LMFDB - Embedded newform 6027.2.a.x.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6027,2,Mod(1,6027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.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:	$48.1258372982$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.1197392.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 8x^{3} + 6x^{2} + 14x - 2 $ x^5 - 2x^4 - 8x^3 + 6x^2 + 14x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 861)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-1.68791$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.68791 q^{2} +1.00000 q^{3} +5.22488 q^{4} -2.62470 q^{5} +2.68791 q^{6} +8.66818 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.68791 q^{2} +1.00000 q^{3} +5.22488 q^{4} -2.62470 q^{5} +2.68791 q^{6} +8.66818 q^{8} +1.00000 q^{9} -7.05495 q^{10} -1.39982 q^{11} +5.22488 q^{12} +3.54123 q^{13} -2.62470 q^{15} +12.8496 q^{16} +6.91355 q^{17} +2.68791 q^{18} +1.86930 q^{19} -13.7137 q^{20} -3.76260 q^{22} -3.18565 q^{23} +8.66818 q^{24} +1.88903 q^{25} +9.51851 q^{26} +1.00000 q^{27} +6.33660 q^{29} -7.05495 q^{30} -4.66894 q^{31} +17.2022 q^{32} -1.39982 q^{33} +18.5830 q^{34} +5.22488 q^{36} -8.47427 q^{37} +5.02452 q^{38} +3.54123 q^{39} -22.7513 q^{40} +1.00000 q^{41} +5.62470 q^{43} -7.31389 q^{44} -2.62470 q^{45} -8.56276 q^{46} +1.51595 q^{47} +12.8496 q^{48} +5.07755 q^{50} +6.91355 q^{51} +18.5025 q^{52} -1.61967 q^{53} +2.68791 q^{54} +3.67410 q^{55} +1.86930 q^{57} +17.0322 q^{58} -7.98747 q^{59} -13.7137 q^{60} +8.59847 q^{61} -12.5497 q^{62} +20.5388 q^{64} -9.29465 q^{65} -3.76260 q^{66} +10.4911 q^{67} +36.1224 q^{68} -3.18565 q^{69} +15.8074 q^{71} +8.66818 q^{72} -10.4540 q^{73} -22.7781 q^{74} +1.88903 q^{75} +9.76686 q^{76} +9.51851 q^{78} -1.53398 q^{79} -33.7262 q^{80} +1.00000 q^{81} +2.68791 q^{82} +10.8401 q^{83} -18.1460 q^{85} +15.1187 q^{86} +6.33660 q^{87} -12.1339 q^{88} +17.2254 q^{89} -7.05495 q^{90} -16.6446 q^{92} -4.66894 q^{93} +4.07475 q^{94} -4.90635 q^{95} +17.2022 q^{96} -1.03922 q^{97} -1.39982 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 3 q^{2} + 5 q^{3} + 11 q^{4} + 9 q^{5} + 3 q^{6} + 9 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + 3 * q^2 + 5 * q^3 + 11 * q^4 + 9 * q^5 + 3 * q^6 + 9 * q^8 + 5 * q^9	$ 5 q + 3 q^{2} + 5 q^{3} + 11 q^{4} + 9 q^{5} + 3 q^{6} + 9 q^{8} + 5 q^{9} - 9 q^{10} + 11 q^{12} + 3 q^{13} + 9 q^{15} + 27 q^{16} + 16 q^{17} + 3 q^{18} - 4 q^{19} + 7 q^{20} - 6 q^{22} - 3 q^{23} + 9 q^{24} + 20 q^{25} - 17 q^{26} + 5 q^{27} + 13 q^{29} - 9 q^{30} + 4 q^{31} + 21 q^{32} + 4 q^{34} + 11 q^{36} + 17 q^{37} - 4 q^{38} + 3 q^{39} - 37 q^{40} + 5 q^{41} + 6 q^{43} + 32 q^{44} + 9 q^{45} + 27 q^{46} + 15 q^{47} + 27 q^{48} - 14 q^{50} + 16 q^{51} + 17 q^{52} + 11 q^{53} + 3 q^{54} + 16 q^{55} - 4 q^{57} + 9 q^{58} - 12 q^{59} + 7 q^{60} - 12 q^{61} - 8 q^{62} + 19 q^{64} - 19 q^{65} - 6 q^{66} + 11 q^{67} + 28 q^{68} - 3 q^{69} + 18 q^{71} + 9 q^{72} - 12 q^{73} - 27 q^{74} + 20 q^{75} + 26 q^{76} - 17 q^{78} + 23 q^{79} + 7 q^{80} + 5 q^{81} + 3 q^{82} + 2 q^{83} + 20 q^{85} + 18 q^{86} + 13 q^{87} - 22 q^{88} + 28 q^{89} - 9 q^{90} - 7 q^{92} + 4 q^{93} + 3 q^{94} - 10 q^{95} + 21 q^{96} - 3 q^{97}+O(q^{100}) $ 5 * q + 3 * q^2 + 5 * q^3 + 11 * q^4 + 9 * q^5 + 3 * q^6 + 9 * q^8 + 5 * q^9 - 9 * q^10 + 11 * q^12 + 3 * q^13 + 9 * q^15 + 27 * q^16 + 16 * q^17 + 3 * q^18 - 4 * q^19 + 7 * q^20 - 6 * q^22 - 3 * q^23 + 9 * q^24 + 20 * q^25 - 17 * q^26 + 5 * q^27 + 13 * q^29 - 9 * q^30 + 4 * q^31 + 21 * q^32 + 4 * q^34 + 11 * q^36 + 17 * q^37 - 4 * q^38 + 3 * q^39 - 37 * q^40 + 5 * q^41 + 6 * q^43 + 32 * q^44 + 9 * q^45 + 27 * q^46 + 15 * q^47 + 27 * q^48 - 14 * q^50 + 16 * q^51 + 17 * q^52 + 11 * q^53 + 3 * q^54 + 16 * q^55 - 4 * q^57 + 9 * q^58 - 12 * q^59 + 7 * q^60 - 12 * q^61 - 8 * q^62 + 19 * q^64 - 19 * q^65 - 6 * q^66 + 11 * q^67 + 28 * q^68 - 3 * q^69 + 18 * q^71 + 9 * q^72 - 12 * q^73 - 27 * q^74 + 20 * q^75 + 26 * q^76 - 17 * q^78 + 23 * q^79 + 7 * q^80 + 5 * q^81 + 3 * q^82 + 2 * q^83 + 20 * q^85 + 18 * q^86 + 13 * q^87 - 22 * q^88 + 28 * q^89 - 9 * q^90 - 7 * q^92 + 4 * q^93 + 3 * q^94 - 10 * q^95 + 21 * q^96 - 3 * q^97

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 $

$2$	2.68791	1.90064	0.950321	−	0.311273i	$-0.100755\pi$
$2$	2.68791	1.90064	0.950321	+	0.311273i	$0.100755\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.22488	2.61244
$5$	−2.62470	−1.17380	−0.586900	−	0.809660i	$-0.699652\pi$
$5$	−2.62470	−1.17380	−0.586900	+	0.809660i	$0.699652\pi$
$6$	2.68791	1.09734
$7$	0	0
$7$	0	0
$8$	8.66818	3.06467
$9$	1.00000	0.333333
$10$	−7.05495	−2.23097
$11$	−1.39982	−0.422062	−0.211031	−	0.977479i	$-0.567682\pi$
$11$	−1.39982	−0.422062	−0.211031	+	0.977479i	$0.567682\pi$
$12$	5.22488	1.50829
$13$	3.54123	0.982160	0.491080	−	0.871114i	$-0.336602\pi$
$13$	3.54123	0.982160	0.491080	+	0.871114i	$0.336602\pi$
$14$	0	0
$15$	−2.62470	−0.677694
$16$	12.8496	3.21239
$17$	6.91355	1.67678	0.838391	−	0.545070i	$-0.183497\pi$
$17$	6.91355	1.67678	0.838391	+	0.545070i	$0.183497\pi$
$18$	2.68791	0.633547
$19$	1.86930	0.428847	0.214423	−	0.976741i	$-0.431213\pi$
$19$	1.86930	0.428847	0.214423	+	0.976741i	$0.431213\pi$
$20$	−13.7137	−3.06648
$21$	0	0
$22$	−3.76260	−0.802188
$23$	−3.18565	−0.664255	−0.332127	−	0.943235i	$-0.607766\pi$
$23$	−3.18565	−0.664255	−0.332127	+	0.943235i	$0.607766\pi$
$24$	8.66818	1.76939
$25$	1.88903	0.377806
$26$	9.51851	1.86673
$27$	1.00000	0.192450
$28$	0	0
$29$	6.33660	1.17668	0.588339	−	0.808614i	$-0.299782\pi$
$29$	6.33660	1.17668	0.588339	+	0.808614i	$0.299782\pi$
$30$	−7.05495	−1.28805
$31$	−4.66894	−0.838567	−0.419283	−	0.907855i	$-0.637719\pi$
$31$	−4.66894	−0.838567	−0.419283	+	0.907855i	$0.637719\pi$
$32$	17.2022	3.04094
