LMFDB - Embedded newform 983.4.a.b.1.18

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			1.18
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)

$f(q)$	$=$	$q-4.27714 q^{2} +9.48940 q^{3} +10.2939 q^{4} -14.7336 q^{5} -40.5875 q^{6} +26.9751 q^{7} -9.81140 q^{8} +63.0488 q^{9} +O(q^{10})$	\(q-4.27714 q^{2} +9.48940 q^{3} +10.2939 q^{4} -14.7336 q^{5} -40.5875 q^{6} +26.9751 q^{7} -9.81140 q^{8} +63.0488 q^{9} +63.0176 q^{10} -12.3523 q^{11} +97.6831 q^{12} +84.6449 q^{13} -115.376 q^{14} -139.813 q^{15} -40.3866 q^{16} +67.6093 q^{17} -269.668 q^{18} +102.840 q^{19} -151.666 q^{20} +255.978 q^{21} +52.8326 q^{22} +179.626 q^{23} -93.1043 q^{24} +92.0786 q^{25} -362.038 q^{26} +342.081 q^{27} +277.680 q^{28} -203.664 q^{29} +597.999 q^{30} -61.4065 q^{31} +251.230 q^{32} -117.216 q^{33} -289.174 q^{34} -397.441 q^{35} +649.019 q^{36} -185.774 q^{37} -439.859 q^{38} +803.230 q^{39} +144.557 q^{40} -159.713 q^{41} -1094.85 q^{42} +52.6030 q^{43} -127.154 q^{44} -928.935 q^{45} -768.284 q^{46} -221.920 q^{47} -383.245 q^{48} +384.659 q^{49} -393.833 q^{50} +641.572 q^{51} +871.328 q^{52} -369.839 q^{53} -1463.13 q^{54} +181.994 q^{55} -264.664 q^{56} +975.886 q^{57} +871.100 q^{58} +412.393 q^{59} -1439.22 q^{60} -302.082 q^{61} +262.644 q^{62} +1700.75 q^{63} -751.454 q^{64} -1247.12 q^{65} +501.350 q^{66} +523.886 q^{67} +695.964 q^{68} +1704.54 q^{69} +1699.91 q^{70} +48.6325 q^{71} -618.597 q^{72} +869.802 q^{73} +794.579 q^{74} +873.771 q^{75} +1058.62 q^{76} -333.206 q^{77} -3435.53 q^{78} -1107.59 q^{79} +595.040 q^{80} +1543.83 q^{81} +683.116 q^{82} -1427.19 q^{83} +2635.02 q^{84} -996.127 q^{85} -224.990 q^{86} -1932.65 q^{87} +121.194 q^{88} +1169.08 q^{89} +3973.18 q^{90} +2283.31 q^{91} +1849.05 q^{92} -582.711 q^{93} +949.181 q^{94} -1515.20 q^{95} +2384.03 q^{96} +136.084 q^{97} -1645.24 q^{98} -778.799 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.27714	−1.51220	−0.756098	−	0.654458i	$-0.772897\pi$
$2$	−4.27714	−1.51220	−0.756098	+	0.654458i	$0.772897\pi$
$3$	9.48940	1.82624	0.913118	−	0.407695i	$-0.133667\pi$
$3$	9.48940	1.82624	0.913118	+	0.407695i	$0.133667\pi$
$4$	10.2939	1.28674
$5$	−14.7336	−1.31781	−0.658906	−	0.752225i	$-0.728981\pi$
$5$	−14.7336	−1.31781	−0.658906	+	0.752225i	$0.728981\pi$
$6$	−40.5875	−2.76163
$7$	26.9751	1.45652	0.728261	−	0.685300i	$-0.240329\pi$
$7$	26.9751	1.45652	0.728261	+	0.685300i	$0.240329\pi$
$8$	−9.81140	−0.433607
$9$	63.0488	2.33514
$10$	63.0176	1.99279
$11$	−12.3523	−0.338579	−0.169289	−	0.985566i	$-0.554147\pi$
$11$	−12.3523	−0.338579	−0.169289	+	0.985566i	$0.554147\pi$
$12$	97.6831	2.34989
$13$	84.6449	1.80587	0.902934	−	0.429779i	$-0.141409\pi$
$13$	84.6449	1.80587	0.902934	+	0.429779i	$0.141409\pi$
$14$	−115.376	−2.20255
$15$	−139.813	−2.40664
$16$	−40.3866	−0.631041
$17$	67.6093	0.964568	0.482284	−	0.876015i	$-0.339807\pi$
$17$	67.6093	0.964568	0.482284	+	0.876015i	$0.339807\pi$
$18$	−269.668	−3.53119
$19$	102.840	1.24174	0.620869	−	0.783915i	$-0.286780\pi$
$19$	102.840	1.24174	0.620869	+	0.783915i	$0.286780\pi$
$20$	−151.666	−1.69568
$21$	255.978	2.65995
$22$	52.8326	0.511998
$23$	179.626	1.62846	0.814230	−	0.580543i	$-0.197160\pi$
$23$	179.626	1.62846	0.814230	+	0.580543i	$0.197160\pi$
$24$	−93.1043	−0.791869
$25$	92.0786	0.736629
$26$	−362.038	−2.73083
$27$	342.081	2.43828
$28$	277.680	1.87416
$29$	−203.664	−1.30412	−0.652060	−	0.758167i	$-0.726095\pi$
$29$	−203.664	−1.30412	−0.652060	+	0.758167i	$0.726095\pi$
$30$	597.999	3.63931
$31$	−61.4065	−0.355772	−0.177886	−	0.984051i	$-0.556926\pi$
$31$	−61.4065	−0.355772	−0.177886	+	0.984051i	$0.556926\pi$
$32$	251.230	1.38786
$33$	−117.216	−0.618325
$34$	−289.174	−1.45862
$35$	−397.441	−1.91942
$36$	649.019	3.00472
$37$	−185.774	−0.825432	−0.412716	−	0.910860i	$-0.635420\pi$
$37$	−185.774	−0.825432	−0.412716	+	0.910860i	$0.635420\pi$
$38$	−439.859	−1.87775
$39$	803.230	3.29794
$40$	144.557	0.571412
$41$	−159.713	−0.608367	−0.304183	−	0.952614i	$-0.598384\pi$
$41$	−159.713	−0.608367	−0.304183	+	0.952614i	$0.598384\pi$
$42$	−1094.85	−4.02237
$43$	52.6030	0.186555	0.0932776	−	0.995640i	$-0.470266\pi$
$43$	52.6030	0.186555	0.0932776	+	0.995640i	$0.470266\pi$
$44$	−127.154	−0.435663
$45$	−928.935	−3.07728
$46$	−768.284	−2.46255
$47$	−221.920	−0.688730	−0.344365	−	0.938836i	$-0.611906\pi$
$47$	−221.920	−0.688730	−0.344365	+	0.938836i	$0.611906\pi$
$48$	−383.245	−1.15243
$49$	384.659	1.12145
$50$	−393.833	−1.11393
$51$	641.572	1.76153
$52$	871.328	2.32368
$53$	−369.839	−0.958515	−0.479258	−	0.877674i	$-0.659094\pi$
$53$	−369.839	−0.958515	−0.479258	+	0.877674i	$0.659094\pi$
$54$	−1463.13	−3.68716
$55$	181.994	0.446183
$56$	−264.664	−0.631557
$57$	975.886	2.26771
$58$	871.100	1.97209
$59$	412.393	0.909982	0.454991	−	0.890496i	$-0.349642\pi$
$59$	412.393	0.909982	0.454991	+	0.890496i	$0.349642\pi$
$60$	−1439.22	−3.09671
$61$	−302.082	−0.634059	−0.317030	−	0.948416i	$-0.602685\pi$
$61$	−302.082	−0.634059	−0.317030	+	0.948416i	$0.602685\pi$
$62$	262.644	0.537998
$63$	1700.75	3.40118
$64$	−751.454	−1.46768
$65$	−1247.12	−2.37979
$66$	501.350	0.935029
$67$	523.886	0.955266	0.477633	−	0.878559i	$-0.341495\pi$
$67$	523.886	0.955266	0.477633	+	0.878559i	$0.341495\pi$
$68$	695.964	1.24115
$69$	1704.54	2.97395
$70$	1699.91	2.90254
$71$	48.6325	0.0812904	0.0406452	−	0.999174i	$-0.487059\pi$
$71$	48.6325	0.0812904	0.0406452	+	0.999174i	$0.487059\pi$
$72$	−618.597	−1.01253
$73$	869.802	1.39456	0.697278	−	0.716801i	$-0.254394\pi$
