LMFDB - Embedded newform 6031.2.a.c.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6031,2,Mod(1,6031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6031, 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("6031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.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:	$48.1577774590$
Analytic rank:	$1$
Dimension:	$110$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.27127 q^{2} -0.567339 q^{3} +3.15866 q^{4} -3.83448 q^{5} +1.28858 q^{6} +2.52768 q^{7} -2.63164 q^{8} -2.67813 q^{9} +O(q^{10})$	\(q-2.27127 q^{2} -0.567339 q^{3} +3.15866 q^{4} -3.83448 q^{5} +1.28858 q^{6} +2.52768 q^{7} -2.63164 q^{8} -2.67813 q^{9} +8.70914 q^{10} +4.61563 q^{11} -1.79203 q^{12} +2.80251 q^{13} -5.74103 q^{14} +2.17545 q^{15} -0.340172 q^{16} -6.62907 q^{17} +6.08275 q^{18} +2.55425 q^{19} -12.1118 q^{20} -1.43405 q^{21} -10.4833 q^{22} -5.91027 q^{23} +1.49303 q^{24} +9.70325 q^{25} -6.36526 q^{26} +3.22142 q^{27} +7.98408 q^{28} +1.34441 q^{29} -4.94103 q^{30} +0.239798 q^{31} +6.03589 q^{32} -2.61862 q^{33} +15.0564 q^{34} -9.69232 q^{35} -8.45930 q^{36} -1.00000 q^{37} -5.80138 q^{38} -1.58997 q^{39} +10.0910 q^{40} -1.83841 q^{41} +3.25711 q^{42} +8.62403 q^{43} +14.5792 q^{44} +10.2692 q^{45} +13.4238 q^{46} +10.4736 q^{47} +0.192993 q^{48} -0.610858 q^{49} -22.0387 q^{50} +3.76093 q^{51} +8.85220 q^{52} -9.81488 q^{53} -7.31671 q^{54} -17.6985 q^{55} -6.65192 q^{56} -1.44912 q^{57} -3.05351 q^{58} -10.4567 q^{59} +6.87151 q^{60} -11.6078 q^{61} -0.544645 q^{62} -6.76943 q^{63} -13.0288 q^{64} -10.7462 q^{65} +5.94760 q^{66} +5.89350 q^{67} -20.9390 q^{68} +3.35312 q^{69} +22.0139 q^{70} +9.98309 q^{71} +7.04786 q^{72} -4.48716 q^{73} +2.27127 q^{74} -5.50503 q^{75} +8.06800 q^{76} +11.6668 q^{77} +3.61126 q^{78} +4.17171 q^{79} +1.30438 q^{80} +6.20674 q^{81} +4.17552 q^{82} -17.7232 q^{83} -4.52968 q^{84} +25.4190 q^{85} -19.5875 q^{86} -0.762734 q^{87} -12.1466 q^{88} -3.81214 q^{89} -23.3242 q^{90} +7.08384 q^{91} -18.6685 q^{92} -0.136046 q^{93} -23.7884 q^{94} -9.79421 q^{95} -3.42440 q^{96} -1.15032 q^{97} +1.38742 q^{98} -12.3612 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9}+O(q^{10}) $ 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9} - 17 q^{10} - 9 q^{11} - 21 q^{13} - 29 q^{14} - 23 q^{15} + 79 q^{16} - 76 q^{17} - 31 q^{18} - 27 q^{19} - 67 q^{20} - 30 q^{21} - 28 q^{22} - 32 q^{23} - 63 q^{24} + 66 q^{25} - 55 q^{26} - 4 q^{28} - 81 q^{29} - 48 q^{30} - 30 q^{31} - 73 q^{32} - 53 q^{33} - 23 q^{34} - 78 q^{35} + 7 q^{36} - 110 q^{37} - 50 q^{38} - 64 q^{39} - 37 q^{40} - 123 q^{41} - 63 q^{42} - 40 q^{43} - 31 q^{44} - 73 q^{45} + 16 q^{46} - 37 q^{47} - 29 q^{48} + 46 q^{49} - 58 q^{50} - 73 q^{51} - 39 q^{52} - 16 q^{53} - 53 q^{54} - 59 q^{55} - 113 q^{56} - 39 q^{57} + 11 q^{58} - 93 q^{59} - 18 q^{60} - 66 q^{61} - 40 q^{62} - 21 q^{63} + 23 q^{64} - 92 q^{65} - 31 q^{66} + q^{67} - 121 q^{68} - 80 q^{69} - 3 q^{70} - 75 q^{71} - 114 q^{72} - 39 q^{73} + 9 q^{74} - 25 q^{75} - 58 q^{76} - 31 q^{77} + 68 q^{78} - 36 q^{79} - 82 q^{80} - 50 q^{81} - 18 q^{82} - 57 q^{83} - 9 q^{84} - 14 q^{85} - 58 q^{86} - 58 q^{87} - 15 q^{88} - 181 q^{89} + 8 q^{90} - 55 q^{91} - 116 q^{92} - 86 q^{93} - 39 q^{94} - 70 q^{95} - 127 q^{96} - 91 q^{97} - 19 q^{98} - 21 q^{99}+O(q^{100}) \) 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9 - 17 * q^10 - 9 * q^11 - 21 * q^13 - 29 * q^14 - 23 * q^15 + 79 * q^16 - 76 * q^17 - 31 * q^18 - 27 * q^19 - 67 * q^20 - 30 * q^21 - 28 * q^22 - 32 * q^23 - 63 * q^24 + 66 * q^25 - 55 * q^26 - 4 * q^28 - 81 * q^29 - 48 * q^30 - 30 * q^31 - 73 * q^32 - 53 * q^33 - 23 * q^34 - 78 * q^35 + 7 * q^36 - 110 * q^37 - 50 * q^38 - 64 * q^39 - 37 * q^40 - 123 * q^41 - 63 * q^42 - 40 * q^43 - 31 * q^44 - 73 * q^45 + 16 * q^46 - 37 * q^47 - 29 * q^48 + 46 * q^49 - 58 * q^50 - 73 * q^51 - 39 * q^52 - 16 * q^53 - 53 * q^54 - 59 * q^55 - 113 * q^56 - 39 * q^57 + 11 * q^58 - 93 * q^59 - 18 * q^60 - 66 * q^61 - 40 * q^62 - 21 * q^63 + 23 * q^64 - 92 * q^65 - 31 * q^66 + q^67 - 121 * q^68 - 80 * q^69 - 3 * q^70 - 75 * q^71 - 114 * q^72 - 39 * q^73 + 9 * q^74 - 25 * q^75 - 58 * q^76 - 31 * q^77 + 68 * q^78 - 36 * q^79 - 82 * q^80 - 50 * q^81 - 18 * q^82 - 57 * q^83 - 9 * q^84 - 14 * q^85 - 58 * q^86 - 58 * q^87 - 15 * q^88 - 181 * q^89 + 8 * q^90 - 55 * q^91 - 116 * q^92 - 86 * q^93 - 39 * q^94 - 70 * q^95 - 127 * q^96 - 91 * q^97 - 19 * q^98 - 21 * 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 $

$2$	−2.27127	−1.60603	−0.803015	−	0.595959i	$-0.796772\pi$
$2$	−2.27127	−1.60603	−0.803015	+	0.595959i	$0.796772\pi$
$3$	−0.567339	−0.327553	−0.163777	−	0.986497i	$-0.552368\pi$
$3$	−0.567339	−0.327553	−0.163777	+	0.986497i	$0.552368\pi$
$4$	3.15866	1.57933
$5$	−3.83448	−1.71483	−0.857416	−	0.514624i	$-0.827932\pi$
$5$	−3.83448	−1.71483	−0.857416	+	0.514624i	$0.827932\pi$
$6$	1.28858	0.526060
$7$	2.52768	0.955371	0.477686	−	0.878531i	$-0.341476\pi$
$7$	2.52768	0.955371	0.477686	+	0.878531i	$0.341476\pi$
$8$	−2.63164	−0.930424
$9$	−2.67813	−0.892709
$10$	8.70914	2.75407
$11$	4.61563	1.39166	0.695832	−	0.718205i	$-0.255036\pi$
$11$	4.61563	1.39166	0.695832	+	0.718205i	$0.255036\pi$
$12$	−1.79203	−0.517315
$13$	2.80251	0.777277	0.388639	−	0.921390i	$-0.372945\pi$
$13$	2.80251	0.777277	0.388639	+	0.921390i	$0.372945\pi$
$14$	−5.74103	−1.53436
$15$	2.17545	0.561699
$16$	−0.340172	−0.0850429
$17$	−6.62907	−1.60778	−0.803892	−	0.594775i	$-0.797241\pi$
$17$	−6.62907	−1.60778	−0.803892	+	0.594775i	$0.797241\pi$
$18$	6.08275	1.43372
$19$	2.55425	0.585984	0.292992	−	0.956115i	$-0.405349\pi$
$19$	2.55425	0.585984	0.292992	+	0.956115i	$0.405349\pi$
$20$	−12.1118	−2.70829
$21$	−1.43405	−0.312935
$22$	−10.4833	−2.23505
$23$	−5.91027	−1.23238	−0.616188	−	0.787599i	$-0.711324\pi$
$23$	−5.91027	−1.23238	−0.616188	+	0.787599i	$0.711324\pi$
$24$	1.49303	0.304763
$25$	9.70325	1.94065
$26$	−6.36526	−1.24833
$27$	3.22142	0.619963
$28$	7.98408	1.50885
$29$	1.34441	0.249650	0.124825	−	0.992179i	$-0.460163\pi$
$29$	1.34441	0.249650	0.124825	+	0.992179i	$0.460163\pi$
