LMFDB - Embedded newform 483.4.a.c.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,4,Mod(1,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("483.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	483.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:	$28.4979225328$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 34x^{5} + 7x^{4} + 295x^{3} + 84x^{2} - 524x - 288 $ x^7 - x^6 - 34x^5 + 7x^4 + 295x^3 + 84x^2 - 524*x - 288
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$5.21883$ of defining polynomial
Character	$\chi$	$=$	483.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.21883 q^{2} +3.00000 q^{3} +9.79849 q^{4} -19.6249 q^{5} +12.6565 q^{6} +7.00000 q^{7} +7.58752 q^{8} +9.00000 q^{9} -82.7940 q^{10} -40.2869 q^{11} +29.3955 q^{12} +19.9125 q^{13} +29.5318 q^{14} -58.8746 q^{15} -46.3775 q^{16} -96.9123 q^{17} +37.9694 q^{18} -124.169 q^{19} -192.294 q^{20} +21.0000 q^{21} -169.963 q^{22} +23.0000 q^{23} +22.7626 q^{24} +260.136 q^{25} +84.0074 q^{26} +27.0000 q^{27} +68.5894 q^{28} +89.9718 q^{29} -248.382 q^{30} +88.3213 q^{31} -256.359 q^{32} -120.861 q^{33} -408.856 q^{34} -137.374 q^{35} +88.1864 q^{36} -226.078 q^{37} -523.848 q^{38} +59.7375 q^{39} -148.904 q^{40} -93.7541 q^{41} +88.5953 q^{42} +303.996 q^{43} -394.751 q^{44} -176.624 q^{45} +97.0330 q^{46} +158.489 q^{47} -139.132 q^{48} +49.0000 q^{49} +1097.47 q^{50} -290.737 q^{51} +195.112 q^{52} -503.202 q^{53} +113.908 q^{54} +790.626 q^{55} +53.1127 q^{56} -372.507 q^{57} +379.575 q^{58} -875.210 q^{59} -576.883 q^{60} +255.292 q^{61} +372.612 q^{62} +63.0000 q^{63} -710.513 q^{64} -390.780 q^{65} -509.890 q^{66} +320.964 q^{67} -949.594 q^{68} +69.0000 q^{69} -579.558 q^{70} +715.635 q^{71} +68.2877 q^{72} -1108.33 q^{73} -953.783 q^{74} +780.408 q^{75} -1216.67 q^{76} -282.008 q^{77} +252.022 q^{78} +996.266 q^{79} +910.153 q^{80} +81.0000 q^{81} -395.532 q^{82} -1045.70 q^{83} +205.768 q^{84} +1901.89 q^{85} +1282.51 q^{86} +269.915 q^{87} -305.678 q^{88} +440.889 q^{89} -745.146 q^{90} +139.387 q^{91} +225.365 q^{92} +264.964 q^{93} +668.638 q^{94} +2436.80 q^{95} -769.076 q^{96} +1568.23 q^{97} +206.722 q^{98} -362.582 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 6 q^{2} + 21 q^{3} + 18 q^{4} - 41 q^{5} - 18 q^{6} + 49 q^{7} - 33 q^{8} + 63 q^{9} + q^{10} - 126 q^{11} + 54 q^{12} - 87 q^{13} - 42 q^{14} - 123 q^{15} + 2 q^{16} - 204 q^{17} - 54 q^{18} - 286 q^{19}+ \cdots - 1134 q^{99}+O(q^{100}) $ 7 * q - 6 * q^2 + 21 * q^3 + 18 * q^4 - 41 * q^5 - 18 * q^6 + 49 * q^7 - 33 * q^8 + 63 * q^9 + q^10 - 126 * q^11 + 54 * q^12 - 87 * q^13 - 42 * q^14 - 123 * q^15 + 2 * q^16 - 204 * q^17 - 54 * q^18 - 286 * q^19 - 418 * q^20 + 147 * q^21 + 329 * q^22 + 161 * q^23 - 99 * q^24 + 440 * q^25 - 360 * q^26 + 189 * q^27 + 126 * q^28 - 329 * q^29 + 3 * q^30 + 296 * q^31 - 270 * q^32 - 378 * q^33 - 919 * q^34 - 287 * q^35 + 162 * q^36 - 691 * q^37 - 367 * q^38 - 261 * q^39 + 138 * q^40 - 343 * q^41 - 126 * q^42 - 171 * q^43 - 1279 * q^44 - 369 * q^45 - 138 * q^46 - 1403 * q^47 + 6 * q^48 + 343 * q^49 + 230 * q^50 - 612 * q^51 + 2157 * q^52 - 1024 * q^53 - 162 * q^54 - 158 * q^55 - 231 * q^56 - 858 * q^57 + 2608 * q^58 - 1388 * q^59 - 1254 * q^60 - 52 * q^61 - 309 * q^62 + 441 * q^63 - 187 * q^64 - 1067 * q^65 + 987 * q^66 - 1148 * q^67 + 1293 * q^68 + 483 * q^69 + 7 * q^70 - 1590 * q^71 - 297 * q^72 - 802 * q^73 - 878 * q^74 + 1320 * q^75 - 2505 * q^76 - 882 * q^77 - 1080 * q^78 + 618 * q^79 + 195 * q^80 + 567 * q^81 - 1040 * q^82 - 1818 * q^83 + 378 * q^84 - 1526 * q^85 + 1188 * q^86 - 987 * q^87 + 1664 * q^88 - 354 * q^89 + 9 * q^90 - 609 * q^91 + 414 * q^92 + 888 * q^93 + 663 * q^94 + 78 * q^95 - 810 * q^96 - 1575 * q^97 - 294 * q^98 - 1134 * q^99

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 $

$2$	4.21883	1.49158	0.745790	−	0.666181i	$-0.232072\pi$
$2$	4.21883	1.49158	0.745790	+	0.666181i	$0.232072\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	9.79849	1.22481
$5$	−19.6249	−1.75530	−0.877651	−	0.479300i	$-0.840891\pi$
$5$	−19.6249	−1.75530	−0.877651	+	0.479300i	$0.840891\pi$
$6$	12.6565	0.861164
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	7.58752	0.335324
$9$	9.00000	0.333333
$10$	−82.7940	−2.61817
$11$	−40.2869	−1.10427	−0.552135	−	0.833755i	$-0.686187\pi$
$11$	−40.2869	−1.10427	−0.552135	+	0.833755i	$0.686187\pi$
$12$	29.3955	0.707145
$13$	19.9125	0.424826	0.212413	−	0.977180i	$-0.431868\pi$
$13$	19.9125	0.424826	0.212413	+	0.977180i	$0.431868\pi$
$14$	29.5318	0.563764
$15$	−58.8746	−1.01342
$16$	−46.3775	−0.724648
$17$	−96.9123	−1.38263	−0.691314	−	0.722554i	$-0.742968\pi$
$17$	−96.9123	−1.38263	−0.691314	+	0.722554i	$0.742968\pi$
$18$	37.9694	0.497193
$19$	−124.169	−1.49928	−0.749640	−	0.661846i	$-0.769773\pi$
$19$	−124.169	−1.49928	−0.749640	+	0.661846i	$0.769773\pi$
$20$	−192.294	−2.14991
$21$	21.0000	0.218218
$22$	−169.963	−1.64711
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	22.7626	0.193600
$25$	260.136	2.08109
$26$	84.0074	0.633661
$27$	27.0000	0.192450
$28$	68.5894	0.462935
$29$	89.9718	0.576115	0.288058	−	0.957613i	$-0.406990\pi$
$29$	89.9718	0.576115	0.288058	+	0.957613i	$0.406990\pi$
$30$	−248.382	−1.51160
$31$	88.3213	0.511709	0.255855	−	0.966715i	$-0.417643\pi$
$31$	88.3213	0.511709	0.255855	+	0.966715i	$0.417643\pi$
