LMFDB - Embedded newform 147.4.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,4,Mod(1,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, 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("147.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	147.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:	$8.67328077084$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	147.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.414214 q^{2} -3.00000 q^{3} -7.82843 q^{4} +0.100505 q^{5} +1.24264 q^{6} +6.55635 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-0.414214 q^{2} -3.00000 q^{3} -7.82843 q^{4} +0.100505 q^{5} +1.24264 q^{6} +6.55635 q^{8} +9.00000 q^{9} -0.0416306 q^{10} -43.9411 q^{11} +23.4853 q^{12} +16.6447 q^{13} -0.301515 q^{15} +59.9117 q^{16} +121.640 q^{17} -3.72792 q^{18} +127.113 q^{19} -0.786797 q^{20} +18.2010 q^{22} +53.5980 q^{23} -19.6690 q^{24} -124.990 q^{25} -6.89444 q^{26} -27.0000 q^{27} +235.681 q^{29} +0.124892 q^{30} +18.7107 q^{31} -77.2670 q^{32} +131.823 q^{33} -50.3848 q^{34} -70.4558 q^{36} -191.882 q^{37} -52.6518 q^{38} -49.9340 q^{39} +0.658946 q^{40} +319.713 q^{41} -218.579 q^{43} +343.990 q^{44} +0.904546 q^{45} -22.2010 q^{46} -401.553 q^{47} -179.735 q^{48} +51.7725 q^{50} -364.919 q^{51} -130.302 q^{52} +643.117 q^{53} +11.1838 q^{54} -4.41631 q^{55} -381.338 q^{57} -97.6224 q^{58} +11.6123 q^{59} +2.36039 q^{60} +12.2426 q^{61} -7.75022 q^{62} -447.288 q^{64} +1.67287 q^{65} -54.6030 q^{66} +669.048 q^{67} -952.247 q^{68} -160.794 q^{69} +822.098 q^{71} +59.0071 q^{72} -515.100 q^{73} +79.4802 q^{74} +374.970 q^{75} -995.092 q^{76} +20.6833 q^{78} -805.754 q^{79} +6.02143 q^{80} +81.0000 q^{81} -132.429 q^{82} +394.863 q^{83} +12.2254 q^{85} +90.5382 q^{86} -707.044 q^{87} -288.093 q^{88} -673.418 q^{89} -0.374675 q^{90} -419.588 q^{92} -56.1320 q^{93} +166.329 q^{94} +12.7755 q^{95} +231.801 q^{96} +1091.11 q^{97} -395.470 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 6 q^{3} - 10 q^{4} + 20 q^{5} - 6 q^{6} - 18 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 6 * q^3 - 10 * q^4 + 20 * q^5 - 6 * q^6 - 18 * q^8 + 18 * q^9	\( 2 q + 2 q^{2} - 6 q^{3} - 10 q^{4} + 20 q^{5} - 6 q^{6} - 18 q^{8} + 18 q^{9} + 48 q^{10} - 20 q^{11} + 30 q^{12} + 104 q^{13} - 60 q^{15} + 18 q^{16} + 116 q^{17} + 18 q^{18} + 192 q^{19} - 44 q^{20} + 76 q^{22} + 28 q^{23} + 54 q^{24} + 146 q^{25} + 204 q^{26} - 54 q^{27} + 296 q^{29} - 144 q^{30} - 104 q^{31} + 18 q^{32} + 60 q^{33} - 64 q^{34} - 90 q^{36} - 248 q^{37} + 104 q^{38} - 312 q^{39} - 488 q^{40} + 20 q^{41} - 720 q^{43} + 292 q^{44} + 180 q^{45} - 84 q^{46} - 96 q^{47} - 54 q^{48} + 706 q^{50} - 348 q^{51} - 320 q^{52} + 268 q^{53} - 54 q^{54} + 472 q^{55} - 576 q^{57} + 48 q^{58} - 616 q^{59} + 132 q^{60} + 16 q^{61} - 304 q^{62} + 118 q^{64} + 1740 q^{65} - 228 q^{66} - 144 q^{67} - 940 q^{68} - 84 q^{69} + 988 q^{71} - 162 q^{72} + 104 q^{73} - 56 q^{74} - 438 q^{75} - 1136 q^{76} - 612 q^{78} - 944 q^{79} - 828 q^{80} + 162 q^{81} - 856 q^{82} + 1016 q^{83} - 100 q^{85} - 1120 q^{86} - 888 q^{87} - 876 q^{88} - 388 q^{89} + 432 q^{90} - 364 q^{92} + 312 q^{93} + 904 q^{94} + 1304 q^{95} - 54 q^{96} + 488 q^{97} - 180 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 6 * q^3 - 10 * q^4 + 20 * q^5 - 6 * q^6 - 18 * q^8 + 18 * q^9 + 48 * q^10 - 20 * q^11 + 30 * q^12 + 104 * q^13 - 60 * q^15 + 18 * q^16 + 116 * q^17 + 18 * q^18 + 192 * q^19 - 44 * q^20 + 76 * q^22 + 28 * q^23 + 54 * q^24 + 146 * q^25 + 204 * q^26 - 54 * q^27 + 296 * q^29 - 144 * q^30 - 104 * q^31 + 18 * q^32 + 60 * q^33 - 64 * q^34 - 90 * q^36 - 248 * q^37 + 104 * q^38 - 312 * q^39 - 488 * q^40 + 20 * q^41 - 720 * q^43 + 292 * q^44 + 180 * q^45 - 84 * q^46 - 96 * q^47 - 54 * q^48 + 706 * q^50 - 348 * q^51 - 320 * q^52 + 268 * q^53 - 54 * q^54 + 472 * q^55 - 576 * q^57 + 48 * q^58 - 616 * q^59 + 132 * q^60 + 16 * q^61 - 304 * q^62 + 118 * q^64 + 1740 * q^65 - 228 * q^66 - 144 * q^67 - 940 * q^68 - 84 * q^69 + 988 * q^71 - 162 * q^72 + 104 * q^73 - 56 * q^74 - 438 * q^75 - 1136 * q^76 - 612 * q^78 - 944 * q^79 - 828 * q^80 + 162 * q^81 - 856 * q^82 + 1016 * q^83 - 100 * q^85 - 1120 * q^86 - 888 * q^87 - 876 * q^88 - 388 * q^89 + 432 * q^90 - 364 * q^92 + 312 * q^93 + 904 * q^94 + 1304 * q^95 - 54 * q^96 + 488 * q^97 - 180 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.414214	−0.146447	−0.0732233	−	0.997316i	$-0.523329\pi$
$2$	−0.414214	−0.146447	−0.0732233	+	0.997316i	$0.523329\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−7.82843	−0.978553
$5$	0.100505	0.00898945	0.00449472	−	0.999990i	$-0.498569\pi$
$5$	0.100505	0.00898945	0.00449472	+	0.999990i	$0.498569\pi$
$6$	1.24264	0.0845510
$7$	0	0
$7$	0	0
$8$	6.55635	0.289752
$9$	9.00000	0.333333
$10$	−0.0416306	−0.00131647
$11$	−43.9411	−1.20443	−0.602216	−	0.798333i	$-0.705715\pi$
$11$	−43.9411	−1.20443	−0.602216	+	0.798333i	$0.705715\pi$
$12$	23.4853	0.564968
$13$	16.6447	0.355108	0.177554	−	0.984111i	$-0.443182\pi$
$13$	16.6447	0.355108	0.177554	+	0.984111i	$0.443182\pi$
$14$	0	0
$15$	−0.301515	−0.00519006
$16$	59.9117	0.936120
$17$	121.640	1.73541	0.867704	−	0.497081i	$-0.165595\pi$
$17$	121.640	1.73541	0.867704	+	0.497081i	$0.165595\pi$
$18$	−3.72792	−0.0488155
$19$	127.113	1.53482	0.767412	−	0.641154i	$-0.221544\pi$
$19$	127.113	1.53482	0.767412	+	0.641154i	$0.221544\pi$
$20$	−0.786797	−0.00879665
$21$	0	0
$22$	18.2010	0.176385
$23$	53.5980	0.485911	0.242955	−	0.970037i	$-0.421883\pi$
$23$	53.5980	0.485911	0.242955	+	0.970037i	$0.421883\pi$
$24$	−19.6690	−0.167289
$25$	−124.990	−0.999919
$26$	−6.89444	−0.0520043
$27$	−27.0000	−0.192450
$28$	0	0
$29$	235.681	1.50913	0.754567	−	0.656223i	$-0.227847\pi$
$29$	235.681	1.50913	0.754567	+	0.656223i	$0.227847\pi$
$30$	0.124892	0.000760067 0
$31$	18.7107	0.108404	0.0542022	−	0.998530i	$-0.482738\pi$
$31$	18.7107	0.108404	0.0542022	+	0.998530i	$0.482738\pi$
$32$	−77.2670	−0.426844
$33$	131.823	0.695379
$34$	−50.3848	−0.254145
$35$	0	0
