LMFDB - Embedded newform 6005.2.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.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:	$47.9501664138$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.2777.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} + x + 2 $ x^4 - x^3 - 4*x^2 + x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.825785$ of defining polynomial
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.59615 q^{2} -0.452290 q^{3} +4.74002 q^{4} -1.00000 q^{5} -1.17422 q^{6} -1.17422 q^{7} +7.11351 q^{8} -2.79543 q^{9} +O(q^{10})$	\(q+2.59615 q^{2} -0.452290 q^{3} +4.74002 q^{4} -1.00000 q^{5} -1.17422 q^{6} -1.17422 q^{7} +7.11351 q^{8} -2.79543 q^{9} -2.59615 q^{10} -0.904581 q^{11} -2.14386 q^{12} -1.59615 q^{13} -3.04844 q^{14} +0.452290 q^{15} +8.98774 q^{16} +1.22266 q^{17} -7.25738 q^{18} +1.22963 q^{19} -4.74002 q^{20} +0.531086 q^{21} -2.34843 q^{22} -2.82578 q^{23} -3.21737 q^{24} +1.00000 q^{25} -4.14386 q^{26} +2.62122 q^{27} -5.56580 q^{28} -5.34314 q^{29} +1.17422 q^{30} +2.36652 q^{31} +9.10654 q^{32} +0.409133 q^{33} +3.17422 q^{34} +1.17422 q^{35} -13.2504 q^{36} -8.52004 q^{37} +3.19231 q^{38} +0.721925 q^{39} -7.11351 q^{40} -3.00965 q^{41} +1.37878 q^{42} -0.990346 q^{43} -4.28773 q^{44} +2.79543 q^{45} -7.33617 q^{46} -9.52848 q^{47} -4.06507 q^{48} -5.62122 q^{49} +2.59615 q^{50} -0.552997 q^{51} -7.56580 q^{52} +9.04844 q^{53} +6.80509 q^{54} +0.904581 q^{55} -8.35280 q^{56} -0.556150 q^{57} -13.8716 q^{58} -11.0511 q^{59} +2.14386 q^{60} +0.217373 q^{61} +6.14386 q^{62} +3.28244 q^{63} +5.66651 q^{64} +1.59615 q^{65} +1.06217 q^{66} -0.125771 q^{67} +5.79543 q^{68} +1.27807 q^{69} +3.04844 q^{70} +3.18118 q^{71} -19.8854 q^{72} -9.41934 q^{73} -22.1194 q^{74} -0.452290 q^{75} +5.82847 q^{76} +1.06217 q^{77} +1.87423 q^{78} +6.36652 q^{79} -8.98774 q^{80} +7.20075 q^{81} -7.81353 q^{82} -4.05013 q^{83} +2.51736 q^{84} -1.22266 q^{85} -2.57109 q^{86} +2.41665 q^{87} -6.43475 q^{88} +10.5690 q^{89} +7.25738 q^{90} +1.87423 q^{91} -13.3943 q^{92} -1.07036 q^{93} -24.7374 q^{94} -1.22963 q^{95} -4.11880 q^{96} +6.19231 q^{97} -14.5936 q^{98} +2.52869 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} - 7 q^{6} - 7 q^{7} + 9 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 4 * q^5 - 7 * q^6 - 7 * q^7 + 9 * q^8 + 2 * q^9	\( 4 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} - 7 q^{6} - 7 q^{7} + 9 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{13} - 4 q^{14} + 2 q^{15} + 6 q^{16} - q^{17} - q^{18} + 11 q^{19} - 2 q^{20} + 5 q^{21} - 14 q^{22} - 9 q^{23} + 11 q^{24} + 4 q^{25} - 8 q^{26} - 5 q^{27} - 3 q^{28} - 8 q^{29} + 7 q^{30} - 5 q^{31} + 5 q^{32} + 28 q^{33} + 15 q^{34} + 7 q^{35} - 13 q^{36} + 4 q^{37} - 4 q^{38} + 5 q^{39} - 9 q^{40} + 3 q^{41} + 21 q^{42} - 19 q^{43} - 2 q^{45} - 4 q^{46} + 4 q^{47} - 5 q^{48} - 7 q^{49} + 2 q^{50} - 20 q^{51} - 11 q^{52} + 28 q^{53} - q^{54} + 4 q^{55} - 5 q^{56} + 2 q^{57} - 9 q^{59} - 23 q^{61} + 16 q^{62} - 22 q^{63} + 21 q^{64} - 2 q^{65} + 10 q^{66} - 11 q^{67} + 10 q^{68} + 3 q^{69} + 4 q^{70} + 27 q^{71} - 38 q^{72} + 18 q^{73} - 20 q^{74} - 2 q^{75} - 6 q^{76} + 10 q^{77} - 3 q^{78} + 11 q^{79} - 6 q^{80} + 8 q^{81} + q^{82} - 2 q^{83} - q^{84} + q^{85} - 9 q^{86} - 19 q^{87} + 22 q^{88} + q^{89} + q^{90} - 3 q^{91} - 5 q^{92} - 11 q^{93} - 37 q^{94} - 11 q^{95} - 15 q^{96} + 8 q^{97} - 5 q^{98} - 22 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 4 * q^5 - 7 * q^6 - 7 * q^7 + 9 * q^8 + 2 * q^9 - 2 * q^10 - 4 * q^11 + 2 * q^13 - 4 * q^14 + 2 * q^15 + 6 * q^16 - q^17 - q^18 + 11 * q^19 - 2 * q^20 + 5 * q^21 - 14 * q^22 - 9 * q^23 + 11 * q^24 + 4 * q^25 - 8 * q^26 - 5 * q^27 - 3 * q^28 - 8 * q^29 + 7 * q^30 - 5 * q^31 + 5 * q^32 + 28 * q^33 + 15 * q^34 + 7 * q^35 - 13 * q^36 + 4 * q^37 - 4 * q^38 + 5 * q^39 - 9 * q^40 + 3 * q^41 + 21 * q^42 - 19 * q^43 - 2 * q^45 - 4 * q^46 + 4 * q^47 - 5 * q^48 - 7 * q^49 + 2 * q^50 - 20 * q^51 - 11 * q^52 + 28 * q^53 - q^54 + 4 * q^55 - 5 * q^56 + 2 * q^57 - 9 * q^59 - 23 * q^61 + 16 * q^62 - 22 * q^63 + 21 * q^64 - 2 * q^65 + 10 * q^66 - 11 * q^67 + 10 * q^68 + 3 * q^69 + 4 * q^70 + 27 * q^71 - 38 * q^72 + 18 * q^73 - 20 * q^74 - 2 * q^75 - 6 * q^76 + 10 * q^77 - 3 * q^78 + 11 * q^79 - 6 * q^80 + 8 * q^81 + q^82 - 2 * q^83 - q^84 + q^85 - 9 * q^86 - 19 * q^87 + 22 * q^88 + q^89 + q^90 - 3 * q^91 - 5 * q^92 - 11 * q^93 - 37 * q^94 - 11 * q^95 - 15 * q^96 + 8 * q^97 - 5 * q^98 - 22 * 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 $

$2$	2.59615	1.83576	0.917879	−	0.396860i	$-0.129900\pi$
$2$	2.59615	1.83576	0.917879	+	0.396860i	$0.129900\pi$
$3$	−0.452290	−0.261130	−0.130565	−	0.991440i	$-0.541679\pi$
$3$	−0.452290	−0.261130	−0.130565	+	0.991440i	$0.541679\pi$
$4$	4.74002	2.37001
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.17422	−0.479371
$7$	−1.17422	−0.443812	−0.221906	−	0.975068i	$-0.571228\pi$
$7$	−1.17422	−0.443812	−0.221906	+	0.975068i	$0.571228\pi$
$8$	7.11351	2.51501
$9$	−2.79543	−0.931811
$10$	−2.59615	−0.820976
$11$	−0.904581	−0.272741	−0.136371	−	0.990658i	$-0.543544\pi$
$11$	−0.904581	−0.272741	−0.136371	+	0.990658i	$0.543544\pi$
$12$	−2.14386	−0.618880
$13$	−1.59615	−0.442694	−0.221347	−	0.975195i	$-0.571045\pi$
$13$	−1.59615	−0.442694	−0.221347	+	0.975195i	$0.571045\pi$
$14$	−3.04844	−0.814731
$15$	0.452290	0.116781
$16$	8.98774	2.24694
$17$	1.22266	0.296539	0.148269	−	0.988947i	$-0.452630\pi$
$17$	1.22266	0.296539	0.148269	+	0.988947i	$0.452630\pi$
$18$	−7.25738	−1.71058
$19$	1.22963	0.282096	0.141048	−	0.990003i	$-0.454953\pi$
$19$	1.22963	0.282096	0.141048	+	0.990003i	$0.454953\pi$
$20$	−4.74002	−1.05990
$21$	0.531086	0.115893
$22$	−2.34843	−0.500687
$23$	−2.82578	−0.589217	−0.294608	−	0.955618i	$-0.595189\pi$
$23$	−2.82578	−0.589217	−0.294608	+	0.955618i	$0.595189\pi$
$24$	−3.21737	−0.656743
$25$	1.00000	0.200000
$26$	−4.14386	−0.812679
$27$	2.62122	0.504454
$28$	−5.56580	−1.05184
$29$	−5.34314	−0.992197	−0.496098	−	0.868266i	$-0.665234\pi$
$29$	−5.34314	−0.992197	−0.496098	+	0.868266i	$0.665234\pi$
$30$	1.17422	0.214381
$31$	2.36652	0.425040	0.212520	−	0.977157i	$-0.431833\pi$
