LMFDB - Embedded newform 7381.2.a.u.1.34

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7381,2,Mod(1,7381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7381, 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("7381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7381 = 11^{2} \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7381.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:	$58.9375817319$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	no (minimal twist has level 671)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.34
Character	$\chi$	$=$	7381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.00503809 q^{2} -2.81406 q^{3} -1.99997 q^{4} -3.65915 q^{5} -0.0141775 q^{6} -1.90549 q^{7} -0.0201523 q^{8} +4.91895 q^{9} +O(q^{10})$	\(q+0.00503809 q^{2} -2.81406 q^{3} -1.99997 q^{4} -3.65915 q^{5} -0.0141775 q^{6} -1.90549 q^{7} -0.0201523 q^{8} +4.91895 q^{9} -0.0184351 q^{10} +5.62805 q^{12} +2.71183 q^{13} -0.00960005 q^{14} +10.2971 q^{15} +3.99985 q^{16} +7.54184 q^{17} +0.0247821 q^{18} -3.93803 q^{19} +7.31820 q^{20} +5.36217 q^{21} +7.91436 q^{23} +0.0567097 q^{24} +8.38937 q^{25} +0.0136625 q^{26} -5.40003 q^{27} +3.81093 q^{28} -3.46565 q^{29} +0.0518776 q^{30} -4.86975 q^{31} +0.0604561 q^{32} +0.0379965 q^{34} +6.97248 q^{35} -9.83777 q^{36} +10.3475 q^{37} -0.0198402 q^{38} -7.63127 q^{39} +0.0737401 q^{40} -2.47225 q^{41} +0.0270151 q^{42} +10.7064 q^{43} -17.9992 q^{45} +0.0398733 q^{46} +0.872623 q^{47} -11.2558 q^{48} -3.36910 q^{49} +0.0422664 q^{50} -21.2232 q^{51} -5.42360 q^{52} +4.57016 q^{53} -0.0272059 q^{54} +0.0383999 q^{56} +11.0819 q^{57} -0.0174603 q^{58} +6.72813 q^{59} -20.5939 q^{60} -1.00000 q^{61} -0.0245343 q^{62} -9.37301 q^{63} -7.99939 q^{64} -9.92300 q^{65} +5.63613 q^{67} -15.0835 q^{68} -22.2715 q^{69} +0.0351280 q^{70} -0.241391 q^{71} -0.0991278 q^{72} +4.26248 q^{73} +0.0521318 q^{74} -23.6082 q^{75} +7.87596 q^{76} -0.0384470 q^{78} +5.88494 q^{79} -14.6360 q^{80} +0.439193 q^{81} -0.0124554 q^{82} +9.32486 q^{83} -10.7242 q^{84} -27.5967 q^{85} +0.0539398 q^{86} +9.75256 q^{87} -10.9928 q^{89} -0.0906815 q^{90} -5.16737 q^{91} -15.8285 q^{92} +13.7038 q^{93} +0.00439636 q^{94} +14.4098 q^{95} -0.170127 q^{96} -0.111688 q^{97} -0.0169739 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 5 q^{2} + 19 q^{3} + 73 q^{4} + 21 q^{5} + q^{6} - 6 q^{7} - 3 q^{8} + 81 q^{9}+O(q^{10}) $ 64 * q - 5 * q^2 + 19 * q^3 + 73 * q^4 + 21 * q^5 + q^6 - 6 * q^7 - 3 * q^8 + 81 * q^9	\( 64 q - 5 q^{2} + 19 q^{3} + 73 q^{4} + 21 q^{5} + q^{6} - 6 q^{7} - 3 q^{8} + 81 q^{9} + 4 q^{10} + 41 q^{12} + q^{13} + 41 q^{14} + 28 q^{15} + 107 q^{16} - 13 q^{17} - 38 q^{18} + q^{19} + 65 q^{20} - q^{21} + 52 q^{23} - 3 q^{24} + 87 q^{25} + 37 q^{26} + 88 q^{27} + q^{28} - 19 q^{29} + 19 q^{30} + 45 q^{31} + 24 q^{32} - 23 q^{34} - 10 q^{35} + 146 q^{36} + 26 q^{37} - 4 q^{38} + 6 q^{39} - 84 q^{40} + 12 q^{41} + 28 q^{42} - 5 q^{43} + 71 q^{45} + 5 q^{46} + 63 q^{47} + 85 q^{48} + 78 q^{49} - 14 q^{50} - 22 q^{51} + 24 q^{52} + 86 q^{53} + 114 q^{54} + 119 q^{56} + 29 q^{57} + q^{58} + 119 q^{59} - 22 q^{60} - 64 q^{61} - 13 q^{62} + 28 q^{63} + 135 q^{64} + 30 q^{65} + 2 q^{67} - 59 q^{68} + 63 q^{69} - 2 q^{70} + 126 q^{71} - 48 q^{72} - 8 q^{73} + 27 q^{74} + 107 q^{75} + 82 q^{76} - 13 q^{78} + 5 q^{79} + 119 q^{80} + 96 q^{81} - 27 q^{82} - 14 q^{83} - 182 q^{84} + 52 q^{85} + 60 q^{86} + 8 q^{87} + 59 q^{89} + 45 q^{90} + 83 q^{91} + 111 q^{92} - 7 q^{93} - 21 q^{94} + 26 q^{95} + 86 q^{96} - 39 q^{97} + 57 q^{98}+O(q^{100}) \) 64 * q - 5 * q^2 + 19 * q^3 + 73 * q^4 + 21 * q^5 + q^6 - 6 * q^7 - 3 * q^8 + 81 * q^9 + 4 * q^10 + 41 * q^12 + q^13 + 41 * q^14 + 28 * q^15 + 107 * q^16 - 13 * q^17 - 38 * q^18 + q^19 + 65 * q^20 - q^21 + 52 * q^23 - 3 * q^24 + 87 * q^25 + 37 * q^26 + 88 * q^27 + q^28 - 19 * q^29 + 19 * q^30 + 45 * q^31 + 24 * q^32 - 23 * q^34 - 10 * q^35 + 146 * q^36 + 26 * q^37 - 4 * q^38 + 6 * q^39 - 84 * q^40 + 12 * q^41 + 28 * q^42 - 5 * q^43 + 71 * q^45 + 5 * q^46 + 63 * q^47 + 85 * q^48 + 78 * q^49 - 14 * q^50 - 22 * q^51 + 24 * q^52 + 86 * q^53 + 114 * q^54 + 119 * q^56 + 29 * q^57 + q^58 + 119 * q^59 - 22 * q^60 - 64 * q^61 - 13 * q^62 + 28 * q^63 + 135 * q^64 + 30 * q^65 + 2 * q^67 - 59 * q^68 + 63 * q^69 - 2 * q^70 + 126 * q^71 - 48 * q^72 - 8 * q^73 + 27 * q^74 + 107 * q^75 + 82 * q^76 - 13 * q^78 + 5 * q^79 + 119 * q^80 + 96 * q^81 - 27 * q^82 - 14 * q^83 - 182 * q^84 + 52 * q^85 + 60 * q^86 + 8 * q^87 + 59 * q^89 + 45 * q^90 + 83 * q^91 + 111 * q^92 - 7 * q^93 - 21 * q^94 + 26 * q^95 + 86 * q^96 - 39 * q^97 + 57 * q^98

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 $

$2$	0.00503809	0.00356247	0.00178124	−	0.999998i	$-0.499433\pi$
$2$	0.00503809	0.00356247	0.00178124	+	0.999998i	$0.499433\pi$
$3$	−2.81406	−1.62470	−0.812350	−	0.583170i	$-0.801812\pi$
$3$	−2.81406	−1.62470	−0.812350	+	0.583170i	$0.801812\pi$
$4$	−1.99997	−0.999987
$5$	−3.65915	−1.63642	−0.818211	−	0.574919i	$-0.805034\pi$
$5$	−3.65915	−1.63642	−0.818211	+	0.574919i	$0.805034\pi$
$6$	−0.0141775	−0.00578795
$7$	−1.90549	−0.720208	−0.360104	−	0.932912i	$-0.617259\pi$
$7$	−1.90549	−0.720208	−0.360104	+	0.932912i	$0.617259\pi$
$8$	−0.0201523	−0.00712490
$9$	4.91895	1.63965
$10$	−0.0184351	−0.00582970
$11$	0	0
$11$	0	0
$12$	5.62805	1.62468
$13$	2.71183	0.752127	0.376064	−	0.926594i	$-0.377277\pi$
$13$	2.71183	0.752127	0.376064	+	0.926594i	$0.377277\pi$
$14$	−0.00960005	−0.00256572
$15$	10.2971	2.65869
$16$	3.99985	0.999962
$17$	7.54184	1.82917	0.914583	−	0.404399i	$-0.132519\pi$
$17$	7.54184	1.82917	0.914583	+	0.404399i	$0.132519\pi$
$18$	0.0247821	0.00584120
$19$	−3.93803	−0.903446	−0.451723	−	0.892158i	$-0.649190\pi$
$19$	−3.93803	−0.903446	−0.451723	+	0.892158i	$0.649190\pi$
$20$	7.31820	1.63640
$21$	5.36217	1.17012
$22$	0	0
$23$	7.91436	1.65026	0.825129	−	0.564945i	$-0.191103\pi$
$23$	7.91436	1.65026	0.825129	+	0.564945i	$0.191103\pi$
$24$	0.0567097	0.0115758
$25$	8.38937	1.67787
$26$	0.0136625	0.00267943
$27$	−5.40003	−1.03924
$28$	3.81093	0.720199
$29$	−3.46565	−0.643556	−0.321778	−	0.946815i	$-0.604280\pi$
