LMFDB - Embedded newform 525.4.a.n.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,4,Mod(1,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("525.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	525.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:	$30.9760027530$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{57}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 14 $ x^2 - x - 14
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$4.27492$ of defining polynomial
Character	$\chi$	$=$	525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.27492 q^{2} -3.00000 q^{3} +19.8248 q^{4} -15.8248 q^{6} -7.00000 q^{7} +62.3746 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+5.27492 q^{2} -3.00000 q^{3} +19.8248 q^{4} -15.8248 q^{6} -7.00000 q^{7} +62.3746 q^{8} +9.00000 q^{9} +34.7492 q^{11} -59.4743 q^{12} +37.2990 q^{13} -36.9244 q^{14} +170.423 q^{16} +10.5498 q^{17} +47.4743 q^{18} -58.5980 q^{19} +21.0000 q^{21} +183.299 q^{22} +125.347 q^{23} -187.124 q^{24} +196.749 q^{26} -27.0000 q^{27} -138.773 q^{28} -35.4020 q^{29} +291.794 q^{31} +399.969 q^{32} -104.248 q^{33} +55.6495 q^{34} +178.423 q^{36} +259.897 q^{37} -309.100 q^{38} -111.897 q^{39} -338.248 q^{41} +110.773 q^{42} -6.80397 q^{43} +688.894 q^{44} +661.196 q^{46} -250.694 q^{47} -511.268 q^{48} +49.0000 q^{49} -31.6495 q^{51} +739.444 q^{52} +536.900 q^{53} -142.423 q^{54} -436.622 q^{56} +175.794 q^{57} -186.743 q^{58} -35.8904 q^{59} +57.7940 q^{61} +1539.19 q^{62} -63.0000 q^{63} +746.423 q^{64} -549.897 q^{66} -481.691 q^{67} +209.148 q^{68} -376.042 q^{69} +363.752 q^{71} +561.371 q^{72} -581.299 q^{73} +1370.94 q^{74} -1161.69 q^{76} -243.244 q^{77} -590.248 q^{78} -693.691 q^{79} +81.0000 q^{81} -1784.23 q^{82} -1334.39 q^{83} +416.320 q^{84} -35.8904 q^{86} +106.206 q^{87} +2167.47 q^{88} -353.038 q^{89} -261.093 q^{91} +2484.98 q^{92} -875.382 q^{93} -1322.39 q^{94} -1199.91 q^{96} -1445.88 q^{97} +258.471 q^{98} +312.743 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} - 6 q^{3} + 17 q^{4} - 9 q^{6} - 14 q^{7} + 87 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q + 3 * q^2 - 6 * q^3 + 17 * q^4 - 9 * q^6 - 14 * q^7 + 87 * q^8 + 18 * q^9	$ 2 q + 3 q^{2} - 6 q^{3} + 17 q^{4} - 9 q^{6} - 14 q^{7} + 87 q^{8} + 18 q^{9} - 6 q^{11} - 51 q^{12} - 16 q^{13} - 21 q^{14} + 137 q^{16} + 6 q^{17} + 27 q^{18} + 64 q^{19} + 42 q^{21} + 276 q^{22} - 6 q^{23} - 261 q^{24} + 318 q^{26} - 54 q^{27} - 119 q^{28} - 252 q^{29} + 40 q^{31} + 279 q^{32} + 18 q^{33} + 66 q^{34} + 153 q^{36} + 248 q^{37} - 588 q^{38} + 48 q^{39} - 450 q^{41} + 63 q^{42} - 376 q^{43} + 804 q^{44} + 960 q^{46} + 12 q^{47} - 411 q^{48} + 98 q^{49} - 18 q^{51} + 890 q^{52} + 1104 q^{53} - 81 q^{54} - 609 q^{56} - 192 q^{57} + 306 q^{58} + 804 q^{59} - 428 q^{61} + 2112 q^{62} - 126 q^{63} + 1289 q^{64} - 828 q^{66} - 148 q^{67} + 222 q^{68} + 18 q^{69} + 954 q^{71} + 783 q^{72} - 1072 q^{73} + 1398 q^{74} - 1508 q^{76} + 42 q^{77} - 954 q^{78} - 572 q^{79} + 162 q^{81} - 1530 q^{82} - 1944 q^{83} + 357 q^{84} + 804 q^{86} + 756 q^{87} + 1164 q^{88} + 366 q^{89} + 112 q^{91} + 2856 q^{92} - 120 q^{93} - 1920 q^{94} - 837 q^{96} - 808 q^{97} + 147 q^{98} - 54 q^{99}+O(q^{100}) $ 2 * q + 3 * q^2 - 6 * q^3 + 17 * q^4 - 9 * q^6 - 14 * q^7 + 87 * q^8 + 18 * q^9 - 6 * q^11 - 51 * q^12 - 16 * q^13 - 21 * q^14 + 137 * q^16 + 6 * q^17 + 27 * q^18 + 64 * q^19 + 42 * q^21 + 276 * q^22 - 6 * q^23 - 261 * q^24 + 318 * q^26 - 54 * q^27 - 119 * q^28 - 252 * q^29 + 40 * q^31 + 279 * q^32 + 18 * q^33 + 66 * q^34 + 153 * q^36 + 248 * q^37 - 588 * q^38 + 48 * q^39 - 450 * q^41 + 63 * q^42 - 376 * q^43 + 804 * q^44 + 960 * q^46 + 12 * q^47 - 411 * q^48 + 98 * q^49 - 18 * q^51 + 890 * q^52 + 1104 * q^53 - 81 * q^54 - 609 * q^56 - 192 * q^57 + 306 * q^58 + 804 * q^59 - 428 * q^61 + 2112 * q^62 - 126 * q^63 + 1289 * q^64 - 828 * q^66 - 148 * q^67 + 222 * q^68 + 18 * q^69 + 954 * q^71 + 783 * q^72 - 1072 * q^73 + 1398 * q^74 - 1508 * q^76 + 42 * q^77 - 954 * q^78 - 572 * q^79 + 162 * q^81 - 1530 * q^82 - 1944 * q^83 + 357 * q^84 + 804 * q^86 + 756 * q^87 + 1164 * q^88 + 366 * q^89 + 112 * q^91 + 2856 * q^92 - 120 * q^93 - 1920 * q^94 - 837 * q^96 - 808 * q^97 + 147 * q^98 - 54 * 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 $

$2$	5.27492	1.86496	0.932482	−	0.361215i	$-0.117638\pi$
$2$	5.27492	1.86496	0.932482	+	0.361215i	$0.117638\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	19.8248	2.47809
$5$	0	0
$5$	0	0
$6$	−15.8248	−1.07674
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	62.3746	2.75659
$9$	9.00000	0.333333
$10$	0	0
$11$	34.7492	0.952479	0.476240	−	0.879316i	$-0.342000\pi$
$11$	34.7492	0.952479	0.476240	+	0.879316i	$0.342000\pi$
$12$	−59.4743	−1.43073
$13$	37.2990	0.795760	0.397880	−	0.917437i	$-0.369746\pi$
$13$	37.2990	0.795760	0.397880	+	0.917437i	$0.369746\pi$
$14$	−36.9244	−0.704890
$15$	0	0
$16$	170.423	2.66286
$17$	10.5498	0.150512	0.0752562	−	0.997164i	$-0.476023\pi$
$17$	10.5498	0.150512	0.0752562	+	0.997164i	$0.476023\pi$
$18$	47.4743	0.621655
$19$	−58.5980	−0.707542	−0.353771	−	0.935332i	$-0.615101\pi$
$19$	−58.5980	−0.707542	−0.353771	+	0.935332i	$0.615101\pi$
$20$	0	0
$21$	21.0000	0.218218
$22$	183.299	1.77634
$23$	125.347	1.13638	0.568189	−	0.822898i	$-0.307644\pi$
$23$	125.347	1.13638	0.568189	+	0.822898i	$0.307644\pi$
$24$	−187.124	−1.59152
$25$	0	0
$26$	196.749	1.48406
$27$	−27.0000	−0.192450
$28$	−138.773	−0.936631
$29$	−35.4020	−0.226689	−0.113345	−	0.993556i	$-0.536156\pi$
$29$	−35.4020	−0.226689	−0.113345	+	0.993556i	$0.536156\pi$
$30$	0	0
$31$	291.794	1.69057	0.845286	−	0.534313i	$-0.179430\pi$
$31$	291.794	1.69057	0.845286	+	0.534313i	$0.179430\pi$
$32$	399.969	2.20954
$33$	−104.248	−0.549914
$34$	55.6495	0.280700
$35$	0	0
$36$	178.423	0.826031
