LMFDB - Embedded newform 2009.2.a.p.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2009,2,Mod(1,2009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2009, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2009 = 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2009.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:	$16.0419457661$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 10x^{5} - x^{4} + 30x^{3} + 7x^{2} - 25x - 11 $ x^7 - 10x^5 - x^4 + 30x^3 + 7x^2 - 25x - 11
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.95500$ of defining polynomial
Character	$\chi$	$=$	2009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.822027 q^{2} +0.955000 q^{3} -1.32427 q^{4} +3.05691 q^{5} +0.785036 q^{6} -2.73264 q^{8} -2.08797 q^{9} +O(q^{10})$	\(q+0.822027 q^{2} +0.955000 q^{3} -1.32427 q^{4} +3.05691 q^{5} +0.785036 q^{6} -2.73264 q^{8} -2.08797 q^{9} +2.51286 q^{10} -6.35985 q^{11} -1.26468 q^{12} -3.93133 q^{13} +2.91935 q^{15} +0.402240 q^{16} +2.97254 q^{17} -1.71637 q^{18} +5.53594 q^{19} -4.04818 q^{20} -5.22797 q^{22} -5.46467 q^{23} -2.60967 q^{24} +4.34471 q^{25} -3.23166 q^{26} -4.85902 q^{27} -5.86753 q^{29} +2.39979 q^{30} -10.6583 q^{31} +5.79593 q^{32} -6.07366 q^{33} +2.44351 q^{34} +2.76505 q^{36} -0.638151 q^{37} +4.55069 q^{38} -3.75443 q^{39} -8.35344 q^{40} +1.00000 q^{41} -0.978093 q^{43} +8.42217 q^{44} -6.38275 q^{45} -4.49210 q^{46} +3.60757 q^{47} +0.384139 q^{48} +3.57147 q^{50} +2.83877 q^{51} +5.20616 q^{52} -2.10130 q^{53} -3.99424 q^{54} -19.4415 q^{55} +5.28683 q^{57} -4.82327 q^{58} +5.71771 q^{59} -3.86602 q^{60} -6.61771 q^{61} -8.76141 q^{62} +3.95993 q^{64} -12.0177 q^{65} -4.99271 q^{66} +2.82804 q^{67} -3.93645 q^{68} -5.21876 q^{69} -0.220124 q^{71} +5.70568 q^{72} +6.59628 q^{73} -0.524578 q^{74} +4.14920 q^{75} -7.33110 q^{76} -3.08624 q^{78} +1.73659 q^{79} +1.22961 q^{80} +1.62356 q^{81} +0.822027 q^{82} -11.9972 q^{83} +9.08679 q^{85} -0.804018 q^{86} -5.60350 q^{87} +17.3792 q^{88} -2.25846 q^{89} -5.24680 q^{90} +7.23671 q^{92} -10.1787 q^{93} +2.96552 q^{94} +16.9229 q^{95} +5.53512 q^{96} +10.9438 q^{97} +13.2792 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} - 7 q^{3} + 9 q^{4} - 4 q^{5} + 4 q^{6} - 12 q^{8} + 6 q^{9}+O(q^{10}) $ 7 * q - q^2 - 7 * q^3 + 9 * q^4 - 4 * q^5 + 4 * q^6 - 12 * q^8 + 6 * q^9	$ 7 q - q^{2} - 7 q^{3} + 9 q^{4} - 4 q^{5} + 4 q^{6} - 12 q^{8} + 6 q^{9} - 8 q^{10} - 12 q^{12} - q^{13} - 4 q^{15} + 5 q^{16} + 11 q^{17} + 16 q^{18} - 9 q^{19} - 12 q^{20} + 3 q^{23} + 23 q^{24} + 31 q^{25} - 10 q^{26} - 22 q^{27} - 14 q^{29} + 6 q^{30} - 34 q^{31} - 20 q^{32} - 12 q^{33} - 15 q^{34} + q^{36} + 7 q^{37} + 39 q^{38} - 22 q^{39} - 50 q^{40} + 7 q^{41} - 3 q^{43} + 26 q^{44} + 4 q^{45} - 8 q^{46} - 17 q^{47} - 17 q^{48} + 11 q^{50} + 8 q^{51} + 25 q^{52} + 24 q^{53} - 68 q^{54} - 48 q^{55} + 22 q^{57} - 38 q^{58} - 4 q^{59} - 6 q^{60} - 16 q^{61} - 24 q^{62} + 8 q^{64} - 6 q^{65} + 12 q^{66} - 24 q^{67} + 10 q^{68} - 35 q^{69} - 12 q^{71} - 11 q^{72} - 14 q^{73} - 6 q^{74} + 19 q^{75} - 42 q^{76} - 29 q^{78} - 8 q^{79} + 92 q^{80} + 15 q^{81} - q^{82} - 14 q^{83} + 16 q^{85} + 35 q^{86} + 20 q^{87} + 22 q^{88} + 19 q^{89} - 24 q^{90} - 10 q^{92} + 2 q^{93} + 20 q^{94} - 8 q^{95} + 25 q^{96} - 23 q^{97} + 24 q^{99}+O(q^{100}) $ 7 * q - q^2 - 7 * q^3 + 9 * q^4 - 4 * q^5 + 4 * q^6 - 12 * q^8 + 6 * q^9 - 8 * q^10 - 12 * q^12 - q^13 - 4 * q^15 + 5 * q^16 + 11 * q^17 + 16 * q^18 - 9 * q^19 - 12 * q^20 + 3 * q^23 + 23 * q^24 + 31 * q^25 - 10 * q^26 - 22 * q^27 - 14 * q^29 + 6 * q^30 - 34 * q^31 - 20 * q^32 - 12 * q^33 - 15 * q^34 + q^36 + 7 * q^37 + 39 * q^38 - 22 * q^39 - 50 * q^40 + 7 * q^41 - 3 * q^43 + 26 * q^44 + 4 * q^45 - 8 * q^46 - 17 * q^47 - 17 * q^48 + 11 * q^50 + 8 * q^51 + 25 * q^52 + 24 * q^53 - 68 * q^54 - 48 * q^55 + 22 * q^57 - 38 * q^58 - 4 * q^59 - 6 * q^60 - 16 * q^61 - 24 * q^62 + 8 * q^64 - 6 * q^65 + 12 * q^66 - 24 * q^67 + 10 * q^68 - 35 * q^69 - 12 * q^71 - 11 * q^72 - 14 * q^73 - 6 * q^74 + 19 * q^75 - 42 * q^76 - 29 * q^78 - 8 * q^79 + 92 * q^80 + 15 * q^81 - q^82 - 14 * q^83 + 16 * q^85 + 35 * q^86 + 20 * q^87 + 22 * q^88 + 19 * q^89 - 24 * q^90 - 10 * q^92 + 2 * q^93 + 20 * q^94 - 8 * q^95 + 25 * q^96 - 23 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.822027	0.581261	0.290630	−	0.956835i	$-0.406135\pi$
$2$	0.822027	0.581261	0.290630	+	0.956835i	$0.406135\pi$
$3$	0.955000	0.551370	0.275685	−	0.961248i	$-0.411095\pi$
$3$	0.955000	0.551370	0.275685	+	0.961248i	$0.411095\pi$
$4$	−1.32427	−0.662136
$5$	3.05691	1.36709	0.683546	−	0.729907i	$-0.260437\pi$
$5$	3.05691	1.36709	0.683546	+	0.729907i	$0.260437\pi$
$6$	0.785036	0.320490
$7$	0	0
$7$	0	0
$8$	−2.73264	−0.966134
$9$	−2.08797	−0.695991
$10$	2.51286	0.794637
$11$	−6.35985	−1.91757	−0.958784	−	0.284137i	$-0.908293\pi$
$11$	−6.35985	−1.91757	−0.958784	+	0.284137i	$0.908293\pi$
$12$	−1.26468	−0.365082
$13$	−3.93133	−1.09036	−0.545178	−	0.838320i	$-0.683538\pi$
$13$	−3.93133	−1.09036	−0.545178	+	0.838320i	$0.683538\pi$
$14$	0	0
$15$	2.91935	0.753774
$16$	0.402240	0.100560
$17$	2.97254	0.720946	0.360473	−	0.932770i	$-0.382615\pi$
$17$	2.97254	0.720946	0.360473	+	0.932770i	$0.382615\pi$
$18$	−1.71637	−0.404552
$19$	5.53594	1.27003	0.635016	−	0.772499i	$-0.280993\pi$
$19$	5.53594	1.27003	0.635016	+	0.772499i	$0.280993\pi$
$20$	−4.04818	−0.905201
$21$	0	0
$22$	−5.22797	−1.11461
$23$	−5.46467	−1.13946	−0.569731	−	0.821831i	$-0.692953\pi$
$23$	−5.46467	−1.13946	−0.569731	+	0.821831i	$0.692953\pi$
$24$	−2.60967	−0.532697
$25$	4.34471	0.868943
$26$	−3.23166	−0.633781
$27$	−4.85902	−0.935118
$28$	0	0
$29$	−5.86753	−1.08957	−0.544787	−	0.838575i	$-0.683389\pi$
$29$	−5.86753	−1.08957	−0.544787	+	0.838575i	$0.683389\pi$
$30$	2.39979	0.438139
$31$	−10.6583	−1.91429	−0.957143	−	0.289614i	$-0.906473\pi$