$73$	869.802	1.39456	0.697278	+	0.716801i	$0.254394\pi$
$74$	794.579	1.24822
$75$	873.771	1.34526
$76$	1058.62	1.59779
$77$	−333.206	−0.493147
$78$	−3435.53	−4.98714
$79$	−1107.59	−1.57738	−0.788690	−	0.614791i	$-0.789241\pi$
$79$	−1107.59	−1.57738	−0.788690	+	0.614791i	$0.789241\pi$
$80$	595.040	0.831593
$81$	1543.83	2.11774
$82$	683.116	0.919970
$83$	−1427.19	−1.88740	−0.943701	−	0.330801i	$-0.892681\pi$
$83$	−1427.19	−1.88740	−0.943701	+	0.330801i	$0.892681\pi$
$84$	2635.02	3.42267
$85$	−996.127	−1.27112
$86$	−224.990	−0.282108
$87$	−1932.65	−2.38163
$88$	121.194	0.146810
$89$	1169.08	1.39238	0.696190	−	0.717858i	$-0.254877\pi$
$89$	1169.08	1.39238	0.696190	+	0.717858i	$0.254877\pi$
$90$	3973.18	4.65345
$91$	2283.31	2.63028
$92$	1849.05	2.09540
$93$	−582.711	−0.649724
$94$	949.181	1.04150
$95$	−1515.20	−1.63638
$96$	2384.03	2.53457
$97$	136.084	0.142445	0.0712227	−	0.997460i	$-0.477310\pi$
$97$	136.084	0.142445	0.0712227	+	0.997460i	$0.477310\pi$
$98$	−1645.24	−1.69586
$99$	−778.799	−0.790629
$100$	947.849	0.947849
$101$	−2.86121	−0.00281883	−0.00140941	−	0.999999i	$-0.500449\pi$
$101$	−2.86121	−0.00281883	−0.00140941	+	0.999999i	$0.500449\pi$
$102$	−2744.09	−2.66378
$103$	1301.78	1.24532	0.622661	−	0.782492i	$-0.286052\pi$
$103$	1301.78	1.24532	0.622661	+	0.782492i	$0.286052\pi$
$104$	−830.485	−0.783037
$105$	−3771.48	−3.50532
$106$	1581.85	1.44946
$107$	−188.812	−0.170590	−0.0852952	−	0.996356i	$-0.527183\pi$
$107$	−188.812	−0.170590	−0.0852952	+	0.996356i	$0.527183\pi$
$108$	3521.36	3.13743
$109$	1218.62	1.07085	0.535423	−	0.844584i	$-0.320152\pi$
$109$	1218.62	1.07085	0.535423	+	0.844584i	$0.320152\pi$
$110$	−778.414	−0.674717
$111$	−1762.88	−1.50743
$112$	−1089.43	−0.919124
$113$	−1067.41	−0.888618	−0.444309	−	0.895874i	$-0.646551\pi$
$113$	−1067.41	−0.888618	−0.444309	+	0.895874i	$0.646551\pi$
$114$	−4174.00	−3.42922
$115$	−2646.53	−2.14600
$116$	−2096.50	−1.67806
$117$	5336.76	4.21695
$118$	−1763.86	−1.37607
$119$	1823.77	1.40491
$120$	1371.76	1.04353
$121$	−1178.42	−0.885364
$122$	1292.05	0.958822
$123$	−1515.58	−1.11102
$124$	−632.114	−0.457786
$125$	485.050	0.347074
$126$	−7274.34	−5.14326
$127$	1153.05	0.805642	0.402821	−	0.915279i	$-0.368030\pi$
$127$	1153.05	0.805642	0.402821	+	0.915279i	$0.368030\pi$
$128$	1204.23	0.831563
$129$	499.171	0.340694
$130$	5334.12	3.59872
$131$	−1151.22	−0.767806	−0.383903	−	0.923373i	$-0.625420\pi$
$131$	−1151.22	−0.767806	−0.383903	+	0.923373i	$0.625420\pi$
$132$	−1206.61	−0.795623
$133$	2774.11	1.80862
$134$	−2240.73	−1.44455
$135$	−5040.09	−3.21320
$136$	−663.342	−0.418243
$137$	−623.254	−0.388673	−0.194336	−	0.980935i	$-0.562255\pi$
$137$	−623.254	−0.388673	−0.194336	+	0.980935i	$0.562255\pi$
$138$	−7290.56	−4.49720
$139$	−1114.77	−0.680243	−0.340122	−	0.940381i	$-0.610468\pi$
$139$	−1114.77	−0.680243	−0.340122	+	0.940381i	$0.610468\pi$
$140$	−4091.22	−2.46980
$141$	−2105.88	−1.25778
$142$	−208.008	−0.122927
$143$	−1045.56	−0.611429
$144$	−2546.33	−1.47357
$145$	3000.70	1.71859
$146$	−3720.26	−2.10884
$147$	3650.18	2.04804
$148$	−1912.34	−1.06212
$149$	−2867.44	−1.57657	−0.788287	−	0.615307i	$-0.789032\pi$
$149$	−2867.44	−1.57657	−0.788287	+	0.615307i	$0.789032\pi$
$150$	−3737.24	−2.03430
$151$	3164.66	1.70554	0.852769	−	0.522288i	$-0.174922\pi$
$151$	3164.66	1.70554	0.852769	+	0.522288i	$0.174922\pi$
$152$	−1009.00	−0.538426
$153$	4262.68	2.25240
$154$	1425.17	0.745736
$155$	904.738	0.468841
$156$	8268.38	4.24359
$157$	−2708.97	−1.37707	−0.688533	−	0.725205i	$-0.741745\pi$
$157$	−2708.97	−1.37707	−0.688533	+	0.725205i	$0.741745\pi$
$158$	4737.30	2.38531
$159$	−3509.55	−1.75048
$160$	−3701.52	−1.82894
$161$	4845.43	2.37188
$162$	−6603.18	−3.20244
$163$	−3770.23	−1.81170	−0.905851	−	0.423597i	$-0.860767\pi$
$163$	−3770.23	−1.81170	−0.905851	+	0.423597i	$0.860767\pi$
$164$	−1644.08	−0.782809
$165$	1727.02	0.814836
$166$	6104.28	2.85412
$167$	382.909	0.177427	0.0887137	−	0.996057i	$-0.471724\pi$
$167$	382.909	0.177427	0.0887137	+	0.996057i	$0.471724\pi$
$168$	−2511.50	−1.15337
$169$	4967.77	2.26116
$170$	4260.57	1.92218
$171$	6483.91	2.89963
$172$	541.490	0.240048
$173$	−2205.67	−0.969328	−0.484664	−	0.874700i	$-0.661058\pi$
$173$	−2205.67	−0.969328	−0.484664	+	0.874700i	$0.661058\pi$
$174$	8266.22	3.60150
$175$	2483.83	1.07292
$176$	498.869	0.213657
$177$	3913.36	1.66184
$178$	−5000.30	−2.10555
$179$	2675.31	1.11710	0.558552	−	0.829469i	$-0.311357\pi$
$179$	2675.31	1.11710	0.558552	+	0.829469i	$0.311357\pi$
$180$	−9562.38	−3.95965
$181$	3323.79	1.36495	0.682474	−	0.730910i	$-0.260904\pi$
$181$	3323.79	1.36495	0.682474	+	0.730910i	$0.260904\pi$
$182$	−9766.03	−3.97751
$183$	−2866.58	−1.15794
$184$	−1762.38	−0.706111
$185$	2737.11	1.08776
$186$	2492.34	0.982511
$187$	−835.132	−0.326582
$188$	−2284.42	−0.886216
$189$	9227.70	3.55141
$190$	6480.70	2.47452
$191$	2511.12	0.951301	0.475651	−	0.879634i	$-0.342213\pi$
$191$	2511.12	0.951301	0.475651	+	0.879634i	$0.342213\pi$
$192$	−7130.85	−2.68034
$193$	2847.22	1.06190	0.530951	−	0.847402i	$-0.321835\pi$
$193$	2847.22	1.06190	0.530951	+	0.847402i	$0.321835\pi$
$194$	−582.049	−0.215405
$195$	−11834.5	−4.34607
$196$	3959.64	1.44302
$197$	1965.24	0.710749	0.355374	−	0.934724i	$-0.384353\pi$
$197$	1965.24	0.710749	0.355374	+	0.934724i	$0.384353\pi$
$198$	3331.03	1.19559
$199$	−224.604	−0.0800087	−0.0400044	−	0.999200i	$-0.512737\pi$
$199$	−224.604	−0.0800087	−0.0400044	+	0.999200i	$0.512737\pi$
$200$	−903.420	−0.319407
