LMFDB - Embedded newform 4011.2.a.m.1.9

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			1.9
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)

$f(q)$	$=$	$q-1.16967 q^{2} +1.00000 q^{3} -0.631883 q^{4} +0.467682 q^{5} -1.16967 q^{6} -1.00000 q^{7} +3.07842 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.16967 q^{2} +1.00000 q^{3} -0.631883 q^{4} +0.467682 q^{5} -1.16967 q^{6} -1.00000 q^{7} +3.07842 q^{8} +1.00000 q^{9} -0.547032 q^{10} -3.62740 q^{11} -0.631883 q^{12} +4.55596 q^{13} +1.16967 q^{14} +0.467682 q^{15} -2.33696 q^{16} +1.72418 q^{17} -1.16967 q^{18} +0.971711 q^{19} -0.295521 q^{20} -1.00000 q^{21} +4.24284 q^{22} +2.32891 q^{23} +3.07842 q^{24} -4.78127 q^{25} -5.32895 q^{26} +1.00000 q^{27} +0.631883 q^{28} +2.66935 q^{29} -0.547032 q^{30} -1.00878 q^{31} -3.42339 q^{32} -3.62740 q^{33} -2.01672 q^{34} -0.467682 q^{35} -0.631883 q^{36} +5.94021 q^{37} -1.13658 q^{38} +4.55596 q^{39} +1.43972 q^{40} +5.57010 q^{41} +1.16967 q^{42} -9.08320 q^{43} +2.29209 q^{44} +0.467682 q^{45} -2.72405 q^{46} +10.0719 q^{47} -2.33696 q^{48} +1.00000 q^{49} +5.59249 q^{50} +1.72418 q^{51} -2.87884 q^{52} -8.29110 q^{53} -1.16967 q^{54} -1.69647 q^{55} -3.07842 q^{56} +0.971711 q^{57} -3.12225 q^{58} -5.00342 q^{59} -0.295521 q^{60} -5.39722 q^{61} +1.17994 q^{62} -1.00000 q^{63} +8.67813 q^{64} +2.13074 q^{65} +4.24284 q^{66} +8.14196 q^{67} -1.08948 q^{68} +2.32891 q^{69} +0.547032 q^{70} -8.75283 q^{71} +3.07842 q^{72} +6.18807 q^{73} -6.94806 q^{74} -4.78127 q^{75} -0.614008 q^{76} +3.62740 q^{77} -5.32895 q^{78} +7.79820 q^{79} -1.09295 q^{80} +1.00000 q^{81} -6.51515 q^{82} +3.87868 q^{83} +0.631883 q^{84} +0.806370 q^{85} +10.6243 q^{86} +2.66935 q^{87} -11.1667 q^{88} +0.195326 q^{89} -0.547032 q^{90} -4.55596 q^{91} -1.47160 q^{92} -1.00878 q^{93} -11.7807 q^{94} +0.454452 q^{95} -3.42339 q^{96} +5.23706 q^{97} -1.16967 q^{98} -3.62740 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.16967	−0.827078	−0.413539	−	0.910486i	$-0.635707\pi$
$2$	−1.16967	−0.827078	−0.413539	+	0.910486i	$0.635707\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.631883	−0.315942
$5$	0.467682	0.209154	0.104577	−	0.994517i	$-0.466651\pi$
$5$	0.467682	0.209154	0.104577	+	0.994517i	$0.466651\pi$
$6$	−1.16967	−0.477514
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	3.07842	1.08839
$9$	1.00000	0.333333
$10$	−0.547032	−0.172987
$11$	−3.62740	−1.09370	−0.546851	−	0.837230i	$-0.684174\pi$
$11$	−3.62740	−1.09370	−0.546851	+	0.837230i	$0.684174\pi$
$12$	−0.631883	−0.182409
$13$	4.55596	1.26360	0.631798	−	0.775133i	$-0.282317\pi$
$13$	4.55596	1.26360	0.631798	+	0.775133i	$0.282317\pi$
$14$	1.16967	0.312606
$15$	0.467682	0.120755
$16$	−2.33696	−0.584239
$17$	1.72418	0.418176	0.209088	−	0.977897i	$-0.432950\pi$
$17$	1.72418	0.418176	0.209088	+	0.977897i	$0.432950\pi$
$18$	−1.16967	−0.275693
$19$	0.971711	0.222926	0.111463	−	0.993769i	$-0.464446\pi$
$19$	0.971711	0.222926	0.111463	+	0.993769i	$0.464446\pi$
$20$	−0.295521	−0.0660804
$21$	−1.00000	−0.218218
$22$	4.24284	0.904577
$23$	2.32891	0.485612	0.242806	−	0.970075i	$-0.421932\pi$
$23$	2.32891	0.485612	0.242806	+	0.970075i	$0.421932\pi$
$24$	3.07842	0.628380
$25$	−4.78127	−0.956255
$26$	−5.32895	−1.04509
$27$	1.00000	0.192450
$28$	0.631883	0.119415
$29$	2.66935	0.495687	0.247843	−	0.968800i	$-0.420278\pi$
$29$	2.66935	0.495687	0.247843	+	0.968800i	$0.420278\pi$
$30$	−0.547032	−0.0998738
$31$	−1.00878	−0.181183	−0.0905913	−	0.995888i	$-0.528876\pi$
$31$	−1.00878	−0.181183	−0.0905913	+	0.995888i	$0.528876\pi$
$32$	−3.42339	−0.605175
$33$	−3.62740	−0.631449
$34$	−2.01672	−0.345864
$35$	−0.467682	−0.0790527
$36$	−0.631883	−0.105314
$37$	5.94021	0.976565	0.488283	−	0.872686i	$-0.337624\pi$
$37$	5.94021	0.976565	0.488283	+	0.872686i	$0.337624\pi$
$38$	−1.13658	−0.184377
$39$	4.55596	0.729538
$40$	1.43972	0.227640
$41$	5.57010	0.869903	0.434951	−	0.900454i	$-0.356766\pi$
$41$	5.57010	0.869903	0.434951	+	0.900454i	$0.356766\pi$
$42$	1.16967	0.180483
$43$	−9.08320	−1.38517	−0.692587	−	0.721334i	$-0.743529\pi$
$43$	−9.08320	−1.38517	−0.692587	+	0.721334i	$0.743529\pi$
$44$	2.29209	0.345546
$45$	0.467682	0.0697179
$46$	−2.72405	−0.401639
$47$	10.0719	1.46913	0.734567	−	0.678536i	$-0.237385\pi$
$47$	10.0719	1.46913	0.734567	+	0.678536i	$0.237385\pi$
$48$	−2.33696	−0.337311
$49$	1.00000	0.142857
$50$	5.59249	0.790897
$51$	1.72418	0.241434
$52$	−2.87884	−0.399223
$53$	−8.29110	−1.13887	−0.569435	−	0.822037i	$-0.692838\pi$
$53$	−8.29110	−1.13887	−0.569435	+	0.822037i	$0.692838\pi$
$54$	−1.16967	−0.159171
$55$	−1.69647	−0.228752
$56$	−3.07842	−0.411371
$57$	0.971711	0.128706
$58$	−3.12225	−0.409972
$59$	−5.00342	−0.651390	−0.325695	−	0.945475i	$-0.605598\pi$
$59$	−5.00342	−0.651390	−0.325695	+	0.945475i	$0.605598\pi$
$60$	−0.295521	−0.0381515
$61$	−5.39722	−0.691044	−0.345522	−	0.938411i	$-0.612298\pi$
$61$	−5.39722	−0.691044	−0.345522	+	0.938411i	$0.612298\pi$
$62$	1.17994	0.149852
$63$	−1.00000	−0.125988
$64$	8.67813	1.08477
$65$	2.13074	0.264286
$66$	4.24284	0.522258
$67$	8.14196	0.994699	0.497349	−	0.867550i	$-0.334307\pi$
$67$	8.14196	0.994699	0.497349	+	0.867550i	$0.334307\pi$
$68$	−1.08948	−0.132119
$69$	2.32891	0.280368
$70$	0.547032	0.0653828
$71$	−8.75283	−1.03877	−0.519385	−	0.854540i	$-0.673839\pi$
$71$	−8.75283	−1.03877	−0.519385	+	0.854540i	$0.673839\pi$
$72$	3.07842	0.362796
$73$	6.18807	0.724258	0.362129	−	0.932128i	$-0.382050\pi$
$73$	6.18807	0.724258	0.362129	+	0.932128i	$0.382050\pi$
$74$	−6.94806	−0.807696
$75$	−4.78127	−0.552094