$31$	−10.6583	−1.91429	−0.957143	+	0.289614i	$0.906473\pi$
$32$	5.79593	1.02459
$33$	−6.07366	−1.05729
$34$	2.44351	0.419058
$35$	0	0
$36$	2.76505	0.460841
$37$	−0.638151	−0.104911	−0.0524557	−	0.998623i	$-0.516705\pi$
$37$	−0.638151	−0.104911	−0.0524557	+	0.998623i	$0.516705\pi$
$38$	4.55069	0.738220
$39$	−3.75443	−0.601189
$40$	−8.35344	−1.32080
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−0.978093	−0.149158	−0.0745789	−	0.997215i	$-0.523761\pi$
$43$	−0.978093	−0.149158	−0.0745789	+	0.997215i	$0.523761\pi$
$44$	8.42217	1.26969
$45$	−6.38275	−0.951485
$46$	−4.49210	−0.662325
$47$	3.60757	0.526218	0.263109	−	0.964766i	$-0.415252\pi$
$47$	3.60757	0.526218	0.263109	+	0.964766i	$0.415252\pi$
$48$	0.384139	0.0554457
$49$	0	0
$50$	3.57147	0.505082
$51$	2.83877	0.397508
$52$	5.20616	0.721964
$53$	−2.10130	−0.288636	−0.144318	−	0.989531i	$-0.546099\pi$
$53$	−2.10130	−0.288636	−0.144318	+	0.989531i	$0.546099\pi$
$54$	−3.99424	−0.543548
$55$	−19.4415	−2.62149
$56$	0	0
$57$	5.28683	0.700258
$58$	−4.82327	−0.633326
$59$	5.71771	0.744383	0.372191	−	0.928156i	$-0.378606\pi$
$59$	5.71771	0.744383	0.372191	+	0.928156i	$0.378606\pi$
$60$	−3.86602	−0.499101
$61$	−6.61771	−0.847311	−0.423655	−	0.905823i	$-0.639253\pi$
$61$	−6.61771	−0.847311	−0.423655	+	0.905823i	$0.639253\pi$
$62$	−8.76141	−1.11270
$63$	0	0
$64$	3.95993	0.494992
$65$	−12.0177	−1.49062
$66$	−4.99271	−0.614560
$67$	2.82804	0.345500	0.172750	−	0.984966i	$-0.444735\pi$
$67$	2.82804	0.345500	0.172750	+	0.984966i	$0.444735\pi$
$68$	−3.93645	−0.477364
$69$	−5.21876	−0.628265
$70$	0	0
$71$	−0.220124	−0.0261239	−0.0130619	−	0.999915i	$-0.504158\pi$
$71$	−0.220124	−0.0261239	−0.0130619	+	0.999915i	$0.504158\pi$
$72$	5.70568	0.672421
$73$	6.59628	0.772036	0.386018	−	0.922491i	$-0.373850\pi$
$73$	6.59628	0.772036	0.386018	+	0.922491i	$0.373850\pi$
$74$	−0.524578	−0.0609809
$75$	4.14920	0.479109
$76$	−7.33110	−0.840934
$77$	0	0
$78$	−3.08624	−0.349448
$79$	1.73659	0.195381	0.0976906	−	0.995217i	$-0.468854\pi$
$79$	1.73659	0.195381	0.0976906	+	0.995217i	$0.468854\pi$
$80$	1.22961	0.137475
$81$	1.62356	0.180395
$82$	0.822027	0.0907777
$83$	−11.9972	−1.31686	−0.658432	−	0.752640i	$-0.728780\pi$
$83$	−11.9972	−1.31686	−0.658432	+	0.752640i	$0.728780\pi$
$84$	0	0
$85$	9.08679	0.985600
$86$	−0.804018	−0.0866995
$87$	−5.60350	−0.600758
$88$	17.3792	1.85263
$89$	−2.25846	−0.239396	−0.119698	−	0.992810i	$-0.538193\pi$
$89$	−2.25846	−0.239396	−0.119698	+	0.992810i	$0.538193\pi$
$90$	−5.24680	−0.553061
$91$	0	0
$92$	7.23671	0.754479
$93$	−10.1787	−1.05548
$94$	2.96552	0.305870
$95$	16.9229	1.73625
$96$	5.53512	0.564926
$97$	10.9438	1.11117	0.555585	−	0.831460i	$-0.312494\pi$
$97$	10.9438	1.11117	0.555585	+	0.831460i	$0.312494\pi$
$98$	0	0
$99$	13.2792	1.33461
$100$	−5.75358	−0.575358
$101$	17.3262	1.72402	0.862008	−	0.506894i	$-0.169207\pi$
$101$	17.3262	1.72402	0.862008	+	0.506894i	$0.169207\pi$
$102$	2.33355	0.231056
$103$	−19.9672	−1.96742	−0.983712	−	0.179754i	$-0.942470\pi$
$103$	−19.9672	−1.96742	−0.983712	+	0.179754i	$0.942470\pi$
$104$	10.7429	1.05343
$105$	0	0
$106$	−1.72732	−0.167773
$107$	7.39198	0.714609	0.357305	−	0.933988i	$-0.383696\pi$
$107$	7.39198	0.714609	0.357305	+	0.933988i	$0.383696\pi$
$108$	6.43466	0.619176
$109$	−13.5056	−1.29360	−0.646800	−	0.762660i	$-0.723893\pi$
$109$	−13.5056	−1.29360	−0.646800	+	0.762660i	$0.723893\pi$
$110$	−15.9814	−1.52377
$111$	−0.609435	−0.0578450
$112$	0	0
$113$	4.25728	0.400492	0.200246	−	0.979746i	$-0.435826\pi$
$113$	4.25728	0.400492	0.200246	+	0.979746i	$0.435826\pi$
$114$	4.34592	0.407032
$115$	−16.7050	−1.55775
$116$	7.77021	0.721446
$117$	8.20853	0.758878
$118$	4.70011	0.432681
$119$	0	0
$120$	−7.97754	−0.728247
$121$	29.4477	2.67706
$122$	−5.43993	−0.492508
$123$	0.955000	0.0861095
$124$	14.1145	1.26752
$125$	−2.00315	−0.179167
$126$	0	0
$127$	−18.8997	−1.67708	−0.838540	−	0.544841i	$-0.816590\pi$
$127$	−18.8997	−1.67708	−0.838540	+	0.544841i	$0.816590\pi$
$128$	−8.33670	−0.736867
$129$	−0.934079	−0.0822411
$130$	−9.87891	−0.866438
$131$	15.3441	1.34062	0.670310	−	0.742081i	$-0.266161\pi$
$131$	15.3441	1.34062	0.670310	+	0.742081i	$0.266161\pi$
$132$	8.04318	0.700069
$133$	0	0
$134$	2.32472	0.200825
$135$	−14.8536	−1.27839
$136$	−8.12288	−0.696531
$137$	10.3150	0.881271	0.440635	−	0.897686i	$-0.354753\pi$
$137$	10.3150	0.881271	0.440635	+	0.897686i	$0.354753\pi$
$138$	−4.28996	−0.365186
$139$	4.26552	0.361797	0.180898	−	0.983502i	$-0.442099\pi$
$139$	4.26552	0.361797	0.180898	+	0.983502i	$0.442099\pi$
$140$	0	0
$141$	3.44523	0.290141
$142$	−0.180948	−0.0151848
$143$	25.0027	2.09083
$144$	−0.839867	−0.0699889
$145$	−17.9365	−1.48955
$146$	5.42232	0.448754
$147$	0	0
$148$	0.845086	0.0694656
$149$	−22.8606	−1.87281	−0.936406	−	0.350919i	$-0.885869\pi$
$149$	−22.8606	−1.87281	−0.936406	+	0.350919i	$0.885869\pi$
$150$	3.41076	0.278487
$151$	−6.37211	−0.518555	−0.259277	−	0.965803i	$-0.583484\pi$
$151$	−6.37211	−0.518555	−0.259277	+	0.965803i	$0.583484\pi$
$152$	−15.1277	−1.22702
$153$	−6.20658	−0.501772
$154$	0	0
$155$	−32.5815	−2.61701
$156$	4.97188	0.398069
$157$	2.75316	0.219726	0.109863	−	0.993947i	$-0.464959\pi$
$157$	2.75316	0.219726	0.109863	+	0.993947i	$0.464959\pi$
$158$	1.42752	0.113567
$159$	−2.00674	−0.159145
$160$	17.7177	1.40070
$161$	0	0
$162$	1.33461	0.104857
$163$	18.1869	1.42451	0.712253	−	0.701923i	$-0.247675\pi$
$163$	18.1869	1.42451	0.712253	+	0.701923i	$0.247675\pi$
$164$	−1.32427	−0.103408
$165$	−18.5666	−1.44541
$166$	−9.86202	−0.765441
$167$	−11.4115	−0.883048	−0.441524	−	0.897249i	$-0.645562\pi$
$167$	−11.4115	−0.883048	−0.441524	+	0.897249i	$0.645562\pi$
$168$	0	0
$169$	2.45539	0.188876
$170$	7.46958	0.572891
$171$	−11.5589	−0.883932
$172$	1.29526	0.0987627
$173$	−3.47112	−0.263904	−0.131952	−	0.991256i	$-0.542125\pi$
