LMFDB - Embedded newform 539.4.a.n.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,4,Mod(1,539)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, 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("539.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	539.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:	$31.8020294931$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 67x^{8} - x^{7} + 1529x^{6} + 194x^{5} - 14053x^{4} - 4705x^{3} + 47798x^{2} + 25312x - 25480 $ x^10 - 67x^8 - x^7 + 1529x^6 + 194x^5 - 14053x^4 - 4705x^3 + 47798x^2 + 25312*x - 25480
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 77)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-1.34862$ of defining polynomial
Character	$\chi$	$=$	539.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.34862 q^{2} +5.81456 q^{3} -6.18124 q^{4} +21.0471 q^{5} -7.84160 q^{6} +19.1250 q^{8} +6.80905 q^{9} +O(q^{10})$	\(q-1.34862 q^{2} +5.81456 q^{3} -6.18124 q^{4} +21.0471 q^{5} -7.84160 q^{6} +19.1250 q^{8} +6.80905 q^{9} -28.3844 q^{10} -11.0000 q^{11} -35.9411 q^{12} -8.28092 q^{13} +122.379 q^{15} +23.6576 q^{16} +19.3649 q^{17} -9.18280 q^{18} +76.8944 q^{19} -130.097 q^{20} +14.8348 q^{22} +95.1994 q^{23} +111.204 q^{24} +317.980 q^{25} +11.1678 q^{26} -117.401 q^{27} +249.317 q^{29} -165.043 q^{30} -149.280 q^{31} -184.905 q^{32} -63.9601 q^{33} -26.1158 q^{34} -42.0884 q^{36} -144.779 q^{37} -103.701 q^{38} -48.1499 q^{39} +402.526 q^{40} +286.779 q^{41} -219.067 q^{43} +67.9936 q^{44} +143.311 q^{45} -128.387 q^{46} -130.455 q^{47} +137.558 q^{48} -428.832 q^{50} +112.598 q^{51} +51.1863 q^{52} +197.832 q^{53} +158.329 q^{54} -231.518 q^{55} +447.107 q^{57} -336.233 q^{58} +237.195 q^{59} -756.456 q^{60} +322.003 q^{61} +201.321 q^{62} +60.1054 q^{64} -174.289 q^{65} +86.2576 q^{66} -1029.62 q^{67} -119.699 q^{68} +553.542 q^{69} +973.085 q^{71} +130.223 q^{72} +216.732 q^{73} +195.252 q^{74} +1848.91 q^{75} -475.302 q^{76} +64.9357 q^{78} +849.594 q^{79} +497.923 q^{80} -866.481 q^{81} -386.755 q^{82} +896.056 q^{83} +407.575 q^{85} +295.437 q^{86} +1449.67 q^{87} -210.375 q^{88} -33.6768 q^{89} -193.271 q^{90} -588.450 q^{92} -867.997 q^{93} +175.934 q^{94} +1618.40 q^{95} -1075.14 q^{96} -795.023 q^{97} -74.8996 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 54 q^{4} + 10 q^{5} + 53 q^{6} + 3 q^{8} + 76 q^{9}+O(q^{10}) $ 10 * q + 54 * q^4 + 10 * q^5 + 53 * q^6 + 3 * q^8 + 76 * q^9	\( 10 q + 54 q^{4} + 10 q^{5} + 53 q^{6} + 3 q^{8} + 76 q^{9} + 63 q^{10} - 110 q^{11} + 55 q^{12} + 162 q^{13} + 30 q^{15} + 286 q^{16} + 200 q^{17} - 252 q^{18} + 252 q^{19} + 96 q^{20} + 134 q^{23} + 786 q^{24} + 86 q^{25} + 363 q^{26} + 174 q^{27} + 148 q^{29} - 316 q^{30} + 530 q^{31} - 731 q^{32} + 102 q^{34} + 1287 q^{36} - 902 q^{37} + 66 q^{38} - 208 q^{39} + 2163 q^{40} + 168 q^{41} + 118 q^{43} - 594 q^{44} + 58 q^{45} - 210 q^{46} + 288 q^{47} - 850 q^{48} + 2325 q^{50} - 1022 q^{51} + 1663 q^{52} - 608 q^{53} + 2312 q^{54} - 110 q^{55} + 828 q^{57} - 1951 q^{58} - 464 q^{59} - 818 q^{60} + 3484 q^{61} - 809 q^{62} + 3045 q^{64} - 1560 q^{65} - 583 q^{66} + 142 q^{67} + 1145 q^{68} + 1716 q^{69} + 334 q^{71} - 1176 q^{72} + 1466 q^{73} - 3460 q^{74} + 2982 q^{75} + 3387 q^{76} + 5420 q^{78} + 578 q^{79} + 2911 q^{80} + 118 q^{81} - 307 q^{82} + 546 q^{83} + 2582 q^{85} + 2597 q^{86} + 1516 q^{87} - 33 q^{88} + 3150 q^{89} - 1836 q^{90} + 2163 q^{92} - 1484 q^{93} + 5700 q^{94} - 1338 q^{95} + 5429 q^{96} + 1654 q^{97} - 836 q^{99}+O(q^{100}) \) 10 * q + 54 * q^4 + 10 * q^5 + 53 * q^6 + 3 * q^8 + 76 * q^9 + 63 * q^10 - 110 * q^11 + 55 * q^12 + 162 * q^13 + 30 * q^15 + 286 * q^16 + 200 * q^17 - 252 * q^18 + 252 * q^19 + 96 * q^20 + 134 * q^23 + 786 * q^24 + 86 * q^25 + 363 * q^26 + 174 * q^27 + 148 * q^29 - 316 * q^30 + 530 * q^31 - 731 * q^32 + 102 * q^34 + 1287 * q^36 - 902 * q^37 + 66 * q^38 - 208 * q^39 + 2163 * q^40 + 168 * q^41 + 118 * q^43 - 594 * q^44 + 58 * q^45 - 210 * q^46 + 288 * q^47 - 850 * q^48 + 2325 * q^50 - 1022 * q^51 + 1663 * q^52 - 608 * q^53 + 2312 * q^54 - 110 * q^55 + 828 * q^57 - 1951 * q^58 - 464 * q^59 - 818 * q^60 + 3484 * q^61 - 809 * q^62 + 3045 * q^64 - 1560 * q^65 - 583 * q^66 + 142 * q^67 + 1145 * q^68 + 1716 * q^69 + 334 * q^71 - 1176 * q^72 + 1466 * q^73 - 3460 * q^74 + 2982 * q^75 + 3387 * q^76 + 5420 * q^78 + 578 * q^79 + 2911 * q^80 + 118 * q^81 - 307 * q^82 + 546 * q^83 + 2582 * q^85 + 2597 * q^86 + 1516 * q^87 - 33 * q^88 + 3150 * q^89 - 1836 * q^90 + 2163 * q^92 - 1484 * q^93 + 5700 * q^94 - 1338 * q^95 + 5429 * q^96 + 1654 * q^97 - 836 * 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 $

$2$	−1.34862	−0.476808	−0.238404	−	0.971166i	$-0.576624\pi$
$2$	−1.34862	−0.476808	−0.238404	+	0.971166i	$0.576624\pi$
$3$	5.81456	1.11901	0.559506	−	0.828826i	$-0.310991\pi$
$3$	5.81456	1.11901	0.559506	+	0.828826i	$0.310991\pi$
$4$	−6.18124	−0.772655
$5$	21.0471	1.88251	0.941254	−	0.337699i	$-0.109649\pi$
$5$	21.0471	1.88251	0.941254	+	0.337699i	$0.109649\pi$
$6$	−7.84160	−0.533553
$7$	0	0
$7$	0	0
$8$	19.1250	0.845215
$9$	6.80905	0.252187
$10$	−28.3844	−0.897594
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−35.9411	−0.864610
$13$	−8.28092	−0.176670	−0.0883352	−	0.996091i	$-0.528155\pi$
$13$	−8.28092	−0.176670	−0.0883352	+	0.996091i	$0.528155\pi$
$14$	0	0
$15$	122.379	2.10655
$16$	23.6576	0.369650
$17$	19.3649	0.276275	0.138138	−	0.990413i	$-0.455888\pi$
$17$	19.3649	0.276275	0.138138	+	0.990413i	$0.455888\pi$
$18$	−9.18280	−0.120245
$19$	76.8944	0.928462	0.464231	−	0.885714i	$-0.346331\pi$
$19$	76.8944	0.928462	0.464231	+	0.885714i	$0.346331\pi$
$20$	−130.097	−1.45453
$21$	0	0
$22$	14.8348	0.143763
$23$	95.1994	0.863063	0.431531	−	0.902098i	$-0.357973\pi$
$23$	95.1994	0.863063	0.431531	+	0.902098i	$0.357973\pi$
$24$	111.204	0.945806
$25$	317.980	2.54384
$26$	11.1678	0.0842378
