LMFDB - Embedded newform 6223.2.a.l.1.15

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			1.15
Root			$2.02020$ 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)

$f(q)$	$=$	$q+2.02020 q^{2} +2.71861 q^{3} +2.08119 q^{4} +3.61502 q^{5} +5.49211 q^{6} +0.164016 q^{8} +4.39082 q^{9} +O(q^{10})$	\(q+2.02020 q^{2} +2.71861 q^{3} +2.08119 q^{4} +3.61502 q^{5} +5.49211 q^{6} +0.164016 q^{8} +4.39082 q^{9} +7.30304 q^{10} +1.71540 q^{11} +5.65793 q^{12} -0.128672 q^{13} +9.82781 q^{15} -3.83103 q^{16} -6.97582 q^{17} +8.87031 q^{18} -2.84568 q^{19} +7.52353 q^{20} +3.46544 q^{22} +7.59356 q^{23} +0.445894 q^{24} +8.06836 q^{25} -0.259942 q^{26} +3.78109 q^{27} +2.66087 q^{29} +19.8541 q^{30} +6.90740 q^{31} -8.06746 q^{32} +4.66350 q^{33} -14.0925 q^{34} +9.13812 q^{36} +3.46102 q^{37} -5.74883 q^{38} -0.349808 q^{39} +0.592920 q^{40} +3.74696 q^{41} -3.42381 q^{43} +3.57007 q^{44} +15.8729 q^{45} +15.3405 q^{46} -3.23711 q^{47} -10.4151 q^{48} +16.2997 q^{50} -18.9645 q^{51} -0.267790 q^{52} -7.71522 q^{53} +7.63853 q^{54} +6.20120 q^{55} -7.73629 q^{57} +5.37547 q^{58} +2.24701 q^{59} +20.4535 q^{60} -11.8098 q^{61} +13.9543 q^{62} -8.63579 q^{64} -0.465151 q^{65} +9.42118 q^{66} +6.26607 q^{67} -14.5180 q^{68} +20.6439 q^{69} +13.9605 q^{71} +0.720163 q^{72} -10.9034 q^{73} +6.99194 q^{74} +21.9347 q^{75} -5.92240 q^{76} -0.706680 q^{78} +8.03030 q^{79} -13.8493 q^{80} -2.89317 q^{81} +7.56958 q^{82} -1.88020 q^{83} -25.2177 q^{85} -6.91676 q^{86} +7.23384 q^{87} +0.281353 q^{88} -17.7992 q^{89} +32.0663 q^{90} +15.8036 q^{92} +18.7785 q^{93} -6.53959 q^{94} -10.2872 q^{95} -21.9323 q^{96} +11.5017 q^{97} +7.53201 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.02020	1.42849	0.714247	−	0.699894i	$-0.246769\pi$
$2$	2.02020	1.42849	0.714247	+	0.699894i	$0.246769\pi$
$3$	2.71861	1.56959	0.784794	−	0.619757i	$-0.212769\pi$
$3$	2.71861	1.56959	0.784794	+	0.619757i	$0.212769\pi$
$4$	2.08119	1.04059
$5$	3.61502	1.61669	0.808343	−	0.588712i	$-0.200365\pi$
$5$	3.61502	1.61669	0.808343	+	0.588712i	$0.200365\pi$
$6$	5.49211	2.24215
$7$	0	0
$7$	0	0
$8$	0.164016	0.0579883
$9$	4.39082	1.46361
$10$	7.30304	2.30942
$11$	1.71540	0.517213	0.258606	−	0.965983i	$-0.416737\pi$
$11$	1.71540	0.517213	0.258606	+	0.965983i	$0.416737\pi$
$12$	5.65793	1.63330
$13$	−0.128672	−0.0356871	−0.0178436	−	0.999841i	$-0.505680\pi$
$13$	−0.128672	−0.0356871	−0.0178436	+	0.999841i	$0.505680\pi$
$14$	0	0
$15$	9.82781	2.53753
$16$	−3.83103	−0.957758
$17$	−6.97582	−1.69189	−0.845943	−	0.533273i	$-0.820962\pi$
$17$	−6.97582	−1.69189	−0.845943	+	0.533273i	$0.820962\pi$
$18$	8.87031	2.09075
$19$	−2.84568	−0.652844	−0.326422	−	0.945224i	$-0.605843\pi$
$19$	−2.84568	−0.652844	−0.326422	+	0.945224i	$0.605843\pi$
$20$	7.52353	1.68231
$21$	0	0
$22$	3.46544	0.738835
$23$	7.59356	1.58337	0.791684	−	0.610931i	$-0.209205\pi$
$23$	7.59356	1.58337	0.791684	+	0.610931i	$0.209205\pi$
$24$	0.445894	0.0910178
$25$	8.06836	1.61367
$26$	−0.259942	−0.0509788
$27$	3.78109	0.727671
$28$	0	0
$29$	2.66087	0.494110	0.247055	−	0.969001i	$-0.420537\pi$
$29$	2.66087	0.494110	0.247055	+	0.969001i	$0.420537\pi$
$30$	19.8541	3.62485
$31$	6.90740	1.24061	0.620303	−	0.784362i	$-0.287010\pi$
$31$	6.90740	1.24061	0.620303	+	0.784362i	$0.287010\pi$
$32$	−8.06746	−1.42614
$33$	4.66350	0.811811
$34$	−14.0925	−2.41685
$35$	0	0
$36$	9.13812	1.52302
$37$	3.46102	0.568988	0.284494	−	0.958678i	$-0.408174\pi$
$37$	3.46102	0.568988	0.284494	+	0.958678i	$0.408174\pi$
$38$	−5.74883	−0.932584
$39$	−0.349808	−0.0560141
$40$	0.592920	0.0937489
$41$	3.74696	0.585176	0.292588	−	0.956239i	$-0.405483\pi$
$41$	3.74696	0.585176	0.292588	+	0.956239i	$0.405483\pi$
$42$	0	0
$43$	−3.42381	−0.522126	−0.261063	−	0.965322i	$-0.584073\pi$
$43$	−3.42381	−0.522126	−0.261063	+	0.965322i	$0.584073\pi$
$44$	3.57007	0.538208
$45$	15.8729	2.36619
$46$	15.3405	2.26183
$47$	−3.23711	−0.472180	−0.236090	−	0.971731i	$-0.575866\pi$
$47$	−3.23711	−0.472180	−0.236090	+	0.971731i	$0.575866\pi$
$48$	−10.4151	−1.50329
$49$	0	0
$50$	16.2997	2.30512
$51$	−18.9645	−2.65556
$52$	−0.267790	−0.0371358
$53$	−7.71522	−1.05977	−0.529884	−	0.848070i	$-0.677764\pi$
$53$	−7.71522	−1.05977	−0.529884	+	0.848070i	$0.677764\pi$
$54$	7.63853	1.03947
$55$	6.20120	0.836170
$56$	0	0
$57$	−7.73629	−1.02470
$58$	5.37547	0.705833
$59$	2.24701	0.292536	0.146268	−	0.989245i	$-0.453274\pi$
$59$	2.24701	0.292536	0.146268	+	0.989245i	$0.453274\pi$
$60$	20.4535	2.64054
$61$	−11.8098	−1.51209	−0.756045	−	0.654520i	$-0.772871\pi$
$61$	−11.8098	−1.51209	−0.756045	+	0.654520i	$0.772871\pi$
$62$	13.9543	1.77220
$63$	0	0
$64$	−8.63579	−1.07947
$65$	−0.465151	−0.0576949
$66$	9.42118	1.15967
$67$	6.26607	0.765522	0.382761	−	0.923847i	$-0.374973\pi$
$67$	6.26607	0.765522	0.382761	+	0.923847i	$0.374973\pi$
$68$	−14.5180	−1.76057
$69$	20.6439	2.48523
$70$	0	0
$71$	13.9605	1.65681	0.828404	−	0.560131i	$-0.189249\pi$
$71$	13.9605	1.65681	0.828404	+	0.560131i	$0.189249\pi$
$72$	0.720163	0.0848721
$73$	−10.9034	−1.27615	−0.638075	−	0.769974i	$-0.720269\pi$
$73$	−10.9034	−1.27615	−0.638075	+	0.769974i	$0.720269\pi$
$74$	6.99194	0.812796
$75$	21.9347	2.53280
$76$	−5.92240	−0.679346
$77$	0	0
$78$	−0.706680	−0.0800158
