LMFDB - Embedded newform 147.4.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("147.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	147.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$8.67328077084$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.57516.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 24x + 6 $ x^3 - x^2 - 24*x + 6
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			$-4.55637$ 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)

$f(q)$	$=$	$q-4.55637 q^{2} -3.00000 q^{3} +12.7605 q^{4} +17.8732 q^{5} +13.6691 q^{6} -21.6905 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-4.55637 q^{2} -3.00000 q^{3} +12.7605 q^{4} +17.8732 q^{5} +13.6691 q^{6} -21.6905 q^{8} +9.00000 q^{9} -81.4369 q^{10} -11.3942 q^{11} -38.2814 q^{12} -13.0987 q^{13} -53.6196 q^{15} -3.25412 q^{16} +53.2674 q^{17} -41.0073 q^{18} -42.4223 q^{19} +228.071 q^{20} +51.9159 q^{22} +152.085 q^{23} +65.0714 q^{24} +194.451 q^{25} +59.6823 q^{26} -27.0000 q^{27} +186.493 q^{29} +244.311 q^{30} -157.874 q^{31} +188.351 q^{32} +34.1825 q^{33} -242.706 q^{34} +114.844 q^{36} +3.74588 q^{37} +193.291 q^{38} +39.2960 q^{39} -387.678 q^{40} -39.3230 q^{41} +429.439 q^{43} -145.395 q^{44} +160.859 q^{45} -692.957 q^{46} +21.1869 q^{47} +9.76236 q^{48} -885.992 q^{50} -159.802 q^{51} -167.145 q^{52} +365.904 q^{53} +123.022 q^{54} -203.650 q^{55} +127.267 q^{57} -849.732 q^{58} -226.578 q^{59} -684.212 q^{60} +651.973 q^{61} +719.331 q^{62} -832.161 q^{64} -234.115 q^{65} -155.748 q^{66} +145.433 q^{67} +679.717 q^{68} -456.256 q^{69} -368.962 q^{71} -195.214 q^{72} +608.906 q^{73} -17.0676 q^{74} -583.354 q^{75} -541.328 q^{76} -179.047 q^{78} +910.237 q^{79} -58.1615 q^{80} +81.0000 q^{81} +179.170 q^{82} -327.929 q^{83} +952.058 q^{85} -1956.68 q^{86} -559.480 q^{87} +247.144 q^{88} -37.6118 q^{89} -732.932 q^{90} +1940.68 q^{92} +473.621 q^{93} -96.5352 q^{94} -758.222 q^{95} -565.052 q^{96} +722.013 q^{97} -102.547 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} - 9 q^{3} + 25 q^{4} + 11 q^{5} - 3 q^{6} + 39 q^{8} + 27 q^{9}+O(q^{10}) $ 3 * q + q^2 - 9 * q^3 + 25 * q^4 + 11 * q^5 - 3 * q^6 + 39 * q^8 + 27 * q^9	\( 3 q + q^{2} - 9 q^{3} + 25 q^{4} + 11 q^{5} - 3 q^{6} + 39 q^{8} + 27 q^{9} - 55 q^{10} + 35 q^{11} - 75 q^{12} + 62 q^{13} - 33 q^{15} + 241 q^{16} + 48 q^{17} + 9 q^{18} - 202 q^{19} + 439 q^{20} - 7 q^{22} + 216 q^{23} - 117 q^{24} + 130 q^{25} + 274 q^{26} - 81 q^{27} + 53 q^{29} + 165 q^{30} - 95 q^{31} + 683 q^{32} - 105 q^{33} - 24 q^{34} + 225 q^{36} + 262 q^{37} - 398 q^{38} - 186 q^{39} + 21 q^{40} + 244 q^{41} + 360 q^{43} - 905 q^{44} + 99 q^{45} - 1056 q^{46} - 210 q^{47} - 723 q^{48} - 1378 q^{50} - 144 q^{51} + 324 q^{52} + 393 q^{53} - 27 q^{54} - 1031 q^{55} + 606 q^{57} - 1249 q^{58} + 1143 q^{59} - 1317 q^{60} - 70 q^{61} + 1059 q^{62} - 399 q^{64} - 472 q^{65} + 21 q^{66} - 628 q^{67} + 1944 q^{68} - 648 q^{69} + 318 q^{71} + 351 q^{72} + 988 q^{73} + 1002 q^{74} - 390 q^{75} - 2340 q^{76} - 822 q^{78} + 861 q^{79} + 175 q^{80} + 243 q^{81} + 124 q^{82} + 519 q^{83} + 1800 q^{85} - 3208 q^{86} - 159 q^{87} - 891 q^{88} + 1766 q^{89} - 495 q^{90} - 672 q^{92} + 285 q^{93} - 3294 q^{94} - 736 q^{95} - 2049 q^{96} + 19 q^{97} + 315 q^{99}+O(q^{100}) \) 3 * q + q^2 - 9 * q^3 + 25 * q^4 + 11 * q^5 - 3 * q^6 + 39 * q^8 + 27 * q^9 - 55 * q^10 + 35 * q^11 - 75 * q^12 + 62 * q^13 - 33 * q^15 + 241 * q^16 + 48 * q^17 + 9 * q^18 - 202 * q^19 + 439 * q^20 - 7 * q^22 + 216 * q^23 - 117 * q^24 + 130 * q^25 + 274 * q^26 - 81 * q^27 + 53 * q^29 + 165 * q^30 - 95 * q^31 + 683 * q^32 - 105 * q^33 - 24 * q^34 + 225 * q^36 + 262 * q^37 - 398 * q^38 - 186 * q^39 + 21 * q^40 + 244 * q^41 + 360 * q^43 - 905 * q^44 + 99 * q^45 - 1056 * q^46 - 210 * q^47 - 723 * q^48 - 1378 * q^50 - 144 * q^51 + 324 * q^52 + 393 * q^53 - 27 * q^54 - 1031 * q^55 + 606 * q^57 - 1249 * q^58 + 1143 * q^59 - 1317 * q^60 - 70 * q^61 + 1059 * q^62 - 399 * q^64 - 472 * q^65 + 21 * q^66 - 628 * q^67 + 1944 * q^68 - 648 * q^69 + 318 * q^71 + 351 * q^72 + 988 * q^73 + 1002 * q^74 - 390 * q^75 - 2340 * q^76 - 822 * q^78 + 861 * q^79 + 175 * q^80 + 243 * q^81 + 124 * q^82 + 519 * q^83 + 1800 * q^85 - 3208 * q^86 - 159 * q^87 - 891 * q^88 + 1766 * q^89 - 495 * q^90 - 672 * q^92 + 285 * q^93 - 3294 * q^94 - 736 * q^95 - 2049 * q^96 + 19 * q^97 + 315 * 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 $

$2$	−4.55637	−1.61092	−0.805459	−	0.592651i	$-0.798081\pi$
$2$	−4.55637	−1.61092	−0.805459	+	0.592651i	$0.798081\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	12.7605	1.59506
$5$	17.8732	1.59863	0.799314	−	0.600914i	$-0.205196\pi$
$5$	17.8732	1.59863	0.799314	+	0.600914i	$0.205196\pi$
$6$	13.6691	0.930064
$7$	0	0
$7$	0	0
$8$	−21.6905	−0.958592
$9$	9.00000	0.333333
$10$	−81.4369	−2.57526
$11$	−11.3942	−0.312315	−0.156158	−	0.987732i	$-0.549911\pi$
$11$	−11.3942	−0.312315	−0.156158	+	0.987732i	$0.549911\pi$
$12$	−38.2814	−0.920908
$13$	−13.0987	−0.279455	−0.139728	−	0.990190i	$-0.544623\pi$
$13$	−13.0987	−0.279455	−0.139728	+	0.990190i	$0.544623\pi$
$14$	0	0
$15$	−53.6196	−0.922968
$16$	−3.25412	−0.0508456
$17$	53.2674	0.759955	0.379977	−	0.924996i	$-0.375932\pi$
$17$	53.2674	0.759955	0.379977	+	0.924996i	$0.375932\pi$
$18$	−41.0073	−0.536973
$19$	−42.4223	−0.512228	−0.256114	−	0.966647i	$-0.582442\pi$
$19$	−42.4223	−0.512228	−0.256114	+	0.966647i	$0.582442\pi$
$20$	228.071	2.54991
$21$	0	0
$22$	51.9159	0.503114
$23$	152.085	1.37878	0.689391	−	0.724389i	$-0.257878\pi$
$23$	152.085	1.37878	0.689391	+	0.724389i	$0.257878\pi$
$24$	65.0714	0.553443
$25$	194.451	1.55561
$26$	59.6823	0.450180
$27$	−27.0000	−0.192450
$28$	0	0
$29$	186.493	1.19417	0.597085	−	0.802178i	$-0.296325\pi$
$29$	186.493	1.19417	0.597085	+	0.802178i	$0.296325\pi$
$30$	244.311	1.48683
$31$	−157.874	−0.914676	−0.457338	−	0.889293i	$-0.651197\pi$
$31$	−157.874	−0.914676	−0.457338	+	0.889293i	$0.651197\pi$
