LMFDB - Embedded newform 4015.2.a.h.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.93175 q^{2} -1.55022 q^{3} +1.73167 q^{4} +1.00000 q^{5} +2.99464 q^{6} +5.03826 q^{7} +0.518349 q^{8} -0.596820 q^{9} +O(q^{10})$	\(q-1.93175 q^{2} -1.55022 q^{3} +1.73167 q^{4} +1.00000 q^{5} +2.99464 q^{6} +5.03826 q^{7} +0.518349 q^{8} -0.596820 q^{9} -1.93175 q^{10} +1.00000 q^{11} -2.68447 q^{12} +4.93475 q^{13} -9.73267 q^{14} -1.55022 q^{15} -4.46466 q^{16} -1.88345 q^{17} +1.15291 q^{18} -5.80475 q^{19} +1.73167 q^{20} -7.81041 q^{21} -1.93175 q^{22} +2.09112 q^{23} -0.803554 q^{24} +1.00000 q^{25} -9.53271 q^{26} +5.57586 q^{27} +8.72460 q^{28} +7.08062 q^{29} +2.99464 q^{30} +0.155442 q^{31} +7.58792 q^{32} -1.55022 q^{33} +3.63837 q^{34} +5.03826 q^{35} -1.03349 q^{36} -2.57766 q^{37} +11.2134 q^{38} -7.64994 q^{39} +0.518349 q^{40} +3.66097 q^{41} +15.0878 q^{42} -6.60752 q^{43} +1.73167 q^{44} -0.596820 q^{45} -4.03952 q^{46} +0.494115 q^{47} +6.92120 q^{48} +18.3841 q^{49} -1.93175 q^{50} +2.91977 q^{51} +8.54535 q^{52} -0.831913 q^{53} -10.7712 q^{54} +1.00000 q^{55} +2.61157 q^{56} +8.99864 q^{57} -13.6780 q^{58} +7.98834 q^{59} -2.68447 q^{60} +12.2714 q^{61} -0.300275 q^{62} -3.00693 q^{63} -5.72867 q^{64} +4.93475 q^{65} +2.99464 q^{66} +4.93466 q^{67} -3.26152 q^{68} -3.24169 q^{69} -9.73267 q^{70} +8.14192 q^{71} -0.309361 q^{72} +1.00000 q^{73} +4.97939 q^{74} -1.55022 q^{75} -10.0519 q^{76} +5.03826 q^{77} +14.7778 q^{78} -10.7148 q^{79} -4.46466 q^{80} -6.85335 q^{81} -7.07208 q^{82} +2.33014 q^{83} -13.5250 q^{84} -1.88345 q^{85} +12.7641 q^{86} -10.9765 q^{87} +0.518349 q^{88} -6.49569 q^{89} +1.15291 q^{90} +24.8625 q^{91} +3.62112 q^{92} -0.240969 q^{93} -0.954507 q^{94} -5.80475 q^{95} -11.7629 q^{96} -11.1355 q^{97} -35.5135 q^{98} -0.596820 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) $ 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * 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 $

$2$	−1.93175	−1.36596	−0.682978	−	0.730439i	$-0.739315\pi$
$2$	−1.93175	−1.36596	−0.682978	+	0.730439i	$0.739315\pi$
$3$	−1.55022	−0.895020	−0.447510	−	0.894279i	$-0.647689\pi$
$3$	−1.55022	−0.895020	−0.447510	+	0.894279i	$0.647689\pi$
$4$	1.73167	0.865835
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.99464	1.22256
$7$	5.03826	1.90428	0.952142	−	0.305657i	$-0.0988762\pi$
$7$	5.03826	1.90428	0.952142	+	0.305657i	$0.0988762\pi$
$8$	0.518349	0.183264
$9$	−0.596820	−0.198940
$10$	−1.93175	−0.610874
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.68447	−0.774939
$13$	4.93475	1.36865	0.684326	−	0.729176i	$-0.260096\pi$
$13$	4.93475	1.36865	0.684326	+	0.729176i	$0.260096\pi$
$14$	−9.73267	−2.60117
$15$	−1.55022	−0.400265
$16$	−4.46466	−1.11616
$17$	−1.88345	−0.456805	−0.228402	−	0.973567i	$-0.573350\pi$
$17$	−1.88345	−0.456805	−0.228402	+	0.973567i	$0.573350\pi$
$18$	1.15291	0.271743
$19$	−5.80475	−1.33170	−0.665851	−	0.746085i	$-0.731931\pi$
$19$	−5.80475	−1.33170	−0.665851	+	0.746085i	$0.731931\pi$
$20$	1.73167	0.387213
$21$	−7.81041	−1.70437
$22$	−1.93175	−0.411851
$23$	2.09112	0.436028	0.218014	−	0.975946i	$-0.430042\pi$
$23$	2.09112	0.436028	0.218014	+	0.975946i	$0.430042\pi$
$24$	−0.803554	−0.164025
$25$	1.00000	0.200000
$26$	−9.53271	−1.86952
$27$	5.57586	1.07307
$28$	8.72460	1.64879
$29$	7.08062	1.31484	0.657420	−	0.753525i	$-0.271648\pi$
$29$	7.08062	1.31484	0.657420	+	0.753525i	$0.271648\pi$
$30$	2.99464	0.546744
$31$	0.155442	0.0279182	0.0139591	−	0.999903i	$-0.495557\pi$
$31$	0.155442	0.0279182	0.0139591	+	0.999903i	$0.495557\pi$
$32$	7.58792	1.34137
$33$	−1.55022	−0.269859
$34$	3.63837	0.623975
$35$	5.03826	0.851621
$36$	−1.03349	−0.172249
$37$	−2.57766	−0.423764	−0.211882	−	0.977295i	$-0.567959\pi$
$37$	−2.57766	−0.423764	−0.211882	+	0.977295i	$0.567959\pi$
$38$	11.2134	1.81905
$39$	−7.64994	−1.22497
$40$	0.518349	0.0819581
$41$	3.66097	0.571747	0.285873	−	0.958267i	$-0.407716\pi$
$41$	3.66097	0.571747	0.285873	+	0.958267i	$0.407716\pi$
$42$	15.0878	2.32809
$43$	−6.60752	−1.00764	−0.503818	−	0.863810i	$-0.668072\pi$
$43$	−6.60752	−1.00764	−0.503818	+	0.863810i	$0.668072\pi$
$44$	1.73167	0.261059
$45$	−0.596820	−0.0889686
$46$	−4.03952	−0.595595
$47$	0.494115	0.0720740	0.0360370	−	0.999350i	$-0.488527\pi$
$47$	0.494115	0.0720740	0.0360370	+	0.999350i	$0.488527\pi$
$48$	6.92120	0.998990
$49$	18.3841	2.62629
$50$	−1.93175	−0.273191
$51$	2.91977	0.408849
$52$	8.54535	1.18503
$53$	−0.831913	−0.114272	−0.0571361	−	0.998366i	$-0.518197\pi$
$53$	−0.831913	−0.114272	−0.0571361	+	0.998366i	$0.518197\pi$
$54$	−10.7712	−1.46577
$55$	1.00000	0.134840
$56$	2.61157	0.348986
$57$	8.99864	1.19190
$58$	−13.6780	−1.79601
$59$	7.98834	1.03999	0.519996	−	0.854168i	$-0.325933\pi$
$59$	7.98834	1.03999	0.519996	+	0.854168i	$0.325933\pi$
$60$	−2.68447	−0.346563
$61$	12.2714	1.57119	0.785594	−	0.618742i	$-0.212358\pi$
$61$	12.2714	1.57119	0.785594	+	0.618742i	$0.212358\pi$
$62$	−0.300275	−0.0381350
$63$	−3.00693	−0.378838
$64$	−5.72867	−0.716084
$65$	4.93475	0.612080
$66$	2.99464	0.368615
$67$	4.93466	0.602865	0.301432	−	0.953488i	$-0.402535\pi$
$67$	4.93466	0.602865	0.301432	+	0.953488i	$0.402535\pi$
$68$	−3.26152	−0.395517
$69$	−3.24169	−0.390254
$70$	−9.73267	−1.16328
$71$	8.14192	0.966269	0.483134	−	0.875546i	$-0.339498\pi$
$71$	8.14192	0.966269	0.483134	+	0.875546i	$0.339498\pi$
$72$	−0.309361	−0.0364585
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	4.97939	0.578843
$75$	−1.55022	−0.179004
$76$	−10.0519	−1.15303
