LMFDB - Embedded newform 4033.2.a.d.1.67

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			1.67
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)

$f(q)$	$=$	$q+1.95930 q^{2} -1.67058 q^{3} +1.83884 q^{4} +2.80907 q^{5} -3.27317 q^{6} +3.08365 q^{7} -0.315757 q^{8} -0.209148 q^{9} +O(q^{10})$	\(q+1.95930 q^{2} -1.67058 q^{3} +1.83884 q^{4} +2.80907 q^{5} -3.27317 q^{6} +3.08365 q^{7} -0.315757 q^{8} -0.209148 q^{9} +5.50380 q^{10} -1.74546 q^{11} -3.07194 q^{12} -2.73274 q^{13} +6.04179 q^{14} -4.69278 q^{15} -4.29634 q^{16} -0.616715 q^{17} -0.409782 q^{18} -5.70306 q^{19} +5.16543 q^{20} -5.15150 q^{21} -3.41987 q^{22} -4.59172 q^{23} +0.527498 q^{24} +2.89086 q^{25} -5.35424 q^{26} +5.36115 q^{27} +5.67035 q^{28} -7.61428 q^{29} -9.19456 q^{30} -9.29142 q^{31} -7.78630 q^{32} +2.91594 q^{33} -1.20833 q^{34} +8.66219 q^{35} -0.384589 q^{36} -1.00000 q^{37} -11.1740 q^{38} +4.56527 q^{39} -0.886981 q^{40} -2.53549 q^{41} -10.0933 q^{42} -4.26193 q^{43} -3.20962 q^{44} -0.587509 q^{45} -8.99654 q^{46} +4.53650 q^{47} +7.17741 q^{48} +2.50891 q^{49} +5.66405 q^{50} +1.03027 q^{51} -5.02507 q^{52} +4.14659 q^{53} +10.5041 q^{54} -4.90311 q^{55} -0.973683 q^{56} +9.52745 q^{57} -14.9186 q^{58} -11.7155 q^{59} -8.62929 q^{60} +12.7258 q^{61} -18.2046 q^{62} -0.644938 q^{63} -6.66298 q^{64} -7.67644 q^{65} +5.71319 q^{66} +7.61438 q^{67} -1.13404 q^{68} +7.67086 q^{69} +16.9718 q^{70} +13.4769 q^{71} +0.0660397 q^{72} +3.33881 q^{73} -1.95930 q^{74} -4.82943 q^{75} -10.4870 q^{76} -5.38239 q^{77} +8.94471 q^{78} -3.75881 q^{79} -12.0687 q^{80} -8.32881 q^{81} -4.96777 q^{82} -2.28548 q^{83} -9.47279 q^{84} -1.73239 q^{85} -8.35039 q^{86} +12.7203 q^{87} +0.551140 q^{88} +11.6178 q^{89} -1.15111 q^{90} -8.42681 q^{91} -8.44345 q^{92} +15.5221 q^{93} +8.88834 q^{94} -16.0203 q^{95} +13.0077 q^{96} +11.4355 q^{97} +4.91569 q^{98} +0.365059 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.95930	1.38543	0.692716	−	0.721211i	$-0.256414\pi$
$2$	1.95930	1.38543	0.692716	+	0.721211i	$0.256414\pi$
$3$	−1.67058	−0.964512	−0.482256	−	0.876030i	$-0.660183\pi$
$3$	−1.67058	−0.964512	−0.482256	+	0.876030i	$0.660183\pi$
$4$	1.83884	0.919421
$5$	2.80907	1.25625	0.628127	−	0.778111i	$-0.283822\pi$
$5$	2.80907	1.25625	0.628127	+	0.778111i	$0.283822\pi$
$6$	−3.27317	−1.33627
$7$	3.08365	1.16551	0.582755	−	0.812648i	$-0.301975\pi$
$7$	3.08365	1.16551	0.582755	+	0.812648i	$0.301975\pi$
$8$	−0.315757	−0.111637
$9$	−0.209148	−0.0697158
$10$	5.50380	1.74045
$11$	−1.74546	−0.526276	−0.263138	−	0.964758i	$-0.584757\pi$
$11$	−1.74546	−0.526276	−0.263138	+	0.964758i	$0.584757\pi$
$12$	−3.07194	−0.886793
$13$	−2.73274	−0.757925	−0.378962	−	0.925412i	$-0.623719\pi$
$13$	−2.73274	−0.757925	−0.378962	+	0.925412i	$0.623719\pi$
$14$	6.04179	1.61474
$15$	−4.69278	−1.21167
$16$	−4.29634	−1.07409
$17$	−0.616715	−0.149575	−0.0747877	−	0.997199i	$-0.523828\pi$
$17$	−0.616715	−0.149575	−0.0747877	+	0.997199i	$0.523828\pi$
$18$	−0.409782	−0.0965865
$19$	−5.70306	−1.30837	−0.654186	−	0.756333i	$-0.726989\pi$
$19$	−5.70306	−1.30837	−0.654186	+	0.756333i	$0.726989\pi$
$20$	5.16543	1.15503
$21$	−5.15150	−1.12415
$22$	−3.41987	−0.729119
$23$	−4.59172	−0.957440	−0.478720	−	0.877968i	$-0.658899\pi$
$23$	−4.59172	−0.957440	−0.478720	+	0.877968i	$0.658899\pi$
$24$	0.527498	0.107675
$25$	2.89086	0.578172
$26$	−5.35424	−1.05005
$27$	5.36115	1.03175
$28$	5.67035	1.07159
$29$	−7.61428	−1.41394	−0.706969	−	0.707245i	$-0.749938\pi$
$29$	−7.61428	−1.41394	−0.706969	+	0.707245i	$0.749938\pi$
$30$	−9.19456	−1.67869
$31$	−9.29142	−1.66879	−0.834394	−	0.551169i	$-0.814182\pi$
$31$	−9.29142	−1.66879	−0.834394	+	0.551169i	$0.814182\pi$
$32$	−7.78630	−1.37644
$33$	2.91594	0.507600
$34$	−1.20833	−0.207226
$35$	8.66219	1.46418
$36$	−0.384589	−0.0640982
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−11.1740	−1.81266
$39$	4.56527	0.731028
$40$	−0.886981	−0.140244
$41$	−2.53549	−0.395977	−0.197988	−	0.980204i	$-0.563441\pi$
$41$	−2.53549	−0.395977	−0.197988	+	0.980204i	$0.563441\pi$
$42$	−10.0933	−1.55743
$43$	−4.26193	−0.649939	−0.324969	−	0.945725i	$-0.605354\pi$
$43$	−4.26193	−0.649939	−0.324969	+	0.945725i	$0.605354\pi$
$44$	−3.20962	−0.483869
$45$	−0.587509	−0.0875807
$46$	−8.99654	−1.32647
$47$	4.53650	0.661716	0.330858	−	0.943681i	$-0.392662\pi$
$47$	4.53650	0.661716	0.330858	+	0.943681i	$0.392662\pi$
$48$	7.17741	1.03597
$49$	2.50891	0.358415
$50$	5.66405	0.801018
$51$	1.03027	0.144267
$52$	−5.02507	−0.696852
$53$	4.14659	0.569578	0.284789	−	0.958590i	$-0.408076\pi$
$53$	4.14659	0.569578	0.284789	+	0.958590i	$0.408076\pi$
$54$	10.5041	1.42942
$55$	−4.90311	−0.661136
$56$	−0.973683	−0.130114
$57$	9.52745	1.26194
$58$	−14.9186	−1.95891
$59$	−11.7155	−1.52523	−0.762617	−	0.646851i	$-0.776086\pi$
$59$	−11.7155	−1.52523	−0.762617	+	0.646851i	$0.776086\pi$
$60$	−8.62929	−1.11404
$61$	12.7258	1.62937	0.814686	−	0.579903i	$-0.196909\pi$
$61$	12.7258	1.62937	0.814686	+	0.579903i	$0.196909\pi$
$62$	−18.2046	−2.31199
$63$	−0.644938	−0.0812546
$64$	−6.66298	−0.832872
$65$	−7.67644	−0.952145
$66$	5.71319	0.703245
$67$	7.61438	0.930245	0.465122	−	0.885246i	$-0.346010\pi$
$67$	7.61438	0.930245	0.465122	+	0.885246i	$0.346010\pi$
$68$	−1.13404	−0.137523
$69$	7.67086	0.923463
$70$	16.9718	2.02852
$71$	13.4769	1.59942	0.799708	−	0.600389i	$-0.204988\pi$
$71$	13.4769	1.59942	0.799708	+	0.600389i	$0.204988\pi$
$72$	0.0660397	0.00778285
$73$	3.33881	0.390778	0.195389	−	0.980726i	$-0.437403\pi$
