LMFDB - Embedded newform 490.4.a.v.1.3

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:	$0$
Dimension:	$3$
Coefficient field:	3.3.115880.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 66x + 90 $ x^3 - x^2 - 66*x + 90
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 70)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-8.28165$ 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)

$f(q)$	$=$	$q+2.00000 q^{2} +7.28165 q^{3} +4.00000 q^{4} -5.00000 q^{5} +14.5633 q^{6} +8.00000 q^{8} +26.0224 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +7.28165 q^{3} +4.00000 q^{4} -5.00000 q^{5} +14.5633 q^{6} +8.00000 q^{8} +26.0224 q^{9} -10.0000 q^{10} +41.1042 q^{11} +29.1266 q^{12} +24.5857 q^{13} -36.4083 q^{15} +16.0000 q^{16} +93.3798 q^{17} +52.0449 q^{18} -54.6306 q^{19} -20.0000 q^{20} +82.2083 q^{22} -136.419 q^{23} +58.2532 q^{24} +25.0000 q^{25} +49.1715 q^{26} -7.11822 q^{27} +282.700 q^{29} -72.8165 q^{30} +54.6531 q^{31} +32.0000 q^{32} +299.306 q^{33} +186.760 q^{34} +104.090 q^{36} +212.288 q^{37} -109.261 q^{38} +179.025 q^{39} -40.0000 q^{40} -417.658 q^{41} +193.045 q^{43} +164.417 q^{44} -130.112 q^{45} -272.837 q^{46} -126.150 q^{47} +116.506 q^{48} +50.0000 q^{50} +679.959 q^{51} +98.3430 q^{52} +437.660 q^{53} -14.2364 q^{54} -205.521 q^{55} -397.801 q^{57} +565.401 q^{58} -419.862 q^{59} -145.633 q^{60} +323.615 q^{61} +109.306 q^{62} +64.0000 q^{64} -122.929 q^{65} +598.612 q^{66} +57.2086 q^{67} +373.519 q^{68} -993.353 q^{69} -1064.55 q^{71} +208.180 q^{72} -687.247 q^{73} +424.575 q^{74} +182.041 q^{75} -218.523 q^{76} +358.050 q^{78} +716.030 q^{79} -80.0000 q^{80} -754.438 q^{81} -835.316 q^{82} -236.392 q^{83} -466.899 q^{85} +386.090 q^{86} +2058.53 q^{87} +328.833 q^{88} +457.594 q^{89} -260.224 q^{90} -545.675 q^{92} +397.965 q^{93} -252.300 q^{94} +273.153 q^{95} +233.013 q^{96} -1838.74 q^{97} +1069.63 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 6 q^{2} - 4 q^{3} + 12 q^{4} - 15 q^{5} - 8 q^{6} + 24 q^{8} + 57 q^{9}+O(q^{10}) $ 3 * q + 6 * q^2 - 4 * q^3 + 12 * q^4 - 15 * q^5 - 8 * q^6 + 24 * q^8 + 57 * q^9	\( 3 q + 6 q^{2} - 4 q^{3} + 12 q^{4} - 15 q^{5} - 8 q^{6} + 24 q^{8} + 57 q^{9} - 30 q^{10} + 41 q^{11} - 16 q^{12} + q^{13} + 20 q^{15} + 48 q^{16} - 30 q^{17} + 114 q^{18} - 49 q^{19} - 60 q^{20} + 82 q^{22} + 145 q^{23} - 32 q^{24} + 75 q^{25} + 2 q^{26} - 118 q^{27} + 268 q^{29} + 40 q^{30} + 28 q^{31} + 96 q^{32} + 626 q^{33} - 60 q^{34} + 228 q^{36} + 813 q^{37} - 98 q^{38} + 114 q^{39} - 120 q^{40} - 313 q^{41} + 360 q^{43} + 164 q^{44} - 285 q^{45} + 290 q^{46} + 977 q^{47} - 64 q^{48} + 150 q^{50} + 1632 q^{51} + 4 q^{52} + 325 q^{53} - 236 q^{54} - 205 q^{55} + 250 q^{57} + 536 q^{58} + 272 q^{59} + 80 q^{60} + 902 q^{61} + 56 q^{62} + 192 q^{64} - 5 q^{65} + 1252 q^{66} - 170 q^{67} - 120 q^{68} - 2264 q^{69} - 1080 q^{71} + 456 q^{72} + 584 q^{73} + 1626 q^{74} - 100 q^{75} - 196 q^{76} + 228 q^{78} - 310 q^{79} - 240 q^{80} + 147 q^{81} - 626 q^{82} - 626 q^{83} + 150 q^{85} + 720 q^{86} + 1846 q^{87} + 328 q^{88} + 400 q^{89} - 570 q^{90} + 580 q^{92} - 372 q^{93} + 1954 q^{94} + 245 q^{95} - 128 q^{96} - 1626 q^{97} - 2611 q^{99}+O(q^{100}) \) 3 * q + 6 * q^2 - 4 * q^3 + 12 * q^4 - 15 * q^5 - 8 * q^6 + 24 * q^8 + 57 * q^9 - 30 * q^10 + 41 * q^11 - 16 * q^12 + q^13 + 20 * q^15 + 48 * q^16 - 30 * q^17 + 114 * q^18 - 49 * q^19 - 60 * q^20 + 82 * q^22 + 145 * q^23 - 32 * q^24 + 75 * q^25 + 2 * q^26 - 118 * q^27 + 268 * q^29 + 40 * q^30 + 28 * q^31 + 96 * q^32 + 626 * q^33 - 60 * q^34 + 228 * q^36 + 813 * q^37 - 98 * q^38 + 114 * q^39 - 120 * q^40 - 313 * q^41 + 360 * q^43 + 164 * q^44 - 285 * q^45 + 290 * q^46 + 977 * q^47 - 64 * q^48 + 150 * q^50 + 1632 * q^51 + 4 * q^52 + 325 * q^53 - 236 * q^54 - 205 * q^55 + 250 * q^57 + 536 * q^58 + 272 * q^59 + 80 * q^60 + 902 * q^61 + 56 * q^62 + 192 * q^64 - 5 * q^65 + 1252 * q^66 - 170 * q^67 - 120 * q^68 - 2264 * q^69 - 1080 * q^71 + 456 * q^72 + 584 * q^73 + 1626 * q^74 - 100 * q^75 - 196 * q^76 + 228 * q^78 - 310 * q^79 - 240 * q^80 + 147 * q^81 - 626 * q^82 - 626 * q^83 + 150 * q^85 + 720 * q^86 + 1846 * q^87 + 328 * q^88 + 400 * q^89 - 570 * q^90 + 580 * q^92 - 372 * q^93 + 1954 * q^94 + 245 * q^95 - 128 * q^96 - 1626 * q^97 - 2611 * 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
$3$	7.28165	1.40135	0.700677	−	0.713478i	$-0.252881\pi$
$3$	7.28165	1.40135	0.700677	+	0.713478i	$0.252881\pi$
$4$	4.00000	0.500000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	14.5633	0.990907
$7$	0	0
$7$	0	0
$8$	8.00000	0.353553
$9$	26.0224	0.963794
$10$	−10.0000	−0.316228
$11$	41.1042	1.12667	0.563335	−	0.826229i	$-0.309518\pi$
$11$	41.1042	1.12667	0.563335	+	0.826229i	$0.309518\pi$
$12$	29.1266	0.700677
$13$	24.5857	0.524528	0.262264	−	0.964996i	$-0.415531\pi$
$13$	24.5857	0.524528	0.262264	+	0.964996i	$0.415531\pi$
$14$	0	0
$15$	−36.4083	−0.626705
$16$	16.0000	0.250000
$17$	93.3798	1.33223	0.666116	−	0.745848i	$-0.267956\pi$
$17$	93.3798	1.33223	0.666116	+	0.745848i	$0.267956\pi$
$18$	52.0449	0.681505
$19$	−54.6306	−0.659638	−0.329819	−	0.944044i	$-0.606988\pi$
$19$	−54.6306	−0.659638	−0.329819	+	0.944044i	$0.606988\pi$
$20$	−20.0000	−0.223607
$21$	0	0
$22$	82.2083	0.796676
$23$	−136.419	−1.23675	−0.618375	−	0.785883i	$-0.712209\pi$
$23$	−136.419	−1.23675	−0.618375	+	0.785883i	$0.712209\pi$
$24$	58.2532	0.495454
$25$	25.0000	0.200000
$26$	49.1715	0.370897
$27$	−7.11822	−0.0507371
$28$	0	0
$29$	282.700	1.81021	0.905106	−	0.425186i	$-0.139791\pi$
$29$	282.700	1.81021	0.905106	+	0.425186i	$0.139791\pi$
$30$	−72.8165	−0.443147
$31$	54.6531	0.316645	0.158322	−	0.987387i	$-0.449391\pi$
$31$	54.6531	0.316645	0.158322	+	0.987387i	$0.449391\pi$
$32$	32.0000	0.176777
$33$	299.306	1.57886
$34$	186.760	0.942030
$35$	0	0
$36$	104.090	0.481897
$37$	212.288	0.943240	0.471620	−	0.881802i	$-0.343669\pi$
$37$	212.288	0.943240	0.471620	+	0.881802i	$0.343669\pi$
