LMFDB - Embedded newform 983.4.a.b.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [983,4,Mod(1,983)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(983, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("983.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 983 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	983.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:	$57.9988775356$
Analytic rank:	$0$
Dimension:	$136$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	983.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.14175 q^{2} -9.46258 q^{3} +18.4375 q^{4} +15.7096 q^{5} +48.6542 q^{6} +4.70054 q^{7} -53.6672 q^{8} +62.5405 q^{9} +O(q^{10})$	\(q-5.14175 q^{2} -9.46258 q^{3} +18.4375 q^{4} +15.7096 q^{5} +48.6542 q^{6} +4.70054 q^{7} -53.6672 q^{8} +62.5405 q^{9} -80.7748 q^{10} -23.5432 q^{11} -174.467 q^{12} -61.4007 q^{13} -24.1690 q^{14} -148.654 q^{15} +128.443 q^{16} +94.6975 q^{17} -321.567 q^{18} -116.492 q^{19} +289.647 q^{20} -44.4793 q^{21} +121.053 q^{22} +177.731 q^{23} +507.830 q^{24} +121.792 q^{25} +315.707 q^{26} -336.305 q^{27} +86.6665 q^{28} -241.827 q^{29} +764.339 q^{30} -93.8285 q^{31} -231.082 q^{32} +222.779 q^{33} -486.910 q^{34} +73.8437 q^{35} +1153.09 q^{36} +340.013 q^{37} +598.973 q^{38} +581.009 q^{39} -843.091 q^{40} +378.815 q^{41} +228.701 q^{42} +177.344 q^{43} -434.078 q^{44} +982.487 q^{45} -913.847 q^{46} -44.3813 q^{47} -1215.40 q^{48} -320.905 q^{49} -626.223 q^{50} -896.083 q^{51} -1132.08 q^{52} -140.013 q^{53} +1729.20 q^{54} -369.854 q^{55} -252.265 q^{56} +1102.32 q^{57} +1243.41 q^{58} -265.869 q^{59} -2740.81 q^{60} +243.846 q^{61} +482.442 q^{62} +293.974 q^{63} +160.623 q^{64} -964.581 q^{65} -1145.47 q^{66} -376.539 q^{67} +1745.99 q^{68} -1681.79 q^{69} -379.686 q^{70} -835.481 q^{71} -3356.37 q^{72} +1000.02 q^{73} -1748.26 q^{74} -1152.47 q^{75} -2147.83 q^{76} -110.666 q^{77} -2987.40 q^{78} +1209.78 q^{79} +2017.78 q^{80} +1493.72 q^{81} -1947.77 q^{82} -1337.89 q^{83} -820.089 q^{84} +1487.66 q^{85} -911.857 q^{86} +2288.31 q^{87} +1263.50 q^{88} +657.497 q^{89} -5051.70 q^{90} -288.617 q^{91} +3276.92 q^{92} +887.860 q^{93} +228.197 q^{94} -1830.05 q^{95} +2186.63 q^{96} -1130.46 q^{97} +1650.01 q^{98} -1472.40 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q + 17 q^{2} + 25 q^{3} + 601 q^{4} + 50 q^{5} + 61 q^{6} + 223 q^{7} + 207 q^{8} + 1443 q^{9}+O(q^{10}) $ 136 * q + 17 * q^2 + 25 * q^3 + 601 * q^4 + 50 * q^5 + 61 * q^6 + 223 * q^7 + 207 * q^8 + 1443 * q^9	\( 136 q + 17 q^{2} + 25 q^{3} + 601 q^{4} + 50 q^{5} + 61 q^{6} + 223 q^{7} + 207 q^{8} + 1443 q^{9} + 257 q^{10} + 204 q^{11} + 296 q^{12} + 530 q^{13} + 103 q^{14} + 226 q^{15} + 2737 q^{16} + 664 q^{17} + 949 q^{18} + 421 q^{19} + 500 q^{20} + 684 q^{21} + 905 q^{22} + 617 q^{23} + 917 q^{24} + 5430 q^{25} + 572 q^{26} + 886 q^{27} + 2728 q^{28} + 688 q^{29} + 712 q^{30} + 1019 q^{31} + 2363 q^{32} + 1764 q^{33} + 1260 q^{34} + 834 q^{35} + 7190 q^{36} + 3303 q^{37} + 384 q^{38} + 1950 q^{39} + 2766 q^{40} + 1975 q^{41} + 448 q^{42} + 3021 q^{43} + 2038 q^{44} + 2266 q^{45} + 2742 q^{46} + 1293 q^{47} + 2589 q^{48} + 10447 q^{49} + 2191 q^{50} + 1032 q^{51} + 4983 q^{52} + 2415 q^{53} + 1878 q^{54} + 2612 q^{55} + 1540 q^{56} + 7908 q^{57} + 5743 q^{58} + 1059 q^{59} + 2611 q^{60} + 4312 q^{61} + 3258 q^{62} + 5605 q^{63} + 13735 q^{64} + 3554 q^{65} + 433 q^{66} + 5715 q^{67} + 5881 q^{68} + 1398 q^{69} + 4287 q^{70} + 2530 q^{71} + 9891 q^{72} + 14106 q^{73} + 2318 q^{74} + 2621 q^{75} + 4651 q^{76} + 4750 q^{77} + 6639 q^{78} + 4791 q^{79} + 4812 q^{80} + 19932 q^{81} + 5380 q^{82} + 4284 q^{83} + 9282 q^{84} + 12058 q^{85} + 2451 q^{86} + 6984 q^{87} + 11197 q^{88} + 5313 q^{89} + 5405 q^{90} + 6298 q^{91} + 6588 q^{92} + 5700 q^{93} + 4743 q^{94} + 5778 q^{95} + 9613 q^{96} + 15382 q^{97} + 6640 q^{98} + 8542 q^{99}+O(q^{100}) \) 136 * q + 17 * q^2 + 25 * q^3 + 601 * q^4 + 50 * q^5 + 61 * q^6 + 223 * q^7 + 207 * q^8 + 1443 * q^9 + 257 * q^10 + 204 * q^11 + 296 * q^12 + 530 * q^13 + 103 * q^14 + 226 * q^15 + 2737 * q^16 + 664 * q^17 + 949 * q^18 + 421 * q^19 + 500 * q^20 + 684 * q^21 + 905 * q^22 + 617 * q^23 + 917 * q^24 + 5430 * q^25 + 572 * q^26 + 886 * q^27 + 2728 * q^28 + 688 * q^29 + 712 * q^30 + 1019 * q^31 + 2363 * q^32 + 1764 * q^33 + 1260 * q^34 + 834 * q^35 + 7190 * q^36 + 3303 * q^37 + 384 * q^38 + 1950 * q^39 + 2766 * q^40 + 1975 * q^41 + 448 * q^42 + 3021 * q^43 + 2038 * q^44 + 2266 * q^45 + 2742 * q^46 + 1293 * q^47 + 2589 * q^48 + 10447 * q^49 + 2191 * q^50 + 1032 * q^51 + 4983 * q^52 + 2415 * q^53 + 1878 * q^54 + 2612 * q^55 + 1540 * q^56 + 7908 * q^57 + 5743 * q^58 + 1059 * q^59 + 2611 * q^60 + 4312 * q^61 + 3258 * q^62 + 5605 * q^63 + 13735 * q^64 + 3554 * q^65 + 433 * q^66 + 5715 * q^67 + 5881 * q^68 + 1398 * q^69 + 4287 * q^70 + 2530 * q^71 + 9891 * q^72 + 14106 * q^73 + 2318 * q^74 + 2621 * q^75 + 4651 * q^76 + 4750 * q^77 + 6639 * q^78 + 4791 * q^79 + 4812 * q^80 + 19932 * q^81 + 5380 * q^82 + 4284 * q^83 + 9282 * q^84 + 12058 * q^85 + 2451 * q^86 + 6984 * q^87 + 11197 * q^88 + 5313 * q^89 + 5405 * q^90 + 6298 * q^91 + 6588 * q^92 + 5700 * q^93 + 4743 * q^94 + 5778 * q^95 + 9613 * q^96 + 15382 * q^97 + 6640 * q^98 + 8542 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−5.14175	−1.81788	−0.908941	−	0.416925i	$-0.863108\pi$
$2$	−5.14175	−1.81788	−0.908941	+	0.416925i	$0.863108\pi$
$3$	−9.46258	−1.82108	−0.910538	−	0.413426i	$-0.864332\pi$
$3$	−9.46258	−1.82108	−0.910538	+	0.413426i	$0.864332\pi$
$4$	18.4375	2.30469
$5$	15.7096	1.40511	0.702555	−	0.711629i	$-0.252042\pi$
$5$	15.7096	1.40511	0.702555	+	0.711629i	$0.252042\pi$
$6$	48.6542	3.31050
$7$	4.70054	0.253805	0.126903	−	0.991915i	$-0.459496\pi$
$7$	4.70054	0.253805	0.126903	+	0.991915i	$0.459496\pi$
$8$	−53.6672	−2.37178
$9$	62.5405	2.31632
$10$	−80.7748	−2.55432
$11$	−23.5432	−0.645321	−0.322660	−	0.946515i	$-0.604577\pi$
$11$	−23.5432	−0.645321	−0.322660	+	0.946515i	$0.604577\pi$
$12$	−174.467	−4.19702
$13$	−61.4007	−1.30996	−0.654980	−	0.755646i	$-0.727323\pi$
$13$	−61.4007	−1.30996	−0.654980	+	0.755646i	$0.727323\pi$
$14$	−24.1690	−0.461388
$15$	−148.654	−2.55881
$16$	128.443	2.00692
$17$	94.6975	1.35103	0.675515	−	0.737346i	$-0.263921\pi$
