LMFDB - Embedded newform 4033.2.a.d.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.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:	$32.2036671352$
Analytic rank:	$1$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.08653 q^{2} +2.88703 q^{3} +2.35363 q^{4} -4.18679 q^{5} -6.02388 q^{6} -1.99666 q^{7} -0.737856 q^{8} +5.33492 q^{9} +O(q^{10})$	\(q-2.08653 q^{2} +2.88703 q^{3} +2.35363 q^{4} -4.18679 q^{5} -6.02388 q^{6} -1.99666 q^{7} -0.737856 q^{8} +5.33492 q^{9} +8.73588 q^{10} +3.06980 q^{11} +6.79498 q^{12} +0.158092 q^{13} +4.16610 q^{14} -12.0874 q^{15} -3.16769 q^{16} -3.54579 q^{17} -11.1315 q^{18} +4.28964 q^{19} -9.85414 q^{20} -5.76441 q^{21} -6.40523 q^{22} -1.05297 q^{23} -2.13021 q^{24} +12.5292 q^{25} -0.329864 q^{26} +6.74097 q^{27} -4.69940 q^{28} -7.99932 q^{29} +25.2207 q^{30} +1.29591 q^{31} +8.08521 q^{32} +8.86258 q^{33} +7.39842 q^{34} +8.35960 q^{35} +12.5564 q^{36} -1.00000 q^{37} -8.95048 q^{38} +0.456415 q^{39} +3.08925 q^{40} -0.110396 q^{41} +12.0276 q^{42} +3.87431 q^{43} +7.22515 q^{44} -22.3362 q^{45} +2.19706 q^{46} -3.80279 q^{47} -9.14521 q^{48} -3.01335 q^{49} -26.1426 q^{50} -10.2368 q^{51} +0.372089 q^{52} +8.59885 q^{53} -14.0653 q^{54} -12.8526 q^{55} +1.47325 q^{56} +12.3843 q^{57} +16.6909 q^{58} -11.5903 q^{59} -28.4492 q^{60} -10.5347 q^{61} -2.70396 q^{62} -10.6520 q^{63} -10.5347 q^{64} -0.661897 q^{65} -18.4921 q^{66} +3.45692 q^{67} -8.34547 q^{68} -3.03996 q^{69} -17.4426 q^{70} +8.33434 q^{71} -3.93640 q^{72} +13.1132 q^{73} +2.08653 q^{74} +36.1721 q^{75} +10.0962 q^{76} -6.12934 q^{77} -0.952325 q^{78} +1.18523 q^{79} +13.2625 q^{80} +3.45659 q^{81} +0.230346 q^{82} +0.476753 q^{83} -13.5673 q^{84} +14.8455 q^{85} -8.08387 q^{86} -23.0942 q^{87} -2.26507 q^{88} +1.85481 q^{89} +46.6052 q^{90} -0.315655 q^{91} -2.47831 q^{92} +3.74132 q^{93} +7.93465 q^{94} -17.9598 q^{95} +23.3422 q^{96} -5.50030 q^{97} +6.28745 q^{98} +16.3771 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) $ 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.08653	−1.47540	−0.737701	−	0.675127i	$-0.764089\pi$
$2$	−2.08653	−1.47540	−0.737701	+	0.675127i	$0.764089\pi$
$3$	2.88703	1.66683	0.833413	−	0.552651i	$-0.186384\pi$
$3$	2.88703	1.66683	0.833413	+	0.552651i	$0.186384\pi$
$4$	2.35363	1.17681
$5$	−4.18679	−1.87239	−0.936195	−	0.351482i	$-0.885678\pi$
$5$	−4.18679	−1.87239	−0.936195	+	0.351482i	$0.885678\pi$
$6$	−6.02388	−2.45924
$7$	−1.99666	−0.754667	−0.377333	−	0.926077i	$-0.623159\pi$
$7$	−1.99666	−0.754667	−0.377333	+	0.926077i	$0.623159\pi$
$8$	−0.737856	−0.260871
$9$	5.33492	1.77831
$10$	8.73588	2.76253
$11$	3.06980	0.925578	0.462789	−	0.886468i	$-0.346849\pi$
$11$	3.06980	0.925578	0.462789	+	0.886468i	$0.346849\pi$
$12$	6.79498	1.96154
$13$	0.158092	0.0438467	0.0219234	−	0.999760i	$-0.493021\pi$
$13$	0.158092	0.0438467	0.0219234	+	0.999760i	$0.493021\pi$
$14$	4.16610	1.11344
$15$	−12.0874	−3.12095
$16$	−3.16769	−0.791923
$17$	−3.54579	−0.859981	−0.429991	−	0.902833i	$-0.641483\pi$
$17$	−3.54579	−0.859981	−0.429991	+	0.902833i	$0.641483\pi$
$18$	−11.1315	−2.62372
$19$	4.28964	0.984111	0.492055	−	0.870564i	$-0.336246\pi$
$19$	4.28964	0.984111	0.492055	+	0.870564i	$0.336246\pi$
$20$	−9.85414	−2.20345
$21$	−5.76441	−1.25790
$22$	−6.40523	−1.36560
$23$	−1.05297	−0.219560	−0.109780	−	0.993956i	$-0.535015\pi$
$23$	−1.05297	−0.219560	−0.109780	+	0.993956i	$0.535015\pi$
$24$	−2.13021	−0.434827
$25$	12.5292	2.50584
$26$	−0.329864	−0.0646916
$27$	6.74097	1.29730
$28$	−4.69940	−0.888102
$29$	−7.99932	−1.48544	−0.742718	−	0.669604i	$-0.766464\pi$
$29$	−7.99932	−1.48544	−0.742718	+	0.669604i	$0.766464\pi$
$30$	25.2207	4.60465
$31$	1.29591	0.232752	0.116376	−	0.993205i	$-0.462872\pi$
$31$	1.29591	0.232752	0.116376	+	0.993205i	$0.462872\pi$
$32$	8.08521	1.42928
$33$	8.86258	1.54278
$34$	7.39842	1.26882
$35$	8.35960	1.41303
$36$	12.5564	2.09273
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−8.95048	−1.45196
$39$	0.456415	0.0730849
$40$	3.08925	0.488453
$41$	−0.110396	−0.0172410	−0.00862051	−	0.999963i	$-0.502744\pi$
$41$	−0.110396	−0.0172410	−0.00862051	+	0.999963i	$0.502744\pi$
$42$	12.0276	1.85591
$43$	3.87431	0.590826	0.295413	−	0.955370i	$-0.404543\pi$
$43$	3.87431	0.590826	0.295413	+	0.955370i	$0.404543\pi$
$44$	7.22515	1.08923
$45$	−22.3362	−3.32968
$46$	2.19706	0.323940
$47$	−3.80279	−0.554693	−0.277347	−	0.960770i	$-0.589455\pi$
$47$	−3.80279	−0.554693	−0.277347	+	0.960770i	$0.589455\pi$
$48$	−9.14521	−1.32000
$49$	−3.01335	−0.430478
$50$	−26.1426	−3.69713
$51$	−10.2368	−1.43344
$52$	0.372089	0.0515995
$53$	8.59885	1.18114	0.590571	−	0.806986i	$-0.298902\pi$
$53$	8.59885	1.18114	0.590571	+	0.806986i	$0.298902\pi$
$54$	−14.0653	−1.91404
$55$	−12.8526	−1.73304
$56$	1.47325	0.196871
$57$	12.3843	1.64034
$58$	16.6909	2.19162
$59$	−11.5903	−1.50893	−0.754466	−	0.656339i	$-0.772104\pi$
$59$	−11.5903	−1.50893	−0.754466	+	0.656339i	$0.772104\pi$
$60$	−28.4492	−3.67277
$61$	−10.5347	−1.34883	−0.674417	−	0.738351i	$-0.735605\pi$
$61$	−10.5347	−1.34883	−0.674417	+	0.738351i	$0.735605\pi$
$62$	−2.70396	−0.343403
$63$	−10.6520	−1.34203
$64$	−10.5347	−1.31684
$65$	−0.661897	−0.0820982
$66$	−18.4921	−2.27622
$67$	3.45692	0.422330	0.211165	−	0.977450i	$-0.432274\pi$
$67$	3.45692	0.422330	0.211165	+	0.977450i	$0.432274\pi$
$68$	−8.34547	−1.01204
$69$	−3.03996	−0.365968
$70$	−17.4426	−2.08479
$71$	8.33434	0.989104	0.494552	−	0.869148i	$-0.335332\pi$
$71$	8.33434	0.989104	0.494552	+	0.869148i	$0.335332\pi$
$72$	−3.93640	−0.463909