$30$	−4.94103	−0.902105
$31$	0.239798	0.0430689	0.0215345	−	0.999768i	$-0.493145\pi$
$31$	0.239798	0.0430689	0.0215345	+	0.999768i	$0.493145\pi$
$32$	6.03589	1.06701
$33$	−2.61862	−0.455844
$34$	15.0564	2.58215
$35$	−9.69232	−1.63830
$36$	−8.45930	−1.40988
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−5.80138	−0.941108
$39$	−1.58997	−0.254600
$40$	10.0910	1.59552
$41$	−1.83841	−0.287111	−0.143556	−	0.989642i	$-0.545854\pi$
$41$	−1.83841	−0.287111	−0.143556	+	0.989642i	$0.545854\pi$
$42$	3.25711	0.502583
$43$	8.62403	1.31515	0.657576	−	0.753388i	$-0.271582\pi$
$43$	8.62403	1.31515	0.657576	+	0.753388i	$0.271582\pi$
$44$	14.5792	2.19790
$45$	10.2692	1.53085
$46$	13.4238	1.97923
$47$	10.4736	1.52774	0.763868	−	0.645372i	$-0.223298\pi$
$47$	10.4736	1.52774	0.763868	+	0.645372i	$0.223298\pi$
$48$	0.192993	0.0278561
$49$	−0.610858	−0.0872654
$50$	−22.0387	−3.11674
$51$	3.76093	0.526635
$52$	8.85220	1.22758
$53$	−9.81488	−1.34818	−0.674089	−	0.738651i	$-0.735463\pi$
$53$	−9.81488	−1.34818	−0.674089	+	0.738651i	$0.735463\pi$
$54$	−7.31671	−0.995679
$55$	−17.6985	−2.38647
$56$	−6.65192	−0.888901
$57$	−1.44912	−0.191941
$58$	−3.05351	−0.400946
$59$	−10.4567	−1.36135	−0.680673	−	0.732588i	$-0.738312\pi$
$59$	−10.4567	−1.36135	−0.680673	+	0.732588i	$0.738312\pi$
$60$	6.87151	0.887109
$61$	−11.6078	−1.48623	−0.743115	−	0.669164i	$-0.766653\pi$
$61$	−11.6078	−1.48623	−0.743115	+	0.669164i	$0.766653\pi$
$62$	−0.544645	−0.0691700
$63$	−6.76943	−0.852869
$64$	−13.0288	−1.62860
$65$	−10.7462	−1.33290
$66$	5.94760	0.732099
$67$	5.89350	0.720006	0.360003	−	0.932951i	$-0.382776\pi$
$67$	5.89350	0.720006	0.360003	+	0.932951i	$0.382776\pi$
$68$	−20.9390	−2.53923
$69$	3.35312	0.403668
$70$	22.0139	2.63116
$71$	9.98309	1.18478	0.592388	−	0.805653i	$-0.298185\pi$
$71$	9.98309	1.18478	0.592388	+	0.805653i	$0.298185\pi$
$72$	7.04786	0.830598
$73$	−4.48716	−0.525183	−0.262591	−	0.964907i	$-0.584577\pi$
$73$	−4.48716	−0.525183	−0.262591	+	0.964907i	$0.584577\pi$
$74$	2.27127	0.264030
$75$	−5.50503	−0.635666
$76$	8.06800	0.925463
$77$	11.6668	1.32956
$78$	3.61126	0.408895
$79$	4.17171	0.469354	0.234677	−	0.972073i	$-0.424597\pi$
$79$	4.17171	0.469354	0.234677	+	0.972073i	$0.424597\pi$
$80$	1.30438	0.145834
$81$	6.20674	0.689638
$82$	4.17552	0.461110
$83$	−17.7232	−1.94537	−0.972685	−	0.232128i	$-0.925431\pi$
$83$	−17.7232	−1.94537	−0.972685	+	0.232128i	$0.925431\pi$
$84$	−4.52968	−0.494228
$85$	25.4190	2.75708
$86$	−19.5875	−2.11217
$87$	−0.762734	−0.0817737
$88$	−12.1466	−1.29484
$89$	−3.81214	−0.404086	−0.202043	−	0.979377i	$-0.564758\pi$
$89$	−3.81214	−0.404086	−0.202043	+	0.979377i	$0.564758\pi$
$90$	−23.3242	−2.45858
$91$	7.08384	0.742589
$92$	−18.6685	−1.94633
$93$	−0.136046	−0.0141074
$94$	−23.7884	−2.45359
$95$	−9.79421	−1.00486
$96$	−3.42440	−0.349501
$97$	−1.15032	−0.116797	−0.0583984	−	0.998293i	$-0.518599\pi$
$97$	−1.15032	−0.116797	−0.0583984	+	0.998293i	$0.518599\pi$
$98$	1.38742	0.140151
$99$	−12.3612	−1.24235
$100$	30.6493	3.06493
$101$	−2.91123	−0.289678	−0.144839	−	0.989455i	$-0.546266\pi$
$101$	−2.91123	−0.289678	−0.144839	+	0.989455i	$0.546266\pi$
$102$	−8.54207	−0.845791
$103$	−18.3774	−1.81078	−0.905390	−	0.424581i	$-0.860421\pi$
$103$	−18.3774	−1.81078	−0.905390	+	0.424581i	$0.860421\pi$
$104$	−7.37520	−0.723198
$105$	5.49883	0.536631
$106$	22.2922	2.16521
$107$	8.08327	0.781439	0.390719	−	0.920510i	$-0.372226\pi$
$107$	8.08327	0.781439	0.390719	+	0.920510i	$0.372226\pi$
$108$	10.1754	0.979127
$109$	−4.59477	−0.440099	−0.220050	−	0.975489i	$-0.570622\pi$
$109$	−4.59477	−0.440099	−0.220050	+	0.975489i	$0.570622\pi$
$110$	40.1981	3.83274
$111$	0.567339	0.0538494
$112$	−0.859844	−0.0812476
$113$	16.0394	1.50886	0.754429	−	0.656382i	$-0.227914\pi$
$113$	16.0394	1.50886	0.754429	+	0.656382i	$0.227914\pi$
$114$	3.29135	0.308263
$115$	22.6628	2.11332
$116$	4.24653	0.394280
$117$	−7.50549	−0.693882
$118$	23.7500	2.18636
$119$	−16.7561	−1.53603
$120$	−5.72499	−0.522618
$121$	10.3040	0.936727
$122$	26.3645	2.38693
$123$	1.04300	0.0940443
$124$	0.757440	0.0680201
$125$	−18.0345	−1.61306
$126$	15.3752	1.36973
$127$	13.1266	1.16479	0.582396	−	0.812905i	$-0.302115\pi$
$127$	13.1266	1.16479	0.582396	+	0.812905i	$0.302115\pi$
$128$	17.5201	1.54857
$129$	−4.89275	−0.430782
$130$	24.4075	2.14068
$131$	8.97195	0.783883	0.391942	−	0.919990i	$-0.371804\pi$
$131$	8.97195	0.783883	0.391942	+	0.919990i	$0.371804\pi$
$132$	−8.27135	−0.719929
$133$	6.45630	0.559833
$134$	−13.3857	−1.15635
$135$	−12.3525	−1.06313
$136$	17.4453	1.49592
$137$	17.4909	1.49435	0.747176	−	0.664627i	$-0.231409\pi$
$137$	17.4909	1.49435	0.747176	+	0.664627i	$0.231409\pi$
$138$	−7.61584	−0.648304
$139$	17.7226	1.50321	0.751606	−	0.659612i	$-0.229279\pi$
$139$	17.7226	1.50321	0.751606	+	0.659612i	$0.229279\pi$
$140$	−30.6148	−2.58742
$141$	−5.94210	−0.500415
$142$	−22.6743	−1.90278
$143$	12.9354	1.08171
$144$	0.911023	0.0759186
$145$	−5.15510	−0.428108
$146$	10.1916	0.843459
$147$	0.346563	0.0285841
$148$	−3.15866	−0.259641
$149$	−1.41593	−0.115997	−0.0579986	−	0.998317i	$-0.518472\pi$
$149$	−1.41593	−0.115997	−0.0579986	+	0.998317i	$0.518472\pi$
$150$	12.5034	1.02090
$151$	−8.92252	−0.726104	−0.363052	−	0.931769i	$-0.618265\pi$
$151$	−8.92252	−0.726104	−0.363052	+	0.931769i	$0.618265\pi$
$152$	−6.72185	−0.545214
$153$	17.7535	1.43528
$154$	−26.4984	−2.13531
$155$	−0.919499	−0.0738559
$156$	−5.02219	−0.402097
$157$	14.4339	1.15195	0.575974	−	0.817468i	$-0.304623\pi$
$157$	14.4339	1.15195	0.575974	+	0.817468i	$0.304623\pi$
$158$	−9.47508	−0.753797
$159$	5.56836	0.441600
$160$	−23.1445	−1.82974
$161$	−14.9392	−1.17738
$162$	−14.0972	−1.10758
$163$	−1.00000	−0.0783260
$163$	−1.00000	−0.0783260
$164$	−5.80692	−0.453444
$165$	10.0411	0.781695
$166$	40.2541	3.12432
$167$	14.2648	1.10385	0.551923	−	0.833895i	$-0.313894\pi$
$167$	14.2648	1.10385	0.551923	+	0.833895i	$0.313894\pi$
$168$	3.77389	0.291162
$169$	−5.14592	−0.395840
$170$	−57.7335	−4.42795
$171$	−6.84059	−0.523113
$172$	27.2404	2.07706
$173$	9.57240	0.727776	0.363888	−	0.931443i	$-0.381449\pi$
