LMFDB - Embedded newform 6223.2.a.r.1.11

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:	$40$
Twist minimal:	no (minimal twist has level 889)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-1.73616 q^{2} +2.58223 q^{3} +1.01424 q^{4} -1.04688 q^{5} -4.48316 q^{6} +1.71143 q^{8} +3.66791 q^{9} +O(q^{10})$	\(q-1.73616 q^{2} +2.58223 q^{3} +1.01424 q^{4} -1.04688 q^{5} -4.48316 q^{6} +1.71143 q^{8} +3.66791 q^{9} +1.81755 q^{10} -0.881511 q^{11} +2.61900 q^{12} +1.98510 q^{13} -2.70329 q^{15} -4.99980 q^{16} -4.10832 q^{17} -6.36807 q^{18} +3.13815 q^{19} -1.06179 q^{20} +1.53044 q^{22} +8.65636 q^{23} +4.41931 q^{24} -3.90404 q^{25} -3.44645 q^{26} +1.72470 q^{27} +4.60277 q^{29} +4.69334 q^{30} +2.88140 q^{31} +5.25757 q^{32} -2.27626 q^{33} +7.13268 q^{34} +3.72014 q^{36} +2.48630 q^{37} -5.44832 q^{38} +5.12598 q^{39} -1.79167 q^{40} +0.398758 q^{41} -4.28434 q^{43} -0.894064 q^{44} -3.83987 q^{45} -15.0288 q^{46} +10.0466 q^{47} -12.9106 q^{48} +6.77802 q^{50} -10.6086 q^{51} +2.01337 q^{52} -10.9916 q^{53} -2.99434 q^{54} +0.922838 q^{55} +8.10342 q^{57} -7.99113 q^{58} -12.0028 q^{59} -2.74179 q^{60} +8.62464 q^{61} -5.00256 q^{62} +0.871632 q^{64} -2.07817 q^{65} +3.95195 q^{66} +2.59127 q^{67} -4.16682 q^{68} +22.3527 q^{69} +11.4224 q^{71} +6.27738 q^{72} -4.55265 q^{73} -4.31661 q^{74} -10.0811 q^{75} +3.18284 q^{76} -8.89951 q^{78} -10.2861 q^{79} +5.23420 q^{80} -6.55017 q^{81} -0.692306 q^{82} -9.46370 q^{83} +4.30093 q^{85} +7.43829 q^{86} +11.8854 q^{87} -1.50865 q^{88} +4.36603 q^{89} +6.66662 q^{90} +8.77963 q^{92} +7.44043 q^{93} -17.4425 q^{94} -3.28527 q^{95} +13.5762 q^{96} +16.1469 q^{97} -3.23330 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 3 q^{2} + 6 q^{3} + 39 q^{4} + 24 q^{5} - 9 q^{8} + 42 q^{9}+O(q^{10}) $ 40 * q - 3 * q^2 + 6 * q^3 + 39 * q^4 + 24 * q^5 - 9 * q^8 + 42 * q^9	$ 40 q - 3 q^{2} + 6 q^{3} + 39 q^{4} + 24 q^{5} - 9 q^{8} + 42 q^{9} + 15 q^{10} + 4 q^{11} + 29 q^{12} + 7 q^{13} + 8 q^{15} + 29 q^{16} + 56 q^{17} - 12 q^{18} + 6 q^{19} + 45 q^{20} + 3 q^{22} - 7 q^{23} + 2 q^{24} + 48 q^{25} + 32 q^{26} + 54 q^{27} - 14 q^{29} + 2 q^{30} - 2 q^{31} - 31 q^{32} + 70 q^{33} - 5 q^{34} + 67 q^{36} + 45 q^{38} - 15 q^{39} + 15 q^{40} + 38 q^{41} + 27 q^{43} - 24 q^{44} + 66 q^{45} - 24 q^{46} + 69 q^{47} + 34 q^{48} + 26 q^{50} - 26 q^{51} + 41 q^{52} - 8 q^{53} + 8 q^{54} + 24 q^{55} + 12 q^{57} - 21 q^{58} + 45 q^{59} - 10 q^{60} - 5 q^{61} + 27 q^{62} + 65 q^{64} + q^{65} + 52 q^{66} + 11 q^{67} + 78 q^{68} + 47 q^{69} + 15 q^{71} - 95 q^{72} + 64 q^{73} - 23 q^{74} + 4 q^{75} - 31 q^{76} + 76 q^{78} - 12 q^{79} + 110 q^{80} + 72 q^{81} - 38 q^{82} + 103 q^{83} + 30 q^{85} - 45 q^{86} + 17 q^{87} + 2 q^{88} + 78 q^{89} + 75 q^{90} - 51 q^{92} - 85 q^{93} + 48 q^{94} - 15 q^{95} - 128 q^{96} + 65 q^{97} + 65 q^{99}+O(q^{100}) $ 40 * q - 3 * q^2 + 6 * q^3 + 39 * q^4 + 24 * q^5 - 9 * q^8 + 42 * q^9 + 15 * q^10 + 4 * q^11 + 29 * q^12 + 7 * q^13 + 8 * q^15 + 29 * q^16 + 56 * q^17 - 12 * q^18 + 6 * q^19 + 45 * q^20 + 3 * q^22 - 7 * q^23 + 2 * q^24 + 48 * q^25 + 32 * q^26 + 54 * q^27 - 14 * q^29 + 2 * q^30 - 2 * q^31 - 31 * q^32 + 70 * q^33 - 5 * q^34 + 67 * q^36 + 45 * q^38 - 15 * q^39 + 15 * q^40 + 38 * q^41 + 27 * q^43 - 24 * q^44 + 66 * q^45 - 24 * q^46 + 69 * q^47 + 34 * q^48 + 26 * q^50 - 26 * q^51 + 41 * q^52 - 8 * q^53 + 8 * q^54 + 24 * q^55 + 12 * q^57 - 21 * q^58 + 45 * q^59 - 10 * q^60 - 5 * q^61 + 27 * q^62 + 65 * q^64 + q^65 + 52 * q^66 + 11 * q^67 + 78 * q^68 + 47 * q^69 + 15 * q^71 - 95 * q^72 + 64 * q^73 - 23 * q^74 + 4 * q^75 - 31 * q^76 + 76 * q^78 - 12 * q^79 + 110 * q^80 + 72 * q^81 - 38 * q^82 + 103 * q^83 + 30 * q^85 - 45 * q^86 + 17 * q^87 + 2 * q^88 + 78 * q^89 + 75 * q^90 - 51 * q^92 - 85 * q^93 + 48 * q^94 - 15 * q^95 - 128 * q^96 + 65 * q^97 + 65 * 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 $

$2$	−1.73616	−1.22765	−0.613824	−	0.789443i	$-0.710370\pi$
$2$	−1.73616	−1.22765	−0.613824	+	0.789443i	$0.710370\pi$
$3$	2.58223	1.49085	0.745425	−	0.666589i	$-0.232246\pi$
$3$	2.58223	1.49085	0.745425	+	0.666589i	$0.232246\pi$
$4$	1.01424	0.507120
$5$	−1.04688	−0.468180	−0.234090	−	0.972215i	$-0.575211\pi$
$5$	−1.04688	−0.468180	−0.234090	+	0.972215i	$0.575211\pi$
$6$	−4.48316	−1.83024
$7$	0	0
$7$	0	0
$8$	1.71143	0.605083
$9$	3.66791	1.22264
$10$	1.81755	0.574761
$11$	−0.881511	−0.265785	−0.132893	−	0.991130i	$-0.542427\pi$
$11$	−0.881511	−0.265785	−0.132893	+	0.991130i	$0.542427\pi$
$12$	2.61900	0.756041
$13$	1.98510	0.550568	0.275284	−	0.961363i	$-0.411228\pi$
$13$	1.98510	0.550568	0.275284	+	0.961363i	$0.411228\pi$
$14$	0	0
$15$	−2.70329	−0.697987
$16$	−4.99980	−1.24995
$17$	−4.10832	−0.996413	−0.498206	−	0.867058i	$-0.666008\pi$
$17$	−4.10832	−0.996413	−0.498206	+	0.867058i	$0.666008\pi$
$18$	−6.36807	−1.50097
$19$	3.13815	0.719940	0.359970	−	0.932964i	$-0.382787\pi$
$19$	3.13815	0.719940	0.359970	+	0.932964i	$0.382787\pi$
$20$	−1.06179	−0.237424
$21$	0	0
$22$	1.53044	0.326291
$23$	8.65636	1.80498	0.902488	−	0.430715i	$-0.141739\pi$
$23$	8.65636	1.80498	0.902488	+	0.430715i	$0.141739\pi$
$24$	4.41931	0.902088
$25$	−3.90404	−0.780807
$26$	−3.44645	−0.675904
$27$	1.72470	0.331918
$28$	0	0
$29$	4.60277	0.854713	0.427356	−	0.904083i	$-0.359445\pi$
$29$	4.60277	0.854713	0.427356	+	0.904083i	$0.359445\pi$
$30$	4.69334	0.856883
$31$	2.88140	0.517514	0.258757	−	0.965942i	$-0.416687\pi$
$31$	2.88140	0.517514	0.258757	+	0.965942i	$0.416687\pi$
$32$	5.25757	0.929415
$33$	−2.27626	−0.396246
$34$	7.13268	1.22324
$35$	0	0
$36$	3.72014	0.620024
$37$	2.48630	0.408746	0.204373	−	0.978893i	$-0.434485\pi$
$37$	2.48630	0.408746	0.204373	+	0.978893i	$0.434485\pi$
$38$	−5.44832	−0.883833
$39$	5.12598	0.820814
$40$	−1.79167	−0.283288
