LMFDB - Embedded newform 490.4.a.r.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,4,Mod(1,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("490.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	490.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:	$28.9109359028$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{46}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 46 $ x^2 - 46
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$6.78233$ of defining polynomial
Character	$\chi$	$=$	490.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} +5.78233 q^{3} +4.00000 q^{4} +5.00000 q^{5} -11.5647 q^{6} -8.00000 q^{8} +6.43534 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} +5.78233 q^{3} +4.00000 q^{4} +5.00000 q^{5} -11.5647 q^{6} -8.00000 q^{8} +6.43534 q^{9} -10.0000 q^{10} -20.4353 q^{11} +23.1293 q^{12} -53.1293 q^{13} +28.9116 q^{15} +16.0000 q^{16} +27.7414 q^{17} -12.8707 q^{18} -143.129 q^{19} +20.0000 q^{20} +40.8707 q^{22} -200.735 q^{23} -46.2586 q^{24} +25.0000 q^{25} +106.259 q^{26} -118.912 q^{27} +113.082 q^{29} -57.8233 q^{30} -105.470 q^{31} -32.0000 q^{32} -118.164 q^{33} -55.4827 q^{34} +25.7414 q^{36} -1.38796 q^{37} +286.259 q^{38} -307.211 q^{39} -40.0000 q^{40} -226.729 q^{41} +268.558 q^{43} -81.7414 q^{44} +32.1767 q^{45} +401.470 q^{46} +27.7414 q^{47} +92.5173 q^{48} -50.0000 q^{50} +160.410 q^{51} -212.517 q^{52} +74.2586 q^{53} +237.823 q^{54} -102.177 q^{55} -827.621 q^{57} -226.164 q^{58} +665.362 q^{59} +115.647 q^{60} +509.845 q^{61} +210.940 q^{62} +64.0000 q^{64} -265.647 q^{65} +236.328 q^{66} -981.416 q^{67} +110.965 q^{68} -1160.72 q^{69} -144.707 q^{71} -51.4827 q^{72} +735.552 q^{73} +2.77592 q^{74} +144.558 q^{75} -572.517 q^{76} +614.423 q^{78} +146.069 q^{79} +80.0000 q^{80} -861.341 q^{81} +453.457 q^{82} +712.356 q^{83} +138.707 q^{85} -537.116 q^{86} +653.877 q^{87} +163.483 q^{88} -606.457 q^{89} -64.3534 q^{90} -802.940 q^{92} -609.862 q^{93} -55.4827 q^{94} -715.647 q^{95} -185.035 q^{96} +771.552 q^{97} -131.508 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{2} - 2 q^{3} + 8 q^{4} + 10 q^{5} + 4 q^{6} - 16 q^{8} + 40 q^{9}+O(q^{10}) $ 2 * q - 4 * q^2 - 2 * q^3 + 8 * q^4 + 10 * q^5 + 4 * q^6 - 16 * q^8 + 40 * q^9	\( 2 q - 4 q^{2} - 2 q^{3} + 8 q^{4} + 10 q^{5} + 4 q^{6} - 16 q^{8} + 40 q^{9} - 20 q^{10} - 68 q^{11} - 8 q^{12} - 52 q^{13} - 10 q^{15} + 32 q^{16} + 164 q^{17} - 80 q^{18} - 232 q^{19} + 40 q^{20} + 136 q^{22} - 198 q^{23} + 16 q^{24} + 50 q^{25} + 104 q^{26} - 170 q^{27} - 18 q^{29} + 20 q^{30} + 196 q^{31} - 64 q^{32} + 252 q^{33} - 328 q^{34} + 160 q^{36} + 160 q^{37} + 464 q^{38} - 316 q^{39} - 80 q^{40} + 62 q^{41} + 198 q^{43} - 272 q^{44} + 200 q^{45} + 396 q^{46} + 164 q^{47} - 32 q^{48} - 100 q^{50} - 900 q^{51} - 208 q^{52} + 40 q^{53} + 340 q^{54} - 340 q^{55} - 136 q^{57} + 36 q^{58} - 80 q^{59} - 40 q^{60} - 174 q^{61} - 392 q^{62} + 128 q^{64} - 260 q^{65} - 504 q^{66} - 1054 q^{67} + 656 q^{68} - 1182 q^{69} - 832 q^{71} - 320 q^{72} + 820 q^{73} - 320 q^{74} - 50 q^{75} - 928 q^{76} + 632 q^{78} - 576 q^{79} + 160 q^{80} - 1370 q^{81} - 124 q^{82} - 298 q^{83} + 820 q^{85} - 396 q^{86} + 1674 q^{87} + 544 q^{88} - 182 q^{89} - 400 q^{90} - 792 q^{92} - 2956 q^{93} - 328 q^{94} - 1160 q^{95} + 64 q^{96} + 892 q^{97} - 1728 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 - 2 * q^3 + 8 * q^4 + 10 * q^5 + 4 * q^6 - 16 * q^8 + 40 * q^9 - 20 * q^10 - 68 * q^11 - 8 * q^12 - 52 * q^13 - 10 * q^15 + 32 * q^16 + 164 * q^17 - 80 * q^18 - 232 * q^19 + 40 * q^20 + 136 * q^22 - 198 * q^23 + 16 * q^24 + 50 * q^25 + 104 * q^26 - 170 * q^27 - 18 * q^29 + 20 * q^30 + 196 * q^31 - 64 * q^32 + 252 * q^33 - 328 * q^34 + 160 * q^36 + 160 * q^37 + 464 * q^38 - 316 * q^39 - 80 * q^40 + 62 * q^41 + 198 * q^43 - 272 * q^44 + 200 * q^45 + 396 * q^46 + 164 * q^47 - 32 * q^48 - 100 * q^50 - 900 * q^51 - 208 * q^52 + 40 * q^53 + 340 * q^54 - 340 * q^55 - 136 * q^57 + 36 * q^58 - 80 * q^59 - 40 * q^60 - 174 * q^61 - 392 * q^62 + 128 * q^64 - 260 * q^65 - 504 * q^66 - 1054 * q^67 + 656 * q^68 - 1182 * q^69 - 832 * q^71 - 320 * q^72 + 820 * q^73 - 320 * q^74 - 50 * q^75 - 928 * q^76 + 632 * q^78 - 576 * q^79 + 160 * q^80 - 1370 * q^81 - 124 * q^82 - 298 * q^83 + 820 * q^85 - 396 * q^86 + 1674 * q^87 + 544 * q^88 - 182 * q^89 - 400 * q^90 - 792 * q^92 - 2956 * q^93 - 328 * q^94 - 1160 * q^95 + 64 * q^96 + 892 * q^97 - 1728 * 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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	5.78233	1.11281	0.556405	−	0.830911i	$-0.312180\pi$
$3$	5.78233	1.11281	0.556405	+	0.830911i	$0.312180\pi$
$4$	4.00000	0.500000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−11.5647	−0.786875
$7$	0	0
$7$	0	0
$8$	−8.00000	−0.353553
$9$	6.43534	0.238346
$10$	−10.0000	−0.316228
$11$	−20.4353	−0.560135	−0.280068	−	0.959980i	$-0.590357\pi$
$11$	−20.4353	−0.560135	−0.280068	+	0.959980i	$0.590357\pi$
$12$	23.1293	0.556405
$13$	−53.1293	−1.13349	−0.566747	−	0.823892i	$-0.691798\pi$
$13$	−53.1293	−1.13349	−0.566747	+	0.823892i	$0.691798\pi$
$14$	0	0
$15$	28.9116	0.497664
$16$	16.0000	0.250000
$17$	27.7414	0.395780	0.197890	−	0.980224i	$-0.436591\pi$
$17$	27.7414	0.395780	0.197890	+	0.980224i	$0.436591\pi$
$18$	−12.8707	−0.168536
$19$	−143.129	−1.72822	−0.864108	−	0.503306i	$-0.832117\pi$
$19$	−143.129	−1.72822	−0.864108	+	0.503306i	$0.832117\pi$
$20$	20.0000	0.223607
$21$	0	0
$22$	40.8707	0.396075
$23$	−200.735	−1.81983	−0.909916	−	0.414793i	$-0.863854\pi$
$23$	−200.735	−1.81983	−0.909916	+	0.414793i	$0.863854\pi$
$24$	−46.2586	−0.393438
$25$	25.0000	0.200000
$26$	106.259	0.801501
$27$	−118.912	−0.847576
$28$	0	0
$29$	113.082	0.724096	0.362048	−	0.932159i	$-0.382078\pi$
$29$	113.082	0.724096	0.362048	+	0.932159i	$0.382078\pi$
$30$	−57.8233	−0.351901
$31$	−105.470	−0.611063	−0.305532	−	0.952182i	$-0.598834\pi$
$31$	−105.470	−0.611063	−0.305532	+	0.952182i	$0.598834\pi$
$32$	−32.0000	−0.176777
$33$	−118.164	−0.623324