$32$	−256.359	−1.41620
$33$	−120.861	−0.637550
$34$	−408.856	−2.06230
$35$	−137.374	−0.663442
$36$	88.1864	0.408270
$37$	−226.078	−1.00451	−0.502256	−	0.864719i	$-0.667497\pi$
$37$	−226.078	−1.00451	−0.502256	+	0.864719i	$0.667497\pi$
$38$	−523.848	−2.23630
$39$	59.7375	0.245273
$40$	−148.904	−0.588596
$41$	−93.7541	−0.357120	−0.178560	−	0.983929i	$-0.557144\pi$
$41$	−93.7541	−0.357120	−0.178560	+	0.983929i	$0.557144\pi$
$42$	88.5953	0.325489
$43$	303.996	1.07812	0.539058	−	0.842269i	$-0.318780\pi$
$43$	303.996	1.07812	0.539058	+	0.842269i	$0.318780\pi$
$44$	−394.751	−1.35252
$45$	−176.624	−0.585101
$46$	97.0330	0.311016
$47$	158.489	0.491873	0.245936	−	0.969286i	$-0.420905\pi$
$47$	158.489	0.491873	0.245936	+	0.969286i	$0.420905\pi$
$48$	−139.132	−0.418376
$49$	49.0000	0.142857
$50$	1097.47	3.10411
$51$	−290.737	−0.798261
$52$	195.112	0.520331
$53$	−503.202	−1.30415	−0.652076	−	0.758153i	$-0.726102\pi$
$53$	−503.202	−1.30415	−0.652076	+	0.758153i	$0.726102\pi$
$54$	113.908	0.287055
$55$	790.626	1.93833
$56$	53.1127	0.126741
$57$	−372.507	−0.865610
$58$	379.575	0.859322
$59$	−875.210	−1.93123	−0.965615	−	0.259975i	$-0.916286\pi$
$59$	−875.210	−1.93123	−0.965615	+	0.259975i	$0.916286\pi$
$60$	−576.883	−1.24125
$61$	255.292	0.535848	0.267924	−	0.963440i	$-0.413662\pi$
$61$	255.292	0.535848	0.267924	+	0.963440i	$0.413662\pi$
$62$	372.612	0.763255
$63$	63.0000	0.125988
$64$	−710.513	−1.38772
$65$	−390.780	−0.745697
$66$	−509.890	−0.950957
$67$	320.964	0.585254	0.292627	−	0.956227i	$-0.405471\pi$
$67$	320.964	0.585254	0.292627	+	0.956227i	$0.405471\pi$
$68$	−949.594	−1.69346
$69$	69.0000	0.120386
$70$	−579.558	−0.989577
$71$	715.635	1.19620	0.598101	−	0.801421i	$-0.295922\pi$
$71$	715.635	1.19620	0.598101	+	0.801421i	$0.295922\pi$
$72$	68.2877	0.111775
$73$	−1108.33	−1.77699	−0.888496	−	0.458885i	$-0.848249\pi$
$73$	−1108.33	−1.77699	−0.888496	+	0.458885i	$0.848249\pi$
$74$	−953.783	−1.49831
$75$	780.408	1.20152
$76$	−1216.67	−1.83634
$77$	−282.008	−0.417375
$78$	252.022	0.365845
$79$	996.266	1.41884	0.709422	−	0.704784i	$-0.248956\pi$
$79$	996.266	1.41884	0.709422	+	0.704784i	$0.248956\pi$
$80$	910.153	1.27198
$81$	81.0000	0.111111
$82$	−395.532	−0.532674
$83$	−1045.70	−1.38290	−0.691449	−	0.722425i	$-0.743027\pi$
$83$	−1045.70	−1.38290	−0.691449	+	0.722425i	$0.743027\pi$
$84$	205.768	0.267276
$85$	1901.89	2.42693
$86$	1282.51	1.60810
$87$	269.915	0.332620
$88$	−305.678	−0.370288
$89$	440.889	0.525103	0.262551	−	0.964918i	$-0.415436\pi$
$89$	440.889	0.525103	0.262551	+	0.964918i	$0.415436\pi$
$90$	−745.146	−0.872725
$91$	139.387	0.160569
$92$	225.365	0.255391
$93$	264.964	0.295435
$94$	668.638	0.733668
