LMFDB - Embedded newform 4021.2.a.c.1.16

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:	$0$
Dimension:	$182$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
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)

$f(q)$	$=$	$q-2.43939 q^{2} +2.42778 q^{3} +3.95064 q^{4} -0.884079 q^{5} -5.92232 q^{6} -2.32249 q^{7} -4.75837 q^{8} +2.89413 q^{9} +O(q^{10})$	\(q-2.43939 q^{2} +2.42778 q^{3} +3.95064 q^{4} -0.884079 q^{5} -5.92232 q^{6} -2.32249 q^{7} -4.75837 q^{8} +2.89413 q^{9} +2.15662 q^{10} -2.97896 q^{11} +9.59129 q^{12} +3.34842 q^{13} +5.66545 q^{14} -2.14635 q^{15} +3.70626 q^{16} -6.80216 q^{17} -7.05992 q^{18} -7.19923 q^{19} -3.49267 q^{20} -5.63849 q^{21} +7.26684 q^{22} +8.56369 q^{23} -11.5523 q^{24} -4.21840 q^{25} -8.16810 q^{26} -0.257026 q^{27} -9.17530 q^{28} +3.41779 q^{29} +5.23579 q^{30} -10.7466 q^{31} +0.475725 q^{32} -7.23226 q^{33} +16.5931 q^{34} +2.05326 q^{35} +11.4337 q^{36} +9.75798 q^{37} +17.5618 q^{38} +8.12923 q^{39} +4.20677 q^{40} -5.19947 q^{41} +13.7545 q^{42} +7.94121 q^{43} -11.7688 q^{44} -2.55864 q^{45} -20.8902 q^{46} +6.64250 q^{47} +8.99798 q^{48} -1.60606 q^{49} +10.2903 q^{50} -16.5142 q^{51} +13.2284 q^{52} +12.2727 q^{53} +0.626986 q^{54} +2.63363 q^{55} +11.0512 q^{56} -17.4782 q^{57} -8.33733 q^{58} +8.40932 q^{59} -8.47945 q^{60} +11.9365 q^{61} +26.2153 q^{62} -6.72158 q^{63} -8.57299 q^{64} -2.96026 q^{65} +17.6423 q^{66} -5.88524 q^{67} -26.8729 q^{68} +20.7908 q^{69} -5.00871 q^{70} +9.94930 q^{71} -13.7713 q^{72} -4.02077 q^{73} -23.8036 q^{74} -10.2414 q^{75} -28.4415 q^{76} +6.91858 q^{77} -19.8304 q^{78} +6.30567 q^{79} -3.27662 q^{80} -9.30640 q^{81} +12.6836 q^{82} +6.34019 q^{83} -22.2756 q^{84} +6.01364 q^{85} -19.3717 q^{86} +8.29766 q^{87} +14.1750 q^{88} +1.76592 q^{89} +6.24153 q^{90} -7.77665 q^{91} +33.8320 q^{92} -26.0905 q^{93} -16.2037 q^{94} +6.36469 q^{95} +1.15496 q^{96} +0.725924 q^{97} +3.91781 q^{98} -8.62149 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9}+O(q^{10}) $ 182 * q + 18 * q^2 + 28 * q^3 + 208 * q^4 + 22 * q^5 + 18 * q^6 + 14 * q^7 + 54 * q^8 + 238 * q^9	\( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9} + 7 q^{10} + 138 q^{11} + 47 q^{12} + 5 q^{13} + 72 q^{14} + 41 q^{15} + 256 q^{16} + 29 q^{17} + 35 q^{18} + 48 q^{19} + 56 q^{20} + 22 q^{21} + 19 q^{22} + 91 q^{23} + 46 q^{24} + 230 q^{25} + 88 q^{26} + 103 q^{27} + 15 q^{28} + 75 q^{29} + 18 q^{30} + 43 q^{31} + 116 q^{32} + 15 q^{33} + 13 q^{34} + 185 q^{35} + 364 q^{36} + 15 q^{37} + 53 q^{38} + 80 q^{39} - 13 q^{40} + 68 q^{41} + 32 q^{42} + 82 q^{43} + 259 q^{44} + 37 q^{45} + 13 q^{46} + 121 q^{47} + 53 q^{48} + 244 q^{49} + 93 q^{50} + 144 q^{51} - 16 q^{52} + 101 q^{53} + 47 q^{54} + 49 q^{55} + 199 q^{56} + 3 q^{57} + 4 q^{58} + 254 q^{59} + 24 q^{60} + 8 q^{61} + 37 q^{62} + 19 q^{63} + 326 q^{64} + 65 q^{65} + 41 q^{66} + 91 q^{67} + 50 q^{68} + 50 q^{69} + 5 q^{70} + 212 q^{71} + 77 q^{72} + 5 q^{73} + 101 q^{74} + 127 q^{75} + 22 q^{76} + 87 q^{77} - 20 q^{78} + 86 q^{79} + 71 q^{80} + 358 q^{81} - 20 q^{82} + 139 q^{83} - 30 q^{84} + 25 q^{85} + 82 q^{86} + 36 q^{87} - 8 q^{88} + 100 q^{89} - 87 q^{90} + 74 q^{91} + 171 q^{92} + 50 q^{93} - 13 q^{94} + 217 q^{95} + 42 q^{96} + 20 q^{97} + 47 q^{98} + 389 q^{99}+O(q^{100}) \) 182 * q + 18 * q^2 + 28 * q^3 + 208 * q^4 + 22 * q^5 + 18 * q^6 + 14 * q^7 + 54 * q^8 + 238 * q^9 + 7 * q^10 + 138 * q^11 + 47 * q^12 + 5 * q^13 + 72 * q^14 + 41 * q^15 + 256 * q^16 + 29 * q^17 + 35 * q^18 + 48 * q^19 + 56 * q^20 + 22 * q^21 + 19 * q^22 + 91 * q^23 + 46 * q^24 + 230 * q^25 + 88 * q^26 + 103 * q^27 + 15 * q^28 + 75 * q^29 + 18 * q^30 + 43 * q^31 + 116 * q^32 + 15 * q^33 + 13 * q^34 + 185 * q^35 + 364 * q^36 + 15 * q^37 + 53 * q^38 + 80 * q^39 - 13 * q^40 + 68 * q^41 + 32 * q^42 + 82 * q^43 + 259 * q^44 + 37 * q^45 + 13 * q^46 + 121 * q^47 + 53 * q^48 + 244 * q^49 + 93 * q^50 + 144 * q^51 - 16 * q^52 + 101 * q^53 + 47 * q^54 + 49 * q^55 + 199 * q^56 + 3 * q^57 + 4 * q^58 + 254 * q^59 + 24 * q^60 + 8 * q^61 + 37 * q^62 + 19 * q^63 + 326 * q^64 + 65 * q^65 + 41 * q^66 + 91 * q^67 + 50 * q^68 + 50 * q^69 + 5 * q^70 + 212 * q^71 + 77 * q^72 + 5 * q^73 + 101 * q^74 + 127 * q^75 + 22 * q^76 + 87 * q^77 - 20 * q^78 + 86 * q^79 + 71 * q^80 + 358 * q^81 - 20 * q^82 + 139 * q^83 - 30 * q^84 + 25 * q^85 + 82 * q^86 + 36 * q^87 - 8 * q^88 + 100 * q^89 - 87 * q^90 + 74 * q^91 + 171 * q^92 + 50 * q^93 - 13 * q^94 + 217 * q^95 + 42 * q^96 + 20 * q^97 + 47 * q^98 + 389 * 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 $

$2$	−2.43939	−1.72491	−0.862456	−	0.506133i	$-0.831075\pi$
$2$	−2.43939	−1.72491	−0.862456	+	0.506133i	$0.831075\pi$
$3$	2.42778	1.40168	0.700841	−	0.713318i	$-0.252808\pi$
$3$	2.42778	1.40168	0.700841	+	0.713318i	$0.252808\pi$
$4$	3.95064	1.97532
$5$	−0.884079	−0.395372	−0.197686	−	0.980265i	$-0.563343\pi$
$5$	−0.884079	−0.395372	−0.197686	+	0.980265i	$0.563343\pi$
$6$	−5.92232	−2.41778
$7$	−2.32249	−0.877817	−0.438908	−	0.898532i	$-0.644635\pi$
$7$	−2.32249	−0.877817	−0.438908	+	0.898532i	$0.644635\pi$
$8$	−4.75837	−1.68234
$9$	2.89413	0.964711
$10$	2.15662	0.681982
$11$	−2.97896	−0.898189	−0.449095	−	0.893484i	$-0.648253\pi$
$11$	−2.97896	−0.898189	−0.449095	+	0.893484i	$0.648253\pi$
$12$	9.59129	2.76877
$13$	3.34842	0.928684	0.464342	−	0.885656i	$-0.346291\pi$
$13$	3.34842	0.928684	0.464342	+	0.885656i	$0.346291\pi$
$14$	5.66545	1.51416
$15$	−2.14635	−0.554186
$16$	3.70626	0.926564
$17$	−6.80216	−1.64977	−0.824883	−	0.565304i	$-0.808759\pi$
$17$	−6.80216	−1.64977	−0.824883	+	0.565304i	$0.808759\pi$
$18$	−7.05992	−1.66404
$19$	−7.19923	−1.65162	−0.825809	−	0.563951i	$-0.809281\pi$
$19$	−7.19923	−1.65162	−0.825809	+	0.563951i	$0.809281\pi$
$20$	−3.49267	−0.780986
$21$	−5.63849	−1.23042
$22$	7.26684	1.54930
$23$	8.56369	1.78565	0.892826	−	0.450402i	$-0.148719\pi$
$23$	8.56369	1.78565	0.892826	+	0.450402i	$0.148719\pi$
$24$	−11.5523	−2.35810
$25$	−4.21840	−0.843681
$26$	−8.16810	−1.60190
$27$	−0.257026	−0.0494646
$28$	−9.17530	−1.73397
$29$	3.41779	0.634668	0.317334	−	0.948314i	$-0.397212\pi$
$29$	3.41779	0.634668	0.317334	+	0.948314i	$0.397212\pi$