$173$	−3.47112	−0.263904	−0.131952	+	0.991256i	$0.542125\pi$
$174$	−4.60622	−0.349197
$175$	0	0
$176$	−2.55819	−0.192831
$177$	5.46042	0.410430
$178$	−1.85651	−0.139151
$179$	5.05668	0.377954	0.188977	−	0.981982i	$-0.439483\pi$
$179$	5.05668	0.377954	0.188977	+	0.981982i	$0.439483\pi$
$180$	8.45250	0.630012
$181$	−7.55435	−0.561510	−0.280755	−	0.959779i	$-0.590585\pi$
$181$	−7.55435	−0.561510	−0.280755	+	0.959779i	$0.590585\pi$
$182$	0	0
$183$	−6.31992	−0.467182
$184$	14.9330	1.10087
$185$	−1.95077	−0.143424
$186$	−8.36715	−0.613509
$187$	−18.9049	−1.38246
$188$	−4.77740	−0.348428
$189$	0	0
$190$	13.9111	1.00922
$191$	−21.7343	−1.57264	−0.786318	−	0.617822i	$-0.788015\pi$
$191$	−21.7343	−1.57264	−0.786318	+	0.617822i	$0.788015\pi$
$192$	3.78174	0.272923
$193$	5.61590	0.404241	0.202121	−	0.979361i	$-0.435217\pi$
$193$	5.61590	0.404241	0.202121	+	0.979361i	$0.435217\pi$
$194$	8.99606	0.645879
$195$	−11.4770	−0.821882
$196$	0	0
$197$	−10.8298	−0.771592	−0.385796	−	0.922584i	$-0.626073\pi$
$197$	−10.8298	−0.771592	−0.385796	+	0.922584i	$0.626073\pi$
$198$	10.9159	0.775756
$199$	2.42131	0.171642	0.0858211	−	0.996311i	$-0.472649\pi$
$199$	2.42131	0.171642	0.0858211	+	0.996311i	$0.472649\pi$
$200$	−11.8725	−0.839516
$201$	2.70078	0.190498
$202$	14.2426	1.00210
$203$	0	0
$204$	−3.75931	−0.263204
$205$	3.05691	0.213504
$206$	−16.4135	−1.14359
$207$	11.4101	0.793056
$208$	−1.58134	−0.109646
$209$	−35.2078	−2.43537
$210$	0	0
$211$	−12.5587	−0.864579	−0.432290	−	0.901735i	$-0.642294\pi$
$211$	−12.5587	−0.864579	−0.432290	+	0.901735i	$0.642294\pi$
$212$	2.78269	0.191116
$213$	−0.210218	−0.0144039
$214$	6.07640	0.415374
$215$	−2.98994	−0.203912
$216$	13.2779	0.903450
$217$	0	0
$218$	−11.1019	−0.751919
$219$	6.29945	0.425677
$220$	25.7458	1.73578
$221$	−11.6860	−0.786088
$222$	−0.500972	−0.0336230
$223$	21.7495	1.45645	0.728227	−	0.685336i	$-0.240345\pi$
$223$	21.7495	1.45645	0.728227	+	0.685336i	$0.240345\pi$
$224$	0	0
$225$	−9.07165	−0.604777
$226$	3.49960	0.232790
$227$	−18.1957	−1.20769	−0.603845	−	0.797102i	$-0.706365\pi$
$227$	−18.1957	−1.20769	−0.603845	+	0.797102i	$0.706365\pi$
$228$	−7.00120	−0.463666
$229$	8.98397	0.593677	0.296839	−	0.954928i	$-0.404068\pi$
$229$	8.98397	0.593677	0.296839	+	0.954928i	$0.404068\pi$
$230$	−13.7320	−0.905459
$231$	0	0
$232$	16.0339	1.05267
$233$	23.1755	1.51828	0.759139	−	0.650929i	$-0.225620\pi$
$233$	23.1755	1.51828	0.759139	+	0.650929i	$0.225620\pi$
$234$	6.74763	0.441106
$235$	11.0280	0.719389
$236$	−7.57181	−0.492883
$237$	1.65844	0.107727
$238$	0	0
$239$	8.06581	0.521734	0.260867	−	0.965375i	$-0.415992\pi$
$239$	8.06581	0.521734	0.260867	+	0.965375i	$0.415992\pi$
$240$	1.17428	0.0757995
$241$	3.47050	0.223555	0.111777	−	0.993733i	$-0.464346\pi$
$241$	3.47050	0.223555	0.111777	+	0.993733i	$0.464346\pi$
$242$	24.2068	1.55607
$243$	16.1276	1.03458
$244$	8.76365	0.561035
$245$	0	0
$246$	0.785036	0.0500521
$247$	−21.7636	−1.38479
$248$	29.1253	1.84946
$249$	−11.4573	−0.726079
$250$	−1.64664	−0.104143
$251$	−2.68175	−0.169271	−0.0846353	−	0.996412i	$-0.526973\pi$
$251$	−2.68175	−0.169271	−0.0846353	+	0.996412i	$0.526973\pi$
$252$	0	0
$253$	34.7545	2.18500
$254$	−15.5361	−0.974820
$255$	8.67789	0.543430
$256$	−14.7729	−0.923303
$257$	0.187770	0.0117128	0.00585638	−	0.999983i	$-0.498136\pi$
$257$	0.187770	0.0117128	0.00585638	+	0.999983i	$0.498136\pi$
$258$	−0.767838	−0.0478035
$259$	0	0
$260$	15.9148	0.986992
$261$	12.2513	0.758334
$262$	12.6133	0.779250
$263$	0.0347674	0.00214385	0.00107192	−	0.999999i	$-0.499659\pi$
$263$	0.0347674	0.00214385	0.00107192	+	0.999999i	$0.499659\pi$
$264$	16.5971	1.02148
$265$	−6.42349	−0.394592
$266$	0	0
$267$	−2.15683	−0.131996
$268$	−3.74509	−0.228768
$269$	21.4744	1.30932	0.654658	−	0.755925i	$-0.272812\pi$
$269$	21.4744	1.30932	0.654658	+	0.755925i	$0.272812\pi$
$270$	−12.2101	−0.743080
$271$	16.7462	1.01726	0.508629	−	0.860986i	$-0.330152\pi$
$271$	16.7462	1.01726	0.508629	+	0.860986i	$0.330152\pi$
$272$	1.19567	0.0724983
$273$	0	0
$274$	8.47921	0.512248
$275$	−27.6317	−1.66626
$276$	6.91106	0.415997
$277$	−18.3894	−1.10491	−0.552456	−	0.833542i	$-0.686309\pi$
$277$	−18.3894	−1.10491	−0.552456	+	0.833542i	$0.686309\pi$
$278$	3.50637	0.210298
$279$	22.2543	1.33233
$280$	0	0
$281$	−27.7980	−1.65829	−0.829145	−	0.559034i	$-0.811172\pi$
$281$	−27.7980	−1.65829	−0.829145	+	0.559034i	$0.811172\pi$
$282$	2.83207	0.168647
$283$	−21.5264	−1.27961	−0.639807	−	0.768536i	$-0.720986\pi$
$283$	−21.5264	−1.27961	−0.639807	+	0.768536i	$0.720986\pi$
$284$	0.291504	0.0172976
$285$	16.1614	0.957317
$286$	20.5529	1.21532
$287$	0	0
$288$	−12.1018	−0.713103
$289$	−8.16402	−0.480237
$290$	−14.7443	−0.865816
$291$	10.4513	0.612665
$292$	−8.73527	−0.511193
$293$	−11.9975	−0.700902	−0.350451	−	0.936581i	$-0.613972\pi$
$293$	−11.9975	−0.700902	−0.350451	+	0.936581i	$0.613972\pi$
$294$	0	0
$295$	17.4786	1.01764
$296$	1.74384	0.101359
$297$	30.9026	1.79315
$298$	−18.7920	−1.08859
$299$	21.4834	1.24242
$300$	−5.49467	−0.317235
$301$	0	0
$302$	−5.23804	−0.301416
$303$	16.5465	0.950571
$304$	2.22678	0.127714
$305$	−20.2298	−1.15835
$306$	−5.10198	−0.291661
$307$	23.6664	1.35071	0.675355	−	0.737493i	$-0.263990\pi$
$307$	23.6664	1.35071	0.675355	+	0.737493i	$0.263990\pi$
$308$	0	0
$309$	−19.0687	−1.08478
$310$	−26.7829	−1.52116
$311$	−27.1376	−1.53883	−0.769416	−	0.638748i	$-0.779453\pi$
$311$	−27.1376	−1.53883	−0.769416	+	0.638748i	$0.779453\pi$
$312$	10.2595	0.580830
$313$	−3.56482	−0.201496	−0.100748	−	0.994912i	$-0.532124\pi$
$313$	−3.56482	−0.201496	−0.100748	+	0.994912i	$0.532124\pi$
$314$	2.26317	0.127718
$315$	0	0
$316$	−2.29971	−0.129369
$317$	33.7784	1.89718	0.948592	−	0.316501i	$-0.102508\pi$
$317$	33.7784	1.89718	0.948592	+	0.316501i	$0.102508\pi$
$318$	−1.64960	−0.0925047
$319$	37.3166	2.08933
$320$	12.1052	0.676699