$31$	2.36652	0.425040	0.212520	+	0.977157i	$0.431833\pi$
$32$	9.10654	1.60982
$33$	0.409133	0.0712209
$34$	3.17422	0.544373
$35$	1.17422	0.198479
$36$	−13.2504	−2.20840
$37$	−8.52004	−1.40069	−0.700343	−	0.713806i	$-0.746970\pi$
$37$	−8.52004	−1.40069	−0.700343	+	0.713806i	$0.746970\pi$
$38$	3.19231	0.517861
$39$	0.721925	0.115601
$40$	−7.11351	−1.12475
$41$	−3.00965	−0.470029	−0.235014	−	0.971992i	$-0.575514\pi$
$41$	−3.00965	−0.470029	−0.235014	+	0.971992i	$0.575514\pi$
$42$	1.37878	0.212751
$43$	−0.990346	−0.151026	−0.0755132	−	0.997145i	$-0.524059\pi$
$43$	−0.990346	−0.151026	−0.0755132	+	0.997145i	$0.524059\pi$
$44$	−4.28773	−0.646399
$45$	2.79543	0.416719
$46$	−7.33617	−1.08166
$47$	−9.52848	−1.38987	−0.694936	−	0.719072i	$-0.744567\pi$
$47$	−9.52848	−1.38987	−0.694936	+	0.719072i	$0.744567\pi$
$48$	−4.06507	−0.586742
$49$	−5.62122	−0.803031
$50$	2.59615	0.367152
$51$	−0.552997	−0.0774351
$52$	−7.56580	−1.04919
$53$	9.04844	1.24290	0.621450	−	0.783454i	$-0.286544\pi$
$53$	9.04844	1.24290	0.621450	+	0.783454i	$0.286544\pi$
$54$	6.80509	0.926055
$55$	0.904581	0.121974
$56$	−8.35280	−1.11619
$57$	−0.556150	−0.0736638
$58$	−13.8716	−1.82143
$59$	−11.0511	−1.43873	−0.719367	−	0.694630i	$-0.755568\pi$
$59$	−11.0511	−1.43873	−0.719367	+	0.694630i	$0.755568\pi$
$60$	2.14386	0.276772
$61$	0.217373	0.0278317	0.0139159	−	0.999903i	$-0.495570\pi$
$61$	0.217373	0.0278317	0.0139159	+	0.999903i	$0.495570\pi$
$62$	6.14386	0.780272
$63$	3.28244	0.413549
$64$	5.66651	0.708314
$65$	1.59615	0.197979
$66$	1.06217	0.130744
$67$	−0.125771	−0.0153653	−0.00768266	−	0.999970i	$-0.502445\pi$
$67$	−0.125771	−0.0153653	−0.00768266	+	0.999970i	$0.502445\pi$
$68$	5.79543	0.702800
$69$	1.27807	0.153862
$70$	3.04844	0.364359
$71$	3.18118	0.377537	0.188769	−	0.982022i	$-0.439550\pi$
$71$	3.18118	0.377537	0.188769	+	0.982022i	$0.439550\pi$
$72$	−19.8854	−2.34351
$73$	−9.41934	−1.10245	−0.551225	−	0.834357i	$-0.685839\pi$
$73$	−9.41934	−1.10245	−0.551225	+	0.834357i	$0.685839\pi$
$74$	−22.1194	−2.57132
$75$	−0.452290	−0.0522260
$76$	5.82847	0.668571
$77$	1.06217	0.121046
$78$	1.87423	0.212215
$79$	6.36652	0.716290	0.358145	−	0.933666i	$-0.383409\pi$
$79$	6.36652	0.716290	0.358145	+	0.933666i	$0.383409\pi$
$80$	−8.98774	−1.00486
$81$	7.20075	0.800083
$82$	−7.81353	−0.862860
$83$	−4.05013	−0.444559	−0.222280	−	0.974983i	$-0.571350\pi$
$83$	−4.05013	−0.444559	−0.222280	+	0.974983i	$0.571350\pi$
$84$	2.51736	0.274666
$85$	−1.22266	−0.132616
$86$	−2.57109	−0.277248
$87$	2.41665	0.259092
$88$	−6.43475	−0.685946
$89$	10.5690	1.12031	0.560154	−	0.828389i	$-0.310742\pi$
$89$	10.5690	1.12031	0.560154	+	0.828389i	$0.310742\pi$
$90$	7.25738	0.764995
$91$	1.87423	0.196473
$92$	−13.3943	−1.39645
$93$	−1.07036	−0.110991
$94$	−24.7374	−2.55147
$95$	−1.22963	−0.126157
$96$	−4.11880	−0.420373
$97$	6.19231	0.628734	0.314367	−	0.949302i	$-0.398208\pi$
$97$	6.19231	0.628734	0.314367	+	0.949302i	$0.398208\pi$
$98$	−14.5936	−1.47417
$99$	2.52869	0.254143
$100$	4.74002	0.474002
$101$	−12.0261	−1.19664	−0.598319	−	0.801258i	$-0.704165\pi$
$101$	−12.0261	−1.19664	−0.598319	+	0.801258i	$0.704165\pi$
$102$	−1.43567	−0.142152
$103$	−1.19231	−0.117482	−0.0587409	−	0.998273i	$-0.518709\pi$
$103$	−1.19231	−0.117482	−0.0587409	+	0.998273i	$0.518709\pi$
$104$	−11.3543	−1.11338
$105$	−0.531086	−0.0518287
$106$	23.4912	2.28166
$107$	0.246253	0.0238062	0.0119031	−	0.999929i	$-0.496211\pi$
$107$	0.246253	0.0238062	0.0119031	+	0.999929i	$0.496211\pi$
$108$	12.4246	1.19556
$109$	−9.75283	−0.934151	−0.467076	−	0.884217i	$-0.654692\pi$
$109$	−9.75283	−0.934151	−0.467076	+	0.884217i	$0.654692\pi$
$110$	2.34843	0.223914
$111$	3.85353	0.365761
$112$	−10.5535	−0.997216
$113$	10.7981	1.01580	0.507901	−	0.861416i	$-0.330422\pi$
$113$	10.7981	1.01580	0.507901	+	0.861416i	$0.330422\pi$
$114$	−1.44385	−0.135229
$115$	2.82578	0.263506
$116$	−25.3266	−2.35152
$117$	4.46194	0.412507
$118$	−28.6904	−2.64117
$119$	−1.43567	−0.131607
$120$	3.21737	0.293705
$121$	−10.1817	−0.925612
$122$	0.564333	0.0510923
$123$	1.36124	0.122739
$124$	11.2174	1.00735
$125$	−1.00000	−0.0894427
$126$	8.52173	0.759176
$127$	−15.3878	−1.36544	−0.682722	−	0.730678i	$-0.739204\pi$
$127$	−15.3878	−1.36544	−0.682722	+	0.730678i	$0.739204\pi$
$128$	−3.50195	−0.309532
$129$	0.447924	0.0394375
$130$	4.14386	0.363441
$131$	−15.4769	−1.35222	−0.676111	−	0.736800i	$-0.736336\pi$
$131$	−15.4769	−1.35222	−0.676111	+	0.736800i	$0.736336\pi$
$132$	1.93930	0.168794
$133$	−1.44385	−0.125198
$134$	−0.326520	−0.0282070
$135$	−2.62122	−0.225599
$136$	8.69741	0.745797
$137$	−9.04966	−0.773165	−0.386582	−	0.922255i	$-0.626344\pi$
$137$	−9.04966	−0.773165	−0.386582	+	0.922255i	$0.626344\pi$
$138$	3.31808	0.282454
$139$	−0.303138	−0.0257118	−0.0128559	−	0.999917i	$-0.504092\pi$
$139$	−0.303138	−0.0257118	−0.0128559	+	0.999917i	$0.504092\pi$
$140$	5.56580	0.470396
$141$	4.30964	0.362937
$142$	8.25885	0.693067
$143$	1.44385	0.120741
$144$	−25.1246	−2.09372
$145$	5.34314	0.443724
$146$	−24.4541	−2.02383
$147$	2.54242	0.209695
$148$	−40.3852	−3.31964
$149$	−2.82532	−0.231459	−0.115729	−	0.993281i	$-0.536921\pi$
$149$	−2.82532	−0.231459	−0.115729	+	0.993281i	$0.536921\pi$
$150$	−1.17422	−0.0958743
$151$	9.01234	0.733414	0.366707	−	0.930337i	$-0.380485\pi$
$151$	9.01234	0.733414	0.366707	+	0.930337i	$0.380485\pi$
$152$	8.74699	0.709474
$153$	−3.41787	−0.276318
$154$	2.75756	0.222211
$155$	−2.36652	−0.190084
$156$	3.42194	0.273974
$157$	10.6277	0.848184	0.424092	−	0.905619i	$-0.360593\pi$
$157$	10.6277	0.848184	0.424092	+	0.905619i	$0.360593\pi$
$158$	16.5285	1.31494
$159$	−4.09252	−0.324558
$160$	−9.10654	−0.719936
$161$	3.31808	0.261501
$162$	18.6943	1.46876
$163$	0.206505	0.0161747	0.00808734	−	0.999967i	$-0.497426\pi$
$163$	0.206505	0.0161747	0.00808734	+	0.999967i	$0.497426\pi$
$164$	−14.2658	−1.11397
$165$	−0.409133	−0.0318510
$166$	−10.5148	−0.816103
$167$	7.43306	0.575188	0.287594	−	0.957752i	$-0.407145\pi$
$167$	7.43306	0.575188	0.287594	+	0.957752i	$0.407145\pi$
$168$	3.77789	0.291470
$169$	−10.4523	−0.804022
$170$	−3.17422	−0.243451
$171$	−3.43735	−0.262861
$172$	−4.69426	−0.357934
