LMFDB - Embedded newform 4022.2.a.e.1.5

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:	$46$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.71162 q^{3} +1.00000 q^{4} -3.39235 q^{5} +2.71162 q^{6} -1.76888 q^{7} -1.00000 q^{8} +4.35289 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.71162 q^{3} +1.00000 q^{4} -3.39235 q^{5} +2.71162 q^{6} -1.76888 q^{7} -1.00000 q^{8} +4.35289 q^{9} +3.39235 q^{10} -0.0397045 q^{11} -2.71162 q^{12} +5.20065 q^{13} +1.76888 q^{14} +9.19878 q^{15} +1.00000 q^{16} +2.00343 q^{17} -4.35289 q^{18} -5.14151 q^{19} -3.39235 q^{20} +4.79653 q^{21} +0.0397045 q^{22} -7.87513 q^{23} +2.71162 q^{24} +6.50806 q^{25} -5.20065 q^{26} -3.66853 q^{27} -1.76888 q^{28} +1.96747 q^{29} -9.19878 q^{30} +3.77979 q^{31} -1.00000 q^{32} +0.107663 q^{33} -2.00343 q^{34} +6.00066 q^{35} +4.35289 q^{36} +2.56333 q^{37} +5.14151 q^{38} -14.1022 q^{39} +3.39235 q^{40} -3.33638 q^{41} -4.79653 q^{42} +6.92677 q^{43} -0.0397045 q^{44} -14.7665 q^{45} +7.87513 q^{46} -3.26808 q^{47} -2.71162 q^{48} -3.87107 q^{49} -6.50806 q^{50} -5.43255 q^{51} +5.20065 q^{52} +1.38926 q^{53} +3.66853 q^{54} +0.134692 q^{55} +1.76888 q^{56} +13.9418 q^{57} -1.96747 q^{58} -14.2794 q^{59} +9.19878 q^{60} -5.97046 q^{61} -3.77979 q^{62} -7.69974 q^{63} +1.00000 q^{64} -17.6424 q^{65} -0.107663 q^{66} -11.7991 q^{67} +2.00343 q^{68} +21.3544 q^{69} -6.00066 q^{70} -5.45041 q^{71} -4.35289 q^{72} +7.62952 q^{73} -2.56333 q^{74} -17.6474 q^{75} -5.14151 q^{76} +0.0702324 q^{77} +14.1022 q^{78} -11.9323 q^{79} -3.39235 q^{80} -3.11101 q^{81} +3.33638 q^{82} -7.86205 q^{83} +4.79653 q^{84} -6.79634 q^{85} -6.92677 q^{86} -5.33502 q^{87} +0.0397045 q^{88} +2.20737 q^{89} +14.7665 q^{90} -9.19931 q^{91} -7.87513 q^{92} -10.2494 q^{93} +3.26808 q^{94} +17.4418 q^{95} +2.71162 q^{96} +9.64140 q^{97} +3.87107 q^{98} -0.172829 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9}+O(q^{10}) $ 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9	\( 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9} - 14 q^{10} - 6 q^{11} + 8 q^{12} + 37 q^{13} - 28 q^{14} + 9 q^{15} + 46 q^{16} + 6 q^{17} - 58 q^{18} + 18 q^{19} + 14 q^{20} + 19 q^{21} + 6 q^{22} - 4 q^{23} - 8 q^{24} + 86 q^{25} - 37 q^{26} + 32 q^{27} + 28 q^{28} + 15 q^{29} - 9 q^{30} + 18 q^{31} - 46 q^{32} + 37 q^{33} - 6 q^{34} - 2 q^{35} + 58 q^{36} + 74 q^{37} - 18 q^{38} - 3 q^{39} - 14 q^{40} - 18 q^{41} - 19 q^{42} + 25 q^{43} - 6 q^{44} + 94 q^{45} + 4 q^{46} + 18 q^{47} + 8 q^{48} + 92 q^{49} - 86 q^{50} - 10 q^{51} + 37 q^{52} + 17 q^{53} - 32 q^{54} + 37 q^{55} - 28 q^{56} + 43 q^{57} - 15 q^{58} - 24 q^{59} + 9 q^{60} + 46 q^{61} - 18 q^{62} + 80 q^{63} + 46 q^{64} + 24 q^{65} - 37 q^{66} + 61 q^{67} + 6 q^{68} + 59 q^{69} + 2 q^{70} - 8 q^{71} - 58 q^{72} + 101 q^{73} - 74 q^{74} + 34 q^{75} + 18 q^{76} + 40 q^{77} + 3 q^{78} + 9 q^{79} + 14 q^{80} + 58 q^{81} + 18 q^{82} + 18 q^{83} + 19 q^{84} + 60 q^{85} - 25 q^{86} + 20 q^{87} + 6 q^{88} - 25 q^{89} - 94 q^{90} + 51 q^{91} - 4 q^{92} + 63 q^{93} - 18 q^{94} - 31 q^{95} - 8 q^{96} + 76 q^{97} - 92 q^{98} + 21 q^{99}+O(q^{100}) \) 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9 - 14 * q^10 - 6 * q^11 + 8 * q^12 + 37 * q^13 - 28 * q^14 + 9 * q^15 + 46 * q^16 + 6 * q^17 - 58 * q^18 + 18 * q^19 + 14 * q^20 + 19 * q^21 + 6 * q^22 - 4 * q^23 - 8 * q^24 + 86 * q^25 - 37 * q^26 + 32 * q^27 + 28 * q^28 + 15 * q^29 - 9 * q^30 + 18 * q^31 - 46 * q^32 + 37 * q^33 - 6 * q^34 - 2 * q^35 + 58 * q^36 + 74 * q^37 - 18 * q^38 - 3 * q^39 - 14 * q^40 - 18 * q^41 - 19 * q^42 + 25 * q^43 - 6 * q^44 + 94 * q^45 + 4 * q^46 + 18 * q^47 + 8 * q^48 + 92 * q^49 - 86 * q^50 - 10 * q^51 + 37 * q^52 + 17 * q^53 - 32 * q^54 + 37 * q^55 - 28 * q^56 + 43 * q^57 - 15 * q^58 - 24 * q^59 + 9 * q^60 + 46 * q^61 - 18 * q^62 + 80 * q^63 + 46 * q^64 + 24 * q^65 - 37 * q^66 + 61 * q^67 + 6 * q^68 + 59 * q^69 + 2 * q^70 - 8 * q^71 - 58 * q^72 + 101 * q^73 - 74 * q^74 + 34 * q^75 + 18 * q^76 + 40 * q^77 + 3 * q^78 + 9 * q^79 + 14 * q^80 + 58 * q^81 + 18 * q^82 + 18 * q^83 + 19 * q^84 + 60 * q^85 - 25 * q^86 + 20 * q^87 + 6 * q^88 - 25 * q^89 - 94 * q^90 + 51 * q^91 - 4 * q^92 + 63 * q^93 - 18 * q^94 - 31 * q^95 - 8 * q^96 + 76 * q^97 - 92 * q^98 + 21 * 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
$3$	−2.71162	−1.56556	−0.782778	−	0.622301i	$-0.786198\pi$
$3$	−2.71162	−1.56556	−0.782778	+	0.622301i	$0.786198\pi$
$4$	1.00000	0.500000
$5$	−3.39235	−1.51711	−0.758553	−	0.651611i	$-0.774093\pi$
$5$	−3.39235	−1.51711	−0.758553	+	0.651611i	$0.774093\pi$
$6$	2.71162	1.10701
$7$	−1.76888	−0.668573	−0.334287	−	0.942471i	$-0.608495\pi$
$7$	−1.76888	−0.668573	−0.334287	+	0.942471i	$0.608495\pi$
$8$	−1.00000	−0.353553
$9$	4.35289	1.45096
$10$	3.39235	1.07276
$11$	−0.0397045	−0.0119713	−0.00598567	−	0.999982i	$-0.501905\pi$
$11$	−0.0397045	−0.0119713	−0.00598567	+	0.999982i	$0.501905\pi$
$12$	−2.71162	−0.782778
$13$	5.20065	1.44240	0.721200	−	0.692727i	$-0.243591\pi$
$13$	5.20065	1.44240	0.721200	+	0.692727i	$0.243591\pi$
$14$	1.76888	0.472753
$15$	9.19878	2.37511
$16$	1.00000	0.250000
$17$	2.00343	0.485903	0.242952	−	0.970038i	$-0.421884\pi$
$17$	2.00343	0.485903	0.242952	+	0.970038i	$0.421884\pi$
$18$	−4.35289	−1.02599
$19$	−5.14151	−1.17954	−0.589772	−	0.807570i	$-0.700782\pi$
$19$	−5.14151	−1.17954	−0.589772	+	0.807570i	$0.700782\pi$
$20$	−3.39235	−0.758553
$21$	4.79653	1.04669
$22$	0.0397045	0.00846502
$23$	−7.87513	−1.64208	−0.821039	−	0.570872i	$-0.806605\pi$
$23$	−7.87513	−1.64208	−0.821039	+	0.570872i	$0.806605\pi$
$24$	2.71162	0.553507
$25$	6.50806	1.30161
$26$	−5.20065	−1.01993
$27$	−3.66853	−0.706009
$28$	−1.76888	−0.334287
$29$	1.96747	0.365349	0.182675	−	0.983173i	$-0.441525\pi$
$29$	1.96747	0.365349	0.182675	+	0.983173i	$0.441525\pi$
$30$	−9.19878	−1.67946
$31$	3.77979	0.678871	0.339435	−	0.940629i	$-0.389764\pi$
$31$	3.77979	0.678871	0.339435	+	0.940629i	$0.389764\pi$
$32$	−1.00000	−0.176777
$33$	0.107663	0.0187418
$34$	−2.00343	−0.343585
$35$	6.00066	1.01430
$36$	4.35289	0.725482
$37$	2.56333	0.421409	0.210705	−	0.977550i	$-0.432424\pi$