$38$	−109.261	−0.466435
$39$	179.025	0.735049
$40$	−40.0000	−0.158114
$41$	−417.658	−1.59091	−0.795454	−	0.606014i	$-0.792767\pi$
$41$	−417.658	−1.59091	−0.795454	+	0.606014i	$0.792767\pi$
$42$	0	0
$43$	193.045	0.684631	0.342315	−	0.939585i	$-0.388789\pi$
$43$	193.045	0.684631	0.342315	+	0.939585i	$0.388789\pi$
$44$	164.417	0.563335
$45$	−130.112	−0.431022
$46$	−272.837	−0.874515
$47$	−126.150	−0.391508	−0.195754	−	0.980653i	$-0.562715\pi$
$47$	−126.150	−0.391508	−0.195754	+	0.980653i	$0.562715\pi$
$48$	116.506	0.350339
$49$	0	0
$50$	50.0000	0.141421
$51$	679.959	1.86693
$52$	98.3430	0.262264
$53$	437.660	1.13429	0.567143	−	0.823619i	$-0.308049\pi$
$53$	437.660	1.13429	0.567143	+	0.823619i	$0.308049\pi$
$54$	−14.2364	−0.0358766
$55$	−205.521	−0.503862
$56$	0	0
$57$	−397.801	−0.924387
$58$	565.401	1.28001
$59$	−419.862	−0.926465	−0.463232	−	0.886237i	$-0.653310\pi$
$59$	−419.862	−0.926465	−0.463232	+	0.886237i	$0.653310\pi$
$60$	−145.633	−0.313352
$61$	323.615	0.679256	0.339628	−	0.940560i	$-0.389699\pi$
$61$	323.615	0.679256	0.339628	+	0.940560i	$0.389699\pi$
$62$	109.306	0.223902
$63$	0	0
$64$	64.0000	0.125000
$65$	−122.929	−0.234576
$66$	598.612	1.11643
$67$	57.2086	0.104316	0.0521578	−	0.998639i	$-0.483390\pi$
$67$	57.2086	0.104316	0.0521578	+	0.998639i	$0.483390\pi$
$68$	373.519	0.666116
$69$	−993.353	−1.73313
$70$	0	0
$71$	−1064.55	−1.77942	−0.889709	−	0.456529i	$-0.849093\pi$
$71$	−1064.55	−1.77942	−0.889709	+	0.456529i	$0.849093\pi$
$72$	208.180	0.340753
$73$	−687.247	−1.10187	−0.550933	−	0.834550i	$-0.685728\pi$
$73$	−687.247	−1.10187	−0.550933	+	0.834550i	$0.685728\pi$
$74$	424.575	0.666971
$75$	182.041	0.280271
$76$	−218.523	−0.329819
$77$	0	0
$78$	358.050	0.519758
$79$	716.030	1.01974	0.509872	−	0.860250i	$-0.329693\pi$
$79$	716.030	1.01974	0.509872	+	0.860250i	$0.329693\pi$
$80$	−80.0000	−0.111803
$81$	−754.438	−1.03489
$82$	−835.316	−1.12494
$83$	−236.392	−0.312619	−0.156310	−	0.987708i	$-0.549960\pi$
$83$	−236.392	−0.312619	−0.156310	+	0.987708i	$0.549960\pi$
$84$	0	0
$85$	−466.899	−0.595792
$86$	386.090	0.484107
$87$	2058.53	2.53675
$88$	328.833	0.398338
$89$	457.594	0.544999	0.272499	−	0.962156i	$-0.412150\pi$
$89$	457.594	0.544999	0.272499	+	0.962156i	$0.412150\pi$
$90$	−260.224	−0.304778
$91$	0	0
$92$	−545.675	−0.618375
$93$	397.965	0.443731
$94$	−252.300	−0.276838
$95$	273.153	0.294999
$96$	233.013	0.247727
$97$	−1838.74	−1.92470	−0.962348	−	0.271821i	$-0.912374\pi$
$97$	−1838.74	−1.92470	−0.962348	+	0.271821i	$0.912374\pi$
$98$	0	0
$99$	1069.63	1.08588
$100$	100.000	0.100000
$101$	−1648.34	−1.62392	−0.811962	−	0.583711i	$-0.801600\pi$
$101$	−1648.34	−1.62392	−0.811962	+	0.583711i	$0.801600\pi$
$102$	1359.92	1.32012
$103$	−1016.70	−0.972605	−0.486302	−	0.873791i	$-0.661655\pi$
$103$	−1016.70	−0.972605	−0.486302	+	0.873791i	$0.661655\pi$
$104$	196.686	0.185449
$105$	0	0
$106$	875.319	0.802061
$107$	−1573.02	−1.42121	−0.710604	−	0.703593i	$-0.751578\pi$
$107$	−1573.02	−1.42121	−0.710604	+	0.703593i	$0.751578\pi$
$108$	−28.4729	−0.0253686
$109$	914.530	0.803634	0.401817	−	0.915720i	$-0.368379\pi$
$109$	914.530	0.803634	0.401817	+	0.915720i	$0.368379\pi$
$110$	−411.042	−0.356284
$111$	1545.80	1.32181
$112$	0	0
$113$	1222.24	1.01751	0.508754	−	0.860912i	$-0.330106\pi$
$113$	1222.24	1.01751	0.508754	+	0.860912i	$0.330106\pi$
$114$	−795.602	−0.653640
$115$	682.094	0.553092
$116$	1130.80	0.905106
$117$	639.781	0.505537
$118$	−839.724	−0.655109
$119$	0	0
$120$	−291.266	−0.221574
$121$	358.552	0.269385
$122$	647.229	0.480306
$123$	−3041.24	−2.22942
$124$	218.612	0.158322
$125$	−125.000	−0.0894427
$126$	0	0
$127$	−1356.92	−0.948087	−0.474044	−	0.880501i	$-0.657206\pi$
$127$	−1356.92	−0.948087	−0.474044	+	0.880501i	$0.657206\pi$
$128$	128.000	0.0883883
$129$	1405.69	0.959410
$130$	−245.857	−0.165870
$131$	1486.80	0.991620	0.495810	−	0.868431i	$-0.334871\pi$
$131$	1486.80	0.991620	0.495810	+	0.868431i	$0.334871\pi$
$132$	1197.22	0.789432
$133$	0	0
$134$	114.417	0.0737623
$135$	35.5911	0.0226903
$136$	747.039	0.471015
$137$	−1356.74	−0.846087	−0.423043	−	0.906109i	$-0.639038\pi$
$137$	−1356.74	−0.846087	−0.423043	+	0.906109i	$0.639038\pi$
$138$	−1986.71	−1.22551
$139$	679.088	0.414385	0.207192	−	0.978300i	$-0.433567\pi$
$139$	679.088	0.414385	0.207192	+	0.978300i	$0.433567\pi$
$140$	0	0
$141$	−918.580	−0.548641
$142$	−2129.10	−1.25824
$143$	1010.58	0.590970
$144$	416.359	0.240949
$145$	−1413.50	−0.809551
$146$	−1374.49	−0.779136
$147$	0	0
$148$	849.151	0.471620
$149$	2604.74	1.43214	0.716068	−	0.698031i	$-0.245940\pi$
$149$	2604.74	1.43214	0.716068	+	0.698031i	$0.245940\pi$
$150$	364.083	0.198181
$151$	961.852	0.518374	0.259187	−	0.965827i	$-0.416545\pi$
$151$	961.852	0.518374	0.259187	+	0.965827i	$0.416545\pi$
$152$	−437.045	−0.233217
$153$	2429.97	1.28400
$154$	0	0
$155$	−273.265	−0.141608
$156$	716.099	0.367525
$157$	1962.26	0.997488	0.498744	−	0.866749i	$-0.333795\pi$
$157$	1962.26	0.997488	0.498744	+	0.866749i	$0.333795\pi$
$158$	1432.06	0.721067
$159$	3186.88	1.58954
$160$	−160.000	−0.0790569
$161$	0	0
$162$	−1508.88	−0.731781
$163$	−2464.15	−1.18409	−0.592046	−	0.805904i	$-0.701680\pi$
$163$	−2464.15	−1.18409	−0.592046	+	0.805904i	$0.701680\pi$
$164$	−1670.63	−0.795454
$165$	−1496.53	−0.706089
$166$	−472.784	−0.221055
$167$	3356.76	1.55541	0.777707	−	0.628627i	$-0.216383\pi$
$167$	3356.76	1.55541	0.777707	+	0.628627i	$0.216383\pi$
$168$	0	0
$169$	−1592.54	−0.724871
$170$	−933.798	−0.421289
$171$	−1421.62	−0.635756
$172$	772.181	0.342315
$173$	−162.849	−0.0715673	−0.0357837	−	0.999360i	$-0.511393\pi$
$173$	−162.849	−0.0715673	−0.0357837	+	0.999360i	$0.511393\pi$
$174$	4117.05	1.79375
$175$	0	0
$176$	657.667	0.281668
$177$	−3057.29	−1.29831
$178$	915.188	0.385372
$179$	−17.5832	−0.00734207	−0.00367104	−	0.999993i	$-0.501169\pi$
$179$	−17.5832	−0.00734207	−0.00367104	+	0.999993i	$0.501169\pi$
$180$	−520.449	−0.215511
$181$	−2045.90	−0.840168	−0.420084	−	0.907485i	$-0.637999\pi$