$29$	−3.46565	−0.643556	−0.321778	+	0.946815i	$0.604280\pi$
$30$	0.0518776	0.00947152
$31$	−4.86975	−0.874633	−0.437317	−	0.899308i	$-0.644071\pi$
$31$	−4.86975	−0.874633	−0.437317	+	0.899308i	$0.644071\pi$
$32$	0.0604561	0.0106872
$33$	0	0
$34$	0.0379965	0.00651635
$35$	6.97248	1.17856
$36$	−9.83777	−1.63963
$37$	10.3475	1.70112	0.850560	−	0.525877i	$-0.176263\pi$
$37$	10.3475	1.70112	0.850560	+	0.525877i	$0.176263\pi$
$38$	−0.0198402	−0.00321850
$39$	−7.63127	−1.22198
$40$	0.0737401	0.0116593
$41$	−2.47225	−0.386101	−0.193050	−	0.981189i	$-0.561838\pi$
$41$	−2.47225	−0.386101	−0.193050	+	0.981189i	$0.561838\pi$
$42$	0.0270151	0.00416852
$43$	10.7064	1.63271	0.816354	−	0.577552i	$-0.195992\pi$
$43$	10.7064	1.63271	0.816354	+	0.577552i	$0.195992\pi$
$44$	0	0
$45$	−17.9992	−2.68316
$46$	0.0398733	0.00587899
$47$	0.872623	0.127285	0.0636426	−	0.997973i	$-0.479728\pi$
$47$	0.872623	0.127285	0.0636426	+	0.997973i	$0.479728\pi$
$48$	−11.2558	−1.62464
$49$	−3.36910	−0.481300
$50$	0.0422664	0.00597738
$51$	−21.2232	−2.97184
$52$	−5.42360	−0.752118
$53$	4.57016	0.627760	0.313880	−	0.949463i	$-0.398371\pi$
$53$	4.57016	0.627760	0.313880	+	0.949463i	$0.398371\pi$
$54$	−0.0272059	−0.00370225
$55$	0	0
$56$	0.0383999	0.00513141
$57$	11.0819	1.46783
$58$	−0.0174603	−0.00229265
$59$	6.72813	0.875927	0.437964	−	0.898993i	$-0.355700\pi$
$59$	6.72813	0.875927	0.437964	+	0.898993i	$0.355700\pi$
$60$	−20.5939	−2.65866
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−0.0245343	−0.00311586
$63$	−9.37301	−1.18089
$64$	−7.99939	−0.999924
$65$	−9.92300	−1.23080
$66$	0	0
$67$	5.63613	0.688562	0.344281	−	0.938867i	$-0.388123\pi$
$67$	5.63613	0.688562	0.344281	+	0.938867i	$0.388123\pi$
$68$	−15.0835	−1.82914
$69$	−22.2715	−2.68117
$70$	0.0351280	0.00419860
$71$	−0.241391	−0.0286478	−0.0143239	−	0.999897i	$-0.504560\pi$
$71$	−0.241391	−0.0286478	−0.0143239	+	0.999897i	$0.504560\pi$
$72$	−0.0991278	−0.0116823
$73$	4.26248	0.498885	0.249443	−	0.968390i	$-0.419753\pi$
$73$	4.26248	0.498885	0.249443	+	0.968390i	$0.419753\pi$
$74$	0.0521318	0.00606019
$75$	−23.6082	−2.72604
$76$	7.87596	0.903434
$77$	0	0
$78$	−0.0384470	−0.00435327
$79$	5.88494	0.662107	0.331054	−	0.943612i	$-0.392596\pi$
$79$	5.88494	0.662107	0.331054	+	0.943612i	$0.392596\pi$
$80$	−14.6360	−1.63636
$81$	0.439193	0.0487992
$82$	−0.0124554	−0.00137547
$83$	9.32486	1.02354	0.511768	−	0.859124i	$-0.328991\pi$
$83$	9.32486	1.02354	0.511768	+	0.859124i	$0.328991\pi$
$84$	−10.7242	−1.17011
$85$	−27.5967	−2.99328
$86$	0.0539398	0.00581648
$87$	9.75256	1.04558
$88$	0	0
$89$	−10.9928	−1.16524	−0.582618	−	0.812746i	$-0.697972\pi$
$89$	−10.9928	−1.16524	−0.582618	+	0.812746i	$0.697972\pi$
$90$	−0.0906815	−0.00955866
$91$	−5.16737	−0.541688
$92$	−15.8285	−1.65024
$93$	13.7038	1.42102
$94$	0.00439636	0.000453450 0
$95$	14.4098	1.47842
$96$	−0.170127	−0.0173635
$97$	−0.111688	−0.0113402	−0.00567008	−	0.999984i	$-0.501805\pi$
$97$	−0.111688	−0.0113402	−0.00567008	+	0.999984i	$0.501805\pi$
$98$	−0.0169739	−0.00171462
$99$	0	0
$100$	−16.7785	−1.67785
$101$	−12.4551	−1.23932	−0.619662	−	0.784868i	$-0.712731\pi$
$101$	−12.4551	−1.23932	−0.619662	+	0.784868i	$0.712731\pi$
$102$	−0.106925	−0.0105871
$103$	−9.84987	−0.970537	−0.485268	−	0.874365i	$-0.661278\pi$
$103$	−9.84987	−0.970537	−0.485268	+	0.874365i	$0.661278\pi$
$104$	−0.0546495	−0.00535883
$105$	−19.6210	−1.91481
$106$	0.0230249	0.00223638
$107$	18.5957	1.79772	0.898858	−	0.438240i	$-0.144398\pi$
$107$	18.5957	1.79772	0.898858	+	0.438240i	$0.144398\pi$
$108$	10.7999	1.03922
$109$	14.1489	1.35521	0.677607	−	0.735424i	$-0.263017\pi$
$109$	14.1489	1.35521	0.677607	+	0.735424i	$0.263017\pi$
$110$	0	0
$111$	−29.1185	−2.76381
$112$	−7.62168	−0.720181
$113$	−0.849759	−0.0799386	−0.0399693	−	0.999201i	$-0.512726\pi$
$113$	−0.849759	−0.0799386	−0.0399693	+	0.999201i	$0.512726\pi$
$114$	0.0558314	0.00522909
$115$	−28.9598	−2.70052
$116$	6.93122	0.643548
$117$	13.3394	1.23322
$118$	0.0338969	0.00312047
$119$	−14.3709	−1.31738
$120$	−0.207509	−0.0189429
$121$	0	0
$122$	−0.00503809	−0.000456128 0
$123$	6.95707	0.627298
$124$	9.73938	0.874622
$125$	−12.4022	−1.10929
$126$	−0.0472221	−0.00420688
$127$	−3.35366	−0.297589	−0.148794	−	0.988868i	$-0.547539\pi$
$127$	−3.35366	−0.297589	−0.148794	+	0.988868i	$0.547539\pi$
$128$	−0.161214	−0.0142494
$129$	−30.1284	−2.65266
$130$	−0.0499930	−0.00438468
$131$	−4.77761	−0.417422	−0.208711	−	0.977977i	$-0.566927\pi$
$131$	−4.77761	−0.417422	−0.208711	+	0.977977i	$0.566927\pi$
$132$	0	0
$133$	7.50388	0.650669
$134$	0.0283953	0.00245298
$135$	19.7595	1.70063
$136$	−0.151985	−0.0130326
$137$	−9.27989	−0.792835	−0.396417	−	0.918070i	$-0.629747\pi$
$137$	−9.27989	−0.792835	−0.396417	+	0.918070i	$0.629747\pi$
$138$	−0.112206	−0.00955160
$139$	19.8170	1.68085	0.840427	−	0.541925i	$-0.182304\pi$
$139$	19.8170	1.68085	0.840427	+	0.541925i	$0.182304\pi$
$140$	−13.9448	−1.17855
$141$	−2.45562	−0.206800
$142$	−0.00121615	−0.000102057 0
$143$	0	0
$144$	19.6750	1.63959
$145$	12.6813	1.05313
$146$	0.0214748	0.00177726
$147$	9.48086	0.781968
$148$	−20.6948	−1.70110
$149$	−13.6434	−1.11771	−0.558857	−	0.829264i	$-0.688760\pi$
$149$	−13.6434	−1.11771	−0.558857	+	0.829264i	$0.688760\pi$
$150$	−0.118940	−0.00971144
$151$	10.7319	0.873351	0.436675	−	0.899619i	$-0.356156\pi$
$151$	10.7319	0.873351	0.436675	+	0.899619i	$0.356156\pi$
$152$	0.0793601	0.00643696
$153$	37.0979	2.99919
$154$	0	0
$155$	17.8191	1.43127
$156$	15.2623	1.22197
$157$	0.854547	0.0682003	0.0341001	−	0.999418i	$-0.489143\pi$
$157$	0.854547	0.0682003	0.0341001	+	0.999418i	$0.489143\pi$
$158$	0.0296489	0.00235874
$159$	−12.8607	−1.01992
$160$	−0.221218	−0.0174888
$161$	−15.0807	−1.18853
$162$	0.00221269	0.000173846 0
$163$	15.7920	1.23693	0.618463	−	0.785814i	$-0.287756\pi$
$163$	15.7920	1.23693	0.618463	+	0.785814i	$0.287756\pi$
$164$	4.94444	0.386096
$165$	0	0
$166$	0.0469795	0.00364632
$167$	−10.7391	−0.831017	−0.415509	−	0.909589i	$-0.636396\pi$
$167$	−10.7391	−0.831017	−0.415509	+	0.909589i	$0.636396\pi$
$168$	−0.108060	−0.00833700
$169$	−5.64596	−0.434305
$170$	−0.139035	−0.0106635
$171$	−19.3709	−1.48133
