LMFDB - Embedded newform 2541.2.a.w.1.1

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:	$0$
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:	$\Z[a_1, \ldots, a_{5}]$
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			1.1
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)

$f(q)$	$=$	$q-2.23607 q^{2} -1.00000 q^{3} +3.00000 q^{4} +1.61803 q^{5} +2.23607 q^{6} +1.00000 q^{7} -2.23607 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.23607 q^{2} -1.00000 q^{3} +3.00000 q^{4} +1.61803 q^{5} +2.23607 q^{6} +1.00000 q^{7} -2.23607 q^{8} +1.00000 q^{9} -3.61803 q^{10} -3.00000 q^{12} -1.23607 q^{13} -2.23607 q^{14} -1.61803 q^{15} -1.00000 q^{16} -1.85410 q^{17} -2.23607 q^{18} -3.85410 q^{19} +4.85410 q^{20} -1.00000 q^{21} +6.61803 q^{23} +2.23607 q^{24} -2.38197 q^{25} +2.76393 q^{26} -1.00000 q^{27} +3.00000 q^{28} -6.00000 q^{29} +3.61803 q^{30} +8.09017 q^{31} +6.70820 q^{32} +4.14590 q^{34} +1.61803 q^{35} +3.00000 q^{36} +2.38197 q^{37} +8.61803 q^{38} +1.23607 q^{39} -3.61803 q^{40} +9.61803 q^{41} +2.23607 q^{42} -3.70820 q^{43} +1.61803 q^{45} -14.7984 q^{46} -4.47214 q^{47} +1.00000 q^{48} +1.00000 q^{49} +5.32624 q^{50} +1.85410 q^{51} -3.70820 q^{52} +11.2361 q^{53} +2.23607 q^{54} -2.23607 q^{56} +3.85410 q^{57} +13.4164 q^{58} -1.23607 q^{59} -4.85410 q^{60} -18.0902 q^{62} +1.00000 q^{63} -13.0000 q^{64} -2.00000 q^{65} -5.56231 q^{68} -6.61803 q^{69} -3.61803 q^{70} +12.9443 q^{71} -2.23607 q^{72} +0.291796 q^{73} -5.32624 q^{74} +2.38197 q^{75} -11.5623 q^{76} -2.76393 q^{78} -10.0000 q^{79} -1.61803 q^{80} +1.00000 q^{81} -21.5066 q^{82} +7.52786 q^{83} -3.00000 q^{84} -3.00000 q^{85} +8.29180 q^{86} +6.00000 q^{87} +3.38197 q^{89} -3.61803 q^{90} -1.23607 q^{91} +19.8541 q^{92} -8.09017 q^{93} +10.0000 q^{94} -6.23607 q^{95} -6.70820 q^{96} -6.00000 q^{97} -2.23607 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} + 6 q^{4} + q^{5} + 2 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^3 + 6 * q^4 + q^5 + 2 * q^7 + 2 * q^9	$ 2 q - 2 q^{3} + 6 q^{4} + q^{5} + 2 q^{7} + 2 q^{9} - 5 q^{10} - 6 q^{12} + 2 q^{13} - q^{15} - 2 q^{16} + 3 q^{17} - q^{19} + 3 q^{20} - 2 q^{21} + 11 q^{23} - 7 q^{25} + 10 q^{26} - 2 q^{27} + 6 q^{28} - 12 q^{29} + 5 q^{30} + 5 q^{31} + 15 q^{34} + q^{35} + 6 q^{36} + 7 q^{37} + 15 q^{38} - 2 q^{39} - 5 q^{40} + 17 q^{41} + 6 q^{43} + q^{45} - 5 q^{46} + 2 q^{48} + 2 q^{49} - 5 q^{50} - 3 q^{51} + 6 q^{52} + 18 q^{53} + q^{57} + 2 q^{59} - 3 q^{60} - 25 q^{62} + 2 q^{63} - 26 q^{64} - 4 q^{65} + 9 q^{68} - 11 q^{69} - 5 q^{70} + 8 q^{71} + 14 q^{73} + 5 q^{74} + 7 q^{75} - 3 q^{76} - 10 q^{78} - 20 q^{79} - q^{80} + 2 q^{81} - 5 q^{82} + 24 q^{83} - 6 q^{84} - 6 q^{85} + 30 q^{86} + 12 q^{87} + 9 q^{89} - 5 q^{90} + 2 q^{91} + 33 q^{92} - 5 q^{93} + 20 q^{94} - 8 q^{95} - 12 q^{97}+O(q^{100}) $ 2 * q - 2 * q^3 + 6 * q^4 + q^5 + 2 * q^7 + 2 * q^9 - 5 * q^10 - 6 * q^12 + 2 * q^13 - q^15 - 2 * q^16 + 3 * q^17 - q^19 + 3 * q^20 - 2 * q^21 + 11 * q^23 - 7 * q^25 + 10 * q^26 - 2 * q^27 + 6 * q^28 - 12 * q^29 + 5 * q^30 + 5 * q^31 + 15 * q^34 + q^35 + 6 * q^36 + 7 * q^37 + 15 * q^38 - 2 * q^39 - 5 * q^40 + 17 * q^41 + 6 * q^43 + q^45 - 5 * q^46 + 2 * q^48 + 2 * q^49 - 5 * q^50 - 3 * q^51 + 6 * q^52 + 18 * q^53 + q^57 + 2 * q^59 - 3 * q^60 - 25 * q^62 + 2 * q^63 - 26 * q^64 - 4 * q^65 + 9 * q^68 - 11 * q^69 - 5 * q^70 + 8 * q^71 + 14 * q^73 + 5 * q^74 + 7 * q^75 - 3 * q^76 - 10 * q^78 - 20 * q^79 - q^80 + 2 * q^81 - 5 * q^82 + 24 * q^83 - 6 * q^84 - 6 * q^85 + 30 * q^86 + 12 * q^87 + 9 * q^89 - 5 * q^90 + 2 * q^91 + 33 * q^92 - 5 * q^93 + 20 * q^94 - 8 * q^95 - 12 * 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 $

$2$	−2.23607	−1.58114	−0.790569	−	0.612372i	$-0.790215\pi$
$2$	−2.23607	−1.58114	−0.790569	+	0.612372i	$0.790215\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.00000	1.50000
$5$	1.61803	0.723607	0.361803	−	0.932254i	$-0.382161\pi$
$5$	1.61803	0.723607	0.361803	+	0.932254i	$0.382161\pi$
$6$	2.23607	0.912871
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.23607	−0.790569
$9$	1.00000	0.333333
$10$	−3.61803	−1.14412
$11$	0	0
$11$	0	0
$12$	−3.00000	−0.866025
$13$	−1.23607	−0.342824	−0.171412	−	0.985199i	$-0.554833\pi$
$13$	−1.23607	−0.342824	−0.171412	+	0.985199i	$0.554833\pi$
$14$	−2.23607	−0.597614
$15$	−1.61803	−0.417775
$16$	−1.00000	−0.250000
$17$	−1.85410	−0.449686	−0.224843	−	0.974395i	$-0.572187\pi$
$17$	−1.85410	−0.449686	−0.224843	+	0.974395i	$0.572187\pi$
$18$	−2.23607	−0.527046
$19$	−3.85410	−0.884192	−0.442096	−	0.896968i	$-0.645765\pi$
$19$	−3.85410	−0.884192	−0.442096	+	0.896968i	$0.645765\pi$
$20$	4.85410	1.08541
$21$	−1.00000	−0.218218
$22$	0	0
$23$	6.61803	1.37996	0.689978	−	0.723831i	$-0.257620\pi$
$23$	6.61803	1.37996	0.689978	+	0.723831i	$0.257620\pi$
$24$	2.23607	0.456435
$25$	−2.38197	−0.476393
$26$	2.76393	0.542052
$27$	−1.00000	−0.192450
$28$	3.00000	0.566947
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	3.61803	0.660560
$31$	8.09017	1.45304	0.726519	−	0.687147i	$-0.241137\pi$
$31$	8.09017	1.45304	0.726519	+	0.687147i	$0.241137\pi$
$32$	6.70820	1.18585
$33$	0	0
$34$	4.14590	0.711016
$35$	1.61803	0.273498
$36$	3.00000	0.500000
$37$	2.38197	0.391593	0.195796	−	0.980645i	$-0.437271\pi$
$37$	2.38197	0.391593	0.195796	+	0.980645i	$0.437271\pi$
$38$	8.61803	1.39803
$39$	1.23607	0.197929
$40$	−3.61803	−0.572061
$41$	9.61803	1.50208	0.751042	−	0.660254i	$-0.229551\pi$
$41$	9.61803	1.50208	0.751042	+	0.660254i	$0.229551\pi$
$42$	2.23607	0.345033
$43$	−3.70820	−0.565496	−0.282748	−	0.959194i	$-0.591246\pi$
$43$	−3.70820	−0.565496	−0.282748	+	0.959194i	$0.591246\pi$
$44$	0	0
$45$	1.61803	0.241202
$46$	−14.7984	−2.18190
$47$	−4.47214	−0.652328	−0.326164	−	0.945313i	$-0.605756\pi$