$73$	3.33881	0.390778	0.195389	+	0.980726i	$0.437403\pi$
$74$	−1.95930	−0.227764
$75$	−4.82943	−0.557654
$76$	−10.4870	−1.20295
$77$	−5.38239	−0.613380
$78$	8.94471	1.01279
$79$	−3.75881	−0.422899	−0.211450	−	0.977389i	$-0.567818\pi$
$79$	−3.75881	−0.422899	−0.211450	+	0.977389i	$0.567818\pi$
$80$	−12.0687	−1.34932
$81$	−8.32881	−0.925424
$82$	−4.96777	−0.548599
$83$	−2.28548	−0.250864	−0.125432	−	0.992102i	$-0.540032\pi$
$83$	−2.28548	−0.250864	−0.125432	+	0.992102i	$0.540032\pi$
$84$	−9.47279	−1.03357
$85$	−1.73239	−0.187905
$86$	−8.35039	−0.900446
$87$	12.7203	1.36376
$88$	0.551140	0.0587518
$89$	11.6178	1.23148	0.615740	−	0.787950i	$-0.288857\pi$
$89$	11.6178	1.23148	0.615740	+	0.787950i	$0.288857\pi$
$90$	−1.15111	−0.121337
$91$	−8.42681	−0.883369
$92$	−8.44345	−0.880290
$93$	15.5221	1.60957
$94$	8.88834	0.916762
$95$	−16.0203	−1.64365
$96$	13.0077	1.32759
$97$	11.4355	1.16110	0.580548	−	0.814226i	$-0.302838\pi$
$97$	11.4355	1.16110	0.580548	+	0.814226i	$0.302838\pi$
$98$	4.91569	0.496560
$99$	0.365059	0.0366898
$100$	5.31584	0.531584
$101$	9.95204	0.990265	0.495133	−	0.868817i	$-0.335119\pi$
$101$	9.95204	0.990265	0.495133	+	0.868817i	$0.335119\pi$
$102$	2.01861	0.199873
$103$	−12.8265	−1.26383	−0.631914	−	0.775038i	$-0.717731\pi$
$103$	−12.8265	−1.26383	−0.631914	+	0.775038i	$0.717731\pi$
$104$	0.862879	0.0846123
$105$	−14.4709	−1.41222
$106$	8.12440	0.789111
$107$	−0.920030	−0.0889427	−0.0444713	−	0.999011i	$-0.514160\pi$
$107$	−0.920030	−0.0889427	−0.0444713	+	0.999011i	$0.514160\pi$
$108$	9.85831	0.948616
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	−9.60665	−0.915959
$111$	1.67058	0.158565
$112$	−13.2484	−1.25186
$113$	−5.50559	−0.517922	−0.258961	−	0.965888i	$-0.583380\pi$
$113$	−5.50559	−0.517922	−0.258961	+	0.965888i	$0.583380\pi$
$114$	18.6671	1.74833
$115$	−12.8985	−1.20279
$116$	−14.0015	−1.30000
$117$	0.571545	0.0528393
$118$	−22.9542	−2.11311
$119$	−1.90173	−0.174332
$120$	1.48178	0.135267
$121$	−7.95337	−0.723034
$122$	24.9336	2.25738
$123$	4.23575	0.381925
$124$	−17.0854	−1.53432
$125$	−5.92471	−0.529923
$126$	−1.26362	−0.112573
$127$	−9.11494	−0.808820	−0.404410	−	0.914578i	$-0.632523\pi$
$127$	−9.11494	−0.808820	−0.404410	+	0.914578i	$0.632523\pi$
$128$	2.51785	0.222549
$129$	7.11992	0.626874
$130$	−15.0404	−1.31913
$131$	1.29821	0.113425	0.0567127	−	0.998391i	$-0.481938\pi$
$131$	1.29821	0.113425	0.0567127	+	0.998391i	$0.481938\pi$
$132$	5.36195	0.466698
$133$	−17.5863	−1.52492
$134$	14.9188	1.28879
$135$	15.0598	1.29614
$136$	0.194732	0.0166981
$137$	13.4624	1.15017	0.575087	−	0.818092i	$-0.304968\pi$
$137$	13.4624	1.15017	0.575087	+	0.818092i	$0.304968\pi$
$138$	15.0295	1.27939
$139$	8.01993	0.680241	0.340121	−	0.940382i	$-0.389532\pi$
$139$	8.01993	0.680241	0.340121	+	0.940382i	$0.389532\pi$
$140$	15.9284	1.34619
$141$	−7.57860	−0.638233
$142$	26.4053	2.21588
$143$	4.76988	0.398877
$144$	0.898570	0.0748808
$145$	−21.3890	−1.77626
$146$	6.54171	0.541396
$147$	−4.19134	−0.345696
$148$	−1.83884	−0.151152
$149$	−7.71772	−0.632260	−0.316130	−	0.948716i	$-0.602384\pi$
$149$	−7.71772	−0.632260	−0.316130	+	0.948716i	$0.602384\pi$
$150$	−9.46228	−0.772592
$151$	−7.66855	−0.624058	−0.312029	−	0.950073i	$-0.601009\pi$
$151$	−7.66855	−0.624058	−0.312029	+	0.950073i	$0.601009\pi$
$152$	1.80078	0.146063
$153$	0.128984	0.0104278
$154$	−10.5457	−0.849796
$155$	−26.1002	−2.09642
$156$	8.39480	0.672122
$157$	15.0840	1.20384	0.601918	−	0.798558i	$-0.294403\pi$
$157$	15.0840	1.20384	0.601918	+	0.798558i	$0.294403\pi$
$158$	−7.36463	−0.585898
$159$	−6.92723	−0.549365
$160$	−21.8722	−1.72915
$161$	−14.1593	−1.11591
$162$	−16.3186	−1.28211
$163$	19.3744	1.51752	0.758758	−	0.651372i	$-0.225806\pi$
$163$	19.3744	1.51752	0.758758	+	0.651372i	$0.225806\pi$
$164$	−4.66236	−0.364069
$165$	8.19107	0.637674
$166$	−4.47794	−0.347555
$167$	17.5972	1.36171	0.680855	−	0.732418i	$-0.261608\pi$
$167$	17.5972	1.36171	0.680855	+	0.732418i	$0.261608\pi$
$168$	1.62662	0.125496
$169$	−5.53215	−0.425550
$170$	−3.39427	−0.260329
$171$	1.19278	0.0912143
$172$	−7.83702	−0.597567
$173$	−17.1623	−1.30482	−0.652411	−	0.757865i	$-0.726242\pi$
$173$	−17.1623	−1.30482	−0.652411	+	0.757865i	$0.726242\pi$
$174$	24.9228	1.88940
$175$	8.91441	0.673866
$176$	7.49910	0.565266
$177$	19.5718	1.47111
$178$	22.7626	1.70613
$179$	18.2808	1.36637	0.683186	−	0.730244i	$-0.260594\pi$
$179$	18.2808	1.36637	0.683186	+	0.730244i	$0.260594\pi$
$180$	−1.08034	−0.0805236
$181$	−11.4692	−0.852499	−0.426250	−	0.904606i	$-0.640165\pi$
$181$	−11.4692	−0.852499	−0.426250	+	0.904606i	$0.640165\pi$
$182$	−16.5106	−1.22385
$183$	−21.2595	−1.57155
$184$	1.44987	0.106886
$185$	−2.80907	−0.206527
$186$	30.4124	2.22994
$187$	1.07645	0.0787179
$188$	8.34190	0.608395
$189$	16.5319	1.20252
$190$	−31.3885	−2.27716
$191$	−17.9270	−1.29715	−0.648577	−	0.761149i	$-0.724635\pi$
$191$	−17.9270	−1.29715	−0.648577	+	0.761149i	$0.724635\pi$
$192$	11.1311	0.803315
$193$	−23.2667	−1.67477	−0.837386	−	0.546612i	$-0.815917\pi$
$193$	−23.2667	−1.67477	−0.837386	+	0.546612i	$0.815917\pi$
$194$	22.4055	1.60862
$195$	12.8241	0.918356
$196$	4.61348	0.329535
$197$	−4.99505	−0.355882	−0.177941	−	0.984041i	$-0.556944\pi$
$197$	−4.99505	−0.355882	−0.177941	+	0.984041i	$0.556944\pi$
$198$	0.715258	0.0508312
$199$	−7.20349	−0.510642	−0.255321	−	0.966856i	$-0.582181\pi$
$199$	−7.20349	−0.510642	−0.255321	+	0.966856i	$0.582181\pi$
$200$	−0.912808	−0.0645453
$201$	−12.7205	−0.897233
$202$	19.4990	1.37194
$203$	−23.4798	−1.64796
