LMFDB - Embedded newform 6011.2.a.e.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6011,2,Mod(1,6011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6011, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6011.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:	$47.9980766550$
Analytic rank:	$1$
Dimension:	$221$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.53639 q^{2} -0.500202 q^{3} +4.43325 q^{4} +0.151225 q^{5} +1.26871 q^{6} +0.853062 q^{7} -6.17167 q^{8} -2.74980 q^{9} +O(q^{10})$	\(q-2.53639 q^{2} -0.500202 q^{3} +4.43325 q^{4} +0.151225 q^{5} +1.26871 q^{6} +0.853062 q^{7} -6.17167 q^{8} -2.74980 q^{9} -0.383566 q^{10} +2.93082 q^{11} -2.21752 q^{12} +0.184956 q^{13} -2.16369 q^{14} -0.0756433 q^{15} +6.78724 q^{16} -4.47898 q^{17} +6.97455 q^{18} -3.96721 q^{19} +0.670421 q^{20} -0.426703 q^{21} -7.43368 q^{22} +4.43908 q^{23} +3.08709 q^{24} -4.97713 q^{25} -0.469121 q^{26} +2.87606 q^{27} +3.78184 q^{28} +2.46629 q^{29} +0.191861 q^{30} -0.368226 q^{31} -4.87171 q^{32} -1.46600 q^{33} +11.3604 q^{34} +0.129005 q^{35} -12.1906 q^{36} +4.49103 q^{37} +10.0624 q^{38} -0.0925156 q^{39} -0.933314 q^{40} +1.47922 q^{41} +1.08228 q^{42} +7.00139 q^{43} +12.9931 q^{44} -0.415839 q^{45} -11.2592 q^{46} -4.26629 q^{47} -3.39499 q^{48} -6.27229 q^{49} +12.6239 q^{50} +2.24040 q^{51} +0.819959 q^{52} -3.22344 q^{53} -7.29480 q^{54} +0.443214 q^{55} -5.26482 q^{56} +1.98441 q^{57} -6.25546 q^{58} +13.8938 q^{59} -0.335346 q^{60} +6.00924 q^{61} +0.933962 q^{62} -2.34575 q^{63} -1.21794 q^{64} +0.0279701 q^{65} +3.71835 q^{66} -2.49795 q^{67} -19.8565 q^{68} -2.22044 q^{69} -0.327206 q^{70} -12.7735 q^{71} +16.9709 q^{72} +3.03953 q^{73} -11.3910 q^{74} +2.48957 q^{75} -17.5877 q^{76} +2.50017 q^{77} +0.234655 q^{78} -1.16850 q^{79} +1.02640 q^{80} +6.81078 q^{81} -3.75187 q^{82} +0.370414 q^{83} -1.89169 q^{84} -0.677336 q^{85} -17.7582 q^{86} -1.23364 q^{87} -18.0880 q^{88} +10.1518 q^{89} +1.05473 q^{90} +0.157779 q^{91} +19.6796 q^{92} +0.184187 q^{93} +10.8210 q^{94} -0.599943 q^{95} +2.43684 q^{96} +2.19448 q^{97} +15.9089 q^{98} -8.05915 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9}+O(q^{10}) $ 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9	\( 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9} - 61 q^{10} - 50 q^{11} - 43 q^{12} - 87 q^{13} - 41 q^{14} - 62 q^{15} + 129 q^{16} - 29 q^{17} - 61 q^{18} - 107 q^{19} - 59 q^{20} - 163 q^{21} - 70 q^{22} - 31 q^{23} - 98 q^{24} + 119 q^{25} - 23 q^{26} - 41 q^{27} - 112 q^{28} - 152 q^{29} - 66 q^{30} - 117 q^{31} - 93 q^{32} - 60 q^{33} - 80 q^{34} - 21 q^{35} + 92 q^{36} - 231 q^{37} + 2 q^{38} - 81 q^{39} - 143 q^{40} - 81 q^{41} - 6 q^{42} - 126 q^{43} - 115 q^{44} - 156 q^{45} - 205 q^{46} - 4 q^{47} - 55 q^{48} + 103 q^{49} - 61 q^{50} - 106 q^{51} - 164 q^{52} - 87 q^{53} - 110 q^{54} - 62 q^{55} - 73 q^{56} - 136 q^{57} - 128 q^{58} - 76 q^{59} - 148 q^{60} - 345 q^{61} + 5 q^{62} - 74 q^{63} - 25 q^{64} - 110 q^{65} - 34 q^{66} - 104 q^{67} - 48 q^{68} - 133 q^{69} - 92 q^{70} - 39 q^{71} - 177 q^{72} - 175 q^{73} - 44 q^{74} - 23 q^{75} - 268 q^{76} - 81 q^{77} - 19 q^{78} - 272 q^{79} - 60 q^{80} + 77 q^{81} - 13 q^{82} - 40 q^{83} - 221 q^{84} - 376 q^{85} - 82 q^{86} - 3 q^{87} - 234 q^{88} - 92 q^{89} - 91 q^{90} - 205 q^{91} - 11 q^{92} - 125 q^{93} - 126 q^{94} - 56 q^{95} - 148 q^{96} - 133 q^{97} - 4 q^{98} - 195 q^{99}+O(q^{100}) \) 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9 - 61 * q^10 - 50 * q^11 - 43 * q^12 - 87 * q^13 - 41 * q^14 - 62 * q^15 + 129 * q^16 - 29 * q^17 - 61 * q^18 - 107 * q^19 - 59 * q^20 - 163 * q^21 - 70 * q^22 - 31 * q^23 - 98 * q^24 + 119 * q^25 - 23 * q^26 - 41 * q^27 - 112 * q^28 - 152 * q^29 - 66 * q^30 - 117 * q^31 - 93 * q^32 - 60 * q^33 - 80 * q^34 - 21 * q^35 + 92 * q^36 - 231 * q^37 + 2 * q^38 - 81 * q^39 - 143 * q^40 - 81 * q^41 - 6 * q^42 - 126 * q^43 - 115 * q^44 - 156 * q^45 - 205 * q^46 - 4 * q^47 - 55 * q^48 + 103 * q^49 - 61 * q^50 - 106 * q^51 - 164 * q^52 - 87 * q^53 - 110 * q^54 - 62 * q^55 - 73 * q^56 - 136 * q^57 - 128 * q^58 - 76 * q^59 - 148 * q^60 - 345 * q^61 + 5 * q^62 - 74 * q^63 - 25 * q^64 - 110 * q^65 - 34 * q^66 - 104 * q^67 - 48 * q^68 - 133 * q^69 - 92 * q^70 - 39 * q^71 - 177 * q^72 - 175 * q^73 - 44 * q^74 - 23 * q^75 - 268 * q^76 - 81 * q^77 - 19 * q^78 - 272 * q^79 - 60 * q^80 + 77 * q^81 - 13 * q^82 - 40 * q^83 - 221 * q^84 - 376 * q^85 - 82 * q^86 - 3 * q^87 - 234 * q^88 - 92 * q^89 - 91 * q^90 - 205 * q^91 - 11 * q^92 - 125 * q^93 - 126 * q^94 - 56 * q^95 - 148 * q^96 - 133 * q^97 - 4 * q^98 - 195 * 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 $

$2$	−2.53639	−1.79350	−0.896748	−	0.442542i	$-0.854077\pi$
$2$	−2.53639	−1.79350	−0.896748	+	0.442542i	$0.854077\pi$
$3$	−0.500202	−0.288792	−0.144396	−	0.989520i	$-0.546124\pi$
$3$	−0.500202	−0.288792	−0.144396	+	0.989520i	$0.546124\pi$
$4$	4.43325	2.21663
$5$	0.151225	0.0676301	0.0338150	−	0.999428i	$-0.489234\pi$
$5$	0.151225	0.0676301	0.0338150	+	0.999428i	$0.489234\pi$
$6$	1.26871	0.517947
$7$	0.853062	0.322427	0.161214	−	0.986920i	$-0.448459\pi$
$7$	0.853062	0.322427	0.161214	+	0.986920i	$0.448459\pi$
$8$	−6.17167	−2.18202
$9$	−2.74980	−0.916599
$10$	−0.383566	−0.121294
$11$	2.93082	0.883674	0.441837	−	0.897095i	$-0.354327\pi$
$11$	2.93082	0.883674	0.441837	+	0.897095i	$0.354327\pi$
$12$	−2.21752	−0.640144
$13$	0.184956	0.0512977	0.0256488	−	0.999671i	$-0.491835\pi$
$13$	0.184956	0.0512977	0.0256488	+	0.999671i	$0.491835\pi$
$14$	−2.16369	−0.578272
$15$	−0.0756433	−0.0195310
$16$	6.78724	1.69681
$17$	−4.47898	−1.08631	−0.543156	−	0.839632i	$-0.682771\pi$
$17$	−4.47898	−1.08631	−0.543156	+	0.839632i	$0.682771\pi$
$18$	6.97455	1.64392
$19$	−3.96721	−0.910141	−0.455070	−	0.890456i	$-0.650386\pi$
$19$	−3.96721	−0.910141	−0.455070	+	0.890456i	$0.650386\pi$
$20$	0.670421	0.149911
$21$	−0.426703	−0.0931143
$22$	−7.43368	−1.58487
$23$	4.43908	0.925612	0.462806	−	0.886460i	$-0.346843\pi$
$23$	4.43908	0.925612	0.462806	+	0.886460i	$0.346843\pi$
$24$	3.08709	0.630149
$25$	−4.97713	−0.995426
$26$	−0.469121	−0.0920022
$27$	2.87606	0.553498
$28$	3.78184	0.714701
$29$	2.46629	0.457978	0.228989	−	0.973429i	$-0.426458\pi$