$41$	0.398758	0.0622755	0.0311377	−	0.999515i	$-0.490087\pi$
$41$	0.398758	0.0622755	0.0311377	+	0.999515i	$0.490087\pi$
$42$	0	0
$43$	−4.28434	−0.653356	−0.326678	−	0.945136i	$-0.605929\pi$
$43$	−4.28434	−0.653356	−0.326678	+	0.945136i	$0.605929\pi$
$44$	−0.894064	−0.134785
$45$	−3.83987	−0.572414
$46$	−15.0288	−2.21588
$47$	10.0466	1.46545	0.732724	−	0.680525i	$-0.238248\pi$
$47$	10.0466	1.46545	0.732724	+	0.680525i	$0.238248\pi$
$48$	−12.9106	−1.86349
$49$	0	0
$50$	6.77802	0.958557
$51$	−10.6086	−1.48550
$52$	2.01337	0.279204
$53$	−10.9916	−1.50982	−0.754909	−	0.655829i	$-0.772319\pi$
$53$	−10.9916	−1.50982	−0.754909	+	0.655829i	$0.772319\pi$
$54$	−2.99434	−0.407479
$55$	0.922838	0.124436
$56$	0	0
$57$	8.10342	1.07332
$58$	−7.99113	−1.04929
$59$	−12.0028	−1.56263	−0.781315	−	0.624137i	$-0.785451\pi$
$59$	−12.0028	−1.56263	−0.781315	+	0.624137i	$0.785451\pi$
$60$	−2.74179	−0.353963
$61$	8.62464	1.10427	0.552136	−	0.833754i	$-0.313813\pi$
$61$	8.62464	1.10427	0.552136	+	0.833754i	$0.313813\pi$
$62$	−5.00256	−0.635325
$63$	0	0
$64$	0.871632	0.108954
$65$	−2.07817	−0.257765
$66$	3.95195	0.486451
$67$	2.59127	0.316574	0.158287	−	0.987393i	$-0.449403\pi$
$67$	2.59127	0.316574	0.158287	+	0.987393i	$0.449403\pi$
$68$	−4.16682	−0.505301
$69$	22.3527	2.69095
$70$	0	0
$71$	11.4224	1.35559	0.677794	−	0.735252i	$-0.262936\pi$
$71$	11.4224	1.35559	0.677794	+	0.735252i	$0.262936\pi$
$72$	6.27738	0.739796
$73$	−4.55265	−0.532847	−0.266424	−	0.963856i	$-0.585842\pi$
$73$	−4.55265	−0.532847	−0.266424	+	0.963856i	$0.585842\pi$
$74$	−4.31661	−0.501796
$75$	−10.0811	−1.16407
$76$	3.18284	0.365096
$77$	0	0
$78$	−8.89951	−1.00767
$79$	−10.2861	−1.15728	−0.578638	−	0.815584i	$-0.696416\pi$
$79$	−10.2861	−1.15728	−0.578638	+	0.815584i	$0.696416\pi$
$80$	5.23420	0.585202
$81$	−6.55017	−0.727796
$82$	−0.692306	−0.0764524
$83$	−9.46370	−1.03878	−0.519388	−	0.854538i	$-0.673840\pi$
$83$	−9.46370	−1.03878	−0.519388	+	0.854538i	$0.673840\pi$
$84$	0	0
$85$	4.30093	0.466501
$86$	7.43829	0.802092
$87$	11.8854	1.27425
$88$	−1.50865	−0.160822
$89$	4.36603	0.462798	0.231399	−	0.972859i	$-0.425670\pi$
$89$	4.36603	0.462798	0.231399	+	0.972859i	$0.425670\pi$
$90$	6.66662	0.702724
$91$	0	0
$92$	8.77963	0.915340
$93$	7.44043	0.771536
$94$	−17.4425	−1.79906
$95$	−3.28527	−0.337062
$96$	13.5762	1.38562
$97$	16.1469	1.63947	0.819737	−	0.572740i	$-0.194120\pi$
$97$	16.1469	1.63947	0.819737	+	0.572740i	$0.194120\pi$
$98$	0	0
$99$	−3.23330	−0.324959
$100$	−3.95963	−0.395963
$101$	9.10526	0.906007	0.453003	−	0.891509i	$-0.350353\pi$
$101$	9.10526	0.906007	0.453003	+	0.891509i	$0.350353\pi$
$102$	18.4182	1.82368
$103$	15.7829	1.55514	0.777569	−	0.628797i	$-0.216453\pi$
$103$	15.7829	1.55514	0.777569	+	0.628797i	$0.216453\pi$
$104$	3.39737	0.333139
$105$	0	0
$106$	19.0832	1.85353
$107$	10.3274	0.998384	0.499192	−	0.866491i	$-0.333630\pi$
$107$	10.3274	0.998384	0.499192	+	0.866491i	$0.333630\pi$
$108$	1.74926	0.168322
$109$	−4.40004	−0.421447	−0.210723	−	0.977546i	$-0.567582\pi$
$109$	−4.40004	−0.421447	−0.210723	+	0.977546i	$0.567582\pi$
$110$	−1.60219	−0.152763
$111$	6.42020	0.609379
$112$	0	0
$113$	7.57453	0.712552	0.356276	−	0.934381i	$-0.384046\pi$
$113$	7.57453	0.712552	0.356276	+	0.934381i	$0.384046\pi$
$114$	−14.0688	−1.31766
$115$	−9.06220	−0.845054
$116$	4.66832	0.433442
$117$	7.28117	0.673144
$118$	20.8387	1.91836
$119$	0	0
$120$	−4.62650	−0.422340
$121$	−10.2229	−0.929358
$122$	−14.9737	−1.35566
$123$	1.02968	0.0928434
$124$	2.92243	0.262442
$125$	9.32148	0.833739
$126$	0	0
$127$	−1.00000	−0.0887357
$127$	−1.00000	−0.0887357
$128$	−12.0284	−1.06317
$129$	−11.0632	−0.974057
$130$	3.60803	0.316445
$131$	3.72095	0.325101	0.162550	−	0.986700i	$-0.448028\pi$
$131$	3.72095	0.325101	0.162550	+	0.986700i	$0.448028\pi$
$132$	−2.30868	−0.200945
$133$	0	0
$134$	−4.49885	−0.388642
$135$	−1.80556	−0.155397
$136$	−7.03111	−0.602912
$137$	3.51102	0.299967	0.149983	−	0.988689i	$-0.452078\pi$
$137$	3.51102	0.299967	0.149983	+	0.988689i	$0.452078\pi$
$138$	−38.8078	−3.30354
$139$	−9.89452	−0.839242	−0.419621	−	0.907699i	$-0.637837\pi$
$139$	−9.89452	−0.839242	−0.419621	+	0.907699i	$0.637837\pi$
$140$	0	0
$141$	25.9427	2.18477
$142$	−19.8310	−1.66418
$143$	−1.74989	−0.146333
$144$	−18.3388	−1.52823
$145$	−4.81856	−0.400160
$146$	7.90411	0.654149
$147$	0	0
$148$	2.52171	0.207283
$149$	1.79314	0.146900	0.0734501	−	0.997299i	$-0.476599\pi$
$149$	1.79314	0.146900	0.0734501	+	0.997299i	$0.476599\pi$
$150$	17.5024	1.42907
$151$	21.8835	1.78085	0.890426	−	0.455128i	$-0.150406\pi$
$151$	21.8835	1.78085	0.890426	+	0.455128i	$0.150406\pi$
$152$	5.37073	0.435623
$153$	−15.0689	−1.21825
$154$	0	0
$155$	−3.01649	−0.242290
$156$	5.19898	0.416252
$157$	−3.83983	−0.306452	−0.153226	−	0.988191i	$-0.548966\pi$
$157$	−3.83983	−0.306452	−0.153226	+	0.988191i	$0.548966\pi$
$158$	17.8583	1.42073
$159$	−28.3829	−2.25091
$160$	−5.50406	−0.435134
$161$	0	0
$162$	11.3721	0.893478
$163$	9.32553	0.730432	0.365216	−	0.930923i	$-0.380995\pi$
$163$	9.32553	0.730432	0.365216	+	0.930923i	$0.380995\pi$
$164$	0.404436	0.0315812
$165$	2.38298	0.185515
$166$	16.4305	1.27525
$167$	−6.51625	−0.504243	−0.252121	−	0.967696i	$-0.581128\pi$
$167$	−6.51625	−0.504243	−0.252121	+	0.967696i	$0.581128\pi$
$168$	0	0
$169$	−9.05938	−0.696875
$170$	−7.46708	−0.572699
$171$	11.5104	0.880225
$172$	−4.34536	−0.331330
$173$	−2.95213	−0.224446	−0.112223	−	0.993683i	$-0.535797\pi$
$173$	−2.95213	−0.224446	−0.112223	+	0.993683i	$0.535797\pi$
$174$	−20.6349	−1.56433
$175$	0	0
$176$	4.40737	0.332218
$177$	−30.9940	−2.32965
$178$	−7.58010	−0.568153
$179$	18.4806	1.38130	0.690652	−	0.723187i	$-0.257324\pi$
$179$	18.4806	1.38130	0.690652	+	0.723187i	$0.257324\pi$
$180$	−3.89456	−0.290283
