LMFDB - Embedded newform 147.4.a.i.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:	$1$
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			1.1
Root			$4.27492$ 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)

$f(q)$	$=$	$q-5.27492 q^{2} -3.00000 q^{3} +19.8248 q^{4} -10.5498 q^{5} +15.8248 q^{6} -62.3746 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-5.27492 q^{2} -3.00000 q^{3} +19.8248 q^{4} -10.5498 q^{5} +15.8248 q^{6} -62.3746 q^{8} +9.00000 q^{9} +55.6495 q^{10} +34.7492 q^{11} -59.4743 q^{12} +37.2990 q^{13} +31.6495 q^{15} +170.423 q^{16} +10.5498 q^{17} -47.4743 q^{18} +58.5980 q^{19} -209.148 q^{20} -183.299 q^{22} -125.347 q^{23} +187.124 q^{24} -13.7010 q^{25} -196.749 q^{26} -27.0000 q^{27} -35.4020 q^{29} -166.949 q^{30} -291.794 q^{31} -399.969 q^{32} -104.248 q^{33} -55.6495 q^{34} +178.423 q^{36} -259.897 q^{37} -309.100 q^{38} -111.897 q^{39} +658.042 q^{40} +338.248 q^{41} +6.80397 q^{43} +688.894 q^{44} -94.9485 q^{45} +661.196 q^{46} -250.694 q^{47} -511.268 q^{48} +72.2716 q^{50} -31.6495 q^{51} +739.444 q^{52} -536.900 q^{53} +142.423 q^{54} -366.598 q^{55} -175.794 q^{57} +186.743 q^{58} +35.8904 q^{59} +627.444 q^{60} -57.7940 q^{61} +1539.19 q^{62} +746.423 q^{64} -393.498 q^{65} +549.897 q^{66} +481.691 q^{67} +209.148 q^{68} +376.042 q^{69} +363.752 q^{71} -561.371 q^{72} -581.299 q^{73} +1370.94 q^{74} +41.1030 q^{75} +1161.69 q^{76} +590.248 q^{78} -693.691 q^{79} -1797.93 q^{80} +81.0000 q^{81} -1784.23 q^{82} -1334.39 q^{83} -111.299 q^{85} -35.8904 q^{86} +106.206 q^{87} -2167.47 q^{88} +353.038 q^{89} +500.846 q^{90} -2484.98 q^{92} +875.382 q^{93} +1322.39 q^{94} -618.199 q^{95} +1199.91 q^{96} -1445.88 q^{97} +312.743 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} - 6 q^{3} + 17 q^{4} - 6 q^{5} + 9 q^{6} - 87 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q - 3 * q^2 - 6 * q^3 + 17 * q^4 - 6 * q^5 + 9 * q^6 - 87 * q^8 + 18 * q^9	\( 2 q - 3 q^{2} - 6 q^{3} + 17 q^{4} - 6 q^{5} + 9 q^{6} - 87 q^{8} + 18 q^{9} + 66 q^{10} - 6 q^{11} - 51 q^{12} - 16 q^{13} + 18 q^{15} + 137 q^{16} + 6 q^{17} - 27 q^{18} - 64 q^{19} - 222 q^{20} - 276 q^{22} + 6 q^{23} + 261 q^{24} - 118 q^{25} - 318 q^{26} - 54 q^{27} - 252 q^{29} - 198 q^{30} - 40 q^{31} - 279 q^{32} + 18 q^{33} - 66 q^{34} + 153 q^{36} - 248 q^{37} - 588 q^{38} + 48 q^{39} + 546 q^{40} + 450 q^{41} + 376 q^{43} + 804 q^{44} - 54 q^{45} + 960 q^{46} + 12 q^{47} - 411 q^{48} - 165 q^{50} - 18 q^{51} + 890 q^{52} - 1104 q^{53} + 81 q^{54} - 552 q^{55} + 192 q^{57} - 306 q^{58} - 804 q^{59} + 666 q^{60} + 428 q^{61} + 2112 q^{62} + 1289 q^{64} - 636 q^{65} + 828 q^{66} + 148 q^{67} + 222 q^{68} - 18 q^{69} + 954 q^{71} - 783 q^{72} - 1072 q^{73} + 1398 q^{74} + 354 q^{75} + 1508 q^{76} + 954 q^{78} - 572 q^{79} - 1950 q^{80} + 162 q^{81} - 1530 q^{82} - 1944 q^{83} - 132 q^{85} + 804 q^{86} + 756 q^{87} - 1164 q^{88} - 366 q^{89} + 594 q^{90} - 2856 q^{92} + 120 q^{93} + 1920 q^{94} - 1176 q^{95} + 837 q^{96} - 808 q^{97} - 54 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 - 6 * q^3 + 17 * q^4 - 6 * q^5 + 9 * q^6 - 87 * q^8 + 18 * q^9 + 66 * q^10 - 6 * q^11 - 51 * q^12 - 16 * q^13 + 18 * q^15 + 137 * q^16 + 6 * q^17 - 27 * q^18 - 64 * q^19 - 222 * q^20 - 276 * q^22 + 6 * q^23 + 261 * q^24 - 118 * q^25 - 318 * q^26 - 54 * q^27 - 252 * q^29 - 198 * q^30 - 40 * q^31 - 279 * q^32 + 18 * q^33 - 66 * q^34 + 153 * q^36 - 248 * q^37 - 588 * q^38 + 48 * q^39 + 546 * q^40 + 450 * q^41 + 376 * q^43 + 804 * q^44 - 54 * q^45 + 960 * q^46 + 12 * q^47 - 411 * q^48 - 165 * q^50 - 18 * q^51 + 890 * q^52 - 1104 * q^53 + 81 * q^54 - 552 * q^55 + 192 * q^57 - 306 * q^58 - 804 * q^59 + 666 * q^60 + 428 * q^61 + 2112 * q^62 + 1289 * q^64 - 636 * q^65 + 828 * q^66 + 148 * q^67 + 222 * q^68 - 18 * q^69 + 954 * q^71 - 783 * q^72 - 1072 * q^73 + 1398 * q^74 + 354 * q^75 + 1508 * q^76 + 954 * q^78 - 572 * q^79 - 1950 * q^80 + 162 * q^81 - 1530 * q^82 - 1944 * q^83 - 132 * q^85 + 804 * q^86 + 756 * q^87 - 1164 * q^88 - 366 * q^89 + 594 * q^90 - 2856 * q^92 + 120 * q^93 + 1920 * q^94 - 1176 * q^95 + 837 * q^96 - 808 * q^97 - 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	$-0.882362\pi$
$2$	−5.27492	−1.86496	−0.932482	+	0.361215i	$0.882362\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	19.8248	2.47809
$5$	−10.5498	−0.943606	−0.471803	−	0.881704i	$-0.656397\pi$
$5$	−10.5498	−0.943606	−0.471803	+	0.881704i	$0.656397\pi$
$6$	15.8248	1.07674
$7$	0	0
$7$	0	0
$8$	−62.3746	−2.75659
$9$	9.00000	0.333333
$10$	55.6495	1.75979
$11$	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	$0.369746\pi$