$37$	259.897	1.15478	0.577389	−	0.816469i	$-0.304072\pi$
$37$	259.897	1.15478	0.577389	+	0.816469i	$0.304072\pi$
$38$	−309.100	−1.31954
$39$	−111.897	−0.459432
$40$	0	0
$41$	−338.248	−1.28842	−0.644212	−	0.764847i	$-0.722815\pi$
$41$	−338.248	−1.28842	−0.644212	+	0.764847i	$0.722815\pi$
$42$	110.773	0.406969
$43$	−6.80397	−0.0241301	−0.0120651	−	0.999927i	$-0.503841\pi$
$43$	−6.80397	−0.0241301	−0.0120651	+	0.999927i	$0.503841\pi$
$44$	688.894	2.36033
$45$	0	0
$46$	661.196	2.11931
$47$	−250.694	−0.778033	−0.389016	−	0.921231i	$-0.627185\pi$
$47$	−250.694	−0.778033	−0.389016	+	0.921231i	$0.627185\pi$
$48$	−511.268	−1.53740
$49$	49.0000	0.142857
$50$	0	0
$51$	−31.6495	−0.0868984
$52$	739.444	1.97197
$53$	536.900	1.39149	0.695745	−	0.718289i	$-0.255075\pi$
$53$	536.900	1.39149	0.695745	+	0.718289i	$0.255075\pi$
$54$	−142.423	−0.358913
$55$	0	0
$56$	−436.622	−1.04189
$57$	175.794	0.408500
$58$	−186.743	−0.422767
$59$	−35.8904	−0.0791955	−0.0395977	−	0.999216i	$-0.512608\pi$
$59$	−35.8904	−0.0791955	−0.0395977	+	0.999216i	$0.512608\pi$
$60$	0	0
$61$	57.7940	0.121308	0.0606538	−	0.998159i	$-0.480681\pi$
$61$	57.7940	0.121308	0.0606538	+	0.998159i	$0.480681\pi$
$62$	1539.19	3.15286
$63$	−63.0000	−0.125988
$64$	746.423	1.45786
$65$	0	0
$66$	−549.897	−1.02557
$67$	−481.691	−0.878327	−0.439164	−	0.898407i	$-0.644725\pi$
$67$	−481.691	−0.878327	−0.439164	+	0.898407i	$0.644725\pi$
$68$	209.148	0.372984
$69$	−376.042	−0.656088
$70$	0	0
$71$	363.752	0.608021	0.304010	−	0.952669i	$-0.401674\pi$
$71$	363.752	0.608021	0.304010	+	0.952669i	$0.401674\pi$
$72$	561.371	0.918864
$73$	−581.299	−0.931999	−0.465999	−	0.884785i	$-0.654305\pi$
$73$	−581.299	−0.931999	−0.465999	+	0.884785i	$0.654305\pi$
$74$	1370.94	2.15362
$75$	0	0
$76$	−1161.69	−1.75336
$77$	−243.244	−0.360003
$78$	−590.248	−0.856825
$79$	−693.691	−0.987928	−0.493964	−	0.869482i	$-0.664453\pi$
$79$	−693.691	−0.987928	−0.493964	+	0.869482i	$0.664453\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	−1784.23	−2.40287
$83$	−1334.39	−1.76468	−0.882341	−	0.470611i	$-0.844033\pi$
$83$	−1334.39	−1.76468	−0.882341	+	0.470611i	$0.844033\pi$
$84$	416.320	0.540764
$85$	0	0
$86$	−35.8904	−0.0450019
$87$	106.206	0.130879
$88$	2167.47	2.62560
$89$	−353.038	−0.420472	−0.210236	−	0.977651i	$-0.567423\pi$
$89$	−353.038	−0.420472	−0.210236	+	0.977651i	$0.567423\pi$
$90$	0	0
$91$	−261.093	−0.300769
$92$	2484.98	2.81605
$93$	−875.382	−0.976053
$94$	−1322.39	−1.45100
$95$	0	0
$96$	−1199.91	−1.27568
$97$	−1445.88	−1.51347	−0.756735	−	0.653722i	$-0.773207\pi$
$97$	−1445.88	−1.51347	−0.756735	+	0.653722i	$0.773207\pi$
$98$	258.471	0.266424
$99$	312.743	0.317493
$100$	0	0
$101$	474.852	0.467817	0.233909	−	0.972259i	$-0.424848\pi$
$101$	474.852	0.467817	0.233909	+	0.972259i	$0.424848\pi$
$102$	−166.949	−0.162062
$103$	1999.59	1.91287	0.956433	−	0.291951i	$-0.0943044\pi$
$103$	1999.59	1.91287	0.956433	+	0.291951i	$0.0943044\pi$
$104$	2326.51	2.19359
$105$	0	0
$106$	2832.10	2.59508
$107$	−1166.74	−1.05414	−0.527068	−	0.849823i	$-0.676709\pi$
$107$	−1166.74	−1.05414	−0.527068	+	0.849823i	$0.676709\pi$
$108$	−535.268	−0.476909
$109$	−1337.18	−1.17503	−0.587515	−	0.809213i	$-0.699894\pi$
$109$	−1337.18	−1.17503	−0.587515	+	0.809213i	$0.699894\pi$
$110$	0	0
$111$	−779.691	−0.666712
$112$	−1192.96	−1.00646
$113$	−906.578	−0.754723	−0.377361	−	0.926066i	$-0.623169\pi$
$113$	−906.578	−0.754723	−0.377361	+	0.926066i	$0.623169\pi$
$114$	927.299	0.761838
$115$	0	0
$116$	−701.836	−0.561757
$117$	335.691	0.265253
$118$	−189.319	−0.147697
$119$	−73.8488	−0.0568883
$120$	0	0
$121$	−123.495	−0.0927836
$122$	304.859	0.226235
$123$	1014.74	0.743872
$124$	5784.74	4.18940
$125$	0	0
$126$	−332.320	−0.234963
$127$	1714.89	1.19820	0.599101	−	0.800674i	$-0.295525\pi$
$127$	1714.89	1.19820	0.599101	+	0.800674i	$0.295525\pi$
$128$	737.564	0.509313
$129$	20.4119	0.0139315
$130$	0	0
$131$	470.611	0.313874	0.156937	−	0.987609i	$-0.449838\pi$
$131$	470.611	0.313874	0.156937	+	0.987609i	$0.449838\pi$
$132$	−2066.68	−1.36274
$133$	410.186	0.267426
$134$	−2540.88	−1.63805
$135$	0	0
$136$	658.042	0.414901
$137$	443.910	0.276831	0.138415	−	0.990374i	$-0.455799\pi$
$137$	443.910	0.276831	0.138415	+	0.990374i	$0.455799\pi$
$138$	−1983.59	−1.22358
$139$	1669.98	1.01904	0.509518	−	0.860460i	$-0.329824\pi$
$139$	1669.98	1.01904	0.509518	+	0.860460i	$0.329824\pi$
$140$	0	0
$141$	752.083	0.449197
$142$	1918.76	1.13394
$143$	1296.11	0.757945
$144$	1533.80	0.887619
$145$	0	0
$146$	−3066.30	−1.73814
$147$	−147.000	−0.0824786
$148$	5152.39	2.86165
$149$	743.871	0.408995	0.204497	−	0.978867i	$-0.434444\pi$
$149$	743.871	0.408995	0.204497	+	0.978867i	$0.434444\pi$
$150$	0	0
$151$	606.764	0.327005	0.163503	−	0.986543i	$-0.447721\pi$
$151$	606.764	0.327005	0.163503	+	0.986543i	$0.447721\pi$
$152$	−3655.03	−1.95041
$153$	94.9485	0.0501708
$154$	−1283.09	−0.671393
$155$	0	0
$156$	−2218.33	−1.13852
$157$	−3114.78	−1.58336	−0.791678	−	0.610939i	$-0.790792\pi$
$157$	−3114.78	−1.58336	−0.791678	+	0.610939i	$0.790792\pi$
$158$	−3659.16	−1.84245
$159$	−1610.70	−0.803377
$160$	0	0
$161$	−877.430	−0.429511
$162$	427.268	0.207218
$163$	−2413.07	−1.15955	−0.579774	−	0.814777i	$-0.696859\pi$
$163$	−2413.07	−1.15955	−0.579774	+	0.814777i	$0.696859\pi$
$164$	−6705.67	−3.19284
$165$	0	0
$166$	−7038.81	−3.29107
$167$	610.475	0.282874	0.141437	−	0.989947i	$-0.454828\pi$
$167$	610.475	0.282874	0.141437	+	0.989947i	$0.454828\pi$
$168$	1309.87	0.601538
$169$	−805.784	−0.366766
$170$	0	0
$171$	−527.382	−0.235847
$172$	−134.887	−0.0597968
$173$	−3793.81	−1.66727	−0.833636	−	0.552315i	$-0.813745\pi$
$173$	−3793.81	−1.66727	−0.833636	+	0.552315i	$0.813745\pi$
$174$	560.228	0.244085
$175$	0	0
$176$	5922.05	2.53631
$177$	107.671	0.0457235
$178$	−1862.25	−0.784165
$179$	−2804.68	−1.17112	−0.585562	−	0.810627i	$-0.699126\pi$