$47$	−4.47214	−0.652328	−0.326164	+	0.945313i	$0.605756\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	5.32624	0.753244
$51$	1.85410	0.259626
$52$	−3.70820	−0.514235
$53$	11.2361	1.54339	0.771696	−	0.635991i	$-0.219409\pi$
$53$	11.2361	1.54339	0.771696	+	0.635991i	$0.219409\pi$
$54$	2.23607	0.304290
$55$	0	0
$56$	−2.23607	−0.298807
$57$	3.85410	0.510488
$58$	13.4164	1.76166
$59$	−1.23607	−0.160922	−0.0804612	−	0.996758i	$-0.525639\pi$
$59$	−1.23607	−0.160922	−0.0804612	+	0.996758i	$0.525639\pi$
$60$	−4.85410	−0.626662
$61$	0	0		−	1.00000i	$-0.5\pi$
$61$	0	0			1.00000i	$0.5\pi$
$62$	−18.0902	−2.29745
$63$	1.00000	0.125988
$64$	−13.0000	−1.62500
$65$	−2.00000	−0.248069
$66$	0	0
$67$	0	0		−	1.00000i	$-0.5\pi$
$67$	0	0			1.00000i	$0.5\pi$
$68$	−5.56231	−0.674529
$69$	−6.61803	−0.796718
$70$	−3.61803	−0.432438
$71$	12.9443	1.53620	0.768101	−	0.640328i	$-0.221202\pi$
$71$	12.9443	1.53620	0.768101	+	0.640328i	$0.221202\pi$
$72$	−2.23607	−0.263523
$73$	0.291796	0.0341521	0.0170761	−	0.999854i	$-0.494564\pi$
$73$	0.291796	0.0341521	0.0170761	+	0.999854i	$0.494564\pi$
$74$	−5.32624	−0.619163
$75$	2.38197	0.275046
$76$	−11.5623	−1.32629
$77$	0	0
$78$	−2.76393	−0.312954
$79$	−10.0000	−1.12509	−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000	−1.12509	−0.562544	+	0.826767i	$0.690177\pi$
$80$	−1.61803	−0.180902
$81$	1.00000	0.111111
$82$	−21.5066	−2.37500
$83$	7.52786	0.826290	0.413145	−	0.910665i	$-0.364430\pi$
$83$	7.52786	0.826290	0.413145	+	0.910665i	$0.364430\pi$
$84$	−3.00000	−0.327327
$85$	−3.00000	−0.325396
$86$	8.29180	0.894127
$87$	6.00000	0.643268
$88$	0	0
$89$	3.38197	0.358488	0.179244	−	0.983805i	$-0.442635\pi$
$89$	3.38197	0.358488	0.179244	+	0.983805i	$0.442635\pi$
$90$	−3.61803	−0.381374
$91$	−1.23607	−0.129575
$92$	19.8541	2.06993
$93$	−8.09017	−0.838912
$94$	10.0000	1.03142
$95$	−6.23607	−0.639807
$96$	−6.70820	−0.684653
$97$	−6.00000	−0.609208	−0.304604	−	0.952479i	$-0.598524\pi$
$97$	−6.00000	−0.609208	−0.304604	+	0.952479i	$0.598524\pi$
$98$	−2.23607	−0.225877
$99$	0	0
$100$	−7.14590	−0.714590
$101$	17.7984	1.77100	0.885502	−	0.464635i	$-0.153815\pi$
$101$	17.7984	1.77100	0.885502	+	0.464635i	$0.153815\pi$
$102$	−4.14590	−0.410505
$103$	−14.3262	−1.41161	−0.705803	−	0.708408i	$-0.749414\pi$
$103$	−14.3262	−1.41161	−0.705803	+	0.708408i	$0.749414\pi$
$104$	2.76393	0.271026
$105$	−1.61803	−0.157904
$106$	−25.1246	−2.44032
$107$	−8.79837	−0.850571	−0.425285	−	0.905059i	$-0.639826\pi$
$107$	−8.79837	−0.850571	−0.425285	+	0.905059i	$0.639826\pi$
$108$	−3.00000	−0.288675
$109$	2.56231	0.245424	0.122712	−	0.992442i	$-0.460841\pi$
$109$	2.56231	0.245424	0.122712	+	0.992442i	$0.460841\pi$
$110$	0	0
$111$	−2.38197	−0.226086
$112$	−1.00000	−0.0944911
$113$	−0.763932	−0.0718647	−0.0359323	−	0.999354i	$-0.511440\pi$
$113$	−0.763932	−0.0718647	−0.0359323	+	0.999354i	$0.511440\pi$
$114$	−8.61803	−0.807153
$115$	10.7082	0.998545
$116$	−18.0000	−1.67126
$117$	−1.23607	−0.114275
$118$	2.76393	0.254441
$119$	−1.85410	−0.169965
$120$	3.61803	0.330280
$121$	0	0
$122$	0	0
$123$	−9.61803	−0.867229
$124$	24.2705	2.17956
$125$	−11.9443	−1.06833
$126$	−2.23607	−0.199205
$127$	13.7082	1.21641	0.608203	−	0.793781i	$-0.291891\pi$
$127$	13.7082	1.21641	0.608203	+	0.793781i	$0.291891\pi$
$128$	15.6525	1.38350
$129$	3.70820	0.326489
$130$	4.47214	0.392232
$131$	14.6525	1.28019	0.640096	−	0.768295i	$-0.278894\pi$
$131$	14.6525	1.28019	0.640096	+	0.768295i	$0.278894\pi$
$132$	0	0
$133$	−3.85410	−0.334193
$134$	0	0
$135$	−1.61803	−0.139258
$136$	4.14590	0.355508
$137$	−14.1803	−1.21151	−0.605754	−	0.795652i	$-0.707128\pi$
$137$	−14.1803	−1.21151	−0.605754	+	0.795652i	$0.707128\pi$
$138$	14.7984	1.25972
$139$	19.8541	1.68400	0.842001	−	0.539475i	$-0.181377\pi$
$139$	19.8541	1.68400	0.842001	+	0.539475i	$0.181377\pi$
$140$	4.85410	0.410246
$141$	4.47214	0.376622
$142$	−28.9443	−2.42895
$143$	0	0
$144$	−1.00000	−0.0833333
$145$	−9.70820	−0.806222
$146$	−0.652476	−0.0539993
$147$	−1.00000	−0.0824786
$148$	7.14590	0.587389
$149$	12.9443	1.06044	0.530218	−	0.847861i	$-0.322110\pi$
$149$	12.9443	1.06044	0.530218	+	0.847861i	$0.322110\pi$
$150$	−5.32624	−0.434886
$151$	−24.4721	−1.99151	−0.995757	−	0.0920207i	$-0.970667\pi$
$151$	−24.4721	−1.99151	−0.995757	+	0.0920207i	$0.970667\pi$
$152$	8.61803	0.699015
$153$	−1.85410	−0.149895
$154$	0	0
$155$	13.0902	1.05143
$156$	3.70820	0.296894
$157$	17.1246	1.36669	0.683346	−	0.730094i	$-0.260524\pi$
$157$	17.1246	1.36669	0.683346	+	0.730094i	$0.260524\pi$
$158$	22.3607	1.77892
$159$	−11.2361	−0.891078
$160$	10.8541	0.858092
$161$	6.61803	0.521574
$162$	−2.23607	−0.175682
$163$	−10.0000	−0.783260	−0.391630	−	0.920123i	$-0.628089\pi$
$163$	−10.0000	−0.783260	−0.391630	+	0.920123i	$0.628089\pi$
$164$	28.8541	2.25313
$165$	0	0
$166$	−16.8328	−1.30648
$167$	−16.7639	−1.29723	−0.648616	−	0.761116i	$-0.724652\pi$
$167$	−16.7639	−1.29723	−0.648616	+	0.761116i	$0.724652\pi$
$168$	2.23607	0.172516
$169$	−11.4721	−0.882472
$170$	6.70820	0.514496
$171$	−3.85410	−0.294731
$172$	−11.1246	−0.848244
$173$	−11.3820	−0.865355	−0.432677	−	0.901549i	$-0.642431\pi$
$173$	−11.3820	−0.865355	−0.432677	+	0.901549i	$0.642431\pi$
$174$	−13.4164	−1.01710
$175$	−2.38197	−0.180060
$176$	0	0
$177$	1.23607	0.0929086
$178$	−7.56231	−0.566819
$179$	9.79837	0.732365	0.366182	−	0.930543i	$-0.380665\pi$
$179$	9.79837	0.732365	0.366182	+	0.930543i	$0.380665\pi$
$180$	4.85410	0.361803
$181$	15.8885	1.18099	0.590493	−	0.807043i	$-0.298933\pi$
$181$	15.8885	1.18099	0.590493	+	0.807043i	$0.298933\pi$
$182$	2.76393	0.204876
$183$	0	0
$184$	−14.7984	−1.09095
$185$	3.85410	0.283359
$186$	18.0902	1.32644
$187$	0	0
$188$	−13.4164	−0.978492
$189$	−1.00000	−0.0727393
$190$	13.9443	1.01162