$181$	−2045.90	−0.840168	−0.420084	+	0.907485i	$0.637999\pi$
$182$	0	0
$183$	2356.45	0.951878
$184$	−1091.35	−0.437257
$185$	−1061.44	−0.421830
$186$	795.929	0.313765
$187$	3838.30	1.50099
$188$	−504.600	−0.195754
$189$	0	0
$190$	546.306	0.208596
$191$	−1515.73	−0.574210	−0.287105	−	0.957899i	$-0.592693\pi$
$191$	−1515.73	−0.574210	−0.287105	+	0.957899i	$0.592693\pi$
$192$	466.026	0.175169
$193$	−2863.80	−1.06809	−0.534043	−	0.845457i	$-0.679328\pi$
$193$	−2863.80	−1.06809	−0.534043	+	0.845457i	$0.679328\pi$
$194$	−3677.47	−1.36097
$195$	−895.124	−0.328724
$196$	0	0
$197$	−1118.96	−0.404683	−0.202342	−	0.979315i	$-0.564855\pi$
$197$	−1118.96	−0.404683	−0.202342	+	0.979315i	$0.564855\pi$
$198$	2139.26	0.767832
$199$	−3322.65	−1.18360	−0.591801	−	0.806084i	$-0.701583\pi$
$199$	−3322.65	−1.18360	−0.591801	+	0.806084i	$0.701583\pi$
$200$	200.000	0.0707107
$201$	416.573	0.146183
$202$	−3296.69	−1.14829
$203$	0	0
$204$	2719.84	0.933464
$205$	2088.29	0.711475
$206$	−2033.40	−0.687735
$207$	−3549.95	−1.19197
$208$	393.372	0.131132
$209$	−2245.55	−0.743195
$210$	0	0
$211$	−2796.60	−0.912446	−0.456223	−	0.889865i	$-0.650798\pi$
$211$	−2796.60	−0.912446	−0.456223	+	0.889865i	$0.650798\pi$
$212$	1750.64	0.567143
$213$	−7751.67	−2.49359
$214$	−3146.03	−1.00495
$215$	−965.226	−0.306176
$216$	−56.9458	−0.0179383
$217$	0	0
$218$	1829.06	0.568255
$219$	−5004.29	−1.54410
$220$	−822.083	−0.251931
$221$	2295.81	0.698792
$222$	3091.61	0.934663
$223$	−758.978	−0.227914	−0.113957	−	0.993486i	$-0.536353\pi$
$223$	−758.978	−0.227914	−0.113957	+	0.993486i	$0.536353\pi$
$224$	0	0
$225$	650.561	0.192759
$226$	2444.47	0.719487
$227$	−193.601	−0.0566067	−0.0283034	−	0.999599i	$-0.509010\pi$
$227$	−193.601	−0.0566067	−0.0283034	+	0.999599i	$0.509010\pi$
$228$	−1591.20	−0.462194
$229$	690.389	0.199223	0.0996117	−	0.995026i	$-0.468240\pi$
$229$	690.389	0.199223	0.0996117	+	0.995026i	$0.468240\pi$
$230$	1364.19	0.391095
$231$	0	0
$232$	2261.60	0.640006
$233$	−910.261	−0.255936	−0.127968	−	0.991778i	$-0.540846\pi$
$233$	−910.261	−0.255936	−0.127968	+	0.991778i	$0.540846\pi$
$234$	1279.56	0.357468
$235$	630.749	0.175087
$236$	−1679.45	−0.463232
$237$	5213.88	1.42902
$238$	0	0
$239$	5465.11	1.47912	0.739558	−	0.673093i	$-0.235035\pi$
$239$	5465.11	1.47912	0.739558	+	0.673093i	$0.235035\pi$
$240$	−582.532	−0.156676
$241$	−4267.99	−1.14077	−0.570385	−	0.821377i	$-0.693206\pi$
$241$	−4267.99	−1.14077	−0.570385	+	0.821377i	$0.693206\pi$
$242$	717.104	0.190484
$243$	−5301.37	−1.39952
$244$	1294.46	0.339628
$245$	0	0
$246$	−6082.48	−1.57644
$247$	−1343.13	−0.345999
$248$	437.225	0.111951
$249$	−1721.33	−0.438091
$250$	−250.000	−0.0632456
$251$	1702.89	0.428228	0.214114	−	0.976809i	$-0.431314\pi$
$251$	1702.89	0.428228	0.214114	+	0.976809i	$0.431314\pi$
$252$	0	0
$253$	−5607.38	−1.39341
$254$	−2713.84	−0.670399
$255$	−3399.80	−0.834916
$256$	256.000	0.0625000
$257$	−5940.85	−1.44195	−0.720973	−	0.692964i	$-0.756305\pi$
$257$	−5940.85	−1.44195	−0.720973	+	0.692964i	$0.756305\pi$
$258$	2811.38	0.678405
$259$	0	0
$260$	−491.715	−0.117288
$261$	7356.55	1.74467
$262$	2973.60	0.701181
$263$	2353.68	0.551841	0.275921	−	0.961180i	$-0.411017\pi$
$263$	2353.68	0.551841	0.275921	+	0.961180i	$0.411017\pi$
$264$	2394.45	0.558213
$265$	−2188.30	−0.507268
$266$	0	0
$267$	3332.04	0.763736
$268$	228.835	0.0521578
$269$	7194.69	1.63074	0.815368	−	0.578942i	$-0.196534\pi$
$269$	7194.69	1.63074	0.815368	+	0.578942i	$0.196534\pi$
$270$	71.1822	0.0160445
$271$	−4716.51	−1.05722	−0.528612	−	0.848864i	$-0.677287\pi$
$271$	−4716.51	−1.05722	−0.528612	+	0.848864i	$0.677287\pi$
$272$	1494.08	0.333058
$273$	0	0
$274$	−2713.47	−0.598274
$275$	1027.60	0.225334
$276$	−3973.41	−0.866563
$277$	3559.84	0.772165	0.386083	−	0.922464i	$-0.373828\pi$
$277$	3559.84	0.772165	0.386083	+	0.922464i	$0.373828\pi$
$278$	1358.18	0.293014
$279$	1422.21	0.305180
$280$	0	0
$281$	−1362.86	−0.289329	−0.144665	−	0.989481i	$-0.546210\pi$
$281$	−1362.86	−0.289329	−0.144665	+	0.989481i	$0.546210\pi$
$282$	−1837.16	−0.387948
$283$	767.583	0.161230	0.0806149	−	0.996745i	$-0.474312\pi$
$283$	767.583	0.161230	0.0806149	+	0.996745i	$0.474312\pi$
$284$	−4258.19	−0.889709
$285$	1989.01	0.413398
$286$	2021.15	0.417879
$287$	0	0
$288$	832.718	0.170376
$289$	3806.79	0.774840
$290$	−2827.00	−0.572439
$291$	−13389.0	−2.69718
$292$	−2748.99	−0.550933
$293$	−2446.59	−0.487820	−0.243910	−	0.969798i	$-0.578430\pi$
$293$	−2446.59	−0.487820	−0.243910	+	0.969798i	$0.578430\pi$
$294$	0	0
$295$	2099.31	0.414328
$296$	1698.30	0.333486
$297$	−292.588	−0.0571640
$298$	5209.47	1.01267
$299$	−3353.96	−0.648710
$300$	728.165	0.140135
$301$	0	0
$302$	1923.70	0.366546
$303$	−12002.7	−2.27569
$304$	−874.090	−0.164910
$305$	−1618.07	−0.303772
$306$	4859.94	0.907923
$307$	5027.81	0.934697	0.467349	−	0.884073i	$-0.345209\pi$
$307$	5027.81	0.934697	0.467349	+	0.884073i	$0.345209\pi$
$308$	0	0
$309$	−7403.24	−1.36296
$310$	−546.531	−0.100132
$311$	5426.39	0.989396	0.494698	−	0.869065i	$-0.335279\pi$
$311$	5426.39	0.989396	0.494698	+	0.869065i	$0.335279\pi$
$312$	1432.20	0.259879
$313$	3072.61	0.554870	0.277435	−	0.960744i	$-0.410516\pi$
$313$	3072.61	0.554870	0.277435	+	0.960744i	$0.410516\pi$
$314$	3924.52	0.705330
$315$	0	0
$316$	2864.12	0.509872
$317$	−1733.39	−0.307120	−0.153560	−	0.988139i	$-0.549074\pi$
$317$	−1733.39	−0.307120	−0.153560	+	0.988139i	$0.549074\pi$
$318$	6373.77	1.12397
$319$	11620.2	2.03951
$320$	−320.000	−0.0559017
$321$	−11454.2	−1.99161
$322$	0	0
$323$	−5101.40	−0.878791
$324$	−3017.75	−0.517447
$325$	614.644	0.104906
$326$	−4928.29	−0.837279
$327$	6659.29	1.12618
$328$	−3341.26	−0.562471
$329$	0	0
$330$	−2993.06	−0.499281
$331$	−1313.45	−0.218108	−0.109054	−	0.994036i	$-0.534782\pi$
$331$	−1313.45	−0.218108	−0.109054	+	0.994036i	$0.534782\pi$
$332$	−945.569	−0.156310
$333$	5524.24	0.909089
$334$	6713.53	1.09984
$335$	−286.043	−0.0466514
$336$	0	0