$14$	0	0
$15$	31.6495	0.544791
$16$	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	$-0.384899\pi$
$19$	58.5980	0.707542	0.353771	+	0.935332i	$0.384899\pi$
$20$	−209.148	−2.33834
$21$	0	0
$22$	−183.299	−1.77634
$23$	−125.347	−1.13638	−0.568189	−	0.822898i	$-0.692356\pi$
$23$	−125.347	−1.13638	−0.568189	+	0.822898i	$0.692356\pi$
$24$	187.124	1.59152
$25$	−13.7010	−0.109608
$26$	−196.749	−1.48406
$27$	−27.0000	−0.192450
$28$	0	0
$29$	−35.4020	−0.226689	−0.113345	−	0.993556i	$-0.536156\pi$
$29$	−35.4020	−0.226689	−0.113345	+	0.993556i	$0.536156\pi$
$30$	−166.949	−1.01602
$31$	−291.794	−1.69057	−0.845286	−	0.534313i	$-0.820570\pi$
$31$	−291.794	−1.69057	−0.845286	+	0.534313i	$0.820570\pi$
$32$	−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	$-0.695928\pi$
$37$	−259.897	−1.15478	−0.577389	+	0.816469i	$0.695928\pi$
$38$	−309.100	−1.31954
$39$	−111.897	−0.459432
$40$	658.042	2.60114
$41$	338.248	1.28842	0.644212	−	0.764847i	$-0.277185\pi$
$41$	338.248	1.28842	0.644212	+	0.764847i	$0.277185\pi$
$42$	0	0
$43$	6.80397	0.0241301	0.0120651	−	0.999927i	$-0.496159\pi$
$43$	6.80397	0.0241301	0.0120651	+	0.999927i	$0.496159\pi$
$44$	688.894	2.36033
$45$	−94.9485	−0.314535
$46$	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
$49$	0	0
$50$	72.2716	0.204415
$51$	−31.6495	−0.0868984
$52$	739.444	1.97197
$53$	−536.900	−1.39149	−0.695745	−	0.718289i	$-0.744925\pi$
$53$	−536.900	−1.39149	−0.695745	+	0.718289i	$0.744925\pi$
$54$	142.423	0.358913
$55$	−366.598	−0.898765
$56$	0	0
$57$	−175.794	−0.408500
$58$	186.743	0.422767
$59$	35.8904	0.0791955	0.0395977	−	0.999216i	$-0.487392\pi$
$59$	35.8904	0.0791955	0.0395977	+	0.999216i	$0.487392\pi$
$60$	627.444	1.35004
$61$	−57.7940	−0.121308	−0.0606538	−	0.998159i	$-0.519319\pi$
$61$	−57.7940	−0.121308	−0.0606538	+	0.998159i	$0.519319\pi$
$62$	1539.19	3.15286
$63$	0	0
$64$	746.423	1.45786
$65$	−393.498	−0.750884
$66$	549.897	1.02557
$67$	481.691	0.878327	0.439164	−	0.898407i	$-0.355275\pi$
$67$	481.691	0.878327	0.439164	+	0.898407i	$0.355275\pi$
$68$	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
$75$	41.1030	0.0632822
$76$	1161.69	1.75336
$77$	0	0
$78$	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	$0.664453\pi$
$80$	−1797.93	−2.51269
$81$	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	$0.844033\pi$
$84$	0	0
$85$	−111.299	−0.142024
$86$	−35.8904	−0.0450019
$87$	106.206	0.130879
$88$	−2167.47	−2.62560
$89$	353.038	0.420472	0.210236	−	0.977651i	$-0.432577\pi$
$89$	353.038	0.420472	0.210236	+	0.977651i	$0.432577\pi$
$90$	500.846	0.586597
$91$	0	0
$92$	−2484.98	−2.81605
$93$	875.382	0.976053
$94$	1322.39	1.45100
$95$	−618.199	−0.667641
$96$	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	$0.773207\pi$
$98$	0	0
$99$	312.743	0.317493
$100$	−271.619	−0.271619
$101$	−474.852	−0.467817	−0.233909	−	0.972259i	$-0.575152\pi$
$101$	−474.852	−0.467817	−0.233909	+	0.972259i	$0.575152\pi$
$102$	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	$-0.323291\pi$
$107$	1166.74	1.05414	0.527068	+	0.849823i	$0.323291\pi$
$108$	−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	$0.699894\pi$
$110$	1933.77	1.67616
$111$	779.691	0.666712
$112$	0	0
$113$	906.578	0.754723	0.377361	−	0.926066i	$-0.376831\pi$
$113$	906.578	0.754723	0.377361	+	0.926066i	$0.376831\pi$
$114$	927.299	0.761838
$115$	1322.39	1.07229
$116$	−701.836	−0.561757
$117$	335.691	0.265253
$118$	−189.319	−0.147697
$119$	0	0
$120$	−1974.12	−1.50177
$121$	−123.495	−0.0927836
$122$	304.859	0.226235
$123$	−1014.74	−0.743872
$124$	−5784.74	−4.18940
$125$	1463.27	1.04703
$126$	0	0
$127$	−1714.89	−1.19820	−0.599101	−	0.800674i	$-0.704475\pi$
$127$	−1714.89	−1.19820	−0.599101	+	0.800674i	$0.704475\pi$
$128$	−737.564	−0.509313
$129$	−20.4119	−0.0139315
$130$	2075.67	1.40037
$131$	−470.611	−0.313874	−0.156937	−	0.987609i	$-0.550162\pi$
$131$	−470.611	−0.313874	−0.156937	+	0.987609i	$0.550162\pi$
$132$	−2066.68	−1.36274
$133$	0	0
$134$	−2540.88	−1.63805
$135$	284.846	0.181597
$136$	−658.042	−0.414901
$137$	−443.910	−0.276831	−0.138415	−	0.990374i	$-0.544201\pi$
$137$	−443.910	−0.276831	−0.138415	+	0.990374i	$0.544201\pi$
$138$	−1983.59	−1.22358
$139$	−1669.98	−1.01904	−0.509518	−	0.860460i	$-0.670176\pi$
$139$	−1669.98	−1.01904	−0.509518	+	0.860460i	$0.670176\pi$
$140$	0	0
$141$	752.083	0.449197
$142$	−1918.76	−1.13394
$143$	1296.11	0.757945
$144$	1533.80	0.887619
$145$	373.485	0.213905
$146$	3066.30	1.73814
$147$	0	0
$148$	−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	$0.434444\pi$
$150$	−216.815	−0.118019
$151$	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
$154$	0	0
$155$	3078.38	1.59523