$36$	−70.4558	−0.326184
$37$	−191.882	−0.852574	−0.426287	−	0.904588i	$-0.640179\pi$
$37$	−191.882	−0.852574	−0.426287	+	0.904588i	$0.640179\pi$
$38$	−52.6518	−0.224770
$39$	−49.9340	−0.205021
$40$	0.658946	0.00260471
$41$	319.713	1.21782	0.608912	−	0.793238i	$-0.291606\pi$
$41$	319.713	1.21782	0.608912	+	0.793238i	$0.291606\pi$
$42$	0	0
$43$	−218.579	−0.775184	−0.387592	−	0.921831i	$-0.626693\pi$
$43$	−218.579	−0.775184	−0.387592	+	0.921831i	$0.626693\pi$
$44$	343.990	1.17860
$45$	0.904546	0.00299648
$46$	−22.2010	−0.0711600
$47$	−401.553	−1.24623	−0.623113	−	0.782132i	$-0.714132\pi$
$47$	−401.553	−1.24623	−0.623113	+	0.782132i	$0.714132\pi$
$48$	−179.735	−0.540469
$49$	0	0
$50$	51.7725	0.146435
$51$	−364.919	−1.00194
$52$	−130.302	−0.347492
$53$	643.117	1.66677	0.833386	−	0.552692i	$-0.186399\pi$
$53$	643.117	1.66677	0.833386	+	0.552692i	$0.186399\pi$
$54$	11.1838	0.0281837
$55$	−4.41631	−0.0108272
$56$	0	0
$57$	−381.338	−0.886131
$58$	−97.6224	−0.221008
$59$	11.6123	0.0256235	0.0128118	−	0.999918i	$-0.495922\pi$
$59$	11.6123	0.0256235	0.0128118	+	0.999918i	$0.495922\pi$
$60$	2.36039	0.00507875
$61$	12.2426	0.0256969	0.0128484	−	0.999917i	$-0.495910\pi$
$61$	12.2426	0.0256969	0.0128484	+	0.999917i	$0.495910\pi$
$62$	−7.75022	−0.0158755
$63$	0	0
$64$	−447.288	−0.873610
$65$	1.67287	0.00319222
$66$	−54.6030	−0.101836
$67$	669.048	1.21996	0.609979	−	0.792417i	$-0.291178\pi$
$67$	669.048	1.21996	0.609979	+	0.792417i	$0.291178\pi$
$68$	−952.247	−1.69819
$69$	−160.794	−0.280541
$70$	0	0
$71$	822.098	1.37416	0.687078	−	0.726584i	$-0.258893\pi$
$71$	822.098	1.37416	0.687078	+	0.726584i	$0.258893\pi$
$72$	59.0071	0.0965841
$73$	−515.100	−0.825861	−0.412930	−	0.910763i	$-0.635495\pi$
$73$	−515.100	−0.825861	−0.412930	+	0.910763i	$0.635495\pi$
$74$	79.4802	0.124857
$75$	374.970	0.577304
$76$	−995.092	−1.50191
$77$	0	0
$78$	20.6833	0.0300247
$79$	−805.754	−1.14752	−0.573762	−	0.819022i	$-0.694517\pi$
$79$	−805.754	−1.14752	−0.573762	+	0.819022i	$0.694517\pi$
$80$	6.02143	0.00841520
$81$	81.0000	0.111111
$82$	−132.429	−0.178346
$83$	394.863	0.522191	0.261095	−	0.965313i	$-0.415916\pi$
$83$	394.863	0.522191	0.261095	+	0.965313i	$0.415916\pi$
$84$	0	0
$85$	12.2254	0.0156004
$86$	90.5382	0.113523
$87$	−707.044	−0.871299
$88$	−288.093	−0.348987
$89$	−673.418	−0.802047	−0.401024	−	0.916068i	$-0.631345\pi$
$89$	−673.418	−0.802047	−0.401024	+	0.916068i	$0.631345\pi$
$90$	−0.374675	−0.000438825 0
$91$	0	0
$92$	−419.588	−0.475490
$93$	−56.1320	−0.0625873
$94$	166.329	0.182505
$95$	12.7755	0.0137972
$96$	231.801	0.246439
$97$	1091.11	1.14212	0.571061	−	0.820908i	$-0.306532\pi$
$97$	1091.11	1.14212	0.571061	+	0.820908i	$0.306532\pi$
$98$	0	0
$99$	−395.470	−0.401477
$100$	978.474	0.978474
$101$	1370.79	1.35048	0.675242	−	0.737597i	$-0.264039\pi$
$101$	1370.79	1.35048	0.675242	+	0.737597i	$0.264039\pi$
$102$	151.154	0.146730
$103$	1413.96	1.35263	0.676316	−	0.736611i	$-0.263575\pi$
$103$	1413.96	1.35263	0.676316	+	0.736611i	$0.263575\pi$
$104$	109.128	0.102893
$105$	0	0
$106$	−266.388	−0.244093
$107$	−343.539	−0.310385	−0.155192	−	0.987884i	$-0.549600\pi$
$107$	−343.539	−0.310385	−0.155192	+	0.987884i	$0.549600\pi$
$108$	211.368	0.188323
$109$	−317.657	−0.279138	−0.139569	−	0.990212i	$-0.544572\pi$
$109$	−317.657	−0.279138	−0.139569	+	0.990212i	$0.544572\pi$
$110$	1.82929	0.00158560
$111$	575.647	0.492234
$112$	0	0
$113$	798.373	0.664643	0.332321	−	0.943166i	$-0.392168\pi$
$113$	798.373	0.664643	0.332321	+	0.943166i	$0.392168\pi$
$114$	157.955	0.129771
$115$	5.38687	0.00436807
$116$	−1845.01	−1.47677
$117$	149.802	0.118369
$118$	−4.80996	−0.00375248
$119$	0	0
$120$	−1.97684	−0.00150383
$121$	599.823	0.450656
$122$	−5.07107	−0.00376322
$123$	−959.138	−0.703110
$124$	−146.475	−0.106080
$125$	−25.1253	−0.0179782
$126$	0	0
$127$	1071.40	0.748593	0.374297	−	0.927309i	$-0.377884\pi$
$127$	1071.40	0.748593	0.374297	+	0.927309i	$0.377884\pi$
$128$	803.409	0.554781
$129$	655.736	0.447553
$130$	−0.692927	−0.000467490 0
$131$	2515.02	1.67739	0.838695	−	0.544601i	$-0.183319\pi$
$131$	2515.02	1.67739	0.838695	+	0.544601i	$0.183319\pi$
$132$	−1031.97	−0.680465
$133$	0	0
$134$	−277.129	−0.178659
$135$	−2.71364	−0.00173002
$136$	797.512	0.502839
$137$	251.064	0.156568	0.0782841	−	0.996931i	$-0.475056\pi$
$137$	251.064	0.156568	0.0782841	+	0.996931i	$0.475056\pi$
$138$	66.6030	0.0410842
$139$	−886.067	−0.540685	−0.270343	−	0.962764i	$-0.587137\pi$
$139$	−886.067	−0.540685	−0.270343	+	0.962764i	$0.587137\pi$
$140$	0	0
$141$	1204.66	0.719508
$142$	−340.524	−0.201240
$143$	−731.385	−0.427703
$144$	539.205	0.312040
$145$	23.6872	0.0135663
$146$	213.361	0.120945
$147$	0	0
$148$	1502.14	0.834289
$149$	582.626	0.320339	0.160170	−	0.987090i	$-0.448796\pi$
$149$	582.626	0.320339	0.160170	+	0.987090i	$0.448796\pi$
$150$	−155.318	−0.0845442
$151$	−2811.76	−1.51535	−0.757676	−	0.652631i	$-0.773665\pi$
$151$	−2811.76	−1.51535	−0.757676	+	0.652631i	$0.773665\pi$
$152$	833.395	0.444719
$153$	1094.76	0.578469
$154$	0	0
$155$	1.88052	0.000974496 0
$156$	390.905	0.200624
$157$	1691.34	0.859770	0.429885	−	0.902884i	$-0.358554\pi$
$157$	1691.34	0.859770	0.429885	+	0.902884i	$0.358554\pi$
$158$	333.754	0.168051
$159$	−1929.35	−0.962311
$160$	−7.76573	−0.00383709
$161$	0	0
$162$	−33.5513	−0.0162718
$163$	−40.7232	−0.0195686	−0.00978432	−	0.999952i	$-0.503114\pi$
$163$	−40.7232	−0.0195686	−0.00978432	+	0.999952i	$0.503114\pi$
$164$	−2502.85	−1.19170
$165$	13.2489	0.00625107
$166$	−163.558	−0.0764731
$167$	−2900.47	−1.34398	−0.671990	−	0.740560i	$-0.734560\pi$
$167$	−2900.47	−1.34398	−0.671990	+	0.740560i	$0.734560\pi$
$168$	0	0
$169$	−1919.96	−0.873899
$170$	−5.06393	−0.00228462
$171$	1144.01	0.511608
$172$	1711.13	0.758559
$173$	2146.15	0.943171	0.471585	−	0.881820i	$-0.343682\pi$
$173$	2146.15	0.943171	0.471585	+	0.881820i	$0.343682\pi$
$174$	292.867	0.127599
$175$	0	0
$176$	−2632.59	−1.12749
$177$	−34.8368	−0.0147938
$178$	278.939	0.117457
$179$	1203.54	0.502552	0.251276	−	0.967916i	$-0.419150\pi$