$337$	10083.5	1.62991	0.814957	−	0.579522i	$-0.196761\pi$
$337$	10083.5	1.62991	0.814957	+	0.579522i	$0.196761\pi$
$338$	−3185.08	−0.512561
$339$	8899.91	1.42589
$340$	−1867.60	−0.297896
$341$	2246.47	0.356754
$342$	−2843.25	−0.449547
$343$	0	0
$344$	1544.36	0.242053
$345$	4966.77	0.775078
$346$	−325.697	−0.0506058
$347$	11595.0	1.79381	0.896907	−	0.442219i	$-0.145808\pi$
$347$	11595.0	1.79381	0.896907	+	0.442219i	$0.145808\pi$
$348$	8234.10	1.26837
$349$	−1188.76	−0.182330	−0.0911649	−	0.995836i	$-0.529059\pi$
$349$	−1188.76	−0.182330	−0.0911649	+	0.995836i	$0.529059\pi$
$350$	0	0
$351$	−175.007	−0.0266130
$352$	1315.33	0.199169
$353$	6308.85	0.951236	0.475618	−	0.879652i	$-0.342224\pi$
$353$	6308.85	0.951236	0.475618	+	0.879652i	$0.342224\pi$
$354$	−6114.58	−0.918040
$355$	5322.74	0.795780
$356$	1830.38	0.272499
$357$	0	0
$358$	−35.1664	−0.00519163
$359$	−8551.60	−1.25720	−0.628602	−	0.777727i	$-0.716373\pi$
$359$	−8551.60	−1.25720	−0.628602	+	0.777727i	$0.716373\pi$
$360$	−1040.90	−0.152389
$361$	−3874.49	−0.564877
$362$	−4091.80	−0.594089
$363$	2610.85	0.377504
$364$	0	0
$365$	3436.23	0.492769
$366$	4712.90	0.673079
$367$	8819.59	1.25444	0.627219	−	0.778843i	$-0.284193\pi$
$367$	8819.59	1.25444	0.627219	+	0.778843i	$0.284193\pi$
$368$	−2182.70	−0.309188
$369$	−10868.5	−1.53331
$370$	−2122.88	−0.298279
$371$	0	0
$372$	1591.86	0.221866
$373$	−2422.58	−0.336291	−0.168145	−	0.985762i	$-0.553778\pi$
$373$	−2422.58	−0.336291	−0.168145	+	0.985762i	$0.553778\pi$
$374$	7676.60	1.06136
$375$	−910.206	−0.125341
$376$	−1009.20	−0.138419
$377$	6950.40	0.949506
$378$	0	0
$379$	−9950.49	−1.34861	−0.674304	−	0.738454i	$-0.735556\pi$
$379$	−9950.49	−1.34861	−0.674304	+	0.738454i	$0.735556\pi$
$380$	1092.61	0.147500
$381$	−9880.61	−1.32861
$382$	−3031.45	−0.406028
$383$	−11287.5	−1.50592	−0.752959	−	0.658067i	$-0.771374\pi$
$383$	−11287.5	−1.50592	−0.752959	+	0.658067i	$0.771374\pi$
$384$	932.051	0.123863
$385$	0	0
$386$	−5727.59	−0.755251
$387$	5023.51	0.659843
$388$	−7354.95	−0.962348
$389$	6537.20	0.852054	0.426027	−	0.904710i	$-0.359913\pi$
$389$	6537.20	0.852054	0.426027	+	0.904710i	$0.359913\pi$
$390$	−1790.25	−0.232443
$391$	−12738.8	−1.64764
$392$	0	0
$393$	10826.4	1.38961
$394$	−2237.92	−0.286154
$395$	−3580.15	−0.456043
$396$	4278.52	0.542939
$397$	10684.2	1.35070	0.675348	−	0.737499i	$-0.263994\pi$
$397$	10684.2	1.35070	0.675348	+	0.737499i	$0.263994\pi$
$398$	−6645.31	−0.836933
$399$	0	0
$400$	400.000	0.0500000
$401$	4088.74	0.509182	0.254591	−	0.967049i	$-0.418059\pi$
$401$	4088.74	0.509182	0.254591	+	0.967049i	$0.418059\pi$
$402$	833.147	0.103367
$403$	1343.69	0.166089
$404$	−6593.37	−0.811962
$405$	3772.19	0.462819
$406$	0	0
$407$	8725.91	1.06272
$408$	5439.67	0.660059
$409$	10184.1	1.23122	0.615611	−	0.788050i	$-0.288909\pi$
$409$	10184.1	1.23122	0.615611	+	0.788050i	$0.288909\pi$
$410$	4176.58	0.503089
$411$	−9879.29	−1.18567
$412$	−4066.79	−0.486302
$413$	0	0
$414$	−7099.90	−0.842852
$415$	1181.96	0.139808
$416$	786.744	0.0927243
$417$	4944.88	0.580700
$418$	−4491.09	−0.525518
$419$	−5367.88	−0.625867	−0.312933	−	0.949775i	$-0.601312\pi$
$419$	−5367.88	−0.625867	−0.312933	+	0.949775i	$0.601312\pi$
$420$	0	0
$421$	−6633.31	−0.767904	−0.383952	−	0.923353i	$-0.625437\pi$
$421$	−6633.31	−0.767904	−0.383952	+	0.923353i	$0.625437\pi$
$422$	−5593.21	−0.645197
$423$	−3282.73	−0.377333
$424$	3501.28	0.401031
$425$	2334.50	0.266446
$426$	−15503.3	−1.76324
$427$	0	0
$428$	−6292.06	−0.710604
$429$	7358.67	0.828158
$430$	−1930.45	−0.216499
$431$	925.656	0.103451	0.0517254	−	0.998661i	$-0.483528\pi$
$431$	925.656	0.103451	0.0517254	+	0.998661i	$0.483528\pi$
$432$	−113.892	−0.0126843
$433$	−3164.31	−0.351194	−0.175597	−	0.984462i	$-0.556186\pi$
$433$	−3164.31	−0.351194	−0.175597	+	0.984462i	$0.556186\pi$
$434$	0	0
$435$	−10292.6	−1.13447
$436$	3658.12	0.401817
$437$	7452.64	0.815808
$438$	−10008.6	−1.09185
$439$	4639.89	0.504442	0.252221	−	0.967670i	$-0.418839\pi$
$439$	4639.89	0.504442	0.252221	+	0.967670i	$0.418839\pi$
$440$	−1644.17	−0.178142
$441$	0	0
$442$	4591.62	0.494121
$443$	15641.6	1.67755	0.838774	−	0.544479i	$-0.183273\pi$
$443$	15641.6	1.67755	0.838774	+	0.544479i	$0.183273\pi$
$444$	6183.22	0.660907
$445$	−2287.97	−0.243731
$446$	−1517.96	−0.161160
$447$	18966.8	2.00693
$448$	0	0
$449$	14829.7	1.55870	0.779348	−	0.626591i	$-0.215550\pi$
$449$	14829.7	1.55870	0.779348	+	0.626591i	$0.215550\pi$
$450$	1301.12	0.136301
$451$	−17167.5	−1.79243
$452$	4888.95	0.508754
$453$	7003.87	0.726425
$454$	−387.201	−0.0400270
$455$	0	0
$456$	−3182.41	−0.326820
$457$	11124.9	1.13873	0.569364	−	0.822085i	$-0.307189\pi$
$457$	11124.9	1.13873	0.569364	+	0.822085i	$0.307189\pi$
$458$	1380.78	0.140872
$459$	−664.698	−0.0675936
$460$	2728.37	0.276546
$461$	8851.07	0.894220	0.447110	−	0.894479i	$-0.352453\pi$
$461$	8851.07	0.894220	0.447110	+	0.894479i	$0.352453\pi$
$462$	0	0
$463$	−2481.12	−0.249044	−0.124522	−	0.992217i	$-0.539740\pi$
$463$	−2481.12	−0.249044	−0.124522	+	0.992217i	$0.539740\pi$
$464$	4523.21	0.452553
$465$	−1989.82	−0.198443
$466$	−1820.52	−0.180974
$467$	1861.20	0.184425	0.0922123	−	0.995739i	$-0.470606\pi$
$467$	1861.20	0.184425	0.0922123	+	0.995739i	$0.470606\pi$
$468$	2559.12	0.252768
$469$	0	0
$470$	1261.50	0.123806
$471$	14288.5	1.39783
$472$	−3358.90	−0.327555
$473$	7934.96	0.771353
$474$	10427.8	1.01047
$475$	−1365.77	−0.131928
$476$	0	0
$477$	11389.0	1.09322
$478$	10930.2	1.04589
$479$	−14997.2	−1.43056	−0.715280	−	0.698838i	$-0.753701\pi$
$479$	−14997.2	−1.43056	−0.715280	+	0.698838i	$0.753701\pi$
$480$	−1165.06	−0.110787
$481$	5219.25	0.494755
$482$	−8535.99	−0.806646
$483$	0	0
$484$	1434.21	0.134693
$485$	9193.69	0.860750
$486$	−10602.7	−0.989608
$487$	−17786.5	−1.65500	−0.827498	−	0.561468i	$-0.810237\pi$
$487$	−17786.5	−1.65500	−0.827498	+	0.561468i	$0.810237\pi$
$488$	2588.92	0.240153
$489$	−17943.1	−1.65933
$490$	0	0
$491$	233.660	0.0214765	0.0107382	−	0.999942i	$-0.496582\pi$
