LMFDB - Embedded newform 245.4.a.m.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,4,Mod(1,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, 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("245.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	245.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:	$14.4554679514$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 37x^{3} + 21x^{2} + 288x + 64 $ x^5 - x^4 - 37x^3 + 21x^2 + 288*x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 35)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-5.02529$ of defining polynomial
Character	$\chi$	$=$	245.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.02529 q^{2} -8.34382 q^{3} +17.2535 q^{4} -5.00000 q^{5} +41.9301 q^{6} -46.5017 q^{8} +42.6193 q^{9} +O(q^{10})$	\(q-5.02529 q^{2} -8.34382 q^{3} +17.2535 q^{4} -5.00000 q^{5} +41.9301 q^{6} -46.5017 q^{8} +42.6193 q^{9} +25.1265 q^{10} -0.888695 q^{11} -143.960 q^{12} -25.9574 q^{13} +41.7191 q^{15} +95.6563 q^{16} -96.3100 q^{17} -214.174 q^{18} -89.0785 q^{19} -86.2677 q^{20} +4.46595 q^{22} -116.532 q^{23} +388.002 q^{24} +25.0000 q^{25} +130.443 q^{26} -130.325 q^{27} -222.663 q^{29} -209.651 q^{30} -12.9193 q^{31} -108.687 q^{32} +7.41511 q^{33} +483.986 q^{34} +735.334 q^{36} +91.2579 q^{37} +447.645 q^{38} +216.584 q^{39} +232.509 q^{40} -98.4403 q^{41} +392.032 q^{43} -15.3331 q^{44} -213.097 q^{45} +585.606 q^{46} -220.282 q^{47} -798.139 q^{48} -125.632 q^{50} +803.594 q^{51} -447.856 q^{52} -228.703 q^{53} +654.919 q^{54} +4.44347 q^{55} +743.254 q^{57} +1118.95 q^{58} +13.5393 q^{59} +719.802 q^{60} +205.946 q^{61} +64.9233 q^{62} -219.067 q^{64} +129.787 q^{65} -37.2631 q^{66} +325.684 q^{67} -1661.69 q^{68} +972.320 q^{69} -583.883 q^{71} -1981.87 q^{72} -950.353 q^{73} -458.597 q^{74} -208.595 q^{75} -1536.92 q^{76} -1088.40 q^{78} +451.485 q^{79} -478.282 q^{80} -63.3158 q^{81} +494.691 q^{82} +164.928 q^{83} +481.550 q^{85} -1970.07 q^{86} +1857.86 q^{87} +41.3258 q^{88} +884.901 q^{89} +1070.87 q^{90} -2010.59 q^{92} +107.796 q^{93} +1106.98 q^{94} +445.392 q^{95} +906.865 q^{96} +62.1494 q^{97} -37.8756 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} - 8 q^{3} + 35 q^{4} - 25 q^{5} + 16 q^{6} + 33 q^{8} + 81 q^{9}+O(q^{10}) $ 5 * q + q^2 - 8 * q^3 + 35 * q^4 - 25 * q^5 + 16 * q^6 + 33 * q^8 + 81 * q^9	\( 5 q + q^{2} - 8 q^{3} + 35 q^{4} - 25 q^{5} + 16 q^{6} + 33 q^{8} + 81 q^{9} - 5 q^{10} + 47 q^{11} - 98 q^{12} + q^{13} + 40 q^{15} + 171 q^{16} - 2 q^{17} - 51 q^{18} - 21 q^{19} - 175 q^{20} + 523 q^{22} + 201 q^{23} + 848 q^{24} + 125 q^{25} - 47 q^{26} - 518 q^{27} + 190 q^{29} - 80 q^{30} + 388 q^{31} - 95 q^{32} - 262 q^{33} + 130 q^{34} + 1229 q^{36} - 145 q^{37} + 835 q^{38} + 14 q^{39} - 165 q^{40} - 281 q^{41} + 568 q^{43} + 1091 q^{44} - 405 q^{45} + 337 q^{46} - 473 q^{47} + 70 q^{48} + 25 q^{50} + 732 q^{51} - 379 q^{52} + 351 q^{53} - 774 q^{54} - 235 q^{55} + 954 q^{57} + 1818 q^{58} + 708 q^{59} + 490 q^{60} + 1944 q^{61} + 448 q^{62} - 125 q^{64} - 5 q^{65} + 1482 q^{66} + 1118 q^{67} - 3118 q^{68} + 374 q^{69} + 864 q^{71} - 2219 q^{72} - 1652 q^{73} - 3285 q^{74} - 200 q^{75} + 691 q^{76} - 5574 q^{78} + 218 q^{79} - 855 q^{80} - 455 q^{81} + 1027 q^{82} - 1502 q^{83} + 10 q^{85} - 4264 q^{86} + 390 q^{87} + 2131 q^{88} + 2322 q^{89} + 255 q^{90} - 2957 q^{92} - 2288 q^{93} - 2677 q^{94} + 105 q^{95} + 4592 q^{96} + 598 q^{97} + 35 q^{99}+O(q^{100}) \) 5 * q + q^2 - 8 * q^3 + 35 * q^4 - 25 * q^5 + 16 * q^6 + 33 * q^8 + 81 * q^9 - 5 * q^10 + 47 * q^11 - 98 * q^12 + q^13 + 40 * q^15 + 171 * q^16 - 2 * q^17 - 51 * q^18 - 21 * q^19 - 175 * q^20 + 523 * q^22 + 201 * q^23 + 848 * q^24 + 125 * q^25 - 47 * q^26 - 518 * q^27 + 190 * q^29 - 80 * q^30 + 388 * q^31 - 95 * q^32 - 262 * q^33 + 130 * q^34 + 1229 * q^36 - 145 * q^37 + 835 * q^38 + 14 * q^39 - 165 * q^40 - 281 * q^41 + 568 * q^43 + 1091 * q^44 - 405 * q^45 + 337 * q^46 - 473 * q^47 + 70 * q^48 + 25 * q^50 + 732 * q^51 - 379 * q^52 + 351 * q^53 - 774 * q^54 - 235 * q^55 + 954 * q^57 + 1818 * q^58 + 708 * q^59 + 490 * q^60 + 1944 * q^61 + 448 * q^62 - 125 * q^64 - 5 * q^65 + 1482 * q^66 + 1118 * q^67 - 3118 * q^68 + 374 * q^69 + 864 * q^71 - 2219 * q^72 - 1652 * q^73 - 3285 * q^74 - 200 * q^75 + 691 * q^76 - 5574 * q^78 + 218 * q^79 - 855 * q^80 - 455 * q^81 + 1027 * q^82 - 1502 * q^83 + 10 * q^85 - 4264 * q^86 + 390 * q^87 + 2131 * q^88 + 2322 * q^89 + 255 * q^90 - 2957 * q^92 - 2288 * q^93 - 2677 * q^94 + 105 * q^95 + 4592 * q^96 + 598 * q^97 + 35 * 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 $

$2$	−5.02529	−1.77671	−0.888354	−	0.459159i	$-0.848151\pi$
$2$	−5.02529	−1.77671	−0.888354	+	0.459159i	$0.848151\pi$
$3$	−8.34382	−1.60577	−0.802884	−	0.596135i	$-0.796702\pi$
$3$	−8.34382	−1.60577	−0.802884	+	0.596135i	$0.796702\pi$
$4$	17.2535	2.15669
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	41.9301	2.85298
$7$	0	0
$7$	0	0
$8$	−46.5017	−2.05511
$9$	42.6193	1.57849
$10$	25.1265	0.794568
$11$	−0.888695	−0.0243592	−0.0121796	−	0.999926i	$-0.503877\pi$
$11$	−0.888695	−0.0243592	−0.0121796	+	0.999926i	$0.503877\pi$
$12$	−143.960	−3.46315
$13$	−25.9574	−0.553791	−0.276895	−	0.960900i	$-0.589306\pi$
$13$	−25.9574	−0.553791	−0.276895	+	0.960900i	$0.589306\pi$
$14$	0	0
$15$	41.7191	0.718122
$16$	95.6563	1.49463
$17$	−96.3100	−1.37404	−0.687018	−	0.726640i	$-0.741081\pi$
$17$	−96.3100	−1.37404	−0.687018	+	0.726640i	$0.741081\pi$
$18$	−214.174	−2.80452
$19$	−89.0785	−1.07558	−0.537789	−	0.843079i	$-0.680740\pi$
$19$	−89.0785	−1.07558	−0.537789	+	0.843079i	$0.680740\pi$
$20$	−86.2677	−0.964502
$21$	0	0
$22$	4.46595	0.0432793
$23$	−116.532	−1.05646	−0.528230	−	0.849102i	$-0.677144\pi$
$23$	−116.532	−1.05646	−0.528230	+	0.849102i	$0.677144\pi$
$24$	388.002	3.30002
$25$	25.0000	0.200000
$26$	130.443	0.983924
$27$	−130.325	−0.928926
$28$	0	0
$29$	−222.663	−1.42578	−0.712888	−	0.701277i	$-0.752613\pi$
$29$	−222.663	−1.42578	−0.712888	+	0.701277i	$0.752613\pi$