$29$	2.46629	0.457978	0.228989	+	0.973429i	$0.426458\pi$
$30$	0.191861	0.0350288
$31$	−0.368226	−0.0661353	−0.0330676	−	0.999453i	$-0.510528\pi$
$31$	−0.368226	−0.0661353	−0.0330676	+	0.999453i	$0.510528\pi$
$32$	−4.87171	−0.861205
$33$	−1.46600	−0.255198
$34$	11.3604	1.94830
$35$	0.129005	0.0218058
$36$	−12.1906	−2.03176
$37$	4.49103	0.738321	0.369160	−	0.929366i	$-0.379645\pi$
$37$	4.49103	0.738321	0.369160	+	0.929366i	$0.379645\pi$
$38$	10.0624	1.63233
$39$	−0.0925156	−0.0148144
$40$	−0.933314	−0.147570
$41$	1.47922	0.231015	0.115507	−	0.993307i	$-0.463151\pi$
$41$	1.47922	0.231015	0.115507	+	0.993307i	$0.463151\pi$
$42$	1.08228	0.167000
$43$	7.00139	1.06770	0.533851	−	0.845579i	$-0.320744\pi$
$43$	7.00139	1.06770	0.533851	+	0.845579i	$0.320744\pi$
$44$	12.9931	1.95878
$45$	−0.415839	−0.0619897
$46$	−11.2592	−1.66008
$47$	−4.26629	−0.622303	−0.311151	−	0.950360i	$-0.600715\pi$
$47$	−4.26629	−0.622303	−0.311151	+	0.950360i	$0.600715\pi$
$48$	−3.39499	−0.490025
$49$	−6.27229	−0.896041
$50$	12.6239	1.78529
$51$	2.24040	0.313718
$52$	0.819959	0.113708
$53$	−3.22344	−0.442773	−0.221387	−	0.975186i	$-0.571058\pi$
$53$	−3.22344	−0.442773	−0.221387	+	0.975186i	$0.571058\pi$
$54$	−7.29480	−0.992697
$55$	0.443214	0.0597630
$56$	−5.26482	−0.703541
$57$	1.98441	0.262841
$58$	−6.25546	−0.821382
$59$	13.8938	1.80882	0.904410	−	0.426664i	$-0.140311\pi$
$59$	13.8938	1.80882	0.904410	+	0.426664i	$0.140311\pi$
$60$	−0.335346	−0.0432930
$61$	6.00924	0.769404	0.384702	−	0.923041i	$-0.374304\pi$
$61$	6.00924	0.769404	0.384702	+	0.923041i	$0.374304\pi$
$62$	0.933962	0.118613
$63$	−2.34575	−0.295536
$64$	−1.21794	−0.152242
$65$	0.0279701	0.00346927
$66$	3.71835	0.457697
$67$	−2.49795	−0.305173	−0.152586	−	0.988290i	$-0.548760\pi$
$67$	−2.49795	−0.305173	−0.152586	+	0.988290i	$0.548760\pi$
$68$	−19.8565	−2.40795
$69$	−2.22044	−0.267309
$70$	−0.327206	−0.0391085
$71$	−12.7735	−1.51594	−0.757970	−	0.652289i	$-0.773809\pi$
$71$	−12.7735	−1.51594	−0.757970	+	0.652289i	$0.773809\pi$
$72$	16.9709	2.00003
$73$	3.03953	0.355750	0.177875	−	0.984053i	$-0.443078\pi$
$73$	3.03953	0.355750	0.177875	+	0.984053i	$0.443078\pi$
$74$	−11.3910	−1.32417
$75$	2.48957	0.287471
$76$	−17.5877	−2.01744
$77$	2.50017	0.284921
$78$	0.234655	0.0265695
$79$	−1.16850	−0.131466	−0.0657331	−	0.997837i	$-0.520939\pi$
$79$	−1.16850	−0.131466	−0.0657331	+	0.997837i	$0.520939\pi$
$80$	1.02640	0.114755
$81$	6.81078	0.756753
$82$	−3.75187	−0.414324
$83$	0.370414	0.0406582	0.0203291	−	0.999793i	$-0.493529\pi$
$83$	0.370414	0.0406582	0.0203291	+	0.999793i	$0.493529\pi$
$84$	−1.89169	−0.206400
$85$	−0.677336	−0.0734674
$86$	−17.7582	−1.91492
$87$	−1.23364	−0.132260
$88$	−18.0880	−1.92819
$89$	10.1518	1.07609	0.538044	−	0.842916i	$-0.319163\pi$
$89$	10.1518	1.07609	0.538044	+	0.842916i	$0.319163\pi$
$90$	1.05473	0.111178
$91$	0.157779	0.0165398
$92$	19.6796	2.05174
$93$	0.184187	0.0190993
$94$	10.8210	1.11610
$95$	−0.599943	−0.0615529
$96$	2.43684	0.248709
$97$	2.19448	0.222815	0.111408	−	0.993775i	$-0.464464\pi$
$97$	2.19448	0.222815	0.111408	+	0.993775i	$0.464464\pi$
$98$	15.9089	1.60705
$99$	−8.05915	−0.809975
$100$	−22.0649	−2.20649
$101$	−5.45924	−0.543215	−0.271607	−	0.962408i	$-0.587555\pi$
$101$	−5.45924	−0.543215	−0.271607	+	0.962408i	$0.587555\pi$
$102$	−5.68251	−0.562653
$103$	4.74846	0.467880	0.233940	−	0.972251i	$-0.424838\pi$
$103$	4.74846	0.467880	0.233940	+	0.972251i	$0.424838\pi$
$104$	−1.14149	−0.111932
$105$	−0.0645284	−0.00629733
$106$	8.17589	0.794112
$107$	−13.5179	−1.30682	−0.653411	−	0.757004i	$-0.726663\pi$
$107$	−13.5179	−1.30682	−0.653411	+	0.757004i	$0.726663\pi$
$108$	12.7503	1.22690
$109$	7.16814	0.686584	0.343292	−	0.939229i	$-0.388458\pi$
$109$	7.16814	0.686584	0.343292	+	0.939229i	$0.388458\pi$
$110$	−1.12416	−0.107185
$111$	−2.24642	−0.213221
$112$	5.78993	0.547097
$113$	13.3248	1.25349	0.626745	−	0.779225i	$-0.284387\pi$
$113$	13.3248	1.25349	0.626745	+	0.779225i	$0.284387\pi$
$114$	−5.03323	−0.471405
$115$	0.671302	0.0625992
$116$	10.9337	1.01517
$117$	−0.508593	−0.0470194
$118$	−35.2401	−3.24411
$119$	−3.82085	−0.350257
$120$	0.466846	0.0426170
$121$	−2.41031	−0.219119
$122$	−15.2417	−1.37992
$123$	−0.739908	−0.0667153
$124$	−1.63244	−0.146597
$125$	−1.50880	−0.134951
$126$	5.94972	0.530043
$127$	−19.7587	−1.75330	−0.876652	−	0.481126i	$-0.840228\pi$
$127$	−19.7587	−1.75330	−0.876652	+	0.481126i	$0.840228\pi$
$128$	12.8326	1.13425
$129$	−3.50211	−0.308344
$130$	−0.0709430	−0.00622211
$131$	2.44180	0.213341	0.106670	−	0.994294i	$-0.465981\pi$
$131$	2.44180	0.213341	0.106670	+	0.994294i	$0.465981\pi$
$132$	−6.49916	−0.565679
$133$	−3.38428	−0.293454
$134$	6.33576	0.547326
$135$	0.434934	0.0374331
$136$	27.6428	2.37035
$137$	1.16085	0.0991785	0.0495892	−	0.998770i	$-0.484209\pi$
$137$	1.16085	0.0991785	0.0495892	+	0.998770i	$0.484209\pi$
$138$	5.63189	0.479418
$139$	−16.2022	−1.37426	−0.687128	−	0.726537i	$-0.741129\pi$
$139$	−16.2022	−1.37426	−0.687128	+	0.726537i	$0.741129\pi$
$140$	0.571910	0.0483353
$141$	2.13401	0.179716
$142$	32.3986	2.71883
$143$	0.542073	0.0453304
$144$	−18.6635	−1.55529
$145$	0.372965	0.0309731
$146$	−7.70942	−0.638036
$147$	3.13741	0.258769
$148$	19.9099	1.63658
$149$	9.88255	0.809610	0.404805	−	0.914403i	$-0.367339\pi$
$149$	9.88255	0.809610	0.404805	+	0.914403i	$0.367339\pi$
$150$	−6.31452	−0.515578
$151$	−22.4003	−1.82291	−0.911455	−	0.411401i	$-0.865040\pi$
$151$	−22.4003	−1.82291	−0.911455	+	0.411401i	$0.865040\pi$
$152$	24.4843	1.98594
$153$	12.3163	0.995713
$154$	−6.34139	−0.511004
$155$	−0.0556851	−0.00447273
$156$	−0.410145	−0.0328379
$157$	−16.2778	−1.29911	−0.649555	−	0.760315i	$-0.725045\pi$
$157$	−16.2778	−1.29911	−0.649555	+	0.760315i	$0.725045\pi$
$158$	2.96376	0.235784
$159$	1.61237	0.127869
$160$	−0.736727	−0.0582434
$161$	3.78681	0.298442
$162$	−17.2748	−1.35723
$163$	−2.11262	−0.165473	−0.0827365	−	0.996571i	$-0.526366\pi$
$163$	−2.11262	−0.165473	−0.0827365	+	0.996571i	$0.526366\pi$
$164$	6.55775	0.512074
$165$	−0.221697	−0.0172591
$166$	−0.939513	−0.0729203
$167$	−16.5172	−1.27814	−0.639070	−	0.769149i	$-0.720680\pi$
$167$	−16.5172	−1.27814	−0.639070	+	0.769149i	$0.720680\pi$
$168$	2.63347	0.203177
$169$	−12.9658	−0.997369
$170$	1.71799	0.131764
