LMFDB - Embedded newform 4033.2.a.e.1.1

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:	$0$
Dimension:	$82$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$	$=$	$q-2.75814 q^{2} +1.25704 q^{3} +5.60732 q^{4} +1.25507 q^{5} -3.46708 q^{6} +2.38515 q^{7} -9.94947 q^{8} -1.41986 q^{9} +O(q^{10})$	\(q-2.75814 q^{2} +1.25704 q^{3} +5.60732 q^{4} +1.25507 q^{5} -3.46708 q^{6} +2.38515 q^{7} -9.94947 q^{8} -1.41986 q^{9} -3.46166 q^{10} -4.34393 q^{11} +7.04861 q^{12} -4.19052 q^{13} -6.57856 q^{14} +1.57767 q^{15} +16.2274 q^{16} +6.23808 q^{17} +3.91616 q^{18} -8.62095 q^{19} +7.03759 q^{20} +2.99822 q^{21} +11.9812 q^{22} +1.33700 q^{23} -12.5069 q^{24} -3.42479 q^{25} +11.5580 q^{26} -5.55593 q^{27} +13.3743 q^{28} +8.63999 q^{29} -4.35144 q^{30} +2.64779 q^{31} -24.8583 q^{32} -5.46049 q^{33} -17.2055 q^{34} +2.99353 q^{35} -7.96159 q^{36} -1.00000 q^{37} +23.7778 q^{38} -5.26764 q^{39} -12.4873 q^{40} +5.54332 q^{41} -8.26950 q^{42} +0.869458 q^{43} -24.3578 q^{44} -1.78202 q^{45} -3.68764 q^{46} +4.50020 q^{47} +20.3984 q^{48} -1.31107 q^{49} +9.44604 q^{50} +7.84150 q^{51} -23.4976 q^{52} -9.77876 q^{53} +15.3240 q^{54} -5.45195 q^{55} -23.7310 q^{56} -10.8369 q^{57} -23.8303 q^{58} +7.40026 q^{59} +8.84651 q^{60} +4.66071 q^{61} -7.30296 q^{62} -3.38657 q^{63} +36.1079 q^{64} -5.25941 q^{65} +15.0608 q^{66} -1.17172 q^{67} +34.9789 q^{68} +1.68066 q^{69} -8.25658 q^{70} +14.2401 q^{71} +14.1268 q^{72} +5.38858 q^{73} +2.75814 q^{74} -4.30509 q^{75} -48.3404 q^{76} -10.3609 q^{77} +14.5289 q^{78} +7.54515 q^{79} +20.3665 q^{80} -2.72443 q^{81} -15.2892 q^{82} +5.13075 q^{83} +16.8120 q^{84} +7.82924 q^{85} -2.39808 q^{86} +10.8608 q^{87} +43.2198 q^{88} +18.6815 q^{89} +4.91506 q^{90} -9.99501 q^{91} +7.49700 q^{92} +3.32837 q^{93} -12.4122 q^{94} -10.8199 q^{95} -31.2478 q^{96} +4.65603 q^{97} +3.61610 q^{98} +6.16776 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9}+O(q^{10}) $ 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9	\( 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9} + 13 q^{10} + 2 q^{11} + 36 q^{12} + 23 q^{13} + 24 q^{14} + 35 q^{15} + 104 q^{16} + 43 q^{17} + 42 q^{18} + 15 q^{19} + 59 q^{20} + 9 q^{21} + 6 q^{22} + 70 q^{23} + 15 q^{24} + 98 q^{25} + 10 q^{26} + 65 q^{27} + 37 q^{28} + 27 q^{29} + 17 q^{30} + 59 q^{31} + 46 q^{32} + 16 q^{33} - 16 q^{34} + 80 q^{35} + 88 q^{36} - 82 q^{37} + 82 q^{38} + 13 q^{39} + 14 q^{40} + 3 q^{41} + 62 q^{42} + 7 q^{43} - 11 q^{44} + 42 q^{45} - 11 q^{46} + 123 q^{47} + 45 q^{48} + 105 q^{49} + 27 q^{50} + 3 q^{51} - 30 q^{52} + 82 q^{53} - 27 q^{54} + 37 q^{55} + 66 q^{56} + 29 q^{57} - 34 q^{58} + 60 q^{59} + 94 q^{60} + 9 q^{61} - 2 q^{62} + 106 q^{63} + 93 q^{64} + 9 q^{65} + 63 q^{66} + 113 q^{68} + 48 q^{69} + 47 q^{70} + 59 q^{71} + 63 q^{72} + 21 q^{73} - 10 q^{74} + 77 q^{75} + 22 q^{76} + 30 q^{77} + 29 q^{78} + 55 q^{79} + 88 q^{80} + 42 q^{81} + 4 q^{82} + 92 q^{83} + 43 q^{84} - 7 q^{85} + 17 q^{86} + 147 q^{87} - 13 q^{88} + 100 q^{89} + 91 q^{90} + 28 q^{91} + 127 q^{92} + 3 q^{93} + 30 q^{94} + 48 q^{95} - 31 q^{96} + 53 q^{97} + 101 q^{98} - 20 q^{99}+O(q^{100}) \) 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9 + 13 * q^10 + 2 * q^11 + 36 * q^12 + 23 * q^13 + 24 * q^14 + 35 * q^15 + 104 * q^16 + 43 * q^17 + 42 * q^18 + 15 * q^19 + 59 * q^20 + 9 * q^21 + 6 * q^22 + 70 * q^23 + 15 * q^24 + 98 * q^25 + 10 * q^26 + 65 * q^27 + 37 * q^28 + 27 * q^29 + 17 * q^30 + 59 * q^31 + 46 * q^32 + 16 * q^33 - 16 * q^34 + 80 * q^35 + 88 * q^36 - 82 * q^37 + 82 * q^38 + 13 * q^39 + 14 * q^40 + 3 * q^41 + 62 * q^42 + 7 * q^43 - 11 * q^44 + 42 * q^45 - 11 * q^46 + 123 * q^47 + 45 * q^48 + 105 * q^49 + 27 * q^50 + 3 * q^51 - 30 * q^52 + 82 * q^53 - 27 * q^54 + 37 * q^55 + 66 * q^56 + 29 * q^57 - 34 * q^58 + 60 * q^59 + 94 * q^60 + 9 * q^61 - 2 * q^62 + 106 * q^63 + 93 * q^64 + 9 * q^65 + 63 * q^66 + 113 * q^68 + 48 * q^69 + 47 * q^70 + 59 * q^71 + 63 * q^72 + 21 * q^73 - 10 * q^74 + 77 * q^75 + 22 * q^76 + 30 * q^77 + 29 * q^78 + 55 * q^79 + 88 * q^80 + 42 * q^81 + 4 * q^82 + 92 * q^83 + 43 * q^84 - 7 * q^85 + 17 * q^86 + 147 * q^87 - 13 * q^88 + 100 * q^89 + 91 * q^90 + 28 * q^91 + 127 * q^92 + 3 * q^93 + 30 * q^94 + 48 * q^95 - 31 * q^96 + 53 * q^97 + 101 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.75814	−1.95030	−0.975148	−	0.221553i	$-0.928888\pi$
$2$	−2.75814	−1.95030	−0.975148	+	0.221553i	$0.928888\pi$
$3$	1.25704	0.725751	0.362875	−	0.931838i	$-0.381795\pi$
$3$	1.25704	0.725751	0.362875	+	0.931838i	$0.381795\pi$
$4$	5.60732	2.80366
$5$	1.25507	0.561286	0.280643	−	0.959812i	$-0.409452\pi$
$5$	1.25507	0.561286	0.280643	+	0.959812i	$0.409452\pi$
$6$	−3.46708	−1.41543
$7$	2.38515	0.901501	0.450751	−	0.892650i	$-0.351156\pi$
$7$	2.38515	0.901501	0.450751	+	0.892650i	$0.351156\pi$
$8$	−9.94947	−3.51767
$9$	−1.41986	−0.473286
$10$	−3.46166	−1.09467
$11$	−4.34393	−1.30975	−0.654873	−	0.755739i	$-0.727278\pi$
$11$	−4.34393	−1.30975	−0.654873	+	0.755739i	$0.727278\pi$
$12$	7.04861	2.03476
$13$	−4.19052	−1.16224	−0.581121	−	0.813818i	$-0.697386\pi$
$13$	−4.19052	−1.16224	−0.581121	+	0.813818i	$0.697386\pi$
$14$	−6.57856	−1.75820
$15$	1.57767	0.407353
$16$	16.2274	4.05684
$17$	6.23808	1.51296	0.756478	−	0.654019i	$-0.226918\pi$
$17$	6.23808	1.51296	0.756478	+	0.654019i	$0.226918\pi$
$18$	3.91616	0.923048
$19$	−8.62095	−1.97778	−0.988891	−	0.148641i	$-0.952510\pi$
$19$	−8.62095	−1.97778	−0.988891	+	0.148641i	$0.952510\pi$
$20$	7.03759	1.57365
$21$	2.99822	0.654265
$22$	11.9812	2.55439
$23$	1.33700	0.278784	0.139392	−	0.990237i	$-0.455485\pi$
$23$	1.33700	0.278784	0.139392	+	0.990237i	$0.455485\pi$
$24$	−12.5069	−2.55295
$25$	−3.42479	−0.684959
$26$	11.5580	2.26671
$27$	−5.55593	−1.06924
$28$	13.3743	2.52750
$29$	8.63999	1.60441	0.802203	−	0.597051i	$-0.203661\pi$
$29$	8.63999	1.60441	0.802203	+	0.597051i	$0.203661\pi$
$30$	−4.35144	−0.794460
$31$	2.64779	0.475557	0.237778	−	0.971319i	$-0.423581\pi$
$31$	2.64779	0.475557	0.237778	+	0.971319i	$0.423581\pi$
$32$	−24.8583	−4.39437
$33$	−5.46049	−0.950549