$179$	−2804.68	−1.17112	−0.585562	+	0.810627i	$0.699126\pi$
$180$	0	0
$181$	3106.04	1.27553	0.637763	−	0.770232i	$-0.279860\pi$
$181$	3106.04	1.27553	0.637763	+	0.770232i	$0.279860\pi$
$182$	−1377.24	−0.560924
$183$	−173.382	−0.0700370
$184$	7818.48	3.13253
$185$	0	0
$186$	−4617.57	−1.82030
$187$	366.598	0.143360
$188$	−4969.95	−1.92804
$189$	189.000	0.0727393
$190$	0	0
$191$	261.952	0.0992365	0.0496182	−	0.998768i	$-0.484200\pi$
$191$	261.952	0.0992365	0.0496182	+	0.998768i	$0.484200\pi$
$192$	−2239.27	−0.841694
$193$	−4051.07	−1.51089	−0.755447	−	0.655210i	$-0.772580\pi$
$193$	−4051.07	−1.51089	−0.755447	+	0.655210i	$0.772580\pi$
$194$	−7626.88	−2.82257
$195$	0	0
$196$	971.413	0.354013
$197$	2874.83	1.03971	0.519855	−	0.854254i	$-0.325986\pi$
$197$	2874.83	1.03971	0.519855	+	0.854254i	$0.325986\pi$
$198$	1649.69	0.592113
$199$	−3066.97	−1.09252	−0.546261	−	0.837615i	$-0.683949\pi$
$199$	−3066.97	−1.09252	−0.546261	+	0.837615i	$0.683949\pi$
$200$	0	0
$201$	1445.07	0.507103
$202$	2504.81	0.872463
$203$	247.814	0.0856804
$204$	−627.444	−0.215342
$205$	0	0
$206$	10547.7	3.56743
$207$	1128.12	0.378793
$208$	6356.60	2.11899
$209$	−2036.23	−0.673919
$210$	0	0
$211$	595.422	0.194268	0.0971340	−	0.995271i	$-0.469032\pi$
$211$	595.422	0.194268	0.0971340	+	0.995271i	$0.469032\pi$
$212$	10643.9	3.44824
$213$	−1091.26	−0.351041
$214$	−6154.44	−1.96593
$215$	0	0
$216$	−1684.11	−0.530507
$217$	−2042.56	−0.638976
$218$	−7053.49	−2.19139
$219$	1743.90	0.538090
$220$	0	0
$221$	393.498	0.119772
$222$	−4112.81	−1.24339
$223$	3779.79	1.13504	0.567520	−	0.823360i	$-0.307903\pi$
$223$	3779.79	1.13504	0.567520	+	0.823360i	$0.307903\pi$
$224$	−2799.79	−0.835127
$225$	0	0
$226$	−4782.12	−1.40753
$227$	−1827.62	−0.534376	−0.267188	−	0.963644i	$-0.586094\pi$
$227$	−1827.62	−0.534376	−0.267188	+	0.963644i	$0.586094\pi$
$228$	3485.07	1.01230
$229$	−850.249	−0.245354	−0.122677	−	0.992447i	$-0.539148\pi$
$229$	−850.249	−0.245354	−0.122677	+	0.992447i	$0.539148\pi$
$230$	0	0
$231$	729.733	0.207848
$232$	−2208.18	−0.624890
$233$	6591.10	1.85321	0.926604	−	0.376039i	$-0.122714\pi$
$233$	6591.10	1.85321	0.926604	+	0.376039i	$0.122714\pi$
$234$	1770.74	0.494688
$235$	0	0
$236$	−711.518	−0.196254
$237$	2081.07	0.570381
$238$	−389.547	−0.106095
$239$	−182.556	−0.0494083	−0.0247042	−	0.999695i	$-0.507864\pi$
$239$	−182.556	−0.0494083	−0.0247042	+	0.999695i	$0.507864\pi$
$240$	0	0
$241$	1523.90	0.407315	0.203657	−	0.979042i	$-0.434717\pi$
$241$	1523.90	0.407315	0.203657	+	0.979042i	$0.434717\pi$
$242$	−651.426	−0.173038
$243$	−243.000	−0.0641500
$244$	1145.75	0.300612
$245$	0	0
$246$	5352.68	1.38730
$247$	−2185.65	−0.563034
$248$	18200.5	4.66022
$249$	4003.18	1.01884
$250$	0	0
$251$	2357.73	0.592903	0.296451	−	0.955048i	$-0.404197\pi$
$251$	2357.73	0.592903	0.296451	+	0.955048i	$0.404197\pi$
$252$	−1248.96	−0.312210
$253$	4355.71	1.08238
$254$	9045.89	2.23460
$255$	0	0
$256$	−2080.79	−0.508006
$257$	−2782.55	−0.675372	−0.337686	−	0.941259i	$-0.609644\pi$
$257$	−2782.55	−0.675372	−0.337686	+	0.941259i	$0.609644\pi$
$258$	107.671	0.0259818
$259$	−1819.28	−0.436465
$260$	0	0
$261$	−318.618	−0.0755630
$262$	2482.44	0.585364
$263$	−2043.78	−0.479183	−0.239591	−	0.970874i	$-0.577013\pi$
$263$	−2043.78	−0.479183	−0.239591	+	0.970874i	$0.577013\pi$
$264$	−6502.40	−1.51589
$265$	0	0
$266$	2163.70	0.498740
$267$	1059.11	0.242759
$268$	−9549.41	−2.17658
$269$	3452.84	0.782614	0.391307	−	0.920260i	$-0.372023\pi$
$269$	3452.84	0.782614	0.391307	+	0.920260i	$0.372023\pi$
$270$	0	0
$271$	2644.29	0.592728	0.296364	−	0.955075i	$-0.404226\pi$
$271$	2644.29	0.592728	0.296364	+	0.955075i	$0.404226\pi$
$272$	1797.93	0.400793
$273$	783.279	0.173649
$274$	2341.59	0.516280
$275$	0	0
$276$	−7454.93	−1.62585
$277$	−2679.49	−0.581208	−0.290604	−	0.956843i	$-0.593856\pi$
$277$	−2679.49	−0.581208	−0.290604	+	0.956843i	$0.593856\pi$
$278$	8809.01	1.90046
$279$	2626.15	0.563524
$280$	0	0
$281$	−1019.69	−0.216476	−0.108238	−	0.994125i	$-0.534521\pi$
$281$	−1019.69	−0.216476	−0.108238	+	0.994125i	$0.534521\pi$
$282$	3967.18	0.837737
$283$	−432.206	−0.0907844	−0.0453922	−	0.998969i	$-0.514454\pi$
$283$	−432.206	−0.0907844	−0.0453922	+	0.998969i	$0.514454\pi$
$284$	7211.30	1.50673
$285$	0	0
$286$	6836.87	1.41354
$287$	2367.73	0.486979
$288$	3599.72	0.736513
$289$	−4801.70	−0.977346
$290$	0	0
$291$	4337.63	0.873802
$292$	−11524.1	−2.30958
$293$	2245.92	0.447809	0.223904	−	0.974611i	$-0.428120\pi$
$293$	2245.92	0.447809	0.223904	+	0.974611i	$0.428120\pi$
$294$	−775.413	−0.153820
$295$	0	0
$296$	16211.0	3.18325
$297$	−938.228	−0.183305
$298$	3923.86	0.762761
$299$	4675.33	0.904284
$300$	0	0
$301$	47.6278	0.00912034
$302$	3200.63	0.609853
$303$	−1424.56	−0.270094
$304$	−9986.44	−1.88408
$305$	0	0
$306$	500.846	0.0935668
$307$	3197.08	0.594354	0.297177	−	0.954822i	$-0.403955\pi$
$307$	3197.08	0.594354	0.297177	+	0.954822i	$0.403955\pi$
$308$	−4822.26	−0.892122
$309$	−5998.76	−1.10439
$310$	0	0
$311$	−3355.60	−0.611829	−0.305915	−	0.952059i	$-0.598962\pi$
$311$	−3355.60	−0.611829	−0.305915	+	0.952059i	$0.598962\pi$
$312$	−6979.53	−1.26647
$313$	2256.39	0.407472	0.203736	−	0.979026i	$-0.434692\pi$
$313$	2256.39	0.407472	0.203736	+	0.979026i	$0.434692\pi$
$314$	−16430.2	−2.95290
$315$	0	0
$316$	−13752.3	−2.44818
$317$	6139.19	1.08773	0.543866	−	0.839172i	$-0.316960\pi$
$317$	6139.19	1.08773	0.543866	+	0.839172i	$0.316960\pi$
$318$	−8496.31	−1.49827
$319$	−1230.19	−0.215917
$320$	0	0
$321$	3500.21	0.608606
$322$	−4628.37	−0.801022
$323$	−618.199	−0.106494
$324$	1605.80	0.275344
$325$	0	0
$326$	−12728.8	−2.16252
$327$	4011.53	0.678404
$328$	−21098.0	−3.55166
$329$	1754.86	0.294069
$330$	0	0
$331$	7029.81	1.16735	0.583676	−	0.811987i	$-0.301614\pi$
$331$	7029.81	1.16735	0.583676	+	0.811987i	$0.301614\pi$
$332$	−26454.0	−4.37305
$333$	2339.07	0.384926
$334$	3220.21	0.527550
$335$	0	0