$27$	−117.401	−0.836811
$28$	0	0
$29$	249.317	1.59645	0.798224	−	0.602361i	$-0.205773\pi$
$29$	249.317	1.59645	0.798224	+	0.602361i	$0.205773\pi$
$30$	−165.043	−1.00442
$31$	−149.280	−0.864887	−0.432443	−	0.901661i	$-0.642348\pi$
$31$	−149.280	−0.864887	−0.432443	+	0.901661i	$0.642348\pi$
$32$	−184.905	−1.02147
$33$	−63.9601	−0.337395
$34$	−26.1158	−0.131730
$35$	0	0
$36$	−42.0884	−0.194854
$37$	−144.779	−0.643286	−0.321643	−	0.946861i	$-0.604235\pi$
$37$	−144.779	−0.643286	−0.321643	+	0.946861i	$0.604235\pi$
$38$	−103.701	−0.442698
$39$	−48.1499	−0.197696
$40$	402.526	1.59112
$41$	286.779	1.09237	0.546187	−	0.837663i	$-0.316079\pi$
$41$	286.779	1.09237	0.546187	+	0.837663i	$0.316079\pi$
$42$	0	0
$43$	−219.067	−0.776915	−0.388458	−	0.921467i	$-0.626992\pi$
$43$	−219.067	−0.776915	−0.388458	+	0.921467i	$0.626992\pi$
$44$	67.9936	0.232964
$45$	143.311	0.474744
$46$	−128.387	−0.411515
$47$	−130.455	−0.404869	−0.202435	−	0.979296i	$-0.564885\pi$
$47$	−130.455	−0.404869	−0.202435	+	0.979296i	$0.564885\pi$
$48$	137.558	0.413642
$49$	0	0
$50$	−428.832	−1.21292
$51$	112.598	0.309155
$52$	51.1863	0.136505
$53$	197.832	0.512723	0.256361	−	0.966581i	$-0.417476\pi$
$53$	197.832	0.512723	0.256361	+	0.966581i	$0.417476\pi$
$54$	158.329	0.398998
$55$	−231.518	−0.567598
$56$	0	0
$57$	447.107	1.03896
$58$	−336.233	−0.761198
$59$	237.195	0.523392	0.261696	−	0.965150i	$-0.415718\pi$
$59$	237.195	0.523392	0.261696	+	0.965150i	$0.415718\pi$
$60$	−756.456	−1.62763
$61$	322.003	0.675872	0.337936	−	0.941169i	$-0.390271\pi$
$61$	322.003	0.675872	0.337936	+	0.941169i	$0.390271\pi$
$62$	201.321	0.412385
$63$	0	0
$64$	60.1054	0.117393
$65$	−174.289	−0.332583
$66$	86.2576	0.160872
$67$	−1029.62	−1.87743	−0.938715	−	0.344694i	$-0.887983\pi$
$67$	−1029.62	−1.87743	−0.938715	+	0.344694i	$0.887983\pi$
$68$	−119.699	−0.213465
$69$	553.542	0.965777
$70$	0	0
$71$	973.085	1.62653	0.813267	−	0.581891i	$-0.197687\pi$
$71$	973.085	1.62653	0.813267	+	0.581891i	$0.197687\pi$
$72$	130.223	0.213152
$73$	216.732	0.347488	0.173744	−	0.984791i	$-0.444414\pi$
$73$	216.732	0.347488	0.173744	+	0.984791i	$0.444414\pi$
$74$	195.252	0.306724
$75$	1848.91	2.84658
$76$	−475.302	−0.717380
$77$	0	0
$78$	64.9357	0.0942630
$79$	849.594	1.20996	0.604980	−	0.796241i	$-0.293181\pi$
$79$	849.594	1.20996	0.604980	+	0.796241i	$0.293181\pi$
$80$	497.923	0.695869
$81$	−866.481	−1.18859
$82$	−386.755	−0.520853
$83$	896.056	1.18500	0.592499	−	0.805571i	$-0.298141\pi$
$83$	896.056	1.18500	0.592499	+	0.805571i	$0.298141\pi$
$84$	0	0
$85$	407.575	0.520090
$86$	295.437	0.370439
$87$	1449.67	1.78644
$88$	−210.375	−0.254842
$89$	−33.6768	−0.0401094	−0.0200547	−	0.999799i	$-0.506384\pi$
$89$	−33.6768	−0.0401094	−0.0200547	+	0.999799i	$0.506384\pi$
$90$	−193.271	−0.226362
$91$	0	0
$92$	−588.450	−0.666849
$93$	−867.997	−0.967819
$94$	175.934	0.193045
$95$	1618.40	1.74784
$96$	−1075.14	−1.14303
$97$	−795.023	−0.832189	−0.416095	−	0.909321i	$-0.636602\pi$
$97$	−795.023	−0.832189	−0.416095	+	0.909321i	$0.636602\pi$
$98$	0	0
$99$	−74.8996	−0.0760373
$100$	−1965.51	−1.96551
$101$	−1426.89	−1.40575	−0.702873	−	0.711315i	$-0.748100\pi$
$101$	−1426.89	−1.40575	−0.702873	+	0.711315i	$0.748100\pi$
$102$	−151.852	−0.147407
$103$	−1370.23	−1.31081	−0.655403	−	0.755280i	$-0.727501\pi$
$103$	−1370.23	−1.31081	−0.655403	+	0.755280i	$0.727501\pi$
$104$	−158.373	−0.149324
$105$	0	0
$106$	−266.799	−0.244470
$107$	921.088	0.832196	0.416098	−	0.909320i	$-0.363397\pi$
$107$	921.088	0.832196	0.416098	+	0.909320i	$0.363397\pi$
$108$	725.686	0.646566
$109$	461.232	0.405302	0.202651	−	0.979251i	$-0.435044\pi$
$109$	461.232	0.405302	0.202651	+	0.979251i	$0.435044\pi$
$110$	312.229	0.270635
$111$	−841.828	−0.719845
$112$	0	0
$113$	1464.16	1.21891	0.609454	−	0.792822i	$-0.291389\pi$
$113$	1464.16	1.21891	0.609454	+	0.792822i	$0.291389\pi$
$114$	−602.975	−0.495384
$115$	2003.67	1.62472
$116$	−1541.09	−1.23350
$117$	−56.3853	−0.0445540
$118$	−319.885	−0.249557
$119$	0	0
$120$	2340.51	1.78049
$121$	121.000	0.0909091
$122$	−434.258	−0.322261
$123$	1667.49	1.22238
$124$	922.735	0.668259
$125$	4061.66	2.90629
$126$	0	0
$127$	−2219.70	−1.55092	−0.775459	−	0.631398i	$-0.782481\pi$
$127$	−2219.70	−1.55092	−0.775459	+	0.631398i	$0.782481\pi$
$128$	1398.18	0.965493
$129$	−1273.78	−0.869377
$130$	235.049	0.158578
$131$	1604.00	1.06979	0.534895	−	0.844919i	$-0.320351\pi$
$131$	1604.00	1.06979	0.534895	+	0.844919i	$0.320351\pi$
$132$	395.353	0.260690
$133$	0	0
$134$	1388.56	0.895173
$135$	−2470.96	−1.57530
$136$	370.354	0.233512
$137$	1672.95	1.04328	0.521640	−	0.853166i	$-0.325320\pi$
$137$	1672.95	1.04328	0.521640	+	0.853166i	$0.325320\pi$
$138$	−746.515	−0.460490
$139$	−454.502	−0.277340	−0.138670	−	0.990339i	$-0.544283\pi$
$139$	−454.502	−0.277340	−0.138670	+	0.990339i	$0.544283\pi$
$140$	0	0
$141$	−758.539	−0.453054
$142$	−1312.32	−0.775544
$143$	91.0902	0.0532681
$144$	161.086	0.0932209
$145$	5247.39	3.00533
$146$	−292.289	−0.165685
$147$	0	0
$148$	894.916	0.497038
$149$	2651.12	1.45764	0.728819	−	0.684707i	$-0.240070\pi$
$149$	2651.12	1.45764	0.728819	+	0.684707i	$0.240070\pi$
$150$	−2493.47	−1.35727
$151$	16.8578	0.00908521	0.00454260	−	0.999990i	$-0.498554\pi$
$151$	16.8578	0.00908521	0.00454260	+	0.999990i	$0.498554\pi$
$152$	1470.61	0.784750
$153$	131.857	0.0696730
$154$	0	0
$155$	−3141.91	−1.62816
$156$	297.626	0.152751
$157$	−1479.12	−0.751889	−0.375944	−	0.926642i	$-0.622682\pi$
$157$	−1479.12	−0.751889	−0.375944	+	0.926642i	$0.622682\pi$
$158$	−1145.78	−0.576918
$159$	1150.30	0.573743
$160$	−3891.72	−1.92292
$161$	0	0
$162$	1168.55	0.566728
$163$	−1157.15	−0.556042	−0.278021	−	0.960575i	$-0.589679\pi$
$163$	−1157.15	−0.556042	−0.278021	+	0.960575i	$0.589679\pi$
$164$	−1772.65	−0.844028
$165$	−1346.17	−0.635148
$166$	−1208.43	−0.565016
$167$	1250.95	0.579651	0.289825	−	0.957080i	$-0.406403\pi$