$95$	2436.80	2.63169
$96$	−769.076	−0.817641
$97$	1568.23	1.64155	0.820774	−	0.571253i	$-0.193543\pi$
$97$	1568.23	1.64155	0.820774	+	0.571253i	$0.193543\pi$
$98$	206.722	0.213083
$99$	−362.582	−0.368090
$100$	2548.94	2.54894
$101$	356.643	0.351360	0.175680	−	0.984447i	$-0.443788\pi$
$101$	356.643	0.351360	0.175680	+	0.984447i	$0.443788\pi$
$102$	−1226.57	−1.19067
$103$	−509.370	−0.487279	−0.243639	−	0.969866i	$-0.578341\pi$
$103$	−509.370	−0.487279	−0.243639	+	0.969866i	$0.578341\pi$
$104$	151.087	0.142454
$105$	−412.122	−0.383038
$106$	−2122.92	−1.94525
$107$	−1001.85	−0.905164	−0.452582	−	0.891723i	$-0.649497\pi$
$107$	−1001.85	−0.905164	−0.452582	+	0.891723i	$0.649497\pi$
$108$	264.559	0.235715
$109$	51.9487	0.0456494	0.0228247	−	0.999739i	$-0.492734\pi$
$109$	51.9487	0.0456494	0.0228247	+	0.999739i	$0.492734\pi$
$110$	3335.51	2.89117
$111$	−678.233	−0.579955
$112$	−324.642	−0.273891
$113$	1489.87	1.24031	0.620154	−	0.784480i	$-0.287070\pi$
$113$	1489.87	1.24031	0.620154	+	0.784480i	$0.287070\pi$
$114$	−1571.54	−1.29113
$115$	−451.372	−0.366006
$116$	881.588	0.705633
$117$	179.212	0.141609
$118$	−3692.36	−2.88059
$119$	−678.386	−0.522584
$120$	−446.713	−0.339826
$121$	292.036	0.219411
$122$	1077.03	0.799261
$123$	−281.262	−0.206184
$124$	865.416	0.626747
$125$	−2652.03	−1.89764
$126$	265.786	0.187921
$127$	496.178	0.346682	0.173341	−	0.984862i	$-0.444544\pi$
$127$	496.178	0.346682	0.173341	+	0.984862i	$0.444544\pi$
$128$	−946.661	−0.653701
$129$	911.988	0.622450
$130$	−1648.63	−1.11227
$131$	1807.83	1.20573	0.602864	−	0.797844i	$-0.294026\pi$
$131$	1807.83	1.20573	0.602864	+	0.797844i	$0.294026\pi$
$132$	−1184.25	−0.780879
$133$	−869.183	−0.566675
$134$	1354.09	0.872953
$135$	−529.872	−0.337808
$136$	−735.324	−0.463629
$137$	1558.86	0.972135	0.486067	−	0.873921i	$-0.338431\pi$
$137$	1558.86	0.972135	0.486067	+	0.873921i	$0.338431\pi$
$138$	291.099	0.179565
$139$	−1888.65	−1.15247	−0.576233	−	0.817285i	$-0.695478\pi$
$139$	−1888.65	−1.15247	−0.576233	+	0.817285i	$0.695478\pi$
$140$	−1346.06	−0.812591
$141$	475.468	0.283983
$142$	3019.14	1.78423
$143$	−802.213	−0.469122
$144$	−417.397	−0.241549
$145$	−1765.69	−1.01126
$146$	−4675.86	−2.65053
$147$	147.000	0.0824786
$148$	−2215.22	−1.23034
$149$	2235.01	1.22885	0.614426	−	0.788975i	$-0.289388\pi$
$149$	2235.01	1.22885	0.614426	+	0.788975i	$0.289388\pi$
$150$	3292.40	1.79216
$151$	−2834.17	−1.52742	−0.763712	−	0.645557i	$-0.776625\pi$
$151$	−2834.17	−1.52742	−0.763712	+	0.645557i	$0.776625\pi$
$152$	−942.136	−0.502745
$153$	−872.211	−0.460876
$154$	−1189.74	−0.622548
$155$	−1733.30	−0.898204
$156$	585.337	0.300413
$157$	−915.070	−0.465163	−0.232581	−	0.972577i	$-0.574717\pi$