$76$	−0.614008	−0.0704316
$77$	3.62740	0.413381
$78$	−5.32895	−0.603385
$79$	7.79820	0.877366	0.438683	−	0.898642i	$-0.355445\pi$
$79$	7.79820	0.877366	0.438683	+	0.898642i	$0.355445\pi$
$80$	−1.09295	−0.122196
$81$	1.00000	0.111111
$82$	−6.51515	−0.719478
$83$	3.87868	0.425741	0.212870	−	0.977080i	$-0.431719\pi$
$83$	3.87868	0.425741	0.212870	+	0.977080i	$0.431719\pi$
$84$	0.631883	0.0689441
$85$	0.806370	0.0874632
$86$	10.6243	1.14565
$87$	2.66935	0.286185
$88$	−11.1667	−1.19037
$89$	0.195326	0.0207045	0.0103523	−	0.999946i	$-0.496705\pi$
$89$	0.195326	0.0207045	0.0103523	+	0.999946i	$0.496705\pi$
$90$	−0.547032	−0.0576622
$91$	−4.55596	−0.477595
$92$	−1.47160	−0.153425
$93$	−1.00878	−0.104606
$94$	−11.7807	−1.21509
$95$	0.454452	0.0466258
$96$	−3.42339	−0.349398
$97$	5.23706	0.531743	0.265872	−	0.964008i	$-0.414340\pi$
$97$	5.23706	0.531743	0.265872	+	0.964008i	$0.414340\pi$
$98$	−1.16967	−0.118154
$99$	−3.62740	−0.364567
$100$	3.02121	0.302121
$101$	4.82887	0.480490	0.240245	−	0.970712i	$-0.422772\pi$
$101$	4.82887	0.480490	0.240245	+	0.970712i	$0.422772\pi$
$102$	−2.01672	−0.199685
$103$	8.72225	0.859428	0.429714	−	0.902965i	$-0.358614\pi$
$103$	8.72225	0.859428	0.429714	+	0.902965i	$0.358614\pi$
$104$	14.0252	1.37528
$105$	−0.467682	−0.0456411
$106$	9.69781	0.941934
$107$	−2.78193	−0.268939	−0.134470	−	0.990918i	$-0.542933\pi$
$107$	−2.78193	−0.268939	−0.134470	+	0.990918i	$0.542933\pi$
$108$	−0.631883	−0.0608030
$109$	−19.1144	−1.83082	−0.915412	−	0.402518i	$-0.868135\pi$
$109$	−19.1144	−1.83082	−0.915412	+	0.402518i	$0.868135\pi$
$110$	1.98430	0.189196
$111$	5.94021	0.563820
$112$	2.33696	0.220822
$113$	12.1647	1.14436	0.572180	−	0.820128i	$-0.306098\pi$
$113$	12.1647	1.14436	0.572180	+	0.820128i	$0.306098\pi$
$114$	−1.13658	−0.106450
$115$	1.08919	0.101568
$116$	−1.68672	−0.156608
$117$	4.55596	0.421199
$118$	5.85233	0.538750
$119$	−1.72418	−0.158056
$120$	1.43972	0.131428
$121$	2.15803	0.196185
$122$	6.31294	0.571547
$123$	5.57010	0.502239
$124$	0.637433	0.0572432
$125$	−4.57453	−0.409158
$126$	1.16967	0.104202
$127$	−18.4352	−1.63586	−0.817929	−	0.575319i	$-0.804878\pi$
$127$	−18.4352	−1.63586	−0.817929	+	0.575319i	$0.804878\pi$
$128$	−3.30373	−0.292011
$129$	−9.08320	−0.799731
$130$	−2.49226	−0.218585
$131$	13.5293	1.18206	0.591031	−	0.806649i	$-0.298721\pi$
$131$	13.5293	1.18206	0.591031	+	0.806649i	$0.298721\pi$
$132$	2.29209	0.199501
$133$	−0.971711	−0.0842580
$134$	−9.52337	−0.822694
$135$	0.467682	0.0402517
$136$	5.30777	0.455137
$137$	10.0095	0.855170	0.427585	−	0.903975i	$-0.359364\pi$
$137$	10.0095	0.855170	0.427585	+	0.903975i	$0.359364\pi$
$138$	−2.72405	−0.231886
$139$	13.5112	1.14601	0.573004	−	0.819552i	$-0.305778\pi$
$139$	13.5112	1.14601	0.573004	+	0.819552i	$0.305778\pi$
$140$	0.295521	0.0249760
$141$	10.0719	0.848205
$142$	10.2379	0.859144
$143$	−16.5263	−1.38200
$144$	−2.33696	−0.194746
$145$	1.24841	0.103675
$146$	−7.23796	−0.599018
$147$	1.00000	0.0824786
$148$	−3.75352	−0.308538
$149$	2.64666	0.216822	0.108411	−	0.994106i	$-0.465424\pi$
$149$	2.64666	0.216822	0.108411	+	0.994106i	$0.465424\pi$
$150$	5.59249	0.456625
$151$	1.19469	0.0972225	0.0486113	−	0.998818i	$-0.484520\pi$
$151$	1.19469	0.0972225	0.0486113	+	0.998818i	$0.484520\pi$
$152$	2.99134	0.242629
$153$	1.72418	0.139392
$154$	−4.24284	−0.341898
$155$	−0.471789	−0.0378950
$156$	−2.87884	−0.230491
$157$	22.2900	1.77894	0.889468	−	0.456997i	$-0.151075\pi$
$157$	22.2900	1.77894	0.889468	+	0.456997i	$0.151075\pi$
$158$	−9.12128	−0.725650
$159$	−8.29110	−0.657527
$160$	−1.60106	−0.126575
$161$	−2.32891	−0.183544
$162$	−1.16967	−0.0918976
$163$	14.9322	1.16958	0.584789	−	0.811185i	$-0.301177\pi$
$163$	14.9322	1.16958	0.584789	+	0.811185i	$0.301177\pi$
$164$	−3.51965	−0.274839
$165$	−1.69647	−0.132070
$166$	−4.53676	−0.352121
$167$	5.41270	0.418847	0.209424	−	0.977825i	$-0.432841\pi$
$167$	5.41270	0.418847	0.209424	+	0.977825i	$0.432841\pi$
$168$	−3.07842	−0.237505
$169$	7.75680	0.596677
$170$	−0.943183	−0.0723389
$171$	0.971711	0.0743086
$172$	5.73952	0.437634
$173$	7.87266	0.598547	0.299273	−	0.954167i	$-0.403256\pi$
$173$	7.87266	0.598547	0.299273	+	0.954167i	$0.403256\pi$
$174$	−3.12225	−0.236697
$175$	4.78127	0.361430
$176$	8.47708	0.638984
$177$	−5.00342	−0.376080
$178$	−0.228466	−0.0171243
$179$	4.51976	0.337823	0.168911	−	0.985631i	$-0.445975\pi$
$179$	4.51976	0.337823	0.168911	+	0.985631i	$0.445975\pi$
$180$	−0.295521	−0.0220268
$181$	17.1968	1.27823	0.639115	−	0.769111i	$-0.279301\pi$
$181$	17.1968	1.27823	0.639115	+	0.769111i	$0.279301\pi$
$182$	5.32895	0.395008
$183$	−5.39722	−0.398974
$184$	7.16938	0.528533
$185$	2.77813	0.204252
$186$	1.17994	0.0865172
$187$	−6.25431	−0.457360
$188$	−6.36425	−0.464161
$189$	−1.00000	−0.0727393
$190$	−0.531557	−0.0385632
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	8.67813	0.626290
$193$	−15.0025	−1.07990	−0.539951	−	0.841697i	$-0.681557\pi$
$193$	−15.0025	−1.07990	−0.539951	+	0.841697i	$0.681557\pi$
$194$	−6.12561	−0.439793
$195$	2.13074	0.152586
$196$	−0.631883	−0.0451345
$197$	13.0181	0.927499	0.463749	−	0.885966i	$-0.346504\pi$
$197$	13.0181	0.927499	0.463749	+	0.885966i	$0.346504\pi$
$198$	4.24284	0.301526
$199$	−23.2829	−1.65048	−0.825241	−	0.564781i	$-0.808961\pi$
$199$	−23.2829	−1.65048	−0.825241	+	0.564781i	$0.808961\pi$
$200$	−14.7188	−1.04077
$201$	8.14196	0.574290
$202$	−5.64816	−0.397403
$203$	−2.66935	−0.187352
$204$	−1.08948	−0.0762791
$205$	2.60503	0.181943
$206$	−10.2021	−0.710814
$207$	2.32891	0.161871
$208$	−10.6471	−0.738243