$30$	−209.651	−1.27589
$31$	−12.9193	−0.0748508	−0.0374254	−	0.999299i	$-0.511916\pi$
$31$	−12.9193	−0.0748508	−0.0374254	+	0.999299i	$0.511916\pi$
$32$	−108.687	−0.600417
$33$	7.41511	0.0391153
$34$	483.986	2.44126
$35$	0	0
$36$	735.334	3.40432
$37$	91.2579	0.405478	0.202739	−	0.979233i	$-0.435016\pi$
$37$	91.2579	0.405478	0.202739	+	0.979233i	$0.435016\pi$
$38$	447.645	1.91099
$39$	216.584	0.889259
$40$	232.509	0.919071
$41$	−98.4403	−0.374971	−0.187485	−	0.982267i	$-0.560034\pi$
$41$	−98.4403	−0.374971	−0.187485	+	0.982267i	$0.560034\pi$
$42$	0	0
$43$	392.032	1.39033	0.695166	−	0.718850i	$-0.255331\pi$
$43$	392.032	1.39033	0.695166	+	0.718850i	$0.255331\pi$
$44$	−15.3331	−0.0525354
$45$	−213.097	−0.705924
$46$	585.606	1.87702
$47$	−220.282	−0.683647	−0.341823	−	0.939764i	$-0.611044\pi$
$47$	−220.282	−0.683647	−0.341823	+	0.939764i	$0.611044\pi$
$48$	−798.139	−2.40003
$49$	0	0
$50$	−125.632	−0.355342
$51$	803.594	2.20638
$52$	−447.856	−1.19436
$53$	−228.703	−0.592732	−0.296366	−	0.955074i	$-0.595775\pi$
$53$	−228.703	−0.592732	−0.296366	+	0.955074i	$0.595775\pi$
$54$	654.919	1.65043
$55$	4.44347	0.0108938
$56$	0	0
$57$	743.254	1.72713
$58$	1118.95	2.53319
$59$	13.5393	0.0298756	0.0149378	−	0.999888i	$-0.495245\pi$
$59$	13.5393	0.0298756	0.0149378	+	0.999888i	$0.495245\pi$
$60$	719.802	1.54877
$61$	205.946	0.432273	0.216136	−	0.976363i	$-0.430654\pi$
$61$	205.946	0.432273	0.216136	+	0.976363i	$0.430654\pi$
$62$	64.9233	0.132988
$63$	0	0
$64$	−219.067	−0.427865
$65$	129.787	0.247663
$66$	−37.2631	−0.0694965
$67$	325.684	0.593861	0.296930	−	0.954899i	$-0.404037\pi$
$67$	325.684	0.593861	0.296930	+	0.954899i	$0.404037\pi$
$68$	−1661.69	−2.96337
$69$	972.320	1.69643
$70$	0	0
$71$	−583.883	−0.975975	−0.487987	−	0.872851i	$-0.662269\pi$
$71$	−583.883	−0.975975	−0.487987	+	0.872851i	$0.662269\pi$
$72$	−1981.87	−3.24397
$73$	−950.353	−1.52370	−0.761852	−	0.647751i	$-0.775710\pi$
$73$	−950.353	−1.52370	−0.761852	+	0.647751i	$0.775710\pi$
$74$	−458.597	−0.720417
$75$	−208.595	−0.321154
$76$	−1536.92	−2.31969
$77$	0	0
$78$	−1088.40	−1.57995
$79$	451.485	0.642988	0.321494	−	0.946912i	$-0.395815\pi$
$79$	451.485	0.642988	0.321494	+	0.946912i	$0.395815\pi$
$80$	−478.282	−0.668419
$81$	−63.3158	−0.0868529
$82$	494.691	0.666213
$83$	164.928	0.218111	0.109056	−	0.994036i	$-0.465217\pi$
$83$	164.928	0.218111	0.109056	+	0.994036i	$0.465217\pi$
$84$	0	0
$85$	481.550	0.614488
$86$	−1970.07	−2.47021
$87$	1857.86	2.28947
$88$	41.3258	0.0500608
$89$	884.901	1.05392	0.526962	−	0.849889i	$-0.323331\pi$
$89$	884.901	1.05392	0.526962	+	0.849889i	$0.323331\pi$
$90$	1070.87	1.25422
$91$	0	0
$92$	−2010.59	−2.27846
$93$	107.796	0.120193
$94$	1106.98	1.21464
$95$	445.392	0.481014
$96$	906.865	0.964130
$97$	62.1494	0.0650548	0.0325274	−	0.999471i	$-0.489644\pi$
$97$	62.1494	0.0650548	0.0325274	+	0.999471i	$0.489644\pi$
$98$	0	0
$99$	−37.8756	−0.0384509
$100$	431.339	0.431339
$101$	−562.733	−0.554396	−0.277198	−	0.960813i	$-0.589406\pi$
$101$	−562.733	−0.554396	−0.277198	+	0.960813i	$0.589406\pi$
$102$	−4038.29	−3.92010
$103$	−417.039	−0.398952	−0.199476	−	0.979903i	$-0.563924\pi$
$103$	−417.039	−0.398952	−0.199476	+	0.979903i	$0.563924\pi$
$104$	1207.06	1.13810
$105$	0	0
$106$	1149.30	1.05311
$107$	1979.39	1.78837	0.894183	−	0.447701i	$-0.147757\pi$
$107$	1979.39	1.78837	0.894183	+	0.447701i	$0.147757\pi$
$108$	−2248.56	−2.00341
$109$	1408.40	1.23762	0.618808	−	0.785542i	$-0.287616\pi$
$109$	1408.40	1.23762	0.618808	+	0.785542i	$0.287616\pi$
$110$	−22.3297	−0.0193551
$111$	−761.439	−0.651104
$112$	0	0
$113$	−850.468	−0.708011	−0.354006	−	0.935243i	$-0.615181\pi$
$113$	−850.468	−0.708011	−0.354006	+	0.935243i	$0.615181\pi$
$114$	−3735.07	−3.06861
$115$	582.659	0.472463
$116$	−3841.73	−3.07496
$117$	−1106.28	−0.874154
$118$	−68.0387	−0.0530803
$119$	0	0
$120$	−1940.01	−1.47582
$121$	−1330.21	−0.999407
$122$	−1034.94	−0.768023
$123$	821.368	0.602116
$124$	−222.904	−0.161430
$125$	−125.000	−0.0894427
$126$	0	0
$127$	885.282	0.618552	0.309276	−	0.950972i	$-0.399913\pi$
$127$	885.282	0.618552	0.309276	+	0.950972i	$0.399913\pi$
$128$	1970.37	1.36061
$129$	−3271.04	−2.23255
$130$	−652.216	−0.440024
$131$	1807.09	1.20524	0.602620	−	0.798028i	$-0.294123\pi$
$131$	1807.09	1.20524	0.602620	+	0.798028i	$0.294123\pi$
$132$	127.937	0.0843597
$133$	0	0
$134$	−1636.66	−1.05512
$135$	651.623	0.415428
$136$	4478.58	2.82379
$137$	1931.87	1.20475	0.602374	−	0.798214i	$-0.294222\pi$
$137$	1931.87	1.20475	0.602374	+	0.798214i	$0.294222\pi$
$138$	−4886.19	−3.01406
$139$	2597.93	1.58528	0.792640	−	0.609690i	$-0.208706\pi$
$139$	2597.93	1.58528	0.792640	+	0.609690i	$0.208706\pi$
$140$	0	0
$141$	1837.99	1.09778
$142$	2934.18	1.73402
$143$	23.0682	0.0134899
$144$	4076.81	2.35926
$145$	1113.32	0.637627
$146$	4775.80	2.70718
$147$	0	0
$148$	1574.52	0.874492
$149$	−2923.55	−1.60743	−0.803713	−	0.595017i	$-0.797145\pi$
$149$	−2923.55	−1.60743	−0.803713	+	0.595017i	$0.797145\pi$
$150$	1048.25	0.570597
$151$	265.714	0.143202	0.0716009	−	0.997433i	$-0.477189\pi$
$151$	265.714	0.143202	0.0716009	+	0.997433i	$0.477189\pi$
$152$	4142.30	2.21043
$153$	−4104.67	−2.16891
$154$	0	0
$155$	64.5965	0.0334743
$156$	3736.83	1.91786
$157$	1748.45	0.888798	0.444399	−	0.895829i	$-0.353417\pi$
$157$	1748.45	0.888798	0.444399	+	0.895829i	$0.353417\pi$
$158$	−2268.84	−1.14240
$159$	1908.26	0.951791
$160$	543.435	0.268515
$161$	0	0
$162$	318.180	0.154312
$163$	−3261.20	−1.56710	−0.783548	−	0.621331i	$-0.786592\pi$
$163$	−3261.20	−1.56710	−0.783548	+	0.621331i	$0.786592\pi$
$164$	−1698.44	−0.808696
$165$	−37.0755	−0.0174929
$166$	−828.812	−0.387520
$167$	1244.32	0.576579	0.288289	−	0.957543i	$-0.406914\pi$
$167$	1244.32	0.576579	0.288289	+	0.957543i	$0.406914\pi$
$168$	0	0
$169$	−1523.22	−0.693316
$170$	−2419.93	−1.09177
$171$	−3796.46	−1.69779
$172$	6763.93	2.99852
$173$	3800.34	1.67014	0.835071	−	0.550142i	$-0.185426\pi$
$173$	3800.34	1.67014	0.835071	+	0.550142i	$0.185426\pi$
$174$	−9336.30	−4.06772