$167$	1250.95	0.579651	0.289825	+	0.957080i	$0.406403\pi$
$168$	0	0
$169$	−2128.43	−0.968788
$170$	−549.661	−0.247983
$171$	523.578	0.234146
$172$	1354.10	0.600287
$173$	−3038.40	−1.33529	−0.667646	−	0.744479i	$-0.732698\pi$
$173$	−3038.40	−1.33529	−0.667646	+	0.744479i	$0.732698\pi$
$174$	−1955.04	−0.851790
$175$	0	0
$176$	−260.233	−0.111454
$177$	1379.18	0.585682
$178$	45.4171	0.0191245
$179$	−605.544	−0.252852	−0.126426	−	0.991976i	$-0.540351\pi$
$179$	−605.544	−0.252852	−0.126426	+	0.991976i	$0.540351\pi$
$180$	−885.838	−0.366814
$181$	3122.40	1.28224	0.641122	−	0.767439i	$-0.278469\pi$
$181$	3122.40	1.28224	0.641122	+	0.767439i	$0.278469\pi$
$182$	0	0
$183$	1872.30	0.756309
$184$	1820.69	0.729474
$185$	−3047.18	−1.21099
$186$	1170.59	0.461463
$187$	−213.014	−0.0833001
$188$	806.375	0.312824
$189$	0	0
$190$	−2182.60	−0.833382
$191$	−1594.54	−0.604068	−0.302034	−	0.953297i	$-0.597666\pi$
$191$	−1594.54	−0.604068	−0.302034	+	0.953297i	$0.597666\pi$
$192$	349.486	0.131365
$193$	−2748.91	−1.02524	−0.512620	−	0.858616i	$-0.671325\pi$
$193$	−2748.91	−1.02524	−0.512620	+	0.858616i	$0.671325\pi$
$194$	1072.18	0.396794
$195$	−1013.41	−0.372165
$196$	0	0
$197$	−2488.91	−0.900140	−0.450070	−	0.892993i	$-0.648601\pi$
$197$	−2488.91	−0.900140	−0.450070	+	0.892993i	$0.648601\pi$
$198$	101.011	0.0362552
$199$	418.884	0.149216	0.0746078	−	0.997213i	$-0.476230\pi$
$199$	418.884	0.149216	0.0746078	+	0.997213i	$0.476230\pi$
$200$	6081.37	2.15009
$201$	−5986.77	−2.10087
$202$	1924.32	0.670271
$203$	0	0
$204$	−695.996	−0.238870
$205$	6035.86	2.05640
$206$	1847.92	0.625002
$207$	648.218	0.217653
$208$	−195.907	−0.0653061
$209$	−845.838	−0.279942
$210$	0	0
$211$	1900.56	0.620095	0.310048	−	0.950721i	$-0.399655\pi$
$211$	1900.56	0.620095	0.310048	+	0.950721i	$0.399655\pi$
$212$	−1222.85	−0.396158
$213$	5658.06	1.82011
$214$	−1242.19	−0.396797
$215$	−4610.71	−1.46255
$216$	−2245.31	−0.707285
$217$	0	0
$218$	−622.024	−0.193251
$219$	1260.20	0.388843
$220$	1431.07	0.438557
$221$	−160.359	−0.0488096
$222$	1135.30	0.343227
$223$	−4308.68	−1.29386	−0.646929	−	0.762550i	$-0.723947\pi$
$223$	−4308.68	−1.29386	−0.646929	+	0.762550i	$0.723947\pi$
$224$	0	0
$225$	2165.14	0.641523
$226$	−1974.59	−0.581184
$227$	−34.7514	−0.0101609	−0.00508046	−	0.999987i	$-0.501617\pi$
$227$	−34.7514	−0.0101609	−0.00508046	+	0.999987i	$0.501617\pi$
$228$	−2763.67	−0.802757
$229$	−2146.45	−0.619393	−0.309697	−	0.950835i	$-0.600228\pi$
$229$	−2146.45	−0.619393	−0.309697	+	0.950835i	$0.600228\pi$
$230$	−2702.18	−0.774680
$231$	0	0
$232$	4768.19	1.34934
$233$	−2711.81	−0.762474	−0.381237	−	0.924477i	$-0.624502\pi$
$233$	−2711.81	−0.762474	−0.381237	+	0.924477i	$0.624502\pi$
$234$	76.0420	0.0212437
$235$	−2745.70	−0.762170
$236$	−1466.16	−0.404401
$237$	4940.01	1.35396
$238$	0	0
$239$	−5433.14	−1.47046	−0.735231	−	0.677817i	$-0.762926\pi$
$239$	−5433.14	−1.47046	−0.735231	+	0.677817i	$0.762926\pi$
$240$	2895.20	0.778685
$241$	3246.78	0.867815	0.433907	−	0.900957i	$-0.357135\pi$
$241$	3246.78	0.867815	0.433907	+	0.900957i	$0.357135\pi$
$242$	−163.182	−0.0433461
$243$	−1868.37	−0.493234
$244$	−1990.37	−0.522216
$245$	0	0
$246$	−2248.81	−0.582840
$247$	−636.756	−0.164032
$248$	−2854.99	−0.731015
$249$	5210.17	1.32603
$250$	−5477.62	−1.38574
$251$	−4160.93	−1.04636	−0.523179	−	0.852223i	$-0.675254\pi$
$251$	−4160.93	−1.04636	−0.523179	+	0.852223i	$0.675254\pi$
$252$	0	0
$253$	−1047.19	−0.260223
$254$	2993.52	0.739489
$255$	2369.86	0.581987
$256$	−2366.45	−0.577748
$257$	−2846.39	−0.690867	−0.345434	−	0.938443i	$-0.612268\pi$
$257$	−2846.39	−0.690867	−0.345434	+	0.938443i	$0.612268\pi$
$258$	1717.83	0.414526
$259$	0	0
$260$	1077.32	0.256972
$261$	1697.61	0.402604
$262$	−2163.18	−0.510083
$263$	1442.13	0.338120	0.169060	−	0.985606i	$-0.445927\pi$
$263$	1442.13	0.338120	0.169060	+	0.985606i	$0.445927\pi$
$264$	−1223.24	−0.285171
$265$	4163.79	0.965205
$266$	0	0
$267$	−195.816	−0.0448829
$268$	6364.31	1.45060
$269$	−7485.88	−1.69674	−0.848368	−	0.529407i	$-0.822415\pi$
$269$	−7485.88	−1.69674	−0.848368	+	0.529407i	$0.822415\pi$
$270$	3332.37	0.751117
$271$	−4141.11	−0.928245	−0.464123	−	0.885771i	$-0.653630\pi$
$271$	−4141.11	−0.928245	−0.464123	+	0.885771i	$0.653630\pi$
$272$	458.127	0.102125
$273$	0	0
$274$	−2256.16	−0.497444
$275$	−3497.78	−0.766996
$276$	−3421.57	−0.746212
$277$	592.679	0.128558	0.0642791	−	0.997932i	$-0.479525\pi$
$277$	592.679	0.128558	0.0642791	+	0.997932i	$0.479525\pi$
$278$	612.948	0.132238
$279$	−1016.46	−0.218113
$280$	0	0
$281$	−4711.43	−1.00022	−0.500108	−	0.865963i	$-0.666706\pi$
$281$	−4711.43	−1.00022	−0.500108	+	0.865963i	$0.666706\pi$
$282$	1022.98	0.216019
$283$	−8623.53	−1.81136	−0.905681	−	0.423960i	$-0.860640\pi$
$283$	−8623.53	−1.81136	−0.905681	+	0.423960i	$0.860640\pi$
$284$	−6014.87	−1.25675
$285$	9410.29	1.95585
$286$	−122.846	−0.0253986
$287$	0	0
$288$	−1259.03	−0.257601
$289$	−4538.00	−0.923672
$290$	−7076.71	−1.43296
$291$	−4622.71	−0.931230
$292$	−1339.67	−0.268488
$293$	7014.63	1.39863	0.699315	−	0.714813i	$-0.253488\pi$
$293$	7014.63	1.39863	0.699315	+	0.714813i	$0.253488\pi$
$294$	0	0
$295$	4992.26	0.985290
$296$	−2768.91	−0.543715
$297$	1291.42	0.252308
$298$	−3575.34	−0.695012
$299$	−788.339	−0.152478
$300$	−11428.6	−2.19943
$301$	0	0
$302$	−22.7347	−0.00433190
$303$	−8296.70	−1.57305
$304$	1819.13	0.343206
$305$	6777.21	1.27233
$306$	−177.824	−0.0332206
$307$	3210.62	0.596872	0.298436	−	0.954430i	$-0.403535\pi$
$307$	3210.62	0.596872	0.298436	+	0.954430i	$0.403535\pi$
$308$	0	0
$309$	−7967.29	−1.46681
$310$	4237.23	0.776317
$311$	3164.37	0.576961	0.288480	−	0.957486i	$-0.406850\pi$
$311$	3164.37	0.576961	0.288480	+	0.957486i	$0.406850\pi$
$312$	−920.868	−0.167096
$313$	−222.600	−0.0401983	−0.0200992	−	0.999798i	$-0.506398\pi$
$313$	−222.600	−0.0401983	−0.0200992	+	0.999798i	$0.506398\pi$
$314$	1994.76	0.358506
$315$	0	0