$79$	8.03030	0.903479	0.451740	−	0.892150i	$-0.350804\pi$
$79$	8.03030	0.903479	0.451740	+	0.892150i	$0.350804\pi$
$80$	−13.8493	−1.54839
$81$	−2.89317	−0.321463
$82$	7.56958	0.835921
$83$	−1.88020	−0.206379	−0.103190	−	0.994662i	$-0.532905\pi$
$83$	−1.88020	−0.206379	−0.103190	+	0.994662i	$0.532905\pi$
$84$	0	0
$85$	−25.2177	−2.73525
$86$	−6.91676	−0.745853
$87$	7.23384	0.775549
$88$	0.281353	0.0299923
$89$	−17.7992	−1.88671	−0.943357	−	0.331778i	$-0.892351\pi$
$89$	−17.7992	−1.88671	−0.943357	+	0.331778i	$0.892351\pi$
$90$	32.0663	3.38009
$91$	0	0
$92$	15.8036	1.64764
$93$	18.7785	1.94724
$94$	−6.53959	−0.674507
$95$	−10.2872	−1.05544
$96$	−21.9323	−2.23845
$97$	11.5017	1.16782	0.583912	−	0.811817i	$-0.301521\pi$
$97$	11.5017	1.16782	0.583912	+	0.811817i	$0.301521\pi$
$98$	0	0
$99$	7.53201	0.756996
$100$	16.7918	1.67918
$101$	14.7154	1.46424	0.732118	−	0.681177i	$-0.238532\pi$
$101$	14.7154	1.46424	0.732118	+	0.681177i	$0.238532\pi$
$102$	−38.3120	−3.79346
$103$	−6.34329	−0.625023	−0.312511	−	0.949914i	$-0.601170\pi$
$103$	−6.34329	−0.625023	−0.312511	+	0.949914i	$0.601170\pi$
$104$	−0.0211042	−0.00206944
$105$	0	0
$106$	−15.5863	−1.51387
$107$	−8.71742	−0.842745	−0.421372	−	0.906888i	$-0.638451\pi$
$107$	−8.71742	−0.842745	−0.421372	+	0.906888i	$0.638451\pi$
$108$	7.86915	0.757210
$109$	−1.07211	−0.102690	−0.0513448	−	0.998681i	$-0.516351\pi$
$109$	−1.07211	−0.102690	−0.0513448	+	0.998681i	$0.516351\pi$
$110$	12.5276	1.19446
$111$	9.40915	0.893077
$112$	0	0
$113$	−0.0606933	−0.00570954	−0.00285477	−	0.999996i	$-0.500909\pi$
$113$	−0.0606933	−0.00570954	−0.00285477	+	0.999996i	$0.500909\pi$
$114$	−15.6288	−1.46377
$115$	27.4509	2.55981
$116$	5.53776	0.514168
$117$	−0.564974	−0.0522319
$118$	4.53941	0.417886
$119$	0	0
$120$	1.61192	0.147147
$121$	−8.05740	−0.732491
$122$	−23.8581	−2.16001
$123$	10.1865	0.918486
$124$	14.3756	1.29097
$125$	11.0922	0.992115
$126$	0	0
$127$	−1.00000	−0.0887357
$127$	−1.00000	−0.0887357
$128$	−1.31104	−0.115881
$129$	−9.30798	−0.819522
$130$	−0.939696	−0.0824168
$131$	−9.72799	−0.849938	−0.424969	−	0.905208i	$-0.639715\pi$
$131$	−9.72799	−0.849938	−0.424969	+	0.905208i	$0.639715\pi$
$132$	9.70562	0.844765
$133$	0	0
$134$	12.6587	1.09354
$135$	13.6687	1.17641
$136$	−1.14414	−0.0981096
$137$	−5.18763	−0.443209	−0.221605	−	0.975137i	$-0.571129\pi$
$137$	−5.18763	−0.443209	−0.221605	+	0.975137i	$0.571129\pi$
$138$	41.7047	3.55014
$139$	5.92853	0.502851	0.251426	−	0.967877i	$-0.419101\pi$
$139$	5.92853	0.502851	0.251426	+	0.967877i	$0.419101\pi$
$140$	0	0
$141$	−8.80042	−0.741129
$142$	28.2030	2.36674
$143$	−0.220724	−0.0184578
$144$	−16.8214	−1.40178
$145$	9.61908	0.798821
$146$	−22.0270	−1.82297
$147$	0	0
$148$	7.20304	0.592086
$149$	11.5470	0.945970	0.472985	−	0.881070i	$-0.343176\pi$
$149$	11.5470	0.945970	0.472985	+	0.881070i	$0.343176\pi$
$150$	44.3124	3.61809
$151$	−2.29824	−0.187028	−0.0935142	−	0.995618i	$-0.529810\pi$
$151$	−2.29824	−0.187028	−0.0935142	+	0.995618i	$0.529810\pi$
$152$	−0.466737	−0.0378573
$153$	−30.6296	−2.47625
$154$	0	0
$155$	24.9704	2.00567
$156$	−0.728016	−0.0582879
$157$	15.2530	1.21733	0.608663	−	0.793429i	$-0.291706\pi$
$157$	15.2530	1.21733	0.608663	+	0.793429i	$0.291706\pi$
$158$	16.2228	1.29061
$159$	−20.9747	−1.66340
$160$	−29.1640	−2.30562
$161$	0	0
$162$	−5.84476	−0.459208
$163$	−3.33315	−0.261073	−0.130536	−	0.991444i	$-0.541670\pi$
$163$	−3.33315	−0.261073	−0.130536	+	0.991444i	$0.541670\pi$
$164$	7.79812	0.608931
$165$	16.8586	1.31244
$166$	−3.79838	−0.294811
$167$	−17.4055	−1.34688	−0.673439	−	0.739243i	$-0.735184\pi$
$167$	−17.4055	−1.34688	−0.673439	+	0.739243i	$0.735184\pi$
$168$	0	0
$169$	−12.9834	−0.998726
$170$	−50.9447	−3.90728
$171$	−12.4949	−0.955507
$172$	−7.12559	−0.543321
$173$	−16.4037	−1.24715	−0.623575	−	0.781764i	$-0.714320\pi$
$173$	−16.4037	−1.24715	−0.623575	+	0.781764i	$0.714320\pi$
$174$	14.6138	1.10787
$175$	0	0
$176$	−6.57175	−0.495365
$177$	6.10875	0.459162
$178$	−35.9579	−2.69516
$179$	8.11019	0.606184	0.303092	−	0.952961i	$-0.401981\pi$
$179$	8.11019	0.606184	0.303092	+	0.952961i	$0.401981\pi$
$180$	33.0345	2.46224
$181$	−10.8706	−0.808007	−0.404004	−	0.914757i	$-0.632382\pi$
$181$	−10.8706	−0.808007	−0.404004	+	0.914757i	$0.632382\pi$
$182$	0	0
$183$	−32.1062	−2.37336
$184$	1.24546	0.0918168
$185$	12.5117	0.919875
$186$	37.9363	2.78162
$187$	−11.9663	−0.875065
$188$	−6.73703	−0.491348
$189$	0	0
$190$	−20.7821	−1.50769
$191$	9.47154	0.685336	0.342668	−	0.939456i	$-0.388669\pi$
$191$	9.47154	0.685336	0.342668	+	0.939456i	$0.388669\pi$
$192$	−23.4773	−1.69433
$193$	−22.3797	−1.61092	−0.805462	−	0.592647i	$-0.798083\pi$
$193$	−22.3797	−1.61092	−0.805462	+	0.592647i	$0.798083\pi$
$194$	23.2358	1.66823
$195$	−1.26456	−0.0905572
$196$	0	0
$197$	−8.09567	−0.576793	−0.288396	−	0.957511i	$-0.593122\pi$
$197$	−8.09567	−0.576793	−0.288396	+	0.957511i	$0.593122\pi$
$198$	15.2161	1.08136
$199$	−23.4903	−1.66518	−0.832591	−	0.553888i	$-0.813143\pi$
$199$	−23.4903	−1.66518	−0.832591	+	0.553888i	$0.813143\pi$
$200$	1.32334	0.0935741
$201$	17.0350	1.20155
$202$	29.7280	2.09165
$203$	0	0
$204$	−39.4687	−2.76336
$205$	13.5453	0.946046
$206$	−12.8147	−0.892841
$207$	33.3420	2.31743