$491$	233.660	0.0214765	0.0107382	+	0.999942i	$0.496582\pi$
$492$	−12165.0	−1.11471
$493$	26398.5	2.41162
$494$	−2686.27	−0.244658
$495$	−5348.15	−0.485619
$496$	874.449	0.0791612
$497$	0	0
$498$	−3442.65	−0.309777
$499$	−1694.46	−0.152013	−0.0760063	−	0.997107i	$-0.524217\pi$
$499$	−1694.46	−0.152013	−0.0760063	+	0.997107i	$0.524217\pi$
$500$	−500.000	−0.0447214
$501$	24442.8	2.17969
$502$	3405.77	0.302803
$503$	10061.6	0.891898	0.445949	−	0.895058i	$-0.352866\pi$
$503$	10061.6	0.891898	0.445949	+	0.895058i	$0.352866\pi$
$504$	0	0
$505$	8241.72	0.726241
$506$	−11214.8	−0.985290
$507$	−11596.3	−1.01580
$508$	−5427.68	−0.474044
$509$	5309.05	0.462317	0.231159	−	0.972916i	$-0.425748\pi$
$509$	5309.05	0.462317	0.231159	+	0.972916i	$0.425748\pi$
$510$	−6799.59	−0.590375
$511$	0	0
$512$	512.000	0.0441942
$513$	388.873	0.0334681
$514$	−11881.7	−1.01961
$515$	5083.49	0.434962
$516$	5622.75	0.479705
$517$	−5185.29	−0.441100
$518$	0	0
$519$	−1185.81	−0.100291
$520$	−983.430	−0.0829351
$521$	−10080.0	−0.847622	−0.423811	−	0.905751i	$-0.639308\pi$
$521$	−10080.0	−0.847622	−0.423811	+	0.905751i	$0.639308\pi$
$522$	14713.1	1.23367
$523$	8611.69	0.720006	0.360003	−	0.932951i	$-0.382776\pi$
$523$	8611.69	0.720006	0.360003	+	0.932951i	$0.382776\pi$
$524$	5947.20	0.495810
$525$	0	0
$526$	4707.36	0.390211
$527$	5103.49	0.421844
$528$	4788.90	0.394716
$529$	6443.06	0.529552
$530$	−4376.60	−0.358693
$531$	−10925.8	−0.892921
$532$	0	0
$533$	−10268.4	−0.834475
$534$	6664.08	0.540043
$535$	7865.08	0.635583
$536$	457.669	0.0368812
$537$	−128.035	−0.0102888
$538$	14389.4	1.15311
$539$	0	0
$540$	142.364	0.0113452
$541$	5580.89	0.443514	0.221757	−	0.975102i	$-0.428821\pi$
$541$	5580.89	0.443514	0.221757	+	0.975102i	$0.428821\pi$
$542$	−9433.02	−0.747570
$543$	−14897.5	−1.17737
$544$	2988.15	0.235507
$545$	−4572.65	−0.359396
$546$	0	0
$547$	9188.68	0.718244	0.359122	−	0.933291i	$-0.383076\pi$
$547$	9188.68	0.718244	0.359122	+	0.933291i	$0.383076\pi$
$548$	−5426.95	−0.423043
$549$	8421.24	0.654663
$550$	2055.21	0.159335
$551$	−15444.1	−1.19408
$552$	−7946.83	−0.612753
$553$	0	0
$554$	7119.67	0.546003
$555$	−7729.02	−0.591133
$556$	2716.35	0.207192
$557$	2561.10	0.194825	0.0974124	−	0.995244i	$-0.468943\pi$
$557$	2561.10	0.194825	0.0974124	+	0.995244i	$0.468943\pi$
$558$	2844.41	0.215795
$559$	4746.16	0.359108
$560$	0	0
$561$	27949.2	2.10341
$562$	−2725.72	−0.204587
$563$	13354.5	0.999687	0.499843	−	0.866116i	$-0.333391\pi$
$563$	13354.5	0.999687	0.499843	+	0.866116i	$0.333391\pi$
$564$	−3674.32	−0.274320
$565$	−6111.19	−0.455044
$566$	1535.17	0.114007
$567$	0	0
$568$	−8516.39	−0.629119
$569$	−24106.3	−1.77608	−0.888038	−	0.459770i	$-0.847932\pi$
$569$	−24106.3	−1.77608	−0.888038	+	0.459770i	$0.847932\pi$
$570$	3978.01	0.292317
$571$	−17525.7	−1.28446	−0.642230	−	0.766512i	$-0.721991\pi$
$571$	−17525.7	−1.28446	−0.642230	+	0.766512i	$0.721991\pi$
$572$	4042.31	0.295485
$573$	−11037.0	−0.804671
$574$	0	0
$575$	−3410.47	−0.247350
$576$	1665.44	0.120474
$577$	20907.5	1.50848	0.754238	−	0.656601i	$-0.228006\pi$
$577$	20907.5	1.50848	0.754238	+	0.656601i	$0.228006\pi$
$578$	7613.58	0.547895
$579$	−20853.2	−1.49677
$580$	−5654.01	−0.404776
$581$	0	0
$582$	−26778.1	−1.90719
$583$	17989.6	1.27797
$584$	−5497.97	−0.389568
$585$	−3198.91	−0.226083
$586$	−4893.18	−0.344941
$587$	17083.5	1.20121	0.600605	−	0.799546i	$-0.294927\pi$
$587$	17083.5	1.20121	0.600605	+	0.799546i	$0.294927\pi$
$588$	0	0
$589$	−2985.73	−0.208871
$590$	4198.62	0.292974
$591$	−8147.87	−0.567104
$592$	3396.60	0.235810
$593$	5836.79	0.404196	0.202098	−	0.979365i	$-0.435224\pi$
$593$	5836.79	0.404196	0.202098	+	0.979365i	$0.435224\pi$
$594$	−585.177	−0.0404210
$595$	0	0
$596$	10418.9	0.716068
$597$	−24194.4	−1.65865
$598$	−6707.91	−0.458707
$599$	465.568	0.0317572	0.0158786	−	0.999874i	$-0.494945\pi$
$599$	465.568	0.0317572	0.0158786	+	0.999874i	$0.494945\pi$
$600$	1456.33	0.0990907
$601$	11738.0	0.796678	0.398339	−	0.917238i	$-0.369587\pi$
$601$	11738.0	0.796678	0.398339	+	0.917238i	$0.369587\pi$
$602$	0	0
$603$	1488.71	0.100539
$604$	3847.41	0.259187
$605$	−1792.76	−0.120473
$606$	−24005.3	−1.60916
$607$	−4121.44	−0.275591	−0.137796	−	0.990461i	$-0.544002\pi$
$607$	−4121.44	−0.275591	−0.137796	+	0.990461i	$0.544002\pi$
$608$	−1748.18	−0.116609
$609$	0	0
$610$	−3236.15	−0.214799
$611$	−3101.49	−0.205357
$612$	9719.88	0.641998
$613$	17234.6	1.13556	0.567779	−	0.823181i	$-0.307803\pi$
$613$	17234.6	1.13556	0.567779	+	0.823181i	$0.307803\pi$
$614$	10055.6	0.660931
$615$	15206.2	0.997029
$616$	0	0
$617$	−18219.3	−1.18879	−0.594395	−	0.804174i	$-0.702608\pi$
$617$	−18219.3	−1.18879	−0.594395	+	0.804174i	$0.702608\pi$
$618$	−14806.5	−0.963761
$619$	−19448.2	−1.26283	−0.631413	−	0.775447i	$-0.717525\pi$
$619$	−19448.2	−1.26283	−0.631413	+	0.775447i	$0.717525\pi$
$620$	−1093.06	−0.0708039
$621$	971.058	0.0627492
$622$	10852.8	0.699609
$623$	0	0
$624$	2864.40	0.183762
$625$	625.000	0.0400000
$626$	6145.22	0.392352
$627$	−16351.3	−1.04148
$628$	7849.05	0.498744
$629$	19823.4	1.25661
$630$	0	0
$631$	−24510.7	−1.54637	−0.773183	−	0.634183i	$-0.781337\pi$
$631$	−24510.7	−1.54637	−0.773183	+	0.634183i	$0.781337\pi$
$632$	5728.24	0.360534
$633$	−20363.9	−1.27866
$634$	−3466.78	−0.217166
$635$	6784.60	0.423998
$636$	12747.5	0.794769
$637$	0	0
$638$	23240.3	1.44215
$639$	−27702.1	−1.71499
$640$	−640.000	−0.0395285
$641$	12244.3	0.754478	0.377239	−	0.926116i	$-0.376873\pi$
$641$	12244.3	0.754478	0.377239	+	0.926116i	$0.376873\pi$
$642$	−22908.3	−1.40828
$643$	−689.647	−0.0422971	−0.0211485	−	0.999776i	$-0.506732\pi$
$643$	−689.647	−0.0422971	−0.0211485	+	0.999776i	$0.506732\pi$
$644$	0	0
$645$	−7028.44	−0.429061
$646$	−10202.8	−0.621399
$647$	−11457.4	−0.696191	−0.348095	−	0.937459i	$-0.613171\pi$
$647$	−11457.4	−0.696191	−0.348095	+	0.937459i	$0.613171\pi$
$648$	−6035.51	−0.365891
$649$	−17258.1	−1.04382
$650$	1229.29	0.0741794
$651$	0	0
