LMFDB - Embedded newform 4033.2.a.f.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.2036671352$
Analytic rank:	$0$
Dimension:	$85$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
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)

$f(q)$	$=$	$q-2.62495 q^{2} +2.49737 q^{3} +4.89034 q^{4} +0.915854 q^{5} -6.55547 q^{6} +2.77253 q^{7} -7.58698 q^{8} +3.23688 q^{9} +O(q^{10})$	\(q-2.62495 q^{2} +2.49737 q^{3} +4.89034 q^{4} +0.915854 q^{5} -6.55547 q^{6} +2.77253 q^{7} -7.58698 q^{8} +3.23688 q^{9} -2.40407 q^{10} +3.08728 q^{11} +12.2130 q^{12} -5.11135 q^{13} -7.27774 q^{14} +2.28723 q^{15} +10.1347 q^{16} -0.311928 q^{17} -8.49662 q^{18} +5.58279 q^{19} +4.47883 q^{20} +6.92405 q^{21} -8.10393 q^{22} +6.75058 q^{23} -18.9475 q^{24} -4.16121 q^{25} +13.4170 q^{26} +0.591568 q^{27} +13.5586 q^{28} -5.41237 q^{29} -6.00385 q^{30} +8.83960 q^{31} -11.4291 q^{32} +7.71008 q^{33} +0.818793 q^{34} +2.53923 q^{35} +15.8294 q^{36} +1.00000 q^{37} -14.6545 q^{38} -12.7650 q^{39} -6.94856 q^{40} +4.63897 q^{41} -18.1752 q^{42} -11.3400 q^{43} +15.0978 q^{44} +2.96451 q^{45} -17.7199 q^{46} +7.62852 q^{47} +25.3102 q^{48} +0.686928 q^{49} +10.9230 q^{50} -0.779000 q^{51} -24.9962 q^{52} +12.8607 q^{53} -1.55283 q^{54} +2.82749 q^{55} -21.0351 q^{56} +13.9423 q^{57} +14.2072 q^{58} +2.95362 q^{59} +11.1853 q^{60} -7.40494 q^{61} -23.2035 q^{62} +8.97434 q^{63} +9.73142 q^{64} -4.68125 q^{65} -20.2385 q^{66} -4.29048 q^{67} -1.52543 q^{68} +16.8587 q^{69} -6.66535 q^{70} -2.69005 q^{71} -24.5581 q^{72} +3.23107 q^{73} -2.62495 q^{74} -10.3921 q^{75} +27.3017 q^{76} +8.55957 q^{77} +33.5073 q^{78} -2.50044 q^{79} +9.28193 q^{80} -8.23326 q^{81} -12.1771 q^{82} +12.4005 q^{83} +33.8609 q^{84} -0.285680 q^{85} +29.7669 q^{86} -13.5167 q^{87} -23.4231 q^{88} -8.44240 q^{89} -7.78166 q^{90} -14.1714 q^{91} +33.0126 q^{92} +22.0758 q^{93} -20.0244 q^{94} +5.11302 q^{95} -28.5428 q^{96} +0.983838 q^{97} -1.80315 q^{98} +9.99313 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9}+O(q^{10}) $ 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9} + 9 q^{10} + 37 q^{11} + 44 q^{12} + 14 q^{13} + 26 q^{14} + 27 q^{15} + 85 q^{16} + 34 q^{17} + 3 q^{18} + 15 q^{19} + 15 q^{20} + 17 q^{21} + q^{22} + 72 q^{23} + 15 q^{24} + 85 q^{25} + 33 q^{26} + 69 q^{27} + 7 q^{28} + 19 q^{29} - 9 q^{30} + 23 q^{31} + 51 q^{32} + 32 q^{33} + 49 q^{34} + 40 q^{35} + 121 q^{36} + 85 q^{37} + 84 q^{38} + 39 q^{39} + 22 q^{40} + 55 q^{41} - 28 q^{42} + 78 q^{44} + 28 q^{45} + 17 q^{46} + 184 q^{47} + 97 q^{48} + 88 q^{49} + 26 q^{50} + 27 q^{51} + 73 q^{52} + 64 q^{53} + 31 q^{54} + 39 q^{55} + 68 q^{56} - 33 q^{57} + 28 q^{58} + 60 q^{59} - 22 q^{60} + 7 q^{61} + 70 q^{62} + 28 q^{63} + 102 q^{64} + 17 q^{65} - 15 q^{66} + 82 q^{67} + 92 q^{68} + 22 q^{69} - 41 q^{70} + 113 q^{71} - 19 q^{73} + 11 q^{74} + 45 q^{75} + 34 q^{76} + 64 q^{77} + 29 q^{78} + 23 q^{79} + 54 q^{80} + 149 q^{81} + 4 q^{82} + 100 q^{83} - 49 q^{84} - 5 q^{85} - 24 q^{86} + 65 q^{87} + 14 q^{88} + 84 q^{89} - 21 q^{90} + 32 q^{91} + 95 q^{92} + 19 q^{93} - 47 q^{94} + 102 q^{95} + 29 q^{96} + 7 q^{97} + 26 q^{98} + 107 q^{99}+O(q^{100}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9 + 9 * q^10 + 37 * q^11 + 44 * q^12 + 14 * q^13 + 26 * q^14 + 27 * q^15 + 85 * q^16 + 34 * q^17 + 3 * q^18 + 15 * q^19 + 15 * q^20 + 17 * q^21 + q^22 + 72 * q^23 + 15 * q^24 + 85 * q^25 + 33 * q^26 + 69 * q^27 + 7 * q^28 + 19 * q^29 - 9 * q^30 + 23 * q^31 + 51 * q^32 + 32 * q^33 + 49 * q^34 + 40 * q^35 + 121 * q^36 + 85 * q^37 + 84 * q^38 + 39 * q^39 + 22 * q^40 + 55 * q^41 - 28 * q^42 + 78 * q^44 + 28 * q^45 + 17 * q^46 + 184 * q^47 + 97 * q^48 + 88 * q^49 + 26 * q^50 + 27 * q^51 + 73 * q^52 + 64 * q^53 + 31 * q^54 + 39 * q^55 + 68 * q^56 - 33 * q^57 + 28 * q^58 + 60 * q^59 - 22 * q^60 + 7 * q^61 + 70 * q^62 + 28 * q^63 + 102 * q^64 + 17 * q^65 - 15 * q^66 + 82 * q^67 + 92 * q^68 + 22 * q^69 - 41 * q^70 + 113 * q^71 - 19 * q^73 + 11 * q^74 + 45 * q^75 + 34 * q^76 + 64 * q^77 + 29 * q^78 + 23 * q^79 + 54 * q^80 + 149 * q^81 + 4 * q^82 + 100 * q^83 - 49 * q^84 - 5 * q^85 - 24 * q^86 + 65 * q^87 + 14 * q^88 + 84 * q^89 - 21 * q^90 + 32 * q^91 + 95 * q^92 + 19 * q^93 - 47 * q^94 + 102 * q^95 + 29 * q^96 + 7 * q^97 + 26 * q^98 + 107 * 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 $

$2$	−2.62495	−1.85612	−0.928058	−	0.372435i	$-0.878523\pi$
$2$	−2.62495	−1.85612	−0.928058	+	0.372435i	$0.878523\pi$
$3$	2.49737	1.44186	0.720930	−	0.693008i	$-0.243715\pi$
$3$	2.49737	1.44186	0.720930	+	0.693008i	$0.243715\pi$
$4$	4.89034	2.44517
$5$	0.915854	0.409582	0.204791	−	0.978806i	$-0.434348\pi$
$5$	0.915854	0.409582	0.204791	+	0.978806i	$0.434348\pi$
$6$	−6.55547	−2.67626
$7$	2.77253	1.04792	0.523959	−	0.851743i	$-0.324454\pi$
$7$	2.77253	1.04792	0.523959	+	0.851743i	$0.324454\pi$
$8$	−7.58698	−2.68240
$9$	3.23688	1.07896
$10$	−2.40407	−0.760232
$11$	3.08728	0.930849	0.465424	−	0.885088i	$-0.345902\pi$
$11$	3.08728	0.930849	0.465424	+	0.885088i	$0.345902\pi$
$12$	12.2130	3.52559
$13$	−5.11135	−1.41763	−0.708817	−	0.705393i	$-0.750771\pi$
$13$	−5.11135	−1.41763	−0.708817	+	0.705393i	$0.750771\pi$
$14$	−7.27774	−1.94506
$15$	2.28723	0.590560
$16$	10.1347	2.53368
$17$	−0.311928	−0.0756536	−0.0378268	−	0.999284i	$-0.512044\pi$
$17$	−0.311928	−0.0756536	−0.0378268	+	0.999284i	$0.512044\pi$
$18$	−8.49662	−2.00267
$19$	5.58279	1.28078	0.640390	−	0.768050i	$-0.278773\pi$
$19$	5.58279	1.28078	0.640390	+	0.768050i	$0.278773\pi$
$20$	4.47883	1.00150
$21$	6.92405	1.51095
$22$	−8.10393	−1.72776
$23$	6.75058	1.40759	0.703796	−	0.710402i	$-0.251487\pi$
$23$	6.75058	1.40759	0.703796	+	0.710402i	$0.251487\pi$
$24$	−18.9475	−3.86765
$25$	−4.16121	−0.832242
$26$	13.4170	2.63129
$27$	0.591568	0.113847
$28$	13.5586	2.56234
$29$	−5.41237	−1.00505	−0.502526	−	0.864562i	$-0.667596\pi$
$29$	−5.41237	−1.00505	−0.502526	+	0.864562i	$0.667596\pi$
$30$	−6.00385	−1.09615
$31$	8.83960	1.58764	0.793820	−	0.608153i	$-0.208089\pi$
$31$	8.83960	1.58764	0.793820	+	0.608153i	$0.208089\pi$