$181$	−16.1506	−1.20046	−0.600232	−	0.799826i	$-0.704925\pi$
$181$	−16.1506	−1.20046	−0.600232	+	0.799826i	$0.704925\pi$
$182$	0	0
$183$	22.2708	1.64631
$184$	14.8148	1.09216
$185$	−2.60287	−0.191367
$186$	−12.9178	−0.947175
$187$	3.62152	0.264832
$188$	10.1897	0.743159
$189$	0	0
$190$	5.70375	0.413793
$191$	21.7672	1.57502	0.787509	−	0.616303i	$-0.211370\pi$
$191$	21.7672	1.57502	0.787509	+	0.616303i	$0.211370\pi$
$192$	2.25076	0.162434
$193$	−1.58370	−0.113998	−0.0569988	−	0.998374i	$-0.518153\pi$
$193$	−1.58370	−0.113998	−0.0569988	+	0.998374i	$0.518153\pi$
$194$	−28.0336	−2.01270
$195$	−5.36631	−0.384289
$196$	0	0
$197$	−12.9381	−0.921799	−0.460899	−	0.887452i	$-0.652473\pi$
$197$	−12.9381	−0.921799	−0.460899	+	0.887452i	$0.652473\pi$
$198$	5.61352	0.398935
$199$	−6.90181	−0.489256	−0.244628	−	0.969617i	$-0.578666\pi$
$199$	−6.90181	−0.489256	−0.244628	+	0.969617i	$0.578666\pi$
$200$	−6.68149	−0.472453
$201$	6.69126	0.471965
$202$	−15.8082	−1.11226
$203$	0	0
$204$	−10.7597	−0.753329
$205$	−0.417452	−0.0291561
$206$	−27.4016	−1.90916
$207$	31.7507	2.20683
$208$	−9.92510	−0.688182
$209$	−2.76631	−0.191350
$210$	0	0
$211$	8.59483	0.591693	0.295846	−	0.955236i	$-0.404398\pi$
$211$	8.59483	0.591693	0.295846	+	0.955236i	$0.404398\pi$
$212$	−11.1482	−0.765660
$213$	29.4952	2.02098
$214$	−17.9299	−1.22566
$215$	4.48521	0.305889
$216$	2.95170	0.200838
$217$	0	0
$218$	7.63915	0.517389
$219$	−11.7560	−0.794396
$220$	0.935980	0.0631038
$221$	−8.15542	−0.548593
$222$	−11.1465	−0.748103
$223$	2.48271	0.166255	0.0831274	−	0.996539i	$-0.473509\pi$
$223$	2.48271	0.166255	0.0831274	+	0.996539i	$0.473509\pi$
$224$	0	0
$225$	−14.3197	−0.954643
$226$	−13.1506	−0.874763
$227$	4.12948	0.274083	0.137042	−	0.990565i	$-0.456241\pi$
$227$	4.12948	0.274083	0.137042	+	0.990565i	$0.456241\pi$
$228$	8.21882	0.544304
$229$	−30.0618	−1.98654	−0.993271	−	0.115814i	$-0.963052\pi$
$229$	−30.0618	−1.98654	−0.993271	+	0.115814i	$0.963052\pi$
$230$	15.7334	1.03743
$231$	0	0
$232$	7.87733	0.517172
$233$	19.9386	1.30622	0.653110	−	0.757263i	$-0.273464\pi$
$233$	19.9386	1.30622	0.653110	+	0.757263i	$0.273464\pi$
$234$	−12.6413	−0.826384
$235$	−10.5176	−0.686094
$236$	−12.1737	−0.792441
$237$	−26.5611	−1.72533
$238$	0	0
$239$	5.70655	0.369126	0.184563	−	0.982821i	$-0.440913\pi$
$239$	5.70655	0.369126	0.184563	+	0.982821i	$0.440913\pi$
$240$	13.5159	0.872448
$241$	20.5773	1.32550	0.662750	−	0.748841i	$-0.269389\pi$
$241$	20.5773	1.32550	0.662750	+	0.748841i	$0.269389\pi$
$242$	17.7486	1.14092
$243$	−22.0881	−1.41695
$244$	8.74746	0.559999
$245$	0	0
$246$	−1.78769	−0.113979
$247$	6.22954	0.396376
$248$	4.93132	0.313139
$249$	−24.4375	−1.54866
$250$	−16.1836	−1.02354
$251$	24.9818	1.57684	0.788418	−	0.615140i	$-0.210900\pi$
$251$	24.9818	1.57684	0.788418	+	0.615140i	$0.210900\pi$
$252$	0	0
$253$	−7.63067	−0.479736
$254$	1.73616	0.108936
$255$	11.1060	0.695483
$256$	19.1400	1.19625
$257$	−1.17374	−0.0732157	−0.0366078	−	0.999330i	$-0.511655\pi$
$257$	−1.17374	−0.0732157	−0.0366078	+	0.999330i	$0.511655\pi$
$258$	19.2074	1.19580
$259$	0	0
$260$	−2.10776	−0.130718
$261$	16.8825	1.04500
$262$	−6.46015	−0.399110
$263$	−2.83494	−0.174810	−0.0874050	−	0.996173i	$-0.527857\pi$
$263$	−2.83494	−0.174810	−0.0874050	+	0.996173i	$0.527857\pi$
$264$	−3.89567	−0.239762
$265$	11.5070	0.706867
$266$	0	0
$267$	11.2741	0.689962
$268$	2.62817	0.160541
$269$	11.3321	0.690928	0.345464	−	0.938432i	$-0.387722\pi$
$269$	11.3321	0.690928	0.345464	+	0.938432i	$0.387722\pi$
$270$	3.13473	0.190773
$271$	14.7715	0.897302	0.448651	−	0.893707i	$-0.351905\pi$
$271$	14.7715	0.897302	0.448651	+	0.893707i	$0.351905\pi$
$272$	20.5407	1.24547
$273$	0	0
$274$	−6.09568	−0.368253
$275$	3.44145	0.207527
$276$	22.6710	1.36464
$277$	28.5329	1.71437	0.857187	−	0.515006i	$-0.172210\pi$
$277$	28.5329	1.71437	0.857187	+	0.515006i	$0.172210\pi$
$278$	17.1784	1.03029
$279$	10.5687	0.632732
$280$	0	0
$281$	5.88946	0.351336	0.175668	−	0.984450i	$-0.443792\pi$
$281$	5.88946	0.351336	0.175668	+	0.984450i	$0.443792\pi$
$282$	−45.0405	−2.68212
$283$	−5.52851	−0.328636	−0.164318	−	0.986407i	$-0.552542\pi$
$283$	−5.52851	−0.328636	−0.164318	+	0.986407i	$0.552542\pi$
$284$	11.5850	0.687446
$285$	−8.48333	−0.502509
$286$	3.03808	0.179645
$287$	0	0
$288$	19.2843	1.13634
$289$	−0.121739	−0.00716114
$290$	8.36578	0.491255
$291$	41.6951	2.44421
$292$	−4.61748	−0.270218
$293$	23.9610	1.39982	0.699908	−	0.714233i	$-0.253224\pi$
$293$	23.9610	1.39982	0.699908	+	0.714233i	$0.253224\pi$
$294$	0	0
$295$	12.5655	0.731592
$296$	4.25514	0.247325
$297$	−1.52034	−0.0882190
$298$	−3.11318	−0.180342
$299$	17.1837	0.993761
$300$	−10.2247	−0.590322
$301$	0	0
$302$	−37.9932	−2.18626
$303$	23.5119	1.35072
$304$	−15.6901	−0.899889
$305$	−9.02899	−0.516998
$306$	26.1620	1.49558
$307$	25.3505	1.44683	0.723415	−	0.690413i	$-0.242571\pi$
$307$	25.3505	1.44683	0.723415	+	0.690413i	$0.242571\pi$
$308$	0	0
$309$	40.7552	2.31848
$310$	5.23709	0.297447
$311$	8.91239	0.505375	0.252688	−	0.967548i	$-0.418686\pi$
$311$	8.91239	0.505375	0.252688	+	0.967548i	$0.418686\pi$
$312$	8.77278	0.496661
$313$	7.82419	0.442249	0.221125	−	0.975246i	$-0.429027\pi$
$313$	7.82419	0.442249	0.221125	+	0.975246i	$0.429027\pi$
$314$	6.66655	0.376215
$315$	0	0
$316$	−10.4326	−0.586879
$317$	−8.28549	−0.465360	−0.232680	−	0.972553i	$-0.574749\pi$
$317$	−8.28549	−0.465360	−0.232680	+	0.972553i	$0.574749\pi$
$318$	49.2773	2.76333
$319$	−4.05739	−0.227170
$320$	−0.912497	−0.0510101
$321$	26.6676	1.48844
$322$	0	0
$323$	−12.8925	−0.717358
$324$	−6.64345	−0.369080
$325$	−7.74990	−0.429887
$326$	−16.1906	−0.896714
$327$	−11.3619	−0.628315
$328$	0.682447	0.0376818
$329$	0	0
$330$	−4.13723	−0.227747
$331$	−9.00852	−0.495153	−0.247577	−	0.968868i	$-0.579634\pi$
