LMFDB - Embedded newform 6223.2.a.l.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6223,2,Mod(1,6223)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6223, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6223.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6223 = 7^{2} \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6223.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:	$49.6909051778$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 8 x^{19} + 152 x^{17} - 274 x^{16} - 1061 x^{15} + 3125 x^{14} + 2977 x^{13} - 15474 x^{12} + \cdots + 31 $ x^20 - 8x^19 + 152x^17 - 274x^16 - 1061x^15 + 3125x^14 + 2977x^13 - 15474x^12 - 56x^11 + 39579x^10 - 17664x^9 - 52271x^8 + 35701x^7 + 32493x^6 - 25504x^5 - 8607x^4 + 6812x^3 + 609x^2 - 425x + 31
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 889)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$1.78791$ of defining polynomial
Character	$\chi$	$=$	6223.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.78791 q^{2} -1.55116 q^{3} +1.19664 q^{4} -2.61034 q^{5} -2.77333 q^{6} -1.43634 q^{8} -0.593917 q^{9} +O(q^{10})$	\(q+1.78791 q^{2} -1.55116 q^{3} +1.19664 q^{4} -2.61034 q^{5} -2.77333 q^{6} -1.43634 q^{8} -0.593917 q^{9} -4.66707 q^{10} -3.67427 q^{11} -1.85617 q^{12} -4.83827 q^{13} +4.04904 q^{15} -4.96133 q^{16} -2.98581 q^{17} -1.06187 q^{18} -4.34824 q^{19} -3.12363 q^{20} -6.56928 q^{22} +2.59876 q^{23} +2.22799 q^{24} +1.81388 q^{25} -8.65041 q^{26} +5.57472 q^{27} -1.91937 q^{29} +7.23934 q^{30} -1.05650 q^{31} -5.99776 q^{32} +5.69937 q^{33} -5.33837 q^{34} -0.710704 q^{36} -7.32285 q^{37} -7.77428 q^{38} +7.50490 q^{39} +3.74934 q^{40} +1.13826 q^{41} -7.87546 q^{43} -4.39677 q^{44} +1.55033 q^{45} +4.64636 q^{46} -2.04802 q^{47} +7.69580 q^{48} +3.24306 q^{50} +4.63145 q^{51} -5.78966 q^{52} -12.5047 q^{53} +9.96713 q^{54} +9.59110 q^{55} +6.74480 q^{57} -3.43167 q^{58} -4.81235 q^{59} +4.84524 q^{60} +10.9771 q^{61} -1.88893 q^{62} -0.800808 q^{64} +12.6295 q^{65} +10.1900 q^{66} -1.31670 q^{67} -3.57293 q^{68} -4.03108 q^{69} +7.73820 q^{71} +0.853068 q^{72} +6.77819 q^{73} -13.0926 q^{74} -2.81361 q^{75} -5.20327 q^{76} +13.4181 q^{78} +0.216655 q^{79} +12.9508 q^{80} -6.86551 q^{81} +2.03511 q^{82} +3.43302 q^{83} +7.79398 q^{85} -14.0807 q^{86} +2.97724 q^{87} +5.27751 q^{88} -9.32688 q^{89} +2.77185 q^{90} +3.10977 q^{92} +1.63879 q^{93} -3.66168 q^{94} +11.3504 q^{95} +9.30345 q^{96} -0.511430 q^{97} +2.18221 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 8 q^{2} + 24 q^{4} - 3 q^{5} - 6 q^{6} + 24 q^{8} + 30 q^{9}+O(q^{10}) $ 20 * q + 8 * q^2 + 24 * q^4 - 3 * q^5 - 6 * q^6 + 24 * q^8 + 30 * q^9	$ 20 q + 8 q^{2} + 24 q^{4} - 3 q^{5} - 6 q^{6} + 24 q^{8} + 30 q^{9} + 8 q^{10} + 26 q^{11} + 4 q^{12} + 4 q^{13} + 10 q^{15} + 24 q^{16} - 4 q^{17} + 5 q^{18} - q^{19} + 2 q^{20} + q^{22} + 31 q^{23} + 6 q^{24} + 27 q^{25} - 4 q^{26} + 18 q^{27} + 16 q^{29} - 5 q^{30} - 6 q^{31} + 41 q^{32} + 18 q^{33} + 10 q^{34} + 18 q^{36} + 2 q^{37} - 3 q^{38} + 43 q^{39} + 38 q^{40} - 25 q^{41} + 13 q^{43} + 66 q^{44} + 2 q^{45} + 20 q^{46} - 19 q^{47} + 16 q^{48} - 4 q^{50} + 4 q^{51} - 20 q^{52} + 24 q^{53} - 5 q^{54} + 3 q^{55} - 4 q^{57} + 12 q^{58} - 23 q^{59} + 24 q^{60} + 27 q^{61} - 7 q^{62} + 2 q^{64} + 26 q^{65} - 26 q^{66} + 9 q^{67} + 25 q^{68} + 3 q^{69} + 63 q^{71} + 27 q^{72} + 21 q^{73} + 21 q^{74} + 52 q^{75} + 10 q^{76} - 70 q^{78} + 18 q^{79} + 23 q^{80} + 40 q^{81} + 42 q^{82} + q^{83} - 41 q^{85} - 12 q^{86} + 9 q^{87} + 57 q^{88} + 16 q^{89} - q^{90} + 17 q^{92} - 41 q^{93} - 7 q^{94} + 75 q^{95} + 81 q^{96} + 32 q^{97} + 15 q^{99}+O(q^{100}) $ 20 * q + 8 * q^2 + 24 * q^4 - 3 * q^5 - 6 * q^6 + 24 * q^8 + 30 * q^9 + 8 * q^10 + 26 * q^11 + 4 * q^12 + 4 * q^13 + 10 * q^15 + 24 * q^16 - 4 * q^17 + 5 * q^18 - q^19 + 2 * q^20 + q^22 + 31 * q^23 + 6 * q^24 + 27 * q^25 - 4 * q^26 + 18 * q^27 + 16 * q^29 - 5 * q^30 - 6 * q^31 + 41 * q^32 + 18 * q^33 + 10 * q^34 + 18 * q^36 + 2 * q^37 - 3 * q^38 + 43 * q^39 + 38 * q^40 - 25 * q^41 + 13 * q^43 + 66 * q^44 + 2 * q^45 + 20 * q^46 - 19 * q^47 + 16 * q^48 - 4 * q^50 + 4 * q^51 - 20 * q^52 + 24 * q^53 - 5 * q^54 + 3 * q^55 - 4 * q^57 + 12 * q^58 - 23 * q^59 + 24 * q^60 + 27 * q^61 - 7 * q^62 + 2 * q^64 + 26 * q^65 - 26 * q^66 + 9 * q^67 + 25 * q^68 + 3 * q^69 + 63 * q^71 + 27 * q^72 + 21 * q^73 + 21 * q^74 + 52 * q^75 + 10 * q^76 - 70 * q^78 + 18 * q^79 + 23 * q^80 + 40 * q^81 + 42 * q^82 + q^83 - 41 * q^85 - 12 * q^86 + 9 * q^87 + 57 * q^88 + 16 * q^89 - q^90 + 17 * q^92 - 41 * q^93 - 7 * q^94 + 75 * q^95 + 81 * q^96 + 32 * q^97 + 15 * 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 $

$2$	1.78791	1.26425	0.632123	−	0.774868i	$-0.282184\pi$
$2$	1.78791	1.26425	0.632123	+	0.774868i	$0.282184\pi$
$3$	−1.55116	−0.895560	−0.447780	−	0.894144i	$-0.647785\pi$
$3$	−1.55116	−0.895560	−0.447780	+	0.894144i	$0.647785\pi$
$4$	1.19664	0.598319
$5$	−2.61034	−1.16738	−0.583690	−	0.811977i	$-0.698392\pi$
$5$	−2.61034	−1.16738	−0.583690	+	0.811977i	$0.698392\pi$
$6$	−2.77333	−1.13221
$7$	0	0
$7$	0	0
$8$	−1.43634	−0.507824
$9$	−0.593917	−0.197972
$10$	−4.66707	−1.47586
$11$	−3.67427	−1.10783	−0.553917	−	0.832572i	$-0.686868\pi$
$11$	−3.67427	−1.10783	−0.553917	+	0.832572i	$0.686868\pi$
$12$	−1.85617	−0.535831
$13$	−4.83827	−1.34189	−0.670947	−	0.741505i	$-0.734112\pi$
$13$	−4.83827	−1.34189	−0.670947	+	0.741505i	$0.734112\pi$
$14$	0	0
$15$	4.04904	1.04546
$16$	−4.96133	−1.24033
$17$	−2.98581	−0.724165	−0.362082	−	0.932146i	$-0.617934\pi$
$17$	−2.98581	−0.724165	−0.362082	+	0.932146i	$0.617934\pi$
$18$	−1.06187	−0.250286
$19$	−4.34824	−0.997555	−0.498778	−	0.866730i	$-0.666218\pi$
$19$	−4.34824	−0.997555	−0.498778	+	0.866730i	$0.666218\pi$
$20$	−3.12363	−0.698466
$21$	0	0
$22$	−6.56928	−1.40058
$23$	2.59876	0.541878	0.270939	−	0.962596i	$-0.412666\pi$