$34$	−17.2055	−2.95072
$35$	2.99353	0.506000
$36$	−7.96159	−1.32693
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	23.7778	3.85726
$39$	−5.26764	−0.843497
$40$	−12.4873	−1.97442
$41$	5.54332	0.865722	0.432861	−	0.901461i	$-0.357504\pi$
$41$	5.54332	0.865722	0.432861	+	0.901461i	$0.357504\pi$
$42$	−8.26950	−1.27601
$43$	0.869458	0.132591	0.0662956	−	0.997800i	$-0.478882\pi$
$43$	0.869458	0.132591	0.0662956	+	0.997800i	$0.478882\pi$
$44$	−24.3578	−3.67208
$45$	−1.78202	−0.265648
$46$	−3.68764	−0.543712
$47$	4.50020	0.656421	0.328211	−	0.944605i	$-0.393554\pi$
$47$	4.50020	0.656421	0.328211	+	0.944605i	$0.393554\pi$
$48$	20.3984	2.94425
$49$	−1.31107	−0.187295
$50$	9.44604	1.33587
$51$	7.84150	1.09803
$52$	−23.4976	−3.25853
$53$	−9.77876	−1.34322	−0.671608	−	0.740907i	$-0.734396\pi$
$53$	−9.77876	−1.34322	−0.671608	+	0.740907i	$0.734396\pi$
$54$	15.3240	2.08533
$55$	−5.45195	−0.735141
$56$	−23.7310	−3.17118
$57$	−10.8369	−1.43538
$58$	−23.8303	−3.12907
$59$	7.40026	0.963432	0.481716	−	0.876327i	$-0.340014\pi$
$59$	7.40026	0.963432	0.481716	+	0.876327i	$0.340014\pi$
$60$	8.84651	1.14208
$61$	4.66071	0.596743	0.298372	−	0.954450i	$-0.403557\pi$
$61$	4.66071	0.596743	0.298372	+	0.954450i	$0.403557\pi$
$62$	−7.30296	−0.927476
$63$	−3.38657	−0.426668
$64$	36.1079	4.51349
$65$	−5.25941	−0.652349
$66$	15.0608	1.85385
$67$	−1.17172	−0.143148	−0.0715741	−	0.997435i	$-0.522802\pi$
$67$	−1.17172	−0.143148	−0.0715741	+	0.997435i	$0.522802\pi$
$68$	34.9789	4.24181
$69$	1.68066	0.202328
$70$	−8.25658	−0.986850
$71$	14.2401	1.68999	0.844997	−	0.534771i	$-0.179602\pi$
$71$	14.2401	1.68999	0.844997	+	0.534771i	$0.179602\pi$
$72$	14.1268	1.66486
$73$	5.38858	0.630686	0.315343	−	0.948978i	$-0.397880\pi$
$73$	5.38858	0.630686	0.315343	+	0.948978i	$0.397880\pi$
$74$	2.75814	0.320627
$75$	−4.30509	−0.497109
$76$	−48.3404	−5.54502
$77$	−10.3609	−1.18074
$78$	14.5289	1.64507
$79$	7.54515	0.848896	0.424448	−	0.905452i	$-0.360468\pi$
$79$	7.54515	0.848896	0.424448	+	0.905452i	$0.360468\pi$
$80$	20.3665	2.27705
$81$	−2.72443	−0.302715
$82$	−15.2892	−1.68841
$83$	5.13075	0.563172	0.281586	−	0.959536i	$-0.409139\pi$
$83$	5.13075	0.563172	0.281586	+	0.959536i	$0.409139\pi$
$84$	16.8120	1.83434
$85$	7.82924	0.849201
$86$	−2.39808	−0.258592
$87$	10.8608	1.16440
$88$	43.2198	4.60725
$89$	18.6815	1.98024	0.990119	−	0.140229i	$-0.0447840\pi$
$89$	18.6815	1.98024	0.990119	+	0.140229i	$0.0447840\pi$
$90$	4.91506	0.518093
$91$	−9.99501	−1.04776
$92$	7.49700	0.781616
$93$	3.32837	0.345136
$94$	−12.4122	−1.28022
$95$	−10.8199	−1.11010
$96$	−31.2478	−3.18922
$97$	4.65603	0.472748	0.236374	−	0.971662i	$-0.424041\pi$
$97$	4.65603	0.472748	0.236374	+	0.971662i	$0.424041\pi$
$98$	3.61610	0.365281
$99$	6.16776	0.619884
$100$	−19.2039	−1.92039
$101$	−0.116683	−0.0116104	−0.00580521	−	0.999983i	$-0.501848\pi$
$101$	−0.116683	−0.0116104	−0.00580521	+	0.999983i	$0.501848\pi$
$102$	−21.6279	−2.14148
$103$	14.2705	1.40611	0.703057	−	0.711133i	$-0.251818\pi$
$103$	14.2705	1.40611	0.703057	+	0.711133i	$0.251818\pi$
$104$	41.6934	4.08838
$105$	3.76298	0.367230
$106$	26.9711	2.61967
$107$	2.82254	0.272865	0.136432	−	0.990649i	$-0.456436\pi$
$107$	2.82254	0.272865	0.136432	+	0.990649i	$0.456436\pi$
$108$	−31.1538	−2.99778
$109$	1.00000	0.0957826
$109$	1.00000	0.0957826
$110$	15.0372	1.43374
$111$	−1.25704	−0.119313
$112$	38.7047	3.65725
$113$	19.0646	1.79345	0.896725	−	0.442588i	$-0.145940\pi$
$113$	19.0646	1.79345	0.896725	+	0.442588i	$0.145940\pi$
$114$	29.8895	2.79941
$115$	1.67804	0.156478
$116$	48.4472	4.49821
$117$	5.94994	0.550072
$118$	−20.4109	−1.87898
$119$	14.8787	1.36393
$120$	−15.6970	−1.43293
$121$	7.86976	0.715432
$122$	−12.8549	−1.16383
$123$	6.96816	0.628298
$124$	14.8470	1.33330
$125$	−10.5737	−0.945743
$126$	9.34062	0.832129
$127$	−0.232971	−0.0206728	−0.0103364	−	0.999947i	$-0.503290\pi$
$127$	−0.232971	−0.0206728	−0.0103364	+	0.999947i	$0.503290\pi$
$128$	−49.8740	−4.40828
$129$	1.09294	0.0962281
$130$	14.5062	1.27227
$131$	−3.82136	−0.333874	−0.166937	−	0.985968i	$-0.553388\pi$
$131$	−3.82136	−0.333874	−0.166937	+	0.985968i	$0.553388\pi$
$132$	−30.6187	−2.66501
$133$	−20.5623	−1.78297
$134$	3.23176	0.279182
$135$	−6.97309	−0.600148
$136$	−62.0656	−5.32208
$137$	−4.97380	−0.424941	−0.212470	−	0.977168i	$-0.568151\pi$
$137$	−4.97380	−0.424941	−0.212470	+	0.977168i	$0.568151\pi$
$138$	−4.63550	−0.394600
$139$	−0.185802	−0.0157595	−0.00787977	−	0.999969i	$-0.502508\pi$
$139$	−0.185802	−0.0157595	−0.00787977	+	0.999969i	$0.502508\pi$
$140$	16.7857	1.41865
$141$	5.65691	0.476398
$142$	−39.2763	−3.29599
$143$	18.2033	1.52224
$144$	−23.0405	−1.92004
$145$	10.8438	0.900530
$146$	−14.8624	−1.23002
$147$	−1.64806	−0.135930
$148$	−5.60732	−0.460919
$149$	14.1196	1.15672	0.578359	−	0.815782i	$-0.303693\pi$
$149$	14.1196	1.15672	0.578359	+	0.815782i	$0.303693\pi$
$150$	11.8740	0.969511
$151$	3.38384	0.275373	0.137686	−	0.990476i	$-0.456033\pi$
$151$	3.38384	0.275373	0.137686	+	0.990476i	$0.456033\pi$
$152$	85.7739	6.95718
$153$	−8.85718	−0.716061
$154$	28.5768	2.30279
$155$	3.32316	0.266923
$156$	−29.5373	−2.36488
$157$	17.0998	1.36472	0.682358	−	0.731018i	$-0.260954\pi$
$157$	17.0998	1.36472	0.682358	+	0.731018i	$0.260954\pi$
$158$	−20.8106	−1.65560
$159$	−12.2923	−0.974840
$160$	−31.1990	−2.46650
$161$	3.18895	0.251325
$162$	7.51436	0.590384
$163$	23.7820	1.86275	0.931375	−	0.364061i	$-0.118610\pi$
$163$	23.7820	1.86275	0.931375	+	0.364061i	$0.118610\pi$
$164$	31.0832	2.42719
$165$	−6.85331	−0.533529
$166$	−14.1513	−1.09835
$167$	11.0745	0.856972	0.428486	−	0.903548i	$-0.359047\pi$
$167$	11.0745	0.856972	0.428486	+	0.903548i	$0.359047\pi$
$168$	−29.8307	−2.30149
$169$	4.56045	0.350804
$170$	−21.5941	−1.65619
$171$	12.2405	0.936056
$172$	4.87533	0.371740
$173$	4.24058	0.322406	0.161203	−	0.986921i	$-0.448463\pi$
$173$	4.24058	0.322406	0.161203	+	0.986921i	$0.448463\pi$
$174$	−29.9555	−2.27092
$175$	−8.16864	−0.617491
$176$	−70.4906	−5.31343
$177$	9.30241	0.699212
$178$	−51.5262	−3.86205
$179$	18.3809	1.37385	0.686927	−	0.726726i	$-0.258959\pi$
