LMFDB - Embedded newform 4013.2.a.c.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4013,2,Mod(1,4013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4013, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4013.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:	$32.0439663311$
Analytic rank:	$0$
Dimension:	$176$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	4013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.53190 q^{2} +1.30897 q^{3} +4.41050 q^{4} -0.932957 q^{5} -3.31419 q^{6} +0.385559 q^{7} -6.10313 q^{8} -1.28658 q^{9} +O(q^{10})$	\(q-2.53190 q^{2} +1.30897 q^{3} +4.41050 q^{4} -0.932957 q^{5} -3.31419 q^{6} +0.385559 q^{7} -6.10313 q^{8} -1.28658 q^{9} +2.36215 q^{10} +3.41589 q^{11} +5.77323 q^{12} +5.74810 q^{13} -0.976195 q^{14} -1.22122 q^{15} +6.63150 q^{16} -7.07331 q^{17} +3.25750 q^{18} +5.92606 q^{19} -4.11480 q^{20} +0.504687 q^{21} -8.64869 q^{22} -4.84546 q^{23} -7.98884 q^{24} -4.12959 q^{25} -14.5536 q^{26} -5.61103 q^{27} +1.70051 q^{28} +6.46039 q^{29} +3.09199 q^{30} +6.54793 q^{31} -4.58400 q^{32} +4.47132 q^{33} +17.9089 q^{34} -0.359710 q^{35} -5.67448 q^{36} +11.4584 q^{37} -15.0042 q^{38} +7.52412 q^{39} +5.69396 q^{40} -8.49962 q^{41} -1.27781 q^{42} +0.246799 q^{43} +15.0658 q^{44} +1.20033 q^{45} +12.2682 q^{46} +7.79076 q^{47} +8.68046 q^{48} -6.85134 q^{49} +10.4557 q^{50} -9.25878 q^{51} +25.3520 q^{52} +7.08735 q^{53} +14.2065 q^{54} -3.18688 q^{55} -2.35311 q^{56} +7.75706 q^{57} -16.3570 q^{58} -5.86013 q^{59} -5.38618 q^{60} -1.71324 q^{61} -16.5787 q^{62} -0.496054 q^{63} -1.65679 q^{64} -5.36273 q^{65} -11.3209 q^{66} +8.13854 q^{67} -31.1968 q^{68} -6.34259 q^{69} +0.910747 q^{70} -3.64091 q^{71} +7.85219 q^{72} -7.26244 q^{73} -29.0114 q^{74} -5.40553 q^{75} +26.1369 q^{76} +1.31703 q^{77} -19.0503 q^{78} -17.3113 q^{79} -6.18690 q^{80} -3.48494 q^{81} +21.5201 q^{82} +14.7707 q^{83} +2.22592 q^{84} +6.59909 q^{85} -0.624869 q^{86} +8.45648 q^{87} -20.8476 q^{88} +2.82512 q^{89} -3.03911 q^{90} +2.21623 q^{91} -21.3709 q^{92} +8.57108 q^{93} -19.7254 q^{94} -5.52876 q^{95} -6.00034 q^{96} +15.5180 q^{97} +17.3469 q^{98} -4.39484 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9}+O(q^{10}) $ 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9	\( 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9} + 43 q^{10} + 18 q^{11} + 95 q^{12} + 95 q^{13} + 2 q^{14} + 36 q^{15} + 225 q^{16} + 35 q^{17} + 46 q^{18} + 127 q^{19} + 4 q^{20} + 32 q^{21} + 60 q^{22} + 35 q^{23} + 26 q^{24} + 207 q^{25} + 19 q^{26} + 191 q^{27} + 87 q^{28} + 16 q^{29} + 28 q^{30} + 93 q^{31} + 73 q^{32} + 70 q^{33} + 45 q^{34} + 73 q^{35} + 206 q^{36} + 64 q^{37} + 35 q^{38} + 72 q^{39} + 139 q^{40} + 19 q^{41} + 35 q^{42} + 261 q^{43} + 11 q^{44} + 12 q^{45} + 58 q^{46} + 40 q^{47} + 130 q^{48} + 234 q^{49} - 14 q^{50} + 76 q^{51} + 263 q^{52} + 17 q^{53} + 28 q^{54} + 170 q^{55} - 10 q^{56} + 60 q^{57} + 52 q^{58} + 69 q^{59} + 37 q^{60} + 110 q^{61} + 71 q^{62} + 101 q^{63} + 250 q^{64} - q^{65} + 43 q^{66} + 190 q^{67} + 48 q^{68} + 45 q^{69} + 14 q^{70} + 9 q^{71} + 98 q^{72} + 182 q^{73} - 23 q^{74} + 219 q^{75} + 197 q^{76} + 25 q^{77} - 26 q^{78} + 105 q^{79} + 20 q^{80} + 236 q^{81} + 107 q^{82} + 130 q^{83} + 38 q^{84} + 73 q^{85} - 24 q^{86} + 171 q^{87} + 165 q^{88} + 40 q^{89} + 45 q^{90} + 182 q^{91} - 4 q^{92} + 23 q^{93} + 98 q^{94} + 30 q^{95} - 2 q^{96} + 168 q^{97} + 82 q^{98} + 50 q^{99}+O(q^{100}) \) 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9 + 43 * q^10 + 18 * q^11 + 95 * q^12 + 95 * q^13 + 2 * q^14 + 36 * q^15 + 225 * q^16 + 35 * q^17 + 46 * q^18 + 127 * q^19 + 4 * q^20 + 32 * q^21 + 60 * q^22 + 35 * q^23 + 26 * q^24 + 207 * q^25 + 19 * q^26 + 191 * q^27 + 87 * q^28 + 16 * q^29 + 28 * q^30 + 93 * q^31 + 73 * q^32 + 70 * q^33 + 45 * q^34 + 73 * q^35 + 206 * q^36 + 64 * q^37 + 35 * q^38 + 72 * q^39 + 139 * q^40 + 19 * q^41 + 35 * q^42 + 261 * q^43 + 11 * q^44 + 12 * q^45 + 58 * q^46 + 40 * q^47 + 130 * q^48 + 234 * q^49 - 14 * q^50 + 76 * q^51 + 263 * q^52 + 17 * q^53 + 28 * q^54 + 170 * q^55 - 10 * q^56 + 60 * q^57 + 52 * q^58 + 69 * q^59 + 37 * q^60 + 110 * q^61 + 71 * q^62 + 101 * q^63 + 250 * q^64 - q^65 + 43 * q^66 + 190 * q^67 + 48 * q^68 + 45 * q^69 + 14 * q^70 + 9 * q^71 + 98 * q^72 + 182 * q^73 - 23 * q^74 + 219 * q^75 + 197 * q^76 + 25 * q^77 - 26 * q^78 + 105 * q^79 + 20 * q^80 + 236 * q^81 + 107 * q^82 + 130 * q^83 + 38 * q^84 + 73 * q^85 - 24 * q^86 + 171 * q^87 + 165 * q^88 + 40 * q^89 + 45 * q^90 + 182 * q^91 - 4 * q^92 + 23 * q^93 + 98 * q^94 + 30 * q^95 - 2 * q^96 + 168 * q^97 + 82 * 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 $

$2$	−2.53190	−1.79032	−0.895160	−	0.445744i	$-0.852939\pi$
$2$	−2.53190	−1.79032	−0.895160	+	0.445744i	$0.852939\pi$
$3$	1.30897	0.755737	0.377868	−	0.925859i	$-0.376657\pi$
$3$	1.30897	0.755737	0.377868	+	0.925859i	$0.376657\pi$
$4$	4.41050	2.20525
$5$	−0.932957	−0.417231	−0.208615	−	0.977998i	$-0.566896\pi$
$5$	−0.932957	−0.417231	−0.208615	+	0.977998i	$0.566896\pi$
$6$	−3.31419	−1.35301
$7$	0.385559	0.145727	0.0728637	−	0.997342i	$-0.476786\pi$
$7$	0.385559	0.145727	0.0728637	+	0.997342i	$0.476786\pi$
$8$	−6.10313	−2.15778
$9$	−1.28658	−0.428862
$10$	2.36215	0.746977
$11$	3.41589	1.02993	0.514965	−	0.857211i	$-0.327805\pi$
$11$	3.41589	1.02993	0.514965	+	0.857211i	$0.327805\pi$
$12$	5.77323	1.66659
$13$	5.74810	1.59424	0.797118	−	0.603823i	$-0.206357\pi$
$13$	5.74810	1.59424	0.797118	+	0.603823i	$0.206357\pi$
$14$	−0.976195	−0.260899
$15$	−1.22122	−0.315317
$16$	6.63150	1.65787
$17$	−7.07331	−1.71553	−0.857765	−	0.514043i	$-0.828147\pi$
$17$	−7.07331	−1.71553	−0.857765	+	0.514043i	$0.828147\pi$
$18$	3.25750	0.767800
$19$	5.92606	1.35953	0.679766	−	0.733429i	$-0.262081\pi$
$19$	5.92606	1.35953	0.679766	+	0.733429i	$0.262081\pi$
$20$	−4.11480	−0.920098
$21$	0.504687	0.110132
$22$	−8.64869	−1.84391
$23$	−4.84546	−1.01035	−0.505174	−	0.863017i	$-0.668572\pi$
$23$	−4.84546	−1.01035	−0.505174	+	0.863017i	$0.668572\pi$
$24$	−7.98884	−1.63072
$25$	−4.12959	−0.825918
$26$	−14.5536	−2.85420
$27$	−5.61103	−1.07984
$28$	1.70051	0.321365