$204$	1.89451	0.132642
$205$	−7.12236	−0.497447
$206$	−25.1308	−1.75095
$207$	0.960347	0.0667487
$208$	11.7408	0.814076
$209$	9.95447	0.688565
$210$	−28.3528	−1.95653
$211$	9.87651	0.679927	0.339963	−	0.940439i	$-0.389585\pi$
$211$	9.87651	0.679927	0.339963	+	0.940439i	$0.389585\pi$
$212$	7.62492	0.523682
$213$	−22.5143	−1.54266
$214$	−1.80261	−0.123224
$215$	−11.9721	−0.816488
$216$	−1.69282	−0.115182
$217$	−28.6515	−1.94499
$218$	−1.95930	−0.132700
$219$	−5.57776	−0.376910
$220$	−9.01605	−0.607862
$221$	1.68532	0.113367
$222$	3.27317	0.219681
$223$	15.6991	1.05129	0.525643	−	0.850705i	$-0.323825\pi$
$223$	15.6991	1.05129	0.525643	+	0.850705i	$0.323825\pi$
$224$	−24.0102	−1.60425
$225$	−0.604616	−0.0403078
$226$	−10.7871	−0.717546
$227$	12.7172	0.844070	0.422035	−	0.906580i	$-0.361316\pi$
$227$	12.7172	0.844070	0.422035	+	0.906580i	$0.361316\pi$
$228$	17.5195	1.16026
$229$	−8.06017	−0.532631	−0.266315	−	0.963886i	$-0.585806\pi$
$229$	−8.06017	−0.532631	−0.266315	+	0.963886i	$0.585806\pi$
$230$	−25.2719	−1.66638
$231$	8.99174	0.591613
$232$	2.40426	0.157847
$233$	−0.541469	−0.0354728	−0.0177364	−	0.999843i	$-0.505646\pi$
$233$	−0.541469	−0.0354728	−0.0177364	+	0.999843i	$0.505646\pi$
$234$	1.11983	0.0732053
$235$	12.7433	0.831283
$236$	−21.5430	−1.40233
$237$	6.27941	0.407892
$238$	−3.72606	−0.241525
$239$	−21.2988	−1.37771	−0.688853	−	0.724901i	$-0.741885\pi$
$239$	−21.2988	−1.37771	−0.688853	+	0.724901i	$0.741885\pi$
$240$	20.1618	1.30144
$241$	13.7250	0.884104	0.442052	−	0.896989i	$-0.354251\pi$
$241$	13.7250	0.884104	0.442052	+	0.896989i	$0.354251\pi$
$242$	−15.5830	−1.00171
$243$	−2.16947	−0.139171
$244$	23.4007	1.49808
$245$	7.04769	0.450260
$246$	8.29909	0.529130
$247$	15.5850	0.991648
$248$	2.93383	0.186298
$249$	3.81809	0.241962
$250$	−11.6083	−0.734172
$251$	−17.5471	−1.10756	−0.553782	−	0.832661i	$-0.686816\pi$
$251$	−17.5471	−1.10756	−0.553782	+	0.832661i	$0.686816\pi$
$252$	−1.18594	−0.0747071
$253$	8.01467	0.503878
$254$	−17.8589	−1.12057
$255$	2.89411	0.181236
$256$	18.2592	1.14120
$257$	−4.23478	−0.264159	−0.132079	−	0.991239i	$-0.542165\pi$
$257$	−4.23478	−0.264159	−0.132079	+	0.991239i	$0.542165\pi$
$258$	13.9500	0.868491
$259$	−3.08365	−0.191609
$260$	−14.1158	−0.875422
$261$	1.59251	0.0985738
$262$	2.54358	0.157143
$263$	18.8082	1.15977	0.579883	−	0.814700i	$-0.303098\pi$
$263$	18.8082	1.15977	0.579883	+	0.814700i	$0.303098\pi$
$264$	−0.920726	−0.0566668
$265$	11.6481	0.715534
$266$	−34.4567	−2.11268
$267$	−19.4084	−1.18778
$268$	14.0016	0.855287
$269$	−25.2112	−1.53715	−0.768577	−	0.639758i	$-0.779035\pi$
$269$	−25.2112	−1.53715	−0.768577	+	0.639758i	$0.779035\pi$
$270$	29.5067	1.79572
$271$	−2.31253	−0.140476	−0.0702381	−	0.997530i	$-0.522376\pi$
$271$	−2.31253	−0.140476	−0.0702381	+	0.997530i	$0.522376\pi$
$272$	2.64962	0.160657
$273$	14.0777	0.852021
$274$	26.3769	1.59349
$275$	−5.04588	−0.304278
$276$	14.1055	0.849051
$277$	−7.84739	−0.471504	−0.235752	−	0.971813i	$-0.575755\pi$
$277$	−7.84739	−0.471504	−0.235752	+	0.971813i	$0.575755\pi$
$278$	15.7134	0.942428
$279$	1.94328	0.116341
$280$	−2.73514	−0.163456
$281$	−23.8497	−1.42275	−0.711377	−	0.702811i	$-0.751928\pi$
$281$	−23.8497	−1.42275	−0.711377	+	0.702811i	$0.751928\pi$
$282$	−14.8487	−0.884228
$283$	−10.8917	−0.647443	−0.323721	−	0.946152i	$-0.604934\pi$
$283$	−10.8917	−0.647443	−0.323721	+	0.946152i	$0.604934\pi$
$284$	24.7819	1.47054
$285$	26.7633	1.58532
$286$	9.34561	0.552617
$287$	−7.81857	−0.461515
$288$	1.62848	0.0959594
$289$	−16.6197	−0.977627
$290$	−41.9075	−2.46089
$291$	−19.1039	−1.11989
$292$	6.13954	0.359289
$293$	19.7382	1.15312	0.576560	−	0.817055i	$-0.304395\pi$
$293$	19.7382	1.15312	0.576560	+	0.817055i	$0.304395\pi$
$294$	−8.21208	−0.478938
$295$	−32.9097	−1.91608
$296$	0.315757	0.0183530
$297$	−9.35768	−0.542987
$298$	−15.1213	−0.875953
$299$	12.5480	0.725667
$300$	−8.88055	−0.512719
$301$	−13.1423	−0.757511
$302$	−15.0250	−0.864589
$303$	−16.6257	−0.955123
$304$	24.5023	1.40530
$305$	35.7476	2.04690
$306$	0.252719	0.0144470
$307$	−20.8185	−1.18818	−0.594088	−	0.804400i	$-0.702487\pi$
$307$	−20.8185	−1.18818	−0.594088	+	0.804400i	$0.702487\pi$
$308$	−9.89736	−0.563955
$309$	21.4277	1.21898
$310$	−51.1381	−2.90445
$311$	−34.9009	−1.97905	−0.989524	−	0.144371i	$-0.953884\pi$
$311$	−34.9009	−1.97905	−0.989524	+	0.144371i	$0.953884\pi$
$312$	−1.44151	−0.0816096
$313$	17.1628	0.970097	0.485049	−	0.874487i	$-0.338802\pi$
$313$	17.1628	0.970097	0.485049	+	0.874487i	$0.338802\pi$
$314$	29.5541	1.66783
$315$	−1.81167	−0.102076
$316$	−6.91186	−0.388823
$317$	20.7259	1.16408	0.582040	−	0.813160i	$-0.302255\pi$
$317$	20.7259	1.16408	0.582040	+	0.813160i	$0.302255\pi$
$318$	−13.5725	−0.761108
$319$	13.2904	0.744121
$320$	−18.7168	−1.04630
$321$	1.53699	0.0857863
$322$	−27.7422	−1.54601
$323$	3.51717	0.195700
$324$	−15.3154	−0.850854
$325$	−7.89996	−0.438211
$326$	37.9601	2.10242
$327$	1.67058	0.0923835
$328$	0.800597	0.0442056
$329$	13.9890	0.771237
$330$	16.0487	0.883453
$331$	−30.5902	−1.68139	−0.840694	−	0.541511i	$-0.817852\pi$
$331$	−30.5902	−1.68139	−0.840694	+	0.541511i	$0.817852\pi$
$332$	−4.20264	−0.230650
$333$	0.209148	0.0114612
$334$	34.4781	1.88656
$335$	21.3893	1.16862
$336$	22.1326	1.20743
$337$	18.1511	0.988752	0.494376	−	0.869248i	$-0.335397\pi$
$337$	18.1511	0.988752	0.494376	+	0.869248i	$0.335397\pi$
$338$	−10.8391	−0.589571
$339$	9.19755	0.499542
$340$	−3.18560	−0.172763
$341$	16.2178	0.878243
$342$	2.33701	0.126371
$343$	−13.8490	−0.747774
