LMFDB - Embedded newform 4021.2.a.c.1.14

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			1.14
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)

$f(q)$	$=$	$q-2.51316 q^{2} +2.70275 q^{3} +4.31595 q^{4} +0.484778 q^{5} -6.79244 q^{6} +2.96790 q^{7} -5.82035 q^{8} +4.30486 q^{9} +O(q^{10})$	\(q-2.51316 q^{2} +2.70275 q^{3} +4.31595 q^{4} +0.484778 q^{5} -6.79244 q^{6} +2.96790 q^{7} -5.82035 q^{8} +4.30486 q^{9} -1.21832 q^{10} +3.13793 q^{11} +11.6650 q^{12} +4.52321 q^{13} -7.45881 q^{14} +1.31023 q^{15} +5.99555 q^{16} +3.62509 q^{17} -10.8188 q^{18} -1.37279 q^{19} +2.09228 q^{20} +8.02151 q^{21} -7.88611 q^{22} -4.23363 q^{23} -15.7310 q^{24} -4.76499 q^{25} -11.3675 q^{26} +3.52673 q^{27} +12.8093 q^{28} +6.76545 q^{29} -3.29282 q^{30} -0.0594343 q^{31} -3.42705 q^{32} +8.48104 q^{33} -9.11042 q^{34} +1.43878 q^{35} +18.5796 q^{36} +2.74582 q^{37} +3.45004 q^{38} +12.2251 q^{39} -2.82158 q^{40} +7.61675 q^{41} -20.1593 q^{42} -10.2127 q^{43} +13.5432 q^{44} +2.08690 q^{45} +10.6398 q^{46} +3.92142 q^{47} +16.2045 q^{48} +1.80846 q^{49} +11.9752 q^{50} +9.79772 q^{51} +19.5220 q^{52} +10.7523 q^{53} -8.86321 q^{54} +1.52120 q^{55} -17.2743 q^{56} -3.71031 q^{57} -17.0026 q^{58} -2.81911 q^{59} +5.65491 q^{60} -9.58142 q^{61} +0.149368 q^{62} +12.7764 q^{63} -3.37839 q^{64} +2.19275 q^{65} -21.3142 q^{66} -4.29092 q^{67} +15.6457 q^{68} -11.4424 q^{69} -3.61587 q^{70} -1.63004 q^{71} -25.0558 q^{72} -8.09746 q^{73} -6.90069 q^{74} -12.8786 q^{75} -5.92490 q^{76} +9.31308 q^{77} -30.7236 q^{78} +0.429789 q^{79} +2.90651 q^{80} -3.38273 q^{81} -19.1421 q^{82} +14.0976 q^{83} +34.6205 q^{84} +1.75736 q^{85} +25.6660 q^{86} +18.2853 q^{87} -18.2639 q^{88} +14.7254 q^{89} -5.24472 q^{90} +13.4245 q^{91} -18.2721 q^{92} -0.160636 q^{93} -9.85515 q^{94} -0.665499 q^{95} -9.26246 q^{96} -16.3011 q^{97} -4.54494 q^{98} +13.5084 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.51316	−1.77707	−0.888535	−	0.458809i	$-0.848276\pi$
$2$	−2.51316	−1.77707	−0.888535	+	0.458809i	$0.848276\pi$
$3$	2.70275	1.56043	0.780217	−	0.625509i	$-0.215109\pi$
$3$	2.70275	1.56043	0.780217	+	0.625509i	$0.215109\pi$
$4$	4.31595	2.15798
$5$	0.484778	0.216799	0.108400	−	0.994107i	$-0.465427\pi$
$5$	0.484778	0.216799	0.108400	+	0.994107i	$0.465427\pi$
$6$	−6.79244	−2.77300
$7$	2.96790	1.12176	0.560881	−	0.827896i	$-0.310462\pi$
$7$	2.96790	1.12176	0.560881	+	0.827896i	$0.310462\pi$
$8$	−5.82035	−2.05781
$9$	4.30486	1.43495
$10$	−1.21832	−0.385268
$11$	3.13793	0.946122	0.473061	−	0.881030i	$-0.343149\pi$
$11$	3.13793	0.946122	0.473061	+	0.881030i	$0.343149\pi$
$12$	11.6650	3.36738
$13$	4.52321	1.25451	0.627256	−	0.778813i	$-0.284178\pi$
$13$	4.52321	1.25451	0.627256	+	0.778813i	$0.284178\pi$
$14$	−7.45881	−1.99345
$15$	1.31023	0.338301
$16$	5.99555	1.49889
$17$	3.62509	0.879214	0.439607	−	0.898190i	$-0.355118\pi$
$17$	3.62509	0.879214	0.439607	+	0.898190i	$0.355118\pi$
$18$	−10.8188	−2.55002
$19$	−1.37279	−0.314940	−0.157470	−	0.987524i	$-0.550334\pi$
$19$	−1.37279	−0.314940	−0.157470	+	0.987524i	$0.550334\pi$
$20$	2.09228	0.467848
$21$	8.02151	1.75044
$22$	−7.88611	−1.68132
$23$	−4.23363	−0.882773	−0.441386	−	0.897317i	$-0.645513\pi$
$23$	−4.23363	−0.882773	−0.441386	+	0.897317i	$0.645513\pi$
$24$	−15.7310	−3.21107
$25$	−4.76499	−0.952998
$26$	−11.3675	−2.22936
$27$	3.52673	0.678719
$28$	12.8093	2.42074
$29$	6.76545	1.25631	0.628156	−	0.778087i	$-0.283810\pi$
$29$	6.76545	1.25631	0.628156	+	0.778087i	$0.283810\pi$
$30$	−3.29282	−0.601185
$31$	−0.0594343	−0.0106747	−0.00533736	−	0.999986i	$-0.501699\pi$
$31$	−0.0594343	−0.0106747	−0.00533736	+	0.999986i	$0.501699\pi$
$32$	−3.42705	−0.605823
$33$	8.48104	1.47636
$34$	−9.11042	−1.56242
$35$	1.43878	0.243197
$36$	18.5796	3.09660
$37$	2.74582	0.451411	0.225705	−	0.974196i	$-0.427531\pi$
$37$	2.74582	0.451411	0.225705	+	0.974196i	$0.427531\pi$
$38$	3.45004	0.559670
$39$	12.2251	1.95758
$40$	−2.82158	−0.446131
$41$	7.61675	1.18954	0.594769	−	0.803897i	$-0.297244\pi$
$41$	7.61675	1.18954	0.594769	+	0.803897i	$0.297244\pi$
$42$	−20.1593	−3.11065
$43$	−10.2127	−1.55741	−0.778707	−	0.627387i	$-0.784124\pi$
$43$	−10.2127	−1.55741	−0.778707	+	0.627387i	$0.784124\pi$
$44$	13.5432	2.04171
$45$	2.08690	0.311097
$46$	10.6398	1.56875
$47$	3.92142	0.571999	0.285999	−	0.958230i	$-0.407675\pi$
$47$	3.92142	0.571999	0.285999	+	0.958230i	$0.407675\pi$
$48$	16.2045	2.33892
$49$	1.80846	0.258351
$50$	11.9752	1.69354
$51$	9.79772	1.37195
$52$	19.5220	2.70721
$53$	10.7523	1.47694	0.738470	−	0.674287i	$-0.235549\pi$
$53$	10.7523	1.47694	0.738470	+	0.674287i	$0.235549\pi$
$54$	−8.86321	−1.20613
$55$	1.52120	0.205119
$56$	−17.2743	−2.30837
$57$	−3.71031	−0.491443
$58$	−17.0026	−2.23255
$59$	−2.81911	−0.367017	−0.183508	−	0.983018i	$-0.558745\pi$
$59$	−2.81911	−0.367017	−0.183508	+	0.983018i	$0.558745\pi$
$60$	5.65491	0.730046
$61$	−9.58142	−1.22677	−0.613387	−	0.789782i	$-0.710193\pi$
$61$	−9.58142	−1.22677	−0.613387	+	0.789782i	$0.710193\pi$
$62$	0.149368	0.0189697
$63$	12.7764	1.60968
$64$	−3.37839	−0.422299
$65$	2.19275	0.271977
$66$	−21.3142	−2.62360
$67$	−4.29092	−0.524219	−0.262109	−	0.965038i	$-0.584418\pi$
$67$	−4.29092	−0.524219	−0.262109	+	0.965038i	$0.584418\pi$
$68$	15.6457	1.89732
$69$	−11.4424	−1.37751
$70$	−3.61587	−0.432179
$71$	−1.63004	−0.193450	−0.0967252	−	0.995311i	$-0.530837\pi$
$71$	−1.63004	−0.193450	−0.0967252	+	0.995311i	$0.530837\pi$
$72$	−25.0558	−2.95286
$73$	−8.09746	−0.947736	−0.473868	−	0.880596i	$-0.657143\pi$