$208$	0.492946	0.0341796
$209$	−4.88148	−0.337659
$210$	0	0
$211$	−22.1116	−1.52223	−0.761114	−	0.648618i	$-0.775347\pi$
$211$	−22.1116	−1.52223	−0.761114	+	0.648618i	$0.775347\pi$
$212$	−16.0568	−1.10279
$213$	37.9532	2.60051
$214$	−17.6109	−1.20386
$215$	−12.3771	−0.844113
$216$	0.620158	0.0421964
$217$	0	0
$218$	−2.16587	−0.146692
$219$	−29.6421	−2.00303
$220$	12.9059	0.870114
$221$	0.897592	0.0603786
$222$	19.0083	1.27576
$223$	22.7679	1.52465	0.762327	−	0.647192i	$-0.224057\pi$
$223$	22.7679	1.52465	0.762327	+	0.647192i	$0.224057\pi$
$224$	0	0
$225$	35.4267	2.36178
$226$	−0.122612	−0.00815605
$227$	−14.8676	−0.986800	−0.493400	−	0.869802i	$-0.664246\pi$
$227$	−14.8676	−0.986800	−0.493400	+	0.869802i	$0.664246\pi$
$228$	−16.1007	−1.06629
$229$	13.3091	0.879487	0.439743	−	0.898123i	$-0.355069\pi$
$229$	13.3091	0.879487	0.439743	+	0.898123i	$0.355069\pi$
$230$	55.4561	3.65667
$231$	0	0
$232$	0.436424	0.0286526
$233$	−15.5911	−1.02140	−0.510702	−	0.859758i	$-0.670615\pi$
$233$	−15.5911	−1.02140	−0.510702	+	0.859758i	$0.670615\pi$
$234$	−1.14136	−0.0746129
$235$	−11.7022	−0.763367
$236$	4.67646	0.304412
$237$	21.8312	1.41809
$238$	0	0
$239$	20.7092	1.33956	0.669782	−	0.742557i	$-0.266387\pi$
$239$	20.7092	1.33956	0.669782	+	0.742557i	$0.266387\pi$
$240$	−37.6507	−2.43034
$241$	−18.0593	−1.16330	−0.581652	−	0.813438i	$-0.697594\pi$
$241$	−18.0593	−1.16330	−0.581652	+	0.813438i	$0.697594\pi$
$242$	−16.2775	−1.04636
$243$	−19.2086	−1.23224
$244$	−24.5784	−1.57347
$245$	0	0
$246$	20.5787	1.31205
$247$	0.366159	0.0232981
$248$	1.13292	0.0719407
$249$	−5.11153	−0.323930
$250$	22.4084	1.41723
$251$	−19.5647	−1.23491	−0.617457	−	0.786604i	$-0.711837\pi$
$251$	−19.5647	−1.23491	−0.617457	+	0.786604i	$0.711837\pi$
$252$	0	0
$253$	13.0260	0.818938
$254$	−2.02020	−0.126758
$255$	−68.5571	−4.29321
$256$	14.6230	0.913938
$257$	15.1899	0.947522	0.473761	−	0.880653i	$-0.342896\pi$
$257$	15.1899	0.947522	0.473761	+	0.880653i	$0.342896\pi$
$258$	−18.8039	−1.17068
$259$	0	0
$260$	−0.968067	−0.0600369
$261$	11.6834	0.723183
$262$	−19.6524	−1.21413
$263$	8.41039	0.518607	0.259304	−	0.965796i	$-0.416507\pi$
$263$	8.41039	0.518607	0.259304	+	0.965796i	$0.416507\pi$
$264$	0.764887	0.0470755
$265$	−27.8907	−1.71331
$266$	0	0
$267$	−48.3891	−2.96136
$268$	13.0409	0.796598
$269$	−30.2487	−1.84430	−0.922148	−	0.386838i	$-0.873567\pi$
$269$	−30.2487	−1.84430	−0.922148	+	0.386838i	$0.873567\pi$
$270$	27.6134	1.68050
$271$	−29.7564	−1.80758	−0.903788	−	0.427981i	$-0.859225\pi$
$271$	−29.7564	−1.80758	−0.903788	+	0.427981i	$0.859225\pi$
$272$	26.7246	1.62042
$273$	0	0
$274$	−10.4800	−0.633121
$275$	13.8405	0.834612
$276$	42.9639	2.58612
$277$	−10.9909	−0.660378	−0.330189	−	0.943915i	$-0.607113\pi$
$277$	−10.9909	−0.660378	−0.330189	+	0.943915i	$0.607113\pi$
$278$	11.9768	0.718320
$279$	30.3292	1.81576
$280$	0	0
$281$	−6.49905	−0.387701	−0.193850	−	0.981031i	$-0.562098\pi$
$281$	−6.49905	−0.387701	−0.193850	+	0.981031i	$0.562098\pi$
$282$	−17.7786	−1.05870
$283$	−8.01715	−0.476570	−0.238285	−	0.971195i	$-0.576585\pi$
$283$	−8.01715	−0.476570	−0.238285	+	0.971195i	$0.576585\pi$
$284$	29.0545	1.72407
$285$	−27.9668	−1.65661
$286$	−0.445905	−0.0263669
$287$	0	0
$288$	−35.4228	−2.08731
$289$	31.6621	1.86248
$290$	19.4324	1.14111
$291$	31.2687	1.83300
$292$	−22.6921	−1.32795
$293$	16.6829	0.974628	0.487314	−	0.873227i	$-0.337977\pi$
$293$	16.6829	0.974628	0.487314	+	0.873227i	$0.337977\pi$
$294$	0	0
$295$	8.12300	0.472939
$296$	0.567662	0.0329947
$297$	6.48608	0.376361
$298$	23.3273	1.35131
$299$	−0.977077	−0.0565058
$300$	45.6502	2.63562
$301$	0	0
$302$	−4.64290	−0.267169
$303$	40.0054	2.29825
$304$	10.9019	0.625267
$305$	−42.6926	−2.44457
$306$	−61.8777	−3.53731
$307$	24.1991	1.38111	0.690557	−	0.723278i	$-0.257365\pi$
$307$	24.1991	1.38111	0.690557	+	0.723278i	$0.257365\pi$
$308$	0	0
$309$	−17.2449	−0.981028
$310$	50.4451	2.86509
$311$	−12.2359	−0.693835	−0.346917	−	0.937896i	$-0.612772\pi$
$311$	−12.2359	−0.693835	−0.346917	+	0.937896i	$0.612772\pi$
$312$	−0.0573740	−0.00324816
$313$	5.94552	0.336061	0.168030	−	0.985782i	$-0.446259\pi$
$313$	5.94552	0.336061	0.168030	+	0.985782i	$0.446259\pi$
$314$	30.8141	1.73894
$315$	0	0
$316$	16.7126	0.940155
$317$	16.4175	0.922099	0.461049	−	0.887374i	$-0.347473\pi$
$317$	16.4175	0.922099	0.461049	+	0.887374i	$0.347473\pi$
$318$	−42.3729	−2.37615
$319$	4.56445	0.255560
$320$	−31.2185	−1.74517
$321$	−23.6992	−1.32276
$322$	0	0
$323$	19.8510	1.10454
$324$	−6.02123	−0.334513
$325$	−1.03817	−0.0575873
$326$	−6.73362	−0.372940
$327$	−2.91465	−0.161180
$328$	0.614560	0.0339334
$329$	0	0
$330$	34.0577	1.87482
$331$	−7.59580	−0.417503	−0.208751	−	0.977969i	$-0.566940\pi$
$331$	−7.59580	−0.417503	−0.208751	+	0.977969i	$0.566940\pi$
$332$	−3.91306	−0.214757
$333$	15.1967	0.832775
$334$	−35.1625	−1.92401
$335$	22.6520	1.23761
$336$	0	0
$337$	3.34888	0.182425	0.0912127	−	0.995831i	$-0.470926\pi$
$337$	3.34888	0.182425	0.0912127	+	0.995831i	$0.470926\pi$
$338$	−26.2291	−1.42667
$339$	−0.165001	−0.00896163
$340$	−52.4829	−2.84628
$341$	11.8490	0.641657
$342$	−25.2421	−1.36494
$343$	0	0
$344$	−0.561558	−0.0302772
$345$	74.6281	4.01784
$346$	−33.1387	−1.78155
