LMFDB - Embedded newform 4021.2.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4021,2,Mod(1,4021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4021, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4021 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4021.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:	$32.1078466528$
Analytic rank:	$1$
Dimension:	$151$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	4021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.72951 q^{2} +0.628920 q^{3} +5.45022 q^{4} +1.83150 q^{5} -1.71664 q^{6} -2.53691 q^{7} -9.41739 q^{8} -2.60446 q^{9} +O(q^{10})$	\(q-2.72951 q^{2} +0.628920 q^{3} +5.45022 q^{4} +1.83150 q^{5} -1.71664 q^{6} -2.53691 q^{7} -9.41739 q^{8} -2.60446 q^{9} -4.99910 q^{10} +3.43188 q^{11} +3.42775 q^{12} +5.46789 q^{13} +6.92451 q^{14} +1.15187 q^{15} +14.8044 q^{16} +0.123834 q^{17} +7.10889 q^{18} -1.26319 q^{19} +9.98208 q^{20} -1.59551 q^{21} -9.36735 q^{22} -1.37392 q^{23} -5.92279 q^{24} -1.64560 q^{25} -14.9247 q^{26} -3.52476 q^{27} -13.8267 q^{28} -7.05644 q^{29} -3.14403 q^{30} -1.63404 q^{31} -21.5740 q^{32} +2.15838 q^{33} -0.338007 q^{34} -4.64635 q^{35} -14.1949 q^{36} -0.641721 q^{37} +3.44789 q^{38} +3.43887 q^{39} -17.2480 q^{40} -2.31400 q^{41} +4.35496 q^{42} +7.89631 q^{43} +18.7045 q^{44} -4.77007 q^{45} +3.75012 q^{46} -5.95186 q^{47} +9.31080 q^{48} -0.564108 q^{49} +4.49169 q^{50} +0.0778820 q^{51} +29.8012 q^{52} +3.20889 q^{53} +9.62086 q^{54} +6.28550 q^{55} +23.8910 q^{56} -0.794447 q^{57} +19.2606 q^{58} -11.8837 q^{59} +6.27793 q^{60} -4.94365 q^{61} +4.46013 q^{62} +6.60727 q^{63} +29.2776 q^{64} +10.0145 q^{65} -5.89132 q^{66} -6.90838 q^{67} +0.674924 q^{68} -0.864085 q^{69} +12.6822 q^{70} +5.23276 q^{71} +24.5272 q^{72} +5.44103 q^{73} +1.75158 q^{74} -1.03495 q^{75} -6.88467 q^{76} -8.70636 q^{77} -9.38642 q^{78} -10.9935 q^{79} +27.1143 q^{80} +5.59659 q^{81} +6.31608 q^{82} -6.95586 q^{83} -8.69588 q^{84} +0.226803 q^{85} -21.5530 q^{86} -4.43794 q^{87} -32.3194 q^{88} +8.27466 q^{89} +13.0199 q^{90} -13.8715 q^{91} -7.48815 q^{92} -1.02768 q^{93} +16.2456 q^{94} -2.31354 q^{95} -13.5683 q^{96} -2.92550 q^{97} +1.53974 q^{98} -8.93820 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) $ 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9	\( 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9} - 7 q^{10} - 126 q^{11} - 47 q^{12} - 10 q^{13} - 58 q^{14} - 50 q^{15} + 74 q^{16} - 39 q^{17} - 47 q^{18} - 48 q^{19} - 64 q^{20} - 50 q^{21} - 7 q^{22} - 91 q^{23} - 44 q^{24} + 102 q^{25} - 94 q^{26} - 92 q^{27} - 27 q^{28} - 79 q^{29} - 12 q^{30} - 33 q^{31} - 102 q^{32} - 7 q^{33} - 17 q^{34} - 183 q^{35} - 6 q^{36} - 24 q^{37} - 77 q^{38} - 81 q^{39} - 37 q^{40} - 62 q^{41} + 4 q^{42} - 74 q^{43} - 209 q^{44} - 35 q^{45} - 37 q^{46} - 127 q^{47} - 59 q^{48} + 75 q^{49} - 79 q^{50} - 138 q^{51} - 12 q^{52} - 104 q^{53} - 43 q^{54} - 49 q^{55} - 167 q^{56} - 19 q^{57} - 32 q^{58} - 207 q^{59} - 94 q^{60} - 57 q^{61} - 69 q^{62} - 49 q^{63} - 4 q^{64} - 78 q^{65} - 51 q^{66} - 92 q^{67} - 80 q^{68} - 84 q^{69} + 5 q^{70} - 217 q^{71} - 79 q^{72} + 2 q^{73} - 113 q^{74} - 173 q^{75} - 70 q^{76} - 85 q^{77} - 46 q^{78} - 70 q^{79} - 95 q^{80} - 49 q^{81} - 12 q^{82} - 109 q^{83} - 114 q^{84} - 25 q^{85} - 136 q^{86} - 60 q^{87} - 2 q^{88} - 144 q^{89} - 55 q^{90} - 62 q^{91} - 175 q^{92} - 42 q^{93} - 15 q^{94} - 189 q^{95} - 64 q^{96} - 24 q^{97} - 37 q^{98} - 293 q^{99}+O(q^{100}) \) 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9 - 7 * q^10 - 126 * q^11 - 47 * q^12 - 10 * q^13 - 58 * q^14 - 50 * q^15 + 74 * q^16 - 39 * q^17 - 47 * q^18 - 48 * q^19 - 64 * q^20 - 50 * q^21 - 7 * q^22 - 91 * q^23 - 44 * q^24 + 102 * q^25 - 94 * q^26 - 92 * q^27 - 27 * q^28 - 79 * q^29 - 12 * q^30 - 33 * q^31 - 102 * q^32 - 7 * q^33 - 17 * q^34 - 183 * q^35 - 6 * q^36 - 24 * q^37 - 77 * q^38 - 81 * q^39 - 37 * q^40 - 62 * q^41 + 4 * q^42 - 74 * q^43 - 209 * q^44 - 35 * q^45 - 37 * q^46 - 127 * q^47 - 59 * q^48 + 75 * q^49 - 79 * q^50 - 138 * q^51 - 12 * q^52 - 104 * q^53 - 43 * q^54 - 49 * q^55 - 167 * q^56 - 19 * q^57 - 32 * q^58 - 207 * q^59 - 94 * q^60 - 57 * q^61 - 69 * q^62 - 49 * q^63 - 4 * q^64 - 78 * q^65 - 51 * q^66 - 92 * q^67 - 80 * q^68 - 84 * q^69 + 5 * q^70 - 217 * q^71 - 79 * q^72 + 2 * q^73 - 113 * q^74 - 173 * q^75 - 70 * q^76 - 85 * q^77 - 46 * q^78 - 70 * q^79 - 95 * q^80 - 49 * q^81 - 12 * q^82 - 109 * q^83 - 114 * q^84 - 25 * q^85 - 136 * q^86 - 60 * q^87 - 2 * q^88 - 144 * q^89 - 55 * q^90 - 62 * q^91 - 175 * q^92 - 42 * q^93 - 15 * q^94 - 189 * q^95 - 64 * q^96 - 24 * q^97 - 37 * q^98 - 293 * 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 $

$2$	−2.72951	−1.93005	−0.965027	−	0.262151i	$-0.915568\pi$
$2$	−2.72951	−1.93005	−0.965027	+	0.262151i	$0.915568\pi$
$3$	0.628920	0.363107	0.181554	−	0.983381i	$-0.441887\pi$
$3$	0.628920	0.363107	0.181554	+	0.983381i	$0.441887\pi$
$4$	5.45022	2.72511
$5$	1.83150	0.819072	0.409536	−	0.912294i	$-0.365691\pi$
$5$	1.83150	0.819072	0.409536	+	0.912294i	$0.365691\pi$
$6$	−1.71664	−0.700817
$7$	−2.53691	−0.958860	−0.479430	−	0.877580i	$-0.659157\pi$
$7$	−2.53691	−0.958860	−0.479430	+	0.877580i	$0.659157\pi$
$8$	−9.41739	−3.32955
$9$	−2.60446	−0.868153
$10$	−4.99910	−1.58085
$11$	3.43188	1.03475	0.517376	−	0.855758i	$-0.326909\pi$
$11$	3.43188	1.03475	0.517376	+	0.855758i	$0.326909\pi$
$12$	3.42775	0.989507
$13$	5.46789	1.51652	0.758260	−	0.651952i	$-0.226050\pi$
$13$	5.46789	1.51652	0.758260	+	0.651952i	$0.226050\pi$
$14$	6.92451	1.85065
$15$	1.15187	0.297411
$16$	14.8044	3.70110
$17$	0.123834	0.0300343	0.0150171	−	0.999887i	$-0.495220\pi$
$17$	0.123834	0.0300343	0.0150171	+	0.999887i	$0.495220\pi$
$18$	7.10889	1.67558
$19$	−1.26319	−0.289796	−0.144898	−	0.989447i	$-0.546285\pi$
$19$	−1.26319	−0.289796	−0.144898	+	0.989447i	$0.546285\pi$
$20$	9.98208	2.23206
$21$	−1.59551	−0.348169
$22$	−9.36735	−1.99713
$23$	−1.37392	−0.286482	−0.143241	−	0.989688i	$-0.545752\pi$
$23$	−1.37392	−0.286482	−0.143241	+	0.989688i	$0.545752\pi$
$24$	−5.92279	−1.20898
$25$	−1.64560	−0.329121
$26$	−14.9247	−2.92697
$27$	−3.52476	−0.678340
$28$	−13.8267	−2.61300