$37$	2.56333	0.421409	0.210705	+	0.977550i	$0.432424\pi$
$38$	5.14151	0.834063
$39$	−14.1022	−2.25816
$40$	3.39235	0.536378
$41$	−3.33638	−0.521055	−0.260527	−	0.965466i	$-0.583896\pi$
$41$	−3.33638	−0.521055	−0.260527	+	0.965466i	$0.583896\pi$
$42$	−4.79653	−0.740120
$43$	6.92677	1.05632	0.528161	−	0.849144i	$-0.322882\pi$
$43$	6.92677	1.05632	0.528161	+	0.849144i	$0.322882\pi$
$44$	−0.0397045	−0.00598567
$45$	−14.7665	−2.20127
$46$	7.87513	1.16112
$47$	−3.26808	−0.476699	−0.238349	−	0.971179i	$-0.576606\pi$
$47$	−3.26808	−0.476699	−0.238349	+	0.971179i	$0.576606\pi$
$48$	−2.71162	−0.391389
$49$	−3.87107	−0.553010
$50$	−6.50806	−0.920378
$51$	−5.43255	−0.760709
$52$	5.20065	0.721200
$53$	1.38926	0.190830	0.0954149	−	0.995438i	$-0.469582\pi$
$53$	1.38926	0.190830	0.0954149	+	0.995438i	$0.469582\pi$
$54$	3.66853	0.499224
$55$	0.134692	0.0181618
$56$	1.76888	0.236376
$57$	13.9418	1.84664
$58$	−1.96747	−0.258341
$59$	−14.2794	−1.85902	−0.929510	−	0.368797i	$-0.879770\pi$
$59$	−14.2794	−1.85902	−0.929510	+	0.368797i	$0.879770\pi$
$60$	9.19878	1.18756
$61$	−5.97046	−0.764439	−0.382220	−	0.924072i	$-0.624840\pi$
$61$	−5.97046	−0.764439	−0.382220	+	0.924072i	$0.624840\pi$
$62$	−3.77979	−0.480034
$63$	−7.69974	−0.970076
$64$	1.00000	0.125000
$65$	−17.6424	−2.18827
$66$	−0.107663	−0.0132525
$67$	−11.7991	−1.44149	−0.720743	−	0.693203i	$-0.756199\pi$
$67$	−11.7991	−1.44149	−0.720743	+	0.693203i	$0.756199\pi$
$68$	2.00343	0.242952
$69$	21.3544	2.57077
$70$	−6.00066	−0.717216
$71$	−5.45041	−0.646845	−0.323422	−	0.946255i	$-0.604833\pi$
$71$	−5.45041	−0.646845	−0.323422	+	0.946255i	$0.604833\pi$
$72$	−4.35289	−0.512993
$73$	7.62952	0.892968	0.446484	−	0.894792i	$-0.352676\pi$
$73$	7.62952	0.892968	0.446484	+	0.894792i	$0.352676\pi$
$74$	−2.56333	−0.297981
$75$	−17.6474	−2.03774
$76$	−5.14151	−0.589772
$77$	0.0702324	0.00800372
$78$	14.1022	1.59676
$79$	−11.9323	−1.34249	−0.671245	−	0.741235i	$-0.734240\pi$
$79$	−11.9323	−1.34249	−0.671245	+	0.741235i	$0.734240\pi$
$80$	−3.39235	−0.379277
$81$	−3.11101	−0.345667
$82$	3.33638	0.368441
$83$	−7.86205	−0.862972	−0.431486	−	0.902120i	$-0.642011\pi$
$83$	−7.86205	−0.862972	−0.431486	+	0.902120i	$0.642011\pi$
$84$	4.79653	0.523344
$85$	−6.79634	−0.737167
$86$	−6.92677	−0.746933
$87$	−5.33502	−0.571974
$88$	0.0397045	0.00423251
$89$	2.20737	0.233981	0.116991	−	0.993133i	$-0.462675\pi$
$89$	2.20737	0.233981	0.116991	+	0.993133i	$0.462675\pi$
$90$	14.7665	1.55653
$91$	−9.19931	−0.964350
$92$	−7.87513	−0.821039
$93$	−10.2494	−1.06281
$94$	3.26808	0.337077
$95$	17.4418	1.78949
$96$	2.71162	0.276754
$97$	9.64140	0.978936	0.489468	−	0.872021i	$-0.337191\pi$
$97$	9.64140	0.978936	0.489468	+	0.872021i	$0.337191\pi$
$98$	3.87107	0.391037
$99$	−0.172829	−0.0173700
$100$	6.50806	0.650806
$101$	−7.30416	−0.726791	−0.363396	−	0.931635i	$-0.618383\pi$
$101$	−7.30416	−0.726791	−0.363396	+	0.931635i	$0.618383\pi$
$102$	5.43255	0.537902
$103$	−0.838448	−0.0826147	−0.0413074	−	0.999146i	$-0.513152\pi$
$103$	−0.838448	−0.0826147	−0.0413074	+	0.999146i	$0.513152\pi$
$104$	−5.20065	−0.509965
$105$	−16.2715	−1.58794
$106$	−1.38926	−0.134937
$107$	0.636058	0.0614900	0.0307450	−	0.999527i	$-0.490212\pi$
$107$	0.636058	0.0614900	0.0307450	+	0.999527i	$0.490212\pi$
$108$	−3.66853	−0.353005
$109$	−3.52869	−0.337987	−0.168993	−	0.985617i	$-0.554052\pi$
$109$	−3.52869	−0.337987	−0.168993	+	0.985617i	$0.554052\pi$
$110$	−0.134692	−0.0128423
$111$	−6.95079	−0.659740
$112$	−1.76888	−0.167143
$113$	−7.56783	−0.711922	−0.355961	−	0.934501i	$-0.615846\pi$
$113$	−7.56783	−0.711922	−0.355961	+	0.934501i	$0.615846\pi$
$114$	−13.9418	−1.30577
$115$	26.7152	2.49121
$116$	1.96747	0.182675
$117$	22.6379	2.09287
$118$	14.2794	1.31453
$119$	−3.54382	−0.324862
$120$	−9.19878	−0.839730
$121$	−10.9984	−0.999857
$122$	5.97046	0.540540
$123$	9.04700	0.815740
$124$	3.77979	0.339435
$125$	−5.11586	−0.457576
$126$	7.69974	0.685947
$127$	−13.0192	−1.15527	−0.577635	−	0.816295i	$-0.696024\pi$
$127$	−13.0192	−1.15527	−0.577635	+	0.816295i	$0.696024\pi$
$128$	−1.00000	−0.0883883
$129$	−18.7828	−1.65373
$130$	17.6424	1.54734
$131$	19.5293	1.70628	0.853139	−	0.521683i	$-0.174696\pi$
$131$	19.5293	1.70628	0.853139	+	0.521683i	$0.174696\pi$
$132$	0.107663	0.00937090
$133$	9.09470	0.788611
$134$	11.7991	1.01928
$135$	12.4450	1.07109
$136$	−2.00343	−0.171793
$137$	−8.38477	−0.716360	−0.358180	−	0.933653i	$-0.616603\pi$
$137$	−8.38477	−0.716360	−0.358180	+	0.933653i	$0.616603\pi$
$138$	−21.3544	−1.81781
$139$	15.6523	1.32761	0.663804	−	0.747906i	$-0.268941\pi$
$139$	15.6523	1.32761	0.663804	+	0.747906i	$0.268941\pi$
$140$	6.00066	0.507148
$141$	8.86180	0.746298
$142$	5.45041	0.457388
$143$	−0.206489	−0.0172675
$144$	4.35289	0.362741
$145$	−6.67434	−0.554273
$146$	−7.62952	−0.631424
$147$	10.4969	0.865768
$148$	2.56333	0.210705
$149$	3.35558	0.274900	0.137450	−	0.990509i	$-0.456109\pi$
$149$	3.35558	0.274900	0.137450	+	0.990509i	$0.456109\pi$
$150$	17.6474	1.44090
$151$	6.97705	0.567784	0.283892	−	0.958856i	$-0.408374\pi$
$151$	6.97705	0.567784	0.283892	+	0.958856i	$0.408374\pi$
$152$	5.14151	0.417031
$153$	8.72072	0.705028
$154$	−0.0702324	−0.00565948
$155$	−12.8224	−1.02992
$156$	−14.1022	−1.12908
$157$	−13.2317	−1.05601	−0.528004	−	0.849242i	$-0.677059\pi$
$157$	−13.2317	−1.05601	−0.528004	+	0.849242i	$0.677059\pi$
$158$	11.9323	0.949284
$159$	−3.76715	−0.298755
$160$	3.39235	0.268189
$161$	13.9302	1.09785
$162$	3.11101	0.244424
$163$	13.7334	1.07568	0.537840	−	0.843047i	$-0.319240\pi$
$163$	13.7334	1.07568	0.537840	+	0.843047i	$0.319240\pi$
$164$	−3.33638	−0.260527
$165$	−0.365232	−0.0284333
$166$	7.86205	0.610214
$167$	6.38547	0.494123	0.247061	−	0.969000i	$-0.420535\pi$
$167$	6.38547	0.494123	0.247061	+	0.969000i	$0.420535\pi$
$168$	−4.79653	−0.370060
$169$	14.0467	1.08052
$170$	6.79634	0.521256
$171$	−22.3804	−1.71147
$172$	6.92677	0.528161
$173$	6.22285	0.473114	0.236557	−	0.971618i	$-0.423981\pi$
$173$	6.22285	0.473114	0.236557	+	0.971618i	$0.423981\pi$
$174$	5.33502	0.404447
$175$	−11.5120	−0.870222
$176$	−0.0397045	−0.00299284
$177$	38.7203	2.91040
$178$	−2.20737	−0.165450