$321$	7.05934	0.394014
$322$	0	0
$323$	16.4558	0.915625
$324$	−2.15003	−0.119446
$325$	−17.0805	−0.947457
$326$	14.9501	0.828009
$327$	−12.8978	−0.713252
$328$	−2.73264	−0.150885
$329$	0	0
$330$	−15.2623	−0.840161
$331$	−2.64492	−0.145378	−0.0726890	−	0.997355i	$-0.523158\pi$
$331$	−2.64492	−0.145378	−0.0726890	+	0.997355i	$0.523158\pi$
$332$	15.8876	0.871943
$333$	1.33244	0.0730175
$334$	−9.38056	−0.513281
$335$	8.64506	0.472330
$336$	0	0
$337$	−0.0598022	−0.00325763	−0.00162882	−	0.999999i	$-0.500518\pi$
$337$	−0.0598022	−0.00325763	−0.00162882	+	0.999999i	$0.500518\pi$
$338$	2.01840	0.109786
$339$	4.06571	0.220819
$340$	−12.0334	−0.652601
$341$	67.7852	3.67077
$342$	−9.50173	−0.513795
$343$	0	0
$344$	2.67278	0.144106
$345$	−15.9533	−0.858897
$346$	−2.85335	−0.153397
$347$	−23.4272	−1.25764	−0.628819	−	0.777552i	$-0.716461\pi$
$347$	−23.4272	−1.25764	−0.628819	+	0.777552i	$0.716461\pi$
$348$	7.42055	0.397783
$349$	16.5820	0.887616	0.443808	−	0.896122i	$-0.353627\pi$
$349$	16.5820	0.887616	0.443808	+	0.896122i	$0.353627\pi$
$350$	0	0
$351$	19.1024	1.01961
$352$	−36.8613	−1.96471
$353$	−26.9710	−1.43552	−0.717760	−	0.696291i	$-0.754832\pi$
$353$	−26.9710	−1.43552	−0.717760	+	0.696291i	$0.754832\pi$
$354$	4.48861	0.238567
$355$	−0.672899	−0.0357138
$356$	2.99081	0.158513
$357$	0	0
$358$	4.15672	0.219690
$359$	5.11293	0.269850	0.134925	−	0.990856i	$-0.456921\pi$
$359$	5.11293	0.269850	0.134925	+	0.990856i	$0.456921\pi$
$360$	17.4418	0.919262
$361$	11.6467	0.612983
$362$	−6.20988	−0.326384
$363$	28.1226	1.47605
$364$	0	0
$365$	20.1642	1.05545
$366$	−5.19514	−0.271554
$367$	−27.7435	−1.44820	−0.724101	−	0.689694i	$-0.757745\pi$
$367$	−27.7435	−1.44820	−0.724101	+	0.689694i	$0.757745\pi$
$368$	−2.19811	−0.114584
$369$	−2.08797	−0.108696
$370$	−1.60359	−0.0833666
$371$	0	0
$372$	13.4793	0.698871
$373$	−0.00430766	−0.000223042 0	−0.000111521	−	1.00000i	$-0.500035\pi$
$373$	−0.00430766	−0.000223042 0	−0.000111521		1.00000i	$0.500035\pi$
$374$	−15.5403	−0.803571
$375$	−1.91301	−0.0987874
$376$	−9.85819	−0.508397
$377$	23.0672	1.18802
$378$	0	0
$379$	−1.97788	−0.101597	−0.0507985	−	0.998709i	$-0.516177\pi$
$379$	−1.97788	−0.101597	−0.0507985	+	0.998709i	$0.516177\pi$
$380$	−22.4105	−1.14964
$381$	−18.0492	−0.924691
$382$	−17.8662	−0.914112
$383$	−29.7948	−1.52244	−0.761222	−	0.648492i	$-0.775400\pi$
$383$	−29.7948	−1.52244	−0.761222	+	0.648492i	$0.775400\pi$
$384$	−7.96155	−0.406286
$385$	0	0
$386$	4.61642	0.234969
$387$	2.04223	0.103812
$388$	−14.4925	−0.735745
$389$	23.9644	1.21504	0.607521	−	0.794304i	$-0.292164\pi$
$389$	23.9644	1.21504	0.607521	+	0.794304i	$0.292164\pi$
$390$	−9.43436	−0.477728
$391$	−16.2439	−0.821491
$392$	0	0
$393$	14.6536	0.739177
$394$	−8.90239	−0.448496
$395$	5.30859	0.267104
$396$	−17.5853	−0.883693
$397$	18.3115	0.919029	0.459514	−	0.888170i	$-0.348023\pi$
$397$	18.3115	0.919029	0.459514	+	0.888170i	$0.348023\pi$
$398$	1.99038	0.0997688
$399$	0	0
$400$	1.74762	0.0873809
$401$	26.1392	1.30533	0.652665	−	0.757646i	$-0.273651\pi$
$401$	26.1392	1.30533	0.652665	+	0.757646i	$0.273651\pi$
$402$	2.22011	0.110729
$403$	41.9013	2.08725
$404$	−22.9445	−1.14153
$405$	4.96308	0.246617
$406$	0	0
$407$	4.05855	0.201175
$408$	−7.75735	−0.384046
$409$	22.3687	1.10606	0.553029	−	0.833162i	$-0.313472\pi$
$409$	22.3687	1.10606	0.553029	+	0.833162i	$0.313472\pi$
$410$	2.51286	0.124102
$411$	9.85084	0.485906
$412$	26.4420	1.30270
$413$	0	0
$414$	9.37940	0.460972
$415$	−36.6744	−1.80028
$416$	−22.7858	−1.11716
$417$	4.07358	0.199484
$418$	−28.9417	−1.41559
$419$	14.6458	0.715492	0.357746	−	0.933819i	$-0.383545\pi$
$419$	14.6458	0.715492	0.357746	+	0.933819i	$0.383545\pi$
$420$	0	0
$421$	1.06190	0.0517537	0.0258769	−	0.999665i	$-0.491762\pi$
$421$	1.06190	0.0517537	0.0258769	+	0.999665i	$0.491762\pi$
$422$	−10.3236	−0.502546
$423$	−7.53251	−0.366243
$424$	5.74210	0.278861
$425$	12.9148	0.626461
$426$	−0.172805	−0.00837243
$427$	0	0
$428$	−9.78899	−0.473169
$429$	23.8776	1.15282
$430$	−2.45781	−0.118526
$431$	30.5689	1.47245	0.736225	−	0.676736i	$-0.236606\pi$
$431$	30.5689	1.47245	0.736225	+	0.676736i	$0.236606\pi$
$432$	−1.95449	−0.0940355
$433$	12.6956	0.610112	0.305056	−	0.952334i	$-0.401325\pi$
$433$	12.6956	0.610112	0.305056	+	0.952334i	$0.401325\pi$
$434$	0	0
$435$	−17.1294	−0.821292
$436$	17.8851	0.856539
$437$	−30.2521	−1.44715
$438$	5.17832	0.247430
$439$	2.06944	0.0987690	0.0493845	−	0.998780i	$-0.484274\pi$
$439$	2.06944	0.0987690	0.0493845	+	0.998780i	$0.484274\pi$
$440$	53.1267	2.53271
$441$	0	0
$442$	−9.60624	−0.456922
$443$	13.4245	0.637818	0.318909	−	0.947785i	$-0.396684\pi$
$443$	13.4245	0.637818	0.318909	+	0.947785i	$0.396684\pi$
$444$	0.807057	0.0383013
$445$	−6.90390	−0.327276
$446$	17.8787	0.846579
$447$	−21.8319	−1.03261
$448$	0	0
$449$	22.7008	1.07132	0.535659	−	0.844434i	$-0.320063\pi$
$449$	22.7008	1.07132	0.535659	+	0.844434i	$0.320063\pi$
$450$	−7.45714	−0.351533
$451$	−6.35985	−0.299474
$452$	−5.63780	−0.265180
$453$	−6.08537	−0.285915
$454$	−14.9573	−0.701983
$455$	0	0
$456$	−14.4470	−0.676543
$457$	22.9642	1.07422	0.537110	−	0.843512i	$-0.319516\pi$
$457$	22.9642	1.07422	0.537110	+	0.843512i	$0.319516\pi$
$458$	7.38506	0.345081
$459$	−14.4436	−0.674170
$460$	22.1220	1.03144
$461$	−26.6031	−1.23903	−0.619514	−	0.784985i	$-0.712670\pi$
$461$	−26.6031	−1.23903	−0.619514	+	0.784985i	$0.712670\pi$
$462$	0	0
$463$	−24.2740	−1.12811	−0.564053	−	0.825738i	$-0.690759\pi$
$463$	−24.2740	−1.12811	−0.564053	+	0.825738i	$0.690759\pi$
$464$	−2.36016	−0.109567
$465$	−31.1153	−1.44294
$466$	19.0509	0.882515
$467$	−15.2419	−0.705313	−0.352656	−	0.935753i	$-0.614722\pi$
$467$	−15.2419	−0.705313	−0.352656	+	0.935753i	$0.614722\pi$
$468$	−10.8703	−0.502481
$469$	0	0
$470$	9.06533	0.418152
$471$	2.62927	0.121150
$472$	−15.6245	−0.719174