$17$	94.6975	1.35103	0.675515	+	0.737346i	$0.263921\pi$
$18$	−321.567	−4.21079
$19$	−116.492	−1.40659	−0.703293	−	0.710900i	$-0.748288\pi$
$19$	−116.492	−1.40659	−0.703293	+	0.710900i	$0.748288\pi$
$20$	289.647	3.23835
$21$	−44.4793	−0.462199
$22$	121.053	1.17312
$23$	177.731	1.61128	0.805640	−	0.592405i	$-0.201822\pi$
$23$	177.731	1.61128	0.805640	+	0.592405i	$0.201822\pi$
$24$	507.830	4.31918
$25$	121.792	0.974335
$26$	315.707	2.38135
$27$	−336.305	−2.39711
$28$	86.6665	0.584944
$29$	−241.827	−1.54849	−0.774243	−	0.632888i	$-0.781869\pi$
$29$	−241.827	−1.54849	−0.774243	+	0.632888i	$0.781869\pi$
$30$	764.339	4.65162
$31$	−93.8285	−0.543616	−0.271808	−	0.962351i	$-0.587622\pi$
$31$	−93.8285	−0.543616	−0.271808	+	0.962351i	$0.587622\pi$
$32$	−231.082	−1.27656
$33$	222.779	1.17518
$34$	−486.910	−2.45601
$35$	73.8437	0.356625
$36$	1153.09	5.33840
$37$	340.013	1.51075	0.755375	−	0.655293i	$-0.227455\pi$
$37$	340.013	1.51075	0.755375	+	0.655293i	$0.227455\pi$
$38$	598.973	2.55701
$39$	581.009	2.38554
$40$	−843.091	−3.33261
$41$	378.815	1.44295	0.721475	−	0.692440i	$-0.243464\pi$
$41$	378.815	1.44295	0.721475	+	0.692440i	$0.243464\pi$
$42$	228.701	0.840223
$43$	177.344	0.628946	0.314473	−	0.949266i	$-0.398172\pi$
$43$	177.344	0.628946	0.314473	+	0.949266i	$0.398172\pi$
$44$	−434.078	−1.48727
$45$	982.487	3.25468
$46$	−913.847	−2.92912
$47$	−44.3813	−0.137738	−0.0688689	−	0.997626i	$-0.521939\pi$
$47$	−44.3813	−0.137738	−0.0688689	+	0.997626i	$0.521939\pi$
$48$	−1215.40	−3.65475
$49$	−320.905	−0.935583
$50$	−626.223	−1.77123
$51$	−896.083	−2.46033
$52$	−1132.08	−3.01906
$53$	−140.013	−0.362873	−0.181436	−	0.983403i	$-0.558075\pi$
$53$	−140.013	−0.362873	−0.181436	+	0.983403i	$0.558075\pi$
$54$	1729.20	4.35766
$55$	−369.854	−0.906747
$56$	−252.265	−0.601970
$57$	1102.32	2.56150
$58$	1243.41	2.81496
$59$	−265.869	−0.586664	−0.293332	−	0.956011i	$-0.594764\pi$
$59$	−265.869	−0.586664	−0.293332	+	0.956011i	$0.594764\pi$
$60$	−2740.81	−5.89728
$61$	243.846	0.511825	0.255912	−	0.966700i	$-0.417624\pi$
$61$	243.846	0.511825	0.255912	+	0.966700i	$0.417624\pi$
$62$	482.442	0.988230
$63$	293.974	0.587893
$64$	160.623	0.313716
$65$	−964.581	−1.84064
$66$	−1145.47	−2.13633
$67$	−376.539	−0.686590	−0.343295	−	0.939228i	$-0.611543\pi$
$67$	−376.539	−0.686590	−0.343295	+	0.939228i	$0.611543\pi$
$68$	1745.99	3.11371
$69$	−1681.79	−2.93426
$70$	−379.686	−0.648301
$71$	−835.481	−1.39653	−0.698263	−	0.715841i	$-0.746044\pi$
$71$	−835.481	−1.39653	−0.698263	+	0.715841i	$0.746044\pi$
$72$	−3356.37	−5.49378
$73$	1000.02	1.60333	0.801667	−	0.597771i	$-0.203947\pi$
$73$	1000.02	1.60333	0.801667	+	0.597771i	$0.203947\pi$
$74$	−1748.26	−2.74636
$75$	−1152.47	−1.77434
$76$	−2147.83	−3.24175
$77$	−110.666	−0.163786
$78$	−2987.40	−4.33662
$79$	1209.78	1.72292	0.861459	−	0.507828i	$-0.169551\pi$
$79$	1209.78	1.72292	0.861459	+	0.507828i	$0.169551\pi$
$80$	2017.78	2.81994
$81$	1493.72	2.04900
$82$	−1947.77	−2.62311
$83$	−1337.89	−1.76931	−0.884657	−	0.466243i	$-0.845607\pi$
$83$	−1337.89	−1.76931	−0.884657	+	0.466243i	$0.845607\pi$
$84$	−820.089	−1.06523
$85$	1487.66	1.89835
$86$	−911.857	−1.14335
$87$	2288.31	2.81991
$88$	1263.50	1.53056
$89$	657.497	0.783084	0.391542	−	0.920160i	$-0.371942\pi$
$89$	657.497	0.783084	0.391542	+	0.920160i	$0.371942\pi$
$90$	−5051.70	−5.91662
$91$	−288.617	−0.332475
$92$	3276.92	3.71351
$93$	887.860	0.989966
$94$	228.197	0.250391
$95$	−1830.05	−1.97641
$96$	2186.63	2.32471
$97$	−1130.46	−1.18331	−0.591655	−	0.806191i	$-0.701525\pi$
$97$	−1130.46	−1.18331	−0.591655	+	0.806191i	$0.701525\pi$
$98$	1650.01	1.70078
$99$	−1472.40	−1.49477
$100$	2245.54	2.24554
$101$	−486.056	−0.478855	−0.239428	−	0.970914i	$-0.576960\pi$
$101$	−486.056	−0.478855	−0.239428	+	0.970914i	$0.576960\pi$
$102$	4607.43	4.47258
$103$	1847.33	1.76722	0.883608	−	0.468228i	$-0.155107\pi$
$103$	1847.33	1.76722	0.883608	+	0.468228i	$0.155107\pi$
$104$	3295.20	3.10693
$105$	−698.752	−0.649440
$106$	719.911	0.659660
$107$	399.574	0.361011	0.180506	−	0.983574i	$-0.442227\pi$
$107$	399.574	0.361011	0.180506	+	0.983574i	$0.442227\pi$
$108$	−6200.64	−5.52460
$109$	2162.89	1.90062	0.950308	−	0.311311i	$-0.100768\pi$
$109$	2162.89	1.90062	0.950308	+	0.311311i	$0.100768\pi$
$110$	1901.69	1.64836
$111$	−3217.40	−2.75119
$112$	603.750	0.509366
$113$	−300.463	−0.250134	−0.125067	−	0.992148i	$-0.539915\pi$
$113$	−300.463	−0.250134	−0.125067	+	0.992148i	$0.539915\pi$
$114$	−5667.83	−4.65650
$115$	2792.08	2.26403
$116$	−4458.69	−3.56879
$117$	−3840.03	−3.03428
$118$	1367.03	1.06649
$119$	445.130	0.342899
$120$	7977.82	6.06893
$121$	−776.720	−0.583561
$122$	−1253.80	−0.930437
$123$	−3584.57	−2.62772
$124$	−1729.97	−1.25287
$125$	−50.3975	−0.0360615
$126$	−1511.54	−1.06872
$127$	−177.424	−0.123967	−0.0619835	−	0.998077i	$-0.519743\pi$
$127$	−177.424	−0.123967	−0.0619835	+	0.998077i	$0.519743\pi$
$128$	1022.77	0.706260
$129$	−1678.13	−1.14536
$130$	4959.63	3.34607
$131$	146.809	0.0979144	0.0489572	−	0.998801i	$-0.484410\pi$
$131$	146.809	0.0979144	0.0489572	+	0.998801i	$0.484410\pi$
$132$	4107.50	2.70842
$133$	−547.576	−0.356999
$134$	1936.07	1.24814
$135$	−5283.22	−3.36820
$136$	−5082.15	−3.20434
$137$	−655.800	−0.408969	−0.204485	−	0.978870i	$-0.565552\pi$
$137$	−655.800	−0.408969	−0.204485	+	0.978870i	$0.565552\pi$
$138$	8647.35	5.33414
$139$	−1899.46	−1.15906	−0.579531	−	0.814950i	$-0.696764\pi$
$139$	−1899.46	−1.15906	−0.579531	+	0.814950i	$0.696764\pi$
$140$	1361.50	0.821910
$141$	419.962	0.250831
$142$	4295.83	2.53872
$143$	1445.57	0.845345
$144$	8032.87	4.64865
$145$	−3799.00	−2.17579
$146$	−5141.84	−2.91467
$147$	3036.59	1.70377
$148$	6269.00	3.48182
$149$	−1176.00	−0.646589	−0.323294	−	0.946298i	$-0.604790\pi$
$149$	−1176.00	−0.646589	−0.323294	+	0.946298i	$0.604790\pi$
$150$	5925.69	3.22554
$151$	676.475	0.364574	0.182287	−	0.983245i	$-0.441650\pi$
$151$	676.475	0.364574	0.182287	+	0.983245i	$0.441650\pi$
$152$	6251.81	3.33611
$153$	5922.43	3.12941
$154$	569.015	0.297743
$155$	−1474.01	−0.763841
$156$	10712.4	5.49793
$157$	3012.68	1.53145	0.765726	−	0.643167i	$-0.222380\pi$
$157$	3012.68	1.53145	0.765726	+	0.643167i	$0.222380\pi$
$158$	−6220.36	−3.13206
$159$	1324.88	0.660819
$160$	−3630.21	−1.79371