$331$	−9.00852	−0.495153	−0.247577	+	0.968868i	$0.579634\pi$
$332$	−9.59848	−0.526785
$333$	9.11953	0.499747
$334$	11.3132	0.619033
$335$	−2.71276	−0.148214
$336$	0	0
$337$	−18.7790	−1.02295	−0.511477	−	0.859297i	$-0.670902\pi$
$337$	−18.7790	−1.02295	−0.511477	+	0.859297i	$0.670902\pi$
$338$	15.7285	0.855518
$339$	19.5592	1.06231
$340$	4.36217	0.236572
$341$	−2.53998	−0.137548
$342$	−19.9839	−1.08061
$343$	0	0
$344$	−7.33237	−0.395335
$345$	−23.4007	−1.25985
$346$	5.12535	0.275541
$347$	6.25097	0.335570	0.167785	−	0.985824i	$-0.446339\pi$
$347$	6.25097	0.335570	0.167785	+	0.985824i	$0.446339\pi$
$348$	12.0547	0.646198
$349$	−29.5780	−1.58328	−0.791638	−	0.610990i	$-0.790771\pi$
$349$	−29.5780	−1.58328	−0.791638	+	0.610990i	$0.790771\pi$
$350$	0	0
$351$	3.42370	0.182743
$352$	−4.63460	−0.247025
$353$	13.6098	0.724378	0.362189	−	0.932105i	$-0.382029\pi$
$353$	13.6098	0.724378	0.362189	+	0.932105i	$0.382029\pi$
$354$	53.8104	2.85999
$355$	−11.9579	−0.634659
$356$	4.42820	0.234694
$357$	0	0
$358$	−32.0852	−1.69576
$359$	−0.269626	−0.0142303	−0.00711516	−	0.999975i	$-0.502265\pi$
$359$	−0.269626	−0.0142303	−0.00711516	+	0.999975i	$0.502265\pi$
$360$	−6.57168	−0.346358
$361$	−9.15204	−0.481686
$362$	28.0400	1.47375
$363$	−26.3980	−1.38553
$364$	0	0
$365$	4.76609	0.249469
$366$	−38.6656	−2.02108
$367$	−2.56606	−0.133947	−0.0669736	−	0.997755i	$-0.521334\pi$
$367$	−2.56606	−0.133947	−0.0669736	+	0.997755i	$0.521334\pi$
$368$	−43.2800	−2.25613
$369$	1.46261	0.0761403
$370$	4.51899	0.234931
$371$	0	0
$372$	7.54639	0.391262
$373$	−8.75285	−0.453205	−0.226603	−	0.973987i	$-0.572762\pi$
$373$	−8.75285	−0.453205	−0.226603	+	0.973987i	$0.572762\pi$
$374$	−6.28753	−0.325121
$375$	24.0702	1.24298
$376$	17.1941	0.886718
$377$	9.13696	0.470577
$378$	0	0
$379$	−10.4552	−0.537048	−0.268524	−	0.963273i	$-0.586536\pi$
$379$	−10.4552	−0.537048	−0.268524	+	0.963273i	$0.586536\pi$
$380$	−3.33206	−0.170931
$381$	−2.58223	−0.132292
$382$	−37.7912	−1.93357
$383$	−7.11337	−0.363476	−0.181738	−	0.983347i	$-0.558172\pi$
$383$	−7.11337	−0.363476	−0.181738	+	0.983347i	$0.558172\pi$
$384$	−31.0602	−1.58503
$385$	0	0
$386$	2.74956	0.139949
$387$	−15.7146	−0.798817
$388$	16.3769	0.831411
$389$	−5.88970	−0.298620	−0.149310	−	0.988790i	$-0.547705\pi$
$389$	−5.88970	−0.298620	−0.149310	+	0.988790i	$0.547705\pi$
$390$	9.31675	0.471772
$391$	−35.5631	−1.79850
$392$	0	0
$393$	9.60835	0.484677
$394$	22.4625	1.13164
$395$	10.7683	0.541814
$396$	−3.27935	−0.164793
$397$	2.59063	0.130020	0.0650101	−	0.997885i	$-0.479292\pi$
$397$	2.59063	0.130020	0.0650101	+	0.997885i	$0.479292\pi$
$398$	11.9826	0.600634
$399$	0	0
$400$	19.5194	0.975969
$401$	26.6439	1.33053	0.665266	−	0.746606i	$-0.268318\pi$
$401$	26.6439	1.33053	0.665266	+	0.746606i	$0.268318\pi$
$402$	−11.6171	−0.579407
$403$	5.71986	0.284927
$404$	9.23492	0.459455
$405$	6.85726	0.340740
$406$	0	0
$407$	−2.19170	−0.108639
$408$	−18.1559	−0.898852
$409$	12.7671	0.631291	0.315646	−	0.948877i	$-0.397779\pi$
$409$	12.7671	0.631291	0.315646	+	0.948877i	$0.397779\pi$
$410$	0.724763	0.0357935
$411$	9.06626	0.447205
$412$	16.0077	0.788642
$413$	0	0
$414$	−55.1243	−2.70921
$415$	9.90739	0.486335
$416$	10.4368	0.511706
$417$	−25.5499	−1.25118
$418$	4.80275	0.234910
$419$	−8.63072	−0.421638	−0.210819	−	0.977525i	$-0.567613\pi$
$419$	−8.63072	−0.421638	−0.210819	+	0.977525i	$0.567613\pi$
$420$	0	0
$421$	15.0255	0.732299	0.366149	−	0.930556i	$-0.380676\pi$
$421$	15.0255	0.732299	0.366149	+	0.930556i	$0.380676\pi$
$422$	−14.9220	−0.726391
$423$	36.8501	1.79171
$424$	−18.8115	−0.913565
$425$	16.0390	0.778006
$426$	−51.2083	−2.48105
$427$	0	0
$428$	10.4744	0.506301
$429$	−4.51861	−0.218161
$430$	−7.78702	−0.375524
$431$	34.5636	1.66487	0.832434	−	0.554124i	$-0.186947\pi$
$431$	34.5636	1.66487	0.832434	+	0.554124i	$0.186947\pi$
$432$	−8.62313	−0.414881
$433$	14.2180	0.683276	0.341638	−	0.939832i	$-0.389018\pi$
$433$	14.2180	0.683276	0.341638	+	0.939832i	$0.389018\pi$
$434$	0	0
$435$	−12.4426	−0.596579
$436$	−4.46270	−0.213724
$437$	27.1649	1.29947
$438$	20.4102	0.975239
$439$	29.0770	1.38777	0.693885	−	0.720086i	$-0.255898\pi$
$439$	29.0770	1.38777	0.693885	+	0.720086i	$0.255898\pi$
$440$	1.57938	0.0752938
$441$	0	0
$442$	14.1591	0.673479
$443$	−28.9753	−1.37666	−0.688328	−	0.725399i	$-0.741655\pi$
$443$	−28.9753	−1.37666	−0.688328	+	0.725399i	$0.741655\pi$
$444$	6.51163	0.309028
$445$	−4.57072	−0.216673
$446$	−4.31038	−0.204102
$447$	4.63031	0.219006
$448$	0	0
$449$	−39.7735	−1.87703	−0.938515	−	0.345239i	$-0.887798\pi$
$449$	−39.7735	−1.87703	−0.938515	+	0.345239i	$0.887798\pi$
$450$	24.8612	1.17197
$451$	−0.351509	−0.0165519
$452$	7.68240	0.361350
$453$	56.5082	2.65499
$454$	−7.16943	−0.336478
$455$	0	0
$456$	13.8684	0.649450
$457$	−40.5481	−1.89676	−0.948380	−	0.317135i	$-0.897279\pi$
$457$	−40.5481	−1.89676	−0.948380	+	0.317135i	$0.897279\pi$
$458$	52.1921	2.43877
$459$	−7.08560	−0.330727
$460$	−9.19125	−0.428544
$461$	−7.51338	−0.349933	−0.174967	−	0.984574i	$-0.555982\pi$
$461$	−7.51338	−0.349933	−0.174967	+	0.984574i	$0.555982\pi$
$462$	0	0
$463$	0.417864	0.0194198	0.00970988	−	0.999953i	$-0.496909\pi$
$463$	0.417864	0.0194198	0.00970988	+	0.999953i	$0.496909\pi$
$464$	−23.0129	−1.06835
$465$	−7.78926	−0.361218
$466$	−34.6165	−1.60358
$467$	−41.2799	−1.91020	−0.955102	−	0.296277i	$-0.904255\pi$
$467$	−41.2799	−1.91020	−0.955102	+	0.296277i	$0.904255\pi$
$468$	7.38486	0.341365
$469$	0	0
$470$	18.2603	0.842283
$471$	−9.91532	−0.456874
$472$	−20.5420	−0.945520
$473$	3.77669	0.173653
$474$	46.1142	2.11810
$475$	−12.2514	−0.562135
$476$	0	0
$477$	−40.3164	−1.84596
$478$	−9.90747	−0.453157
$479$	37.2720	1.70300	0.851501	−	0.524353i	$-0.175693\pi$