$29$	−7.05644	−1.31035	−0.655174	−	0.755478i	$-0.727405\pi$
$29$	−7.05644	−1.31035	−0.655174	+	0.755478i	$0.727405\pi$
$30$	−3.14403	−0.574019
$31$	−1.63404	−0.293483	−0.146741	−	0.989175i	$-0.546878\pi$
$31$	−1.63404	−0.293483	−0.146741	+	0.989175i	$0.546878\pi$
$32$	−21.5740	−3.81378
$33$	2.15838	0.375726
$34$	−0.338007	−0.0579677
$35$	−4.64635	−0.785376
$36$	−14.1949	−2.36581
$37$	−0.641721	−0.105498	−0.0527492	−	0.998608i	$-0.516798\pi$
$37$	−0.641721	−0.105498	−0.0527492	+	0.998608i	$0.516798\pi$
$38$	3.44789	0.559322
$39$	3.43887	0.550660
$40$	−17.2480	−2.72714
$41$	−2.31400	−0.361386	−0.180693	−	0.983540i	$-0.557834\pi$
$41$	−2.31400	−0.361386	−0.180693	+	0.983540i	$0.557834\pi$
$42$	4.35496	0.671985
$43$	7.89631	1.20418	0.602088	−	0.798430i	$-0.294336\pi$
$43$	7.89631	1.20418	0.602088	+	0.798430i	$0.294336\pi$
$44$	18.7045	2.81981
$45$	−4.77007	−0.711080
$46$	3.75012	0.552925
$47$	−5.95186	−0.868168	−0.434084	−	0.900872i	$-0.642928\pi$
$47$	−5.95186	−0.868168	−0.434084	+	0.900872i	$0.642928\pi$
$48$	9.31080	1.34390
$49$	−0.564108	−0.0805869
$50$	4.49169	0.635221
$51$	0.0778820	0.0109057
$52$	29.8012	4.13268
$53$	3.20889	0.440775	0.220387	−	0.975412i	$-0.429268\pi$
$53$	3.20889	0.440775	0.220387	+	0.975412i	$0.429268\pi$
$54$	9.62086	1.30923
$55$	6.28550	0.847536
$56$	23.8910	3.19257
$57$	−0.794447	−0.105227
$58$	19.2606	2.52904
$59$	−11.8837	−1.54713	−0.773566	−	0.633716i	$-0.781529\pi$
$59$	−11.8837	−1.54713	−0.773566	+	0.633716i	$0.781529\pi$
$60$	6.27793	0.810477
$61$	−4.94365	−0.632970	−0.316485	−	0.948598i	$-0.602503\pi$
$61$	−4.94365	−0.632970	−0.316485	+	0.948598i	$0.602503\pi$
$62$	4.46013	0.566437
$63$	6.60727	0.832438
$64$	29.2776	3.65970
$65$	10.0145	1.24214
$66$	−5.89132	−0.725171
$67$	−6.90838	−0.843993	−0.421997	−	0.906597i	$-0.638671\pi$
$67$	−6.90838	−0.843993	−0.421997	+	0.906597i	$0.638671\pi$
$68$	0.674924	0.0818466
$69$	−0.864085	−0.104024
$70$	12.6822	1.51582
$71$	5.23276	0.621015	0.310507	−	0.950571i	$-0.399501\pi$
$71$	5.23276	0.621015	0.310507	+	0.950571i	$0.399501\pi$
$72$	24.5272	2.89056
$73$	5.44103	0.636825	0.318412	−	0.947952i	$-0.396850\pi$
$73$	5.44103	0.636825	0.318412	+	0.947952i	$0.396850\pi$
$74$	1.75158	0.203617
$75$	−1.03495	−0.119506
$76$	−6.88467	−0.789726
$77$	−8.70636	−0.992182
$78$	−9.38642	−1.06280
$79$	−10.9935	−1.23687	−0.618433	−	0.785837i	$-0.712232\pi$
$79$	−10.9935	−1.23687	−0.618433	+	0.785837i	$0.712232\pi$
$80$	27.1143	3.03147
$81$	5.59659	0.621843
$82$	6.31608	0.697494
$83$	−6.95586	−0.763505	−0.381752	−	0.924265i	$-0.624679\pi$
$83$	−6.95586	−0.763505	−0.381752	+	0.924265i	$0.624679\pi$
$84$	−8.69588	−0.948799
$85$	0.226803	0.0246002
$86$	−21.5530	−2.32412
$87$	−4.43794	−0.475797
$88$	−32.3194	−3.44526
$89$	8.27466	0.877112	0.438556	−	0.898704i	$-0.355490\pi$
$89$	8.27466	0.877112	0.438556	+	0.898704i	$0.355490\pi$
$90$	13.0199	1.37242
$91$	−13.8715	−1.45413
$92$	−7.48815	−0.780694
$93$	−1.02768	−0.106566
$94$	16.2456	1.67561
$95$	−2.31354	−0.237364
$96$	−13.5683	−1.38481
$97$	−2.92550	−0.297040	−0.148520	−	0.988909i	$-0.547451\pi$
$97$	−2.92550	−0.297040	−0.148520	+	0.988909i	$0.547451\pi$
$98$	1.53974	0.155537
$99$	−8.93820	−0.898323
$100$	−8.96890	−0.896890
$101$	−1.07475	−0.106942	−0.0534709	−	0.998569i	$-0.517028\pi$
$101$	−1.07475	−0.106942	−0.0534709	+	0.998569i	$0.517028\pi$
$102$	−0.212580	−0.0210485
$103$	−2.94286	−0.289969	−0.144984	−	0.989434i	$-0.546313\pi$
$103$	−2.94286	−0.289969	−0.144984	+	0.989434i	$0.546313\pi$
$104$	−51.4933	−5.04933
$105$	−2.92218	−0.285176
$106$	−8.75868	−0.850719
$107$	6.48781	0.627200	0.313600	−	0.949555i	$-0.398465\pi$
$107$	6.48781	0.627200	0.313600	+	0.949555i	$0.398465\pi$
$108$	−19.2107	−1.84855
$109$	1.17695	0.112731	0.0563657	−	0.998410i	$-0.482049\pi$
$109$	1.17695	0.112731	0.0563657	+	0.998410i	$0.482049\pi$
$110$	−17.1563	−1.63579
$111$	−0.403592	−0.0383072
$112$	−37.5574	−3.54884
$113$	1.16685	0.109768	0.0548841	−	0.998493i	$-0.482521\pi$
$113$	1.16685	0.109768	0.0548841	+	0.998493i	$0.482521\pi$
$114$	2.16845	0.203094
$115$	−2.51633	−0.234649
$116$	−38.4591	−3.57084
$117$	−14.2409	−1.31657
$118$	32.4368	2.98605
$119$	−0.314156	−0.0287987
$120$	−10.8476	−0.990245
$121$	0.777814	0.0707104
$122$	13.4937	1.22167
$123$	−1.45532	−0.131222
$124$	−8.90588	−0.799772
$125$	−12.1714	−1.08865
$126$	−18.0346	−1.60665
$127$	20.2569	1.79751	0.898755	−	0.438451i	$-0.144473\pi$
$127$	20.2569	1.79751	0.898755	+	0.438451i	$0.144473\pi$
$128$	−36.7654	−3.24963
$129$	4.96615	0.437245
$130$	−27.3345	−2.39740
$131$	−6.36968	−0.556522	−0.278261	−	0.960506i	$-0.589758\pi$
$131$	−6.36968	−0.556522	−0.278261	+	0.960506i	$0.589758\pi$
$132$	11.7636	1.02389
$133$	3.20460	0.277874
$134$	18.8565	1.62895
$135$	−6.45560	−0.555609
$136$	−1.16620	−0.100001
$137$	−13.9292	−1.19005	−0.595027	−	0.803706i	$-0.702859\pi$
$137$	−13.9292	−1.19005	−0.595027	+	0.803706i	$0.702859\pi$
$138$	2.35853	0.200771
$139$	0.717028	0.0608176	0.0304088	−	0.999538i	$-0.490319\pi$
$139$	0.717028	0.0608176	0.0304088	+	0.999538i	$0.490319\pi$
$140$	−25.3236	−2.14023
$141$	−3.74324	−0.315238
$142$	−14.2829	−1.19859
$143$	18.7652	1.56922
$144$	−38.5575	−3.21312
$145$	−12.9239	−1.07327
$146$	−14.8513	−1.22911
$147$	−0.354779	−0.0292617
$148$	−3.49752	−0.287494
$149$	6.55378	0.536906	0.268453	−	0.963293i	$-0.413488\pi$
$149$	6.55378	0.536906	0.268453	+	0.963293i	$0.413488\pi$
$150$	2.82491	0.230653
$151$	−8.30979	−0.676241	−0.338120	−	0.941103i	$-0.609791\pi$
$151$	−8.30979	−0.676241	−0.338120	+	0.941103i	$0.609791\pi$
$152$	11.8960	0.964891
$153$	−0.322522	−0.0260743
$154$	23.7641	1.91496
$155$	−2.99275	−0.240383
$156$	18.7426	1.50061
$157$	−1.53490	−0.122498	−0.0612491	−	0.998123i	$-0.519508\pi$
$157$	−1.53490	−0.122498	−0.0612491	+	0.998123i	$0.519508\pi$
$158$	30.0069	2.38722
$159$	2.01813	0.160048
$160$	−39.5128	−3.12376
$161$	3.48550	0.274696
$162$	−15.2759	−1.20019
$163$	9.27137	0.726189	0.363095	−	0.931752i	$-0.381720\pi$
$163$	9.27137	0.726189	0.363095	+	0.931752i	$0.381720\pi$
$164$	−12.6118	−0.984815
$165$	3.95308	0.307747
$166$	18.9861	1.47361
$167$	12.2626	0.948906	0.474453	−	0.880281i	$-0.342646\pi$
$167$	12.2626	0.948906	0.474453	+	0.880281i	$0.342646\pi$