$23$	2.59876	0.541878	0.270939	+	0.962596i	$0.412666\pi$
$24$	2.22799	0.454786
$25$	1.81388	0.362776
$26$	−8.65041	−1.69648
$27$	5.57472	1.07286
$28$	0	0
$29$	−1.91937	−0.356418	−0.178209	−	0.983993i	$-0.557030\pi$
$29$	−1.91937	−0.356418	−0.178209	+	0.983993i	$0.557030\pi$
$30$	7.23934	1.32172
$31$	−1.05650	−0.189752	−0.0948762	−	0.995489i	$-0.530246\pi$
$31$	−1.05650	−0.189752	−0.0948762	+	0.995489i	$0.530246\pi$
$32$	−5.99776	−1.06026
$33$	5.69937	0.992132
$34$	−5.33837	−0.915523
$35$	0	0
$36$	−0.710704	−0.118451
$37$	−7.32285	−1.20387	−0.601934	−	0.798546i	$-0.705603\pi$
$37$	−7.32285	−1.20387	−0.601934	+	0.798546i	$0.705603\pi$
$38$	−7.77428	−1.26116
$39$	7.50490	1.20175
$40$	3.74934	0.592823
$41$	1.13826	0.177766	0.0888831	−	0.996042i	$-0.471670\pi$
$41$	1.13826	0.177766	0.0888831	+	0.996042i	$0.471670\pi$
$42$	0	0
$43$	−7.87546	−1.20100	−0.600498	−	0.799626i	$-0.705031\pi$
$43$	−7.87546	−1.20100	−0.600498	+	0.799626i	$0.705031\pi$
$44$	−4.39677	−0.662839
$45$	1.55033	0.231109
$46$	4.64636	0.685068
$47$	−2.04802	−0.298734	−0.149367	−	0.988782i	$-0.547724\pi$
$47$	−2.04802	−0.298734	−0.149367	+	0.988782i	$0.547724\pi$
$48$	7.69580	1.11079
$49$	0	0
$50$	3.24306	0.458638
$51$	4.63145	0.648533
$52$	−5.78966	−0.802881
$53$	−12.5047	−1.71765	−0.858823	−	0.512272i	$-0.828804\pi$
$53$	−12.5047	−1.71765	−0.858823	+	0.512272i	$0.828804\pi$
$54$	9.96713	1.35635
$55$	9.59110	1.29326
$56$	0	0
$57$	6.74480	0.893370
$58$	−3.43167	−0.450600
$59$	−4.81235	−0.626514	−0.313257	−	0.949668i	$-0.601420\pi$
$59$	−4.81235	−0.626514	−0.313257	+	0.949668i	$0.601420\pi$
$60$	4.84524	0.625518
$61$	10.9771	1.40548	0.702738	−	0.711449i	$-0.251961\pi$
$61$	10.9771	1.40548	0.702738	+	0.711449i	$0.251961\pi$
$62$	−1.88893	−0.239894
$63$	0	0
$64$	−0.800808	−0.100101
$65$	12.6295	1.56650
$66$	10.1900	1.25430
$67$	−1.31670	−0.160860	−0.0804302	−	0.996760i	$-0.525629\pi$
$67$	−1.31670	−0.160860	−0.0804302	+	0.996760i	$0.525629\pi$
$68$	−3.57293	−0.433282
$69$	−4.03108	−0.485285
$70$	0	0
$71$	7.73820	0.918356	0.459178	−	0.888344i	$-0.348144\pi$
$71$	7.73820	0.918356	0.459178	+	0.888344i	$0.348144\pi$
$72$	0.853068	0.100535
$73$	6.77819	0.793327	0.396663	−	0.917964i	$-0.370168\pi$
$73$	6.77819	0.793327	0.396663	+	0.917964i	$0.370168\pi$
$74$	−13.0926	−1.52199
$75$	−2.81361	−0.324887
$76$	−5.20327	−0.596856
$77$	0	0
$78$	13.4181	1.51930
$79$	0.216655	0.0243756	0.0121878	−	0.999926i	$-0.496120\pi$
$79$	0.216655	0.0243756	0.0121878	+	0.999926i	$0.496120\pi$
$80$	12.9508	1.44794
$81$	−6.86551	−0.762835
$82$	2.03511	0.224740
$83$	3.43302	0.376823	0.188412	−	0.982090i	$-0.439666\pi$
$83$	3.43302	0.376823	0.188412	+	0.982090i	$0.439666\pi$
$84$	0	0
$85$	7.79398	0.845376
$86$	−14.0807	−1.51836
$87$	2.97724	0.319194
$88$	5.27751	0.562584
$89$	−9.32688	−0.988648	−0.494324	−	0.869278i	$-0.664584\pi$
$89$	−9.32688	−0.988648	−0.494324	+	0.869278i	$0.664584\pi$
$90$	2.77185	0.292179
$91$	0	0
$92$	3.10977	0.324216
$93$	1.63879	0.169935
$94$	−3.66168	−0.377673
$95$	11.3504	1.16453
$96$	9.30345	0.949530
$97$	−0.511430	−0.0519279	−0.0259639	−	0.999663i	$-0.508266\pi$
$97$	−0.511430	−0.0519279	−0.0259639	+	0.999663i	$0.508266\pi$
$98$	0	0
$99$	2.18221	0.219321
$100$	2.17056	0.217056
$101$	−6.15736	−0.612680	−0.306340	−	0.951922i	$-0.599104\pi$
$101$	−6.15736	−0.612680	−0.306340	+	0.951922i	$0.599104\pi$
$102$	8.28064	0.819906
$103$	−15.9846	−1.57501	−0.787503	−	0.616311i	$-0.788626\pi$
$103$	−15.9846	−1.57501	−0.787503	+	0.616311i	$0.788626\pi$
$104$	6.94941	0.681445
$105$	0	0
$106$	−22.3573	−2.17153
$107$	17.6482	1.70611	0.853056	−	0.521820i	$-0.174747\pi$
$107$	17.6482	1.70611	0.853056	+	0.521820i	$0.174747\pi$
$108$	6.67093	0.641910
$109$	−19.2144	−1.84040	−0.920202	−	0.391445i	$-0.871975\pi$
$109$	−19.2144	−1.84040	−0.920202	+	0.391445i	$0.871975\pi$
$110$	17.1481	1.63500
$111$	11.3589	1.07814
$112$	0	0
$113$	8.54280	0.803639	0.401820	−	0.915719i	$-0.368378\pi$
$113$	8.54280	0.803639	0.401820	+	0.915719i	$0.368378\pi$
$114$	12.0591	1.12944
$115$	−6.78364	−0.632578
$116$	−2.29679	−0.213252
$117$	2.87353	0.265658
$118$	−8.60407	−0.792068
$119$	0	0
$120$	−5.81581	−0.530909
$121$	2.50027	0.227297
$122$	19.6261	1.77687
$123$	−1.76562	−0.159200
$124$	−1.26424	−0.113533
$125$	8.31686	0.743883
$126$	0	0
$127$	−1.00000	−0.0887357
$127$	−1.00000	−0.0887357
$128$	10.5637	0.933711
$129$	12.2161	1.07556
$130$	22.5805	1.98044
$131$	−8.10827	−0.708422	−0.354211	−	0.935165i	$-0.615251\pi$
$131$	−8.10827	−0.708422	−0.354211	+	0.935165i	$0.615251\pi$
$132$	6.82008	0.593612
$133$	0	0
$134$	−2.35415	−0.203367
$135$	−14.5519	−1.25243
$136$	4.28864	0.367748
$137$	−7.16460	−0.612113	−0.306057	−	0.952013i	$-0.599010\pi$
$137$	−7.16460	−0.612113	−0.306057	+	0.952013i	$0.599010\pi$
$138$	−7.20722	−0.613519
$139$	17.8437	1.51348	0.756740	−	0.653716i	$-0.226791\pi$
$139$	17.8437	1.51348	0.756740	+	0.653716i	$0.226791\pi$
$140$	0	0
$141$	3.17679	0.267534
$142$	13.8352	1.16103
$143$	17.7771	1.48660
$144$	2.94662	0.245552
$145$	5.01021	0.416075
$146$	12.1188	1.00296
$147$	0	0
$148$	−8.76280	−0.720298
$149$	−9.67559	−0.792655	−0.396328	−	0.918109i	$-0.629716\pi$
$149$	−9.67559	−0.792655	−0.396328	+	0.918109i	$0.629716\pi$
$150$	−5.03049	−0.410738
$151$	7.11519	0.579026	0.289513	−	0.957174i	$-0.406507\pi$
$151$	7.11519	0.579026	0.289513	+	0.957174i	$0.406507\pi$
$152$	6.24556	0.506582
$153$	1.77332	0.143365
$154$	0	0
$155$	2.75782	0.221513
$156$	8.98066	0.719028
$157$	−17.7565	−1.41712	−0.708562	−	0.705649i	$-0.750656\pi$
$157$	−17.7565	−1.41712	−0.708562	+	0.705649i	$0.750656\pi$
$158$	0.387361	0.0308168
$159$	19.3967	1.53826
$160$	15.6562	1.23773
$161$	0	0
$162$	−12.2749	−0.964411
$163$	13.3104	1.04255	0.521277	−	0.853388i	$-0.325456\pi$
$163$	13.3104	1.04255	0.521277	+	0.853388i	$0.325456\pi$
$164$	1.36208	0.106361
$165$	−14.8773	−1.15820
$166$	6.13795	0.476397