$30$	5.23579	0.955921
$31$	−10.7466	−1.93015	−0.965077	−	0.261965i	$-0.915630\pi$
$31$	−10.7466	−1.93015	−0.965077	+	0.261965i	$0.915630\pi$
$32$	0.475725	0.0840970
$33$	−7.23226	−1.25897
$34$	16.5931	2.84570
$35$	2.05326	0.347064
$36$	11.4337	1.90561
$37$	9.75798	1.60420	0.802101	−	0.597188i	$-0.203715\pi$
$37$	9.75798	1.60420	0.802101	+	0.597188i	$0.203715\pi$
$38$	17.5618	2.84889
$39$	8.12923	1.30172
$40$	4.20677	0.665149
$41$	−5.19947	−0.812021	−0.406011	−	0.913868i	$-0.633080\pi$
$41$	−5.19947	−0.812021	−0.406011	+	0.913868i	$0.633080\pi$
$42$	13.7545	2.12236
$43$	7.94121	1.21102	0.605512	−	0.795836i	$-0.292968\pi$
$43$	7.94121	1.21102	0.605512	+	0.795836i	$0.292968\pi$
$44$	−11.7688	−1.77421
$45$	−2.55864	−0.381420
$46$	−20.8902	−3.08009
$47$	6.64250	0.968908	0.484454	−	0.874817i	$-0.339018\pi$
$47$	6.64250	0.968908	0.484454	+	0.874817i	$0.339018\pi$
$48$	8.99798	1.29875
$49$	−1.60606	−0.229437
$50$	10.2903	1.45527
$51$	−16.5142	−2.31245
$52$	13.2284	1.83445
$53$	12.2727	1.68579	0.842894	−	0.538080i	$-0.180850\pi$
$53$	12.2727	1.68579	0.842894	+	0.538080i	$0.180850\pi$
$54$	0.626986	0.0853220
$55$	2.63363	0.355119
$56$	11.0512	1.47678
$57$	−17.4782	−2.31504
$58$	−8.33733	−1.09475
$59$	8.40932	1.09480	0.547400	−	0.836871i	$-0.315618\pi$
$59$	8.40932	1.09480	0.547400	+	0.836871i	$0.315618\pi$
$60$	−8.47945	−1.09469
$61$	11.9365	1.52831	0.764154	−	0.645034i	$-0.223157\pi$
$61$	11.9365	1.52831	0.764154	+	0.645034i	$0.223157\pi$
$62$	26.2153	3.32935
$63$	−6.72158	−0.846839
$64$	−8.57299	−1.07162
$65$	−2.96026	−0.367176
$66$	17.6423	2.17162
$67$	−5.88524	−0.718997	−0.359498	−	0.933146i	$-0.617052\pi$
$67$	−5.88524	−0.718997	−0.359498	+	0.933146i	$0.617052\pi$
$68$	−26.8729	−3.25881
$69$	20.7908	2.50291
$70$	−5.00871	−0.598655
$71$	9.94930	1.18076	0.590382	−	0.807124i	$-0.298977\pi$
$71$	9.94930	1.18076	0.590382	+	0.807124i	$0.298977\pi$
$72$	−13.7713	−1.62297
$73$	−4.02077	−0.470595	−0.235298	−	0.971923i	$-0.575606\pi$
$73$	−4.02077	−0.470595	−0.235298	+	0.971923i	$0.575606\pi$
$74$	−23.8036	−2.76711
$75$	−10.2414	−1.18257
$76$	−28.4415	−3.26247
$77$	6.91858	0.788446
$78$	−19.8304	−2.24535
$79$	6.30567	0.709444	0.354722	−	0.934972i	$-0.384576\pi$
$79$	6.30567	0.709444	0.354722	+	0.934972i	$0.384576\pi$
$80$	−3.27662	−0.366337
$81$	−9.30640	−1.03404
$82$	12.6836	1.40066
$83$	6.34019	0.695926	0.347963	−	0.937508i	$-0.386874\pi$
$83$	6.34019	0.695926	0.347963	+	0.937508i	$0.386874\pi$
$84$	−22.2756	−2.43047
$85$	6.01364	0.652271
$86$	−19.3717	−2.08891
$87$	8.29766	0.889602
$88$	14.1750	1.51106
$89$	1.76592	0.187187	0.0935934	−	0.995611i	$-0.470165\pi$
$89$	1.76592	0.187187	0.0935934	+	0.995611i	$0.470165\pi$
$90$	6.24153	0.657915
$91$	−7.77665	−0.815215
$92$	33.8320	3.52723
$93$	−26.0905	−2.70546
$94$	−16.2037	−1.67128
$95$	6.36469	0.653003
$96$	1.15496	0.117877
$97$	0.725924	0.0737064	0.0368532	−	0.999321i	$-0.488267\pi$
$97$	0.725924	0.0737064	0.0368532	+	0.999321i	$0.488267\pi$
$98$	3.91781	0.395759
$99$	−8.62149	−0.866493
$100$	−16.6654	−1.66654
$101$	−6.14466	−0.611416	−0.305708	−	0.952125i	$-0.598893\pi$
$101$	−6.14466	−0.611416	−0.305708	+	0.952125i	$0.598893\pi$
$102$	40.2845	3.98876
$103$	−3.26907	−0.322111	−0.161056	−	0.986945i	$-0.551490\pi$
$103$	−3.26907	−0.322111	−0.161056	+	0.986945i	$0.551490\pi$
$104$	−15.9330	−1.56236
$105$	4.98487	0.486474
$106$	−29.9380	−2.90783
$107$	−2.42116	−0.234062	−0.117031	−	0.993128i	$-0.537338\pi$
$107$	−2.42116	−0.234062	−0.117031	+	0.993128i	$0.537338\pi$
$108$	−1.01541	−0.0977083
$109$	5.94698	0.569617	0.284809	−	0.958584i	$-0.408070\pi$
$109$	5.94698	0.569617	0.284809	+	0.958584i	$0.408070\pi$
$110$	−6.42446	−0.612548
$111$	23.6903	2.24858
$112$	−8.60772	−0.813353
$113$	20.6149	1.93929	0.969645	−	0.244517i	$-0.0786292\pi$
$113$	20.6149	1.93929	0.969645	+	0.244517i	$0.0786292\pi$
$114$	42.6361	3.99324
$115$	−7.57097	−0.705997
$116$	13.5025	1.25367
$117$	9.69076	0.895911
$118$	−20.5136	−1.88843
$119$	15.7979	1.44819
$120$	10.2131	0.932327
$121$	−2.12582	−0.193256
$122$	−29.1177	−2.63619
$123$	−12.6232	−1.13820
$124$	−42.4561	−3.81267
$125$	8.14980	0.728940
$126$	16.3966	1.46072
$127$	10.5281	0.934221	0.467110	−	0.884199i	$-0.345295\pi$
$127$	10.5281	0.934221	0.467110	+	0.884199i	$0.345295\pi$
$128$	19.9614	1.76436
$129$	19.2795	1.69747
$130$	7.22125	0.633345
$131$	17.7871	1.55407	0.777035	−	0.629457i	$-0.216723\pi$
$131$	17.7871	1.55407	0.777035	+	0.629457i	$0.216723\pi$
$132$	−28.5720	−2.48688
$133$	16.7201	1.44982
$134$	14.3564	1.24021
$135$	0.227231	0.0195569
$136$	32.3672	2.77546
$137$	8.29817	0.708961	0.354480	−	0.935063i	$-0.384658\pi$
$137$	8.29817	0.708961	0.354480	+	0.935063i	$0.384658\pi$
$138$	−50.7169	−4.31731
$139$	−6.79937	−0.576715	−0.288357	−	0.957523i	$-0.593109\pi$
$139$	−6.79937	−0.576715	−0.288357	+	0.957523i	$0.593109\pi$
$140$	8.11168	0.685562
$141$	16.1266	1.35810
$142$	−24.2702	−2.03671
$143$	−9.97479	−0.834134
$144$	10.7264	0.893866
$145$	−3.02160	−0.250930
$146$	9.80823	0.811735
$147$	−3.89917	−0.321598
$148$	38.5502	3.16881
$149$	3.88833	0.318544	0.159272	−	0.987235i	$-0.449085\pi$
$149$	3.88833	0.318544	0.159272	+	0.987235i	$0.449085\pi$
$150$	24.9827	2.03983
$151$	0.719362	0.0585408	0.0292704	−	0.999572i	$-0.490682\pi$
$151$	0.719362	0.0585408	0.0292704	+	0.999572i	$0.490682\pi$
$152$	34.2566	2.77858
$153$	−19.6863	−1.59155
$154$	−16.8771	−1.36000
$155$	9.50088	0.763129
$156$	32.1156	2.57131
$157$	8.26999	0.660017	0.330008	−	0.943978i	$-0.392948\pi$
$157$	8.26999	0.660017	0.330008	+	0.943978i	$0.392948\pi$
$158$	−15.3820	−1.22373
$159$	29.7955	2.36294
$160$	−0.420578	−0.0332496
$161$	−19.8890	−1.56748
$162$	22.7020	1.78363
$163$	3.84395	0.301081	0.150541	−	0.988604i	$-0.451899\pi$
$163$	3.84395	0.301081	0.150541	+	0.988604i	$0.451899\pi$
$164$	−20.5412	−1.60400
$165$	6.39389	0.497763
$166$	−15.4662	−1.20041
$167$	−0.647722	−0.0501222	−0.0250611	−	0.999686i	$-0.507978\pi$
$167$	−0.647722	−0.0501222	−0.0250611	+	0.999686i	$0.507978\pi$
$168$	26.8300	2.06998
$169$	−1.78810	−0.137546
$170$	−14.6696	−1.12511
$171$	−20.8355	−1.59333
$172$	31.3728	2.39216
