LMFDB - Embedded newform 4011.2.a.m.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:	$29$
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)

$f(q)$	$=$	$q-0.220924 q^{2} +1.00000 q^{3} -1.95119 q^{4} +3.22358 q^{5} -0.220924 q^{6} -1.00000 q^{7} +0.872912 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.220924 q^{2} +1.00000 q^{3} -1.95119 q^{4} +3.22358 q^{5} -0.220924 q^{6} -1.00000 q^{7} +0.872912 q^{8} +1.00000 q^{9} -0.712166 q^{10} +6.18240 q^{11} -1.95119 q^{12} -0.227405 q^{13} +0.220924 q^{14} +3.22358 q^{15} +3.70954 q^{16} +2.91165 q^{17} -0.220924 q^{18} +5.03246 q^{19} -6.28983 q^{20} -1.00000 q^{21} -1.36584 q^{22} +8.84250 q^{23} +0.872912 q^{24} +5.39149 q^{25} +0.0502392 q^{26} +1.00000 q^{27} +1.95119 q^{28} -6.58100 q^{29} -0.712166 q^{30} +6.91797 q^{31} -2.56535 q^{32} +6.18240 q^{33} -0.643253 q^{34} -3.22358 q^{35} -1.95119 q^{36} -11.1160 q^{37} -1.11179 q^{38} -0.227405 q^{39} +2.81391 q^{40} -0.197199 q^{41} +0.220924 q^{42} -5.41599 q^{43} -12.0631 q^{44} +3.22358 q^{45} -1.95352 q^{46} -13.3167 q^{47} +3.70954 q^{48} +1.00000 q^{49} -1.19111 q^{50} +2.91165 q^{51} +0.443711 q^{52} -3.35626 q^{53} -0.220924 q^{54} +19.9295 q^{55} -0.872912 q^{56} +5.03246 q^{57} +1.45390 q^{58} -8.04248 q^{59} -6.28983 q^{60} -10.8774 q^{61} -1.52834 q^{62} -1.00000 q^{63} -6.85233 q^{64} -0.733060 q^{65} -1.36584 q^{66} +13.1548 q^{67} -5.68119 q^{68} +8.84250 q^{69} +0.712166 q^{70} +14.6519 q^{71} +0.872912 q^{72} -1.97765 q^{73} +2.45578 q^{74} +5.39149 q^{75} -9.81930 q^{76} -6.18240 q^{77} +0.0502392 q^{78} +13.6434 q^{79} +11.9580 q^{80} +1.00000 q^{81} +0.0435659 q^{82} -4.68599 q^{83} +1.95119 q^{84} +9.38595 q^{85} +1.19652 q^{86} -6.58100 q^{87} +5.39669 q^{88} -8.45572 q^{89} -0.712166 q^{90} +0.227405 q^{91} -17.2534 q^{92} +6.91797 q^{93} +2.94199 q^{94} +16.2226 q^{95} -2.56535 q^{96} +6.77323 q^{97} -0.220924 q^{98} +6.18240 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9}+O(q^{10}) $ 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9} + 11 q^{11} + 40 q^{12} + 13 q^{13} - 6 q^{14} + 22 q^{15} + 58 q^{16} + 17 q^{17} + 6 q^{18} + 3 q^{19} + 52 q^{20} - 29 q^{21} + 17 q^{22} + 36 q^{23} + 15 q^{24} + 57 q^{25} + 25 q^{26} + 29 q^{27} - 40 q^{28} + 20 q^{29} + 6 q^{31} + 46 q^{32} + 11 q^{33} + 18 q^{34} - 22 q^{35} + 40 q^{36} + 22 q^{37} + 8 q^{38} + 13 q^{39} + 6 q^{40} + 26 q^{41} - 6 q^{42} + 21 q^{43} + 22 q^{44} + 22 q^{45} + 28 q^{46} + 41 q^{47} + 58 q^{48} + 29 q^{49} + 18 q^{50} + 17 q^{51} + 2 q^{52} + 37 q^{53} + 6 q^{54} + 7 q^{55} - 15 q^{56} + 3 q^{57} + 9 q^{58} + 27 q^{59} + 52 q^{60} + 20 q^{61} - 12 q^{62} - 29 q^{63} + 59 q^{64} + 3 q^{65} + 17 q^{66} + 30 q^{67} + 33 q^{68} + 36 q^{69} + 68 q^{71} + 15 q^{72} + q^{73} + 21 q^{74} + 57 q^{75} + 11 q^{76} - 11 q^{77} + 25 q^{78} + 34 q^{79} + 110 q^{80} + 29 q^{81} - 49 q^{82} + 13 q^{83} - 40 q^{84} + 27 q^{85} + 35 q^{86} + 20 q^{87} + 17 q^{88} + 61 q^{89} - 13 q^{91} + 86 q^{92} + 6 q^{93} - 19 q^{94} + 25 q^{95} + 46 q^{96} - 3 q^{97} + 6 q^{98} + 11 q^{99}+O(q^{100}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9 + 11 * q^11 + 40 * q^12 + 13 * q^13 - 6 * q^14 + 22 * q^15 + 58 * q^16 + 17 * q^17 + 6 * q^18 + 3 * q^19 + 52 * q^20 - 29 * q^21 + 17 * q^22 + 36 * q^23 + 15 * q^24 + 57 * q^25 + 25 * q^26 + 29 * q^27 - 40 * q^28 + 20 * q^29 + 6 * q^31 + 46 * q^32 + 11 * q^33 + 18 * q^34 - 22 * q^35 + 40 * q^36 + 22 * q^37 + 8 * q^38 + 13 * q^39 + 6 * q^40 + 26 * q^41 - 6 * q^42 + 21 * q^43 + 22 * q^44 + 22 * q^45 + 28 * q^46 + 41 * q^47 + 58 * q^48 + 29 * q^49 + 18 * q^50 + 17 * q^51 + 2 * q^52 + 37 * q^53 + 6 * q^54 + 7 * q^55 - 15 * q^56 + 3 * q^57 + 9 * q^58 + 27 * q^59 + 52 * q^60 + 20 * q^61 - 12 * q^62 - 29 * q^63 + 59 * q^64 + 3 * q^65 + 17 * q^66 + 30 * q^67 + 33 * q^68 + 36 * q^69 + 68 * q^71 + 15 * q^72 + q^73 + 21 * q^74 + 57 * q^75 + 11 * q^76 - 11 * q^77 + 25 * q^78 + 34 * q^79 + 110 * q^80 + 29 * q^81 - 49 * q^82 + 13 * q^83 - 40 * q^84 + 27 * q^85 + 35 * q^86 + 20 * q^87 + 17 * q^88 + 61 * q^89 - 13 * q^91 + 86 * q^92 + 6 * q^93 - 19 * q^94 + 25 * q^95 + 46 * q^96 - 3 * q^97 + 6 * q^98 + 11 * 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 $

$2$	−0.220924	−0.156217	−0.0781083	−	0.996945i	$-0.524888\pi$
$2$	−0.220924	−0.156217	−0.0781083	+	0.996945i	$0.524888\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.95119	−0.975596
$5$	3.22358	1.44163	0.720815	−	0.693127i	$-0.243768\pi$
$5$	3.22358	1.44163	0.720815	+	0.693127i	$0.243768\pi$
$6$	−0.220924	−0.0901917
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0.872912	0.308621
$9$	1.00000	0.333333
$10$	−0.712166	−0.225207
$11$	6.18240	1.86406	0.932032	−	0.362377i	$-0.118035\pi$
$11$	6.18240	1.86406	0.932032	+	0.362377i	$0.118035\pi$
$12$	−1.95119	−0.563261
$13$	−0.227405	−0.0630709	−0.0315354	−	0.999503i	$-0.510040\pi$
$13$	−0.227405	−0.0630709	−0.0315354	+	0.999503i	$0.510040\pi$
$14$	0.220924	0.0590444
$15$	3.22358	0.832326
$16$	3.70954	0.927385
$17$	2.91165	0.706179	0.353090	−	0.935590i	$-0.385131\pi$
$17$	2.91165	0.706179	0.353090	+	0.935590i	$0.385131\pi$
$18$	−0.220924	−0.0520722
$19$	5.03246	1.15453	0.577263	−	0.816558i	$-0.304121\pi$
$19$	5.03246	1.15453	0.577263	+	0.816558i	$0.304121\pi$
$20$	−6.28983	−1.40645
$21$	−1.00000	−0.218218
$22$	−1.36584	−0.291198
$23$	8.84250	1.84379	0.921894	−	0.387442i	$-0.126641\pi$
$23$	8.84250	1.84379	0.921894	+	0.387442i	$0.126641\pi$
$24$	0.872912	0.178182
$25$	5.39149	1.07830
$26$	0.0502392	0.00985272
$27$	1.00000	0.192450
$28$	1.95119	0.368741
$29$	−6.58100	−1.22206	−0.611031	−	0.791607i	$-0.709245\pi$
$29$	−6.58100	−1.22206	−0.611031	+	0.791607i	$0.709245\pi$
$30$	−0.712166	−0.130023
$31$	6.91797	1.24250	0.621252	−	0.783611i	$-0.286624\pi$
$31$	6.91797	1.24250	0.621252	+	0.783611i	$0.286624\pi$
$32$	−2.56535	−0.453494
$33$	6.18240	1.07622
$34$	−0.643253	−0.110317
$35$	−3.22358	−0.544885
$36$	−1.95119	−0.325199
$37$	−11.1160	−1.82746	−0.913728	−	0.406327i	$-0.866809\pi$
$37$	−11.1160	−1.82746	−0.913728	+	0.406327i	$0.866809\pi$
$38$	−1.11179	−0.180356
$39$	−0.227405	−0.0364140
