LMFDB - Embedded newform 4022.2.a.f.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4022,2,Mod(1,4022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4022, 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("4022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4022 = 2 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4022.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:	$32.1158316930$
Analytic rank:	$0$
Dimension:	$50$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	4022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.49143 q^{3} +1.00000 q^{4} +2.52331 q^{5} -2.49143 q^{6} +1.07230 q^{7} +1.00000 q^{8} +3.20721 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.49143 q^{3} +1.00000 q^{4} +2.52331 q^{5} -2.49143 q^{6} +1.07230 q^{7} +1.00000 q^{8} +3.20721 q^{9} +2.52331 q^{10} +3.78431 q^{11} -2.49143 q^{12} +3.19901 q^{13} +1.07230 q^{14} -6.28663 q^{15} +1.00000 q^{16} -1.39908 q^{17} +3.20721 q^{18} +2.39669 q^{19} +2.52331 q^{20} -2.67155 q^{21} +3.78431 q^{22} +8.17419 q^{23} -2.49143 q^{24} +1.36707 q^{25} +3.19901 q^{26} -0.516245 q^{27} +1.07230 q^{28} +6.40392 q^{29} -6.28663 q^{30} -5.65216 q^{31} +1.00000 q^{32} -9.42832 q^{33} -1.39908 q^{34} +2.70574 q^{35} +3.20721 q^{36} -7.08052 q^{37} +2.39669 q^{38} -7.97009 q^{39} +2.52331 q^{40} +4.40289 q^{41} -2.67155 q^{42} -9.04539 q^{43} +3.78431 q^{44} +8.09277 q^{45} +8.17419 q^{46} +7.69695 q^{47} -2.49143 q^{48} -5.85018 q^{49} +1.36707 q^{50} +3.48571 q^{51} +3.19901 q^{52} -1.93801 q^{53} -0.516245 q^{54} +9.54896 q^{55} +1.07230 q^{56} -5.97119 q^{57} +6.40392 q^{58} +1.51620 q^{59} -6.28663 q^{60} -1.36191 q^{61} -5.65216 q^{62} +3.43908 q^{63} +1.00000 q^{64} +8.07207 q^{65} -9.42832 q^{66} -2.26610 q^{67} -1.39908 q^{68} -20.3654 q^{69} +2.70574 q^{70} +9.10967 q^{71} +3.20721 q^{72} -2.42541 q^{73} -7.08052 q^{74} -3.40596 q^{75} +2.39669 q^{76} +4.05790 q^{77} -7.97009 q^{78} -12.5503 q^{79} +2.52331 q^{80} -8.33544 q^{81} +4.40289 q^{82} +14.2698 q^{83} -2.67155 q^{84} -3.53031 q^{85} -9.04539 q^{86} -15.9549 q^{87} +3.78431 q^{88} -10.1769 q^{89} +8.09277 q^{90} +3.43029 q^{91} +8.17419 q^{92} +14.0819 q^{93} +7.69695 q^{94} +6.04759 q^{95} -2.49143 q^{96} -12.2522 q^{97} -5.85018 q^{98} +12.1371 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9}+O(q^{10}) $ 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9} + 11 q^{10} + 21 q^{11} + 18 q^{12} + 26 q^{13} + 30 q^{14} + 17 q^{15} + 50 q^{16} + 24 q^{17} + 66 q^{18} + 39 q^{19} + 11 q^{20} - q^{21} + 21 q^{22} + 28 q^{23} + 18 q^{24} + 79 q^{25} + 26 q^{26} + 66 q^{27} + 30 q^{28} - 5 q^{29} + 17 q^{30} + 60 q^{31} + 50 q^{32} + 37 q^{33} + 24 q^{34} + 38 q^{35} + 66 q^{36} + 35 q^{37} + 39 q^{38} + 37 q^{39} + 11 q^{40} + 42 q^{41} - q^{42} + 44 q^{43} + 21 q^{44} + 31 q^{45} + 28 q^{46} + 60 q^{47} + 18 q^{48} + 92 q^{49} + 79 q^{50} + 26 q^{51} + 26 q^{52} - 2 q^{53} + 66 q^{54} + 33 q^{55} + 30 q^{56} + 15 q^{57} - 5 q^{58} + 65 q^{59} + 17 q^{60} + 15 q^{61} + 60 q^{62} + 56 q^{63} + 50 q^{64} + 6 q^{65} + 37 q^{66} + 48 q^{67} + 24 q^{68} - 9 q^{69} + 38 q^{70} + 34 q^{71} + 66 q^{72} + 91 q^{73} + 35 q^{74} + 54 q^{75} + 39 q^{76} - 6 q^{77} + 37 q^{78} + 29 q^{79} + 11 q^{80} + 66 q^{81} + 42 q^{82} + 43 q^{83} - q^{84} + 44 q^{86} + 32 q^{87} + 21 q^{88} + 38 q^{89} + 31 q^{90} + 55 q^{91} + 28 q^{92} - 15 q^{93} + 60 q^{94} + 9 q^{95} + 18 q^{96} + 80 q^{97} + 92 q^{98} + 20 q^{99}+O(q^{100}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9 + 11 * q^10 + 21 * q^11 + 18 * q^12 + 26 * q^13 + 30 * q^14 + 17 * q^15 + 50 * q^16 + 24 * q^17 + 66 * q^18 + 39 * q^19 + 11 * q^20 - q^21 + 21 * q^22 + 28 * q^23 + 18 * q^24 + 79 * q^25 + 26 * q^26 + 66 * q^27 + 30 * q^28 - 5 * q^29 + 17 * q^30 + 60 * q^31 + 50 * q^32 + 37 * q^33 + 24 * q^34 + 38 * q^35 + 66 * q^36 + 35 * q^37 + 39 * q^38 + 37 * q^39 + 11 * q^40 + 42 * q^41 - q^42 + 44 * q^43 + 21 * q^44 + 31 * q^45 + 28 * q^46 + 60 * q^47 + 18 * q^48 + 92 * q^49 + 79 * q^50 + 26 * q^51 + 26 * q^52 - 2 * q^53 + 66 * q^54 + 33 * q^55 + 30 * q^56 + 15 * q^57 - 5 * q^58 + 65 * q^59 + 17 * q^60 + 15 * q^61 + 60 * q^62 + 56 * q^63 + 50 * q^64 + 6 * q^65 + 37 * q^66 + 48 * q^67 + 24 * q^68 - 9 * q^69 + 38 * q^70 + 34 * q^71 + 66 * q^72 + 91 * q^73 + 35 * q^74 + 54 * q^75 + 39 * q^76 - 6 * q^77 + 37 * q^78 + 29 * q^79 + 11 * q^80 + 66 * q^81 + 42 * q^82 + 43 * q^83 - q^84 + 44 * q^86 + 32 * q^87 + 21 * q^88 + 38 * q^89 + 31 * q^90 + 55 * q^91 + 28 * q^92 - 15 * q^93 + 60 * q^94 + 9 * q^95 + 18 * q^96 + 80 * q^97 + 92 * q^98 + 20 * 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
$3$	−2.49143	−1.43843	−0.719213	−	0.694790i	$-0.755497\pi$
$3$	−2.49143	−1.43843	−0.719213	+	0.694790i	$0.755497\pi$
$4$	1.00000	0.500000
$5$	2.52331	1.12846	0.564228	−	0.825619i	$-0.309174\pi$
$5$	2.52331	1.12846	0.564228	+	0.825619i	$0.309174\pi$
$6$	−2.49143	−1.01712
$7$	1.07230	0.405291	0.202645	−	0.979252i	$-0.435046\pi$
$7$	1.07230	0.405291	0.202645	+	0.979252i	$0.435046\pi$
$8$	1.00000	0.353553
$9$	3.20721	1.06907
$10$	2.52331	0.797939
$11$	3.78431	1.14101	0.570506	−	0.821294i	$-0.306747\pi$
$11$	3.78431	1.14101	0.570506	+	0.821294i	$0.306747\pi$
$12$	−2.49143	−0.719213
$13$	3.19901	0.887245	0.443622	−	0.896214i	$-0.353693\pi$
$13$	3.19901	0.887245	0.443622	+	0.896214i	$0.353693\pi$
$14$	1.07230	0.286584
$15$	−6.28663	−1.62320
$16$	1.00000	0.250000
$17$	−1.39908	−0.339327	−0.169664	−	0.985502i	$-0.554268\pi$
$17$	−1.39908	−0.339327	−0.169664	+	0.985502i	$0.554268\pi$
$18$	3.20721	0.755946
$19$	2.39669	0.549839	0.274920	−	0.961467i	$-0.411349\pi$
$19$	2.39669	0.549839	0.274920	+	0.961467i	$0.411349\pi$
$20$	2.52331	0.564228
$21$	−2.67155	−0.582980
$22$	3.78431	0.806817
$23$	8.17419	1.70444	0.852218	−	0.523187i	$-0.175257\pi$
$23$	8.17419	1.70444	0.852218	+	0.523187i	$0.175257\pi$
$24$	−2.49143	−0.508560
$25$	1.36707	0.273414
$26$	3.19901	0.627377
$27$	−0.516245	−0.0993513
$28$	1.07230	0.202645
$29$	6.40392	1.18918	0.594589	−	0.804030i	$-0.297315\pi$
$29$	6.40392	1.18918	0.594589	+	0.804030i	$0.297315\pi$
$30$	−6.28663	−1.14778
