LMFDB - Embedded newform 4021.2.a.c.1.18

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			1.18
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)

$f(q)$	$=$	$q-2.37596 q^{2} -0.498603 q^{3} +3.64520 q^{4} -0.0295149 q^{5} +1.18466 q^{6} +0.657526 q^{7} -3.90895 q^{8} -2.75139 q^{9} +O(q^{10})$	\(q-2.37596 q^{2} -0.498603 q^{3} +3.64520 q^{4} -0.0295149 q^{5} +1.18466 q^{6} +0.657526 q^{7} -3.90895 q^{8} -2.75139 q^{9} +0.0701264 q^{10} -4.45743 q^{11} -1.81751 q^{12} +0.156749 q^{13} -1.56226 q^{14} +0.0147162 q^{15} +1.99711 q^{16} +6.00344 q^{17} +6.53721 q^{18} -5.59795 q^{19} -0.107588 q^{20} -0.327845 q^{21} +10.5907 q^{22} -0.738501 q^{23} +1.94901 q^{24} -4.99913 q^{25} -0.372431 q^{26} +2.86766 q^{27} +2.39682 q^{28} -5.02270 q^{29} -0.0349652 q^{30} -1.90424 q^{31} +3.07284 q^{32} +2.22249 q^{33} -14.2640 q^{34} -0.0194068 q^{35} -10.0294 q^{36} -3.95606 q^{37} +13.3005 q^{38} -0.0781558 q^{39} +0.115372 q^{40} +0.419506 q^{41} +0.778947 q^{42} +2.02327 q^{43} -16.2482 q^{44} +0.0812072 q^{45} +1.75465 q^{46} -0.977061 q^{47} -0.995764 q^{48} -6.56766 q^{49} +11.8777 q^{50} -2.99333 q^{51} +0.571384 q^{52} +5.26118 q^{53} -6.81347 q^{54} +0.131561 q^{55} -2.57023 q^{56} +2.79116 q^{57} +11.9337 q^{58} -10.2966 q^{59} +0.0536437 q^{60} +10.0091 q^{61} +4.52442 q^{62} -1.80911 q^{63} -11.2952 q^{64} -0.00462644 q^{65} -5.28056 q^{66} -10.8505 q^{67} +21.8838 q^{68} +0.368219 q^{69} +0.0461099 q^{70} +1.58693 q^{71} +10.7551 q^{72} -7.04644 q^{73} +9.39945 q^{74} +2.49258 q^{75} -20.4057 q^{76} -2.93088 q^{77} +0.185695 q^{78} +13.9398 q^{79} -0.0589444 q^{80} +6.82436 q^{81} -0.996731 q^{82} +17.0742 q^{83} -1.19506 q^{84} -0.177191 q^{85} -4.80723 q^{86} +2.50433 q^{87} +17.4239 q^{88} -6.81812 q^{89} -0.192945 q^{90} +0.103067 q^{91} -2.69199 q^{92} +0.949463 q^{93} +2.32146 q^{94} +0.165223 q^{95} -1.53213 q^{96} -4.94802 q^{97} +15.6045 q^{98} +12.2642 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.37596	−1.68006	−0.840030	−	0.542540i	$-0.817463\pi$
$2$	−2.37596	−1.68006	−0.840030	+	0.542540i	$0.817463\pi$
$3$	−0.498603	−0.287869	−0.143934	−	0.989587i	$-0.545975\pi$
$3$	−0.498603	−0.287869	−0.143934	+	0.989587i	$0.545975\pi$
$4$	3.64520	1.82260
$5$	−0.0295149	−0.0131995	−0.00659973	−	0.999978i	$-0.502101\pi$
$5$	−0.0295149	−0.0131995	−0.00659973	+	0.999978i	$0.502101\pi$
$6$	1.18466	0.483637
$7$	0.657526	0.248521	0.124261	−	0.992250i	$-0.460344\pi$
$7$	0.657526	0.248521	0.124261	+	0.992250i	$0.460344\pi$
$8$	−3.90895	−1.38202
$9$	−2.75139	−0.917132
$10$	0.0701264	0.0221759
$11$	−4.45743	−1.34397	−0.671983	−	0.740566i	$-0.734557\pi$
$11$	−4.45743	−1.34397	−0.671983	+	0.740566i	$0.734557\pi$
$12$	−1.81751	−0.524670
$13$	0.156749	0.0434745	0.0217372	−	0.999764i	$-0.493080\pi$
$13$	0.156749	0.0434745	0.0217372	+	0.999764i	$0.493080\pi$
$14$	−1.56226	−0.417531
$15$	0.0147162	0.00379972
$16$	1.99711	0.499277
$17$	6.00344	1.45605	0.728024	−	0.685552i	$-0.240439\pi$
$17$	6.00344	1.45605	0.728024	+	0.685552i	$0.240439\pi$
$18$	6.53721	1.54084
$19$	−5.59795	−1.28426	−0.642129	−	0.766596i	$-0.721949\pi$
$19$	−5.59795	−1.28426	−0.642129	+	0.766596i	$0.721949\pi$
$20$	−0.107588	−0.0240574
$21$	−0.327845	−0.0715415
$22$	10.5907	2.25794
$23$	−0.738501	−0.153988	−0.0769941	−	0.997032i	$-0.524532\pi$
$23$	−0.738501	−0.153988	−0.0769941	+	0.997032i	$0.524532\pi$
$24$	1.94901	0.397841
$25$	−4.99913	−0.999826
$26$	−0.372431	−0.0730397
$27$	2.86766	0.551882
$28$	2.39682	0.452956
$29$	−5.02270	−0.932691	−0.466346	−	0.884603i	$-0.654430\pi$
$29$	−5.02270	−0.932691	−0.466346	+	0.884603i	$0.654430\pi$
$30$	−0.0349652	−0.00638375
$31$	−1.90424	−0.342012	−0.171006	−	0.985270i	$-0.554702\pi$
$31$	−1.90424	−0.342012	−0.171006	+	0.985270i	$0.554702\pi$
$32$	3.07284	0.543207
$33$	2.22249	0.386886
$34$	−14.2640	−2.44625
$35$	−0.0194068	−0.00328035
$36$	−10.0294	−1.67157
$37$	−3.95606	−0.650372	−0.325186	−	0.945650i	$-0.605427\pi$
$37$	−3.95606	−0.650372	−0.325186	+	0.945650i	$0.605427\pi$
$38$	13.3005	2.15763
$39$	−0.0781558	−0.0125149
$40$	0.115372	0.0182419
$41$	0.419506	0.0655158	0.0327579	−	0.999463i	$-0.489571\pi$
$41$	0.419506	0.0655158	0.0327579	+	0.999463i	$0.489571\pi$
$42$	0.778947	0.120194
$43$	2.02327	0.308546	0.154273	−	0.988028i	$-0.450696\pi$
$43$	2.02327	0.308546	0.154273	+	0.988028i	$0.450696\pi$
$44$	−16.2482	−2.44952
$45$	0.0812072	0.0121056
$46$	1.75465	0.258709
$47$	−0.977061	−0.142519	−0.0712595	−	0.997458i	$-0.522702\pi$
$47$	−0.977061	−0.142519	−0.0712595	+	0.997458i	$0.522702\pi$
$48$	−0.995764	−0.143726
$49$	−6.56766	−0.938237
$50$	11.8777	1.67977
$51$	−2.99333	−0.419151
$52$	0.571384	0.0792366
$53$	5.26118	0.722679	0.361340	−	0.932434i	$-0.382320\pi$
$53$	5.26118	0.722679	0.361340	+	0.932434i	$0.382320\pi$
$54$	−6.81347	−0.927196
$55$	0.131561	0.0177396
$56$	−2.57023	−0.343462
$57$	2.79116	0.369698
$58$	11.9337	1.56698
$59$	−10.2966	−1.34051	−0.670254	−	0.742131i	$-0.733815\pi$
$59$	−10.2966	−1.34051	−0.670254	+	0.742131i	$0.733815\pi$
$60$	0.0536437	0.00692537
$61$	10.0091	1.28154	0.640770	−	0.767733i	$-0.278615\pi$
$61$	10.0091	1.28154	0.640770	+	0.767733i	$0.278615\pi$
$62$	4.52442	0.574602
$63$	−1.80911	−0.227927
$64$	−11.2952	−1.41190
$65$	−0.00462644	−0.000573840 0
$66$	−5.28056	−0.649992
$67$	−10.8505	−1.32559	−0.662797	−	0.748799i	$-0.730631\pi$
$67$	−10.8505	−1.32559	−0.662797	+	0.748799i	$0.730631\pi$
$68$	21.8838	2.65380
$69$	0.368219	0.0443284
$70$	0.0461099	0.00551119
$71$	1.58693	0.188334	0.0941669	−	0.995556i	$-0.469981\pi$
$71$	1.58693	0.188334	0.0941669	+	0.995556i	$0.469981\pi$
$72$	10.7551	1.26750