$32$	−11.4291	−2.02041
$33$	7.71008	1.34215
$34$	0.818793	0.140422
$35$	2.53923	0.429209
$36$	15.8294	2.63824
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	−14.6545	−2.37728
$39$	−12.7650	−2.04403
$40$	−6.94856	−1.09866
$41$	4.63897	0.724486	0.362243	−	0.932084i	$-0.382011\pi$
$41$	4.63897	0.724486	0.362243	+	0.932084i	$0.382011\pi$
$42$	−18.1752	−2.80450
$43$	−11.3400	−1.72933	−0.864667	−	0.502346i	$-0.832471\pi$
$43$	−11.3400	−1.72933	−0.864667	+	0.502346i	$0.832471\pi$
$44$	15.0978	2.27608
$45$	2.96451	0.441922
$46$	−17.7199	−2.61266
$47$	7.62852	1.11273	0.556367	−	0.830937i	$-0.312195\pi$
$47$	7.62852	1.11273	0.556367	+	0.830937i	$0.312195\pi$
$48$	25.3102	3.65321
$49$	0.686928	0.0981325
$50$	10.9230	1.54474
$51$	−0.779000	−0.109082
$52$	−24.9962	−3.46635
$53$	12.8607	1.76656	0.883278	−	0.468850i	$-0.155331\pi$
$53$	12.8607	1.76656	0.883278	+	0.468850i	$0.155331\pi$
$54$	−1.55283	−0.211314
$55$	2.82749	0.381259
$56$	−21.0351	−2.81094
$57$	13.9423	1.84671
$58$	14.2072	1.86549
$59$	2.95362	0.384529	0.192264	−	0.981343i	$-0.438417\pi$
$59$	2.95362	0.384529	0.192264	+	0.981343i	$0.438417\pi$
$60$	11.1853	1.44402
$61$	−7.40494	−0.948105	−0.474053	−	0.880496i	$-0.657209\pi$
$61$	−7.40494	−0.948105	−0.474053	+	0.880496i	$0.657209\pi$
$62$	−23.2035	−2.94684
$63$	8.97434	1.13066
$64$	9.73142	1.21643
$65$	−4.68125	−0.580638
$66$	−20.2385	−2.49119
$67$	−4.29048	−0.524166	−0.262083	−	0.965045i	$-0.584409\pi$
$67$	−4.29048	−0.524166	−0.262083	+	0.965045i	$0.584409\pi$
$68$	−1.52543	−0.184986
$69$	16.8587	2.02955
$70$	−6.66535	−0.796661
$71$	−2.69005	−0.319250	−0.159625	−	0.987178i	$-0.551028\pi$
$71$	−2.69005	−0.319250	−0.159625	+	0.987178i	$0.551028\pi$
$72$	−24.5581	−2.89420
$73$	3.23107	0.378168	0.189084	−	0.981961i	$-0.439448\pi$
$73$	3.23107	0.378168	0.189084	+	0.981961i	$0.439448\pi$
$74$	−2.62495	−0.305144
$75$	−10.3921	−1.19998
$76$	27.3017	3.13172
$77$	8.55957	0.975453
$78$	33.5073	3.79395
$79$	−2.50044	−0.281321	−0.140661	−	0.990058i	$-0.544923\pi$
$79$	−2.50044	−0.281321	−0.140661	+	0.990058i	$0.544923\pi$
$80$	9.28193	1.03775
$81$	−8.23326	−0.914807
$82$	−12.1771	−1.34473
$83$	12.4005	1.36113	0.680564	−	0.732689i	$-0.261735\pi$
$83$	12.4005	1.36113	0.680564	+	0.732689i	$0.261735\pi$
$84$	33.8609	3.69453
$85$	−0.285680	−0.0309864
$86$	29.7669	3.20985
$87$	−13.5167	−1.44914
$88$	−23.4231	−2.49691
$89$	−8.44240	−0.894892	−0.447446	−	0.894311i	$-0.647666\pi$
$89$	−8.44240	−0.894892	−0.447446	+	0.894311i	$0.647666\pi$
$90$	−7.78166	−0.820259
$91$	−14.1714	−1.48556
$92$	33.0126	3.44180
$93$	22.0758	2.28915
$94$	−20.0244	−2.06536
$95$	5.11302	0.524585
$96$	−28.5428	−2.91314
$97$	0.983838	0.0998937	0.0499468	−	0.998752i	$-0.484095\pi$
$97$	0.983838	0.0998937	0.0499468	+	0.998752i	$0.484095\pi$
$98$	−1.80315	−0.182145
$99$	9.99313	1.00435
$100$	−20.3497	−2.03497
$101$	−5.09642	−0.507112	−0.253556	−	0.967321i	$-0.581600\pi$
$101$	−5.09642	−0.507112	−0.253556	+	0.967321i	$0.581600\pi$
$102$	2.04483	0.202469
$103$	6.86124	0.676058	0.338029	−	0.941136i	$-0.390240\pi$
$103$	6.86124	0.676058	0.338029	+	0.941136i	$0.390240\pi$
$104$	38.7797	3.80266
$105$	6.34141	0.618859
$106$	−33.7587	−3.27893
$107$	11.8027	1.14101	0.570505	−	0.821294i	$-0.306747\pi$
$107$	11.8027	1.14101	0.570505	+	0.821294i	$0.306747\pi$
$108$	2.89296	0.278376
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	−7.42202	−0.707661
$111$	2.49737	0.237040
$112$	28.0988	2.65509
$113$	20.6389	1.94155	0.970774	−	0.239996i	$-0.0771462\pi$
$113$	20.6389	1.94155	0.970774	+	0.239996i	$0.0771462\pi$
$114$	−36.5978	−3.42770
$115$	6.18254	0.576525
$116$	−26.4683	−2.45752
$117$	−16.5448	−1.52957
$118$	−7.75309	−0.713730
$119$	−0.864829	−0.0792788
$120$	−17.3532	−1.58412
$121$	−1.46873	−0.133521
$122$	19.4376	1.75979
$123$	11.5853	1.04461
$124$	43.2286	3.88205
$125$	−8.39033	−0.750454
$126$	−23.5571	−2.09864
$127$	2.69862	0.239464	0.119732	−	0.992806i	$-0.461797\pi$
$127$	2.69862	0.239464	0.119732	+	0.992806i	$0.461797\pi$
$128$	−2.68616	−0.237425
$129$	−28.3202	−2.49346
$130$	12.2880	1.07773
$131$	6.83118	0.596843	0.298422	−	0.954434i	$-0.403540\pi$
$131$	6.83118	0.596843	0.298422	+	0.954434i	$0.403540\pi$
$132$	37.7049	3.28179
$133$	15.4785	1.34215
$134$	11.2623	0.972913
$135$	0.541789	0.0466298
$136$	2.36659	0.202933
$137$	5.26696	0.449987	0.224994	−	0.974360i	$-0.427764\pi$
$137$	5.26696	0.449987	0.224994	+	0.974360i	$0.427764\pi$
$138$	−44.2532	−3.76708
$139$	18.0099	1.52758	0.763789	−	0.645466i	$-0.223337\pi$
$139$	18.0099	1.52758	0.763789	+	0.645466i	$0.223337\pi$
$140$	12.4177	1.04949
$141$	19.0513	1.60441
$142$	7.06123	0.592565
$143$	−15.7801	−1.31960
$144$	32.8048	2.73374
$145$	−4.95694	−0.411651
$146$	−8.48137	−0.701923
$147$	1.71552	0.141493
$148$	4.89034	0.401983
$149$	−4.00260	−0.327905	−0.163953	−	0.986468i	$-0.552424\pi$
$149$	−4.00260	−0.327905	−0.163953	+	0.986468i	$0.552424\pi$
$150$	27.2787	2.22730
$151$	−12.8623	−1.04672	−0.523361	−	0.852111i	$-0.675322\pi$
$151$	−12.8623	−1.04672	−0.523361	+	0.852111i	$0.675322\pi$
$152$	−42.3565	−3.43557
$153$	−1.00967	−0.0816271
$154$	−22.4684	−1.81056
$155$	8.09578	0.650269
$156$	−62.4249	−4.99799
$157$	17.1050	1.36513	0.682564	−	0.730826i	$-0.260865\pi$
$157$	17.1050	1.36513	0.682564	+	0.730826i	$0.260865\pi$
$158$	6.56351	0.522165
$159$	32.1180	2.54713
$160$	−10.4674	−0.827522
$161$	18.7162	1.47504
$162$	21.6119	1.69799
$163$	−3.00302	−0.235215	−0.117607	−	0.993060i	$-0.537522\pi$
$163$	−3.00302	−0.235215	−0.117607	+	0.993060i	$0.537522\pi$
$164$	22.6861	1.77149
$165$	7.06131	0.549722
$166$	−32.5505	−2.52641
$167$	−13.1879	−1.02051	−0.510254	−	0.860023i	$-0.670449\pi$
$167$	−13.1879	−1.02051	−0.510254	+	0.860023i	$0.670449\pi$
$168$	−52.5326	−4.05298
$169$	13.1259	1.00968
$170$	0.749895	0.0575143
$171$	18.0708	1.38191
$172$	−55.4564	−4.22851
$173$	8.80846	0.669695	0.334847	−	0.942272i	$-0.391315\pi$
$173$	8.80846	0.669695	0.334847	+	0.942272i	$0.391315\pi$
$174$	35.4806	2.68978
$175$	−11.5371	−0.872122
$176$	31.2887	2.35847
$177$	7.37630	0.554436
$178$	22.1608	1.66102
