LMFDB - Embedded newform 2009.2.a.s.1.8

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:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 3 x^{16} - 25 x^{15} + 77 x^{14} + 247 x^{13} - 790 x^{12} - 1231 x^{11} + 4173 x^{10} + \cdots - 464 $ x^17 - 3x^16 - 25x^15 + 77x^14 + 247x^13 - 790x^12 - 1231x^11 + 4173x^10 + 3251x^9 - 12183x^8 - 4259x^7 + 19567x^6 + 2029x^5 - 16136x^4 + 299x^3 + 5775x^2 - 312x - 464
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 287)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-0.290774$ 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)

$f(q)$	$=$	$q-0.290774 q^{2} -1.26632 q^{3} -1.91545 q^{4} +3.23790 q^{5} +0.368212 q^{6} +1.13851 q^{8} -1.39645 q^{9} +O(q^{10})$	\(q-0.290774 q^{2} -1.26632 q^{3} -1.91545 q^{4} +3.23790 q^{5} +0.368212 q^{6} +1.13851 q^{8} -1.39645 q^{9} -0.941496 q^{10} -3.38547 q^{11} +2.42556 q^{12} -2.06267 q^{13} -4.10020 q^{15} +3.49985 q^{16} -1.31987 q^{17} +0.406050 q^{18} +3.39003 q^{19} -6.20203 q^{20} +0.984407 q^{22} -2.82090 q^{23} -1.44171 q^{24} +5.48397 q^{25} +0.599770 q^{26} +5.56729 q^{27} +4.41169 q^{29} +1.19223 q^{30} +5.50884 q^{31} -3.29469 q^{32} +4.28707 q^{33} +0.383783 q^{34} +2.67482 q^{36} -4.83103 q^{37} -0.985733 q^{38} +2.61199 q^{39} +3.68638 q^{40} +1.00000 q^{41} +8.33525 q^{43} +6.48470 q^{44} -4.52155 q^{45} +0.820246 q^{46} -11.7439 q^{47} -4.43191 q^{48} -1.59460 q^{50} +1.67137 q^{51} +3.95094 q^{52} -0.654278 q^{53} -1.61882 q^{54} -10.9618 q^{55} -4.29285 q^{57} -1.28281 q^{58} -2.95421 q^{59} +7.85373 q^{60} -3.12732 q^{61} -1.60183 q^{62} -6.04169 q^{64} -6.67870 q^{65} -1.24657 q^{66} +15.7172 q^{67} +2.52814 q^{68} +3.57215 q^{69} +7.52354 q^{71} -1.58987 q^{72} -9.83043 q^{73} +1.40474 q^{74} -6.94444 q^{75} -6.49344 q^{76} -0.759498 q^{78} +11.7647 q^{79} +11.3322 q^{80} -2.86060 q^{81} -0.290774 q^{82} +12.3648 q^{83} -4.27359 q^{85} -2.42367 q^{86} -5.58659 q^{87} -3.85440 q^{88} +3.04716 q^{89} +1.31475 q^{90} +5.40330 q^{92} -6.97593 q^{93} +3.41483 q^{94} +10.9766 q^{95} +4.17211 q^{96} -12.8792 q^{97} +4.72762 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 3 q^{2} + q^{3} + 25 q^{4} - q^{5} + 2 q^{6} + 9 q^{8} + 26 q^{9}+O(q^{10}) $ 17 * q + 3 * q^2 + q^3 + 25 * q^4 - q^5 + 2 * q^6 + 9 * q^8 + 26 * q^9	$ 17 q + 3 q^{2} + q^{3} + 25 q^{4} - q^{5} + 2 q^{6} + 9 q^{8} + 26 q^{9} - 2 q^{10} + 15 q^{11} + 4 q^{12} - 5 q^{13} + 24 q^{15} + 33 q^{16} + 4 q^{17} + 10 q^{18} + 5 q^{19} - 26 q^{20} + 16 q^{22} + 12 q^{23} + 16 q^{24} + 24 q^{25} + 31 q^{26} - 11 q^{27} + 14 q^{29} - 33 q^{30} - 3 q^{31} + 16 q^{32} + 4 q^{33} - 24 q^{34} + 57 q^{36} + 24 q^{37} + 45 q^{39} + 36 q^{40} + 17 q^{41} + 14 q^{43} - 9 q^{44} - 21 q^{45} + 44 q^{46} + 19 q^{47} - 60 q^{48} - 4 q^{50} + 2 q^{51} - 25 q^{52} + 4 q^{53} + 68 q^{54} + 9 q^{55} - 12 q^{57} - q^{58} - 27 q^{59} + 66 q^{60} - q^{61} - 23 q^{62} + 75 q^{64} + 22 q^{65} - 16 q^{66} + 49 q^{67} + 45 q^{68} + 12 q^{69} + 40 q^{71} - 23 q^{72} - 14 q^{73} + 33 q^{74} + 27 q^{75} - 9 q^{76} - 12 q^{78} + 61 q^{79} - 82 q^{80} + 53 q^{81} + 3 q^{82} - 18 q^{83} - 13 q^{85} - 4 q^{86} - 17 q^{87} + 74 q^{88} + 18 q^{89} - 20 q^{90} + 28 q^{92} - 36 q^{93} - 5 q^{94} + 20 q^{95} + 148 q^{96} + 26 q^{97} + 38 q^{99}+O(q^{100}) $ 17 * q + 3 * q^2 + q^3 + 25 * q^4 - q^5 + 2 * q^6 + 9 * q^8 + 26 * q^9 - 2 * q^10 + 15 * q^11 + 4 * q^12 - 5 * q^13 + 24 * q^15 + 33 * q^16 + 4 * q^17 + 10 * q^18 + 5 * q^19 - 26 * q^20 + 16 * q^22 + 12 * q^23 + 16 * q^24 + 24 * q^25 + 31 * q^26 - 11 * q^27 + 14 * q^29 - 33 * q^30 - 3 * q^31 + 16 * q^32 + 4 * q^33 - 24 * q^34 + 57 * q^36 + 24 * q^37 + 45 * q^39 + 36 * q^40 + 17 * q^41 + 14 * q^43 - 9 * q^44 - 21 * q^45 + 44 * q^46 + 19 * q^47 - 60 * q^48 - 4 * q^50 + 2 * q^51 - 25 * q^52 + 4 * q^53 + 68 * q^54 + 9 * q^55 - 12 * q^57 - q^58 - 27 * q^59 + 66 * q^60 - q^61 - 23 * q^62 + 75 * q^64 + 22 * q^65 - 16 * q^66 + 49 * q^67 + 45 * q^68 + 12 * q^69 + 40 * q^71 - 23 * q^72 - 14 * q^73 + 33 * q^74 + 27 * q^75 - 9 * q^76 - 12 * q^78 + 61 * q^79 - 82 * q^80 + 53 * q^81 + 3 * q^82 - 18 * q^83 - 13 * q^85 - 4 * q^86 - 17 * q^87 + 74 * q^88 + 18 * q^89 - 20 * q^90 + 28 * q^92 - 36 * q^93 - 5 * q^94 + 20 * q^95 + 148 * q^96 + 26 * q^97 + 38 * 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 $

$2$	−0.290774	−0.205608	−0.102804	−	0.994702i	$-0.532781\pi$
$2$	−0.290774	−0.205608	−0.102804	+	0.994702i	$0.532781\pi$
$3$	−1.26632	−0.731107	−0.365554	−	0.930790i	$-0.619120\pi$
$3$	−1.26632	−0.731107	−0.365554	+	0.930790i	$0.619120\pi$
$4$	−1.91545	−0.957725
$5$	3.23790	1.44803	0.724016	−	0.689784i	$-0.242294\pi$
$5$	3.23790	1.44803	0.724016	+	0.689784i	$0.242294\pi$
$6$	0.368212	0.150322
$7$	0	0
$7$	0	0
$8$	1.13851	0.402525
$9$	−1.39645	−0.465482
$10$	−0.941496	−0.297727
$11$	−3.38547	−1.02076	−0.510379	−	0.859950i	$-0.670495\pi$
$11$	−3.38547	−1.02076	−0.510379	+	0.859950i	$0.670495\pi$
$12$	2.42556	0.700200
$13$	−2.06267	−0.572081	−0.286041	−	0.958218i	$-0.592339\pi$
$13$	−2.06267	−0.572081	−0.286041	+	0.958218i	$0.592339\pi$
$14$	0	0
$15$	−4.10020	−1.05867
$16$	3.49985	0.874963
$17$	−1.31987	−0.320115	−0.160057	−	0.987108i	$-0.551168\pi$
$17$	−1.31987	−0.320115	−0.160057	+	0.987108i	$0.551168\pi$
$18$	0.406050	0.0957070
$19$	3.39003	0.777727	0.388863	−	0.921295i	$-0.372868\pi$
$19$	3.39003	0.777727	0.388863	+	0.921295i	$0.372868\pi$
$20$	−6.20203	−1.38682
$21$	0	0
$22$	0.984407	0.209876
$23$	−2.82090	−0.588199	−0.294100	−	0.955775i	$-0.595020\pi$
$23$	−2.82090	−0.588199	−0.294100	+	0.955775i	$0.595020\pi$
$24$	−1.44171	−0.294289
$25$	5.48397	1.09679
$26$	0.599770	0.117625
$27$	5.56729	1.07142
$28$	0	0
$29$	4.41169	0.819231	0.409615	−	0.912258i	$-0.365663\pi$
$29$	4.41169	0.819231	0.409615	+	0.912258i	$0.365663\pi$
$30$	1.19223	0.217671
$31$	5.50884	0.989417	0.494708	−	0.869059i	$-0.335275\pi$