$73$	−7.04644	−0.824724	−0.412362	−	0.911020i	$-0.635296\pi$
$73$	−7.04644	−0.824724	−0.412362	+	0.911020i	$0.635296\pi$
$74$	9.39945	1.09266
$75$	2.49258	0.287819
$76$	−20.4057	−2.34069
$77$	−2.93088	−0.334004
$78$	0.185695	0.0210259
$79$	13.9398	1.56835	0.784173	−	0.620542i	$-0.213087\pi$
$79$	13.9398	1.56835	0.784173	+	0.620542i	$0.213087\pi$
$80$	−0.0589444	−0.00659018
$81$	6.82436	0.758262
$82$	−0.996731	−0.110070
$83$	17.0742	1.87414	0.937068	−	0.349146i	$-0.113528\pi$
$83$	17.0742	1.87414	0.937068	+	0.349146i	$0.113528\pi$
$84$	−1.19506	−0.130392
$85$	−0.177191	−0.0192191
$86$	−4.80723	−0.518376
$87$	2.50433	0.268493
$88$	17.4239	1.85739
$89$	−6.81812	−0.722719	−0.361360	−	0.932426i	$-0.617687\pi$
$89$	−6.81812	−0.722719	−0.361360	+	0.932426i	$0.617687\pi$
$90$	−0.192945	−0.0203382
$91$	0.103067	0.0108043
$92$	−2.69199	−0.280659
$93$	0.949463	0.0984547
$94$	2.32146	0.239441
$95$	0.165223	0.0169515
$96$	−1.53213	−0.156372
$97$	−4.94802	−0.502395	−0.251198	−	0.967936i	$-0.580824\pi$
$97$	−4.94802	−0.502395	−0.251198	+	0.967936i	$0.580824\pi$
$98$	15.6045	1.57629
$99$	12.2642	1.23259
$100$	−18.2228	−1.82228
$101$	15.4652	1.53884	0.769421	−	0.638742i	$-0.220545\pi$
$101$	15.4652	1.53884	0.769421	+	0.638742i	$0.220545\pi$
$102$	7.11206	0.704198
$103$	19.8540	1.95627	0.978137	−	0.207962i	$-0.0666832\pi$
$103$	19.8540	1.95627	0.978137	+	0.207962i	$0.0666832\pi$
$104$	−0.612725	−0.0600826
$105$	0.00967630	0.000944310 0
$106$	−12.5004	−1.21414
$107$	12.0161	1.16164	0.580819	−	0.814033i	$-0.302732\pi$
$107$	12.0161	1.16164	0.580819	+	0.814033i	$0.302732\pi$
$108$	10.4532	1.00586
$109$	−19.6990	−1.88682	−0.943412	−	0.331624i	$-0.892404\pi$
$109$	−19.6990	−1.88682	−0.943412	+	0.331624i	$0.892404\pi$
$110$	−0.312583	−0.0298037
$111$	1.97250	0.187222
$112$	1.31315	0.124081
$113$	−8.21943	−0.773219	−0.386609	−	0.922244i	$-0.626354\pi$
$113$	−8.21943	−0.773219	−0.386609	+	0.922244i	$0.626354\pi$
$114$	−6.63169	−0.621115
$115$	0.0217968	0.00203256
$116$	−18.3088	−1.69992
$117$	−0.431279	−0.0398718
$118$	24.4645	2.25214
$119$	3.94742	0.361859
$120$	−0.0575250	−0.00525129
$121$	8.86870	0.806245
$122$	−23.7814	−2.15306
$123$	−0.209167	−0.0188600
$124$	−6.94136	−0.623353
$125$	0.295123	0.0263966
$126$	4.29839	0.382931
$127$	11.3325	1.00560	0.502800	−	0.864403i	$-0.332303\pi$
$127$	11.3325	1.00560	0.502800	+	0.864403i	$0.332303\pi$
$128$	20.6912	1.82886
$129$	−1.00881	−0.0888209
$130$	0.0109923	0.000964085 0
$131$	−4.91002	−0.428990	−0.214495	−	0.976725i	$-0.568811\pi$
$131$	−4.91002	−0.428990	−0.214495	+	0.976725i	$0.568811\pi$
$132$	8.10143	0.705139
$133$	−3.68080	−0.319166
$134$	25.7803	2.22708
$135$	−0.0846389	−0.00728455
$136$	−23.4671	−2.01229
$137$	−10.3214	−0.881815	−0.440907	−	0.897553i	$-0.645343\pi$
$137$	−10.3214	−0.881815	−0.440907	+	0.897553i	$0.645343\pi$
$138$	−0.874876	−0.0744744
$139$	−6.15448	−0.522016	−0.261008	−	0.965337i	$-0.584055\pi$
$139$	−6.15448	−0.522016	−0.261008	+	0.965337i	$0.584055\pi$
$140$	−0.0707418	−0.00597877
$141$	0.487166	0.0410268
$142$	−3.77048	−0.316412
$143$	−0.698700	−0.0584282
$144$	−5.49483	−0.457902
$145$	0.148244	0.0123110
$146$	16.7421	1.38559
$147$	3.27466	0.270089
$148$	−14.4206	−1.18537
$149$	13.8826	1.13731	0.568653	−	0.822577i	$-0.307465\pi$
$149$	13.8826	1.13731	0.568653	+	0.822577i	$0.307465\pi$
$150$	−5.92229	−0.483553
$151$	−6.94603	−0.565260	−0.282630	−	0.959229i	$-0.591207\pi$
$151$	−6.94603	−0.565260	−0.282630	+	0.959229i	$0.591207\pi$
$152$	21.8821	1.77487
$153$	−16.5178	−1.33539
$154$	6.96366	0.561147
$155$	0.0562036	0.00451438
$156$	−0.284894	−0.0228098
$157$	−5.32416	−0.424914	−0.212457	−	0.977170i	$-0.568147\pi$
$157$	−5.32416	−0.424914	−0.212457	+	0.977170i	$0.568147\pi$
$158$	−33.1204	−2.63492
$159$	−2.62324	−0.208037
$160$	−0.0906946	−0.00717004
$161$	−0.485584	−0.0382694
$162$	−16.2144	−1.27393
$163$	−4.38657	−0.343583	−0.171791	−	0.985133i	$-0.554956\pi$
$163$	−4.38657	−0.343583	−0.171791	+	0.985133i	$0.554956\pi$
$164$	1.52918	0.119409
$165$	−0.0655966	−0.00510669
$166$	−40.5677	−3.14866
$167$	−13.2836	−1.02792	−0.513959	−	0.857815i	$-0.671822\pi$
$167$	−13.2836	−1.02792	−0.513959	+	0.857815i	$0.671822\pi$
$168$	1.28153	0.0988719
$169$	−12.9754	−0.998110
$170$	0.420999	0.0322892
$171$	15.4022	1.17783
$172$	7.37525	0.562357
$173$	6.12214	0.465458	0.232729	−	0.972542i	$-0.425235\pi$
$173$	6.12214	0.465458	0.232729	+	0.972542i	$0.425235\pi$
$174$	−5.95020	−0.451084
$175$	−3.28706	−0.248478
$176$	−8.90196	−0.671011
$177$	5.13394	0.385891
$178$	16.1996	1.21421
$179$	16.5579	1.23760	0.618799	−	0.785549i	$-0.287619\pi$
$179$	16.5579	1.23760	0.618799	+	0.785549i	$0.287619\pi$
$180$	0.296017	0.0220638
$181$	−8.77442	−0.652198	−0.326099	−	0.945336i	$-0.605734\pi$
$181$	−8.77442	−0.652198	−0.326099	+	0.945336i	$0.605734\pi$
$182$	−0.244883	−0.0181519
$183$	−4.99059	−0.368915
$184$	2.88676	0.212815
$185$	0.116763	0.00858456
$186$	−2.25589	−0.165410
$187$	−26.7599	−1.95688
$188$	−3.56159	−0.259755
$189$	1.88556	0.137155
$190$	−0.392564	−0.0284796
$191$	7.64775	0.553372	0.276686	−	0.960960i	$-0.410764\pi$
$191$	7.64775	0.553372	0.276686	+	0.960960i	$0.410764\pi$
$192$	5.63181	0.406441
$193$	−25.2658	−1.81867	−0.909335	−	0.416065i	$-0.863409\pi$
$193$	−25.2658	−1.81867	−0.909335	+	0.416065i	$0.863409\pi$
$194$	11.7563	0.844055
$195$	0.00230676	0.000165191 0
$196$	−23.9405	−1.71003
$197$	16.5541	1.17943	0.589714	−	0.807612i	$-0.299241\pi$
$197$	16.5541	1.17943	0.589714	+	0.807612i	$0.299241\pi$
$198$	−29.1392	−2.07083
$199$	−0.685891	−0.0486216	−0.0243108	−	0.999704i	$-0.507739\pi$
$199$	−0.685891	−0.0486216	−0.0243108	+	0.999704i	$0.507739\pi$