$167$	−9.83583	−0.761120	−0.380560	−	0.924756i	$-0.624269\pi$
$167$	−9.83583	−0.761120	−0.380560	+	0.924756i	$0.624269\pi$
$168$	0	0
$169$	10.4088	0.800679
$170$	13.9350	1.06876
$171$	2.58249	0.197488
$172$	−9.42408	−0.718579
$173$	2.08214	0.158302	0.0791512	−	0.996863i	$-0.474779\pi$
$173$	2.08214	0.158302	0.0791512	+	0.996863i	$0.474779\pi$
$174$	5.32305	0.403540
$175$	0	0
$176$	18.2293	1.37408
$177$	7.46470	0.561081
$178$	−16.6757	−1.24989
$179$	−21.6013	−1.61456	−0.807279	−	0.590170i	$-0.799061\pi$
$179$	−21.6013	−1.61456	−0.807279	+	0.590170i	$0.799061\pi$
$180$	1.85518	0.138277
$181$	−1.76440	−0.131147	−0.0655735	−	0.997848i	$-0.520888\pi$
$181$	−1.76440	−0.131147	−0.0655735	+	0.997848i	$0.520888\pi$
$182$	0	0
$183$	−17.0272	−1.25869
$184$	−3.73270	−0.275179
$185$	19.1151	1.40537
$186$	2.93002	0.214839
$187$	10.9707	0.802255
$188$	−2.45073	−0.178738
$189$	0	0
$190$	20.2935	1.47225
$191$	−11.2136	−0.811384	−0.405692	−	0.914010i	$-0.632969\pi$
$191$	−11.2136	−0.811384	−0.405692	+	0.914010i	$0.632969\pi$
$192$	1.24218	0.0896465
$193$	14.3214	1.03088	0.515438	−	0.856927i	$-0.327629\pi$
$193$	14.3214	1.03088	0.515438	+	0.856927i	$0.327629\pi$
$194$	−0.914393	−0.0656496
$195$	−19.5904	−1.40289
$196$	0	0
$197$	−8.77144	−0.624939	−0.312470	−	0.949928i	$-0.601156\pi$
$197$	−8.77144	−0.624939	−0.312470	+	0.949928i	$0.601156\pi$
$198$	3.90161	0.277275
$199$	7.29620	0.517214	0.258607	−	0.965983i	$-0.416737\pi$
$199$	7.29620	0.517214	0.258607	+	0.965983i	$0.416737\pi$
$200$	−2.60535	−0.184226
$201$	2.04241	0.144060
$202$	−11.0088	−0.774578
$203$	0	0
$204$	5.54217	0.388030
$205$	−2.97124	−0.207521
$206$	−28.5790	−1.99120
$207$	−1.54345	−0.107277
$208$	24.0043	1.66440
$209$	15.9766	1.10513
$210$	0	0
$211$	14.4229	0.992913	0.496457	−	0.868062i	$-0.334634\pi$
$211$	14.4229	0.992913	0.496457	+	0.868062i	$0.334634\pi$
$212$	−14.9636	−1.02770
$213$	−12.0032	−0.822443
$214$	31.5534	2.15695
$215$	20.5576	1.40202
$216$	−8.00721	−0.544822
$217$	0	0
$218$	−34.3537	−2.32672
$219$	−10.5140	−0.710472
$220$	11.4771	0.773784
$221$	14.4461	0.971752
$222$	20.3087	1.36303
$223$	−12.8364	−0.859590	−0.429795	−	0.902926i	$-0.641414\pi$
$223$	−12.8364	−0.859590	−0.429795	+	0.902926i	$0.641414\pi$
$224$	0	0
$225$	−1.07729	−0.0718196
$226$	15.2738	1.01600
$227$	−17.7170	−1.17592	−0.587960	−	0.808890i	$-0.700069\pi$
$227$	−17.7170	−1.17592	−0.587960	+	0.808890i	$0.700069\pi$
$228$	8.07108	0.534521
$229$	−7.21401	−0.476715	−0.238358	−	0.971177i	$-0.576609\pi$
$229$	−7.21401	−0.476715	−0.238358	+	0.971177i	$0.576609\pi$
$230$	−12.1286	−0.799734
$231$	0	0
$232$	2.75687	0.180998
$233$	19.5177	1.27865	0.639323	−	0.768938i	$-0.279215\pi$
$233$	19.5177	1.27865	0.639323	+	0.768938i	$0.279215\pi$
$234$	5.13762	0.335857
$235$	5.34602	0.348736
$236$	−5.75864	−0.374855
$237$	−0.336066	−0.0218298
$238$	0	0
$239$	−18.9197	−1.22381	−0.611907	−	0.790930i	$-0.709597\pi$
$239$	−18.9197	−1.22381	−0.611907	+	0.790930i	$0.709597\pi$
$240$	−20.0887	−1.29672
$241$	−22.4343	−1.44512	−0.722561	−	0.691307i	$-0.757035\pi$
$241$	−22.4343	−1.44512	−0.722561	+	0.691307i	$0.757035\pi$
$242$	4.47027	0.287360
$243$	−6.07470	−0.389692
$244$	13.1356	0.840923
$245$	0	0
$246$	−3.15677	−0.201268
$247$	21.0380	1.33861
$248$	1.51749	0.0963608
$249$	−5.32515	−0.337468
$250$	14.8698	0.940451
$251$	−1.97098	−0.124407	−0.0622035	−	0.998063i	$-0.519813\pi$
$251$	−1.97098	−0.124407	−0.0622035	+	0.998063i	$0.519813\pi$
$252$	0	0
$253$	−9.54854	−0.600311
$254$	−1.78791	−0.112184
$255$	−12.0897	−0.757084
$256$	20.4887	1.28054
$257$	−19.7692	−1.23317	−0.616585	−	0.787288i	$-0.711484\pi$
$257$	−19.7692	−1.23317	−0.616585	+	0.787288i	$0.711484\pi$
$258$	21.8413	1.35978
$259$	0	0
$260$	15.1130	0.937267
$261$	1.13995	0.0705609
$262$	−14.4969	−0.895621
$263$	13.9744	0.861698	0.430849	−	0.902424i	$-0.358214\pi$
$263$	13.9744	0.861698	0.430849	+	0.902424i	$0.358214\pi$
$264$	−8.18624	−0.503828
$265$	32.6414	2.00515
$266$	0	0
$267$	14.4674	0.885393
$268$	−1.57561	−0.0962459
$269$	−22.2765	−1.35822	−0.679110	−	0.734036i	$-0.737634\pi$
$269$	−22.2765	−1.35822	−0.679110	+	0.734036i	$0.737634\pi$
$270$	−26.0176	−1.58338
$271$	22.3273	1.35628	0.678142	−	0.734931i	$-0.262785\pi$
$271$	22.3273	1.35628	0.678142	+	0.734931i	$0.262785\pi$
$272$	14.8136	0.898206
$273$	0	0
$274$	−12.8097	−0.773862
$275$	−6.66468	−0.401895
$276$	−4.82374	−0.290355
$277$	−30.9057	−1.85694	−0.928472	−	0.371403i	$-0.878877\pi$
$277$	−30.9057	−1.85694	−0.928472	+	0.371403i	$0.878877\pi$
$278$	31.9030	1.91341
$279$	0.627472	0.0375657
$280$	0	0
$281$	−0.0969246	−0.00578204	−0.00289102	−	0.999996i	$-0.500920\pi$
$281$	−0.0969246	−0.00578204	−0.00289102	+	0.999996i	$0.500920\pi$
$282$	5.67983	0.338229
$283$	−18.5673	−1.10371	−0.551856	−	0.833939i	$-0.686080\pi$
$283$	−18.5673	−1.10371	−0.551856	+	0.833939i	$0.686080\pi$
$284$	9.25983	0.549470
$285$	−17.6062	−1.04290
$286$	31.7839	1.87942
$287$	0	0
$288$	3.56217	0.209903
$289$	−8.08495	−0.475585
$290$	8.95783	0.526022
$291$	0.793308	0.0465045
$292$	8.11104	0.474663
$293$	12.1959	0.712491	0.356246	−	0.934392i	$-0.384057\pi$
$293$	12.1959	0.712491	0.356246	+	0.934392i	$0.384057\pi$
$294$	0	0
$295$	12.5619	0.731380
$296$	10.5181	0.611353
$297$	−20.4830	−1.18855
$298$	−17.2991	−1.00211
$299$	−12.5735	−0.727143
$300$	−3.36687	−0.194386
$301$	0	0
$302$	12.7214	0.732032
$303$	9.55102	0.548692
$304$	21.5731	1.23730
$305$	−28.6540	−1.64072
$306$	3.17055	0.181248
$307$	9.15964	0.522768	0.261384	−	0.965235i	$-0.415821\pi$
$307$	9.15964	0.522768	0.261384	+	0.965235i	$0.415821\pi$
$308$	0	0
$309$	24.7945	1.41051
$310$	4.93074	0.280047
$311$	−19.6147	−1.11225	−0.556125	−	0.831099i	$-0.687712\pi$
$311$	−19.6147	−1.11225	−0.556125	+	0.831099i	$0.687712\pi$
$312$	−10.7796	−0.610275
$313$	22.3298	1.26215	0.631076	−	0.775721i	$-0.282613\pi$
$313$	22.3298	1.26215	0.631076	+	0.775721i	$0.282613\pi$