$31$	5.50884	0.989417	0.494708	+	0.869059i	$0.335275\pi$
$32$	−3.29469	−0.582424
$33$	4.28707	0.746283
$34$	0.383783	0.0658182
$35$	0	0
$36$	2.67482	0.445804
$37$	−4.83103	−0.794217	−0.397108	−	0.917772i	$-0.629986\pi$
$37$	−4.83103	−0.794217	−0.397108	+	0.917772i	$0.629986\pi$
$38$	−0.985733	−0.159907
$39$	2.61199	0.418253
$40$	3.68638	0.582868
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	8.33525	1.27111	0.635557	−	0.772054i	$-0.280771\pi$
$43$	8.33525	1.27111	0.635557	+	0.772054i	$0.280771\pi$
$44$	6.48470	0.977605
$45$	−4.52155	−0.674032
$46$	0.820246	0.120939
$47$	−11.7439	−1.71303	−0.856514	−	0.516124i	$-0.827374\pi$
$47$	−11.7439	−1.71303	−0.856514	+	0.516124i	$0.827374\pi$
$48$	−4.43191	−0.639692
$49$	0	0
$50$	−1.59460	−0.225510
$51$	1.67137	0.234038
$52$	3.95094	0.547897
$53$	−0.654278	−0.0898720	−0.0449360	−	0.998990i	$-0.514308\pi$
$53$	−0.654278	−0.0898720	−0.0449360	+	0.998990i	$0.514308\pi$
$54$	−1.61882	−0.220294
$55$	−10.9618	−1.47809
$56$	0	0
$57$	−4.29285	−0.568602
$58$	−1.28281	−0.168441
$59$	−2.95421	−0.384605	−0.192303	−	0.981336i	$-0.561596\pi$
$59$	−2.95421	−0.384605	−0.192303	+	0.981336i	$0.561596\pi$
$60$	7.85373	1.01391
$61$	−3.12732	−0.400413	−0.200206	−	0.979754i	$-0.564161\pi$
$61$	−3.12732	−0.400413	−0.200206	+	0.979754i	$0.564161\pi$
$62$	−1.60183	−0.203432
$63$	0	0
$64$	−6.04169	−0.755212
$65$	−6.67870	−0.828391
$66$	−1.24657	−0.153442
$67$	15.7172	1.92016	0.960079	−	0.279729i	$-0.0902445\pi$
$67$	15.7172	1.92016	0.960079	+	0.279729i	$0.0902445\pi$
$68$	2.52814	0.306582
$69$	3.57215	0.430037
$70$	0	0
$71$	7.52354	0.892880	0.446440	−	0.894814i	$-0.352692\pi$
$71$	7.52354	0.892880	0.446440	+	0.894814i	$0.352692\pi$
$72$	−1.58987	−0.187368
$73$	−9.83043	−1.15057	−0.575283	−	0.817955i	$-0.695108\pi$
$73$	−9.83043	−1.15057	−0.575283	+	0.817955i	$0.695108\pi$
$74$	1.40474	0.163298
$75$	−6.94444	−0.801875
$76$	−6.49344	−0.744848
$77$	0	0
$78$	−0.759498	−0.0859963
$79$	11.7647	1.32363	0.661815	−	0.749667i	$-0.269786\pi$
$79$	11.7647	1.32363	0.661815	+	0.749667i	$0.269786\pi$
$80$	11.3322	1.26697
$81$	−2.86060	−0.317845
$82$	−0.290774	−0.0321106
$83$	12.3648	1.35722	0.678608	−	0.734501i	$-0.262584\pi$
$83$	12.3648	1.35722	0.678608	+	0.734501i	$0.262584\pi$
$84$	0	0
$85$	−4.27359	−0.463536
$86$	−2.42367	−0.261351
$87$	−5.58659	−0.598946
$88$	−3.85440	−0.410880
$89$	3.04716	0.322999	0.161499	−	0.986873i	$-0.448367\pi$
$89$	3.04716	0.322999	0.161499	+	0.986873i	$0.448367\pi$
$90$	1.31475	0.138587
$91$	0	0
$92$	5.40330	0.563333
$93$	−6.97593	−0.723370
$94$	3.41483	0.352213
$95$	10.9766	1.12617
$96$	4.17211	0.425815
$97$	−12.8792	−1.30769	−0.653844	−	0.756629i	$-0.726845\pi$
$97$	−12.8792	−1.30769	−0.653844	+	0.756629i	$0.726845\pi$
$98$	0	0
$99$	4.72762	0.475144
$100$	−10.5043	−1.05043
$101$	12.8128	1.27492	0.637459	−	0.770484i	$-0.279985\pi$
$101$	12.8128	1.27492	0.637459	+	0.770484i	$0.279985\pi$
$102$	−0.485990	−0.0481202
$103$	9.31581	0.917914	0.458957	−	0.888459i	$-0.348223\pi$
$103$	9.31581	0.917914	0.458957	+	0.888459i	$0.348223\pi$
$104$	−2.34837	−0.230277
$105$	0	0
$106$	0.190247	0.0184784
$107$	16.6873	1.61322	0.806611	−	0.591083i	$-0.201299\pi$
$107$	16.6873	1.61322	0.806611	+	0.591083i	$0.201299\pi$
$108$	−10.6639	−1.02613
$109$	17.9627	1.72051	0.860256	−	0.509862i	$-0.170304\pi$
$109$	17.9627	1.72051	0.860256	+	0.509862i	$0.170304\pi$
$110$	3.18741	0.303907
$111$	6.11761	0.580658
$112$	0	0
$113$	−10.6231	−0.999333	−0.499667	−	0.866218i	$-0.666544\pi$
$113$	−10.6231	−0.999333	−0.499667	+	0.866218i	$0.666544\pi$
$114$	1.24825	0.116909
$115$	−9.13379	−0.851731
$116$	−8.45038	−0.784598
$117$	2.88040	0.266293
$118$	0.859007	0.0790780
$119$	0	0
$120$	−4.66812	−0.426139
$121$	0.461402	0.0419456
$122$	0.909345	0.0823282
$123$	−1.26632	−0.114180
$124$	−10.5519	−0.947589
$125$	1.56705	0.140162
$126$	0	0
$127$	16.1140	1.42988	0.714942	−	0.699184i	$-0.246453\pi$
$127$	16.1140	1.42988	0.714942	+	0.699184i	$0.246453\pi$
$128$	8.34615	0.737702
$129$	−10.5550	−0.929320
$130$	1.94199	0.170324
$131$	13.5152	1.18083	0.590415	−	0.807100i	$-0.298964\pi$
$131$	13.5152	1.18083	0.590415	+	0.807100i	$0.298964\pi$
$132$	−8.21167	−0.714734
$133$	0	0
$134$	−4.57015	−0.394801
$135$	18.0263	1.55146
$136$	−1.50268	−0.128854
$137$	15.6112	1.33376	0.666879	−	0.745166i	$-0.267630\pi$
$137$	15.6112	1.33376	0.666879	+	0.745166i	$0.267630\pi$
$138$	−1.03869	−0.0884191
$139$	−12.2150	−1.03606	−0.518030	−	0.855363i	$-0.673334\pi$
$139$	−12.2150	−1.03606	−0.518030	+	0.855363i	$0.673334\pi$
$140$	0	0
$141$	14.8715	1.25241
$142$	−2.18765	−0.183584
$143$	6.98310	0.583956
$144$	−4.88735	−0.407279
$145$	14.2846	1.18627
$146$	2.85843	0.236566
$147$	0	0
$148$	9.25360	0.760641
$149$	−4.23323	−0.346800	−0.173400	−	0.984852i	$-0.555475\pi$
$149$	−4.23323	−0.346800	−0.173400	+	0.984852i	$0.555475\pi$
$150$	2.01926	0.164872
$151$	−5.54319	−0.451099	−0.225549	−	0.974232i	$-0.572418\pi$
$151$	−5.54319	−0.451099	−0.225549	+	0.974232i	$0.572418\pi$
$152$	3.85959	0.313054
$153$	1.84312	0.149008
$154$	0	0
$155$	17.8371	1.43271
$156$	−5.00313	−0.400571
$157$	10.2633	0.819099	0.409550	−	0.912288i	$-0.365686\pi$
$157$	10.2633	0.819099	0.409550	+	0.912288i	$0.365686\pi$
$158$	−3.42087	−0.272149
$159$	0.828522	0.0657061
$160$	−10.6679	−0.843369
$161$	0	0
$162$	0.831789	0.0653515
$163$	−10.6936	−0.837585	−0.418793	−	0.908082i	$-0.637547\pi$
$163$	−10.6936	−0.837585	−0.418793	+	0.908082i	$0.637547\pi$
$164$	−1.91545	−0.149572
$165$	13.8811	1.08064
$166$	−3.59537	−0.279055
$167$	15.3153	1.18513	0.592566	−	0.805522i	$-0.298115\pi$
$167$	15.3153	1.18513	0.592566	+	0.805522i	$0.298115\pi$
$168$	0	0
$169$	−8.74540	−0.672723
$170$	1.24265	0.0953068
$171$	−4.73400	−0.362018
$172$	−15.9658	−1.21738
$173$	5.20785	0.395946	0.197973	−	0.980207i	$-0.436564\pi$