$40$	2.81391	0.444918
$41$	−0.197199	−0.0307973	−0.0153986	−	0.999881i	$-0.504902\pi$
$41$	−0.197199	−0.0307973	−0.0153986	+	0.999881i	$0.504902\pi$
$42$	0.220924	0.0340893
$43$	−5.41599	−0.825931	−0.412966	−	0.910747i	$-0.635507\pi$
$43$	−5.41599	−0.825931	−0.412966	+	0.910747i	$0.635507\pi$
$44$	−12.0631	−1.81857
$45$	3.22358	0.480544
$46$	−1.95352	−0.288030
$47$	−13.3167	−1.94245	−0.971224	−	0.238169i	$-0.923453\pi$
$47$	−13.3167	−1.94245	−0.971224	+	0.238169i	$0.923453\pi$
$48$	3.70954	0.535426
$49$	1.00000	0.142857
$50$	−1.19111	−0.168448
$51$	2.91165	0.407713
$52$	0.443711	0.0615317
$53$	−3.35626	−0.461018	−0.230509	−	0.973070i	$-0.574039\pi$
$53$	−3.35626	−0.461018	−0.230509	+	0.973070i	$0.574039\pi$
$54$	−0.220924	−0.0300639
$55$	19.9295	2.68729
$56$	−0.872912	−0.116648
$57$	5.03246	0.666566
$58$	1.45390	0.190906
$59$	−8.04248	−1.04704	−0.523521	−	0.852013i	$-0.675382\pi$
$59$	−8.04248	−1.04704	−0.523521	+	0.852013i	$0.675382\pi$
$60$	−6.28983	−0.812014
$61$	−10.8774	−1.39270	−0.696351	−	0.717701i	$-0.745194\pi$
$61$	−10.8774	−1.39270	−0.696351	+	0.717701i	$0.745194\pi$
$62$	−1.52834	−0.194100
$63$	−1.00000	−0.125988
$64$	−6.85233	−0.856541
$65$	−0.733060	−0.0909249
$66$	−1.36584	−0.168123
$67$	13.1548	1.60712	0.803559	−	0.595226i	$-0.202937\pi$
$67$	13.1548	1.60712	0.803559	+	0.595226i	$0.202937\pi$
$68$	−5.68119	−0.688946
$69$	8.84250	1.06451
$70$	0.712166	0.0851201
$71$	14.6519	1.73886	0.869431	−	0.494055i	$-0.164486\pi$
$71$	14.6519	1.73886	0.869431	+	0.494055i	$0.164486\pi$
$72$	0.872912	0.102874
$73$	−1.97765	−0.231467	−0.115733	−	0.993280i	$-0.536922\pi$
$73$	−1.97765	−0.231467	−0.115733	+	0.993280i	$0.536922\pi$
$74$	2.45578	0.285479
$75$	5.39149	0.622556
$76$	−9.81930	−1.12635
$77$	−6.18240	−0.704550
$78$	0.0502392	0.00568847
$79$	13.6434	1.53501	0.767504	−	0.641045i	$-0.221499\pi$
$79$	13.6434	1.53501	0.767504	+	0.641045i	$0.221499\pi$
$80$	11.9580	1.33695
$81$	1.00000	0.111111
$82$	0.0435659	0.00481105
$83$	−4.68599	−0.514355	−0.257177	−	0.966364i	$-0.582792\pi$
$83$	−4.68599	−0.514355	−0.257177	+	0.966364i	$0.582792\pi$
$84$	1.95119	0.212893
$85$	9.38595	1.01805
$86$	1.19652	0.129024
$87$	−6.58100	−0.705558
$88$	5.39669	0.575289
$89$	−8.45572	−0.896304	−0.448152	−	0.893957i	$-0.647918\pi$
$89$	−8.45572	−0.896304	−0.448152	+	0.893957i	$0.647918\pi$
$90$	−0.712166	−0.0750689
$91$	0.227405	0.0238385
$92$	−17.2534	−1.79879
$93$	6.91797	0.717360
$94$	2.94199	0.303443
$95$	16.2226	1.66440
$96$	−2.56535	−0.261825
$97$	6.77323	0.687717	0.343858	−	0.939022i	$-0.388266\pi$
$97$	6.77323	0.687717	0.343858	+	0.939022i	$0.388266\pi$
$98$	−0.220924	−0.0223167
$99$	6.18240	0.621354
$100$	−10.5198	−1.05198
$101$	13.0143	1.29497	0.647486	−	0.762077i	$-0.275820\pi$
$101$	13.0143	1.29497	0.647486	+	0.762077i	$0.275820\pi$
$102$	−0.643253	−0.0636915
$103$	12.3472	1.21660	0.608301	−	0.793706i	$-0.291851\pi$
$103$	12.3472	1.21660	0.608301	+	0.793706i	$0.291851\pi$
$104$	−0.198505	−0.0194650
$105$	−3.22358	−0.314590
$106$	0.741478	0.0720187
$107$	−12.1760	−1.17710	−0.588548	−	0.808462i	$-0.700300\pi$
$107$	−12.1760	−1.17710	−0.588548	+	0.808462i	$0.700300\pi$
$108$	−1.95119	−0.187754
$109$	1.37940	0.132122	0.0660611	−	0.997816i	$-0.478957\pi$
$109$	1.37940	0.132122	0.0660611	+	0.997816i	$0.478957\pi$
$110$	−4.40290	−0.419800
$111$	−11.1160	−1.05508
$112$	−3.70954	−0.350518
$113$	−4.31209	−0.405647	−0.202824	−	0.979215i	$-0.565012\pi$
$113$	−4.31209	−0.405647	−0.202824	+	0.979215i	$0.565012\pi$
$114$	−1.11179	−0.104129
$115$	28.5045	2.65806
$116$	12.8408	1.19224
$117$	−0.227405	−0.0210236
$118$	1.77677	0.163565
$119$	−2.91165	−0.266911
$120$	2.81391	0.256873
$121$	27.2221	2.47473
$122$	2.40307	0.217563
$123$	−0.197199	−0.0177808
$124$	−13.4983	−1.21218
$125$	1.26201	0.112878
$126$	0.220924	0.0196815
$127$	−17.0894	−1.51643	−0.758217	−	0.652002i	$-0.773929\pi$
$127$	−17.0894	−1.51643	−0.758217	+	0.652002i	$0.773929\pi$
$128$	6.64454	0.587300
$129$	−5.41599	−0.476852
$130$	0.161950	0.0142040
$131$	−11.9207	−1.04152	−0.520760	−	0.853703i	$-0.674351\pi$
$131$	−11.9207	−1.04152	−0.520760	+	0.853703i	$0.674351\pi$
$132$	−12.0631	−1.04995
$133$	−5.03246	−0.436370
$134$	−2.90621	−0.251059
$135$	3.22358	0.277442
$136$	2.54162	0.217942
$137$	7.31183	0.624692	0.312346	−	0.949968i	$-0.398885\pi$
$137$	7.31183	0.624692	0.312346	+	0.949968i	$0.398885\pi$
$138$	−1.95352	−0.166294
$139$	7.82224	0.663474	0.331737	−	0.943372i	$-0.392365\pi$
$139$	7.82224	0.663474	0.331737	+	0.943372i	$0.392365\pi$
$140$	6.28983	0.531588
$141$	−13.3167	−1.12147
$142$	−3.23695	−0.271639
$143$	−1.40591	−0.117568
$144$	3.70954	0.309128
$145$	−21.2144	−1.76176
$146$	0.436910	0.0361590
$147$	1.00000	0.0824786
$148$	21.6894	1.78286
$149$	11.3929	0.933343	0.466672	−	0.884431i	$-0.345453\pi$
$149$	11.3929	0.933343	0.466672	+	0.884431i	$0.345453\pi$
$150$	−1.19111	−0.0972536
$151$	−19.4170	−1.58013	−0.790067	−	0.613021i	$-0.789954\pi$
$151$	−19.4170	−1.58013	−0.790067	+	0.613021i	$0.789954\pi$
$152$	4.39290	0.356311
$153$	2.91165	0.235393
$154$	1.36584	0.110062
$155$	22.3007	1.79123
$156$	0.443711	0.0355253
$157$	−2.20938	−0.176328	−0.0881639	−	0.996106i	$-0.528100\pi$
$157$	−2.20938	−0.176328	−0.0881639	+	0.996106i	$0.528100\pi$
$158$	−3.01416	−0.239794
$159$	−3.35626	−0.266169
$160$	−8.26962	−0.653771
$161$	−8.84250	−0.696886
$162$	−0.220924	−0.0173574
$163$	8.91703	0.698436	0.349218	−	0.937042i	$-0.386447\pi$
$163$	8.91703	0.698436	0.349218	+	0.937042i	$0.386447\pi$
$164$	0.384773	0.0300457
$165$	19.9295	1.55151
$166$	1.03525	0.0803508
$167$	−4.64763	−0.359645	−0.179822	−	0.983699i	$-0.557552\pi$
$167$	−4.64763	−0.359645	−0.179822	+	0.983699i	$0.557552\pi$
$168$	−0.872912	−0.0673466
$169$	−12.9483	−0.996022
$170$	−2.07358	−0.159036
$171$	5.03246	0.384842
$172$	10.5676	0.805776
$173$	6.97363	0.530195	0.265098	−	0.964222i	$-0.414596\pi$
$173$	6.97363	0.530195	0.265098	+	0.964222i	$0.414596\pi$
$174$	1.45390	0.110220
$175$	−5.39149	−0.407559
$176$	22.9338	1.72870
$177$	−8.04248	−0.604510
$178$	1.86807	0.140018
$179$	−12.2707	−0.917154	−0.458577	−	0.888655i	$-0.651641\pi$