$29$	6.46039	1.19966	0.599832	−	0.800126i	$-0.295234\pi$
$29$	6.46039	1.19966	0.599832	+	0.800126i	$0.295234\pi$
$30$	3.09199	0.564518
$31$	6.54793	1.17604	0.588022	−	0.808845i	$-0.299907\pi$
$31$	6.54793	1.17604	0.588022	+	0.808845i	$0.299907\pi$
$32$	−4.58400	−0.810344
$33$	4.47132	0.778357
$34$	17.9089	3.07135
$35$	−0.359710	−0.0608020
$36$	−5.67448	−0.945747
$37$	11.4584	1.88374	0.941872	−	0.335973i	$-0.109065\pi$
$37$	11.4584	1.88374	0.941872	+	0.335973i	$0.109065\pi$
$38$	−15.0042	−2.43400
$39$	7.52412	1.20482
$40$	5.69396	0.900294
$41$	−8.49962	−1.32742	−0.663709	−	0.747991i	$-0.731018\pi$
$41$	−8.49962	−1.32742	−0.663709	+	0.747991i	$0.731018\pi$
$42$	−1.27781	−0.197171
$43$	0.246799	0.0376365	0.0188182	−	0.999823i	$-0.494010\pi$
$43$	0.246799	0.0376365	0.0188182	+	0.999823i	$0.494010\pi$
$44$	15.0658	2.27125
$45$	1.20033	0.178934
$46$	12.2682	1.80885
$47$	7.79076	1.13640	0.568199	−	0.822891i	$-0.307640\pi$
$47$	7.79076	1.13640	0.568199	+	0.822891i	$0.307640\pi$
$48$	8.68046	1.25292
$49$	−6.85134	−0.978763
$50$	10.4557	1.47866
$51$	−9.25878	−1.29649
$52$	25.3520	3.51569
$53$	7.08735	0.973523	0.486762	−	0.873535i	$-0.338178\pi$
$53$	7.08735	0.973523	0.486762	+	0.873535i	$0.338178\pi$
$54$	14.2065	1.93327
$55$	−3.18688	−0.429719
$56$	−2.35311	−0.314448
$57$	7.75706	1.02745
$58$	−16.3570	−2.14778
$59$	−5.86013	−0.762924	−0.381462	−	0.924385i	$-0.624579\pi$
$59$	−5.86013	−0.762924	−0.381462	+	0.924385i	$0.624579\pi$
$60$	−5.38618	−0.695352
$61$	−1.71324	−0.219358	−0.109679	−	0.993967i	$-0.534982\pi$
$61$	−1.71324	−0.219358	−0.109679	+	0.993967i	$0.534982\pi$
$62$	−16.5787	−2.10549
$63$	−0.496054	−0.0624969
$64$	−1.65679	−0.207098
$65$	−5.36273	−0.665165
$66$	−11.3209	−1.39351
$67$	8.13854	0.994281	0.497141	−	0.867670i	$-0.334383\pi$
$67$	8.13854	0.994281	0.497141	+	0.867670i	$0.334383\pi$
$68$	−31.1968	−3.78317
$69$	−6.34259	−0.763558
$70$	0.910747	0.108855
$71$	−3.64091	−0.432097	−0.216048	−	0.976383i	$-0.569317\pi$
$71$	−3.64091	−0.432097	−0.216048	+	0.976383i	$0.569317\pi$
$72$	7.85219	0.925390
$73$	−7.26244	−0.850005	−0.425002	−	0.905192i	$-0.639727\pi$
$73$	−7.26244	−0.850005	−0.425002	+	0.905192i	$0.639727\pi$
$74$	−29.0114	−3.37250
$75$	−5.40553	−0.624177
$76$	26.1369	2.99810
$77$	1.31703	0.150089
$78$	−19.0503	−2.15702
$79$	−17.3113	−1.94767	−0.973835	−	0.227254i	$-0.927025\pi$
$79$	−17.3113	−1.94767	−0.973835	+	0.227254i	$0.927025\pi$
$80$	−6.18690	−0.691716
$81$	−3.48494	−0.387216
$82$	21.5201	2.37650
$83$	14.7707	1.62129	0.810646	−	0.585536i	$-0.199116\pi$
$83$	14.7707	1.62129	0.810646	+	0.585536i	$0.199116\pi$
$84$	2.22592	0.242868
$85$	6.59909	0.715772
$86$	−0.624869	−0.0673814
$87$	8.45648	0.906630
$88$	−20.8476	−2.22237
$89$	2.82512	0.299462	0.149731	−	0.988727i	$-0.452159\pi$
$89$	2.82512	0.299462	0.149731	+	0.988727i	$0.452159\pi$
$90$	−3.03911	−0.320350
$91$	2.21623	0.232324
$92$	−21.3709	−2.22807
$93$	8.57108	0.888779
$94$	−19.7254	−2.03452
$95$	−5.52876	−0.567239
$96$	−6.00034	−0.612407
$97$	15.5180	1.57561	0.787805	−	0.615924i	$-0.211217\pi$
$97$	15.5180	1.57561	0.787805	+	0.615924i	$0.211217\pi$
$98$	17.3469	1.75230
$99$	−4.39484	−0.441698
$100$	−18.2136	−1.82136
$101$	15.1014	1.50265	0.751324	−	0.659934i	$-0.229416\pi$
$101$	15.1014	1.50265	0.751324	+	0.659934i	$0.229416\pi$
$102$	23.4423	2.32113
$103$	15.4351	1.52087	0.760433	−	0.649416i	$-0.224987\pi$
$103$	15.4351	1.52087	0.760433	+	0.649416i	$0.224987\pi$
$104$	−35.0814	−3.44002
$105$	−0.470851	−0.0459503
$106$	−17.9444	−1.74292
$107$	−6.58394	−0.636493	−0.318247	−	0.948008i	$-0.603094\pi$
$107$	−6.58394	−0.636493	−0.318247	+	0.948008i	$0.603094\pi$
$108$	−24.7474	−2.38132
$109$	−1.84877	−0.177080	−0.0885402	−	0.996073i	$-0.528220\pi$
$109$	−1.84877	−0.177080	−0.0885402	+	0.996073i	$0.528220\pi$
$110$	8.06885	0.769335
$111$	14.9987	1.42361
$112$	2.55683	0.241598
$113$	−8.60867	−0.809836	−0.404918	−	0.914353i	$-0.632700\pi$
$113$	−8.60867	−0.809836	−0.404918	+	0.914353i	$0.632700\pi$
$114$	−19.6401	−1.83946
$115$	4.52061	0.421549
$116$	28.4935	2.64556
$117$	−7.39542	−0.683707
$118$	14.8372	1.36588
$119$	−2.72718	−0.250000
$120$	7.45325	0.680385
$121$	0.668331	0.0607574
$122$	4.33774	0.392721
$123$	−11.1258	−1.00318
$124$	28.8796	2.59347
$125$	8.51751	0.761830
$126$	1.25596	0.111890
$127$	9.95075	0.882987	0.441493	−	0.897265i	$-0.354449\pi$
$127$	9.95075	0.882987	0.441493	+	0.897265i	$0.354449\pi$
$128$	13.3628	1.18112
$129$	0.323054	0.0284433
$130$	13.5779	1.19086
$131$	7.93533	0.693313	0.346657	−	0.937992i	$-0.387317\pi$
$131$	7.93533	0.693313	0.346657	+	0.937992i	$0.387317\pi$
$132$	19.7207	1.71647
$133$	2.28484	0.198121
$134$	−20.6059	−1.78008
$135$	5.23485	0.450544
$136$	43.1693	3.70174
$137$	6.63337	0.566727	0.283363	−	0.959013i	$-0.408550\pi$
$137$	6.63337	0.566727	0.283363	+	0.959013i	$0.408550\pi$
$138$	16.0588	1.36701
$139$	−13.2941	−1.12759	−0.563795	−	0.825914i	$-0.690659\pi$
$139$	−13.2941	−1.12759	−0.563795	+	0.825914i	$0.690659\pi$
$140$	−1.58650	−0.134084
$141$	10.1979	0.858819
$142$	9.21841	0.773592
$143$	19.6349	1.64195
$144$	−8.53198	−0.710998
$145$	−6.02726	−0.500537
$146$	18.3878	1.52178
$147$	−8.96824	−0.739688
$148$	50.5371	4.15412
$149$	9.28872	0.760962	0.380481	−	0.924789i	$-0.375759\pi$
$149$	9.28872	0.760962	0.380481	+	0.924789i	$0.375759\pi$
$150$	13.6862	1.11748
$151$	7.02403	0.571608	0.285804	−	0.958288i	$-0.407739\pi$
$151$	7.02403	0.571608	0.285804	+	0.958288i	$0.407739\pi$
$152$	−36.1675	−2.93357
$153$	9.10041	0.735725
$154$	−3.33458	−0.268708
$155$	−6.10894	−0.490682
$156$	33.1851	2.65694
$157$	−11.8793	−0.948073	−0.474036	−	0.880505i	$-0.657203\pi$
$157$	−11.8793	−0.948073	−0.474036	+	0.880505i	$0.657203\pi$
$158$	43.8304	3.48696
$159$	9.27717	0.735727
$160$	4.27667	0.338101
$161$	−1.86821	−0.147236
$162$	8.82352	0.693241
$163$	−8.52100	−0.667417	−0.333708	−	0.942676i	$-0.608300\pi$
$163$	−8.52100	−0.667417	−0.333708	+	0.942676i	$0.608300\pi$
$164$	−37.4875	−2.92729
$165$	−4.17155	−0.324755
$166$	−37.3978	−2.90263
$167$	−14.1536	−1.09524	−0.547619	−	0.836728i	$-0.684466\pi$
$167$	−14.1536	−1.09524	−0.547619	+	0.836728i	$0.684466\pi$
$168$	−3.08017	−0.237640