$179$	−22.7234	−1.69843	−0.849214	−	0.528049i	$-0.822924\pi$
$179$	−22.7234	−1.69843	−0.849214	+	0.528049i	$0.822924\pi$
$180$	−14.7665	−1.10063
$181$	11.9564	0.888713	0.444357	−	0.895850i	$-0.353432\pi$
$181$	11.9564	0.888713	0.444357	+	0.895850i	$0.353432\pi$
$182$	9.19931	0.681898
$183$	16.1896	1.19677
$184$	7.87513	0.580562
$185$	−8.69573	−0.639323
$186$	10.2494	0.751520
$187$	−0.0795451	−0.00581691
$188$	−3.26808	−0.238349
$189$	6.48919	0.472019
$190$	−17.4418	−1.26536
$191$	13.0028	0.940850	0.470425	−	0.882440i	$-0.344101\pi$
$191$	13.0028	0.940850	0.470425	+	0.882440i	$0.344101\pi$
$192$	−2.71162	−0.195694
$193$	−14.4227	−1.03817	−0.519084	−	0.854723i	$-0.673727\pi$
$193$	−14.4227	−1.03817	−0.519084	+	0.854723i	$0.673727\pi$
$194$	−9.64140	−0.692212
$195$	47.8396	3.42586
$196$	−3.87107	−0.276505
$197$	15.4340	1.09963	0.549815	−	0.835287i	$-0.314698\pi$
$197$	15.4340	1.09963	0.549815	+	0.835287i	$0.314698\pi$
$198$	0.172829	0.0122824
$199$	−10.2717	−0.728143	−0.364072	−	0.931371i	$-0.618614\pi$
$199$	−10.2717	−0.728143	−0.364072	+	0.931371i	$0.618614\pi$
$200$	−6.50806	−0.460189
$201$	31.9946	2.25672
$202$	7.30416	0.513919
$203$	−3.48021	−0.244263
$204$	−5.43255	−0.380354
$205$	11.3182	0.790495
$206$	0.838448	0.0584174
$207$	−34.2796	−2.38260
$208$	5.20065	0.360600
$209$	0.204141	0.0141207
$210$	16.2715	1.12284
$211$	19.1879	1.32095	0.660474	−	0.750849i	$-0.270355\pi$
$211$	19.1879	1.32095	0.660474	+	0.750849i	$0.270355\pi$
$212$	1.38926	0.0954149
$213$	14.7794	1.01267
$214$	−0.636058	−0.0434800
$215$	−23.4980	−1.60255
$216$	3.66853	0.249612
$217$	−6.68599	−0.453875
$218$	3.52869	0.238993
$219$	−20.6884	−1.39799
$220$	0.134692	0.00908090
$221$	10.4191	0.700867
$222$	6.95079	0.466506
$223$	25.4649	1.70525	0.852626	−	0.522521i	$-0.175008\pi$
$223$	25.4649	1.70525	0.852626	+	0.522521i	$0.175008\pi$
$224$	1.76888	0.118188
$225$	28.3289	1.88859
$226$	7.56783	0.503405
$227$	11.4520	0.760094	0.380047	−	0.924967i	$-0.375908\pi$
$227$	11.4520	0.760094	0.380047	+	0.924967i	$0.375908\pi$
$228$	13.9418	0.923320
$229$	−11.0475	−0.730040	−0.365020	−	0.931000i	$-0.618938\pi$
$229$	−11.0475	−0.730040	−0.365020	+	0.931000i	$0.618938\pi$
$230$	−26.7152	−1.76155
$231$	−0.190444	−0.0125303
$232$	−1.96747	−0.129170
$233$	−9.77393	−0.640311	−0.320156	−	0.947365i	$-0.603735\pi$
$233$	−9.77393	−0.640311	−0.320156	+	0.947365i	$0.603735\pi$
$234$	−22.6379	−1.47988
$235$	11.0865	0.723203
$236$	−14.2794	−0.929510
$237$	32.3559	2.10174
$238$	3.54382	0.229712
$239$	−23.6011	−1.52663	−0.763315	−	0.646026i	$-0.776430\pi$
$239$	−23.6011	−1.52663	−0.763315	+	0.646026i	$0.776430\pi$
$240$	9.19878	0.593778
$241$	−29.1321	−1.87656	−0.938282	−	0.345872i	$-0.887583\pi$
$241$	−29.1321	−1.87656	−0.938282	+	0.345872i	$0.887583\pi$
$242$	10.9984	0.707005
$243$	19.4415	1.24717
$244$	−5.97046	−0.382220
$245$	13.1320	0.838975
$246$	−9.04700	−0.576815
$247$	−26.7392	−1.70137
$248$	−3.77979	−0.240017
$249$	21.3189	1.35103
$250$	5.11586	0.323555
$251$	−23.5362	−1.48559	−0.742796	−	0.669518i	$-0.766501\pi$
$251$	−23.5362	−1.48559	−0.742796	+	0.669518i	$0.766501\pi$
$252$	−7.69974	−0.485038
$253$	0.312678	0.0196579
$254$	13.0192	0.816899
$255$	18.4291	1.15408
$256$	1.00000	0.0625000
$257$	−15.2232	−0.949600	−0.474800	−	0.880094i	$-0.657480\pi$
$257$	−15.2232	−0.949600	−0.474800	+	0.880094i	$0.657480\pi$
$258$	18.7828	1.16936
$259$	−4.53422	−0.281743
$260$	−17.6424	−1.09414
$261$	8.56416	0.530108
$262$	−19.5293	−1.20652
$263$	−5.45516	−0.336380	−0.168190	−	0.985755i	$-0.553792\pi$
$263$	−5.45516	−0.336380	−0.168190	+	0.985755i	$0.553792\pi$
$264$	−0.107663	−0.00662623
$265$	−4.71287	−0.289509
$266$	−9.09470	−0.557632
$267$	−5.98556	−0.366311
$268$	−11.7991	−0.720743
$269$	2.89942	0.176781	0.0883903	−	0.996086i	$-0.471828\pi$
$269$	2.89942	0.176781	0.0883903	+	0.996086i	$0.471828\pi$
$270$	−12.4450	−0.757376
$271$	−8.86327	−0.538406	−0.269203	−	0.963084i	$-0.586760\pi$
$271$	−8.86327	−0.538406	−0.269203	+	0.963084i	$0.586760\pi$
$272$	2.00343	0.121476
$273$	24.9450	1.50974
$274$	8.38477	0.506543
$275$	−0.258399	−0.0155820
$276$	21.3544	1.28538
$277$	7.07556	0.425129	0.212564	−	0.977147i	$-0.431818\pi$
$277$	7.07556	0.425129	0.212564	+	0.977147i	$0.431818\pi$
$278$	−15.6523	−0.938761
$279$	16.4530	0.985017
$280$	−6.00066	−0.358608
$281$	25.9212	1.54633	0.773164	−	0.634206i	$-0.218673\pi$
$281$	25.9212	1.54633	0.773164	+	0.634206i	$0.218673\pi$
$282$	−8.86180	−0.527713
$283$	2.13969	0.127191	0.0635956	−	0.997976i	$-0.479743\pi$
$283$	2.13969	0.127191	0.0635956	+	0.997976i	$0.479743\pi$
$284$	−5.45041	−0.323422
$285$	−47.2956	−2.80155
$286$	0.206489	0.0122099
$287$	5.90165	0.348363
$288$	−4.35289	−0.256497
$289$	−12.9863	−0.763898
$290$	6.67434	0.391930
$291$	−26.1438	−1.53258
$292$	7.62952	0.446484
$293$	27.7063	1.61862	0.809309	−	0.587383i	$-0.199842\pi$
$293$	27.7063	1.61862	0.809309	+	0.587383i	$0.199842\pi$
$294$	−10.4969	−0.612190
$295$	48.4408	2.82033
$296$	−2.56333	−0.148991
$297$	0.145657	0.00845188
$298$	−3.35558	−0.194384
$299$	−40.9558	−2.36853
$300$	−17.6474	−1.01887
$301$	−12.2526	−0.706229
$302$	−6.97705	−0.401484
$303$	19.8061	1.13783
$304$	−5.14151	−0.294886
$305$	20.2539	1.15974
$306$	−8.72072	−0.498530
$307$	18.7643	1.07094	0.535468	−	0.844556i	$-0.320135\pi$
$307$	18.7643	1.07094	0.535468	+	0.844556i	$0.320135\pi$
$308$	0.0702324	0.00400186
$309$	2.27355	0.129338
$310$	12.8224	0.728263
$311$	−15.1706	−0.860246	−0.430123	−	0.902770i	$-0.641530\pi$
$311$	−15.1706	−0.860246	−0.430123	+	0.902770i	$0.641530\pi$
$312$	14.1022	0.798379
$313$	−10.8853	−0.615274	−0.307637	−	0.951504i	$-0.599538\pi$
$313$	−10.8853	−0.615274	−0.307637	+	0.951504i	$0.599538\pi$
$314$	13.2317	0.746710
$315$	26.1202	1.47171
$316$	−11.9323	−0.671245
$317$	13.0453	0.732695	0.366348	−	0.930478i	$-0.380608\pi$
$317$	13.0453	0.732695	0.366348	+	0.930478i	$0.380608\pi$
$318$	3.76715	0.211252
$319$	−0.0781171	−0.00437372
$320$	−3.39235	−0.189638
$321$	−1.72475	−0.0962660
$322$	−13.9302	−0.776297
$323$	−10.3007	−0.573144
$324$	−3.11101	−0.172834
$325$	33.8461	1.87744
$326$	−13.7334	−0.760621