$173$	21.3097	1.62015	0.810074	−	0.586328i	$-0.199427\pi$
$173$	21.3097	1.62015	0.810074	+	0.586328i	$0.199427\pi$
$174$	6.27400	0.475631
$175$	−1.17422	−0.0887623
$176$	−8.13014	−0.612832
$177$	4.99832	0.375697
$178$	27.4386	2.05661
$179$	10.0569	0.751687	0.375843	−	0.926683i	$-0.377353\pi$
$179$	10.0569	0.751687	0.375843	+	0.926683i	$0.377353\pi$
$180$	13.2504	0.987627
$181$	−19.1205	−1.42121	−0.710607	−	0.703589i	$-0.751580\pi$
$181$	−19.1205	−1.42121	−0.710607	+	0.703589i	$0.751580\pi$
$182$	4.86579	0.360676
$183$	−0.0983156	−0.00726770
$184$	−20.1013	−1.48188
$185$	8.52004	0.626406
$186$	−2.77881	−0.203752
$187$	−1.10599	−0.0808783
$188$	−45.1652	−3.29401
$189$	−3.07787	−0.223882
$190$	−3.19231	−0.231594
$191$	−2.21209	−0.160061	−0.0800304	−	0.996792i	$-0.525502\pi$
$191$	−2.21209	−0.160061	−0.0800304	+	0.996792i	$0.525502\pi$
$192$	−2.56291	−0.184962
$193$	−0.709587	−0.0510772	−0.0255386	−	0.999674i	$-0.508130\pi$
$193$	−0.709587	−0.0510772	−0.0255386	+	0.999674i	$0.508130\pi$
$194$	16.0762	1.15420
$195$	−0.721925	−0.0516981
$196$	−26.6447	−1.90319
$197$	−18.8174	−1.34069	−0.670343	−	0.742051i	$-0.733853\pi$
$197$	−18.8174	−1.34069	−0.670343	+	0.742051i	$0.733853\pi$
$198$	6.56488	0.466546
$199$	26.4524	1.87516	0.937579	−	0.347771i	$-0.113061\pi$
$199$	26.4524	1.87516	0.937579	+	0.347771i	$0.113061\pi$
$200$	7.11351	0.503001
$201$	0.0568848	0.00401234
$202$	−31.2215	−2.19674
$203$	6.27400	0.440349
$204$	−2.62122	−0.183522
$205$	3.00965	0.210203
$206$	−3.09542	−0.215668
$207$	7.89929	0.549039
$208$	−14.3458	−0.994704
$209$	−1.11230	−0.0769393
$210$	−1.37878	−0.0951450
$211$	23.1967	1.59693	0.798463	−	0.602045i	$-0.205647\pi$
$211$	23.1967	1.59693	0.798463	+	0.602045i	$0.205647\pi$
$212$	42.8898	2.94568
$213$	−1.43882	−0.0985862
$214$	0.639312	0.0437025
$215$	0.990346	0.0675410
$216$	18.6461	1.26870
$217$	−2.77881	−0.188638
$218$	−25.3198	−1.71488
$219$	4.26027	0.287883
$220$	4.28773	0.289079
$221$	−1.95156	−0.131276
$222$	10.0044	0.671449
$223$	5.80341	0.388625	0.194312	−	0.980940i	$-0.437752\pi$
$223$	5.80341	0.388625	0.194312	+	0.980940i	$0.437752\pi$
$224$	−10.6930	−0.714459
$225$	−2.79543	−0.186362
$226$	28.0336	1.86477
$227$	6.42916	0.426719	0.213359	−	0.976974i	$-0.431559\pi$
$227$	6.42916	0.426719	0.213359	+	0.976974i	$0.431559\pi$
$228$	−2.63616	−0.174584
$229$	16.9105	1.11748	0.558739	−	0.829344i	$-0.311286\pi$
$229$	16.9105	1.11748	0.558739	+	0.829344i	$0.311286\pi$
$230$	7.33617	0.483733
$231$	−0.480410	−0.0316087
$232$	−38.0085	−2.49538
$233$	22.3637	1.46510	0.732548	−	0.680716i	$-0.238331\pi$
$233$	22.3637	1.46510	0.732548	+	0.680716i	$0.238331\pi$
$234$	11.5839	0.757263
$235$	9.52848	0.621570
$236$	−52.3826	−3.40981
$237$	−2.87952	−0.187045
$238$	−3.72721	−0.241599
$239$	17.6425	1.14120	0.570598	−	0.821229i	$-0.306711\pi$
$239$	17.6425	1.14120	0.570598	+	0.821229i	$0.306711\pi$
$240$	4.06507	0.262399
$241$	−25.6723	−1.65370	−0.826851	−	0.562422i	$-0.809870\pi$
$241$	−25.6723	−1.65370	−0.826851	+	0.562422i	$0.809870\pi$
$242$	−26.4334	−1.69920
$243$	−11.1205	−0.713379
$244$	1.03035	0.0659615
$245$	5.62122	0.359126
$246$	3.53398	0.225318
$247$	−1.96268	−0.124882
$248$	16.8343	1.06898
$249$	1.83183	0.116088
$250$	−2.59615	−0.164195
$251$	11.1715	0.705141	0.352570	−	0.935785i	$-0.385308\pi$
$251$	11.1715	0.705141	0.352570	+	0.935785i	$0.385308\pi$
$252$	15.5588	0.980114
$253$	2.55615	0.160704
$254$	−39.9490	−2.50663
$255$	0.552997	0.0346300
$256$	−20.4246	−1.27654
$257$	9.73573	0.607298	0.303649	−	0.952784i	$-0.401795\pi$
$257$	9.73573	0.607298	0.303649	+	0.952784i	$0.401795\pi$
$258$	1.16288	0.0723977
$259$	10.0044	0.621641
$260$	7.56580	0.469211
$261$	14.9364	0.924540
$262$	−40.1804	−2.48235
$263$	1.14970	0.0708936	0.0354468	−	0.999372i	$-0.488715\pi$
$263$	1.14970	0.0708936	0.0354468	+	0.999372i	$0.488715\pi$
$264$	2.91037	0.179121
$265$	−9.04844	−0.555842
$266$	−3.74846	−0.229833
$267$	−4.78024	−0.292546
$268$	−0.596155	−0.0364159
$269$	1.90076	0.115892	0.0579458	−	0.998320i	$-0.481545\pi$
$269$	1.90076	0.115892	0.0579458	+	0.998320i	$0.481545\pi$
$270$	−6.80509	−0.414144
$271$	−13.4412	−0.816498	−0.408249	−	0.912871i	$-0.633860\pi$
$271$	−13.4412	−0.816498	−0.408249	+	0.912871i	$0.633860\pi$
$272$	10.9890	0.666303
$273$	−0.847696	−0.0513049
$274$	−23.4943	−1.41934
$275$	−0.904581	−0.0545483
$276$	6.05810	0.364655
$277$	−2.23177	−0.134094	−0.0670469	−	0.997750i	$-0.521358\pi$
$277$	−2.23177	−0.134094	−0.0670469	+	0.997750i	$0.521358\pi$
$278$	−0.786994	−0.0472007
$279$	−6.61546	−0.396057
$280$	8.35280	0.499175
$281$	18.4789	1.10236	0.551180	−	0.834387i	$-0.314178\pi$
$281$	18.4789	1.10236	0.551180	+	0.834387i	$0.314178\pi$
$282$	11.1885	0.666265
$283$	30.6493	1.82191	0.910956	−	0.412504i	$-0.135346\pi$
$283$	30.6493	1.82191	0.910956	+	0.412504i	$0.135346\pi$
$284$	15.0789	0.894767
$285$	0.556150	0.0329435
$286$	3.74846	0.221651
$287$	3.53398	0.208604
$288$	−25.4567	−1.50005
$289$	−15.5051	−0.912065
$290$	13.8716	0.814570
$291$	−2.80072	−0.164181
$292$	−44.6478	−2.61282
$293$	4.29617	0.250985	0.125492	−	0.992095i	$-0.459949\pi$
$293$	4.29617	0.250985	0.125492	+	0.992095i	$0.459949\pi$
$294$	6.60052	0.384950
$295$	11.0511	0.643422
$296$	−60.6074	−3.52274
$297$	−2.37110	−0.137585
$298$	−7.33496	−0.424903
$299$	4.51039	0.260843
$300$	−2.14386	−0.123776
$301$	1.16288	0.0670273
$302$	23.3974	1.34637
$303$	5.43927	0.312478
$304$	11.0516	0.633853
$305$	−0.217373	−0.0124467
$306$	−8.87331	−0.507253
$307$	−31.6878	−1.80852	−0.904258	−	0.426987i	$-0.859575\pi$
$307$	−31.6878	−1.80852	−0.904258	+	0.426987i	$0.859575\pi$
$308$	5.03472	0.286880
$309$	0.539270	0.0306780
$310$	−6.14386	−0.348948
$311$	2.64942	0.150235	0.0751174	−	0.997175i	$-0.476067\pi$
$311$	2.64942	0.150235	0.0751174	+	0.997175i	$0.476067\pi$
$312$	5.13542	0.290736
$313$	2.59729	0.146807	0.0734037	−	0.997302i	$-0.476614\pi$
$313$	2.59729	0.146807	0.0734037	+	0.997302i	$0.476614\pi$
$314$	27.5912	1.55706
$315$	−3.28244	−0.184945
$316$	30.1774	1.69761
$317$	−2.56727	−0.144192	−0.0720962	−	0.997398i	$-0.522969\pi$
$317$	−2.56727	−0.144192	−0.0720962	+	0.997398i	$0.522969\pi$
$318$	−10.6248	−0.595811
$319$	4.83330	0.270613