$32$	188.351	1.04050
$33$	34.1825	0.180315
$34$	−242.706	−1.22423
$35$	0	0
$36$	114.844	0.531686
$37$	3.74588	0.0166438	0.00832188	−	0.999965i	$-0.497351\pi$
$37$	3.74588	0.0166438	0.00832188	+	0.999965i	$0.497351\pi$
$38$	193.291	0.825158
$39$	39.2960	0.161344
$40$	−387.678	−1.53243
$41$	−39.3230	−0.149786	−0.0748930	−	0.997192i	$-0.523862\pi$
$41$	−39.3230	−0.149786	−0.0748930	+	0.997192i	$0.523862\pi$
$42$	0	0
$43$	429.439	1.52300	0.761498	−	0.648168i	$-0.224464\pi$
$43$	429.439	1.52300	0.761498	+	0.648168i	$0.224464\pi$
$44$	−145.395	−0.498161
$45$	160.859	0.532876
$46$	−692.957	−2.22111
$47$	21.1869	0.0657537	0.0328768	−	0.999459i	$-0.489533\pi$
$47$	21.1869	0.0657537	0.0328768	+	0.999459i	$0.489533\pi$
$48$	9.76236	0.0293557
$49$	0	0
$50$	−885.992	−2.50596
$51$	−159.802	−0.438760
$52$	−167.145	−0.445748
$53$	365.904	0.948317	0.474158	−	0.880440i	$-0.342752\pi$
$53$	365.904	0.948317	0.474158	+	0.880440i	$0.342752\pi$
$54$	123.022	0.310021
$55$	−203.650	−0.499276
$56$	0	0
$57$	127.267	0.295735
$58$	−849.732	−1.92371
$59$	−226.578	−0.499964	−0.249982	−	0.968250i	$-0.580425\pi$
$59$	−226.578	−0.499964	−0.249982	+	0.968250i	$0.580425\pi$
$60$	−684.212	−1.47219
$61$	651.973	1.36847	0.684235	−	0.729262i	$-0.260136\pi$
$61$	651.973	1.36847	0.684235	+	0.729262i	$0.260136\pi$
$62$	719.331	1.47347
$63$	0	0
$64$	−832.161	−1.62532
$65$	−234.115	−0.446745
$66$	−155.748	−0.290473
$67$	145.433	0.265186	0.132593	−	0.991171i	$-0.457670\pi$
$67$	145.433	0.265186	0.132593	+	0.991171i	$0.457670\pi$
$68$	679.717	1.21217
$69$	−456.256	−0.796041
$70$	0	0
$71$	−368.962	−0.616728	−0.308364	−	0.951268i	$-0.599782\pi$
$71$	−368.962	−0.616728	−0.308364	+	0.951268i	$0.599782\pi$
$72$	−195.214	−0.319531
$73$	608.906	0.976261	0.488130	−	0.872771i	$-0.337679\pi$
$73$	608.906	0.976261	0.488130	+	0.872771i	$0.337679\pi$
$74$	−17.0676	−0.0268117
$75$	−583.354	−0.898133
$76$	−541.328	−0.817034
$77$	0	0
$78$	−179.047	−0.259911
$79$	910.237	1.29633	0.648163	−	0.761502i	$-0.275538\pi$
$79$	910.237	1.29633	0.648163	+	0.761502i	$0.275538\pi$
$80$	−58.1615	−0.0812832
$81$	81.0000	0.111111
$82$	179.170	0.241293
$83$	−327.929	−0.433674	−0.216837	−	0.976208i	$-0.569574\pi$
$83$	−327.929	−0.433674	−0.216837	+	0.976208i	$0.569574\pi$
$84$	0	0
$85$	952.058	1.21489
$86$	−1956.68	−2.45342
$87$	−559.480	−0.689455
$88$	247.144	0.299383
$89$	−37.6118	−0.0447960	−0.0223980	−	0.999749i	$-0.507130\pi$
$89$	−37.6118	−0.0447960	−0.0223980	+	0.999749i	$0.507130\pi$
$90$	−732.932	−0.858420
$91$	0	0
$92$	1940.68	2.19924
$93$	473.621	0.528089
$94$	−96.5352	−0.105924
$95$	−758.222	−0.818863
$96$	−565.052	−0.600733
$97$	722.013	0.755766	0.377883	−	0.925853i	$-0.376652\pi$
$97$	722.013	0.755766	0.377883	+	0.925853i	$0.376652\pi$
$98$	0	0
$99$	−102.547	−0.104105
$100$	2481.29	2.48129
$101$	1518.67	1.49617	0.748087	−	0.663601i	$-0.230973\pi$
$101$	1518.67	1.49617	0.748087	+	0.663601i	$0.230973\pi$
$102$	728.117	0.706807
$103$	−1051.88	−1.00626	−0.503132	−	0.864210i	$-0.667819\pi$
$103$	−1051.88	−1.00626	−0.503132	+	0.864210i	$0.667819\pi$
$104$	284.116	0.267883
$105$	0	0
$106$	−1667.19	−1.52766
$107$	766.520	0.692545	0.346273	−	0.938134i	$-0.387447\pi$
$107$	766.520	0.692545	0.346273	+	0.938134i	$0.387447\pi$
$108$	−344.533	−0.306969
$109$	−1427.05	−1.25400	−0.627002	−	0.779018i	$-0.715718\pi$
$109$	−1427.05	−1.25400	−0.627002	+	0.779018i	$0.715718\pi$
$110$	927.904	0.804292
$111$	−11.2376	−0.00960928
$112$	0	0
$113$	362.564	0.301833	0.150917	−	0.988546i	$-0.451778\pi$
$113$	362.564	0.301833	0.150917	+	0.988546i	$0.451778\pi$
$114$	−579.874	−0.476405
$115$	2718.25	2.20416
$116$	2379.74	1.90477
$117$	−117.888	−0.0931517
$118$	1032.37	0.805402
$119$	0	0
$120$	1163.03	0.884750
$121$	−1201.17	−0.902459
$122$	−2970.63	−2.20449
$123$	117.969	0.0864789
$124$	−2014.54	−1.45896
$125$	1241.32	0.888216
$126$	0	0
$127$	974.777	0.681082	0.340541	−	0.940230i	$-0.389390\pi$
$127$	974.777	0.681082	0.340541	+	0.940230i	$0.389390\pi$
$128$	2284.83	1.57775
$129$	−1288.32	−0.879302
$130$	1066.71	0.719670
$131$	−1792.70	−1.19564	−0.597821	−	0.801629i	$-0.703967\pi$
$131$	−1792.70	−1.19564	−0.597821	+	0.801629i	$0.703967\pi$
$132$	436.184	0.287613
$133$	0	0
$134$	−662.647	−0.427194
$135$	−482.577	−0.307656
$136$	−1155.39	−0.728486
$137$	1684.42	1.05043	0.525217	−	0.850969i	$-0.323984\pi$
$137$	1684.42	1.05043	0.525217	+	0.850969i	$0.323984\pi$
$138$	2078.87	1.28236
$139$	315.089	0.192270	0.0961350	−	0.995368i	$-0.469352\pi$
$139$	315.089	0.192270	0.0961350	+	0.995368i	$0.469352\pi$
$140$	0	0
$141$	−63.5606	−0.0379629
$142$	1681.13	0.993499
$143$	149.248	0.0872781
$144$	−29.2871	−0.0169485
$145$	3333.23	1.90903
$146$	−2774.40	−1.57268
$147$	0	0
$148$	47.7992	0.0265478
$149$	1893.77	1.04123	0.520617	−	0.853790i	$-0.325702\pi$
$149$	1893.77	1.04123	0.520617	+	0.853790i	$0.325702\pi$
$150$	2657.98	1.44682
$151$	−2011.84	−1.08425	−0.542124	−	0.840299i	$-0.682380\pi$
$151$	−2011.84	−1.08425	−0.542124	+	0.840299i	$0.682380\pi$
$152$	920.159	0.491018
$153$	479.406	0.253318
$154$	0	0
$155$	−2821.71	−1.46223
$156$	501.436	0.257352
$157$	−3828.50	−1.94616	−0.973082	−	0.230460i	$-0.925977\pi$
$157$	−3828.50	−1.94616	−0.973082	+	0.230460i	$0.925977\pi$
$158$	−4147.38	−2.08827
$159$	−1097.71	−0.547511
$160$	3366.43	1.66337
$161$	0	0
$162$	−369.066	−0.178991
$163$	−3509.26	−1.68630	−0.843148	−	0.537682i	$-0.819300\pi$
$163$	−3509.26	−1.68630	−0.843148	+	0.537682i	$0.819300\pi$
$164$	−501.780	−0.238917
$165$	610.950	0.288257
$166$	1494.17	0.698613
$167$	−343.008	−0.158939	−0.0794694	−	0.996837i	$-0.525323\pi$
$167$	−343.008	−0.158939	−0.0794694	+	0.996837i	$0.525323\pi$
$168$	0	0
$169$	−2025.42	−0.921905
$170$	−4337.93	−1.95708
$171$	−381.800	−0.170743
$172$	5479.84	2.42927
$173$	−4187.21	−1.84016	−0.920081	−	0.391729i	$-0.871877\pi$
$173$	−4187.21	−1.84016	−0.920081	+	0.391729i	$0.871877\pi$
$174$	2549.20	1.11066
$175$	0	0
$176$	37.0779	0.0158798
$177$	679.733	0.288654
$178$	171.373	0.0721627