$73$	13.1132	1.53479	0.767395	−	0.641175i	$-0.221553\pi$
$73$	13.1132	1.53479	0.767395	+	0.641175i	$0.221553\pi$
$74$	2.08653	0.242555
$75$	36.1721	4.17680
$76$	10.0962	1.15812
$77$	−6.12934	−0.698503
$78$	−0.952325	−0.107830
$79$	1.18523	0.133349	0.0666746	−	0.997775i	$-0.478761\pi$
$79$	1.18523	0.133349	0.0666746	+	0.997775i	$0.478761\pi$
$80$	13.2625	1.48279
$81$	3.45659	0.384066
$82$	0.230346	0.0254374
$83$	0.476753	0.0523304	0.0261652	−	0.999658i	$-0.491670\pi$
$83$	0.476753	0.0523304	0.0261652	+	0.999658i	$0.491670\pi$
$84$	−13.5673	−1.48031
$85$	14.8455	1.61022
$86$	−8.08387	−0.871707
$87$	−23.0942	−2.47596
$88$	−2.26507	−0.241457
$89$	1.85481	0.196609	0.0983046	−	0.995156i	$-0.468658\pi$
$89$	1.85481	0.196609	0.0983046	+	0.995156i	$0.468658\pi$
$90$	46.6052	4.91262
$91$	−0.315655	−0.0330897
$92$	−2.47831	−0.258381
$93$	3.74132	0.387957
$94$	7.93465	0.818396
$95$	−17.9598	−1.84264
$96$	23.3422	2.38236
$97$	−5.50030	−0.558471	−0.279236	−	0.960223i	$-0.590081\pi$
$97$	−5.50030	−0.558471	−0.279236	+	0.960223i	$0.590081\pi$
$98$	6.28745	0.635128
$99$	16.3771	1.64596
$100$	29.4891	2.94891
$101$	−4.35362	−0.433201	−0.216600	−	0.976260i	$-0.569497\pi$
$101$	−4.35362	−0.433201	−0.216600	+	0.976260i	$0.569497\pi$
$102$	21.3594	2.11490
$103$	10.3794	1.02272	0.511358	−	0.859368i	$-0.329143\pi$
$103$	10.3794	1.02272	0.511358	+	0.859368i	$0.329143\pi$
$104$	−0.116649	−0.0114384
$105$	24.1344	2.35527
$106$	−17.9418	−1.74266
$107$	0.428744	0.0414482	0.0207241	−	0.999785i	$-0.493403\pi$
$107$	0.428744	0.0414482	0.0207241	+	0.999785i	$0.493403\pi$
$108$	15.8657	1.52668
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	26.8174	2.55694
$111$	−2.88703	−0.274024
$112$	6.32481	0.597638
$113$	−0.0188257	−0.00177098	−0.000885488	−	1.00000i	$-0.500282\pi$
$113$	−0.0188257	−0.00177098	−0.000885488		1.00000i	$0.500282\pi$
$114$	−25.8403	−2.42016
$115$	4.40858	0.411102
$116$	−18.8274	−1.74808
$117$	0.843406	0.0779729
$118$	24.1836	2.22628
$119$	7.07974	0.648999
$120$	8.91873	0.814165
$121$	−1.57636	−0.143305
$122$	21.9811	1.99007
$123$	−0.318717	−0.0287378
$124$	3.05008	0.273906
$125$	−31.5232	−2.81952
$126$	22.2258	1.98003
$127$	−7.48308	−0.664016	−0.332008	−	0.943277i	$-0.607726\pi$
$127$	−7.48308	−0.664016	−0.332008	+	0.943277i	$0.607726\pi$
$128$	5.81057	0.513587
$129$	11.1852	0.984804
$130$	1.38107	0.121128
$131$	−1.39904	−0.122234	−0.0611172	−	0.998131i	$-0.519466\pi$
$131$	−1.39904	−0.122234	−0.0611172	+	0.998131i	$0.519466\pi$
$132$	20.8592	1.81556
$133$	−8.56496	−0.742676
$134$	−7.21299	−0.623108
$135$	−28.2230	−2.42905
$136$	2.61628	0.224344
$137$	−22.2379	−1.89991	−0.949957	−	0.312381i	$-0.898873\pi$
$137$	−22.2379	−1.89991	−0.949957	+	0.312381i	$0.898873\pi$
$138$	6.34298	0.539951
$139$	6.16989	0.523323	0.261662	−	0.965160i	$-0.415730\pi$
$139$	6.16989	0.523323	0.261662	+	0.965160i	$0.415730\pi$
$140$	19.6754	1.66287
$141$	−10.9787	−0.924577
$142$	−17.3899	−1.45933
$143$	0.485309	0.0405836
$144$	−16.8994	−1.40828
$145$	33.4915	2.78132
$146$	−27.3612	−2.26443
$147$	−8.69961	−0.717531
$148$	−2.35363	−0.193467
$149$	17.9682	1.47201	0.736007	−	0.676974i	$-0.236709\pi$
$149$	17.9682	1.47201	0.736007	+	0.676974i	$0.236709\pi$
$150$	−75.4744	−6.16246
$151$	−8.44332	−0.687107	−0.343554	−	0.939133i	$-0.611631\pi$
$151$	−8.44332	−0.687107	−0.343554	+	0.939133i	$0.611631\pi$
$152$	−3.16514	−0.256726
$153$	−18.9165	−1.52931
$154$	12.7891	1.03057
$155$	−5.42569	−0.435802
$156$	1.07423	0.0860073
$157$	−18.7783	−1.49867	−0.749336	−	0.662190i	$-0.769627\pi$
$157$	−18.7783	−1.49867	−0.749336	+	0.662190i	$0.769627\pi$
$158$	−2.47303	−0.196744
$159$	24.8251	1.96876
$160$	−33.8511	−2.67616
$161$	2.10243	0.165695
$162$	−7.21230	−0.566652
$163$	11.4355	0.895700	0.447850	−	0.894109i	$-0.352190\pi$
$163$	11.4355	0.895700	0.447850	+	0.894109i	$0.352190\pi$
$164$	−0.259832	−0.0202895
$165$	−37.1057	−2.88868
$166$	−0.994761	−0.0772084
$167$	−12.1767	−0.942258	−0.471129	−	0.882064i	$-0.656153\pi$
$167$	−12.1767	−0.942258	−0.471129	+	0.882064i	$0.656153\pi$
$168$	4.25330	0.328149
$169$	−12.9750	−0.998077
$170$	−30.9756	−2.37572
$171$	22.8849	1.75005
$172$	9.11867	0.695292
$173$	−18.1908	−1.38302	−0.691510	−	0.722367i	$-0.743054\pi$
$173$	−18.1908	−1.38302	−0.691510	+	0.722367i	$0.743054\pi$
$174$	48.1869	3.65304
$175$	−25.0166	−1.89108
$176$	−9.72417	−0.732987
$177$	−33.4616	−2.51513
$178$	−3.87012	−0.290078
$179$	−8.66274	−0.647483	−0.323742	−	0.946145i	$-0.604941\pi$
$179$	−8.66274	−0.647483	−0.323742	+	0.946145i	$0.604941\pi$
$180$	−52.5710	−3.91841
$181$	−16.9078	−1.25675	−0.628374	−	0.777912i	$-0.716279\pi$
$181$	−16.9078	−1.25675	−0.628374	+	0.777912i	$0.716279\pi$
$182$	0.658626	0.0488206
$183$	−30.4140	−2.24827
$184$	0.776942	0.0572769
$185$	4.18679	0.307819
$186$	−7.80639	−0.572392
$187$	−10.8849	−0.795980
$188$	−8.95034	−0.652771
$189$	−13.4594	−0.979029
$190$	37.4738	2.71863
$191$	0.249458	0.0180502	0.00902508	−	0.999959i	$-0.497127\pi$
$191$	0.249458	0.0180502	0.00902508	+	0.999959i	$0.497127\pi$
$192$	−30.4139	−2.19494
$193$	−3.13628	−0.225754	−0.112877	−	0.993609i	$-0.536007\pi$
$193$	−3.13628	−0.225754	−0.112877	+	0.993609i	$0.536007\pi$
$194$	11.4766	0.823970
$195$	−1.91091	−0.136843
$196$	−7.09229	−0.506592
$197$	−24.4710	−1.74348	−0.871742	−	0.489965i	$-0.837010\pi$
$197$	−24.4710	−1.74348	−0.871742	+	0.489965i	$0.837010\pi$
$198$	−34.1714	−2.42846
$199$	−1.83804	−0.130295	−0.0651476	−	0.997876i	$-0.520752\pi$
$199$	−1.83804	−0.130295	−0.0651476	+	0.997876i	$0.520752\pi$
