LMFDB - Embedded newform 4021.2.a.c.1.6

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			1.6
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)

$f(q)$	$=$	$q-2.67278 q^{2} +1.10671 q^{3} +5.14375 q^{4} +3.24617 q^{5} -2.95798 q^{6} -3.43903 q^{7} -8.40257 q^{8} -1.77520 q^{9} +O(q^{10})$	\(q-2.67278 q^{2} +1.10671 q^{3} +5.14375 q^{4} +3.24617 q^{5} -2.95798 q^{6} -3.43903 q^{7} -8.40257 q^{8} -1.77520 q^{9} -8.67630 q^{10} -2.27752 q^{11} +5.69262 q^{12} -3.44803 q^{13} +9.19177 q^{14} +3.59256 q^{15} +12.1707 q^{16} -5.49021 q^{17} +4.74472 q^{18} -0.347015 q^{19} +16.6975 q^{20} -3.80599 q^{21} +6.08731 q^{22} +2.23757 q^{23} -9.29917 q^{24} +5.53762 q^{25} +9.21583 q^{26} -5.28474 q^{27} -17.6895 q^{28} +6.37715 q^{29} -9.60211 q^{30} +10.8237 q^{31} -15.7245 q^{32} -2.52054 q^{33} +14.6741 q^{34} -11.1637 q^{35} -9.13120 q^{36} +3.96782 q^{37} +0.927494 q^{38} -3.81596 q^{39} -27.2762 q^{40} +5.47844 q^{41} +10.1726 q^{42} -5.58528 q^{43} -11.7150 q^{44} -5.76261 q^{45} -5.98054 q^{46} -2.84315 q^{47} +13.4694 q^{48} +4.82691 q^{49} -14.8008 q^{50} -6.07605 q^{51} -17.7358 q^{52} +3.71252 q^{53} +14.1250 q^{54} -7.39321 q^{55} +28.8967 q^{56} -0.384043 q^{57} -17.0447 q^{58} -3.70961 q^{59} +18.4792 q^{60} -2.17698 q^{61} -28.9294 q^{62} +6.10497 q^{63} +17.6867 q^{64} -11.1929 q^{65} +6.73686 q^{66} +1.96066 q^{67} -28.2403 q^{68} +2.47634 q^{69} +29.8380 q^{70} -3.44116 q^{71} +14.9163 q^{72} -7.97336 q^{73} -10.6051 q^{74} +6.12851 q^{75} -1.78496 q^{76} +7.83245 q^{77} +10.1992 q^{78} +11.3082 q^{79} +39.5082 q^{80} -0.523053 q^{81} -14.6427 q^{82} +10.8931 q^{83} -19.5771 q^{84} -17.8221 q^{85} +14.9282 q^{86} +7.05762 q^{87} +19.1370 q^{88} -1.22373 q^{89} +15.4022 q^{90} +11.8579 q^{91} +11.5095 q^{92} +11.9787 q^{93} +7.59912 q^{94} -1.12647 q^{95} -17.4024 q^{96} +12.7331 q^{97} -12.9013 q^{98} +4.04305 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.67278	−1.88994	−0.944971	−	0.327155i	$-0.893910\pi$
$2$	−2.67278	−1.88994	−0.944971	+	0.327155i	$0.893910\pi$
$3$	1.10671	0.638957	0.319478	−	0.947594i	$-0.396492\pi$
$3$	1.10671	0.638957	0.319478	+	0.947594i	$0.396492\pi$
$4$	5.14375	2.57188
$5$	3.24617	1.45173	0.725866	−	0.687837i	$-0.241439\pi$
$5$	3.24617	1.45173	0.725866	+	0.687837i	$0.241439\pi$
$6$	−2.95798	−1.20759
$7$	−3.43903	−1.29983	−0.649915	−	0.760007i	$-0.725196\pi$
$7$	−3.43903	−1.29983	−0.649915	+	0.760007i	$0.725196\pi$
$8$	−8.40257	−2.97076
$9$	−1.77520	−0.591734
$10$	−8.67630	−2.74369
$11$	−2.27752	−0.686698	−0.343349	−	0.939208i	$-0.611561\pi$
$11$	−2.27752	−0.686698	−0.343349	+	0.939208i	$0.611561\pi$
$12$	5.69262	1.64332
$13$	−3.44803	−0.956312	−0.478156	−	0.878275i	$-0.658695\pi$
$13$	−3.44803	−0.956312	−0.478156	+	0.878275i	$0.658695\pi$
$14$	9.19177	2.45660
$15$	3.59256	0.927594
$16$	12.1707	3.04268
$17$	−5.49021	−1.33157	−0.665785	−	0.746143i	$-0.731903\pi$
$17$	−5.49021	−1.33157	−0.665785	+	0.746143i	$0.731903\pi$
$18$	4.74472	1.11834
$19$	−0.347015	−0.0796106	−0.0398053	−	0.999207i	$-0.512674\pi$
$19$	−0.347015	−0.0796106	−0.0398053	+	0.999207i	$0.512674\pi$
$20$	16.6975	3.73367
$21$	−3.80599	−0.830536
$22$	6.08731	1.29782
$23$	2.23757	0.466566	0.233283	−	0.972409i	$-0.425053\pi$
$23$	2.23757	0.466566	0.233283	+	0.972409i	$0.425053\pi$
$24$	−9.29917	−1.89819
$25$	5.53762	1.10752
$26$	9.21583	1.80737
$27$	−5.28474	−1.01705
$28$	−17.6895	−3.34300
$29$	6.37715	1.18421	0.592103	−	0.805862i	$-0.298298\pi$
$29$	6.37715	1.18421	0.592103	+	0.805862i	$0.298298\pi$
$30$	−9.60211	−1.75310
$31$	10.8237	1.94400	0.971999	−	0.234983i	$-0.0755035\pi$
$31$	10.8237	1.94400	0.971999	+	0.234983i	$0.0755035\pi$
$32$	−15.7245	−2.77972
$33$	−2.52054	−0.438770
$34$	14.6741	2.51659
$35$	−11.1637	−1.88700
$36$	−9.13120	−1.52187
$37$	3.96782	0.652306	0.326153	−	0.945317i	$-0.394247\pi$
$37$	3.96782	0.652306	0.326153	+	0.945317i	$0.394247\pi$
$38$	0.927494	0.150459
$39$	−3.81596	−0.611042
$40$	−27.2762	−4.31274
$41$	5.47844	0.855589	0.427794	−	0.903876i	$-0.359291\pi$
$41$	5.47844	0.855589	0.427794	+	0.903876i	$0.359291\pi$
$42$	10.1726	1.56966
$43$	−5.58528	−0.851747	−0.425873	−	0.904783i	$-0.640033\pi$
$43$	−5.58528	−0.851747	−0.425873	+	0.904783i	$0.640033\pi$
$44$	−11.7150	−1.76610
$45$	−5.76261	−0.859039
$46$	−5.98054	−0.881783
$47$	−2.84315	−0.414716	−0.207358	−	0.978265i	$-0.566487\pi$
$47$	−2.84315	−0.414716	−0.207358	+	0.978265i	$0.566487\pi$
$48$	13.4694	1.94414
$49$	4.82691	0.689559
$50$	−14.8008	−2.09315
$51$	−6.07605	−0.850817
$52$	−17.7358	−2.45952
$53$	3.71252	0.509953	0.254977	−	0.966947i	$-0.417932\pi$
$53$	3.71252	0.509953	0.254977	+	0.966947i	$0.417932\pi$
$54$	14.1250	1.92216
$55$	−7.39321	−0.996900
$56$	28.8967	3.86148
$57$	−0.384043	−0.0508678
$58$	−17.0447	−2.23808
$59$	−3.70961	−0.482950	−0.241475	−	0.970407i	$-0.577631\pi$
$59$	−3.70961	−0.482950	−0.241475	+	0.970407i	$0.577631\pi$
$60$	18.4792	2.38566
$61$	−2.17698	−0.278734	−0.139367	−	0.990241i	$-0.544507\pi$
$61$	−2.17698	−0.278734	−0.139367	+	0.990241i	$0.544507\pi$
$62$	−28.9294	−3.67404
$63$	6.10497	0.769154
$64$	17.6867	2.21084
$65$	−11.1929	−1.38831
$66$	6.73686	0.829250
$67$	1.96066	0.239533	0.119767	−	0.992802i	$-0.461785\pi$
$67$	1.96066	0.239533	0.119767	+	0.992802i	$0.461785\pi$
$68$	−28.2403	−3.42464
$69$	2.47634	0.298116
$70$	29.8380	3.56633
$71$	−3.44116	−0.408390	−0.204195	−	0.978930i	$-0.565458\pi$
$71$	−3.44116	−0.408390	−0.204195	+	0.978930i	$0.565458\pi$
$72$	14.9163	1.75790
