LMFDB - Embedded newform 2541.2.a.x.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2541,2,Mod(1,2541)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2541, 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("2541.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2541 = 3 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2541.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:	$20.2899871536$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 231)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	2541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.61803 q^{2} -1.00000 q^{3} +0.618034 q^{4} +0.618034 q^{5} -1.61803 q^{6} +1.00000 q^{7} -2.23607 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.61803 q^{2} -1.00000 q^{3} +0.618034 q^{4} +0.618034 q^{5} -1.61803 q^{6} +1.00000 q^{7} -2.23607 q^{8} +1.00000 q^{9} +1.00000 q^{10} -0.618034 q^{12} +0.236068 q^{13} +1.61803 q^{14} -0.618034 q^{15} -4.85410 q^{16} -5.47214 q^{17} +1.61803 q^{18} +2.47214 q^{19} +0.381966 q^{20} -1.00000 q^{21} -7.70820 q^{23} +2.23607 q^{24} -4.61803 q^{25} +0.381966 q^{26} -1.00000 q^{27} +0.618034 q^{28} -4.23607 q^{29} -1.00000 q^{30} +3.00000 q^{31} -3.38197 q^{32} -8.85410 q^{34} +0.618034 q^{35} +0.618034 q^{36} +6.00000 q^{37} +4.00000 q^{38} -0.236068 q^{39} -1.38197 q^{40} +3.14590 q^{41} -1.61803 q^{42} +2.52786 q^{43} +0.618034 q^{45} -12.4721 q^{46} -11.8541 q^{47} +4.85410 q^{48} +1.00000 q^{49} -7.47214 q^{50} +5.47214 q^{51} +0.145898 q^{52} +7.56231 q^{53} -1.61803 q^{54} -2.23607 q^{56} -2.47214 q^{57} -6.85410 q^{58} -2.38197 q^{59} -0.381966 q^{60} -9.94427 q^{61} +4.85410 q^{62} +1.00000 q^{63} +4.23607 q^{64} +0.145898 q^{65} +8.76393 q^{67} -3.38197 q^{68} +7.70820 q^{69} +1.00000 q^{70} -13.4721 q^{71} -2.23607 q^{72} -9.61803 q^{73} +9.70820 q^{74} +4.61803 q^{75} +1.52786 q^{76} -0.381966 q^{78} -5.09017 q^{79} -3.00000 q^{80} +1.00000 q^{81} +5.09017 q^{82} +0.472136 q^{83} -0.618034 q^{84} -3.38197 q^{85} +4.09017 q^{86} +4.23607 q^{87} -14.3262 q^{89} +1.00000 q^{90} +0.236068 q^{91} -4.76393 q^{92} -3.00000 q^{93} -19.1803 q^{94} +1.52786 q^{95} +3.38197 q^{96} -18.7082 q^{97} +1.61803 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 2 q^{3} - q^{4} - q^{5} - q^{6} + 2 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q + q^2 - 2 * q^3 - q^4 - q^5 - q^6 + 2 * q^7 + 2 * q^9	$ 2 q + q^{2} - 2 q^{3} - q^{4} - q^{5} - q^{6} + 2 q^{7} + 2 q^{9} + 2 q^{10} + q^{12} - 4 q^{13} + q^{14} + q^{15} - 3 q^{16} - 2 q^{17} + q^{18} - 4 q^{19} + 3 q^{20} - 2 q^{21} - 2 q^{23} - 7 q^{25} + 3 q^{26} - 2 q^{27} - q^{28} - 4 q^{29} - 2 q^{30} + 6 q^{31} - 9 q^{32} - 11 q^{34} - q^{35} - q^{36} + 12 q^{37} + 8 q^{38} + 4 q^{39} - 5 q^{40} + 13 q^{41} - q^{42} + 14 q^{43} - q^{45} - 16 q^{46} - 17 q^{47} + 3 q^{48} + 2 q^{49} - 6 q^{50} + 2 q^{51} + 7 q^{52} - 5 q^{53} - q^{54} + 4 q^{57} - 7 q^{58} - 7 q^{59} - 3 q^{60} - 2 q^{61} + 3 q^{62} + 2 q^{63} + 4 q^{64} + 7 q^{65} + 22 q^{67} - 9 q^{68} + 2 q^{69} + 2 q^{70} - 18 q^{71} - 17 q^{73} + 6 q^{74} + 7 q^{75} + 12 q^{76} - 3 q^{78} + q^{79} - 6 q^{80} + 2 q^{81} - q^{82} - 8 q^{83} + q^{84} - 9 q^{85} - 3 q^{86} + 4 q^{87} - 13 q^{89} + 2 q^{90} - 4 q^{91} - 14 q^{92} - 6 q^{93} - 16 q^{94} + 12 q^{95} + 9 q^{96} - 24 q^{97} + q^{98}+O(q^{100}) $ 2 * q + q^2 - 2 * q^3 - q^4 - q^5 - q^6 + 2 * q^7 + 2 * q^9 + 2 * q^10 + q^12 - 4 * q^13 + q^14 + q^15 - 3 * q^16 - 2 * q^17 + q^18 - 4 * q^19 + 3 * q^20 - 2 * q^21 - 2 * q^23 - 7 * q^25 + 3 * q^26 - 2 * q^27 - q^28 - 4 * q^29 - 2 * q^30 + 6 * q^31 - 9 * q^32 - 11 * q^34 - q^35 - q^36 + 12 * q^37 + 8 * q^38 + 4 * q^39 - 5 * q^40 + 13 * q^41 - q^42 + 14 * q^43 - q^45 - 16 * q^46 - 17 * q^47 + 3 * q^48 + 2 * q^49 - 6 * q^50 + 2 * q^51 + 7 * q^52 - 5 * q^53 - q^54 + 4 * q^57 - 7 * q^58 - 7 * q^59 - 3 * q^60 - 2 * q^61 + 3 * q^62 + 2 * q^63 + 4 * q^64 + 7 * q^65 + 22 * q^67 - 9 * q^68 + 2 * q^69 + 2 * q^70 - 18 * q^71 - 17 * q^73 + 6 * q^74 + 7 * q^75 + 12 * q^76 - 3 * q^78 + q^79 - 6 * q^80 + 2 * q^81 - q^82 - 8 * q^83 + q^84 - 9 * q^85 - 3 * q^86 + 4 * q^87 - 13 * q^89 + 2 * q^90 - 4 * q^91 - 14 * q^92 - 6 * q^93 - 16 * q^94 + 12 * q^95 + 9 * q^96 - 24 * q^97 + q^98

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 $

$2$	1.61803	1.14412	0.572061	−	0.820211i	$-0.306144\pi$
$2$	1.61803	1.14412	0.572061	+	0.820211i	$0.306144\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.618034	0.309017
$5$	0.618034	0.276393	0.138197	−	0.990405i	$-0.455869\pi$
$5$	0.618034	0.276393	0.138197	+	0.990405i	$0.455869\pi$
$6$	−1.61803	−0.660560
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.23607	−0.790569
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	0	0
$11$	0	0
$12$	−0.618034	−0.178411
$13$	0.236068	0.0654735	0.0327367	−	0.999464i	$-0.489578\pi$
$13$	0.236068	0.0654735	0.0327367	+	0.999464i	$0.489578\pi$
$14$	1.61803	0.432438
$15$	−0.618034	−0.159576
$16$	−4.85410	−1.21353
$17$	−5.47214	−1.32719	−0.663594	−	0.748093i	$-0.730970\pi$
$17$	−5.47214	−1.32719	−0.663594	+	0.748093i	$0.730970\pi$
$18$	1.61803	0.381374
$19$	2.47214	0.567147	0.283573	−	0.958951i	$-0.408480\pi$
$19$	2.47214	0.567147	0.283573	+	0.958951i	$0.408480\pi$
$20$	0.381966	0.0854102
$21$	−1.00000	−0.218218
$22$	0	0
$23$	−7.70820	−1.60727	−0.803636	−	0.595121i	$-0.797104\pi$
$23$	−7.70820	−1.60727	−0.803636	+	0.595121i	$0.797104\pi$
$24$	2.23607	0.456435
$25$	−4.61803	−0.923607
$26$	0.381966	0.0749097
$27$	−1.00000	−0.192450
$28$	0.618034	0.116797
$29$	−4.23607	−0.786618	−0.393309	−	0.919406i	$-0.628670\pi$
$29$	−4.23607	−0.786618	−0.393309	+	0.919406i	$0.628670\pi$
$30$	−1.00000	−0.182574
$31$	3.00000	0.538816	0.269408	−	0.963026i	$-0.413172\pi$
$31$	3.00000	0.538816	0.269408	+	0.963026i	$0.413172\pi$
$32$	−3.38197	−0.597853
$33$	0	0
$34$	−8.85410	−1.51847
$35$	0.618034	0.104467
$36$	0.618034	0.103006
$37$	6.00000	0.986394	0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000	0.986394	0.493197	+	0.869918i	$0.335828\pi$