$77$	5.03826	0.574163
$78$	14.7778	1.67326
$79$	−10.7148	−1.20550	−0.602752	−	0.797928i	$-0.705929\pi$
$79$	−10.7148	−1.20550	−0.602752	+	0.797928i	$0.705929\pi$
$80$	−4.46466	−0.499164
$81$	−6.85335	−0.761483
$82$	−7.07208	−0.780981
$83$	2.33014	0.255766	0.127883	−	0.991789i	$-0.459182\pi$
$83$	2.33014	0.255766	0.127883	+	0.991789i	$0.459182\pi$
$84$	−13.5250	−1.47570
$85$	−1.88345	−0.204289
$86$	12.7641	1.37639
$87$	−10.9765	−1.17681
$88$	0.518349	0.0552561
$89$	−6.49569	−0.688541	−0.344271	−	0.938870i	$-0.611874\pi$
$89$	−6.49569	−0.688541	−0.344271	+	0.938870i	$0.611874\pi$
$90$	1.15291	0.121527
$91$	24.8625	2.60630
$92$	3.62112	0.377528
$93$	−0.240969	−0.0249873
$94$	−0.954507	−0.0984499
$95$	−5.80475	−0.595555
$96$	−11.7629	−1.20055
$97$	−11.1355	−1.13064	−0.565320	−	0.824872i	$-0.691247\pi$
$97$	−11.1355	−1.13064	−0.565320	+	0.824872i	$0.691247\pi$
$98$	−35.5135	−3.58740
$99$	−0.596820	−0.0599826
$100$	1.73167	0.173167
$101$	−6.87548	−0.684136	−0.342068	−	0.939675i	$-0.611127\pi$
$101$	−6.87548	−0.684136	−0.342068	+	0.939675i	$0.611127\pi$
$102$	−5.64027	−0.558470
$103$	−1.32182	−0.130243	−0.0651216	−	0.997877i	$-0.520744\pi$
$103$	−1.32182	−0.130243	−0.0651216	+	0.997877i	$0.520744\pi$
$104$	2.55792	0.250825
$105$	−7.81041	−0.762218
$106$	1.60705	0.156091
$107$	5.62131	0.543433	0.271716	−	0.962377i	$-0.412409\pi$
$107$	5.62131	0.543433	0.271716	+	0.962377i	$0.412409\pi$
$108$	9.65555	0.929105
$109$	−7.60288	−0.728224	−0.364112	−	0.931355i	$-0.618627\pi$
$109$	−7.60288	−0.728224	−0.364112	+	0.931355i	$0.618627\pi$
$110$	−1.93175	−0.184185
$111$	3.99593	0.379277
$112$	−22.4941	−2.12549
$113$	12.0398	1.13261	0.566305	−	0.824196i	$-0.308372\pi$
$113$	12.0398	1.13261	0.566305	+	0.824196i	$0.308372\pi$
$114$	−17.3832	−1.62808
$115$	2.09112	0.194998
$116$	12.2613	1.13843
$117$	−2.94515	−0.272280
$118$	−15.4315	−1.42058
$119$	−9.48933	−0.869886
$120$	−0.803554	−0.0733541
$121$	1.00000	0.0909091
$122$	−23.7053	−2.14617
$123$	−5.67530	−0.511725
$124$	0.269174	0.0241725
$125$	1.00000	0.0894427
$126$	5.80865	0.517476
$127$	−10.9666	−0.973124	−0.486562	−	0.873646i	$-0.661749\pi$
$127$	−10.9666	−0.973124	−0.486562	+	0.873646i	$0.661749\pi$
$128$	−4.10947	−0.363229
$129$	10.2431	0.901855
$130$	−9.53271	−0.836074
$131$	20.4822	1.78954	0.894769	−	0.446530i	$-0.147340\pi$
$131$	20.4822	1.78954	0.894769	+	0.446530i	$0.147340\pi$
$132$	−2.68447	−0.233653
$133$	−29.2459	−2.53594
$134$	−9.53255	−0.823487
$135$	5.57586	0.479894
$136$	−0.976286	−0.0837158
$137$	11.3844	0.972639	0.486319	−	0.873781i	$-0.338339\pi$
$137$	11.3844	0.972639	0.486319	+	0.873781i	$0.338339\pi$
$138$	6.26214	0.533069
$139$	−13.6259	−1.15573	−0.577865	−	0.816132i	$-0.696114\pi$
$139$	−13.6259	−1.15573	−0.577865	+	0.816132i	$0.696114\pi$
$140$	8.72460	0.737363
$141$	−0.765986	−0.0645077
$142$	−15.7282	−1.31988
$143$	4.93475	0.412664
$144$	2.66460	0.222050
$145$	7.08062	0.588014
$146$	−1.93175	−0.159873
$147$	−28.4993	−2.35059
$148$	−4.46365	−0.366909
$149$	8.90186	0.729269	0.364635	−	0.931151i	$-0.381194\pi$
$149$	8.90186	0.729269	0.364635	+	0.931151i	$0.381194\pi$
$150$	2.99464	0.244511
$151$	−17.8913	−1.45597	−0.727986	−	0.685592i	$-0.759543\pi$
$151$	−17.8913	−1.45597	−0.727986	+	0.685592i	$0.759543\pi$
$152$	−3.00889	−0.244053
$153$	1.12408	0.0908767
$154$	−9.73267	−0.784281
$155$	0.155442	0.0124854
$156$	−13.2472	−1.06062
$157$	−6.52351	−0.520633	−0.260317	−	0.965523i	$-0.583827\pi$
$157$	−6.52351	−0.520633	−0.260317	+	0.965523i	$0.583827\pi$
$158$	20.6983	1.64667
$159$	1.28965	0.102276
$160$	7.58792	0.599878
$161$	10.5356	0.830321
$162$	13.2390	1.04015
$163$	14.5035	1.13600	0.567999	−	0.823029i	$-0.307718\pi$
$163$	14.5035	1.13600	0.567999	+	0.823029i	$0.307718\pi$
$164$	6.33958	0.495038
$165$	−1.55022	−0.120684
$166$	−4.50125	−0.349365
$167$	2.45982	0.190347	0.0951733	−	0.995461i	$-0.469659\pi$
$167$	2.45982	0.190347	0.0951733	+	0.995461i	$0.469659\pi$
$168$	−4.04851	−0.312350
$169$	11.3517	0.873209
$170$	3.63837	0.279050
$171$	3.46439	0.264929
$172$	−11.4420	−0.872447
$173$	−20.2070	−1.53631	−0.768156	−	0.640263i	$-0.778825\pi$
$173$	−20.2070	−1.53631	−0.768156	+	0.640263i	$0.778825\pi$
$174$	21.2039	1.60747
$175$	5.03826	0.380857
$176$	−4.46466	−0.336536
$177$	−12.3837	−0.930814
$178$	12.5481	0.940517
$179$	−13.6978	−1.02382	−0.511910	−	0.859039i	$-0.671062\pi$
$179$	−13.6978	−1.02382	−0.511910	+	0.859039i	$0.671062\pi$
$180$	−1.03349	−0.0770321
$181$	19.9045	1.47949	0.739743	−	0.672889i	$-0.234947\pi$
$181$	19.9045	1.47949	0.739743	+	0.672889i	$0.234947\pi$
$182$	−48.0283	−3.56009
$183$	−19.0233	−1.40624
$184$	1.08393	0.0799082
$185$	−2.57766	−0.189513
$186$	0.465493	0.0341316
$187$	−1.88345	−0.137732
$188$	0.855643	0.0624042
$189$	28.0926	2.04344
$190$	11.2134	0.813502
$191$	−4.80342	−0.347563	−0.173782	−	0.984784i	$-0.555599\pi$
$191$	−4.80342	−0.347563	−0.173782	+	0.984784i	$0.555599\pi$
$192$	8.88070	0.640909
$193$	−13.6923	−0.985596	−0.492798	−	0.870144i	$-0.664026\pi$
$193$	−13.6923	−0.985596	−0.492798	+	0.870144i	$0.664026\pi$
$194$	21.5110	1.54440
$195$	−7.64994	−0.547824
$196$	31.8351	2.27394
$197$	12.9944	0.925815	0.462907	−	0.886407i	$-0.346806\pi$
$197$	12.9944	0.925815	0.462907	+	0.886407i	$0.346806\pi$
$198$	1.15291	0.0819336
$199$	10.4918	0.743747	0.371873	−	0.928283i	$-0.378716\pi$
$199$	10.4918	0.743747	0.371873	+	0.928283i	$0.378716\pi$
$200$	0.518349	0.0366528
$201$	−7.64981	−0.539576
$202$	13.2817	0.934499
$203$	35.6740	2.50383
$204$	5.05607	0.353996
$205$	3.66097	0.255693