$171$	10.9090	0.834234
$172$	31.0389	2.36670
$173$	20.1502	1.53199	0.765997	−	0.642844i	$-0.222246\pi$
$173$	20.1502	1.53199	0.765997	+	0.642844i	$0.222246\pi$
$174$	3.12899	0.237208
$175$	−4.24580	−0.320952
$176$	19.8922	1.49943
$177$	−6.94972	−0.522373
$178$	−25.7489	−1.92996
$179$	8.35924	0.624799	0.312399	−	0.949951i	$-0.398867\pi$
$179$	8.35924	0.624799	0.312399	+	0.949951i	$0.398867\pi$
$180$	−1.84352	−0.137408
$181$	−5.78853	−0.430258	−0.215129	−	0.976586i	$-0.569017\pi$
$181$	−5.78853	−0.430258	−0.215129	+	0.976586i	$0.569017\pi$
$182$	−0.400189	−0.0296640
$183$	−3.00583	−0.222198
$184$	−27.3965	−2.01970
$185$	0.679158	0.0499327
$186$	−0.467170	−0.0342546
$187$	−13.1271	−0.959947
$188$	−18.9136	−1.37941
$189$	2.45346	0.178463
$190$	1.52169	0.110395
$191$	−11.6714	−0.844511	−0.422255	−	0.906477i	$-0.638761\pi$
$191$	−11.6714	−0.844511	−0.422255	+	0.906477i	$0.638761\pi$
$192$	0.609215	0.0439663
$193$	−9.70832	−0.698820	−0.349410	−	0.936970i	$-0.613618\pi$
$193$	−9.70832	−0.698820	−0.349410	+	0.936970i	$0.613618\pi$
$194$	−5.56604	−0.399618
$195$	−0.0139907	−0.00100190
$196$	−27.8066	−1.98619
$197$	−5.30672	−0.378088	−0.189044	−	0.981969i	$-0.560539\pi$
$197$	−5.30672	−0.378088	−0.189044	+	0.981969i	$0.560539\pi$
$198$	20.4411	1.45269
$199$	−15.6892	−1.11217	−0.556087	−	0.831124i	$-0.687698\pi$
$199$	−15.6892	−1.11217	−0.556087	+	0.831124i	$0.687698\pi$
$200$	30.7172	2.17204
$201$	1.24948	0.0881314
$202$	13.8467	0.974253
$203$	2.10390	0.147665
$204$	9.93225	0.695397
$205$	0.223695	0.0156236
$206$	−12.0439	−0.839140
$207$	−12.2066	−0.848415
$208$	1.25534	0.0870424
$209$	−11.6272	−0.804268
$210$	0.163669	0.0112942
$211$	18.7291	1.28936	0.644681	−	0.764452i	$-0.276990\pi$
$211$	18.7291	1.28936	0.644681	+	0.764452i	$0.276990\pi$
$212$	−14.2903	−0.981464
$213$	6.38935	0.437791
$214$	34.2865	2.34378
$215$	1.05879	0.0722087
$216$	−17.7501	−1.20774
$217$	−0.314119	−0.0213238
$218$	−18.1812	−1.23138
$219$	−1.52038	−0.102738
$220$	1.96488	0.132472
$221$	−0.828416	−0.0557253
$222$	5.69780	0.382411
$223$	14.2425	0.953751	0.476875	−	0.878971i	$-0.341769\pi$
$223$	14.2425	0.953751	0.476875	+	0.878971i	$0.341769\pi$
$224$	−4.15587	−0.277676
$225$	13.6861	0.912407
$226$	−33.7968	−2.24813
$227$	9.82918	0.652386	0.326193	−	0.945303i	$-0.394234\pi$
$227$	9.82918	0.652386	0.326193	+	0.945303i	$0.394234\pi$
$228$	8.79739	0.582621
$229$	27.5723	1.82203	0.911015	−	0.412372i	$-0.135300\pi$
$229$	27.5723	1.82203	0.911015	+	0.412372i	$0.135300\pi$
$230$	−1.70268	−0.112271
$231$	−1.25059	−0.0822827
$232$	−15.2211	−0.999316
$233$	−20.1532	−1.32028	−0.660141	−	0.751141i	$-0.729504\pi$
$233$	−20.1532	−1.32028	−0.660141	+	0.751141i	$0.729504\pi$
$234$	1.28999	0.0843291
$235$	−0.645172	−0.0420864
$236$	61.5948	4.00948
$237$	0.584485	0.0379664
$238$	9.69115	0.628184
$239$	22.4613	1.45290	0.726452	−	0.687217i	$-0.241168\pi$
$239$	22.4613	1.45290	0.726452	+	0.687217i	$0.241168\pi$
$240$	−0.513409	−0.0331404
$241$	−18.1781	−1.17096	−0.585478	−	0.810688i	$-0.699093\pi$
$241$	−18.1781	−1.17096	−0.585478	+	0.810688i	$0.699093\pi$
$242$	6.11349	0.392990
$243$	−12.0350	−0.772043
$244$	26.6405	1.70548
$245$	−0.948529	−0.0605993
$246$	1.87669	0.119654
$247$	−0.733761	−0.0466881
$248$	2.27257	0.144308
$249$	−0.185282	−0.0117418
$250$	3.82689	0.242034
$251$	−28.6638	−1.80925	−0.904623	−	0.426213i	$-0.859847\pi$
$251$	−28.6638	−1.80925	−0.904623	+	0.426213i	$0.859847\pi$
$252$	−10.3993	−0.655094
$253$	13.0101	0.817940
$254$	50.1158	3.14454
$255$	0.338805	0.0212168
$256$	−30.1125	−1.88203
$257$	24.8470	1.54991	0.774957	−	0.632014i	$-0.217772\pi$
$257$	24.8470	1.54991	0.774957	+	0.632014i	$0.217772\pi$
$258$	8.88270	0.553013
$259$	3.83112	0.238055
$260$	0.123999	0.00769007
$261$	−6.78179	−0.419782
$262$	−6.19334	−0.382626
$263$	2.71564	0.167453	0.0837266	−	0.996489i	$-0.473318\pi$
$263$	2.71564	0.167453	0.0837266	+	0.996489i	$0.473318\pi$
$264$	9.04768	0.556846
$265$	−0.487466	−0.0299448
$266$	8.58383	0.526308
$267$	−5.07796	−0.310766
$268$	−11.0740	−0.676454
$269$	−21.8784	−1.33395	−0.666976	−	0.745079i	$-0.732412\pi$
$269$	−21.8784	−1.33395	−0.666976	+	0.745079i	$0.732412\pi$
$270$	−1.10316	−0.0671362
$271$	−27.4137	−1.66527	−0.832633	−	0.553826i	$-0.813167\pi$
$271$	−27.4137	−1.66527	−0.832633	+	0.553826i	$0.813167\pi$
$272$	−30.3999	−1.84327
$273$	−0.0789215	−0.00477655
$274$	−2.94437	−0.177876
$275$	−14.5871	−0.879633
$276$	−9.84377	−0.592525
$277$	20.3739	1.22415	0.612076	−	0.790799i	$-0.290335\pi$
$277$	20.3739	1.22415	0.612076	+	0.790799i	$0.290335\pi$
$278$	41.0951	2.46472
$279$	1.01255	0.0606195
$280$	−0.796175	−0.0475805
$281$	28.4368	1.69640	0.848200	−	0.529676i	$-0.177687\pi$
$281$	28.4368	1.69640	0.848200	+	0.529676i	$0.177687\pi$
$282$	−5.41267	−0.322320
$283$	11.6753	0.694026	0.347013	−	0.937860i	$-0.387196\pi$
$283$	11.6753	0.694026	0.347013	+	0.937860i	$0.387196\pi$
$284$	−56.6284	−3.36028
$285$	0.300093	0.0177760
$286$	−1.37491	−0.0813000
$287$	1.26186	0.0744855
$288$	13.3962	0.789380
$289$	3.06128	0.180076
$290$	−0.945984	−0.0555501
$291$	−1.09768	−0.0643472
$292$	13.4750	0.788566
$293$	6.54869	0.382579	0.191289	−	0.981534i	$-0.438733\pi$
$293$	6.54869	0.382579	0.191289	+	0.981534i	$0.438733\pi$
$294$	−7.95769	−0.464102
$295$	2.10110	0.122331
$296$	−27.7172	−1.61103
$297$	8.42921	0.489112
$298$	−25.0660	−1.45203
$299$	0.821036	0.0474817
$300$	11.0369	0.637216
$301$	5.97261	0.344256
$302$	56.8158	3.26938
$303$	2.73072	0.156876
$304$	−26.9264	−1.54434
$305$	0.908750	0.0520348
$306$	−31.2389	−1.78581
$307$	8.10852	0.462777	0.231389	−	0.972861i	$-0.425673\pi$
$307$	8.10852	0.462777	0.231389	+	0.972861i	$0.425673\pi$
$308$	11.0839	0.631563
$309$	−2.37519	−0.135120
$310$	0.141239	0.00802183
$311$	15.2198	0.863036	0.431518	−	0.902104i	$-0.357978\pi$
$311$	15.2198	0.863036	0.431518	+	0.902104i	$0.357978\pi$
$312$	0.570976	0.0323252
$313$	−17.1253	−0.967981	−0.483990	−	0.875073i	$-0.660813\pi$
$313$	−17.1253	−0.967981	−0.483990	+	0.875073i	$0.660813\pi$
$314$	41.2868	2.32995
$315$	−0.354737	−0.0199871
$316$	−5.18025	−0.291412
$317$	17.7474	0.996794	0.498397	−	0.866949i	$-0.333922\pi$
$317$	17.7474	0.996794	0.498397	+	0.866949i	$0.333922\pi$
$318$	−4.08960	−0.229333
$319$	7.22824	0.404704