$173$	11.4878	0.873401	0.436700	−	0.899607i	$-0.356147\pi$
$173$	11.4878	0.873401	0.436700	+	0.899607i	$0.356147\pi$
$174$	−20.2412	−1.53448
$175$	9.79718	0.740597
$176$	−11.0408	−0.832230
$177$	20.4160	1.53456
$178$	−4.30776	−0.322881
$179$	4.77474	0.356881	0.178441	−	0.983951i	$-0.442895\pi$
$179$	4.77474	0.356881	0.178441	+	0.983951i	$0.442895\pi$
$180$	−10.1083	−0.753425
$181$	−12.7568	−0.948206	−0.474103	−	0.880469i	$-0.657228\pi$
$181$	−12.7568	−0.948206	−0.474103	+	0.880469i	$0.657228\pi$
$182$	18.9703	1.40617
$183$	28.9791	2.14220
$184$	−40.7492	−3.00407
$185$	−8.62683	−0.634257
$186$	63.6450	4.66668
$187$	20.2633	1.48180
$188$	26.2421	1.91390
$189$	0.596938	0.0434209
$190$	−15.5260	−1.12637
$191$	−12.3429	−0.893099	−0.446550	−	0.894759i	$-0.647347\pi$
$191$	−12.3429	−0.893099	−0.446550	+	0.894759i	$0.647347\pi$
$192$	−20.8134	−1.50207
$193$	1.47453	0.106139	0.0530694	−	0.998591i	$-0.483100\pi$
$193$	1.47453	0.106139	0.0530694	+	0.998591i	$0.483100\pi$
$194$	−1.77081	−0.127137
$195$	−7.18688	−0.514663
$196$	−6.34497	−0.453212
$197$	−19.6125	−1.39733	−0.698667	−	0.715447i	$-0.746223\pi$
$197$	−19.6125	−1.39733	−0.698667	+	0.715447i	$0.746223\pi$
$198$	21.0312	1.49462
$199$	27.6776	1.96201	0.981006	−	0.193979i	$-0.0621392\pi$
$199$	27.6776	1.96201	0.981006	+	0.193979i	$0.0621392\pi$
$200$	20.0727	1.41936
$201$	−14.2881	−1.00780
$202$	14.9892	1.05464
$203$	−7.93777	−0.557122
$204$	−65.2415	−4.56782
$205$	4.59674	0.321051
$206$	7.97455	0.555613
$207$	24.7844	1.72264
$208$	12.4101	0.860485
$209$	21.4462	1.48346
$210$	−12.1601	−0.839124
$211$	6.28482	0.432665	0.216332	−	0.976320i	$-0.430590\pi$
$211$	6.28482	0.432665	0.216332	+	0.976320i	$0.430590\pi$
$212$	48.4851	3.32997
$213$	24.1547	1.65506
$214$	5.90616	0.403737
$215$	−7.02066	−0.478805
$216$	1.22302	0.0832161
$217$	24.9589	1.69432
$218$	−14.5070	−0.982539
$219$	−9.76155	−0.659624
$220$	10.4045	0.701473
$221$	−22.7765	−1.53211
$222$	−57.7899	−3.87860
$223$	7.42341	0.497109	0.248554	−	0.968618i	$-0.420045\pi$
$223$	7.42341	0.497109	0.248554	+	0.968618i	$0.420045\pi$
$224$	−1.10486	−0.0738218
$225$	−12.2086	−0.813908
$226$	−50.2879	−3.34510
$227$	−16.7064	−1.10884	−0.554421	−	0.832236i	$-0.687060\pi$
$227$	−16.7064	−1.10884	−0.554421	+	0.832236i	$0.687060\pi$
$228$	−69.0499	−4.57294
$229$	−10.9961	−0.726645	−0.363322	−	0.931663i	$-0.618358\pi$
$229$	−10.9961	−0.726645	−0.363322	+	0.931663i	$0.618358\pi$
$230$	18.4686	1.21778
$231$	16.7968	1.10515
$232$	−16.2631	−1.06773
$233$	−27.8048	−1.82156	−0.910778	−	0.412897i	$-0.864517\pi$
$233$	−27.8048	−1.82156	−0.910778	+	0.412897i	$0.864517\pi$
$234$	−23.6396	−1.54537
$235$	−5.87249	−0.383079
$236$	33.2222	2.16258
$237$	15.3088	0.994414
$238$	−38.5373	−2.49800
$239$	−24.9097	−1.61127	−0.805637	−	0.592410i	$-0.798177\pi$
$239$	−24.9097	−1.61127	−0.805637	+	0.592410i	$0.798177\pi$
$240$	−7.95493	−0.513488
$241$	−3.80003	−0.244781	−0.122391	−	0.992482i	$-0.539056\pi$
$241$	−3.80003	−0.244781	−0.122391	+	0.992482i	$0.539056\pi$
$242$	5.18571	0.333350
$243$	−21.8228	−1.39994
$244$	47.1566	3.01889
$245$	1.41988	0.0907131
$246$	30.7929	1.96329
$247$	−24.1060	−1.53383
$248$	51.1365	3.24717
$249$	15.3926	0.975466
$250$	−19.8806	−1.25736
$251$	−12.5268	−0.790684	−0.395342	−	0.918534i	$-0.629374\pi$
$251$	−12.5268	−0.790684	−0.395342	+	0.918534i	$0.629374\pi$
$252$	−26.5545	−1.67278
$253$	−25.5108	−1.60385
$254$	−25.6822	−1.61145
$255$	14.5998	0.914276
$256$	−31.5478	−1.97174
$257$	9.90052	0.617577	0.308789	−	0.951131i	$-0.400076\pi$
$257$	9.90052	0.617577	0.308789	+	0.951131i	$0.400076\pi$
$258$	−47.0304	−2.92798
$259$	−22.6628	−1.40820
$260$	−11.6949	−0.725289
$261$	9.89154	0.612271
$262$	−43.3898	−2.68063
$263$	−4.14253	−0.255440	−0.127720	−	0.991810i	$-0.540766\pi$
$263$	−4.14253	−0.255440	−0.127720	+	0.991810i	$0.540766\pi$
$264$	34.4138	2.11802
$265$	−10.8501	−0.666513
$266$	−40.7869	−2.50081
$267$	4.28726	0.262376
$268$	−23.2504	−1.42025
$269$	15.4875	0.944289	0.472144	−	0.881521i	$-0.343480\pi$
$269$	15.4875	0.944289	0.472144	+	0.881521i	$0.343480\pi$
$270$	−0.554305	−0.0337339
$271$	16.2698	0.988317	0.494159	−	0.869372i	$-0.335476\pi$
$271$	16.2698	0.988317	0.494159	+	0.869372i	$0.335476\pi$
$272$	−25.2105	−1.52861
$273$	−18.8800	−1.14267
$274$	−20.2425	−1.22289
$275$	12.5664	0.757785
$276$	82.1368	4.94405
$277$	−33.0537	−1.98601	−0.993003	−	0.118091i	$-0.962323\pi$
$277$	−33.0537	−1.98601	−0.993003	+	0.118091i	$0.962323\pi$
$278$	16.5863	0.994782
$279$	−31.1022	−1.86204
$280$	−9.77017	−0.583879
$281$	7.23313	0.431493	0.215746	−	0.976449i	$-0.430782\pi$
$281$	7.23313	0.431493	0.215746	+	0.976449i	$0.430782\pi$
$282$	−39.3390	−2.34260
$283$	−25.9736	−1.54397	−0.771985	−	0.635641i	$-0.780736\pi$
$283$	−25.9736	−1.54397	−0.771985	+	0.635641i	$0.780736\pi$
$284$	39.3061	2.33239
$285$	15.4521	0.915302
$286$	24.3324	1.43881
$287$	12.0757	0.712806
$288$	1.37681	0.0811293
$289$	29.2694	1.72173
$290$	7.37086	0.432832
$291$	1.76239	0.103313
$292$	−15.8846	−0.929575
$293$	−9.90570	−0.578697	−0.289349	−	0.957224i	$-0.593439\pi$
$293$	−9.90570	−0.578697	−0.289349	+	0.957224i	$0.593439\pi$
$294$	9.51160	0.554728
$295$	−7.43450	−0.432853
$296$	−46.4321	−2.69881
$297$	0.765668	0.0444286
$298$	−9.48516	−0.549460
$299$	28.6748	1.65831
$300$	−40.4599	−2.33596
$301$	−18.4433	−1.06306
$302$	−1.75481	−0.100978
$303$	−14.9179	−0.857010
$304$	−26.6822	−1.53033
$305$	−10.5528	−0.604250
$306$	48.0227	2.74528
$307$	5.15335	0.294117	0.147059	−	0.989128i	$-0.453019\pi$
$307$	5.15335	0.294117	0.147059	+	0.989128i	$0.453019\pi$
$308$	27.3328	1.55743
$309$	−7.93659	−0.451497
$310$	−23.1764	−1.31633
$311$	34.3646	1.94864	0.974319	−	0.225171i	$-0.0722941\pi$
$311$	34.3646	1.94864	0.974319	+	0.225171i	$0.0722941\pi$
$312$	−38.6819	−2.18993
$313$	6.53289	0.369261	0.184631	−	0.982808i	$-0.440891\pi$
$313$	6.53289	0.369261	0.184631	+	0.982808i	$0.440891\pi$
$314$	−20.1737	−1.13847
$315$	5.94240	0.334817
$316$	24.9114	1.40138
$317$	−12.4013	−0.696528	−0.348264	−	0.937396i	$-0.613229\pi$
$317$	−12.4013	−0.696528	−0.348264	+	0.937396i	$0.613229\pi$
$318$	−72.6829	−4.07586
$319$	−10.1815	−0.570052