$73$	−8.09746	−0.947736	−0.473868	+	0.880596i	$0.657143\pi$
$74$	−6.90069	−0.802188
$75$	−12.8786	−1.48709
$76$	−5.92490	−0.679633
$77$	9.31308	1.06132
$78$	−30.7236	−3.47876
$79$	0.429789	0.0483550	0.0241775	−	0.999708i	$-0.492303\pi$
$79$	0.429789	0.0483550	0.0241775	+	0.999708i	$0.492303\pi$
$80$	2.90651	0.324958
$81$	−3.38273	−0.375859
$82$	−19.1421	−2.11389
$83$	14.0976	1.54742	0.773709	−	0.633542i	$-0.218399\pi$
$83$	14.0976	1.54742	0.773709	+	0.633542i	$0.218399\pi$
$84$	34.6205	3.77740
$85$	1.75736	0.190613
$86$	25.6660	2.76764
$87$	18.2853	1.96039
$88$	−18.2639	−1.94693
$89$	14.7254	1.56089	0.780445	−	0.625224i	$-0.214992\pi$
$89$	14.7254	1.56089	0.780445	+	0.625224i	$0.214992\pi$
$90$	−5.24472	−0.552842
$91$	13.4245	1.40726
$92$	−18.2721	−1.90500
$93$	−0.160636	−0.0166572
$94$	−9.85515	−1.01648
$95$	−0.665499	−0.0682787
$96$	−9.26246	−0.945346
$97$	−16.3011	−1.65513	−0.827564	−	0.561371i	$-0.810274\pi$
$97$	−16.3011	−1.65513	−0.827564	+	0.561371i	$0.810274\pi$
$98$	−4.54494	−0.459109
$99$	13.5084	1.35764
$100$	−20.5655	−2.05655
$101$	−11.0810	−1.10260	−0.551300	−	0.834307i	$-0.685868\pi$
$101$	−11.0810	−1.10260	−0.551300	+	0.834307i	$0.685868\pi$
$102$	−24.6232	−2.43806
$103$	4.21217	0.415037	0.207519	−	0.978231i	$-0.433461\pi$
$103$	4.21217	0.415037	0.207519	+	0.978231i	$0.433461\pi$
$104$	−26.3267	−2.58154
$105$	3.88865	0.379494
$106$	−27.0222	−2.62462
$107$	0.788823	0.0762583	0.0381292	−	0.999273i	$-0.487860\pi$
$107$	0.788823	0.0762583	0.0381292	+	0.999273i	$0.487860\pi$
$108$	15.2212	1.46466
$109$	−6.47396	−0.620093	−0.310046	−	0.950721i	$-0.600345\pi$
$109$	−6.47396	−0.620093	−0.310046	+	0.950721i	$0.600345\pi$
$110$	−3.82301	−0.364510
$111$	7.42128	0.704397
$112$	17.7942	1.68140
$113$	0.0690810	0.00649859	0.00324930	−	0.999995i	$-0.498966\pi$
$113$	0.0690810	0.00649859	0.00324930	+	0.999995i	$0.498966\pi$
$114$	9.32459	0.873328
$115$	−2.05237	−0.191385
$116$	29.1994	2.71109
$117$	19.4718	1.80017
$118$	7.08486	0.652214
$119$	10.7589	0.986269
$120$	−7.62603	−0.696158
$121$	−1.15339	−0.104854
$122$	24.0796	2.18006
$123$	20.5862	1.85619
$124$	−0.256516	−0.0230358
$125$	−4.73385	−0.423409
$126$	−32.1092	−2.86051
$127$	7.17065	0.636292	0.318146	−	0.948042i	$-0.396940\pi$
$127$	7.17065	0.636292	0.318146	+	0.948042i	$0.396940\pi$
$128$	15.3445	1.35628
$129$	−27.6023	−2.43024
$130$	−5.51073	−0.483323
$131$	−0.658129	−0.0575010	−0.0287505	−	0.999587i	$-0.509153\pi$
$131$	−0.658129	−0.0575010	−0.0287505	+	0.999587i	$0.509153\pi$
$132$	36.6038	3.18595
$133$	−4.07431	−0.353288
$134$	10.7837	0.931574
$135$	1.70968	0.147146
$136$	−21.0993	−1.80925
$137$	−13.7361	−1.17355	−0.586775	−	0.809750i	$-0.699603\pi$
$137$	−13.7361	−1.17355	−0.586775	+	0.809750i	$0.699603\pi$
$138$	28.7567	2.44793
$139$	−1.88453	−0.159844	−0.0799221	−	0.996801i	$-0.525467\pi$
$139$	−1.88453	−0.159844	−0.0799221	+	0.996801i	$0.525467\pi$
$140$	6.20969	0.524814
$141$	10.5986	0.892566
$142$	4.09655	0.343775
$143$	14.1935	1.18692
$144$	25.8100	2.15084
$145$	3.27974	0.272368
$146$	20.3502	1.68419
$147$	4.88782	0.403140
$148$	11.8509	0.974134
$149$	−12.1671	−0.996766	−0.498383	−	0.866957i	$-0.666073\pi$
$149$	−12.1671	−0.996766	−0.498383	+	0.866957i	$0.666073\pi$
$150$	32.3659	2.64266
$151$	20.4080	1.66078	0.830391	−	0.557181i	$-0.188117\pi$
$151$	20.4080	1.66078	0.830391	+	0.557181i	$0.188117\pi$
$152$	7.99013	0.648085
$153$	15.6055	1.26163
$154$	−23.4052	−1.88605
$155$	−0.0288124	−0.00231427
$156$	52.7630	4.22442
$157$	13.9029	1.10958	0.554788	−	0.831992i	$-0.312800\pi$
$157$	13.9029	1.10958	0.554788	+	0.831992i	$0.312800\pi$
$158$	−1.08013	−0.0859303
$159$	29.0607	2.30467
$160$	−1.66136	−0.131342
$161$	−12.5650	−0.990261
$162$	8.50134	0.667928
$163$	−10.0802	−0.789545	−0.394772	−	0.918779i	$-0.629177\pi$
$163$	−10.0802	−0.789545	−0.394772	+	0.918779i	$0.629177\pi$
$164$	32.8736	2.56699
$165$	4.11142	0.320074
$166$	−35.4296	−2.74987
$167$	−16.3025	−1.26152	−0.630762	−	0.775976i	$-0.717258\pi$
$167$	−16.3025	−1.26152	−0.630762	+	0.775976i	$0.717258\pi$
$168$	−46.6880	−3.60206
$169$	7.45941	0.573801
$170$	−4.41653	−0.338732
$171$	−5.90968	−0.451924
$172$	−44.0773	−3.36087
$173$	−11.8880	−0.903831	−0.451916	−	0.892061i	$-0.649259\pi$
$173$	−11.8880	−0.903831	−0.451916	+	0.892061i	$0.649259\pi$
$174$	−45.9539	−3.48375
$175$	−14.1420	−1.06904
$176$	18.8136	1.41813
$177$	−7.61935	−0.572706
$178$	−37.0073	−2.77381
$179$	1.97542	0.147650	0.0738249	−	0.997271i	$-0.476479\pi$
$179$	1.97542	0.147650	0.0738249	+	0.997271i	$0.476479\pi$
$180$	9.00698	0.671341
$181$	12.7156	0.945145	0.472573	−	0.881292i	$-0.343325\pi$
$181$	12.7156	0.945145	0.472573	+	0.881292i	$0.343325\pi$
$182$	−33.7377	−2.50081
$183$	−25.8962	−1.91430
$184$	24.6412	1.81657
$185$	1.33112	0.0978656
$186$	0.403704	0.0296010
$187$	11.3753	0.831843
$188$	16.9247	1.23436
$189$	10.4670	0.761361
$190$	1.67250	0.121336
$191$	−13.7488	−0.994827	−0.497414	−	0.867513i	$-0.665717\pi$
$191$	−13.7488	−0.994827	−0.497414	+	0.867513i	$0.665717\pi$
$192$	−9.13096	−0.658970
$193$	4.29631	0.309255	0.154627	−	0.987973i	$-0.450582\pi$
$193$	4.29631	0.309255	0.154627	+	0.987973i	$0.450582\pi$
$194$	40.9673	2.94128
$195$	5.92646	0.424403
$196$	7.80523	0.557516
$197$	−21.6056	−1.53934	−0.769668	−	0.638444i	$-0.779578\pi$
$197$	−21.6056	−1.53934	−0.769668	+	0.638444i	$0.779578\pi$
$198$	−33.9486	−2.41262
$199$	0.833060	0.0590541	0.0295270	−	0.999564i	$-0.490600\pi$
$199$	0.833060	0.0590541	0.0295270	+	0.999564i	$0.490600\pi$
$200$	27.7339	1.96109
$201$	−11.5973	−0.818009