$179$	18.3809	1.37385	0.686927	+	0.726726i	$0.258959\pi$
$180$	−9.99237	−0.744787
$181$	−9.67304	−0.718991	−0.359496	−	0.933147i	$-0.617051\pi$
$181$	−9.67304	−0.718991	−0.359496	+	0.933147i	$0.617051\pi$
$182$	27.5676	2.04345
$183$	5.85869	0.433087
$184$	−13.3025	−0.980671
$185$	−1.25507	−0.0922748
$186$	−9.18009	−0.673117
$187$	−27.0978	−1.98159
$188$	25.2340	1.84038
$189$	−13.2517	−0.963920
$190$	29.8428	2.16503
$191$	−10.5585	−0.763989	−0.381995	−	0.924165i	$-0.624763\pi$
$191$	−10.5585	−0.763989	−0.381995	+	0.924165i	$0.624763\pi$
$192$	45.3890	3.27567
$193$	−26.1904	−1.88523	−0.942613	−	0.333887i	$-0.891639\pi$
$193$	−26.1904	−1.88523	−0.942613	+	0.333887i	$0.891639\pi$
$194$	−12.8420	−0.921999
$195$	−6.61127	−0.473443
$196$	−7.35157	−0.525112
$197$	−15.6977	−1.11842	−0.559208	−	0.829027i	$-0.688895\pi$
$197$	−15.6977	−1.11842	−0.559208	+	0.829027i	$0.688895\pi$
$198$	−17.0115	−1.20896
$199$	0.0502232	0.00356023	0.00178012	−	0.999998i	$-0.499433\pi$
$199$	0.0502232	0.00356023	0.00178012	+	0.999998i	$0.499433\pi$
$200$	34.0749	2.40946
$201$	−1.47289	−0.103890
$202$	0.321828	0.0226438
$203$	20.6077	1.44637
$204$	43.9698	3.07850
$205$	6.95727	0.485917
$206$	−39.3600	−2.74234
$207$	−1.89835	−0.131945
$208$	−68.0011	−4.71502
$209$	37.4488	2.59039
$210$	−10.3788	−0.716207
$211$	−11.7141	−0.806435	−0.403218	−	0.915104i	$-0.632108\pi$
$211$	−11.7141	−0.806435	−0.403218	+	0.915104i	$0.632108\pi$
$212$	−54.8326	−3.76592
$213$	17.9004	1.22651
$214$	−7.78494	−0.532167
$215$	1.09123	0.0744215
$216$	55.2785	3.76123
$217$	6.31536	0.428715
$218$	−2.75814	−0.186805
$219$	6.77365	0.457721
$220$	−30.5708	−2.06108
$221$	−26.1408	−1.75842
$222$	3.46708	0.232695
$223$	18.4652	1.23652	0.618259	−	0.785974i	$-0.287838\pi$
$223$	18.4652	1.23652	0.618259	+	0.785974i	$0.287838\pi$
$224$	−59.2908	−3.96153
$225$	4.86272	0.324181
$226$	−52.5829	−3.49776
$227$	−16.8565	−1.11881	−0.559404	−	0.828895i	$-0.688970\pi$
$227$	−16.8565	−1.11881	−0.559404	+	0.828895i	$0.688970\pi$
$228$	−60.7657	−4.02431
$229$	−18.7728	−1.24054	−0.620271	−	0.784388i	$-0.712977\pi$
$229$	−18.7728	−1.24054	−0.620271	+	0.784388i	$0.712977\pi$
$230$	−4.62825	−0.305178
$231$	−13.0241	−0.856921
$232$	−85.9633	−5.64377
$233$	10.8932	0.713634	0.356817	−	0.934174i	$-0.383862\pi$
$233$	10.8932	0.713634	0.356817	+	0.934174i	$0.383862\pi$
$234$	−16.4107	−1.07280
$235$	5.64807	0.368440
$236$	41.4956	2.70113
$237$	9.48454	0.616087
$238$	−41.0376	−2.66007
$239$	3.78859	0.245063	0.122532	−	0.992465i	$-0.460899\pi$
$239$	3.78859	0.245063	0.122532	+	0.992465i	$0.460899\pi$
$240$	25.6015	1.65257
$241$	−13.2201	−0.851579	−0.425789	−	0.904822i	$-0.640004\pi$
$241$	−13.2201	−0.851579	−0.425789	+	0.904822i	$0.640004\pi$
$242$	−21.7059	−1.39531
$243$	13.2431	0.849543
$244$	26.1341	1.67306
$245$	−1.64548	−0.105126
$246$	−19.2191	−1.22537
$247$	36.1263	2.29866
$248$	−26.3441	−1.67285
$249$	6.44954	0.408723
$250$	29.1638	1.84448
$251$	20.4228	1.28908	0.644538	−	0.764572i	$-0.277050\pi$
$251$	20.4228	1.28908	0.644538	+	0.764572i	$0.277050\pi$
$252$	−18.9896	−1.19623
$253$	−5.80785	−0.365137
$254$	0.642566	0.0403182
$255$	9.84165	0.616308
$256$	65.3433	4.08396
$257$	−18.0816	−1.12790	−0.563950	−	0.825809i	$-0.690719\pi$
$257$	−18.0816	−1.12790	−0.563950	+	0.825809i	$0.690719\pi$
$258$	−3.01448	−0.187673
$259$	−2.38515	−0.148206
$260$	−29.4912	−1.82896
$261$	−12.2676	−0.759343
$262$	10.5398	0.651153
$263$	6.03079	0.371874	0.185937	−	0.982562i	$-0.440468\pi$
$263$	6.03079	0.371874	0.185937	+	0.982562i	$0.440468\pi$
$264$	54.3289	3.34371
$265$	−12.2730	−0.753927
$266$	56.7135	3.47733
$267$	23.4834	1.43716
$268$	−6.57020	−0.401339
$269$	−1.57224	−0.0958611	−0.0479305	−	0.998851i	$-0.515263\pi$
$269$	−1.57224	−0.0958611	−0.0479305	+	0.998851i	$0.515263\pi$
$270$	19.2327	1.17047
$271$	−25.9927	−1.57895	−0.789473	−	0.613785i	$-0.789646\pi$
$271$	−25.9927	−1.57895	−0.789473	+	0.613785i	$0.789646\pi$
$272$	101.228	6.13782
$273$	−12.5641	−0.760414
$274$	13.7184	0.828761
$275$	14.8771	0.897121
$276$	9.42401	0.567259
$277$	15.3266	0.920888	0.460444	−	0.887689i	$-0.347690\pi$
$277$	15.3266	0.920888	0.460444	+	0.887689i	$0.347690\pi$
$278$	0.512468	0.0307358
$279$	−3.75948	−0.225074
$280$	−29.7841	−1.77994
$281$	−24.7496	−1.47644	−0.738218	−	0.674563i	$-0.764332\pi$
$281$	−24.7496	−1.47644	−0.738218	+	0.674563i	$0.764332\pi$
$282$	−15.6025	−0.929118
$283$	11.3790	0.676410	0.338205	−	0.941073i	$-0.390180\pi$
$283$	11.3790	0.676410	0.338205	+	0.941073i	$0.390180\pi$
$284$	79.8490	4.73817
$285$	−13.6010	−0.805657
$286$	−50.2073	−2.96882
$287$	13.2216	0.780449
$288$	35.2953	2.07979
$289$	21.9137	1.28904
$290$	−29.9087	−1.75630
$291$	5.85280	0.343097
$292$	30.2155	1.76823
$293$	−18.9512	−1.10714	−0.553569	−	0.832803i	$-0.686735\pi$
$293$	−18.9512	−1.10714	−0.553569	+	0.832803i	$0.686735\pi$
$294$	4.54558	0.265103
$295$	9.28787	0.540761
$296$	9.94947	0.578301
$297$	24.1346	1.40043
$298$	−38.9437	−2.25595
$299$	−5.60274	−0.324015
$300$	−24.1400	−1.39372
$301$	2.07379	0.119531
$302$	−9.33308	−0.537059
$303$	−0.146675	−0.00842627
$304$	−139.895	−8.02355
$305$	5.84953	0.334943
$306$	24.4293	1.39653
$307$	−4.17983	−0.238555	−0.119278	−	0.992861i	$-0.538058\pi$
$307$	−4.17983	−0.238555	−0.119278	+	0.992861i	$0.538058\pi$
$308$	−58.0970	−3.31038
$309$	17.9386	1.02049
$310$	−9.16574	−0.520579
$311$	−23.1985	−1.31547	−0.657734	−	0.753250i	$-0.728485\pi$
$311$	−23.1985	−1.31547	−0.657734	+	0.753250i	$0.728485\pi$
$312$	52.4102	2.96714
$313$	20.3327	1.14927	0.574637	−	0.818408i	$-0.305143\pi$
$313$	20.3327	1.14927	0.574637	+	0.818408i	$0.305143\pi$
$314$	−47.1637	−2.66160
$315$	−4.25039	−0.239482
$316$	42.3081	2.38001
$317$	−23.6398	−1.32775	−0.663873	−	0.747845i	$-0.731088\pi$
$317$	−23.6398	−1.32775	−0.663873	+	0.747845i	$0.731088\pi$
$318$	33.9037	1.90123
$319$	−37.5315	−2.10136
$320$	45.3181	2.53336
$321$	3.54803	0.198032
$322$	−8.79556	−0.490158
$323$	−53.7782	−2.99230
$324$	−15.2768	−0.848709
$325$	14.3517	0.796087
$326$	−65.5940	−3.63292
$327$	1.25704	0.0695143