$344$	1.34573	0.0725571
$345$	21.5480	1.16010
$346$	−33.6259	−1.80774
$347$	18.9330	1.01638	0.508189	−	0.861246i	$-0.330315\pi$
$347$	18.9330	1.01638	0.508189	+	0.861246i	$0.330315\pi$
$348$	23.3906	1.25387
$349$	−2.31535	−0.123938	−0.0619689	−	0.998078i	$-0.519738\pi$
$349$	−2.31535	−0.123938	−0.0619689	+	0.998078i	$0.519738\pi$
$350$	17.4660	0.933595
$351$	−14.6506	−0.781992
$352$	13.5907	0.724385
$353$	22.1500	1.17893	0.589463	−	0.807795i	$-0.299339\pi$
$353$	22.1500	1.17893	0.589463	+	0.807795i	$0.299339\pi$
$354$	38.3470	2.03812
$355$	37.8576	2.00927
$356$	21.3632	1.13225
$357$	3.17701	0.168145
$358$	35.8175	1.89302
$359$	−31.1224	−1.64258	−0.821289	−	0.570513i	$-0.806745\pi$
$359$	−31.1224	−1.64258	−0.821289	+	0.570513i	$0.806745\pi$
$360$	0.185510	0.00977723
$361$	13.5249	0.711839
$362$	−22.4716	−1.18108
$363$	13.2868	0.697375
$364$	−15.4956	−0.812188
$365$	9.37894	0.490916
$366$	−41.6537	−2.17727
$367$	−7.27062	−0.379524	−0.189762	−	0.981830i	$-0.560772\pi$
$367$	−7.27062	−0.379524	−0.189762	+	0.981830i	$0.560772\pi$
$368$	19.7276	1.02837
$369$	0.530291	0.0276059
$370$	−5.50380	−0.286129
$371$	12.7866	0.663849
$372$	28.5427	1.47987
$373$	8.09036	0.418903	0.209452	−	0.977819i	$-0.432832\pi$
$373$	8.09036	0.418903	0.209452	+	0.977819i	$0.432832\pi$
$374$	2.10909	0.109058
$375$	9.89774	0.511117
$376$	−1.43243	−0.0738718
$377$	20.8078	1.07166
$378$	32.3909	1.66601
$379$	−12.4875	−0.641442	−0.320721	−	0.947174i	$-0.603925\pi$
$379$	−12.4875	−0.641442	−0.320721	+	0.947174i	$0.603925\pi$
$380$	−29.4588	−1.51120
$381$	15.2273	0.780117
$382$	−35.1243	−1.79712
$383$	−32.0929	−1.63987	−0.819935	−	0.572456i	$-0.805991\pi$
$383$	−32.0929	−1.63987	−0.819935	+	0.572456i	$0.805991\pi$
$384$	−4.20628	−0.214651
$385$	−15.1195	−0.770561
$386$	−45.5863	−2.32028
$387$	0.891373	0.0453110
$388$	21.0280	1.06754
$389$	−1.78570	−0.0905384	−0.0452692	−	0.998975i	$-0.514415\pi$
$389$	−1.78570	−0.0905384	−0.0452692	+	0.998975i	$0.514415\pi$
$390$	25.1263	1.27232
$391$	2.83178	0.143209
$392$	−0.792204	−0.0400123
$393$	−2.16877	−0.109400
$394$	−9.78678	−0.493051
$395$	−10.5588	−0.531269
$396$	0.671285	0.0337333
$397$	−12.8867	−0.646763	−0.323381	−	0.946269i	$-0.604820\pi$
$397$	−12.8867	−0.646763	−0.323381	+	0.946269i	$0.604820\pi$
$398$	−14.1138	−0.707459
$399$	29.3793	1.47081
$400$	−12.4201	−0.621007
$401$	−2.97844	−0.148736	−0.0743680	−	0.997231i	$-0.523694\pi$
$401$	−2.97844	−0.148736	−0.0743680	+	0.997231i	$0.523694\pi$
$402$	−24.9232	−1.24305
$403$	25.3910	1.26482
$404$	18.3002	0.910470
$405$	−23.3962	−1.16257
$406$	−46.0039	−2.28313
$407$	1.74546	0.0865192
$408$	−0.325316	−0.0161055
$409$	1.63918	0.0810523	0.0405262	−	0.999178i	$-0.487097\pi$
$409$	1.63918	0.0810523	0.0405262	+	0.999178i	$0.487097\pi$
$410$	−13.9548	−0.689179
$411$	−22.4901	−1.10936
$412$	−23.5858	−1.16199
$413$	−36.1266	−1.77768
$414$	1.88160	0.0924758
$415$	−6.42007	−0.315149
$416$	21.2779	1.04323
$417$	−13.3980	−0.656101
$418$	19.5038	0.953960
$419$	25.1688	1.22958	0.614789	−	0.788691i	$-0.289241\pi$
$419$	25.1688	1.22958	0.614789	+	0.788691i	$0.289241\pi$
$420$	−26.6097	−1.29842
$421$	10.5060	0.512033	0.256016	−	0.966672i	$-0.417590\pi$
$421$	10.5060	0.512033	0.256016	+	0.966672i	$0.417590\pi$
$422$	19.3510	0.941992
$423$	−0.948797	−0.0461321
$424$	−1.30931	−0.0635859
$425$	−1.78284	−0.0864803
$426$	−44.1122	−2.13725
$427$	39.2419	1.89905
$428$	−1.69179	−0.0817758
$429$	−7.96849	−0.384722
$430$	−23.4568	−1.13119
$431$	−6.76947	−0.326074	−0.163037	−	0.986620i	$-0.552129\pi$
$431$	−6.76947	−0.326074	−0.163037	+	0.986620i	$0.552129\pi$
$432$	−23.0334	−1.10819
$433$	17.8076	0.855776	0.427888	−	0.903832i	$-0.359258\pi$
$433$	17.8076	0.855776	0.427888	+	0.903832i	$0.359258\pi$
$434$	−56.1368	−2.69465
$435$	35.7322	1.71323
$436$	−1.83884	−0.0880646
$437$	26.1869	1.25269
$438$	−10.9285	−0.522183
$439$	16.8160	0.802586	0.401293	−	0.915950i	$-0.368561\pi$
$439$	16.8160	0.802586	0.401293	+	0.915950i	$0.368561\pi$
$440$	1.54819	0.0738071
$441$	−0.524732	−0.0249872
$442$	3.30204	0.157062
$443$	12.8732	0.611626	0.305813	−	0.952092i	$-0.401072\pi$
$443$	12.8732	0.611626	0.305813	+	0.952092i	$0.401072\pi$
$444$	3.07194	0.145788
$445$	32.6351	1.54705
$446$	30.7591	1.45649
$447$	12.8931	0.609823
$448$	−20.5463	−0.970721
$449$	−32.0736	−1.51365	−0.756824	−	0.653618i	$-0.773250\pi$
$449$	−32.0736	−1.51365	−0.756824	+	0.653618i	$0.773250\pi$
$450$	−1.18462	−0.0558436
$451$	4.42559	0.208393
$452$	−10.1239	−0.476188
$453$	12.8110	0.601911
$454$	24.9167	1.16940
$455$	−23.6715	−1.10974
$456$	−3.00835	−0.140879
$457$	38.8052	1.81523	0.907616	−	0.419801i	$-0.137900\pi$
$457$	38.8052	1.81523	0.907616	+	0.419801i	$0.137900\pi$
$458$	−15.7923	−0.737924
$459$	−3.30630	−0.154325
$460$	−23.7182	−1.10587
$461$	−11.0080	−0.512693	−0.256346	−	0.966585i	$-0.582519\pi$
$461$	−11.0080	−0.512693	−0.256346	+	0.966585i	$0.582519\pi$
$462$	17.6175	0.819639
$463$	16.8248	0.781913	0.390956	−	0.920409i	$-0.372144\pi$
$463$	16.8248	0.781913	0.390956	+	0.920409i	$0.372144\pi$
$464$	32.7136	1.51869
$465$	43.6026	2.02202
$466$	−1.06090	−0.0491452
$467$	−14.6605	−0.678405	−0.339203	−	0.940713i	$-0.610157\pi$
$467$	−14.6605	−0.678405	−0.339203	+	0.940713i	$0.610157\pi$
$468$	1.05098	0.0485816
$469$	23.4801	1.08421
$470$	24.9679	1.15169
$471$	−25.1991	−1.16111
$472$	3.69926	0.170272
$473$	7.43903	0.342047
$474$	12.3032	0.565106
$475$	−16.4868	−0.756465
$476$	−3.49699	−0.160284
$477$	−0.867249	−0.0397086
$478$	−41.7307	−1.90872