$31$	−5.65216	−1.01516	−0.507579	−	0.861605i	$-0.669459\pi$
$31$	−5.65216	−1.01516	−0.507579	+	0.861605i	$0.669459\pi$
$32$	1.00000	0.176777
$33$	−9.42832	−1.64126
$34$	−1.39908	−0.239941
$35$	2.70574	0.457353
$36$	3.20721	0.534535
$37$	−7.08052	−1.16403	−0.582015	−	0.813178i	$-0.697736\pi$
$37$	−7.08052	−1.16403	−0.582015	+	0.813178i	$0.697736\pi$
$38$	2.39669	0.388795
$39$	−7.97009	−1.27624
$40$	2.52331	0.398970
$41$	4.40289	0.687616	0.343808	−	0.939040i	$-0.388283\pi$
$41$	4.40289	0.687616	0.343808	+	0.939040i	$0.388283\pi$
$42$	−2.67155	−0.412229
$43$	−9.04539	−1.37941	−0.689705	−	0.724091i	$-0.742260\pi$
$43$	−9.04539	−1.37941	−0.689705	+	0.724091i	$0.742260\pi$
$44$	3.78431	0.570506
$45$	8.09277	1.20640
$46$	8.17419	1.20522
$47$	7.69695	1.12272	0.561358	−	0.827573i	$-0.310279\pi$
$47$	7.69695	1.12272	0.561358	+	0.827573i	$0.310279\pi$
$48$	−2.49143	−0.359607
$49$	−5.85018	−0.835740
$50$	1.36707	0.193333
$51$	3.48571	0.488097
$52$	3.19901	0.443622
$53$	−1.93801	−0.266206	−0.133103	−	0.991102i	$-0.542494\pi$
$53$	−1.93801	−0.266206	−0.133103	+	0.991102i	$0.542494\pi$
$54$	−0.516245	−0.0702520
$55$	9.54896	1.28758
$56$	1.07230	0.143292
$57$	−5.97119	−0.790903
$58$	6.40392	0.840876
$59$	1.51620	0.197392	0.0986961	−	0.995118i	$-0.468533\pi$
$59$	1.51620	0.197392	0.0986961	+	0.995118i	$0.468533\pi$
$60$	−6.28663	−0.811601
$61$	−1.36191	−0.174375	−0.0871873	−	0.996192i	$-0.527788\pi$
$61$	−1.36191	−0.174375	−0.0871873	+	0.996192i	$0.527788\pi$
$62$	−5.65216	−0.717825
$63$	3.43908	0.433284
$64$	1.00000	0.125000
$65$	8.07207	1.00122
$66$	−9.42832	−1.16055
$67$	−2.26610	−0.276848	−0.138424	−	0.990373i	$-0.544204\pi$
$67$	−2.26610	−0.276848	−0.138424	+	0.990373i	$0.544204\pi$
$68$	−1.39908	−0.169664
$69$	−20.3654	−2.45170
$70$	2.70574	0.323397
$71$	9.10967	1.08112	0.540559	−	0.841306i	$-0.318213\pi$
$71$	9.10967	1.08112	0.540559	+	0.841306i	$0.318213\pi$
$72$	3.20721	0.377973
$73$	−2.42541	−0.283873	−0.141936	−	0.989876i	$-0.545333\pi$
$73$	−2.42541	−0.283873	−0.141936	+	0.989876i	$0.545333\pi$
$74$	−7.08052	−0.823094
$75$	−3.40596	−0.393286
$76$	2.39669	0.274920
$77$	4.05790	0.462441
$78$	−7.97009	−0.902435
$79$	−12.5503	−1.41202	−0.706008	−	0.708204i	$-0.749506\pi$
$79$	−12.5503	−1.41202	−0.706008	+	0.708204i	$0.749506\pi$
$80$	2.52331	0.282114
$81$	−8.33544	−0.926160
$82$	4.40289	0.486218
$83$	14.2698	1.56632	0.783159	−	0.621821i	$-0.213607\pi$
$83$	14.2698	1.56632	0.783159	+	0.621821i	$0.213607\pi$
$84$	−2.67155	−0.291490
$85$	−3.53031	−0.382916
$86$	−9.04539	−0.975390
$87$	−15.9549	−1.71054
$88$	3.78431	0.403408
$89$	−10.1769	−1.07875	−0.539375	−	0.842066i	$-0.681339\pi$
$89$	−10.1769	−1.07875	−0.539375	+	0.842066i	$0.681339\pi$
$90$	8.09277	0.853052
$91$	3.43029	0.359592
$92$	8.17419	0.852218
$93$	14.0819	1.46023
$94$	7.69695	0.793880
$95$	6.04759	0.620470
$96$	−2.49143	−0.254280
$97$	−12.2522	−1.24402	−0.622010	−	0.783009i	$-0.713684\pi$
$97$	−12.2522	−1.24402	−0.622010	+	0.783009i	$0.713684\pi$
$98$	−5.85018	−0.590957
$99$	12.1371	1.21982
$100$	1.36707	0.136707
$101$	8.49917	0.845700	0.422850	−	0.906200i	$-0.361030\pi$
$101$	8.49917	0.845700	0.422850	+	0.906200i	$0.361030\pi$
$102$	3.48571	0.345137
$103$	2.19298	0.216080	0.108040	−	0.994147i	$-0.465542\pi$
$103$	2.19298	0.216080	0.108040	+	0.994147i	$0.465542\pi$
$104$	3.19901	0.313688
$105$	−6.74114	−0.657868
$106$	−1.93801	−0.188236
$107$	2.60833	0.252157	0.126079	−	0.992020i	$-0.459761\pi$
$107$	2.60833	0.252157	0.126079	+	0.992020i	$0.459761\pi$
$108$	−0.516245	−0.0496757
$109$	7.02773	0.673135	0.336567	−	0.941659i	$-0.390734\pi$
$109$	7.02773	0.673135	0.336567	+	0.941659i	$0.390734\pi$
$110$	9.54896	0.910458
$111$	17.6406	1.67437
$112$	1.07230	0.101323
$113$	−9.15068	−0.860823	−0.430412	−	0.902633i	$-0.641632\pi$
$113$	−9.15068	−0.860823	−0.430412	+	0.902633i	$0.641632\pi$
$114$	−5.97119	−0.559253
$115$	20.6260	1.92338
$116$	6.40392	0.594589
$117$	10.2599	0.948526
$118$	1.51620	0.139577
$119$	−1.50023	−0.137526
$120$	−6.28663	−0.573888
$121$	3.32098	0.301907
$122$	−1.36191	−0.123301
$123$	−10.9695	−0.989085
$124$	−5.65216	−0.507579
$125$	−9.16699	−0.819921
$126$	3.43908	0.306378
$127$	18.5189	1.64328	0.821642	−	0.570004i	$-0.193058\pi$
$127$	18.5189	1.64328	0.821642	+	0.570004i	$0.193058\pi$
$128$	1.00000	0.0883883
$129$	22.5359	1.98418
$130$	8.07207	0.707967
$131$	−7.55459	−0.660047	−0.330024	−	0.943973i	$-0.607057\pi$
$131$	−7.55459	−0.660047	−0.330024	+	0.943973i	$0.607057\pi$
$132$	−9.42832	−0.820630
$133$	2.56997	0.222845
$134$	−2.26610	−0.195761
$135$	−1.30264	−0.112114
$136$	−1.39908	−0.119970
$137$	−3.87673	−0.331211	−0.165606	−	0.986192i	$-0.552958\pi$
$137$	−3.87673	−0.331211	−0.165606	+	0.986192i	$0.552958\pi$
$138$	−20.3654	−1.73362
$139$	−13.0645	−1.10811	−0.554056	−	0.832479i	$-0.686921\pi$
$139$	−13.0645	−1.10811	−0.554056	+	0.832479i	$0.686921\pi$
$140$	2.70574	0.228676
$141$	−19.1764	−1.61494
$142$	9.10967	0.764467
$143$	12.1060	1.01236
$144$	3.20721	0.267267
$145$	16.1590	1.34194
$146$	−2.42541	−0.200728
$147$	14.5753	1.20215
$148$	−7.08052	−0.582015
$149$	−10.4102	−0.852835	−0.426418	−	0.904526i	$-0.640225\pi$
$149$	−10.4102	−0.852835	−0.426418	+	0.904526i	$0.640225\pi$
$150$	−3.40596	−0.278095
$151$	−14.6847	−1.19503	−0.597513	−	0.801859i	$-0.703844\pi$
$151$	−14.6847	−1.19503	−0.597513	+	0.801859i	$0.703844\pi$
$152$	2.39669	0.194398
$153$	−4.48715	−0.362764
$154$	4.05790	0.326995
$155$	−14.2621	−1.14556
$156$	−7.97009	−0.638118
$157$	3.31066	0.264219	0.132110	−	0.991235i	$-0.457825\pi$
$157$	3.31066	0.264219	0.132110	+	0.991235i	$0.457825\pi$
$158$	−12.5503	−0.998446
$159$	4.82841	0.382917
$160$	2.52331	0.199485
$161$	8.76516	0.690792
$162$	−8.33544	−0.654894
$163$	6.55856	0.513706	0.256853	−	0.966450i	$-0.417314\pi$
$163$	6.55856	0.513706	0.256853	+	0.966450i	$0.417314\pi$
$164$	4.40289	0.343808
$165$	−23.7905	−1.85209
$166$	14.2698	1.10755
$167$	5.13963	0.397716	0.198858	−	0.980028i	$-0.436277\pi$
$167$	5.13963	0.397716	0.198858	+	0.980028i	$0.436277\pi$
$168$	−2.67155	−0.206115
$169$	−2.76636	−0.212797
$170$	−3.53031	−0.270762
$171$	7.68670	0.587816
$172$	−9.04539	−0.689705