$209$	−3.52478	−0.243814
$210$	0.547032	0.0377488
$211$	−26.0714	−1.79483	−0.897414	−	0.441189i	$-0.854557\pi$
$211$	−26.0714	−1.79483	−0.897414	+	0.441189i	$0.854557\pi$
$212$	5.23901	0.359816
$213$	−8.75283	−0.599734
$214$	3.25392	0.222434
$215$	−4.24805	−0.289715
$216$	3.07842	0.209460
$217$	1.00878	0.0684806
$218$	22.3574	1.51423
$219$	6.18807	0.418151
$220$	1.07197	0.0722723
$221$	7.85532	0.528406
$222$	−6.94806	−0.466323
$223$	−16.4458	−1.10129	−0.550646	−	0.834739i	$-0.685618\pi$
$223$	−16.4458	−1.10129	−0.550646	+	0.834739i	$0.685618\pi$
$224$	3.42339	0.228735
$225$	−4.78127	−0.318752
$226$	−14.2287	−0.946476
$227$	22.6455	1.50303	0.751517	−	0.659713i	$-0.229322\pi$
$227$	22.6455	1.50303	0.751517	+	0.659713i	$0.229322\pi$
$228$	−0.614008	−0.0406637
$229$	−6.52289	−0.431044	−0.215522	−	0.976499i	$-0.569145\pi$
$229$	−6.52289	−0.431044	−0.215522	+	0.976499i	$0.569145\pi$
$230$	−1.27399	−0.0840043
$231$	3.62740	0.238665
$232$	8.21740	0.539499
$233$	13.3009	0.871368	0.435684	−	0.900100i	$-0.356506\pi$
$233$	13.3009	0.871368	0.435684	+	0.900100i	$0.356506\pi$
$234$	−5.32895	−0.348364
$235$	4.71044	0.307275
$236$	3.16158	0.205801
$237$	7.79820	0.506547
$238$	2.01672	0.130724
$239$	−18.0696	−1.16882	−0.584411	−	0.811458i	$-0.698674\pi$
$239$	−18.0696	−1.16882	−0.584411	+	0.811458i	$0.698674\pi$
$240$	−1.09295	−0.0705498
$241$	6.66237	0.429161	0.214580	−	0.976706i	$-0.431162\pi$
$241$	6.66237	0.429161	0.214580	+	0.976706i	$0.431162\pi$
$242$	−2.52418	−0.162260
$243$	1.00000	0.0641500
$244$	3.41042	0.218330
$245$	0.467682	0.0298791
$246$	−6.51515	−0.415391
$247$	4.42708	0.281688
$248$	−3.10546	−0.197197
$249$	3.87868	0.245801
$250$	5.35066	0.338406
$251$	6.06306	0.382697	0.191348	−	0.981522i	$-0.438714\pi$
$251$	6.06306	0.382697	0.191348	+	0.981522i	$0.438714\pi$
$252$	0.631883	0.0398049
$253$	−8.44790	−0.531115
$254$	21.5630	1.35298
$255$	0.806370	0.0504969
$256$	−13.4920	−0.843250
$257$	13.1532	0.820472	0.410236	−	0.911979i	$-0.365446\pi$
$257$	13.1532	0.820472	0.410236	+	0.911979i	$0.365446\pi$
$258$	10.6243	0.661440
$259$	−5.94021	−0.369107
$260$	−1.34638	−0.0834990
$261$	2.66935	0.165229
$262$	−15.8248	−0.977658
$263$	30.9457	1.90820	0.954098	−	0.299494i	$-0.0968177\pi$
$263$	30.9457	1.90820	0.954098	+	0.299494i	$0.0968177\pi$
$264$	−11.1667	−0.687261
$265$	−3.87760	−0.238199
$266$	1.13658	0.0696880
$267$	0.195326	0.0119538
$268$	−5.14477	−0.314267
$269$	21.9079	1.33575	0.667874	−	0.744275i	$-0.267205\pi$
$269$	21.9079	1.33575	0.667874	+	0.744275i	$0.267205\pi$
$270$	−0.547032	−0.0332913
$271$	16.4864	1.00148	0.500738	−	0.865599i	$-0.333062\pi$
$271$	16.4864	1.00148	0.500738	+	0.865599i	$0.333062\pi$
$272$	−4.02934	−0.244315
$273$	−4.55596	−0.275739
$274$	−11.7078	−0.707293
$275$	17.3436	1.04586
$276$	−1.47160	−0.0885800
$277$	26.9311	1.61813	0.809067	−	0.587716i	$-0.199973\pi$
$277$	26.9311	1.61813	0.809067	+	0.587716i	$0.199973\pi$
$278$	−15.8036	−0.947839
$279$	−1.00878	−0.0603942
$280$	−1.43972	−0.0860399
$281$	7.96047	0.474882	0.237441	−	0.971402i	$-0.423691\pi$
$281$	7.96047	0.474882	0.237441	+	0.971402i	$0.423691\pi$
$282$	−11.7807	−0.701532
$283$	−2.86934	−0.170565	−0.0852824	−	0.996357i	$-0.527179\pi$
$283$	−2.86934	−0.170565	−0.0852824	+	0.996357i	$0.527179\pi$
$284$	5.53077	0.328191
$285$	0.454452	0.0269194
$286$	19.3302	1.14302
$287$	−5.57010	−0.328792
$288$	−3.42339	−0.201725
$289$	−14.0272	−0.825129
$290$	−1.46022	−0.0857471
$291$	5.23706	0.307002
$292$	−3.91014	−0.228823
$293$	23.8210	1.39164	0.695819	−	0.718217i	$-0.255041\pi$
$293$	23.8210	1.39164	0.695819	+	0.718217i	$0.255041\pi$
$294$	−1.16967	−0.0682163
$295$	−2.34001	−0.136241
$296$	18.2865	1.06288
$297$	−3.62740	−0.210483
$298$	−3.09570	−0.179329
$299$	10.6104	0.613618
$300$	3.02121	0.174429
$301$	9.08320	0.523547
$302$	−1.39739	−0.0804106
$303$	4.82887	0.277411
$304$	−2.27085	−0.130242
$305$	−2.52419	−0.144534
$306$	−2.01672	−0.115288
$307$	14.6571	0.836526	0.418263	−	0.908326i	$-0.362639\pi$
$307$	14.6571	0.836526	0.418263	+	0.908326i	$0.362639\pi$
$308$	−2.29209	−0.130604
$309$	8.72225	0.496191
$310$	0.551836	0.0313422
$311$	25.1341	1.42522	0.712611	−	0.701559i	$-0.247512\pi$
$311$	25.1341	1.42522	0.712611	+	0.701559i	$0.247512\pi$
$312$	14.0252	0.794019
$313$	16.6856	0.943127	0.471563	−	0.881832i	$-0.343690\pi$
$313$	16.6856	0.943127	0.471563	+	0.881832i	$0.343690\pi$
$314$	−26.0719	−1.47132
$315$	−0.467682	−0.0263509
$316$	−4.92755	−0.277196
$317$	−10.0578	−0.564900	−0.282450	−	0.959282i	$-0.591147\pi$
$317$	−10.0578	−0.564900	−0.282450	+	0.959282i	$0.591147\pi$
$318$	9.69781	0.543826
$319$	−9.68282	−0.542134
$320$	4.05861	0.226883
$321$	−2.78193	−0.155272
$322$	2.72405	0.151805
$323$	1.67541	0.0932223
$324$	−0.631883	−0.0351046
$325$	−21.7833	−1.20832
$326$	−17.4656	−0.967332
$327$	−19.1144	−1.05703
$328$	17.1471	0.946791
$329$	−10.0719	−0.555281
$330$	1.98430	0.109232
$331$	−13.5534	−0.744961	−0.372481	−	0.928040i	$-0.621493\pi$
$331$	−13.5534	−0.744961	−0.372481	+	0.928040i	$0.621493\pi$
$332$	−2.45087	−0.134509
$333$	5.94021	0.325522
$334$	−6.33105	−0.346420
$335$	3.80785	0.208045
$336$	2.33696	0.127491
$337$	−7.97972	−0.434683	−0.217342	−	0.976096i	$-0.569739\pi$
$337$	−7.97972	−0.434683	−0.217342	+	0.976096i	$0.569739\pi$
$338$	−9.07286	−0.493498
$339$	12.1647	0.660697
$340$	−0.509532	−0.0276333
$341$	3.65926	0.198160
$342$	−1.13658	−0.0614590
$343$	−1.00000	−0.0539949
$344$	−27.9619	−1.50761
$345$	1.08919	0.0586401
$346$	−9.20837	−0.495045
$347$	34.1625	1.83394	0.916971	−	0.398955i	$-0.130627\pi$
