LMFDB - Embedded newform 4033.2.a.d.1.74

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.2036671352$
Analytic rank:	$1$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.74
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)

$f(q)$	$=$	$q+2.41408 q^{2} -3.32951 q^{3} +3.82777 q^{4} +0.246258 q^{5} -8.03770 q^{6} +3.51170 q^{7} +4.41239 q^{8} +8.08565 q^{9} +O(q^{10})$	\(q+2.41408 q^{2} -3.32951 q^{3} +3.82777 q^{4} +0.246258 q^{5} -8.03770 q^{6} +3.51170 q^{7} +4.41239 q^{8} +8.08565 q^{9} +0.594487 q^{10} -5.06069 q^{11} -12.7446 q^{12} +2.29244 q^{13} +8.47752 q^{14} -0.819919 q^{15} +2.99631 q^{16} -7.51584 q^{17} +19.5194 q^{18} -5.50590 q^{19} +0.942621 q^{20} -11.6922 q^{21} -12.2169 q^{22} -3.95169 q^{23} -14.6911 q^{24} -4.93936 q^{25} +5.53414 q^{26} -16.9327 q^{27} +13.4420 q^{28} +4.89294 q^{29} -1.97935 q^{30} +7.61908 q^{31} -1.59146 q^{32} +16.8496 q^{33} -18.1438 q^{34} +0.864785 q^{35} +30.9500 q^{36} -1.00000 q^{37} -13.2917 q^{38} -7.63271 q^{39} +1.08659 q^{40} -6.91725 q^{41} -28.2260 q^{42} +6.54367 q^{43} -19.3712 q^{44} +1.99116 q^{45} -9.53968 q^{46} -13.1925 q^{47} -9.97624 q^{48} +5.33203 q^{49} -11.9240 q^{50} +25.0241 q^{51} +8.77495 q^{52} +8.83631 q^{53} -40.8769 q^{54} -1.24624 q^{55} +15.4950 q^{56} +18.3320 q^{57} +11.8119 q^{58} -4.19328 q^{59} -3.13847 q^{60} +3.69939 q^{61} +18.3931 q^{62} +28.3944 q^{63} -9.83452 q^{64} +0.564533 q^{65} +40.6763 q^{66} +4.19323 q^{67} -28.7690 q^{68} +13.1572 q^{69} +2.08766 q^{70} -13.4595 q^{71} +35.6770 q^{72} -4.40081 q^{73} -2.41408 q^{74} +16.4456 q^{75} -21.0753 q^{76} -17.7716 q^{77} -18.4260 q^{78} +4.45280 q^{79} +0.737865 q^{80} +32.1207 q^{81} -16.6988 q^{82} +5.03966 q^{83} -44.7553 q^{84} -1.85084 q^{85} +15.7969 q^{86} -16.2911 q^{87} -22.3297 q^{88} -2.19007 q^{89} +4.80681 q^{90} +8.05037 q^{91} -15.1262 q^{92} -25.3678 q^{93} -31.8476 q^{94} -1.35587 q^{95} +5.29879 q^{96} +13.1153 q^{97} +12.8719 q^{98} -40.9190 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) $ 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.41408	1.70701	0.853506	−	0.521084i	$-0.174472\pi$
$2$	2.41408	1.70701	0.853506	+	0.521084i	$0.174472\pi$
$3$	−3.32951	−1.92229	−0.961147	−	0.276036i	$-0.910979\pi$
$3$	−3.32951	−1.92229	−0.961147	+	0.276036i	$0.910979\pi$
$4$	3.82777	1.91389
$5$	0.246258	0.110130	0.0550650	−	0.998483i	$-0.482463\pi$
$5$	0.246258	0.110130	0.0550650	+	0.998483i	$0.482463\pi$
$6$	−8.03770	−3.28138
$7$	3.51170	1.32730	0.663649	−	0.748044i	$-0.269007\pi$
$7$	3.51170	1.32730	0.663649	+	0.748044i	$0.269007\pi$
$8$	4.41239	1.56002
$9$	8.08565	2.69522
$10$	0.594487	0.187993
$11$	−5.06069	−1.52586	−0.762928	−	0.646483i	$-0.776239\pi$
$11$	−5.06069	−1.52586	−0.762928	+	0.646483i	$0.776239\pi$
$12$	−12.7446	−3.67905
$13$	2.29244	0.635809	0.317905	−	0.948123i	$-0.397021\pi$
$13$	2.29244	0.635809	0.317905	+	0.948123i	$0.397021\pi$
$14$	8.47752	2.26571
$15$	−0.819919	−0.211702
$16$	2.99631	0.749077
$17$	−7.51584	−1.82286	−0.911430	−	0.411455i	$-0.865021\pi$
$17$	−7.51584	−1.82286	−0.911430	+	0.411455i	$0.865021\pi$
$18$	19.5194	4.60076
$19$	−5.50590	−1.26314	−0.631570	−	0.775319i	$-0.717589\pi$
$19$	−5.50590	−1.26314	−0.631570	+	0.775319i	$0.717589\pi$
$20$	0.942621	0.210776
$21$	−11.6922	−2.55146
$22$	−12.2169	−2.60465
$23$	−3.95169	−0.823983	−0.411992	−	0.911188i	$-0.635167\pi$
$23$	−3.95169	−0.823983	−0.411992	+	0.911188i	$0.635167\pi$
$24$	−14.6911	−2.99881
$25$	−4.93936	−0.987871
$26$	5.53414	1.08533
$27$	−16.9327	−3.25870
$28$	13.4420	2.54030
$29$	4.89294	0.908595	0.454298	−	0.890850i	$-0.349890\pi$
$29$	4.89294	0.908595	0.454298	+	0.890850i	$0.349890\pi$
$30$	−1.97935	−0.361378
$31$	7.61908	1.36843	0.684214	−	0.729281i	$-0.260145\pi$
$31$	7.61908	1.36843	0.684214	+	0.729281i	$0.260145\pi$
$32$	−1.59146	−0.281333
$33$	16.8496	2.93314
$34$	−18.1438	−3.11164
$35$	0.864785	0.146175
$36$	30.9500	5.15834
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−13.2917	−2.15619
$39$	−7.63271	−1.22221
$40$	1.08659	0.171805
$41$	−6.91725	−1.08029	−0.540147	−	0.841571i	$-0.681631\pi$
$41$	−6.91725	−1.08029	−0.540147	+	0.841571i	$0.681631\pi$
$42$	−28.2260	−4.35536
$43$	6.54367	0.997900	0.498950	−	0.866631i	$-0.333719\pi$
$43$	6.54367	0.997900	0.498950	+	0.866631i	$0.333719\pi$
$44$	−19.3712	−2.92032
$45$	1.99116	0.296824
$46$	−9.53968	−1.40655
$47$	−13.1925	−1.92432	−0.962159	−	0.272490i	$-0.912153\pi$
$47$	−13.1925	−1.92432	−0.962159	+	0.272490i	$0.912153\pi$
$48$	−9.97624	−1.43995
$49$	5.33203	0.761719
$50$	−11.9240	−1.68631
$51$	25.0241	3.50407
$52$	8.77495	1.21687
$53$	8.83631	1.21376	0.606880	−	0.794793i	$-0.292421\pi$
$53$	8.83631	1.21376	0.606880	+	0.794793i	$0.292421\pi$
$54$	−40.8769	−5.56264
$55$	−1.24624	−0.168043
$56$	15.4950	2.07060
$57$	18.3320	2.42813
$58$	11.8119	1.55098
$59$	−4.19328	−0.545919	−0.272959	−	0.962026i	$-0.588002\pi$
$59$	−4.19328	−0.545919	−0.272959	+	0.962026i	$0.588002\pi$
$60$	−3.13847	−0.405174
$61$	3.69939	0.473658	0.236829	−	0.971551i	$-0.423892\pi$
$61$	3.69939	0.473658	0.236829	+	0.971551i	$0.423892\pi$
$62$	18.3931	2.33592
$63$	28.3944	3.57735
$64$	−9.83452	−1.22932
$65$	0.564533	0.0700217
$66$	40.6763	5.00691
$67$	4.19323	0.512285	0.256142	−	0.966639i	$-0.417548\pi$
$67$	4.19323	0.512285	0.256142	+	0.966639i	$0.417548\pi$
$68$	−28.7690	−3.48875
$69$	13.1572	1.58394
$70$	2.08766	0.249523
$71$	−13.4595	−1.59735	−0.798674	−	0.601764i	$-0.794465\pi$
$71$	−13.4595	−1.59735	−0.798674	+	0.601764i	$0.794465\pi$