$473$	6.22052	0.286020
$474$	1.36328	0.0626177
$475$	24.0521	1.10359
$476$	0	0
$477$	4.38746	0.200888
$478$	6.63031	0.303264
$479$	−17.8727	−0.816626	−0.408313	−	0.912842i	$-0.633883\pi$
$479$	−17.8727	−0.816626	−0.408313	+	0.912842i	$0.633883\pi$
$480$	16.9204	0.772306
$481$	2.50879	0.114391
$482$	2.85285	0.129944
$483$	0	0
$484$	−38.9968	−1.77258
$485$	33.4541	1.51907
$486$	13.2573	0.601362
$487$	−4.68920	−0.212488	−0.106244	−	0.994340i	$-0.533882\pi$
$487$	−4.68920	−0.212488	−0.106244	+	0.994340i	$0.533882\pi$
$488$	18.0838	0.818616
$489$	17.3685	0.785429
$490$	0	0
$491$	11.2926	0.509630	0.254815	−	0.966990i	$-0.417985\pi$
$491$	11.2926	0.509630	0.254815	+	0.966990i	$0.417985\pi$
$492$	−1.26468	−0.0570162
$493$	−17.4415	−0.785524
$494$	−17.8903	−0.804923
$495$	40.5934	1.82454
$496$	−4.28719	−0.192501
$497$	0	0
$498$	−9.41824	−0.422041
$499$	12.4988	0.559523	0.279761	−	0.960070i	$-0.409745\pi$
$499$	12.4988	0.559523	0.279761	+	0.960070i	$0.409745\pi$
$500$	2.65272	0.118633
$501$	−10.8980	−0.486886
$502$	−2.20447	−0.0983904
$503$	0.599712	0.0267398	0.0133699	−	0.999911i	$-0.495744\pi$
$503$	0.599712	0.0267398	0.0133699	+	0.999911i	$0.495744\pi$
$504$	0	0
$505$	52.9645	2.35689
$506$	28.5691	1.27005
$507$	2.34490	0.104141
$508$	25.0284	1.11045
$509$	33.6164	1.49002	0.745011	−	0.667052i	$-0.232444\pi$
$509$	33.6164	1.49002	0.745011	+	0.667052i	$0.232444\pi$
$510$	7.13345	0.315875
$511$	0	0
$512$	4.52971	0.200187
$513$	−26.8992	−1.18763
$514$	0.154352	0.00680816
$515$	−61.0379	−2.68965
$516$	1.23697	0.0544548
$517$	−22.9436	−1.00906
$518$	0	0
$519$	−3.31492	−0.145509
$520$	32.8402	1.44014
$521$	−31.1062	−1.36279	−0.681394	−	0.731917i	$-0.738626\pi$
$521$	−31.1062	−1.36279	−0.681394	+	0.731917i	$0.738626\pi$
$522$	10.0709	0.440790
$523$	22.7561	0.995054	0.497527	−	0.867449i	$-0.334242\pi$
$523$	22.7561	0.995054	0.497527	+	0.867449i	$0.334242\pi$
$524$	−20.3198	−0.887673
$525$	0	0
$526$	0.0285797	0.00124614
$527$	−31.6822	−1.38010
$528$	−2.44307	−0.106321
$529$	6.86260	0.298374
$530$	−5.28028	−0.229361
$531$	−11.9384	−0.518084
$532$	0	0
$533$	−3.93133	−0.170285
$534$	−1.77297	−0.0767239
$535$	22.5966	0.976937
$536$	−7.72801	−0.333799
$537$	4.82913	0.208392
$538$	17.6525	0.761055
$539$	0	0
$540$	19.6702	0.846470
$541$	−18.7053	−0.804204	−0.402102	−	0.915595i	$-0.631720\pi$
$541$	−18.7053	−0.804204	−0.402102	+	0.915595i	$0.631720\pi$
$542$	13.7658	0.591292
$543$	−7.21440	−0.309600
$544$	17.2286	0.738671
$545$	−41.2854	−1.76847
$546$	0	0
$547$	−25.6732	−1.09771	−0.548854	−	0.835918i	$-0.684936\pi$
$547$	−25.6732	−1.09771	−0.548854	+	0.835918i	$0.684936\pi$
$548$	−13.6599	−0.583521
$549$	13.8176	0.589721
$550$	−22.7140	−0.968529
$551$	−32.4823	−1.38379
$552$	14.2610	0.606988
$553$	0	0
$554$	−15.1166	−0.642242
$555$	−1.86299	−0.0790795
$556$	−5.64871	−0.239559
$557$	−6.20343	−0.262848	−0.131424	−	0.991326i	$-0.541955\pi$
$557$	−6.20343	−0.262848	−0.131424	+	0.991326i	$0.541955\pi$
$558$	18.2936	0.774429
$559$	3.84521	0.162635
$560$	0	0
$561$	−18.0542	−0.762248
$562$	−22.8507	−0.963899
$563$	31.2307	1.31622	0.658108	−	0.752923i	$-0.271357\pi$
$563$	31.2307	1.31622	0.658108	+	0.752923i	$0.271357\pi$
$564$	−4.56242	−0.192113
$565$	13.0141	0.547509
$566$	−17.6953	−0.743789
$567$	0	0
$568$	0.601519	0.0252392
$569$	−1.04621	−0.0438594	−0.0219297	−	0.999760i	$-0.506981\pi$
$569$	−1.04621	−0.0438594	−0.0219297	+	0.999760i	$0.506981\pi$
$570$	13.2851	0.556451
$571$	−45.6353	−1.90978	−0.954888	−	0.296966i	$-0.904025\pi$
$571$	−45.6353	−1.90978	−0.954888	+	0.296966i	$0.904025\pi$
$572$	−33.1104	−1.38441
$573$	−20.7562	−0.867104
$574$	0	0
$575$	−23.7424	−0.990128
$576$	−8.26824	−0.344510
$577$	−36.2026	−1.50714	−0.753568	−	0.657370i	$-0.771669\pi$
$577$	−36.2026	−1.50714	−0.753568	+	0.657370i	$0.771669\pi$
$578$	−6.71104	−0.279143
$579$	5.36318	0.222886
$580$	23.7528	0.986283
$581$	0	0
$582$	8.59124	0.356118
$583$	13.3639	0.553478
$584$	−18.0253	−0.745891
$585$	25.0927	1.03746
$586$	−9.86228	−0.407407
$587$	−35.0186	−1.44537	−0.722686	−	0.691177i	$-0.757093\pi$
$587$	−35.0186	−1.44537	−0.722686	+	0.691177i	$0.757093\pi$
$588$	0	0
$589$	−59.0037	−2.43121
$590$	14.3678	0.591515
$591$	−10.3425	−0.425432
$592$	−0.256690	−0.0105499
$593$	5.00531	0.205544	0.102772	−	0.994705i	$-0.467229\pi$
$593$	5.00531	0.205544	0.102772	+	0.994705i	$0.467229\pi$
$594$	25.4028	1.04229
$595$	0	0
$596$	30.2736	1.24006
$597$	2.31235	0.0946383
$598$	17.6600	0.722170
$599$	5.44607	0.222520	0.111260	−	0.993791i	$-0.464511\pi$
$599$	5.44607	0.222520	0.111260	+	0.993791i	$0.464511\pi$
$600$	−11.3383	−0.462884
$601$	−7.04481	−0.287364	−0.143682	−	0.989624i	$-0.545894\pi$
$601$	−7.04481	−0.287364	−0.143682	+	0.989624i	$0.545894\pi$
$602$	0	0
$603$	−5.90487	−0.240465
$604$	8.43840	0.343354
$605$	90.0190	3.65979
$606$	13.6017	0.552529
$607$	4.02945	0.163550	0.0817751	−	0.996651i	$-0.473941\pi$
$607$	4.02945	0.163550	0.0817751	+	0.996651i	$0.473941\pi$
$608$	32.0860	1.30126
$609$	0	0
$610$	−16.6294	−0.673305
$611$	−14.1826	−0.573765
$612$	8.21920	0.332242
$613$	−42.1491	−1.70239	−0.851193	−	0.524852i	$-0.824121\pi$
$613$	−42.1491	−1.70239	−0.851193	+	0.524852i	$0.824121\pi$
$614$	19.4544	0.785115
$615$	2.91935	0.117720
$616$	0	0
$617$	−41.6677	−1.67748	−0.838738	−	0.544535i	$-0.816706\pi$
$617$	−41.6677	−1.67748	−0.838738	+	0.544535i	$0.816706\pi$
$618$	−15.6749	−0.630539
$619$	−42.9096	−1.72468	−0.862340	−	0.506329i	$-0.831002\pi$
$619$	−42.9096	−1.72468	−0.862340	+	0.506329i	$0.831002\pi$
$620$	43.1467	1.73282
$621$	26.5529	1.06553
$622$	−22.3078	−0.894463
$623$	0	0
$624$	−1.51018	−0.0604556
$625$	−27.8470	−1.11388
$626$	−2.93038	−0.117122
$627$	−33.6234	−1.34279
$628$	−3.64594	−0.145489
$629$	−1.89693	−0.0756355
$630$	0	0
$631$	43.0580	1.71411	0.857056	−	0.515223i	$-0.172291\pi$