$347$	34.1625	1.83394	0.916971	+	0.398955i	$0.130627\pi$
$348$	−1.68672	−0.0904177
$349$	−11.7735	−0.630220	−0.315110	−	0.949055i	$-0.602041\pi$
$349$	−11.7735	−0.630220	−0.315110	+	0.949055i	$0.602041\pi$
$350$	−5.59249	−0.298931
$351$	4.55596	0.243179
$352$	12.4180	0.661882
$353$	−5.09764	−0.271320	−0.135660	−	0.990755i	$-0.543315\pi$
$353$	−5.09764	−0.271320	−0.135660	+	0.990755i	$0.543315\pi$
$354$	5.85233	0.311048
$355$	−4.09354	−0.217263
$356$	−0.123423	−0.00654142
$357$	−1.72418	−0.0912535
$358$	−5.28661	−0.279406
$359$	−12.1086	−0.639069	−0.319534	−	0.947575i	$-0.603527\pi$
$359$	−12.1086	−0.639069	−0.319534	+	0.947575i	$0.603527\pi$
$360$	1.43972	0.0758801
$361$	−18.0558	−0.950304
$362$	−20.1145	−1.05720
$363$	2.15803	0.113267
$364$	2.87884	0.150892
$365$	2.89405	0.151481
$366$	6.31294	0.329983
$367$	−18.4480	−0.962980	−0.481490	−	0.876452i	$-0.659904\pi$
$367$	−18.4480	−0.962980	−0.481490	+	0.876452i	$0.659904\pi$
$368$	−5.44257	−0.283713
$369$	5.57010	0.289968
$370$	−3.24948	−0.168933
$371$	8.29110	0.430452
$372$	0.637433	0.0330494
$373$	27.3026	1.41367	0.706837	−	0.707376i	$-0.250121\pi$
$373$	27.3026	1.41367	0.706837	+	0.707376i	$0.250121\pi$
$374$	7.31545	0.378273
$375$	−4.57453	−0.236228
$376$	31.0055	1.59899
$377$	12.1615	0.626348
$378$	1.16967	0.0601611
$379$	−30.0623	−1.54420	−0.772099	−	0.635502i	$-0.780793\pi$
$379$	−30.0623	−1.54420	−0.772099	+	0.635502i	$0.780793\pi$
$380$	−0.287161	−0.0147310
$381$	−18.4352	−0.944463
$382$	1.16967	0.0598453
$383$	−6.28605	−0.321202	−0.160601	−	0.987019i	$-0.551343\pi$
$383$	−6.28605	−0.321202	−0.160601	+	0.987019i	$0.551343\pi$
$384$	−3.30373	−0.168593
$385$	1.69647	0.0864601
$386$	17.5479	0.893163
$387$	−9.08320	−0.461725
$388$	−3.30921	−0.168000
$389$	12.2787	0.622557	0.311278	−	0.950319i	$-0.399243\pi$
$389$	12.2787	0.622557	0.311278	+	0.950319i	$0.399243\pi$
$390$	−2.49226	−0.126200
$391$	4.01548	0.203071
$392$	3.07842	0.155484
$393$	13.5293	0.682464
$394$	−15.2268	−0.767114
$395$	3.64708	0.183504
$396$	2.29209	0.115182
$397$	−33.9341	−1.70310	−0.851551	−	0.524272i	$-0.824338\pi$
$397$	−33.9341	−1.70310	−0.851551	+	0.524272i	$0.824338\pi$
$398$	27.2332	1.36508
$399$	−0.971711	−0.0486464
$400$	11.1736	0.558681
$401$	−5.95200	−0.297229	−0.148614	−	0.988895i	$-0.547481\pi$
$401$	−5.95200	−0.297229	−0.148614	+	0.988895i	$0.547481\pi$
$402$	−9.52337	−0.474982
$403$	−4.59597	−0.228942
$404$	−3.05128	−0.151807
$405$	0.467682	0.0232393
$406$	3.12225	0.154955
$407$	−21.5475	−1.06807
$408$	5.30777	0.262774
$409$	38.9302	1.92497	0.962486	−	0.271330i	$-0.0874636\pi$
$409$	38.9302	1.92497	0.962486	+	0.271330i	$0.0874636\pi$
$410$	−3.04702	−0.150481
$411$	10.0095	0.493733
$412$	−5.51144	−0.271529
$413$	5.00342	0.246202
$414$	−2.72405	−0.133880
$415$	1.81399	0.0890453
$416$	−15.5968	−0.764697
$417$	13.5112	0.661648
$418$	4.12282	0.201654
$419$	−13.9657	−0.682271	−0.341136	−	0.940014i	$-0.610812\pi$
$419$	−13.9657	−0.682271	−0.341136	+	0.940014i	$0.610812\pi$
$420$	0.295521	0.0144199
$421$	12.2297	0.596040	0.298020	−	0.954560i	$-0.403674\pi$
$421$	12.2297	0.596040	0.298020	+	0.954560i	$0.403674\pi$
$422$	30.4948	1.48446
$423$	10.0719	0.489711
$424$	−25.5235	−1.23953
$425$	−8.24380	−0.399883
$426$	10.2379	0.496027
$427$	5.39722	0.261190
$428$	1.75785	0.0849691
$429$	−16.5263	−0.797897
$430$	4.96880	0.239617
$431$	−14.6845	−0.707328	−0.353664	−	0.935373i	$-0.615064\pi$
$431$	−14.6845	−0.707328	−0.353664	+	0.935373i	$0.615064\pi$
$432$	−2.33696	−0.112437
$433$	19.4631	0.935339	0.467669	−	0.883903i	$-0.345094\pi$
$433$	19.4631	0.935339	0.467669	+	0.883903i	$0.345094\pi$
$434$	−1.17994	−0.0566388
$435$	1.24841	0.0598566
$436$	12.0780	0.578434
$437$	2.26303	0.108255
$438$	−7.23796	−0.345843
$439$	−29.0348	−1.38576	−0.692878	−	0.721055i	$-0.743657\pi$
$439$	−29.0348	−1.38576	−0.692878	+	0.721055i	$0.743657\pi$
$440$	−5.22245	−0.248971
$441$	1.00000	0.0476190
$442$	−9.18810	−0.437033
$443$	−2.06480	−0.0981017	−0.0490509	−	0.998796i	$-0.515620\pi$
$443$	−2.06480	−0.0981017	−0.0490509	+	0.998796i	$0.515620\pi$
$444$	−3.75352	−0.178134
$445$	0.0913506	0.00433043
$446$	19.2361	0.910854
$447$	2.64666	0.125183
$448$	−8.67813	−0.410003
$449$	4.64732	0.219320	0.109660	−	0.993969i	$-0.465024\pi$
$449$	4.64732	0.219320	0.109660	+	0.993969i	$0.465024\pi$
$450$	5.59249	0.263632
$451$	−20.2050	−0.951415
$452$	−7.68669	−0.361551
$453$	1.19469	0.0561315
$454$	−26.4877	−1.24313
$455$	−2.13074	−0.0998908
$456$	2.99134	0.140082
$457$	15.6066	0.730045	0.365022	−	0.930999i	$-0.381061\pi$
$457$	15.6066	0.730045	0.365022	+	0.930999i	$0.381061\pi$
$458$	7.62959	0.356507
$459$	1.72418	0.0804781
$460$	−0.688242	−0.0320894
$461$	−0.367844	−0.0171322	−0.00856609	−	0.999963i	$-0.502727\pi$
$461$	−0.367844	−0.0171322	−0.00856609	+	0.999963i	$0.502727\pi$
$462$	−4.24284	−0.197395
$463$	18.6963	0.868890	0.434445	−	0.900698i	$-0.356945\pi$
$463$	18.6963	0.868890	0.434445	+	0.900698i	$0.356945\pi$
$464$	−6.23816	−0.289600
$465$	−0.471789	−0.0218787
$466$	−15.5576	−0.720690
$467$	22.4362	1.03823	0.519113	−	0.854706i	$-0.326262\pi$
$467$	22.4362	1.03823	0.519113	+	0.854706i	$0.326262\pi$
$468$	−2.87884	−0.133074
$469$	−8.14196	−0.375961
$470$	−5.50963	−0.254140
$471$	22.2900	1.02707
$472$	−15.4026	−0.708964
$473$	32.9484	1.51497
$474$	−9.12128	−0.418954
$475$	−4.64602	−0.213174
$476$	1.08948	0.0499364
$477$	−8.29110	−0.379623
$478$	21.1353	0.966707
$479$	17.4940	0.799319	0.399660	−	0.916664i	$-0.369128\pi$
$479$	17.4940	0.799319	0.399660	+	0.916664i	$0.369128\pi$
$480$	−1.60106	−0.0730779