$191$	16.0902	1.16424	0.582122	−	0.813102i	$-0.302223\pi$
$191$	16.0902	1.16424	0.582122	+	0.813102i	$0.302223\pi$
$192$	13.0000	0.938194
$193$	−15.1459	−1.09023	−0.545113	−	0.838363i	$-0.683513\pi$
$193$	−15.1459	−1.09023	−0.545113	+	0.838363i	$0.683513\pi$
$194$	13.4164	0.963242
$195$	2.00000	0.143223
$196$	3.00000	0.214286
$197$	13.5279	0.963820	0.481910	−	0.876221i	$-0.339943\pi$
$197$	13.5279	0.963820	0.481910	+	0.876221i	$0.339943\pi$
$198$	0	0
$199$	19.8541	1.40742	0.703710	−	0.710487i	$-0.251525\pi$
$199$	19.8541	1.40742	0.703710	+	0.710487i	$0.251525\pi$
$200$	5.32624	0.376622
$201$	0	0
$202$	−39.7984	−2.80020
$203$	−6.00000	−0.421117
$204$	5.56231	0.389439
$205$	15.5623	1.08692
$206$	32.0344	2.23195
$207$	6.61803	0.459985
$208$	1.23607	0.0857059
$209$	0	0
$210$	3.61803	0.249668
$211$	26.3607	1.81474	0.907372	−	0.420328i	$-0.138085\pi$
$211$	26.3607	1.81474	0.907372	+	0.420328i	$0.138085\pi$
$212$	33.7082	2.31509
$213$	−12.9443	−0.886927
$214$	19.6738	1.34487
$215$	−6.00000	−0.409197
$216$	2.23607	0.152145
$217$	8.09017	0.549197
$218$	−5.72949	−0.388050
$219$	−0.291796	−0.0197178
$220$	0	0
$221$	2.29180	0.154163
$222$	5.32624	0.357474
$223$	17.3820	1.16398	0.581991	−	0.813195i	$-0.302274\pi$
$223$	17.3820	1.16398	0.581991	+	0.813195i	$0.302274\pi$
$224$	6.70820	0.448211
$225$	−2.38197	−0.158798
$226$	1.70820	0.113628
$227$	3.52786	0.234153	0.117076	−	0.993123i	$-0.462648\pi$
$227$	3.52786	0.234153	0.117076	+	0.993123i	$0.462648\pi$
$228$	11.5623	0.765732
$229$	−6.18034	−0.408408	−0.204204	−	0.978928i	$-0.565461\pi$
$229$	−6.18034	−0.408408	−0.204204	+	0.978928i	$0.565461\pi$
$230$	−23.9443	−1.57884
$231$	0	0
$232$	13.4164	0.880830
$233$	−2.29180	−0.150141	−0.0750703	−	0.997178i	$-0.523918\pi$
$233$	−2.29180	−0.150141	−0.0750703	+	0.997178i	$0.523918\pi$
$234$	2.76393	0.180684
$235$	−7.23607	−0.472029
$236$	−3.70820	−0.241384
$237$	10.0000	0.649570
$238$	4.14590	0.268739
$239$	10.0344	0.649074	0.324537	−	0.945873i	$-0.394792\pi$
$239$	10.0344	0.649074	0.324537	+	0.945873i	$0.394792\pi$
$240$	1.61803	0.104444
$241$	12.0000	0.772988	0.386494	−	0.922292i	$-0.373686\pi$
$241$	12.0000	0.772988	0.386494	+	0.922292i	$0.373686\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	0	0
$245$	1.61803	0.103372
$246$	21.5066	1.37121
$247$	4.76393	0.303122
$248$	−18.0902	−1.14873
$249$	−7.52786	−0.477059
$250$	26.7082	1.68918
$251$	14.2918	0.902090	0.451045	−	0.892501i	$-0.351051\pi$
$251$	14.2918	0.902090	0.451045	+	0.892501i	$0.351051\pi$
$252$	3.00000	0.188982
$253$	0	0
$254$	−30.6525	−1.92331
$255$	3.00000	0.187867
$256$	−9.00000	−0.562500
$257$	−31.4508	−1.96185	−0.980925	−	0.194386i	$-0.937728\pi$
$257$	−31.4508	−1.96185	−0.980925	+	0.194386i	$0.937728\pi$
$258$	−8.29180	−0.516225
$259$	2.38197	0.148008
$260$	−6.00000	−0.372104
$261$	−6.00000	−0.371391
$262$	−32.7639	−2.02416
$263$	4.14590	0.255647	0.127824	−	0.991797i	$-0.459201\pi$
$263$	4.14590	0.255647	0.127824	+	0.991797i	$0.459201\pi$
$264$	0	0
$265$	18.1803	1.11681
$266$	8.61803	0.528406
$267$	−3.38197	−0.206973
$268$	0	0
$269$	13.4164	0.818013	0.409006	−	0.912532i	$-0.365875\pi$
$269$	13.4164	0.818013	0.409006	+	0.912532i	$0.365875\pi$
$270$	3.61803	0.220187
$271$	15.5066	0.941958	0.470979	−	0.882145i	$-0.343901\pi$
$271$	15.5066	0.941958	0.470979	+	0.882145i	$0.343901\pi$
$272$	1.85410	0.112421
$273$	1.23607	0.0748102
$274$	31.7082	1.91556
$275$	0	0
$276$	−19.8541	−1.19508
$277$	11.0902	0.666344	0.333172	−	0.942866i	$-0.391881\pi$
$277$	11.0902	0.666344	0.333172	+	0.942866i	$0.391881\pi$
$278$	−44.3951	−2.66264
$279$	8.09017	0.484346
$280$	−3.61803	−0.216219
$281$	−9.05573	−0.540219	−0.270110	−	0.962830i	$-0.587060\pi$
$281$	−9.05573	−0.540219	−0.270110	+	0.962830i	$0.587060\pi$
$282$	−10.0000	−0.595491
$283$	16.2705	0.967181	0.483591	−	0.875294i	$-0.339332\pi$
$283$	16.2705	0.967181	0.483591	+	0.875294i	$0.339332\pi$
$284$	38.8328	2.30430
$285$	6.23607	0.369393
$286$	0	0
$287$	9.61803	0.567735
$288$	6.70820	0.395285
$289$	−13.5623	−0.797783
$290$	21.7082	1.27475
$291$	6.00000	0.351726
$292$	0.875388	0.0512282
$293$	33.2148	1.94043	0.970214	−	0.242249i	$-0.0778851\pi$
$293$	33.2148	1.94043	0.970214	+	0.242249i	$0.0778851\pi$
$294$	2.23607	0.130410
$295$	−2.00000	−0.116445
$296$	−5.32624	−0.309581
$297$	0	0
$298$	−28.9443	−1.67670
$299$	−8.18034	−0.473081
$300$	7.14590	0.412569
$301$	−3.70820	−0.213737
$302$	54.7214	3.14886
$303$	−17.7984	−1.02249
$304$	3.85410	0.221048
$305$	0	0
$306$	4.14590	0.237005
$307$	2.56231	0.146239	0.0731193	−	0.997323i	$-0.476705\pi$
$307$	2.56231	0.146239	0.0731193	+	0.997323i	$0.476705\pi$
$308$	0	0
$309$	14.3262	0.814991
$310$	−29.2705	−1.66245
$311$	−10.6525	−0.604046	−0.302023	−	0.953301i	$-0.597662\pi$
$311$	−10.6525	−0.604046	−0.302023	+	0.953301i	$0.597662\pi$
$312$	−2.76393	−0.156477
$313$	−30.1803	−1.70589	−0.852947	−	0.521998i	$-0.825187\pi$
$313$	−30.1803	−1.70589	−0.852947	+	0.521998i	$0.825187\pi$
$314$	−38.2918	−2.16093
$315$	1.61803	0.0911659
$316$	−30.0000	−1.68763
$317$	11.2361	0.631080	0.315540	−	0.948912i	$-0.397814\pi$
$317$	11.2361	0.631080	0.315540	+	0.948912i	$0.397814\pi$
$318$	25.1246	1.40892
$319$	0	0
$320$	−21.0344	−1.17586
$321$	8.79837	0.491077
$322$	−14.7984	−0.824681
$323$	7.14590	0.397608
$324$	3.00000	0.166667
$325$	2.94427	0.163319
$326$	22.3607	1.23844
$327$	−2.56231	−0.141696
$328$	−21.5066	−1.18750
$329$	−4.47214	−0.246557
$330$	0	0
$331$	−9.41641	−0.517573	−0.258786	−	0.965935i	$-0.583323\pi$
$331$	−9.41641	−0.517573	−0.258786	+	0.965935i	$0.583323\pi$
$332$	22.5836	1.23944
$333$	2.38197	0.130531
$334$	37.4853	2.05110
$335$	0	0
$336$	1.00000	0.0545545
$337$	15.9098	0.866664	0.433332	−	0.901234i	$-0.357338\pi$
$337$	15.9098	0.866664	0.433332	+	0.901234i	$0.357338\pi$
$338$	25.6525	1.39531