$652$	−9856.59	−0.592046
$653$	−1126.22	−0.0674922	−0.0337461	−	0.999430i	$-0.510744\pi$
$653$	−1126.22	−0.0674922	−0.0337461	+	0.999430i	$0.510744\pi$
$654$	13318.6	0.796326
$655$	−7433.99	−0.443466
$656$	−6682.53	−0.397727
$657$	−17883.8	−1.06197
$658$	0	0
$659$	12717.3	0.751741	0.375870	−	0.926672i	$-0.377344\pi$
$659$	12717.3	0.751741	0.375870	+	0.926672i	$0.377344\pi$
$660$	−5986.12	−0.353045
$661$	4794.08	0.282100	0.141050	−	0.990002i	$-0.454952\pi$
$661$	4794.08	0.282100	0.141050	+	0.990002i	$0.454952\pi$
$662$	−2626.90	−0.154226
$663$	16717.3	0.979255
$664$	−1891.14	−0.110528
$665$	0	0
$666$	11048.5	0.642823
$667$	−38565.6	−2.23878
$668$	13427.1	0.777707
$669$	−5526.61	−0.319389
$670$	−572.086	−0.0329875
$671$	13301.9	0.765297
$672$	0	0
$673$	−6992.05	−0.400481	−0.200240	−	0.979747i	$-0.564172\pi$
$673$	−6992.05	−0.400481	−0.200240	+	0.979747i	$0.564172\pi$
$674$	20166.9	1.15252
$675$	−177.955	−0.0101474
$676$	−6370.16	−0.362435
$677$	−1799.00	−0.102129	−0.0510644	−	0.998695i	$-0.516261\pi$
$677$	−1799.00	−0.102129	−0.0510644	+	0.998695i	$0.516261\pi$
$678$	17799.8	1.00826
$679$	0	0
$680$	−3735.19	−0.210644
$681$	−1409.73	−0.0793261
$682$	4492.94	0.252263
$683$	22666.5	1.26985	0.634925	−	0.772574i	$-0.281031\pi$
$683$	22666.5	1.26985	0.634925	+	0.772574i	$0.281031\pi$
$684$	−5686.49	−0.317878
$685$	6783.69	0.378382
$686$	0	0
$687$	5027.17	0.279183
$688$	3088.72	0.171158
$689$	10760.2	0.594964
$690$	9933.53	0.548063
$691$	−7358.23	−0.405095	−0.202547	−	0.979272i	$-0.564922\pi$
$691$	−7358.23	−0.405095	−0.202547	+	0.979272i	$0.564922\pi$
$692$	−651.394	−0.0357837
$693$	0	0
$694$	23190.1	1.26842
$695$	−3395.44	−0.185318
$696$	16468.2	0.896876
$697$	−39000.8	−2.11946
$698$	−2377.53	−0.128927
$699$	−6628.20	−0.358658
$700$	0	0
$701$	9879.57	0.532306	0.266153	−	0.963931i	$-0.414247\pi$
$701$	9879.57	0.532306	0.266153	+	0.963931i	$0.414247\pi$
$702$	−350.013	−0.0188182
$703$	−11597.4	−0.622197
$704$	2630.67	0.140834
$705$	4592.90	0.245360
$706$	12617.7	0.672626
$707$	0	0
$708$	−12229.2	−0.649153
$709$	9562.75	0.506540	0.253270	−	0.967396i	$-0.418494\pi$
$709$	9562.75	0.506540	0.253270	+	0.967396i	$0.418494\pi$
$710$	10645.5	0.562701
$711$	18632.9	0.982823
$712$	3660.75	0.192686
$713$	−7455.70	−0.391610
$714$	0	0
$715$	−5052.88	−0.264290
$716$	−70.3329	−0.00367104
$717$	39795.0	2.07276
$718$	−17103.2	−0.888978
$719$	9784.30	0.507501	0.253750	−	0.967270i	$-0.418336\pi$
$719$	9784.30	0.507501	0.253750	+	0.967270i	$0.418336\pi$
$720$	−2081.80	−0.107755
$721$	0	0
$722$	−7748.99	−0.399429
$723$	−31078.0	−1.59862
$724$	−8183.59	−0.420084
$725$	7067.51	0.362042
$726$	5221.70	0.266936
$727$	−24810.7	−1.26572	−0.632861	−	0.774266i	$-0.718119\pi$
$727$	−24810.7	−1.26572	−0.632861	+	0.774266i	$0.718119\pi$
$728$	0	0
$729$	−18232.9	−0.926325
$730$	6872.47	0.348440
$731$	18026.5	0.912086
$732$	9425.79	0.475939
$733$	11766.1	0.592893	0.296447	−	0.955049i	$-0.404198\pi$
$733$	11766.1	0.592893	0.296447	+	0.955049i	$0.404198\pi$
$734$	17639.2	0.887022
$735$	0	0
$736$	−4365.40	−0.218629
$737$	2351.51	0.117529
$738$	−21737.0	−1.08421
$739$	−1747.18	−0.0869703	−0.0434851	−	0.999054i	$-0.513846\pi$
$739$	−1747.18	−0.0869703	−0.0434851	+	0.999054i	$0.513846\pi$
$740$	−4245.75	−0.210915
$741$	−9780.24	−0.484867
$742$	0	0
$743$	23037.6	1.13751	0.568753	−	0.822508i	$-0.307426\pi$
$743$	23037.6	1.13751	0.568753	+	0.822508i	$0.307426\pi$
$744$	3183.72	0.156883
$745$	−13023.7	−0.640471
$746$	−4845.16	−0.237793
$747$	−6151.50	−0.301301
$748$	15353.2	0.750493
$749$	0	0
$750$	−1820.41	−0.0886294
$751$	−34234.1	−1.66341	−0.831705	−	0.555218i	$-0.812635\pi$
$751$	−34234.1	−1.66341	−0.831705	+	0.555218i	$0.812635\pi$
$752$	−2018.40	−0.0978769
$753$	12399.8	0.600099
$754$	13900.8	0.671402
$755$	−4809.26	−0.231824
$756$	0	0
$757$	−36791.0	−1.76643	−0.883217	−	0.468964i	$-0.844627\pi$
$757$	−36791.0	−1.76643	−0.883217	+	0.468964i	$0.844627\pi$
$758$	−19901.0	−0.953610
$759$	−40831.0	−1.95266
$760$	2185.23	0.104298
$761$	−18758.4	−0.893552	−0.446776	−	0.894646i	$-0.647428\pi$
$761$	−18758.4	−0.893552	−0.446776	+	0.894646i	$0.647428\pi$
$762$	−19761.2	−0.939467
$763$	0	0
$764$	−6062.90	−0.287105
$765$	−12149.9	−0.574221
$766$	−22575.1	−1.06485
$767$	−10322.6	−0.485956
$768$	1864.10	0.0875847
$769$	−201.237	−0.00943665	−0.00471832	−	0.999989i	$-0.501502\pi$
$769$	−201.237	−0.00943665	−0.00471832	+	0.999989i	$0.501502\pi$
$770$	0	0
$771$	−43259.2	−2.02068
$772$	−11455.2	−0.534043
$773$	−21391.4	−0.995338	−0.497669	−	0.867367i	$-0.665811\pi$
$773$	−21391.4	−0.995338	−0.497669	+	0.867367i	$0.665811\pi$
$774$	10047.0	0.466580
$775$	1366.33	0.0633289
$776$	−14709.9	−0.680483
$777$	0	0
$778$	13074.4	0.602493
$779$	22816.9	1.04942
$780$	−3580.50	−0.164362
$781$	−43757.4	−2.00482
$782$	−25477.5	−1.16506
$783$	−2012.32	−0.0918449
$784$	0	0
$785$	−9811.31	−0.446090
$786$	21652.7	0.982603
$787$	−3767.00	−0.170621	−0.0853106	−	0.996354i	$-0.527188\pi$
$787$	−3767.00	−0.170621	−0.0853106	+	0.996354i	$0.527188\pi$
$788$	−4475.84	−0.202342
$789$	17138.7	0.773325
$790$	−7160.30	−0.322471
$791$	0	0
$792$	8557.05	0.383916
$793$	7956.30	0.356288
$794$	21368.5	0.955086
$795$	−15934.4	−0.710863
$796$	−13290.6	−0.591801
$797$	17338.4	0.770587	0.385293	−	0.922794i	$-0.374100\pi$
$797$	17338.4	0.770587	0.385293	+	0.922794i	$0.374100\pi$
$798$	0	0
$799$	−11779.9	−0.521579
$800$	800.000	0.0353553
$801$	11907.7	0.525266
$802$	8177.48	0.360046
$803$	−28248.7	−1.24144
$804$	1666.29	0.0730916
$805$	0	0
$806$	2687.37	0.117443
$807$	52389.3	2.28524
$808$	−13186.7	−0.574144
$809$	1110.73	0.0482711	0.0241356	−	0.999709i	$-0.492317\pi$
$809$	1110.73	0.0482711	0.0241356	+	0.999709i	$0.492317\pi$
$810$	7544.38	0.327263
$811$	−7784.82	−0.337068	−0.168534	−	0.985696i	$-0.553903\pi$
$811$	−7784.82	−0.337068	−0.168534	+	0.985696i	$0.553903\pi$
$812$	0	0
$813$	−34344.0	−1.48155
$814$	17451.8	0.751457
$815$	12320.7	0.529542
$816$	10879.3	0.466732