$631$	43.0580	1.71411	0.857056	+	0.515223i	$0.172291\pi$
$632$	−4.74547	−0.188765
$633$	−11.9936	−0.476703
$634$	27.7668	1.10276
$635$	−57.7748	−2.29272
$636$	2.65747	0.105376
$637$	0	0
$638$	30.6753	1.21445
$639$	0.459612	0.0181820
$640$	−25.4846	−1.00737
$641$	2.75069	0.108646	0.0543228	−	0.998523i	$-0.482700\pi$
$641$	2.75069	0.108646	0.0543228	+	0.998523i	$0.482700\pi$
$642$	5.80297	0.229025
$643$	−9.20668	−0.363076	−0.181538	−	0.983384i	$-0.558108\pi$
$643$	−9.20668	−0.363076	−0.181538	+	0.983384i	$0.558108\pi$
$644$	0	0
$645$	−2.85540	−0.112431
$646$	13.5271	0.532217
$647$	−26.7278	−1.05078	−0.525389	−	0.850862i	$-0.676080\pi$
$647$	−26.7278	−1.05078	−0.525389	+	0.850862i	$0.676080\pi$
$648$	−4.43660	−0.174286
$649$	−36.3638	−1.42740
$650$	−14.0407	−0.550720
$651$	0	0
$652$	−24.0844	−0.943217
$653$	44.1976	1.72959	0.864793	−	0.502128i	$-0.167449\pi$
$653$	44.1976	1.72959	0.864793	+	0.502128i	$0.167449\pi$
$654$	−10.6024	−0.414585
$655$	46.9056	1.83275
$656$	0.402240	0.0157048
$657$	−13.7729	−0.537330
$658$	0	0
$659$	−12.5368	−0.488364	−0.244182	−	0.969729i	$-0.578519\pi$
$659$	−12.5368	−0.488364	−0.244182	+	0.969729i	$0.578519\pi$
$660$	24.5873	0.957059
$661$	−13.5827	−0.528304	−0.264152	−	0.964481i	$-0.585092\pi$
$661$	−13.5827	−0.528304	−0.264152	+	0.964481i	$0.585092\pi$
$662$	−2.17420	−0.0845025
$663$	−11.1602	−0.433425
$664$	32.7840	1.27227
$665$	0	0
$666$	1.09530	0.0424422
$667$	32.0641	1.24153
$668$	15.1119	0.584698
$669$	20.7708	0.803044
$670$	7.10647	0.274547
$671$	42.0876	1.62478
$672$	0	0
$673$	−24.2900	−0.936313	−0.468156	−	0.883646i	$-0.655082\pi$
$673$	−24.2900	−0.936313	−0.468156	+	0.883646i	$0.655082\pi$
$674$	−0.0491590	−0.00189353
$675$	−21.1110	−0.812564
$676$	−3.25161	−0.125062
$677$	16.2649	0.625110	0.312555	−	0.949900i	$-0.398815\pi$
$677$	16.2649	0.625110	0.312555	+	0.949900i	$0.398815\pi$
$678$	3.34212	0.128353
$679$	0	0
$680$	−24.8309	−0.952222
$681$	−17.3769	−0.665884
$682$	55.7212	2.13368
$683$	8.24211	0.315376	0.157688	−	0.987489i	$-0.449596\pi$
$683$	8.24211	0.315376	0.157688	+	0.987489i	$0.449596\pi$
$684$	15.3071	0.585283
$685$	31.5321	1.20478
$686$	0	0
$687$	8.57970	0.327336
$688$	−0.393428	−0.0149993
$689$	8.26091	0.314716
$690$	−13.1140	−0.499243
$691$	−41.0224	−1.56056	−0.780282	−	0.625428i	$-0.784924\pi$
$691$	−41.0224	−1.56056	−0.780282	+	0.625428i	$0.784924\pi$
$692$	4.59670	0.174740
$693$	0	0
$694$	−19.2578	−0.731015
$695$	13.0393	0.494610
$696$	15.3123	0.580413
$697$	2.97254	0.112593
$698$	13.6309	0.515937
$699$	22.1326	0.837132
$700$	0	0
$701$	33.5039	1.26543	0.632713	−	0.774386i	$-0.281941\pi$
$701$	33.5039	1.26543	0.632713	+	0.774386i	$0.281941\pi$
$702$	15.7027	0.592660
$703$	−3.53277	−0.133241
$704$	−25.1846	−0.949180
$705$	10.5318	0.396649
$706$	−22.1709	−0.834411
$707$	0	0
$708$	−7.23108	−0.271761
$709$	−2.21529	−0.0831968	−0.0415984	−	0.999134i	$-0.513245\pi$
$709$	−2.21529	−0.0831968	−0.0415984	+	0.999134i	$0.513245\pi$
$710$	−0.553141	−0.0207590
$711$	−3.62595	−0.135984
$712$	6.17155	0.231289
$713$	58.2441	2.18126
$714$	0	0
$715$	76.4311	2.85836
$716$	−6.69641	−0.250257
$717$	7.70286	0.287668
$718$	4.20296	0.156853
$719$	−10.5205	−0.392347	−0.196174	−	0.980569i	$-0.562852\pi$
$719$	−10.5205	−0.392347	−0.196174	+	0.980569i	$0.562852\pi$
$720$	−2.56740	−0.0956813
$721$	0	0
$722$	9.57388	0.356303
$723$	3.31433	0.123261
$724$	10.0040	0.371796
$725$	−25.4927	−0.946777
$726$	23.1175	0.857971
$727$	−42.8588	−1.58954	−0.794772	−	0.606908i	$-0.792410\pi$
$727$	−42.8588	−1.58954	−0.794772	+	0.606908i	$0.792410\pi$
$728$	0	0
$729$	10.5311	0.390042
$730$	16.5756	0.613489
$731$	−2.90742	−0.107535
$732$	8.36929	0.309338
$733$	−10.7435	−0.396819	−0.198410	−	0.980119i	$-0.563578\pi$
$733$	−10.7435	−0.396819	−0.198410	+	0.980119i	$0.563578\pi$
$734$	−22.8059	−0.841782
$735$	0	0
$736$	−31.6729	−1.16748
$737$	−17.9859	−0.662519
$738$	−1.71637	−0.0631805
$739$	22.5097	0.828033	0.414017	−	0.910269i	$-0.364126\pi$
$739$	22.5097	0.828033	0.414017	+	0.910269i	$0.364126\pi$
$740$	2.58335	0.0949660
$741$	−20.7843	−0.763530
$742$	0	0
$743$	−10.5627	−0.387509	−0.193755	−	0.981050i	$-0.562067\pi$
$743$	−10.5627	−0.387509	−0.193755	+	0.981050i	$0.562067\pi$
$744$	27.8147	1.01974
$745$	−69.8828	−2.56031
$746$	−0.00354101	−0.000129646 0
$747$	25.0498	0.916526
$748$	25.0352	0.915378
$749$	0	0
$750$	−1.57255	−0.0574212
$751$	−0.0181360	−0.000661792 0	−0.000330896	−	1.00000i	$-0.500105\pi$
$751$	−0.0181360	−0.000661792 0	−0.000330896		1.00000i	$0.500105\pi$
$752$	1.45111	0.0529165
$753$	−2.56107	−0.0933307
$754$	18.9619	0.690551
$755$	−19.4790	−0.708913
$756$	0	0
$757$	−3.18683	−0.115827	−0.0579137	−	0.998322i	$-0.518445\pi$
$757$	−3.18683	−0.115827	−0.0579137	+	0.998322i	$0.518445\pi$
$758$	−1.62587	−0.0590543
$759$	33.1905	1.20474
$760$	−46.2442	−1.67745
$761$	33.7668	1.22404	0.612022	−	0.790841i	$-0.290356\pi$
$761$	33.7668	1.22404	0.612022	+	0.790841i	$0.290356\pi$
$762$	−14.8370	−0.537486
$763$	0	0
$764$	28.7821	1.04130
$765$	−18.9730	−0.685969
$766$	−24.4921	−0.884936
$767$	−22.4782	−0.811642
$768$	−14.1081	−0.509082
$769$	15.5278	0.559946	0.279973	−	0.960008i	$-0.409674\pi$
$769$	15.5278	0.559946	0.279973	+	0.960008i	$0.409674\pi$
$770$	0	0
$771$	0.179320	0.00645806
$772$	−7.43697	−0.267663
$773$	17.8559	0.642233	0.321116	−	0.947040i	$-0.395942\pi$
$773$	17.8559	0.642233	0.321116	+	0.947040i	$0.395942\pi$
$774$	1.67877	0.0603421
$775$	−46.3073	−1.66341
$776$	−29.9053	−1.07354
$777$	0	0
$778$	19.6994	0.706256
$779$	5.53594	0.198346
$780$	15.1986	0.544197
$781$	1.39995	0.0500943
$782$	−13.3529	−0.477500
$783$	28.5104	1.01888
$784$	0	0
$785$	8.41618	0.300386
$786$	12.0457	0.429655
$787$	19.2373	0.685734	0.342867	−	0.939384i	$-0.388602\pi$
$787$	19.2373	0.685734	0.342867	+	0.939384i	$0.388602\pi$
$788$	14.3416	0.510899
$789$	0.0332029	0.00118205