$316$	−5251.54	−0.934881
$317$	−4048.48	−0.717304	−0.358652	−	0.933471i	$-0.616764\pi$
$317$	−4048.48	−0.717304	−0.358652	+	0.933471i	$0.616764\pi$
$318$	−1551.32	−0.273565
$319$	−2742.49	−0.481347
$320$	1265.04	0.220994
$321$	5355.72	0.931237
$322$	0	0
$323$	1489.05	0.256511
$324$	5355.93	0.918369
$325$	−2633.17	−0.449421
$326$	1560.55	0.265125
$327$	2681.86	0.453538
$328$	5484.66	0.923292
$329$	0	0
$330$	1815.47	0.302844
$331$	−9958.20	−1.65363	−0.826816	−	0.562472i	$-0.809850\pi$
$331$	−9958.20	−1.65363	−0.826816	+	0.562472i	$0.809850\pi$
$332$	−5538.73	−0.915595
$333$	−985.811	−0.162229
$334$	−1687.06	−0.276382
$335$	−21670.4	−3.53428
$336$	0	0
$337$	−2266.24	−0.366321	−0.183160	−	0.983083i	$-0.558633\pi$
$337$	−2266.24	−0.366321	−0.183160	+	0.983083i	$0.558633\pi$
$338$	2870.43	0.461925
$339$	8513.43	1.36397
$340$	−2519.31	−0.401850
$341$	1642.08	0.260773
$342$	−706.105	−0.111643
$343$	0	0
$344$	−4189.66	−0.656660
$345$	11650.4	1.81808
$346$	4097.63	0.636677
$347$	6211.32	0.960926	0.480463	−	0.877015i	$-0.340469\pi$
$347$	6211.32	0.960926	0.480463	+	0.877015i	$0.340469\pi$
$348$	−8960.73	−1.38030
$349$	10197.4	1.56405	0.782026	−	0.623246i	$-0.214186\pi$
$349$	10197.4	1.56405	0.782026	+	0.623246i	$0.214186\pi$
$350$	0	0
$351$	972.192	0.147840
$352$	2033.96	0.307984
$353$	2885.07	0.435005	0.217503	−	0.976060i	$-0.430209\pi$
$353$	2885.07	0.435005	0.217503	+	0.976060i	$0.430209\pi$
$354$	−1859.99	−0.279258
$355$	20480.6	3.06196
$356$	208.164	0.0309907
$357$	0	0
$358$	816.646	0.120562
$359$	2038.05	0.299622	0.149811	−	0.988715i	$-0.452133\pi$
$359$	2038.05	0.299622	0.149811	+	0.988715i	$0.452133\pi$
$360$	2740.82	0.401261
$361$	−946.256	−0.137958
$362$	−4210.92	−0.611384
$363$	703.561	0.101728
$364$	0	0
$365$	4561.58	0.654149
$366$	−2525.01	−0.360614
$367$	−1312.84	−0.186729	−0.0933645	−	0.995632i	$-0.529762\pi$
$367$	−1312.84	−0.186729	−0.0933645	+	0.995632i	$0.529762\pi$
$368$	2252.19	0.319031
$369$	1952.69	0.275483
$370$	4109.48	0.577410
$371$	0	0
$372$	5365.30	0.747789
$373$	−5101.38	−0.708149	−0.354074	−	0.935217i	$-0.615204\pi$
$373$	−5101.38	−0.708149	−0.354074	+	0.935217i	$0.615204\pi$
$374$	287.274	0.0397181
$375$	23616.7	3.25217
$376$	−2494.96	−0.342202
$377$	−2064.57	−0.282045
$378$	0	0
$379$	−2249.30	−0.304852	−0.152426	−	0.988315i	$-0.548709\pi$
$379$	−2249.30	−0.304852	−0.152426	+	0.988315i	$0.548709\pi$
$380$	−10003.7	−1.35047
$381$	−12906.6	−1.73550
$382$	2150.42	0.288024
$383$	−10221.2	−1.36365	−0.681826	−	0.731514i	$-0.738814\pi$
$383$	−10221.2	−1.36365	−0.681826	+	0.731514i	$0.738814\pi$
$384$	8129.81	1.08040
$385$	0	0
$386$	3707.23	0.488842
$387$	−1491.64	−0.195928
$388$	4914.23	0.642995
$389$	4926.32	0.642093	0.321047	−	0.947063i	$-0.395965\pi$
$389$	4926.32	0.642093	0.321047	+	0.947063i	$0.395965\pi$
$390$	1366.71	0.177451
$391$	1843.53	0.238443
$392$	0	0
$393$	9326.56	1.19711
$394$	3356.59	0.429194
$395$	17881.5	2.27776
$396$	462.972	0.0587506
$397$	11583.2	1.46434	0.732172	−	0.681120i	$-0.238507\pi$
$397$	11583.2	1.46434	0.732172	+	0.681120i	$0.238507\pi$
$398$	−564.914	−0.0711471
$399$	0	0
$400$	7522.63	0.940329
$401$	−5794.40	−0.721592	−0.360796	−	0.932645i	$-0.617495\pi$
$401$	−5794.40	−0.721592	−0.360796	+	0.932645i	$0.617495\pi$
$402$	8073.85	1.00171
$403$	1236.18	0.152800
$404$	8819.92	1.08616
$405$	−18236.9	−2.23753
$406$	0	0
$407$	1592.57	0.193958
$408$	2153.45	0.261303
$409$	5674.97	0.686087	0.343043	−	0.939320i	$-0.388542\pi$
$409$	5674.97	0.686087	0.343043	+	0.939320i	$0.388542\pi$
$410$	−8140.06	−0.980509
$411$	9727.43	1.16744
$412$	8469.73	1.01280
$413$	0	0
$414$	−874.196	−0.103779
$415$	18859.4	2.23077
$416$	1531.19	0.180463
$417$	−2642.73	−0.310347
$418$	1140.71	0.133478
$419$	5319.71	0.620250	0.310125	−	0.950696i	$-0.399629\pi$
$419$	5319.71	0.620250	0.310125	+	0.950696i	$0.399629\pi$
$420$	0	0
$421$	−4140.13	−0.479281	−0.239641	−	0.970862i	$-0.577030\pi$
$421$	−4140.13	−0.479281	−0.239641	+	0.970862i	$0.577030\pi$
$422$	−2563.13	−0.295666
$423$	−888.277	−0.102103
$424$	3783.54	0.433361
$425$	6157.64	0.702799
$426$	−7630.54	−0.867842
$427$	0	0
$428$	−5693.46	−0.643000
$429$	529.649	0.0596076
$430$	6218.08	0.697354
$431$	−11817.9	−1.32076	−0.660379	−	0.750933i	$-0.729604\pi$
$431$	−11817.9	−1.32076	−0.660379	+	0.750933i	$0.729604\pi$
$432$	−2777.43	−0.309327
$433$	−102.294	−0.0113532	−0.00567659	−	0.999984i	$-0.501807\pi$
$433$	−102.294	−0.0113532	−0.00567659	+	0.999984i	$0.501807\pi$
$434$	0	0
$435$	30511.3	3.36299
$436$	−2850.98	−0.313159
$437$	7320.30	0.801321
$438$	−1699.53	−0.185403
$439$	4653.47	0.505918	0.252959	−	0.967477i	$-0.418596\pi$
$439$	4653.47	0.505918	0.252959	+	0.967477i	$0.418596\pi$
$440$	−4427.79	−0.479742
$441$	0	0
$442$	216.263	0.0232728
$443$	5754.47	0.617163	0.308581	−	0.951198i	$-0.400146\pi$
$443$	5754.47	0.617163	0.308581	+	0.951198i	$0.400146\pi$
$444$	5203.54	0.556191
$445$	−708.799	−0.0755063
$446$	5810.75	0.616922
$447$	15415.1	1.63111
$448$	0	0
$449$	4993.23	0.524822	0.262411	−	0.964956i	$-0.415482\pi$
$449$	4993.23	0.524822	0.262411	+	0.964956i	$0.415482\pi$
$450$	−2919.94	−0.305883
$451$	−3154.57	−0.329363
$452$	−9050.31	−0.941794
$453$	98.0205	0.0101665
$454$	46.8663	0.00484481
$455$	0	0
$456$	8550.93	0.878144
$457$	8183.04	0.837608	0.418804	−	0.908077i	$-0.362450\pi$
$457$	8183.04	0.837608	0.418804	+	0.908077i	$0.362450\pi$
$458$	2894.73	0.295331
$459$	−2273.47	−0.231190
$460$	−12385.2	−1.25535
$461$	−1748.63	−0.176663	−0.0883315	−	0.996091i	$-0.528153\pi$
$461$	−1748.63	−0.176663	−0.0883315	+	0.996091i	$0.528153\pi$
$462$	0	0
$463$	−1283.24	−0.128806	−0.0644031	−	0.997924i	$-0.520514\pi$
$463$	−1283.24	−0.128806	−0.0644031	+	0.997924i	$0.520514\pi$
$464$	5898.23	0.590126
$465$	−18268.8	−1.82193
$466$	3657.19	0.363553
$467$	7448.83	0.738096	0.369048	−	0.929410i	$-0.379684\pi$
$467$	7448.83	0.738096	0.369048	+	0.929410i	$0.379684\pi$