$336$	3578.88	0.581083
$337$	−10328.4	−1.66951	−0.834757	−	0.550619i	$-0.814392\pi$
$337$	−10328.4	−1.66951	−0.834757	+	0.550619i	$0.814392\pi$
$338$	−4250.44	−0.684005
$339$	2719.73	0.435740
$340$	0	0
$341$	10139.6	1.61024
$342$	−2781.90	−0.439847
$343$	−343.000	−0.0539949
$344$	−424.395	−0.0665170
$345$	0	0
$346$	−20012.0	−3.10940
$347$	−1967.54	−0.304389	−0.152194	−	0.988351i	$-0.548634\pi$
$347$	−1967.54	−0.304389	−0.152194	+	0.988351i	$0.548634\pi$
$348$	2105.51	0.324330
$349$	−4365.46	−0.669564	−0.334782	−	0.942296i	$-0.608663\pi$
$349$	−4365.46	−0.669564	−0.334782	+	0.942296i	$0.608663\pi$
$350$	0	0
$351$	−1007.07	−0.153144
$352$	13898.6	2.10454
$353$	6071.59	0.915462	0.457731	−	0.889091i	$-0.348662\pi$
$353$	6071.59	0.915462	0.457731	+	0.889091i	$0.348662\pi$
$354$	567.957	0.0852728
$355$	0	0
$356$	−6998.90	−1.04197
$357$	221.547	0.0328445
$358$	−14794.4	−2.18411
$359$	9638.04	1.41693	0.708463	−	0.705748i	$-0.249389\pi$
$359$	9638.04	1.41693	0.708463	+	0.705748i	$0.249389\pi$
$360$	0	0
$361$	−3425.27	−0.499384
$362$	16384.1	2.37881
$363$	370.485	0.0535687
$364$	−5176.10	−0.745334
$365$	0	0
$366$	−914.576	−0.130617
$367$	−522.725	−0.0743488	−0.0371744	−	0.999309i	$-0.511836\pi$
$367$	−522.725	−0.0743488	−0.0371744	+	0.999309i	$0.511836\pi$
$368$	21362.0	3.02601
$369$	−3044.23	−0.429475
$370$	0	0
$371$	−3758.30	−0.525934
$372$	−17354.2	−2.41875
$373$	−3229.84	−0.448351	−0.224175	−	0.974549i	$-0.571969\pi$
$373$	−3229.84	−0.448351	−0.224175	+	0.974549i	$0.571969\pi$
$374$	1933.77	0.267361
$375$	0	0
$376$	−15637.0	−2.14472
$377$	−1320.46	−0.180390
$378$	996.959	0.135656
$379$	6639.71	0.899892	0.449946	−	0.893056i	$-0.351443\pi$
$379$	6639.71	0.899892	0.449946	+	0.893056i	$0.351443\pi$
$380$	0	0
$381$	−5144.66	−0.691782
$382$	1381.77	0.185073
$383$	14224.4	1.89774	0.948871	−	0.315664i	$-0.102227\pi$
$383$	14224.4	1.89774	0.948871	+	0.315664i	$0.102227\pi$
$384$	−2212.69	−0.294052
$385$	0	0
$386$	−21369.1	−2.81777
$387$	−61.2358	−0.00804338
$388$	−28664.2	−3.75052
$389$	2921.82	0.380828	0.190414	−	0.981704i	$-0.439017\pi$
$389$	2921.82	0.380828	0.190414	+	0.981704i	$0.439017\pi$
$390$	0	0
$391$	1322.39	0.171039
$392$	3056.35	0.393799
$393$	−1411.83	−0.181215
$394$	15164.5	1.93902
$395$	0	0
$396$	6200.04	0.786778
$397$	−811.940	−0.102645	−0.0513226	−	0.998682i	$-0.516344\pi$
$397$	−811.940	−0.102645	−0.0513226	+	0.998682i	$0.516344\pi$
$398$	−16178.0	−2.03751
$399$	−1230.56	−0.154398
$400$	0	0
$401$	2338.63	0.291237	0.145618	−	0.989341i	$-0.453483\pi$
$401$	2338.63	0.291237	0.145618	+	0.989341i	$0.453483\pi$
$402$	7622.64	0.945728
$403$	10883.6	1.34529
$404$	9413.83	1.15930
$405$	0	0
$406$	1307.20	0.159791
$407$	9031.21	1.09990
$408$	−1974.12	−0.239543
$409$	−2727.57	−0.329755	−0.164877	−	0.986314i	$-0.552723\pi$
$409$	−2727.57	−0.329755	−0.164877	+	0.986314i	$0.552723\pi$
$410$	0	0
$411$	−1331.73	−0.159828
$412$	39641.3	4.74026
$413$	251.233	0.0299331
$414$	5950.76	0.706435
$415$	0	0
$416$	14918.5	1.75826
$417$	−5009.94	−0.588340
$418$	−10741.0	−1.25684
$419$	13306.3	1.55144	0.775721	−	0.631076i	$-0.217386\pi$
$419$	13306.3	1.55144	0.775721	+	0.631076i	$0.217386\pi$
$420$	0	0
$421$	−11007.5	−1.27428	−0.637138	−	0.770750i	$-0.719882\pi$
$421$	−11007.5	−1.27428	−0.637138	+	0.770750i	$0.719882\pi$
$422$	3140.80	0.362303
$423$	−2256.25	−0.259344
$424$	33488.9	3.83577
$425$	0	0
$426$	−5756.29	−0.654679
$427$	−404.558	−0.0458500
$428$	−23130.2	−2.61225
$429$	−3888.33	−0.437600
$430$	0	0
$431$	−6525.62	−0.729300	−0.364650	−	0.931145i	$-0.618811\pi$
$431$	−6525.62	−0.729300	−0.364650	+	0.931145i	$0.618811\pi$
$432$	−4601.41	−0.512467
$433$	11716.3	1.30034	0.650171	−	0.759788i	$-0.274697\pi$
$433$	11716.3	1.30034	0.650171	+	0.759788i	$0.274697\pi$
$434$	−10774.3	−1.19167
$435$	0	0
$436$	−26509.2	−2.91183
$437$	−7345.10	−0.804036
$438$	9198.91	1.00352
$439$	−14611.4	−1.58853	−0.794264	−	0.607573i	$-0.792143\pi$
$439$	−14611.4	−1.58853	−0.794264	+	0.607573i	$0.792143\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	2075.67	0.223370
$443$	15239.8	1.63446	0.817228	−	0.576314i	$-0.195510\pi$
$443$	15239.8	1.63446	0.817228	+	0.576314i	$0.195510\pi$
$444$	−15457.2	−1.65217
$445$	0	0
$446$	19938.1	2.11681
$447$	−2231.61	−0.236133
$448$	−5224.96	−0.551018
$449$	10678.8	1.12241	0.561206	−	0.827676i	$-0.310338\pi$
$449$	10678.8	1.12241	0.561206	+	0.827676i	$0.310338\pi$
$450$	0	0
$451$	−11753.8	−1.22720
$452$	−17972.7	−1.87027
$453$	−1820.29	−0.188796
$454$	−9640.53	−0.996592
$455$	0	0
$456$	10965.1	1.12607
$457$	−4228.23	−0.432797	−0.216399	−	0.976305i	$-0.569431\pi$
$457$	−4228.23	−0.432797	−0.216399	+	0.976305i	$0.569431\pi$
$458$	−4484.99	−0.457577
$459$	−284.846	−0.0289661
$460$	0	0
$461$	910.121	0.0919492	0.0459746	−	0.998943i	$-0.485361\pi$
$461$	910.121	0.0919492	0.0459746	+	0.998943i	$0.485361\pi$
$462$	3849.28	0.387629
$463$	−4456.16	−0.447290	−0.223645	−	0.974671i	$-0.571796\pi$
$463$	−4456.16	−0.447290	−0.223645	+	0.974671i	$0.571796\pi$
$464$	−6033.30	−0.603640
$465$	0	0
$466$	34767.5	3.45617
$467$	4429.42	0.438907	0.219453	−	0.975623i	$-0.429573\pi$
$467$	4429.42	0.438907	0.219453	+	0.975623i	$0.429573\pi$
$468$	6654.99	0.657323
$469$	3371.84	0.331977
$470$	0	0
$471$	9344.35	0.914151
$472$	−2238.65	−0.218310
$473$	−236.432	−0.0229835
$474$	10977.5	1.06374
$475$	0	0
$476$	−1464.03	−0.140975
$477$	4832.10	0.463830
$478$	−962.970	−0.0921448
$479$	2752.85	0.262591	0.131296	−	0.991343i	$-0.458086\pi$
$479$	2752.85	0.262591	0.131296	+	0.991343i	$0.458086\pi$
$480$	0	0
$481$	9693.90	0.918927
$482$	8038.43	0.759628
$483$	2632.29	0.247978
$484$	−2448.26	−0.229927
$485$	0	0
$486$	−1281.80	−0.119638
$487$	670.598	0.0623977	0.0311989	−	0.999513i	$-0.490067\pi$
$487$	670.598	0.0623977	0.0311989	+	0.999513i	$0.490067\pi$
$488$	3604.88	0.334396
$489$	7239.22	0.669466
$490$	0	0