$38$	4.00000	0.648886
$39$	−0.236068	−0.0378011
$40$	−1.38197	−0.218508
$41$	3.14590	0.491307	0.245653	−	0.969358i	$-0.420998\pi$
$41$	3.14590	0.491307	0.245653	+	0.969358i	$0.420998\pi$
$42$	−1.61803	−0.249668
$43$	2.52786	0.385496	0.192748	−	0.981248i	$-0.438260\pi$
$43$	2.52786	0.385496	0.192748	+	0.981248i	$0.438260\pi$
$44$	0	0
$45$	0.618034	0.0921311
$46$	−12.4721	−1.83892
$47$	−11.8541	−1.72910	−0.864549	−	0.502548i	$-0.832396\pi$
$47$	−11.8541	−1.72910	−0.864549	+	0.502548i	$0.832396\pi$
$48$	4.85410	0.700629
$49$	1.00000	0.142857
$50$	−7.47214	−1.05672
$51$	5.47214	0.766252
$52$	0.145898	0.0202324
$53$	7.56231	1.03876	0.519381	−	0.854543i	$-0.326162\pi$
$53$	7.56231	1.03876	0.519381	+	0.854543i	$0.326162\pi$
$54$	−1.61803	−0.220187
$55$	0	0
$56$	−2.23607	−0.298807
$57$	−2.47214	−0.327442
$58$	−6.85410	−0.899988
$59$	−2.38197	−0.310106	−0.155053	−	0.987906i	$-0.549555\pi$
$59$	−2.38197	−0.310106	−0.155053	+	0.987906i	$0.549555\pi$
$60$	−0.381966	−0.0493116
$61$	−9.94427	−1.27323	−0.636617	−	0.771180i	$-0.719667\pi$
$61$	−9.94427	−1.27323	−0.636617	+	0.771180i	$0.719667\pi$
$62$	4.85410	0.616472
$63$	1.00000	0.125988
$64$	4.23607	0.529508
$65$	0.145898	0.0180964
$66$	0	0
$67$	8.76393	1.07068	0.535342	−	0.844635i	$-0.320183\pi$
$67$	8.76393	1.07068	0.535342	+	0.844635i	$0.320183\pi$
$68$	−3.38197	−0.410124
$69$	7.70820	0.927959
$70$	1.00000	0.119523
$71$	−13.4721	−1.59885	−0.799424	−	0.600767i	$-0.794862\pi$
$71$	−13.4721	−1.59885	−0.799424	+	0.600767i	$0.794862\pi$
$72$	−2.23607	−0.263523
$73$	−9.61803	−1.12571	−0.562853	−	0.826557i	$-0.690296\pi$
$73$	−9.61803	−1.12571	−0.562853	+	0.826557i	$0.690296\pi$
$74$	9.70820	1.12856
$75$	4.61803	0.533245
$76$	1.52786	0.175258
$77$	0	0
$78$	−0.381966	−0.0432491
$79$	−5.09017	−0.572689	−0.286344	−	0.958127i	$-0.592440\pi$
$79$	−5.09017	−0.572689	−0.286344	+	0.958127i	$0.592440\pi$
$80$	−3.00000	−0.335410
$81$	1.00000	0.111111
$82$	5.09017	0.562115
$83$	0.472136	0.0518237	0.0259118	−	0.999664i	$-0.491751\pi$
$83$	0.472136	0.0518237	0.0259118	+	0.999664i	$0.491751\pi$
$84$	−0.618034	−0.0674330
$85$	−3.38197	−0.366826
$86$	4.09017	0.441054
$87$	4.23607	0.454154
$88$	0	0
$89$	−14.3262	−1.51858	−0.759289	−	0.650753i	$-0.774453\pi$
$89$	−14.3262	−1.51858	−0.759289	+	0.650753i	$0.774453\pi$
$90$	1.00000	0.105409
$91$	0.236068	0.0247466
$92$	−4.76393	−0.496674
$93$	−3.00000	−0.311086
$94$	−19.1803	−1.97830
$95$	1.52786	0.156756
$96$	3.38197	0.345170
$97$	−18.7082	−1.89953	−0.949765	−	0.312963i	$-0.898678\pi$
$97$	−18.7082	−1.89953	−0.949765	+	0.312963i	$0.898678\pi$
$98$	1.61803	0.163446
$99$	0	0
$100$	−2.85410	−0.285410
$101$	−6.76393	−0.673036	−0.336518	−	0.941677i	$-0.609249\pi$
$101$	−6.76393	−0.673036	−0.336518	+	0.941677i	$0.609249\pi$
$102$	8.85410	0.876687
$103$	−6.52786	−0.643210	−0.321605	−	0.946874i	$-0.604222\pi$
$103$	−6.52786	−0.643210	−0.321605	+	0.946874i	$0.604222\pi$
$104$	−0.527864	−0.0517613
$105$	−0.618034	−0.0603139
$106$	12.2361	1.18847
$107$	−10.2361	−0.989558	−0.494779	−	0.869019i	$-0.664751\pi$
$107$	−10.2361	−0.989558	−0.494779	+	0.869019i	$0.664751\pi$
$108$	−0.618034	−0.0594703
$109$	10.8541	1.03963	0.519817	−	0.854278i	$-0.326000\pi$
$109$	10.8541	1.03963	0.519817	+	0.854278i	$0.326000\pi$
$110$	0	0
$111$	−6.00000	−0.569495
$112$	−4.85410	−0.458670
$113$	11.1803	1.05176	0.525879	−	0.850559i	$-0.323736\pi$
$113$	11.1803	1.05176	0.525879	+	0.850559i	$0.323736\pi$
$114$	−4.00000	−0.374634
$115$	−4.76393	−0.444239
$116$	−2.61803	−0.243078
$117$	0.236068	0.0218245
$118$	−3.85410	−0.354799
$119$	−5.47214	−0.501630
$120$	1.38197	0.126156
$121$	0	0
$122$	−16.0902	−1.45674
$123$	−3.14590	−0.283656
$124$	1.85410	0.166503
$125$	−5.94427	−0.531672
$126$	1.61803	0.144146
$127$	−8.32624	−0.738834	−0.369417	−	0.929264i	$-0.620443\pi$
$127$	−8.32624	−0.738834	−0.369417	+	0.929264i	$0.620443\pi$
$128$	13.6180	1.20368
$129$	−2.52786	−0.222566
$130$	0.236068	0.0207045
$131$	−0.145898	−0.0127472	−0.00637359	−	0.999980i	$-0.502029\pi$
$131$	−0.145898	−0.0127472	−0.00637359	+	0.999980i	$0.502029\pi$
$132$	0	0
$133$	2.47214	0.214361
$134$	14.1803	1.22499
$135$	−0.618034	−0.0531919
$136$	12.2361	1.04923
$137$	−1.52786	−0.130534	−0.0652671	−	0.997868i	$-0.520790\pi$
$137$	−1.52786	−0.130534	−0.0652671	+	0.997868i	$0.520790\pi$
$138$	12.4721	1.06170
$139$	−0.381966	−0.0323979	−0.0161990	−	0.999869i	$-0.505157\pi$
$139$	−0.381966	−0.0323979	−0.0161990	+	0.999869i	$0.505157\pi$
$140$	0.381966	0.0322820
$141$	11.8541	0.998295
$142$	−21.7984	−1.82928
$143$	0	0
$144$	−4.85410	−0.404508
$145$	−2.61803	−0.217416
$146$	−15.5623	−1.28795
$147$	−1.00000	−0.0824786
$148$	3.70820	0.304812
$149$	3.61803	0.296401	0.148200	−	0.988957i	$-0.452652\pi$
$149$	3.61803	0.296401	0.148200	+	0.988957i	$0.452652\pi$
$150$	7.47214	0.610097
$151$	9.32624	0.758958	0.379479	−	0.925200i	$-0.376103\pi$
$151$	9.32624	0.758958	0.379479	+	0.925200i	$0.376103\pi$
$152$	−5.52786	−0.448369
$153$	−5.47214	−0.442396
$154$	0	0
$155$	1.85410	0.148925
$156$	−0.145898	−0.0116812
$157$	17.7984	1.42046	0.710232	−	0.703967i	$-0.248590\pi$
$157$	17.7984	1.42046	0.710232	+	0.703967i	$0.248590\pi$
$158$	−8.23607	−0.655226
$159$	−7.56231	−0.599730
$160$	−2.09017	−0.165242
$161$	−7.70820	−0.607492
$162$	1.61803	0.127125
$163$	−2.67376	−0.209425	−0.104713	−	0.994503i	$-0.533392\pi$
$163$	−2.67376	−0.209425	−0.104713	+	0.994503i	$0.533392\pi$
$164$	1.94427	0.151822
$165$	0	0
$166$	0.763932	0.0592926
$167$	8.85410	0.685151	0.342575	−	0.939490i	$-0.388701\pi$
$167$	8.85410	0.685151	0.342575	+	0.939490i	$0.388701\pi$
$168$	2.23607	0.172516
$169$	−12.9443	−0.995713
$170$	−5.47214	−0.419694
$171$	2.47214	0.189049
$172$	1.56231	0.119125
$173$	13.7984	1.04907	0.524535	−	0.851389i	$-0.324239\pi$
$173$	13.7984	1.04907	0.524535	+	0.851389i	$0.324239\pi$
$174$	6.85410	0.519608
$175$	−4.61803	−0.349091
$176$	0	0
$177$	2.38197	0.179040
$178$	−23.1803	−1.73744
$179$	−5.29180	−0.395527	−0.197764	−	0.980250i	$-0.563368\pi$