$320$	−5.66651	−0.316768
$321$	−0.111378	−0.00621652
$322$	8.61425	0.480053
$323$	1.50342	0.0836525
$324$	34.1317	1.89620
$325$	−1.59615	−0.0885387
$326$	0.536118	0.0296928
$327$	4.41111	0.243935
$328$	−21.4092	−1.18213
$329$	11.1885	0.616842
$330$	−1.06217	−0.0584707
$331$	11.5907	0.637080	0.318540	−	0.947909i	$-0.396807\pi$
$331$	11.5907	0.637080	0.318540	+	0.947909i	$0.396807\pi$
$332$	−19.1977	−1.05361
$333$	23.8172	1.30518
$334$	19.2974	1.05591
$335$	0.125771	0.00687158
$336$	4.77327	0.260403
$337$	−18.8186	−1.02512	−0.512558	−	0.858652i	$-0.671302\pi$
$337$	−18.8186	−1.02512	−0.512558	+	0.858652i	$0.671302\pi$
$338$	−27.1358	−1.47599
$339$	−4.88388	−0.265256
$340$	−5.79543	−0.314302
$341$	−2.14071	−0.115926
$342$	−8.92389	−0.482549
$343$	14.8200	0.800206
$344$	−7.04484	−0.379832
$345$	−1.27807	−0.0688092
$346$	55.3233	2.97420
$347$	−15.3441	−0.823717	−0.411858	−	0.911248i	$-0.635120\pi$
$347$	−15.3441	−0.823717	−0.411858	+	0.911248i	$0.635120\pi$
$348$	11.4550	0.614051
$349$	28.5259	1.52696	0.763478	−	0.645834i	$-0.223490\pi$
$349$	28.5259	1.52696	0.763478	+	0.645834i	$0.223490\pi$
$350$	−3.04844	−0.162946
$351$	−4.18387	−0.223318
$352$	−8.23760	−0.439066
$353$	18.0353	0.959920	0.479960	−	0.877290i	$-0.340651\pi$
$353$	18.0353	0.959920	0.479960	+	0.877290i	$0.340651\pi$
$354$	12.9764	0.689688
$355$	−3.18118	−0.168840
$356$	50.0971	2.65514
$357$	0.649338	0.0343666
$358$	26.1092	1.37992
$359$	−8.96965	−0.473400	−0.236700	−	0.971583i	$-0.576066\pi$
$359$	−8.96965	−0.473400	−0.236700	+	0.971583i	$0.576066\pi$
$360$	19.8854	1.04805
$361$	−17.4880	−0.920422
$362$	−49.6397	−2.60901
$363$	4.60510	0.241705
$364$	8.88388	0.465642
$365$	9.41934	0.493031
$366$	−0.255242	−0.0133417
$367$	10.8470	0.566210	0.283105	−	0.959089i	$-0.408635\pi$
$367$	10.8470	0.566210	0.283105	+	0.959089i	$0.408635\pi$
$368$	−25.3974	−1.32393
$369$	8.41329	0.437978
$370$	22.1194	1.14993
$371$	−10.6248	−0.551613
$372$	−5.07351	−0.263049
$373$	−16.8259	−0.871210	−0.435605	−	0.900138i	$-0.643466\pi$
$373$	−16.8259	−0.871210	−0.435605	+	0.900138i	$0.643466\pi$
$374$	−2.87133	−0.148473
$375$	0.452290	0.0233562
$376$	−67.7810	−3.49554
$377$	8.52848	0.439239
$378$	−7.99064	−0.410994
$379$	20.9415	1.07569	0.537847	−	0.843043i	$-0.319238\pi$
$379$	20.9415	1.07569	0.537847	+	0.843043i	$0.319238\pi$
$380$	−5.82847	−0.298994
$381$	6.95974	0.356558
$382$	−5.74292	−0.293833
$383$	15.2974	0.781660	0.390830	−	0.920463i	$-0.372188\pi$
$383$	15.2974	0.781660	0.390830	+	0.920463i	$0.372188\pi$
$384$	1.58390	0.0808279
$385$	−1.06217	−0.0541333
$386$	−1.84220	−0.0937653
$387$	2.76845	0.140728
$388$	29.3517	1.49011
$389$	−6.50984	−0.330062	−0.165031	−	0.986288i	$-0.552772\pi$
$389$	−6.50984	−0.330062	−0.165031	+	0.986288i	$0.552772\pi$
$390$	−1.87423	−0.0949053
$391$	−3.45497	−0.174726
$392$	−39.9866	−2.01963
$393$	7.00004	0.353106
$394$	−48.8529	−2.46118
$395$	−6.36652	−0.320335
$396$	11.9861	0.602322
$397$	15.5893	0.782403	0.391201	−	0.920305i	$-0.372060\pi$
$397$	15.5893	0.782403	0.391201	+	0.920305i	$0.372060\pi$
$398$	68.6744	3.44234
$399$	0.653039	0.0326929
$400$	8.98774	0.449387
$401$	8.82847	0.440873	0.220436	−	0.975401i	$-0.429252\pi$
$401$	8.82847	0.440873	0.220436	+	0.975401i	$0.429252\pi$
$402$	0.147682	0.00736569
$403$	−3.77734	−0.188163
$404$	−57.0038	−2.83604
$405$	−7.20075	−0.357808
$406$	16.2883	0.808374
$407$	7.70707	0.382025
$408$	−3.93375	−0.194750
$409$	20.7329	1.02517	0.512587	−	0.858635i	$-0.328687\pi$
$409$	20.7329	1.02517	0.512587	+	0.858635i	$0.328687\pi$
$410$	7.81353	0.385883
$411$	4.09307	0.201896
$412$	−5.65157	−0.278433
$413$	12.9764	0.638527
$414$	20.5078	1.00790
$415$	4.05013	0.198813
$416$	−14.5355	−0.712659
$417$	0.137106	0.00671413
$418$	−2.88770	−0.141242
$419$	−16.5755	−0.809764	−0.404882	−	0.914369i	$-0.632687\pi$
$419$	−16.5755	−0.809764	−0.404882	+	0.914369i	$0.632687\pi$
$420$	−2.51736	−0.122835
$421$	−4.19063	−0.204239	−0.102119	−	0.994772i	$-0.532562\pi$
$421$	−4.19063	−0.204239	−0.102119	+	0.994772i	$0.532562\pi$
$422$	60.2222	2.93157
$423$	26.6362	1.29510
$424$	64.3662	3.12590
$425$	1.22266	0.0593077
$426$	−3.73540	−0.180981
$427$	−0.255242	−0.0123520
$428$	1.16725	0.0564210
$429$	−0.653039	−0.0315290
$430$	2.57109	0.123989
$431$	7.76240	0.373902	0.186951	−	0.982369i	$-0.440140\pi$
$431$	7.76240	0.373902	0.186951	+	0.982369i	$0.440140\pi$
$432$	23.5588	1.13347
$433$	−4.56727	−0.219489	−0.109745	−	0.993960i	$-0.535003\pi$
$433$	−4.56727	−0.219489	−0.109745	+	0.993960i	$0.535003\pi$
$434$	−7.21422	−0.346294
$435$	−2.41665	−0.115870
$436$	−46.2286	−2.21395
$437$	−3.47467	−0.166216
$438$	11.0603	0.528483
$439$	−20.5919	−0.982797	−0.491398	−	0.870935i	$-0.663514\pi$
$439$	−20.5919	−0.982797	−0.491398	+	0.870935i	$0.663514\pi$
$440$	6.43475	0.306764
$441$	15.7137	0.748273
$442$	−5.06654	−0.240991
$443$	−30.7294	−1.46000	−0.730000	−	0.683447i	$-0.760480\pi$
$443$	−30.7294	−1.46000	−0.730000	+	0.683447i	$0.760480\pi$
$444$	18.2658	0.866857
$445$	−10.5690	−0.501017
$446$	15.0665	0.713421
$447$	1.27786	0.0604409
$448$	−6.65370	−0.314358
$449$	−8.15953	−0.385072	−0.192536	−	0.981290i	$-0.561671\pi$
$449$	−8.15953	−0.385072	−0.192536	+	0.981290i	$0.561671\pi$
$450$	−7.25738	−0.342116
$451$	2.72247	0.128196
$452$	51.1833	2.40746
$453$	−4.07619	−0.191516
$454$	16.6911	0.783352
$455$	−1.87423	−0.0878652
$456$	−3.95618	−0.185265
$457$	−21.6435	−1.01244	−0.506219	−	0.862405i	$-0.668957\pi$
$457$	−21.6435	−1.01244	−0.506219	+	0.862405i	$0.668957\pi$
$458$	43.9023	2.05142
$459$	3.20486	0.149590
$460$	13.3943	0.624511
$461$	−11.5152	−0.536317	−0.268159	−	0.963375i	$-0.586415\pi$
$461$	−11.5152	−0.536317	−0.268159	+	0.963375i	$0.586415\pi$
$462$	−1.24722	−0.0580259
$463$	−30.6684	−1.42528	−0.712642	−	0.701528i	$-0.752502\pi$
$463$	−30.6684	−1.42528	−0.712642	+	0.701528i	$0.752502\pi$
$464$	−48.0228	−2.22940
$465$	1.07036	0.0496366
$466$	58.0597	2.68956
$467$	−23.2541	−1.07607	−0.538036	−	0.842922i	$-0.680834\pi$
$467$	−23.2541	−1.07607	−0.538036	+	0.842922i	$0.680834\pi$
$468$	21.1497	0.977645
$469$	0.147682	0.00681931
$470$	24.7374	1.14105
$471$	−4.80681	−0.221486
$472$	−78.6124	−3.61843
