LMFDB - Embedded newform 2009.2.a.s.1.1

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			1.1
Root			$-2.76801$ 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)

$f(q)$	$=$	$q-2.76801 q^{2} -2.85049 q^{3} +5.66188 q^{4} -3.02107 q^{5} +7.89019 q^{6} -10.1361 q^{8} +5.12530 q^{9} +O(q^{10})$	\(q-2.76801 q^{2} -2.85049 q^{3} +5.66188 q^{4} -3.02107 q^{5} +7.89019 q^{6} -10.1361 q^{8} +5.12530 q^{9} +8.36234 q^{10} -0.809408 q^{11} -16.1392 q^{12} -3.86586 q^{13} +8.61152 q^{15} +16.7332 q^{16} -0.828004 q^{17} -14.1869 q^{18} -1.89207 q^{19} -17.1049 q^{20} +2.24045 q^{22} -0.475366 q^{23} +28.8930 q^{24} +4.12684 q^{25} +10.7007 q^{26} -6.05815 q^{27} -2.61064 q^{29} -23.8368 q^{30} +0.449043 q^{31} -26.0453 q^{32} +2.30721 q^{33} +2.29192 q^{34} +29.0189 q^{36} +3.25880 q^{37} +5.23726 q^{38} +11.0196 q^{39} +30.6219 q^{40} +1.00000 q^{41} -6.10120 q^{43} -4.58277 q^{44} -15.4839 q^{45} +1.31582 q^{46} -5.67973 q^{47} -47.6977 q^{48} -11.4231 q^{50} +2.36022 q^{51} -21.8880 q^{52} -13.0084 q^{53} +16.7690 q^{54} +2.44527 q^{55} +5.39331 q^{57} +7.22629 q^{58} -9.52954 q^{59} +48.7574 q^{60} -11.7095 q^{61} -1.24296 q^{62} +38.6274 q^{64} +11.6790 q^{65} -6.38638 q^{66} +5.13357 q^{67} -4.68806 q^{68} +1.35503 q^{69} -1.45987 q^{71} -51.9507 q^{72} +8.74088 q^{73} -9.02038 q^{74} -11.7635 q^{75} -10.7127 q^{76} -30.5023 q^{78} -10.6884 q^{79} -50.5520 q^{80} +1.89279 q^{81} -2.76801 q^{82} -6.30118 q^{83} +2.50146 q^{85} +16.8882 q^{86} +7.44162 q^{87} +8.20427 q^{88} -3.07544 q^{89} +42.8595 q^{90} -2.69147 q^{92} -1.27999 q^{93} +15.7216 q^{94} +5.71605 q^{95} +74.2419 q^{96} -15.8551 q^{97} -4.14846 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.76801	−1.95728	−0.978640	−	0.205583i	$-0.934091\pi$
$2$	−2.76801	−1.95728	−0.978640	+	0.205583i	$0.934091\pi$
$3$	−2.85049	−1.64573	−0.822866	−	0.568236i	$-0.807626\pi$
$3$	−2.85049	−1.64573	−0.822866	+	0.568236i	$0.807626\pi$
$4$	5.66188	2.83094
$5$	−3.02107	−1.35106	−0.675531	−	0.737332i	$-0.736086\pi$
$5$	−3.02107	−1.35106	−0.675531	+	0.737332i	$0.736086\pi$
$6$	7.89019	3.22116
$7$	0	0
$7$	0	0
$8$	−10.1361	−3.58367
$9$	5.12530	1.70843
$10$	8.36234	2.64441
$11$	−0.809408	−0.244046	−0.122023	−	0.992527i	$-0.538938\pi$
$11$	−0.809408	−0.244046	−0.122023	+	0.992527i	$0.538938\pi$
$12$	−16.1392	−4.65897
$13$	−3.86586	−1.07220	−0.536098	−	0.844156i	$-0.680102\pi$
$13$	−3.86586	−1.07220	−0.536098	+	0.844156i	$0.680102\pi$
$14$	0	0
$15$	8.61152	2.22349
$16$	16.7332	4.18329
$17$	−0.828004	−0.200821	−0.100410	−	0.994946i	$-0.532016\pi$
$17$	−0.828004	−0.200821	−0.100410	+	0.994946i	$0.532016\pi$
$18$	−14.1869	−3.34388
$19$	−1.89207	−0.434069	−0.217035	−	0.976164i	$-0.569638\pi$
$19$	−1.89207	−0.434069	−0.217035	+	0.976164i	$0.569638\pi$
$20$	−17.1049	−3.82478
$21$	0	0
$22$	2.24045	0.477665
$23$	−0.475366	−0.0991206	−0.0495603	−	0.998771i	$-0.515782\pi$
$23$	−0.475366	−0.0991206	−0.0495603	+	0.998771i	$0.515782\pi$
$24$	28.8930	5.89775
$25$	4.12684	0.825368
$26$	10.7007	2.09859
$27$	−6.05815	−1.16589
$28$	0	0
$29$	−2.61064	−0.484784	−0.242392	−	0.970178i	$-0.577932\pi$
$29$	−2.61064	−0.484784	−0.242392	+	0.970178i	$0.577932\pi$
$30$	−23.8368	−4.35198
$31$	0.449043	0.0806505	0.0403253	−	0.999187i	$-0.487161\pi$
$31$	0.449043	0.0806505	0.0403253	+	0.999187i	$0.487161\pi$
$32$	−26.0453	−4.60421
$33$	2.30721	0.401634
$34$	2.29192	0.393062
$35$	0	0
$36$	29.0189	4.83648
$37$	3.25880	0.535743	0.267871	−	0.963455i	$-0.413680\pi$
$37$	3.25880	0.535743	0.267871	+	0.963455i	$0.413680\pi$
$38$	5.23726	0.849595
$39$	11.0196	1.76455
$40$	30.6219	4.84175
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−6.10120	−0.930425	−0.465212	−	0.885199i	$-0.654022\pi$
$43$	−6.10120	−0.930425	−0.465212	+	0.885199i	$0.654022\pi$
$44$	−4.58277	−0.690879
$45$	−15.4839	−2.30820
$46$	1.31582	0.194007
$47$	−5.67973	−0.828474	−0.414237	−	0.910169i	$-0.635952\pi$
$47$	−5.67973	−0.828474	−0.414237	+	0.910169i	$0.635952\pi$
$48$	−47.6977	−6.88458
$49$	0	0
$50$	−11.4231	−1.61548
$51$	2.36022	0.330497
$52$	−21.8880	−3.03532
$53$	−13.0084	−1.78684	−0.893422	−	0.449218i	$-0.851703\pi$
$53$	−13.0084	−1.78684	−0.893422	+	0.449218i	$0.851703\pi$
$54$	16.7690	2.28197
$55$	2.44527	0.329721
$56$	0	0
$57$	5.39331	0.714362
$58$	7.22629	0.948858
$59$	−9.52954	−1.24064	−0.620321	−	0.784348i	$-0.712997\pi$
$59$	−9.52954	−1.24064	−0.620321	+	0.784348i	$0.712997\pi$
$60$	48.7574	6.29456
$61$	−11.7095	−1.49925	−0.749623	−	0.661865i	$-0.769765\pi$
$61$	−11.7095	−1.49925	−0.749623	+	0.661865i	$0.769765\pi$
$62$	−1.24296	−0.157856
$63$	0	0
$64$	38.6274	4.82842
$65$	11.6790	1.44860
$66$	−6.38638	−0.786109
$67$	5.13357	0.627165	0.313583	−	0.949561i	$-0.398471\pi$
$67$	5.13357	0.627165	0.313583	+	0.949561i	$0.398471\pi$
$68$	−4.68806	−0.568511
$69$	1.35503	0.163126
$70$	0	0
$71$	−1.45987	−0.173255	−0.0866273	−	0.996241i	$-0.527609\pi$
$71$	−1.45987	−0.173255	−0.0866273	+	0.996241i	$0.527609\pi$
$72$	−51.9507	−6.12245
$73$	8.74088	1.02304	0.511521	−	0.859271i	$-0.329082\pi$
$73$	8.74088	1.02304	0.511521	+	0.859271i	$0.329082\pi$
$74$	−9.02038	−1.04860
$75$	−11.7635	−1.35833
$76$	−10.7127	−1.22883
$77$	0	0
$78$	−30.5023	−3.45371
$79$	−10.6884	−1.20254	−0.601269	−	0.799047i	$-0.705338\pi$