$175$	0	0
$176$	−85.0093	−0.0364080
$177$	−112.969	−0.0479733
$178$	−4446.88	−1.87252
$179$	1701.63	0.710534	0.355267	−	0.934765i	$-0.384390\pi$
$179$	1701.63	0.710534	0.355267	+	0.934765i	$0.384390\pi$
$180$	−3676.67	−1.52246
$181$	−2366.84	−0.971966	−0.485983	−	0.873968i	$-0.661538\pi$
$181$	−2366.84	−0.971966	−0.485983	+	0.873968i	$0.661538\pi$
$182$	0	0
$183$	−1718.37	−0.694130
$184$	5418.93	2.17114
$185$	−456.289	−0.181335
$186$	−541.708	−0.213548
$187$	85.5902	0.0334705
$188$	−3800.64	−1.47442
$189$	0	0
$190$	−2238.23	−0.854621
$191$	−2230.48	−0.844982	−0.422491	−	0.906367i	$-0.638844\pi$
$191$	−2230.48	−0.844982	−0.422491	+	0.906367i	$0.638844\pi$
$192$	1827.85	0.687052
$193$	−235.689	−0.0879028	−0.0439514	−	0.999034i	$-0.513995\pi$
$193$	−235.689	−0.0879028	−0.0439514	+	0.999034i	$0.513995\pi$
$194$	−312.319	−0.115583
$195$	−1082.92	−0.397689
$196$	0	0
$197$	3232.17	1.16895	0.584473	−	0.811413i	$-0.301301\pi$
$197$	3232.17	1.16895	0.584473	+	0.811413i	$0.301301\pi$
$198$	190.336	0.0683160
$199$	3792.29	1.35090	0.675448	−	0.737408i	$-0.263950\pi$
$199$	3792.29	1.35090	0.675448	+	0.737408i	$0.263950\pi$
$200$	−1162.54	−0.411021
$201$	−2717.45	−0.953603
$202$	2827.90	0.985000
$203$	0	0
$204$	13864.8	4.75849
$205$	492.201	0.167692
$206$	2095.74	0.708821
$207$	−4966.51	−1.66761
$208$	−2482.99	−0.827712
$209$	79.1636	0.0262003
$210$	0	0
$211$	728.206	0.237591	0.118796	−	0.992919i	$-0.462097\pi$
$211$	728.206	0.237591	0.118796	+	0.992919i	$0.462097\pi$
$212$	−3945.94	−1.27834
$213$	4871.82	1.56719
$214$	−9947.03	−3.17741
$215$	−1960.16	−0.621775
$216$	6060.32	1.90904
$217$	0	0
$218$	−7077.61	−2.19888
$219$	7929.57	2.44672
$220$	76.6657	0.0234945
$221$	2499.95	0.760928
$222$	3826.45	1.15682
$223$	3994.75	1.19959	0.599795	−	0.800154i	$-0.295249\pi$
$223$	3994.75	1.19959	0.599795	+	0.800154i	$0.295249\pi$
$224$	0	0
$225$	1065.48	0.315699
$226$	4273.85	1.25793
$227$	465.315	0.136053	0.0680265	−	0.997684i	$-0.478330\pi$
$227$	465.315	0.136053	0.0680265	+	0.997684i	$0.478330\pi$
$228$	12823.8	3.72489
$229$	−5090.75	−1.46902	−0.734512	−	0.678596i	$-0.762589\pi$
$229$	−5090.75	−1.46902	−0.734512	+	0.678596i	$0.762589\pi$
$230$	−2928.03	−0.839429
$231$	0	0
$232$	10354.2	2.93012
$233$	−1659.26	−0.466530	−0.233265	−	0.972413i	$-0.574941\pi$
$233$	−1659.26	−0.466530	−0.233265	+	0.972413i	$0.574941\pi$
$234$	5559.40	1.55312
$235$	1101.41	0.305736
$236$	233.600	0.0644325
$237$	−3767.11	−1.03249
$238$	0	0
$239$	−1300.53	−0.351983	−0.175992	−	0.984392i	$-0.556313\pi$
$239$	−1300.53	−0.351983	−0.175992	+	0.984392i	$0.556313\pi$
$240$	3990.70	1.07333
$241$	896.001	0.239488	0.119744	−	0.992805i	$-0.461793\pi$
$241$	896.001	0.239488	0.119744	+	0.992805i	$0.461793\pi$
$242$	6684.69	1.77565
$243$	4047.06	1.06839
$244$	3553.29	0.932280
$245$	0	0
$246$	−4127.61	−1.06978
$247$	2312.24	0.595645
$248$	600.770	0.153826
$249$	−1376.13	−0.350236
$250$	628.161	0.158914
$251$	383.031	0.0963216	0.0481608	−	0.998840i	$-0.484664\pi$
$251$	383.031	0.0963216	0.0481608	+	0.998840i	$0.484664\pi$
$252$	0	0
$253$	103.561	0.0257345
$254$	−4448.80	−1.09899
$255$	−4017.97	−0.986725
$256$	−8149.15	−1.98954
$257$	7323.87	1.77763	0.888815	−	0.458267i	$-0.151530\pi$
$257$	7323.87	1.77763	0.888815	+	0.458267i	$0.151530\pi$
$258$	16437.9	3.96659
$259$	0	0
$260$	2239.28	0.534132
$261$	−9489.75	−2.25058
$262$	−9081.17	−2.14136
$263$	−6762.89	−1.58562	−0.792810	−	0.609469i	$-0.791383\pi$
$263$	−6762.89	−1.58562	−0.792810	+	0.609469i	$0.791383\pi$
$264$	−344.815	−0.0803860
$265$	1143.52	0.265078
$266$	0	0
$267$	−7383.45	−1.69236
$268$	5619.21	1.28077
$269$	−1918.70	−0.434888	−0.217444	−	0.976073i	$-0.569772\pi$
$269$	−1918.70	−0.434888	−0.217444	+	0.976073i	$0.569772\pi$
$270$	−3274.60	−0.738095
$271$	1428.96	0.320308	0.160154	−	0.987092i	$-0.448801\pi$
$271$	1428.96	0.320308	0.160154	+	0.987092i	$0.448801\pi$
$272$	−9212.67	−2.05368
$273$	0	0
$274$	−9708.19	−2.14049
$275$	−22.2174	−0.00487185
$276$	16776.0	3.65868
$277$	−6269.22	−1.35986	−0.679930	−	0.733277i	$-0.737990\pi$
$277$	−6269.22	−1.35986	−0.679930	+	0.733277i	$0.737990\pi$
$278$	−13055.4	−2.81658
$279$	−550.612	−0.118152
$280$	0	0
$281$	486.921	0.103371	0.0516856	−	0.998663i	$-0.483541\pi$
$281$	486.921	0.103371	0.0516856	+	0.998663i	$0.483541\pi$
$282$	−9236.44	−1.95043
$283$	6054.15	1.27167	0.635834	−	0.771826i	$-0.280656\pi$
$283$	6054.15	1.27167	0.635834	+	0.771826i	$0.280656\pi$
$284$	−10074.1	−2.10488
$285$	−3716.27	−0.772396
$286$	−115.924	−0.0239676
$287$	0	0
$288$	−4632.17	−0.947753
$289$	4362.62	0.887976
$290$	−5594.74	−1.13288
$291$	−518.563	−0.104463
$292$	−16397.0	−3.28616
$293$	−2506.54	−0.499773	−0.249887	−	0.968275i	$-0.580393\pi$
$293$	−2506.54	−0.499773	−0.249887	+	0.968275i	$0.580393\pi$
$294$	0	0
$295$	−67.6963	−0.0133608
$296$	−4243.65	−0.833301
$297$	115.819	0.0226279
$298$	14691.7	2.85593
$299$	3024.86	0.585057
$300$	−3599.01	−0.692630
$301$	0	0
$302$	−1335.29	−0.254428
$303$	4695.34	0.890232
$304$	−8520.92	−1.60759
$305$	−1029.73	−0.193318
$306$	20627.1	3.85351
$307$	−5201.02	−0.966898	−0.483449	−	0.875372i	$-0.660616\pi$
$307$	−5201.02	−0.966898	−0.483449	+	0.875372i	$0.660616\pi$
$308$	0	0
$309$	3479.70	0.640625
$310$	−324.616	−0.0594741
$311$	−3263.68	−0.595069	−0.297534	−	0.954711i	$-0.596164\pi$
$311$	−3263.68	−0.595069	−0.297534	+	0.954711i	$0.596164\pi$
$312$	−10071.5	−1.82752
$313$	−3986.24	−0.719857	−0.359929	−	0.932980i	$-0.617199\pi$
$313$	−3986.24	−0.719857	−0.359929	+	0.932980i	$0.617199\pi$
$314$	−8786.46	−1.57914
$315$	0	0
$316$	7789.72	1.38673
$317$	−6429.56	−1.13918	−0.569590	−	0.821929i	$-0.692898\pi$
$317$	−6429.56	−1.13918	−0.569590	+	0.821929i	$0.692898\pi$
$318$	−9589.55	−1.69105
$319$	197.880	0.0347308
$320$	1095.33	0.191347
$321$	−16515.7	−2.87170
$322$	0	0
$323$	8579.15	1.47788
$324$	−1092.42	−0.187315
$325$	−648.934	−0.110758
$326$	16388.5	2.78427
$327$	−11751.4	−1.98733
$328$	4577.64	0.770604
$329$	0	0
$330$	186.315	0.0310798