$72$	35.6770	4.20458
$73$	−4.40081	−0.515076	−0.257538	−	0.966268i	$-0.582911\pi$
$73$	−4.40081	−0.515076	−0.257538	+	0.966268i	$0.582911\pi$
$74$	−2.41408	−0.280631
$75$	16.4456	1.89898
$76$	−21.0753	−2.41751
$77$	−17.7716	−2.02527
$78$	−18.4260	−2.08633
$79$	4.45280	0.500979	0.250489	−	0.968119i	$-0.419408\pi$
$79$	4.45280	0.500979	0.250489	+	0.968119i	$0.419408\pi$
$80$	0.737865	0.0824958
$81$	32.1207	3.56897
$82$	−16.6988	−1.84407
$83$	5.03966	0.553175	0.276588	−	0.960989i	$-0.410796\pi$
$83$	5.03966	0.553175	0.276588	+	0.960989i	$0.410796\pi$
$84$	−44.7553	−4.88320
$85$	−1.85084	−0.200752
$86$	15.7969	1.70343
$87$	−16.2911	−1.74659
$88$	−22.3297	−2.38036
$89$	−2.19007	−0.232147	−0.116074	−	0.993241i	$-0.537031\pi$
$89$	−2.19007	−0.232147	−0.116074	+	0.993241i	$0.537031\pi$
$90$	4.80681	0.506682
$91$	8.05037	0.843908
$92$	−15.1262	−1.57701
$93$	−25.3678	−2.63052
$94$	−31.8476	−3.28483
$95$	−1.35587	−0.139110
$96$	5.29879	0.540805
$97$	13.1153	1.33166	0.665831	−	0.746103i	$-0.268077\pi$
$97$	13.1153	1.33166	0.665831	+	0.746103i	$0.268077\pi$
$98$	12.8719	1.30026
$99$	−40.9190	−4.11251
$100$	−18.9067	−1.89067
$101$	−14.1992	−1.41288	−0.706439	−	0.707774i	$-0.749699\pi$
$101$	−14.1992	−1.41288	−0.706439	+	0.707774i	$0.749699\pi$
$102$	60.4101	5.98149
$103$	−16.0881	−1.58521	−0.792604	−	0.609737i	$-0.791275\pi$
$103$	−16.0881	−1.58521	−0.792604	+	0.609737i	$0.791275\pi$
$104$	10.1152	0.991872
$105$	−2.87931	−0.280992
$106$	21.3315	2.07190
$107$	−9.85253	−0.952480	−0.476240	−	0.879315i	$-0.658001\pi$
$107$	−9.85253	−0.952480	−0.476240	+	0.879315i	$0.658001\pi$
$108$	−64.8146	−6.23679
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	−3.00851	−0.286851
$111$	3.32951	0.316023
$112$	10.5221	0.994248
$113$	2.04391	0.192275	0.0961374	−	0.995368i	$-0.469351\pi$
$113$	2.04391	0.192275	0.0961374	+	0.995368i	$0.469351\pi$
$114$	44.2548	4.14484
$115$	−0.973135	−0.0907453
$116$	18.7291	1.73895
$117$	18.5359	1.71364
$118$	−10.1229	−0.931889
$119$	−26.3934	−2.41948
$120$	−3.61780	−0.330259
$121$	14.6106	1.32824
$122$	8.93062	0.808540
$123$	23.0311	2.07664
$124$	29.1641	2.61902
$125$	−2.44765	−0.218924
$126$	68.5462	6.10658
$127$	−1.54683	−0.137259	−0.0686296	−	0.997642i	$-0.521863\pi$
$127$	−1.54683	−0.137259	−0.0686296	+	0.997642i	$0.521863\pi$
$128$	−20.5584	−1.81712
$129$	−21.7872	−1.91826
$130$	1.36283	0.119528
$131$	1.56273	0.136536	0.0682682	−	0.997667i	$-0.478253\pi$
$131$	1.56273	0.136536	0.0682682	+	0.997667i	$0.478253\pi$
$132$	64.4966	5.61371
$133$	−19.3351	−1.67656
$134$	10.1228	0.874476
$135$	−4.16982	−0.358881
$136$	−33.1628	−2.84369
$137$	−4.17516	−0.356708	−0.178354	−	0.983966i	$-0.557077\pi$
$137$	−4.17516	−0.356708	−0.178354	+	0.983966i	$0.557077\pi$
$138$	31.7625	2.70380
$139$	13.5354	1.14806	0.574028	−	0.818836i	$-0.305380\pi$
$139$	13.5354	1.14806	0.574028	+	0.818836i	$0.305380\pi$
$140$	3.31020	0.279763
$141$	43.9244	3.69910
$142$	−32.4923	−2.72669
$143$	−11.6013	−0.970153
$144$	24.2271	2.01892
$145$	1.20493	0.100064
$146$	−10.6239	−0.879241
$147$	−17.7531	−1.46425
$148$	−3.82777	−0.314641
$149$	7.45974	0.611126	0.305563	−	0.952172i	$-0.401155\pi$
$149$	7.45974	0.611126	0.305563	+	0.952172i	$0.401155\pi$
$150$	39.7011	3.24158
$151$	−14.9176	−1.21398	−0.606990	−	0.794709i	$-0.707623\pi$
$151$	−14.9176	−1.21398	−0.606990	+	0.794709i	$0.707623\pi$
$152$	−24.2942	−1.97052
$153$	−60.7705	−4.91300
$154$	−42.9021	−3.45715
$155$	1.87626	0.150705
$156$	−29.2163	−2.33918
$157$	−21.1909	−1.69122	−0.845611	−	0.533800i	$-0.820763\pi$
$157$	−21.1909	−1.69122	−0.845611	+	0.533800i	$0.820763\pi$
$158$	10.7494	0.855176
$159$	−29.4206	−2.33320
$160$	−0.391910	−0.0309832
$161$	−13.8771	−1.09367
$162$	77.5420	6.09227
$163$	−12.0449	−0.943428	−0.471714	−	0.881752i	$-0.656364\pi$
$163$	−12.0449	−0.943428	−0.471714	+	0.881752i	$0.656364\pi$
$164$	−26.4777	−2.06756
$165$	4.14936	0.323027
$166$	12.1661	0.944276
$167$	−6.40640	−0.495742	−0.247871	−	0.968793i	$-0.579731\pi$
$167$	−6.40640	−0.495742	−0.247871	+	0.968793i	$0.579731\pi$
$168$	−51.5907	−3.98031
$169$	−7.74471	−0.595747
$170$	−4.46807	−0.342685
$171$	−44.5188	−3.40443
$172$	25.0477	1.90987
$173$	8.74308	0.664724	0.332362	−	0.943152i	$-0.392154\pi$
$173$	8.74308	0.664724	0.332362	+	0.943152i	$0.392154\pi$
$174$	−39.3280	−2.98144
$175$	−17.3455	−1.31120
$176$	−15.1634	−1.14298
$177$	13.9616	1.04942
$178$	−5.28700	−0.396278
$179$	23.1016	1.72669	0.863346	−	0.504612i	$-0.168364\pi$
$179$	23.1016	1.72669	0.863346	+	0.504612i	$0.168364\pi$
$180$	7.62170	0.568088
$181$	12.2530	0.910760	0.455380	−	0.890297i	$-0.349503\pi$
$181$	12.2530	0.910760	0.455380	+	0.890297i	$0.349503\pi$
$182$	19.4342	1.44056
$183$	−12.3172	−0.910511
$184$	−17.4364	−1.28543
$185$	−0.246258	−0.0181053
$186$	−61.2399	−4.49033
$187$	38.0354	2.78142
$188$	−50.4977	−3.68293
$189$	−59.4626	−4.32527
$190$	−3.27318	−0.237462
$191$	−5.19074	−0.375589	−0.187794	−	0.982208i	$-0.560134\pi$
$191$	−5.19074	−0.375589	−0.187794	+	0.982208i	$0.560134\pi$
$192$	32.7442	2.36311
$193$	3.10161	0.223259	0.111629	−	0.993750i	$-0.464393\pi$
$193$	3.10161	0.223259	0.111629	+	0.993750i	$0.464393\pi$
$194$	31.6615	2.27316
$195$	−1.87962	−0.134602
$196$	20.4098	1.45784
$197$	22.5086	1.60367	0.801834	−	0.597546i	$-0.203858\pi$
$197$	22.5086	1.60367	0.801834	+	0.597546i	$0.203858\pi$
$198$	−98.7816	−7.02010
$199$	−5.47997	−0.388465	−0.194232	−	0.980956i	$-0.562222\pi$
$199$	−5.47997	−0.388465	−0.194232	+	0.980956i	$0.562222\pi$