$206$	2.55344	0.177906
$207$	−1.24802	−0.0867434
$208$	−22.0320	−1.52764
$209$	−5.80475	−0.401523
$210$	15.0878	1.04116
$211$	20.6162	1.41928	0.709639	−	0.704566i	$-0.248858\pi$
$211$	20.6162	1.41928	0.709639	+	0.704566i	$0.248858\pi$
$212$	−1.44060	−0.0989407
$213$	−12.6218	−0.864829
$214$	−10.8590	−0.742305
$215$	−6.60752	−0.450629
$216$	2.89024	0.196656
$217$	0.783156	0.0531641
$218$	14.6869	0.994721
$219$	−1.55022	−0.104754
$220$	1.73167	0.116749
$221$	−9.29437	−0.625207
$222$	−7.71915	−0.518076
$223$	−0.515177	−0.0344988	−0.0172494	−	0.999851i	$-0.505491\pi$
$223$	−0.515177	−0.0344988	−0.0172494	+	0.999851i	$0.505491\pi$
$224$	38.2299	2.55434
$225$	−0.596820	−0.0397880
$226$	−23.2579	−1.54710
$227$	−28.9941	−1.92441	−0.962204	−	0.272329i	$-0.912206\pi$
$227$	−28.9941	−1.92441	−0.962204	+	0.272329i	$0.912206\pi$
$228$	15.5827	1.03199
$229$	−18.8631	−1.24651	−0.623254	−	0.782019i	$-0.714190\pi$
$229$	−18.8631	−1.24651	−0.623254	+	0.782019i	$0.714190\pi$
$230$	−4.03952	−0.266358
$231$	−7.81041	−0.513887
$232$	3.67023	0.240962
$233$	11.2385	0.736259	0.368129	−	0.929775i	$-0.379998\pi$
$233$	11.2385	0.736259	0.368129	+	0.929775i	$0.379998\pi$
$234$	5.68931	0.371922
$235$	0.494115	0.0322325
$236$	13.8332	0.900462
$237$	16.6102	1.07895
$238$	18.3310	1.18823
$239$	29.2160	1.88983	0.944915	−	0.327317i	$-0.106145\pi$
$239$	29.2160	1.88983	0.944915	+	0.327317i	$0.106145\pi$
$240$	6.92120	0.446762
$241$	15.4868	0.997595	0.498797	−	0.866719i	$-0.333775\pi$
$241$	15.4868	0.997595	0.498797	+	0.866719i	$0.333775\pi$
$242$	−1.93175	−0.124178
$243$	−6.10339	−0.391533
$244$	21.2500	1.36039
$245$	18.3841	1.17451
$246$	10.9633	0.698993
$247$	−28.6450	−1.82264
$248$	0.0805731	0.00511639
$249$	−3.61223	−0.228916
$250$	−1.93175	−0.122175
$251$	16.8859	1.06583	0.532915	−	0.846169i	$-0.321096\pi$
$251$	16.8859	1.06583	0.532915	+	0.846169i	$0.321096\pi$
$252$	−5.20701	−0.328011
$253$	2.09112	0.131467
$254$	21.1847	1.32924
$255$	2.91977	0.182843
$256$	19.3958	1.21224
$257$	3.41553	0.213055	0.106527	−	0.994310i	$-0.466027\pi$
$257$	3.41553	0.213055	0.106527	+	0.994310i	$0.466027\pi$
$258$	−19.7871	−1.23189
$259$	−12.9869	−0.806966
$260$	8.54535	0.529960
$261$	−4.22586	−0.261574
$262$	−39.5665	−2.44443
$263$	−20.8884	−1.28804	−0.644018	−	0.765010i	$-0.722734\pi$
$263$	−20.8884	−1.28804	−0.644018	+	0.765010i	$0.722734\pi$
$264$	−0.803554	−0.0494553
$265$	−0.831913	−0.0511040
$266$	56.4958	3.46398
$267$	10.0697	0.616258
$268$	8.54520	0.521981
$269$	6.76940	0.412738	0.206369	−	0.978474i	$-0.433835\pi$
$269$	6.76940	0.412738	0.206369	+	0.978474i	$0.433835\pi$
$270$	−10.7712	−0.655513
$271$	8.18356	0.497116	0.248558	−	0.968617i	$-0.420043\pi$
$271$	8.18356	0.497116	0.248558	+	0.968617i	$0.420043\pi$
$272$	8.40898	0.509869
$273$	−38.5424	−2.33269
$274$	−21.9919	−1.32858
$275$	1.00000	0.0603023
$276$	−5.61354	−0.337895
$277$	−18.5592	−1.11511	−0.557557	−	0.830138i	$-0.688261\pi$
$277$	−18.5592	−1.11511	−0.557557	+	0.830138i	$0.688261\pi$
$278$	26.3218	1.57868
$279$	−0.0927708	−0.00555404
$280$	2.61157	0.156071
$281$	1.44112	0.0859699	0.0429850	−	0.999076i	$-0.486313\pi$
$281$	1.44112	0.0859699	0.0429850	+	0.999076i	$0.486313\pi$
$282$	1.47970	0.0881146
$283$	17.6781	1.05085	0.525426	−	0.850839i	$-0.323906\pi$
$283$	17.6781	1.05085	0.525426	+	0.850839i	$0.323906\pi$
$284$	14.0991	0.836629
$285$	8.99864	0.533034
$286$	−9.53271	−0.563681
$287$	18.4449	1.08877
$288$	−4.52862	−0.266852
$289$	−13.4526	−0.791329
$290$	−13.6780	−0.803201
$291$	17.2625	1.01194
$292$	1.73167	0.101338
$293$	−20.6008	−1.20351	−0.601755	−	0.798680i	$-0.705532\pi$
$293$	−20.6008	−1.20351	−0.601755	+	0.798680i	$0.705532\pi$
$294$	55.0537	3.21079
$295$	7.98834	0.465099
$296$	−1.33612	−0.0776606
$297$	5.57586	0.323544
$298$	−17.1962	−0.996149
$299$	10.3191	0.596771
$300$	−2.68447	−0.154988
$301$	−33.2904	−1.91883
$302$	34.5615	1.98879
$303$	10.6585	0.612315
$304$	25.9163	1.48640
$305$	12.2714	0.702657
$306$	−2.17145	−0.124134
$307$	4.01236	0.228997	0.114499	−	0.993423i	$-0.463474\pi$
$307$	4.01236	0.228997	0.114499	+	0.993423i	$0.463474\pi$
$308$	8.72460	0.497130
$309$	2.04912	0.116570
$310$	−0.300275	−0.0170545
$311$	−19.3873	−1.09935	−0.549677	−	0.835377i	$-0.685249\pi$
$311$	−19.3873	−1.09935	−0.549677	+	0.835377i	$0.685249\pi$
$312$	−3.96533	−0.224493
$313$	−21.2151	−1.19915	−0.599575	−	0.800319i	$-0.704664\pi$
$313$	−21.2151	−1.19915	−0.599575	+	0.800319i	$0.704664\pi$
$314$	12.6018	0.711162
$315$	−3.00693	−0.169421
$316$	−18.5544	−1.04377
$317$	19.5399	1.09747	0.548734	−	0.835997i	$-0.315110\pi$
$317$	19.5399	1.09747	0.548734	+	0.835997i	$0.315110\pi$
$318$	−2.49128	−0.139704
$319$	7.08062	0.396439
$320$	−5.72867	−0.320243
$321$	−8.71426	−0.486383
$322$	−20.3522	−1.13418
$323$	10.9330	0.608328
$324$	−11.8677	−0.659318
$325$	4.93475	0.273730
$326$	−28.0171	−1.55172
$327$	11.7861	0.651774
$328$	1.89766	0.104781
$329$	2.48948	0.137249
$330$	2.99464	0.164850
$331$	−26.3665	−1.44923	−0.724617	−	0.689151i	$-0.757984\pi$
$331$	−26.3665	−1.44923	−0.724617	+	0.689151i	$0.757984\pi$
$332$	4.03503	0.221451
$333$	1.53840	0.0843036
$334$	−4.75177	−0.260005
$335$	4.93466	0.269609
$336$	34.8708	1.90236
$337$	12.1864	0.663834	0.331917	−	0.943309i	$-0.392305\pi$
$337$	12.1864	0.663834	0.331917	+	0.943309i	$0.392305\pi$
$338$	−21.9287	−1.19277
$339$	−18.6644	−1.01371
$340$	−3.26152	−0.176881
$341$	0.155442	0.00841765
$342$	−6.69235	−0.361881
$343$	57.3559	3.09693
$344$	−3.42500	−0.184663
$345$	−3.24169	−0.174527