$157$	−915.070	−0.465163	−0.232581	+	0.972577i	$0.574717\pi$
$158$	4203.07	2.11632
$159$	−1509.61	−0.752953
$160$	5031.01	2.48585
$161$	161.000	0.0788110
$162$	341.725	0.165731
$163$	1410.65	0.677855	0.338927	−	0.940813i	$-0.389936\pi$
$163$	1410.65	0.677855	0.338927	+	0.940813i	$0.389936\pi$
$164$	−918.649	−0.437405
$165$	2371.88	1.11909
$166$	−4411.63	−2.06270
$167$	−3275.53	−1.51777	−0.758886	−	0.651223i	$-0.774256\pi$
$167$	−3275.53	−1.51777	−0.758886	+	0.651223i	$0.774256\pi$
$168$	159.338	0.0731738
$169$	−1800.49	−0.819523
$170$	8023.75	3.61996
$171$	−1117.52	−0.499760
$172$	2978.70	1.32049
$173$	1116.33	0.490594	0.245297	−	0.969448i	$-0.421114\pi$
$173$	1116.33	0.490594	0.245297	+	0.969448i	$0.421114\pi$
$174$	1138.73	0.496130
$175$	1820.95	0.786577
$176$	1868.41	0.800207
$177$	−2625.63	−1.11500
$178$	1860.03	0.783233
$179$	−2980.95	−1.24473	−0.622365	−	0.782727i	$-0.713828\pi$
$179$	−2980.95	−1.24473	−0.622365	+	0.782727i	$0.713828\pi$
$180$	−1730.65	−0.716638
$181$	−4151.36	−1.70480	−0.852398	−	0.522894i	$-0.824852\pi$
$181$	−4151.36	−1.70480	−0.852398	+	0.522894i	$0.824852\pi$
$182$	588.051	0.239502
$183$	765.875	0.309372
$184$	174.513	0.0699200
$185$	4436.75	1.76322
$186$	1117.84	0.440666
$187$	3904.30	1.52679
$188$	1552.95	0.602451
$189$	189.000	0.0727393
$190$	10280.4	3.92538
$191$	−4065.39	−1.54011	−0.770056	−	0.637977i	$-0.779772\pi$
$191$	−4065.39	−1.54011	−0.770056	+	0.637977i	$0.779772\pi$
$192$	−2131.54	−0.801201
$193$	2574.86	0.960323	0.480162	−	0.877180i	$-0.340578\pi$
$193$	2574.86	0.960323	0.480162	+	0.877180i	$0.340578\pi$
$194$	6616.11	2.44850
$195$	−1172.34	−0.430529
$196$	480.126	0.174973
$197$	−3305.71	−1.19554	−0.597771	−	0.801667i	$-0.703947\pi$
$197$	−3305.71	−1.19554	−0.597771	+	0.801667i	$0.703947\pi$
$198$	−1529.67	−0.549035
$199$	1245.53	0.443684	0.221842	−	0.975083i	$-0.428793\pi$
$199$	1245.53	0.443684	0.221842	+	0.975083i	$0.428793\pi$
$200$	1973.79	0.697839
$201$	962.893	0.337897
$202$	1504.62	0.524081
$203$	629.803	0.217751
$204$	−2848.78	−0.977719
$205$	1839.91	0.626854
$206$	−2148.94	−0.726815
$207$	207.000	0.0695048
$208$	−923.492	−0.307849
$209$	5002.39	1.65561
$210$	−1738.67	−0.571333
$211$	3277.40	1.06932	0.534658	−	0.845068i	$-0.320440\pi$
$211$	3277.40	1.06932	0.534658	+	0.845068i	$0.320440\pi$
$212$	−4930.62	−1.59734
$213$	2146.91	0.690627
$214$	−4226.63	−1.35012
$215$	−5965.89	−1.89242
$216$	204.863	0.0645332
$217$	618.249	0.193408
$218$	219.163	0.0680897
$219$	−3324.99	−1.02595
$220$	7746.94	2.37409
$221$	−1929.77	−0.587376
$222$	−2861.35	−0.865050
$223$	318.327	0.0955907	0.0477953	−	0.998857i	$-0.484780\pi$