$179$	−5.29180	−0.395527	−0.197764	+	0.980250i	$0.563368\pi$
$180$	0.381966	0.0284701
$181$	−9.47214	−0.704058	−0.352029	−	0.935989i	$-0.614508\pi$
$181$	−9.47214	−0.704058	−0.352029	+	0.935989i	$0.614508\pi$
$182$	0.381966	0.0283132
$183$	9.94427	0.735102
$184$	17.2361	1.27066
$185$	3.70820	0.272633
$186$	−4.85410	−0.355920
$187$	0	0
$188$	−7.32624	−0.534321
$189$	−1.00000	−0.0727393
$190$	2.47214	0.179348
$191$	−11.7639	−0.851208	−0.425604	−	0.904909i	$-0.639938\pi$
$191$	−11.7639	−0.851208	−0.425604	+	0.904909i	$0.639938\pi$
$192$	−4.23607	−0.305712
$193$	9.41641	0.677808	0.338904	−	0.940821i	$-0.389944\pi$
$193$	9.41641	0.677808	0.338904	+	0.940821i	$0.389944\pi$
$194$	−30.2705	−2.17330
$195$	−0.145898	−0.0104480
$196$	0.618034	0.0441453
$197$	26.6525	1.89891	0.949455	−	0.313903i	$-0.101637\pi$
$197$	26.6525	1.89891	0.949455	+	0.313903i	$0.101637\pi$
$198$	0	0
$199$	25.2148	1.78743	0.893714	−	0.448637i	$-0.148090\pi$
$199$	25.2148	1.78743	0.893714	+	0.448637i	$0.148090\pi$
$200$	10.3262	0.730175
$201$	−8.76393	−0.618160
$202$	−10.9443	−0.770036
$203$	−4.23607	−0.297314
$204$	3.38197	0.236785
$205$	1.94427	0.135794
$206$	−10.5623	−0.735911
$207$	−7.70820	−0.535757
$208$	−1.14590	−0.0794537
$209$	0	0
$210$	−1.00000	−0.0690066
$211$	5.29180	0.364302	0.182151	−	0.983271i	$-0.441694\pi$
$211$	5.29180	0.364302	0.182151	+	0.983271i	$0.441694\pi$
$212$	4.67376	0.320995
$213$	13.4721	0.923096
$214$	−16.5623	−1.13218
$215$	1.56231	0.106548
$216$	2.23607	0.152145
$217$	3.00000	0.203653
$218$	17.5623	1.18947
$219$	9.61803	0.649927
$220$	0	0
$221$	−1.29180	−0.0868956
$222$	−9.70820	−0.651572
$223$	2.05573	0.137662	0.0688309	−	0.997628i	$-0.478073\pi$
$223$	2.05573	0.137662	0.0688309	+	0.997628i	$0.478073\pi$
$224$	−3.38197	−0.225967
$225$	−4.61803	−0.307869
$226$	18.0902	1.20334
$227$	12.0902	0.802453	0.401226	−	0.915979i	$-0.368584\pi$
$227$	12.0902	0.802453	0.401226	+	0.915979i	$0.368584\pi$
$228$	−1.52786	−0.101185
$229$	−25.1246	−1.66028	−0.830141	−	0.557554i	$-0.811740\pi$
$229$	−25.1246	−1.66028	−0.830141	+	0.557554i	$0.811740\pi$
$230$	−7.70820	−0.508264
$231$	0	0
$232$	9.47214	0.621876
$233$	20.2361	1.32571	0.662854	−	0.748748i	$-0.269345\pi$
$233$	20.2361	1.32571	0.662854	+	0.748748i	$0.269345\pi$
$234$	0.381966	0.0249699
$235$	−7.32624	−0.477911
$236$	−1.47214	−0.0958279
$237$	5.09017	0.330642
$238$	−8.85410	−0.573926
$239$	19.3820	1.25372	0.626858	−	0.779134i	$-0.284341\pi$
$239$	19.3820	1.25372	0.626858	+	0.779134i	$0.284341\pi$
$240$	3.00000	0.193649
$241$	16.4164	1.05747	0.528737	−	0.848786i	$-0.322666\pi$
$241$	16.4164	1.05747	0.528737	+	0.848786i	$0.322666\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	−6.14590	−0.393451
$245$	0.618034	0.0394847
$246$	−5.09017	−0.324537
$247$	0.583592	0.0371331
$248$	−6.70820	−0.425971
$249$	−0.472136	−0.0299204
$250$	−9.61803	−0.608298
$251$	3.94427	0.248960	0.124480	−	0.992222i	$-0.460274\pi$
$251$	3.94427	0.248960	0.124480	+	0.992222i	$0.460274\pi$
$252$	0.618034	0.0389325
$253$	0	0
$254$	−13.4721	−0.845317
$255$	3.38197	0.211787
$256$	13.5623	0.847644
$257$	−11.8885	−0.741587	−0.370793	−	0.928715i	$-0.620914\pi$
$257$	−11.8885	−0.741587	−0.370793	+	0.928715i	$0.620914\pi$
$258$	−4.09017	−0.254643
$259$	6.00000	0.372822
$260$	0.0901699	0.00559210
$261$	−4.23607	−0.262206
$262$	−0.236068	−0.0145843
$263$	22.7082	1.40025	0.700124	−	0.714021i	$-0.253128\pi$
$263$	22.7082	1.40025	0.700124	+	0.714021i	$0.253128\pi$
$264$	0	0
$265$	4.67376	0.287107
$266$	4.00000	0.245256
$267$	14.3262	0.876752
$268$	5.41641	0.330860
$269$	−6.81966	−0.415802	−0.207901	−	0.978150i	$-0.566663\pi$
$269$	−6.81966	−0.415802	−0.207901	+	0.978150i	$0.566663\pi$
$270$	−1.00000	−0.0608581
$271$	−18.1246	−1.10099	−0.550496	−	0.834838i	$-0.685561\pi$
$271$	−18.1246	−1.10099	−0.550496	+	0.834838i	$0.685561\pi$
$272$	26.5623	1.61058
$273$	−0.236068	−0.0142875
$274$	−2.47214	−0.149347
$275$	0	0
$276$	4.76393	0.286755
$277$	0.472136	0.0283679	0.0141840	−	0.999899i	$-0.495485\pi$
$277$	0.472136	0.0283679	0.0141840	+	0.999899i	$0.495485\pi$
$278$	−0.618034	−0.0370672
$279$	3.00000	0.179605
$280$	−1.38197	−0.0825883
$281$	−4.14590	−0.247324	−0.123662	−	0.992324i	$-0.539464\pi$
$281$	−4.14590	−0.247324	−0.123662	+	0.992324i	$0.539464\pi$
$282$	19.1803	1.14217
$283$	22.8885	1.36058	0.680291	−	0.732942i	$-0.261853\pi$
$283$	22.8885	1.36058	0.680291	+	0.732942i	$0.261853\pi$
$284$	−8.32624	−0.494071
$285$	−1.52786	−0.0905029
$286$	0	0
$287$	3.14590	0.185696
$288$	−3.38197	−0.199284
$289$	12.9443	0.761428
$290$	−4.23607	−0.248750
$291$	18.7082	1.09669
$292$	−5.94427	−0.347862
$293$	−5.70820	−0.333477	−0.166738	−	0.986001i	$-0.553324\pi$
$293$	−5.70820	−0.333477	−0.166738	+	0.986001i	$0.553324\pi$
$294$	−1.61803	−0.0943657
$295$	−1.47214	−0.0857111
$296$	−13.4164	−0.779813
$297$	0	0
$298$	5.85410	0.339119
$299$	−1.81966	−0.105234
$300$	2.85410	0.164782
$301$	2.52786	0.145704
$302$	15.0902	0.868342
$303$	6.76393	0.388578
$304$	−12.0000	−0.688247
$305$	−6.14590	−0.351913
$306$	−8.85410	−0.506155
$307$	−25.9443	−1.48072	−0.740359	−	0.672212i	$-0.765344\pi$
$307$	−25.9443	−1.48072	−0.740359	+	0.672212i	$0.765344\pi$
$308$	0	0
$309$	6.52786	0.371357
$310$	3.00000	0.170389
$311$	−17.7984	−1.00925	−0.504627	−	0.863338i	$-0.668370\pi$
$311$	−17.7984	−1.00925	−0.504627	+	0.863338i	$0.668370\pi$
$312$	0.527864	0.0298844
$313$	20.9098	1.18189	0.590947	−	0.806711i	$-0.298754\pi$
$313$	20.9098	1.18189	0.590947	+	0.806711i	$0.298754\pi$
$314$	28.7984	1.62519
$315$	0.618034	0.0348223
$316$	−3.14590	−0.176971
$317$	0.888544	0.0499056	0.0249528	−	0.999689i	$-0.492056\pi$
$317$	0.888544	0.0499056	0.0249528	+	0.999689i	$0.492056\pi$
$318$	−12.2361	−0.686165
$319$	0	0
$320$	2.61803	0.146353
$321$	10.2361	0.571322
$322$	−12.4721	−0.695045
$323$	−13.5279	−0.752710
$324$	0.618034	0.0343352
$325$	−1.09017	−0.0604717
$326$	−4.32624	−0.239608
$327$	−10.8541	−0.600233
$328$	−7.03444	−0.388412
$329$	−11.8541	−0.653538
