LMFDB - Embedded newform 6026.2.a.k.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.52794 q^{3} +1.00000 q^{4} +1.80988 q^{5} -1.52794 q^{6} +2.28195 q^{7} +1.00000 q^{8} -0.665396 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.52794 q^{3} +1.00000 q^{4} +1.80988 q^{5} -1.52794 q^{6} +2.28195 q^{7} +1.00000 q^{8} -0.665396 q^{9} +1.80988 q^{10} +6.02486 q^{11} -1.52794 q^{12} -1.69567 q^{13} +2.28195 q^{14} -2.76539 q^{15} +1.00000 q^{16} +4.34232 q^{17} -0.665396 q^{18} +7.78968 q^{19} +1.80988 q^{20} -3.48668 q^{21} +6.02486 q^{22} -1.00000 q^{23} -1.52794 q^{24} -1.72432 q^{25} -1.69567 q^{26} +5.60051 q^{27} +2.28195 q^{28} +2.33595 q^{29} -2.76539 q^{30} +4.63734 q^{31} +1.00000 q^{32} -9.20563 q^{33} +4.34232 q^{34} +4.13006 q^{35} -0.665396 q^{36} -3.98719 q^{37} +7.78968 q^{38} +2.59088 q^{39} +1.80988 q^{40} -6.85263 q^{41} -3.48668 q^{42} +3.29895 q^{43} +6.02486 q^{44} -1.20429 q^{45} -1.00000 q^{46} -2.24991 q^{47} -1.52794 q^{48} -1.79272 q^{49} -1.72432 q^{50} -6.63480 q^{51} -1.69567 q^{52} +0.341940 q^{53} +5.60051 q^{54} +10.9043 q^{55} +2.28195 q^{56} -11.9022 q^{57} +2.33595 q^{58} -10.7395 q^{59} -2.76539 q^{60} +9.39809 q^{61} +4.63734 q^{62} -1.51840 q^{63} +1.00000 q^{64} -3.06897 q^{65} -9.20563 q^{66} +9.80160 q^{67} +4.34232 q^{68} +1.52794 q^{69} +4.13006 q^{70} -16.5302 q^{71} -0.665396 q^{72} -0.667746 q^{73} -3.98719 q^{74} +2.63466 q^{75} +7.78968 q^{76} +13.7484 q^{77} +2.59088 q^{78} -11.1363 q^{79} +1.80988 q^{80} -6.56106 q^{81} -6.85263 q^{82} +16.8765 q^{83} -3.48668 q^{84} +7.85909 q^{85} +3.29895 q^{86} -3.56920 q^{87} +6.02486 q^{88} -1.05088 q^{89} -1.20429 q^{90} -3.86943 q^{91} -1.00000 q^{92} -7.08559 q^{93} -2.24991 q^{94} +14.0984 q^{95} -1.52794 q^{96} -8.59298 q^{97} -1.79272 q^{98} -4.00892 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9}+O(q^{10}) $ 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9} + 10 q^{10} + 9 q^{11} - 3 q^{12} + 19 q^{13} + 14 q^{14} + 14 q^{15} + 35 q^{16} + 28 q^{17} + 54 q^{18} + 21 q^{19} + 10 q^{20} + 28 q^{21} + 9 q^{22} - 35 q^{23} - 3 q^{24} + 81 q^{25} + 19 q^{26} - 21 q^{27} + 14 q^{28} + 35 q^{29} + 14 q^{30} + 5 q^{31} + 35 q^{32} + 26 q^{33} + 28 q^{34} - 7 q^{35} + 54 q^{36} + 51 q^{37} + 21 q^{38} + 21 q^{39} + 10 q^{40} + 3 q^{41} + 28 q^{42} + 43 q^{43} + 9 q^{44} + 2 q^{45} - 35 q^{46} + 10 q^{47} - 3 q^{48} + 85 q^{49} + 81 q^{50} + 26 q^{51} + 19 q^{52} + 39 q^{53} - 21 q^{54} + 2 q^{55} + 14 q^{56} + 50 q^{57} + 35 q^{58} - 42 q^{59} + 14 q^{60} + 47 q^{61} + 5 q^{62} + 23 q^{63} + 35 q^{64} + 61 q^{65} + 26 q^{66} + 22 q^{67} + 28 q^{68} + 3 q^{69} - 7 q^{70} + 54 q^{72} + 30 q^{73} + 51 q^{74} - 26 q^{75} + 21 q^{76} + 2 q^{77} + 21 q^{78} + 55 q^{79} + 10 q^{80} + 67 q^{81} + 3 q^{82} + 20 q^{83} + 28 q^{84} + 28 q^{85} + 43 q^{86} + 29 q^{87} + 9 q^{88} - 31 q^{89} + 2 q^{90} + 32 q^{91} - 35 q^{92} + 11 q^{93} + 10 q^{94} + 16 q^{95} - 3 q^{96} + 36 q^{97} + 85 q^{98} - 9 q^{99}+O(q^{100}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9 + 10 * q^10 + 9 * q^11 - 3 * q^12 + 19 * q^13 + 14 * q^14 + 14 * q^15 + 35 * q^16 + 28 * q^17 + 54 * q^18 + 21 * q^19 + 10 * q^20 + 28 * q^21 + 9 * q^22 - 35 * q^23 - 3 * q^24 + 81 * q^25 + 19 * q^26 - 21 * q^27 + 14 * q^28 + 35 * q^29 + 14 * q^30 + 5 * q^31 + 35 * q^32 + 26 * q^33 + 28 * q^34 - 7 * q^35 + 54 * q^36 + 51 * q^37 + 21 * q^38 + 21 * q^39 + 10 * q^40 + 3 * q^41 + 28 * q^42 + 43 * q^43 + 9 * q^44 + 2 * q^45 - 35 * q^46 + 10 * q^47 - 3 * q^48 + 85 * q^49 + 81 * q^50 + 26 * q^51 + 19 * q^52 + 39 * q^53 - 21 * q^54 + 2 * q^55 + 14 * q^56 + 50 * q^57 + 35 * q^58 - 42 * q^59 + 14 * q^60 + 47 * q^61 + 5 * q^62 + 23 * q^63 + 35 * q^64 + 61 * q^65 + 26 * q^66 + 22 * q^67 + 28 * q^68 + 3 * q^69 - 7 * q^70 + 54 * q^72 + 30 * q^73 + 51 * q^74 - 26 * q^75 + 21 * q^76 + 2 * q^77 + 21 * q^78 + 55 * q^79 + 10 * q^80 + 67 * q^81 + 3 * q^82 + 20 * q^83 + 28 * q^84 + 28 * q^85 + 43 * q^86 + 29 * q^87 + 9 * q^88 - 31 * q^89 + 2 * q^90 + 32 * q^91 - 35 * q^92 + 11 * q^93 + 10 * q^94 + 16 * q^95 - 3 * q^96 + 36 * q^97 + 85 * q^98 - 9 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.52794	−0.882157	−0.441079	−	0.897468i	$-0.645404\pi$
$3$	−1.52794	−0.882157	−0.441079	+	0.897468i	$0.645404\pi$
$4$	1.00000	0.500000
$5$	1.80988	0.809404	0.404702	−	0.914449i	$-0.367375\pi$
$5$	1.80988	0.809404	0.404702	+	0.914449i	$0.367375\pi$
$6$	−1.52794	−0.623779
$7$	2.28195	0.862495	0.431247	−	0.902234i	$-0.358074\pi$
$7$	2.28195	0.862495	0.431247	+	0.902234i	$0.358074\pi$
$8$	1.00000	0.353553
$9$	−0.665396	−0.221799
$10$	1.80988	0.572335
$11$	6.02486	1.81656	0.908282	−	0.418359i	$-0.137395\pi$
$11$	6.02486	1.81656	0.908282	+	0.418359i	$0.137395\pi$
$12$	−1.52794	−0.441079
$13$	−1.69567	−0.470294	−0.235147	−	0.971960i	$-0.575557\pi$
$13$	−1.69567	−0.470294	−0.235147	+	0.971960i	$0.575557\pi$
$14$	2.28195	0.609876
$15$	−2.76539	−0.714022
$16$	1.00000	0.250000
$17$	4.34232	1.05317	0.526583	−	0.850124i	$-0.323473\pi$
$17$	4.34232	1.05317	0.526583	+	0.850124i	$0.323473\pi$
$18$	−0.665396	−0.156835
$19$	7.78968	1.78708	0.893538	−	0.448988i	$-0.148215\pi$
$19$	7.78968	1.78708	0.893538	+	0.448988i	$0.148215\pi$
$20$	1.80988	0.404702
$21$	−3.48668	−0.760856
$22$	6.02486	1.28450
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.52794	−0.311890
$25$	−1.72432	−0.344865
$26$	−1.69567	−0.332548
$27$	5.60051	1.07782
$28$	2.28195	0.431247
$29$	2.33595	0.433776	0.216888	−	0.976197i	$-0.430409\pi$
$29$	2.33595	0.433776	0.216888	+	0.976197i	$0.430409\pi$
$30$	−2.76539	−0.504890
$31$	4.63734	0.832892	0.416446	−	0.909161i	$-0.363276\pi$
$31$	4.63734	0.832892	0.416446	+	0.909161i	$0.363276\pi$
$32$	1.00000	0.176777
$33$	−9.20563	−1.60249
$34$	4.34232	0.744701
$35$	4.13006	0.698107
$36$	−0.665396	−0.110899
$37$	−3.98719	−0.655491	−0.327745	−	0.944766i	$-0.606289\pi$
$37$	−3.98719	−0.655491	−0.327745	+	0.944766i	$0.606289\pi$
$38$	7.78968	1.26365
$39$	2.59088	0.414874
$40$	1.80988	0.286168
$41$	−6.85263	−1.07020	−0.535100	−	0.844789i	$-0.679726\pi$