$346$	39.0350	2.09853
$347$	−7.37707	−0.396022	−0.198011	−	0.980200i	$-0.563448\pi$
$347$	−7.37707	−0.396022	−0.198011	+	0.980200i	$0.563448\pi$
$348$	−19.0077	−1.01892
$349$	−2.44699	−0.130984	−0.0654921	−	0.997853i	$-0.520862\pi$
$349$	−2.44699	−0.130984	−0.0654921	+	0.997853i	$0.520862\pi$
$350$	−9.73267	−0.520233
$351$	27.5155	1.46867
$352$	7.58792	0.404438
$353$	11.5591	0.615228	0.307614	−	0.951511i	$-0.400469\pi$
$353$	11.5591	0.615228	0.307614	+	0.951511i	$0.400469\pi$
$354$	23.9222	1.27145
$355$	8.14192	0.432128
$356$	−11.2484	−0.596163
$357$	14.7105	0.778565
$358$	26.4607	1.39849
$359$	20.3984	1.07659	0.538293	−	0.842758i	$-0.319069\pi$
$359$	20.3984	1.07659	0.538293	+	0.842758i	$0.319069\pi$
$360$	−0.309361	−0.0163047
$361$	14.6952	0.773430
$362$	−38.4505	−2.02091
$363$	−1.55022	−0.0813654
$364$	43.0537	2.25663
$365$	1.00000	0.0523424
$366$	36.7483	1.92087
$367$	31.4652	1.64247	0.821234	−	0.570592i	$-0.193286\pi$
$367$	31.4652	1.64247	0.821234	+	0.570592i	$0.193286\pi$
$368$	−9.33613	−0.486679
$369$	−2.18494	−0.113743
$370$	4.97939	0.258866
$371$	−4.19140	−0.217606
$372$	−0.417279	−0.0216349
$373$	−9.05849	−0.469031	−0.234516	−	0.972112i	$-0.575350\pi$
$373$	−9.05849	−0.469031	−0.234516	+	0.972112i	$0.575350\pi$
$374$	3.63837	0.188136
$375$	−1.55022	−0.0800530
$376$	0.256124	0.0132086
$377$	34.9411	1.79956
$378$	−54.2680	−2.79125
$379$	−4.54049	−0.233229	−0.116615	−	0.993177i	$-0.537204\pi$
$379$	−4.54049	−0.233229	−0.116615	+	0.993177i	$0.537204\pi$
$380$	−10.0519	−0.515652
$381$	17.0006	0.870965
$382$	9.27902	0.474756
$383$	13.7088	0.700487	0.350244	−	0.936659i	$-0.386099\pi$
$383$	13.7088	0.700487	0.350244	+	0.936659i	$0.386099\pi$
$384$	6.37057	0.325097
$385$	5.03826	0.256773
$386$	26.4502	1.34628
$387$	3.94350	0.200459
$388$	−19.2830	−0.978947
$389$	−6.70658	−0.340037	−0.170019	−	0.985441i	$-0.554383\pi$
$389$	−6.70658	−0.340037	−0.170019	+	0.985441i	$0.554383\pi$
$390$	14.7778	0.748303
$391$	−3.93852	−0.199180
$392$	9.52935	0.481305
$393$	−31.7519	−1.60167
$394$	−25.1020	−1.26462
$395$	−10.7148	−0.539118
$396$	−1.03349	−0.0519350
$397$	1.51931	0.0762521	0.0381261	−	0.999273i	$-0.487861\pi$
$397$	1.51931	0.0762521	0.0381261	+	0.999273i	$0.487861\pi$
$398$	−20.2676	−1.01593
$399$	45.3375	2.26971
$400$	−4.46466	−0.223233
$401$	8.98064	0.448472	0.224236	−	0.974535i	$-0.428011\pi$
$401$	8.98064	0.448472	0.224236	+	0.974535i	$0.428011\pi$
$402$	14.7775	0.737037
$403$	0.767066	0.0382103
$404$	−11.9061	−0.592348
$405$	−6.85335	−0.340546
$406$	−68.9134	−3.42011
$407$	−2.57766	−0.127770
$408$	1.51346	0.0749273
$409$	18.8030	0.929747	0.464874	−	0.885377i	$-0.346100\pi$
$409$	18.8030	0.929747	0.464874	+	0.885377i	$0.346100\pi$
$410$	−7.07208	−0.349265
$411$	−17.6484	−0.870531
$412$	−2.28896	−0.112769
$413$	40.2473	1.98044
$414$	2.41087	0.118488
$415$	2.33014	0.114382
$416$	37.4445	1.83587
$417$	21.1231	1.03440
$418$	11.2134	0.548463
$419$	−36.2214	−1.76953	−0.884766	−	0.466035i	$-0.845682\pi$
$419$	−36.2214	−1.76953	−0.884766	+	0.466035i	$0.845682\pi$
$420$	−13.5250	−0.659955
$421$	29.7990	1.45231	0.726156	−	0.687530i	$-0.241305\pi$
$421$	29.7990	1.45231	0.726156	+	0.687530i	$0.241305\pi$
$422$	−39.8254	−1.93867
$423$	−0.294897	−0.0143384
$424$	−0.431221	−0.0209419
$425$	−1.88345	−0.0913609
$426$	24.3821	1.18132
$427$	61.8264	2.99199
$428$	9.73425	0.470523
$429$	−7.64994	−0.369343
$430$	12.7641	0.615539
$431$	29.1183	1.40258	0.701291	−	0.712876i	$-0.252608\pi$
$431$	29.1183	1.40258	0.701291	+	0.712876i	$0.252608\pi$
$432$	−24.8943	−1.19773
$433$	5.29947	0.254676	0.127338	−	0.991859i	$-0.459357\pi$
$433$	5.29947	0.254676	0.127338	+	0.991859i	$0.459357\pi$
$434$	−1.51286	−0.0726198
$435$	−10.9765	−0.526284
$436$	−13.1657	−0.630521
$437$	−12.1384	−0.580659
$438$	2.99464	0.143089
$439$	0.706813	0.0337344	0.0168672	−	0.999858i	$-0.494631\pi$
$439$	0.706813	0.0337344	0.0168672	+	0.999858i	$0.494631\pi$
$440$	0.518349	0.0247113
$441$	−10.9720	−0.522475
$442$	17.9544	0.854005
$443$	−7.82679	−0.371862	−0.185931	−	0.982563i	$-0.559530\pi$
$443$	−7.82679	−0.371862	−0.185931	+	0.982563i	$0.559530\pi$
$444$	6.91963	0.328391
$445$	−6.49569	−0.307925
$446$	0.995195	0.0471238
$447$	−13.7998	−0.652710
$448$	−28.8625	−1.36363
$449$	24.0263	1.13387	0.566935	−	0.823762i	$-0.308129\pi$
$449$	24.0263	1.13387	0.566935	+	0.823762i	$0.308129\pi$
$450$	1.15291	0.0543486
$451$	3.66097	0.172388
$452$	20.8490	0.980653
$453$	27.7354	1.30312
$454$	56.0095	2.62866
$455$	24.8625	1.16557
$456$	4.66443	0.218432
$457$	22.4896	1.05202	0.526008	−	0.850479i	$-0.323688\pi$
$457$	22.4896	1.05202	0.526008	+	0.850479i	$0.323688\pi$
$458$	36.4388	1.70267
$459$	−10.5019	−0.490186
$460$	3.62112	0.168836
$461$	−0.829128	−0.0386163	−0.0193082	−	0.999814i	$-0.506146\pi$
$461$	−0.829128	−0.0386163	−0.0193082	+	0.999814i	$0.506146\pi$
$462$	15.0878	0.701947
$463$	20.7013	0.962073	0.481036	−	0.876701i	$-0.340260\pi$
$463$	20.7013	0.962073	0.481036	+	0.876701i	$0.340260\pi$
$464$	−31.6126	−1.46758
$465$	−0.240969	−0.0111747
$466$	−21.7100	−1.00570
$467$	−12.9160	−0.597679	−0.298840	−	0.954303i	$-0.596600\pi$
$467$	−12.9160	−0.597679	−0.298840	+	0.954303i	$0.596600\pi$
$468$	−5.10003	−0.235749
$469$	24.8621	1.14803
$470$	−0.954507	−0.0440281
$471$	10.1129	0.465977
$472$	4.14074	0.190593
$473$	−6.60752	−0.303814
$474$	−32.0869	−1.47380
$475$	−5.80475	−0.266340
$476$	−16.4324	−0.753177
$477$	0.496502	0.0227333
$478$	−56.4382	−2.58142
$479$	−30.7438	−1.40472	−0.702360	−	0.711822i	$-0.747870\pi$