$200$	−9.24475	−0.653702
$201$	9.98023	0.703951
$202$	9.08397	0.639146
$203$	15.9719	1.12101
$204$	−24.0936	−1.68689
$205$	0.462206	0.0322819
$206$	−21.6570	−1.50892
$207$	−5.61752	−0.390445
$208$	−0.500786	−0.0347233
$209$	13.1683	0.910872
$210$	−50.3572	−3.47498
$211$	19.6474	1.35258	0.676291	−	0.736635i	$-0.263586\pi$
$211$	19.6474	1.35258	0.676291	+	0.736635i	$0.263586\pi$
$212$	20.2385	1.38998
$213$	24.0614	1.64866
$214$	−0.894589	−0.0611529
$215$	−16.2209	−1.10626
$216$	−4.97386	−0.338428
$217$	−2.58749	−0.175650
$218$	2.08653	0.141318
$219$	37.8583	2.55822
$220$	−30.2502	−2.03947
$221$	−0.560560	−0.0377074
$222$	6.02388	0.404296
$223$	−28.5126	−1.90935	−0.954673	−	0.297655i	$-0.903795\pi$
$223$	−28.5126	−1.90935	−0.954673	+	0.297655i	$0.903795\pi$
$224$	−16.1434	−1.07863
$225$	66.8423	4.45615
$226$	0.0392805	0.00261290
$227$	−27.4752	−1.82359	−0.911796	−	0.410643i	$-0.865304\pi$
$227$	−27.4752	−1.82359	−0.911796	+	0.410643i	$0.865304\pi$
$228$	29.1480	1.93038
$229$	18.1710	1.20077	0.600387	−	0.799710i	$-0.295013\pi$
$229$	18.1710	1.20077	0.600387	+	0.799710i	$0.295013\pi$
$230$	−9.19865	−0.606541
$231$	−17.6956	−1.16428
$232$	5.90234	0.387508
$233$	−19.8201	−1.29846	−0.649230	−	0.760592i	$-0.724909\pi$
$233$	−19.8201	−1.29846	−0.649230	+	0.760592i	$0.724909\pi$
$234$	−1.75980	−0.115041
$235$	15.9215	1.03860
$236$	−27.2793	−1.77573
$237$	3.42180	0.222270
$238$	−14.7721	−0.957535
$239$	−8.85584	−0.572836	−0.286418	−	0.958105i	$-0.592465\pi$
$239$	−8.85584	−0.572836	−0.286418	+	0.958105i	$0.592465\pi$
$240$	38.2891	2.47155
$241$	7.69249	0.495517	0.247759	−	0.968822i	$-0.420306\pi$
$241$	7.69249	0.495517	0.247759	+	0.968822i	$0.420306\pi$
$242$	3.28913	0.211433
$243$	−10.2436	−0.657129
$244$	−24.7948	−1.58733
$245$	12.6162	0.806022
$246$	0.665014	0.0423998
$247$	0.678157	0.0431501
$248$	−0.956193	−0.0607183
$249$	1.37640	0.0872256
$250$	65.7743	4.15993
$251$	−31.4555	−1.98545	−0.992727	−	0.120383i	$-0.961588\pi$
$251$	−31.4555	−1.98545	−0.992727	+	0.120383i	$0.961588\pi$
$252$	−25.0709	−1.57932
$253$	−3.23241	−0.203220
$254$	15.6137	0.979692
$255$	42.8593	2.68395
$256$	8.94542	0.559089
$257$	0.406951	0.0253849	0.0126925	−	0.999919i	$-0.495960\pi$
$257$	0.406951	0.0253849	0.0126925	+	0.999919i	$0.495960\pi$
$258$	−23.3384	−1.45298
$259$	1.99666	0.124066
$260$	−1.55786	−0.0966143
$261$	−42.6757	−2.64156
$262$	2.91914	0.180345
$263$	0.648543	0.0399909	0.0199954	−	0.999800i	$-0.493635\pi$
$263$	0.648543	0.0399909	0.0199954	+	0.999800i	$0.493635\pi$
$264$	−6.53930	−0.402466
$265$	−36.0016	−2.21156
$266$	17.8711	1.09575
$267$	5.35487	0.327713
$268$	8.13631	0.497004
$269$	0.582066	0.0354892	0.0177446	−	0.999843i	$-0.494351\pi$
$269$	0.582066	0.0354892	0.0177446	+	0.999843i	$0.494351\pi$
$270$	58.8883	3.58383
$271$	18.5576	1.12729	0.563647	−	0.826016i	$-0.309398\pi$
$271$	18.5576	1.12729	0.563647	+	0.826016i	$0.309398\pi$
$272$	11.2320	0.681039
$273$	−0.911306	−0.0551547
$274$	46.4002	2.80314
$275$	38.4621	2.31935
$276$	−7.15493	−0.430676
$277$	−12.0589	−0.724549	−0.362274	−	0.932071i	$-0.618000\pi$
$277$	−12.0589	−0.724549	−0.362274	+	0.932071i	$0.618000\pi$
$278$	−12.8737	−0.772113
$279$	6.91356	0.413904
$280$	−6.16818	−0.368619
$281$	14.9185	0.889962	0.444981	−	0.895540i	$-0.353210\pi$
$281$	14.9185	0.889962	0.444981	+	0.895540i	$0.353210\pi$
$282$	22.9075	1.36412
$283$	2.97531	0.176864	0.0884318	−	0.996082i	$-0.471814\pi$
$283$	2.97531	0.176864	0.0884318	+	0.996082i	$0.471814\pi$
$284$	19.6159	1.16399
$285$	−51.8505	−3.07136
$286$	−1.01261	−0.0598771
$287$	0.220424	0.0130112
$288$	43.1339	2.54169
$289$	−4.42736	−0.260433
$290$	−69.8811	−4.10356
$291$	−15.8795	−0.930873
$292$	30.8637	1.80616
$293$	22.5892	1.31967	0.659837	−	0.751409i	$-0.270625\pi$
$293$	22.5892	1.31967	0.659837	+	0.751409i	$0.270625\pi$
$294$	18.1520	1.05865
$295$	48.5263	2.82531
$296$	0.737856	0.0428870
$297$	20.6934	1.20075
$298$	−37.4913	−2.17181
$299$	−0.166466	−0.00962699
$300$	85.1358	4.91531
$301$	−7.73568	−0.445877
$302$	17.6173	1.01376
$303$	−12.5690	−0.722070
$304$	−13.5883	−0.779340
$305$	44.1067	2.52554
$306$	39.4700	2.25635
$307$	1.08596	0.0619788	0.0309894	−	0.999520i	$-0.490134\pi$
$307$	1.08596	0.0619788	0.0309894	+	0.999520i	$0.490134\pi$
$308$	−14.4262	−0.822008
$309$	29.9657	1.70469
$310$	11.3209	0.642984
$311$	−26.2601	−1.48907	−0.744536	−	0.667582i	$-0.767329\pi$
$311$	−26.2601	−1.48907	−0.744536	+	0.667582i	$0.767329\pi$
$312$	−0.336768	−0.0190657
$313$	−29.8583	−1.68769	−0.843844	−	0.536588i	$-0.819713\pi$
$313$	−29.8583	−1.68769	−0.843844	+	0.536588i	$0.819713\pi$
$314$	39.1816	2.21114
$315$	44.5978	2.51280
$316$	2.78960	0.156927
$317$	−5.37419	−0.301844	−0.150922	−	0.988546i	$-0.548224\pi$
$317$	−5.37419	−0.301844	−0.150922	+	0.988546i	$0.548224\pi$
$318$	−51.7984	−2.90471
$319$	−24.5563	−1.37489
$320$	44.1065	2.46563
$321$	1.23780	0.0690870
$322$	−4.38679	−0.244466
$323$	−15.2102	−0.846317
$324$	8.13553	0.451974
$325$	1.98076	0.109873
$326$	−23.8606	−1.32152
$327$	−2.88703	−0.159653
$328$	0.0814566	0.00449769
$329$	7.59288	0.418609
$330$	77.4224	4.26196
$331$	5.39626	0.296605	0.148303	−	0.988942i	$-0.452619\pi$
$331$	5.39626	0.296605	0.148303	+	0.988942i	$0.452619\pi$
$332$	1.12210	0.0615831
$333$	−5.33492	−0.292352
$334$	25.4070	1.39021
$335$	−14.4734	−0.790767
$336$	18.2599	0.996158
$337$	−4.63676	−0.252581	−0.126290	−	0.991993i	$-0.540307\pi$
$337$	−4.63676	−0.252581	−0.126290	+	0.991993i	$0.540307\pi$
$338$	27.0728	1.47257
$339$	−0.0543504	−0.00295191
$340$	34.9407	1.89493