$161$	835.431	0.408952
$162$	−7680.34	−3.72484
$163$	−1056.87	−0.507854	−0.253927	−	0.967223i	$-0.581722\pi$
$163$	−1056.87	−0.507854	−0.253927	+	0.967223i	$0.581722\pi$
$164$	6984.42	3.32556
$165$	3499.77	1.65125
$166$	6879.11	3.21640
$167$	1171.97	0.543052	0.271526	−	0.962431i	$-0.412472\pi$
$167$	1171.97	0.543052	0.271526	+	0.962431i	$0.412472\pi$
$168$	2387.08	1.09623
$169$	1573.05	0.715998
$170$	−7649.17	−3.45097
$171$	−7285.48	−3.25810
$172$	3269.79	1.44953
$173$	−1444.60	−0.634859	−0.317429	−	0.948282i	$-0.602820\pi$
$173$	−1444.60	−0.634859	−0.317429	+	0.948282i	$0.602820\pi$
$174$	−11765.9	−5.12626
$175$	572.488	0.247292
$176$	−3023.95	−1.29510
$177$	2515.81	1.06836
$178$	−3380.68	−1.42355
$179$	−558.131	−0.233054	−0.116527	−	0.993188i	$-0.537176\pi$
$179$	−558.131	−0.233054	−0.116527	+	0.993188i	$0.537176\pi$
$180$	18114.7	7.50103
$181$	1178.72	0.484052	0.242026	−	0.970270i	$-0.422188\pi$
$181$	1178.72	0.484052	0.242026	+	0.970270i	$0.422188\pi$
$182$	1483.99	0.604401
$183$	−2307.42	−0.932072
$184$	−9538.31	−3.82160
$185$	5341.47	2.12277
$186$	−4565.15	−1.79964
$187$	−2229.48	−0.871848
$188$	−818.282	−0.317443
$189$	−1580.82	−0.608399
$190$	9409.63	3.59288
$191$	3392.32	1.28513	0.642565	−	0.766231i	$-0.277870\pi$
$191$	3392.32	1.28513	0.642565	+	0.766231i	$0.277870\pi$
$192$	−1519.91	−0.571301
$193$	−1703.87	−0.635476	−0.317738	−	0.948178i	$-0.602923\pi$
$193$	−1703.87	−0.635476	−0.317738	+	0.948178i	$0.602923\pi$
$194$	5812.55	2.15112
$195$	9127.43	3.35194
$196$	−5916.70	−2.15623
$197$	900.881	0.325813	0.162906	−	0.986642i	$-0.447913\pi$
$197$	900.881	0.325813	0.162906	+	0.986642i	$0.447913\pi$
$198$	7570.71	2.71731
$199$	−3630.12	−1.29313	−0.646563	−	0.762860i	$-0.723794\pi$
$199$	−3630.12	−1.29313	−0.646563	+	0.762860i	$0.723794\pi$
$200$	−6536.23	−2.31091
$201$	3563.03	1.25033
$202$	2499.18	0.870502
$203$	−1136.72	−0.393014
$204$	−16521.6	−5.67030
$205$	5951.04	2.02751
$206$	−9498.52	−3.21259
$207$	11115.4	3.73223
$208$	−7886.47	−2.62898
$209$	2742.59	0.907699
$210$	3592.81	1.18061
$211$	−4698.35	−1.53293	−0.766464	−	0.642287i	$-0.777986\pi$
$211$	−4698.35	−1.53293	−0.766464	+	0.642287i	$0.777986\pi$
$212$	−2581.50	−0.836311
$213$	7905.81	2.54318
$214$	−2054.51	−0.656276
$215$	2786.00	0.883739
$216$	18048.5	5.68541
$217$	−441.045	−0.137973
$218$	−11121.0	−3.45510
$219$	−9462.77	−2.91979
$220$	−6819.20	−2.08977
$221$	−5814.49	−1.76980
$222$	16543.1	5.00134
$223$	−2759.91	−0.828776	−0.414388	−	0.910100i	$-0.636004\pi$
$223$	−2759.91	−0.828776	−0.414388	+	0.910100i	$0.636004\pi$
$224$	−1086.21	−0.323998
$225$	7616.93	2.25687
$226$	1544.90	0.454714
$227$	−162.585	−0.0475380	−0.0237690	−	0.999717i	$-0.507567\pi$
$227$	−162.585	−0.0475380	−0.0237690	+	0.999717i	$0.507567\pi$
$228$	20324.0	5.90347
$229$	−1257.93	−0.362996	−0.181498	−	0.983391i	$-0.558095\pi$
$229$	−1257.93	−0.362996	−0.181498	+	0.983391i	$0.558095\pi$
$230$	−14356.2	−4.11573
$231$	1047.18	0.298267
$232$	12978.2	3.67266
$233$	2766.45	0.777839	0.388919	−	0.921272i	$-0.372848\pi$
$233$	2766.45	0.777839	0.388919	+	0.921272i	$0.372848\pi$
$234$	19744.5	5.51597
$235$	−697.213	−0.193537
$236$	−4901.97	−1.35208
$237$	−11447.6	−3.13756
$238$	−2288.74	−0.623349
$239$	2083.33	0.563846	0.281923	−	0.959437i	$-0.409028\pi$
$239$	2083.33	0.563846	0.281923	+	0.959437i	$0.409028\pi$
$240$	−19093.5	−5.13532
$241$	2102.47	0.561958	0.280979	−	0.959714i	$-0.409341\pi$
$241$	2102.47	0.561958	0.280979	+	0.959714i	$0.409341\pi$
$242$	3993.69	1.06084
$243$	−5054.23	−1.33428
$244$	4495.93	1.17960
$245$	−5041.29	−1.31460
$246$	18430.9	4.77689
$247$	7152.70	1.84257
$248$	5035.51	1.28934
$249$	12659.9	3.22205
$250$	259.131	0.0655556
$251$	−4737.18	−1.19127	−0.595634	−	0.803256i	$-0.703099\pi$
$251$	−4737.18	−1.19127	−0.595634	+	0.803256i	$0.703099\pi$
$252$	5420.16	1.35491
$253$	−4184.35	−1.03979
$254$	912.267	0.225357
$255$	−14077.1	−3.45703
$256$	−6543.82	−1.59761
$257$	−3401.60	−0.825625	−0.412813	−	0.910816i	$-0.635454\pi$
$257$	−3401.60	−0.825625	−0.412813	+	0.910816i	$0.635454\pi$
$258$	8628.53	2.08213
$259$	1598.24	0.383437
$260$	−17784.5	−4.24211
$261$	−15124.0	−3.58678
$262$	−754.856	−0.177997
$263$	4924.12	1.15450	0.577252	−	0.816566i	$-0.304125\pi$
$263$	4924.12	1.15450	0.577252	+	0.816566i	$0.304125\pi$
$264$	−11955.9	−2.78726
$265$	−2199.55	−0.509877
$266$	2815.50	0.648982
$267$	−6221.62	−1.42606
$268$	−6942.45	−1.58238
$269$	−1253.80	−0.284184	−0.142092	−	0.989853i	$-0.545383\pi$
$269$	−1253.80	−0.284184	−0.142092	+	0.989853i	$0.545383\pi$
$270$	27165.0	6.12299
$271$	7725.05	1.73160	0.865799	−	0.500391i	$-0.166810\pi$
$271$	7725.05	1.73160	0.865799	+	0.500391i	$0.166810\pi$
$272$	12163.2	2.71140
$273$	2731.06	0.605462
$274$	3371.96	0.743458
$275$	−2867.37	−0.628759
$276$	−31008.1	−6.76257
$277$	6915.91	1.50013	0.750066	−	0.661363i	$-0.230022\pi$
$277$	6915.91	1.50013	0.750066	+	0.661363i	$0.230022\pi$
$278$	9766.52	2.10704
$279$	−5868.08	−1.25919
$280$	−3962.98	−0.845834
$281$	269.881	0.0572945	0.0286472	−	0.999590i	$-0.490880\pi$
$281$	269.881	0.0572945	0.0286472	+	0.999590i	$0.490880\pi$
$282$	−2159.34	−0.455981
$283$	−1095.56	−0.230120	−0.115060	−	0.993359i	$-0.536706\pi$
$283$	−1095.56	−0.230120	−0.115060	+	0.993359i	$0.536706\pi$
$284$	−15404.2	−3.21856
$285$	17317.0	3.59919
$286$	−7432.74	−1.53674
$287$	1780.64	0.366229
$288$	−14452.0	−2.95691
$289$	4054.61	0.825282
$290$	19533.5	3.95534
$291$	10697.1	2.15490
$292$	18437.9	3.69519
$293$	2405.21	0.479569	0.239785	−	0.970826i	$-0.422923\pi$
$293$	2405.21	0.479569	0.239785	+	0.970826i	$0.422923\pi$
$294$	−15613.4	−3.09725
$295$	−4176.70	−0.824328
$296$	−18247.5	−3.58316
$297$	7917.69	1.54690
$298$	6046.69	1.17542
$299$	−10912.8	−2.11071
$300$	−21248.6	−4.08930
$301$	833.613	0.159630
$302$	−3478.26	−0.662753
$303$	4599.35	0.872032
$304$	−14962.6	−2.82290
$305$	3830.73	0.719170
$306$	−30451.6	−5.68890
$307$	6512.28	1.21067	0.605335	−	0.795971i	$-0.293039\pi$
$307$	6512.28	1.21067	0.605335	+	0.795971i	$0.293039\pi$
$308$	−2040.40	−0.377476
$309$	−17480.5	−3.21823
$310$	7578.98	1.38857
$311$	1611.77	0.293874	0.146937	−	0.989146i	$-0.453059\pi$
$311$	1611.77	0.293874	0.146937	+	0.989146i	$0.453059\pi$
$312$	−31181.1	−5.65796
$313$	2683.19	0.484546	0.242273	−	0.970208i	$-0.422107\pi$