$491$	−8244.70	−0.757797	−0.378898	−	0.925438i	$-0.623697\pi$
$491$	−8244.70	−0.757797	−0.378898	+	0.925438i	$0.623697\pi$
$492$	20117.0	1.84338
$493$	−373.485	−0.0341195
$494$	−11529.1	−1.05004
$495$	0	0
$496$	49728.3	4.50175
$497$	−2546.27	−0.229810
$498$	21116.4	1.90010
$499$	8164.91	0.732488	0.366244	−	0.930519i	$-0.380644\pi$
$499$	8164.91	0.732488	0.366244	+	0.930519i	$0.380644\pi$
$500$	0	0
$501$	−1831.43	−0.163317
$502$	12436.8	1.10574
$503$	−8175.59	−0.724715	−0.362357	−	0.932039i	$-0.618028\pi$
$503$	−8175.59	−0.724715	−0.362357	+	0.932039i	$0.618028\pi$
$504$	−3929.60	−0.347298
$505$	0	0
$506$	22976.0	2.01859
$507$	2417.35	0.211752
$508$	33997.2	2.96926
$509$	−878.448	−0.0764961	−0.0382480	−	0.999268i	$-0.512178\pi$
$509$	−878.448	−0.0764961	−0.0382480	+	0.999268i	$0.512178\pi$
$510$	0	0
$511$	4069.09	0.352262
$512$	−16876.5	−1.45673
$513$	1582.15	0.136167
$514$	−14677.7	−1.25955
$515$	0	0
$516$	404.661	0.0345237
$517$	−8711.42	−0.741060
$518$	−9596.55	−0.813992
$519$	11381.4	0.962600
$520$	0	0
$521$	11712.6	0.984910	0.492455	−	0.870338i	$-0.336100\pi$
$521$	11712.6	0.984910	0.492455	+	0.870338i	$0.336100\pi$
$522$	−1680.68	−0.140922
$523$	7341.82	0.613834	0.306917	−	0.951736i	$-0.400703\pi$
$523$	7341.82	0.613834	0.306917	+	0.951736i	$0.400703\pi$
$524$	9329.75	0.777809
$525$	0	0
$526$	−10780.8	−0.893659
$527$	3078.38	0.254452
$528$	−17766.1	−1.46434
$529$	3544.92	0.291355
$530$	0	0
$531$	−323.014	−0.0263985
$532$	8131.84	0.662707
$533$	−12616.3	−1.02528
$534$	5586.74	0.452738
$535$	0	0
$536$	−30045.3	−2.42119
$537$	8414.03	0.676149
$538$	18213.4	1.45955
$539$	1702.71	0.136068
$540$	0	0
$541$	−15868.7	−1.26109	−0.630545	−	0.776153i	$-0.717169\pi$
$541$	−15868.7	−1.26109	−0.630545	+	0.776153i	$0.717169\pi$
$542$	13948.4	1.10542
$543$	−9318.13	−0.736426
$544$	4219.61	0.332563
$545$	0	0
$546$	4131.73	0.323850
$547$	−2315.26	−0.180975	−0.0904875	−	0.995898i	$-0.528843\pi$
$547$	−2315.26	−0.180975	−0.0904875	+	0.995898i	$0.528843\pi$
$548$	8800.41	0.686013
$549$	520.146	0.0404359
$550$	0	0
$551$	2074.49	0.160392
$552$	−23455.4	−1.80857
$553$	4855.84	0.373402
$554$	−14134.1	−1.08393
$555$	0	0
$556$	33106.9	2.52526
$557$	4819.05	0.366588	0.183294	−	0.983058i	$-0.441324\pi$
$557$	4819.05	0.366588	0.183294	+	0.983058i	$0.441324\pi$
$558$	13852.7	1.05095
$559$	−253.781	−0.0192018
$560$	0	0
$561$	−1099.79	−0.0827689
$562$	−5378.79	−0.403720
$563$	−2540.86	−0.190203	−0.0951017	−	0.995468i	$-0.530318\pi$
$563$	−2540.86	−0.190203	−0.0951017	+	0.995468i	$0.530318\pi$
$564$	14909.9	1.11315
$565$	0	0
$566$	−2279.85	−0.169310
$567$	−567.000	−0.0419961
$568$	22688.9	1.67607
$569$	−24220.0	−1.78445	−0.892227	−	0.451587i	$-0.850858\pi$
$569$	−24220.0	−1.78445	−0.892227	+	0.451587i	$0.850858\pi$
$570$	0	0
$571$	−11772.1	−0.862778	−0.431389	−	0.902166i	$-0.641976\pi$
$571$	−11772.1	−0.862778	−0.431389	+	0.902166i	$0.641976\pi$
$572$	25695.1	1.87826
$573$	−785.855	−0.0572942
$574$	12489.6	0.908198
$575$	0	0
$576$	6717.80	0.485952
$577$	−10584.3	−0.763655	−0.381827	−	0.924234i	$-0.624705\pi$
$577$	−10584.3	−0.763655	−0.381827	+	0.924234i	$0.624705\pi$
$578$	−25328.6	−1.82272
$579$	12153.2	0.872315
$580$	0	0
$581$	9340.74	0.666987
$582$	22880.6	1.62961
$583$	18656.8	1.32536
$584$	−36258.3	−2.56914
$585$	0	0
$586$	11847.0	0.835148
$587$	8712.63	0.612621	0.306311	−	0.951932i	$-0.400905\pi$
$587$	8712.63	0.612621	0.306311	+	0.951932i	$0.400905\pi$
$588$	−2914.24	−0.204390
$589$	−17098.6	−1.19615
$590$	0	0
$591$	−8624.48	−0.600277
$592$	44292.4	3.07501
$593$	15362.9	1.06387	0.531937	−	0.846784i	$-0.321464\pi$
$593$	15362.9	1.06387	0.531937	+	0.846784i	$0.321464\pi$
$594$	−4949.07	−0.341857
$595$	0	0
$596$	14747.0	1.01353
$597$	9200.91	0.630768
$598$	24662.0	1.68646
$599$	26003.8	1.77377	0.886883	−	0.461994i	$-0.152866\pi$
$599$	26003.8	1.77377	0.886883	+	0.461994i	$0.152866\pi$
$600$	0	0
$601$	20567.7	1.39596	0.697982	−	0.716115i	$-0.254082\pi$
$601$	20567.7	1.39596	0.697982	+	0.716115i	$0.254082\pi$
$602$	251.233	0.0170091
$603$	−4335.22	−0.292776
$604$	12029.0	0.810349
$605$	0	0
$606$	−7514.42	−0.503717
$607$	−19642.1	−1.31342	−0.656711	−	0.754142i	$-0.728053\pi$
$607$	−19642.1	−1.31342	−0.656711	+	0.754142i	$0.728053\pi$
$608$	−23437.4	−1.56334
$609$	−743.442	−0.0494676
$610$	0	0
$611$	−9350.65	−0.619127
$612$	1882.33	0.124328
$613$	−8454.59	−0.557060	−0.278530	−	0.960428i	$-0.589847\pi$
$613$	−8454.59	−0.557060	−0.278530	+	0.960428i	$0.589847\pi$
$614$	16864.3	1.10845
$615$	0	0
$616$	−15172.3	−0.992383
$617$	24168.4	1.57696	0.788479	−	0.615061i	$-0.210869\pi$
$617$	24168.4	1.57696	0.788479	+	0.615061i	$0.210869\pi$
$618$	−31643.0	−2.05966
$619$	−2037.56	−0.132305	−0.0661523	−	0.997810i	$-0.521072\pi$
$619$	−2037.56	−0.132305	−0.0661523	+	0.997810i	$0.521072\pi$
$620$	0	0
$621$	−3384.37	−0.218696
$622$	−17700.5	−1.14104
$623$	2471.27	0.158923
$624$	−19069.8	−1.22340
$625$	0	0
$626$	11902.3	0.759921
$627$	6108.70	0.389088
$628$	−61749.8	−3.92370
$629$	2741.87	0.173808
$630$	0	0
$631$	12339.5	0.778489	0.389244	−	0.921135i	$-0.372736\pi$
$631$	12339.5	0.778489	0.389244	+	0.921135i	$0.372736\pi$
$632$	−43268.7	−2.72332
$633$	−1786.27	−0.112161
$634$	32383.7	2.02858
$635$	0	0
$636$	−31931.7	−1.99084
$637$	1827.65	0.113680
$638$	−6489.15	−0.402677
$639$	3273.77	0.202674
$640$	0	0
$641$	−10222.6	−0.629906	−0.314953	−	0.949107i	$-0.601989\pi$
$641$	−10222.6	−0.629906	−0.314953	+	0.949107i	$0.601989\pi$
$642$	18463.3	1.13503
$643$	1211.75	0.0743187	0.0371594	−	0.999309i	$-0.488169\pi$
$643$	1211.75	0.0743187	0.0371594	+	0.999309i	$0.488169\pi$
$644$	−17394.8	−1.06437
$645$	0	0
$646$	−3260.95	−0.198607
$647$	2817.22	0.171184	0.0855922	−	0.996330i	$-0.472722\pi$
$647$	2817.22	0.171184	0.0855922	+	0.996330i	$0.472722\pi$
$648$	5052.34	0.306288
$649$	−1247.16	−0.0754320
$650$	0	0
$651$	6127.67	0.368913