$202$	27.8483	1.95940
$203$	20.0792	1.40928
$204$	42.2865	2.96065
$205$	3.69244	0.257891
$206$	−10.5858	−0.737551
$207$	−18.2252	−1.26674
$208$	27.1191	1.88037
$209$	−4.30772	−0.297971
$210$	−9.77279	−0.674387
$211$	16.2090	1.11587	0.557936	−	0.829884i	$-0.311593\pi$
$211$	16.2090	1.11587	0.557936	+	0.829884i	$0.311593\pi$
$212$	46.4064	3.18720
$213$	−4.40560	−0.301867
$214$	−1.98243	−0.135516
$215$	−4.95087	−0.337647
$216$	−20.5268	−1.39667
$217$	−0.176395	−0.0119745
$218$	16.2701	1.10195
$219$	−21.8854	−1.47888
$220$	6.56543	0.442641
$221$	16.3970	1.10298
$222$	−18.6508	−1.25176
$223$	14.8511	0.994504	0.497252	−	0.867606i	$-0.334342\pi$
$223$	14.8511	0.994504	0.497252	+	0.867606i	$0.334342\pi$
$224$	−10.1712	−0.679589
$225$	−20.5126	−1.36751
$226$	−0.173611	−0.0115485
$227$	8.28055	0.549599	0.274800	−	0.961502i	$-0.411388\pi$
$227$	8.28055	0.549599	0.274800	+	0.961502i	$0.411388\pi$
$228$	−16.0135	−1.06052
$229$	0.00577772	0.000381803 0	0.000190901	−	1.00000i	$-0.499939\pi$
$229$	0.00577772	0.000381803 0	0.000190901		1.00000i	$0.499939\pi$
$230$	5.15793	0.340104
$231$	25.1709	1.65613
$232$	−39.3773	−2.58525
$233$	7.91680	0.518647	0.259323	−	0.965791i	$-0.416500\pi$
$233$	7.91680	0.518647	0.259323	+	0.965791i	$0.416500\pi$
$234$	−48.9357	−3.19902
$235$	1.90102	0.124009
$236$	−12.1671	−0.792014
$237$	1.16161	0.0754548
$238$	−27.0389	−1.75267
$239$	−12.6538	−0.818504	−0.409252	−	0.912421i	$-0.634210\pi$
$239$	−12.6538	−0.818504	−0.409252	+	0.912421i	$0.634210\pi$
$240$	7.85558	0.507075
$241$	−4.54700	−0.292898	−0.146449	−	0.989218i	$-0.546784\pi$
$241$	−4.54700	−0.292898	−0.146449	+	0.989218i	$0.546784\pi$
$242$	2.89866	0.186333
$243$	−19.7229	−1.26522
$244$	−41.3529	−2.64735
$245$	0.876702	0.0560104
$246$	−51.7363	−3.29859
$247$	−6.20942	−0.395096
$248$	0.345929	0.0219665
$249$	38.1024	2.41464
$250$	11.8969	0.752427
$251$	−30.7528	−1.94110	−0.970551	−	0.240895i	$-0.922559\pi$
$251$	−30.7528	−1.94110	−0.970551	+	0.240895i	$0.922559\pi$
$252$	55.1425	3.47365
$253$	−13.2848	−0.835210
$254$	−18.0210	−1.13074
$255$	4.74972	0.297439
$256$	−31.8064	−1.98790
$257$	−13.3152	−0.830577	−0.415288	−	0.909690i	$-0.636319\pi$
$257$	−13.3152	−0.830577	−0.415288	+	0.909690i	$0.636319\pi$
$258$	69.3688	4.31871
$259$	8.14935	0.506376
$260$	9.46382	0.586921
$261$	29.1243	1.80275
$262$	1.65398	0.102183
$263$	4.16468	0.256805	0.128403	−	0.991722i	$-0.459015\pi$
$263$	4.16468	0.256805	0.128403	+	0.991722i	$0.459015\pi$
$264$	−49.3627	−3.03806
$265$	5.21247	0.320199
$266$	10.2394	0.627817
$267$	39.7991	2.43567
$268$	−18.5194	−1.13125
$269$	14.3388	0.874254	0.437127	−	0.899400i	$-0.355996\pi$
$269$	14.3388	0.874254	0.437127	+	0.899400i	$0.355996\pi$
$270$	−4.29669	−0.261488
$271$	−24.7220	−1.50175	−0.750877	−	0.660442i	$-0.770369\pi$
$271$	−24.7220	−1.50175	−0.750877	+	0.660442i	$0.770369\pi$
$272$	21.7344	1.31784
$273$	36.2830	2.19594
$274$	34.5209	2.08548
$275$	−14.9522	−0.901652
$276$	−49.3851	−2.97263
$277$	−4.42113	−0.265640	−0.132820	−	0.991140i	$-0.542403\pi$
$277$	−4.42113	−0.265640	−0.132820	+	0.991140i	$0.542403\pi$
$278$	4.73613	0.284054
$279$	−0.255857	−0.0153177
$280$	−8.37418	−0.500453
$281$	−18.3091	−1.09223	−0.546115	−	0.837710i	$-0.683894\pi$
$281$	−18.3091	−1.09223	−0.546115	+	0.837710i	$0.683894\pi$
$282$	−26.6360	−1.58615
$283$	26.9138	1.59986	0.799929	−	0.600095i	$-0.204870\pi$
$283$	26.9138	1.59986	0.799929	+	0.600095i	$0.204870\pi$
$284$	−7.03518	−0.417461
$285$	−1.79868	−0.106544
$286$	−35.6705	−2.10924
$287$	22.6058	1.33438
$288$	−14.7530	−0.869328
$289$	−3.85872	−0.226984
$290$	−8.24250	−0.484016
$291$	−44.0579	−2.58272
$292$	−34.9483	−2.04519
$293$	−15.2067	−0.888387	−0.444194	−	0.895931i	$-0.646510\pi$
$293$	−15.2067	−0.888387	−0.444194	+	0.895931i	$0.646510\pi$
$294$	−12.2839	−0.716409
$295$	−1.36664	−0.0795690
$296$	−15.9817	−0.928916
$297$	11.0666	0.642150
$298$	30.5778	1.77132
$299$	−19.1496	−1.10745
$300$	−55.5834	−3.20911
$301$	−30.3102	−1.74705
$302$	−51.2886	−2.95133
$303$	−29.9492	−1.72053
$304$	−8.23064	−0.472060
$305$	−4.64486	−0.265964
$306$	−39.2191	−2.24201
$307$	−18.0340	−1.02925	−0.514627	−	0.857414i	$-0.672070\pi$
$307$	−18.0340	−1.02925	−0.514627	+	0.857414i	$0.672070\pi$
$308$	40.1948	2.29031
$309$	11.3844	0.647639
$310$	0.0724102	0.00411262
$311$	12.6542	0.717556	0.358778	−	0.933423i	$-0.383193\pi$
$311$	12.6542	0.717556	0.358778	+	0.933423i	$0.383193\pi$
$312$	−71.1544	−4.02833
$313$	16.8262	0.951073	0.475537	−	0.879696i	$-0.342254\pi$
$313$	16.8262	0.951073	0.475537	+	0.879696i	$0.342254\pi$
$314$	−34.9403	−1.97179
$315$	6.19373	0.348977
$316$	1.85495	0.104349
$317$	33.9970	1.90946	0.954730	−	0.297474i	$-0.0961440\pi$
$317$	33.9970	1.90946	0.954730	+	0.297474i	$0.0961440\pi$
$318$	−73.0342	−4.09555
$319$	21.2295	1.18862
$320$	−1.63777	−0.0915542
$321$	2.13199	0.118996
$322$	31.5778	1.75976
$323$	−4.97649	−0.276899
$324$	−14.5997	−0.811095
$325$	−21.5530	−1.19555
$326$	25.3332	1.40308
$327$	−17.4975	−0.967614
$328$	−44.3322	−2.44784
$329$	11.6384	0.641647
$330$	−10.3327	−0.568794
$331$	−14.3154	−0.786843	−0.393422	−	0.919358i	$-0.628709\pi$
$331$	−14.3154	−0.786843	−0.393422	+	0.919358i	$0.628709\pi$
$332$	60.8448	3.33929
$333$	11.8204	0.647754
$334$	40.9707	2.24182
$335$	−2.08014	−0.113650
$336$	48.0934	2.62371
$337$	−19.6286	−1.06924	−0.534619	−	0.845093i	$-0.679545\pi$
$337$	−19.6286	−1.06924	−0.534619	+	0.845093i	$0.679545\pi$
$338$	−18.7467	−1.01968
$339$	0.186709	0.0101406
$340$	7.58470	0.411338
$341$	−0.186501	−0.0100996