$331$	−5773.29	−0.958696	−0.479348	−	0.877625i	$-0.659127\pi$
$331$	−5773.29	−0.958696	−0.479348	+	0.877625i	$0.659127\pi$
$332$	2845.59	0.470398
$333$	3889.35	0.640045
$334$	−6253.09	−1.02441
$335$	−1628.42	−0.265582
$336$	0	0
$337$	−10674.0	−1.72536	−0.862681	−	0.505748i	$-0.831217\pi$
$337$	−10674.0	−1.72536	−0.862681	+	0.505748i	$0.831217\pi$
$338$	7654.60	1.23182
$339$	7096.15	1.13690
$340$	8308.45	1.32526
$341$	11.4813	0.00182331
$342$	19078.3	3.01648
$343$	0	0
$344$	−18230.1	−2.85728
$345$	−4861.60	−0.758666
$346$	−19097.8	−2.96736
$347$	8501.97	1.31530	0.657651	−	0.753323i	$-0.271550\pi$
$347$	8501.97	1.31530	0.657651	+	0.753323i	$0.271550\pi$
$348$	32054.7	4.93768
$349$	4158.79	0.637865	0.318933	−	0.947777i	$-0.396676\pi$
$349$	4158.79	0.637865	0.318933	+	0.947777i	$0.396676\pi$
$350$	0	0
$351$	3382.89	0.514430
$352$	96.5896	0.0146257
$353$	−5043.63	−0.760469	−0.380234	−	0.924890i	$-0.624157\pi$
$353$	−5043.63	−0.760469	−0.380234	+	0.924890i	$0.624157\pi$
$354$	567.703	0.0852346
$355$	2919.42	0.436469
$356$	15267.7	2.27299
$357$	0	0
$358$	−8551.17	−1.26241
$359$	9501.30	1.39682	0.698412	−	0.715696i	$-0.253890\pi$
$359$	9501.30	1.39682	0.698412	+	0.715696i	$0.253890\pi$
$360$	9909.36	1.45075
$361$	1075.97	0.156870
$362$	11894.1	1.72690
$363$	11099.0	1.60482
$364$	0	0
$365$	4751.77	0.681421
$366$	8635.33	1.23327
$367$	−6606.52	−0.939666	−0.469833	−	0.882755i	$-0.655686\pi$
$367$	−6606.52	−0.939666	−0.469833	+	0.882755i	$0.655686\pi$
$368$	−11147.0	−1.57902
$369$	−4195.46	−0.591888
$370$	2292.99	0.322180
$371$	0	0
$372$	1859.87	0.259220
$373$	−8719.88	−1.21045	−0.605226	−	0.796054i	$-0.706917\pi$
$373$	−8719.88	−1.21045	−0.605226	+	0.796054i	$0.706917\pi$
$374$	−430.116	−0.0594673
$375$	1042.98	0.143624
$376$	10243.5	1.40497
$377$	5779.75	0.789582
$378$	0	0
$379$	11457.2	1.55281	0.776405	−	0.630235i	$-0.217041\pi$
$379$	11457.2	1.55281	0.776405	+	0.630235i	$0.217041\pi$
$380$	7684.59	1.03740
$381$	−7386.63	−0.993251
$382$	11208.8	1.50129
$383$	−4797.61	−0.640069	−0.320034	−	0.947406i	$-0.603694\pi$
$383$	−4797.61	−0.640069	−0.320034	+	0.947406i	$0.603694\pi$
$384$	−16440.4	−2.18482
$385$	0	0
$386$	1184.40	0.156178
$387$	16708.1	2.19463
$388$	1072.30	0.140303
$389$	390.521	0.0509003	0.0254501	−	0.999676i	$-0.491898\pi$
$389$	390.521	0.0509003	0.0254501	+	0.999676i	$0.491898\pi$
$390$	5441.98	0.706577
$391$	11223.2	1.45161
$392$	0	0
$393$	−15078.1	−1.93534
$394$	−16242.6	−2.07688
$395$	−2257.43	−0.287553
$396$	−653.487	−0.0829267
$397$	15361.7	1.94202	0.971009	−	0.239041i	$-0.0768331\pi$
$397$	15361.7	1.94202	0.971009	+	0.239041i	$0.0768331\pi$
$398$	−19057.3	−2.40015
$399$	0	0
$400$	2391.41	0.298926
$401$	7181.72	0.894359	0.447180	−	0.894444i	$-0.352428\pi$
$401$	7181.72	0.894359	0.447180	+	0.894444i	$0.352428\pi$
$402$	13656.0	1.69427
$403$	335.351	0.0414517
$404$	−9709.14	−1.19566
$405$	316.579	0.0388418
$406$	0	0
$407$	−81.1004	−0.00987714
$408$	−37368.5	−4.53435
$409$	2177.35	0.263235	0.131617	−	0.991301i	$-0.457983\pi$
$409$	2177.35	0.263235	0.131617	+	0.991301i	$0.457983\pi$
$410$	−2473.46	−0.297940
$411$	−16119.1	−1.93455
$412$	−7195.40	−0.860417
$413$	0	0
$414$	24958.1	2.96286
$415$	−824.641	−0.0975422
$416$	2821.23	0.332505
$417$	−21676.7	−2.54559
$418$	−397.820	−0.0465503
$419$	6832.55	0.796639	0.398320	−	0.917247i	$-0.369593\pi$
$419$	6832.55	0.796639	0.398320	+	0.917247i	$0.369593\pi$
$420$	0	0
$421$	2198.26	0.254482	0.127241	−	0.991872i	$-0.459388\pi$
$421$	2198.26	0.254482	0.127241	+	0.991872i	$0.459388\pi$
$422$	−3659.44	−0.422130
$423$	−9388.25	−1.07913
$424$	10635.1	1.21813
$425$	−2407.75	−0.274807
$426$	−24482.3	−2.78444
$427$	0	0
$428$	34151.5	3.85696
$429$	−192.477	−0.0216617
$430$	9850.36	1.10471
$431$	12854.6	1.43663	0.718313	−	0.695720i	$-0.244915\pi$
$431$	12854.6	1.43663	0.718313	+	0.695720i	$0.244915\pi$
$432$	−12466.4	−1.38840
$433$	−4590.69	−0.509502	−0.254751	−	0.967007i	$-0.581993\pi$
$433$	−4590.69	−0.509502	−0.254751	+	0.967007i	$0.581993\pi$
$434$	0	0
$435$	−9289.31	−1.02388
$436$	24299.9	2.66916
$437$	10380.5	1.13631
$438$	−39848.4	−4.34710
$439$	2598.82	0.282540	0.141270	−	0.989971i	$-0.454881\pi$
$439$	2598.82	0.282540	0.141270	+	0.989971i	$0.454881\pi$
$440$	−206.629	−0.0223879
$441$	0	0
$442$	−12563.0	−1.35195
$443$	1708.96	0.183285	0.0916426	−	0.995792i	$-0.470788\pi$
$443$	1708.96	0.183285	0.0916426	+	0.995792i	$0.470788\pi$
$444$	−13137.5	−1.40423
$445$	−4424.50	−0.471329
$446$	−20074.8	−2.13132
$447$	24393.6	2.58115
$448$	0	0
$449$	−1428.21	−0.150115	−0.0750573	−	0.997179i	$-0.523914\pi$
$449$	−1428.21	−0.150115	−0.0750573	+	0.997179i	$0.523914\pi$
$450$	−5354.36	−0.560904
$451$	87.4834	0.00913399
$452$	−14673.6	−1.52696
$453$	−2217.07	−0.229949
$454$	−2338.34	−0.241727
$455$	0	0
$456$	−34562.6	−3.54944
$457$	13802.7	1.41283	0.706417	−	0.707796i	$-0.250310\pi$
$457$	13802.7	1.41283	0.706417	+	0.707796i	$0.250310\pi$
$458$	25582.5	2.61003
$459$	12551.6	1.27638
$460$	10052.9	1.01896
$461$	9698.29	0.979815	0.489907	−	0.871775i	$-0.337031\pi$
$461$	9698.29	0.979815	0.489907	+	0.871775i	$0.337031\pi$
$462$	0	0
$463$	2757.52	0.276788	0.138394	−	0.990377i	$-0.455806\pi$
$463$	2757.52	0.276788	0.138394	+	0.990377i	$0.455806\pi$
$464$	−21299.2	−2.13101
$465$	−538.982	−0.0537520
$466$	8338.24	0.828887
$467$	−5292.92	−0.524469	−0.262235	−	0.965004i	$-0.584459\pi$
$467$	−5292.92	−0.524469	−0.262235	+	0.965004i	$0.584459\pi$
$468$	−19087.3	−1.88528
$469$	0	0
$470$	−5534.90	−0.543204
$471$	−14588.7	−1.42720
$472$	−629.599	−0.0613975
$473$	−348.396	−0.0338674
$474$	18930.8	1.83443
$475$	−2226.96	−0.215116
$476$	0	0
$477$	−9747.18	−0.935624
$478$	6535.52	0.625371
$479$	9319.53	0.888977	0.444489	−	0.895784i	$-0.353385\pi$
$479$	9319.53	0.888977	0.444489	+	0.895784i	$0.353385\pi$
$480$	−4534.32	−0.431172
$481$	−2368.81	−0.224550
$482$	−4502.67	−0.425500
$483$	0	0
$484$	−22950.8	−2.15541
$485$	−310.747	−0.0290934
$486$	−20337.7	−1.89822
$487$	−3499.65	−0.325635	−0.162818	−	0.986656i	$-0.552058\pi$