$33$	−1.39982	−0.243678
$34$	18.5830	3.18696
$35$	0	0
$36$	5.22488	0.870813
$37$	−8.47427	−1.39316	−0.696581	−	0.717479i	$-0.745296\pi$
$37$	−8.47427	−1.39316	−0.696581	+	0.717479i	$0.745296\pi$
$38$	5.02452	0.815084
$39$	3.54123	0.567050
$40$	−22.7513	−3.59730
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	5.62470	0.857758	0.428879	−	0.903362i	$-0.358909\pi$
$43$	5.62470	0.857758	0.428879	+	0.903362i	$0.358909\pi$
$44$	−7.31389	−1.10261
$45$	−2.62470	−0.391267
$46$	−8.56276	−1.26251
$47$	1.51595	0.221124	0.110562	−	0.993869i	$-0.464735\pi$
$47$	1.51595	0.221124	0.110562	+	0.993869i	$0.464735\pi$
$48$	12.8496	1.85468
$49$	0	0
$50$	5.07755	0.718074
$51$	6.91355	0.968090
$52$	18.5025	2.56583
$53$	−1.61967	−0.222479	−0.111240	−	0.993794i	$-0.535482\pi$
$53$	−1.61967	−0.222479	−0.111240	+	0.993794i	$0.535482\pi$
$54$	2.68791	0.365779
$55$	3.67410	0.495416
$56$	0	0
$57$	1.86930	0.247595
$58$	17.0322	2.23644
$59$	−7.98747	−1.03988	−0.519940	−	0.854203i	$-0.674046\pi$
$59$	−7.98747	−1.03988	−0.519940	+	0.854203i	$0.674046\pi$
$60$	−13.7137	−1.77043
$61$	8.59847	1.10092	0.550461	−	0.834861i	$-0.314452\pi$
$61$	8.59847	1.10092	0.550461	+	0.834861i	$0.314452\pi$
$62$	−12.5497	−1.59381
$63$	0	0
$64$	20.5388	2.56735
$65$	−9.29465	−1.15286
$66$	−3.76260	−0.463144
$67$	10.4911	1.28169	0.640844	−	0.767671i	$-0.278585\pi$
$67$	10.4911	1.28169	0.640844	+	0.767671i	$0.278585\pi$
$68$	36.1224	4.38049
$69$	−3.18565	−0.383508
$70$	0	0
$71$	15.8074	1.87599	0.937994	−	0.346650i	$-0.112681\pi$
$71$	15.8074	1.87599	0.937994	+	0.346650i	$0.112681\pi$
$72$	8.66818	1.02156
$73$	−10.4540	−1.22355	−0.611775	−	0.791032i	$-0.709544\pi$
$73$	−10.4540	−1.22355	−0.611775	+	0.791032i	$0.709544\pi$
$74$	−22.7781	−2.64790
$75$	1.88903	0.218126
$76$	9.76686	1.12034
$77$	0	0
$78$	9.51851	1.07776
$79$	−1.53398	−0.172586	−0.0862929	−	0.996270i	$-0.527502\pi$
$79$	−1.53398	−0.172586	−0.0862929	+	0.996270i	$0.527502\pi$
$80$	−33.7262	−3.77071
$81$	1.00000	0.111111
$82$	2.68791	0.296830
$83$	10.8401	1.18986	0.594930	−	0.803777i	$-0.297180\pi$
$83$	10.8401	1.18986	0.594930	+	0.803777i	$0.297180\pi$
$84$	0	0
$85$	−18.1460	−1.96821
$86$	15.1187	1.63029
$87$	6.33660	0.679355
$88$	−12.1339	−1.29348
$89$	17.2254	1.82589	0.912944	−	0.408084i	$-0.133803\pi$
$89$	17.2254	1.82589	0.912944	+	0.408084i	$0.133803\pi$
$90$	−7.05495	−0.743657
$91$	0	0
$92$	−16.6446	−1.73532
$93$	−4.66894	−0.484147
$94$	4.07475	0.420278
$95$	−4.90635	−0.503380
$96$	17.2022	1.75569
$97$	−1.03922	−0.105517	−0.0527585	−	0.998607i	$-0.516801\pi$
$97$	−1.03922	−0.105517	−0.0527585	+	0.998607i	$0.516801\pi$
$98$	0	0
$99$	−1.39982	−0.140687
$100$	9.86994	0.986994
$101$	−14.8770	−1.48032	−0.740160	−	0.672431i	$-0.765250\pi$
$101$	−14.8770	−1.48032	−0.740160	+	0.672431i	$0.765250\pi$
$102$	18.5830	1.83999
$103$	6.38537	0.629169	0.314585	−	0.949229i	$-0.398135\pi$
$103$	6.38537	0.629169	0.314585	+	0.949229i	$0.398135\pi$
$104$	30.6960	3.00999
$105$	0	0
$106$	−4.35354	−0.422853
$107$	−20.0285	−1.93623	−0.968116	−	0.250501i	$-0.919405\pi$
$107$	−20.0285	−1.93623	−0.968116	+	0.250501i	$0.919405\pi$
$108$	5.22488	0.502764
$109$	−4.76909	−0.456796	−0.228398	−	0.973568i	$-0.573349\pi$
$109$	−4.76909	−0.456796	−0.228398	+	0.973568i	$0.573349\pi$
$110$	9.87567	0.941608
$111$	−8.47427	−0.804342
$112$	0	0
$113$	−3.98454	−0.374834	−0.187417	−	0.982280i	$-0.560012\pi$
$113$	−3.98454	−0.374834	−0.187417	+	0.982280i	$0.560012\pi$
$114$	5.02452	0.470589
$115$	8.36137	0.779702
$116$	33.1080	3.07400
$117$	3.54123	0.327387
$118$	−21.4696	−1.97644
$119$	0	0
$120$	−22.7513	−2.07690
$121$	−9.04050	−0.821864
$122$	23.1119	2.09246
$123$	1.00000	0.0901670
$124$	−24.3946	−2.19070
$125$	8.16535	0.730331
$126$	0	0
$127$	5.48680	0.486874	0.243437	−	0.969917i	$-0.421725\pi$
$127$	5.48680	0.486874	0.243437	+	0.969917i	$0.421725\pi$
$128$	20.8021	1.83866
$129$	5.62470	0.495227
$130$	−24.9832	−2.19117
$131$	−6.78817	−0.593086	−0.296543	−	0.955020i	$-0.595834\pi$
$131$	−6.78817	−0.593086	−0.296543	+	0.955020i	$0.595834\pi$
$132$	−7.31389	−0.636592
$133$	0	0
$134$	28.1991	2.43603
$135$	−2.62470	−0.225898
$136$	59.9279	5.13877
$137$	10.5490	0.901258	0.450629	−	0.892711i	$-0.351200\pi$
$137$	10.5490	0.901258	0.450629	+	0.892711i	$0.351200\pi$
$138$	−8.56276	−0.728911
$139$	−14.4505	−1.22568	−0.612838	−	0.790209i	$-0.709972\pi$
$139$	−14.4505	−1.22568	−0.612838	+	0.790209i	$0.709972\pi$
$140$	0	0
$141$	1.51595	0.127666
$142$	42.4888	3.56558
$143$	−4.95709	−0.414532
$144$	12.8496	1.07080
$145$	−16.6317	−1.38118
$146$	−28.0995	−2.32553
$147$	0	0
$148$	−44.2770	−3.63955
$149$	22.3696	1.83259	0.916295	−	0.400505i	$-0.131165\pi$
$149$	22.3696	1.83259	0.916295	+	0.400505i	$0.131165\pi$
$150$	5.07755	0.414580
$151$	9.72314	0.791258	0.395629	−	0.918410i	$-0.370527\pi$
$151$	9.72314	0.791258	0.395629	+	0.918410i	$0.370527\pi$
$152$	16.2034	1.31427
$153$	6.91355	0.558927
$154$	0	0
$155$	12.2546	0.984309
$156$	18.5025	1.48138
$157$	15.7834	1.25965	0.629825	−	0.776737i	$-0.283127\pi$
$157$	15.7834	1.25965	0.629825	+	0.776737i	$0.283127\pi$
$158$	−4.12320	−0.328024
$159$	−1.61967	−0.128448
$160$	−45.1504	−3.56946
$161$	0	0
$162$	2.68791	0.211182
$163$	−1.83704	−0.143888	−0.0719442	−	0.997409i	$-0.522920\pi$
$163$	−1.83704	−0.143888	−0.0719442	+	0.997409i	$0.522920\pi$
$164$	5.22488	0.407994
$165$	3.67410	0.286029
$166$	29.1374	2.26150
$167$	−4.13815	−0.320220	−0.160110	−	0.987099i	$-0.551185\pi$
$167$	−4.13815	−0.320220	−0.160110	+	0.987099i	$0.551185\pi$
$168$	0	0
$169$	−0.459700	−0.0353616
$170$	−48.7748	−3.74085
$171$	1.86930	0.142949
$172$	29.3883	2.24084
$173$	2.85554	0.217103	0.108551	−	0.994091i	$-0.465379\pi$
$173$	2.85554	0.217103	0.108551	+	0.994091i	$0.465379\pi$
$174$	17.0322	1.29121
$175$	0	0