$179$	1203.54	0.502552	0.251276	+	0.967916i	$0.419150\pi$
$180$	−7.08117	−0.00293222
$181$	2990.47	1.22807	0.614033	−	0.789280i	$-0.289546\pi$
$181$	2990.47	1.22807	0.614033	+	0.789280i	$0.289546\pi$
$182$	0	0
$183$	−36.7279	−0.0148361
$184$	351.407	0.140794
$185$	−19.2851	−0.00766417
$186$	23.2506	0.00916570
$187$	−5344.98	−2.09018
$188$	3143.53	1.21950
$189$	0	0
$190$	−5.29177	−0.00202056
$191$	−2807.41	−1.06354	−0.531772	−	0.846887i	$-0.678474\pi$
$191$	−2807.41	−1.06354	−0.531772	+	0.846887i	$0.678474\pi$
$192$	1341.87	0.504379
$193$	3336.37	1.24434	0.622169	−	0.782883i	$-0.286252\pi$
$193$	3336.37	1.24434	0.622169	+	0.782883i	$0.286252\pi$
$194$	−451.954	−0.167260
$195$	−5.01862	−0.00184303
$196$	0	0
$197$	−4226.65	−1.52861	−0.764305	−	0.644855i	$-0.776918\pi$
$197$	−4226.65	−1.52861	−0.764305	+	0.644855i	$0.776918\pi$
$198$	163.809	0.0587950
$199$	−4385.69	−1.56228	−0.781140	−	0.624356i	$-0.785361\pi$
$199$	−4385.69	−1.56228	−0.781140	+	0.624356i	$0.785361\pi$
$200$	−819.477	−0.289729
$201$	−2007.14	−0.704343
$202$	−567.800	−0.197774
$203$	0	0
$204$	2856.74	0.980450
$205$	32.1328	0.0109476
$206$	−585.680	−0.198088
$207$	482.382	0.161970
$208$	997.210	0.332423
$209$	−5585.48	−1.84859
$210$	0	0
$211$	2291.56	0.747665	0.373833	−	0.927496i	$-0.378043\pi$
$211$	2291.56	0.747665	0.373833	+	0.927496i	$0.378043\pi$
$212$	−5034.59	−1.63103
$213$	−2466.29	−0.793369
$214$	142.299	0.0454548
$215$	−21.9683	−0.00696848
$216$	−177.021	−0.0557629
$217$	0	0
$218$	131.578	0.0408788
$219$	1545.30	0.476811
$220$	34.5727	0.0105950
$221$	2024.65	0.616257
$222$	−238.441	−0.0720860
$223$	217.970	0.0654544	0.0327272	−	0.999464i	$-0.489581\pi$
$223$	217.970	0.0654544	0.0327272	+	0.999464i	$0.489581\pi$
$224$	0	0
$225$	−1124.91	−0.333306
$226$	−330.697	−0.0973347
$227$	−1835.36	−0.536639	−0.268320	−	0.963330i	$-0.586468\pi$
$227$	−1835.36	−0.536639	−0.268320	+	0.963330i	$0.586468\pi$
$228$	2985.28	0.867126
$229$	−2774.01	−0.800488	−0.400244	−	0.916409i	$-0.631075\pi$
$229$	−2774.01	−0.800488	−0.400244	+	0.916409i	$0.631075\pi$
$230$	−2.23131	−0.000639689 0
$231$	0	0
$232$	1545.21	0.437275
$233$	−988.712	−0.277994	−0.138997	−	0.990293i	$-0.544388\pi$
$233$	−988.712	−0.277994	−0.138997	+	0.990293i	$0.544388\pi$
$234$	−62.0500	−0.0173348
$235$	−40.3581	−0.0112029
$236$	−90.9058	−0.0250740
$237$	2417.26	0.662524
$238$	0	0
$239$	−837.928	−0.226783	−0.113391	−	0.993550i	$-0.536171\pi$
$239$	−837.928	−0.226783	−0.113391	+	0.993550i	$0.536171\pi$
$240$	−18.0643	−0.00485852
$241$	3454.99	0.923466	0.461733	−	0.887019i	$-0.347228\pi$
$241$	3454.99	0.923466	0.461733	+	0.887019i	$0.347228\pi$
$242$	−248.455	−0.0659970
$243$	−243.000	−0.0641500
$244$	−95.8406	−0.0251458
$245$	0	0
$246$	397.288	0.102968
$247$	2115.75	0.545028
$248$	122.674	0.0314104
$249$	−1184.59	−0.301487
$250$	10.4072	0.00263284
$251$	−5635.01	−1.41705	−0.708523	−	0.705688i	$-0.750638\pi$
$251$	−5635.01	−1.41705	−0.708523	+	0.705688i	$0.750638\pi$
$252$	0	0
$253$	−2355.16	−0.585246
$254$	−443.788	−0.109629
$255$	−36.6762	−0.00900687
$256$	3245.52	0.792364
$257$	2271.16	0.551248	0.275624	−	0.961265i	$-0.411115\pi$
$257$	2271.16	0.551248	0.275624	+	0.961265i	$0.411115\pi$
$258$	−271.615	−0.0655426
$259$	0	0
$260$	−13.0960	−0.00312376
$261$	2121.13	0.503045
$262$	−1041.75	−0.245648
$263$	163.867	0.0384201	0.0192101	−	0.999815i	$-0.493885\pi$
$263$	163.867	0.0384201	0.0192101	+	0.999815i	$0.493885\pi$
$264$	864.280	0.201488
$265$	64.6365	0.0149834
$266$	0	0
$267$	2020.26	0.463062
$268$	−5237.59	−1.19379
$269$	5167.10	1.17116	0.585582	−	0.810613i	$-0.300866\pi$
$269$	5167.10	1.17116	0.585582	+	0.810613i	$0.300866\pi$
$270$	1.12403	0.000253356 0
$271$	1622.27	0.363638	0.181819	−	0.983332i	$-0.441801\pi$
$271$	1622.27	0.363638	0.181819	+	0.983332i	$0.441801\pi$
$272$	7287.63	1.62455
$273$	0	0
$274$	−103.994	−0.0229289
$275$	5492.20	1.20433
$276$	1258.76	0.274524
$277$	−4612.37	−1.00047	−0.500235	−	0.865890i	$-0.666753\pi$
$277$	−4612.37	−1.00047	−0.500235	+	0.865890i	$0.666753\pi$
$278$	367.021	0.0791815
$279$	168.396	0.0361348
$280$	0	0
$281$	−2125.22	−0.451174	−0.225587	−	0.974223i	$-0.572430\pi$
$281$	−2125.22	−0.451174	−0.225587	+	0.974223i	$0.572430\pi$
$282$	−498.987	−0.105370
$283$	−2571.54	−0.540149	−0.270075	−	0.962839i	$-0.587048\pi$
$283$	−2571.54	−0.540149	−0.270075	+	0.962839i	$0.587048\pi$
$284$	−6435.73	−1.34468
$285$	−38.3264	−0.00796583
$286$	302.950	0.0626356
$287$	0	0
$288$	−695.403	−0.142281
$289$	9883.19	2.01164
$290$	−9.81154	−0.00198674
$291$	−3273.34	−0.659404
$292$	4032.42	0.808149
$293$	3324.96	0.662957	0.331478	−	0.943463i	$-0.392453\pi$
$293$	3324.96	0.662957	0.331478	+	0.943463i	$0.392453\pi$
$294$	0	0
$295$	1.16709	0.000230341 0
$296$	−1258.05	−0.247035
$297$	1186.41	0.231793
$298$	−241.331	−0.0469126
$299$	892.120	0.172551
$300$	−2935.42	−0.564922
$301$	0	0
$302$	1164.67	0.221918
$303$	−4112.37	−0.779702
$304$	7615.54	1.43678
$305$	1.23045	0.000231001 0
$306$	−453.463	−0.0847149
$307$	−887.096	−0.164916	−0.0824580	−	0.996595i	$-0.526277\pi$
$307$	−887.096	−0.164916	−0.0824580	+	0.996595i	$0.526277\pi$
$308$	0	0
$309$	−4241.87	−0.780943
$310$	−0.778936	−0.000142712 0
$311$	−4510.82	−0.822460	−0.411230	−	0.911532i	$-0.634901\pi$
$311$	−4510.82	−0.822460	−0.411230	+	0.911532i	$0.634901\pi$
$312$	−327.385	−0.0594055
$313$	3715.78	0.671018	0.335509	−	0.942037i	$-0.391092\pi$
$313$	3715.78	0.671018	0.335509	+	0.942037i	$0.391092\pi$
$314$	−700.577	−0.125910
$315$	0	0
$316$	6307.79	1.12291
$317$	6954.52	1.23219	0.616096	−	0.787671i	$-0.288713\pi$
$317$	6954.52	1.23219	0.616096	+	0.787671i	$0.288713\pi$
$318$	799.163	0.140927
$319$	−10356.1	−1.81765
$320$	−44.9548	−0.00785327
$321$	1030.62	0.179201
$322$	0	0
$323$	15461.9	2.66355
$324$	−634.103	−0.108728
$325$	−2080.41	−0.355079
$326$	16.8681	0.00286576
$327$	952.971	0.161160
$328$	2096.15	0.352867
$329$	0	0
$330$	−5.48788	−0.000915448 0
$331$	−9863.18	−1.63785	−0.818926	−	0.573899i	$-0.805430\pi$