$320$	−0.184183	−0.0102961
$321$	6.76167	0.377400
$322$	−9.60481	−0.535255
$323$	17.7691	0.988697
$324$	30.1939	1.67744
$325$	−0.920552	−0.0510630
$326$	5.35841	0.296775
$327$	−3.58552	−0.198280
$328$	−9.12925	−0.504078
$329$	−3.63941	−0.200647
$330$	0.562308	0.0309541
$331$	−16.9139	−0.929672	−0.464836	−	0.885397i	$-0.653887\pi$
$331$	−16.9139	−0.929672	−0.464836	+	0.885397i	$0.653887\pi$
$332$	1.64214	0.0901241
$333$	−12.3494	−0.676744
$334$	41.8940	2.29234
$335$	−0.377753	−0.0206389
$336$	−2.89614	−0.157997
$337$	27.8079	1.51479	0.757397	−	0.652955i	$-0.226471\pi$
$337$	27.8079	1.51479	0.757397	+	0.652955i	$0.226471\pi$
$338$	32.8863	1.78878
$339$	−6.66508	−0.361998
$340$	−3.00280	−0.162850
$341$	−1.07920	−0.0584421
$342$	−27.6695	−1.49620
$343$	−11.3221	−0.611335
$344$	−43.2103	−2.32974
$345$	−0.335787	−0.0180781
$346$	−51.1088	−2.74763
$347$	22.2077	1.19217	0.596086	−	0.802921i	$-0.296722\pi$
$347$	22.2077	1.19217	0.596086	+	0.802921i	$0.296722\pi$
$348$	−5.46905	−0.293172
$349$	−33.1087	−1.77227	−0.886135	−	0.463427i	$-0.846620\pi$
$349$	−33.1087	−1.77227	−0.886135	+	0.463427i	$0.846620\pi$
$350$	10.7690	0.575627
$351$	0.531946	0.0283932
$352$	−14.2781	−0.761025
$353$	5.58939	0.297493	0.148747	−	0.988875i	$-0.452476\pi$
$353$	5.58939	0.297493	0.148747	+	0.988875i	$0.452476\pi$
$354$	17.6272	0.936873
$355$	−1.93168	−0.102523
$356$	45.0055	2.38529
$357$	1.91120	0.101151
$358$	−21.2023	−1.12057
$359$	16.9789	0.896114	0.448057	−	0.894005i	$-0.352116\pi$
$359$	16.9789	0.896114	0.448057	+	0.894005i	$0.352116\pi$
$360$	2.56643	0.135262
$361$	−3.26124	−0.171644
$362$	14.6820	0.771667
$363$	1.20564	0.0632799
$364$	0.699475	0.0366625
$365$	0.459654	0.0240594
$366$	7.62396	0.398511
$367$	−1.85769	−0.0969707	−0.0484853	−	0.998824i	$-0.515439\pi$
$367$	−1.85769	−0.0969707	−0.0484853	+	0.998824i	$0.515439\pi$
$368$	30.1291	1.57059
$369$	−4.06755	−0.211748
$370$	−1.72261	−0.0895541
$371$	−2.74979	−0.142762
$372$	0.816549	0.0423361
$373$	−2.35892	−0.122141	−0.0610703	−	0.998133i	$-0.519451\pi$
$373$	−2.35892	−0.122141	−0.0610703	+	0.998133i	$0.519451\pi$
$374$	33.2953	1.72166
$375$	0.754703	0.0389727
$376$	26.3302	1.35787
$377$	0.456156	0.0234932
$378$	−6.22292	−0.320072
$379$	9.24104	0.474680	0.237340	−	0.971427i	$-0.423724\pi$
$379$	9.24104	0.474680	0.237340	+	0.971427i	$0.423724\pi$
$380$	−2.65970	−0.136440
$381$	9.88336	0.506340
$382$	29.6031	1.51463
$383$	−1.18899	−0.0607546	−0.0303773	−	0.999539i	$-0.509671\pi$
$383$	−1.18899	−0.0607546	−0.0303773	+	0.999539i	$0.509671\pi$
$384$	−6.41889	−0.327562
$385$	0.378089	0.0192692
$386$	24.6240	1.25333
$387$	−19.2524	−0.978654
$388$	9.72867	0.493898
$389$	5.01245	0.254141	0.127071	−	0.991894i	$-0.459443\pi$
$389$	5.01245	0.254141	0.127071	+	0.991894i	$0.459443\pi$
$390$	0.0354859	0.00179690
$391$	−19.8826	−1.00550
$392$	38.7105	1.95518
$393$	−1.22139	−0.0616111
$394$	13.4599	0.678100
$395$	−0.176707	−0.00889107
$396$	−35.7283	−1.79541
$397$	23.3938	1.17410	0.587050	−	0.809551i	$-0.300289\pi$
$397$	23.3938	1.17410	0.587050	+	0.809551i	$0.300289\pi$
$398$	39.7938	1.99468
$399$	1.69282	0.0847471
$400$	−33.7810	−1.68905
$401$	−37.0915	−1.85226	−0.926131	−	0.377202i	$-0.876886\pi$
$401$	−37.0915	−1.85226	−0.926131	+	0.377202i	$0.876886\pi$
$402$	−3.16916	−0.158063
$403$	−0.0681057	−0.00339259
$404$	−24.2022	−1.20410
$405$	1.02996	0.0511793
$406$	−5.33629	−0.264836
$407$	13.1624	0.652435
$408$	−13.8270	−0.684539
$409$	−32.7763	−1.62068	−0.810342	−	0.585957i	$-0.800719\pi$
$409$	−32.7763	−1.62068	−0.810342	+	0.585957i	$0.800719\pi$
$410$	−0.567378	−0.0280208
$411$	−0.580662	−0.0286419
$412$	21.0511	1.03711
$413$	11.8523	0.583213
$414$	30.9606	1.52163
$415$	0.0560160	0.00274972
$416$	−0.901054	−0.0441778
$417$	8.10439	0.396874
$418$	29.4910	1.44245
$419$	−8.84528	−0.432120	−0.216060	−	0.976380i	$-0.569321\pi$
$419$	−8.84528	−0.432120	−0.216060	+	0.976380i	$0.569321\pi$
$420$	−0.286071	−0.0139588
$421$	−21.5808	−1.05178	−0.525891	−	0.850552i	$-0.676268\pi$
$421$	−21.5808	−1.05178	−0.525891	+	0.850552i	$0.676268\pi$
$422$	−47.5042	−2.31247
$423$	11.7314	0.570402
$424$	19.8940	0.966139
$425$	22.2925	1.08134
$426$	−16.2059	−0.785177
$427$	5.12625	0.248077
$428$	−59.9282	−2.89674
$429$	−0.271146	−0.0130911
$430$	−2.68549	−0.129506
$431$	−9.87814	−0.475813	−0.237907	−	0.971288i	$-0.576461\pi$
$431$	−9.87814	−0.475813	−0.237907	+	0.971288i	$0.576461\pi$
$432$	19.5205	0.939182
$433$	−40.5812	−1.95021	−0.975105	−	0.221745i	$-0.928825\pi$
$433$	−40.5812	−1.95021	−0.975105	+	0.221745i	$0.928825\pi$
$434$	0.796728	0.0382441
$435$	−0.186558	−0.00894478
$436$	31.7782	1.52190
$437$	−17.6108	−0.842437
$438$	3.85627	0.184260
$439$	−31.4280	−1.49998	−0.749988	−	0.661451i	$-0.769941\pi$
$439$	−31.4280	−1.49998	−0.749988	+	0.661451i	$0.769941\pi$
$440$	−2.73537	−0.130404
$441$	17.2475	0.821310
$442$	2.10118	0.0999431
$443$	30.2814	1.43871	0.719357	−	0.694640i	$-0.244437\pi$
$443$	30.2814	1.43871	0.719357	+	0.694640i	$0.244437\pi$
$444$	−9.95897	−0.472632
$445$	1.53521	0.0727760
$446$	−36.1246	−1.71055
$447$	−4.94328	−0.233809
$448$	−1.03898	−0.0490870
$449$	−36.9384	−1.74323	−0.871615	−	0.490190i	$-0.836927\pi$
$449$	−36.9384	−1.74323	−0.871615	+	0.490190i	$0.836927\pi$
$450$	−34.7132	−1.63640
$451$	4.33532	0.204142
$452$	59.0721	2.77852
$453$	11.2047	0.526441
$454$	−24.9306	−1.17005
$455$	0.0238602	0.00111858
$456$	−12.2471	−0.573524
$457$	−36.0632	−1.68697	−0.843483	−	0.537156i	$-0.819499\pi$
$457$	−36.0632	−1.68697	−0.843483	+	0.537156i	$0.819499\pi$
$458$	−69.9341	−3.26780
$459$	−12.8818	−0.601272
$460$	2.97605	0.138759
$461$	21.6628	1.00894	0.504469	−	0.863430i	$-0.331688\pi$
$461$	21.6628	1.00894	0.504469	+	0.863430i	$0.331688\pi$
$462$	3.17198	0.147574
$463$	0.633338	0.0294337	0.0147168	−	0.999892i	$-0.495315\pi$
$463$	0.633338	0.0294337	0.0147168	+	0.999892i	$0.495315\pi$
$464$	16.7393	0.777102
$465$	0.0278538	0.00129169
$466$	51.1164	2.36792
$467$	37.1869	1.72081	0.860403	−	0.509614i	$-0.170212\pi$
$467$	37.1869	1.72081	0.860403	+	0.509614i	$0.170212\pi$
$468$	−2.25472	−0.104225
$469$	−2.13090	−0.0983959
$470$	1.63641	0.0754818
$471$	8.14219	0.375172
$472$	−85.7481	−3.94688
$473$	20.5198	0.943500
$474$	−1.48248	−0.0680926
$475$	19.7453	0.905978