$479$	−30.7438	−1.40472	−0.702360	+	0.711822i	$0.747870\pi$
$480$	−11.7629	−0.536903
$481$	−12.7201	−0.579985
$482$	−29.9167	−1.36267
$483$	−16.3325	−0.743153
$484$	1.73167	0.0787122
$485$	−11.1355	−0.505637
$486$	11.7902	0.534816
$487$	−2.24109	−0.101554	−0.0507768	−	0.998710i	$-0.516170\pi$
$487$	−2.24109	−0.101554	−0.0507768	+	0.998710i	$0.516170\pi$
$488$	6.36085	0.287942
$489$	−22.4835	−1.01674
$490$	−35.5135	−1.60433
$491$	−26.5097	−1.19637	−0.598183	−	0.801360i	$-0.704110\pi$
$491$	−26.5097	−1.19637	−0.598183	+	0.801360i	$0.704110\pi$
$492$	−9.82774	−0.443069
$493$	−13.3360	−0.600625
$494$	55.3350	2.48964
$495$	−0.596820	−0.0268251
$496$	−0.693995	−0.0311613
$497$	41.0211	1.84005
$498$	6.97793	0.312689
$499$	−16.7668	−0.750583	−0.375292	−	0.926907i	$-0.622457\pi$
$499$	−16.7668	−0.750583	−0.375292	+	0.926907i	$0.622457\pi$
$500$	1.73167	0.0774426
$501$	−3.81326	−0.170364
$502$	−32.6195	−1.45588
$503$	−18.2376	−0.813175	−0.406588	−	0.913612i	$-0.633281\pi$
$503$	−18.2376	−0.813175	−0.406588	+	0.913612i	$0.633281\pi$
$504$	−1.55864	−0.0694273
$505$	−6.87548	−0.305955
$506$	−4.03952	−0.179579
$507$	−17.5977	−0.781539
$508$	−18.9904	−0.842564
$509$	5.26211	0.233239	0.116620	−	0.993177i	$-0.462794\pi$
$509$	5.26211	0.233239	0.116620	+	0.993177i	$0.462794\pi$
$510$	−5.64027	−0.249755
$511$	5.03826	0.222879
$512$	−29.2490	−1.29264
$513$	−32.3665	−1.42902
$514$	−6.59795	−0.291023
$515$	−1.32182	−0.0582465
$516$	17.7377	0.780857
$517$	0.494115	0.0217311
$518$	25.0875	1.10228
$519$	31.3253	1.37503
$520$	2.55792	0.112172
$521$	30.3204	1.32836	0.664181	−	0.747572i	$-0.268780\pi$
$521$	30.3204	1.32836	0.664181	+	0.747572i	$0.268780\pi$
$522$	8.16331	0.357298
$523$	1.53755	0.0672325	0.0336163	−	0.999435i	$-0.489298\pi$
$523$	1.53755	0.0672325	0.0336163	+	0.999435i	$0.489298\pi$
$524$	35.4684	1.54944
$525$	−7.81041	−0.340874
$526$	40.3513	1.75940
$527$	−0.292768	−0.0127532
$528$	6.92120	0.301207
$529$	−18.6272	−0.809880
$530$	1.60705	0.0698058
$531$	−4.76760	−0.206896
$532$	−50.6442	−2.19570
$533$	18.0659	0.782523
$534$	−19.4522	−0.841781
$535$	5.62131	0.243030
$536$	2.55788	0.110483
$537$	21.2346	0.916340
$538$	−13.0768	−0.563781
$539$	18.3841	0.791858
$540$	9.65555	0.415509
$541$	5.17801	0.222620	0.111310	−	0.993786i	$-0.464495\pi$
$541$	5.17801	0.222620	0.111310	+	0.993786i	$0.464495\pi$
$542$	−15.8086	−0.679038
$543$	−30.8563	−1.32417
$544$	−14.2915	−0.612743
$545$	−7.60288	−0.325671
$546$	74.4544	3.18635
$547$	−16.2447	−0.694572	−0.347286	−	0.937759i	$-0.612897\pi$
$547$	−16.2447	−0.694572	−0.347286	+	0.937759i	$0.612897\pi$
$548$	19.7141	0.842144
$549$	−7.32380	−0.312572
$550$	−1.93175	−0.0823702
$551$	−41.1013	−1.75097
$552$	−1.68033	−0.0715194
$553$	−53.9837	−2.29562
$554$	35.8518	1.52320
$555$	3.99593	0.169618
$556$	−23.5955	−1.00067
$557$	7.56535	0.320554	0.160277	−	0.987072i	$-0.448761\pi$
$557$	7.56535	0.320554	0.160277	+	0.987072i	$0.448761\pi$
$558$	0.179210	0.00758657
$559$	−32.6064	−1.37910
$560$	−22.4941	−0.950550
$561$	2.91977	0.123273
$562$	−2.78388	−0.117431
$563$	29.7103	1.25214	0.626070	−	0.779767i	$-0.284662\pi$
$563$	29.7103	1.25214	0.626070	+	0.779767i	$0.284662\pi$
$564$	−1.32643	−0.0558530
$565$	12.0398	0.506519
$566$	−34.1497	−1.43542
$567$	−34.5289	−1.45008
$568$	4.22035	0.177082
$569$	36.1059	1.51364	0.756819	−	0.653624i	$-0.226752\pi$
$569$	36.1059	1.51364	0.756819	+	0.653624i	$0.226752\pi$
$570$	−17.3832	−0.728100
$571$	14.4335	0.604022	0.302011	−	0.953304i	$-0.402342\pi$
$571$	14.4335	0.604022	0.302011	+	0.953304i	$0.402342\pi$
$572$	8.54535	0.357299
$573$	7.44635	0.311076
$574$	−35.6310	−1.48721
$575$	2.09112	0.0872056
$576$	3.41898	0.142458
$577$	−32.8442	−1.36732	−0.683660	−	0.729801i	$-0.739613\pi$
$577$	−32.8442	−1.36732	−0.683660	+	0.729801i	$0.739613\pi$
$578$	25.9871	1.08092
$579$	21.2261	0.882128
$580$	12.2613	0.509123
$581$	11.7398	0.487051
$582$	−33.3468	−1.38227
$583$	−0.831913	−0.0344543
$584$	0.518349	0.0214494
$585$	−2.94515	−0.121767
$586$	39.7956	1.64394
$587$	−21.8084	−0.900130	−0.450065	−	0.892996i	$-0.648599\pi$
$587$	−21.8084	−0.900130	−0.450065	+	0.892996i	$0.648599\pi$
$588$	−49.3514	−2.03522
$589$	−0.902302	−0.0371787
$590$	−15.4315	−0.635304
$591$	−20.1442	−0.828623
$592$	11.5084	0.472990
$593$	2.68288	0.110173	0.0550863	−	0.998482i	$-0.482457\pi$
$593$	2.68288	0.110173	0.0550863	+	0.998482i	$0.482457\pi$
$594$	−10.7712	−0.441947
$595$	−9.48933	−0.389025
$596$	15.4151	0.631426
$597$	−16.2647	−0.665668
$598$	−19.9340	−0.815162
$599$	−11.9206	−0.487063	−0.243531	−	0.969893i	$-0.578306\pi$
$599$	−11.9206	−0.487063	−0.243531	+	0.969893i	$0.578306\pi$
$600$	−0.803554	−0.0328050
$601$	40.4224	1.64886	0.824431	−	0.565962i	$-0.191495\pi$
$601$	40.4224	1.64886	0.824431	+	0.565962i	$0.191495\pi$
$602$	64.3088	2.62103
$603$	−2.94510	−0.119934
$604$	−30.9818	−1.26063
$605$	1.00000	0.0406558
$606$	−20.5896	−0.836395
$607$	−22.6150	−0.917914	−0.458957	−	0.888458i	$-0.651777\pi$
$607$	−22.6150	−0.917914	−0.458957	+	0.888458i	$0.651777\pi$
$608$	−44.0460	−1.78630
$609$	−55.3026	−2.24097
$610$	−23.7053	−0.959798
$611$	2.43833	0.0986443
$612$	1.94654	0.0786842
$613$	16.9075	0.682888	0.341444	−	0.939902i	$-0.389084\pi$
$613$	16.9075	0.682888	0.341444	+	0.939902i	$0.389084\pi$
$614$	−7.75089	−0.312800
$615$	−5.67530	−0.228850
$616$	2.61157	0.105223
$617$	16.0878	0.647672	0.323836	−	0.946113i	$-0.395027\pi$
$617$	16.0878	0.647672	0.323836	+	0.946113i	$0.395027\pi$
$618$	−3.95839	−0.159230
$619$	−26.1103	−1.04946	−0.524730	−	0.851269i	$-0.675834\pi$