$331$	−9863.18	−1.63785	−0.818926	+	0.573899i	$0.805430\pi$
$332$	−3091.16	−0.510992
$333$	−1726.94	−0.284191
$334$	1201.41	0.196821
$335$	67.2427	0.0109668
$336$	0	0
$337$	−5945.06	−0.960974	−0.480487	−	0.877002i	$-0.659540\pi$
$337$	−5945.06	−0.960974	−0.480487	+	0.877002i	$0.659540\pi$
$338$	795.272	0.127979
$339$	−2395.12	−0.383732
$340$	−95.7056	−0.0152658
$341$	−822.168	−0.130566
$342$	−473.866	−0.0749232
$343$	0	0
$344$	−1433.08	−0.224612
$345$	−16.1606	−0.00252191
$346$	−888.963	−0.138124
$347$	1169.57	0.180939	0.0904697	−	0.995899i	$-0.471163\pi$
$347$	1169.57	0.180939	0.0904697	+	0.995899i	$0.471163\pi$
$348$	5535.04	0.852613
$349$	−9176.66	−1.40749	−0.703747	−	0.710451i	$-0.748491\pi$
$349$	−9176.66	−1.40749	−0.703747	+	0.710451i	$0.748491\pi$
$350$	0	0
$351$	−449.406	−0.0683405
$352$	3395.20	0.514104
$353$	10587.2	1.59632	0.798158	−	0.602448i	$-0.205808\pi$
$353$	10587.2	1.59632	0.798158	+	0.602448i	$0.205808\pi$
$354$	14.4299	0.00216649
$355$	82.6250	0.0123529
$356$	5271.81	0.784846
$357$	0	0
$358$	−498.522	−0.0735970
$359$	8615.21	1.26656	0.633278	−	0.773924i	$-0.281709\pi$
$359$	8615.21	1.26656	0.633278	+	0.773924i	$0.281709\pi$
$360$	5.93052	0.000868238 0
$361$	9298.64	1.35568
$362$	−1238.69	−0.179846
$363$	−1799.47	−0.260186
$364$	0	0
$365$	−51.7701	−0.00742403
$366$	15.2132	0.00217270
$367$	8297.79	1.18022	0.590110	−	0.807323i	$-0.299084\pi$
$367$	8297.79	1.18022	0.590110	+	0.807323i	$0.299084\pi$
$368$	3211.15	0.454871
$369$	2877.41	0.405941
$370$	7.98817	0.00112239
$371$	0	0
$372$	439.426	0.0612450
$373$	−5123.86	−0.711269	−0.355634	−	0.934625i	$-0.615735\pi$
$373$	−5123.86	−0.711269	−0.355634	+	0.934625i	$0.615735\pi$
$374$	2213.96	0.306100
$375$	75.3758	0.0103797
$376$	−2632.72	−0.361097
$377$	3922.83	0.535905
$378$	0	0
$379$	−1502.49	−0.203635	−0.101817	−	0.994803i	$-0.532466\pi$
$379$	−1502.49	−0.203635	−0.101817	+	0.994803i	$0.532466\pi$
$380$	−100.012	−0.0135013
$381$	−3214.20	−0.432200
$382$	1162.87	0.155753
$383$	−10872.9	−1.45060	−0.725301	−	0.688431i	$-0.758300\pi$
$383$	−10872.9	−1.45060	−0.725301	+	0.688431i	$0.758300\pi$
$384$	−2410.23	−0.320303
$385$	0	0
$386$	−1381.97	−0.182229
$387$	−1967.21	−0.258395
$388$	−8541.71	−1.11763
$389$	4618.99	0.602036	0.301018	−	0.953618i	$-0.402674\pi$
$389$	4618.99	0.602036	0.301018	+	0.953618i	$0.402674\pi$
$390$	2.07878	0.000269905 0
$391$	6519.64	0.843254
$392$	0	0
$393$	−7545.05	−0.968442
$394$	1750.73	0.223860
$395$	−80.9824	−0.0103156
$396$	3095.91	0.392867
$397$	9606.95	1.21451	0.607253	−	0.794508i	$-0.292271\pi$
$397$	9606.95	1.21451	0.607253	+	0.794508i	$0.292271\pi$
$398$	1816.61	0.228791
$399$	0	0
$400$	−7488.36	−0.936044
$401$	−10501.0	−1.30772	−0.653862	−	0.756614i	$-0.726852\pi$
$401$	−10501.0	−1.30772	−0.653862	+	0.756614i	$0.726852\pi$
$402$	831.386	0.103149
$403$	311.433	0.0384952
$404$	−10731.1	−1.32152
$405$	8.14091	0.000998827 0
$406$	0	0
$407$	8431.52	1.02687
$408$	−2392.54	−0.290314
$409$	−12066.9	−1.45885	−0.729427	−	0.684059i	$-0.760213\pi$
$409$	−12066.9	−1.45885	−0.729427	+	0.684059i	$0.760213\pi$
$410$	−13.3098	−0.00160323
$411$	−753.192	−0.0903947
$412$	−11069.0	−1.32362
$413$	0	0
$414$	−199.809	−0.0237200
$415$	39.6857	0.00469421
$416$	−1286.08	−0.151576
$417$	2658.20	0.312165
$418$	2313.58	0.270720
$419$	−6366.31	−0.742278	−0.371139	−	0.928577i	$-0.621033\pi$
$419$	−6366.31	−0.742278	−0.371139	+	0.928577i	$0.621033\pi$
$420$	0	0
$421$	−4731.84	−0.547781	−0.273890	−	0.961761i	$-0.588311\pi$
$421$	−4731.84	−0.547781	−0.273890	+	0.961761i	$0.588311\pi$
$422$	−949.194	−0.109493
$423$	−3613.98	−0.415408
$424$	4216.50	0.482951
$425$	−15203.7	−1.73527
$426$	1021.57	0.116186
$427$	0	0
$428$	2689.37	0.303728
$429$	2194.16	0.246934
$430$	9.09955	0.00102051
$431$	3752.78	0.419409	0.209704	−	0.977765i	$-0.432750\pi$
$431$	3752.78	0.419409	0.209704	+	0.977765i	$0.432750\pi$
$432$	−1617.62	−0.180156
$433$	11709.2	1.29956	0.649780	−	0.760122i	$-0.274861\pi$
$433$	11709.2	1.29956	0.649780	+	0.760122i	$0.274861\pi$
$434$	0	0
$435$	−71.0615	−0.00783250
$436$	2486.75	0.273151
$437$	6812.98	0.745788
$438$	−640.084	−0.0698274
$439$	−14924.7	−1.62259	−0.811296	−	0.584635i	$-0.801238\pi$
$439$	−14924.7	−1.62259	−0.811296	+	0.584635i	$0.801238\pi$
$440$	−28.9548	−0.00313720
$441$	0	0
$442$	−838.638	−0.0902487
$443$	−8517.66	−0.913513	−0.456756	−	0.889592i	$-0.650989\pi$
$443$	−8517.66	−0.913513	−0.456756	+	0.889592i	$0.650989\pi$
$444$	−4506.41	−0.481677
$445$	−67.6820	−0.00720996
$446$	−90.2860	−0.00958557
$447$	−1747.88	−0.184948
$448$	0	0
$449$	−5965.73	−0.627038	−0.313519	−	0.949582i	$-0.601508\pi$
$449$	−5965.73	−0.627038	−0.313519	+	0.949582i	$0.601508\pi$
$450$	465.953	0.0488116
$451$	−14048.5	−1.46678
$452$	−6250.01	−0.650389
$453$	8435.29	0.874889
$454$	760.231	0.0785890
$455$	0	0
$456$	−2500.19	−0.256759
$457$	−13860.6	−1.41875	−0.709376	−	0.704830i	$-0.751023\pi$
$457$	−13860.6	−1.41875	−0.709376	+	0.704830i	$0.751023\pi$
$458$	1149.03	0.117229
$459$	−3284.27	−0.333979
$460$	−42.1707	−0.00427439
$461$	−149.312	−0.0150850	−0.00754249	−	0.999972i	$-0.502401\pi$
$461$	−149.312	−0.0150850	−0.00754249	+	0.999972i	$0.502401\pi$
$462$	0	0
$463$	5403.95	0.542425	0.271213	−	0.962519i	$-0.412575\pi$
$463$	5403.95	0.542425	0.271213	+	0.962519i	$0.412575\pi$
$464$	14120.1	1.41273
$465$	−5.64155	−0.000562625 0
$466$	409.538	0.0407113
$467$	3704.66	0.367090	0.183545	−	0.983011i	$-0.441243\pi$
$467$	3704.66	0.367090	0.183545	+	0.983011i	$0.441243\pi$
$468$	−1172.71	−0.115831
$469$	0	0
$470$	16.7169	0.00164062
$471$	−5074.03	−0.496389
$472$	76.1341	0.00742448
$473$	9604.59	0.933657
$474$	−1001.26	−0.0970244
$475$	−15887.8	−1.53470
$476$	0	0
$477$	5788.05	0.555591
$478$	347.081	0.0332115
$479$	−10671.8	−1.01796	−0.508982	−	0.860777i	$-0.669978\pi$
$479$	−10671.8	−1.01796	−0.508982	+	0.860777i	$0.669978\pi$
$480$	23.2972	0.00221535
$481$	−3193.82	−0.302756
$482$	−1431.10	−0.135238
$483$	0	0
$484$	−4695.67	−0.440990
$485$	109.662	0.0102670
$486$	100.654	0.00939455