$179$	−14.6016	−1.09138	−0.545688	−	0.837988i	$-0.683732\pi$
$179$	−14.6016	−1.09138	−0.545688	+	0.837988i	$0.683732\pi$
$180$	14.4974	1.08057
$181$	17.1855	1.27739	0.638693	−	0.769461i	$-0.279475\pi$
$181$	17.1855	1.27739	0.638693	+	0.769461i	$0.279475\pi$
$182$	37.1991	2.75738
$183$	−18.4929	−1.36703
$184$	−51.2165	−3.77573
$185$	0.915854	0.0673349
$186$	−57.9477	−4.24893
$187$	−0.963007	−0.0704220
$188$	37.3060	2.72082
$189$	1.64014	0.119303
$190$	−13.4214	−0.973691
$191$	−20.5170	−1.48456	−0.742279	−	0.670091i	$-0.766255\pi$
$191$	−20.5170	−1.48456	−0.742279	+	0.670091i	$0.766255\pi$
$192$	24.3030	1.75392
$193$	1.47202	0.105958	0.0529792	−	0.998596i	$-0.483128\pi$
$193$	1.47202	0.105958	0.0529792	+	0.998596i	$0.483128\pi$
$194$	−2.58252	−0.185414
$195$	−11.6908	−0.837198
$196$	3.35931	0.239951
$197$	−8.38377	−0.597319	−0.298659	−	0.954360i	$-0.596539\pi$
$197$	−8.38377	−0.597319	−0.298659	+	0.954360i	$0.596539\pi$
$198$	−26.2314	−1.86419
$199$	−7.88280	−0.558797	−0.279398	−	0.960175i	$-0.590135\pi$
$199$	−7.88280	−0.558797	−0.279398	+	0.960175i	$0.590135\pi$
$200$	31.5710	2.23241
$201$	−10.7149	−0.755773
$202$	13.3778	0.941260
$203$	−15.0060	−1.05321
$204$	−3.80957	−0.266723
$205$	4.24862	0.296737
$206$	−18.0104	−1.25484
$207$	21.8508	1.51873
$208$	−51.8021	−3.59183
$209$	17.2356	1.19221
$210$	−16.6459	−1.14867
$211$	−1.41650	−0.0975162	−0.0487581	−	0.998811i	$-0.515526\pi$
$211$	−1.41650	−0.0975162	−0.0487581	+	0.998811i	$0.515526\pi$
$212$	62.8933	4.31953
$213$	−6.71805	−0.460313
$214$	−30.9815	−2.11785
$215$	−10.3858	−0.708305
$216$	−4.48821	−0.305384
$217$	24.5081	1.66372
$218$	2.62495	0.177784
$219$	8.06918	0.545265
$220$	13.8274	0.932243
$221$	1.59437	0.107249
$222$	−6.55547	−0.439974
$223$	6.32104	0.423288	0.211644	−	0.977347i	$-0.432118\pi$
$223$	6.32104	0.423288	0.211644	+	0.977347i	$0.432118\pi$
$224$	−31.6876	−2.11722
$225$	−13.4693	−0.897955
$226$	−54.1761	−3.60374
$227$	11.4149	0.757634	0.378817	−	0.925472i	$-0.376331\pi$
$227$	11.4149	0.757634	0.378817	+	0.925472i	$0.376331\pi$
$228$	68.1827	4.51551
$229$	0.101449	0.00670391	0.00335195	−	0.999994i	$-0.498933\pi$
$229$	0.101449	0.00670391	0.00335195	+	0.999994i	$0.498933\pi$
$230$	−16.2288	−1.07010
$231$	21.3764	1.40647
$232$	41.0635	2.69595
$233$	20.4082	1.33698	0.668492	−	0.743719i	$-0.266940\pi$
$233$	20.4082	1.33698	0.668492	+	0.743719i	$0.266940\pi$
$234$	43.4292	2.83906
$235$	6.98661	0.455756
$236$	14.4442	0.940238
$237$	−6.24453	−0.405626
$238$	2.27013	0.147151
$239$	−10.3833	−0.671642	−0.335821	−	0.941926i	$-0.609014\pi$
$239$	−10.3833	−0.671642	−0.335821	+	0.941926i	$0.609014\pi$
$240$	23.1804	1.49629
$241$	8.52476	0.549128	0.274564	−	0.961569i	$-0.411467\pi$
$241$	8.52476	0.549128	0.274564	+	0.961569i	$0.411467\pi$
$242$	3.85533	0.247830
$243$	−22.3362	−1.43287
$244$	−36.2127	−2.31828
$245$	0.629125	0.0401934
$246$	−30.4107	−1.93891
$247$	−28.5356	−1.81568
$248$	−67.0658	−4.25869
$249$	30.9686	1.96256
$250$	22.0242	1.39293
$251$	−20.0318	−1.26440	−0.632199	−	0.774806i	$-0.717847\pi$
$251$	−20.0318	−1.26440	−0.632199	+	0.774806i	$0.717847\pi$
$252$	43.8875	2.76466
$253$	20.8409	1.31026
$254$	−7.08372	−0.444472
$255$	−0.713450	−0.0446780
$256$	−12.4118	−0.775738
$257$	24.9607	1.55700	0.778501	−	0.627643i	$-0.215980\pi$
$257$	24.9607	1.55700	0.778501	+	0.627643i	$0.215980\pi$
$258$	74.3390	4.62815
$259$	2.77253	0.172277
$260$	−22.8929	−1.41976
$261$	−17.5192	−1.08441
$262$	−17.9315	−1.10781
$263$	−26.6623	−1.64407	−0.822035	−	0.569437i	$-0.807161\pi$
$263$	−26.6623	−1.64407	−0.822035	+	0.569437i	$0.807161\pi$
$264$	−58.4962	−3.60019
$265$	11.7785	0.723550
$266$	−40.6301	−2.49119
$267$	−21.0838	−1.29031
$268$	−20.9819	−1.28167
$269$	−18.7869	−1.14545	−0.572727	−	0.819746i	$-0.694115\pi$
$269$	−18.7869	−1.14545	−0.572727	+	0.819746i	$0.694115\pi$
$270$	−1.42217	−0.0865504
$271$	−1.23039	−0.0747406	−0.0373703	−	0.999301i	$-0.511898\pi$
$271$	−1.23039	−0.0747406	−0.0373703	+	0.999301i	$0.511898\pi$
$272$	−3.16130	−0.191682
$273$	−35.3912	−2.14197
$274$	−13.8255	−0.835229
$275$	−12.8468	−0.774692
$276$	82.4448	4.96259
$277$	−17.9773	−1.08015	−0.540074	−	0.841617i	$-0.681604\pi$
$277$	−17.9773	−1.08015	−0.540074	+	0.841617i	$0.681604\pi$
$278$	−47.2750	−2.83536
$279$	28.6127	1.71300
$280$	−19.2651	−1.15131
$281$	19.4732	1.16167	0.580837	−	0.814020i	$-0.302725\pi$
$281$	19.4732	1.16167	0.580837	+	0.814020i	$0.302725\pi$
$282$	−50.0085	−2.97796
$283$	−22.2775	−1.32426	−0.662130	−	0.749389i	$-0.730347\pi$
$283$	−22.2775	−1.32426	−0.662130	+	0.749389i	$0.730347\pi$
$284$	−13.1552	−0.780620
$285$	12.7691	0.756378
$286$	41.4220	2.44934
$287$	12.8617	0.759202
$288$	−36.9947	−2.17993
$289$	−16.9027	−0.994277
$290$	13.0117	0.764073
$291$	2.45701	0.144033
$292$	15.8010	0.924684
$293$	−28.3324	−1.65520	−0.827599	−	0.561319i	$-0.810294\pi$
$293$	−28.3324	−1.65520	−0.827599	+	0.561319i	$0.810294\pi$
$294$	−4.50313	−0.262628
$295$	2.70509	0.157496
$296$	−7.58698	−0.440984
$297$	1.82633	0.105975
$298$	10.5066	0.608631
$299$	−34.5046	−1.99545
$300$	−50.8209	−2.93414
$301$	−31.4405	−1.81220
$302$	33.7629	1.94284
$303$	−12.7277	−0.731185
$304$	56.5801	3.24509
$305$	−6.78184	−0.388327
$306$	2.65033	0.151509
$307$	−1.17159	−0.0668664	−0.0334332	−	0.999441i	$-0.510644\pi$
$307$	−1.17159	−0.0668664	−0.0334332	+	0.999441i	$0.510644\pi$
$308$	41.8592	2.38515
$309$	17.1351	0.974781
$310$	−21.2510	−1.20697
$311$	−9.62845	−0.545979	−0.272990	−	0.962017i	$-0.588012\pi$
$311$	−9.62845	−0.545979	−0.272990	+	0.962017i	$0.588012\pi$
$312$	96.8474	5.48290
$313$	−33.9059	−1.91648	−0.958238	−	0.285971i	$-0.907684\pi$
$313$	−33.9059	−1.91648	−0.958238	+	0.285971i	$0.907684\pi$
$314$	−44.8997	−2.53384
$315$	8.21918	0.463098
$316$	−12.2280	−0.687878
$317$	−4.74609	−0.266567	−0.133283	−	0.991078i	$-0.542552\pi$
$317$	−4.74609	−0.266567	−0.133283	+	0.991078i	$0.542552\pi$
$318$	−84.3081	−4.72776
$319$	−16.7095	−0.935551
$320$	8.91256	0.498227
$321$	29.4758	1.64518
$322$	−49.1290	−2.73785
$323$	−1.74143	−0.0968956
$324$	−40.2634	−2.23686