$201$	4971.36	1.74454
$202$	12.2378	0.00426262
$203$	−5493.87	−1.89948
$204$	6604.29	2.26663
$205$	2353.15	0.801713
$206$	−5567.89	−1.88317
$207$	11325.2	3.80268
$208$	−3418.52	−1.13958
$209$	−1270.31	−0.420426
$210$	16131.1	5.30073
$211$	−1066.32	−0.347906	−0.173953	−	0.984754i	$-0.555654\pi$
$211$	−1066.32	−0.347906	−0.173953	+	0.984754i	$0.555654\pi$
$212$	−3807.09	−1.23336
$213$	461.494	0.148455
$214$	807.576	0.257966
$215$	−775.030	−0.245845
$216$	−3356.30	−1.05726
$217$	−1656.45	−0.518190
$218$	−5212.19	−1.61933
$219$	8253.90	2.54679
$220$	1873.43	0.574122
$221$	5722.78	1.74188
$222$	7540.08	2.27954
$223$	−2065.00	−0.620101	−0.310051	−	0.950720i	$-0.600346\pi$
$223$	−2065.00	−0.620101	−0.310051	+	0.950720i	$0.600346\pi$
$224$	6776.98	2.02145
$225$	5805.44	1.72013
$226$	4565.48	1.34377
$227$	5107.43	1.49336	0.746678	−	0.665185i	$-0.231647\pi$
$227$	5107.43	1.49336	0.746678	+	0.665185i	$0.231647\pi$
$228$	10045.7	2.91795
$229$	−2917.20	−0.841807	−0.420904	−	0.907105i	$-0.638287\pi$
$229$	−2917.20	−0.841807	−0.420904	+	0.907105i	$0.638287\pi$
$230$	11319.6	3.24518
$231$	−3161.93	−0.900604
$232$	1998.23	0.565475
$233$	−4131.14	−1.16155	−0.580773	−	0.814066i	$-0.697250\pi$
$233$	−4131.14	−1.16155	−0.580773	+	0.814066i	$0.697250\pi$
$234$	−22826.1	−6.37687
$235$	3269.67	0.907616
$236$	4245.14	1.17091
$237$	−10510.3	−2.88067
$238$	−7800.52	−2.12451
$239$	−1117.16	−0.302357	−0.151179	−	0.988506i	$-0.548307\pi$
$239$	−1117.16	−0.302357	−0.151179	+	0.988506i	$0.548307\pi$
$240$	5646.57	1.51869
$241$	−1445.53	−0.386368	−0.193184	−	0.981163i	$-0.561881\pi$
$241$	−1445.53	−0.386368	−0.193184	+	0.981163i	$0.561881\pi$
$242$	5040.27	1.33885
$243$	5413.85	1.42921
$244$	−3109.60	−0.815869
$245$	−5667.40	−1.47787
$246$	6482.36	1.68008
$247$	8704.85	2.24241
$248$	602.484	0.154265
$249$	−13543.2	−3.44684
$250$	−2074.63	−0.524844
$251$	−3019.57	−0.759338	−0.379669	−	0.925122i	$-0.623962\pi$
$251$	−3019.57	−0.759338	−0.379669	+	0.925122i	$0.623962\pi$
$252$	17507.4	4.37643
$253$	−2218.80	−0.551362
$254$	−4931.75	−1.21829
$255$	−9452.65	−2.32137
$256$	860.970	0.210198
$257$	4942.98	1.19975	0.599873	−	0.800095i	$-0.295218\pi$
$257$	4942.98	1.19975	0.599873	+	0.800095i	$0.295218\pi$
$258$	−2135.02	−0.515196
$259$	−5011.27	−1.20226
$260$	−12837.8	−3.06218
$261$	−12840.8	−3.04530
$262$	4923.93	1.16107
$263$	−1498.31	−0.351292	−0.175646	−	0.984453i	$-0.556201\pi$
$263$	−1498.31	−0.351292	−0.175646	+	0.984453i	$0.556201\pi$
$264$	1150.06	0.268110
$265$	5449.06	1.26314
$266$	−11865.3	−2.73498
$267$	11093.8	2.54282
$268$	5392.84	1.22918
$269$	5684.47	1.28843	0.644216	−	0.764844i	$-0.277184\pi$
$269$	5684.47	1.28843	0.644216	+	0.764844i	$0.277184\pi$
$270$	21557.2	4.85899
$271$	4604.27	1.03206	0.516032	−	0.856569i	$-0.327409\pi$
$271$	4604.27	1.03206	0.516032	+	0.856569i	$0.327409\pi$
$272$	−2730.51	−0.608682
$273$	21667.2	4.80352
$274$	2665.74	0.587750
$275$	−1137.39	−0.249407
$276$	17546.4	3.82670
$277$	−9081.72	−1.96992	−0.984959	−	0.172786i	$-0.944723\pi$
$277$	−9081.72	−1.96992	−0.984959	+	0.172786i	$0.944723\pi$
$278$	4768.04	1.02866
$279$	−3871.61	−0.830778
$280$	3899.45	0.832274
$281$	1882.61	0.399670	0.199835	−	0.979830i	$-0.435959\pi$
$281$	1882.61	0.399670	0.199835	+	0.979830i	$0.435959\pi$
$282$	9007.16	1.90202
$283$	−1129.06	−0.237157	−0.118578	−	0.992945i	$-0.537834\pi$
$283$	−1129.06	−0.237157	−0.118578	+	0.992945i	$0.537834\pi$
$284$	500.619	0.104600
$285$	−14378.3	−2.98841
$286$	4472.02	0.924601
$287$	−4308.29	−0.886099
$288$	15839.8	3.24086
$289$	−341.985	−0.0696083
$290$	−12834.4	−2.59884
$291$	1291.35	0.260139
$292$	8953.66	1.79443
$293$	−4226.06	−0.842625	−0.421312	−	0.906916i	$-0.638430\pi$
$293$	−4226.06	−0.842625	−0.421312	+	0.906916i	$0.638430\pi$
$294$	−15612.3	−3.09704
$295$	−6076.02	−1.19919
$296$	1822.70	0.357913
$297$	−4225.50	−0.825551
$298$	12264.4	2.38409
$299$	15204.4	2.94078
$300$	8994.53	1.73100
$301$	1418.97	0.271722
$302$	−13535.7	−2.57911
$303$	−27.1512	−0.00514784
$304$	−4153.34	−0.783587
$305$	4450.75	0.835571
$306$	−18232.1	−3.40608
$307$	10083.5	1.87458	0.937292	−	0.348545i	$-0.113324\pi$
$307$	10083.5	1.87458	0.937292	+	0.348545i	$0.113324\pi$
$308$	−3429.99	−0.634552
$309$	12353.1	2.27425
$310$	−3869.69	−0.708980
$311$	−497.371	−0.0906859	−0.0453429	−	0.998971i	$-0.514438\pi$
$311$	−497.371	−0.0906859	−0.0453429	+	0.998971i	$0.514438\pi$
$312$	−7880.81	−1.43001
$313$	5888.41	1.06336	0.531682	−	0.846944i	$-0.321560\pi$
$313$	5888.41	1.06336	0.531682	+	0.846944i	$0.321560\pi$
$314$	11586.6	2.08239
$315$	−25058.2	−4.48212
$316$	−11401.4	−2.02968
$317$	10861.9	1.92450	0.962252	−	0.272160i	$-0.0877381\pi$
$317$	10861.9	1.92450	0.962252	+	0.272160i	$0.0877381\pi$
$318$	15010.8	2.64706
$319$	2515.73	0.441547
$320$	11071.6	1.93413
$321$	−1791.72	−0.311538
$322$	−20724.6	−3.58676
$323$	6952.91	1.19774
$324$	15892.1	2.72498
$325$	7793.99	1.33025
$326$	16125.8	2.73965
$327$	11563.9	1.95562
$328$	1567.01	0.263792
$329$	−5986.31	−1.00315
$330$	−7386.69	−1.23219
$331$	−49.8544	−0.00827868	−0.00413934	−	0.999991i	$-0.501318\pi$
$331$	−49.8544	−0.00827868	−0.00413934	+	0.999991i	$0.501318\pi$
$332$	−14691.4	−2.42859
$333$	−11712.8	−1.92750
$334$	−1637.75	−0.268305
$335$	−7718.72	−1.25886
$336$	−10338.1	−1.67854
$337$	1905.56	0.308020	0.154010	−	0.988069i	$-0.450781\pi$
$337$	1905.56	0.308020	0.154010	+	0.988069i	$0.450781\pi$
$338$	−21247.8	−3.41932
$339$	−10129.1	−1.62283
$340$	−10254.1	−1.63560
$341$	758.514	0.120457