$173$	16.9796	1.29093	0.645466	−	0.763789i	$-0.276663\pi$
$173$	16.9796	1.29093	0.645466	+	0.763789i	$0.276663\pi$
$174$	−15.9549	−1.20954
$175$	1.46591	0.110812
$176$	3.78431	0.285253
$177$	−3.77750	−0.283934
$178$	−10.1769	−0.762791
$179$	21.4883	1.60611	0.803056	−	0.595903i	$-0.203206\pi$
$179$	21.4883	1.60611	0.803056	+	0.595903i	$0.203206\pi$
$180$	8.09277	0.603199
$181$	−3.63131	−0.269913	−0.134957	−	0.990852i	$-0.543089\pi$
$181$	−3.63131	−0.269913	−0.134957	+	0.990852i	$0.543089\pi$
$182$	3.43029	0.254270
$183$	3.39310	0.250825
$184$	8.17419	0.602609
$185$	−17.8663	−1.31356
$186$	14.0819	1.03254
$187$	−5.29455	−0.387176
$188$	7.69695	0.561358
$189$	−0.553568	−0.0402662
$190$	6.04759	0.438738
$191$	−2.25550	−0.163202	−0.0816010	−	0.996665i	$-0.526003\pi$
$191$	−2.25550	−0.163202	−0.0816010	+	0.996665i	$0.526003\pi$
$192$	−2.49143	−0.179803
$193$	0.0242992	0.00174909	0.000874547	−	1.00000i	$-0.499722\pi$
$193$	0.0242992	0.00174909	0.000874547		1.00000i	$0.499722\pi$
$194$	−12.2522	−0.879655
$195$	−20.1110	−1.44018
$196$	−5.85018	−0.417870
$197$	−3.09311	−0.220375	−0.110187	−	0.993911i	$-0.535145\pi$
$197$	−3.09311	−0.220375	−0.110187	+	0.993911i	$0.535145\pi$
$198$	12.1371	0.862543
$199$	15.0314	1.06555	0.532773	−	0.846258i	$-0.321150\pi$
$199$	15.0314	1.06555	0.532773	+	0.846258i	$0.321150\pi$
$200$	1.36707	0.0966665
$201$	5.64582	0.398226
$202$	8.49917	0.598000
$203$	6.86691	0.481963
$204$	3.48571	0.244049
$205$	11.1098	0.775945
$206$	2.19298	0.152792
$207$	26.2163	1.82216
$208$	3.19901	0.221811
$209$	9.06983	0.627373
$210$	−6.74114	−0.465183
$211$	5.19118	0.357376	0.178688	−	0.983906i	$-0.442815\pi$
$211$	5.19118	0.357376	0.178688	+	0.983906i	$0.442815\pi$
$212$	−1.93801	−0.133103
$213$	−22.6961	−1.55511
$214$	2.60833	0.178302
$215$	−22.8243	−1.55660
$216$	−0.516245	−0.0351260
$217$	−6.06080	−0.411434
$218$	7.02773	0.475978
$219$	6.04273	0.408330
$220$	9.54896	0.643791
$221$	−4.47567	−0.301066
$222$	17.6406	1.18396
$223$	−2.27370	−0.152258	−0.0761292	−	0.997098i	$-0.524256\pi$
$223$	−2.27370	−0.152258	−0.0761292	+	0.997098i	$0.524256\pi$
$224$	1.07230	0.0716459
$225$	4.38448	0.292299
$226$	−9.15068	−0.608694
$227$	5.38813	0.357623	0.178811	−	0.983883i	$-0.442775\pi$
$227$	5.38813	0.357623	0.178811	+	0.983883i	$0.442775\pi$
$228$	−5.97119	−0.395452
$229$	28.0699	1.85491	0.927457	−	0.373929i	$-0.121990\pi$
$229$	28.0699	1.85491	0.927457	+	0.373929i	$0.121990\pi$
$230$	20.6260	1.36004
$231$	−10.1100	−0.665187
$232$	6.40392	0.420438
$233$	1.35100	0.0885069	0.0442535	−	0.999020i	$-0.485909\pi$
$233$	1.35100	0.0885069	0.0442535	+	0.999020i	$0.485909\pi$
$234$	10.2599	0.670709
$235$	19.4218	1.26694
$236$	1.51620	0.0986961
$237$	31.2681	2.03108
$238$	−1.50023	−0.0972456
$239$	10.2842	0.665230	0.332615	−	0.943063i	$-0.392069\pi$
$239$	10.2842	0.665230	0.332615	+	0.943063i	$0.392069\pi$
$240$	−6.28663	−0.405800
$241$	17.5635	1.13136	0.565681	−	0.824624i	$-0.308613\pi$
$241$	17.5635	1.13136	0.565681	+	0.824624i	$0.308613\pi$
$242$	3.32098	0.213480
$243$	22.3159	1.43156
$244$	−1.36191	−0.0871873
$245$	−14.7618	−0.943096
$246$	−10.9695	−0.699388
$247$	7.66704	0.487842
$248$	−5.65216	−0.358913
$249$	−35.5523	−2.25303
$250$	−9.16699	−0.579771
$251$	−10.1839	−0.642800	−0.321400	−	0.946943i	$-0.604153\pi$
$251$	−10.1839	−0.642800	−0.321400	+	0.946943i	$0.604153\pi$
$252$	3.43908	0.216642
$253$	30.9336	1.94478
$254$	18.5189	1.16198
$255$	8.79551	0.550796
$256$	1.00000	0.0625000
$257$	3.19573	0.199344	0.0996720	−	0.995020i	$-0.468221\pi$
$257$	3.19573	0.199344	0.0996720	+	0.995020i	$0.468221\pi$
$258$	22.5359	1.40303
$259$	−7.59243	−0.471770
$260$	8.07207	0.500609
$261$	20.5387	1.27131
$262$	−7.55459	−0.466724
$263$	6.20599	0.382677	0.191339	−	0.981524i	$-0.438717\pi$
$263$	6.20599	0.382677	0.191339	+	0.981524i	$0.438717\pi$
$264$	−9.42832	−0.580273
$265$	−4.89019	−0.300402
$266$	2.56997	0.157575
$267$	25.3550	1.55170
$268$	−2.26610	−0.138424
$269$	−3.74032	−0.228051	−0.114026	−	0.993478i	$-0.536375\pi$
$269$	−3.74032	−0.228051	−0.114026	+	0.993478i	$0.536375\pi$
$270$	−1.30264	−0.0792763
$271$	5.98443	0.363528	0.181764	−	0.983342i	$-0.441819\pi$
$271$	5.98443	0.363528	0.181764	+	0.983342i	$0.441819\pi$
$272$	−1.39908	−0.0848318
$273$	−8.54631	−0.517246
$274$	−3.87673	−0.234202
$275$	5.17341	0.311969
$276$	−20.3654	−1.22585
$277$	5.54957	0.333441	0.166721	−	0.986004i	$-0.446682\pi$
$277$	5.54957	0.333441	0.166721	+	0.986004i	$0.446682\pi$
$278$	−13.0645	−0.783554
$279$	−18.1277	−1.08527
$280$	2.70574	0.161699
$281$	7.85462	0.468567	0.234284	−	0.972168i	$-0.424726\pi$
$281$	7.85462	0.468567	0.234284	+	0.972168i	$0.424726\pi$
$282$	−19.1764	−1.14194
$283$	23.3724	1.38935	0.694673	−	0.719326i	$-0.255549\pi$
$283$	23.3724	1.38935	0.694673	+	0.719326i	$0.255549\pi$
$284$	9.10967	0.540559
$285$	−15.0671	−0.892500
$286$	12.1060	0.715844
$287$	4.72121	0.278684
$288$	3.20721	0.188987
$289$	−15.0426	−0.884857
$290$	16.1590	0.948892
$291$	30.5254	1.78943
$292$	−2.42541	−0.141936
$293$	24.5052	1.43161	0.715804	−	0.698301i	$-0.246060\pi$
$293$	24.5052	1.43161	0.715804	+	0.698301i	$0.246060\pi$
$294$	14.5753	0.850048
$295$	3.82583	0.222749
$296$	−7.08052	−0.411547
$297$	−1.95363	−0.113361
$298$	−10.4102	−0.603046
$299$	26.1493	1.51225
$300$	−3.40596	−0.196643
$301$	−9.69935	−0.559061
$302$	−14.6847	−0.845011
$303$	−21.1751	−1.21648
$304$	2.39669	0.137460
$305$	−3.43651	−0.196774
$306$	−4.48715	−0.256513
$307$	−5.48236	−0.312895	−0.156447	−	0.987686i	$-0.550004\pi$
$307$	−5.48236	−0.312895	−0.156447	+	0.987686i	$0.550004\pi$
$308$	4.05790	0.231221
$309$	−5.46364	−0.310816
$310$	−14.2621	−0.810034
$311$	−15.4523	−0.876218	−0.438109	−	0.898922i	$-0.644352\pi$
$311$	−15.4523	−0.876218	−0.438109	+	0.898922i	$0.644352\pi$
$312$	−7.97009	−0.451218
$313$	16.2054	0.915985	0.457992	−	0.888956i	$-0.348569\pi$
$313$	16.2054	0.915985	0.457992	+	0.888956i	$0.348569\pi$
$314$	3.31066	0.186831
$315$	8.67786	0.488942
$316$	−12.5503	−0.706008
$317$	6.71978	0.377421	0.188710	−	0.982033i	$-0.439569\pi$
$317$	6.71978	0.377421	0.188710	+	0.982033i	$0.439569\pi$
$318$	4.82841	0.270764
$319$	24.2344	1.35687
$320$	2.52331	0.141057