$325$	21.2694	1.17981
$326$	7.88277	0.436586
$327$	−2.49737	−0.138105
$328$	−35.1958	−1.94336
$329$	21.1503	1.16605
$330$	−18.5355	−1.02035
$331$	−10.7828	−0.592676	−0.296338	−	0.955083i	$-0.595765\pi$
$331$	−10.7828	−0.592676	−0.296338	+	0.955083i	$0.595765\pi$
$332$	60.6425	3.32819
$333$	3.23688	0.177380
$334$	34.6175	1.89418
$335$	−3.92945	−0.214689
$336$	70.1733	3.82827
$337$	−11.0289	−0.600781	−0.300391	−	0.953816i	$-0.597117\pi$
$337$	−11.0289	−0.600781	−0.300391	+	0.953816i	$0.597117\pi$
$338$	−34.4548	−1.87409
$339$	51.5431	2.79944
$340$	−1.39707	−0.0757669
$341$	27.2903	1.47785
$342$	−47.4349	−2.56498
$343$	−17.5032	−0.945083
$344$	86.0363	4.63877
$345$	15.4401	0.831268
$346$	−23.1217	−1.24303
$347$	−14.5936	−0.783426	−0.391713	−	0.920087i	$-0.628117\pi$
$347$	−14.5936	−0.783426	−0.391713	+	0.920087i	$0.628117\pi$
$348$	−66.1013	−3.54340
$349$	−16.4844	−0.882389	−0.441194	−	0.897412i	$-0.645445\pi$
$349$	−16.4844	−0.882389	−0.441194	+	0.897412i	$0.645445\pi$
$350$	30.2842	1.61876
$351$	−3.02371	−0.161394
$352$	−35.2849	−1.88069
$353$	3.53753	0.188284	0.0941418	−	0.995559i	$-0.469989\pi$
$353$	3.53753	0.188284	0.0941418	+	0.995559i	$0.469989\pi$
$354$	−19.3624	−1.02910
$355$	−2.46369	−0.130759
$356$	−41.2862	−2.18816
$357$	−2.15980	−0.114309
$358$	38.3284	2.02572
$359$	10.3635	0.546964	0.273482	−	0.961877i	$-0.411825\pi$
$359$	10.3635	0.546964	0.273482	+	0.961877i	$0.411825\pi$
$360$	−22.4916	−1.18541
$361$	12.1676	0.640399
$362$	−45.1109	−2.37098
$363$	−3.66796	−0.192518
$364$	−69.3028	−3.63245
$365$	2.95918	0.154891
$366$	48.5429	2.53738
$367$	15.7341	0.821311	0.410656	−	0.911791i	$-0.365300\pi$
$367$	15.7341	0.821311	0.410656	+	0.911791i	$0.365300\pi$
$368$	68.4152	3.56639
$369$	15.0158	0.781690
$370$	−2.40407	−0.124981
$371$	35.6567	1.85121
$372$	107.958	5.59736
$373$	31.6788	1.64027	0.820134	−	0.572171i	$-0.193899\pi$
$373$	31.6788	1.64027	0.820134	+	0.572171i	$0.193899\pi$
$374$	2.52784	0.130712
$375$	−20.9538	−1.08205
$376$	−57.8774	−2.98480
$377$	27.6645	1.42479
$378$	−4.30528	−0.221440
$379$	7.84041	0.402735	0.201367	−	0.979516i	$-0.435462\pi$
$379$	7.84041	0.402735	0.201367	+	0.979516i	$0.435462\pi$
$380$	25.0044	1.28270
$381$	6.73946	0.345273
$382$	53.8560	2.75551
$383$	30.5171	1.55935	0.779675	−	0.626185i	$-0.215384\pi$
$383$	30.5171	1.55935	0.779675	+	0.626185i	$0.215384\pi$
$384$	−6.70835	−0.342334
$385$	7.83931	0.399528
$386$	−3.86397	−0.196671
$387$	−36.7062	−1.86588
$388$	4.81130	0.244257
$389$	2.60412	0.132034	0.0660171	−	0.997818i	$-0.478971\pi$
$389$	2.60412	0.132034	0.0660171	+	0.997818i	$0.478971\pi$
$390$	30.6878	1.55394
$391$	−2.10569	−0.106489
$392$	−5.21170	−0.263231
$393$	17.0600	0.860564
$394$	22.0069	1.10869
$395$	−2.29004	−0.115224
$396$	48.8698	2.45580
$397$	−15.0405	−0.754859	−0.377430	−	0.926038i	$-0.623192\pi$
$397$	−15.0405	−0.754859	−0.377430	+	0.926038i	$0.623192\pi$
$398$	20.6919	1.03719
$399$	38.6555	1.93520
$400$	−42.1727	−2.10864
$401$	−19.7617	−0.986850	−0.493425	−	0.869788i	$-0.664255\pi$
$401$	−19.7617	−0.986850	−0.493425	+	0.869788i	$0.664255\pi$
$402$	28.1261	1.40280
$403$	−45.1823	−2.25069
$404$	−24.9232	−1.23998
$405$	−7.54047	−0.374689
$406$	39.3898	1.95488
$407$	3.08728	0.153031
$408$	5.91026	0.292601
$409$	10.9404	0.540970	0.270485	−	0.962724i	$-0.412816\pi$
$409$	10.9404	0.540970	0.270485	+	0.962724i	$0.412816\pi$
$410$	−11.1524	−0.550778
$411$	13.1536	0.648818
$412$	33.5538	1.65308
$413$	8.18901	0.402955
$414$	−57.3571	−2.81895
$415$	11.3570	0.557494
$416$	58.4183	2.86419
$417$	44.9774	2.20255
$418$	−45.2426	−2.21289
$419$	−2.45686	−0.120026	−0.0600128	−	0.998198i	$-0.519114\pi$
$419$	−2.45686	−0.120026	−0.0600128	+	0.998198i	$0.519114\pi$
$420$	31.0117	1.51321
$421$	30.9934	1.51052	0.755262	−	0.655423i	$-0.227510\pi$
$421$	30.9934	1.51052	0.755262	+	0.655423i	$0.227510\pi$
$422$	3.71825	0.181001
$423$	24.6926	1.20059
$424$	−97.5740	−4.73861
$425$	1.29800	0.0629621
$426$	17.6345	0.854395
$427$	−20.5304	−0.993537
$428$	57.7192	2.78996
$429$	−39.4089	−1.90268
$430$	27.2621	1.31470
$431$	36.5313	1.75965	0.879826	−	0.475295i	$-0.157659\pi$
$431$	36.5313	1.75965	0.879826	+	0.475295i	$0.157659\pi$
$432$	5.99537	0.288453
$433$	−20.8301	−1.00103	−0.500516	−	0.865727i	$-0.666856\pi$
$433$	−20.8301	−1.00103	−0.500516	+	0.865727i	$0.666856\pi$
$434$	−64.3323	−3.08805
$435$	−12.3793	−0.593543
$436$	−4.89034	−0.234205
$437$	37.6871	1.80282
$438$	−21.1812	−1.01207
$439$	−21.8879	−1.04465	−0.522327	−	0.852745i	$-0.674936\pi$
$439$	−21.8879	−1.04465	−0.522327	+	0.852745i	$0.674936\pi$
$440$	−21.4521	−1.02269
$441$	2.22350	0.105881
$442$	−4.18514	−0.199067
$443$	27.5200	1.30752	0.653758	−	0.756704i	$-0.273192\pi$
$443$	27.5200	1.30752	0.653758	+	0.756704i	$0.273192\pi$
$444$	12.2130	0.579603
$445$	−7.73200	−0.366532
$446$	−16.5924	−0.785672
$447$	−9.99598	−0.472794
$448$	26.9807	1.27472
$449$	20.3484	0.960302	0.480151	−	0.877186i	$-0.340582\pi$
$449$	20.3484	0.960302	0.480151	+	0.877186i	$0.340582\pi$
$450$	35.3562	1.66671
$451$	14.3218	0.674387
$452$	100.931	4.74741
$453$	−32.1220	−1.50923
$454$	−29.9635	−1.40626
$455$	−12.9789	−0.608461
$456$	−105.780	−4.95361
$457$	−4.17012	−0.195070	−0.0975350	−	0.995232i	$-0.531096\pi$
$457$	−4.17012	−0.195070	−0.0975350	+	0.995232i	$0.531096\pi$
$458$	−0.266297	−0.0124432
$459$	−0.184526	−0.00861295
$460$	30.2347	1.40970
$461$	−28.8920	−1.34564	−0.672818	−	0.739808i	$-0.734916\pi$
$461$	−28.8920	−1.34564	−0.672818	+	0.739808i	$0.734916\pi$
$462$	−56.1120	−2.61057
$463$	29.3546	1.36423	0.682113	−	0.731247i	$-0.261061\pi$
$463$	29.3546	1.36423	0.682113	+	0.731247i	$0.261061\pi$
$464$	−54.8529	−2.54648
$465$	20.2182	0.937596
$466$	−53.5704	−2.48160
$467$	36.5212	1.69000	0.845000	−	0.534767i	$-0.179600\pi$
$467$	36.5212	1.69000	0.845000	+	0.534767i	$0.179600\pi$
$468$	−80.9097	−3.74005
$469$	−11.8955	−0.549283
$470$	−18.3395	−0.845936
$471$	42.7176	1.96832
$472$	−22.4091	−1.03146
$473$	−35.0097	−1.60975
$474$	16.3915	0.752889
$475$	−23.2312	−1.06592
$476$	−4.22931	−0.193850
$477$	41.6286	1.90604