$342$	−27732.6	−4.38481
$343$	1123.75	0.176900
$344$	−516.109	−0.0808916
$345$	−25114.0	−3.91911
$346$	9433.95	1.46582
$347$	−558.565	−0.0864131	−0.0432065	−	0.999066i	$-0.513757\pi$
$347$	−558.565	−0.0864131	−0.0432065	+	0.999066i	$0.513757\pi$
$348$	−19894.5	−3.06454
$349$	−5894.50	−0.904084	−0.452042	−	0.891997i	$-0.649304\pi$
$349$	−5894.50	−0.904084	−0.452042	+	0.891997i	$0.649304\pi$
$350$	−10623.7	−1.62246
$351$	28955.5	4.40322
$352$	−3103.28	−0.469902
$353$	−3824.87	−0.576706	−0.288353	−	0.957524i	$-0.593108\pi$
$353$	−3824.87	−0.576706	−0.288353	+	0.957524i	$0.593108\pi$
$354$	−16738.0	−2.51303
$355$	−716.531	−0.107125
$356$	12034.4	1.79163
$357$	17306.5	2.56571
$358$	−11442.7	−1.68928
$359$	7655.79	1.12551	0.562754	−	0.826625i	$-0.309742\pi$
$359$	7655.79	1.12551	0.562754	+	0.826625i	$0.309742\pi$
$360$	9114.15	1.33433
$361$	3716.97	0.541912
$362$	−14216.3	−2.06407
$363$	−11182.5	−1.61688
$364$	23504.2	3.38449
$365$	−12815.3	−1.83776
$366$	12260.7	1.75104
$367$	2113.61	0.300625	0.150313	−	0.988639i	$-0.451972\pi$
$367$	2113.61	0.300625	0.150313	+	0.988639i	$0.451972\pi$
$368$	−7254.48	−1.02762
$369$	−10069.7	−1.42062
$370$	−11707.0	−1.64491
$371$	−9976.46	−1.39610
$372$	−5998.38	−0.836026
$373$	1780.63	0.247179	0.123589	−	0.992333i	$-0.460559\pi$
$373$	1780.63	0.247179	0.123589	+	0.992333i	$0.460559\pi$
$374$	3571.98	0.493857
$375$	4602.84	0.633839
$376$	2177.34	0.298638
$377$	−17239.1	−2.35507
$378$	−39468.1	−5.37043
$379$	−1048.32	−0.142080	−0.0710400	−	0.997473i	$-0.522632\pi$
$379$	−1048.32	−0.142080	−0.0710400	+	0.997473i	$0.522632\pi$
$380$	−15597.3	−2.10559
$381$	10941.7	1.47129
$382$	−10740.4	−1.43855
$383$	10647.0	1.42046	0.710228	−	0.703972i	$-0.248592\pi$
$383$	10647.0	1.42046	0.710228	+	0.703972i	$0.248592\pi$
$384$	11427.4	1.51863
$385$	4909.32	0.649875
$386$	−12177.9	−1.60581
$387$	3316.55	0.435633
$388$	1400.83	0.183290
$389$	−11239.6	−1.46496	−0.732482	−	0.680786i	$-0.761638\pi$
$389$	−11239.6	−1.46496	−0.732482	+	0.680786i	$0.761638\pi$
$390$	50617.6	6.57211
$391$	12144.4	1.57076
$392$	−3774.04	−0.486270
$393$	−10924.4	−1.40220
$394$	−8405.60	−1.07479
$395$	16318.7	2.07869
$396$	−8016.90	−1.01733
$397$	3971.38	0.502060	0.251030	−	0.967979i	$-0.419231\pi$
$397$	3971.38	0.502060	0.251030	+	0.967979i	$0.419231\pi$
$398$	960.661	0.120989
$399$	26324.7	3.30296
$400$	−3718.74	−0.464843
$401$	6149.65	0.765833	0.382916	−	0.923783i	$-0.374920\pi$
$401$	6149.65	0.765833	0.382916	+	0.923783i	$0.374920\pi$
$402$	−21263.2	−2.63809
$403$	−5197.75	−0.642478
$404$	−29.4531	−0.00362710
$405$	−22746.2	−2.79078
$406$	23498.0	2.87238
$407$	2294.74	0.279474
$408$	−6294.72	−0.763811
$409$	7419.25	0.896964	0.448482	−	0.893792i	$-0.351965\pi$
$409$	7419.25	0.896964	0.448482	+	0.893792i	$0.351965\pi$
$410$	−10064.8	−1.21235
$411$	−5914.30	−0.709808
$412$	13400.4	1.60240
$413$	11124.4	1.32541
$414$	−48439.4	−5.75040
$415$	21027.6	2.48724
$416$	21265.4	2.50630
$417$	−10578.5	−1.24229
$418$	5433.28	0.635767
$419$	−3310.69	−0.386009	−0.193005	−	0.981198i	$-0.561823\pi$
$419$	−3310.69	−0.386009	−0.193005	+	0.981198i	$0.561823\pi$
$420$	−38823.3	−4.51043
$421$	−3875.17	−0.448609	−0.224305	−	0.974519i	$-0.572011\pi$
$421$	−3875.17	−0.448609	−0.224305	+	0.974519i	$0.572011\pi$
$422$	4560.78	0.526103
$423$	−13991.8	−1.60828
$424$	3628.64	0.415619
$425$	6225.37	0.710529
$426$	−1973.87	−0.224494
$427$	−8148.70	−0.923520
$428$	−1943.62	−0.219505
$429$	−9921.76	−1.11661
$430$	3314.91	0.371766
$431$	8223.59	0.919063	0.459532	−	0.888161i	$-0.348017\pi$
$431$	8223.59	0.919063	0.459532	+	0.888161i	$0.348017\pi$
$432$	−13815.5	−1.53866
$433$	−10793.6	−1.19794	−0.598971	−	0.800770i	$-0.704424\pi$
$433$	−10793.6	−1.19794	−0.598971	+	0.800770i	$0.704424\pi$
$434$	7084.87	0.783605
$435$	28474.9	3.13854
$436$	12544.3	1.37790
$437$	18472.6	2.02212
$438$	−35303.1	−3.85125
$439$	−10099.0	−1.09795	−0.548976	−	0.835838i	$-0.684982\pi$
$439$	−10099.0	−1.09795	−0.548976	+	0.835838i	$0.684982\pi$
$440$	−1785.62	−0.193468
$441$	24252.3	2.61875
$442$	−24477.1	−2.63407
$443$	7894.23	0.846650	0.423325	−	0.905978i	$-0.360863\pi$
$443$	7894.23	0.846650	0.423325	+	0.905978i	$0.360863\pi$
$444$	−18146.9	−1.93967
$445$	−17224.7	−1.83490
$446$	8832.29	0.937715
$447$	−27210.3	−2.87920
$448$	−20270.6	−2.13771
$449$	−11804.2	−1.24070	−0.620351	−	0.784324i	$-0.713010\pi$
$449$	−11804.2	−1.24070	−0.620351	+	0.784324i	$0.713010\pi$
$450$	−24830.7	−2.60118
$451$	1972.83	0.205980
$452$	−10987.9	−1.14342
$453$	30030.7	3.11472
$454$	−21845.2	−2.25825
$455$	−33641.3	−3.46622
$456$	−9574.81	−0.983293
$457$	−18260.7	−1.86915	−0.934574	−	0.355769i	$-0.884219\pi$
$457$	−18260.7	−1.86915	−0.934574	+	0.355769i	$0.884219\pi$
$458$	12477.3	1.27298
$459$	23127.9	2.35189
$460$	−27243.2	−2.76135
$461$	−7361.01	−0.743680	−0.371840	−	0.928297i	$-0.621273\pi$
$461$	−7361.01	−0.743680	−0.371840	+	0.928297i	$0.621273\pi$
$462$	13524.0	1.36189
$463$	−11496.3	−1.15395	−0.576974	−	0.816762i	$-0.695767\pi$
$463$	−11496.3	−1.15395	−0.576974	+	0.816762i	$0.695767\pi$
$464$	8225.30	0.822953
$465$	8585.43	0.856214
$466$	17669.5	1.75649
$467$	1634.32	0.161943	0.0809715	−	0.996716i	$-0.474198\pi$
$467$	1634.32	0.161943	0.0809715	+	0.996716i	$0.474198\pi$
$468$	54936.2	5.42612
$469$	14131.9	1.39137
$470$	−13984.8	−1.37249
$471$	−25706.5	−2.51485
$472$	−4046.15	−0.394574
$473$	−649.769	−0.0631637
$474$	44954.1	4.35614
$475$	9469.32	0.914700
$476$	18773.7	1.80776
$477$	−23317.9	−2.23827
$478$	4778.27	0.457223