$223$	318.327	0.0955907	0.0477953	+	0.998857i	$0.484780\pi$
$224$	−1794.51	−0.535272
$225$	2341.22	0.693696
$226$	6285.48	1.85002
$227$	−4910.01	−1.43563	−0.717817	−	0.696232i	$-0.754859\pi$
$227$	−4910.01	−1.43563	−0.717817	+	0.696232i	$0.754859\pi$
$228$	−3650.01	−1.06021
$229$	2031.19	0.586135	0.293068	−	0.956092i	$-0.405324\pi$
$229$	2031.19	0.586135	0.293068	+	0.956092i	$0.405324\pi$
$230$	−1904.26	−0.545927
$231$	−846.025	−0.240971
$232$	682.663	0.193186
$233$	−4737.30	−1.33198	−0.665989	−	0.745962i	$-0.731990\pi$
$233$	−4737.30	−1.33198	−0.665989	+	0.745962i	$0.731990\pi$
$234$	756.066	0.211220
$235$	−3110.33	−0.863386
$236$	−8575.74	−2.36539
$237$	2988.80	0.819170
$238$	−2861.99	−0.779477
$239$	−182.095	−0.0492834	−0.0246417	−	0.999696i	$-0.507844\pi$
$239$	−182.095	−0.0492834	−0.0246417	+	0.999696i	$0.507844\pi$
$240$	2730.46	0.734376
$241$	−3501.67	−0.935943	−0.467971	−	0.883744i	$-0.655015\pi$
$241$	−3501.67	−0.935943	−0.467971	+	0.883744i	$0.655015\pi$
$242$	1232.05	0.327269
$243$	243.000	0.0641500
$244$	2501.47	0.656313
$245$	−961.619	−0.250758
$246$	−1186.60	−0.307539
$247$	−2472.52	−0.636933
$248$	670.140	0.171589
$249$	−3137.10	−0.798417
$250$	−11188.4	−2.83048
$251$	1913.06	0.481082	0.240541	−	0.970639i	$-0.422675\pi$
$251$	1913.06	0.481082	0.240541	+	0.970639i	$0.422675\pi$
$252$	617.305	0.154312
$253$	−926.599	−0.230256
$254$	2093.29	0.517105
$255$	5705.68	1.40119
$256$	1690.31	0.412673
$257$	5251.40	1.27460	0.637302	−	0.770614i	$-0.280050\pi$
$257$	5251.40	1.27460	0.637302	+	0.770614i	$0.280050\pi$
$258$	3847.52	0.928435
$259$	−1582.54	−0.379670
$260$	−3829.06	−0.913339
$261$	809.746	0.192038
$262$	7626.90	1.79844
$263$	4282.52	1.00407	0.502037	−	0.864846i	$-0.332584\pi$
$263$	4282.52	1.00407	0.502037	+	0.864846i	$0.332584\pi$
$264$	−917.034	−0.213786
$265$	9875.28	2.28918
$266$	−3666.93	−0.845241
$267$	1322.67	0.303168
$268$	3144.97	0.716826
$269$	−5511.78	−1.24929	−0.624646	−	0.780908i	$-0.714757\pi$
$269$	−5511.78	−1.24929	−0.624646	+	0.780908i	$0.714757\pi$
$270$	−2235.44	−0.503868
$271$	−2590.12	−0.580585	−0.290293	−	0.956938i	$-0.593753\pi$
$271$	−2590.12	−0.580585	−0.290293	+	0.956938i	$0.593753\pi$
$272$	4494.55	1.00192
$273$	418.162	0.0927045
$274$	6576.56	1.45002
$275$	−10480.1	−2.29808
$276$	676.096	0.147450
$277$	−3780.85	−0.820107	−0.410053	−	0.912062i	$-0.634490\pi$
$277$	−3780.85	−0.820107	−0.410053	+	0.912062i	$0.634490\pi$
$278$	−7967.87	−1.71900
$279$	794.892	0.170570
$280$	−1042.33	−0.222468
$281$	409.840	0.0870072	0.0435036	−	0.999053i	$-0.486148\pi$
$281$	409.840	0.0870072	0.0435036	+	0.999053i	$0.486148\pi$
$282$	2005.91	0.423583
