0.568957	0.284478	−	0.958682i	$-0.408180\pi$
$991$	17.9108	0.568957	0.284478	+	0.958682i	$0.408180\pi$
$992$	−19.8647	−0.630704
$993$	−30.0894	−0.954857
$994$	0.246370	0.00781440
$995$	−28.6121	−0.907064
$996$	2.86238	0.0906981
$997$	−12.5531	−0.397560	−0.198780	−	0.980044i	$-0.563698\pi$
$997$	−12.5531	−0.397560	−0.198780	+	0.980044i	$0.563698\pi$
$998$	4.91703	0.155646
$999$	4.80152	0.151913

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.j.1.14	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.j.1.14	✓	26	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q+0.272327 q^{2} -1.00000 q^{3} -1.92584 q^{4} -2.12381 q^{5} -0.272327 q^{6} -1.00000 q^{7} -1.06911 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.272327 q^{2} -1.00000 q^{3} -1.92584 q^{4} -2.12381 q^{5} -0.272327 q^{6} -1.00000 q^{7} -1.06911 q^{8} +1.00000 q^{9} -0.578372 q^{10} +3.95929 q^{11} +1.92584 q^{12} -6.83710 q^{13} -0.272327 q^{14} +2.12381 q^{15} +3.56053 q^{16} -3.01361 q^{17} +0.272327 q^{18} -4.39515 q^{19} +4.09012 q^{20} +1.00000 q^{21} +1.07822 q^{22} -0.487418 q^{23} +1.06911 q^{24} -0.489426 q^{25} -1.86193 q^{26} -1.00000 q^{27} +1.92584 q^{28} +4.16162 q^{29} +0.578372 q^{30} -6.39176 q^{31} +3.10786 q^{32} -3.95929 q^{33} -0.820689 q^{34} +2.12381 q^{35} -1.92584 q^{36} -4.80152 q^{37} -1.19692 q^{38} +6.83710 q^{39} +2.27059 q^{40} -10.9800 q^{41} +0.272327 q^{42} -8.26929 q^{43} -7.62496 q^{44} -2.12381 q^{45} -0.132737 q^{46} -4.00681 q^{47} -3.56053 q^{48} +1.00000 q^{49} -0.133284 q^{50} +3.01361 q^{51} +13.1672 q^{52} -2.58889 q^{53} -0.272327 q^{54} -8.40879 q^{55} +1.06911 q^{56} +4.39515 q^{57} +1.13332 q^{58} +6.83089 q^{59} -4.09012 q^{60} -9.24318 q^{61} -1.74065 q^{62} -1.00000 q^{63} -6.27470 q^{64} +14.5207 q^{65} -1.07822 q^{66} +9.95956 q^{67} +5.80373 q^{68} +0.487418 q^{69} +0.578372 q^{70} -0.904685 q^{71} -1.06911 q^{72} -16.9543 q^{73} -1.30759 q^{74} +0.489426 q^{75} +8.46434 q^{76} -3.95929 q^{77} +1.86193 q^{78} +14.4473 q^{79} -7.56189 q^{80} +1.00000 q^{81} -2.99016 q^{82} +1.48631 q^{83} -1.92584 q^{84} +6.40034 q^{85} -2.25196 q^{86} -4.16162 q^{87} -4.23293 q^{88} +0.491165 q^{89} -0.578372 q^{90} +6.83710 q^{91} +0.938689 q^{92} +6.39176 q^{93} -1.09116 q^{94} +9.33447 q^{95} -3.10786 q^{96} +4.97786 q^{97} +0.272327 q^{98} +3.95929 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9}+O(q^{10}) \) 26 * q - 26 * q^3 + 34 * q^4 + 2 * q^5 - 26 * q^7 + 26 * q^9	\( 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9} - q^{10} + 13 q^{11} - 34 q^{12} - q^{13} - 2 q^{15} + 54 q^{16} + q^{19} - 22 q^{20} + 26 q^{21} + 17 q^{22} - 3 q^{23} + 48 q^{25} + 6 q^{26} - 26 q^{27} - 34 q^{28} + 23 q^{29} + q^{30} + 18 q^{31} + 10 q^{32} - 13 q^{33} - 19 q^{34} - 2 q^{35} + 34 q^{36} + 23 q^{37} - 15 q^{38} + q^{39} + 14 q^{40} - 4 q^{41} + 5 q^{43} + 60 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{47} - 54 q^{48} + 26 q^{49} + 26 q^{50} + 19 q^{52} + 31 q^{53} + 41 q^{55} - q^{57} + 19 q^{58} - 2 q^{59} + 22 q^{60} - 2 q^{61} - 35 q^{62} - 26 q^{63} + 132 q^{64} + 40 q^{65} - 17 q^{66} + 47 q^{67} - 60 q^{68} + 3 q^{69} + q^{70} + 16 q^{71} - 23 q^{73} + 34 q^{74} - 48 q^{75} + 72 q^{76} - 13 q^{77} - 6 q^{78} + 14 q^{79} - 21 q^{80} + 26 q^{81} + 60 q^{82} - 4 q^{83} + 34 q^{84} + 36 q^{85} + 21 q^{86} - 23 q^{87} + 67 q^{88} + 14 q^{89} - q^{90} + q^{91} + 20 q^{92} - 18 q^{93} + 58 q^{94} - 4 q^{95} - 10 q^{96} + 48 q^{97} + 13 q^{99}+O(q^{100}) \) 26 * q - 26 * q^3 + 34 * q^4 + 2 * q^5 - 26 * q^7 + 26 * q^9 - q^10 + 13 * q^11 - 34 * q^12 - q^13 - 2 * q^15 + 54 * q^16 + q^19 - 22 * q^20 + 26 * q^21 + 17 * q^22 - 3 * q^23 + 48 * q^25 + 6 * q^26 - 26 * q^27 - 34 * q^28 + 23 * q^29 + q^30 + 18 * q^31 + 10 * q^32 - 13 * q^33 - 19 * q^34 - 2 * q^35 + 34 * q^36 + 23 * q^37 - 15 * q^38 + q^39 + 14 * q^40 - 4 * q^41 + 5 * q^43 + 60 * q^44 + 2 * q^45 + 8 * q^46 - 20 * q^47 - 54 * q^48 + 26 * q^49 + 26 * q^50 + 19 * q^52 + 31 * q^53 + 41 * q^55 - q^57 + 19 * q^58 - 2 * q^59 + 22 * q^60 - 2 * q^61 - 35 * q^62 - 26 * q^63 + 132 * q^64 + 40 * q^65 - 17 * q^66 + 47 * q^67 - 60 * q^68 + 3 * q^69 + q^70 + 16 * q^71 - 23 * q^73 + 34 * q^74 - 48 * q^75 + 72 * q^76 - 13 * q^77 - 6 * q^78 + 14 * q^79 - 21 * q^80 + 26 * q^81 + 60 * q^82 - 4 * q^83 + 34 * q^84 + 36 * q^85 + 21 * q^86 - 23 * q^87 + 67 * q^88 + 14 * q^89 - q^90 + q^91 + 20 * q^92 - 18 * q^93 + 58 * q^94 - 4 * q^95 - 10 * q^96 + 48 * q^97 + 13 * q^99

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