$168$	15.0256	1.15925
$169$	16.8979	1.29984
$170$	−0.619060	−0.0474798
$171$	3.28993	0.251587
$172$	43.0366	3.28151
$173$	−2.24250	−0.170494	−0.0852469	−	0.996360i	$-0.527168\pi$
$173$	−2.24250	−0.170494	−0.0852469	+	0.996360i	$0.527168\pi$
$174$	12.1134	0.918314
$175$	4.17474	0.315581
$176$	50.8070	3.82972
$177$	−7.47393	−0.561775
$178$	−22.5857	−1.69287
$179$	−23.9546	−1.79045	−0.895227	−	0.445610i	$-0.852987\pi$
$179$	−23.9546	−1.79045	−0.895227	+	0.445610i	$0.852987\pi$
$180$	−25.9979	−1.93777
$181$	−10.0121	−0.744196	−0.372098	−	0.928193i	$-0.621362\pi$
$181$	−10.0121	−0.744196	−0.372098	+	0.928193i	$0.621362\pi$
$182$	37.8625	2.80655
$183$	−3.10916	−0.229836
$184$	12.9387	0.953856
$185$	−1.17531	−0.0864107
$186$	2.80507	0.205677
$187$	0.424985	0.0310780
$188$	−32.4389	−2.36585
$189$	8.94198	0.650433
$190$	6.31482	0.458125
$191$	−18.9222	−1.36916	−0.684579	−	0.728938i	$-0.740014\pi$
$191$	−18.9222	−1.36916	−0.684579	+	0.728938i	$0.740014\pi$
$192$	18.4133	1.32886
$193$	2.76091	0.198735	0.0993674	−	0.995051i	$-0.468318\pi$
$193$	2.76091	0.198735	0.0993674	+	0.995051i	$0.468318\pi$
$194$	7.98518	0.573303
$195$	6.29829	0.451030
$196$	−3.07451	−0.219608
$197$	−12.7889	−0.911173	−0.455587	−	0.890191i	$-0.650570\pi$
$197$	−12.7889	−0.911173	−0.455587	+	0.890191i	$0.650570\pi$
$198$	24.3969	1.73381
$199$	16.2911	1.15484	0.577421	−	0.816446i	$-0.304059\pi$
$199$	16.2911	1.15484	0.577421	+	0.816446i	$0.304059\pi$
$200$	15.4973	1.09582
$201$	−4.34482	−0.306460
$202$	2.93354	0.206403
$203$	17.9015	1.25644
$204$	0.424474	0.0297191
$205$	−4.23809	−0.296001
$206$	8.03256	0.559655
$207$	3.57831	0.248710
$208$	80.9490	5.61280
$209$	−4.33513	−0.299867
$210$	7.97612	0.550404
$211$	−4.45151	−0.306455	−0.153227	−	0.988191i	$-0.548967\pi$
$211$	−4.45151	−0.306455	−0.153227	+	0.988191i	$0.548967\pi$
$212$	17.4891	1.20116
$213$	3.29099	0.225495
$214$	−17.7085	−1.21053
$215$	14.4621	0.986307
$216$	33.1940	2.25857
$217$	4.14541	0.281409
$218$	−3.21249	−0.217578
$219$	3.42198	0.231236
$220$	34.2573	2.30963
$221$	0.677113	0.0455476
$222$	1.10161	0.0739350
$223$	11.8928	0.796398	0.398199	−	0.917299i	$-0.369635\pi$
$223$	11.8928	0.796398	0.398199	+	0.917299i	$0.369635\pi$
$224$	54.7312	3.65688
$225$	4.28591	0.285727
$226$	−3.18493	−0.211859
$227$	−9.88541	−0.656118	−0.328059	−	0.944657i	$-0.606394\pi$
$227$	−9.88541	−0.656118	−0.328059	+	0.944657i	$0.606394\pi$
$228$	−4.32991	−0.286755
$229$	−3.96804	−0.262215	−0.131108	−	0.991368i	$-0.541853\pi$
$229$	−3.96804	−0.262215	−0.131108	+	0.991368i	$0.541853\pi$
$230$	6.86835	0.452886
$231$	−5.47561	−0.360269
$232$	66.4533	4.36287
$233$	−2.35821	−0.154491	−0.0772456	−	0.997012i	$-0.524613\pi$
$233$	−2.35821	−0.154491	−0.0772456	+	0.997012i	$0.524613\pi$
$234$	38.8707	2.54106
$235$	−10.9008	−0.711092
$236$	−64.7690	−4.21610
$237$	−6.91404	−0.449115
$238$	0.857492	0.0555830
$239$	−9.34727	−0.604624	−0.302312	−	0.953209i	$-0.597759\pi$
$239$	−9.34727	−0.604624	−0.302312	+	0.953209i	$0.597759\pi$
$240$	17.0527	1.10075
$241$	22.3098	1.43710	0.718551	−	0.695474i	$-0.244806\pi$
$241$	22.3098	1.43710	0.718551	+	0.695474i	$0.244806\pi$
$242$	−2.12305	−0.136475
$243$	14.0941	0.904136
$244$	−26.9440	−1.72491
$245$	−1.03316	−0.0660065
$246$	3.97231	0.253265
$247$	−6.90700	−0.439482
$248$	15.3884	0.977165
$249$	−4.37468	−0.277234
$250$	33.2220	2.10115
$251$	−21.6150	−1.36433	−0.682164	−	0.731199i	$-0.738961\pi$
$251$	−21.6150	−1.36433	−0.682164	+	0.731199i	$0.738961\pi$
$252$	36.0110	2.26848
$253$	−4.71513	−0.296437
$254$	−55.2914	−3.46929
$255$	0.142641	0.00893252
$256$	41.7962	2.61226
$257$	−15.8669	−0.989751	−0.494876	−	0.868964i	$-0.664786\pi$
$257$	−15.8669	−0.989751	−0.494876	+	0.868964i	$0.664786\pi$
$258$	−13.5552	−0.843907
$259$	1.62799	0.101158
$260$	54.5809	3.38497
$261$	18.3782	1.13758
$262$	17.3861	1.07412
$263$	−30.3974	−1.87439	−0.937193	−	0.348811i	$-0.886586\pi$
$263$	−30.3974	−1.87439	−0.937193	+	0.348811i	$0.886586\pi$
$264$	−20.3263	−1.25100
$265$	5.87708	0.361026
$266$	−8.74698	−0.536312
$267$	5.20410	0.318486
$268$	−37.6522	−2.29997
$269$	−3.61366	−0.220329	−0.110164	−	0.993913i	$-0.535138\pi$
$269$	−3.61366	−0.220329	−0.110164	+	0.993913i	$0.535138\pi$
$270$	17.6206	1.07236
$271$	−26.5172	−1.61081	−0.805403	−	0.592728i	$-0.798051\pi$
$271$	−26.5172	−1.61081	−0.805403	+	0.592728i	$0.798051\pi$
$272$	1.83330	0.111160
$273$	−8.72409	−0.528006
$274$	38.0199	2.29687
$275$	−5.64752	−0.340558
$276$	−4.70945	−0.283476
$277$	20.9807	1.26061	0.630303	−	0.776350i	$-0.282931\pi$
$277$	20.9807	1.26061	0.630303	+	0.776350i	$0.282931\pi$
$278$	−1.95714	−0.117381
$279$	4.25580	0.254788
$280$	43.7565	2.61495
$281$	31.7646	1.89492	0.947459	−	0.319879i	$-0.103642\pi$
$281$	31.7646	1.89492	0.947459	+	0.319879i	$0.103642\pi$
$282$	10.2172	0.608426
$283$	15.6277	0.928971	0.464486	−	0.885581i	$-0.346239\pi$
$283$	15.6277	0.928971	0.464486	+	0.885581i	$0.346239\pi$
$284$	28.5197	1.69233
$285$	−1.45503	−0.0861886
$286$	−51.2197	−3.02868
$287$	5.87039	0.346518
$288$	56.1886	3.31094
$289$	−16.9847	−0.999098
$290$	35.2758	2.07147
$291$	−1.83991	−0.107857
$292$	29.6548	1.73542
$293$	−12.0163	−0.702000	−0.351000	−	0.936376i	$-0.614158\pi$
$293$	−12.0163	−0.702000	−0.351000	+	0.936376i	$0.614158\pi$
$294$	0.968372	0.0564766
$295$	−21.7651	−1.26721
$296$	6.04334	0.351262
$297$	−12.0966	−0.701913
$298$	−17.8886	−1.03626
$299$	−7.51244	−0.434456
$300$	−5.64072	−0.325667
$301$	−20.0322	−1.15464
$302$	22.6816	1.30518
$303$	−0.675933	−0.0388314
$304$	−18.7008	−1.07257
$305$	−9.05431	−0.518448
$306$	0.880326	0.0503249
$307$	22.5471	1.28683	0.643415	−	0.765518i	$-0.277517\pi$
$307$	22.5471	1.28683	0.643415	+	0.765518i	$0.277517\pi$
$308$	−47.4515	−2.70380
$309$	−1.85083	−0.105290
$310$	8.16873	0.463953
$311$	18.4347	1.04534	0.522668	−	0.852536i	$-0.324937\pi$
$311$	18.4347	1.04534	0.522668	+	0.852536i	$0.324937\pi$
$312$	−32.3852	−1.83345
$313$	2.14911	0.121475	0.0607375	−	0.998154i	$-0.480655\pi$
$313$	2.14911	0.121475	0.0607375	+	0.998154i	$0.480655\pi$
$314$	4.18952	0.236428
$315$	12.1012	0.681826
$316$	−59.9170	−3.37059
$317$	−9.98952	−0.561067	−0.280534	−	0.959844i	$-0.590511\pi$