$156$	−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
$160$	4219.61	2.08493
$161$	0	0
$162$	−427.268	−0.207218
$163$	2413.07	1.15955	0.579774	−	0.814777i	$-0.303141\pi$
$163$	2413.07	1.15955	0.579774	+	0.814777i	$0.303141\pi$
$164$	6705.67	3.19284
$165$	1099.79	0.518902
$166$	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	$0.454828\pi$
$168$	0	0
$169$	−805.784	−0.366766
$170$	587.093	0.264870
$171$	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	$0.699126\pi$
$180$	−1882.33	−0.779448
$181$	−3106.04	−1.27553	−0.637763	−	0.770232i	$-0.720140\pi$
$181$	−3106.04	−1.27553	−0.637763	+	0.770232i	$0.720140\pi$
$182$	0	0
$183$	173.382	0.0700370
$184$	7818.48	3.13253
$185$	2741.87	1.08966
$186$	−4617.57	−1.82030
$187$	366.598	0.143360
$188$	−4969.95	−1.92804
$189$	0	0
$190$	3260.95	1.24513
$191$	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	$-0.227420\pi$
$193$	4051.07	1.51089	0.755447	+	0.655210i	$0.227420\pi$
$194$	7626.88	2.82257
$195$	1180.50	0.433523
$196$	0	0
$197$	−2874.83	−1.03971	−0.519855	−	0.854254i	$-0.674014\pi$
$197$	−2874.83	−1.03971	−0.519855	+	0.854254i	$0.674014\pi$
$198$	−1649.69	−0.592113
$199$	3066.97	1.09252	0.546261	−	0.837615i	$-0.316051\pi$
$199$	3066.97	1.09252	0.546261	+	0.837615i	$0.316051\pi$
$200$	854.594	0.302145
$201$	−1445.07	−0.507103
$202$	2504.81	0.872463
$203$	0	0
$204$	−627.444	−0.215342
$205$	−3568.46	−1.21576
$206$	−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
$215$	−71.7808	−0.0227693
$216$	1684.11	0.530507
$217$	0	0
$218$	7053.49	2.19139
$219$	1743.90	0.538090
$220$	−7267.71	−2.22722
$221$	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	$0.307903\pi$
$224$	0	0
$225$	−123.309	−0.0365360
$226$	−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	$-0.460852\pi$
$229$	850.249	0.245354	0.122677	+	0.992447i	$0.460852\pi$
$230$	−6975.51	−1.99979
$231$	0	0
$232$	2208.18	0.624890
$233$	−6591.10	−1.85321	−0.926604	−	0.376039i	$-0.877286\pi$
$233$	−6591.10	−1.85321	−0.926604	+	0.376039i	$0.877286\pi$
$234$	−1770.74	−0.494688
$235$	2644.78	0.734156
$236$	711.518	0.196254
$237$	2081.07	0.570381
$238$	0	0
$239$	−182.556	−0.0494083	−0.0247042	−	0.999695i	$-0.507864\pi$
$239$	−182.556	−0.0494083	−0.0247042	+	0.999695i	$0.507864\pi$
$240$	5393.80	1.45070
$241$	−1523.90	−0.407315	−0.203657	−	0.979042i	$-0.565283\pi$
$241$	−1523.90	−0.407315	−0.203657	+	0.979042i	$0.565283\pi$
$242$	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
$250$	−7718.64	−1.95268
$251$	−2357.73	−0.592903	−0.296451	−	0.955048i	$-0.595803\pi$
$251$	−2357.73	−0.592903	−0.296451	+	0.955048i	$0.595803\pi$
$252$	0	0
$253$	−4355.71	−1.08238
$254$	9045.89	2.23460
$255$	333.897	0.0819978
$256$	−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
$259$	0	0
$260$	−7801.01	−1.86076
$261$	−318.618	−0.0755630
$262$	2482.44	0.585364
$263$	2043.78	0.479183	0.239591	−	0.970874i	$-0.422987\pi$
$263$	2043.78	0.479183	0.239591	+	0.970874i	$0.422987\pi$
$264$	6502.40	1.51589
$265$	5664.21	1.31302
$266$	0	0
$267$	−1059.11	−0.242759
$268$	9549.41	2.17658
$269$	−3452.84	−0.782614	−0.391307	−	0.920260i	$-0.627977\pi$
$269$	−3452.84	−0.782614	−0.391307	+	0.920260i	$0.627977\pi$
$270$	−1502.54	−0.338672
$271$	−2644.29	−0.592728	−0.296364	−	0.955075i	$-0.595774\pi$
$271$	−2644.29	−0.592728	−0.296364	+	0.955075i	$0.595774\pi$
$272$	1797.93	0.400793
$273$	0	0
$274$	2341.59	0.516280
$275$	−476.098	−0.104399
$276$	7454.93	1.62585
$277$	2679.49	0.581208	0.290604	−	0.956843i	$-0.406144\pi$
$277$	2679.49	0.581208	0.290604	+	0.956843i	$0.406144\pi$
$278$	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
$285$	1854.60	0.385463
$286$	−6836.87	−1.41354
$287$	0	0
$288$	−3599.72	−0.736513
$289$	−4801.70	−0.977346
$290$	−1970.10	−0.398926
$291$	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	$0.428120\pi$
$294$	0	0
$295$	−378.638	−0.0747293
$296$	16211.0	3.18325
$297$	−938.228	−0.183305
$298$	−3923.86	−0.762761
$299$	−4675.33	−0.904284
$300$	814.856	0.156819
$301$	0	0
$302$	−3200.63	−0.609853
$303$	1424.56	0.270094
$304$	9986.44	1.88408
$305$	609.718	0.114467
$306$	−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	$0.403955\pi$
$308$	0	0
$309$	−5998.76	−1.10439
$310$	−16238.2	−2.97506
$311$	3355.60	0.611829	0.305915	−	0.952059i	$-0.401038\pi$
$311$	3355.60	0.611829	0.305915	+	0.952059i	$0.401038\pi$
$312$	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	$-0.683040\pi$
$317$	−6139.19	−1.08773	−0.543866	+	0.839172i	$0.683040\pi$
$318$	−8496.31	−1.49827
$319$	−1230.19	−0.215917
$320$	−7874.64	−1.37564
$321$	−3500.21	−0.608606
$322$	0	0
$323$	618.199	0.106494
$324$	1605.80	0.275344