$173$	9.57240	0.727776	0.363888	+	0.931443i	$0.381449\pi$
$174$	1.73237	0.131331
$175$	24.5267	1.85404
$176$	−1.57011	−0.118351
$177$	5.93249	0.445913
$178$	8.65839	0.648974
$179$	5.64773	0.422131	0.211066	−	0.977472i	$-0.432307\pi$
$179$	5.64773	0.422131	0.211066	+	0.977472i	$0.432307\pi$
$180$	32.4370	2.41771
$181$	17.2697	1.28365	0.641824	−	0.766852i	$-0.278178\pi$
$181$	17.2697	1.28365	0.641824	+	0.766852i	$0.278178\pi$
$182$	−16.0893	−1.19262
$183$	6.58557	0.486819
$184$	15.5537	1.14663
$185$	3.83448	0.281917
$186$	0.308998	0.0226568
$187$	−30.5973	−2.23750
$188$	33.0827	2.41280
$189$	8.14271	0.592295
$190$	22.2453	1.61384
$191$	−11.5667	−0.836939	−0.418469	−	0.908231i	$-0.637433\pi$
$191$	−11.5667	−0.836939	−0.418469	+	0.908231i	$0.637433\pi$
$192$	7.39174	0.533453
$193$	5.33635	0.384119	0.192059	−	0.981383i	$-0.438483\pi$
$193$	5.33635	0.384119	0.192059	+	0.981383i	$0.438483\pi$
$194$	2.61268	0.187579
$195$	6.09673	0.436596
$196$	−1.92949	−0.137821
$197$	−18.5968	−1.32497	−0.662484	−	0.749076i	$-0.730498\pi$
$197$	−18.5968	−1.32497	−0.662484	+	0.749076i	$0.730498\pi$
$198$	28.0757	1.99525
$199$	24.6744	1.74913	0.874563	−	0.484912i	$-0.161149\pi$
$199$	24.6744	1.74913	0.874563	+	0.484912i	$0.161149\pi$
$200$	−25.5354	−1.80563
$201$	−3.34361	−0.235840
$202$	6.61219	0.465232
$203$	3.39822	0.238509
$204$	11.8795	0.831731
$205$	7.04935	0.492348
$206$	41.7400	2.90817
$207$	15.8284	1.10015
$208$	−0.953336	−0.0661019
$209$	11.7894	0.815493
$210$	−12.4893	−0.861845
$211$	−10.5847	−0.728678	−0.364339	−	0.931266i	$-0.618705\pi$
$211$	−10.5847	−0.728678	−0.364339	+	0.931266i	$0.618705\pi$
$212$	−31.0019	−2.12922
$213$	−5.66380	−0.388077
$214$	−18.3593	−1.25501
$215$	−33.0687	−2.25527
$216$	−8.47761	−0.576828
$217$	0.606130	0.0411468
$218$	10.4360	0.706813
$219$	2.54574	0.172025
$220$	−55.9037	−3.76903
$221$	−18.5780	−1.24969
$222$	−1.28858	−0.0864838
$223$	6.66541	0.446349	0.223175	−	0.974778i	$-0.428358\pi$
$223$	6.66541	0.446349	0.223175	+	0.974778i	$0.428358\pi$
$224$	15.2568	1.01939
$225$	−25.9865	−1.73243
$226$	−36.4297	−2.42327
$227$	−20.9711	−1.39190	−0.695952	−	0.718089i	$-0.745017\pi$
$227$	−20.9711	−1.39190	−0.695952	+	0.718089i	$0.745017\pi$
$228$	−4.57729	−0.303138
$229$	−6.10816	−0.403638	−0.201819	−	0.979423i	$-0.564685\pi$
$229$	−6.10816	−0.403638	−0.201819	+	0.979423i	$0.564685\pi$
$230$	−51.4733	−3.39405
$231$	−6.61903	−0.435500
$232$	−3.53799	−0.232280
$233$	−5.49643	−0.360083	−0.180042	−	0.983659i	$-0.557623\pi$
$233$	−5.49643	−0.360083	−0.180042	+	0.983659i	$0.557623\pi$
$234$	17.0470	1.11440
$235$	−40.1610	−2.61981
$236$	−33.0292	−2.15002
$237$	−2.36677	−0.153739
$238$	38.0577	2.46691
$239$	4.62710	0.299302	0.149651	−	0.988739i	$-0.452185\pi$
$239$	4.62710	0.299302	0.149651	+	0.988739i	$0.452185\pi$
$240$	−0.740026	−0.0477685
$241$	1.15505	0.0744033	0.0372017	−	0.999308i	$-0.488156\pi$
$241$	1.15505	0.0744033	0.0372017	+	0.999308i	$0.488156\pi$
$242$	−23.4032	−1.50441
$243$	−13.1856	−0.845856
$244$	−36.6652	−2.34725
$245$	2.34232	0.149646
$246$	−2.36894	−0.151038
$247$	7.15831	0.455472
$248$	−0.631060	−0.0400724
$249$	10.0550	0.637212
$250$	40.9612	2.59061
$251$	−25.2841	−1.59592	−0.797958	−	0.602712i	$-0.794087\pi$
$251$	−25.2841	−1.59592	−0.797958	+	0.602712i	$0.794087\pi$
$252$	−21.3824	−1.34696
$253$	−27.2796	−1.71505
$254$	−29.8139	−1.87069
$255$	−14.4212	−0.903090
$256$	−13.7353	−0.858457
$257$	10.2202	0.637518	0.318759	−	0.947836i	$-0.396734\pi$
$257$	10.2202	0.637518	0.318759	+	0.947836i	$0.396734\pi$
$258$	11.1127	0.691849
$259$	−2.52768	−0.157062
$260$	−33.9436	−2.10509
$261$	−3.60049	−0.222865
$262$	−20.3777	−1.25894
$263$	25.8582	1.59449	0.797243	−	0.603659i	$-0.206291\pi$
$263$	25.8582	1.59449	0.797243	+	0.603659i	$0.206291\pi$
$264$	6.89126	0.424128
$265$	37.6350	2.31190
$266$	−14.6640	−0.899108
$267$	2.16277	0.132360
$268$	18.6156	1.13713
$269$	3.85895	0.235284	0.117642	−	0.993056i	$-0.462466\pi$
$269$	3.85895	0.235284	0.117642	+	0.993056i	$0.462466\pi$
$270$	28.0558	1.70742
$271$	−23.1019	−1.40334	−0.701669	−	0.712503i	$-0.747562\pi$
$271$	−23.1019	−1.40334	−0.701669	+	0.712503i	$0.747562\pi$
$272$	2.25502	0.136731
$273$	−4.01894	−0.243237
$274$	−39.7266	−2.39997
$275$	44.7865	2.70073
$276$	10.5914	0.637526
$277$	12.1378	0.729293	0.364646	−	0.931146i	$-0.381190\pi$
$277$	12.1378	0.729293	0.364646	+	0.931146i	$0.381190\pi$
$278$	−40.2528	−2.41420
$279$	−0.642208	−0.0384480
$280$	25.5067	1.52432
$281$	−8.62795	−0.514700	−0.257350	−	0.966318i	$-0.582849\pi$
$281$	−8.62795	−0.514700	−0.257350	+	0.966318i	$0.582849\pi$
$282$	13.4961	0.803681
$283$	−27.8261	−1.65409	−0.827045	−	0.562135i	$-0.809980\pi$
$283$	−27.8261	−1.65409	−0.827045	+	0.562135i	$0.809980\pi$
$284$	31.5332	1.87115
$285$	5.55663	0.329147
$286$	−29.3797	−1.73726
$287$	−4.64690	−0.274298
$288$	−16.1649	−0.952525
$289$	26.9445	1.58497
$290$	11.7086	0.687554
$291$	0.652619	0.0382572
$292$	−14.1734	−0.829438
$293$	27.9344	1.63194	0.815971	−	0.578092i	$-0.196203\pi$
$293$	27.9344	1.63194	0.815971	+	0.578092i	$0.196203\pi$
$294$	−0.787138	−0.0459068
$295$	40.0960	2.33448
$296$	2.63164	0.152961
$297$	14.8689	0.862780
$298$	3.21595	0.186295
$299$	−16.5636	−0.957898
$300$	−17.3885	−1.00393
$301$	21.7988	1.25646
$302$	20.2654	1.16615
$303$	1.65165	0.0948850
$304$	−0.868882	−0.0498338
$305$	44.5100	2.54864
$306$	−40.3229	−2.30511
$307$	−11.0008	−0.627847	−0.313924	−	0.949448i	$-0.601644\pi$
$307$	−11.0008	−0.627847	−0.313924	+	0.949448i	$0.601644\pi$
$308$	36.8515	2.09981
$309$	10.4262	0.593127
$310$	2.08843	0.118615
$311$	−12.4686	−0.707031	−0.353515	−	0.935429i	$-0.615014\pi$
$311$	−12.4686	−0.707031	−0.353515	+	0.935429i	$0.615014\pi$
$312$	4.18423	0.236886
$313$	23.6854	1.33878	0.669389	−	0.742912i	$-0.266556\pi$
$313$	23.6854	1.33878	0.669389	+	0.742912i	$0.266556\pi$
$314$	−32.7832	−1.85006
$315$	25.9573	1.46253
$316$	13.1770	0.741266
$317$	−24.8565	−1.39608	−0.698041	−	0.716058i	$-0.745944\pi$
$317$	−24.8565	−1.39608	−0.698041	+	0.716058i	$0.745944\pi$
$318$	−12.6472	−0.709222
$319$	6.20528	0.347429
$320$	49.9587	2.79278
$321$	−4.58595	−0.255963