$339$	0.763932	0.0414911
$340$	−9.00000	−0.488094
$341$	0	0
$342$	8.61803	0.466010
$343$	1.00000	0.0539949
$344$	8.29180	0.447064
$345$	−10.7082	−0.576510
$346$	25.4508	1.36825
$347$	23.5066	1.26190	0.630950	−	0.775824i	$-0.282665\pi$
$347$	23.5066	1.26190	0.630950	+	0.775824i	$0.282665\pi$
$348$	18.0000	0.964901
$349$	−8.29180	−0.443850	−0.221925	−	0.975064i	$-0.571234\pi$
$349$	−8.29180	−0.443850	−0.221925	+	0.975064i	$0.571234\pi$
$350$	5.32624	0.284699
$351$	1.23607	0.0659764
$352$	0	0
$353$	−18.0000	−0.958043	−0.479022	−	0.877803i	$-0.659008\pi$
$353$	−18.0000	−0.958043	−0.479022	+	0.877803i	$0.659008\pi$
$354$	−2.76393	−0.146901
$355$	20.9443	1.11161
$356$	10.1459	0.537732
$357$	1.85410	0.0981295
$358$	−21.9098	−1.15797
$359$	26.5623	1.40190	0.700952	−	0.713208i	$-0.252759\pi$
$359$	26.5623	1.40190	0.700952	+	0.713208i	$0.252759\pi$
$360$	−3.61803	−0.190687
$361$	−4.14590	−0.218205
$362$	−35.5279	−1.86730
$363$	0	0
$364$	−3.70820	−0.194363
$365$	0.472136	0.0247127
$366$	0	0
$367$	36.2705	1.89331	0.946653	−	0.322256i	$-0.104441\pi$
$367$	36.2705	1.89331	0.946653	+	0.322256i	$0.104441\pi$
$368$	−6.61803	−0.344989
$369$	9.61803	0.500695
$370$	−8.61803	−0.448030
$371$	11.2361	0.583348
$372$	−24.2705	−1.25837
$373$	0.673762	0.0348861	0.0174430	−	0.999848i	$-0.494447\pi$
$373$	0.673762	0.0348861	0.0174430	+	0.999848i	$0.494447\pi$
$374$	0	0
$375$	11.9443	0.616800
$376$	10.0000	0.515711
$377$	7.41641	0.381964
$378$	2.23607	0.115011
$379$	30.4721	1.56525	0.782624	−	0.622494i	$-0.213881\pi$
$379$	30.4721	1.56525	0.782624	+	0.622494i	$0.213881\pi$
$380$	−18.7082	−0.959711
$381$	−13.7082	−0.702293
$382$	−35.9787	−1.84083
$383$	32.8328	1.67768	0.838839	−	0.544379i	$-0.183235\pi$
$383$	32.8328	1.67768	0.838839	+	0.544379i	$0.183235\pi$
$384$	−15.6525	−0.798762
$385$	0	0
$386$	33.8673	1.72380
$387$	−3.70820	−0.188499
$388$	−18.0000	−0.913812
$389$	10.7639	0.545753	0.272877	−	0.962049i	$-0.412025\pi$
$389$	10.7639	0.545753	0.272877	+	0.962049i	$0.412025\pi$
$390$	−4.47214	−0.226455
$391$	−12.2705	−0.620546
$392$	−2.23607	−0.112938
$393$	−14.6525	−0.739120
$394$	−30.2492	−1.52393
$395$	−16.1803	−0.814121
$396$	0	0
$397$	−36.5410	−1.83394	−0.916971	−	0.398955i	$-0.869373\pi$
$397$	−36.5410	−1.83394	−0.916971	+	0.398955i	$0.869373\pi$
$398$	−44.3951	−2.22533
$399$	3.85410	0.192946
$400$	2.38197	0.119098
$401$	−19.4164	−0.969609	−0.484805	−	0.874623i	$-0.661109\pi$
$401$	−19.4164	−0.969609	−0.484805	+	0.874623i	$0.661109\pi$
$402$	0	0
$403$	−10.0000	−0.498135
$404$	53.3951	2.65651
$405$	1.61803	0.0804008
$406$	13.4164	0.665845
$407$	0	0
$408$	−4.14590	−0.205253
$409$	0.180340	0.00891723	0.00445862	−	0.999990i	$-0.498581\pi$
$409$	0.180340	0.00891723	0.00445862	+	0.999990i	$0.498581\pi$
$410$	−34.7984	−1.71857
$411$	14.1803	0.699465
$412$	−42.9787	−2.11741
$413$	−1.23607	−0.0608229
$414$	−14.7984	−0.727300
$415$	12.1803	0.597909
$416$	−8.29180	−0.406539
$417$	−19.8541	−0.972260
$418$	0	0
$419$	1.23607	0.0603859	0.0301929	−	0.999544i	$-0.490388\pi$
$419$	1.23607	0.0603859	0.0301929	+	0.999544i	$0.490388\pi$
$420$	−4.85410	−0.236856
$421$	−14.7984	−0.721229	−0.360614	−	0.932715i	$-0.617433\pi$
$421$	−14.7984	−0.721229	−0.360614	+	0.932715i	$0.617433\pi$
$422$	−58.9443	−2.86936
$423$	−4.47214	−0.217443
$424$	−25.1246	−1.22016
$425$	4.41641	0.214227
$426$	28.9443	1.40235
$427$	0	0
$428$	−26.3951	−1.27586
$429$	0	0
$430$	13.4164	0.646997
$431$	3.90983	0.188330	0.0941649	−	0.995557i	$-0.469982\pi$
$431$	3.90983	0.188330	0.0941649	+	0.995557i	$0.469982\pi$
$432$	1.00000	0.0481125
$433$	−26.7639	−1.28619	−0.643096	−	0.765785i	$-0.722350\pi$
$433$	−26.7639	−1.28619	−0.643096	+	0.765785i	$0.722350\pi$
$434$	−18.0902	−0.868356
$435$	9.70820	0.465473
$436$	7.68692	0.368137
$437$	−25.5066	−1.22015
$438$	0.652476	0.0311765
$439$	−4.85410	−0.231674	−0.115837	−	0.993268i	$-0.536955\pi$
$439$	−4.85410	−0.231674	−0.115837	+	0.993268i	$0.536955\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	−5.12461	−0.243753
$443$	22.6180	1.07462	0.537308	−	0.843386i	$-0.319441\pi$
$443$	22.6180	1.07462	0.537308	+	0.843386i	$0.319441\pi$
$444$	−7.14590	−0.339129
$445$	5.47214	0.259404
$446$	−38.8673	−1.84042
$447$	−12.9443	−0.612243
$448$	−13.0000	−0.614192
$449$	−6.11146	−0.288417	−0.144209	−	0.989547i	$-0.546064\pi$
$449$	−6.11146	−0.288417	−0.144209	+	0.989547i	$0.546064\pi$
$450$	5.32624	0.251081
$451$	0	0
$452$	−2.29180	−0.107797
$453$	24.4721	1.14980
$454$	−7.88854	−0.370228
$455$	−2.00000	−0.0937614
$456$	−8.61803	−0.403576
$457$	−5.41641	−0.253369	−0.126684	−	0.991943i	$-0.540434\pi$
$457$	−5.41641	−0.253369	−0.126684	+	0.991943i	$0.540434\pi$
$458$	13.8197	0.645750
$459$	1.85410	0.0865421
$460$	32.1246	1.49782
$461$	−6.00000	−0.279448	−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000	−0.279448	−0.139724	+	0.990190i	$0.544622\pi$
$462$	0	0
$463$	3.41641	0.158774	0.0793870	−	0.996844i	$-0.474704\pi$
$463$	3.41641	0.158774	0.0793870	+	0.996844i	$0.474704\pi$
$464$	6.00000	0.278543
$465$	−13.0902	−0.607042
$466$	5.12461	0.237393
$467$	3.81966	0.176753	0.0883764	−	0.996087i	$-0.471832\pi$
$467$	3.81966	0.176753	0.0883764	+	0.996087i	$0.471832\pi$
$468$	−3.70820	−0.171412
$469$	0	0
$470$	16.1803	0.746343
$471$	−17.1246	−0.789060
$472$	2.76393	0.127220
$473$	0	0
$474$	−22.3607	−1.02706
$475$	9.18034	0.421223
$476$	−5.56231	−0.254948
$477$	11.2361	0.514464
$478$	−22.4377	−1.02628
$479$	16.9443	0.774204	0.387102	−	0.922037i	$-0.373476\pi$
$479$	16.9443	0.774204	0.387102	+	0.922037i	$0.373476\pi$
$480$	−10.8541	−0.495420
$481$	−2.94427	−0.134247
$482$	−26.8328	−1.22220
$483$	−6.61803	−0.301131
$484$	0	0
$485$	−9.70820	−0.440827
$486$	2.23607	0.101430
$487$	14.2918	0.647623	0.323812	−	0.946122i	$-0.395036\pi$