$347$	−14.0552	−0.754522	−0.377261	−	0.926107i	$-0.623134\pi$
$347$	−14.0552	−0.754522	−0.377261	+	0.926107i	$0.623134\pi$
$348$	15.0550	0.807032
$349$	30.4812	1.63162	0.815810	−	0.578319i	$-0.196291\pi$
$349$	30.4812	1.63162	0.815810	+	0.578319i	$0.196291\pi$
$350$	0	0
$351$	−0.486519	−0.0259685
$352$	−13.8389	−0.737618
$353$	19.9490	1.06178	0.530888	−	0.847442i	$-0.321859\pi$
$353$	19.9490	1.06178	0.530888	+	0.847442i	$0.321859\pi$
$354$	12.3409	0.655909
$355$	50.4675	2.67854
$356$	−37.0435	−1.96330
$357$	0	0
$358$	16.3842	0.865930
$359$	32.0511	1.69159	0.845797	−	0.533505i	$-0.179125\pi$
$359$	32.0511	1.69159	0.845797	+	0.533505i	$0.179125\pi$
$360$	2.60340	0.137211
$361$	−10.9021	−0.573795
$362$	−21.9608	−1.15423
$363$	−21.9049	−1.14971
$364$	0	0
$365$	−39.4161	−2.06313
$366$	−64.8608	−3.39033
$367$	31.5922	1.64910	0.824549	−	0.565791i	$-0.191429\pi$
$367$	31.5922	1.64910	0.824549	+	0.565791i	$0.191429\pi$
$368$	−29.0912	−1.51648
$369$	16.4522	0.856468
$370$	25.2760	1.31404
$371$	0	0
$372$	39.0816	2.02629
$373$	22.1743	1.14814	0.574070	−	0.818806i	$-0.305364\pi$
$373$	22.1743	1.14814	0.574070	+	0.818806i	$0.305364\pi$
$374$	−24.1743	−1.25002
$375$	30.1553	1.55721
$376$	−0.530936	−0.0273809
$377$	−0.342378	−0.0176334
$378$	0	0
$379$	30.5459	1.56904	0.784519	−	0.620105i	$-0.212910\pi$
$379$	30.5459	1.56904	0.784519	+	0.620105i	$0.212910\pi$
$380$	−21.4096	−1.09829
$381$	−2.71861	−0.139278
$382$	19.1344	0.978999
$383$	15.8165	0.808185	0.404092	−	0.914718i	$-0.367587\pi$
$383$	15.8165	0.808185	0.404092	+	0.914718i	$0.367587\pi$
$384$	−3.56421	−0.181886
$385$	0	0
$386$	−45.2113	−2.30119
$387$	−15.0333	−0.764186
$388$	23.9373	1.21523
$389$	−5.46371	−0.277021	−0.138511	−	0.990361i	$-0.544231\pi$
$389$	−5.46371	−0.277021	−0.138511	+	0.990361i	$0.544231\pi$
$390$	−2.55466	−0.129360
$391$	−52.9714	−2.67888
$392$	0	0
$393$	−26.4466	−1.33405
$394$	−16.3548	−0.823945
$395$	29.0297	1.46064
$396$	15.6755	0.787725
$397$	20.9152	1.04971	0.524853	−	0.851193i	$-0.324120\pi$
$397$	20.9152	1.04971	0.524853	+	0.851193i	$0.324120\pi$
$398$	−47.4549	−2.37870
$399$	0	0
$400$	−30.9102	−1.54551
$401$	32.3399	1.61498	0.807488	−	0.589884i	$-0.200826\pi$
$401$	32.3399	1.61498	0.807488	+	0.589884i	$0.200826\pi$
$402$	34.4140	1.71641
$403$	−0.888788	−0.0442737
$404$	30.6255	1.52368
$405$	−10.4589	−0.519705
$406$	0	0
$407$	5.93704	0.294288
$408$	−3.11048	−0.153992
$409$	4.21818	0.208576	0.104288	−	0.994547i	$-0.466744\pi$
$409$	4.21818	0.208576	0.104288	+	0.994547i	$0.466744\pi$
$410$	27.3642	1.35142
$411$	−14.1031	−0.695656
$412$	−13.2016	−0.650395
$413$	0	0
$414$	67.3573	3.31043
$415$	−6.79697	−0.333650
$416$	1.03805	0.0508948
$417$	16.1173	0.789269
$418$	−9.86155	−0.482344
$419$	24.3115	1.18770	0.593848	−	0.804578i	$-0.297608\pi$
$419$	24.3115	1.18770	0.593848	+	0.804578i	$0.297608\pi$
$420$	0	0
$421$	−27.5365	−1.34205	−0.671024	−	0.741436i	$-0.734145\pi$
$421$	−27.5365	−1.34205	−0.671024	+	0.741436i	$0.734145\pi$
$422$	−44.6698	−2.17449
$423$	−14.2135	−0.691086
$424$	−1.26542	−0.0614541
$425$	−56.2835	−2.73015
$426$	76.6728	3.71481
$427$	0	0
$428$	−18.1426	−0.876955
$429$	−0.600061	−0.0289712
$430$	−25.0042	−1.20581
$431$	7.91245	0.381129	0.190565	−	0.981675i	$-0.438968\pi$
$431$	7.91245	0.381129	0.190565	+	0.981675i	$0.438968\pi$
$432$	−14.4855	−0.696932
$433$	−2.59840	−0.124871	−0.0624355	−	0.998049i	$-0.519887\pi$
$433$	−2.59840	−0.124871	−0.0624355	+	0.998049i	$0.519887\pi$
$434$	0	0
$435$	26.1505	1.25382
$436$	−2.23127	−0.106858
$437$	−21.6089	−1.03369
$438$	−59.8829	−2.86131
$439$	35.6823	1.70302	0.851511	−	0.524336i	$-0.175686\pi$
$439$	35.6823	1.70302	0.851511	+	0.524336i	$0.175686\pi$
$440$	1.01710	0.0484881
$441$	0	0
$442$	1.81331	0.0862504
$443$	−5.93840	−0.282142	−0.141071	−	0.989999i	$-0.545055\pi$
$443$	−5.93840	−0.282142	−0.141071	+	0.989999i	$0.545055\pi$
$444$	19.5822	0.929331
$445$	−64.3446	−3.05022
$446$	45.9957	2.17796
$447$	31.3919	1.48478
$448$	0	0
$449$	−41.2502	−1.94672	−0.973358	−	0.229293i	$-0.926359\pi$
$449$	−41.2502	−1.94672	−0.973358	+	0.229293i	$0.926359\pi$
$450$	71.5689	3.37379
$451$	6.42753	0.302661
$452$	−0.126314	−0.00594132
$453$	−6.24802	−0.293558
$454$	−30.0355	−1.40964
$455$	0	0
$456$	−1.26887	−0.0594204
$457$	−30.1065	−1.40832	−0.704161	−	0.710040i	$-0.748677\pi$
$457$	−30.1065	−1.40832	−0.704161	+	0.710040i	$0.748677\pi$
$458$	26.8869	1.25634
$459$	−26.3762	−1.23114
$460$	57.1304	2.66372
$461$	−33.2839	−1.55019	−0.775093	−	0.631847i	$-0.782297\pi$
$461$	−33.2839	−1.55019	−0.775093	+	0.631847i	$0.782297\pi$
$462$	0	0
$463$	18.7729	0.872449	0.436224	−	0.899838i	$-0.356315\pi$
$463$	18.7729	0.872449	0.436224	+	0.899838i	$0.356315\pi$
$464$	−10.1939	−0.473238
$465$	67.8847	3.14808
$466$	−31.4970	−1.45907
$467$	24.4057	1.12936	0.564682	−	0.825309i	$-0.308999\pi$
$467$	24.4057	1.12936	0.564682	+	0.825309i	$0.308999\pi$
$468$	−1.17582	−0.0543522
$469$	0	0
$470$	−23.6407	−1.09047
$471$	41.4670	1.91070
$472$	0.368546	0.0169637
$473$	−5.87320	−0.270050
$474$	44.1033	2.02573
$475$	−22.9600	−1.05348
$476$	0	0
$477$	−33.8762	−1.55108
$478$	41.8366	1.91356
$479$	17.0333	0.778272	0.389136	−	0.921180i	$-0.372774\pi$
$479$	17.0333	0.778272	0.389136	+	0.921180i	$0.372774\pi$
$480$	−79.2855	−3.61887