$313$	2683.19	0.484546	0.242273	+	0.970208i	$0.422107\pi$
$314$	−15490.4	−2.78400
$315$	4618.22	0.826055
$316$	22305.3	3.97079
$317$	3268.02	0.579023	0.289511	−	0.957175i	$-0.406507\pi$
$317$	3268.02	0.579023	0.289511	+	0.957175i	$0.406507\pi$
$318$	−6812.22	−1.20129
$319$	5693.37	0.999271
$320$	2523.32	0.440806
$321$	−3781.00	−0.657429
$322$	−4295.58	−0.743426
$323$	−11031.5	−1.90034
$324$	27540.6	4.72232
$325$	−7478.11	−1.27634
$326$	5434.14	0.923218
$327$	−20466.5	−3.46117
$328$	−20329.9	−3.42236
$329$	−208.616	−0.0349586
$330$	−17994.9	−3.00179
$331$	7759.47	1.28852	0.644258	−	0.764808i	$-0.277166\pi$
$331$	7759.47	1.28852	0.644258	+	0.764808i	$0.277166\pi$
$332$	−24667.5	−4.07772
$333$	21264.6	3.49937
$334$	−6025.97	−0.987205
$335$	−5915.27	−0.964734
$336$	−5713.04	−0.927594
$337$	1589.46	0.256924	0.128462	−	0.991714i	$-0.458996\pi$
$337$	1589.46	0.256924	0.128462	+	0.991714i	$0.458996\pi$
$338$	−8088.21	−1.30160
$339$	2843.15	0.455513
$340$	27428.8	4.37511
$341$	2209.02	0.350807
$342$	37460.1	5.92283
$343$	−3120.71	−0.491261
$344$	−9517.55	−1.49172
$345$	−26420.3	−4.12296
$346$	7427.74	1.15410
$347$	−4227.65	−0.654040	−0.327020	−	0.945017i	$-0.606044\pi$
$347$	−4227.65	−0.654040	−0.327020	+	0.945017i	$0.606044\pi$
$348$	42190.7	6.49903
$349$	9195.27	1.41035	0.705174	−	0.709034i	$-0.250869\pi$
$349$	9195.27	1.41035	0.705174	+	0.709034i	$0.250869\pi$
$350$	−2943.59	−0.449547
$351$	20649.4	3.14012
$352$	5440.40	0.823790
$353$	5126.18	0.772915	0.386458	−	0.922307i	$-0.373699\pi$
$353$	5126.18	0.772915	0.386458	+	0.922307i	$0.373699\pi$
$354$	−12935.6	−1.94215
$355$	−13125.1	−1.96227
$356$	12122.6	1.80477
$357$	−4212.08	−0.624445
$358$	2869.77	0.423664
$359$	1254.18	0.184381	0.0921907	−	0.995741i	$-0.470613\pi$
$359$	1254.18	0.184381	0.0921907	+	0.995741i	$0.470613\pi$
$360$	−52727.3	−7.71937
$361$	6711.42	0.978484
$362$	−6060.67	−0.879950
$363$	7349.77	1.06271
$364$	−5321.38	−0.766253
$365$	15709.9	2.25286
$366$	11864.1	1.69440
$367$	−6422.87	−0.913545	−0.456773	−	0.889584i	$-0.650995\pi$
$367$	−6422.87	−0.913545	−0.456773	+	0.889584i	$0.650995\pi$
$368$	22828.2	3.23370
$369$	23691.3	3.34233
$370$	−27464.5	−3.85895
$371$	−658.137	−0.0920991
$372$	16370.0	2.28157
$373$	5749.46	0.798112	0.399056	−	0.916927i	$-0.369338\pi$
$373$	5749.46	0.798112	0.399056	+	0.916927i	$0.369338\pi$
$374$	11463.4	1.58492
$375$	476.891	0.0656708
$376$	2381.82	0.326683
$377$	14848.3	2.02846
$378$	8128.16	1.10600
$379$	241.902	0.0327855	0.0163927	−	0.999866i	$-0.494782\pi$
$379$	241.902	0.0327855	0.0163927	+	0.999866i	$0.494782\pi$
$380$	−33741.6	−4.55501
$381$	1678.89	0.225753
$382$	−17442.5	−2.33621
$383$	−10022.5	−1.33714	−0.668569	−	0.743651i	$-0.733093\pi$
$383$	−10022.5	−1.33714	−0.668569	+	0.743651i	$0.733093\pi$
$384$	−9678.08	−1.28615
$385$	−1738.51	−0.230137
$386$	8760.84	1.15522
$387$	11091.2	1.45684
$388$	−20842.9	−2.72716
$389$	5288.62	0.689315	0.344657	−	0.938729i	$-0.387995\pi$
$389$	5288.62	0.689315	0.344657	+	0.938729i	$0.387995\pi$
$390$	−46930.9	−6.09344
$391$	16830.7	2.17689
$392$	17222.1	2.21899
$393$	−1389.19	−0.178309
$394$	−4632.10	−0.592289
$395$	19005.1	2.42089
$396$	−27147.5	−3.44498
$397$	5685.81	0.718798	0.359399	−	0.933184i	$-0.382982\pi$
$397$	5685.81	0.718798	0.359399	+	0.933184i	$0.382982\pi$
$398$	18665.1	2.35075
$399$	5181.49	0.650122
$400$	15643.3	1.95541
$401$	−3134.28	−0.390321	−0.195160	−	0.980771i	$-0.562523\pi$
$401$	−3134.28	−0.390321	−0.195160	+	0.980771i	$0.562523\pi$
$402$	−18320.2	−2.27295
$403$	5761.14	0.712116
$404$	−8961.68	−1.10361
$405$	23465.8	2.87907
$406$	5844.71	0.714453
$407$	−8004.98	−0.974919
$408$	48090.2	5.83535
$409$	−6891.72	−0.833187	−0.416594	−	0.909093i	$-0.636776\pi$
$409$	−6891.72	−0.833187	−0.416594	+	0.909093i	$0.636776\pi$
$410$	−30598.7	−3.68576
$411$	6205.57	0.744764
$412$	34060.3	4.07289
$413$	−1249.73	−0.148899
$414$	−57152.4	−6.78476
$415$	−21017.8	−2.48608
$416$	14188.6	1.67224
$417$	17973.8	2.11074
$418$	−14101.7	−1.65009
$419$	11779.8	1.37346	0.686729	−	0.726913i	$-0.259046\pi$
$419$	11779.8	1.37346	0.686729	+	0.726913i	$0.259046\pi$
$420$	−12883.3	−1.49676
$421$	4332.50	0.501552	0.250776	−	0.968045i	$-0.419314\pi$
$421$	4332.50	0.501552	0.250776	+	0.968045i	$0.419314\pi$
$422$	24157.7	2.78668
$423$	−2775.63	−0.319044
$424$	7514.10	0.860654
$425$	11533.4	1.31636
$426$	−40649.7	−4.62320
$427$	1146.21	0.129904
$428$	7367.15	0.832021
$429$	−13678.8	−1.53944
$430$	−14324.9	−1.60653
$431$	15550.2	1.73788	0.868941	−	0.494916i	$-0.164801\pi$
$431$	15550.2	1.73788	0.868941	+	0.494916i	$0.164801\pi$
$432$	−43195.9	−4.81080
$433$	−11298.4	−1.25396	−0.626980	−	0.779035i	$-0.715709\pi$
$433$	−11298.4	−1.25396	−0.626980	+	0.779035i	$0.715709\pi$
$434$	2267.74	0.250818
$435$	35948.4	3.96229
$436$	39878.4	4.38034
$437$	−20704.2	−2.26640
$438$	48655.1	5.30784
$439$	2904.59	0.315782	0.157891	−	0.987457i	$-0.449531\pi$
$439$	2904.59	0.315782	0.157891	+	0.987457i	$0.449531\pi$
$440$	19849.0	2.15060
$441$	−20069.6	−2.16710
$442$	29896.6	3.21728
$443$	−13350.5	−1.43183	−0.715915	−	0.698188i	$-0.753990\pi$
$443$	−13350.5	−1.43183	−0.715915	+	0.698188i	$0.753990\pi$
$444$	−59320.9	−6.34065
$445$	10329.0	1.10032
$446$	14190.7	1.50662
$447$	11128.0	1.17749
$448$	755.014	0.0796228
$449$	4848.80	0.509641	0.254821	−	0.966988i	$-0.417984\pi$
$449$	4848.80	0.509641	0.254821	+	0.966988i	$0.417984\pi$
$450$	−39164.3	−4.10272
$451$	−8918.50	−0.931166
$452$	−5539.79	−0.576482
$453$	−6401.20	−0.663918
$454$	835.970	0.0864185
$455$	−4534.06	−0.467164
$456$	−59158.2	−6.07530
$457$	15648.9	1.60180	0.800902	−	0.598795i	$-0.204354\pi$
$457$	15648.9	1.60180	0.800902	+	0.598795i	$0.204354\pi$
$458$	6467.94	0.659884
$459$	−31847.2	−3.23857
$460$	51479.1	5.21789
$461$	883.473	0.0892570	0.0446285	−	0.999004i	$-0.485790\pi$
$461$	883.473	0.0892570	0.0446285	+	0.999004i	$0.485790\pi$
$462$	−5384.35	−0.542213
$463$	−7812.34	−0.784169	−0.392084	−	0.919929i	$-0.628246\pi$
$463$	−7812.34	−0.784169	−0.392084	+	0.919929i	$0.628246\pi$
$464$	−31060.9	−3.10768
$465$	13947.9	1.39101
$466$	−14224.4	−1.41402
$467$	6401.96	0.634363	0.317182	−	0.948365i	$-0.397264\pi$
$467$	6401.96	0.634363	0.317182	+	0.948365i	$0.397264\pi$
$468$	−70800.8	−6.99309