$342$	14.8519	0.803101
$343$	−15.4080	−0.831954
$344$	59.4413	3.20486
$345$	−5.54705	−0.298643
$346$	29.8765	1.60617
$347$	−9.29048	−0.498739	−0.249370	−	0.968408i	$-0.580223\pi$
$347$	−9.29048	−0.498739	−0.249370	+	0.968408i	$0.580223\pi$
$348$	78.9186	4.23048
$349$	−11.1560	−0.597168	−0.298584	−	0.954383i	$-0.596514\pi$
$349$	−11.1560	−0.597168	−0.298584	+	0.954383i	$0.596514\pi$
$350$	35.5412	1.89975
$351$	15.9521	0.851461
$352$	−10.7538	−0.573182
$353$	−22.6827	−1.20728	−0.603640	−	0.797257i	$-0.706283\pi$
$353$	−22.6827	−1.20728	−0.603640	+	0.797257i	$0.706283\pi$
$354$	19.1486	1.01774
$355$	−0.790208	−0.0419399
$356$	63.5542	3.36837
$357$	29.0787	1.53901
$358$	−4.96454	−0.262384
$359$	1.50439	0.0793985	0.0396992	−	0.999212i	$-0.487360\pi$
$359$	1.50439	0.0793985	0.0396992	+	0.999212i	$0.487360\pi$
$360$	−12.1465	−0.640178
$361$	−17.1154	−0.900813
$362$	−31.9564	−1.67959
$363$	−3.11734	−0.163618
$364$	57.9393	3.03685
$365$	−3.92547	−0.205469
$366$	65.0812	3.40185
$367$	27.2566	1.42278	0.711391	−	0.702797i	$-0.248066\pi$
$367$	27.2566	1.42278	0.711391	+	0.702797i	$0.248066\pi$
$368$	−25.3829	−1.32318
$369$	32.7891	1.70693
$370$	−3.34530	−0.173914
$371$	31.9117	1.65678
$372$	−0.693298	−0.0359458
$373$	−6.15028	−0.318449	−0.159225	−	0.987242i	$-0.550899\pi$
$373$	−6.15028	−0.318449	−0.159225	+	0.987242i	$0.550899\pi$
$374$	−28.5879	−1.47824
$375$	−12.7944	−0.660701
$376$	−22.8241	−1.17706
$377$	30.6015	1.57606
$378$	−26.3052	−1.35299
$379$	37.8658	1.94504	0.972518	−	0.232829i	$-0.0747981\pi$
$379$	37.8658	1.94504	0.972518	+	0.232829i	$0.0747981\pi$
$380$	−2.87226	−0.147344
$381$	19.3805	0.992892
$382$	34.5529	1.76788
$383$	−8.60332	−0.439609	−0.219805	−	0.975544i	$-0.570542\pi$
$383$	−8.60332	−0.439609	−0.219805	+	0.975544i	$0.570542\pi$
$384$	41.4724	2.11638
$385$	4.51478	0.230094
$386$	−10.7973	−0.549568
$387$	−43.9641	−2.23482
$388$	−70.3549	−3.57173
$389$	11.5494	0.585575	0.292788	−	0.956177i	$-0.405417\pi$
$389$	11.5494	0.585575	0.292788	+	0.956177i	$0.405417\pi$
$390$	−14.8941	−0.754193
$391$	−15.3473	−0.776146
$392$	−10.5259	−0.531637
$393$	−1.77876	−0.0897265
$394$	54.2983	2.73551
$395$	0.208352	0.0104833
$396$	58.3015	2.92976
$397$	9.91542	0.497640	0.248820	−	0.968550i	$-0.419957\pi$
$397$	9.91542	0.497640	0.248820	+	0.968550i	$0.419957\pi$
$398$	−2.09361	−0.104943
$399$	−11.0119	−0.551282
$400$	−28.5687	−1.42844
$401$	22.6094	1.12906	0.564530	−	0.825413i	$-0.309057\pi$
$401$	22.6094	1.12906	0.564530	+	0.825413i	$0.309057\pi$
$402$	29.1458	1.45366
$403$	−0.268834	−0.0133916
$404$	−47.8250	−2.37939
$405$	−1.63987	−0.0814860
$406$	−50.4622	−2.50440
$407$	8.61621	0.427089
$408$	−57.0262	−2.82322
$409$	−7.89175	−0.390222	−0.195111	−	0.980781i	$-0.562507\pi$
$409$	−7.89175	−0.390222	−0.195111	+	0.980781i	$0.562507\pi$
$410$	−9.27967	−0.458290
$411$	−37.1252	−1.83125
$412$	18.1795	0.895641
$413$	−8.36685	−0.411706
$414$	45.8028	2.25108
$415$	6.83423	0.335479
$416$	−15.5013	−0.760012
$417$	−5.09343	−0.249426
$418$	10.8260	0.529516
$419$	17.5606	0.857890	0.428945	−	0.903331i	$-0.358885\pi$
$419$	17.5606	0.857890	0.428945	+	0.903331i	$0.358885\pi$
$420$	16.7832	0.818938
$421$	−38.4077	−1.87188	−0.935938	−	0.352164i	$-0.885446\pi$
$421$	−38.4077	−1.87188	−0.935938	+	0.352164i	$0.885446\pi$
$422$	−40.7357	−1.98298
$423$	16.8812	0.820792
$424$	−62.5821	−3.03925
$425$	−17.2735	−0.837889
$426$	11.0720	0.536438
$427$	−28.4367	−1.37615
$428$	3.40452	0.164564
$429$	38.3615	1.85211
$430$	12.4423	0.600021
$431$	3.07944	0.148332	0.0741658	−	0.997246i	$-0.476371\pi$
$431$	3.07944	0.148332	0.0741658	+	0.997246i	$0.476371\pi$
$432$	21.1447	1.01732
$433$	−0.886168	−0.0425865	−0.0212933	−	0.999773i	$-0.506778\pi$
$433$	−0.886168	−0.0425865	−0.0212933	+	0.999773i	$0.506778\pi$
$434$	0.443309	0.0212795
$435$	8.86432	0.425012
$436$	−27.9413	−1.33815
$437$	5.81189	0.278020
$438$	55.0015	2.62807
$439$	−6.16130	−0.294063	−0.147031	−	0.989132i	$-0.546972\pi$
$439$	−6.16130	−0.294063	−0.147031	+	0.989132i	$0.546972\pi$
$440$	−8.85392	−0.422094
$441$	7.78518	0.370723
$442$	−41.2083	−1.96008
$443$	22.0175	1.04608	0.523041	−	0.852308i	$-0.324798\pi$
$443$	22.0175	1.04608	0.523041	+	0.852308i	$0.324798\pi$
$444$	32.0299	1.52007
$445$	7.13856	0.338400
$446$	−37.3232	−1.76730
$447$	−32.8846	−1.55539
$448$	−10.0267	−0.473719
$449$	17.2638	0.814731	0.407366	−	0.913265i	$-0.366447\pi$
$449$	17.2638	0.814731	0.407366	+	0.913265i	$0.366447\pi$
$450$	51.5515	2.43016
$451$	23.9008	1.12545
$452$	0.298150	0.0140238
$453$	55.1578	2.59154
$454$	−20.8103	−0.976676
$455$	6.50788	0.305094
$456$	21.5953	1.01129
$457$	39.2914	1.83797	0.918987	−	0.394288i	$-0.129009\pi$
$457$	39.2914	1.83797	0.918987	+	0.394288i	$0.129009\pi$
$458$	−0.0145203	−0.000678490 0
$459$	12.7847	0.596739
$460$	−8.85794	−0.413003
$461$	2.94723	0.137266	0.0686331	−	0.997642i	$-0.478136\pi$
$461$	2.94723	0.137266	0.0686331	+	0.997642i	$0.478136\pi$
$462$	−63.2585	−2.94305
$463$	−14.7814	−0.686950	−0.343475	−	0.939162i	$-0.611604\pi$
$463$	−14.7814	−0.686950	−0.343475	+	0.939162i	$0.611604\pi$
$464$	40.5626	1.88307
$465$	−0.0778729	−0.00361127
$466$	−19.8961	−0.921671
$467$	42.3501	1.95973	0.979864	−	0.199667i	$-0.0639860\pi$
$467$	42.3501	1.95973	0.979864	+	0.199667i	$0.0639860\pi$
$468$	84.0394	3.88472
$469$	−12.7350	−0.588049
$470$	−4.77756	−0.220372
$471$	37.5762	1.73142
$472$	16.4082	0.755249
$473$	−32.0466	−1.47350
$474$	−2.91931	−0.134089
$475$	6.54134	0.300137
$476$	46.4350	2.12835
$477$	46.2871	2.11934
$478$	31.8009	1.45454