$328$	−55.1531	−3.04532
$329$	10.7336	0.591765
$330$	18.9024	1.04054
$331$	27.4345	1.50794	0.753969	−	0.656910i	$-0.228137\pi$
$331$	27.4345	1.50794	0.753969	+	0.656910i	$0.228137\pi$
$332$	28.7697	1.57894
$333$	1.41986	0.0778077
$334$	−30.5450	−1.67135
$335$	−1.47059	−0.0803470
$336$	48.6532	2.65425
$337$	−6.73198	−0.366714	−0.183357	−	0.983046i	$-0.558696\pi$
$337$	−6.73198	−0.366714	−0.183357	+	0.983046i	$0.558696\pi$
$338$	−12.5784	−0.684172
$339$	23.9650	1.30160
$340$	43.9010	2.38087
$341$	−11.5018	−0.622858
$342$	−33.7610	−1.82559
$343$	−19.8231	−1.07035
$344$	−8.65065	−0.466412
$345$	2.10935	0.113564
$346$	−11.6961	−0.628787
$347$	16.7341	0.898334	0.449167	−	0.893448i	$-0.351721\pi$
$347$	16.7341	0.898334	0.449167	+	0.893448i	$0.351721\pi$
$348$	60.8999	3.26458
$349$	−21.8942	−1.17197	−0.585986	−	0.810321i	$-0.699293\pi$
$349$	−21.8942	−1.17197	−0.585986	+	0.810321i	$0.699293\pi$
$350$	22.5302	1.20429
$351$	23.2822	1.24271
$352$	107.983	5.75551
$353$	2.21935	0.118124	0.0590620	−	0.998254i	$-0.481189\pi$
$353$	2.21935	0.118124	0.0590620	+	0.998254i	$0.481189\pi$
$354$	−25.6573	−1.36367
$355$	17.8724	0.948569
$356$	104.753	5.55191
$357$	18.7031	0.989875
$358$	−50.6971	−2.67943
$359$	−16.8065	−0.887014	−0.443507	−	0.896271i	$-0.646266\pi$
$359$	−16.8065	−0.887014	−0.443507	+	0.896271i	$0.646266\pi$
$360$	17.7302	0.934463
$361$	55.3208	2.91162
$362$	26.6796	1.40225
$363$	9.89258	0.519226
$364$	−56.0452	−2.93757
$365$	6.76306	0.353995
$366$	−16.1591	−0.844648
$367$	31.7140	1.65546	0.827728	−	0.561129i	$-0.189633\pi$
$367$	31.7140	1.65546	0.827728	+	0.561129i	$0.189633\pi$
$368$	21.6960	1.13098
$369$	−7.87073	−0.409734
$370$	3.46166	0.179963
$371$	−23.3238	−1.21091
$372$	18.6632	0.967642
$373$	6.16915	0.319426	0.159713	−	0.987163i	$-0.448943\pi$
$373$	6.16915	0.319426	0.159713	+	0.987163i	$0.448943\pi$
$374$	74.7394	3.86468
$375$	−13.2916	−0.686374
$376$	−44.7746	−2.30907
$377$	−36.2061	−1.86471
$378$	36.5500	1.87993
$379$	5.69260	0.292409	0.146205	−	0.989254i	$-0.453294\pi$
$379$	5.69260	0.292409	0.146205	+	0.989254i	$0.453294\pi$
$380$	−60.6707	−3.11234
$381$	−0.292853	−0.0150033
$382$	29.1219	1.49001
$383$	−18.1379	−0.926801	−0.463401	−	0.886149i	$-0.653371\pi$
$383$	−18.1379	−0.926801	−0.463401	+	0.886149i	$0.653371\pi$
$384$	−62.6934	−3.19931
$385$	−13.0037	−0.662731
$386$	72.2367	3.67675
$387$	−1.23451	−0.0627535
$388$	26.1078	1.32542
$389$	18.5628	0.941171	0.470585	−	0.882354i	$-0.344043\pi$
$389$	18.5628	0.941171	0.470585	+	0.882354i	$0.344043\pi$
$390$	18.2348	0.923354
$391$	8.34033	0.421789
$392$	13.0444	0.658843
$393$	−4.80359	−0.242309
$394$	43.2965	2.18124
$395$	9.46972	0.476473
$396$	34.5846	1.73794
$397$	−24.7674	−1.24304	−0.621520	−	0.783398i	$-0.713484\pi$
$397$	−24.7674	−1.24304	−0.621520	+	0.783398i	$0.713484\pi$
$398$	−0.138522	−0.00694351
$399$	−25.8475	−1.29399
$400$	−55.5753	−2.77877
$401$	−8.11149	−0.405069	−0.202534	−	0.979275i	$-0.564918\pi$
$401$	−8.11149	−0.405069	−0.202534	+	0.979275i	$0.564918\pi$
$402$	4.06244	0.202616
$403$	−11.0956	−0.552711
$404$	−0.654280	−0.0325517
$405$	−3.41936	−0.169910
$406$	−56.8387	−2.82086
$407$	4.34393	0.215321
$408$	−78.0188	−3.86250
$409$	−8.69395	−0.429888	−0.214944	−	0.976626i	$-0.568957\pi$
$409$	−8.69395	−0.429888	−0.214944	+	0.976626i	$0.568957\pi$
$410$	−19.1891	−0.947682
$411$	−6.25226	−0.308401
$412$	80.0192	3.94226
$413$	17.6507	0.868536
$414$	5.23592	0.257331
$415$	6.43946	0.316101
$416$	104.169	5.10732
$417$	−0.233560	−0.0114375
$418$	−103.289	−5.05203
$419$	−16.0386	−0.783539	−0.391770	−	0.920063i	$-0.628137\pi$
$419$	−16.0386	−0.783539	−0.391770	+	0.920063i	$0.628137\pi$
$420$	21.1002	1.02959
$421$	−19.7347	−0.961810	−0.480905	−	0.876773i	$-0.659692\pi$
$421$	−19.7347	−0.961810	−0.480905	+	0.876773i	$0.659692\pi$
$422$	32.3092	1.57279
$423$	−6.38964	−0.310675
$424$	97.2934	4.72499
$425$	−21.3641	−1.03631
$426$	−49.3717	−2.39207
$427$	11.1165	0.537965
$428$	15.8269	0.765020
$429$	22.8823	1.10477
$430$	−3.00977	−0.145144
$431$	−11.1196	−0.535614	−0.267807	−	0.963473i	$-0.586299\pi$
$431$	−11.1196	−0.535614	−0.267807	+	0.963473i	$0.586299\pi$
$432$	−90.1580	−4.33773
$433$	19.6937	0.946419	0.473210	−	0.880950i	$-0.343095\pi$
$433$	19.6937	0.946419	0.473210	+	0.880950i	$0.343095\pi$
$434$	−17.4186	−0.836121
$435$	13.6311	0.653560
$436$	5.60732	0.268542
$437$	−11.5262	−0.551375
$438$	−18.6827	−0.892692
$439$	−14.2216	−0.678758	−0.339379	−	0.940650i	$-0.610217\pi$
$439$	−14.2216	−0.678758	−0.339379	+	0.940650i	$0.610217\pi$
$440$	54.2440	2.58598
$441$	1.86153	0.0886442
$442$	72.0999	3.42944
$443$	−15.1748	−0.720976	−0.360488	−	0.932764i	$-0.617390\pi$
$443$	−15.1748	−0.720976	−0.360488	+	0.932764i	$0.617390\pi$
$444$	−7.04861	−0.334512
$445$	23.4467	1.11148
$446$	−50.9294	−2.41158
$447$	17.7488	0.839490
$448$	86.1228	4.06892
$449$	31.6796	1.49505	0.747527	−	0.664232i	$-0.231241\pi$
$449$	31.6796	1.49505	0.747527	+	0.664232i	$0.231241\pi$
$450$	−13.4120	−0.632249
$451$	−24.0798	−1.13387
$452$	106.901	5.02822
$453$	4.25361	0.199852
$454$	46.4926	2.18201
$455$	−12.5445	−0.588094
$456$	107.821	5.04918
$457$	−12.0030	−0.561478	−0.280739	−	0.959784i	$-0.590580\pi$
$457$	−12.0030	−0.561478	−0.280739	+	0.959784i	$0.590580\pi$
$458$	51.7779	2.41942
$459$	−34.6583	−1.61771
$460$	9.40928	0.438710
$461$	−17.3015	−0.805812	−0.402906	−	0.915241i	$-0.632000\pi$
$461$	−17.3015	−0.805812	−0.402906	+	0.915241i	$0.632000\pi$
$462$	35.9222	1.67125
$463$	35.2855	1.63986	0.819928	−	0.572466i	$-0.194013\pi$
$463$	35.2855	1.63986	0.819928	+	0.572466i	$0.194013\pi$
$464$	140.204	6.50882
$465$	4.17734	0.193720
$466$	−30.0448	−1.39180
$467$	−0.544554	−0.0251990	−0.0125995	−	0.999921i	$-0.504011\pi$
$467$	−0.544554	−0.0251990	−0.0125995	+	0.999921i	$0.504011\pi$
$468$	33.3632	1.54221
$469$	−2.79472	−0.129048
$470$	−15.5782	−0.718567
$471$	21.4951	0.990444
$472$	−73.6287	−3.38904
$473$	−3.77687	−0.173661
$474$	−26.1597	−1.20155
$475$	29.5250	1.35470
$476$	83.4298	3.82400
$477$	13.8844	0.635725
$478$	−10.4494	−0.477946