$330$	0	0
$331$	−32.7082	−1.79781	−0.898903	−	0.438148i	$-0.855635\pi$
$331$	−32.7082	−1.79781	−0.898903	+	0.438148i	$0.855635\pi$
$332$	0.291796	0.0160144
$333$	6.00000	0.328798
$334$	14.3262	0.783897
$335$	5.41641	0.295930
$336$	4.85410	0.264813
$337$	−0.236068	−0.0128594	−0.00642972	−	0.999979i	$-0.502047\pi$
$337$	−0.236068	−0.0128594	−0.00642972	+	0.999979i	$0.502047\pi$
$338$	−20.9443	−1.13922
$339$	−11.1803	−0.607233
$340$	−2.09017	−0.113355
$341$	0	0
$342$	4.00000	0.216295
$343$	1.00000	0.0539949
$344$	−5.65248	−0.304761
$345$	4.76393	0.256481
$346$	22.3262	1.20027
$347$	−8.47214	−0.454808	−0.227404	−	0.973800i	$-0.573024\pi$
$347$	−8.47214	−0.454808	−0.227404	+	0.973800i	$0.573024\pi$
$348$	2.61803	0.140341
$349$	1.67376	0.0895944	0.0447972	−	0.998996i	$-0.485736\pi$
$349$	1.67376	0.0895944	0.0447972	+	0.998996i	$0.485736\pi$
$350$	−7.47214	−0.399402
$351$	−0.236068	−0.0126004
$352$	0	0
$353$	36.1246	1.92272	0.961360	−	0.275296i	$-0.0887758\pi$
$353$	36.1246	1.92272	0.961360	+	0.275296i	$0.0887758\pi$
$354$	3.85410	0.204843
$355$	−8.32624	−0.441911
$356$	−8.85410	−0.469266
$357$	5.47214	0.289616
$358$	−8.56231	−0.452532
$359$	−12.6180	−0.665954	−0.332977	−	0.942935i	$-0.608053\pi$
$359$	−12.6180	−0.665954	−0.332977	+	0.942935i	$0.608053\pi$
$360$	−1.38197	−0.0728360
$361$	−12.8885	−0.678344
$362$	−15.3262	−0.805529
$363$	0	0
$364$	0.145898	0.00764713
$365$	−5.94427	−0.311137
$366$	16.0902	0.841047
$367$	−5.00000	−0.260998	−0.130499	−	0.991448i	$-0.541658\pi$
$367$	−5.00000	−0.260998	−0.130499	+	0.991448i	$0.541658\pi$
$368$	37.4164	1.95047
$369$	3.14590	0.163769
$370$	6.00000	0.311925
$371$	7.56231	0.392615
$372$	−1.85410	−0.0961307
$373$	33.7082	1.74534	0.872672	−	0.488306i	$-0.162385\pi$
$373$	33.7082	1.74534	0.872672	+	0.488306i	$0.162385\pi$
$374$	0	0
$375$	5.94427	0.306961
$376$	26.5066	1.36697
$377$	−1.00000	−0.0515026
$378$	−1.61803	−0.0832227
$379$	−13.0902	−0.672397	−0.336198	−	0.941791i	$-0.609141\pi$
$379$	−13.0902	−0.672397	−0.336198	+	0.941791i	$0.609141\pi$
$380$	0.944272	0.0484401
$381$	8.32624	0.426566
$382$	−19.0344	−0.973887
$383$	−18.3262	−0.936427	−0.468214	−	0.883615i	$-0.655102\pi$
$383$	−18.3262	−0.936427	−0.468214	+	0.883615i	$0.655102\pi$
$384$	−13.6180	−0.694942
$385$	0	0
$386$	15.2361	0.775495
$387$	2.52786	0.128499
$388$	−11.5623	−0.586987
$389$	−12.7639	−0.647157	−0.323579	−	0.946201i	$-0.604886\pi$
$389$	−12.7639	−0.647157	−0.323579	+	0.946201i	$0.604886\pi$
$390$	−0.236068	−0.0119538
$391$	42.1803	2.13315
$392$	−2.23607	−0.112938
$393$	0.145898	0.00735958
$394$	43.1246	2.17259
$395$	−3.14590	−0.158287
$396$	0	0
$397$	9.56231	0.479918	0.239959	−	0.970783i	$-0.422866\pi$
$397$	9.56231	0.479918	0.239959	+	0.970783i	$0.422866\pi$
$398$	40.7984	2.04504
$399$	−2.47214	−0.123762
$400$	22.4164	1.12082
$401$	−14.7426	−0.736213	−0.368106	−	0.929784i	$-0.619994\pi$
$401$	−14.7426	−0.736213	−0.368106	+	0.929784i	$0.619994\pi$
$402$	−14.1803	−0.707251
$403$	0.708204	0.0352782
$404$	−4.18034	−0.207980
$405$	0.618034	0.0307104
$406$	−6.85410	−0.340163
$407$	0	0
$408$	−12.2361	−0.605776
$409$	−32.7984	−1.62178	−0.810888	−	0.585202i	$-0.801015\pi$
$409$	−32.7984	−1.62178	−0.810888	+	0.585202i	$0.801015\pi$
$410$	3.14590	0.155365
$411$	1.52786	0.0753640
$412$	−4.03444	−0.198763
$413$	−2.38197	−0.117209
$414$	−12.4721	−0.612972
$415$	0.291796	0.0143237
$416$	−0.798374	−0.0391435
$417$	0.381966	0.0187050
$418$	0	0
$419$	−33.3820	−1.63082	−0.815408	−	0.578887i	$-0.803487\pi$
$419$	−33.3820	−1.63082	−0.815408	+	0.578887i	$0.803487\pi$
$420$	−0.381966	−0.0186380
$421$	24.8541	1.21131	0.605657	−	0.795726i	$-0.292910\pi$
$421$	24.8541	1.21131	0.605657	+	0.795726i	$0.292910\pi$
$422$	8.56231	0.416807
$423$	−11.8541	−0.576366
$424$	−16.9098	−0.821214
$425$	25.2705	1.22580
$426$	21.7984	1.05613
$427$	−9.94427	−0.481237
$428$	−6.32624	−0.305790
$429$	0	0
$430$	2.52786	0.121904
$431$	13.8541	0.667329	0.333664	−	0.942692i	$-0.391715\pi$
$431$	13.8541	0.667329	0.333664	+	0.942692i	$0.391715\pi$
$432$	4.85410	0.233543
$433$	10.9443	0.525948	0.262974	−	0.964803i	$-0.415297\pi$
$433$	10.9443	0.525948	0.262974	+	0.964803i	$0.415297\pi$
$434$	4.85410	0.233004
$435$	2.61803	0.125525
$436$	6.70820	0.321265
$437$	−19.0557	−0.911559
$438$	15.5623	0.743596
$439$	−4.34752	−0.207496	−0.103748	−	0.994604i	$-0.533084\pi$
$439$	−4.34752	−0.207496	−0.103748	+	0.994604i	$0.533084\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	−2.09017	−0.0994192
$443$	−6.65248	−0.316069	−0.158034	−	0.987434i	$-0.550516\pi$
$443$	−6.65248	−0.316069	−0.158034	+	0.987434i	$0.550516\pi$
$444$	−3.70820	−0.175984
$445$	−8.85410	−0.419725
$446$	3.32624	0.157502
$447$	−3.61803	−0.171127
$448$	4.23607	0.200135
$449$	28.5967	1.34956	0.674782	−	0.738017i	$-0.264238\pi$
$449$	28.5967	1.34956	0.674782	+	0.738017i	$0.264238\pi$
$450$	−7.47214	−0.352240
$451$	0	0
$452$	6.90983	0.325011
$453$	−9.32624	−0.438185
$454$	19.5623	0.918105
$455$	0.145898	0.00683981
$456$	5.52786	0.258866
$457$	23.7426	1.11063	0.555317	−	0.831639i	$-0.312597\pi$
$457$	23.7426	1.11063	0.555317	+	0.831639i	$0.312597\pi$
$458$	−40.6525	−1.89957
$459$	5.47214	0.255417
$460$	−2.94427	−0.137277
$461$	34.3050	1.59774	0.798870	−	0.601503i	$-0.205431\pi$
$461$	34.3050	1.59774	0.798870	+	0.601503i	$0.205431\pi$
$462$	0	0
$463$	31.9787	1.48618	0.743088	−	0.669193i	$-0.233360\pi$
$463$	31.9787	1.48618	0.743088	+	0.669193i	$0.233360\pi$
$464$	20.5623	0.954581
$465$	−1.85410	−0.0859819
$466$	32.7426	1.51677
$467$	−13.2918	−0.615071	−0.307535	−	0.951537i	$-0.599504\pi$
$467$	−13.2918	−0.615071	−0.307535	+	0.951537i	$0.599504\pi$
$468$	0.145898	0.00674414
$469$	8.76393	0.404681
$470$	−11.8541	−0.546789
$471$	−17.7984	−0.820106
$472$	5.32624	0.245160
$473$	0	0
$474$	8.23607	0.378295
$475$	−11.4164	−0.523821
$476$	−3.38197	−0.155012
$477$	7.56231	0.346254
$478$	31.3607	1.43440
$479$	−32.6180	−1.49036	−0.745178	−	0.666866i	$-0.767636\pi$
$479$	−32.6180	−1.49036	−0.745178	+	0.666866i	$0.767636\pi$