$173$	5.20785	0.395946	0.197973	+	0.980207i	$0.436564\pi$
$174$	1.62444	0.123148
$175$	0	0
$176$	−11.8486	−0.893125
$177$	3.74096	0.281188
$178$	−0.886036	−0.0664112
$179$	−9.93049	−0.742240	−0.371120	−	0.928585i	$-0.621026\pi$
$179$	−9.93049	−0.742240	−0.371120	+	0.928585i	$0.621026\pi$
$180$	8.66080	0.645538
$181$	18.9915	1.41163	0.705815	−	0.708396i	$-0.250581\pi$
$181$	18.9915	1.41163	0.705815	+	0.708396i	$0.250581\pi$
$182$	0	0
$183$	3.96018	0.292745
$184$	−3.21163	−0.236765
$185$	−15.6424	−1.15005
$186$	2.02842	0.148731
$187$	4.46837	0.326759
$188$	22.4949	1.64061
$189$	0	0
$190$	−3.19170	−0.231550
$191$	6.01766	0.435423	0.217711	−	0.976013i	$-0.430141\pi$
$191$	6.01766	0.435423	0.217711	+	0.976013i	$0.430141\pi$
$192$	7.65069	0.552141
$193$	17.2067	1.23857	0.619284	−	0.785167i	$-0.287423\pi$
$193$	17.2067	1.23857	0.619284	+	0.785167i	$0.287423\pi$
$194$	3.74495	0.268872
$195$	8.45735	0.605643
$196$	0	0
$197$	−2.34296	−0.166929	−0.0834644	−	0.996511i	$-0.526598\pi$
$197$	−2.34296	−0.166929	−0.0834644	+	0.996511i	$0.526598\pi$
$198$	−1.37467	−0.0976936
$199$	13.6796	0.969720	0.484860	−	0.874592i	$-0.338871\pi$
$199$	13.6796	0.969720	0.484860	+	0.874592i	$0.338871\pi$
$200$	6.24357	0.441487
$201$	−19.9029	−1.40384
$202$	−3.72562	−0.262134
$203$	0	0
$204$	−3.20142	−0.224144
$205$	3.23790	0.226144
$206$	−2.70880	−0.188731
$207$	3.93924	0.273796
$208$	−7.21903	−0.500550
$209$	−11.4768	−0.793870
$210$	0	0
$211$	4.56610	0.314344	0.157172	−	0.987571i	$-0.449762\pi$
$211$	4.56610	0.314344	0.157172	+	0.987571i	$0.449762\pi$
$212$	1.25324	0.0860727
$213$	−9.52717	−0.652791
$214$	−4.85223	−0.331692
$215$	26.9887	1.84061
$216$	6.33842	0.431275
$217$	0	0
$218$	−5.22308	−0.353752
$219$	12.4484	0.841187
$220$	20.9968	1.41560
$221$	2.72245	0.183132
$222$	−1.77884	−0.119388
$223$	−9.72735	−0.651392	−0.325696	−	0.945475i	$-0.605599\pi$
$223$	−9.72735	−0.651392	−0.325696	+	0.945475i	$0.605599\pi$
$224$	0	0
$225$	−7.65807	−0.510538
$226$	3.08891	0.205471
$227$	−4.21956	−0.280062	−0.140031	−	0.990147i	$-0.544720\pi$
$227$	−4.21956	−0.280062	−0.140031	+	0.990147i	$0.544720\pi$
$228$	8.22274	0.544564
$229$	1.28581	0.0849690	0.0424845	−	0.999097i	$-0.486473\pi$
$229$	1.28581	0.0849690	0.0424845	+	0.999097i	$0.486473\pi$
$230$	2.65587	0.175123
$231$	0	0
$232$	5.02276	0.329760
$233$	7.03841	0.461102	0.230551	−	0.973060i	$-0.425947\pi$
$233$	7.03841	0.461102	0.230551	+	0.973060i	$0.425947\pi$
$234$	−0.837547	−0.0547521
$235$	−38.0256	−2.48052
$236$	5.65864	0.368346
$237$	−14.8978	−0.967716
$238$	0	0
$239$	−17.0994	−1.10607	−0.553035	−	0.833158i	$-0.686530\pi$
$239$	−17.0994	−1.10607	−0.553035	+	0.833158i	$0.686530\pi$
$240$	−14.3501	−0.926294
$241$	18.7507	1.20784	0.603918	−	0.797047i	$-0.293606\pi$
$241$	18.7507	1.20784	0.603918	+	0.797047i	$0.293606\pi$
$242$	−0.134164	−0.00862437
$243$	−13.0794	−0.839046
$244$	5.99024	0.383486
$245$	0	0
$246$	0.368212	0.0234763
$247$	−6.99251	−0.444923
$248$	6.27188	0.398265
$249$	−15.6578	−0.992271
$250$	−0.455659	−0.0288184
$251$	18.5700	1.17213	0.586063	−	0.810265i	$-0.300677\pi$
$251$	18.5700	1.17213	0.586063	+	0.810265i	$0.300677\pi$
$252$	0	0
$253$	9.55008	0.600409
$254$	−4.68553	−0.293996
$255$	5.41171	0.338895
$256$	9.65654	0.603534
$257$	−9.98111	−0.622605	−0.311302	−	0.950311i	$-0.600765\pi$
$257$	−9.98111	−0.622605	−0.311302	+	0.950311i	$0.600765\pi$
$258$	3.06913	0.191076
$259$	0	0
$260$	12.7927	0.793371
$261$	−6.16069	−0.381337
$262$	−3.92987	−0.242788
$263$	1.89909	0.117103	0.0585513	−	0.998284i	$-0.481352\pi$
$263$	1.89909	0.117103	0.0585513	+	0.998284i	$0.481352\pi$
$264$	4.88088	0.300397
$265$	−2.11848	−0.130137
$266$	0	0
$267$	−3.85867	−0.236147
$268$	−30.1055	−1.83898
$269$	−19.3155	−1.17768	−0.588842	−	0.808248i	$-0.700416\pi$
$269$	−19.3155	−1.17768	−0.588842	+	0.808248i	$0.700416\pi$
$270$	−5.24158	−0.318992
$271$	−13.3770	−0.812597	−0.406299	−	0.913740i	$-0.633181\pi$
$271$	−13.3770	−0.812597	−0.406299	+	0.913740i	$0.633181\pi$
$272$	−4.61934	−0.280088
$273$	0	0
$274$	−4.53934	−0.274232
$275$	−18.5658	−1.11956
$276$	−6.84228	−0.411857
$277$	5.36491	0.322346	0.161173	−	0.986926i	$-0.448472\pi$
$277$	5.36491	0.322346	0.161173	+	0.986926i	$0.448472\pi$
$278$	3.55179	0.213023
$279$	−7.69280	−0.460556
$280$	0	0
$281$	−4.66530	−0.278309	−0.139154	−	0.990271i	$-0.544438\pi$
$281$	−4.66530	−0.278309	−0.139154	+	0.990271i	$0.544438\pi$
$282$	−4.32425	−0.257505
$283$	−8.49963	−0.505251	−0.252625	−	0.967564i	$-0.581294\pi$
$283$	−8.49963	−0.505251	−0.252625	+	0.967564i	$0.581294\pi$
$284$	−14.4110	−0.855134
$285$	−13.8998	−0.823353
$286$	−2.03050	−0.120066
$287$	0	0
$288$	4.60085	0.271108
$289$	−15.2580	−0.897527
$290$	−4.15359	−0.243907
$291$	16.3092	0.956061
$292$	18.8297	1.10193
$293$	−19.0779	−1.11454	−0.557271	−	0.830330i	$-0.688152\pi$
$293$	−19.0779	−1.11454	−0.557271	+	0.830330i	$0.688152\pi$
$294$	0	0
$295$	−9.56542	−0.556920
$296$	−5.50018	−0.319692
$297$	−18.8479	−1.09366
$298$	1.23091	0.0713049
$299$	5.81859	0.336498
$300$	13.3017	0.767976
$301$	0	0
$302$	1.61182	0.0927497
$303$	−16.2250	−0.932103
$304$	11.8646	0.680482
$305$	−10.1260	−0.579810
$306$	−0.535932	−0.0306372
$307$	−0.654055	−0.0373289	−0.0186645	−	0.999826i	$-0.505941\pi$
$307$	−0.654055	−0.0373289	−0.0186645	+	0.999826i	$0.505941\pi$
$308$	0	0
$309$	−11.7967	−0.671094
$310$	−5.18655	−0.294576
$311$	24.9772	1.41632	0.708162	−	0.706050i	$-0.249524\pi$
$311$	24.9772	1.41632	0.708162	+	0.706050i	$0.249524\pi$
$312$	2.97378	0.168357
$313$	−18.6850	−1.05614	−0.528069	−	0.849202i	$-0.677084\pi$
$313$	−18.6850	−1.05614	−0.528069	+	0.849202i	$0.677084\pi$
$314$	−2.98430	−0.168414
$315$	0	0
$316$	−22.5347	−1.26767
$317$	19.6586	1.10414	0.552069	−	0.833798i	$-0.313838\pi$
$317$	19.6586	1.10414	0.552069	+	0.833798i	$0.313838\pi$
$318$	−0.240913	−0.0135097
$319$	−14.9356	−0.836236