$481$	27.0634	1.23398
$482$	−7.79274	−0.354949
$483$	−2.32891	−0.105969
$484$	−1.36363	−0.0619830
$485$	2.44928	0.111216
$486$	−1.16967	−0.0530571
$487$	−39.3002	−1.78086	−0.890432	−	0.455116i	$-0.849598\pi$
$487$	−39.3002	−1.78086	−0.890432	+	0.455116i	$0.849598\pi$
$488$	−16.6149	−0.752123
$489$	14.9322	0.675256
$490$	−0.547032	−0.0247124
$491$	12.5677	0.567171	0.283585	−	0.958947i	$-0.408476\pi$
$491$	12.5677	0.567171	0.283585	+	0.958947i	$0.408476\pi$
$492$	−3.51965	−0.158678
$493$	4.60246	0.207284
$494$	−5.17820	−0.232978
$495$	−1.69647	−0.0762507
$496$	2.35748	0.105854
$497$	8.75283	0.392618
$498$	−4.53676	−0.203297
$499$	15.6534	0.700740	0.350370	−	0.936611i	$-0.386056\pi$
$499$	15.6534	0.700740	0.350370	+	0.936611i	$0.386056\pi$
$500$	2.89057	0.129270
$501$	5.41270	0.241822
$502$	−7.09174	−0.316520
$503$	1.64175	0.0732022	0.0366011	−	0.999330i	$-0.488347\pi$
$503$	1.64175	0.0732022	0.0366011	+	0.999330i	$0.488347\pi$
$504$	−3.07842	−0.137124
$505$	2.25838	0.100496
$506$	9.88121	0.439273
$507$	7.75680	0.344492
$508$	11.6489	0.516836
$509$	10.8712	0.481859	0.240930	−	0.970543i	$-0.422548\pi$
$509$	10.8712	0.481859	0.240930	+	0.970543i	$0.422548\pi$
$510$	−0.943183	−0.0417649
$511$	−6.18807	−0.273744
$512$	22.3886	0.989445
$513$	0.971711	0.0429021
$514$	−15.3848	−0.678595
$515$	4.07924	0.179753
$516$	5.73952	0.252668
$517$	−36.5347	−1.60680
$518$	6.94806	0.305280
$519$	7.87266	0.345571
$520$	6.55933	0.287645
$521$	34.7692	1.52327	0.761633	−	0.648009i	$-0.224398\pi$
$521$	34.7692	1.52327	0.761633	+	0.648009i	$0.224398\pi$
$522$	−3.12225	−0.136657
$523$	0.771067	0.0337164	0.0168582	−	0.999858i	$-0.494634\pi$
$523$	0.771067	0.0337164	0.0168582	+	0.999858i	$0.494634\pi$
$524$	−8.54895	−0.373463
$525$	4.78127	0.208672
$526$	−36.1962	−1.57823
$527$	−1.73933	−0.0757663
$528$	8.47708	0.368917
$529$	−17.5762	−0.764181
$530$	4.53549	0.197009
$531$	−5.00342	−0.217130
$532$	0.614008	0.0266206
$533$	25.3772	1.09921
$534$	−0.228466	−0.00988670
$535$	−1.30106	−0.0562496
$536$	25.0644	1.08262
$537$	4.51976	0.195042
$538$	−25.6249	−1.10477
$539$	−3.62740	−0.156243
$540$	−0.295521	−0.0127172
$541$	−15.3415	−0.659582	−0.329791	−	0.944054i	$-0.606978\pi$
$541$	−15.3415	−0.659582	−0.329791	+	0.944054i	$0.606978\pi$
$542$	−19.2835	−0.828298
$543$	17.1968	0.737986
$544$	−5.90255	−0.253070
$545$	−8.93945	−0.382924
$546$	5.32895	0.228058
$547$	−9.32539	−0.398725	−0.199362	−	0.979926i	$-0.563887\pi$
$547$	−9.32539	−0.398725	−0.199362	+	0.979926i	$0.563887\pi$
$548$	−6.32484	−0.270184
$549$	−5.39722	−0.230348
$550$	−20.2862	−0.865006
$551$	2.59384	0.110501
$552$	7.16938	0.305149
$553$	−7.79820	−0.331613
$554$	−31.5004	−1.33832
$555$	2.77813	0.117925
$556$	−8.53753	−0.362072
$557$	−28.0705	−1.18939	−0.594693	−	0.803953i	$-0.702726\pi$
$557$	−28.0705	−1.18939	−0.594693	+	0.803953i	$0.702726\pi$
$558$	1.17994	0.0499507
$559$	−41.3827	−1.75030
$560$	1.09295	0.0461857
$561$	−6.25431	−0.264057
$562$	−9.31108	−0.392764
$563$	−11.4656	−0.483218	−0.241609	−	0.970374i	$-0.577675\pi$
$563$	−11.4656	−0.483218	−0.241609	+	0.970374i	$0.577675\pi$
$564$	−6.36425	−0.267983
$565$	5.68922	0.239347
$566$	3.35617	0.141070
$567$	−1.00000	−0.0419961
$568$	−26.9449	−1.13058
$569$	29.1557	1.22227	0.611136	−	0.791525i	$-0.290713\pi$
$569$	29.1557	1.22227	0.611136	+	0.791525i	$0.290713\pi$
$570$	−0.531557	−0.0222645
$571$	44.6561	1.86880	0.934400	−	0.356225i	$-0.115936\pi$
$571$	44.6561	1.86880	0.934400	+	0.356225i	$0.115936\pi$
$572$	10.4427	0.436631
$573$	−1.00000	−0.0417756
$574$	6.51515	0.271937
$575$	−11.1352	−0.464369
$576$	8.67813	0.361589
$577$	18.0813	0.752736	0.376368	−	0.926470i	$-0.377173\pi$
$577$	18.0813	0.752736	0.376368	+	0.926470i	$0.377173\pi$
$578$	16.4071	0.682446
$579$	−15.0025	−0.623481
$580$	−0.788849	−0.0327552
$581$	−3.87868	−0.160915
$582$	−6.12561	−0.253915
$583$	30.0751	1.24558
$584$	19.0495	0.788273
$585$	2.13074	0.0880954
$586$	−27.8626	−1.15099
$587$	10.1127	0.417397	0.208699	−	0.977980i	$-0.433077\pi$
$587$	10.1127	0.417397	0.208699	+	0.977980i	$0.433077\pi$
$588$	−0.631883	−0.0260584
$589$	−0.980245	−0.0403903
$590$	2.73703	0.112682
$591$	13.0181	0.535492
$592$	−13.8820	−0.570548
$593$	39.7697	1.63315	0.816574	−	0.577241i	$-0.195871\pi$
$593$	39.7697	1.63315	0.816574	+	0.577241i	$0.195871\pi$
$594$	4.24284	0.174086
$595$	−0.806370	−0.0330580
$596$	−1.67238	−0.0685033
$597$	−23.2829	−0.952906
$598$	−12.4107	−0.507510
$599$	−36.1114	−1.47547	−0.737736	−	0.675089i	$-0.764105\pi$
$599$	−36.1114	−1.47547	−0.737736	+	0.675089i	$0.764105\pi$
$600$	−14.7188	−0.600892
$601$	4.15209	0.169367	0.0846837	−	0.996408i	$-0.473012\pi$
$601$	4.15209	0.169367	0.0846837	+	0.996408i	$0.473012\pi$
$602$	−10.6243	−0.433014
$603$	8.14196	0.331566
$604$	−0.754905	−0.0307167
$605$	1.00927	0.0410328
$606$	−5.64816	−0.229441
$607$	2.33717	0.0948626	0.0474313	−	0.998875i	$-0.484896\pi$
$607$	2.33717	0.0948626	0.0474313	+	0.998875i	$0.484896\pi$
$608$	−3.32654	−0.134909
$609$	−2.66935	−0.108168
$610$	2.95245	0.119541
$611$	45.8871	1.85639
$612$	−1.08948	−0.0440398
$613$	24.1019	0.973468	0.486734	−	0.873550i	$-0.338188\pi$
$613$	24.1019	0.973468	0.486734	+	0.873550i	$0.338188\pi$
$614$	−17.1439	−0.691872
$615$	2.60503	0.105045
$616$	11.1667	0.449918
$617$	−1.58274	−0.0637188	−0.0318594	−	0.999492i	$-0.510143\pi$
$617$	−1.58274	−0.0637188	−0.0318594	+	0.999492i	$0.510143\pi$
$618$	−10.2021	−0.410389
$619$	−9.14658	−0.367632	−0.183816	−	0.982961i	$-0.558845\pi$
$619$	−9.14658	−0.367632	−0.183816	+	0.982961i	$0.558845\pi$
$620$	0.298116	0.0119726