$179$	−1970.29	−0.822716	−0.411358	−	0.911474i	$-0.634945\pi$
$179$	−1970.29	−0.822716	−0.411358	+	0.911474i	$0.634945\pi$
$180$	2052.63	0.849969
$181$	−3613.10	−1.48376	−0.741878	−	0.670535i	$-0.766065\pi$
$181$	−3613.10	−1.48376	−0.741878	+	0.670535i	$0.766065\pi$
$182$	0	0
$183$	−1955.92	−0.790086
$184$	−3298.80	−1.32169
$185$	66.9509	0.0266072
$186$	−2157.99	−0.850708
$187$	−606.936	−0.237345
$188$	270.355	0.104881
$189$	0	0
$190$	3454.74	1.31912
$191$	1907.77	0.722729	0.361365	−	0.932425i	$-0.382311\pi$
$191$	1907.77	0.722729	0.361365	+	0.932425i	$0.382311\pi$
$192$	2496.48	0.938376
$193$	2399.93	0.895080	0.447540	−	0.894264i	$-0.352300\pi$
$193$	2399.93	0.895080	0.447540	+	0.894264i	$0.352300\pi$
$194$	−3289.75	−1.21748
$195$	702.346	0.257928
$196$	0	0
$197$	1514.32	0.547668	0.273834	−	0.961777i	$-0.411708\pi$
$197$	1514.32	0.547668	0.273834	+	0.961777i	$0.411708\pi$
$198$	467.243	0.167705
$199$	1367.78	0.487232	0.243616	−	0.969872i	$-0.421666\pi$
$199$	1367.78	0.487232	0.243616	+	0.969872i	$0.421666\pi$
$200$	−4217.74	−1.49120
$201$	−436.300	−0.153105
$202$	−6919.63	−2.41021
$203$	0	0
$204$	−2039.15	−0.699848
$205$	−702.828	−0.239452
$206$	4792.76	1.62101
$207$	1368.77	0.459594
$208$	42.6246	0.0142091
$209$	483.366	0.159977
$210$	0	0
$211$	4302.52	1.40378	0.701891	−	0.712285i	$-0.252339\pi$
$211$	4302.52	1.40378	0.701891	+	0.712285i	$0.252339\pi$
$212$	4669.11	1.51262
$213$	1106.89	0.356068
$214$	−3492.55	−1.11563
$215$	7675.45	2.43470
$216$	585.642	0.184481
$217$	0	0
$218$	6502.16	2.02010
$219$	−1826.72	−0.563644
$220$	−2598.67	−0.796374
$221$	−697.731	−0.212373
$222$	51.2028	0.0154798
$223$	−1497.19	−0.449592	−0.224796	−	0.974406i	$-0.572172\pi$
$223$	−1497.19	−0.449592	−0.224796	+	0.974406i	$0.572172\pi$
$224$	0	0
$225$	1750.06	0.518537
$226$	−1651.97	−0.486229
$227$	1603.32	0.468795	0.234397	−	0.972141i	$-0.424688\pi$
$227$	1603.32	0.468795	0.234397	+	0.972141i	$0.424688\pi$
$228$	1623.98	0.471715
$229$	1010.52	0.291603	0.145802	−	0.989314i	$-0.453424\pi$
$229$	1010.52	0.291603	0.145802	+	0.989314i	$0.453424\pi$
$230$	−12385.4	−3.55072
$231$	0	0
$232$	−4045.13	−1.14472
$233$	198.217	0.0557323	0.0278661	−	0.999612i	$-0.491129\pi$
$233$	198.217	0.0557323	0.0278661	+	0.999612i	$0.491129\pi$
$234$	537.141	0.150060
$235$	378.677	0.105116
$236$	−2891.24	−0.797472
$237$	−2730.71	−0.748434
$238$	0	0
$239$	−1201.19	−0.325098	−0.162549	−	0.986700i	$-0.551972\pi$
$239$	−1201.19	−0.325098	−0.162549	+	0.986700i	$0.551972\pi$
$240$	174.485	0.0469289
$241$	−2732.69	−0.730407	−0.365204	−	0.930928i	$-0.619001\pi$
$241$	−2732.69	−0.730407	−0.365204	+	0.930928i	$0.619001\pi$
$242$	5472.99	1.45379
$243$	−243.000	−0.0641500
$244$	8319.49	2.18279
$245$	0	0
$246$	−537.510	−0.139311
$247$	555.675	0.143145
$248$	3424.35	0.876801
$249$	983.788	0.250382
$250$	−5655.91	−1.43084
$251$	7565.82	1.90259	0.951295	−	0.308281i	$-0.0997537\pi$
$251$	7565.82	1.90259	0.951295	+	0.308281i	$0.0997537\pi$
$252$	0	0
$253$	−1732.88	−0.430615
$254$	−4441.44	−1.09717
$255$	−2856.18	−0.701414
$256$	−3753.22	−0.916313
$257$	5008.68	1.21569	0.607846	−	0.794055i	$-0.292034\pi$
$257$	5008.68	1.21569	0.607846	+	0.794055i	$0.292034\pi$
$258$	5870.04	1.41648
$259$	0	0
$260$	−2987.42	−0.712584
$261$	1678.44	0.398057
$262$	8168.21	1.92608
$263$	−6248.81	−1.46509	−0.732544	−	0.680720i	$-0.761667\pi$
$263$	−6248.81	−1.46509	−0.732544	+	0.680720i	$0.761667\pi$
$264$	−741.433	−0.172849
$265$	6539.88	1.51601
$266$	0	0
$267$	112.835	0.0258630
$268$	1855.80	0.422988
$269$	−3588.45	−0.813351	−0.406676	−	0.913573i	$-0.633312\pi$
$269$	−3588.45	−0.813351	−0.406676	+	0.913573i	$0.633312\pi$
$270$	2198.80	0.495609
$271$	−1983.14	−0.444529	−0.222264	−	0.974986i	$-0.571345\pi$
$271$	−1983.14	−0.444529	−0.222264	+	0.974986i	$0.571345\pi$
$272$	−173.338	−0.0386404
$273$	0	0
$274$	−7674.81	−1.69216
$275$	−2215.61	−0.485841
$276$	−5822.05	−1.26973
$277$	7363.91	1.59731	0.798654	−	0.601790i	$-0.205546\pi$
$277$	7363.91	1.59731	0.798654	+	0.601790i	$0.205546\pi$
$278$	−1435.66	−0.309731
$279$	−1420.86	−0.304892
$280$	0	0
$281$	−5312.05	−1.12772	−0.563861	−	0.825869i	$-0.690685\pi$
$281$	−5312.05	−1.12772	−0.563861	+	0.825869i	$0.690685\pi$
$282$	289.606	0.0611552
$283$	−1091.76	−0.229324	−0.114662	−	0.993405i	$-0.536578\pi$
$283$	−1091.76	−0.229324	−0.114662	+	0.993405i	$0.536578\pi$
$284$	−4708.13	−0.983718
$285$	2274.67	0.472770
$286$	−680.030	−0.140598
$287$	0	0
$288$	1695.16	0.346833
$289$	−2075.59	−0.422469
$290$	−15187.4	−3.07530
$291$	−2166.04	−0.436341
$292$	7769.92	1.55719
$293$	−7191.86	−1.43397	−0.716985	−	0.697089i	$-0.754478\pi$
$293$	−7191.86	−1.43397	−0.716985	+	0.697089i	$0.754478\pi$
$294$	0	0
$295$	−4049.67	−0.799257
$296$	−81.2499	−0.0159546
$297$	307.642	0.0601051
$298$	−8628.73	−1.67734
$299$	−1992.12	−0.385308
$300$	−7443.88	−1.43257
$301$	0	0
$302$	9166.69	1.74663
$303$	−4556.02	−0.863816
$304$	138.047	0.0260446
$305$	11652.9	2.18767
$306$	−2184.35	−0.408075
$307$	541.355	0.100641	0.0503204	−	0.998733i	$-0.483976\pi$
$307$	541.355	0.100641	0.0503204	+	0.998733i	$0.483976\pi$
$308$	0	0
$309$	3155.65	0.580966
$310$	12856.7	2.35553
$311$	54.0168	0.00984892	0.00492446	−	0.999988i	$-0.498432\pi$
$311$	54.0168	0.00984892	0.00492446	+	0.999988i	$0.498432\pi$
$312$	−852.348	−0.154663
$313$	3772.94	0.681340	0.340670	−	0.940183i	$-0.389346\pi$
$313$	3772.94	0.681340	0.340670	+	0.940183i	$0.389346\pi$
$314$	17444.1	3.13511
$315$	0	0
$316$	11615.1	2.06772
$317$	1719.24	0.304612	0.152306	−	0.988333i	$-0.451330\pi$
$317$	1719.24	0.304612	0.152306	+	0.988333i	$0.451330\pi$
$318$	5001.58	0.881996
$319$	−2124.93	−0.372957
$320$	−14873.4	−2.59827
$321$	−2299.56	−0.399841
$322$	0	0
$323$	−2259.72	−0.389270
$324$	1033.60	0.177229
$325$	−2547.06	−0.434724
$326$	15989.5	2.71649
$327$	4281.15	0.724000
$328$	852.934	0.143584
$329$	0	0
$330$	−2783.71	−0.464358
$331$	8408.21	1.39625	0.698123	−	0.715978i	$-0.254019\pi$