$341$	3.97817	0.215430
$342$	−47.7501	−2.58203
$343$	19.9933	1.07953
$344$	−2.85868	−0.154130
$345$	12.7277	0.685235
$346$	37.9557	2.04051
$347$	−26.9002	−1.44408	−0.722040	−	0.691851i	$-0.756796\pi$
$347$	−26.9002	−1.44408	−0.722040	+	0.691851i	$0.756796\pi$
$348$	−54.3552	−2.91375
$349$	−2.90982	−0.155759	−0.0778795	−	0.996963i	$-0.524815\pi$
$349$	−2.90982	−0.155759	−0.0778795	+	0.996963i	$0.524815\pi$
$350$	52.1980	2.79010
$351$	1.06569	0.0568824
$352$	24.8199	1.32291
$353$	−8.09966	−0.431101	−0.215551	−	0.976493i	$-0.569155\pi$
$353$	−8.09966	−0.431101	−0.215551	+	0.976493i	$0.569155\pi$
$354$	69.8188	3.71083
$355$	−34.8941	−1.85199
$356$	4.36552	0.231372
$357$	20.4394	1.08177
$358$	18.0751	0.955299
$359$	−27.8454	−1.46962	−0.734811	−	0.678272i	$-0.762729\pi$
$359$	−27.8454	−1.46962	−0.734811	+	0.678272i	$0.762729\pi$
$360$	16.4809	0.868618
$361$	−0.598986	−0.0315256
$362$	35.2787	1.85421
$363$	−4.55099	−0.238865
$364$	−0.742935	−0.0389404
$365$	−54.9024	−2.87372
$366$	63.4600	3.31710
$367$	12.4733	0.651099	0.325550	−	0.945525i	$-0.394451\pi$
$367$	12.4733	0.651099	0.325550	+	0.945525i	$0.394451\pi$
$368$	3.33550	0.173875
$369$	−0.588955	−0.0306598
$370$	−8.73588	−0.454157
$371$	−17.1690	−0.891369
$372$	8.80567	0.456553
$373$	8.61311	0.445970	0.222985	−	0.974822i	$-0.428420\pi$
$373$	8.61311	0.445970	0.222985	+	0.974822i	$0.428420\pi$
$374$	22.7116	1.17439
$375$	−91.0083	−4.69965
$376$	2.80591	0.144704
$377$	−1.26463	−0.0651316
$378$	28.0836	1.44446
$379$	4.81080	0.247114	0.123557	−	0.992337i	$-0.460570\pi$
$379$	4.81080	0.247114	0.123557	+	0.992337i	$0.460570\pi$
$380$	−42.2707	−2.16844
$381$	−21.6039	−1.10680
$382$	−0.520503	−0.0266313
$383$	8.51216	0.434951	0.217476	−	0.976066i	$-0.430218\pi$
$383$	8.51216	0.434951	0.217476	+	0.976066i	$0.430218\pi$
$384$	16.7753	0.856060
$385$	25.6623	1.30787
$386$	6.54396	0.333079
$387$	20.6691	1.05067
$388$	−12.9457	−0.657216
$389$	11.5429	0.585249	0.292624	−	0.956227i	$-0.405471\pi$
$389$	11.5429	0.585249	0.292624	+	0.956227i	$0.405471\pi$
$390$	3.98719	0.201899
$391$	3.73362	0.188817
$392$	2.22341	0.112299
$393$	−4.03906	−0.203743
$394$	51.0595	2.57234
$395$	−4.96232	−0.249681
$396$	38.5456	1.93699
$397$	8.01852	0.402438	0.201219	−	0.979546i	$-0.435510\pi$
$397$	8.01852	0.402438	0.201219	+	0.979546i	$0.435510\pi$
$398$	3.83513	0.192238
$399$	−24.7272	−1.23791
$400$	−39.6887	−1.98443
$401$	30.6008	1.52813	0.764065	−	0.645139i	$-0.223201\pi$
$401$	30.6008	1.52813	0.764065	+	0.645139i	$0.223201\pi$
$402$	−20.8241	−1.03861
$403$	0.204872	0.0102054
$404$	−10.2468	−0.509797
$405$	−14.4720	−0.719120
$406$	−33.3260	−1.65394
$407$	−3.06980	−0.152164
$408$	7.55328	0.373943
$409$	−13.2434	−0.654844	−0.327422	−	0.944878i	$-0.606180\pi$
$409$	−13.2434	−0.654844	−0.327422	+	0.944878i	$0.606180\pi$
$410$	−0.964410	−0.0476288
$411$	−64.2014	−3.16682
$412$	24.4293	1.20355
$413$	23.1420	1.13874
$414$	11.7212	0.576064
$415$	−1.99606	−0.0979829
$416$	1.27821	0.0626692
$417$	17.8126	0.872289
$418$	−27.4762	−1.34390
$419$	−17.2542	−0.842924	−0.421462	−	0.906846i	$-0.638483\pi$
$419$	−17.2542	−0.842924	−0.421462	+	0.906846i	$0.638483\pi$
$420$	56.8033	2.77172
$421$	−8.73585	−0.425759	−0.212880	−	0.977078i	$-0.568284\pi$
$421$	−8.73585	−0.425759	−0.212880	+	0.977078i	$0.568284\pi$
$422$	−40.9949	−1.99560
$423$	−20.2876	−0.986415
$424$	−6.34471	−0.308126
$425$	−44.4260	−2.15498
$426$	−50.2051	−2.43244
$427$	21.0343	1.01792
$428$	1.00910	0.0487769
$429$	1.40110	0.0676457
$430$	33.8455	1.63217
$431$	9.41660	0.453582	0.226791	−	0.973943i	$-0.427177\pi$
$431$	9.41660	0.453582	0.226791	+	0.973943i	$0.427177\pi$
$432$	−21.3533	−1.02736
$433$	−32.3039	−1.55242	−0.776212	−	0.630472i	$-0.782862\pi$
$433$	−32.3039	−1.55242	−0.776212	+	0.630472i	$0.782862\pi$
$434$	5.39888	0.259155
$435$	96.6907	4.63597
$436$	−2.35363	−0.112718
$437$	−4.51688	−0.216071
$438$	−78.9926	−3.77441
$439$	25.3124	1.20809	0.604047	−	0.796949i	$-0.293554\pi$
$439$	25.3124	1.20809	0.604047	+	0.796949i	$0.293554\pi$
$440$	9.48335	0.452101
$441$	−16.0759	−0.765521
$442$	1.16963	0.0556336
$443$	34.6939	1.64836	0.824178	−	0.566331i	$-0.191638\pi$
$443$	34.6939	1.64836	0.824178	+	0.566331i	$0.191638\pi$
$444$	−6.79498	−0.322476
$445$	−7.76569	−0.368129
$446$	59.4926	2.81706
$447$	51.8747	2.45359
$448$	21.0342	0.993773
$449$	20.4845	0.966722	0.483361	−	0.875421i	$-0.339416\pi$
$449$	20.4845	0.966722	0.483361	+	0.875421i	$0.339416\pi$
$450$	−139.469	−6.57462
$451$	−0.338894	−0.0159579
$452$	−0.0443088	−0.00208411
$453$	−24.3761	−1.14529
$454$	57.3279	2.69053
$455$	1.32158	0.0619568
$456$	−9.13783	−0.427918
$457$	−8.29217	−0.387891	−0.193946	−	0.981012i	$-0.562129\pi$
$457$	−8.29217	−0.387891	−0.193946	+	0.981012i	$0.562129\pi$
$458$	−37.9144	−1.77163
$459$	−23.9021	−1.11565
$460$	10.3761	0.483790
$461$	4.11590	0.191697	0.0958483	−	0.995396i	$-0.469444\pi$
$461$	4.11590	0.191697	0.0958483	+	0.995396i	$0.469444\pi$
$462$	36.9224	1.71779
$463$	−13.7422	−0.638656	−0.319328	−	0.947644i	$-0.603457\pi$
$463$	−13.7422	−0.638656	−0.319328	+	0.947644i	$0.603457\pi$
$464$	25.3394	1.17635
$465$	−15.6641	−0.726406
$466$	41.3554	1.91575
$467$	−23.1326	−1.07045	−0.535224	−	0.844710i	$-0.679773\pi$
$467$	−23.1326	−1.07045	−0.535224	+	0.844710i	$0.679773\pi$
$468$	1.98506	0.0917596
$469$	−6.90230	−0.318719
$470$	−33.2207	−1.53236
$471$	−54.2134	−2.49802
$472$	8.55199	0.393637
$473$	11.8933	0.546856
$474$	−7.13970	−0.327937
$475$	53.7458	2.46603
$476$	16.6631	0.763751
$477$	45.8741	2.10043