$176$	−17.9871	−1.35583
$177$	−7.98747	−0.600375
$178$	46.3004	3.47036
$179$	−22.3216	−1.66840	−0.834198	−	0.551465i	$-0.814069\pi$
$179$	−22.3216	−1.66840	−0.834198	+	0.551465i	$0.814069\pi$
$180$	−13.7137	−1.02216
$181$	−14.1841	−1.05429	−0.527147	−	0.849774i	$-0.676738\pi$
$181$	−14.1841	−1.05429	−0.527147	+	0.849774i	$0.676738\pi$
$182$	0	0
$183$	8.59847	0.635617
$184$	−27.6138	−2.03572
$185$	22.2424	1.63529
$186$	−12.5497	−0.920189
$187$	−9.67773	−0.707705
$188$	7.92067	0.577674
$189$	0	0
$190$	−13.1878	−0.956746
$191$	−3.91577	−0.283335	−0.141668	−	0.989914i	$-0.545246\pi$
$191$	−3.91577	−0.283335	−0.141668	+	0.989914i	$0.545246\pi$
$192$	20.5388	1.48226
$193$	−2.87153	−0.206697	−0.103349	−	0.994645i	$-0.532956\pi$
$193$	−2.87153	−0.206697	−0.103349	+	0.994645i	$0.532956\pi$
$194$	−2.79334	−0.200550
$195$	−9.29465	−0.665604
$196$	0	0
$197$	−2.00000	−0.142494	−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000	−0.142494	−0.0712470	+	0.997459i	$0.522698\pi$
$198$	−3.76260	−0.267396
$199$	−21.7609	−1.54259	−0.771294	−	0.636479i	$-0.780390\pi$
$199$	−21.7609	−1.54259	−0.771294	+	0.636479i	$0.780390\pi$
$200$	16.3745	1.15785
$201$	10.4911	0.739982
$202$	−39.9881	−2.81356
$203$	0	0
$204$	36.1224	2.52908
$205$	−2.62470	−0.183317
$206$	17.1633	1.19582
$207$	−3.18565	−0.221418
$208$	45.5033	3.15508
$209$	−2.61669	−0.181000
$210$	0	0
$211$	10.9173	0.751577	0.375789	−	0.926705i	$-0.377372\pi$
$211$	10.9173	0.751577	0.375789	+	0.926705i	$0.377372\pi$
$212$	−8.46258	−0.581213
$213$	15.8074	1.08310
$214$	−53.8350	−3.68008
$215$	−14.7631	−1.00684
$216$	8.66818	0.589795
$217$	0	0
$218$	−12.8189	−0.868205
$219$	−10.4540	−0.706417
$220$	19.1967	1.29424
$221$	24.4824	1.64687
$222$	−22.7781	−1.52877
$223$	−2.97331	−0.199107	−0.0995537	−	0.995032i	$-0.531741\pi$
$223$	−2.97331	−0.199107	−0.0995537	+	0.995032i	$0.531741\pi$
$224$	0	0
$225$	1.88903	0.125935
$226$	−10.7101	−0.712424
$227$	−25.9233	−1.72059	−0.860295	−	0.509796i	$-0.829721\pi$
$227$	−25.9233	−1.72059	−0.860295	+	0.509796i	$0.829721\pi$
$228$	9.76686	0.646826
$229$	−5.81487	−0.384257	−0.192129	−	0.981370i	$-0.561539\pi$
$229$	−5.81487	−0.384257	−0.192129	+	0.981370i	$0.561539\pi$
$230$	22.4746	1.48193
$231$	0	0
$232$	54.9268	3.60612
$233$	−29.4249	−1.92769	−0.963846	−	0.266459i	$-0.914146\pi$
$233$	−29.4249	−1.92769	−0.963846	+	0.266459i	$0.914146\pi$
$234$	9.51851	0.622245
$235$	−3.97892	−0.259556
$236$	−41.7335	−2.71662
$237$	−1.53398	−0.0996425
$238$	0	0
$239$	10.7362	0.694466	0.347233	−	0.937779i	$-0.387121\pi$
$239$	10.7362	0.694466	0.347233	+	0.937779i	$0.387121\pi$
$240$	−33.7262	−2.17702
$241$	−2.59912	−0.167424	−0.0837119	−	0.996490i	$-0.526678\pi$
$241$	−2.59912	−0.167424	−0.0837119	+	0.996490i	$0.526678\pi$
$242$	−24.3001	−1.56207
$243$	1.00000	0.0641500
$244$	44.9260	2.87609
$245$	0	0
$246$	2.68791	0.171375
$247$	6.61962	0.421196
$248$	−40.4712	−2.56993
$249$	10.8401	0.686966
$250$	21.9478	1.38810
$251$	3.52028	0.222198	0.111099	−	0.993809i	$-0.464563\pi$
$251$	3.52028	0.222198	0.111099	+	0.993809i	$0.464563\pi$
$252$	0	0
$253$	4.45934	0.280357
$254$	14.7480	0.925374
$255$	−18.1460	−1.13634
$256$	14.8367	0.927292
$257$	−4.65463	−0.290348	−0.145174	−	0.989406i	$-0.546374\pi$
$257$	−4.65463	−0.290348	−0.145174	+	0.989406i	$0.546374\pi$
$258$	15.1187	0.941249
$259$	0	0
$260$	−48.5634	−3.01177
$261$	6.33660	0.392226
$262$	−18.2460	−1.12724
$263$	−22.5213	−1.38872	−0.694360	−	0.719628i	$-0.744313\pi$
$263$	−22.5213	−1.38872	−0.694360	+	0.719628i	$0.744313\pi$
$264$	−12.1339	−0.746790
$265$	4.25115	0.261146
$266$	0	0
$267$	17.2254	1.05418
$268$	54.8145	3.34833
$269$	23.5217	1.43414	0.717072	−	0.696999i	$-0.245482\pi$
$269$	23.5217	1.43414	0.717072	+	0.696999i	$0.245482\pi$
$270$	−7.05495	−0.429351
$271$	−25.2940	−1.53650	−0.768252	−	0.640148i	$-0.778873\pi$
$271$	−25.2940	−1.53650	−0.768252	+	0.640148i	$0.778873\pi$
$272$	88.8361	5.38648
$273$	0	0
$274$	28.3547	1.71297
$275$	−2.64430	−0.159457
$276$	−16.6446	−1.00189
$277$	16.2239	0.974798	0.487399	−	0.873179i	$-0.337946\pi$
$277$	16.2239	0.974798	0.487399	+	0.873179i	$0.337946\pi$
$278$	−38.8417	−2.32957
$279$	−4.66894	−0.279522
$280$	0	0
$281$	−22.9900	−1.37147	−0.685734	−	0.727853i	$-0.740519\pi$
$281$	−22.9900	−1.37147	−0.685734	+	0.727853i	$0.740519\pi$
$282$	4.07475	0.242648
$283$	−13.3171	−0.791620	−0.395810	−	0.918332i	$-0.629536\pi$
$283$	−13.3171	−0.791620	−0.395810	+	0.918332i	$0.629536\pi$
$284$	82.5915	4.90090
$285$	−4.90635	−0.290627
$286$	−13.3242	−0.787877
$287$	0	0
$288$	17.2022	1.01365
$289$	30.7971	1.81160
$290$	−44.7045	−2.62514
$291$	−1.03922	−0.0609202
$292$	−54.6209	−3.19645
$293$	21.2544	1.24170	0.620849	−	0.783930i	$-0.286788\pi$
$293$	21.2544	1.24170	0.620849	+	0.783930i	$0.286788\pi$
$294$	0	0
$295$	20.9647	1.22061
$296$	−73.4565	−4.26957
$297$	−1.39982	−0.0812258
$298$	60.1275	3.48309
$299$	−11.2811	−0.652404
$300$	9.86994	0.569842
$301$	0	0
$302$	26.1349	1.50390
$303$	−14.8770	−0.854663
$304$	24.0197	1.37762
$305$	−22.5684	−1.29226
$306$	18.5830	1.06232
$307$	−23.3494	−1.33262	−0.666309	−	0.745675i	$-0.732127\pi$
$307$	−23.3494	−1.33262	−0.666309	+	0.745675i	$0.732127\pi$
$308$	0	0
$309$	6.38537	0.363251
$310$	32.9392	1.87082
$311$	30.4611	1.72729	0.863645	−	0.504100i	$-0.168176\pi$
$311$	30.4611	1.72729	0.863645	+	0.504100i	$0.168176\pi$
$312$	30.6960	1.73782
$313$	−22.6822	−1.28207	−0.641037	−	0.767510i	$-0.721496\pi$
$313$	−22.6822	−1.28207	−0.641037	+	0.767510i	$0.721496\pi$
$314$	42.4243	2.39414
$315$	0	0
$316$	−8.01484	−0.450870
$317$	22.4268	1.25961	0.629807	−	0.776752i	$-0.283134\pi$
$317$	22.4268	1.25961	0.629807	+	0.776752i	$0.283134\pi$
$318$	−4.35354	−0.244134
$319$	−8.87011	−0.496631
$320$	−53.9080	−3.01355
$321$	−20.0285	−1.11788
$322$	0	0
$323$	12.9235	0.719083