$473$	0.895848	0.0411911
$474$	−7.47567	−0.343369
$475$	1.22963	0.0564193
$476$	−6.80509	−0.311911
$477$	−25.2943	−1.15815
$478$	45.8026	2.09496
$479$	29.5772	1.35142	0.675709	−	0.737169i	$-0.263838\pi$
$479$	29.5772	1.35142	0.675709	+	0.737169i	$0.263838\pi$
$480$	4.11880	0.187997
$481$	13.5993	0.620075
$482$	−66.6494	−3.03580
$483$	−1.50074	−0.0682858
$484$	−48.2616	−2.19371
$485$	−6.19231	−0.281178
$486$	−28.8705	−1.30959
$487$	−27.1780	−1.23155	−0.615776	−	0.787921i	$-0.711158\pi$
$487$	−27.1780	−1.23155	−0.615776	+	0.787921i	$0.711158\pi$
$488$	1.54628	0.0699970
$489$	−0.0934000	−0.00422369
$490$	14.5936	0.659269
$491$	−30.8639	−1.39287	−0.696434	−	0.717620i	$-0.745231\pi$
$491$	−30.8639	−1.39287	−0.696434	+	0.717620i	$0.745231\pi$
$492$	6.45229	0.290892
$493$	−6.53285	−0.294225
$494$	−5.09542	−0.229254
$495$	−2.52869	−0.113656
$496$	21.2697	0.955038
$497$	−3.73540	−0.167555
$498$	4.75572	0.213109
$499$	−24.5066	−1.09706	−0.548532	−	0.836129i	$-0.684813\pi$
$499$	−24.5066	−1.09706	−0.548532	+	0.836129i	$0.684813\pi$
$500$	−4.74002	−0.211980
$501$	−3.36190	−0.150199
$502$	29.0030	1.29447
$503$	9.54846	0.425745	0.212872	−	0.977080i	$-0.431718\pi$
$503$	9.54846	0.425745	0.212872	+	0.977080i	$0.431718\pi$
$504$	23.3497	1.04008
$505$	12.0261	0.535153
$506$	6.63616	0.295013
$507$	4.72747	0.209954
$508$	−72.9383	−3.23612
$509$	−1.13413	−0.0502694	−0.0251347	−	0.999684i	$-0.508001\pi$
$509$	−1.13413	−0.0502694	−0.0251347	+	0.999684i	$0.508001\pi$
$510$	1.43567	0.0635724
$511$	11.0603	0.489280
$512$	−46.0216	−2.03389
$513$	3.22313	0.142305
$514$	25.2755	1.11485
$515$	1.19231	0.0525394
$516$	2.12317	0.0934672
$517$	8.61928	0.379076
$518$	25.9729	1.14118
$519$	−9.63818	−0.423069
$520$	11.3543	0.497918
$521$	27.0866	1.18668	0.593342	−	0.804950i	$-0.297808\pi$
$521$	27.0866	1.18668	0.593342	+	0.804950i	$0.297808\pi$
$522$	38.7772	1.69723
$523$	6.02636	0.263514	0.131757	−	0.991282i	$-0.457938\pi$
$523$	6.02636	0.263514	0.131757	+	0.991282i	$0.457938\pi$
$524$	−73.3607	−3.20478
$525$	0.531086	0.0231785
$526$	2.98480	0.130144
$527$	2.89346	0.126041
$528$	3.67718	0.160029
$529$	−15.0149	−0.652824
$530$	−23.4912	−1.02039
$531$	30.8927	1.34063
$532$	−6.84388	−0.296720
$533$	4.80387	0.208079
$534$	−12.4102	−0.537043
$535$	−0.246253	−0.0106465
$536$	−0.894670	−0.0386439
$537$	−4.54863	−0.196288
$538$	4.93468	0.212749
$539$	5.08484	0.219020
$540$	−12.4246	−0.534671
$541$	9.54544	0.410391	0.205195	−	0.978721i	$-0.434217\pi$
$541$	9.54544	0.410391	0.205195	+	0.978721i	$0.434217\pi$
$542$	−34.8956	−1.49889
$543$	8.64801	0.371122
$544$	11.1342	0.477375
$545$	9.75283	0.417765
$546$	−2.20075	−0.0941834
$547$	25.5774	1.09361	0.546805	−	0.837260i	$-0.315844\pi$
$547$	25.5774	1.09361	0.546805	+	0.837260i	$0.315844\pi$
$548$	−42.8956	−1.83241
$549$	−0.607651	−0.0259339
$550$	−2.34843	−0.100137
$551$	−6.57009	−0.279895
$552$	9.09160	0.386964
$553$	−7.47567	−0.317898
$554$	−5.79401	−0.246164
$555$	−3.85353	−0.163573
$556$	−1.43688	−0.0609373
$557$	−1.72802	−0.0732185	−0.0366092	−	0.999330i	$-0.511656\pi$
$557$	−1.72802	−0.0732185	−0.0366092	+	0.999330i	$0.511656\pi$
$558$	−17.1748	−0.727066
$559$	1.58075	0.0668584
$560$	10.5535	0.445969
$561$	0.500231	0.0211198
$562$	47.9741	2.02367
$563$	−29.4710	−1.24206	−0.621028	−	0.783789i	$-0.713285\pi$
$563$	−29.4710	−1.24206	−0.621028	+	0.783789i	$0.713285\pi$
$564$	20.4278	0.860165
$565$	−10.7981	−0.454280
$566$	79.5703	3.34459
$567$	−8.45523	−0.355086
$568$	22.6294	0.949509
$569$	−27.5541	−1.15513	−0.577564	−	0.816345i	$-0.695997\pi$
$569$	−27.5541	−1.15513	−0.577564	+	0.816345i	$0.695997\pi$
$570$	1.44385	0.0604762
$571$	30.1035	1.25979	0.629895	−	0.776680i	$-0.283098\pi$
$571$	30.1035	1.25979	0.629895	+	0.776680i	$0.283098\pi$
$572$	6.84388	0.286157
$573$	1.00050	0.0417967
$574$	9.17476	0.382947
$575$	−2.82578	−0.117843
$576$	−15.8404	−0.660015
$577$	11.1776	0.465331	0.232665	−	0.972557i	$-0.425255\pi$
$577$	11.1776	0.465331	0.232665	+	0.972557i	$0.425255\pi$
$578$	−40.2536	−1.67433
$579$	0.320939	0.0133378
$580$	25.3266	1.05163
$581$	4.75572	0.197301
$582$	−7.27111	−0.301397
$583$	−8.18505	−0.338990
$584$	−67.0046	−2.77267
$585$	−4.46194	−0.184479
$586$	11.1535	0.460748
$587$	−6.26603	−0.258627	−0.129313	−	0.991604i	$-0.541277\pi$
$587$	−6.26603	−0.258627	−0.129313	+	0.991604i	$0.541277\pi$
$588$	12.0511	0.496980
$589$	2.90995	0.119902
$590$	28.6904	1.18117
$591$	8.51094	0.350093
$592$	−76.5760	−3.14725
$593$	32.8762	1.35007	0.675033	−	0.737788i	$-0.264129\pi$
$593$	32.8762	1.35007	0.675033	+	0.737788i	$0.264129\pi$
$594$	−6.15575	−0.252573
$595$	1.43567	0.0588566
$596$	−13.3921	−0.548560
$597$	−11.9641	−0.489660
$598$	11.7097	0.478844
$599$	−14.6940	−0.600382	−0.300191	−	0.953879i	$-0.597051\pi$
$599$	−14.6940	−0.600382	−0.300191	+	0.953879i	$0.597051\pi$
$600$	−3.21737	−0.131349
$601$	12.9725	0.529161	0.264581	−	0.964364i	$-0.414766\pi$
$601$	12.9725	0.529161	0.264581	+	0.964364i	$0.414766\pi$
$602$	3.01902	0.123046
$603$	0.351583	0.0143176
$604$	42.7187	1.73820
$605$	10.1817	0.413946
$606$	14.1212	0.573634
$607$	16.7592	0.680237	0.340118	−	0.940383i	$-0.389533\pi$
$607$	16.7592	0.680237	0.340118	+	0.940383i	$0.389533\pi$
$608$	11.1977	0.454126
$609$	−2.83767	−0.114988
$610$	−0.564333	−0.0228492
$611$	15.2089	0.615288
$612$	−16.2007	−0.654876
$613$	−13.2791	−0.536338	−0.268169	−	0.963372i	$-0.586419\pi$
$613$	−13.2791	−0.536338	−0.268169	+	0.963372i	$0.586419\pi$
$614$	−82.2663	−3.32000
$615$	−1.36124	−0.0548904
$616$	7.55578	0.304431
$617$	−10.4731	−0.421630	−0.210815	−	0.977526i	$-0.567612\pi$
$617$	−10.4731	−0.421630	−0.210815	+	0.977526i	$0.567612\pi$
$618$	1.40003	0.0563174
$619$	−35.3334	−1.42017	−0.710085	−	0.704116i	$-0.751343\pi$
$619$	−35.3334	−1.42017	−0.710085	+	0.704116i	$0.751343\pi$
$620$	−11.2174	−0.450501
$621$	−7.40700	−0.297233
$622$	6.87830	0.275795
$623$	−12.4102	−0.497205
$624$	6.48848	0.259747
$625$	1.00000	0.0400000
$626$	6.74296	0.269503
$627$	0.503082	0.0200912
$628$	50.3756	2.01021
$629$	−10.4171	−0.415358
$630$	−8.52173	−0.339514
$631$	−42.3389	−1.68549	−0.842743	−	0.538316i	$-0.819061\pi$
$631$	−42.3389	−1.68549	−0.842743	+	0.538316i	$0.819061\pi$