$317$	−9.98952	−0.561067	−0.280534	+	0.959844i	$0.590511\pi$
$318$	−5.50851	−0.308902
$319$	−24.2169	−1.35588
$320$	53.6219	2.99755
$321$	4.08031	0.227741
$322$	−9.51371	−0.530178
$323$	−0.156427	−0.00870381
$324$	30.5026	1.69459
$325$	−8.99799	−0.499118
$326$	−25.3063	−1.40158
$327$	0.740208	0.0409336
$328$	21.7918	1.20325
$329$	15.0993	0.832452
$330$	−10.7900	−0.593967
$331$	−1.77054	−0.0973179	−0.0486589	−	0.998815i	$-0.515495\pi$
$331$	−1.77054	−0.0973179	−0.0486589	+	0.998815i	$0.515495\pi$
$332$	−37.9109	−2.08063
$333$	1.67134	0.0915887
$334$	−33.4708	−1.83144
$335$	−12.6527	−0.691291
$336$	−23.6206	−1.28861
$337$	10.7742	0.586907	0.293454	−	0.955973i	$-0.405195\pi$
$337$	10.7742	0.586907	0.293454	+	0.955973i	$0.405195\pi$
$338$	−46.1228	−2.50875
$339$	0.733857	0.0398576
$340$	1.23612	0.0670383
$341$	−5.60784	−0.303681
$342$	−8.97990	−0.485577
$343$	19.1894	1.03613
$344$	−74.3627	−4.00937
$345$	−1.58257	−0.0852029
$346$	6.12091	0.329062
$347$	−36.3103	−1.94924	−0.974619	−	0.223869i	$-0.928131\pi$
$347$	−36.3103	−1.94924	−0.974619	+	0.223869i	$0.928131\pi$
$348$	−24.1877	−1.29660
$349$	−7.07464	−0.378697	−0.189348	−	0.981910i	$-0.560638\pi$
$349$	−7.07464	−0.378697	−0.189348	+	0.981910i	$0.560638\pi$
$350$	−11.3950	−0.609088
$351$	−19.2730	−1.02872
$352$	−74.0394	−3.94631
$353$	−7.23970	−0.385330	−0.192665	−	0.981265i	$-0.561713\pi$
$353$	−7.23970	−0.385330	−0.192665	+	0.981265i	$0.561713\pi$
$354$	20.4002	1.08426
$355$	9.58381	0.508656
$356$	45.0987	2.39022
$357$	−0.197579	−0.0104570
$358$	65.3844	3.45567
$359$	−11.5298	−0.608522	−0.304261	−	0.952589i	$-0.598409\pi$
$359$	−11.5298	−0.608522	−0.304261	+	0.952589i	$0.598409\pi$
$360$	44.9216	2.36758
$361$	−17.4043	−0.916018
$362$	27.3282	1.43634
$363$	0.489183	0.0256755
$364$	−75.6028	−3.96267
$365$	9.96526	0.521605
$366$	8.48649	0.443596
$367$	−4.77450	−0.249227	−0.124614	−	0.992205i	$-0.539769\pi$
$367$	−4.77450	−0.249227	−0.124614	+	0.992205i	$0.539769\pi$
$368$	−20.3401	−1.06030
$369$	6.02671	0.313738
$370$	3.20803	0.166777
$371$	−8.14064	−0.422641
$372$	−5.60109	−0.290403
$373$	28.1395	1.45701	0.728505	−	0.685041i	$-0.240216\pi$
$373$	28.1395	1.45701	0.728505	+	0.685041i	$0.240216\pi$
$374$	−1.16000	−0.0599822
$375$	−7.65486	−0.395295
$376$	56.0510	2.89061
$377$	−38.5839	−1.98717
$378$	−24.4072	−1.25537
$379$	−17.2459	−0.885861	−0.442930	−	0.896556i	$-0.646061\pi$
$379$	−17.2459	−0.885861	−0.442930	+	0.896556i	$0.646061\pi$
$380$	−12.6093	−0.646842
$381$	12.7400	0.652689
$382$	51.6482	2.64255
$383$	−25.2542	−1.29043	−0.645214	−	0.764002i	$-0.723232\pi$
$383$	−25.2542	−1.29043	−0.645214	+	0.764002i	$0.723232\pi$
$384$	−23.1225	−1.17996
$385$	−15.9457	−0.812669
$386$	−7.53593	−0.383569
$387$	−20.5656	−1.04541
$388$	−15.9446	−0.809465
$389$	−7.85567	−0.398298	−0.199149	−	0.979969i	$-0.563818\pi$
$389$	−7.85567	−0.398298	−0.199149	+	0.979969i	$0.563818\pi$
$390$	−17.1912	−0.870512
$391$	−0.170138	−0.00860427
$392$	5.31243	0.268318
$393$	−4.00602	−0.202077
$394$	34.9075	1.75861
$395$	−20.1346	−1.01308
$396$	−48.7151	−2.44803
$397$	29.6548	1.48833	0.744167	−	0.667994i	$-0.232847\pi$
$397$	29.6548	1.48833	0.744167	+	0.667994i	$0.232847\pi$
$398$	−44.4666	−2.22891
$399$	2.01544	0.100898
$400$	−24.3622	−1.21811
$401$	−15.4803	−0.773048	−0.386524	−	0.922279i	$-0.626324\pi$
$401$	−15.4803	−0.773048	−0.386524	+	0.922279i	$0.626324\pi$
$402$	11.8592	0.591485
$403$	−8.93477	−0.445072
$404$	−5.85763	−0.291428
$405$	10.2502	0.509334
$406$	−48.8624	−2.42500
$407$	−2.20231	−0.109165
$408$	−0.733445	−0.0363109
$409$	28.5809	1.41324	0.706618	−	0.707595i	$-0.250220\pi$
$409$	28.5809	1.41324	0.706618	+	0.707595i	$0.250220\pi$
$410$	11.5679	0.571298
$411$	−8.76037	−0.432117
$412$	−16.0392	−0.790196
$413$	30.1479	1.48348
$414$	−9.76704	−0.480024
$415$	−12.7397	−0.625366
$416$	−117.964	−5.78368
$417$	0.450954	0.0220833
$418$	11.8328	0.578759
$419$	21.7383	1.06199	0.530993	−	0.847376i	$-0.321819\pi$
$419$	21.7383	1.06199	0.530993	+	0.847376i	$0.321819\pi$
$420$	−15.9265	−0.777135
$421$	17.0513	0.831031	0.415515	−	0.909586i	$-0.363601\pi$
$421$	17.0513	0.831031	0.415515	+	0.909586i	$0.363601\pi$
$422$	12.1504	0.591474
$423$	15.5014	0.753703
$424$	−30.2193	−1.46758
$425$	−0.203782	−0.00988490
$426$	−8.98279	−0.435217
$427$	12.5416	0.606930
$428$	35.3600	1.70919
$429$	11.8018	0.569796
$430$	−39.4744	−1.90363
$431$	−31.4807	−1.51637	−0.758186	−	0.652039i	$-0.773914\pi$
$431$	−31.4807	−1.51637	−0.758186	+	0.652039i	$0.773914\pi$
$432$	−52.1820	−2.51061
$433$	−20.4832	−0.984358	−0.492179	−	0.870494i	$-0.663799\pi$
$433$	−20.4832	−0.984358	−0.492179	+	0.870494i	$0.663799\pi$
$434$	−11.3149	−0.543134
$435$	−8.12809	−0.389712
$436$	6.41463	0.307205
$437$	1.73552	0.0830213
$438$	−9.34031	−0.446297
$439$	−20.0267	−0.955822	−0.477911	−	0.878408i	$-0.658606\pi$
$439$	−20.0267	−0.955822	−0.477911	+	0.878408i	$0.658606\pi$
$440$	−59.1930	−2.82191
$441$	1.46920	0.0699617
$442$	−1.84819	−0.0879093
$443$	7.55793	0.359088	0.179544	−	0.983750i	$-0.442538\pi$
$443$	7.55793	0.359088	0.179544	+	0.983750i	$0.442538\pi$
$444$	−2.19966	−0.104391
$445$	15.1550	0.718418
$446$	−32.4614	−1.53709
$447$	4.12180	0.194955
$448$	−74.2744	−3.50914
$449$	−31.6401	−1.49319	−0.746594	−	0.665280i	$-0.768312\pi$
$449$	−31.6401	−1.49319	−0.746594	+	0.665280i	$0.768312\pi$
$450$	−11.6984	−0.551469
$451$	−7.94137	−0.373944
$452$	6.35959	0.299130
$453$	−5.22619	−0.245548
$454$	26.9823	1.26634
$455$	−25.4057	−1.19104
$456$	7.48162	0.350359
$457$	24.9191	1.16567	0.582833	−	0.812592i	$-0.301944\pi$
$457$	24.9191	1.16567	0.582833	+	0.812592i	$0.301944\pi$
$458$	10.8308	0.506089
$459$	−0.436486	−0.0203734
$460$	−13.7146	−0.639445
$461$	27.8469	1.29696	0.648480	−	0.761232i	$-0.275405\pi$
$461$	27.8469	1.29696	0.648480	+	0.761232i	$0.275405\pi$
$462$	14.9457	0.695338
$463$	31.9607	1.48534	0.742670	−	0.669657i	$-0.233559\pi$
$463$	31.9607	1.48534	0.742670	+	0.669657i	$0.233559\pi$
$464$	−104.466	−4.84973
$465$	−1.88220	−0.0872850
$466$	6.43674	0.298176
$467$	15.8143	0.731797	0.365899	−	0.930655i	$-0.380762\pi$
$467$	15.8143	0.731797	0.365899	+	0.930655i	$0.380762\pi$
$468$	−77.6160	−3.58780
$469$	17.5259	0.809272
$470$	29.7539	1.37245