$34$	−55.4827	−0.279859
$35$	0	0
$36$	25.7414	0.119173
$37$	−1.38796	−0.00616701	−0.00308350	−	0.999995i	$-0.500982\pi$
$37$	−1.38796	−0.00616701	−0.00308350	+	0.999995i	$0.500982\pi$
$38$	286.259	1.22203
$39$	−307.211	−1.26136
$40$	−40.0000	−0.158114
$41$	−226.729	−0.863635	−0.431818	−	0.901961i	$-0.642128\pi$
$41$	−226.729	−0.863635	−0.431818	+	0.901961i	$0.642128\pi$
$42$	0	0
$43$	268.558	0.952436	0.476218	−	0.879327i	$-0.342007\pi$
$43$	268.558	0.952436	0.476218	+	0.879327i	$0.342007\pi$
$44$	−81.7414	−0.280068
$45$	32.1767	0.106592
$46$	401.470	1.28682
$47$	27.7414	0.0860956	0.0430478	−	0.999073i	$-0.486293\pi$
$47$	27.7414	0.0860956	0.0430478	+	0.999073i	$0.486293\pi$
$48$	92.5173	0.278202
$49$	0	0
$50$	−50.0000	−0.141421
$51$	160.410	0.440428
$52$	−212.517	−0.566747
$53$	74.2586	0.192457	0.0962284	−	0.995359i	$-0.469322\pi$
$53$	74.2586	0.192457	0.0962284	+	0.995359i	$0.469322\pi$
$54$	237.823	0.599327
$55$	−102.177	−0.250500
$56$	0	0
$57$	−827.621	−1.92318
$58$	−226.164	−0.512013
$59$	665.362	1.46818	0.734091	−	0.679051i	$-0.237608\pi$
$59$	665.362	1.46818	0.734091	+	0.679051i	$0.237608\pi$
$60$	115.647	0.248832
$61$	509.845	1.07015	0.535074	−	0.844806i	$-0.320284\pi$
$61$	509.845	1.07015	0.535074	+	0.844806i	$0.320284\pi$
$62$	210.940	0.432087
$63$	0	0
$64$	64.0000	0.125000
$65$	−265.647	−0.506914
$66$	236.328	0.440757
$67$	−981.416	−1.78954	−0.894769	−	0.446529i	$-0.852660\pi$
$67$	−981.416	−1.78954	−0.894769	+	0.446529i	$0.852660\pi$
$68$	110.965	0.197890
$69$	−1160.72	−2.02513
$70$	0	0
$71$	−144.707	−0.241881	−0.120940	−	0.992660i	$-0.538591\pi$
$71$	−144.707	−0.241881	−0.120940	+	0.992660i	$0.538591\pi$
$72$	−51.4827	−0.0842680
$73$	735.552	1.17931	0.589656	−	0.807654i	$-0.299263\pi$
$73$	735.552	1.17931	0.589656	+	0.807654i	$0.299263\pi$
$74$	2.77592	0.00436073
$75$	144.558	0.222562
$76$	−572.517	−0.864108
$77$	0	0
$78$	614.423	0.891919
$79$	146.069	0.208026	0.104013	−	0.994576i	$-0.466832\pi$
$79$	146.069	0.208026	0.104013	+	0.994576i	$0.466832\pi$
$80$	80.0000	0.111803
$81$	−861.341	−1.18154
$82$	453.457	0.610682
$83$	712.356	0.942063	0.471031	−	0.882116i	$-0.343882\pi$
$83$	712.356	0.942063	0.471031	+	0.882116i	$0.343882\pi$
$84$	0	0
$85$	138.707	0.176998
$86$	−537.116	−0.673474
$87$	653.877	0.805781
$88$	163.483	0.198038
$89$	−606.457	−0.722296	−0.361148	−	0.932509i	$-0.617615\pi$
$89$	−606.457	−0.722296	−0.361148	+	0.932509i	$0.617615\pi$
$90$	−64.3534	−0.0753716
$91$	0	0
$92$	−802.940	−0.909916
$93$	−609.862	−0.679997
$94$	−55.4827	−0.0608788
$95$	−715.647	−0.772882
$96$	−185.035	−0.196719
$97$	771.552	0.807621	0.403810	−	0.914843i	$-0.367686\pi$
$97$	771.552	0.807621	0.403810	+	0.914843i	$0.367686\pi$
$98$	0	0
$99$	−131.508	−0.133506
$100$	100.000	0.100000
$101$	−1465.41	−1.44370	−0.721850	−	0.692049i	$-0.756708\pi$
$101$	−1465.41	−1.44370	−0.721850	+	0.692049i	$0.756708\pi$
$102$	−320.819	−0.311430
$103$	436.312	0.417390	0.208695	−	0.977981i	$-0.433078\pi$
$103$	436.312	0.417390	0.208695	+	0.977981i	$0.433078\pi$
$104$	425.035	0.400751
$105$	0	0
$106$	−148.517	−0.136087
$107$	−2184.33	−1.97353	−0.986763	−	0.162172i	$-0.948150\pi$
$107$	−2184.33	−1.97353	−0.986763	+	0.162172i	$0.948150\pi$
$108$	−475.647	−0.423788
$109$	−65.0256	−0.0571406	−0.0285703	−	0.999592i	$-0.509095\pi$
$109$	−65.0256	−0.0571406	−0.0285703	+	0.999592i	$0.509095\pi$
$110$	204.353	0.177130
$111$	−8.02564	−0.00686270
$112$	0	0
$113$	−613.767	−0.510959	−0.255479	−	0.966815i	$-0.582233\pi$
$113$	−613.767	−0.510959	−0.255479	+	0.966815i	$0.582233\pi$
$114$	1655.24	1.35989
$115$	−1003.67	−0.813854
$116$	452.328	0.362048
$117$	−341.905	−0.270164
$118$	−1330.72	−1.03816
$119$	0	0
$120$	−231.293	−0.175951
$121$	−913.397	−0.686249
$122$	−1019.69	−0.756708
$123$	−1311.02	−0.961062
$124$	−421.880	−0.305532
$125$	125.000	0.0894427
$126$	0	0
$127$	−2490.47	−1.74010	−0.870052	−	0.492961i	$-0.835915\pi$
$127$	−2490.47	−1.74010	−0.870052	+	0.492961i	$0.835915\pi$
$128$	−128.000	−0.0883883
$129$	1552.89	1.05988
$130$	531.293	0.358442
$131$	−2389.20	−1.59348	−0.796738	−	0.604325i	$-0.793443\pi$
$131$	−2389.20	−1.59348	−0.796738	+	0.604325i	$0.793443\pi$
$132$	−472.656	−0.311662
$133$	0	0
$134$	1962.83	1.26539
$135$	−594.558	−0.379048
$136$	−221.931	−0.139930
$137$	1738.86	1.08439	0.542194	−	0.840254i	$-0.317594\pi$
$137$	1738.86	1.08439	0.542194	+	0.840254i	$0.317594\pi$
$138$	2321.43	1.43198
$139$	697.332	0.425517	0.212759	−	0.977105i	$-0.431755\pi$
$139$	697.332	0.425517	0.212759	+	0.977105i	$0.431755\pi$
$140$	0	0
$141$	160.410	0.0958080
$142$	289.414	0.171036
$143$	1085.72	0.634910
$144$	102.965	0.0595865
$145$	565.410	0.323826
$146$	−1471.10	−0.833900
$147$	0	0
$148$	−5.55184	−0.00308350
$149$	−1639.86	−0.901630	−0.450815	−	0.892618i	$-0.648867\pi$
$149$	−1639.86	−0.901630	−0.450815	+	0.892618i	$0.648867\pi$
$150$	−289.116	−0.157375
$151$	2829.31	1.52481	0.762403	−	0.647103i	$-0.224020\pi$
$151$	2829.31	1.52481	0.762403	+	0.647103i	$0.224020\pi$
$152$	1145.03	0.611017
$153$	178.525	0.0943327
$154$	0	0
$155$	−527.349	−0.273276
$156$	−1228.85	−0.630682
$157$	−2591.12	−1.31716	−0.658580	−	0.752511i	$-0.728842\pi$
$157$	−2591.12	−1.31716	−0.658580	+	0.752511i	$0.728842\pi$
$158$	−292.138	−0.147097
$159$	429.388	0.214168
$160$	−160.000	−0.0790569
$161$	0	0
$162$	1722.68	0.835473
$163$	3472.54	1.66865	0.834325	−	0.551273i	$-0.185858\pi$
$163$	3472.54	1.66865	0.834325	+	0.551273i	$0.185858\pi$
$164$	−906.914	−0.431818
$165$	−590.819	−0.278759
$166$	−1424.71	−0.666139
$167$	798.576	0.370034	0.185017	−	0.982735i	$-0.440766\pi$
$167$	798.576	0.370034	0.185017	+	0.982735i	$0.440766\pi$
$168$	0	0
$169$	625.725	0.284809
$170$	−277.414	−0.125157
$171$	−921.086	−0.411913
$172$	1074.23	0.476218
$173$	2198.89	0.966349	0.483175	−	0.875524i	$-0.339484\pi$
$173$	2198.89	0.966349	0.483175	+	0.875524i	$0.339484\pi$
$174$	−1307.75	−0.569773
$175$	0	0
$176$	−326.965	−0.140034
$177$	3847.34	1.63381
$178$	1212.91	0.510740
$179$	−2336.57	−0.975663	−0.487832	−	0.872938i	$-0.662212\pi$