$320$	7.57920	0.423690
$321$	−5.87805	−0.328081
$322$	48.5172	2.70376
$323$	48.9703	2.72478
$324$	−36.7662	−2.04257
$325$	−14.1250	−0.783513
$326$	−9.37690	−0.519338
$327$	14.4380	0.798422
$328$	24.7410	1.36609
$329$	−15.4271	−0.850524
$330$	−15.5972	−0.858598
$331$	28.5067	1.56687	0.783434	−	0.621475i	$-0.213466\pi$
$331$	28.5067	1.56687	0.783434	+	0.621475i	$0.213466\pi$
$332$	25.0478	1.37467
$333$	28.2409	1.54759
$334$	1.58005	0.0864563
$335$	5.20302	0.284271
$336$	−20.8977	−1.14006
$337$	−8.21002	−0.447228	−0.223614	−	0.974678i	$-0.571786\pi$
$337$	−8.21002	−0.447228	−0.223614	+	0.974678i	$0.571786\pi$
$338$	4.36188	0.237255
$339$	50.0486	2.71827
$340$	23.7577	1.28844
$341$	32.0138	1.73364
$342$	50.8260	2.74836
$343$	19.9875	1.07922
$344$	−37.7872	−2.03735
$345$	−18.3807	−0.989582
$346$	−28.0232	−1.50654
$347$	9.22725	0.495345	0.247672	−	0.968844i	$-0.420334\pi$
$347$	9.22725	0.495345	0.247672	+	0.968844i	$0.420334\pi$
$348$	32.7810	1.75725
$349$	−2.67451	−0.143163	−0.0715815	−	0.997435i	$-0.522805\pi$
$349$	−2.67451	−0.143163	−0.0715815	+	0.997435i	$0.522805\pi$
$350$	−23.8992	−1.27746
$351$	−0.860629	−0.0459370
$352$	−1.41716	−0.0755350
$353$	−14.7483	−0.784970	−0.392485	−	0.919758i	$-0.628385\pi$
$353$	−14.7483	−0.784970	−0.392485	+	0.919758i	$0.628385\pi$
$354$	−49.8027	−2.64698
$355$	−8.79596	−0.466841
$356$	6.97649	0.369753
$357$	38.3539	2.02990
$358$	−11.6475	−0.615588
$359$	30.2466	1.59636	0.798178	−	0.602422i	$-0.205798\pi$
$359$	30.2466	1.59636	0.798178	+	0.602422i	$0.205798\pi$
$360$	12.1750	0.641676
$361$	32.8289	1.72784
$362$	31.1189	1.63557
$363$	−5.16103	−0.270884
$364$	−30.7227	−1.61031
$365$	3.55467	0.186060
$366$	−70.6915	−3.69510
$367$	14.1937	0.740904	0.370452	−	0.928852i	$-0.379203\pi$
$367$	14.1937	0.740904	0.370452	+	0.928852i	$0.379203\pi$
$368$	31.7392	1.65452
$369$	−15.0480	−0.783366
$370$	21.0442	1.09404
$371$	−28.5032	−1.47981
$372$	−103.074	−5.34415
$373$	−16.3402	−0.846065	−0.423033	−	0.906114i	$-0.639034\pi$
$373$	−16.3402	−0.846065	−0.423033	+	0.906114i	$0.639034\pi$
$374$	−49.4302	−2.55598
$375$	19.7859	1.02174
$376$	−31.6075	−1.63003
$377$	11.4442	0.589406
$378$	−1.45617	−0.0748971
$379$	−37.3333	−1.91768	−0.958841	−	0.283943i	$-0.908357\pi$
$379$	−37.3333	−1.91768	−0.958841	+	0.283943i	$0.908357\pi$
$380$	25.1446	1.28989
$381$	25.5600	1.30948
$382$	30.1091	1.54052
$383$	−2.59413	−0.132554	−0.0662769	−	0.997801i	$-0.521112\pi$
$383$	−2.59413	−0.132554	−0.0662769	+	0.997801i	$0.521112\pi$
$384$	48.4620	2.47307
$385$	−6.11657	−0.311729
$386$	−3.59695	−0.183080
$387$	22.9829	1.16829
$388$	2.86786	0.145594
$389$	9.43876	0.478564	0.239282	−	0.970950i	$-0.423088\pi$
$389$	9.43876	0.478564	0.239282	+	0.970950i	$0.423088\pi$
$390$	17.5316	0.887748
$391$	−58.2515	−2.94591
$392$	7.64223	0.385991
$393$	43.1833	2.17831
$394$	47.8426	2.41028
$395$	−5.57471	−0.280494
$396$	−34.0604	−1.71160
$397$	−14.9403	−0.749831	−0.374916	−	0.927059i	$-0.622328\pi$
$397$	−14.9403	−0.749831	−0.374916	+	0.927059i	$0.622328\pi$
$398$	−67.5165	−3.38430
$399$	40.5928	2.03218
$400$	−15.6345	−0.781724
$401$	−4.88637	−0.244014	−0.122007	−	0.992529i	$-0.538933\pi$
$401$	−4.88637	−0.244014	−0.122007	+	0.992529i	$0.538933\pi$
$402$	34.8543	1.73837
$403$	−35.9843	−1.79250
$404$	−24.2753	−1.20774
$405$	8.22759	0.408832
$406$	19.3633	0.960986
$407$	−29.0686	−1.44088
$408$	78.5805	3.89031
$409$	−7.98945	−0.395053	−0.197526	−	0.980298i	$-0.563291\pi$
$409$	−7.98945	−0.395053	−0.197526	+	0.980298i	$0.563291\pi$
$410$	−11.2133	−0.553784
$411$	20.1462	0.993737
$412$	−12.9149	−0.636272
$413$	−19.5305	−0.961034
$414$	−60.4590	−2.97140
$415$	−5.60522	−0.275150
$416$	1.59292	0.0780996
$417$	−16.5074	−0.808370
$418$	−52.3157	−2.55884
$419$	24.9445	1.21862	0.609308	−	0.792933i	$-0.291447\pi$
$419$	24.9445	1.21862	0.609308	+	0.792933i	$0.291447\pi$
$420$	19.6934	0.960940
$421$	−6.47142	−0.315398	−0.157699	−	0.987487i	$-0.550408\pi$
$421$	−6.47142	−0.315398	−0.157699	+	0.987487i	$0.550408\pi$
$422$	−15.3311	−0.746309
$423$	19.2243	0.934716
$424$	−58.3981	−2.83606
$425$	28.6943	1.39188
$426$	−58.9229	−2.85482
$427$	−27.7223	−1.34157
$428$	−9.56512	−0.462348
$429$	−24.2166	−1.16919
$430$	17.1261	0.825896
$431$	13.9923	0.673986	0.336993	−	0.941507i	$-0.390590\pi$
$431$	13.9923	0.673986	0.336993	+	0.941507i	$0.390590\pi$
$432$	−0.952602	−0.0458321
$433$	8.25570	0.396744	0.198372	−	0.980127i	$-0.436435\pi$
$433$	8.25570	0.396744	0.198372	+	0.980127i	$0.436435\pi$
$434$	−60.8846	−2.92256
$435$	−7.33578	−0.351724
$436$	23.4943	1.12518
$437$	−61.6520	−2.94921
$438$	23.8123	1.13779
$439$	20.3042	0.969069	0.484534	−	0.874772i	$-0.338989\pi$
$439$	20.3042	0.969069	0.484534	+	0.874772i	$0.338989\pi$
$440$	−12.5318	−0.597430
$441$	−4.64815	−0.221341
$442$	55.5607	2.64275
$443$	11.1356	0.529067	0.264534	−	0.964376i	$-0.414782\pi$
$443$	11.1356	0.529067	0.264534	+	0.964376i	$0.414782\pi$
$444$	93.5916	4.44166
$445$	−1.56121	−0.0740084
$446$	−18.1086	−0.857468
$447$	9.44002	0.446497
$448$	19.9106	0.940689
$449$	27.7913	1.31155	0.655775	−	0.754956i	$-0.272342\pi$
$449$	27.7913	1.31155	0.655775	+	0.754956i	$0.272342\pi$
$450$	29.7816	1.40392
$451$	15.4890	0.729349
$452$	81.4421	3.83072
$453$	1.74646	0.0820556
$454$	40.7535	1.91266
$455$	6.87517	0.322313
$456$	83.1676	3.89468
$457$	24.4119	1.14194	0.570970	−	0.820971i	$-0.306567\pi$
$457$	24.4119	1.14194	0.570970	+	0.820971i	$0.306567\pi$
$458$	26.8239	1.25340
$459$	1.74833	0.0816050
$460$	−29.9102	−1.39457
$461$	−27.4425	−1.27813	−0.639063	−	0.769155i	$-0.720678\pi$
$461$	−27.4425	−1.27813	−0.639063	+	0.769155i	$0.720678\pi$
$462$	−40.9740	−1.90628
$463$	−14.2830	−0.663786	−0.331893	−	0.943317i	$-0.607687\pi$
$463$	−14.2830	−0.663786	−0.331893	+	0.943317i	$0.607687\pi$
$464$	12.6672	0.588060
$465$	23.0661	1.06966
$466$	67.8269	3.14202
$467$	−14.3434	−0.663735	−0.331867	−	0.943326i	$-0.607679\pi$
$467$	−14.3434	−0.663735	−0.331867	+	0.943326i	$0.607679\pi$
$468$	38.2847	1.76971
$469$	13.6684	0.631147
$470$	14.3253	0.660778
$471$	20.0777	0.925133
$472$	−40.0146	−1.84182
$473$	−23.6565	−1.08773
$474$	−37.3442	−1.71528
$475$	30.3693	1.39344