$478$	27.2557	1.24665
$479$	23.1199	1.05638	0.528188	−	0.849127i	$-0.322871\pi$
$479$	23.1199	1.05638	0.528188	+	0.849127i	$0.322871\pi$
$480$	−26.1411	−1.19317
$481$	−5.11135	−0.233057
$482$	−22.3770	−1.01925
$483$	46.7413	2.12680
$484$	−7.18257	−0.326480
$485$	0.901052	0.0409147
$486$	58.6314	2.65957
$487$	33.4896	1.51756	0.758779	−	0.651348i	$-0.225796\pi$
$487$	33.4896	1.51756	0.758779	+	0.651348i	$0.225796\pi$
$488$	56.1811	2.54320
$489$	−7.49967	−0.339147
$490$	−1.65142	−0.0746035
$491$	29.3470	1.32441	0.662205	−	0.749323i	$-0.269621\pi$
$491$	29.3470	1.32441	0.662205	+	0.749323i	$0.269621\pi$
$492$	56.6558	2.55424
$493$	1.68827	0.0760358
$494$	74.9044	3.37011
$495$	9.15225	0.411363
$496$	89.5869	4.02257
$497$	−7.45824	−0.334548
$498$	−81.2909	−3.64273
$499$	−6.80632	−0.304693	−0.152346	−	0.988327i	$-0.548683\pi$
$499$	−6.80632	−0.304693	−0.152346	+	0.988327i	$0.548683\pi$
$500$	−41.0315	−1.83499
$501$	−32.9351	−1.47143
$502$	52.5824	2.34687
$503$	17.5390	0.782027	0.391014	−	0.920385i	$-0.372125\pi$
$503$	17.5390	0.782027	0.391014	+	0.920385i	$0.372125\pi$
$504$	−68.0881	−3.03288
$505$	−4.66757	−0.207704
$506$	−54.7062	−2.43199
$507$	32.7803	1.45582
$508$	13.1972	0.585529
$509$	−10.9100	−0.483577	−0.241788	−	0.970329i	$-0.577734\pi$
$509$	−10.9100	−0.483577	−0.241788	+	0.970329i	$0.577734\pi$
$510$	1.87277	0.0829276
$511$	8.95823	0.396289
$512$	37.9526	1.67729
$513$	3.30260	0.145813
$514$	−65.5203	−2.88998
$515$	6.28390	0.276902
$516$	−138.495	−6.09692
$517$	23.5513	1.03579
$518$	−7.27774	−0.319766
$519$	21.9980	0.965606
$520$	35.5165	1.55750
$521$	−0.811856	−0.0355681	−0.0177840	−	0.999842i	$-0.505661\pi$
$521$	−0.811856	−0.0355681	−0.0177840	+	0.999842i	$0.505661\pi$
$522$	45.9869	2.01279
$523$	−44.1589	−1.93093	−0.965466	−	0.260529i	$-0.916103\pi$
$523$	−44.1589	−1.93093	−0.965466	+	0.260529i	$0.916103\pi$
$524$	33.4068	1.45938
$525$	−28.8124	−1.25748
$526$	69.9872	3.05159
$527$	−2.75732	−0.120111
$528$	78.1395	3.40059
$529$	22.5703	0.981318
$530$	−30.9180	−1.34299
$531$	9.56051	0.414891
$532$	75.6949	3.28179
$533$	−23.7114	−1.02706
$534$	55.3439	2.39496
$535$	10.8096	0.467338
$536$	32.5518	1.40602
$537$	−36.4657	−1.57361
$538$	49.3145	2.12610
$539$	2.12074	0.0913466
$540$	2.64953	0.114018
$541$	35.0167	1.50549	0.752743	−	0.658314i	$-0.228730\pi$
$541$	35.0167	1.50549	0.752743	+	0.658314i	$0.228730\pi$
$542$	3.22969	0.138727
$543$	42.9186	1.84181
$544$	3.56507	0.152851
$545$	−0.915854	−0.0392309
$546$	92.9000	3.97575
$547$	7.53892	0.322341	0.161170	−	0.986927i	$-0.448473\pi$
$547$	7.53892	0.322341	0.161170	+	0.986927i	$0.448473\pi$
$548$	25.7572	1.10029
$549$	−23.9689	−1.02297
$550$	33.7222	1.43792
$551$	−30.2161	−1.28725
$552$	−127.907	−5.44407
$553$	−6.93254	−0.294802
$554$	47.1893	2.00488
$555$	2.28723	0.0970875
$556$	88.0744	3.73519
$557$	−41.9938	−1.77933	−0.889667	−	0.456609i	$-0.849064\pi$
$557$	−41.9938	−1.77933	−0.889667	+	0.456609i	$0.849064\pi$
$558$	−75.1067	−3.17952
$559$	57.9627	2.45156
$560$	25.7344	1.08748
$561$	−2.40499	−0.101539
$562$	−51.1161	−2.15620
$563$	−10.2205	−0.430742	−0.215371	−	0.976532i	$-0.569096\pi$
$563$	−10.2205	−0.430742	−0.215371	+	0.976532i	$0.569096\pi$
$564$	93.1671	3.92304
$565$	18.9022	0.795224
$566$	58.4772	2.45798
$567$	−22.8270	−0.958643
$568$	20.4093	0.856356
$569$	7.91378	0.331763	0.165882	−	0.986146i	$-0.446953\pi$
$569$	7.91378	0.331763	0.165882	+	0.986146i	$0.446953\pi$
$570$	−33.5183	−1.40393
$571$	−21.5305	−0.901022	−0.450511	−	0.892771i	$-0.648758\pi$
$571$	−21.5305	−0.901022	−0.450511	+	0.892771i	$0.648758\pi$
$572$	−77.1702	−3.22665
$573$	−51.2386	−2.14052
$574$	−33.7613	−1.40917
$575$	−28.0906	−1.17146
$576$	31.4994	1.31247
$577$	−13.0018	−0.541274	−0.270637	−	0.962682i	$-0.587234\pi$
$577$	−13.0018	−0.541274	−0.270637	+	0.962682i	$0.587234\pi$
$578$	44.3687	1.84549
$579$	3.67618	0.152777
$580$	−24.2411	−1.00656
$581$	34.3807	1.42635
$582$	−6.44952	−0.267341
$583$	39.7046	1.64440
$584$	−24.5140	−1.01440
$585$	−15.1526	−0.626484
$586$	74.3711	3.07224
$587$	−38.9953	−1.60951	−0.804754	−	0.593608i	$-0.797703\pi$
$587$	−38.9953	−1.60951	−0.804754	+	0.593608i	$0.797703\pi$
$588$	8.38945	0.345975
$589$	49.3497	2.03342
$590$	−7.10070	−0.292331
$591$	−20.9374	−0.861249
$592$	10.1347	0.416535
$593$	−33.7818	−1.38725	−0.693627	−	0.720334i	$-0.743988\pi$
$593$	−33.7818	−1.38725	−0.693627	+	0.720334i	$0.743988\pi$
$594$	−4.79402	−0.196701
$595$	−0.792057	−0.0324712
$596$	−19.5740	−0.801784
$597$	−19.6863	−0.805707
$598$	90.5726	3.70379
$599$	−30.7155	−1.25500	−0.627501	−	0.778616i	$-0.715922\pi$
$599$	−30.7155	−1.25500	−0.627501	+	0.778616i	$0.715922\pi$
$600$	78.8446	3.21882
$601$	−42.5521	−1.73574	−0.867868	−	0.496795i	$-0.834510\pi$
$601$	−42.5521	−1.73574	−0.867868	+	0.496795i	$0.834510\pi$
$602$	82.5296	3.36366
$603$	−13.8878	−0.565553
$604$	−62.9011	−2.55941
$605$	−1.34514	−0.0546877
$606$	33.4094	1.35716
$607$	−0.357441	−0.0145081	−0.00725405	−	0.999974i	$-0.502309\pi$
$607$	−0.357441	−0.0145081	−0.00725405	+	0.999974i	$0.502309\pi$
$608$	−63.8065	−2.58770
$609$	−37.4755	−1.51858
$610$	17.8020	0.720780
$611$	−38.9920	−1.57745
$612$	−4.93763	−0.199592
$613$	42.3848	1.71191	0.855953	−	0.517054i	$-0.172971\pi$
$613$	42.3848	1.71191	0.855953	+	0.517054i	$0.172971\pi$
$614$	3.07537	0.124112
$615$	10.6104	0.427853
$616$	−64.9412	−2.61656
$617$	−15.5147	−0.624599	−0.312299	−	0.949984i	$-0.601099\pi$
$617$	−15.5147	−0.624599	−0.312299	+	0.949984i	$0.601099\pi$
$618$	−44.9787	−1.80931
$619$	−25.5528	−1.02705	−0.513527	−	0.858073i	$-0.671662\pi$
$619$	−25.5528	−1.02705	−0.513527	+	0.858073i	$0.671662\pi$
$620$	39.5911	1.59002
$621$	3.99342	0.160251
$622$	25.2741	1.01340
$623$	−23.4068	−0.937774
$624$	−129.369	−5.17891
$625$	13.1217	0.524870
$626$	89.0012	3.55720
$627$	43.0438	1.71900
$628$	83.6492	3.33797
$629$	−0.311928	−0.0124374
$630$	−21.5749	−0.859565
$631$	0.588235	0.0234173	0.0117086	−	0.999931i	$-0.496273\pi$
$631$	0.588235	0.0234173	0.0117086	+	0.999931i	$0.496273\pi$
$632$	18.9708	0.754617
$633$	−3.53754	−0.140605