$487$	5853.92	0.544695	0.272348	−	0.962199i	$-0.412200\pi$
$487$	5853.92	0.544695	0.272348	+	0.962199i	$0.412200\pi$
$488$	80.2670	0.00744573
$489$	122.170	0.0112980
$490$	0	0
$491$	4065.31	0.373656	0.186828	−	0.982393i	$-0.440179\pi$
$491$	4065.31	0.373656	0.186828	+	0.982393i	$0.440179\pi$
$492$	7508.54	0.688031
$493$	28668.2	2.61896
$494$	−876.371	−0.0798174
$495$	−39.7468	−0.00360906
$496$	1120.99	0.101480
$497$	0	0
$498$	490.673	0.0441517
$499$	4811.19	0.431620	0.215810	−	0.976435i	$-0.430761\pi$
$499$	4811.19	0.431620	0.215810	+	0.976435i	$0.430761\pi$
$500$	196.691	0.0175926
$501$	8701.40	0.775947
$502$	2334.10	0.207522
$503$	17001.2	1.50705	0.753526	−	0.657418i	$-0.228351\pi$
$503$	17001.2	1.50705	0.753526	+	0.657418i	$0.228351\pi$
$504$	0	0
$505$	137.771	0.0121401
$506$	975.537	0.0857074
$507$	5759.87	0.504546
$508$	−8387.37	−0.732538
$509$	13797.2	1.20148	0.600738	−	0.799446i	$-0.294874\pi$
$509$	13797.2	1.20148	0.600738	+	0.799446i	$0.294874\pi$
$510$	15.1918	0.00131903
$511$	0	0
$512$	−7771.61	−0.670820
$513$	−3432.04	−0.295377
$514$	−940.744	−0.0807284
$515$	142.110	0.0121594
$516$	−5133.38	−0.437954
$517$	17644.7	1.50099
$518$	0	0
$519$	−6438.44	−0.544540
$520$	10.9679	0.000924954 0
$521$	3936.61	0.331029	0.165515	−	0.986207i	$-0.447072\pi$
$521$	3936.61	0.331029	0.165515	+	0.986207i	$0.447072\pi$
$522$	−878.601	−0.0736692
$523$	17459.3	1.45973	0.729866	−	0.683590i	$-0.239582\pi$
$523$	17459.3	1.45973	0.729866	+	0.683590i	$0.239582\pi$
$524$	−19688.6	−1.64142
$525$	0	0
$526$	−67.8760	−0.00562649
$527$	2275.96	0.188126
$528$	7897.76	0.650958
$529$	−9294.26	−0.763891
$530$	−26.7733	−0.00219426
$531$	104.510	0.00854118
$532$	0	0
$533$	5321.51	0.432458
$534$	−836.817	−0.0678139
$535$	−34.5274	−0.00279019
$536$	4386.51	0.353486
$537$	−3610.62	−0.290148
$538$	−2140.28	−0.171513
$539$	0	0
$540$	21.2435	0.00169292
$541$	19101.3	1.51798	0.758992	−	0.651100i	$-0.225692\pi$
$541$	19101.3	1.51798	0.758992	+	0.651100i	$0.225692\pi$
$542$	−671.967	−0.0532536
$543$	−8971.41	−0.709024
$544$	−9398.73	−0.740749
$545$	−31.9261	−0.00250929
$546$	0	0
$547$	15413.5	1.20481	0.602407	−	0.798189i	$-0.294208\pi$
$547$	15413.5	1.20481	0.602407	+	0.798189i	$0.294208\pi$
$548$	−1965.44	−0.153210
$549$	110.184	0.00856563
$550$	−2274.94	−0.176371
$551$	29958.1	2.31626
$552$	−1054.22	−0.0812874
$553$	0	0
$554$	1910.51	0.146516
$555$	57.8554	0.00442491
$556$	6936.51	0.529089
$557$	−20492.9	−1.55891	−0.779453	−	0.626460i	$-0.784503\pi$
$557$	−20492.9	−1.55891	−0.779453	+	0.626460i	$0.784503\pi$
$558$	−69.7519	−0.00529182
$559$	−3638.17	−0.275274
$560$	0	0
$561$	16034.9	1.20677
$562$	880.294	0.0660729
$563$	−7142.49	−0.534671	−0.267336	−	0.963603i	$-0.586143\pi$
$563$	−7142.49	−0.534671	−0.267336	+	0.963603i	$0.586143\pi$
$564$	−9430.59	−0.704077
$565$	80.2406	0.00597477
$566$	1065.17	0.0791030
$567$	0	0
$568$	5389.96	0.398165
$569$	4097.91	0.301922	0.150961	−	0.988540i	$-0.451763\pi$
$569$	4097.91	0.301922	0.150961	+	0.988540i	$0.451763\pi$
$570$	15.8753	0.00116657
$571$	−2838.48	−0.208033	−0.104016	−	0.994576i	$-0.533169\pi$
$571$	−2838.48	−0.208033	−0.104016	+	0.994576i	$0.533169\pi$
$572$	5725.60	0.418530
$573$	8422.23	0.614038
$574$	0	0
$575$	−6699.21	−0.485872
$576$	−4025.60	−0.291203
$577$	−15464.5	−1.11576	−0.557881	−	0.829921i	$-0.688385\pi$
$577$	−15464.5	−1.11576	−0.557881	+	0.829921i	$0.688385\pi$
$578$	−4093.75	−0.294598
$579$	−10009.1	−0.718418
$580$	−185.433	−0.0132753
$581$	0	0
$582$	1355.86	0.0965675
$583$	−28259.3	−2.00751
$584$	−3377.17	−0.239295
$585$	15.0559	0.00106407
$586$	−1377.24	−0.0970878
$587$	14003.6	0.984652	0.492326	−	0.870411i	$-0.336147\pi$
$587$	14003.6	0.984652	0.492326	+	0.870411i	$0.336147\pi$
$588$	0	0
$589$	2378.36	0.166382
$590$	−0.483425	−3.37327e−5 0
$591$	12679.9	0.882543
$592$	−11496.0	−0.798112
$593$	6504.50	0.450435	0.225217	−	0.974309i	$-0.427691\pi$
$593$	6504.50	0.450435	0.225217	+	0.974309i	$0.427691\pi$
$594$	−491.427	−0.0339453
$595$	0	0
$596$	−4561.04	−0.313469
$597$	13157.1	0.901982
$598$	−369.528	−0.0252695
$599$	−12616.1	−0.860567	−0.430284	−	0.902694i	$-0.641586\pi$
$599$	−12616.1	−0.860567	−0.430284	+	0.902694i	$0.641586\pi$
$600$	2458.43	0.167275
$601$	8270.87	0.561358	0.280679	−	0.959802i	$-0.409440\pi$
$601$	8270.87	0.561358	0.280679	+	0.959802i	$0.409440\pi$
$602$	0	0
$603$	6021.43	0.406653
$604$	22011.7	1.48285
$605$	60.2852	0.00405114
$606$	1703.40	0.114185
$607$	3811.84	0.254889	0.127445	−	0.991846i	$-0.459323\pi$
$607$	3811.84	0.254889	0.127445	+	0.991846i	$0.459323\pi$
$608$	−9821.62	−0.655130
$609$	0	0
$610$	−0.509668	−3.38293e−5 0
$611$	−6683.72	−0.442544
$612$	−8570.22	−0.566063
$613$	11359.3	0.748445	0.374222	−	0.927339i	$-0.377910\pi$
$613$	11359.3	0.748445	0.374222	+	0.927339i	$0.377910\pi$
$614$	367.447	0.0241514
$615$	−96.3983	−0.00632057
$616$	0	0
$617$	−18272.2	−1.19224	−0.596118	−	0.802896i	$-0.703291\pi$
$617$	−18272.2	−1.19224	−0.596118	+	0.802896i	$0.703291\pi$
$618$	1757.04	0.114366
$619$	29600.2	1.92203	0.961013	−	0.276503i	$-0.0891756\pi$
$619$	29600.2	1.92203	0.961013	+	0.276503i	$0.0891756\pi$
$620$	−14.7215	−0.000953596 0
$621$	−1447.15	−0.0935136
$622$	1868.44	0.120447
$623$	0	0
$624$	−2991.63	−0.191925
$625$	15621.2	0.999758
$626$	−1539.13	−0.0982682
$627$	16756.4	1.06728
$628$	−13240.6	−0.841331
$629$	−23340.5	−1.47956
$630$	0	0
$631$	7185.41	0.453322	0.226661	−	0.973974i	$-0.427219\pi$
$631$	7185.41	0.453322	0.226661	+	0.973974i	$0.427219\pi$
$632$	−5282.81	−0.332498
$633$	−6874.67	−0.431665
$634$	−2880.66	−0.180450
$635$	107.681	0.00672944
$636$	15103.8	0.941673
$637$	0	0
$638$	4289.64	0.266189
$639$	7398.88	0.458052
$640$	80.7467	0.00498718
$641$	−232.982	−0.0143561	−0.00717803	−	0.999974i	$-0.502285\pi$
$641$	−232.982	−0.0143561	−0.00717803	+	0.999974i	$0.502285\pi$
$642$	−426.896	−0.0262433
$643$	−1837.96	−0.112725	−0.0563624	−	0.998410i	$-0.517950\pi$
$643$	−1837.96	−0.112725	−0.0563624	+	0.998410i	$0.517950\pi$
$644$	0	0
$645$	65.9048	0.00402325
$646$	−6404.54	−0.390067