$314$	−31.7471	−1.79159
$315$	0	0
$316$	0.259258	0.0145844
$317$	6.48966	0.364496	0.182248	−	0.983253i	$-0.441663\pi$
$317$	6.48966	0.364496	0.182248	+	0.983253i	$0.441663\pi$
$318$	34.6796	1.94473
$319$	7.05229	0.394852
$320$	2.09038	0.116856
$321$	−27.3750	−1.52792
$322$	0	0
$323$	12.9830	0.722394
$324$	−8.21553	−0.456419
$325$	−8.77603	−0.486807
$326$	23.7979	1.31804
$327$	29.8045	1.64819
$328$	−1.63493	−0.0902738
$329$	0	0
$330$	−26.5993	−1.46424
$331$	11.6043	0.637830	0.318915	−	0.947783i	$-0.396682\pi$
$331$	11.6043	0.637830	0.318915	+	0.947783i	$0.396682\pi$
$332$	4.10809	0.225461
$333$	4.34916	0.238333
$334$	−17.5856	−0.962243
$335$	3.43703	0.187785
$336$	0	0
$337$	9.73516	0.530308	0.265154	−	0.964206i	$-0.414577\pi$
$337$	9.73516	0.530308	0.265154	+	0.964206i	$0.414577\pi$
$338$	18.6101	1.01226
$339$	−13.2512	−0.719707
$340$	9.32657	0.505804
$341$	3.88186	0.210214
$342$	4.61728	0.249674
$343$	0	0
$344$	11.3119	0.609894
$345$	10.5225	0.566511
$346$	3.72269	0.200133
$347$	3.20316	0.171955	0.0859774	−	0.996297i	$-0.472599\pi$
$347$	3.20316	0.171955	0.0859774	+	0.996297i	$0.472599\pi$
$348$	3.56268	0.190980
$349$	18.6426	0.997916	0.498958	−	0.866626i	$-0.333716\pi$
$349$	18.6426	0.997916	0.498958	+	0.866626i	$0.333716\pi$
$350$	0	0
$351$	−26.9720	−1.43966
$352$	22.0374	1.17460
$353$	23.8815	1.27108	0.635541	−	0.772067i	$-0.280777\pi$
$353$	23.8815	1.27108	0.635541	+	0.772067i	$0.280777\pi$
$354$	13.3462	0.709345
$355$	−20.1993	−1.07207
$356$	−11.1609	−0.591527
$357$	0	0
$358$	−38.6213	−2.04120
$359$	4.40641	0.232561	0.116281	−	0.993216i	$-0.462903\pi$
$359$	4.40641	0.232561	0.116281	+	0.993216i	$0.462903\pi$
$360$	−2.22680	−0.117363
$361$	−0.0927956	−0.00488398
$362$	−3.15460	−0.165802
$363$	−3.87831	−0.203558
$364$	0	0
$365$	−17.6934	−0.926114
$366$	−30.4432	−1.59129
$367$	−6.38739	−0.333419	−0.166710	−	0.986006i	$-0.553314\pi$
$367$	−6.38739	−0.333419	−0.166710	+	0.986006i	$0.553314\pi$
$368$	−12.8933	−0.672110
$369$	−0.676031	−0.0351928
$370$	34.1762	1.77674
$371$	0	0
$372$	1.96104	0.101675
$373$	25.2092	1.30528	0.652642	−	0.757666i	$-0.273661\pi$
$373$	25.2092	1.30528	0.652642	+	0.757666i	$0.273661\pi$
$374$	19.6146	1.01425
$375$	−12.9007	−0.666192
$376$	2.94165	0.151704
$377$	9.28643	0.478275
$378$	0	0
$379$	−28.5137	−1.46465	−0.732326	−	0.680955i	$-0.761565\pi$
$379$	−28.5137	−1.46465	−0.732326	+	0.680955i	$0.761565\pi$
$380$	13.5823	0.696758
$381$	1.55116	0.0794681
$382$	−20.0489	−1.02579
$383$	4.36258	0.222917	0.111459	−	0.993769i	$-0.464448\pi$
$383$	4.36258	0.222917	0.111459	+	0.993769i	$0.464448\pi$
$384$	−16.3860	−0.836194
$385$	0	0
$386$	25.6054	1.30328
$387$	4.67737	0.237764
$388$	−0.611997	−0.0310694
$389$	18.0882	0.917109	0.458554	−	0.888666i	$-0.348367\pi$
$389$	18.0882	0.917109	0.458554	+	0.888666i	$0.348367\pi$
$390$	−35.0259	−1.77360
$391$	−7.75939	−0.392409
$392$	0	0
$393$	12.5772	0.634435
$394$	−15.6826	−0.790077
$395$	−0.565544	−0.0284556
$396$	2.61132	0.131224
$397$	−3.34162	−0.167711	−0.0838556	−	0.996478i	$-0.526723\pi$
$397$	−3.34162	−0.167711	−0.0838556	+	0.996478i	$0.526723\pi$
$398$	13.0450	0.653885
$399$	0	0
$400$	−8.99926	−0.449963
$401$	9.47634	0.473226	0.236613	−	0.971604i	$-0.423963\pi$
$401$	9.47634	0.473226	0.236613	+	0.971604i	$0.423963\pi$
$402$	3.65165	0.182128
$403$	5.11162	0.254628
$404$	−7.36813	−0.366578
$405$	17.9213	0.890518
$406$	0	0
$407$	26.9061	1.33369
$408$	−6.65235	−0.329340
$409$	−37.4637	−1.85246	−0.926231	−	0.376957i	$-0.876970\pi$
$409$	−37.4637	−1.85246	−0.926231	+	0.376957i	$0.876970\pi$
$410$	−5.31233	−0.262357
$411$	11.1134	0.548184
$412$	−19.1277	−0.942356
$413$	0	0
$414$	−2.75955	−0.135624
$415$	−8.96136	−0.439896
$416$	29.0187	1.42276
$417$	−27.6783	−1.35541
$418$	28.5648	1.39715
$419$	−4.82140	−0.235541	−0.117770	−	0.993041i	$-0.537575\pi$
$419$	−4.82140	−0.235541	−0.117770	+	0.993041i	$0.537575\pi$
$420$	0	0
$421$	−29.3062	−1.42830	−0.714149	−	0.699994i	$-0.753186\pi$
$421$	−29.3062	−1.42830	−0.714149	+	0.699994i	$0.753186\pi$
$422$	25.7869	1.25529
$423$	1.21635	0.0591410
$424$	17.9610	0.872262
$425$	−5.41589	−0.262709
$426$	−21.4606	−1.03977
$427$	0	0
$428$	21.1185	1.02080
$429$	−27.5751	−1.33134
$430$	36.7553	1.77250
$431$	40.1333	1.93315	0.966576	−	0.256380i	$-0.0825297\pi$
$431$	40.1333	1.93315	0.966576	+	0.256380i	$0.0825297\pi$
$432$	−27.6581	−1.33070
$433$	16.8897	0.811665	0.405833	−	0.913947i	$-0.366982\pi$
$433$	16.8897	0.811665	0.405833	+	0.913947i	$0.366982\pi$
$434$	0	0
$435$	−7.77161	−0.372620
$436$	−22.9927	−1.10115
$437$	−11.3000	−0.540553
$438$	−18.7982	−0.898211
$439$	−20.7918	−0.992340	−0.496170	−	0.868225i	$-0.665261\pi$
$439$	−20.7918	−0.992340	−0.496170	+	0.868225i	$0.665261\pi$
$440$	−13.7761	−0.656750
$441$	0	0
$442$	25.8285	1.22853
$443$	−3.18205	−0.151184	−0.0755918	−	0.997139i	$-0.524085\pi$
$443$	−3.18205	−0.151184	−0.0755918	+	0.997139i	$0.524085\pi$
$444$	13.5925	0.645070
$445$	24.3463	1.15413
$446$	−22.9504	−1.08673
$447$	15.0083	0.709870
$448$	0	0
$449$	−21.1543	−0.998333	−0.499167	−	0.866506i	$-0.666360\pi$
$449$	−21.1543	−0.998333	−0.499167	+	0.866506i	$0.666360\pi$
$450$	−1.92611	−0.0907976
$451$	−4.18227	−0.196935
$452$	10.2226	0.480833
$453$	−11.0368	−0.518553
$454$	−31.6765	−1.48665
$455$	0	0
$456$	−9.68784	−0.453675
$457$	−27.3549	−1.27961	−0.639804	−	0.768538i	$-0.720984\pi$
$457$	−27.3549	−1.27961	−0.639804	+	0.768538i	$0.720984\pi$
$458$	−12.8980	−0.602685
$459$	−16.6451	−0.776925
$460$	−8.11757	−0.378483
$461$	−17.2554	−0.803663	−0.401831	−	0.915714i	$-0.631626\pi$
$461$	−17.2554	−0.803663	−0.401831	+	0.915714i	$0.631626\pi$
$462$	0	0
$463$	−25.2987	−1.17573	−0.587865	−	0.808959i	$-0.700031\pi$
$463$	−25.2987	−1.17573	−0.587865	+	0.808959i	$0.700031\pi$
$464$	9.52263	0.442077
$465$	−4.27780	−0.198378
$466$	34.8960	1.61652
$467$	−21.6496	−1.00182	−0.500912	−	0.865498i	$-0.667002\pi$