$479$	−22.1200	−1.01069	−0.505344	−	0.862918i	$-0.668634\pi$
$479$	−22.1200	−1.01069	−0.505344	+	0.862918i	$0.668634\pi$
$480$	−4.49024	−0.204950
$481$	12.4199	0.566300
$482$	11.4273	0.520501
$483$	−33.9601	−1.54524
$484$	−4.97800	−0.226273
$485$	−7.90243	−0.358831
$486$	49.5666	2.24839
$487$	32.4192	1.46905	0.734527	−	0.678579i	$-0.237404\pi$
$487$	32.4192	1.46905	0.734527	+	0.678579i	$0.237404\pi$
$488$	55.7672	2.52446
$489$	−27.2444	−1.23203
$490$	−2.20329	−0.0995344
$491$	21.8562	0.986356	0.493178	−	0.869928i	$-0.335835\pi$
$491$	21.8562	0.986356	0.493178	+	0.869928i	$0.335835\pi$
$492$	88.8491	4.00563
$493$	24.5254	1.10457
$494$	15.6052	0.702113
$495$	6.54856	0.294336
$496$	−0.356341	−0.0160002
$497$	−4.83781	−0.217005
$498$	−95.7573	−4.29099
$499$	2.37873	0.106487	0.0532433	−	0.998582i	$-0.483044\pi$
$499$	2.37873	0.106487	0.0532433	+	0.998582i	$0.483044\pi$
$500$	−20.4311	−0.913706
$501$	−44.0616	−1.96852
$502$	77.2867	3.44947
$503$	29.3348	1.30797	0.653986	−	0.756506i	$-0.273095\pi$
$503$	29.3348	1.30797	0.653986	+	0.756506i	$0.273095\pi$
$504$	−74.3634	−3.31241
$505$	−5.37182	−0.239043
$506$	33.3869	1.48423
$507$	20.1609	0.895378
$508$	30.9482	1.37310
$509$	10.8082	0.479065	0.239532	−	0.970888i	$-0.423006\pi$
$509$	10.8082	0.479065	0.239532	+	0.970888i	$0.423006\pi$
$510$	−11.9368	−0.528570
$511$	−24.0325	−1.06313
$512$	49.2454	2.17636
$513$	−4.84146	−0.213756
$514$	33.4631	1.47599
$515$	2.04197	0.0899798
$516$	−119.130	−5.24441
$517$	12.3052	0.541180
$518$	−20.4806	−0.899865
$519$	−32.1304	−1.41037
$520$	−12.7626	−0.559677
$521$	43.5919	1.90980	0.954898	−	0.296934i	$-0.0959642\pi$
$521$	43.5919	1.90980	0.954898	+	0.296934i	$0.0959642\pi$
$522$	−73.1940	−3.20361
$523$	−12.9319	−0.565472	−0.282736	−	0.959198i	$-0.591242\pi$
$523$	−12.9319	−0.565472	−0.282736	+	0.959198i	$0.591242\pi$
$524$	−2.84045	−0.124086
$525$	−38.2224	−1.66816
$526$	−10.4665	−0.456361
$527$	−0.215455	−0.00938535
$528$	50.8485	2.21290
$529$	−5.07639	−0.220713
$530$	−13.0998	−0.569017
$531$	−12.1359	−0.526653
$532$	−17.5845	−0.762387
$533$	34.4522	1.49229
$534$	−100.021	−4.32835
$535$	0.382404	0.0165328
$536$	24.9747	1.07874
$537$	5.33907	0.230398
$538$	−36.0357	−1.55361
$539$	5.67482	0.244432
$540$	7.37890	0.317537
$541$	21.3104	0.916204	0.458102	−	0.888900i	$-0.348530\pi$
$541$	21.3104	0.916204	0.458102	+	0.888900i	$0.348530\pi$
$542$	62.1302	2.66872
$543$	34.3672	1.47484
$544$	−12.4234	−0.532647
$545$	−3.13843	−0.134436
$546$	−91.1847	−3.90235
$547$	10.9206	0.466932	0.233466	−	0.972365i	$-0.424993\pi$
$547$	10.9206	0.466932	0.233466	+	0.972365i	$0.424993\pi$
$548$	−59.2842	−2.53250
$549$	−41.2467	−1.76037
$550$	37.5772	1.60230
$551$	−9.28754	−0.395663
$552$	66.5991	2.83465
$553$	1.27557	0.0542429
$554$	11.1110	0.472060
$555$	3.59767	0.152713
$556$	−8.13356	−0.344940
$557$	−15.7760	−0.668450	−0.334225	−	0.942493i	$-0.608475\pi$
$557$	−15.7760	−0.668450	−0.334225	+	0.942493i	$0.608475\pi$
$558$	0.643008	0.0272207
$559$	−46.1939	−1.95380
$560$	8.62625	0.364526
$561$	30.7446	1.29804
$562$	46.0137	1.94097
$563$	−44.3071	−1.86732	−0.933660	−	0.358160i	$-0.883404\pi$
$563$	−44.3071	−1.86732	−0.933660	+	0.358160i	$0.883404\pi$
$564$	45.7432	1.92614
$565$	0.0334889	0.00140889
$566$	−67.6385	−2.84306
$567$	−10.0396	−0.421625
$568$	9.48742	0.398083
$569$	13.2734	0.556450	0.278225	−	0.960516i	$-0.410254\pi$
$569$	13.2734	0.556450	0.278225	+	0.960516i	$0.410254\pi$
$570$	4.52036	0.189337
$571$	41.0484	1.71782	0.858911	−	0.512124i	$-0.171141\pi$
$571$	41.0484	1.71782	0.858911	+	0.512124i	$0.171141\pi$
$572$	61.2585	2.56135
$573$	−37.1596	−1.55236
$574$	−56.8119	−2.37128
$575$	20.1732	0.841281
$576$	−14.5435	−0.605980
$577$	−5.60979	−0.233539	−0.116769	−	0.993159i	$-0.537254\pi$
$577$	−5.60979	−0.233539	−0.116769	+	0.993159i	$0.537254\pi$
$578$	9.69757	0.403366
$579$	11.6118	0.482572
$580$	14.1552	0.587763
$581$	41.8405	1.73583
$582$	110.724	4.58967
$583$	33.7399	1.39736
$584$	47.1301	1.95026
$585$	9.43950	0.390275
$586$	38.2169	1.57873
$587$	−8.26898	−0.341297	−0.170649	−	0.985332i	$-0.554586\pi$
$587$	−8.26898	−0.341297	−0.170649	+	0.985332i	$0.554586\pi$
$588$	21.0956	0.869968
$589$	0.0815909	0.00336189
$590$	3.43459	0.141400
$591$	−58.3946	−2.40203
$592$	16.4627	0.676614
$593$	−2.72469	−0.111890	−0.0559449	−	0.998434i	$-0.517817\pi$
$593$	−2.72469	−0.111890	−0.0559449	+	0.998434i	$0.517817\pi$
$594$	−27.8121	−1.14115
$595$	5.21569	0.213822
$596$	−52.5126	−2.15100
$597$	2.25155	0.0921500
$598$	48.1259	1.96801
$599$	−47.0132	−1.92091	−0.960453	−	0.278441i	$-0.910182\pi$
$599$	−47.0132	−1.92091	−0.960453	+	0.278441i	$0.910182\pi$
$600$	74.9579	3.06014
$601$	−14.2921	−0.582988	−0.291494	−	0.956573i	$-0.594152\pi$
$601$	−14.2921	−0.582988	−0.291494	+	0.956573i	$0.594152\pi$
$602$	76.1742	3.10463
$603$	−18.4718	−0.752231
$604$	88.0801	3.58393
$605$	−0.559140	−0.0227323
$606$	75.2669	3.05751
$607$	19.9601	0.810157	0.405078	−	0.914282i	$-0.367244\pi$
$607$	19.9601	0.810157	0.405078	+	0.914282i	$0.367244\pi$
$608$	4.70462	0.190798
$609$	54.2691	2.19909
$610$	11.6733	0.472636
$611$	17.7374	0.717579
$612$	67.3527	2.72257
$613$	−44.9660	−1.81616	−0.908079	−	0.418799i	$-0.862451\pi$
$613$	−44.9660	−1.81616	−0.908079	+	0.418799i	$0.862451\pi$
$614$	45.3223	1.82906
$615$	9.97973	0.402422
$616$	−54.2054	−2.18400
$617$	−19.4898	−0.784632	−0.392316	−	0.919831i	$-0.628326\pi$
$617$	−19.4898	−0.784632	−0.392316	+	0.919831i	$0.628326\pi$
$618$	−28.6109	−1.15090
$619$	22.8871	0.919912	0.459956	−	0.887942i	$-0.347865\pi$