$479$	−3.63708	−0.166182	−0.0830912	−	0.996542i	$-0.526479\pi$
$479$	−3.63708	−0.166182	−0.0830912	+	0.996542i	$0.526479\pi$
$480$	−39.2183	−1.79006
$481$	4.19052	0.191071
$482$	36.4627	1.66083
$483$	4.00863	0.182399
$484$	44.1282	2.00583
$485$	5.84365	0.265347
$486$	−36.5262	−1.65686
$487$	10.5889	0.479830	0.239915	−	0.970794i	$-0.422880\pi$
$487$	10.5889	0.479830	0.239915	+	0.970794i	$0.422880\pi$
$488$	−46.3716	−2.09914
$489$	29.8949	1.35189
$490$	4.53847	0.205027
$491$	5.80992	0.262198	0.131099	−	0.991369i	$-0.458149\pi$
$491$	5.80992	0.262198	0.131099	+	0.991369i	$0.458149\pi$
$492$	39.0727	1.76153
$493$	53.8970	2.42740
$494$	−99.6412	−4.48307
$495$	7.74099	0.347932
$496$	42.9666	1.92926
$497$	33.9649	1.52353
$498$	−17.7887	−0.797131
$499$	−38.8583	−1.73954	−0.869768	−	0.493461i	$-0.835732\pi$
$499$	−38.8583	−1.73954	−0.869768	+	0.493461i	$0.835732\pi$
$500$	−59.2902	−2.65154
$501$	13.9211	0.621948
$502$	−56.3289	−2.51408
$503$	−3.68776	−0.164429	−0.0822146	−	0.996615i	$-0.526199\pi$
$503$	−3.68776	−0.164429	−0.0822146	+	0.996615i	$0.526199\pi$
$504$	33.6946	1.50088
$505$	−0.146446	−0.00651676
$506$	16.0189	0.712125
$507$	5.73266	0.254596
$508$	−1.30634	−0.0579596
$509$	−13.3060	−0.589780	−0.294890	−	0.955531i	$-0.595283\pi$
$509$	−13.3060	−0.589780	−0.294890	+	0.955531i	$0.595283\pi$
$510$	−27.1446	−1.20198
$511$	12.8526	0.568564
$512$	−80.4778	−3.55665
$513$	47.8974	2.11472
$514$	49.8715	2.19974
$515$	17.9105	0.789232
$516$	6.12847	0.269791
$517$	−19.5486	−0.859744
$518$	6.57856	0.289046
$519$	5.33057	0.233986
$520$	52.3283	2.29475
$521$	30.5432	1.33812	0.669061	−	0.743208i	$-0.266697\pi$
$521$	30.5432	1.33812	0.669061	+	0.743208i	$0.266697\pi$
$522$	33.8356	1.48094
$523$	7.34207	0.321046	0.160523	−	0.987032i	$-0.448682\pi$
$523$	7.34207	0.321046	0.160523	+	0.987032i	$0.448682\pi$
$524$	−21.4276	−0.936068
$525$	−10.2683	−0.448145
$526$	−16.6337	−0.725265
$527$	16.5171	0.719497
$528$	−88.6093	−3.85622
$529$	−21.2124	−0.922279
$530$	33.8507	1.47038
$531$	−10.5073	−0.455979
$532$	−115.299	−4.99885
$533$	−23.2294	−1.00618
$534$	−64.7704	−2.80289
$535$	3.54249	0.153155
$536$	11.6580	0.503548
$537$	23.1055	0.997076
$538$	4.33645	0.186958
$539$	5.69519	0.245309
$540$	−39.1003	−1.68261
$541$	−1.26386	−0.0543377	−0.0271688	−	0.999631i	$-0.508649\pi$
$541$	−1.26386	−0.0543377	−0.0271688	+	0.999631i	$0.508649\pi$
$542$	71.6915	3.07941
$543$	−12.1594	−0.521809
$544$	−155.068	−6.64850
$545$	1.25507	0.0537614
$546$	34.6535	1.48303
$547$	−4.31002	−0.184283	−0.0921416	−	0.995746i	$-0.529371\pi$
$547$	−4.31002	−0.184283	−0.0921416	+	0.995746i	$0.529371\pi$
$548$	−27.8897	−1.19139
$549$	−6.61755	−0.282430
$550$	−41.0330	−1.74965
$551$	−74.4850	−3.17317
$552$	−16.7217	−0.711723
$553$	17.9963	0.765281
$554$	−42.2729	−1.79601
$555$	−1.57767	−0.0669685
$556$	−1.04185	−0.0441844
$557$	16.1442	0.684052	0.342026	−	0.939691i	$-0.388887\pi$
$557$	16.1442	0.684052	0.342026	+	0.939691i	$0.388887\pi$
$558$	10.3692	0.438961
$559$	−3.64348	−0.154103
$560$	48.5772	2.05276
$561$	−34.0630	−1.43814
$562$	68.2627	2.87949
$563$	10.8722	0.458209	0.229105	−	0.973402i	$-0.426420\pi$
$563$	10.8722	0.458209	0.229105	+	0.973402i	$0.426420\pi$
$564$	31.7201	1.33566
$565$	23.9275	1.00664
$566$	−31.3848	−1.31920
$567$	−6.49818	−0.272898
$568$	−141.682	−5.94484
$569$	−24.2218	−1.01543	−0.507716	−	0.861524i	$-0.669510\pi$
$569$	−24.2218	−1.01543	−0.507716	+	0.861524i	$0.669510\pi$
$570$	37.5135	1.57127
$571$	2.55600	0.106965	0.0534827	−	0.998569i	$-0.482968\pi$
$571$	2.55600	0.106965	0.0534827	+	0.998569i	$0.482968\pi$
$572$	102.072	4.26784
$573$	−13.2725	−0.554466
$574$	−36.4671	−1.52211
$575$	−4.57896	−0.190956
$576$	−51.2681	−2.13617
$577$	−5.45630	−0.227149	−0.113574	−	0.993529i	$-0.536230\pi$
$577$	−5.45630	−0.227149	−0.113574	+	0.993529i	$0.536230\pi$
$578$	−60.4408	−2.51401
$579$	−32.9223	−1.36820
$580$	60.8047	2.52478
$581$	12.2376	0.507701
$582$	−16.1428	−0.669141
$583$	42.4783	1.75927
$584$	−53.6135	−2.21854
$585$	7.46761	0.308748
$586$	52.2699	2.15925
$587$	31.2694	1.29063	0.645313	−	0.763918i	$-0.276727\pi$
$587$	31.2694	1.29063	0.645313	+	0.763918i	$0.276727\pi$
$588$	−9.24120	−0.381100
$589$	−22.8264	−0.940547
$590$	−25.6172	−1.05464
$591$	−19.7326	−0.811692
$592$	−16.2274	−0.666940
$593$	23.6951	0.973043	0.486522	−	0.873669i	$-0.338266\pi$
$593$	23.6951	0.973043	0.486522	+	0.873669i	$0.338266\pi$
$594$	−66.5664	−2.73125
$595$	18.6739	0.765556
$596$	79.1728	3.24304
$597$	0.0631325	0.00258384
$598$	15.4531	0.631925
$599$	8.60870	0.351742	0.175871	−	0.984413i	$-0.443726\pi$
$599$	8.60870	0.351742	0.175871	+	0.984413i	$0.443726\pi$
$600$	42.8334	1.74867
$601$	34.4352	1.40464	0.702321	−	0.711861i	$-0.252147\pi$
$601$	34.4352	1.40464	0.702321	+	0.711861i	$0.252147\pi$
$602$	−5.71979	−0.233121
$603$	1.66367	0.0677500
$604$	18.9742	0.772051
$605$	9.87711	0.401562
$606$	0.404550	0.0164337
$607$	−30.6085	−1.24236	−0.621179	−	0.783668i	$-0.713346\pi$
$607$	−30.6085	−1.24236	−0.621179	+	0.783668i	$0.713346\pi$
$608$	214.302	8.69111
$609$	25.9046	1.04971
$610$	−16.1338	−0.653239
$611$	−18.8582	−0.762920
$612$	−49.6650	−2.00759
$613$	26.4882	1.06985	0.534925	−	0.844900i	$-0.320340\pi$
$613$	26.4882	1.06985	0.534925	+	0.844900i	$0.320340\pi$
$614$	11.5285	0.465253
$615$	8.74555	0.352655
$616$	103.086	4.15344
$617$	−19.6697	−0.791874	−0.395937	−	0.918278i	$-0.629580\pi$
$617$	−19.6697	−0.791874	−0.395937	+	0.918278i	$0.629580\pi$
$618$	−49.4770	−1.99026
$619$	−33.6407	−1.35213	−0.676067	−	0.736840i	$-0.736317\pi$
$619$	−33.6407	−1.35213	−0.676067	+	0.736840i	$0.736317\pi$
$620$	18.6340	0.748361
$621$	−7.42829	−0.298087
$622$	63.9847	2.56555
$623$	44.5582	1.78519
$624$	−85.4799	−3.42193
$625$	3.85317	0.154127
$626$	−56.0804	−2.24143
$627$	47.0746	1.87998
$628$	95.8842	3.82620
$629$	−6.23808	−0.248729
$630$	11.7232	0.467062
$631$	−0.123738	−0.00492594	−0.00246297	−	0.999997i	$-0.500784\pi$
$631$	−0.123738	−0.00492594	−0.00246297	+	0.999997i	$0.500784\pi$
$632$	−75.0703	−2.98614
$633$	−14.7251	−0.585271
$634$	65.2019	2.58950
$635$	−0.292396	−0.0116034