$468$	348.531	0.0344249
$469$	0	0
$470$	3702.90	0.363408
$471$	−8600.42	−0.841372
$472$	4536.36	0.442379
$473$	2409.73	0.234249
$474$	−6662.18	−0.645578
$475$	24450.8	2.36186
$476$	0	0
$477$	1347.05	0.129302
$478$	7327.21	0.701127
$479$	−12399.4	−1.18277	−0.591383	−	0.806391i	$-0.701418\pi$
$479$	−12399.4	−1.18277	−0.591383	+	0.806391i	$0.701418\pi$
$480$	−22628.6	−2.15177
$481$	1198.91	0.113650
$482$	−4378.65	−0.413781
$483$	0	0
$484$	−747.930	−0.0702413
$485$	−16732.9	−1.56660
$486$	2519.71	0.235177
$487$	−2121.79	−0.197428	−0.0987138	−	0.995116i	$-0.531473\pi$
$487$	−2121.79	−0.197428	−0.0987138	+	0.995116i	$0.531473\pi$
$488$	6158.31	0.571257
$489$	−6728.31	−0.622218
$490$	0	0
$491$	−7367.38	−0.677159	−0.338580	−	0.940938i	$-0.609946\pi$
$491$	−7367.38	−0.677159	−0.338580	+	0.940938i	$0.609946\pi$
$492$	−10307.2	−0.944478
$493$	4827.99	0.441059
$494$	858.739	0.0782116
$495$	−1576.42	−0.143141
$496$	−3531.61	−0.319705
$497$	0	0
$498$	−7026.51	−0.632260
$499$	5996.89	0.537992	0.268996	−	0.963141i	$-0.413308\pi$
$499$	5996.89	0.537992	0.268996	+	0.963141i	$0.413308\pi$
$500$	−25106.1	−2.24556
$501$	7273.74	0.648636
$502$	5611.50	0.498911
$503$	−11911.3	−1.05587	−0.527933	−	0.849286i	$-0.677033\pi$
$503$	−11911.3	−1.05587	−0.527933	+	0.849286i	$0.677033\pi$
$504$	0	0
$505$	−30031.8	−2.64633
$506$	1412.26	0.124076
$507$	−12375.9	−1.08408
$508$	13720.5	1.19832
$509$	−13590.6	−1.18348	−0.591740	−	0.806129i	$-0.701559\pi$
$509$	−13590.6	−1.18348	−0.591740	+	0.806129i	$0.701559\pi$
$510$	−3196.04	−0.277496
$511$	0	0
$512$	−7994.03	−0.690018
$513$	−9027.50	−0.776947
$514$	3838.69	0.329411
$515$	−28839.4	−2.46760
$516$	7873.50	0.671728
$517$	1435.01	0.122073
$518$	0	0
$519$	−17667.0	−1.49421
$520$	−3333.29	−0.281105
$521$	13671.0	1.14960	0.574798	−	0.818295i	$-0.305081\pi$
$521$	13671.0	1.14960	0.574798	+	0.818295i	$0.305081\pi$
$522$	−2289.43	−0.191964
$523$	−6244.50	−0.522090	−0.261045	−	0.965327i	$-0.584067\pi$
$523$	−6244.50	−0.522090	−0.261045	+	0.965327i	$0.584067\pi$
$524$	−9914.72	−0.826577
$525$	0	0
$526$	−1944.88	−0.161218
$527$	−2890.79	−0.238947
$528$	−1513.14	−0.124718
$529$	−3104.08	−0.255123
$530$	−5615.34	−0.460217
$531$	1615.07	0.131993
$532$	0	0
$533$	−2374.80	−0.192990
$534$	264.080	0.0214005
$535$	19386.2	1.56662
$536$	−19691.5	−1.58683
$537$	−3520.97	−0.282944
$538$	10095.6	0.809017
$539$	0	0
$540$	15273.6	1.21717
$541$	−20862.8	−1.65797	−0.828987	−	0.559268i	$-0.811082\pi$
$541$	−20862.8	−1.65797	−0.828987	+	0.559268i	$0.811082\pi$
$542$	5584.76	0.442594
$543$	18155.4	1.43485
$544$	−3580.67	−0.282206
$545$	9707.58	0.762985
$546$	0	0
$547$	15139.8	1.18342	0.591709	−	0.806152i	$-0.298454\pi$
$547$	15139.8	1.18342	0.591709	+	0.806152i	$0.298454\pi$
$548$	−10340.9	−0.806095
$549$	2192.53	0.170446
$550$	4717.15	0.365709
$551$	19171.1	1.48224
$552$	10586.5	0.816289
$553$	0	0
$554$	−799.296	−0.0612976
$555$	−17718.0	−1.35511
$556$	2809.38	0.214288
$557$	−5640.85	−0.429104	−0.214552	−	0.976713i	$-0.568829\pi$
$557$	−5640.85	−0.429104	−0.214552	+	0.976713i	$0.568829\pi$
$558$	1370.81	0.103998
$559$	1814.07	0.137258
$560$	0	0
$561$	−1238.58	−0.0932138
$562$	6353.91	0.476910
$563$	−2771.63	−0.207478	−0.103739	−	0.994605i	$-0.533081\pi$
$563$	−2771.63	−0.207478	−0.103739	+	0.994605i	$0.533081\pi$
$564$	4688.71	0.350054
$565$	30816.3	2.29460
$566$	11629.8	0.863671
$567$	0	0
$568$	18610.3	1.37477
$569$	7809.90	0.575409	0.287705	−	0.957719i	$-0.407108\pi$
$569$	7809.90	0.575409	0.287705	+	0.957719i	$0.407108\pi$
$570$	−12690.9	−0.932564
$571$	−10743.5	−0.787391	−0.393696	−	0.919241i	$-0.628804\pi$
$571$	−10743.5	−0.787391	−0.393696	+	0.919241i	$0.628804\pi$
$572$	−563.050	−0.0411579
$573$	−9271.55	−0.675959
$574$	0	0
$575$	30271.5	2.19549
$576$	409.261	0.0296051
$577$	12535.7	0.904452	0.452226	−	0.891903i	$-0.350630\pi$
$577$	12535.7	0.904452	0.452226	+	0.891903i	$0.350630\pi$
$578$	6120.02	0.440414
$579$	−15983.7	−1.14726
$580$	−32435.4	−2.32208
$581$	0	0
$582$	6234.25	0.444017
$583$	−2176.15	−0.154592
$584$	4145.01	0.293702
$585$	−1186.75	−0.0838733
$586$	−9460.03	−0.666878
$587$	151.029	0.0106195	0.00530975	−	0.999986i	$-0.498310\pi$
$587$	151.029	0.0106195	0.00530975	+	0.999986i	$0.498310\pi$
$588$	0	0
$589$	−11478.8	−0.803015
$590$	−6732.64	−0.469794
$591$	−14471.9	−1.00727
$592$	−3425.13	−0.237790
$593$	−15160.7	−1.04988	−0.524939	−	0.851140i	$-0.675912\pi$
$593$	−15160.7	−1.04988	−0.524939	+	0.851140i	$0.675912\pi$
$594$	−1741.62	−0.120302
$595$	0	0
$596$	−16387.2	−1.12625
$597$	2435.63	0.166974
$598$	1063.17	0.0727025
$599$	8616.13	0.587722	0.293861	−	0.955848i	$-0.405060\pi$
$599$	8616.13	0.587722	0.293861	+	0.955848i	$0.405060\pi$
$600$	35360.5	2.40598
$601$	−7485.64	−0.508063	−0.254031	−	0.967196i	$-0.581757\pi$
$601$	−7485.64	−0.508063	−0.254031	+	0.967196i	$0.581757\pi$
$602$	0	0
$603$	−7010.72	−0.473464
$604$	−104.202	−0.00701973
$605$	2546.70	0.171137
$606$	11189.1	0.750041
$607$	−18726.3	−1.25218	−0.626092	−	0.779749i	$-0.715347\pi$
$607$	−18726.3	−1.25218	−0.626092	+	0.779749i	$0.715347\pi$
$608$	−14218.2	−0.948393
$609$	0	0
$610$	−9139.86	−0.606659
$611$	1080.29	0.0715284
$612$	−815.037	−0.0538332
$613$	−27282.2	−1.79758	−0.898790	−	0.438380i	$-0.855553\pi$
$613$	−27282.2	−1.79758	−0.898790	+	0.438380i	$0.855553\pi$
$614$	−4329.89	−0.284593
$615$	35095.9	2.30114
$616$	0	0
$617$	7269.34	0.474315	0.237158	−	0.971471i	$-0.423784\pi$
$617$	7269.34	0.474315	0.237158	+	0.971471i	$0.423784\pi$
$618$	10744.8	0.699384
$619$	1564.61	0.101594	0.0507972	−	0.998709i	$-0.483824\pi$
$619$	1564.61	0.101594	0.0507972	+	0.998709i	$0.483824\pi$
$620$	19420.9	1.25800
$621$	−11176.5	−0.722221
$622$	−4267.52	−0.275099
$623$	0	0
$624$	−1139.11	−0.0730783
$625$	45738.6	2.92727
$626$	300.201	0.0191669
$627$	−4918.17	−0.313258
$628$	9142.78	0.580950
$629$	−2803.64	−0.177724
$630$	0	0
$631$	11114.9	0.701229	0.350614	−	0.936520i	$-0.385973\pi$