$172$	−21.4125	−1.63269
$173$	5.73563	0.436072	0.218036	−	0.975941i	$-0.430035\pi$
$173$	5.73563	0.436072	0.218036	+	0.975941i	$0.430035\pi$
$174$	0.0491343	0.00372487
$175$	−15.9859	−1.20842
$176$	0	0
$177$	−18.9334	−1.42312
$178$	−0.0553828	−0.00415112
$179$	22.5806	1.68775	0.843875	−	0.536540i	$-0.180269\pi$
$179$	22.5806	1.68775	0.843875	+	0.536540i	$0.180269\pi$
$180$	35.9979	2.68312
$181$	−1.00159	−0.0744474	−0.0372237	−	0.999307i	$-0.511851\pi$
$181$	−1.00159	−0.0744474	−0.0372237	+	0.999307i	$0.511851\pi$
$182$	−0.0260337	−0.00192975
$183$	2.81406	0.208021
$184$	−0.159492	−0.0117579
$185$	−37.8631	−2.78375
$186$	0.0690410	0.00506233
$187$	0	0
$188$	−1.74522	−0.127284
$189$	10.2897	0.748467
$190$	0.0725981	0.00526682
$191$	12.1301	0.877704	0.438852	−	0.898559i	$-0.355385\pi$
$191$	12.1301	0.877704	0.438852	+	0.898559i	$0.355385\pi$
$192$	22.5108	1.62458
$193$	1.11525	0.0802775	0.0401387	−	0.999194i	$-0.487220\pi$
$193$	1.11525	0.0802775	0.0401387	+	0.999194i	$0.487220\pi$
$194$	−0.000562693 0	−4.03990e−5 0
$195$	27.9239	1.99967
$196$	6.73812	0.481294
$197$	−4.36453	−0.310960	−0.155480	−	0.987839i	$-0.549692\pi$
$197$	−4.36453	−0.310960	−0.155480	+	0.987839i	$0.549692\pi$
$198$	0	0
$199$	−5.07935	−0.360066	−0.180033	−	0.983661i	$-0.557620\pi$
$199$	−5.07935	−0.360066	−0.180033	+	0.983661i	$0.557620\pi$
$200$	−0.169065	−0.0119547
$201$	−15.8604	−1.11871
$202$	−0.0627498	−0.00441506
$203$	6.60377	0.463494
$204$	42.4459	2.97181
$205$	9.04634	0.631824
$206$	−0.0496246	−0.00345751
$207$	38.9303	2.70584
$208$	10.8469	0.752099
$209$	0	0
$210$	−0.0988524	−0.00682146
$211$	−12.5525	−0.864151	−0.432075	−	0.901837i	$-0.642219\pi$
$211$	−12.5525	−0.864151	−0.432075	+	0.901837i	$0.642219\pi$
$212$	−9.14020	−0.627752
$213$	0.679289	0.0465441
$214$	0.0936870	0.00640431
$215$	−39.1763	−2.67180
$216$	0.108823	0.00740446
$217$	9.27927	0.629918
$218$	0.0712833	0.00482791
$219$	−11.9949	−0.810538
$220$	0	0
$221$	20.4522	1.37576
$222$	−0.146702	−0.00984599
$223$	−0.147299	−0.00986388	−0.00493194	−	0.999988i	$-0.501570\pi$
$223$	−0.147299	−0.00986388	−0.00493194	+	0.999988i	$0.501570\pi$
$224$	−0.115199	−0.00769703
$225$	41.2669	2.75112
$226$	−0.00428117	−0.000284779 0
$227$	8.24958	0.547544	0.273772	−	0.961795i	$-0.411729\pi$
$227$	8.24958	0.547544	0.273772	+	0.961795i	$0.411729\pi$
$228$	−22.1634	−1.46781
$229$	12.0123	0.793797	0.396899	−	0.917862i	$-0.370086\pi$
$229$	12.0123	0.793797	0.396899	+	0.917862i	$0.370086\pi$
$230$	−0.145902	−0.00962051
$231$	0	0
$232$	0.0698407	0.00458527
$233$	4.84881	0.317656	0.158828	−	0.987306i	$-0.449228\pi$
$233$	4.84881	0.317656	0.158828	+	0.987306i	$0.449228\pi$
$234$	0.0672050	0.00439333
$235$	−3.19306	−0.208292
$236$	−13.4561	−0.875916
$237$	−16.5606	−1.07573
$238$	−0.0724020	−0.00469313
$239$	21.7953	1.40982	0.704911	−	0.709295i	$-0.250987\pi$
$239$	21.7953	1.40982	0.704911	+	0.709295i	$0.250987\pi$
$240$	41.1867	2.65859
$241$	6.09801	0.392808	0.196404	−	0.980523i	$-0.437074\pi$
$241$	6.09801	0.392808	0.196404	+	0.980523i	$0.437074\pi$
$242$	0	0
$243$	14.9642	0.959953
$244$	1.99997	0.128035
$245$	12.3280	0.787610
$246$	0.0350504	0.00223473
$247$	−10.6793	−0.679506
$248$	0.0981365	0.00623167
$249$	−26.2407	−1.66294
$250$	−0.0624835	−0.00395180
$251$	−3.93423	−0.248326	−0.124163	−	0.992262i	$-0.539625\pi$
$251$	−3.93423	−0.248326	−0.124163	+	0.992262i	$0.539625\pi$
$252$	18.7458	1.18087
$253$	0	0
$254$	−0.0168960	−0.00106015
$255$	77.6589	4.86319
$256$	15.9980	0.999873
$257$	23.8495	1.48769	0.743846	−	0.668351i	$-0.233000\pi$
$257$	23.8495	1.48769	0.743846	+	0.668351i	$0.233000\pi$
$258$	−0.151790	−0.00945003
$259$	−19.7171	−1.22516
$260$	19.8457	1.23078
$261$	−17.0474	−1.05521
$262$	−0.0240700	−0.00148705
$263$	10.4846	0.646511	0.323255	−	0.946312i	$-0.395223\pi$
$263$	10.4846	0.646511	0.323255	+	0.946312i	$0.395223\pi$
$264$	0	0
$265$	−16.7229	−1.02728
$266$	0.0378053	0.00231799
$267$	30.9345	1.89316
$268$	−11.2721	−0.688554
$269$	2.74074	0.167106	0.0835530	−	0.996503i	$-0.473373\pi$
$269$	2.74074	0.167106	0.0835530	+	0.996503i	$0.473373\pi$
$270$	0.0995504	0.00605844
$271$	4.93312	0.299666	0.149833	−	0.988711i	$-0.452126\pi$
$271$	4.93312	0.299666	0.149833	+	0.988711i	$0.452126\pi$
$272$	30.1662	1.82910
$273$	14.5413	0.880080
$274$	−0.0467530	−0.00282445
$275$	0	0
$276$	44.5424	2.68114
$277$	−9.75927	−0.586378	−0.293189	−	0.956055i	$-0.594716\pi$
$277$	−9.75927	−0.586378	−0.293189	+	0.956055i	$0.594716\pi$
$278$	0.0998398	0.00598799
$279$	−23.9540	−1.43409
$280$	−0.140511	−0.00839714
$281$	−21.5105	−1.28321	−0.641603	−	0.767037i	$-0.721730\pi$
$281$	−21.5105	−1.28321	−0.641603	+	0.767037i	$0.721730\pi$
$282$	−0.0123716	−0.000736720 0
$283$	18.4042	1.09402	0.547009	−	0.837127i	$-0.315766\pi$
$283$	18.4042	1.09402	0.547009	+	0.837127i	$0.315766\pi$
$284$	0.482776	0.0286475
$285$	−40.5502	−2.40198
$286$	0	0
$287$	4.71086	0.278073
$288$	0.297380	0.0175233
$289$	39.8794	2.34584
$290$	0.0638898	0.00375174
$291$	0.314296	0.0184244
$292$	−8.52485	−0.498879
$293$	−27.1663	−1.58707	−0.793535	−	0.608524i	$-0.791762\pi$
$293$	−27.1663	−1.58707	−0.793535	+	0.608524i	$0.791762\pi$
$294$	0.0477655	0.00278574
$295$	−24.6192	−1.43339
$296$	−0.208526	−0.0121203
$297$	0	0
$298$	−0.0687369	−0.00398182
$299$	21.4624	1.24120
$300$	47.2158	2.72601
$301$	−20.4009	−1.17589
$302$	0.0540684	0.00311129
$303$	35.0493	2.01353
$304$	−15.7515	−0.903411
$305$	3.65915	0.209522
$306$	0.186903	0.0106845
$307$	22.0219	1.25686	0.628429	−	0.777867i	$-0.283698\pi$
$307$	22.0219	1.25686	0.628429	+	0.777867i	$0.283698\pi$
$308$	0	0
$309$	27.7182	1.57683
$310$	0.0897746	0.00509885
$311$	−5.41146	−0.306856	−0.153428	−	0.988160i	$-0.549031\pi$
$311$	−5.41146	−0.306856	−0.153428	+	0.988160i	$0.549031\pi$
$312$	0.153787	0.00870649
$313$	−30.6912	−1.73477	−0.867383	−	0.497640i	$-0.834200\pi$
$313$	−30.6912	−1.73477	−0.867383	+	0.497640i	$0.834200\pi$
$314$	0.00430529	0.000242962 0
$315$	34.2972	1.93243
$316$	−11.7697	−0.662099
$317$	−11.4260	−0.641748	−0.320874	−	0.947122i	$-0.603977\pi$
$317$	−11.4260	−0.641748	−0.320874	+	0.947122i	$0.603977\pi$
$318$	−0.0647935	−0.00363344
$319$	0	0
$320$	29.2710	1.63630