$327$	9.56846	0.529137
$328$	3.33638	0.184221
$329$	5.78084	0.318708
$330$	0.365232	0.0201054
$331$	9.55393	0.525131	0.262566	−	0.964914i	$-0.415431\pi$
$331$	9.55393	0.525131	0.262566	+	0.964914i	$0.415431\pi$
$332$	−7.86205	−0.431486
$333$	11.1579	0.611450
$334$	−6.38547	−0.349398
$335$	40.0266	2.18689
$336$	4.79653	0.261672
$337$	33.1525	1.80593	0.902965	−	0.429715i	$-0.141386\pi$
$337$	33.1525	1.80593	0.902965	+	0.429715i	$0.141386\pi$
$338$	−14.0467	−0.764041
$339$	20.5211	1.11455
$340$	−6.79634	−0.368583
$341$	−0.150075	−0.00812700
$342$	22.3804	1.21020
$343$	19.2296	1.03830
$344$	−6.92677	−0.373466
$345$	−72.4416	−3.90012
$346$	−6.22285	−0.334542
$347$	−2.60917	−0.140068	−0.0700338	−	0.997545i	$-0.522311\pi$
$347$	−2.60917	−0.140068	−0.0700338	+	0.997545i	$0.522311\pi$
$348$	−5.33502	−0.285987
$349$	21.5683	1.15452	0.577262	−	0.816559i	$-0.304121\pi$
$349$	21.5683	1.15452	0.577262	+	0.816559i	$0.304121\pi$
$350$	11.5120	0.615340
$351$	−19.0787	−1.01835
$352$	0.0397045	0.00211625
$353$	17.6887	0.941477	0.470738	−	0.882273i	$-0.343988\pi$
$353$	17.6887	0.941477	0.470738	+	0.882273i	$0.343988\pi$
$354$	−38.7203	−2.05796
$355$	18.4897	0.981332
$356$	2.20737	0.116991
$357$	9.60951	0.508589
$358$	22.7234	1.20097
$359$	−12.6956	−0.670048	−0.335024	−	0.942210i	$-0.608744\pi$
$359$	−12.6956	−0.670048	−0.335024	+	0.942210i	$0.608744\pi$
$360$	14.7665	0.778265
$361$	7.43512	0.391322
$362$	−11.9564	−0.628415
$363$	29.8236	1.56533
$364$	−9.19931	−0.482175
$365$	−25.8820	−1.35473
$366$	−16.1896	−0.846246
$367$	2.97302	0.155191	0.0775953	−	0.996985i	$-0.475276\pi$
$367$	2.97302	0.155191	0.0775953	+	0.996985i	$0.475276\pi$
$368$	−7.87513	−0.410520
$369$	−14.5229	−0.756032
$370$	8.69573	0.452069
$371$	−2.45744	−0.127584
$372$	−10.2494	−0.531405
$373$	−21.8117	−1.12937	−0.564683	−	0.825308i	$-0.691001\pi$
$373$	−21.8117	−1.12937	−0.564683	+	0.825308i	$0.691001\pi$
$374$	0.0795451	0.00411318
$375$	13.8723	0.716361
$376$	3.26808	0.168538
$377$	10.2321	0.526979
$378$	−6.48919	−0.333768
$379$	28.7843	1.47855	0.739274	−	0.673405i	$-0.235169\pi$
$379$	28.7843	1.47855	0.739274	+	0.673405i	$0.235169\pi$
$380$	17.4418	0.894746
$381$	35.3032	1.80864
$382$	−13.0028	−0.665281
$383$	15.4306	0.788467	0.394233	−	0.919010i	$-0.371010\pi$
$383$	15.4306	0.788467	0.394233	+	0.919010i	$0.371010\pi$
$384$	2.71162	0.138377
$385$	−0.238253	−0.0121425
$386$	14.4227	0.734096
$387$	30.1515	1.53269
$388$	9.64140	0.489468
$389$	−5.09427	−0.258290	−0.129145	−	0.991626i	$-0.541223\pi$
$389$	−5.09427	−0.258290	−0.129145	+	0.991626i	$0.541223\pi$
$390$	−47.8396	−2.42245
$391$	−15.7773	−0.797891
$392$	3.87107	0.195519
$393$	−52.9559	−2.67127
$394$	−15.4340	−0.777555
$395$	40.4786	2.03670
$396$	−0.172829	−0.00868500
$397$	14.6890	0.737219	0.368610	−	0.929584i	$-0.379834\pi$
$397$	14.6890	0.737219	0.368610	+	0.929584i	$0.379834\pi$
$398$	10.2717	0.514875
$399$	−24.6614	−1.23461
$400$	6.50806	0.325403
$401$	−25.4458	−1.27070	−0.635352	−	0.772222i	$-0.719145\pi$
$401$	−25.4458	−1.27070	−0.635352	+	0.772222i	$0.719145\pi$
$402$	−31.9946	−1.59575
$403$	19.6574	0.979203
$404$	−7.30416	−0.363396
$405$	10.5536	0.524414
$406$	3.48021	0.172720
$407$	−0.101776	−0.00504483
$408$	5.43255	0.268951
$409$	13.7335	0.679079	0.339540	−	0.940592i	$-0.389729\pi$
$409$	13.7335	0.679079	0.339540	+	0.940592i	$0.389729\pi$
$410$	−11.3182	−0.558965
$411$	22.7363	1.12150
$412$	−0.838448	−0.0413074
$413$	25.2585	1.24289
$414$	34.2796	1.68475
$415$	26.6709	1.30922
$416$	−5.20065	−0.254983
$417$	−42.4430	−2.07844
$418$	−0.204141	−0.00998485
$419$	11.5424	0.563884	0.281942	−	0.959431i	$-0.409021\pi$
$419$	11.5424	0.563884	0.281942	+	0.959431i	$0.409021\pi$
$420$	−16.2715	−0.793969
$421$	−18.2162	−0.887805	−0.443903	−	0.896075i	$-0.646406\pi$
$421$	−18.2162	−0.887805	−0.443903	+	0.896075i	$0.646406\pi$
$422$	−19.1879	−0.934051
$423$	−14.2256	−0.691673
$424$	−1.38926	−0.0674685
$425$	13.0384	0.632457
$426$	−14.7794	−0.716067
$427$	10.5610	0.511084
$428$	0.636058	0.0307450
$429$	0.559920	0.0270332
$430$	23.4980	1.13318
$431$	5.41501	0.260832	0.130416	−	0.991459i	$-0.458369\pi$
$431$	5.41501	0.260832	0.130416	+	0.991459i	$0.458369\pi$
$432$	−3.66853	−0.176502
$433$	21.7928	1.04729	0.523647	−	0.851935i	$-0.324571\pi$
$433$	21.7928	1.04729	0.523647	+	0.851935i	$0.324571\pi$
$434$	6.68599	0.320938
$435$	18.0983	0.867746
$436$	−3.52869	−0.168993
$437$	40.4901	1.93690
$438$	20.6884	0.988529
$439$	−17.1307	−0.817605	−0.408803	−	0.912623i	$-0.634054\pi$
$439$	−17.1307	−0.817605	−0.408803	+	0.912623i	$0.634054\pi$
$440$	−0.134692	−0.00642117
$441$	−16.8503	−0.802398
$442$	−10.4191	−0.495588
$443$	−26.3518	−1.25201	−0.626007	−	0.779818i	$-0.715312\pi$
$443$	−26.3518	−1.25201	−0.626007	+	0.779818i	$0.715312\pi$
$444$	−6.95079	−0.329870
$445$	−7.48819	−0.354974
$446$	−25.4649	−1.20580
$447$	−9.09907	−0.430371
$448$	−1.76888	−0.0835716
$449$	−13.5298	−0.638512	−0.319256	−	0.947669i	$-0.603433\pi$
$449$	−13.5298	−0.638512	−0.319256	+	0.947669i	$0.603433\pi$
$450$	−28.3289	−1.33544
$451$	0.132469	0.00623772
$452$	−7.56783	−0.355961
$453$	−18.9191	−0.888898
$454$	−11.4520	−0.537468
$455$	31.2073	1.46302
$456$	−13.9418	−0.652886
$457$	12.1800	0.569755	0.284877	−	0.958564i	$-0.408047\pi$
$457$	12.1800	0.569755	0.284877	+	0.958564i	$0.408047\pi$
$458$	11.0475	0.516216
$459$	−7.34965	−0.343052
$460$	26.7152	1.24560
$461$	−31.8210	−1.48205	−0.741027	−	0.671476i	$-0.765661\pi$
$461$	−31.8210	−1.48205	−0.741027	+	0.671476i	$0.765661\pi$
$462$	0.190444	0.00886024
$463$	−0.866649	−0.0402766	−0.0201383	−	0.999797i	$-0.506411\pi$
$463$	−0.866649	−0.0402766	−0.0201383	+	0.999797i	$0.506411\pi$
$464$	1.96747	0.0913373
$465$	34.7695	1.61240
$466$	9.77393	0.452768
$467$	−19.6124	−0.907556	−0.453778	−	0.891115i	$-0.649924\pi$
$467$	−19.6124	−0.907556	−0.453778	+	0.891115i	$0.649924\pi$
$468$	22.6379	1.04644
$469$	20.8711	0.963738
$470$	−11.0865	−0.511381
$471$	35.8795	1.65324
$472$	14.2794	0.657263
$473$	−0.275024	−0.0126456
$474$	−32.3559	−1.48616
$475$	−33.4612	−1.53531
$476$	−3.54382	−0.162431
$477$	6.04731	0.276887
$478$	23.6011	1.07949