$469$	−1769.94	−0.174260
$470$	3584.89	0.351827
$471$	−28507.7	−2.78889
$472$	14268.4	1.39144
$473$	−4175.24	−0.405872
$474$	58860.7	5.70372
$475$	−14187.8	−1.37049
$476$	8207.09	0.790276
$477$	−8756.49	−0.840528
$478$	−10711.9	−1.02500
$479$	17227.4	1.64330	0.821650	−	0.569992i	$-0.193054\pi$
$479$	17227.4	1.64330	0.821650	+	0.569992i	$0.193054\pi$
$480$	34351.1	3.26647
$481$	−20877.0	−1.97902
$482$	−10810.3	−1.02157
$483$	−7905.34	−0.744732
$484$	−14320.8	−1.34493
$485$	−17759.1	−1.66268
$486$	25987.6	2.42556
$487$	15081.7	1.40332	0.701658	−	0.712514i	$-0.252443\pi$
$487$	15081.7	1.40332	0.701658	+	0.712514i	$0.252443\pi$
$488$	−13086.5	−1.21393
$489$	10000.7	0.924840
$490$	25921.0	2.38978
$491$	2161.31	0.198653	0.0993263	−	0.995055i	$-0.468331\pi$
$491$	2161.31	0.198653	0.0993263	+	0.995055i	$0.468331\pi$
$492$	−66090.7	−6.05609
$493$	−22900.4	−2.09205
$494$	−36777.4	−3.34958
$495$	−23130.9	−2.10031
$496$	−12051.6	−1.09099
$497$	−3927.22	−0.354446
$498$	−65094.2	−5.85731
$499$	−5498.00	−0.493235	−0.246618	−	0.969113i	$-0.579319\pi$
$499$	−5498.00	−0.493235	−0.246618	+	0.969113i	$0.579319\pi$
$500$	−929.207	−0.0831108
$501$	−11089.9	−0.988939
$502$	24357.4	2.16558
$503$	9966.28	0.883448	0.441724	−	0.897151i	$-0.354367\pi$
$503$	9966.28	0.883448	0.441724	+	0.897151i	$0.354367\pi$
$504$	−15776.8	−1.39435
$505$	−7635.75	−0.672845
$506$	21514.8	1.89022
$507$	−14885.1	−1.30389
$508$	−3271.26	−0.285706
$509$	−7990.51	−0.695821	−0.347911	−	0.937528i	$-0.613109\pi$
$509$	−7990.51	−0.695821	−0.347911	+	0.937528i	$0.613109\pi$
$510$	72380.9	6.28447
$511$	4700.63	0.406935
$512$	25464.5	2.19801
$513$	39176.9	3.37174
$514$	17490.1	1.50089
$515$	29020.9	2.48313
$516$	−30940.6	−2.63970
$517$	1044.88	0.0888851
$518$	−8217.77	−0.697042
$519$	13669.6	1.15613
$520$	51766.4	4.36559
$521$	−1283.13	−0.107898	−0.0539490	−	0.998544i	$-0.517181\pi$
$521$	−1283.13	−0.107898	−0.0539490	+	0.998544i	$0.517181\pi$
$522$	77763.6	6.52035
$523$	20046.4	1.67603	0.838017	−	0.545643i	$-0.183715\pi$
$523$	20046.4	1.67603	0.838017	+	0.545643i	$0.183715\pi$
$524$	2706.80	0.225663
$525$	−5417.22	−0.450337
$526$	−25318.6	−2.09875
$527$	−8885.32	−0.734442
$528$	28614.3	2.35848
$529$	19421.2	1.59622
$530$	11309.5	0.926895
$531$	−16627.6	−1.35890
$532$	−10096.0	−0.822773
$533$	−23259.5	−1.89021
$534$	31990.0	2.59240
$535$	6277.14	0.507261
$536$	20207.8	1.62844
$537$	5281.36	0.424409
$538$	6446.71	0.516612
$539$	7555.12	0.603751
$540$	−97409.7	−7.76267
$541$	20920.8	1.66258	0.831289	−	0.555840i	$-0.187603\pi$
$541$	20920.8	1.66258	0.831289	+	0.555840i	$0.187603\pi$
$542$	−39720.2	−3.14784
$543$	−11153.7	−0.881496
$544$	−21882.9	−1.72467
$545$	33978.1	2.67058
$546$	−14042.4	−1.10066
$547$	12966.5	1.01355	0.506773	−	0.862080i	$-0.330838\pi$
$547$	12966.5	1.01355	0.506773	+	0.862080i	$0.330838\pi$
$548$	−12091.3	−0.942549
$549$	15250.3	1.18555
$550$	14743.3	1.14301
$551$	28170.9	2.17808
$552$	90257.1	6.95942
$553$	5686.60	0.437286
$554$	−35559.8	−2.72706
$555$	−50544.1	−3.86573
$556$	−35021.3	−2.67128
$557$	−7893.73	−0.600481	−0.300241	−	0.953863i	$-0.597067\pi$
$557$	−7893.73	−0.600481	−0.300241	+	0.953863i	$0.597067\pi$
$558$	30172.2	2.28905
$559$	−10889.0	−0.823895
$560$	9484.68	0.715716
$561$	21096.6	1.58770
$562$	−1387.66	−0.104155
$563$	−7247.06	−0.542500	−0.271250	−	0.962509i	$-0.587437\pi$
$563$	−7247.06	−0.542500	−0.271250	+	0.962509i	$0.587437\pi$
$564$	7743.06	0.578088
$565$	−4720.15	−0.351466
$566$	5633.07	0.418332
$567$	7021.30	0.520048
$568$	44837.9	3.31225
$569$	4658.21	0.343203	0.171601	−	0.985166i	$-0.445106\pi$
$569$	4658.21	0.343203	0.171601	+	0.985166i	$0.445106\pi$
$570$	−89039.5	−6.54290
$571$	−6819.51	−0.499803	−0.249902	−	0.968271i	$-0.580398\pi$
$571$	−6819.51	−0.499803	−0.249902	+	0.968271i	$0.580398\pi$
$572$	26652.7	1.94826
$573$	−32100.1	−2.34032
$574$	−9155.58	−0.665760
$575$	21646.2	1.56993
$576$	10045.4	0.726665
$577$	−3991.14	−0.287961	−0.143980	−	0.989581i	$-0.545990\pi$
$577$	−3991.14	−0.287961	−0.143980	+	0.989581i	$0.545990\pi$
$578$	−20847.8	−1.50027
$579$	16123.0	1.15725
$580$	−70044.3	−5.01454
$581$	−6288.83	−0.449061
$582$	−55001.7	−3.91734
$583$	3296.35	0.234169
$584$	−53668.2	−3.80275
$585$	−60325.4	−4.26350
$586$	−12367.0	−0.871800
$587$	9122.38	0.641433	0.320716	−	0.947175i	$-0.396076\pi$
$587$	9122.38	0.641433	0.320716	+	0.947175i	$0.396076\pi$
$588$	55987.3	3.92666
$589$	10930.3	0.764643
$590$	21475.5	1.49853
$591$	−8524.67	−0.593330
$592$	43672.1	3.03195
$593$	11609.3	0.803938	0.401969	−	0.915653i	$-0.368326\pi$
$593$	11609.3	0.803938	0.401969	+	0.915653i	$0.368326\pi$
$594$	−40710.7	−2.81209
$595$	6992.81	0.481811
$596$	−21682.6	−1.49019
$597$	34350.3	2.35488
$598$	56110.8	3.83703
$599$	−15952.6	−1.08816	−0.544079	−	0.839034i	$-0.683121\pi$
$599$	−15952.6	−1.08816	−0.544079	+	0.839034i	$0.683121\pi$
$600$	61849.6	4.20833
$601$	3162.59	0.214650	0.107325	−	0.994224i	$-0.465771\pi$
$601$	3162.59	0.214650	0.107325	+	0.994224i	$0.465771\pi$
$602$	−4286.22	−0.290188
$603$	−23548.9	−1.59036
$604$	12472.5	0.840232
$605$	−12202.0	−0.819968
$606$	−23648.7	−1.58525
$607$	359.742	0.0240552	0.0120276	−	0.999928i	$-0.496171\pi$
$607$	359.742	0.0240552	0.0120276	+	0.999928i	$0.496171\pi$
$608$	26919.2	1.79559
$609$	10756.3	0.715709
$610$	−19696.6	−1.30737
$611$	2725.04	0.180431
$612$	109195.	7.21233
$613$	23570.5	1.55302	0.776511	−	0.630103i	$-0.216987\pi$
$613$	23570.5	1.55302	0.776511	+	0.630103i	$0.216987\pi$
$614$	−33484.5	−2.20085
$615$	−56312.2	−3.69224
$616$	5939.11	0.388464
$617$	−4523.60	−0.295160	−0.147580	−	0.989050i	$-0.547148\pi$
$617$	−4523.60	−0.295160	−0.147580	+	0.989050i	$0.547148\pi$
$618$	89880.5	5.85036
$619$	5734.65	0.372367	0.186183	−	0.982515i	$-0.440388\pi$
$619$	5734.65	0.372367	0.186183	+	0.982515i	$0.440388\pi$
$620$	−27177.1	−1.76042
$621$	−59771.8	−3.86241
$622$	−8287.29	−0.534228
$623$	3090.59	0.198751
$624$	74626.4	4.78757
$625$	−16015.7	−1.02501
$626$	−13796.3	−0.880846
$627$	−25952.0	−1.65299
$628$	55546.4	3.52953
$629$	32198.4	2.04107
$630$	−23745.7	−1.50167
$631$	−9094.45	−0.573763	−0.286882	−	0.957966i	$-0.592619\pi$
$631$	−9094.45	−0.573763	−0.286882	+	0.957966i	$0.592619\pi$
$632$	−64925.3	−4.08637
$633$	44458.5	2.79158
$634$	−16803.3	−1.05259