$480$	2.09017	0.0954028
$481$	1.41641	0.0645826
$482$	26.5623	1.20988
$483$	7.70820	0.350735
$484$	0	0
$485$	−11.5623	−0.525017
$486$	−1.61803	−0.0733955
$487$	−17.6180	−0.798349	−0.399175	−	0.916875i	$-0.630703\pi$
$487$	−17.6180	−0.798349	−0.399175	+	0.916875i	$0.630703\pi$
$488$	22.2361	1.00658
$489$	2.67376	0.120912
$490$	1.00000	0.0451754
$491$	21.7082	0.979678	0.489839	−	0.871813i	$-0.337056\pi$
$491$	21.7082	0.979678	0.489839	+	0.871813i	$0.337056\pi$
$492$	−1.94427	−0.0876545
$493$	23.1803	1.04399
$494$	0.944272	0.0424848
$495$	0	0
$496$	−14.5623	−0.653867
$497$	−13.4721	−0.604308
$498$	−0.763932	−0.0342326
$499$	7.00000	0.313363	0.156682	−	0.987649i	$-0.449920\pi$
$499$	7.00000	0.313363	0.156682	+	0.987649i	$0.449920\pi$
$500$	−3.67376	−0.164296
$501$	−8.85410	−0.395572
$502$	6.38197	0.284841
$503$	−34.0132	−1.51657	−0.758286	−	0.651922i	$-0.773963\pi$
$503$	−34.0132	−1.51657	−0.758286	+	0.651922i	$0.773963\pi$
$504$	−2.23607	−0.0996024
$505$	−4.18034	−0.186023
$506$	0	0
$507$	12.9443	0.574875
$508$	−5.14590	−0.228312
$509$	−28.1246	−1.24660	−0.623301	−	0.781982i	$-0.714209\pi$
$509$	−28.1246	−1.24660	−0.623301	+	0.781982i	$0.714209\pi$
$510$	5.47214	0.242310
$511$	−9.61803	−0.425477
$512$	−5.29180	−0.233867
$513$	−2.47214	−0.109147
$514$	−19.2361	−0.848467
$515$	−4.03444	−0.177779
$516$	−1.56231	−0.0687767
$517$	0	0
$518$	9.70820	0.426554
$519$	−13.7984	−0.605681
$520$	−0.326238	−0.0143065
$521$	−18.4164	−0.806837	−0.403419	−	0.915015i	$-0.632178\pi$
$521$	−18.4164	−0.806837	−0.403419	+	0.915015i	$0.632178\pi$
$522$	−6.85410	−0.299996
$523$	37.5410	1.64155	0.820777	−	0.571249i	$-0.193541\pi$
$523$	37.5410	1.64155	0.820777	+	0.571249i	$0.193541\pi$
$524$	−0.0901699	−0.00393909
$525$	4.61803	0.201548
$526$	36.7426	1.60206
$527$	−16.4164	−0.715110
$528$	0	0
$529$	36.4164	1.58332
$530$	7.56231	0.328486
$531$	−2.38197	−0.103369
$532$	1.52786	0.0662413
$533$	0.742646	0.0321676
$534$	23.1803	1.00311
$535$	−6.32624	−0.273507
$536$	−19.5967	−0.846451
$537$	5.29180	0.228358
$538$	−11.0344	−0.475729
$539$	0	0
$540$	−0.381966	−0.0164372
$541$	40.0344	1.72122	0.860608	−	0.509269i	$-0.170084\pi$
$541$	40.0344	1.72122	0.860608	+	0.509269i	$0.170084\pi$
$542$	−29.3262	−1.25967
$543$	9.47214	0.406488
$544$	18.5066	0.793463
$545$	6.70820	0.287348
$546$	−0.381966	−0.0163466
$547$	−39.0689	−1.67046	−0.835232	−	0.549897i	$-0.814667\pi$
$547$	−39.0689	−1.67046	−0.835232	+	0.549897i	$0.814667\pi$
$548$	−0.944272	−0.0403373
$549$	−9.94427	−0.424411
$550$	0	0
$551$	−10.4721	−0.446128
$552$	−17.2361	−0.733616
$553$	−5.09017	−0.216456
$554$	0.763932	0.0324564
$555$	−3.70820	−0.157404
$556$	−0.236068	−0.0100115
$557$	−46.5410	−1.97201	−0.986003	−	0.166727i	$-0.946680\pi$
$557$	−46.5410	−1.97201	−0.986003	+	0.166727i	$0.946680\pi$
$558$	4.85410	0.205491
$559$	0.596748	0.0252397
$560$	−3.00000	−0.126773
$561$	0	0
$562$	−6.70820	−0.282969
$563$	10.0557	0.423798	0.211899	−	0.977292i	$-0.432035\pi$
$563$	10.0557	0.423798	0.211899	+	0.977292i	$0.432035\pi$
$564$	7.32624	0.308490
$565$	6.90983	0.290699
$566$	37.0344	1.55667
$567$	1.00000	0.0419961
$568$	30.1246	1.26400
$569$	25.2918	1.06029	0.530144	−	0.847908i	$-0.322138\pi$
$569$	25.2918	1.06029	0.530144	+	0.847908i	$0.322138\pi$
$570$	−2.47214	−0.103546
$571$	−18.0557	−0.755609	−0.377804	−	0.925885i	$-0.623321\pi$
$571$	−18.0557	−0.755609	−0.377804	+	0.925885i	$0.623321\pi$
$572$	0	0
$573$	11.7639	0.491445
$574$	5.09017	0.212460
$575$	35.5967	1.48449
$576$	4.23607	0.176503
$577$	43.8541	1.82567	0.912835	−	0.408328i	$-0.133888\pi$
$577$	43.8541	1.82567	0.912835	+	0.408328i	$0.133888\pi$
$578$	20.9443	0.871167
$579$	−9.41641	−0.391333
$580$	−1.61803	−0.0671852
$581$	0.472136	0.0195875
$582$	30.2705	1.25475
$583$	0	0
$584$	21.5066	0.889949
$585$	0.145898	0.00603214
$586$	−9.23607	−0.381538
$587$	48.2492	1.99146	0.995729	−	0.0923211i	$-0.0294286\pi$
$587$	48.2492	1.99146	0.995729	+	0.0923211i	$0.0294286\pi$
$588$	−0.618034	−0.0254873
$589$	7.41641	0.305588
$590$	−2.38197	−0.0980640
$591$	−26.6525	−1.09634
$592$	−29.1246	−1.19701
$593$	−10.0000	−0.410651	−0.205325	−	0.978694i	$-0.565825\pi$
$593$	−10.0000	−0.410651	−0.205325	+	0.978694i	$0.565825\pi$
$594$	0	0
$595$	−3.38197	−0.138647
$596$	2.23607	0.0915929
$597$	−25.2148	−1.03197
$598$	−2.94427	−0.120400
$599$	5.56231	0.227270	0.113635	−	0.993523i	$-0.463751\pi$
$599$	5.56231	0.227270	0.113635	+	0.993523i	$0.463751\pi$
$600$	−10.3262	−0.421567
$601$	31.4164	1.28150	0.640751	−	0.767749i	$-0.278623\pi$
$601$	31.4164	1.28150	0.640751	+	0.767749i	$0.278623\pi$
$602$	4.09017	0.166703
$603$	8.76393	0.356895
$604$	5.76393	0.234531
$605$	0	0
$606$	10.9443	0.444581
$607$	−46.1591	−1.87354	−0.936769	−	0.349948i	$-0.886199\pi$
$607$	−46.1591	−1.87354	−0.936769	+	0.349948i	$0.886199\pi$
$608$	−8.36068	−0.339070
$609$	4.23607	0.171654
$610$	−9.94427	−0.402632
$611$	−2.79837	−0.113210
$612$	−3.38197	−0.136708
$613$	−4.43769	−0.179237	−0.0896184	−	0.995976i	$-0.528565\pi$
$613$	−4.43769	−0.179237	−0.0896184	+	0.995976i	$0.528565\pi$
$614$	−41.9787	−1.69412
$615$	−1.94427	−0.0784006
$616$	0	0
$617$	14.3262	0.576753	0.288376	−	0.957517i	$-0.406885\pi$
$617$	14.3262	0.576753	0.288376	+	0.957517i	$0.406885\pi$
$618$	10.5623	0.424878
$619$	0.180340	0.00724847	0.00362424	−	0.999993i	$-0.498846\pi$
$619$	0.180340	0.00724847	0.00362424	+	0.999993i	$0.498846\pi$
$620$	1.14590	0.0460204
$621$	7.70820	0.309320
$622$	−28.7984	−1.15471
$623$	−14.3262	−0.573969
$624$	1.14590	0.0458726
$625$	19.4164	0.776656
$626$	33.8328	1.35223
$627$	0	0
$628$	11.0000	0.438948
$629$	−32.8328	−1.30913
$630$	1.00000	0.0398410
$631$	−12.7082	−0.505906	−0.252953	−	0.967479i	$-0.581402\pi$
$631$	−12.7082	−0.505906	−0.252953	+	0.967479i	$0.581402\pi$
$632$	11.3820	0.452750
$633$	−5.29180	−0.210330
$634$	1.43769	0.0570981
$635$	−5.14590	−0.204209
$636$	−4.67376	−0.185327
$637$	0.236068	0.00935335
$638$	0	0
$639$	−13.4721	−0.532949
$640$	8.41641	0.332688