$478$	18.4780	0.845165
$479$	−28.2284	−1.28979	−0.644893	−	0.764272i	$-0.723098\pi$
$479$	−28.2284	−1.28979	−0.644893	+	0.764272i	$0.723098\pi$
$480$	−97.7290	−4.46070
$481$	−0.158092	−0.00720836
$482$	−16.0507	−0.731087
$483$	6.06977	0.276184
$484$	−3.71016	−0.168644
$485$	23.0286	1.04568
$486$	21.3737	0.969531
$487$	24.1370	1.09375	0.546876	−	0.837214i	$-0.315817\pi$
$487$	24.1370	1.09375	0.546876	+	0.837214i	$0.315817\pi$
$488$	7.77311	0.351872
$489$	33.0147	1.49298
$490$	−26.3242	−1.18921
$491$	30.4537	1.37436	0.687179	−	0.726488i	$-0.258849\pi$
$491$	30.4537	1.37436	0.687179	+	0.726488i	$0.258849\pi$
$492$	−0.750141	−0.0338190
$493$	28.3639	1.27745
$494$	−1.41500	−0.0636637
$495$	−68.5675	−3.08188
$496$	−4.10504	−0.184322
$497$	−16.6408	−0.746444
$498$	−2.87190	−0.128693
$499$	26.1562	1.17091	0.585457	−	0.810704i	$-0.300915\pi$
$499$	26.1562	1.17091	0.585457	+	0.810704i	$0.300915\pi$
$500$	−74.1939	−3.31805
$501$	−35.1543	−1.57058
$502$	65.6330	2.92935
$503$	28.7989	1.28408	0.642039	−	0.766672i	$-0.278089\pi$
$503$	28.7989	1.28408	0.642039	+	0.766672i	$0.278089\pi$
$504$	7.85965	0.350097
$505$	18.2277	0.811121
$506$	6.74454	0.299831
$507$	−37.4592	−1.66362
$508$	−17.6124	−0.781423
$509$	20.1854	0.894703	0.447351	−	0.894358i	$-0.352367\pi$
$509$	20.1854	0.894703	0.447351	+	0.894358i	$0.352367\pi$
$510$	−89.4274	−3.95991
$511$	−26.1827	−1.15825
$512$	−30.2861	−1.33847
$513$	28.9163	1.27669
$514$	−0.849117	−0.0374530
$515$	−43.4565	−1.91492
$516$	26.3258	1.15893
$517$	−11.6738	−0.513412
$518$	−4.16610	−0.183048
$519$	−52.5172	−2.30525
$520$	0.488384	0.0214171
$521$	−41.7702	−1.82998	−0.914992	−	0.403472i	$-0.867803\pi$
$521$	−41.7702	−1.82998	−0.914992	+	0.403472i	$0.867803\pi$
$522$	89.0444	3.89737
$523$	0.815699	0.0356680	0.0178340	−	0.999841i	$-0.494323\pi$
$523$	0.815699	0.0356680	0.0178340	+	0.999841i	$0.494323\pi$
$524$	−3.29281	−0.143847
$525$	−72.2235	−3.15209
$526$	−1.35321	−0.0590027
$527$	−4.59502	−0.200162
$528$	−28.0739	−1.22176
$529$	−21.8912	−0.951793
$530$	75.1185	3.26294
$531$	−61.8335	−2.68334
$532$	−20.1587	−0.873991
$533$	−0.0174527	−0.000755962 0
$534$	−11.1731	−0.483509
$535$	−1.79506	−0.0776073
$536$	−2.55071	−0.110174
$537$	−25.0095	−1.07924
$538$	−1.21450	−0.0523609
$539$	−9.25035	−0.398441
$540$	−66.4264	−2.85854
$541$	37.5645	1.61502	0.807511	−	0.589852i	$-0.200814\pi$
$541$	37.5645	1.61502	0.807511	+	0.589852i	$0.200814\pi$
$542$	−38.7211	−1.66321
$543$	−48.8133	−2.09478
$544$	−28.6685	−1.22915
$545$	4.18679	0.179342
$546$	1.90147	0.0813754
$547$	34.6399	1.48109	0.740547	−	0.672005i	$-0.234567\pi$
$547$	34.6399	1.48109	0.740547	+	0.672005i	$0.234567\pi$
$548$	−52.3398	−2.23584
$549$	−56.2019	−2.39864
$550$	−80.2525	−3.42198
$551$	−34.3142	−1.46183
$552$	2.24305	0.0954706
$553$	−2.36651	−0.100634
$554$	25.1613	1.06900
$555$	12.0874	0.513080
$556$	14.5216	0.615854
$557$	−26.0112	−1.10213	−0.551064	−	0.834463i	$-0.685778\pi$
$557$	−26.0112	−1.10213	−0.551064	+	0.834463i	$0.685778\pi$
$558$	−14.4254	−0.610675
$559$	0.612496	0.0259058
$560$	−26.4806	−1.11901
$561$	−31.4249	−1.32676
$562$	−31.1279	−1.31305
$563$	−0.0410395	−0.00172961	−0.000864805	−	1.00000i	$-0.500275\pi$
$563$	−0.0410395	−0.00172961	−0.000864805		1.00000i	$0.500275\pi$
$564$	−25.8399	−1.08805
$565$	0.0788194	0.00331596
$566$	−6.20808	−0.260945
$567$	−6.90164	−0.289842
$568$	−6.14954	−0.258029
$569$	−26.4683	−1.10961	−0.554804	−	0.831981i	$-0.687207\pi$
$569$	−26.4683	−1.10961	−0.554804	+	0.831981i	$0.687207\pi$
$570$	108.188	4.53149
$571$	14.5483	0.608828	0.304414	−	0.952540i	$-0.401539\pi$
$571$	14.5483	0.608828	0.304414	+	0.952540i	$0.401539\pi$
$572$	1.14224	0.0477593
$573$	0.720192	0.0300865
$574$	−0.459922	−0.0191968
$575$	−13.1929	−0.550183
$576$	−56.2017	−2.34174
$577$	−8.48698	−0.353318	−0.176659	−	0.984272i	$-0.556529\pi$
$577$	−8.48698	−0.353318	−0.176659	+	0.984272i	$0.556529\pi$
$578$	9.23783	0.384243
$579$	−9.05452	−0.376293
$580$	78.8265	3.27309
$581$	−0.951913	−0.0394920
$582$	33.1332	1.37341
$583$	26.3967	1.09324
$584$	−9.67568	−0.400383
$585$	−3.53116	−0.145996
$586$	−47.1331	−1.94705
$587$	20.2853	0.837264	0.418632	−	0.908156i	$-0.362510\pi$
$587$	20.2853	0.837264	0.418632	+	0.908156i	$0.362510\pi$
$588$	−20.4756	−0.844401
$589$	5.55898	0.229054
$590$	−101.252	−4.16847
$591$	−70.6483	−2.90608
$592$	3.16769	0.130191
$593$	−10.7798	−0.442675	−0.221337	−	0.975197i	$-0.571042\pi$
$593$	−10.7798	−0.442675	−0.221337	+	0.975197i	$0.571042\pi$
$594$	−43.1775	−1.77159
$595$	−29.6414	−1.21518
$596$	42.2905	1.73229
$597$	−5.30647	−0.217179
$598$	0.347338	0.0142037
$599$	35.7897	1.46233	0.731164	−	0.682202i	$-0.238978\pi$
$599$	35.7897	1.46233	0.731164	+	0.682202i	$0.238978\pi$
$600$	−26.6898	−1.08961
$601$	28.9614	1.18136	0.590681	−	0.806905i	$-0.298859\pi$
$601$	28.9614	1.18136	0.590681	+	0.806905i	$0.298859\pi$
$602$	16.1408	0.657848
$603$	18.4424	0.751033
$604$	−19.8724	−0.808597
$605$	6.59988	0.268323
$606$	26.2257	1.06534
$607$	19.0091	0.771556	0.385778	−	0.922592i	$-0.373933\pi$
$607$	19.0091	0.771556	0.385778	+	0.922592i	$0.373933\pi$
$608$	34.6827	1.40657
$609$	46.1114	1.86853
$610$	−92.0302	−3.72619
$611$	−0.601189	−0.0243215
$612$	−44.5224	−1.79971
$613$	−40.4964	−1.63564	−0.817818	−	0.575477i	$-0.804816\pi$
$613$	−40.4964	−1.63564	−0.817818	+	0.575477i	$0.804816\pi$
$614$	−2.26589	−0.0914437
$615$	1.33440	0.0538083
$616$	4.52257	0.182219
$617$	−2.83996	−0.114333	−0.0571663	−	0.998365i	$-0.518207\pi$
$617$	−2.83996	−0.114333	−0.0571663	+	0.998365i	$0.518207\pi$