$169$	20.0407	1.54159
$170$	−16.7082	−1.28146
$171$	−7.62438	−0.583051
$172$	1.08851	0.0829978
$173$	−20.3117	−1.54427	−0.772136	−	0.635458i	$-0.780811\pi$
$173$	−20.3117	−1.54427	−0.772136	+	0.635458i	$0.780811\pi$
$174$	−21.4109	−1.62316
$175$	−1.59220	−0.120359
$176$	22.6525	1.70750
$177$	−7.67076	−0.576570
$178$	−7.15291	−0.536133
$179$	−19.5290	−1.45967	−0.729834	−	0.683625i	$-0.760403\pi$
$179$	−19.5290	−1.45967	−0.729834	+	0.683625i	$0.760403\pi$
$180$	5.29404	0.394595
$181$	16.4363	1.22170	0.610849	−	0.791747i	$-0.290828\pi$
$181$	16.4363	1.22170	0.610849	+	0.791747i	$0.290828\pi$
$182$	−5.61127	−0.415935
$183$	−2.24259	−0.165777
$184$	29.5725	2.18011
$185$	−10.6902	−0.785956
$186$	−21.7011	−1.59120
$187$	−24.1617	−1.76688
$188$	34.3611	2.50604
$189$	−2.16338	−0.157363
$190$	13.9982	1.01554
$191$	12.6429	0.914805	0.457403	−	0.889260i	$-0.348780\pi$
$191$	12.6429	0.914805	0.457403	+	0.889260i	$0.348780\pi$
$192$	−2.16869	−0.156512
$193$	5.56398	0.400504	0.200252	−	0.979744i	$-0.435824\pi$
$193$	5.56398	0.400504	0.200252	+	0.979744i	$0.435824\pi$
$194$	−39.2899	−2.82085
$195$	−7.01968	−0.502690
$196$	−30.2178	−2.15842
$197$	23.4442	1.67033	0.835165	−	0.549999i	$-0.185372\pi$
$197$	23.4442	1.67033	0.835165	+	0.549999i	$0.185372\pi$
$198$	11.1273	0.790781
$199$	−5.43348	−0.385169	−0.192584	−	0.981280i	$-0.561687\pi$
$199$	−5.43348	−0.385169	−0.192584	+	0.981280i	$0.561687\pi$
$200$	25.2034	1.78215
$201$	10.6531	0.751415
$202$	−38.2352	−2.69022
$203$	2.49086	0.174824
$204$	−40.8358	−2.85908
$205$	7.92978	0.553840
$206$	−39.0801	−2.72284
$207$	6.23410	0.433300
$208$	38.1185	2.64304
$209$	20.2428	1.40022
$210$	1.19215	0.0822658
$211$	6.36073	0.437891	0.218945	−	0.975737i	$-0.429738\pi$
$211$	6.36073	0.437891	0.218945	+	0.975737i	$0.429738\pi$
$212$	31.2588	2.14686
$213$	−4.76586	−0.326552
$214$	16.6698	1.13953
$215$	−0.230253	−0.0157031
$216$	34.2449	2.33007
$217$	2.52461	0.171382
$218$	4.68090	0.317031
$219$	−9.50636	−0.642380
$220$	−14.0557	−0.947637
$221$	−40.6581	−2.73496
$222$	−37.9752	−2.54873
$223$	9.61075	0.643584	0.321792	−	0.946810i	$-0.395715\pi$
$223$	9.61075	0.643584	0.321792	+	0.946810i	$0.395715\pi$
$224$	−1.76740	−0.118089
$225$	5.31307	0.354205
$226$	21.7963	1.44987
$227$	8.14996	0.540932	0.270466	−	0.962730i	$-0.412822\pi$
$227$	8.14996	0.540932	0.270466	+	0.962730i	$0.412822\pi$
$228$	34.2125	2.26578
$229$	−3.72265	−0.246000	−0.123000	−	0.992407i	$-0.539252\pi$
$229$	−3.72265	−0.246000	−0.123000	+	0.992407i	$0.539252\pi$
$230$	−11.4457	−0.754708
$231$	1.72396	0.113428
$232$	−39.4286	−2.58861
$233$	5.27225	0.345396	0.172698	−	0.984975i	$-0.444751\pi$
$233$	5.27225	0.345396	0.172698	+	0.984975i	$0.444751\pi$
$234$	18.7244	1.22406
$235$	−7.26844	−0.474141
$236$	−25.8461	−1.68244
$237$	−22.6600	−1.47193
$238$	6.90493	0.447580
$239$	4.82023	0.311795	0.155897	−	0.987773i	$-0.450173\pi$
$239$	4.82023	0.311795	0.155897	+	0.987773i	$0.450173\pi$
$240$	−8.09850	−0.522756
$241$	−21.5006	−1.38497	−0.692487	−	0.721431i	$-0.743485\pi$
$241$	−21.5006	−1.38497	−0.692487	+	0.721431i	$0.743485\pi$
$242$	−1.69215	−0.108775
$243$	12.2714	0.787210
$244$	−7.55623	−0.483738
$245$	6.39201	0.408370
$246$	28.1693	1.79601
$247$	34.0636	2.16742
$248$	−39.9629	−2.53765
$249$	19.3344	1.22527
$250$	−21.5655	−1.36392
$251$	6.82848	0.431010	0.215505	−	0.976503i	$-0.430860\pi$
$251$	6.82848	0.431010	0.215505	+	0.976503i	$0.430860\pi$
$252$	−2.18784	−0.137821
$253$	−16.5516	−1.04059
$254$	−25.1943	−1.58083
$255$	8.63805	0.540935
$256$	−30.5197	−1.90748
$257$	11.6454	0.726419	0.363209	−	0.931708i	$-0.381681\pi$
$257$	11.6454	0.726419	0.363209	+	0.931708i	$0.381681\pi$
$258$	−0.817938	−0.0509226
$259$	4.41787	0.274513
$260$	−23.6523	−1.46685
$261$	−8.31184	−0.514490
$262$	−20.0914	−1.24125
$263$	6.30112	0.388544	0.194272	−	0.980948i	$-0.437766\pi$
$263$	6.30112	0.388544	0.194272	+	0.980948i	$0.437766\pi$
$264$	−27.2890	−1.67952
$265$	−6.61220	−0.406184
$266$	−5.78499	−0.354700
$267$	3.69801	0.226315
$268$	35.8950	2.19264
$269$	−32.2776	−1.96800	−0.984002	−	0.178160i	$-0.942985\pi$
$269$	−32.2776	−1.96800	−0.984002	+	0.178160i	$0.942985\pi$
$270$	−13.2541	−0.806619
$271$	17.0793	1.03749	0.518746	−	0.854929i	$-0.326399\pi$
$271$	17.0793	1.03749	0.518746	+	0.854929i	$0.326399\pi$
$272$	−46.9066	−2.84413
$273$	2.90099	0.175576
$274$	−16.7950	−1.01462
$275$	−14.1062	−0.850639
$276$	−27.9740	−1.68384
$277$	20.7570	1.24717	0.623583	−	0.781757i	$-0.285676\pi$
$277$	20.7570	1.24717	0.623583	+	0.781757i	$0.285676\pi$
$278$	33.6593	2.01875
$279$	−8.42447	−0.504360
$280$	2.19535	0.131198
$281$	20.7811	1.23970	0.619848	−	0.784722i	$-0.287194\pi$
$281$	20.7811	1.23970	0.619848	+	0.784722i	$0.287194\pi$
$282$	−25.8200	−1.53756
$283$	−19.1766	−1.13993	−0.569964	−	0.821669i	$-0.693043\pi$
$283$	−19.1766	−1.13993	−0.569964	+	0.821669i	$0.693043\pi$
$284$	−16.0582	−0.952881
$285$	−7.23701	−0.428683
$286$	−49.7136	−2.93962
$287$	−3.27710	−0.193441
$288$	5.89770	0.347525
$289$	33.0317	1.94304
$290$	15.2604	0.896122
$291$	20.3126	1.19075
$292$	−32.0310	−1.87447
$293$	24.9314	1.45651	0.728255	−	0.685307i	$-0.240332\pi$
$293$	24.9314	1.45651	0.728255	+	0.685307i	$0.240332\pi$
$294$	22.7066	1.32428
$295$	5.46725	0.318316
$296$	−69.9319	−4.06471
$297$	−19.1667	−1.11216
$298$	−23.5181	−1.36237
$299$	−27.8522	−1.61074
$300$	−23.8411	−1.37647
$301$	0.0951555	0.00548467
$302$	−17.7841	−1.02336
$303$	19.7674	1.13561
$304$	39.2986	2.25393
$305$	1.59838	0.0915228
$306$	−23.0413	−1.31718
$307$	−19.3166	−1.10246	−0.551228	−	0.834355i	$-0.685841\pi$
$307$	−19.3166	−1.10246	−0.551228	+	0.834355i	$0.685841\pi$
$308$	5.80875	0.330984
$309$	20.2042	1.14937
$310$	15.4672	0.878478
$311$	19.7511	1.11998	0.559990	−	0.828500i	$-0.310805\pi$
$311$	19.7511	1.11998	0.559990	+	0.828500i	$0.310805\pi$
$312$	−45.9207	−2.59975
$313$	19.0275	1.07550	0.537749	−	0.843105i	$-0.319275\pi$
$313$	19.0275	1.07550	0.537749	+	0.843105i	$0.319275\pi$
$314$	30.0772	1.69735
$315$	0.462797	0.0260757
$316$	−76.3513	−4.29510
$317$	−1.24449	−0.0698976	−0.0349488	−	0.999389i	$-0.511127\pi$
$317$	−1.24449	−0.0698976	−0.0349488	+	0.999389i	$0.511127\pi$