$634$	12.4582	0.494779
$635$	2.47154	0.0980801
$636$	157.068	6.22815
$637$	−3.51113	−0.139116
$638$	43.8615	1.73649
$639$	−8.70735	−0.344457
$640$	−2.46013	−0.0972452
$641$	42.5528	1.68073	0.840367	−	0.542018i	$-0.182340\pi$
$641$	42.5528	1.68073	0.840367	+	0.542018i	$0.182340\pi$
$642$	−77.3723	−3.05364
$643$	−11.3746	−0.448569	−0.224285	−	0.974524i	$-0.572005\pi$
$643$	−11.3746	−0.448569	−0.224285	+	0.974524i	$0.572005\pi$
$644$	91.5285	3.60673
$645$	−25.9372	−1.02128
$646$	4.57115	0.179850
$647$	32.6647	1.28418	0.642091	−	0.766628i	$-0.278067\pi$
$647$	32.6647	1.28418	0.642091	+	0.766628i	$0.278067\pi$
$648$	62.4656	2.45388
$649$	9.11864	0.357938
$650$	−55.8310	−2.18987
$651$	61.2058	2.39884
$652$	−14.6858	−0.575140
$653$	36.0416	1.41042	0.705209	−	0.708999i	$-0.250853\pi$
$653$	36.0416	1.41042	0.705209	+	0.708999i	$0.250853\pi$
$654$	6.55547	0.256339
$655$	6.25636	0.244456
$656$	47.0147	1.83562
$657$	10.4586	0.408027
$658$	−55.5184	−2.16433
$659$	−14.8904	−0.580050	−0.290025	−	0.957019i	$-0.593664\pi$
$659$	−14.8904	−0.580050	−0.290025	+	0.957019i	$0.593664\pi$
$660$	34.5322	1.34416
$661$	−22.6126	−0.879527	−0.439763	−	0.898114i	$-0.644938\pi$
$661$	−22.6126	−0.879527	−0.439763	+	0.898114i	$0.644938\pi$
$662$	28.3042	1.10008
$663$	3.98174	0.154638
$664$	−94.0821	−3.65109
$665$	14.1760	0.549722
$666$	−8.49662	−0.329237
$667$	−36.5366	−1.41470
$668$	−64.4932	−2.49532
$669$	15.7860	0.610322
$670$	10.3146	0.398488
$671$	−22.8611	−0.882543
$672$	−79.1359	−3.05273
$673$	39.3898	1.51837	0.759183	−	0.650878i	$-0.225599\pi$
$673$	39.3898	1.51837	0.759183	+	0.650878i	$0.225599\pi$
$674$	28.9502	1.11512
$675$	−2.46164	−0.0947485
$676$	64.1901	2.46885
$677$	13.7814	0.529661	0.264830	−	0.964295i	$-0.414684\pi$
$677$	13.7814	0.529661	0.264830	+	0.964295i	$0.414684\pi$
$678$	−135.298	−5.19608
$679$	2.72772	0.104680
$680$	2.16745	0.0831179
$681$	28.5073	1.09240
$682$	−71.6355	−2.74307
$683$	−15.4366	−0.590666	−0.295333	−	0.955394i	$-0.595431\pi$
$683$	−15.4366	−0.590666	−0.295333	+	0.955394i	$0.595431\pi$
$684$	88.3723	3.37900
$685$	4.82377	0.184307
$686$	45.9449	1.75418
$687$	0.253355	0.00966609
$688$	−114.928	−4.38158
$689$	−65.7356	−2.50433
$690$	−40.5295	−1.54293
$691$	−34.2472	−1.30282	−0.651412	−	0.758724i	$-0.725823\pi$
$691$	−34.2472	−1.30282	−0.651412	+	0.758724i	$0.725823\pi$
$692$	43.0763	1.63752
$693$	27.7063	1.05247
$694$	38.3074	1.45413
$695$	16.4944	0.625669
$696$	102.551	3.88718
$697$	−1.44702	−0.0548100
$698$	43.2706	1.63782
$699$	50.9669	1.92774
$700$	−56.4203	−2.13249
$701$	30.1425	1.13847	0.569233	−	0.822177i	$-0.307240\pi$
$701$	30.1425	1.13847	0.569233	+	0.822177i	$0.307240\pi$
$702$	7.93707	0.299565
$703$	5.58279	0.210559
$704$	30.0436	1.13231
$705$	17.4482	0.657136
$706$	−9.28582	−0.349476
$707$	−14.1300	−0.531412
$708$	36.0726	1.35569
$709$	−37.7185	−1.41655	−0.708274	−	0.705937i	$-0.750526\pi$
$709$	−37.7185	−1.41655	−0.708274	+	0.705937i	$0.750526\pi$
$710$	6.46705	0.242704
$711$	−8.09361	−0.303534
$712$	64.0523	2.40046
$713$	59.6724	2.23475
$714$	5.66936	0.212171
$715$	−14.4523	−0.540486
$716$	−71.4068	−2.66860
$717$	−25.9311	−0.968413
$718$	−27.2036	−1.01523
$719$	2.07831	0.0775078	0.0387539	−	0.999249i	$-0.487661\pi$
$719$	2.07831	0.0775078	0.0387539	+	0.999249i	$0.487661\pi$
$720$	30.0444	1.11969
$721$	19.0230	0.708454
$722$	−31.9392	−1.18866
$723$	21.2895	0.791765
$724$	84.0428	3.12343
$725$	22.5220	0.836447
$726$	9.62819	0.357336
$727$	−36.8618	−1.36713	−0.683564	−	0.729890i	$-0.739571\pi$
$727$	−36.8618	−1.36713	−0.683564	+	0.729890i	$0.739571\pi$
$728$	107.518	3.98488
$729$	−31.0821	−1.15119
$730$	−7.76770	−0.287495
$731$	3.53726	0.130830
$732$	−90.4365	−3.34263
$733$	−35.7912	−1.32198	−0.660988	−	0.750396i	$-0.729863\pi$
$733$	−35.7912	−1.32198	−0.660988	+	0.750396i	$0.729863\pi$
$734$	−41.3010	−1.52445
$735$	1.57116	0.0579532
$736$	−77.1533	−2.84391
$737$	−13.2459	−0.487919
$738$	−39.4156	−1.45091
$739$	−34.1041	−1.25454	−0.627269	−	0.778803i	$-0.715827\pi$
$739$	−34.1041	−1.25454	−0.627269	+	0.778803i	$0.715827\pi$
$740$	4.47883	0.164645
$741$	−71.2641	−2.61795
$742$	−93.5970	−3.43605
$743$	10.3748	0.380615	0.190308	−	0.981724i	$-0.439051\pi$
$743$	10.3748	0.380615	0.190308	+	0.981724i	$0.439051\pi$
$744$	−167.488	−6.14043
$745$	−3.66579	−0.134304
$746$	−83.1552	−3.04453
$747$	40.1388	1.46860
$748$	−4.70943	−0.172194
$749$	32.7234	1.19569
$750$	55.0026	2.00841
$751$	40.2692	1.46945	0.734723	−	0.678367i	$-0.237312\pi$
$751$	40.2692	1.46945	0.734723	+	0.678367i	$0.237312\pi$
$752$	77.3129	2.81931
$753$	−50.0270	−1.82308
$754$	−72.6178	−2.64459
$755$	−11.7800	−0.428719
$756$	8.02083	0.291715
$757$	−4.88608	−0.177588	−0.0887938	−	0.996050i	$-0.528301\pi$
$757$	−4.88608	−0.177588	−0.0887938	+	0.996050i	$0.528301\pi$
$758$	−20.5806	−0.747522
$759$	52.0475	1.88921
$760$	−38.7924	−1.40715
$761$	−27.7179	−1.00477	−0.502387	−	0.864643i	$-0.667545\pi$
$761$	−27.7179	−1.00477	−0.502387	+	0.864643i	$0.667545\pi$
$762$	−17.6907	−0.640867
$763$	−2.77253	−0.100372
$764$	−100.335	−3.63000
$765$	−0.924711	−0.0334330
$766$	−80.1056	−2.89433
$767$	−15.0970	−0.545121
$768$	−30.9969	−1.11851
$769$	3.32049	0.119740	0.0598699	−	0.998206i	$-0.480931\pi$
$769$	3.32049	0.119740	0.0598699	+	0.998206i	$0.480931\pi$
$770$	−20.5778	−0.741571
$771$	62.3361	2.24498
$772$	7.19868	0.259086
$773$	−2.72115	−0.0978729	−0.0489364	−	0.998802i	$-0.515583\pi$
$773$	−2.72115	−0.0978729	−0.0489364	+	0.998802i	$0.515583\pi$
$774$	96.3517	3.46329
$775$	−36.7835	−1.32130
$776$	−7.46436	−0.267955
$777$	6.92405	0.248399
$778$	−6.83568	−0.245071
$779$	25.8984	0.927908
$780$	−57.1721	−2.04709
$781$	−8.30492	−0.297173
$782$	5.52733	0.197657
$783$	−3.20178	−0.114422
$784$	6.96182	0.248637
$785$	15.6657	0.559132
$786$	−44.7816	−1.59731
$787$	−15.5636	−0.554783	−0.277392	−	0.960757i	$-0.589470\pi$
$787$	−15.5636	−0.554783	−0.277392	+	0.960757i	$0.589470\pi$
$788$	−40.9994	−1.46054
$789$	−66.5858	−2.37052
$790$	6.01122	0.213870
$791$	57.2221	2.03458
$792$	−75.8176	−2.69406
$793$	37.8492	1.34407
$794$	39.4804	1.40111