$179$	−12.2707	−0.917154	−0.458577	+	0.888655i	$0.651641\pi$
$180$	−6.28983	−0.468816
$181$	7.10240	0.527917	0.263959	−	0.964534i	$-0.414972\pi$
$181$	7.10240	0.527917	0.263959	+	0.964534i	$0.414972\pi$
$182$	−0.0502392	−0.00372398
$183$	−10.8774	−0.804077
$184$	7.71873	0.569032
$185$	−35.8333	−2.63452
$186$	−1.52834	−0.112064
$187$	18.0010	1.31636
$188$	25.9835	1.89504
$189$	−1.00000	−0.0727393
$190$	−3.58395	−0.260007
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	−6.85233	−0.494524
$193$	−12.9405	−0.931476	−0.465738	−	0.884923i	$-0.654211\pi$
$193$	−12.9405	−0.931476	−0.465738	+	0.884923i	$0.654211\pi$
$194$	−1.49637	−0.107433
$195$	−0.733060	−0.0524955
$196$	−1.95119	−0.139371
$197$	14.6416	1.04317	0.521584	−	0.853200i	$-0.325341\pi$
$197$	14.6416	1.04317	0.521584	+	0.853200i	$0.325341\pi$
$198$	−1.36584	−0.0970659
$199$	4.88880	0.346558	0.173279	−	0.984873i	$-0.444564\pi$
$199$	4.88880	0.346558	0.173279	+	0.984873i	$0.444564\pi$
$200$	4.70630	0.332786
$201$	13.1548	0.927870
$202$	−2.87517	−0.202296
$203$	6.58100	0.461896
$204$	−5.68119	−0.397763
$205$	−0.635687	−0.0443983
$206$	−2.72778	−0.190054
$207$	8.84250	0.614596
$208$	−0.843568	−0.0584909
$209$	31.1127	2.15211
$210$	0.712166	0.0491441
$211$	22.7370	1.56528	0.782639	−	0.622476i	$-0.213873\pi$
$211$	22.7370	1.56528	0.782639	+	0.622476i	$0.213873\pi$
$212$	6.54871	0.449767
$213$	14.6519	1.00393
$214$	2.68996	0.183882
$215$	−17.4589	−1.19069
$216$	0.872912	0.0593942
$217$	−6.91797	−0.469623
$218$	−0.304741	−0.0206397
$219$	−1.97765	−0.133637
$220$	−38.8863	−2.62171
$221$	−0.662125	−0.0445393
$222$	2.45578	0.164821
$223$	11.7774	0.788672	0.394336	−	0.918966i	$-0.370975\pi$
$223$	11.7774	0.788672	0.394336	+	0.918966i	$0.370975\pi$
$224$	2.56535	0.171405
$225$	5.39149	0.359433
$226$	0.952643	0.0633689
$227$	0.794694	0.0527457	0.0263729	−	0.999652i	$-0.491604\pi$
$227$	0.794694	0.0527457	0.0263729	+	0.999652i	$0.491604\pi$
$228$	−9.81930	−0.650299
$229$	9.46318	0.625344	0.312672	−	0.949861i	$-0.398776\pi$
$229$	9.46318	0.625344	0.312672	+	0.949861i	$0.398776\pi$
$230$	−6.29733	−0.415234
$231$	−6.18240	−0.406772
$232$	−5.74464	−0.377154
$233$	3.11310	0.203946	0.101973	−	0.994787i	$-0.467484\pi$
$233$	3.11310	0.203946	0.101973	+	0.994787i	$0.467484\pi$
$234$	0.0502392	0.00328424
$235$	−42.9277	−2.80029
$236$	15.6924	1.02149
$237$	13.6434	0.886237
$238$	0.643253	0.0416959
$239$	−15.1032	−0.976948	−0.488474	−	0.872579i	$-0.662446\pi$
$239$	−15.1032	−0.976948	−0.488474	+	0.872579i	$0.662446\pi$
$240$	11.9580	0.771886
$241$	−21.8651	−1.40846	−0.704228	−	0.709974i	$-0.748707\pi$
$241$	−21.8651	−1.40846	−0.704228	+	0.709974i	$0.748707\pi$
$242$	−6.01400	−0.386595
$243$	1.00000	0.0641500
$244$	21.2238	1.35872
$245$	3.22358	0.205947
$246$	0.0435659	0.00277766
$247$	−1.14441	−0.0728169
$248$	6.03878	0.383463
$249$	−4.68599	−0.296963
$250$	−0.278808	−0.0176334
$251$	6.12527	0.386624	0.193312	−	0.981137i	$-0.438077\pi$
$251$	6.12527	0.386624	0.193312	+	0.981137i	$0.438077\pi$
$252$	1.95119	0.122914
$253$	54.6679	3.43694
$254$	3.77544	0.236892
$255$	9.38595	0.587771
$256$	12.2367	0.764795
$257$	−25.1551	−1.56913	−0.784567	−	0.620044i	$-0.787115\pi$
$257$	−25.1551	−1.56913	−0.784567	+	0.620044i	$0.787115\pi$
$258$	1.19652	0.0744922
$259$	11.1160	0.690713
$260$	1.43034	0.0887060
$261$	−6.58100	−0.407354
$262$	2.63357	0.162703
$263$	8.60510	0.530613	0.265306	−	0.964164i	$-0.414527\pi$
$263$	8.60510	0.530613	0.265306	+	0.964164i	$0.414527\pi$
$264$	5.39669	0.332143
$265$	−10.8192	−0.664617
$266$	1.11179	0.0681682
$267$	−8.45572	−0.517482
$268$	−25.6676	−1.56790
$269$	6.46544	0.394205	0.197102	−	0.980383i	$-0.436847\pi$
$269$	6.46544	0.394205	0.197102	+	0.980383i	$0.436847\pi$
$270$	−0.712166	−0.0433411
$271$	14.4997	0.880791	0.440396	−	0.897804i	$-0.354838\pi$
$271$	14.4997	0.880791	0.440396	+	0.897804i	$0.354838\pi$
$272$	10.8009	0.654900
$273$	0.227405	0.0137632
$274$	−1.61536	−0.0975873
$275$	33.3324	2.01002
$276$	−17.2534	−1.03853
$277$	−2.61445	−0.157087	−0.0785434	−	0.996911i	$-0.525027\pi$
$277$	−2.61445	−0.157087	−0.0785434	+	0.996911i	$0.525027\pi$
$278$	−1.72812	−0.103646
$279$	6.91797	0.414168
$280$	−2.81391	−0.168163
$281$	−4.76934	−0.284515	−0.142258	−	0.989830i	$-0.545436\pi$
$281$	−4.76934	−0.284515	−0.142258	+	0.989830i	$0.545436\pi$
$282$	2.94199	0.175193
$283$	−29.8010	−1.77148	−0.885742	−	0.464177i	$-0.846350\pi$
$283$	−29.8010	−1.77148	−0.885742	+	0.464177i	$0.846350\pi$
$284$	−28.5887	−1.69643
$285$	16.2226	0.960941
$286$	0.310599	0.0183661
$287$	0.197199	0.0116403
$288$	−2.56535	−0.151165
$289$	−8.52229	−0.501311
$290$	4.68677	0.275217
$291$	6.77323	0.397054
$292$	3.85878	0.225818
$293$	−4.81235	−0.281140	−0.140570	−	0.990071i	$-0.544894\pi$
$293$	−4.81235	−0.281140	−0.140570	+	0.990071i	$0.544894\pi$
$294$	−0.220924	−0.0128845
$295$	−25.9256	−1.50945
$296$	−9.70327	−0.563991
$297$	6.18240	0.358739
$298$	−2.51696	−0.145804
$299$	−2.01083	−0.116289
$300$	−10.5198	−0.607363
$301$	5.41599	0.312173
$302$	4.28968	0.246843
$303$	13.0143	0.747653
$304$	18.6681	1.07069
$305$	−35.0641	−2.00776
$306$	−0.643253	−0.0367723
$307$	−25.0006	−1.42686	−0.713431	−	0.700726i	$-0.752860\pi$
$307$	−25.0006	−1.42686	−0.713431	+	0.700726i	$0.752860\pi$
$308$	12.0631	0.687356
$309$	12.3472	0.702406
$310$	−4.92675	−0.279820
$311$	32.7606	1.85768	0.928842	−	0.370477i	$-0.120806\pi$
$311$	32.7606	1.85768	0.928842	+	0.370477i	$0.120806\pi$
$312$	−0.198505	−0.0112381
$313$	−15.2399	−0.861411	−0.430705	−	0.902493i	$-0.641735\pi$
$313$	−15.2399	−0.861411	−0.430705	+	0.902493i	$0.641735\pi$
$314$	0.488105	0.0275453
$315$	−3.22358	−0.181628
$316$	−26.6210	−1.49755
$317$	12.2835	0.689912	0.344956	−	0.938619i	$-0.387894\pi$
$317$	12.2835	0.689912	0.344956	+	0.938619i	$0.387894\pi$
$318$	0.741478	0.0415800
$319$	−40.6864	−2.27800
$320$	−22.0891	−1.23482
$321$	−12.1760	−0.679596
$322$	1.95352	0.108865
$323$	14.6528	0.815302
$324$	−1.95119	−0.108400
$325$	−1.22605	−0.0680092
$326$	−1.96998	−0.109107
$327$	1.37940	0.0762808
$328$	−0.172137	−0.00950469
$329$	13.3167	0.734176
$330$	−4.40290	−0.242371