$325$	−511.033	−0.0872216
$326$	−12728.8	−2.16252
$327$	4011.53	0.678404
$328$	−21098.0	−3.55166
$329$	0	0
$330$	−5801.32	−0.967734
$331$	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
$335$	−5081.76	−0.828795
$336$	0	0
$337$	10328.4	1.66951	0.834757	−	0.550619i	$-0.185608\pi$
$337$	10328.4	1.66951	0.834757	+	0.550619i	$0.185608\pi$
$338$	4250.44	0.684005
$339$	−2719.73	−0.435740
$340$	−2206.48	−0.351950
$341$	−10139.6	−1.61024
$342$	−2781.90	−0.439847
$343$	0	0
$344$	−424.395	−0.0665170
$345$	−3967.18	−0.619089
$346$	20012.0	3.10940
$347$	1967.54	0.304389	0.152194	−	0.988351i	$-0.451366\pi$
$347$	1967.54	0.304389	0.152194	+	0.988351i	$0.451366\pi$
$348$	2105.51	0.324330
$349$	4365.46	0.669564	0.334782	−	0.942296i	$-0.391337\pi$
$349$	4365.46	0.669564	0.334782	+	0.942296i	$0.391337\pi$
$350$	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
$355$	−3837.53	−0.573732
$356$	6998.90	1.04197
$357$	0	0
$358$	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	$0.249389\pi$
$360$	5922.37	0.867046
$361$	−3425.27	−0.499384
$362$	16384.1	2.37881
$363$	370.485	0.0535687
$364$	0	0
$365$	6132.61	0.879439
$366$	−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
$370$	−14463.1	−2.03217
$371$	0	0
$372$	17354.2	2.41875
$373$	3229.84	0.448351	0.224175	−	0.974549i	$-0.428031\pi$
$373$	3229.84	0.448351	0.224175	+	0.974549i	$0.428031\pi$
$374$	−1933.77	−0.267361
$375$	−4389.82	−0.604505
$376$	15637.0	2.14472
$377$	−1320.46	−0.180390
$378$	0	0
$379$	6639.71	0.899892	0.449946	−	0.893056i	$-0.351443\pi$
$379$	6639.71	0.899892	0.449946	+	0.893056i	$0.351443\pi$
$380$	−12255.6	−1.65448
$381$	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	$0.439017\pi$
$390$	−6227.01	−0.808505
$391$	−1322.39	−0.171039
$392$	0	0
$393$	1411.83	0.181215
$394$	15164.5	1.93902
$395$	7318.33	0.932215
$396$	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
$399$	0	0
$400$	−2334.96	−0.291870
$401$	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
$405$	−854.537	−0.104845
$406$	0	0
$407$	−9031.21	−1.09990
$408$	1974.12	0.239543
$409$	2727.57	0.329755	0.164877	−	0.986314i	$-0.447277\pi$
$409$	2727.57	0.329755	0.164877	+	0.986314i	$0.447277\pi$
$410$	18823.3	2.26736
$411$	1331.73	0.159828
$412$	39641.3	4.74026
$413$	0	0
$414$	5950.76	0.706435
$415$	14077.6	1.66516
$416$	−14918.5	−1.75826
$417$	5009.94	0.588340
$418$	−10741.0	−1.25684
$419$	−13306.3	−1.55144	−0.775721	−	0.631076i	$-0.782614\pi$
$419$	−13306.3	−1.55144	−0.775721	+	0.631076i	$0.782614\pi$
$420$	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
$425$	−144.543	−0.0164974
$426$	5756.29	0.654679
$427$	0	0
$428$	23130.2	2.61225
$429$	−3888.33	−0.437600
$430$	378.638	0.0424640
$431$	−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	$0.274697\pi$
$434$	0	0
$435$	−1120.46	−0.123498
$436$	−26509.2	−2.91183
$437$	−7345.10	−0.804036
$438$	−9198.91	−1.00352
$439$	14611.4	1.58853	0.794264	−	0.607573i	$-0.207857\pi$
$439$	14611.4	1.58853	0.794264	+	0.607573i	$0.207857\pi$
$440$	22866.4	2.47753
$441$	0	0
$442$	−2075.67	−0.223370
$443$	−15239.8	−1.63446	−0.817228	−	0.576314i	$-0.804490\pi$
$443$	−15239.8	−1.63446	−0.817228	+	0.576314i	$0.804490\pi$
$444$	15457.2	1.65217
$445$	−3724.50	−0.396760
$446$	−19938.1	−2.11681
$447$	−2231.61	−0.236133
$448$	0	0
$449$	10678.8	1.12241	0.561206	−	0.827676i	$-0.310338\pi$
$449$	10678.8	1.12241	0.561206	+	0.827676i	$0.310338\pi$
$450$	650.444	0.0681383
$451$	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	$-0.430569\pi$
$457$	4228.23	0.432797	0.216399	+	0.976305i	$0.430569\pi$
$458$	−4484.99	−0.457577
$459$	−284.846	−0.0289661
$460$	26216.1	2.65724
$461$	−910.121	−0.0919492	−0.0459746	−	0.998943i	$-0.514639\pi$
$461$	−910.121	−0.0919492	−0.0459746	+	0.998943i	$0.514639\pi$
$462$	0	0
$463$	4456.16	0.447290	0.223645	−	0.974671i	$-0.428204\pi$
$463$	4456.16	0.447290	0.223645	+	0.974671i	$0.428204\pi$
$464$	−6033.30	−0.603640
$465$	−9235.14	−0.921009
$466$	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
$469$	0	0
$470$	−13951.0	−1.36918
$471$	9344.35	0.914151
$472$	−2238.65	−0.218310
$473$	236.432	0.0229835
$474$	−10977.5	−1.06374
$475$	−802.851	−0.0775523
$476$	0	0
$477$	−4832.10	−0.463830
$478$	962.970	0.0921448
$479$	−2752.85	−0.262591	−0.131296	−	0.991343i	$-0.541914\pi$
$479$	−2752.85	−0.262591	−0.131296	+	0.991343i	$0.541914\pi$
$480$	−12658.8	−1.20374
$481$	−9693.90	−0.918927
$482$	8038.43	0.759628
$483$	0	0
$484$	−2448.26	−0.229927
$485$	15253.8	1.42812
$486$	1281.80	0.119638
$487$	−670.598	−0.0623977	−0.0311989	−	0.999513i	$-0.509933\pi$
$487$	−670.598	−0.0623977	−0.0311989	+	0.999513i	$0.509933\pi$