$647$	−18594.7	−1.12988	−0.564941	−	0.825131i	$-0.691101\pi$
$647$	−18594.7	−1.12988	−0.564941	+	0.825131i	$0.691101\pi$
$648$	531.064	0.0321947
$649$	−510.256	−0.0308618
$650$	861.736	0.0520001
$651$	0	0
$652$	318.799	0.0191490
$653$	−28864.7	−1.72980	−0.864902	−	0.501940i	$-0.832620\pi$
$653$	−28864.7	−1.72980	−0.864902	+	0.501940i	$0.832620\pi$
$654$	−394.733	−0.0236014
$655$	252.772	0.0150788
$656$	19154.5	1.14003
$657$	−4635.90	−0.275287
$658$	0	0
$659$	−29066.3	−1.71815	−0.859076	−	0.511847i	$-0.828961\pi$
$659$	−29066.3	−1.71815	−0.859076	+	0.511847i	$0.828961\pi$
$660$	−103.718	−0.00611701
$661$	−3979.51	−0.234168	−0.117084	−	0.993122i	$-0.537355\pi$
$661$	−3979.51	−0.234168	−0.117084	+	0.993122i	$0.537355\pi$
$662$	4085.46	0.239858
$663$	−6073.95	−0.355796
$664$	2588.86	0.151306
$665$	0	0
$666$	715.322	0.0416189
$667$	12632.0	0.733305
$668$	22706.1	1.31516
$669$	−653.909	−0.0377901
$670$	−27.8528	−0.00160604
$671$	−537.955	−0.0309501
$672$	0	0
$673$	−184.229	−0.0105520	−0.00527601	−	0.999986i	$-0.501679\pi$
$673$	−184.229	−0.0105520	−0.00527601	+	0.999986i	$0.501679\pi$
$674$	2462.52	0.140731
$675$	3374.73	0.192435
$676$	15030.2	0.855156
$677$	−16683.5	−0.947116	−0.473558	−	0.880763i	$-0.657031\pi$
$677$	−16683.5	−0.947116	−0.473558	+	0.880763i	$0.657031\pi$
$678$	992.091	0.0561962
$679$	0	0
$680$	80.1540	0.00452024
$681$	5506.08	0.309829
$682$	340.553	0.0191209
$683$	17808.2	0.997676	0.498838	−	0.866695i	$-0.333760\pi$
$683$	17808.2	0.997676	0.498838	+	0.866695i	$0.333760\pi$
$684$	−8955.83	−0.500636
$685$	25.2332	0.00140746
$686$	0	0
$687$	8322.03	0.462162
$688$	−13095.4	−0.725666
$689$	10704.5	0.591883
$690$	6.69394	0.000369325 0
$691$	−20145.7	−1.10908	−0.554542	−	0.832156i	$-0.687106\pi$
$691$	−20145.7	−1.10908	−0.554542	+	0.832156i	$0.687106\pi$
$692$	−16801.0	−0.922943
$693$	0	0
$694$	−484.453	−0.0264980
$695$	−89.0542	−0.00486046
$696$	−4635.63	−0.252461
$697$	38889.7	2.11342
$698$	3801.10	0.206123
$699$	2966.14	0.160500
$700$	0	0
$701$	−2719.67	−0.146534	−0.0732672	−	0.997312i	$-0.523343\pi$
$701$	−2719.67	−0.146534	−0.0732672	+	0.997312i	$0.523343\pi$
$702$	186.150	0.0100082
$703$	−24390.7	−1.30855
$704$	19654.4	1.05220
$705$	121.074	0.00646798
$706$	−4385.36	−0.233775
$707$	0	0
$708$	272.717	0.0144765
$709$	−625.708	−0.0331438	−0.0165719	−	0.999863i	$-0.505275\pi$
$709$	−625.708	−0.0331438	−0.0165719	+	0.999863i	$0.505275\pi$
$710$	−34.2244	−0.00180904
$711$	−7251.79	−0.382508
$712$	−4415.17	−0.232395
$713$	1002.85	0.0526749
$714$	0	0
$715$	−73.5079	−0.00384481
$716$	−9421.82	−0.491774
$717$	2513.78	0.130933
$718$	−3568.54	−0.185483
$719$	−9577.54	−0.496776	−0.248388	−	0.968661i	$-0.579901\pi$
$719$	−9577.54	−0.496776	−0.248388	+	0.968661i	$0.579901\pi$
$720$	54.1929	0.00280507
$721$	0	0
$722$	−3851.62	−0.198535
$723$	−10365.0	−0.533163
$724$	−23410.7	−1.20173
$725$	−29457.8	−1.50901
$726$	745.364	0.0381034
$727$	−16741.2	−0.854053	−0.427027	−	0.904239i	$-0.640439\pi$
$727$	−16741.2	−0.854053	−0.427027	+	0.904239i	$0.640439\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	21.4439	0.00108722
$731$	−26587.8	−1.34526
$732$	287.522	0.0145179
$733$	−6496.04	−0.327335	−0.163668	−	0.986516i	$-0.552332\pi$
$733$	−6496.04	−0.327335	−0.163668	+	0.986516i	$0.552332\pi$
$734$	−3437.06	−0.172839
$735$	0	0
$736$	−4141.36	−0.207408
$737$	−29398.7	−1.46936
$738$	−1191.86	−0.0594487
$739$	499.280	0.0248529	0.0124265	−	0.999923i	$-0.496044\pi$
$739$	499.280	0.0248529	0.0124265	+	0.999923i	$0.496044\pi$
$740$	150.972	0.00749980
$741$	−6347.24	−0.314672
$742$	0	0
$743$	−6367.30	−0.314393	−0.157196	−	0.987567i	$-0.550246\pi$
$743$	−6367.30	−0.314393	−0.157196	+	0.987567i	$0.550246\pi$
$744$	−368.021	−0.0181348
$745$	58.5568	0.00287967
$746$	2122.37	0.104163
$747$	3553.77	0.174064
$748$	41842.8	2.04535
$749$	0	0
$750$	−31.2217	−0.00152007
$751$	496.098	0.0241050	0.0120525	−	0.999927i	$-0.496163\pi$
$751$	496.098	0.0241050	0.0120525	+	0.999927i	$0.496163\pi$
$752$	−24057.7	−1.16662
$753$	16905.0	0.818132
$754$	−1624.89	−0.0784815
$755$	−282.597	−0.0136222
$756$	0	0
$757$	13025.9	0.625408	0.312704	−	0.949851i	$-0.398765\pi$
$757$	13025.9	0.625408	0.312704	+	0.949851i	$0.398765\pi$
$758$	622.350	0.0298216
$759$	7065.47	0.337892
$760$	83.7604	0.00399778
$761$	−25474.6	−1.21347	−0.606736	−	0.794904i	$-0.707521\pi$
$761$	−25474.6	−1.21347	−0.606736	+	0.794904i	$0.707521\pi$
$762$	1331.36	0.0632943
$763$	0	0
$764$	21977.6	1.04074
$765$	110.029	0.00520012
$766$	4503.72	0.212436
$767$	193.282	0.00909911
$768$	−9736.57	−0.457472
$769$	−29054.0	−1.36244	−0.681218	−	0.732080i	$-0.738550\pi$
$769$	−29054.0	−1.36244	−0.681218	+	0.732080i	$0.738550\pi$
$770$	0	0
$771$	−6813.47	−0.318263
$772$	−26118.5	−1.21765
$773$	1897.35	0.0882834	0.0441417	−	0.999025i	$-0.485945\pi$
$773$	1897.35	0.0882834	0.0441417	+	0.999025i	$0.485945\pi$
$774$	814.844	0.0378410
$775$	−2338.65	−0.108396
$776$	7153.72	0.330933
$777$	0	0
$778$	−1913.25	−0.0881662
$779$	40639.6	1.86914
$780$	39.2879	0.00180350
$781$	−36123.9	−1.65508
$782$	−2700.52	−0.123492
$783$	−6363.39	−0.290433
$784$	0	0
$785$	169.989	0.00772886
$786$	3125.26	0.141825
$787$	42650.3	1.93179	0.965895	−	0.258936i	$-0.0833718\pi$
$787$	42650.3	1.93179	0.965895	+	0.258936i	$0.0833718\pi$
$788$	33088.0	1.49583
$789$	−491.602	−0.0221819
$790$	33.5440	0.00151069
$791$	0	0
$792$	−2592.84	−0.116329
$793$	203.775	0.00912516
$794$	−3979.33	−0.177860
$795$	−193.910	−0.00865064
$796$	34333.1	1.52877
$797$	36822.8	1.63655	0.818275	−	0.574828i	$-0.194931\pi$
$797$	36822.8	1.63655	0.818275	+	0.574828i	$0.194931\pi$
$798$	0	0
$799$	−48844.8	−2.16271
$800$	9657.60	0.426810
$801$	−6060.77	−0.267349
$802$	4349.68	0.191512
$803$	22634.1	0.994693
$804$	15712.8	0.689238
$805$	0	0
$806$	−129.000	−0.00563750
$807$	−15501.3	−0.676172
$808$	8987.38	0.391306
$809$	5081.94	0.220855	0.110427	−	0.993884i	$-0.464778\pi$
$809$	5081.94	0.220855	0.110427	+	0.993884i	$0.464778\pi$
$810$	−3.37208	−0.000146275 0
$811$	11873.4	0.514097	0.257048	−	0.966399i	$-0.417250\pi$