$631$	11114.9	0.701229	0.350614	+	0.936520i	$0.385973\pi$
$632$	16248.5	1.02268
$633$	11050.9	0.693894
$634$	5459.84	0.342016
$635$	−46718.2	−2.91962
$636$	−7110.31	−0.443305
$637$	0	0
$638$	3698.56	0.229510
$639$	6625.79	0.410191
$640$	29427.7	1.81755
$641$	1176.08	0.0724685	0.0362342	−	0.999343i	$-0.488464\pi$
$641$	1176.08	0.0724685	0.0362342	+	0.999343i	$0.488464\pi$
$642$	−7222.80	−0.444021
$643$	−27766.1	−1.70294	−0.851469	−	0.524405i	$-0.824288\pi$
$643$	−27766.1	−1.70294	−0.851469	+	0.524405i	$0.824288\pi$
$644$	0	0
$645$	−26809.2	−1.63661
$646$	−2008.16	−0.122306
$647$	7162.70	0.435232	0.217616	−	0.976034i	$-0.430172\pi$
$647$	7162.70	0.435232	0.217616	+	0.976034i	$0.430172\pi$
$648$	−16571.5	−1.00461
$649$	−2609.14	−0.157809
$650$	3551.13	0.214287
$651$	0	0
$652$	7152.61	0.429629
$653$	−1282.36	−0.0768492	−0.0384246	−	0.999262i	$-0.512234\pi$
$653$	−1282.36	−0.0768492	−0.0384246	+	0.999262i	$0.512234\pi$
$654$	−3616.79	−0.216250
$655$	33759.6	2.01389
$656$	6784.50	0.403796
$657$	1475.74	0.0876320
$658$	0	0
$659$	26204.1	1.54896	0.774482	−	0.632596i	$-0.218010\pi$
$659$	26204.1	1.54896	0.774482	+	0.632596i	$0.218010\pi$
$660$	8321.02	0.490750
$661$	−404.148	−0.0237815	−0.0118907	−	0.999929i	$-0.503785\pi$
$661$	−404.148	−0.0237815	−0.0118907	+	0.999929i	$0.503785\pi$
$662$	13429.8	0.788465
$663$	−932.417	−0.0546185
$664$	17137.1	1.00158
$665$	0	0
$666$	1329.48	0.0773518
$667$	23734.8	1.37783
$668$	−7732.44	−0.447870
$669$	−25053.1	−1.44784
$670$	29225.1	1.68517
$671$	−3542.03	−0.203783
$672$	0	0
$673$	8520.96	0.488052	0.244026	−	0.969769i	$-0.421532\pi$
$673$	8520.96	0.488052	0.244026	+	0.969769i	$0.421532\pi$
$674$	3056.29	0.174665
$675$	−37331.2	−2.12871
$676$	13156.3	0.748538
$677$	28527.6	1.61951	0.809754	−	0.586770i	$-0.199601\pi$
$677$	28527.6	1.61951	0.809754	+	0.586770i	$0.199601\pi$
$678$	−11481.3	−0.650352
$679$	0	0
$680$	7794.88	0.439588
$681$	−202.064	−0.0113702
$682$	−2214.54	−0.124339
$683$	1513.54	0.0847934	0.0423967	−	0.999101i	$-0.486501\pi$
$683$	1513.54	0.0847934	0.0423967	+	0.999101i	$0.486501\pi$
$684$	−3236.36	−0.180914
$685$	35210.6	1.96398
$686$	0	0
$687$	−12480.6	−0.693108
$688$	−5182.59	−0.287186
$689$	−1638.23	−0.0905829
$690$	−15712.0	−0.866876
$691$	3150.35	0.173437	0.0867186	−	0.996233i	$-0.472362\pi$
$691$	3150.35	0.173437	0.0867186	+	0.996233i	$0.472362\pi$
$692$	18781.1	1.03172
$693$	0	0
$694$	−8376.68	−0.458177
$695$	−9565.93	−0.522096
$696$	27724.9	1.50993
$697$	5553.45	0.301796
$698$	−13752.4	−0.745752
$699$	−15768.0	−0.853218
$700$	0	0
$701$	2741.85	0.147729	0.0738646	−	0.997268i	$-0.476467\pi$
$701$	2741.85	0.147729	0.0738646	+	0.997268i	$0.476467\pi$
$702$	−1311.11	−0.0704911
$703$	−11132.7	−0.597267
$704$	−661.159	−0.0353954
$705$	−15965.0	−0.852877
$706$	−3890.85	−0.207414
$707$	0	0
$708$	−8525.05	−0.452530
$709$	−9343.90	−0.494947	−0.247474	−	0.968895i	$-0.579600\pi$
$709$	−9343.90	−0.494947	−0.247474	+	0.968895i	$0.579600\pi$
$710$	−27620.4	−1.45997
$711$	5784.93	0.305136
$712$	−644.070	−0.0339011
$713$	−14211.4	−0.746452
$714$	0	0
$715$	1917.18	0.100278
$716$	3743.01	0.195367
$717$	−31591.3	−1.64546
$718$	−2748.55	−0.142862
$719$	−23249.1	−1.20591	−0.602953	−	0.797777i	$-0.706009\pi$
$719$	−23249.1	−1.20591	−0.602953	+	0.797777i	$0.706009\pi$
$720$	3390.39	0.175489
$721$	0	0
$722$	1276.14	0.0657796
$723$	18878.6	0.971095
$724$	−19300.3	−0.990732
$725$	79277.7	4.06110
$726$	−948.833	−0.0485048
$727$	−3483.84	−0.177728	−0.0888641	−	0.996044i	$-0.528324\pi$
$727$	−3483.84	−0.177728	−0.0888641	+	0.996044i	$0.528324\pi$
$728$	0	0
$729$	12531.3	0.636655
$730$	−6151.82	−0.311903
$731$	−4242.20	−0.214642
$732$	−11573.1	−0.584366
$733$	3813.19	0.192147	0.0960733	−	0.995374i	$-0.469372\pi$
$733$	3813.19	0.192147	0.0960733	+	0.995374i	$0.469372\pi$
$734$	1770.51	0.0890338
$735$	0	0
$736$	−17602.9	−0.881590
$737$	11325.8	0.566066
$738$	−2633.43	−0.131352
$739$	−11561.3	−0.575493	−0.287747	−	0.957707i	$-0.592906\pi$
$739$	−11561.3	−0.575493	−0.287747	+	0.957707i	$0.592906\pi$
$740$	18835.4	0.935678
$741$	−3702.45	−0.183553
$742$	0	0
$743$	12410.9	0.612800	0.306400	−	0.951903i	$-0.400875\pi$
$743$	12410.9	0.612800	0.306400	+	0.951903i	$0.400875\pi$
$744$	−16600.5	−0.818015
$745$	55798.3	2.74401
$746$	6879.80	0.337651
$747$	6101.29	0.298842
$748$	1316.69	0.0643622
$749$	0	0
$750$	−31849.9	−1.55066
$751$	−24759.7	−1.20305	−0.601527	−	0.798852i	$-0.705441\pi$
$751$	−24759.7	−1.20305	−0.601527	+	0.798852i	$0.705441\pi$
$752$	−3086.26	−0.149660
$753$	−24194.0	−1.17089
$754$	2784.32	0.134481
$755$	354.807	0.0171030
$756$	0	0
$757$	−25482.3	−1.22347	−0.611736	−	0.791062i	$-0.709529\pi$
$757$	−25482.3	−1.22347	−0.611736	+	0.791062i	$0.709529\pi$
$758$	3033.44	0.145356
$759$	−6088.96	−0.291193
$760$	30952.0	1.47730
$761$	28832.5	1.37343	0.686713	−	0.726928i	$-0.259053\pi$
$761$	28832.5	1.37343	0.686713	+	0.726928i	$0.259053\pi$
$762$	17406.0	0.827497
$763$	0	0
$764$	9856.23	0.466736
$765$	2775.20	0.131160
$766$	13784.5	0.650200
$767$	−1964.19	−0.0924679
$768$	−13759.9	−0.646506
$769$	13927.6	0.653110	0.326555	−	0.945178i	$-0.394112\pi$
$769$	13927.6	0.653110	0.326555	+	0.945178i	$0.394112\pi$
$770$	0	0
$771$	−16550.5	−0.773089
$772$	16991.7	0.792156
$773$	−38374.0	−1.78553	−0.892766	−	0.450520i	$-0.851238\pi$
$773$	−38374.0	−1.78553	−0.892766	+	0.450520i	$0.851238\pi$
$774$	2011.64	0.0934200
$775$	−47468.0	−2.20013
$776$	−15204.8	−0.703379
$777$	0	0
$778$	−6643.71	−0.306155
$779$	22051.7	1.01423
$780$	6264.16	0.287555
$781$	−10703.9	−0.490418
$782$	−2486.21	−0.113691
$783$	−29270.1	−1.33593
$784$	0	0
$785$	−31131.1	−1.41544
$786$	−12577.9	−0.570789
$787$	4598.43	0.208280	0.104140	−	0.994563i	$-0.466791\pi$
$787$	4598.43	0.208280	0.104140	+	0.994563i	$0.466791\pi$
$788$	15384.6	0.695498
$789$	8385.34	0.378360
$790$	−24115.2	−1.08605
$791$	0	0
$792$	−1432.46	−0.0642679