$200$	19.5413	1.38178
$201$	5.41008	0.381597
$202$	−36.7447	−2.58535
$203$	−3.30255	−0.231794
$204$	−10.9113	−0.763945
$205$	−0.0123817	−0.000864774 0
$206$	−47.1724	−3.28666
$207$	2.03191	0.141227
$208$	0.313045	0.0217058
$209$	24.9525	1.72600
$210$	−0.0229905	−0.00158650
$211$	−6.83583	−0.470598	−0.235299	−	0.971923i	$-0.575607\pi$
$211$	−6.83583	−0.470598	−0.235299	+	0.971923i	$0.575607\pi$
$212$	19.1781	1.31716
$213$	−0.791248	−0.0542154
$214$	−28.5498	−1.95162
$215$	−0.0597167	−0.00407265
$216$	−11.2095	−0.762713
$217$	−1.25209	−0.0849974
$218$	46.8042	3.16998
$219$	3.51338	0.237412
$220$	0.479566	0.0323323
$221$	0.941035	0.0633009
$222$	−4.68660	−0.314544
$223$	12.8583	0.861053	0.430527	−	0.902578i	$-0.358328\pi$
$223$	12.8583	0.861053	0.430527	+	0.902578i	$0.358328\pi$
$224$	2.02047	0.134998
$225$	13.7546	0.916972
$226$	19.5291	1.29905
$227$	2.44971	0.162593	0.0812965	−	0.996690i	$-0.474094\pi$
$227$	2.44971	0.162593	0.0812965	+	0.996690i	$0.474094\pi$
$228$	10.1743	0.673812
$229$	−2.21029	−0.146060	−0.0730302	−	0.997330i	$-0.523267\pi$
$229$	−2.21029	−0.146060	−0.0730302	+	0.997330i	$0.523267\pi$
$230$	−0.0517884	−0.00341483
$231$	1.46134	0.0961494
$232$	19.6334	1.28900
$233$	−16.4282	−1.07625	−0.538123	−	0.842866i	$-0.680867\pi$
$233$	−16.4282	−1.07625	−0.538123	+	0.842866i	$0.680867\pi$
$234$	1.02470	0.0669870
$235$	0.0288379	0.00188118
$236$	−37.5334	−2.44321
$237$	−6.95042	−0.451478
$238$	−9.37892	−0.607945
$239$	5.30737	0.343305	0.171653	−	0.985158i	$-0.445089\pi$
$239$	5.30737	0.343305	0.171653	+	0.985158i	$0.445089\pi$
$240$	0.0293899	0.00189711
$241$	0.956378	0.0616057	0.0308029	−	0.999525i	$-0.490194\pi$
$241$	0.956378	0.0616057	0.0308029	+	0.999525i	$0.490194\pi$
$242$	−21.0717	−1.35454
$243$	−12.0056	−0.770162
$244$	36.4854	2.33574
$245$	0.193844	0.0123842
$246$	0.496973	0.0316859
$247$	−0.877476	−0.0558324
$248$	7.44359	0.472668
$249$	−8.51325	−0.539505
$250$	−0.701203	−0.0443479
$251$	27.6300	1.74399	0.871996	−	0.489514i	$-0.162826\pi$
$251$	27.6300	1.74399	0.871996	+	0.489514i	$0.162826\pi$
$252$	−6.59459	−0.415420
$253$	3.29182	0.206955
$254$	−26.9257	−1.68947
$255$	0.0883480	0.00553257
$256$	−26.5713	−1.66071
$257$	23.9213	1.49217	0.746084	−	0.665851i	$-0.231932\pi$
$257$	23.9213	1.49217	0.746084	+	0.665851i	$0.231932\pi$
$258$	2.39690	0.149224
$259$	−2.60121	−0.161631
$260$	−0.0168643	−0.00104588
$261$	13.8194	0.855400
$262$	11.6660	0.720729
$263$	−21.2230	−1.30867	−0.654335	−	0.756205i	$-0.727051\pi$
$263$	−21.2230	−1.30867	−0.654335	+	0.756205i	$0.727051\pi$
$264$	−8.68759	−0.534685
$265$	−0.155283	−0.00953898
$266$	8.74544	0.536218
$267$	3.39954	0.208048
$268$	−39.5522	−2.41603
$269$	−5.99684	−0.365634	−0.182817	−	0.983147i	$-0.558522\pi$
$269$	−5.99684	−0.365634	−0.182817	+	0.983147i	$0.558522\pi$
$270$	0.201099	0.0122385
$271$	12.1626	0.738827	0.369414	−	0.929265i	$-0.379559\pi$
$271$	12.1626	0.738827	0.369414	+	0.929265i	$0.379559\pi$
$272$	11.9895	0.726970
$273$	−0.0513894	−0.00311023
$274$	24.5232	1.48150
$275$	22.2833	1.34373
$276$	1.34223	0.0807930
$277$	−11.3457	−0.681696	−0.340848	−	0.940118i	$-0.610714\pi$
$277$	−11.3457	−0.681696	−0.340848	+	0.940118i	$0.610714\pi$
$278$	14.6228	0.877018
$279$	5.23933	0.313670
$280$	0.0758602	0.00453351
$281$	−10.2451	−0.611168	−0.305584	−	0.952165i	$-0.598852\pi$
$281$	−10.2451	−0.611168	−0.305584	+	0.952165i	$0.598852\pi$
$282$	−1.15749	−0.0689274
$283$	23.6453	1.40557	0.702783	−	0.711405i	$-0.251941\pi$
$283$	23.6453	1.40557	0.702783	+	0.711405i	$0.251941\pi$
$284$	5.78468	0.343258
$285$	−0.0823808	−0.00487982
$286$	1.66009	0.0981629
$287$	0.275836	0.0162821
$288$	−8.45460	−0.498192
$289$	19.0413	1.12008
$290$	−0.352223	−0.0206833
$291$	2.46710	0.144624
$292$	−25.6857	−1.50314
$293$	25.0921	1.46590	0.732948	−	0.680285i	$-0.238144\pi$
$293$	25.0921	1.46590	0.732948	+	0.680285i	$0.238144\pi$
$294$	−7.78047	−0.453766
$295$	0.303905	0.0176940
$296$	15.4640	0.898828
$297$	−12.7824	−0.741711
$298$	−32.9845	−1.91074
$299$	−0.115760	−0.00669455
$300$	9.08597	0.524579
$301$	1.33035	0.0766804
$302$	16.5035	0.949670
$303$	−7.71098	−0.442985
$304$	−11.1797	−0.641200
$305$	−0.295419	−0.0169156
$306$	39.2458	2.24353
$307$	28.1817	1.60842	0.804208	−	0.594348i	$-0.202590\pi$
$307$	28.1817	1.60842	0.804208	+	0.594348i	$0.202590\pi$
$308$	−10.6836	−0.608757
$309$	−9.89928	−0.563150
$310$	−0.133538	−0.00758444
$311$	−14.1401	−0.801809	−0.400904	−	0.916120i	$-0.631304\pi$
$311$	−14.1401	−0.801809	−0.400904	+	0.916120i	$0.631304\pi$
$312$	0.305507	0.0172959
$313$	6.30785	0.356541	0.178270	−	0.983982i	$-0.442950\pi$
$313$	6.30785	0.356541	0.178270	+	0.983982i	$0.442950\pi$
$314$	12.6500	0.713881
$315$	0.0533958	0.00300851
$316$	50.8133	2.85847
$317$	13.1028	0.735929	0.367965	−	0.929840i	$-0.380055\pi$
$317$	13.1028	0.735929	0.367965	+	0.929840i	$0.380055\pi$
$318$	6.23273	0.349514
$319$	22.3883	1.25351
$320$	0.333376	0.0186363
$321$	−5.99126	−0.334399
$322$	1.15373	0.0642948
$323$	−33.6070	−1.86994
$324$	24.8762	1.38201
$325$	−0.783610	−0.0434669
$326$	10.4223	0.577240
$327$	9.82200	0.543158
$328$	−1.63983	−0.0905442
$329$	−0.642443	−0.0354190
$330$	0.155855	0.00857954
$331$	−22.4703	−1.23508	−0.617539	−	0.786540i	$-0.711870\pi$
$331$	−22.4703	−1.23508	−0.617539	+	0.786540i	$0.711870\pi$
$332$	62.2389	3.41581
$333$	10.8847	0.596477
$334$	31.5614	1.72696
$335$	0.320250	0.0174971
$336$	−0.654740	−0.0357190
$337$	16.4788	0.897658	0.448829	−	0.893618i	$-0.351841\pi$
$337$	16.4788	0.897658	0.448829	+	0.893618i	$0.351841\pi$
$338$	30.8292	1.67688
$339$	4.09823	0.222586
$340$	−0.645897	−0.0350287
$341$	8.48804	0.459653