$621$	2.32891	0.0934560
$622$	−29.3985	−1.17877
$623$	−0.195326	−0.00782558
$624$	−10.6471	−0.426225
$625$	21.7669	0.870678
$626$	−19.5166	−0.780039
$627$	−3.52478	−0.140766
$628$	−14.0847	−0.562040
$629$	10.2420	0.408376
$630$	0.547032	0.0217943
$631$	25.6139	1.01967	0.509836	−	0.860271i	$-0.329706\pi$
$631$	25.6139	1.01967	0.509836	+	0.860271i	$0.329706\pi$
$632$	24.0061	0.954913
$633$	−26.0714	−1.03624
$634$	11.7642	0.467216
$635$	−8.62181	−0.342146
$636$	5.23901	0.207740
$637$	4.55596	0.180514
$638$	11.3257	0.448387
$639$	−8.75283	−0.346257
$640$	−1.54510	−0.0610753
$641$	−25.6478	−1.01303	−0.506515	−	0.862231i	$-0.669066\pi$
$641$	−25.6478	−1.01303	−0.506515	+	0.862231i	$0.669066\pi$
$642$	3.25392	0.128422
$643$	−12.0553	−0.475413	−0.237706	−	0.971337i	$-0.576396\pi$
$643$	−12.0553	−0.475413	−0.237706	+	0.971337i	$0.576396\pi$
$644$	1.47160	0.0579892
$645$	−4.24805	−0.167267
$646$	−1.95967	−0.0771021
$647$	29.2461	1.14978	0.574892	−	0.818229i	$-0.305044\pi$
$647$	29.2461	1.14978	0.574892	+	0.818229i	$0.305044\pi$
$648$	3.07842	0.120932
$649$	18.1494	0.712427
$650$	25.4792	0.999375
$651$	1.00878	0.0395373
$652$	−9.43539	−0.369518
$653$	−15.8319	−0.619549	−0.309774	−	0.950810i	$-0.600254\pi$
$653$	−15.8319	−0.619549	−0.309774	+	0.950810i	$0.600254\pi$
$654$	22.3574	0.874244
$655$	6.32742	0.247233
$656$	−13.0171	−0.508231
$657$	6.18807	0.241419
$658$	11.7807	0.459260
$659$	−37.6544	−1.46681	−0.733404	−	0.679793i	$-0.762070\pi$
$659$	−37.6544	−1.46681	−0.733404	+	0.679793i	$0.762070\pi$
$660$	1.07197	0.0417264
$661$	−22.2601	−0.865816	−0.432908	−	0.901438i	$-0.642512\pi$
$661$	−22.2601	−0.865816	−0.432908	+	0.901438i	$0.642512\pi$
$662$	15.8529	0.616141
$663$	7.85532	0.305075
$664$	11.9402	0.463370
$665$	−0.454452	−0.0176229
$666$	−6.94806	−0.269232
$667$	6.21669	0.240711
$668$	−3.42020	−0.132331
$669$	−16.4458	−0.635831
$670$	−4.45391	−0.172070
$671$	19.5779	0.755796
$672$	3.42339	0.132060
$673$	8.27447	0.318957	0.159479	−	0.987201i	$-0.449019\pi$
$673$	8.27447	0.318957	0.159479	+	0.987201i	$0.449019\pi$
$674$	9.33360	0.359517
$675$	−4.78127	−0.184031
$676$	−4.90139	−0.188515
$677$	15.4313	0.593072	0.296536	−	0.955022i	$-0.404168\pi$
$677$	15.4313	0.593072	0.296536	+	0.955022i	$0.404168\pi$
$678$	−14.2287	−0.546448
$679$	−5.23706	−0.200980
$680$	2.48235	0.0951937
$681$	22.6455	0.867777
$682$	−4.28011	−0.163894
$683$	−48.4702	−1.85466	−0.927330	−	0.374245i	$-0.877902\pi$
$683$	−48.4702	−1.85466	−0.927330	+	0.374245i	$0.877902\pi$
$684$	−0.614008	−0.0234772
$685$	4.68127	0.178862
$686$	1.16967	0.0446580
$687$	−6.52289	−0.248864
$688$	21.2270	0.809273
$689$	−37.7739	−1.43907
$690$	−1.27399	−0.0484999
$691$	−5.51109	−0.209652	−0.104826	−	0.994491i	$-0.533429\pi$
$691$	−5.51109	−0.209652	−0.104826	+	0.994491i	$0.533429\pi$
$692$	−4.97460	−0.189106
$693$	3.62740	0.137794
$694$	−39.9587	−1.51681
$695$	6.31897	0.239692
$696$	8.21740	0.311480
$697$	9.60387	0.363773
$698$	13.7710	0.521241
$699$	13.3009	0.503085
$700$	−3.02121	−0.114191
$701$	−17.0525	−0.644063	−0.322032	−	0.946729i	$-0.604366\pi$
$701$	−17.0525	−0.644063	−0.322032	+	0.946729i	$0.604366\pi$
$702$	−5.32895	−0.201128
$703$	5.77217	0.217702
$704$	−31.4791	−1.18641
$705$	4.71044	0.177405
$706$	5.96253	0.224403
$707$	−4.82887	−0.181608
$708$	3.16158	0.118819
$709$	15.0188	0.564042	0.282021	−	0.959408i	$-0.408995\pi$
$709$	15.0188	0.564042	0.282021	+	0.959408i	$0.408995\pi$
$710$	4.78807	0.179693
$711$	7.79820	0.292455
$712$	0.601296	0.0225345
$713$	−2.34937	−0.0879844
$714$	2.01672	0.0754738
$715$	−7.72906	−0.289050
$716$	−2.85596	−0.106732
$717$	−18.0696	−0.674820
$718$	14.1630	0.528560
$719$	21.1723	0.789592	0.394796	−	0.918769i	$-0.370815\pi$
$719$	21.1723	0.789592	0.394796	+	0.918769i	$0.370815\pi$
$720$	−1.09295	−0.0407319
$721$	−8.72225	−0.324833
$722$	21.1192	0.785976
$723$	6.66237	0.247776
$724$	−10.8664	−0.403846
$725$	−12.7629	−0.474003
$726$	−2.52418	−0.0936810
$727$	34.5072	1.27980	0.639901	−	0.768458i	$-0.278976\pi$
$727$	34.5072	1.27980	0.639901	+	0.768458i	$0.278976\pi$
$728$	−14.0252	−0.519808
$729$	1.00000	0.0370370
$730$	−3.38507	−0.125287
$731$	−15.6611	−0.579247
$732$	3.41042	0.126053
$733$	8.99307	0.332167	0.166083	−	0.986112i	$-0.446888\pi$
$733$	8.99307	0.332167	0.166083	+	0.986112i	$0.446888\pi$
$734$	21.5780	0.796460
$735$	0.467682	0.0172507
$736$	−7.97277	−0.293880
$737$	−29.5342	−1.08790
$738$	−6.51515	−0.239826
$739$	−20.7711	−0.764077	−0.382038	−	0.924146i	$-0.624778\pi$
$739$	−20.7711	−0.764077	−0.382038	+	0.924146i	$0.624778\pi$
$740$	−1.75546	−0.0645318
$741$	4.42708	0.162633
$742$	−9.69781	−0.356018
$743$	−46.6775	−1.71243	−0.856216	−	0.516618i	$-0.827191\pi$
$743$	−46.6775	−1.71243	−0.856216	+	0.516618i	$0.827191\pi$
$744$	−3.10546	−0.113852
$745$	1.23779	0.0453492
$746$	−31.9349	−1.16922
$747$	3.87868	0.141914
$748$	3.95199	0.144499
$749$	2.78193	0.101649
$750$	5.35066	0.195379
$751$	−7.47625	−0.272812	−0.136406	−	0.990653i	$-0.543555\pi$
$751$	−7.47625	−0.272812	−0.136406	+	0.990653i	$0.543555\pi$
$752$	−23.5375	−0.858326
$753$	6.06306	0.220950
$754$	−14.2249	−0.518039
$755$	0.558736	0.0203345
$756$	0.631883	0.0229814
$757$	−11.9692	−0.435028	−0.217514	−	0.976057i	$-0.569795\pi$
$757$	−11.9692	−0.435028	−0.217514	+	0.976057i	$0.569795\pi$
$758$	35.1629	1.27717
$759$	−8.44790	−0.306639
$760$	1.39899	0.0507469
$761$	−42.8606	−1.55370	−0.776849	−	0.629688i	$-0.783183\pi$
$761$	−42.8606	−1.55370	−0.776849	+	0.629688i	$0.783183\pi$
$762$	21.5630	0.781145
$763$	19.1144	0.691986
$764$	0.631883	0.0228607