$200$	−21.7944	−1.54109
$201$	−13.9614	−0.984762
$202$	−34.2781	−2.41180
$203$	17.1825	1.20598
$204$	95.7866	6.70640
$205$	−1.70343	−0.118973
$206$	−38.8380	−2.70597
$207$	−31.9519	−2.22081
$208$	6.86886	0.476270
$209$	27.8637	1.92737
$210$	−6.95088	−0.479656
$211$	5.83899	0.401973	0.200986	−	0.979594i	$-0.435585\pi$
$211$	5.83899	0.401973	0.200986	+	0.979594i	$0.435585\pi$
$212$	33.8234	2.32300
$213$	44.8136	3.07057
$214$	−23.7848	−1.62589
$215$	1.61143	0.109899
$216$	−74.7138	−5.08363
$217$	26.7559	1.81631
$218$	−2.41408	−0.163502
$219$	14.6526	0.990128
$220$	−4.77031	−0.321614
$221$	−17.2296	−1.15899
$222$	8.03770	0.539455
$223$	9.93204	0.665098	0.332549	−	0.943086i	$-0.392091\pi$
$223$	9.93204	0.665098	0.332549	+	0.943086i	$0.392091\pi$
$224$	−5.58873	−0.373413
$225$	−39.9379	−2.66253
$226$	4.93416	0.328215
$227$	−16.0747	−1.06692	−0.533458	−	0.845827i	$-0.679108\pi$
$227$	−16.0747	−1.06692	−0.533458	+	0.845827i	$0.679108\pi$
$228$	70.1706	4.64716
$229$	−11.2207	−0.741486	−0.370743	−	0.928735i	$-0.620897\pi$
$229$	−11.2207	−0.741486	−0.370743	+	0.928735i	$0.620897\pi$
$230$	−2.34922	−0.154903
$231$	59.1708	3.89316
$232$	21.5895	1.41742
$233$	−15.8092	−1.03569	−0.517847	−	0.855473i	$-0.673266\pi$
$233$	−15.8092	−1.03569	−0.517847	+	0.855473i	$0.673266\pi$
$234$	44.7471	2.92521
$235$	−3.24875	−0.211925
$236$	−16.0509	−1.04483
$237$	−14.8256	−0.963029
$238$	−63.7157	−4.13008
$239$	−8.97551	−0.580578	−0.290289	−	0.956939i	$-0.593751\pi$
$239$	−8.97551	−0.580578	−0.290289	+	0.956939i	$0.593751\pi$
$240$	−2.45673	−0.158581
$241$	22.1051	1.42391	0.711956	−	0.702224i	$-0.247809\pi$
$241$	22.1051	1.42391	0.711956	+	0.702224i	$0.247809\pi$
$242$	35.2711	2.26732
$243$	−56.1482	−3.60191
$244$	14.1604	0.906529
$245$	1.31306	0.0838881
$246$	55.5988	3.54485
$247$	−12.6220	−0.803116
$248$	33.6184	2.13477
$249$	−16.7796	−1.06337
$250$	−5.90881	−0.373706
$251$	6.67902	0.421576	0.210788	−	0.977532i	$-0.432397\pi$
$251$	6.67902	0.421576	0.210788	+	0.977532i	$0.432397\pi$
$252$	108.687	6.84665
$253$	19.9983	1.25728
$254$	−3.73418	−0.234303
$255$	6.16239	0.385904
$256$	−29.9605	−1.87253
$257$	12.0657	0.752636	0.376318	−	0.926491i	$-0.377190\pi$
$257$	12.0657	0.752636	0.376318	+	0.926491i	$0.377190\pi$
$258$	−52.5961	−3.27449
$259$	−3.51170	−0.218206
$260$	2.16090	0.134014
$261$	39.5625	2.44886
$262$	3.77256	0.233069
$263$	6.33121	0.390399	0.195200	−	0.980764i	$-0.437465\pi$
$263$	6.33121	0.390399	0.195200	+	0.980764i	$0.437465\pi$
$264$	74.3471	4.57575
$265$	2.17601	0.133671
$266$	−46.6764	−2.86191
$267$	7.29187	0.446255
$268$	16.0507	0.980455
$269$	−11.0809	−0.675616	−0.337808	−	0.941215i	$-0.609686\pi$
$269$	−11.0809	−0.675616	−0.337808	+	0.941215i	$0.609686\pi$
$270$	−10.0663	−0.612614
$271$	−25.3939	−1.54257	−0.771286	−	0.636488i	$-0.780386\pi$
$271$	−25.3939	−1.54257	−0.771286	+	0.636488i	$0.780386\pi$
$272$	−22.5198	−1.36546
$273$	−26.8038	−1.62224
$274$	−10.0792	−0.608904
$275$	24.9966	1.50735
$276$	50.3627	3.03148
$277$	−7.42263	−0.445982	−0.222991	−	0.974820i	$-0.571582\pi$
$277$	−7.42263	−0.445982	−0.222991	+	0.974820i	$0.571582\pi$
$278$	32.6755	1.95975
$279$	61.6052	3.68821
$280$	3.81577	0.228036
$281$	21.0587	1.25626	0.628128	−	0.778110i	$-0.283822\pi$
$281$	21.0587	1.25626	0.628128	+	0.778110i	$0.283822\pi$
$282$	106.037	6.31441
$283$	−3.17673	−0.188837	−0.0944184	−	0.995533i	$-0.530099\pi$
$283$	−3.17673	−0.188837	−0.0944184	+	0.995533i	$0.530099\pi$
$284$	−51.5199	−3.05714
$285$	4.51439	0.267410
$286$	−28.0066	−1.65606
$287$	−24.2913	−1.43387
$288$	−12.8680	−0.758254
$289$	39.4879	2.32282
$290$	2.90878	0.170810
$291$	−43.6677	−2.55985
$292$	−16.8453	−0.985798
$293$	−9.06120	−0.529361	−0.264680	−	0.964336i	$-0.585266\pi$
$293$	−9.06120	−0.529361	−0.264680	+	0.964336i	$0.585266\pi$
$294$	−42.8573	−2.49949
$295$	−1.03263	−0.0601220
$296$	−4.41239	−0.256465
$297$	85.6913	4.97231
$298$	18.0084	1.04320
$299$	−9.05901	−0.523896
$300$	62.9502	3.63443
$301$	22.9794	1.32451
$302$	−36.0124	−2.07228
$303$	47.2765	2.71597
$304$	−16.4974	−0.946189
$305$	0.911005	0.0521640
$306$	−146.705	−8.38655
$307$	−6.62980	−0.378382	−0.189191	−	0.981940i	$-0.560587\pi$
$307$	−6.62980	−0.378382	−0.189191	+	0.981940i	$0.560587\pi$
$308$	−68.0258	−3.87613
$309$	53.5655	3.04724
$310$	4.52944	0.257255
$311$	−16.0717	−0.911341	−0.455671	−	0.890149i	$-0.650600\pi$
$311$	−16.0717	−0.911341	−0.455671	+	0.890149i	$0.650600\pi$
$312$	−33.6785	−1.90667
$313$	0.123693	0.00699156	0.00349578	−	0.999994i	$-0.498887\pi$
$313$	0.123693	0.00699156	0.00349578	+	0.999994i	$0.498887\pi$
$314$	−51.1566	−2.88693
$315$	6.99234	0.393974
$316$	17.0443	0.958817
$317$	−2.10202	−0.118061	−0.0590307	−	0.998256i	$-0.518801\pi$
$317$	−2.10202	−0.118061	−0.0590307	+	0.998256i	$0.518801\pi$
$318$	−71.0236	−3.98281
$319$	−24.7616	−1.38639
$320$	−2.42183	−0.135385
$321$	32.8041	1.83095
$322$	−33.5005	−1.86691
$323$	41.3815	2.30253
$324$	122.951	6.83061
$325$	−11.3232	−0.628098
$326$	−29.0773	−1.61044
$327$	3.32951	0.184122
$328$	−30.5216	−1.68527
$329$	−46.3279	−2.55414
$330$	10.0169	0.551411
$331$	−9.06000	−0.497983	−0.248991	−	0.968506i	$-0.580099\pi$
$331$	−9.06000	−0.497983	−0.248991	+	0.968506i	$0.580099\pi$
$332$	19.2907	1.05871
$333$	−8.08565	−0.443091
$334$	−15.4656	−0.846238
$335$	1.03262	0.0564179
$336$	−35.0335	−1.91124
$337$	29.1115	1.58580	0.792902	−	0.609349i	$-0.208569\pi$
$337$	29.1115	1.58580	0.792902	+	0.609349i	$0.208569\pi$
$338$	−18.6963	−1.01695
$339$	−6.80522	−0.369609