$342$	−36.5950	−1.97883
$343$	−8.92109	−0.481693
$344$	−7.90887	−0.426418
$345$	−0.0108680	−0.000585111 0
$346$	−14.5460	−0.781997
$347$	−8.65180	−0.464453	−0.232226	−	0.972662i	$-0.574601\pi$
$347$	−8.65180	−0.464453	−0.232226	+	0.972662i	$0.574601\pi$
$348$	9.12880	0.489355
$349$	28.0219	1.49998	0.749989	−	0.661450i	$-0.230059\pi$
$349$	28.0219	1.49998	0.749989	+	0.661450i	$0.230059\pi$
$350$	7.80993	0.417458
$351$	0.449505	0.0239928
$352$	−13.6970	−0.730051
$353$	−25.7662	−1.37140	−0.685698	−	0.727886i	$-0.740503\pi$
$353$	−25.7662	−1.37140	−0.685698	+	0.727886i	$0.740503\pi$
$354$	−12.1981	−0.648320
$355$	−0.0468380	−0.00248591
$356$	−24.8534	−1.31723
$357$	−1.96819	−0.104168
$358$	−39.3411	−2.07924
$359$	−3.74436	−0.197620	−0.0988100	−	0.995106i	$-0.531504\pi$
$359$	−3.74436	−0.197620	−0.0988100	+	0.995106i	$0.531504\pi$
$360$	−0.317434	−0.0167303
$361$	12.3371	0.649320
$362$	20.8477	1.09573
$363$	−4.42196	−0.232093
$364$	0.375699	0.0196920
$365$	0.207975	0.0108859
$366$	11.8575	0.619800
$367$	−33.8475	−1.76682	−0.883412	−	0.468598i	$-0.844759\pi$
$367$	−33.8475	−1.76682	−0.883412	+	0.468598i	$0.844759\pi$
$368$	−1.47487	−0.0768827
$369$	−1.15423	−0.0600866
$370$	−0.277424	−0.0144226
$371$	3.45936	0.179601
$372$	3.46099	0.179444
$373$	24.8199	1.28513	0.642563	−	0.766233i	$-0.277871\pi$
$373$	24.8199	1.28513	0.642563	+	0.766233i	$0.277871\pi$
$374$	63.5806	3.28767
$375$	−0.147150	−0.00759877
$376$	3.81928	0.196964
$377$	−0.787304	−0.0405482
$378$	−4.48003	−0.230428
$379$	28.2451	1.45085	0.725426	−	0.688301i	$-0.241643\pi$
$379$	28.2451	1.45085	0.725426	+	0.688301i	$0.241643\pi$
$380$	0.602272	0.0308959
$381$	−5.65044	−0.289481
$382$	−18.1708	−0.929698
$383$	−0.650955	−0.0332622	−0.0166311	−	0.999862i	$-0.505294\pi$
$383$	−0.650955	−0.0332622	−0.0166311	+	0.999862i	$0.505294\pi$
$384$	−10.3167	−0.526473
$385$	0.0865045	0.00440868
$386$	60.0305	3.05547
$387$	−5.56682	−0.282978
$388$	−18.0366	−0.915667
$389$	8.48432	0.430172	0.215086	−	0.976595i	$-0.430997\pi$
$389$	8.48432	0.430172	0.215086	+	0.976595i	$0.430997\pi$
$390$	−0.00548078	−0.000277530 0
$391$	−4.43355	−0.224214
$392$	25.6726	1.29666
$393$	2.44815	0.123493
$394$	−39.3318	−1.98151
$395$	−0.411431	−0.0207013
$396$	44.7053	2.24653
$397$	26.8928	1.34971	0.674856	−	0.737949i	$-0.264206\pi$
$397$	26.8928	1.34971	0.674856	+	0.737949i	$0.264206\pi$
$398$	1.62965	0.0816871
$399$	1.83526	0.0918778
$400$	−9.98379	−0.499190
$401$	25.1385	1.25536	0.627678	−	0.778473i	$-0.284006\pi$
$401$	25.1385	1.25536	0.627678	+	0.778473i	$0.284006\pi$
$402$	−12.8541	−0.641107
$403$	−0.298489	−0.0148688
$404$	56.3737	2.80470
$405$	−0.201420	−0.0100087
$406$	7.84674	0.389427
$407$	17.6339	0.874078
$408$	11.7008	0.579275
$409$	13.1694	0.651187	0.325594	−	0.945510i	$-0.394436\pi$
$409$	13.1694	0.651187	0.325594	+	0.945510i	$0.394436\pi$
$410$	0.0294184	0.00145287
$411$	5.14627	0.253847
$412$	72.3719	3.56551
$413$	−6.77031	−0.333145
$414$	−4.82774	−0.237271
$415$	−0.503943	−0.0247376
$416$	0.481666	0.0236156
$417$	3.06864	0.150272
$418$	−59.2862	−2.89978
$419$	−19.7758	−0.966113	−0.483056	−	0.875589i	$-0.660473\pi$
$419$	−19.7758	−0.966113	−0.483056	+	0.875589i	$0.660473\pi$
$420$	0.0352721	0.00172110
$421$	−27.4337	−1.33704	−0.668518	−	0.743696i	$-0.733071\pi$
$421$	−27.4337	−1.33704	−0.668518	+	0.743696i	$0.733071\pi$
$422$	16.2417	0.790633
$423$	2.68828	0.130709
$424$	−20.5657	−0.998758
$425$	−30.0120	−1.45579
$426$	1.87998	0.0910851
$427$	6.58127	0.318490
$428$	43.8010	2.11720
$429$	0.348374	0.0168197
$430$	0.141885	0.00684229
$431$	23.3969	1.12699	0.563494	−	0.826120i	$-0.309457\pi$
$431$	23.3969	1.12699	0.563494	+	0.826120i	$0.309457\pi$
$432$	5.72703	0.275542
$433$	8.47742	0.407399	0.203699	−	0.979033i	$-0.434703\pi$
$433$	8.47742	0.407399	0.203699	+	0.979033i	$0.434703\pi$
$434$	2.97492	0.142801
$435$	−0.0739152	−0.00354396
$436$	−71.8069	−3.43893
$437$	4.13410	0.197761
$438$	−8.34766	−0.398867
$439$	39.3458	1.87787	0.938937	−	0.344090i	$-0.111813\pi$
$439$	39.3458	1.87787	0.938937	+	0.344090i	$0.111813\pi$
$440$	−0.514264	−0.0245166
$441$	18.0702	0.860487
$442$	−2.23587	−0.106349
$443$	11.5949	0.550890	0.275445	−	0.961317i	$-0.411175\pi$
$443$	11.5949	0.550890	0.275445	+	0.961317i	$0.411175\pi$
$444$	7.19018	0.341231
$445$	0.201236	0.00953951
$446$	−30.5508	−1.44662
$447$	−6.92191	−0.327395
$448$	−7.42687	−0.350886
$449$	−0.159910	−0.00754661	−0.00377331	−	0.999993i	$-0.501201\pi$
$449$	−0.159910	−0.00754661	−0.00377331	+	0.999993i	$0.501201\pi$
$450$	−32.6804	−1.54057
$451$	−1.86992	−0.0880510
$452$	−29.9615	−1.40927
$453$	3.46331	0.162721
$454$	−5.82042	−0.273166
$455$	−0.00304201	−0.000142611 0
$456$	−10.9105	−0.510930
$457$	−14.0258	−0.656100	−0.328050	−	0.944660i	$-0.606391\pi$
$457$	−14.0258	−0.656100	−0.328050	+	0.944660i	$0.606391\pi$
$458$	5.25158	0.245390
$459$	17.2158	0.803567
$460$	0.0794538	0.00370455
$461$	28.6061	1.33232	0.666159	−	0.745810i	$-0.267937\pi$
$461$	28.6061	1.33232	0.666159	+	0.745810i	$0.267937\pi$
$462$	−3.47210	−0.161537
$463$	−1.97727	−0.0918914	−0.0459457	−	0.998944i	$-0.514630\pi$
$463$	−1.97727	−0.0918914	−0.0459457	+	0.998944i	$0.514630\pi$
$464$	−10.0309	−0.465671
$465$	−0.0280233	−0.00129955
$466$	39.0328	1.80816
$467$	−19.9870	−0.924890	−0.462445	−	0.886648i	$-0.653028\pi$
$467$	−19.9870	−0.924890	−0.462445	+	0.886648i	$0.653028\pi$
$468$	−1.57210	−0.0726704
$469$	−7.13446	−0.329439
$470$	−0.0685177	−0.00316049
$471$	2.65464	0.122320
$472$	40.2490	1.85261
$473$	−9.01860	−0.414676
$474$	16.5139	0.758510
$475$	27.9849	1.28403
$476$	14.3891	0.659525
$477$	−14.4756	−0.662792