$179$	−2336.57	−0.975663	−0.487832	+	0.872938i	$0.662212\pi$
$180$	128.707	0.0532958
$181$	2243.52	0.921324	0.460662	−	0.887576i	$-0.347612\pi$
$181$	2243.52	0.921324	0.460662	+	0.887576i	$0.347612\pi$
$182$	0	0
$183$	2948.09	1.19087
$184$	1605.88	0.643408
$185$	−6.93980	−0.00275797
$186$	1219.72	0.480830
$187$	−566.904	−0.221691
$188$	110.965	0.0430478
$189$	0	0
$190$	1431.29	0.546510
$191$	−415.099	−0.157254	−0.0786269	−	0.996904i	$-0.525054\pi$
$191$	−415.099	−0.157254	−0.0786269	+	0.996904i	$0.525054\pi$
$192$	370.069	0.139101
$193$	1820.21	0.678867	0.339434	−	0.940630i	$-0.389765\pi$
$193$	1820.21	0.678867	0.339434	+	0.940630i	$0.389765\pi$
$194$	−1543.10	−0.571074
$195$	−1536.06	−0.564099
$196$	0	0
$197$	343.337	0.124171	0.0620856	−	0.998071i	$-0.480225\pi$
$197$	343.337	0.124171	0.0620856	+	0.998071i	$0.480225\pi$
$198$	263.017	0.0944030
$199$	2432.41	0.866479	0.433239	−	0.901279i	$-0.357370\pi$
$199$	2432.41	0.866479	0.433239	+	0.901279i	$0.357370\pi$
$200$	−200.000	−0.0707107
$201$	−5674.87	−1.99142
$202$	2930.82	1.02085
$203$	0	0
$204$	641.639	0.220214
$205$	−1133.64	−0.386229
$206$	−872.625	−0.295139
$207$	−1291.80	−0.433749
$208$	−850.069	−0.283374
$209$	2924.90	0.968035
$210$	0	0
$211$	310.965	0.101459	0.0507293	−	0.998712i	$-0.483845\pi$
$211$	310.965	0.101459	0.0507293	+	0.998712i	$0.483845\pi$
$212$	297.035	0.0962284
$213$	−836.742	−0.269167
$214$	4368.66	1.39549
$215$	1342.79	0.425942
$216$	951.293	0.299663
$217$	0	0
$218$	130.051	0.0404045
$219$	4253.20	1.31235
$220$	−408.707	−0.125250
$221$	−1473.88	−0.448615
$222$	16.0513	0.00485266
$223$	2999.59	0.900750	0.450375	−	0.892840i	$-0.351290\pi$
$223$	2999.59	0.900750	0.450375	+	0.892840i	$0.351290\pi$
$224$	0	0
$225$	160.884	0.0476692
$226$	1227.53	0.361302
$227$	6145.54	1.79689	0.898445	−	0.439086i	$-0.144698\pi$
$227$	6145.54	1.79689	0.898445	+	0.439086i	$0.144698\pi$
$228$	−3310.48	−0.961588
$229$	−1422.05	−0.410357	−0.205179	−	0.978725i	$-0.565778\pi$
$229$	−1422.05	−0.410357	−0.205179	+	0.978725i	$0.565778\pi$
$230$	2007.35	0.575481
$231$	0	0
$232$	−904.656	−0.256007
$233$	3515.64	0.988486	0.494243	−	0.869324i	$-0.335445\pi$
$233$	3515.64	0.988486	0.494243	+	0.869324i	$0.335445\pi$
$234$	683.810	0.191035
$235$	138.707	0.0385031
$236$	2661.45	0.734091
$237$	844.620	0.231493
$238$	0	0
$239$	−4332.94	−1.17270	−0.586348	−	0.810059i	$-0.699435\pi$
$239$	−4332.94	−1.17270	−0.586348	+	0.810059i	$0.699435\pi$
$240$	462.586	0.124416
$241$	−6600.26	−1.76415	−0.882075	−	0.471109i	$-0.843854\pi$
$241$	−6600.26	−1.76415	−0.882075	+	0.471109i	$0.843854\pi$
$242$	1826.79	0.485251
$243$	−1769.94	−0.467250
$244$	2039.38	0.535074
$245$	0	0
$246$	2622.04	0.679573
$247$	7604.36	1.95892
$248$	843.759	0.216043
$249$	4119.08	1.04834
$250$	−250.000	−0.0632456
$251$	−3659.19	−0.920182	−0.460091	−	0.887872i	$-0.652183\pi$
$251$	−3659.19	−0.920182	−0.460091	+	0.887872i	$0.652183\pi$
$252$	0	0
$253$	4102.09	1.01935
$254$	4980.93	1.23044
$255$	802.048	0.196966
$256$	256.000	0.0625000
$257$	−3843.24	−0.932820	−0.466410	−	0.884569i	$-0.654453\pi$
$257$	−3843.24	−0.932820	−0.466410	+	0.884569i	$0.654453\pi$
$258$	−3105.78	−0.749449
$259$	0	0
$260$	−1062.59	−0.253457
$261$	727.721	0.172585
$262$	4778.40	1.12676
$263$	−462.377	−0.108408	−0.0542041	−	0.998530i	$-0.517262\pi$
$263$	−462.377	−0.108408	−0.0542041	+	0.998530i	$0.517262\pi$
$264$	945.311	0.220378
$265$	371.293	0.0860693
$266$	0	0
$267$	−3506.73	−0.803778
$268$	−3925.66	−0.894769
$269$	−678.880	−0.153874	−0.0769368	−	0.997036i	$-0.524514\pi$
$269$	−678.880	−0.153874	−0.0769368	+	0.997036i	$0.524514\pi$
$270$	1189.12	0.268027
$271$	887.810	0.199006	0.0995030	−	0.995037i	$-0.468275\pi$
$271$	887.810	0.199006	0.0995030	+	0.995037i	$0.468275\pi$
$272$	443.862	0.0989451
$273$	0	0
$274$	−3477.73	−0.766778
$275$	−510.884	−0.112027
$276$	−4642.86	−1.01256
$277$	−5414.86	−1.17454	−0.587269	−	0.809392i	$-0.699797\pi$
$277$	−5414.86	−1.17454	−0.587269	+	0.809392i	$0.699797\pi$
$278$	−1394.66	−0.300886
$279$	−678.735	−0.145644
$280$	0	0
$281$	−1424.10	−0.302331	−0.151165	−	0.988508i	$-0.548303\pi$
$281$	−1424.10	−0.302331	−0.151165	+	0.988508i	$0.548303\pi$
$282$	−320.819	−0.0677465
$283$	4164.94	0.874841	0.437420	−	0.899257i	$-0.355892\pi$
$283$	4164.94	0.874841	0.437420	+	0.899257i	$0.355892\pi$
$284$	−578.827	−0.120940
$285$	−4138.10	−0.860071
$286$	−2171.43	−0.448949
$287$	0	0
$288$	−205.931	−0.0421340
$289$	−4143.42	−0.843358
$290$	−1130.82	−0.228979
$291$	4461.37	0.898728
$292$	2942.21	0.589656
$293$	6486.84	1.29340	0.646698	−	0.762746i	$-0.276149\pi$
$293$	6486.84	1.29340	0.646698	+	0.762746i	$0.276149\pi$
$294$	0	0
$295$	3326.81	0.656591
$296$	11.1037	0.00218037
$297$	2430.00	0.474757
$298$	3279.73	0.637548
$299$	10664.9	2.06277
$300$	578.233	0.111281
$301$	0	0
$302$	−5658.61	−1.07820
$303$	−8473.48	−1.60656
$304$	−2290.07	−0.432054
$305$	2549.23	0.478584
$306$	−357.050	−0.0667033
$307$	4307.13	0.800719	0.400359	−	0.916358i	$-0.368885\pi$
$307$	4307.13	0.800719	0.400359	+	0.916358i	$0.368885\pi$
$308$	0	0
$309$	2522.90	0.464475
$310$	1054.70	0.193235
$311$	−2646.85	−0.482602	−0.241301	−	0.970450i	$-0.577574\pi$
$311$	−2646.85	−0.482602	−0.241301	+	0.970450i	$0.577574\pi$
$312$	2457.69	0.445959
$313$	634.766	0.114630	0.0573148	−	0.998356i	$-0.481746\pi$
$313$	634.766	0.114630	0.0573148	+	0.998356i	$0.481746\pi$
$314$	5182.24	0.931372
$315$	0	0
$316$	584.276	0.104013
$317$	7219.04	1.27906	0.639530	−	0.768766i	$-0.279129\pi$
$317$	7219.04	1.27906	0.639530	+	0.768766i	$0.279129\pi$
$318$	−858.776	−0.151440
$319$	−2310.87	−0.405592
$320$	320.000	0.0559017
$321$	−12630.5	−2.19616
$322$	0	0
$323$	−3970.60	−0.683994
$324$	−3445.36	−0.590769
$325$	−1328.23	−0.226699
$326$	−6945.07	−1.17991
$327$	−376.000	−0.0635866
$328$	1813.83	0.305341
$329$	0	0
$330$	1181.64	0.197112
$331$	−8398.10	−1.39457	−0.697283	−	0.716796i	$-0.745608\pi$
$331$	−8398.10	−1.39457	−0.697283	+	0.716796i	$0.745608\pi$
$332$	2849.42	0.471031