$487$	14.2918	0.647623	0.323812	+	0.946122i	$0.395036\pi$
$488$	0	0
$489$	10.0000	0.452216
$490$	−3.61803	−0.163446
$491$	−36.5066	−1.64752	−0.823759	−	0.566940i	$-0.808127\pi$
$491$	−36.5066	−1.64752	−0.823759	+	0.566940i	$0.808127\pi$
$492$	−28.8541	−1.30084
$493$	11.1246	0.501027
$494$	−10.6525	−0.479278
$495$	0	0
$496$	−8.09017	−0.363259
$497$	12.9443	0.580630
$498$	16.8328	0.754297
$499$	−19.1246	−0.856135	−0.428068	−	0.903747i	$-0.640805\pi$
$499$	−19.1246	−0.856135	−0.428068	+	0.903747i	$0.640805\pi$
$500$	−35.8328	−1.60249
$501$	16.7639	0.748957
$502$	−31.9574	−1.42633
$503$	−5.52786	−0.246475	−0.123238	−	0.992377i	$-0.539328\pi$
$503$	−5.52786	−0.246475	−0.123238	+	0.992377i	$0.539328\pi$
$504$	−2.23607	−0.0996024
$505$	28.7984	1.28151
$506$	0	0
$507$	11.4721	0.509495
$508$	41.1246	1.82461
$509$	−15.9098	−0.705191	−0.352595	−	0.935776i	$-0.614701\pi$
$509$	−15.9098	−0.705191	−0.352595	+	0.935776i	$0.614701\pi$
$510$	−6.70820	−0.297044
$511$	0.291796	0.0129083
$512$	−11.1803	−0.494106
$513$	3.85410	0.170163
$514$	70.3262	3.10196
$515$	−23.1803	−1.02145
$516$	11.1246	0.489734
$517$	0	0
$518$	−5.32624	−0.234021
$519$	11.3820	0.499613
$520$	4.47214	0.196116
$521$	3.32624	0.145725	0.0728626	−	0.997342i	$-0.476787\pi$
$521$	3.32624	0.145725	0.0728626	+	0.997342i	$0.476787\pi$
$522$	13.4164	0.587220
$523$	19.8541	0.868159	0.434080	−	0.900875i	$-0.357074\pi$
$523$	19.8541	0.868159	0.434080	+	0.900875i	$0.357074\pi$
$524$	43.9574	1.92029
$525$	2.38197	0.103958
$526$	−9.27051	−0.404213
$527$	−15.0000	−0.653410
$528$	0	0
$529$	20.7984	0.904277
$530$	−40.6525	−1.76583
$531$	−1.23607	−0.0536408
$532$	−11.5623	−0.501290
$533$	−11.8885	−0.514950
$534$	7.56231	0.327253
$535$	−14.2361	−0.615479
$536$	0	0
$537$	−9.79837	−0.422831
$538$	−30.0000	−1.29339
$539$	0	0
$540$	−4.85410	−0.208887
$541$	−0.673762	−0.0289673	−0.0144836	−	0.999895i	$-0.504610\pi$
$541$	−0.673762	−0.0289673	−0.0144836	+	0.999895i	$0.504610\pi$
$542$	−34.6738	−1.48937
$543$	−15.8885	−0.681843
$544$	−12.4377	−0.533262
$545$	4.14590	0.177591
$546$	−2.76393	−0.118285
$547$	−27.5279	−1.17701	−0.588503	−	0.808495i	$-0.700283\pi$
$547$	−27.5279	−1.17701	−0.588503	+	0.808495i	$0.700283\pi$
$548$	−42.5410	−1.81726
$549$	0	0
$550$	0	0
$551$	23.1246	0.985142
$552$	14.7984	0.629861
$553$	−10.0000	−0.425243
$554$	−24.7984	−1.05358
$555$	−3.85410	−0.163598
$556$	59.5623	2.52600
$557$	−22.3607	−0.947452	−0.473726	−	0.880672i	$-0.657091\pi$
$557$	−22.3607	−0.947452	−0.473726	+	0.880672i	$0.657091\pi$
$558$	−18.0902	−0.765818
$559$	4.58359	0.193865
$560$	−1.61803	−0.0683744
$561$	0	0
$562$	20.2492	0.854162
$563$	−18.4721	−0.778508	−0.389254	−	0.921131i	$-0.627267\pi$
$563$	−18.4721	−0.778508	−0.389254	+	0.921131i	$0.627267\pi$
$564$	13.4164	0.564933
$565$	−1.23607	−0.0520018
$566$	−36.3820	−1.52925
$567$	1.00000	0.0419961
$568$	−28.9443	−1.21447
$569$	−37.5967	−1.57614	−0.788069	−	0.615587i	$-0.788919\pi$
$569$	−37.5967	−1.57614	−0.788069	+	0.615587i	$0.788919\pi$
$570$	−13.9443	−0.584061
$571$	46.6525	1.95235	0.976173	−	0.216995i	$-0.0696256\pi$
$571$	46.6525	1.95235	0.976173	+	0.216995i	$0.0696256\pi$
$572$	0	0
$573$	−16.0902	−0.672176
$574$	−21.5066	−0.897667
$575$	−15.7639	−0.657401
$576$	−13.0000	−0.541667
$577$	−22.2918	−0.928020	−0.464010	−	0.885830i	$-0.653590\pi$
$577$	−22.2918	−0.928020	−0.464010	+	0.885830i	$0.653590\pi$
$578$	30.3262	1.26141
$579$	15.1459	0.629442
$580$	−29.1246	−1.20933
$581$	7.52786	0.312308
$582$	−13.4164	−0.556128
$583$	0	0
$584$	−0.652476	−0.0269996
$585$	−2.00000	−0.0826898
$586$	−74.2705	−3.06809
$587$	25.4164	1.04905	0.524524	−	0.851396i	$-0.324243\pi$
$587$	25.4164	1.04905	0.524524	+	0.851396i	$0.324243\pi$
$588$	−3.00000	−0.123718
$589$	−31.1803	−1.28476
$590$	4.47214	0.184115
$591$	−13.5279	−0.556462
$592$	−2.38197	−0.0978982
$593$	−15.5066	−0.636779	−0.318389	−	0.947960i	$-0.603142\pi$
$593$	−15.5066	−0.636779	−0.318389	+	0.947960i	$0.603142\pi$
$594$	0	0
$595$	−3.00000	−0.122988
$596$	38.8328	1.59065
$597$	−19.8541	−0.812574
$598$	18.2918	0.748007
$599$	−21.3820	−0.873643	−0.436822	−	0.899548i	$-0.643896\pi$
$599$	−21.3820	−0.873643	−0.436822	+	0.899548i	$0.643896\pi$
$600$	−5.32624	−0.217443
$601$	12.4721	0.508749	0.254375	−	0.967106i	$-0.418130\pi$
$601$	12.4721	0.508749	0.254375	+	0.967106i	$0.418130\pi$
$602$	8.29180	0.337948
$603$	0	0
$604$	−73.4164	−2.98727
$605$	0	0
$606$	39.7984	1.61670
$607$	34.9787	1.41974	0.709871	−	0.704332i	$-0.248753\pi$
$607$	34.9787	1.41974	0.709871	+	0.704332i	$0.248753\pi$
$608$	−25.8541	−1.04852
$609$	6.00000	0.243132
$610$	0	0
$611$	5.52786	0.223633
$612$	−5.56231	−0.224843
$613$	24.9787	1.00888	0.504440	−	0.863447i	$-0.331699\pi$
$613$	24.9787	1.00888	0.504440	+	0.863447i	$0.331699\pi$
$614$	−5.72949	−0.231223
$615$	−15.5623	−0.627533
$616$	0	0
$617$	44.0689	1.77415	0.887073	−	0.461629i	$-0.152735\pi$
$617$	44.0689	1.77415	0.887073	+	0.461629i	$0.152735\pi$
$618$	−32.0344	−1.28861
$619$	23.6869	0.952058	0.476029	−	0.879430i	$-0.342076\pi$
$619$	23.6869	0.952058	0.476029	+	0.879430i	$0.342076\pi$
$620$	39.2705	1.57714
$621$	−6.61803	−0.265573
$622$	23.8197	0.955081
$623$	3.38197	0.135496
$624$	−1.23607	−0.0494823
$625$	−7.41641	−0.296656
$626$	67.4853	2.69725
$627$	0	0
$628$	51.3738	2.05004
$629$	−4.41641	−0.176094
$630$	−3.61803	−0.144146
$631$	17.3050	0.688899	0.344450	−	0.938805i	$-0.388066\pi$
$631$	17.3050	0.688899	0.344450	+	0.938805i	$0.388066\pi$
$632$	22.3607	0.889460
$633$	−26.3607	−1.04774
$634$	−25.1246	−0.997826
$635$	22.1803	0.880200
$636$	−33.7082	−1.33662
$637$	−1.23607	−0.0489748
$638$	0	0
$639$	12.9443	0.512067
$640$	25.3262	1.00111
$641$	17.2361	0.680784	0.340392	−	0.940284i	$-0.389440\pi$
$641$	17.2361	0.680784	0.340392	+	0.940284i	$0.389440\pi$