$331$	−21.1515	−1.16259	−0.581295	−	0.813693i	$-0.697454\pi$
$331$	−21.1515	−1.16259	−0.581295	+	0.813693i	$0.697454\pi$
$332$	9.14328	0.501803
$333$	−11.1160	−0.609152
$334$	1.02677	0.0561825
$335$	42.4057	2.31687
$336$	−3.70954	−0.202372
$337$	−25.6534	−1.39743	−0.698714	−	0.715401i	$-0.746244\pi$
$337$	−25.6534	−1.39743	−0.698714	+	0.715401i	$0.746244\pi$
$338$	2.86058	0.155595
$339$	−4.31209	−0.234201
$340$	−18.3138	−0.993205
$341$	42.7697	2.31611
$342$	−1.11179	−0.0601187
$343$	−1.00000	−0.0539949
$344$	−4.72769	−0.254900
$345$	28.5045	1.53463
$346$	−1.54064	−0.0828254
$347$	−10.1228	−0.543418	−0.271709	−	0.962379i	$-0.587589\pi$
$347$	−10.1228	−0.543418	−0.271709	+	0.962379i	$0.587589\pi$
$348$	12.8408	0.688339
$349$	14.7040	0.787088	0.393544	−	0.919306i	$-0.371249\pi$
$349$	14.7040	0.787088	0.393544	+	0.919306i	$0.371249\pi$
$350$	1.19111	0.0636674
$351$	−0.227405	−0.0121380
$352$	−15.8600	−0.845342
$353$	7.35064	0.391235	0.195618	−	0.980680i	$-0.437329\pi$
$353$	7.35064	0.391235	0.195618	+	0.980680i	$0.437329\pi$
$354$	1.77677	0.0944345
$355$	47.2317	2.50680
$356$	16.4987	0.874431
$357$	−2.91165	−0.154101
$358$	2.71088	0.143275
$359$	−9.91380	−0.523231	−0.261615	−	0.965172i	$-0.584255\pi$
$359$	−9.91380	−0.523231	−0.261615	+	0.965172i	$0.584255\pi$
$360$	2.81391	0.148306
$361$	6.32566	0.332929
$362$	−1.56909	−0.0824695
$363$	27.2221	1.42879
$364$	−0.443711	−0.0232568
$365$	−6.37513	−0.333690
$366$	2.40307	0.125610
$367$	−13.7436	−0.717413	−0.358706	−	0.933450i	$-0.616782\pi$
$367$	−13.7436	−0.717413	−0.358706	+	0.933450i	$0.616782\pi$
$368$	32.8016	1.70990
$369$	−0.197199	−0.0102658
$370$	7.91642	0.411555
$371$	3.35626	0.174248
$372$	−13.4983	−0.699854
$373$	10.0293	0.519299	0.259650	−	0.965703i	$-0.416393\pi$
$373$	10.0293	0.519299	0.259650	+	0.965703i	$0.416393\pi$
$374$	−3.97685	−0.205638
$375$	1.26201	0.0651699
$376$	−11.6244	−0.599480
$377$	1.49655	0.0770765
$378$	0.220924	0.0113631
$379$	−0.853720	−0.0438527	−0.0219263	−	0.999760i	$-0.506980\pi$
$379$	−0.853720	−0.0438527	−0.0219263	+	0.999760i	$0.506980\pi$
$380$	−31.6533	−1.62378
$381$	−17.0894	−0.875514
$382$	0.220924	0.0113034
$383$	−4.13058	−0.211063	−0.105531	−	0.994416i	$-0.533654\pi$
$383$	−4.13058	−0.211063	−0.105531	+	0.994416i	$0.533654\pi$
$384$	6.64454	0.339078
$385$	−19.9295	−1.01570
$386$	2.85886	0.145512
$387$	−5.41599	−0.275310
$388$	−13.2159	−0.670934
$389$	14.4476	0.732524	0.366262	−	0.930512i	$-0.380637\pi$
$389$	14.4476	0.732524	0.366262	+	0.930512i	$0.380637\pi$
$390$	0.161950	0.00820067
$391$	25.7463	1.30204
$392$	0.872912	0.0440887
$393$	−11.9207	−0.601322
$394$	−3.23467	−0.162960
$395$	43.9808	2.21291
$396$	−12.0631	−0.606191
$397$	30.3175	1.52159	0.760795	−	0.648992i	$-0.224809\pi$
$397$	30.3175	1.52159	0.760795	+	0.648992i	$0.224809\pi$
$398$	−1.08005	−0.0541381
$399$	−5.03246	−0.251938
$400$	20.0000	0.999998
$401$	23.0914	1.15313	0.576564	−	0.817052i	$-0.304393\pi$
$401$	23.0914	1.15313	0.576564	+	0.817052i	$0.304393\pi$
$402$	−2.90621	−0.144949
$403$	−1.57318	−0.0783658
$404$	−25.3934	−1.26337
$405$	3.22358	0.160181
$406$	−1.45390	−0.0721558
$407$	−68.7234	−3.40649
$408$	2.54162	0.125829
$409$	26.0236	1.28678	0.643392	−	0.765537i	$-0.277526\pi$
$409$	26.0236	1.28678	0.643392	+	0.765537i	$0.277526\pi$
$410$	0.140438	0.00693575
$411$	7.31183	0.360666
$412$	−24.0917	−1.18691
$413$	8.04248	0.395745
$414$	−1.95352	−0.0960102
$415$	−15.1057	−0.741509
$416$	0.583374	0.0286023
$417$	7.82224	0.383057
$418$	−6.87353	−0.336195
$419$	12.3778	0.604696	0.302348	−	0.953198i	$-0.402230\pi$
$419$	12.3778	0.604696	0.302348	+	0.953198i	$0.402230\pi$
$420$	6.28983	0.306912
$421$	−0.362254	−0.0176552	−0.00882758	−	0.999961i	$-0.502810\pi$
$421$	−0.362254	−0.0176552	−0.00882758	+	0.999961i	$0.502810\pi$
$422$	−5.02314	−0.244523
$423$	−13.3167	−0.647482
$424$	−2.92972	−0.142280
$425$	15.6981	0.761472
$426$	−3.23695	−0.156831
$427$	10.8774	0.526392
$428$	23.7577	1.14837
$429$	−1.40591	−0.0678780
$430$	3.85709	0.186005
$431$	6.49717	0.312958	0.156479	−	0.987681i	$-0.449986\pi$
$431$	6.49717	0.312958	0.156479	+	0.987681i	$0.449986\pi$
$432$	3.70954	0.178475
$433$	17.9572	0.862966	0.431483	−	0.902121i	$-0.357990\pi$
$433$	17.9572	0.862966	0.431483	+	0.902121i	$0.357990\pi$
$434$	1.52834	0.0733629
$435$	−21.2144	−1.01715
$436$	−2.69147	−0.128898
$437$	44.4995	2.12870
$438$	0.436910	0.0208764
$439$	9.23787	0.440899	0.220450	−	0.975398i	$-0.429248\pi$
$439$	9.23787	0.440899	0.220450	+	0.975398i	$0.429248\pi$
$440$	17.3967	0.829355
$441$	1.00000	0.0476190
$442$	0.146279	0.00695778
$443$	−7.78226	−0.369746	−0.184873	−	0.982762i	$-0.559187\pi$
$443$	−7.78226	−0.369746	−0.184873	+	0.982762i	$0.559187\pi$
$444$	21.6894	1.02933
$445$	−27.2577	−1.29214
$446$	−2.60190	−0.123204
$447$	11.3929	0.538866
$448$	6.85233	0.323742
$449$	−41.0451	−1.93704	−0.968519	−	0.248939i	$-0.919918\pi$
$449$	−41.0451	−1.93704	−0.968519	+	0.248939i	$0.919918\pi$
$450$	−1.19111	−0.0561494
$451$	−1.21916	−0.0574081
$452$	8.41372	0.395748
$453$	−19.4170	−0.912290
$454$	−0.175567	−0.00823976
$455$	0.733060	0.0343664
$456$	4.39290	0.205716
$457$	27.8024	1.30054	0.650270	−	0.759703i	$-0.274656\pi$
$457$	27.8024	1.30054	0.650270	+	0.759703i	$0.274656\pi$
$458$	−2.09064	−0.0976892
$459$	2.91165	0.135904
$460$	−55.6178	−2.59320
$461$	−12.9299	−0.602203	−0.301102	−	0.953592i	$-0.597354\pi$
$461$	−12.9299	−0.602203	−0.301102	+	0.953592i	$0.597354\pi$
$462$	1.36584	0.0635446
$463$	−8.04632	−0.373944	−0.186972	−	0.982365i	$-0.559867\pi$
$463$	−8.04632	−0.373944	−0.186972	+	0.982365i	$0.559867\pi$
$464$	−24.4125	−1.13332
$465$	22.3007	1.03417
$466$	−0.687758	−0.0318598
$467$	−11.5229	−0.533217	−0.266609	−	0.963805i	$-0.585903\pi$
$467$	−11.5229	−0.533217	−0.266609	+	0.963805i	$0.585903\pi$
$468$	0.443711	0.0205106
$469$	−13.1548	−0.607433
$470$	9.48374	0.437452
$471$	−2.20938	−0.101803
$472$	−7.02038	−0.323139
$473$	−33.4838	−1.53959
$474$	−3.01416	−0.138445
$475$	27.1325	1.24492
$476$	5.68119	0.260397
$477$	−3.35626	−0.153673
$478$	3.33666	0.152615
$479$	28.9489	1.32271	0.661355	−	0.750073i	$-0.269982\pi$