$333$	−8.93199	−0.00146988
$334$	−1597.15	−0.261654
$335$	−4907.08	−0.800306
$336$	0	0
$337$	11964.8	1.93401	0.967007	−	0.254748i	$-0.0819926\pi$
$337$	11964.8	1.93401	0.967007	+	0.254748i	$0.0819926\pi$
$338$	−1251.45	−0.201390
$339$	−3549.00	−0.568600
$340$	554.827	0.0884992
$341$	2155.31	0.342278
$342$	1842.17	0.291267
$343$	0	0
$344$	−2148.47	−0.336737
$345$	−5803.58	−0.905664
$346$	−4397.78	−0.683312
$347$	−9014.24	−1.39455	−0.697276	−	0.716803i	$-0.745605\pi$
$347$	−9014.24	−1.39455	−0.697276	+	0.716803i	$0.745605\pi$
$348$	2615.51	0.402891
$349$	4439.73	0.680955	0.340477	−	0.940253i	$-0.389411\pi$
$349$	4439.73	0.680955	0.340477	+	0.940253i	$0.389411\pi$
$350$	0	0
$351$	6317.70	0.960723
$352$	653.931	0.0990188
$353$	−8903.85	−1.34250	−0.671252	−	0.741229i	$-0.734243\pi$
$353$	−8903.85	−1.34250	−0.671252	+	0.741229i	$0.734243\pi$
$354$	−7694.69	−1.15528
$355$	−723.534	−0.108172
$356$	−2425.83	−0.361148
$357$	0	0
$358$	4673.15	0.689898
$359$	−10567.2	−1.55352	−0.776760	−	0.629797i	$-0.783138\pi$
$359$	−10567.2	−1.55352	−0.776760	+	0.629797i	$0.783138\pi$
$360$	−257.414	−0.0376858
$361$	13627.0	1.98673
$362$	−4487.04	−0.651475
$363$	−5281.56	−0.763664
$364$	0	0
$365$	3677.76	0.527405
$366$	−5896.18	−0.842072
$367$	−3593.28	−0.511084	−0.255542	−	0.966798i	$-0.582254\pi$
$367$	−3593.28	−0.511084	−0.255542	+	0.966798i	$0.582254\pi$
$368$	−3211.76	−0.454958
$369$	−1459.08	−0.205844
$370$	13.8796	0.00195018
$371$	0	0
$372$	−2439.45	−0.339998
$373$	8762.21	1.21633	0.608163	−	0.793812i	$-0.291907\pi$
$373$	8762.21	1.21633	0.608163	+	0.793812i	$0.291907\pi$
$374$	1133.81	0.156759
$375$	722.791	0.0995327
$376$	−221.931	−0.0304394
$377$	−6007.97	−0.820759
$378$	0	0
$379$	−13221.6	−1.79195	−0.895974	−	0.444106i	$-0.853521\pi$
$379$	−13221.6	−1.79195	−0.895974	+	0.444106i	$0.853521\pi$
$380$	−2862.59	−0.386441
$381$	−14400.7	−1.93640
$382$	830.197	0.111195
$383$	−7109.63	−0.948525	−0.474263	−	0.880383i	$-0.657285\pi$
$383$	−7109.63	−0.948525	−0.474263	+	0.880383i	$0.657285\pi$
$384$	−740.138	−0.0983594
$385$	0	0
$386$	−3640.41	−0.480032
$387$	1728.26	0.227009
$388$	3086.21	0.403810
$389$	−5282.31	−0.688493	−0.344247	−	0.938879i	$-0.611866\pi$
$389$	−5282.31	−0.688493	−0.344247	+	0.938879i	$0.611866\pi$
$390$	3072.11	0.398878
$391$	−5568.66	−0.720254
$392$	0	0
$393$	−13815.1	−1.77323
$394$	−686.673	−0.0878023
$395$	730.346	0.0930321
$396$	−526.033	−0.0667530
$397$	11937.1	1.50908	0.754538	−	0.656256i	$-0.227861\pi$
$397$	11937.1	1.50908	0.754538	+	0.656256i	$0.227861\pi$
$398$	−4864.83	−0.612693
$399$	0	0
$400$	400.000	0.0500000
$401$	−4144.05	−0.516070	−0.258035	−	0.966136i	$-0.583075\pi$
$401$	−4144.05	−0.516070	−0.258035	+	0.966136i	$0.583075\pi$
$402$	11349.7	1.40814
$403$	5603.54	0.692636
$404$	−5861.64	−0.721850
$405$	−4306.70	−0.528399
$406$	0	0
$407$	28.3634	0.00345436
$408$	−1283.28	−0.155715
$409$	8288.13	1.00201	0.501004	−	0.865445i	$-0.332964\pi$
$409$	8288.13	1.00201	0.501004	+	0.865445i	$0.332964\pi$
$410$	2267.29	0.273105
$411$	10054.7	1.20672
$412$	1745.25	0.208695
$413$	0	0
$414$	2583.60	0.306707
$415$	3561.78	0.421303
$416$	1700.14	0.200375
$417$	4032.20	0.473520
$418$	−5849.79	−0.684504
$419$	−404.482	−0.0471604	−0.0235802	−	0.999722i	$-0.507507\pi$
$419$	−404.482	−0.0471604	−0.0235802	+	0.999722i	$0.507507\pi$
$420$	0	0
$421$	−1345.62	−0.155776	−0.0778879	−	0.996962i	$-0.524818\pi$
$421$	−1345.62	−0.155776	−0.0778879	+	0.996962i	$0.524818\pi$
$422$	−621.931	−0.0717420
$423$	178.525	0.0205205
$424$	−594.069	−0.0680437
$425$	693.534	0.0791561
$426$	1673.48	0.190330
$427$	0	0
$428$	−8737.32	−0.986763
$429$	6277.97	0.706534
$430$	−2685.58	−0.301187
$431$	−2877.79	−0.321620	−0.160810	−	0.986985i	$-0.551411\pi$
$431$	−2877.79	−0.321620	−0.160810	+	0.986985i	$0.551411\pi$
$432$	−1902.59	−0.211894
$433$	702.525	0.0779704	0.0389852	−	0.999240i	$-0.487587\pi$
$433$	702.525	0.0779704	0.0389852	+	0.999240i	$0.487587\pi$
$434$	0	0
$435$	3269.39	0.360356
$436$	−260.103	−0.0285703
$437$	28731.1	3.14506
$438$	−8506.41	−0.927972
$439$	11009.5	1.19694	0.598468	−	0.801146i	$-0.295776\pi$
$439$	11009.5	1.19694	0.598468	+	0.801146i	$0.295776\pi$
$440$	817.414	0.0885651
$441$	0	0
$442$	2947.76	0.317219
$443$	−16642.9	−1.78494	−0.892471	−	0.451105i	$-0.851030\pi$
$443$	−16642.9	−1.78494	−0.892471	+	0.451105i	$0.851030\pi$
$444$	−32.1026	−0.00343135
$445$	−3032.29	−0.323020
$446$	−5999.18	−0.636926
$447$	−9482.23	−1.00334
$448$	0	0
$449$	−8698.08	−0.914226	−0.457113	−	0.889409i	$-0.651117\pi$
$449$	−8698.08	−0.914226	−0.457113	+	0.889409i	$0.651117\pi$
$450$	−321.767	−0.0337072
$451$	4633.27	0.483753
$452$	−2455.07	−0.255479
$453$	16360.0	1.69682
$454$	−12291.1	−1.27059
$455$	0	0
$456$	6620.97	0.679946
$457$	6488.46	0.664152	0.332076	−	0.943253i	$-0.392251\pi$
$457$	6488.46	0.664152	0.332076	+	0.943253i	$0.392251\pi$
$458$	2844.10	0.290166
$459$	−3298.77	−0.335454
$460$	−4014.70	−0.406927
$461$	8797.74	0.888832	0.444416	−	0.895820i	$-0.353411\pi$
$461$	8797.74	0.888832	0.444416	+	0.895820i	$0.353411\pi$
$462$	0	0
$463$	−538.084	−0.0540106	−0.0270053	−	0.999635i	$-0.508597\pi$
$463$	−538.084	−0.0540106	−0.0270053	+	0.999635i	$0.508597\pi$
$464$	1809.31	0.181024
$465$	−3049.31	−0.304104
$466$	−7031.28	−0.698965
$467$	−9566.10	−0.947893	−0.473947	−	0.880554i	$-0.657171\pi$
$467$	−9566.10	−0.947893	−0.473947	+	0.880554i	$0.657171\pi$
$468$	−1367.62	−0.135082
$469$	0	0
$470$	−277.414	−0.0272258
$471$	−14982.7	−1.46575
$472$	−5322.90	−0.519081
$473$	−5488.08	−0.533493
$474$	−1689.24	−0.163691
$475$	−3578.23	−0.345643
$476$	0	0
$477$	477.880	0.0458713
$478$	8665.87	0.829221
$479$	4111.74	0.392214	0.196107	−	0.980583i	$-0.437170\pi$
$479$	4111.74	0.392214	0.196107	+	0.980583i	$0.437170\pi$
$480$	−925.173	−0.0879753
$481$	73.7414	0.00699026
$482$	13200.5	1.24744
$483$	0	0
$484$	−3653.59	−0.343124
$485$	3857.76	0.361179
$486$	3539.88	0.330396
$487$	−3571.73	−0.332342	−0.166171	−	0.986097i	$-0.553140\pi$
$487$	−3571.73	−0.332342	−0.166171	+	0.986097i	$0.553140\pi$