$618$	−62.5244	−2.51510
$619$	0.302818	0.0121713	0.00608564	−	0.999981i	$-0.498063\pi$
$619$	0.302818	0.0121713	0.00608564	+	0.999981i	$0.498063\pi$
$620$	−12.7701	−0.512858
$621$	−7.09806	−0.284835
$622$	54.7926	2.19698
$623$	−3.70342	−0.148374
$624$	−1.44578	−0.0578776
$625$	69.3350	2.77340
$626$	62.3003	2.49002
$627$	38.0173	1.51826
$628$	−44.1971	−1.76366
$629$	3.54579	0.141380
$630$	−93.0548	−3.70739
$631$	23.5429	0.937227	0.468613	−	0.883403i	$-0.344754\pi$
$631$	23.5429	0.937227	0.468613	+	0.883403i	$0.344754\pi$
$632$	−0.874531	−0.0347870
$633$	56.7225	2.25452
$634$	11.2134	0.445342
$635$	31.3301	1.24330
$636$	58.4290	2.31686
$637$	−0.476385	−0.0188751
$638$	51.2375	2.02851
$639$	44.4630	1.75893
$640$	−24.3277	−0.961635
$641$	−4.73413	−0.186987	−0.0934935	−	0.995620i	$-0.529803\pi$
$641$	−4.73413	−0.186987	−0.0934935	+	0.995620i	$0.529803\pi$
$642$	−2.58270	−0.101931
$643$	9.65759	0.380858	0.190429	−	0.981701i	$-0.439012\pi$
$643$	9.65759	0.380858	0.190429	+	0.981701i	$0.439012\pi$
$644$	4.94834	0.194992
$645$	−46.8302	−1.84394
$646$	31.7366	1.24866
$647$	34.6508	1.36226	0.681132	−	0.732160i	$-0.261488\pi$
$647$	34.6508	1.36226	0.681132	+	0.732160i	$0.261488\pi$
$648$	−2.55047	−0.100192
$649$	−35.5799	−1.39664
$650$	−4.13293	−0.162107
$651$	−7.47014	−0.292778
$652$	26.9150	1.05407
$653$	−9.15488	−0.358258	−0.179129	−	0.983826i	$-0.557328\pi$
$653$	−9.15488	−0.358258	−0.179129	+	0.983826i	$0.557328\pi$
$654$	6.02388	0.235552
$655$	5.85748	0.228871
$656$	0.349702	0.0136536
$657$	69.9581	2.72932
$658$	−15.8428	−0.617617
$659$	9.19005	0.357994	0.178997	−	0.983850i	$-0.442715\pi$
$659$	9.19005	0.357994	0.178997	+	0.983850i	$0.442715\pi$
$660$	−87.3331	−3.39944
$661$	0.209045	0.00813091	0.00406546	−	0.999992i	$-0.498706\pi$
$661$	0.209045	0.00813091	0.00406546	+	0.999992i	$0.498706\pi$
$662$	−11.2595	−0.437612
$663$	−1.61835	−0.0628516
$664$	−0.351775	−0.0136515
$665$	35.8597	1.39058
$666$	11.1315	0.431336
$667$	8.42307	0.326143
$668$	−28.6593	−1.10886
$669$	−82.3167	−3.18255
$670$	30.1993	1.16670
$671$	−32.3395	−1.24845
$672$	−46.6065	−1.79788
$673$	−34.4177	−1.32671	−0.663353	−	0.748307i	$-0.730867\pi$
$673$	−34.4177	−1.32671	−0.663353	+	0.748307i	$0.730867\pi$
$674$	9.67477	0.372658
$675$	84.4590	3.25083
$676$	−30.5383	−1.17455
$677$	−7.74387	−0.297621	−0.148811	−	0.988866i	$-0.547544\pi$
$677$	−7.74387	−0.297621	−0.148811	+	0.988866i	$0.547544\pi$
$678$	0.113404	0.00435525
$679$	10.9822	0.421460
$680$	−10.9538	−0.420060
$681$	−79.3216	−3.03961
$682$	−8.30059	−0.317846
$683$	−1.52810	−0.0584710	−0.0292355	−	0.999573i	$-0.509307\pi$
$683$	−1.52810	−0.0584710	−0.0292355	+	0.999573i	$0.509307\pi$
$684$	53.8625	2.05948
$685$	93.1055	3.55738
$686$	−41.7166	−1.59275
$687$	52.4602	2.00148
$688$	−12.2726	−0.467889
$689$	1.35941	0.0517893
$690$	−26.5567	−1.01100
$691$	8.93879	0.340048	0.170024	−	0.985440i	$-0.445616\pi$
$691$	8.93879	0.340048	0.170024	+	0.985440i	$0.445616\pi$
$692$	−42.8143	−1.62756
$693$	−32.6995	−1.24215
$694$	56.1283	2.13060
$695$	−25.8320	−0.979865
$696$	17.0402	0.645908
$697$	0.391443	0.0148269
$698$	6.07144	0.229807
$699$	−57.2212	−2.16431
$700$	−58.8797	−2.22544
$701$	−49.3797	−1.86505	−0.932523	−	0.361110i	$-0.882398\pi$
$701$	−49.3797	−1.86505	−0.932523	+	0.361110i	$0.882398\pi$
$702$	−2.22360	−0.0839244
$703$	−4.28964	−0.161787
$704$	−32.3393	−1.21883
$705$	45.9657	1.73117
$706$	16.9002	0.636048
$707$	8.69269	0.326922
$708$	−78.7561	−2.95984
$709$	22.5113	0.845430	0.422715	−	0.906263i	$-0.361077\pi$
$709$	22.5113	0.845430	0.422715	+	0.906263i	$0.361077\pi$
$710$	72.8078	2.73243
$711$	6.32312	0.237135
$712$	−1.36858	−0.0512897
$713$	−1.36456	−0.0511030
$714$	−42.6475	−1.59604
$715$	−2.03189	−0.0759883
$716$	−20.3889	−0.761967
$717$	−25.5670	−0.954818
$718$	58.1003	2.16828
$719$	0.654194	0.0243973	0.0121987	−	0.999926i	$-0.496117\pi$
$719$	0.654194	0.0243973	0.0121987	+	0.999926i	$0.496117\pi$
$720$	70.7542	2.63685
$721$	−20.7242	−0.771810
$722$	1.24980	0.0465129
$723$	22.2084	0.825940
$724$	−39.7947	−1.47896
$725$	−100.225	−3.72227
$726$	9.49579	0.352422
$727$	−7.06728	−0.262111	−0.131055	−	0.991375i	$-0.541837\pi$
$727$	−7.06728	−0.262111	−0.131055	+	0.991375i	$0.541837\pi$
$728$	0.232908	0.00863215
$729$	−39.9434	−1.47939
$730$	114.556	4.23990
$731$	−13.7375	−0.508099
$732$	−71.5833	−2.64580
$733$	−45.6776	−1.68714	−0.843570	−	0.537019i	$-0.819550\pi$
$733$	−45.6776	−1.68714	−0.843570	+	0.537019i	$0.819550\pi$
$734$	−26.0259	−0.960634
$735$	36.4234	1.34350
$736$	−8.51351	−0.313812
$737$	10.6120	0.390900
$738$	1.22888	0.0452355
$739$	16.9935	0.625117	0.312559	−	0.949898i	$-0.398814\pi$
$739$	16.9935	0.625117	0.312559	+	0.949898i	$0.398814\pi$
$740$	9.85414	0.362245
$741$	1.95786	0.0719236
$742$	35.8237	1.31513
$743$	−26.2424	−0.962739	−0.481370	−	0.876518i	$-0.659861\pi$
$743$	−26.2424	−0.962739	−0.481370	+	0.876518i	$0.659861\pi$
$744$	−2.76055	−0.101207
$745$	−75.2292	−2.75618
$746$	−17.9716	−0.657986
$747$	2.54344	0.0930594
$748$	−25.6189	−0.936720
$749$	−0.856056	−0.0312796
$750$	189.892	6.93388
$751$	47.1976	1.72226	0.861132	−	0.508382i	$-0.169756\pi$
$751$	47.1976	1.72226	0.861132	+	0.508382i	$0.169756\pi$
$752$	12.0461	0.439275
$753$	−90.8129	−3.30941
$754$	2.63869	0.0960953
$755$	35.3504	1.28653
$756$	−31.6785	−1.15213
$757$	−37.8309	−1.37499	−0.687494	−	0.726190i	$-0.741289\pi$
$757$	−37.8309	−1.37499	−0.687494	+	0.726190i	$0.741289\pi$
$758$	−10.0379	−0.364593
$759$	−9.33206	−0.338732
$760$	13.2518	0.480692