$283$	1403.87	0.294882	0.147441	−	0.989071i	$-0.452896\pi$
$283$	1403.87	0.294882	0.147441	+	0.989071i	$0.452896\pi$
$284$	7012.15	1.46512
$285$	7310.41	1.51941
$286$	−3384.40	−0.699733
$287$	−656.279	−0.134979
$288$	−2307.23	−0.472065
$289$	4478.99	0.911662
$290$	−7449.12	−1.50837
$291$	4704.70	0.947748
$292$	−10860.0	−2.17648
$293$	612.849	0.122195	0.0610973	−	0.998132i	$-0.480540\pi$
$293$	612.849	0.122195	0.0610973	+	0.998132i	$0.480540\pi$
$294$	620.167	0.123023
$295$	17175.9	3.38989
$296$	−1715.37	−0.336837
$297$	−1087.75	−0.212517
$298$	9429.10	1.83293
$299$	457.987	0.0885823
$300$	7646.82	1.47163
$301$	2127.97	0.407489
$302$	−11956.8	−2.27828
$303$	1069.93	0.202858
$304$	5758.65	1.08645
$305$	−5010.07	−0.940576
$306$	−3679.70	−0.687434
$307$	−4347.74	−0.808269	−0.404135	−	0.914700i	$-0.632427\pi$
$307$	−4347.74	−0.808269	−0.404135	+	0.914700i	$0.632427\pi$
$308$	−2763.26	−0.511205
$309$	−1528.11	−0.281331
$310$	−7312.47	−1.33974
$311$	−5921.52	−1.07967	−0.539837	−	0.841769i	$-0.681514\pi$
$311$	−5921.52	−1.07967	−0.539837	+	0.841769i	$0.681514\pi$
$312$	453.260	0.0822461
$313$	−5781.42	−1.04404	−0.522021	−	0.852933i	$-0.674822\pi$
$313$	−5781.42	−1.04404	−0.522021	+	0.852933i	$0.674822\pi$
$314$	−3860.52	−0.693828
$315$	−1236.37	−0.221147
$316$	9761.90	1.73782
$317$	−1010.66	−0.179067	−0.0895333	−	0.995984i	$-0.528538\pi$
$317$	−1010.66	−0.179067	−0.0895333	+	0.995984i	$0.528538\pi$
$318$	−6368.76	−1.12309
$319$	−3624.69	−0.636187
$320$	13943.7	2.43587
$321$	−3005.55	−0.522597
$322$	679.231	0.117553
$323$	12033.5	2.07295
$324$	793.678	0.136090
$325$	5179.96	0.884099
$326$	5951.27	1.01107
$327$	155.846	0.0263557
$328$	−711.362	−0.119751
$329$	1109.42	0.185910
$330$	10006.5	1.66922
$331$	−4151.00	−0.689304	−0.344652	−	0.938730i	$-0.612003\pi$
$331$	−4151.00	−0.689304	−0.344652	+	0.938730i	$0.612003\pi$
$332$	−10246.3	−1.69379
$333$	−2034.70	−0.334837
$334$	−13818.9	−2.26388
$335$	−6298.88	−1.02730
$336$	−973.927	−0.158131
$337$	−9856.55	−1.59324	−0.796618	−	0.604484i	$-0.793379\pi$
$337$	−9856.55	−1.59324	−0.796618	+	0.604484i	$0.793379\pi$
$338$	−7595.96	−1.22238
$339$	4469.60	0.716092
$340$	18635.7	2.97253
$341$	−3558.19	−0.565065
$342$	−4714.63	−0.745432
$343$	343.000	0.0539949
$344$	2306.58	0.361518
$345$	−1354.12	−0.211314
$346$	4709.59	0.731761
$347$	1538.53	0.238020	0.119010	−	0.992893i	$-0.462028\pi$
$347$	1538.53	0.238020	0.119010	+	0.992893i	$0.462028\pi$
$348$	2644.76	0.407397
$349$	10721.6	1.64445	0.822223	−	0.569166i	$-0.192734\pi$
$349$	10721.6	1.64445	0.822223	+	0.569166i	$0.192734\pi$
$350$	7682.28	1.17324
$351$	537.637	0.0817577
$352$	10327.9	1.56386
$353$	1412.76	0.213013	0.106507	−	0.994312i	$-0.466033\pi$