$619$	22.8871	0.919912	0.459956	+	0.887942i	$0.347865\pi$
$620$	−0.124353	−0.00499414
$621$	−14.9308	−0.599154
$622$	−31.8021	−1.27515
$623$	43.7036	1.75095
$624$	73.2963	2.93420
$625$	21.5301	0.861203
$626$	−42.2869	−1.69012
$627$	−11.6427	−0.464965
$628$	60.0044	2.39444
$629$	9.95386	0.396886
$630$	−15.5658	−0.620157
$631$	22.3756	0.890757	0.445378	−	0.895342i	$-0.353069\pi$
$631$	22.3756	0.890757	0.445378	+	0.895342i	$0.353069\pi$
$632$	−2.50152	−0.0995053
$633$	43.8089	1.74125
$634$	−85.4397	−3.39324
$635$	3.47617	0.137948
$636$	125.425	4.97342
$637$	8.18004	0.324105
$638$	−53.3530	−2.11227
$639$	−7.01711	−0.277593
$640$	7.43869	0.294040
$641$	21.5004	0.849216	0.424608	−	0.905377i	$-0.360412\pi$
$641$	21.5004	0.849216	0.424608	+	0.905377i	$0.360412\pi$
$642$	−5.35803	−0.211464
$643$	0.741143	0.0292278	0.0146139	−	0.999893i	$-0.495348\pi$
$643$	0.741143	0.0292278	0.0146139	+	0.999893i	$0.495348\pi$
$644$	−54.2300	−2.13696
$645$	−13.3810	−0.526875
$646$	12.5067	0.492069
$647$	12.0396	0.473326	0.236663	−	0.971592i	$-0.423946\pi$
$647$	12.0396	0.473326	0.236663	+	0.971592i	$0.423946\pi$
$648$	19.6887	0.773445
$649$	−8.84617	−0.347242
$650$	54.1662	2.12457
$651$	−0.476753	−0.0186854
$652$	−43.5058	−1.70382
$653$	−27.1665	−1.06311	−0.531554	−	0.847024i	$-0.678392\pi$
$653$	−27.1665	−1.06311	−0.531554	+	0.847024i	$0.678392\pi$
$654$	43.9739	1.71952
$655$	−0.319046	−0.0124662
$656$	45.6666	1.78298
$657$	−34.8585	−1.35996
$658$	−29.2492	−1.14025
$659$	−18.8971	−0.736127	−0.368064	−	0.929801i	$-0.619979\pi$
$659$	−18.8971	−0.736127	−0.368064	+	0.929801i	$0.619979\pi$
$660$	17.7447	0.690712
$661$	21.6179	0.840840	0.420420	−	0.907330i	$-0.361883\pi$
$661$	21.6179	0.840840	0.420420	+	0.907330i	$0.361883\pi$
$662$	35.9767	1.39828
$663$	44.3171	1.72113
$664$	−82.0533	−3.18428
$665$	−1.97514	−0.0765925
$666$	−29.7065	−1.15110
$667$	−28.6424	−1.10904
$668$	−70.3608	−2.72234
$669$	40.1389	1.55186
$670$	5.22772	0.201965
$671$	−30.0658	−1.16068
$672$	−27.4901	−1.06045
$673$	2.70360	0.104216	0.0521081	−	0.998641i	$-0.483406\pi$
$673$	2.70360	0.104216	0.0521081	+	0.998641i	$0.483406\pi$
$674$	49.3297	1.90011
$675$	−16.8048	−0.646818
$676$	32.1945	1.23825
$677$	11.9421	0.458974	0.229487	−	0.973312i	$-0.426295\pi$
$677$	11.9421	0.458974	0.229487	+	0.973312i	$0.426295\pi$
$678$	−0.469228	−0.0180206
$679$	−48.3802	−1.85666
$680$	−10.2285	−0.392244
$681$	22.3803	0.857614
$682$	0.468705	0.0179477
$683$	1.59807	0.0611484	0.0305742	−	0.999533i	$-0.490266\pi$
$683$	1.59807	0.0611484	0.0305742	+	0.999533i	$0.490266\pi$
$684$	−25.5059	−0.975243
$685$	−6.65894	−0.254425
$686$	38.7227	1.47844
$687$	0.0156157	0.000595778 0
$688$	−61.2305	−2.33439
$689$	48.6348	1.85284
$690$	13.9406	0.530709
$691$	2.64298	0.100544	0.0502718	−	0.998736i	$-0.483991\pi$
$691$	2.64298	0.100544	0.0502718	+	0.998736i	$0.483991\pi$
$692$	−51.3083	−1.95045
$693$	40.0915	1.52295
$694$	23.3484	0.886294
$695$	−0.913581	−0.0346541
$696$	−106.427	−4.03411
$697$	27.6114	1.04586
$698$	28.0368	1.06121
$699$	21.3971	0.809314
$700$	−61.0364	−2.30696
$701$	−9.39744	−0.354936	−0.177468	−	0.984127i	$-0.556791\pi$
$701$	−9.39744	−0.354936	−0.177468	+	0.984127i	$0.556791\pi$
$702$	−40.0901	−1.51311
$703$	−3.76944	−0.142167
$704$	−10.6012	−0.399546
$705$	5.13799	0.193508
$706$	57.0052	2.14542
$707$	−32.8873	−1.23686
$708$	−32.8848	−1.23589
$709$	20.1731	0.757618	0.378809	−	0.925475i	$-0.376334\pi$
$709$	20.1731	0.757618	0.378809	+	0.925475i	$0.376334\pi$
$710$	1.98592	0.0745301
$711$	1.85018	0.0693873
$712$	−85.7071	−3.21201
$713$	0.251623	0.00942334
$714$	−73.0793	−2.73492
$715$	6.88070	0.257324
$716$	8.52582	0.318625
$717$	−34.2000	−1.27722
$718$	−3.78076	−0.141097
$719$	−6.12517	−0.228430	−0.114215	−	0.993456i	$-0.536435\pi$
$719$	−6.12517	−0.228430	−0.114215	+	0.993456i	$0.536435\pi$
$720$	12.5121	0.466300
$721$	12.5013	0.465574
$722$	43.0138	1.60081
$723$	−12.2894	−0.457048
$724$	54.8801	2.03960
$725$	−32.2373	−1.19726
$726$	7.83436	0.290760
$727$	35.5726	1.31931	0.659657	−	0.751567i	$-0.270701\pi$
$727$	35.5726	1.31931	0.659657	+	0.751567i	$0.270701\pi$
$728$	−78.1351	−2.89588
$729$	−43.1578	−1.59844
$730$	9.86532	0.365132
$731$	−37.0218	−1.36930
$732$	−111.767	−4.13102
$733$	−11.7171	−0.432780	−0.216390	−	0.976307i	$-0.569428\pi$
$733$	−11.7171	−0.432780	−0.216390	+	0.976307i	$0.569428\pi$
$734$	−68.5000	−2.52838
$735$	2.36951	0.0874006
$736$	14.5089	0.534803
$737$	−13.4646	−0.495975
$738$	−82.4041	−3.03334
$739$	3.65661	0.134511	0.0672553	−	0.997736i	$-0.478576\pi$
$739$	3.65661	0.134511	0.0672553	+	0.997736i	$0.478576\pi$
$740$	5.74503	0.211192
$741$	−16.7825	−0.616521
$742$	−80.1992	−2.94421
$743$	−13.7608	−0.504836	−0.252418	−	0.967618i	$-0.581226\pi$
$743$	−13.7608	−0.504836	−0.252418	+	0.967618i	$0.581226\pi$
$744$	0.934959	0.0342773
$745$	−5.89833	−0.216098
$746$	15.4566	0.565907
$747$	60.6884	2.22047
$748$	49.0952	1.79510
$749$	2.34115	0.0855438
$750$	32.1544	1.17411
$751$	37.8983	1.38293	0.691463	−	0.722411i	$-0.256966\pi$
$751$	37.8983	1.38293	0.691463	+	0.722411i	$0.256966\pi$
$752$	23.5111	0.857362
$753$	−83.1173	−3.02896
$754$	−76.9064	−2.80077
$755$	9.89337	0.360056
$756$	45.1750	1.64300
$757$	−31.1854	−1.13345	−0.566726	−	0.823907i	$-0.691790\pi$
$757$	−31.1854	−1.13345	−0.566726	+	0.823907i	$0.691790\pi$
$758$	−95.1627	−3.45646
$759$	−35.9056	−1.30329
$760$	3.87344	0.140504
$761$	14.0175	0.508132	0.254066	−	0.967187i	$-0.418232\pi$
$761$	14.0175	0.508132	0.254066	+	0.967187i	$0.418232\pi$
$762$	−48.7062	−1.76444