$479$	−4.65212	−0.212561	−0.106280	−	0.994336i	$-0.533894\pi$
$479$	−4.65212	−0.212561	−0.106280	+	0.994336i	$0.533894\pi$
$480$	36.5394	1.66779
$481$	2.73274	0.124602
$482$	26.8913	1.22487
$483$	23.6543	1.07631
$484$	−14.6250	−0.664772
$485$	32.1230	1.45863
$486$	−4.25063	−0.192812
$487$	−8.49170	−0.384796	−0.192398	−	0.981317i	$-0.561626\pi$
$487$	−8.49170	−0.384796	−0.192398	+	0.981317i	$0.561626\pi$
$488$	−4.01825	−0.181898
$489$	−32.3665	−1.46366
$490$	13.8085	0.623805
$491$	−1.12803	−0.0509072	−0.0254536	−	0.999676i	$-0.508103\pi$
$491$	−1.12803	−0.0509072	−0.0254536	+	0.999676i	$0.508103\pi$
$492$	7.78887	0.351149
$493$	4.69584	0.211490
$494$	30.5356	1.37386
$495$	1.02547	0.0460916
$496$	39.9191	1.79242
$497$	41.5581	1.86414
$498$	7.48077	0.335221
$499$	19.7216	0.882860	0.441430	−	0.897296i	$-0.354471\pi$
$499$	19.7216	0.882860	0.441430	+	0.897296i	$0.354471\pi$
$500$	−10.8946	−0.487222
$501$	−29.3975	−1.31339
$502$	−34.3800	−1.53446
$503$	−27.5149	−1.22683	−0.613415	−	0.789760i	$-0.710205\pi$
$503$	−27.5149	−1.22683	−0.613415	+	0.789760i	$0.710205\pi$
$504$	0.203643	0.00907100
$505$	27.9560	1.24402
$506$	15.7031	0.698088
$507$	9.24193	0.410449
$508$	−16.7609	−0.743646
$509$	17.2000	0.762375	0.381188	−	0.924498i	$-0.375515\pi$
$509$	17.2000	0.762375	0.381188	+	0.924498i	$0.375515\pi$
$510$	5.67042	0.251090
$511$	10.2957	0.455456
$512$	30.7394	1.35850
$513$	−30.5750	−1.34992
$514$	−8.29720	−0.365974
$515$	−36.0304	−1.58769
$516$	13.0924	0.576361
$517$	−7.91827	−0.348245
$518$	−6.04179	−0.265461
$519$	28.6710	1.25852
$520$	2.42389	0.106294
$521$	−3.15207	−0.138095	−0.0690473	−	0.997613i	$-0.521996\pi$
$521$	−3.15207	−0.138095	−0.0690473	+	0.997613i	$0.521996\pi$
$522$	3.12020	0.136567
$523$	5.17131	0.226126	0.113063	−	0.993588i	$-0.463934\pi$
$523$	5.17131	0.226126	0.113063	+	0.993588i	$0.463934\pi$
$524$	2.38721	0.104286
$525$	−14.8923	−0.649952
$526$	36.8509	1.60678
$527$	5.73016	0.249610
$528$	−12.5279	−0.545206
$529$	−1.91609	−0.0833084
$530$	22.8220	0.991324
$531$	2.45028	0.106333
$532$	−32.3384	−1.40205
$533$	6.92882	0.300121
$534$	−38.0269	−1.64558
$535$	−2.58443	−0.111735
$536$	−2.40429	−0.103850
$537$	−30.5397	−1.31788
$538$	−49.3962	−2.12962
$539$	−4.37920	−0.188625
$540$	27.6927	1.19170
$541$	−28.9932	−1.24651	−0.623257	−	0.782017i	$-0.714191\pi$
$541$	−28.9932	−1.24651	−0.623257	+	0.782017i	$0.714191\pi$
$542$	−4.53093	−0.194620
$543$	19.1603	0.822246
$544$	4.80193	0.205881
$545$	−2.80907	−0.120327
$546$	27.5824	1.18042
$547$	6.87023	0.293750	0.146875	−	0.989155i	$-0.453079\pi$
$547$	6.87023	0.293750	0.146875	+	0.989155i	$0.453079\pi$
$548$	24.7553	1.05749
$549$	−2.66157	−0.113593
$550$	−9.88638	−0.421556
$551$	43.4248	1.84996
$552$	−2.42212	−0.103092
$553$	−11.5909	−0.492894
$554$	−15.3754	−0.653237
$555$	4.69278	0.199198
$556$	14.7474	0.625428
$557$	10.3657	0.439207	0.219603	−	0.975589i	$-0.429524\pi$
$557$	10.3657	0.439207	0.219603	+	0.975589i	$0.429524\pi$
$558$	3.80745	0.161182
$559$	11.6467	0.492605
$560$	−37.2157	−1.57265
$561$	−1.79830	−0.0759244
$562$	−46.7286	−1.97113
$563$	−37.8073	−1.59339	−0.796694	−	0.604383i	$-0.793420\pi$
$563$	−37.8073	−1.59339	−0.796694	+	0.604383i	$0.793420\pi$
$564$	−13.9358	−0.586805
$565$	−15.4656	−0.650641
$566$	−21.3400	−0.896988
$567$	−25.6832	−1.07859
$568$	−4.25543	−0.178554
$569$	28.6009	1.19901	0.599507	−	0.800370i	$-0.295363\pi$
$569$	28.6009	1.19901	0.599507	+	0.800370i	$0.295363\pi$
$570$	52.4371	2.19635
$571$	−11.6382	−0.487042	−0.243521	−	0.969896i	$-0.578303\pi$
$571$	−11.6382	−0.487042	−0.243521	+	0.969896i	$0.578303\pi$
$572$	8.77106	0.366736
$573$	29.9486	1.25112
$574$	−15.3189	−0.639398
$575$	−13.2740	−0.553565
$576$	1.39354	0.0580644
$577$	25.8406	1.07576	0.537880	−	0.843021i	$-0.319225\pi$
$577$	25.8406	1.07576	0.537880	+	0.843021i	$0.319225\pi$
$578$	−32.5628	−1.35444
$579$	38.8689	1.61534
$580$	−39.3311	−1.63313
$581$	−7.04763	−0.292385
$582$	−37.4302	−1.55153
$583$	−7.23771	−0.299755
$584$	−1.05425	−0.0436252
$585$	1.60551	0.0663796
$586$	38.6730	1.59757
$587$	−11.8719	−0.490005	−0.245002	−	0.969522i	$-0.578789\pi$
$587$	−11.8719	−0.490005	−0.245002	+	0.969522i	$0.578789\pi$
$588$	−7.70721	−0.317840
$589$	52.9895	2.18340
$590$	−64.4799	−2.65460
$591$	8.34465	0.343253
$592$	4.29634	0.176579
$593$	21.1578	0.868848	0.434424	−	0.900708i	$-0.356952\pi$
$593$	21.1578	0.868848	0.434424	+	0.900708i	$0.356952\pi$
$594$	−18.3345	−0.752272
$595$	−5.34210	−0.219005
$596$	−14.1917	−0.581313
$597$	12.0340	0.492520
$598$	24.5852	1.00536
$599$	−34.1872	−1.39685	−0.698426	−	0.715682i	$-0.746116\pi$
$599$	−34.1872	−1.39685	−0.698426	+	0.715682i	$0.746116\pi$
$600$	1.52492	0.0622547
$601$	29.9818	1.22298	0.611491	−	0.791251i	$-0.290570\pi$
$601$	29.9818	1.22298	0.611491	+	0.791251i	$0.290570\pi$
$602$	−25.7497	−1.04948
$603$	−1.59253	−0.0648528
$604$	−14.1013	−0.573772
$605$	−22.3416	−0.908313
$606$	−32.5747	−1.32326
$607$	−15.3876	−0.624563	−0.312282	−	0.949990i	$-0.601093\pi$
$607$	−15.3876	−0.624563	−0.312282	+	0.949990i	$0.601093\pi$
$608$	44.4058	1.80089
$609$	39.2250	1.58948
$610$	70.0402	2.83584
$611$	−12.3970	−0.501531
$612$	0.237182	0.00958751
$613$	11.2226	0.453276	0.226638	−	0.973979i	$-0.427226\pi$
$613$	11.2226	0.453276	0.226638	+	0.973979i	$0.427226\pi$
$614$	−40.7896	−1.64614
$615$	11.8985	0.479794
$616$	1.69952	0.0684758
$617$	32.4744	1.30737	0.653685	−	0.756766i	$-0.273222\pi$
$617$	32.4744	1.30737	0.653685	+	0.756766i	$0.273222\pi$
$618$	41.9832	1.68881
$619$	−34.7147	−1.39530	−0.697651	−	0.716438i	$-0.745771\pi$