$635$	−2787.26	−0.174187
$636$	24427.6	1.52298
$637$	19703.8	1.22558
$638$	−29273.8	−1.81656
$639$	−52251.4	−3.23480
$640$	16067.4	0.992373
$641$	−27288.5	−1.68148	−0.840741	−	0.541437i	$-0.817880\pi$
$641$	−27288.5	−1.68148	−0.840741	+	0.541437i	$0.817880\pi$
$642$	19440.9	1.19513
$643$	−11548.0	−0.708254	−0.354127	−	0.935197i	$-0.615222\pi$
$643$	−11548.0	−0.708254	−0.354127	+	0.935197i	$0.615222\pi$
$644$	15403.3	0.942508
$645$	−26362.8	−1.60936
$646$	56721.2	3.45459
$647$	27349.1	1.66183	0.830917	−	0.556397i	$-0.187817\pi$
$647$	27349.1	1.66183	0.830917	+	0.556397i	$0.187817\pi$
$648$	−80163.8	−4.85977
$649$	6259.39	0.378587
$650$	38450.5	2.32024
$651$	4173.43	0.251259
$652$	−19486.0	−1.17045
$653$	−3544.40	−0.212409	−0.106205	−	0.994344i	$-0.533870\pi$
$653$	−3544.40	−0.212409	−0.106205	+	0.994344i	$0.533870\pi$
$654$	105234.	6.29199
$655$	2306.32	0.137581
$656$	48656.0	2.89588
$657$	62541.7	3.71383
$658$	1072.65	0.0635506
$659$	30988.1	1.83175	0.915876	−	0.401460i	$-0.131497\pi$
$659$	30988.1	1.83175	0.915876	+	0.401460i	$0.131497\pi$
$660$	64527.2	3.80564
$661$	−1883.07	−0.110806	−0.0554032	−	0.998464i	$-0.517644\pi$
$661$	−1883.07	−0.110806	−0.0554032	+	0.998464i	$0.517644\pi$
$662$	−39897.2	−2.34237
$663$	55020.1	3.22293
$664$	71801.0	4.19642
$665$	−8602.21	−0.501623
$666$	−109337.	−6.36145
$667$	−42980.1	−2.49505
$668$	21608.2	1.25157
$669$	26115.9	1.50926
$670$	30414.8	1.75377
$671$	−5740.91	−0.330291
$672$	10278.4	0.590024
$673$	−2703.36	−0.154839	−0.0774197	−	0.996999i	$-0.524668\pi$
$673$	−2703.36	−0.154839	−0.0774197	+	0.996999i	$0.524668\pi$
$674$	−8172.60	−0.467058
$675$	−40959.3	−2.33559
$676$	29003.1	1.65015
$677$	26945.8	1.52970	0.764852	−	0.644206i	$-0.222812\pi$
$677$	26945.8	1.52970	0.764852	+	0.644206i	$0.222812\pi$
$678$	−14618.8	−0.828068
$679$	−5313.78	−0.300330
$680$	−79838.6	−4.50245
$681$	1538.47	0.0865704
$682$	−11358.2	−0.637725
$683$	15532.1	0.870162	0.435081	−	0.900391i	$-0.356720\pi$
$683$	15532.1	0.870162	0.435081	+	0.900391i	$0.356720\pi$
$684$	−134326.	−7.50891
$685$	−10302.4	−0.574647
$686$	16045.9	0.893055
$687$	11903.2	0.661044
$688$	22778.5	1.26224
$689$	8596.90	0.475349
$690$	135847.	7.49506
$691$	−7013.54	−0.386118	−0.193059	−	0.981187i	$-0.561841\pi$
$691$	−7013.54	−0.386118	−0.193059	+	0.981187i	$0.561841\pi$
$692$	−26634.8	−1.46315
$693$	−6921.09	−0.379380
$694$	21737.5	1.18897
$695$	−29839.7	−1.62861
$696$	−122807.	−6.68820
$697$	35872.8	1.94947
$698$	−47279.7	−2.56385
$699$	−26177.8	−1.41650
$700$	10555.3	0.569931
$701$	−10263.3	−0.552982	−0.276491	−	0.961016i	$-0.589172\pi$
$701$	−10263.3	−0.552982	−0.276491	+	0.961016i	$0.589172\pi$
$702$	−106174.	−5.70837
$703$	−39608.8	−2.12500
$704$	−3781.56	−0.202448
$705$	6597.44	0.352445
$706$	−26357.5	−1.40507
$707$	−2284.73	−0.121536
$708$	46385.3	2.46224
$709$	35296.8	1.86968	0.934838	−	0.355073i	$-0.115544\pi$
$709$	35296.8	1.86968	0.934838	+	0.355073i	$0.115544\pi$
$710$	67485.9	3.56718
$711$	75660.0	3.99082
$712$	−35286.0	−1.85730
$713$	−16676.2	−0.875918
$714$	21657.4	1.13517
$715$	22709.3	1.18780
$716$	−10290.6	−0.537118
$717$	−19713.6	−1.02681
$718$	−6448.66	−0.335184
$719$	−35801.1	−1.85696	−0.928482	−	0.371377i	$-0.878886\pi$
$719$	−35801.1	−1.85696	−0.928482	+	0.371377i	$0.878886\pi$
$720$	126193.	6.53187
$721$	8683.47	0.448529
$722$	−34508.4	−1.77877
$723$	−19894.8	−1.02337
$724$	21732.7	1.11559
$725$	−29452.5	−1.50875
$726$	−37790.7	−1.93188
$727$	−11949.4	−0.609599	−0.304799	−	0.952417i	$-0.598589\pi$
$727$	−11949.4	−0.609599	−0.304799	+	0.952417i	$0.598589\pi$
$728$	15489.2	0.788557
$729$	7495.61	0.380817
$730$	−80776.4	−4.09544
$731$	16794.0	0.849726
$732$	−42543.1	−2.14814
$733$	−8741.79	−0.440499	−0.220249	−	0.975444i	$-0.570687\pi$
$733$	−8741.79	−0.440499	−0.220249	+	0.975444i	$0.570687\pi$
$734$	33024.8	1.66072
$735$	47703.7	2.39398
$736$	−41070.4	−2.05689
$737$	8864.91	0.443071
$738$	−121815.	−6.07596
$739$	10459.0	0.520626	0.260313	−	0.965524i	$-0.416174\pi$
$739$	10459.0	0.520626	0.260313	+	0.965524i	$0.416174\pi$
$740$	98483.6	4.89234
$741$	−67683.0	−3.35546
$742$	3383.97	0.167425
$743$	−21049.3	−1.03933	−0.519665	−	0.854370i	$-0.673943\pi$
$743$	−21049.3	−1.03933	−0.519665	+	0.854370i	$0.673943\pi$
$744$	−47649.0	−2.34798
$745$	−18474.5	−0.908529
$746$	−29562.3	−1.45087
$747$	−83672.6	−4.09829
$748$	−41106.1	−2.00934
$749$	1878.21	0.0916267
$750$	−2452.05	−0.119382
$751$	4798.97	0.233178	0.116589	−	0.993180i	$-0.462804\pi$
$751$	4798.97	0.233178	0.116589	+	0.993180i	$0.462804\pi$
$752$	−5700.45	−0.276428
$753$	44826.0	2.16939
$754$	−76346.4	−3.68749
$755$	10627.2	0.512267
$756$	−29146.4	−1.40217
$757$	28060.7	1.34727	0.673634	−	0.739065i	$-0.264732\pi$
$757$	28060.7	1.34727	0.673634	+	0.739065i	$0.264732\pi$
$758$	−1243.80	−0.0596001
$759$	39594.7	1.89354
$760$	98213.4	4.68760
$761$	−23814.2	−1.13438	−0.567190	−	0.823587i	$-0.691969\pi$
$761$	−23814.2	−1.13438	−0.567190	+	0.823587i	$0.691969\pi$
$762$	−8632.41	−0.410393
$763$	10166.8	0.482387
$764$	62546.1	2.96183
$765$	93039.1	4.39717
$766$	51532.9	2.43076
$767$	16324.5	0.768507
$768$	61921.5	2.90937
$769$	30123.7	1.41260	0.706299	−	0.707913i	$-0.250363\pi$
$769$	30123.7	1.41260	0.706299	+	0.707913i	$0.250363\pi$
$770$	8939.00	0.418362
$771$	32187.9	1.50353
$772$	−31415.1	−1.46458
$773$	−32009.0	−1.48937	−0.744686	−	0.667415i	$-0.767401\pi$
$773$	−32009.0	−1.48937	−0.744686	+	0.667415i	$0.767401\pi$
$774$	−57028.0	−2.64836
$775$	−11427.6	−0.529664
$776$	60668.7	2.80655
$777$	−15123.5	−0.698267
$778$	−27192.7	−1.25309
$779$	−44129.0	−2.02963
$780$	168287.	7.72520
$781$	19669.9	0.901208
$782$	−86539.0	−3.95732
$783$	81327.6	3.71189
$784$	−41217.9	−1.87764
$785$	47328.0	2.15186
$786$	7142.89	0.324145
$787$	15302.9	0.693123	0.346562	−	0.938027i	$-0.387349\pi$
$787$	15302.9	0.693123	0.346562	+	0.938027i	$0.387349\pi$
$788$	16610.0	0.750899
$789$	−46594.9	−2.10244
$790$	−97719.5	−4.40089
$791$	−1412.34	−0.0634854
$792$	79019.6	3.54525
$793$	−14972.3	−0.670471
$794$	−29235.0	−1.30669
$795$	20813.4	0.928524
$796$	−66930.4	−2.98026
$797$	8966.39	0.398502	0.199251	−	0.979949i	$-0.436149\pi$
$797$	8966.39	0.398502	0.199251	+	0.979949i	$0.436149\pi$
$798$	−26641.9	−1.18185
$799$	−4202.80	−0.186088
$800$	−28143.9	−1.24380