$79$	−10.6884	−1.20254	−0.601269	+	0.799047i	$0.705338\pi$
$80$	−50.5520	−5.65189
$81$	1.89279	0.210310
$82$	−2.76801	−0.305676
$83$	−6.30118	−0.691644	−0.345822	−	0.938300i	$-0.612400\pi$
$83$	−6.30118	−0.691644	−0.345822	+	0.938300i	$0.612400\pi$
$84$	0	0
$85$	2.50146	0.271321
$86$	16.8882	1.82110
$87$	7.44162	0.797825
$88$	8.20427	0.874578
$89$	−3.07544	−0.325996	−0.162998	−	0.986626i	$-0.552116\pi$
$89$	−3.07544	−0.325996	−0.162998	+	0.986626i	$0.552116\pi$
$90$	42.8595	4.51779
$91$	0	0
$92$	−2.69147	−0.280605
$93$	−1.27999	−0.132729
$94$	15.7216	1.62156
$95$	5.71605	0.586455
$96$	74.2419	7.57729
$97$	−15.8551	−1.60984	−0.804918	−	0.593386i	$-0.797791\pi$
$97$	−15.8551	−1.60984	−0.804918	+	0.593386i	$0.797791\pi$
$98$	0	0
$99$	−4.14846	−0.416936
$100$	23.3657	2.33657
$101$	2.85892	0.284474	0.142237	−	0.989833i	$-0.454571\pi$
$101$	2.85892	0.284474	0.142237	+	0.989833i	$0.454571\pi$
$102$	−6.53311	−0.646874
$103$	−9.74855	−0.960553	−0.480277	−	0.877117i	$-0.659464\pi$
$103$	−9.74855	−0.960553	−0.480277	+	0.877117i	$0.659464\pi$
$104$	39.1848	3.84239
$105$	0	0
$106$	36.0075	3.49735
$107$	−14.8849	−1.43898	−0.719489	−	0.694504i	$-0.755624\pi$
$107$	−14.8849	−1.43898	−0.719489	+	0.694504i	$0.755624\pi$
$108$	−34.3005	−3.30057
$109$	−9.75957	−0.934798	−0.467399	−	0.884047i	$-0.654809\pi$
$109$	−9.75957	−0.934798	−0.467399	+	0.884047i	$0.654809\pi$
$110$	−6.76855	−0.645356
$111$	−9.28917	−0.881689
$112$	0	0
$113$	−20.3338	−1.91284	−0.956420	−	0.291996i	$-0.905681\pi$
$113$	−20.3338	−1.91284	−0.956420	+	0.291996i	$0.905681\pi$
$114$	−14.9288	−1.39821
$115$	1.43611	0.133918
$116$	−14.7812	−1.37240
$117$	−19.8137	−1.83177
$118$	26.3779	2.42828
$119$	0	0
$120$	−87.2876	−7.96823
$121$	−10.3449	−0.940442
$122$	32.4120	2.93444
$123$	−2.85049	−0.257020
$124$	2.54243	0.228317
$125$	2.63787	0.235939
$126$	0	0
$127$	7.82133	0.694031	0.347015	−	0.937859i	$-0.387195\pi$
$127$	7.82133	0.694031	0.347015	+	0.937859i	$0.387195\pi$
$128$	−54.8304	−4.84637
$129$	17.3914	1.53123
$130$	−32.3276	−2.83532
$131$	−2.45252	−0.214278	−0.107139	−	0.994244i	$-0.534169\pi$
$131$	−2.45252	−0.214278	−0.107139	+	0.994244i	$0.534169\pi$
$132$	13.0632	1.13700
$133$	0	0
$134$	−14.2098	−1.22754
$135$	18.3021	1.57519
$136$	8.39276	0.719674
$137$	13.3576	1.14121	0.570607	−	0.821223i	$-0.306708\pi$
$137$	13.3576	1.14121	0.570607	+	0.821223i	$0.306708\pi$
$138$	−3.75073	−0.319283
$139$	−9.08568	−0.770638	−0.385319	−	0.922784i	$-0.625909\pi$
$139$	−9.08568	−0.770638	−0.385319	+	0.922784i	$0.625909\pi$
$140$	0	0
$141$	16.1900	1.36345
$142$	4.04093	0.339108
$143$	3.12905	0.261665
$144$	85.7625	7.14687
$145$	7.88693	0.654974
$146$	−24.1949	−2.00238
$147$	0	0
$148$	18.4509	1.51666
$149$	2.94081	0.240921	0.120460	−	0.992718i	$-0.461563\pi$
$149$	2.94081	0.240921	0.120460	+	0.992718i	$0.461563\pi$
$150$	32.5616	2.65864
$151$	1.91810	0.156093	0.0780464	−	0.996950i	$-0.475132\pi$
$151$	1.91810	0.156093	0.0780464	+	0.996950i	$0.475132\pi$
$152$	19.1782	1.55556
$153$	−4.24377	−0.343088
$154$	0	0
$155$	−1.35659	−0.108964
$156$	62.3916	4.99533
$157$	10.5089	0.838702	0.419351	−	0.907824i	$-0.362258\pi$
$157$	10.5089	0.838702	0.419351	+	0.907824i	$0.362258\pi$
$158$	29.5856	2.35370
$159$	37.0804	2.94067
$160$	78.6846	6.22057
$161$	0	0
$162$	−5.23927	−0.411636
$163$	18.0875	1.41672	0.708362	−	0.705849i	$-0.249434\pi$
$163$	18.0875	1.41672	0.708362	+	0.705849i	$0.249434\pi$
$164$	5.66188	0.442119
$165$	−6.97023	−0.542632
$166$	17.4417	1.35374
$167$	19.0456	1.47380	0.736898	−	0.676004i	$-0.236290\pi$
$167$	19.0456	1.47380	0.736898	+	0.676004i	$0.236290\pi$
$168$	0	0
$169$	1.94485	0.149604
$170$	−6.92406	−0.531051
$171$	−9.69740	−0.741579
$172$	−34.5443	−2.63398
$173$	−4.63435	−0.352343	−0.176172	−	0.984359i	$-0.556371\pi$
$173$	−4.63435	−0.352343	−0.176172	+	0.984359i	$0.556371\pi$
$174$	−20.5985	−1.56157
$175$	0	0
$176$	−13.5440	−1.02091
$177$	27.1639	2.04176
$178$	8.51284	0.638065
$179$	−10.7836	−0.806002	−0.403001	−	0.915200i	$-0.632033\pi$
$179$	−10.7836	−0.806002	−0.403001	+	0.915200i	$0.632033\pi$
$180$	−87.6679	−6.53438
$181$	19.6683	1.46193	0.730965	−	0.682415i	$-0.239070\pi$
$181$	19.6683	1.46193	0.730965	+	0.682415i	$0.239070\pi$
$182$	0	0
$183$	33.3778	2.46736
$184$	4.81837	0.355215
$185$	−9.84504	−0.723822
$186$	3.54304	0.259788
$187$	0.670193	0.0490094
$188$	−32.1580	−2.34536
$189$	0	0
$190$	−15.8221	−1.14786
$191$	23.2230	1.68035	0.840177	−	0.542312i	$-0.182451\pi$
$191$	23.2230	1.68035	0.840177	+	0.542312i	$0.182451\pi$
$192$	−110.107	−7.94629
$193$	−14.7682	−1.06304	−0.531518	−	0.847047i	$-0.678378\pi$
$193$	−14.7682	−1.06304	−0.531518	+	0.847047i	$0.678378\pi$
$194$	43.8870	3.15090
$195$	−33.2909	−2.38401
$196$	0	0
$197$	−22.0210	−1.56893	−0.784466	−	0.620172i	$-0.787063\pi$
$197$	−22.0210	−1.56893	−0.784466	+	0.620172i	$0.787063\pi$
$198$	11.4830	0.816059
$199$	−7.15240	−0.507020	−0.253510	−	0.967333i	$-0.581585\pi$
$199$	−7.15240	−0.507020	−0.253510	+	0.967333i	$0.581585\pi$
$200$	−41.8302	−2.95784
$201$	−14.6332	−1.03215
$202$	−7.91353	−0.556794
$203$	0	0
$204$	13.3633	0.935617
$205$	−3.02107	−0.211000
$206$	26.9841	1.88007
$207$	−2.43639	−0.169341
$208$	−64.6880	−4.48531