$479$	33.1602	1.51513	0.757563	−	0.652762i	$-0.226390\pi$
$479$	33.1602	1.51513	0.757563	+	0.652762i	$0.226390\pi$
$480$	−9.19878	−0.419865
$481$	13.3310	0.607841
$482$	29.1321	1.32693
$483$	−37.7733	−1.71874
$484$	−10.9984	−0.499928
$485$	−32.7070	−1.48515
$486$	−19.4415	−0.881883
$487$	10.6370	0.482011	0.241005	−	0.970524i	$-0.422523\pi$
$487$	10.6370	0.482011	0.241005	+	0.970524i	$0.422523\pi$
$488$	5.97046	0.270270
$489$	−37.2397	−1.68404
$490$	−13.1320	−0.593245
$491$	−0.792484	−0.0357643	−0.0178821	−	0.999840i	$-0.505692\pi$
$491$	−0.792484	−0.0357643	−0.0178821	+	0.999840i	$0.505692\pi$
$492$	9.04700	0.407870
$493$	3.94168	0.177524
$494$	26.7392	1.20305
$495$	0.586298	0.0263521
$496$	3.77979	0.169718
$497$	9.64111	0.432463
$498$	−21.3189	−0.955323
$499$	23.4936	1.05172	0.525860	−	0.850571i	$-0.323744\pi$
$499$	23.4936	1.05172	0.525860	+	0.850571i	$0.323744\pi$
$500$	−5.11586	−0.228788
$501$	−17.3150	−0.773577
$502$	23.5362	1.05047
$503$	−5.93995	−0.264849	−0.132425	−	0.991193i	$-0.542276\pi$
$503$	−5.93995	−0.264849	−0.132425	+	0.991193i	$0.542276\pi$
$504$	7.69974	0.342974
$505$	24.7783	1.10262
$506$	−0.312678	−0.0139002
$507$	−38.0894	−1.69161
$508$	−13.0192	−0.577635
$509$	−21.4055	−0.948782	−0.474391	−	0.880314i	$-0.657332\pi$
$509$	−21.4055	−0.948782	−0.474391	+	0.880314i	$0.657332\pi$
$510$	−18.4291	−0.816055
$511$	−13.4957	−0.597014
$512$	−1.00000	−0.0441942
$513$	18.8618	0.832768
$514$	15.2232	0.671468
$515$	2.84431	0.125335
$516$	−18.7828	−0.826866
$517$	0.129757	0.00570672
$518$	4.53422	0.199222
$519$	−16.8740	−0.740687
$520$	17.6424	0.773672
$521$	−30.7299	−1.34630	−0.673151	−	0.739505i	$-0.735059\pi$
$521$	−30.7299	−1.34630	−0.673151	+	0.739505i	$0.735059\pi$
$522$	−8.56416	−0.374843
$523$	−10.9276	−0.477830	−0.238915	−	0.971040i	$-0.576792\pi$
$523$	−10.9276	−0.477830	−0.238915	+	0.971040i	$0.576792\pi$
$524$	19.5293	0.853139
$525$	31.2161	1.36238
$526$	5.45516	0.237856
$527$	7.57255	0.329866
$528$	0.107663	0.00468545
$529$	39.0177	1.69642
$530$	4.71287	0.204714
$531$	−62.1567	−2.69737
$532$	9.09470	0.394305
$533$	−17.3513	−0.751569
$534$	5.98556	0.259021
$535$	−2.15773	−0.0932869
$536$	11.7991	0.509642
$537$	61.6173	2.65898
$538$	−2.89942	−0.125003
$539$	0.153699	0.00662027
$540$	12.4450	0.535546
$541$	5.41511	0.232814	0.116407	−	0.993202i	$-0.462862\pi$
$541$	5.41511	0.232814	0.116407	+	0.993202i	$0.462862\pi$
$542$	8.86327	0.380710
$543$	−32.4213	−1.39133
$544$	−2.00343	−0.0858964
$545$	11.9706	0.512762
$546$	−24.9450	−1.06755
$547$	−39.1331	−1.67321	−0.836606	−	0.547806i	$-0.815463\pi$
$547$	−39.1331	−1.67321	−0.836606	+	0.547806i	$0.815463\pi$
$548$	−8.38477	−0.358180
$549$	−25.9888	−1.10917
$550$	0.258399	0.0110182
$551$	−10.1157	−0.430945
$552$	−21.3544	−0.908903
$553$	21.1068	0.897553
$554$	−7.07556	−0.300612
$555$	23.5795	1.00089
$556$	15.6523	0.663804
$557$	−12.5339	−0.531079	−0.265540	−	0.964100i	$-0.585550\pi$
$557$	−12.5339	−0.531079	−0.265540	+	0.964100i	$0.585550\pi$
$558$	−16.4530	−0.696512
$559$	36.0237	1.52364
$560$	6.00066	0.253574
$561$	0.215696	0.00910670
$562$	−25.9212	−1.09342
$563$	38.3359	1.61566	0.807832	−	0.589413i	$-0.200641\pi$
$563$	38.3359	1.61566	0.807832	+	0.589413i	$0.200641\pi$
$564$	8.86180	0.373149
$565$	25.6728	1.08006
$566$	−2.13969	−0.0899378
$567$	5.50299	0.231104
$568$	5.45041	0.228694
$569$	2.45018	0.102717	0.0513585	−	0.998680i	$-0.483645\pi$
$569$	2.45018	0.102717	0.0513585	+	0.998680i	$0.483645\pi$
$570$	47.2956	1.98099
$571$	−0.492888	−0.0206267	−0.0103134	−	0.999947i	$-0.503283\pi$
$571$	−0.492888	−0.0206267	−0.0103134	+	0.999947i	$0.503283\pi$
$572$	−0.206489	−0.00863373
$573$	−35.2587	−1.47295
$574$	−5.90165	−0.246330
$575$	−51.2518	−2.13735
$576$	4.35289	0.181371
$577$	38.2079	1.59062	0.795308	−	0.606206i	$-0.207309\pi$
$577$	38.2079	1.59062	0.795308	+	0.606206i	$0.207309\pi$
$578$	12.9863	0.540157
$579$	39.1089	1.62531
$580$	−6.67434	−0.277137
$581$	13.9070	0.576960
$582$	26.1438	1.08370
$583$	−0.0551599	−0.00228449
$584$	−7.62952	−0.315712
$585$	−76.7956	−3.17511
$586$	−27.7063	−1.14454
$587$	6.63134	0.273705	0.136852	−	0.990591i	$-0.456301\pi$
$587$	6.63134	0.273705	0.136852	+	0.990591i	$0.456301\pi$
$588$	10.4969	0.432884
$589$	−19.4338	−0.800757
$590$	−48.4408	−1.99427
$591$	−41.8512	−1.72153
$592$	2.56333	0.105352
$593$	42.2330	1.73430	0.867150	−	0.498047i	$-0.165949\pi$
$593$	42.2330	1.73430	0.867150	+	0.498047i	$0.165949\pi$
$594$	−0.145657	−0.00597638
$595$	12.0219	0.492850
$596$	3.35558	0.137450
$597$	27.8530	1.13995
$598$	40.9558	1.67481
$599$	−2.40391	−0.0982210	−0.0491105	−	0.998793i	$-0.515639\pi$
$599$	−2.40391	−0.0982210	−0.0491105	+	0.998793i	$0.515639\pi$
$600$	17.6474	0.720452
$601$	2.92793	0.119433	0.0597163	−	0.998215i	$-0.480980\pi$
$601$	2.92793	0.119433	0.0597163	+	0.998215i	$0.480980\pi$
$602$	12.2526	0.499379
$603$	−51.3601	−2.09154
$604$	6.97705	0.283892
$605$	37.3105	1.51689
$606$	−19.8061	−0.804569
$607$	−38.8555	−1.57710	−0.788549	−	0.614972i	$-0.789167\pi$
$607$	−38.8555	−1.57710	−0.788549	+	0.614972i	$0.789167\pi$
$608$	5.14151	0.208516
$609$	9.43700	0.382407
$610$	−20.2539	−0.820057
$611$	−16.9961	−0.687590
$612$	8.72072	0.352514
$613$	−21.4483	−0.866290	−0.433145	−	0.901324i	$-0.642596\pi$
$613$	−21.4483	−0.866290	−0.433145	+	0.901324i	$0.642596\pi$
$614$	−18.7643	−0.757266
$615$	−30.6906	−1.23756
$616$	−0.0702324	−0.00282974
$617$	−32.4416	−1.30605	−0.653024	−	0.757337i	$-0.726500\pi$
$617$	−32.4416	−1.30605	−0.653024	+	0.757337i	$0.726500\pi$
$618$	−2.27355	−0.0914558
$619$	−44.2612	−1.77901	−0.889503	−	0.456928i	$-0.848950\pi$
$619$	−44.2612	−1.77901	−0.889503	+	0.456928i	$0.848950\pi$
$620$	−12.8224	−0.514960
$621$	28.8902	1.15932
$622$	15.1706	0.608286
$623$	−3.90458	−0.156434
$624$	−14.1022	−0.564539
$625$	−15.1855	−0.607419
$626$	10.8853	0.435064
$627$	−0.553553	−0.0221068
$628$	−13.2317	−0.528004
$629$	5.13546	0.204764
$630$	−26.1202	−1.04065
$631$	−13.2655	−0.528091	−0.264045	−	0.964510i	$-0.585057\pi$
$631$	−13.2655	−0.528091	−0.264045	+	0.964510i	$0.585057\pi$
$632$	11.9323	0.474642
$633$	−52.0303	−2.06802
$634$	−13.0453	−0.518094