$476$	−16.9388	−0.776388
$477$	8.86381	0.405846
$478$	−56.9707	−2.60578
$479$	28.7419	1.31325	0.656626	−	0.754216i	$-0.271983\pi$
$479$	28.7419	1.31325	0.656626	+	0.754216i	$0.271983\pi$
$480$	0.368512	0.0168202
$481$	0.830645	0.0378741
$482$	46.1068	2.10011
$483$	−1.89417	−0.0861877
$484$	−10.6855	−0.485706
$485$	0.331861	0.0150690
$486$	30.5253	1.38466
$487$	19.1334	0.867017	0.433509	−	0.901149i	$-0.357275\pi$
$487$	19.1334	0.867017	0.433509	+	0.901149i	$0.357275\pi$
$488$	−37.0871	−1.67885
$489$	1.05674	0.0477873
$490$	2.40584	0.108685
$491$	−35.5642	−1.60499	−0.802495	−	0.596659i	$-0.796494\pi$
$491$	−35.5642	−1.60499	−0.802495	+	0.596659i	$0.796494\pi$
$492$	−3.28020	−0.147883
$493$	−11.0465	−0.497507
$494$	1.86110	0.0837349
$495$	−1.21875	−0.0547787
$496$	−2.49924	−0.112219
$497$	−10.8966	−0.488780
$498$	0.469946	0.0210588
$499$	12.9472	0.579596	0.289798	−	0.957088i	$-0.406412\pi$
$499$	12.9472	0.579596	0.289798	+	0.957088i	$0.406412\pi$
$500$	−6.68888	−0.299136
$501$	8.26194	0.369116
$502$	72.7026	3.24487
$503$	−33.5840	−1.49744	−0.748719	−	0.662887i	$-0.769331\pi$
$503$	−33.5840	−1.49744	−0.748719	+	0.662887i	$0.769331\pi$
$504$	14.4772	0.644865
$505$	−0.825576	−0.0367376
$506$	−32.9987	−1.46697
$507$	6.48552	0.288032
$508$	−87.5955	−3.88642
$509$	−41.1477	−1.82384	−0.911919	−	0.410370i	$-0.865400\pi$
$509$	−41.1477	−1.82384	−0.911919	+	0.410370i	$0.865400\pi$
$510$	−0.859341	−0.0380522
$511$	2.59291	0.114703
$512$	50.7118	2.24117
$513$	−11.4099	−0.503761
$514$	−63.0216	−2.77976
$515$	0.718088	0.0316427
$516$	−15.5257	−0.683483
$517$	−12.5037	−0.549913
$518$	−9.71721	−0.426950
$519$	−10.0792	−0.442428
$520$	−0.172622	−0.00756999
$521$	−2.09619	−0.0918356	−0.0459178	−	0.998945i	$-0.514621\pi$
$521$	−2.09619	−0.0918356	−0.0459178	+	0.998945i	$0.514621\pi$
$522$	17.2012	0.752878
$523$	3.19341	0.139638	0.0698191	−	0.997560i	$-0.477758\pi$
$523$	3.19341	0.139638	0.0698191	+	0.997560i	$0.477758\pi$
$524$	10.8251	0.472897
$525$	2.12376	0.0926884
$526$	−6.88790	−0.300327
$527$	1.64928	0.0718436
$528$	−9.95010	−0.433023
$529$	−3.29458	−0.143242
$530$	1.23640	0.0537059
$531$	−38.2052	−1.65796
$532$	−15.0034	−0.650478
$533$	0.273591	0.0118505
$534$	12.8797	0.557357
$535$	−2.04425	−0.0883804
$536$	15.4165	0.665892
$537$	−4.18131	−0.180437
$538$	55.4922	2.39244
$539$	−18.3829	−0.791808
$540$	1.92817	0.0829753
$541$	−25.2328	−1.08484	−0.542421	−	0.840107i	$-0.682492\pi$
$541$	−25.2328	−1.08484	−0.542421	+	0.840107i	$0.682492\pi$
$542$	69.5318	2.98665
$543$	2.89544	0.124255
$544$	21.8203	0.935538
$545$	1.08401	0.0464337
$546$	0.200175	0.00856672
$547$	6.28182	0.268591	0.134296	−	0.990941i	$-0.457123\pi$
$547$	6.28182	0.268591	0.134296	+	0.990941i	$0.457123\pi$
$548$	5.14636	0.219842
$549$	−16.5242	−0.705235
$550$	36.9984	1.57762
$551$	−9.78428	−0.416824
$552$	13.7038	0.583273
$553$	−0.996800	−0.0423883
$554$	−51.6762	−2.19551
$555$	−0.339716	−0.0144202
$556$	−71.8286	−3.04621
$557$	15.5424	0.658552	0.329276	−	0.944234i	$-0.393195\pi$
$557$	15.5424	0.658552	0.329276	+	0.944234i	$0.393195\pi$
$558$	−2.56821	−0.108721
$559$	1.29495	0.0547706
$560$	0.875585	0.0370002
$561$	6.56619	0.277225
$562$	−72.1268	−3.04249
$563$	−25.7820	−1.08658	−0.543292	−	0.839544i	$-0.682822\pi$
$563$	−25.7820	−1.08658	−0.543292	+	0.839544i	$0.682822\pi$
$564$	9.46061	0.398364
$565$	2.01504	0.0847736
$566$	−29.6131	−1.24473
$567$	5.81002	0.243998
$568$	78.8341	3.30781
$569$	4.00562	0.167924	0.0839622	−	0.996469i	$-0.473242\pi$
$569$	4.00562	0.167924	0.0839622	+	0.996469i	$0.473242\pi$
$570$	−0.761152	−0.0318811
$571$	−42.9179	−1.79606	−0.898030	−	0.439934i	$-0.855002\pi$
$571$	−42.9179	−1.79606	−0.898030	+	0.439934i	$0.855002\pi$
$572$	2.40315	0.100481
$573$	5.83805	0.243888
$574$	−3.20057	−0.133589
$575$	−22.0939	−0.921378
$576$	3.34908	0.139545
$577$	−5.52829	−0.230146	−0.115073	−	0.993357i	$-0.536710\pi$
$577$	−5.52829	−0.230146	−0.115073	+	0.993357i	$0.536710\pi$
$578$	−7.76460	−0.322965
$579$	4.85612	0.201814
$580$	1.65345	0.0686558
$581$	0.315986	0.0131093
$582$	2.78414	0.115407
$583$	−9.44731	−0.391268
$584$	−18.7590	−0.776253
$585$	−0.0769121	−0.00317993
$586$	−16.6100	−0.686154
$587$	7.69529	0.317618	0.158809	−	0.987309i	$-0.449235\pi$
$587$	7.69529	0.317618	0.158809	+	0.987309i	$0.449235\pi$
$588$	13.9089	0.573595
$589$	1.46083	0.0601924
$590$	−5.32920	−0.219400
$591$	2.65444	0.109189
$592$	30.4817	1.25279
$593$	−38.1296	−1.56579	−0.782897	−	0.622152i	$-0.786259\pi$
$593$	−38.1296	−1.56579	−0.782897	+	0.622152i	$0.786259\pi$
$594$	−21.3797	−0.877221
$595$	−0.577809	−0.0236879
$596$	43.8119	1.79460
$597$	7.84775	0.321187
$598$	−2.08246	−0.0851583
$599$	21.2967	0.870160	0.435080	−	0.900392i	$-0.356720\pi$
$599$	21.2967	0.870160	0.435080	+	0.900392i	$0.356720\pi$
$600$	−15.3648	−0.627267
$601$	−21.6157	−0.881722	−0.440861	−	0.897575i	$-0.645327\pi$
$601$	−21.6157	−0.881722	−0.440861	+	0.897575i	$0.645327\pi$
$602$	−15.1489	−0.617421
$603$	6.86885	0.279721
$604$	−99.3062	−4.04071
$605$	−0.364501	−0.0148191
$606$	−6.92617	−0.281356
$607$	3.31588	0.134587	0.0672937	−	0.997733i	$-0.478564\pi$
$607$	3.31588	0.134587	0.0672937	+	0.997733i	$0.478564\pi$
$608$	19.3271	0.783818
$609$	−1.05237	−0.0426443
$610$	−2.30494	−0.0933243
$611$	−0.789078	−0.0319227
$612$	54.6013	2.20713
$613$	−12.5301	−0.506086	−0.253043	−	0.967455i	$-0.581431\pi$
$613$	−12.5301	−0.506086	−0.253043	+	0.967455i	$0.581431\pi$
$614$	−20.5663	−0.829989
$615$	−0.111893	−0.00451196
$616$	−15.4302	−0.621701
$617$	−41.2391	−1.66022	−0.830112	−	0.557596i	$-0.811724\pi$
$617$	−41.2391	−1.66022	−0.830112	+	0.557596i	$0.811724\pi$
$618$	6.02440	0.242337
$619$	4.78034	0.192138	0.0960691	−	0.995375i	$-0.469373\pi$
$619$	4.78034	0.192138	0.0960691	+	0.995375i	$0.469373\pi$
$620$	−0.246866	−0.00991438
$621$	12.7671	0.512325
$622$	−38.6033	−1.54785
$623$	8.66011	0.346960
$624$	−0.627926	−0.0251371
$625$	24.6575	0.986299
$626$	43.4364	1.73607
$627$	5.81594	0.232266
$628$	−72.1636	−2.87964
$629$	−20.1152	−0.802047
$630$	0.899749	0.0358469
$631$	−15.1902	−0.604711	−0.302355	−	0.953195i	$-0.597773\pi$
$631$	−15.1902	−0.604711	−0.302355	+	0.953195i	$0.597773\pi$
$632$	7.21159	0.286861
$633$	−9.36832	−0.372357
$634$	−45.0143	−1.78775