$73$	−7.97336	−0.933211	−0.466606	−	0.884465i	$-0.654523\pi$
$73$	−7.97336	−0.933211	−0.466606	+	0.884465i	$0.654523\pi$
$74$	−10.6051	−1.23282
$75$	6.12851	0.707660
$76$	−1.78496	−0.204749
$77$	7.83245	0.892590
$78$	10.1992	1.15483
$79$	11.3082	1.27227	0.636134	−	0.771579i	$-0.280533\pi$
$79$	11.3082	1.27227	0.636134	+	0.771579i	$0.280533\pi$
$80$	39.5082	4.41715
$81$	−0.523053	−0.0581170
$82$	−14.6427	−1.61701
$83$	10.8931	1.19567	0.597836	−	0.801618i	$-0.296027\pi$
$83$	10.8931	1.19567	0.597836	+	0.801618i	$0.296027\pi$
$84$	−19.5771	−2.13604
$85$	−17.8221	−1.93308
$86$	14.9282	1.60975
$87$	7.05762	0.756657
$88$	19.1370	2.04001
$89$	−1.22373	−0.129715	−0.0648576	−	0.997895i	$-0.520659\pi$
$89$	−1.22373	−0.129715	−0.0648576	+	0.997895i	$0.520659\pi$
$90$	15.4022	1.62353
$91$	11.8579	1.24304
$92$	11.5095	1.19995
$93$	11.9787	1.24213
$94$	7.59912	0.783790
$95$	−1.12647	−0.115573
$96$	−17.4024	−1.77612
$97$	12.7331	1.29285	0.646423	−	0.762979i	$-0.276264\pi$
$97$	12.7331	1.29285	0.646423	+	0.762979i	$0.276264\pi$
$98$	−12.9013	−1.30323
$99$	4.04305	0.406342
$100$	28.4841	2.84841
$101$	8.04284	0.800292	0.400146	−	0.916451i	$-0.368959\pi$
$101$	8.04284	0.800292	0.400146	+	0.916451i	$0.368959\pi$
$102$	16.2399	1.60799
$103$	6.10715	0.601755	0.300878	−	0.953663i	$-0.402720\pi$
$103$	6.10715	0.601755	0.300878	+	0.953663i	$0.402720\pi$
$104$	28.9723	2.84097
$105$	−12.3549	−1.20571
$106$	−9.92274	−0.963782
$107$	3.93571	0.380479	0.190240	−	0.981738i	$-0.439073\pi$
$107$	3.93571	0.380479	0.190240	+	0.981738i	$0.439073\pi$
$108$	−27.1834	−2.61573
$109$	−11.4769	−1.09929	−0.549644	−	0.835399i	$-0.685236\pi$
$109$	−11.4769	−1.09929	−0.549644	+	0.835399i	$0.685236\pi$
$110$	19.7604	1.88408
$111$	4.39121	0.416796
$112$	−41.8554	−3.95496
$113$	6.36371	0.598648	0.299324	−	0.954152i	$-0.403239\pi$
$113$	6.36371	0.598648	0.299324	+	0.954152i	$0.403239\pi$
$114$	1.02646	0.0961371
$115$	7.26354	0.677329
$116$	32.8025	3.04563
$117$	6.12095	0.565882
$118$	9.91497	0.912747
$119$	18.8810	1.73082
$120$	−30.1867	−2.75565
$121$	−5.81291	−0.528446
$122$	5.81860	0.526791
$123$	6.06302	0.546684
$124$	55.6746	4.99973
$125$	1.74519	0.156095
$126$	−16.3172	−1.45366
$127$	13.4266	1.19142	0.595708	−	0.803201i	$-0.296872\pi$
$127$	13.4266	1.19142	0.595708	+	0.803201i	$0.296872\pi$
$128$	−15.8237	−1.39863
$129$	−6.18126	−0.544229
$130$	29.9162	2.62382
$131$	7.81422	0.682731	0.341366	−	0.939931i	$-0.389111\pi$
$131$	7.81422	0.682731	0.341366	+	0.939931i	$0.389111\pi$
$132$	−12.9651	−1.12846
$133$	1.19339	0.103480
$134$	−5.24043	−0.452704
$135$	−17.1552	−1.47648
$136$	46.1318	3.95577
$137$	−0.373168	−0.0318819	−0.0159409	−	0.999873i	$-0.505074\pi$
$137$	−0.373168	−0.0318819	−0.0159409	+	0.999873i	$0.505074\pi$
$138$	−6.61870	−0.563421
$139$	14.2735	1.21066	0.605329	−	0.795975i	$-0.293041\pi$
$139$	14.2735	1.21066	0.605329	+	0.795975i	$0.293041\pi$
$140$	−57.4232	−4.85314
$141$	−3.14653	−0.264986
$142$	9.19746	0.771834
$143$	7.85296	0.656697
$144$	−21.6055	−1.80045
$145$	20.7013	1.71915
$146$	21.3110	1.76371
$147$	5.34197	0.440598
$148$	20.4095	1.67765
$149$	5.81108	0.476062	0.238031	−	0.971258i	$-0.423498\pi$
$149$	5.81108	0.476062	0.238031	+	0.971258i	$0.423498\pi$
$150$	−16.3802	−1.33744
$151$	12.4973	1.01702	0.508508	−	0.861057i	$-0.330197\pi$
$151$	12.4973	1.01702	0.508508	+	0.861057i	$0.330197\pi$
$152$	2.91581	0.236504
$153$	9.74623	0.787936
$154$	−20.9344	−1.68694
$155$	35.1357	2.82216
$156$	−19.6284	−1.57153
$157$	−22.3982	−1.78757	−0.893785	−	0.448495i	$-0.851960\pi$
$157$	−22.3982	−1.78757	−0.893785	+	0.448495i	$0.851960\pi$
$158$	−30.2242	−2.40451
$159$	4.10866	0.325838
$160$	−51.0444	−4.03541
$161$	−7.69507	−0.606457
$162$	1.39800	0.109838
$163$	−25.0480	−1.96191	−0.980957	−	0.194226i	$-0.937781\pi$
$163$	−25.0480	−1.96191	−0.980957	+	0.194226i	$0.937781\pi$
$164$	28.1798	2.20047
$165$	−8.18211	−0.636976
$166$	−29.1148	−2.25975
$167$	6.43151	0.497685	0.248843	−	0.968544i	$-0.419950\pi$
$167$	6.43151	0.497685	0.248843	+	0.968544i	$0.419950\pi$
$168$	31.9801	2.46732
$169$	−1.11107	−0.0854669
$170$	47.6347	3.65341
$171$	0.616021	0.0471083
$172$	−28.7293	−2.19059
$173$	−12.5915	−0.957311	−0.478655	−	0.878003i	$-0.658876\pi$
$173$	−12.5915	−0.957311	−0.478655	+	0.878003i	$0.658876\pi$
$174$	−18.8635	−1.43004
$175$	−19.0440	−1.43959
$176$	−27.7190	−2.08940
$177$	−4.10545	−0.308584
$178$	3.27077	0.245154
$179$	22.8656	1.70905	0.854527	−	0.519407i	$-0.173847\pi$
$179$	22.8656	1.70905	0.854527	+	0.519407i	$0.173847\pi$
$180$	−29.6414	−2.20934
$181$	20.0942	1.49359	0.746795	−	0.665055i	$-0.231592\pi$
$181$	20.0942	1.49359	0.746795	+	0.665055i	$0.231592\pi$
$182$	−31.6935	−2.34928
$183$	−2.40928	−0.178099
$184$	−18.8014	−1.38605
$185$	12.8802	0.946973
$186$	−32.0164	−2.34756
$187$	12.5040	0.914387
$188$	−14.6245	−1.06660
$189$	18.1744	1.32199
$190$	3.01080	0.218427
$191$	−0.239839	−0.0173541	−0.00867707	−	0.999962i	$-0.502762\pi$
$191$	−0.239839	−0.0173541	−0.00867707	+	0.999962i	$0.502762\pi$
$192$	19.5740	1.41263
$193$	−3.73606	−0.268927	−0.134464	−	0.990919i	$-0.542931\pi$
$193$	−3.73606	−0.268927	−0.134464	+	0.990919i	$0.542931\pi$
$194$	−34.0327	−2.44340
$195$	−12.3872	−0.887069
$196$	24.8285	1.77346
$197$	0.176131	0.0125488	0.00627441	−	0.999980i	$-0.498003\pi$
$197$	0.176131	0.0125488	0.00627441	+	0.999980i	$0.498003\pi$
$198$	−10.8062	−0.767963
$199$	−3.99883	−0.283470	−0.141735	−	0.989905i	$-0.545268\pi$
$199$	−3.99883	−0.283470	−0.141735	+	0.989905i	$0.545268\pi$
$200$	−46.5302	−3.29018