$322$	33.9310	1.89090
$323$	−16.9323	−0.942136
$324$	19.6050	1.08917
$325$	27.1935	1.50842
$326$	2.27127	0.125794
$327$	2.60679	0.144156
$328$	4.83803	0.267135
$329$	26.4739	1.45956
$330$	−22.8060	−1.25543
$331$	−32.1264	−1.76583	−0.882915	−	0.469533i	$-0.844422\pi$
$331$	−32.1264	−1.76583	−0.882915	+	0.469533i	$0.844422\pi$
$332$	−55.9815	−3.07239
$333$	2.67813	0.146760
$334$	−32.3993	−1.77281
$335$	−22.5985	−1.23469
$336$	0.487823	0.0266129
$337$	−24.9376	−1.35844	−0.679218	−	0.733937i	$-0.737681\pi$
$337$	−24.9376	−1.35844	−0.679218	+	0.733937i	$0.737681\pi$
$338$	11.6878	0.635731
$339$	−9.09976	−0.494231
$340$	80.2902	4.35435
$341$	1.10682	0.0599374
$342$	15.5368	0.840136
$343$	−19.2378	−1.03874
$344$	−22.6953	−1.22365
$345$	−12.8575	−0.692224
$346$	−21.7415	−1.16883
$347$	19.8200	1.06399	0.531996	−	0.846747i	$-0.321442\pi$
$347$	19.8200	1.06399	0.531996	+	0.846747i	$0.321442\pi$
$348$	−2.40922	−0.129148
$349$	33.9727	1.81852	0.909260	−	0.416229i	$-0.136649\pi$
$349$	33.9727	1.81852	0.909260	+	0.416229i	$0.136649\pi$
$350$	−55.7066	−2.97764
$351$	9.02808	0.481883
$352$	27.8594	1.48491
$353$	−23.7852	−1.26596	−0.632978	−	0.774169i	$-0.718168\pi$
$353$	−23.7852	−1.26596	−0.632978	+	0.774169i	$0.718168\pi$
$354$	−13.4743	−0.716150
$355$	−38.2800	−2.03169
$356$	−12.0413	−0.638186
$357$	9.50640	0.503132
$358$	−12.8275	−0.677955
$359$	12.5694	0.663386	0.331693	−	0.943387i	$-0.392380\pi$
$359$	12.5694	0.663386	0.331693	+	0.943387i	$0.392380\pi$
$360$	−27.0249	−1.42434
$361$	−12.4758	−0.656623
$362$	−39.2242	−2.06158
$363$	−5.84586	−0.306828
$364$	22.3755	1.17279
$365$	17.2059	0.900600
$366$	−14.9576	−0.781846
$367$	−18.6814	−0.975159	−0.487580	−	0.873078i	$-0.662120\pi$
$367$	−18.6814	−0.975159	−0.487580	+	0.873078i	$0.662120\pi$
$368$	2.01050	0.104805
$369$	4.92350	0.256307
$370$	−8.70914	−0.452767
$371$	−24.8088	−1.28801
$372$	−0.429725	−0.0222802
$373$	−13.0573	−0.676079	−0.338040	−	0.941132i	$-0.609764\pi$
$373$	−13.0573	−0.676079	−0.338040	+	0.941132i	$0.609764\pi$
$374$	69.4947	3.59348
$375$	10.2317	0.528361
$376$	−27.5628	−1.42144
$377$	3.76772	0.194047
$378$	−18.4943	−0.951243
$379$	12.0476	0.618846	0.309423	−	0.950925i	$-0.399864\pi$
$379$	12.0476	0.618846	0.309423	+	0.950925i	$0.399864\pi$
$380$	−30.9366	−1.58701
$381$	−7.44720	−0.381532
$382$	26.2711	1.34415
$383$	22.3415	1.14160	0.570798	−	0.821091i	$-0.306634\pi$
$383$	22.3415	1.14160	0.570798	+	0.821091i	$0.306634\pi$
$384$	−9.93984	−0.507240
$385$	−44.7361	−2.27996
$386$	−12.1203	−0.616906
$387$	−23.0963	−1.17405
$388$	−3.63346	−0.184461
$389$	27.4060	1.38954	0.694770	−	0.719232i	$-0.255506\pi$
$389$	27.4060	1.38954	0.694770	+	0.719232i	$0.255506\pi$
$390$	−13.8473	−0.701186
$391$	39.1795	1.98139
$392$	1.60756	0.0811938
$393$	−5.09014	−0.256763
$394$	42.2383	2.12794
$395$	−15.9964	−0.804864
$396$	−39.0450	−1.96208
$397$	−24.2494	−1.21704	−0.608521	−	0.793538i	$-0.708237\pi$
$397$	−24.2494	−1.21704	−0.608521	+	0.793538i	$0.708237\pi$
$398$	−56.0423	−2.80915
$399$	−3.66291	−0.183375
$400$	−3.30077	−0.165038
$401$	12.2955	0.614010	0.307005	−	0.951708i	$-0.400673\pi$
$401$	12.2955	0.614010	0.307005	+	0.951708i	$0.400673\pi$
$402$	7.59424	0.378767
$403$	0.672036	0.0334765
$404$	−9.19560	−0.457498
$405$	−23.7996	−1.18261
$406$	−7.71828	−0.383052
$407$	−4.61563	−0.228788
$408$	−9.89739	−0.489994
$409$	32.9928	1.63139	0.815694	−	0.578484i	$-0.196355\pi$
$409$	32.9928	1.63139	0.815694	+	0.578484i	$0.196355\pi$
$410$	−16.0110	−0.790726
$411$	−9.92328	−0.489479
$412$	−58.0480	−2.85982
$413$	−26.4311	−1.30059
$414$	−35.9506	−1.76688
$415$	67.9591	3.33598
$416$	16.9157	0.829359
$417$	−10.0547	−0.492382
$418$	−26.7770	−1.30971
$419$	−34.0840	−1.66511	−0.832555	−	0.553942i	$-0.813123\pi$
$419$	−34.0840	−1.66511	−0.832555	+	0.553942i	$0.813123\pi$
$420$	17.3690	0.847518
$421$	−14.3584	−0.699787	−0.349894	−	0.936789i	$-0.613782\pi$
$421$	−14.3584	−0.699787	−0.349894	+	0.936789i	$0.613782\pi$
$422$	24.0406	1.17028
$423$	−28.0497	−1.36382
$424$	25.8292	1.25438
$425$	−64.3235	−3.12015
$426$	12.8640	0.623263
$427$	−29.3408	−1.41990
$428$	25.5323	1.23415
$429$	−7.33873	−0.354317
$430$	75.1079	3.62203
$431$	−33.7345	−1.62493	−0.812466	−	0.583008i	$-0.801876\pi$
$431$	−33.7345	−1.62493	−0.812466	+	0.583008i	$0.801876\pi$
$432$	−1.09584	−0.0527234
$433$	−36.6185	−1.75977	−0.879886	−	0.475185i	$-0.842381\pi$
$433$	−36.6185	−1.75977	−0.879886	+	0.475185i	$0.842381\pi$
$434$	−1.37669	−0.0660830
$435$	2.92469	0.140228
$436$	−14.5133	−0.695063
$437$	−15.0963	−0.722153
$438$	−5.78206	−0.276278
$439$	−26.8793	−1.28288	−0.641439	−	0.767174i	$-0.721662\pi$
$439$	−26.8793	−1.28288	−0.641439	+	0.767174i	$0.721662\pi$
$440$	46.5761	2.22043
$441$	1.63595	0.0779026
$442$	42.1957	2.00705
$443$	16.3135	0.775079	0.387539	−	0.921853i	$-0.373325\pi$
$443$	16.3135	0.775079	0.387539	+	0.921853i	$0.373325\pi$
$444$	1.79203	0.0850461
$445$	14.6176	0.692939
$446$	−15.1390	−0.716850
$447$	0.803310	0.0379953
$448$	−32.9326	−1.55592
$449$	−21.4854	−1.01396	−0.506979	−	0.861959i	$-0.669238\pi$
$449$	−21.4854	−1.01396	−0.506979	+	0.861959i	$0.669238\pi$
$450$	59.0224	2.78234
$451$	−8.48541	−0.399563
$452$	50.6630	2.38299
$453$	5.06209	0.237838
$454$	47.6311	2.23544
$455$	−27.1629	−1.27341
$456$	3.81356	0.178586
$457$	−5.64301	−0.263969	−0.131984	−	0.991252i	$-0.542135\pi$
$457$	−5.64301	−0.263969	−0.131984	+	0.991252i	$0.542135\pi$
$458$	13.8733	0.648255
$459$	−21.3550	−0.996767
$460$	71.5842	3.33763
$461$	−27.5009	−1.28085	−0.640423	−	0.768023i	$-0.721241\pi$
$461$	−27.5009	−1.28085	−0.640423	+	0.768023i	$0.721241\pi$
$462$	15.0336	0.699426
$463$	0.738210	0.0343075	0.0171538	−	0.999853i	$-0.494540\pi$
$463$	0.738210	0.0343075	0.0171538	+	0.999853i	$0.494540\pi$
$464$	−0.457329	−0.0212310
$465$	0.521667	0.0241917
$466$	12.4839	0.578304
$467$	−4.77538	−0.220978	−0.110489	−	0.993877i	$-0.535242\pi$
$467$	−4.77538	−0.220978	−0.110489	+	0.993877i	$0.535242\pi$
$468$	−23.7073	−1.09587
$469$	14.8969	0.687873
$470$	91.2163	4.20750
$471$	−8.18889	−0.377324
$472$	27.5182	1.26663
$473$	39.8053	1.83025
$474$	5.37558	0.246909