$318$	−23.4888	−1.31719
$319$	22.0680	1.23557
$320$	1.54571	0.0864078
$321$	−8.61821	−0.481021
$322$	4.73011	0.263599
$323$	−41.9169	−2.33232
$324$	−15.3703	−0.853908
$325$	−23.7373	−1.31671
$326$	21.5743	1.19489
$327$	−2.42000	−0.133826
$328$	51.8743	2.86428
$329$	3.00379	0.165605
$330$	10.5619	0.581415
$331$	−25.0529	−1.37703	−0.688517	−	0.725220i	$-0.741738\pi$
$331$	−25.0529	−1.37703	−0.688517	+	0.725220i	$0.741738\pi$
$332$	65.1460	3.57535
$333$	−14.7422	−0.807865
$334$	35.8354	1.96083
$335$	−7.59291	−0.414845
$336$	3.34683	0.182584
$337$	17.5595	0.956526	0.478263	−	0.878217i	$-0.341267\pi$
$337$	17.5595	0.956526	0.478263	+	0.878217i	$0.341267\pi$
$338$	−50.7409	−2.75994
$339$	−11.2685	−0.612023
$340$	29.1053	1.57846
$341$	22.3670	1.21124
$342$	19.3041	1.04385
$343$	−5.34051	−0.288360
$344$	−1.50625	−0.0812114
$345$	5.91736	0.318580
$346$	51.4272	2.76474
$347$	−5.22110	−0.280283	−0.140142	−	0.990131i	$-0.544756\pi$
$347$	−5.22110	−0.280283	−0.140142	+	0.990131i	$0.544756\pi$
$348$	37.2973	1.99935
$349$	12.2311	0.654717	0.327358	−	0.944900i	$-0.393842\pi$
$349$	12.2311	0.654717	0.327358	+	0.944900i	$0.393842\pi$
$350$	4.03128	0.215481
$351$	−32.2528	−1.72153
$352$	−15.6584	−0.834598
$353$	−15.0819	−0.802731	−0.401366	−	0.915918i	$-0.631464\pi$
$353$	−15.0819	−0.802731	−0.401366	+	0.915918i	$0.631464\pi$
$354$	19.4216	1.03225
$355$	3.39681	0.180284
$356$	12.4602	0.660388
$357$	−3.56980	−0.188934
$358$	49.4455	2.61327
$359$	−20.5164	−1.08281	−0.541406	−	0.840761i	$-0.682108\pi$
$359$	−20.5164	−1.08281	−0.541406	+	0.840761i	$0.682108\pi$
$360$	−7.32576	−0.386101
$361$	16.1182	0.848325
$362$	−41.6149	−2.18723
$363$	0.874829	0.0459166
$364$	9.77468	0.512333
$365$	6.77555	0.354648
$366$	5.67799	0.296794
$367$	17.4475	0.910752	0.455376	−	0.890299i	$-0.349505\pi$
$367$	17.4475	0.910752	0.455376	+	0.890299i	$0.349505\pi$
$368$	−32.1327	−1.67503
$369$	10.9355	0.569278
$370$	27.0664	1.40711
$371$	2.73259	0.141869
$372$	37.8027	1.95998
$373$	26.3687	1.36532	0.682659	−	0.730737i	$-0.260823\pi$
$373$	26.3687	1.36532	0.682659	+	0.730737i	$0.260823\pi$
$374$	61.1748	3.16328
$375$	11.1492	0.575743
$376$	−47.5480	−2.45210
$377$	37.1350	1.91255
$378$	5.47746	0.281730
$379$	19.7573	1.01487	0.507433	−	0.861691i	$-0.330594\pi$
$379$	19.7573	1.01487	0.507433	+	0.861691i	$0.330594\pi$
$380$	−24.3846	−1.25090
$381$	13.0253	0.667306
$382$	−32.0104	−1.63780
$383$	9.68817	0.495042	0.247521	−	0.968883i	$-0.420384\pi$
$383$	9.68817	0.495042	0.247521	+	0.968883i	$0.420384\pi$
$384$	17.4916	0.892613
$385$	−1.22873	−0.0626219
$386$	−14.0874	−0.717031
$387$	−0.317528	−0.0161408
$388$	68.4420	3.47461
$389$	−1.49453	−0.0757756	−0.0378878	−	0.999282i	$-0.512063\pi$
$389$	−1.49453	−0.0757756	−0.0378878	+	0.999282i	$0.512063\pi$
$390$	17.7731	0.899976
$391$	34.2735	1.73328
$392$	41.8146	2.11196
$393$	10.3872	0.523963
$394$	−59.3583	−2.99043
$395$	16.1507	0.812629
$396$	−19.3834	−0.974054
$397$	18.4911	0.928044	0.464022	−	0.885824i	$-0.346406\pi$
$397$	18.4911	0.928044	0.464022	+	0.885824i	$0.346406\pi$
$398$	13.7570	0.689576
$399$	2.99080	0.149727
$400$	−27.3854	−1.36927
$401$	−18.8337	−0.940512	−0.470256	−	0.882530i	$-0.655838\pi$
$401$	−18.8337	−0.940512	−0.470256	+	0.882530i	$0.655838\pi$
$402$	−26.9727	−1.34527
$403$	37.6382	1.87489
$404$	66.6048	3.31371
$405$	3.25130	0.161559
$406$	−6.30659	−0.312991
$407$	39.1405	1.94012
$408$	56.5076	2.79754
$409$	−29.7676	−1.47191	−0.735956	−	0.677030i	$-0.763267\pi$
$409$	−29.7676	−1.47191	−0.735956	+	0.677030i	$0.763267\pi$
$410$	−20.0774	−0.991550
$411$	8.68291	0.428296
$412$	68.0765	3.35389
$413$	−2.25942	−0.111179
$414$	−15.7841	−0.775746
$415$	−13.7804	−0.676453
$416$	−26.3493	−1.29188
$417$	−17.4016	−0.852162
$418$	−51.2526	−2.50685
$419$	1.93304	0.0944352	0.0472176	−	0.998885i	$-0.484965\pi$
$419$	1.93304	0.0944352	0.0472176	+	0.998885i	$0.484965\pi$
$420$	−2.07669	−0.101332
$421$	9.38489	0.457392	0.228696	−	0.973498i	$-0.426554\pi$
$421$	9.38489	0.457392	0.228696	+	0.973498i	$0.426554\pi$
$422$	−16.1047	−0.783965
$423$	−10.0235	−0.487358
$424$	−43.2550	−2.10065
$425$	29.2099	1.41689
$426$	12.0667	0.584632
$427$	−0.660554	−0.0319664
$428$	−29.0384	−1.40363
$429$	25.7016	1.24089
$430$	0.582976	0.0281136
$431$	26.5648	1.27958	0.639791	−	0.768549i	$-0.279021\pi$
$431$	26.5648	1.27958	0.639791	+	0.768549i	$0.279021\pi$
$432$	−37.2095	−1.79024
$433$	2.78344	0.133763	0.0668817	−	0.997761i	$-0.478695\pi$
$433$	2.78344	0.133763	0.0668817	+	0.997761i	$0.478695\pi$
$434$	−6.39205	−0.306828
$435$	−7.88953	−0.378274
$436$	−8.15401	−0.390506
$437$	−28.7145	−1.37360
$438$	24.0691	1.15007
$439$	−9.60310	−0.458331	−0.229165	−	0.973388i	$-0.573600\pi$
$439$	−9.60310	−0.458331	−0.229165	+	0.973388i	$0.573600\pi$
$440$	19.4500	0.927240
$441$	8.81484	0.419754
$442$	102.942	4.89646
$443$	−34.9185	−1.65903	−0.829513	−	0.558487i	$-0.811382\pi$
$443$	−34.9185	−1.65903	−0.829513	+	0.558487i	$0.811382\pi$
$444$	66.1518	3.13942
$445$	−2.63571	−0.124945
$446$	−24.3334	−1.15222
$447$	12.1587	0.575087
$448$	−0.638788	−0.0301799
$449$	15.7578	0.743657	0.371829	−	0.928301i	$-0.378731\pi$
$449$	15.7578	0.743657	0.371829	+	0.928301i	$0.378731\pi$
$450$	−13.4521	−0.634140
$451$	−29.0338	−1.36715
$452$	−37.9685	−1.78589
$453$	9.19429	0.431985
$454$	−20.6349	−0.968442
$455$	−2.06765	−0.0969328
$456$	−47.3424	−2.21701
$457$	−4.07989	−0.190849	−0.0954246	−	0.995437i	$-0.530421\pi$
$457$	−4.07989	−0.190849	−0.0954246	+	0.995437i	$0.530421\pi$
$458$	9.42537	0.440419
$459$	39.6886	1.85250
$460$	19.9381	0.929620
$461$	15.7060	0.731502	0.365751	−	0.930713i	$-0.380812\pi$
$461$	15.7060	0.731502	0.365751	+	0.930713i	$0.380812\pi$
$462$	−4.36488	−0.203072
$463$	−5.71241	−0.265478	−0.132739	−	0.991151i	$-0.542377\pi$
$463$	−5.71241	−0.265478	−0.132739	+	0.991151i	$0.542377\pi$
$464$	42.8420	1.98889
$465$	−7.99645	−0.370826
$466$	−13.3488	−0.618370
$467$	1.66030	0.0768296	0.0384148	−	0.999262i	$-0.487769\pi$
$467$	1.66030	0.0768296	0.0384148	+	0.999262i	$0.487769\pi$
$468$	−32.6175	−1.50774
$469$	3.13789	0.144894
$470$	18.4029	0.848864
$471$	−15.5497	−0.716494
$472$	35.7651	1.64622
$473$	0.843039	0.0387630