$324$	5.22488	0.290271
$325$	6.68949	0.371066
$326$	−4.93781	−0.273480
$327$	−4.76909	−0.263731
$328$	8.66818	0.478620
$329$	0	0
$330$	9.87567	0.543638
$331$	−17.2696	−0.949225	−0.474613	−	0.880195i	$-0.657412\pi$
$331$	−17.2696	−0.949225	−0.474613	+	0.880195i	$0.657412\pi$
$332$	56.6384	3.10844
$333$	−8.47427	−0.464387
$334$	−11.1230	−0.608623
$335$	−27.5358	−1.50444
$336$	0	0
$337$	−11.2919	−0.615111	−0.307555	−	0.951530i	$-0.599511\pi$
$337$	−11.2919	−0.615111	−0.307555	+	0.951530i	$0.599511\pi$
$338$	−1.23563	−0.0672097
$339$	−3.98454	−0.216410
$340$	−94.8104	−5.14181
$341$	6.53568	0.353927
$342$	5.02452	0.271695
$343$	0	0
$344$	48.7559	2.62874
$345$	8.36137	0.450161
$346$	7.67545	0.412635
$347$	12.5005	0.671061	0.335531	−	0.942029i	$-0.391084\pi$
$347$	12.5005	0.671061	0.335531	+	0.942029i	$0.391084\pi$
$348$	33.1080	1.77477
$349$	−30.9543	−1.65695	−0.828473	−	0.560029i	$-0.810790\pi$
$349$	−30.9543	−1.65695	−0.828473	+	0.560029i	$0.810790\pi$
$350$	0	0
$351$	3.54123	0.189017
$352$	−24.0799	−1.28347
$353$	−22.0000	−1.17094	−0.585470	−	0.810694i	$-0.699090\pi$
$353$	−22.0000	−1.17094	−0.585470	+	0.810694i	$0.699090\pi$
$354$	−21.4696	−1.14110
$355$	−41.4895	−2.20204
$356$	90.0006	4.77002
$357$	0	0
$358$	−59.9985	−3.17102
$359$	−32.0824	−1.69324	−0.846622	−	0.532195i	$-0.821367\pi$
$359$	−32.0824	−1.69324	−0.846622	+	0.532195i	$0.821367\pi$
$360$	−22.7513	−1.19910
$361$	−15.5057	−0.816090
$362$	−38.1256	−2.00384
$363$	−9.04050	−0.474503
$364$	0	0
$365$	27.4386	1.43620
$366$	23.1119	1.20808
$367$	−34.3183	−1.79140	−0.895700	−	0.444660i	$-0.853325\pi$
$367$	−34.3183	−1.79140	−0.895700	+	0.444660i	$0.853325\pi$
$368$	−40.9343	−2.13385
$369$	1.00000	0.0520579
$370$	59.7856	3.10810
$371$	0	0
$372$	−24.3946	−1.26480
$373$	23.0479	1.19337	0.596687	−	0.802474i	$-0.296483\pi$
$373$	23.0479	1.19337	0.596687	+	0.802474i	$0.296483\pi$
$374$	−26.0129	−1.34509
$375$	8.16535	0.421657
$376$	13.1406	0.677673
$377$	22.4394	1.15569
$378$	0	0
$379$	−23.7560	−1.22026	−0.610132	−	0.792299i	$-0.708884\pi$
$379$	−23.7560	−1.22026	−0.610132	+	0.792299i	$0.708884\pi$
$380$	−25.6350	−1.31505
$381$	5.48680	0.281097
$382$	−10.5253	−0.538519
$383$	11.0187	0.563028	0.281514	−	0.959557i	$-0.409163\pi$
$383$	11.0187	0.563028	0.281514	+	0.959557i	$0.409163\pi$
$384$	20.8021	1.06155
$385$	0	0
$386$	−7.71842	−0.392857
$387$	5.62470	0.285919
$388$	−5.42980	−0.275656
$389$	−22.3985	−1.13565	−0.567825	−	0.823149i	$-0.692215\pi$
$389$	−22.3985	−1.13565	−0.567825	+	0.823149i	$0.692215\pi$
$390$	−24.9832	−1.26507
$391$	−22.0242	−1.11381
$392$	0	0
$393$	−6.78817	−0.342418
$394$	−5.37583	−0.270830
$395$	4.02622	0.202581
$396$	−7.31389	−0.367537
$397$	−5.82984	−0.292591	−0.146296	−	0.989241i	$-0.546735\pi$
$397$	−5.82984	−0.292591	−0.146296	+	0.989241i	$0.546735\pi$
$398$	−58.4914	−2.93191
$399$	0	0
$400$	24.2732	1.21366
$401$	−26.7217	−1.33442	−0.667209	−	0.744871i	$-0.732511\pi$
$401$	−26.7217	−1.33442	−0.667209	+	0.744871i	$0.732511\pi$
$402$	28.1991	1.40644
$403$	−16.5338	−0.823607
$404$	−77.7306	−3.86724
$405$	−2.62470	−0.130422
$406$	0	0
$407$	11.8625	0.588000
$408$	59.9279	2.96687
$409$	24.9451	1.23346	0.616729	−	0.787176i	$-0.288457\pi$
$409$	24.9451	1.23346	0.616729	+	0.787176i	$0.288457\pi$
$410$	−7.05495	−0.348419
$411$	10.5490	0.520341
$412$	33.3628	1.64366
$413$	0	0
$414$	−8.56276	−0.420837
$415$	−28.4521	−1.39666
$416$	60.9168	2.98669
$417$	−14.4505	−0.707644
$418$	−7.03342	−0.344016
$419$	12.6042	0.615753	0.307877	−	0.951426i	$-0.400382\pi$
$419$	12.6042	0.615753	0.307877	+	0.951426i	$0.400382\pi$
$420$	0	0
$421$	−4.25143	−0.207202	−0.103601	−	0.994619i	$-0.533037\pi$
$421$	−4.25143	−0.207202	−0.103601	+	0.994619i	$0.533037\pi$
$422$	29.3447	1.42848
$423$	1.51595	0.0737082
$424$	−14.0396	−0.681824
$425$	13.0599	0.633498
$426$	42.4888	2.05859
$427$	0	0
$428$	−104.647	−5.05829
$429$	−4.95709	−0.239330
$430$	−39.6820	−1.91363
$431$	36.5221	1.75921	0.879605	−	0.475705i	$-0.157807\pi$
$431$	36.5221	1.75921	0.879605	+	0.475705i	$0.157807\pi$
$432$	12.8496	0.618225
$433$	−6.95602	−0.334285	−0.167143	−	0.985933i	$-0.553454\pi$
$433$	−6.95602	−0.334285	−0.167143	+	0.985933i	$0.553454\pi$
$434$	0	0
$435$	−16.6317	−0.797427
$436$	−24.9179	−1.19335
$437$	−5.95494	−0.284864
$438$	−28.0995	−1.34265
$439$	−20.8023	−0.992839	−0.496420	−	0.868083i	$-0.665352\pi$
$439$	−20.8023	−0.992839	−0.496420	+	0.868083i	$0.665352\pi$
$440$	31.8478	1.51828
$441$	0	0
$442$	65.8067	3.13010
$443$	−11.6904	−0.555429	−0.277714	−	0.960664i	$-0.589577\pi$
$443$	−11.6904	−0.555429	−0.277714	+	0.960664i	$0.589577\pi$
$444$	−44.2770	−2.10129
$445$	−45.2114	−2.14323
$446$	−7.99199	−0.378432
$447$	22.3696	1.05805
$448$	0	0
$449$	25.3476	1.19623	0.598113	−	0.801412i	$-0.295917\pi$
$449$	25.3476	1.19623	0.598113	+	0.801412i	$0.295917\pi$
$450$	5.07755	0.239358
$451$	−1.39982	−0.0659150
$452$	−20.8187	−0.979230
$453$	9.72314	0.456833
$454$	−69.6796	−3.27023
$455$	0	0
$456$	16.2034	0.758796
$457$	5.09099	0.238146	0.119073	−	0.992885i	$-0.462008\pi$
$457$	5.09099	0.238146	0.119073	+	0.992885i	$0.462008\pi$
$458$	−15.6299	−0.730335
$459$	6.91355	0.322697
$460$	43.6871	2.03692
$461$	2.07089	0.0964510	0.0482255	−	0.998836i	$-0.484643\pi$
$461$	2.07089	0.0964510	0.0482255	+	0.998836i	$0.484643\pi$
$462$	0	0
$463$	−12.4011	−0.576326	−0.288163	−	0.957581i	$-0.593044\pi$
$463$	−12.4011	−0.576326	−0.288163	+	0.957581i	$0.593044\pi$
$464$	81.4226	3.77995
$465$	12.2546	0.568291
$466$	−79.0917	−3.66385
$467$	−2.75506	−0.127489	−0.0637445	−	0.997966i	$-0.520304\pi$
$467$	−2.75506	−0.127489	−0.0637445	+	0.997966i	$0.520304\pi$
$468$	18.5025	0.855277
$469$	0	0
$470$	−10.6950	−0.493323
$471$	15.7834	0.727259
$472$	−69.2369	−3.18689
$473$	−7.87357	−0.362027
$474$	−4.12320	−0.189385