$635$	44.1658	1.75267
$636$	−3.76715	−0.149377
$637$	−20.1321	−0.797661
$638$	0.0781171	0.00309269
$639$	−23.7250	−0.938548
$640$	3.39235	0.134095
$641$	30.5406	1.20628	0.603141	−	0.797634i	$-0.293915\pi$
$641$	30.5406	1.20628	0.603141	+	0.797634i	$0.293915\pi$
$642$	1.72475	0.0680703
$643$	−11.3033	−0.445757	−0.222879	−	0.974846i	$-0.571545\pi$
$643$	−11.3033	−0.445757	−0.222879	+	0.974846i	$0.571545\pi$
$644$	13.9302	0.548925
$645$	63.7178	2.50889
$646$	10.3007	0.405274
$647$	−6.33251	−0.248956	−0.124478	−	0.992222i	$-0.539726\pi$
$647$	−6.33251	−0.248956	−0.124478	+	0.992222i	$0.539726\pi$
$648$	3.11101	0.122212
$649$	0.566956	0.0222550
$650$	−33.8461	−1.32755
$651$	18.1299	0.710566
$652$	13.7334	0.537840
$653$	9.33124	0.365159	0.182580	−	0.983191i	$-0.441555\pi$
$653$	9.33124	0.365159	0.182580	+	0.983191i	$0.441555\pi$
$654$	−9.56846	−0.374157
$655$	−66.2501	−2.58861
$656$	−3.33638	−0.130264
$657$	33.2105	1.29566
$658$	−5.78084	−0.225361
$659$	4.72733	0.184150	0.0920752	−	0.995752i	$-0.470650\pi$
$659$	4.72733	0.184150	0.0920752	+	0.995752i	$0.470650\pi$
$660$	−0.365232	−0.0142167
$661$	−14.1795	−0.551519	−0.275759	−	0.961227i	$-0.588929\pi$
$661$	−14.1795	−0.551519	−0.275759	+	0.961227i	$0.588929\pi$
$662$	−9.55393	−0.371324
$663$	−28.2527	−1.09725
$664$	7.86205	0.305107
$665$	−30.8524	−1.19641
$666$	−11.1579	−0.432360
$667$	−15.4940	−0.599932
$668$	6.38547	0.247061
$669$	−69.0510	−2.66967
$670$	−40.0266	−1.54636
$671$	0.237054	0.00915136
$672$	−4.79653	−0.185030
$673$	−7.93744	−0.305966	−0.152983	−	0.988229i	$-0.548888\pi$
$673$	−7.93744	−0.305966	−0.152983	+	0.988229i	$0.548888\pi$
$674$	−33.1525	−1.27698
$675$	−23.8750	−0.918950
$676$	14.0467	0.540258
$677$	22.8178	0.876960	0.438480	−	0.898741i	$-0.355517\pi$
$677$	22.8178	0.876960	0.438480	+	0.898741i	$0.355517\pi$
$678$	−20.5211	−0.788108
$679$	−17.0545	−0.654490
$680$	6.79634	0.260628
$681$	−31.0534	−1.18997
$682$	0.150075	0.00574665
$683$	−33.4297	−1.27915	−0.639577	−	0.768727i	$-0.720890\pi$
$683$	−33.4297	−1.27915	−0.639577	+	0.768727i	$0.720890\pi$
$684$	−22.3804	−0.855737
$685$	28.4441	1.08679
$686$	−19.2296	−0.734190
$687$	29.9567	1.14292
$688$	6.92677	0.264081
$689$	7.22506	0.275253
$690$	72.4416	2.75780
$691$	−1.69238	−0.0643810	−0.0321905	−	0.999482i	$-0.510248\pi$
$691$	−1.69238	−0.0643810	−0.0321905	+	0.999482i	$0.510248\pi$
$692$	6.22285	0.236557
$693$	0.305714	0.0116131
$694$	2.60917	0.0990427
$695$	−53.0980	−2.01412
$696$	5.33502	0.202223
$697$	−6.68420	−0.253182
$698$	−21.5683	−0.816372
$699$	26.5032	1.00244
$700$	−11.5120	−0.435111
$701$	−14.7732	−0.557976	−0.278988	−	0.960295i	$-0.589999\pi$
$701$	−14.7732	−0.557976	−0.278988	+	0.960295i	$0.589999\pi$
$702$	19.0787	0.720081
$703$	−13.1794	−0.497070
$704$	−0.0397045	−0.00149642
$705$	−30.0624	−1.13221
$706$	−17.6887	−0.665725
$707$	12.9202	0.485913
$708$	38.7203	1.45520
$709$	39.2275	1.47322	0.736610	−	0.676317i	$-0.236425\pi$
$709$	39.2275	1.47322	0.736610	+	0.676317i	$0.236425\pi$
$710$	−18.4897	−0.693907
$711$	−51.9401	−1.94791
$712$	−2.20737	−0.0827249
$713$	−29.7664	−1.11476
$714$	−9.60951	−0.359627
$715$	0.700483	0.0261966
$716$	−22.7234	−0.849214
$717$	63.9973	2.39002
$718$	12.6956	0.473795
$719$	−16.3364	−0.609246	−0.304623	−	0.952473i	$-0.598530\pi$
$719$	−16.3364	−0.609246	−0.304623	+	0.952473i	$0.598530\pi$
$720$	−14.7665	−0.550317
$721$	1.48311	0.0552340
$722$	−7.43512	−0.276706
$723$	78.9952	2.93786
$724$	11.9564	0.444357
$725$	12.8044	0.475542
$726$	−29.8236	−1.10686
$727$	19.8865	0.737551	0.368776	−	0.929518i	$-0.379777\pi$
$727$	19.8865	0.737551	0.368776	+	0.929518i	$0.379777\pi$
$728$	9.19931	0.340949
$729$	−43.3849	−1.60685
$730$	25.8820	0.957937
$731$	13.8773	0.513271
$732$	16.1896	0.598386
$733$	27.8982	1.03045	0.515223	−	0.857056i	$-0.327709\pi$
$733$	27.8982	1.03045	0.515223	+	0.857056i	$0.327709\pi$
$734$	−2.97302	−0.109736
$735$	−35.6091	−1.31346
$736$	7.87513	0.290281
$737$	0.468475	0.0172565
$738$	14.5229	0.534595
$739$	19.4846	0.716752	0.358376	−	0.933577i	$-0.383331\pi$
$739$	19.4846	0.716752	0.358376	+	0.933577i	$0.383331\pi$
$740$	−8.69573	−0.319661
$741$	72.5065	2.66359
$742$	2.45744	0.0902153
$743$	25.1347	0.922104	0.461052	−	0.887373i	$-0.347472\pi$
$743$	25.1347	0.922104	0.461052	+	0.887373i	$0.347472\pi$
$744$	10.2494	0.375760
$745$	−11.3833	−0.417052
$746$	21.8117	0.798582
$747$	−34.2227	−1.25214
$748$	−0.0795451	−0.00290846
$749$	−1.12511	−0.0411106
$750$	−13.8723	−0.506544
$751$	2.49787	0.0911486	0.0455743	−	0.998961i	$-0.485488\pi$
$751$	2.49787	0.0911486	0.0455743	+	0.998961i	$0.485488\pi$
$752$	−3.26808	−0.119175
$753$	63.8213	2.32578
$754$	−10.2321	−0.372631
$755$	−23.6686	−0.861389
$756$	6.48919	0.236009
$757$	−24.9134	−0.905494	−0.452747	−	0.891639i	$-0.649556\pi$
$757$	−24.9134	−0.905494	−0.452747	+	0.891639i	$0.649556\pi$
$758$	−28.7843	−1.04549
$759$	−0.847864	−0.0307755
$760$	−17.4418	−0.632681
$761$	21.9662	0.796274	0.398137	−	0.917326i	$-0.369657\pi$
$761$	21.9662	0.796274	0.398137	+	0.917326i	$0.369657\pi$
$762$	−35.3032	−1.27890
$763$	6.24182	0.225969
$764$	13.0028	0.470425
$765$	−29.5837	−1.06960
$766$	−15.4306	−0.557530
$767$	−74.2621	−2.68145
$768$	−2.71162	−0.0978472
$769$	22.5418	0.812879	0.406440	−	0.913678i	$-0.366770\pi$
$769$	22.5418	0.812879	0.406440	+	0.913678i	$0.366770\pi$
$770$	0.238253	0.00858604
$771$	41.2797	1.48665
$772$	−14.4227	−0.519084
$773$	44.9742	1.61761	0.808805	−	0.588077i	$-0.200115\pi$
$773$	44.9742	1.61761	0.808805	+	0.588077i	$0.200115\pi$
$774$	−30.1515	−1.08377
$775$	24.5991	0.883626
$776$	−9.64140	−0.346106
$777$	12.2951	0.441084
$778$	5.09427	0.182639
$779$	17.1540	0.614606
$780$	47.8396	1.71293
$781$	0.216406	0.00774360
$782$	15.7773	0.564194
$783$	−7.21771	−0.257940
$784$	−3.87107	−0.138252
$785$	44.8867	1.60208
$786$	52.9559	1.88888
$787$	37.1705	1.32499	0.662493	−	0.749068i	$-0.269499\pi$
$787$	37.1705	1.32499	0.662493	+	0.749068i	$0.269499\pi$
$788$	15.4340	0.549815
$789$	14.7923	0.526621
$790$	−40.4786	−1.44016
$791$	13.3866	0.475972
$792$	0.172829	0.00614122
$793$	−31.0503	−1.10263
$794$	−14.6890	−0.521293