$201$	2.16988	0.153051
$202$	−21.4967	−1.51251
$203$	−21.9312	−1.53927
$204$	−31.2537	−2.18820
$205$	17.7839	1.24208
$206$	−16.3231	−1.13728
$207$	−3.97214	−0.276083
$208$	−41.9650	−2.90975
$209$	0.790332	0.0546684
$210$	33.0219	2.27873
$211$	−12.1585	−0.837027	−0.418514	−	0.908211i	$-0.637449\pi$
$211$	−12.1585	−0.837027	−0.418514	+	0.908211i	$0.637449\pi$
$212$	19.0963	1.31154
$213$	−3.80835	−0.260944
$214$	−10.5193	−0.719084
$215$	−18.1308	−1.23651
$216$	44.4054	3.02141
$217$	−37.2231	−2.52687
$218$	30.6752	2.07759
$219$	−8.82417	−0.596282
$220$	−38.0289	−2.56391
$221$	18.9304	1.27340
$222$	−11.7368	−0.787719
$223$	13.2985	0.890536	0.445268	−	0.895397i	$-0.353108\pi$
$223$	13.2985	0.890536	0.445268	+	0.895397i	$0.353108\pi$
$224$	54.0770	3.61317
$225$	−9.83039	−0.655359
$226$	−17.0088	−1.13141
$227$	11.2209	0.744757	0.372379	−	0.928081i	$-0.378542\pi$
$227$	11.2209	0.744757	0.372379	+	0.928081i	$0.378542\pi$
$228$	−1.97542	−0.130826
$229$	15.7519	1.04091	0.520456	−	0.853889i	$-0.325762\pi$
$229$	15.7519	1.04091	0.520456	+	0.853889i	$0.325762\pi$
$230$	−19.4138	−1.28011
$231$	8.66822	0.570327
$232$	−53.5844	−3.51799
$233$	−0.633162	−0.0414798	−0.0207399	−	0.999785i	$-0.506602\pi$
$233$	−0.633162	−0.0414798	−0.0207399	+	0.999785i	$0.506602\pi$
$234$	−16.3600	−1.06948
$235$	−9.22936	−0.602057
$236$	−19.0813	−1.24209
$237$	12.5148	0.812925
$238$	−50.4647	−3.27114
$239$	6.53177	0.422505	0.211253	−	0.977431i	$-0.432246\pi$
$239$	6.53177	0.422505	0.211253	+	0.977431i	$0.432246\pi$
$240$	43.7239	2.82237
$241$	−4.54729	−0.292917	−0.146458	−	0.989217i	$-0.546787\pi$
$241$	−4.54729	−0.292917	−0.146458	+	0.989217i	$0.546787\pi$
$242$	15.5366	0.998733
$243$	15.2754	0.979915
$244$	−11.1979	−0.716870
$245$	15.6690	1.00105
$246$	−16.2051	−1.03320
$247$	1.19652	0.0761326
$248$	−90.9471	−5.77515
$249$	12.0554	0.763983
$250$	−4.66452	−0.295010
$251$	−5.20968	−0.328832	−0.164416	−	0.986391i	$-0.552574\pi$
$251$	−5.20968	−0.328832	−0.164416	+	0.986391i	$0.552574\pi$
$252$	31.4025	1.97817
$253$	−5.09611	−0.320390
$254$	−35.8863	−2.25170
$255$	−19.7239	−1.23516
$256$	6.91982	0.432488
$257$	4.40294	0.274648	0.137324	−	0.990526i	$-0.456150\pi$
$257$	4.40294	0.274648	0.137324	+	0.990526i	$0.456150\pi$
$258$	16.5211	1.02856
$259$	−13.6455	−0.847887
$260$	−57.5735	−3.57056
$261$	−11.3207	−0.700735
$262$	−20.8857	−1.29032
$263$	5.88678	0.362994	0.181497	−	0.983391i	$-0.441906\pi$
$263$	5.88678	0.362994	0.181497	+	0.983391i	$0.441906\pi$
$264$	21.1790	1.30348
$265$	12.0515	0.740315
$266$	−3.18968	−0.195572
$267$	−1.35431	−0.0828825
$268$	10.0852	0.616050
$269$	31.9198	1.94619	0.973094	−	0.230410i	$-0.0740066\pi$
$269$	31.9198	1.94619	0.973094	+	0.230410i	$0.0740066\pi$
$270$	45.8520	2.79046
$271$	−1.68710	−0.102484	−0.0512421	−	0.998686i	$-0.516318\pi$
$271$	−1.68710	−0.102484	−0.0512421	+	0.998686i	$0.516318\pi$
$272$	−66.8197	−4.05154
$273$	13.1232	0.794251
$274$	0.997395	0.0602548
$275$	−12.6120	−0.760534
$276$	12.7377	0.766717
$277$	18.5601	1.11517	0.557584	−	0.830120i	$-0.311728\pi$
$277$	18.5601	1.11517	0.557584	+	0.830120i	$0.311728\pi$
$278$	−38.1498	−2.28807
$279$	−19.2143	−1.15033
$280$	93.8035	5.60583
$281$	−21.0030	−1.25294	−0.626468	−	0.779447i	$-0.715500\pi$
$281$	−21.0030	−1.25294	−0.626468	+	0.779447i	$0.715500\pi$
$282$	8.41000	0.500808
$283$	−25.2342	−1.50002	−0.750009	−	0.661428i	$-0.769951\pi$
$283$	−25.2342	−1.50002	−0.750009	+	0.661428i	$0.769951\pi$
$284$	−17.7005	−1.05033
$285$	−1.24667	−0.0738463
$286$	−20.9892	−1.24112
$287$	−18.8405	−1.11212
$288$	27.9141	1.64486
$289$	13.1424	0.773081
$290$	−55.3300	−3.24909
$291$	14.0918	0.826074
$292$	−41.0130	−2.40011
$293$	33.9528	1.98355	0.991773	−	0.128010i	$-0.0408589\pi$
$293$	33.9528	1.98355	0.991773	+	0.128010i	$0.0408589\pi$
$294$	−14.2779	−0.832705
$295$	−12.0420	−0.701113
$296$	−33.3399	−1.93784
$297$	12.0361	0.698405
$298$	−15.5317	−0.899729
$299$	−7.71522	−0.446183
$300$	31.5236	1.82001
$301$	19.2079	1.10713
$302$	−33.4026	−1.92210
$303$	8.90106	0.511352
$304$	−4.22341	−0.242229
$305$	−7.06685	−0.404647
$306$	−26.0495	−1.48915
$307$	19.9358	1.13780	0.568899	−	0.822407i	$-0.307370\pi$
$307$	19.9358	1.13780	0.568899	+	0.822407i	$0.307370\pi$
$308$	40.2882	2.29563
$309$	6.75882	0.384496
$310$	−93.9099	−5.33372
$311$	29.5566	1.67600	0.838000	−	0.545670i	$-0.183725\pi$
$311$	29.5566	1.67600	0.838000	+	0.545670i	$0.183725\pi$
$312$	32.0638	1.81526
$313$	−18.0966	−1.02288	−0.511441	−	0.859318i	$-0.670888\pi$
$313$	−18.0966	−1.02288	−0.511441	+	0.859318i	$0.670888\pi$
$314$	59.8654	3.37840
$315$	19.8178	1.11660
$316$	58.1664	3.27212
$317$	24.7495	1.39007	0.695035	−	0.718976i	$-0.255389\pi$
$317$	24.7495	1.39007	0.695035	+	0.718976i	$0.255389\pi$
$318$	−10.9816	−0.615815
$319$	−14.5241	−0.813192
$320$	57.4140	3.20954
$321$	4.35567	0.243110
$322$	20.5672	1.14617
$323$	1.90518	0.106007
$324$	−2.69045	−0.149470
$325$	−19.0939	−1.05914
$326$	66.9479	3.70790
$327$	−12.7015	−0.702397
$328$	−46.0330	−2.54175
$329$	9.77768	0.539061
$330$	21.8690	1.20385
$331$	5.13309	0.282140	0.141070	−	0.990000i	$-0.454946\pi$
$331$	5.13309	0.282140	0.141070	+	0.990000i	$0.454946\pi$
$332$	56.0314	3.07512
$333$	−7.04369	−0.385992
$334$	−17.1900	−0.940596
$335$	6.36465	0.347738
$336$	−46.3216	−2.52705
$337$	−13.6291	−0.742425	−0.371213	−	0.928548i	$-0.621058\pi$
$337$	−13.6291	−0.742425	−0.371213	+	0.928548i	$0.621058\pi$
$338$	2.96964	0.161527
$339$	7.04276	0.382510
$340$	−91.6727	−4.97165
$341$	−24.6512	−1.33494