$41$	−6.85263	−1.07020	−0.535100	+	0.844789i	$0.679726\pi$
$42$	−3.48668	−0.538007
$43$	3.29895	0.503085	0.251542	−	0.967846i	$-0.419062\pi$
$43$	3.29895	0.503085	0.251542	+	0.967846i	$0.419062\pi$
$44$	6.02486	0.908282
$45$	−1.20429	−0.179525
$46$	−1.00000	−0.147442
$47$	−2.24991	−0.328182	−0.164091	−	0.986445i	$-0.552469\pi$
$47$	−2.24991	−0.328182	−0.164091	+	0.986445i	$0.552469\pi$
$48$	−1.52794	−0.220539
$49$	−1.79272	−0.256102
$50$	−1.72432	−0.243856
$51$	−6.63480	−0.929058
$52$	−1.69567	−0.235147
$53$	0.341940	0.0469690	0.0234845	−	0.999724i	$-0.492524\pi$
$53$	0.341940	0.0469690	0.0234845	+	0.999724i	$0.492524\pi$
$54$	5.60051	0.762133
$55$	10.9043	1.47033
$56$	2.28195	0.304938
$57$	−11.9022	−1.57648
$58$	2.33595	0.306726
$59$	−10.7395	−1.39816	−0.699080	−	0.715043i	$-0.746407\pi$
$59$	−10.7395	−1.39816	−0.699080	+	0.715043i	$0.746407\pi$
$60$	−2.76539	−0.357011
$61$	9.39809	1.20330	0.601651	−	0.798759i	$-0.294510\pi$
$61$	9.39809	1.20330	0.601651	+	0.798759i	$0.294510\pi$
$62$	4.63734	0.588943
$63$	−1.51840	−0.191300
$64$	1.00000	0.125000
$65$	−3.06897	−0.380658
$66$	−9.20563	−1.13313
$67$	9.80160	1.19746	0.598728	−	0.800953i	$-0.295673\pi$
$67$	9.80160	1.19746	0.598728	+	0.800953i	$0.295673\pi$
$68$	4.34232	0.526583
$69$	1.52794	0.183942
$70$	4.13006	0.493636
$71$	−16.5302	−1.96178	−0.980890	−	0.194565i	$-0.937670\pi$
$71$	−16.5302	−1.96178	−0.980890	+	0.194565i	$0.937670\pi$
$72$	−0.665396	−0.0784177
$73$	−0.667746	−0.0781537	−0.0390769	−	0.999236i	$-0.512442\pi$
$73$	−0.667746	−0.0781537	−0.0390769	+	0.999236i	$0.512442\pi$
$74$	−3.98719	−0.463502
$75$	2.63466	0.304225
$76$	7.78968	0.893538
$77$	13.7484	1.56678
$78$	2.59088	0.293360
$79$	−11.1363	−1.25294	−0.626468	−	0.779447i	$-0.715500\pi$
$79$	−11.1363	−1.25294	−0.626468	+	0.779447i	$0.715500\pi$
$80$	1.80988	0.202351
$81$	−6.56106	−0.729007
$82$	−6.85263	−0.756746
$83$	16.8765	1.85243	0.926217	−	0.376990i	$-0.123041\pi$
$83$	16.8765	1.85243	0.926217	+	0.376990i	$0.123041\pi$
$84$	−3.48668	−0.380428
$85$	7.85909	0.852437
$86$	3.29895	0.355735
$87$	−3.56920	−0.382658
$88$	6.02486	0.642252
$89$	−1.05088	−0.111393	−0.0556966	−	0.998448i	$-0.517738\pi$
$89$	−1.05088	−0.111393	−0.0556966	+	0.998448i	$0.517738\pi$
$90$	−1.20429	−0.126943
$91$	−3.86943	−0.405627
$92$	−1.00000	−0.104257
$93$	−7.08559	−0.734741
$94$	−2.24991	−0.232060
$95$	14.0984	1.44647
$96$	−1.52794	−0.155945
$97$	−8.59298	−0.872485	−0.436243	−	0.899829i	$-0.643691\pi$
$97$	−8.59298	−0.872485	−0.436243	+	0.899829i	$0.643691\pi$
$98$	−1.79272	−0.181092
$99$	−4.00892	−0.402911
$100$	−1.72432	−0.172432
$101$	5.13075	0.510529	0.255264	−	0.966871i	$-0.417838\pi$
$101$	5.13075	0.510529	0.255264	+	0.966871i	$0.417838\pi$
$102$	−6.63480	−0.656943
$103$	0.118201	0.0116467	0.00582334	−	0.999983i	$-0.498146\pi$
$103$	0.118201	0.0116467	0.00582334	+	0.999983i	$0.498146\pi$
$104$	−1.69567	−0.166274
$105$	−6.31048	−0.615840
$106$	0.341940	0.0332121
$107$	9.75541	0.943091	0.471546	−	0.881842i	$-0.343696\pi$
$107$	9.75541	0.943091	0.471546	+	0.881842i	$0.343696\pi$
$108$	5.60051	0.538909
$109$	−8.86003	−0.848637	−0.424318	−	0.905513i	$-0.639486\pi$
$109$	−8.86003	−0.848637	−0.424318	+	0.905513i	$0.639486\pi$
$110$	10.9043	1.03968
$111$	6.09220	0.578246
$112$	2.28195	0.215624
$113$	−9.30219	−0.875076	−0.437538	−	0.899200i	$-0.644149\pi$
$113$	−9.30219	−0.875076	−0.437538	+	0.899200i	$0.644149\pi$
$114$	−11.9022	−1.11474
$115$	−1.80988	−0.168772
$116$	2.33595	0.216888
$117$	1.12829	0.104311
$118$	−10.7395	−0.988649
$119$	9.90894	0.908351
$120$	−2.76539	−0.252445
$121$	25.2989	2.29990
$122$	9.39809	0.850863
$123$	10.4704	0.944085
$124$	4.63734	0.416446
$125$	−12.1702	−1.08854
$126$	−1.51840	−0.135270
$127$	−15.2690	−1.35490	−0.677452	−	0.735567i	$-0.736916\pi$
$127$	−15.2690	−1.35490	−0.677452	+	0.735567i	$0.736916\pi$
$128$	1.00000	0.0883883
$129$	−5.04060	−0.443800
$130$	−3.06897	−0.269166
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−9.20563	−0.801247
$133$	17.7756	1.54134
$134$	9.80160	0.846729
$135$	10.1363	0.872391
$136$	4.34232	0.372351
$137$	9.51548	0.812963	0.406481	−	0.913659i	$-0.366756\pi$
$137$	9.51548	0.812963	0.406481	+	0.913659i	$0.366756\pi$
$138$	1.52794	0.130067
$139$	16.9557	1.43816	0.719080	−	0.694927i	$-0.244563\pi$
$139$	16.9557	1.43816	0.719080	+	0.694927i	$0.244563\pi$
$140$	4.13006	0.349054
$141$	3.43772	0.289509
$142$	−16.5302	−1.38719
$143$	−10.2162	−0.854320
$144$	−0.665396	−0.0554497
$145$	4.22780	0.351100
$146$	−0.667746	−0.0552630
$147$	2.73917	0.225923
$148$	−3.98719	−0.327745
$149$	−17.0773	−1.39903	−0.699513	−	0.714620i	$-0.746600\pi$
$149$	−17.0773	−1.39903	−0.699513	+	0.714620i	$0.746600\pi$
$150$	2.63466	0.215119
$151$	18.8555	1.53444	0.767218	−	0.641386i	$-0.221640\pi$
$151$	18.8555	1.53444	0.767218	+	0.641386i	$0.221640\pi$
$152$	7.78968	0.631827
$153$	−2.88936	−0.233591
$154$	13.7484	1.10788
$155$	8.39305	0.674146
$156$	2.59088	0.207437
$157$	−1.45596	−0.116198	−0.0580990	−	0.998311i	$-0.518504\pi$
$157$	−1.45596	−0.116198	−0.0580990	+	0.998311i	$0.518504\pi$
$158$	−11.1363	−0.885960
$159$	−0.522464	−0.0414341
$160$	1.80988	0.143084
$161$	−2.28195	−0.179843
$162$	−6.56106	−0.515485
$163$	−15.8676	−1.24285	−0.621425	−	0.783474i	$-0.713446\pi$
$163$	−15.8676	−1.24285	−0.621425	+	0.783474i	$0.713446\pi$
$164$	−6.85263	−0.535100
$165$	−16.6611	−1.29707
$166$	16.8765	1.30987
$167$	−12.3314	−0.954231	−0.477116	−	0.878841i	$-0.658318\pi$
$167$	−12.3314	−0.954231	−0.477116	+	0.878841i	$0.658318\pi$
$168$	−3.48668	−0.269003
$169$	−10.1247	−0.778823
$170$	7.85909	0.602764
$171$	−5.18322	−0.396371
$172$	3.29895	0.251542
$173$	3.44630	0.262017	0.131009	−	0.991381i	$-0.458178\pi$
$173$	3.44630	0.262017	0.131009	+	0.991381i	$0.458178\pi$
$174$	−3.56920	−0.270580
$175$	−3.93481	−0.297444
$176$	6.02486	0.454141
$177$	16.4093	1.23340
$178$	−1.05088	−0.0787669
$179$	−12.0078	−0.897508	−0.448754	−	0.893655i	$-0.648132\pi$
$179$	−12.0078	−0.897508	−0.448754	+	0.893655i	$0.648132\pi$
$180$	−1.20429	−0.0897624
$181$	1.02743	0.0763686	0.0381843	−	0.999271i	$-0.487843\pi$