$761$	27.9204	1.01211	0.506056	−	0.862500i	$-0.331103\pi$
$761$	27.9204	1.01211	0.506056	+	0.862500i	$0.331103\pi$
$762$	45.0772	1.63297
$763$	1.99666	0.0722840
$764$	0.587131	0.0212417
$765$	79.1994	2.86346
$766$	−17.7609	−0.641728
$767$	−1.83234	−0.0661618
$768$	25.8256	0.931903
$769$	27.4464	0.989743	0.494871	−	0.868966i	$-0.335215\pi$
$769$	27.4464	0.989743	0.494871	+	0.868966i	$0.335215\pi$
$770$	−53.5452	−1.92963
$771$	1.17488	0.0423122
$772$	−7.38164	−0.265671
$773$	14.6265	0.526079	0.263039	−	0.964785i	$-0.415275\pi$
$773$	14.6265	0.526079	0.263039	+	0.964785i	$0.415275\pi$
$774$	−43.1268	−1.55016
$775$	16.2367	0.583239
$776$	4.05843	0.145689
$777$	5.76441	0.206797
$778$	−24.0847	−0.863478
$779$	−0.473561	−0.0169671
$780$	−4.49758	−0.161039
$781$	25.5847	0.915493
$782$	−7.79034	−0.278582
$783$	−53.9232	−1.92706
$784$	9.54535	0.340906
$785$	78.6208	2.80610
$786$	8.42763	0.300604
$787$	2.66927	0.0951491	0.0475746	−	0.998868i	$-0.484851\pi$
$787$	2.66927	0.0951491	0.0475746	+	0.998868i	$0.484851\pi$
$788$	−57.5955	−2.05176
$789$	1.87236	0.0666578
$790$	10.3541	0.368381
$791$	0.0375886	0.00133650
$792$	−12.0839	−0.429384
$793$	−1.66545	−0.0591420
$794$	−16.7309	−0.593758
$795$	−103.937	−3.68628
$796$	−4.32606	−0.153333
$797$	−52.0129	−1.84239	−0.921195	−	0.389102i	$-0.872786\pi$
$797$	−52.0129	−1.84239	−0.921195	+	0.389102i	$0.872786\pi$
$798$	51.5943	1.82642
$799$	13.4839	0.477026
$800$	101.301	3.58154
$801$	9.89524	0.349631
$802$	−63.8496	−2.25461
$803$	40.2550	1.42057
$804$	23.4897	0.828419
$805$	−8.80243	−0.310245
$806$	−0.427473	−0.0150571
$807$	1.68044	0.0591543
$808$	3.21234	0.113010
$809$	0.926175	0.0325626	0.0162813	−	0.999867i	$-0.494817\pi$
$809$	0.926175	0.0325626	0.0162813	+	0.999867i	$0.494817\pi$
$810$	30.1964	1.06099
$811$	43.2951	1.52030	0.760149	−	0.649749i	$-0.225126\pi$
$811$	43.2951	1.52030	0.760149	+	0.649749i	$0.225126\pi$
$812$	37.5920	1.31922
$813$	53.5763	1.87900
$814$	6.40523	0.224503
$815$	−47.8782	−1.67710
$816$	32.4270	1.13517
$817$	16.6194	0.581439
$818$	27.6328	0.966159
$819$	−1.68400	−0.0588436
$820$	1.08786	0.0379898
$821$	−9.91403	−0.346002	−0.173001	−	0.984922i	$-0.555346\pi$
$821$	−9.91403	−0.346002	−0.173001	+	0.984922i	$0.555346\pi$
$822$	133.959	4.67234
$823$	−22.0778	−0.769582	−0.384791	−	0.923004i	$-0.625727\pi$
$823$	−22.0778	−0.769582	−0.384791	+	0.923004i	$0.625727\pi$
$824$	−7.65852	−0.266797
$825$	111.041	3.86595
$826$	−48.2865	−1.68010
$827$	26.1769	0.910258	0.455129	−	0.890425i	$-0.349593\pi$
$827$	26.1769	0.910258	0.455129	+	0.890425i	$0.349593\pi$
$828$	−13.2216	−0.459481
$829$	39.0943	1.35780	0.678900	−	0.734231i	$-0.262457\pi$
$829$	39.0943	1.35780	0.678900	+	0.734231i	$0.262457\pi$
$830$	4.16485	0.144564
$831$	−34.8143	−1.20770
$832$	−1.66545	−0.0577390
$833$	10.6847	0.370203
$834$	−37.1667	−1.28698
$835$	50.9811	1.76427
$836$	30.9933	1.07193
$837$	8.73567	0.301949
$838$	36.0015	1.24365
$839$	50.8751	1.75640	0.878201	−	0.478291i	$-0.158744\pi$
$839$	50.8751	1.75640	0.878201	+	0.478291i	$0.158744\pi$
$840$	−17.8077	−0.614424
$841$	34.9891	1.20652
$842$	18.2277	0.628166
$843$	43.0700	1.48341
$844$	46.2426	1.59174
$845$	54.3236	1.86879
$846$	42.3307	1.45536
$847$	3.14745	0.108148
$848$	−27.2385	−0.935374
$849$	8.58978	0.294801
$850$	92.6963	3.17946
$851$	1.05297	0.0360955
$852$	56.6317	1.94017
$853$	−8.56741	−0.293342	−0.146671	−	0.989185i	$-0.546856\pi$
$853$	−8.56741	−0.293342	−0.146671	+	0.989185i	$0.546856\pi$
$854$	−43.8888	−1.50184
$855$	−95.8142	−3.27678
$856$	−0.316351	−0.0108127
$857$	−32.8619	−1.12254	−0.561271	−	0.827632i	$-0.689688\pi$
$857$	−32.8619	−1.12254	−0.561271	+	0.827632i	$0.689688\pi$
$858$	−2.92344	−0.0998047
$859$	−33.7271	−1.15075	−0.575376	−	0.817889i	$-0.695144\pi$
$859$	−33.7271	−1.15075	−0.575376	+	0.817889i	$0.695144\pi$
$860$	−38.1780	−1.30186
$861$	0.636370	0.0216874
$862$	−19.6481	−0.669216
$863$	17.0282	0.579646	0.289823	−	0.957080i	$-0.406404\pi$
$863$	17.0282	0.579646	0.289823	+	0.957080i	$0.406404\pi$
$864$	54.5021	1.85420
$865$	76.1610	2.58955
$866$	67.4031	2.29045
$867$	−12.7819	−0.434096
$868$	−6.08998	−0.206707
$869$	3.63842	0.123425
$870$	−201.749	−6.83992
$871$	0.546511	0.0185178
$872$	0.737856	0.0249869
$873$	−29.3437	−0.993132
$874$	9.42462	0.318792
$875$	62.9412	2.12780
$876$	89.1043	3.01055
$877$	10.0570	0.339600	0.169800	−	0.985479i	$-0.445688\pi$
$877$	10.0570	0.339600	0.169800	+	0.985479i	$0.445688\pi$
$878$	−52.8151	−1.78242
$879$	65.2155	2.19966
$880$	40.7130	1.37244
$881$	57.3994	1.93384	0.966918	−	0.255088i	$-0.0821043\pi$
$881$	57.3994	1.93384	0.966918	+	0.255088i	$0.0821043\pi$
$882$	33.5430	1.12945
$883$	−33.7958	−1.13732	−0.568659	−	0.822573i	$-0.692538\pi$
$883$	−33.7958	−1.13732	−0.568659	+	0.822573i	$0.692538\pi$
$884$	−1.31935	−0.0443745
$885$	140.097	4.70930
$886$	−72.3900	−2.43199
$887$	−17.6359	−0.592157	−0.296078	−	0.955164i	$-0.595679\pi$
$887$	−17.6359	−0.592157	−0.296078	+	0.955164i	$0.595679\pi$
$888$	2.13021	0.0714851
$889$	14.9412	0.501111
$890$	16.2034	0.543138
$891$	10.6110	0.355483
$892$	−67.1081	−2.24695
$893$	−16.3126	−0.545880
$894$	−108.238	−3.62003
$895$	36.2691	1.21234
$896$	−11.6017	−0.387587
$897$	−0.480592	−0.0160465
$898$	−42.7415	−1.42630
$899$	−10.3664	−0.345738
$900$	157.322	5.24406
$901$	−30.4897	−1.01576
$902$	0.707114	0.0235443
$903$	−22.3331	−0.743199
$904$	0.0138907	0.000461997 0
$905$	70.7894	2.35312
$906$	50.8615	1.68976
$907$	−29.6536	−0.984633	−0.492317	−	0.870416i	$-0.663850\pi$
$907$	−29.6536	−0.984633	−0.492317	+	0.870416i	$0.663850\pi$