$793$	−2666.48	−0.119407
$794$	−15621.3	−0.698210
$795$	24210.6	1.08008
$796$	−2589.22	−0.115292
$797$	−14874.1	−0.661064	−0.330532	−	0.943795i	$-0.607228\pi$
$797$	−14874.1	−0.661064	−0.330532	+	0.943795i	$0.607228\pi$
$798$	0	0
$799$	−2526.25	−0.111855
$800$	−58796.1	−2.59845
$801$	−229.307	−0.0101151
$802$	7814.41	0.344060
$803$	−2384.06	−0.104772
$804$	37005.6	1.62324
$805$	0	0
$806$	−1667.13	−0.0728561
$807$	−43527.1	−1.89867
$808$	−27289.2	−1.18816
$809$	−9724.48	−0.422614	−0.211307	−	0.977420i	$-0.567772\pi$
$809$	−9724.48	−0.422614	−0.211307	+	0.977420i	$0.567772\pi$
$810$	24594.6	1.06687
$811$	6523.79	0.282468	0.141234	−	0.989976i	$-0.454893\pi$
$811$	6523.79	0.282468	0.141234	+	0.989976i	$0.454893\pi$
$812$	0	0
$813$	−24078.7	−1.03872
$814$	−2147.77	−0.0924807
$815$	−24354.6	−1.04675
$816$	2663.80	0.114279
$817$	−16845.0	−0.721336
$818$	−7653.36	−0.327131
$819$	0	0
$820$	−37309.1	−1.58889
$821$	−14486.1	−0.615796	−0.307898	−	0.951419i	$-0.599626\pi$
$821$	−14486.1	−0.615796	−0.307898	+	0.951419i	$0.599626\pi$
$822$	−13118.6	−0.556645
$823$	−1895.40	−0.0802788	−0.0401394	−	0.999194i	$-0.512780\pi$
$823$	−1895.40	−0.0802788	−0.0401394	+	0.999194i	$0.512780\pi$
$824$	−26205.7	−1.10791
$825$	−20338.0	−0.858277
$826$	0	0
$827$	−4280.88	−0.180001	−0.0900005	−	0.995942i	$-0.528687\pi$
$827$	−4280.88	−0.180001	−0.0900005	+	0.995942i	$0.528687\pi$
$828$	−4006.79	−0.168171
$829$	42842.1	1.79490	0.897448	−	0.441120i	$-0.145419\pi$
$829$	42842.1	1.79490	0.897448	+	0.441120i	$0.145419\pi$
$830$	−25434.0	−1.06365
$831$	3446.17	0.143858
$832$	−497.728	−0.0207399
$833$	0	0
$834$	3564.02	0.147976
$835$	26328.9	1.09120
$836$	5228.33	0.216298
$837$	17525.7	0.723747
$838$	−7174.24	−0.295740
$839$	20777.5	0.854969	0.427484	−	0.904023i	$-0.359400\pi$
$839$	20777.5	0.854969	0.427484	+	0.904023i	$0.359400\pi$
$840$	0	0
$841$	37769.9	1.54864
$842$	5583.44	0.228525
$843$	−27394.9	−1.11925
$844$	−11747.8	−0.479119
$845$	−44797.2	−1.82375
$846$	1197.94	0.0486834
$847$	0	0
$848$	4680.23	0.189528
$849$	−50142.0	−2.02694
$850$	−8304.29	−0.335100
$851$	−13782.9	−0.555196
$852$	−34973.8	−1.40632
$853$	46917.6	1.88327	0.941634	−	0.336638i	$-0.109290\pi$
$853$	46917.6	1.88327	0.941634	+	0.336638i	$0.109290\pi$
$854$	0	0
$855$	11019.8	0.440782
$856$	17615.8	0.703384
$857$	5623.95	0.224166	0.112083	−	0.993699i	$-0.464248\pi$
$857$	5623.95	0.224166	0.112083	+	0.993699i	$0.464248\pi$
$858$	−714.292	−0.0284214
$859$	12977.5	0.515468	0.257734	−	0.966216i	$-0.417024\pi$
$859$	12977.5	0.515468	0.257734	+	0.966216i	$0.417024\pi$
$860$	28499.9	1.13005
$861$	0	0
$862$	15937.8	0.629747
$863$	41575.1	1.63990	0.819949	−	0.572436i	$-0.194001\pi$
$863$	41575.1	1.63990	0.819949	+	0.572436i	$0.194001\pi$
$864$	21708.1	0.854775
$865$	−63949.5	−2.51370
$866$	137.955	0.00541329
$867$	−26386.5	−1.03360
$868$	0	0
$869$	−9345.54	−0.364817
$870$	−41147.9	−1.60350
$871$	8526.18	0.331686
$872$	8821.07	0.342568
$873$	−5413.36	−0.209868
$874$	−9872.26	−0.382076
$875$	0	0
$876$	−7789.61	−0.300441
$877$	21089.5	0.812020	0.406010	−	0.913869i	$-0.366920\pi$
$877$	21089.5	0.812020	0.406010	+	0.913869i	$0.366920\pi$
$878$	−6275.74	−0.241226
$879$	40786.9	1.56508
$880$	−5477.15	−0.209812
$881$	38649.6	1.47802	0.739012	−	0.673692i	$-0.235293\pi$
$881$	38649.6	1.47802	0.739012	+	0.673692i	$0.235293\pi$
$882$	0	0
$883$	−35642.7	−1.35841	−0.679203	−	0.733951i	$-0.737674\pi$
$883$	−35642.7	−1.35841	−0.679203	+	0.733951i	$0.737674\pi$
$884$	991.218	0.0377130
$885$	29027.8	1.10255
$886$	−7760.57	−0.294268
$887$	22755.9	0.861406	0.430703	−	0.902494i	$-0.358266\pi$
$887$	22755.9	0.861406	0.430703	+	0.902494i	$0.358266\pi$
$888$	−16100.0	−0.608424
$889$	0	0
$890$	955.897	0.0360020
$891$	9531.29	0.358373
$892$	26633.0	0.999706
$893$	−10031.3	−0.375906
$894$	−20789.0	−0.777727
$895$	−12744.9	−0.475996
$896$	0	0
$897$	−4583.84	−0.170624
$898$	−6733.95	−0.250239
$899$	−37218.0	−1.38075
$900$	−13383.2	−0.495676
$901$	3830.99	0.141653
$902$	4254.30	0.157043
$903$	0	0
$904$	28002.1	1.03024
$905$	65717.4	2.41384
$906$	−132.192	−0.00484744
$907$	−6907.96	−0.252894	−0.126447	−	0.991973i	$-0.540357\pi$
$907$	−6907.96	−0.252894	−0.126447	+	0.991973i	$0.540357\pi$
$908$	214.807	0.00785089
$909$	−9715.74	−0.354511
$910$	0	0
$911$	2637.98	0.0959388	0.0479694	−	0.998849i	$-0.484725\pi$
$911$	2637.98	0.0959388	0.0479694	+	0.998849i	$0.484725\pi$
$912$	10577.5	0.384051
$913$	−9856.61	−0.357291
$914$	−11035.8	−0.399378
$915$	39406.5	1.42376
$916$	13267.7	0.478577
$917$	0	0
$918$	3066.03	0.110233
$919$	19439.9	0.697784	0.348892	−	0.937163i	$-0.386558\pi$
$919$	19439.9	0.697784	0.348892	+	0.937163i	$0.386558\pi$
$920$	38320.2	1.37324
$921$	18668.3	0.667907
$922$	2358.22	0.0842342
$923$	−8058.04	−0.287360
$924$	0	0
$925$	−46036.9	−1.63642
$926$	1730.60	0.0614157
$927$	−9329.98	−0.330568
$928$	−46100.0	−1.63072
$929$	24151.6	0.852946	0.426473	−	0.904500i	$-0.359756\pi$
$929$	24151.6	0.852946	0.426473	+	0.904500i	$0.359756\pi$
$930$	24637.6	0.868708
$931$	0	0
$932$	16762.3	0.589129
$933$	18399.4	0.645626
$934$	−10045.6	−0.351930
$935$	−4483.32	−0.156813
$936$	−1078.37	−0.0376577
$937$	−27580.8	−0.961607	−0.480804	−	0.876828i	$-0.659655\pi$
$937$	−27580.8	−0.961607	−0.480804	+	0.876828i	$0.659655\pi$
$938$	0	0
$939$	−1294.32	−0.0449824
$940$	16971.8	0.588894
$941$	12561.9	0.435183	0.217592	−	0.976040i	$-0.430180\pi$
$941$	12561.9	0.435183	0.217592	+	0.976040i	$0.430180\pi$
$942$	11598.7	0.401173
$943$	27301.2	0.942788
$944$	5611.46	0.193472
$945$	0	0
$946$	−3249.80	−0.111692
$947$	15723.8	0.539550	0.269775	−	0.962923i	$-0.413051\pi$
$947$	15723.8	0.539550	0.269775	+	0.962923i	$0.413051\pi$
$948$	−30535.4	−1.04614
$949$	−1794.74	−0.0613908
$950$	−32974.8	−1.12615
$951$	−23540.1	−0.802671
$952$	0	0
$953$	42826.1	1.45569	0.727846	−	0.685741i	$-0.240522\pi$
$953$	42826.1	1.45569	0.727846	+	0.685741i	$0.240522\pi$