$481$	−0.445336	−0.0203056
$482$	−36.4834	−1.66177
$483$	0	0
$484$	−16.7690	−0.762226
$485$	41.5790	1.88800
$486$	−38.8052	−1.76024
$487$	39.6345	1.79601	0.898006	−	0.439984i	$-0.145016\pi$
$487$	39.6345	1.79601	0.898006	+	0.439984i	$0.145016\pi$
$488$	−1.93699	−0.0876835
$489$	−9.06152	−0.409776
$490$	0	0
$491$	4.67486	0.210974	0.105487	−	0.994421i	$-0.466360\pi$
$491$	4.67486	0.210974	0.105487	+	0.994421i	$0.466360\pi$
$492$	21.2000	0.955771
$493$	−18.5617	−0.835978
$494$	0.739712	0.0332812
$495$	27.2284	1.22382
$496$	−26.4625	−1.18820
$497$	0	0
$498$	−10.3263	−0.462732
$499$	−30.8849	−1.38260	−0.691299	−	0.722569i	$-0.742961\pi$
$499$	−30.8849	−1.38260	−0.691299	+	0.722569i	$0.742961\pi$
$500$	23.0849	1.03239
$501$	−47.3187	−2.11404
$502$	−39.5246	−1.76407
$503$	6.68857	0.298229	0.149114	−	0.988820i	$-0.452358\pi$
$503$	6.68857	0.298229	0.149114	+	0.988820i	$0.452358\pi$
$504$	0	0
$505$	53.1964	2.36721
$506$	26.3151	1.16985
$507$	−35.2969	−1.56759
$508$	−2.08119	−0.0923378
$509$	32.6130	1.44554	0.722772	−	0.691086i	$-0.242867\pi$
$509$	32.6130	1.44554	0.722772	+	0.691086i	$0.242867\pi$
$510$	−138.499	−6.13283
$511$	0	0
$512$	32.1634	1.42144
$513$	−10.7598	−0.475056
$514$	30.6866	1.35353
$515$	−22.9311	−1.01047
$516$	−19.3717	−0.852790
$517$	−5.55293	−0.244218
$518$	0	0
$519$	−44.5952	−1.95751
$520$	−0.0762921	−0.00334563
$521$	34.6072	1.51617	0.758085	−	0.652156i	$-0.226135\pi$
$521$	34.6072	1.51617	0.758085	+	0.652156i	$0.226135\pi$
$522$	23.6027	1.03306
$523$	31.0308	1.35688	0.678440	−	0.734656i	$-0.262656\pi$
$523$	31.0308	1.35688	0.678440	+	0.734656i	$0.262656\pi$
$524$	−20.2458	−0.884441
$525$	0	0
$526$	16.9906	0.740827
$527$	−48.1848	−2.09896
$528$	−17.8660	−0.777518
$529$	34.6622	1.50705
$530$	−56.3446	−2.44745
$531$	9.86623	0.428158
$532$	0	0
$533$	−0.482128	−0.0208833
$534$	−97.7554	−4.23029
$535$	−31.5136	−1.36245
$536$	1.02773	0.0443913
$537$	22.0484	0.951459
$538$	−61.1083	−2.63456
$539$	0	0
$540$	28.4471	1.22417
$541$	23.4032	1.00618	0.503090	−	0.864234i	$-0.332196\pi$
$541$	23.4032	1.00618	0.503090	+	0.864234i	$0.332196\pi$
$542$	−60.1138	−2.58211
$543$	−29.5530	−1.26824
$544$	56.2772	2.41287
$545$	−3.87570	−0.166017
$546$	0	0
$547$	−13.6374	−0.583094	−0.291547	−	0.956556i	$-0.594170\pi$
$547$	−13.6374	−0.583094	−0.291547	+	0.956556i	$0.594170\pi$
$548$	−10.7964	−0.461201
$549$	−51.8547	−2.21310
$550$	27.9604	1.19224
$551$	−7.57197	−0.322577
$552$	3.38593	0.144115
$553$	0	0
$554$	−22.2037	−0.943346
$555$	34.0143	1.44382
$556$	12.3384	0.523264
$557$	9.93529	0.420972	0.210486	−	0.977597i	$-0.432495\pi$
$557$	9.93529	0.420972	0.210486	+	0.977597i	$0.432495\pi$
$558$	61.2708	2.59380
$559$	0.440547	0.0186332
$560$	0	0
$561$	−32.5317	−1.37349
$562$	−13.1293	−0.553828
$563$	−21.9020	−0.923059	−0.461530	−	0.887125i	$-0.652699\pi$
$563$	−21.9020	−0.923059	−0.461530	+	0.887125i	$0.652699\pi$
$564$	−18.3153	−0.771214
$565$	−0.219407	−0.00923054
$566$	−16.1962	−0.680777
$567$	0	0
$568$	2.28974	0.0960755
$569$	31.1582	1.30622	0.653110	−	0.757263i	$-0.273464\pi$
$569$	31.1582	1.30622	0.653110	+	0.757263i	$0.273464\pi$
$570$	−56.4984	−2.36646
$571$	−17.3603	−0.726508	−0.363254	−	0.931690i	$-0.618334\pi$
$571$	−17.3603	−0.726508	−0.363254	+	0.931690i	$0.618334\pi$
$572$	−0.459367	−0.0192071
$573$	25.7494	1.07570
$574$	0	0
$575$	61.2676	2.55504
$576$	−37.9182	−1.57992
$577$	−14.3014	−0.595374	−0.297687	−	0.954663i	$-0.596215\pi$
$577$	−14.3014	−0.595374	−0.297687	+	0.954663i	$0.596215\pi$
$578$	63.9637	2.66054
$579$	−60.8415	−2.52849
$580$	20.0191	0.831248
$581$	0	0
$582$	63.1689	2.61843
$583$	−13.2347	−0.548125
$584$	−1.78833	−0.0740018
$585$	−2.04239	−0.0844426
$586$	33.7028	1.39225
$587$	−27.0893	−1.11810	−0.559048	−	0.829135i	$-0.688833\pi$
$587$	−27.0893	−1.11810	−0.559048	+	0.829135i	$0.688833\pi$
$588$	0	0
$589$	−19.6563	−0.809923
$590$	16.4100	0.675591
$591$	−22.0089	−0.905327
$592$	−13.2593	−0.544953
$593$	23.0423	0.946234	0.473117	−	0.881000i	$-0.343129\pi$
$593$	23.0423	0.946234	0.473117	+	0.881000i	$0.343129\pi$
$594$	13.1031	0.537629
$595$	0	0
$596$	24.0316	0.984371
$597$	−63.8608	−2.61365
$598$	−1.97389	−0.0807182
$599$	−31.2334	−1.27616	−0.638080	−	0.769970i	$-0.720271\pi$
$599$	−31.2334	−1.27616	−0.638080	+	0.769970i	$0.720271\pi$
$600$	3.59763	0.146873
$601$	26.2495	1.07074	0.535369	−	0.844618i	$-0.320173\pi$
$601$	26.2495	1.07074	0.535369	+	0.844618i	$0.320173\pi$
$602$	0	0
$603$	27.5132	1.12042
$604$	−4.78308	−0.194621
$605$	−29.1277	−1.18421
$606$	80.8187	3.28303
$607$	29.2334	1.18655	0.593275	−	0.805000i	$-0.297835\pi$
$607$	29.2334	1.18655	0.593275	+	0.805000i	$0.297835\pi$
$608$	22.9574	0.931047
$609$	0	0
$610$	−86.2474	−3.49206
$611$	0.416524	0.0168508
$612$	−63.7459	−2.57678
$613$	−0.319186	−0.0128918	−0.00644589	−	0.999979i	$-0.502052\pi$
$613$	−0.319186	−0.0128918	−0.00644589	+	0.999979i	$0.502052\pi$
$614$	48.8869	1.97291
$615$	36.8244	1.48490
$616$	0	0
$617$	30.3544	1.22202	0.611010	−	0.791623i	$-0.290763\pi$
$617$	30.3544	1.22202	0.611010	+	0.791623i	$0.290763\pi$
$618$	−34.8381	−1.40139
$619$	−5.15089	−0.207032	−0.103516	−	0.994628i	$-0.533009\pi$
$619$	−5.15089	−0.207032	−0.103516	+	0.994628i	$0.533009\pi$
$620$	51.9681	2.08709