$642$	−19.6738	−0.776461
$643$	−23.2705	−0.917699	−0.458850	−	0.888514i	$-0.651738\pi$
$643$	−23.2705	−0.917699	−0.458850	+	0.888514i	$0.651738\pi$
$644$	19.8541	0.782361
$645$	6.00000	0.236250
$646$	−15.9787	−0.628674
$647$	27.5279	1.08223	0.541116	−	0.840948i	$-0.318002\pi$
$647$	27.5279	1.08223	0.541116	+	0.840948i	$0.318002\pi$
$648$	−2.23607	−0.0878410
$649$	0	0
$650$	−6.58359	−0.258230
$651$	−8.09017	−0.317079
$652$	−30.0000	−1.17489
$653$	−28.3607	−1.10984	−0.554920	−	0.831904i	$-0.687251\pi$
$653$	−28.3607	−1.10984	−0.554920	+	0.831904i	$0.687251\pi$
$654$	5.72949	0.224041
$655$	23.7082	0.926356
$656$	−9.61803	−0.375521
$657$	0.291796	0.0113840
$658$	10.0000	0.389841
$659$	−19.1459	−0.745818	−0.372909	−	0.927868i	$-0.621640\pi$
$659$	−19.1459	−0.745818	−0.372909	+	0.927868i	$0.621640\pi$
$660$	0	0
$661$	34.5410	1.34349	0.671745	−	0.740782i	$-0.265545\pi$
$661$	34.5410	1.34349	0.671745	+	0.740782i	$0.265545\pi$
$662$	21.0557	0.818354
$663$	−2.29180	−0.0890060
$664$	−16.8328	−0.653240
$665$	−6.23607	−0.241824
$666$	−5.32624	−0.206388
$667$	−39.7082	−1.53751
$668$	−50.2918	−1.94585
$669$	−17.3820	−0.672026
$670$	0	0
$671$	0	0
$672$	−6.70820	−0.258775
$673$	8.83282	0.340480	0.170240	−	0.985403i	$-0.445546\pi$
$673$	8.83282	0.340480	0.170240	+	0.985403i	$0.445546\pi$
$674$	−35.5755	−1.37032
$675$	2.38197	0.0916819
$676$	−34.4164	−1.32371
$677$	−10.3607	−0.398193	−0.199097	−	0.979980i	$-0.563801\pi$
$677$	−10.3607	−0.398193	−0.199097	+	0.979980i	$0.563801\pi$
$678$	−1.70820	−0.0656032
$679$	−6.00000	−0.230259
$680$	6.70820	0.257248
$681$	−3.52786	−0.135188
$682$	0	0
$683$	2.20163	0.0842429	0.0421214	−	0.999112i	$-0.486588\pi$
$683$	2.20163	0.0842429	0.0421214	+	0.999112i	$0.486588\pi$
$684$	−11.5623	−0.442096
$685$	−22.9443	−0.876656
$686$	−2.23607	−0.0853735
$687$	6.18034	0.235795
$688$	3.70820	0.141374
$689$	−13.8885	−0.529111
$690$	23.9443	0.911543
$691$	6.25735	0.238041	0.119020	−	0.992892i	$-0.462025\pi$
$691$	6.25735	0.238041	0.119020	+	0.992892i	$0.462025\pi$
$692$	−34.1459	−1.29803
$693$	0	0
$694$	−52.5623	−1.99524
$695$	32.1246	1.21856
$696$	−13.4164	−0.508548
$697$	−17.8328	−0.675466
$698$	18.5410	0.701788
$699$	2.29180	0.0866837
$700$	−7.14590	−0.270090
$701$	−9.59675	−0.362464	−0.181232	−	0.983440i	$-0.558009\pi$
$701$	−9.59675	−0.362464	−0.181232	+	0.983440i	$0.558009\pi$
$702$	−2.76393	−0.104318
$703$	−9.18034	−0.346243
$704$	0	0
$705$	7.23607	0.272526
$706$	40.2492	1.51480
$707$	17.7984	0.669377
$708$	3.70820	0.139363
$709$	21.0344	0.789965	0.394983	−	0.918689i	$-0.370751\pi$
$709$	21.0344	0.789965	0.394983	+	0.918689i	$0.370751\pi$
$710$	−46.8328	−1.75760
$711$	−10.0000	−0.375029
$712$	−7.56231	−0.283409
$713$	53.5410	2.00513
$714$	−4.14590	−0.155156
$715$	0	0
$716$	29.3951	1.09855
$717$	−10.0344	−0.374743
$718$	−59.3951	−2.21661
$719$	−37.0132	−1.38036	−0.690179	−	0.723639i	$-0.742468\pi$
$719$	−37.0132	−1.38036	−0.690179	+	0.723639i	$0.742468\pi$
$720$	−1.61803	−0.0603006
$721$	−14.3262	−0.533537
$722$	9.27051	0.345013
$723$	−12.0000	−0.446285
$724$	47.6656	1.77148
$725$	14.2918	0.530784
$726$	0	0
$727$	−12.1459	−0.450466	−0.225233	−	0.974305i	$-0.572314\pi$
$727$	−12.1459	−0.450466	−0.225233	+	0.974305i	$0.572314\pi$
$728$	2.76393	0.102438
$729$	1.00000	0.0370370
$730$	−1.05573	−0.0390742
$731$	6.87539	0.254295
$732$	0	0
$733$	40.0689	1.47998	0.739989	−	0.672619i	$-0.234831\pi$
$733$	40.0689	1.47998	0.739989	+	0.672619i	$0.234831\pi$
$734$	−81.1033	−2.99358
$735$	−1.61803	−0.0596821
$736$	44.3951	1.63643
$737$	0	0
$738$	−21.5066	−0.791668
$739$	0.875388	0.0322017	0.0161008	−	0.999870i	$-0.494875\pi$
$739$	0.875388	0.0322017	0.0161008	+	0.999870i	$0.494875\pi$
$740$	11.5623	0.425039
$741$	−4.76393	−0.175007
$742$	−25.1246	−0.922354
$743$	−0.673762	−0.0247179	−0.0123590	−	0.999924i	$-0.503934\pi$
$743$	−0.673762	−0.0247179	−0.0123590	+	0.999924i	$0.503934\pi$
$744$	18.0902	0.663218
$745$	20.9443	0.767339
$746$	−1.50658	−0.0551597
$747$	7.52786	0.275430
$748$	0	0
$749$	−8.79837	−0.321486
$750$	−26.7082	−0.975246
$751$	24.0000	0.875772	0.437886	−	0.899030i	$-0.355727\pi$
$751$	24.0000	0.875772	0.437886	+	0.899030i	$0.355727\pi$
$752$	4.47214	0.163082
$753$	−14.2918	−0.520822
$754$	−16.5836	−0.603939
$755$	−39.5967	−1.44107
$756$	−3.00000	−0.109109
$757$	−9.56231	−0.347548	−0.173774	−	0.984786i	$-0.555596\pi$
$757$	−9.56231	−0.347548	−0.173774	+	0.984786i	$0.555596\pi$
$758$	−68.1378	−2.47488
$759$	0	0
$760$	13.9443	0.505812
$761$	−25.4164	−0.921344	−0.460672	−	0.887570i	$-0.652392\pi$
$761$	−25.4164	−0.921344	−0.460672	+	0.887570i	$0.652392\pi$
$762$	30.6525	1.11042
$763$	2.56231	0.0927617
$764$	48.2705	1.74637
$765$	−3.00000	−0.108465
$766$	−73.4164	−2.65264
$767$	1.52786	0.0551680
$768$	9.00000	0.324760
$769$	18.9443	0.683148	0.341574	−	0.939855i	$-0.389040\pi$
$769$	18.9443	0.683148	0.341574	+	0.939855i	$0.389040\pi$
$770$	0	0
$771$	31.4508	1.13267
$772$	−45.4377	−1.63534
$773$	−0.472136	−0.0169815	−0.00849077	−	0.999964i	$-0.502703\pi$
$773$	−0.472136	−0.0169815	−0.00849077	+	0.999964i	$0.502703\pi$
$774$	8.29180	0.298042
$775$	−19.2705	−0.692217
$776$	13.4164	0.481621
$777$	−2.38197	−0.0854526
$778$	−24.0689	−0.862911
$779$	−37.0689	−1.32813
$780$	6.00000	0.214834
$781$	0	0
$782$	27.4377	0.981170
$783$	6.00000	0.214423
$784$	−1.00000	−0.0357143
$785$	27.7082	0.988948
$786$	32.7639	1.16865
$787$	−19.1459	−0.682478	−0.341239	−	0.939977i	$-0.610846\pi$
$787$	−19.1459	−0.682478	−0.341239	+	0.939977i	$0.610846\pi$
$788$	40.5836	1.44573
$789$	−4.14590	−0.147598
$790$	36.1803	1.28724
$791$	−0.763932	−0.0271623
$792$	0	0
$793$	0	0
$794$	81.7082	2.89972
$795$	−18.1803	−0.644790
$796$	59.5623	2.11113
$797$	21.4377	0.759362	0.379681	−	0.925117i	$-0.376034\pi$