$478$	−12.6101	−0.576773
$479$	20.5263	0.937871	0.468936	−	0.883232i	$-0.344638\pi$
$479$	20.5263	0.937871	0.468936	+	0.883232i	$0.344638\pi$
$480$	0.0452206	0.00206403
$481$	−0.620110	−0.0282746
$482$	−2.27232	−0.103501
$483$	0.242114	0.0110166
$484$	32.3282	1.46946
$485$	0.146040	0.00663135
$486$	28.5250	1.29392
$487$	27.4394	1.24340	0.621700	−	0.783255i	$-0.286442\pi$
$487$	27.4394	1.24340	0.621700	+	0.783255i	$0.286442\pi$
$488$	−39.1252	−1.77111
$489$	2.18716	0.0989068
$490$	−0.460566	−0.0208063
$491$	20.7433	0.936133	0.468066	−	0.883693i	$-0.344951\pi$
$491$	20.7433	0.936133	0.468066	+	0.883693i	$0.344951\pi$
$492$	−0.762457	−0.0343742
$493$	−30.1534	−1.35804
$494$	2.08485	0.0938019
$495$	−0.361975	−0.0162696
$496$	−3.80298	−0.170759
$497$	1.04345	0.0468050
$498$	20.2272	0.906402
$499$	17.1012	0.765553	0.382777	−	0.923841i	$-0.374968\pi$
$499$	17.1012	0.765553	0.382777	+	0.923841i	$0.374968\pi$
$500$	1.07579	0.0481106
$501$	6.62326	0.295906
$502$	−65.6479	−2.93001
$503$	20.8610	0.930145	0.465073	−	0.885273i	$-0.346028\pi$
$503$	20.8610	0.930145	0.465073	+	0.885273i	$0.346028\pi$
$504$	7.07172	0.315000
$505$	−0.456453	−0.0203119
$506$	−7.82124	−0.347697
$507$	6.46959	0.287325
$508$	41.3094	1.83281
$509$	21.3811	0.947700	0.473850	−	0.880606i	$-0.342864\pi$
$509$	21.3811	0.947700	0.473850	+	0.880606i	$0.342864\pi$
$510$	−0.209912	−0.00929504
$511$	−4.63322	−0.204961
$512$	21.7499	0.961221
$513$	−16.0531	−0.708760
$514$	−56.8361	−2.50693
$515$	−0.585989	−0.0258218
$516$	−3.67732	−0.161885
$517$	4.35518	0.191541
$518$	6.18038	0.271550
$519$	−3.05252	−0.133991
$520$	0.0180845	0.000793059 0
$521$	−24.0673	−1.05441	−0.527203	−	0.849739i	$-0.676759\pi$
$521$	−24.0673	−1.05441	−0.527203	+	0.849739i	$0.676759\pi$
$522$	−32.8344	−1.43712
$523$	14.2105	0.621383	0.310691	−	0.950511i	$-0.399439\pi$
$523$	14.2105	0.621383	0.310691	+	0.950511i	$0.399439\pi$
$524$	−17.8980	−0.781878
$525$	1.63894	0.0715291
$526$	50.4252	2.19864
$527$	−11.4320	−0.497987
$528$	4.43855	0.193163
$529$	−22.4546	−0.976288
$530$	0.368948	0.0160261
$531$	28.3301	1.22942
$532$	−13.4173	−0.581712
$533$	0.0657573	0.00284826
$534$	−8.07718	−0.349534
$535$	−0.354653	−0.0153330
$536$	42.4139	1.83200
$537$	−8.25584	−0.356266
$538$	14.2483	0.614286
$539$	29.2749	1.26096
$540$	−0.308526	−0.0132768
$541$	−12.1114	−0.520709	−0.260355	−	0.965513i	$-0.583840\pi$
$541$	−12.1114	−0.520709	−0.260355	+	0.965513i	$0.583840\pi$
$542$	−28.8980	−1.24127
$543$	4.37496	0.187747
$544$	18.4476	0.790935
$545$	0.581415	0.0249051
$546$	0.122099	0.00522537
$547$	−29.9125	−1.27897	−0.639483	−	0.768806i	$-0.720851\pi$
$547$	−29.9125	−1.27897	−0.639483	+	0.768806i	$0.720851\pi$
$548$	−37.6235	−1.60720
$549$	−27.5391	−1.17534
$550$	−52.9443	−2.25755
$551$	28.1168	1.19782
$552$	−1.43935	−0.0612628
$553$	9.16576	0.389768
$554$	26.9569	1.14529
$555$	−0.0582183	−0.00247123
$556$	−22.4343	−0.951428
$557$	27.1723	1.15133	0.575664	−	0.817686i	$-0.304743\pi$
$557$	27.1723	1.15133	0.575664	+	0.817686i	$0.304743\pi$
$558$	−12.4485	−0.526985
$559$	0.317147	0.0134139
$560$	−0.0387575	−0.00163780
$561$	13.3426	0.563324
$562$	24.3419	1.02680
$563$	44.9519	1.89450	0.947248	−	0.320501i	$-0.103851\pi$
$563$	44.9519	1.89450	0.947248	+	0.320501i	$0.103851\pi$
$564$	1.77582	0.0747755
$565$	0.242596	0.0102061
$566$	−56.1803	−2.36143
$567$	4.48719	0.188444
$568$	−6.20322	−0.260281
$569$	−33.1186	−1.38841	−0.694203	−	0.719780i	$-0.744243\pi$
$569$	−33.1186	−1.38841	−0.694203	+	0.719780i	$0.744243\pi$
$570$	0.195734	0.00819839
$571$	37.3184	1.56173	0.780863	−	0.624703i	$-0.214780\pi$
$571$	37.3184	1.56173	0.780863	+	0.624703i	$0.214780\pi$
$572$	−2.54690	−0.106491
$573$	−3.81319	−0.159298
$574$	−0.655376	−0.0273549
$575$	3.69186	0.153961
$576$	31.0775	1.29489
$577$	−16.3285	−0.679766	−0.339883	−	0.940468i	$-0.610387\pi$
$577$	−16.3285	−0.679766	−0.339883	+	0.940468i	$0.610387\pi$
$578$	−45.2414	−1.88179
$579$	12.5976	0.523538
$580$	0.540381	0.0224381
$581$	11.2267	0.465763
$582$	−5.86174	−0.242977
$583$	−23.4514	−0.971256
$584$	27.5442	1.13979
$585$	0.0127292	0.000526287 0
$586$	−59.6179	−2.46279
$587$	5.64687	0.233071	0.116536	−	0.993187i	$-0.462821\pi$
$587$	5.64687	0.233071	0.116536	+	0.993187i	$0.462821\pi$
$588$	11.9368	0.492265
$589$	10.6599	0.439232
$590$	−0.722066	−0.0297270
$591$	−8.25391	−0.339520
$592$	−7.90067	−0.324715
$593$	40.0781	1.64581	0.822905	−	0.568179i	$-0.192352\pi$
$593$	40.0781	1.64581	0.822905	+	0.568179i	$0.192352\pi$
$594$	30.3706	1.24612
$595$	−0.116508	−0.00477635
$596$	50.6049	2.07286
$597$	0.341988	0.0139966
$598$	0.275041	0.0112473
$599$	−33.2751	−1.35958	−0.679792	−	0.733405i	$-0.737930\pi$
$599$	−33.2751	−1.35958	−0.679792	+	0.733405i	$0.737930\pi$
$600$	−9.74337	−0.397771
$601$	23.8250	0.971844	0.485922	−	0.874002i	$-0.338484\pi$
$601$	23.8250	0.971844	0.485922	+	0.874002i	$0.338484\pi$
$602$	−3.16087	−0.128828
$603$	29.8539	1.21574
$604$	−25.3197	−1.03024
$605$	−0.261759	−0.0106420
$606$	18.3210	0.744241
$607$	−16.4592	−0.668059	−0.334029	−	0.942563i	$-0.608408\pi$
$607$	−16.4592	−0.668059	−0.334029	+	0.942563i	$0.608408\pi$
$608$	−17.2016	−0.697618
$609$	1.64666	0.0667262
$610$	0.701905	0.0284193
$611$	−0.153154	−0.00619594
$612$	−60.2109	−2.43388
$613$	−21.5048	−0.868570	−0.434285	−	0.900776i	$-0.642999\pi$
$613$	−21.5048	−0.868570	−0.434285	+	0.900776i	$0.642999\pi$
$614$	−66.9588	−2.70224
$615$	0.00617355	0.000248941 0
$616$	11.4566	0.461601
$617$	2.29292	0.0923094	0.0461547	−	0.998934i	$-0.485303\pi$
$617$	2.29292	0.0923094	0.0461547	+	0.998934i	$0.485303\pi$
$618$	23.5203	0.946126
$619$	−28.4893	−1.14508	−0.572541	−	0.819876i	$-0.694042\pi$