$652$	−47838.6	−2.87347
$653$	−20986.2	−1.25766	−0.628831	−	0.777542i	$-0.716466\pi$
$653$	−20986.2	−1.25766	−0.628831	+	0.777542i	$0.716466\pi$
$654$	21160.5	1.26520
$655$	0	0
$656$	−57645.1	−3.43089
$657$	−5231.69	−0.310666
$658$	9256.74	0.548428
$659$	−2384.09	−0.140927	−0.0704635	−	0.997514i	$-0.522448\pi$
$659$	−2384.09	−0.140927	−0.0704635	+	0.997514i	$0.522448\pi$
$660$	0	0
$661$	−7577.10	−0.445862	−0.222931	−	0.974834i	$-0.571562\pi$
$661$	−7577.10	−0.445862	−0.222931	+	0.974834i	$0.571562\pi$
$662$	37081.7	2.17707
$663$	−1180.50	−0.0691503
$664$	−83232.2	−4.86451
$665$	0	0
$666$	12338.4	0.717874
$667$	−4437.54	−0.257605
$668$	12102.5	0.700989
$669$	−11339.4	−0.655315
$670$	0	0
$671$	2008.30	0.115543
$672$	8399.36	0.482161
$673$	−11724.6	−0.671547	−0.335774	−	0.941943i	$-0.608998\pi$
$673$	−11724.6	−0.671547	−0.335774	+	0.941943i	$0.608998\pi$
$674$	−54481.7	−3.11358
$675$	0	0
$676$	−15974.5	−0.908880
$677$	−32304.3	−1.83390	−0.916952	−	0.398997i	$-0.869358\pi$
$677$	−32304.3	−1.83390	−0.916952	+	0.398997i	$0.869358\pi$
$678$	14346.4	0.812639
$679$	10121.1	0.572038
$680$	0	0
$681$	5482.85	0.308522
$682$	53485.6	3.00303
$683$	−33367.1	−1.86934	−0.934669	−	0.355519i	$-0.884304\pi$
$683$	−33367.1	−1.86934	−0.934669	+	0.355519i	$0.884304\pi$
$684$	−10455.2	−0.584452
$685$	0	0
$686$	−1809.30	−0.100699
$687$	2550.75	0.141655
$688$	−1159.55	−0.0642551
$689$	20025.8	1.10729
$690$	0	0
$691$	−1043.67	−0.0574577	−0.0287288	−	0.999587i	$-0.509146\pi$
$691$	−1043.67	−0.0574577	−0.0287288	+	0.999587i	$0.509146\pi$
$692$	−75211.3	−4.13166
$693$	−2189.20	−0.120001
$694$	−10378.6	−0.567674
$695$	0	0
$696$	6624.55	0.360780
$697$	−3568.46	−0.193924
$698$	−23027.4	−1.24871
$699$	−19773.3	−1.06995
$700$	0	0
$701$	−11305.7	−0.609143	−0.304572	−	0.952489i	$-0.598513\pi$
$701$	−11305.7	−0.609143	−0.304572	+	0.952489i	$0.598513\pi$
$702$	−5312.23	−0.285608
$703$	−15229.4	−0.817055
$704$	25937.6	1.38858
$705$	0	0
$706$	32027.1	1.70730
$707$	−3323.97	−0.176818
$708$	2134.55	0.113307
$709$	−13306.8	−0.704860	−0.352430	−	0.935838i	$-0.614645\pi$
$709$	−13306.8	−0.704860	−0.352430	+	0.935838i	$0.614645\pi$
$710$	0	0
$711$	−6243.22	−0.329309
$712$	−22020.6	−1.15907
$713$	36575.6	1.92113
$714$	1168.64	0.0612538
$715$	0	0
$716$	−55602.0	−2.90216
$717$	547.669	0.0285259
$718$	50839.9	2.64252
$719$	10701.2	0.555062	0.277531	−	0.960717i	$-0.410484\pi$
$719$	10701.2	0.555062	0.277531	+	0.960717i	$0.410484\pi$
$720$	0	0
$721$	−13997.1	−0.722996
$722$	−18068.0	−0.931333
$723$	−4571.69	−0.235163
$724$	61576.5	3.16088
$725$	0	0
$726$	1954.28	0.0999037
$727$	2121.14	0.108210	0.0541051	−	0.998535i	$-0.482769\pi$
$727$	2121.14	0.108210	0.0541051	+	0.998535i	$0.482769\pi$
$728$	−16285.6	−0.829098
$729$	729.000	0.0370370
$730$	0	0
$731$	−71.7808	−0.00363189
$732$	−3437.26	−0.173558
$733$	21584.0	1.08762	0.543809	−	0.839209i	$-0.316981\pi$
$733$	21584.0	1.08762	0.543809	+	0.839209i	$0.316981\pi$
$734$	−2757.33	−0.138658
$735$	0	0
$736$	50135.0	2.51087
$737$	−16738.4	−0.836588
$738$	−16058.0	−0.800955
$739$	−9945.21	−0.495048	−0.247524	−	0.968882i	$-0.579617\pi$
$739$	−9945.21	−0.495048	−0.247524	+	0.968882i	$0.579617\pi$
$740$	0	0
$741$	6556.94	0.325068
$742$	−19824.7	−0.980848
$743$	−2867.01	−0.141562	−0.0707808	−	0.997492i	$-0.522549\pi$
$743$	−2867.01	−0.141562	−0.0707808	+	0.997492i	$0.522549\pi$
$744$	−54601.6	−2.69058
$745$	0	0
$746$	−17037.1	−0.836158
$747$	−12009.5	−0.588227
$748$	7267.71	0.355259
$749$	8167.15	0.398426
$750$	0	0
$751$	−10824.1	−0.525934	−0.262967	−	0.964805i	$-0.584701\pi$
$751$	−10824.1	−0.525934	−0.262967	+	0.964805i	$0.584701\pi$
$752$	−42724.0	−2.07179
$753$	−7073.19	−0.342313
$754$	−6965.31	−0.336421
$755$	0	0
$756$	3746.88	0.180255
$757$	14512.0	0.696761	0.348381	−	0.937353i	$-0.386732\pi$
$757$	14512.0	0.696761	0.348381	+	0.937353i	$0.386732\pi$
$758$	35023.9	1.67827
$759$	−13067.1	−0.624910
$760$	0	0
$761$	−33075.8	−1.57556	−0.787778	−	0.615959i	$-0.788769\pi$
$761$	−33075.8	−1.57556	−0.787778	+	0.615959i	$0.788769\pi$
$762$	−27137.7	−1.29015
$763$	9360.23	0.444120
$764$	5193.13	0.245917
$765$	0	0
$766$	75032.8	3.53922
$767$	−1338.68	−0.0630206
$768$	6242.38	0.293297
$769$	6728.44	0.315518	0.157759	−	0.987478i	$-0.449573\pi$
$769$	6728.44	0.315518	0.157759	+	0.987478i	$0.449573\pi$
$770$	0	0
$771$	8347.65	0.389926
$772$	−80311.5	−3.74414
$773$	24233.3	1.12757	0.563784	−	0.825922i	$-0.309345\pi$
$773$	24233.3	1.12757	0.563784	+	0.825922i	$0.309345\pi$
$774$	−323.014	−0.0150006
$775$	0	0
$776$	−90186.0	−4.17202
$777$	5457.84	0.251993
$778$	15412.4	0.710231
$779$	19820.6	0.911615
$780$	0	0
$781$	12640.1	0.579127
$782$	6975.51	0.318982
$783$	955.854	0.0436263
$784$	8350.72	0.380408
$785$	0	0
$786$	−7447.31	−0.337960
$787$	17200.4	0.779069	0.389535	−	0.921012i	$-0.372636\pi$
$787$	17200.4	0.779069	0.389535	+	0.921012i	$0.372636\pi$
$788$	56992.7	2.57650
$789$	6131.35	0.276656
$790$	0	0
$791$	6346.05	0.285258
$792$	19507.2	0.875199
$793$	2155.66	0.0965318
$794$	−4282.92	−0.191430
$795$	0	0
$796$	−60801.9	−2.70737
$797$	4208.87	0.187059	0.0935295	−	0.995617i	$-0.470185\pi$
$797$	4208.87	0.187059	0.0935295	+	0.995617i	$0.470185\pi$
$798$	−6491.09	−0.287948
$799$	−2644.78	−0.117104
$800$	0	0
$801$	−3177.34	−0.140157
$802$	12336.1	0.543146
$803$	−20199.7	−0.887709
$804$	28648.2	1.25665
$805$	0	0
$806$	57410.2	2.50892
$807$	−10358.5	−0.451842
$808$	29618.7	1.28958
$809$	−23632.1	−1.02702	−0.513511	−	0.858083i	$-0.671656\pi$
$809$	−23632.1	−1.02702	−0.513511	+	0.858083i	$0.671656\pi$
$810$	0	0
$811$	28425.1	1.23075	0.615377	−	0.788233i	$-0.289004\pi$
$811$	28425.1	1.23075	0.615377	+	0.788233i	$0.289004\pi$
$812$	4912.85	0.212324
$813$	−7932.88	−0.342212
$814$	47638.9	2.05128
$815$	0	0
$816$	−5393.80	−0.231398
$817$	398.699	0.0170731
$818$	−14387.7	−0.614981
$819$	−2349.84	−0.100256