$320$	−19.5624	−1.09357
$321$	−21.1314	−1.17944
$322$	0	0
$323$	−4.47439	−0.248962
$324$	5.47934	0.304408
$325$	−11.3116	−0.627456
$326$	3.10941	0.172214
$327$	−22.7464	−1.25788
$328$	1.13851	0.0628638
$329$	0	0
$330$	−4.03626	−0.222189
$331$	22.6387	1.24434	0.622168	−	0.782884i	$-0.286252\pi$
$331$	22.6387	1.24434	0.622168	+	0.782884i	$0.286252\pi$
$332$	−23.6842	−1.29984
$333$	6.74627	0.369693
$334$	−4.45329	−0.243673
$335$	50.8906	2.78045
$336$	0	0
$337$	11.0787	0.603494	0.301747	−	0.953388i	$-0.402430\pi$
$337$	11.0787	0.603494	0.301747	+	0.953388i	$0.402430\pi$
$338$	2.54294	0.138317
$339$	13.4521	0.730620
$340$	8.18585	0.443940
$341$	−18.6500	−1.00995
$342$	1.37652	0.0744338
$343$	0	0
$344$	9.48977	0.511654
$345$	11.5663	0.622707
$346$	−1.51431	−0.0814098
$347$	−14.7425	−0.791420	−0.395710	−	0.918375i	$-0.629502\pi$
$347$	−14.7425	−0.791420	−0.395710	+	0.918375i	$0.629502\pi$
$348$	10.7008	0.573625
$349$	−20.4958	−1.09712	−0.548558	−	0.836112i	$-0.684823\pi$
$349$	−20.4958	−1.09712	−0.548558	+	0.836112i	$0.684823\pi$
$350$	0	0
$351$	−11.4835	−0.612942
$352$	11.1541	0.594514
$353$	11.3923	0.606351	0.303175	−	0.952935i	$-0.401953\pi$
$353$	11.3923	0.606351	0.303175	+	0.952935i	$0.401953\pi$
$354$	−1.08777	−0.0578145
$355$	24.3604	1.29292
$356$	−5.83669	−0.309344
$357$	0	0
$358$	2.88753	0.152611
$359$	37.1713	1.96182	0.980912	−	0.194453i	$-0.0622931\pi$
$359$	37.1713	1.96182	0.980912	+	0.194453i	$0.0622931\pi$
$360$	−5.14783	−0.271315
$361$	−7.50768	−0.395141
$362$	−5.52225	−0.290243
$363$	−0.584280	−0.0306668
$364$	0	0
$365$	−31.8299	−1.66605
$366$	−1.15152	−0.0601908
$367$	−23.7871	−1.24168	−0.620838	−	0.783939i	$-0.713208\pi$
$367$	−23.7871	−1.24168	−0.620838	+	0.783939i	$0.713208\pi$
$368$	−9.87274	−0.514652
$369$	−1.39645	−0.0726961
$370$	4.54840	0.236460
$371$	0	0
$372$	13.3620	0.692790
$373$	18.1458	0.939554	0.469777	−	0.882785i	$-0.344334\pi$
$373$	18.1458	0.939554	0.469777	+	0.882785i	$0.344334\pi$
$374$	−1.29929	−0.0671844
$375$	−1.98439	−0.102473
$376$	−13.3706	−0.689536
$377$	−9.09986	−0.468666
$378$	0	0
$379$	1.46342	0.0751709	0.0375854	−	0.999293i	$-0.488033\pi$
$379$	1.46342	0.0751709	0.0375854	+	0.999293i	$0.488033\pi$
$380$	−21.0251	−1.07856
$381$	−20.4054	−1.04540
$382$	−1.74978	−0.0895266
$383$	−30.0911	−1.53758	−0.768792	−	0.639499i	$-0.779142\pi$
$383$	−30.0911	−1.53758	−0.768792	+	0.639499i	$0.779142\pi$
$384$	−10.5689	−0.539339
$385$	0	0
$386$	−5.00327	−0.254660
$387$	−11.6397	−0.591680
$388$	24.6695	1.25241
$389$	−29.4127	−1.49128	−0.745642	−	0.666346i	$-0.767857\pi$
$389$	−29.4127	−1.49128	−0.745642	+	0.666346i	$0.767857\pi$
$390$	−2.45918	−0.124525
$391$	3.72322	0.188291
$392$	0	0
$393$	−17.1145	−0.863313
$394$	0.681271	0.0343220
$395$	38.0928	1.91666
$396$	−9.05553	−0.455057
$397$	−9.70025	−0.486841	−0.243421	−	0.969921i	$-0.578270\pi$
$397$	−9.70025	−0.486841	−0.243421	+	0.969921i	$0.578270\pi$
$398$	−3.97767	−0.199382
$399$	0	0
$400$	19.1931	0.959655
$401$	28.2337	1.40992	0.704961	−	0.709246i	$-0.250965\pi$
$401$	28.2337	1.40992	0.704961	+	0.709246i	$0.250965\pi$
$402$	5.78725	0.288642
$403$	−11.3629	−0.566027
$404$	−24.5422	−1.22102
$405$	−9.26233	−0.460249
$406$	0	0
$407$	16.3553	0.810702
$408$	1.90287	0.0942061
$409$	10.4609	0.517261	0.258630	−	0.965976i	$-0.416729\pi$
$409$	10.4609	0.517261	0.258630	+	0.965976i	$0.416729\pi$
$410$	−0.941496	−0.0464972
$411$	−19.7687	−0.975120
$412$	−17.8440	−0.879109
$413$	0	0
$414$	−1.14543	−0.0562947
$415$	40.0360	1.96529
$416$	6.79585	0.333194
$417$	15.4680	0.757471
$418$	3.33717	0.163226
$419$	14.8903	0.727441	0.363720	−	0.931508i	$-0.381506\pi$
$419$	14.8903	0.727441	0.363720	+	0.931508i	$0.381506\pi$
$420$	0	0
$421$	8.18953	0.399134	0.199567	−	0.979884i	$-0.436047\pi$
$421$	8.18953	0.399134	0.199567	+	0.979884i	$0.436047\pi$
$422$	−1.32770	−0.0646317
$423$	16.3998	0.797383
$424$	−0.744903	−0.0361757
$425$	−7.23811	−0.351100
$426$	2.77025	0.134219
$427$	0	0
$428$	−31.9637	−1.54502
$429$	−8.84280	−0.426935
$430$	−7.84760	−0.378445
$431$	−29.2562	−1.40922	−0.704612	−	0.709593i	$-0.748879\pi$
$431$	−29.2562	−1.40922	−0.704612	+	0.709593i	$0.748879\pi$
$432$	19.4847	0.937457
$433$	19.8146	0.952228	0.476114	−	0.879384i	$-0.342045\pi$
$433$	19.8146	0.952228	0.476114	+	0.879384i	$0.342045\pi$
$434$	0	0
$435$	−18.0888	−0.867292
$436$	−34.4066	−1.64778
$437$	−9.56295	−0.457458
$438$	−3.61968	−0.172955
$439$	−24.7629	−1.18187	−0.590935	−	0.806719i	$-0.701241\pi$
$439$	−24.7629	−1.18187	−0.590935	+	0.806719i	$0.701241\pi$
$440$	−12.4801	−0.594967
$441$	0	0
$442$	−0.791617	−0.0376534
$443$	−34.0005	−1.61541	−0.807707	−	0.589584i	$-0.799292\pi$
$443$	−34.0005	−1.61541	−0.807707	+	0.589584i	$0.799292\pi$
$444$	−11.7180	−0.556110
$445$	9.86640	0.467712
$446$	2.82846	0.133932
$447$	5.36060	0.253548
$448$	0	0
$449$	−22.2494	−1.05001	−0.525006	−	0.851098i	$-0.675937\pi$
$449$	−22.2494	−1.05001	−0.525006	+	0.851098i	$0.675937\pi$
$450$	2.22677	0.104971
$451$	−3.38547	−0.159416
$452$	20.3479	0.957087
$453$	7.01943	0.329802
$454$	1.22694	0.0575831
$455$	0	0
$456$	−4.88746	−0.228876
$457$	35.9711	1.68266	0.841328	−	0.540525i	$-0.181774\pi$
$457$	35.9711	1.68266	0.841328	+	0.540525i	$0.181774\pi$
$458$	−0.373882	−0.0174703
$459$	−7.34807	−0.342979
$460$	17.4953	0.815724
$461$	−10.6347	−0.495310	−0.247655	−	0.968848i	$-0.579660\pi$
$461$	−10.6347	−0.495310	−0.247655	+	0.968848i	$0.579660\pi$
$462$	0	0
$463$	26.8603	1.24830	0.624152	−	0.781303i	$-0.285445\pi$
$463$	26.8603	1.24830	0.624152	+	0.781303i	$0.285445\pi$
$464$	15.4403	0.716796
$465$	−22.5873	−1.04746
$466$	−2.04659	−0.0948064
$467$	−13.0940	−0.605919	−0.302960	−	0.953003i	$-0.597975\pi$
$467$	−13.0940	−0.605919	−0.302960	+	0.953003i	$0.597975\pi$
$468$	−5.51727	−0.255036
$469$	0	0
$470$	11.0569	0.510015
$471$	−12.9966	−0.598850
$472$	−3.36340	−0.154813