$632$	45.2884	1.80147
$633$	−10.4916	−0.417005
$634$	−6.66504	−0.264703
$635$	15.3878	0.610645
$636$	−19.3986	−0.769206
$637$	8.97233	0.355497
$638$	12.5480	0.496780
$639$	−8.89279	−0.351793
$640$	3.50195	0.138427
$641$	−36.3728	−1.43664	−0.718320	−	0.695713i	$-0.755089\pi$
$641$	−36.3728	−1.43664	−0.718320	+	0.695713i	$0.755089\pi$
$642$	−0.289155	−0.0114120
$643$	11.1027	0.437849	0.218924	−	0.975742i	$-0.429745\pi$
$643$	11.1027	0.437849	0.218924	+	0.975742i	$0.429745\pi$
$644$	15.7278	0.619761
$645$	−0.447924	−0.0176370
$646$	3.90311	0.153566
$647$	14.5536	0.572162	0.286081	−	0.958205i	$-0.407647\pi$
$647$	14.5536	0.572162	0.286081	+	0.958205i	$0.407647\pi$
$648$	51.2226	2.01221
$649$	9.99664	0.392402
$650$	−4.14386	−0.162536
$651$	1.25683	0.0492590
$652$	0.978835	0.0383342
$653$	−40.4031	−1.58109	−0.790547	−	0.612401i	$-0.790204\pi$
$653$	−40.4031	−1.58109	−0.790547	+	0.612401i	$0.790204\pi$
$654$	11.4519	0.447805
$655$	15.4769	0.604732
$656$	−27.0500	−1.05612
$657$	26.3311	1.02728
$658$	29.0471	1.13237
$659$	−17.9447	−0.699025	−0.349512	−	0.936932i	$-0.613653\pi$
$659$	−17.9447	−0.699025	−0.349512	+	0.936932i	$0.613653\pi$
$660$	−1.93930	−0.0754871
$661$	3.43856	0.133745	0.0668723	−	0.997762i	$-0.478698\pi$
$661$	3.43856	0.133745	0.0668723	+	0.997762i	$0.478698\pi$
$662$	30.0911	1.16953
$663$	0.882669	0.0342800
$664$	−28.8106	−1.11807
$665$	1.44385	0.0559901
$666$	61.8332	2.39599
$667$	15.0986	0.584619
$668$	35.2329	1.36320
$669$	−2.62482	−0.101482
$670$	0.326520	0.0126146
$671$	−0.196631	−0.00759086
$672$	4.83636	0.186567
$673$	24.0825	0.928312	0.464156	−	0.885754i	$-0.346358\pi$
$673$	24.0825	0.928312	0.464156	+	0.885754i	$0.346358\pi$
$674$	−48.8561	−1.88187
$675$	2.62122	0.100891
$676$	−49.5441	−1.90554
$677$	−2.61480	−0.100495	−0.0502474	−	0.998737i	$-0.516001\pi$
$677$	−2.61480	−0.100495	−0.0502474	+	0.998737i	$0.516001\pi$
$678$	−12.6793	−0.486946
$679$	−7.27111	−0.279039
$680$	−8.69741	−0.333530
$681$	−2.90785	−0.111429
$682$	−5.55762	−0.212812
$683$	27.4169	1.04908	0.524540	−	0.851386i	$-0.324237\pi$
$683$	27.4169	1.04908	0.524540	+	0.851386i	$0.324237\pi$
$684$	−16.2931	−0.622982
$685$	9.04966	0.345770
$686$	38.4751	1.46899
$687$	−7.64845	−0.291807
$688$	−8.90097	−0.339346
$689$	−14.4427	−0.550224
$690$	−3.31808	−0.126317
$691$	4.15666	0.158127	0.0790633	−	0.996870i	$-0.474807\pi$
$691$	4.15666	0.158127	0.0790633	+	0.996870i	$0.474807\pi$
$692$	101.008	3.83977
$693$	−2.96923	−0.112792
$694$	−39.8358	−1.51215
$695$	0.303138	0.0114987
$696$	17.1909	0.651619
$697$	−3.67978	−0.139382
$698$	74.0576	2.80312
$699$	−10.1149	−0.382580
$700$	−5.56580	−0.210368
$701$	25.3609	0.957866	0.478933	−	0.877851i	$-0.341024\pi$
$701$	25.3609	0.957866	0.478933	+	0.877851i	$0.341024\pi$
$702$	−10.8620	−0.409959
$703$	−10.4765	−0.395129
$704$	−5.12582	−0.193186
$705$	−4.30964	−0.162310
$706$	46.8223	1.76218
$707$	14.1212	0.531082
$708$	23.6921	0.890405
$709$	23.6181	0.886998	0.443499	−	0.896275i	$-0.353737\pi$
$709$	23.6181	0.886998	0.443499	+	0.896275i	$0.353737\pi$
$710$	−8.25885	−0.309949
$711$	−17.7972	−0.667447
$712$	75.1824	2.81758
$713$	−6.68729	−0.250441
$714$	1.68578	0.0630888
$715$	−1.44385	−0.0539969
$716$	47.6698	1.78151
$717$	−7.97951	−0.298000
$718$	−23.2866	−0.869048
$719$	−0.0337594	−0.00125901	−0.000629507	−	1.00000i	$-0.500200\pi$
$719$	−0.0337594	−0.00125901	−0.000629507		1.00000i	$0.500200\pi$
$720$	25.1246	0.936340
$721$	1.40003	0.0521398
$722$	−45.4016	−1.68967
$723$	11.6114	0.431831
$724$	−90.6315	−3.36829
$725$	−5.34314	−0.198439
$726$	11.9555	0.443712
$727$	−36.1204	−1.33963	−0.669815	−	0.742528i	$-0.733627\pi$
$727$	−36.1204	−1.33963	−0.669815	+	0.742528i	$0.733627\pi$
$728$	13.3324	0.494130
$729$	−16.5726	−0.613799
$730$	24.4541	0.905085
$731$	−1.21086	−0.0447852
$732$	−0.466018	−0.0172245
$733$	37.4642	1.38377	0.691885	−	0.722007i	$-0.256780\pi$
$733$	37.4642	1.38377	0.691885	+	0.722007i	$0.256780\pi$
$734$	28.1606	1.03943
$735$	−2.54242	−0.0937787
$736$	−25.7331	−0.948536
$737$	0.113770	0.00419076
$738$	21.8422	0.804022
$739$	15.5868	0.573371	0.286686	−	0.958025i	$-0.407447\pi$
$739$	15.5868	0.573371	0.286686	+	0.958025i	$0.407447\pi$
$740$	40.3852	1.48459
$741$	0.887701	0.0326105
$742$	−27.5837	−1.01263
$743$	−6.63688	−0.243484	−0.121742	−	0.992562i	$-0.538848\pi$
$743$	−6.63688	−0.243484	−0.121742	+	0.992562i	$0.538848\pi$
$744$	−7.61399	−0.279143
$745$	2.82532	0.103512
$746$	−43.6826	−1.59933
$747$	11.3219	0.414245
$748$	−5.24244	−0.191682
$749$	−0.289155	−0.0105655
$750$	1.17422	0.0428763
$751$	9.63335	0.351526	0.175763	−	0.984433i	$-0.443761\pi$
$751$	9.63335	0.351526	0.175763	+	0.984433i	$0.443761\pi$
$752$	−85.6396	−3.12295
$753$	−5.05277	−0.184133
$754$	22.1413	0.806337
$755$	−9.01234	−0.327993
$756$	−14.5892	−0.530604
$757$	2.90728	0.105667	0.0528334	−	0.998603i	$-0.483175\pi$
$757$	2.90728	0.105667	0.0528334	+	0.998603i	$0.483175\pi$
$758$	54.3674	1.97471
$759$	−1.15612	−0.0419646
$760$	−8.74699	−0.317287
$761$	14.0584	0.509618	0.254809	−	0.966991i	$-0.417987\pi$
$761$	14.0584	0.509618	0.254809	+	0.966991i	$0.417987\pi$
$762$	18.0686	0.654555
$763$	11.4519	0.414587
$764$	−10.4853	−0.379346
$765$	3.41787	0.123573
$766$	39.7144	1.43494
$767$	17.6393	0.636919
$768$	9.23786	0.333342
$769$	−11.5598	−0.416857	−0.208428	−	0.978038i	$-0.566835\pi$
$769$	−11.5598	−0.416857	−0.208428	+	0.978038i	$0.566835\pi$
$770$	−2.75756	−0.0993757
$771$	−4.40338	−0.158584
$772$	−3.36345	−0.121053
$773$	20.7860	0.747620	0.373810	−	0.927505i	$-0.378051\pi$
$773$	20.7860	0.747620	0.373810	+	0.927505i	$0.378051\pi$
$774$	7.18731	0.258343
$775$	2.36652	0.0850081
$776$	44.0491	1.58127
$777$	−4.52488	−0.162329
$778$	−16.9006	−0.605914
$779$	−3.70076	−0.132594
$780$	−3.42194	−0.122525
$781$	−2.87764	−0.102970
$782$	−8.96965	−0.320754
$783$	−14.0055	−0.500517
$784$	−50.5221	−1.80436
$785$	−10.6277	−0.379320
$786$	18.1732	0.648217
$787$	9.07355	0.323437	0.161719	−	0.986837i	$-0.448296\pi$
$787$	9.07355	0.323437	0.161719	+	0.986837i	$0.448296\pi$
$788$	−89.1950	−3.17744
$789$	−0.519999	−0.0185124
$790$	−16.5285	−0.588057
$791$	−12.6793	−0.450825
$792$	17.9879	0.639172