$321$	−52.3295	−2.92075
$322$	−0.0759782	−0.00423410
$323$	−29.7000	−1.65255
$324$	−0.878374	−0.0487986
$325$	22.7506	1.26197
$326$	0.0795616	0.00440651
$327$	−39.8158	−2.20182
$328$	0.0498214	0.00275093
$329$	−1.66278	−0.0916718
$330$	0	0
$331$	−25.7195	−1.41367	−0.706835	−	0.707378i	$-0.749878\pi$
$331$	−25.7195	−1.41367	−0.706835	+	0.707378i	$0.749878\pi$
$332$	−18.6495	−1.02352
$333$	50.8989	2.78924
$334$	−0.0541047	−0.00296047
$335$	−20.6234	−1.12678
$336$	21.4479	1.17008
$337$	20.6728	1.12612	0.563060	−	0.826416i	$-0.309624\pi$
$337$	20.6728	1.12612	0.563060	+	0.826416i	$0.309624\pi$
$338$	−0.0284449	−0.00154720
$339$	2.39128	0.129876
$340$	55.1927	2.99325
$341$	0	0
$342$	−0.0975927	−0.00527721
$343$	19.7582	1.06684
$344$	−0.215758	−0.0116329
$345$	81.4947	4.38753
$346$	0.0288966	0.00155349
$347$	−17.5472	−0.941985	−0.470992	−	0.882137i	$-0.656104\pi$
$347$	−17.5472	−0.941985	−0.470992	+	0.882137i	$0.656104\pi$
$348$	−19.5049	−1.04557
$349$	−29.8659	−1.59868	−0.799342	−	0.600876i	$-0.794818\pi$
$349$	−29.8659	−1.59868	−0.799342	+	0.600876i	$0.794818\pi$
$350$	−0.0805383	−0.00430496
$351$	−14.6440	−0.781638
$352$	0	0
$353$	−17.1563	−0.913136	−0.456568	−	0.889689i	$-0.650921\pi$
$353$	−17.1563	−0.913136	−0.456568	+	0.889689i	$0.650921\pi$
$354$	−0.0953881	−0.00506982
$355$	0.883286	0.0468799
$356$	21.9853	1.16522
$357$	40.4406	2.14035
$358$	0.113763	0.00601256
$359$	−19.8604	−1.04819	−0.524096	−	0.851659i	$-0.675597\pi$
$359$	−19.8604	−1.04819	−0.524096	+	0.851659i	$0.675597\pi$
$360$	0.362724	0.0191172
$361$	−3.49194	−0.183786
$362$	−0.00504609	−0.000265217 0
$363$	0	0
$364$	10.3346	0.541681
$365$	−15.5970	−0.816386
$366$	0.0141775	0.000741070 0
$367$	−5.35609	−0.279586	−0.139793	−	0.990181i	$-0.544644\pi$
$367$	−5.35609	−0.279586	−0.139793	+	0.990181i	$0.544644\pi$
$368$	31.6562	1.65019
$369$	−12.1609	−0.633070
$370$	−0.190758	−0.00991703
$371$	−8.70840	−0.452118
$372$	−27.4072	−1.42100
$373$	−2.08390	−0.107900	−0.0539500	−	0.998544i	$-0.517181\pi$
$373$	−2.08390	−0.107900	−0.0539500	+	0.998544i	$0.517181\pi$
$374$	0	0
$375$	34.9006	1.80226
$376$	−0.0175853	−0.000906894 0
$377$	−9.39827	−0.484036
$378$	0.0518406	0.00266639
$379$	27.9335	1.43485	0.717423	−	0.696637i	$-0.245321\pi$
$379$	27.9335	1.43485	0.717423	+	0.696637i	$0.245321\pi$
$380$	−28.8193	−1.47840
$381$	9.43739	0.483492
$382$	0.0611126	0.00312680
$383$	10.3093	0.526780	0.263390	−	0.964689i	$-0.415159\pi$
$383$	10.3093	0.526780	0.263390	+	0.964689i	$0.415159\pi$
$384$	0.453666	0.0231510
$385$	0	0
$386$	0.00561874	0.000285986 0
$387$	52.6641	2.67707
$388$	0.223373	0.0113400
$389$	33.1205	1.67928	0.839638	−	0.543146i	$-0.182767\pi$
$389$	33.1205	1.67928	0.839638	+	0.543146i	$0.182767\pi$
$390$	0.140683	0.00712378
$391$	59.6888	3.01859
$392$	0.0678950	0.00342921
$393$	13.4445	0.678185
$394$	−0.0219889	−0.00110778
$395$	−21.5339	−1.08349
$396$	0	0
$397$	30.3815	1.52480	0.762401	−	0.647105i	$-0.224021\pi$
$397$	30.3815	1.52480	0.762401	+	0.647105i	$0.224021\pi$
$398$	−0.0255903	−0.00128272
$399$	−21.1164	−1.05714
$400$	33.5562	1.67781
$401$	−19.0673	−0.952176	−0.476088	−	0.879398i	$-0.657946\pi$
$401$	−19.0673	−0.952176	−0.476088	+	0.879398i	$0.657946\pi$
$402$	−0.0799063	−0.00398536
$403$	−13.2060	−0.657835
$404$	24.9098	1.23931
$405$	−1.60707	−0.0798560
$406$	0.0332704	0.00165118
$407$	0	0
$408$	0.427695	0.0211741
$409$	−11.3850	−0.562953	−0.281476	−	0.959568i	$-0.590824\pi$
$409$	−11.3850	−0.562953	−0.281476	+	0.959568i	$0.590824\pi$
$410$	0.0455763	0.00225085
$411$	26.1142	1.28812
$412$	19.6995	0.970524
$413$	−12.8204	−0.630850
$414$	0.196134	0.00963948
$415$	−34.1210	−1.67494
$416$	0.163947	0.00803816
$417$	−55.7662	−2.73088
$418$	0	0
$419$	28.0403	1.36986	0.684929	−	0.728610i	$-0.259833\pi$
$419$	28.0403	1.36986	0.684929	+	0.728610i	$0.259833\pi$
$420$	39.2415	1.91479
$421$	−30.4168	−1.48242	−0.741211	−	0.671272i	$-0.765748\pi$
$421$	−30.4168	−1.48242	−0.741211	+	0.671272i	$0.765748\pi$
$422$	−0.0632408	−0.00307851
$423$	4.29239	0.208703
$424$	−0.0920990	−0.00447272
$425$	63.2713	3.06911
$426$	0.00342232	0.000165812 0
$427$	1.90549	0.0922132
$428$	−37.1910	−1.79769
$429$	0	0
$430$	−0.197374	−0.00951820
$431$	−17.3102	−0.833802	−0.416901	−	0.908952i	$-0.636884\pi$
$431$	−17.3102	−0.833802	−0.416901	+	0.908952i	$0.636884\pi$
$432$	−21.5993	−1.03920
$433$	−23.6278	−1.13548	−0.567739	−	0.823209i	$-0.692182\pi$
$433$	−23.6278	−1.13548	−0.567739	+	0.823209i	$0.692182\pi$
$434$	0.0467499	0.00224406
$435$	−35.6861	−1.71102
$436$	−28.2974	−1.35520
$437$	−31.1670	−1.49092
$438$	−0.0604313	−0.00288752
$439$	−15.7669	−0.752511	−0.376256	−	0.926516i	$-0.622789\pi$
$439$	−15.7669	−0.752511	−0.376256	+	0.926516i	$0.622789\pi$
$440$	0	0
$441$	−16.5724	−0.789163
$442$	0.103040	0.00490112
$443$	10.2740	0.488134	0.244067	−	0.969758i	$-0.421518\pi$
$443$	10.2740	0.488134	0.244067	+	0.969758i	$0.421518\pi$
$444$	58.2364	2.76378
$445$	40.2243	1.90682
$446$	−0.000742107 0	−3.51398e−5 0
$447$	38.3935	1.81595
$448$	15.2428	0.720153
$449$	−19.2879	−0.910252	−0.455126	−	0.890427i	$-0.650406\pi$
$449$	−19.2879	−0.910252	−0.455126	+	0.890427i	$0.650406\pi$
$450$	0.207906	0.00980080
$451$	0	0
$452$	1.69950	0.0799376
$453$	−30.2003	−1.41893
$454$	0.0415622	0.00195061
$455$	18.9082	0.886430
$456$	−0.223324	−0.0104581
$457$	−8.74866	−0.409245	−0.204623	−	0.978841i	$-0.565597\pi$
$457$	−8.74866	−0.409245	−0.204623	+	0.978841i	$0.565597\pi$
$458$	0.0605193	0.00282788
$459$	−40.7262	−1.90094
$460$	57.9189	2.70048
$461$	−2.97591	−0.138602	−0.0693009	−	0.997596i	$-0.522077\pi$
$461$	−2.97591	−0.138602	−0.0693009	+	0.997596i	$0.522077\pi$
$462$	0	0
$463$	−26.7760	−1.24439	−0.622194	−	0.782863i	$-0.713758\pi$
$463$	−26.7760	−1.24439	−0.622194	+	0.782863i	$0.713758\pi$
$464$	−13.8621	−0.643531
$465$	−50.1442	−2.32538
$466$	0.0244288	0.00113164
$467$	10.0843	0.466645	0.233323	−	0.972399i	$-0.425040\pi$
$467$	10.0843	0.466645	0.233323	+	0.972399i	$0.425040\pi$
$468$	−26.6784	−1.23321
$469$	−10.7396	−0.495908
$470$	−0.0160869	−0.000742035 0
$471$	−2.40475	−0.110805
$472$	−0.135587	−0.00624089
$473$	0	0
$474$	−0.0834338	−0.00383224