$621$	28.7119	1.15217
$622$	−24.7189	−0.991138
$623$	0	0
$624$	1.34013	0.0536479
$625$	−0.243359	−0.00973436
$626$	12.0111	0.480061
$627$	−13.2708	−0.529986
$628$	31.7444	1.26674
$629$	−24.1435	−0.962663
$630$	0	0
$631$	21.2141	0.844518	0.422259	−	0.906475i	$-0.361237\pi$
$631$	21.2141	0.844518	0.422259	+	0.906475i	$0.361237\pi$
$632$	1.31710	0.0523912
$633$	−60.1129	−2.38927
$634$	33.1666	1.31721
$635$	−3.61502	−0.143458
$636$	−43.6522	−1.73092
$637$	0	0
$638$	9.22108	0.365066
$639$	61.2981	2.42492
$640$	−4.73945	−0.187343
$641$	−31.9569	−1.26222	−0.631111	−	0.775693i	$-0.717401\pi$
$641$	−31.9569	−1.26222	−0.631111	+	0.775693i	$0.717401\pi$
$642$	−47.8771	−1.88956
$643$	−28.8328	−1.13706	−0.568528	−	0.822664i	$-0.692487\pi$
$643$	−28.8328	−1.13706	−0.568528	+	0.822664i	$0.692487\pi$
$644$	0	0
$645$	−33.6485	−1.32491
$646$	40.1028	1.57783
$647$	−13.1212	−0.515846	−0.257923	−	0.966165i	$-0.583038\pi$
$647$	−13.1212	−0.515846	−0.257923	+	0.966165i	$0.583038\pi$
$648$	−0.474525	−0.0186411
$649$	3.85453	0.151304
$650$	−2.09731	−0.0822631
$651$	0	0
$652$	−6.93691	−0.271671
$653$	−17.8784	−0.699636	−0.349818	−	0.936818i	$-0.613757\pi$
$653$	−17.8784	−0.699636	−0.349818	+	0.936818i	$0.613757\pi$
$654$	−5.88816	−0.230245
$655$	−35.1669	−1.37408
$656$	−14.3547	−0.560457
$657$	−47.8750	−1.86778
$658$	0	0
$659$	13.2593	0.516507	0.258254	−	0.966077i	$-0.416853\pi$
$659$	13.2593	0.516507	0.258254	+	0.966077i	$0.416853\pi$
$660$	35.0860	1.36572
$661$	46.4942	1.80841	0.904207	−	0.427095i	$-0.140463\pi$
$661$	46.4942	1.80841	0.904207	+	0.427095i	$0.140463\pi$
$662$	−15.3450	−0.596400
$663$	2.44020	0.0947695
$664$	−0.308383	−0.0119676
$665$	0	0
$666$	30.7003	1.18961
$667$	20.2054	0.782358
$668$	−36.2241	−1.40155
$669$	61.8971	2.39308
$670$	45.7614	1.76792
$671$	−20.2585	−0.782072
$672$	0	0
$673$	17.3390	0.668370	0.334185	−	0.942508i	$-0.391539\pi$
$673$	17.3390	0.668370	0.334185	+	0.942508i	$0.391539\pi$
$674$	6.76540	0.260593
$675$	30.5072	1.17422
$676$	−27.0210	−1.03927
$677$	−18.6695	−0.717529	−0.358764	−	0.933428i	$-0.616802\pi$
$677$	−18.6695	−0.717529	−0.358764	+	0.933428i	$0.616802\pi$
$678$	−0.333334	−0.0128016
$679$	0	0
$680$	−4.13611	−0.158612
$681$	−40.4193	−1.54887
$682$	23.9372	0.916604
$683$	0.402900	0.0154166	0.00770828	−	0.999970i	$-0.497546\pi$
$683$	0.402900	0.0154166	0.00770828	+	0.999970i	$0.497546\pi$
$684$	−26.0042	−0.994295
$685$	−18.7534	−0.716530
$686$	0	0
$687$	36.1821	1.38043
$688$	13.1167	0.500070
$689$	0.992732	0.0378201
$690$	150.763	5.73946
$691$	−16.9046	−0.643083	−0.321541	−	0.946896i	$-0.604201\pi$
$691$	−16.9046	−0.643083	−0.321541	+	0.946896i	$0.604201\pi$
$692$	−34.1392	−1.29778
$693$	0	0
$694$	−28.3942	−1.07783
$695$	21.4317	0.812952
$696$	1.18646	0.0449728
$697$	−26.1381	−0.990052
$698$	61.5780	2.33076
$699$	−42.3860	−1.60318
$700$	0	0
$701$	22.1749	0.837535	0.418767	−	0.908094i	$-0.362462\pi$
$701$	22.1749	0.837535	0.418767	+	0.908094i	$0.362462\pi$
$702$	−0.982864	−0.0370958
$703$	−9.84896	−0.371461
$704$	−14.8138	−0.558317
$705$	−31.8137	−1.19817
$706$	40.3008	1.51674
$707$	0	0
$708$	12.7135	0.477801
$709$	34.6461	1.30116	0.650580	−	0.759438i	$-0.274526\pi$
$709$	34.6461	1.30116	0.650580	+	0.759438i	$0.274526\pi$
$710$	101.954	3.82628
$711$	35.2596	1.32234
$712$	−2.91935	−0.109407
$713$	52.4518	1.96434
$714$	0	0
$715$	−0.797920	−0.0298405
$716$	16.8788	0.630791
$717$	56.3001	2.10256
$718$	64.7495	2.41643
$719$	−37.4182	−1.39546	−0.697732	−	0.716359i	$-0.745807\pi$
$719$	−37.4182	−1.39546	−0.697732	+	0.716359i	$0.745807\pi$
$720$	−60.8096	−2.26624
$721$	0	0
$722$	−22.0244	−0.819662
$723$	−49.0962	−1.82591
$724$	−22.6238	−0.840808
$725$	21.4688	0.797332
$726$	−44.2522	−1.64235
$727$	−8.52854	−0.316306	−0.158153	−	0.987415i	$-0.550554\pi$
$727$	−8.52854	−0.316306	−0.158153	+	0.987415i	$0.550554\pi$
$728$	0	0
$729$	−43.5412	−1.61264
$730$	−79.6282	−2.94717
$731$	23.8839	0.883377
$732$	−66.8190	−2.46970
$733$	40.2487	1.48662	0.743310	−	0.668947i	$-0.233255\pi$
$733$	40.2487	1.48662	0.743310	+	0.668947i	$0.233255\pi$
$734$	63.8223	2.35572
$735$	0	0
$736$	−61.2608	−2.25810
$737$	10.7488	0.395938
$738$	33.2367	1.22346
$739$	−16.8878	−0.621229	−0.310614	−	0.950536i	$-0.600535\pi$
$739$	−16.8878	−0.621229	−0.310614	+	0.950536i	$0.600535\pi$
$740$	26.0391	0.957217
$741$	0.995442	0.0365685
$742$	0	0
$743$	24.6759	0.905270	0.452635	−	0.891696i	$-0.350484\pi$
$743$	24.6759	0.905270	0.452635	+	0.891696i	$0.350484\pi$
$744$	3.07997	0.112917
$745$	41.7428	1.52934
$746$	44.7963	1.64011
$747$	−8.25564	−0.302058
$748$	−24.9042	−0.910587
$749$	0	0
$750$	60.9195	2.22447
$751$	23.8276	0.869482	0.434741	−	0.900556i	$-0.356840\pi$
$751$	23.8276	0.869482	0.434741	+	0.900556i	$0.356840\pi$
$752$	12.4015	0.452235
$753$	−53.1888	−1.93831
$754$	−0.691671	−0.0251892
$755$	−8.30820	−0.302366
$756$	0	0
$757$	7.97693	0.289927	0.144963	−	0.989437i	$-0.453694\pi$
$757$	7.97693	0.289927	0.144963	+	0.989437i	$0.453694\pi$
$758$	61.7087	2.24136
$759$	35.4126	1.28539
$760$	−1.68726	−0.0612034
$761$	7.00869	0.254065	0.127032	−	0.991899i	$-0.459455\pi$
$761$	7.00869	0.254065	0.127032	+	0.991899i	$0.459455\pi$
$762$	−5.49211	−0.198958
$763$	0	0
$764$	19.7121	0.713157
$765$	−110.727	−4.00333