$209$	1.53145	0.105933
$210$	0	0
$211$	17.5087	1.20535	0.602673	−	0.797988i	$-0.294102\pi$
$211$	17.5087	1.20535	0.602673	+	0.797988i	$0.294102\pi$
$212$	−73.6522	−5.05845
$213$	4.16134	0.285131
$214$	41.2016	2.81648
$215$	18.4321	1.25706
$216$	61.4062	4.17816
$217$	0	0
$218$	27.0146	1.82966
$219$	−24.9158	−1.68365
$220$	13.8449	0.933420
$221$	3.20095	0.215319
$222$	25.7125	1.72571
$223$	9.22671	0.617866	0.308933	−	0.951084i	$-0.400028\pi$
$223$	9.22671	0.617866	0.308933	+	0.951084i	$0.400028\pi$
$224$	0	0
$225$	21.1513	1.41009
$226$	56.2841	3.74396
$227$	21.8853	1.45258	0.726290	−	0.687388i	$-0.241243\pi$
$227$	21.8853	1.45258	0.726290	+	0.687388i	$0.241243\pi$
$228$	30.5363	2.02232
$229$	−8.91465	−0.589097	−0.294548	−	0.955637i	$-0.595169\pi$
$229$	−8.91465	−0.589097	−0.294548	+	0.955637i	$0.595169\pi$
$230$	−3.97517	−0.262115
$231$	0	0
$232$	26.4618	1.73730
$233$	0.537037	0.0351825	0.0175912	−	0.999845i	$-0.494400\pi$
$233$	0.537037	0.0351825	0.0175912	+	0.999845i	$0.494400\pi$
$234$	54.8445	3.58529
$235$	17.1588	1.11932
$236$	−53.9552	−3.51218
$237$	30.4672	1.97906
$238$	0	0
$239$	14.2066	0.918951	0.459476	−	0.888190i	$-0.348037\pi$
$239$	14.2066	0.918951	0.459476	+	0.888190i	$0.348037\pi$
$240$	144.098	9.30149
$241$	−7.18725	−0.462972	−0.231486	−	0.972838i	$-0.574359\pi$
$241$	−7.18725	−0.462972	−0.231486	+	0.972838i	$0.574359\pi$
$242$	28.6347	1.84071
$243$	12.7790	0.819776
$244$	−66.2978	−4.24428
$245$	0	0
$246$	7.89019	0.503060
$247$	7.31445	0.465407
$248$	−4.55156	−0.289025
$249$	17.9614	1.13826
$250$	−7.30166	−0.461798
$251$	7.54012	0.475928	0.237964	−	0.971274i	$-0.423520\pi$
$251$	7.54012	0.475928	0.237964	+	0.971274i	$0.423520\pi$
$252$	0	0
$253$	0.384765	0.0241900
$254$	−21.6495	−1.35841
$255$	−7.13038	−0.446521
$256$	74.5164	4.65727
$257$	19.7370	1.23116	0.615579	−	0.788075i	$-0.288922\pi$
$257$	19.7370	1.23116	0.615579	+	0.788075i	$0.288922\pi$
$258$	−48.1397	−2.99704
$259$	0	0
$260$	66.1252	4.10091
$261$	−13.3803	−0.828222
$262$	6.78860	0.419401
$263$	0.286751	0.0176818	0.00884092	−	0.999961i	$-0.497186\pi$
$263$	0.286751	0.0176818	0.00884092	+	0.999961i	$0.497186\pi$
$264$	−23.3862	−1.43932
$265$	39.2993	2.41414
$266$	0	0
$267$	8.76651	0.536501
$268$	29.0657	1.77547
$269$	−18.2027	−1.10984	−0.554920	−	0.831904i	$-0.687251\pi$
$269$	−18.2027	−1.10984	−0.554920	+	0.831904i	$0.687251\pi$
$270$	−50.6603	−3.08309
$271$	−4.82169	−0.292897	−0.146448	−	0.989218i	$-0.546784\pi$
$271$	−4.82169	−0.292897	−0.146448	+	0.989218i	$0.546784\pi$
$272$	−13.8551	−0.840091
$273$	0	0
$274$	−36.9739	−2.23367
$275$	−3.34030	−0.201427
$276$	7.67200	0.461800
$277$	−14.4367	−0.867416	−0.433708	−	0.901054i	$-0.642795\pi$
$277$	−14.4367	−0.867416	−0.433708	+	0.901054i	$0.642795\pi$
$278$	25.1493	1.50835
$279$	2.30148	0.137786
$280$	0	0
$281$	−4.23994	−0.252934	−0.126467	−	0.991971i	$-0.540364\pi$
$281$	−4.23994	−0.252934	−0.126467	+	0.991971i	$0.540364\pi$
$282$	−44.8142	−2.66864
$283$	−22.5254	−1.33900	−0.669498	−	0.742813i	$-0.733491\pi$
$283$	−22.5254	−1.33900	−0.669498	+	0.742813i	$0.733491\pi$
$284$	−8.26561	−0.490474
$285$	−16.2936	−0.965147
$286$	−8.66126	−0.512151
$287$	0	0
$288$	−133.490	−7.86598
$289$	−16.3144	−0.959671
$290$	−21.8311	−1.28197
$291$	45.1947	2.64936
$292$	49.4899	2.89617
$293$	13.5665	0.792565	0.396282	−	0.918129i	$-0.370300\pi$
$293$	13.5665	0.792565	0.396282	+	0.918129i	$0.370300\pi$
$294$	0	0
$295$	28.7894	1.67618
$296$	−33.0316	−1.91992
$297$	4.90351	0.284531
$298$	−8.14019	−0.471549
$299$	1.83770	0.106277
$300$	−66.6037	−3.84537
$301$	0	0
$302$	−5.30932	−0.305517
$303$	−8.14934	−0.468167
$304$	−31.6602	−1.81584
$305$	35.3751	2.02557
$306$	11.7468	0.671520
$307$	−26.6357	−1.52018	−0.760090	−	0.649817i	$-0.774845\pi$
$307$	−26.6357	−1.52018	−0.760090	+	0.649817i	$0.774845\pi$
$308$	0	0
$309$	27.7882	1.58081
$310$	3.75505	0.213273
$311$	9.43307	0.534900	0.267450	−	0.963572i	$-0.413819\pi$
$311$	9.43307	0.534900	0.267450	+	0.963572i	$0.413819\pi$
$312$	−111.696	−6.32354
$313$	−12.1547	−0.687023	−0.343511	−	0.939148i	$-0.611616\pi$
$313$	−12.1547	−0.687023	−0.343511	+	0.939148i	$0.611616\pi$
$314$	−29.0888	−1.64157
$315$	0	0
$316$	−60.5165	−3.40432
$317$	14.4001	0.808789	0.404394	−	0.914585i	$-0.367482\pi$
$317$	14.4001	0.808789	0.404394	+	0.914585i	$0.367482\pi$
$318$	−102.639	−5.75571
$319$	2.11308	0.118310
$320$	−116.696	−6.52350
$321$	42.4293	2.36817
$322$	0	0
$323$	1.56664	0.0871701
$324$	10.7168	0.595377
$325$	−15.9538	−0.884956
$326$	−50.0665	−2.77292
$327$	27.8196	1.53843
$328$	−10.1361	−0.559675
$329$	0	0
$330$	19.2937	1.06208
$331$	−4.76156	−0.261719	−0.130859	−	0.991401i	$-0.541774\pi$
$331$	−4.76156	−0.261719	−0.130859	+	0.991401i	$0.541774\pi$
$332$	−35.6765	−1.95800
$333$	16.7023	0.915281
$334$	−52.7185	−2.88463
$335$	−15.5088	−0.847339
$336$	0	0
$337$	−8.79898	−0.479311	−0.239655	−	0.970858i	$-0.577034\pi$
$337$	−8.79898	−0.479311	−0.239655	+	0.970858i	$0.577034\pi$
$338$	−5.38335	−0.292816
$339$	57.9612	3.14802
$340$	14.1630	0.768094
$341$	−0.363459	−0.0196824
$342$	26.8425	1.45148
$343$	0	0
$344$	61.8426	3.33433
$345$	−4.09362	−0.220393
$346$	12.8279	0.689634
$347$	−26.0201	−1.39683	−0.698416	−	0.715692i	$-0.746112\pi$