$487$	−3499.65	−0.325635	−0.162818	+	0.986656i	$0.552058\pi$
$488$	−9576.83	−0.888367
$489$	27210.8	2.51639
$490$	0	0
$491$	−54.5901	−0.00501755	−0.00250877	−	0.999997i	$-0.500799\pi$
$491$	−54.5901	−0.00501755	−0.00250877	+	0.999997i	$0.500799\pi$
$492$	14171.5	1.29858
$493$	21444.7	1.95907
$494$	−11619.7	−1.05829
$495$	189.378	0.0171958
$496$	−1235.81	−0.111874
$497$	0	0
$498$	6915.45	0.622267
$499$	−7930.98	−0.711502	−0.355751	−	0.934581i	$-0.615775\pi$
$499$	−7930.98	−0.711502	−0.355751	+	0.934581i	$0.615775\pi$
$500$	−2156.69	−0.192900
$501$	−10382.4	−0.925852
$502$	−1924.84	−0.171135
$503$	−21662.2	−1.92022	−0.960109	−	0.279625i	$-0.909790\pi$
$503$	−21662.2	−1.92022	−0.960109	+	0.279625i	$0.909790\pi$
$504$	0	0
$505$	2813.66	0.247934
$506$	−520.425	−0.0457228
$507$	12709.4	1.11331
$508$	15274.2	1.33403
$509$	6913.22	0.602010	0.301005	−	0.953623i	$-0.402678\pi$
$509$	6913.22	0.602010	0.301005	+	0.953623i	$0.402678\pi$
$510$	20191.5	1.75312
$511$	0	0
$512$	25188.9	2.17422
$513$	11609.1	0.999133
$514$	−36804.6	−3.15833
$515$	2085.19	0.178417
$516$	−56437.0	−4.81493
$517$	195.763	0.0166531
$518$	0	0
$519$	−31709.4	−2.68186
$520$	−6035.31	−0.508973
$521$	2680.16	0.225374	0.112687	−	0.993631i	$-0.464054\pi$
$521$	2680.16	0.225374	0.112687	+	0.993631i	$0.464054\pi$
$522$	47688.8	3.99862
$523$	835.518	0.0698559	0.0349280	−	0.999390i	$-0.488880\pi$
$523$	835.518	0.0698559	0.0349280	+	0.999390i	$0.488880\pi$
$524$	31178.8	2.59933
$525$	0	0
$526$	33985.5	2.81718
$527$	1244.26	0.102848
$528$	709.302	0.0584629
$529$	1412.67	0.116106
$530$	−5746.50	−0.470966
$531$	577.034	0.0471585
$532$	0	0
$533$	2555.25	0.207655
$534$	37104.0	3.00683
$535$	−9896.97	−0.799782
$536$	−15144.9	−1.22045
$537$	−14198.1	−1.14095
$538$	9642.00	0.772669
$539$	0	0
$540$	11242.8	0.895951
$541$	10319.5	0.820090	0.410045	−	0.912065i	$-0.365513\pi$
$541$	10319.5	0.820090	0.410045	+	0.912065i	$0.365513\pi$
$542$	−7180.96	−0.569093
$543$	19748.5	1.56075
$544$	10467.7	0.824994
$545$	−7042.00	−0.553479
$546$	0	0
$547$	12465.4	0.974373	0.487186	−	0.873298i	$-0.338023\pi$
$547$	12465.4	0.974373	0.487186	+	0.873298i	$0.338023\pi$
$548$	33331.5	2.59827
$549$	8777.27	0.682340
$550$	111.649	0.00865585
$551$	19834.5	1.53354
$552$	−45214.6	−3.48634
$553$	0	0
$554$	31504.7	2.41607
$555$	3807.19	0.291183
$556$	44823.6	3.41896
$557$	−8750.27	−0.665639	−0.332819	−	0.942991i	$-0.608000\pi$
$557$	−8750.27	−0.665639	−0.332819	+	0.942991i	$0.608000\pi$
$558$	2766.98	0.209921
$559$	−10176.1	−0.769952
$560$	0	0
$561$	−714.149	−0.0537458
$562$	−2446.92	−0.183660
$563$	−12033.1	−0.900774	−0.450387	−	0.892833i	$-0.648714\pi$
$563$	−12033.1	−0.900774	−0.450387	+	0.892833i	$0.648714\pi$
$564$	31711.8	2.36757
$565$	4252.34	0.316632
$566$	−30423.9	−2.25938
$567$	0	0
$568$	27151.6	2.00573
$569$	−12824.3	−0.944856	−0.472428	−	0.881369i	$-0.656622\pi$
$569$	−12824.3	−0.944856	−0.472428	+	0.881369i	$0.656622\pi$
$570$	18675.3	1.37232
$571$	−21514.0	−1.57676	−0.788382	−	0.615186i	$-0.789081\pi$
$571$	−21514.0	−1.57676	−0.788382	+	0.615186i	$0.789081\pi$
$572$	398.008	0.0290936
$573$	18610.7	1.35685
$574$	0	0
$575$	−2913.30	−0.211292
$576$	−9336.48	−0.675382
$577$	−9538.51	−0.688203	−0.344102	−	0.938932i	$-0.611816\pi$
$577$	−9538.51	−0.688203	−0.344102	+	0.938932i	$0.611816\pi$
$578$	−21923.5	−1.57767
$579$	1966.54	0.141152
$580$	19208.6	1.37517
$581$	0	0
$582$	2605.93	0.185600
$583$	203.247	0.0144385
$584$	44193.1	3.13137
$585$	5531.42	0.390934
$586$	12596.1	0.887952
$587$	−25729.6	−1.80916	−0.904579	−	0.426306i	$-0.859815\pi$
$587$	−25729.6	−1.80916	−0.904579	+	0.426306i	$0.859815\pi$
$588$	0	0
$589$	1150.83	0.0805080
$590$	340.194	0.0237382
$591$	−26968.6	−1.87706
$592$	8729.39	0.606040
$593$	15379.9	1.06505	0.532526	−	0.846414i	$-0.321243\pi$
$593$	15379.9	1.06505	0.532526	+	0.846414i	$0.321243\pi$
$594$	−582.023	−0.0402032
$595$	0	0
$596$	−50441.6	−3.46672
$597$	−31642.2	−2.16923
$598$	−15200.8	−1.03948
$599$	12267.5	0.836791	0.418395	−	0.908265i	$-0.362593\pi$
$599$	12267.5	0.836791	0.418395	+	0.908265i	$0.362593\pi$
$600$	9700.05	0.660005
$601$	−17025.4	−1.15554	−0.577770	−	0.816200i	$-0.696077\pi$
$601$	−17025.4	−1.15554	−0.577770	+	0.816200i	$0.696077\pi$
$602$	0	0
$603$	13880.4	0.937405
$604$	4584.50	0.308842
$605$	6651.05	0.446948
$606$	−23595.5	−1.58168
$607$	−25674.7	−1.71681	−0.858407	−	0.512970i	$-0.828545\pi$
$607$	−25674.7	−1.71681	−0.858407	+	0.512970i	$0.828545\pi$
$608$	9681.67	0.645796
$609$	0	0
$610$	5174.69	0.343470
$611$	5717.93	0.378597
$612$	−70820.0	−4.67766
$613$	−12436.0	−0.819389	−0.409695	−	0.912223i	$-0.634365\pi$
$613$	−12436.0	−0.819389	−0.409695	+	0.912223i	$0.634365\pi$
$614$	26136.6	1.71790
$615$	−4106.84	−0.269274
$616$	0	0
$617$	9794.06	0.639050	0.319525	−	0.947578i	$-0.396477\pi$
$617$	9794.06	0.639050	0.319525	+	0.947578i	$0.396477\pi$
$618$	−17486.5	−1.13820
$619$	−18198.0	−1.18164	−0.590822	−	0.806802i	$-0.701197\pi$
$619$	−18198.0	−1.18164	−0.590822	+	0.806802i	$0.701197\pi$
$620$	1114.52	0.0721938
$621$	15187.0	0.981372
$622$	16401.0	1.05726
$623$	0	0
$624$	20717.6	1.32911
$625$	625.000	0.0400000
$626$	20032.0	1.27898
$627$	−660.526	−0.0420716
$628$	30166.9	1.91686
$629$	−8789.05	−0.557142
$630$	0	0
$631$	92.7119	0.00584914	0.00292457	−	0.999996i	$-0.499069\pi$
$631$	92.7119	0.00584914	0.00292457	+	0.999996i	$0.499069\pi$
$632$	−20994.8	−1.32141
$633$	−6076.02	−0.381516
$634$	32310.4	2.02399
$635$	−4426.41	−0.276625
$636$	32924.2	2.05272
$637$	0	0
$638$	−994.403	−0.0617066
$639$	−24884.7	−1.54057
$640$	−9851.85	−0.608482
$641$	12888.6	0.794179	0.397090	−	0.917780i	$-0.370020\pi$
$641$	12888.6	0.794179	0.397090	+	0.917780i	$0.370020\pi$
$642$	82996.2	5.10218
$643$	24478.5	1.50130	0.750651	−	0.660699i	$-0.229740\pi$
$643$	24478.5	1.50130	0.750651	+	0.660699i	$0.229740\pi$
$644$	0	0
$645$	16355.2	0.998427
$646$	−43112.7	−2.62577
$647$	6675.03	0.405599	0.202799	−	0.979220i	$-0.434996\pi$
$647$	6675.03	0.405599	0.202799	+	0.979220i	$0.434996\pi$