$817$	−10546.2	−0.451609
$818$	20368.2	0.870606
$819$	0	0
$820$	8353.16	0.355738
$821$	33642.5	1.43012	0.715062	−	0.699061i	$-0.246398\pi$
$821$	33642.5	1.43012	0.715062	+	0.699061i	$0.246398\pi$
$822$	−19758.6	−0.838394
$823$	−19358.4	−0.819918	−0.409959	−	0.912104i	$-0.634457\pi$
$823$	−19358.4	−0.819918	−0.409959	+	0.912104i	$0.634457\pi$
$824$	−8133.59	−0.343868
$825$	7482.65	0.315773
$826$	0	0
$827$	12660.1	0.532329	0.266165	−	0.963928i	$-0.414244\pi$
$827$	12660.1	0.532329	0.266165	+	0.963928i	$0.414244\pi$
$828$	−14199.8	−0.595987
$829$	−23367.9	−0.979011	−0.489506	−	0.872000i	$-0.662823\pi$
$829$	−23367.9	−0.979011	−0.489506	+	0.872000i	$0.662823\pi$
$830$	2363.92	0.0988589
$831$	25921.5	1.08208
$832$	1573.49	0.0655660
$833$	0	0
$834$	9889.76	0.410617
$835$	−16783.8	−0.695602
$836$	−8982.19	−0.371597
$837$	−389.033	−0.0160656
$838$	−10735.8	−0.442554
$839$	16798.4	0.691234	0.345617	−	0.938376i	$-0.387670\pi$
$839$	16798.4	0.691234	0.345617	+	0.938376i	$0.387670\pi$
$840$	0	0
$841$	55530.5	2.27687
$842$	−13266.6	−0.542990
$843$	−9923.89	−0.405453
$844$	−11186.4	−0.456223
$845$	7962.71	0.324172
$846$	−6565.46	−0.266815
$847$	0	0
$848$	7002.55	0.283572
$849$	5589.27	0.225940
$850$	4668.99	0.188406
$851$	−28960.0	−1.16655
$852$	−31006.7	−1.24680
$853$	−34874.8	−1.39987	−0.699936	−	0.714205i	$-0.746788\pi$
$853$	−34874.8	−1.39987	−0.699936	+	0.714205i	$0.746788\pi$
$854$	0	0
$855$	7108.11	0.284319
$856$	−12584.1	−0.502473
$857$	−18631.7	−0.742644	−0.371322	−	0.928504i	$-0.621095\pi$
$857$	−18631.7	−0.742644	−0.371322	+	0.928504i	$0.621095\pi$
$858$	14717.3	0.585596
$859$	7082.15	0.281304	0.140652	−	0.990059i	$-0.455080\pi$
$859$	7082.15	0.281304	0.140652	+	0.990059i	$0.455080\pi$
$860$	−3860.90	−0.153088
$861$	0	0
$862$	1851.31	0.0731508
$863$	15698.0	0.619196	0.309598	−	0.950867i	$-0.399805\pi$
$863$	15698.0	0.619196	0.309598	+	0.950867i	$0.399805\pi$
$864$	−227.783	−0.00896914
$865$	814.243	0.0320059
$866$	−6328.63	−0.248332
$867$	27719.7	1.08583
$868$	0	0
$869$	29431.8	1.14891
$870$	−20585.3	−0.802190
$871$	1406.52	0.0547164
$872$	7316.24	0.284127
$873$	−47848.4	−1.85501
$874$	14905.3	0.576863
$875$	0	0
$876$	−20017.2	−0.772052
$877$	9135.32	0.351742	0.175871	−	0.984413i	$-0.443726\pi$
$877$	9135.32	0.351742	0.175871	+	0.984413i	$0.443726\pi$
$878$	9279.79	0.356694
$879$	−17815.2	−0.683609
$880$	−3288.33	−0.125966
$881$	−7831.72	−0.299498	−0.149749	−	0.988724i	$-0.547846\pi$
$881$	−7831.72	−0.299498	−0.149749	+	0.988724i	$0.547846\pi$
$882$	0	0
$883$	−1731.92	−0.0660064	−0.0330032	−	0.999455i	$-0.510507\pi$
$883$	−1731.92	−0.0660064	−0.0330032	+	0.999455i	$0.510507\pi$
$884$	9183.25	0.349396
$885$	15286.5	0.580620
$886$	31283.2	1.18621
$887$	4482.85	0.169695	0.0848475	−	0.996394i	$-0.472960\pi$
$887$	4482.85	0.169695	0.0848475	+	0.996394i	$0.472960\pi$
$888$	12366.4	0.467332
$889$	0	0
$890$	−4575.94	−0.172344
$891$	−31010.6	−1.16599
$892$	−3035.91	−0.113957
$893$	6891.65	0.258253
$894$	37933.5	1.41911
$895$	87.9161	0.00328347
$896$	0	0
$897$	−24422.3	−0.909073
$898$	29659.3	1.10216
$899$	15450.4	0.573194
$900$	2602.24	0.0963794
$901$	40868.6	1.51113
$902$	−34335.0	−1.26744
$903$	0	0
$904$	9777.90	0.359743
$905$	10229.5	0.375735
$906$	14007.7	0.513660
$907$	22581.5	0.826687	0.413344	−	0.910575i	$-0.364361\pi$
$907$	22581.5	0.826687	0.413344	+	0.910575i	$0.364361\pi$
$908$	−774.403	−0.0283034
$909$	−42893.9	−1.56513
$910$	0	0
$911$	−7640.75	−0.277881	−0.138940	−	0.990301i	$-0.544370\pi$
$911$	−7640.75	−0.277881	−0.138940	+	0.990301i	$0.544370\pi$
$912$	−6364.82	−0.231097
$913$	−9716.70	−0.352219
$914$	22249.7	0.805203
$915$	−11782.2	−0.425693
$916$	2761.56	0.0996117
$917$	0	0
$918$	−1329.40	−0.0477959
$919$	−22273.6	−0.799497	−0.399748	−	0.916625i	$-0.630902\pi$
$919$	−22273.6	−0.799497	−0.399748	+	0.916625i	$0.630902\pi$
$920$	5456.75	0.195547
$921$	36610.7	1.30984
$922$	17702.1	0.632309
$923$	−26172.7	−0.933354
$924$	0	0
$925$	5307.19	0.188648
$926$	−4962.25	−0.176101
$927$	−26457.0	−0.937391
$928$	9046.41	0.320003
$929$	−8272.45	−0.292153	−0.146077	−	0.989273i	$-0.546665\pi$
$929$	−8272.45	−0.292153	−0.146077	+	0.989273i	$0.546665\pi$
$930$	−3979.65	−0.140320
$931$	0	0
$932$	−3641.04	−0.127968
$933$	39513.1	1.38649
$934$	3722.41	0.130408
$935$	−19191.5	−0.671261
$936$	5118.25	0.178734
$937$	51472.4	1.79459	0.897294	−	0.441433i	$-0.145530\pi$
$937$	51472.4	1.79459	0.897294	+	0.441433i	$0.145530\pi$
$938$	0	0
$939$	22373.7	0.777569
$940$	2523.00	0.0875437
$941$	10032.8	0.347568	0.173784	−	0.984784i	$-0.444401\pi$
$941$	10032.8	0.347568	0.173784	+	0.984784i	$0.444401\pi$
$942$	28577.0	0.988418
$943$	56976.3	1.96756
$944$	−6717.80	−0.231616
$945$	0	0
$946$	15869.9	0.545429
$947$	45353.6	1.55628	0.778138	−	0.628094i	$-0.216165\pi$
$947$	45353.6	1.55628	0.778138	+	0.628094i	$0.216165\pi$
$948$	20855.5	0.714511
$949$	−16896.5	−0.577959
$950$	−2731.53	−0.0932869
$951$	−12621.9	−0.430383
$952$	0	0
$953$	33334.0	1.13305	0.566524	−	0.824045i	$-0.308288\pi$
$953$	33334.0	1.13305	0.566524	+	0.824045i	$0.308288\pi$
$954$	22777.9	0.773022
$955$	7578.63	0.256794
$956$	21860.4	0.739558
$957$	84614.0	2.85808
$958$	−29994.3	−1.01156
$959$	0	0
$960$	−2330.13	−0.0783381
$961$	−26804.0	−0.899736
$962$	10438.5	0.349845
$963$	−40933.7	−1.36975
$964$	−17072.0	−0.570385
$965$	14319.0	0.477663
$966$	0	0
$967$	−1586.10	−0.0527461	−0.0263730	−	0.999652i	$-0.508396\pi$
$967$	−1586.10	−0.0527461	−0.0263730	+	0.999652i	$0.508396\pi$
$968$	2868.42	0.0952421
$969$	−37146.6	−1.23150
$970$	18387.4	0.608642
$971$	11576.6	0.382606	0.191303	−	0.981531i	$-0.438729\pi$
$971$	11576.6	0.382606	0.191303	+	0.981531i	$0.438729\pi$
$972$	−21205.5	−0.699759
$973$	0	0
$974$	−35573.0	−1.17026
$975$	4475.62	0.147010
$976$	5177.83	0.169814
$977$	2736.82	0.0896200	0.0448100	−	0.998996i	$-0.485732\pi$
$977$	2736.82	0.0896200	0.0448100	+	0.998996i	$0.485732\pi$
$978$	−35886.1	−1.17332
$979$	18809.0	0.614034
$980$	0	0