$795$	12.7795	0.453243
$796$	−10.2717	−0.364072
$797$	10.6073	0.375728	0.187864	−	0.982195i	$-0.439844\pi$
$797$	10.6073	0.375728	0.187864	+	0.982195i	$0.439844\pi$
$798$	24.6614	0.873004
$799$	−6.54737	−0.231629
$800$	−6.50806	−0.230095
$801$	9.60846	0.339498
$802$	25.4458	0.898524
$803$	−0.302926	−0.0106900
$804$	31.9946	1.12836
$805$	−47.2560	−1.66555
$806$	−19.6574	−0.692401
$807$	−7.86213	−0.276760
$808$	7.30416	0.256959
$809$	−15.6112	−0.548859	−0.274430	−	0.961607i	$-0.588489\pi$
$809$	−15.6112	−0.548859	−0.274430	+	0.961607i	$0.588489\pi$
$810$	−10.5536	−0.370817
$811$	53.8427	1.89067	0.945336	−	0.326097i	$-0.105734\pi$
$811$	53.8427	1.89067	0.945336	+	0.326097i	$0.105734\pi$
$812$	−3.48021	−0.122131
$813$	24.0338	0.842904
$814$	0.101776	0.00356724
$815$	−46.5884	−1.63192
$816$	−5.43255	−0.190177
$817$	−35.6141	−1.24598
$818$	−13.7335	−0.480181
$819$	−40.0436	−1.39924
$820$	11.3182	0.395248
$821$	47.6151	1.66178	0.830889	−	0.556438i	$-0.187832\pi$
$821$	47.6151	1.66178	0.830889	+	0.556438i	$0.187832\pi$
$822$	−22.7363	−0.793021
$823$	38.1746	1.33068	0.665341	−	0.746539i	$-0.268286\pi$
$823$	38.1746	1.33068	0.665341	+	0.746539i	$0.268286\pi$
$824$	0.838448	0.0292087
$825$	0.700680	0.0243945
$826$	−25.2585	−0.878857
$827$	26.1294	0.908607	0.454303	−	0.890847i	$-0.349888\pi$
$827$	26.1294	0.908607	0.454303	+	0.890847i	$0.349888\pi$
$828$	−34.2796	−1.19130
$829$	55.2481	1.91885	0.959423	−	0.281969i	$-0.0909876\pi$
$829$	55.2481	1.91885	0.959423	+	0.281969i	$0.0909876\pi$
$830$	−26.6709	−0.925759
$831$	−19.1862	−0.665563
$832$	5.20065	0.180300
$833$	−7.75542	−0.268709
$834$	42.4430	1.46968
$835$	−21.6618	−0.749637
$836$	0.204141	0.00706036
$837$	−13.8663	−0.479289
$838$	−11.5424	−0.398726
$839$	−30.9881	−1.06983	−0.534914	−	0.844907i	$-0.679656\pi$
$839$	−30.9881	−1.06983	−0.534914	+	0.844907i	$0.679656\pi$
$840$	16.2715	0.561421
$841$	−25.1291	−0.866520
$842$	18.2162	0.627773
$843$	−70.2885	−2.42086
$844$	19.1879	0.660474
$845$	−47.6514	−1.63926
$846$	14.2256	0.489086
$847$	19.4549	0.668477
$848$	1.38926	0.0477075
$849$	−5.80202	−0.199125
$850$	−13.0384	−0.447215
$851$	−20.1866	−0.691987
$852$	14.7794	0.506336
$853$	−26.8397	−0.918975	−0.459488	−	0.888184i	$-0.651967\pi$
$853$	−26.8397	−0.918975	−0.459488	+	0.888184i	$0.651967\pi$
$854$	−10.5610	−0.361391
$855$	75.9223	2.59649
$856$	−0.636058	−0.0217400
$857$	−6.97169	−0.238148	−0.119074	−	0.992885i	$-0.537993\pi$
$857$	−6.97169	−0.238148	−0.119074	+	0.992885i	$0.537993\pi$
$858$	−0.559920	−0.0191153
$859$	8.63701	0.294691	0.147346	−	0.989085i	$-0.452927\pi$
$859$	8.63701	0.294691	0.147346	+	0.989085i	$0.452927\pi$
$860$	−23.4980	−0.801277
$861$	−16.0030	−0.545382
$862$	−5.41501	−0.184436
$863$	−12.3192	−0.419351	−0.209675	−	0.977771i	$-0.567241\pi$
$863$	−12.3192	−0.419351	−0.209675	+	0.977771i	$0.567241\pi$
$864$	3.66853	0.124806
$865$	−21.1101	−0.717765
$866$	−21.7928	−0.740549
$867$	35.2138	1.19592
$868$	−6.68599	−0.226937
$869$	0.473766	0.0160714
$870$	−18.0983	−0.613589
$871$	−61.3628	−2.07920
$872$	3.52869	0.119496
$873$	41.9680	1.42040
$874$	−40.4901	−1.36960
$875$	9.04933	0.305923
$876$	−20.6884	−0.698995
$877$	28.7429	0.970580	0.485290	−	0.874353i	$-0.338714\pi$
$877$	28.7429	0.970580	0.485290	+	0.874353i	$0.338714\pi$
$878$	17.1307	0.578134
$879$	−75.1290	−2.53404
$880$	0.134692	0.00454045
$881$	−29.8093	−1.00430	−0.502150	−	0.864781i	$-0.667457\pi$
$881$	−29.8093	−1.00430	−0.502150	+	0.864781i	$0.667457\pi$
$882$	16.8503	0.567381
$883$	−15.2733	−0.513986	−0.256993	−	0.966413i	$-0.582732\pi$
$883$	−15.2733	−0.513986	−0.256993	+	0.966413i	$0.582732\pi$
$884$	10.4191	0.350433
$885$	−131.353	−4.41538
$886$	26.3518	0.885307
$887$	−43.6465	−1.46551	−0.732753	−	0.680495i	$-0.761765\pi$
$887$	−43.6465	−1.46551	−0.732753	+	0.680495i	$0.761765\pi$
$888$	6.95079	0.233253
$889$	23.0294	0.772382
$890$	7.48819	0.251005
$891$	0.123521	0.00413810
$892$	25.4649	0.852626
$893$	16.8029	0.562287
$894$	9.09907	0.304318
$895$	77.0858	2.57670
$896$	1.76888	0.0590941
$897$	111.057	3.70807
$898$	13.5298	0.451496
$899$	7.43661	0.248025
$900$	28.3289	0.944296
$901$	2.78329	0.0927249
$902$	−0.132469	−0.00441074
$903$	33.2245	1.10564
$904$	7.56783	0.251702
$905$	−40.5604	−1.34827
$906$	18.9191	0.628546
$907$	−31.7954	−1.05575	−0.527875	−	0.849322i	$-0.677011\pi$
$907$	−31.7954	−1.05575	−0.527875	+	0.849322i	$0.677011\pi$
$908$	11.4520	0.380047
$909$	−31.7942	−1.05455
$910$	−31.2073	−1.03451
$911$	−10.2502	−0.339605	−0.169802	−	0.985478i	$-0.554313\pi$
$911$	−10.2502	−0.339605	−0.169802	+	0.985478i	$0.554313\pi$
$912$	13.9418	0.461660
$913$	0.312158	0.0103309
$914$	−12.1800	−0.402878
$915$	−54.9209	−1.81563
$916$	−11.0475	−0.365020
$917$	−34.5449	−1.14077
$918$	7.34965	0.242575
$919$	30.8823	1.01871	0.509357	−	0.860555i	$-0.329883\pi$
$919$	30.8823	1.01871	0.509357	+	0.860555i	$0.329883\pi$
$920$	−26.7152	−0.880775
$921$	−50.8817	−1.67661
$922$	31.8210	1.04797
$923$	−28.3457	−0.933008
$924$	−0.190444	−0.00626513
$925$	16.6823	0.548511
$926$	0.866649	0.0284798
$927$	−3.64967	−0.119871
$928$	−1.96747	−0.0645852
$929$	−15.3561	−0.503817	−0.251908	−	0.967751i	$-0.581058\pi$
$929$	−15.3561	−0.503817	−0.251908	+	0.967751i	$0.581058\pi$
$930$	−34.7695	−1.14014
$931$	19.9031	0.652299
$932$	−9.77393	−0.320156
$933$	41.1370	1.34676
$934$	19.6124	0.641739
$935$	0.269845	0.00882488
$936$	−22.6379	−0.739941
$937$	−24.2454	−0.792062	−0.396031	−	0.918237i	$-0.629613\pi$
$937$	−24.2454	−0.792062	−0.396031	+	0.918237i	$0.629613\pi$
$938$	−20.8711	−0.681466
$939$	29.5168	0.963246
$940$	11.0865	0.361601
$941$	52.5077	1.71170	0.855851	−	0.517222i	$-0.173034\pi$
$941$	52.5077	1.71170	0.855851	+	0.517222i	$0.173034\pi$
$942$	−35.8795	−1.16902
$943$	26.2744	0.855613
$944$	−14.2794	−0.464755
$945$	−22.0136	−0.716103
$946$	0.275024	0.00894179
$947$	−40.3676	−1.31177	−0.655885	−	0.754861i	$-0.727704\pi$
$947$	−40.3676	−1.31177	−0.655885	+	0.754861i	$0.727704\pi$
$948$	32.3559	1.05087
$949$	39.6784	1.28802
$950$	33.4612	1.08563
$951$	−35.3738	−1.14708
$952$	3.54382	0.114856
$953$	1.50624	0.0487918	0.0243959	−	0.999702i	$-0.492234\pi$