$479$	28.9489	1.32271	0.661355	+	0.750073i	$0.269982\pi$
$480$	−8.26962	−0.377455
$481$	2.52783	0.115259
$482$	4.83053	0.220024
$483$	−8.84250	−0.402348
$484$	−53.1155	−2.41434
$485$	21.8341	0.991434
$486$	−0.220924	−0.0100213
$487$	−39.1858	−1.77568	−0.887839	−	0.460155i	$-0.847794\pi$
$487$	−39.1858	−1.77568	−0.887839	+	0.460155i	$0.847794\pi$
$488$	−9.49498	−0.429817
$489$	8.91703	0.403242
$490$	−0.712166	−0.0321724
$491$	−21.3304	−0.962627	−0.481313	−	0.876549i	$-0.659840\pi$
$491$	−21.3304	−0.962627	−0.481313	+	0.876549i	$0.659840\pi$
$492$	0.384773	0.0173469
$493$	−19.1616	−0.862994
$494$	0.252827	0.0113752
$495$	19.9295	0.895764
$496$	25.6625	1.15228
$497$	−14.6519	−0.657228
$498$	1.03525	0.0463905
$499$	10.0853	0.451482	0.225741	−	0.974187i	$-0.427520\pi$
$499$	10.0853	0.451482	0.225741	+	0.974187i	$0.427520\pi$
$500$	−2.46243	−0.110123
$501$	−4.64763	−0.207641
$502$	−1.35322	−0.0603970
$503$	−0.385190	−0.0171748	−0.00858738	−	0.999963i	$-0.502733\pi$
$503$	−0.385190	−0.0171748	−0.00858738	+	0.999963i	$0.502733\pi$
$504$	−0.872912	−0.0388826
$505$	41.9527	1.86687
$506$	−12.0774	−0.536907
$507$	−12.9483	−0.575054
$508$	33.3446	1.47943
$509$	−37.8051	−1.67568	−0.837841	−	0.545915i	$-0.816182\pi$
$509$	−37.8051	−1.67568	−0.837841	+	0.545915i	$0.816182\pi$
$510$	−2.07358	−0.0918196
$511$	1.97765	0.0874862
$512$	−15.9925	−0.706774
$513$	5.03246	0.222189
$514$	5.55736	0.245125
$515$	39.8021	1.75389
$516$	10.5676	0.465215
$517$	−82.3295	−3.62085
$518$	−2.45578	−0.107901
$519$	6.97363	0.306108
$520$	−0.639897	−0.0280613
$521$	19.4955	0.854115	0.427058	−	0.904224i	$-0.359550\pi$
$521$	19.4955	0.854115	0.427058	+	0.904224i	$0.359550\pi$
$522$	1.45390	0.0636355
$523$	−23.6604	−1.03460	−0.517298	−	0.855805i	$-0.673062\pi$
$523$	−23.6604	−1.03460	−0.517298	+	0.855805i	$0.673062\pi$
$524$	23.2597	1.01610
$525$	−5.39149	−0.235304
$526$	−1.90107	−0.0828906
$527$	20.1427	0.877431
$528$	22.9338	0.998068
$529$	55.1898	2.39956
$530$	2.39022	0.103824
$531$	−8.04248	−0.349014
$532$	9.81930	0.425721
$533$	0.0448440	0.00194241
$534$	1.86807	0.0808392
$535$	−39.2503	−1.69694
$536$	11.4830	0.495990
$537$	−12.2707	−0.529519
$538$	−1.42837	−0.0615814
$539$	6.18240	0.266295
$540$	−6.28983	−0.270671
$541$	35.1673	1.51196	0.755980	−	0.654594i	$-0.227160\pi$
$541$	35.1673	1.51196	0.755980	+	0.654594i	$0.227160\pi$
$542$	−3.20332	−0.137594
$543$	7.10240	0.304793
$544$	−7.46940	−0.320248
$545$	4.44660	0.190471
$546$	−0.0502392	−0.00215004
$547$	26.2614	1.12286	0.561428	−	0.827525i	$-0.310252\pi$
$547$	26.2614	1.12286	0.561428	+	0.827525i	$0.310252\pi$
$548$	−14.2668	−0.609447
$549$	−10.8774	−0.464234
$550$	−7.36391	−0.313998
$551$	−33.1186	−1.41090
$552$	7.71873	0.328531
$553$	−13.6434	−0.580178
$554$	0.577593	0.0245396
$555$	−35.8333	−1.52104
$556$	−15.2627	−0.647283
$557$	6.24147	0.264460	0.132230	−	0.991219i	$-0.457786\pi$
$557$	6.24147	0.264460	0.132230	+	0.991219i	$0.457786\pi$
$558$	−1.52834	−0.0647000
$559$	1.23163	0.0520922
$560$	−11.9580	−0.505318
$561$	18.0010	0.760002
$562$	1.05366	0.0444460
$563$	−37.8180	−1.59384	−0.796920	−	0.604085i	$-0.793539\pi$
$563$	−37.8180	−1.59384	−0.796920	+	0.604085i	$0.793539\pi$
$564$	25.9835	1.09410
$565$	−13.9004	−0.584794
$566$	6.58374	0.276735
$567$	−1.00000	−0.0419961
$568$	12.7898	0.536649
$569$	9.72451	0.407673	0.203836	−	0.979005i	$-0.434659\pi$
$569$	9.72451	0.407673	0.203836	+	0.979005i	$0.434659\pi$
$570$	−3.58395	−0.150115
$571$	−3.78962	−0.158591	−0.0792953	−	0.996851i	$-0.525267\pi$
$571$	−3.78962	−0.158591	−0.0792953	+	0.996851i	$0.525267\pi$
$572$	2.74320	0.114699
$573$	−1.00000	−0.0417756
$574$	−0.0435659	−0.00181840
$575$	47.6743	1.98815
$576$	−6.85233	−0.285514
$577$	−12.8837	−0.536355	−0.268177	−	0.963370i	$-0.586421\pi$
$577$	−12.8837	−0.536355	−0.268177	+	0.963370i	$0.586421\pi$
$578$	1.88278	0.0783132
$579$	−12.9405	−0.537788
$580$	41.3934	1.71877
$581$	4.68599	0.194408
$582$	−1.49637	−0.0620264
$583$	−20.7497	−0.859367
$584$	−1.72632	−0.0714355
$585$	−0.733060	−0.0303083
$586$	1.06316	0.0439188
$587$	8.23595	0.339934	0.169967	−	0.985450i	$-0.445634\pi$
$587$	8.23595	0.339934	0.169967	+	0.985450i	$0.445634\pi$
$588$	−1.95119	−0.0804658
$589$	34.8144	1.43450
$590$	5.72758	0.235801
$591$	14.6416	0.602274
$592$	−41.2351	−1.69475
$593$	−10.4460	−0.428967	−0.214483	−	0.976728i	$-0.568807\pi$
$593$	−10.4460	−0.428967	−0.214483	+	0.976728i	$0.568807\pi$
$594$	−1.36584	−0.0560410
$595$	−9.38595	−0.384786
$596$	−22.2298	−0.910566
$597$	4.88880	0.200085
$598$	0.444240	0.0181663
$599$	−35.4252	−1.44744	−0.723718	−	0.690096i	$-0.757568\pi$
$599$	−35.4252	−1.44744	−0.723718	+	0.690096i	$0.757568\pi$
$600$	4.70630	0.192134
$601$	−19.5602	−0.797877	−0.398939	−	0.916978i	$-0.630621\pi$
$601$	−19.5602	−0.797877	−0.398939	+	0.916978i	$0.630621\pi$
$602$	−1.19652	−0.0487666
$603$	13.1548	0.535706
$604$	37.8863	1.54157
$605$	87.7526	3.56765
$606$	−2.87517	−0.116796
$607$	21.3404	0.866182	0.433091	−	0.901350i	$-0.357423\pi$
$607$	21.3404	0.866182	0.433091	+	0.901350i	$0.357423\pi$
$608$	−12.9100	−0.523570
$609$	6.58100	0.266676
$610$	7.74649	0.313646
$611$	3.02830	0.122512
$612$	−5.68119	−0.229649
$613$	−40.8678	−1.65063	−0.825317	−	0.564669i	$-0.809004\pi$
$613$	−40.8678	−1.65063	−0.825317	+	0.564669i	$0.809004\pi$
$614$	5.52323	0.222900
$615$	−0.635687	−0.0256334
$616$	−5.39669	−0.217439
$617$	5.57286	0.224355	0.112177	−	0.993688i	$-0.464218\pi$
$617$	5.57286	0.224355	0.112177	+	0.993688i	$0.464218\pi$
$618$	−2.72778	−0.109728
$619$	−3.68112	−0.147957	−0.0739784	−	0.997260i	$-0.523570\pi$
$619$	−3.68112	−0.147957	−0.0739784	+	0.997260i	$0.523570\pi$
$620$	−43.5129	−1.74752
$621$	8.84250	0.354837
$622$	−7.23759	−0.290201
$623$	8.45572	0.338771
$624$	−0.843568	−0.0337698
$625$	−22.8893	−0.915571
$626$	3.36686	0.134567
$627$	31.1127	1.24252
$628$	4.31093	0.172025
$629$	−32.3658	−1.29051
$630$	0.712166	0.0283734
$631$	12.3596	0.492028	0.246014	−	0.969266i	$-0.420879\pi$
$631$	12.3596	0.492028	0.246014	+	0.969266i	$0.420879\pi$
$632$	11.9095	0.473736
$633$	22.7370	0.903714
$634$	−2.71372	−0.107776