$981$	23798.3	0.774537
$982$	467.321	0.0151861
$983$	45724.9	1.48362	0.741810	−	0.670610i	$-0.233968\pi$
$983$	45724.9	1.48362	0.741810	+	0.670610i	$0.233968\pi$
$984$	−24329.9	−0.788221
$985$	5594.80	0.180980
$986$	52797.0	1.70527
$987$	0	0
$988$	−5372.54	−0.172999
$989$	−26335.0	−0.846717
$990$	−10696.3	−0.343385
$991$	31832.0	1.02036	0.510180	−	0.860068i	$-0.329579\pi$
$991$	31832.0	1.02036	0.510180	+	0.860068i	$0.329579\pi$
$992$	1748.90	0.0559754
$993$	−9564.10	−0.305647
$994$	0	0
$995$	16613.3	0.529323
$996$	−6885.30	−0.219045
$997$	35316.4	1.12185	0.560923	−	0.827868i	$-0.310446\pi$
$997$	35316.4	1.12185	0.560923	+	0.827868i	$0.310446\pi$
$998$	−3388.91	−0.107489
$999$	−1511.11	−0.0478573

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.4.a.v.1.3		3
5.4	even	2		2450.4.a.ce.1.1		3
7.2	even	3		490.4.e.y.361.1		6
7.3	odd	6		70.4.e.e.51.3	yes	6
7.4	even	3		490.4.e.y.471.1		6
7.5	odd	6		70.4.e.e.11.3	✓	6
7.6	odd	2		490.4.a.w.1.1		3
21.5	even	6		630.4.k.r.361.3		6
21.17	even	6		630.4.k.r.541.3		6
28.3	even	6		560.4.q.m.401.1		6
28.19	even	6		560.4.q.m.81.1		6
35.3	even	12		350.4.j.i.149.4		12
35.12	even	12		350.4.j.i.249.4		12
35.17	even	12		350.4.j.i.149.3		12
35.19	odd	6		350.4.e.k.151.1		6
35.24	odd	6		350.4.e.k.51.1		6
35.33	even	12		350.4.j.i.249.3		12
35.34	odd	2		2450.4.a.cb.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.4.e.e.11.3	✓	6	7.5	odd	6
70.4.e.e.51.3	yes	6	7.3	odd	6
350.4.e.k.51.1		6	35.24	odd	6
350.4.e.k.151.1		6	35.19	odd	6
350.4.j.i.149.3		12	35.17	even	12
350.4.j.i.149.4		12	35.3	even	12
350.4.j.i.249.3		12	35.33	even	12
350.4.j.i.249.4		12	35.12	even	12
490.4.a.v.1.3		3	1.1	even	1	trivial
490.4.a.w.1.1		3	7.6	odd	2
490.4.e.y.361.1		6	7.2	even	3
490.4.e.y.471.1		6	7.4	even	3
560.4.q.m.81.1		6	28.19	even	6
560.4.q.m.401.1		6	28.3	even	6
630.4.k.r.361.3		6	21.5	even	6
630.4.k.r.541.3		6	21.17	even	6
2450.4.a.cb.1.3		3	35.34	odd	2
2450.4.a.ce.1.1		3	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)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +7.28165 q^{3} +4.00000 q^{4} -5.00000 q^{5} +14.5633 q^{6} +8.00000 q^{8} +26.0224 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +7.28165 q^{3} +4.00000 q^{4} -5.00000 q^{5} +14.5633 q^{6} +8.00000 q^{8} +26.0224 q^{9} -10.0000 q^{10} +41.1042 q^{11} +29.1266 q^{12} +24.5857 q^{13} -36.4083 q^{15} +16.0000 q^{16} +93.3798 q^{17} +52.0449 q^{18} -54.6306 q^{19} -20.0000 q^{20} +82.2083 q^{22} -136.419 q^{23} +58.2532 q^{24} +25.0000 q^{25} +49.1715 q^{26} -7.11822 q^{27} +282.700 q^{29} -72.8165 q^{30} +54.6531 q^{31} +32.0000 q^{32} +299.306 q^{33} +186.760 q^{34} +104.090 q^{36} +212.288 q^{37} -109.261 q^{38} +179.025 q^{39} -40.0000 q^{40} -417.658 q^{41} +193.045 q^{43} +164.417 q^{44} -130.112 q^{45} -272.837 q^{46} -126.150 q^{47} +116.506 q^{48} +50.0000 q^{50} +679.959 q^{51} +98.3430 q^{52} +437.660 q^{53} -14.2364 q^{54} -205.521 q^{55} -397.801 q^{57} +565.401 q^{58} -419.862 q^{59} -145.633 q^{60} +323.615 q^{61} +109.306 q^{62} +64.0000 q^{64} -122.929 q^{65} +598.612 q^{66} +57.2086 q^{67} +373.519 q^{68} -993.353 q^{69} -1064.55 q^{71} +208.180 q^{72} -687.247 q^{73} +424.575 q^{74} +182.041 q^{75} -218.523 q^{76} +358.050 q^{78} +716.030 q^{79} -80.0000 q^{80} -754.438 q^{81} -835.316 q^{82} -236.392 q^{83} -466.899 q^{85} +386.090 q^{86} +2058.53 q^{87} +328.833 q^{88} +457.594 q^{89} -260.224 q^{90} -545.675 q^{92} +397.965 q^{93} -252.300 q^{94} +273.153 q^{95} +233.013 q^{96} -1838.74 q^{97} +1069.63 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 6 q^{2} - 4 q^{3} + 12 q^{4} - 15 q^{5} - 8 q^{6} + 24 q^{8} + 57 q^{9}+O(q^{10}) \) 3 * q + 6 * q^2 - 4 * q^3 + 12 * q^4 - 15 * q^5 - 8 * q^6 + 24 * q^8 + 57 * q^9	\( 3 q + 6 q^{2} - 4 q^{3} + 12 q^{4} - 15 q^{5} - 8 q^{6} + 24 q^{8} + 57 q^{9} - 30 q^{10} + 41 q^{11} - 16 q^{12} + q^{13} + 20 q^{15} + 48 q^{16} - 30 q^{17} + 114 q^{18} - 49 q^{19} - 60 q^{20} + 82 q^{22} + 145 q^{23} - 32 q^{24} + 75 q^{25} + 2 q^{26} - 118 q^{27} + 268 q^{29} + 40 q^{30} + 28 q^{31} + 96 q^{32} + 626 q^{33} - 60 q^{34} + 228 q^{36} + 813 q^{37} - 98 q^{38} + 114 q^{39} - 120 q^{40} - 313 q^{41} + 360 q^{43} + 164 q^{44} - 285 q^{45} + 290 q^{46} + 977 q^{47} - 64 q^{48} + 150 q^{50} + 1632 q^{51} + 4 q^{52} + 325 q^{53} - 236 q^{54} - 205 q^{55} + 250 q^{57} + 536 q^{58} + 272 q^{59} + 80 q^{60} + 902 q^{61} + 56 q^{62} + 192 q^{64} - 5 q^{65} + 1252 q^{66} - 170 q^{67} - 120 q^{68} - 2264 q^{69} - 1080 q^{71} + 456 q^{72} + 584 q^{73} + 1626 q^{74} - 100 q^{75} - 196 q^{76} + 228 q^{78} - 310 q^{79} - 240 q^{80} + 147 q^{81} - 626 q^{82} - 626 q^{83} + 150 q^{85} + 720 q^{86} + 1846 q^{87} + 328 q^{88} + 400 q^{89} - 570 q^{90} + 580 q^{92} - 372 q^{93} + 1954 q^{94} + 245 q^{95} - 128 q^{96} - 1626 q^{97} - 2611 q^{99}+O(q^{100}) \) 3 * q + 6 * q^2 - 4 * q^3 + 12 * q^4 - 15 * q^5 - 8 * q^6 + 24 * q^8 + 57 * q^9 - 30 * q^10 + 41 * q^11 - 16 * q^12 + q^13 + 20 * q^15 + 48 * q^16 - 30 * q^17 + 114 * q^18 - 49 * q^19 - 60 * q^20 + 82 * q^22 + 145 * q^23 - 32 * q^24 + 75 * q^25 + 2 * q^26 - 118 * q^27 + 268 * q^29 + 40 * q^30 + 28 * q^31 + 96 * q^32 + 626 * q^33 - 60 * q^34 + 228 * q^36 + 813 * q^37 - 98 * q^38 + 114 * q^39 - 120 * q^40 - 313 * q^41 + 360 * q^43 + 164 * q^44 - 285 * q^45 + 290 * q^46 + 977 * q^47 - 64 * q^48 + 150 * q^50 + 1632 * q^51 + 4 * q^52 + 325 * q^53 - 236 * q^54 - 205 * q^55 + 250 * q^57 + 536 * q^58 + 272 * q^59 + 80 * q^60 + 902 * q^61 + 56 * q^62 + 192 * q^64 - 5 * q^65 + 1252 * q^66 - 170 * q^67 - 120 * q^68 - 2264 * q^69 - 1080 * q^71 + 456 * q^72 + 584 * q^73 + 1626 * q^74 - 100 * q^75 - 196 * q^76 + 228 * q^78 - 310 * q^79 - 240 * q^80 + 147 * q^81 - 626 * q^82 - 626 * q^83 + 150 * q^85 + 720 * q^86 + 1846 * q^87 + 328 * q^88 + 400 * q^89 - 570 * q^90 + 580 * q^92 - 372 * q^93 + 1954 * q^94 + 245 * q^95 - 128 * q^96 - 1626 * q^97 - 2611 * q^99

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