$641$	−6.32624	−0.249871	−0.124936	−	0.992165i	$-0.539872\pi$
$641$	−6.32624	−0.249871	−0.124936	+	0.992165i	$0.539872\pi$
$642$	16.5623	0.653662
$643$	−29.8885	−1.17869	−0.589345	−	0.807882i	$-0.700614\pi$
$643$	−29.8885	−1.17869	−0.589345	+	0.807882i	$0.700614\pi$
$644$	−4.76393	−0.187725
$645$	−1.56231	−0.0615157
$646$	−21.8885	−0.861193
$647$	−20.8885	−0.821213	−0.410607	−	0.911813i	$-0.634683\pi$
$647$	−20.8885	−0.821213	−0.410607	+	0.911813i	$0.634683\pi$
$648$	−2.23607	−0.0878410
$649$	0	0
$650$	−1.76393	−0.0691871
$651$	−3.00000	−0.117579
$652$	−1.65248	−0.0647159
$653$	−8.81966	−0.345140	−0.172570	−	0.984997i	$-0.555207\pi$
$653$	−8.81966	−0.345140	−0.172570	+	0.984997i	$0.555207\pi$
$654$	−17.5623	−0.686741
$655$	−0.0901699	−0.00352323
$656$	−15.2705	−0.596213
$657$	−9.61803	−0.375235
$658$	−19.1803	−0.747727
$659$	−14.8885	−0.579975	−0.289988	−	0.957030i	$-0.593651\pi$
$659$	−14.8885	−0.579975	−0.289988	+	0.957030i	$0.593651\pi$
$660$	0	0
$661$	−30.5967	−1.19008	−0.595038	−	0.803698i	$-0.702863\pi$
$661$	−30.5967	−1.19008	−0.595038	+	0.803698i	$0.702863\pi$
$662$	−52.9230	−2.05691
$663$	1.29180	0.0501692
$664$	−1.05573	−0.0409702
$665$	1.52786	0.0592480
$666$	9.70820	0.376185
$667$	32.6525	1.26431
$668$	5.47214	0.211723
$669$	−2.05573	−0.0794790
$670$	8.76393	0.338580
$671$	0	0
$672$	3.38197	0.130462
$673$	35.9443	1.38555	0.692775	−	0.721154i	$-0.256388\pi$
$673$	35.9443	1.38555	0.692775	+	0.721154i	$0.256388\pi$
$674$	−0.381966	−0.0147128
$675$	4.61803	0.177748
$676$	−8.00000	−0.307692
$677$	−29.3262	−1.12710	−0.563549	−	0.826082i	$-0.690565\pi$
$677$	−29.3262	−1.12710	−0.563549	+	0.826082i	$0.690565\pi$
$678$	−18.0902	−0.694749
$679$	−18.7082	−0.717955
$680$	7.56231	0.290001
$681$	−12.0902	−0.463296
$682$	0	0
$683$	−6.52786	−0.249782	−0.124891	−	0.992170i	$-0.539858\pi$
$683$	−6.52786	−0.249782	−0.124891	+	0.992170i	$0.539858\pi$
$684$	1.52786	0.0584193
$685$	−0.944272	−0.0360788
$686$	1.61803	0.0617768
$687$	25.1246	0.958564
$688$	−12.2705	−0.467809
$689$	1.78522	0.0680114
$690$	7.70820	0.293446
$691$	−30.0344	−1.14256	−0.571282	−	0.820754i	$-0.693554\pi$
$691$	−30.0344	−1.14256	−0.571282	+	0.820754i	$0.693554\pi$
$692$	8.52786	0.324181
$693$	0	0
$694$	−13.7082	−0.520356
$695$	−0.236068	−0.00895457
$696$	−9.47214	−0.359040
$697$	−17.2148	−0.652056
$698$	2.70820	0.102507
$699$	−20.2361	−0.765398
$700$	−2.85410	−0.107875
$701$	−16.0557	−0.606416	−0.303208	−	0.952924i	$-0.598058\pi$
$701$	−16.0557	−0.606416	−0.303208	+	0.952924i	$0.598058\pi$
$702$	−0.381966	−0.0144164
$703$	14.8328	0.559430
$704$	0	0
$705$	7.32624	0.275922
$706$	58.4508	2.19983
$707$	−6.76393	−0.254384
$708$	1.47214	0.0553263
$709$	7.70820	0.289488	0.144744	−	0.989469i	$-0.453764\pi$
$709$	7.70820	0.289488	0.144744	+	0.989469i	$0.453764\pi$
$710$	−13.4721	−0.505600
$711$	−5.09017	−0.190896
$712$	32.0344	1.20054
$713$	−23.1246	−0.866024
$714$	8.85410	0.331356
$715$	0	0
$716$	−3.27051	−0.122225
$717$	−19.3820	−0.723833
$718$	−20.4164	−0.761934
$719$	22.4508	0.837275	0.418638	−	0.908153i	$-0.362508\pi$
$719$	22.4508	0.837275	0.418638	+	0.908153i	$0.362508\pi$
$720$	−3.00000	−0.111803
$721$	−6.52786	−0.243110
$722$	−20.8541	−0.776109
$723$	−16.4164	−0.610533
$724$	−5.85410	−0.217566
$725$	19.5623	0.726526
$726$	0	0
$727$	27.0344	1.00265	0.501326	−	0.865258i	$-0.332846\pi$
$727$	27.0344	1.00265	0.501326	+	0.865258i	$0.332846\pi$
$728$	−0.527864	−0.0195639
$729$	1.00000	0.0370370
$730$	−9.61803	−0.355979
$731$	−13.8328	−0.511625
$732$	6.14590	0.227159
$733$	−44.4164	−1.64056	−0.820279	−	0.571964i	$-0.806182\pi$
$733$	−44.4164	−1.64056	−0.820279	+	0.571964i	$0.806182\pi$
$734$	−8.09017	−0.298614
$735$	−0.618034	−0.0227965
$736$	26.0689	0.960912
$737$	0	0
$738$	5.09017	0.187372
$739$	46.8541	1.72356	0.861778	−	0.507286i	$-0.169351\pi$
$739$	46.8541	1.72356	0.861778	+	0.507286i	$0.169351\pi$
$740$	2.29180	0.0842481
$741$	−0.583592	−0.0214388
$742$	12.2361	0.449200
$743$	−26.9098	−0.987226	−0.493613	−	0.869682i	$-0.664324\pi$
$743$	−26.9098	−0.987226	−0.493613	+	0.869682i	$0.664324\pi$
$744$	6.70820	0.245935
$745$	2.23607	0.0819232
$746$	54.5410	1.99689
$747$	0.472136	0.0172746
$748$	0	0
$749$	−10.2361	−0.374018
$750$	9.61803	0.351201
$751$	30.4377	1.11069	0.555344	−	0.831621i	$-0.312587\pi$
$751$	30.4377	1.11069	0.555344	+	0.831621i	$0.312587\pi$
$752$	57.5410	2.09831
$753$	−3.94427	−0.143737
$754$	−1.61803	−0.0589253
$755$	5.76393	0.209771
$756$	−0.618034	−0.0224777
$757$	10.8754	0.395273	0.197636	−	0.980275i	$-0.436673\pi$
$757$	10.8754	0.395273	0.197636	+	0.980275i	$0.436673\pi$
$758$	−21.1803	−0.769305
$759$	0	0
$760$	−3.41641	−0.123926
$761$	−24.1459	−0.875288	−0.437644	−	0.899148i	$-0.644187\pi$
$761$	−24.1459	−0.875288	−0.437644	+	0.899148i	$0.644187\pi$
$762$	13.4721	0.488044
$763$	10.8541	0.392945
$764$	−7.27051	−0.263038
$765$	−3.38197	−0.122275
$766$	−29.6525	−1.07139
$767$	−0.562306	−0.0203037
$768$	−13.5623	−0.489388
$769$	−17.7771	−0.641058	−0.320529	−	0.947239i	$-0.603861\pi$
$769$	−17.7771	−0.641058	−0.320529	+	0.947239i	$0.603861\pi$
$770$	0	0
$771$	11.8885	0.428155
$772$	5.81966	0.209454
$773$	−13.0557	−0.469582	−0.234791	−	0.972046i	$-0.575441\pi$
$773$	−13.0557	−0.469582	−0.234791	+	0.972046i	$0.575441\pi$
$774$	4.09017	0.147018
$775$	−13.8541	−0.497654
$776$	41.8328	1.50171
$777$	−6.00000	−0.215249
$778$	−20.6525	−0.740427
$779$	7.77709	0.278643
$780$	−0.0901699	−0.00322860
$781$	0	0
$782$	68.2492	2.44059
$783$	4.23607	0.151385
$784$	−4.85410	−0.173361
$785$	11.0000	0.392607
$786$	0.236068	0.00842027
$787$	19.5623	0.697321	0.348660	−	0.937249i	$-0.386637\pi$
$787$	19.5623	0.697321	0.348660	+	0.937249i	$0.386637\pi$
$788$	16.4721	0.586796
$789$	−22.7082	−0.808433
$790$	−5.09017	−0.181100
$791$	11.1803	0.397527
$792$	0	0
$793$	−2.34752	−0.0833630
$794$	15.4721	0.549086
$795$	−4.67376	−0.165761
$796$	15.5836	0.552346
$797$	43.8541	1.55339	0.776696	−	0.629876i	$-0.216894\pi$
$797$	43.8541	1.55339	0.776696	+	0.629876i	$0.216894\pi$