$765$	0.806370	0.0291544
$766$	7.35258	0.265659
$767$	−22.7954	−0.823094
$768$	−13.4920	−0.486851
$769$	17.8036	0.642014	0.321007	−	0.947077i	$-0.395979\pi$
$769$	17.8036	0.642014	0.321007	+	0.947077i	$0.395979\pi$
$770$	−1.98430	−0.0715093
$771$	13.1532	0.473700
$772$	9.47981	0.341186
$773$	−4.61346	−0.165935	−0.0829673	−	0.996552i	$-0.526440\pi$
$773$	−4.61346	−0.165935	−0.0829673	+	0.996552i	$0.526440\pi$
$774$	10.6243	0.381883
$775$	4.82326	0.173257
$776$	16.1219	0.578742
$777$	−5.94021	−0.213104
$778$	−14.3620	−0.514903
$779$	5.41252	0.193924
$780$	−1.34638	−0.0482082
$781$	31.7500	1.13611
$782$	−4.69676	−0.167956
$783$	2.66935	0.0953949
$784$	−2.33696	−0.0834627
$785$	10.4246	0.372071
$786$	−15.8248	−0.564451
$787$	−43.4609	−1.54921	−0.774607	−	0.632442i	$-0.782053\pi$
$787$	−43.4609	−1.54921	−0.774607	+	0.632442i	$0.782053\pi$
$788$	−8.22590	−0.293035
$789$	30.9457	1.10170
$790$	−4.26586	−0.151772
$791$	−12.1647	−0.432528
$792$	−11.1667	−0.396790
$793$	−24.5896	−0.873201
$794$	39.6915	1.40860
$795$	−3.87760	−0.137524
$796$	14.7121	0.521456
$797$	40.3494	1.42925	0.714625	−	0.699508i	$-0.246598\pi$
$797$	40.3494	1.42925	0.714625	+	0.699508i	$0.246598\pi$
$798$	1.13658	0.0402344
$799$	17.3658	0.614357
$800$	16.3682	0.578702
$801$	0.195326	0.00690151
$802$	6.96185	0.245831
$803$	−22.4466	−0.792123
$804$	−5.14477	−0.181442
$805$	−1.08919	−0.0383889
$806$	5.37575	0.189353
$807$	21.9079	0.771194
$808$	14.8653	0.522959
$809$	−19.0869	−0.671059	−0.335529	−	0.942030i	$-0.608915\pi$
$809$	−19.0869	−0.671059	−0.335529	+	0.942030i	$0.608915\pi$
$810$	−0.547032	−0.0192207
$811$	12.2966	0.431790	0.215895	−	0.976417i	$-0.430733\pi$
$811$	12.2966	0.431790	0.215895	+	0.976417i	$0.430733\pi$
$812$	1.68672	0.0591923
$813$	16.4864	0.578202
$814$	25.2034	0.883379
$815$	6.98351	0.244622
$816$	−4.02934	−0.141055
$817$	−8.82624	−0.308791
$818$	−45.5353	−1.59210
$819$	−4.55596	−0.159198
$820$	−1.64608	−0.0574835
$821$	−1.41050	−0.0492267	−0.0246134	−	0.999697i	$-0.507835\pi$
$821$	−1.41050	−0.0492267	−0.0246134	+	0.999697i	$0.507835\pi$
$822$	−11.7078	−0.408356
$823$	−29.3338	−1.02251	−0.511256	−	0.859428i	$-0.670820\pi$
$823$	−29.3338	−1.02251	−0.511256	+	0.859428i	$0.670820\pi$
$824$	26.8508	0.935390
$825$	17.3436	0.603826
$826$	−5.85233	−0.203629
$827$	17.5677	0.610890	0.305445	−	0.952210i	$-0.401195\pi$
$827$	17.5677	0.610890	0.305445	+	0.952210i	$0.401195\pi$
$828$	−1.47160	−0.0511417
$829$	−49.9435	−1.73461	−0.867305	−	0.497778i	$-0.834150\pi$
$829$	−49.9435	−1.73461	−0.867305	+	0.497778i	$0.834150\pi$
$830$	−2.12176	−0.0736474
$831$	26.9311	0.934230
$832$	39.5372	1.37071
$833$	1.72418	0.0597395
$834$	−15.8036	−0.547235
$835$	2.53142	0.0876035
$836$	2.22725	0.0770312
$837$	−1.00878	−0.0348686
$838$	16.3352	0.564292
$839$	−21.1736	−0.730995	−0.365497	−	0.930812i	$-0.619101\pi$
$839$	−21.1736	−0.730995	−0.365497	+	0.930812i	$0.619101\pi$
$840$	−1.43972	−0.0496752
$841$	−21.8745	−0.754295
$842$	−14.3047	−0.492972
$843$	7.96047	0.274173
$844$	16.4741	0.567061
$845$	3.62772	0.124797
$846$	−11.7807	−0.405030
$847$	−2.15803	−0.0741509
$848$	19.3759	0.665372
$849$	−2.86934	−0.0984756
$850$	9.64248	0.330734
$851$	13.8342	0.474232
$852$	5.53077	0.189481
$853$	6.57309	0.225058	0.112529	−	0.993648i	$-0.464105\pi$
$853$	6.57309	0.225058	0.112529	+	0.993648i	$0.464105\pi$
$854$	−6.31294	−0.216025
$855$	0.454452	0.0155419
$856$	−8.56395	−0.292710
$857$	−3.03248	−0.103587	−0.0517937	−	0.998658i	$-0.516494\pi$
$857$	−3.03248	−0.103587	−0.0517937	+	0.998658i	$0.516494\pi$
$858$	19.3302	0.659923
$859$	−15.7970	−0.538988	−0.269494	−	0.963002i	$-0.586856\pi$
$859$	−15.7970	−0.538988	−0.269494	+	0.963002i	$0.586856\pi$
$860$	2.68427	0.0915329
$861$	−5.57010	−0.189828
$862$	17.1760	0.585015
$863$	12.3974	0.422014	0.211007	−	0.977485i	$-0.432326\pi$
$863$	12.3974	0.422014	0.211007	+	0.977485i	$0.432326\pi$
$864$	−3.42339	−0.116466
$865$	3.68190	0.125188
$866$	−22.7654	−0.773598
$867$	−14.0272	−0.476388
$868$	−0.637433	−0.0216359
$869$	−28.2872	−0.959577
$870$	−1.46022	−0.0495061
$871$	37.0945	1.25690
$872$	−58.8421	−1.99264
$873$	5.23706	0.177248
$874$	−2.64699	−0.0895357
$875$	4.57453	0.154647
$876$	−3.91014	−0.132111
$877$	−49.3351	−1.66593	−0.832964	−	0.553327i	$-0.813358\pi$
$877$	−49.3351	−1.66593	−0.832964	+	0.553327i	$0.813358\pi$
$878$	33.9610	1.14613
$879$	23.8210	0.803463
$880$	3.96458	0.133646
$881$	52.3958	1.76526	0.882629	−	0.470070i	$-0.155771\pi$
$881$	52.3958	1.76526	0.882629	+	0.470070i	$0.155771\pi$
$882$	−1.16967	−0.0393847
$883$	−27.4667	−0.924329	−0.462164	−	0.886794i	$-0.652927\pi$
$883$	−27.4667	−0.924329	−0.462164	+	0.886794i	$0.652927\pi$
$884$	−4.96365	−0.166946
$885$	−2.34001	−0.0786586
$886$	2.41513	0.0811378
$887$	24.7717	0.831751	0.415876	−	0.909421i	$-0.363475\pi$
$887$	24.7717	0.831751	0.415876	+	0.909421i	$0.363475\pi$
$888$	18.2865	0.613654
$889$	18.4352	0.618296
$890$	−0.106850	−0.00358161
$891$	−3.62740	−0.121522
$892$	10.3918	0.347944
$893$	9.78695	0.327508
$894$	−3.09570	−0.103536
$895$	2.11381	0.0706570
$896$	3.30373	0.110370
$897$	10.6104	0.354272
$898$	−5.43581	−0.181395
$899$	−2.69280	−0.0898098
$900$	3.02121	0.100707
$901$	−14.2954	−0.476248
$902$	23.6330	0.786894
$903$	9.08320	0.302270
$904$	37.4482	1.24551
$905$	8.04265	0.267347
$906$	−1.39739	−0.0464251
$907$	−29.3557	−0.974740	−0.487370	−	0.873196i	$-0.662044\pi$
$907$	−29.3557	−0.974740	−0.487370	+	0.873196i	$0.662044\pi$
$908$	−14.3093	−0.474871
$909$	4.82887	0.160163
$910$	2.49226	0.0826175
$911$	−39.5507	−1.31037	−0.655186	−	0.755467i	$-0.727410\pi$