$340$	−7.08459	−0.384216
$341$	−38.5578	−2.08802
$342$	−107.472	−5.81141
$343$	−5.85740	−0.316270
$344$	28.8732	1.55674
$345$	3.24006	0.174439
$346$	21.1065	1.13469
$347$	9.71901	0.521744	0.260872	−	0.965373i	$-0.415990\pi$
$347$	9.71901	0.521744	0.260872	+	0.965373i	$0.415990\pi$
$348$	−62.3586	−3.34277
$349$	17.1723	0.919210	0.459605	−	0.888123i	$-0.347991\pi$
$349$	17.1723	0.919210	0.459605	+	0.888123i	$0.347991\pi$
$350$	−41.8735	−2.23823
$351$	−38.8173	−2.07191
$352$	8.05389	0.429274
$353$	−23.6353	−1.25798	−0.628991	−	0.777413i	$-0.716532\pi$
$353$	−23.6353	−1.25798	−0.628991	+	0.777413i	$0.716532\pi$
$354$	33.7043	1.79137
$355$	−3.31451	−0.175916
$356$	−8.38310	−0.444303
$357$	87.8771	4.65095
$358$	55.7690	2.94748
$359$	−18.2338	−0.962342	−0.481171	−	0.876627i	$-0.659788\pi$
$359$	−18.2338	−0.962342	−0.481171	+	0.876627i	$0.659788\pi$
$360$	8.78576	0.463050
$361$	11.3149	0.595523
$362$	29.5798	1.55468
$363$	−48.6462	−2.55326
$364$	30.8150	1.61514
$365$	−1.08374	−0.0567254
$366$	−29.7346	−1.55425
$367$	−6.12612	−0.319781	−0.159890	−	0.987135i	$-0.551114\pi$
$367$	−6.12612	−0.319781	−0.159890	+	0.987135i	$0.551114\pi$
$368$	−11.8405	−0.617227
$369$	−55.9305	−2.91162
$370$	−0.594487	−0.0309059
$371$	31.0305	1.61102
$372$	−97.1023	−5.03452
$373$	31.4488	1.62835	0.814177	−	0.580616i	$-0.197188\pi$
$373$	31.4488	1.62835	0.814177	+	0.580616i	$0.197188\pi$
$374$	91.8204	4.74792
$375$	8.14947	0.420837
$376$	−58.2103	−3.00196
$377$	11.2168	0.577693
$378$	−143.547	−7.38328
$379$	−6.30320	−0.323773	−0.161887	−	0.986809i	$-0.551758\pi$
$379$	−6.30320	−0.323773	−0.161887	+	0.986809i	$0.551758\pi$
$380$	−5.18998	−0.266240
$381$	5.15020	0.263853
$382$	−12.5308	−0.641134
$383$	−0.784369	−0.0400794	−0.0200397	−	0.999799i	$-0.506379\pi$
$383$	−0.784369	−0.0400794	−0.0200397	+	0.999799i	$0.506379\pi$
$384$	68.4494	3.49304
$385$	−4.37641	−0.223042
$386$	7.48753	0.381105
$387$	52.9098	2.68956
$388$	50.2026	2.54865
$389$	0.330769	0.0167706	0.00838532	−	0.999965i	$-0.497331\pi$
$389$	0.330769	0.0167706	0.00838532	+	0.999965i	$0.497331\pi$
$390$	−4.53755	−0.229768
$391$	29.7003	1.50201
$392$	23.5270	1.18829
$393$	−5.20313	−0.262463
$394$	54.3374	2.73748
$395$	1.09654	0.0551728
$396$	−156.629	−7.87088
$397$	−12.3299	−0.618821	−0.309411	−	0.950929i	$-0.600132\pi$
$397$	−12.3299	−0.618821	−0.309411	+	0.950929i	$0.600132\pi$
$398$	−13.2291	−0.663114
$399$	64.3763	3.22285
$400$	−14.7998	−0.739991
$401$	−33.9003	−1.69290	−0.846450	−	0.532468i	$-0.821265\pi$
$401$	−33.9003	−1.69290	−0.846450	+	0.532468i	$0.821265\pi$
$402$	−33.7039	−1.68100
$403$	17.4663	0.870059
$404$	−54.3515	−2.70409
$405$	7.91000	0.393051
$406$	41.4799	2.05862
$407$	5.06069	0.250849
$408$	110.416	5.46641
$409$	10.0631	0.497589	0.248795	−	0.968556i	$-0.419966\pi$
$409$	10.0631	0.497589	0.248795	+	0.968556i	$0.419966\pi$
$410$	−4.11221	−0.203088
$411$	13.9012	0.685697
$412$	−61.5816	−3.03391
$413$	−14.7255	−0.724597
$414$	−77.1345	−3.79095
$415$	1.24106	0.0609212
$416$	−3.64833	−0.178874
$417$	−45.0662	−2.20690
$418$	67.2651	3.29004
$419$	21.3114	1.04113	0.520564	−	0.853823i	$-0.325722\pi$
$419$	21.3114	1.04113	0.520564	+	0.853823i	$0.325722\pi$
$420$	−11.0214	−0.537787
$421$	31.8108	1.55036	0.775182	−	0.631738i	$-0.217658\pi$
$421$	31.8108	1.55036	0.775182	+	0.631738i	$0.217658\pi$
$422$	14.0958	0.686172
$423$	−106.670	−5.18645
$424$	38.9892	1.89348
$425$	37.1234	1.80075
$426$	108.183	5.24150
$427$	12.9911	0.628686
$428$	−37.7132	−1.82294
$429$	38.6268	1.86492
$430$	3.89012	0.187598
$431$	19.1864	0.924175	0.462087	−	0.886834i	$-0.347101\pi$
$431$	19.1864	0.924175	0.462087	+	0.886834i	$0.347101\pi$
$432$	−50.7356	−2.44102
$433$	−12.4956	−0.600499	−0.300249	−	0.953861i	$-0.597070\pi$
$433$	−12.4956	−0.600499	−0.300249	+	0.953861i	$0.597070\pi$
$434$	64.5909	3.10046
$435$	−4.01181	−0.192352
$436$	−3.82777	−0.183317
$437$	21.7576	1.04081
$438$	35.3724	1.69016
$439$	−11.6371	−0.555409	−0.277705	−	0.960667i	$-0.589574\pi$
$439$	−11.6371	−0.555409	−0.277705	+	0.960667i	$0.589574\pi$
$440$	−5.49888	−0.262149
$441$	43.1129	2.05300
$442$	−41.5937	−1.97841
$443$	3.04326	0.144590	0.0722948	−	0.997383i	$-0.476968\pi$
$443$	3.04326	0.144590	0.0722948	+	0.997383i	$0.476968\pi$
$444$	12.7446	0.604833
$445$	−0.539323	−0.0255664
$446$	23.9767	1.13533
$447$	−24.8373	−1.17476
$448$	−34.5359	−1.63167
$449$	23.2729	1.09832	0.549159	−	0.835718i	$-0.314948\pi$
$449$	23.2729	1.09832	0.549159	+	0.835718i	$0.314948\pi$
$450$	−96.4132	−4.54496
$451$	35.0061	1.64837
$452$	7.82362	0.367992
$453$	49.6685	2.33363
$454$	−38.8056	−1.82124
$455$	1.98247	0.0929396
$456$	80.8877	3.78792
$457$	−16.8972	−0.790415	−0.395208	−	0.918592i	$-0.629327\pi$
$457$	−16.8972	−0.790415	−0.395208	+	0.918592i	$0.629327\pi$
$458$	−27.0877	−1.26572
$459$	127.264	5.94016
$460$	−3.72494	−0.173676
$461$	−12.2736	−0.571640	−0.285820	−	0.958283i	$-0.592266\pi$
$461$	−12.2736	−0.571640	−0.285820	+	0.958283i	$0.592266\pi$
$462$	142.843	6.64566
$463$	31.6911	1.47281	0.736404	−	0.676542i	$-0.236522\pi$
$463$	31.6911	1.47281	0.736404	+	0.676542i	$0.236522\pi$
$464$	14.6607	0.680607
$465$	−6.24704	−0.289699
$466$	−38.1646	−1.76794
$467$	−20.1411	−0.932021	−0.466011	−	0.884779i	$-0.654309\pi$
$467$	−20.1411	−0.932021	−0.466011	+	0.884779i	$0.654309\pi$
$468$	70.9512	3.27972
$469$	14.7254	0.679954
$470$	−7.84274	−0.361758
$471$	70.5555	3.25103
$472$	−18.5024	−0.851642
$473$	−33.1155	−1.52265
$474$	−35.7902	−1.64390
$475$	27.1956	1.24782