$798$	−4.00000	−0.141598
$799$	64.8673	2.29484
$800$	15.6180	0.552181
$801$	−14.3262	−0.506193
$802$	−23.8541	−0.842318
$803$	0	0
$804$	−5.41641	−0.191022
$805$	−4.76393	−0.167907
$806$	1.14590	0.0403625
$807$	6.81966	0.240063
$808$	15.1246	0.532082
$809$	−19.3951	−0.681896	−0.340948	−	0.940082i	$-0.610748\pi$
$809$	−19.3951	−0.681896	−0.340948	+	0.940082i	$0.610748\pi$
$810$	1.00000	0.0351364
$811$	−34.2918	−1.20415	−0.602074	−	0.798440i	$-0.705659\pi$
$811$	−34.2918	−1.20415	−0.602074	+	0.798440i	$0.705659\pi$
$812$	−2.61803	−0.0918750
$813$	18.1246	0.635658
$814$	0	0
$815$	−1.65248	−0.0578837
$816$	−26.5623	−0.929867
$817$	6.24922	0.218633
$818$	−53.0689	−1.85551
$819$	0.236068	0.00824888
$820$	1.20163	0.0419626
$821$	36.1803	1.26270	0.631351	−	0.775497i	$-0.282501\pi$
$821$	36.1803	1.26270	0.631351	+	0.775497i	$0.282501\pi$
$822$	2.47214	0.0862256
$823$	13.5279	0.471552	0.235776	−	0.971807i	$-0.424237\pi$
$823$	13.5279	0.471552	0.235776	+	0.971807i	$0.424237\pi$
$824$	14.5967	0.508502
$825$	0	0
$826$	−3.85410	−0.134101
$827$	−24.0557	−0.836500	−0.418250	−	0.908332i	$-0.637356\pi$
$827$	−24.0557	−0.836500	−0.418250	+	0.908332i	$0.637356\pi$
$828$	−4.76393	−0.165558
$829$	−16.3262	−0.567034	−0.283517	−	0.958967i	$-0.591501\pi$
$829$	−16.3262	−0.567034	−0.283517	+	0.958967i	$0.591501\pi$
$830$	0.472136	0.0163881
$831$	−0.472136	−0.0163782
$832$	1.00000	0.0346688
$833$	−5.47214	−0.189598
$834$	0.618034	0.0214008
$835$	5.47214	0.189371
$836$	0	0
$837$	−3.00000	−0.103695
$838$	−54.0132	−1.86585
$839$	−23.4721	−0.810348	−0.405174	−	0.914240i	$-0.632789\pi$
$839$	−23.4721	−0.810348	−0.405174	+	0.914240i	$0.632789\pi$
$840$	1.38197	0.0476824
$841$	−11.0557	−0.381232
$842$	40.2148	1.38589
$843$	4.14590	0.142792
$844$	3.27051	0.112576
$845$	−8.00000	−0.275208
$846$	−19.1803	−0.659434
$847$	0	0
$848$	−36.7082	−1.26056
$849$	−22.8885	−0.785533
$850$	40.8885	1.40247
$851$	−46.2492	−1.58540
$852$	8.32624	0.285252
$853$	−0.201626	−0.00690355	−0.00345177	−	0.999994i	$-0.501099\pi$
$853$	−0.201626	−0.00690355	−0.00345177	+	0.999994i	$0.501099\pi$
$854$	−16.0902	−0.550594
$855$	1.52786	0.0522518
$856$	22.8885	0.782314
$857$	14.0557	0.480135	0.240067	−	0.970756i	$-0.422830\pi$
$857$	14.0557	0.480135	0.240067	+	0.970756i	$0.422830\pi$
$858$	0	0
$859$	−29.6525	−1.01173	−0.505865	−	0.862613i	$-0.668827\pi$
$859$	−29.6525	−1.01173	−0.505865	+	0.862613i	$0.668827\pi$
$860$	0.965558	0.0329253
$861$	−3.14590	−0.107212
$862$	22.4164	0.763506
$863$	−49.2492	−1.67646	−0.838232	−	0.545314i	$-0.816410\pi$
$863$	−49.2492	−1.67646	−0.838232	+	0.545314i	$0.816410\pi$
$864$	3.38197	0.115057
$865$	8.52786	0.289956
$866$	17.7082	0.601749
$867$	−12.9443	−0.439611
$868$	1.85410	0.0629323
$869$	0	0
$870$	4.23607	0.143616
$871$	2.06888	0.0701015
$872$	−24.2705	−0.821903
$873$	−18.7082	−0.633177
$874$	−30.8328	−1.04294
$875$	−5.94427	−0.200953
$876$	5.94427	0.200838
$877$	18.8541	0.636658	0.318329	−	0.947980i	$-0.396878\pi$
$877$	18.8541	0.636658	0.318329	+	0.947980i	$0.396878\pi$
$878$	−7.03444	−0.237401
$879$	5.70820	0.192533
$880$	0	0
$881$	−18.7082	−0.630295	−0.315148	−	0.949043i	$-0.602054\pi$
$881$	−18.7082	−0.630295	−0.315148	+	0.949043i	$0.602054\pi$
$882$	1.61803	0.0544820
$883$	−32.9098	−1.10750	−0.553752	−	0.832682i	$-0.686804\pi$
$883$	−32.9098	−1.10750	−0.553752	+	0.832682i	$0.686804\pi$
$884$	−0.798374	−0.0268522
$885$	1.47214	0.0494853
$886$	−10.7639	−0.361621
$887$	−25.2918	−0.849215	−0.424608	−	0.905377i	$-0.639588\pi$
$887$	−25.2918	−0.849215	−0.424608	+	0.905377i	$0.639588\pi$
$888$	13.4164	0.450225
$889$	−8.32624	−0.279253
$890$	−14.3262	−0.480217
$891$	0	0
$892$	1.27051	0.0425398
$893$	−29.3050	−0.980653
$894$	−5.85410	−0.195790
$895$	−3.27051	−0.109321
$896$	13.6180	0.454947
$897$	1.81966	0.0607567
$898$	46.2705	1.54407
$899$	−12.7082	−0.423842
$900$	−2.85410	−0.0951367
$901$	−41.3820	−1.37863
$902$	0	0
$903$	−2.52786	−0.0841220
$904$	−25.0000	−0.831488
$905$	−5.85410	−0.194597
$906$	−15.0902	−0.501337
$907$	−49.5066	−1.64384	−0.821919	−	0.569604i	$-0.807097\pi$
$907$	−49.5066	−1.64384	−0.821919	+	0.569604i	$0.807097\pi$
$908$	7.47214	0.247972
$909$	−6.76393	−0.224345
$910$	0.236068	0.00782558
$911$	−43.0902	−1.42764	−0.713821	−	0.700329i	$-0.753037\pi$
$911$	−43.0902	−1.42764	−0.713821	+	0.700329i	$0.753037\pi$
$912$	12.0000	0.397360
$913$	0	0
$914$	38.4164	1.27070
$915$	6.14590	0.203177
$916$	−15.5279	−0.513055
$917$	−0.145898	−0.00481798
$918$	8.85410	0.292229
$919$	4.00000	0.131948	0.0659739	−	0.997821i	$-0.478985\pi$
$919$	4.00000	0.131948	0.0659739	+	0.997821i	$0.478985\pi$
$920$	10.6525	0.351202
$921$	25.9443	0.854893
$922$	55.5066	1.82801
$923$	−3.18034	−0.104682
$924$	0	0
$925$	−27.7082	−0.911040
$926$	51.7426	1.70037
$927$	−6.52786	−0.214403
$928$	14.3262	0.470282
$929$	25.8885	0.849376	0.424688	−	0.905340i	$-0.360384\pi$
$929$	25.8885	0.849376	0.424688	+	0.905340i	$0.360384\pi$
$930$	−3.00000	−0.0983739
$931$	2.47214	0.0810210
$932$	12.5066	0.409667
$933$	17.7984	0.582693
$934$	−21.5066	−0.703717
$935$	0	0
$936$	−0.527864	−0.0172538
$937$	−18.1246	−0.592105	−0.296053	−	0.955172i	$-0.595670\pi$
$937$	−18.1246	−0.592105	−0.296053	+	0.955172i	$0.595670\pi$
$938$	14.1803	0.463005
$939$	−20.9098	−0.682367
$940$	−4.52786	−0.147683
$941$	51.5967	1.68201	0.841003	−	0.541031i	$-0.181966\pi$
$941$	51.5967	1.68201	0.841003	+	0.541031i	$0.181966\pi$
$942$	−28.7984	−0.938302
$943$	−24.2492	−0.789663
$944$	11.5623	0.376321
$945$	−0.618034	−0.0201046
$946$	0	0
$947$	−41.9787	−1.36412	−0.682062	−	0.731294i	$-0.738917\pi$
$947$	−41.9787	−1.36412	−0.682062	+	0.731294i	$0.738917\pi$
$948$	3.14590	0.102174
$949$	−2.27051	−0.0737039
$950$	−18.4721	−0.599315
$951$	−0.888544	−0.0288130
$952$	12.2361	0.396573
$953$	−19.0344	−0.616586	−0.308293	−	0.951291i	$-0.599758\pi$
$953$	−19.0344	−0.616586	−0.308293	+	0.951291i	$0.599758\pi$
$954$	12.2361	0.396157
$955$	−7.27051	−0.235268
$956$	11.9787	0.387419
$957$	0	0
$958$	−52.7771	−1.70515