$474$	57.3728	2.63522
$475$	−24.4722	−1.12286
$476$	−12.0282	−0.551312
$477$	−9.11848	−0.417507
$478$	−12.2043	−0.558213
$479$	−19.6143	−0.896200	−0.448100	−	0.893984i	$-0.647899\pi$
$479$	−19.6143	−0.896200	−0.448100	+	0.893984i	$0.647899\pi$
$480$	5.59806	0.255515
$481$	65.8638	3.00313
$482$	54.4372	2.47955
$483$	−2.44544	−0.111271
$484$	2.94767	0.133985
$485$	−14.4776	−0.657394
$486$	−31.0699	−1.40936
$487$	−26.0501	−1.18044	−0.590222	−	0.807241i	$-0.700960\pi$
$487$	−26.0501	−1.18044	−0.590222	+	0.807241i	$0.700960\pi$
$488$	10.4561	0.473326
$489$	−11.1538	−0.504391
$490$	−16.1839	−0.731114
$491$	4.23691	0.191209	0.0956044	−	0.995419i	$-0.469522\pi$
$491$	4.23691	0.191209	0.0956044	+	0.995419i	$0.469522\pi$
$492$	−49.0702	−2.21226
$493$	−45.6963	−2.05806
$494$	−86.2455	−3.88037
$495$	4.10019	0.184290
$496$	43.4226	1.94973
$497$	−1.40379	−0.0629684
$498$	−48.9528	−2.19363
$499$	27.2858	1.22148	0.610740	−	0.791831i	$-0.290872\pi$
$499$	27.2858	1.22148	0.610740	+	0.791831i	$0.290872\pi$
$500$	37.5665	1.68002
$501$	−18.5267	−0.827712
$502$	−17.2890	−0.771646
$503$	−3.25762	−0.145250	−0.0726251	−	0.997359i	$-0.523138\pi$
$503$	−3.25762	−0.145250	−0.0726251	+	0.997359i	$0.523138\pi$
$504$	3.02748	0.134855
$505$	−14.0890	−0.626951
$506$	41.9069	1.86299
$507$	26.2328	1.16504
$508$	43.8878	1.94721
$509$	34.5399	1.53095	0.765476	−	0.643464i	$-0.222503\pi$
$509$	34.5399	1.53095	0.765476	+	0.643464i	$0.222503\pi$
$510$	−21.8706	−0.968448
$511$	−2.80010	−0.123869
$512$	50.5470	2.23388
$513$	−33.2513	−1.46808
$514$	−29.4849	−1.30052
$515$	−14.4003	−0.634552
$516$	1.42483	0.0627245
$517$	26.6124	1.17041
$518$	−11.1856	−0.491467
$519$	−26.5875	−1.16706
$520$	32.7295	1.43528
$521$	7.23420	0.316936	0.158468	−	0.987364i	$-0.449345\pi$
$521$	7.23420	0.316936	0.158468	+	0.987364i	$0.449345\pi$
$522$	21.0447	0.921102
$523$	22.7804	0.996119	0.498059	−	0.867143i	$-0.334046\pi$
$523$	22.7804	0.996119	0.498059	+	0.867143i	$0.334046\pi$
$524$	34.9988	1.52893
$525$	−2.08415	−0.0909597
$526$	−15.9538	−0.695618
$527$	−46.3155	−2.01754
$528$	29.6515	1.29042
$529$	0.478513	0.0208049
$530$	16.7414	0.727200
$531$	7.53956	0.327189
$532$	10.0773	0.436906
$533$	−48.8567	−2.11622
$534$	−9.36298	−0.405176
$535$	6.14253	0.265565
$536$	−49.6706	−2.14544
$537$	−25.5630	−1.10312
$538$	81.7237	3.52336
$539$	−23.4035	−1.00806
$540$	23.0883	0.993562
$541$	19.3149	0.830412	0.415206	−	0.909727i	$-0.363710\pi$
$541$	19.3149	0.830412	0.415206	+	0.909727i	$0.363710\pi$
$542$	−43.2429	−1.85744
$543$	21.5147	0.923283
$544$	32.4240	1.39017
$545$	1.72483	0.0738834
$546$	−7.34501	−0.314337
$547$	27.3187	1.16806	0.584031	−	0.811731i	$-0.301475\pi$
$547$	27.3187	1.16806	0.584031	+	0.811731i	$0.301475\pi$
$548$	29.2565	1.24977
$549$	2.20423	0.0940741
$550$	35.7156	1.52292
$551$	38.2846	1.63098
$552$	38.7096	1.64759
$553$	−6.67451	−0.283829
$554$	−52.5545	−2.23283
$555$	−13.9931	−0.593976
$556$	−58.6336	−2.48662
$557$	34.8325	1.47590	0.737951	−	0.674855i	$-0.235794\pi$
$557$	34.8325	1.47590	0.737951	+	0.674855i	$0.235794\pi$
$558$	21.3299	0.902966
$559$	1.41863	0.0600015
$560$	−2.38541	−0.100802
$561$	−31.6270	−1.33529
$562$	−52.6156	−2.21945
$563$	11.2474	0.474023	0.237012	−	0.971507i	$-0.423832\pi$
$563$	11.2474	0.474023	0.237012	+	0.971507i	$0.423832\pi$
$564$	44.9778	1.89391
$565$	8.03152	0.337889
$566$	48.5531	2.04084
$567$	−1.34365	−0.0564280
$568$	22.2210	0.932371
$569$	−3.83638	−0.160829	−0.0804147	−	0.996761i	$-0.525624\pi$
$569$	−3.83638	−0.160829	−0.0804147	+	0.996761i	$0.525624\pi$
$570$	18.3233	0.767480
$571$	21.5263	0.900846	0.450423	−	0.892815i	$-0.351273\pi$
$571$	21.5263	0.900846	0.450423	+	0.892815i	$0.351273\pi$
$572$	86.5997	3.62092
$573$	16.5492	0.691352
$574$	8.29728	0.346322
$575$	20.0098	0.834466
$576$	2.13160	0.0888165
$577$	−24.1686	−1.00615	−0.503077	−	0.864242i	$-0.667799\pi$
$577$	−24.1686	−1.00615	−0.503077	+	0.864242i	$0.667799\pi$
$578$	−83.6328	−3.47867
$579$	7.28311	0.302676
$580$	−26.5832	−1.10381
$581$	5.69496	0.236267
$582$	−51.4295	−2.13182
$583$	24.2097	1.00266
$584$	44.3236	1.83413
$585$	6.89961	0.285264
$586$	−63.1238	−2.60762
$587$	10.7408	0.443319	0.221660	−	0.975124i	$-0.428853\pi$
$587$	10.7408	0.443319	0.221660	+	0.975124i	$0.428853\pi$
$588$	−39.5544	−1.63120
$589$	38.8034	1.59887
$590$	−13.8425	−0.569887
$591$	30.6879	1.26233
$592$	75.9861	3.12301
$593$	32.1925	1.32199	0.660993	−	0.750392i	$-0.270135\pi$
$593$	32.1925	1.32199	0.660993	+	0.750392i	$0.270135\pi$
$594$	48.5281	1.99113
$595$	2.54434	0.104308
$596$	40.9679	1.67811
$597$	−7.11228	−0.291086
$598$	70.5189	2.88373
$599$	−0.539314	−0.0220358	−0.0110179	−	0.999939i	$-0.503507\pi$
$599$	−0.539314	−0.0220358	−0.0110179	+	0.999939i	$0.503507\pi$
$600$	32.9907	1.34684
$601$	−13.2673	−0.541183	−0.270591	−	0.962694i	$-0.587219\pi$
$601$	−13.2673	−0.541183	−0.270591	+	0.962694i	$0.587219\pi$
$602$	−0.240924	−0.00981932
$603$	−10.4709	−0.426409
$604$	30.9795	1.26054
$605$	−0.623524	−0.0253499
$606$	−50.0489	−2.03310
$607$	27.5323	1.11750	0.558750	−	0.829336i	$-0.311281\pi$
$607$	27.5323	1.11750	0.558750	+	0.829336i	$0.311281\pi$
$608$	−27.1650	−1.10169
$609$	3.26047	0.132121
$610$	−4.04693	−0.163855
$611$	44.7821	1.81169
$612$	40.1373	1.62246
$613$	11.1044	0.448501	0.224250	−	0.974532i	$-0.428007\pi$
$613$	11.1044	0.448501	0.224250	+	0.974532i	$0.428007\pi$
$614$	48.9076	1.97375
$615$	10.3799	0.418557
$616$	−8.03799	−0.323860
$617$	30.3821	1.22314	0.611568	−	0.791192i	$-0.290539\pi$
$617$	30.3821	1.22314	0.611568	+	0.791192i	$0.290539\pi$
$618$	−51.1548	−2.05775
$619$	−8.57168	−0.344525	−0.172263	−	0.985051i	$-0.555108\pi$
$619$	−8.57168	−0.344525	−0.172263	+	0.985051i	$0.555108\pi$
$620$	−26.9435	−1.08208
$621$	27.1880	1.09102
$622$	−50.0076	−2.00512
$623$	1.08925	0.0436399
$624$	49.8962	1.99745
$625$	12.7015	0.508059
$626$	−48.1757	−1.92549
$627$	26.4973	1.05820
$628$	−52.3937	−2.09074
$629$	−81.0485	−3.23162
$630$	−1.17175	−0.0466838
$631$	3.21510	0.127991	0.0639956	−	0.997950i	$-0.479616\pi$
$631$	3.21510	0.127991	0.0639956	+	0.997950i	$0.479616\pi$
$632$	105.653	4.20265
$633$	8.32604	0.330930
$634$	3.15092	0.125139