$763$	−19.2141	−0.695597
$764$	−59.3391	−2.14681
$765$	7.56522	0.273521
$766$	21.6215	0.781216
$767$	−12.7514	−0.460427
$768$	−85.9648	−3.10199
$769$	39.3118	1.41762	0.708810	−	0.705399i	$-0.249232\pi$
$769$	39.3118	1.41762	0.708810	+	0.705399i	$0.249232\pi$
$770$	−11.3463	−0.408894
$771$	−35.9876	−1.29606
$772$	18.5427	0.667365
$773$	11.8819	0.427361	0.213680	−	0.976904i	$-0.431455\pi$
$773$	11.8819	0.427361	0.213680	+	0.976904i	$0.431455\pi$
$774$	110.489	3.97143
$775$	0.283204	0.0101730
$776$	94.8783	3.40593
$777$	22.0257	0.790166
$778$	−29.0253	−1.04061
$779$	−10.4562	−0.374633
$780$	25.5783	0.915852
$781$	−5.11496	−0.183028
$782$	38.5701	1.37926
$783$	23.8599	0.852682
$784$	10.8427	0.387240
$785$	6.73984	0.240555
$786$	4.47030	0.159450
$787$	−21.6360	−0.771239	−0.385619	−	0.922658i	$-0.626012\pi$
$787$	−21.6360	−0.771239	−0.385619	+	0.922658i	$0.626012\pi$
$788$	−93.2488	−3.32185
$789$	11.2561	0.400727
$790$	−0.523622	−0.0186296
$791$	0.205026	0.00728988
$792$	−78.6235	−2.79376
$793$	−43.3387	−1.53900
$794$	−24.9190	−0.884342
$795$	14.0880	0.499650
$796$	3.59545	0.127437
$797$	−26.2348	−0.929284	−0.464642	−	0.885499i	$-0.653817\pi$
$797$	−26.2348	−0.929284	−0.464642	+	0.885499i	$0.653817\pi$
$798$	27.6745	0.979667
$799$	14.2155	0.502909
$800$	16.3299	0.577348
$801$	63.3909	2.23981
$802$	−56.8210	−2.00642
$803$	−25.4093	−0.896673
$804$	−50.0533	−1.76525
$805$	−6.09124	−0.214688
$806$	0.675621	0.0237977
$807$	38.7543	1.36422
$808$	64.4953	2.26894
$809$	45.2800	1.59196	0.795980	−	0.605323i	$-0.206956\pi$
$809$	45.2800	1.59196	0.795980	+	0.605323i	$0.206956\pi$
$810$	4.12126	0.144806
$811$	−31.9929	−1.12342	−0.561711	−	0.827333i	$-0.689857\pi$
$811$	−31.9929	−1.12342	−0.561711	+	0.827333i	$0.689857\pi$
$812$	86.6609	3.04120
$813$	−66.8174	−2.34339
$814$	−21.6539	−0.758968
$815$	−4.88667	−0.171173
$816$	58.7427	2.05641
$817$	14.0198	0.490492
$818$	19.8332	0.693452
$819$	57.7904	2.01936
$820$	15.9364	0.556523
$821$	4.09832	0.143032	0.0715162	−	0.997439i	$-0.477216\pi$
$821$	4.09832	0.143032	0.0715162	+	0.997439i	$0.477216\pi$
$822$	93.3013	3.25426
$823$	−15.6424	−0.545261	−0.272630	−	0.962119i	$-0.587894\pi$
$823$	−15.6424	−0.545261	−0.272630	+	0.962119i	$0.587894\pi$
$824$	−24.5163	−0.854067
$825$	−40.4121	−1.40697
$826$	21.0272	0.731630
$827$	−27.3942	−0.952590	−0.476295	−	0.879286i	$-0.658021\pi$
$827$	−27.3942	−0.952590	−0.476295	+	0.879286i	$0.658021\pi$
$828$	−78.6591	−2.73359
$829$	−27.6632	−0.960784	−0.480392	−	0.877054i	$-0.659506\pi$
$829$	−27.6632	−0.960784	−0.480392	+	0.877054i	$0.659506\pi$
$830$	−17.1755	−0.596170
$831$	−11.9492	−0.414513
$832$	−15.2812	−0.529779
$833$	6.55583	0.227146
$834$	12.8006	0.443248
$835$	−7.90308	−0.273498
$836$	−18.5919	−0.643015
$837$	−0.209608	−0.00724513
$838$	−44.1325	−1.52453
$839$	−34.3497	−1.18588	−0.592942	−	0.805245i	$-0.702034\pi$
$839$	−34.3497	−1.18588	−0.592942	+	0.805245i	$0.702034\pi$
$840$	−22.6333	−0.780924
$841$	16.7713	0.578320
$842$	96.5246	3.32646
$843$	−49.4850	−1.70435
$844$	69.9573	2.40803
$845$	3.61616	0.124400
$846$	−42.4251	−1.45860
$847$	−3.42317	−0.117621
$848$	64.4659	2.21377
$849$	72.7412	2.49647
$850$	43.4111	1.48899
$851$	−11.6248	−0.398493
$852$	−19.0144	−0.651421
$853$	−24.2248	−0.829442	−0.414721	−	0.909949i	$-0.636121\pi$
$853$	−24.2248	−0.829442	−0.414721	+	0.909949i	$0.636121\pi$
$854$	71.4659	2.44551
$855$	−2.86488	−0.0979769
$856$	−4.59123	−0.156925
$857$	−1.75534	−0.0599611	−0.0299806	−	0.999550i	$-0.509545\pi$
$857$	−1.75534	−0.0599611	−0.0299806	+	0.999550i	$0.509545\pi$
$858$	−96.4085	−3.29133
$859$	4.86882	0.166122	0.0830610	−	0.996544i	$-0.473530\pi$
$859$	4.86882	0.166122	0.0830610	+	0.996544i	$0.473530\pi$
$860$	−21.3677	−0.728633
$861$	61.0979	2.08221
$862$	−7.73912	−0.263596
$863$	14.0720	0.479018	0.239509	−	0.970894i	$-0.423014\pi$
$863$	14.0720	0.479018	0.239509	+	0.970894i	$0.423014\pi$
$864$	−12.0863	−0.411183
$865$	−5.76306	−0.195950
$866$	2.22708	0.0756792
$867$	−10.4292	−0.354193
$868$	−0.761314	−0.0258407
$869$	1.34865	0.0457497
$870$	−22.2774	−0.755276
$871$	−19.4087	−0.657639
$872$	37.6807	1.27603
$873$	−70.1741	−2.37503
$874$	−14.6062	−0.494061
$875$	−14.0496	−0.474964
$876$	−94.4565	−3.19139
$877$	−13.7812	−0.465358	−0.232679	−	0.972554i	$-0.574749\pi$
$877$	−13.7812	−0.465358	−0.232679	+	0.972554i	$0.574749\pi$
$878$	15.4843	0.522570
$879$	−41.1000	−1.38627
$880$	9.12043	0.307450
$881$	40.4296	1.36211	0.681055	−	0.732233i	$-0.261522\pi$
$881$	40.4296	1.36211	0.681055	+	0.732233i	$0.261522\pi$
$882$	−19.5654	−0.658800
$883$	−21.1476	−0.711672	−0.355836	−	0.934548i	$-0.615804\pi$
$883$	−21.1476	−0.711672	−0.355836	+	0.934548i	$0.615804\pi$
$884$	70.7689	2.38021
$885$	−3.69369	−0.124162
$886$	−55.3333	−1.85896
$887$	32.3085	1.08481	0.542407	−	0.840116i	$-0.317513\pi$
$887$	32.3085	1.08481	0.542407	+	0.840116i	$0.317513\pi$
$888$	−43.1945	−1.44951
$889$	21.2818	0.713769
$890$	−17.9403	−0.601360
$891$	−10.6148	−0.355608
$892$	64.0967	2.14612
$893$	−5.38330	−0.180145
$894$	82.6441	2.76403
$895$	0.957640	0.0320104
$896$	45.5411	1.52142
$897$	−51.7566	−1.72810
$898$	−43.3867	−1.44783
$899$	−0.402100	−0.0134108
$900$	−88.5316	−2.95105
$901$	38.9780	1.29855
$902$	−60.0665	−2.00000
$903$	−81.9209	−2.72616
$904$	−0.402076	−0.0133728
$905$	6.16426	0.204907
$906$	−138.620	−4.60535
$907$	−56.3750	−1.87190	−0.935951	−	0.352131i	$-0.885457\pi$
$907$	−56.3750	−1.87190	−0.935951	+	0.352131i	$0.885457\pi$
$908$	35.7385	1.18602
$909$	−47.7022	−1.58218
$910$	−16.3553	−0.542173