$347$	−26.0201	−1.39683	−0.698416	+	0.715692i	$0.746112\pi$
$348$	42.1336	2.25860
$349$	−14.7488	−0.789488	−0.394744	−	0.918791i	$-0.629167\pi$
$349$	−14.7488	−0.789488	−0.394744	+	0.918791i	$0.629167\pi$
$350$	0	0
$351$	23.4199	1.25006
$352$	21.0813	1.12364
$353$	11.0539	0.588341	0.294170	−	0.955753i	$-0.404957\pi$
$353$	11.0539	0.588341	0.294170	+	0.955753i	$0.404957\pi$
$354$	−75.1899	−3.99630
$355$	4.41036	0.234078
$356$	−17.4128	−0.922875
$357$	0	0
$358$	29.8490	1.57757
$359$	23.7540	1.25369	0.626845	−	0.779144i	$-0.284346\pi$
$359$	23.7540	1.25369	0.626845	+	0.779144i	$0.284346\pi$
$360$	156.947	8.27181
$361$	−15.4201	−0.811584
$362$	−54.4420	−2.86141
$363$	29.4879	1.54771
$364$	0	0
$365$	−26.4068	−1.38219
$366$	−92.3901	−4.82931
$367$	21.1330	1.10313	0.551567	−	0.834130i	$-0.314030\pi$
$367$	21.1330	1.10313	0.551567	+	0.834130i	$0.314030\pi$
$368$	−7.95438	−0.414650
$369$	5.12530	0.266812
$370$	27.2512	1.41672
$371$	0	0
$372$	−7.24718	−0.375749
$373$	8.91618	0.461662	0.230831	−	0.972994i	$-0.425855\pi$
$373$	8.91618	0.461662	0.230831	+	0.972994i	$0.425855\pi$
$374$	−1.85510	−0.0959250
$375$	−7.51923	−0.388292
$376$	57.5705	2.96897
$377$	10.0924	0.519784
$378$	0	0
$379$	2.48486	0.127639	0.0638194	−	0.997961i	$-0.479672\pi$
$379$	2.48486	0.127639	0.0638194	+	0.997961i	$0.479672\pi$
$380$	32.3636	1.66022
$381$	−22.2946	−1.14219
$382$	−64.2814	−3.28892
$383$	−12.1522	−0.620950	−0.310475	−	0.950582i	$-0.600488\pi$
$383$	−12.1522	−0.620950	−0.310475	+	0.950582i	$0.600488\pi$
$384$	156.294	7.97582
$385$	0	0
$386$	40.8785	2.08066
$387$	−31.2705	−1.58957
$388$	−89.7695	−4.55735
$389$	−33.0103	−1.67369	−0.836844	−	0.547441i	$-0.815602\pi$
$389$	−33.0103	−1.67369	−0.836844	+	0.547441i	$0.815602\pi$
$390$	92.1496	4.66618
$391$	0.393605	0.0199055
$392$	0	0
$393$	6.99088	0.352643
$394$	60.9544	3.07084
$395$	32.2903	1.62470
$396$	−23.4881	−1.18032
$397$	17.1194	0.859198	0.429599	−	0.903020i	$-0.358655\pi$
$397$	17.1194	0.859198	0.429599	+	0.903020i	$0.358655\pi$
$398$	19.7979	0.992380
$399$	0	0
$400$	69.0551	3.45276
$401$	15.5316	0.775611	0.387805	−	0.921741i	$-0.373233\pi$
$401$	15.5316	0.775611	0.387805	+	0.921741i	$0.373233\pi$
$402$	40.5048	2.02020
$403$	−1.73594	−0.0864732
$404$	16.1869	0.805328
$405$	−5.71826	−0.284142
$406$	0	0
$407$	−2.63770	−0.130746
$408$	−23.9235	−1.18439
$409$	1.10843	0.0548083	0.0274041	−	0.999624i	$-0.491276\pi$
$409$	1.10843	0.0548083	0.0274041	+	0.999624i	$0.491276\pi$
$410$	8.36234	0.412987
$411$	−38.0756	−1.87813
$412$	−55.1952	−2.71927
$413$	0	0
$414$	6.74396	0.331448
$415$	19.0363	0.934454
$416$	100.687	4.93661
$417$	25.8987	1.26826
$418$	−4.23908	−0.207340
$419$	−5.74205	−0.280518	−0.140259	−	0.990115i	$-0.544793\pi$
$419$	−5.74205	−0.280518	−0.140259	+	0.990115i	$0.544793\pi$
$420$	0	0
$421$	−24.9380	−1.21541	−0.607703	−	0.794165i	$-0.707909\pi$
$421$	−24.9380	−1.21541	−0.607703	+	0.794165i	$0.707909\pi$
$422$	−48.4641	−2.35920
$423$	−29.1103	−1.41539
$424$	131.855	6.40345
$425$	−3.41704	−0.165751
$426$	−11.5186	−0.558080
$427$	0	0
$428$	−84.2766	−4.07367
$429$	−8.91934	−0.430630
$430$	−51.0204	−2.46042
$431$	15.8925	0.765517	0.382758	−	0.923848i	$-0.374974\pi$
$431$	15.8925	0.765517	0.382758	+	0.923848i	$0.374974\pi$
$432$	−101.372	−4.87726
$433$	6.34096	0.304727	0.152364	−	0.988325i	$-0.451312\pi$
$433$	6.34096	0.304727	0.152364	+	0.988325i	$0.451312\pi$
$434$	0	0
$435$	−22.4816	−1.07791
$436$	−55.2576	−2.64636
$437$	0.899423	0.0430252
$438$	68.9672	3.29538
$439$	−30.3726	−1.44961	−0.724803	−	0.688956i	$-0.758069\pi$
$439$	−30.3726	−1.44961	−0.724803	+	0.688956i	$0.758069\pi$
$440$	−24.7856	−1.18161
$441$	0	0
$442$	−8.86025	−0.421439
$443$	29.3469	1.39431	0.697157	−	0.716918i	$-0.254448\pi$
$443$	29.3469	1.39431	0.697157	+	0.716918i	$0.254448\pi$
$444$	−52.5942	−2.49601
$445$	9.29110	0.440440
$446$	−25.5396	−1.20934
$447$	−8.38275	−0.396491
$448$	0	0
$449$	35.1178	1.65731	0.828656	−	0.559758i	$-0.189106\pi$
$449$	35.1178	1.65731	0.828656	+	0.559758i	$0.189106\pi$
$450$	−58.5470	−2.75993
$451$	−0.809408	−0.0381135
$452$	−115.127	−5.41514
$453$	−5.46753	−0.256887
$454$	−60.5788	−2.84310
$455$	0	0
$456$	−54.6674	−2.56003
$457$	4.90137	0.229276	0.114638	−	0.993407i	$-0.463429\pi$
$457$	4.90137	0.229276	0.114638	+	0.993407i	$0.463429\pi$
$458$	24.6759	1.15303
$459$	5.01617	0.234135
$460$	8.13110	0.379114
$461$	1.55339	0.0723486	0.0361743	−	0.999345i	$-0.488483\pi$
$461$	1.55339	0.0723486	0.0361743	+	0.999345i	$0.488483\pi$
$462$	0	0
$463$	−6.30847	−0.293179	−0.146590	−	0.989197i	$-0.546830\pi$
$463$	−6.30847	−0.293179	−0.146590	+	0.989197i	$0.546830\pi$
$464$	−43.6843	−2.02799
$465$	3.86695	0.179325
$466$	−1.48652	−0.0688619
$467$	21.0062	0.972049	0.486024	−	0.873945i	$-0.338447\pi$
$467$	21.0062	0.972049	0.486024	+	0.873945i	$0.338447\pi$
$468$	−112.183	−5.18565
$469$	0	0
$470$	−47.4959	−2.19082
$471$	−29.9555	−1.38028
$472$	96.5928	4.44604
$473$	4.93836	0.227066
$474$	−84.3335	−3.87356
$475$	−7.80825	−0.358267
$476$	0	0
$477$	−66.6721	−3.05270
$478$	−39.3241	−1.79864
$479$	−0.510272	−0.0233149	−0.0116575	−	0.999932i	$-0.503711\pi$
$479$	−0.510272	−0.0233149	−0.0116575	+	0.999932i	$0.503711\pi$
$480$	−224.290	−10.2374