$479$	1197.86	0.114262	0.0571310	−	0.998367i	$-0.481805\pi$
$479$	1197.86	0.114262	0.0571310	+	0.998367i	$0.481805\pi$
$480$	−35125.3	−3.34009
$481$	−15724.8	−1.49062
$482$	6182.72	0.584264
$483$	45980.3	4.33162
$484$	−12130.6	−1.13923
$485$	−2005.00	−0.187716
$486$	−23155.8	−2.16125
$487$	−17362.7	−1.61557	−0.807783	−	0.589481i	$-0.799332\pi$
$487$	−17362.7	−1.61557	−0.807783	+	0.589481i	$0.799332\pi$
$488$	2963.84	0.274932
$489$	−35777.3	−3.30860
$490$	24240.3	2.23482
$491$	11504.1	1.05738	0.528690	−	0.848815i	$-0.322683\pi$
$491$	11504.1	1.05738	0.528690	+	0.848815i	$0.322683\pi$
$492$	−15601.3	−1.42960
$493$	−13769.6	−1.25791
$494$	−37231.8	−3.39097
$495$	11474.5	1.04190
$496$	2480.00	0.224507
$497$	1311.87	0.118401
$498$	57926.0	5.21230
$499$	−13205.7	−1.18470	−0.592351	−	0.805680i	$-0.701800\pi$
$499$	−13205.7	−1.18470	−0.592351	+	0.805680i	$0.701800\pi$
$500$	4993.07	0.446594
$501$	3633.58	0.324024
$502$	12915.1	1.14827
$503$	−3277.09	−0.290493	−0.145247	−	0.989395i	$-0.546398\pi$
$503$	−3277.09	−0.290493	−0.145247	+	0.989395i	$0.546398\pi$
$504$	−16686.7	−1.47477
$505$	42.1560	0.00371468
$506$	9490.10	0.833768
$507$	47141.1	4.12941
$508$	11869.4	1.03665
$509$	12824.0	1.11673	0.558363	−	0.829597i	$-0.311430\pi$
$509$	12824.0	1.11673	0.558363	+	0.829597i	$0.311430\pi$
$510$	40430.3	3.51036
$511$	23463.0	2.03120
$512$	−13316.3	−1.14942
$513$	35179.5	3.02771
$514$	−21141.8	−1.81425
$515$	−19179.9	−1.64110
$516$	5138.42	0.438384
$517$	2741.22	0.233189
$518$	21433.9	1.81805
$519$	−20930.5	−1.77022
$520$	12236.0	1.03190
$521$	−18107.8	−1.52268	−0.761340	−	0.648353i	$-0.775458\pi$
$521$	−18107.8	−1.52268	−0.761340	+	0.648353i	$0.775458\pi$
$522$	54921.8	4.60510
$523$	10631.6	0.888887	0.444443	−	0.895807i	$-0.353402\pi$
$523$	10631.6	0.888887	0.444443	+	0.895807i	$0.353402\pi$
$524$	−11850.6	−0.987967
$525$	23570.1	1.95940
$526$	6408.49	0.531223
$527$	−4151.65	−0.343167
$528$	4733.97	0.390188
$529$	20098.4	1.65188
$530$	−23306.4	−1.91012
$531$	26000.9	2.12494
$532$	28556.5	2.32722
$533$	−13518.9	−1.09863
$534$	−47449.9	−3.84524
$535$	2781.88	0.224806
$536$	−5140.05	−0.414210
$537$	25387.1	2.04010
$538$	−24313.3	−1.94836
$539$	−4751.43	−0.379700
$540$	−51882.2	−4.13455
$541$	−9959.32	−0.791469	−0.395734	−	0.918365i	$-0.629510\pi$
$541$	−9959.32	−0.791469	−0.395734	+	0.918365i	$0.629510\pi$
$542$	−19693.1	−1.56068
$543$	31540.8	2.49272
$544$	16985.5	1.33869
$545$	−17954.6	−1.41117
$546$	−92673.8	−7.26387
$547$	−12237.6	−0.956569	−0.478284	−	0.878205i	$-0.658741\pi$
$547$	−12237.6	−0.956569	−0.478284	+	0.878205i	$0.658741\pi$
$548$	−6415.72	−0.500120
$549$	−19045.9	−1.48062
$550$	4864.75	0.377152
$551$	−20944.7	−1.61937
$552$	−16723.9	−1.28953
$553$	−29877.3	−2.29749
$554$	38843.8	2.97891
$555$	25973.5	1.98651
$556$	−11475.4	−0.875296
$557$	−21319.1	−1.62176	−0.810878	−	0.585215i	$-0.801010\pi$
$557$	−21319.1	−1.62176	−0.810878	+	0.585215i	$0.801010\pi$
$558$	16559.4	1.25630
$559$	4452.57	0.336894
$560$	16051.3	1.21123
$561$	−7924.91	−0.596417
$562$	−8052.20	−0.604380
$563$	−11136.6	−0.833662	−0.416831	−	0.908984i	$-0.636859\pi$
$563$	−11136.6	−0.833662	−0.416831	+	0.908984i	$0.636859\pi$
$564$	−21677.8	−1.61844
$565$	15726.8	1.17103
$566$	4829.13	0.358628
$567$	41645.1	3.08453
$568$	−477.153	−0.0352481
$569$	14885.0	1.09668	0.548339	−	0.836256i	$-0.315260\pi$
$569$	14885.0	1.09668	0.548339	+	0.836256i	$0.315260\pi$
$570$	61498.0	4.51907
$571$	16093.3	1.17948	0.589740	−	0.807593i	$-0.299230\pi$
$571$	16093.3	1.17948	0.589740	+	0.807593i	$0.299230\pi$
$572$	−10762.9	−0.786750
$573$	23829.1	1.73730
$574$	18427.2	1.33996
$575$	16539.7	1.19957
$576$	−47378.3	−3.42725
$577$	−19700.0	−1.42136	−0.710679	−	0.703517i	$-0.751612\pi$
$577$	−19700.0	−1.42136	−0.710679	+	0.703517i	$0.751612\pi$
$578$	1462.72	0.105261
$579$	27018.4	1.93929
$580$	30889.0	2.21137
$581$	−38498.6	−2.74904
$582$	−5523.29	−0.393381
$583$	4568.38	0.324533
$584$	−8533.97	−0.604689
$585$	−78629.6	−5.55715
$586$	18075.4	1.27421
$587$	4279.47	0.300907	0.150454	−	0.988617i	$-0.451927\pi$
$587$	4279.47	0.300907	0.150454	+	0.988617i	$0.451927\pi$
$588$	37574.7	2.63529
$589$	−6315.02	−0.441776
$590$	25988.0	1.81340
$591$	18648.9	1.29800
$592$	7502.76	0.520881
$593$	−7280.95	−0.504204	−0.252102	−	0.967701i	$-0.581122\pi$
$593$	−7280.95	−0.504204	−0.252102	+	0.967701i	$0.581122\pi$
$594$	18073.1	1.24840
$595$	−26870.7	−1.85141
$596$	−29517.2	−2.02864
$597$	−2131.36	−0.146115
$598$	−65031.4	−4.44704
$599$	−6407.48	−0.437066	−0.218533	−	0.975830i	$-0.570127\pi$
$599$	−6407.48	−0.437066	−0.218533	+	0.975830i	$0.570127\pi$
$600$	−8572.92	−0.583313
$601$	24092.1	1.63517	0.817587	−	0.575806i	$-0.195311\pi$
$601$	24092.1	1.63517	0.817587	+	0.575806i	$0.195311\pi$
$602$	−6069.14	−0.410897
$603$	33030.4	2.23068
$604$	32576.7	2.19458
$605$	17362.4	1.16674
$606$	116.130	0.00778456
$607$	−13981.5	−0.934913	−0.467457	−	0.884016i	$-0.654830\pi$
$607$	−13981.5	−0.934913	−0.467457	+	0.884016i	$0.654830\pi$
$608$	25836.4	1.72336
$609$	−52133.5	−3.46890
$610$	−19036.5	−1.26355
$611$	−18784.4	−1.24376
$612$	43879.7	2.89825
$613$	−1179.18	−0.0776945	−0.0388472	−	0.999245i	$-0.512369\pi$
$613$	−1179.18	−0.0776945	−0.0388472	+	0.999245i	$0.512369\pi$
$614$	−43128.6	−2.83474
$615$	22330.0	1.46412
$616$	3269.22	0.213832
$617$	1632.18	0.106498	0.0532490	−	0.998581i	$-0.483042\pi$
$617$	1632.18	0.106498	0.0532490	+	0.998581i	$0.483042\pi$
$618$	−52836.0	−3.43912