$648$	2944.29	0.178492
$649$	−12.0323	−0.000727747 0
$650$	3261.08	0.196785
$651$	0	0
$652$	−56267.2	−3.37974
$653$	2382.08	0.142753	0.0713767	−	0.997449i	$-0.477261\pi$
$653$	2382.08	0.142753	0.0713767	+	0.997449i	$0.477261\pi$
$654$	59054.3	3.53090
$655$	−9035.47	−0.539000
$656$	−9416.44	−0.560442
$657$	−40503.4	−2.40516
$658$	0	0
$659$	−384.150	−0.0227077	−0.0113538	−	0.999936i	$-0.503614\pi$
$659$	−384.150	−0.0227077	−0.0113538	+	0.999936i	$0.503614\pi$
$660$	−639.684	−0.0377268
$661$	29320.5	1.72532	0.862660	−	0.505784i	$-0.168797\pi$
$661$	29320.5	1.72532	0.862660	+	0.505784i	$0.168797\pi$
$662$	29012.4	1.70332
$663$	−20859.2	−1.22187
$664$	−7669.44	−0.448241
$665$	0	0
$666$	−19545.1	−1.13717
$667$	25947.4	1.50628
$668$	21469.0	1.24350
$669$	−33331.5	−1.92626
$670$	8183.29	0.471863
$671$	−183.023	−0.0105298
$672$	0	0
$673$	−24841.9	−1.42286	−0.711431	−	0.702756i	$-0.751952\pi$
$673$	−24841.9	−1.42286	−0.711431	+	0.702756i	$0.751952\pi$
$674$	53639.7	3.06547
$675$	−3258.12	−0.185785
$676$	−26280.9	−1.49527
$677$	−483.632	−0.0274556	−0.0137278	−	0.999906i	$-0.504370\pi$
$677$	−483.632	−0.0274556	−0.0137278	+	0.999906i	$0.504370\pi$
$678$	−35660.2	−2.01994
$679$	0	0
$680$	−22392.9	−1.26284
$681$	−3882.50	−0.218470
$682$	−57.6970	−0.00323949
$683$	−6436.97	−0.360620	−0.180310	−	0.983610i	$-0.557710\pi$
$683$	−6436.97	−0.360620	−0.180310	+	0.983610i	$0.557710\pi$
$684$	−65502.4	−3.66162
$685$	−9659.33	−0.538780
$686$	0	0
$687$	42476.3	2.35891
$688$	37500.3	2.07803
$689$	5936.53	0.328250
$690$	24431.0	1.34793
$691$	−17783.5	−0.979042	−0.489521	−	0.871992i	$-0.662828\pi$
$691$	−17783.5	−0.979042	−0.489521	+	0.871992i	$0.662828\pi$
$692$	65569.4	3.60198
$693$	0	0
$694$	−42724.9	−2.33691
$695$	−12989.7	−0.708959
$696$	−86393.8	−4.70510
$697$	9480.79	0.515223
$698$	−20899.1	−1.13330
$699$	13844.5	0.749139
$700$	0	0
$701$	23546.2	1.26866	0.634328	−	0.773064i	$-0.281277\pi$
$701$	23546.2	1.26866	0.634328	+	0.773064i	$0.281277\pi$
$702$	−17000.0	−0.913993
$703$	−8129.11	−0.436124
$704$	194.684	0.0104225
$705$	−9189.95	−0.490941
$706$	25345.7	1.35113
$707$	0	0
$708$	−1949.12	−0.103464
$709$	−23563.8	−1.24818	−0.624088	−	0.781354i	$-0.714529\pi$
$709$	−23563.8	−1.24818	−0.624088	+	0.781354i	$0.714529\pi$
$710$	−14670.9	−0.775478
$711$	19242.0	1.01495
$712$	−41149.4	−2.16593
$713$	1505.51	0.0790769
$714$	0	0
$715$	−115.341	−0.00603287
$716$	29359.1	1.53240
$717$	10851.3	0.565204
$718$	−47746.8	−2.48175
$719$	25106.5	1.30224	0.651122	−	0.758973i	$-0.274299\pi$
$719$	25106.5	1.30224	0.651122	+	0.758973i	$0.274299\pi$
$720$	−20384.0	−1.05509
$721$	0	0
$722$	−5407.07	−0.278712
$723$	−7476.07	−0.384562
$724$	−40836.4	−2.09623
$725$	−5566.58	−0.285155
$726$	−55775.9	−2.85129
$727$	−20502.4	−1.04593	−0.522965	−	0.852354i	$-0.675174\pi$
$727$	−20502.4	−1.04593	−0.522965	+	0.852354i	$0.675174\pi$
$728$	0	0
$729$	−32058.4	−1.62874
$730$	−23879.0	−1.21069
$731$	−37756.6	−1.91037
$732$	−29648.0	−1.49703
$733$	9984.38	0.503112	0.251556	−	0.967843i	$-0.419058\pi$
$733$	9984.38	0.503112	0.251556	+	0.967843i	$0.419058\pi$
$734$	33199.7	1.66951
$735$	0	0
$736$	12665.5	0.634316
$737$	−289.434	−0.0144660
$738$	21083.4	1.05161
$739$	−20692.0	−1.03000	−0.514999	−	0.857191i	$-0.672208\pi$
$739$	−20692.0	−1.03000	−0.514999	+	0.857191i	$0.672208\pi$
$740$	−7872.61	−0.391085
$741$	−19292.9	−0.956469
$742$	0	0
$743$	4015.42	0.198266	0.0991330	−	0.995074i	$-0.468393\pi$
$743$	4015.42	0.198266	0.0991330	+	0.995074i	$0.468393\pi$
$744$	−5012.72	−0.247010
$745$	14617.7	0.718863
$746$	43819.9	2.15062
$747$	7029.12	0.344287
$748$	1476.73	0.0721855
$749$	0	0
$750$	−5241.26	−0.255179
$751$	19406.6	0.942950	0.471475	−	0.881879i	$-0.343722\pi$
$751$	19406.6	0.942950	0.471475	+	0.881879i	$0.343722\pi$
$752$	−21071.3	−1.02180
$753$	−3195.94	−0.154670
$754$	−29044.9	−1.40286
$755$	−1328.57	−0.0640418
$756$	0	0
$757$	−14626.8	−0.702274	−0.351137	−	0.936324i	$-0.614205\pi$
$757$	−14626.8	−0.702274	−0.351137	+	0.936324i	$0.614205\pi$
$758$	−57575.6	−2.75889
$759$	−864.096	−0.0413237
$760$	−20711.5	−0.988533
$761$	−22296.4	−1.06208	−0.531040	−	0.847347i	$-0.678199\pi$
$761$	−22296.4	−1.06208	−0.531040	+	0.847347i	$0.678199\pi$
$762$	37120.0	1.76472
$763$	0	0
$764$	−38483.6	−1.82237
$765$	20523.3	0.969964
$766$	24109.4	1.13722
$767$	−351.443	−0.0165448
$768$	67995.0	3.19474
$769$	−8658.29	−0.406015	−0.203008	−	0.979177i	$-0.565072\pi$
$769$	−8658.29	−0.406015	−0.203008	+	0.979177i	$0.565072\pi$
$770$	0	0
$771$	−61109.1	−2.85446
$772$	−4066.46	−0.189579
$773$	4583.16	0.213253	0.106627	−	0.994299i	$-0.465995\pi$
$773$	4583.16	0.213253	0.106627	+	0.994299i	$0.465995\pi$
$774$	−83963.1	−3.89921
$775$	−322.983	−0.0149702
$776$	−2890.05	−0.133694
$777$	0	0
$778$	−1962.48	−0.0904350
$779$	8768.91	0.403310
$780$	−18684.2	−0.857693
$781$	518.894	0.0237740
$782$	−56399.8	−2.57909
$783$	29018.5	1.32444
$784$	0	0
$785$	−8742.24	−0.397483
$786$	75771.6	3.43853
$787$	21374.1	0.968111	0.484055	−	0.875037i	$-0.339163\pi$
$787$	21374.1	0.968111	0.484055	+	0.875037i	$0.339163\pi$
$788$	55766.3	2.52106
$789$	56428.4	2.54614
$790$	11344.2	0.510898
$791$	0	0
$792$	1761.28	0.0790206
$793$	−5345.81	−0.239389
$794$	−77197.0	−3.45040
$795$	−9541.29	−0.425654
$796$	65430.4	2.91347
$797$	13930.6	0.619131	0.309565	−	0.950878i	$-0.399816\pi$
$797$	13930.6	0.619131	0.309565	+	0.950878i	$0.399816\pi$
$798$	0	0
$799$	21215.3	0.939355
$800$	−2717.18	−0.120083
$801$	37713.9	1.66361
$802$	−36090.2	−1.58902
$803$	844.574	0.0371163
$804$	−46885.6	−2.05663
$805$	0	0
$806$	−1685.24	−0.0736476
$807$	16009.2	0.698330
$808$	26168.1	1.13934
$809$	23831.6	1.03569	0.517845	−	0.855475i	$-0.326734\pi$
$809$	23831.6	1.03569	0.517845	+	0.855475i	$0.326734\pi$
$810$	−1590.90	−0.0690106
$811$	14512.4	0.628358	0.314179	−	0.949364i	$-0.398271\pi$
$811$	14512.4	0.628358	0.314179	+	0.949364i	$0.398271\pi$
$812$	0	0
$813$	−11923.0	−0.514340
$814$	407.553	0.0175488
$815$	16306.0	0.700827
$816$	76868.8	3.29773
$817$	−34921.6	−1.49541