$959$	−1.52786	−0.0493373
$960$	−2.61803	−0.0844967
$961$	−22.0000	−0.709677
$962$	2.29180	0.0738905
$963$	−10.2361	−0.329853
$964$	10.1459	0.326777
$965$	5.81966	0.187341
$966$	12.4721	0.401284
$967$	17.3475	0.557859	0.278929	−	0.960312i	$-0.410020\pi$
$967$	17.3475	0.557859	0.278929	+	0.960312i	$0.410020\pi$
$968$	0	0
$969$	13.5279	0.434578
$970$	−18.7082	−0.600684
$971$	16.4164	0.526828	0.263414	−	0.964683i	$-0.415152\pi$
$971$	16.4164	0.526828	0.263414	+	0.964683i	$0.415152\pi$
$972$	−0.618034	−0.0198234
$973$	−0.381966	−0.0122453
$974$	−28.5066	−0.913410
$975$	1.09017	0.0349134
$976$	48.2705	1.54510
$977$	−28.7771	−0.920661	−0.460330	−	0.887748i	$-0.652269\pi$
$977$	−28.7771	−0.920661	−0.460330	+	0.887748i	$0.652269\pi$
$978$	4.32624	0.138338
$979$	0	0
$980$	0.381966	0.0122015
$981$	10.8541	0.346545
$982$	35.1246	1.12087
$983$	1.40325	0.0447568	0.0223784	−	0.999750i	$-0.492876\pi$
$983$	1.40325	0.0447568	0.0223784	+	0.999750i	$0.492876\pi$
$984$	7.03444	0.224250
$985$	16.4721	0.524846
$986$	37.5066	1.19445
$987$	11.8541	0.377320
$988$	0.360680	0.0114748
$989$	−19.4853	−0.619596
$990$	0	0
$991$	−26.3820	−0.838051	−0.419025	−	0.907975i	$-0.637628\pi$
$991$	−26.3820	−0.838051	−0.419025	+	0.907975i	$0.637628\pi$
$992$	−10.1459	−0.322133
$993$	32.7082	1.03796
$994$	−21.7984	−0.691402
$995$	15.5836	0.494033
$996$	−0.291796	−0.00924591
$997$	−57.1935	−1.81134	−0.905668	−	0.423987i	$-0.860630\pi$
$997$	−57.1935	−1.81134	−0.905668	+	0.423987i	$0.860630\pi$
$998$	11.3262	0.358526
$999$	−6.00000	−0.189832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2541.2.a.x.1.2		2
3.2	odd	2		7623.2.a.z.1.1		2
11.7	odd	10		231.2.j.b.148.1	yes	4
11.8	odd	10		231.2.j.b.64.1	✓	4
11.10	odd	2		2541.2.a.p.1.1		2
33.8	even	10		693.2.m.d.64.1		4
33.29	even	10		693.2.m.d.379.1		4
33.32	even	2		7623.2.a.bo.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.b.64.1	✓	4	11.8	odd	10
231.2.j.b.148.1	yes	4	11.7	odd	10
693.2.m.d.64.1		4	33.8	even	10
693.2.m.d.379.1		4	33.29	even	10
2541.2.a.p.1.1		2	11.10	odd	2
2541.2.a.x.1.2		2	1.1	even	1	trivial
7623.2.a.z.1.1		2	3.2	odd	2
7623.2.a.bo.1.2		2	33.32	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2541 = 3 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2541.a (trivial)

\(f(q)\)	\(=\)	\(q+1.61803 q^{2} -1.00000 q^{3} +0.618034 q^{4} +0.618034 q^{5} -1.61803 q^{6} +1.00000 q^{7} -2.23607 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.61803 q^{2} -1.00000 q^{3} +0.618034 q^{4} +0.618034 q^{5} -1.61803 q^{6} +1.00000 q^{7} -2.23607 q^{8} +1.00000 q^{9} +1.00000 q^{10} -0.618034 q^{12} +0.236068 q^{13} +1.61803 q^{14} -0.618034 q^{15} -4.85410 q^{16} -5.47214 q^{17} +1.61803 q^{18} +2.47214 q^{19} +0.381966 q^{20} -1.00000 q^{21} -7.70820 q^{23} +2.23607 q^{24} -4.61803 q^{25} +0.381966 q^{26} -1.00000 q^{27} +0.618034 q^{28} -4.23607 q^{29} -1.00000 q^{30} +3.00000 q^{31} -3.38197 q^{32} -8.85410 q^{34} +0.618034 q^{35} +0.618034 q^{36} +6.00000 q^{37} +4.00000 q^{38} -0.236068 q^{39} -1.38197 q^{40} +3.14590 q^{41} -1.61803 q^{42} +2.52786 q^{43} +0.618034 q^{45} -12.4721 q^{46} -11.8541 q^{47} +4.85410 q^{48} +1.00000 q^{49} -7.47214 q^{50} +5.47214 q^{51} +0.145898 q^{52} +7.56231 q^{53} -1.61803 q^{54} -2.23607 q^{56} -2.47214 q^{57} -6.85410 q^{58} -2.38197 q^{59} -0.381966 q^{60} -9.94427 q^{61} +4.85410 q^{62} +1.00000 q^{63} +4.23607 q^{64} +0.145898 q^{65} +8.76393 q^{67} -3.38197 q^{68} +7.70820 q^{69} +1.00000 q^{70} -13.4721 q^{71} -2.23607 q^{72} -9.61803 q^{73} +9.70820 q^{74} +4.61803 q^{75} +1.52786 q^{76} -0.381966 q^{78} -5.09017 q^{79} -3.00000 q^{80} +1.00000 q^{81} +5.09017 q^{82} +0.472136 q^{83} -0.618034 q^{84} -3.38197 q^{85} +4.09017 q^{86} +4.23607 q^{87} -14.3262 q^{89} +1.00000 q^{90} +0.236068 q^{91} -4.76393 q^{92} -3.00000 q^{93} -19.1803 q^{94} +1.52786 q^{95} +3.38197 q^{96} -18.7082 q^{97} +1.61803 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 2 q^{3} - q^{4} - q^{5} - q^{6} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q + q^2 - 2 * q^3 - q^4 - q^5 - q^6 + 2 * q^7 + 2 * q^9	\( 2 q + q^{2} - 2 q^{3} - q^{4} - q^{5} - q^{6} + 2 q^{7} + 2 q^{9} + 2 q^{10} + q^{12} - 4 q^{13} + q^{14} + q^{15} - 3 q^{16} - 2 q^{17} + q^{18} - 4 q^{19} + 3 q^{20} - 2 q^{21} - 2 q^{23} - 7 q^{25} + 3 q^{26} - 2 q^{27} - q^{28} - 4 q^{29} - 2 q^{30} + 6 q^{31} - 9 q^{32} - 11 q^{34} - q^{35} - q^{36} + 12 q^{37} + 8 q^{38} + 4 q^{39} - 5 q^{40} + 13 q^{41} - q^{42} + 14 q^{43} - q^{45} - 16 q^{46} - 17 q^{47} + 3 q^{48} + 2 q^{49} - 6 q^{50} + 2 q^{51} + 7 q^{52} - 5 q^{53} - q^{54} + 4 q^{57} - 7 q^{58} - 7 q^{59} - 3 q^{60} - 2 q^{61} + 3 q^{62} + 2 q^{63} + 4 q^{64} + 7 q^{65} + 22 q^{67} - 9 q^{68} + 2 q^{69} + 2 q^{70} - 18 q^{71} - 17 q^{73} + 6 q^{74} + 7 q^{75} + 12 q^{76} - 3 q^{78} + q^{79} - 6 q^{80} + 2 q^{81} - q^{82} - 8 q^{83} + q^{84} - 9 q^{85} - 3 q^{86} + 4 q^{87} - 13 q^{89} + 2 q^{90} - 4 q^{91} - 14 q^{92} - 6 q^{93} - 16 q^{94} + 12 q^{95} + 9 q^{96} - 24 q^{97} + q^{98}+O(q^{100}) \) 2 * q + q^2 - 2 * q^3 - q^4 - q^5 - q^6 + 2 * q^7 + 2 * q^9 + 2 * q^10 + q^12 - 4 * q^13 + q^14 + q^15 - 3 * q^16 - 2 * q^17 + q^18 - 4 * q^19 + 3 * q^20 - 2 * q^21 - 2 * q^23 - 7 * q^25 + 3 * q^26 - 2 * q^27 - q^28 - 4 * q^29 - 2 * q^30 + 6 * q^31 - 9 * q^32 - 11 * q^34 - q^35 - q^36 + 12 * q^37 + 8 * q^38 + 4 * q^39 - 5 * q^40 + 13 * q^41 - q^42 + 14 * q^43 - q^45 - 16 * q^46 - 17 * q^47 + 3 * q^48 + 2 * q^49 - 6 * q^50 + 2 * q^51 + 7 * q^52 - 5 * q^53 - q^54 + 4 * q^57 - 7 * q^58 - 7 * q^59 - 3 * q^60 - 2 * q^61 + 3 * q^62 + 2 * q^63 + 4 * q^64 + 7 * q^65 + 22 * q^67 - 9 * q^68 + 2 * q^69 + 2 * q^70 - 18 * q^71 - 17 * q^73 + 6 * q^74 + 7 * q^75 + 12 * q^76 - 3 * q^78 + q^79 - 6 * q^80 + 2 * q^81 - q^82 - 8 * q^83 + q^84 - 9 * q^85 - 3 * q^86 + 4 * q^87 - 13 * q^89 + 2 * q^90 - 4 * q^91 - 14 * q^92 - 6 * q^93 - 16 * q^94 + 12 * q^95 + 9 * q^96 - 24 * q^97 + q^98

Introduction

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