$475$	24.7845	1.13719
$476$	−52.9270	−2.42590
$477$	26.2855	1.20353
$478$	−10.5094	−0.480688
$479$	20.9303	0.956332	0.478166	−	0.878269i	$-0.341302\pi$
$479$	20.9303	0.956332	0.478166	+	0.878269i	$0.341302\pi$
$480$	13.1308	0.599336
$481$	−2.80251	−0.127784
$482$	−2.62343	−0.119494
$483$	8.47560	0.385653
$484$	32.5469	1.47940
$485$	4.41087	0.200287
$486$	29.9480	1.35847
$487$	11.4985	0.521048	0.260524	−	0.965467i	$-0.416105\pi$
$487$	11.4985	0.521048	0.260524	+	0.965467i	$0.416105\pi$
$488$	30.5476	1.38282
$489$	0.567339	0.0256559
$490$	−5.32005	−0.240335
$491$	13.7007	0.618304	0.309152	−	0.951013i	$-0.399955\pi$
$491$	13.7007	0.618304	0.309152	+	0.951013i	$0.399955\pi$
$492$	3.29449	0.148527
$493$	−8.91216	−0.401384
$494$	−16.2584	−0.731502
$495$	47.3989	2.13042
$496$	−0.0815723	−0.00366271
$497$	25.2340	1.13190
$498$	−22.8377	−1.02338
$499$	−10.3034	−0.461243	−0.230622	−	0.973043i	$-0.574076\pi$
$499$	−10.3034	−0.461243	−0.230622	+	0.973043i	$0.574076\pi$
$500$	−56.9649	−2.54755
$501$	−8.09300	−0.361569
$502$	57.4269	2.56309
$503$	−25.7775	−1.14936	−0.574680	−	0.818378i	$-0.694874\pi$
$503$	−25.7775	−1.14936	−0.574680	+	0.818378i	$0.694874\pi$
$504$	17.8147	0.793530
$505$	11.1631	0.496750
$506$	61.9592	2.75442
$507$	2.91948	0.129659
$508$	41.4624	1.83959
$509$	−13.4325	−0.595386	−0.297693	−	0.954662i	$-0.596217\pi$
$509$	−13.4325	−0.595386	−0.297693	+	0.954662i	$0.596217\pi$
$510$	32.7544	1.45039
$511$	−11.3421	−0.501745
$512$	−3.84366	−0.169867
$513$	8.22830	0.363288
$514$	−23.2128	−1.02387
$515$	70.4678	3.10518
$516$	−15.4545	−0.680348
$517$	48.3424	2.12610
$518$	5.74103	0.252246
$519$	−5.43079	−0.238385
$520$	28.2801	1.24016
$521$	−16.2058	−0.709988	−0.354994	−	0.934869i	$-0.615517\pi$
$521$	−16.2058	−0.709988	−0.354994	+	0.934869i	$0.615517\pi$
$522$	8.17769	0.357928
$523$	−15.5057	−0.678015	−0.339008	−	0.940784i	$-0.610091\pi$
$523$	−15.5057	−0.678015	−0.339008	+	0.940784i	$0.610091\pi$
$524$	28.3394	1.23801
$525$	−13.9149	−0.607297
$526$	−58.7309	−2.56079
$527$	−1.58963	−0.0692455
$528$	0.890781	0.0387663
$529$	11.9312	0.518749
$530$	−85.4791	−3.71298
$531$	28.0043	1.21529
$532$	20.3933	0.884161
$533$	−5.15217	−0.223165
$534$	−4.91224	−0.212573
$535$	−30.9951	−1.34004
$536$	−15.5096	−0.669911
$537$	−3.20418	−0.138270
$538$	−8.76471	−0.377874
$539$	−2.81949	−0.121444
$540$	−39.0173	−1.67904
$541$	−41.4269	−1.78108	−0.890541	−	0.454902i	$-0.849674\pi$
$541$	−41.4269	−1.78108	−0.890541	+	0.454902i	$0.849674\pi$
$542$	52.4706	2.25380
$543$	−9.79778	−0.420463
$544$	−40.0123	−1.71552
$545$	17.6186	0.754696
$546$	9.12809	0.390646
$547$	−9.42671	−0.403057	−0.201529	−	0.979483i	$-0.564591\pi$
$547$	−9.42671	−0.403057	−0.201529	+	0.979483i	$0.564591\pi$
$548$	55.2480	2.36008
$549$	31.0872	1.32677
$550$	−101.722	−4.33745
$551$	3.43395	0.146291
$552$	−8.82420	−0.375583
$553$	10.5447	0.448408
$554$	−27.5683	−1.17127
$555$	−2.17545	−0.0923427
$556$	55.9798	2.37407
$557$	−20.6517	−0.875040	−0.437520	−	0.899209i	$-0.644143\pi$
$557$	−20.6517	−0.875040	−0.437520	+	0.899209i	$0.644143\pi$
$558$	1.45863	0.0617486
$559$	24.1690	1.02224
$560$	3.29705	0.139326
$561$	17.3590	0.732899
$562$	19.5964	0.826624
$563$	17.1119	0.721181	0.360590	−	0.932724i	$-0.382575\pi$
$563$	17.1119	0.721181	0.360590	+	0.932724i	$0.382575\pi$
$564$	−18.7691	−0.790321
$565$	−61.5027	−2.58744
$566$	63.2006	2.65652
$567$	15.6886	0.658861
$568$	−26.2719	−1.10234
$569$	−15.5978	−0.653894	−0.326947	−	0.945043i	$-0.606020\pi$
$569$	−15.5978	−0.653894	−0.326947	+	0.945043i	$0.606020\pi$
$570$	−12.6206	−0.528619
$571$	22.0356	0.922160	0.461080	−	0.887359i	$-0.347462\pi$
$571$	22.0356	0.922160	0.461080	+	0.887359i	$0.347462\pi$
$572$	40.8584	1.70838
$573$	6.56225	0.274142
$574$	10.5544	0.440531
$575$	−57.3488	−2.39161
$576$	34.8928	1.45387
$577$	20.9961	0.874080	0.437040	−	0.899442i	$-0.356027\pi$
$577$	20.9961	0.874080	0.437040	+	0.899442i	$0.356027\pi$
$578$	−61.1983	−2.54551
$579$	−3.02752	−0.125819
$580$	−16.2832	−0.676125
$581$	−44.7984	−1.85855
$582$	−1.48227	−0.0614422
$583$	−45.3018	−1.87621
$584$	11.8086	0.488643
$585$	28.7796	1.18989
$586$	−63.4464	−2.62095
$587$	−35.6268	−1.47048	−0.735239	−	0.677808i	$-0.762930\pi$
$587$	−35.6268	−1.47048	−0.735239	+	0.677808i	$0.762930\pi$
$588$	1.09468	0.0451437
$589$	0.612502	0.0252377
$590$	−91.0688	−3.74924
$591$	10.5507	0.433997
$592$	0.340172	0.0139810
$593$	25.4873	1.04664	0.523319	−	0.852137i	$-0.324694\pi$
$593$	25.4873	1.04664	0.523319	+	0.852137i	$0.324694\pi$
$594$	−33.7712	−1.38565
$595$	64.2511	2.63404
$596$	−4.47244	−0.183198
$597$	−13.9988	−0.572932
$598$	37.6204	1.53841
$599$	−20.9950	−0.857833	−0.428917	−	0.903344i	$-0.641105\pi$
$599$	−20.9950	−0.857833	−0.428917	+	0.903344i	$0.641105\pi$
$600$	14.4872	0.591439
$601$	2.26263	0.0922946	0.0461473	−	0.998935i	$-0.485306\pi$
$601$	2.26263	0.0922946	0.0461473	+	0.998935i	$0.485306\pi$
$602$	−49.5108	−2.01791
$603$	−15.7836	−0.642756
$604$	−28.1832	−1.14676
$605$	−39.5105	−1.60633
$606$	−3.75135	−0.152388
$607$	−30.5459	−1.23982	−0.619911	−	0.784672i	$-0.712831\pi$
$607$	−30.5459	−1.23982	−0.619911	+	0.784672i	$0.712831\pi$
$608$	15.4172	0.625248
$609$	−1.92794	−0.0781242
$610$	−101.094	−4.09318
$611$	29.3525	1.18748
$612$	56.0773	2.26679
$613$	27.7361	1.12025	0.560125	−	0.828408i	$-0.310753\pi$
$613$	27.7361	1.12025	0.560125	+	0.828408i	$0.310753\pi$
$614$	24.9857	1.00834
$615$	−3.99937	−0.161270
$616$	−30.7028	−1.23705
$617$	−1.80590	−0.0727029	−0.0363514	−	0.999339i	$-0.511574\pi$
$617$	−1.80590	−0.0727029	−0.0363514	+	0.999339i	$0.511574\pi$
$618$	−23.6807	−0.952579
$619$	2.70528	0.108734	0.0543672	−	0.998521i	$-0.482686\pi$
$619$	2.70528	0.108734	0.0543672	+	0.998521i	$0.482686\pi$
$620$	−2.90439	−0.116643
$621$	−19.0395	−0.764027
$622$	28.3196	1.13551
$623$	−9.63585	−0.386052
$624$	0.540864	0.0216519
$625$	20.6367	0.825470
$626$	−53.7959	−2.15012
$627$	−6.68861	−0.267117
$628$	45.5917	1.81931
$629$	6.62907	0.264318
$630$	−58.9559	−2.34886
$631$	−30.4882	−1.21372	−0.606858	−	0.794811i	$-0.707570\pi$
$631$	−30.4882	−1.21372	−0.606858	+	0.794811i	$0.707570\pi$