$488$	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
$495$	−3299.38	−0.299588
$496$	−49728.3	−4.50175
$497$	0	0
$498$	−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	$0.380644\pi$
$500$	29009.0	2.59465
$501$	−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	$0.618028\pi$
$504$	0	0
$505$	5009.61	0.441435
$506$	22976.0	2.01859
$507$	2417.35	0.211752
$508$	−33997.2	−2.96926
$509$	878.448	0.0764961	0.0382480	−	0.999268i	$-0.487822\pi$
$509$	878.448	0.0764961	0.0382480	+	0.999268i	$0.487822\pi$
$510$	−1761.28	−0.152923
$511$	0	0
$512$	16876.5	1.45673
$513$	−1582.15	−0.136167
$514$	14677.7	1.25955
$515$	−21095.3	−1.80499
$516$	−404.661	−0.0345237
$517$	−8711.42	−0.741060
$518$	0	0
$519$	11381.4	0.962600
$520$	24544.3	2.06988
$521$	−11712.6	−0.984910	−0.492455	−	0.870338i	$-0.663900\pi$
$521$	−11712.6	−0.984910	−0.492455	+	0.870338i	$0.663900\pi$
$522$	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
$530$	−29878.2	−2.44873
$531$	323.014	0.0263985
$532$	0	0
$533$	12616.3	1.02528
$534$	5586.74	0.452738
$535$	−12308.9	−0.994690
$536$	−30045.3	−2.42119
$537$	8414.03	0.676149
$538$	18213.4	1.45955
$539$	0	0
$540$	5646.99	0.450015
$541$	−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
$545$	14107.0	1.10877
$546$	0	0
$547$	2315.26	0.180975	0.0904875	−	0.995898i	$-0.471157\pi$
$547$	2315.26	0.180975	0.0904875	+	0.995898i	$0.471157\pi$
$548$	−8800.41	−0.686013
$549$	−520.146	−0.0404359
$550$	2511.38	0.194701
$551$	−2074.49	−0.160392
$552$	−23455.4	−1.80857
$553$	0	0
$554$	−14134.1	−1.08393
$555$	−8225.61	−0.629113
$556$	−33106.9	−2.52526
$557$	−4819.05	−0.366588	−0.183294	−	0.983058i	$-0.558676\pi$
$557$	−4819.05	−0.366588	−0.183294	+	0.983058i	$0.558676\pi$
$558$	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
$565$	−9564.25	−0.712161
$566$	2279.85	0.169310
$567$	0	0
$568$	−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	$0.850858\pi$
$570$	−9782.85	−0.718875
$571$	−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
$574$	0	0
$575$	1717.38	0.124556
$576$	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
$580$	7404.25	0.530077
$581$	0	0
$582$	−22880.6	−1.62961
$583$	−18656.8	−1.32536
$584$	36258.3	2.56914
$585$	−3541.49	−0.250295
$586$	−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	$0.400905\pi$
$588$	0	0
$589$	−17098.6	−1.19615
$590$	1997.28	0.139368
$591$	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	$0.152866\pi$
$600$	−2563.78	−0.174443
$601$	−20567.7	−1.39596	−0.697982	−	0.716115i	$-0.745918\pi$
$601$	−20567.7	−1.39596	−0.697982	+	0.716115i	$0.745918\pi$
$602$	0	0
$603$	4335.22	0.292776
$604$	12029.0	0.810349
$605$	1302.85	0.0875512
$606$	−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
$609$	0	0
$610$	−3216.21	−0.213476
$611$	−9350.65	−0.619127
$612$	1882.33	0.124328
$613$	8454.59	0.557060	0.278530	−	0.960428i	$-0.410153\pi$
$613$	8454.59	0.557060	0.278530	+	0.960428i	$0.410153\pi$
$614$	−16864.3	−1.10845
$615$	10705.4	0.701922
$616$	0	0
$617$	−24168.4	−1.57696	−0.788479	−	0.615061i	$-0.789131\pi$
$617$	−24168.4	−1.57696	−0.788479	+	0.615061i	$0.789131\pi$
$618$	31643.0	2.05966
$619$	2037.56	0.132305	0.0661523	−	0.997810i	$-0.478928\pi$
$619$	2037.56	0.132305	0.0661523	+	0.997810i	$0.478928\pi$
$620$	61028.1	3.95314
$621$	3384.37	0.218696
$622$	−17700.5	−1.14104
$623$	0	0
$624$	−19069.8	−1.22340
$625$	−13724.7	−0.878378
$626$	−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
$635$	18091.8	1.13063
$636$	31931.7	1.99084
$637$	0	0
$638$	6489.15	0.402677
$639$	3273.77	0.202674
$640$	7781.18	0.480591
$641$	−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	$0.488169\pi$
$644$	0	0
$645$	215.342	0.0131459
$646$	−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
$650$	2695.66	0.162665
$651$	0	0
$652$	47838.6	2.87347
$653$	20986.2	1.25766	0.628831	−	0.777542i	$-0.283534\pi$
$653$	20986.2	1.25766	0.628831	+	0.777542i	$0.283534\pi$
$654$	−21160.5	−1.26520
$655$	4964.87	0.296173
$656$	57645.1	3.43089
$657$	−5231.69	−0.310666
$658$	0	0
$659$	−2384.09	−0.140927	−0.0704635	−	0.997514i	$-0.522448\pi$
$659$	−2384.09	−0.140927	−0.0704635	+	0.997514i	$0.522448\pi$
$660$	21803.1	1.28589
$661$	7577.10	0.445862	0.222931	−	0.974834i	$-0.428438\pi$
$661$	7577.10	0.445862	0.222931	+	0.974834i	$0.428438\pi$
$662$	−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
$670$	26805.9	1.54567
$671$	−2008.30	−0.115543
$672$	0	0
$673$	11724.6	0.671547	0.335774	−	0.941943i	$-0.391002\pi$
$673$	11724.6	0.671547	0.335774	+	0.941943i	$0.391002\pi$
$674$	−54481.7	−3.11358
$675$	369.927	0.0210941
$676$	−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
$679$	0	0