$766$	31.9524	1.15449
$767$	−0.289127	−0.0104398
$768$	39.7542	1.43451
$769$	4.84305	0.174645	0.0873224	−	0.996180i	$-0.472169\pi$
$769$	4.84305	0.174645	0.0873224	+	0.996180i	$0.472169\pi$
$770$	0	0
$771$	41.2954	1.48722
$772$	−46.5763	−1.67632
$773$	−11.7074	−0.421088	−0.210544	−	0.977584i	$-0.567523\pi$
$773$	−11.7074	−0.421088	−0.210544	+	0.977584i	$0.567523\pi$
$774$	−30.3702	−1.09164
$775$	55.7314	2.00193
$776$	1.88647	0.0677202
$777$	0	0
$778$	−11.0378	−0.395723
$779$	−10.6626	−0.382029
$780$	−2.63179	−0.0942332
$781$	23.9479	0.856923
$782$	−107.012	−3.82676
$783$	10.0610	0.359550
$784$	0	0
$785$	55.1400	1.96803
$786$	−53.4272	−1.90569
$787$	−8.61915	−0.307240	−0.153620	−	0.988130i	$-0.549093\pi$
$787$	−8.61915	−0.307240	−0.153620	+	0.988130i	$0.549093\pi$
$788$	−16.8486	−0.600207
$789$	22.8645	0.813999
$790$	58.6456	2.08652
$791$	0	0
$792$	1.23537	0.0438969
$793$	1.51959	0.0539621
$794$	42.2528	1.49950
$795$	−75.8238	−2.68919
$796$	−48.8877	−1.73278
$797$	23.2723	0.824348	0.412174	−	0.911105i	$-0.364770\pi$
$797$	23.2723	0.824348	0.412174	+	0.911105i	$0.364770\pi$
$798$	0	0
$799$	22.5815	0.798875
$800$	−65.0912	−2.30132
$801$	−78.1532	−2.76141
$802$	65.3329	2.30698
$803$	−18.7037	−0.660041
$804$	35.4530	1.25033
$805$	0	0
$806$	−1.79553	−0.0632447
$807$	−82.2343	−2.89478
$808$	2.41356	0.0849086
$809$	12.1938	0.428711	0.214356	−	0.976756i	$-0.431235\pi$
$809$	12.1938	0.428711	0.214356	+	0.976756i	$0.431235\pi$
$810$	−21.1289	−0.742395
$811$	3.35628	0.117855	0.0589275	−	0.998262i	$-0.481232\pi$
$811$	3.35628	0.117855	0.0589275	+	0.998262i	$0.481232\pi$
$812$	0	0
$813$	−80.8961	−2.83715
$814$	11.9940	0.420389
$815$	−12.0494	−0.422072
$816$	72.6537	2.54339
$817$	9.74306	0.340867
$818$	8.52155	0.297949
$819$	0	0
$820$	28.1904	0.984450
$821$	18.9649	0.661881	0.330941	−	0.943652i	$-0.392634\pi$
$821$	18.9649	0.661881	0.330941	+	0.943652i	$0.392634\pi$
$822$	−28.4911	−0.993740
$823$	−43.1458	−1.50397	−0.751983	−	0.659182i	$-0.770903\pi$
$823$	−43.1458	−1.50397	−0.751983	+	0.659182i	$0.770903\pi$
$824$	−1.04040	−0.0362440
$825$	37.6268	1.31000
$826$	0	0
$827$	6.35206	0.220883	0.110441	−	0.993883i	$-0.464774\pi$
$827$	6.35206	0.220883	0.110441	+	0.993883i	$0.464774\pi$
$828$	69.3909	2.41150
$829$	30.1984	1.04883	0.524417	−	0.851462i	$-0.324283\pi$
$829$	30.1984	1.04883	0.524417	+	0.851462i	$0.324283\pi$
$830$	−13.7312	−0.476617
$831$	−29.8799	−1.03652
$832$	1.11118	0.0385233
$833$	0	0
$834$	32.5602	1.12747
$835$	−62.9212	−2.17748
$836$	−10.1593	−0.351366
$837$	26.1175	0.902753
$838$	49.1140	1.69662
$839$	−14.3431	−0.495178	−0.247589	−	0.968865i	$-0.579638\pi$
$839$	−14.3431	−0.495178	−0.247589	+	0.968865i	$0.579638\pi$
$840$	0	0
$841$	−21.9198	−0.755855
$842$	−55.6291	−1.91711
$843$	−17.6683	−0.608530
$844$	−46.0185	−1.58402
$845$	−46.9354	−1.61463
$846$	−28.7141	−0.987212
$847$	0	0
$848$	29.5573	1.01500
$849$	−21.7955	−0.748019
$850$	−113.704	−3.90000
$851$	26.2815	0.900918
$852$	78.9876	2.70607
$853$	−14.8706	−0.509160	−0.254580	−	0.967052i	$-0.581937\pi$
$853$	−14.8706	−0.509160	−0.254580	+	0.967052i	$0.581937\pi$
$854$	0	0
$855$	−45.1692	−1.54475
$856$	−1.42979	−0.0488694
$857$	−2.03231	−0.0694223	−0.0347111	−	0.999397i	$-0.511051\pi$
$857$	−2.03231	−0.0694223	−0.0347111	+	0.999397i	$0.511051\pi$
$858$	−1.21224	−0.0413852
$859$	−40.7276	−1.38961	−0.694803	−	0.719200i	$-0.744509\pi$
$859$	−40.7276	−1.38961	−0.694803	+	0.719200i	$0.744509\pi$
$860$	−25.7591	−0.878379
$861$	0	0
$862$	15.9847	0.544441
$863$	−2.68462	−0.0913854	−0.0456927	−	0.998956i	$-0.514550\pi$
$863$	−2.68462	−0.0913854	−0.0456927	+	0.998956i	$0.514550\pi$
$864$	−30.5038	−1.03776
$865$	−59.2997	−2.01625
$866$	−5.24927	−0.178377
$867$	86.0769	2.92332
$868$	0	0
$869$	13.7752	0.467291
$870$	52.8291	1.79107
$871$	−0.806266	−0.0273193
$872$	−0.175843	−0.00595480
$873$	50.5020	1.70924
$874$	−43.6541	−1.47662
$875$	0	0
$876$	−61.6908	−2.08434
$877$	43.2007	1.45878	0.729392	−	0.684096i	$-0.239803\pi$
$877$	43.2007	1.45878	0.729392	+	0.684096i	$0.239803\pi$
$878$	72.0852	2.43276
$879$	45.3544	1.52976
$880$	−23.7570	−0.800849
$881$	19.7471	0.665298	0.332649	−	0.943051i	$-0.392058\pi$
$881$	19.7471	0.665298	0.332649	+	0.943051i	$0.392058\pi$
$882$	0	0
$883$	14.7255	0.495554	0.247777	−	0.968817i	$-0.420300\pi$
$883$	14.7255	0.495554	0.247777	+	0.968817i	$0.420300\pi$
$884$	1.86806	0.0628296
$885$	22.0832	0.742320
$886$	−11.9967	−0.403038
$887$	24.4301	0.820281	0.410140	−	0.912022i	$-0.365480\pi$
$887$	24.4301	0.820281	0.410140	+	0.912022i	$0.365480\pi$
$888$	1.54325	0.0517880
$889$	0	0
$890$	−129.989	−4.35723
$891$	−4.96294	−0.166265
$892$	47.3844	1.58655
$893$	9.21177	0.308260
$894$	63.4177	2.12100
$895$	29.3185	0.980008
$896$	0	0
$897$	−2.65629	−0.0886909
$898$	−83.3334	−2.78087
$899$	18.3797	0.612996
$900$	73.7296	2.45765
$901$	53.8201	1.79301
$902$	12.9849	0.432349
$903$	0	0
$904$	−0.00995465	−0.000331087 0
$905$	−39.2975	−1.30629
$906$	−12.6222	−0.419345
$907$	18.8141	0.624713	0.312357	−	0.949965i	$-0.398882\pi$
$907$	18.8141	0.624713	0.312357	+	0.949965i	$0.398882\pi$
$908$	−30.9424	−1.02686
$909$	64.6126	2.14307
$910$	0	0
$911$	−16.9197	−0.560573	−0.280287	−	0.959916i	$-0.590430\pi$