$820$	0	0
$821$	39409.6	1.67528	0.837640	−	0.546223i	$-0.183935\pi$
$821$	39409.6	1.67528	0.837640	+	0.546223i	$0.183935\pi$
$822$	−7024.77	−0.298074
$823$	−16346.6	−0.692352	−0.346176	−	0.938170i	$-0.612520\pi$
$823$	−16346.6	−0.692352	−0.346176	+	0.938170i	$0.612520\pi$
$824$	124723.	5.27300
$825$	0	0
$826$	1325.23	0.0558241
$827$	3738.87	0.157211	0.0786054	−	0.996906i	$-0.474953\pi$
$827$	3738.87	0.157211	0.0786054	+	0.996906i	$0.474953\pi$
$828$	22364.8	0.938684
$829$	−45196.2	−1.89352	−0.946761	−	0.321937i	$-0.895666\pi$
$829$	−45196.2	−1.89352	−0.946761	+	0.321937i	$0.895666\pi$
$830$	0	0
$831$	8038.46	0.335561
$832$	27840.8	1.16010
$833$	516.942	0.0215018
$834$	−26427.0	−1.09723
$835$	0	0
$836$	−40367.8	−1.67004
$837$	−7878.44	−0.325351
$838$	70189.5	2.89338
$839$	15899.7	0.654254	0.327127	−	0.944980i	$-0.393920\pi$
$839$	15899.7	0.654254	0.327127	+	0.944980i	$0.393920\pi$
$840$	0	0
$841$	−23135.7	−0.948612
$842$	−58063.4	−2.37648
$843$	3059.07	0.124982
$844$	11804.1	0.481414
$845$	0	0
$846$	−11901.5	−0.483668
$847$	864.465	0.0350689
$848$	91500.0	3.70534
$849$	1296.62	0.0524144
$850$	0	0
$851$	32577.4	1.31227
$852$	−21633.9	−0.869913
$853$	−33926.7	−1.36182	−0.680908	−	0.732369i	$-0.738415\pi$
$853$	−33926.7	−1.36182	−0.680908	+	0.732369i	$0.738415\pi$
$854$	−2134.01	−0.0855086
$855$	0	0
$856$	−72774.7	−2.90583
$857$	35432.4	1.41231	0.706154	−	0.708058i	$-0.250428\pi$
$857$	35432.4	1.41231	0.706154	+	0.708058i	$0.250428\pi$
$858$	−20510.6	−0.816108
$859$	−6780.17	−0.269309	−0.134655	−	0.990893i	$-0.542992\pi$
$859$	−6780.17	−0.269309	−0.134655	+	0.990893i	$0.542992\pi$
$860$	0	0
$861$	−7103.20	−0.281157
$862$	−34422.1	−1.36012
$863$	30675.1	1.20995	0.604977	−	0.796243i	$-0.293182\pi$
$863$	30675.1	1.20995	0.604977	+	0.796243i	$0.293182\pi$
$864$	−10799.2	−0.425226
$865$	0	0
$866$	61802.4	2.42509
$867$	14405.1	0.564271
$868$	−40493.2	−1.58344
$869$	−24105.2	−0.940981
$870$	0	0
$871$	−17966.6	−0.698938
$872$	−83405.8	−3.23908
$873$	−13012.9	−0.504490
$874$	−38744.8	−1.49950
$875$	0	0
$876$	34572.3	1.33344
$877$	−40861.3	−1.57330	−0.786652	−	0.617397i	$-0.788187\pi$
$877$	−40861.3	−1.57330	−0.786652	+	0.617397i	$0.788187\pi$
$878$	−77073.9	−2.96255
$879$	−6737.76	−0.258543
$880$	0	0
$881$	−43839.0	−1.67647	−0.838236	−	0.545308i	$-0.816413\pi$
$881$	−43839.0	−1.67647	−0.838236	+	0.545308i	$0.816413\pi$
$882$	2326.24	0.0888079
$883$	−44625.1	−1.70074	−0.850371	−	0.526183i	$-0.823623\pi$
$883$	−44625.1	−1.70074	−0.850371	+	0.526183i	$0.823623\pi$
$884$	7801.01	0.296806
$885$	0	0
$886$	80388.6	3.04820
$887$	43967.5	1.66436	0.832178	−	0.554509i	$-0.187094\pi$
$887$	43967.5	1.66436	0.832178	+	0.554509i	$0.187094\pi$
$888$	−48632.9	−1.83785
$889$	−12004.2	−0.452878
$890$	0	0
$891$	2814.68	0.105831
$892$	74933.5	2.81273
$893$	14690.2	0.550491
$894$	−11771.6	−0.440380
$895$	0	0
$896$	−5162.95	−0.192502
$897$	−14026.0	−0.522089
$898$	56329.7	2.09326
$899$	−10330.1	−0.383234
$900$	0	0
$901$	5664.21	0.209436
$902$	−62000.4	−2.28868
$903$	−142.883	−0.00526563
$904$	−56547.4	−2.08046
$905$	0	0
$906$	−9601.89	−0.352099
$907$	13584.3	0.497309	0.248654	−	0.968592i	$-0.420012\pi$
$907$	13584.3	0.497309	0.248654	+	0.968592i	$0.420012\pi$
$908$	−36232.1	−1.32423
$909$	4273.67	0.155939
$910$	0	0
$911$	−16421.6	−0.597226	−0.298613	−	0.954374i	$-0.596524\pi$
$911$	−16421.6	−0.597226	−0.298613	+	0.954374i	$0.596524\pi$
$912$	29959.3	1.08778
$913$	−46369.0	−1.68082
$914$	−22303.6	−0.807152
$915$	0	0
$916$	−16856.0	−0.608010
$917$	−3294.28	−0.118633
$918$	−1502.54	−0.0540208
$919$	−29487.3	−1.05843	−0.529214	−	0.848488i	$-0.677513\pi$
$919$	−29487.3	−1.05843	−0.529214	+	0.848488i	$0.677513\pi$
$920$	0	0
$921$	−9591.23	−0.343151
$922$	4800.81	0.171482
$923$	13567.6	0.483839
$924$	14466.8	0.515067
$925$	0	0
$926$	−23505.9	−0.834181
$927$	17996.3	0.637622
$928$	−14159.7	−0.500878
$929$	3441.85	0.121554	0.0607769	−	0.998151i	$-0.480642\pi$
$929$	3441.85	0.121554	0.0607769	+	0.998151i	$0.480642\pi$
$930$	0	0
$931$	−2871.30	−0.101077
$932$	130667.	4.59242
$933$	10066.8	0.353240
$934$	23364.8	0.818545
$935$	0	0
$936$	20938.6	0.731196
$937$	−5646.60	−0.196869	−0.0984346	−	0.995144i	$-0.531384\pi$
$937$	−5646.60	−0.196869	−0.0984346	+	0.995144i	$0.531384\pi$
$938$	17786.2	0.619125
$939$	−6769.18	−0.235254
$940$	0	0
$941$	−44680.1	−1.54785	−0.773927	−	0.633275i	$-0.781710\pi$
$941$	−44680.1	−1.54785	−0.773927	+	0.633275i	$0.781710\pi$
$942$	49290.7	1.70486
$943$	−42398.4	−1.46414
$944$	−6116.54	−0.210886
$945$	0	0
$946$	−1247.16	−0.0428633
$947$	48924.6	1.67881	0.839406	−	0.543505i	$-0.182903\pi$
$947$	48924.6	1.67881	0.839406	+	0.543505i	$0.182903\pi$
$948$	41256.8	1.41346
$949$	−21681.9	−0.741647
$950$	0	0
$951$	−18417.6	−0.628002
$952$	−4606.29	−0.156818
$953$	−52014.3	−1.76801	−0.884003	−	0.467482i	$-0.845161\pi$
$953$	−52014.3	−1.76801	−0.884003	+	0.467482i	$0.845161\pi$
$954$	25488.9	0.865026
$955$	0	0
$956$	−3619.14	−0.122439
$957$	3690.57	0.124660
$958$	14521.1	0.489723
$959$	−3107.37	−0.104632
$960$	0	0
$961$	55352.8	1.85804
$962$	51134.5	1.71377
$963$	−10500.6	−0.351379
$964$	30210.9	1.00936
$965$	0	0
$966$	13885.1	0.462470
$967$	47117.7	1.56691	0.783456	−	0.621448i	$-0.213455\pi$
$967$	47117.7	1.56691	0.783456	+	0.621448i	$0.213455\pi$
$968$	−7702.95	−0.255767
$969$	1854.60	0.0614843
$970$	0	0
$971$	−8195.04	−0.270846	−0.135423	−	0.990788i	$-0.543239\pi$
$971$	−8195.04	−0.270846	−0.135423	+	0.990788i	$0.543239\pi$
$972$	−4817.41	−0.158970
$973$	−11689.9	−0.385159
$974$	3537.35	0.116370
$975$	0	0
$976$	9849.42	0.323025
$977$	−4643.51	−0.152056	−0.0760282	−	0.997106i	$-0.524224\pi$
$977$	−4643.51	−0.152056	−0.0760282	+	0.997106i	$0.524224\pi$
$978$	38186.3	1.24853
$979$	−12267.8	−0.400490
$980$	0	0
$981$	−12034.6	−0.391677
$982$	−43490.1	−1.41326
$983$	−43986.5	−1.42721	−0.713607	−	0.700546i	$-0.752940\pi$