$632$	−10.9784	−0.436699
$633$	6.00509	0.238681
$634$	56.4558	2.24215
$635$	−50.3335	−1.99742
$636$	17.5886	0.697432
$637$	−1.71194	−0.0678294
$638$	−14.0939	−0.557981
$639$	−26.7360	−1.05766
$640$	−67.1806	−2.65554
$641$	3.47169	0.137123	0.0685617	−	0.997647i	$-0.478159\pi$
$641$	3.47169	0.137123	0.0685617	+	0.997647i	$0.478159\pi$
$642$	10.4159	0.411084
$643$	13.5649	0.534947	0.267474	−	0.963565i	$-0.413811\pi$
$643$	13.5649	0.534947	0.267474	+	0.963565i	$0.413811\pi$
$644$	−47.1880	−1.85947
$645$	18.7612	0.738720
$646$	38.4577	1.51310
$647$	−8.64318	−0.339798	−0.169899	−	0.985461i	$-0.554344\pi$
$647$	−8.64318	−0.339798	−0.169899	+	0.985461i	$0.554344\pi$
$648$	−16.3339	−0.641656
$649$	−48.2642	−1.89453
$650$	−61.7637	−2.42257
$651$	−0.343881	−0.0134778
$652$	−3.15866	−0.123703
$653$	15.2834	0.598086	0.299043	−	0.954240i	$-0.403333\pi$
$653$	15.2834	0.598086	0.299043	+	0.954240i	$0.403333\pi$
$654$	−5.92073	−0.231519
$655$	−34.4028	−1.34423
$656$	0.625375	0.0244168
$657$	12.0172	0.468835
$658$	−60.1295	−2.34409
$659$	−4.63708	−0.180635	−0.0903174	−	0.995913i	$-0.528788\pi$
$659$	−4.63708	−0.180635	−0.0903174	+	0.995913i	$0.528788\pi$
$660$	31.7163	1.23456
$661$	−17.2995	−0.672872	−0.336436	−	0.941706i	$-0.609222\pi$
$661$	−17.2995	−0.672872	−0.336436	+	0.941706i	$0.609222\pi$
$662$	72.9678	2.83597
$663$	10.5400	0.409341
$664$	46.6409	1.81002
$665$	−24.7566	−0.960019
$666$	−6.08275	−0.235702
$667$	−7.94580	−0.307663
$668$	45.0578	1.74334
$669$	−3.78155	−0.146203
$670$	51.3273	1.98295
$671$	−53.5774	−2.06833
$672$	−8.65576	−0.333903
$673$	−7.88635	−0.303997	−0.151998	−	0.988381i	$-0.548571\pi$
$673$	−7.88635	−0.303997	−0.151998	+	0.988381i	$0.548571\pi$
$674$	56.6399	2.18169
$675$	31.2582	1.20313
$676$	−16.2542	−0.625162
$677$	2.41404	0.0927790	0.0463895	−	0.998923i	$-0.485228\pi$
$677$	2.41404	0.0927790	0.0463895	+	0.998923i	$0.485228\pi$
$678$	20.6680	0.793750
$679$	−2.90763	−0.111584
$680$	−66.8937	−2.56525
$681$	11.8977	0.455922
$682$	−2.51388	−0.0962613
$683$	46.3373	1.77305	0.886524	−	0.462683i	$-0.153113\pi$
$683$	46.3373	1.77305	0.886524	+	0.462683i	$0.153113\pi$
$684$	−21.6071	−0.826169
$685$	−67.0687	−2.56256
$686$	43.6942	1.66825
$687$	3.46539	0.132213
$688$	−2.93365	−0.111844
$689$	−27.5063	−1.04791
$690$	29.2028	1.11173
$691$	−18.9721	−0.721734	−0.360867	−	0.932617i	$-0.617519\pi$
$691$	−18.9721	−0.721734	−0.360867	+	0.932617i	$0.617519\pi$
$692$	30.2360	1.14940
$693$	−31.2452	−1.18691
$694$	−45.0165	−1.70880
$695$	−67.9570	−2.57776
$696$	2.00724	0.0760842
$697$	12.1869	0.461613
$698$	−77.1613	−2.92060
$699$	3.11834	0.117946
$700$	77.4714	2.92815
$701$	11.6859	0.441369	0.220685	−	0.975345i	$-0.429171\pi$
$701$	11.6859	0.441369	0.220685	+	0.975345i	$0.429171\pi$
$702$	−20.5052	−0.773919
$703$	−2.55425	−0.0963352
$704$	−60.1361	−2.26646
$705$	22.7849	0.858128
$706$	54.0225	2.03316
$707$	−7.35865	−0.276750
$708$	18.7387	0.704245
$709$	32.1886	1.20887	0.604434	−	0.796655i	$-0.293399\pi$
$709$	32.1886	1.20887	0.604434	+	0.796655i	$0.293399\pi$
$710$	86.9442	3.26296
$711$	−11.1724	−0.418997
$712$	10.0322	0.375971
$713$	−1.41727	−0.0530771
$714$	−21.5916	−0.808045
$715$	−49.6004	−1.85495
$716$	17.8393	0.666685
$717$	−2.62513	−0.0980373
$718$	−28.5484	−1.06542
$719$	−33.8176	−1.26118	−0.630592	−	0.776115i	$-0.717188\pi$
$719$	−33.8176	−1.26118	−0.630592	+	0.776115i	$0.717188\pi$
$720$	−3.49330	−0.130188
$721$	−46.4521	−1.72997
$722$	28.3360	1.05456
$723$	−0.655305	−0.0243710
$724$	54.5492	2.02731
$725$	13.0451	0.484483
$726$	13.2775	0.492775
$727$	25.7146	0.953703	0.476852	−	0.878984i	$-0.341778\pi$
$727$	25.7146	0.953703	0.476852	+	0.878984i	$0.341778\pi$
$728$	−18.6421	−0.690922
$729$	−11.1395	−0.412575
$730$	−39.0793	−1.44639
$731$	−57.1693	−2.11448
$732$	20.8016	0.768849
$733$	−21.4245	−0.791334	−0.395667	−	0.918394i	$-0.629486\pi$
$733$	−21.4245	−0.791334	−0.395667	+	0.918394i	$0.629486\pi$
$734$	42.4304	1.56614
$735$	−1.32889	−0.0490169
$736$	−35.6737	−1.31495
$737$	27.2022	1.00201
$738$	−11.1826	−0.411637
$739$	16.5713	0.609586	0.304793	−	0.952419i	$-0.401413\pi$
$739$	16.5713	0.609586	0.304793	+	0.952419i	$0.401413\pi$
$740$	12.1118	0.445240
$741$	−4.06119	−0.149191
$742$	56.3475	2.06858
$743$	−44.5828	−1.63558	−0.817792	−	0.575514i	$-0.804802\pi$
$743$	−44.5828	−1.63558	−0.817792	+	0.575514i	$0.804802\pi$
$744$	0.358025	0.0131258
$745$	5.42935	0.198916
$746$	29.6566	1.08580
$747$	47.4649	1.73665
$748$	−96.6465	−3.53375
$749$	20.4319	0.746564
$750$	−23.2389	−0.848564
$751$	31.0833	1.13424	0.567122	−	0.823634i	$-0.308057\pi$
$751$	31.0833	1.13424	0.567122	+	0.823634i	$0.308057\pi$
$752$	−3.56283	−0.129923
$753$	14.3446	0.522748
$754$	−8.55750	−0.311646
$755$	34.2132	1.24515
$756$	25.7201	0.935430
$757$	9.62747	0.349916	0.174958	−	0.984576i	$-0.444021\pi$
$757$	9.62747	0.349916	0.174958	+	0.984576i	$0.444021\pi$
$758$	−27.3634	−0.993885
$759$	15.4768	0.561771
$760$	25.7748	0.934950
$761$	20.5944	0.746545	0.373273	−	0.927722i	$-0.378236\pi$
$761$	20.5944	0.746545	0.373273	+	0.927722i	$0.378236\pi$
$762$	16.9146	0.612751
$763$	−11.6141	−0.420458
$764$	−36.5354	−1.32180
$765$	−68.0754	−2.46127
$766$	−50.7435	−1.83344
$767$	−29.3050	−1.05814
$768$	7.79257	0.281190
$769$	38.0184	1.37098	0.685489	−	0.728083i	$-0.259588\pi$
$769$	38.0184	1.37098	0.685489	+	0.728083i	$0.259588\pi$
$770$	101.608	3.66169
$771$	−5.79831	−0.208821
$772$	16.8557	0.606651
$773$	−0.0694173	−0.00249677	−0.00124838	−	0.999999i	$-0.500397\pi$
$773$	−0.0694173	−0.00249677	−0.00124838	+	0.999999i	$0.500397\pi$
$774$	52.4578	1.88556
$775$	2.32681	0.0835816
$776$	3.02721	0.108671
$777$	1.43405	0.0514462
$778$	−62.2464	−2.23164
$779$	−4.69575	−0.168243
$780$	19.2575	0.689529
$781$	46.0782	1.64881
$782$	−88.9873	−3.18218
$783$	4.33090	0.154774
$784$	0.207797	0.00742130
$785$	−55.3464	−1.97540
$786$	11.5611	0.412370
$787$	−6.98834	−0.249107	−0.124554	−	0.992213i	$-0.539750\pi$
$787$	−6.98834	−0.249107	−0.124554	+	0.992213i	$0.539750\pi$
$788$	−58.7410	−2.09256
$789$	−14.6704	−0.522279
$790$	36.3320	1.29264
$791$	40.5423	1.44152
$792$	32.5303	1.15591