$801$	41120.2	1.81387
$802$	16115.7	0.709557
$803$	−23543.6	−1.03467
$804$	65693.5	2.88163
$805$	13124.3	0.574622
$806$	−29622.3	−1.29454
$807$	11864.2	0.517520
$808$	26085.3	1.13574
$809$	26717.1	1.16109	0.580545	−	0.814228i	$-0.302839\pi$
$809$	26717.1	1.16109	0.580545	+	0.814228i	$0.302839\pi$
$810$	−120655.	−5.23381
$811$	18933.9	0.819801	0.409900	−	0.912130i	$-0.365563\pi$
$811$	18933.9	0.819801	0.409900	+	0.912130i	$0.365563\pi$
$812$	−20958.3	−0.905777
$813$	−73098.9	−3.15337
$814$	41159.5	1.77229
$815$	−16603.0	−0.713590
$816$	−115095.	−4.93767
$817$	−20659.2	−0.884667
$818$	35435.5	1.51464
$819$	−18050.2	−0.770118
$820$	109723.	4.67278
$821$	16772.2	0.712976	0.356488	−	0.934300i	$-0.383974\pi$
$821$	16772.2	0.712976	0.356488	+	0.934300i	$0.383974\pi$
$822$	−31907.4	−1.35389
$823$	−26574.6	−1.12555	−0.562777	−	0.826609i	$-0.690267\pi$
$823$	−26574.6	−1.12555	−0.562777	+	0.826609i	$0.690267\pi$
$824$	−99141.2	−4.19144
$825$	27132.7	1.14502
$826$	6425.78	0.270680
$827$	2102.90	0.0884218	0.0442109	−	0.999022i	$-0.485923\pi$
$827$	2102.90	0.0884218	0.0442109	+	0.999022i	$0.485923\pi$
$828$	204940.	8.60165
$829$	29478.8	1.23503	0.617516	−	0.786558i	$-0.288139\pi$
$829$	29478.8	1.23503	0.617516	+	0.786558i	$0.288139\pi$
$830$	108068.	4.51940
$831$	−65442.4	−2.73185
$832$	−9862.34	−0.410956
$833$	−30388.9	−1.26400
$834$	−92416.5	−3.83708
$835$	18411.2	0.763048
$836$	50566.7	2.09197
$837$	31555.0	1.30311
$838$	−60568.6	−2.49679
$839$	4081.86	0.167964	0.0839818	−	0.996467i	$-0.473236\pi$
$839$	4081.86	0.167964	0.0839818	+	0.996467i	$0.473236\pi$
$840$	37500.1	1.54033
$841$	34091.2	1.39781
$842$	−22276.6	−0.911762
$843$	−2553.77	−0.104338
$844$	−86626.0	−3.53293
$845$	24712.0	1.00606
$846$	14271.6	0.579985
$847$	−3651.00	−0.148111
$848$	−17983.6	−0.728256
$849$	10366.8	0.419067
$850$	−59301.7	−2.39298
$851$	60430.8	2.43424
$852$	145764.	5.86125
$853$	−10477.7	−0.420575	−0.210288	−	0.977640i	$-0.567440\pi$
$853$	−10477.7	−0.420575	−0.210288	+	0.977640i	$0.567440\pi$
$854$	−5893.52	−0.236150
$855$	−114452.	−4.57799
$856$	−21444.0	−0.856239
$857$	6053.66	0.241294	0.120647	−	0.992695i	$-0.461503\pi$
$857$	6053.66	0.241294	0.120647	+	0.992695i	$0.461503\pi$
$858$	70332.9	2.79851
$859$	7988.13	0.317289	0.158645	−	0.987336i	$-0.449288\pi$
$859$	7988.13	0.317289	0.158645	+	0.987336i	$0.449288\pi$
$860$	51367.1	2.03675
$861$	−16849.4	−0.666930
$862$	−79955.2	−3.15926
$863$	42185.4	1.66397	0.831986	−	0.554796i	$-0.187204\pi$
$863$	42185.4	1.66397	0.831986	+	0.554796i	$0.187204\pi$
$864$	77714.0	3.06005
$865$	−22694.0	−0.892047
$866$	58093.3	2.27955
$867$	−38367.1	−1.50290
$868$	−8131.79	−0.317985
$869$	−28482.0	−1.11183
$870$	−184838.	−7.20296
$871$	23119.7	0.899406
$872$	−116076.	−4.50784
$873$	−70699.7	−2.74092
$874$	106456.	4.12005
$875$	−236.896	−0.00915262
$876$	−174470.	−6.72922
$877$	−6847.41	−0.263649	−0.131825	−	0.991273i	$-0.542084\pi$
$877$	−6847.41	−0.263649	−0.131825	+	0.991273i	$0.542084\pi$
$878$	−14934.6	−0.574055
$879$	−22759.5	−0.873332
$880$	−47505.0	−1.81977
$881$	1422.25	0.0543891	0.0271946	−	0.999630i	$-0.491343\pi$
$881$	1422.25	0.0543891	0.0271946	+	0.999630i	$0.491343\pi$
$882$	103193.	3.93954
$883$	−4670.88	−0.178016	−0.0890078	−	0.996031i	$-0.528370\pi$
$883$	−4670.88	−0.178016	−0.0890078	+	0.996031i	$0.528370\pi$
$884$	−107205.	−4.07884
$885$	39522.3	1.50116
$886$	68644.8	2.60290
$887$	−25881.4	−0.979720	−0.489860	−	0.871801i	$-0.662952\pi$
$887$	−25881.4	−0.979720	−0.489860	+	0.871801i	$0.662952\pi$
$888$	172669.	6.52521
$889$	−833.988	−0.0314635
$890$	−53109.2	−2.00025
$891$	−35166.9	−1.32226
$892$	−50885.9	−1.91007
$893$	5170.07	0.193740
$894$	−57217.4	−2.14053
$895$	−8768.02	−0.327467
$896$	4807.59	0.179253
$897$	103263.	3.84377
$898$	−24931.3	−0.926467
$899$	22690.2	0.841782
$900$	140437.	5.20139
$901$	−13258.9	−0.490252
$902$	45856.7	1.69275
$903$	−7888.13	−0.290698
$904$	16125.0	0.593262
$905$	18517.2	0.680147
$906$	32913.3	1.20692
$907$	44222.4	1.61894	0.809471	−	0.587160i	$-0.199754\pi$
$907$	44222.4	1.61894	0.809471	+	0.587160i	$0.199754\pi$
$908$	−2997.67	−0.109561
$909$	−30398.2	−1.10918
$910$	23313.0	0.849250
$911$	−47874.9	−1.74113	−0.870563	−	0.492057i	$-0.836245\pi$
$911$	−47874.9	−1.74113	−0.870563	+	0.492057i	$0.836245\pi$
$912$	141584.	5.14071
$913$	31498.3	1.14177
$914$	−80462.7	−2.91189
$915$	−36248.6	−1.30966
$916$	−23193.1	−0.836595
$917$	690.083	0.0248512
$918$	163750.	5.88733
$919$	22038.3	0.791052	0.395526	−	0.918455i	$-0.370562\pi$
$919$	22038.3	0.791052	0.395526	+	0.918455i	$0.370562\pi$
$920$	−149843.	−5.36977
$921$	−61623.0	−2.20472
$922$	−4542.60	−0.162259
$923$	51299.1	1.82940
$924$	19307.5	0.687413
$925$	41410.8	1.47198
$926$	40169.1	1.42553
$927$	115533.	4.09343
$928$	55881.8	1.97673
$929$	47134.0	1.66460	0.832301	−	0.554324i	$-0.187023\pi$
$929$	47134.0	1.66460	0.832301	+	0.554324i	$0.187023\pi$
$930$	−71716.8	−2.52869
$931$	37382.9	1.31598
$932$	51006.6	1.79268
$933$	−15251.5	−0.535167
$934$	−32917.3	−1.15320
$935$	−35024.2	−1.22504
$936$	206084.	7.19664
$937$	−45063.3	−1.57114	−0.785568	−	0.618776i	$-0.787629\pi$
$937$	−45063.3	−1.57114	−0.785568	+	0.618776i	$0.787629\pi$
$938$	9100.56	0.316784
$939$	−25389.9	−0.882394
$940$	−12854.9	−0.446043
$941$	−34259.5	−1.18685	−0.593426	−	0.804889i	$-0.702225\pi$
$941$	−34259.5	−1.18685	−0.593426	+	0.804889i	$0.702225\pi$
$942$	146580.	5.06987
$943$	67327.1	2.32500
$944$	−34148.9	−1.17739
$945$	−24834.0	−0.854868
$946$	21468.0	0.737828
$947$	35512.1	1.21857	0.609287	−	0.792950i	$-0.291456\pi$
$947$	35512.1	1.21857	0.609287	+	0.792950i	$0.291456\pi$
$948$	−211066.	−7.23112
$949$	−61401.9	−2.10031
$950$	72950.1	2.49138
$951$	−30923.9	−1.05444
$952$	−23888.8	−0.813279
$953$	−1593.02	−0.0541478	−0.0270739	−	0.999633i	$-0.508619\pi$
$953$	−1593.02	−0.0541478	−0.0270739	+	0.999633i	$0.508619\pi$
$954$	45023.6	1.52798
$955$	53292.1	1.80575
$956$	38411.4	1.29949
$957$	−53874.0	−1.81975
$958$	−88579.0	−2.98732
$959$	−3082.62	−0.103799
$960$	−23877.1	−0.802740
$961$	−20987.2	−0.704482
$962$	107344.	3.59763
$963$	24989.5	0.836216
$964$	38764.3	1.29514
$965$	−26767.1	−0.892915
$966$	40647.2	1.35383
$967$	43252.0	1.43836	0.719178	−	0.694826i	$-0.244519\pi$
$967$	43252.0	1.43836	0.719178	+	0.694826i	$0.244519\pi$