$476$	62.4118	2.86064
$477$	35.5189	1.62630
$478$	60.7645	2.77930
$479$	26.6639	1.21830	0.609152	−	0.793054i	$-0.291510\pi$
$479$	26.6639	1.21830	0.609152	+	0.793054i	$0.291510\pi$
$480$	−1.02107	−0.0466054
$481$	32.6738	1.48980
$482$	9.26976	0.422226
$483$	−48.2863	−2.19710
$484$	−8.39834	−0.381743
$485$	−0.641774	−0.0291414
$486$	53.2345	2.41476
$487$	1.57885	0.0715444	0.0357722	−	0.999360i	$-0.488611\pi$
$487$	1.57885	0.0715444	0.0357722	+	0.999360i	$0.488611\pi$
$488$	−56.7981	−2.57113
$489$	9.33227	0.422020
$490$	−3.46366	−0.156472
$491$	−13.6611	−0.616515	−0.308258	−	0.951303i	$-0.599746\pi$
$491$	−13.6611	−0.616515	−0.308258	+	0.951303i	$0.599746\pi$
$492$	−49.8697	−2.24830
$493$	−23.2484	−1.04705
$494$	58.8041	2.64572
$495$	7.62208	0.342587
$496$	−39.8298	−1.78841
$497$	−23.1071	−1.03649
$498$	−37.5486	−1.68259
$499$	39.1386	1.75208	0.876042	−	0.482235i	$-0.160175\pi$
$499$	39.1386	1.75208	0.876042	+	0.482235i	$0.160175\pi$
$500$	32.1969	1.43989
$501$	−1.57253	−0.0702553
$502$	30.5578	1.36386
$503$	−11.3580	−0.506429	−0.253214	−	0.967410i	$-0.581488\pi$
$503$	−11.3580	−0.506429	−0.253214	+	0.967410i	$0.581488\pi$
$504$	31.9837	1.42467
$505$	5.43236	0.241737
$506$	62.2310	2.76650
$507$	−4.34112	−0.192796
$508$	41.5928	1.84538
$509$	−27.8265	−1.23339	−0.616694	−	0.787203i	$-0.711528\pi$
$509$	−27.8265	−1.23339	−0.616694	+	0.787203i	$0.711528\pi$
$510$	−35.6147	−1.57705
$511$	9.33817	0.413096
$512$	37.0346	1.63671
$513$	1.85039	0.0816966
$514$	−24.1513	−1.06527
$515$	2.89012	0.127354
$516$	76.1665	3.35304
$517$	−19.7877	−0.870263
$518$	55.2834	2.42901
$519$	27.8899	1.22423
$520$	14.0860	0.617713
$521$	3.59709	0.157591	0.0787957	−	0.996891i	$-0.474893\pi$
$521$	3.59709	0.157591	0.0787957	+	0.996891i	$0.474893\pi$
$522$	−24.1293	−1.05611
$523$	−21.2783	−0.930434	−0.465217	−	0.885197i	$-0.654024\pi$
$523$	−21.2783	−0.930434	−0.465217	+	0.885197i	$0.654024\pi$
$524$	70.2705	3.06978
$525$	23.7854	1.03808
$526$	10.1053	0.440611
$527$	73.1004	3.18430
$528$	−26.8046	−1.16652
$529$	50.3367	2.18855
$530$	26.4675	1.14968
$531$	24.3377	1.05617
$532$	66.0551	2.86385
$533$	−17.4100	−0.754111
$534$	−10.4583	−0.452576
$535$	2.14050	0.0925417
$536$	28.0041	1.20959
$537$	11.5920	0.500234
$538$	−37.7801	−1.62881
$539$	4.78439	0.206078
$540$	0.897707	0.0386311
$541$	9.51090	0.408905	0.204453	−	0.978876i	$-0.434459\pi$
$541$	9.51090	0.408905	0.204453	+	0.978876i	$0.434459\pi$
$542$	−39.6883	−1.70476
$543$	−30.9708	−1.32908
$544$	−3.23595	−0.138740
$545$	−5.25760	−0.225211
$546$	46.0558	1.97101
$547$	16.9236	0.723600	0.361800	−	0.932256i	$-0.382162\pi$
$547$	16.9236	0.723600	0.361800	+	0.932256i	$0.382162\pi$
$548$	32.7831	1.40042
$549$	34.5457	1.47437
$550$	−30.6545	−1.30711
$551$	−24.6055	−1.04823
$552$	−98.9301	−4.21075
$553$	−14.6448	−0.622762
$554$	80.6310	3.42568
$555$	−20.9441	−0.889026
$556$	−26.8618	−1.13920
$557$	−1.96515	−0.0832661	−0.0416331	−	0.999133i	$-0.513256\pi$
$557$	−1.96515	−0.0832661	−0.0416331	+	0.999133i	$0.513256\pi$
$558$	75.8705	3.21185
$559$	26.5905	1.12466
$560$	7.60991	0.321577
$561$	49.1950	2.07701
$562$	−17.6445	−0.744286
$563$	0.677297	0.0285447	0.0142723	−	0.999898i	$-0.495457\pi$
$563$	0.677297	0.0285447	0.0142723	+	0.999898i	$0.495457\pi$
$564$	63.7102	2.68268
$565$	−18.2252	−0.766741
$566$	63.3598	2.66321
$567$	21.6140	0.907701
$568$	−47.3424	−1.98644
$569$	−39.5533	−1.65816	−0.829081	−	0.559129i	$-0.811136\pi$
$569$	−39.5533	−1.65816	−0.829081	+	0.559129i	$0.811136\pi$
$570$	−37.6937	−1.57882
$571$	−37.1992	−1.55674	−0.778370	−	0.627806i	$-0.783953\pi$
$571$	−37.1992	−1.55674	−0.778370	+	0.627806i	$0.783953\pi$
$572$	−39.4068	−1.64768
$573$	−29.9658	−1.25184
$574$	−29.4574	−1.22953
$575$	−36.1251	−1.50652
$576$	−24.8114	−1.03381
$577$	28.4895	1.18603	0.593016	−	0.805191i	$-0.297937\pi$
$577$	28.4895	1.18603	0.593016	+	0.805191i	$0.297937\pi$
$578$	−71.3994	−2.96983
$579$	3.57983	0.148773
$580$	−11.9372	−0.495666
$581$	−14.7250	−0.610896
$582$	−4.29915	−0.178206
$583$	−36.5599	−1.51416
$584$	19.1323	0.791700
$585$	−8.56740	−0.354218
$586$	24.1639	0.998201
$587$	5.31467	0.219360	0.109680	−	0.993967i	$-0.465017\pi$
$587$	5.31467	0.219360	0.109680	+	0.993967i	$0.465017\pi$
$588$	−15.4042	−0.635258
$589$	77.3676	3.18788
$590$	18.1357	0.746634
$591$	−47.6149	−1.95862
$592$	36.1656	1.48640
$593$	42.6266	1.75047	0.875233	−	0.483701i	$-0.160708\pi$
$593$	42.6266	1.75047	0.875233	+	0.483701i	$0.160708\pi$
$594$	−1.86777	−0.0766353
$595$	−13.9666	−0.572575
$596$	15.3614	0.629226
$597$	67.1952	2.75011
$598$	−69.9491	−2.86043
$599$	34.8685	1.42469	0.712344	−	0.701830i	$-0.247633\pi$
$599$	34.8685	1.42469	0.712344	+	0.701830i	$0.247633\pi$
$600$	48.7322	1.98948
$601$	23.8474	0.972754	0.486377	−	0.873749i	$-0.338318\pi$
$601$	23.8474	0.972754	0.486377	+	0.873749i	$0.338318\pi$
$602$	44.9906	1.83368
$603$	−17.0327	−0.693624
$604$	2.84194	0.115637
$605$	1.87939	0.0764081
$606$	36.3906	1.47827
$607$	0.488918	0.0198446	0.00992229	−	0.999951i	$-0.496842\pi$
$607$	0.488918	0.0198446	0.00992229	+	0.999951i	$0.496842\pi$
$608$	−3.42485	−0.138896
$609$	−19.2712	−0.780908
$610$	25.7424	1.04228
$611$	22.2419	0.899810
$612$	−77.7736	−3.14381
$613$	14.2270	0.574623	0.287311	−	0.957837i	$-0.407239\pi$
$613$	14.2270	0.574623	0.287311	+	0.957837i	$0.407239\pi$
$614$	−12.5710	−0.507326
$615$	11.1599	0.450011
$616$	−32.9212	−1.32643
$617$	−11.6910	−0.470660	−0.235330	−	0.971916i	$-0.575617\pi$
$617$	−11.6910	−0.470660	−0.235330	+	0.971916i	$0.575617\pi$
$618$	19.3605	0.778792
$619$	−13.1558	−0.528775	−0.264387	−	0.964417i	$-0.585170\pi$
$619$	−13.1558	−0.528775	−0.264387	+	0.964417i	$0.585170\pi$
$620$	37.5345	1.50742
$621$	−2.20109	−0.0883266
$622$	−83.8288	−3.36123
$623$	−4.10132	−0.164316
$624$	30.1290	1.20613
$625$	13.8870	0.555479
$626$	−15.9363	−0.636942
$627$	52.0667	2.07934
$628$	32.6717	1.30374
$629$	−66.3753	−2.64656
$630$	−14.4959	−0.577529
$631$	−1.00773	−0.0401169	−0.0200585	−	0.999799i	$-0.506385\pi$
$631$	−1.00773	−0.0401169	−0.0200585	+	0.999799i	$0.506385\pi$
$632$	−30.0047	−1.19352
$633$	15.2582	0.606458
$634$	30.2517	1.20145
$635$	−9.30770	−0.369365