$481$	−12.5980	−0.574421
$482$	19.8944	0.906165
$483$	0	0
$484$	−58.5714	−2.66234
$485$	47.8992	2.17499
$486$	−35.3725	−1.60453
$487$	10.9455	0.495988	0.247994	−	0.968762i	$-0.420229\pi$
$487$	10.9455	0.495988	0.247994	+	0.968762i	$0.420229\pi$
$488$	118.689	5.37280
$489$	−51.5583	−2.33155
$490$	0	0
$491$	1.52841	0.0689760	0.0344880	−	0.999405i	$-0.489020\pi$
$491$	1.52841	0.0689760	0.0344880	+	0.999405i	$0.489020\pi$
$492$	−16.1392	−0.727609
$493$	2.16162	0.0973546
$494$	−20.2465	−0.910932
$495$	12.5328	0.563306
$496$	7.51392	0.337385
$497$	0	0
$498$	−49.7175	−2.22789
$499$	−29.5904	−1.32465	−0.662324	−	0.749218i	$-0.730430\pi$
$499$	−29.5904	−1.32465	−0.662324	+	0.749218i	$0.730430\pi$
$500$	14.9353	0.667928
$501$	−54.2894	−2.42547
$502$	−20.8711	−0.931525
$503$	29.9673	1.33618	0.668088	−	0.744082i	$-0.267113\pi$
$503$	29.9673	1.33618	0.668088	+	0.744082i	$0.267113\pi$
$504$	0	0
$505$	−8.63700	−0.384341
$506$	−1.06503	−0.0473465
$507$	−5.54377	−0.246207
$508$	44.2835	1.96476
$509$	−9.94634	−0.440864	−0.220432	−	0.975402i	$-0.570747\pi$
$509$	−9.94634	−0.440864	−0.220432	+	0.975402i	$0.570747\pi$
$510$	19.7370	0.873967
$511$	0	0
$512$	−96.6013	−4.26922
$513$	11.4624	0.506078
$514$	−54.6321	−2.40972
$515$	29.4510	1.29777
$516$	98.4682	4.33482
$517$	4.59722	0.202185
$518$	0	0
$519$	13.2102	0.579862
$520$	−118.380	−5.19131
$521$	−31.9204	−1.39846	−0.699230	−	0.714897i	$-0.746474\pi$
$521$	−31.9204	−1.39846	−0.699230	+	0.714897i	$0.746474\pi$
$522$	37.0369	1.62106
$523$	13.5725	0.593484	0.296742	−	0.954958i	$-0.404100\pi$
$523$	13.5725	0.593484	0.296742	+	0.954958i	$0.404100\pi$
$524$	−13.8859	−0.606607
$525$	0	0
$526$	−0.793731	−0.0346083
$527$	−0.371810	−0.0161963
$528$	38.6069	1.68015
$529$	−22.7740	−0.990175
$530$	−108.781	−4.72514
$531$	−48.8418	−2.11955
$532$	0	0
$533$	−3.86586	−0.167449
$534$	−24.2658	−1.05008
$535$	44.9683	1.94415
$536$	−52.0345	−2.24755
$537$	30.7385	1.32646
$538$	50.3854	2.17227
$539$	0	0
$540$	103.624	4.45927
$541$	−3.85715	−0.165832	−0.0829159	−	0.996557i	$-0.526423\pi$
$541$	−3.85715	−0.165832	−0.0829159	+	0.996557i	$0.526423\pi$
$542$	13.3465	0.573280
$543$	−56.0642	−2.40595
$544$	21.5656	0.924619
$545$	29.4843	1.26297
$546$	0	0
$547$	3.96156	0.169384	0.0846920	−	0.996407i	$-0.473009\pi$
$547$	3.96156	0.169384	0.0846920	+	0.996407i	$0.473009\pi$
$548$	75.6290	3.23071
$549$	−60.0146	−2.56136
$550$	9.24598	0.394250
$551$	4.93951	0.210430
$552$	−13.7347	−0.584589
$553$	0	0
$554$	39.9609	1.69777
$555$	28.0632	1.19122
$556$	−51.4421	−2.18163
$557$	−7.17809	−0.304145	−0.152073	−	0.988369i	$-0.548595\pi$
$557$	−7.17809	−0.304145	−0.152073	+	0.988369i	$0.548595\pi$
$558$	−6.37052	−0.269686
$559$	23.5864	0.997597
$560$	0	0
$561$	−1.91038	−0.0806563
$562$	11.7362	0.495062
$563$	−24.9483	−1.05145	−0.525723	−	0.850656i	$-0.676205\pi$
$563$	−24.9483	−1.05145	−0.525723	+	0.850656i	$0.676205\pi$
$564$	91.6660	3.85984
$565$	61.4296	2.58436
$566$	62.3506	2.62079
$567$	0	0
$568$	14.7974	0.620886
$569$	−35.7525	−1.49882	−0.749412	−	0.662104i	$-0.769664\pi$
$569$	−35.7525	−1.49882	−0.749412	+	0.662104i	$0.769664\pi$
$570$	45.1008	1.88906
$571$	32.9225	1.37777	0.688883	−	0.724873i	$-0.258101\pi$
$571$	32.9225	1.37777	0.688883	+	0.724873i	$0.258101\pi$
$572$	17.7163	0.740758
$573$	−66.1968	−2.76541
$574$	0	0
$575$	−1.96176	−0.0818110
$576$	197.977	8.24904
$577$	−13.0378	−0.542770	−0.271385	−	0.962471i	$-0.587482\pi$
$577$	−13.0378	−0.542770	−0.271385	+	0.962471i	$0.587482\pi$
$578$	45.1585	1.87834
$579$	42.0965	1.74947
$580$	44.6549	1.85419
$581$	0	0
$582$	−125.099	−5.18554
$583$	10.5291	0.436072
$584$	−88.5988	−3.66624
$585$	59.8584	2.47484
$586$	−37.5523	−1.55127
$587$	20.5144	0.846721	0.423360	−	0.905961i	$-0.360850\pi$
$587$	20.5144	0.846721	0.423360	+	0.905961i	$0.360850\pi$
$588$	0	0
$589$	−0.849619	−0.0350079
$590$	−79.6893	−3.28076
$591$	62.7707	2.58204
$592$	54.5300	2.24117
$593$	−25.8242	−1.06047	−0.530236	−	0.847850i	$-0.677897\pi$
$593$	−25.8242	−1.06047	−0.530236	+	0.847850i	$0.677897\pi$
$594$	−13.5730	−0.556906
$595$	0	0
$596$	16.6505	0.682032
$597$	20.3879	0.834419
$598$	−5.08676	−0.208013
$599$	8.13168	0.332252	0.166126	−	0.986105i	$-0.446874\pi$
$599$	8.13168	0.332252	0.166126	+	0.986105i	$0.446874\pi$
$600$	119.237	4.86782
$601$	−16.8215	−0.686163	−0.343082	−	0.939306i	$-0.611471\pi$
$601$	−16.8215	−0.686163	−0.343082	+	0.939306i	$0.611471\pi$
$602$	0	0
$603$	26.3111	1.07147
$604$	10.8601	0.441890
$605$	31.2525	1.27059
$606$	22.5575	0.916334
$607$	2.45843	0.0997848	0.0498924	−	0.998755i	$-0.484112\pi$
$607$	2.45843	0.0997848	0.0498924	+	0.998755i	$0.484112\pi$
$608$	49.2794	1.99854
$609$	0	0
$610$	−97.9188	−3.96462
$611$	21.9570	0.888286
$612$	−24.0277	−0.971263
$613$	22.9107	0.925355	0.462678	−	0.886527i	$-0.346889\pi$
$613$	22.9107	0.925355	0.462678	+	0.886527i	$0.346889\pi$
$614$	73.7280	2.97542
$615$	8.61152	0.347250
$616$	0	0
$617$	−31.6529	−1.27430	−0.637149	−	0.770741i	$-0.719886\pi$
$617$	−31.6529	−1.27430	−0.637149	+	0.770741i	$0.719886\pi$
$618$	−76.9179	−3.09409
$619$	4.60395	0.185049	0.0925243	−	0.995710i	$-0.470506\pi$
$619$	4.60395	0.185049	0.0925243	+	0.995710i	$0.470506\pi$
$620$	−7.68085	−0.308470
$621$	2.87984	0.115564