$331$	8408.21	1.39625	0.698123	+	0.715978i	$0.254019\pi$
$332$	−4184.53	−0.691735
$333$	33.7129	0.00554792
$334$	1562.87	0.256037
$335$	2599.36	0.423935
$336$	0	0
$337$	2789.46	0.450894	0.225447	−	0.974255i	$-0.427616\pi$
$337$	2789.46	0.450894	0.225447	+	0.974255i	$0.427616\pi$
$338$	9228.58	1.48511
$339$	−1087.69	−0.174263
$340$	12148.7	1.93781
$341$	1798.84	0.285667
$342$	1739.62	0.275053
$343$	0	0
$344$	−9314.72	−1.45993
$345$	−8154.76	−1.27257
$346$	19078.5	2.96435
$347$	−3471.96	−0.537132	−0.268566	−	0.963261i	$-0.586550\pi$
$347$	−3471.96	−0.537132	−0.268566	+	0.963261i	$0.586550\pi$
$348$	−7139.23	−1.09972
$349$	−6626.12	−1.01630	−0.508149	−	0.861269i	$-0.669670\pi$
$349$	−6626.12	−1.01630	−0.508149	+	0.861269i	$0.669670\pi$
$350$	0	0
$351$	353.664	0.0537812
$352$	−2146.10	−0.324964
$353$	9468.40	1.42763	0.713813	−	0.700337i	$-0.246967\pi$
$353$	9468.40	1.42763	0.713813	+	0.700337i	$0.246967\pi$
$354$	−3097.11	−0.464999
$355$	−6594.53	−0.985919
$356$	−479.944	−0.0714522
$357$	0	0
$358$	8977.35	1.32533
$359$	−6279.55	−0.923182	−0.461591	−	0.887093i	$-0.652721\pi$
$359$	−6279.55	−0.923182	−0.461591	+	0.887093i	$0.652721\pi$
$360$	−3489.10	−0.510811
$361$	−5059.35	−0.737622
$362$	16462.6	2.39021
$363$	3603.52	0.521035
$364$	0	0
$365$	10883.1	1.56068
$366$	8911.89	1.27276
$367$	−10827.8	−1.54008	−0.770038	−	0.637998i	$-0.779763\pi$
$367$	−10827.8	−1.54008	−0.770038	+	0.637998i	$0.779763\pi$
$368$	−494.904	−0.0701050
$369$	−353.907	−0.0499286
$370$	−305.053	−0.0428620
$371$	0	0
$372$	6043.63	0.842332
$373$	5239.23	0.727284	0.363642	−	0.931539i	$-0.381533\pi$
$373$	5239.23	0.727284	0.363642	+	0.931539i	$0.381533\pi$
$374$	2765.42	0.382344
$375$	−3723.96	−0.512812
$376$	−459.553	−0.0630310
$377$	−2442.81	−0.333717
$378$	0	0
$379$	−11050.4	−1.49768	−0.748839	−	0.662751i	$-0.769389\pi$
$379$	−11050.4	−1.49768	−0.748839	+	0.662751i	$0.769389\pi$
$380$	−9675.27	−1.30613
$381$	−2924.33	−0.393223
$382$	−8692.49	−1.16426
$383$	−10468.0	−1.39658	−0.698292	−	0.715813i	$-0.746056\pi$
$383$	−10468.0	−1.39658	−0.698292	+	0.715813i	$0.746056\pi$
$384$	−6854.48	−0.910915
$385$	0	0
$386$	−10934.9	−1.44190
$387$	3864.95	0.507665
$388$	9213.22	1.20549
$389$	−11614.0	−1.51377	−0.756884	−	0.653550i	$-0.773279\pi$
$389$	−11614.0	−1.51377	−0.756884	+	0.653550i	$0.773279\pi$
$390$	−3200.14	−0.415501
$391$	8101.19	1.04781
$392$	0	0
$393$	5378.11	0.690304
$394$	−6899.78	−0.882248
$395$	16268.9	2.07234
$396$	−1308.55	−0.166054
$397$	−6707.30	−0.847934	−0.423967	−	0.905678i	$-0.639363\pi$
$397$	−6707.30	−0.847934	−0.423967	+	0.905678i	$0.639363\pi$
$398$	−6232.10	−0.784892
$399$	0	0
$400$	−632.768	−0.0790960
$401$	5526.38	0.688215	0.344107	−	0.938930i	$-0.388182\pi$
$401$	5526.38	0.688215	0.344107	+	0.938930i	$0.388182\pi$
$402$	1987.94	0.246640
$403$	2067.94	0.255611
$404$	19379.0	2.38649
$405$	1447.73	0.177625
$406$	0	0
$407$	−42.6811	−0.00519810
$408$	3466.18	0.420592
$409$	−1318.91	−0.159452	−0.0797258	−	0.996817i	$-0.525404\pi$
$409$	−1318.91	−0.159452	−0.0797258	+	0.996817i	$0.525404\pi$
$410$	3202.34	0.385738
$411$	−5053.25	−0.606468
$412$	−13422.5	−1.60505
$413$	0	0
$414$	−6236.61	−0.740369
$415$	−5861.15	−0.693283
$416$	−2467.14	−0.290773
$417$	−945.268	−0.111007
$418$	−2202.39	−0.257709
$419$	3656.13	0.426286	0.213143	−	0.977021i	$-0.431630\pi$
$419$	3656.13	0.426286	0.213143	+	0.977021i	$0.431630\pi$
$420$	0	0
$421$	−135.389	−0.0156733	−0.00783663	−	0.999969i	$-0.502495\pi$
$421$	−135.389	−0.0156733	−0.00783663	+	0.999969i	$0.502495\pi$
$422$	−19603.9	−2.26138
$423$	190.682	0.0219179
$424$	−7936.63	−0.909049
$425$	10357.9	1.18219
$426$	−5043.38	−0.573597
$427$	0	0
$428$	9781.16	1.10465
$429$	−447.745	−0.0503900
$430$	−34972.1	−3.92211
$431$	8389.16	0.937568	0.468784	−	0.883313i	$-0.344692\pi$
$431$	8389.16	0.937568	0.468784	+	0.883313i	$0.344692\pi$
$432$	87.8612	0.00978524
$433$	−8243.02	−0.914859	−0.457430	−	0.889246i	$-0.651230\pi$
$433$	−8243.02	−0.914859	−0.457430	+	0.889246i	$0.651230\pi$
$434$	0	0
$435$	−9999.70	−1.10218
$436$	−18209.8	−2.00021
$437$	−6451.81	−0.706252
$438$	8323.19	0.907985
$439$	−18283.2	−1.98772	−0.993859	−	0.110649i	$-0.964707\pi$
$439$	−18283.2	−1.98772	−0.993859	+	0.110649i	$0.964707\pi$
$440$	4417.26	0.478602
$441$	0	0
$442$	3179.12	0.342116
$443$	1210.44	0.129818	0.0649092	−	0.997891i	$-0.479324\pi$
$443$	1210.44	0.129818	0.0649092	+	0.997891i	$0.479324\pi$
$444$	−143.398	−0.0153274
$445$	−672.243	−0.0716121
$446$	6821.72	0.724256
$447$	−5681.32	−0.601157
$448$	0	0
$449$	−8301.16	−0.872508	−0.436254	−	0.899824i	$-0.643695\pi$
$449$	−8301.16	−0.872508	−0.436254	+	0.899824i	$0.643695\pi$
$450$	−7973.93	−0.835321
$451$	448.052	0.0467804
$452$	4626.49	0.481442
$453$	6035.52	0.625990
$454$	−7305.34	−0.755190
$455$	0	0
$456$	−2760.48	−0.283489
$457$	−12293.8	−1.25838	−0.629188	−	0.777253i	$-0.716612\pi$
$457$	−12293.8	−1.25838	−0.629188	+	0.777253i	$0.716612\pi$
$458$	−4604.31	−0.469749
$459$	−1438.22	−0.146253
$460$	34686.2	3.51577
$461$	19434.2	1.96343	0.981717	−	0.190346i	$-0.0609609\pi$
$461$	19434.2	1.96343	0.981717	+	0.190346i	$0.0609609\pi$
$462$	0	0
$463$	−12491.1	−1.25380	−0.626902	−	0.779098i	$-0.715678\pi$
$463$	−12491.1	−1.25380	−0.626902	+	0.779098i	$0.715678\pi$
$464$	−606.871	−0.0607183
$465$	8465.13	0.844217
$466$	−903.149	−0.0897802
$467$	3385.17	0.335433	0.167716	−	0.985835i	$-0.446361\pi$
$467$	3385.17	0.335433	0.167716	+	0.985835i	$0.446361\pi$
$468$	−1504.31	−0.148583
$469$	0	0
$470$	−1725.39	−0.169333
$471$	11485.5	1.12362
$472$	4914.57	0.479262
$473$	−4893.09	−0.475654
$474$	12442.1	1.20567
$475$	−8249.07	−0.796828
$476$	0	0
$477$	3293.14	0.316106
$478$	5473.05	0.523706
$479$	5979.41	0.570368	0.285184	−	0.958473i	$-0.407945\pi$
$479$	5979.41	0.570368	0.285184	+	0.958473i	$0.407945\pi$
$480$	−10099.3	−0.960349
$481$	−49.0661	−0.00465119
$482$	12451.1	1.17663
$483$	0	0
$484$	−15327.5	−1.43948
$485$	12904.7	1.20819
$486$	1107.20	0.103340