$181$	1.02743	0.0763686	0.0381843	+	0.999271i	$0.487843\pi$
$182$	−3.86943	−0.286821
$183$	−14.3597	−1.06150
$184$	−1.00000	−0.0737210
$185$	−7.21635	−0.530557
$186$	−7.08559	−0.519541
$187$	26.1618	1.91314
$188$	−2.24991	−0.164091
$189$	12.7801	0.929613
$190$	14.0984	1.02281
$191$	10.4675	0.757400	0.378700	−	0.925519i	$-0.376371\pi$
$191$	10.4675	0.757400	0.378700	+	0.925519i	$0.376371\pi$
$192$	−1.52794	−0.110270
$193$	−21.9038	−1.57667	−0.788336	−	0.615245i	$-0.789057\pi$
$193$	−21.9038	−1.57667	−0.788336	+	0.615245i	$0.789057\pi$
$194$	−8.59298	−0.616940
$195$	4.68920	0.335801
$196$	−1.79272	−0.128051
$197$	12.8481	0.915390	0.457695	−	0.889109i	$-0.348675\pi$
$197$	12.8481	0.915390	0.457695	+	0.889109i	$0.348675\pi$
$198$	−4.00892	−0.284901
$199$	−2.25359	−0.159753	−0.0798764	−	0.996805i	$-0.525453\pi$
$199$	−2.25359	−0.159753	−0.0798764	+	0.996805i	$0.525453\pi$
$200$	−1.72432	−0.121928
$201$	−14.9763	−1.05634
$202$	5.13075	0.360998
$203$	5.33052	0.374129
$204$	−6.63480	−0.464529
$205$	−12.4025	−0.866225
$206$	0.118201	0.00823544
$207$	0.665396	0.0462482
$208$	−1.69567	−0.117574
$209$	46.9317	3.24634
$210$	−6.31048	−0.435465
$211$	8.58768	0.591200	0.295600	−	0.955312i	$-0.404480\pi$
$211$	8.58768	0.591200	0.295600	+	0.955312i	$0.404480\pi$
$212$	0.341940	0.0234845
$213$	25.2572	1.73060
$214$	9.75541	0.666866
$215$	5.97071	0.407199
$216$	5.60051	0.381066
$217$	10.5822	0.718365
$218$	−8.86003	−0.600077
$219$	1.02028	0.0689439
$220$	10.9043	0.735167
$221$	−7.36314	−0.495298
$222$	6.09220	0.408881
$223$	−15.5613	−1.04206	−0.521032	−	0.853537i	$-0.674453\pi$
$223$	−15.5613	−1.04206	−0.521032	+	0.853537i	$0.674453\pi$
$224$	2.28195	0.152469
$225$	1.14736	0.0764905
$226$	−9.30219	−0.618772
$227$	7.57344	0.502667	0.251333	−	0.967901i	$-0.419131\pi$
$227$	7.57344	0.502667	0.251333	+	0.967901i	$0.419131\pi$
$228$	−11.9022	−0.788241
$229$	18.0351	1.19180	0.595898	−	0.803060i	$-0.296796\pi$
$229$	18.0351	1.19180	0.595898	+	0.803060i	$0.296796\pi$
$230$	−1.80988	−0.119340
$231$	−21.0068	−1.38214
$232$	2.33595	0.153363
$233$	6.84394	0.448361	0.224181	−	0.974548i	$-0.428029\pi$
$233$	6.84394	0.448361	0.224181	+	0.974548i	$0.428029\pi$
$234$	1.12829	0.0737588
$235$	−4.07207	−0.265632
$236$	−10.7395	−0.699080
$237$	17.0157	1.10529
$238$	9.90894	0.642301
$239$	27.1525	1.75635	0.878176	−	0.478338i	$-0.158761\pi$
$239$	27.1525	1.75635	0.878176	+	0.478338i	$0.158761\pi$
$240$	−2.76539	−0.178505
$241$	−26.1645	−1.68540	−0.842702	−	0.538381i	$-0.819036\pi$
$241$	−26.1645	−1.68540	−0.842702	+	0.538381i	$0.819036\pi$
$242$	25.2989	1.62628
$243$	−6.77662	−0.434720
$244$	9.39809	0.601651
$245$	−3.24461	−0.207290
$246$	10.4704	0.667569
$247$	−13.2087	−0.840452
$248$	4.63734	0.294472
$249$	−25.7863	−1.63414
$250$	−12.1702	−0.769713
$251$	9.77762	0.617158	0.308579	−	0.951199i	$-0.400147\pi$
$251$	9.77762	0.617158	0.308579	+	0.951199i	$0.400147\pi$
$252$	−1.51840	−0.0956502
$253$	−6.02486	−0.378780
$254$	−15.2690	−0.958061
$255$	−12.0082	−0.751984
$256$	1.00000	0.0625000
$257$	14.0589	0.876973	0.438486	−	0.898738i	$-0.355515\pi$
$257$	14.0589	0.876973	0.438486	+	0.898738i	$0.355515\pi$
$258$	−5.04060	−0.313814
$259$	−9.09856	−0.565357
$260$	−3.06897	−0.190329
$261$	−1.55433	−0.0962109
$262$	−1.00000	−0.0617802
$263$	26.9954	1.66461	0.832303	−	0.554321i	$-0.187022\pi$
$263$	26.9954	1.66461	0.832303	+	0.554321i	$0.187022\pi$
$264$	−9.20563	−0.566567
$265$	0.618871	0.0380169
$266$	17.7756	1.08989
$267$	1.60568	0.0982663
$268$	9.80160	0.598728
$269$	1.34876	0.0822355	0.0411177	−	0.999154i	$-0.486908\pi$
$269$	1.34876	0.0822355	0.0411177	+	0.999154i	$0.486908\pi$
$270$	10.1363	0.616874
$271$	0.704170	0.0427753	0.0213876	−	0.999771i	$-0.493192\pi$
$271$	0.704170	0.0427753	0.0213876	+	0.999771i	$0.493192\pi$
$272$	4.34232	0.263292
$273$	5.91226	0.357826
$274$	9.51548	0.574851
$275$	−10.3888	−0.626468
$276$	1.52794	0.0919712
$277$	24.0457	1.44477	0.722384	−	0.691492i	$-0.243046\pi$
$277$	24.0457	1.44477	0.722384	+	0.691492i	$0.243046\pi$
$278$	16.9557	1.01693
$279$	−3.08567	−0.184734
$280$	4.13006	0.246818
$281$	−17.6746	−1.05438	−0.527190	−	0.849748i	$-0.676754\pi$
$281$	−17.6746	−1.05438	−0.527190	+	0.849748i	$0.676754\pi$
$282$	3.43772	0.204713
$283$	−20.4176	−1.21370	−0.606850	−	0.794816i	$-0.707567\pi$
$283$	−20.4176	−1.21370	−0.606850	+	0.794816i	$0.707567\pi$
$284$	−16.5302	−0.980890
$285$	−21.5415	−1.27601
$286$	−10.2162	−0.604095
$287$	−15.6373	−0.923043
$288$	−0.665396	−0.0392088
$289$	1.85571	0.109159
$290$	4.22780	0.248265
$291$	13.1296	0.769669
$292$	−0.667746	−0.0390769
$293$	−9.22251	−0.538785	−0.269392	−	0.963030i	$-0.586823\pi$
$293$	−9.22251	−0.538785	−0.269392	+	0.963030i	$0.586823\pi$
$294$	2.73917	0.159751
$295$	−19.4372	−1.13168
$296$	−3.98719	−0.231751
$297$	33.7423	1.95793
$298$	−17.0773	−0.989260
$299$	1.69567	0.0980632
$300$	2.63466	0.152112
$301$	7.52803	0.433908
$302$	18.8555	1.08501
$303$	−7.83948	−0.450366
$304$	7.78968	0.446769
$305$	17.0094	0.973958
$306$	−2.88936	−0.165174
$307$	−25.6122	−1.46177	−0.730883	−	0.682502i	$-0.760892\pi$
$307$	−25.6122	−1.46177	−0.730883	+	0.682502i	$0.760892\pi$
$308$	13.7484	0.783388
$309$	−0.180604	−0.0102742
$310$	8.39305	0.476693
$311$	−8.89342	−0.504299	−0.252150	−	0.967688i	$-0.581138\pi$
$311$	−8.89342	−0.504299	−0.252150	+	0.967688i	$0.581138\pi$
$312$	2.59088	0.146680
$313$	1.72337	0.0974109	0.0487054	−	0.998813i	$-0.484490\pi$
$313$	1.72337	0.0974109	0.0487054	+	0.998813i	$0.484490\pi$
$314$	−1.45596	−0.0821644
$315$	−2.74812	−0.154839
$316$	−11.1363	−0.626468
$317$	32.7597	1.83997	0.919984	−	0.391955i	$-0.128201\pi$
$317$	32.7597	1.83997	0.919984	+	0.391955i	$0.128201\pi$
$318$	−0.522464	−0.0292983
$319$	14.0738	0.787981
$320$	1.80988	0.101176
$321$	−14.9057	−0.831955
$322$	−2.28195	−0.127168
$323$	33.8253	1.88209
$324$	−6.56106	−0.364503
$325$	2.92388	0.162188
$326$	−15.8676	−0.878828
$327$	13.5376	0.748631
$328$	−6.85263	−0.378373
$329$	−5.13417	−0.283056
$330$	−16.6611	−0.917164
$331$	−3.03858	−0.167016	−0.0835079	−	0.996507i	$-0.526612\pi$