$622$	−26.1108	−1.04695
$623$	0	0
$624$	184.393	7.38161
$625$	−28.6034	−1.14414
$626$	33.6443	1.34470
$627$	−4.36539	−0.174337
$628$	59.5002	2.37432
$629$	−2.69830	−0.107588
$630$	0	0
$631$	−5.46440	−0.217534	−0.108767	−	0.994067i	$-0.534690\pi$
$631$	−5.46440	−0.217534	−0.108767	+	0.994067i	$0.534690\pi$
$632$	108.339	4.30949
$633$	−49.9083	−1.98368
$634$	−39.8596	−1.58303
$635$	−23.6288	−0.937679
$636$	209.945	8.32486
$637$	0	0
$638$	−5.84902	−0.231565
$639$	−7.48227	−0.295994
$640$	165.646	6.54774
$641$	36.9536	1.45958	0.729789	−	0.683672i	$-0.239618\pi$
$641$	36.9536	1.45958	0.729789	+	0.683672i	$0.239618\pi$
$642$	−117.445	−4.63518
$643$	21.6513	0.853843	0.426922	−	0.904289i	$-0.359598\pi$
$643$	21.6513	0.853843	0.426922	+	0.904289i	$0.359598\pi$
$644$	0	0
$645$	−52.5406	−2.06879
$646$	−4.33647	−0.170616
$647$	−17.9487	−0.705637	−0.352818	−	0.935692i	$-0.614777\pi$
$647$	−17.9487	−0.705637	−0.352818	+	0.935692i	$0.614777\pi$
$648$	−19.1856	−0.753682
$649$	7.71329	0.302773
$650$	44.1602	1.73211
$651$	0	0
$652$	102.409	4.01066
$653$	35.3145	1.38196	0.690982	−	0.722872i	$-0.257178\pi$
$653$	35.3145	1.38196	0.690982	+	0.722872i	$0.257178\pi$
$654$	−77.0049	−3.01113
$655$	7.40922	0.289502
$656$	16.7332	0.653320
$657$	44.7996	1.74780
$658$	0	0
$659$	−5.81071	−0.226353	−0.113177	−	0.993575i	$-0.536103\pi$
$659$	−5.81071	−0.226353	−0.113177	+	0.993575i	$0.536103\pi$
$660$	−39.4647	−1.53616
$661$	36.6871	1.42696	0.713482	−	0.700674i	$-0.247117\pi$
$661$	36.6871	1.42696	0.713482	+	0.700674i	$0.247117\pi$
$662$	13.1800	0.512257
$663$	−9.12427	−0.354357
$664$	63.8696	2.47862
$665$	0	0
$666$	−46.2322	−1.79146
$667$	1.24101	0.0480521
$668$	107.834	4.17223
$669$	−26.3006	−1.01684
$670$	42.9287	1.65848
$671$	9.47775	0.365885
$672$	0	0
$673$	−45.8608	−1.76780	−0.883902	−	0.467672i	$-0.845093\pi$
$673$	−45.8608	−1.76780	−0.883902	+	0.467672i	$0.845093\pi$
$674$	24.3557	0.938145
$675$	−25.0010	−0.962289
$676$	11.0115	0.423519
$677$	−19.8902	−0.764441	−0.382221	−	0.924071i	$-0.624841\pi$
$677$	−19.8902	−0.764441	−0.382221	+	0.924071i	$0.624841\pi$
$678$	−160.437	−6.16155
$679$	0	0
$680$	−25.3551	−0.972323
$681$	−62.3839	−2.39056
$682$	1.00606	0.0385240
$683$	−8.49824	−0.325176	−0.162588	−	0.986694i	$-0.551984\pi$
$683$	−8.49824	−0.325176	−0.162588	+	0.986694i	$0.551984\pi$
$684$	−54.9056	−2.09937
$685$	−40.3541	−1.54185
$686$	0	0
$687$	25.4111	0.969496
$688$	−102.092	−3.89224
$689$	50.2887	1.91585
$690$	11.3312	0.431371
$691$	31.2384	1.18837	0.594183	−	0.804330i	$-0.297476\pi$
$691$	31.2384	1.18837	0.594183	+	0.804330i	$0.297476\pi$
$692$	−26.2392	−0.997463
$693$	0	0
$694$	72.0239	2.73399
$695$	27.4484	1.04118
$696$	−75.4292	−2.85914
$697$	−0.828004	−0.0313629
$698$	40.8250	1.54525
$699$	−1.53082	−0.0579009
$700$	0	0
$701$	20.3738	0.769508	0.384754	−	0.923019i	$-0.374286\pi$
$701$	20.3738	0.769508	0.384754	+	0.923019i	$0.374286\pi$
$702$	−64.8266	−2.44672
$703$	−6.16585	−0.232550
$704$	−31.2653	−1.17836
$705$	−48.9111	−1.84210
$706$	−30.5974	−1.15155
$707$	0	0
$708$	153.799	5.78011
$709$	48.0124	1.80314	0.901571	−	0.432630i	$-0.142414\pi$
$709$	48.0124	1.80314	0.901571	+	0.432630i	$0.142414\pi$
$710$	−12.2079	−0.458155
$711$	−54.7812	−2.05446
$712$	31.1730	1.16826
$713$	−0.213460	−0.00799413
$714$	0	0
$715$	−9.45308	−0.353525
$716$	−61.0553	−2.28174
$717$	−40.4959	−1.51235
$718$	−65.7514	−2.45382
$719$	−3.33151	−0.124244	−0.0621221	−	0.998069i	$-0.519787\pi$
$719$	−3.33151	−0.124244	−0.0621221	+	0.998069i	$0.519787\pi$
$720$	−259.094	−9.65587
$721$	0	0
$722$	42.6830	1.58850
$723$	20.4872	0.761927
$724$	111.359	4.13864
$725$	−10.7737	−0.400126
$726$	−81.6229	−3.02931
$727$	32.9605	1.22244	0.611219	−	0.791461i	$-0.290679\pi$
$727$	32.9605	1.22244	0.611219	+	0.791461i	$0.290679\pi$
$728$	0	0
$729$	−42.1049	−1.55944
$730$	73.0942	2.70534
$731$	5.05182	0.186848
$732$	188.981	6.98495
$733$	−35.7714	−1.32125	−0.660623	−	0.750718i	$-0.729708\pi$
$733$	−35.7714	−1.32125	−0.660623	+	0.750718i	$0.729708\pi$
$734$	−58.4964	−2.15914
$735$	0	0
$736$	12.3811	0.456372
$737$	−4.15515	−0.153057
$738$	−14.1869	−0.522226
$739$	19.1912	0.705961	0.352980	−	0.935631i	$-0.385168\pi$
$739$	19.1912	0.705961	0.352980	+	0.935631i	$0.385168\pi$
$740$	−55.7415	−2.04910
$741$	−20.8498	−0.765936
$742$	0	0
$743$	5.15568	0.189144	0.0945718	−	0.995518i	$-0.469852\pi$
$743$	5.15568	0.189144	0.0945718	+	0.995518i	$0.469852\pi$
$744$	12.9742	0.475657
$745$	−8.88438	−0.325499
$746$	−24.6801	−0.903602
$747$	−32.2954	−1.18163
$748$	3.79456	0.138743
$749$	0	0
$750$	20.8133	0.759995
$751$	19.9981	0.729741	0.364871	−	0.931058i	$-0.381113\pi$
$751$	19.9981	0.729741	0.364871	+	0.931058i	$0.381113\pi$
$752$	−95.0399	−3.46575
$753$	−21.4930	−0.783250
$754$	−27.9358	−1.01736
$755$	−5.79471	−0.210891
$756$	0	0
$757$	−1.81127	−0.0658319	−0.0329159	−	0.999458i	$-0.510479\pi$
$757$	−1.81127	−0.0658319	−0.0329159	+	0.999458i	$0.510479\pi$
$758$	−6.87813	−0.249825
$759$	−1.09677	−0.0398102
$760$	−57.9387	−2.10166
$761$	23.7203	0.859860	0.429930	−	0.902862i	$-0.358538\pi$
$761$	23.7203	0.859860	0.429930	+	0.902862i	$0.358538\pi$
$762$	61.7118	2.23558
$763$	0	0
$764$	131.486	4.75698
$765$	12.8207	0.463534
$766$	33.6375	1.21537