$479$	37.2720	1.70300	0.851501	+	0.524353i	$0.175693\pi$
$480$	−14.2127	−0.648720
$481$	4.93556	0.225042
$482$	−35.7254	−1.62725
$483$	0	0
$484$	−10.3685	−0.471296
$485$	−16.9040	−0.767569
$486$	38.3485	1.73952
$487$	−12.9320	−0.586006	−0.293003	−	0.956112i	$-0.594655\pi$
$487$	−12.9320	−0.586006	−0.293003	+	0.956112i	$0.594655\pi$
$488$	14.7605	0.668176
$489$	24.0807	1.08897
$490$	0	0
$491$	−10.6756	−0.481785	−0.240892	−	0.970552i	$-0.577440\pi$
$491$	−10.6756	−0.481785	−0.240892	+	0.970552i	$0.577440\pi$
$492$	1.04435	0.0470828
$493$	−18.9096	−0.851647
$494$	−10.8155	−0.486610
$495$	3.38489	0.152139
$496$	−14.4064	−0.646866
$497$	0	0
$498$	42.4273	1.90121
$499$	9.67013	0.432895	0.216447	−	0.976294i	$-0.430553\pi$
$499$	9.67013	0.432895	0.216447	+	0.976294i	$0.430553\pi$
$500$	9.45423	0.422806
$501$	−16.8265	−0.751750
$502$	−43.3723	−1.93580
$503$	16.4749	0.734581	0.367291	−	0.930106i	$-0.380285\pi$
$503$	16.4749	0.734581	0.367291	+	0.930106i	$0.380285\pi$
$504$	0	0
$505$	−9.53214	−0.424175
$506$	13.2480	0.588947
$507$	−23.3934	−1.03894
$508$	−1.01424	−0.0449997
$509$	6.85390	0.303794	0.151897	−	0.988396i	$-0.451462\pi$
$509$	6.85390	0.303794	0.151897	+	0.988396i	$0.451462\pi$
$510$	−19.2817	−0.853809
$511$	0	0
$512$	−9.17314	−0.405399
$513$	5.41235	0.238961
$514$	2.03779	0.0898831
$515$	−16.5229	−0.728085
$516$	−11.2207	−0.493964
$517$	−8.85619	−0.389495
$518$	0	0
$519$	−7.62306	−0.334615
$520$	−3.55664	−0.155969
$521$	25.6572	1.12406	0.562032	−	0.827116i	$-0.310020\pi$
$521$	25.6572	1.12406	0.562032	+	0.827116i	$0.310020\pi$
$522$	−29.3107	−1.28290
$523$	−15.8218	−0.691838	−0.345919	−	0.938264i	$-0.612433\pi$
$523$	−15.8218	−0.691838	−0.345919	+	0.938264i	$0.612433\pi$
$524$	3.77394	0.164865
$525$	0	0
$526$	4.92190	0.214605
$527$	−11.8377	−0.515658
$528$	11.3809	0.495288
$529$	51.9326	2.25794
$530$	−19.9779	−0.867784
$531$	−44.0251	−1.91053
$532$	0	0
$533$	0.791574	0.0342869
$534$	−19.5736	−0.847031
$535$	−10.8115	−0.467424
$536$	4.43478	0.191554
$537$	47.7211	2.05932
$538$	−19.6742	−0.848216
$539$	0	0
$540$	−1.83127	−0.0788052
$541$	10.5432	0.453289	0.226644	−	0.973978i	$-0.427225\pi$
$541$	10.5432	0.453289	0.226644	+	0.973978i	$0.427225\pi$
$542$	−25.6456	−1.10157
$543$	−41.7046	−1.78971
$544$	−21.5997	−0.926082
$545$	4.60632	0.197313
$546$	0	0
$547$	−24.5216	−1.04847	−0.524234	−	0.851574i	$-0.675648\pi$
$547$	−24.5216	−1.04847	−0.524234	+	0.851574i	$0.675648\pi$
$548$	3.56102	0.152119
$549$	31.6344	1.35012
$550$	−5.97490	−0.254770
$551$	14.4442	0.615342
$552$	38.2552	1.62825
$553$	0	0
$554$	−49.5375	−2.10465
$555$	−6.72120	−0.285299
$556$	−10.0354	−0.425597
$557$	−21.8674	−0.926553	−0.463276	−	0.886214i	$-0.653326\pi$
$557$	−21.8674	−0.926553	−0.463276	+	0.886214i	$0.653326\pi$
$558$	−18.3489	−0.776772
$559$	−8.50485	−0.359717
$560$	0	0
$561$	9.35161	0.394825
$562$	−10.2250	−0.431317
$563$	−21.4116	−0.902391	−0.451195	−	0.892425i	$-0.649002\pi$
$563$	−21.4116	−0.902391	−0.451195	+	0.892425i	$0.649002\pi$
$564$	26.3121	1.10794
$565$	−7.92965	−0.333603
$566$	9.59835	0.403449
$567$	0	0
$568$	19.5486	0.820243
$569$	16.8701	0.707232	0.353616	−	0.935391i	$-0.384952\pi$
$569$	16.8701	0.707232	0.353616	+	0.935391i	$0.384952\pi$
$570$	14.7284	0.616904
$571$	−16.3172	−0.682854	−0.341427	−	0.939908i	$-0.610910\pi$
$571$	−16.3172	−0.682854	−0.341427	+	0.939908i	$0.610910\pi$
$572$	−1.77481	−0.0742084
$573$	56.2079	2.34812
$574$	0	0
$575$	−33.7947	−1.40934
$576$	3.19707	0.133211
$577$	2.91913	0.121525	0.0607624	−	0.998152i	$-0.480647\pi$
$577$	2.91913	0.121525	0.0607624	+	0.998152i	$0.480647\pi$
$578$	0.211359	0.00879136
$579$	−4.08949	−0.169953
$580$	−4.88718	−0.202929
$581$	0	0
$582$	−72.3893	−3.00063
$583$	9.68925	0.401288
$584$	−7.79155	−0.322417
$585$	−7.62253	−0.315153
$586$	−41.6001	−1.71848
$587$	44.4697	1.83546	0.917730	−	0.397204i	$-0.130019\pi$
$587$	44.4697	1.83546	0.917730	+	0.397204i	$0.130019\pi$
$588$	0	0
$589$	9.04225	0.372579
$590$	−21.8157	−0.898138
$591$	−33.4090	−1.37426
$592$	−12.4310	−0.510911
$593$	−5.85169	−0.240300	−0.120150	−	0.992756i	$-0.538338\pi$
$593$	−5.85169	−0.240300	−0.120150	+	0.992756i	$0.538338\pi$
$594$	2.63955	0.108302
$595$	0	0
$596$	1.81868	0.0744960
$597$	−17.8220	−0.729408
$598$	−29.8337	−1.21999
$599$	25.8583	1.05654	0.528271	−	0.849076i	$-0.322841\pi$
$599$	25.8583	1.05654	0.528271	+	0.849076i	$0.322841\pi$
$600$	−17.2532	−0.704357
$601$	−7.74060	−0.315746	−0.157873	−	0.987459i	$-0.550464\pi$
$601$	−7.74060	−0.315746	−0.157873	+	0.987459i	$0.550464\pi$
$602$	0	0
$603$	9.50455	0.387055
$604$	22.1951	0.903107
$605$	10.7022	0.435107
$606$	−40.8203	−1.65821
$607$	40.9282	1.66122	0.830611	−	0.556852i	$-0.187991\pi$
$607$	40.9282	1.66122	0.830611	+	0.556852i	$0.187991\pi$
$608$	16.4990	0.669124
$609$	0	0
$610$	15.6757	0.634692
$611$	19.9435	0.806829
$612$	−15.2835	−0.617800
$613$	1.96513	0.0793710	0.0396855	−	0.999212i	$-0.487364\pi$
$613$	1.96513	0.0793710	0.0396855	+	0.999212i	$0.487364\pi$
$614$	−44.0125	−1.77620
$615$	−1.07796	−0.0434675
$616$	0	0
$617$	27.0054	1.08720	0.543599	−	0.839345i	$-0.317061\pi$
$617$	27.0054	1.08720	0.543599	+	0.839345i	$0.317061\pi$
$618$	−70.7573	−2.84628
$619$	−7.32786	−0.294532	−0.147266	−	0.989097i	$-0.547047\pi$
$619$	−7.32786	−0.294532	−0.147266	+	0.989097i	$0.547047\pi$
$620$	−3.05944	−0.122870
$621$	14.9296	0.599104
$622$	−15.4733	−0.620423
$623$	0	0
$624$	−25.6289	−1.02598
$625$	9.76168	0.390467
$626$	−13.5840	−0.542927
$627$	−7.14325	−0.285274
$628$	−3.89451	−0.155408
$629$	−10.2145	−0.407279
$630$	0	0
$631$	−10.0132	−0.398620	−0.199310	−	0.979937i	$-0.563870\pi$
$631$	−10.0132	−0.398620	−0.199310	+	0.979937i	$0.563870\pi$
$632$	−17.6040	−0.700248
$633$	22.1938	0.882126
$634$	14.3849	0.571298
$635$	1.04688	0.0415443
$636$	−28.7871	−1.14148