$473$	−28.2187	−1.29750
$474$	4.33189	0.198970
$475$	18.5908	0.853006
$476$	0	0
$477$	0.913664	0.0418338
$478$	4.97207	0.227417
$479$	−21.7648	−0.994460	−0.497230	−	0.867619i	$-0.665649\pi$
$479$	−21.7648	−0.994460	−0.497230	+	0.867619i	$0.665649\pi$
$480$	13.5089	0.616593
$481$	9.96481	0.454356
$482$	−5.45220	−0.248341
$483$	0	0
$484$	−0.883792	−0.0401724
$485$	−41.7016	−1.89357
$486$	3.80316	0.172515
$487$	−1.19003	−0.0539254	−0.0269627	−	0.999636i	$-0.508584\pi$
$487$	−1.19003	−0.0539254	−0.0269627	+	0.999636i	$0.508584\pi$
$488$	−3.56049	−0.161176
$489$	13.5414	0.612365
$490$	0	0
$491$	26.3045	1.18711	0.593553	−	0.804795i	$-0.297725\pi$
$491$	26.3045	1.18711	0.593553	+	0.804795i	$0.297725\pi$
$492$	2.42556	0.109353
$493$	−5.82284	−0.262248
$494$	2.03324	0.0914798
$495$	15.3076	0.688024
$496$	19.2801	0.865703
$497$	0	0
$498$	4.55287	0.204019
$499$	8.24392	0.369048	0.184524	−	0.982828i	$-0.440926\pi$
$499$	8.24392	0.369048	0.184524	+	0.982828i	$0.440926\pi$
$500$	−3.00162	−0.134236
$501$	−19.3940	−0.866459
$502$	−5.39967	−0.240999
$503$	−35.9004	−1.60072	−0.800359	−	0.599521i	$-0.795358\pi$
$503$	−35.9004	−1.60072	−0.800359	+	0.599521i	$0.795358\pi$
$504$	0	0
$505$	41.4864	1.84612
$506$	−2.77692	−0.123449
$507$	11.0744	0.491833
$508$	−30.8655	−1.36944
$509$	28.6449	1.26966	0.634832	−	0.772651i	$-0.281069\pi$
$509$	28.6449	1.26966	0.634832	+	0.772651i	$0.281069\pi$
$510$	−1.57359	−0.0696795
$511$	0	0
$512$	−19.5002	−0.861794
$513$	18.8733	0.833276
$514$	2.90225	0.128013
$515$	30.1636	1.32917
$516$	20.2177	0.890033
$517$	39.7587	1.74859
$518$	0	0
$519$	−6.59478	−0.289479
$520$	−7.60378	−0.333448
$521$	−9.87892	−0.432803	−0.216402	−	0.976304i	$-0.569432\pi$
$521$	−9.87892	−0.432803	−0.216402	+	0.976304i	$0.569432\pi$
$522$	1.79137	0.0784061
$523$	2.64852	0.115811	0.0579057	−	0.998322i	$-0.481558\pi$
$523$	2.64852	0.115811	0.0579057	+	0.998322i	$0.481558\pi$
$524$	−25.8877	−1.13091
$525$	0	0
$526$	−0.552205	−0.0240773
$527$	−7.27093	−0.316727
$528$	15.0041	0.652970
$529$	−15.0425	−0.654022
$530$	0.616000	0.0267573
$531$	4.12539	0.179027
$532$	0	0
$533$	−2.06267	−0.0893441
$534$	1.12200	0.0485538
$535$	54.0317	2.33600
$536$	17.8942	0.772911
$537$	12.5751	0.542657
$538$	5.61644	0.242142
$539$	0	0
$540$	−34.5285	−1.48587
$541$	−16.6006	−0.713716	−0.356858	−	0.934159i	$-0.616152\pi$
$541$	−16.6006	−0.713716	−0.356858	+	0.934159i	$0.616152\pi$
$542$	3.88970	0.167077
$543$	−24.0493	−1.03205
$544$	4.34855	0.186442
$545$	58.1613	2.49136
$546$	0	0
$547$	23.1422	0.989491	0.494746	−	0.869038i	$-0.335261\pi$
$547$	23.1422	0.989491	0.494746	+	0.869038i	$0.335261\pi$
$548$	−29.9025	−1.27737
$549$	4.36714	0.186385
$550$	5.39846	0.230191
$551$	14.9558	0.637138
$552$	4.06694	0.173100
$553$	0	0
$554$	−1.55998	−0.0662771
$555$	19.8082	0.840810
$556$	23.3972	0.992261
$557$	30.6690	1.29949	0.649743	−	0.760154i	$-0.274876\pi$
$557$	30.6690	1.29949	0.649743	+	0.760154i	$0.274876\pi$
$558$	2.23687	0.0946941
$559$	−17.1928	−0.727180
$560$	0	0
$561$	−5.65836	−0.238896
$562$	1.35655	0.0572226
$563$	14.8120	0.624252	0.312126	−	0.950041i	$-0.398959\pi$
$563$	14.8120	0.624252	0.312126	+	0.950041i	$0.398959\pi$
$564$	−28.4856	−1.19946
$565$	−34.3964	−1.44707
$566$	2.47147	0.103884
$567$	0	0
$568$	8.56564	0.359406
$569$	−33.9102	−1.42159	−0.710794	−	0.703400i	$-0.751664\pi$
$569$	−33.9102	−1.42159	−0.710794	+	0.703400i	$0.751664\pi$
$570$	4.04170	0.169288
$571$	−23.8463	−0.997938	−0.498969	−	0.866620i	$-0.666288\pi$
$571$	−23.8463	−0.997938	−0.498969	+	0.866620i	$0.666288\pi$
$572$	−13.3758	−0.559269
$573$	−7.62026	−0.318341
$574$	0	0
$575$	−15.4698	−0.645134
$576$	8.43690	0.351537
$577$	19.8932	0.828164	0.414082	−	0.910240i	$-0.364103\pi$
$577$	19.8932	0.828164	0.414082	+	0.910240i	$0.364103\pi$
$578$	4.43662	0.184539
$579$	−21.7891	−0.905526
$580$	−27.3614	−1.13612
$581$	0	0
$582$	−4.74229	−0.196574
$583$	2.21504	0.0917375
$584$	−11.1921	−0.463131
$585$	9.32645	0.385601
$586$	5.54736	0.229159
$587$	10.9628	0.452484	0.226242	−	0.974071i	$-0.427356\pi$
$587$	10.9628	0.452484	0.226242	+	0.974071i	$0.427356\pi$
$588$	0	0
$589$	18.6751	0.769496
$590$	2.78138	0.114507
$591$	2.96692	0.122043
$592$	−16.9079	−0.694910
$593$	−38.8866	−1.59688	−0.798440	−	0.602074i	$-0.794341\pi$
$593$	−38.8866	−1.59688	−0.798440	+	0.602074i	$0.794341\pi$
$594$	5.48047	0.224867
$595$	0	0
$596$	8.10854	0.332139
$597$	−17.3227	−0.708969
$598$	−1.69189	−0.0691867
$599$	38.4136	1.56954	0.784769	−	0.619789i	$-0.212782\pi$
$599$	38.4136	1.56954	0.784769	+	0.619789i	$0.212782\pi$
$600$	−7.90632	−0.322774
$601$	25.7763	1.05144	0.525719	−	0.850658i	$-0.323796\pi$
$601$	25.7763	1.05144	0.525719	+	0.850658i	$0.323796\pi$
$602$	0	0
$603$	−21.9482	−0.893799
$604$	10.6177	0.432029
$605$	1.49397	0.0607386
$606$	4.71781	0.191648
$607$	4.40529	0.178805	0.0894026	−	0.995996i	$-0.471504\pi$
$607$	4.40529	0.178805	0.0894026	+	0.995996i	$0.471504\pi$
$608$	−11.1691	−0.452967
$609$	0	0
$610$	2.94436	0.119214
$611$	24.2238	0.979991
$612$	−3.53041	−0.142708
$613$	9.52086	0.384544	0.192272	−	0.981342i	$-0.438414\pi$
$613$	9.52086	0.384544	0.192272	+	0.981342i	$0.438414\pi$
$614$	0.190182	0.00767513
$615$	−4.10020	−0.165336
$616$	0	0
$617$	−10.0267	−0.403661	−0.201830	−	0.979420i	$-0.564689\pi$
$617$	−10.0267	−0.403661	−0.201830	+	0.979420i	$0.564689\pi$
$618$	3.43019	0.137982
$619$	43.1136	1.73288	0.866441	−	0.499280i	$-0.166402\pi$
$619$	43.1136	1.73288	0.866441	+	0.499280i	$0.166402\pi$
$620$	−34.1660	−1.37214
$621$	−15.7048	−0.630211
$622$	−7.26271	−0.291208
$623$	0	0
$624$	9.14157	0.365956
$625$	−22.3459	−0.893836
$626$	5.43311	0.217151
$627$	14.5333	0.580404
$628$	−19.6588	−0.784472
$629$	6.37631	0.254240
$630$	0	0
$631$	−12.8524	−0.511648	−0.255824	−	0.966723i	$-0.582347\pi$
$631$	−12.8524	−0.511648	−0.255824	+	0.966723i	$0.582347\pi$