$635$	−2.98802	−0.118576
$636$	7.14805	0.283439
$637$	−1.16010	−0.0459648
$638$	−18.3336	−0.725834
$639$	35.1247	1.38951
$640$	1.94061	0.0767095
$641$	−19.0110	−0.750890	−0.375445	−	0.926845i	$-0.622510\pi$
$641$	−19.0110	−0.750890	−0.375445	+	0.926845i	$0.622510\pi$
$642$	−17.1502	−0.676864
$643$	−20.5754	−0.811413	−0.405706	−	0.914003i	$-0.632974\pi$
$643$	−20.5754	−0.811413	−0.405706	+	0.914003i	$0.632974\pi$
$644$	16.7879	0.661535
$645$	−0.529608	−0.0208533
$646$	−45.0692	−1.77322
$647$	−15.4771	−0.608467	−0.304233	−	0.952597i	$-0.598400\pi$
$647$	−15.4771	−0.608467	−0.304233	+	0.952597i	$0.598400\pi$
$648$	−42.0339	−1.65125
$649$	40.7202	1.59841
$650$	2.33488	0.0915814
$651$	0.157123	0.00615814
$652$	−9.36577	−0.366792
$653$	−17.5274	−0.685901	−0.342951	−	0.939353i	$-0.611426\pi$
$653$	−17.5274	−0.685901	−0.342951	+	0.939353i	$0.611426\pi$
$654$	9.09427	0.355614
$655$	0.369262	0.0144283
$656$	10.0398	0.391988
$657$	−8.35809	−0.326080
$658$	9.23095	0.359860
$659$	−29.7433	−1.15864	−0.579318	−	0.815102i	$-0.696681\pi$
$659$	−29.7433	−1.15864	−0.579318	+	0.815102i	$0.696681\pi$
$660$	−0.982838	−0.0382569
$661$	37.9998	1.47802	0.739010	−	0.673694i	$-0.235294\pi$
$661$	37.9998	1.47802	0.739010	+	0.673694i	$0.235294\pi$
$662$	42.9002	1.66736
$663$	0.414376	0.0160930
$664$	−2.28607	−0.0887169
$665$	−0.511789	−0.0198463
$666$	31.3229	1.21374
$667$	10.9480	0.423910
$668$	−73.2249	−2.83316
$669$	−7.12415	−0.275436
$670$	0.958128	0.0370157
$671$	17.6120	0.679903
$672$	2.07878	0.0801905
$673$	−40.6234	−1.56592	−0.782958	−	0.622075i	$-0.786290\pi$
$673$	−40.6234	−1.56592	−0.782958	+	0.622075i	$0.786290\pi$
$674$	−70.5316	−2.71678
$675$	−14.3145	−0.550967
$676$	−57.4807	−2.21079
$677$	−19.9671	−0.767400	−0.383700	−	0.923458i	$-0.625350\pi$
$677$	−19.9671	−0.767400	−0.383700	+	0.923458i	$0.625350\pi$
$678$	16.9052	0.649241
$679$	1.87202	0.0718417
$680$	4.18030	0.160307
$681$	−4.91658	−0.188404
$682$	2.73727	0.104816
$683$	−21.4830	−0.822026	−0.411013	−	0.911630i	$-0.634825\pi$
$683$	−21.4830	−0.822026	−0.411013	+	0.911630i	$0.634825\pi$
$684$	48.3625	1.84919
$685$	0.175551	0.00670745
$686$	28.7172	1.09643
$687$	−13.7917	−0.526188
$688$	47.5201	1.81169
$689$	−0.596196	−0.0227132
$690$	0.851685	0.0324231
$691$	−4.82747	−0.183646	−0.0918229	−	0.995775i	$-0.529269\pi$
$691$	−4.82747	−0.183646	−0.0918229	+	0.995775i	$0.529269\pi$
$692$	89.3312	3.39586
$693$	−6.87495	−0.261158
$694$	−56.3273	−2.13816
$695$	−2.45019	−0.0929410
$696$	7.61364	0.288594
$697$	−6.62539	−0.250955
$698$	83.9765	3.17856
$699$	10.0807	0.381287
$700$	−18.8227	−0.711432
$701$	0.0711186	0.00268611	0.00134306	−	0.999999i	$-0.499572\pi$
$701$	0.0711186	0.00268611	0.00134306	+	0.999999i	$0.499572\pi$
$702$	−1.34922	−0.0509231
$703$	−17.8169	−0.671976
$704$	−3.56955	−0.134532
$705$	0.322717	0.0121542
$706$	−14.1769	−0.533553
$707$	−4.65707	−0.175147
$708$	−30.8099	−1.15791
$709$	47.3436	1.77802	0.889012	−	0.457883i	$-0.151392\pi$
$709$	47.3436	1.77802	0.889012	+	0.457883i	$0.151392\pi$
$710$	4.89950	0.183875
$711$	3.21313	0.120502
$712$	−62.6536	−2.34804
$713$	−1.63458	−0.0612156
$714$	−4.84753	−0.181414
$715$	0.0819753	0.00306570
$716$	37.0586	1.38495
$717$	−11.2352	−0.419587
$718$	−43.0651	−1.60718
$719$	−44.9493	−1.67633	−0.838163	−	0.545419i	$-0.816370\pi$
$719$	−44.9493	−1.67633	−0.838163	+	0.545419i	$0.816370\pi$
$720$	−2.82240	−0.105185
$721$	4.05073	0.150857
$722$	8.27176	0.307843
$723$	9.09274	0.338163
$724$	−25.6620	−0.953722
$725$	−12.2750	−0.455883
$726$	−3.05798	−0.113492
$727$	−9.96873	−0.369720	−0.184860	−	0.982765i	$-0.559183\pi$
$727$	−9.96873	−0.369720	−0.184860	+	0.982765i	$0.559183\pi$
$728$	−0.973762	−0.0360900
$729$	−14.4124	−0.533794
$730$	−1.16586	−0.0431505
$731$	−31.3591	−1.15986
$732$	−13.3256	−0.492529
$733$	19.6497	0.725780	0.362890	−	0.931832i	$-0.381790\pi$
$733$	19.6497	0.725780	0.362890	+	0.931832i	$0.381790\pi$
$734$	4.71182	0.173916
$735$	0.474456	0.0175006
$736$	−21.6259	−0.797142
$737$	−7.32102	−0.269673
$738$	10.3169	0.379769
$739$	14.2595	0.524543	0.262272	−	0.964994i	$-0.415528\pi$
$739$	14.2595	0.524543	0.262272	+	0.964994i	$0.415528\pi$
$740$	3.01088	0.110682
$741$	0.367029	0.0134831
$742$	6.97454	0.256043
$743$	−34.9035	−1.28048	−0.640242	−	0.768173i	$-0.721166\pi$
$743$	−34.9035	−1.28048	−0.640242	+	0.768173i	$0.721166\pi$
$744$	−1.13674	−0.0416751
$745$	1.49449	0.0547540
$746$	5.98314	0.219058
$747$	−1.01856	−0.0372673
$748$	−58.1957	−2.12784
$749$	−11.5316	−0.421355
$750$	−1.91422	−0.0698974
$751$	5.21468	0.190286	0.0951432	−	0.995464i	$-0.469669\pi$
$751$	5.21468	0.190286	0.0951432	+	0.995464i	$0.469669\pi$
$752$	−28.9564	−1.05593
$753$	14.3377	0.522496
$754$	−1.15699	−0.0421350
$755$	−3.38749	−0.123283
$756$	10.8768	0.395586
$757$	37.5752	1.36569	0.682847	−	0.730561i	$-0.260741\pi$
$757$	37.5752	1.36569	0.682847	+	0.730561i	$0.260741\pi$
$758$	−23.4389	−0.851337
$759$	−6.50770	−0.236214
$760$	3.70265	0.134309
$761$	−33.9424	−1.23041	−0.615205	−	0.788367i	$-0.710927\pi$
$761$	−33.9424	−1.23041	−0.615205	+	0.788367i	$0.710927\pi$
$762$	−25.0680	−0.908118
$763$	6.11487	0.221373
$764$	−51.7422	−1.87197
$765$	1.86254	0.0673402
$766$	3.01574	0.108963
$767$	2.56975	0.0927883
$768$	15.0623	0.543516
$769$	35.1145	1.26626	0.633131	−	0.774044i	$-0.281769\pi$
$769$	35.1145	1.26626	0.633131	+	0.774044i	$0.281769\pi$
$770$	−0.958979	−0.0345592
$771$	−12.4285	−0.447603
$772$	−43.0394	−1.54902
$773$	13.0178	0.468219	0.234110	−	0.972210i	$-0.424783\pi$
$773$	13.0178	0.468219	0.234110	+	0.972210i	$0.424783\pi$
$774$	48.8315	1.75521
$775$	1.83271	0.0658328
$776$	−13.5436	−0.486186
$777$	−1.91634	−0.0687482
$778$	−12.7135	−0.455801
$779$	−5.86837	−0.210256
$780$	−0.0620244	−0.00222083
$781$	−37.4369	−1.33960
$782$	50.4298	1.80337
$783$	7.09320	0.253490
$784$	−42.5715	−1.52041
$785$	−2.46162	−0.0878589
$786$	3.09793	0.110499
$787$	−0.702577	−0.0250442	−0.0125221	−	0.999922i	$-0.503986\pi$
$787$	−0.702577	−0.0250442	−0.0125221	+	0.999922i	$0.503986\pi$
$788$	−23.5261	−0.838081
$789$	−1.35837	−0.0483592
$790$	0.448196	0.0159461
$791$	11.3669	0.404159
$792$	49.7385	1.76738
$793$	1.11145	0.0394686
$794$	−59.3356	−2.10574
$795$	0.243832	0.00864782
$796$	−69.5540	−2.46528