$637$	0	0
$638$	7.04427	0.278885
$639$	41.8963	1.65739
$640$	12.5924	0.497756
$641$	13.2531	0.523466	0.261733	−	0.965140i	$-0.415706\pi$
$641$	13.2531	0.523466	0.261733	+	0.965140i	$0.415706\pi$
$642$	−46.2992	−1.82728
$643$	36.3250	1.43252	0.716259	−	0.697834i	$-0.245853\pi$
$643$	36.3250	1.43252	0.716259	+	0.697834i	$0.245853\pi$
$644$	0	0
$645$	11.5818	0.456034
$646$	22.3834	0.880663
$647$	20.9195	0.822429	0.411214	−	0.911539i	$-0.365105\pi$
$647$	20.9195	0.822429	0.411214	+	0.911539i	$0.365105\pi$
$648$	−11.2102	−0.440377
$649$	10.5806	0.415324
$650$	13.4550	0.527750
$651$	0	0
$652$	9.45834	0.370417
$653$	−26.9588	−1.05498	−0.527489	−	0.849562i	$-0.676866\pi$
$653$	−26.9588	−1.05498	−0.527489	+	0.849562i	$0.676866\pi$
$654$	19.7260	0.771349
$655$	−3.89540	−0.152206
$656$	−1.99371	−0.0778412
$657$	−16.6987	−0.651479
$658$	0	0
$659$	35.5482	1.38476	0.692380	−	0.721533i	$-0.256562\pi$
$659$	35.5482	1.38476	0.692380	+	0.721533i	$0.256562\pi$
$660$	2.41692	0.0940783
$661$	−48.5419	−1.88806	−0.944031	−	0.329856i	$-0.893000\pi$
$661$	−48.5419	−1.88806	−0.944031	+	0.329856i	$0.893000\pi$
$662$	15.6402	0.607874
$663$	−21.0592	−0.817870
$664$	−16.1965	−0.628546
$665$	0	0
$666$	−15.8329	−0.613514
$667$	39.8432	1.54274
$668$	−6.60905	−0.255712
$669$	6.41093	0.247861
$670$	4.70977	0.181954
$671$	−7.60271	−0.293499
$672$	0	0
$673$	−17.2708	−0.665742	−0.332871	−	0.942972i	$-0.608017\pi$
$673$	−17.2708	−0.665742	−0.332871	+	0.942972i	$0.608017\pi$
$674$	32.6032	1.25583
$675$	−6.73328	−0.259164
$676$	−9.18839	−0.353400
$677$	42.5206	1.63420	0.817100	−	0.576496i	$-0.195580\pi$
$677$	42.5206	1.63420	0.817100	+	0.576496i	$0.195580\pi$
$678$	−33.9578	−1.30414
$679$	0	0
$680$	7.36075	0.282272
$681$	10.6633	0.408617
$682$	4.40981	0.168860
$683$	−22.3583	−0.855516	−0.427758	−	0.903893i	$-0.640696\pi$
$683$	−22.3583	−0.855516	−0.427758	+	0.903893i	$0.640696\pi$
$684$	11.6744	0.446380
$685$	−3.67563	−0.140438
$686$	0	0
$687$	−77.6266	−2.96164
$688$	21.4209	0.816662
$689$	−21.8195	−0.831257
$690$	40.6272	1.54665
$691$	7.25800	0.276107	0.138054	−	0.990425i	$-0.455915\pi$
$691$	7.25800	0.276107	0.138054	+	0.990425i	$0.455915\pi$
$692$	−2.99417	−0.113821
$693$	0	0
$694$	−10.8527	−0.411962
$695$	10.3584	0.392917
$696$	20.3411	0.771026
$697$	−1.63822	−0.0620521
$698$	51.3521	1.94371
$699$	51.4860	1.94738
$700$	0	0
$701$	21.6538	0.817853	0.408926	−	0.912567i	$-0.365903\pi$
$701$	21.6538	0.817853	0.408926	+	0.912567i	$0.365903\pi$
$702$	−5.94407	−0.224345
$703$	7.80238	0.294272
$704$	−0.768353	−0.0289584
$705$	−27.1589	−1.02286
$706$	−23.6288	−0.889282
$707$	0	0
$708$	−31.4353	−1.18141
$709$	−26.3619	−0.990042	−0.495021	−	0.868881i	$-0.664840\pi$
$709$	−26.3619	−0.990042	−0.495021	+	0.868881i	$0.664840\pi$
$710$	20.7608	0.779138
$711$	−37.7285	−1.41493
$712$	7.47216	0.280031
$713$	24.9424	0.934100
$714$	0	0
$715$	1.83193	0.0685102
$716$	18.7438	0.700488
$717$	14.7356	0.550312
$718$	0.468113	0.0174698
$719$	−17.9316	−0.668735	−0.334367	−	0.942443i	$-0.608523\pi$
$719$	−17.9316	−0.668735	−0.334367	+	0.942443i	$0.608523\pi$
$720$	19.1986	0.715489
$721$	0	0
$722$	15.8894	0.591341
$723$	53.1353	1.97612
$724$	−16.3806	−0.608780
$725$	−17.9694	−0.667366
$726$	45.8310	1.70095
$727$	37.7814	1.40124	0.700618	−	0.713537i	$-0.252908\pi$
$727$	37.7814	1.40124	0.700618	+	0.713537i	$0.252908\pi$
$728$	0	0
$729$	−37.3861	−1.38467
$730$	−8.27468	−0.306260
$731$	17.6014	0.651013
$732$	22.5880	0.834875
$733$	−15.1978	−0.561342	−0.280671	−	0.959804i	$-0.590557\pi$
$733$	−15.1978	−0.561342	−0.280671	+	0.959804i	$0.590557\pi$
$734$	4.45508	0.164440
$735$	0	0
$736$	45.5114	1.67757
$737$	−2.28423	−0.0841408
$738$	−2.53931	−0.0934735
$739$	6.42376	0.236302	0.118151	−	0.992996i	$-0.462303\pi$
$739$	6.42376	0.236302	0.118151	+	0.992996i	$0.462303\pi$
$740$	−2.63993	−0.0970459
$741$	16.0861	0.590937
$742$	0	0
$743$	−43.2857	−1.58800	−0.793999	−	0.607919i	$-0.792005\pi$
$743$	−43.2857	−1.58800	−0.793999	+	0.607919i	$0.792005\pi$
$744$	12.7338	0.466843
$745$	−1.87721	−0.0687757
$746$	15.1963	0.556377
$747$	−34.7120	−1.27005
$748$	3.67310	0.134302
$749$	0	0
$750$	−41.7897	−1.52594
$751$	28.0579	1.02385	0.511924	−	0.859031i	$-0.328933\pi$
$751$	28.0579	1.02385	0.511924	+	0.859031i	$0.328933\pi$
$752$	−50.2310	−1.83174
$753$	64.5087	2.35083
$754$	−15.8632	−0.577704
$755$	−22.9094	−0.833760
$756$	0	0
$757$	46.8117	1.70140	0.850700	−	0.525652i	$-0.176179\pi$
$757$	46.8117	1.70140	0.850700	+	0.525652i	$0.176179\pi$
$758$	18.1519	0.659306
$759$	−19.7041	−0.715215
$760$	−5.62252	−0.203950
$761$	−32.7918	−1.18870	−0.594351	−	0.804205i	$-0.702591\pi$
$761$	−32.7918	−1.18870	−0.594351	+	0.804205i	$0.702591\pi$
$762$	4.48316	0.162408
$763$	0	0
$764$	22.0772	0.798724
$765$	15.7754	0.570361
$766$	12.3499	0.446221
$767$	−23.8267	−0.860333
$768$	49.4238	1.78343
$769$	−3.48451	−0.125655	−0.0628273	−	0.998024i	$-0.520012\pi$
$769$	−3.48451	−0.125655	−0.0628273	+	0.998024i	$0.520012\pi$
$770$	0	0
$771$	−3.03086	−0.109154
$772$	−1.60626	−0.0578105
$773$	−13.8137	−0.496846	−0.248423	−	0.968652i	$-0.579912\pi$
$773$	−13.8137	−0.496846	−0.248423	+	0.968652i	$0.579912\pi$
$774$	27.2830	0.980667
$775$	−11.2491	−0.404079
$776$	27.6344	0.992017
$777$	0	0
$778$	10.2254	0.366600
$779$	1.25136	0.0448346
$780$	−5.44273	−0.194881
$781$	−10.0690	−0.360295
$782$	61.7431	2.20793
$783$	7.93838	0.283695
$784$	0	0
$785$	4.01985	0.143475
$786$	−16.6816	−0.595013
$787$	4.37308	0.155884	0.0779418	−	0.996958i	$-0.475165\pi$
$787$	4.37308	0.155884	0.0779418	+	0.996958i	$0.475165\pi$
$788$	−13.1223	−0.467463
$789$	−7.32047	−0.260616
$790$	−18.6955	−0.665157
$791$	0	0
$792$	−5.53358	−0.196627
$793$	17.1208	0.607977
$794$	−4.49774	−0.159619
$795$	29.7136	1.05383
$796$	−7.00009	−0.248112