$635$	−9.28362	−0.368409
$636$	40.9169	1.62246
$637$	−39.3822	−1.56038
$638$	−55.8739	−2.21207
$639$	4.68434	0.185310
$640$	−12.4669	−0.492798
$641$	−28.3875	−1.12124	−0.560620	−	0.828073i	$-0.689437\pi$
$641$	−28.3875	−1.12124	−0.560620	+	0.828073i	$0.689437\pi$
$642$	21.8204	0.861183
$643$	−5.93369	−0.234002	−0.117001	−	0.993132i	$-0.537328\pi$
$643$	−5.93369	−0.234002	−0.117001	+	0.993132i	$0.537328\pi$
$644$	−8.23974	−0.324691
$645$	−0.301395	−0.0118674
$646$	106.129	4.17559
$647$	−10.7236	−0.421588	−0.210794	−	0.977531i	$-0.567605\pi$
$647$	−10.7236	−0.421588	−0.210794	+	0.977531i	$0.567605\pi$
$648$	21.2691	0.835528
$649$	−20.0176	−0.785759
$650$	60.1004	2.35733
$651$	3.30465	0.129520
$652$	−37.5819	−1.47182
$653$	−15.6107	−0.610894	−0.305447	−	0.952209i	$-0.598806\pi$
$653$	−15.6107	−0.610894	−0.305447	+	0.952209i	$0.598806\pi$
$654$	6.12719	0.239592
$655$	−7.40332	−0.289272
$656$	−56.3652	−2.20069
$657$	9.34375	0.364534
$658$	−7.60530	−0.296485
$659$	−5.70008	−0.222043	−0.111022	−	0.993818i	$-0.535412\pi$
$659$	−5.70008	−0.222043	−0.111022	+	0.993818i	$0.535412\pi$
$660$	−18.3986	−0.716165
$661$	7.40890	0.288173	0.144086	−	0.989565i	$-0.453976\pi$
$661$	7.40890	0.288173	0.144086	+	0.989565i	$0.453976\pi$
$662$	63.4314	2.46533
$663$	−53.2204	−2.06691
$664$	−90.1473	−3.49840
$665$	−2.13166	−0.0826623
$666$	37.3256	1.44634
$667$	−31.3036	−1.21208
$668$	−62.4244	−2.41527
$669$	12.5802	0.486380
$670$	19.2245	0.742705
$671$	−5.85224	−0.225923
$672$	−2.31348	−0.0892445
$673$	4.43099	0.170802	0.0854010	−	0.996347i	$-0.472783\pi$
$673$	4.43099	0.170802	0.0854010	+	0.996347i	$0.472783\pi$
$674$	−44.4588	−1.71249
$675$	23.1713	0.891863
$676$	88.3894	3.39959
$677$	−33.0018	−1.26836	−0.634182	−	0.773184i	$-0.718663\pi$
$677$	−33.0018	−1.26836	−0.634182	+	0.773184i	$0.718663\pi$
$678$	28.5308	1.09572
$679$	5.98309	0.229610
$680$	−40.2751	−1.54448
$681$	10.6681	0.408802
$682$	−56.6310	−2.16851
$683$	−15.8510	−0.606520	−0.303260	−	0.952908i	$-0.598075\pi$
$683$	−15.8510	−0.606520	−0.303260	+	0.952908i	$0.598075\pi$
$684$	−33.6273	−1.28577
$685$	−6.18865	−0.236456
$686$	13.5216	0.516257
$687$	−4.87286	−0.185911
$688$	1.63665	0.0623966
$689$	40.7388	1.55203
$690$	−14.9821	−0.570361
$691$	−20.9196	−0.795819	−0.397909	−	0.917425i	$-0.630264\pi$
$691$	−20.9196	−0.795819	−0.397909	+	0.917425i	$0.630264\pi$
$692$	−89.5848	−3.40550
$693$	−1.69447	−0.0643675
$694$	13.2193	0.501797
$695$	12.4028	0.470466
$696$	−51.6110	−1.95631
$697$	60.1204	2.27722
$698$	−30.9679	−1.17215
$699$	6.90124	0.261029
$700$	−7.02239	−0.265422
$701$	12.0605	0.455520	0.227760	−	0.973717i	$-0.426860\pi$
$701$	12.0605	0.455520	0.227760	+	0.973717i	$0.426860\pi$
$702$	81.6607	3.08208
$703$	67.9029	2.56101
$704$	−5.65940	−0.213297
$705$	−9.51421	−0.358326
$706$	38.1859	1.43715
$707$	5.82248	0.218977
$708$	−33.8319	−1.27148
$709$	−1.44243	−0.0541717	−0.0270858	−	0.999633i	$-0.508623\pi$
$709$	−1.44243	−0.0541717	−0.0270858	+	0.999633i	$0.508623\pi$
$710$	−8.60038	−0.322767
$711$	22.2724	0.835281
$712$	−17.2421	−0.646174
$713$	−31.7278	−1.18821
$714$	9.03837	0.338253
$715$	−18.3185	−0.685074
$716$	−86.1327	−3.21893
$717$	6.30956	0.235635
$718$	51.9453	1.93858
$719$	28.3355	1.05674	0.528368	−	0.849016i	$-0.322804\pi$
$719$	28.3355	1.05674	0.528368	+	0.849016i	$0.322804\pi$
$720$	7.95997	0.296651
$721$	5.95114	0.221632
$722$	−40.8096	−1.51877
$723$	−28.1437	−1.04668
$724$	72.4921	2.69415
$725$	−26.6788	−0.990824
$726$	−2.21498	−0.0822055
$727$	−10.2065	−0.378537	−0.189269	−	0.981925i	$-0.560612\pi$
$727$	−10.2065	−0.378537	−0.189269	+	0.981925i	$0.560612\pi$
$728$	−13.5259	−0.501305
$729$	26.5178	0.982140
$730$	−17.1550	−0.634934
$731$	−1.74569	−0.0645665
$732$	−9.89092	−0.365579
$733$	23.2848	0.860045	0.430023	−	0.902818i	$-0.358506\pi$
$733$	23.2848	0.860045	0.430023	+	0.902818i	$0.358506\pi$
$734$	−44.1752	−1.63054
$735$	8.36698	0.308621
$736$	22.2116	0.818730
$737$	27.8004	1.02404
$738$	−27.6875	−1.01919
$739$	3.27656	0.120530	0.0602651	−	0.998182i	$-0.480805\pi$
$739$	3.27656	0.120530	0.0602651	+	0.998182i	$0.480805\pi$
$740$	−47.1489	−1.73323
$741$	44.5884	1.63800
$742$	−6.91864	−0.253991
$743$	−8.11887	−0.297853	−0.148926	−	0.988848i	$-0.547582\pi$
$743$	−8.11887	−0.297853	−0.148926	+	0.988848i	$0.547582\pi$
$744$	−52.3104	−1.91779
$745$	−8.66598	−0.317497
$746$	−66.7628	−2.44436
$747$	−19.0037	−0.695310
$748$	−106.565	−3.89640
$749$	−2.53849	−0.0927546
$750$	−28.2286	−1.03076
$751$	19.2599	0.702805	0.351403	−	0.936224i	$-0.385705\pi$
$751$	19.2599	0.702805	0.351403	+	0.936224i	$0.385705\pi$
$752$	51.6644	1.88401
$753$	8.93831	0.325730
$754$	−94.0219	−3.42407
$755$	−6.55312	−0.238493
$756$	−9.54159	−0.347024
$757$	32.2604	1.17253	0.586263	−	0.810121i	$-0.300599\pi$
$757$	32.2604	1.17253	0.586263	+	0.810121i	$0.300599\pi$
$758$	−50.0235	−1.81694
$759$	−21.6656	−0.786412
$760$	33.7427	1.22398
$761$	−17.4036	−0.630880	−0.315440	−	0.948945i	$-0.602152\pi$
$761$	−17.4036	−0.630880	−0.315440	+	0.948945i	$0.602152\pi$
$762$	−32.9787	−1.19469
$763$	−0.712811	−0.0258055
$764$	55.7613	2.01737
$765$	−8.49029	−0.306967
$766$	−24.5294	−0.886284
$767$	−33.6846	−1.21628
$768$	−39.9495	−1.44155
$769$	48.8409	1.76125	0.880623	−	0.473817i	$-0.157124\pi$
$769$	48.8409	1.76125	0.880623	+	0.473817i	$0.157124\pi$
$770$	3.11102	0.112113
$771$	15.2435	0.548981
$772$	24.5399	0.883212
$773$	2.76724	0.0995306	0.0497653	−	0.998761i	$-0.484153\pi$
$773$	2.76724	0.0995306	0.0497653	+	0.998761i	$0.484153\pi$
$774$	0.803947	0.0288973
$775$	−27.0403	−0.971316
$776$	−94.7082	−3.39982
$777$	5.78288	0.207460
$778$	3.78399	0.135663
$779$	−50.3692	−1.80467
$780$	−30.9603	−1.10856
$781$	−12.4370	−0.445030
$782$	−86.7768	−3.10313
$783$	−36.2494	−1.29545
$784$	−45.4347	−1.62267
$785$	11.0829	0.395565
$786$	−26.2992	−0.938061
$787$	−2.95386	−0.105294	−0.0526468	−	0.998613i	$-0.516766\pi$
$787$	−2.95386	−0.105294	−0.0526468	+	0.998613i	$0.516766\pi$
$788$	103.401	3.68350
$789$	8.24801	0.293637
$790$	−40.8918	−1.45487
$791$	−3.31915	−0.118015
$792$	26.8223	0.953088
$793$	−9.84787	−0.349708
$794$	−46.8176	−1.66150
$795$	−8.65520	−0.306968
$796$	−23.9643	−0.849393