$797$	0.300054	0.0106285	0.00531423	−	0.999986i	$-0.498308\pi$
$797$	0.300054	0.0106285	0.00531423	+	0.999986i	$0.498308\pi$
$798$	−4.29365	−0.151994
$799$	19.1087	0.676016
$800$	24.2471	0.857266
$801$	−27.9154	−0.986342
$802$	94.0784	3.32202
$803$	8.90831	0.314367
$804$	5.53926	0.195355
$805$	0.572662	0.0201837
$806$	0.172742	0.00608459
$807$	10.9436	0.385235
$808$	33.6926	1.18530
$809$	−30.9153	−1.08692	−0.543462	−	0.839434i	$-0.682887\pi$
$809$	−30.9153	−1.08692	−0.543462	+	0.839434i	$0.682887\pi$
$810$	−2.61238	−0.0917898
$811$	11.7338	0.412029	0.206014	−	0.978549i	$-0.433951\pi$
$811$	11.7338	0.412029	0.206014	+	0.978549i	$0.433951\pi$
$812$	9.32710	0.327317
$813$	13.7124	0.480915
$814$	−33.3849	−1.17014
$815$	−0.319481	−0.0111909
$816$	15.2061	0.532320
$817$	−27.7760	−0.971758
$818$	83.1333	2.90669
$819$	−0.433861	−0.0151603
$820$	0.991698	0.0346316
$821$	44.1692	1.54152	0.770759	−	0.637127i	$-0.219877\pi$
$821$	44.1692	1.54152	0.770759	+	0.637127i	$0.219877\pi$
$822$	1.47278	0.0513692
$823$	46.4187	1.61805	0.809027	−	0.587772i	$-0.199995\pi$
$823$	46.4187	1.61805	0.809027	+	0.587772i	$0.199995\pi$
$824$	−29.3059	−1.02092
$825$	7.29648	0.254031
$826$	−30.0620	−1.04599
$827$	−45.6708	−1.58813	−0.794065	−	0.607833i	$-0.792039\pi$
$827$	−45.6708	−1.58813	−0.794065	+	0.607833i	$0.792039\pi$
$828$	−54.1148	−1.88062
$829$	−29.8416	−1.03644	−0.518221	−	0.855247i	$-0.673406\pi$
$829$	−29.8416	−1.03644	−0.518221	+	0.855247i	$0.673406\pi$
$830$	−0.142078	−0.00493161
$831$	−10.1911	−0.353525
$832$	−0.225265	−0.00780967
$833$	28.0935	0.973381
$834$	−20.5559	−0.711792
$835$	−2.49782	−0.0864406
$836$	−51.5462	−1.78276
$837$	−1.05904	−0.0366058
$838$	22.4350	0.775006
$839$	−12.0853	−0.417230	−0.208615	−	0.977998i	$-0.566896\pi$
$839$	−12.0853	−0.417230	−0.208615	+	0.977998i	$0.566896\pi$
$840$	0.398248	0.0137409
$841$	−22.9174	−0.790256
$842$	54.7371	1.88637
$843$	−14.2242	−0.489907
$844$	83.0307	2.85804
$845$	−1.96076	−0.0674521
$846$	−29.7555	−1.02301
$847$	−2.05615	−0.0706500
$848$	−21.8783	−0.751302
$849$	−5.84003	−0.200429
$850$	−56.5423	−1.93939
$851$	19.9360	0.683398
$852$	28.3256	0.970420
$853$	0.544219	0.0186337	0.00931685	−	0.999957i	$-0.497034\pi$
$853$	0.544219	0.0186337	0.00931685	+	0.999957i	$0.497034\pi$
$854$	−13.0021	−0.444924
$855$	1.64972	0.0564193
$856$	83.4279	2.85151
$857$	−7.64059	−0.260997	−0.130499	−	0.991448i	$-0.541658\pi$
$857$	−7.64059	−0.260997	−0.130499	+	0.991448i	$0.541658\pi$
$858$	0.687732	0.0234788
$859$	31.3812	1.07071	0.535356	−	0.844627i	$-0.320177\pi$
$859$	31.3812	1.07071	0.535356	+	0.844627i	$0.320177\pi$
$860$	4.69388	0.160060
$861$	−0.631187	−0.0215108
$862$	25.0548	0.853369
$863$	−6.19799	−0.210982	−0.105491	−	0.994420i	$-0.533641\pi$
$863$	−6.19799	−0.210982	−0.105491	+	0.994420i	$0.533641\pi$
$864$	−14.0113	−0.476676
$865$	3.04723	0.103609
$866$	102.930	3.49769
$867$	−1.53126	−0.0520044
$868$	−1.39257	−0.0472669
$869$	−3.42465	−0.116173
$870$	0.473184	0.0160424
$871$	−0.462011	−0.0156547
$872$	−44.2394	−1.49814
$873$	−6.03436	−0.204232
$874$	44.6677	1.51091
$875$	−1.28710	−0.0435118
$876$	−6.74023	−0.227731
$877$	37.0555	1.25127	0.625637	−	0.780114i	$-0.284839\pi$
$877$	37.0555	1.25127	0.625637	+	0.780114i	$0.284839\pi$
$878$	79.7136	2.69020
$879$	−3.27567	−0.110486
$880$	3.00820	0.101406
$881$	16.7425	0.564068	0.282034	−	0.959404i	$-0.408991\pi$
$881$	16.7425	0.564068	0.282034	+	0.959404i	$0.408991\pi$
$882$	−43.7464	−1.47302
$883$	−3.68899	−0.124144	−0.0620722	−	0.998072i	$-0.519771\pi$
$883$	−3.68899	−0.124144	−0.0620722	+	0.998072i	$0.519771\pi$
$884$	−3.67258	−0.123522
$885$	−1.05097	−0.0353281
$886$	−76.8054	−2.58033
$887$	44.9101	1.50793	0.753967	−	0.656913i	$-0.228138\pi$
$887$	44.9101	1.50793	0.753967	+	0.656913i	$0.228138\pi$
$888$	13.8642	0.465252
$889$	−16.8554	−0.565312
$890$	−3.89389	−0.130523
$891$	19.9611	0.668724
$892$	63.1408	2.11411
$893$	16.9253	0.566383
$894$	12.5381	0.419335
$895$	1.26413	0.0422552
$896$	10.9470	0.365713
$897$	−0.410684	−0.0137123
$898$	93.6900	3.12648
$899$	−0.908150	−0.0302885
$900$	60.6740	2.02247
$901$	14.4377	0.480990
$902$	−10.9960	−0.366128
$903$	−2.98752	−0.0994183
$904$	−82.2362	−2.73513
$905$	−0.875374	−0.0290984
$906$	−28.4194	−0.944171
$907$	−31.8120	−1.05630	−0.528151	−	0.849151i	$-0.677114\pi$
$907$	−31.8120	−1.05630	−0.528151	+	0.849151i	$0.677114\pi$
$908$	43.5753	1.44610
$909$	15.0118	0.497910
$910$	−0.0605188	−0.00200618
$911$	−53.3966	−1.76911	−0.884553	−	0.466439i	$-0.845537\pi$
$911$	−53.3966	−1.76911	−0.884553	+	0.466439i	$0.845537\pi$
$912$	13.4687	0.445992
$913$	1.08562	0.0359286
$914$	91.4702	3.02557
$915$	−0.454559	−0.0150272
$916$	122.235	4.03876
$917$	2.08300	0.0687869
$918$	32.6733	1.07838
$919$	−0.557782	−0.0183995	−0.00919976	−	0.999958i	$-0.502928\pi$
$919$	−0.557782	−0.0183995	−0.00919976	+	0.999958i	$0.502928\pi$
$920$	−4.14306	−0.136592
$921$	−4.05590	−0.133646
$922$	−54.9452	−1.80952
$923$	−2.36255	−0.0777642
$924$	−5.54418	−0.182390
$925$	−22.3524	−0.734944
$926$	−1.60639	−0.0527892
$927$	−13.0573	−0.428858
$928$	−12.0150	−0.394413
$929$	27.3328	0.896760	0.448380	−	0.893843i	$-0.352001\pi$
$929$	27.3328	0.896760	0.448380	+	0.893843i	$0.352001\pi$
$930$	−0.0706480	−0.00231664
$931$	24.8835	0.815523
$932$	−89.3445	−2.92658
$933$	−7.61298	−0.249238
$934$	−94.3204	−3.08626
$935$	−1.98515	−0.0649213
$936$	3.13887	0.102597
$937$	−21.8368	−0.713376	−0.356688	−	0.934224i	$-0.616094\pi$
$937$	−21.8368	−0.713376	−0.356688	+	0.934224i	$0.616094\pi$
$938$	5.40479	0.176473
$939$	8.56613	0.279545
$940$	−2.86021	−0.0932898
$941$	−48.9050	−1.59426	−0.797129	−	0.603809i	$-0.793649\pi$
$941$	−48.9050	−1.59426	−0.797129	+	0.603809i	$0.793649\pi$
$942$	−20.6517	−0.672870
$943$	6.56636	0.213830
$944$	94.3006	3.06922
$945$	0.371025	0.0120695
$946$	−52.0461	−1.69216
$947$	6.14090	0.199552	0.0997761	−	0.995010i	$-0.468187\pi$
$947$	6.14090	0.199552	0.0997761	+	0.995010i	$0.468187\pi$
$948$	2.59117	0.0841573
$949$	0.562181	0.0182492
$950$	−50.0818	−1.62487
$951$	−8.87730	−0.287866
$952$	23.5810	0.764266
$953$	−3.49298	−0.113149	−0.0565744	−	0.998398i	$-0.518018\pi$
$953$	−3.49298	−0.113149	−0.0565744	+	0.998398i	$0.518018\pi$
$954$	−22.4820	−0.727883
$955$	−1.76501	−0.0571143