$797$	21.4377	0.759362	0.379681	+	0.925117i	$0.376034\pi$
$798$	−8.61803	−0.305075
$799$	8.29180	0.293343
$800$	−15.9787	−0.564933
$801$	3.38197	0.119496
$802$	43.4164	1.53309
$803$	0	0
$804$	0	0
$805$	10.7082	0.377415
$806$	22.3607	0.787621
$807$	−13.4164	−0.472280
$808$	−39.7984	−1.40010
$809$	2.76393	0.0971747	0.0485873	−	0.998819i	$-0.484528\pi$
$809$	2.76393	0.0971747	0.0485873	+	0.998819i	$0.484528\pi$
$810$	−3.61803	−0.127125
$811$	35.4164	1.24364	0.621819	−	0.783161i	$-0.286394\pi$
$811$	35.4164	1.24364	0.621819	+	0.783161i	$0.286394\pi$
$812$	−18.0000	−0.631676
$813$	−15.5066	−0.543839
$814$	0	0
$815$	−16.1803	−0.566773
$816$	−1.85410	−0.0649066
$817$	14.2918	0.500007
$818$	−0.403252	−0.0140994
$819$	−1.23607	−0.0431917
$820$	46.6869	1.63038
$821$	6.94427	0.242357	0.121178	−	0.992631i	$-0.461333\pi$
$821$	6.94427	0.242357	0.121178	+	0.992631i	$0.461333\pi$
$822$	−31.7082	−1.10595
$823$	−48.8328	−1.70220	−0.851102	−	0.525000i	$-0.824065\pi$
$823$	−48.8328	−1.70220	−0.851102	+	0.525000i	$0.824065\pi$
$824$	32.0344	1.11597
$825$	0	0
$826$	2.76393	0.0961695
$827$	−52.8673	−1.83837	−0.919187	−	0.393821i	$-0.871153\pi$
$827$	−52.8673	−1.83837	−0.919187	+	0.393821i	$0.871153\pi$
$828$	19.8541	0.689978
$829$	50.2492	1.74523	0.872614	−	0.488411i	$-0.162423\pi$
$829$	50.2492	1.74523	0.872614	+	0.488411i	$0.162423\pi$
$830$	−27.2361	−0.945378
$831$	−11.0902	−0.384714
$832$	16.0689	0.557088
$833$	−1.85410	−0.0642408
$834$	44.3951	1.53728
$835$	−27.1246	−0.938686
$836$	0	0
$837$	−8.09017	−0.279637
$838$	−2.76393	−0.0954784
$839$	40.2492	1.38956	0.694779	−	0.719224i	$-0.255502\pi$
$839$	40.2492	1.38956	0.694779	+	0.719224i	$0.255502\pi$
$840$	3.61803	0.124834
$841$	7.00000	0.241379
$842$	33.0902	1.14036
$843$	9.05573	0.311896
$844$	79.0820	2.72212
$845$	−18.5623	−0.638563
$846$	10.0000	0.343807
$847$	0	0
$848$	−11.2361	−0.385848
$849$	−16.2705	−0.558402
$850$	−9.87539	−0.338723
$851$	15.7639	0.540381
$852$	−38.8328	−1.33039
$853$	−28.2918	−0.968693	−0.484346	−	0.874876i	$-0.660943\pi$
$853$	−28.2918	−0.968693	−0.484346	+	0.874876i	$0.660943\pi$
$854$	0	0
$855$	−6.23607	−0.213269
$856$	19.6738	0.672435
$857$	10.3607	0.353914	0.176957	−	0.984219i	$-0.443375\pi$
$857$	10.3607	0.353914	0.176957	+	0.984219i	$0.443375\pi$
$858$	0	0
$859$	12.0000	0.409435	0.204717	−	0.978821i	$-0.434372\pi$
$859$	12.0000	0.409435	0.204717	+	0.978821i	$0.434372\pi$
$860$	−18.0000	−0.613795
$861$	−9.61803	−0.327782
$862$	−8.74265	−0.297776
$863$	3.32624	0.113226	0.0566132	−	0.998396i	$-0.481970\pi$
$863$	3.32624	0.113226	0.0566132	+	0.998396i	$0.481970\pi$
$864$	−6.70820	−0.228218
$865$	−18.4164	−0.626177
$866$	59.8460	2.03365
$867$	13.5623	0.460600
$868$	24.2705	0.823795
$869$	0	0
$870$	−21.7082	−0.735977
$871$	0	0
$872$	−5.72949	−0.194025
$873$	−6.00000	−0.203069
$874$	57.0344	1.92922
$875$	−11.9443	−0.403790
$876$	−0.875388	−0.0295766
$877$	3.52786	0.119128	0.0595638	−	0.998225i	$-0.481029\pi$
$877$	3.52786	0.119128	0.0595638	+	0.998225i	$0.481029\pi$
$878$	10.8541	0.366308
$879$	−33.2148	−1.12031
$880$	0	0
$881$	−4.32624	−0.145755	−0.0728773	−	0.997341i	$-0.523218\pi$
$881$	−4.32624	−0.145755	−0.0728773	+	0.997341i	$0.523218\pi$
$882$	−2.23607	−0.0752923
$883$	−29.5967	−0.996010	−0.498005	−	0.867174i	$-0.665934\pi$
$883$	−29.5967	−0.996010	−0.498005	+	0.867174i	$0.665934\pi$
$884$	6.87539	0.231244
$885$	2.00000	0.0672293
$886$	−50.5755	−1.69912
$887$	−21.5967	−0.725148	−0.362574	−	0.931955i	$-0.618102\pi$
$887$	−21.5967	−0.725148	−0.362574	+	0.931955i	$0.618102\pi$
$888$	5.32624	0.178737
$889$	13.7082	0.459758
$890$	−12.2361	−0.410154
$891$	0	0
$892$	52.1459	1.74597
$893$	17.2361	0.576783
$894$	28.9443	0.968041
$895$	15.8541	0.529944
$896$	15.6525	0.522913
$897$	8.18034	0.273134
$898$	13.6656	0.456028
$899$	−48.5410	−1.61893
$900$	−7.14590	−0.238197
$901$	−20.8328	−0.694042
$902$	0	0
$903$	3.70820	0.123401
$904$	1.70820	0.0568140
$905$	25.7082	0.854570
$906$	−54.7214	−1.81800
$907$	29.7082	0.986445	0.493222	−	0.869903i	$-0.335819\pi$
$907$	29.7082	0.986445	0.493222	+	0.869903i	$0.335819\pi$
$908$	10.5836	0.351229
$909$	17.7984	0.590335
$910$	4.47214	0.148250
$911$	16.9443	0.561389	0.280694	−	0.959797i	$-0.409435\pi$
$911$	16.9443	0.561389	0.280694	+	0.959797i	$0.409435\pi$
$912$	−3.85410	−0.127622
$913$	0	0
$914$	12.1115	0.400611
$915$	0	0
$916$	−18.5410	−0.612613
$917$	14.6525	0.483867
$918$	−4.14590	−0.136835
$919$	−21.5279	−0.710139	−0.355069	−	0.934840i	$-0.615543\pi$
$919$	−21.5279	−0.710139	−0.355069	+	0.934840i	$0.615543\pi$
$920$	−23.9443	−0.789419
$921$	−2.56231	−0.0844308
$922$	13.4164	0.441846
$923$	−16.0000	−0.526646
$924$	0	0
$925$	−5.67376	−0.186552
$926$	−7.63932	−0.251044
$927$	−14.3262	−0.470535
$928$	−40.2492	−1.32125
$929$	57.2705	1.87898	0.939492	−	0.342570i	$-0.111297\pi$
$929$	57.2705	1.87898	0.939492	+	0.342570i	$0.111297\pi$
$930$	29.2705	0.959818
$931$	−3.85410	−0.126313
$932$	−6.87539	−0.225211
$933$	10.6525	0.348746
$934$	−8.54102	−0.279471
$935$	0	0
$936$	2.76393	0.0903419
$937$	−24.0689	−0.786296	−0.393148	−	0.919475i	$-0.628614\pi$
$937$	−24.0689	−0.786296	−0.393148	+	0.919475i	$0.628614\pi$
$938$	0	0
$939$	30.1803	0.984898
$940$	−21.7082	−0.708044
$941$	−38.5066	−1.25528	−0.627639	−	0.778504i	$-0.715979\pi$
$941$	−38.5066	−1.25528	−0.627639	+	0.778504i	$0.715979\pi$
$942$	38.2918	1.24761
$943$	63.6525	2.07281
$944$	1.23607	0.0402306
$945$	−1.61803	−0.0526346
$946$	0	0
$947$	7.14590	0.232210	0.116105	−	0.993237i	$-0.462959\pi$
$947$	7.14590	0.232210	0.116105	+	0.993237i	$0.462959\pi$
$948$	30.0000	0.974355
$949$	−0.360680	−0.0117082
$950$	−20.5279	−0.666012
$951$	−11.2361	−0.364354
$952$	4.14590	0.134369
$953$	−23.8885	−0.773826	−0.386913	−	0.922116i	$-0.626459\pi$
$953$	−23.8885	−0.773826	−0.386913	+	0.922116i	$0.626459\pi$