$321$	−6.49847	−0.362709
$322$	8.76516	0.488464
$323$	−3.35317	−0.186575
$324$	−8.33544	−0.463080
$325$	4.37327	0.242585
$326$	6.55856	0.363245
$327$	−17.5091	−0.968255
$328$	4.40289	0.243109
$329$	8.25343	0.455026
$330$	−23.7905	−1.30963
$331$	−24.7060	−1.35797	−0.678983	−	0.734154i	$-0.737579\pi$
$331$	−24.7060	−1.35797	−0.678983	+	0.734154i	$0.737579\pi$
$332$	14.2698	0.783159
$333$	−22.7087	−1.24443
$334$	5.13963	0.281228
$335$	−5.71806	−0.312411
$336$	−2.67155	−0.145745
$337$	9.67930	0.527265	0.263633	−	0.964623i	$-0.415079\pi$
$337$	9.67930	0.527265	0.263633	+	0.964623i	$0.415079\pi$
$338$	−2.76636	−0.150470
$339$	22.7982	1.23823
$340$	−3.53031	−0.191458
$341$	−21.3895	−1.15831
$342$	7.68670	0.415649
$343$	−13.7792	−0.744008
$344$	−9.04539	−0.487695
$345$	−51.3881	−2.76664
$346$	16.9796	0.912827
$347$	−27.1869	−1.45947	−0.729736	−	0.683729i	$-0.760357\pi$
$347$	−27.1869	−1.45947	−0.729736	+	0.683729i	$0.760357\pi$
$348$	−15.9549	−0.855272
$349$	−10.7692	−0.576463	−0.288231	−	0.957561i	$-0.593067\pi$
$349$	−10.7692	−0.576463	−0.288231	+	0.957561i	$0.593067\pi$
$350$	1.46591	0.0783560
$351$	−1.65147	−0.0881490
$352$	3.78431	0.201704
$353$	−19.6091	−1.04369	−0.521843	−	0.853042i	$-0.674755\pi$
$353$	−19.6091	−1.04369	−0.521843	+	0.853042i	$0.674755\pi$
$354$	−3.77750	−0.200772
$355$	22.9865	1.22000
$356$	−10.1769	−0.539375
$357$	3.73772	0.197821
$358$	21.4883	1.13569
$359$	36.6494	1.93428	0.967141	−	0.254239i	$-0.0818251\pi$
$359$	36.6494	1.93428	0.967141	+	0.254239i	$0.0818251\pi$
$360$	8.09277	0.426526
$361$	−13.2559	−0.697677
$362$	−3.63131	−0.190857
$363$	−8.27397	−0.434271
$364$	3.43029	0.179796
$365$	−6.12005	−0.320338
$366$	3.39310	0.177360
$367$	6.16431	0.321774	0.160887	−	0.986973i	$-0.448564\pi$
$367$	6.16431	0.321774	0.160887	+	0.986973i	$0.448564\pi$
$368$	8.17419	0.426109
$369$	14.1210	0.735109
$370$	−17.8663	−0.928825
$371$	−2.07812	−0.107891
$372$	14.0819	0.730115
$373$	−35.5582	−1.84113	−0.920567	−	0.390586i	$-0.872273\pi$
$373$	−35.5582	−1.84113	−0.920567	+	0.390586i	$0.872273\pi$
$374$	−5.29455	−0.273775
$375$	22.8389	1.17940
$376$	7.69695	0.396940
$377$	20.4862	1.05509
$378$	−0.553568	−0.0284725
$379$	−13.3839	−0.687484	−0.343742	−	0.939064i	$-0.611695\pi$
$379$	−13.3839	−0.687484	−0.343742	+	0.939064i	$0.611695\pi$
$380$	6.04759	0.310235
$381$	−46.1384	−2.36374
$382$	−2.25550	−0.115401
$383$	12.3067	0.628842	0.314421	−	0.949284i	$-0.398190\pi$
$383$	12.3067	0.628842	0.314421	+	0.949284i	$0.398190\pi$
$384$	−2.49143	−0.127140
$385$	10.2393	0.521845
$386$	0.0242992	0.00123680
$387$	−29.0105	−1.47468
$388$	−12.2522	−0.622010
$389$	−15.1614	−0.768713	−0.384357	−	0.923185i	$-0.625577\pi$
$389$	−15.1614	−0.768713	−0.384357	+	0.923185i	$0.625577\pi$
$390$	−20.1110	−1.01836
$391$	−11.4364	−0.578361
$392$	−5.85018	−0.295479
$393$	18.8217	0.949429
$394$	−3.09311	−0.155828
$395$	−31.6682	−1.59340
$396$	12.1371	0.609910
$397$	7.03601	0.353127	0.176564	−	0.984289i	$-0.443502\pi$
$397$	7.03601	0.353127	0.176564	+	0.984289i	$0.443502\pi$
$398$	15.0314	0.753455
$399$	−6.40289	−0.320546
$400$	1.36707	0.0683535
$401$	−28.2976	−1.41312	−0.706558	−	0.707655i	$-0.749753\pi$
$401$	−28.2976	−1.41312	−0.706558	+	0.707655i	$0.749753\pi$
$402$	5.64582	0.281588
$403$	−18.0813	−0.900694
$404$	8.49917	0.422850
$405$	−21.0329	−1.04513
$406$	6.86691	0.340799
$407$	−26.7949	−1.32817
$408$	3.48571	0.172568
$409$	16.0688	0.794553	0.397277	−	0.917699i	$-0.369955\pi$
$409$	16.0688	0.794553	0.397277	+	0.917699i	$0.369955\pi$
$410$	11.1098	0.548676
$411$	9.65859	0.476423
$412$	2.19298	0.108040
$413$	1.62582	0.0800012
$414$	26.2163	1.28846
$415$	36.0072	1.76752
$416$	3.19901	0.156844
$417$	32.5491	1.59394
$418$	9.06983	0.443620
$419$	7.88655	0.385283	0.192642	−	0.981269i	$-0.438294\pi$
$419$	7.88655	0.385283	0.192642	+	0.981269i	$0.438294\pi$
$420$	−6.74114	−0.328934
$421$	−18.8633	−0.919342	−0.459671	−	0.888089i	$-0.652033\pi$
$421$	−18.8633	−0.919342	−0.459671	+	0.888089i	$0.652033\pi$
$422$	5.19118	0.252703
$423$	24.6857	1.20026
$424$	−1.93801	−0.0941180
$425$	−1.91264	−0.0927768
$426$	−22.6961	−1.09963
$427$	−1.46037	−0.0706723
$428$	2.60833	0.126079
$429$	−30.1613	−1.45620
$430$	−22.8243	−1.10068
$431$	6.27794	0.302397	0.151199	−	0.988503i	$-0.451687\pi$
$431$	6.27794	0.302397	0.151199	+	0.988503i	$0.451687\pi$
$432$	−0.516245	−0.0248378
$433$	−38.0188	−1.82707	−0.913534	−	0.406762i	$-0.866658\pi$
$433$	−38.0188	−1.82707	−0.913534	+	0.406762i	$0.866658\pi$
$434$	−6.06080	−0.290928
$435$	−40.2591	−1.93027
$436$	7.02773	0.336567
$437$	19.5910	0.937166
$438$	6.04273	0.288733
$439$	−3.33830	−0.159328	−0.0796642	−	0.996822i	$-0.525385\pi$
$439$	−3.33830	−0.159328	−0.0796642	+	0.996822i	$0.525385\pi$
$440$	9.54896	0.455229
$441$	−18.7627	−0.893464
$442$	−4.47567	−0.212886
$443$	4.62217	0.219606	0.109803	−	0.993953i	$-0.464978\pi$
$443$	4.62217	0.219606	0.109803	+	0.993953i	$0.464978\pi$
$444$	17.6406	0.837186
$445$	−25.6794	−1.21732
$446$	−2.27370	−0.107663
$447$	25.9362	1.22674
$448$	1.07230	0.0506613
$449$	−23.3357	−1.10128	−0.550640	−	0.834743i	$-0.685616\pi$
$449$	−23.3357	−1.10128	−0.550640	+	0.834743i	$0.685616\pi$
$450$	4.38448	0.206686
$451$	16.6619	0.784578
$452$	−9.15068	−0.430412
$453$	36.5859	1.71896
$454$	5.38813	0.252878
$455$	8.65567	0.405784
$456$	−5.97119	−0.279627
$457$	−8.84805	−0.413894	−0.206947	−	0.978352i	$-0.566353\pi$
$457$	−8.84805	−0.413894	−0.206947	+	0.978352i	$0.566353\pi$
$458$	28.0699	1.31162
$459$	0.722269	0.0337126
$460$	20.6260	0.961691
$461$	−32.3687	−1.50756	−0.753781	−	0.657125i	$-0.771772\pi$
$461$	−32.3687	−1.50756	−0.753781	+	0.657125i	$0.771772\pi$
$462$	−10.1100	−0.470359
$463$	8.19253	0.380739	0.190370	−	0.981712i	$-0.439031\pi$
$463$	8.19253	0.380739	0.190370	+	0.981712i	$0.439031\pi$
$464$	6.40392	0.297294
$465$	35.5331	1.64781
$466$	1.35100	0.0625839
$467$	2.78068	0.128675	0.0643373	−	0.997928i	$-0.479507\pi$
$467$	2.78068	0.128675	0.0643373	+	0.997928i	$0.479507\pi$
$468$	10.2599	0.474263
$469$	−2.42993	−0.112204
$470$	19.4218	0.895859
$471$	−8.24826	−0.380060
$472$	1.51620	0.0697887
$473$	−34.2305	−1.57392