$331$	−3.03858	−0.167016	−0.0835079	+	0.996507i	$0.526612\pi$
$332$	16.8765	0.926217
$333$	2.65306	0.145387
$334$	−12.3314	−0.674743
$335$	17.7397	0.969226
$336$	−3.48668	−0.190214
$337$	15.2619	0.831367	0.415683	−	0.909509i	$-0.363542\pi$
$337$	15.2619	0.831367	0.415683	+	0.909509i	$0.363542\pi$
$338$	−10.1247	−0.550711
$339$	14.2132	0.771955
$340$	7.85909	0.426219
$341$	27.9393	1.51300
$342$	−5.18322	−0.280277
$343$	−20.0645	−1.08338
$344$	3.29895	0.177867
$345$	2.76539	0.148884
$346$	3.44630	0.185274
$347$	−4.13738	−0.222106	−0.111053	−	0.993814i	$-0.535422\pi$
$347$	−4.13738	−0.222106	−0.111053	+	0.993814i	$0.535422\pi$
$348$	−3.56920	−0.191329
$349$	29.9158	1.60136	0.800678	−	0.599096i	$-0.204473\pi$
$349$	29.9158	1.60136	0.800678	+	0.599096i	$0.204473\pi$
$350$	−3.93481	−0.210325
$351$	−9.49662	−0.506892
$352$	6.02486	0.321126
$353$	−33.9771	−1.80842	−0.904209	−	0.427089i	$-0.859539\pi$
$353$	−33.9771	−1.80842	−0.904209	+	0.427089i	$0.859539\pi$
$354$	16.4093	0.872144
$355$	−29.9178	−1.58787
$356$	−1.05088	−0.0556966
$357$	−15.1403	−0.801308
$358$	−12.0078	−0.634634
$359$	5.96865	0.315013	0.157507	−	0.987518i	$-0.449654\pi$
$359$	5.96865	0.315013	0.157507	+	0.987518i	$0.449654\pi$
$360$	−1.20429	−0.0634716
$361$	41.6791	2.19364
$362$	1.02743	0.0540008
$363$	−38.6553	−2.02888
$364$	−3.86943	−0.202813
$365$	−1.20854	−0.0632580
$366$	−14.3597	−0.750595
$367$	−1.83382	−0.0957248	−0.0478624	−	0.998854i	$-0.515241\pi$
$367$	−1.83382	−0.0957248	−0.0478624	+	0.998854i	$0.515241\pi$
$368$	−1.00000	−0.0521286
$369$	4.55971	0.237369
$370$	−7.21635	−0.375160
$371$	0.780289	0.0405106
$372$	−7.08559	−0.367371
$373$	−21.6187	−1.11937	−0.559686	−	0.828705i	$-0.689078\pi$
$373$	−21.6187	−1.11937	−0.559686	+	0.828705i	$0.689078\pi$
$374$	26.1618	1.35280
$375$	18.5954	0.960263
$376$	−2.24991	−0.116030
$377$	−3.96101	−0.204002
$378$	12.7801	0.657336
$379$	15.1858	0.780042	0.390021	−	0.920806i	$-0.372468\pi$
$379$	15.1858	0.780042	0.390021	+	0.920806i	$0.372468\pi$
$380$	14.0984	0.723233
$381$	23.3301	1.19524
$382$	10.4675	0.535563
$383$	9.39948	0.480291	0.240145	−	0.970737i	$-0.422805\pi$
$383$	9.39948	0.480291	0.240145	+	0.970737i	$0.422805\pi$
$384$	−1.52794	−0.0779724
$385$	24.8830	1.26816
$386$	−21.9038	−1.11488
$387$	−2.19511	−0.111584
$388$	−8.59298	−0.436243
$389$	29.1454	1.47773	0.738866	−	0.673853i	$-0.235362\pi$
$389$	29.1454	1.47773	0.738866	+	0.673853i	$0.235362\pi$
$390$	4.68920	0.237447
$391$	−4.34232	−0.219600
$392$	−1.79272	−0.0905459
$393$	1.52794	0.0770744
$394$	12.8481	0.647278
$395$	−20.1555	−1.01413
$396$	−4.00892	−0.201456
$397$	9.89027	0.496378	0.248189	−	0.968712i	$-0.420165\pi$
$397$	9.89027	0.496378	0.248189	+	0.968712i	$0.420165\pi$
$398$	−2.25359	−0.112962
$399$	−27.1601	−1.35971
$400$	−1.72432	−0.0862161
$401$	37.7100	1.88315	0.941573	−	0.336809i	$-0.109348\pi$
$401$	37.7100	1.88315	0.941573	+	0.336809i	$0.109348\pi$
$402$	−14.9763	−0.746948
$403$	−7.86341	−0.391704
$404$	5.13075	0.255264
$405$	−11.8748	−0.590061
$406$	5.33052	0.264549
$407$	−24.0223	−1.19074
$408$	−6.63480	−0.328472
$409$	24.7635	1.22448	0.612238	−	0.790673i	$-0.290269\pi$
$409$	24.7635	1.22448	0.612238	+	0.790673i	$0.290269\pi$
$410$	−12.4025	−0.612514
$411$	−14.5391	−0.717161
$412$	0.118201	0.00582334
$413$	−24.5069	−1.20591
$414$	0.665396	0.0327024
$415$	30.5445	1.49937
$416$	−1.69567	−0.0831371
$417$	−25.9072	−1.26868
$418$	46.9317	2.29551
$419$	−10.0729	−0.492093	−0.246046	−	0.969258i	$-0.579132\pi$
$419$	−10.0729	−0.492093	−0.246046	+	0.969258i	$0.579132\pi$
$420$	−6.31048	−0.307920
$421$	22.3802	1.09074	0.545372	−	0.838194i	$-0.316389\pi$
$421$	22.3802	1.09074	0.545372	+	0.838194i	$0.316389\pi$
$422$	8.58768	0.418042
$423$	1.49708	0.0727905
$424$	0.341940	0.0166061
$425$	−7.48755	−0.363200
$426$	25.2572	1.22372
$427$	21.4459	1.03784
$428$	9.75541	0.471546
$429$	15.6097	0.753644
$430$	5.97071	0.287933
$431$	−18.3001	−0.881482	−0.440741	−	0.897634i	$-0.645284\pi$
$431$	−18.3001	−0.881482	−0.440741	+	0.897634i	$0.645284\pi$
$432$	5.60051	0.269455
$433$	−14.4655	−0.695169	−0.347584	−	0.937649i	$-0.612998\pi$
$433$	−14.4655	−0.695169	−0.347584	+	0.937649i	$0.612998\pi$
$434$	10.5822	0.507961
$435$	−6.45983	−0.309725
$436$	−8.86003	−0.424318
$437$	−7.78968	−0.372631
$438$	1.02028	0.0487507
$439$	9.42760	0.449955	0.224977	−	0.974364i	$-0.427769\pi$
$439$	9.42760	0.449955	0.224977	+	0.974364i	$0.427769\pi$
$440$	10.9043	0.519842
$441$	1.19287	0.0568032
$442$	−7.36314	−0.350229
$443$	10.7546	0.510966	0.255483	−	0.966814i	$-0.417766\pi$
$443$	10.7546	0.510966	0.255483	+	0.966814i	$0.417766\pi$
$444$	6.09220	0.289123
$445$	−1.90197	−0.0901621
$446$	−15.5613	−0.736851
$447$	26.0931	1.23416
$448$	2.28195	0.107812
$449$	−20.4012	−0.962791	−0.481396	−	0.876503i	$-0.659870\pi$
$449$	−20.4012	−0.962791	−0.481396	+	0.876503i	$0.659870\pi$
$450$	1.14736	0.0540870
$451$	−41.2861	−1.94409
$452$	−9.30219	−0.437538
$453$	−28.8100	−1.35361
$454$	7.57344	0.355439
$455$	−7.00322	−0.328316
$456$	−11.9022	−0.557370
$457$	4.22736	0.197747	0.0988737	−	0.995100i	$-0.468476\pi$
$457$	4.22736	0.197747	0.0988737	+	0.995100i	$0.468476\pi$
$458$	18.0351	0.842726
$459$	24.3192	1.13512
$460$	−1.80988	−0.0843862
$461$	19.8212	0.923166	0.461583	−	0.887097i	$-0.347282\pi$
$461$	19.8212	0.923166	0.461583	+	0.887097i	$0.347282\pi$
$462$	−21.0068	−0.977323
$463$	−24.9229	−1.15827	−0.579133	−	0.815233i	$-0.696609\pi$
$463$	−24.9229	−1.15827	−0.579133	+	0.815233i	$0.696609\pi$
$464$	2.33595	0.108444
$465$	−12.8241	−0.594703
$466$	6.84394	0.317039
$467$	11.9021	0.550766	0.275383	−	0.961335i	$-0.411195\pi$
$467$	11.9021	0.550766	0.275383	+	0.961335i	$0.411195\pi$
$468$	1.12829	0.0521554
$469$	22.3667	1.03280
$470$	−4.07207	−0.187830
$471$	2.22462	0.102505
$472$	−10.7395	−0.494325
$473$	19.8757	0.913886
$474$	17.0157	0.781556
$475$	−13.4319	−0.616299
$476$	9.90894	0.454175
$477$	−0.227525	−0.0104177
$478$	27.1525	1.24193
$479$	−6.75608	−0.308693	−0.154347	−	0.988017i	$-0.549327\pi$
$479$	−6.75608	−0.308693	−0.154347	+	0.988017i	$0.549327\pi$
$480$	−2.76539	−0.126222