$797$	14.2741	0.505614	0.252807	−	0.967517i	$-0.418646\pi$
$797$	14.2741	0.505614	0.252807	+	0.967517i	$0.418646\pi$
$798$	−7.57240	−0.268060
$799$	−55.1064	−1.94953
$800$	18.9300	0.669278
$801$	−3.63476	−0.128428
$802$	47.6851	1.68382
$803$	−24.8077	−0.875446
$804$	46.9857	1.65706
$805$	1.74296	0.0614313
$806$	−95.2960	−3.35666
$807$	−42.2506	−1.48729
$808$	−92.1659	−3.24239
$809$	−44.2992	−1.55748	−0.778738	−	0.627349i	$-0.784140\pi$
$809$	−44.2992	−1.55748	−0.778738	+	0.627349i	$0.784140\pi$
$810$	−8.23196	−0.289242
$811$	30.3659	1.06629	0.533145	−	0.846024i	$-0.321010\pi$
$811$	30.3659	1.06629	0.533145	+	0.846024i	$0.321010\pi$
$812$	10.9859	0.385530
$813$	22.3563	0.784071
$814$	−99.0998	−3.47345
$815$	7.94973	0.278467
$816$	−61.3996	−2.14942
$817$	1.46255	0.0511680
$818$	75.3684	2.63519
$819$	−2.85137	−0.0996349
$820$	34.9743	1.22135
$821$	43.0962	1.50407	0.752034	−	0.659124i	$-0.229073\pi$
$821$	43.0962	1.50407	0.752034	+	0.659124i	$0.229073\pi$
$822$	−21.9842	−0.766788
$823$	−25.0342	−0.872639	−0.436319	−	0.899792i	$-0.643718\pi$
$823$	−25.0342	−0.872639	−0.436319	+	0.899792i	$0.643718\pi$
$824$	−94.2024	−3.28170
$825$	−18.4647	−0.642859
$826$	5.72063	0.199046
$827$	−26.4506	−0.919779	−0.459890	−	0.887976i	$-0.652111\pi$
$827$	−26.4506	−0.919779	−0.459890	+	0.887976i	$0.652111\pi$
$828$	27.4955	0.955534
$829$	1.35149	0.0469392	0.0234696	−	0.999725i	$-0.492529\pi$
$829$	1.35149	0.0469392	0.0234696	+	0.999725i	$0.492529\pi$
$830$	34.8905	1.21107
$831$	27.1704	0.942529
$832$	−9.52338	−0.330164
$833$	48.4617	1.67910
$834$	44.0591	1.52564
$835$	13.2047	0.456967
$836$	89.2808	3.08784
$837$	−36.7407	−1.26994
$838$	−4.89426	−0.169069
$839$	19.6885	0.679722	0.339861	−	0.940476i	$-0.389620\pi$
$839$	19.6885	0.679722	0.339861	+	0.940476i	$0.389620\pi$
$840$	2.87366	0.0991508
$841$	12.7366	0.439193
$842$	−23.7616	−0.818878
$843$	27.2019	0.936884
$844$	28.0540	0.965658
$845$	−18.6971	−0.643200
$846$	25.3784	0.872527
$847$	0.257681	0.00885402
$848$	46.9998	1.61398
$849$	−25.1017	−0.861486
$850$	−73.9564	−2.53668
$851$	−55.5211	−1.90324
$852$	−21.0198	−0.720128
$853$	−35.4808	−1.21484	−0.607420	−	0.794381i	$-0.707796\pi$
$853$	−35.4808	−1.21484	−0.607420	+	0.794381i	$0.707796\pi$
$854$	1.67245	0.0572302
$855$	7.11322	0.243267
$856$	40.1826	1.37341
$857$	32.8319	1.12152	0.560759	−	0.827979i	$-0.310509\pi$
$857$	32.8319	1.12152	0.560759	+	0.827979i	$0.310509\pi$
$858$	−65.0738	−2.22158
$859$	26.7550	0.912868	0.456434	−	0.889757i	$-0.349126\pi$
$859$	26.7550	0.912868	0.456434	+	0.889757i	$0.349126\pi$
$860$	−1.01553	−0.0346293
$861$	−4.28964	−0.146191
$862$	−67.2593	−2.29086
$863$	−1.88148	−0.0640463	−0.0320232	−	0.999487i	$-0.510195\pi$
$863$	−1.88148	−0.0640463	−0.0320232	+	0.999487i	$0.510195\pi$
$864$	25.7210	0.875045
$865$	18.9500	0.644318
$866$	−7.04738	−0.239480
$867$	43.2377	1.46843
$868$	11.1348	0.377940
$869$	−59.1335	−2.00597
$870$	19.9755	0.677232
$871$	46.7812	1.58512
$872$	11.2833	0.382101
$873$	−19.9652	−0.675719
$874$	72.7021	2.45919
$875$	3.28400	0.111020
$876$	−41.9278	−1.41661
$877$	−3.69970	−0.124930	−0.0624650	−	0.998047i	$-0.519896\pi$
$877$	−3.69970	−0.124930	−0.0624650	+	0.998047i	$0.519896\pi$
$878$	24.3140	0.820559
$879$	32.6346	1.10074
$880$	−21.1338	−0.712420
$881$	7.85428	0.264617	0.132309	−	0.991209i	$-0.457761\pi$
$881$	7.85428	0.264617	0.132309	+	0.991209i	$0.457761\pi$
$882$	−22.3182	−0.751495
$883$	3.10947	0.104642	0.0523210	−	0.998630i	$-0.483338\pi$
$883$	3.10947	0.104642	0.0523210	+	0.998630i	$0.483338\pi$
$884$	−179.323	−6.03127
$885$	7.15649	0.240563
$886$	88.4099	2.97019
$887$	−16.4183	−0.551273	−0.275637	−	0.961262i	$-0.588889\pi$
$887$	−16.4183	−0.551273	−0.275637	+	0.961262i	$0.588889\pi$
$888$	−91.5391	−3.07185
$889$	3.83660	0.128675
$890$	6.67336	0.223691
$891$	−11.9042	−0.398806
$892$	42.3882	1.41926
$893$	46.1685	1.54497
$894$	−30.7846	−1.02959
$895$	18.2197	0.609019
$896$	5.15215	0.172121
$897$	−36.4579	−1.21729
$898$	−39.8971	−1.33138
$899$	42.3022	1.41086
$900$	23.4333	0.781109
$901$	−50.1311	−1.67011
$902$	73.5105	2.44763
$903$	0.124556	0.00414497
$904$	52.5399	1.74745
$905$	−15.3343	−0.509730
$906$	−23.2790	−0.773392
$907$	−43.7327	−1.45212	−0.726060	−	0.687632i	$-0.758650\pi$
$907$	−43.7327	−1.45212	−0.726060	+	0.687632i	$0.758650\pi$
$908$	35.9454	1.19289
$909$	−19.4293	−0.644428
$910$	5.23507	0.173541
$911$	23.1473	0.766903	0.383451	−	0.923561i	$-0.374735\pi$
$911$	23.1473	0.766903	0.383451	+	0.923561i	$0.374735\pi$
$912$	51.4409	1.70338
$913$	50.4551	1.66982
$914$	10.3299	0.341681
$915$	2.09224	0.0691672
$916$	−16.4188	−0.542491
$917$	3.05954	0.101035
$918$	−100.487	−3.31658
$919$	−18.7654	−0.619015	−0.309507	−	0.950897i	$-0.600164\pi$
$919$	−18.7654	−0.619015	−0.309507	+	0.950897i	$0.600164\pi$
$920$	−27.5899	−0.909611
$921$	−25.2849	−0.833167
$922$	−39.7660	−1.30962
$923$	−20.9283	−0.688865
$924$	7.60350	0.250137
$925$	−47.3184	−1.55582
$926$	14.4632	0.475291
$927$	−19.8586	−0.652241
$928$	−29.6144	−0.972140
$929$	−34.1521	−1.12049	−0.560247	−	0.828326i	$-0.689294\pi$
$929$	−34.1521	−1.12049	−0.560247	+	0.828326i	$0.689294\pi$
$930$	20.2462	0.663898
$931$	−40.6015	−1.33066
$932$	23.2532	0.761685
$933$	25.8536	0.846410
$934$	−4.20371	−0.137550
$935$	22.5418	0.737196
$936$	45.1352	1.47529
$937$	−25.0073	−0.816954	−0.408477	−	0.912769i	$-0.633940\pi$
$937$	−25.0073	−0.816954	−0.408477	+	0.912769i	$0.633940\pi$
$938$	−7.94480	−0.259407
$939$	24.9065	0.812794
$940$	−32.0574	−1.04560
$941$	−54.5519	−1.77834	−0.889171	−	0.457575i	$-0.848718\pi$
$941$	−54.5519	−1.77834	−0.889171	+	0.457575i	$0.848718\pi$
$942$	39.3703	1.28275
$943$	41.1846	1.34115
$944$	−38.8614	−1.26483
$945$	2.01834	0.0656567
$946$	−2.13449	−0.0693982
$947$	28.4184	0.923474	0.461737	−	0.887017i	$-0.347226\pi$
$947$	28.4184	0.923474	0.461737	+	0.887017i	$0.347226\pi$
$948$	−99.9420	−3.24597
$949$	−41.7453	−1.35511
$950$	61.9611	2.01028
$951$	−1.62901	−0.0528242
$952$	16.6443	0.539445
$953$	22.0064	0.712856	0.356428	−	0.934323i	$-0.383994\pi$
$953$	22.0064	0.712856	0.356428	+	0.934323i	$0.383994\pi$
$954$	23.0871	0.747471
$955$	−11.7952	−0.381685