$956$	99.5769	3.22055
$957$	−3.61558	−0.116875
$958$	−72.9006	−2.35531
$959$	0.990280	0.0319778
$960$	0.0921288	0.00297344
$961$	−30.8644	−0.995626
$962$	−2.10684	−0.0679271
$963$	37.1714	1.19783
$964$	−80.5883	−2.59557
$965$	−1.46814	−0.0472612
$966$	4.80435	0.154577
$967$	−61.1163	−1.96537	−0.982684	−	0.185287i	$-0.940678\pi$
$967$	−61.1163	−1.96537	−0.982684	+	0.185287i	$0.940678\pi$
$968$	14.8757	0.478122
$969$	−8.88813	−0.285528
$970$	−0.841727	−0.0270262
$971$	32.9774	1.05829	0.529147	−	0.848530i	$-0.322512\pi$
$971$	32.9774	1.05829	0.529147	+	0.848530i	$0.322512\pi$
$972$	−53.3540	−1.71133
$973$	−13.8215	−0.443097
$974$	−48.5297	−1.55499
$975$	0.460462	0.0147466
$976$	40.7861	1.30553
$977$	−42.8045	−1.36944	−0.684718	−	0.728808i	$-0.740075\pi$
$977$	−42.8045	−1.36944	−0.684718	+	0.728808i	$0.740075\pi$
$978$	−2.68029	−0.0857063
$979$	29.7531	0.950912
$980$	−4.20507	−0.134326
$981$	−19.7109	−0.629322
$982$	90.2045	2.87854
$983$	38.8663	1.23964	0.619821	−	0.784743i	$-0.287205\pi$
$983$	38.8663	1.23964	0.619821	+	0.784743i	$0.287205\pi$
$984$	4.56647	0.145574
$985$	−0.802512	−0.0255701
$986$	28.0181	0.892278
$987$	1.82044	0.0579453
$988$	−3.25295	−0.103490
$989$	31.0797	0.988277
$990$	3.09122	0.0982454
$991$	12.3750	0.393105	0.196553	−	0.980493i	$-0.437025\pi$
$991$	12.3750	0.393105	0.196553	+	0.980493i	$0.437025\pi$
$992$	1.79389	0.0569560
$993$	8.46037	0.268482
$994$	27.6380	0.876625
$995$	−2.37260	−0.0752165
$996$	−0.821402	−0.0260271
$997$	−1.92311	−0.0609055	−0.0304528	−	0.999536i	$-0.509695\pi$
$997$	−1.92311	−0.0609055	−0.0304528	+	0.999536i	$0.509695\pi$
$998$	−32.8391	−1.03950
$999$	12.9165	0.408659

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6011.2.a.e.1.12	✓	221

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6011.2.a.e.1.12	✓	221	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:	\( N \)	\(=\)	\( 6011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.53639 q^{2} -0.500202 q^{3} +4.43325 q^{4} +0.151225 q^{5} +1.26871 q^{6} +0.853062 q^{7} -6.17167 q^{8} -2.74980 q^{9} +O(q^{10})\)	\(q-2.53639 q^{2} -0.500202 q^{3} +4.43325 q^{4} +0.151225 q^{5} +1.26871 q^{6} +0.853062 q^{7} -6.17167 q^{8} -2.74980 q^{9} -0.383566 q^{10} +2.93082 q^{11} -2.21752 q^{12} +0.184956 q^{13} -2.16369 q^{14} -0.0756433 q^{15} +6.78724 q^{16} -4.47898 q^{17} +6.97455 q^{18} -3.96721 q^{19} +0.670421 q^{20} -0.426703 q^{21} -7.43368 q^{22} +4.43908 q^{23} +3.08709 q^{24} -4.97713 q^{25} -0.469121 q^{26} +2.87606 q^{27} +3.78184 q^{28} +2.46629 q^{29} +0.191861 q^{30} -0.368226 q^{31} -4.87171 q^{32} -1.46600 q^{33} +11.3604 q^{34} +0.129005 q^{35} -12.1906 q^{36} +4.49103 q^{37} +10.0624 q^{38} -0.0925156 q^{39} -0.933314 q^{40} +1.47922 q^{41} +1.08228 q^{42} +7.00139 q^{43} +12.9931 q^{44} -0.415839 q^{45} -11.2592 q^{46} -4.26629 q^{47} -3.39499 q^{48} -6.27229 q^{49} +12.6239 q^{50} +2.24040 q^{51} +0.819959 q^{52} -3.22344 q^{53} -7.29480 q^{54} +0.443214 q^{55} -5.26482 q^{56} +1.98441 q^{57} -6.25546 q^{58} +13.8938 q^{59} -0.335346 q^{60} +6.00924 q^{61} +0.933962 q^{62} -2.34575 q^{63} -1.21794 q^{64} +0.0279701 q^{65} +3.71835 q^{66} -2.49795 q^{67} -19.8565 q^{68} -2.22044 q^{69} -0.327206 q^{70} -12.7735 q^{71} +16.9709 q^{72} +3.03953 q^{73} -11.3910 q^{74} +2.48957 q^{75} -17.5877 q^{76} +2.50017 q^{77} +0.234655 q^{78} -1.16850 q^{79} +1.02640 q^{80} +6.81078 q^{81} -3.75187 q^{82} +0.370414 q^{83} -1.89169 q^{84} -0.677336 q^{85} -17.7582 q^{86} -1.23364 q^{87} -18.0880 q^{88} +10.1518 q^{89} +1.05473 q^{90} +0.157779 q^{91} +19.6796 q^{92} +0.184187 q^{93} +10.8210 q^{94} -0.599943 q^{95} +2.43684 q^{96} +2.19448 q^{97} +15.9089 q^{98} -8.05915 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9}+O(q^{10}) \) 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9	\( 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9} - 61 q^{10} - 50 q^{11} - 43 q^{12} - 87 q^{13} - 41 q^{14} - 62 q^{15} + 129 q^{16} - 29 q^{17} - 61 q^{18} - 107 q^{19} - 59 q^{20} - 163 q^{21} - 70 q^{22} - 31 q^{23} - 98 q^{24} + 119 q^{25} - 23 q^{26} - 41 q^{27} - 112 q^{28} - 152 q^{29} - 66 q^{30} - 117 q^{31} - 93 q^{32} - 60 q^{33} - 80 q^{34} - 21 q^{35} + 92 q^{36} - 231 q^{37} + 2 q^{38} - 81 q^{39} - 143 q^{40} - 81 q^{41} - 6 q^{42} - 126 q^{43} - 115 q^{44} - 156 q^{45} - 205 q^{46} - 4 q^{47} - 55 q^{48} + 103 q^{49} - 61 q^{50} - 106 q^{51} - 164 q^{52} - 87 q^{53} - 110 q^{54} - 62 q^{55} - 73 q^{56} - 136 q^{57} - 128 q^{58} - 76 q^{59} - 148 q^{60} - 345 q^{61} + 5 q^{62} - 74 q^{63} - 25 q^{64} - 110 q^{65} - 34 q^{66} - 104 q^{67} - 48 q^{68} - 133 q^{69} - 92 q^{70} - 39 q^{71} - 177 q^{72} - 175 q^{73} - 44 q^{74} - 23 q^{75} - 268 q^{76} - 81 q^{77} - 19 q^{78} - 272 q^{79} - 60 q^{80} + 77 q^{81} - 13 q^{82} - 40 q^{83} - 221 q^{84} - 376 q^{85} - 82 q^{86} - 3 q^{87} - 234 q^{88} - 92 q^{89} - 91 q^{90} - 205 q^{91} - 11 q^{92} - 125 q^{93} - 126 q^{94} - 56 q^{95} - 148 q^{96} - 133 q^{97} - 4 q^{98} - 195 q^{99}+O(q^{100}) \) 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9 - 61 * q^10 - 50 * q^11 - 43 * q^12 - 87 * q^13 - 41 * q^14 - 62 * q^15 + 129 * q^16 - 29 * q^17 - 61 * q^18 - 107 * q^19 - 59 * q^20 - 163 * q^21 - 70 * q^22 - 31 * q^23 - 98 * q^24 + 119 * q^25 - 23 * q^26 - 41 * q^27 - 112 * q^28 - 152 * q^29 - 66 * q^30 - 117 * q^31 - 93 * q^32 - 60 * q^33 - 80 * q^34 - 21 * q^35 + 92 * q^36 - 231 * q^37 + 2 * q^38 - 81 * q^39 - 143 * q^40 - 81 * q^41 - 6 * q^42 - 126 * q^43 - 115 * q^44 - 156 * q^45 - 205 * q^46 - 4 * q^47 - 55 * q^48 + 103 * q^49 - 61 * q^50 - 106 * q^51 - 164 * q^52 - 87 * q^53 - 110 * q^54 - 62 * q^55 - 73 * q^56 - 136 * q^57 - 128 * q^58 - 76 * q^59 - 148 * q^60 - 345 * q^61 + 5 * q^62 - 74 * q^63 - 25 * q^64 - 110 * q^65 - 34 * q^66 - 104 * q^67 - 48 * q^68 - 133 * q^69 - 92 * q^70 - 39 * q^71 - 177 * q^72 - 175 * q^73 - 44 * q^74 - 23 * q^75 - 268 * q^76 - 81 * q^77 - 19 * q^78 - 272 * q^79 - 60 * q^80 + 77 * q^81 - 13 * q^82 - 40 * q^83 - 221 * q^84 - 376 * q^85 - 82 * q^86 - 3 * q^87 - 234 * q^88 - 92 * q^89 - 91 * q^90 - 205 * q^91 - 11 * q^92 - 125 * q^93 - 126 * q^94 - 56 * q^95 - 148 * q^96 - 133 * q^97 - 4 * q^98 - 195 * q^99

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