$481$	6.76097	0.308274
$482$	−26.1645	−1.19176
$483$	3.48668	0.158649
$484$	25.2989	1.14995
$485$	−15.5523	−0.706193
$486$	−6.77662	−0.307394
$487$	9.75491	0.442037	0.221019	−	0.975270i	$-0.429062\pi$
$487$	9.75491	0.442037	0.221019	+	0.975270i	$0.429062\pi$
$488$	9.39809	0.425431
$489$	24.2448	1.09639
$490$	−3.24461	−0.146576
$491$	7.18628	0.324312	0.162156	−	0.986765i	$-0.448155\pi$
$491$	7.18628	0.324312	0.162156	+	0.986765i	$0.448155\pi$
$492$	10.4704	0.472043
$493$	10.1434	0.456838
$494$	−13.2087	−0.594289
$495$	−7.25567	−0.326118
$496$	4.63734	0.208223
$497$	−37.7211	−1.69202
$498$	−25.7863	−1.15551
$499$	0.655241	0.0293326	0.0146663	−	0.999892i	$-0.495331\pi$
$499$	0.655241	0.0293326	0.0146663	+	0.999892i	$0.495331\pi$
$500$	−12.1702	−0.544270
$501$	18.8416	0.841782
$502$	9.77762	0.436396
$503$	−20.0250	−0.892869	−0.446434	−	0.894816i	$-0.647306\pi$
$503$	−20.0250	−0.892869	−0.446434	+	0.894816i	$0.647306\pi$
$504$	−1.51840	−0.0676349
$505$	9.28606	0.413224
$506$	−6.02486	−0.267838
$507$	15.4699	0.687044
$508$	−15.2690	−0.677452
$509$	25.9611	1.15070	0.575352	−	0.817906i	$-0.304865\pi$
$509$	25.9611	1.15070	0.575352	+	0.817906i	$0.304865\pi$
$510$	−12.0082	−0.531733
$511$	−1.52376	−0.0674072
$512$	1.00000	0.0441942
$513$	43.6262	1.92614
$514$	14.0589	0.620113
$515$	0.213930	0.00942687
$516$	−5.04060	−0.221900
$517$	−13.5554	−0.596164
$518$	−9.09856	−0.399768
$519$	−5.26574	−0.231140
$520$	−3.06897	−0.134583
$521$	−11.9486	−0.523478	−0.261739	−	0.965139i	$-0.584296\pi$
$521$	−11.9486	−0.523478	−0.261739	+	0.965139i	$0.584296\pi$
$522$	−1.55433	−0.0680314
$523$	0.380426	0.0166349	0.00831743	−	0.999965i	$-0.497352\pi$
$523$	0.380426	0.0166349	0.00831743	+	0.999965i	$0.497352\pi$
$524$	−1.00000	−0.0436852
$525$	6.01216	0.262392
$526$	26.9954	1.17705
$527$	20.1368	0.877174
$528$	−9.20563	−0.400624
$529$	1.00000	0.0434783
$530$	0.618871	0.0268820
$531$	7.14601	0.310110
$532$	17.7756	0.770672
$533$	11.6198	0.503309
$534$	1.60568	0.0694848
$535$	17.6562	0.763342
$536$	9.80160	0.423365
$537$	18.3473	0.791743
$538$	1.34876	0.0581493
$539$	−10.8009	−0.465226
$540$	10.1363	0.436196
$541$	−27.3742	−1.17691	−0.588454	−	0.808531i	$-0.700263\pi$
$541$	−27.3742	−1.17691	−0.588454	+	0.808531i	$0.700263\pi$
$542$	0.704170	0.0302467
$543$	−1.56986	−0.0673691
$544$	4.34232	0.186175
$545$	−16.0356	−0.686890
$546$	5.91226	0.253021
$547$	−13.3377	−0.570280	−0.285140	−	0.958486i	$-0.592040\pi$
$547$	−13.3377	−0.570280	−0.285140	+	0.958486i	$0.592040\pi$
$548$	9.51548	0.406481
$549$	−6.25345	−0.266891
$550$	−10.3888	−0.442980
$551$	18.1963	0.775190
$552$	1.52794	0.0650335
$553$	−25.4125	−1.08065
$554$	24.0457	1.02160
$555$	11.0262	0.468035
$556$	16.9557	0.719080
$557$	−24.8858	−1.05445	−0.527224	−	0.849727i	$-0.676767\pi$
$557$	−24.8858	−1.05445	−0.527224	+	0.849727i	$0.676767\pi$
$558$	−3.08567	−0.130627
$559$	−5.59393	−0.236598
$560$	4.13006	0.174527
$561$	−39.9738	−1.68769
$562$	−17.6746	−0.745559
$563$	−13.5545	−0.571255	−0.285627	−	0.958341i	$-0.592202\pi$
$563$	−13.5545	−0.571255	−0.285627	+	0.958341i	$0.592202\pi$
$564$	3.43772	0.144754
$565$	−16.8359	−0.708290
$566$	−20.4176	−0.858215
$567$	−14.9720	−0.628765
$568$	−16.5302	−0.693594
$569$	−5.93904	−0.248977	−0.124489	−	0.992221i	$-0.539729\pi$
$569$	−5.93904	−0.248977	−0.124489	+	0.992221i	$0.539729\pi$
$570$	−21.5415	−0.902276
$571$	−22.3116	−0.933713	−0.466857	−	0.884333i	$-0.654614\pi$
$571$	−22.3116	−0.933713	−0.466857	+	0.884333i	$0.654614\pi$
$572$	−10.2162	−0.427160
$573$	−15.9937	−0.668146
$574$	−15.6373	−0.652690
$575$	1.72432	0.0719092
$576$	−0.665396	−0.0277248
$577$	3.96427	0.165035	0.0825175	−	0.996590i	$-0.473704\pi$
$577$	3.96427	0.165035	0.0825175	+	0.996590i	$0.473704\pi$
$578$	1.85571	0.0771874
$579$	33.4677	1.39087
$580$	4.22780	0.175550
$581$	38.5112	1.59772
$582$	13.1296	0.544238
$583$	2.06014	0.0853222
$584$	−0.667746	−0.0276315
$585$	2.04208	0.0844296
$586$	−9.22251	−0.380979
$587$	−29.7182	−1.22660	−0.613301	−	0.789849i	$-0.710159\pi$
$587$	−29.7182	−1.22660	−0.613301	+	0.789849i	$0.710159\pi$
$588$	2.73917	0.112961
$589$	36.1234	1.48844
$590$	−19.4372	−0.800217
$591$	−19.6311	−0.807517
$592$	−3.98719	−0.163873
$593$	12.5963	0.517269	0.258634	−	0.965975i	$-0.416728\pi$
$593$	12.5963	0.517269	0.258634	+	0.965975i	$0.416728\pi$
$594$	33.7423	1.38446
$595$	17.9340	0.735223
$596$	−17.0773	−0.699513
$597$	3.44335	0.140927
$598$	1.69567	0.0693411
$599$	11.0986	0.453478	0.226739	−	0.973956i	$-0.427194\pi$
$599$	11.0986	0.453478	0.226739	+	0.973956i	$0.427194\pi$
$600$	2.63466	0.107560
$601$	11.4126	0.465528	0.232764	−	0.972533i	$-0.425223\pi$
$601$	11.4126	0.465528	0.232764	+	0.972533i	$0.425223\pi$
$602$	7.52803	0.306819
$603$	−6.52195	−0.265594
$604$	18.8555	0.767218
$605$	45.7881	1.86155
$606$	−7.83948	−0.318457
$607$	39.7313	1.61264	0.806322	−	0.591476i	$-0.201455\pi$
$607$	39.7313	1.61264	0.806322	+	0.591476i	$0.201455\pi$
$608$	7.78968	0.315913
$609$	−8.14472	−0.330041
$610$	17.0094	0.688692
$611$	3.81510	0.154342
$612$	−2.88936	−0.116795
$613$	−6.28305	−0.253770	−0.126885	−	0.991917i	$-0.540498\pi$
$613$	−6.28305	−0.253770	−0.126885	+	0.991917i	$0.540498\pi$
$614$	−25.6122	−1.03363
$615$	18.9502	0.764147
$616$	13.7484	0.553939
$617$	−27.3424	−1.10076	−0.550381	−	0.834914i	$-0.685518\pi$
$617$	−27.3424	−1.10076	−0.550381	+	0.834914i	$0.685518\pi$
$618$	−0.180604	−0.00726495
$619$	−16.6078	−0.667523	−0.333762	−	0.942657i	$-0.608318\pi$
$619$	−16.6078	−0.667523	−0.333762	+	0.942657i	$0.608318\pi$
$620$	8.39305	0.337073
$621$	−5.60051	−0.224741
$622$	−8.89342	−0.356593
$623$	−2.39806	−0.0960761
$624$	2.59088	0.103718
$625$	−13.4051	−0.536204
$626$	1.72337	0.0688799
$627$	−71.7089	−2.86378
$628$	−1.45596	−0.0580990
$629$	−17.3137	−0.690341
$630$	−2.74812	−0.109488
$631$	9.45493	0.376395	0.188197	−	0.982131i	$-0.439736\pi$
$631$	9.45493	0.376395	0.188197	+	0.982131i	$0.439736\pi$
$632$	−11.1363	−0.442980
$633$	−13.1215	−0.521532
$634$	32.7597	1.30105
$635$	−27.6351	−1.09666
$636$	−0.522464	−0.0207170
$637$	3.03986	0.120444