$956$	21.2596	0.687585
$957$	28.8864	0.933766
$958$	49.6613	1.60448
$959$	2.55755	0.0825877
$960$	2.02330	0.0653016
$961$	11.8754	0.383078
$962$	−166.760	−5.37657
$963$	8.47079	0.272968
$964$	−94.8282	−3.05421
$965$	−5.19096	−0.167103
$966$	6.19160	0.199211
$967$	29.6829	0.954539	0.477269	−	0.878757i	$-0.341627\pi$
$967$	29.6829	0.954539	0.477269	+	0.878757i	$0.341627\pi$
$968$	−4.07891	−0.131101
$969$	−54.8681	−1.76262
$970$	36.6558	1.17695
$971$	−51.5578	−1.65457	−0.827284	−	0.561784i	$-0.810115\pi$
$971$	−51.5578	−1.65457	−0.827284	+	0.561784i	$0.810115\pi$
$972$	54.1229	1.73599
$973$	−5.12566	−0.164321
$974$	65.9562	2.11337
$975$	−31.0716	−0.995086
$976$	−11.3613	−0.363667
$977$	−47.3187	−1.51386	−0.756929	−	0.653497i	$-0.773301\pi$
$977$	−47.3187	−1.51386	−0.756929	+	0.653497i	$0.773301\pi$
$978$	28.2402	0.903022
$979$	9.65031	0.308425
$980$	28.1919	0.900559
$981$	2.37860	0.0759430
$982$	−10.7274	−0.342325
$983$	60.2262	1.92092	0.960459	−	0.278420i	$-0.0898108\pi$
$983$	60.2262	1.92092	0.960459	+	0.278420i	$0.0898108\pi$
$984$	67.9021	2.16464
$985$	−21.8724	−0.696914
$986$	115.698	3.68458
$987$	3.93189	0.125153
$988$	150.237	4.77969
$989$	−1.19586	−0.0380260
$990$	−10.3813	−0.329938
$991$	−53.3573	−1.69495	−0.847475	−	0.530836i	$-0.821878\pi$
$991$	−53.3573	−1.69495	−0.847475	+	0.530836i	$0.821878\pi$
$992$	−30.0157	−0.952999
$993$	−32.7937	−1.04068
$994$	3.55424	0.112734
$995$	5.06920	0.160704
$996$	85.2745	2.70203
$997$	−43.3011	−1.37136	−0.685680	−	0.727903i	$-0.740495\pi$
$997$	−43.3011	−1.37136	−0.685680	+	0.727903i	$0.740495\pi$
$998$	−69.0848	−2.18684
$999$	−64.2932	−2.03415

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4013.2.a.c.1.13	✓	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4013.2.a.c.1.13	✓	176	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:	\( N \)	\(=\)	\( 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.53190 q^{2} +1.30897 q^{3} +4.41050 q^{4} -0.932957 q^{5} -3.31419 q^{6} +0.385559 q^{7} -6.10313 q^{8} -1.28658 q^{9} +O(q^{10})\)	\(q-2.53190 q^{2} +1.30897 q^{3} +4.41050 q^{4} -0.932957 q^{5} -3.31419 q^{6} +0.385559 q^{7} -6.10313 q^{8} -1.28658 q^{9} +2.36215 q^{10} +3.41589 q^{11} +5.77323 q^{12} +5.74810 q^{13} -0.976195 q^{14} -1.22122 q^{15} +6.63150 q^{16} -7.07331 q^{17} +3.25750 q^{18} +5.92606 q^{19} -4.11480 q^{20} +0.504687 q^{21} -8.64869 q^{22} -4.84546 q^{23} -7.98884 q^{24} -4.12959 q^{25} -14.5536 q^{26} -5.61103 q^{27} +1.70051 q^{28} +6.46039 q^{29} +3.09199 q^{30} +6.54793 q^{31} -4.58400 q^{32} +4.47132 q^{33} +17.9089 q^{34} -0.359710 q^{35} -5.67448 q^{36} +11.4584 q^{37} -15.0042 q^{38} +7.52412 q^{39} +5.69396 q^{40} -8.49962 q^{41} -1.27781 q^{42} +0.246799 q^{43} +15.0658 q^{44} +1.20033 q^{45} +12.2682 q^{46} +7.79076 q^{47} +8.68046 q^{48} -6.85134 q^{49} +10.4557 q^{50} -9.25878 q^{51} +25.3520 q^{52} +7.08735 q^{53} +14.2065 q^{54} -3.18688 q^{55} -2.35311 q^{56} +7.75706 q^{57} -16.3570 q^{58} -5.86013 q^{59} -5.38618 q^{60} -1.71324 q^{61} -16.5787 q^{62} -0.496054 q^{63} -1.65679 q^{64} -5.36273 q^{65} -11.3209 q^{66} +8.13854 q^{67} -31.1968 q^{68} -6.34259 q^{69} +0.910747 q^{70} -3.64091 q^{71} +7.85219 q^{72} -7.26244 q^{73} -29.0114 q^{74} -5.40553 q^{75} +26.1369 q^{76} +1.31703 q^{77} -19.0503 q^{78} -17.3113 q^{79} -6.18690 q^{80} -3.48494 q^{81} +21.5201 q^{82} +14.7707 q^{83} +2.22592 q^{84} +6.59909 q^{85} -0.624869 q^{86} +8.45648 q^{87} -20.8476 q^{88} +2.82512 q^{89} -3.03911 q^{90} +2.21623 q^{91} -21.3709 q^{92} +8.57108 q^{93} -19.7254 q^{94} -5.52876 q^{95} -6.00034 q^{96} +15.5180 q^{97} +17.3469 q^{98} -4.39484 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9}+O(q^{10}) \) 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9	\( 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9} + 43 q^{10} + 18 q^{11} + 95 q^{12} + 95 q^{13} + 2 q^{14} + 36 q^{15} + 225 q^{16} + 35 q^{17} + 46 q^{18} + 127 q^{19} + 4 q^{20} + 32 q^{21} + 60 q^{22} + 35 q^{23} + 26 q^{24} + 207 q^{25} + 19 q^{26} + 191 q^{27} + 87 q^{28} + 16 q^{29} + 28 q^{30} + 93 q^{31} + 73 q^{32} + 70 q^{33} + 45 q^{34} + 73 q^{35} + 206 q^{36} + 64 q^{37} + 35 q^{38} + 72 q^{39} + 139 q^{40} + 19 q^{41} + 35 q^{42} + 261 q^{43} + 11 q^{44} + 12 q^{45} + 58 q^{46} + 40 q^{47} + 130 q^{48} + 234 q^{49} - 14 q^{50} + 76 q^{51} + 263 q^{52} + 17 q^{53} + 28 q^{54} + 170 q^{55} - 10 q^{56} + 60 q^{57} + 52 q^{58} + 69 q^{59} + 37 q^{60} + 110 q^{61} + 71 q^{62} + 101 q^{63} + 250 q^{64} - q^{65} + 43 q^{66} + 190 q^{67} + 48 q^{68} + 45 q^{69} + 14 q^{70} + 9 q^{71} + 98 q^{72} + 182 q^{73} - 23 q^{74} + 219 q^{75} + 197 q^{76} + 25 q^{77} - 26 q^{78} + 105 q^{79} + 20 q^{80} + 236 q^{81} + 107 q^{82} + 130 q^{83} + 38 q^{84} + 73 q^{85} - 24 q^{86} + 171 q^{87} + 165 q^{88} + 40 q^{89} + 45 q^{90} + 182 q^{91} - 4 q^{92} + 23 q^{93} + 98 q^{94} + 30 q^{95} - 2 q^{96} + 168 q^{97} + 82 q^{98} + 50 q^{99}+O(q^{100}) \) 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9 + 43 * q^10 + 18 * q^11 + 95 * q^12 + 95 * q^13 + 2 * q^14 + 36 * q^15 + 225 * q^16 + 35 * q^17 + 46 * q^18 + 127 * q^19 + 4 * q^20 + 32 * q^21 + 60 * q^22 + 35 * q^23 + 26 * q^24 + 207 * q^25 + 19 * q^26 + 191 * q^27 + 87 * q^28 + 16 * q^29 + 28 * q^30 + 93 * q^31 + 73 * q^32 + 70 * q^33 + 45 * q^34 + 73 * q^35 + 206 * q^36 + 64 * q^37 + 35 * q^38 + 72 * q^39 + 139 * q^40 + 19 * q^41 + 35 * q^42 + 261 * q^43 + 11 * q^44 + 12 * q^45 + 58 * q^46 + 40 * q^47 + 130 * q^48 + 234 * q^49 - 14 * q^50 + 76 * q^51 + 263 * q^52 + 17 * q^53 + 28 * q^54 + 170 * q^55 - 10 * q^56 + 60 * q^57 + 52 * q^58 + 69 * q^59 + 37 * q^60 + 110 * q^61 + 71 * q^62 + 101 * q^63 + 250 * q^64 - q^65 + 43 * q^66 + 190 * q^67 + 48 * q^68 + 45 * q^69 + 14 * q^70 + 9 * q^71 + 98 * q^72 + 182 * q^73 - 23 * q^74 + 219 * q^75 + 197 * q^76 + 25 * q^77 - 26 * q^78 + 105 * q^79 + 20 * q^80 + 236 * q^81 + 107 * q^82 + 130 * q^83 + 38 * q^84 + 73 * q^85 - 24 * q^86 + 171 * q^87 + 165 * q^88 + 40 * q^89 + 45 * q^90 + 182 * q^91 - 4 * q^92 + 23 * q^93 + 98 * q^94 + 30 * q^95 - 2 * q^96 + 168 * q^97 + 82 * q^98 + 50 * q^99

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