$795$	29.4154	1.04326
$796$	−38.5496	−1.36635
$797$	48.8218	1.72936	0.864679	−	0.502325i	$-0.167522\pi$
$797$	48.8218	1.72936	0.864679	+	0.502325i	$0.167522\pi$
$798$	−101.469	−3.59195
$799$	−2.37955	−0.0841823
$800$	47.5591	1.68147
$801$	−27.3270	−0.965552
$802$	51.8733	1.83171
$803$	9.97519	0.352017
$804$	−52.3997	−1.84799
$805$	17.1413	0.604151
$806$	118.601	4.17754
$807$	−46.9178	−1.65158
$808$	38.6664	1.36028
$809$	7.27769	0.255870	0.127935	−	0.991783i	$-0.459165\pi$
$809$	7.27769	0.255870	0.127935	+	0.991783i	$0.459165\pi$
$810$	19.7933	0.695466
$811$	−35.5030	−1.24668	−0.623339	−	0.781952i	$-0.714224\pi$
$811$	−35.5030	−1.24668	−0.623339	+	0.781952i	$0.714224\pi$
$812$	−73.3842	−2.57528
$813$	−3.07273	−0.107765
$814$	−8.10393	−0.284043
$815$	−2.75033	−0.0963398
$816$	−7.89495	−0.276379
$817$	−63.3089	−2.21490
$818$	−28.7180	−1.00410
$819$	−45.8710	−1.60286
$820$	20.7772	0.725571
$821$	8.93883	0.311967	0.155984	−	0.987760i	$-0.450145\pi$
$821$	8.93883	0.311967	0.155984	+	0.987760i	$0.450145\pi$
$822$	−34.5274	−1.20428
$823$	24.2143	0.844057	0.422028	−	0.906583i	$-0.361318\pi$
$823$	24.2143	0.844057	0.422028	+	0.906583i	$0.361318\pi$
$824$	−52.0561	−1.81346
$825$	−32.0833	−1.11700
$826$	−21.4957	−0.747931
$827$	−10.2997	−0.358155	−0.179078	−	0.983835i	$-0.557311\pi$
$827$	−10.2997	−0.358155	−0.179078	+	0.983835i	$0.557311\pi$
$828$	106.858	3.71356
$829$	−10.6592	−0.370211	−0.185105	−	0.982719i	$-0.559263\pi$
$829$	−10.6592	−0.370211	−0.185105	+	0.982719i	$0.559263\pi$
$830$	−29.8115	−1.03477
$831$	−44.8959	−1.55742
$832$	−49.7407	−1.72445
$833$	−0.214272	−0.00742408
$834$	−118.063	−4.08820
$835$	−12.0782	−0.417982
$836$	84.2880	2.91516
$837$	5.22922	0.180748
$838$	6.44913	0.222781
$839$	10.6957	0.369256	0.184628	−	0.982808i	$-0.440892\pi$
$839$	10.6957	0.369256	0.184628	+	0.982808i	$0.440892\pi$
$840$	−48.1122	−1.66003
$841$	0.293738	0.0101289
$842$	−81.3558	−2.80371
$843$	48.6319	1.67497
$844$	−6.92719	−0.238444
$845$	12.0214	0.413549
$846$	−64.8166	−2.22844
$847$	−4.07209	−0.139919
$848$	130.340	4.47589
$849$	−55.6353	−1.90940
$850$	−3.40717	−0.116865
$851$	6.75058	0.231407
$852$	−32.8535	−1.12554
$853$	14.6907	0.502999	0.251499	−	0.967857i	$-0.419076\pi$
$853$	14.6907	0.502999	0.251499	+	0.967857i	$0.419076\pi$
$854$	53.8912	1.84412
$855$	16.5502	0.566006
$856$	−89.5469	−3.06065
$857$	11.4796	0.392137	0.196068	−	0.980590i	$-0.437183\pi$
$857$	11.4796	0.392137	0.196068	+	0.980590i	$0.437183\pi$
$858$	103.446	3.53160
$859$	39.7116	1.35494	0.677471	−	0.735550i	$-0.263076\pi$
$859$	39.7116	1.35494	0.677471	+	0.735550i	$0.263076\pi$
$860$	−50.7900	−1.73192
$861$	32.1205	1.09466
$862$	−95.8928	−3.26612
$863$	14.0470	0.478165	0.239082	−	0.970999i	$-0.423153\pi$
$863$	14.0470	0.478165	0.239082	+	0.970999i	$0.423153\pi$
$864$	−6.76111	−0.230018
$865$	8.06726	0.274295
$866$	54.6780	1.85803
$867$	−42.2124	−1.43361
$868$	119.853	4.06807
$869$	−7.71954	−0.261868
$870$	32.4951	1.10169
$871$	21.9302	0.743075
$872$	7.58698	0.256927
$873$	3.18456	0.107781
$874$	−98.9265	−3.34624
$875$	−23.2625	−0.786414
$876$	39.4610	1.33326
$877$	42.3028	1.42847	0.714233	−	0.699908i	$-0.246776\pi$
$877$	42.3028	1.42847	0.714233	+	0.699908i	$0.246776\pi$
$878$	57.4546	1.93900
$879$	−70.7567	−2.38656
$880$	28.6559	0.965989
$881$	−20.7693	−0.699734	−0.349867	−	0.936799i	$-0.613773\pi$
$881$	−20.7693	−0.699734	−0.349867	+	0.936799i	$0.613773\pi$
$882$	−5.83657	−0.196527
$883$	22.4329	0.754927	0.377464	−	0.926024i	$-0.376796\pi$
$883$	22.4329	0.754927	0.377464	+	0.926024i	$0.376796\pi$
$884$	7.79702	0.262242
$885$	6.75561	0.227087
$886$	−72.2385	−2.42690
$887$	−35.5623	−1.19406	−0.597032	−	0.802217i	$-0.703654\pi$
$887$	−35.5623	−1.19406	−0.597032	+	0.802217i	$0.703654\pi$
$888$	−18.9475	−0.635837
$889$	7.48200	0.250938
$890$	20.2961	0.680326
$891$	−25.4184	−0.851547
$892$	30.9120	1.03501
$893$	42.5884	1.42517
$894$	26.2389	0.877560
$895$	−13.3729	−0.447008
$896$	−7.44746	−0.248802
$897$	−86.1708	−2.87716
$898$	−53.4135	−1.78243
$899$	−47.8432	−1.59566
$900$	−65.8695	−2.19565
$901$	−4.01162	−0.133646
$902$	−37.5939	−1.25174
$903$	−78.5187	−2.61294
$904$	−156.587	−5.20801
$905$	15.7394	0.523195
$906$	84.3186	2.80130
$907$	−23.5567	−0.782186	−0.391093	−	0.920351i	$-0.627903\pi$
$907$	−23.5567	−0.782186	−0.391093	+	0.920351i	$0.627903\pi$
$908$	55.8227	1.85254
$909$	−16.4965	−0.547153
$910$	34.0689	1.12937
$911$	−53.8620	−1.78453	−0.892264	−	0.451514i	$-0.850884\pi$
$911$	−53.8620	−1.78453	−0.892264	+	0.451514i	$0.850884\pi$
$912$	141.302	4.67896
$913$	38.2837	1.26700
$914$	10.9463	0.362073
$915$	−16.9368	−0.559913
$916$	0.496117	0.0163922
$917$	18.9397	0.625443
$918$	0.484372	0.0159866
$919$	48.6339	1.60428	0.802142	−	0.597133i	$-0.203693\pi$
$919$	48.6339	1.60428	0.802142	+	0.597133i	$0.203693\pi$
$920$	−46.9068	−1.54647
$921$	−2.92591	−0.0964119
$922$	75.8400	2.49766
$923$	13.7498	0.452579
$924$	104.538	3.43905
$925$	−4.16121	−0.136820
$926$	−77.0543	−2.53216
$927$	22.2090	0.729439
$928$	61.8587	2.03061
$929$	−50.8799	−1.66932	−0.834658	−	0.550769i	$-0.814335\pi$
$929$	−50.8799	−1.66932	−0.834658	+	0.550769i	$0.814335\pi$
$930$	−53.0717	−1.74029
$931$	3.83498	0.125686
$932$	99.8029	3.26915
$933$	−24.0458	−0.787225
$934$	−95.8662	−3.13684
$935$	−0.881974	−0.0288436
$936$	125.525	4.10291
$937$	−37.9815	−1.24080	−0.620400	−	0.784286i	$-0.713030\pi$
$937$	−37.9815	−1.24080	−0.620400	+	0.784286i	$0.713030\pi$
$938$	31.2250	1.01953
$939$	−84.6758	−2.76329
$940$	34.1669	1.11440
$941$	5.15932	0.168189	0.0840946	−	0.996458i	$-0.473200\pi$
$941$	5.15932	0.168189	0.0840946	+	0.996458i	$0.473200\pi$
$942$	−112.131	−3.65343
$943$	31.3158	1.01978
$944$	29.9341	0.974273
$945$	1.50213	0.0488642
$946$	91.8986	2.98788
$947$	−19.0304	−0.618406	−0.309203	−	0.950996i	$-0.600062\pi$
$947$	−19.0304	−0.618406	−0.309203	+	0.950996i	$0.600062\pi$
$948$	−30.5379	−0.991823
$949$	−16.5151	−0.536103
$950$	60.9806	1.97847
$951$	−11.8528	−0.384352
$952$	6.56144	0.212657
$953$	−37.4951	−1.21459	−0.607293	−	0.794478i	$-0.707745\pi$