$636$	−68.9266	−2.73312
$637$	5.49405	0.217682
$638$	103.517	4.09828
$639$	−20.2190	−0.799850
$640$	−62.5954	−2.47430
$641$	−45.9698	−1.81570	−0.907849	−	0.419298i	$-0.862276\pi$
$641$	−45.9698	−1.81570	−0.907849	+	0.419298i	$0.862276\pi$
$642$	−9.78596	−0.386221
$643$	−16.7281	−0.659692	−0.329846	−	0.944035i	$-0.606997\pi$
$643$	−16.7281	−0.659692	−0.329846	+	0.944035i	$0.606997\pi$
$644$	17.8815	0.704628
$645$	1.37172	0.0540115
$646$	148.328	5.83587
$647$	1.42017	0.0558328	0.0279164	−	0.999610i	$-0.491113\pi$
$647$	1.42017	0.0558328	0.0279164	+	0.999610i	$0.491113\pi$
$648$	27.1067	1.06485
$649$	−32.1463	−1.26185
$650$	−39.5838	−1.55261
$651$	7.93865	0.311140
$652$	133.353	5.22252
$653$	39.9174	1.56209	0.781045	−	0.624475i	$-0.214687\pi$
$653$	39.9174	1.56209	0.781045	+	0.624475i	$0.214687\pi$
$654$	−3.46708	−0.135574
$655$	−4.79608	−0.187399
$656$	89.9535	3.51209
$657$	−7.65102	−0.298495
$658$	−29.6048	−1.15412
$659$	−33.7434	−1.31445	−0.657227	−	0.753692i	$-0.728271\pi$
$659$	−33.7434	−1.31445	−0.657227	+	0.753692i	$0.728271\pi$
$660$	−38.4287	−1.49583
$661$	18.8057	0.731455	0.365728	−	0.930722i	$-0.380820\pi$
$661$	18.8057	0.731455	0.365728	+	0.930722i	$0.380820\pi$
$662$	−75.6681	−2.94093
$663$	−32.8600	−1.27618
$664$	−51.0482	−1.98105
$665$	−25.8071	−1.00076
$666$	−3.91616	−0.151748
$667$	11.5517	0.447284
$668$	62.0984	2.40266
$669$	23.2114	0.897404
$670$	4.05609	0.156701
$671$	−20.2458	−0.781581
$672$	−74.5307	−2.87509
$673$	45.1145	1.73904	0.869518	−	0.493901i	$-0.164430\pi$
$673$	45.1145	1.73904	0.869518	+	0.493901i	$0.164430\pi$
$674$	18.5677	0.715202
$675$	19.0279	0.732384
$676$	25.5719	0.983535
$677$	−9.06201	−0.348281	−0.174141	−	0.984721i	$-0.555715\pi$
$677$	−9.06201	−0.348281	−0.174141	+	0.984721i	$0.555715\pi$
$678$	−66.0986	−2.53850
$679$	11.1053	0.426183
$680$	−77.8968	−2.98721
$681$	−21.1893	−0.811976
$682$	31.7236	1.21476
$683$	38.2738	1.46451	0.732254	−	0.681032i	$-0.238469\pi$
$683$	38.2738	1.46451	0.732254	+	0.681032i	$0.238469\pi$
$684$	68.6365	2.62438
$685$	−6.24249	−0.238513
$686$	54.6749	2.08750
$687$	−23.5981	−0.900324
$688$	14.1090	0.537901
$689$	40.9781	1.56114
$690$	−5.81789	−0.221483
$691$	−6.52529	−0.248234	−0.124117	−	0.992268i	$-0.539610\pi$
$691$	−6.52529	−0.248234	−0.124117	+	0.992268i	$0.539610\pi$
$692$	23.7783	0.903915
$693$	14.7110	0.558826
$694$	−46.1550	−1.75202
$695$	−0.233195	−0.00884561
$696$	−108.059	−4.09597
$697$	34.5797	1.30980
$698$	60.3873	2.28569
$699$	13.6931	0.517921
$700$	−45.8041	−1.73123
$701$	−12.1342	−0.458303	−0.229151	−	0.973391i	$-0.573595\pi$
$701$	−12.1342	−0.458303	−0.229151	+	0.973391i	$0.573595\pi$
$702$	−64.2155	−2.42366
$703$	8.62095	0.325145
$704$	−156.850	−5.91152
$705$	7.09984	0.267395
$706$	−6.12126	−0.230377
$707$	−0.278307	−0.0104668
$708$	52.1615	1.96035
$709$	−27.4134	−1.02953	−0.514766	−	0.857331i	$-0.672121\pi$
$709$	−27.4134	−1.02953	−0.514766	+	0.857331i	$0.672121\pi$
$710$	−49.2946	−1.84999
$711$	−10.7130	−0.401770
$712$	−185.871	−6.96582
$713$	3.54010	0.132578
$714$	−51.5858	−1.93055
$715$	22.8465	0.854411
$716$	103.068	3.85182
$717$	4.76239	0.177855
$718$	46.3547	1.72994
$719$	8.65479	0.322769	0.161385	−	0.986892i	$-0.448404\pi$
$719$	8.65479	0.322769	0.161385	+	0.986892i	$0.448404\pi$
$720$	−28.9175	−1.07769
$721$	34.0373	1.26761
$722$	−152.582	−5.67853
$723$	−16.6181	−0.618034
$724$	−54.2398	−2.01581
$725$	−29.5902	−1.09895
$726$	−27.2851	−1.01264
$727$	−23.4223	−0.868684	−0.434342	−	0.900748i	$-0.643019\pi$
$727$	−23.4223	−0.868684	−0.434342	+	0.900748i	$0.643019\pi$
$728$	99.4450	3.68568
$729$	24.8203	0.919271
$730$	−18.6535	−0.690395
$731$	5.42375	0.200605
$732$	32.8515	1.21423
$733$	9.11720	0.336751	0.168376	−	0.985723i	$-0.446148\pi$
$733$	9.11720	0.336751	0.168376	+	0.985723i	$0.446148\pi$
$734$	−87.4715	−3.22863
$735$	−2.06844	−0.0762954
$736$	−33.2357	−1.22508
$737$	5.08987	0.187488
$738$	21.7085	0.799102
$739$	−20.8406	−0.766634	−0.383317	−	0.923617i	$-0.625218\pi$
$739$	−20.8406	−0.766634	−0.383317	+	0.923617i	$0.625218\pi$
$740$	−7.03759	−0.258707
$741$	45.4121	1.66825
$742$	64.3302	2.36164
$743$	−31.8288	−1.16768	−0.583842	−	0.811867i	$-0.698451\pi$
$743$	−31.8288	−1.16768	−0.583842	+	0.811867i	$0.698451\pi$
$744$	−33.1155	−1.21407
$745$	17.7211	0.649250
$746$	−17.0154	−0.622976
$747$	−7.28493	−0.266541
$748$	−151.946	−5.55569
$749$	6.73217	0.245988
$750$	36.6600	1.33863
$751$	42.5080	1.55114	0.775569	−	0.631263i	$-0.217463\pi$
$751$	42.5080	1.55114	0.775569	+	0.631263i	$0.217463\pi$
$752$	73.0263	2.66299
$753$	25.6722	0.935548
$754$	99.8612	3.63673
$755$	4.24696	0.154563
$756$	−74.3065	−2.70250
$757$	−11.0716	−0.402404	−0.201202	−	0.979550i	$-0.564485\pi$
$757$	−11.0716	−0.402404	−0.201202	+	0.979550i	$0.564485\pi$
$758$	−15.7010	−0.570285
$759$	−7.30069	−0.264998
$760$	107.652	3.90497
$761$	38.4906	1.39528	0.697642	−	0.716447i	$-0.254233\pi$
$761$	38.4906	1.39528	0.697642	+	0.716447i	$0.254233\pi$
$762$	0.807729	0.0292609
$763$	2.38515	0.0863482
$764$	−59.2051	−2.14196
$765$	−11.1164	−0.401915
$766$	50.0267	1.80754
$767$	−31.0110	−1.11974
$768$	82.1390	2.96393
$769$	−15.8554	−0.571759	−0.285880	−	0.958266i	$-0.592286\pi$
$769$	−15.8554	−0.571759	−0.285880	+	0.958266i	$0.592286\pi$
$770$	35.8660	1.29252
$771$	−22.7293	−0.818574
$772$	−146.858	−5.28553
$773$	50.2707	1.80811	0.904056	−	0.427415i	$-0.140576\pi$
$773$	50.2707	1.80811	0.904056	+	0.427415i	$0.140576\pi$
$774$	3.40494	0.122388
$775$	−9.06812	−0.325737
$776$	−46.3250	−1.66297
$777$	−2.99822	−0.107561
$778$	−51.1987	−1.83556
$779$	−47.7887	−1.71221
$780$	−37.0715	−1.32737
$781$	−61.8582	−2.21346
$782$	−23.0038	−0.822614
$783$	−48.0032	−1.71549
$784$	−21.2752	−0.759827
$785$	21.4616	0.765996
$786$	13.2490	0.472575
$787$	11.2433	0.400779	0.200390	−	0.979716i	$-0.435779\pi$
$787$	11.2433	0.400779	0.200390	+	0.979716i	$0.435779\pi$
$788$	−88.0221	−3.13566
$789$	7.58093	0.269888
$790$	−26.1188	−0.929264
$791$	45.4720	1.61680
$792$	−61.3660	−2.18054
$793$	−19.5308	−0.693559
$794$	68.3118	2.42430
$795$	−15.4277	−0.547163
$796$	0.281617	0.00998167