$619$	−26.1103	−1.04946	−0.524730	+	0.851269i	$0.675834\pi$
$620$	0.269174	0.0108103
$621$	11.6598	0.467891
$622$	37.4515	1.50167
$623$	−32.7270	−1.31118
$624$	34.1544	1.36727
$625$	1.00000	0.0400000
$626$	40.9824	1.63799
$627$	8.99864	0.359371
$628$	−11.2966	−0.450782
$629$	4.85490	0.193577
$630$	5.80865	0.231422
$631$	−7.64708	−0.304425	−0.152213	−	0.988348i	$-0.548640\pi$
$631$	−7.64708	−0.304425	−0.152213	+	0.988348i	$0.548640\pi$
$632$	−5.55398	−0.220925
$633$	−31.9596	−1.27028
$634$	−37.7462	−1.49909
$635$	−10.9666	−0.435194
$636$	2.23324	0.0885539
$637$	90.7207	3.59448
$638$	−13.6780	−0.541518
$639$	−4.85926	−0.192229
$640$	−4.10947	−0.162441
$641$	−29.0050	−1.14563	−0.572815	−	0.819685i	$-0.694149\pi$
$641$	−29.0050	−1.14563	−0.572815	+	0.819685i	$0.694149\pi$
$642$	16.8338	0.664377
$643$	39.1775	1.54501	0.772506	−	0.635008i	$-0.219003\pi$
$643$	39.1775	1.54501	0.772506	+	0.635008i	$0.219003\pi$
$644$	18.2442	0.718921
$645$	10.2431	0.403322
$646$	−21.1198	−0.830949
$647$	42.1918	1.65873	0.829365	−	0.558708i	$-0.188703\pi$
$647$	42.1918	1.65873	0.829365	+	0.558708i	$0.188703\pi$
$648$	−3.55242	−0.139552
$649$	7.98834	0.313570
$650$	−9.53271	−0.373904
$651$	−1.21406	−0.0475829
$652$	25.1152	0.983587
$653$	−30.7023	−1.20147	−0.600736	−	0.799447i	$-0.705126\pi$
$653$	−30.7023	−1.20147	−0.600736	+	0.799447i	$0.705126\pi$
$654$	−22.7679	−0.890295
$655$	20.4822	0.800306
$656$	−16.3450	−0.638164
$657$	−0.596820	−0.0232842
$658$	−4.80906	−0.187476
$659$	34.9234	1.36042	0.680211	−	0.733016i	$-0.261888\pi$
$659$	34.9234	1.36042	0.680211	+	0.733016i	$0.261888\pi$
$660$	−2.68447	−0.104493
$661$	22.9407	0.892291	0.446145	−	0.894961i	$-0.352796\pi$
$661$	22.9407	0.892291	0.446145	+	0.894961i	$0.352796\pi$
$662$	50.9336	1.97959
$663$	14.4083	0.559572
$664$	1.20782	0.0468727
$665$	−29.2459	−1.13411
$666$	−2.97180	−0.115155
$667$	14.8064	0.573307
$668$	4.25960	0.164809
$669$	0.798638	0.0308771
$670$	−9.53255	−0.368274
$671$	12.2714	0.473731
$672$	−59.2648	−2.28619
$673$	30.9844	1.19436	0.597180	−	0.802107i	$-0.296288\pi$
$673$	30.9844	1.19436	0.597180	+	0.802107i	$0.296288\pi$
$674$	−23.5411	−0.906768
$675$	5.57586	0.214615
$676$	19.6574	0.756055
$677$	47.8263	1.83811	0.919057	−	0.394126i	$-0.128953\pi$
$677$	47.8263	1.83811	0.919057	+	0.394126i	$0.128953\pi$
$678$	36.0549	1.38468
$679$	−56.1036	−2.15306
$680$	−0.976286	−0.0374388
$681$	44.9473	1.72238
$682$	−0.300275	−0.0114981
$683$	−2.35139	−0.0899733	−0.0449867	−	0.998988i	$-0.514325\pi$
$683$	−2.35139	−0.0899733	−0.0449867	+	0.998988i	$0.514325\pi$
$684$	5.99918	0.229384
$685$	11.3844	0.434977
$686$	−110.797	−4.23026
$687$	29.2419	1.11565
$688$	29.5003	1.12469
$689$	−4.10528	−0.156399
$690$	6.26214	0.238396
$691$	−36.4761	−1.38762	−0.693808	−	0.720160i	$-0.744068\pi$
$691$	−36.4761	−1.38762	−0.693808	+	0.720160i	$0.744068\pi$
$692$	−34.9919	−1.33019
$693$	−3.00693	−0.114224
$694$	14.2507	0.540949
$695$	−13.6259	−0.516858
$696$	−5.68966	−0.215666
$697$	−6.89526	−0.261177
$698$	4.72697	0.178918
$699$	−17.4221	−0.658966
$700$	8.72460	0.329759
$701$	−1.95771	−0.0739417	−0.0369709	−	0.999316i	$-0.511771\pi$
$701$	−1.95771	−0.0739417	−0.0369709	+	0.999316i	$0.511771\pi$
$702$	−53.1531	−2.00613
$703$	14.9627	0.564327
$704$	−5.72867	−0.215907
$705$	−0.765986	−0.0288487
$706$	−22.3293	−0.840374
$707$	−34.6404	−1.30279
$708$	−21.4444	−0.805931
$709$	−22.7895	−0.855877	−0.427939	−	0.903808i	$-0.640760\pi$
$709$	−22.7895	−0.855877	−0.427939	+	0.903808i	$0.640760\pi$
$710$	−15.7282	−0.590268
$711$	6.39478	0.239823
$712$	−3.36703	−0.126185
$713$	0.325047	0.0121731
$714$	−28.4171	−1.06348
$715$	4.93475	0.184549
$716$	−23.7200	−0.886459
$717$	−45.2913	−1.69143
$718$	−39.4047	−1.47057
$719$	−28.1303	−1.04908	−0.524541	−	0.851385i	$-0.675763\pi$
$719$	−28.1303	−1.04908	−0.524541	+	0.851385i	$0.675763\pi$
$720$	2.66460	0.0993037
$721$	−6.65969	−0.248020
$722$	−28.3874	−1.05647
$723$	−24.0080	−0.892867
$724$	34.4679	1.28099
$725$	7.08062	0.262968
$726$	2.99464	0.111142
$727$	13.7962	0.511673	0.255837	−	0.966720i	$-0.417649\pi$
$727$	13.7962	0.511673	0.255837	+	0.966720i	$0.417649\pi$
$728$	12.8875	0.477641
$729$	30.0216	1.11191
$730$	−1.93175	−0.0714974
$731$	12.4450	0.460293
$732$	−32.9421	−1.21757
$733$	25.4547	0.940190	0.470095	−	0.882616i	$-0.344220\pi$
$733$	25.4547	0.940190	0.470095	+	0.882616i	$0.344220\pi$
$734$	−60.7829	−2.24354
$735$	−28.4993	−1.05121
$736$	15.8672	0.584874
$737$	4.93466	0.181771
$738$	4.22076	0.155368
$739$	−51.2472	−1.88516	−0.942579	−	0.333984i	$-0.891607\pi$
$739$	−51.2472	−1.88516	−0.942579	+	0.333984i	$0.891607\pi$
$740$	−4.46365	−0.164087
$741$	44.4060	1.63130
$742$	8.09674	0.297241
$743$	−23.3817	−0.857791	−0.428896	−	0.903354i	$-0.641097\pi$
$743$	−23.3817	−0.857791	−0.428896	+	0.903354i	$0.641097\pi$
$744$	−0.124906	−0.00457927
$745$	8.90186	0.326139
$746$	17.4988	0.640676
$747$	−1.39067	−0.0508821
$748$	−3.26152	−0.119253
$749$	28.3216	1.03485
$750$	2.99464	0.109349
$751$	38.4156	1.40181	0.700903	−	0.713257i	$-0.252781\pi$
$751$	38.4156	1.40181	0.700903	+	0.713257i	$0.252781\pi$
$752$	−2.20605	−0.0804465
$753$	−26.1769	−0.953939
$754$	−67.4975	−2.45812
$755$	−17.8913	−0.651130
$756$	48.6471	1.76928
$757$	−19.8109	−0.720040	−0.360020	−	0.932945i	$-0.617230\pi$
$757$	−19.8109	−0.720040	−0.360020	+	0.932945i	$0.617230\pi$
$758$	8.77110	0.318581
$759$	−3.24169	−0.117666
$760$	−3.00889	−0.109144
$761$	34.5569	1.25269	0.626343	−	0.779547i	$-0.284551\pi$