$953$	−37.4951	−1.21459	−0.607293	+	0.794478i	$0.707745\pi$
$954$	−109.273	−3.53783
$955$	−18.7906	−0.608049
$956$	−50.7780	−1.64228
$957$	−41.7298	−1.34893
$958$	−60.6886	−1.96076
$959$	14.6028	0.471550
$960$	22.2580	0.718373
$961$	47.1385	1.52060
$962$	13.4170	0.432582
$963$	38.2039	1.23110
$964$	41.6889	1.34271
$965$	1.34816	0.0433987
$966$	−122.693	−3.94760
$967$	−20.8946	−0.671926	−0.335963	−	0.941875i	$-0.609062\pi$
$967$	−20.8946	−0.671926	−0.335963	+	0.941875i	$0.609062\pi$
$968$	11.1432	0.358156
$969$	−4.34900	−0.139710
$970$	−2.36521	−0.0759424
$971$	−12.5698	−0.403384	−0.201692	−	0.979449i	$-0.564644\pi$
$971$	−12.5698	−0.403384	−0.201692	+	0.979449i	$0.564644\pi$
$972$	−109.232	−3.50361
$973$	49.9330	1.60078
$974$	−87.9084	−2.81677
$975$	53.1177	1.70113
$976$	−75.0470	−2.40220
$977$	−17.6853	−0.565803	−0.282901	−	0.959149i	$-0.591297\pi$
$977$	−17.6853	−0.565803	−0.282901	+	0.959149i	$0.591297\pi$
$978$	19.6862	0.629496
$979$	−26.0640	−0.833009
$980$	3.07664	0.0982795
$981$	−3.23688	−0.103345
$982$	−77.0341	−2.45826
$983$	−43.3426	−1.38241	−0.691207	−	0.722657i	$-0.742921\pi$
$983$	−43.3426	−1.38241	−0.691207	+	0.722657i	$0.742921\pi$
$984$	−87.8970	−2.80206
$985$	−7.67830	−0.244651
$986$	−4.43161	−0.141131
$987$	52.8202	1.68129
$988$	−139.549	−4.43964
$989$	−76.5516	−2.43420
$990$	−24.0241	−0.763537
$991$	13.8247	0.439157	0.219579	−	0.975595i	$-0.429532\pi$
$991$	13.8247	0.439157	0.219579	+	0.975595i	$0.429532\pi$
$992$	−101.029	−3.20767
$993$	−26.9287	−0.854556
$994$	19.5775	0.620960
$995$	−7.21949	−0.228873
$996$	151.447	4.79878
$997$	−27.7601	−0.879172	−0.439586	−	0.898200i	$-0.644875\pi$
$997$	−27.7601	−0.879172	−0.439586	+	0.898200i	$0.644875\pi$
$998$	17.8662	0.565545
$999$	0.591568	0.0187164

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.f.1.4	✓	85

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.f.1.4	✓	85	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)

\(f(q)\)	\(=\)	\(q-2.62495 q^{2} +2.49737 q^{3} +4.89034 q^{4} +0.915854 q^{5} -6.55547 q^{6} +2.77253 q^{7} -7.58698 q^{8} +3.23688 q^{9} +O(q^{10})\)	\(q-2.62495 q^{2} +2.49737 q^{3} +4.89034 q^{4} +0.915854 q^{5} -6.55547 q^{6} +2.77253 q^{7} -7.58698 q^{8} +3.23688 q^{9} -2.40407 q^{10} +3.08728 q^{11} +12.2130 q^{12} -5.11135 q^{13} -7.27774 q^{14} +2.28723 q^{15} +10.1347 q^{16} -0.311928 q^{17} -8.49662 q^{18} +5.58279 q^{19} +4.47883 q^{20} +6.92405 q^{21} -8.10393 q^{22} +6.75058 q^{23} -18.9475 q^{24} -4.16121 q^{25} +13.4170 q^{26} +0.591568 q^{27} +13.5586 q^{28} -5.41237 q^{29} -6.00385 q^{30} +8.83960 q^{31} -11.4291 q^{32} +7.71008 q^{33} +0.818793 q^{34} +2.53923 q^{35} +15.8294 q^{36} +1.00000 q^{37} -14.6545 q^{38} -12.7650 q^{39} -6.94856 q^{40} +4.63897 q^{41} -18.1752 q^{42} -11.3400 q^{43} +15.0978 q^{44} +2.96451 q^{45} -17.7199 q^{46} +7.62852 q^{47} +25.3102 q^{48} +0.686928 q^{49} +10.9230 q^{50} -0.779000 q^{51} -24.9962 q^{52} +12.8607 q^{53} -1.55283 q^{54} +2.82749 q^{55} -21.0351 q^{56} +13.9423 q^{57} +14.2072 q^{58} +2.95362 q^{59} +11.1853 q^{60} -7.40494 q^{61} -23.2035 q^{62} +8.97434 q^{63} +9.73142 q^{64} -4.68125 q^{65} -20.2385 q^{66} -4.29048 q^{67} -1.52543 q^{68} +16.8587 q^{69} -6.66535 q^{70} -2.69005 q^{71} -24.5581 q^{72} +3.23107 q^{73} -2.62495 q^{74} -10.3921 q^{75} +27.3017 q^{76} +8.55957 q^{77} +33.5073 q^{78} -2.50044 q^{79} +9.28193 q^{80} -8.23326 q^{81} -12.1771 q^{82} +12.4005 q^{83} +33.8609 q^{84} -0.285680 q^{85} +29.7669 q^{86} -13.5167 q^{87} -23.4231 q^{88} -8.44240 q^{89} -7.78166 q^{90} -14.1714 q^{91} +33.0126 q^{92} +22.0758 q^{93} -20.0244 q^{94} +5.11302 q^{95} -28.5428 q^{96} +0.983838 q^{97} -1.80315 q^{98} +9.99313 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9}+O(q^{10}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9} + 9 q^{10} + 37 q^{11} + 44 q^{12} + 14 q^{13} + 26 q^{14} + 27 q^{15} + 85 q^{16} + 34 q^{17} + 3 q^{18} + 15 q^{19} + 15 q^{20} + 17 q^{21} + q^{22} + 72 q^{23} + 15 q^{24} + 85 q^{25} + 33 q^{26} + 69 q^{27} + 7 q^{28} + 19 q^{29} - 9 q^{30} + 23 q^{31} + 51 q^{32} + 32 q^{33} + 49 q^{34} + 40 q^{35} + 121 q^{36} + 85 q^{37} + 84 q^{38} + 39 q^{39} + 22 q^{40} + 55 q^{41} - 28 q^{42} + 78 q^{44} + 28 q^{45} + 17 q^{46} + 184 q^{47} + 97 q^{48} + 88 q^{49} + 26 q^{50} + 27 q^{51} + 73 q^{52} + 64 q^{53} + 31 q^{54} + 39 q^{55} + 68 q^{56} - 33 q^{57} + 28 q^{58} + 60 q^{59} - 22 q^{60} + 7 q^{61} + 70 q^{62} + 28 q^{63} + 102 q^{64} + 17 q^{65} - 15 q^{66} + 82 q^{67} + 92 q^{68} + 22 q^{69} - 41 q^{70} + 113 q^{71} - 19 q^{73} + 11 q^{74} + 45 q^{75} + 34 q^{76} + 64 q^{77} + 29 q^{78} + 23 q^{79} + 54 q^{80} + 149 q^{81} + 4 q^{82} + 100 q^{83} - 49 q^{84} - 5 q^{85} - 24 q^{86} + 65 q^{87} + 14 q^{88} + 84 q^{89} - 21 q^{90} + 32 q^{91} + 95 q^{92} + 19 q^{93} - 47 q^{94} + 102 q^{95} + 29 q^{96} + 7 q^{97} + 26 q^{98} + 107 q^{99}+O(q^{100}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9 + 9 * q^10 + 37 * q^11 + 44 * q^12 + 14 * q^13 + 26 * q^14 + 27 * q^15 + 85 * q^16 + 34 * q^17 + 3 * q^18 + 15 * q^19 + 15 * q^20 + 17 * q^21 + q^22 + 72 * q^23 + 15 * q^24 + 85 * q^25 + 33 * q^26 + 69 * q^27 + 7 * q^28 + 19 * q^29 - 9 * q^30 + 23 * q^31 + 51 * q^32 + 32 * q^33 + 49 * q^34 + 40 * q^35 + 121 * q^36 + 85 * q^37 + 84 * q^38 + 39 * q^39 + 22 * q^40 + 55 * q^41 - 28 * q^42 + 78 * q^44 + 28 * q^45 + 17 * q^46 + 184 * q^47 + 97 * q^48 + 88 * q^49 + 26 * q^50 + 27 * q^51 + 73 * q^52 + 64 * q^53 + 31 * q^54 + 39 * q^55 + 68 * q^56 - 33 * q^57 + 28 * q^58 + 60 * q^59 - 22 * q^60 + 7 * q^61 + 70 * q^62 + 28 * q^63 + 102 * q^64 + 17 * q^65 - 15 * q^66 + 82 * q^67 + 92 * q^68 + 22 * q^69 - 41 * q^70 + 113 * q^71 - 19 * q^73 + 11 * q^74 + 45 * q^75 + 34 * q^76 + 64 * q^77 + 29 * q^78 + 23 * q^79 + 54 * q^80 + 149 * q^81 + 4 * q^82 + 100 * q^83 - 49 * q^84 - 5 * q^85 - 24 * q^86 + 65 * q^87 + 14 * q^88 + 84 * q^89 - 21 * q^90 + 32 * q^91 + 95 * q^92 + 19 * q^93 - 47 * q^94 + 102 * q^95 + 29 * q^96 + 7 * q^97 + 26 * q^98 + 107 * q^99

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