$793$	−32.5311	−1.15521
$794$	55.0769	1.95461
$795$	−21.3518	−0.757269
$796$	77.9383	2.76245
$797$	−20.1437	−0.713527	−0.356764	−	0.934195i	$-0.616120\pi$
$797$	−20.1437	−0.713527	−0.356764	+	0.934195i	$0.616120\pi$
$798$	8.31946	0.294506
$799$	−69.4304	−2.45627
$800$	58.5678	2.07068
$801$	10.2094	0.360731
$802$	−27.9265	−0.986119
$803$	−20.7111	−0.730878
$804$	−10.5613	−0.372470
$805$	57.2842	2.01900
$806$	−1.52637	−0.0537642
$807$	−2.18933	−0.0770681
$808$	7.66130	0.269524
$809$	−13.8538	−0.487073	−0.243536	−	0.969892i	$-0.578308\pi$
$809$	−13.8538	−0.487073	−0.243536	+	0.969892i	$0.578308\pi$
$810$	54.0554	1.89931
$811$	−33.4729	−1.17539	−0.587697	−	0.809081i	$-0.699965\pi$
$811$	−33.4729	−1.17539	−0.587697	+	0.809081i	$0.699965\pi$
$812$	10.7338	0.376684
$813$	13.1066	0.459668
$814$	10.4833	0.367440
$815$	3.83448	0.134316
$816$	−1.27936	−0.0447866
$817$	22.0279	0.770659
$818$	−74.9355	−2.62006
$819$	−18.9714	−0.662916
$820$	22.2665	0.777581
$821$	−12.7888	−0.446333	−0.223167	−	0.974780i	$-0.571639\pi$
$821$	−12.7888	−0.446333	−0.223167	+	0.974780i	$0.571639\pi$
$822$	22.5384	0.786119
$823$	−36.0052	−1.25506	−0.627531	−	0.778591i	$-0.715935\pi$
$823$	−36.0052	−1.25506	−0.627531	+	0.778591i	$0.715935\pi$
$824$	48.3627	1.68479
$825$	−25.4091	−0.884633
$826$	60.0322	2.08879
$827$	−48.6303	−1.69104	−0.845520	−	0.533944i	$-0.820709\pi$
$827$	−48.6303	−1.69104	−0.845520	+	0.533944i	$0.820709\pi$
$828$	49.9967	1.73751
$829$	−45.3389	−1.57469	−0.787343	−	0.616516i	$-0.788544\pi$
$829$	−45.3389	−1.57469	−0.787343	+	0.616516i	$0.788544\pi$
$830$	−154.354	−5.35769
$831$	−6.88627	−0.238882
$832$	−36.5134	−1.26587
$833$	4.04942	0.140304
$834$	22.8370	0.790780
$835$	−54.6983	−1.89291
$836$	37.2389	1.28793
$837$	0.772489	0.0267011
$838$	77.4139	2.67422
$839$	−31.1886	−1.07675	−0.538375	−	0.842706i	$-0.680961\pi$
$839$	−31.1886	−1.07675	−0.538375	+	0.842706i	$0.680961\pi$
$840$	−14.4709	−0.499294
$841$	−27.1926	−0.937675
$842$	32.6119	1.12388
$843$	4.89497	0.168592
$844$	−33.4334	−1.15082
$845$	19.7319	0.678799
$846$	63.7085	2.19034
$847$	26.0452	0.894922
$848$	3.33874	0.114653
$849$	15.7868	0.541803
$850$	146.096	5.01105
$851$	5.91027	0.202601
$852$	−17.8900	−0.612902
$853$	14.7594	0.505352	0.252676	−	0.967551i	$-0.418689\pi$
$853$	14.7594	0.505352	0.252676	+	0.967551i	$0.418689\pi$
$854$	66.6409	2.28040
$855$	26.2301	0.897052
$856$	−21.2722	−0.727069
$857$	−54.6259	−1.86599	−0.932993	−	0.359894i	$-0.882813\pi$
$857$	−54.6259	−1.86599	−0.932993	+	0.359894i	$0.882813\pi$
$858$	16.6682	0.569044
$859$	−53.6268	−1.82972	−0.914861	−	0.403769i	$-0.867700\pi$
$859$	−53.6268	−1.82972	−0.914861	+	0.403769i	$0.867700\pi$
$860$	−104.453	−3.56181
$861$	2.63637	0.0898472
$862$	76.6201	2.60969
$863$	54.1652	1.84380	0.921902	−	0.387423i	$-0.126635\pi$
$863$	54.1652	1.84380	0.921902	+	0.387423i	$0.126635\pi$
$864$	19.4442	0.661504
$865$	−36.7052	−1.24801
$866$	83.1704	2.82625
$867$	−15.2867	−0.519162
$868$	1.91456	0.0649845
$869$	19.2551	0.653183
$870$	−6.64276	−0.225211
$871$	16.5166	0.559644
$872$	12.0918	0.409479
$873$	3.08069	0.104266
$874$	34.2877	1.15980
$875$	−45.5854	−1.54107
$876$	8.04114	0.271685
$877$	33.7571	1.13990	0.569948	−	0.821681i	$-0.306963\pi$
$877$	33.7571	1.13990	0.569948	+	0.821681i	$0.306963\pi$
$878$	61.0501	2.06034
$879$	−15.8482	−0.534548
$880$	6.02054	0.202952
$881$	−51.6841	−1.74128	−0.870641	−	0.491919i	$-0.836296\pi$
$881$	−51.6841	−1.74128	−0.870641	+	0.491919i	$0.836296\pi$
$882$	−3.71569	−0.125114
$883$	26.9050	0.905426	0.452713	−	0.891656i	$-0.350456\pi$
$883$	26.9050	0.905426	0.452713	+	0.891656i	$0.350456\pi$
$884$	−58.6818	−1.97368
$885$	−22.7480	−0.764666
$886$	−37.0524	−1.24480
$887$	8.07572	0.271156	0.135578	−	0.990767i	$-0.456711\pi$
$887$	8.07572	0.271156	0.135578	+	0.990767i	$0.456711\pi$
$888$	−1.49303	−0.0501028
$889$	33.1797	1.11281
$890$	−33.2004	−1.11288
$891$	28.6480	0.959744
$892$	21.0538	0.704933
$893$	26.7522	0.895229
$894$	−1.82453	−0.0610216
$895$	−21.6561	−0.723884
$896$	44.2852	1.47946
$897$	9.39717	0.313762
$898$	48.7991	1.62845
$899$	0.322385	0.0107522
$900$	−82.0827	−2.73609
$901$	65.0635	2.16758
$902$	19.2727	0.641709
$903$	−12.3673	−0.411557
$904$	−42.2098	−1.40388
$905$	−66.2204	−2.20124
$906$	−11.4974	−0.381975
$907$	−0.432609	−0.0143645	−0.00718227	−	0.999974i	$-0.502286\pi$
$907$	−0.432609	−0.0143645	−0.00718227	+	0.999974i	$0.502286\pi$
$908$	−66.2408	−2.19828
$909$	7.79665	0.258598
$910$	61.6942	2.04514
$911$	−55.0793	−1.82486	−0.912430	−	0.409233i	$-0.865796\pi$
$911$	−55.0793	−1.82486	−0.912430	+	0.409233i	$0.865796\pi$
$912$	0.492950	0.0163232
$913$	−81.8035	−2.70730
$914$	12.8168	0.423942
$915$	−25.2522	−0.834814
$916$	−19.2936	−0.637479
$917$	22.6782	0.748900
$918$	48.5030	1.60084
$919$	50.6202	1.66981	0.834903	−	0.550396i	$-0.185523\pi$
$919$	50.6202	1.66981	0.834903	+	0.550396i	$0.185523\pi$
$920$	−59.6403	−1.96628
$921$	6.24116	0.205653
$922$	62.4620	2.05708
$923$	27.9778	0.920899
$924$	−20.9073	−0.687799
$925$	−9.70325	−0.319041
$926$	−1.67667	−0.0550989
$927$	49.2170	1.61650
$928$	8.11470	0.266378
$929$	−11.5539	−0.379071	−0.189535	−	0.981874i	$-0.560698\pi$
$929$	−11.5539	−0.379071	−0.189535	+	0.981874i	$0.560698\pi$
$930$	−1.18485	−0.0388527
$931$	−1.56028	−0.0511361
$932$	−17.3614	−0.568691
$933$	7.07393	0.231590
$934$	10.8462	0.354897
$935$	117.325	3.83693
$936$	19.7517	0.645605
$937$	20.5853	0.672494	0.336247	−	0.941774i	$-0.390842\pi$
$937$	20.5853	0.672494	0.336247	+	0.941774i	$0.390842\pi$
$938$	−33.8348	−1.10475
$939$	−13.4376	−0.438521
$940$	−126.855	−4.13755
$941$	−10.2574	−0.334383	−0.167191	−	0.985924i	$-0.553470\pi$
$941$	−10.2574	−0.334383	−0.167191	+	0.985924i	$0.553470\pi$
$942$	18.5992	0.605994
$943$	10.8655	0.353829
$944$	3.55707	0.115773
$945$	−31.2231	−1.01569
$946$	−90.4086	−2.93944
$947$	13.3228	0.432932	0.216466	−	0.976290i	$-0.430547\pi$
$947$	13.3228	0.432932	0.216466	+	0.976290i	$0.430547\pi$
$948$	−7.47584	−0.242804
$949$	−12.5753	−0.408213
$950$	−56.2922	−1.82636
$951$	14.1021	0.457291
$952$	44.0960	1.42916
$953$	39.4873	1.27912	0.639559	−	0.768742i	$-0.279117\pi$