$811$	11873.4	0.514097	0.257048	+	0.966399i	$0.417250\pi$
$812$	0	0
$813$	−4866.82	−0.209947
$814$	−3492.45	−0.150381
$815$	−4.09289	−0.000175911 0
$816$	−21862.9	−0.937935
$817$	−27784.1	−1.18977
$818$	4998.29	0.213644
$819$	0	0
$820$	−251.549	−0.0107128
$821$	16969.4	0.721361	0.360681	−	0.932689i	$-0.382544\pi$
$821$	16969.4	0.721361	0.360681	+	0.932689i	$0.382544\pi$
$822$	311.982	0.0132380
$823$	3995.94	0.169246	0.0846231	−	0.996413i	$-0.473031\pi$
$823$	3995.94	0.169246	0.0846231	+	0.996413i	$0.473031\pi$
$824$	9270.39	0.391929
$825$	−16476.6	−0.695323
$826$	0	0
$827$	−13589.7	−0.571417	−0.285708	−	0.958317i	$-0.592229\pi$
$827$	−13589.7	−0.571417	−0.285708	+	0.958317i	$0.592229\pi$
$828$	−3776.29	−0.158497
$829$	−30646.0	−1.28393	−0.641966	−	0.766733i	$-0.721881\pi$
$829$	−30646.0	−1.28393	−0.641966	+	0.766733i	$0.721881\pi$
$830$	−16.4384	−0.000687451 0
$831$	13837.1	0.577622
$832$	−7444.96	−0.310226
$833$	0	0
$834$	−1101.06	−0.0457155
$835$	−291.511	−0.0120816
$836$	43725.5	1.80894
$837$	−505.188	−0.0208624
$838$	2637.01	0.108704
$839$	−7497.57	−0.308516	−0.154258	−	0.988031i	$-0.549299\pi$
$839$	−7497.57	−0.308516	−0.154258	+	0.988031i	$0.549299\pi$
$840$	0	0
$841$	31156.6	1.27749
$842$	1959.99	0.0802207
$843$	6375.65	0.260485
$844$	−17939.3	−0.731630
$845$	−192.965	−0.00785586
$846$	1496.96	0.0608351
$847$	0	0
$848$	38530.2	1.56030
$849$	7714.62	0.311855
$850$	6297.59	0.254124
$851$	−10284.5	−0.414275
$852$	19307.2	0.776354
$853$	−10347.6	−0.415352	−0.207676	−	0.978198i	$-0.566590\pi$
$853$	−10347.6	−0.415352	−0.207676	+	0.978198i	$0.566590\pi$
$854$	0	0
$855$	114.979	0.00459907
$856$	−2252.36	−0.0899348
$857$	1550.00	0.0617817	0.0308909	−	0.999523i	$-0.490166\pi$
$857$	1550.00	0.0617817	0.0308909	+	0.999523i	$0.490166\pi$
$858$	−908.849	−0.0361627
$859$	15187.5	0.603250	0.301625	−	0.953427i	$-0.402471\pi$
$859$	15187.5	0.603250	0.301625	+	0.953427i	$0.402471\pi$
$860$	171.977	0.00681903
$861$	0	0
$862$	−1554.45	−0.0614210
$863$	41550.2	1.63892	0.819459	−	0.573138i	$-0.194274\pi$
$863$	41550.2	1.63892	0.819459	+	0.573138i	$0.194274\pi$
$864$	2086.21	0.0821462
$865$	215.699	0.00847858
$866$	−4850.12	−0.190316
$867$	−29649.6	−1.16142
$868$	0	0
$869$	35405.8	1.38212
$870$	29.4346	0.00114704
$871$	11136.1	0.433216
$872$	−2082.67	−0.0808808
$873$	9820.03	0.380707
$874$	−2822.03	−0.109218
$875$	0	0
$876$	−12097.3	−0.466585
$877$	27837.4	1.07184	0.535919	−	0.844269i	$-0.319965\pi$
$877$	27837.4	1.07184	0.535919	+	0.844269i	$0.319965\pi$
$878$	6182.02	0.237623
$879$	−9974.89	−0.382758
$880$	−264.588	−0.0101355
$881$	−2587.85	−0.0989635	−0.0494817	−	0.998775i	$-0.515757\pi$
$881$	−2587.85	−0.0989635	−0.0494817	+	0.998775i	$0.515757\pi$
$882$	0	0
$883$	−16382.0	−0.624346	−0.312173	−	0.950025i	$-0.601057\pi$
$883$	−16382.0	−0.624346	−0.312173	+	0.950025i	$0.601057\pi$
$884$	−15849.8	−0.603040
$885$	−3.50127	−0.000132988 0
$886$	3528.13	0.133781
$887$	−22980.2	−0.869896	−0.434948	−	0.900456i	$-0.643233\pi$
$887$	−22980.2	−0.869896	−0.434948	+	0.900456i	$0.643233\pi$
$888$	3774.14	0.142626
$889$	0	0
$890$	28.0348	0.00105587
$891$	−3559.23	−0.133826
$892$	−1706.36	−0.0640506
$893$	−51042.5	−1.91274
$894$	723.994	0.0270850
$895$	120.962	0.00451766
$896$	0	0
$897$	−2676.36	−0.0996222
$898$	2471.09	0.0918276
$899$	4409.76	0.163597
$900$	8806.27	0.326158
$901$	78228.5	2.89253
$902$	5819.10	0.214806
$903$	0	0
$904$	5234.42	0.192582
$905$	300.557	0.0110396
$906$	−3494.01	−0.128125
$907$	−22715.4	−0.831590	−0.415795	−	0.909458i	$-0.636497\pi$
$907$	−22715.4	−0.831590	−0.415795	+	0.909458i	$0.636497\pi$
$908$	14368.0	0.525130
$909$	12337.1	0.450161
$910$	0	0
$911$	34922.3	1.27006	0.635031	−	0.772487i	$-0.280987\pi$
$911$	34922.3	1.27006	0.635031	+	0.772487i	$0.280987\pi$
$912$	−22846.6	−0.829525
$913$	−17350.7	−0.628943
$914$	5741.24	0.207772
$915$	−3.69134	−0.000133368 0
$916$	21716.1	0.783320
$917$	0	0
$918$	1360.39	0.0489102
$919$	11702.6	0.420059	0.210030	−	0.977695i	$-0.432644\pi$
$919$	11702.6	0.420059	0.210030	+	0.977695i	$0.432644\pi$
$920$	35.3182	0.00126566
$921$	2661.29	0.0952144
$922$	61.8473	0.00220914
$923$	13683.5	0.487973
$924$	0	0
$925$	23983.3	0.852505
$926$	−2238.39	−0.0794364
$927$	12725.6	0.450878
$928$	−18210.4	−0.644165
$929$	−53096.5	−1.87518	−0.937588	−	0.347747i	$-0.886947\pi$
$929$	−53096.5	−1.87518	−0.937588	+	0.347747i	$0.886947\pi$
$930$	2.33681	8.23946e−5 0
$931$	0	0
$932$	7740.06	0.272032
$933$	13532.5	0.474848
$934$	−1534.52	−0.0537591
$935$	−537.198	−0.0187896
$936$	982.154	0.0342978
$937$	−39020.6	−1.36046	−0.680229	−	0.733000i	$-0.738120\pi$
$937$	−39020.6	−1.36046	−0.680229	+	0.733000i	$0.738120\pi$
$938$	0	0
$939$	−11147.4	−0.387412
$940$	315.941	0.0109626
$941$	30743.8	1.06506	0.532528	−	0.846412i	$-0.321242\pi$
$941$	30743.8	1.06506	0.532528	+	0.846412i	$0.321242\pi$
$942$	2101.73	0.0726944
$943$	17136.0	0.591754
$944$	695.710	0.0239867
$945$	0	0
$946$	−3978.35	−0.136731
$947$	16300.3	0.559332	0.279666	−	0.960097i	$-0.409776\pi$
$947$	16300.3	0.559332	0.279666	+	0.960097i	$0.409776\pi$
$948$	−18923.4	−0.648315
$949$	−8573.66	−0.293269
$950$	6580.94	0.224752
$951$	−20863.6	−0.711406
$952$	0	0
$953$	−11512.7	−0.391325	−0.195663	−	0.980671i	$-0.562686\pi$
$953$	−11512.7	−0.391325	−0.195663	+	0.980671i	$0.562686\pi$
$954$	−2397.49	−0.0813644
$955$	−282.159	−0.00956068
$956$	6559.65	0.221919
$957$	31068.3	1.04942
$958$	4420.39	0.149078
$959$	0	0
$960$	134.864	0.00453409
$961$	−29440.9	−0.988248
$962$	1322.92	0.0443375
$963$	−3091.85	−0.103462
$964$	−27047.1	−0.903661
$965$	335.322	0.0111859
$966$	0	0
$967$	−18178.4	−0.604528	−0.302264	−	0.953224i	$-0.597742\pi$
$967$	−18178.4	−0.604528	−0.302264	+	0.953224i	$0.597742\pi$
$968$	3932.65	0.130579
$969$	−46385.8	−1.53780
$970$	−45.4237	−0.00150357
$971$	−28276.7	−0.934543	−0.467271	−	0.884114i	$-0.654763\pi$
$971$	−28276.7	−0.934543	−0.467271	+	0.884114i	$0.654763\pi$
$972$	1902.31	0.0627742
$973$	0	0
$974$	−2424.77	−0.0797688