$619$	26723.2	1.73521	0.867605	−	0.497255i	$-0.165659\pi$
$619$	26723.2	1.73521	0.867605	+	0.497255i	$0.165659\pi$
$620$	9313.30	0.603276
$621$	61446.6	3.97064
$622$	2127.32	0.137135
$623$	31536.0	2.02803
$624$	−32439.7	−2.08114
$625$	−18656.4	−1.19401
$626$	−25185.6	−1.60801
$627$	−12054.5	−0.767797
$628$	−27885.9	−1.77192
$629$	−12560.0	−0.796185
$630$	107177.	6.77784
$631$	−3868.74	−0.244076	−0.122038	−	0.992525i	$-0.538943\pi$
$631$	−3868.74	−0.244076	−0.122038	+	0.992525i	$0.538943\pi$
$632$	10867.0	0.683963
$633$	−10118.7	−0.635359
$634$	−46458.1	−2.91023
$635$	−16988.5	−1.06168
$636$	−36127.0	−2.25241
$637$	32559.4	2.02520
$638$	−10760.1	−0.667707
$639$	3066.22	0.189824
$640$	−17742.6	−1.09584
$641$	−2299.27	−0.141678	−0.0708392	−	0.997488i	$-0.522568\pi$
$641$	−2299.27	−0.141678	−0.0708392	+	0.997488i	$0.522568\pi$
$642$	7663.41	0.471107
$643$	14601.2	0.895516	0.447758	−	0.894155i	$-0.352223\pi$
$643$	14601.2	0.895516	0.447758	+	0.894155i	$0.352223\pi$
$644$	49878.5	3.05200
$645$	−7354.57	−0.448971
$646$	−29738.6	−1.81122
$647$	−15672.4	−0.952310	−0.476155	−	0.879361i	$-0.657970\pi$
$647$	−15672.4	−0.952310	−0.476155	+	0.879361i	$0.657970\pi$
$648$	−15147.2	−0.918266
$649$	−5094.01	−0.308101
$650$	−33336.0	−2.01161
$651$	−15718.7	−0.946337
$652$	−38810.5	−2.33119
$653$	14447.1	0.865786	0.432893	−	0.901445i	$-0.357493\pi$
$653$	14447.1	0.865786	0.432893	+	0.901445i	$0.357493\pi$
$654$	−49460.5	−2.95728
$655$	16961.6	1.01182
$656$	6450.28	0.383904
$657$	54839.9	3.25648
$658$	25604.3	1.51696
$659$	−5353.33	−0.316444	−0.158222	−	0.987404i	$-0.550576\pi$
$659$	−5353.33	−0.316444	−0.158222	+	0.987404i	$0.550576\pi$
$660$	17777.8	1.04848
$661$	−18140.4	−1.06744	−0.533722	−	0.845660i	$-0.679207\pi$
$661$	−18140.4	−1.06744	−0.533722	+	0.845660i	$0.679207\pi$
$662$	213.234	0.0125190
$663$	54305.8	3.18109
$664$	14002.7	0.818390
$665$	−40872.6	−2.38342
$666$	50097.3	2.91476
$667$	−36583.3	−2.12371
$668$	3941.63	0.228303
$669$	−19595.6	−1.13245
$670$	33014.0	1.90365
$671$	3731.41	0.214679
$672$	64309.5	3.69165
$673$	−15720.0	−0.900390	−0.450195	−	0.892930i	$-0.648646\pi$
$673$	−15720.0	−0.900390	−0.450195	+	0.892930i	$0.648646\pi$
$674$	−8150.36	−0.465787
$675$	31498.4	1.79611
$676$	51137.8	2.90952
$677$	−5659.65	−0.321297	−0.160648	−	0.987012i	$-0.551359\pi$
$677$	−5659.65	−0.321297	−0.160648	+	0.987012i	$0.551359\pi$
$678$	43323.6	2.45403
$679$	3670.88	0.207475
$680$	9773.40	0.551166
$681$	48466.4	2.72722
$682$	−3244.27	−0.182155
$683$	12097.5	0.677744	0.338872	−	0.940833i	$-0.389955\pi$
$683$	12097.5	0.677744	0.338872	+	0.940833i	$0.389955\pi$
$684$	66744.8	3.73107
$685$	9182.76	0.512197
$686$	−4806.42	−0.267507
$687$	−27682.5	−1.53734
$688$	−2124.46	−0.117724
$689$	−31305.0	−1.73095
$690$	107416.	5.92647
$691$	13833.0	0.761549	0.380775	−	0.924668i	$-0.375657\pi$
$691$	13833.0	0.761549	0.380775	+	0.924668i	$0.375657\pi$
$692$	−22705.0	−1.24727
$693$	−21008.2	−1.15157
$694$	2389.06	0.130674
$695$	16424.6	0.896433
$696$	18962.0	1.03269
$697$	−10798.1	−0.586811
$698$	25211.6	1.36715
$699$	−39202.1	−2.12126
$700$	25568.4	1.38056
$701$	−16016.1	−0.862938	−0.431469	−	0.902128i	$-0.642005\pi$
$701$	−16016.1	−0.862938	−0.431469	+	0.902128i	$0.642005\pi$
$702$	−123847.	−6.65853
$703$	−19104.9	−1.02497
$704$	9282.21	0.496927
$705$	31027.2	1.65752
$706$	16359.5	0.872093
$707$	−77.1817	−0.00410568
$708$	40283.8	2.13836
$709$	−8105.84	−0.429367	−0.214683	−	0.976684i	$-0.568872\pi$
$709$	−8105.84	−0.429367	−0.214683	+	0.976684i	$0.568872\pi$
$710$	3064.70	0.161995
$711$	−69831.9	−3.68341
$712$	−11470.3	−0.603745
$713$	−11030.2	−0.579360
$714$	−74022.3	−3.87985
$715$	15404.9	0.805748
$716$	27539.4	1.43742
$717$	−10601.2	−0.552176
$718$	−32744.9	−1.70199
$719$	32273.4	1.67399	0.836993	−	0.547213i	$-0.184311\pi$
$719$	32273.4	1.67399	0.836993	+	0.547213i	$0.184311\pi$
$720$	37516.5	1.94189
$721$	35115.7	1.81384
$722$	−15898.0	−0.819477
$723$	−13717.2	−0.705599
$724$	34214.9	1.75633
$725$	−18753.1	−0.960652
$726$	47829.1	2.44505
$727$	−29841.8	−1.52238	−0.761191	−	0.648528i	$-0.775385\pi$
$727$	−29841.8	−1.52238	−0.761191	+	0.648528i	$0.775385\pi$
$728$	−22402.5	−1.14051
$729$	9690.70	0.492339
$730$	54812.8	2.77906
$731$	3556.45	0.179945
$732$	−29508.3	−1.48997
$733$	28157.5	1.41885	0.709427	−	0.704779i	$-0.248954\pi$
$733$	28157.5	1.41885	0.709427	+	0.704779i	$0.248954\pi$
$734$	−9040.20	−0.454605
$735$	−53780.3	−2.69893
$736$	45127.4	2.26008
$737$	−6471.21	−0.323433
$738$	43069.6	2.14826
$739$	−4474.12	−0.222710	−0.111355	−	0.993781i	$-0.535519\pi$
$739$	−4474.12	−0.222710	−0.111355	+	0.993781i	$0.535519\pi$
$740$	28175.6	1.39967
$741$	82603.8	4.09518
$742$	42670.7	2.11117
$743$	−24345.7	−1.20209	−0.601047	−	0.799214i	$-0.705250\pi$
$743$	−24345.7	−1.20209	−0.601047	+	0.799214i	$0.705250\pi$
$744$	5717.21	0.281725
$745$	42247.6	2.07763
$746$	−7616.02	−0.373783
$747$	−89982.5	−4.40735
$748$	−8596.78	−0.420227
$749$	−5093.24	−0.248468
$750$	−19687.0	−0.958489
$751$	−22873.7	−1.11141	−0.555707	−	0.831378i	$-0.687552\pi$
$751$	−22873.7	−1.11141	−0.555707	+	0.831378i	$0.687552\pi$
$752$	8962.58	0.434617
$753$	−28653.9	−1.38673
$754$	73734.2	3.56133
$755$	−46626.8	−2.24758
$756$	94989.2	4.56974
$757$	−17493.2	−0.839894	−0.419947	−	0.907549i	$-0.637951\pi$
$757$	−17493.2	−0.839894	−0.419947	+	0.907549i	$0.637951\pi$
$758$	4483.79	0.214853
$759$	−21055.1	−1.00692
$760$	14866.2	0.709544
$761$	6112.69	0.291176	0.145588	−	0.989345i	$-0.453493\pi$