$619$	−28.4893	−1.14508	−0.572541	+	0.819876i	$0.694042\pi$
$620$	0.204874	0.00822792
$621$	−2.11777	−0.0849834
$622$	33.5963	1.34709
$623$	−4.48309	−0.179611
$624$	−0.156085	−0.00624842
$625$	24.9869	0.999477
$626$	−14.9872	−0.599010
$627$	−12.4414	−0.496862
$628$	−19.4076	−0.774450
$629$	−23.7499	−0.946972
$630$	−0.126867	−0.00505448
$631$	13.8016	0.549431	0.274716	−	0.961526i	$-0.411416\pi$
$631$	13.8016	0.549431	0.274716	+	0.961526i	$0.411416\pi$
$632$	−54.4898	−2.16749
$633$	3.40837	0.135470
$634$	−31.1319	−1.23641
$635$	−0.334479	−0.0132734
$636$	−9.56226	−0.379168
$637$	−1.02948	−0.0407894
$638$	−53.1938	−2.10596
$639$	−4.36627	−0.172727
$640$	−0.610700	−0.0241400
$641$	−6.33443	−0.250195	−0.125097	−	0.992144i	$-0.539924\pi$
$641$	−6.33443	−0.250195	−0.125097	+	0.992144i	$0.539924\pi$
$642$	14.2350	0.561811
$643$	31.6847	1.24952	0.624760	−	0.780817i	$-0.285197\pi$
$643$	31.6847	1.24952	0.624760	+	0.780817i	$0.285197\pi$
$644$	−1.77005	−0.0697498
$645$	0.0297750	0.00117239
$646$	79.8489	3.14161
$647$	32.0932	1.26171	0.630857	−	0.775899i	$-0.282704\pi$
$647$	32.0932	1.26171	0.630857	+	0.775899i	$0.282704\pi$
$648$	−26.6760	−1.04793
$649$	45.8966	1.80160
$650$	1.86183	0.0730270
$651$	0.624296	0.0244681
$652$	−15.9900	−0.626215
$653$	12.7554	0.499159	0.249580	−	0.968354i	$-0.419708\pi$
$653$	12.7554	0.499159	0.249580	+	0.968354i	$0.419708\pi$
$654$	−23.3367	−0.912537
$655$	0.144919	0.00566244
$656$	0.837798	0.0327105
$657$	19.3875	0.756380
$658$	1.52642	0.0595061
$659$	8.89963	0.346680	0.173340	−	0.984862i	$-0.444544\pi$
$659$	8.89963	0.346680	0.173340	+	0.984862i	$0.444544\pi$
$660$	−0.239113	−0.00930746
$661$	−5.63017	−0.218988	−0.109494	−	0.993987i	$-0.534923\pi$
$661$	−5.63017	−0.218988	−0.109494	+	0.993987i	$0.534923\pi$
$662$	53.3886	2.07501
$663$	−0.469203	−0.0182223
$664$	−66.7421	−2.59010
$665$	0.108638	0.00421282
$666$	−25.8616	−1.00212
$667$	3.70927	0.143623
$668$	−48.4216	−1.87349
$669$	−6.41118	−0.247870
$670$	−0.760903	−0.0293963
$671$	−44.6151	−1.72235
$672$	−1.00741	−0.0388618
$673$	−38.7553	−1.49391	−0.746954	−	0.664876i	$-0.768484\pi$
$673$	−38.7553	−1.49391	−0.746954	+	0.664876i	$0.768484\pi$
$674$	−39.1531	−1.50812
$675$	−14.3358	−0.551786
$676$	−47.2981	−1.81916
$677$	−20.0724	−0.771443	−0.385722	−	0.922615i	$-0.626047\pi$
$677$	−20.0724	−0.771443	−0.385722	+	0.922615i	$0.626047\pi$
$678$	−9.73726	−0.373957
$679$	−3.25345	−0.124856
$680$	0.692630	0.0265611
$681$	−1.22143	−0.0468055
$682$	−20.1673	−0.772245
$683$	−25.8564	−0.989367	−0.494683	−	0.869073i	$-0.664716\pi$
$683$	−25.8564	−0.989367	−0.494683	+	0.869073i	$0.664716\pi$
$684$	56.1441	2.14672
$685$	0.304635	0.0116395
$686$	21.1962	0.809274
$687$	1.10206	0.0420462
$688$	4.04069	0.154050
$689$	0.824687	0.0314181
$690$	0.0258219	0.000983022 0
$691$	46.0582	1.75214	0.876069	−	0.482186i	$-0.160157\pi$
$691$	46.0582	1.75214	0.876069	+	0.482186i	$0.160157\pi$
$692$	22.3165	0.848344
$693$	8.06400	0.306326
$694$	20.5564	0.780309
$695$	0.181649	0.00689033
$696$	−9.78930	−0.371063
$697$	2.51848	0.0953941
$698$	−66.5790	−2.52005
$699$	8.19115	0.309818
$700$	−11.9820	−0.452877
$701$	−1.31333	−0.0496037	−0.0248019	−	0.999692i	$-0.507895\pi$
$701$	−1.31333	−0.0496037	−0.0248019	+	0.999692i	$0.507895\pi$
$702$	−1.06801	−0.0403093
$703$	22.1458	0.835246
$704$	50.3474	1.89754
$705$	−0.0143787	−0.000541532 0
$706$	61.2196	2.30403
$707$	10.1687	0.382435
$708$	18.7143	0.703325
$709$	−28.8698	−1.08423	−0.542114	−	0.840305i	$-0.682376\pi$
$709$	−28.8698	−1.08423	−0.542114	+	0.840305i	$0.682376\pi$
$710$	0.111286	0.00417647
$711$	−38.3538	−1.43838
$712$	26.6517	0.998814
$713$	1.40629	0.0526659
$714$	4.67636	0.175008
$715$	0.0206221	0.000771221 0
$716$	60.3571	2.25565
$717$	−2.64627	−0.0988268
$718$	8.89647	0.332013
$719$	27.3764	1.02097	0.510483	−	0.859888i	$-0.329467\pi$
$719$	27.3764	1.02097	0.510483	+	0.859888i	$0.329467\pi$
$720$	0.162179	0.00604407
$721$	13.0545	0.486176
$722$	−29.3125	−1.09090
$723$	−0.476853	−0.0177344
$724$	−31.9846	−1.18870
$725$	25.1091	0.932529
$726$	10.5064	0.389930
$727$	31.7094	1.17604	0.588018	−	0.808848i	$-0.299909\pi$
$727$	31.7094	1.17604	0.588018	+	0.808848i	$0.299909\pi$
$728$	−0.402882	−0.0149318
$729$	−14.4870	−0.536556
$730$	−0.494141	−0.0182890
$731$	12.1466	0.449258
$732$	−18.1917	−0.672386
$733$	−15.0106	−0.554429	−0.277214	−	0.960808i	$-0.589411\pi$
$733$	−15.0106	−0.554429	−0.277214	+	0.960808i	$0.589411\pi$
$734$	80.4203	2.96837
$735$	−0.0966512	−0.00356503
$736$	−2.26930	−0.0836474
$737$	48.3652	1.78155
$738$	2.74240	0.100949
$739$	11.8917	0.437445	0.218723	−	0.975787i	$-0.429811\pi$
$739$	11.8917	0.437445	0.218723	+	0.975787i	$0.429811\pi$
$740$	0.425624	0.0156462
$741$	0.437512	0.0160724
$742$	−8.21932	−0.301741
$743$	−27.9983	−1.02716	−0.513579	−	0.858042i	$-0.671681\pi$
$743$	−27.9983	−1.02716	−0.513579	+	0.858042i	$0.671681\pi$
$744$	−3.71140	−0.136067
$745$	−0.409744	−0.0150118
$746$	−58.9712	−2.15909
$747$	−46.9779	−1.71883
$748$	−97.5454	−3.56661
$749$	7.90088	0.288692
$750$	0.349622	0.0127664
$751$	−9.68439	−0.353388	−0.176694	−	0.984266i	$-0.556540\pi$
$751$	−9.68439	−0.353388	−0.176694	+	0.984266i	$0.556540\pi$
$752$	−1.95129	−0.0711564
$753$	−13.7764	−0.502041
$754$	1.87061	0.0681235
$755$	0.205011	0.00746113
$756$	6.87326	0.249978
$757$	34.1001	1.23939	0.619695	−	0.784843i	$-0.287256\pi$
$757$	34.1001	1.23939	0.619695	+	0.784843i	$0.287256\pi$
$758$	−67.1092	−2.43752
$759$	−1.64131	−0.0595759
$760$	−0.645848	−0.0234274
$761$	−39.3124	−1.42507	−0.712536	−	0.701636i	$-0.752453\pi$
$761$	−39.3124	−1.42507	−0.712536	+	0.701636i	$0.752453\pi$