$911$	−7.76455	−0.257251	−0.128625	−	0.991693i	$-0.541057\pi$
$911$	−7.76455	−0.257251	−0.128625	+	0.991693i	$0.541057\pi$
$912$	−22.2454	−0.736618
$913$	44.2374	1.46404
$914$	−98.7454	−3.26621
$915$	−12.5539	−0.415019
$916$	0.0249364	0.000823921 0
$917$	−1.95326	−0.0645024
$918$	−32.1299	−1.06045
$919$	18.0425	0.595169	0.297584	−	0.954696i	$-0.403819\pi$
$919$	18.0425	0.595169	0.297584	+	0.954696i	$0.403819\pi$
$920$	11.9455	0.393832
$921$	−48.7414	−1.60608
$922$	−7.40685	−0.243931
$923$	−7.37302	−0.242686
$924$	108.637	3.57388
$925$	−13.0838	−0.430194
$926$	37.1480	1.22076
$927$	18.1328	0.595560
$928$	−23.1855	−0.761102
$929$	−2.04658	−0.0671461	−0.0335731	−	0.999436i	$-0.510689\pi$
$929$	−2.04658	−0.0671461	−0.0335731	+	0.999436i	$0.510689\pi$
$930$	0.195707	0.00641747
$931$	−2.48264	−0.0813652
$932$	34.1685	1.11923
$933$	34.2013	1.11970
$934$	−106.432	−3.48257
$935$	5.51449	0.180343
$936$	−113.333	−3.70440
$937$	25.4127	0.830197	0.415099	−	0.909776i	$-0.363747\pi$
$937$	25.4127	0.830197	0.415099	+	0.909776i	$0.363747\pi$
$938$	32.0051	1.04500
$939$	45.4770	1.48409
$940$	8.20472	0.267608
$941$	−2.60689	−0.0849821	−0.0424910	−	0.999097i	$-0.513529\pi$
$941$	−2.60689	−0.0849821	−0.0424910	+	0.999097i	$0.513529\pi$
$942$	−94.4348	−3.07685
$943$	−32.2465	−1.05009
$944$	−16.9021	−0.550117
$945$	5.07417	0.165063
$946$	80.5381	2.61852
$947$	11.1009	0.360731	0.180366	−	0.983600i	$-0.442272\pi$
$947$	11.1009	0.360731	0.180366	+	0.983600i	$0.442272\pi$
$948$	5.01347	0.162830
$949$	−36.6265	−1.18895
$950$	−16.4394	−0.533364
$951$	91.8854	2.97959
$952$	−62.6208	−2.02955
$953$	7.52033	0.243607	0.121804	−	0.992554i	$-0.461132\pi$
$953$	7.52033	0.243607	0.121804	+	0.992554i	$0.461132\pi$
$954$	−116.327	−3.76622
$955$	−6.66511	−0.215678
$956$	−54.6131	−1.76631
$957$	57.3781	1.85477
$958$	55.5910	1.79606
$959$	−40.7673	−1.31645
$960$	−4.42649	−0.142864
$961$	−30.9965	−0.999886
$962$	−31.2132	−1.00636
$963$	3.39577	0.109427
$964$	−19.6247	−0.632068
$965$	2.08276	0.0670463
$966$	85.3470	2.74600
$967$	−10.0449	−0.323023	−0.161512	−	0.986871i	$-0.551637\pi$
$967$	−10.0449	−0.323023	−0.161512	+	0.986871i	$0.551637\pi$
$968$	6.71317	0.215769
$969$	−13.4502	−0.432083
$970$	19.8600	0.637667
$971$	55.2319	1.77248	0.886239	−	0.463229i	$-0.153309\pi$
$971$	55.2319	1.77248	0.886239	+	0.463229i	$0.153309\pi$
$972$	−85.1230	−2.73032
$973$	−5.59312	−0.179307
$974$	−81.4745	−2.61061
$975$	−58.2525	−1.86557
$976$	−57.4459	−1.83880
$977$	15.3680	0.491666	0.245833	−	0.969312i	$-0.420939\pi$
$977$	15.3680	0.491666	0.245833	+	0.969312i	$0.420939\pi$
$978$	68.4693	2.18941
$979$	46.2073	1.47679
$980$	3.78380	0.120869
$981$	−27.8695	−0.889805
$982$	−54.9280	−1.75282
$983$	41.3629	1.31927	0.659636	−	0.751585i	$-0.270710\pi$
$983$	41.3629	1.31927	0.659636	+	0.751585i	$0.270710\pi$
$984$	−119.819	−3.81969
$985$	−10.4739	−0.333727
$986$	−61.6361	−1.96289
$987$	31.4557	1.00125
$988$	−26.7996	−0.852608
$989$	43.2366	1.37484
$990$	−16.4576	−0.523055
$991$	37.6402	1.19568	0.597839	−	0.801616i	$-0.296026\pi$
$991$	37.6402	1.19568	0.597839	+	0.801616i	$0.296026\pi$
$992$	0.203684	0.00646698
$993$	−38.6909	−1.22782
$994$	12.1582	0.385634
$995$	0.403849	0.0128029
$996$	164.448	5.21074
$997$	36.4487	1.15434	0.577172	−	0.816623i	$-0.304156\pi$
$997$	36.4487	1.15434	0.577172	+	0.816623i	$0.304156\pi$
$998$	−5.97812	−0.189234
$999$	9.68377	0.306381

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4021.2.a.c.1.14	✓	182

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4021.2.a.c.1.14	✓	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)

\(f(q)\)	\(=\)	\(q-2.51316 q^{2} +2.70275 q^{3} +4.31595 q^{4} +0.484778 q^{5} -6.79244 q^{6} +2.96790 q^{7} -5.82035 q^{8} +4.30486 q^{9} +O(q^{10})\)	\(q-2.51316 q^{2} +2.70275 q^{3} +4.31595 q^{4} +0.484778 q^{5} -6.79244 q^{6} +2.96790 q^{7} -5.82035 q^{8} +4.30486 q^{9} -1.21832 q^{10} +3.13793 q^{11} +11.6650 q^{12} +4.52321 q^{13} -7.45881 q^{14} +1.31023 q^{15} +5.99555 q^{16} +3.62509 q^{17} -10.8188 q^{18} -1.37279 q^{19} +2.09228 q^{20} +8.02151 q^{21} -7.88611 q^{22} -4.23363 q^{23} -15.7310 q^{24} -4.76499 q^{25} -11.3675 q^{26} +3.52673 q^{27} +12.8093 q^{28} +6.76545 q^{29} -3.29282 q^{30} -0.0594343 q^{31} -3.42705 q^{32} +8.48104 q^{33} -9.11042 q^{34} +1.43878 q^{35} +18.5796 q^{36} +2.74582 q^{37} +3.45004 q^{38} +12.2251 q^{39} -2.82158 q^{40} +7.61675 q^{41} -20.1593 q^{42} -10.2127 q^{43} +13.5432 q^{44} +2.08690 q^{45} +10.6398 q^{46} +3.92142 q^{47} +16.2045 q^{48} +1.80846 q^{49} +11.9752 q^{50} +9.79772 q^{51} +19.5220 q^{52} +10.7523 q^{53} -8.86321 q^{54} +1.52120 q^{55} -17.2743 q^{56} -3.71031 q^{57} -17.0026 q^{58} -2.81911 q^{59} +5.65491 q^{60} -9.58142 q^{61} +0.149368 q^{62} +12.7764 q^{63} -3.37839 q^{64} +2.19275 q^{65} -21.3142 q^{66} -4.29092 q^{67} +15.6457 q^{68} -11.4424 q^{69} -3.61587 q^{70} -1.63004 q^{71} -25.0558 q^{72} -8.09746 q^{73} -6.90069 q^{74} -12.8786 q^{75} -5.92490 q^{76} +9.31308 q^{77} -30.7236 q^{78} +0.429789 q^{79} +2.90651 q^{80} -3.38273 q^{81} -19.1421 q^{82} +14.0976 q^{83} +34.6205 q^{84} +1.75736 q^{85} +25.6660 q^{86} +18.2853 q^{87} -18.2639 q^{88} +14.7254 q^{89} -5.24472 q^{90} +13.4245 q^{91} -18.2721 q^{92} -0.160636 q^{93} -9.85515 q^{94} -0.665499 q^{95} -9.26246 q^{96} -16.3011 q^{97} -4.54494 q^{98} +13.5084 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9}+O(q^{10}) \) 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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