$488$	−4078.76	−0.378354
$489$	20079.3	1.85689
$490$	0	0
$491$	21626.1	1.98772	0.993861	−	0.110634i	$-0.0352881\pi$
$491$	21626.1	1.98772	0.993861	+	0.110634i	$0.0352881\pi$
$492$	−5244.08	−0.480531
$493$	3137.05	0.286583
$494$	−15208.7	−1.38517
$495$	−657.542	−0.0597057
$496$	−1687.52	−0.152766
$497$	0	0
$498$	−8238.15	−0.741286
$499$	170.407	0.0152875	0.00764377	−	0.999971i	$-0.497567\pi$
$499$	170.407	0.0152875	0.00764377	+	0.999971i	$0.497567\pi$
$500$	500.000	0.0447214
$501$	4617.63	0.411777
$502$	7318.37	0.650667
$503$	−57.5343	−0.00510005	−0.00255003	−	0.999997i	$-0.500812\pi$
$503$	−57.5343	−0.00510005	−0.00255003	+	0.999997i	$0.500812\pi$
$504$	0	0
$505$	−7327.05	−0.645642
$506$	−8204.17	−0.720791
$507$	3618.15	0.316938
$508$	−9961.86	−0.870052
$509$	−2127.18	−0.185237	−0.0926187	−	0.995702i	$-0.529524\pi$
$509$	−2127.18	−0.185237	−0.0926187	+	0.995702i	$0.529524\pi$
$510$	−1604.10	−0.139276
$511$	0	0
$512$	−512.000	−0.0441942
$513$	17019.7	1.46480
$514$	7686.48	0.659604
$515$	2181.56	0.186662
$516$	6211.57	0.529940
$517$	−566.904	−0.0482252
$518$	0	0
$519$	12714.7	1.07536
$520$	2125.17	0.179221
$521$	6823.57	0.573793	0.286896	−	0.957962i	$-0.407376\pi$
$521$	6823.57	0.573793	0.286896	+	0.957962i	$0.407376\pi$
$522$	−1455.44	−0.122036
$523$	10746.7	0.898513	0.449257	−	0.893403i	$-0.351689\pi$
$523$	10746.7	0.898513	0.449257	+	0.893403i	$0.351689\pi$
$524$	−9556.79	−0.796738
$525$	0	0
$526$	924.753	0.0766562
$527$	−2925.88	−0.241847
$528$	−1890.62	−0.155831
$529$	28127.5	2.31179
$530$	−742.586	−0.0608602
$531$	4281.83	0.349935
$532$	0	0
$533$	12045.9	0.978925
$534$	7013.47	0.568357
$535$	−10921.7	−0.882587
$536$	7851.33	0.632697
$537$	−13510.8	−1.08573
$538$	1357.76	0.108805
$539$	0	0
$540$	−2378.23	−0.189524
$541$	−14896.8	−1.18385	−0.591926	−	0.805992i	$-0.701632\pi$
$541$	−14896.8	−1.18385	−0.591926	+	0.805992i	$0.701632\pi$
$542$	−1775.62	−0.140719
$543$	12972.8	1.02526
$544$	−887.724	−0.0699648
$545$	−325.128	−0.0255541
$546$	0	0
$547$	7150.91	0.558960	0.279480	−	0.960152i	$-0.409838\pi$
$547$	7150.91	0.558960	0.279480	+	0.960152i	$0.409838\pi$
$548$	6955.45	0.542194
$549$	3281.03	0.255065
$550$	1021.77	0.0792151
$551$	−16185.3	−1.25140
$552$	9285.73	0.715990
$553$	0	0
$554$	10829.7	0.830524
$555$	−40.1282	−0.00306909
$556$	2789.33	0.212759
$557$	−12197.3	−0.927856	−0.463928	−	0.885873i	$-0.653560\pi$
$557$	−12197.3	−0.927856	−0.463928	+	0.885873i	$0.653560\pi$
$558$	1357.47	0.102986
$559$	−14268.3	−1.07958
$560$	0	0
$561$	−3278.03	−0.246699
$562$	2848.21	0.213780
$563$	−6040.23	−0.452159	−0.226079	−	0.974109i	$-0.572591\pi$
$563$	−6040.23	−0.452159	−0.226079	+	0.974109i	$0.572591\pi$
$564$	641.639	0.0479040
$565$	−3068.84	−0.228508
$566$	−8329.88	−0.618606
$567$	0	0
$568$	1157.65	0.0855178
$569$	5156.95	0.379948	0.189974	−	0.981789i	$-0.439160\pi$
$569$	5156.95	0.379948	0.189974	+	0.981789i	$0.439160\pi$
$570$	8276.21	0.608162
$571$	−13464.2	−0.986795	−0.493398	−	0.869804i	$-0.664245\pi$
$571$	−13464.2	−0.986795	−0.493398	+	0.869804i	$0.664245\pi$
$572$	4342.86	0.317455
$573$	−2400.24	−0.174994
$574$	0	0
$575$	−5018.37	−0.363966
$576$	411.862	0.0297932
$577$	−5180.09	−0.373744	−0.186872	−	0.982384i	$-0.559835\pi$
$577$	−5180.09	−0.373744	−0.186872	+	0.982384i	$0.559835\pi$
$578$	8286.83	0.596344
$579$	10525.0	0.755450
$580$	2261.64	0.161913
$581$	0	0
$582$	−8922.73	−0.635497
$583$	−1517.50	−0.107802
$584$	−5884.41	−0.416950
$585$	−1709.53	−0.120821
$586$	−12973.7	−0.914569
$587$	−1803.06	−0.126781	−0.0633905	−	0.997989i	$-0.520191\pi$
$587$	−1803.06	−0.126781	−0.0633905	+	0.997989i	$0.520191\pi$
$588$	0	0
$589$	15095.8	1.05605
$590$	−6653.62	−0.464280
$591$	1985.29	0.138179
$592$	−22.2074	−0.00154175
$593$	−17231.6	−1.19328	−0.596642	−	0.802507i	$-0.703499\pi$
$593$	−17231.6	−1.19328	−0.596642	+	0.802507i	$0.703499\pi$
$594$	−4860.00	−0.335704
$595$	0	0
$596$	−6559.45	−0.450815
$597$	14065.0	0.964226
$598$	−21329.8	−1.45860
$599$	−2931.67	−0.199975	−0.0999874	−	0.994989i	$-0.531880\pi$
$599$	−2931.67	−0.199975	−0.0999874	+	0.994989i	$0.531880\pi$
$600$	−1156.47	−0.0786875
$601$	−5877.40	−0.398909	−0.199454	−	0.979907i	$-0.563917\pi$
$601$	−5877.40	−0.398909	−0.199454	+	0.979907i	$0.563917\pi$
$602$	0	0
$603$	−6315.75	−0.426529
$604$	11317.2	0.762403
$605$	−4566.98	−0.306900
$606$	16947.0	1.13601
$607$	22425.3	1.49953	0.749765	−	0.661705i	$-0.230167\pi$
$607$	22425.3	1.49953	0.749765	+	0.661705i	$0.230167\pi$
$608$	4580.14	0.305508
$609$	0	0
$610$	−5098.45	−0.338410
$611$	−1473.88	−0.0975888
$612$	714.100	0.0471663
$613$	26204.0	1.72654	0.863272	−	0.504739i	$-0.168411\pi$
$613$	26204.0	1.72654	0.863272	+	0.504739i	$0.168411\pi$
$614$	−8614.25	−0.566194
$615$	−6555.10	−0.429800
$616$	0	0
$617$	−9424.07	−0.614909	−0.307454	−	0.951563i	$-0.599477\pi$
$617$	−9424.07	−0.614909	−0.307454	+	0.951563i	$0.599477\pi$
$618$	−5045.80	−0.328434
$619$	−10551.8	−0.685157	−0.342578	−	0.939489i	$-0.611300\pi$
$619$	−10551.8	−0.685157	−0.342578	+	0.939489i	$0.611300\pi$
$620$	−2109.40	−0.136638
$621$	23869.7	1.54245
$622$	5293.71	0.341251
$623$	0	0
$624$	−4915.38	−0.315341
$625$	625.000	0.0400000
$626$	−1269.53	−0.0810554
$627$	16912.7	1.07724
$628$	−10364.5	−0.658580
$629$	−38.5039	−0.00244078
$630$	0	0
$631$	4238.56	0.267408	0.133704	−	0.991021i	$-0.457313\pi$
$631$	4238.56	0.267408	0.133704	+	0.991021i	$0.457313\pi$
$632$	−1168.55	−0.0735483
$633$	1798.10	0.112904
$634$	−14438.1	−0.904432
$635$	−12452.3	−0.778198
$636$	1717.55	0.107084
$637$	0	0
$638$	4621.74	0.286797
$639$	−931.237	−0.0576513
$640$	−640.000	−0.0395285
$641$	−18319.7	−1.12883	−0.564417	−	0.825490i	$-0.690899\pi$
$641$	−18319.7	−1.12883	−0.564417	+	0.825490i	$0.690899\pi$
$642$	25261.0	1.55292
$643$	−3583.89	−0.219806	−0.109903	−	0.993942i	$-0.535054\pi$
$643$	−3583.89	−0.219806	−0.109903	+	0.993942i	$0.535054\pi$
$644$	0	0
$645$	7764.46	0.473993
$646$	7941.20	0.483657
$647$	−7974.68	−0.484570	−0.242285	−	0.970205i	$-0.577897\pi$