$632$	13.3942	0.532794
$633$	−5.78213	−0.229819
$634$	−5.71622	−0.227020
$635$	52.1754	2.07052
$636$	−1.58699	−0.0629284
$637$	0	0
$638$	4.34290	0.171937
$639$	−10.5062	−0.415619
$640$	27.0240	1.06822
$641$	−10.2331	−0.404185	−0.202093	−	0.979366i	$-0.564774\pi$
$641$	−10.2331	−0.404185	−0.202093	+	0.979366i	$0.564774\pi$
$642$	6.14446	0.242502
$643$	−5.37422	−0.211939	−0.105969	−	0.994369i	$-0.533795\pi$
$643$	−5.37422	−0.211939	−0.105969	+	0.994369i	$0.533795\pi$
$644$	0	0
$645$	−34.1762	−1.34568
$646$	1.30104	0.0511886
$647$	−16.7144	−0.657109	−0.328555	−	0.944485i	$-0.606561\pi$
$647$	−16.7144	−0.657109	−0.328555	+	0.944485i	$0.606561\pi$
$648$	−3.25683	−0.127940
$649$	10.0014	0.392589
$650$	3.28912	0.129010
$651$	0	0
$652$	20.4830	0.802176
$653$	−31.1508	−1.21902	−0.609512	−	0.792777i	$-0.708635\pi$
$653$	−31.1508	−1.21902	−0.609512	+	0.792777i	$0.708635\pi$
$654$	6.61407	0.258630
$655$	43.7609	1.70988
$656$	3.49985	0.136646
$657$	13.7277	0.535567
$658$	0	0
$659$	4.26432	0.166114	0.0830571	−	0.996545i	$-0.473532\pi$
$659$	4.26432	0.166114	0.0830571	+	0.996545i	$0.473532\pi$
$660$	−26.5885	−1.03496
$661$	−30.1930	−1.17437	−0.587186	−	0.809452i	$-0.699764\pi$
$661$	−30.1930	−1.17437	−0.587186	+	0.809452i	$0.699764\pi$
$662$	−6.58275	−0.255846
$663$	−3.44747	−0.133889
$664$	14.0775	0.546313
$665$	0	0
$666$	−1.96164	−0.0760120
$667$	−12.4450	−0.481871
$668$	−29.3357	−1.13503
$669$	12.3179	0.476237
$670$	−14.7977	−0.571684
$671$	10.5875	0.408724
$672$	0	0
$673$	4.60838	0.177640	0.0888200	−	0.996048i	$-0.471690\pi$
$673$	4.60838	0.177640	0.0888200	+	0.996048i	$0.471690\pi$
$674$	−3.22139	−0.124083
$675$	30.5308	1.17513
$676$	16.7514	0.644284
$677$	28.5937	1.09894	0.549472	−	0.835512i	$-0.314829\pi$
$677$	28.5937	1.09894	0.549472	+	0.835512i	$0.314829\pi$
$678$	−3.91153	−0.150222
$679$	0	0
$680$	−4.86553	−0.186585
$681$	5.34330	0.204756
$682$	5.42294	0.207655
$683$	−17.6472	−0.675253	−0.337626	−	0.941280i	$-0.609624\pi$
$683$	−17.6472	−0.675253	−0.337626	+	0.941280i	$0.609624\pi$
$684$	9.06773	0.346713
$685$	50.5475	1.93132
$686$	0	0
$687$	−1.62825	−0.0621215
$688$	29.1721	1.11218
$689$	1.34956	0.0514141
$690$	−3.36317	−0.128034
$691$	9.44651	0.359362	0.179681	−	0.983725i	$-0.442493\pi$
$691$	9.44651	0.359362	0.179681	+	0.983725i	$0.442493\pi$
$692$	−9.97539	−0.379207
$693$	0	0
$694$	4.28674	0.162723
$695$	−39.5508	−1.50025
$696$	−6.36040	−0.241090
$697$	−1.31987	−0.0499935
$698$	5.95965	0.225576
$699$	−8.91285	−0.337115
$700$	0	0
$701$	−46.0660	−1.73989	−0.869944	−	0.493150i	$-0.835845\pi$
$701$	−46.0660	−1.73989	−0.869944	+	0.493150i	$0.835845\pi$
$702$	3.33909	0.126026
$703$	−16.3773	−0.617683
$704$	20.4540	0.770888
$705$	48.1524	1.81352
$706$	−3.31259	−0.124671
$707$	0	0
$708$	−7.16562	−0.269301
$709$	28.3067	1.06308	0.531540	−	0.847033i	$-0.321613\pi$
$709$	28.3067	1.06308	0.531540	+	0.847033i	$0.321613\pi$
$710$	−7.08338	−0.265835
$711$	−16.4287	−0.616126
$712$	3.46923	0.130015
$713$	−15.5399	−0.581974
$714$	0	0
$715$	22.6105	0.845587
$716$	19.0214	0.710862
$717$	21.6533	0.808656
$718$	−10.8084	−0.403367
$719$	−17.4745	−0.651689	−0.325844	−	0.945423i	$-0.605649\pi$
$719$	−17.4745	−0.651689	−0.325844	+	0.945423i	$0.605649\pi$
$720$	−15.8247	−0.589753
$721$	0	0
$722$	2.18304	0.0812443
$723$	−23.7442	−0.883058
$724$	−36.3774	−1.35195
$725$	24.1936	0.898528
$726$	0.169894	0.00630534
$727$	−32.3822	−1.20099	−0.600495	−	0.799629i	$-0.705030\pi$
$727$	−32.3822	−1.20099	−0.600495	+	0.799629i	$0.705030\pi$
$728$	0	0
$729$	25.1445	0.931278
$730$	9.25532	0.342555
$731$	−11.0014	−0.406902
$732$	−7.58553	−0.280369
$733$	−51.5781	−1.90508	−0.952540	−	0.304413i	$-0.901540\pi$
$733$	−51.5781	−1.90508	−0.952540	+	0.304413i	$0.901540\pi$
$734$	6.91667	0.255299
$735$	0	0
$736$	9.29400	0.342581
$737$	−53.2100	−1.96002
$738$	0.406050	0.0149469
$739$	48.0308	1.76684	0.883421	−	0.468580i	$-0.155234\pi$
$739$	48.0308	1.76684	0.883421	+	0.468580i	$0.155234\pi$
$740$	29.9622	1.10143
$741$	8.85472	0.325286
$742$	0	0
$743$	−5.85228	−0.214699	−0.107350	−	0.994221i	$-0.534236\pi$
$743$	−5.85228	−0.214699	−0.107350	+	0.994221i	$0.534236\pi$
$744$	−7.94217	−0.291174
$745$	−13.7068	−0.502177
$746$	−5.27633	−0.193180
$747$	−17.2668	−0.631760
$748$	−8.55893	−0.312946
$749$	0	0
$750$	0.577008	0.0210693
$751$	39.0587	1.42527	0.712636	−	0.701534i	$-0.247501\pi$
$751$	39.0587	1.42527	0.712636	+	0.701534i	$0.247501\pi$
$752$	−41.1020	−1.49884
$753$	−23.5154	−0.856951
$754$	2.64600	0.0963617
$755$	−17.9483	−0.653205
$756$	0	0
$757$	−35.2763	−1.28214	−0.641069	−	0.767483i	$-0.721509\pi$
$757$	−35.2763	−1.28214	−0.641069	+	0.767483i	$0.721509\pi$
$758$	−0.425525	−0.0154558
$759$	−12.0934	−0.438963
$760$	12.4970	0.453312
$761$	13.7633	0.498921	0.249460	−	0.968385i	$-0.419747\pi$
$761$	13.7633	0.498921	0.249460	+	0.968385i	$0.419747\pi$
$762$	5.93335	0.214943
$763$	0	0
$764$	−11.5265	−0.417015
$765$	5.96784	0.215768
$766$	8.74972	0.316140
$767$	6.09355	0.220025
$768$	−12.2282	−0.441248
$769$	3.81571	0.137598	0.0687990	−	0.997631i	$-0.478083\pi$
$769$	3.81571	0.137598	0.0687990	+	0.997631i	$0.478083\pi$
$770$	0	0
$771$	12.6392	0.455191
$772$	−32.9586	−1.18621
$773$	31.7824	1.14313	0.571567	−	0.820556i	$-0.306336\pi$
$773$	31.7824	1.14313	0.571567	+	0.820556i	$0.306336\pi$
$774$	3.38453	0.121654
$775$	30.2103	1.08519
$776$	−14.6632	−0.526377
$777$	0	0
$778$	8.55246	0.306621
$779$	3.39003	0.121460
$780$	−16.1996	−0.580040
$781$	−25.4707	−0.911414
$782$	−1.08261	−0.0387142
$783$	24.5612	0.877744
$784$	0	0
$785$	33.2315	1.18608
$786$	4.97646	0.177504
$787$	−44.9735	−1.60313	−0.801567	−	0.597906i	$-0.796000\pi$
$787$	−44.9735	−1.60313	−0.801567	+	0.597906i	$0.796000\pi$
$788$	4.48782	0.159872
$789$	−2.40484	−0.0856146
$790$	−11.0764	−0.394081
$791$	0	0
$792$	5.38245	0.191257
$793$	6.45063	0.229069
$794$	2.82058	0.100099