$635$	−55.0890	−2.18614
$636$	6.54871	0.259673
$637$	−0.227405	−0.00901012
$638$	8.98859	0.355862
$639$	14.6519	0.579620
$640$	21.4192	0.846670
$641$	−40.3307	−1.59297	−0.796483	−	0.604661i	$-0.793309\pi$
$641$	−40.3307	−1.59297	−0.796483	+	0.604661i	$0.793309\pi$
$642$	2.68996	0.106164
$643$	−34.3024	−1.35276	−0.676378	−	0.736555i	$-0.736451\pi$
$643$	−34.3024	−1.35276	−0.676378	+	0.736555i	$0.736451\pi$
$644$	17.2534	0.679880
$645$	−17.4589	−0.687444
$646$	−3.23714	−0.127364
$647$	18.4969	0.727187	0.363594	−	0.931558i	$-0.381550\pi$
$647$	18.4969	0.727187	0.363594	+	0.931558i	$0.381550\pi$
$648$	0.872912	0.0342912
$649$	−49.7218	−1.95175
$650$	0.270864	0.0106242
$651$	−6.91797	−0.271137
$652$	−17.3988	−0.681392
$653$	1.66160	0.0650235	0.0325118	−	0.999471i	$-0.489649\pi$
$653$	1.66160	0.0650235	0.0325118	+	0.999471i	$0.489649\pi$
$654$	−0.304741	−0.0119163
$655$	−38.4275	−1.50149
$656$	−0.731516	−0.0285609
$657$	−1.97765	−0.0771556
$658$	−2.94199	−0.114691
$659$	15.9230	0.620271	0.310136	−	0.950692i	$-0.399626\pi$
$659$	15.9230	0.620271	0.310136	+	0.950692i	$0.399626\pi$
$660$	−38.8863	−1.51365
$661$	−19.0854	−0.742338	−0.371169	−	0.928565i	$-0.621043\pi$
$661$	−19.0854	−0.742338	−0.371169	+	0.928565i	$0.621043\pi$
$662$	4.67286	0.181616
$663$	−0.662125	−0.0257148
$664$	−4.09046	−0.158741
$665$	−16.2226	−0.629084
$666$	2.45578	0.0951597
$667$	−58.1925	−2.25322
$668$	9.06842	0.350868
$669$	11.7774	0.455340
$670$	−9.36842	−0.361934
$671$	−67.2482	−2.59609
$672$	2.56535	0.0989605
$673$	−8.09917	−0.312200	−0.156100	−	0.987741i	$-0.549892\pi$
$673$	−8.09917	−0.312200	−0.156100	+	0.987741i	$0.549892\pi$
$674$	5.66744	0.218302
$675$	5.39149	0.207519
$676$	25.2646	0.971715
$677$	−6.35068	−0.244077	−0.122038	−	0.992525i	$-0.538943\pi$
$677$	−6.35068	−0.244077	−0.122038	+	0.992525i	$0.538943\pi$
$678$	0.952643	0.0365860
$679$	−6.77323	−0.259933
$680$	8.19311	0.314191
$681$	0.794694	0.0304528
$682$	−9.44884	−0.361815
$683$	30.6945	1.17449	0.587247	−	0.809408i	$-0.300212\pi$
$683$	30.6945	1.17449	0.587247	+	0.809408i	$0.300212\pi$
$684$	−9.81930	−0.375450
$685$	23.5703	0.900575
$686$	0.220924	0.00843491
$687$	9.46318	0.361043
$688$	−20.0908	−0.765956
$689$	0.763231	0.0290768
$690$	−6.29733	−0.239735
$691$	−8.97570	−0.341452	−0.170726	−	0.985319i	$-0.554611\pi$
$691$	−8.97570	−0.341452	−0.170726	+	0.985319i	$0.554611\pi$
$692$	−13.6069	−0.517257
$693$	−6.18240	−0.234850
$694$	2.23636	0.0848910
$695$	25.2157	0.956484
$696$	−5.74464	−0.217750
$697$	−0.574174	−0.0217484
$698$	−3.24846	−0.122956
$699$	3.11310	0.117748
$700$	10.5198	0.397613
$701$	29.4265	1.11142	0.555712	−	0.831375i	$-0.312446\pi$
$701$	29.4265	1.11142	0.555712	+	0.831375i	$0.312446\pi$
$702$	0.0502392	0.00189616
$703$	−55.9407	−2.10984
$704$	−42.3638	−1.59665
$705$	−42.9277	−1.61675
$706$	−1.62393	−0.0611174
$707$	−13.0143	−0.489454
$708$	15.6924	0.589757
$709$	27.5102	1.03317	0.516584	−	0.856236i	$-0.327203\pi$
$709$	27.5102	1.03317	0.516584	+	0.856236i	$0.327203\pi$
$710$	−10.4346	−0.391603
$711$	13.6434	0.511669
$712$	−7.38110	−0.276618
$713$	61.1722	2.29092
$714$	0.643253	0.0240731
$715$	−4.53207	−0.169490
$716$	23.9425	0.894772
$717$	−15.1032	−0.564041
$718$	2.19019	0.0817373
$719$	37.0784	1.38279	0.691396	−	0.722476i	$-0.256996\pi$
$719$	37.0784	1.38279	0.691396	+	0.722476i	$0.256996\pi$
$720$	11.9580	0.445649
$721$	−12.3472	−0.459833
$722$	−1.39749	−0.0520091
$723$	−21.8651	−0.813173
$724$	−13.8581	−0.515034
$725$	−35.4814	−1.31775
$726$	−6.01400	−0.223200
$727$	3.66364	0.135877	0.0679384	−	0.997690i	$-0.478358\pi$
$727$	3.66364	0.135877	0.0679384	+	0.997690i	$0.478358\pi$
$728$	0.198505	0.00735708
$729$	1.00000	0.0370370
$730$	1.40842	0.0521279
$731$	−15.7695	−0.583255
$732$	21.2238	0.784455
$733$	23.7769	0.878219	0.439110	−	0.898433i	$-0.355294\pi$
$733$	23.7769	0.878219	0.439110	+	0.898433i	$0.355294\pi$
$734$	3.03630	0.112072
$735$	3.22358	0.118904
$736$	−22.6841	−0.836147
$737$	81.3284	2.99577
$738$	0.0435659	0.00160368
$739$	4.62040	0.169964	0.0849821	−	0.996382i	$-0.472917\pi$
$739$	4.62040	0.169964	0.0849821	+	0.996382i	$0.472917\pi$
$740$	69.9176	2.57022
$741$	−1.14441	−0.0420409
$742$	−0.741478	−0.0272205
$743$	21.0604	0.772632	0.386316	−	0.922367i	$-0.373747\pi$
$743$	21.0604	0.772632	0.386316	+	0.922367i	$0.373747\pi$
$744$	6.03878	0.221393
$745$	36.7260	1.34554
$746$	−2.21572	−0.0811232
$747$	−4.68599	−0.171452
$748$	−35.1234	−1.28424
$749$	12.1760	0.444900
$750$	−0.278808	−0.0101806
$751$	−29.7163	−1.08436	−0.542181	−	0.840262i	$-0.682401\pi$
$751$	−29.7163	−1.08436	−0.542181	+	0.840262i	$0.682401\pi$
$752$	−49.3990	−1.80140
$753$	6.12527	0.223217
$754$	−0.330624	−0.0120406
$755$	−62.5923	−2.27797
$756$	1.95119	0.0709642
$757$	31.6489	1.15030	0.575149	−	0.818049i	$-0.304944\pi$
$757$	31.6489	1.15030	0.575149	+	0.818049i	$0.304944\pi$
$758$	0.188607	0.00685052
$759$	54.6679	1.98432
$760$	14.1609	0.513669
$761$	−7.86613	−0.285147	−0.142573	−	0.989784i	$-0.545538\pi$
$761$	−7.86613	−0.285147	−0.142573	+	0.989784i	$0.545538\pi$
$762$	3.77544	0.136770
$763$	−1.37940	−0.0499375
$764$	1.95119	0.0705917
$765$	9.38595	0.339350
$766$	0.912544	0.0329716
$767$	1.82890	0.0660378
$768$	12.2367	0.441555
$769$	7.32349	0.264092	0.132046	−	0.991244i	$-0.457845\pi$
$769$	7.32349	0.264092	0.132046	+	0.991244i	$0.457845\pi$
$770$	4.40290	0.158669
$771$	−25.1551	−0.905940
$772$	25.2494	0.908745
$773$	6.00278	0.215905	0.107952	−	0.994156i	$-0.465571\pi$
$773$	6.00278	0.215905	0.107952	+	0.994156i	$0.465571\pi$
$774$	1.19652	0.0430081
$775$	37.2982	1.33979
$776$	5.91243	0.212244
$777$	11.1160	0.398783
$778$	−3.19182	−0.114432
$779$	−0.992395	−0.0355562
$780$	1.43034	0.0512144
$781$	90.5839	3.24135
$782$	−5.68796	−0.203401
$783$	−6.58100	−0.235186
$784$	3.70954	0.132484
$785$	−7.12213	−0.254200
$786$	2.63357	0.0939365
$787$	−25.8459	−0.921307	−0.460653	−	0.887580i	$-0.652385\pi$
$787$	−25.8459	−0.921307	−0.460653	+	0.887580i	$0.652385\pi$
$788$	−28.5685	−1.01771
$789$	8.60510	0.306350
$790$	−9.71640	−0.345694
$791$	4.31209	0.153320
$792$	5.39669	0.191763
$793$	2.47357	0.0878390