$790$	4.36381	0.155257
$791$	0	0
$792$	−36.2873	−1.28941
$793$	26.0164	0.923870
$794$	15.0526	0.534195
$795$	−6.13443	−0.217566
$796$	−3.20647	−0.113650
$797$	−29.2883	−1.03745	−0.518723	−	0.854943i	$-0.673592\pi$
$797$	−29.2883	−1.03745	−0.518723	+	0.854943i	$0.673592\pi$
$798$	0	0
$799$	10.7236	0.379375
$800$	25.1817	0.890307
$801$	4.71560	0.166617
$802$	21.4871	0.758737
$803$	−41.9514	−1.48043
$804$	−3.57656	−0.126136
$805$	0	0
$806$	34.4440	1.21324
$807$	20.5081	0.721918
$808$	−47.3461	−1.66563
$809$	11.6219	0.408603	0.204302	−	0.978908i	$-0.434508\pi$
$809$	11.6219	0.408603	0.204302	+	0.978908i	$0.434508\pi$
$810$	4.07978	0.143349
$811$	−19.1655	−0.672992	−0.336496	−	0.941685i	$-0.609242\pi$
$811$	−19.1655	−0.672992	−0.336496	+	0.941685i	$0.609242\pi$
$812$	0	0
$813$	15.9926	0.560886
$814$	3.33623	0.116935
$815$	55.5957	1.94743
$816$	1.14187	0.0399734
$817$	−5.41467	−0.189435
$818$	18.3876	0.642908
$819$	0	0
$820$	−4.04818	−0.141369
$821$	9.67126	0.337529	0.168765	−	0.985656i	$-0.446022\pi$
$821$	9.67126	0.337529	0.168765	+	0.985656i	$0.446022\pi$
$822$	8.09765	0.282438
$823$	26.9298	0.938715	0.469358	−	0.883008i	$-0.344485\pi$
$823$	26.9298	0.938715	0.469358	+	0.883008i	$0.344485\pi$
$824$	54.5631	1.90080
$825$	−26.3883	−0.918723
$826$	0	0
$827$	38.3103	1.33218	0.666090	−	0.745871i	$-0.267967\pi$
$827$	38.3103	1.33218	0.666090	+	0.745871i	$0.267967\pi$
$828$	−15.1101	−0.525111
$829$	4.40565	0.153015	0.0765073	−	0.997069i	$-0.475623\pi$
$829$	4.40565	0.153015	0.0765073	+	0.997069i	$0.475623\pi$
$830$	−30.1473	−1.04643
$831$	−17.5619	−0.609215
$832$	−15.5678	−0.539717
$833$	0	0
$834$	3.34859	0.115952
$835$	−34.8840	−1.20721
$836$	46.6247	1.61255
$837$	51.7889	1.79008
$838$	12.0392	0.415888
$839$	−21.9824	−0.758918	−0.379459	−	0.925209i	$-0.623890\pi$
$839$	−21.9824	−0.758918	−0.379459	+	0.925209i	$0.623890\pi$
$840$	0	0
$841$	5.42792	0.187170
$842$	0.872908	0.0300824
$843$	−26.5471	−0.914331
$844$	16.6312	0.572469
$845$	7.50592	0.258212
$846$	−6.19192	−0.212883
$847$	0	0
$848$	−0.845226	−0.0290252
$849$	−20.5578	−0.705540
$850$	10.6163	0.364137
$851$	3.48729	0.119543
$852$	0.278386	0.00953735
$853$	34.1692	1.16993	0.584966	−	0.811058i	$-0.301108\pi$
$853$	34.1692	1.16993	0.584966	+	0.811058i	$0.301108\pi$
$854$	0	0
$855$	−35.3346	−1.20842
$856$	−20.1996	−0.690409
$857$	−12.4354	−0.424784	−0.212392	−	0.977185i	$-0.568125\pi$
$857$	−12.4354	−0.424784	−0.212392	+	0.977185i	$0.568125\pi$
$858$	19.6280	0.670090
$859$	−24.6897	−0.842402	−0.421201	−	0.906967i	$-0.638391\pi$
$859$	−24.6897	−0.842402	−0.421201	+	0.906967i	$0.638391\pi$
$860$	3.95950	0.135018
$861$	0	0
$862$	25.1284	0.855878
$863$	−31.5754	−1.07484	−0.537420	−	0.843314i	$-0.680601\pi$
$863$	−31.5754	−1.07484	−0.537420	+	0.843314i	$0.680601\pi$
$864$	−28.1625	−0.958109
$865$	−10.6109	−0.360782
$866$	10.4361	0.354634
$867$	−7.79664	−0.264788
$868$	0	0
$869$	−11.0444	−0.374657
$870$	−14.0808	−0.477385
$871$	−11.1180	−0.376718
$872$	36.9059	1.24979
$873$	−22.8503	−0.773365
$874$	−24.8680	−0.841174
$875$	0	0
$876$	−8.34218	−0.281856
$877$	−32.4785	−1.09672	−0.548361	−	0.836242i	$-0.684748\pi$
$877$	−32.4785	−1.09672	−0.548361	+	0.836242i	$0.684748\pi$
$878$	1.70114	0.0574105
$879$	−11.4576	−0.386456
$880$	−7.82015	−0.263617
$881$	0.106076	0.00357378	0.00178689	−	0.999998i	$-0.499431\pi$
$881$	0.106076	0.00357378	0.00178689	+	0.999998i	$0.499431\pi$
$882$	0	0
$883$	−10.1039	−0.340024	−0.170012	−	0.985442i	$-0.554381\pi$
$883$	−10.1039	−0.340024	−0.170012	+	0.985442i	$0.554381\pi$
$884$	15.4755	0.520497
$885$	16.6920	0.561096
$886$	11.0353	0.370738
$887$	0.556726	0.0186930	0.00934652	−	0.999956i	$-0.497025\pi$
$887$	0.556726	0.0186930	0.00934652	+	0.999956i	$0.497025\pi$
$888$	1.66537	0.0558860
$889$	0	0
$890$	−5.67519	−0.190233
$891$	−10.3256	−0.345920
$892$	−28.8022	−0.964370
$893$	19.9713	0.668314
$894$	−17.9464	−0.600217
$895$	15.4578	0.516698
$896$	0	0
$897$	20.5167	0.685033
$898$	18.6607	0.622715
$899$	62.5379	2.08576
$900$	12.0133	0.400444
$901$	−6.24619	−0.208091
$902$	−5.22797	−0.174072
$903$	0	0
$904$	−11.6336	−0.386929
$905$	−23.0930	−0.767636
$906$	−5.00233	−0.166191
$907$	42.7608	1.41985	0.709924	−	0.704278i	$-0.248729\pi$
$907$	42.7608	1.41985	0.709924	+	0.704278i	$0.248729\pi$
$908$	24.0960	0.799655
$909$	−36.1766	−1.19990
$910$	0	0
$911$	40.3198	1.33586	0.667928	−	0.744226i	$-0.267181\pi$
$911$	40.3198	1.33586	0.667928	+	0.744226i	$0.267181\pi$
$912$	2.12657	0.0704179
$913$	76.3004	2.52518
$914$	18.8772	0.624402
$915$	−19.3194	−0.638681
$916$	−11.8972	−0.393095
$917$	0	0
$918$	−11.8730	−0.391869
$919$	−51.2014	−1.68898	−0.844489	−	0.535573i	$-0.820096\pi$
$919$	−51.2014	−1.68898	−0.844489	+	0.535573i	$0.820096\pi$
$920$	45.6488	1.50500
$921$	22.6014	0.744741
$922$	−21.8684	−0.720199
$923$	0.865380	0.0284843
$924$	0	0
$925$	−2.77259	−0.0911621
$926$	−19.9538	−0.655724
$927$	41.6909	1.36931
$928$	−34.0078	−1.11636
$929$	28.5589	0.936988	0.468494	−	0.883467i	$-0.344797\pi$
$929$	28.5589	0.936988	0.468494	+	0.883467i	$0.344797\pi$
$930$	−25.5776	−0.838724
$931$	0	0
$932$	−30.6907	−1.00531
$933$	−25.9164	−0.848466
$934$	−12.5293	−0.409971
$935$	−57.7906	−1.88995
$936$	−22.4309	−0.733179
$937$	−44.5918	−1.45675	−0.728376	−	0.685178i	$-0.759724\pi$
$937$	−44.5918	−1.45675	−0.728376	+	0.685178i	$0.759724\pi$
$938$	0	0
$939$	−3.40441	−0.111099
$940$	−14.6041	−0.476333
$941$	16.8388	0.548929	0.274464	−	0.961597i	$-0.411499\pi$
$941$	16.8388	0.548929	0.274464	+	0.961597i	$0.411499\pi$
$942$	2.16133	0.0704200
$943$	−5.46467	−0.177954
$944$	2.29989	0.0748551
$945$	0	0
$946$	5.11344	0.166252
$947$	−19.9942	−0.649725	−0.324862	−	0.945761i	$-0.605318\pi$
$947$	−19.9942	−0.649725	−0.324862	+	0.945761i	$0.605318\pi$
$948$	−2.19623	−0.0713301
$949$	−25.9322	−0.841794
$950$	19.7715	0.641471