$795$	2.68267	0.0951445
$796$	−26.2026	−0.928725
$797$	−26.7786	−0.948547	−0.474274	−	0.880378i	$-0.657289\pi$
$797$	−26.7786	−0.948547	−0.474274	+	0.880378i	$0.657289\pi$
$798$	0	0
$799$	15.5004	0.548365
$800$	−18.0680	−0.638800
$801$	−4.25520	−0.150350
$802$	−8.20962	−0.289892
$803$	33.2806	1.17445
$804$	38.1230	1.34449
$805$	0	0
$806$	3.30404	0.116380
$807$	24.4595	0.861014
$808$	14.5875	0.513186
$809$	−17.2766	−0.607413	−0.303706	−	0.952766i	$-0.598224\pi$
$809$	−17.2766	−0.607413	−0.303706	+	0.952766i	$0.598224\pi$
$810$	2.69325	0.0946310
$811$	0.379424	0.0133234	0.00666168	−	0.999978i	$-0.497880\pi$
$811$	0.379424	0.0133234	0.00666168	+	0.999978i	$0.497880\pi$
$812$	0	0
$813$	16.9395	0.594096
$814$	−4.75570	−0.166687
$815$	−34.6247	−1.21285
$816$	5.84953	0.204775
$817$	28.2568	0.988579
$818$	−3.04177	−0.106353
$819$	0	0
$820$	−6.20203	−0.216584
$821$	48.2382	1.68352	0.841762	−	0.539849i	$-0.181519\pi$
$821$	48.2382	1.68352	0.841762	+	0.539849i	$0.181519\pi$
$822$	5.74824	0.200493
$823$	43.4211	1.51356	0.756782	−	0.653668i	$-0.226771\pi$
$823$	43.4211	1.51356	0.756782	+	0.653668i	$0.226771\pi$
$824$	10.6062	0.369483
$825$	23.5102	0.818520
$826$	0	0
$827$	32.6835	1.13652	0.568258	−	0.822851i	$-0.307618\pi$
$827$	32.6835	1.13652	0.568258	+	0.822851i	$0.307618\pi$
$828$	−7.54542	−0.262221
$829$	−5.75590	−0.199911	−0.0999553	−	0.994992i	$-0.531870\pi$
$829$	−5.75590	−0.199911	−0.0999553	+	0.994992i	$0.531870\pi$
$830$	−11.6414	−0.404080
$831$	−6.79367	−0.235670
$832$	12.4620	0.432042
$833$	0	0
$834$	−4.49769	−0.155742
$835$	49.5893	1.71611
$836$	21.9833	0.760310
$837$	30.6693	1.06009
$838$	−4.32973	−0.149568
$839$	−20.6974	−0.714555	−0.357278	−	0.933998i	$-0.616295\pi$
$839$	−20.6974	−0.714555	−0.357278	+	0.933998i	$0.616295\pi$
$840$	0	0
$841$	−9.53697	−0.328861
$842$	−2.38130	−0.0820652
$843$	5.90774	0.203474
$844$	−8.74615	−0.301055
$845$	−28.3167	−0.974124
$846$	−4.76862	−0.163949
$847$	0	0
$848$	−2.28988	−0.0786347
$849$	10.7632	0.369392
$850$	2.10466	0.0721891
$851$	13.6279	0.467157
$852$	18.2488	0.625194
$853$	−14.3782	−0.492301	−0.246150	−	0.969232i	$-0.579166\pi$
$853$	−14.3782	−0.492301	−0.246150	+	0.969232i	$0.579166\pi$
$854$	0	0
$855$	−15.3282	−0.524213
$856$	18.9987	0.649361
$857$	−34.6754	−1.18449	−0.592245	−	0.805758i	$-0.701758\pi$
$857$	−34.6754	−1.18449	−0.592245	+	0.805758i	$0.701758\pi$
$858$	2.57126	0.0877813
$859$	42.8934	1.46350	0.731751	−	0.681572i	$-0.238703\pi$
$859$	42.8934	1.46350	0.731751	+	0.681572i	$0.238703\pi$
$860$	−51.6954	−1.76280
$861$	0	0
$862$	8.50695	0.289748
$863$	−49.9157	−1.69915	−0.849575	−	0.527468i	$-0.823142\pi$
$863$	−49.9157	−1.69915	−0.849575	+	0.527468i	$0.823142\pi$
$864$	−18.3425	−0.624024
$865$	16.8625	0.573342
$866$	−5.76157	−0.195786
$867$	19.3214	0.656188
$868$	0	0
$869$	−39.8290	−1.35111
$870$	5.25976	0.178322
$871$	−32.4193	−1.09849
$872$	20.4507	0.692549
$873$	17.9852	0.608705
$874$	2.78066	0.0940572
$875$	0	0
$876$	−23.8443	−0.805626
$877$	10.8772	0.367295	0.183648	−	0.982992i	$-0.441209\pi$
$877$	10.8772	0.367295	0.183648	+	0.982992i	$0.441209\pi$
$878$	7.20042	0.243002
$879$	24.1586	0.814850
$880$	−38.3647	−1.29327
$881$	36.5632	1.23185	0.615923	−	0.787806i	$-0.288783\pi$
$881$	36.5632	1.23185	0.615923	+	0.787806i	$0.288783\pi$
$882$	0	0
$883$	−33.8141	−1.13794	−0.568968	−	0.822360i	$-0.692657\pi$
$883$	−33.8141	−1.13794	−0.568968	+	0.822360i	$0.692657\pi$
$884$	−5.21471	−0.175390
$885$	12.1128	0.407169
$886$	9.88647	0.332143
$887$	23.4261	0.786571	0.393285	−	0.919416i	$-0.371338\pi$
$887$	23.4261	0.786571	0.393285	+	0.919416i	$0.371338\pi$
$888$	6.96497	0.233729
$889$	0	0
$890$	−2.86889	−0.0961656
$891$	9.68448	0.324442
$892$	18.6323	0.623854
$893$	−39.8123	−1.33227
$894$	−1.55872	−0.0521315
$895$	−32.1539	−1.07479
$896$	0	0
$897$	−7.36817	−0.246016
$898$	6.46954	0.215891
$899$	24.3033	0.810561
$900$	14.6687	0.488955
$901$	0.863559	0.0287693
$902$	0.984407	0.0327772
$903$	0	0
$904$	−12.0945	−0.402256
$905$	61.4927	2.04408
$906$	−2.04107	−0.0678100
$907$	−55.6327	−1.84725	−0.923627	−	0.383292i	$-0.874790\pi$
$907$	−55.6327	−1.84725	−0.923627	+	0.383292i	$0.874790\pi$
$908$	8.08237	0.268223
$909$	−17.8923	−0.593452
$910$	0	0
$911$	21.9284	0.726519	0.363259	−	0.931688i	$-0.381664\pi$
$911$	21.9284	0.726519	0.363259	+	0.931688i	$0.381664\pi$
$912$	−15.0243	−0.497505
$913$	−41.8607	−1.38539
$914$	−10.4595	−0.345968
$915$	12.8226	0.423904
$916$	−2.46291	−0.0813770
$917$	0	0
$918$	2.13663	0.0705193
$919$	20.9389	0.690710	0.345355	−	0.938472i	$-0.387759\pi$
$919$	20.9389	0.690710	0.345355	+	0.938472i	$0.387759\pi$
$920$	−10.3989	−0.342843
$921$	0.828240	0.0272914
$922$	3.09231	0.101840
$923$	−15.5186	−0.510800
$924$	0	0
$925$	−26.4932	−0.871092
$926$	−7.81028	−0.256662
$927$	−13.0090	−0.427272
$928$	−14.5352	−0.477140
$929$	−57.3750	−1.88241	−0.941206	−	0.337833i	$-0.890306\pi$
$929$	−57.3750	−1.88241	−0.941206	+	0.337833i	$0.890306\pi$
$930$	6.56781	0.215367
$931$	0	0
$932$	−13.4817	−0.441609
$933$	−31.6290	−1.03549
$934$	3.80740	0.124582
$935$	14.4681	0.473158
$936$	3.27937	0.107190
$937$	−28.8379	−0.942093	−0.471046	−	0.882108i	$-0.656124\pi$
$937$	−28.8379	−0.942093	−0.471046	+	0.882108i	$0.656124\pi$
$938$	0	0
$939$	23.6611	0.772150
$940$	72.8362	2.37565
$941$	−47.7182	−1.55557	−0.777784	−	0.628532i	$-0.783656\pi$
$941$	−47.7182	−1.55557	−0.777784	+	0.628532i	$0.783656\pi$
$942$	3.77906	0.123128
$943$	−2.82090	−0.0918613
$944$	−10.3393	−0.336515
$945$	0	0
$946$	8.20527	0.266776
$947$	4.96728	0.161415	0.0807075	−	0.996738i	$-0.474282\pi$
$947$	4.96728	0.161415	0.0807075	+	0.996738i	$0.474282\pi$
$948$	28.5360	0.926806
$949$	20.2769	0.658217
$950$	−5.40574	−0.175385
$951$	−24.8940	−0.807244
$952$	0	0
$953$	−21.5046	−0.696603	−0.348301	−	0.937383i	$-0.613241\pi$
$953$	−21.5046	−0.696603	−0.348301	+	0.937383i	$0.613241\pi$