$487$	−1114.96	−0.103745	−0.0518725	−	0.998654i	$-0.516519\pi$
$487$	−1114.96	−0.103745	−0.0518725	+	0.998654i	$0.516519\pi$
$488$	−14141.6	−1.31180
$489$	10527.8	0.973583
$490$	0	0
$491$	1086.23	0.0998387	0.0499194	−	0.998753i	$-0.484104\pi$
$491$	1086.23	0.0998387	0.0499194	+	0.998753i	$0.484104\pi$
$492$	1505.34	0.137939
$493$	9934.01	0.907516
$494$	−2531.86	−0.230595
$495$	−1832.85	−0.166425
$496$	513.740	0.0465073
$497$	0	0
$498$	−4482.50	−0.403344
$499$	−2213.50	−0.198577	−0.0992884	−	0.995059i	$-0.531657\pi$
$499$	−2213.50	−0.198577	−0.0992884	+	0.995059i	$0.531657\pi$
$500$	15839.8	1.41676
$501$	1029.02	0.0917634
$502$	−34472.6	−3.06492
$503$	−2643.32	−0.234314	−0.117157	−	0.993113i	$-0.537378\pi$
$503$	−2643.32	−0.234314	−0.117157	+	0.993113i	$0.537378\pi$
$504$	0	0
$505$	27143.5	2.39183
$506$	7895.66	0.693685
$507$	6076.27	0.532262
$508$	12438.6	1.08637
$509$	−665.169	−0.0579236	−0.0289618	−	0.999581i	$-0.509220\pi$
$509$	−665.169	−0.0579236	−0.0289618	+	0.999581i	$0.509220\pi$
$510$	13013.8	1.12992
$511$	0	0
$512$	−1177.58	−0.101645
$513$	1145.40	0.0985784
$514$	−22821.4	−1.95838
$515$	−18800.5	−1.60864
$516$	−16439.5	−1.40254
$517$	−241.406	−0.0205359
$518$	0	0
$519$	12561.6	1.06242
$520$	5078.07	0.428246
$521$	−11762.0	−0.989063	−0.494531	−	0.869160i	$-0.664660\pi$
$521$	−11762.0	−0.989063	−0.494531	+	0.869160i	$0.664660\pi$
$522$	−7647.59	−0.641237
$523$	10122.6	0.846330	0.423165	−	0.906053i	$-0.360919\pi$
$523$	10122.6	0.846330	0.423165	+	0.906053i	$0.360919\pi$
$524$	−22875.7	−1.90712
$525$	0	0
$526$	28471.9	2.36014
$527$	−8409.52	−0.695112
$528$	−111.234	−0.00916823
$529$	10963.0	0.901042
$530$	−29798.1	−2.44216
$531$	−2039.20	−0.166655
$532$	0	0
$533$	515.079	0.0418585
$534$	−514.119	−0.0416631
$535$	13700.2	1.10712
$536$	−3154.51	−0.254206
$537$	5910.86	0.474995
$538$	16350.3	1.31024
$539$	0	0
$540$	−6157.90	−0.490730
$541$	16118.0	1.28090	0.640449	−	0.768001i	$-0.278748\pi$
$541$	16118.0	1.28090	0.640449	+	0.768001i	$0.278748\pi$
$542$	9035.92	0.716100
$543$	10839.3	0.856647
$544$	10032.9	0.790733
$545$	−25505.9	−2.00469
$546$	0	0
$547$	−626.100	−0.0489399	−0.0244699	−	0.999701i	$-0.507790\pi$
$547$	−626.100	−0.0489399	−0.0244699	+	0.999701i	$0.507790\pi$
$548$	21493.9	1.67550
$549$	5867.76	0.456156
$550$	10095.1	0.782650
$551$	−7911.47	−0.611688
$552$	9896.41	0.763078
$553$	0	0
$554$	−33552.7	−2.57313
$555$	−200.853	−0.0153617
$556$	4020.69	0.306682
$557$	20771.2	1.58008	0.790039	−	0.613057i	$-0.210060\pi$
$557$	20771.2	1.58008	0.790039	+	0.613057i	$0.210060\pi$
$558$	6473.97	0.491156
$559$	−5625.08	−0.425609
$560$	0	0
$561$	1820.81	0.137031
$562$	24203.6	1.81667
$563$	−5521.72	−0.413344	−0.206672	−	0.978410i	$-0.566263\pi$
$563$	−5521.72	−0.413344	−0.206672	+	0.978410i	$0.566263\pi$
$564$	−811.064	−0.0605531
$565$	6480.18	0.482519
$566$	4974.48	0.369422
$567$	0	0
$568$	8002.95	0.591191
$569$	7574.81	0.558089	0.279044	−	0.960278i	$-0.409982\pi$
$569$	7574.81	0.558089	0.279044	+	0.960278i	$0.409982\pi$
$570$	−10364.2	−0.761595
$571$	−331.248	−0.0242772	−0.0121386	−	0.999926i	$-0.503864\pi$
$571$	−331.248	−0.0242772	−0.0121386	+	0.999926i	$0.503864\pi$
$572$	1904.48	0.139214
$573$	−5723.31	−0.417268
$574$	0	0
$575$	29573.2	2.14485
$576$	−7489.45	−0.541772
$577$	2038.11	0.147050	0.0735248	−	0.997293i	$-0.476575\pi$
$577$	2038.11	0.147050	0.0735248	+	0.997293i	$0.476575\pi$
$578$	9457.14	0.680563
$579$	−7199.78	−0.516775
$580$	42533.6	3.04502
$581$	0	0
$582$	9869.26	0.702911
$583$	−4169.17	−0.296174
$584$	−13207.4	−0.935835
$585$	−2107.04	−0.148915
$586$	32768.8	2.31001
$587$	5232.90	0.367947	0.183973	−	0.982931i	$-0.441104\pi$
$587$	5232.90	0.367947	0.183973	+	0.982931i	$0.441104\pi$
$588$	0	0
$589$	6697.36	0.468523
$590$	18451.8	1.28754
$591$	−4542.95	−0.316196
$592$	−12.1895	−0.000846262 0
$593$	−5720.24	−0.396125	−0.198062	−	0.980189i	$-0.563465\pi$
$593$	−5720.24	−0.396125	−0.198062	+	0.980189i	$0.563465\pi$
$594$	−1401.73	−0.0968244
$595$	0	0
$596$	24165.5	1.66083
$597$	−4103.33	−0.281304
$598$	9076.81	0.620700
$599$	18088.4	1.23384	0.616922	−	0.787024i	$-0.288379\pi$
$599$	18088.4	1.23384	0.616922	+	0.787024i	$0.288379\pi$
$600$	12653.2	0.860943
$601$	−1821.43	−0.123623	−0.0618117	−	0.998088i	$-0.519688\pi$
$601$	−1821.43	−0.123623	−0.0618117	+	0.998088i	$0.519688\pi$
$602$	0	0
$603$	1308.90	0.0883955
$604$	−25672.0	−1.72944
$605$	−21468.8	−1.44270
$606$	20758.9	1.39154
$607$	2372.20	0.158624	0.0793120	−	0.996850i	$-0.474728\pi$
$607$	2372.20	0.158624	0.0793120	+	0.996850i	$0.474728\pi$
$608$	−7990.26	−0.532974
$609$	0	0
$610$	−53094.7	−3.52416
$611$	−277.520	−0.0183752
$612$	6117.45	0.404058
$613$	9725.08	0.640770	0.320385	−	0.947287i	$-0.396188\pi$
$613$	9725.08	0.640770	0.320385	+	0.947287i	$0.396188\pi$
$614$	−2466.61	−0.162124
$615$	2108.48	0.138248
$616$	0	0
$617$	−5329.51	−0.347744	−0.173872	−	0.984768i	$-0.555628\pi$
$617$	−5329.51	−0.347744	−0.173872	+	0.984768i	$0.555628\pi$
$618$	−14378.3	−0.935890
$619$	−15976.6	−1.03740	−0.518702	−	0.854955i	$-0.673585\pi$
$619$	−15976.6	−1.03740	−0.518702	+	0.854955i	$0.673585\pi$
$620$	−36006.3	−2.33234
$621$	−4106.31	−0.265347
$622$	−246.120	−0.0158658
$623$	0	0
$624$	−127.874	−0.00820361
$625$	−2120.06	−0.135684
$626$	−17190.9	−1.09758
$627$	−1450.10	−0.0923625
$628$	−48853.5	−3.10425
$629$	199.533	0.0126485
$630$	0	0
$631$	−4199.98	−0.264974	−0.132487	−	0.991185i	$-0.542296\pi$
$631$	−4199.98	−0.264974	−0.132487	+	0.991185i	$0.542296\pi$
$632$	−19743.5	−1.24265
$633$	−12907.6	−0.810474
$634$	−7833.47	−0.490705
$635$	17422.4	1.08880
$636$	−14007.3	−0.873312
$637$	0	0
$638$	9681.97	0.600804
$639$	−3320.66	−0.205576
$640$	40837.2	2.52224
$641$	2648.51	0.163198	0.0815988	−	0.996665i	$-0.473997\pi$
$641$	2648.51	0.163198	0.0815988	+	0.996665i	$0.473997\pi$
$642$	10477.6	0.644112
$643$	13.4305	0.000823715 0	0.000411857	−	1.00000i	$-0.499869\pi$
$643$	13.4305	0.000823715 0	0.000411857		1.00000i	$0.499869\pi$
$644$	0	0
$645$	−23026.3	−1.40568