$954$	−25.1246	−0.813439
$955$	26.0344	0.842455
$956$	30.1033	0.973611
$957$	0	0
$958$	−37.8885	−1.22412
$959$	−14.1803	−0.457907
$960$	21.0344	0.678884
$961$	34.4508	1.11132
$962$	6.58359	0.212264
$963$	−8.79837	−0.283524
$964$	36.0000	1.15948
$965$	−24.5066	−0.788895
$966$	14.7984	0.476130
$967$	−48.3607	−1.55517	−0.777587	−	0.628775i	$-0.783557\pi$
$967$	−48.3607	−1.55517	−0.777587	+	0.628775i	$0.783557\pi$
$968$	0	0
$969$	−7.14590	−0.229559
$970$	21.7082	0.697008
$971$	−12.5410	−0.402460	−0.201230	−	0.979544i	$-0.564494\pi$
$971$	−12.5410	−0.402460	−0.201230	+	0.979544i	$0.564494\pi$
$972$	−3.00000	−0.0962250
$973$	19.8541	0.636493
$974$	−31.9574	−1.02398
$975$	−2.94427	−0.0942922
$976$	0	0
$977$	−58.3607	−1.86712	−0.933562	−	0.358417i	$-0.883317\pi$
$977$	−58.3607	−1.86712	−0.933562	+	0.358417i	$0.883317\pi$
$978$	−22.3607	−0.715016
$979$	0	0
$980$	4.85410	0.155059
$981$	2.56231	0.0818081
$982$	81.6312	2.60496
$983$	6.94427	0.221488	0.110744	−	0.993849i	$-0.464677\pi$
$983$	6.94427	0.221488	0.110744	+	0.993849i	$0.464677\pi$
$984$	21.5066	0.685605
$985$	21.8885	0.697427
$986$	−24.8754	−0.792194
$987$	4.47214	0.142350
$988$	14.2918	0.454683
$989$	−24.5410	−0.780359
$990$	0	0
$991$	−28.7639	−0.913716	−0.456858	−	0.889540i	$-0.651025\pi$
$991$	−28.7639	−0.913716	−0.456858	+	0.889540i	$0.651025\pi$
$992$	54.2705	1.72309
$993$	9.41641	0.298821
$994$	−28.9443	−0.918057
$995$	32.1246	1.01842
$996$	−22.5836	−0.715588
$997$	58.4296	1.85048	0.925241	−	0.379379i	$-0.123862\pi$
$997$	58.4296	1.85048	0.925241	+	0.379379i	$0.123862\pi$
$998$	42.7639	1.35367
$999$	−2.38197	−0.0753621

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2541.2.a.w.1.1		2
3.2	odd	2		7623.2.a.bk.1.2		2
11.5	even	5		231.2.j.e.190.1	yes	4
11.9	even	5		231.2.j.e.169.1	✓	4
11.10	odd	2		2541.2.a.v.1.2		2
33.5	odd	10		693.2.m.a.190.1		4
33.20	odd	10		693.2.m.a.631.1		4
33.32	even	2		7623.2.a.bj.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.e.169.1	✓	4	11.9	even	5
231.2.j.e.190.1	yes	4	11.5	even	5
693.2.m.a.190.1		4	33.5	odd	10
693.2.m.a.631.1		4	33.20	odd	10
2541.2.a.v.1.2		2	11.10	odd	2
2541.2.a.w.1.1		2	1.1	even	1	trivial
7623.2.a.bj.1.1		2	33.32	even	2
7623.2.a.bk.1.2		2	3.2	odd	2

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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)

\(f(q)\)	\(=\)	\(q-2.23607 q^{2} -1.00000 q^{3} +3.00000 q^{4} +1.61803 q^{5} +2.23607 q^{6} +1.00000 q^{7} -2.23607 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.23607 q^{2} -1.00000 q^{3} +3.00000 q^{4} +1.61803 q^{5} +2.23607 q^{6} +1.00000 q^{7} -2.23607 q^{8} +1.00000 q^{9} -3.61803 q^{10} -3.00000 q^{12} -1.23607 q^{13} -2.23607 q^{14} -1.61803 q^{15} -1.00000 q^{16} -1.85410 q^{17} -2.23607 q^{18} -3.85410 q^{19} +4.85410 q^{20} -1.00000 q^{21} +6.61803 q^{23} +2.23607 q^{24} -2.38197 q^{25} +2.76393 q^{26} -1.00000 q^{27} +3.00000 q^{28} -6.00000 q^{29} +3.61803 q^{30} +8.09017 q^{31} +6.70820 q^{32} +4.14590 q^{34} +1.61803 q^{35} +3.00000 q^{36} +2.38197 q^{37} +8.61803 q^{38} +1.23607 q^{39} -3.61803 q^{40} +9.61803 q^{41} +2.23607 q^{42} -3.70820 q^{43} +1.61803 q^{45} -14.7984 q^{46} -4.47214 q^{47} +1.00000 q^{48} +1.00000 q^{49} +5.32624 q^{50} +1.85410 q^{51} -3.70820 q^{52} +11.2361 q^{53} +2.23607 q^{54} -2.23607 q^{56} +3.85410 q^{57} +13.4164 q^{58} -1.23607 q^{59} -4.85410 q^{60} -18.0902 q^{62} +1.00000 q^{63} -13.0000 q^{64} -2.00000 q^{65} -5.56231 q^{68} -6.61803 q^{69} -3.61803 q^{70} +12.9443 q^{71} -2.23607 q^{72} +0.291796 q^{73} -5.32624 q^{74} +2.38197 q^{75} -11.5623 q^{76} -2.76393 q^{78} -10.0000 q^{79} -1.61803 q^{80} +1.00000 q^{81} -21.5066 q^{82} +7.52786 q^{83} -3.00000 q^{84} -3.00000 q^{85} +8.29180 q^{86} +6.00000 q^{87} +3.38197 q^{89} -3.61803 q^{90} -1.23607 q^{91} +19.8541 q^{92} -8.09017 q^{93} +10.0000 q^{94} -6.23607 q^{95} -6.70820 q^{96} -6.00000 q^{97} -2.23607 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} + 6 q^{4} + q^{5} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^3 + 6 * q^4 + q^5 + 2 * q^7 + 2 * q^9	\( 2 q - 2 q^{3} + 6 q^{4} + q^{5} + 2 q^{7} + 2 q^{9} - 5 q^{10} - 6 q^{12} + 2 q^{13} - q^{15} - 2 q^{16} + 3 q^{17} - q^{19} + 3 q^{20} - 2 q^{21} + 11 q^{23} - 7 q^{25} + 10 q^{26} - 2 q^{27} + 6 q^{28} - 12 q^{29} + 5 q^{30} + 5 q^{31} + 15 q^{34} + q^{35} + 6 q^{36} + 7 q^{37} + 15 q^{38} - 2 q^{39} - 5 q^{40} + 17 q^{41} + 6 q^{43} + q^{45} - 5 q^{46} + 2 q^{48} + 2 q^{49} - 5 q^{50} - 3 q^{51} + 6 q^{52} + 18 q^{53} + q^{57} + 2 q^{59} - 3 q^{60} - 25 q^{62} + 2 q^{63} - 26 q^{64} - 4 q^{65} + 9 q^{68} - 11 q^{69} - 5 q^{70} + 8 q^{71} + 14 q^{73} + 5 q^{74} + 7 q^{75} - 3 q^{76} - 10 q^{78} - 20 q^{79} - q^{80} + 2 q^{81} - 5 q^{82} + 24 q^{83} - 6 q^{84} - 6 q^{85} + 30 q^{86} + 12 q^{87} + 9 q^{89} - 5 q^{90} + 2 q^{91} + 33 q^{92} - 5 q^{93} + 20 q^{94} - 8 q^{95} - 12 q^{97}+O(q^{100}) \) 2 * q - 2 * q^3 + 6 * q^4 + q^5 + 2 * q^7 + 2 * q^9 - 5 * q^10 - 6 * q^12 + 2 * q^13 - q^15 - 2 * q^16 + 3 * q^17 - q^19 + 3 * q^20 - 2 * q^21 + 11 * q^23 - 7 * q^25 + 10 * q^26 - 2 * q^27 + 6 * q^28 - 12 * q^29 + 5 * q^30 + 5 * q^31 + 15 * q^34 + q^35 + 6 * q^36 + 7 * q^37 + 15 * q^38 - 2 * q^39 - 5 * q^40 + 17 * q^41 + 6 * q^43 + q^45 - 5 * q^46 + 2 * q^48 + 2 * q^49 - 5 * q^50 - 3 * q^51 + 6 * q^52 + 18 * q^53 + q^57 + 2 * q^59 - 3 * q^60 - 25 * q^62 + 2 * q^63 - 26 * q^64 - 4 * q^65 + 9 * q^68 - 11 * q^69 - 5 * q^70 + 8 * q^71 + 14 * q^73 + 5 * q^74 + 7 * q^75 - 3 * q^76 - 10 * q^78 - 20 * q^79 - q^80 + 2 * q^81 - 5 * q^82 + 24 * q^83 - 6 * q^84 - 6 * q^85 + 30 * q^86 + 12 * q^87 + 9 * q^89 - 5 * q^90 + 2 * q^91 + 33 * q^92 - 5 * q^93 + 20 * q^94 - 8 * q^95 - 12 * q^97

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