$818$	−10941.8	−0.467692
$819$	0	0
$820$	8492.22	0.361660
$821$	−395.767	−0.0168238	−0.00841191	−	0.999965i	$-0.502678\pi$
$821$	−395.767	−0.0168238	−0.00841191	+	0.999965i	$0.502678\pi$
$822$	81003.4	3.43712
$823$	17250.2	0.730625	0.365312	−	0.930885i	$-0.380962\pi$
$823$	17250.2	0.730625	0.365312	+	0.930885i	$0.380962\pi$
$824$	19393.0	0.819888
$825$	185.378	0.00782306
$826$	0	0
$827$	43760.3	1.84002	0.920009	−	0.391897i	$-0.128181\pi$
$827$	43760.3	1.84002	0.920009	+	0.391897i	$0.128181\pi$
$828$	−85689.8	−3.59653
$829$	15250.8	0.638939	0.319470	−	0.947597i	$-0.396495\pi$
$829$	15250.8	0.638939	0.319470	+	0.947597i	$0.396495\pi$
$830$	4144.06	0.173304
$831$	52309.3	2.18362
$832$	5686.40	0.236948
$833$	0	0
$834$	108932.	4.52278
$835$	−6221.62	−0.257854
$836$	1365.85	0.0565059
$837$	1683.70	0.0695309
$838$	−34335.5	−1.41540
$839$	−15948.9	−0.656276	−0.328138	−	0.944630i	$-0.606421\pi$
$839$	−15948.9	−0.656276	−0.328138	+	0.944630i	$0.606421\pi$
$840$	0	0
$841$	25189.9	1.03284
$842$	−11046.9	−0.452140
$843$	−4062.78	−0.165990
$844$	12564.1	0.512411
$845$	7616.08	0.310060
$846$	47178.7	1.91730
$847$	0	0
$848$	−21876.9	−0.885916
$849$	−50514.8	−2.04200
$850$	12099.6	0.488252
$851$	−10634.4	−0.428371
$852$	84056.1	3.37995
$853$	−18372.1	−0.737456	−0.368728	−	0.929537i	$-0.620207\pi$
$853$	−18372.1	−0.737456	−0.368728	+	0.929537i	$0.620207\pi$
$854$	0	0
$855$	18982.3	0.759276
$856$	−92045.2	−3.67528
$857$	−45484.2	−1.81296	−0.906482	−	0.422244i	$-0.861242\pi$
$857$	−45484.2	−1.81296	−0.906482	+	0.422244i	$0.861242\pi$
$858$	967.251	0.0384865
$859$	−35623.5	−1.41497	−0.707485	−	0.706728i	$-0.750170\pi$
$859$	−35623.5	−1.41497	−0.707485	+	0.706728i	$0.750170\pi$
$860$	−33819.7	−1.34098
$861$	0	0
$862$	−64598.3	−2.55247
$863$	7274.95	0.286955	0.143478	−	0.989654i	$-0.454172\pi$
$863$	7274.95	0.286955	0.143478	+	0.989654i	$0.454172\pi$
$864$	14164.6	0.557743
$865$	−19001.7	−0.746911
$866$	23069.5	0.905236
$867$	−36400.9	−1.42588
$868$	0	0
$869$	−401.233	−0.0156627
$870$	46681.5	1.81914
$871$	−8453.90	−0.328874
$872$	−65493.0	−2.54343
$873$	2648.76	0.102688
$874$	−52164.9	−2.01888
$875$	0	0
$876$	136813.	5.27682
$877$	20656.4	0.795345	0.397672	−	0.917527i	$-0.369818\pi$
$877$	20656.4	0.795345	0.397672	+	0.917527i	$0.369818\pi$
$878$	−13059.8	−0.501990
$879$	20914.1	0.802520
$880$	425.046	0.0162822
$881$	13163.2	0.503383	0.251691	−	0.967808i	$-0.419013\pi$
$881$	13163.2	0.503383	0.251691	+	0.967808i	$0.419013\pi$
$882$	0	0
$883$	−1426.38	−0.0543620	−0.0271810	−	0.999631i	$-0.508653\pi$
$883$	−1426.38	−0.0543620	−0.0271810	+	0.999631i	$0.508653\pi$
$884$	43133.1	1.64109
$885$	564.846	0.0214543
$886$	−8588.04	−0.325644
$887$	36168.2	1.36912	0.684560	−	0.728957i	$-0.259994\pi$
$887$	36168.2	1.36912	0.684560	+	0.728957i	$0.259994\pi$
$888$	35408.2	1.33809
$889$	0	0
$890$	22234.4	0.837415
$891$	56.2684	0.00211567
$892$	68923.6	2.58715
$893$	19622.4	0.735316
$894$	−122585.	−4.58596
$895$	−8508.14	−0.317761
$896$	0	0
$897$	−25238.9	−0.939466
$898$	7177.17	0.266710
$899$	2876.66	0.106721
$900$	18383.3	0.680865
$901$	22026.4	0.814436
$902$	−439.629	−0.0162284
$903$	0	0
$904$	39548.2	1.45504
$905$	11834.2	0.434676
$906$	11141.4	0.408552
$907$	212.271	0.00777105	0.00388552	−	0.999992i	$-0.498763\pi$
$907$	212.271	0.00777105	0.00388552	+	0.999992i	$0.498763\pi$
$908$	8028.33	0.293425
$909$	−23983.3	−0.875111
$910$	0	0
$911$	−36810.6	−1.33874	−0.669369	−	0.742930i	$-0.733436\pi$
$911$	−36810.6	−1.33874	−0.669369	+	0.742930i	$0.733436\pi$
$912$	71097.0	2.58142
$913$	−146.571	−0.00531302
$914$	−69362.8	−2.51019
$915$	8591.87	0.310425
$916$	−87833.5	−3.16823
$917$	0	0
$918$	−63075.3	−2.26775
$919$	32727.7	1.17474	0.587371	−	0.809318i	$-0.300163\pi$
$919$	32727.7	1.17474	0.587371	+	0.809318i	$0.300163\pi$
$920$	−27094.7	−0.970961
$921$	43396.3	1.55261
$922$	−48736.7	−1.74084
$923$	15156.1	0.540486
$924$	0	0
$925$	2281.45	0.0810957
$926$	−13857.3	−0.491771
$927$	−17773.9	−0.629743
$928$	24200.6	0.856060
$929$	−6359.40	−0.224591	−0.112296	−	0.993675i	$-0.535820\pi$
$929$	−6359.40	−0.224591	−0.112296	+	0.993675i	$0.535820\pi$
$930$	2708.54	0.0955016
$931$	0	0
$932$	−28628.0	−1.00616
$933$	27231.6	0.955543
$934$	26598.5	0.931829
$935$	−427.951	−0.0149684
$936$	51444.2	1.79648
$937$	29540.8	1.02994	0.514971	−	0.857208i	$-0.327803\pi$
$937$	29540.8	1.02994	0.514971	+	0.857208i	$0.327803\pi$
$938$	0	0
$939$	33260.4	1.15592
$940$	19003.2	0.659379
$941$	−19002.1	−0.658291	−0.329145	−	0.944279i	$-0.606761\pi$
$941$	−19002.1	−0.658291	−0.329145	+	0.944279i	$0.606761\pi$
$942$	73312.6	2.53573
$943$	11471.4	0.396141
$944$	1295.12	0.0446530
$945$	0	0
$946$	1750.79	0.0601725
$947$	21320.8	0.731609	0.365804	−	0.930692i	$-0.380794\pi$
$947$	21320.8	0.731609	0.365804	+	0.930692i	$0.380794\pi$
$948$	−64996.0	−2.22676
$949$	24668.7	0.843813
$950$	11191.1	0.382198
$951$	53647.1	1.82926
$952$	0	0
$953$	16523.3	0.561640	0.280820	−	0.959760i	$-0.409394\pi$
$953$	16523.3	0.561640	0.280820	+	0.959760i	$0.409394\pi$
$954$	48982.4	1.66233
$955$	11152.4	0.377888
$956$	−22438.7	−0.759120
$957$	−1651.07	−0.0557697
$958$	−46833.3	−1.57945
$959$	0	0
$960$	−9139.27	−0.307259
$961$	−29624.1	−0.994397
$962$	11904.0	0.398960
$963$	84360.4	2.82292
$964$	15459.2	0.516501
$965$	1178.44	0.0393113
$966$	0	0
$967$	11517.9	0.383031	0.191515	−	0.981490i	$-0.438660\pi$
$967$	11517.9	0.383031	0.191515	+	0.981490i	$0.438660\pi$
$968$	61857.1	2.05389
$969$	−71582.9	−2.37314
$970$	1561.59	0.0516904
$971$	−20328.0	−0.671838	−0.335919	−	0.941891i	$-0.609047\pi$
$971$	−20328.0	−0.671838	−0.335919	+	0.941891i	$0.609047\pi$
$972$	69826.1	2.30419
$973$	0	0
$974$	17586.8	0.578559
$975$	5414.59	0.177852
$976$	19700.0	0.646088
$977$	−2142.66	−0.0701635	−0.0350817	−	0.999384i	$-0.511169\pi$
$977$	−2142.66	−0.0701635	−0.0350817	+	0.999384i	$0.511169\pi$
$978$	−136742.	−4.47090
$979$	−786.407	−0.0256728
$980$	0	0
$981$	60025.0	1.95357
$982$	274.331	0.00891472
$983$	−23277.0	−0.755260	−0.377630	−	0.925957i	$-0.623261\pi$