$647$	−7974.68	−0.484570	−0.242285	+	0.970205i	$0.577897\pi$
$648$	6890.72	0.417736
$649$	−13596.9	−0.822381
$650$	2656.47	0.160300
$651$	0	0
$652$	13890.1	0.834325
$653$	20010.0	1.19916	0.599579	−	0.800315i	$-0.295335\pi$
$653$	20010.0	1.19916	0.599579	+	0.800315i	$0.295335\pi$
$654$	751.999	0.0449625
$655$	−11946.0	−0.712624
$656$	−3627.66	−0.215909
$657$	4733.53	0.281084
$658$	0	0
$659$	−12398.6	−0.732897	−0.366448	−	0.930438i	$-0.619426\pi$
$659$	−12398.6	−0.732897	−0.366448	+	0.930438i	$0.619426\pi$
$660$	−2363.28	−0.139379
$661$	−25974.6	−1.52844	−0.764218	−	0.644958i	$-0.776875\pi$
$661$	−25974.6	−1.52844	−0.764218	+	0.644958i	$0.776875\pi$
$662$	16796.2	0.986107
$663$	−8522.46	−0.499223
$664$	−5698.85	−0.333070
$665$	0	0
$666$	17.8640	0.00103936
$667$	−22699.5	−1.31773
$668$	3194.30	0.185017
$669$	17344.6	1.00236
$670$	9814.16	0.565902
$671$	−10418.9	−0.599427
$672$	0	0
$673$	−23005.5	−1.31768	−0.658839	−	0.752284i	$-0.728952\pi$
$673$	−23005.5	−1.31768	−0.658839	+	0.752284i	$0.728952\pi$
$674$	−23929.6	−1.36755
$675$	−2972.79	−0.169515
$676$	2502.90	0.142404
$677$	−12121.1	−0.688111	−0.344055	−	0.938949i	$-0.611801\pi$
$677$	−12121.1	−0.688111	−0.344055	+	0.938949i	$0.611801\pi$
$678$	7098.01	0.402061
$679$	0	0
$680$	−1109.65	−0.0625784
$681$	35535.6	1.99960
$682$	−4310.63	−0.242027
$683$	−14223.1	−0.796823	−0.398412	−	0.917207i	$-0.630438\pi$
$683$	−14223.1	−0.796823	−0.398412	+	0.917207i	$0.630438\pi$
$684$	−3684.34	−0.205957
$685$	8694.31	0.484953
$686$	0	0
$687$	−8222.77	−0.456650
$688$	4296.93	0.238109
$689$	−3945.31	−0.218149
$690$	11607.2	0.640401
$691$	2442.82	0.134485	0.0672425	−	0.997737i	$-0.478580\pi$
$691$	2442.82	0.134485	0.0672425	+	0.997737i	$0.478580\pi$
$692$	8795.55	0.483175
$693$	0	0
$694$	18028.5	0.986097
$695$	3486.66	0.190297
$696$	−5231.02	−0.284887
$697$	−6289.76	−0.341810
$698$	−8879.46	−0.481508
$699$	20328.6	1.10000
$700$	0	0
$701$	5484.01	0.295475	0.147738	−	0.989027i	$-0.452801\pi$
$701$	5484.01	0.295475	0.147738	+	0.989027i	$0.452801\pi$
$702$	−12635.4	−0.679333
$703$	198.658	0.0106579
$704$	−1307.86	−0.0700169
$705$	802.048	0.0428467
$706$	17807.7	0.949294
$707$	0	0
$708$	15389.4	0.816904
$709$	10856.6	0.575074	0.287537	−	0.957770i	$-0.407164\pi$
$709$	10856.6	0.575074	0.287537	+	0.957770i	$0.407164\pi$
$710$	1447.07	0.0764894
$711$	940.004	0.0495822
$712$	4851.66	0.255370
$713$	21171.5	1.11203
$714$	0	0
$715$	5428.58	0.283940
$716$	−9346.29	−0.487832
$717$	−25054.5	−1.30499
$718$	21134.3	1.09850
$719$	−10679.7	−0.553943	−0.276971	−	0.960878i	$-0.589331\pi$
$719$	−10679.7	−0.553943	−0.276971	+	0.960878i	$0.589331\pi$
$720$	514.827	0.0266479
$721$	0	0
$722$	−27254.0	−1.40483
$723$	−38164.9	−1.96316
$724$	8974.09	0.460662
$725$	2827.05	0.144819
$726$	10563.1	0.539992
$727$	−18540.2	−0.945831	−0.472916	−	0.881108i	$-0.656798\pi$
$727$	−18540.2	−0.945831	−0.472916	+	0.881108i	$0.656798\pi$
$728$	0	0
$729$	13021.8	0.661577
$730$	−7355.52	−0.372931
$731$	7450.17	0.376956
$732$	11792.4	0.595435
$733$	−14239.0	−0.717501	−0.358750	−	0.933434i	$-0.616797\pi$
$733$	−14239.0	−0.717501	−0.358750	+	0.933434i	$0.616797\pi$
$734$	7186.57	0.361391
$735$	0	0
$736$	6423.52	0.321704
$737$	20055.6	1.00238
$738$	2918.15	0.145554
$739$	4765.10	0.237195	0.118597	−	0.992942i	$-0.462160\pi$
$739$	4765.10	0.237195	0.118597	+	0.992942i	$0.462160\pi$
$740$	−27.7592	−0.00137898
$741$	43970.9	2.17991
$742$	0	0
$743$	13720.9	0.677485	0.338743	−	0.940879i	$-0.389998\pi$
$743$	13720.9	0.677485	0.338743	+	0.940879i	$0.389998\pi$
$744$	4878.89	0.240415
$745$	−8199.31	−0.403221
$746$	−17524.4	−0.860073
$747$	4584.25	0.224537
$748$	−2267.62	−0.110845
$749$	0	0
$750$	−1445.58	−0.0703803
$751$	25957.9	1.26127	0.630636	−	0.776079i	$-0.282794\pi$
$751$	25957.9	1.26127	0.630636	+	0.776079i	$0.282794\pi$
$752$	443.862	0.0215239
$753$	−21158.6	−1.02399
$754$	12015.9	0.580364
$755$	14146.5	0.681914
$756$	0	0
$757$	−7731.70	−0.371220	−0.185610	−	0.982624i	$-0.559426\pi$
$757$	−7731.70	−0.371220	−0.185610	+	0.982624i	$0.559426\pi$
$758$	26443.2	1.26710
$759$	23719.6	1.13434
$760$	5725.17	0.273255
$761$	24447.7	1.16456	0.582278	−	0.812989i	$-0.302161\pi$
$761$	24447.7	1.16456	0.582278	+	0.812989i	$0.302161\pi$
$762$	28801.4	1.36924
$763$	0	0
$764$	−1660.39	−0.0786269
$765$	892.625	0.0421869
$766$	14219.3	0.670709
$767$	−35350.2	−1.66418
$768$	1480.28	0.0695506
$769$	38807.0	1.81979	0.909893	−	0.414843i	$-0.136164\pi$
$769$	38807.0	1.81979	0.909893	+	0.414843i	$0.136164\pi$
$770$	0	0
$771$	−22222.9	−1.03805
$772$	7280.83	0.339434
$773$	35375.7	1.64602	0.823012	−	0.568023i	$-0.192292\pi$
$773$	35375.7	1.64602	0.823012	+	0.568023i	$0.192292\pi$
$774$	−3456.53	−0.160520
$775$	−2636.75	−0.122213
$776$	−6172.41	−0.285537
$777$	0	0
$778$	10564.6	0.486838
$779$	32451.5	1.49255
$780$	−6144.23	−0.282049
$781$	2957.13	0.135486
$782$	11137.3	0.509296
$783$	−13446.8	−0.613727
$784$	0	0
$785$	−12955.6	−0.589052
$786$	27630.3	1.25387
$787$	−20972.1	−0.949904	−0.474952	−	0.880012i	$-0.657535\pi$
$787$	−20972.1	−0.949904	−0.474952	+	0.880012i	$0.657535\pi$
$788$	1373.35	0.0620856
$789$	−2673.61	−0.120638
$790$	−1460.69	−0.0657836
$791$	0	0
$792$	1052.07	0.0472015
$793$	−27087.7	−1.21301
$794$	−23874.1	−1.06708
$795$	2146.94	0.0957788
$796$	9729.66	0.433239
$797$	−873.157	−0.0388065	−0.0194033	−	0.999812i	$-0.506177\pi$
$797$	−873.157	−0.0388065	−0.0194033	+	0.999812i	$0.506177\pi$
$798$	0	0
$799$	769.583	0.0340750
$800$	−800.000	−0.0353553
$801$	−3902.76	−0.172156
$802$	8288.10	0.364917
$803$	−15031.3	−0.660575
$804$	−22699.5	−0.995708
$805$	0	0
$806$	−11207.1	−0.489768
$807$	−3925.51	−0.171232
$808$	11723.3	0.510425
$809$	1871.57	0.0813359	0.0406679	−	0.999173i	$-0.487051\pi$
$809$	1871.57	0.0813359	0.0406679	+	0.999173i	$0.487051\pi$
$810$	8613.41	0.373635
$811$	−39990.1	−1.73150	−0.865748	−	0.500480i	$-0.833157\pi$
$811$	−39990.1	−1.73150	−0.865748	+	0.500480i	$0.833157\pi$
$812$	0	0
$813$	5133.61	0.221456
$814$	−56.7269	−0.00244260