$619$	−34.7147	−1.39530	−0.697651	+	0.716438i	$0.745771\pi$
$620$	−47.9942	−1.92749
$621$	−24.6169	−0.987843
$622$	−68.3812	−2.74183
$623$	35.8251	1.43530
$624$	−19.6140	−0.785187
$625$	−31.0972	−1.24389
$626$	33.6269	1.34400
$627$	−16.6298	−0.664129
$628$	27.7371	1.10683
$629$	0.616715	0.0245900
$630$	−3.54961	−0.141420
$631$	12.2209	0.486508	0.243254	−	0.969963i	$-0.421785\pi$
$631$	12.2209	0.486508	0.243254	+	0.969963i	$0.421785\pi$
$632$	1.18687	0.0472111
$633$	−16.4995	−0.655798
$634$	40.6081	1.61275
$635$	−25.6045	−1.01608
$636$	−12.7381	−0.505098
$637$	−6.85618	−0.271652
$638$	26.0399	1.03093
$639$	−2.81866	−0.111505
$640$	7.07281	0.279578
$641$	−5.54437	−0.218990	−0.109495	−	0.993987i	$-0.534923\pi$
$641$	−5.54437	−0.218990	−0.109495	+	0.993987i	$0.534923\pi$
$642$	3.01142	0.118851
$643$	−21.5926	−0.851530	−0.425765	−	0.904834i	$-0.639995\pi$
$643$	−21.5926	−0.851530	−0.425765	+	0.904834i	$0.639995\pi$
$644$	−26.0367	−1.02599
$645$	20.0003	0.787512
$646$	6.89117	0.271129
$647$	−36.1128	−1.41974	−0.709869	−	0.704333i	$-0.751246\pi$
$647$	−36.1128	−1.41974	−0.709869	+	0.704333i	$0.751246\pi$
$648$	2.62988	0.103311
$649$	20.4490	0.802694
$650$	−15.4784	−0.607111
$651$	47.8647	1.87597
$652$	35.6264	1.39524
$653$	39.5675	1.54840	0.774198	−	0.632944i	$-0.218154\pi$
$653$	39.5675	1.54840	0.774198	+	0.632944i	$0.218154\pi$
$654$	3.27317	0.127991
$655$	3.64677	0.142491
$656$	10.8933	0.425313
$657$	−0.698303	−0.0272434
$658$	27.4085	1.06850
$659$	35.7608	1.39304	0.696522	−	0.717536i	$-0.254730\pi$
$659$	35.7608	1.39304	0.696522	+	0.717536i	$0.254730\pi$
$660$	15.0621	0.586291
$661$	−17.8403	−0.693907	−0.346954	−	0.937882i	$-0.612784\pi$
$661$	−17.8403	−0.693907	−0.346954	+	0.937882i	$0.612784\pi$
$662$	−59.9352	−2.32945
$663$	−2.81547	−0.109344
$664$	0.721656	0.0280057
$665$	−49.4010	−1.91569
$666$	0.409782	0.0158787
$667$	34.9627	1.35376
$668$	32.3584	1.25198
$669$	−26.2266	−1.01398
$670$	41.9080	1.61905
$671$	−22.2124	−0.857499
$672$	40.1111	1.54732
$673$	−13.0951	−0.504778	−0.252389	−	0.967626i	$-0.581216\pi$
$673$	−13.0951	−0.504778	−0.252389	+	0.967626i	$0.581216\pi$
$674$	35.5633	1.36985
$675$	15.4983	0.596532
$676$	−10.1728	−0.391260
$677$	19.3950	0.745410	0.372705	−	0.927950i	$-0.378430\pi$
$677$	19.3950	0.745410	0.372705	+	0.927950i	$0.378430\pi$
$678$	18.0207	0.692082
$679$	35.2630	1.35327
$680$	0.547015	0.0209771
$681$	−21.2451	−0.814116
$682$	31.7755	1.21675
$683$	−20.6540	−0.790303	−0.395152	−	0.918616i	$-0.629308\pi$
$683$	−20.6540	−0.790303	−0.395152	+	0.918616i	$0.629308\pi$
$684$	2.19334	0.0838643
$685$	37.8169	1.44491
$686$	−27.1342	−1.03599
$687$	13.4652	0.513729
$688$	18.3107	0.698090
$689$	−11.3315	−0.431697
$690$	42.2188	1.60724
$691$	−10.6990	−0.407011	−0.203506	−	0.979074i	$-0.565233\pi$
$691$	−10.6990	−0.407011	−0.203506	+	0.979074i	$0.565233\pi$
$692$	−31.5587	−1.19968
$693$	1.12571	0.0427623
$694$	37.0954	1.40812
$695$	22.5285	0.854555
$696$	−4.01652	−0.152246
$697$	1.56367	0.0592284
$698$	−4.53645	−0.171707
$699$	0.904570	0.0342140
$700$	16.3922	0.619566
$701$	42.7036	1.61289	0.806446	−	0.591308i	$-0.201388\pi$
$701$	42.7036	1.61289	0.806446	+	0.591308i	$0.201388\pi$
$702$	−28.7049	−1.08340
$703$	5.70306	0.215095
$704$	11.6300	0.438321
$705$	−21.2888	−0.801782
$706$	43.3984	1.63332
$707$	30.6886	1.15416
$708$	35.9894	1.35257
$709$	11.5801	0.434898	0.217449	−	0.976072i	$-0.430226\pi$
$709$	11.5801	0.434898	0.217449	+	0.976072i	$0.430226\pi$
$710$	74.1742	2.78371
$711$	0.786146	0.0294828
$712$	−3.66838	−0.137478
$713$	42.6636	1.59776
$714$	6.22470	0.232954
$715$	13.3989	0.501091
$716$	33.6155	1.25627
$717$	35.5815	1.32881
$718$	−60.9780	−2.27568
$719$	−47.6323	−1.77639	−0.888193	−	0.459470i	$-0.848039\pi$
$719$	−47.6323	−1.77639	−0.888193	+	0.459470i	$0.848039\pi$
$720$	2.52414	0.0940693
$721$	−39.5523	−1.47301
$722$	26.4994	0.986204
$723$	−22.9288	−0.852730
$724$	−21.0900	−0.783806
$725$	−22.0118	−0.817499
$726$	26.0327	0.966165
$727$	43.6391	1.61849	0.809243	−	0.587475i	$-0.199878\pi$
$727$	43.6391	1.61849	0.809243	+	0.587475i	$0.199878\pi$
$728$	2.66082	0.0986165
$729$	28.6107	1.05966
$730$	18.3761	0.680131
$731$	2.62840	0.0972148
$732$	−39.0929	−1.44492
$733$	37.0153	1.36719	0.683596	−	0.729861i	$-0.260415\pi$
$733$	37.0153	1.36719	0.683596	+	0.729861i	$0.260415\pi$
$734$	−14.2453	−0.525804
$735$	−11.7738	−0.434282
$736$	35.7525	1.31786
$737$	−13.2906	−0.489566
$738$	1.03900	0.0382460
$739$	31.6106	1.16281	0.581407	−	0.813613i	$-0.302502\pi$
$739$	31.6106	1.16281	0.581407	+	0.813613i	$0.302502\pi$
$740$	−5.16543	−0.189885
$741$	−26.0360	−0.956457
$742$	25.0528	0.919718
$743$	−52.1834	−1.91442	−0.957212	−	0.289387i	$-0.906548\pi$
$743$	−52.1834	−1.91442	−0.957212	+	0.289387i	$0.906548\pi$
$744$	−4.90120	−0.179687
$745$	−21.6796	−0.794279
$746$	15.8514	0.580362
$747$	0.478003	0.0174892
$748$	1.97942	0.0723749
$749$	−2.83705	−0.103664
$750$	19.3926	0.708118
$751$	−39.7390	−1.45010	−0.725048	−	0.688699i	$-0.758182\pi$
$751$	−39.7390	−1.45010	−0.725048	+	0.688699i	$0.758182\pi$
$752$	−19.4903	−0.710740
$753$	29.3140	1.06826
$754$	40.7687	1.48471
$755$	−21.5415	−0.783975
$756$	30.3996	1.10562
$757$	−51.6586	−1.87756	−0.938782	−	0.344512i	$-0.888045\pi$
$757$	−51.6586	−1.87756	−0.938782	+	0.344512i	$0.888045\pi$
$758$	−24.4668	−0.888674
$759$	−13.3892	−0.485996
$760$	5.05851	0.183492
$761$	−50.4266	−1.82796	−0.913981	−	0.405757i	$-0.867008\pi$
$761$	−50.4266	−1.82796	−0.913981	+	0.405757i	$0.867008\pi$