$911$	−16.9197	−0.560573	−0.280287	+	0.959916i	$0.590430\pi$
$912$	29.6380	0.981411
$913$	−3.22530	−0.106742
$914$	−60.8210	−2.01178
$915$	−116.064	−3.83697
$916$	27.6986	0.915189
$917$	0	0
$918$	−53.2851	−1.75867
$919$	24.6905	0.814465	0.407232	−	0.913325i	$-0.366494\pi$
$919$	24.6905	0.814465	0.407232	+	0.913325i	$0.366494\pi$
$920$	4.50237	0.148439
$921$	65.7878	2.16778
$922$	−67.2400	−2.21443
$923$	−1.79632	−0.0591268
$924$	0	0
$925$	27.9248	0.918161
$926$	37.9248	1.24629
$927$	−27.8522	−0.914787
$928$	−21.4664	−0.704670
$929$	23.2303	0.762163	0.381081	−	0.924541i	$-0.375552\pi$
$929$	23.2303	0.762163	0.381081	+	0.924541i	$0.375552\pi$
$930$	137.140	4.49701
$931$	0	0
$932$	−32.4479	−1.06287
$933$	−33.2646	−1.08903
$934$	49.3044	1.61329
$935$	−43.2585	−1.41470
$936$	−0.0926647	−0.00302884
$937$	21.0118	0.686426	0.343213	−	0.939258i	$-0.388485\pi$
$937$	21.0118	0.686426	0.343213	+	0.939258i	$0.388485\pi$
$938$	0	0
$939$	16.1635	0.527477
$940$	−24.3545	−0.794355
$941$	−10.1636	−0.331325	−0.165662	−	0.986183i	$-0.552976\pi$
$941$	−10.1636	−0.331325	−0.165662	+	0.986183i	$0.552976\pi$
$942$	83.7714	2.72942
$943$	28.4528	0.926549
$944$	−8.60839	−0.280179
$945$	0	0
$946$	−11.8650	−0.385765
$947$	−15.0463	−0.488938	−0.244469	−	0.969657i	$-0.578614\pi$
$947$	−15.0463	−0.488938	−0.244469	+	0.969657i	$0.578614\pi$
$948$	45.4349	1.47566
$949$	1.40296	0.0455421
$950$	−46.3836	−1.50488
$951$	44.6327	1.44732
$952$	0	0
$953$	−8.04449	−0.260586	−0.130293	−	0.991476i	$-0.541592\pi$
$953$	−8.04449	−0.260586	−0.130293	+	0.991476i	$0.541592\pi$
$954$	−68.4364	−2.21571
$955$	34.2398	1.10797
$956$	43.0997	1.39394
$957$	12.4089	0.401124
$958$	34.4106	1.11176
$959$	0	0
$960$	−84.8709	−2.73920
$961$	16.7122	0.539104
$962$	−0.899665	−0.0290064
$963$	−38.2766	−1.23345
$964$	−37.5849	−1.21053
$965$	−80.9029	−2.60436
$966$	0	0
$967$	26.6596	0.857316	0.428658	−	0.903467i	$-0.358987\pi$
$967$	26.6596	0.857316	0.428658	+	0.903467i	$0.358987\pi$
$968$	−1.32154	−0.0424759
$969$	53.9670	1.73367
$970$	83.9977	2.69700
$971$	−9.74863	−0.312848	−0.156424	−	0.987690i	$-0.549997\pi$
$971$	−9.74863	−0.312848	−0.156424	+	0.987690i	$0.549997\pi$
$972$	−39.9768	−1.28226
$973$	0	0
$974$	80.0694	2.56559
$975$	−2.82238	−0.0903884
$976$	45.2437	1.44822
$977$	−37.6924	−1.20589	−0.602943	−	0.797784i	$-0.706005\pi$
$977$	−37.6924	−1.20589	−0.602943	+	0.797784i	$0.706005\pi$
$978$	−18.3060	−0.585363
$979$	−30.5328	−0.975833
$980$	0	0
$981$	−4.70745	−0.150297
$982$	9.44414	0.301375
$983$	54.1582	1.72738	0.863690	−	0.504024i	$-0.168148\pi$
$983$	54.1582	1.72738	0.863690	+	0.504024i	$0.168148\pi$
$984$	1.67075	0.0532614
$985$	−29.2660	−0.932493
$986$	−37.4983	−1.19419
$987$	0	0
$988$	0.762046	0.0242439
$989$	−25.9989	−0.826717
$990$	55.0066	1.74822
$991$	−32.7359	−1.03989	−0.519945	−	0.854200i	$-0.674048\pi$
$991$	−32.7359	−1.03989	−0.519945	+	0.854200i	$0.674048\pi$
$992$	−55.7252	−1.76928
$993$	−20.6500	−0.655307
$994$	0	0
$995$	−84.9178	−2.69208
$996$	−10.6381	−0.337080
$997$	10.5223	0.333246	0.166623	−	0.986021i	$-0.446714\pi$
$997$	10.5223	0.333246	0.166623	+	0.986021i	$0.446714\pi$
$998$	−62.3935	−1.97503
$999$	13.0864	0.414036

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6223.2.a.l.1.15		20
7.6	odd	2		889.2.a.d.1.15	✓	20
21.20	even	2		8001.2.a.w.1.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
889.2.a.d.1.15	✓	20	7.6	odd	2
6223.2.a.l.1.15		20	1.1	even	1	trivial
8001.2.a.w.1.6		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)

\(f(q)\)	\(=\)	\(q+2.02020 q^{2} +2.71861 q^{3} +2.08119 q^{4} +3.61502 q^{5} +5.49211 q^{6} +0.164016 q^{8} +4.39082 q^{9} +O(q^{10})\)	\(q+2.02020 q^{2} +2.71861 q^{3} +2.08119 q^{4} +3.61502 q^{5} +5.49211 q^{6} +0.164016 q^{8} +4.39082 q^{9} +7.30304 q^{10} +1.71540 q^{11} +5.65793 q^{12} -0.128672 q^{13} +9.82781 q^{15} -3.83103 q^{16} -6.97582 q^{17} +8.87031 q^{18} -2.84568 q^{19} +7.52353 q^{20} +3.46544 q^{22} +7.59356 q^{23} +0.445894 q^{24} +8.06836 q^{25} -0.259942 q^{26} +3.78109 q^{27} +2.66087 q^{29} +19.8541 q^{30} +6.90740 q^{31} -8.06746 q^{32} +4.66350 q^{33} -14.0925 q^{34} +9.13812 q^{36} +3.46102 q^{37} -5.74883 q^{38} -0.349808 q^{39} +0.592920 q^{40} +3.74696 q^{41} -3.42381 q^{43} +3.57007 q^{44} +15.8729 q^{45} +15.3405 q^{46} -3.23711 q^{47} -10.4151 q^{48} +16.2997 q^{50} -18.9645 q^{51} -0.267790 q^{52} -7.71522 q^{53} +7.63853 q^{54} +6.20120 q^{55} -7.73629 q^{57} +5.37547 q^{58} +2.24701 q^{59} +20.4535 q^{60} -11.8098 q^{61} +13.9543 q^{62} -8.63579 q^{64} -0.465151 q^{65} +9.42118 q^{66} +6.26607 q^{67} -14.5180 q^{68} +20.6439 q^{69} +13.9605 q^{71} +0.720163 q^{72} -10.9034 q^{73} +6.99194 q^{74} +21.9347 q^{75} -5.92240 q^{76} -0.706680 q^{78} +8.03030 q^{79} -13.8493 q^{80} -2.89317 q^{81} +7.56958 q^{82} -1.88020 q^{83} -25.2177 q^{85} -6.91676 q^{86} +7.23384 q^{87} +0.281353 q^{88} -17.7992 q^{89} +32.0663 q^{90} +15.8036 q^{92} +18.7785 q^{93} -6.53959 q^{94} -10.2872 q^{95} -21.9323 q^{96} +11.5017 q^{97} +7.53201 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 8 q^{2} + 24 q^{4} - 3 q^{5} - 6 q^{6} + 24 q^{8} + 30 q^{9}+O(q^{10}) \) 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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