$680$	6942.23	0.391503
$681$	5482.85	0.308522
$682$	53485.6	3.00303
$683$	33367.1	1.86934	0.934669	−	0.355519i	$-0.115696\pi$
$683$	33367.1	1.86934	0.934669	+	0.355519i	$0.115696\pi$
$684$	10455.2	0.584452
$685$	4683.18	0.261219
$686$	0	0
$687$	−2550.75	−0.141655
$688$	1159.55	0.0642551
$689$	−20025.8	−1.10729
$690$	20926.5	1.15458
$691$	1043.67	0.0574577	0.0287288	−	0.999587i	$-0.490854\pi$
$691$	1043.67	0.0574577	0.0287288	+	0.999587i	$0.490854\pi$
$692$	−75211.3	−4.13166
$693$	0	0
$694$	−10378.6	−0.567674
$695$	17618.0	0.961567
$696$	−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
$705$	−7934.35	−0.423865
$706$	−32027.1	−1.70730
$707$	0	0
$708$	−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	$0.614645\pi$
$710$	20242.6	1.06999
$711$	−6243.22	−0.329309
$712$	−22020.6	−1.15907
$713$	36575.6	1.92113
$714$	0	0
$715$	−13673.7	−0.715201
$716$	−55602.0	−2.90216
$717$	547.669	0.0285259
$718$	−50839.9	−2.64252
$719$	−10701.2	−0.555062	−0.277531	−	0.960717i	$-0.589516\pi$
$719$	−10701.2	−0.555062	−0.277531	+	0.960717i	$0.589516\pi$
$720$	−16181.4	−0.837562
$721$	0	0
$722$	18068.0	0.931333
$723$	4571.69	0.235163
$724$	−61576.5	−3.16088
$725$	485.042	0.0248469
$726$	−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	$0.482769\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	−32349.0	−1.64012
$731$	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	$0.579617\pi$
$740$	54356.9	2.70027
$741$	−6556.94	−0.325068
$742$	0	0
$743$	2867.01	0.141562	0.0707808	−	0.997492i	$-0.477451\pi$
$743$	2867.01	0.141562	0.0707808	+	0.997492i	$0.477451\pi$
$744$	−54601.6	−2.69058
$745$	−7847.71	−0.385930
$746$	−17037.1	−0.836158
$747$	−12009.5	−0.588227
$748$	7267.71	0.355259
$749$	0	0
$750$	23155.9	1.12738
$751$	−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
$755$	−6401.26	−0.308564
$756$	0	0
$757$	−14512.0	−0.696761	−0.348381	−	0.937353i	$-0.613268\pi$
$757$	−14512.0	−0.696761	−0.348381	+	0.937353i	$0.613268\pi$
$758$	−35023.9	−1.67827
$759$	13067.1	0.624910
$760$	38559.9	1.84042
$761$	33075.8	1.57556	0.787778	−	0.615959i	$-0.211231\pi$
$761$	33075.8	1.57556	0.787778	+	0.615959i	$0.211231\pi$
$762$	−27137.7	−1.29015
$763$	0	0
$764$	5193.13	0.245917
$765$	−1001.69	−0.0473415
$766$	−75032.8	−3.53922
$767$	1338.68	0.0630206
$768$	6242.38	0.293297
$769$	−6728.44	−0.315518	−0.157759	−	0.987478i	$-0.550427\pi$
$769$	−6728.44	−0.315518	−0.157759	+	0.987478i	$0.550427\pi$
$770$	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
$775$	3997.87	0.185300
$776$	90186.0	4.17202
$777$	0	0
$778$	−15412.4	−0.710231
$779$	19820.6	0.911615
$780$	23403.0	1.07431
$781$	12640.1	0.579127
$782$	6975.51	0.318982
$783$	955.854	0.0436263
$784$	0	0
$785$	32860.5	1.49406
$786$	−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
$790$	−38603.6	−1.73855
$791$	0	0
$792$	−19507.2	−0.875199
$793$	−2155.66	−0.0965318
$794$	4282.92	0.191430
$795$	−16992.6	−0.758071
$796$	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	$0.470185\pi$
$798$	0	0
$799$	−2644.78	−0.117104
$800$	5479.98	0.242183
$801$	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	$0.671656\pi$
$810$	4507.61	0.195532
$811$	−28425.1	−1.23075	−0.615377	−	0.788233i	$-0.710996\pi$
$811$	−28425.1	−1.23075	−0.615377	+	0.788233i	$0.710996\pi$
$812$	0	0
$813$	7932.88	0.342212
$814$	47638.9	2.05128
$815$	−25457.5	−1.09416
$816$	−5393.80	−0.231398
$817$	398.699	0.0170731
$818$	−14387.7	−0.614981
$819$	0	0
$820$	−70743.7	−3.01278
$821$	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	$-0.387480\pi$
$823$	16346.6	0.692352	0.346176	+	0.938170i	$0.387480\pi$
$824$	−124723.	−5.27300
$825$	1428.29	0.0602749
$826$	0	0
$827$	−3738.87	−0.157211	−0.0786054	−	0.996906i	$-0.525047\pi$
$827$	−3738.87	−0.157211	−0.0786054	+	0.996906i	$0.525047\pi$
$828$	−22364.8	−0.938684
$829$	45196.2	1.89352	0.946761	−	0.321937i	$-0.104334\pi$
$829$	45196.2	1.89352	0.946761	+	0.321937i	$0.104334\pi$
$830$	−74258.3	−3.10547
$831$	−8038.46	−0.335561
$832$	27840.8	1.16010
$833$	0	0
$834$	−26427.0	−1.09723
$835$	−6440.41	−0.266922
$836$	40367.8	1.67004
$837$	7878.44	0.325351
$838$	70189.5	2.89338
$839$	−15899.7	−0.654254	−0.327127	−	0.944980i	$-0.606080\pi$
$839$	−15899.7	−0.654254	−0.327127	+	0.944980i	$0.606080\pi$
$840$	0	0
$841$	−23135.7	−0.948612
$842$	58063.4	2.37648
$843$	3059.07	0.124982
$844$	11804.1	0.481414
$845$	8500.89	0.346082
$846$	11901.5	0.483668
$847$	0	0
$848$	−91500.0	−3.70534
$849$	1296.62	0.0524144
$850$	762.453	0.0307670
$851$	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	$0.738415\pi$
$854$	0	0
$855$	−5563.79	−0.222547
$856$	−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	$-0.457008\pi$