$646$	10296.1	0.627083
$647$	11624.1	0.706324	0.353162	−	0.935562i	$-0.385106\pi$
$647$	11624.1	0.706324	0.353162	+	0.935562i	$0.385106\pi$
$648$	−1756.93	−0.106510
$649$	2581.66	0.156146
$650$	11605.3	0.700305
$651$	0	0
$652$	−44779.8	−2.68974
$653$	−28516.6	−1.70894	−0.854471	−	0.519499i	$-0.826119\pi$
$653$	−28516.6	−1.70894	−0.854471	+	0.519499i	$0.826119\pi$
$654$	−19506.5	−1.16630
$655$	−32041.3	−1.91139
$656$	127.962	0.00761595
$657$	5480.15	0.325420
$658$	0	0
$659$	18048.6	1.06688	0.533440	−	0.845838i	$-0.320899\pi$
$659$	18048.6	1.06688	0.533440	+	0.845838i	$0.320899\pi$
$660$	7796.01	0.459787
$661$	17841.4	1.04985	0.524926	−	0.851148i	$-0.324093\pi$
$661$	17841.4	1.04985	0.524926	+	0.851148i	$0.324093\pi$
$662$	−38310.9	−2.24924
$663$	2093.19	0.122614
$664$	7112.94	0.415716
$665$	0	0
$666$	−153.608	−0.00893725
$667$	28362.9	1.64650
$668$	−4376.95	−0.253517
$669$	4491.56	0.259572
$670$	−11843.6	−0.682924
$671$	−7428.68	−0.427394
$672$	0	0
$673$	−6826.13	−0.390978	−0.195489	−	0.980706i	$-0.562629\pi$
$673$	−6826.13	−0.390978	−0.195489	+	0.980706i	$0.562629\pi$
$674$	−12709.8	−0.726354
$675$	−5250.19	−0.299378
$676$	−25845.4	−1.47049
$677$	−21286.9	−1.20845	−0.604225	−	0.796814i	$-0.706517\pi$
$677$	−21286.9	−1.20845	−0.604225	+	0.796814i	$0.706517\pi$
$678$	4955.92	0.280724
$679$	0	0
$680$	−20650.6	−1.16458
$681$	−4809.97	−0.270659
$682$	−8196.16	−0.460187
$683$	−20696.8	−1.15951	−0.579753	−	0.814793i	$-0.696851\pi$
$683$	−20696.8	−1.15951	−0.579753	+	0.814793i	$0.696851\pi$
$684$	−4871.95	−0.272345
$685$	30105.9	1.67925
$686$	0	0
$687$	−3031.56	−0.168357
$688$	−1397.44	−0.0774376
$689$	−4792.86	−0.265012
$690$	37156.1	2.05001
$691$	31341.9	1.72548	0.862738	−	0.505652i	$-0.168748\pi$
$691$	31341.9	1.72548	0.862738	+	0.505652i	$0.168748\pi$
$692$	−53430.8	−2.93517
$693$	0	0
$694$	15819.5	0.865276
$695$	5631.66	0.307368
$696$	12135.4	0.660906
$697$	−2094.63	−0.113831
$698$	30191.0	1.63717
$699$	−594.651	−0.0321770
$700$	0	0
$701$	−9213.32	−0.496408	−0.248204	−	0.968708i	$-0.579840\pi$
$701$	−9213.32	−0.496408	−0.248204	+	0.968708i	$0.579840\pi$
$702$	−1611.42	−0.0866371
$703$	−158.909	−0.00852541
$704$	9481.77	0.507610
$705$	−1136.03	−0.0606886
$706$	−43141.5	−2.29979
$707$	0	0
$708$	8673.71	0.460421
$709$	14516.5	0.768942	0.384471	−	0.923137i	$-0.374384\pi$
$709$	14516.5	0.768942	0.384471	+	0.923137i	$0.374384\pi$
$710$	30047.1	1.58824
$711$	8192.14	0.432108
$712$	815.817	0.0429411
$713$	−24010.3	−1.26114
$714$	0	0
$715$	2667.54	0.139525
$716$	−25141.8	−1.31228
$717$	3603.56	0.187695
$718$	28611.9	1.48717
$719$	25882.4	1.34249	0.671246	−	0.741235i	$-0.265760\pi$
$719$	25882.4	1.34249	0.671246	+	0.741235i	$0.265760\pi$
$720$	−523.454	−0.0270944
$721$	0	0
$722$	23052.3	1.18825
$723$	8198.08	0.421701
$724$	−46104.9	−2.36668
$725$	36263.9	1.85767
$726$	−16419.0	−0.839345
$727$	32181.2	1.64172	0.820862	−	0.571127i	$-0.193494\pi$
$727$	32181.2	1.64172	0.820862	+	0.571127i	$0.193494\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	−49587.4	−2.51412
$731$	22875.1	1.15741
$732$	−24958.5	−1.26023
$733$	20836.1	1.04993	0.524966	−	0.851123i	$-0.324078\pi$
$733$	20836.1	1.04993	0.524966	+	0.851123i	$0.324078\pi$
$734$	49335.5	2.48094
$735$	0	0
$736$	28645.4	1.43462
$737$	−1657.09	−0.0828217
$738$	1612.53	0.0804310
$739$	26434.9	1.31586	0.657931	−	0.753078i	$-0.271432\pi$
$739$	26434.9	1.31586	0.657931	+	0.753078i	$0.271432\pi$
$740$	854.325	0.0424400
$741$	−1667.03	−0.0826447
$742$	0	0
$743$	9954.69	0.491524	0.245762	−	0.969330i	$-0.420962\pi$
$743$	9954.69	0.491524	0.245762	+	0.969330i	$0.420962\pi$
$744$	−10273.1	−0.506221
$745$	33847.8	1.66455
$746$	−23871.8	−1.17160
$747$	−2951.36	−0.144558
$748$	−7744.79	−0.378580
$749$	0	0
$750$	16967.7	0.826098
$751$	−33204.5	−1.61338	−0.806692	−	0.590973i	$-0.798744\pi$
$751$	−33204.5	−1.61338	−0.806692	+	0.590973i	$0.798744\pi$
$752$	−68.9446	−0.00334329
$753$	−22697.5	−1.09846
$754$	11130.4	0.537591
$755$	−35958.1	−1.73331
$756$	0	0
$757$	1964.06	0.0942998	0.0471499	−	0.998888i	$-0.484986\pi$
$757$	1964.06	0.0942998	0.0471499	+	0.998888i	$0.484986\pi$
$758$	50349.6	2.41264
$759$	5198.65	0.248615
$760$	16446.2	0.784955
$761$	−38553.8	−1.83650	−0.918248	−	0.396005i	$-0.870396\pi$
$761$	−38553.8	−1.83650	−0.918248	+	0.396005i	$0.870396\pi$
$762$	13324.3	0.633450
$763$	0	0
$764$	24344.0	1.15280
$765$	8568.53	0.404962
$766$	47696.2	2.24978
$767$	2967.87	0.139718
$768$	11259.7	0.529034
$769$	−19715.0	−0.924501	−0.462251	−	0.886749i	$-0.652958\pi$
$769$	−19715.0	−0.924501	−0.462251	+	0.886749i	$0.652958\pi$
$770$	0	0
$771$	−15026.0	−0.701880
$772$	30624.2	1.42771
$773$	−14700.7	−0.684019	−0.342010	−	0.939696i	$-0.611108\pi$
$773$	−14700.7	−0.684019	−0.342010	+	0.939696i	$0.611108\pi$
$774$	−17610.1	−0.817807
$775$	−30698.8	−1.42288
$776$	−15660.8	−0.724471
$777$	0	0
$778$	52917.8	2.43856
$779$	1668.17	0.0767246
$780$	8962.26	0.411411
$781$	4204.01	0.192614
$782$	−36912.0	−1.68794
$783$	−5035.32	−0.229818
$784$	0	0
$785$	−68427.6	−3.11119
$786$	−24504.6	−1.11202
$787$	−23918.6	−1.08336	−0.541681	−	0.840584i	$-0.682212\pi$
$787$	−23918.6	−1.08336	−0.541681	+	0.840584i	$0.682212\pi$
$788$	19323.4	0.873562
$789$	18746.4	0.845869
$790$	−74126.9	−3.33837
$791$	0	0
$792$	2224.30	0.0997942
$793$	−8539.98	−0.382426
$794$	30560.9	1.36595
$795$	−19619.6	−0.875266
$796$	17453.5	0.777164
$797$	38252.7	1.70010	0.850051	−	0.526700i	$-0.176571\pi$
$797$	38252.7	1.70010	0.850051	+	0.526700i	$0.176571\pi$
$798$	0	0
$799$	1128.57	0.0499698
$800$	36625.1	1.61861
$801$	−338.506	−0.0149320
$802$	−25180.2	−1.10866
$803$	−6937.96	−0.304901
$804$	−5567.39	−0.244212
$805$	0	0
$806$	−9422.27	−0.411769
$807$	10765.3	0.469589
$808$	−32940.7	−1.43422
$809$	−31435.6	−1.36615	−0.683075	−	0.730348i	$-0.739358\pi$
$809$	−31435.6	−1.36615	−0.683075	+	0.730348i	$0.739358\pi$
$810$	−6596.39	−0.286140
$811$	11467.0	0.496501	0.248250	−	0.968696i	$-0.420144\pi$