$471$	−0.965329	−0.0444800
$472$	111.914	5.15125
$473$	27.0992	1.24602
$474$	18.8719	0.866816
$475$	2.07871	0.0953779
$476$	−1.71222	−0.0784795
$477$	−8.35741	−0.382660
$478$	25.5134	1.16696
$479$	21.7018	0.991580	0.495790	−	0.868442i	$-0.334879\pi$
$479$	21.7018	0.991580	0.495790	+	0.868442i	$0.334879\pi$
$480$	−24.8504	−1.13426
$481$	−3.50886	−0.159990
$482$	−60.8948	−2.77368
$483$	2.19210	0.0997441
$484$	4.23925	0.192693
$485$	−5.35806	−0.243297
$486$	−38.4699	−1.74503
$487$	−25.0869	−1.13679	−0.568397	−	0.822755i	$-0.692436\pi$
$487$	−25.0869	−1.13679	−0.568397	+	0.822755i	$0.692436\pi$
$488$	46.5563	2.10751
$489$	5.83095	0.263685
$490$	2.82003	0.127396
$491$	−2.19816	−0.0992015	−0.0496007	−	0.998769i	$-0.515795\pi$
$491$	−2.19816	−0.0992015	−0.0496007	+	0.998769i	$0.515795\pi$
$492$	−7.93181	−0.357594
$493$	−0.873830	−0.0393553
$494$	18.8527	0.848223
$495$	−16.3703	−0.735791
$496$	−24.1910	−1.08621
$497$	−13.2750	−0.595466
$498$	11.9407	0.535077
$499$	−21.7034	−0.971576	−0.485788	−	0.874077i	$-0.661467\pi$
$499$	−21.7034	−0.971576	−0.485788	+	0.874077i	$0.661467\pi$
$500$	−66.3369	−2.96668
$501$	7.71218	0.344555
$502$	58.9984	2.63323
$503$	−23.7337	−1.05823	−0.529116	−	0.848549i	$-0.677476\pi$
$503$	−23.7337	−1.05823	−0.529116	+	0.848549i	$0.677476\pi$
$504$	−62.2232	−2.77164
$505$	−1.96841	−0.0875931
$506$	12.8700	0.572140
$507$	10.6274	0.471980
$508$	110.405	4.89841
$509$	−0.401088	−0.0177779	−0.00888896	−	0.999960i	$-0.502829\pi$
$509$	−0.401088	−0.0177779	−0.00888896	+	0.999960i	$0.502829\pi$
$510$	−0.389340	−0.0172402
$511$	−13.8034	−0.610626
$512$	−40.5524	−1.79218
$513$	4.45245	0.196580
$514$	43.3089	1.91027
$515$	−5.38985	−0.237505
$516$	27.0666	1.19154
$517$	−20.4261	−0.898338
$518$	−4.44360	−0.195241
$519$	−1.41035	−0.0619076
$520$	−94.3100	−4.13577
$521$	−6.95860	−0.304862	−0.152431	−	0.988314i	$-0.548710\pi$
$521$	−6.95860	−0.304862	−0.152431	+	0.988314i	$0.548710\pi$
$522$	−50.1635	−2.19560
$523$	−5.52654	−0.241659	−0.120829	−	0.992673i	$-0.538555\pi$
$523$	−5.52654	−0.241659	−0.120829	+	0.992673i	$0.538555\pi$
$524$	−34.7161	−1.51658
$525$	2.62558	0.114590
$526$	82.9701	3.61767
$527$	−0.202351	−0.00881453
$528$	31.9536	1.39060
$529$	−21.1123	−0.917928
$530$	−16.0415	−0.696800
$531$	30.9507	1.34315
$532$	17.4658	0.757236
$533$	−12.6527	−0.548049
$534$	−14.2046	−0.614695
$535$	11.8824	0.513722
$536$	65.0589	2.81012
$537$	−15.0656	−0.650127
$538$	9.86351	0.425246
$539$	−1.93595	−0.0833874
$540$	−35.1844	−1.51410
$541$	−36.1513	−1.55427	−0.777134	−	0.629336i	$-0.783327\pi$
$541$	−36.1513	−1.55427	−0.777134	+	0.629336i	$0.783327\pi$
$542$	72.3789	3.10894
$543$	−6.29684	−0.270223
$544$	−2.67160	−0.114544
$545$	2.15558	0.0923351
$546$	23.8125	1.01908
$547$	−43.9759	−1.88027	−0.940136	−	0.340799i	$-0.889303\pi$
$547$	−43.9759	−1.88027	−0.940136	+	0.340799i	$0.889303\pi$
$548$	−75.9173	−3.24303
$549$	12.8755	0.549515
$550$	15.4149	0.657296
$551$	8.91364	0.379734
$552$	8.13743	0.346352
$553$	27.8895	1.18598
$554$	−57.2669	−2.43304
$555$	−0.739178	−0.0313764
$556$	3.90796	0.165734
$557$	16.7883	0.711344	0.355672	−	0.934611i	$-0.384252\pi$
$557$	16.7883	0.711344	0.355672	+	0.934611i	$0.384252\pi$
$558$	−11.6162	−0.491754
$559$	43.1762	1.82616
$560$	−68.7864	−2.90676
$561$	0.267282	0.0112846
$562$	−86.7017	−3.65729
$563$	21.1070	0.889554	0.444777	−	0.895641i	$-0.353283\pi$
$563$	21.1070	0.889554	0.444777	+	0.895641i	$0.353283\pi$
$564$	−20.4015	−0.859058
$565$	2.13709	0.0899081
$566$	−42.6560	−1.79296
$567$	−14.1980	−0.596260
$568$	−49.2790	−2.06770
$569$	−15.1025	−0.633128	−0.316564	−	0.948571i	$-0.602529\pi$
$569$	−15.1025	−0.633128	−0.316564	+	0.948571i	$0.602529\pi$
$570$	3.97152	0.166349
$571$	10.5265	0.440522	0.220261	−	0.975441i	$-0.429309\pi$
$571$	10.5265	0.440522	0.220261	+	0.975441i	$0.429309\pi$
$572$	102.274	4.27630
$573$	−11.9005	−0.497152
$574$	−16.0233	−0.668799
$575$	2.26093	0.0942871
$576$	−76.2522	−3.17718
$577$	−26.8004	−1.11572	−0.557858	−	0.829936i	$-0.688377\pi$
$577$	−26.8004	−1.11572	−0.557858	+	0.829936i	$0.688377\pi$
$578$	46.3598	1.92831
$579$	1.73639	0.0721621
$580$	−70.4379	−2.92478
$581$	17.6464	0.732094
$582$	5.02204	0.208170
$583$	11.0125	0.456092
$584$	−51.2403	−2.12034
$585$	−26.0822	−1.07837
$586$	32.7986	1.35490
$587$	3.82339	0.157808	0.0789040	−	0.996882i	$-0.474858\pi$
$587$	3.82339	0.157808	0.0789040	+	0.996882i	$0.474858\pi$
$588$	−1.93362	−0.0797412
$589$	2.06411	0.0850501
$590$	59.4080	2.44579
$591$	−8.04322	−0.330854
$592$	−9.50031	−0.390460
$593$	−9.63743	−0.395762	−0.197881	−	0.980226i	$-0.563406\pi$
$593$	−9.63743	−0.395762	−0.197881	+	0.980226i	$0.563406\pi$
$594$	33.0176	1.35473
$595$	−0.575378	−0.0235882
$596$	35.7195	1.46313
$597$	10.2458	0.419332
$598$	20.5053	0.838523
$599$	17.5458	0.716903	0.358452	−	0.933548i	$-0.383305\pi$
$599$	17.5458	0.716903	0.358452	+	0.933548i	$0.383305\pi$
$600$	9.74656	0.397902
$601$	47.1128	1.92177	0.960885	−	0.276947i	$-0.0893228\pi$
$601$	47.1128	1.92177	0.960885	+	0.276947i	$0.0893228\pi$
$602$	54.6781	2.22851
$603$	17.9926	0.732715
$604$	−45.2901	−1.84283
$605$	1.42457	0.0579169
$606$	1.84497	0.0749466
$607$	−11.9722	−0.485936	−0.242968	−	0.970034i	$-0.578121\pi$
$607$	−11.9722	−0.485936	−0.242968	+	0.970034i	$0.578121\pi$
$608$	27.2521	1.10522
$609$	11.2586	0.456223
$610$	24.7138	1.00063
$611$	−32.5441	−1.31659
$612$	−1.75781	−0.0710554
$613$	−15.6808	−0.633343	−0.316671	−	0.948535i	$-0.602565\pi$
$613$	−15.6808	−0.633343	−0.316671	+	0.948535i	$0.602565\pi$
$614$	−61.5424	−2.48365
$615$	−2.66542	−0.107480
$616$	81.9912	3.30352
$617$	−11.0792	−0.446032	−0.223016	−	0.974815i	$-0.571590\pi$
$617$	−11.0792	−0.446032	−0.223016	+	0.974815i	$0.571590\pi$
$618$	5.05184	0.203215
$619$	−32.3926	−1.30197	−0.650984	−	0.759091i	$-0.725644\pi$
$619$	−32.3926	−1.30197	−0.650984	+	0.759091i	$0.725644\pi$
$620$	−16.3111	−0.655071
$621$	4.84273	0.194332
$622$	−50.3177	−2.01756
$623$	−20.9920	−0.841028
$624$	50.9105	2.03805
$625$	−14.0640	−0.562559
$626$	−5.86601	−0.234453
$627$	−2.72645	−0.108884
$628$	−8.36552	−0.333821
$629$	−0.0794672	−0.00316856
$630$	−33.0304	−1.31596
$631$	40.8768	1.62728	0.813640	−	0.581370i	$-0.197483\pi$