$467$	−21.6496	−1.00182	−0.500912	+	0.865498i	$0.667002\pi$
$468$	3.43858	0.158948
$469$	0	0
$470$	9.55822	0.440888
$471$	27.5431	1.26912
$472$	6.91218	0.318159
$473$	28.9366	1.33051
$474$	−0.600857	−0.0275983
$475$	−7.88718	−0.361889
$476$	0	0
$477$	7.42673	0.340047
$478$	−33.8268	−1.54720
$479$	30.3805	1.38812	0.694060	−	0.719917i	$-0.255820\pi$
$479$	30.3805	1.38812	0.694060	+	0.719917i	$0.255820\pi$
$480$	−24.2852	−1.10846
$481$	35.4299	1.61546
$482$	−40.1107	−1.82699
$483$	0	0
$484$	2.99192	0.135996
$485$	1.33501	0.0606195
$486$	−10.8610	−0.492667
$487$	26.9970	1.22335	0.611675	−	0.791109i	$-0.290496\pi$
$487$	26.9970	1.22335	0.611675	+	0.791109i	$0.290496\pi$
$488$	−15.7669	−0.713734
$489$	−20.6466	−0.933669
$490$	0	0
$491$	16.6883	0.753131	0.376565	−	0.926390i	$-0.377105\pi$
$491$	16.6883	0.753131	0.376565	+	0.926390i	$0.377105\pi$
$492$	−2.11280	−0.0952525
$493$	5.73087	0.258105
$494$	37.6141	1.69234
$495$	−5.69632	−0.256030
$496$	5.24163	0.235356
$497$	0	0
$498$	−9.52092	−0.426642
$499$	−16.8527	−0.754429	−0.377214	−	0.926126i	$-0.623118\pi$
$499$	−16.8527	−0.754429	−0.377214	+	0.926126i	$0.623118\pi$
$500$	9.95228	0.445079
$501$	15.2569	0.681628
$502$	−3.52394	−0.157281
$503$	16.4139	0.731860	0.365930	−	0.930642i	$-0.380751\pi$
$503$	16.4139	0.731860	0.365930	+	0.930642i	$0.380751\pi$
$504$	0	0
$505$	16.0728	0.715230
$506$	−17.0720	−0.758942
$507$	−16.1457	−0.717056
$508$	−1.19664	−0.0530922
$509$	−16.1583	−0.716206	−0.358103	−	0.933682i	$-0.616576\pi$
$509$	−16.1583	−0.716206	−0.358103	+	0.933682i	$0.616576\pi$
$510$	−21.6153	−0.957141
$511$	0	0
$512$	15.5045	0.685210
$513$	−24.2402	−1.07023
$514$	−35.3457	−1.55903
$515$	41.7251	1.83863
$516$	14.6182	0.643531
$517$	7.52496	0.330948
$518$	0	0
$519$	−3.22973	−0.141769
$520$	−18.1403	−0.795506
$521$	−13.5649	−0.594290	−0.297145	−	0.954832i	$-0.596035\pi$
$521$	−13.5649	−0.594290	−0.297145	+	0.954832i	$0.596035\pi$
$522$	2.03813	0.0892064
$523$	18.5963	0.813159	0.406579	−	0.913615i	$-0.366721\pi$
$523$	18.5963	0.813159	0.406579	+	0.913615i	$0.366721\pi$
$524$	−9.70266	−0.423863
$525$	0	0
$526$	24.9850	1.08940
$527$	3.15450	0.137412
$528$	−28.2765	−1.23057
$529$	−16.2465	−0.706368
$530$	58.3601	2.53500
$531$	2.85813	0.124032
$532$	0	0
$533$	−5.50720	−0.238543
$534$	25.8666	1.11936
$535$	−46.0677	−1.99168
$536$	1.89123	0.0816887
$537$	33.5070	1.44593
$538$	−39.8284	−1.71713
$539$	0	0
$540$	−17.4134	−0.749353
$541$	−18.9711	−0.815631	−0.407815	−	0.913064i	$-0.633709\pi$
$541$	−18.9711	−0.815631	−0.407815	+	0.913064i	$0.633709\pi$
$542$	39.9192	1.71468
$543$	2.73686	0.117450
$544$	17.9081	0.767806
$545$	50.1561	2.14845
$546$	0	0
$547$	−32.6463	−1.39585	−0.697927	−	0.716169i	$-0.745894\pi$
$547$	−32.6463	−1.39585	−0.697927	+	0.716169i	$0.745894\pi$
$548$	−8.57344	−0.366239
$549$	−6.51949	−0.278245
$550$	−11.9159	−0.508095
$551$	8.34588	0.355547
$552$	5.79000	0.246439
$553$	0	0
$554$	−55.2568	−2.34763
$555$	−29.6505	−1.25859
$556$	21.3524	0.905544
$557$	16.4123	0.695412	0.347706	−	0.937604i	$-0.386961\pi$
$557$	16.4123	0.695412	0.347706	+	0.937604i	$0.386961\pi$
$558$	1.12187	0.0474923
$559$	38.1036	1.61161
$560$	0	0
$561$	−17.0172	−0.718467
$562$	−0.173293	−0.00730992
$563$	16.9970	0.716340	0.358170	−	0.933656i	$-0.383401\pi$
$563$	16.9970	0.716340	0.358170	+	0.933656i	$0.383401\pi$
$564$	3.80147	0.160071
$565$	−22.2996	−0.938152
$566$	−33.1968	−1.39536
$567$	0	0
$568$	−11.1147	−0.466363
$569$	−3.38733	−0.142004	−0.0710022	−	0.997476i	$-0.522620\pi$
$569$	−3.38733	−0.142004	−0.0710022	+	0.997476i	$0.522620\pi$
$570$	−31.4784	−1.31849
$571$	22.6320	0.947118	0.473559	−	0.880762i	$-0.342969\pi$
$571$	22.6320	0.947118	0.473559	+	0.880762i	$0.342969\pi$
$572$	21.2728	0.889459
$573$	17.3940	0.726643
$574$	0	0
$575$	4.71383	0.196580
$576$	0.475614	0.0198172
$577$	−39.6115	−1.64905	−0.824525	−	0.565826i	$-0.808558\pi$
$577$	−39.6115	−1.64905	−0.824525	+	0.565826i	$0.808558\pi$
$578$	−14.4552	−0.601257
$579$	−22.2147	−0.923210
$580$	5.99541	0.248946
$581$	0	0
$582$	1.41837	0.0587932
$583$	45.9455	1.90287
$584$	−9.73580	−0.402870
$585$	−7.50089	−0.310124
$586$	21.8052	0.900765
$587$	10.6810	0.440850	0.220425	−	0.975404i	$-0.429256\pi$
$587$	10.6810	0.440850	0.220425	+	0.975404i	$0.429256\pi$
$588$	0	0
$589$	4.59390	0.189289
$590$	22.4595	0.924645
$591$	13.6059	0.559671
$592$	36.3311	1.49320
$593$	−40.2803	−1.65412	−0.827058	−	0.562117i	$-0.809987\pi$
$593$	−40.2803	−1.65412	−0.827058	+	0.562117i	$0.809987\pi$
$594$	−36.6219	−1.50262
$595$	0	0
$596$	−11.5782	−0.474261
$597$	−11.3175	−0.463196
$598$	−22.4803	−0.919288
$599$	−38.7977	−1.58523	−0.792616	−	0.609721i	$-0.791281\pi$
$599$	−38.7977	−1.58523	−0.792616	+	0.609721i	$0.791281\pi$
$600$	4.04130	0.164986
$601$	8.76032	0.357341	0.178670	−	0.983909i	$-0.442820\pi$
$601$	8.76032	0.357341	0.178670	+	0.983909i	$0.442820\pi$
$602$	0	0
$603$	0.782010	0.0318459
$604$	8.51431	0.346442
$605$	−6.52655	−0.265342
$606$	17.0764	0.693681
$607$	7.86010	0.319032	0.159516	−	0.987195i	$-0.449007\pi$
$607$	7.86010	0.319032	0.159516	+	0.987195i	$0.449007\pi$
$608$	26.0797	1.05767
$609$	0	0
$610$	−51.2309	−2.07428
$611$	9.90885	0.400869
$612$	2.12203	0.0857778
$613$	17.3298	0.699943	0.349971	−	0.936760i	$-0.386191\pi$
$613$	17.3298	0.699943	0.349971	+	0.936760i	$0.386191\pi$
$614$	16.3766	0.660908
$615$	4.60886	0.185847
$616$	0	0
$617$	−13.2526	−0.533531	−0.266766	−	0.963761i	$-0.585955\pi$
$617$	−13.2526	−0.533531	−0.266766	+	0.963761i	$0.585955\pi$
$618$	44.3305	1.78323
$619$	25.3342	1.01827	0.509134	−	0.860687i	$-0.329966\pi$
$619$	25.3342	1.01827	0.509134	+	0.860687i	$0.329966\pi$
$620$	3.30011	0.132536
$621$	14.4874	0.581357
$622$	−35.0695	−1.40616
$623$	0	0
$624$	−37.2343	−1.49057
$625$	−30.7792	−1.23117
$626$	39.9237	1.59567
$627$	−24.7822	−0.989706
$628$	−21.2481	−0.847892
$629$	21.8646	0.871799
$630$	0	0