$636$	117.711	4.66755
$637$	−5.37776	−0.213075
$638$	24.8366	0.983289
$639$	28.7946	1.13910
$640$	−17.6475	−0.697578
$641$	−1.07815	−0.0425844	−0.0212922	−	0.999773i	$-0.506778\pi$
$641$	−1.07815	−0.0425844	−0.0212922	+	0.999773i	$0.506778\pi$
$642$	14.3389	0.565910
$643$	−32.5518	−1.28372	−0.641859	−	0.766823i	$-0.721837\pi$
$643$	−32.5518	−1.28372	−0.641859	+	0.766823i	$0.721837\pi$
$644$	−78.5743	−3.09626
$645$	−17.0446	−0.671132
$646$	−119.458	−4.70001
$647$	42.9241	1.68752	0.843761	−	0.536720i	$-0.180337\pi$
$647$	42.9241	1.68752	0.843761	+	0.536720i	$0.180337\pi$
$648$	44.2833	1.73961
$649$	−25.0510	−0.983338
$650$	34.4564	1.35149
$651$	60.5949	2.37490
$652$	15.1860	0.594731
$653$	15.5165	0.607209	0.303605	−	0.952798i	$-0.401810\pi$
$653$	15.5165	0.607209	0.303605	+	0.952798i	$0.401810\pi$
$654$	−35.2199	−1.37721
$655$	−15.7252	−0.614436
$656$	−19.2706	−0.752390
$657$	−11.6366	−0.453988
$658$	37.6328	1.46708
$659$	28.9967	1.12955	0.564775	−	0.825245i	$-0.308963\pi$
$659$	28.9967	1.12955	0.564775	+	0.825245i	$0.308963\pi$
$660$	25.2599	0.983241
$661$	−27.8198	−1.08206	−0.541032	−	0.841002i	$-0.681966\pi$
$661$	−27.8198	−1.08206	−0.541032	+	0.841002i	$0.681966\pi$
$662$	−69.5390	−2.70271
$663$	−55.2963	−2.14753
$664$	−30.1689	−1.17078
$665$	−14.7819	−0.573217
$666$	−68.8906	−2.66946
$667$	29.2689	1.13330
$668$	−2.55891	−0.0990073
$669$	18.0224	0.696788
$670$	−12.6922	−0.490342
$671$	−35.5582	−1.37271
$672$	−2.68237	−0.103475
$673$	−9.88280	−0.380954	−0.190477	−	0.981692i	$-0.561003\pi$
$673$	−9.88280	−0.380954	−0.190477	+	0.981692i	$0.561003\pi$
$674$	20.0275	0.771429
$675$	1.08424	0.0417323
$676$	−7.06413	−0.271697
$677$	10.3397	0.397388	0.198694	−	0.980062i	$-0.436330\pi$
$677$	10.3397	0.397388	0.198694	+	0.980062i	$0.436330\pi$
$678$	−122.088	−4.68877
$679$	−1.68595	−0.0647007
$680$	−28.6151	−1.09734
$681$	−40.5595	−1.55424
$682$	−78.0942	−2.99038
$683$	13.4973	0.516460	0.258230	−	0.966083i	$-0.416861\pi$
$683$	13.4973	0.516460	0.258230	+	0.966083i	$0.416861\pi$
$684$	−82.3136	−3.14734
$685$	−7.33624	−0.280303
$686$	−48.7572	−1.86156
$687$	−26.6962	−1.01852
$688$	29.4322	1.12209
$689$	41.0942	1.56556
$690$	44.8377	1.70694
$691$	42.4145	1.61352	0.806762	−	0.590877i	$-0.201218\pi$
$691$	42.4145	1.61352	0.806762	+	0.590877i	$0.201218\pi$
$692$	45.3841	1.72524
$693$	20.0233	0.760622
$694$	−22.5089	−0.854425
$695$	6.01118	0.228017
$696$	−39.4833	−1.49661
$697$	35.3676	1.33964
$698$	6.52417	0.246944
$699$	−67.5041	−2.55324
$700$	38.7051	1.46292
$701$	−26.2712	−0.992248	−0.496124	−	0.868252i	$-0.665244\pi$
$701$	−26.2712	−0.992248	−0.496124	+	0.868252i	$0.665244\pi$
$702$	2.09941	0.0792372
$703$	−70.2500	−2.64953
$704$	25.5386	0.962521
$705$	−14.2571	−0.536955
$706$	35.9768	1.35400
$707$	14.2709	0.536711
$708$	80.6562	3.03125
$709$	9.50043	0.356796	0.178398	−	0.983958i	$-0.442908\pi$
$709$	9.50043	0.356796	0.178398	+	0.983958i	$0.442908\pi$
$710$	21.4568	0.805259
$711$	18.2494	0.684408
$712$	−8.40288	−0.314911
$713$	−92.0309	−3.44658
$714$	−93.5602	−3.50140
$715$	8.81850	0.329793
$716$	18.8633	0.704954
$717$	−60.4753	−2.25849
$718$	−73.7834	−2.75357
$719$	4.18413	0.156042	0.0780208	−	0.996952i	$-0.475140\pi$
$719$	4.18413	0.156042	0.0780208	+	0.996952i	$0.475140\pi$
$720$	−9.48297	−0.353410
$721$	7.59237	0.282755
$722$	−80.0827	−2.98037
$723$	−9.22564	−0.343105
$724$	−50.3975	−1.87301
$725$	−14.4176	−0.535457
$726$	12.5898	0.467250
$727$	−16.5869	−0.615173	−0.307587	−	0.951520i	$-0.599521\pi$
$727$	−16.5869	−0.615173	−0.307587	+	0.951520i	$0.599521\pi$
$728$	37.0042	1.37147
$729$	−25.0619	−0.928220
$730$	−8.67125	−0.320937
$731$	−54.0174	−1.99791
$732$	114.486	4.23153
$733$	23.2490	0.858721	0.429360	−	0.903133i	$-0.358739\pi$
$733$	23.2490	0.858721	0.429360	+	0.903133i	$0.358739\pi$
$734$	−34.6240	−1.27799
$735$	3.44717	0.127151
$736$	4.07396	0.150168
$737$	17.5319	0.645795
$738$	36.7079	1.35124
$739$	1.99890	0.0735306	0.0367653	−	0.999324i	$-0.488295\pi$
$739$	1.99890	0.0735306	0.0367653	+	0.999324i	$0.488295\pi$
$740$	−34.0815	−1.25286
$741$	−58.5242	−2.14994
$742$	69.5305	2.55255
$743$	45.5008	1.66926	0.834631	−	0.550809i	$-0.185681\pi$
$743$	45.5008	1.66926	0.834631	+	0.550809i	$0.185681\pi$
$744$	124.148	4.55150
$745$	−3.43759	−0.125943
$746$	39.8603	1.45939
$747$	18.3493	0.671367
$748$	80.0531	2.92703
$749$	5.62311	0.205464
$750$	−48.2657	−1.76241
$751$	−20.4885	−0.747637	−0.373818	−	0.927502i	$-0.621952\pi$
$751$	−20.4885	−0.747637	−0.373818	+	0.927502i	$0.621952\pi$
$752$	24.6188	0.897756
$753$	−30.4123	−1.10829
$754$	−27.9169	−1.01667
$755$	−0.635973	−0.0231454
$756$	2.35829	0.0857700
$757$	42.4396	1.54249	0.771246	−	0.636537i	$-0.219634\pi$
$757$	42.4396	1.54249	0.771246	+	0.636537i	$0.219634\pi$
$758$	91.0705	3.30783
$759$	−61.9348	−2.24809
$760$	−30.2855	−1.09857
$761$	−39.7287	−1.44016	−0.720081	−	0.693890i	$-0.755895\pi$
$761$	−39.7287	−1.44016	−0.720081	+	0.693890i	$0.755895\pi$
$762$	−62.3509	−2.25874
$763$	−13.8118	−0.500020
$764$	−48.7622	−1.76415
$765$	17.4043	0.629253
$766$	6.32810	0.228644
$767$	28.1579	1.01672
$768$	−76.5912	−2.76375
$769$	−39.9535	−1.44076	−0.720379	−	0.693580i	$-0.756032\pi$
$769$	−39.9535	−1.44076	−0.720379	+	0.693580i	$0.756032\pi$
$770$	14.9207	0.537705
$771$	24.0363	0.865647
$772$	5.82532	0.209658
$773$	37.7309	1.35709	0.678544	−	0.734560i	$-0.262611\pi$
$773$	37.7309	1.35709	0.678544	+	0.734560i	$0.262611\pi$
$774$	−56.0643	−2.01519
$775$	45.3337	1.62843
$776$	−3.45421	−0.123999
$777$	−55.0203	−1.97384
$778$	−23.0248	−0.825481
$779$	37.4322	1.34115
$780$	−28.3928	−1.01662
$781$	−29.6385	−1.06055
$782$	142.098	5.08143
$783$	−0.878460	−0.0313936
$784$	−5.95247	−0.212588
$785$	−7.31132	−0.260952
$786$	−105.341	−3.75739
$787$	21.7057	0.773723	0.386862	−	0.922138i	$-0.373559\pi$
$787$	21.7057	0.773723	0.386862	+	0.922138i	$0.373559\pi$
$788$	−77.4819	−2.76018
$789$	−10.0572	−0.358045
$790$	13.5989	0.483827
$791$	−47.8779	−1.70234
$792$	41.0242	1.45773
$793$	39.9683	1.41931
$794$	36.4452	1.29339
$795$	−26.3416	−0.934239
$796$	109.344	3.87560
$797$	−11.2600	−0.398848	−0.199424	−	0.979913i	$-0.563907\pi$