$951$	32.2584	1.04605
$952$	0	0
$953$	−46.6974	−1.51268	−0.756339	−	0.654180i	$-0.773014\pi$
$953$	−46.6974	−1.51268	−0.756339	+	0.654180i	$0.773014\pi$
$954$	3.60661	0.116768
$955$	−66.4398	−2.14994
$956$	−10.6813	−0.345459
$957$	35.6374	1.15199
$958$	−14.6919	−0.474673
$959$	0	0
$960$	11.5604	0.373112
$961$	82.5993	2.66449
$962$	2.06229	0.0664909
$963$	−15.4343	−0.497362
$964$	−4.59589	−0.148024
$965$	17.1673	0.552635
$966$	0	0
$967$	−3.81245	−0.122600	−0.0613001	−	0.998119i	$-0.519525\pi$
$967$	−3.81245	−0.122600	−0.0613001	+	0.998119i	$0.519525\pi$
$968$	−80.4700	−2.58640
$969$	15.7153	0.504848
$970$	27.5002	0.882977
$971$	−8.89896	−0.285581	−0.142791	−	0.989753i	$-0.545608\pi$
$971$	−8.89896	−0.285581	−0.142791	+	0.989753i	$0.545608\pi$
$972$	−21.3573	−0.685035
$973$	0	0
$974$	−3.85465	−0.123511
$975$	−16.3119	−0.522399
$976$	−2.66191	−0.0852056
$977$	−42.1929	−1.34987	−0.674935	−	0.737877i	$-0.735828\pi$
$977$	−42.1929	−1.34987	−0.674935	+	0.737877i	$0.735828\pi$
$978$	14.2773	0.456539
$979$	14.3634	0.459058
$980$	0	0
$981$	28.1993	0.900334
$982$	9.28285	0.296228
$983$	24.0094	0.765781	0.382891	−	0.923794i	$-0.374929\pi$
$983$	24.0094	0.765781	0.382891	+	0.923794i	$0.374929\pi$
$984$	−2.60967	−0.0831933
$985$	−33.1058	−1.05484
$986$	−14.3373	−0.456594
$987$	0	0
$988$	28.8210	0.916918
$989$	5.34495	0.169960
$990$	33.3688	1.06053
$991$	23.4683	0.745494	0.372747	−	0.927933i	$-0.378416\pi$
$991$	23.4683	0.745494	0.372747	+	0.927933i	$0.378416\pi$
$992$	−61.7748	−1.96135
$993$	−2.52590	−0.0801571
$994$	0	0
$995$	7.40173	0.234651
$996$	15.1726	0.480763
$997$	−29.1430	−0.922968	−0.461484	−	0.887148i	$-0.652683\pi$
$997$	−29.1430	−0.922968	−0.461484	+	0.887148i	$0.652683\pi$
$998$	10.2743	0.325229
$999$	3.10079	0.0981046

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.p.1.5	✓	7
7.6	odd	2		2009.2.a.q.1.5	yes	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2009.2.a.p.1.5	✓	7	1.1	even	1	trivial
2009.2.a.q.1.5	yes	7	7.6	odd	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:	\( N \)	\(=\)	\( 2009 = 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2009.a (trivial)

\(f(q)\)	\(=\)	\(q+0.822027 q^{2} +0.955000 q^{3} -1.32427 q^{4} +3.05691 q^{5} +0.785036 q^{6} -2.73264 q^{8} -2.08797 q^{9} +O(q^{10})\)	\(q+0.822027 q^{2} +0.955000 q^{3} -1.32427 q^{4} +3.05691 q^{5} +0.785036 q^{6} -2.73264 q^{8} -2.08797 q^{9} +2.51286 q^{10} -6.35985 q^{11} -1.26468 q^{12} -3.93133 q^{13} +2.91935 q^{15} +0.402240 q^{16} +2.97254 q^{17} -1.71637 q^{18} +5.53594 q^{19} -4.04818 q^{20} -5.22797 q^{22} -5.46467 q^{23} -2.60967 q^{24} +4.34471 q^{25} -3.23166 q^{26} -4.85902 q^{27} -5.86753 q^{29} +2.39979 q^{30} -10.6583 q^{31} +5.79593 q^{32} -6.07366 q^{33} +2.44351 q^{34} +2.76505 q^{36} -0.638151 q^{37} +4.55069 q^{38} -3.75443 q^{39} -8.35344 q^{40} +1.00000 q^{41} -0.978093 q^{43} +8.42217 q^{44} -6.38275 q^{45} -4.49210 q^{46} +3.60757 q^{47} +0.384139 q^{48} +3.57147 q^{50} +2.83877 q^{51} +5.20616 q^{52} -2.10130 q^{53} -3.99424 q^{54} -19.4415 q^{55} +5.28683 q^{57} -4.82327 q^{58} +5.71771 q^{59} -3.86602 q^{60} -6.61771 q^{61} -8.76141 q^{62} +3.95993 q^{64} -12.0177 q^{65} -4.99271 q^{66} +2.82804 q^{67} -3.93645 q^{68} -5.21876 q^{69} -0.220124 q^{71} +5.70568 q^{72} +6.59628 q^{73} -0.524578 q^{74} +4.14920 q^{75} -7.33110 q^{76} -3.08624 q^{78} +1.73659 q^{79} +1.22961 q^{80} +1.62356 q^{81} +0.822027 q^{82} -11.9972 q^{83} +9.08679 q^{85} -0.804018 q^{86} -5.60350 q^{87} +17.3792 q^{88} -2.25846 q^{89} -5.24680 q^{90} +7.23671 q^{92} -10.1787 q^{93} +2.96552 q^{94} +16.9229 q^{95} +5.53512 q^{96} +10.9438 q^{97} +13.2792 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} - 7 q^{3} + 9 q^{4} - 4 q^{5} + 4 q^{6} - 12 q^{8} + 6 q^{9}+O(q^{10}) \) 7 * q - q^2 - 7 * q^3 + 9 * q^4 - 4 * q^5 + 4 * q^6 - 12 * q^8 + 6 * q^9	\( 7 q - q^{2} - 7 q^{3} + 9 q^{4} - 4 q^{5} + 4 q^{6} - 12 q^{8} + 6 q^{9} - 8 q^{10} - 12 q^{12} - q^{13} - 4 q^{15} + 5 q^{16} + 11 q^{17} + 16 q^{18} - 9 q^{19} - 12 q^{20} + 3 q^{23} + 23 q^{24} + 31 q^{25} - 10 q^{26} - 22 q^{27} - 14 q^{29} + 6 q^{30} - 34 q^{31} - 20 q^{32} - 12 q^{33} - 15 q^{34} + q^{36} + 7 q^{37} + 39 q^{38} - 22 q^{39} - 50 q^{40} + 7 q^{41} - 3 q^{43} + 26 q^{44} + 4 q^{45} - 8 q^{46} - 17 q^{47} - 17 q^{48} + 11 q^{50} + 8 q^{51} + 25 q^{52} + 24 q^{53} - 68 q^{54} - 48 q^{55} + 22 q^{57} - 38 q^{58} - 4 q^{59} - 6 q^{60} - 16 q^{61} - 24 q^{62} + 8 q^{64} - 6 q^{65} + 12 q^{66} - 24 q^{67} + 10 q^{68} - 35 q^{69} - 12 q^{71} - 11 q^{72} - 14 q^{73} - 6 q^{74} + 19 q^{75} - 42 q^{76} - 29 q^{78} - 8 q^{79} + 92 q^{80} + 15 q^{81} - q^{82} - 14 q^{83} + 16 q^{85} + 35 q^{86} + 20 q^{87} + 22 q^{88} + 19 q^{89} - 24 q^{90} - 10 q^{92} + 2 q^{93} + 20 q^{94} - 8 q^{95} + 25 q^{96} - 23 q^{97} + 24 q^{99}+O(q^{100}) \) 7 * q - q^2 - 7 * q^3 + 9 * q^4 - 4 * q^5 + 4 * q^6 - 12 * q^8 + 6 * q^9 - 8 * q^10 - 12 * q^12 - q^13 - 4 * q^15 + 5 * q^16 + 11 * q^17 + 16 * q^18 - 9 * q^19 - 12 * q^20 + 3 * q^23 + 23 * q^24 + 31 * q^25 - 10 * q^26 - 22 * q^27 - 14 * q^29 + 6 * q^30 - 34 * q^31 - 20 * q^32 - 12 * q^33 - 15 * q^34 + q^36 + 7 * q^37 + 39 * q^38 - 22 * q^39 - 50 * q^40 + 7 * q^41 - 3 * q^43 + 26 * q^44 + 4 * q^45 - 8 * q^46 - 17 * q^47 - 17 * q^48 + 11 * q^50 + 8 * q^51 + 25 * q^52 + 24 * q^53 - 68 * q^54 - 48 * q^55 + 22 * q^57 - 38 * q^58 - 4 * q^59 - 6 * q^60 - 16 * q^61 - 24 * q^62 + 8 * q^64 - 6 * q^65 + 12 * q^66 - 24 * q^67 + 10 * q^68 - 35 * q^69 - 12 * q^71 - 11 * q^72 - 14 * q^73 - 6 * q^74 + 19 * q^75 - 42 * q^76 - 29 * q^78 - 8 * q^79 + 92 * q^80 + 15 * q^81 - q^82 - 14 * q^83 + 16 * q^85 + 35 * q^86 + 20 * q^87 + 22 * q^88 + 19 * q^89 - 24 * q^90 - 10 * q^92 + 2 * q^93 + 20 * q^94 - 8 * q^95 + 25 * q^96 - 23 * q^97 + 24 * q^99

Introduction

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