$762$	29.8348	1.08080
$763$	−3.08365	−0.111636
$764$	−32.9649	−1.19263
$765$	0.362326	0.0130999
$766$	−62.8795	−2.27193
$767$	32.0155	1.15601
$768$	−30.5035	−1.10070
$769$	−28.6457	−1.03299	−0.516495	−	0.856290i	$-0.672764\pi$
$769$	−28.6457	−1.03299	−0.516495	+	0.856290i	$0.672764\pi$
$770$	−29.6236	−1.06756
$771$	7.07457	0.254784
$772$	−42.7837	−1.53982
$773$	14.6309	0.526238	0.263119	−	0.964763i	$-0.415249\pi$
$773$	14.6309	0.526238	0.263119	+	0.964763i	$0.415249\pi$
$774$	1.74646	0.0627753
$775$	−26.8602	−0.964847
$776$	−3.61083	−0.129621
$777$	5.15150	0.184809
$778$	−3.49871	−0.125435
$779$	14.4601	0.518085
$780$	23.5816	0.844356
$781$	−23.5234	−0.841734
$782$	5.54830	0.198407
$783$	−40.8213	−1.45884
$784$	−10.7791	−0.384969
$785$	42.3720	1.51232
$786$	−4.24927	−0.151566
$787$	−11.0832	−0.395074	−0.197537	−	0.980295i	$-0.563294\pi$
$787$	−11.0832	−0.395074	−0.197537	+	0.980295i	$0.563294\pi$
$788$	−9.18510	−0.327206
$789$	−31.4207	−1.11861
$790$	−20.6877	−0.736037
$791$	−16.9773	−0.603644
$792$	−0.115270	−0.00409593
$793$	−34.7763	−1.23494
$794$	−25.2488	−0.896046
$795$	−19.4591	−0.690142
$796$	−13.2461	−0.469495
$797$	−5.51901	−0.195493	−0.0977467	−	0.995211i	$-0.531164\pi$
$797$	−5.51901	−0.195493	−0.0977467	+	0.995211i	$0.531164\pi$
$798$	57.5628	2.03770
$799$	−2.79773	−0.0989764
$800$	−22.5091	−0.795817
$801$	−2.42982	−0.0858536
$802$	−5.83564	−0.206064
$803$	−5.82775	−0.205657
$804$	−23.3909	−0.824935
$805$	−39.7743	−1.40186
$806$	49.7485	1.75232
$807$	42.1174	1.48260
$808$	−3.14242	−0.110550
$809$	12.2880	0.432022	0.216011	−	0.976391i	$-0.430695\pi$
$809$	12.2880	0.432022	0.216011	+	0.976391i	$0.430695\pi$
$810$	−45.8401	−1.61066
$811$	38.7368	1.36023	0.680117	−	0.733104i	$-0.261929\pi$
$811$	38.7368	1.36023	0.680117	+	0.733104i	$0.261929\pi$
$812$	−43.1756	−1.51517
$813$	3.86328	0.135491
$814$	3.41987	0.119866
$815$	54.4239	1.90639
$816$	−4.42641	−0.154956
$817$	24.3061	0.850362
$818$	3.21164	0.112292
$819$	1.76245	0.0615848
$820$	−13.0969	−0.457363
$821$	44.4114	1.54997	0.774985	−	0.631980i	$-0.217758\pi$
$821$	44.4114	1.54997	0.774985	+	0.631980i	$0.217758\pi$
$822$	−44.0648	−1.53694
$823$	−32.6669	−1.13870	−0.569348	−	0.822096i	$-0.692804\pi$
$823$	−32.6669	−1.13870	−0.569348	+	0.822096i	$0.692804\pi$
$824$	4.05004	0.141090
$825$	8.42957	0.293480
$826$	−70.7828	−2.46285
$827$	−26.4066	−0.918247	−0.459124	−	0.888372i	$-0.651836\pi$
$827$	−26.4066	−0.918247	−0.459124	+	0.888372i	$0.651836\pi$
$828$	1.76593	0.0613702
$829$	30.9284	1.07419	0.537094	−	0.843522i	$-0.319522\pi$
$829$	30.9284	1.07419	0.537094	+	0.843522i	$0.319522\pi$
$830$	−12.5788	−0.436617
$831$	13.1097	0.454771
$832$	18.2082	0.631254
$833$	−1.54728	−0.0536101
$834$	−26.2506	−0.908983
$835$	49.4316	1.71065
$836$	18.3047	0.633081
$837$	−49.8127	−1.72178
$838$	49.3132	1.70350
$839$	−8.66381	−0.299108	−0.149554	−	0.988754i	$-0.547784\pi$
$839$	−8.66381	−0.299108	−0.149554	+	0.988754i	$0.547784\pi$
$840$	4.56929	0.157655
$841$	28.9773	0.999218
$842$	20.5844	0.709386
$843$	39.8429	1.37226
$844$	18.1613	0.625139
$845$	−15.5402	−0.534599
$846$	−1.85897	−0.0639128
$847$	−24.5254	−0.842704
$848$	−17.8152	−0.611776
$849$	18.1955	0.624467
$850$	−3.49311	−0.119813
$851$	4.59172	0.157402
$852$	−41.4003	−1.41835
$853$	−34.7348	−1.18930	−0.594648	−	0.803986i	$-0.702708\pi$
$853$	−34.7348	−1.18930	−0.594648	+	0.803986i	$0.702708\pi$
$854$	76.8866	2.63100
$855$	3.35060	0.114588
$856$	0.290506	0.00992928
$857$	18.5421	0.633386	0.316693	−	0.948528i	$-0.397427\pi$
$857$	18.5421	0.633386	0.316693	+	0.948528i	$0.397427\pi$
$858$	−15.6126	−0.533006
$859$	−11.3683	−0.387881	−0.193941	−	0.981013i	$-0.562127\pi$
$859$	−11.3683	−0.387881	−0.193941	+	0.981013i	$0.562127\pi$
$860$	−22.0147	−0.750696
$861$	13.0616	0.445137
$862$	−13.2634	−0.451753
$863$	2.65691	0.0904423	0.0452212	−	0.998977i	$-0.485601\pi$
$863$	2.65691	0.0904423	0.0452212	+	0.998977i	$0.485601\pi$
$864$	−41.7435	−1.42014
$865$	−48.2099	−1.63919
$866$	34.8903	1.18562
$867$	27.7646	0.942934
$868$	−52.6856	−1.78826
$869$	6.56086	0.222562
$870$	70.0100	2.37356
$871$	−20.8081	−0.705055
$872$	0.315757	0.0106929
$873$	−2.39170	−0.0809468
$874$	51.3079	1.73551
$875$	−18.2698	−0.617631
$876$	−10.2566	−0.346539
$877$	−13.8740	−0.468490	−0.234245	−	0.972178i	$-0.575262\pi$
$877$	−13.8740	−0.468490	−0.234245	+	0.972178i	$0.575262\pi$
$878$	32.9476	1.11193
$879$	−32.9744	−1.11220
$880$	21.0655	0.710117
$881$	58.4075	1.96780	0.983899	−	0.178727i	$-0.0571980\pi$
$881$	58.4075	1.96780	0.983899	+	0.178727i	$0.0571980\pi$
$882$	−1.02810	−0.0346181
$883$	33.7538	1.13591	0.567953	−	0.823061i	$-0.307736\pi$
$883$	33.7538	1.13591	0.567953	+	0.823061i	$0.307736\pi$
$884$	3.09904	0.104232
$885$	54.9785	1.84808
$886$	25.2225	0.847366
$887$	−8.02813	−0.269558	−0.134779	−	0.990876i	$-0.543032\pi$
$887$	−8.02813	−0.269558	−0.134779	+	0.990876i	$0.543032\pi$
$888$	−0.527498	−0.0177017
$889$	−28.1073	−0.942689
$890$	63.9417	2.14333
$891$	14.5376	0.487028
$892$	28.8681	0.966575
$893$	−25.8719	−0.865771
$894$	25.2614	0.844868
$895$	51.3521	1.71651
$896$	7.76418	0.259383
$897$	−20.9624	−0.699915
$898$	−62.8418	−2.09706
$899$	70.7475	2.35956
$900$	−1.11179	−0.0370598
$901$	−2.55726	−0.0851948
$902$	8.67105	0.288714
$903$	21.9554	0.730628
$904$	1.73843	0.0578192
$905$	−32.2178	−1.07095
$906$	25.1005	0.833907
$907$	−10.0885	−0.334984	−0.167492	−	0.985873i	$-0.553567\pi$
$907$	−10.0885	−0.334984	−0.167492	+	0.985873i	$0.553567\pi$
$908$	23.3849	0.776055
$909$	−2.08144	−0.0690372