$793$	−0.346961	−0.0123209
$794$	40.4721	1.43630
$795$	4.09252	0.145147
$796$	125.385	4.44414
$797$	43.4476	1.53899	0.769496	−	0.638652i	$-0.220508\pi$
$797$	43.4476	1.53899	0.769496	+	0.638652i	$0.220508\pi$
$798$	1.69539	0.0600162
$799$	−11.6501	−0.412151
$800$	9.10654	0.321965
$801$	−29.5448	−1.04391
$802$	22.9201	0.809336
$803$	8.52055	0.300684
$804$	0.269635	0.00950929
$805$	−3.31808	−0.116947
$806$	−9.80656	−0.345421
$807$	−0.859697	−0.0302628
$808$	−85.5476	−3.00955
$809$	−33.3100	−1.17112	−0.585558	−	0.810630i	$-0.699125\pi$
$809$	−33.3100	−1.17112	−0.585558	+	0.810630i	$0.699125\pi$
$810$	−18.6943	−0.656849
$811$	−21.6565	−0.760462	−0.380231	−	0.924892i	$-0.624156\pi$
$811$	−21.6565	−0.760462	−0.380231	+	0.924892i	$0.624156\pi$
$812$	29.7389	1.04363
$813$	6.07935	0.213212
$814$	20.0087	0.701306
$815$	−0.206505	−0.00723354
$816$	−4.97020	−0.173992
$817$	−1.21776	−0.0426040
$818$	53.8258	1.88197
$819$	−5.23928	−0.183075
$820$	14.2658	0.498184
$821$	20.6996	0.722422	0.361211	−	0.932484i	$-0.382363\pi$
$821$	20.6996	0.722422	0.361211	+	0.932484i	$0.382363\pi$
$822$	10.6262	0.370633
$823$	0.177112	0.00617372	0.00308686	−	0.999995i	$-0.499017\pi$
$823$	0.177112	0.00617372	0.00308686	+	0.999995i	$0.499017\pi$
$824$	−8.48151	−0.295467
$825$	0.409133	0.0142442
$826$	33.6888	1.17218
$827$	−10.6057	−0.368796	−0.184398	−	0.982852i	$-0.559033\pi$
$827$	−10.6057	−0.368796	−0.184398	+	0.982852i	$0.559033\pi$
$828$	37.4428	1.30123
$829$	−7.04429	−0.244658	−0.122329	−	0.992490i	$-0.539036\pi$
$829$	−7.04429	−0.244658	−0.122329	+	0.992490i	$0.539036\pi$
$830$	10.5148	0.364972
$831$	1.00941	0.0350159
$832$	−9.04463	−0.313566
$833$	−6.87284	−0.238130
$834$	0.355950	0.0123255
$835$	−7.43306	−0.257232
$836$	−5.27232	−0.182347
$837$	6.20318	0.214413
$838$	−43.0325	−1.48653
$839$	1.90848	0.0658880	0.0329440	−	0.999457i	$-0.489512\pi$
$839$	1.90848	0.0658880	0.0329440	+	0.999457i	$0.489512\pi$
$840$	−3.77789	−0.130350
$841$	−0.450820	−0.0155455
$842$	−10.8795	−0.374933
$843$	−8.35783	−0.287859
$844$	109.953	3.78473
$845$	10.4523	0.359570
$846$	69.1518	2.37749
$847$	11.9555	0.410798
$848$	81.3251	2.79272
$849$	−13.8624	−0.475756
$850$	3.17422	0.108875
$851$	24.0758	0.825308
$852$	−6.82003	−0.233650
$853$	24.4557	0.837348	0.418674	−	0.908137i	$-0.362495\pi$
$853$	24.4557	0.837348	0.418674	+	0.908137i	$0.362495\pi$
$854$	−0.662649	−0.0226754
$855$	3.43735	0.117555
$856$	1.75173	0.0598728
$857$	37.4047	1.27772	0.638861	−	0.769322i	$-0.279406\pi$
$857$	37.4047	1.27772	0.638861	+	0.769322i	$0.279406\pi$
$858$	−1.69539	−0.0578797
$859$	−21.0744	−0.719050	−0.359525	−	0.933135i	$-0.617061\pi$
$859$	−21.0744	−0.719050	−0.359525	+	0.933135i	$0.617061\pi$
$860$	4.69426	0.160073
$861$	−1.59839	−0.0544728
$862$	20.1524	0.686393
$863$	−33.2821	−1.13293	−0.566467	−	0.824084i	$-0.691690\pi$
$863$	−33.2821	−1.13293	−0.566467	+	0.824084i	$0.691690\pi$
$864$	23.8702	0.812082
$865$	−21.3097	−0.724552
$866$	−11.8573	−0.402929
$867$	7.01281	0.238167
$868$	−13.1716	−0.447074
$869$	−5.75903	−0.195362
$870$	−6.27400	−0.212709
$871$	0.200749	0.00680213
$872$	−69.3769	−2.34940
$873$	−17.3102	−0.585861
$874$	−9.02078	−0.305132
$875$	1.17422	0.0396957
$876$	20.1938	0.682285
$877$	18.9012	0.638248	0.319124	−	0.947713i	$-0.396611\pi$
$877$	18.9012	0.638248	0.319124	+	0.947713i	$0.396611\pi$
$878$	−53.4597	−1.80418
$879$	−1.94312	−0.0655396
$880$	8.13014	0.274067
$881$	−57.0309	−1.92142	−0.960709	−	0.277557i	$-0.910475\pi$
$881$	−57.0309	−1.92142	−0.960709	+	0.277557i	$0.910475\pi$
$882$	40.7953	1.37365
$883$	−2.19873	−0.0739931	−0.0369966	−	0.999315i	$-0.511779\pi$
$883$	−2.19873	−0.0739931	−0.0369966	+	0.999315i	$0.511779\pi$
$884$	−9.25041	−0.311125
$885$	−4.99832	−0.168017
$886$	−79.7784	−2.68021
$887$	47.3960	1.59140	0.795702	−	0.605689i	$-0.207102\pi$
$887$	47.3960	1.59140	0.795702	+	0.605689i	$0.207102\pi$
$888$	27.4122	0.919892
$889$	18.0686	0.606000
$890$	−27.4386	−0.919745
$891$	−6.51366	−0.218216
$892$	27.5083	0.921044
$893$	−11.7165	−0.392078
$894$	3.31753	0.110955
$895$	−10.0569	−0.336165
$896$	4.11204	0.137374
$897$	−2.04001	−0.0681138
$898$	−21.1834	−0.706899
$899$	−12.6447	−0.421724
$900$	−13.2504	−0.441680
$901$	11.0632	0.368568
$902$	7.06796	0.235337
$903$	−0.525959	−0.0175028
$904$	76.8126	2.55475
$905$	19.1205	0.635586
$906$	−10.5824	−0.351578
$907$	−15.0409	−0.499426	−0.249713	−	0.968320i	$-0.580336\pi$
$907$	−15.0409	−0.499426	−0.249713	+	0.968320i	$0.580336\pi$
$908$	30.4744	1.01133
$909$	33.6181	1.11504
$910$	−4.86579	−0.161299
$911$	−22.1298	−0.733193	−0.366597	−	0.930380i	$-0.619477\pi$
$911$	−22.1298	−0.733193	−0.366597	+	0.930380i	$0.619477\pi$
$912$	−4.99853	−0.165518
$913$	3.66367	0.121250
$914$	−56.1898	−1.85859
$915$	0.0983156	0.00325021
$916$	80.1561	2.64843
$917$	18.1732	0.600132
$918$	8.32031	0.274611
$919$	−46.0521	−1.51912	−0.759559	−	0.650438i	$-0.774585\pi$
$919$	−46.0521	−1.51912	−0.759559	+	0.650438i	$0.774585\pi$
$920$	20.1013	0.662719
$921$	14.3321	0.472258
$922$	−29.8953	−0.984549
$923$	−5.07766	−0.167133
$924$	−2.27715	−0.0749129
$925$	−8.52004	−0.280137
$926$	−79.6200	−2.61648
$927$	3.33302	0.109471
$928$	−48.6576	−1.59726
$929$	1.19407	0.0391763	0.0195881	−	0.999808i	$-0.493765\pi$
$929$	1.19407	0.0391763	0.0195881	+	0.999808i	$0.493765\pi$
$930$	2.77881	0.0911208
$931$	−6.91202	−0.226532
$932$	106.004	3.47229
$933$	−1.19831	−0.0392308
$934$	−60.3713	−1.97541
$935$	1.10599	0.0361699
$936$	31.7401	1.03746
$937$	−0.426436	−0.0139310	−0.00696552	−	0.999976i	$-0.502217\pi$
$937$	−0.426436	−0.0139310	−0.00696552	+	0.999976i	$0.502217\pi$
$938$	0.383405	0.0125186
$939$	−1.17473	−0.0383358
$940$	45.1652	1.47313
$941$	21.5391	0.702154	0.351077	−	0.936347i	$-0.385816\pi$
$941$	21.5391	0.702154	0.351077	+	0.936347i	$0.385816\pi$
$942$	−12.4792	−0.406595
$943$	8.50463	0.276949
$944$	−99.3247	−3.23274
$945$	3.07787	0.100123
$946$	2.32576	0.0756169
$947$	−16.3233	−0.530436	−0.265218	−	0.964189i	$-0.585444\pi$
$947$	−16.3233	−0.530436	−0.265218	+	0.964189i	$0.585444\pi$
$948$	−13.6490	−0.443298
$949$	15.0347	0.488048
$950$	3.19231	0.103572
$951$	1.16115	0.0376530
$952$	−10.2126	−0.330993