$342$	−1.64649	−0.0890319
$343$	7.47331	0.403521
$344$	46.9307	2.53033
$345$	8.03860	0.432784
$346$	33.6542	1.80926
$347$	24.8300	1.33294	0.666472	−	0.745530i	$-0.267804\pi$
$347$	24.8300	1.33294	0.666472	+	0.745530i	$0.267804\pi$
$348$	36.3027	1.94603
$349$	−17.1373	−0.917336	−0.458668	−	0.888608i	$-0.651673\pi$
$349$	−17.1373	−0.917336	−0.458668	+	0.888608i	$0.651673\pi$
$350$	50.9005	2.72074
$351$	18.2220	0.972617
$352$	35.8128	1.90883
$353$	20.5131	1.09180	0.545902	−	0.837849i	$-0.316187\pi$
$353$	20.5131	1.09180	0.545902	+	0.837849i	$0.316187\pi$
$354$	10.9730	0.583206
$355$	−11.1706	−0.592873
$356$	−6.29458	−0.333612
$357$	20.8957	1.10592
$358$	−61.1147	−3.23001
$359$	13.8828	0.732706	0.366353	−	0.930476i	$-0.380606\pi$
$359$	13.8828	0.732706	0.366353	+	0.930476i	$0.380606\pi$
$360$	48.4207	2.55199
$361$	−18.8796	−0.993662
$362$	−53.7073	−2.82280
$363$	−6.43318	−0.337655
$364$	60.9940	3.19696
$365$	−25.8829	−1.35477
$366$	6.43947	0.336597
$367$	32.4597	1.69438	0.847191	−	0.531289i	$-0.178292\pi$
$367$	32.4597	1.69438	0.847191	+	0.531289i	$0.178292\pi$
$368$	27.2328	1.41961
$369$	−9.72534	−0.506281
$370$	−34.4260	−1.78972
$371$	−12.7674	−0.662853
$372$	61.6154	3.19461
$373$	27.4710	1.42239	0.711196	−	0.702994i	$-0.248154\pi$
$373$	27.4710	1.42239	0.711196	+	0.702994i	$0.248154\pi$
$374$	−33.4206	−1.72814
$375$	1.93142	0.0997379
$376$	23.8898	1.23202
$377$	−21.9886	−1.13247
$378$	−48.5761	−2.49849
$379$	−34.6545	−1.78008	−0.890040	−	0.455883i	$-0.849324\pi$
$379$	−34.6545	−1.78008	−0.890040	+	0.455883i	$0.849324\pi$
$380$	−5.79428	−0.297240
$381$	14.8593	0.761263
$382$	0.641037	0.0327983
$383$	−19.1476	−0.978398	−0.489199	−	0.872172i	$-0.662711\pi$
$383$	−19.1476	−0.978398	−0.489199	+	0.872172i	$0.662711\pi$
$384$	−17.5122	−0.893663
$385$	25.4255	1.29580
$386$	9.98566	0.508257
$387$	9.91499	0.504007
$388$	65.4958	3.32504
$389$	26.8001	1.35882	0.679410	−	0.733758i	$-0.262236\pi$
$389$	26.8001	1.35882	0.679410	+	0.733758i	$0.262236\pi$
$390$	33.1084	1.67651
$391$	−12.2847	−0.621266
$392$	−40.5584	−2.04851
$393$	8.64804	0.436236
$394$	−0.470760	−0.0237165
$395$	36.7082	1.84699
$396$	20.7965	1.04506
$397$	8.41317	0.422245	0.211122	−	0.977460i	$-0.432288\pi$
$397$	8.41317	0.422245	0.211122	+	0.977460i	$0.432288\pi$
$398$	10.6880	0.535741
$399$	1.32074	0.0661195
$400$	67.3967	3.36983
$401$	23.0220	1.14966	0.574831	−	0.818272i	$-0.305068\pi$
$401$	23.0220	1.14966	0.574831	+	0.818272i	$0.305068\pi$
$402$	−5.79961	−0.289258
$403$	−37.3206	−1.85907
$404$	41.3704	2.05825
$405$	−1.69792	−0.0843702
$406$	58.6172	2.90912
$407$	−9.03679	−0.447937
$408$	51.0544	2.52757
$409$	−18.9058	−0.934831	−0.467416	−	0.884038i	$-0.654815\pi$
$409$	−18.9058	−0.934831	−0.467416	+	0.884038i	$0.654815\pi$
$410$	−47.5326	−2.34747
$411$	−0.412987	−0.0203711
$412$	31.4137	1.54764
$413$	12.7574	0.627753
$414$	10.6167	0.521781
$415$	35.3608	1.73579
$416$	54.2186	2.65828
$417$	15.7965	0.773559
$418$	−2.11238	−0.103320
$419$	−16.9245	−0.826815	−0.413407	−	0.910546i	$-0.635661\pi$
$419$	−16.9245	−0.826815	−0.413407	+	0.910546i	$0.635661\pi$
$420$	−63.5506	−3.10095
$421$	−40.4862	−1.97318	−0.986589	−	0.163226i	$-0.947810\pi$
$421$	−40.4862	−1.97318	−0.986589	+	0.163226i	$0.947810\pi$
$422$	32.4971	1.58193
$423$	5.04717	0.245402
$424$	−31.1947	−1.51495
$425$	−30.4027	−1.47475
$426$	10.1789	0.493169
$427$	7.48670	0.362307
$428$	20.2443	0.978547
$429$	8.69092	0.419601
$430$	48.4595	2.33693
$431$	−2.93463	−0.141356	−0.0706781	−	0.997499i	$-0.522516\pi$
$431$	−2.93463	−0.141356	−0.0706781	+	0.997499i	$0.522516\pi$
$432$	−64.3191	−3.09455
$433$	−35.7290	−1.71703	−0.858514	−	0.512791i	$-0.828612\pi$
$433$	−35.7290	−1.71703	−0.858514	+	0.512791i	$0.828612\pi$
$434$	99.4892	4.77563
$435$	22.9102	1.09846
$436$	−59.0343	−2.82723
$437$	−0.776471	−0.0371436
$438$	23.5851	1.12694
$439$	10.0113	0.477812	0.238906	−	0.971043i	$-0.423211\pi$
$439$	10.0113	0.477812	0.238906	+	0.971043i	$0.423211\pi$
$440$	62.1219	2.96155
$441$	−8.56874	−0.408035
$442$	−50.5968	−2.40665
$443$	−1.59235	−0.0756547	−0.0378274	−	0.999284i	$-0.512044\pi$
$443$	−1.59235	−0.0756547	−0.0378274	+	0.999284i	$0.512044\pi$
$444$	22.5873	1.07195
$445$	−3.97244	−0.188312
$446$	−35.5441	−1.68306
$447$	6.43115	0.304183
$448$	−60.8250	−2.87371
$449$	−25.3951	−1.19847	−0.599236	−	0.800573i	$-0.704529\pi$
$449$	−25.3951	−1.19847	−0.599236	+	0.800573i	$0.704529\pi$
$450$	26.2745	1.23859
$451$	−12.4772	−0.587531
$452$	32.7334	1.53965
$453$	13.8308	0.649830
$454$	−29.9910	−1.40755
$455$	38.4927	1.80457
$456$	3.22695	0.151116
$457$	−13.4185	−0.627689	−0.313844	−	0.949474i	$-0.601617\pi$
$457$	−13.4185	−0.627689	−0.313844	+	0.949474i	$0.601617\pi$
$458$	−42.1012	−1.96726
$459$	29.0143	1.35427
$460$	37.3619	1.74201
$461$	10.9757	0.511187	0.255594	−	0.966784i	$-0.417729\pi$
$461$	10.9757	0.511187	0.255594	+	0.966784i	$0.417729\pi$
$462$	−23.1682	−1.07788
$463$	41.2944	1.91911	0.959557	−	0.281514i	$-0.0908365\pi$
$463$	41.2944	1.91911	0.959557	+	0.281514i	$0.0908365\pi$
$464$	77.6144	3.60316
$465$	38.8848	1.80324
$466$	1.69230	0.0783944
$467$	19.3892	0.897224	0.448612	−	0.893727i	$-0.351919\pi$
$467$	19.3892	0.897224	0.448612	+	0.893727i	$0.351919\pi$
$468$	31.4847	1.45538
$469$	−6.74278	−0.311353
$470$	24.6680	1.13785
$471$	−24.7882	−1.14218
$472$	31.1702	1.43473
$473$	12.7206	0.584892
$474$	−33.4494	−1.53638
$475$	−1.92163	−0.0881706
$476$	97.1191	4.45145
$477$	−6.59047	−0.301757
$478$	−17.4580	−0.798510