$910$	−46.3794	−1.53746
$911$	5.43910	0.180205	0.0901027	−	0.995932i	$-0.471280\pi$
$911$	5.43910	0.180205	0.0901027	+	0.995932i	$0.471280\pi$
$912$	−40.9332	−1.35543
$913$	3.98922	0.132024
$914$	76.0310	2.51488
$915$	−59.7194	−1.97426
$916$	−14.8214	−0.489712
$917$	4.00323	0.132198
$918$	−6.47803	−0.213807
$919$	−42.8741	−1.41429	−0.707143	−	0.707071i	$-0.750016\pi$
$919$	−42.8741	−1.41429	−0.707143	+	0.707071i	$0.750016\pi$
$920$	4.07277	0.134275
$921$	34.7791	1.14601
$922$	−21.5679	−0.710301
$923$	−36.8289	−1.21224
$924$	16.5344	0.543941
$925$	−2.89086	−0.0950509
$926$	32.9647	1.08329
$927$	2.68262	0.0881089
$928$	59.2871	1.94619
$929$	42.7879	1.40383	0.701913	−	0.712263i	$-0.252330\pi$
$929$	42.7879	1.40383	0.701913	+	0.712263i	$0.252330\pi$
$930$	85.4304	2.80137
$931$	−14.3085	−0.468941
$932$	−0.995676	−0.0326145
$933$	58.3049	1.90882
$934$	−28.7242	−0.939884
$935$	3.02382	0.0988896
$936$	−0.180469	−0.00589881
$937$	5.10130	0.166652	0.0833261	−	0.996522i	$-0.473446\pi$
$937$	5.10130	0.166652	0.0833261	+	0.996522i	$0.473446\pi$
$938$	46.0045	1.50210
$939$	−28.6719	−0.935671
$940$	23.4330	0.764299
$941$	−26.6351	−0.868279	−0.434139	−	0.900846i	$-0.642947\pi$
$941$	−26.6351	−0.868279	−0.434139	+	0.900846i	$0.642947\pi$
$942$	−49.3726	−1.60864
$943$	11.6423	0.379124
$944$	50.3340	1.63823
$945$	46.4393	1.51067
$946$	14.5753	0.473883
$947$	14.0946	0.458011	0.229006	−	0.973425i	$-0.426453\pi$
$947$	14.0946	0.458011	0.229006	+	0.973425i	$0.426453\pi$
$948$	11.5469	0.375024
$949$	−9.12408	−0.296180
$950$	−32.3025	−1.04803
$951$	−34.6243	−1.12277
$952$	0.600485	0.0194618
$953$	35.6209	1.15387	0.576937	−	0.816789i	$-0.304248\pi$
$953$	35.6209	1.15387	0.576937	+	0.816789i	$0.304248\pi$
$954$	−1.69920	−0.0550136
$955$	−50.3582	−1.62955
$956$	−39.1651	−1.26669
$957$	−22.2028	−0.717714
$958$	−9.11488	−0.294488
$959$	41.5135	1.34054
$960$	31.2679	1.00917
$961$	55.3304	1.78485
$962$	5.35424	0.172628
$963$	0.192422	0.00620071
$964$	25.2381	0.812864
$965$	−65.3577	−2.10394
$966$	46.3457	1.49115
$967$	20.5765	0.661696	0.330848	−	0.943684i	$-0.392665\pi$
$967$	20.5765	0.661696	0.330848	+	0.943684i	$0.392665\pi$
$968$	2.51133	0.0807172
$969$	−5.87572	−0.188755
$970$	62.9385	2.02083
$971$	29.9217	0.960234	0.480117	−	0.877204i	$-0.340594\pi$
$971$	29.9217	0.960234	0.480117	+	0.877204i	$0.340594\pi$
$972$	−3.98931	−0.127957
$973$	24.7307	0.792829
$974$	−16.6378	−0.533108
$975$	13.1975	0.422660
$976$	−54.6744	−1.75009
$977$	−22.7064	−0.726441	−0.363221	−	0.931703i	$-0.618323\pi$
$977$	−22.7064	−0.726441	−0.363221	+	0.931703i	$0.618323\pi$
$978$	−63.4156	−2.02781
$979$	−20.2783	−0.648098
$980$	12.9596	0.413979
$981$	0.209148	0.00667757
$982$	−2.21014	−0.0705285
$983$	−42.4619	−1.35432	−0.677162	−	0.735834i	$-0.736790\pi$
$983$	−42.4619	−1.35432	−0.677162	+	0.735834i	$0.736790\pi$
$984$	−1.33747	−0.0426368
$985$	−14.0314	−0.447078
$986$	9.20055	0.293005
$987$	−23.3698	−0.743868
$988$	28.6583	0.911742
$989$	19.5696	0.622277
$990$	2.00921	0.0638568
$991$	−10.9300	−0.347201	−0.173601	−	0.984816i	$-0.555540\pi$
$991$	−10.9300	−0.347201	−0.173601	+	0.984816i	$0.555540\pi$
$992$	72.3457	2.29698
$993$	51.1034	1.62172
$994$	81.4247	2.58263
$995$	−20.2351	−0.641495
$996$	7.02086	0.222465
$997$	−42.7100	−1.35264	−0.676320	−	0.736608i	$-0.736426\pi$
$997$	−42.7100	−1.35264	−0.676320	+	0.736608i	$0.736426\pi$
$998$	38.6405	1.22314
$999$	−5.36115	−0.169619

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.67	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.67	✓	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)

\(f(q)\)	\(=\)	\(q+1.95930 q^{2} -1.67058 q^{3} +1.83884 q^{4} +2.80907 q^{5} -3.27317 q^{6} +3.08365 q^{7} -0.315757 q^{8} -0.209148 q^{9} +O(q^{10})\)	\(q+1.95930 q^{2} -1.67058 q^{3} +1.83884 q^{4} +2.80907 q^{5} -3.27317 q^{6} +3.08365 q^{7} -0.315757 q^{8} -0.209148 q^{9} +5.50380 q^{10} -1.74546 q^{11} -3.07194 q^{12} -2.73274 q^{13} +6.04179 q^{14} -4.69278 q^{15} -4.29634 q^{16} -0.616715 q^{17} -0.409782 q^{18} -5.70306 q^{19} +5.16543 q^{20} -5.15150 q^{21} -3.41987 q^{22} -4.59172 q^{23} +0.527498 q^{24} +2.89086 q^{25} -5.35424 q^{26} +5.36115 q^{27} +5.67035 q^{28} -7.61428 q^{29} -9.19456 q^{30} -9.29142 q^{31} -7.78630 q^{32} +2.91594 q^{33} -1.20833 q^{34} +8.66219 q^{35} -0.384589 q^{36} -1.00000 q^{37} -11.1740 q^{38} +4.56527 q^{39} -0.886981 q^{40} -2.53549 q^{41} -10.0933 q^{42} -4.26193 q^{43} -3.20962 q^{44} -0.587509 q^{45} -8.99654 q^{46} +4.53650 q^{47} +7.17741 q^{48} +2.50891 q^{49} +5.66405 q^{50} +1.03027 q^{51} -5.02507 q^{52} +4.14659 q^{53} +10.5041 q^{54} -4.90311 q^{55} -0.973683 q^{56} +9.52745 q^{57} -14.9186 q^{58} -11.7155 q^{59} -8.62929 q^{60} +12.7258 q^{61} -18.2046 q^{62} -0.644938 q^{63} -6.66298 q^{64} -7.67644 q^{65} +5.71319 q^{66} +7.61438 q^{67} -1.13404 q^{68} +7.67086 q^{69} +16.9718 q^{70} +13.4769 q^{71} +0.0660397 q^{72} +3.33881 q^{73} -1.95930 q^{74} -4.82943 q^{75} -10.4870 q^{76} -5.38239 q^{77} +8.94471 q^{78} -3.75881 q^{79} -12.0687 q^{80} -8.32881 q^{81} -4.96777 q^{82} -2.28548 q^{83} -9.47279 q^{84} -1.73239 q^{85} -8.35039 q^{86} +12.7203 q^{87} +0.551140 q^{88} +11.6178 q^{89} -1.15111 q^{90} -8.42681 q^{91} -8.44345 q^{92} +15.5221 q^{93} +8.88834 q^{94} -16.0203 q^{95} +13.0077 q^{96} +11.4355 q^{97} +4.91569 q^{98} +0.365059 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 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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