$968$	41684.3	1.38408
$969$	104387.	3.46066
$970$	91312.9	3.02256
$971$	43389.6	1.43402	0.717012	−	0.697061i	$-0.245509\pi$
$971$	43389.6	1.43402	0.717012	+	0.697061i	$0.245509\pi$
$972$	−93187.6	−3.07510
$973$	−8928.47	−0.294176
$974$	−77546.0	−2.55106
$975$	70762.3	2.32431
$976$	31320.3	1.02719
$977$	29113.9	0.953363	0.476681	−	0.879076i	$-0.341840\pi$
$977$	29113.9	0.953363	0.476681	+	0.879076i	$0.341840\pi$
$978$	−51421.0	−1.68125
$979$	−15479.6	−0.505341
$980$	−92949.0	−3.02974
$981$	135268.	4.40243
$982$	−11112.9	−0.361127
$983$	−983.000	−0.0318950
$983$	−983.000	−0.0318950
$984$	192374.	6.23237
$985$	14152.5	0.457803
$986$	117748.	3.80310
$987$	1974.05	0.0636623
$988$	131878.	4.24656
$989$	31519.5	1.01341
$990$	118933.	3.81812
$991$	−10225.3	−0.327767	−0.163883	−	0.986480i	$-0.552402\pi$
$991$	−10225.3	−0.327767	−0.163883	+	0.986480i	$0.552402\pi$
$992$	21682.1	0.693958
$993$	−73424.6	−2.34649
$994$	20192.7	0.644341
$995$	−57027.7	−1.81699
$996$	233418.	7.42584
$997$	−12725.3	−0.404227	−0.202113	−	0.979362i	$-0.564781\pi$
$997$	−12725.3	−0.404227	−0.202113	+	0.979362i	$0.564781\pi$
$998$	28269.3	0.896643
$999$	−114348.	−3.62143

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.4.a.b.1.8	✓	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.4.a.b.1.8	✓	136	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:	\( N \)	\(=\)	\( 983 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	983.a (trivial)

\(f(q)\)	\(=\)	\(q-5.14175 q^{2} -9.46258 q^{3} +18.4375 q^{4} +15.7096 q^{5} +48.6542 q^{6} +4.70054 q^{7} -53.6672 q^{8} +62.5405 q^{9} +O(q^{10})\)	\(q-5.14175 q^{2} -9.46258 q^{3} +18.4375 q^{4} +15.7096 q^{5} +48.6542 q^{6} +4.70054 q^{7} -53.6672 q^{8} +62.5405 q^{9} -80.7748 q^{10} -23.5432 q^{11} -174.467 q^{12} -61.4007 q^{13} -24.1690 q^{14} -148.654 q^{15} +128.443 q^{16} +94.6975 q^{17} -321.567 q^{18} -116.492 q^{19} +289.647 q^{20} -44.4793 q^{21} +121.053 q^{22} +177.731 q^{23} +507.830 q^{24} +121.792 q^{25} +315.707 q^{26} -336.305 q^{27} +86.6665 q^{28} -241.827 q^{29} +764.339 q^{30} -93.8285 q^{31} -231.082 q^{32} +222.779 q^{33} -486.910 q^{34} +73.8437 q^{35} +1153.09 q^{36} +340.013 q^{37} +598.973 q^{38} +581.009 q^{39} -843.091 q^{40} +378.815 q^{41} +228.701 q^{42} +177.344 q^{43} -434.078 q^{44} +982.487 q^{45} -913.847 q^{46} -44.3813 q^{47} -1215.40 q^{48} -320.905 q^{49} -626.223 q^{50} -896.083 q^{51} -1132.08 q^{52} -140.013 q^{53} +1729.20 q^{54} -369.854 q^{55} -252.265 q^{56} +1102.32 q^{57} +1243.41 q^{58} -265.869 q^{59} -2740.81 q^{60} +243.846 q^{61} +482.442 q^{62} +293.974 q^{63} +160.623 q^{64} -964.581 q^{65} -1145.47 q^{66} -376.539 q^{67} +1745.99 q^{68} -1681.79 q^{69} -379.686 q^{70} -835.481 q^{71} -3356.37 q^{72} +1000.02 q^{73} -1748.26 q^{74} -1152.47 q^{75} -2147.83 q^{76} -110.666 q^{77} -2987.40 q^{78} +1209.78 q^{79} +2017.78 q^{80} +1493.72 q^{81} -1947.77 q^{82} -1337.89 q^{83} -820.089 q^{84} +1487.66 q^{85} -911.857 q^{86} +2288.31 q^{87} +1263.50 q^{88} +657.497 q^{89} -5051.70 q^{90} -288.617 q^{91} +3276.92 q^{92} +887.860 q^{93} +228.197 q^{94} -1830.05 q^{95} +2186.63 q^{96} -1130.46 q^{97} +1650.01 q^{98} -1472.40 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q + 17 q^{2} + 25 q^{3} + 601 q^{4} + 50 q^{5} + 61 q^{6} + 223 q^{7} + 207 q^{8} + 1443 q^{9}+O(q^{10}) \) 136 * q + 17 * q^2 + 25 * q^3 + 601 * q^4 + 50 * q^5 + 61 * q^6 + 223 * q^7 + 207 * q^8 + 1443 * q^9	\( 136 q + 17 q^{2} + 25 q^{3} + 601 q^{4} + 50 q^{5} + 61 q^{6} + 223 q^{7} + 207 q^{8} + 1443 q^{9} + 257 q^{10} + 204 q^{11} + 296 q^{12} + 530 q^{13} + 103 q^{14} + 226 q^{15} + 2737 q^{16} + 664 q^{17} + 949 q^{18} + 421 q^{19} + 500 q^{20} + 684 q^{21} + 905 q^{22} + 617 q^{23} + 917 q^{24} + 5430 q^{25} + 572 q^{26} + 886 q^{27} + 2728 q^{28} + 688 q^{29} + 712 q^{30} + 1019 q^{31} + 2363 q^{32} + 1764 q^{33} + 1260 q^{34} + 834 q^{35} + 7190 q^{36} + 3303 q^{37} + 384 q^{38} + 1950 q^{39} + 2766 q^{40} + 1975 q^{41} + 448 q^{42} + 3021 q^{43} + 2038 q^{44} + 2266 q^{45} + 2742 q^{46} + 1293 q^{47} + 2589 q^{48} + 10447 q^{49} + 2191 q^{50} + 1032 q^{51} + 4983 q^{52} + 2415 q^{53} + 1878 q^{54} + 2612 q^{55} + 1540 q^{56} + 7908 q^{57} + 5743 q^{58} + 1059 q^{59} + 2611 q^{60} + 4312 q^{61} + 3258 q^{62} + 5605 q^{63} + 13735 q^{64} + 3554 q^{65} + 433 q^{66} + 5715 q^{67} + 5881 q^{68} + 1398 q^{69} + 4287 q^{70} + 2530 q^{71} + 9891 q^{72} + 14106 q^{73} + 2318 q^{74} + 2621 q^{75} + 4651 q^{76} + 4750 q^{77} + 6639 q^{78} + 4791 q^{79} + 4812 q^{80} + 19932 q^{81} + 5380 q^{82} + 4284 q^{83} + 9282 q^{84} + 12058 q^{85} + 2451 q^{86} + 6984 q^{87} + 11197 q^{88} + 5313 q^{89} + 5405 q^{90} + 6298 q^{91} + 6588 q^{92} + 5700 q^{93} + 4743 q^{94} + 5778 q^{95} + 9613 q^{96} + 15382 q^{97} + 6640 q^{98} + 8542 q^{99}+O(q^{100}) \) 136 * q + 17 * q^2 + 25 * q^3 + 601 * q^4 + 50 * q^5 + 61 * q^6 + 223 * q^7 + 207 * q^8 + 1443 * q^9 + 257 * q^10 + 204 * q^11 + 296 * q^12 + 530 * q^13 + 103 * q^14 + 226 * q^15 + 2737 * q^16 + 664 * q^17 + 949 * q^18 + 421 * q^19 + 500 * q^20 + 684 * q^21 + 905 * q^22 + 617 * q^23 + 917 * q^24 + 5430 * q^25 + 572 * q^26 + 886 * q^27 + 2728 * q^28 + 688 * q^29 + 712 * q^30 + 1019 * q^31 + 2363 * q^32 + 1764 * q^33 + 1260 * q^34 + 834 * q^35 + 7190 * q^36 + 3303 * q^37 + 384 * q^38 + 1950 * q^39 + 2766 * q^40 + 1975 * q^41 + 448 * q^42 + 3021 * q^43 + 2038 * q^44 + 2266 * q^45 + 2742 * q^46 + 1293 * q^47 + 2589 * q^48 + 10447 * q^49 + 2191 * q^50 + 1032 * q^51 + 4983 * q^52 + 2415 * q^53 + 1878 * q^54 + 2612 * q^55 + 1540 * q^56 + 7908 * q^57 + 5743 * q^58 + 1059 * q^59 + 2611 * q^60 + 4312 * q^61 + 3258 * q^62 + 5605 * q^63 + 13735 * q^64 + 3554 * q^65 + 433 * q^66 + 5715 * q^67 + 5881 * q^68 + 1398 * q^69 + 4287 * q^70 + 2530 * q^71 + 9891 * q^72 + 14106 * q^73 + 2318 * q^74 + 2621 * q^75 + 4651 * q^76 + 4750 * q^77 + 6639 * q^78 + 4791 * q^79 + 4812 * q^80 + 19932 * q^81 + 5380 * q^82 + 4284 * q^83 + 9282 * q^84 + 12058 * q^85 + 2451 * q^86 + 6984 * q^87 + 11197 * q^88 + 5313 * q^89 + 5405 * q^90 + 6298 * q^91 + 6588 * q^92 + 5700 * q^93 + 4743 * q^94 + 5778 * q^95 + 9613 * q^96 + 15382 * q^97 + 6640 * q^98 + 8542 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more