$631$	40.8768	1.62728	0.813640	+	0.581370i	$0.197483\pi$
$632$	103.530	4.11821
$633$	−2.79965	−0.111276
$634$	27.2665	1.08289
$635$	37.1005	1.47229
$636$	10.9993	0.436149
$637$	−3.08448	−0.122212
$638$	66.1001	2.61693
$639$	−13.6285	−0.539136
$640$	−67.3358	−2.66168
$641$	−15.9261	−0.629042	−0.314521	−	0.949251i	$-0.601844\pi$
$641$	−15.9261	−0.629042	−0.314521	+	0.949251i	$0.601844\pi$
$642$	−11.1373	−0.439552
$643$	−21.0140	−0.828712	−0.414356	−	0.910115i	$-0.635993\pi$
$643$	−21.0140	−0.828712	−0.414356	+	0.910115i	$0.635993\pi$
$644$	18.9967	0.748576
$645$	9.09551	0.358135
$646$	0.426968	0.0167988
$647$	−19.3185	−0.759488	−0.379744	−	0.925092i	$-0.623988\pi$
$647$	−19.3185	−0.759488	−0.379744	+	0.925092i	$0.623988\pi$
$648$	−52.7052	−2.07046
$649$	−40.7836	−1.60090
$650$	24.5601	0.963326
$651$	2.60713	0.102182
$652$	50.5309	1.97894
$653$	31.0726	1.21597	0.607983	−	0.793950i	$-0.291979\pi$
$653$	31.0726	1.21597	0.607983	+	0.793950i	$0.291979\pi$
$654$	−2.02040	−0.0790040
$655$	−11.6661	−0.455831
$656$	−34.2574	−1.33753
$657$	−14.1709	−0.552861
$658$	−41.2137	−1.60668
$659$	−14.1707	−0.552012	−0.276006	−	0.961156i	$-0.589011\pi$
$659$	−14.1707	−0.552012	−0.276006	+	0.961156i	$0.589011\pi$
$660$	21.5451	0.838642
$661$	−41.3800	−1.60949	−0.804747	−	0.593618i	$-0.797699\pi$
$661$	−41.3800	−1.60949	−0.804747	+	0.593618i	$0.797699\pi$
$662$	4.83271	0.187829
$663$	0.425850	0.0165387
$664$	65.5060	2.54213
$665$	5.86923	0.227599
$666$	−4.56193	−0.176771
$667$	9.69497	0.375391
$668$	66.8336	2.58587
$669$	7.47960	0.289178
$670$	34.5357	1.33423
$671$	−16.9660	−0.654967
$672$	34.4216	1.32784
$673$	24.7627	0.954533	0.477266	−	0.878759i	$-0.341628\pi$
$673$	24.7627	0.954533	0.477266	+	0.878759i	$0.341628\pi$
$674$	−29.4082	−1.13276
$675$	5.80036	0.223256
$676$	92.0970	3.54219
$677$	−40.7319	−1.56545	−0.782727	−	0.622365i	$-0.786172\pi$
$677$	−40.7319	−1.56545	−0.782727	+	0.622365i	$0.786172\pi$
$678$	−2.00307	−0.0769274
$679$	7.42173	0.284820
$680$	−2.13589	−0.0819077
$681$	−6.21714	−0.238241
$682$	15.3066	0.586122
$683$	32.7417	1.25283	0.626413	−	0.779491i	$-0.284522\pi$
$683$	32.7417	1.25283	0.626413	+	0.779491i	$0.284522\pi$
$684$	17.9308	0.685603
$685$	−25.5114	−0.974740
$686$	−52.3777	−1.99979
$687$	−2.49558	−0.0952122
$688$	116.900	4.45678
$689$	17.5459	0.668444
$690$	4.31965	0.164446
$691$	−10.3963	−0.395493	−0.197747	−	0.980253i	$-0.563362\pi$
$691$	−10.3963	−0.395493	−0.197747	+	0.980253i	$0.563362\pi$
$692$	−12.2221	−0.464614
$693$	22.6754	0.861366
$694$	99.1092	3.76214
$695$	1.31324	0.0498140
$696$	41.7938	1.58419
$697$	−0.286553	−0.0108540
$698$	19.3103	0.730905
$699$	−1.48312	−0.0560969
$700$	22.7532	0.859992
$701$	−14.5681	−0.550231	−0.275116	−	0.961411i	$-0.588716\pi$
$701$	−14.5681	−0.550231	−0.275116	+	0.961411i	$0.588716\pi$
$702$	52.6058	1.98548
$703$	0.810617	0.0305730
$704$	100.477	3.78687
$705$	−6.85576	−0.258203
$706$	19.7608	0.743708
$707$	2.72654	0.102542
$708$	−40.7345	−1.53090
$709$	−30.2819	−1.13726	−0.568630	−	0.822593i	$-0.692526\pi$
$709$	−30.2819	−1.13726	−0.568630	+	0.822593i	$0.692526\pi$
$710$	−26.1591	−0.981733
$711$	28.6321	1.07379
$712$	−77.9257	−2.92039
$713$	2.24504	0.0840774
$714$	0.539294	0.0201826
$715$	34.3684	1.28531
$716$	−130.558	−4.87918
$717$	−5.87869	−0.219544
$718$	31.4708	1.17448
$719$	−7.15129	−0.266698	−0.133349	−	0.991069i	$-0.542573\pi$
$719$	−7.15129	−0.266698	−0.133349	+	0.991069i	$0.542573\pi$
$720$	−70.6181	−2.63178
$721$	7.46576	0.278039
$722$	47.5053	1.76796
$723$	14.0311	0.521822
$724$	−54.5683	−2.02802
$725$	11.6121	0.431263
$726$	−1.33523	−0.0495550
$727$	−25.8085	−0.957184	−0.478592	−	0.878037i	$-0.658853\pi$
$727$	−25.8085	−0.957184	−0.478592	+	0.878037i	$0.658853\pi$
$728$	130.634	4.84160
$729$	−7.92570	−0.293544
$730$	−27.2003	−1.00673
$731$	0.977835	0.0361665
$732$	−16.9456	−0.626328
$733$	−17.3730	−0.641687	−0.320844	−	0.947132i	$-0.603966\pi$
$733$	−17.3730	−0.641687	−0.320844	+	0.947132i	$0.603966\pi$
$734$	13.0320	0.481022
$735$	−0.649778	−0.0239674
$736$	29.6409	1.09258
$737$	−23.7088	−0.873323
$738$	−16.4500	−0.605531
$739$	−19.1213	−0.703387	−0.351694	−	0.936115i	$-0.614394\pi$
$739$	−19.1213	−0.703387	−0.351694	+	0.936115i	$0.614394\pi$
$740$	−6.40571	−0.235479
$741$	−4.34395	−0.159579
$742$	22.2200	0.815720
$743$	10.5785	0.388087	0.194044	−	0.980993i	$-0.437840\pi$
$743$	10.5785	0.388087	0.194044	+	0.980993i	$0.437840\pi$
$744$	9.67808	0.354816
$745$	12.0033	0.439765
$746$	−76.8071	−2.81211
$747$	18.1163	0.662839
$748$	2.31626	0.0846909
$749$	−16.4590	−0.601397
$750$	20.8940	0.762941
$751$	−33.1080	−1.20813	−0.604064	−	0.796936i	$-0.706453\pi$
$751$	−33.1080	−1.20813	−0.604064	+	0.796936i	$0.706453\pi$
$752$	−88.1138	−3.21318
$753$	−13.5941	−0.495398
$754$	105.315	3.83534
$755$	−15.2194	−0.553890
$756$	48.7357	1.77250
$757$	5.10969	0.185715	0.0928574	−	0.995679i	$-0.470400\pi$
$757$	5.10969	0.185715	0.0928574	+	0.995679i	$0.470400\pi$
$758$	47.0727	1.70976
$759$	−2.96544	−0.107639
$760$	21.7875	0.790315
$761$	29.9689	1.08637	0.543186	−	0.839613i	$-0.317218\pi$
$761$	29.9689	1.08637	0.543186	+	0.839613i	$0.317218\pi$
$762$	−34.7739	−1.25972
$763$	−2.98581	−0.108094
$764$	−103.130	−3.73111
$765$	−0.590699	−0.0213568
$766$	68.9314	2.49059
$767$	−64.9791	−2.34626
$768$	26.2865	0.948532
$769$	3.06069	0.110371	0.0551856	−	0.998476i	$-0.482425\pi$
$769$	3.06069	0.110371	0.0551856	+	0.998476i	$0.482425\pi$
$770$	43.5240	1.56849
$771$	−9.97903	−0.359386
$772$	15.0476	0.541574
$773$	32.3203	1.16248	0.581240	−	0.813732i	$-0.302568\pi$
$773$	32.3203	1.16248	0.581240	+	0.813732i	$0.302568\pi$
$774$	56.1340	2.01770
$775$	2.68899	0.0965912
$776$	27.5506	0.989009
$777$	1.02387	0.0367313
$778$	21.4421	0.768737
$779$	2.92302	0.104728
$780$	34.3271	1.22911
$781$	17.9582	0.642596
$782$	0.464394	0.0166067
$783$	24.8722	0.888862
$784$	−8.35129	−0.298260
$785$	−2.81117	−0.100335
$786$	10.9345	0.390020
$787$	−11.4294	−0.407416	−0.203708	−	0.979032i	$-0.565299\pi$
$787$	−11.4294	−0.407416	−0.203708	+	0.979032i	$0.565299\pi$
$788$	−69.7024	−2.48305
$789$	−19.1176	−0.680603
$790$	54.9576	1.95530
$791$	−2.96019	−0.105252
$792$	84.1745	2.99101
$793$	−27.0314	−0.959912