$762$	13.4252	0.486345
$763$	−12.9526	−0.468916
$764$	27.8776	1.00858
$765$	0.487522	0.0176264
$766$	1.54664	0.0558825
$767$	−1.61399	−0.0582779
$768$	13.2485	0.478065
$769$	28.9792	1.04502	0.522508	−	0.852634i	$-0.324996\pi$
$769$	28.9792	1.04502	0.522508	+	0.852634i	$0.324996\pi$
$770$	−0.205532	−0.00740685
$771$	−11.9272	−0.429549
$772$	−92.0989	−3.31471
$773$	51.0516	1.83620	0.918099	−	0.396351i	$-0.129724\pi$
$773$	51.0516	1.83620	0.918099	+	0.396351i	$0.129724\pi$
$774$	13.2266	0.475419
$775$	9.51957	0.341953
$776$	19.3416	0.694321
$777$	1.29697	0.0465286
$778$	−20.1584	−0.722715
$779$	−2.34837	−0.0841392
$780$	0.00840861	0.000301077 0
$781$	−7.07362	−0.253114
$782$	10.5339	0.376693
$783$	−14.4034	−0.514736
$784$	−13.1163	−0.468440
$785$	0.157142	0.00560864
$786$	−5.81672	−0.207475
$787$	−5.38902	−0.192098	−0.0960489	−	0.995377i	$-0.530621\pi$
$787$	−5.38902	−0.192098	−0.0960489	+	0.995377i	$0.530621\pi$
$788$	60.3429	2.14963
$789$	10.5819	0.376725
$790$	0.977545	0.0347795
$791$	−5.40449	−0.192161
$792$	−47.9399	−1.70347
$793$	1.56893	0.0557142
$794$	−63.8964	−2.26760
$795$	0.0774248	0.00274597
$796$	−2.50021	−0.0886178
$797$	−30.1130	−1.06666	−0.533328	−	0.845908i	$-0.679059\pi$
$797$	−30.1130	−1.06666	−0.533328	+	0.845908i	$0.679059\pi$
$798$	−4.36051	−0.154360
$799$	−5.86573	−0.207514
$800$	−15.3615	−0.543112
$801$	18.7593	0.662829
$802$	−59.7281	−2.10907
$803$	31.4090	1.10840
$804$	19.7208	0.695500
$805$	0.0143320	0.000505135 0
$806$	0.709200	0.0249805
$807$	2.99004	0.105254
$808$	−60.4525	−2.12671
$809$	−7.54548	−0.265285	−0.132643	−	0.991164i	$-0.542346\pi$
$809$	−7.54548	−0.265285	−0.132643	+	0.991164i	$0.542346\pi$
$810$	0.478567	0.0168151
$811$	−41.0168	−1.44030	−0.720148	−	0.693820i	$-0.755926\pi$
$811$	−41.0168	−1.44030	−0.720148	+	0.693820i	$0.755926\pi$
$812$	−12.0385	−0.422468
$813$	−6.06433	−0.212685
$814$	−41.8974	−1.46850
$815$	0.129469	0.00453511
$816$	−5.97801	−0.209272
$817$	−11.3262	−0.396253
$818$	−31.2901	−1.09403
$819$	−0.283577	−0.00990899
$820$	−0.0451337	−0.00157614
$821$	50.7456	1.77103	0.885516	−	0.464608i	$-0.153805\pi$
$821$	50.7456	1.77103	0.885516	+	0.464608i	$0.153805\pi$
$822$	−12.2274	−0.426478
$823$	28.6693	0.999349	0.499674	−	0.866213i	$-0.333453\pi$
$823$	28.6693	0.999349	0.499674	+	0.866213i	$0.333453\pi$
$824$	−77.6083	−2.70361
$825$	−11.1105	−0.386819
$826$	16.0860	0.559704
$827$	−41.5286	−1.44409	−0.722045	−	0.691846i	$-0.756798\pi$
$827$	−41.5286	−1.44409	−0.722045	+	0.691846i	$0.756798\pi$
$828$	7.40672	0.257401
$829$	44.0067	1.52842	0.764209	−	0.644969i	$-0.223130\pi$
$829$	44.0067	1.52842	0.764209	+	0.644969i	$0.223130\pi$
$830$	1.19735	0.0415607
$831$	5.65700	0.196239
$832$	−1.77051	−0.0613814
$833$	−39.4285	−1.36612
$834$	−7.29099	−0.252466
$835$	0.392065	0.0135680
$836$	90.9569	3.14581
$837$	−5.46074	−0.188751
$838$	46.9867	1.62313
$839$	32.1560	1.11015	0.555074	−	0.831801i	$-0.312690\pi$
$839$	32.1560	1.11015	0.555074	+	0.831801i	$0.312690\pi$
$840$	−0.0378241	−0.00130506
$841$	−3.77253	−0.130087
$842$	65.1814	2.24630
$843$	5.10822	0.175936
$844$	−24.9180	−0.857713
$845$	0.382969	0.0131745
$846$	−6.38726	−0.219598
$847$	5.83140	0.200369
$848$	10.5071	0.360817
$849$	−11.7896	−0.404618
$850$	71.3073	2.44582
$851$	2.92155	0.100150
$852$	−2.88426	−0.0988131
$853$	−21.7053	−0.743177	−0.371588	−	0.928398i	$-0.621187\pi$
$853$	−21.7053	−0.743177	−0.371588	+	0.928398i	$0.621187\pi$
$854$	−15.6369	−0.535082
$855$	−0.454594	−0.0155468
$856$	−46.9702	−1.60541
$857$	−32.4894	−1.10982	−0.554908	−	0.831912i	$-0.687246\pi$
$857$	−32.4894	−1.10982	−0.554908	+	0.831912i	$0.687246\pi$
$858$	−0.827724	−0.0282580
$859$	31.2671	1.06682	0.533410	−	0.845857i	$-0.320910\pi$
$859$	31.2671	1.06682	0.533410	+	0.845857i	$0.320910\pi$
$860$	−0.217680	−0.00742282
$861$	−0.137533	−0.00468710
$862$	−55.5902	−1.89341
$863$	20.0011	0.680844	0.340422	−	0.940273i	$-0.389430\pi$
$863$	20.0011	0.680844	0.340422	+	0.940273i	$0.389430\pi$
$864$	8.81188	0.299786
$865$	−0.180694	−0.00614380
$866$	−20.1420	−0.684454
$867$	−9.49404	−0.322435
$868$	−4.56412	−0.154916
$869$	−62.1356	−2.10780
$870$	0.175620	0.00595407
$871$	−1.70080	−0.0576295
$872$	77.0024	2.60763
$873$	13.6140	0.460763
$874$	−9.82246	−0.332250
$875$	0.194051	0.00656013
$876$	12.8070	0.432708
$877$	28.0725	0.947942	0.473971	−	0.880540i	$-0.342820\pi$
$877$	28.0725	0.947942	0.473971	+	0.880540i	$0.342820\pi$
$878$	−93.4842	−3.15494
$879$	−12.5110	−0.421986
$880$	0.262741	0.00885699
$881$	−5.54995	−0.186982	−0.0934912	−	0.995620i	$-0.529803\pi$
$881$	−5.54995	−0.186982	−0.0934912	+	0.995620i	$0.529803\pi$
$882$	−42.9342	−1.44567
$883$	−57.1603	−1.92360	−0.961798	−	0.273759i	$-0.911733\pi$
$883$	−57.1603	−1.92360	−0.961798	+	0.273759i	$0.911733\pi$
$884$	3.43027	0.115372
$885$	−0.151528	−0.00509355
$886$	−27.5491	−0.925529
$887$	−45.3908	−1.52407	−0.762037	−	0.647533i	$-0.775801\pi$
$887$	−45.3908	−1.52407	−0.762037	+	0.647533i	$0.775801\pi$
$888$	−7.71041	−0.258744
$889$	7.45144	0.249913
$890$	−0.478130	−0.0160270
$891$	−30.4191	−1.01908
$892$	46.8710	1.56936
$893$	5.46954	0.183031
$894$	16.4462	0.550043
$895$	−0.488706	−0.0163356
$896$	13.6050	0.454512
$897$	0.0577181	0.00192715
$898$	0.379940	0.0126788
$899$	9.56444	0.318992
$900$	50.1382	1.67127
$901$	31.5852	1.05226
$902$	4.44286	0.147931
$903$	−0.663319	−0.0220739
$904$	32.1293	1.06860
$905$	0.258976	0.00860866
$906$	−8.22870	−0.273380
$907$	−45.6812	−1.51682	−0.758410	−	0.651778i	$-0.774023\pi$
$907$	−45.6812	−1.51682	−0.758410	+	0.651778i	$0.774023\pi$
$908$	8.92970	0.296342
$909$	−42.5508	−1.41132
$910$	0.00722770	0.000239596 0