$794$	−6.69785	−0.237698
$795$	−10.8192	−0.383717
$796$	−9.53898	−0.338100
$797$	46.3192	1.64071	0.820355	−	0.571854i	$-0.193776\pi$
$797$	46.3192	1.64071	0.820355	+	0.571854i	$0.193776\pi$
$798$	1.11179	0.0393569
$799$	−38.7737	−1.37172
$800$	−13.8311	−0.489002
$801$	−8.45572	−0.298768
$802$	−5.10144	−0.180138
$803$	−12.2266	−0.431469
$804$	−25.6676	−0.905226
$805$	−28.5045	−1.00465
$806$	0.347554	0.0122421
$807$	6.46544	0.227594
$808$	11.3604	0.399656
$809$	−37.4601	−1.31703	−0.658513	−	0.752569i	$-0.728814\pi$
$809$	−37.4601	−1.31703	−0.658513	+	0.752569i	$0.728814\pi$
$810$	−0.712166	−0.0250230
$811$	17.4483	0.612692	0.306346	−	0.951920i	$-0.400894\pi$
$811$	17.4483	0.612692	0.306346	+	0.951920i	$0.400894\pi$
$812$	−12.8408	−0.450624
$813$	14.4997	0.508525
$814$	15.1826	0.532151
$815$	28.7448	1.00689
$816$	10.8009	0.378106
$817$	−27.2558	−0.953559
$818$	−5.74923	−0.201017
$819$	0.227405	0.00794618
$820$	1.24035	0.0433148
$821$	−5.09960	−0.177977	−0.0889886	−	0.996033i	$-0.528363\pi$
$821$	−5.09960	−0.177977	−0.0889886	+	0.996033i	$0.528363\pi$
$822$	−1.61536	−0.0563420
$823$	−26.8120	−0.934606	−0.467303	−	0.884097i	$-0.654774\pi$
$823$	−26.8120	−0.934606	−0.467303	+	0.884097i	$0.654774\pi$
$824$	10.7780	0.375469
$825$	33.3324	1.16048
$826$	−1.77677	−0.0618219
$827$	−51.8823	−1.80412	−0.902062	−	0.431606i	$-0.857947\pi$
$827$	−51.8823	−1.80412	−0.902062	+	0.431606i	$0.857947\pi$
$828$	−17.2534	−0.599598
$829$	−11.0927	−0.385265	−0.192633	−	0.981271i	$-0.561703\pi$
$829$	−11.0927	−0.385265	−0.192633	+	0.981271i	$0.561703\pi$
$830$	3.33721	0.115836
$831$	−2.61445	−0.0906941
$832$	1.55826	0.0540228
$833$	2.91165	0.100883
$834$	−1.72812	−0.0598399
$835$	−14.9820	−0.518475
$836$	−60.7068	−2.09959
$837$	6.91797	0.239120
$838$	−2.73455	−0.0944636
$839$	29.5994	1.02188	0.510942	−	0.859615i	$-0.329297\pi$
$839$	29.5994	1.02188	0.510942	+	0.859615i	$0.329297\pi$
$840$	−2.81391	−0.0970890
$841$	14.3096	0.493435
$842$	0.0800304	0.00275803
$843$	−4.76934	−0.164265
$844$	−44.3642	−1.52708
$845$	−41.7399	−1.43590
$846$	2.94199	0.101148
$847$	−27.2221	−0.935361
$848$	−12.4502	−0.427541
$849$	−29.8010	−1.02277
$850$	−3.46809	−0.118955
$851$	−98.2930	−3.36944
$852$	−28.5887	−0.979433
$853$	37.3179	1.27774	0.638870	−	0.769314i	$-0.279402\pi$
$853$	37.3179	1.27774	0.638870	+	0.769314i	$0.279402\pi$
$854$	−2.40307	−0.0822312
$855$	16.2226	0.554800
$856$	−10.6286	−0.363277
$857$	25.7913	0.881013	0.440506	−	0.897749i	$-0.354799\pi$
$857$	25.7913	0.881013	0.440506	+	0.897749i	$0.354799\pi$
$858$	0.310599	0.0106037
$859$	0.683805	0.0233311	0.0116656	−	0.999932i	$-0.496287\pi$
$859$	0.683805	0.0233311	0.0116656	+	0.999932i	$0.496287\pi$
$860$	34.0657	1.16163
$861$	0.197199	0.00672051
$862$	−1.43538	−0.0488892
$863$	35.9589	1.22406	0.612028	−	0.790836i	$-0.290354\pi$
$863$	35.9589	1.22406	0.612028	+	0.790836i	$0.290354\pi$
$864$	−2.56535	−0.0872750
$865$	22.4801	0.764346
$866$	−3.96716	−0.134810
$867$	−8.52229	−0.289432
$868$	13.4983	0.458162
$869$	84.3492	2.86135
$870$	4.68677	0.158896
$871$	−2.99148	−0.101362
$872$	1.20409	0.0407757
$873$	6.77323	0.229239
$874$	−9.83100	−0.332539
$875$	−1.26201	−0.0426637
$876$	3.85878	0.130376
$877$	49.8450	1.68315	0.841574	−	0.540142i	$-0.181630\pi$
$877$	49.8450	1.68315	0.841574	+	0.540142i	$0.181630\pi$
$878$	−2.04086	−0.0688758
$879$	−4.81235	−0.162317
$880$	73.9292	2.49215
$881$	−52.7041	−1.77565	−0.887823	−	0.460185i	$-0.847783\pi$
$881$	−52.7041	−1.77565	−0.887823	+	0.460185i	$0.847783\pi$
$882$	−0.220924	−0.00743889
$883$	3.10259	0.104411	0.0522053	−	0.998636i	$-0.483375\pi$
$883$	3.10259	0.104411	0.0522053	+	0.998636i	$0.483375\pi$
$884$	1.29193	0.0434524
$885$	−25.9256	−0.871480
$886$	1.71929	0.0577605
$887$	−14.4746	−0.486010	−0.243005	−	0.970025i	$-0.578133\pi$
$887$	−14.4746	−0.486010	−0.243005	+	0.970025i	$0.578133\pi$
$888$	−9.70327	−0.325621
$889$	17.0894	0.573158
$890$	6.02188	0.201854
$891$	6.18240	0.207118
$892$	−22.9799	−0.769425
$893$	−67.0160	−2.24261
$894$	−2.51696	−0.0841799
$895$	−39.5556	−1.32220
$896$	−6.64454	−0.221979
$897$	−2.01083	−0.0671397
$898$	9.06784	0.302598
$899$	−45.5272	−1.51842
$900$	−10.5198	−0.350661
$901$	−9.77226	−0.325561
$902$	0.269342	0.00896810
$903$	5.41599	0.180233
$904$	−3.76408	−0.125191
$905$	22.8952	0.761061
$906$	4.28968	0.142515
$907$	−34.0789	−1.13157	−0.565785	−	0.824553i	$-0.691427\pi$
$907$	−34.0789	−1.13157	−0.565785	+	0.824553i	$0.691427\pi$
$908$	−1.55060	−0.0514585
$909$	13.0143	0.431658
$910$	−0.161950	−0.00536860
$911$	−7.34490	−0.243348	−0.121674	−	0.992570i	$-0.538826\pi$
$911$	−7.34490	−0.243348	−0.121674	+	0.992570i	$0.538826\pi$
$912$	18.6681	0.618163
$913$	−28.9707	−0.958790
$914$	−6.14221	−0.203166
$915$	−35.0641	−1.15918
$916$	−18.4645	−0.610084
$917$	11.9207	0.393658
$918$	−0.643253	−0.0212305
$919$	−46.2597	−1.52597	−0.762983	−	0.646419i	$-0.776266\pi$
$919$	−46.2597	−1.52597	−0.762983	+	0.646419i	$0.776266\pi$
$920$	24.8820	0.820334
$921$	−25.0006	−0.823799
$922$	2.85651	0.0940742
$923$	−3.33192	−0.109671
$924$	12.0631	0.396845
$925$	−59.9317	−1.97054
$926$	1.77762	0.0584163
$927$	12.3472	0.405534
$928$	16.8826	0.554198
$929$	−0.331390	−0.0108725	−0.00543627	−	0.999985i	$-0.501730\pi$
$929$	−0.331390	−0.0108725	−0.00543627	+	0.999985i	$0.501730\pi$
$930$	−4.92675	−0.161554
$931$	5.03246	0.164932
$932$	−6.07426	−0.198969
$933$	32.7606	1.07253
$934$	2.54569	0.0832974
$935$	58.0277	1.89771
$936$	−0.198505	−0.00648833
$937$	6.49524	0.212190	0.106095	−	0.994356i	$-0.466165\pi$
$937$	6.49524	0.212190	0.106095	+	0.994356i	$0.466165\pi$
$938$	2.90621	0.0948912
$939$	−15.2399	−0.497336
$940$	83.7601	2.73195
$941$	−13.7341	−0.447718	−0.223859	−	0.974622i	$-0.571865\pi$
$941$	−13.7341	−0.447718	−0.223859	+	0.974622i	$0.571865\pi$
$942$	0.488105	0.0159033
$943$	−1.74373	−0.0567836
$944$	−29.8339	−0.971010
$945$	−3.22358	−0.104863
$946$	7.39738	0.240509
$947$	11.1341	0.361809	0.180905	−	0.983501i	$-0.442097\pi$
$947$	11.1341	0.361809	0.180905	+	0.983501i	$0.442097\pi$
$948$	−26.6210	−0.864609
$949$	0.449729	0.0145988
$950$	−5.99421	−0.194478
$951$	12.2835	0.398321