$815$	17362.7	0.746243
$816$	2566.56	0.110107
$817$	−38438.6	−1.64602
$818$	−16576.3	−0.708527
$819$	0	0
$820$	−4534.57	−0.193115
$821$	−27502.1	−1.16910	−0.584550	−	0.811357i	$-0.698729\pi$
$821$	−27502.1	−1.16910	−0.584550	+	0.811357i	$0.698729\pi$
$822$	−20109.4	−0.853278
$823$	−1303.62	−0.0552142	−0.0276071	−	0.999619i	$-0.508789\pi$
$823$	−1303.62	−0.0552142	−0.0276071	+	0.999619i	$0.508789\pi$
$824$	−3490.50	−0.147570
$825$	−2954.10	−0.124665
$826$	0	0
$827$	−36754.0	−1.54542	−0.772709	−	0.634760i	$-0.781099\pi$
$827$	−36754.0	−1.54542	−0.772709	+	0.634760i	$0.781099\pi$
$828$	−5167.19	−0.216875
$829$	21461.2	0.899128	0.449564	−	0.893248i	$-0.351579\pi$
$829$	21461.2	0.899128	0.449564	+	0.893248i	$0.351579\pi$
$830$	−7123.56	−0.297906
$831$	−31310.5	−1.30704
$832$	−3400.28	−0.141687
$833$	0	0
$834$	−8064.40	−0.334829
$835$	3992.88	0.165484
$836$	11699.6	0.484017
$837$	12541.6	0.517922
$838$	808.963	0.0333475
$839$	11299.8	0.464973	0.232486	−	0.972600i	$-0.425314\pi$
$839$	11299.8	0.464973	0.232486	+	0.972600i	$0.425314\pi$
$840$	0	0
$841$	−11601.5	−0.475685
$842$	2691.24	0.110150
$843$	−8234.64	−0.336437
$844$	1243.86	0.0507293
$845$	3128.62	0.127370
$846$	−357.050	−0.0145102
$847$	0	0
$848$	1188.14	0.0481142
$849$	24083.1	0.973532
$850$	−1387.07	−0.0559718
$851$	278.612	0.0112229
$852$	−3346.97	−0.134584
$853$	13188.1	0.529370	0.264685	−	0.964335i	$-0.414732\pi$
$853$	13188.1	0.529370	0.264685	+	0.964335i	$0.414732\pi$
$854$	0	0
$855$	−4605.43	−0.184213
$856$	17474.6	0.697746
$857$	−13279.5	−0.529309	−0.264655	−	0.964343i	$-0.585258\pi$
$857$	−13279.5	−0.529309	−0.264655	+	0.964343i	$0.585258\pi$
$858$	−12555.9	−0.499595
$859$	4066.00	0.161502	0.0807509	−	0.996734i	$-0.474268\pi$
$859$	4066.00	0.161502	0.0807509	+	0.996734i	$0.474268\pi$
$860$	5371.16	0.212971
$861$	0	0
$862$	5755.58	0.227420
$863$	18299.4	0.721807	0.360903	−	0.932603i	$-0.382468\pi$
$863$	18299.4	0.721807	0.360903	+	0.932603i	$0.382468\pi$
$864$	3805.17	0.149832
$865$	10994.4	0.432164
$866$	−1405.05	−0.0551334
$867$	−23958.6	−0.938497
$868$	0	0
$869$	−2984.97	−0.116523
$870$	−6538.77	−0.254810
$871$	52142.0	2.02843
$872$	520.205	0.0202023
$873$	4965.20	0.192493
$874$	−57462.1	−2.22390
$875$	0	0
$876$	17012.8	0.656175
$877$	−14113.3	−0.543411	−0.271705	−	0.962381i	$-0.587588\pi$
$877$	−14113.3	−0.543411	−0.271705	+	0.962381i	$0.587588\pi$
$878$	−22019.0	−0.846362
$879$	37509.0	1.43930
$880$	−1634.83	−0.0626250
$881$	14794.7	0.565772	0.282886	−	0.959154i	$-0.408708\pi$
$881$	14794.7	0.565772	0.282886	+	0.959154i	$0.408708\pi$
$882$	0	0
$883$	−10477.5	−0.399314	−0.199657	−	0.979866i	$-0.563983\pi$
$883$	−10477.5	−0.399314	−0.199657	+	0.979866i	$0.563983\pi$
$884$	−5895.52	−0.224307
$885$	19236.7	0.730661
$886$	33285.8	1.26214
$887$	857.232	0.0324499	0.0162249	−	0.999868i	$-0.494835\pi$
$887$	857.232	0.0324499	0.0162249	+	0.999868i	$0.494835\pi$
$888$	64.2051	0.00242633
$889$	0	0
$890$	6064.57	0.228410
$891$	17601.8	0.661821
$892$	11998.4	0.450375
$893$	−3970.60	−0.148792
$894$	18964.5	0.709470
$895$	−11682.9	−0.436330
$896$	0	0
$897$	61668.0	2.29547
$898$	17396.2	0.646456
$899$	−11926.7	−0.442468
$900$	643.534	0.0238346
$901$	2060.04	0.0761706
$902$	−9266.55	−0.342065
$903$	0	0
$904$	4910.14	0.180651
$905$	11217.6	0.412029
$906$	−32720.0	−1.19983
$907$	−52444.7	−1.91995	−0.959977	−	0.280078i	$-0.909640\pi$
$907$	−52444.7	−1.91995	−0.959977	+	0.280078i	$0.909640\pi$
$908$	24582.2	0.898445
$909$	−9430.41	−0.344100
$910$	0	0
$911$	−2743.07	−0.0997606	−0.0498803	−	0.998755i	$-0.515884\pi$
$911$	−2743.07	−0.0997606	−0.0498803	+	0.998755i	$0.515884\pi$
$912$	−13241.9	−0.480794
$913$	−14557.2	−0.527683
$914$	−12976.9	−0.469626
$915$	14740.5	0.532573
$916$	−5688.21	−0.205179
$917$	0	0
$918$	6597.54	0.237202
$919$	−53455.6	−1.91876	−0.959378	−	0.282124i	$-0.908961\pi$
$919$	−53455.6	−1.91876	−0.959378	+	0.282124i	$0.908961\pi$
$920$	8029.40	0.287741
$921$	24905.2	0.891048
$922$	−17595.5	−0.628499
$923$	7688.17	0.274170
$924$	0	0
$925$	−34.6990	−0.00123340
$926$	1076.17	0.0381913
$927$	2807.82	0.0994831
$928$	−3618.62	−0.128003
$929$	8558.80	0.302266	0.151133	−	0.988513i	$-0.451708\pi$
$929$	8558.80	0.302266	0.151133	+	0.988513i	$0.451708\pi$
$930$	6098.62	0.215034
$931$	0	0
$932$	14062.6	0.494243
$933$	−15305.0	−0.537044
$934$	19132.2	0.670262
$935$	−2834.52	−0.0991430
$936$	2735.24	0.0955173
$937$	−13653.3	−0.476022	−0.238011	−	0.971262i	$-0.576495\pi$
$937$	−13653.3	−0.476022	−0.238011	+	0.971262i	$0.576495\pi$
$938$	0	0
$939$	3670.43	0.127561
$940$	554.827	0.0192516
$941$	5269.56	0.182553	0.0912767	−	0.995826i	$-0.470905\pi$
$941$	5269.56	0.182553	0.0912767	+	0.995826i	$0.470905\pi$
$942$	29965.4	1.03644
$943$	45512.3	1.57167
$944$	10645.8	0.367046
$945$	0	0
$946$	10976.2	0.377236
$947$	−39151.7	−1.34346	−0.671731	−	0.740795i	$-0.734449\pi$
$947$	−39151.7	−1.34346	−0.671731	+	0.740795i	$0.734449\pi$
$948$	3378.48	0.115747
$949$	−39079.4	−1.33674
$950$	7156.47	0.244407
$951$	41742.9	1.42335
$952$	0	0
$953$	20474.4	0.695941	0.347971	−	0.937505i	$-0.386871\pi$
$953$	20474.4	0.695941	0.347971	+	0.937505i	$0.386871\pi$
$954$	−955.759	−0.0324359
$955$	−2075.49	−0.0703261
$956$	−17331.7	−0.586348
$957$	−13362.2	−0.451347
$958$	−8223.49	−0.277337
$959$	0	0
$960$	1850.35	0.0622080
$961$	−18667.1	−0.626602
$962$	−147.483	−0.00494286
$963$	−14056.9	−0.470382
$964$	−26401.0	−0.882075
$965$	9101.04	0.303599
$966$	0	0
$967$	2823.17	0.0938852	0.0469426	−	0.998898i	$-0.485052\pi$
$967$	2823.17	0.0938852	0.0469426	+	0.998898i	$0.485052\pi$
$968$	7307.18	0.242626
$969$	−22959.3	−0.761156
$970$	−7715.52	−0.255392
$971$	−8367.21	−0.276536	−0.138268	−	0.990395i	$-0.544154\pi$
$971$	−8367.21	−0.276536	−0.138268	+	0.990395i	$0.544154\pi$
$972$	−7079.76	−0.233625
$973$	0	0
$974$	7143.45	0.235001
$975$	−7680.28	−0.252273
$976$	8157.52	0.267537
$977$	−20786.2	−0.680665	−0.340332	−	0.940305i	$-0.610540\pi$
$977$	−20786.2	−0.680665	−0.340332	+	0.940305i	$0.610540\pi$
$978$	−40158.7	−1.31302