$631$	30.7245	1.22312	0.611561	−	0.791197i	$-0.290542\pi$
$631$	30.7245	1.22312	0.611561	+	0.791197i	$0.290542\pi$
$632$	−0.311191	−0.0123785
$633$	−22.3722	−0.889213
$634$	11.6030	0.460812
$635$	2.61034	0.103588
$636$	23.2108	0.920368
$637$	0	0
$638$	12.6089	0.499191
$639$	−4.59585	−0.181809
$640$	−27.5749	−1.09000
$641$	18.4045	0.726935	0.363468	−	0.931607i	$-0.381593\pi$
$641$	18.4045	0.726935	0.363468	+	0.931607i	$0.381593\pi$
$642$	−48.9442	−1.93167
$643$	−35.7664	−1.41049	−0.705245	−	0.708964i	$-0.749163\pi$
$643$	−35.7664	−1.41049	−0.705245	+	0.708964i	$0.749163\pi$
$644$	0	0
$645$	−31.8881	−1.25559
$646$	23.2125	0.913284
$647$	−20.3216	−0.798923	−0.399461	−	0.916750i	$-0.630803\pi$
$647$	−20.3216	−0.798923	−0.399461	+	0.916750i	$0.630803\pi$
$648$	9.86122	0.387385
$649$	17.6819	0.694074
$650$	−15.6908	−0.615444
$651$	0	0
$652$	15.9278	0.623780
$653$	23.8719	0.934181	0.467090	−	0.884210i	$-0.345302\pi$
$653$	23.8719	0.934181	0.467090	+	0.884210i	$0.345302\pi$
$654$	53.2879	2.08372
$655$	21.1653	0.826998
$656$	−5.64728	−0.220489
$657$	−4.02568	−0.157057
$658$	0	0
$659$	−19.6363	−0.764923	−0.382462	−	0.923971i	$-0.624924\pi$
$659$	−19.6363	−0.764923	−0.382462	+	0.923971i	$0.624924\pi$
$660$	−17.8027	−0.692970
$661$	22.5802	0.878267	0.439133	−	0.898422i	$-0.355286\pi$
$661$	22.5802	0.878267	0.439133	+	0.898422i	$0.355286\pi$
$662$	20.7475	0.806374
$663$	−22.4082	−0.870263
$664$	−4.93100	−0.191360
$665$	0	0
$666$	7.77593	0.301311
$667$	−4.98798	−0.193135
$668$	−11.7699	−0.455392
$669$	19.9113	0.769815
$670$	6.14512	0.237407
$671$	−40.3329	−1.55703
$672$	0	0
$673$	−18.1619	−0.700089	−0.350044	−	0.936733i	$-0.613833\pi$
$673$	−18.1619	−0.700089	−0.350044	+	0.936733i	$0.613833\pi$
$674$	17.4056	0.670440
$675$	10.1119	0.389206
$676$	12.4556	0.479062
$677$	−29.6690	−1.14027	−0.570135	−	0.821551i	$-0.693109\pi$
$677$	−29.6690	−1.14027	−0.570135	+	0.821551i	$0.693109\pi$
$678$	−23.6920	−0.909887
$679$	0	0
$680$	−11.1948	−0.429302
$681$	27.4818	1.05311
$682$	6.94043	0.265763
$683$	−31.8760	−1.21970	−0.609851	−	0.792516i	$-0.708771\pi$
$683$	−31.8760	−1.21970	−0.609851	+	0.792516i	$0.708771\pi$
$684$	3.09031	0.118161
$685$	18.7021	0.714569
$686$	0	0
$687$	11.1900	0.426927
$688$	39.0728	1.48964
$689$	60.5009	2.30490
$690$	18.8133	0.716210
$691$	−31.6487	−1.20397	−0.601987	−	0.798506i	$-0.705624\pi$
$691$	−31.6487	−1.20397	−0.601987	+	0.798506i	$0.705624\pi$
$692$	2.49157	0.0947153
$693$	0	0
$694$	5.72698	0.217393
$695$	−46.5781	−1.76681
$696$	−4.27634	−0.162094
$697$	−3.39862	−0.128732
$698$	33.3314	1.26161
$699$	−30.2750	−1.14510
$700$	0	0
$701$	38.3975	1.45025	0.725127	−	0.688615i	$-0.241781\pi$
$701$	38.3975	1.45025	0.725127	+	0.688615i	$0.241781\pi$
$702$	−48.2236	−1.82008
$703$	31.8415	1.20092
$704$	2.94239	0.110895
$705$	−8.29251	−0.312314
$706$	42.6980	1.60696
$707$	0	0
$708$	8.93254	0.335706
$709$	−32.1618	−1.20786	−0.603930	−	0.797037i	$-0.706399\pi$
$709$	−32.1618	−1.20786	−0.603930	+	0.797037i	$0.706399\pi$
$710$	−36.1147	−1.35536
$711$	−0.128675	−0.00482570
$712$	13.3966	0.502059
$713$	−2.74558	−0.102823
$714$	0	0
$715$	−46.4043	−1.73542
$716$	−25.8490	−0.966021
$717$	29.3474	1.09600
$718$	7.87828	0.294015
$719$	−28.0804	−1.04722	−0.523612	−	0.851957i	$-0.675416\pi$
$719$	−28.0804	−1.04722	−0.523612	+	0.851957i	$0.675416\pi$
$720$	−7.69168	−0.286652
$721$	0	0
$722$	−0.165911	−0.00617455
$723$	34.7991	1.29419
$724$	−2.11135	−0.0784678
$725$	−3.48150	−0.129300
$726$	−6.93408	−0.257348
$727$	−42.9400	−1.59256	−0.796278	−	0.604930i	$-0.793201\pi$
$727$	−42.9400	−1.59256	−0.796278	+	0.604930i	$0.793201\pi$
$728$	0	0
$729$	30.0193	1.11183
$730$	−31.6342	−1.17084
$731$	23.5146	0.869719
$732$	−20.3754	−0.753097
$733$	−10.9962	−0.406153	−0.203076	−	0.979163i	$-0.565094\pi$
$733$	−10.9962	−0.406153	−0.203076	+	0.979163i	$0.565094\pi$
$734$	−11.4201	−0.421524
$735$	0	0
$736$	−15.5867	−0.574534
$737$	4.83791	0.178207
$738$	−1.20869	−0.0444923
$739$	−3.36023	−0.123608	−0.0618040	−	0.998088i	$-0.519685\pi$
$739$	−3.36023	−0.123608	−0.0618040	+	0.998088i	$0.519685\pi$
$740$	22.8739	0.840861
$741$	−32.6331	−1.19881
$742$	0	0
$743$	3.20588	0.117612	0.0588061	−	0.998269i	$-0.481271\pi$
$743$	3.20588	0.117612	0.0588061	+	0.998269i	$0.481271\pi$
$744$	−2.35386	−0.0862969
$745$	25.2566	0.925330
$746$	45.0719	1.65020
$747$	−2.03893	−0.0746006
$748$	13.1279	0.480004
$749$	0	0
$750$	−23.0654	−0.842230
$751$	−11.9997	−0.437876	−0.218938	−	0.975739i	$-0.570259\pi$
$751$	−11.9997	−0.437876	−0.218938	+	0.975739i	$0.570259\pi$
$752$	10.1609	0.370529
$753$	3.05729	0.111414
$754$	16.6033	0.604658
$755$	−18.5731	−0.675943
$756$	0	0
$757$	−45.7149	−1.66154	−0.830768	−	0.556619i	$-0.812098\pi$
$757$	−45.7149	−1.66154	−0.830768	+	0.556619i	$0.812098\pi$
$758$	−50.9801	−1.85168
$759$	14.8113	0.537615
$760$	−16.3030	−0.591374
$761$	53.7416	1.94813	0.974066	−	0.226264i	$-0.0726513\pi$
$761$	53.7416	1.94813	0.974066	+	0.226264i	$0.0726513\pi$
$762$	2.77333	0.100467
$763$	0	0
$764$	−13.4186	−0.485467
$765$	−4.62898	−0.167361
$766$	7.79992	0.281823
$767$	23.2834	0.840716
$768$	−31.7811	−1.14680
$769$	40.0369	1.44377	0.721884	−	0.692014i	$-0.243276\pi$
$769$	40.0369	1.44377	0.721884	+	0.692014i	$0.243276\pi$
$770$	0	0
$771$	30.6651	1.10438
$772$	17.1375	0.616792
$773$	−26.2445	−0.943948	−0.471974	−	0.881613i	$-0.656458\pi$
$773$	−26.2445	−0.943948	−0.471974	+	0.881613i	$0.656458\pi$
$774$	8.36274	0.300592
$775$	−1.91636	−0.0688376
$776$	0.734589	0.0263702
$777$	0	0
$778$	32.3402	1.15945
$779$	−4.94942	−0.177331
$780$	−23.4426	−0.839379
$781$	−28.4323	−1.01739
$782$	−13.8731	−0.496102
$783$	−10.7000	−0.382385
$784$	0	0
$785$	46.3505	1.65432
$786$	22.4869	0.802082
$787$	−17.4932	−0.623564	−0.311782	−	0.950154i	$-0.600926\pi$
$787$	−17.4932	−0.623564	−0.311782	+	0.950154i	$0.600926\pi$
$788$	−10.4962	−0.373913
$789$	−21.6765	−0.771702