$952$	−2.54162	−0.0823742
$953$	−18.3573	−0.594652	−0.297326	−	0.954776i	$-0.596095\pi$
$953$	−18.3573	−0.594652	−0.297326	+	0.954776i	$0.596095\pi$
$954$	0.741478	0.0240062
$955$	−3.22358	−0.104313
$956$	29.4693	0.953106
$957$	−40.6864	−1.31520
$958$	−6.39551	−0.206629
$959$	−7.31183	−0.236111
$960$	−22.0891	−0.712921
$961$	16.8584	0.543818
$962$	−0.558458	−0.0180054
$963$	−12.1760	−0.392365
$964$	42.6631	1.37409
$965$	−41.7147	−1.34284
$966$	1.95352	0.0628534
$967$	−28.1335	−0.904714	−0.452357	−	0.891837i	$-0.649417\pi$
$967$	−28.1335	−0.904714	−0.452357	+	0.891837i	$0.649417\pi$
$968$	23.7625	0.763755
$969$	14.6528	0.470715
$970$	−4.82366	−0.154878
$971$	−47.4098	−1.52145	−0.760726	−	0.649073i	$-0.775157\pi$
$971$	−47.4098	−1.52145	−0.760726	+	0.649073i	$0.775157\pi$
$972$	−1.95119	−0.0625845
$973$	−7.82224	−0.250770
$974$	8.65707	0.277390
$975$	−1.22605	−0.0392651
$976$	−40.3500	−1.29157
$977$	13.8641	0.443553	0.221776	−	0.975098i	$-0.428815\pi$
$977$	13.8641	0.443553	0.221776	+	0.975098i	$0.428815\pi$
$978$	−1.96998	−0.0629932
$979$	−52.2766	−1.67077
$980$	−6.28983	−0.200921
$981$	1.37940	0.0440407
$982$	4.71239	0.150378
$983$	26.4269	0.842886	0.421443	−	0.906855i	$-0.361524\pi$
$983$	26.4269	0.842886	0.421443	+	0.906855i	$0.361524\pi$
$984$	−0.172137	−0.00548753
$985$	47.1983	1.50386
$986$	4.23325	0.134814
$987$	13.3167	0.423877
$988$	2.23296	0.0710399
$989$	−47.8909	−1.52284
$990$	−4.40290	−0.139933
$991$	40.3454	1.28161	0.640807	−	0.767702i	$-0.278600\pi$
$991$	40.3454	1.28161	0.640807	+	0.767702i	$0.278600\pi$
$992$	−17.7470	−0.563469
$993$	−21.1515	−0.671222
$994$	3.23695	0.102670
$995$	15.7594	0.499608
$996$	9.14328	0.289716
$997$	33.8993	1.07360	0.536801	−	0.843709i	$-0.319633\pi$
$997$	33.8993	1.07360	0.536801	+	0.843709i	$0.319633\pi$
$998$	−2.22809	−0.0705290
$999$	−11.1160	−0.351694

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.m.1.14	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.m.1.14	✓	29	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)

\(f(q)\)	\(=\)	\(q-0.220924 q^{2} +1.00000 q^{3} -1.95119 q^{4} +3.22358 q^{5} -0.220924 q^{6} -1.00000 q^{7} +0.872912 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.220924 q^{2} +1.00000 q^{3} -1.95119 q^{4} +3.22358 q^{5} -0.220924 q^{6} -1.00000 q^{7} +0.872912 q^{8} +1.00000 q^{9} -0.712166 q^{10} +6.18240 q^{11} -1.95119 q^{12} -0.227405 q^{13} +0.220924 q^{14} +3.22358 q^{15} +3.70954 q^{16} +2.91165 q^{17} -0.220924 q^{18} +5.03246 q^{19} -6.28983 q^{20} -1.00000 q^{21} -1.36584 q^{22} +8.84250 q^{23} +0.872912 q^{24} +5.39149 q^{25} +0.0502392 q^{26} +1.00000 q^{27} +1.95119 q^{28} -6.58100 q^{29} -0.712166 q^{30} +6.91797 q^{31} -2.56535 q^{32} +6.18240 q^{33} -0.643253 q^{34} -3.22358 q^{35} -1.95119 q^{36} -11.1160 q^{37} -1.11179 q^{38} -0.227405 q^{39} +2.81391 q^{40} -0.197199 q^{41} +0.220924 q^{42} -5.41599 q^{43} -12.0631 q^{44} +3.22358 q^{45} -1.95352 q^{46} -13.3167 q^{47} +3.70954 q^{48} +1.00000 q^{49} -1.19111 q^{50} +2.91165 q^{51} +0.443711 q^{52} -3.35626 q^{53} -0.220924 q^{54} +19.9295 q^{55} -0.872912 q^{56} +5.03246 q^{57} +1.45390 q^{58} -8.04248 q^{59} -6.28983 q^{60} -10.8774 q^{61} -1.52834 q^{62} -1.00000 q^{63} -6.85233 q^{64} -0.733060 q^{65} -1.36584 q^{66} +13.1548 q^{67} -5.68119 q^{68} +8.84250 q^{69} +0.712166 q^{70} +14.6519 q^{71} +0.872912 q^{72} -1.97765 q^{73} +2.45578 q^{74} +5.39149 q^{75} -9.81930 q^{76} -6.18240 q^{77} +0.0502392 q^{78} +13.6434 q^{79} +11.9580 q^{80} +1.00000 q^{81} +0.0435659 q^{82} -4.68599 q^{83} +1.95119 q^{84} +9.38595 q^{85} +1.19652 q^{86} -6.58100 q^{87} +5.39669 q^{88} -8.45572 q^{89} -0.712166 q^{90} +0.227405 q^{91} -17.2534 q^{92} +6.91797 q^{93} +2.94199 q^{94} +16.2226 q^{95} -2.56535 q^{96} +6.77323 q^{97} -0.220924 q^{98} +6.18240 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9}+O(q^{10}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9} + 11 q^{11} + 40 q^{12} + 13 q^{13} - 6 q^{14} + 22 q^{15} + 58 q^{16} + 17 q^{17} + 6 q^{18} + 3 q^{19} + 52 q^{20} - 29 q^{21} + 17 q^{22} + 36 q^{23} + 15 q^{24} + 57 q^{25} + 25 q^{26} + 29 q^{27} - 40 q^{28} + 20 q^{29} + 6 q^{31} + 46 q^{32} + 11 q^{33} + 18 q^{34} - 22 q^{35} + 40 q^{36} + 22 q^{37} + 8 q^{38} + 13 q^{39} + 6 q^{40} + 26 q^{41} - 6 q^{42} + 21 q^{43} + 22 q^{44} + 22 q^{45} + 28 q^{46} + 41 q^{47} + 58 q^{48} + 29 q^{49} + 18 q^{50} + 17 q^{51} + 2 q^{52} + 37 q^{53} + 6 q^{54} + 7 q^{55} - 15 q^{56} + 3 q^{57} + 9 q^{58} + 27 q^{59} + 52 q^{60} + 20 q^{61} - 12 q^{62} - 29 q^{63} + 59 q^{64} + 3 q^{65} + 17 q^{66} + 30 q^{67} + 33 q^{68} + 36 q^{69} + 68 q^{71} + 15 q^{72} + q^{73} + 21 q^{74} + 57 q^{75} + 11 q^{76} - 11 q^{77} + 25 q^{78} + 34 q^{79} + 110 q^{80} + 29 q^{81} - 49 q^{82} + 13 q^{83} - 40 q^{84} + 27 q^{85} + 35 q^{86} + 20 q^{87} + 17 q^{88} + 61 q^{89} - 13 q^{91} + 86 q^{92} + 6 q^{93} - 19 q^{94} + 25 q^{95} + 46 q^{96} - 3 q^{97} + 6 q^{98} + 11 q^{99}+O(q^{100}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9 + 11 * q^11 + 40 * q^12 + 13 * q^13 - 6 * q^14 + 22 * q^15 + 58 * q^16 + 17 * q^17 + 6 * q^18 + 3 * q^19 + 52 * q^20 - 29 * q^21 + 17 * q^22 + 36 * q^23 + 15 * q^24 + 57 * q^25 + 25 * q^26 + 29 * q^27 - 40 * q^28 + 20 * q^29 + 6 * q^31 + 46 * q^32 + 11 * q^33 + 18 * q^34 - 22 * q^35 + 40 * q^36 + 22 * q^37 + 8 * q^38 + 13 * q^39 + 6 * q^40 + 26 * q^41 - 6 * q^42 + 21 * q^43 + 22 * q^44 + 22 * q^45 + 28 * q^46 + 41 * q^47 + 58 * q^48 + 29 * q^49 + 18 * q^50 + 17 * q^51 + 2 * q^52 + 37 * q^53 + 6 * q^54 + 7 * q^55 - 15 * q^56 + 3 * q^57 + 9 * q^58 + 27 * q^59 + 52 * q^60 + 20 * q^61 - 12 * q^62 - 29 * q^63 + 59 * q^64 + 3 * q^65 + 17 * q^66 + 30 * q^67 + 33 * q^68 + 36 * q^69 + 68 * q^71 + 15 * q^72 + q^73 + 21 * q^74 + 57 * q^75 + 11 * q^76 - 11 * q^77 + 25 * q^78 + 34 * q^79 + 110 * q^80 + 29 * q^81 - 49 * q^82 + 13 * q^83 - 40 * q^84 + 27 * q^85 + 35 * q^86 + 20 * q^87 + 17 * q^88 + 61 * q^89 - 13 * q^91 + 86 * q^92 + 6 * q^93 - 19 * q^94 + 25 * q^95 + 46 * q^96 - 3 * q^97 + 6 * q^98 + 11 * q^99

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