$638$	14.0738	0.557186
$639$	10.9992	0.435120
$640$	1.80988	0.0715419
$641$	−41.9323	−1.65623	−0.828114	−	0.560560i	$-0.810586\pi$
$641$	−41.9323	−1.65623	−0.828114	+	0.560560i	$0.810586\pi$
$642$	−14.9057	−0.588281
$643$	−32.2469	−1.27170	−0.635848	−	0.771815i	$-0.719349\pi$
$643$	−32.2469	−1.27170	−0.635848	+	0.771815i	$0.719349\pi$
$644$	−2.28195	−0.0899213
$645$	−9.12290	−0.359214
$646$	33.8253	1.33084
$647$	−18.9864	−0.746432	−0.373216	−	0.927745i	$-0.621745\pi$
$647$	−18.9864	−0.746432	−0.373216	+	0.927745i	$0.621745\pi$
$648$	−6.56106	−0.257743
$649$	−64.7038	−2.53985
$650$	2.92388	0.114684
$651$	−16.1689	−0.633711
$652$	−15.8676	−0.621425
$653$	0.971906	0.0380336	0.0190168	−	0.999819i	$-0.493946\pi$
$653$	0.971906	0.0380336	0.0190168	+	0.999819i	$0.493946\pi$
$654$	13.5376	0.529362
$655$	−1.80988	−0.0707180
$656$	−6.85263	−0.267550
$657$	0.444315	0.0173344
$658$	−5.13417	−0.200151
$659$	−37.2308	−1.45031	−0.725153	−	0.688588i	$-0.758231\pi$
$659$	−37.2308	−1.45031	−0.725153	+	0.688588i	$0.758231\pi$
$660$	−16.6611	−0.648533
$661$	11.0544	0.429965	0.214982	−	0.976618i	$-0.431031\pi$
$661$	11.0544	0.429965	0.214982	+	0.976618i	$0.431031\pi$
$662$	−3.03858	−0.118098
$663$	11.2504	0.436931
$664$	16.8765	0.654935
$665$	32.1718	1.24757
$666$	2.65306	0.102804
$667$	−2.33595	−0.0904485
$668$	−12.3314	−0.477116
$669$	23.7768	0.919265
$670$	17.7397	0.685346
$671$	56.6221	2.18587
$672$	−3.48668	−0.134502
$673$	−2.11137	−0.0813874	−0.0406937	−	0.999172i	$-0.512957\pi$
$673$	−2.11137	−0.0813874	−0.0406937	+	0.999172i	$0.512957\pi$
$674$	15.2619	0.587865
$675$	−9.65709	−0.371701
$676$	−10.1247	−0.389412
$677$	−48.7193	−1.87244	−0.936218	−	0.351419i	$-0.885699\pi$
$677$	−48.7193	−1.87244	−0.936218	+	0.351419i	$0.885699\pi$
$678$	14.2132	0.545854
$679$	−19.6087	−0.752514
$680$	7.85909	0.301382
$681$	−11.5718	−0.443431
$682$	27.9393	1.06985
$683$	−22.3426	−0.854917	−0.427458	−	0.904035i	$-0.640591\pi$
$683$	−22.3426	−0.854917	−0.427458	+	0.904035i	$0.640591\pi$
$684$	−5.18322	−0.198186
$685$	17.2219	0.658016
$686$	−20.0645	−0.766067
$687$	−27.5566	−1.05135
$688$	3.29895	0.125771
$689$	−0.579817	−0.0220893
$690$	2.76539	0.105277
$691$	9.10455	0.346353	0.173177	−	0.984891i	$-0.444597\pi$
$691$	9.10455	0.346353	0.173177	+	0.984891i	$0.444597\pi$
$692$	3.44630	0.131009
$693$	−9.14814	−0.347509
$694$	−4.13738	−0.157053
$695$	30.6878	1.16405
$696$	−3.56920	−0.135290
$697$	−29.7563	−1.12710
$698$	29.9158	1.13233
$699$	−10.4571	−0.395525
$700$	−3.93481	−0.148722
$701$	−13.3806	−0.505377	−0.252689	−	0.967548i	$-0.581315\pi$
$701$	−13.3806	−0.505377	−0.252689	+	0.967548i	$0.581315\pi$
$702$	−9.49662	−0.358427
$703$	−31.0590	−1.17141
$704$	6.02486	0.227070
$705$	6.22188	0.234329
$706$	−33.9771	−1.27875
$707$	11.7081	0.440328
$708$	16.4093	0.616699
$709$	37.3422	1.40241	0.701207	−	0.712958i	$-0.252645\pi$
$709$	37.3422	1.40241	0.701207	+	0.712958i	$0.252645\pi$
$710$	−29.9178	−1.12280
$711$	7.41008	0.277900
$712$	−1.05088	−0.0393834
$713$	−4.63734	−0.173670
$714$	−15.1403	−0.566610
$715$	−18.4901	−0.691490
$716$	−12.0078	−0.448754
$717$	−41.4875	−1.54938
$718$	5.96865	0.222748
$719$	37.6352	1.40356	0.701778	−	0.712396i	$-0.252390\pi$
$719$	37.6352	1.40356	0.701778	+	0.712396i	$0.252390\pi$
$720$	−1.20429	−0.0448812
$721$	0.269728	0.0100452
$722$	41.6791	1.55114
$723$	39.9778	1.48679
$724$	1.02743	0.0381843
$725$	−4.02794	−0.149594
$726$	−38.6553	−1.43463
$727$	−44.6613	−1.65640	−0.828198	−	0.560435i	$-0.810634\pi$
$727$	−44.6613	−1.65640	−0.828198	+	0.560435i	$0.810634\pi$
$728$	−3.86943	−0.143411
$729$	30.0374	1.11250
$730$	−1.20854	−0.0447301
$731$	14.3251	0.529832
$732$	−14.3597	−0.530751
$733$	−18.3943	−0.679408	−0.339704	−	0.940532i	$-0.610327\pi$
$733$	−18.3943	−0.679408	−0.339704	+	0.940532i	$0.610327\pi$
$734$	−1.83382	−0.0676877
$735$	4.95757	0.182863
$736$	−1.00000	−0.0368605
$737$	59.0532	2.17525
$738$	4.55971	0.167845
$739$	−37.6268	−1.38412	−0.692062	−	0.721838i	$-0.743298\pi$
$739$	−37.6268	−1.38412	−0.692062	+	0.721838i	$0.743298\pi$
$740$	−7.21635	−0.265278
$741$	20.1822	0.741410
$742$	0.780289	0.0286453
$743$	34.4481	1.26378	0.631888	−	0.775059i	$-0.282280\pi$
$743$	34.4481	1.26378	0.631888	+	0.775059i	$0.282280\pi$
$744$	−7.08559	−0.259770
$745$	−30.9079	−1.13238
$746$	−21.6187	−0.791516
$747$	−11.2295	−0.410868
$748$	26.1618	0.956572
$749$	22.2613	0.813411
$750$	18.5954	0.679008
$751$	36.4246	1.32915	0.664576	−	0.747221i	$-0.268612\pi$
$751$	36.4246	1.32915	0.664576	+	0.747221i	$0.268612\pi$
$752$	−2.24991	−0.0820456
$753$	−14.9396	−0.544430
$754$	−3.96101	−0.144251
$755$	34.1262	1.24198
$756$	12.7801	0.464807
$757$	9.54009	0.346741	0.173370	−	0.984857i	$-0.444534\pi$
$757$	9.54009	0.346741	0.173370	+	0.984857i	$0.444534\pi$
$758$	15.1858	0.551573
$759$	9.20563	0.334143
$760$	14.0984	0.511403
$761$	−22.7585	−0.824996	−0.412498	−	0.910958i	$-0.635344\pi$
$761$	−22.7585	−0.824996	−0.412498	+	0.910958i	$0.635344\pi$
$762$	23.3301	0.845161
$763$	−20.2181	−0.731945
$764$	10.4675	0.378700
$765$	−5.22941	−0.189070
$766$	9.39948	0.339617
$767$	18.2106	0.657547
$768$	−1.52794	−0.0551348
$769$	48.0325	1.73210	0.866048	−	0.499961i	$-0.166652\pi$
$769$	48.0325	1.73210	0.866048	+	0.499961i	$0.166652\pi$
$770$	24.8830	0.896722
$771$	−21.4812	−0.773628
$772$	−21.9038	−0.788336
$773$	50.6415	1.82145	0.910723	−	0.413017i	$-0.135525\pi$
$773$	50.6415	1.82145	0.910723	+	0.413017i	$0.135525\pi$
$774$	−2.19511	−0.0789015
$775$	−7.99628	−0.287235
$776$	−8.59298	−0.308470
$777$	13.9021	0.498734
$778$	29.1454	1.04491
$779$	−53.3798	−1.91253
$780$	4.68920	0.167900
$781$	−99.5924	−3.56370
$782$	−4.34232	−0.155281
$783$	13.0825	0.467531
$784$	−1.79272	−0.0640256
$785$	−2.63511	−0.0940511
$786$	1.52794	0.0544999
$787$	−48.0740	−1.71365	−0.856826	−	0.515606i	$-0.827567\pi$
$787$	−48.0740	−1.71365	−0.856826	+	0.515606i	$0.827567\pi$
$788$	12.8481	0.457695
$789$	−41.2473	−1.46844
$790$	−20.1555	−0.717100
$791$	−21.2271	−0.754749
$792$	−4.00892	−0.142451
$793$	−15.9361	−0.565906
$794$	9.89027	0.350992
$795$	−0.945598	−0.0335369