$790$	−1.01114	−0.0359749
$791$	0	0
$792$	−3.13440	−0.111376
$793$	−53.1102	−1.88600
$794$	−5.97454	−0.212028
$795$	−50.6319	−1.79573
$796$	8.73091	0.309459
$797$	20.6866	0.732758	0.366379	−	0.930466i	$-0.380597\pi$
$797$	20.6866	0.732758	0.366379	+	0.930466i	$0.380597\pi$
$798$	0	0
$799$	6.11498	0.216333
$800$	−10.8792	−0.384638
$801$	5.53939	0.195725
$802$	16.9429	0.598274
$803$	−24.9049	−0.878875
$804$	2.44402	0.0861940
$805$	0	0
$806$	9.13913	0.321912
$807$	34.5543	1.21637
$808$	8.84407	0.311133
$809$	−24.9709	−0.877930	−0.438965	−	0.898504i	$-0.644655\pi$
$809$	−24.9709	−0.877930	−0.438965	+	0.898504i	$0.644655\pi$
$810$	32.0418	1.12583
$811$	−45.0359	−1.58143	−0.790713	−	0.612187i	$-0.790290\pi$
$811$	−45.0359	−1.58143	−0.790713	+	0.612187i	$0.790290\pi$
$812$	0	0
$813$	−34.6330	−1.21463
$814$	48.1058	1.68611
$815$	−34.7448	−1.21706
$816$	−22.9782	−0.804397
$817$	34.2444	1.19806
$818$	−66.9819	−2.34197
$819$	0	0
$820$	−3.55550	−0.124164
$821$	−21.6733	−0.756404	−0.378202	−	0.925723i	$-0.623458\pi$
$821$	−21.6733	−0.756404	−0.378202	+	0.925723i	$0.623458\pi$
$822$	19.8698	0.693040
$823$	−35.9327	−1.25253	−0.626267	−	0.779609i	$-0.715418\pi$
$823$	−35.9327	−1.25253	−0.626267	+	0.779609i	$0.715418\pi$
$824$	22.9593	0.799825
$825$	10.3380	0.359922
$826$	0	0
$827$	−43.0107	−1.49563	−0.747814	−	0.663908i	$-0.768896\pi$
$827$	−43.0107	−1.49563	−0.747814	+	0.663908i	$0.768896\pi$
$828$	−1.84695	−0.0641858
$829$	−5.33521	−0.185300	−0.0926498	−	0.995699i	$-0.529534\pi$
$829$	−5.33521	−0.185300	−0.0926498	+	0.995699i	$0.529534\pi$
$830$	−16.0221	−0.556137
$831$	47.9395	1.66300
$832$	3.87452	0.134325
$833$	0	0
$834$	−49.4864	−1.71358
$835$	25.6749	0.888516
$836$	19.1182	0.661218
$837$	−5.88968	−0.203577
$838$	−8.62024	−0.297781
$839$	−13.1009	−0.452294	−0.226147	−	0.974093i	$-0.572613\pi$
$839$	−13.1009	−0.452294	−0.226147	+	0.974093i	$0.572613\pi$
$840$	0	0
$841$	−25.3160	−0.872966
$842$	−52.3970	−1.80572
$843$	0.150345	0.00517816
$844$	17.2590	0.594079
$845$	−27.1706	−0.934697
$846$	2.17473	0.0747688
$847$	0	0
$848$	62.0398	2.13045
$849$	28.8008	0.988441
$850$	−9.68316	−0.332130
$851$	−19.0303	−0.652350
$852$	−14.3634	−0.492083
$853$	19.2115	0.657788	0.328894	−	0.944367i	$-0.393324\pi$
$853$	19.2115	0.657788	0.328894	+	0.944367i	$0.393324\pi$
$854$	0	0
$855$	−6.74119	−0.230544
$856$	−25.3488	−0.866403
$857$	38.6562	1.32047	0.660236	−	0.751058i	$-0.270456\pi$
$857$	38.6562	1.32047	0.660236	+	0.751058i	$0.270456\pi$
$858$	−49.3018	−1.68314
$859$	−45.0464	−1.53696	−0.768482	−	0.639872i	$-0.778988\pi$
$859$	−45.0464	−1.53696	−0.768482	+	0.639872i	$0.778988\pi$
$860$	24.6001	0.838855
$861$	0	0
$862$	71.7549	2.44398
$863$	−44.3562	−1.50990	−0.754951	−	0.655782i	$-0.772339\pi$
$863$	−44.3562	−1.50990	−0.754951	+	0.655782i	$0.772339\pi$
$864$	−33.4358	−1.13751
$865$	−5.43510	−0.184799
$866$	30.1973	1.02615
$867$	12.5410	0.425915
$868$	0	0
$869$	−0.796050	−0.0270041
$870$	−13.8950	−0.471084
$871$	6.37054	0.215858
$872$	27.5984	0.934600
$873$	0.303747	0.0102803
$874$	−20.2035	−0.683393
$875$	0	0
$876$	−12.5815	−0.425089
$877$	−50.6435	−1.71011	−0.855055	−	0.518536i	$-0.826477\pi$
$877$	−50.6435	−1.71011	−0.855055	+	0.518536i	$0.826477\pi$
$878$	−37.1740	−1.25456
$879$	−18.9177	−0.638079
$880$	−47.5846	−1.60408
$881$	26.3543	0.887900	0.443950	−	0.896052i	$-0.353577\pi$
$881$	26.3543	0.887900	0.443950	+	0.896052i	$0.353577\pi$
$882$	0	0
$883$	−39.0563	−1.31435	−0.657175	−	0.753738i	$-0.728249\pi$
$883$	−39.0563	−1.31435	−0.657175	+	0.753738i	$0.728249\pi$
$884$	17.2868	0.581418
$885$	−19.4854	−0.654995
$886$	−5.68923	−0.191133
$887$	−24.3759	−0.818464	−0.409232	−	0.912430i	$-0.634203\pi$
$887$	−24.3759	−0.818464	−0.409232	+	0.912430i	$0.634203\pi$
$888$	−16.3152	−0.547503
$889$	0	0
$890$	43.5292	1.45910
$891$	25.2258	0.845094
$892$	−15.3606	−0.514309
$893$	8.90527	0.298003
$894$	26.8336	0.897451
$895$	56.3868	1.88480
$896$	0	0
$897$	19.5034	0.651200
$898$	−37.8221	−1.26214
$899$	2.02781	0.0676312
$900$	−1.28913	−0.0429710
$901$	37.3365	1.24386
$902$	−7.47754	−0.248975
$903$	0	0
$904$	−12.2704	−0.408107
$905$	4.60569	0.153098
$906$	−19.7328	−0.655578
$907$	−35.8315	−1.18977	−0.594883	−	0.803812i	$-0.702802\pi$
$907$	−35.8315	−1.18977	−0.594883	+	0.803812i	$0.702802\pi$
$908$	−21.2009	−0.703575
$909$	3.65696	0.121294
$910$	0	0
$911$	29.2977	0.970677	0.485339	−	0.874326i	$-0.338696\pi$
$911$	29.2977	0.970677	0.485339	+	0.874326i	$0.338696\pi$
$912$	−33.4632	−1.10808
$913$	−12.6139	−0.417458
$914$	−48.9082	−1.61774
$915$	44.4468	1.46937
$916$	−8.63256	−0.285228
$917$	0	0
$918$	−29.7599	−0.982224
$919$	41.9383	1.38342	0.691709	−	0.722177i	$-0.256858\pi$
$919$	41.9383	1.38342	0.691709	+	0.722177i	$0.256858\pi$
$920$	9.74363	0.321238
$921$	−14.2080	−0.468170
$922$	−30.8511	−1.01603
$923$	−37.4395	−1.23234
$924$	0	0
$925$	−13.2828	−0.436734
$926$	−45.2319	−1.48641
$927$	9.49350	0.311807
$928$	11.5119	0.377897
$929$	32.8282	1.07706	0.538530	−	0.842607i	$-0.318980\pi$
$929$	32.8282	1.07706	0.538530	+	0.842607i	$0.318980\pi$
$930$	−7.64835	−0.250799
$931$	0	0
$932$	23.3556	0.765039
$933$	30.4255	0.996086
$934$	−38.7076	−1.26655
$935$	−28.6372	−0.936536
$936$	−4.12737	−0.134907
$937$	−60.4319	−1.97422	−0.987112	−	0.160030i	$-0.948841\pi$
$937$	−60.4319	−1.97422	−0.987112	+	0.160030i	$0.948841\pi$
$938$	0	0
$939$	−34.6369	−1.13033
$940$	6.39725	0.208655
$941$	39.9477	1.30226	0.651129	−	0.758967i	$-0.274296\pi$
$941$	39.9477	1.30226	0.651129	+	0.758967i	$0.274296\pi$
$942$	49.2447	1.60448
$943$	2.95806	0.0963276
$944$	23.8757	0.777086
$945$	0	0
$946$	51.7361	1.68209
$947$	48.3521	1.57123	0.785616	−	0.618714i	$-0.212346\pi$
$947$	48.3521	1.57123	0.785616	+	0.618714i	$0.212346\pi$
$948$	−0.402149	−0.0130612
$949$	−32.7947	−1.06456
$950$	−14.1016	−0.457517
$951$	−10.0665	−0.326428
$952$	0	0