$479$	−11.6141	−0.530662	−0.265331	−	0.964157i	$-0.585481\pi$
$479$	−11.6141	−0.530662	−0.265331	+	0.964157i	$0.585481\pi$
$480$	−56.4911	−2.57845
$481$	−13.6812	−0.623809
$482$	12.1539	0.553595
$483$	−8.51619	−0.387500
$484$	−29.9002	−1.35910
$485$	41.3337	1.87687
$486$	−40.8277	−1.85198
$487$	9.26475	0.419826	0.209913	−	0.977720i	$-0.432682\pi$
$487$	9.26475	0.419826	0.209913	+	0.977720i	$0.432682\pi$
$488$	18.2922	0.828051
$489$	−27.7208	−1.25358
$490$	−41.8797	−1.89193
$491$	−35.2575	−1.59115	−0.795574	−	0.605856i	$-0.792831\pi$
$491$	−35.2575	−1.59115	−0.795574	+	0.605856i	$0.792831\pi$
$492$	31.1867	1.40601
$493$	−35.0118	−1.57685
$494$	−3.19803	−0.143886
$495$	13.1244	0.589900
$496$	131.732	5.91496
$497$	11.8342	0.530838
$498$	−32.2216	−1.44388
$499$	−27.6416	−1.23741	−0.618703	−	0.785625i	$-0.712342\pi$
$499$	−27.6416	−1.23741	−0.618703	+	0.785625i	$0.712342\pi$
$500$	8.97685	0.401457
$501$	7.11779	0.318000
$502$	13.9243	0.621473
$503$	−29.7528	−1.32661	−0.663307	−	0.748347i	$-0.730848\pi$
$503$	−29.7528	−1.32661	−0.663307	+	0.748347i	$0.730848\pi$
$504$	−51.2974	−2.28497
$505$	26.1084	1.16181
$506$	13.6208	0.605518
$507$	−1.22963	−0.0546097
$508$	69.0630	3.06417
$509$	41.2582	1.82874	0.914369	−	0.404881i	$-0.132687\pi$
$509$	41.2582	1.82874	0.914369	+	0.404881i	$0.132687\pi$
$510$	52.7176	2.33437
$511$	27.4206	1.21302
$512$	13.1522	0.581251
$513$	1.83388	0.0809679
$514$	−11.7681	−0.519069
$515$	19.8248	0.873587
$516$	−31.7949	−1.39969
$517$	6.47533	0.284785
$518$	36.4713	1.60246
$519$	−13.9350	−0.611680
$520$	94.0491	4.12432
$521$	−18.2996	−0.801718	−0.400859	−	0.916140i	$-0.631288\pi$
$521$	−18.2996	−0.801718	−0.400859	+	0.916140i	$0.631288\pi$
$522$	30.2578	1.32435
$523$	−9.70344	−0.424302	−0.212151	−	0.977237i	$-0.568047\pi$
$523$	−9.70344	−0.424302	−0.212151	+	0.977237i	$0.568047\pi$
$524$	40.1944	1.75590
$525$	−21.0761	−0.919838
$526$	−15.7341	−0.686038
$527$	−59.4245	−2.58857
$528$	−30.6768	−1.33504
$529$	−17.9933	−0.782316
$530$	−32.2109	−1.39915
$531$	6.58530	0.285778
$532$	6.13852	0.266139
$533$	−18.8898	−0.818210
$534$	3.61978	0.156643
$535$	12.7760	0.552354
$536$	−16.4746	−0.711595
$537$	25.3055	1.09201
$538$	−85.3147	−3.67818
$539$	−10.9934	−0.473518
$540$	−88.2420	−3.79733
$541$	13.8049	0.593521	0.296761	−	0.954952i	$-0.404094\pi$
$541$	13.8049	0.593521	0.296761	+	0.954952i	$0.404094\pi$
$542$	4.50925	0.193689
$543$	22.2384	0.954339
$544$	86.3307	3.70140
$545$	−37.2559	−1.59587
$546$	−35.0754	−1.50109
$547$	18.8065	0.804107	0.402054	−	0.915616i	$-0.368297\pi$
$547$	18.8065	0.804107	0.402054	+	0.915616i	$0.368297\pi$
$548$	−1.91948	−0.0819962
$549$	3.86458	0.164936
$550$	33.7092	1.43736
$551$	−2.21296	−0.0942754
$552$	−20.8076	−0.885629
$553$	−38.8891	−1.65373
$554$	−49.6071	−2.10760
$555$	14.2546	0.605075
$556$	73.4191	3.11366
$557$	24.1122	1.02167	0.510833	−	0.859680i	$-0.329337\pi$
$557$	24.1122	1.02167	0.510833	+	0.859680i	$0.329337\pi$
$558$	51.3556	2.17406
$559$	19.2582	0.814536
$560$	−135.870	−5.74154
$561$	13.8383	0.584254
$562$	56.1365	2.36797
$563$	−27.3218	−1.15148	−0.575739	−	0.817634i	$-0.695285\pi$
$563$	−27.3218	−1.15148	−0.575739	+	0.817634i	$0.695285\pi$
$564$	−16.1850	−0.681511
$565$	20.6577	0.869075
$566$	67.4455	2.83495
$567$	1.79879	0.0755422
$568$	28.9146	1.21323
$569$	25.9031	1.08591	0.542957	−	0.839760i	$-0.317305\pi$
$569$	25.9031	1.08591	0.542957	+	0.839760i	$0.317305\pi$
$570$	3.33207	0.139565
$571$	7.22429	0.302327	0.151164	−	0.988509i	$-0.451698\pi$
$571$	7.22429	0.302327	0.151164	+	0.988509i	$0.451698\pi$
$572$	40.3937	1.68895
$573$	−0.265431	−0.0110885
$574$	50.3565	2.10184
$575$	12.3908	0.516733
$576$	−31.3975	−1.30823
$577$	15.9846	0.665446	0.332723	−	0.943025i	$-0.392033\pi$
$577$	15.9846	0.665446	0.332723	+	0.943025i	$0.392033\pi$
$578$	−35.1267	−1.46108
$579$	−4.13472	−0.171833
$580$	106.482	4.42144
$581$	−37.4616	−1.55417
$582$	−37.6642	−1.56123
$583$	−8.45533	−0.350184
$584$	66.9967	2.77234
$585$	19.8697	0.821509
$586$	−90.7485	−3.74878
$587$	−22.7804	−0.940246	−0.470123	−	0.882601i	$-0.655790\pi$
$587$	−22.7804	−0.940246	−0.470123	+	0.882601i	$0.655790\pi$
$588$	27.4778	1.13317
$589$	−3.75599	−0.154763
$590$	32.1857	1.32506
$591$	0.194925	0.00801816
$592$	48.2912	1.98476
$593$	−16.7738	−0.688818	−0.344409	−	0.938820i	$-0.611921\pi$
$593$	−16.7738	−0.688818	−0.344409	+	0.938820i	$0.611921\pi$
$594$	−32.1699	−1.31995
$595$	61.2908	2.51268
$596$	29.8908	1.22437
$597$	−4.42553	−0.181125
$598$	20.6211	0.843260
$599$	10.6632	0.435685	0.217842	−	0.975984i	$-0.430098\pi$
$599$	10.6632	0.435685	0.217842	+	0.975984i	$0.430098\pi$
$600$	−51.4952	−2.10228
$601$	6.87252	0.280336	0.140168	−	0.990128i	$-0.455236\pi$
$601$	6.87252	0.280336	0.140168	+	0.990128i	$0.455236\pi$
$602$	−51.3386	−2.09240
$603$	−3.48058	−0.141740
$604$	64.2831	2.61564
$605$	−18.8697	−0.767162
$606$	−23.7906	−0.966426
$607$	15.5738	0.632122	0.316061	−	0.948739i	$-0.397640\pi$
$607$	15.5738	0.632122	0.316061	+	0.948739i	$0.397640\pi$
$608$	5.45663	0.221296
$609$	−24.2714	−0.983525
$610$	18.8881	0.764759
$611$	9.80328	0.396598
$612$	50.1322	2.02647
$613$	−43.5205	−1.75778	−0.878889	−	0.477026i	$-0.841715\pi$
$613$	−43.5205	−1.75778	−0.878889	+	0.477026i	$0.841715\pi$
$614$	−53.2841	−2.15037
$615$	19.6816	0.793639
$616$	−65.8127	−2.65167
$617$	5.00808	0.201618	0.100809	−	0.994906i	$-0.467857\pi$
$617$	5.00808	0.201618	0.100809	+	0.994906i	$0.467857\pi$
$618$	−18.0648	−0.726674
$619$	29.6613	1.19219	0.596095	−	0.802914i	$-0.296718\pi$