$953$	39.4873	1.27912	0.639559	+	0.768742i	$0.279117\pi$
$954$	−59.7014	−1.93290
$955$	44.3524	1.43521
$956$	14.6154	0.472697
$957$	−3.52049	−0.113801
$958$	−47.5384	−1.53590
$959$	44.2114	1.42766
$960$	−28.3435	−0.914782
$961$	−30.9425	−0.998145
$962$	6.36526	0.205224
$963$	−21.6480	−0.697597
$964$	3.64842	0.117508
$965$	−20.4621	−0.658699
$966$	−19.2504	−0.619371
$967$	−21.5102	−0.691720	−0.345860	−	0.938286i	$-0.612413\pi$
$967$	−21.5102	−0.691720	−0.345860	+	0.938286i	$0.612413\pi$
$968$	−27.1164	−0.871554
$969$	9.60633	0.308600
$970$	−10.0183	−0.321667
$971$	26.2017	0.840852	0.420426	−	0.907327i	$-0.361881\pi$
$971$	26.2017	0.840852	0.420426	+	0.907327i	$0.361881\pi$
$972$	−41.6488	−1.33589
$973$	44.7970	1.43613
$974$	−26.1162	−0.836818
$975$	−15.4279	−0.494089
$976$	3.94865	0.126393
$977$	−40.3498	−1.29090	−0.645452	−	0.763801i	$-0.723331\pi$
$977$	−40.3498	−1.29090	−0.645452	+	0.763801i	$0.723331\pi$
$978$	−1.28858	−0.0412042
$979$	−17.5954	−0.562352
$980$	7.39861	0.236340
$981$	12.3054	0.392881
$982$	−31.1180	−0.993015
$983$	20.6814	0.659635	0.329817	−	0.944045i	$-0.393013\pi$
$983$	20.6814	0.659635	0.329817	+	0.944045i	$0.393013\pi$
$984$	−2.74480	−0.0875011
$985$	71.3091	2.27210
$986$	20.2419	0.644634
$987$	−15.0197	−0.478082
$988$	22.6107	0.719342
$989$	−50.9703	−1.62076
$990$	−107.656	−3.42152
$991$	−57.5824	−1.82916	−0.914582	−	0.404400i	$-0.867480\pi$
$991$	−57.5824	−1.82916	−0.914582	+	0.404400i	$0.867480\pi$
$992$	1.44739	0.0459548
$993$	18.2266	0.578403
$994$	−57.3133	−1.81787
$995$	−94.6137	−2.99946
$996$	31.7605	1.00637
$997$	53.6877	1.70031	0.850154	−	0.526534i	$-0.176509\pi$
$997$	53.6877	1.70031	0.850154	+	0.526534i	$0.176509\pi$
$998$	23.4018	0.740771
$999$	−3.22142	−0.101921

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.c.1.15	✓	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.c.1.15	✓	110	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:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.27127 q^{2} -0.567339 q^{3} +3.15866 q^{4} -3.83448 q^{5} +1.28858 q^{6} +2.52768 q^{7} -2.63164 q^{8} -2.67813 q^{9} +O(q^{10})\)	\(q-2.27127 q^{2} -0.567339 q^{3} +3.15866 q^{4} -3.83448 q^{5} +1.28858 q^{6} +2.52768 q^{7} -2.63164 q^{8} -2.67813 q^{9} +8.70914 q^{10} +4.61563 q^{11} -1.79203 q^{12} +2.80251 q^{13} -5.74103 q^{14} +2.17545 q^{15} -0.340172 q^{16} -6.62907 q^{17} +6.08275 q^{18} +2.55425 q^{19} -12.1118 q^{20} -1.43405 q^{21} -10.4833 q^{22} -5.91027 q^{23} +1.49303 q^{24} +9.70325 q^{25} -6.36526 q^{26} +3.22142 q^{27} +7.98408 q^{28} +1.34441 q^{29} -4.94103 q^{30} +0.239798 q^{31} +6.03589 q^{32} -2.61862 q^{33} +15.0564 q^{34} -9.69232 q^{35} -8.45930 q^{36} -1.00000 q^{37} -5.80138 q^{38} -1.58997 q^{39} +10.0910 q^{40} -1.83841 q^{41} +3.25711 q^{42} +8.62403 q^{43} +14.5792 q^{44} +10.2692 q^{45} +13.4238 q^{46} +10.4736 q^{47} +0.192993 q^{48} -0.610858 q^{49} -22.0387 q^{50} +3.76093 q^{51} +8.85220 q^{52} -9.81488 q^{53} -7.31671 q^{54} -17.6985 q^{55} -6.65192 q^{56} -1.44912 q^{57} -3.05351 q^{58} -10.4567 q^{59} +6.87151 q^{60} -11.6078 q^{61} -0.544645 q^{62} -6.76943 q^{63} -13.0288 q^{64} -10.7462 q^{65} +5.94760 q^{66} +5.89350 q^{67} -20.9390 q^{68} +3.35312 q^{69} +22.0139 q^{70} +9.98309 q^{71} +7.04786 q^{72} -4.48716 q^{73} +2.27127 q^{74} -5.50503 q^{75} +8.06800 q^{76} +11.6668 q^{77} +3.61126 q^{78} +4.17171 q^{79} +1.30438 q^{80} +6.20674 q^{81} +4.17552 q^{82} -17.7232 q^{83} -4.52968 q^{84} +25.4190 q^{85} -19.5875 q^{86} -0.762734 q^{87} -12.1466 q^{88} -3.81214 q^{89} -23.3242 q^{90} +7.08384 q^{91} -18.6685 q^{92} -0.136046 q^{93} -23.7884 q^{94} -9.79421 q^{95} -3.42440 q^{96} -1.15032 q^{97} +1.38742 q^{98} -12.3612 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9}+O(q^{10}) \) 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9} - 17 q^{10} - 9 q^{11} - 21 q^{13} - 29 q^{14} - 23 q^{15} + 79 q^{16} - 76 q^{17} - 31 q^{18} - 27 q^{19} - 67 q^{20} - 30 q^{21} - 28 q^{22} - 32 q^{23} - 63 q^{24} + 66 q^{25} - 55 q^{26} - 4 q^{28} - 81 q^{29} - 48 q^{30} - 30 q^{31} - 73 q^{32} - 53 q^{33} - 23 q^{34} - 78 q^{35} + 7 q^{36} - 110 q^{37} - 50 q^{38} - 64 q^{39} - 37 q^{40} - 123 q^{41} - 63 q^{42} - 40 q^{43} - 31 q^{44} - 73 q^{45} + 16 q^{46} - 37 q^{47} - 29 q^{48} + 46 q^{49} - 58 q^{50} - 73 q^{51} - 39 q^{52} - 16 q^{53} - 53 q^{54} - 59 q^{55} - 113 q^{56} - 39 q^{57} + 11 q^{58} - 93 q^{59} - 18 q^{60} - 66 q^{61} - 40 q^{62} - 21 q^{63} + 23 q^{64} - 92 q^{65} - 31 q^{66} + q^{67} - 121 q^{68} - 80 q^{69} - 3 q^{70} - 75 q^{71} - 114 q^{72} - 39 q^{73} + 9 q^{74} - 25 q^{75} - 58 q^{76} - 31 q^{77} + 68 q^{78} - 36 q^{79} - 82 q^{80} - 50 q^{81} - 18 q^{82} - 57 q^{83} - 9 q^{84} - 14 q^{85} - 58 q^{86} - 58 q^{87} - 15 q^{88} - 181 q^{89} + 8 q^{90} - 55 q^{91} - 116 q^{92} - 86 q^{93} - 39 q^{94} - 70 q^{95} - 127 q^{96} - 91 q^{97} - 19 q^{98} - 21 q^{99}+O(q^{100}) \) 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9 - 17 * q^10 - 9 * q^11 - 21 * q^13 - 29 * q^14 - 23 * q^15 + 79 * q^16 - 76 * q^17 - 31 * q^18 - 27 * q^19 - 67 * q^20 - 30 * q^21 - 28 * q^22 - 32 * q^23 - 63 * q^24 + 66 * q^25 - 55 * q^26 - 4 * q^28 - 81 * q^29 - 48 * q^30 - 30 * q^31 - 73 * q^32 - 53 * q^33 - 23 * q^34 - 78 * q^35 + 7 * q^36 - 110 * q^37 - 50 * q^38 - 64 * q^39 - 37 * q^40 - 123 * q^41 - 63 * q^42 - 40 * q^43 - 31 * q^44 - 73 * q^45 + 16 * q^46 - 37 * q^47 - 29 * q^48 + 46 * q^49 - 58 * q^50 - 73 * q^51 - 39 * q^52 - 16 * q^53 - 53 * q^54 - 59 * q^55 - 113 * q^56 - 39 * q^57 + 11 * q^58 - 93 * q^59 - 18 * q^60 - 66 * q^61 - 40 * q^62 - 21 * q^63 + 23 * q^64 - 92 * q^65 - 31 * q^66 + q^67 - 121 * q^68 - 80 * q^69 - 3 * q^70 - 75 * q^71 - 114 * q^72 - 39 * q^73 + 9 * q^74 - 25 * q^75 - 58 * q^76 - 31 * q^77 + 68 * q^78 - 36 * q^79 - 82 * q^80 - 50 * q^81 - 18 * q^82 - 57 * q^83 - 9 * q^84 - 14 * q^85 - 58 * q^86 - 58 * q^87 - 15 * q^88 - 181 * q^89 + 8 * q^90 - 55 * q^91 - 116 * q^92 - 86 * q^93 - 39 * q^94 - 70 * q^95 - 127 * q^96 - 91 * q^97 - 19 * q^98 - 21 * q^99

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