$954$	−1816.65	−0.0616522
$955$	−33560.4	−1.13716
$956$	33583.5	1.13616
$957$	−15946.3	−0.538633
$958$	16722.1	0.563951
$959$	0	0
$960$	7355.66	0.247295
$961$	−7506.46	−0.251971
$962$	−1616.86	−0.0541890
$963$	6271.74	0.209869
$964$	−20069.1	−0.670521
$965$	−57856.6	−1.93002
$966$	0	0
$967$	42695.2	1.41984	0.709920	−	0.704282i	$-0.248731\pi$
$967$	42695.2	1.41984	0.709920	+	0.704282i	$0.248731\pi$
$968$	2314.13	0.0768377
$969$	8658.17	0.287039
$970$	22566.3	0.746968
$971$	−38230.5	−1.26352	−0.631759	−	0.775165i	$-0.717667\pi$
$971$	−38230.5	−1.26352	−0.631759	+	0.775165i	$0.717667\pi$
$972$	11548.8	0.381099
$973$	0	0
$974$	2861.47	0.0941350
$975$	−15310.7	−0.502907
$976$	7617.80	0.249836
$977$	17071.2	0.559013	0.279507	−	0.960144i	$-0.409829\pi$
$977$	17071.2	0.559013	0.279507	+	0.960144i	$0.409829\pi$
$978$	9073.90	0.296678
$979$	370.445	0.0120934
$980$	0	0
$981$	3140.55	0.102212
$982$	9935.76	0.322875
$983$	22703.5	0.736654	0.368327	−	0.929696i	$-0.379931\pi$
$983$	22703.5	0.736654	0.368327	+	0.929696i	$0.379931\pi$
$984$	31890.9	1.03317
$985$	−52384.3	−1.69452
$986$	−6511.11	−0.210300
$987$	0	0
$988$	3935.94	0.126740
$989$	−20855.0	−0.670526
$990$	2125.98	0.0682506
$991$	−4211.29	−0.134991	−0.0674955	−	0.997720i	$-0.521501\pi$
$991$	−4211.29	−0.134991	−0.0674955	+	0.997720i	$0.521501\pi$
$992$	27602.7	0.883453
$993$	−57902.5	−1.85043
$994$	0	0
$995$	8816.29	0.280900
$996$	−32205.3	−1.02456
$997$	17670.6	0.561319	0.280660	−	0.959807i	$-0.409447\pi$
$997$	17670.6	0.561319	0.280660	+	0.959807i	$0.409447\pi$
$998$	−8087.50	−0.256519
$999$	16997.3	0.538309

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.4.a.n.1.5		10
7.2	even	3		77.4.e.c.67.6	yes	20
7.4	even	3		77.4.e.c.23.6	✓	20
7.6	odd	2		539.4.a.m.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.4.e.c.23.6	✓	20	7.4	even	3
77.4.e.c.67.6	yes	20	7.2	even	3
539.4.a.m.1.5		10	7.6	odd	2
539.4.a.n.1.5		10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	539.a (trivial)

\(f(q)\)	\(=\)	\(q-1.34862 q^{2} +5.81456 q^{3} -6.18124 q^{4} +21.0471 q^{5} -7.84160 q^{6} +19.1250 q^{8} +6.80905 q^{9} +O(q^{10})\)	\(q-1.34862 q^{2} +5.81456 q^{3} -6.18124 q^{4} +21.0471 q^{5} -7.84160 q^{6} +19.1250 q^{8} +6.80905 q^{9} -28.3844 q^{10} -11.0000 q^{11} -35.9411 q^{12} -8.28092 q^{13} +122.379 q^{15} +23.6576 q^{16} +19.3649 q^{17} -9.18280 q^{18} +76.8944 q^{19} -130.097 q^{20} +14.8348 q^{22} +95.1994 q^{23} +111.204 q^{24} +317.980 q^{25} +11.1678 q^{26} -117.401 q^{27} +249.317 q^{29} -165.043 q^{30} -149.280 q^{31} -184.905 q^{32} -63.9601 q^{33} -26.1158 q^{34} -42.0884 q^{36} -144.779 q^{37} -103.701 q^{38} -48.1499 q^{39} +402.526 q^{40} +286.779 q^{41} -219.067 q^{43} +67.9936 q^{44} +143.311 q^{45} -128.387 q^{46} -130.455 q^{47} +137.558 q^{48} -428.832 q^{50} +112.598 q^{51} +51.1863 q^{52} +197.832 q^{53} +158.329 q^{54} -231.518 q^{55} +447.107 q^{57} -336.233 q^{58} +237.195 q^{59} -756.456 q^{60} +322.003 q^{61} +201.321 q^{62} +60.1054 q^{64} -174.289 q^{65} +86.2576 q^{66} -1029.62 q^{67} -119.699 q^{68} +553.542 q^{69} +973.085 q^{71} +130.223 q^{72} +216.732 q^{73} +195.252 q^{74} +1848.91 q^{75} -475.302 q^{76} +64.9357 q^{78} +849.594 q^{79} +497.923 q^{80} -866.481 q^{81} -386.755 q^{82} +896.056 q^{83} +407.575 q^{85} +295.437 q^{86} +1449.67 q^{87} -210.375 q^{88} -33.6768 q^{89} -193.271 q^{90} -588.450 q^{92} -867.997 q^{93} +175.934 q^{94} +1618.40 q^{95} -1075.14 q^{96} -795.023 q^{97} -74.8996 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 54 q^{4} + 10 q^{5} + 53 q^{6} + 3 q^{8} + 76 q^{9}+O(q^{10}) \) 10 * q + 54 * q^4 + 10 * q^5 + 53 * q^6 + 3 * q^8 + 76 * q^9	\( 10 q + 54 q^{4} + 10 q^{5} + 53 q^{6} + 3 q^{8} + 76 q^{9} + 63 q^{10} - 110 q^{11} + 55 q^{12} + 162 q^{13} + 30 q^{15} + 286 q^{16} + 200 q^{17} - 252 q^{18} + 252 q^{19} + 96 q^{20} + 134 q^{23} + 786 q^{24} + 86 q^{25} + 363 q^{26} + 174 q^{27} + 148 q^{29} - 316 q^{30} + 530 q^{31} - 731 q^{32} + 102 q^{34} + 1287 q^{36} - 902 q^{37} + 66 q^{38} - 208 q^{39} + 2163 q^{40} + 168 q^{41} + 118 q^{43} - 594 q^{44} + 58 q^{45} - 210 q^{46} + 288 q^{47} - 850 q^{48} + 2325 q^{50} - 1022 q^{51} + 1663 q^{52} - 608 q^{53} + 2312 q^{54} - 110 q^{55} + 828 q^{57} - 1951 q^{58} - 464 q^{59} - 818 q^{60} + 3484 q^{61} - 809 q^{62} + 3045 q^{64} - 1560 q^{65} - 583 q^{66} + 142 q^{67} + 1145 q^{68} + 1716 q^{69} + 334 q^{71} - 1176 q^{72} + 1466 q^{73} - 3460 q^{74} + 2982 q^{75} + 3387 q^{76} + 5420 q^{78} + 578 q^{79} + 2911 q^{80} + 118 q^{81} - 307 q^{82} + 546 q^{83} + 2582 q^{85} + 2597 q^{86} + 1516 q^{87} - 33 q^{88} + 3150 q^{89} - 1836 q^{90} + 2163 q^{92} - 1484 q^{93} + 5700 q^{94} - 1338 q^{95} + 5429 q^{96} + 1654 q^{97} - 836 q^{99}+O(q^{100}) \) 10 * q + 54 * q^4 + 10 * q^5 + 53 * q^6 + 3 * q^8 + 76 * q^9 + 63 * q^10 - 110 * q^11 + 55 * q^12 + 162 * q^13 + 30 * q^15 + 286 * q^16 + 200 * q^17 - 252 * q^18 + 252 * q^19 + 96 * q^20 + 134 * q^23 + 786 * q^24 + 86 * q^25 + 363 * q^26 + 174 * q^27 + 148 * q^29 - 316 * q^30 + 530 * q^31 - 731 * q^32 + 102 * q^34 + 1287 * q^36 - 902 * q^37 + 66 * q^38 - 208 * q^39 + 2163 * q^40 + 168 * q^41 + 118 * q^43 - 594 * q^44 + 58 * q^45 - 210 * q^46 + 288 * q^47 - 850 * q^48 + 2325 * q^50 - 1022 * q^51 + 1663 * q^52 - 608 * q^53 + 2312 * q^54 - 110 * q^55 + 828 * q^57 - 1951 * q^58 - 464 * q^59 - 818 * q^60 + 3484 * q^61 - 809 * q^62 + 3045 * q^64 - 1560 * q^65 - 583 * q^66 + 142 * q^67 + 1145 * q^68 + 1716 * q^69 + 334 * q^71 - 1176 * q^72 + 1466 * q^73 - 3460 * q^74 + 2982 * q^75 + 3387 * q^76 + 5420 * q^78 + 578 * q^79 + 2911 * q^80 + 118 * q^81 - 307 * q^82 + 546 * q^83 + 2582 * q^85 + 2597 * q^86 + 1516 * q^87 - 33 * q^88 + 3150 * q^89 - 1836 * q^90 + 2163 * q^92 - 1484 * q^93 + 5700 * q^94 - 1338 * q^95 + 5429 * q^96 + 1654 * q^97 - 836 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more