$794$	−80.9432	−2.87257
$795$	3.69622	0.131091
$796$	88.7898	3.14707
$797$	52.6358	1.86446	0.932229	−	0.361870i	$-0.117862\pi$
$797$	52.6358	1.86446	0.932229	+	0.361870i	$0.117862\pi$
$798$	−5.50115	−0.194739
$799$	−0.737045	−0.0260748
$800$	35.5022	1.25519
$801$	−21.5510	−0.761467
$802$	42.2535	1.49202
$803$	18.6730	0.658955
$804$	−23.6802	−0.835137
$805$	6.38370	0.224996
$806$	24.3875	0.859014
$807$	−2.27270	−0.0800030
$808$	10.1214	0.356068
$809$	16.3504	0.574851	0.287426	−	0.957803i	$-0.407201\pi$
$809$	16.3504	0.574851	0.287426	+	0.957803i	$0.407201\pi$
$810$	−27.9779	−0.983042
$811$	−39.8462	−1.39919	−0.699595	−	0.714540i	$-0.746636\pi$
$811$	−39.8462	−1.39919	−0.699595	+	0.714540i	$0.746636\pi$
$812$	97.5672	3.42394
$813$	−16.6772	−0.584895
$814$	6.01123	0.210693
$815$	16.9805	0.594802
$816$	1.15300	0.0403630
$817$	−9.97456	−0.348966
$818$	−78.0119	−2.72762
$819$	36.1278	1.26241
$820$	−23.0985	−0.806635
$821$	28.7619	1.00380	0.501898	−	0.864927i	$-0.332635\pi$
$821$	28.7619	1.00380	0.501898	+	0.864927i	$0.332635\pi$
$822$	23.9115	0.834010
$823$	−14.0505	−0.489769	−0.244884	−	0.969552i	$-0.578750\pi$
$823$	−14.0505	−0.489769	−0.244884	+	0.969552i	$0.578750\pi$
$824$	27.7141	0.965465
$825$	−3.55184	−0.123659
$826$	−82.2891	−2.86320
$827$	4.51232	0.156909	0.0784543	−	0.996918i	$-0.475002\pi$
$827$	4.51232	0.156909	0.0784543	+	0.996918i	$0.475002\pi$
$828$	19.5026	0.677762
$829$	27.0836	0.940654	0.470327	−	0.882492i	$-0.344136\pi$
$829$	27.0836	0.940654	0.470327	+	0.882492i	$0.344136\pi$
$830$	34.7730	1.20699
$831$	13.1952	0.457735
$832$	160.087	5.55000
$833$	−0.0698560	−0.00242037
$834$	−1.23088	−0.0426220
$835$	22.4589	0.777223
$836$	−23.6274	−0.817170
$837$	5.75960	0.199081
$838$	−59.3349	−2.04969
$839$	−17.5657	−0.606436	−0.303218	−	0.952921i	$-0.598061\pi$
$839$	−17.5657	−0.606436	−0.303218	+	0.952921i	$0.598061\pi$
$840$	27.5193	0.949507
$841$	20.7933	0.717012
$842$	−46.5417	−1.60393
$843$	19.9774	0.688058
$844$	−24.2617	−0.835122
$845$	30.9484	1.06466
$846$	−42.3111	−1.45469
$847$	−1.97324	−0.0678014
$848$	47.5057	1.63135
$849$	9.82859	0.337316
$850$	0.556226	0.0190784
$851$	0.881673	0.0302233
$852$	17.9366	0.614498
$853$	−36.1209	−1.23676	−0.618378	−	0.785881i	$-0.712210\pi$
$853$	−36.1209	−1.23676	−0.618378	+	0.785881i	$0.712210\pi$
$854$	−34.2324	−1.17141
$855$	6.02551	0.206068
$856$	−61.0982	−2.08829
$857$	−9.11634	−0.311408	−0.155704	−	0.987804i	$-0.549765\pi$
$857$	−9.11634	−0.311408	−0.155704	+	0.987804i	$0.549765\pi$
$858$	−32.2131	−1.09974
$859$	3.78056	0.128991	0.0644955	−	0.997918i	$-0.479456\pi$
$859$	3.78056	0.128991	0.0644955	+	0.997918i	$0.479456\pi$
$860$	78.8216	2.68779
$861$	3.69201	0.125823
$862$	85.9268	2.92668
$863$	−35.5105	−1.20879	−0.604395	−	0.796685i	$-0.706585\pi$
$863$	−35.5105	−1.20879	−0.604395	+	0.796685i	$0.706585\pi$
$864$	76.0431	2.58704
$865$	−4.10713	−0.139647
$866$	55.9089	1.89986
$867$	−10.6820	−0.362780
$868$	22.5934	0.766869
$869$	−37.7284	−1.27985
$870$	22.1857	0.752165
$871$	−37.7743	−1.27993
$872$	−11.0838	−0.375345
$873$	7.61935	0.257876
$874$	−4.73712	−0.160236
$875$	30.8778	1.04386
$876$	18.6505	0.630142
$877$	−8.59983	−0.290396	−0.145198	−	0.989403i	$-0.546382\pi$
$877$	−8.59983	−0.290396	−0.145198	+	0.989403i	$0.546382\pi$
$878$	54.6630	1.84479
$879$	−7.55730	−0.254901
$880$	93.0531	3.13682
$881$	−2.09939	−0.0707303	−0.0353651	−	0.999374i	$-0.511259\pi$
$881$	−2.09939	−0.0707303	−0.0353651	+	0.999374i	$0.511259\pi$
$882$	−4.01018	−0.135030
$883$	48.3351	1.62661	0.813304	−	0.581840i	$-0.197667\pi$
$883$	48.3351	1.62661	0.813304	+	0.581840i	$0.197667\pi$
$884$	3.69041	0.124122
$885$	−13.6885	−0.460134
$886$	−20.6294	−0.693060
$887$	−42.2610	−1.41899	−0.709493	−	0.704712i	$-0.751076\pi$
$887$	−42.2610	−1.41899	−0.709493	+	0.704712i	$0.751076\pi$
$888$	3.80078	0.127546
$889$	−51.3899	−1.72356
$890$	−41.3658	−1.38659
$891$	19.2068	0.643453
$892$	64.8181	2.17027
$893$	7.51834	0.251592
$894$	−11.2505	−0.376273
$895$	−43.8730	−1.46651
$896$	93.2703	3.11594
$897$	−4.72473	−0.157754
$898$	86.3619	2.88193
$899$	11.5305	0.384564
$900$	23.3591	0.778637
$901$	0.397371	0.0132383
$902$	21.6760	0.721733
$903$	−12.5987	−0.419257
$904$	−10.9887	−0.365479
$905$	−18.3372	−0.609551
$906$	14.2649	0.473921
$907$	20.0542	0.665889	0.332945	−	0.942946i	$-0.391958\pi$
$907$	20.0542	0.665889	0.332945	+	0.942946i	$0.391958\pi$
$908$	−53.8776	−1.78799
$909$	2.79915	0.0928419
$910$	69.3451	2.29877
$911$	14.5287	0.481356	0.240678	−	0.970605i	$-0.422630\pi$
$911$	14.5287	0.481356	0.240678	+	0.970605i	$0.422630\pi$
$912$	−11.7613	−0.389456
$913$	−23.8717	−0.790038
$914$	−68.0168	−2.24980
$915$	−5.69444	−0.188252
$916$	−21.6266	−0.714565
$917$	16.1593	0.533626
$918$	1.19139	0.0393218
$919$	−13.3443	−0.440188	−0.220094	−	0.975479i	$-0.570636\pi$
$919$	−13.3443	−0.440188	−0.220094	+	0.975479i	$0.570636\pi$
$920$	23.6973	0.781277
$921$	14.1803	0.467257
$922$	−76.0083	−2.50320
$923$	28.6122	0.941782
$924$	−29.8432	−0.981771
$925$	1.05602	0.0347217
$926$	−87.2370	−2.86679
$927$	7.66456	0.251737
$928$	152.236	4.99738
$929$	15.3510	0.503651	0.251826	−	0.967773i	$-0.418969\pi$
$929$	15.3510	0.503651	0.251826	+	0.967773i	$0.418969\pi$
$930$	5.13748	0.168465
$931$	0.712577	0.0233538
$932$	−12.8527	−0.421005
$933$	11.5940	0.379569
$934$	−43.1652	−1.41241
$935$	0.778361	0.0254551
$936$	134.112	4.38359
$937$	−19.2014	−0.627283	−0.313641	−	0.949541i	$-0.601549\pi$
$937$	−19.2014	−0.627283	−0.313641	+	0.949541i	$0.601549\pi$
$938$	−47.8371	−1.56194
$939$	1.35162	0.0441084
$940$	−59.4119	−1.93780
$941$	41.9318	1.36694	0.683468	−	0.729980i	$-0.260471\pi$
$941$	41.9318	1.36694	0.683468	+	0.729980i	$0.260471\pi$
$942$	2.63487	0.0858488
$943$	3.17924	0.103530
$944$	−175.932	−5.72610
$945$	16.3772	0.532752
$946$	−73.9675	−2.40489
$947$	43.9735	1.42895	0.714474	−	0.699662i	$-0.246666\pi$
$947$	43.9735	1.42895	0.714474	+	0.699662i	$0.246666\pi$
$948$	−37.6830	−1.22389
$949$	29.7510	0.965758
$950$	−5.67387	−0.184085
$951$	−6.28261	−0.203728
$952$	2.95853	0.0958866
$953$	13.6231	0.441297	0.220648	−	0.975353i	$-0.429183\pi$
$953$	13.6231	0.441297	0.220648	+	0.975353i	$0.429183\pi$
$954$	22.8116	0.738554