$983$	−23277.0	−0.755260	−0.377630	+	0.925957i	$0.623261\pi$
$984$	−38195.0	−1.23741
$985$	−16160.8	−0.522769
$986$	−107766.	−3.48069
$987$	0	0
$988$	39894.4	1.28462
$989$	−45684.2	−1.46883
$990$	−951.678	−0.0305518
$991$	7542.57	0.241774	0.120887	−	0.992666i	$-0.461426\pi$
$991$	7542.57	0.241774	0.120887	+	0.992666i	$0.461426\pi$
$992$	1404.16	0.0449417
$993$	48171.2	1.53944
$994$	0	0
$995$	−18961.4	−0.604139
$996$	−23743.1	−0.755351
$997$	−48108.9	−1.52821	−0.764104	−	0.645093i	$-0.776819\pi$
$997$	−48108.9	−1.52821	−0.764104	+	0.645093i	$0.776819\pi$
$998$	39855.5	1.26413
$999$	−11893.2	−0.376659

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.a.m.1.1		5
3.2	odd	2		2205.4.a.bu.1.5		5
5.4	even	2		1225.4.a.bg.1.5		5
7.2	even	3		35.4.e.c.11.5	✓	10
7.3	odd	6		245.4.e.o.226.5		10
7.4	even	3		35.4.e.c.16.5	yes	10
7.5	odd	6		245.4.e.o.116.5		10
7.6	odd	2		245.4.a.n.1.1		5
21.2	odd	6		315.4.j.g.46.1		10
21.11	odd	6		315.4.j.g.226.1		10
21.20	even	2		2205.4.a.bt.1.5		5
28.11	odd	6		560.4.q.n.401.2		10
28.23	odd	6		560.4.q.n.81.2		10
35.2	odd	12		175.4.k.d.74.2		20
35.4	even	6		175.4.e.d.51.1		10
35.9	even	6		175.4.e.d.151.1		10
35.18	odd	12		175.4.k.d.149.2		20
35.23	odd	12		175.4.k.d.74.9		20
35.32	odd	12		175.4.k.d.149.9		20
35.34	odd	2		1225.4.a.bf.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.e.c.11.5	✓	10	7.2	even	3
35.4.e.c.16.5	yes	10	7.4	even	3
175.4.e.d.51.1		10	35.4	even	6
175.4.e.d.151.1		10	35.9	even	6
175.4.k.d.74.2		20	35.2	odd	12
175.4.k.d.74.9		20	35.23	odd	12
175.4.k.d.149.2		20	35.18	odd	12
175.4.k.d.149.9		20	35.32	odd	12
245.4.a.m.1.1		5	1.1	even	1	trivial
245.4.a.n.1.1		5	7.6	odd	2
245.4.e.o.116.5		10	7.5	odd	6
245.4.e.o.226.5		10	7.3	odd	6
315.4.j.g.46.1		10	21.2	odd	6
315.4.j.g.226.1		10	21.11	odd	6
560.4.q.n.81.2		10	28.23	odd	6
560.4.q.n.401.2		10	28.11	odd	6
1225.4.a.bf.1.5		5	35.34	odd	2
1225.4.a.bg.1.5		5	5.4	even	2
2205.4.a.bt.1.5		5	21.20	even	2
2205.4.a.bu.1.5		5	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	245.a (trivial)

\(f(q)\)	\(=\)	\(q-5.02529 q^{2} -8.34382 q^{3} +17.2535 q^{4} -5.00000 q^{5} +41.9301 q^{6} -46.5017 q^{8} +42.6193 q^{9} +O(q^{10})\)	\(q-5.02529 q^{2} -8.34382 q^{3} +17.2535 q^{4} -5.00000 q^{5} +41.9301 q^{6} -46.5017 q^{8} +42.6193 q^{9} +25.1265 q^{10} -0.888695 q^{11} -143.960 q^{12} -25.9574 q^{13} +41.7191 q^{15} +95.6563 q^{16} -96.3100 q^{17} -214.174 q^{18} -89.0785 q^{19} -86.2677 q^{20} +4.46595 q^{22} -116.532 q^{23} +388.002 q^{24} +25.0000 q^{25} +130.443 q^{26} -130.325 q^{27} -222.663 q^{29} -209.651 q^{30} -12.9193 q^{31} -108.687 q^{32} +7.41511 q^{33} +483.986 q^{34} +735.334 q^{36} +91.2579 q^{37} +447.645 q^{38} +216.584 q^{39} +232.509 q^{40} -98.4403 q^{41} +392.032 q^{43} -15.3331 q^{44} -213.097 q^{45} +585.606 q^{46} -220.282 q^{47} -798.139 q^{48} -125.632 q^{50} +803.594 q^{51} -447.856 q^{52} -228.703 q^{53} +654.919 q^{54} +4.44347 q^{55} +743.254 q^{57} +1118.95 q^{58} +13.5393 q^{59} +719.802 q^{60} +205.946 q^{61} +64.9233 q^{62} -219.067 q^{64} +129.787 q^{65} -37.2631 q^{66} +325.684 q^{67} -1661.69 q^{68} +972.320 q^{69} -583.883 q^{71} -1981.87 q^{72} -950.353 q^{73} -458.597 q^{74} -208.595 q^{75} -1536.92 q^{76} -1088.40 q^{78} +451.485 q^{79} -478.282 q^{80} -63.3158 q^{81} +494.691 q^{82} +164.928 q^{83} +481.550 q^{85} -1970.07 q^{86} +1857.86 q^{87} +41.3258 q^{88} +884.901 q^{89} +1070.87 q^{90} -2010.59 q^{92} +107.796 q^{93} +1106.98 q^{94} +445.392 q^{95} +906.865 q^{96} +62.1494 q^{97} -37.8756 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} - 8 q^{3} + 35 q^{4} - 25 q^{5} + 16 q^{6} + 33 q^{8} + 81 q^{9}+O(q^{10}) \) 5 * q + q^2 - 8 * q^3 + 35 * q^4 - 25 * q^5 + 16 * q^6 + 33 * q^8 + 81 * q^9	\( 5 q + q^{2} - 8 q^{3} + 35 q^{4} - 25 q^{5} + 16 q^{6} + 33 q^{8} + 81 q^{9} - 5 q^{10} + 47 q^{11} - 98 q^{12} + q^{13} + 40 q^{15} + 171 q^{16} - 2 q^{17} - 51 q^{18} - 21 q^{19} - 175 q^{20} + 523 q^{22} + 201 q^{23} + 848 q^{24} + 125 q^{25} - 47 q^{26} - 518 q^{27} + 190 q^{29} - 80 q^{30} + 388 q^{31} - 95 q^{32} - 262 q^{33} + 130 q^{34} + 1229 q^{36} - 145 q^{37} + 835 q^{38} + 14 q^{39} - 165 q^{40} - 281 q^{41} + 568 q^{43} + 1091 q^{44} - 405 q^{45} + 337 q^{46} - 473 q^{47} + 70 q^{48} + 25 q^{50} + 732 q^{51} - 379 q^{52} + 351 q^{53} - 774 q^{54} - 235 q^{55} + 954 q^{57} + 1818 q^{58} + 708 q^{59} + 490 q^{60} + 1944 q^{61} + 448 q^{62} - 125 q^{64} - 5 q^{65} + 1482 q^{66} + 1118 q^{67} - 3118 q^{68} + 374 q^{69} + 864 q^{71} - 2219 q^{72} - 1652 q^{73} - 3285 q^{74} - 200 q^{75} + 691 q^{76} - 5574 q^{78} + 218 q^{79} - 855 q^{80} - 455 q^{81} + 1027 q^{82} - 1502 q^{83} + 10 q^{85} - 4264 q^{86} + 390 q^{87} + 2131 q^{88} + 2322 q^{89} + 255 q^{90} - 2957 q^{92} - 2288 q^{93} - 2677 q^{94} + 105 q^{95} + 4592 q^{96} + 598 q^{97} + 35 q^{99}+O(q^{100}) \) 5 * q + q^2 - 8 * q^3 + 35 * q^4 - 25 * q^5 + 16 * q^6 + 33 * q^8 + 81 * q^9 - 5 * q^10 + 47 * q^11 - 98 * q^12 + q^13 + 40 * q^15 + 171 * q^16 - 2 * q^17 - 51 * q^18 - 21 * q^19 - 175 * q^20 + 523 * q^22 + 201 * q^23 + 848 * q^24 + 125 * q^25 - 47 * q^26 - 518 * q^27 + 190 * q^29 - 80 * q^30 + 388 * q^31 - 95 * q^32 - 262 * q^33 + 130 * q^34 + 1229 * q^36 - 145 * q^37 + 835 * q^38 + 14 * q^39 - 165 * q^40 - 281 * q^41 + 568 * q^43 + 1091 * q^44 - 405 * q^45 + 337 * q^46 - 473 * q^47 + 70 * q^48 + 25 * q^50 + 732 * q^51 - 379 * q^52 + 351 * q^53 - 774 * q^54 - 235 * q^55 + 954 * q^57 + 1818 * q^58 + 708 * q^59 + 490 * q^60 + 1944 * q^61 + 448 * q^62 - 125 * q^64 - 5 * q^65 + 1482 * q^66 + 1118 * q^67 - 3118 * q^68 + 374 * q^69 + 864 * q^71 - 2219 * q^72 - 1652 * q^73 - 3285 * q^74 - 200 * q^75 + 691 * q^76 - 5574 * q^78 + 218 * q^79 - 855 * q^80 - 455 * q^81 + 1027 * q^82 - 1502 * q^83 + 10 * q^85 - 4264 * q^86 + 390 * q^87 + 2131 * q^88 + 2322 * q^89 + 255 * q^90 - 2957 * q^92 - 2288 * q^93 - 2677 * q^94 + 105 * q^95 + 4592 * q^96 + 598 * q^97 + 35 * q^99

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