$797$	−11.2600	−0.398848	−0.199424	+	0.979913i	$0.563907\pi$
$798$	−99.0218	−3.50533
$799$	−45.1833	−1.59847
$800$	−2.00680	−0.0709511
$801$	5.11080	0.180581
$802$	11.9198	0.420902
$803$	11.9777	0.422683
$804$	−56.4470	−1.99073
$805$	17.5835	0.619736
$806$	87.7797	3.09191
$807$	37.6003	1.32359
$808$	29.2385	1.02861
$809$	−40.2845	−1.41633	−0.708163	−	0.706049i	$-0.750476\pi$
$809$	−40.2845	−1.41633	−0.708163	+	0.706049i	$0.750476\pi$
$810$	−20.0703	−0.705199
$811$	12.8997	0.452970	0.226485	−	0.974015i	$-0.427277\pi$
$811$	12.8997	0.452970	0.226485	+	0.974015i	$0.427277\pi$
$812$	−31.3592	−1.10049
$813$	39.4994	1.38531
$814$	70.9097	2.48539
$815$	−3.39835	−0.119039
$816$	−61.2057	−2.14263
$817$	−57.1706	−2.00015
$818$	19.4894	0.681431
$819$	−22.5067	−0.786446
$820$	18.1601	0.634177
$821$	36.5109	1.27424	0.637119	−	0.770765i	$-0.280126\pi$
$821$	36.5109	1.27424	0.637119	+	0.770765i	$0.280126\pi$
$822$	−49.1444	−1.71411
$823$	−2.07993	−0.0725018	−0.0362509	−	0.999343i	$-0.511542\pi$
$823$	−2.07993	−0.0725018	−0.0362509	+	0.999343i	$0.511542\pi$
$824$	15.5554	0.541899
$825$	30.5086	1.06217
$826$	47.6426	1.65770
$827$	−10.1603	−0.353308	−0.176654	−	0.984273i	$-0.556527\pi$
$827$	−10.1603	−0.353308	−0.176654	+	0.984273i	$0.556527\pi$
$828$	97.9143	3.40276
$829$	13.0702	0.453947	0.226973	−	0.973901i	$-0.427117\pi$
$829$	13.0702	0.453947	0.226973	+	0.973901i	$0.427117\pi$
$830$	13.6733	0.474609
$831$	−80.2473	−2.78375
$832$	−28.7059	−0.995200
$833$	10.9247	0.378518
$834$	40.2680	1.39437
$835$	0.572637	0.0198169
$836$	84.7261	2.93031
$837$	2.76216	0.0954743
$838$	−60.8493	−2.10201
$839$	−34.0134	−1.17427	−0.587136	−	0.809488i	$-0.699745\pi$
$839$	−34.0134	−1.17427	−0.587136	+	0.809488i	$0.699745\pi$
$840$	−23.7198	−0.818412
$841$	−17.3187	−0.597197
$842$	15.7863	0.544033
$843$	17.5605	0.604815
$844$	24.8290	0.854651
$845$	1.58082	0.0543819
$846$	−46.8956	−1.61230
$847$	4.93718	0.169644
$848$	45.4858	1.56199
$849$	−63.0583	−2.16415
$850$	−69.9966	−2.40086
$851$	83.5643	2.86455
$852$	95.4266	3.26926
$853$	−8.43024	−0.288646	−0.144323	−	0.989531i	$-0.546100\pi$
$853$	−8.43024	−0.288646	−0.144323	+	0.989531i	$0.546100\pi$
$854$	67.6255	2.31410
$855$	18.4202	0.629959
$856$	11.5208	0.393772
$857$	43.8258	1.49706	0.748530	−	0.663101i	$-0.230760\pi$
$857$	43.8258	1.49706	0.748530	+	0.663101i	$0.230760\pi$
$858$	59.0739	2.01675
$859$	0.0282549	0.000964045 0	0.000482022	−	1.00000i	$-0.499847\pi$
$859$	0.0282549	0.000964045 0	0.000482022		1.00000i	$0.499847\pi$
$860$	−27.7361	−0.945792
$861$	29.3172	0.999127
$862$	−34.1327	−1.16257
$863$	41.3125	1.40629	0.703147	−	0.711044i	$-0.251778\pi$
$863$	41.3125	1.40629	0.703147	+	0.711044i	$0.251778\pi$
$864$	−0.122273	−0.00415983
$865$	−10.1561	−0.345318
$866$	−20.1389	−0.684348
$867$	71.0596	2.41331
$868$	98.6037	3.34683
$869$	−18.7843	−0.637214
$870$	17.8949	0.606692
$871$	−19.7062	−0.667721
$872$	−28.2979	−0.958288
$873$	2.10092	0.0711053
$874$	150.393	5.08713
$875$	−18.9278	−0.639876
$876$	−38.5643	−1.30297
$877$	19.3889	0.654716	0.327358	−	0.944900i	$-0.393842\pi$
$877$	19.3889	0.654716	0.327358	+	0.944900i	$0.393842\pi$
$878$	−49.5300	−1.67156
$879$	−24.0489	−0.811149
$880$	9.76091	0.329040
$881$	11.0886	0.373585	0.186792	−	0.982399i	$-0.440191\pi$
$881$	11.0886	0.373585	0.186792	+	0.982399i	$0.440191\pi$
$882$	11.3387	0.381793
$883$	7.49814	0.252333	0.126166	−	0.992009i	$-0.459733\pi$
$883$	7.49814	0.252333	0.126166	+	0.992009i	$0.459733\pi$
$884$	−89.9815	−3.02641
$885$	−18.0494	−0.606723
$886$	−27.1641	−0.912594
$887$	4.72508	0.158653	0.0793263	−	0.996849i	$-0.474723\pi$
$887$	4.72508	0.158653	0.0793263	+	0.996849i	$0.474723\pi$
$888$	−112.727	−3.78287
$889$	−24.4514	−0.820075
$890$	3.80840	0.127658
$891$	27.7234	0.928767
$892$	29.3272	0.981948
$893$	−47.8209	−1.60027
$894$	−23.0279	−0.770168
$895$	−4.22125	−0.141101
$896$	−46.3601	−1.54878
$897$	69.6162	2.32442
$898$	−67.7938	−2.26231
$899$	−36.7298	−1.22501
$900$	−48.2318	−1.60773
$901$	−83.4810	−2.78116
$902$	−37.7838	−1.25806
$903$	−44.7765	−1.49007
$904$	−98.0935	−3.26254
$905$	11.2780	0.374894
$906$	−4.26029	−0.141539
$907$	−7.34147	−0.243770	−0.121885	−	0.992544i	$-0.538894\pi$
$907$	−7.34147	−0.243770	−0.121885	+	0.992544i	$0.538894\pi$
$908$	−66.0009	−2.19032
$909$	−17.7834	−0.589839
$910$	−16.7712	−0.555961
$911$	3.78017	0.125243	0.0626213	−	0.998037i	$-0.480054\pi$
$911$	3.78017	0.125243	0.0626213	+	0.998037i	$0.480054\pi$
$912$	−64.7786	−2.14503
$913$	−18.8871	−0.625073
$914$	−59.5502	−1.96974
$915$	−25.6198	−0.846966
$916$	−43.4417	−1.43535
$917$	−41.3104	−1.36419
$918$	−4.26486	−0.140761
$919$	18.2945	0.603480	0.301740	−	0.953390i	$-0.402433\pi$
$919$	18.2945	0.603480	0.301740	+	0.953390i	$0.402433\pi$
$920$	36.0255	1.18772
$921$	12.5112	0.412258
$922$	66.9431	2.20465
$923$	33.3144	1.09656
$924$	66.3581	2.18302
$925$	−41.1631	−1.35344
$926$	34.8418	1.14497
$927$	−9.46112	−0.310744
$928$	1.62593	0.0533737
$929$	−34.4125	−1.12904	−0.564518	−	0.825421i	$-0.690938\pi$
$929$	−34.4125	−1.12904	−0.564518	+	0.825421i	$0.690938\pi$
$930$	−56.2672	−1.84508
$931$	11.5624	0.378943
$932$	−109.847	−3.59815
$933$	83.4298	2.73137
$934$	34.9893	1.14488
$935$	−17.9144	−0.585863
$936$	−46.1122	−1.50722
$937$	−4.03906	−0.131950	−0.0659751	−	0.997821i	$-0.521016\pi$
$937$	−4.03906	−0.131950	−0.0659751	+	0.997821i	$0.521016\pi$
$938$	−33.3426	−1.08867
$939$	15.8605	0.517586
$940$	−23.2001	−0.756704
$941$	18.0112	0.587147	0.293574	−	0.955936i	$-0.405155\pi$
$941$	18.0112	0.587147	0.293574	+	0.955936i	$0.405155\pi$
$942$	−48.9775	−1.59577
$943$	−44.5267	−1.44999
$944$	31.1671	1.01440
$945$	−0.527740	−0.0171674
$946$	57.7076	1.87623
$947$	−43.1605	−1.40253	−0.701264	−	0.712902i	$-0.747380\pi$
$947$	−43.1605	−1.40253	−0.701264	+	0.712902i	$0.747380\pi$
$948$	60.4795	1.96428
$949$	−13.4632	−0.437034
$950$	−74.0826	−2.40356
$951$	−30.1077	−0.976310
$952$	−75.1723	−2.43635
$953$	31.2044	1.01081	0.505405	−	0.862882i	$-0.331343\pi$
$953$	31.2044	1.01081	0.505405	+	0.862882i	$0.331343\pi$
$954$	−86.6445	−2.80522
$955$	10.9121	0.353106
$956$	−98.4091	−3.18278
$957$	−24.7184	−0.799031