$811$	11467.0	0.496501	0.248250	+	0.968696i	$0.420144\pi$
$812$	0	0
$813$	5949.43	0.256649
$814$	194.471	0.00837371
$815$	−62721.7	−2.69576
$816$	520.015	0.0223090
$817$	−18217.8	−0.780121
$818$	6009.42	0.256864
$819$	0	0
$820$	−8968.42	−0.381940
$821$	−5030.57	−0.213847	−0.106923	−	0.994267i	$-0.534100\pi$
$821$	−5030.57	−0.213847	−0.106923	+	0.994267i	$0.534100\pi$
$822$	23024.4	0.976970
$823$	−13985.2	−0.592336	−0.296168	−	0.955136i	$-0.595709\pi$
$823$	−13985.2	−0.592336	−0.296168	+	0.955136i	$0.595709\pi$
$824$	22815.8	0.964596
$825$	6646.83	0.280500
$826$	0	0
$827$	−13939.5	−0.586125	−0.293063	−	0.956093i	$-0.594674\pi$
$827$	−13939.5	−0.586125	−0.293063	+	0.956093i	$0.594674\pi$
$828$	17466.1	0.733080
$829$	−20104.4	−0.842286	−0.421143	−	0.906994i	$-0.638371\pi$
$829$	−20104.4	−0.842286	−0.421143	+	0.906994i	$0.638371\pi$
$830$	26705.5	1.11682
$831$	−22091.7	−0.922207
$832$	10900.2	0.454203
$833$	0	0
$834$	4306.99	0.178823
$835$	−6130.66	−0.254084
$836$	6167.98	0.255172
$837$	4262.59	0.176030
$838$	−16658.7	−0.686711
$839$	15949.5	0.656302	0.328151	−	0.944625i	$-0.393575\pi$
$839$	15949.5	0.656302	0.328151	+	0.944625i	$0.393575\pi$
$840$	0	0
$841$	10390.8	0.426043
$842$	616.881	0.0252484
$843$	15936.1	0.651091
$844$	54902.2	2.23911
$845$	−36200.8	−1.47378
$846$	−868.817	−0.0353080
$847$	0	0
$848$	−1190.70	−0.0482177
$849$	3275.29	0.132400
$850$	−47194.5	−1.90442
$851$	569.694	0.0229481
$852$	14124.4	0.567950
$853$	11802.0	0.473730	0.236865	−	0.971543i	$-0.423880\pi$
$853$	11802.0	0.473730	0.236865	+	0.971543i	$0.423880\pi$
$854$	0	0
$855$	−6824.00	−0.272954
$856$	−16626.2	−0.663868
$857$	9595.28	0.382460	0.191230	−	0.981545i	$-0.438752\pi$
$857$	9595.28	0.382460	0.191230	+	0.981545i	$0.438752\pi$
$858$	2040.09	0.0811742
$859$	21840.9	0.867521	0.433760	−	0.901028i	$-0.357186\pi$
$859$	21840.9	0.867521	0.433760	+	0.901028i	$0.357186\pi$
$860$	97942.3	3.88350
$861$	0	0
$862$	−38224.1	−1.51035
$863$	−26531.6	−1.04652	−0.523260	−	0.852173i	$-0.675284\pi$
$863$	−26531.6	−1.04652	−0.523260	+	0.852173i	$0.675284\pi$
$864$	−5085.47	−0.200244
$865$	−74838.9	−2.94173
$866$	37558.2	1.47376
$867$	6226.77	0.243912
$868$	0	0
$869$	−10371.4	−0.404862
$870$	45562.3	1.77552
$871$	−1904.98	−0.0741077
$872$	30953.3	1.20208
$873$	6498.11	0.251922
$874$	29396.8	1.13771
$875$	0	0
$876$	−23309.8	−0.899046
$877$	−6832.46	−0.263074	−0.131537	−	0.991311i	$-0.541991\pi$
$877$	−6832.46	−0.263074	−0.131537	+	0.991311i	$0.541991\pi$
$878$	83304.9	3.20205
$879$	21575.6	0.827903
$880$	662.701	0.0253860
$881$	−3994.77	−0.152766	−0.0763832	−	0.997079i	$-0.524337\pi$
$881$	−3994.77	−0.152766	−0.0763832	+	0.997079i	$0.524337\pi$
$882$	0	0
$883$	13727.0	0.523161	0.261580	−	0.965182i	$-0.415756\pi$
$883$	13727.0	0.523161	0.261580	+	0.965182i	$0.415756\pi$
$884$	−8903.38	−0.338748
$885$	12149.0	0.461451
$886$	−5515.19	−0.209127
$887$	44119.4	1.67011	0.835054	−	0.550169i	$-0.185437\pi$
$887$	44119.4	1.67011	0.835054	+	0.550169i	$0.185437\pi$
$888$	243.750	0.00921138
$889$	0	0
$890$	3062.99	0.115361
$891$	−922.926	−0.0347017
$892$	−19104.8	−0.717125
$893$	−898.796	−0.0336809
$894$	25886.2	0.968415
$895$	−35215.3	−1.31522
$896$	0	0
$897$	5976.35	0.222458
$898$	37823.1	1.40554
$899$	−29442.4	−1.09228
$900$	22331.6	0.827098
$901$	19490.7	0.720678
$902$	−2041.49	−0.0753594
$903$	0	0
$904$	−7864.18	−0.289335
$905$	−64577.7	−2.37197
$906$	−27500.1	−1.00842
$907$	36905.8	1.35109	0.675545	−	0.737319i	$-0.263908\pi$
$907$	36905.8	1.35109	0.675545	+	0.737319i	$0.263908\pi$
$908$	20459.2	0.747755
$909$	13668.1	0.498725
$910$	0	0
$911$	−3169.56	−0.115271	−0.0576356	−	0.998338i	$-0.518356\pi$
$911$	−3169.56	−0.115271	−0.0576356	+	0.998338i	$0.518356\pi$
$912$	−414.141	−0.0150368
$913$	3736.48	0.135443
$914$	56014.9	2.02714
$915$	−34958.6	−1.26305
$916$	12894.7	0.465124
$917$	0	0
$918$	6553.05	0.235602
$919$	8727.00	0.313250	0.156625	−	0.987658i	$-0.449939\pi$
$919$	8727.00	0.313250	0.156625	+	0.987658i	$0.449939\pi$
$920$	−58960.2	−2.11289
$921$	−1624.06	−0.0581050
$922$	−88549.5	−3.16293
$923$	4832.91	0.172348
$924$	0	0
$925$	728.392	0.0258912
$926$	56914.1	2.01978
$927$	−9466.95	−0.335421
$928$	35126.1	1.24253
$929$	19405.1	0.685317	0.342659	−	0.939460i	$-0.388673\pi$
$929$	19405.1	0.685317	0.342659	+	0.939460i	$0.388673\pi$
$930$	−38570.2	−1.35997
$931$	0	0
$932$	2529.34	0.0888963
$933$	−162.050	−0.00568628
$934$	−15424.1	−0.540355
$935$	−10847.9	−0.379427
$936$	2557.05	0.0892945
$937$	−615.692	−0.0214662	−0.0107331	−	0.999942i	$-0.503417\pi$
$937$	−615.692	−0.0214662	−0.0107331	+	0.999942i	$0.503417\pi$
$938$	0	0
$939$	−11318.8	−0.393372
$940$	4832.10	0.167666
$941$	−29602.0	−1.02550	−0.512751	−	0.858537i	$-0.671374\pi$
$941$	−29602.0	−1.02550	−0.512751	+	0.858537i	$0.671374\pi$
$942$	−52332.2	−1.81006
$943$	−5980.46	−0.206522
$944$	737.310	0.0254210
$945$	0	0
$946$	22294.7	0.766240
$947$	13537.4	0.464527	0.232264	−	0.972653i	$-0.425387\pi$
$947$	13537.4	0.464527	0.232264	+	0.972653i	$0.425387\pi$
$948$	−34845.2	−1.19380
$949$	−7975.85	−0.272821
$950$	37585.8	1.28363
$951$	−5157.71	−0.175868
$952$	0	0
$953$	33468.5	1.13762	0.568810	−	0.822469i	$-0.307404\pi$
$953$	33468.5	1.13762	0.568810	+	0.822469i	$0.307404\pi$
$954$	−15004.7	−0.509220
$955$	34097.9	1.15538
$956$	−15327.7	−0.518550
$957$	6374.80	0.215327
$958$	−27244.4	−0.918817
$959$	0	0
$960$	44620.2	1.50011
$961$	−4866.88	−0.163368
$962$	223.563	0.00749268
$963$	6898.68	0.230848
$964$	−34870.4	−1.16504
$965$	42894.4	1.43090
$966$	0	0
$967$	−55733.5	−1.85343	−0.926715	−	0.375764i	$-0.877380\pi$
$967$	−55733.5	−1.85343	−0.926715	+	0.375764i	$0.877380\pi$
$968$	26054.0	0.865090
$969$	6779.17	0.224745
$970$	−58798.4	−1.94629
$971$	−19491.3	−0.644187	−0.322094	−	0.946708i	$-0.604387\pi$
$971$	−19491.3	−0.644187	−0.322094	+	0.946708i	$0.604387\pi$
$972$	−3100.79	−0.102323
$973$	0	0
$974$	5080.18	0.167125
$975$	7641.17	0.250988
$976$	−2121.60	−0.0695807
$977$	−6241.56	−0.204386	−0.102193	−	0.994765i	$-0.532586\pi$