$954$	−0.265670	−0.00860138
$955$	19.4846	0.630506
$956$	32.7531	1.05931
$957$	18.9132	0.611378
$958$	6.32865	0.204469
$959$	0	0
$960$	24.7721	0.799517
$961$	−0.652689	−0.0210545
$962$	−2.89751	−0.0934194
$963$	−23.3029	−0.750925
$964$	−35.9159	−1.15677
$965$	55.7136	1.79348
$966$	0	0
$967$	17.5564	0.564576	0.282288	−	0.959330i	$-0.408907\pi$
$967$	17.5564	0.564576	0.282288	+	0.959330i	$0.408907\pi$
$968$	0.525311	0.0168841
$969$	5.66599	0.182018
$970$	12.1258	0.389335
$971$	−15.1562	−0.486385	−0.243193	−	0.969978i	$-0.578195\pi$
$971$	−15.1562	−0.486385	−0.243193	+	0.969978i	$0.578195\pi$
$972$	25.0530	0.803576
$973$	0	0
$974$	0.346030	0.0110875
$975$	14.3241	0.458737
$976$	−10.9452	−0.350346
$977$	35.6246	1.13973	0.569865	−	0.821738i	$-0.306995\pi$
$977$	35.6246	1.13973	0.569865	+	0.821738i	$0.306995\pi$
$978$	−3.93750	−0.125907
$979$	−10.3161	−0.329703
$980$	0	0
$981$	−25.0839	−0.800867
$982$	−7.64867	−0.244079
$983$	−5.41628	−0.172752	−0.0863762	−	0.996263i	$-0.527529\pi$
$983$	−5.41628	−0.172752	−0.0863762	+	0.996263i	$0.527529\pi$
$984$	−1.44171	−0.0459602
$985$	−7.58626	−0.241718
$986$	1.69313	0.0539203
$987$	0	0
$988$	13.3938	0.426114
$989$	−23.5129	−0.747668
$990$	−4.45104	−0.141463
$991$	49.1888	1.56253	0.781267	−	0.624197i	$-0.214574\pi$
$991$	49.1888	1.56253	0.781267	+	0.624197i	$0.214574\pi$
$992$	−18.1499	−0.576260
$993$	−28.6678	−0.909744
$994$	0	0
$995$	44.2931	1.40418
$996$	29.9917	0.950323
$997$	−28.6596	−0.907658	−0.453829	−	0.891089i	$-0.649942\pi$
$997$	−28.6596	−0.907658	−0.453829	+	0.891089i	$0.649942\pi$
$998$	−2.39712	−0.0758794
$999$	−26.8957	−0.850943

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.s.1.8		17
7.2	even	3		287.2.e.d.165.10	✓	34
7.4	even	3		287.2.e.d.247.10	yes	34
7.6	odd	2		2009.2.a.r.1.8		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.e.d.165.10	✓	34	7.2	even	3
287.2.e.d.247.10	yes	34	7.4	even	3
2009.2.a.r.1.8		17	7.6	odd	2
2009.2.a.s.1.8		17	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2009 = 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2009.a (trivial)

\(f(q)\)	\(=\)	\(q-0.290774 q^{2} -1.26632 q^{3} -1.91545 q^{4} +3.23790 q^{5} +0.368212 q^{6} +1.13851 q^{8} -1.39645 q^{9} +O(q^{10})\)	\(q-0.290774 q^{2} -1.26632 q^{3} -1.91545 q^{4} +3.23790 q^{5} +0.368212 q^{6} +1.13851 q^{8} -1.39645 q^{9} -0.941496 q^{10} -3.38547 q^{11} +2.42556 q^{12} -2.06267 q^{13} -4.10020 q^{15} +3.49985 q^{16} -1.31987 q^{17} +0.406050 q^{18} +3.39003 q^{19} -6.20203 q^{20} +0.984407 q^{22} -2.82090 q^{23} -1.44171 q^{24} +5.48397 q^{25} +0.599770 q^{26} +5.56729 q^{27} +4.41169 q^{29} +1.19223 q^{30} +5.50884 q^{31} -3.29469 q^{32} +4.28707 q^{33} +0.383783 q^{34} +2.67482 q^{36} -4.83103 q^{37} -0.985733 q^{38} +2.61199 q^{39} +3.68638 q^{40} +1.00000 q^{41} +8.33525 q^{43} +6.48470 q^{44} -4.52155 q^{45} +0.820246 q^{46} -11.7439 q^{47} -4.43191 q^{48} -1.59460 q^{50} +1.67137 q^{51} +3.95094 q^{52} -0.654278 q^{53} -1.61882 q^{54} -10.9618 q^{55} -4.29285 q^{57} -1.28281 q^{58} -2.95421 q^{59} +7.85373 q^{60} -3.12732 q^{61} -1.60183 q^{62} -6.04169 q^{64} -6.67870 q^{65} -1.24657 q^{66} +15.7172 q^{67} +2.52814 q^{68} +3.57215 q^{69} +7.52354 q^{71} -1.58987 q^{72} -9.83043 q^{73} +1.40474 q^{74} -6.94444 q^{75} -6.49344 q^{76} -0.759498 q^{78} +11.7647 q^{79} +11.3322 q^{80} -2.86060 q^{81} -0.290774 q^{82} +12.3648 q^{83} -4.27359 q^{85} -2.42367 q^{86} -5.58659 q^{87} -3.85440 q^{88} +3.04716 q^{89} +1.31475 q^{90} +5.40330 q^{92} -6.97593 q^{93} +3.41483 q^{94} +10.9766 q^{95} +4.17211 q^{96} -12.8792 q^{97} +4.72762 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 3 q^{2} + q^{3} + 25 q^{4} - q^{5} + 2 q^{6} + 9 q^{8} + 26 q^{9}+O(q^{10}) \) 17 * q + 3 * q^2 + q^3 + 25 * q^4 - q^5 + 2 * q^6 + 9 * q^8 + 26 * q^9	\( 17 q + 3 q^{2} + q^{3} + 25 q^{4} - q^{5} + 2 q^{6} + 9 q^{8} + 26 q^{9} - 2 q^{10} + 15 q^{11} + 4 q^{12} - 5 q^{13} + 24 q^{15} + 33 q^{16} + 4 q^{17} + 10 q^{18} + 5 q^{19} - 26 q^{20} + 16 q^{22} + 12 q^{23} + 16 q^{24} + 24 q^{25} + 31 q^{26} - 11 q^{27} + 14 q^{29} - 33 q^{30} - 3 q^{31} + 16 q^{32} + 4 q^{33} - 24 q^{34} + 57 q^{36} + 24 q^{37} + 45 q^{39} + 36 q^{40} + 17 q^{41} + 14 q^{43} - 9 q^{44} - 21 q^{45} + 44 q^{46} + 19 q^{47} - 60 q^{48} - 4 q^{50} + 2 q^{51} - 25 q^{52} + 4 q^{53} + 68 q^{54} + 9 q^{55} - 12 q^{57} - q^{58} - 27 q^{59} + 66 q^{60} - q^{61} - 23 q^{62} + 75 q^{64} + 22 q^{65} - 16 q^{66} + 49 q^{67} + 45 q^{68} + 12 q^{69} + 40 q^{71} - 23 q^{72} - 14 q^{73} + 33 q^{74} + 27 q^{75} - 9 q^{76} - 12 q^{78} + 61 q^{79} - 82 q^{80} + 53 q^{81} + 3 q^{82} - 18 q^{83} - 13 q^{85} - 4 q^{86} - 17 q^{87} + 74 q^{88} + 18 q^{89} - 20 q^{90} + 28 q^{92} - 36 q^{93} - 5 q^{94} + 20 q^{95} + 148 q^{96} + 26 q^{97} + 38 q^{99}+O(q^{100}) \) 17 * q + 3 * q^2 + q^3 + 25 * q^4 - q^5 + 2 * q^6 + 9 * q^8 + 26 * q^9 - 2 * q^10 + 15 * q^11 + 4 * q^12 - 5 * q^13 + 24 * q^15 + 33 * q^16 + 4 * q^17 + 10 * q^18 + 5 * q^19 - 26 * q^20 + 16 * q^22 + 12 * q^23 + 16 * q^24 + 24 * q^25 + 31 * q^26 - 11 * q^27 + 14 * q^29 - 33 * q^30 - 3 * q^31 + 16 * q^32 + 4 * q^33 - 24 * q^34 + 57 * q^36 + 24 * q^37 + 45 * q^39 + 36 * q^40 + 17 * q^41 + 14 * q^43 - 9 * q^44 - 21 * q^45 + 44 * q^46 + 19 * q^47 - 60 * q^48 - 4 * q^50 + 2 * q^51 - 25 * q^52 + 4 * q^53 + 68 * q^54 + 9 * q^55 - 12 * q^57 - q^58 - 27 * q^59 + 66 * q^60 - q^61 - 23 * q^62 + 75 * q^64 + 22 * q^65 - 16 * q^66 + 49 * q^67 + 45 * q^68 + 12 * q^69 + 40 * q^71 - 23 * q^72 - 14 * q^73 + 33 * q^74 + 27 * q^75 - 9 * q^76 - 12 * q^78 + 61 * q^79 - 82 * q^80 + 53 * q^81 + 3 * q^82 - 18 * q^83 - 13 * q^85 - 4 * q^86 - 17 * q^87 + 74 * q^88 + 18 * q^89 - 20 * q^90 + 28 * q^92 - 36 * q^93 - 5 * q^94 + 20 * q^95 + 148 * q^96 + 26 * q^97 + 38 * q^99

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