$958$	−65.0437	−2.10147
$959$	−19.2724	−0.622338
$960$	18.4006	0.593878
$961$	84.4904	2.72550
$962$	−79.7042	−2.56977
$963$	−7.00715	−0.225802
$964$	−15.0125	−0.483521
$965$	−1.30360	−0.0419643
$966$	117.789	3.78980
$967$	−11.3402	−0.364678	−0.182339	−	0.983236i	$-0.558367\pi$
$967$	−11.3402	−0.364678	−0.182339	+	0.983236i	$0.558367\pi$
$968$	10.1154	0.325122
$969$	118.889	3.81928
$970$	1.56554	0.0502664
$971$	−17.0792	−0.548098	−0.274049	−	0.961716i	$-0.588363\pi$
$971$	−17.0792	−0.548098	−0.274049	+	0.961716i	$0.588363\pi$
$972$	−86.2141	−2.76532
$973$	15.7914	0.506250
$974$	−3.85143	−0.123408
$975$	−34.2924	−1.09824
$976$	44.2396	1.41607
$977$	37.5366	1.20090	0.600452	−	0.799661i	$-0.294987\pi$
$977$	37.5366	1.20090	0.600452	+	0.799661i	$0.294987\pi$
$978$	−22.7651	−0.727947
$979$	−5.26059	−0.168129
$980$	5.60945	0.179187
$981$	17.2113	0.549516
$982$	33.3247	1.06343
$983$	−14.3420	−0.457439	−0.228719	−	0.973492i	$-0.573454\pi$
$983$	−14.3420	−0.457439	−0.228719	+	0.973492i	$0.573454\pi$
$984$	60.0658	1.91483
$985$	17.3390	0.552466
$986$	56.7119	1.80607
$987$	−37.4537	−1.19216
$988$	−95.2342	−3.02980
$989$	68.0060	2.16247
$990$	−18.5932	−0.590932
$991$	19.4673	0.618399	0.309199	−	0.950997i	$-0.399939\pi$
$991$	19.4673	0.618399	0.309199	+	0.950997i	$0.399939\pi$
$992$	−5.11244	−0.162320
$993$	69.2080	2.19625
$994$	56.3673	1.78786
$995$	−24.4692	−0.775724
$996$	60.8106	1.92686
$997$	45.5435	1.44238	0.721189	−	0.692738i	$-0.243596\pi$
$997$	45.5435	1.44238	0.721189	+	0.692738i	$0.243596\pi$
$998$	−95.4744	−3.02219
$999$	−2.50805	−0.0793512

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4021.2.a.c.1.16	✓	182

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4021.2.a.c.1.16	✓	182	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)

\(f(q)\)	\(=\)	\(q-2.43939 q^{2} +2.42778 q^{3} +3.95064 q^{4} -0.884079 q^{5} -5.92232 q^{6} -2.32249 q^{7} -4.75837 q^{8} +2.89413 q^{9} +O(q^{10})\)	\(q-2.43939 q^{2} +2.42778 q^{3} +3.95064 q^{4} -0.884079 q^{5} -5.92232 q^{6} -2.32249 q^{7} -4.75837 q^{8} +2.89413 q^{9} +2.15662 q^{10} -2.97896 q^{11} +9.59129 q^{12} +3.34842 q^{13} +5.66545 q^{14} -2.14635 q^{15} +3.70626 q^{16} -6.80216 q^{17} -7.05992 q^{18} -7.19923 q^{19} -3.49267 q^{20} -5.63849 q^{21} +7.26684 q^{22} +8.56369 q^{23} -11.5523 q^{24} -4.21840 q^{25} -8.16810 q^{26} -0.257026 q^{27} -9.17530 q^{28} +3.41779 q^{29} +5.23579 q^{30} -10.7466 q^{31} +0.475725 q^{32} -7.23226 q^{33} +16.5931 q^{34} +2.05326 q^{35} +11.4337 q^{36} +9.75798 q^{37} +17.5618 q^{38} +8.12923 q^{39} +4.20677 q^{40} -5.19947 q^{41} +13.7545 q^{42} +7.94121 q^{43} -11.7688 q^{44} -2.55864 q^{45} -20.8902 q^{46} +6.64250 q^{47} +8.99798 q^{48} -1.60606 q^{49} +10.2903 q^{50} -16.5142 q^{51} +13.2284 q^{52} +12.2727 q^{53} +0.626986 q^{54} +2.63363 q^{55} +11.0512 q^{56} -17.4782 q^{57} -8.33733 q^{58} +8.40932 q^{59} -8.47945 q^{60} +11.9365 q^{61} +26.2153 q^{62} -6.72158 q^{63} -8.57299 q^{64} -2.96026 q^{65} +17.6423 q^{66} -5.88524 q^{67} -26.8729 q^{68} +20.7908 q^{69} -5.00871 q^{70} +9.94930 q^{71} -13.7713 q^{72} -4.02077 q^{73} -23.8036 q^{74} -10.2414 q^{75} -28.4415 q^{76} +6.91858 q^{77} -19.8304 q^{78} +6.30567 q^{79} -3.27662 q^{80} -9.30640 q^{81} +12.6836 q^{82} +6.34019 q^{83} -22.2756 q^{84} +6.01364 q^{85} -19.3717 q^{86} +8.29766 q^{87} +14.1750 q^{88} +1.76592 q^{89} +6.24153 q^{90} -7.77665 q^{91} +33.8320 q^{92} -26.0905 q^{93} -16.2037 q^{94} +6.36469 q^{95} +1.15496 q^{96} +0.725924 q^{97} +3.91781 q^{98} -8.62149 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9}+O(q^{10}) \) 182 * q + 18 * q^2 + 28 * q^3 + 208 * q^4 + 22 * q^5 + 18 * q^6 + 14 * q^7 + 54 * q^8 + 238 * q^9	\( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9} + 7 q^{10} + 138 q^{11} + 47 q^{12} + 5 q^{13} + 72 q^{14} + 41 q^{15} + 256 q^{16} + 29 q^{17} + 35 q^{18} + 48 q^{19} + 56 q^{20} + 22 q^{21} + 19 q^{22} + 91 q^{23} + 46 q^{24} + 230 q^{25} + 88 q^{26} + 103 q^{27} + 15 q^{28} + 75 q^{29} + 18 q^{30} + 43 q^{31} + 116 q^{32} + 15 q^{33} + 13 q^{34} + 185 q^{35} + 364 q^{36} + 15 q^{37} + 53 q^{38} + 80 q^{39} - 13 q^{40} + 68 q^{41} + 32 q^{42} + 82 q^{43} + 259 q^{44} + 37 q^{45} + 13 q^{46} + 121 q^{47} + 53 q^{48} + 244 q^{49} + 93 q^{50} + 144 q^{51} - 16 q^{52} + 101 q^{53} + 47 q^{54} + 49 q^{55} + 199 q^{56} + 3 q^{57} + 4 q^{58} + 254 q^{59} + 24 q^{60} + 8 q^{61} + 37 q^{62} + 19 q^{63} + 326 q^{64} + 65 q^{65} + 41 q^{66} + 91 q^{67} + 50 q^{68} + 50 q^{69} + 5 q^{70} + 212 q^{71} + 77 q^{72} + 5 q^{73} + 101 q^{74} + 127 q^{75} + 22 q^{76} + 87 q^{77} - 20 q^{78} + 86 q^{79} + 71 q^{80} + 358 q^{81} - 20 q^{82} + 139 q^{83} - 30 q^{84} + 25 q^{85} + 82 q^{86} + 36 q^{87} - 8 q^{88} + 100 q^{89} - 87 q^{90} + 74 q^{91} + 171 q^{92} + 50 q^{93} - 13 q^{94} + 217 q^{95} + 42 q^{96} + 20 q^{97} + 47 q^{98} + 389 q^{99}+O(q^{100}) \) 182 * q + 18 * q^2 + 28 * q^3 + 208 * q^4 + 22 * q^5 + 18 * q^6 + 14 * q^7 + 54 * q^8 + 238 * q^9 + 7 * q^10 + 138 * q^11 + 47 * q^12 + 5 * q^13 + 72 * q^14 + 41 * q^15 + 256 * q^16 + 29 * q^17 + 35 * q^18 + 48 * q^19 + 56 * q^20 + 22 * q^21 + 19 * q^22 + 91 * q^23 + 46 * q^24 + 230 * q^25 + 88 * q^26 + 103 * q^27 + 15 * q^28 + 75 * q^29 + 18 * q^30 + 43 * q^31 + 116 * q^32 + 15 * q^33 + 13 * q^34 + 185 * q^35 + 364 * q^36 + 15 * q^37 + 53 * q^38 + 80 * q^39 - 13 * q^40 + 68 * q^41 + 32 * q^42 + 82 * q^43 + 259 * q^44 + 37 * q^45 + 13 * q^46 + 121 * q^47 + 53 * q^48 + 244 * q^49 + 93 * q^50 + 144 * q^51 - 16 * q^52 + 101 * q^53 + 47 * q^54 + 49 * q^55 + 199 * q^56 + 3 * q^57 + 4 * q^58 + 254 * q^59 + 24 * q^60 + 8 * q^61 + 37 * q^62 + 19 * q^63 + 326 * q^64 + 65 * q^65 + 41 * q^66 + 91 * q^67 + 50 * q^68 + 50 * q^69 + 5 * q^70 + 212 * q^71 + 77 * q^72 + 5 * q^73 + 101 * q^74 + 127 * q^75 + 22 * q^76 + 87 * q^77 - 20 * q^78 + 86 * q^79 + 71 * q^80 + 358 * q^81 - 20 * q^82 + 139 * q^83 - 30 * q^84 + 25 * q^85 + 82 * q^86 + 36 * q^87 - 8 * q^88 + 100 * q^89 - 87 * q^90 + 74 * q^91 + 171 * q^92 + 50 * q^93 - 13 * q^94 + 217 * q^95 + 42 * q^96 + 20 * q^97 + 47 * q^98 + 389 * q^99

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