$475$	3.53116	0.162021
$476$	0	0
$477$	−1.61967	−0.0741597
$478$	28.8579	1.31993
$479$	30.3308	1.38585	0.692925	−	0.721010i	$-0.256322\pi$
$479$	30.3308	1.38585	0.692925	+	0.721010i	$0.256322\pi$
$480$	−45.1504	−2.06083
$481$	−30.0093	−1.36831
$482$	−6.98620	−0.318213
$483$	0	0
$484$	−47.2355	−2.14707
$485$	2.72764	0.123856
$486$	2.68791	0.121926
$487$	−2.63377	−0.119347	−0.0596737	−	0.998218i	$-0.519006\pi$
$487$	−2.63377	−0.119347	−0.0596737	+	0.998218i	$0.519006\pi$
$488$	74.5331	3.37396
$489$	−1.83704	−0.0830740
$490$	0	0
$491$	18.4155	0.831081	0.415540	−	0.909575i	$-0.363593\pi$
$491$	18.4155	0.831081	0.415540	+	0.909575i	$0.363593\pi$
$492$	5.22488	0.235556
$493$	43.8084	1.97303
$494$	17.7930	0.800543
$495$	3.67410	0.165139
$496$	−59.9939	−2.69381
$497$	0	0
$498$	29.1374	1.30568
$499$	−5.42275	−0.242756	−0.121378	−	0.992606i	$-0.538731\pi$
$499$	−5.42275	−0.242756	−0.121378	+	0.992606i	$0.538731\pi$
$500$	42.6629	1.90794
$501$	−4.13815	−0.184879
$502$	9.46221	0.422319
$503$	20.8039	0.927599	0.463799	−	0.885940i	$-0.346486\pi$
$503$	20.8039	0.927599	0.463799	+	0.885940i	$0.346486\pi$
$504$	0	0
$505$	39.0477	1.73760
$506$	11.9863	0.532857
$507$	−0.459700	−0.0204160
$508$	28.6678	1.27193
$509$	−17.0401	−0.755288	−0.377644	−	0.925951i	$-0.623266\pi$
$509$	−17.0401	−0.755288	−0.377644	+	0.925951i	$0.623266\pi$
$510$	−48.7748	−2.15978
$511$	0	0
$512$	−1.72450	−0.0762130
$513$	1.86930	0.0825316
$514$	−12.5112	−0.551847
$515$	−16.7597	−0.738518
$516$	29.3883	1.29375
$517$	−2.12206	−0.0933282
$518$	0	0
$519$	2.85554	0.125344
$520$	−80.5677	−3.53313
$521$	−15.9195	−0.697445	−0.348723	−	0.937226i	$-0.613384\pi$
$521$	−15.9195	−0.697445	−0.348723	+	0.937226i	$0.613384\pi$
$522$	17.0322	0.745481
$523$	−7.19609	−0.314663	−0.157332	−	0.987546i	$-0.550289\pi$
$523$	−7.19609	−0.314663	−0.157332	+	0.987546i	$0.550289\pi$
$524$	−35.4674	−1.54940
$525$	0	0
$526$	−60.5352	−2.63946
$527$	−32.2789	−1.40609
$528$	−17.9871	−0.782788
$529$	−12.8516	−0.558766
$530$	11.4267	0.496345
$531$	−7.98747	−0.346627
$532$	0	0
$533$	3.54123	0.153388
$534$	46.3004	2.00361
$535$	52.5688	2.27275
$536$	90.9385	3.92794
$537$	−22.3216	−0.963249
$538$	63.2243	2.72579
$539$	0	0
$540$	−13.7137	−0.590144
$541$	−31.5567	−1.35673	−0.678365	−	0.734725i	$-0.737311\pi$
$541$	−31.5567	−1.35673	−0.678365	+	0.734725i	$0.737311\pi$
$542$	−67.9882	−2.92034
$543$	−14.1841	−0.608697
$544$	118.928	5.09899
$545$	12.5174	0.536187
$546$	0	0
$547$	−23.5470	−1.00680	−0.503399	−	0.864054i	$-0.667918\pi$
$547$	−23.5470	−1.00680	−0.503399	+	0.864054i	$0.667918\pi$
$548$	55.1170	2.35448
$549$	8.59847	0.366974
$550$	−7.10766	−0.303071
$551$	11.8450	0.504615
$552$	−27.6138	−1.17532
$553$	0	0
$554$	43.6084	1.85274
$555$	22.2424	0.944136
$556$	−75.5021	−3.20200
$557$	29.3096	1.24189	0.620944	−	0.783855i	$-0.286749\pi$
$557$	29.3096	1.24189	0.620944	+	0.783855i	$0.286749\pi$
$558$	−12.5497	−0.531272
$559$	19.9183	0.842456
$560$	0	0
$561$	−9.67773	−0.408594
$562$	−61.7951	−2.60667
$563$	−3.72899	−0.157158	−0.0785790	−	0.996908i	$-0.525038\pi$
$563$	−3.72899	−0.157158	−0.0785790	+	0.996908i	$0.525038\pi$
$564$	7.92067	0.333520
$565$	10.4582	0.439980
$566$	−35.7952	−1.50459
$567$	0	0
$568$	137.021	5.74928
$569$	15.2846	0.640762	0.320381	−	0.947289i	$-0.396189\pi$
$569$	15.2846	0.640762	0.320381	+	0.947289i	$0.396189\pi$
$570$	−13.1878	−0.552377
$571$	33.7231	1.41127	0.705635	−	0.708576i	$-0.250662\pi$
$571$	33.7231	1.41127	0.705635	+	0.708576i	$0.250662\pi$
$572$	−25.9002	−1.08294
$573$	−3.91577	−0.163584
$574$	0	0
$575$	−6.01779	−0.250959
$576$	20.5388	0.855782
$577$	−9.52359	−0.396472	−0.198236	−	0.980154i	$-0.563521\pi$
$577$	−9.52359	−0.396472	−0.198236	+	0.980154i	$0.563521\pi$
$578$	82.7800	3.44319
$579$	−2.87153	−0.119337
$580$	−86.8984	−3.60826
$581$	0	0
$582$	−2.79334	−0.115788
$583$	2.26725	0.0938999
$584$	−90.6173	−3.74977
$585$	−9.29465	−0.384286
$586$	57.1301	2.36002
$587$	13.2200	0.545647	0.272824	−	0.962064i	$-0.412042\pi$
$587$	13.2200	0.545647	0.272824	+	0.962064i	$0.412042\pi$
$588$	0	0
$589$	−8.72766	−0.359617
$590$	56.3512	2.31994
$591$	−2.00000	−0.0822690
$592$	−108.891	−4.47538
$593$	12.5598	0.515768	0.257884	−	0.966176i	$-0.416975\pi$
$593$	12.5598	0.515768	0.257884	+	0.966176i	$0.416975\pi$
$594$	−3.76260	−0.154381
$595$	0	0
$596$	116.878	4.78753
$597$	−21.7609	−0.890614
$598$	−30.3227	−1.23999
$599$	26.0303	1.06357	0.531784	−	0.846880i	$-0.321522\pi$
$599$	26.0303	1.06357	0.531784	+	0.846880i	$0.321522\pi$
$600$	16.3745	0.668484
$601$	22.6891	0.925506	0.462753	−	0.886487i	$-0.346862\pi$
$601$	22.6891	0.925506	0.462753	+	0.886487i	$0.346862\pi$
$602$	0	0
$603$	10.4911	0.427229
$604$	50.8022	2.06711
$605$	23.7286	0.964704
$606$	−39.9881	−1.62441
$607$	10.5783	0.429361	0.214681	−	0.976684i	$-0.431129\pi$
$607$	10.5783	0.429361	0.214681	+	0.976684i	$0.431129\pi$
$608$	32.1560	1.30410
$609$	0	0
$610$	−60.6618	−2.45613
$611$	5.36834	0.217180
$612$	36.1224	1.46016
$613$	43.5248	1.75795	0.878975	−	0.476868i	$-0.158228\pi$
$613$	43.5248	1.75795	0.878975	+	0.476868i	$0.158228\pi$
$614$	−62.7611	−2.53283
$615$	−2.62470	−0.105838
$616$	0	0
$617$	19.2125	0.773466	0.386733	−	0.922192i	$-0.373604\pi$
$617$	19.2125	0.773466	0.386733	+	0.922192i	$0.373604\pi$
$618$	17.1633	0.690410
$619$	−11.4779	−0.461335	−0.230667	−	0.973033i	$-0.574091\pi$
$619$	−11.4779	−0.461335	−0.230667	+	0.973033i	$0.574091\pi$
$620$	64.0285	2.57145
$621$	−3.18565	−0.127836
$622$	81.8768	3.28296
$623$	0	0
$624$	45.5033	1.82159
$625$	−30.8767	−1.23507
$626$	−60.9678	−2.43676
$627$	−2.61669	−0.104500
$628$	82.4661	3.29076
$629$	−58.5872	−2.33603
$630$	0	0
$631$	16.8067	0.669062	0.334531	−	0.942385i	$-0.391422\pi$
$631$	16.8067	0.669062	0.334531	+	0.942385i	$0.391422\pi$