$955$	−34.6559	−1.12144
$956$	−50.9446	−1.64767
$957$	−15.2305	−0.492332
$958$	−59.2352	−1.91380
$959$	35.3371	1.14110
$960$	33.7239	1.08843
$961$	−28.3299	−0.913868
$962$	9.57747	0.308790
$963$	−16.8972	−0.544506
$964$	121.593	3.91626
$965$	5.05661	0.162778
$966$	−5.98336	−0.192512
$967$	20.0567	0.644981	0.322491	−	0.946573i	$-0.395480\pi$
$967$	20.0567	0.644981	0.322491	+	0.946573i	$0.395480\pi$
$968$	−7.32498	−0.235434
$969$	−0.0983799	−0.00316042
$970$	14.6249	0.469576
$971$	−9.91294	−0.318121	−0.159061	−	0.987269i	$-0.550847\pi$
$971$	−9.91294	−0.318121	−0.159061	+	0.987269i	$0.550847\pi$
$972$	76.8158	2.46387
$973$	−1.81903	−0.0583155
$974$	68.4748	2.19407
$975$	−5.65902	−0.181234
$976$	−73.1879	−2.34269
$977$	−8.44145	−0.270066	−0.135033	−	0.990841i	$-0.543114\pi$
$977$	−8.44145	−0.270066	−0.135033	+	0.990841i	$0.543114\pi$
$978$	−15.9156	−0.508926
$979$	28.3976	0.907593
$980$	−5.63097	−0.179875
$981$	−3.06532	−0.0978681
$982$	5.99989	0.191464
$983$	−5.61813	−0.179190	−0.0895952	−	0.995978i	$-0.528557\pi$
$983$	−5.61813	−0.179190	−0.0895952	+	0.995978i	$0.528557\pi$
$984$	13.7053	0.436910
$985$	−23.4229	−0.746317
$986$	2.38513	0.0759579
$987$	9.49626	0.302269
$988$	−37.6446	−1.19764
$989$	−10.8489	−0.344975
$990$	44.6829	1.42012
$991$	11.9879	0.380808	0.190404	−	0.981706i	$-0.439020\pi$
$991$	11.9879	0.380808	0.190404	+	0.981706i	$0.439020\pi$
$992$	35.2528	1.11928
$993$	−1.11353	−0.0353368
$994$	36.2343	1.14928
$995$	29.8371	0.945899
$996$	−23.8430	−0.755493
$997$	−6.14511	−0.194618	−0.0973088	−	0.995254i	$-0.531023\pi$
$997$	−6.14511	−0.194618	−0.0973088	+	0.995254i	$0.531023\pi$
$998$	59.2395	1.87519
$999$	2.26191	0.0715637

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4021.2.a.b.1.2	✓	151

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4021.2.a.b.1.2	✓	151	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:	\( N \)	\(=\)	\( 4021 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.72951 q^{2} +0.628920 q^{3} +5.45022 q^{4} +1.83150 q^{5} -1.71664 q^{6} -2.53691 q^{7} -9.41739 q^{8} -2.60446 q^{9} +O(q^{10})\)	\(q-2.72951 q^{2} +0.628920 q^{3} +5.45022 q^{4} +1.83150 q^{5} -1.71664 q^{6} -2.53691 q^{7} -9.41739 q^{8} -2.60446 q^{9} -4.99910 q^{10} +3.43188 q^{11} +3.42775 q^{12} +5.46789 q^{13} +6.92451 q^{14} +1.15187 q^{15} +14.8044 q^{16} +0.123834 q^{17} +7.10889 q^{18} -1.26319 q^{19} +9.98208 q^{20} -1.59551 q^{21} -9.36735 q^{22} -1.37392 q^{23} -5.92279 q^{24} -1.64560 q^{25} -14.9247 q^{26} -3.52476 q^{27} -13.8267 q^{28} -7.05644 q^{29} -3.14403 q^{30} -1.63404 q^{31} -21.5740 q^{32} +2.15838 q^{33} -0.338007 q^{34} -4.64635 q^{35} -14.1949 q^{36} -0.641721 q^{37} +3.44789 q^{38} +3.43887 q^{39} -17.2480 q^{40} -2.31400 q^{41} +4.35496 q^{42} +7.89631 q^{43} +18.7045 q^{44} -4.77007 q^{45} +3.75012 q^{46} -5.95186 q^{47} +9.31080 q^{48} -0.564108 q^{49} +4.49169 q^{50} +0.0778820 q^{51} +29.8012 q^{52} +3.20889 q^{53} +9.62086 q^{54} +6.28550 q^{55} +23.8910 q^{56} -0.794447 q^{57} +19.2606 q^{58} -11.8837 q^{59} +6.27793 q^{60} -4.94365 q^{61} +4.46013 q^{62} +6.60727 q^{63} +29.2776 q^{64} +10.0145 q^{65} -5.89132 q^{66} -6.90838 q^{67} +0.674924 q^{68} -0.864085 q^{69} +12.6822 q^{70} +5.23276 q^{71} +24.5272 q^{72} +5.44103 q^{73} +1.75158 q^{74} -1.03495 q^{75} -6.88467 q^{76} -8.70636 q^{77} -9.38642 q^{78} -10.9935 q^{79} +27.1143 q^{80} +5.59659 q^{81} +6.31608 q^{82} -6.95586 q^{83} -8.69588 q^{84} +0.226803 q^{85} -21.5530 q^{86} -4.43794 q^{87} -32.3194 q^{88} +8.27466 q^{89} +13.0199 q^{90} -13.8715 q^{91} -7.48815 q^{92} -1.02768 q^{93} +16.2456 q^{94} -2.31354 q^{95} -13.5683 q^{96} -2.92550 q^{97} +1.53974 q^{98} -8.93820 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) \) 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9	\( 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9} - 7 q^{10} - 126 q^{11} - 47 q^{12} - 10 q^{13} - 58 q^{14} - 50 q^{15} + 74 q^{16} - 39 q^{17} - 47 q^{18} - 48 q^{19} - 64 q^{20} - 50 q^{21} - 7 q^{22} - 91 q^{23} - 44 q^{24} + 102 q^{25} - 94 q^{26} - 92 q^{27} - 27 q^{28} - 79 q^{29} - 12 q^{30} - 33 q^{31} - 102 q^{32} - 7 q^{33} - 17 q^{34} - 183 q^{35} - 6 q^{36} - 24 q^{37} - 77 q^{38} - 81 q^{39} - 37 q^{40} - 62 q^{41} + 4 q^{42} - 74 q^{43} - 209 q^{44} - 35 q^{45} - 37 q^{46} - 127 q^{47} - 59 q^{48} + 75 q^{49} - 79 q^{50} - 138 q^{51} - 12 q^{52} - 104 q^{53} - 43 q^{54} - 49 q^{55} - 167 q^{56} - 19 q^{57} - 32 q^{58} - 207 q^{59} - 94 q^{60} - 57 q^{61} - 69 q^{62} - 49 q^{63} - 4 q^{64} - 78 q^{65} - 51 q^{66} - 92 q^{67} - 80 q^{68} - 84 q^{69} + 5 q^{70} - 217 q^{71} - 79 q^{72} + 2 q^{73} - 113 q^{74} - 173 q^{75} - 70 q^{76} - 85 q^{77} - 46 q^{78} - 70 q^{79} - 95 q^{80} - 49 q^{81} - 12 q^{82} - 109 q^{83} - 114 q^{84} - 25 q^{85} - 136 q^{86} - 60 q^{87} - 2 q^{88} - 144 q^{89} - 55 q^{90} - 62 q^{91} - 175 q^{92} - 42 q^{93} - 15 q^{94} - 189 q^{95} - 64 q^{96} - 24 q^{97} - 37 q^{98} - 293 q^{99}+O(q^{100}) \) 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9 - 7 * q^10 - 126 * q^11 - 47 * q^12 - 10 * q^13 - 58 * q^14 - 50 * q^15 + 74 * q^16 - 39 * q^17 - 47 * q^18 - 48 * q^19 - 64 * q^20 - 50 * q^21 - 7 * q^22 - 91 * q^23 - 44 * q^24 + 102 * q^25 - 94 * q^26 - 92 * q^27 - 27 * q^28 - 79 * q^29 - 12 * q^30 - 33 * q^31 - 102 * q^32 - 7 * q^33 - 17 * q^34 - 183 * q^35 - 6 * q^36 - 24 * q^37 - 77 * q^38 - 81 * q^39 - 37 * q^40 - 62 * q^41 + 4 * q^42 - 74 * q^43 - 209 * q^44 - 35 * q^45 - 37 * q^46 - 127 * q^47 - 59 * q^48 + 75 * q^49 - 79 * q^50 - 138 * q^51 - 12 * q^52 - 104 * q^53 - 43 * q^54 - 49 * q^55 - 167 * q^56 - 19 * q^57 - 32 * q^58 - 207 * q^59 - 94 * q^60 - 57 * q^61 - 69 * q^62 - 49 * q^63 - 4 * q^64 - 78 * q^65 - 51 * q^66 - 92 * q^67 - 80 * q^68 - 84 * q^69 + 5 * q^70 - 217 * q^71 - 79 * q^72 + 2 * q^73 - 113 * q^74 - 173 * q^75 - 70 * q^76 - 85 * q^77 - 46 * q^78 - 70 * q^79 - 95 * q^80 - 49 * q^81 - 12 * q^82 - 109 * q^83 - 114 * q^84 - 25 * q^85 - 136 * q^86 - 60 * q^87 - 2 * q^88 - 144 * q^89 - 55 * q^90 - 62 * q^91 - 175 * q^92 - 42 * q^93 - 15 * q^94 - 189 * q^95 - 64 * q^96 - 24 * q^97 - 37 * q^98 - 293 * q^99

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