$619$	29.6613	1.19219	0.596095	+	0.802914i	$0.296718\pi$
$620$	180.729	7.25826
$621$	−11.8250	−0.474521
$622$	−78.9983	−3.16754
$623$	4.20845	0.168608
$624$	−46.4429	−1.85920
$625$	−22.0229	−0.880916
$626$	48.3683	1.93319
$627$	0.874665	0.0349308
$628$	−115.211	−4.59741
$629$	−21.7842	−0.868592
$630$	−52.9685	−2.11032
$631$	−36.2588	−1.44344	−0.721721	−	0.692184i	$-0.756649\pi$
$631$	−36.2588	−1.44344	−0.721721	+	0.692184i	$0.756649\pi$
$632$	−95.0176	−3.77960
$633$	−13.4559	−0.534824
$634$	−66.1500	−2.62715
$635$	43.5849	1.72961
$636$	21.1340	0.838016
$637$	−16.6433	−0.659434
$638$	38.8196	1.53688
$639$	6.10875	0.241659
$640$	−51.3663	−2.03043
$641$	−42.0527	−1.66098	−0.830492	−	0.557031i	$-0.811940\pi$
$641$	−42.0527	−1.66098	−0.830492	+	0.557031i	$0.811940\pi$
$642$	−11.6418	−0.459464
$643$	−26.0273	−1.02642	−0.513208	−	0.858264i	$-0.671543\pi$
$643$	−26.0273	−1.02642	−0.513208	+	0.858264i	$0.671543\pi$
$644$	−39.5816	−1.55973
$645$	−20.0654	−0.790075
$646$	−5.09213	−0.200347
$647$	3.98674	0.156735	0.0783675	−	0.996925i	$-0.475029\pi$
$647$	3.98674	0.156735	0.0783675	+	0.996925i	$0.475029\pi$
$648$	4.39498	0.172651
$649$	8.44870	0.331641
$650$	51.0338	2.00171
$651$	−41.1950	−1.61456
$652$	−128.841	−5.04580
$653$	−3.03328	−0.118701	−0.0593507	−	0.998237i	$-0.518903\pi$
$653$	−3.03328	−0.118701	−0.0593507	+	0.998237i	$0.518903\pi$
$654$	33.9485	1.32749
$655$	25.3663	0.991142
$656$	66.6765	2.60328
$657$	14.1543	0.552213
$658$	−26.1336	−1.01879
$659$	18.9642	0.738739	0.369369	−	0.929283i	$-0.379574\pi$
$659$	18.9642	0.738739	0.369369	+	0.929283i	$0.379574\pi$
$660$	−42.0868	−1.63823
$661$	6.55636	0.255013	0.127506	−	0.991838i	$-0.459303\pi$
$661$	6.55636	0.255013	0.127506	+	0.991838i	$0.459303\pi$
$662$	−13.7196	−0.533229
$663$	20.9504	0.813646
$664$	−91.5299	−3.55205
$665$	3.87396	0.150226
$666$	18.8262	0.729502
$667$	14.2693	0.552511
$668$	33.0821	1.27999
$669$	14.7176	0.569014
$670$	−17.0113	−0.657204
$671$	4.95812	0.191406
$672$	59.8473	2.30866
$673$	−18.2848	−0.704826	−0.352413	−	0.935845i	$-0.614639\pi$
$673$	−18.2848	−0.704826	−0.352413	+	0.935845i	$0.614639\pi$
$674$	36.4276	1.40314
$675$	−29.2649	−1.12641
$676$	−5.71507	−0.219810
$677$	−18.7096	−0.719068	−0.359534	−	0.933132i	$-0.617064\pi$
$677$	−18.7096	−0.719068	−0.359534	+	0.933132i	$0.617064\pi$
$678$	−18.8237	−0.722921
$679$	−43.7894	−1.68048
$680$	149.752	5.74272
$681$	12.4182	0.475868
$682$	65.8873	2.52296
$683$	29.2550	1.11941	0.559705	−	0.828692i	$-0.310914\pi$
$683$	29.2550	1.11941	0.559705	+	0.828692i	$0.310914\pi$
$684$	3.16866	0.121157
$685$	−1.21137	−0.0462839
$686$	−19.9745	−0.762631
$687$	17.4327	0.665098
$688$	−67.9768	−2.59159
$689$	−12.8009	−0.487675
$690$	−21.4854	−0.817936
$691$	8.73408	0.332260	0.166130	−	0.986104i	$-0.446873\pi$
$691$	8.73408	0.332260	0.166130	+	0.986104i	$0.446873\pi$
$692$	−64.7674	−2.46209
$693$	−13.9042	−0.528176
$694$	−66.3651	−2.51919
$695$	46.3340	1.75755
$696$	−59.3022	−2.24784
$697$	−30.0778	−1.13928
$698$	45.8041	1.73371
$699$	−0.700724	−0.0265038
$700$	−97.9577	−3.70245
$701$	−3.89166	−0.146986	−0.0734929	−	0.997296i	$-0.523415\pi$
$701$	−3.89166	−0.146986	−0.0734929	+	0.997296i	$0.523415\pi$
$702$	−48.7033	−1.83819
$703$	−1.37689	−0.0519305
$704$	−40.2818	−1.51818
$705$	−10.2142	−0.384688
$706$	−54.8271	−2.06345
$707$	−27.6595	−1.04024
$708$	−21.1174	−0.793641
$709$	−50.5093	−1.89692	−0.948459	−	0.316900i	$-0.897358\pi$
$709$	−50.5093	−1.89692	−0.948459	+	0.316900i	$0.897358\pi$
$710$	29.8565	1.12050
$711$	−20.0743	−0.752844
$712$	10.2825	0.385352
$713$	24.2189	0.907004
$714$	−55.8496	−2.09012
$715$	25.4920	0.953348
$716$	117.615	4.39548
$717$	7.22875	0.269963
$718$	−37.1056	−1.38477
$719$	35.9270	1.33985	0.669926	−	0.742428i	$-0.266326\pi$
$719$	35.9270	1.33985	0.669926	+	0.742428i	$0.266326\pi$
$720$	−70.1350	−2.61378
$721$	−21.0026	−0.782180
$722$	50.4610	1.87796
$723$	−5.03251	−0.187161
$724$	103.360	3.84133
$725$	35.3142	1.31154
$726$	17.1945	0.638147
$727$	10.2557	0.380363	0.190181	−	0.981749i	$-0.439092\pi$
$727$	10.2557	0.380363	0.190181	+	0.981749i	$0.439092\pi$
$728$	−99.6366	−3.69278
$729$	18.4745	0.684241
$730$	69.1793	2.56044
$731$	30.6643	1.13416
$732$	−12.3927	−0.458049
$733$	−23.6132	−0.872174	−0.436087	−	0.899904i	$-0.643636\pi$
$733$	−23.6132	−0.872174	−0.436087	+	0.899904i	$0.643636\pi$
$734$	−86.7576	−3.20228
$735$	17.3409	0.639630
$736$	−35.1847	−1.29692
$737$	−4.46545	−0.164487
$738$	25.9937	0.956841
$739$	−42.2987	−1.55598	−0.777991	−	0.628275i	$-0.783761\pi$
$739$	−42.2987	−1.55598	−0.777991	+	0.628275i	$0.783761\pi$
$740$	66.2527	2.43550
$741$	1.32419	0.0486455
$742$	34.1246	1.25275
$743$	−22.0473	−0.808838	−0.404419	−	0.914574i	$-0.632526\pi$
$743$	−22.0473	−0.808838	−0.404419	+	0.914574i	$0.632526\pi$
$744$	−100.652	−3.69007
$745$	18.8637	0.691114
$746$	−73.4238	−2.68824
$747$	−19.3374	−0.707520
$748$	64.3178	2.35169
$749$	−13.5350	−0.494559
$750$	−5.16225	−0.188499
$751$	−10.3954	−0.379333	−0.189666	−	0.981849i	$-0.560741\pi$
$751$	−10.3954	−0.379333	−0.189666	+	0.981849i	$0.560741\pi$
$752$	−34.6032	−1.26185
$753$	−5.76558	−0.210110
$754$	58.7707	2.14030
$755$	40.5684	1.47643
$756$	93.4846	3.40000
$757$	34.6543	1.25953	0.629765	−	0.776785i	$-0.283151\pi$
$757$	34.6543	1.25953	0.629765	+	0.776785i	$0.283151\pi$
$758$	92.6238	3.36425
$759$	−5.63990	−0.204715
$760$	9.46523	0.343340
$761$	23.0660	0.836142	0.418071	−	0.908414i	$-0.362706\pi$
$761$	23.0660	0.836142	0.418071	+	0.908414i	$0.362706\pi$