$767$	36.8399	1.33021
$768$	−212.408	−7.66462
$769$	−47.0762	−1.69761	−0.848806	−	0.528704i	$-0.822678\pi$
$769$	−47.0762	−1.69761	−0.848806	+	0.528704i	$0.822678\pi$
$770$	0	0
$771$	−56.2600	−2.02615
$772$	−83.6157	−3.00939
$773$	−26.4758	−0.952268	−0.476134	−	0.879373i	$-0.657962\pi$
$773$	−26.4758	−0.952268	−0.476134	+	0.879373i	$0.657962\pi$
$774$	86.5571	3.11123
$775$	1.85313	0.0665664
$776$	160.709	5.76912
$777$	0	0
$778$	91.3729	3.27588
$779$	−1.89207	−0.0677903
$780$	−188.489	−6.74900
$781$	1.18163	0.0422820
$782$	−1.08950	−0.0389605
$783$	15.8157	0.565206
$784$	0	0
$785$	−31.7481	−1.13314
$786$	−19.3508	−0.690221
$787$	50.7389	1.80865	0.904324	−	0.426848i	$-0.140376\pi$
$787$	50.7389	1.80865	0.904324	+	0.426848i	$0.140376\pi$
$788$	−124.680	−4.44156
$789$	−0.817382	−0.0290996
$790$	−89.3800	−3.18000
$791$	0	0
$792$	42.0493	1.49416
$793$	45.2672	1.60749
$794$	−47.3867	−1.68169
$795$	−112.022	−3.97302
$796$	−40.4961	−1.43534
$797$	18.9700	0.671953	0.335976	−	0.941870i	$-0.390934\pi$
$797$	18.9700	0.671953	0.335976	+	0.941870i	$0.390934\pi$
$798$	0	0
$799$	4.70284	0.166375
$800$	−107.485	−3.80016
$801$	−15.7625	−0.556942
$802$	−42.9916	−1.51809
$803$	−7.07494	−0.249669
$804$	−82.8514	−2.92194
$805$	0	0
$806$	4.80509	0.169252
$807$	51.8867	1.82650
$808$	−28.9784	−1.01946
$809$	43.5429	1.53089	0.765443	−	0.643503i	$-0.222520\pi$
$809$	43.5429	1.53089	0.765443	+	0.643503i	$0.222520\pi$
$810$	15.8282	0.556146
$811$	32.9946	1.15860	0.579298	−	0.815116i	$-0.303327\pi$
$811$	32.9946	1.15860	0.579298	+	0.815116i	$0.303327\pi$
$812$	0	0
$813$	13.7442	0.482029
$814$	7.30117	0.255906
$815$	−54.6436	−1.91408
$816$	39.4939	1.38256
$817$	11.5439	0.403869
$818$	−3.06814	−0.107275
$819$	0	0
$820$	−17.1049	−0.597330
$821$	34.7604	1.21315	0.606573	−	0.795028i	$-0.292544\pi$
$821$	34.7604	1.21315	0.606573	+	0.795028i	$0.292544\pi$
$822$	105.394	3.67603
$823$	21.5711	0.751922	0.375961	−	0.926636i	$-0.377313\pi$
$823$	21.5711	0.751922	0.375961	+	0.926636i	$0.377313\pi$
$824$	98.8127	3.44230
$825$	9.52149	0.331496
$826$	0	0
$827$	−1.59470	−0.0554532	−0.0277266	−	0.999616i	$-0.508827\pi$
$827$	−1.59470	−0.0554532	−0.0277266	+	0.999616i	$0.508827\pi$
$828$	−13.7946	−0.479394
$829$	36.1338	1.25498	0.627489	−	0.778626i	$-0.284083\pi$
$829$	36.1338	1.25498	0.627489	+	0.778626i	$0.284083\pi$
$830$	−52.6926	−1.82899
$831$	41.1516	1.42753
$832$	−149.328	−5.17701
$833$	0	0
$834$	−71.6878	−2.48234
$835$	−57.5381	−1.99119
$836$	8.67091	0.299890
$837$	−2.72037	−0.0940297
$838$	15.8941	0.549052
$839$	3.43446	0.118571	0.0592853	−	0.998241i	$-0.481118\pi$
$839$	3.43446	0.118571	0.0592853	+	0.998241i	$0.481118\pi$
$840$	0	0
$841$	−22.1845	−0.764984
$842$	69.0287	2.37889
$843$	12.0859	0.416261
$844$	99.1320	3.41226
$845$	−5.87551	−0.202124
$846$	80.5777	2.77032
$847$	0	0
$848$	−217.672	−7.47489
$849$	64.2085	2.20363
$850$	9.45841	0.324421
$851$	−1.54912	−0.0531032
$852$	23.5610	0.807188
$853$	5.93145	0.203089	0.101544	−	0.994831i	$-0.467622\pi$
$853$	5.93145	0.203089	0.101544	+	0.994831i	$0.467622\pi$
$854$	0	0
$855$	29.2965	1.00192
$856$	150.875	5.15682
$857$	15.5223	0.530233	0.265117	−	0.964216i	$-0.414590\pi$
$857$	15.5223	0.530233	0.265117	+	0.964216i	$0.414590\pi$
$858$	24.6888	0.842863
$859$	−20.6119	−0.703268	−0.351634	−	0.936138i	$-0.614374\pi$
$859$	−20.6119	−0.703268	−0.351634	+	0.936138i	$0.614374\pi$
$860$	104.361	3.55867
$861$	0	0
$862$	−43.9907	−1.49833
$863$	−29.6407	−1.00898	−0.504491	−	0.863417i	$-0.668320\pi$
$863$	−29.6407	−1.00898	−0.504491	+	0.863417i	$0.668320\pi$
$864$	157.786	5.36800
$865$	14.0007	0.476037
$866$	−17.5519	−0.596436
$867$	46.5041	1.57936
$868$	0	0
$869$	8.65127	0.293474
$870$	62.2294	2.10977
$871$	−19.8456	−0.672444
$872$	98.9244	3.35000
$873$	−81.2619	−2.75030
$874$	−2.48961	−0.0842124
$875$	0	0
$876$	−141.070	−4.76633
$877$	−25.6980	−0.867760	−0.433880	−	0.900971i	$-0.642856\pi$
$877$	−25.6980	−0.867760	−0.433880	+	0.900971i	$0.642856\pi$
$878$	84.0718	2.83728
$879$	−38.6712	−1.30435
$880$	40.9172	1.37932
$881$	3.71565	0.125183	0.0625917	−	0.998039i	$-0.480063\pi$
$881$	3.71565	0.125183	0.0625917	+	0.998039i	$0.480063\pi$
$882$	0	0
$883$	−11.8979	−0.400395	−0.200198	−	0.979756i	$-0.564158\pi$
$883$	−11.8979	−0.400395	−0.200198	+	0.979756i	$0.564158\pi$
$884$	18.1234	0.609555
$885$	−82.0639	−2.75855
$886$	−81.2326	−2.72906
$887$	−9.80933	−0.329365	−0.164683	−	0.986347i	$-0.552660\pi$
$887$	−9.80933	−0.329365	−0.164683	+	0.986347i	$0.552660\pi$
$888$	94.1563	3.15968
$889$	0	0
$890$	−25.7179	−0.862065
$891$	−1.53204	−0.0513253
$892$	52.2405	1.74914
$893$	10.7464	0.359615
$894$	23.2036	0.776043
$895$	32.5779	1.08896
$896$	0	0
$897$	−5.23834	−0.174903
$898$	−97.2065	−3.24382
$899$	−1.17229	−0.0390981
$900$	119.756	3.99187
$901$	10.7710	0.358835
$902$	2.24045	0.0745988
$903$	0	0
$904$	206.106	6.85498
$905$	−59.4191	−1.97516
$906$	15.1342	0.502799
$907$	−22.3954	−0.743628	−0.371814	−	0.928307i	$-0.621264\pi$
$907$	−22.3954	−0.743628	−0.371814	+	0.928307i	$0.621264\pi$
$908$	123.912	4.11217
$909$	14.6528	0.486004
$910$	0	0
$911$	−26.3926	−0.874425	−0.437213	−	0.899358i	$-0.644034\pi$
$911$	−26.3926	−0.874425	−0.437213	+	0.899358i	$0.644034\pi$
$912$	90.2472	2.98838