$797$	10.8114	0.382960	0.191480	−	0.981497i	$-0.438671\pi$
$797$	10.8114	0.382960	0.191480	+	0.981497i	$0.438671\pi$
$798$	71.2910	2.52367
$799$	28.0726	0.993137
$800$	85.1346	3.00996
$801$	−26.5251	−0.937218
$802$	22.3726	0.790004
$803$	−23.4076	−0.826038
$804$	−8.25898	−0.291272
$805$	4.00237	0.141065
$806$	30.6032	1.07795
$807$	−1.97636	−0.0695712
$808$	1.16094	0.0408416
$809$	44.0854	1.54996	0.774980	−	0.631986i	$-0.217760\pi$
$809$	44.0854	1.54996	0.774980	+	0.631986i	$0.217760\pi$
$810$	9.43107	0.331374
$811$	−39.3783	−1.38276	−0.691379	−	0.722492i	$-0.742996\pi$
$811$	−39.3783	−1.38276	−0.691379	+	0.722492i	$0.742996\pi$
$812$	115.554	4.05514
$813$	−32.6738	−1.14592
$814$	−11.9812	−0.419939
$815$	29.8481	1.04553
$816$	127.247	4.45453
$817$	−7.49556	−0.262236
$818$	23.9791	0.838410
$819$	14.1915	0.495891
$820$	39.0116	1.36234
$821$	−44.5103	−1.55342	−0.776711	−	0.629858i	$-0.783113\pi$
$821$	−44.5103	−1.55342	−0.776711	+	0.629858i	$0.783113\pi$
$822$	17.2446	0.601474
$823$	10.5105	0.366374	0.183187	−	0.983078i	$-0.441359\pi$
$823$	10.5105	0.366374	0.183187	+	0.983078i	$0.441359\pi$
$824$	−141.984	−4.94625
$825$	18.7010	0.651086
$826$	−48.6831	−1.69390
$827$	−39.5348	−1.37476	−0.687380	−	0.726298i	$-0.741239\pi$
$827$	−39.5348	−1.37476	−0.687380	+	0.726298i	$0.741239\pi$
$828$	−10.6447	−0.369928
$829$	6.04907	0.210093	0.105047	−	0.994467i	$-0.466501\pi$
$829$	6.04907	0.210093	0.105047	+	0.994467i	$0.466501\pi$
$830$	−17.7609	−0.616490
$831$	19.2661	0.668335
$832$	−151.311	−5.24577
$833$	−8.17854	−0.283370
$834$	0.644192	0.0223065
$835$	13.8993	0.481006
$836$	209.987	7.26257
$837$	−14.7109	−0.508483
$838$	44.2368	1.52813
$839$	13.1688	0.454638	0.227319	−	0.973820i	$-0.427004\pi$
$839$	13.1688	0.454638	0.227319	+	0.973820i	$0.427004\pi$
$840$	−37.4397	−1.29179
$841$	45.6495	1.57412
$842$	54.4310	1.87581
$843$	−31.1111	−1.07152
$844$	−65.6849	−2.26097
$845$	5.72370	0.196901
$846$	17.6235	0.605908
$847$	18.7705	0.644963
$848$	−158.683	−5.44921
$849$	14.3038	0.490905
$850$	58.9252	2.02112
$851$	−1.33700	−0.0458319
$852$	100.373	3.43873
$853$	5.63477	0.192931	0.0964655	−	0.995336i	$-0.469246\pi$
$853$	5.63477	0.192931	0.0964655	+	0.995336i	$0.469246\pi$
$854$	−30.6608	−1.04919
$855$	15.3627	0.525395
$856$	−28.0827	−0.959848
$857$	−18.2956	−0.624965	−0.312482	−	0.949924i	$-0.601161\pi$
$857$	−18.2956	−0.624965	−0.312482	+	0.949924i	$0.601161\pi$
$858$	−63.1124	−2.15462
$859$	10.3210	0.352147	0.176073	−	0.984377i	$-0.443660\pi$
$859$	10.3210	0.352147	0.176073	+	0.984377i	$0.443660\pi$
$860$	6.11889	0.208652
$861$	16.6201	0.566412
$862$	30.6695	1.04461
$863$	4.08768	0.139146	0.0695731	−	0.997577i	$-0.477836\pi$
$863$	4.08768	0.139146	0.0695731	+	0.997577i	$0.477836\pi$
$864$	138.111	4.69863
$865$	5.32224	0.180962
$866$	−54.3179	−1.84580
$867$	27.5463	0.935521
$868$	35.4122	1.20197
$869$	−32.7756	−1.11184
$870$	−37.5964	−1.27464
$871$	4.91011	0.166373
$872$	−9.94947	−0.336931
$873$	−6.61089	−0.223745
$874$	31.7909	1.07534
$875$	−25.2199	−0.852588
$876$	37.9820	1.28329
$877$	−57.1754	−1.93068	−0.965338	−	0.261002i	$-0.915947\pi$
$877$	−57.1754	−1.93068	−0.965338	+	0.261002i	$0.915947\pi$
$878$	39.2250	1.32378
$879$	−23.8223	−0.803507
$880$	−88.4708	−2.98235
$881$	25.4426	0.857183	0.428592	−	0.903498i	$-0.359010\pi$
$881$	25.4426	0.857183	0.428592	+	0.903498i	$0.359010\pi$
$882$	−5.13435	−0.172882
$883$	−6.35425	−0.213838	−0.106919	−	0.994268i	$-0.534098\pi$
$883$	−6.35425	−0.213838	−0.106919	+	0.994268i	$0.534098\pi$
$884$	−146.580	−4.93001
$885$	11.6752	0.392458
$886$	41.8542	1.40612
$887$	−19.1155	−0.641834	−0.320917	−	0.947107i	$-0.603991\pi$
$887$	−19.1155	−0.641834	−0.320917	+	0.947107i	$0.603991\pi$
$888$	12.5069	0.419702
$889$	−0.555671	−0.0186366
$890$	−64.6691	−2.16771
$891$	11.8348	0.396479
$892$	103.540	3.46677
$893$	−38.7960	−1.29826
$894$	−48.9536	−1.63725
$895$	23.0694	0.771125
$896$	−118.957	−3.97407
$897$	−7.04285	−0.235154
$898$	−87.3767	−2.91580
$899$	22.8769	0.762986
$900$	27.2668	0.908893
$901$	−61.0007	−2.03223
$902$	66.4154	2.21139
$903$	2.60683	0.0867498
$904$	−189.683	−6.30876
$905$	−12.1404	−0.403559
$906$	−11.7320	−0.389771
$907$	49.0647	1.62917	0.814583	−	0.580047i	$-0.196966\pi$
$907$	49.0647	1.62917	0.814583	+	0.580047i	$0.196966\pi$
$908$	−94.5199	−3.13675
$909$	0.165674	0.00549505
$910$	34.5993	1.14696
$911$	32.4699	1.07578	0.537888	−	0.843017i	$-0.319222\pi$
$911$	32.4699	1.07578	0.537888	+	0.843017i	$0.319222\pi$
$912$	−175.854	−5.82309
$913$	−22.2876	−0.737612
$914$	33.1060	1.09505
$915$	7.35308	0.243085
$916$	−105.265	−3.47805
$917$	−9.11451	−0.300988
$918$	95.5923	3.15502
$919$	−6.78879	−0.223941	−0.111971	−	0.993712i	$-0.535716\pi$
$919$	−6.78879	−0.223941	−0.111971	+	0.993712i	$0.535716\pi$
$920$	−16.6956	−0.550437
$921$	−5.25420	−0.173132
$922$	47.7200	1.57157
$923$	−59.6736	−1.96418
$924$	−73.0301	−2.40251
$925$	3.42479	0.112606
$926$	−97.3222	−3.19821
$927$	−20.2621	−0.665494
$928$	−214.776	−7.05036
$929$	10.9723	0.359991	0.179996	−	0.983667i	$-0.442392\pi$
$929$	10.9723	0.359991	0.179996	+	0.983667i	$0.442392\pi$
$930$	−11.5217	−0.377811
$931$	11.3026	0.370429
$932$	61.0814	2.00079
$933$	−29.1614	−0.954703
$934$	1.50195	0.0491455
$935$	−34.0097	−1.11224
$936$	−59.1987	−1.93497
$937$	−58.6047	−1.91453	−0.957266	−	0.289211i	$-0.906607\pi$
$937$	−58.6047	−1.91453	−0.957266	+	0.289211i	$0.906607\pi$
$938$	7.70823	0.251683
$939$	25.5590	0.834087
$940$	31.6705	1.03298
$941$	45.3489	1.47833	0.739166	−	0.673523i	$-0.235220\pi$
$941$	45.3489	1.47833	0.739166	+	0.673523i	$0.235220\pi$
$942$	−59.2865	−1.93166
$943$	7.41144	0.241350
$944$	120.087	3.90849
$945$	−16.6319	−0.541034
$946$	10.4171	0.338690
$947$	−4.94163	−0.160581	−0.0802907	−	0.996771i	$-0.525585\pi$
$947$	−4.94163	−0.160581	−0.0802907	+	0.996771i	$0.525585\pi$
$948$	53.1828	1.72730
$949$	−22.5810	−0.733009
$950$	−81.4339	−2.64206
$951$	−29.7162	−0.963613
$952$	−148.036	−4.79786
$953$	−2.57723	−0.0834848	−0.0417424	−	0.999128i	$-0.513291\pi$
$953$	−2.57723	−0.0834848	−0.0417424	+	0.999128i	$0.513291\pi$