$911$	−17.1272	−0.567449	−0.283725	−	0.958906i	$-0.591570\pi$
$911$	−17.1272	−0.567449	−0.283725	+	0.958906i	$0.591570\pi$
$912$	5.57424	0.184581
$913$	−76.1071	−2.51878
$914$	33.3248	1.10229
$915$	0.147297	0.00486948
$916$	−8.05697	−0.266210
$917$	−3.22846	−0.106613
$918$	−40.9042	−1.35004
$919$	12.2483	0.404033	0.202017	−	0.979382i	$-0.435251\pi$
$919$	12.2483	0.404033	0.202017	+	0.979382i	$0.435251\pi$
$920$	−0.0852025	−0.00280904
$921$	−14.0515	−0.463013
$922$	−67.9670	−2.23837
$923$	0.248750	0.00818771
$924$	5.32690	0.175242
$925$	19.7768	0.650258
$926$	4.69791	0.154383
$927$	−54.6262	−1.79416
$928$	−15.4339	−0.506644
$929$	−53.0967	−1.74205	−0.871023	−	0.491242i	$-0.836543\pi$
$929$	−53.0967	−1.74205	−0.871023	+	0.491242i	$0.836543\pi$
$930$	0.0665824	0.00218332
$931$	36.7655	1.20494
$932$	−59.8841	−1.96157
$933$	7.05028	0.230816
$934$	47.4885	1.55387
$935$	0.789817	0.0258298
$936$	1.68585	0.0551037
$937$	28.0905	0.917676	0.458838	−	0.888520i	$-0.348266\pi$
$937$	28.0905	0.917676	0.458838	+	0.888520i	$0.348266\pi$
$938$	16.9512	0.553477
$939$	−3.14512	−0.102637
$940$	0.105120	0.00342863
$941$	23.8649	0.777974	0.388987	−	0.921243i	$-0.372825\pi$
$941$	23.8649	0.777974	0.388987	+	0.921243i	$0.372825\pi$
$942$	−6.30734	−0.205504
$943$	−0.309806	−0.0100887
$944$	−20.5635	−0.669285
$945$	−0.0556522	−0.00181037
$946$	21.4279	0.696680
$947$	−52.8970	−1.71892	−0.859461	−	0.511202i	$-0.829201\pi$
$947$	−52.8970	−1.71892	−0.859461	+	0.511202i	$0.829201\pi$
$948$	−25.3357	−0.822865
$949$	−1.10453	−0.0358544
$950$	−66.4911	−2.15726
$951$	−6.53312	−0.211851
$952$	−15.4302	−0.500097
$953$	−1.20916	−0.0391687	−0.0195843	−	0.999808i	$-0.506234\pi$
$953$	−1.20916	−0.0391687	−0.0195843	+	0.999808i	$0.506234\pi$
$954$	34.3935	1.11353
$955$	−0.225723	−0.00730422
$956$	19.3464	0.625708
$957$	−11.1629	−0.360845
$958$	−48.7698	−1.57568
$959$	−6.78657	−0.219150
$960$	−0.166222	−0.00536480
$961$	−27.3739	−0.883027
$962$	1.47336	0.0475030
$963$	−33.0610	−1.06537
$964$	3.48619	0.112283
$965$	0.745717	0.0240055
$966$	−0.575253	−0.0185085
$967$	−31.8829	−1.02529	−0.512643	−	0.858602i	$-0.671333\pi$
$967$	−31.8829	−1.02529	−0.512643	+	0.858602i	$0.671333\pi$
$968$	−34.6673	−1.11425
$969$	16.7565	0.538298
$970$	−0.346987	−0.0111411
$971$	29.3748	0.942682	0.471341	−	0.881951i	$-0.343770\pi$
$971$	29.3748	0.942682	0.471341	+	0.881951i	$0.343770\pi$
$972$	−43.7630	−1.40370
$973$	−4.04673	−0.129732
$974$	−65.1951	−2.08899
$975$	0.390711	0.0125128
$976$	19.9893	0.639843
$977$	20.2090	0.646542	0.323271	−	0.946306i	$-0.395218\pi$
$977$	20.2090	0.646542	0.323271	+	0.946306i	$0.395218\pi$
$978$	−5.19661	−0.166169
$979$	30.3913	0.971311
$980$	0.706601	0.0225715
$981$	54.1998	1.73047
$982$	−49.2854	−1.57276
$983$	16.6830	0.532107	0.266053	−	0.963958i	$-0.414280\pi$
$983$	16.6830	0.532107	0.266053	+	0.963958i	$0.414280\pi$
$984$	0.817623	0.0260649
$985$	−0.488592	−0.0155678
$986$	71.6435	2.28159
$987$	0.320324	0.0101960
$988$	−3.19858	−0.101760
$989$	−1.49419	−0.0475125
$990$	0.860040	0.0273339
$991$	−32.5006	−1.03242	−0.516209	−	0.856463i	$-0.672657\pi$
$991$	−32.5006	−1.03242	−0.516209	+	0.856463i	$0.672657\pi$
$992$	−5.85144	−0.185783
$993$	11.2038	0.355540
$994$	−2.47919	−0.0786352
$995$	0.0202440	0.000641779 0
$996$	−31.0325	−0.983304
$997$	3.52907	0.111767	0.0558833	−	0.998437i	$-0.482203\pi$
$997$	3.52907	0.111767	0.0558833	+	0.998437i	$0.482203\pi$
$998$	−40.6318	−1.28618
$999$	−11.3446	−0.358929

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4021.2.a.c.1.18	✓	182

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4021.2.a.c.1.18	✓	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)

\(f(q)\)	\(=\)	\(q-2.37596 q^{2} -0.498603 q^{3} +3.64520 q^{4} -0.0295149 q^{5} +1.18466 q^{6} +0.657526 q^{7} -3.90895 q^{8} -2.75139 q^{9} +O(q^{10})\)	\(q-2.37596 q^{2} -0.498603 q^{3} +3.64520 q^{4} -0.0295149 q^{5} +1.18466 q^{6} +0.657526 q^{7} -3.90895 q^{8} -2.75139 q^{9} +0.0701264 q^{10} -4.45743 q^{11} -1.81751 q^{12} +0.156749 q^{13} -1.56226 q^{14} +0.0147162 q^{15} +1.99711 q^{16} +6.00344 q^{17} +6.53721 q^{18} -5.59795 q^{19} -0.107588 q^{20} -0.327845 q^{21} +10.5907 q^{22} -0.738501 q^{23} +1.94901 q^{24} -4.99913 q^{25} -0.372431 q^{26} +2.86766 q^{27} +2.39682 q^{28} -5.02270 q^{29} -0.0349652 q^{30} -1.90424 q^{31} +3.07284 q^{32} +2.22249 q^{33} -14.2640 q^{34} -0.0194068 q^{35} -10.0294 q^{36} -3.95606 q^{37} +13.3005 q^{38} -0.0781558 q^{39} +0.115372 q^{40} +0.419506 q^{41} +0.778947 q^{42} +2.02327 q^{43} -16.2482 q^{44} +0.0812072 q^{45} +1.75465 q^{46} -0.977061 q^{47} -0.995764 q^{48} -6.56766 q^{49} +11.8777 q^{50} -2.99333 q^{51} +0.571384 q^{52} +5.26118 q^{53} -6.81347 q^{54} +0.131561 q^{55} -2.57023 q^{56} +2.79116 q^{57} +11.9337 q^{58} -10.2966 q^{59} +0.0536437 q^{60} +10.0091 q^{61} +4.52442 q^{62} -1.80911 q^{63} -11.2952 q^{64} -0.00462644 q^{65} -5.28056 q^{66} -10.8505 q^{67} +21.8838 q^{68} +0.368219 q^{69} +0.0461099 q^{70} +1.58693 q^{71} +10.7551 q^{72} -7.04644 q^{73} +9.39945 q^{74} +2.49258 q^{75} -20.4057 q^{76} -2.93088 q^{77} +0.185695 q^{78} +13.9398 q^{79} -0.0589444 q^{80} +6.82436 q^{81} -0.996731 q^{82} +17.0742 q^{83} -1.19506 q^{84} -0.177191 q^{85} -4.80723 q^{86} +2.50433 q^{87} +17.4239 q^{88} -6.81812 q^{89} -0.192945 q^{90} +0.103067 q^{91} -2.69199 q^{92} +0.949463 q^{93} +2.32146 q^{94} +0.165223 q^{95} -1.53213 q^{96} -4.94802 q^{97} +15.6045 q^{98} +12.2642 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9}+O(q^{10}) \) 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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