$796$	−2.25359	−0.0798764
$797$	10.1007	0.357785	0.178893	−	0.983869i	$-0.442749\pi$
$797$	10.1007	0.357785	0.178893	+	0.983869i	$0.442749\pi$
$798$	−27.1601	−0.961458
$799$	−9.76980	−0.345631
$800$	−1.72432	−0.0609640
$801$	0.699252	0.0247069
$802$	37.7100	1.33159
$803$	−4.02307	−0.141971
$804$	−14.9763	−0.528172
$805$	−4.13006	−0.145565
$806$	−7.86341	−0.276977
$807$	−2.06083	−0.0725446
$808$	5.13075	0.180499
$809$	−26.3357	−0.925914	−0.462957	−	0.886381i	$-0.653211\pi$
$809$	−26.3357	−0.925914	−0.462957	+	0.886381i	$0.653211\pi$
$810$	−11.8748	−0.417236
$811$	13.8632	0.486803	0.243402	−	0.969926i	$-0.421737\pi$
$811$	13.8632	0.486803	0.243402	+	0.969926i	$0.421737\pi$
$812$	5.33052	0.187065
$813$	−1.07593	−0.0377345
$814$	−24.0223	−0.841980
$815$	−28.7186	−1.00597
$816$	−6.63480	−0.232265
$817$	25.6978	0.899051
$818$	24.7635	0.865835
$819$	2.57470	0.0899675
$820$	−12.4025	−0.433112
$821$	−26.4347	−0.922579	−0.461289	−	0.887250i	$-0.652613\pi$
$821$	−26.4347	−0.922579	−0.461289	+	0.887250i	$0.652613\pi$
$822$	−14.5391	−0.507109
$823$	11.9261	0.415717	0.207859	−	0.978159i	$-0.433351\pi$
$823$	11.9261	0.415717	0.207859	+	0.978159i	$0.433351\pi$
$824$	0.118201	0.00411772
$825$	15.8735	0.552643
$826$	−24.5069	−0.852705
$827$	23.7163	0.824697	0.412348	−	0.911026i	$-0.364709\pi$
$827$	23.7163	0.824697	0.412348	+	0.911026i	$0.364709\pi$
$828$	0.665396	0.0231241
$829$	34.2832	1.19070	0.595352	−	0.803465i	$-0.297012\pi$
$829$	34.2832	1.19070	0.595352	+	0.803465i	$0.297012\pi$
$830$	30.5445	1.06021
$831$	−36.7404	−1.27451
$832$	−1.69567	−0.0587868
$833$	−7.78454	−0.269718
$834$	−25.9072	−0.897095
$835$	−22.3184	−0.772359
$836$	46.9317	1.62317
$837$	25.9715	0.897706
$838$	−10.0729	−0.347962
$839$	−16.6124	−0.573523	−0.286761	−	0.958002i	$-0.592579\pi$
$839$	−16.6124	−0.573523	−0.286761	+	0.958002i	$0.592579\pi$
$840$	−6.31048	−0.217732
$841$	−23.5433	−0.811839
$842$	22.3802	0.771272
$843$	27.0058	0.930128
$844$	8.58768	0.295600
$845$	−18.3245	−0.630383
$846$	1.49708	0.0514706
$847$	57.7308	1.98365
$848$	0.341940	0.0117423
$849$	31.1969	1.07067
$850$	−7.48755	−0.256821
$851$	3.98719	0.136679
$852$	25.2572	0.865299
$853$	−15.0798	−0.516322	−0.258161	−	0.966102i	$-0.583117\pi$
$853$	−15.0798	−0.516322	−0.258161	+	0.966102i	$0.583117\pi$
$854$	21.4459	0.733865
$855$	−9.38103	−0.320824
$856$	9.75541	0.333433
$857$	−27.4415	−0.937383	−0.468692	−	0.883362i	$-0.655274\pi$
$857$	−27.4415	−0.937383	−0.468692	+	0.883362i	$0.655274\pi$
$858$	15.6097	0.532907
$859$	31.2894	1.06758	0.533790	−	0.845617i	$-0.320767\pi$
$859$	31.2894	1.06758	0.533790	+	0.845617i	$0.320767\pi$
$860$	5.97071	0.203600
$861$	23.8929	0.814269
$862$	−18.3001	−0.623302
$863$	−18.6536	−0.634976	−0.317488	−	0.948262i	$-0.602839\pi$
$863$	−18.6536	−0.634976	−0.317488	+	0.948262i	$0.602839\pi$
$864$	5.60051	0.190533
$865$	6.23740	0.212078
$866$	−14.4655	−0.491558
$867$	−2.83542	−0.0962957
$868$	10.5822	0.359182
$869$	−67.0949	−2.27604
$870$	−6.45983	−0.219009
$871$	−16.6203	−0.563157
$872$	−8.86003	−0.300038
$873$	5.71774	0.193516
$874$	−7.78968	−0.263490
$875$	−27.7718	−0.938860
$876$	1.02028	0.0344719
$877$	23.4818	0.792924	0.396462	−	0.918051i	$-0.370238\pi$
$877$	23.4818	0.792924	0.396462	+	0.918051i	$0.370238\pi$
$878$	9.42760	0.318166
$879$	14.0915	0.475293
$880$	10.9043	0.367584
$881$	35.5924	1.19914	0.599569	−	0.800323i	$-0.295339\pi$
$881$	35.5924	1.19914	0.599569	+	0.800323i	$0.295339\pi$
$882$	1.19287	0.0401659
$883$	−32.1758	−1.08280	−0.541400	−	0.840765i	$-0.682106\pi$
$883$	−32.1758	−1.08280	−0.541400	+	0.840765i	$0.682106\pi$
$884$	−7.36314	−0.247649
$885$	29.6989	0.998317
$886$	10.7546	0.361307
$887$	−39.2975	−1.31948	−0.659741	−	0.751493i	$-0.729334\pi$
$887$	−39.2975	−1.31948	−0.659741	+	0.751493i	$0.729334\pi$
$888$	6.09220	0.204441
$889$	−34.8430	−1.16860
$890$	−1.90197	−0.0637543
$891$	−39.5295	−1.32429
$892$	−15.5613	−0.521032
$893$	−17.5260	−0.586487
$894$	26.0931	0.872683
$895$	−21.7328	−0.726447
$896$	2.28195	0.0762345
$897$	−2.59088	−0.0865071
$898$	−20.4012	−0.680796
$899$	10.8326	0.361288
$900$	1.14736	0.0382453
$901$	1.48481	0.0494662
$902$	−41.2861	−1.37468
$903$	−11.5024	−0.382775
$904$	−9.30219	−0.309386
$905$	1.85954	0.0618131
$906$	−28.8100	−0.957149
$907$	17.1970	0.571018	0.285509	−	0.958376i	$-0.407837\pi$
$907$	17.1970	0.571018	0.285509	+	0.958376i	$0.407837\pi$
$908$	7.57344	0.251333
$909$	−3.41398	−0.113235
$910$	−7.00322	−0.232154
$911$	−20.4081	−0.676150	−0.338075	−	0.941119i	$-0.609776\pi$
$911$	−20.4081	−0.676150	−0.338075	+	0.941119i	$0.609776\pi$
$912$	−11.9022	−0.394120
$913$	101.678	3.36507
$914$	4.22736	0.139828
$915$	−25.9894	−0.859184
$916$	18.0351	0.595898
$917$	−2.28195	−0.0753565
$918$	24.3192	0.802653
$919$	−4.64664	−0.153279	−0.0766393	−	0.997059i	$-0.524419\pi$
$919$	−4.64664	−0.153279	−0.0766393	+	0.997059i	$0.524419\pi$
$920$	−1.80988	−0.0596701
$921$	39.1340	1.28951
$922$	19.8212	0.652777
$923$	28.0299	0.922614
$924$	−21.0068	−0.691072
$925$	6.87521	0.226055
$926$	−24.9229	−0.819018
$927$	−0.0786504	−0.00258322
$928$	2.33595	0.0766814
$929$	−58.2776	−1.91203	−0.956013	−	0.293323i	$-0.905239\pi$
$929$	−58.2776	−1.91203	−0.956013	+	0.293323i	$0.905239\pi$
$930$	−12.8241	−0.420518
$931$	−13.9647	−0.457674
$932$	6.84394	0.224181
$933$	13.5886	0.444871
$934$	11.9021	0.389450
$935$	47.3499	1.54851
$936$	1.12829	0.0368794
$937$	−6.77308	−0.221267	−0.110633	−	0.993861i	$-0.535288\pi$
$937$	−6.77308	−0.221267	−0.110633	+	0.993861i	$0.535288\pi$
$938$	22.3667	0.730300
$939$	−2.63321	−0.0859317
$940$	−4.07207	−0.132816
$941$	−2.81160	−0.0916554	−0.0458277	−	0.998949i	$-0.514593\pi$
$941$	−2.81160	−0.0916554	−0.0458277	+	0.998949i	$0.514593\pi$
$942$	2.22462	0.0724819
$943$	6.85263	0.223152
$944$	−10.7395	−0.349540
$945$	23.1304	0.752433
$946$	19.8757	0.646215
$947$	33.2305	1.07985	0.539924	−	0.841714i	$-0.318453\pi$
$947$	33.2305	1.07985	0.539924	+	0.841714i	$0.318453\pi$
$948$	17.0157	0.552644
$949$	1.13228	0.0367553
$950$	−13.4319	−0.435789
$951$	−50.0549	−1.62314
$952$	9.90894	0.321150