$908$	−64.6664	−2.14603
$909$	−23.2262	−0.770364
$910$	−2.75753	−0.0914112
$911$	−32.5549	−1.07859	−0.539296	−	0.842116i	$-0.681310\pi$
$911$	−32.5549	−1.07859	−0.539296	+	0.842116i	$0.681310\pi$
$912$	−39.2297	−1.29902
$913$	1.46353	0.0484359
$914$	17.3019	0.572296
$915$	127.337	4.20964
$916$	42.7678	1.41309
$917$	2.79340	0.0922463
$918$	49.8725	1.64604
$919$	45.9636	1.51620	0.758099	−	0.652140i	$-0.226128\pi$
$919$	45.9636	1.51620	0.758099	+	0.652140i	$0.226128\pi$
$920$	−3.25289	−0.107245
$921$	3.13519	0.103308
$922$	−8.58797	−0.282830
$923$	1.31759	0.0433690
$924$	−41.6488	−1.37014
$925$	−12.5292	−0.411958
$926$	28.6737	0.942275
$927$	55.3734	1.81870
$928$	−64.6762	−2.12310
$929$	−6.80955	−0.223414	−0.111707	−	0.993741i	$-0.535632\pi$
$929$	−6.80955	−0.223414	−0.111707	+	0.993741i	$0.535632\pi$
$930$	32.6837	1.07174
$931$	−12.9262	−0.423638
$932$	−46.6492	−1.52805
$933$	−75.8135	−2.48202
$934$	48.2669	1.57934
$935$	45.5726	1.49038
$936$	−0.622312	−0.0203409
$937$	−49.0367	−1.60196	−0.800980	−	0.598692i	$-0.795688\pi$
$937$	−49.0367	−1.60196	−0.800980	+	0.598692i	$0.795688\pi$
$938$	14.4019	0.470239
$939$	−86.2016	−2.81308
$940$	37.4732	1.22224
$941$	−39.2197	−1.27853	−0.639263	−	0.768988i	$-0.720760\pi$
$941$	−39.2197	−1.27853	−0.639263	+	0.768988i	$0.720760\pi$
$942$	113.118	3.68559
$943$	0.116244	0.00378544
$944$	36.7146	1.19496
$945$	56.3518	1.83312
$946$	−24.8158	−0.806833
$947$	20.6620	0.671424	0.335712	−	0.941965i	$-0.391023\pi$
$947$	20.6620	0.671424	0.335712	+	0.941965i	$0.391023\pi$
$948$	8.05364	0.261570
$949$	2.07310	0.0672955
$950$	−112.142	−3.63838
$951$	−15.5154	−0.503122
$952$	−5.22383	−0.169305
$953$	−32.9748	−1.06816	−0.534079	−	0.845434i	$-0.679342\pi$
$953$	−32.9748	−1.06816	−0.534079	+	0.845434i	$0.679342\pi$
$954$	−95.7180	−3.09898
$955$	−1.04443	−0.0337969
$956$	−20.8433	−0.674122
$957$	−70.8946	−2.29170
$958$	58.8995	1.90296
$959$	44.4016	1.43380
$960$	127.337	4.10977
$961$	−29.3206	−0.945827
$962$	0.329864	0.0106352
$963$	2.28731	0.0737077
$964$	18.1053	0.583131
$965$	13.1309	0.422700
$966$	−12.6648	−0.407483
$967$	−11.2566	−0.361986	−0.180993	−	0.983484i	$-0.557931\pi$
$967$	−11.2566	−0.361986	−0.180993	+	0.983484i	$0.557931\pi$
$968$	1.16312	0.0373842
$969$	−43.9122	−1.41066
$970$	−48.0500	−1.54279
$971$	−47.6527	−1.52925	−0.764623	−	0.644477i	$-0.777075\pi$
$971$	−47.6527	−1.52925	−0.764623	+	0.644477i	$0.777075\pi$
$972$	−24.1097	−0.773319
$973$	−12.3192	−0.394935
$974$	−50.3627	−1.61373
$975$	5.71852	0.183139
$976$	33.3708	1.06817
$977$	22.4780	0.719136	0.359568	−	0.933119i	$-0.382924\pi$
$977$	22.4780	0.719136	0.359568	+	0.933119i	$0.382924\pi$
$978$	−68.8863	−2.20274
$979$	5.69388	0.181977
$980$	29.6939	0.948538
$981$	−5.33492	−0.170331
$982$	−63.5428	−2.02773
$983$	50.6589	1.61577	0.807884	−	0.589342i	$-0.200613\pi$
$983$	50.6589	1.61577	0.807884	+	0.589342i	$0.200613\pi$
$984$	0.235167	0.00749686
$985$	102.455	3.26448
$986$	−59.1823	−1.88475
$987$	21.9208	0.697748
$988$	1.59613	0.0507796
$989$	−4.07954	−0.129722
$990$	143.068	4.54701
$991$	49.7518	1.58042	0.790209	−	0.612838i	$-0.209972\pi$
$991$	49.7518	1.58042	0.790209	+	0.612838i	$0.209972\pi$
$992$	10.4777	0.332667
$993$	15.5791	0.494389
$994$	34.7217	1.10131
$995$	7.69549	0.243963
$996$	3.23953	0.102648
$997$	5.18402	0.164180	0.0820898	−	0.996625i	$-0.473841\pi$
$997$	5.18402	0.164180	0.0820898	+	0.996625i	$0.473841\pi$
$998$	−54.5759	−1.72757
$999$	−6.74097	−0.213275

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.15	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.15	✓	79	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:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.08653 q^{2} +2.88703 q^{3} +2.35363 q^{4} -4.18679 q^{5} -6.02388 q^{6} -1.99666 q^{7} -0.737856 q^{8} +5.33492 q^{9} +O(q^{10})\)	\(q-2.08653 q^{2} +2.88703 q^{3} +2.35363 q^{4} -4.18679 q^{5} -6.02388 q^{6} -1.99666 q^{7} -0.737856 q^{8} +5.33492 q^{9} +8.73588 q^{10} +3.06980 q^{11} +6.79498 q^{12} +0.158092 q^{13} +4.16610 q^{14} -12.0874 q^{15} -3.16769 q^{16} -3.54579 q^{17} -11.1315 q^{18} +4.28964 q^{19} -9.85414 q^{20} -5.76441 q^{21} -6.40523 q^{22} -1.05297 q^{23} -2.13021 q^{24} +12.5292 q^{25} -0.329864 q^{26} +6.74097 q^{27} -4.69940 q^{28} -7.99932 q^{29} +25.2207 q^{30} +1.29591 q^{31} +8.08521 q^{32} +8.86258 q^{33} +7.39842 q^{34} +8.35960 q^{35} +12.5564 q^{36} -1.00000 q^{37} -8.95048 q^{38} +0.456415 q^{39} +3.08925 q^{40} -0.110396 q^{41} +12.0276 q^{42} +3.87431 q^{43} +7.22515 q^{44} -22.3362 q^{45} +2.19706 q^{46} -3.80279 q^{47} -9.14521 q^{48} -3.01335 q^{49} -26.1426 q^{50} -10.2368 q^{51} +0.372089 q^{52} +8.59885 q^{53} -14.0653 q^{54} -12.8526 q^{55} +1.47325 q^{56} +12.3843 q^{57} +16.6909 q^{58} -11.5903 q^{59} -28.4492 q^{60} -10.5347 q^{61} -2.70396 q^{62} -10.6520 q^{63} -10.5347 q^{64} -0.661897 q^{65} -18.4921 q^{66} +3.45692 q^{67} -8.34547 q^{68} -3.03996 q^{69} -17.4426 q^{70} +8.33434 q^{71} -3.93640 q^{72} +13.1132 q^{73} +2.08653 q^{74} +36.1721 q^{75} +10.0962 q^{76} -6.12934 q^{77} -0.952325 q^{78} +1.18523 q^{79} +13.2625 q^{80} +3.45659 q^{81} +0.230346 q^{82} +0.476753 q^{83} -13.5673 q^{84} +14.8455 q^{85} -8.08387 q^{86} -23.0942 q^{87} -2.26507 q^{88} +1.85481 q^{89} +46.6052 q^{90} -0.315655 q^{91} -2.47831 q^{92} +3.74132 q^{93} +7.93465 q^{94} -17.9598 q^{95} +23.3422 q^{96} -5.50030 q^{97} +6.28745 q^{98} +16.3771 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + q^99

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