$797$	25.0129	0.886002	0.443001	−	0.896521i	$-0.353914\pi$
$797$	25.0129	0.886002	0.443001	+	0.896521i	$0.353914\pi$
$798$	0	0
$799$	−41.2747	−1.46019
$800$	−20.5257	−0.725694
$801$	16.0142	0.565833
$802$	−46.2580	−1.63343
$803$	4.01321	0.141623
$804$	6.78654	0.239343
$805$	0	0
$806$	−9.93058	−0.349790
$807$	29.2620	1.03007
$808$	15.5830	0.548209
$809$	−42.5779	−1.49696	−0.748480	−	0.663157i	$-0.769216\pi$
$809$	−42.5779	−1.49696	−0.748480	+	0.663157i	$0.769216\pi$
$810$	−11.9053	−0.418309
$811$	3.59916	0.126384	0.0631918	−	0.998001i	$-0.479872\pi$
$811$	3.59916	0.126384	0.0631918	+	0.998001i	$0.479872\pi$
$812$	0	0
$813$	38.1433	1.33774
$814$	3.80514	0.133370
$815$	−9.76274	−0.341974
$816$	53.0409	1.85680
$817$	−13.4449	−0.470378
$818$	−22.1657	−0.775004
$819$	0	0
$820$	−0.423397	−0.0147857
$821$	−27.6338	−0.964427	−0.482214	−	0.876054i	$-0.660167\pi$
$821$	−27.6338	−0.964427	−0.482214	+	0.876054i	$0.660167\pi$
$822$	−15.7404	−0.549011
$823$	−42.2944	−1.47429	−0.737145	−	0.675735i	$-0.763826\pi$
$823$	−42.2944	−1.47429	−0.737145	+	0.675735i	$0.763826\pi$
$824$	27.0114	0.940987
$825$	8.88661	0.309392
$826$	0	0
$827$	34.0962	1.18564	0.592821	−	0.805334i	$-0.298014\pi$
$827$	34.0962	1.18564	0.592821	+	0.805334i	$0.298014\pi$
$828$	32.2029	1.11913
$829$	−15.5110	−0.538719	−0.269360	−	0.963040i	$-0.586812\pi$
$829$	−15.5110	−0.538719	−0.269360	+	0.963040i	$0.586812\pi$
$830$	−17.2008	−0.597048
$831$	73.6784	2.55587
$832$	1.73028	0.0599866
$833$	0	0
$834$	44.3587	1.53602
$835$	6.82175	0.236076
$836$	−2.80570	−0.0970373
$837$	4.96954	0.171772
$838$	14.9843	0.517624
$839$	37.2475	1.28593	0.642963	−	0.765898i	$-0.277705\pi$
$839$	37.2475	1.28593	0.642963	+	0.765898i	$0.277705\pi$
$840$	0	0
$841$	−7.81451	−0.269466
$842$	−26.0866	−0.899005
$843$	15.2079	0.523789
$844$	8.71723	0.300060
$845$	9.48411	0.326263
$846$	−63.9775	−2.19959
$847$	0	0
$848$	54.9560	1.88720
$849$	−14.2759	−0.489947
$850$	−27.8462	−0.955118
$851$	21.5223	0.737776
$852$	29.9153	1.02488
$853$	31.7533	1.08721	0.543606	−	0.839341i	$-0.317059\pi$
$853$	31.7533	1.08721	0.543606	+	0.839341i	$0.317059\pi$
$854$	0	0
$855$	−12.0501	−0.412104
$856$	17.6746	0.604105
$857$	27.5926	0.942544	0.471272	−	0.881988i	$-0.343795\pi$
$857$	27.5926	0.942544	0.471272	+	0.881988i	$0.343795\pi$
$858$	7.84502	0.267824
$859$	26.0085	0.887399	0.443700	−	0.896176i	$-0.353666\pi$
$859$	26.0085	0.887399	0.443700	+	0.896176i	$0.353666\pi$
$860$	4.54908	0.155122
$861$	0	0
$862$	−60.0078	−2.04387
$863$	−44.6899	−1.52126	−0.760630	−	0.649185i	$-0.775110\pi$
$863$	−44.6899	−1.52126	−0.760630	+	0.649185i	$0.775110\pi$
$864$	9.06771	0.308490
$865$	3.09053	0.105081
$866$	−24.6848	−0.838822
$867$	−0.314359	−0.0106762
$868$	0	0
$869$	9.06731	0.307587
$870$	21.6024	0.732389
$871$	5.14393	0.174295
$872$	−7.53036	−0.255010
$873$	59.2255	2.00448
$874$	−47.1626	−1.59530
$875$	0	0
$876$	−11.9234	−0.402854
$877$	−18.9995	−0.641567	−0.320783	−	0.947153i	$-0.603946\pi$
$877$	−18.9995	−0.641567	−0.320783	+	0.947153i	$0.603946\pi$
$878$	−50.4823	−1.70369
$879$	61.8728	2.08692
$880$	−4.61400	−0.155538
$881$	46.3443	1.56138	0.780690	−	0.624919i	$-0.214868\pi$
$881$	46.3443	1.56138	0.780690	+	0.624919i	$0.214868\pi$
$882$	0	0
$883$	13.3688	0.449896	0.224948	−	0.974371i	$-0.427779\pi$
$883$	13.3688	0.449896	0.224948	+	0.974371i	$0.427779\pi$
$884$	−8.27156	−0.278203
$885$	32.4470	1.09070
$886$	50.3056	1.69005
$887$	−28.9159	−0.970900	−0.485450	−	0.874264i	$-0.661344\pi$
$887$	−28.9159	−0.970900	−0.485450	+	0.874264i	$0.661344\pi$
$888$	10.9877	0.368725
$889$	0	0
$890$	7.93548	0.265998
$891$	5.77404	0.193438
$892$	2.51807	0.0843112
$893$	31.5277	1.05504
$894$	−8.03895	−0.268863
$895$	−19.3470	−0.646699
$896$	0	0
$897$	44.3724	1.48155
$898$	69.0531	2.30433
$899$	13.2624	0.442326
$900$	−14.5236	−0.484119
$901$	45.1571	1.50440
$902$	0.610275	0.0203199
$903$	0	0
$904$	12.9633	0.431153
$905$	16.9078	0.562034
$906$	−98.1070	−3.25939
$907$	12.3591	0.410379	0.205189	−	0.978722i	$-0.434219\pi$
$907$	12.3591	0.410379	0.205189	+	0.978722i	$0.434219\pi$
$908$	4.18829	0.138993
$909$	33.3973	1.10772
$910$	0	0
$911$	9.34087	0.309477	0.154738	−	0.987955i	$-0.450547\pi$
$911$	9.34087	0.309477	0.154738	+	0.987955i	$0.450547\pi$
$912$	−40.5154	−1.34160
$913$	8.34236	0.276092
$914$	70.3979	2.32856
$915$	−23.3149	−0.770768
$916$	−30.4899	−1.00742
$917$	0	0
$918$	12.3017	0.406017
$919$	−0.270764	−0.00893167	−0.00446584	−	0.999990i	$-0.501422\pi$
$919$	−0.270764	−0.00893167	−0.00446584	+	0.999990i	$0.501422\pi$
$920$	−15.5093	−0.511328
$921$	65.4609	2.15701
$922$	13.0444	0.429595
$923$	22.6746	0.746343
$924$	0	0
$925$	−9.70661	−0.319151
$926$	−0.725477	−0.0238406
$927$	57.8904	1.90137
$928$	24.1994	0.794383
$929$	19.8208	0.650301	0.325150	−	0.945662i	$-0.394585\pi$
$929$	19.8208	0.650301	0.325150	+	0.945662i	$0.394585\pi$
$930$	13.5234	0.443449
$931$	0	0
$932$	20.2225	0.662411
$933$	23.0138	0.753439
$934$	71.6683	2.34506
$935$	−3.79131	−0.123989
$936$	12.4612	0.407308
$937$	−5.40859	−0.176691	−0.0883454	−	0.996090i	$-0.528158\pi$
$937$	−5.40859	−0.176691	−0.0883454	+	0.996090i	$0.528158\pi$
$938$	0	0
$939$	20.2039	0.659328
$940$	−10.6674	−0.347932
$941$	−12.8242	−0.418056	−0.209028	−	0.977910i	$-0.567030\pi$
$941$	−12.8242	−0.418056	−0.209028	+	0.977910i	$0.567030\pi$
$942$	17.2146	0.560881
$943$	3.45179	0.112406
$944$	60.0115	1.95321
$945$	0	0
$946$	−6.55693	−0.213184
$947$	−46.7949	−1.52063	−0.760315	−	0.649555i	$-0.774955\pi$
$947$	−46.7949	−1.52063	−0.760315	+	0.649555i	$0.774955\pi$
$948$	−26.9393	−0.874949
$949$	−9.03746	−0.293369
$950$	21.2704	0.690104
$951$	−21.3950	−0.693782
$952$	0	0
$953$	6.05933	0.196281	0.0981404	−	0.995173i	$-0.468711\pi$
$953$	6.05933	0.196281	0.0981404	+	0.995173i	$0.468711\pi$