$954$	−38.2952	−1.23985
$955$	−13.2517	−0.428816
$956$	21.2438	0.687074
$957$	−47.1786	−1.52507
$958$	10.0316	0.324105
$959$	−11.8633	−0.383085
$960$	56.9665	1.83859
$961$	−23.9892	−0.773846
$962$	−11.5580	−0.372646
$963$	−4.00760	−0.129143
$964$	−74.1290	−2.38754
$965$	−32.8708	−1.05815
$966$	−11.0564	−0.355732
$967$	29.2183	0.939596	0.469798	−	0.882774i	$-0.344327\pi$
$967$	29.2183	0.939596	0.469798	+	0.882774i	$0.344327\pi$
$968$	−78.2999	−2.51665
$969$	−67.6012	−2.17166
$970$	−16.1176	−0.517504
$971$	37.9966	1.21937	0.609684	−	0.792645i	$-0.291296\pi$
$971$	37.9966	1.21937	0.609684	+	0.792645i	$0.291296\pi$
$972$	74.2580	2.38183
$973$	−0.443166	−0.0142073
$974$	−29.2057	−0.935811
$975$	18.0406	0.577761
$976$	75.6310	2.42089
$977$	41.0347	1.31281	0.656407	−	0.754407i	$-0.272075\pi$
$977$	41.0347	1.31281	0.656407	+	0.754407i	$0.272075\pi$
$978$	−82.4541	−2.63659
$979$	−81.1513	−2.59361
$980$	−9.22675	−0.294738
$981$	−1.41986	−0.0453325
$982$	−16.0246	−0.511364
$983$	29.4434	0.939099	0.469550	−	0.882906i	$-0.344416\pi$
$983$	29.4434	0.939099	0.469550	+	0.882906i	$0.344416\pi$
$984$	−69.3295	−2.21014
$985$	−19.7018	−0.627751
$986$	−148.655	−4.73415
$987$	13.4926	0.429474
$988$	202.571	6.44466
$989$	1.16247	0.0369643
$990$	−21.3507	−0.678570
$991$	−1.49719	−0.0475599	−0.0237800	−	0.999717i	$-0.507570\pi$
$991$	−1.49719	−0.0475599	−0.0237800	+	0.999717i	$0.507570\pi$
$992$	−65.8195	−2.08977
$993$	34.4862	1.09439
$994$	−93.6797	−2.97134
$995$	0.0630338	0.00199831
$996$	36.1646	1.14592
$997$	15.4718	0.489996	0.244998	−	0.969524i	$-0.421213\pi$
$997$	15.4718	0.489996	0.244998	+	0.969524i	$0.421213\pi$
$998$	107.176	3.39261
$999$	5.55593	0.175782

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.e.1.1	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.e.1.1	✓	82	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)

\(f(q)\)	\(=\)	\(q-2.75814 q^{2} +1.25704 q^{3} +5.60732 q^{4} +1.25507 q^{5} -3.46708 q^{6} +2.38515 q^{7} -9.94947 q^{8} -1.41986 q^{9} +O(q^{10})\)	\(q-2.75814 q^{2} +1.25704 q^{3} +5.60732 q^{4} +1.25507 q^{5} -3.46708 q^{6} +2.38515 q^{7} -9.94947 q^{8} -1.41986 q^{9} -3.46166 q^{10} -4.34393 q^{11} +7.04861 q^{12} -4.19052 q^{13} -6.57856 q^{14} +1.57767 q^{15} +16.2274 q^{16} +6.23808 q^{17} +3.91616 q^{18} -8.62095 q^{19} +7.03759 q^{20} +2.99822 q^{21} +11.9812 q^{22} +1.33700 q^{23} -12.5069 q^{24} -3.42479 q^{25} +11.5580 q^{26} -5.55593 q^{27} +13.3743 q^{28} +8.63999 q^{29} -4.35144 q^{30} +2.64779 q^{31} -24.8583 q^{32} -5.46049 q^{33} -17.2055 q^{34} +2.99353 q^{35} -7.96159 q^{36} -1.00000 q^{37} +23.7778 q^{38} -5.26764 q^{39} -12.4873 q^{40} +5.54332 q^{41} -8.26950 q^{42} +0.869458 q^{43} -24.3578 q^{44} -1.78202 q^{45} -3.68764 q^{46} +4.50020 q^{47} +20.3984 q^{48} -1.31107 q^{49} +9.44604 q^{50} +7.84150 q^{51} -23.4976 q^{52} -9.77876 q^{53} +15.3240 q^{54} -5.45195 q^{55} -23.7310 q^{56} -10.8369 q^{57} -23.8303 q^{58} +7.40026 q^{59} +8.84651 q^{60} +4.66071 q^{61} -7.30296 q^{62} -3.38657 q^{63} +36.1079 q^{64} -5.25941 q^{65} +15.0608 q^{66} -1.17172 q^{67} +34.9789 q^{68} +1.68066 q^{69} -8.25658 q^{70} +14.2401 q^{71} +14.1268 q^{72} +5.38858 q^{73} +2.75814 q^{74} -4.30509 q^{75} -48.3404 q^{76} -10.3609 q^{77} +14.5289 q^{78} +7.54515 q^{79} +20.3665 q^{80} -2.72443 q^{81} -15.2892 q^{82} +5.13075 q^{83} +16.8120 q^{84} +7.82924 q^{85} -2.39808 q^{86} +10.8608 q^{87} +43.2198 q^{88} +18.6815 q^{89} +4.91506 q^{90} -9.99501 q^{91} +7.49700 q^{92} +3.32837 q^{93} -12.4122 q^{94} -10.8199 q^{95} -31.2478 q^{96} +4.65603 q^{97} +3.61610 q^{98} +6.16776 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9}+O(q^{10}) \) 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9	\( 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9} + 13 q^{10} + 2 q^{11} + 36 q^{12} + 23 q^{13} + 24 q^{14} + 35 q^{15} + 104 q^{16} + 43 q^{17} + 42 q^{18} + 15 q^{19} + 59 q^{20} + 9 q^{21} + 6 q^{22} + 70 q^{23} + 15 q^{24} + 98 q^{25} + 10 q^{26} + 65 q^{27} + 37 q^{28} + 27 q^{29} + 17 q^{30} + 59 q^{31} + 46 q^{32} + 16 q^{33} - 16 q^{34} + 80 q^{35} + 88 q^{36} - 82 q^{37} + 82 q^{38} + 13 q^{39} + 14 q^{40} + 3 q^{41} + 62 q^{42} + 7 q^{43} - 11 q^{44} + 42 q^{45} - 11 q^{46} + 123 q^{47} + 45 q^{48} + 105 q^{49} + 27 q^{50} + 3 q^{51} - 30 q^{52} + 82 q^{53} - 27 q^{54} + 37 q^{55} + 66 q^{56} + 29 q^{57} - 34 q^{58} + 60 q^{59} + 94 q^{60} + 9 q^{61} - 2 q^{62} + 106 q^{63} + 93 q^{64} + 9 q^{65} + 63 q^{66} + 113 q^{68} + 48 q^{69} + 47 q^{70} + 59 q^{71} + 63 q^{72} + 21 q^{73} - 10 q^{74} + 77 q^{75} + 22 q^{76} + 30 q^{77} + 29 q^{78} + 55 q^{79} + 88 q^{80} + 42 q^{81} + 4 q^{82} + 92 q^{83} + 43 q^{84} - 7 q^{85} + 17 q^{86} + 147 q^{87} - 13 q^{88} + 100 q^{89} + 91 q^{90} + 28 q^{91} + 127 q^{92} + 3 q^{93} + 30 q^{94} + 48 q^{95} - 31 q^{96} + 53 q^{97} + 101 q^{98} - 20 q^{99}+O(q^{100}) \) 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9 + 13 * q^10 + 2 * q^11 + 36 * q^12 + 23 * q^13 + 24 * q^14 + 35 * q^15 + 104 * q^16 + 43 * q^17 + 42 * q^18 + 15 * q^19 + 59 * q^20 + 9 * q^21 + 6 * q^22 + 70 * q^23 + 15 * q^24 + 98 * q^25 + 10 * q^26 + 65 * q^27 + 37 * q^28 + 27 * q^29 + 17 * q^30 + 59 * q^31 + 46 * q^32 + 16 * q^33 - 16 * q^34 + 80 * q^35 + 88 * q^36 - 82 * q^37 + 82 * q^38 + 13 * q^39 + 14 * q^40 + 3 * q^41 + 62 * q^42 + 7 * q^43 - 11 * q^44 + 42 * q^45 - 11 * q^46 + 123 * q^47 + 45 * q^48 + 105 * q^49 + 27 * q^50 + 3 * q^51 - 30 * q^52 + 82 * q^53 - 27 * q^54 + 37 * q^55 + 66 * q^56 + 29 * q^57 - 34 * q^58 + 60 * q^59 + 94 * q^60 + 9 * q^61 - 2 * q^62 + 106 * q^63 + 93 * q^64 + 9 * q^65 + 63 * q^66 + 113 * q^68 + 48 * q^69 + 47 * q^70 + 59 * q^71 + 63 * q^72 + 21 * q^73 - 10 * q^74 + 77 * q^75 + 22 * q^76 + 30 * q^77 + 29 * q^78 + 55 * q^79 + 88 * q^80 + 42 * q^81 + 4 * q^82 + 92 * q^83 + 43 * q^84 - 7 * q^85 + 17 * q^86 + 147 * q^87 - 13 * q^88 + 100 * q^89 + 91 * q^90 + 28 * q^91 + 127 * q^92 + 3 * q^93 + 30 * q^94 + 48 * q^95 - 31 * q^96 + 53 * q^97 + 101 * q^98 - 20 * q^99

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