$953$	2.20319	0.0713684	0.0356842	−	0.999363i	$-0.488639\pi$
$953$	2.20319	0.0713684	0.0356842	+	0.999363i	$0.488639\pi$
$954$	−0.227525	−0.00736641
$955$	18.9449	0.613043
$956$	27.1525	0.878176
$957$	−21.5039	−0.695123
$958$	−6.75608	−0.218279
$959$	21.7138	0.701176
$960$	−2.76539	−0.0892527
$961$	−9.49503	−0.306291
$962$	6.76097	0.217982
$963$	−6.49121	−0.209176
$964$	−26.1645	−0.842702
$965$	−39.6434	−1.27616
$966$	3.48668	0.112182
$967$	−3.79915	−0.122172	−0.0610862	−	0.998132i	$-0.519456\pi$
$967$	−3.79915	−0.122172	−0.0610862	+	0.998132i	$0.519456\pi$
$968$	25.2989	0.813138
$969$	−51.6830	−1.66030
$970$	−15.5523	−0.499354
$971$	−0.277635	−0.00890975	−0.00445487	−	0.999990i	$-0.501418\pi$
$971$	−0.277635	−0.00890975	−0.00445487	+	0.999990i	$0.501418\pi$
$972$	−6.77662	−0.217360
$973$	38.6919	1.24041
$974$	9.75491	0.312568
$975$	−4.46752	−0.143075
$976$	9.39809	0.300825
$977$	56.1634	1.79683	0.898413	−	0.439151i	$-0.144721\pi$
$977$	56.1634	1.79683	0.898413	+	0.439151i	$0.144721\pi$
$978$	24.2448	0.775264
$979$	−6.33141	−0.202353
$980$	−3.24461	−0.103645
$981$	5.89543	0.188227
$982$	7.18628	0.229323
$983$	−57.5418	−1.83530	−0.917650	−	0.397391i	$-0.869916\pi$
$983$	−57.5418	−1.83530	−0.917650	+	0.397391i	$0.869916\pi$
$984$	10.4704	0.333784
$985$	23.2536	0.740920
$986$	10.1434	0.323033
$987$	7.84470	0.249700
$988$	−13.2087	−0.420226
$989$	−3.29895	−0.104900
$990$	−7.25567	−0.230600
$991$	42.8725	1.36189	0.680945	−	0.732334i	$-0.261569\pi$
$991$	42.8725	1.36189	0.680945	+	0.732334i	$0.261569\pi$
$992$	4.63734	0.147236
$993$	4.64278	0.147334
$994$	−37.7211	−1.19644
$995$	−4.07874	−0.129305
$996$	−25.7863	−0.817069
$997$	12.5309	0.396858	0.198429	−	0.980115i	$-0.436416\pi$
$997$	12.5309	0.396858	0.198429	+	0.980115i	$0.436416\pi$
$998$	0.655241	0.0207413
$999$	−22.3303	−0.706500

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.k.1.13	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.k.1.13	✓	35	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.52794 q^{3} +1.00000 q^{4} +1.80988 q^{5} -1.52794 q^{6} +2.28195 q^{7} +1.00000 q^{8} -0.665396 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.52794 q^{3} +1.00000 q^{4} +1.80988 q^{5} -1.52794 q^{6} +2.28195 q^{7} +1.00000 q^{8} -0.665396 q^{9} +1.80988 q^{10} +6.02486 q^{11} -1.52794 q^{12} -1.69567 q^{13} +2.28195 q^{14} -2.76539 q^{15} +1.00000 q^{16} +4.34232 q^{17} -0.665396 q^{18} +7.78968 q^{19} +1.80988 q^{20} -3.48668 q^{21} +6.02486 q^{22} -1.00000 q^{23} -1.52794 q^{24} -1.72432 q^{25} -1.69567 q^{26} +5.60051 q^{27} +2.28195 q^{28} +2.33595 q^{29} -2.76539 q^{30} +4.63734 q^{31} +1.00000 q^{32} -9.20563 q^{33} +4.34232 q^{34} +4.13006 q^{35} -0.665396 q^{36} -3.98719 q^{37} +7.78968 q^{38} +2.59088 q^{39} +1.80988 q^{40} -6.85263 q^{41} -3.48668 q^{42} +3.29895 q^{43} +6.02486 q^{44} -1.20429 q^{45} -1.00000 q^{46} -2.24991 q^{47} -1.52794 q^{48} -1.79272 q^{49} -1.72432 q^{50} -6.63480 q^{51} -1.69567 q^{52} +0.341940 q^{53} +5.60051 q^{54} +10.9043 q^{55} +2.28195 q^{56} -11.9022 q^{57} +2.33595 q^{58} -10.7395 q^{59} -2.76539 q^{60} +9.39809 q^{61} +4.63734 q^{62} -1.51840 q^{63} +1.00000 q^{64} -3.06897 q^{65} -9.20563 q^{66} +9.80160 q^{67} +4.34232 q^{68} +1.52794 q^{69} +4.13006 q^{70} -16.5302 q^{71} -0.665396 q^{72} -0.667746 q^{73} -3.98719 q^{74} +2.63466 q^{75} +7.78968 q^{76} +13.7484 q^{77} +2.59088 q^{78} -11.1363 q^{79} +1.80988 q^{80} -6.56106 q^{81} -6.85263 q^{82} +16.8765 q^{83} -3.48668 q^{84} +7.85909 q^{85} +3.29895 q^{86} -3.56920 q^{87} +6.02486 q^{88} -1.05088 q^{89} -1.20429 q^{90} -3.86943 q^{91} -1.00000 q^{92} -7.08559 q^{93} -2.24991 q^{94} +14.0984 q^{95} -1.52794 q^{96} -8.59298 q^{97} -1.79272 q^{98} -4.00892 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9}+O(q^{10}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9} + 10 q^{10} + 9 q^{11} - 3 q^{12} + 19 q^{13} + 14 q^{14} + 14 q^{15} + 35 q^{16} + 28 q^{17} + 54 q^{18} + 21 q^{19} + 10 q^{20} + 28 q^{21} + 9 q^{22} - 35 q^{23} - 3 q^{24} + 81 q^{25} + 19 q^{26} - 21 q^{27} + 14 q^{28} + 35 q^{29} + 14 q^{30} + 5 q^{31} + 35 q^{32} + 26 q^{33} + 28 q^{34} - 7 q^{35} + 54 q^{36} + 51 q^{37} + 21 q^{38} + 21 q^{39} + 10 q^{40} + 3 q^{41} + 28 q^{42} + 43 q^{43} + 9 q^{44} + 2 q^{45} - 35 q^{46} + 10 q^{47} - 3 q^{48} + 85 q^{49} + 81 q^{50} + 26 q^{51} + 19 q^{52} + 39 q^{53} - 21 q^{54} + 2 q^{55} + 14 q^{56} + 50 q^{57} + 35 q^{58} - 42 q^{59} + 14 q^{60} + 47 q^{61} + 5 q^{62} + 23 q^{63} + 35 q^{64} + 61 q^{65} + 26 q^{66} + 22 q^{67} + 28 q^{68} + 3 q^{69} - 7 q^{70} + 54 q^{72} + 30 q^{73} + 51 q^{74} - 26 q^{75} + 21 q^{76} + 2 q^{77} + 21 q^{78} + 55 q^{79} + 10 q^{80} + 67 q^{81} + 3 q^{82} + 20 q^{83} + 28 q^{84} + 28 q^{85} + 43 q^{86} + 29 q^{87} + 9 q^{88} - 31 q^{89} + 2 q^{90} + 32 q^{91} - 35 q^{92} + 11 q^{93} + 10 q^{94} + 16 q^{95} - 3 q^{96} + 36 q^{97} + 85 q^{98} - 9 q^{99}+O(q^{100}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9 + 10 * q^10 + 9 * q^11 - 3 * q^12 + 19 * q^13 + 14 * q^14 + 14 * q^15 + 35 * q^16 + 28 * q^17 + 54 * q^18 + 21 * q^19 + 10 * q^20 + 28 * q^21 + 9 * q^22 - 35 * q^23 - 3 * q^24 + 81 * q^25 + 19 * q^26 - 21 * q^27 + 14 * q^28 + 35 * q^29 + 14 * q^30 + 5 * q^31 + 35 * q^32 + 26 * q^33 + 28 * q^34 - 7 * q^35 + 54 * q^36 + 51 * q^37 + 21 * q^38 + 21 * q^39 + 10 * q^40 + 3 * q^41 + 28 * q^42 + 43 * q^43 + 9 * q^44 + 2 * q^45 - 35 * q^46 + 10 * q^47 - 3 * q^48 + 85 * q^49 + 81 * q^50 + 26 * q^51 + 19 * q^52 + 39 * q^53 - 21 * q^54 + 2 * q^55 + 14 * q^56 + 50 * q^57 + 35 * q^58 - 42 * q^59 + 14 * q^60 + 47 * q^61 + 5 * q^62 + 23 * q^63 + 35 * q^64 + 61 * q^65 + 26 * q^66 + 22 * q^67 + 28 * q^68 + 3 * q^69 - 7 * q^70 + 54 * q^72 + 30 * q^73 + 51 * q^74 - 26 * q^75 + 21 * q^76 + 2 * q^77 + 21 * q^78 + 55 * q^79 + 10 * q^80 + 67 * q^81 + 3 * q^82 + 20 * q^83 + 28 * q^84 + 28 * q^85 + 43 * q^86 + 29 * q^87 + 9 * q^88 - 31 * q^89 + 2 * q^90 + 32 * q^91 - 35 * q^92 + 11 * q^93 + 10 * q^94 + 16 * q^95 - 3 * q^96 + 36 * q^97 + 85 * q^98 - 9 * q^99

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