$979$	12393.2	0.404583
$980$	0	0
$981$	−418.462	−0.0136192
$982$	−43252.2	−1.40553
$983$	−12744.7	−0.413523	−0.206762	−	0.978391i	$-0.566292\pi$
$983$	−12744.7	−0.413523	−0.206762	+	0.978391i	$0.566292\pi$
$984$	10488.2	0.339787
$985$	1716.68	0.0555310
$986$	−6274.09	−0.202645
$987$	0	0
$988$	30417.5	0.979462
$989$	−53909.0	−1.73327
$990$	1315.08	0.0422183
$991$	−7072.58	−0.226708	−0.113354	−	0.993555i	$-0.536159\pi$
$991$	−7072.58	−0.226708	−0.113354	+	0.993555i	$0.536159\pi$
$992$	3375.04	0.108022
$993$	−48560.6	−1.55189
$994$	0	0
$995$	12162.1	0.387501
$996$	16476.3	0.524168
$997$	13372.8	0.424795	0.212398	−	0.977183i	$-0.431873\pi$
$997$	13372.8	0.424795	0.212398	+	0.977183i	$0.431873\pi$
$998$	−340.815	−0.0108099
$999$	165.045	0.00522701

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.4.a.r.1.2		2
5.4	even	2		2450.4.a.bz.1.1		2
7.2	even	3		70.4.e.d.11.1	✓	4
7.3	odd	6		490.4.e.u.471.2		4
7.4	even	3		70.4.e.d.51.1	yes	4
7.5	odd	6		490.4.e.u.361.2		4
7.6	odd	2		490.4.a.t.1.1		2
21.2	odd	6		630.4.k.l.361.1		4
21.11	odd	6		630.4.k.l.541.1		4
28.11	odd	6		560.4.q.j.401.2		4
28.23	odd	6		560.4.q.j.81.2		4
35.2	odd	12		350.4.j.g.249.2		8
35.4	even	6		350.4.e.h.51.2		4
35.9	even	6		350.4.e.h.151.2		4
35.18	odd	12		350.4.j.g.149.2		8
35.23	odd	12		350.4.j.g.249.3		8
35.32	odd	12		350.4.j.g.149.3		8
35.34	odd	2		2450.4.a.bv.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.4.e.d.11.1	✓	4	7.2	even	3
70.4.e.d.51.1	yes	4	7.4	even	3
350.4.e.h.51.2		4	35.4	even	6
350.4.e.h.151.2		4	35.9	even	6
350.4.j.g.149.2		8	35.18	odd	12
350.4.j.g.149.3		8	35.32	odd	12
350.4.j.g.249.2		8	35.2	odd	12
350.4.j.g.249.3		8	35.23	odd	12
490.4.a.r.1.2		2	1.1	even	1	trivial
490.4.a.t.1.1		2	7.6	odd	2
490.4.e.u.361.2		4	7.5	odd	6
490.4.e.u.471.2		4	7.3	odd	6
560.4.q.j.81.2		4	28.23	odd	6
560.4.q.j.401.2		4	28.11	odd	6
630.4.k.l.361.1		4	21.2	odd	6
630.4.k.l.541.1		4	21.11	odd	6
2450.4.a.bv.1.2		2	35.34	odd	2
2450.4.a.bz.1.1		2	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	490.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +5.78233 q^{3} +4.00000 q^{4} +5.00000 q^{5} -11.5647 q^{6} -8.00000 q^{8} +6.43534 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} +5.78233 q^{3} +4.00000 q^{4} +5.00000 q^{5} -11.5647 q^{6} -8.00000 q^{8} +6.43534 q^{9} -10.0000 q^{10} -20.4353 q^{11} +23.1293 q^{12} -53.1293 q^{13} +28.9116 q^{15} +16.0000 q^{16} +27.7414 q^{17} -12.8707 q^{18} -143.129 q^{19} +20.0000 q^{20} +40.8707 q^{22} -200.735 q^{23} -46.2586 q^{24} +25.0000 q^{25} +106.259 q^{26} -118.912 q^{27} +113.082 q^{29} -57.8233 q^{30} -105.470 q^{31} -32.0000 q^{32} -118.164 q^{33} -55.4827 q^{34} +25.7414 q^{36} -1.38796 q^{37} +286.259 q^{38} -307.211 q^{39} -40.0000 q^{40} -226.729 q^{41} +268.558 q^{43} -81.7414 q^{44} +32.1767 q^{45} +401.470 q^{46} +27.7414 q^{47} +92.5173 q^{48} -50.0000 q^{50} +160.410 q^{51} -212.517 q^{52} +74.2586 q^{53} +237.823 q^{54} -102.177 q^{55} -827.621 q^{57} -226.164 q^{58} +665.362 q^{59} +115.647 q^{60} +509.845 q^{61} +210.940 q^{62} +64.0000 q^{64} -265.647 q^{65} +236.328 q^{66} -981.416 q^{67} +110.965 q^{68} -1160.72 q^{69} -144.707 q^{71} -51.4827 q^{72} +735.552 q^{73} +2.77592 q^{74} +144.558 q^{75} -572.517 q^{76} +614.423 q^{78} +146.069 q^{79} +80.0000 q^{80} -861.341 q^{81} +453.457 q^{82} +712.356 q^{83} +138.707 q^{85} -537.116 q^{86} +653.877 q^{87} +163.483 q^{88} -606.457 q^{89} -64.3534 q^{90} -802.940 q^{92} -609.862 q^{93} -55.4827 q^{94} -715.647 q^{95} -185.035 q^{96} +771.552 q^{97} -131.508 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} - 2 q^{3} + 8 q^{4} + 10 q^{5} + 4 q^{6} - 16 q^{8} + 40 q^{9}+O(q^{10}) \) 2 * q - 4 * q^2 - 2 * q^3 + 8 * q^4 + 10 * q^5 + 4 * q^6 - 16 * q^8 + 40 * q^9	\( 2 q - 4 q^{2} - 2 q^{3} + 8 q^{4} + 10 q^{5} + 4 q^{6} - 16 q^{8} + 40 q^{9} - 20 q^{10} - 68 q^{11} - 8 q^{12} - 52 q^{13} - 10 q^{15} + 32 q^{16} + 164 q^{17} - 80 q^{18} - 232 q^{19} + 40 q^{20} + 136 q^{22} - 198 q^{23} + 16 q^{24} + 50 q^{25} + 104 q^{26} - 170 q^{27} - 18 q^{29} + 20 q^{30} + 196 q^{31} - 64 q^{32} + 252 q^{33} - 328 q^{34} + 160 q^{36} + 160 q^{37} + 464 q^{38} - 316 q^{39} - 80 q^{40} + 62 q^{41} + 198 q^{43} - 272 q^{44} + 200 q^{45} + 396 q^{46} + 164 q^{47} - 32 q^{48} - 100 q^{50} - 900 q^{51} - 208 q^{52} + 40 q^{53} + 340 q^{54} - 340 q^{55} - 136 q^{57} + 36 q^{58} - 80 q^{59} - 40 q^{60} - 174 q^{61} - 392 q^{62} + 128 q^{64} - 260 q^{65} - 504 q^{66} - 1054 q^{67} + 656 q^{68} - 1182 q^{69} - 832 q^{71} - 320 q^{72} + 820 q^{73} - 320 q^{74} - 50 q^{75} - 928 q^{76} + 632 q^{78} - 576 q^{79} + 160 q^{80} - 1370 q^{81} - 124 q^{82} - 298 q^{83} + 820 q^{85} - 396 q^{86} + 1674 q^{87} + 544 q^{88} - 182 q^{89} - 400 q^{90} - 792 q^{92} - 2956 q^{93} - 328 q^{94} - 1160 q^{95} + 64 q^{96} + 892 q^{97} - 1728 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 - 2 * q^3 + 8 * q^4 + 10 * q^5 + 4 * q^6 - 16 * q^8 + 40 * q^9 - 20 * q^10 - 68 * q^11 - 8 * q^12 - 52 * q^13 - 10 * q^15 + 32 * q^16 + 164 * q^17 - 80 * q^18 - 232 * q^19 + 40 * q^20 + 136 * q^22 - 198 * q^23 + 16 * q^24 + 50 * q^25 + 104 * q^26 - 170 * q^27 - 18 * q^29 + 20 * q^30 + 196 * q^31 - 64 * q^32 + 252 * q^33 - 328 * q^34 + 160 * q^36 + 160 * q^37 + 464 * q^38 - 316 * q^39 - 80 * q^40 + 62 * q^41 + 198 * q^43 - 272 * q^44 + 200 * q^45 + 396 * q^46 + 164 * q^47 - 32 * q^48 - 100 * q^50 - 900 * q^51 - 208 * q^52 + 40 * q^53 + 340 * q^54 - 340 * q^55 - 136 * q^57 + 36 * q^58 - 80 * q^59 - 40 * q^60 - 174 * q^61 - 392 * q^62 + 128 * q^64 - 260 * q^65 - 504 * q^66 - 1054 * q^67 + 656 * q^68 - 1182 * q^69 - 832 * q^71 - 320 * q^72 + 820 * q^73 - 320 * q^74 - 50 * q^75 - 928 * q^76 + 632 * q^78 - 576 * q^79 + 160 * q^80 - 1370 * q^81 - 124 * q^82 - 298 * q^83 + 820 * q^85 - 396 * q^86 + 1674 * q^87 + 544 * q^88 - 182 * q^89 - 400 * q^90 - 792 * q^92 - 2956 * q^93 - 328 * q^94 - 1160 * q^95 + 64 * q^96 + 892 * q^97 - 1728 * q^99

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