$762$	−39.7155	−1.43874
$763$	39.4694	1.42889
$764$	−1.23367	−0.0446327
$765$	31.6379	1.14387
$766$	51.1774	1.84912
$767$	12.7909	0.461851
$768$	7.65820	0.276342
$769$	−3.42319	−0.123444	−0.0617218	−	0.998093i	$-0.519659\pi$
$769$	−3.42319	−0.123444	−0.0617218	+	0.998093i	$0.519659\pi$
$770$	−67.9567	−2.44899
$771$	4.87277	0.175488
$772$	−19.2174	−0.691648
$773$	−2.24921	−0.0808986	−0.0404493	−	0.999182i	$-0.512879\pi$
$773$	−2.24921	−0.0808986	−0.0404493	+	0.999182i	$0.512879\pi$
$774$	−26.5006	−0.952544
$775$	59.9377	2.15302
$776$	−106.990	−3.84073
$777$	−15.1015	−0.541764
$778$	−71.6309	−2.56809
$779$	−1.90110	−0.0681139
$780$	−63.7170	−2.28143
$781$	7.83730	0.280441
$782$	32.8344	1.17416
$783$	−33.7016	−1.20440
$784$	58.7469	2.09810
$785$	−72.7083	−2.59507
$786$	−23.1143	−0.824460
$787$	−24.9602	−0.889736	−0.444868	−	0.895596i	$-0.646749\pi$
$787$	−24.9602	−0.889736	−0.444868	+	0.895596i	$0.646749\pi$
$788$	0.905975	0.0322740
$789$	6.51493	0.231938
$790$	−98.1130	−3.49070
$791$	−21.8850	−0.778140
$792$	−33.9720	−1.20714
$793$	7.50631	0.266557
$794$	−22.4866	−0.798018
$795$	13.3374	0.473030
$796$	−20.5690	−0.729049
$797$	26.0866	0.924033	0.462017	−	0.886871i	$-0.347126\pi$
$797$	26.0866	0.924033	0.462017	+	0.886871i	$0.347126\pi$
$798$	−3.53004	−0.124962
$799$	15.6095	0.552224
$800$	−87.0762	−3.07861
$801$	2.17237	0.0767569
$802$	−61.5327	−2.17280
$803$	18.1595	0.640834
$804$	11.1613	0.393630
$805$	−24.9795	−0.880412
$806$	99.7497	3.51353
$807$	35.3259	1.24353
$808$	−67.5805	−2.37747
$809$	22.2086	0.780814	0.390407	−	0.920642i	$-0.372334\pi$
$809$	22.2086	0.780814	0.390407	+	0.920642i	$0.372334\pi$
$810$	4.53816	0.159455
$811$	45.4539	1.59610	0.798051	−	0.602590i	$-0.205864\pi$
$811$	45.4539	1.59610	0.798051	+	0.602590i	$0.205864\pi$
$812$	−112.809	−3.95881
$813$	−1.86713	−0.0654829
$814$	24.1534	0.846575
$815$	−81.3102	−2.84817
$816$	−73.9498	−2.58876
$817$	1.93817	0.0678081
$818$	50.5310	1.76678
$819$	−21.0501	−0.735551
$820$	91.4763	3.19449
$821$	6.70398	0.233971	0.116985	−	0.993134i	$-0.462677\pi$
$821$	6.70398	0.233971	0.116985	+	0.993134i	$0.462677\pi$
$822$	1.10382	0.0385002
$823$	−37.9076	−1.32138	−0.660689	−	0.750660i	$-0.729736\pi$
$823$	−37.9076	−1.32138	−0.660689	+	0.750660i	$0.729736\pi$
$824$	−51.3157	−1.78767
$825$	−13.9578	−0.485948
$826$	−34.0979	−1.18642
$827$	34.6432	1.20466	0.602331	−	0.798246i	$-0.294239\pi$
$827$	34.6432	1.20466	0.602331	+	0.798246i	$0.294239\pi$
$828$	−20.4317	−0.710052
$829$	45.0713	1.56539	0.782695	−	0.622405i	$-0.213844\pi$
$829$	45.0713	1.56539	0.782695	+	0.622405i	$0.213844\pi$
$830$	−94.5117	−3.28055
$831$	20.5406	0.712545
$832$	−60.9843	−2.11425
$833$	−26.5007	−0.918196
$834$	−42.2206	−1.46198
$835$	20.8778	0.722505
$836$	4.06528	0.140600
$837$	−57.2006	−1.97714
$838$	45.2354	1.56263
$839$	39.2294	1.35435	0.677175	−	0.735822i	$-0.263204\pi$
$839$	39.2294	1.35435	0.677175	+	0.735822i	$0.263204\pi$
$840$	103.813	3.58188
$841$	11.6680	0.402344
$842$	108.211	3.72919
$843$	−23.2442	−0.800572
$844$	−62.5405	−2.15273
$845$	−3.60672	−0.124075
$846$	−13.4900	−0.463795
$847$	19.9908	0.686891
$848$	45.1840	1.55162
$849$	−27.9269	−0.958447
$850$	81.2596	2.78718
$851$	8.87830	0.304344
$852$	−19.5892	−0.671116
$853$	−17.3166	−0.592910	−0.296455	−	0.955047i	$-0.595804\pi$
$853$	−17.3166	−0.592910	−0.296455	+	0.955047i	$0.595804\pi$
$854$	−20.0103	−0.684739
$855$	1.99971	0.0683886
$856$	−33.0701	−1.13031
$857$	4.03324	0.137773	0.0688864	−	0.997625i	$-0.478055\pi$
$857$	4.03324	0.137773	0.0688864	+	0.997625i	$0.478055\pi$
$858$	−23.2289	−0.793022
$859$	−1.06416	−0.0363088	−0.0181544	−	0.999835i	$-0.505779\pi$
$859$	−1.06416	−0.0363088	−0.0181544	+	0.999835i	$0.505779\pi$
$860$	−93.2602	−3.18014
$861$	−20.8509	−0.710597
$862$	7.84363	0.267155
$863$	−15.3067	−0.521045	−0.260522	−	0.965468i	$-0.583895\pi$
$863$	−15.3067	−0.521045	−0.260522	+	0.965468i	$0.583895\pi$
$864$	83.0999	2.82712
$865$	−40.8740	−1.38976
$866$	95.4958	3.24508
$867$	14.5447	0.493966
$868$	−191.467	−6.49880
$869$	−25.7546	−0.873663
$870$	−61.2341	−2.07603
$871$	−6.76044	−0.229069
$872$	96.4354	3.26571
$873$	−22.6038	−0.765021
$874$	2.07534	0.0701993
$875$	−6.00177	−0.202897
$876$	−45.3894	−1.53356
$877$	18.1945	0.614385	0.307192	−	0.951647i	$-0.400610\pi$
$877$	18.1945	0.614385	0.307192	+	0.951647i	$0.400610\pi$
$878$	−26.7579	−0.903036
$879$	37.5758	1.26740
$880$	−89.9806	−3.03324
$881$	33.7091	1.13569	0.567844	−	0.823136i	$-0.307777\pi$
$881$	33.7091	1.13569	0.567844	+	0.823136i	$0.307777\pi$
$882$	22.9024	0.771163
$883$	42.9496	1.44537	0.722684	−	0.691178i	$-0.242908\pi$
$883$	42.9496	1.44537	0.722684	+	0.691178i	$0.242908\pi$
$884$	97.3734	3.27502
$885$	−13.3270	−0.447981
$886$	4.25600	0.142983
$887$	−45.8266	−1.53871	−0.769354	−	0.638823i	$-0.779422\pi$
$887$	−45.8266	−1.53871	−0.769354	+	0.638823i	$0.779422\pi$
$888$	−36.8975	−1.23820
$889$	−46.1743	−1.54864
$890$	10.6175	0.355898
$891$	1.19126	0.0399088
$892$	68.4044	2.29035
$893$	0.986616	0.0330158
$894$	−17.1891	−0.574888
$895$	74.2256	2.48109
$896$	54.4181	1.81798
$897$	−8.53848	−0.285092
$898$	67.8756	2.26504
$899$	69.0245	2.30210
$900$	−50.5651	−1.68550
$901$	−20.3825	−0.679039
$902$	33.3489	1.11040
$903$	21.2575	0.707406
$904$	−53.4715	−1.77844
$905$	65.2291	2.16829
$906$	−36.9668	−1.22814
$907$	35.0160	1.16269	0.581343	−	0.813658i	$-0.302527\pi$
$907$	35.0160	1.16269	0.581343	+	0.813658i	$0.302527\pi$
$908$	57.7176	1.91542
$909$	−14.2777	−0.473560
$910$	−102.883	−3.41052