$953$	1.50624	0.0487918	0.0243959	+	0.999702i	$0.492234\pi$
$954$	−6.04731	−0.195789
$955$	−44.1101	−1.42737
$956$	−23.6011	−0.763315
$957$	0.211824	0.00684730
$958$	−33.1602	−1.07136
$959$	14.8316	0.478939
$960$	9.19878	0.296889
$961$	−16.7132	−0.539134
$962$	−13.3310	−0.429808
$963$	2.76869	0.0892198
$964$	−29.1321	−0.938282
$965$	48.9269	1.57501
$966$	37.7733	1.21534
$967$	−21.6873	−0.697417	−0.348708	−	0.937231i	$-0.613380\pi$
$967$	−21.6873	−0.697417	−0.348708	+	0.937231i	$0.613380\pi$
$968$	10.9984	0.353503
$969$	27.9315	0.897289
$970$	32.7070	1.05016
$971$	11.2048	0.359578	0.179789	−	0.983705i	$-0.442458\pi$
$971$	11.2048	0.359578	0.179789	+	0.983705i	$0.442458\pi$
$972$	19.4415	0.623585
$973$	−27.6870	−0.887603
$974$	−10.6370	−0.340833
$975$	−91.7778	−2.93924
$976$	−5.97046	−0.191110
$977$	19.6806	0.629637	0.314819	−	0.949152i	$-0.398056\pi$
$977$	19.6806	0.629637	0.314819	+	0.949152i	$0.398056\pi$
$978$	37.2397	1.19079
$979$	−0.0876426	−0.00280107
$980$	13.1320	0.419487
$981$	−15.3600	−0.490407
$982$	0.792484	0.0252892
$983$	51.1289	1.63076	0.815379	−	0.578928i	$-0.196529\pi$
$983$	51.1289	1.63076	0.815379	+	0.578928i	$0.196529\pi$
$984$	−9.04700	−0.288408
$985$	−52.3577	−1.66825
$986$	−3.94168	−0.125529
$987$	−15.6754	−0.498955
$988$	−26.7392	−0.850686
$989$	−54.5492	−1.73456
$990$	−0.586298	−0.0186338
$991$	31.3401	0.995552	0.497776	−	0.867306i	$-0.334150\pi$
$991$	31.3401	0.995552	0.497776	+	0.867306i	$0.334150\pi$
$992$	−3.77979	−0.120009
$993$	−25.9066	−0.822123
$994$	−9.64111	−0.305797
$995$	34.8453	1.10467
$996$	21.3189	0.675516
$997$	−0.299312	−0.00947931	−0.00473966	−	0.999989i	$-0.501509\pi$
$997$	−0.299312	−0.00947931	−0.00473966	+	0.999989i	$0.501509\pi$
$998$	−23.4936	−0.743678
$999$	−9.40367	−0.297519

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.e.1.5	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.e.1.5	✓	46	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.71162 q^{3} +1.00000 q^{4} -3.39235 q^{5} +2.71162 q^{6} -1.76888 q^{7} -1.00000 q^{8} +4.35289 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.71162 q^{3} +1.00000 q^{4} -3.39235 q^{5} +2.71162 q^{6} -1.76888 q^{7} -1.00000 q^{8} +4.35289 q^{9} +3.39235 q^{10} -0.0397045 q^{11} -2.71162 q^{12} +5.20065 q^{13} +1.76888 q^{14} +9.19878 q^{15} +1.00000 q^{16} +2.00343 q^{17} -4.35289 q^{18} -5.14151 q^{19} -3.39235 q^{20} +4.79653 q^{21} +0.0397045 q^{22} -7.87513 q^{23} +2.71162 q^{24} +6.50806 q^{25} -5.20065 q^{26} -3.66853 q^{27} -1.76888 q^{28} +1.96747 q^{29} -9.19878 q^{30} +3.77979 q^{31} -1.00000 q^{32} +0.107663 q^{33} -2.00343 q^{34} +6.00066 q^{35} +4.35289 q^{36} +2.56333 q^{37} +5.14151 q^{38} -14.1022 q^{39} +3.39235 q^{40} -3.33638 q^{41} -4.79653 q^{42} +6.92677 q^{43} -0.0397045 q^{44} -14.7665 q^{45} +7.87513 q^{46} -3.26808 q^{47} -2.71162 q^{48} -3.87107 q^{49} -6.50806 q^{50} -5.43255 q^{51} +5.20065 q^{52} +1.38926 q^{53} +3.66853 q^{54} +0.134692 q^{55} +1.76888 q^{56} +13.9418 q^{57} -1.96747 q^{58} -14.2794 q^{59} +9.19878 q^{60} -5.97046 q^{61} -3.77979 q^{62} -7.69974 q^{63} +1.00000 q^{64} -17.6424 q^{65} -0.107663 q^{66} -11.7991 q^{67} +2.00343 q^{68} +21.3544 q^{69} -6.00066 q^{70} -5.45041 q^{71} -4.35289 q^{72} +7.62952 q^{73} -2.56333 q^{74} -17.6474 q^{75} -5.14151 q^{76} +0.0702324 q^{77} +14.1022 q^{78} -11.9323 q^{79} -3.39235 q^{80} -3.11101 q^{81} +3.33638 q^{82} -7.86205 q^{83} +4.79653 q^{84} -6.79634 q^{85} -6.92677 q^{86} -5.33502 q^{87} +0.0397045 q^{88} +2.20737 q^{89} +14.7665 q^{90} -9.19931 q^{91} -7.87513 q^{92} -10.2494 q^{93} +3.26808 q^{94} +17.4418 q^{95} +2.71162 q^{96} +9.64140 q^{97} +3.87107 q^{98} -0.172829 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9}+O(q^{10}) \) 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9	\( 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9} - 14 q^{10} - 6 q^{11} + 8 q^{12} + 37 q^{13} - 28 q^{14} + 9 q^{15} + 46 q^{16} + 6 q^{17} - 58 q^{18} + 18 q^{19} + 14 q^{20} + 19 q^{21} + 6 q^{22} - 4 q^{23} - 8 q^{24} + 86 q^{25} - 37 q^{26} + 32 q^{27} + 28 q^{28} + 15 q^{29} - 9 q^{30} + 18 q^{31} - 46 q^{32} + 37 q^{33} - 6 q^{34} - 2 q^{35} + 58 q^{36} + 74 q^{37} - 18 q^{38} - 3 q^{39} - 14 q^{40} - 18 q^{41} - 19 q^{42} + 25 q^{43} - 6 q^{44} + 94 q^{45} + 4 q^{46} + 18 q^{47} + 8 q^{48} + 92 q^{49} - 86 q^{50} - 10 q^{51} + 37 q^{52} + 17 q^{53} - 32 q^{54} + 37 q^{55} - 28 q^{56} + 43 q^{57} - 15 q^{58} - 24 q^{59} + 9 q^{60} + 46 q^{61} - 18 q^{62} + 80 q^{63} + 46 q^{64} + 24 q^{65} - 37 q^{66} + 61 q^{67} + 6 q^{68} + 59 q^{69} + 2 q^{70} - 8 q^{71} - 58 q^{72} + 101 q^{73} - 74 q^{74} + 34 q^{75} + 18 q^{76} + 40 q^{77} + 3 q^{78} + 9 q^{79} + 14 q^{80} + 58 q^{81} + 18 q^{82} + 18 q^{83} + 19 q^{84} + 60 q^{85} - 25 q^{86} + 20 q^{87} + 6 q^{88} - 25 q^{89} - 94 q^{90} + 51 q^{91} - 4 q^{92} + 63 q^{93} - 18 q^{94} - 31 q^{95} - 8 q^{96} + 76 q^{97} - 92 q^{98} + 21 q^{99}+O(q^{100}) \) 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9 - 14 * q^10 - 6 * q^11 + 8 * q^12 + 37 * q^13 - 28 * q^14 + 9 * q^15 + 46 * q^16 + 6 * q^17 - 58 * q^18 + 18 * q^19 + 14 * q^20 + 19 * q^21 + 6 * q^22 - 4 * q^23 - 8 * q^24 + 86 * q^25 - 37 * q^26 + 32 * q^27 + 28 * q^28 + 15 * q^29 - 9 * q^30 + 18 * q^31 - 46 * q^32 + 37 * q^33 - 6 * q^34 - 2 * q^35 + 58 * q^36 + 74 * q^37 - 18 * q^38 - 3 * q^39 - 14 * q^40 - 18 * q^41 - 19 * q^42 + 25 * q^43 - 6 * q^44 + 94 * q^45 + 4 * q^46 + 18 * q^47 + 8 * q^48 + 92 * q^49 - 86 * q^50 - 10 * q^51 + 37 * q^52 + 17 * q^53 - 32 * q^54 + 37 * q^55 - 28 * q^56 + 43 * q^57 - 15 * q^58 - 24 * q^59 + 9 * q^60 + 46 * q^61 - 18 * q^62 + 80 * q^63 + 46 * q^64 + 24 * q^65 - 37 * q^66 + 61 * q^67 + 6 * q^68 + 59 * q^69 + 2 * q^70 - 8 * q^71 - 58 * q^72 + 101 * q^73 - 74 * q^74 + 34 * q^75 + 18 * q^76 + 40 * q^77 + 3 * q^78 + 9 * q^79 + 14 * q^80 + 58 * q^81 + 18 * q^82 + 18 * q^83 + 19 * q^84 + 60 * q^85 - 25 * q^86 + 20 * q^87 + 6 * q^88 - 25 * q^89 - 94 * q^90 + 51 * q^91 - 4 * q^92 + 63 * q^93 - 18 * q^94 - 31 * q^95 - 8 * q^96 + 76 * q^97 - 92 * q^98 + 21 * q^99

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