$911$	−39.5507	−1.31037	−0.655186	+	0.755467i	$0.727410\pi$
$912$	−2.27085	−0.0751952
$913$	−14.0695	−0.465633
$914$	−18.2545	−0.603804
$915$	−2.52419	−0.0834470
$916$	4.12170	0.136185
$917$	−13.5293	−0.446777
$918$	−2.01672	−0.0665616
$919$	−7.51991	−0.248059	−0.124029	−	0.992279i	$-0.539582\pi$
$919$	−7.51991	−0.248059	−0.124029	+	0.992279i	$0.539582\pi$
$920$	3.35299	0.110545
$921$	14.6571	0.482968
$922$	0.430254	0.0141697
$923$	−39.8776	−1.31259
$924$	−2.29209	−0.0754044
$925$	−28.4018	−0.933845
$926$	−21.8684	−0.718640
$927$	8.72225	0.286476
$928$	−9.13824	−0.299977
$929$	−23.8560	−0.782690	−0.391345	−	0.920244i	$-0.627990\pi$
$929$	−23.8560	−0.782690	−0.391345	+	0.920244i	$0.627990\pi$
$930$	0.551836	0.0180954
$931$	0.971711	0.0318465
$932$	−8.40459	−0.275302
$933$	25.1341	0.822853
$934$	−26.2429	−0.858694
$935$	−2.92503	−0.0956587
$936$	14.0252	0.458427
$937$	−38.0938	−1.24447	−0.622234	−	0.782831i	$-0.713775\pi$
$937$	−38.0938	−1.24447	−0.622234	+	0.782831i	$0.713775\pi$
$938$	9.52337	0.310949
$939$	16.6856	0.544514
$940$	−2.97645	−0.0970810
$941$	−24.1463	−0.787146	−0.393573	−	0.919293i	$-0.628761\pi$
$941$	−24.1463	−0.787146	−0.393573	+	0.919293i	$0.628761\pi$
$942$	−26.0719	−0.849467
$943$	12.9723	0.422435
$944$	11.6928	0.380568
$945$	−0.467682	−0.0152137
$946$	−38.5386	−1.25300
$947$	−5.90424	−0.191862	−0.0959309	−	0.995388i	$-0.530583\pi$
$947$	−5.90424	−0.191862	−0.0959309	+	0.995388i	$0.530583\pi$
$948$	−4.92755	−0.160039
$949$	28.1926	0.915170
$950$	5.43428	0.176311
$951$	−10.0578	−0.326145
$952$	−5.30777	−0.172026
$953$	−35.1523	−1.13869	−0.569347	−	0.822097i	$-0.692804\pi$
$953$	−35.1523	−1.13869	−0.569347	+	0.822097i	$0.692804\pi$
$954$	9.69781	0.313978
$955$	−0.467682	−0.0151338
$956$	11.4179	0.369280
$957$	−9.68282	−0.313001
$958$	−20.4621	−0.661100
$959$	−10.0095	−0.323224
$960$	4.05861	0.130991
$961$	−29.9824	−0.967173
$962$	−31.6551	−1.02060
$963$	−2.78193	−0.0896464
$964$	−4.20984	−0.135590
$965$	−7.01639	−0.225866
$966$	2.72405	0.0876448
$967$	29.7849	0.957817	0.478908	−	0.877865i	$-0.341033\pi$
$967$	29.7849	0.957817	0.478908	+	0.877865i	$0.341033\pi$
$968$	6.64334	0.213525
$969$	1.67541	0.0538219
$970$	−2.86484	−0.0919844
$971$	−11.6452	−0.373711	−0.186856	−	0.982387i	$-0.559830\pi$
$971$	−11.6452	−0.373711	−0.186856	+	0.982387i	$0.559830\pi$
$972$	−0.631883	−0.0202677
$973$	−13.5112	−0.433151
$974$	45.9681	1.47291
$975$	−21.7833	−0.697624
$976$	12.6131	0.403735
$977$	−44.3851	−1.42000	−0.710002	−	0.704200i	$-0.751306\pi$
$977$	−44.3851	−1.42000	−0.710002	+	0.704200i	$0.751306\pi$
$978$	−17.4656	−0.558490
$979$	−0.708526	−0.0226446
$980$	−0.295521	−0.00944006
$981$	−19.1144	−0.610275
$982$	−14.7000	−0.469094
$983$	−8.55326	−0.272807	−0.136403	−	0.990653i	$-0.543554\pi$
$983$	−8.55326	−0.272807	−0.136403	+	0.990653i	$0.543554\pi$
$984$	17.1471	0.546630
$985$	6.08832	0.193990
$986$	−5.38334	−0.171440
$987$	−10.0719	−0.320591
$988$	−2.79740	−0.0889971
$989$	−21.1540	−0.672657
$990$	1.98430	0.0630653
$991$	24.6757	0.783850	0.391925	−	0.919997i	$-0.371809\pi$
$991$	24.6757	0.783850	0.391925	+	0.919997i	$0.371809\pi$
$992$	3.45345	0.109647
$993$	−13.5534	−0.430104
$994$	−10.2379	−0.324726
$995$	−10.8890	−0.345205
$996$	−2.45087	−0.0776589
$997$	−2.11921	−0.0671159	−0.0335580	−	0.999437i	$-0.510684\pi$
$997$	−2.11921	−0.0671159	−0.0335580	+	0.999437i	$0.510684\pi$
$998$	−18.3092	−0.579567
$999$	5.94021	0.187940

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.m.1.9	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.m.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-1.16967 q^{2} +1.00000 q^{3} -0.631883 q^{4} +0.467682 q^{5} -1.16967 q^{6} -1.00000 q^{7} +3.07842 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.16967 q^{2} +1.00000 q^{3} -0.631883 q^{4} +0.467682 q^{5} -1.16967 q^{6} -1.00000 q^{7} +3.07842 q^{8} +1.00000 q^{9} -0.547032 q^{10} -3.62740 q^{11} -0.631883 q^{12} +4.55596 q^{13} +1.16967 q^{14} +0.467682 q^{15} -2.33696 q^{16} +1.72418 q^{17} -1.16967 q^{18} +0.971711 q^{19} -0.295521 q^{20} -1.00000 q^{21} +4.24284 q^{22} +2.32891 q^{23} +3.07842 q^{24} -4.78127 q^{25} -5.32895 q^{26} +1.00000 q^{27} +0.631883 q^{28} +2.66935 q^{29} -0.547032 q^{30} -1.00878 q^{31} -3.42339 q^{32} -3.62740 q^{33} -2.01672 q^{34} -0.467682 q^{35} -0.631883 q^{36} +5.94021 q^{37} -1.13658 q^{38} +4.55596 q^{39} +1.43972 q^{40} +5.57010 q^{41} +1.16967 q^{42} -9.08320 q^{43} +2.29209 q^{44} +0.467682 q^{45} -2.72405 q^{46} +10.0719 q^{47} -2.33696 q^{48} +1.00000 q^{49} +5.59249 q^{50} +1.72418 q^{51} -2.87884 q^{52} -8.29110 q^{53} -1.16967 q^{54} -1.69647 q^{55} -3.07842 q^{56} +0.971711 q^{57} -3.12225 q^{58} -5.00342 q^{59} -0.295521 q^{60} -5.39722 q^{61} +1.17994 q^{62} -1.00000 q^{63} +8.67813 q^{64} +2.13074 q^{65} +4.24284 q^{66} +8.14196 q^{67} -1.08948 q^{68} +2.32891 q^{69} +0.547032 q^{70} -8.75283 q^{71} +3.07842 q^{72} +6.18807 q^{73} -6.94806 q^{74} -4.78127 q^{75} -0.614008 q^{76} +3.62740 q^{77} -5.32895 q^{78} +7.79820 q^{79} -1.09295 q^{80} +1.00000 q^{81} -6.51515 q^{82} +3.87868 q^{83} +0.631883 q^{84} +0.806370 q^{85} +10.6243 q^{86} +2.66935 q^{87} -11.1667 q^{88} +0.195326 q^{89} -0.547032 q^{90} -4.55596 q^{91} -1.47160 q^{92} -1.00878 q^{93} -11.7807 q^{94} +0.454452 q^{95} -3.42339 q^{96} +5.23706 q^{97} -1.16967 q^{98} -3.62740 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9}+O(q^{10}) \) 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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