$475$	−33.0376	−1.51587
$476$	28.7415	1.31736
$477$	22.4804	1.02931
$478$	0.109807	0.00502245
$479$	22.8572	1.04437	0.522186	−	0.852831i	$-0.325117\pi$
$479$	22.8572	1.04437	0.522186	+	0.852831i	$0.325117\pi$
$480$	0.622521	0.0284141
$481$	28.0607	1.27946
$482$	0.0307224	0.00139937
$483$	42.4381	1.93100
$484$	0	0
$485$	0.408682	0.0185573
$486$	0.0753910	0.00341980
$487$	−38.6685	−1.75224	−0.876118	−	0.482097i	$-0.839875\pi$
$487$	−38.6685	−1.75224	−0.876118	+	0.482097i	$0.839875\pi$
$488$	0.0201523	0.000912250 0
$489$	−44.4397	−2.00963
$490$	0.0621099	0.00280584
$491$	38.6502	1.74426	0.872129	−	0.489275i	$-0.162739\pi$
$491$	38.6502	1.74426	0.872129	+	0.489275i	$0.162739\pi$
$492$	−13.9140	−0.627290
$493$	−26.1374	−1.17717
$494$	−0.0538032	−0.00242072
$495$	0	0
$496$	−19.4783	−0.874600
$497$	0.459968	0.0206324
$498$	−0.132203	−0.00592417
$499$	−13.5029	−0.604471	−0.302236	−	0.953233i	$-0.597733\pi$
$499$	−13.5029	−0.604471	−0.302236	+	0.953233i	$0.597733\pi$
$500$	24.8041	1.10927
$501$	30.2205	1.35015
$502$	−0.0198210	−0.000884655 0
$503$	15.4211	0.687595	0.343797	−	0.939044i	$-0.388287\pi$
$503$	15.4211	0.687595	0.343797	+	0.939044i	$0.388287\pi$
$504$	0.188887	0.00841371
$505$	45.5749	2.02806
$506$	0	0
$507$	15.8881	0.705615
$508$	6.70722	0.297585
$509$	−13.1890	−0.584593	−0.292297	−	0.956328i	$-0.594419\pi$
$509$	−13.1890	−0.584593	−0.292297	+	0.956328i	$0.594419\pi$
$510$	0.391253	0.0173250
$511$	−8.12211	−0.359301
$512$	0.403027	0.0178115
$513$	21.2655	0.938894
$514$	0.120156	0.00529986
$515$	36.0421	1.58821
$516$	60.2561	2.65263
$517$	0	0
$518$	−0.0993366	−0.00436460
$519$	−16.1404	−0.708486
$520$	0.199971	0.00876930
$521$	42.7287	1.87198	0.935990	−	0.352028i	$-0.114508\pi$
$521$	42.7287	1.87198	0.935990	+	0.352028i	$0.114508\pi$
$522$	−0.0858862	−0.00375914
$523$	21.0632	0.921027	0.460514	−	0.887653i	$-0.347665\pi$
$523$	21.0632	0.921027	0.460514	+	0.887653i	$0.347665\pi$
$524$	9.55510	0.417416
$525$	44.9852	1.96332
$526$	0.0528226	0.00230318
$527$	−36.7269	−1.59985
$528$	0	0
$529$	39.6370	1.72335
$530$	−0.0842515	−0.00365965
$531$	33.0953	1.43621
$532$	−15.0076	−0.650661
$533$	−6.70434	−0.290397
$534$	0.155851	0.00674432
$535$	−68.0445	−2.94182
$536$	−0.113581	−0.00490594
$537$	−63.5431	−2.74209
$538$	0.0138081	0.000595310 0
$539$	0	0
$540$	−39.5186	−1.70061
$541$	−12.9012	−0.554664	−0.277332	−	0.960774i	$-0.589450\pi$
$541$	−12.9012	−0.554664	−0.277332	+	0.960774i	$0.589450\pi$
$542$	0.0248535	0.00106755
$543$	2.81853	0.120955
$544$	0.455950	0.0195487
$545$	−51.7728	−2.21770
$546$	0.0732605	0.00313526
$547$	10.6793	0.456613	0.228306	−	0.973589i	$-0.426681\pi$
$547$	10.6793	0.456613	0.228306	+	0.973589i	$0.426681\pi$
$548$	18.5595	0.792824
$549$	−4.91895	−0.209936
$550$	0	0
$551$	13.6478	0.581418
$552$	0.448821	0.0191031
$553$	−11.2137	−0.476855
$554$	−0.0491681	−0.00208895
$555$	106.549	4.52276
$556$	−39.6334	−1.68083
$557$	6.35105	0.269103	0.134551	−	0.990907i	$-0.457041\pi$
$557$	6.35105	0.269103	0.134551	+	0.990907i	$0.457041\pi$
$558$	−0.120683	−0.00510891
$559$	29.0339	1.22800
$560$	27.8888	1.17852
$561$	0	0
$562$	−0.108372	−0.00457139
$563$	−14.8816	−0.627183	−0.313592	−	0.949558i	$-0.601532\pi$
$563$	−14.8816	−0.627183	−0.313592	+	0.949558i	$0.601532\pi$
$564$	4.91117	0.206798
$565$	3.10940	0.130813
$566$	0.0927223	0.00389741
$567$	−0.836878	−0.0351456
$568$	0.00486457	0.000204113 0
$569$	−9.93824	−0.416633	−0.208316	−	0.978062i	$-0.566798\pi$
$569$	−9.93824	−0.416633	−0.208316	+	0.978062i	$0.566798\pi$
$570$	−0.204296	−0.00855700
$571$	−31.1449	−1.30337	−0.651687	−	0.758488i	$-0.725938\pi$
$571$	−31.1449	−1.30337	−0.651687	+	0.758488i	$0.725938\pi$
$572$	0	0
$573$	−34.1349	−1.42601
$574$	0.0237337	0.000990627 0
$575$	66.3965	2.76892
$576$	−39.3486	−1.63952
$577$	2.74696	0.114357	0.0571787	−	0.998364i	$-0.481790\pi$
$577$	2.74696	0.114357	0.0571787	+	0.998364i	$0.481790\pi$
$578$	0.200916	0.00835700
$579$	−3.13838	−0.130427
$580$	−25.3624	−1.05311
$581$	−17.7684	−0.737159
$582$	0.00158345	6.56363e−5 0
$583$	0	0
$584$	−0.0858985	−0.00355451
$585$	−48.8107	−2.01807
$586$	−0.136866	−0.00565389
$587$	−26.5421	−1.09551	−0.547754	−	0.836639i	$-0.684517\pi$
$587$	−26.5421	−1.09551	−0.547754	+	0.836639i	$0.684517\pi$
$588$	−18.9615	−0.781958
$589$	19.1772	0.790184
$590$	−0.124034	−0.00510640
$591$	12.2820	0.505216
$592$	41.3885	1.70106
$593$	11.5587	0.474660	0.237330	−	0.971429i	$-0.423728\pi$
$593$	11.5587	0.474660	0.237330	+	0.971429i	$0.423728\pi$
$594$	0	0
$595$	52.5853	2.15579
$596$	27.2865	1.11770
$597$	14.2936	0.584999
$598$	0.108130	0.00442175
$599$	8.16786	0.333730	0.166865	−	0.985980i	$-0.446636\pi$
$599$	8.16786	0.333730	0.166865	+	0.985980i	$0.446636\pi$
$600$	0.475759	0.0194228
$601$	−18.0714	−0.737147	−0.368574	−	0.929599i	$-0.620154\pi$
$601$	−18.0714	−0.737147	−0.368574	+	0.929599i	$0.620154\pi$
$602$	−0.102782	−0.00418907
$603$	27.7238	1.12900
$604$	−21.4636	−0.873340
$605$	0	0
$606$	0.176582	0.00717315
$607$	−39.7774	−1.61451	−0.807257	−	0.590201i	$-0.799049\pi$
$607$	−39.7774	−1.61451	−0.807257	+	0.590201i	$0.799049\pi$
$608$	−0.238078	−0.00965533
$609$	−18.5834	−0.753039
$610$	0.0184351	0.000746417 0
$611$	2.36641	0.0957346
$612$	−74.1949	−2.99915
$613$	3.61113	0.145852	0.0729261	−	0.997337i	$-0.476766\pi$
$613$	3.61113	0.145852	0.0729261	+	0.997337i	$0.476766\pi$
$614$	0.110949	0.00447752
$615$	−25.4570	−1.02652
$616$	0	0
$617$	27.5412	1.10877	0.554383	−	0.832262i	$-0.312954\pi$
$617$	27.5412	1.10877	0.554383	+	0.832262i	$0.312954\pi$
$618$	0.139647	0.00561741
$619$	−13.5962	−0.546479	−0.273239	−	0.961946i	$-0.588095\pi$
$619$	−13.5962	−0.546479	−0.273239	+	0.961946i	$0.588095\pi$
$620$	−35.6378	−1.43125
$621$	−42.7378	−1.71501
$622$	−0.0272635	−0.00109317
$623$	20.9467	0.839212
$624$	−30.5239	−1.22193
$625$	3.43468	0.137387
$626$	−0.154625	−0.00618006
$627$	0	0
$628$	−1.70907	−0.0681994
$629$	78.0393	3.11163
$630$	0.172793	0.00688423
$631$	30.7520	1.22422	0.612110	−	0.790773i	$-0.290321\pi$
$631$	30.7520	1.22422	0.612110	+	0.790773i	$0.290321\pi$
$632$	−0.118595	−0.00471745
$633$	35.3236	1.40399
$634$	−0.0575653	−0.00228621
$635$	12.2715	0.486981