$474$	31.2681	1.43619
$475$	3.27645	0.150334
$476$	−1.50023	−0.0687630
$477$	−6.21560	−0.284593
$478$	10.2842	0.470388
$479$	−31.2390	−1.42735	−0.713673	−	0.700479i	$-0.752970\pi$
$479$	−31.2390	−1.42735	−0.713673	+	0.700479i	$0.752970\pi$
$480$	−6.28663	−0.286944
$481$	−22.6506	−1.03278
$482$	17.5635	0.799994
$483$	−21.8378	−0.993653
$484$	3.32098	0.150953
$485$	−30.9160	−1.40382
$486$	22.3159	1.01227
$487$	−14.9958	−0.679525	−0.339763	−	0.940511i	$-0.610347\pi$
$487$	−14.9958	−0.679525	−0.339763	+	0.940511i	$0.610347\pi$
$488$	−1.36191	−0.0616507
$489$	−16.3402	−0.738928
$490$	−14.7618	−0.666869
$491$	19.4148	0.876179	0.438089	−	0.898931i	$-0.355655\pi$
$491$	19.4148	0.876179	0.438089	+	0.898931i	$0.355655\pi$
$492$	−10.9695	−0.494542
$493$	−8.95960	−0.403520
$494$	7.66704	0.344956
$495$	30.6255	1.37651
$496$	−5.65216	−0.253790
$497$	9.76828	0.438167
$498$	−35.5523	−1.59314
$499$	6.00622	0.268875	0.134438	−	0.990922i	$-0.457077\pi$
$499$	6.00622	0.268875	0.134438	+	0.990922i	$0.457077\pi$
$500$	−9.16699	−0.409960
$501$	−12.8050	−0.572086
$502$	−10.1839	−0.454529
$503$	−25.0986	−1.11909	−0.559545	−	0.828800i	$-0.689024\pi$
$503$	−25.0986	−1.11909	−0.559545	+	0.828800i	$0.689024\pi$
$504$	3.43908	0.153189
$505$	21.4460	0.954335
$506$	30.9336	1.37517
$507$	6.89217	0.306092
$508$	18.5189	0.821642
$509$	27.0276	1.19798	0.598989	−	0.800758i	$-0.295569\pi$
$509$	27.0276	1.19798	0.598989	+	0.800758i	$0.295569\pi$
$510$	8.79551	0.389472
$511$	−2.60076	−0.115051
$512$	1.00000	0.0441942
$513$	−1.23728	−0.0546273
$514$	3.19573	0.140958
$515$	5.53355	0.243837
$516$	22.5359	0.992089
$517$	29.1276	1.28103
$518$	−7.59243	−0.333592
$519$	−42.3033	−1.85691
$520$	8.07207	0.353984
$521$	0.722074	0.0316346	0.0158173	−	0.999875i	$-0.494965\pi$
$521$	0.722074	0.0316346	0.0158173	+	0.999875i	$0.494965\pi$
$522$	20.5387	0.898954
$523$	−41.5005	−1.81469	−0.907344	−	0.420389i	$-0.861894\pi$
$523$	−41.5005	−1.81469	−0.907344	+	0.420389i	$0.861894\pi$
$524$	−7.55459	−0.330024
$525$	−3.65220	−0.159395
$526$	6.20599	0.270594
$527$	7.90783	0.344471
$528$	−9.42832	−0.410315
$529$	43.8173	1.90510
$530$	−4.89019	−0.212416
$531$	4.86277	0.211026
$532$	2.56997	0.111422
$533$	14.0849	0.610084
$534$	25.3550	1.09722
$535$	6.58162	0.284548
$536$	−2.26610	−0.0978806
$537$	−53.5366	−2.31027
$538$	−3.74032	−0.161257
$539$	−22.1389	−0.953588
$540$	−1.30264	−0.0560568
$541$	−21.4186	−0.920857	−0.460429	−	0.887697i	$-0.652304\pi$
$541$	−21.4186	−0.920857	−0.460429	+	0.887697i	$0.652304\pi$
$542$	5.98443	0.257053
$543$	9.04714	0.388250
$544$	−1.39908	−0.0599851
$545$	17.7331	0.759603
$546$	−8.54631	−0.365748
$547$	−30.6132	−1.30893	−0.654464	−	0.756094i	$-0.727106\pi$
$547$	−30.6132	−1.30893	−0.654464	+	0.756094i	$0.727106\pi$
$548$	−3.87673	−0.165606
$549$	−4.36792	−0.186418
$550$	5.17341	0.220595
$551$	15.3482	0.653857
$552$	−20.3654	−0.866809
$553$	−13.4576	−0.572277
$554$	5.54957	0.235779
$555$	44.5126	1.88946
$556$	−13.0645	−0.554056
$557$	−16.2013	−0.686472	−0.343236	−	0.939249i	$-0.611523\pi$
$557$	−16.2013	−0.686472	−0.343236	+	0.939249i	$0.611523\pi$
$558$	−18.1277	−0.767405
$559$	−28.9363	−1.22387
$560$	2.70574	0.114338
$561$	13.1910	0.556924
$562$	7.85462	0.331327
$563$	20.4826	0.863238	0.431619	−	0.902056i	$-0.357943\pi$
$563$	20.4826	0.863238	0.431619	+	0.902056i	$0.357943\pi$
$564$	−19.1764	−0.807472
$565$	−23.0900	−0.971402
$566$	23.3724	0.982416
$567$	−8.93808	−0.375364
$568$	9.10967	0.382233
$569$	−6.12086	−0.256600	−0.128300	−	0.991735i	$-0.540952\pi$
$569$	−6.12086	−0.256600	−0.128300	+	0.991735i	$0.540952\pi$
$570$	−15.0671	−0.631093
$571$	7.90355	0.330753	0.165377	−	0.986230i	$-0.447116\pi$
$571$	7.90355	0.330753	0.165377	+	0.986230i	$0.447116\pi$
$572$	12.1060	0.506178
$573$	5.61940	0.234754
$574$	4.72121	0.197060
$575$	11.1747	0.466017
$576$	3.20721	0.133634
$577$	−8.00418	−0.333218	−0.166609	−	0.986023i	$-0.553282\pi$
$577$	−8.00418	−0.333218	−0.166609	+	0.986023i	$0.553282\pi$
$578$	−15.0426	−0.625688
$579$	−0.0605397	−0.00251594
$580$	16.1590	0.670968
$581$	15.3015	0.634814
$582$	30.5254	1.26532
$583$	−7.33402	−0.303744
$584$	−2.42541	−0.100364
$585$	25.8888	1.07037
$586$	24.5052	1.01230
$587$	33.1849	1.36969	0.684844	−	0.728690i	$-0.259870\pi$
$587$	33.1849	1.36969	0.684844	+	0.728690i	$0.259870\pi$
$588$	14.5753	0.601075
$589$	−13.5465	−0.558174
$590$	3.82583	0.157507
$591$	7.70625	0.316993
$592$	−7.08052	−0.291008
$593$	19.9060	0.817442	0.408721	−	0.912659i	$-0.365975\pi$
$593$	19.9060	0.817442	0.408721	+	0.912659i	$0.365975\pi$
$594$	−1.95363	−0.0801583
$595$	−3.78554	−0.155192
$596$	−10.4102	−0.426418
$597$	−37.4496	−1.53271
$598$	26.1493	1.06932
$599$	1.18207	0.0482980	0.0241490	−	0.999708i	$-0.492312\pi$
$599$	1.18207	0.0482980	0.0241490	+	0.999708i	$0.492312\pi$
$600$	−3.40596	−0.139048
$601$	−24.3194	−0.992010	−0.496005	−	0.868320i	$-0.665200\pi$
$601$	−24.3194	−0.992010	−0.496005	+	0.868320i	$0.665200\pi$
$602$	−9.69935	−0.395316
$603$	−7.26785	−0.295970
$604$	−14.6847	−0.597513
$605$	8.37984	0.340689
$606$	−21.1751	−0.860179
$607$	13.2884	0.539360	0.269680	−	0.962950i	$-0.413082\pi$
$607$	13.2884	0.539360	0.269680	+	0.962950i	$0.413082\pi$
$608$	2.39669	0.0971988
$609$	−17.1084	−0.693267
$610$	−3.43651	−0.139140
$611$	24.6226	0.996124
$612$	−4.48715	−0.181382
$613$	−0.0871949	−0.00352177	−0.00176088	−	0.999998i	$-0.500561\pi$
$613$	−0.0871949	−0.00352177	−0.00176088	+	0.999998i	$0.500561\pi$
$614$	−5.48236	−0.221250
$615$	−27.6793	−1.11614
$616$	4.05790	0.163498
$617$	−6.83620	−0.275215	−0.137608	−	0.990487i	$-0.543941\pi$
$617$	−6.83620	−0.275215	−0.137608	+	0.990487i	$0.543941\pi$
$618$	−5.46364	−0.219780
$619$	−48.8387	−1.96299	−0.981497	−	0.191477i	$-0.938672\pi$
$619$	−48.8387	−1.96299	−0.981497	+	0.191477i	$0.938672\pi$
$620$	−14.2621	−0.572781
$621$	−4.21988	−0.169338
$622$	−15.4523	−0.619579
$623$	−10.9127	−0.437207
$624$	−7.97009	−0.319059
$625$	−29.9665	−1.19866
$626$	16.2054	0.647699
$627$	−22.5968	−0.902430
$628$	3.31066	0.132110
$629$	9.90623	0.394987
$630$	8.67786	0.345734
$631$	−5.71138	−0.227366	−0.113683	−	0.993517i	$-0.536265\pi$