$476$	−101.028	−4.63061
$477$	71.4473	3.27135
$478$	−21.6676	−0.991052
$479$	29.3547	1.34125	0.670625	−	0.741796i	$-0.266026\pi$
$479$	29.3547	1.34125	0.670625	+	0.741796i	$0.266026\pi$
$480$	1.30487	0.0595589
$481$	−2.29244	−0.104526
$482$	53.3634	2.43063
$483$	46.2041	2.10236
$484$	55.9261	2.54210
$485$	3.22976	0.146656
$486$	−135.546	−6.14850
$487$	33.3404	1.51080	0.755398	−	0.655266i	$-0.227444\pi$
$487$	33.3404	1.51080	0.755398	+	0.655266i	$0.227444\pi$
$488$	16.3232	0.738914
$489$	40.1036	1.81355
$490$	3.16982	0.143198
$491$	27.4862	1.24043	0.620217	−	0.784430i	$-0.287045\pi$
$491$	27.4862	1.24043	0.620217	+	0.784430i	$0.287045\pi$
$492$	88.1577	3.97446
$493$	−36.7745	−1.65624
$494$	−30.4704	−1.37093
$495$	−10.0766	−0.452911
$496$	22.8291	1.02506
$497$	−47.2657	−2.12016
$498$	−40.5073	−1.81518
$499$	−34.0117	−1.52257	−0.761286	−	0.648416i	$-0.775432\pi$
$499$	−34.0117	−1.52257	−0.761286	+	0.648416i	$0.775432\pi$
$500$	−9.36904	−0.418996
$501$	21.3302	0.952963
$502$	16.1237	0.719635
$503$	26.9733	1.20268	0.601340	−	0.798993i	$-0.294634\pi$
$503$	26.9733	1.20268	0.601340	+	0.798993i	$0.294634\pi$
$504$	125.287	5.58073
$505$	−3.49668	−0.155600
$506$	48.2774	2.14619
$507$	25.7861	1.14520
$508$	−5.92093	−0.262699
$509$	−16.8126	−0.745204	−0.372602	−	0.927991i	$-0.621534\pi$
$509$	−16.8126	−0.745204	−0.372602	+	0.927991i	$0.621534\pi$
$510$	14.8765	0.658742
$511$	−15.4543	−0.683660
$512$	−31.2103	−1.37931
$513$	93.2298	4.11620
$514$	29.1275	1.28476
$515$	−3.96183	−0.174579
$516$	−83.3966	−3.67133
$517$	66.7629	2.93623
$518$	−8.47752	−0.372481
$519$	−29.1102	−1.27779
$520$	2.49094	0.109235
$521$	31.1634	1.36529	0.682647	−	0.730749i	$-0.260829\pi$
$521$	31.1634	1.36529	0.682647	+	0.730749i	$0.260829\pi$
$522$	95.5071	4.18023
$523$	8.48206	0.370895	0.185447	−	0.982654i	$-0.440627\pi$
$523$	8.48206	0.370895	0.185447	+	0.982654i	$0.440627\pi$
$524$	5.98178	0.261315
$525$	57.7522	2.52051
$526$	15.2840	0.666416
$527$	−57.2639	−2.49445
$528$	50.4867	2.19715
$529$	−7.38418	−0.321051
$530$	5.25307	0.228179
$531$	−33.9054	−1.47137
$532$	−74.0103	−3.20875
$533$	−15.8574	−0.686861
$534$	17.6031	0.761762
$535$	−2.42627	−0.104897
$536$	18.5022	0.799172
$537$	−76.9170	−3.31921
$538$	−26.7502	−1.15328
$539$	−26.9838	−1.16227
$540$	−15.9611	−0.686858
$541$	20.6894	0.889508	0.444754	−	0.895653i	$-0.353291\pi$
$541$	20.6894	0.889508	0.444754	+	0.895653i	$0.353291\pi$
$542$	−61.3030	−2.63319
$543$	−40.7966	−1.75075
$544$	11.9612	0.512831
$545$	−0.246258	−0.0105485
$546$	−64.7065	−2.76918
$547$	−30.1856	−1.29064	−0.645321	−	0.763912i	$-0.723276\pi$
$547$	−30.1856	−1.29064	−0.645321	+	0.763912i	$0.723276\pi$
$548$	−15.9816	−0.682699
$549$	29.9120	1.27661
$550$	60.3437	2.57306
$551$	−26.9400	−1.14768
$552$	58.0546	2.47097
$553$	15.6369	0.664948
$554$	−17.9188	−0.761297
$555$	0.819919	0.0348036
$556$	51.8104	2.19725
$557$	13.8072	0.585028	0.292514	−	0.956261i	$-0.405508\pi$
$557$	13.8072	0.585028	0.292514	+	0.956261i	$0.405508\pi$
$558$	148.720	6.29581
$559$	15.0010	0.634474
$560$	2.59116	0.109497
$561$	−126.639	−5.34671
$562$	50.8373	2.14444
$563$	28.7056	1.20980	0.604898	−	0.796303i	$-0.293214\pi$
$563$	28.7056	1.20980	0.604898	+	0.796303i	$0.293214\pi$
$564$	168.133	7.07967
$565$	0.503329	0.0211752
$566$	−7.66887	−0.322347
$567$	112.798	4.73709
$568$	−59.3886	−2.49189
$569$	−36.0715	−1.51220	−0.756099	−	0.654457i	$-0.772897\pi$
$569$	−36.0715	−1.51220	−0.756099	+	0.654457i	$0.772897\pi$
$570$	10.8981	0.456471
$571$	−18.6781	−0.781653	−0.390827	−	0.920464i	$-0.627811\pi$
$571$	−18.6781	−0.781653	−0.390827	+	0.920464i	$0.627811\pi$
$572$	−44.4073	−1.85676
$573$	17.2826	0.721992
$574$	−58.6411	−2.44763
$575$	19.5188	0.813990
$576$	−79.5185	−3.31327
$577$	−17.1072	−0.712182	−0.356091	−	0.934451i	$-0.615891\pi$
$577$	−17.1072	−0.712182	−0.356091	+	0.934451i	$0.615891\pi$
$578$	95.3269	3.96508
$579$	−10.3268	−0.429169
$580$	4.61218	0.191510
$581$	17.6978	0.734228
$582$	−105.417	−4.36969
$583$	−44.7178	−1.85202
$584$	−19.4181	−0.803527
$585$	4.56461	0.188723
$586$	−21.8744	−0.903625
$587$	−37.4686	−1.54649	−0.773247	−	0.634105i	$-0.781369\pi$
$587$	−37.4686	−1.54649	−0.773247	+	0.634105i	$0.781369\pi$
$588$	−67.9547	−2.80241
$589$	−41.9499	−1.72852
$590$	−2.49285	−0.102629
$591$	−74.9425	−3.08272
$592$	−2.99631	−0.123147
$593$	2.10137	0.0862928	0.0431464	−	0.999069i	$-0.486262\pi$
$593$	2.10137	0.0862928	0.0431464	+	0.999069i	$0.486262\pi$
$594$	206.865	8.48779
$595$	−6.49959	−0.266457
$596$	28.5542	1.16963
$597$	18.2456	0.746744
$598$	−21.8692	−0.894297
$599$	−0.929673	−0.0379854	−0.0189927	−	0.999820i	$-0.506046\pi$
$599$	−0.929673	−0.0379854	−0.0189927	+	0.999820i	$0.506046\pi$
$600$	72.5646	2.96244
$601$	−38.9616	−1.58928	−0.794638	−	0.607084i	$-0.792339\pi$
$601$	−38.9616	−1.58928	−0.794638	+	0.607084i	$0.792339\pi$
$602$	55.4741	2.26095
$603$	33.9050	1.38072
$604$	−57.1014	−2.32342
$605$	3.59798	0.146279
$606$	114.129	4.63618
$607$	14.7518	0.598758	0.299379	−	0.954134i	$-0.403221\pi$
$607$	14.7518	0.598758	0.299379	+	0.954134i	$0.403221\pi$
$608$	8.76243	0.355363
$609$	−57.2094	−2.31824
$610$	2.19924	0.0890445
$611$	−30.2429	−1.22350
$612$	−232.616	−9.40293
$613$	−15.8186	−0.638907	−0.319454	−	0.947602i	$-0.603499\pi$
$613$	−15.8186	−0.638907	−0.319454	+	0.947602i	$0.603499\pi$
$614$	−16.0048	−0.645903
$615$	5.67159	0.228701
$616$	−78.4154	−3.15944
$617$	21.6594	0.871976	0.435988	−	0.899952i	$-0.356399\pi$
$617$	21.6594	0.871976	0.435988	+	0.899952i	$0.356399\pi$