$761$	6112.69	0.291176	0.145588	+	0.989345i	$0.453493\pi$
$762$	−46799.4	−2.22488
$763$	32872.3	1.55971
$764$	25849.3	1.22408
$765$	−62804.6	−2.96824
$766$	−45538.5	−2.14801
$767$	34907.0	1.64331
$768$	8170.09	0.383871
$769$	23703.4	1.11153	0.555764	−	0.831340i	$-0.312426\pi$
$769$	23703.4	1.11153	0.555764	+	0.831340i	$0.312426\pi$
$770$	−20997.8	−0.982740
$771$	46906.0	2.19102
$772$	29309.0	1.36639
$773$	−41625.0	−1.93680	−0.968400	−	0.249403i	$-0.919766\pi$
$773$	−41625.0	−1.93680	−0.968400	+	0.249403i	$0.919766\pi$
$774$	−14185.4	−0.658762
$775$	−5654.23	−0.262072
$776$	−1335.17	−0.0617653
$777$	−47553.9	−2.19561
$778$	48073.4	2.21532
$779$	−16424.8	−0.755432
$780$	−121823.	−5.59226
$781$	−600.725	−0.0275232
$782$	−51943.1	−2.37530
$783$	−69669.7	−3.17981
$784$	−15535.1	−0.707683
$785$	39912.8	1.81471
$786$	46725.2	2.12040
$787$	33250.4	1.50603	0.753017	−	0.658001i	$-0.228598\pi$
$787$	33250.4	1.50603	0.753017	+	0.658001i	$0.228598\pi$
$788$	20230.0	0.914548
$789$	−14218.1	−0.641543
$790$	−69797.4	−3.14339
$791$	−28793.6	−1.29429
$792$	7641.11	0.342822
$793$	−25569.7	−1.14503
$794$	−16986.1	−0.759213
$795$	51708.3	2.30680
$796$	−2312.05	−0.102950
$797$	6381.01	0.283597	0.141799	−	0.989896i	$-0.454711\pi$
$797$	6381.01	0.283597	0.141799	+	0.989896i	$0.454711\pi$
$798$	−112594.	−4.99473
$799$	−15003.8	−0.664327
$800$	23132.9	1.02234
$801$	73708.8	3.25140
$802$	−26302.9	−1.15809
$803$	−10744.1	−0.472167
$804$	51174.8	2.24477
$805$	−71390.6	−3.12570
$806$	22231.5	0.971553
$807$	53942.2	2.35298
$808$	28.0725	0.00122226
$809$	−32699.6	−1.42109	−0.710543	−	0.703654i	$-0.751550\pi$
$809$	−32699.6	−1.42109	−0.710543	+	0.703654i	$0.751550\pi$
$810$	97288.6	4.22021
$811$	−941.192	−0.0407518	−0.0203759	−	0.999792i	$-0.506486\pi$
$811$	−941.192	−0.0407518	−0.0203759	+	0.999792i	$0.506486\pi$
$812$	−56553.4	−2.44413
$813$	43691.8	1.88479
$814$	−9814.90	−0.422619
$815$	55549.0	2.38748
$816$	−25910.9	−1.11160
$817$	5409.66	0.231653
$818$	−31733.2	−1.35639
$819$	143960.	6.14208
$820$	24223.1	1.03160
$821$	−16185.5	−0.688035	−0.344017	−	0.938963i	$-0.611788\pi$
$821$	−16185.5	−0.688035	−0.344017	+	0.938963i	$0.611788\pi$
$822$	25296.3	1.07337
$823$	26947.5	1.14135	0.570675	−	0.821176i	$-0.306682\pi$
$823$	26947.5	1.14135	0.570675	+	0.821176i	$0.306682\pi$
$824$	−12772.3	−0.539980
$825$	−10793.1	−0.455476
$826$	−47580.4	−2.00428
$827$	35668.2	1.49977	0.749883	−	0.661571i	$-0.230110\pi$
$827$	35668.2	1.49977	0.749883	+	0.661571i	$0.230110\pi$
$828$	116581.	4.89306
$829$	13408.9	0.561773	0.280887	−	0.959741i	$-0.409372\pi$
$829$	13408.9	0.561773	0.280887	+	0.959741i	$0.409372\pi$
$830$	−89938.0	−3.76120
$831$	−86180.1	−3.59754
$832$	−63606.8	−2.65044
$833$	26006.5	1.08172
$834$	45245.8	1.87858
$835$	−5641.62	−0.233816
$836$	−13076.4	−0.540979
$837$	−21006.0	−0.867473
$838$	14160.3	0.583722
$839$	−9770.94	−0.402062	−0.201031	−	0.979585i	$-0.564429\pi$
$839$	−9770.94	−0.402062	−0.201031	+	0.979585i	$0.564429\pi$
$840$	37003.5	1.51993
$841$	17090.1	0.700729
$842$	16574.7	0.678385
$843$	17864.9	0.729892
$844$	−10976.6	−0.447665
$845$	−73193.0	−2.97978
$846$	59844.7	2.43204
$847$	−31788.1	−1.28955
$848$	14936.5	0.604862
$849$	−10714.1	−0.433104
$850$	−26626.8	−1.07446
$851$	−33369.7	−1.34418
$852$	4750.58	0.191024
$853$	−15140.5	−0.607737	−0.303869	−	0.952714i	$-0.598278\pi$
$853$	−15140.5	−0.607737	−0.303869	+	0.952714i	$0.598278\pi$
$854$	34853.1	1.39654
$855$	−95531.2	−3.82117
$856$	1852.51	0.0739691
$857$	13364.6	0.532703	0.266352	−	0.963876i	$-0.414182\pi$
$857$	13364.6	0.532703	0.266352	+	0.963876i	$0.414182\pi$
$858$	42436.8	1.68854
$859$	18132.0	0.720205	0.360103	−	0.932913i	$-0.382742\pi$
$859$	18132.0	0.720205	0.360103	+	0.932913i	$0.382742\pi$
$860$	−7978.10	−0.316338
$861$	−40883.1	−1.61823
$862$	−35173.4	−1.38980
$863$	−4584.66	−0.180838	−0.0904192	−	0.995904i	$-0.528821\pi$
$863$	−4584.66	−0.180838	−0.0904192	+	0.995904i	$0.528821\pi$
$864$	85941.2	3.38401
$865$	32497.4	1.27739
$866$	46165.9	1.81153
$867$	−3245.24	−0.127121
$868$	−17051.4	−0.666775
$869$	13681.3	0.534068
$870$	−121791.	−4.74609
$871$	44344.3	1.72508
$872$	−11956.3	−0.464326
$873$	8579.91	0.332630
$874$	−79010.0	−3.05784
$875$	13084.3	0.505520
$876$	84964.9	3.27705
$877$	45114.1	1.73705	0.868525	−	0.495645i	$-0.165068\pi$
$877$	45114.1	1.73705	0.868525	+	0.495645i	$0.165068\pi$
$878$	43195.0	1.66032
$879$	−40102.8	−1.53883
$880$	−7350.13	−0.281560
$881$	34241.8	1.30946	0.654731	−	0.755862i	$-0.272782\pi$
$881$	34241.8	1.30946	0.654731	+	0.755862i	$0.272782\pi$
$882$	−103730.	−3.96007
$883$	−33874.6	−1.29102	−0.645510	−	0.763752i	$-0.723355\pi$
$883$	−33874.6	−1.29102	−0.645510	+	0.763752i	$0.723355\pi$
$884$	58909.9	2.24135
$885$	−57657.8	−2.19000
$886$	−33764.7	−1.28030
$887$	5808.12	0.219862	0.109931	−	0.993939i	$-0.464937\pi$
$887$	5808.12	0.219862	0.109931	+	0.993939i	$0.464937\pi$
$888$	17296.3	0.653634
$889$	31103.7	1.17343
$890$	73672.4	2.77472
$891$	−19069.9	−0.717022
$892$	−21256.9	−0.797909
$893$	−22822.1	−0.855222
$894$	116382.	4.35392
$895$	−39416.9	−1.47213
$896$	32484.3	1.21119
$897$	144281.	5.37056
$898$	50488.3	1.87619
$899$	12506.3	0.463970
$900$	59760.8	2.21336
$901$	−25004.6	−0.924553
$902$	−8438.08	−0.311483
$903$	13465.2	0.496228
$904$	10472.8	0.385311
$905$	−48971.4	−1.79875
$906$	−128446.	−4.71006
$907$	−17297.6	−0.633248	−0.316624	−	0.948551i	$-0.602549\pi$
$907$	−17297.6	−0.633248	−0.316624	+	0.948551i	$0.602549\pi$
$908$	52575.4	1.92156
$909$	−180.396	−0.00658236