$761$	34.5569	1.25269	0.626343	+	0.779547i	$0.284551\pi$
$762$	−32.8409	−1.18970
$763$	−38.3053	−1.38674
$764$	−8.31793	−0.300932
$765$	1.12408	0.0406413
$766$	−26.4820	−0.956834
$767$	39.4204	1.42339
$768$	−30.0678	−1.08498
$769$	25.3529	0.914249	0.457124	−	0.889403i	$-0.348879\pi$
$769$	25.3529	0.914249	0.457124	+	0.889403i	$0.348879\pi$
$770$	−9.73267	−0.350741
$771$	−5.29482	−0.190688
$772$	−23.7106	−0.853363
$773$	−41.7998	−1.50343	−0.751717	−	0.659486i	$-0.770774\pi$
$773$	−41.7998	−1.50343	−0.751717	+	0.659486i	$0.770774\pi$
$774$	−7.61786	−0.273818
$775$	0.155442	0.00558364
$776$	−5.77207	−0.207205
$777$	20.1325	0.722251
$778$	12.9555	0.464476
$779$	−21.2510	−0.761396
$780$	−13.2472	−0.474325
$781$	8.14192	0.291341
$782$	7.60825	0.272071
$783$	39.4806	1.41092
$784$	−82.0786	−2.93138
$785$	−6.52351	−0.232834
$786$	61.3368	2.18781
$787$	9.97500	0.355570	0.177785	−	0.984069i	$-0.443107\pi$
$787$	9.97500	0.355570	0.177785	+	0.984069i	$0.443107\pi$
$788$	22.5021	0.801603
$789$	32.3817	1.15282
$790$	20.6983	0.736411
$791$	60.6597	2.15681
$792$	−0.309361	−0.0109927
$793$	60.5561	2.15041
$794$	−2.93494	−0.104157
$795$	1.28965	0.0457391
$796$	18.1684	0.643962
$797$	−36.3482	−1.28752	−0.643759	−	0.765228i	$-0.722626\pi$
$797$	−36.3482	−1.28752	−0.643759	+	0.765228i	$0.722626\pi$
$798$	−87.5808	−3.10033
$799$	−0.930642	−0.0329237
$800$	7.58792	0.268274
$801$	3.87675	0.136978
$802$	−17.3484	−0.612592
$803$	1.00000	0.0352892
$804$	−13.2469	−0.467184
$805$	10.5356	0.371331
$806$	−1.48178	−0.0521936
$807$	−10.4941	−0.369408
$808$	−3.56389	−0.125377
$809$	−18.4730	−0.649474	−0.324737	−	0.945804i	$-0.605276\pi$
$809$	−18.4730	−0.649474	−0.324737	+	0.945804i	$0.605276\pi$
$810$	13.2390	0.465170
$811$	19.6901	0.691412	0.345706	−	0.938343i	$-0.387639\pi$
$811$	19.6901	0.691412	0.345706	+	0.938343i	$0.387639\pi$
$812$	61.7756	2.16790
$813$	−12.6863	−0.444928
$814$	4.97939	0.174528
$815$	14.5035	0.508034
$816$	−13.0358	−0.456343
$817$	38.3550	1.34187
$818$	−36.3227	−1.26999
$819$	−14.8385	−0.518497
$820$	6.33958	0.221388
$821$	45.5502	1.58971	0.794856	−	0.606798i	$-0.207546\pi$
$821$	45.5502	1.58971	0.794856	+	0.606798i	$0.207546\pi$
$822$	34.0923	1.18911
$823$	−18.9055	−0.659005	−0.329502	−	0.944155i	$-0.606881\pi$
$823$	−18.9055	−0.659005	−0.329502	+	0.944155i	$0.606881\pi$
$824$	−0.685165	−0.0238689
$825$	−1.55022	−0.0539717
$826$	−77.7479	−2.70519
$827$	27.0676	0.941232	0.470616	−	0.882338i	$-0.344032\pi$
$827$	27.0676	0.941232	0.470616	+	0.882338i	$0.344032\pi$
$828$	−2.16116	−0.0751054
$829$	−0.0508846	−0.00176730	−0.000883648	−	1.00000i	$-0.500281\pi$
$829$	−0.0508846	−0.00176730	−0.000883648		1.00000i	$0.500281\pi$
$830$	−4.50125	−0.156241
$831$	28.7708	0.998050
$832$	−28.2695	−0.980070
$833$	−34.6255	−1.19970
$834$	−40.8046	−1.41295
$835$	2.45982	0.0851256
$836$	−10.0519	−0.347653
$837$	0.866722	0.0299583
$838$	69.9709	2.41710
$839$	10.0560	0.347171	0.173586	−	0.984819i	$-0.444465\pi$
$839$	10.0560	0.347171	0.173586	+	0.984819i	$0.444465\pi$
$840$	−4.04851	−0.139687
$841$	21.1352	0.728802
$842$	−57.5642	−1.98379
$843$	−2.23405	−0.0769448
$844$	35.7004	1.22886
$845$	11.3517	0.390511
$846$	0.569669	0.0195856
$847$	5.03826	0.173117
$848$	3.71421	0.127547
$849$	−27.4049	−0.940534
$850$	3.63837	0.124795
$851$	−5.39018	−0.184773
$852$	−21.8567	−0.748799
$853$	−41.4409	−1.41891	−0.709455	−	0.704751i	$-0.751059\pi$
$853$	−41.4409	−1.41891	−0.709455	+	0.704751i	$0.751059\pi$
$854$	−119.433	−4.08692
$855$	3.46439	0.118480
$856$	2.91380	0.0995916
$857$	1.42104	0.0485419	0.0242709	−	0.999705i	$-0.492274\pi$
$857$	1.42104	0.0485419	0.0242709	+	0.999705i	$0.492274\pi$
$858$	14.7778	0.504506
$859$	−17.0378	−0.581322	−0.290661	−	0.956826i	$-0.593875\pi$
$859$	−17.0378	−0.581322	−0.290661	+	0.956826i	$0.593875\pi$
$860$	−11.4420	−0.390170
$861$	−28.5936	−0.974469
$862$	−56.2494	−1.91586
$863$	−34.3440	−1.16908	−0.584541	−	0.811364i	$-0.698725\pi$
$863$	−34.3440	−1.16908	−0.584541	+	0.811364i	$0.698725\pi$
$864$	42.3092	1.43939
$865$	−20.2070	−0.687059
$866$	−10.2373	−0.347877
$867$	20.8545	0.708255
$868$	1.35617	0.0460313
$869$	−10.7148	−0.363473
$870$	21.2039	0.718881
$871$	24.3513	0.825113
$872$	−3.94094	−0.133457
$873$	6.64589	0.224929
$874$	23.4484	0.793155
$875$	5.03826	0.170324
$876$	−2.68447	−0.0906998
$877$	−10.7392	−0.362636	−0.181318	−	0.983424i	$-0.558036\pi$
$877$	−10.7392	−0.362636	−0.181318	+	0.983424i	$0.558036\pi$
$878$	−1.36539	−0.0460796
$879$	31.9357	1.07717
$880$	−4.46466	−0.150504
$881$	35.0429	1.18063	0.590313	−	0.807174i	$-0.299004\pi$
$881$	35.0429	1.18063	0.590313	+	0.807174i	$0.299004\pi$
$882$	21.1951	0.713677
$883$	−42.7549	−1.43882	−0.719409	−	0.694587i	$-0.755587\pi$
$883$	−42.7549	−1.43882	−0.719409	+	0.694587i	$0.755587\pi$
$884$	−16.0948	−0.541326
$885$	−12.3837	−0.416273
$886$	15.1194	0.507947
$887$	−4.46323	−0.149861	−0.0749303	−	0.997189i	$-0.523873\pi$
$887$	−4.46323	−0.149861	−0.0749303	+	0.997189i	$0.523873\pi$
$888$	2.07129	0.0695078
$889$	−55.2523	−1.85310
$890$	12.5481	0.420612
$891$	−6.85335	−0.229596
$892$	−0.892117	−0.0298703
$893$	−2.86821	−0.0959811
$894$	26.6579	0.891573
$895$	−13.6978	−0.457867
$896$	−20.7046	−0.691691
$897$	−15.9969	−0.534122
$898$	−46.4129	−1.54882
$899$	1.10063	0.0367079
$900$	−1.03349	−0.0344498
$901$	1.56687	0.0522000
$902$	−7.07208	−0.235475
$903$	51.6074	1.71739
$904$	6.24082	0.207567
$905$	19.9045	0.661646
$906$	−53.5779	−1.78001
$907$	35.2083	1.16907	0.584537	−	0.811367i	$-0.301276\pi$
$907$	35.2083	1.16907	0.584537	+	0.811367i	$0.301276\pi$