$631$	−5.71138	−0.227366	−0.113683	+	0.993517i	$0.536265\pi$
$632$	−12.5503	−0.499223
$633$	−12.9335	−0.514059
$634$	6.71978	0.266877
$635$	46.7288	1.85437
$636$	4.82841	0.191459
$637$	−18.7148	−0.741506
$638$	24.2344	0.959449
$639$	29.2166	1.15579
$640$	2.52331	0.0997424
$641$	1.99429	0.0787697	0.0393848	−	0.999224i	$-0.487460\pi$
$641$	1.99429	0.0787697	0.0393848	+	0.999224i	$0.487460\pi$
$642$	−6.49847	−0.256474
$643$	−26.0222	−1.02622	−0.513108	−	0.858324i	$-0.671506\pi$
$643$	−26.0222	−1.02622	−0.513108	+	0.858324i	$0.671506\pi$
$644$	8.76516	0.345396
$645$	56.8650	2.23906
$646$	−3.35317	−0.131929
$647$	33.7948	1.32861	0.664305	−	0.747461i	$-0.268727\pi$
$647$	33.7948	1.32861	0.664305	+	0.747461i	$0.268727\pi$
$648$	−8.33544	−0.327447
$649$	5.73776	0.225227
$650$	4.37327	0.171534
$651$	15.1000	0.591817
$652$	6.55856	0.256853
$653$	−13.2109	−0.516983	−0.258491	−	0.966014i	$-0.583225\pi$
$653$	−13.2109	−0.516983	−0.258491	+	0.966014i	$0.583225\pi$
$654$	−17.5091	−0.684659
$655$	−19.0625	−0.744835
$656$	4.40289	0.171904
$657$	−7.77879	−0.303480
$658$	8.25343	0.321752
$659$	16.3040	0.635113	0.317556	−	0.948239i	$-0.397138\pi$
$659$	16.3040	0.635113	0.317556	+	0.948239i	$0.397138\pi$
$660$	−23.7905	−0.926046
$661$	−21.4561	−0.834547	−0.417274	−	0.908781i	$-0.637014\pi$
$661$	−21.4561	−0.834547	−0.417274	+	0.908781i	$0.637014\pi$
$662$	−24.7060	−0.960227
$663$	11.1508	0.433062
$664$	14.2698	0.553777
$665$	6.48482	0.251471
$666$	−22.7087	−0.879944
$667$	52.3468	2.02688
$668$	5.13963	0.198858
$669$	5.66476	0.219012
$670$	−5.71806	−0.220908
$671$	−5.15388	−0.198963
$672$	−2.67155	−0.103057
$673$	0.0804343	0.00310051	0.00155026	−	0.999999i	$-0.499507\pi$
$673$	0.0804343	0.00310051	0.00155026	+	0.999999i	$0.499507\pi$
$674$	9.67930	0.372833
$675$	−0.705743	−0.0271641
$676$	−2.76636	−0.106398
$677$	36.4723	1.40174	0.700871	−	0.713288i	$-0.252795\pi$
$677$	36.4723	1.40174	0.700871	+	0.713288i	$0.252795\pi$
$678$	22.7982	0.875561
$679$	−13.1380	−0.504189
$680$	−3.53031	−0.135381
$681$	−13.4241	−0.514414
$682$	−21.3895	−0.819047
$683$	−33.7576	−1.29170	−0.645849	−	0.763465i	$-0.723497\pi$
$683$	−33.7576	−1.29170	−0.645849	+	0.763465i	$0.723497\pi$
$684$	7.68670	0.293908
$685$	−9.78217	−0.373758
$686$	−13.7792	−0.526093
$687$	−69.9342	−2.66816
$688$	−9.04539	−0.344852
$689$	−6.19970	−0.236190
$690$	−51.3881	−1.95631
$691$	20.8833	0.794440	0.397220	−	0.917723i	$-0.369975\pi$
$691$	20.8833	0.794440	0.397220	+	0.917723i	$0.369975\pi$
$692$	16.9796	0.645466
$693$	13.0145	0.494382
$694$	−27.1869	−1.03200
$695$	−32.9656	−1.25046
$696$	−15.9549	−0.604769
$697$	−6.16000	−0.233327
$698$	−10.7692	−0.407621
$699$	−3.36592	−0.127311
$700$	1.46591	0.0554061
$701$	−19.8563	−0.749962	−0.374981	−	0.927033i	$-0.622351\pi$
$701$	−19.8563	−0.749962	−0.374981	+	0.927033i	$0.622351\pi$
$702$	−1.65147	−0.0623307
$703$	−16.9698	−0.640030
$704$	3.78431	0.142626
$705$	−48.3879	−1.82239
$706$	−19.6091	−0.737997
$707$	9.11365	0.342754
$708$	−3.77750	−0.141967
$709$	50.0331	1.87903	0.939517	−	0.342502i	$-0.111275\pi$
$709$	50.0331	1.87903	0.939517	+	0.342502i	$0.111275\pi$
$710$	22.9865	0.862667
$711$	−40.2513	−1.50954
$712$	−10.1769	−0.381395
$713$	−46.2018	−1.73027
$714$	3.73772	0.139881
$715$	30.5472	1.14240
$716$	21.4883	0.803056
$717$	−25.6223	−0.956883
$718$	36.6494	1.36774
$719$	40.3205	1.50370	0.751851	−	0.659333i	$-0.229161\pi$
$719$	40.3205	1.50370	0.751851	+	0.659333i	$0.229161\pi$
$720$	8.09277	0.301600
$721$	2.35152	0.0875753
$722$	−13.2559	−0.493332
$723$	−43.7581	−1.62738
$724$	−3.63131	−0.134957
$725$	8.75461	0.325138
$726$	−8.27397	−0.307076
$727$	10.8353	0.401858	0.200929	−	0.979606i	$-0.435604\pi$
$727$	10.8353	0.401858	0.200929	+	0.979606i	$0.435604\pi$
$728$	3.43029	0.127135
$729$	−30.5920	−1.13304
$730$	−6.12005	−0.226513
$731$	12.6552	0.468071
$732$	3.39310	0.125412
$733$	49.4892	1.82793	0.913963	−	0.405797i	$-0.133006\pi$
$733$	49.4892	1.82793	0.913963	+	0.405797i	$0.133006\pi$
$734$	6.16431	0.227529
$735$	36.7779	1.35657
$736$	8.17419	0.301305
$737$	−8.57562	−0.315887
$738$	14.1210	0.519801
$739$	21.8045	0.802091	0.401046	−	0.916058i	$-0.368647\pi$
$739$	21.8045	0.802091	0.401046	+	0.916058i	$0.368647\pi$
$740$	−17.8663	−0.656779
$741$	−19.1019	−0.701725
$742$	−2.07812	−0.0762903
$743$	−43.7617	−1.60546	−0.802731	−	0.596341i	$-0.796620\pi$
$743$	−43.7617	−1.60546	−0.802731	+	0.596341i	$0.796620\pi$
$744$	14.0819	0.516269
$745$	−26.2681	−0.962388
$746$	−35.5582	−1.30188
$747$	45.7664	1.67450
$748$	−5.29455	−0.193588
$749$	2.79691	0.102197
$750$	22.8389	0.833958
$751$	38.6489	1.41032	0.705159	−	0.709049i	$-0.250876\pi$
$751$	38.6489	1.41032	0.705159	+	0.709049i	$0.250876\pi$
$752$	7.69695	0.280679
$753$	25.3724	0.924621
$754$	20.4862	0.746063
$755$	−37.0540	−1.34853
$756$	−0.553568	−0.0201331
$757$	4.15370	0.150969	0.0754844	−	0.997147i	$-0.475950\pi$
$757$	4.15370	0.150969	0.0754844	+	0.997147i	$0.475950\pi$
$758$	−13.3839	−0.486125
$759$	−77.0689	−2.79742
$760$	6.04759	0.219369
$761$	0.0253616	0.000919357 0	0.000459679	−	1.00000i	$-0.499854\pi$
$761$	0.0253616	0.000919357 0	0.000459679		1.00000i	$0.499854\pi$
$762$	−46.1384	−1.67142
$763$	7.53583	0.272815
$764$	−2.25550	−0.0816010
$765$	−11.3224	−0.409364
$766$	12.3067	0.444659
$767$	4.85033	0.175135
$768$	−2.49143	−0.0899016
$769$	31.9502	1.15215	0.576076	−	0.817396i	$-0.304583\pi$
$769$	31.9502	1.15215	0.576076	+	0.817396i	$0.304583\pi$
$770$	10.2393	0.369000
$771$	−7.96192	−0.286742
$772$	0.0242992	0.000874547 0
$773$	−12.5162	−0.450175	−0.225088	−	0.974339i	$-0.572267\pi$
$773$	−12.5162	−0.450175	−0.225088	+	0.974339i	$0.572267\pi$
$774$	−29.0105	−1.04276
$775$	−7.72690	−0.277558
$776$	−12.2522	−0.439827
$777$	18.9160	0.678607
$778$	−15.1614	−0.543562
$779$	10.5524	0.378078
$780$	−20.1110	−0.720088
$781$	34.4738	1.23357
$782$	−11.4364	−0.408963
$783$	−3.30599	−0.118146
$784$	−5.85018	−0.208935
$785$	8.35380	0.298160
$786$	18.8217	0.671348
$787$	−31.3161	−1.11630	−0.558148	−	0.829741i	$-0.688488\pi$
$787$	−31.3161	−1.11630	−0.558148	+	0.829741i	$0.688488\pi$
$788$	−3.09311	−0.110187
$789$	−15.4618	−0.550453
$790$	−31.6682	−1.12670