$911$	49.6207	1.64401	0.822003	−	0.569483i	$-0.192857\pi$
$911$	49.6207	1.64401	0.822003	+	0.569483i	$0.192857\pi$
$912$	−4.67408	−0.154774
$913$	−24.8092	−0.821065
$914$	35.8646	1.18630
$915$	−7.82093	−0.258552
$916$	81.0237	2.67710
$917$	−26.8733	−0.887435
$918$	−77.5490	−2.55950
$919$	38.0155	1.25402	0.627008	−	0.779013i	$-0.284279\pi$
$919$	38.0155	1.25402	0.627008	+	0.779013i	$0.284279\pi$
$920$	−61.0324	−2.01218
$921$	22.0631	0.727004
$922$	−29.3355	−0.966114
$923$	11.8652	0.390549
$924$	44.5872	1.46681
$925$	21.9723	0.722444
$926$	−110.371	−3.62701
$927$	−10.8414	−0.356079
$928$	−100.277	−3.29177
$929$	−41.0179	−1.34575	−0.672876	−	0.739755i	$-0.734941\pi$
$929$	−41.0179	−1.34575	−0.672876	+	0.739755i	$0.734941\pi$
$930$	−103.931	−3.40802
$931$	−1.67501	−0.0548962
$932$	−3.25683	−0.106681
$933$	32.7105	1.07089
$934$	−51.8230	−1.69570
$935$	40.5903	1.32744
$936$	−51.4317	−1.68110
$937$	28.5101	0.931386	0.465693	−	0.884946i	$-0.345805\pi$
$937$	28.5101	0.931386	0.465693	+	0.884946i	$0.345805\pi$
$938$	18.0220	0.588438
$939$	−20.0276	−0.653578
$940$	−47.4735	−1.54842
$941$	10.1914	0.332230	0.166115	−	0.986106i	$-0.446878\pi$
$941$	10.1914	0.332230	0.166115	+	0.986106i	$0.446878\pi$
$942$	66.2534	2.15865
$943$	12.2584	0.399189
$944$	−45.1486	−1.46946
$945$	58.9971	1.91918
$946$	−33.9993	−1.10541
$947$	−0.580655	−0.0188687	−0.00943437	−	0.999955i	$-0.503003\pi$
$947$	−0.580655	−0.0188687	−0.00943437	+	0.999955i	$0.503003\pi$
$948$	64.3731	2.09074
$949$	27.4924	0.892441
$950$	5.13611	0.166637
$951$	27.3904	0.888195
$952$	−158.649	−5.14183
$953$	−22.0475	−0.714187	−0.357094	−	0.934069i	$-0.616232\pi$
$953$	−22.0475	−0.714187	−0.357094	+	0.934069i	$0.616232\pi$
$954$	17.6149	0.570303
$955$	−0.778558	−0.0251935
$956$	33.5978	1.08663
$957$	−16.0739	−0.519594
$958$	31.0419	1.00292
$959$	1.28333	0.0414410
$960$	63.5404	2.05076
$961$	86.1531	2.77913
$962$	36.5668	1.17896
$963$	−6.98668	−0.225143
$964$	−23.3901	−0.753346
$965$	−12.1279	−0.390410
$966$	22.7619	0.732352
$967$	−13.9819	−0.449629	−0.224814	−	0.974402i	$-0.572178\pi$
$967$	−13.9819	−0.449629	−0.224814	+	0.974402i	$0.572178\pi$
$968$	48.8434	1.56989
$969$	2.10848	0.0677340
$970$	−110.476	−3.54717
$971$	−52.9828	−1.70030	−0.850149	−	0.526542i	$-0.823488\pi$
$971$	−52.9828	−1.70030	−0.850149	+	0.526542i	$0.823488\pi$
$972$	78.5727	2.52022
$973$	−49.0868	−1.57365
$974$	−24.7626	−0.793446
$975$	−21.1313	−0.676744
$976$	−26.4954	−0.848097
$977$	−23.2654	−0.744326	−0.372163	−	0.928167i	$-0.621384\pi$
$977$	−23.2654	−0.744326	−0.372163	+	0.928167i	$0.621384\pi$
$978$	74.0916	2.36919
$979$	2.78707	0.0890752
$980$	80.5974	2.57459
$981$	20.3738	0.650486
$982$	94.2355	3.00718
$983$	−60.1389	−1.91813	−0.959067	−	0.283179i	$-0.908611\pi$
$983$	−60.1389	−1.91813	−0.959067	+	0.283179i	$0.908611\pi$
$984$	−50.9450	−1.62407
$985$	0.571751	0.0182175
$986$	93.5790	2.98016
$987$	10.8210	0.344437
$988$	6.15460	0.195804
$989$	−12.4975	−0.397396
$990$	−35.0787	−1.11488
$991$	14.3900	0.457114	0.228557	−	0.973531i	$-0.426599\pi$
$991$	14.3900	0.457114	0.228557	+	0.973531i	$0.426599\pi$
$992$	−170.198	−5.40378
$993$	5.68082	0.180276
$994$	−31.6303	−1.00325
$995$	−12.9809	−0.411522
$996$	62.0103	1.96487
$997$	−17.0780	−0.540867	−0.270434	−	0.962739i	$-0.587167\pi$
$997$	−17.0780	−0.540867	−0.270434	+	0.962739i	$0.587167\pi$
$998$	73.8798	2.33863
$999$	−20.9689	−0.663428

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4021.2.a.c.1.6	✓	182

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4021.2.a.c.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-2.67278 q^{2} +1.10671 q^{3} +5.14375 q^{4} +3.24617 q^{5} -2.95798 q^{6} -3.43903 q^{7} -8.40257 q^{8} -1.77520 q^{9} +O(q^{10})\)	\(q-2.67278 q^{2} +1.10671 q^{3} +5.14375 q^{4} +3.24617 q^{5} -2.95798 q^{6} -3.43903 q^{7} -8.40257 q^{8} -1.77520 q^{9} -8.67630 q^{10} -2.27752 q^{11} +5.69262 q^{12} -3.44803 q^{13} +9.19177 q^{14} +3.59256 q^{15} +12.1707 q^{16} -5.49021 q^{17} +4.74472 q^{18} -0.347015 q^{19} +16.6975 q^{20} -3.80599 q^{21} +6.08731 q^{22} +2.23757 q^{23} -9.29917 q^{24} +5.53762 q^{25} +9.21583 q^{26} -5.28474 q^{27} -17.6895 q^{28} +6.37715 q^{29} -9.60211 q^{30} +10.8237 q^{31} -15.7245 q^{32} -2.52054 q^{33} +14.6741 q^{34} -11.1637 q^{35} -9.13120 q^{36} +3.96782 q^{37} +0.927494 q^{38} -3.81596 q^{39} -27.2762 q^{40} +5.47844 q^{41} +10.1726 q^{42} -5.58528 q^{43} -11.7150 q^{44} -5.76261 q^{45} -5.98054 q^{46} -2.84315 q^{47} +13.4694 q^{48} +4.82691 q^{49} -14.8008 q^{50} -6.07605 q^{51} -17.7358 q^{52} +3.71252 q^{53} +14.1250 q^{54} -7.39321 q^{55} +28.8967 q^{56} -0.384043 q^{57} -17.0447 q^{58} -3.70961 q^{59} +18.4792 q^{60} -2.17698 q^{61} -28.9294 q^{62} +6.10497 q^{63} +17.6867 q^{64} -11.1929 q^{65} +6.73686 q^{66} +1.96066 q^{67} -28.2403 q^{68} +2.47634 q^{69} +29.8380 q^{70} -3.44116 q^{71} +14.9163 q^{72} -7.97336 q^{73} -10.6051 q^{74} +6.12851 q^{75} -1.78496 q^{76} +7.83245 q^{77} +10.1992 q^{78} +11.3082 q^{79} +39.5082 q^{80} -0.523053 q^{81} -14.6427 q^{82} +10.8931 q^{83} -19.5771 q^{84} -17.8221 q^{85} +14.9282 q^{86} +7.05762 q^{87} +19.1370 q^{88} -1.22373 q^{89} +15.4022 q^{90} +11.8579 q^{91} +11.5095 q^{92} +11.9787 q^{93} +7.59912 q^{94} -1.12647 q^{95} -17.4024 q^{96} +12.7331 q^{97} -12.9013 q^{98} +4.04305 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9}+O(q^{10}) \) 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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