$859$	6780.17	0.269309	0.134655	+	0.990893i	$0.457008\pi$
$860$	−1423.04	−0.0564246
$861$	0	0
$862$	34422.1	1.36012
$863$	−30675.1	−1.20995	−0.604977	−	0.796243i	$-0.706818\pi$
$863$	−30675.1	−1.20995	−0.604977	+	0.796243i	$0.706818\pi$
$864$	10799.2	0.425226
$865$	40024.1	1.57325
$866$	−61802.4	−2.42509
$867$	14405.1	0.564271
$868$	0	0
$869$	−24105.2	−0.940981
$870$	5910.31	0.230320
$871$	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	$-0.211813\pi$
$877$	40861.3	1.57330	0.786652	+	0.617397i	$0.211813\pi$
$878$	−77073.9	−2.96255
$879$	−6737.76	−0.258543
$880$	−62476.6	−2.39328
$881$	43839.0	1.67647	0.838236	−	0.545308i	$-0.183587\pi$
$881$	43839.0	1.67647	0.838236	+	0.545308i	$0.183587\pi$
$882$	0	0
$883$	44625.1	1.70074	0.850371	−	0.526183i	$-0.176377\pi$
$883$	44625.1	1.70074	0.850371	+	0.526183i	$0.176377\pi$
$884$	7801.01	0.296806
$885$	1135.91	0.0431450
$886$	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
$889$	0	0
$890$	19646.4	0.739943
$891$	2814.68	0.105831
$892$	74933.5	2.81273
$893$	−14690.2	−0.550491
$894$	11771.6	0.440380
$895$	29588.9	1.10508
$896$	0	0
$897$	14026.0	0.522089
$898$	−56329.7	−2.09326
$899$	10330.1	0.383234
$900$	−2444.57	−0.0905396
$901$	−5664.21	−0.209436
$902$	−62000.4	−2.28868
$903$	0	0
$904$	−56547.4	−2.08046
$905$	32768.2	1.20359
$906$	9601.89	0.352099
$907$	−13584.3	−0.497309	−0.248654	−	0.968592i	$-0.579988\pi$
$907$	−13584.3	−0.497309	−0.248654	+	0.968592i	$0.579988\pi$
$908$	−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
$915$	−1829.15	−0.0660873
$916$	16856.0	0.608010
$917$	0	0
$918$	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	$0.677513\pi$
$920$	−82483.7	−2.95588
$921$	−9591.23	−0.343151
$922$	4800.81	0.171482
$923$	13567.6	0.483839
$924$	0	0
$925$	3560.85	0.126573
$926$	−23505.9	−0.834181
$927$	17996.3	0.637622
$928$	14159.7	0.500878
$929$	−3441.85	−0.121554	−0.0607769	−	0.998151i	$-0.519358\pi$
$929$	−3441.85	−0.121554	−0.0607769	+	0.998151i	$0.519358\pi$
$930$	48714.6	1.71765
$931$	0	0
$932$	−130667.	−4.59242
$933$	−10066.8	−0.353240
$934$	−23364.8	−0.818545
$935$	−3867.55	−0.135275
$936$	−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	$0.531384\pi$
$938$	0	0
$939$	−6769.18	−0.235254
$940$	52432.2	1.81931
$941$	44680.1	1.54785	0.773927	−	0.633275i	$-0.218290\pi$
$941$	44680.1	1.54785	0.773927	+	0.633275i	$0.218290\pi$
$942$	−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	$-0.817097\pi$
$947$	−48924.6	−1.67881	−0.839406	+	0.543505i	$0.817097\pi$
$948$	41256.8	1.41346
$949$	−21681.9	−0.741647
$950$	4234.97	0.144632
$951$	18417.6	0.628002
$952$	0	0
$953$	52014.3	1.76801	0.884003	−	0.467482i	$-0.154839\pi$
$953$	52014.3	1.76801	0.884003	+	0.467482i	$0.154839\pi$
$954$	25488.9	0.865026
$955$	−2763.55	−0.0936401
$956$	−3619.14	−0.122439
$957$	3690.57	0.124660
$958$	14521.1	0.489723
$959$	0	0
$960$	23623.9	0.794228
$961$	55352.8	1.85804
$962$	51134.5	1.71377
$963$	10500.6	0.351379
$964$	−30210.9	−1.00936
$965$	−42738.2	−1.42569
$966$	0	0
$967$	−47117.7	−1.56691	−0.783456	−	0.621448i	$-0.786545\pi$
$967$	−47117.7	−1.56691	−0.783456	+	0.621448i	$0.786545\pi$
$968$	7702.95	0.255767
$969$	−1854.60	−0.0614843
$970$	−80462.3	−2.66339
$971$	8195.04	0.270846	0.135423	−	0.990788i	$-0.456761\pi$
$971$	8195.04	0.270846	0.135423	+	0.990788i	$0.456761\pi$
$972$	−4817.41	−0.158970
$973$	0	0
$974$	3537.35	0.116370
$975$	1533.10	0.0503574
$976$	−9849.42	−0.323025
$977$	4643.51	0.152056	0.0760282	−	0.997106i	$-0.475776\pi$
$977$	4643.51	0.152056	0.0760282	+	0.997106i	$0.475776\pi$
$978$	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
$985$	30329.0	0.981077
$986$	1970.10	0.0636317
$987$	0	0
$988$	43329.9	1.39525
$989$	−852.859	−0.0274210
$990$	17404.0	0.558722
$991$	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
$994$	0	0
$995$	−32356.0	−1.03091
$996$	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	147.4.a.i.1.1		2
3.2	odd	2		441.4.a.r.1.2		2
4.3	odd	2		2352.4.a.bz.1.1		2
7.2	even	3		147.4.e.m.67.2		4
7.3	odd	6		147.4.e.l.79.2		4
7.4	even	3		147.4.e.m.79.2		4
7.5	odd	6		147.4.e.l.67.2		4
7.6	odd	2		21.4.a.c.1.1	✓	2
21.2	odd	6		441.4.e.p.361.1		4
21.5	even	6		441.4.e.q.361.1		4
21.11	odd	6		441.4.e.p.226.1		4
21.17	even	6		441.4.e.q.226.1		4
21.20	even	2		63.4.a.e.1.2		2
28.27	even	2		336.4.a.m.1.2		2
35.13	even	4		525.4.d.g.274.4		4
35.27	even	4		525.4.d.g.274.1		4
35.34	odd	2		525.4.a.n.1.2		2
56.13	odd	2		1344.4.a.bg.1.1		2
56.27	even	2		1344.4.a.bo.1.1		2
84.83	odd	2		1008.4.a.ba.1.1		2
105.104	even	2		1575.4.a.p.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.a.c.1.1	✓	2	7.6	odd	2