$791$	−9.81225	−0.348884
$792$	12.1371	0.431272
$793$	−4.35675	−0.154713
$794$	7.03601	0.249699
$795$	12.1835	0.432106
$796$	15.0314	0.532773
$797$	−39.9789	−1.41613	−0.708063	−	0.706149i	$-0.750431\pi$
$797$	−39.9789	−1.41613	−0.708063	+	0.706149i	$0.750431\pi$
$798$	−6.40289	−0.226660
$799$	−10.7687	−0.380968
$800$	1.36707	0.0483332
$801$	−32.6394	−1.15326
$802$	−28.2976	−0.999225
$803$	−9.17849	−0.323902
$804$	5.64582	0.199113
$805$	22.1172	0.779528
$806$	−18.0813	−0.636887
$807$	9.31873	0.328035
$808$	8.49917	0.299000
$809$	10.9171	0.383824	0.191912	−	0.981412i	$-0.438531\pi$
$809$	10.9171	0.383824	0.191912	+	0.981412i	$0.438531\pi$
$810$	−21.0329	−0.739019
$811$	−46.8405	−1.64479	−0.822397	−	0.568914i	$-0.807364\pi$
$811$	−46.8405	−1.64479	−0.822397	+	0.568914i	$0.807364\pi$
$812$	6.86691	0.240981
$813$	−14.9098	−0.522909
$814$	−26.7949	−0.939159
$815$	16.5492	0.579695
$816$	3.48571	0.122024
$817$	−21.6790	−0.758453
$818$	16.0688	0.561834
$819$	11.0017	0.384429
$820$	11.1098	0.387972
$821$	45.0300	1.57156	0.785779	−	0.618508i	$-0.212263\pi$
$821$	45.0300	1.57156	0.785779	+	0.618508i	$0.212263\pi$
$822$	9.65859	0.336882
$823$	−21.9970	−0.766767	−0.383383	−	0.923589i	$-0.625241\pi$
$823$	−21.9970	−0.766767	−0.383383	+	0.923589i	$0.625241\pi$
$824$	2.19298	0.0763959
$825$	−12.8892	−0.448744
$826$	1.62582	0.0565694
$827$	−20.0445	−0.697016	−0.348508	−	0.937306i	$-0.613312\pi$
$827$	−20.0445	−0.697016	−0.348508	+	0.937306i	$0.613312\pi$
$828$	26.2163	0.911080
$829$	−30.5615	−1.06144	−0.530722	−	0.847546i	$-0.678079\pi$
$829$	−30.5615	−1.06144	−0.530722	+	0.847546i	$0.678079\pi$
$830$	36.0072	1.24983
$831$	−13.8264	−0.479631
$832$	3.19901	0.110906
$833$	8.18488	0.283589
$834$	32.5491	1.12708
$835$	12.9689	0.448806
$836$	9.06983	0.313686
$837$	2.91790	0.100857
$838$	7.88655	0.272436
$839$	−35.3642	−1.22091	−0.610453	−	0.792052i	$-0.709013\pi$
$839$	−35.3642	−1.22091	−0.610453	+	0.792052i	$0.709013\pi$
$840$	−6.74114	−0.232592
$841$	12.0102	0.414144
$842$	−18.8633	−0.650073
$843$	−19.5692	−0.674000
$844$	5.19118	0.178688
$845$	−6.98036	−0.240132
$846$	24.6857	0.848713
$847$	3.56108	0.122360
$848$	−1.93801	−0.0665515
$849$	−58.2307	−1.99847
$850$	−1.91264	−0.0656031
$851$	−57.8775	−1.98401
$852$	−22.6961	−0.777555
$853$	25.7067	0.880182	0.440091	−	0.897953i	$-0.354946\pi$
$853$	25.7067	0.880182	0.440091	+	0.897953i	$0.354946\pi$
$854$	−1.46037	−0.0499729
$855$	19.3959	0.663325
$856$	2.60833	0.0891510
$857$	−10.3538	−0.353679	−0.176839	−	0.984240i	$-0.556587\pi$
$857$	−10.3538	−0.353679	−0.176839	+	0.984240i	$0.556587\pi$
$858$	−30.1613	−1.02969
$859$	−15.3700	−0.524419	−0.262210	−	0.965011i	$-0.584451\pi$
$859$	−15.3700	−0.524419	−0.262210	+	0.965011i	$0.584451\pi$
$860$	−22.8243	−0.778302
$861$	−11.7626	−0.400867
$862$	6.27794	0.213827
$863$	−20.6370	−0.702492	−0.351246	−	0.936283i	$-0.614242\pi$
$863$	−20.6370	−0.702492	−0.351246	+	0.936283i	$0.614242\pi$
$864$	−0.516245	−0.0175630
$865$	42.8446	1.45676
$866$	−38.0188	−1.29193
$867$	37.4775	1.27280
$868$	−6.06080	−0.205717
$869$	−47.4941	−1.61113
$870$	−40.2591	−1.36491
$871$	−7.24927	−0.245632
$872$	7.02773	0.237989
$873$	−39.2953	−1.32994
$874$	19.5910	0.662676
$875$	−9.82975	−0.332306
$876$	6.04273	0.204165
$877$	16.6587	0.562525	0.281263	−	0.959631i	$-0.409247\pi$
$877$	16.6587	0.562525	0.281263	+	0.959631i	$0.409247\pi$
$878$	−3.33830	−0.112662
$879$	−61.0529	−2.05926
$880$	9.54896	0.321895
$881$	−49.1735	−1.65670	−0.828349	−	0.560212i	$-0.810720\pi$
$881$	−49.1735	−1.65670	−0.828349	+	0.560212i	$0.810720\pi$
$882$	−18.7627	−0.631774
$883$	34.0491	1.14584	0.572921	−	0.819610i	$-0.305810\pi$
$883$	34.0491	1.14584	0.572921	+	0.819610i	$0.305810\pi$
$884$	−4.47567	−0.150533
$885$	−9.53178	−0.320407
$886$	4.62217	0.155285
$887$	58.9117	1.97806	0.989030	−	0.147714i	$-0.0471914\pi$
$887$	58.9117	1.97806	0.989030	+	0.147714i	$0.0471914\pi$
$888$	17.6406	0.591980
$889$	19.8577	0.666008
$890$	−25.6794	−0.860776
$891$	−31.5439	−1.05676
$892$	−2.27370	−0.0761292
$893$	18.4472	0.617313
$894$	25.9362	0.867437
$895$	54.2216	1.81243
$896$	1.07230	0.0358230
$897$	−65.1490	−2.17526
$898$	−23.3357	−0.778723
$899$	−36.1960	−1.20720
$900$	4.38448	0.146149
$901$	2.71143	0.0903309
$902$	16.6619	0.554780
$903$	24.1652	0.804169
$904$	−9.15068	−0.304347
$905$	−9.16290	−0.304585
$906$	36.5859	1.21549
$907$	−35.3552	−1.17395	−0.586976	−	0.809604i	$-0.699682\pi$
$907$	−35.3552	−1.17395	−0.586976	+	0.809604i	$0.699682\pi$
$908$	5.38813	0.178811
$909$	27.2586	0.904112
$910$	8.65567	0.286933
$911$	−4.14732	−0.137407	−0.0687033	−	0.997637i	$-0.521886\pi$
$911$	−4.14732	−0.137407	−0.0687033	+	0.997637i	$0.521886\pi$
$912$	−5.97119	−0.197726
$913$	54.0015	1.78719
$914$	−8.84805	−0.292667
$915$	8.56182	0.283045
$916$	28.0699	0.927457
$917$	−8.10077	−0.267511
$918$	0.722269	0.0238384
$919$	−10.5858	−0.349192	−0.174596	−	0.984640i	$-0.555862\pi$
$919$	−10.5858	−0.349192	−0.174596	+	0.984640i	$0.555862\pi$
$920$	20.6260	0.680018
$921$	13.6589	0.450076
$922$	−32.3687	−1.06601
$923$	29.1419	0.959217
$924$	−10.1100	−0.332594
$925$	−9.67957	−0.318262
$926$	8.19253	0.269223
$927$	7.03333	0.231005
$928$	6.40392	0.210219
$929$	33.0378	1.08393	0.541967	−	0.840400i	$-0.317680\pi$
$929$	33.0378	1.08393	0.541967	+	0.840400i	$0.317680\pi$
$930$	35.5331	1.16517
$931$	−14.0211	−0.459522
$932$	1.35100	0.0442535
$933$	38.4982	1.26037
$934$	2.78068	0.0909867
$935$	−13.3598	−0.436911
$936$	10.2599	0.335355
$937$	−3.77215	−0.123231	−0.0616154	−	0.998100i	$-0.519625\pi$
$937$	−3.77215	−0.123231	−0.0616154	+	0.998100i	$0.519625\pi$
$938$	−2.42993	−0.0793402
$939$	−40.3746	−1.31758
$940$	19.4218	0.633468
$941$	−47.7360	−1.55615	−0.778074	−	0.628172i	$-0.783803\pi$
$941$	−47.7360	−1.55615	−0.778074	+	0.628172i	$0.783803\pi$
$942$	−8.24826	−0.268743
$943$	35.9900	1.17200
$944$	1.51620	0.0493481
$945$	−1.39682	−0.0454386
$946$	−34.2305	−1.11293
$947$	−22.2066	−0.721619	−0.360809	−	0.932640i	$-0.617500\pi$
$947$	−22.2066	−0.721619	−0.360809	+	0.932640i	$0.617500\pi$
$948$	31.2681	1.01554
$949$	−7.75890	−0.251865
$950$	3.27645	0.106302
$951$	−16.7418	−0.542892