$910$	143889.	5.24161
$911$	15304.9	0.556614	0.278307	−	0.960492i	$-0.410227\pi$
$911$	15304.9	0.556614	0.278307	+	0.960492i	$0.410227\pi$
$912$	−39412.7	−1.43102
$913$	17629.1	0.639034
$914$	78103.6	2.82652
$915$	42234.9	1.52595
$916$	−30029.4	−1.08319
$917$	−31054.3	−1.11833
$918$	−98921.2	−3.55652
$919$	−13764.3	−0.494063	−0.247031	−	0.969008i	$-0.579455\pi$
$919$	−13764.3	−0.494063	−0.247031	+	0.969008i	$0.579455\pi$
$920$	25966.2	0.930521
$921$	95686.6	3.42343
$922$	31484.1	1.12459
$923$	4116.50	0.146800
$924$	−32548.6	−1.15884
$925$	−17105.8	−0.608037
$926$	49171.3	1.74500
$927$	82075.6	2.90800
$928$	−51166.6	−1.80994
$929$	−11013.1	−0.388943	−0.194471	−	0.980908i	$-0.562299\pi$
$929$	−11013.1	−0.388943	−0.194471	+	0.980908i	$0.562299\pi$
$930$	−36721.1	−1.29476
$931$	39558.1	1.39255
$932$	−42525.6	−1.49461
$933$	−4719.75	−0.165614
$934$	−6990.22	−0.244890
$935$	12304.5	0.430374
$936$	−52361.1	−1.82850
$937$	−9410.58	−0.328101	−0.164050	−	0.986452i	$-0.552456\pi$
$937$	−9410.58	−0.328101	−0.164050	+	0.986452i	$0.552456\pi$
$938$	−60444.1	−2.10402
$939$	55877.5	1.94195
$940$	33657.7	1.16787
$941$	−15885.2	−0.550311	−0.275155	−	0.961400i	$-0.588729\pi$
$941$	−15885.2	−0.550311	−0.275155	+	0.961400i	$0.588729\pi$
$942$	109950.	3.80294
$943$	−28688.6	−0.990700
$944$	−16655.1	−0.574236
$945$	−135957.	−4.68009
$946$	2779.15	0.0955159
$947$	−26030.2	−0.893206	−0.446603	−	0.894732i	$-0.647366\pi$
$947$	−26030.2	−0.893206	−0.446603	+	0.894732i	$0.647366\pi$
$948$	−108192.	−3.70667
$949$	73624.3	2.51838
$950$	−40501.6	−1.38321
$951$	103073.	3.51460
$952$	−17893.7	−0.609180
$953$	24675.0	0.838722	0.419361	−	0.907820i	$-0.362254\pi$
$953$	24675.0	0.838722	0.419361	+	0.907820i	$0.362254\pi$
$954$	99733.9	3.38470
$955$	−36997.9	−1.25364
$956$	−11500.0	−0.389055
$957$	23872.7	0.806370
$958$	−5123.40	−0.172787
$959$	−16812.4	−0.566110
$960$	105063.	3.53218
$961$	−26020.2	−0.873426
$962$	67257.1	2.25411
$963$	−11904.4	−0.398352
$964$	−14880.1	−0.497155
$965$	−41949.7	−1.39939
$966$	−196664.	−6.55027
$967$	−14187.3	−0.471803	−0.235902	−	0.971777i	$-0.575804\pi$
$967$	−14187.3	−0.471803	−0.235902	+	0.971777i	$0.575804\pi$
$968$	11562.0	0.383900
$969$	65978.9	2.18736
$970$	8575.66	0.283864
$971$	7933.45	0.262200	0.131100	−	0.991369i	$-0.458149\pi$
$971$	7933.45	0.262200	0.131100	+	0.991369i	$0.458149\pi$
$972$	55729.7	1.83902
$973$	−30071.2	−0.990789
$974$	74262.8	2.44305
$975$	73960.3	2.42936
$976$	12200.1	0.400117
$977$	−7095.48	−0.232348	−0.116174	−	0.993229i	$-0.537063\pi$
$977$	−7095.48	−0.232348	−0.116174	+	0.993229i	$0.537063\pi$
$978$	153024.	5.00325
$979$	−14440.8	−0.471431
$980$	−58339.7	−1.90163
$981$	76832.2	2.50057
$982$	−49204.7	−1.59897
$983$	−983.000	−0.0318950
$983$	−983.000	−0.0318950
$984$	14870.0	0.481746
$985$	−28955.0	−0.936633
$986$	58894.4	1.90221
$987$	−56806.5	−1.83199
$988$	89607.0	2.88540
$989$	9448.85	0.303798
$990$	−49078.1	−1.57556
$991$	−11162.9	−0.357821	−0.178911	−	0.983865i	$-0.557257\pi$
$991$	−11162.9	−0.357821	−0.178911	+	0.983865i	$0.557257\pi$
$992$	−15427.2	−0.493764
$993$	−473.088	−0.0151188
$994$	−5611.05	−0.179046
$995$	3309.22	0.105436
$996$	−139412.	−4.43519
$997$	5592.24	0.177641	0.0888205	−	0.996048i	$-0.471690\pi$
$997$	5592.24	0.177641	0.0888205	+	0.996048i	$0.471690\pi$
$998$	56482.4	1.79150
$999$	−63549.7	−2.01264

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.4.a.b.1.18	✓	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.4.a.b.1.18	✓	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)

\(f(q)\)	\(=\)	\(q-4.27714 q^{2} +9.48940 q^{3} +10.2939 q^{4} -14.7336 q^{5} -40.5875 q^{6} +26.9751 q^{7} -9.81140 q^{8} +63.0488 q^{9} +O(q^{10})\)	\(q-4.27714 q^{2} +9.48940 q^{3} +10.2939 q^{4} -14.7336 q^{5} -40.5875 q^{6} +26.9751 q^{7} -9.81140 q^{8} +63.0488 q^{9} +63.0176 q^{10} -12.3523 q^{11} +97.6831 q^{12} +84.6449 q^{13} -115.376 q^{14} -139.813 q^{15} -40.3866 q^{16} +67.6093 q^{17} -269.668 q^{18} +102.840 q^{19} -151.666 q^{20} +255.978 q^{21} +52.8326 q^{22} +179.626 q^{23} -93.1043 q^{24} +92.0786 q^{25} -362.038 q^{26} +342.081 q^{27} +277.680 q^{28} -203.664 q^{29} +597.999 q^{30} -61.4065 q^{31} +251.230 q^{32} -117.216 q^{33} -289.174 q^{34} -397.441 q^{35} +649.019 q^{36} -185.774 q^{37} -439.859 q^{38} +803.230 q^{39} +144.557 q^{40} -159.713 q^{41} -1094.85 q^{42} +52.6030 q^{43} -127.154 q^{44} -928.935 q^{45} -768.284 q^{46} -221.920 q^{47} -383.245 q^{48} +384.659 q^{49} -393.833 q^{50} +641.572 q^{51} +871.328 q^{52} -369.839 q^{53} -1463.13 q^{54} +181.994 q^{55} -264.664 q^{56} +975.886 q^{57} +871.100 q^{58} +412.393 q^{59} -1439.22 q^{60} -302.082 q^{61} +262.644 q^{62} +1700.75 q^{63} -751.454 q^{64} -1247.12 q^{65} +501.350 q^{66} +523.886 q^{67} +695.964 q^{68} +1704.54 q^{69} +1699.91 q^{70} +48.6325 q^{71} -618.597 q^{72} +869.802 q^{73} +794.579 q^{74} +873.771 q^{75} +1058.62 q^{76} -333.206 q^{77} -3435.53 q^{78} -1107.59 q^{79} +595.040 q^{80} +1543.83 q^{81} +683.116 q^{82} -1427.19 q^{83} +2635.02 q^{84} -996.127 q^{85} -224.990 q^{86} -1932.65 q^{87} +121.194 q^{88} +1169.08 q^{89} +3973.18 q^{90} +2283.31 q^{91} +1849.05 q^{92} -582.711 q^{93} +949.181 q^{94} -1515.20 q^{95} +2384.03 q^{96} +136.084 q^{97} -1645.24 q^{98} -778.799 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q + 17 q^{2} + 25 q^{3} + 601 q^{4} + 50 q^{5} + 61 q^{6} + 223 q^{7} + 207 q^{8} + 1443 q^{9}+O(q^{10}) \) 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