$636$	25.7211	1.01991
$637$	−9.13644	−0.361999
$638$	0	0
$639$	−1.18739	−0.0469724
$640$	0.589906	0.0233181
$641$	−12.8498	−0.507538	−0.253769	−	0.967265i	$-0.581670\pi$
$641$	−12.8498	−0.507538	−0.253769	+	0.967265i	$0.581670\pi$
$642$	−0.263641	−0.0104051
$643$	−31.5261	−1.24327	−0.621634	−	0.783308i	$-0.713531\pi$
$643$	−31.5261	−1.24327	−0.621634	+	0.783308i	$0.713531\pi$
$644$	30.1611	1.18851
$645$	110.244	4.34087
$646$	−0.149631	−0.00588716
$647$	17.4379	0.685556	0.342778	−	0.939416i	$-0.388632\pi$
$647$	17.4379	0.685556	0.342778	+	0.939416i	$0.388632\pi$
$648$	−0.00885072	−0.000347689 0
$649$	0	0
$650$	0.114620	0.00449575
$651$	−26.1124	−1.02343
$652$	−31.5836	−1.23691
$653$	−8.46512	−0.331266	−0.165633	−	0.986187i	$-0.552967\pi$
$653$	−8.46512	−0.331266	−0.165633	+	0.986187i	$0.552967\pi$
$654$	−0.200596	−0.00784391
$655$	17.4820	0.683078
$656$	−9.88863	−0.386086
$657$	20.9669	0.817996
$658$	−0.00837722	−0.000326578 0
$659$	22.3485	0.870574	0.435287	−	0.900292i	$-0.356647\pi$
$659$	22.3485	0.870574	0.435287	+	0.900292i	$0.356647\pi$
$660$	0	0
$661$	30.7153	1.19469	0.597344	−	0.801985i	$-0.296223\pi$
$661$	30.7153	1.19469	0.597344	+	0.801985i	$0.296223\pi$
$662$	−0.129577	−0.00503616
$663$	−57.5538	−2.23520
$664$	−0.187917	−0.00729259
$665$	−27.4578	−1.06477
$666$	0.256433	0.00993659
$667$	−27.4284	−1.06203
$668$	21.4779	0.831007
$669$	0.414509	0.0160258
$670$	−0.103903	−0.00401411
$671$	0	0
$672$	0.324176	0.0125054
$673$	20.7331	0.799202	0.399601	−	0.916689i	$-0.369149\pi$
$673$	20.7331	0.799202	0.399601	+	0.916689i	$0.369149\pi$
$674$	0.104152	0.00401177
$675$	−45.3029	−1.74371
$676$	11.2918	0.434299
$677$	29.8839	1.14853	0.574265	−	0.818669i	$-0.305288\pi$
$677$	29.8839	1.14853	0.574265	+	0.818669i	$0.305288\pi$
$678$	0.0120475	0.000462680 0
$679$	0.212820	0.00816728
$680$	0.556136	0.0213268
$681$	−23.2148	−0.889594
$682$	0	0
$683$	6.52987	0.249859	0.124929	−	0.992166i	$-0.460130\pi$
$683$	6.52987	0.249859	0.124929	+	0.992166i	$0.460130\pi$
$684$	38.7414	1.48131
$685$	33.9565	1.29741
$686$	0.0995439	0.00380060
$687$	−33.8035	−1.28968
$688$	42.8239	1.63265
$689$	12.3935	0.472155
$690$	0.410578	0.0156304
$691$	−14.8478	−0.564839	−0.282419	−	0.959291i	$-0.591137\pi$
$691$	−14.8478	−0.564839	−0.282419	+	0.959291i	$0.591137\pi$
$692$	−11.4711	−0.436066
$693$	0	0
$694$	−0.0884046	−0.00335579
$695$	−72.5132	−2.75058
$696$	−0.196536	−0.00744968
$697$	−18.6453	−0.706242
$698$	−0.150467	−0.00569526
$699$	−13.6448	−0.516096
$700$	31.9713	1.20840
$701$	36.2693	1.36987	0.684936	−	0.728603i	$-0.259830\pi$
$701$	36.2693	1.36987	0.684936	+	0.728603i	$0.259830\pi$
$702$	−0.0737778	−0.00278456
$703$	−40.7488	−1.53687
$704$	0	0
$705$	8.98546	0.338412
$706$	−0.0864349	−0.00325302
$707$	23.7330	0.892572
$708$	37.8663	1.42310
$709$	16.9372	0.636092	0.318046	−	0.948075i	$-0.396973\pi$
$709$	16.9372	0.636092	0.318046	+	0.948075i	$0.396973\pi$
$710$	0.00445008	0.000167008 0
$711$	28.9477	1.08562
$712$	0.221530	0.00830218
$713$	−38.5410	−1.44337
$714$	0.203744	0.00762492
$715$	0	0
$716$	−45.1605	−1.68773
$717$	−61.3334	−2.29054
$718$	−0.100059	−0.00373416
$719$	−16.6995	−0.622787	−0.311394	−	0.950281i	$-0.600796\pi$
$719$	−16.6995	−0.622787	−0.311394	+	0.950281i	$0.600796\pi$
$720$	−71.9939	−2.68305
$721$	18.7688	0.698988
$722$	−0.0175927	−0.000654733 0
$723$	−17.1602	−0.638194
$724$	2.00315	0.0744465
$725$	−29.0747	−1.07981
$726$	0	0
$727$	−10.6192	−0.393846	−0.196923	−	0.980419i	$-0.563095\pi$
$727$	−10.6192	−0.393846	−0.196923	+	0.980419i	$0.563095\pi$
$728$	0.104134	0.00385947
$729$	−43.4277	−1.60843
$730$	−0.0785793	−0.00290835
$731$	80.7458	2.98649
$732$	−5.62805	−0.208019
$733$	0.502228	0.0185502	0.00927510	−	0.999957i	$-0.497048\pi$
$733$	0.502228	0.0185502	0.00927510	+	0.999957i	$0.497048\pi$
$734$	−0.0269845	−0.000996016 0
$735$	−34.6919	−1.27963
$736$	0.478471	0.0176367
$737$	0	0
$738$	−0.0612676	−0.00225529
$739$	−40.8208	−1.50162	−0.750809	−	0.660519i	$-0.770336\pi$
$739$	−40.8208	−1.50162	−0.750809	+	0.660519i	$0.770336\pi$
$740$	75.7252	2.78371
$741$	30.0521	1.10399
$742$	−0.0438737	−0.00161066
$743$	−20.7273	−0.760410	−0.380205	−	0.924902i	$-0.624147\pi$
$743$	−20.7273	−0.760410	−0.380205	+	0.924902i	$0.624147\pi$
$744$	−0.276162	−0.0101246
$745$	49.9234	1.82905
$746$	−0.0104989	−0.000384391 0
$747$	45.8685	1.67824
$748$	0	0
$749$	−35.4340	−1.29473
$750$	0.175832	0.00642049
$751$	−6.39684	−0.233424	−0.116712	−	0.993166i	$-0.537235\pi$
$751$	−6.39684	−0.233424	−0.116712	+	0.993166i	$0.537235\pi$
$752$	3.49036	0.127280
$753$	11.0712	0.403456
$754$	−0.0473494	−0.00172436
$755$	−39.2697	−1.42917
$756$	−20.5792	−0.748457
$757$	−20.6561	−0.750759	−0.375380	−	0.926871i	$-0.622488\pi$
$757$	−20.6561	−0.750759	−0.375380	+	0.926871i	$0.622488\pi$
$758$	0.140732	0.00511160
$759$	0	0
$760$	−0.290390	−0.0105336
$761$	20.0400	0.726451	0.363226	−	0.931701i	$-0.381675\pi$
$761$	20.0400	0.726451	0.363226	+	0.931701i	$0.381675\pi$
$762$	0.0475465	0.00172243
$763$	−26.9605	−0.976037
$764$	−24.2599	−0.877693
$765$	−135.747	−4.90793
$766$	0.0519392	0.00187664
$767$	18.2456	0.658809
$768$	−45.0193	−1.62449
$769$	−9.49169	−0.342279	−0.171140	−	0.985247i	$-0.554745\pi$
$769$	−9.49169	−0.342279	−0.171140	+	0.985247i	$0.554745\pi$
$770$	0	0
$771$	−67.1140	−2.41705
$772$	−2.23047	−0.0802764
$773$	−10.1627	−0.365529	−0.182764	−	0.983157i	$-0.558505\pi$
$773$	−10.1627	−0.365529	−0.182764	+	0.983157i	$0.558505\pi$
$774$	0.265327	0.00953698
$775$	−40.8542	−1.46752
$776$	0.00225076	8.07975e−5 0
$777$	55.4851	1.99052
$778$	0.166864	0.00598237
$779$	9.73580	0.348821
$780$	−55.8472	−1.99965
$781$	0	0
$782$	0.300718	0.0107536
$783$	18.7146	0.668807
$784$	−13.4759	−0.481282
$785$	−3.12692	−0.111604
$786$	0.0677346	0.00241601
$787$	45.8049	1.63277	0.816384	−	0.577510i	$-0.195975\pi$
$787$	45.8049	1.63277	0.816384	+	0.577510i	$0.195975\pi$
$788$	8.72894	0.310956
$789$	−29.5044	−1.05039
$790$	−0.108490	−0.00385989
$791$	1.61921	0.0575724
$792$	0	0
$793$	−2.71183	−0.0963000
$794$	0.153065	0.00543206
$795$	47.0593	1.66902
$796$	10.1586	0.360061
$797$	52.5440	1.86120	0.930601	−	0.366035i	$-0.119285\pi$