$953$	50.2552	1.62793	0.813963	−	0.580916i	$-0.197306\pi$
$953$	50.2552	1.62793	0.813963	+	0.580916i	$0.197306\pi$
$954$	−65.6680	−2.12608
$955$	2.21209	0.0715814
$956$	83.6256	2.70465
$957$	−2.18606	−0.0706652
$958$	76.7870	2.48088
$959$	10.6262	0.343139
$960$	2.56291	0.0827175
$961$	−25.3996	−0.819341
$962$	35.3059	1.13831
$963$	−0.688385	−0.0221829
$964$	−121.687	−3.91929
$965$	0.709587	0.0228424
$966$	−3.89614	−0.125356
$967$	17.0631	0.548713	0.274357	−	0.961628i	$-0.411535\pi$
$967$	17.0631	0.548713	0.274357	+	0.961628i	$0.411535\pi$
$968$	−72.4279	−2.32792
$969$	−0.679982	−0.0218442
$970$	−16.0762	−0.516175
$971$	−45.1473	−1.44884	−0.724422	−	0.689356i	$-0.757893\pi$
$971$	−45.1473	−1.44884	−0.724422	+	0.689356i	$0.757893\pi$
$972$	−52.7113	−1.69072
$973$	0.355950	0.0114112
$974$	−70.5583	−2.26083
$975$	0.721925	0.0231201
$976$	1.95369	0.0625361
$977$	−22.9284	−0.733544	−0.366772	−	0.930311i	$-0.619537\pi$
$977$	−22.9284	−0.733544	−0.366772	+	0.930311i	$0.619537\pi$
$978$	−0.242481	−0.00775368
$979$	−9.56047	−0.305554
$980$	26.6447	0.851133
$981$	27.2634	0.870453
$982$	−80.1275	−2.55697
$983$	−58.6824	−1.87168	−0.935839	−	0.352429i	$-0.885356\pi$
$983$	−58.6824	−1.87168	−0.935839	+	0.352429i	$0.885356\pi$
$984$	9.68318	0.308688
$985$	18.8174	0.599573
$986$	−16.9603	−0.540126
$987$	−5.06045	−0.161076
$988$	−9.30314	−0.295972
$989$	2.79850	0.0889873
$990$	−6.56488	−0.208646
$991$	46.8097	1.48696	0.743480	−	0.668758i	$-0.233174\pi$
$991$	46.8097	1.48696	0.743480	+	0.668758i	$0.233174\pi$
$992$	21.5509	0.684241
$993$	−5.24234	−0.166361
$994$	−9.69767	−0.307591
$995$	−26.4524	−0.838597
$996$	8.68292	0.275129
$997$	−45.1216	−1.42902	−0.714508	−	0.699627i	$-0.753350\pi$
$997$	−45.1216	−1.42902	−0.714508	+	0.699627i	$0.753350\pi$
$998$	−63.6229	−2.01395
$999$	−22.3329	−0.706581

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.c.1.4	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.c.1.4	✓	4	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:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q+2.59615 q^{2} -0.452290 q^{3} +4.74002 q^{4} -1.00000 q^{5} -1.17422 q^{6} -1.17422 q^{7} +7.11351 q^{8} -2.79543 q^{9} +O(q^{10})\)	\(q+2.59615 q^{2} -0.452290 q^{3} +4.74002 q^{4} -1.00000 q^{5} -1.17422 q^{6} -1.17422 q^{7} +7.11351 q^{8} -2.79543 q^{9} -2.59615 q^{10} -0.904581 q^{11} -2.14386 q^{12} -1.59615 q^{13} -3.04844 q^{14} +0.452290 q^{15} +8.98774 q^{16} +1.22266 q^{17} -7.25738 q^{18} +1.22963 q^{19} -4.74002 q^{20} +0.531086 q^{21} -2.34843 q^{22} -2.82578 q^{23} -3.21737 q^{24} +1.00000 q^{25} -4.14386 q^{26} +2.62122 q^{27} -5.56580 q^{28} -5.34314 q^{29} +1.17422 q^{30} +2.36652 q^{31} +9.10654 q^{32} +0.409133 q^{33} +3.17422 q^{34} +1.17422 q^{35} -13.2504 q^{36} -8.52004 q^{37} +3.19231 q^{38} +0.721925 q^{39} -7.11351 q^{40} -3.00965 q^{41} +1.37878 q^{42} -0.990346 q^{43} -4.28773 q^{44} +2.79543 q^{45} -7.33617 q^{46} -9.52848 q^{47} -4.06507 q^{48} -5.62122 q^{49} +2.59615 q^{50} -0.552997 q^{51} -7.56580 q^{52} +9.04844 q^{53} +6.80509 q^{54} +0.904581 q^{55} -8.35280 q^{56} -0.556150 q^{57} -13.8716 q^{58} -11.0511 q^{59} +2.14386 q^{60} +0.217373 q^{61} +6.14386 q^{62} +3.28244 q^{63} +5.66651 q^{64} +1.59615 q^{65} +1.06217 q^{66} -0.125771 q^{67} +5.79543 q^{68} +1.27807 q^{69} +3.04844 q^{70} +3.18118 q^{71} -19.8854 q^{72} -9.41934 q^{73} -22.1194 q^{74} -0.452290 q^{75} +5.82847 q^{76} +1.06217 q^{77} +1.87423 q^{78} +6.36652 q^{79} -8.98774 q^{80} +7.20075 q^{81} -7.81353 q^{82} -4.05013 q^{83} +2.51736 q^{84} -1.22266 q^{85} -2.57109 q^{86} +2.41665 q^{87} -6.43475 q^{88} +10.5690 q^{89} +7.25738 q^{90} +1.87423 q^{91} -13.3943 q^{92} -1.07036 q^{93} -24.7374 q^{94} -1.22963 q^{95} -4.11880 q^{96} +6.19231 q^{97} -14.5936 q^{98} +2.52869 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} - 7 q^{6} - 7 q^{7} + 9 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 4 * q^5 - 7 * q^6 - 7 * q^7 + 9 * q^8 + 2 * q^9	\( 4 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} - 7 q^{6} - 7 q^{7} + 9 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{13} - 4 q^{14} + 2 q^{15} + 6 q^{16} - q^{17} - q^{18} + 11 q^{19} - 2 q^{20} + 5 q^{21} - 14 q^{22} - 9 q^{23} + 11 q^{24} + 4 q^{25} - 8 q^{26} - 5 q^{27} - 3 q^{28} - 8 q^{29} + 7 q^{30} - 5 q^{31} + 5 q^{32} + 28 q^{33} + 15 q^{34} + 7 q^{35} - 13 q^{36} + 4 q^{37} - 4 q^{38} + 5 q^{39} - 9 q^{40} + 3 q^{41} + 21 q^{42} - 19 q^{43} - 2 q^{45} - 4 q^{46} + 4 q^{47} - 5 q^{48} - 7 q^{49} + 2 q^{50} - 20 q^{51} - 11 q^{52} + 28 q^{53} - q^{54} + 4 q^{55} - 5 q^{56} + 2 q^{57} - 9 q^{59} - 23 q^{61} + 16 q^{62} - 22 q^{63} + 21 q^{64} - 2 q^{65} + 10 q^{66} - 11 q^{67} + 10 q^{68} + 3 q^{69} + 4 q^{70} + 27 q^{71} - 38 q^{72} + 18 q^{73} - 20 q^{74} - 2 q^{75} - 6 q^{76} + 10 q^{77} - 3 q^{78} + 11 q^{79} - 6 q^{80} + 8 q^{81} + q^{82} - 2 q^{83} - q^{84} + q^{85} - 9 q^{86} - 19 q^{87} + 22 q^{88} + q^{89} + q^{90} - 3 q^{91} - 5 q^{92} - 11 q^{93} - 37 q^{94} - 11 q^{95} - 15 q^{96} + 8 q^{97} - 5 q^{98} - 22 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 4 * q^5 - 7 * q^6 - 7 * q^7 + 9 * q^8 + 2 * q^9 - 2 * q^10 - 4 * q^11 + 2 * q^13 - 4 * q^14 + 2 * q^15 + 6 * q^16 - q^17 - q^18 + 11 * q^19 - 2 * q^20 + 5 * q^21 - 14 * q^22 - 9 * q^23 + 11 * q^24 + 4 * q^25 - 8 * q^26 - 5 * q^27 - 3 * q^28 - 8 * q^29 + 7 * q^30 - 5 * q^31 + 5 * q^32 + 28 * q^33 + 15 * q^34 + 7 * q^35 - 13 * q^36 + 4 * q^37 - 4 * q^38 + 5 * q^39 - 9 * q^40 + 3 * q^41 + 21 * q^42 - 19 * q^43 - 2 * q^45 - 4 * q^46 + 4 * q^47 - 5 * q^48 - 7 * q^49 + 2 * q^50 - 20 * q^51 - 11 * q^52 + 28 * q^53 - q^54 + 4 * q^55 - 5 * q^56 + 2 * q^57 - 9 * q^59 - 23 * q^61 + 16 * q^62 - 22 * q^63 + 21 * q^64 - 2 * q^65 + 10 * q^66 - 11 * q^67 + 10 * q^68 + 3 * q^69 + 4 * q^70 + 27 * q^71 - 38 * q^72 + 18 * q^73 - 20 * q^74 - 2 * q^75 - 6 * q^76 + 10 * q^77 - 3 * q^78 + 11 * q^79 - 6 * q^80 + 8 * q^81 + q^82 - 2 * q^83 - q^84 + q^85 - 9 * q^86 - 19 * q^87 + 22 * q^88 + q^89 + q^90 - 3 * q^91 - 5 * q^92 - 11 * q^93 - 37 * q^94 - 11 * q^95 - 15 * q^96 + 8 * q^97 - 5 * q^98 - 22 * q^99

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