63.4.a.e.1.2		2	21.20	even	2
147.4.a.i.1.1		2	1.1	even	1	trivial
147.4.e.l.67.2		4	7.5	odd	6
147.4.e.l.79.2		4	7.3	odd	6
147.4.e.m.67.2		4	7.2	even	3
147.4.e.m.79.2		4	7.4	even	3
336.4.a.m.1.2		2	28.27	even	2
441.4.a.r.1.2		2	3.2	odd	2
441.4.e.p.226.1		4	21.11	odd	6
441.4.e.p.361.1		4	21.2	odd	6
441.4.e.q.226.1		4	21.17	even	6
441.4.e.q.361.1		4	21.5	even	6
525.4.a.n.1.2		2	35.34	odd	2
525.4.d.g.274.1		4	35.27	even	4
525.4.d.g.274.4		4	35.13	even	4
1008.4.a.ba.1.1		2	84.83	odd	2
1344.4.a.bg.1.1		2	56.13	odd	2
1344.4.a.bo.1.1		2	56.27	even	2
1575.4.a.p.1.1		2	105.104	even	2
2352.4.a.bz.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)

\(f(q)\)	\(=\)	\(q-5.27492 q^{2} -3.00000 q^{3} +19.8248 q^{4} -10.5498 q^{5} +15.8248 q^{6} -62.3746 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-5.27492 q^{2} -3.00000 q^{3} +19.8248 q^{4} -10.5498 q^{5} +15.8248 q^{6} -62.3746 q^{8} +9.00000 q^{9} +55.6495 q^{10} +34.7492 q^{11} -59.4743 q^{12} +37.2990 q^{13} +31.6495 q^{15} +170.423 q^{16} +10.5498 q^{17} -47.4743 q^{18} +58.5980 q^{19} -209.148 q^{20} -183.299 q^{22} -125.347 q^{23} +187.124 q^{24} -13.7010 q^{25} -196.749 q^{26} -27.0000 q^{27} -35.4020 q^{29} -166.949 q^{30} -291.794 q^{31} -399.969 q^{32} -104.248 q^{33} -55.6495 q^{34} +178.423 q^{36} -259.897 q^{37} -309.100 q^{38} -111.897 q^{39} +658.042 q^{40} +338.248 q^{41} +6.80397 q^{43} +688.894 q^{44} -94.9485 q^{45} +661.196 q^{46} -250.694 q^{47} -511.268 q^{48} +72.2716 q^{50} -31.6495 q^{51} +739.444 q^{52} -536.900 q^{53} +142.423 q^{54} -366.598 q^{55} -175.794 q^{57} +186.743 q^{58} +35.8904 q^{59} +627.444 q^{60} -57.7940 q^{61} +1539.19 q^{62} +746.423 q^{64} -393.498 q^{65} +549.897 q^{66} +481.691 q^{67} +209.148 q^{68} +376.042 q^{69} +363.752 q^{71} -561.371 q^{72} -581.299 q^{73} +1370.94 q^{74} +41.1030 q^{75} +1161.69 q^{76} +590.248 q^{78} -693.691 q^{79} -1797.93 q^{80} +81.0000 q^{81} -1784.23 q^{82} -1334.39 q^{83} -111.299 q^{85} -35.8904 q^{86} +106.206 q^{87} -2167.47 q^{88} +353.038 q^{89} +500.846 q^{90} -2484.98 q^{92} +875.382 q^{93} +1322.39 q^{94} -618.199 q^{95} +1199.91 q^{96} -1445.88 q^{97} +312.743 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} - 6 q^{3} + 17 q^{4} - 6 q^{5} + 9 q^{6} - 87 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q - 3 * q^2 - 6 * q^3 + 17 * q^4 - 6 * q^5 + 9 * q^6 - 87 * q^8 + 18 * q^9	\( 2 q - 3 q^{2} - 6 q^{3} + 17 q^{4} - 6 q^{5} + 9 q^{6} - 87 q^{8} + 18 q^{9} + 66 q^{10} - 6 q^{11} - 51 q^{12} - 16 q^{13} + 18 q^{15} + 137 q^{16} + 6 q^{17} - 27 q^{18} - 64 q^{19} - 222 q^{20} - 276 q^{22} + 6 q^{23} + 261 q^{24} - 118 q^{25} - 318 q^{26} - 54 q^{27} - 252 q^{29} - 198 q^{30} - 40 q^{31} - 279 q^{32} + 18 q^{33} - 66 q^{34} + 153 q^{36} - 248 q^{37} - 588 q^{38} + 48 q^{39} + 546 q^{40} + 450 q^{41} + 376 q^{43} + 804 q^{44} - 54 q^{45} + 960 q^{46} + 12 q^{47} - 411 q^{48} - 165 q^{50} - 18 q^{51} + 890 q^{52} - 1104 q^{53} + 81 q^{54} - 552 q^{55} + 192 q^{57} - 306 q^{58} - 804 q^{59} + 666 q^{60} + 428 q^{61} + 2112 q^{62} + 1289 q^{64} - 636 q^{65} + 828 q^{66} + 148 q^{67} + 222 q^{68} - 18 q^{69} + 954 q^{71} - 783 q^{72} - 1072 q^{73} + 1398 q^{74} + 354 q^{75} + 1508 q^{76} + 954 q^{78} - 572 q^{79} - 1950 q^{80} + 162 q^{81} - 1530 q^{82} - 1944 q^{83} - 132 q^{85} + 804 q^{86} + 756 q^{87} - 1164 q^{88} - 366 q^{89} + 594 q^{90} - 2856 q^{92} + 120 q^{93} + 1920 q^{94} - 1176 q^{95} + 837 q^{96} - 808 q^{97} - 54 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 - 6 * q^3 + 17 * q^4 - 6 * q^5 + 9 * q^6 - 87 * q^8 + 18 * q^9 + 66 * q^10 - 6 * q^11 - 51 * q^12 - 16 * q^13 + 18 * q^15 + 137 * q^16 + 6 * q^17 - 27 * q^18 - 64 * q^19 - 222 * q^20 - 276 * q^22 + 6 * q^23 + 261 * q^24 - 118 * q^25 - 318 * q^26 - 54 * q^27 - 252 * q^29 - 198 * q^30 - 40 * q^31 - 279 * q^32 + 18 * q^33 - 66 * q^34 + 153 * q^36 - 248 * q^37 - 588 * q^38 + 48 * q^39 + 546 * q^40 + 450 * q^41 + 376 * q^43 + 804 * q^44 - 54 * q^45 + 960 * q^46 + 12 * q^47 - 411 * q^48 - 165 * q^50 - 18 * q^51 + 890 * q^52 - 1104 * q^53 + 81 * q^54 - 552 * q^55 + 192 * q^57 - 306 * q^58 - 804 * q^59 + 666 * q^60 + 428 * q^61 + 2112 * q^62 + 1289 * q^64 - 636 * q^65 + 828 * q^66 + 148 * q^67 + 222 * q^68 - 18 * q^69 + 954 * q^71 - 783 * q^72 - 1072 * q^73 + 1398 * q^74 + 354 * q^75 + 1508 * q^76 + 954 * q^78 - 572 * q^79 - 1950 * q^80 + 162 * q^81 - 1530 * q^82 - 1944 * q^83 - 132 * q^85 + 804 * q^86 + 756 * q^87 - 1164 * q^88 - 366 * q^89 + 594 * q^90 - 2856 * q^92 + 120 * q^93 + 1920 * q^94 - 1176 * q^95 + 837 * q^96 - 808 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more