$632$	−13.2968	−0.528918
$633$	10.9173	0.433923
$634$	60.2812	2.39407
$635$	−14.4012	−0.571493
$636$	−8.46258	−0.335563
$637$	0	0
$638$	−23.8421	−0.943917
$639$	15.8074	0.625330
$640$	−54.5992	−2.15822
$641$	−2.66999	−0.105458	−0.0527290	−	0.998609i	$-0.516792\pi$
$641$	−2.66999	−0.105458	−0.0527290	+	0.998609i	$0.516792\pi$
$642$	−53.8350	−2.12470
$643$	16.9383	0.667982	0.333991	−	0.942576i	$-0.391604\pi$
$643$	16.9383	0.667982	0.333991	+	0.942576i	$0.391604\pi$
$644$	0	0
$645$	−14.7631	−0.581297
$646$	34.7372	1.36672
$647$	50.5412	1.98698	0.993491	−	0.113914i	$-0.0363387\pi$
$647$	50.5412	1.98698	0.993491	+	0.113914i	$0.0363387\pi$
$648$	8.66818	0.340518
$649$	11.1810	0.438894
$650$	17.9808	0.705263
$651$	0	0
$652$	−9.59832	−0.375899
$653$	4.44759	0.174048	0.0870238	−	0.996206i	$-0.472264\pi$
$653$	4.44759	0.174048	0.0870238	+	0.996206i	$0.472264\pi$
$654$	−12.8189	−0.501259
$655$	17.8169	0.696164
$656$	12.8496	0.501691
$657$	−10.4540	−0.407850
$658$	0	0
$659$	−26.3723	−1.02732	−0.513660	−	0.857994i	$-0.671711\pi$
$659$	−26.3723	−1.02732	−0.513660	+	0.857994i	$0.671711\pi$
$660$	19.1967	0.747232
$661$	9.17903	0.357023	0.178511	−	0.983938i	$-0.442872\pi$
$661$	9.17903	0.357023	0.178511	+	0.983938i	$0.442872\pi$
$662$	−46.4193	−1.80414
$663$	24.4824	0.950820
$664$	93.9644	3.64652
$665$	0	0
$666$	−22.7781	−0.882633
$667$	−20.1862	−0.781614
$668$	−21.6213	−0.836554
$669$	−2.97331	−0.114955
$670$	−74.0140	−2.85941
$671$	−12.0363	−0.464657
$672$	0	0
$673$	−25.4678	−0.981713	−0.490857	−	0.871240i	$-0.663316\pi$
$673$	−25.4678	−0.981713	−0.490857	+	0.871240i	$0.663316\pi$
$674$	−30.3517	−1.16910
$675$	1.88903	0.0727088
$676$	−2.40188	−0.0923799
$677$	13.5727	0.521642	0.260821	−	0.965387i	$-0.416007\pi$
$677$	13.5727	0.521642	0.260821	+	0.965387i	$0.416007\pi$
$678$	−10.7101	−0.411318
$679$	0	0
$680$	−157.293	−6.03189
$681$	−25.9233	−0.993383
$682$	17.5673	0.672688
$683$	−6.57535	−0.251599	−0.125799	−	0.992056i	$-0.540150\pi$
$683$	−6.57535	−0.251599	−0.125799	+	0.992056i	$0.540150\pi$
$684$	9.76686	0.373445
$685$	−27.6878	−1.05790
$686$	0	0
$687$	−5.81487	−0.221851
$688$	72.2749	2.75546
$689$	−5.73563	−0.218510
$690$	22.4746	0.855595
$691$	17.3732	0.660909	0.330455	−	0.943822i	$-0.392798\pi$
$691$	17.3732	0.660909	0.330455	+	0.943822i	$0.392798\pi$
$692$	14.9199	0.567168
$693$	0	0
$694$	33.6002	1.27545
$695$	37.9282	1.43870
$696$	54.9268	2.08200
$697$	6.91355	0.261869
$698$	−83.2025	−3.14926
$699$	−29.4249	−1.11295
$700$	0	0
$701$	−30.4807	−1.15124	−0.575619	−	0.817718i	$-0.695239\pi$
$701$	−30.4807	−1.15124	−0.575619	+	0.817718i	$0.695239\pi$
$702$	9.51851	0.359253
$703$	−15.8410	−0.597453
$704$	−28.7506	−1.08358
$705$	−3.97892	−0.149855
$706$	−59.1340	−2.22554
$707$	0	0
$708$	−41.7335	−1.56844
$709$	−19.0530	−0.715550	−0.357775	−	0.933808i	$-0.616465\pi$
$709$	−19.0530	−0.715550	−0.357775	+	0.933808i	$0.616465\pi$
$710$	−111.520	−4.18528
$711$	−1.53398	−0.0575286
$712$	149.313	5.59574
$713$	14.8736	0.557022
$714$	0	0
$715$	13.0108	0.486578
$716$	−116.628	−4.35858
$717$	10.7362	0.400950
$718$	−86.2347	−3.21825
$719$	−50.5857	−1.88653	−0.943265	−	0.332041i	$-0.892263\pi$
$719$	−50.5857	−1.88653	−0.943265	+	0.332041i	$0.892263\pi$
$720$	−33.7262	−1.25690
$721$	0	0
$722$	−41.6780	−1.55109
$723$	−2.59912	−0.0966622
$724$	−74.1101	−2.75428
$725$	11.9700	0.444556
$726$	−24.3001	−0.901861
$727$	17.6776	0.655627	0.327813	−	0.944742i	$-0.393688\pi$
$727$	17.6776	0.655627	0.327813	+	0.944742i	$0.393688\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	73.7526	2.72971
$731$	38.8866	1.43827
$732$	44.9260	1.66051
$733$	−1.97940	−0.0731107	−0.0365554	−	0.999332i	$-0.511639\pi$
$733$	−1.97940	−0.0731107	−0.0365554	+	0.999332i	$0.511639\pi$
$734$	−92.2445	−3.40481
$735$	0	0
$736$	−54.8001	−2.01996
$737$	−14.6856	−0.540951
$738$	2.68791	0.0989434
$739$	−0.787113	−0.0289544	−0.0144772	−	0.999895i	$-0.504608\pi$
$739$	−0.787113	−0.0289544	−0.0144772	+	0.999895i	$0.504608\pi$
$740$	116.214	4.27210
$741$	6.61962	0.243178
$742$	0	0
$743$	2.43797	0.0894403	0.0447201	−	0.999000i	$-0.485760\pi$
$743$	2.43797	0.0894403	0.0447201	+	0.999000i	$0.485760\pi$
$744$	−40.4712	−1.48375
$745$	−58.7134	−2.15109
$746$	61.9507	2.26818
$747$	10.8401	0.396620
$748$	−50.5649	−1.84884
$749$	0	0
$750$	21.9478	0.801419
$751$	21.5459	0.786221	0.393111	−	0.919491i	$-0.371399\pi$
$751$	21.5459	0.786221	0.393111	+	0.919491i	$0.371399\pi$
$752$	19.4793	0.710339
$753$	3.52028	0.128286
$754$	60.3151	2.19654
$755$	−25.5203	−0.928778
$756$	0	0
$757$	37.4266	1.36029	0.680147	−	0.733076i	$-0.261916\pi$
$757$	37.4266	1.36029	0.680147	+	0.733076i	$0.261916\pi$
$758$	−63.8541	−2.31929
$759$	4.45934	0.161864
$760$	−42.5291	−1.54269
$761$	18.6397	0.675687	0.337843	−	0.941202i	$-0.390303\pi$
$761$	18.6397	0.675687	0.337843	+	0.941202i	$0.390303\pi$
$762$	14.7480	0.534265
$763$	0	0
$764$	−20.4594	−0.740196
$765$	−18.1460	−0.656069
$766$	29.6172	1.07011
$767$	−28.2855	−1.02133
$768$	14.8367	0.535372
$769$	34.0439	1.22765	0.613827	−	0.789441i	$-0.289629\pi$
$769$	34.0439	1.22765	0.613827	+	0.789441i	$0.289629\pi$
$770$	0	0
$771$	−4.65463	−0.167632
$772$	−15.0034	−0.539983
$773$	−13.5632	−0.487835	−0.243918	−	0.969796i	$-0.578433\pi$
$773$	−13.5632	−0.487835	−0.243918	+	0.969796i	$0.578433\pi$
$774$	15.1187	0.543430
$775$	−8.81977	−0.316815
$776$	−9.00816	−0.323374
$777$	0	0
$778$	−60.2053	−2.15847
$779$	1.86930	0.0669746
$780$	−48.5634	−1.73885
$781$	−22.1275	−0.791783
$782$	−59.1990	−2.11695
$783$	6.33660	0.226452
$784$	0	0
$785$	−41.4265	−1.47858
$786$	−18.2460	−0.650814
$787$	−7.10873	−0.253399	−0.126699	−	0.991941i	$-0.540438\pi$
$787$	−7.10873	−0.253399	−0.126699	+	0.991941i	$0.540438\pi$
$788$	−10.4498	−0.372257
$789$	−22.5213	−0.801778
$790$	10.8221	0.385034