$975$	6241.24	0.205005
$976$	733.477	0.0240554
$977$	−13947.1	−0.456710	−0.228355	−	0.973578i	$-0.573335\pi$
$977$	−13947.1	−0.456710	−0.228355	+	0.973578i	$0.573335\pi$
$978$	−50.6043	−0.00165455
$979$	29590.8	0.966011
$980$	0	0
$981$	−2858.91	−0.0930459
$982$	−1683.91	−0.0547206
$983$	26576.8	0.862327	0.431164	−	0.902274i	$-0.358103\pi$
$983$	26576.8	0.862327	0.431164	+	0.902274i	$0.358103\pi$
$984$	−6288.45	−0.203728
$985$	−424.799	−0.0137414
$986$	−11874.7	−0.383539
$987$	0	0
$988$	−16563.0	−0.533339
$989$	−11715.4	−0.376671
$990$	16.4636	0.000528534 0
$991$	16249.9	0.520884	0.260442	−	0.965490i	$-0.416132\pi$
$991$	16249.9	0.520884	0.260442	+	0.965490i	$0.416132\pi$
$992$	−1445.72	−0.0462718
$993$	29589.5	0.945615
$994$	0	0
$995$	−440.784	−0.0140440
$996$	9273.47	0.295021
$997$	−18814.1	−0.597642	−0.298821	−	0.954309i	$-0.596593\pi$
$997$	−18814.1	−0.597642	−0.298821	+	0.954309i	$0.596593\pi$
$998$	−1992.86	−0.0632092
$999$	5180.82	0.164078

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.4.a.j.1.1	✓	2
3.2	odd	2		441.4.a.n.1.2		2
4.3	odd	2		2352.4.a.cf.1.1		2
7.2	even	3		147.4.e.k.67.2		4
7.3	odd	6		147.4.e.j.79.2		4
7.4	even	3		147.4.e.k.79.2		4
7.5	odd	6		147.4.e.j.67.2		4
7.6	odd	2		147.4.a.k.1.1	yes	2
21.2	odd	6		441.4.e.v.361.1		4
21.5	even	6		441.4.e.u.361.1		4
21.11	odd	6		441.4.e.v.226.1		4
21.17	even	6		441.4.e.u.226.1		4
21.20	even	2		441.4.a.o.1.2		2
28.27	even	2		2352.4.a.bl.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.4.a.j.1.1	✓	2	1.1	even	1	trivial
147.4.a.k.1.1	yes	2	7.6	odd	2
147.4.e.j.67.2		4	7.5	odd	6
147.4.e.j.79.2		4	7.3	odd	6
147.4.e.k.67.2		4	7.2	even	3
147.4.e.k.79.2		4	7.4	even	3
441.4.a.n.1.2		2	3.2	odd	2
441.4.a.o.1.2		2	21.20	even	2
441.4.e.u.226.1		4	21.17	even	6
441.4.e.u.361.1		4	21.5	even	6
441.4.e.v.226.1		4	21.11	odd	6
441.4.e.v.361.1		4	21.2	odd	6
2352.4.a.bl.1.2		2	28.27	even	2
2352.4.a.cf.1.1		2	4.3	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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	147.a (trivial)

\(f(q)\)	\(=\)	\(q-0.414214 q^{2} -3.00000 q^{3} -7.82843 q^{4} +0.100505 q^{5} +1.24264 q^{6} +6.55635 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-0.414214 q^{2} -3.00000 q^{3} -7.82843 q^{4} +0.100505 q^{5} +1.24264 q^{6} +6.55635 q^{8} +9.00000 q^{9} -0.0416306 q^{10} -43.9411 q^{11} +23.4853 q^{12} +16.6447 q^{13} -0.301515 q^{15} +59.9117 q^{16} +121.640 q^{17} -3.72792 q^{18} +127.113 q^{19} -0.786797 q^{20} +18.2010 q^{22} +53.5980 q^{23} -19.6690 q^{24} -124.990 q^{25} -6.89444 q^{26} -27.0000 q^{27} +235.681 q^{29} +0.124892 q^{30} +18.7107 q^{31} -77.2670 q^{32} +131.823 q^{33} -50.3848 q^{34} -70.4558 q^{36} -191.882 q^{37} -52.6518 q^{38} -49.9340 q^{39} +0.658946 q^{40} +319.713 q^{41} -218.579 q^{43} +343.990 q^{44} +0.904546 q^{45} -22.2010 q^{46} -401.553 q^{47} -179.735 q^{48} +51.7725 q^{50} -364.919 q^{51} -130.302 q^{52} +643.117 q^{53} +11.1838 q^{54} -4.41631 q^{55} -381.338 q^{57} -97.6224 q^{58} +11.6123 q^{59} +2.36039 q^{60} +12.2426 q^{61} -7.75022 q^{62} -447.288 q^{64} +1.67287 q^{65} -54.6030 q^{66} +669.048 q^{67} -952.247 q^{68} -160.794 q^{69} +822.098 q^{71} +59.0071 q^{72} -515.100 q^{73} +79.4802 q^{74} +374.970 q^{75} -995.092 q^{76} +20.6833 q^{78} -805.754 q^{79} +6.02143 q^{80} +81.0000 q^{81} -132.429 q^{82} +394.863 q^{83} +12.2254 q^{85} +90.5382 q^{86} -707.044 q^{87} -288.093 q^{88} -673.418 q^{89} -0.374675 q^{90} -419.588 q^{92} -56.1320 q^{93} +166.329 q^{94} +12.7755 q^{95} +231.801 q^{96} +1091.11 q^{97} -395.470 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 6 q^{3} - 10 q^{4} + 20 q^{5} - 6 q^{6} - 18 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 6 * q^3 - 10 * q^4 + 20 * q^5 - 6 * q^6 - 18 * q^8 + 18 * q^9	\( 2 q + 2 q^{2} - 6 q^{3} - 10 q^{4} + 20 q^{5} - 6 q^{6} - 18 q^{8} + 18 q^{9} + 48 q^{10} - 20 q^{11} + 30 q^{12} + 104 q^{13} - 60 q^{15} + 18 q^{16} + 116 q^{17} + 18 q^{18} + 192 q^{19} - 44 q^{20} + 76 q^{22} + 28 q^{23} + 54 q^{24} + 146 q^{25} + 204 q^{26} - 54 q^{27} + 296 q^{29} - 144 q^{30} - 104 q^{31} + 18 q^{32} + 60 q^{33} - 64 q^{34} - 90 q^{36} - 248 q^{37} + 104 q^{38} - 312 q^{39} - 488 q^{40} + 20 q^{41} - 720 q^{43} + 292 q^{44} + 180 q^{45} - 84 q^{46} - 96 q^{47} - 54 q^{48} + 706 q^{50} - 348 q^{51} - 320 q^{52} + 268 q^{53} - 54 q^{54} + 472 q^{55} - 576 q^{57} + 48 q^{58} - 616 q^{59} + 132 q^{60} + 16 q^{61} - 304 q^{62} + 118 q^{64} + 1740 q^{65} - 228 q^{66} - 144 q^{67} - 940 q^{68} - 84 q^{69} + 988 q^{71} - 162 q^{72} + 104 q^{73} - 56 q^{74} - 438 q^{75} - 1136 q^{76} - 612 q^{78} - 944 q^{79} - 828 q^{80} + 162 q^{81} - 856 q^{82} + 1016 q^{83} - 100 q^{85} - 1120 q^{86} - 888 q^{87} - 876 q^{88} - 388 q^{89} + 432 q^{90} - 364 q^{92} + 312 q^{93} + 904 q^{94} + 1304 q^{95} - 54 q^{96} + 488 q^{97} - 180 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 6 * q^3 - 10 * q^4 + 20 * q^5 - 6 * q^6 - 18 * q^8 + 18 * q^9 + 48 * q^10 - 20 * q^11 + 30 * q^12 + 104 * q^13 - 60 * q^15 + 18 * q^16 + 116 * q^17 + 18 * q^18 + 192 * q^19 - 44 * q^20 + 76 * q^22 + 28 * q^23 + 54 * q^24 + 146 * q^25 + 204 * q^26 - 54 * q^27 + 296 * q^29 - 144 * q^30 - 104 * q^31 + 18 * q^32 + 60 * q^33 - 64 * q^34 - 90 * q^36 - 248 * q^37 + 104 * q^38 - 312 * q^39 - 488 * q^40 + 20 * q^41 - 720 * q^43 + 292 * q^44 + 180 * q^45 - 84 * q^46 - 96 * q^47 - 54 * q^48 + 706 * q^50 - 348 * q^51 - 320 * q^52 + 268 * q^53 - 54 * q^54 + 472 * q^55 - 576 * q^57 + 48 * q^58 - 616 * q^59 + 132 * q^60 + 16 * q^61 - 304 * q^62 + 118 * q^64 + 1740 * q^65 - 228 * q^66 - 144 * q^67 - 940 * q^68 - 84 * q^69 + 988 * q^71 - 162 * q^72 + 104 * q^73 - 56 * q^74 - 438 * q^75 - 1136 * q^76 - 612 * q^78 - 944 * q^79 - 828 * q^80 + 162 * q^81 - 856 * q^82 + 1016 * q^83 - 100 * q^85 - 1120 * q^86 - 888 * q^87 - 876 * q^88 - 388 * q^89 + 432 * q^90 - 364 * q^92 + 312 * q^93 + 904 * q^94 + 1304 * q^95 - 54 * q^96 + 488 * q^97 - 180 * q^99

Introduction

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