$797$	52.5440	1.86120	0.930601	+	0.366035i	$0.119285\pi$
$798$	−0.106386	−0.00376604
$799$	6.58119	0.232826
$800$	0.507189	0.0179318
$801$	−54.0730	−1.91058
$802$	−0.0960629	−0.00339210
$803$	0	0
$804$	31.7204	1.11869
$805$	55.1827	1.94493
$806$	−0.0665329	−0.00234352
$807$	−7.71262	−0.271497
$808$	0.250998	0.00883006
$809$	24.2497	0.852575	0.426287	−	0.904588i	$-0.359821\pi$
$809$	24.2497	0.852575	0.426287	+	0.904588i	$0.359821\pi$
$810$	−0.00809658	−0.000284485 0
$811$	2.78876	0.0979266	0.0489633	−	0.998801i	$-0.484408\pi$
$811$	2.78876	0.0979266	0.0489633	+	0.998801i	$0.484408\pi$
$812$	−13.2074	−0.463488
$813$	−13.8821	−0.486866
$814$	0	0
$815$	−57.7853	−2.02413
$816$	−84.8896	−2.97173
$817$	−42.1620	−1.47506
$818$	−0.0573588	−0.00200550
$819$	−25.4180	−0.888178
$820$	−18.0924	−0.631816
$821$	−29.1297	−1.01663	−0.508317	−	0.861170i	$-0.669732\pi$
$821$	−29.1297	−1.01663	−0.508317	+	0.861170i	$0.669732\pi$
$822$	0.131566	0.00458888
$823$	30.7525	1.07197	0.535983	−	0.844229i	$-0.319941\pi$
$823$	30.7525	1.07197	0.535983	+	0.844229i	$0.319941\pi$
$824$	0.198497	0.00691497
$825$	0	0
$826$	−0.0645903	−0.00224739
$827$	−9.65684	−0.335801	−0.167901	−	0.985804i	$-0.553699\pi$
$827$	−9.65684	−0.335801	−0.167901	+	0.985804i	$0.553699\pi$
$828$	−77.8596	−2.70581
$829$	4.84797	0.168377	0.0841884	−	0.996450i	$-0.473170\pi$
$829$	4.84797	0.168377	0.0841884	+	0.996450i	$0.473170\pi$
$830$	−0.171905	−0.00596691
$831$	27.4632	0.952688
$832$	−21.6930	−0.752070
$833$	−25.4092	−0.880378
$834$	−0.280955	−0.00972869
$835$	39.2960	1.35989
$836$	0	0
$837$	26.2968	0.908951
$838$	0.141270	0.00488008
$839$	29.9786	1.03498	0.517489	−	0.855690i	$-0.326867\pi$
$839$	29.9786	1.03498	0.517489	+	0.855690i	$0.326867\pi$
$840$	0.395407	0.0136428
$841$	−16.9892	−0.585836
$842$	−0.153243	−0.00528109
$843$	60.5318	2.08482
$844$	25.1047	0.864140
$845$	20.6594	0.710705
$846$	0.0216255	0.000743498 0
$847$	0	0
$848$	18.2799	0.627736
$849$	−51.7907	−1.77745
$850$	0.318767	0.0109336
$851$	81.8939	2.80729
$852$	−1.35856	−0.0465435
$853$	−33.2917	−1.13989	−0.569944	−	0.821684i	$-0.693035\pi$
$853$	−33.2917	−1.13989	−0.569944	+	0.821684i	$0.693035\pi$
$854$	0.00960005	0.000328507 0
$855$	70.8812	2.42408
$856$	−0.374746	−0.0128085
$857$	50.8561	1.73721	0.868606	−	0.495503i	$-0.165016\pi$
$857$	50.8561	1.73721	0.868606	+	0.495503i	$0.165016\pi$
$858$	0	0
$859$	13.3141	0.454270	0.227135	−	0.973863i	$-0.427064\pi$
$859$	13.3141	0.454270	0.227135	+	0.973863i	$0.427064\pi$
$860$	78.3515	2.67176
$861$	−13.2566	−0.451785
$862$	−0.0872103	−0.00297039
$863$	−25.4727	−0.867101	−0.433550	−	0.901129i	$-0.642739\pi$
$863$	−25.4727	−0.867101	−0.433550	+	0.901129i	$0.642739\pi$
$864$	−0.326465	−0.0111066
$865$	−20.9875	−0.713597
$866$	−0.119039	−0.00404511
$867$	−112.223	−3.81129
$868$	−18.5583	−0.629910
$869$	0	0
$870$	−0.179790	−0.00609545
$871$	15.2842	0.517887
$872$	−0.285131	−0.00965577
$873$	−0.549386	−0.0185939
$874$	−0.157022	−0.00531135
$875$	23.6323	0.798918
$876$	23.9894	0.810528
$877$	−13.5225	−0.456623	−0.228311	−	0.973588i	$-0.573320\pi$
$877$	−13.5225	−0.456623	−0.228311	+	0.973588i	$0.573320\pi$
$878$	−0.0794350	−0.00268080
$879$	76.4476	2.57851
$880$	0	0
$881$	−25.9810	−0.875321	−0.437661	−	0.899140i	$-0.644193\pi$
$881$	−25.9810	−0.875321	−0.437661	+	0.899140i	$0.644193\pi$
$882$	−0.0834935	−0.00281137
$883$	11.5828	0.389791	0.194896	−	0.980824i	$-0.437563\pi$
$883$	11.5828	0.389791	0.194896	+	0.980824i	$0.437563\pi$
$884$	−40.9039	−1.37575
$885$	69.2800	2.32882
$886$	0.0517615	0.00173896
$887$	−23.9520	−0.804230	−0.402115	−	0.915589i	$-0.631725\pi$
$887$	−23.9520	−0.804230	−0.402115	+	0.915589i	$0.631725\pi$
$888$	0.586804	0.0196919
$889$	6.39036	0.214326
$890$	0.202654	0.00679298
$891$	0	0
$892$	0.294595	0.00986376
$893$	−3.43641	−0.114995
$894$	0.193430	0.00646927
$895$	−82.6256	−2.76187
$896$	0.307192	0.0102626
$897$	−60.3966	−2.01658
$898$	−0.0971742	−0.00324274
$899$	16.8769	0.562875
$900$	−82.5327	−2.75109
$901$	34.4674	1.14828
$902$	0	0
$903$	57.4095	1.91047
$904$	0.0171246	0.000569554 0
$905$	3.66496	0.121827
$906$	−0.152152	−0.00505491
$907$	9.27662	0.308025	0.154013	−	0.988069i	$-0.450780\pi$
$907$	9.27662	0.308025	0.154013	+	0.988069i	$0.450780\pi$
$908$	−16.4989	−0.547537
$909$	−61.2658	−2.03206
$910$	0.0952613	0.00315788
$911$	−22.4563	−0.744012	−0.372006	−	0.928230i	$-0.621330\pi$
$911$	−22.4563	−0.744012	−0.372006	+	0.928230i	$0.621330\pi$
$912$	44.3257	1.46777
$913$	0	0
$914$	−0.0440766	−0.00145792
$915$	−10.2971	−0.340411
$916$	−24.0244	−0.793787
$917$	9.10369	0.300630
$918$	−0.205182	−0.00677203
$919$	−14.7054	−0.485087	−0.242544	−	0.970140i	$-0.577982\pi$
$919$	−14.7054	−0.485087	−0.242544	+	0.970140i	$0.577982\pi$
$920$	0.583605	0.0192409
$921$	−61.9711	−2.04202
$922$	−0.0149929	−0.000493765 0
$923$	−0.654612	−0.0215468
$924$	0	0
$925$	86.8091	2.85427
$926$	−0.134900	−0.00443310
$927$	−48.4510	−1.59134
$928$	−0.209520	−0.00687783
$929$	−22.4216	−0.735627	−0.367814	−	0.929899i	$-0.619894\pi$
$929$	−22.4216	−0.735627	−0.367814	+	0.929899i	$0.619894\pi$
$930$	−0.252631	−0.00828410
$931$	13.2676	0.434829
$932$	−9.69749	−0.317652
$933$	15.2282	0.498549
$934$	0.0508056	0.00166241
$935$	0	0
$936$	−0.268818	−0.00878660
$937$	−39.2122	−1.28101	−0.640503	−	0.767956i	$-0.721274\pi$
$937$	−39.2122	−1.28101	−0.640503	+	0.767956i	$0.721274\pi$
$938$	−0.0541071	−0.00176666
$939$	86.3668	2.81847
$940$	6.38604	0.208290
$941$	47.5495	1.55007	0.775035	−	0.631918i	$-0.217732\pi$
$941$	47.5495	1.55007	0.775035	+	0.631918i	$0.217732\pi$
$942$	−0.0121154	−0.000394740 0
$943$	−19.5663	−0.637166
$944$	26.9115	0.875894
$945$	−37.6516	−1.22481
$946$	0	0
$947$	23.4541	0.762154	0.381077	−	0.924543i	$-0.375553\pi$
$947$	23.4541	0.762154	0.381077	+	0.924543i	$0.375553\pi$
$948$	33.1207	1.07571
$949$	11.5591	0.375225
$950$	−0.166446	−0.00540023
$951$	32.1535	1.04265
$952$	0.289606	0.00938619
$953$	4.30106	0.139325	0.0696624	−	0.997571i	$-0.477808\pi$
$953$	4.30106	0.139325	0.0696624	+	0.997571i	$0.477808\pi$
$954$	0.113258	0.00366687
$955$	−44.3859	−1.43629
$956$	−43.5901	−1.40980
$957$	0	0
$958$	0.115157	0.00372055