$791$	0	0
$792$	−12.1339	−0.431159
$793$	30.4492	1.08128
$794$	−15.6701	−0.556111
$795$	4.25115	0.150773
$796$	−113.698	−4.02992
$797$	19.4787	0.689972	0.344986	−	0.938608i	$-0.387884\pi$
$797$	19.4787	0.689972	0.344986	+	0.938608i	$0.387884\pi$
$798$	0	0
$799$	10.4806	0.370777
$800$	32.4954	1.14889
$801$	17.2254	0.608629
$802$	−71.8256	−2.53625
$803$	14.6337	0.516414
$804$	54.8145	1.93316
$805$	0	0
$806$	−44.4414	−1.56538
$807$	23.5217	0.828004
$808$	−128.957	−4.53668
$809$	−18.2309	−0.640966	−0.320483	−	0.947254i	$-0.603845\pi$
$809$	−18.2309	−0.640966	−0.320483	+	0.947254i	$0.603845\pi$
$810$	−7.05495	−0.247886
$811$	−26.7156	−0.938112	−0.469056	−	0.883168i	$-0.655406\pi$
$811$	−26.7156	−0.938112	−0.469056	+	0.883168i	$0.655406\pi$
$812$	0	0
$813$	−25.2940	−0.887101
$814$	31.8852	1.11758
$815$	4.82168	0.168896
$816$	88.8361	3.10989
$817$	10.5142	0.367847
$818$	67.0504	2.34436
$819$	0	0
$820$	−13.7137	−0.478904
$821$	29.4191	1.02673	0.513366	−	0.858170i	$-0.328398\pi$
$821$	29.4191	1.02673	0.513366	+	0.858170i	$0.328398\pi$
$822$	28.3547	0.988982
$823$	11.8565	0.413292	0.206646	−	0.978416i	$-0.433745\pi$
$823$	11.8565	0.413292	0.206646	+	0.978416i	$0.433745\pi$
$824$	55.3495	1.92819
$825$	−2.64430	−0.0920628
$826$	0	0
$827$	53.7082	1.86762	0.933809	−	0.357771i	$-0.116463\pi$
$827$	53.7082	1.86762	0.933809	+	0.357771i	$0.116463\pi$
$828$	−16.6446	−0.578441
$829$	−13.8687	−0.481678	−0.240839	−	0.970565i	$-0.577423\pi$
$829$	−13.8687	−0.481678	−0.240839	+	0.970565i	$0.577423\pi$
$830$	−76.4767	−2.65455
$831$	16.2239	0.562800
$832$	72.7325	2.52154
$833$	0	0
$834$	−38.8417	−1.34498
$835$	10.8614	0.375874
$836$	−13.6719	−0.472851
$837$	−4.66894	−0.161382
$838$	33.8789	1.17033
$839$	−19.0013	−0.655998	−0.327999	−	0.944678i	$-0.606374\pi$
$839$	−19.0013	−0.655998	−0.327999	+	0.944678i	$0.606374\pi$
$840$	0	0
$841$	11.1526	0.384571
$842$	−11.4275	−0.393817
$843$	−22.9900	−0.791817
$844$	57.0415	1.96345
$845$	1.20657	0.0415074
$846$	4.07475	0.140093
$847$	0	0
$848$	−20.8121	−0.714690
$849$	−13.3171	−0.457042
$850$	35.1039	1.20405
$851$	26.9961	0.925414
$852$	82.5915	2.82954
$853$	4.95243	0.169568	0.0847840	−	0.996399i	$-0.472980\pi$
$853$	4.95243	0.169568	0.0847840	+	0.996399i	$0.472980\pi$
$854$	0	0
$855$	−4.90635	−0.167793
$856$	−173.611	−5.93391
$857$	46.6695	1.59420	0.797100	−	0.603847i	$-0.206366\pi$
$857$	46.6695	1.59420	0.797100	+	0.603847i	$0.206366\pi$
$858$	−13.3242	−0.454881
$859$	13.6354	0.465233	0.232617	−	0.972568i	$-0.425271\pi$
$859$	13.6354	0.465233	0.232617	+	0.972568i	$0.425271\pi$
$860$	−77.1355	−2.63030
$861$	0	0
$862$	98.1683	3.34363
$863$	−29.4944	−1.00400	−0.502000	−	0.864868i	$-0.667402\pi$
$863$	−29.4944	−1.00400	−0.502000	+	0.864868i	$0.667402\pi$
$864$	17.2022	0.585229
$865$	−7.49493	−0.254835
$866$	−18.6972	−0.635356
$867$	30.7971	1.04593
$868$	0	0
$869$	2.14729	0.0728419
$870$	−44.7045	−1.51562
$871$	37.1512	1.25882
$872$	−41.3393	−1.39993
$873$	−1.03922	−0.0351723
$874$	−16.0064	−0.541424
$875$	0	0
$876$	−54.6209	−1.84547
$877$	1.71017	0.0577483	0.0288742	−	0.999583i	$-0.490808\pi$
$877$	1.71017	0.0577483	0.0288742	+	0.999583i	$0.490808\pi$
$878$	−55.9147	−1.88703
$879$	21.2544	0.716894
$880$	47.2107	1.59147
$881$	−4.55585	−0.153490	−0.0767452	−	0.997051i	$-0.524453\pi$
$881$	−4.55585	−0.153490	−0.0767452	+	0.997051i	$0.524453\pi$
$882$	0	0
$883$	−39.9300	−1.34375	−0.671875	−	0.740664i	$-0.734511\pi$
$883$	−39.9300	−1.34375	−0.671875	+	0.740664i	$0.734511\pi$
$884$	127.918	4.30234
$885$	20.9647	0.704720
$886$	−31.4228	−1.05567
$887$	−17.6170	−0.591519	−0.295760	−	0.955262i	$-0.595573\pi$
$887$	−17.6170	−0.591519	−0.295760	+	0.955262i	$0.595573\pi$
$888$	−73.4565	−2.46504
$889$	0	0
$890$	−121.524	−4.07351
$891$	−1.39982	−0.0468958
$892$	−15.5352	−0.520156
$893$	2.83377	0.0948286
$894$	60.1275	2.01097
$895$	58.5874	1.95836
$896$	0	0
$897$	−11.2811	−0.376666
$898$	68.1320	2.27360
$899$	−29.5852	−0.986723
$900$	9.86994	0.328998
$901$	−11.1977	−0.373049
$902$	−3.76260	−0.125281
$903$	0	0
$904$	−34.5387	−1.14874
$905$	37.2289	1.23753
$906$	26.1349	0.868275
$907$	27.4925	0.912873	0.456436	−	0.889756i	$-0.349126\pi$
$907$	27.4925	0.912873	0.456436	+	0.889756i	$0.349126\pi$
$908$	−135.446	−4.49494
$909$	−14.8770	−0.493440
$910$	0	0
$911$	38.2298	1.26661	0.633305	−	0.773902i	$-0.281698\pi$
$911$	38.2298	1.26661	0.633305	+	0.773902i	$0.281698\pi$
$912$	24.0197	0.795372
$913$	−15.1743	−0.502195
$914$	13.6841	0.452631
$915$	−22.5684	−0.746088
$916$	−30.3820	−1.00385
$917$	0	0
$918$	18.5830	0.613331
$919$	29.9823	0.989025	0.494512	−	0.869171i	$-0.335347\pi$
$919$	29.9823	0.989025	0.494512	+	0.869171i	$0.335347\pi$
$920$	72.4779	2.38953
$921$	−23.3494	−0.769388
$922$	5.56638	0.183319
$923$	55.9775	1.84252
$924$	0	0
$925$	−16.0081	−0.526344
$926$	−33.3329	−1.09539
$927$	6.38537	0.209723
$928$	109.003	3.57821
$929$	49.5037	1.62416	0.812081	−	0.583544i	$-0.198335\pi$
$929$	49.5037	1.62416	0.812081	+	0.583544i	$0.198335\pi$
$930$	32.9392	1.08012
$931$	0	0
$932$	−153.742	−5.03598
$933$	30.4611	0.997251
$934$	−7.40536	−0.242311
$935$	25.4011	0.830704
$936$	30.6960	1.00333
$937$	35.7948	1.16937	0.584683	−	0.811262i	$-0.301219\pi$
$937$	35.7948	1.16937	0.584683	+	0.811262i	$0.301219\pi$
$938$	0	0
$939$	−22.6822	−0.740206
$940$	−20.7893	−0.678074
$941$	20.5683	0.670507	0.335253	−	0.942128i	$-0.391178\pi$
$941$	20.5683	0.670507	0.335253	+	0.942128i	$0.391178\pi$
$942$	42.4243	1.38226
$943$	−3.18565	−0.103739
$944$	−102.636	−3.34050
$945$	0	0
$946$	−21.1635	−0.688083
$947$	4.67416	0.151890	0.0759448	−	0.997112i	$-0.475803\pi$
$947$	4.67416	0.151890	0.0759448	+	0.997112i	$0.475803\pi$
$948$	−8.01484	−0.260310
$949$	−37.0201	−1.20172
$950$	9.49146	0.307944
$951$	22.4268	0.727238
$952$	0	0