$977$	−6241.56	−0.204386	−0.102193	+	0.994765i	$0.532586\pi$
$978$	−47968.4	−1.56836
$979$	428.554	0.0139905
$980$	0	0
$981$	−12843.4	−0.418001
$982$	−4949.25	−0.160832
$983$	59694.6	1.93689	0.968444	−	0.249231i	$-0.0801778\pi$
$983$	59694.6	1.93689	0.968444	+	0.249231i	$0.0801778\pi$
$984$	−2558.80	−0.0828980
$985$	27065.7	0.875517
$986$	−45263.0	−1.46193
$987$	0	0
$988$	7090.68	0.228324
$989$	65311.4	2.09988
$990$	8351.14	0.268097
$991$	15561.6	0.498821	0.249411	−	0.968398i	$-0.419763\pi$
$991$	15561.6	0.498821	0.249411	+	0.968398i	$0.419763\pi$
$992$	−29735.6	−0.951720
$993$	−25224.6	−0.806123
$994$	0	0
$995$	24446.6	0.778903
$996$	12553.6	0.399374
$997$	19884.9	0.631657	0.315829	−	0.948816i	$-0.397718\pi$
$997$	19884.9	0.631657	0.315829	+	0.948816i	$0.397718\pi$
$998$	10085.5	0.319891
$999$	−101.139	−0.00320309

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.4.a.l.1.1		3
3.2	odd	2		441.4.a.s.1.3		3
4.3	odd	2		2352.4.a.ci.1.3		3
7.2	even	3		21.4.e.b.4.3	✓	6
7.3	odd	6		147.4.e.n.79.3		6
7.4	even	3		21.4.e.b.16.3	yes	6
7.5	odd	6		147.4.e.n.67.3		6
7.6	odd	2		147.4.a.m.1.1		3
21.2	odd	6		63.4.e.c.46.1		6
21.5	even	6		441.4.e.w.361.1		6
21.11	odd	6		63.4.e.c.37.1		6
21.17	even	6		441.4.e.w.226.1		6
21.20	even	2		441.4.a.t.1.3		3
28.11	odd	6		336.4.q.k.289.1		6
28.23	odd	6		336.4.q.k.193.1		6
28.27	even	2		2352.4.a.cg.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.e.b.4.3	✓	6	7.2	even	3
21.4.e.b.16.3	yes	6	7.4	even	3
63.4.e.c.37.1		6	21.11	odd	6
63.4.e.c.46.1		6	21.2	odd	6
147.4.a.l.1.1		3	1.1	even	1	trivial
147.4.a.m.1.1		3	7.6	odd	2
147.4.e.n.67.3		6	7.5	odd	6
147.4.e.n.79.3		6	7.3	odd	6
336.4.q.k.193.1		6	28.23	odd	6
336.4.q.k.289.1		6	28.11	odd	6
441.4.a.s.1.3		3	3.2	odd	2
441.4.a.t.1.3		3	21.20	even	2
441.4.e.w.226.1		6	21.17	even	6
441.4.e.w.361.1		6	21.5	even	6
2352.4.a.cg.1.1		3	28.27	even	2
2352.4.a.ci.1.3		3	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)

\(f(q)\)	\(=\)	\(q-4.55637 q^{2} -3.00000 q^{3} +12.7605 q^{4} +17.8732 q^{5} +13.6691 q^{6} -21.6905 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-4.55637 q^{2} -3.00000 q^{3} +12.7605 q^{4} +17.8732 q^{5} +13.6691 q^{6} -21.6905 q^{8} +9.00000 q^{9} -81.4369 q^{10} -11.3942 q^{11} -38.2814 q^{12} -13.0987 q^{13} -53.6196 q^{15} -3.25412 q^{16} +53.2674 q^{17} -41.0073 q^{18} -42.4223 q^{19} +228.071 q^{20} +51.9159 q^{22} +152.085 q^{23} +65.0714 q^{24} +194.451 q^{25} +59.6823 q^{26} -27.0000 q^{27} +186.493 q^{29} +244.311 q^{30} -157.874 q^{31} +188.351 q^{32} +34.1825 q^{33} -242.706 q^{34} +114.844 q^{36} +3.74588 q^{37} +193.291 q^{38} +39.2960 q^{39} -387.678 q^{40} -39.3230 q^{41} +429.439 q^{43} -145.395 q^{44} +160.859 q^{45} -692.957 q^{46} +21.1869 q^{47} +9.76236 q^{48} -885.992 q^{50} -159.802 q^{51} -167.145 q^{52} +365.904 q^{53} +123.022 q^{54} -203.650 q^{55} +127.267 q^{57} -849.732 q^{58} -226.578 q^{59} -684.212 q^{60} +651.973 q^{61} +719.331 q^{62} -832.161 q^{64} -234.115 q^{65} -155.748 q^{66} +145.433 q^{67} +679.717 q^{68} -456.256 q^{69} -368.962 q^{71} -195.214 q^{72} +608.906 q^{73} -17.0676 q^{74} -583.354 q^{75} -541.328 q^{76} -179.047 q^{78} +910.237 q^{79} -58.1615 q^{80} +81.0000 q^{81} +179.170 q^{82} -327.929 q^{83} +952.058 q^{85} -1956.68 q^{86} -559.480 q^{87} +247.144 q^{88} -37.6118 q^{89} -732.932 q^{90} +1940.68 q^{92} +473.621 q^{93} -96.5352 q^{94} -758.222 q^{95} -565.052 q^{96} +722.013 q^{97} -102.547 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} - 9 q^{3} + 25 q^{4} + 11 q^{5} - 3 q^{6} + 39 q^{8} + 27 q^{9}+O(q^{10}) \) 3 * q + q^2 - 9 * q^3 + 25 * q^4 + 11 * q^5 - 3 * q^6 + 39 * q^8 + 27 * q^9	\( 3 q + q^{2} - 9 q^{3} + 25 q^{4} + 11 q^{5} - 3 q^{6} + 39 q^{8} + 27 q^{9} - 55 q^{10} + 35 q^{11} - 75 q^{12} + 62 q^{13} - 33 q^{15} + 241 q^{16} + 48 q^{17} + 9 q^{18} - 202 q^{19} + 439 q^{20} - 7 q^{22} + 216 q^{23} - 117 q^{24} + 130 q^{25} + 274 q^{26} - 81 q^{27} + 53 q^{29} + 165 q^{30} - 95 q^{31} + 683 q^{32} - 105 q^{33} - 24 q^{34} + 225 q^{36} + 262 q^{37} - 398 q^{38} - 186 q^{39} + 21 q^{40} + 244 q^{41} + 360 q^{43} - 905 q^{44} + 99 q^{45} - 1056 q^{46} - 210 q^{47} - 723 q^{48} - 1378 q^{50} - 144 q^{51} + 324 q^{52} + 393 q^{53} - 27 q^{54} - 1031 q^{55} + 606 q^{57} - 1249 q^{58} + 1143 q^{59} - 1317 q^{60} - 70 q^{61} + 1059 q^{62} - 399 q^{64} - 472 q^{65} + 21 q^{66} - 628 q^{67} + 1944 q^{68} - 648 q^{69} + 318 q^{71} + 351 q^{72} + 988 q^{73} + 1002 q^{74} - 390 q^{75} - 2340 q^{76} - 822 q^{78} + 861 q^{79} + 175 q^{80} + 243 q^{81} + 124 q^{82} + 519 q^{83} + 1800 q^{85} - 3208 q^{86} - 159 q^{87} - 891 q^{88} + 1766 q^{89} - 495 q^{90} - 672 q^{92} + 285 q^{93} - 3294 q^{94} - 736 q^{95} - 2049 q^{96} + 19 q^{97} + 315 q^{99}+O(q^{100}) \) 3 * q + q^2 - 9 * q^3 + 25 * q^4 + 11 * q^5 - 3 * q^6 + 39 * q^8 + 27 * q^9 - 55 * q^10 + 35 * q^11 - 75 * q^12 + 62 * q^13 - 33 * q^15 + 241 * q^16 + 48 * q^17 + 9 * q^18 - 202 * q^19 + 439 * q^20 - 7 * q^22 + 216 * q^23 - 117 * q^24 + 130 * q^25 + 274 * q^26 - 81 * q^27 + 53 * q^29 + 165 * q^30 - 95 * q^31 + 683 * q^32 - 105 * q^33 - 24 * q^34 + 225 * q^36 + 262 * q^37 - 398 * q^38 - 186 * q^39 + 21 * q^40 + 244 * q^41 + 360 * q^43 - 905 * q^44 + 99 * q^45 - 1056 * q^46 - 210 * q^47 - 723 * q^48 - 1378 * q^50 - 144 * q^51 + 324 * q^52 + 393 * q^53 - 27 * q^54 - 1031 * q^55 + 606 * q^57 - 1249 * q^58 + 1143 * q^59 - 1317 * q^60 - 70 * q^61 + 1059 * q^62 - 399 * q^64 - 472 * q^65 + 21 * q^66 - 628 * q^67 + 1944 * q^68 - 648 * q^69 + 318 * q^71 + 351 * q^72 + 988 * q^73 + 1002 * q^74 - 390 * q^75 - 2340 * q^76 - 822 * q^78 + 861 * q^79 + 175 * q^80 + 243 * q^81 + 124 * q^82 + 519 * q^83 + 1800 * q^85 - 3208 * q^86 - 159 * q^87 - 891 * q^88 + 1766 * q^89 - 495 * q^90 - 672 * q^92 + 285 * q^93 - 3294 * q^94 - 736 * q^95 - 2049 * q^96 + 19 * q^97 + 315 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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