$913$	5.10022	0.168793
$914$	−13.5670	−0.448758
$915$	−100.837	−3.33355
$916$	−50.4737	−1.66770
$917$	0	0
$918$	−13.8848	−0.458267
$919$	−50.3575	−1.66114	−0.830571	−	0.556913i	$-0.811986\pi$
$919$	−50.3575	−1.66114	−0.830571	+	0.556913i	$0.811986\pi$
$920$	−14.5566	−0.479918
$921$	75.9249	2.50181
$922$	−4.29980	−0.141606
$923$	5.64364	0.185763
$924$	0	0
$925$	13.4485	0.442185
$926$	17.4619	0.573834
$927$	−49.9642	−1.64104
$928$	67.9950	2.23205
$929$	19.1637	0.628741	0.314371	−	0.949300i	$-0.398207\pi$
$929$	19.1637	0.628741	0.314371	+	0.949300i	$0.398207\pi$
$930$	−10.7037	−0.350990
$931$	0	0
$932$	3.04064	0.0995995
$933$	−26.8889	−0.880303
$934$	−58.1453	−1.90257
$935$	−2.02470	−0.0662147
$936$	200.834	6.56447
$937$	4.86054	0.158787	0.0793935	−	0.996843i	$-0.474702\pi$
$937$	4.86054	0.158787	0.0793935	+	0.996843i	$0.474702\pi$
$938$	0	0
$939$	34.6468	1.13066
$940$	97.1514	3.16873
$941$	15.9427	0.519718	0.259859	−	0.965647i	$-0.416324\pi$
$941$	15.9427	0.519718	0.259859	+	0.965647i	$0.416324\pi$
$942$	82.9172	2.70159
$943$	−0.475366	−0.0154800
$944$	−159.459	−5.18996
$945$	0	0
$946$	−13.6694	−0.444432
$947$	−32.7906	−1.06555	−0.532775	−	0.846257i	$-0.678851\pi$
$947$	−32.7906	−1.06555	−0.532775	+	0.846257i	$0.678851\pi$
$948$	172.502	5.60259
$949$	−33.7910	−1.09690
$950$	21.6133	0.701229
$951$	−41.0473	−1.33105
$952$	0	0
$953$	−18.3086	−0.593074	−0.296537	−	0.955021i	$-0.595832\pi$
$953$	−18.3086	−0.593074	−0.296537	+	0.955021i	$0.595832\pi$
$954$	184.549	5.97499
$955$	−70.1581	−2.27026
$956$	80.4364	2.60150
$957$	−6.02330	−0.194706
$958$	1.41244	0.0456338
$959$	0	0
$960$	332.641	10.7359
$961$	−30.7984	−0.993495
$962$	34.8715	1.12430
$963$	−76.2896	−2.45840
$964$	−40.6934	−1.31065
$965$	44.6156	1.43623
$966$	0	0
$967$	21.3394	0.686230	0.343115	−	0.939293i	$-0.388518\pi$
$967$	21.3394	0.686230	0.343115	+	0.939293i	$0.388518\pi$
$968$	104.857	3.37023
$969$	−4.46569	−0.143459
$970$	−132.585	−4.25706
$971$	−37.6666	−1.20878	−0.604389	−	0.796690i	$-0.706583\pi$
$971$	−37.6666	−1.20878	−0.604389	+	0.796690i	$0.706583\pi$
$972$	72.3535	2.32074
$973$	0	0
$974$	−30.2973	−0.970787
$975$	45.4761	1.45640
$976$	−195.937	−6.27179
$977$	−15.5512	−0.497527	−0.248764	−	0.968564i	$-0.580024\pi$
$977$	−15.5512	−0.497527	−0.248764	+	0.968564i	$0.580024\pi$
$978$	142.714	4.56349
$979$	2.48928	0.0795578
$980$	0	0
$981$	−50.0207	−1.59704
$982$	−4.23065	−0.135005
$983$	−22.3641	−0.713303	−0.356652	−	0.934237i	$-0.616082\pi$
$983$	−22.3641	−0.713303	−0.356652	+	0.934237i	$0.616082\pi$
$984$	28.8930	0.921074
$985$	66.5269	2.11972
$986$	−5.98340	−0.190550
$987$	0	0
$988$	41.4136	1.31754
$989$	2.90030	0.0922243
$990$	−34.6908	−1.10255
$991$	−15.1727	−0.481977	−0.240989	−	0.970528i	$-0.577472\pi$
$991$	−15.1727	−0.481977	−0.240989	+	0.970528i	$0.577472\pi$
$992$	−11.6955	−0.371332
$993$	13.5728	0.430719
$994$	0	0
$995$	21.6079	0.685016
$996$	101.696	3.22235
$997$	−18.1532	−0.574917	−0.287458	−	0.957793i	$-0.592810\pi$
$997$	−18.1532	−0.574917	−0.287458	+	0.957793i	$0.592810\pi$
$998$	81.9065	2.59270
$999$	−19.7423	−0.624618

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.s.1.1		17
7.2	even	3		287.2.e.d.165.17	✓	34
7.4	even	3		287.2.e.d.247.17	yes	34
7.6	odd	2		2009.2.a.r.1.1		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.e.d.165.17	✓	34	7.2	even	3
287.2.e.d.247.17	yes	34	7.4	even	3
2009.2.a.r.1.1		17	7.6	odd	2
2009.2.a.s.1.1		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)

\(f(q)\)	\(=\)	\(q-2.76801 q^{2} -2.85049 q^{3} +5.66188 q^{4} -3.02107 q^{5} +7.89019 q^{6} -10.1361 q^{8} +5.12530 q^{9} +O(q^{10})\)	\(q-2.76801 q^{2} -2.85049 q^{3} +5.66188 q^{4} -3.02107 q^{5} +7.89019 q^{6} -10.1361 q^{8} +5.12530 q^{9} +8.36234 q^{10} -0.809408 q^{11} -16.1392 q^{12} -3.86586 q^{13} +8.61152 q^{15} +16.7332 q^{16} -0.828004 q^{17} -14.1869 q^{18} -1.89207 q^{19} -17.1049 q^{20} +2.24045 q^{22} -0.475366 q^{23} +28.8930 q^{24} +4.12684 q^{25} +10.7007 q^{26} -6.05815 q^{27} -2.61064 q^{29} -23.8368 q^{30} +0.449043 q^{31} -26.0453 q^{32} +2.30721 q^{33} +2.29192 q^{34} +29.0189 q^{36} +3.25880 q^{37} +5.23726 q^{38} +11.0196 q^{39} +30.6219 q^{40} +1.00000 q^{41} -6.10120 q^{43} -4.58277 q^{44} -15.4839 q^{45} +1.31582 q^{46} -5.67973 q^{47} -47.6977 q^{48} -11.4231 q^{50} +2.36022 q^{51} -21.8880 q^{52} -13.0084 q^{53} +16.7690 q^{54} +2.44527 q^{55} +5.39331 q^{57} +7.22629 q^{58} -9.52954 q^{59} +48.7574 q^{60} -11.7095 q^{61} -1.24296 q^{62} +38.6274 q^{64} +11.6790 q^{65} -6.38638 q^{66} +5.13357 q^{67} -4.68806 q^{68} +1.35503 q^{69} -1.45987 q^{71} -51.9507 q^{72} +8.74088 q^{73} -9.02038 q^{74} -11.7635 q^{75} -10.7127 q^{76} -30.5023 q^{78} -10.6884 q^{79} -50.5520 q^{80} +1.89279 q^{81} -2.76801 q^{82} -6.30118 q^{83} +2.50146 q^{85} +16.8882 q^{86} +7.44162 q^{87} +8.20427 q^{88} -3.07544 q^{89} +42.8595 q^{90} -2.69147 q^{92} -1.27999 q^{93} +15.7216 q^{94} +5.71605 q^{95} +74.2419 q^{96} -15.8551 q^{97} -4.14846 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 3 q^{2} + q^{3} + 25 q^{4} - q^{5} + 2 q^{6} + 9 q^{8} + 26 q^{9}+O(q^{10}) \) 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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