$953$	−13.1277	−0.425249	−0.212624	−	0.977134i	$-0.568201\pi$
$953$	−13.1277	−0.425249	−0.212624	+	0.977134i	$0.568201\pi$
$954$	−4.35354	−0.140951
$955$	10.2777	0.332579
$956$	56.0952	1.81425
$957$	−8.87011	−0.286730
$958$	81.5265	2.63400
$959$	0	0
$960$	−53.9080	−1.73987
$961$	−9.20098	−0.296806
$962$	−80.6624	−2.60066
$963$	−20.0285	−0.645411
$964$	−13.5801	−0.437384
$965$	7.53689	0.242621
$966$	0	0
$967$	−30.1537	−0.969677	−0.484839	−	0.874604i	$-0.661122\pi$
$967$	−30.1537	−0.969677	−0.484839	+	0.874604i	$0.661122\pi$
$968$	−78.3647	−2.51874
$969$	12.9235	0.415163
$970$	7.33166	0.235405
$971$	42.3620	1.35946	0.679731	−	0.733461i	$-0.262096\pi$
$971$	42.3620	1.35946	0.679731	+	0.733461i	$0.262096\pi$
$972$	5.22488	0.167588
$973$	0	0
$974$	−7.07934	−0.226837
$975$	6.68949	0.214235
$976$	110.487	3.53659
$977$	−57.0503	−1.82520	−0.912600	−	0.408853i	$-0.865929\pi$
$977$	−57.0503	−1.82520	−0.912600	+	0.408853i	$0.865929\pi$
$978$	−4.93781	−0.157894
$979$	−24.1125	−0.770638
$980$	0	0
$981$	−4.76909	−0.152265
$982$	49.4993	1.57959
$983$	−11.1579	−0.355881	−0.177940	−	0.984041i	$-0.556943\pi$
$983$	−11.1579	−0.355881	−0.177940	+	0.984041i	$0.556943\pi$
$984$	8.66818	0.276332
$985$	5.24939	0.167260
$986$	117.753	3.75003
$987$	0	0
$988$	34.5867	1.10035
$989$	−17.9183	−0.569770
$990$	9.87567	0.313869
$991$	−34.8764	−1.10789	−0.553943	−	0.832555i	$-0.686877\pi$
$991$	−34.8764	−1.10789	−0.553943	+	0.832555i	$0.686877\pi$
$992$	−80.3159	−2.55003
$993$	−17.2696	−0.548036
$994$	0	0
$995$	57.1157	1.81069
$996$	56.6384	1.79466
$997$	−26.9857	−0.854646	−0.427323	−	0.904099i	$-0.640543\pi$
$997$	−26.9857	−0.854646	−0.427323	+	0.904099i	$0.640543\pi$
$998$	−14.5759	−0.461392
$999$	−8.47427	−0.268114

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.x.1.5		5
7.6	odd	2		861.2.a.k.1.5	✓	5
21.20	even	2		2583.2.a.q.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.a.k.1.5	✓	5	7.6	odd	2
2583.2.a.q.1.1		5	21.20	even	2
6027.2.a.x.1.5		5	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:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q+2.68791 q^{2} +1.00000 q^{3} +5.22488 q^{4} -2.62470 q^{5} +2.68791 q^{6} +8.66818 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.68791 q^{2} +1.00000 q^{3} +5.22488 q^{4} -2.62470 q^{5} +2.68791 q^{6} +8.66818 q^{8} +1.00000 q^{9} -7.05495 q^{10} -1.39982 q^{11} +5.22488 q^{12} +3.54123 q^{13} -2.62470 q^{15} +12.8496 q^{16} +6.91355 q^{17} +2.68791 q^{18} +1.86930 q^{19} -13.7137 q^{20} -3.76260 q^{22} -3.18565 q^{23} +8.66818 q^{24} +1.88903 q^{25} +9.51851 q^{26} +1.00000 q^{27} +6.33660 q^{29} -7.05495 q^{30} -4.66894 q^{31} +17.2022 q^{32} -1.39982 q^{33} +18.5830 q^{34} +5.22488 q^{36} -8.47427 q^{37} +5.02452 q^{38} +3.54123 q^{39} -22.7513 q^{40} +1.00000 q^{41} +5.62470 q^{43} -7.31389 q^{44} -2.62470 q^{45} -8.56276 q^{46} +1.51595 q^{47} +12.8496 q^{48} +5.07755 q^{50} +6.91355 q^{51} +18.5025 q^{52} -1.61967 q^{53} +2.68791 q^{54} +3.67410 q^{55} +1.86930 q^{57} +17.0322 q^{58} -7.98747 q^{59} -13.7137 q^{60} +8.59847 q^{61} -12.5497 q^{62} +20.5388 q^{64} -9.29465 q^{65} -3.76260 q^{66} +10.4911 q^{67} +36.1224 q^{68} -3.18565 q^{69} +15.8074 q^{71} +8.66818 q^{72} -10.4540 q^{73} -22.7781 q^{74} +1.88903 q^{75} +9.76686 q^{76} +9.51851 q^{78} -1.53398 q^{79} -33.7262 q^{80} +1.00000 q^{81} +2.68791 q^{82} +10.8401 q^{83} -18.1460 q^{85} +15.1187 q^{86} +6.33660 q^{87} -12.1339 q^{88} +17.2254 q^{89} -7.05495 q^{90} -16.6446 q^{92} -4.66894 q^{93} +4.07475 q^{94} -4.90635 q^{95} +17.2022 q^{96} -1.03922 q^{97} -1.39982 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 3 q^{2} + 5 q^{3} + 11 q^{4} + 9 q^{5} + 3 q^{6} + 9 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + 3 * q^2 + 5 * q^3 + 11 * q^4 + 9 * q^5 + 3 * q^6 + 9 * q^8 + 5 * q^9	\( 5 q + 3 q^{2} + 5 q^{3} + 11 q^{4} + 9 q^{5} + 3 q^{6} + 9 q^{8} + 5 q^{9} - 9 q^{10} + 11 q^{12} + 3 q^{13} + 9 q^{15} + 27 q^{16} + 16 q^{17} + 3 q^{18} - 4 q^{19} + 7 q^{20} - 6 q^{22} - 3 q^{23} + 9 q^{24} + 20 q^{25} - 17 q^{26} + 5 q^{27} + 13 q^{29} - 9 q^{30} + 4 q^{31} + 21 q^{32} + 4 q^{34} + 11 q^{36} + 17 q^{37} - 4 q^{38} + 3 q^{39} - 37 q^{40} + 5 q^{41} + 6 q^{43} + 32 q^{44} + 9 q^{45} + 27 q^{46} + 15 q^{47} + 27 q^{48} - 14 q^{50} + 16 q^{51} + 17 q^{52} + 11 q^{53} + 3 q^{54} + 16 q^{55} - 4 q^{57} + 9 q^{58} - 12 q^{59} + 7 q^{60} - 12 q^{61} - 8 q^{62} + 19 q^{64} - 19 q^{65} - 6 q^{66} + 11 q^{67} + 28 q^{68} - 3 q^{69} + 18 q^{71} + 9 q^{72} - 12 q^{73} - 27 q^{74} + 20 q^{75} + 26 q^{76} - 17 q^{78} + 23 q^{79} + 7 q^{80} + 5 q^{81} + 3 q^{82} + 2 q^{83} + 20 q^{85} + 18 q^{86} + 13 q^{87} - 22 q^{88} + 28 q^{89} - 9 q^{90} - 7 q^{92} + 4 q^{93} + 3 q^{94} - 10 q^{95} + 21 q^{96} - 3 q^{97}+O(q^{100}) \) 5 * q + 3 * q^2 + 5 * q^3 + 11 * q^4 + 9 * q^5 + 3 * q^6 + 9 * q^8 + 5 * q^9 - 9 * q^10 + 11 * q^12 + 3 * q^13 + 9 * q^15 + 27 * q^16 + 16 * q^17 + 3 * q^18 - 4 * q^19 + 7 * q^20 - 6 * q^22 - 3 * q^23 + 9 * q^24 + 20 * q^25 - 17 * q^26 + 5 * q^27 + 13 * q^29 - 9 * q^30 + 4 * q^31 + 21 * q^32 + 4 * q^34 + 11 * q^36 + 17 * q^37 - 4 * q^38 + 3 * q^39 - 37 * q^40 + 5 * q^41 + 6 * q^43 + 32 * q^44 + 9 * q^45 + 27 * q^46 + 15 * q^47 + 27 * q^48 - 14 * q^50 + 16 * q^51 + 17 * q^52 + 11 * q^53 + 3 * q^54 + 16 * q^55 - 4 * q^57 + 9 * q^58 - 12 * q^59 + 7 * q^60 - 12 * q^61 - 8 * q^62 + 19 * q^64 - 19 * q^65 - 6 * q^66 + 11 * q^67 + 28 * q^68 - 3 * q^69 + 18 * q^71 + 9 * q^72 - 12 * q^73 - 27 * q^74 + 20 * q^75 + 26 * q^76 - 17 * q^78 + 23 * q^79 + 7 * q^80 + 5 * q^81 + 3 * q^82 + 2 * q^83 + 20 * q^85 + 18 * q^86 + 13 * q^87 - 22 * q^88 + 28 * q^89 - 9 * q^90 - 7 * q^92 + 4 * q^93 + 3 * q^94 - 10 * q^95 + 21 * q^96 - 3 * q^97

Introduction

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