$618$	129.311	5.20167
$619$	24.3164	0.977360	0.488680	−	0.872463i	$-0.337479\pi$
$619$	24.3164	0.977360	0.488680	+	0.872463i	$0.337479\pi$
$620$	7.18191	0.288432
$621$	66.9128	2.68512
$622$	−38.7983	−1.55567
$623$	−7.69087	−0.308128
$624$	−22.8700	−0.915531
$625$	24.0940	0.963761
$626$	0.298605	0.0119347
$627$	−92.7724	−3.70497
$628$	−81.1141	−3.23681
$629$	7.51584	0.299676
$630$	16.8801	0.672518
$631$	27.3143	1.08737	0.543683	−	0.839291i	$-0.317030\pi$
$631$	27.3143	1.08737	0.543683	+	0.839291i	$0.317030\pi$
$632$	19.6475	0.781535
$633$	−19.4410	−0.772710
$634$	−5.07445	−0.201532
$635$	−0.380920	−0.0151164
$636$	−112.615	−4.46549
$637$	12.2234	0.484308
$638$	−59.7765	−2.36658
$639$	−108.829	−4.30520
$640$	−5.06267	−0.200120
$641$	−8.19123	−0.323534	−0.161767	−	0.986829i	$-0.551719\pi$
$641$	−8.19123	−0.323534	−0.161767	+	0.986829i	$0.551719\pi$
$642$	79.1917	3.12545
$643$	−36.7011	−1.44735	−0.723675	−	0.690141i	$-0.757548\pi$
$643$	−36.7011	−1.44735	−0.723675	+	0.690141i	$0.757548\pi$
$644$	−53.1185	−2.09316
$645$	−5.36528	−0.211258
$646$	99.8981	3.93044
$647$	1.05932	0.0416462	0.0208231	−	0.999783i	$-0.493371\pi$
$647$	1.05932	0.0416462	0.0208231	+	0.999783i	$0.493371\pi$
$648$	141.729	5.56765
$649$	21.2209	0.832994
$650$	−27.3351	−1.07217
$651$	−89.0842	−3.49148
$652$	−46.1051	−1.80561
$653$	41.2465	1.61410	0.807051	−	0.590482i	$-0.201062\pi$
$653$	41.2465	1.61410	0.807051	+	0.590482i	$0.201062\pi$
$654$	8.03770	0.314299
$655$	0.384835	0.0150368
$656$	−20.7262	−0.809223
$657$	−35.5834	−1.38824
$658$	−111.839	−4.35995
$659$	−23.6282	−0.920422	−0.460211	−	0.887810i	$-0.652226\pi$
$659$	−23.6282	−0.920422	−0.460211	+	0.887810i	$0.652226\pi$
$660$	15.8828	0.618238
$661$	22.1553	0.861742	0.430871	−	0.902413i	$-0.358206\pi$
$661$	22.1553	0.861742	0.430871	+	0.902413i	$0.358206\pi$
$662$	−21.8716	−0.850062
$663$	57.3663	2.22792
$664$	22.2370	0.862962
$665$	−4.76142	−0.184640
$666$	−19.5194	−0.756361
$667$	−19.3353	−0.748667
$668$	−24.5223	−0.948795
$669$	−33.0688	−1.27851
$670$	2.49282	0.0963060
$671$	−18.7215	−0.722734
$672$	18.6077	0.717810
$673$	−1.36208	−0.0525043	−0.0262522	−	0.999655i	$-0.508357\pi$
$673$	−1.36208	−0.0525043	−0.0262522	+	0.999655i	$0.508357\pi$
$674$	70.2775	2.70699
$675$	83.6367	3.21918
$676$	−29.6450	−1.14019
$677$	13.4195	0.515753	0.257876	−	0.966178i	$-0.416977\pi$
$677$	13.4195	0.515753	0.257876	+	0.966178i	$0.416977\pi$
$678$	−16.4283	−0.630926
$679$	46.0572	1.76751
$680$	−8.16662	−0.313176
$681$	53.5209	2.05093
$682$	−93.0817	−3.56428
$683$	31.4629	1.20389	0.601947	−	0.798536i	$-0.294392\pi$
$683$	31.4629	1.20389	0.601947	+	0.798536i	$0.294392\pi$
$684$	−170.408	−6.51570
$685$	−1.02817	−0.0392842
$686$	−14.1402	−0.539876
$687$	37.3595	1.42535
$688$	19.6068	0.747504
$689$	20.2567	0.771720
$690$	7.82177	0.297770
$691$	−14.8216	−0.563842	−0.281921	−	0.959438i	$-0.590972\pi$
$691$	−14.8216	−0.563842	−0.281921	+	0.959438i	$0.590972\pi$
$692$	33.4665	1.27221
$693$	−143.695	−5.45853
$694$	23.4624	0.890622
$695$	3.33320	0.126435
$696$	−71.8826	−2.72470
$697$	51.9890	1.96922
$698$	41.4552	1.56910
$699$	52.6369	1.99091
$700$	−66.3948	−2.50949
$701$	−15.6206	−0.589983	−0.294991	−	0.955500i	$-0.595317\pi$
$701$	−15.6206	−0.589983	−0.294991	+	0.955500i	$0.595317\pi$
$702$	−93.7080	−3.53678
$703$	5.50590	0.207659
$704$	49.7695	1.87576
$705$	10.8167	0.407382
$706$	−57.0575	−2.14739
$707$	−49.8635	−1.87531
$708$	53.4418	2.00846
$709$	24.1739	0.907871	0.453936	−	0.891034i	$-0.350020\pi$
$709$	24.1739	0.907871	0.453936	+	0.891034i	$0.350020\pi$
$710$	−8.00149	−0.300291
$711$	36.0037	1.35025
$712$	−9.66345	−0.362153
$713$	−30.1082	−1.12756
$714$	212.142	7.93922
$715$	−2.85693	−0.106843
$716$	88.4276	3.30470
$717$	29.8841	1.11604
$718$	−44.0178	−1.64273
$719$	10.1136	0.377175	0.188587	−	0.982056i	$-0.439609\pi$
$719$	10.1136	0.377175	0.188587	+	0.982056i	$0.439609\pi$
$720$	5.96612	0.222344
$721$	−56.4966	−2.10404
$722$	27.3151	1.01656
$723$	−73.5991	−2.73718
$724$	46.9018	1.74309
$725$	−24.1680	−0.897575
$726$	−117.436	−4.35845
$727$	−45.1399	−1.67415	−0.837073	−	0.547092i	$-0.815735\pi$
$727$	−45.1399	−1.67415	−0.837073	+	0.547092i	$0.815735\pi$
$728$	35.5214	1.31651
$729$	90.5839	3.35496
$730$	−2.61622	−0.0968308
$731$	−49.1812	−1.81903
$732$	−47.1473	−1.74261
$733$	−27.4710	−1.01466	−0.507332	−	0.861750i	$-0.669368\pi$
$733$	−27.4710	−1.01466	−0.507332	+	0.861750i	$0.669368\pi$
$734$	−14.7889	−0.545869
$735$	−4.37184	−0.161258
$736$	6.28895	0.231814
$737$	−21.2207	−0.781673
$738$	−135.021	−4.97017
$739$	−38.2409	−1.40671	−0.703357	−	0.710837i	$-0.748316\pi$
$739$	−38.2409	−1.40671	−0.703357	+	0.710837i	$0.748316\pi$
$740$	−0.942621	−0.0346514
$741$	42.0250	1.54383
$742$	74.9100	2.75003
$743$	19.9459	0.731742	0.365871	−	0.930665i	$-0.380771\pi$
$743$	19.9459	0.731742	0.365871	+	0.930665i	$0.380771\pi$
$744$	−111.933	−4.10365
$745$	1.83702	0.0673033
$746$	75.9198	2.77962
$747$	40.7489	1.49093
$748$	145.591	5.32333
$749$	−34.5991	−1.26422
$750$	19.6735	0.718373
$751$	−26.4875	−0.966543	−0.483271	−	0.875471i	$-0.660552\pi$
$751$	−26.4875	−0.966543	−0.483271	+	0.875471i	$0.660552\pi$
$752$	−39.5286	−1.44146
$753$	−22.2379	−0.810393
$754$	27.0782	0.986129
$755$	−3.67359	−0.133696
$756$	−227.609	−8.27808
$757$	−29.9728	−1.08938	−0.544690	−	0.838638i	$-0.683353\pi$
$757$	−29.9728	−1.08938	−0.544690	+	0.838638i	$0.683353\pi$
$758$	−15.2164	−0.552685
$759$	−66.5845	−2.41686
$760$	−5.98264	−0.217013