$959$	17.6828	0.571006
$960$	−82.3703	−2.65849
$961$	−7.28551	−0.235017
$962$	0.141373	0.00455804
$963$	91.4713	2.94762
$964$	−12.1959	−0.392803
$965$	−4.08087	−0.131368
$966$	0.213807	0.00687914
$967$	10.3561	0.333030	0.166515	−	0.986039i	$-0.446749\pi$
$967$	10.3561	0.333030	0.166515	+	0.986039i	$0.446749\pi$
$968$	0	0
$969$	83.5776	2.68490
$970$	0.00205898	6.61098e−5 0
$971$	−7.34631	−0.235754	−0.117877	−	0.993028i	$-0.537609\pi$
$971$	−7.34631	−0.235754	−0.117877	+	0.993028i	$0.537609\pi$
$972$	−29.9280	−0.959941
$973$	−37.7611	−1.21056
$974$	−0.194815	−0.00624229
$975$	−64.0215	−2.05033
$976$	−3.99985	−0.128032
$977$	36.8771	1.17980	0.589902	−	0.807475i	$-0.299166\pi$
$977$	36.8771	1.17980	0.589902	+	0.807475i	$0.299166\pi$
$978$	−0.223891	−0.00715925
$979$	0	0
$980$	−24.6558	−0.787600
$981$	69.5975	2.22208
$982$	0.194723	0.00621387
$983$	−6.34023	−0.202222	−0.101111	−	0.994875i	$-0.532240\pi$
$983$	−6.34023	−0.202222	−0.101111	+	0.994875i	$0.532240\pi$
$984$	−0.140201	−0.00446943
$985$	15.9705	0.508861
$986$	−0.131683	−0.00419363
$987$	4.67916	0.148939
$988$	21.3583	0.679497
$989$	84.7341	2.69439
$990$	0	0
$991$	30.4065	0.965894	0.482947	−	0.875650i	$-0.339566\pi$
$991$	30.4065	0.965894	0.482947	+	0.875650i	$0.339566\pi$
$992$	−0.294406	−0.00934741
$993$	72.3762	2.29679
$994$	0.00231736	7.35023e−5 0
$995$	18.5861	0.589219
$996$	52.4808	1.66292
$997$	22.5428	0.713938	0.356969	−	0.934116i	$-0.383810\pi$
$997$	22.5428	0.713938	0.356969	+	0.934116i	$0.383810\pi$
$998$	−0.0680287	−0.00215341
$999$	−55.8769	−1.76787

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7381.2.a.u.1.34		64
11.2	odd	10		671.2.j.c.367.18	yes	128
11.6	odd	10		671.2.j.c.245.18	✓	128
11.10	odd	2		7381.2.a.v.1.31		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.j.c.245.18	✓	128	11.6	odd	10
671.2.j.c.367.18	yes	128	11.2	odd	10
7381.2.a.u.1.34		64	1.1	even	1	trivial
7381.2.a.v.1.31		64	11.10	odd	2

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:	\( N \)	\(=\)	\( 7381 = 11^{2} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7381.a (trivial)

\(f(q)\)	\(=\)	\(q+0.00503809 q^{2} -2.81406 q^{3} -1.99997 q^{4} -3.65915 q^{5} -0.0141775 q^{6} -1.90549 q^{7} -0.0201523 q^{8} +4.91895 q^{9} +O(q^{10})\)	\(q+0.00503809 q^{2} -2.81406 q^{3} -1.99997 q^{4} -3.65915 q^{5} -0.0141775 q^{6} -1.90549 q^{7} -0.0201523 q^{8} +4.91895 q^{9} -0.0184351 q^{10} +5.62805 q^{12} +2.71183 q^{13} -0.00960005 q^{14} +10.2971 q^{15} +3.99985 q^{16} +7.54184 q^{17} +0.0247821 q^{18} -3.93803 q^{19} +7.31820 q^{20} +5.36217 q^{21} +7.91436 q^{23} +0.0567097 q^{24} +8.38937 q^{25} +0.0136625 q^{26} -5.40003 q^{27} +3.81093 q^{28} -3.46565 q^{29} +0.0518776 q^{30} -4.86975 q^{31} +0.0604561 q^{32} +0.0379965 q^{34} +6.97248 q^{35} -9.83777 q^{36} +10.3475 q^{37} -0.0198402 q^{38} -7.63127 q^{39} +0.0737401 q^{40} -2.47225 q^{41} +0.0270151 q^{42} +10.7064 q^{43} -17.9992 q^{45} +0.0398733 q^{46} +0.872623 q^{47} -11.2558 q^{48} -3.36910 q^{49} +0.0422664 q^{50} -21.2232 q^{51} -5.42360 q^{52} +4.57016 q^{53} -0.0272059 q^{54} +0.0383999 q^{56} +11.0819 q^{57} -0.0174603 q^{58} +6.72813 q^{59} -20.5939 q^{60} -1.00000 q^{61} -0.0245343 q^{62} -9.37301 q^{63} -7.99939 q^{64} -9.92300 q^{65} +5.63613 q^{67} -15.0835 q^{68} -22.2715 q^{69} +0.0351280 q^{70} -0.241391 q^{71} -0.0991278 q^{72} +4.26248 q^{73} +0.0521318 q^{74} -23.6082 q^{75} +7.87596 q^{76} -0.0384470 q^{78} +5.88494 q^{79} -14.6360 q^{80} +0.439193 q^{81} -0.0124554 q^{82} +9.32486 q^{83} -10.7242 q^{84} -27.5967 q^{85} +0.0539398 q^{86} +9.75256 q^{87} -10.9928 q^{89} -0.0906815 q^{90} -5.16737 q^{91} -15.8285 q^{92} +13.7038 q^{93} +0.00439636 q^{94} +14.4098 q^{95} -0.170127 q^{96} -0.111688 q^{97} -0.0169739 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 5 q^{2} + 19 q^{3} + 73 q^{4} + 21 q^{5} + q^{6} - 6 q^{7} - 3 q^{8} + 81 q^{9}+O(q^{10}) \) 64 * q - 5 * q^2 + 19 * q^3 + 73 * q^4 + 21 * q^5 + q^6 - 6 * q^7 - 3 * q^8 + 81 * q^9	\( 64 q - 5 q^{2} + 19 q^{3} + 73 q^{4} + 21 q^{5} + q^{6} - 6 q^{7} - 3 q^{8} + 81 q^{9} + 4 q^{10} + 41 q^{12} + q^{13} + 41 q^{14} + 28 q^{15} + 107 q^{16} - 13 q^{17} - 38 q^{18} + q^{19} + 65 q^{20} - q^{21} + 52 q^{23} - 3 q^{24} + 87 q^{25} + 37 q^{26} + 88 q^{27} + q^{28} - 19 q^{29} + 19 q^{30} + 45 q^{31} + 24 q^{32} - 23 q^{34} - 10 q^{35} + 146 q^{36} + 26 q^{37} - 4 q^{38} + 6 q^{39} - 84 q^{40} + 12 q^{41} + 28 q^{42} - 5 q^{43} + 71 q^{45} + 5 q^{46} + 63 q^{47} + 85 q^{48} + 78 q^{49} - 14 q^{50} - 22 q^{51} + 24 q^{52} + 86 q^{53} + 114 q^{54} + 119 q^{56} + 29 q^{57} + q^{58} + 119 q^{59} - 22 q^{60} - 64 q^{61} - 13 q^{62} + 28 q^{63} + 135 q^{64} + 30 q^{65} + 2 q^{67} - 59 q^{68} + 63 q^{69} - 2 q^{70} + 126 q^{71} - 48 q^{72} - 8 q^{73} + 27 q^{74} + 107 q^{75} + 82 q^{76} - 13 q^{78} + 5 q^{79} + 119 q^{80} + 96 q^{81} - 27 q^{82} - 14 q^{83} - 182 q^{84} + 52 q^{85} + 60 q^{86} + 8 q^{87} + 59 q^{89} + 45 q^{90} + 83 q^{91} + 111 q^{92} - 7 q^{93} - 21 q^{94} + 26 q^{95} + 86 q^{96} - 39 q^{97} + 57 q^{98}+O(q^{100}) \) 64 * q - 5 * q^2 + 19 * q^3 + 73 * q^4 + 21 * q^5 + q^6 - 6 * q^7 - 3 * q^8 + 81 * q^9 + 4 * q^10 + 41 * q^12 + q^13 + 41 * q^14 + 28 * q^15 + 107 * q^16 - 13 * q^17 - 38 * q^18 + q^19 + 65 * q^20 - q^21 + 52 * q^23 - 3 * q^24 + 87 * q^25 + 37 * q^26 + 88 * q^27 + q^28 - 19 * q^29 + 19 * q^30 + 45 * q^31 + 24 * q^32 - 23 * q^34 - 10 * q^35 + 146 * q^36 + 26 * q^37 - 4 * q^38 + 6 * q^39 - 84 * q^40 + 12 * q^41 + 28 * q^42 - 5 * q^43 + 71 * q^45 + 5 * q^46 + 63 * q^47 + 85 * q^48 + 78 * q^49 - 14 * q^50 - 22 * q^51 + 24 * q^52 + 86 * q^53 + 114 * q^54 + 119 * q^56 + 29 * q^57 + q^58 + 119 * q^59 - 22 * q^60 - 64 * q^61 - 13 * q^62 + 28 * q^63 + 135 * q^64 + 30 * q^65 + 2 * q^67 - 59 * q^68 + 63 * q^69 - 2 * q^70 + 126 * q^71 - 48 * q^72 - 8 * q^73 + 27 * q^74 + 107 * q^75 + 82 * q^76 - 13 * q^78 + 5 * q^79 + 119 * q^80 + 96 * q^81 - 27 * q^82 - 14 * q^83 - 182 * q^84 + 52 * q^85 + 60 * q^86 + 8 * q^87 + 59 * q^89 + 45 * q^90 + 83 * q^91 + 111 * q^92 - 7 * q^93 - 21 * q^94 + 26 * q^95 + 86 * q^96 - 39 * q^97 + 57 * q^98

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