$954$	69.9955	2.26619
$955$	−22.7877	−0.737392
$956$	5.78782	0.187192
$957$	−10.4771	−0.338677
$958$	−64.7101	−2.09069
$959$	0	0
$960$	−2.35628	−0.0760485
$961$	−22.6976	−0.732179
$962$	−8.56891	−0.276273
$963$	37.8799	1.22066
$964$	20.8703	0.672188
$965$	1.65795	0.0533714
$966$	0	0
$967$	−5.53050	−0.177849	−0.0889245	−	0.996038i	$-0.528343\pi$
$967$	−5.53050	−0.177849	−0.0889245	+	0.996038i	$0.528343\pi$
$968$	−17.4959	−0.562339
$969$	−33.2914	−1.06947
$970$	29.3479	0.942305
$971$	27.1740	0.872055	0.436027	−	0.899933i	$-0.356385\pi$
$971$	27.1740	0.872055	0.436027	+	0.899933i	$0.356385\pi$
$972$	−22.4027	−0.718566
$973$	0	0
$974$	22.4520	0.719409
$975$	−20.0120	−0.640898
$976$	−43.1215	−1.38028
$977$	−26.7020	−0.854274	−0.427137	−	0.904187i	$-0.640478\pi$
$977$	−26.7020	−0.854274	−0.427137	+	0.904187i	$0.640478\pi$
$978$	−41.8078	−1.33687
$979$	−3.84870	−0.123005
$980$	0	0
$981$	−16.1389	−0.515276
$982$	18.5346	0.591462
$983$	−17.3047	−0.551935	−0.275968	−	0.961167i	$-0.588998\pi$
$983$	−17.3047	−0.551935	−0.275968	+	0.961167i	$0.588998\pi$
$984$	1.76223	0.0561780
$985$	13.5446	0.431568
$986$	32.8301	1.04552
$987$	0	0
$988$	6.31825	0.201010
$989$	−37.0868	−1.17929
$990$	−5.87670	−0.186774
$991$	−11.9807	−0.380580	−0.190290	−	0.981728i	$-0.560943\pi$
$991$	−11.9807	−0.380580	−0.190290	+	0.981728i	$0.560943\pi$
$992$	15.1491	0.480986
$993$	−23.2621	−0.738199
$994$	0	0
$995$	7.22538	0.229060
$996$	−24.7855	−0.785358
$997$	−0.178989	−0.00566863	−0.00283431	−	0.999996i	$-0.500902\pi$
$997$	−0.178989	−0.00566863	−0.00283431	+	0.999996i	$0.500902\pi$
$998$	−16.7889	−0.531442
$999$	4.28812	0.135670

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6223.2.a.r.1.11		40
7.3	odd	6		889.2.f.d.128.30	✓	80
7.5	odd	6		889.2.f.d.382.30	yes	80
7.6	odd	2		6223.2.a.q.1.11		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
889.2.f.d.128.30	✓	80	7.3	odd	6
889.2.f.d.382.30	yes	80	7.5	odd	6
6223.2.a.q.1.11		40	7.6	odd	2
6223.2.a.r.1.11		40	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-1.73616 q^{2} +2.58223 q^{3} +1.01424 q^{4} -1.04688 q^{5} -4.48316 q^{6} +1.71143 q^{8} +3.66791 q^{9} +O(q^{10})\)	\(q-1.73616 q^{2} +2.58223 q^{3} +1.01424 q^{4} -1.04688 q^{5} -4.48316 q^{6} +1.71143 q^{8} +3.66791 q^{9} +1.81755 q^{10} -0.881511 q^{11} +2.61900 q^{12} +1.98510 q^{13} -2.70329 q^{15} -4.99980 q^{16} -4.10832 q^{17} -6.36807 q^{18} +3.13815 q^{19} -1.06179 q^{20} +1.53044 q^{22} +8.65636 q^{23} +4.41931 q^{24} -3.90404 q^{25} -3.44645 q^{26} +1.72470 q^{27} +4.60277 q^{29} +4.69334 q^{30} +2.88140 q^{31} +5.25757 q^{32} -2.27626 q^{33} +7.13268 q^{34} +3.72014 q^{36} +2.48630 q^{37} -5.44832 q^{38} +5.12598 q^{39} -1.79167 q^{40} +0.398758 q^{41} -4.28434 q^{43} -0.894064 q^{44} -3.83987 q^{45} -15.0288 q^{46} +10.0466 q^{47} -12.9106 q^{48} +6.77802 q^{50} -10.6086 q^{51} +2.01337 q^{52} -10.9916 q^{53} -2.99434 q^{54} +0.922838 q^{55} +8.10342 q^{57} -7.99113 q^{58} -12.0028 q^{59} -2.74179 q^{60} +8.62464 q^{61} -5.00256 q^{62} +0.871632 q^{64} -2.07817 q^{65} +3.95195 q^{66} +2.59127 q^{67} -4.16682 q^{68} +22.3527 q^{69} +11.4224 q^{71} +6.27738 q^{72} -4.55265 q^{73} -4.31661 q^{74} -10.0811 q^{75} +3.18284 q^{76} -8.89951 q^{78} -10.2861 q^{79} +5.23420 q^{80} -6.55017 q^{81} -0.692306 q^{82} -9.46370 q^{83} +4.30093 q^{85} +7.43829 q^{86} +11.8854 q^{87} -1.50865 q^{88} +4.36603 q^{89} +6.66662 q^{90} +8.77963 q^{92} +7.44043 q^{93} -17.4425 q^{94} -3.28527 q^{95} +13.5762 q^{96} +16.1469 q^{97} -3.23330 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 3 q^{2} + 6 q^{3} + 39 q^{4} + 24 q^{5} - 9 q^{8} + 42 q^{9}+O(q^{10}) \) 40 * q - 3 * q^2 + 6 * q^3 + 39 * q^4 + 24 * q^5 - 9 * q^8 + 42 * q^9	\( 40 q - 3 q^{2} + 6 q^{3} + 39 q^{4} + 24 q^{5} - 9 q^{8} + 42 q^{9} + 15 q^{10} + 4 q^{11} + 29 q^{12} + 7 q^{13} + 8 q^{15} + 29 q^{16} + 56 q^{17} - 12 q^{18} + 6 q^{19} + 45 q^{20} + 3 q^{22} - 7 q^{23} + 2 q^{24} + 48 q^{25} + 32 q^{26} + 54 q^{27} - 14 q^{29} + 2 q^{30} - 2 q^{31} - 31 q^{32} + 70 q^{33} - 5 q^{34} + 67 q^{36} + 45 q^{38} - 15 q^{39} + 15 q^{40} + 38 q^{41} + 27 q^{43} - 24 q^{44} + 66 q^{45} - 24 q^{46} + 69 q^{47} + 34 q^{48} + 26 q^{50} - 26 q^{51} + 41 q^{52} - 8 q^{53} + 8 q^{54} + 24 q^{55} + 12 q^{57} - 21 q^{58} + 45 q^{59} - 10 q^{60} - 5 q^{61} + 27 q^{62} + 65 q^{64} + q^{65} + 52 q^{66} + 11 q^{67} + 78 q^{68} + 47 q^{69} + 15 q^{71} - 95 q^{72} + 64 q^{73} - 23 q^{74} + 4 q^{75} - 31 q^{76} + 76 q^{78} - 12 q^{79} + 110 q^{80} + 72 q^{81} - 38 q^{82} + 103 q^{83} + 30 q^{85} - 45 q^{86} + 17 q^{87} + 2 q^{88} + 78 q^{89} + 75 q^{90} - 51 q^{92} - 85 q^{93} + 48 q^{94} - 15 q^{95} - 128 q^{96} + 65 q^{97} + 65 q^{99}+O(q^{100}) \) 40 * q - 3 * q^2 + 6 * q^3 + 39 * q^4 + 24 * q^5 - 9 * q^8 + 42 * q^9 + 15 * q^10 + 4 * q^11 + 29 * q^12 + 7 * q^13 + 8 * q^15 + 29 * q^16 + 56 * q^17 - 12 * q^18 + 6 * q^19 + 45 * q^20 + 3 * q^22 - 7 * q^23 + 2 * q^24 + 48 * q^25 + 32 * q^26 + 54 * q^27 - 14 * q^29 + 2 * q^30 - 2 * q^31 - 31 * q^32 + 70 * q^33 - 5 * q^34 + 67 * q^36 + 45 * q^38 - 15 * q^39 + 15 * q^40 + 38 * q^41 + 27 * q^43 - 24 * q^44 + 66 * q^45 - 24 * q^46 + 69 * q^47 + 34 * q^48 + 26 * q^50 - 26 * q^51 + 41 * q^52 - 8 * q^53 + 8 * q^54 + 24 * q^55 + 12 * q^57 - 21 * q^58 + 45 * q^59 - 10 * q^60 - 5 * q^61 + 27 * q^62 + 65 * q^64 + q^65 + 52 * q^66 + 11 * q^67 + 78 * q^68 + 47 * q^69 + 15 * q^71 - 95 * q^72 + 64 * q^73 - 23 * q^74 + 4 * q^75 - 31 * q^76 + 76 * q^78 - 12 * q^79 + 110 * q^80 + 72 * q^81 - 38 * q^82 + 103 * q^83 + 30 * q^85 - 45 * q^86 + 17 * q^87 + 2 * q^88 + 78 * q^89 + 75 * q^90 - 51 * q^92 - 85 * q^93 + 48 * q^94 - 15 * q^95 - 128 * q^96 + 65 * q^97 + 65 * q^99

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