$761$	−28.1743	−1.02132	−0.510658	−	0.859784i	$-0.670598\pi$
$761$	−28.1743	−1.02132	−0.510658	+	0.859784i	$0.670598\pi$
$762$	12.4330	0.450400
$763$	−3.51170	−0.127132
$764$	−19.8690	−0.718834
$765$	−14.9652	−0.541069
$766$	−1.89353	−0.0684159
$767$	−9.61286	−0.347100
$768$	99.7539	3.59956
$769$	13.5970	0.490319	0.245159	−	0.969483i	$-0.421160\pi$
$769$	13.5970	0.490319	0.245159	+	0.969483i	$0.421160\pi$
$770$	−10.5650	−0.380736
$771$	−40.1728	−1.44679
$772$	11.8723	0.427292
$773$	12.9735	0.466626	0.233313	−	0.972402i	$-0.425043\pi$
$773$	12.9735	0.466626	0.233313	+	0.972402i	$0.425043\pi$
$774$	127.728	4.59110
$775$	−37.6334	−1.35183
$776$	57.8700	2.07741
$777$	11.6922	0.419457
$778$	0.798501	0.0286277
$779$	38.0857	1.36456
$780$	−7.19475	−0.257614
$781$	68.1144	2.43732
$782$	71.6987	2.56394
$783$	−82.8507	−2.96084
$784$	15.9764	0.570586
$785$	−5.21844	−0.186254
$786$	−12.5608	−0.448028
$787$	−9.18102	−0.327268	−0.163634	−	0.986521i	$-0.552322\pi$
$787$	−9.18102	−0.327268	−0.163634	+	0.986521i	$0.552322\pi$
$788$	86.1577	3.06924
$789$	−21.0798	−0.750462
$790$	2.64713	0.0941806
$791$	7.17759	0.255206
$792$	−180.550	−6.41558
$793$	8.48064	0.301156
$794$	−29.7654	−1.05633
$795$	−7.24506	−0.256956
$796$	−20.9761	−0.743478
$797$	19.2701	0.682583	0.341292	−	0.939957i	$-0.389136\pi$
$797$	19.2701	0.682583	0.341292	+	0.939957i	$0.389136\pi$
$798$	155.409	5.50144
$799$	99.1524	3.50776
$800$	7.86079	0.277921
$801$	−17.7081	−0.625686
$802$	−81.8380	−2.88980
$803$	22.2712	0.785932
$804$	−53.4411	−1.88472
$805$	−3.41736	−0.120446
$806$	42.1651	1.48520
$807$	36.8941	1.29873
$808$	−62.6526	−2.20411
$809$	27.0560	0.951240	0.475620	−	0.879651i	$-0.342224\pi$
$809$	27.0560	0.951240	0.475620	+	0.879651i	$0.342224\pi$
$810$	19.0953	0.670942
$811$	−6.45925	−0.226815	−0.113407	−	0.993549i	$-0.536177\pi$
$811$	−6.45925	−0.226815	−0.113407	+	0.993549i	$0.536177\pi$
$812$	65.7708	2.30810
$813$	84.5494	2.96528
$814$	12.2169	0.428202
$815$	−2.96615	−0.103900
$816$	74.9798	2.62482
$817$	−36.0288	−1.26049
$818$	24.2932	0.849391
$819$	65.0924	2.27451
$820$	−6.52035	−0.227700
$821$	−41.0934	−1.43417	−0.717086	−	0.696985i	$-0.754524\pi$
$821$	−41.0934	−1.43417	−0.717086	+	0.696985i	$0.754524\pi$
$822$	33.5587	1.17049
$823$	−19.2826	−0.672149	−0.336074	−	0.941835i	$-0.609099\pi$
$823$	−19.2826	−0.672149	−0.336074	+	0.941835i	$0.609099\pi$
$824$	−70.9870	−2.47295
$825$	−83.2263	−2.89757
$826$	−35.5486	−1.23689
$827$	−9.68264	−0.336698	−0.168349	−	0.985727i	$-0.553844\pi$
$827$	−9.68264	−0.336698	−0.168349	+	0.985727i	$0.553844\pi$
$828$	−122.305	−4.25038
$829$	25.4892	0.885275	0.442638	−	0.896701i	$-0.354043\pi$
$829$	25.4892	0.885275	0.442638	+	0.896701i	$0.354043\pi$
$830$	2.99601	0.103993
$831$	24.7137	0.857310
$832$	−22.5451	−0.781610
$833$	−40.0747	−1.38851
$834$	−108.793	−3.76721
$835$	−1.57763	−0.0545961
$836$	106.656	3.68877
$837$	−129.012	−4.45930
$838$	51.4473	1.77722
$839$	31.5929	1.09071	0.545354	−	0.838206i	$-0.316395\pi$
$839$	31.5929	1.09071	0.545354	+	0.838206i	$0.316395\pi$
$840$	−12.7046	−0.438352
$841$	−5.05918	−0.174455
$842$	76.7938	2.64649
$843$	−70.1151	−2.41489
$844$	22.3504	0.769331
$845$	−1.90720	−0.0656096
$846$	−257.509	−8.85333
$847$	51.3081	1.76297
$848$	26.4763	0.909200
$849$	10.5769	0.363000
$850$	89.6189	3.07390
$851$	3.95169	0.135462
$852$	171.536	5.87673
$853$	15.7204	0.538255	0.269128	−	0.963105i	$-0.413265\pi$
$853$	15.7204	0.538255	0.269128	+	0.963105i	$0.413265\pi$
$854$	31.3616	1.07317
$855$	−10.9631	−0.374930
$856$	−43.4732	−1.48588
$857$	47.0888	1.60852	0.804261	−	0.594277i	$-0.202562\pi$
$857$	47.0888	1.60852	0.804261	+	0.594277i	$0.202562\pi$
$858$	93.2482	3.18344
$859$	−3.55238	−0.121205	−0.0606027	−	0.998162i	$-0.519302\pi$
$859$	−3.55238	−0.121205	−0.0606027	+	0.998162i	$0.519302\pi$
$860$	6.16820	0.210334
$861$	80.8782	2.75632
$862$	46.3174	1.57758
$863$	−28.3758	−0.965922	−0.482961	−	0.875642i	$-0.660439\pi$
$863$	−28.3758	−0.965922	−0.482961	+	0.875642i	$0.660439\pi$
$864$	26.9478	0.916781
$865$	2.15305	0.0732060
$866$	−30.1653	−1.02506
$867$	−131.475	−4.46514
$868$	102.416	3.47621
$869$	−22.5342	−0.764421
$870$	−9.68483	−0.328347
$871$	9.61274	0.325715
$872$	−4.41239	−0.149422
$873$	106.046	3.58912
$874$	52.5245	1.77667
$875$	−8.59540	−0.290578
$876$	56.0867	1.89499
$877$	9.28176	0.313423	0.156711	−	0.987644i	$-0.449911\pi$
$877$	9.28176	0.313423	0.156711	+	0.987644i	$0.449911\pi$
$878$	−28.0929	−0.948089
$879$	30.1694	1.01759
$880$	−3.73411	−0.125877
$881$	−42.9846	−1.44819	−0.724094	−	0.689701i	$-0.757742\pi$
$881$	−42.9846	−1.44819	−0.724094	+	0.689701i	$0.757742\pi$
$882$	104.078	3.50449
$883$	25.1880	0.847645	0.423823	−	0.905745i	$-0.360688\pi$
$883$	25.1880	0.847645	0.423823	+	0.905745i	$0.360688\pi$
$884$	−65.9512	−2.21818
$885$	3.43815	0.115572
$886$	7.34666	0.246816
$887$	−13.5049	−0.453450	−0.226725	−	0.973959i	$-0.572802\pi$
$887$	−13.5049	−0.453450	−0.226725	+	0.973959i	$0.572802\pi$
$888$	14.6911	0.493001
$889$	−5.43202	−0.182184
$890$	−1.30197	−0.0436421
$891$	−162.553	−5.44574
$892$	38.0176	1.27292
$893$	72.6363	2.43068
$894$	−59.9592	−2.00533
$895$	5.68895	0.190161
$896$	−72.1949	−2.41186
$897$	30.1621	1.00708
$898$	56.1827	1.87484
$899$	37.2797	1.24335
$900$	−152.873	−5.09577
$901$	−66.4123	−2.21252
$902$	84.5074	2.81379
$903$	−76.5102	−2.54610
$904$	9.01852	0.299952
$905$	3.01741	0.100302
$906$	119.904	3.98353
$907$	32.3069	1.07273	0.536367	−	0.843985i	$-0.319796\pi$