$908$	−50.2083	−1.66622
$909$	4.10342	0.136102
$910$	−48.0283	−1.59212
$911$	45.5719	1.50986	0.754932	−	0.655803i	$-0.227670\pi$
$911$	45.5719	1.50986	0.754932	+	0.655803i	$0.227670\pi$
$912$	−40.1759	−1.33036
$913$	2.33014	0.0771164
$914$	−43.4443	−1.43701
$915$	−19.0233	−0.628891
$916$	−32.6646	−1.07927
$917$	103.195	3.40779
$918$	20.2870	0.669572
$919$	−13.0262	−0.429695	−0.214847	−	0.976648i	$-0.568925\pi$
$919$	−13.0262	−0.429695	−0.214847	+	0.976648i	$0.568925\pi$
$920$	1.08393	0.0357360
$921$	−6.22004	−0.204957
$922$	1.60167	0.0527482
$923$	40.1783	1.32249
$924$	−13.5250	−0.444941
$925$	−2.57766	−0.0847528
$926$	−39.9899	−1.31415
$927$	0.788890	0.0259106
$928$	53.7272	1.76368
$929$	58.7904	1.92885	0.964425	−	0.264355i	$-0.0851591\pi$
$929$	58.7904	1.92885	0.964425	+	0.264355i	$0.0851591\pi$
$930$	0.465493	0.0152641
$931$	−106.715	−3.49744
$932$	19.4614	0.637478
$933$	30.0546	0.983943
$934$	24.9504	0.816404
$935$	−1.88345	−0.0615955
$936$	−1.52662	−0.0498990
$937$	5.56584	0.181828	0.0909141	−	0.995859i	$-0.471021\pi$
$937$	5.56584	0.181828	0.0909141	+	0.995859i	$0.471021\pi$
$938$	−48.0275	−1.56815
$939$	32.8881	1.07326
$940$	0.855643	0.0279080
$941$	6.16795	0.201069	0.100535	−	0.994934i	$-0.467945\pi$
$941$	6.16795	0.201069	0.100535	+	0.994934i	$0.467945\pi$
$942$	−19.5356	−0.636504
$943$	7.65551	0.249298
$944$	−35.6652	−1.16080
$945$	28.0926	0.913853
$946$	12.7641	0.414996
$947$	−42.4764	−1.38030	−0.690149	−	0.723667i	$-0.742455\pi$
$947$	−42.4764	−1.38030	−0.690149	+	0.723667i	$0.742455\pi$
$948$	28.7634	0.934193
$949$	4.93475	0.160189
$950$	11.2134	0.363809
$951$	−30.2911	−0.982256
$952$	−4.91878	−0.159419
$953$	−50.8495	−1.64718	−0.823588	−	0.567188i	$-0.808031\pi$
$953$	−50.8495	−1.64718	−0.823588	+	0.567188i	$0.808031\pi$
$954$	−0.959120	−0.0310527
$955$	−4.80342	−0.155435
$956$	50.5925	1.63628
$957$	−10.9765	−0.354821
$958$	59.3895	1.91879
$959$	57.3578	1.85218
$960$	8.88070	0.286623
$961$	−30.9758	−0.999221
$962$	24.5720	0.792234
$963$	−3.35491	−0.108110
$964$	26.8181	0.863752
$965$	−13.6923	−0.440772
$966$	31.5503	1.01511
$967$	−35.1896	−1.13162	−0.565811	−	0.824535i	$-0.691437\pi$
$967$	−35.1896	−1.13162	−0.565811	+	0.824535i	$0.691437\pi$
$968$	0.518349	0.0166604
$969$	−16.9485	−0.544465
$970$	21.5110	0.690678
$971$	−7.12227	−0.228565	−0.114282	−	0.993448i	$-0.536457\pi$
$971$	−7.12227	−0.228565	−0.114282	+	0.993448i	$0.536457\pi$
$972$	−10.5690	−0.339002
$973$	−68.6506	−2.20084
$974$	4.32924	0.138718
$975$	−7.64994	−0.244994
$976$	−54.7875	−1.75371
$977$	29.1255	0.931808	0.465904	−	0.884835i	$-0.345729\pi$
$977$	29.1255	0.931808	0.465904	+	0.884835i	$0.345729\pi$
$978$	43.4326	1.38882
$979$	−6.49569	−0.207603
$980$	31.8351	1.01694
$981$	4.53755	0.144873
$982$	51.2102	1.63418
$983$	−18.5931	−0.593028	−0.296514	−	0.955028i	$-0.595824\pi$
$983$	−18.5931	−0.593028	−0.296514	+	0.955028i	$0.595824\pi$
$984$	−2.94178	−0.0937806
$985$	12.9944	0.414037
$986$	25.7619	0.820427
$987$	−3.85924	−0.122841
$988$	−49.6036	−1.57810
$989$	−13.8171	−0.439358
$990$	1.15291	0.0366418
$991$	41.2954	1.31179	0.655896	−	0.754851i	$-0.272291\pi$
$991$	41.2954	1.31179	0.655896	+	0.754851i	$0.272291\pi$
$992$	1.17948	0.0374486
$993$	40.8739	1.29709
$994$	−79.2427	−2.51343
$995$	10.4918	0.332614
$996$	−6.25518	−0.198203
$997$	−7.10600	−0.225049	−0.112525	−	0.993649i	$-0.535894\pi$
$997$	−7.10600	−0.225049	−0.112525	+	0.993649i	$0.535894\pi$
$998$	32.3892	1.02526
$999$	−14.3726	−0.454730

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.h.1.7	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.h.1.7	✓	37	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.93175 q^{2} -1.55022 q^{3} +1.73167 q^{4} +1.00000 q^{5} +2.99464 q^{6} +5.03826 q^{7} +0.518349 q^{8} -0.596820 q^{9} +O(q^{10})\)	\(q-1.93175 q^{2} -1.55022 q^{3} +1.73167 q^{4} +1.00000 q^{5} +2.99464 q^{6} +5.03826 q^{7} +0.518349 q^{8} -0.596820 q^{9} -1.93175 q^{10} +1.00000 q^{11} -2.68447 q^{12} +4.93475 q^{13} -9.73267 q^{14} -1.55022 q^{15} -4.46466 q^{16} -1.88345 q^{17} +1.15291 q^{18} -5.80475 q^{19} +1.73167 q^{20} -7.81041 q^{21} -1.93175 q^{22} +2.09112 q^{23} -0.803554 q^{24} +1.00000 q^{25} -9.53271 q^{26} +5.57586 q^{27} +8.72460 q^{28} +7.08062 q^{29} +2.99464 q^{30} +0.155442 q^{31} +7.58792 q^{32} -1.55022 q^{33} +3.63837 q^{34} +5.03826 q^{35} -1.03349 q^{36} -2.57766 q^{37} +11.2134 q^{38} -7.64994 q^{39} +0.518349 q^{40} +3.66097 q^{41} +15.0878 q^{42} -6.60752 q^{43} +1.73167 q^{44} -0.596820 q^{45} -4.03952 q^{46} +0.494115 q^{47} +6.92120 q^{48} +18.3841 q^{49} -1.93175 q^{50} +2.91977 q^{51} +8.54535 q^{52} -0.831913 q^{53} -10.7712 q^{54} +1.00000 q^{55} +2.61157 q^{56} +8.99864 q^{57} -13.6780 q^{58} +7.98834 q^{59} -2.68447 q^{60} +12.2714 q^{61} -0.300275 q^{62} -3.00693 q^{63} -5.72867 q^{64} +4.93475 q^{65} +2.99464 q^{66} +4.93466 q^{67} -3.26152 q^{68} -3.24169 q^{69} -9.73267 q^{70} +8.14192 q^{71} -0.309361 q^{72} +1.00000 q^{73} +4.97939 q^{74} -1.55022 q^{75} -10.0519 q^{76} +5.03826 q^{77} +14.7778 q^{78} -10.7148 q^{79} -4.46466 q^{80} -6.85335 q^{81} -7.07208 q^{82} +2.33014 q^{83} -13.5250 q^{84} -1.88345 q^{85} +12.7641 q^{86} -10.9765 q^{87} +0.518349 q^{88} -6.49569 q^{89} +1.15291 q^{90} +24.8625 q^{91} +3.62112 q^{92} -0.240969 q^{93} -0.954507 q^{94} -5.80475 q^{95} -11.7629 q^{96} -11.1355 q^{97} -35.5135 q^{98} -0.596820 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * q^99

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