$952$	−1.50023	−0.0486228
$953$	48.9295	1.58498	0.792491	−	0.609883i	$-0.208784\pi$
$953$	48.9295	1.58498	0.792491	+	0.609883i	$0.208784\pi$
$954$	−6.21560	−0.201237
$955$	−5.69131	−0.184166
$956$	10.2842	0.332615
$957$	−60.3782	−1.95175
$958$	−31.2390	−1.00929
$959$	−4.15701	−0.134237
$960$	−6.28663	−0.202900
$961$	0.946925	0.0305460
$962$	−22.6506	−0.730286
$963$	8.36547	0.269573
$964$	17.5635	0.565681
$965$	0.0613143	0.00197378
$966$	−21.8378	−0.702619
$967$	5.56060	0.178817	0.0894084	−	0.995995i	$-0.471502\pi$
$967$	5.56060	0.178817	0.0894084	+	0.995995i	$0.471502\pi$
$968$	3.32098	0.106740
$969$	8.35418	0.268375
$970$	−30.9160	−0.992652
$971$	−35.2143	−1.13008	−0.565041	−	0.825063i	$-0.691140\pi$
$971$	−35.2143	−1.13008	−0.565041	+	0.825063i	$0.691140\pi$
$972$	22.3159	0.715782
$973$	−14.0090	−0.449108
$974$	−14.9958	−0.480497
$975$	−10.8957	−0.348941
$976$	−1.36191	−0.0435936
$977$	16.7474	0.535795	0.267898	−	0.963447i	$-0.413671\pi$
$977$	16.7474	0.535795	0.267898	+	0.963447i	$0.413671\pi$
$978$	−16.3402	−0.522501
$979$	−38.5125	−1.23087
$980$	−14.7618	−0.471548
$981$	22.5394	0.719628
$982$	19.4148	0.619552
$983$	9.07249	0.289368	0.144684	−	0.989478i	$-0.453784\pi$
$983$	9.07249	0.289368	0.144684	+	0.989478i	$0.453784\pi$
$984$	−10.9695	−0.349694
$985$	−7.80485	−0.248683
$986$	−8.95960	−0.285332
$987$	−20.5628	−0.654521
$988$	7.66704	0.243921
$989$	−73.9387	−2.35111
$990$	30.6255	0.973343
$991$	−31.8886	−1.01297	−0.506487	−	0.862247i	$-0.669056\pi$
$991$	−31.8886	−1.01297	−0.506487	+	0.862247i	$0.669056\pi$
$992$	−5.65216	−0.179456
$993$	61.5532	1.95333
$994$	9.76828	0.309831
$995$	37.9288	1.20242
$996$	−35.5523	−1.12652
$997$	61.9565	1.96218	0.981091	−	0.193547i	$-0.0619993\pi$
$997$	61.9565	1.96218	0.981091	+	0.193547i	$0.0619993\pi$
$998$	6.00622	0.190123
$999$	3.65528	0.115648

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.f.1.7	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.f.1.7	✓	50	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:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.49143 q^{3} +1.00000 q^{4} +2.52331 q^{5} -2.49143 q^{6} +1.07230 q^{7} +1.00000 q^{8} +3.20721 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.49143 q^{3} +1.00000 q^{4} +2.52331 q^{5} -2.49143 q^{6} +1.07230 q^{7} +1.00000 q^{8} +3.20721 q^{9} +2.52331 q^{10} +3.78431 q^{11} -2.49143 q^{12} +3.19901 q^{13} +1.07230 q^{14} -6.28663 q^{15} +1.00000 q^{16} -1.39908 q^{17} +3.20721 q^{18} +2.39669 q^{19} +2.52331 q^{20} -2.67155 q^{21} +3.78431 q^{22} +8.17419 q^{23} -2.49143 q^{24} +1.36707 q^{25} +3.19901 q^{26} -0.516245 q^{27} +1.07230 q^{28} +6.40392 q^{29} -6.28663 q^{30} -5.65216 q^{31} +1.00000 q^{32} -9.42832 q^{33} -1.39908 q^{34} +2.70574 q^{35} +3.20721 q^{36} -7.08052 q^{37} +2.39669 q^{38} -7.97009 q^{39} +2.52331 q^{40} +4.40289 q^{41} -2.67155 q^{42} -9.04539 q^{43} +3.78431 q^{44} +8.09277 q^{45} +8.17419 q^{46} +7.69695 q^{47} -2.49143 q^{48} -5.85018 q^{49} +1.36707 q^{50} +3.48571 q^{51} +3.19901 q^{52} -1.93801 q^{53} -0.516245 q^{54} +9.54896 q^{55} +1.07230 q^{56} -5.97119 q^{57} +6.40392 q^{58} +1.51620 q^{59} -6.28663 q^{60} -1.36191 q^{61} -5.65216 q^{62} +3.43908 q^{63} +1.00000 q^{64} +8.07207 q^{65} -9.42832 q^{66} -2.26610 q^{67} -1.39908 q^{68} -20.3654 q^{69} +2.70574 q^{70} +9.10967 q^{71} +3.20721 q^{72} -2.42541 q^{73} -7.08052 q^{74} -3.40596 q^{75} +2.39669 q^{76} +4.05790 q^{77} -7.97009 q^{78} -12.5503 q^{79} +2.52331 q^{80} -8.33544 q^{81} +4.40289 q^{82} +14.2698 q^{83} -2.67155 q^{84} -3.53031 q^{85} -9.04539 q^{86} -15.9549 q^{87} +3.78431 q^{88} -10.1769 q^{89} +8.09277 q^{90} +3.43029 q^{91} +8.17419 q^{92} +14.0819 q^{93} +7.69695 q^{94} +6.04759 q^{95} -2.49143 q^{96} -12.2522 q^{97} -5.85018 q^{98} +12.1371 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9}+O(q^{10}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9} + 11 q^{10} + 21 q^{11} + 18 q^{12} + 26 q^{13} + 30 q^{14} + 17 q^{15} + 50 q^{16} + 24 q^{17} + 66 q^{18} + 39 q^{19} + 11 q^{20} - q^{21} + 21 q^{22} + 28 q^{23} + 18 q^{24} + 79 q^{25} + 26 q^{26} + 66 q^{27} + 30 q^{28} - 5 q^{29} + 17 q^{30} + 60 q^{31} + 50 q^{32} + 37 q^{33} + 24 q^{34} + 38 q^{35} + 66 q^{36} + 35 q^{37} + 39 q^{38} + 37 q^{39} + 11 q^{40} + 42 q^{41} - q^{42} + 44 q^{43} + 21 q^{44} + 31 q^{45} + 28 q^{46} + 60 q^{47} + 18 q^{48} + 92 q^{49} + 79 q^{50} + 26 q^{51} + 26 q^{52} - 2 q^{53} + 66 q^{54} + 33 q^{55} + 30 q^{56} + 15 q^{57} - 5 q^{58} + 65 q^{59} + 17 q^{60} + 15 q^{61} + 60 q^{62} + 56 q^{63} + 50 q^{64} + 6 q^{65} + 37 q^{66} + 48 q^{67} + 24 q^{68} - 9 q^{69} + 38 q^{70} + 34 q^{71} + 66 q^{72} + 91 q^{73} + 35 q^{74} + 54 q^{75} + 39 q^{76} - 6 q^{77} + 37 q^{78} + 29 q^{79} + 11 q^{80} + 66 q^{81} + 42 q^{82} + 43 q^{83} - q^{84} + 44 q^{86} + 32 q^{87} + 21 q^{88} + 38 q^{89} + 31 q^{90} + 55 q^{91} + 28 q^{92} - 15 q^{93} + 60 q^{94} + 9 q^{95} + 18 q^{96} + 80 q^{97} + 92 q^{98} + 20 q^{99}+O(q^{100}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9 + 11 * q^10 + 21 * q^11 + 18 * q^12 + 26 * q^13 + 30 * q^14 + 17 * q^15 + 50 * q^16 + 24 * q^17 + 66 * q^18 + 39 * q^19 + 11 * q^20 - q^21 + 21 * q^22 + 28 * q^23 + 18 * q^24 + 79 * q^25 + 26 * q^26 + 66 * q^27 + 30 * q^28 - 5 * q^29 + 17 * q^30 + 60 * q^31 + 50 * q^32 + 37 * q^33 + 24 * q^34 + 38 * q^35 + 66 * q^36 + 35 * q^37 + 39 * q^38 + 37 * q^39 + 11 * q^40 + 42 * q^41 - q^42 + 44 * q^43 + 21 * q^44 + 31 * q^45 + 28 * q^46 + 60 * q^47 + 18 * q^48 + 92 * q^49 + 79 * q^50 + 26 * q^51 + 26 * q^52 - 2 * q^53 + 66 * q^54 + 33 * q^55 + 30 * q^56 + 15 * q^57 - 5 * q^58 + 65 * q^59 + 17 * q^60 + 15 * q^61 + 60 * q^62 + 56 * q^63 + 50 * q^64 + 6 * q^65 + 37 * q^66 + 48 * q^67 + 24 * q^68 - 9 * q^69 + 38 * q^70 + 34 * q^71 + 66 * q^72 + 91 * q^73 + 35 * q^74 + 54 * q^75 + 39 * q^76 - 6 * q^77 + 37 * q^78 + 29 * q^79 + 11 * q^80 + 66 * q^81 + 42 * q^82 + 43 * q^83 - q^84 + 44 * q^86 + 32 * q^87 + 21 * q^88 + 38 * q^89 + 31 * q^90 + 55 * q^91 + 28 * q^92 - 15 * q^93 + 60 * q^94 + 9 * q^95 + 18 * q^96 + 80 * q^97 + 92 * q^98 + 20 * q^99

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