$907$	32.3069	1.07273	0.536367	+	0.843985i	$0.319796\pi$
$908$	−61.5303	−2.04196
$909$	−114.810	−3.80801
$910$	4.78584	0.158649
$911$	3.87592	0.128415	0.0642076	−	0.997937i	$-0.479548\pi$
$911$	3.87592	0.128415	0.0642076	+	0.997937i	$0.479548\pi$
$912$	54.9282	1.81885
$913$	−25.5042	−0.844066
$914$	−40.7910	−1.34925
$915$	−3.03320	−0.100275
$916$	−42.9504	−1.41912
$917$	5.48784	0.181225
$918$	307.224	10.1399
$919$	7.29925	0.240780	0.120390	−	0.992727i	$-0.461585\pi$
$919$	7.29925	0.240780	0.120390	+	0.992727i	$0.461585\pi$
$920$	−4.29385	−0.141564
$921$	22.0740	0.727362
$922$	−29.6295	−0.975796
$923$	−30.8551	−1.01561
$924$	226.493	7.45106
$925$	4.93936	0.162405
$926$	76.5047	2.51410
$927$	−130.083	−4.27248
$928$	−7.78692	−0.255618
$929$	51.8707	1.70182	0.850911	−	0.525310i	$-0.176051\pi$
$929$	51.8707	1.70182	0.850911	+	0.525310i	$0.176051\pi$
$930$	−15.0808	−0.494520
$931$	−29.3576	−0.962158
$932$	−60.5140	−1.98220
$933$	53.5108	1.75187
$934$	−48.6223	−1.59097
$935$	9.36652	0.306318
$936$	81.7875	2.67331
$937$	−11.8926	−0.388514	−0.194257	−	0.980951i	$-0.562230\pi$
$937$	−11.8926	−0.388514	−0.194257	+	0.980951i	$0.562230\pi$
$938$	35.5482	1.16069
$939$	−0.411838	−0.0134398
$940$	−12.4355	−0.405601
$941$	−32.9055	−1.07269	−0.536345	−	0.843999i	$-0.680195\pi$
$941$	−32.9055	−1.07269	−0.536345	+	0.843999i	$0.680195\pi$
$942$	170.326	5.54954
$943$	27.3348	0.890144
$944$	−12.5644	−0.408935
$945$	−14.6432	−0.476342
$946$	−79.9434	−2.59918
$947$	−56.8773	−1.84826	−0.924132	−	0.382073i	$-0.875210\pi$
$947$	−56.8773	−1.84826	−0.924132	+	0.382073i	$0.875210\pi$
$948$	−56.7492	−1.84313
$949$	−10.0886	−0.327490
$950$	65.6523	2.13004
$951$	6.99871	0.226949
$952$	−116.458	−3.77442
$953$	−48.2333	−1.56243	−0.781214	−	0.624263i	$-0.785399\pi$
$953$	−48.2333	−1.56243	−0.781214	+	0.624263i	$0.785399\pi$
$954$	172.479	5.58422
$955$	−1.27826	−0.0413636
$956$	−34.3562	−1.11116
$957$	82.4442	2.66504
$958$	70.8645	2.28953
$959$	−14.6619	−0.473457
$960$	8.06352	0.260249
$961$	27.0504	0.872595
$962$	−5.53414	−0.178428
$963$	−79.6640	−2.56714
$964$	84.6132	2.72521
$965$	0.763797	0.0245875
$966$	111.540	3.58875
$967$	52.6156	1.69201	0.846003	−	0.533179i	$-0.179003\pi$
$967$	52.6156	1.69201	0.846003	+	0.533179i	$0.179003\pi$
$968$	64.4677	2.07207
$969$	−137.780	−4.42614
$970$	7.79690	0.250343
$971$	43.8224	1.40633	0.703164	−	0.711028i	$-0.251770\pi$
$971$	43.8224	1.40633	0.703164	+	0.711028i	$0.251770\pi$
$972$	−214.923	−6.89365
$973$	47.5322	1.52381
$974$	80.4862	2.57895
$975$	37.7007	1.20739
$976$	11.0845	0.354806
$977$	−2.24970	−0.0719742	−0.0359871	−	0.999352i	$-0.511458\pi$
$977$	−2.24970	−0.0719742	−0.0359871	+	0.999352i	$0.511458\pi$
$978$	96.8132	3.09574
$979$	11.0833	0.354223
$980$	5.02608	0.160552
$981$	−8.08565	−0.258155
$982$	66.3538	2.11743
$983$	−42.2244	−1.34675	−0.673374	−	0.739302i	$-0.735156\pi$
$983$	−42.2244	−1.34675	−0.673374	+	0.739302i	$0.735156\pi$
$984$	101.622	3.23959
$985$	5.54292	0.176612
$986$	−88.7766	−2.82722
$987$	154.249	4.90981
$988$	−48.3140	−1.53707
$989$	−25.8585	−0.822253
$990$	−24.3258	−0.773124
$991$	56.6291	1.79888	0.899441	−	0.437041i	$-0.143974\pi$
$991$	56.6291	1.79888	0.899441	+	0.437041i	$0.143974\pi$
$992$	−12.1255	−0.384984
$993$	30.1654	0.957270
$994$	−114.103	−3.61913
$995$	−1.34949	−0.0427816
$996$	−64.2286	−2.03516
$997$	9.21440	0.291823	0.145911	−	0.989298i	$-0.453389\pi$
$997$	9.21440	0.291823	0.145911	+	0.989298i	$0.453389\pi$
$998$	−82.1069	−2.59905
$999$	16.9327	0.535727

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.74	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.74	✓	79	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q+2.41408 q^{2} -3.32951 q^{3} +3.82777 q^{4} +0.246258 q^{5} -8.03770 q^{6} +3.51170 q^{7} +4.41239 q^{8} +8.08565 q^{9} +O(q^{10})\)	\(q+2.41408 q^{2} -3.32951 q^{3} +3.82777 q^{4} +0.246258 q^{5} -8.03770 q^{6} +3.51170 q^{7} +4.41239 q^{8} +8.08565 q^{9} +0.594487 q^{10} -5.06069 q^{11} -12.7446 q^{12} +2.29244 q^{13} +8.47752 q^{14} -0.819919 q^{15} +2.99631 q^{16} -7.51584 q^{17} +19.5194 q^{18} -5.50590 q^{19} +0.942621 q^{20} -11.6922 q^{21} -12.2169 q^{22} -3.95169 q^{23} -14.6911 q^{24} -4.93936 q^{25} +5.53414 q^{26} -16.9327 q^{27} +13.4420 q^{28} +4.89294 q^{29} -1.97935 q^{30} +7.61908 q^{31} -1.59146 q^{32} +16.8496 q^{33} -18.1438 q^{34} +0.864785 q^{35} +30.9500 q^{36} -1.00000 q^{37} -13.2917 q^{38} -7.63271 q^{39} +1.08659 q^{40} -6.91725 q^{41} -28.2260 q^{42} +6.54367 q^{43} -19.3712 q^{44} +1.99116 q^{45} -9.53968 q^{46} -13.1925 q^{47} -9.97624 q^{48} +5.33203 q^{49} -11.9240 q^{50} +25.0241 q^{51} +8.77495 q^{52} +8.83631 q^{53} -40.8769 q^{54} -1.24624 q^{55} +15.4950 q^{56} +18.3320 q^{57} +11.8119 q^{58} -4.19328 q^{59} -3.13847 q^{60} +3.69939 q^{61} +18.3931 q^{62} +28.3944 q^{63} -9.83452 q^{64} +0.564533 q^{65} +40.6763 q^{66} +4.19323 q^{67} -28.7690 q^{68} +13.1572 q^{69} +2.08766 q^{70} -13.4595 q^{71} +35.6770 q^{72} -4.40081 q^{73} -2.41408 q^{74} +16.4456 q^{75} -21.0753 q^{76} -17.7716 q^{77} -18.4260 q^{78} +4.45280 q^{79} +0.737865 q^{80} +32.1207 q^{81} -16.6988 q^{82} +5.03966 q^{83} -44.7553 q^{84} -1.85084 q^{85} +15.7969 q^{86} -16.2911 q^{87} -22.3297 q^{88} -2.19007 q^{89} +4.80681 q^{90} +8.05037 q^{91} -15.1262 q^{92} -25.3678 q^{93} -31.8476 q^{94} -1.35587 q^{95} +5.29879 q^{96} +13.1153 q^{97} +12.8719 q^{98} -40.9190 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + q^99

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