$953$	17.5215	0.567578	0.283789	−	0.958887i	$-0.408408\pi$
$953$	17.5215	0.567578	0.283789	+	0.958887i	$0.408408\pi$
$954$	13.2784	0.429903
$955$	29.2712	0.947194
$956$	−22.6400	−0.732231
$957$	−10.9392	−0.353614
$958$	54.3177	1.75493
$959$	0	0
$960$	−3.24251	−0.104651
$961$	−29.8838	−0.963994
$962$	63.3456	2.04234
$963$	−10.4815	−0.337763
$964$	−26.8458	−0.864644
$965$	−37.3837	−1.20342
$966$	0	0
$967$	−33.2691	−1.06986	−0.534930	−	0.844896i	$-0.679662\pi$
$967$	−33.2691	−1.06986	−0.534930	+	0.844896i	$0.679662\pi$
$968$	−3.59124	−0.115427
$969$	−20.1387	−0.646947
$970$	2.38688	0.0766380
$971$	31.8860	1.02327	0.511635	−	0.859203i	$-0.329040\pi$
$971$	31.8860	1.02327	0.511635	+	0.859203i	$0.329040\pi$
$972$	−7.26921	−0.233160
$973$	0	0
$974$	48.2683	1.54662
$975$	13.6130	0.435965
$976$	−54.4611	−1.74326
$977$	−5.55629	−0.177762	−0.0888808	−	0.996042i	$-0.528329\pi$
$977$	−5.55629	−0.177762	−0.0888808	+	0.996042i	$0.528329\pi$
$978$	−36.9143	−1.18039
$979$	34.2695	1.09526
$980$	0	0
$981$	11.4117	0.364349
$982$	29.8372	0.952143
$983$	−39.4972	−1.25977	−0.629883	−	0.776690i	$-0.716897\pi$
$983$	−39.4972	−1.25977	−0.629883	+	0.776690i	$0.716897\pi$
$984$	2.53603	0.0808456
$985$	22.8964	0.729541
$986$	10.2463	0.326309
$987$	0	0
$988$	25.1748	0.800918
$989$	−20.4664	−0.650794
$990$	−10.1845	−0.323686
$991$	−37.6712	−1.19667	−0.598333	−	0.801248i	$-0.704170\pi$
$991$	−37.6712	−1.19667	−0.598333	+	0.801248i	$0.704170\pi$
$992$	6.33661	0.201188
$993$	−18.0001	−0.571215
$994$	0	0
$995$	−19.0456	−0.603785
$996$	−6.37228	−0.201913
$997$	34.4421	1.09079	0.545396	−	0.838179i	$-0.316379\pi$
$997$	34.4421	1.09079	0.545396	+	0.838179i	$0.316379\pi$
$998$	−30.1311	−0.953784
$999$	−40.8228	−1.29158

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6223.2.a.l.1.14		20
7.6	odd	2		889.2.a.d.1.14	✓	20
21.20	even	2		8001.2.a.w.1.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
889.2.a.d.1.14	✓	20	7.6	odd	2
6223.2.a.l.1.14		20	1.1	even	1	trivial
8001.2.a.w.1.7		20	21.20	even	2

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:	\( N \)	\(=\)	\( 6223 = 7^{2} \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6223.a (trivial)

\(f(q)\)	\(=\)	\(q+1.78791 q^{2} -1.55116 q^{3} +1.19664 q^{4} -2.61034 q^{5} -2.77333 q^{6} -1.43634 q^{8} -0.593917 q^{9} +O(q^{10})\)	\(q+1.78791 q^{2} -1.55116 q^{3} +1.19664 q^{4} -2.61034 q^{5} -2.77333 q^{6} -1.43634 q^{8} -0.593917 q^{9} -4.66707 q^{10} -3.67427 q^{11} -1.85617 q^{12} -4.83827 q^{13} +4.04904 q^{15} -4.96133 q^{16} -2.98581 q^{17} -1.06187 q^{18} -4.34824 q^{19} -3.12363 q^{20} -6.56928 q^{22} +2.59876 q^{23} +2.22799 q^{24} +1.81388 q^{25} -8.65041 q^{26} +5.57472 q^{27} -1.91937 q^{29} +7.23934 q^{30} -1.05650 q^{31} -5.99776 q^{32} +5.69937 q^{33} -5.33837 q^{34} -0.710704 q^{36} -7.32285 q^{37} -7.77428 q^{38} +7.50490 q^{39} +3.74934 q^{40} +1.13826 q^{41} -7.87546 q^{43} -4.39677 q^{44} +1.55033 q^{45} +4.64636 q^{46} -2.04802 q^{47} +7.69580 q^{48} +3.24306 q^{50} +4.63145 q^{51} -5.78966 q^{52} -12.5047 q^{53} +9.96713 q^{54} +9.59110 q^{55} +6.74480 q^{57} -3.43167 q^{58} -4.81235 q^{59} +4.84524 q^{60} +10.9771 q^{61} -1.88893 q^{62} -0.800808 q^{64} +12.6295 q^{65} +10.1900 q^{66} -1.31670 q^{67} -3.57293 q^{68} -4.03108 q^{69} +7.73820 q^{71} +0.853068 q^{72} +6.77819 q^{73} -13.0926 q^{74} -2.81361 q^{75} -5.20327 q^{76} +13.4181 q^{78} +0.216655 q^{79} +12.9508 q^{80} -6.86551 q^{81} +2.03511 q^{82} +3.43302 q^{83} +7.79398 q^{85} -14.0807 q^{86} +2.97724 q^{87} +5.27751 q^{88} -9.32688 q^{89} +2.77185 q^{90} +3.10977 q^{92} +1.63879 q^{93} -3.66168 q^{94} +11.3504 q^{95} +9.30345 q^{96} -0.511430 q^{97} +2.18221 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 8 q^{2} + 24 q^{4} - 3 q^{5} - 6 q^{6} + 24 q^{8} + 30 q^{9}+O(q^{10}) \) 20 * q + 8 * q^2 + 24 * q^4 - 3 * q^5 - 6 * q^6 + 24 * q^8 + 30 * q^9	\( 20 q + 8 q^{2} + 24 q^{4} - 3 q^{5} - 6 q^{6} + 24 q^{8} + 30 q^{9} + 8 q^{10} + 26 q^{11} + 4 q^{12} + 4 q^{13} + 10 q^{15} + 24 q^{16} - 4 q^{17} + 5 q^{18} - q^{19} + 2 q^{20} + q^{22} + 31 q^{23} + 6 q^{24} + 27 q^{25} - 4 q^{26} + 18 q^{27} + 16 q^{29} - 5 q^{30} - 6 q^{31} + 41 q^{32} + 18 q^{33} + 10 q^{34} + 18 q^{36} + 2 q^{37} - 3 q^{38} + 43 q^{39} + 38 q^{40} - 25 q^{41} + 13 q^{43} + 66 q^{44} + 2 q^{45} + 20 q^{46} - 19 q^{47} + 16 q^{48} - 4 q^{50} + 4 q^{51} - 20 q^{52} + 24 q^{53} - 5 q^{54} + 3 q^{55} - 4 q^{57} + 12 q^{58} - 23 q^{59} + 24 q^{60} + 27 q^{61} - 7 q^{62} + 2 q^{64} + 26 q^{65} - 26 q^{66} + 9 q^{67} + 25 q^{68} + 3 q^{69} + 63 q^{71} + 27 q^{72} + 21 q^{73} + 21 q^{74} + 52 q^{75} + 10 q^{76} - 70 q^{78} + 18 q^{79} + 23 q^{80} + 40 q^{81} + 42 q^{82} + q^{83} - 41 q^{85} - 12 q^{86} + 9 q^{87} + 57 q^{88} + 16 q^{89} - q^{90} + 17 q^{92} - 41 q^{93} - 7 q^{94} + 75 q^{95} + 81 q^{96} + 32 q^{97} + 15 q^{99}+O(q^{100}) \) 20 * q + 8 * q^2 + 24 * q^4 - 3 * q^5 - 6 * q^6 + 24 * q^8 + 30 * q^9 + 8 * q^10 + 26 * q^11 + 4 * q^12 + 4 * q^13 + 10 * q^15 + 24 * q^16 - 4 * q^17 + 5 * q^18 - q^19 + 2 * q^20 + q^22 + 31 * q^23 + 6 * q^24 + 27 * q^25 - 4 * q^26 + 18 * q^27 + 16 * q^29 - 5 * q^30 - 6 * q^31 + 41 * q^32 + 18 * q^33 + 10 * q^34 + 18 * q^36 + 2 * q^37 - 3 * q^38 + 43 * q^39 + 38 * q^40 - 25 * q^41 + 13 * q^43 + 66 * q^44 + 2 * q^45 + 20 * q^46 - 19 * q^47 + 16 * q^48 - 4 * q^50 + 4 * q^51 - 20 * q^52 + 24 * q^53 - 5 * q^54 + 3 * q^55 - 4 * q^57 + 12 * q^58 - 23 * q^59 + 24 * q^60 + 27 * q^61 - 7 * q^62 + 2 * q^64 + 26 * q^65 - 26 * q^66 + 9 * q^67 + 25 * q^68 + 3 * q^69 + 63 * q^71 + 27 * q^72 + 21 * q^73 + 21 * q^74 + 52 * q^75 + 10 * q^76 - 70 * q^78 + 18 * q^79 + 23 * q^80 + 40 * q^81 + 42 * q^82 + q^83 - 41 * q^85 - 12 * q^86 + 9 * q^87 + 57 * q^88 + 16 * q^89 - q^90 + 17 * q^92 - 41 * q^93 - 7 * q^94 + 75 * q^95 + 81 * q^96 + 32 * q^97 + 15 * q^99

Introduction

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