$983$	−43986.5	−1.42721	−0.713607	+	0.700546i	$0.752940\pi$
$984$	63294.1	2.05055
$985$	0	0
$986$	−1970.10	−0.0636317
$987$	−5264.58	−0.169781
$988$	−43329.9	−1.39525
$989$	−852.859	−0.0274210
$990$	0	0
$991$	1595.21	0.0511337	0.0255668	−	0.999673i	$-0.491861\pi$
$991$	1595.21	0.0511337	0.0255668	+	0.999673i	$0.491861\pi$
$992$	116709.	3.73539
$993$	−21089.4	−0.673971
$994$	−13431.3	−0.428588
$995$	0	0
$996$	79362.0	2.52478
$997$	−21501.2	−0.682998	−0.341499	−	0.939882i	$-0.610935\pi$
$997$	−21501.2	−0.682998	−0.341499	+	0.939882i	$0.610935\pi$
$998$	43069.2	1.36606
$999$	−7017.22	−0.222237

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.4.a.n.1.2		2
3.2	odd	2		1575.4.a.p.1.1		2
5.2	odd	4		525.4.d.g.274.4		4
5.3	odd	4		525.4.d.g.274.1		4
5.4	even	2		21.4.a.c.1.1	✓	2
15.14	odd	2		63.4.a.e.1.2		2
20.19	odd	2		336.4.a.m.1.2		2
35.4	even	6		147.4.e.l.79.2		4
35.9	even	6		147.4.e.l.67.2		4
35.19	odd	6		147.4.e.m.67.2		4
35.24	odd	6		147.4.e.m.79.2		4
35.34	odd	2		147.4.a.i.1.1		2
40.19	odd	2		1344.4.a.bo.1.1		2
40.29	even	2		1344.4.a.bg.1.1		2
60.59	even	2		1008.4.a.ba.1.1		2
105.44	odd	6		441.4.e.q.361.1		4
105.59	even	6		441.4.e.p.226.1		4
105.74	odd	6		441.4.e.q.226.1		4
105.89	even	6		441.4.e.p.361.1		4
105.104	even	2		441.4.a.r.1.2		2
140.139	even	2		2352.4.a.bz.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.a.c.1.1	✓	2	5.4	even	2
63.4.a.e.1.2		2	15.14	odd	2
147.4.a.i.1.1		2	35.34	odd	2
147.4.e.l.67.2		4	35.9	even	6
147.4.e.l.79.2		4	35.4	even	6
147.4.e.m.67.2		4	35.19	odd	6
147.4.e.m.79.2		4	35.24	odd	6
336.4.a.m.1.2		2	20.19	odd	2
441.4.a.r.1.2		2	105.104	even	2
441.4.e.p.226.1		4	105.59	even	6
441.4.e.p.361.1		4	105.89	even	6
441.4.e.q.226.1		4	105.74	odd	6
441.4.e.q.361.1		4	105.44	odd	6
525.4.a.n.1.2		2	1.1	even	1	trivial
525.4.d.g.274.1		4	5.3	odd	4
525.4.d.g.274.4		4	5.2	odd	4
1008.4.a.ba.1.1		2	60.59	even	2
1344.4.a.bg.1.1		2	40.29	even	2
1344.4.a.bo.1.1		2	40.19	odd	2
1575.4.a.p.1.1		2	3.2	odd	2
2352.4.a.bz.1.1		2	140.139	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	525.a (trivial)

\(f(q)\)	\(=\)	\(q+5.27492 q^{2} -3.00000 q^{3} +19.8248 q^{4} -15.8248 q^{6} -7.00000 q^{7} +62.3746 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+5.27492 q^{2} -3.00000 q^{3} +19.8248 q^{4} -15.8248 q^{6} -7.00000 q^{7} +62.3746 q^{8} +9.00000 q^{9} +34.7492 q^{11} -59.4743 q^{12} +37.2990 q^{13} -36.9244 q^{14} +170.423 q^{16} +10.5498 q^{17} +47.4743 q^{18} -58.5980 q^{19} +21.0000 q^{21} +183.299 q^{22} +125.347 q^{23} -187.124 q^{24} +196.749 q^{26} -27.0000 q^{27} -138.773 q^{28} -35.4020 q^{29} +291.794 q^{31} +399.969 q^{32} -104.248 q^{33} +55.6495 q^{34} +178.423 q^{36} +259.897 q^{37} -309.100 q^{38} -111.897 q^{39} -338.248 q^{41} +110.773 q^{42} -6.80397 q^{43} +688.894 q^{44} +661.196 q^{46} -250.694 q^{47} -511.268 q^{48} +49.0000 q^{49} -31.6495 q^{51} +739.444 q^{52} +536.900 q^{53} -142.423 q^{54} -436.622 q^{56} +175.794 q^{57} -186.743 q^{58} -35.8904 q^{59} +57.7940 q^{61} +1539.19 q^{62} -63.0000 q^{63} +746.423 q^{64} -549.897 q^{66} -481.691 q^{67} +209.148 q^{68} -376.042 q^{69} +363.752 q^{71} +561.371 q^{72} -581.299 q^{73} +1370.94 q^{74} -1161.69 q^{76} -243.244 q^{77} -590.248 q^{78} -693.691 q^{79} +81.0000 q^{81} -1784.23 q^{82} -1334.39 q^{83} +416.320 q^{84} -35.8904 q^{86} +106.206 q^{87} +2167.47 q^{88} -353.038 q^{89} -261.093 q^{91} +2484.98 q^{92} -875.382 q^{93} -1322.39 q^{94} -1199.91 q^{96} -1445.88 q^{97} +258.471 q^{98} +312.743 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} - 6 q^{3} + 17 q^{4} - 9 q^{6} - 14 q^{7} + 87 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q + 3 * q^2 - 6 * q^3 + 17 * q^4 - 9 * q^6 - 14 * q^7 + 87 * q^8 + 18 * q^9	\( 2 q + 3 q^{2} - 6 q^{3} + 17 q^{4} - 9 q^{6} - 14 q^{7} + 87 q^{8} + 18 q^{9} - 6 q^{11} - 51 q^{12} - 16 q^{13} - 21 q^{14} + 137 q^{16} + 6 q^{17} + 27 q^{18} + 64 q^{19} + 42 q^{21} + 276 q^{22} - 6 q^{23} - 261 q^{24} + 318 q^{26} - 54 q^{27} - 119 q^{28} - 252 q^{29} + 40 q^{31} + 279 q^{32} + 18 q^{33} + 66 q^{34} + 153 q^{36} + 248 q^{37} - 588 q^{38} + 48 q^{39} - 450 q^{41} + 63 q^{42} - 376 q^{43} + 804 q^{44} + 960 q^{46} + 12 q^{47} - 411 q^{48} + 98 q^{49} - 18 q^{51} + 890 q^{52} + 1104 q^{53} - 81 q^{54} - 609 q^{56} - 192 q^{57} + 306 q^{58} + 804 q^{59} - 428 q^{61} + 2112 q^{62} - 126 q^{63} + 1289 q^{64} - 828 q^{66} - 148 q^{67} + 222 q^{68} + 18 q^{69} + 954 q^{71} + 783 q^{72} - 1072 q^{73} + 1398 q^{74} - 1508 q^{76} + 42 q^{77} - 954 q^{78} - 572 q^{79} + 162 q^{81} - 1530 q^{82} - 1944 q^{83} + 357 q^{84} + 804 q^{86} + 756 q^{87} + 1164 q^{88} + 366 q^{89} + 112 q^{91} + 2856 q^{92} - 120 q^{93} - 1920 q^{94} - 837 q^{96} - 808 q^{97} + 147 q^{98} - 54 q^{99}+O(q^{100}) \) 2 * q + 3 * q^2 - 6 * q^3 + 17 * q^4 - 9 * q^6 - 14 * q^7 + 87 * q^8 + 18 * q^9 - 6 * q^11 - 51 * q^12 - 16 * q^13 - 21 * q^14 + 137 * q^16 + 6 * q^17 + 27 * q^18 + 64 * q^19 + 42 * q^21 + 276 * q^22 - 6 * q^23 - 261 * q^24 + 318 * q^26 - 54 * q^27 - 119 * q^28 - 252 * q^29 + 40 * q^31 + 279 * q^32 + 18 * q^33 + 66 * q^34 + 153 * q^36 + 248 * q^37 - 588 * q^38 + 48 * q^39 - 450 * q^41 + 63 * q^42 - 376 * q^43 + 804 * q^44 + 960 * q^46 + 12 * q^47 - 411 * q^48 + 98 * q^49 - 18 * q^51 + 890 * q^52 + 1104 * q^53 - 81 * q^54 - 609 * q^56 - 192 * q^57 + 306 * q^58 + 804 * q^59 - 428 * q^61 + 2112 * q^62 - 126 * q^63 + 1289 * q^64 - 828 * q^66 - 148 * q^67 + 222 * q^68 + 18 * q^69 + 954 * q^71 + 783 * q^72 - 1072 * q^73 + 1398 * q^74 - 1508 * q^76 + 42 * q^77 - 954 * q^78 - 572 * q^79 + 162 * q^81 - 1530 * q^82 - 1944 * q^83 + 357 * q^84 + 804 * q^86 + 756 * q^87 + 1164 * q^88 + 366 * q^89 + 112 * q^91 + 2856 * q^92 - 120 * q^93 - 1920 * q^94 - 837 * q^96 - 808 * q^97 + 147 * q^98 - 54 * q^99

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