$353$	1412.76	0.213013	0.106507	+	0.994312i	$0.466033\pi$
$354$	−11077.1	−1.66311
$355$	−14044.3	−2.09970
$356$	4320.05	0.643152
$357$	−2035.16	−0.301714
$358$	−12576.1	−1.85662
$359$	4408.28	0.648078	0.324039	−	0.946044i	$-0.394959\pi$
$359$	4408.28	0.648078	0.324039	+	0.946044i	$0.394959\pi$
$360$	−1340.14	−0.196199
$361$	8558.95	1.24784
$362$	−17513.9	−2.54284
$363$	876.107	0.126677
$364$	1365.79	0.196667
$365$	21750.9	3.11916
$366$	3231.09	0.461453
$367$	−580.837	−0.0826142	−0.0413071	−	0.999146i	$-0.513152\pi$
$367$	−580.837	−0.0826142	−0.0413071	+	0.999146i	$0.513152\pi$
$368$	−1066.68	−0.151100
$369$	−843.787	−0.119040
$370$	18717.9	2.62999
$371$	−3522.41	−0.492923
$372$	2596.25	0.361853
$373$	−1388.64	−0.192764	−0.0963820	−	0.995344i	$-0.530727\pi$
$373$	−1388.64	−0.192764	−0.0963820	+	0.995344i	$0.530727\pi$
$374$	16471.6	2.27734
$375$	−7956.08	−1.09560
$376$	1202.54	0.164937
$377$	1791.56	0.244749
$378$	797.358	0.108496
$379$	4206.05	0.570054	0.285027	−	0.958519i	$-0.407997\pi$
$379$	4206.05	0.570054	0.285027	+	0.958519i	$0.407997\pi$
$380$	23877.0	3.22333
$381$	1488.53	0.200157
$382$	−17151.2	−2.29720
$383$	−11891.0	−1.58643	−0.793217	−	0.608939i	$-0.791595\pi$
$383$	−11891.0	−1.58643	−0.793217	+	0.608939i	$0.791595\pi$
$384$	−2839.98	−0.377415
$385$	5534.38	0.732619
$386$	10862.9	1.43240
$387$	2735.96	0.359372
$388$	15366.3	2.01059
$389$	−3493.17	−0.455297	−0.227649	−	0.973743i	$-0.573104\pi$
$389$	−3493.17	−0.455297	−0.227649	+	0.973743i	$0.573104\pi$
$390$	−4945.90	−0.642168
$391$	−2228.98	−0.288298
$392$	371.789	0.0479035
$393$	5423.48	0.696128
$394$	−13946.2	−1.78325
$395$	−19551.6	−2.49050
$396$	−3552.76	−0.450841
$397$	9331.52	1.17969	0.589843	−	0.807518i	$-0.299189\pi$
$397$	9331.52	1.17969	0.589843	+	0.807518i	$0.299189\pi$
$398$	5254.67	0.661790
$399$	−2607.55	−0.327170
$400$	−12064.5	−1.50806
$401$	−2906.48	−0.361952	−0.180976	−	0.983487i	$-0.557926\pi$
$401$	−2906.48	−0.361952	−0.180976	+	0.983487i	$0.557926\pi$
$402$	4062.28	0.504000
$403$	1758.70	0.217387
$404$	3494.57	0.430350
$405$	−1589.62	−0.195034
$406$	2657.03	0.324793
$407$	9107.98	1.10925
$408$	−2205.97	−0.267676
$409$	−5685.56	−0.687366	−0.343683	−	0.939086i	$-0.611675\pi$
$409$	−5685.56	−0.687366	−0.343683	+	0.939086i	$0.611675\pi$
$410$	7762.28	0.935004
$411$	4676.58	0.561262
$412$	−4991.06	−0.596825
$413$	−6126.47	−0.729937
$414$	873.297	0.103672
$415$	20521.7	2.42740
$416$	−5104.74	−0.601636
$417$	−5665.94	−0.665377
$418$	21104.2	2.46947
$419$	−14950.3	−1.74313	−0.871565	−	0.490279i	$-0.836895\pi$
$419$	−14950.3	−1.74313	−0.871565	+	0.490279i	$0.836895\pi$
$420$	−4038.18	−0.469150
$421$	481.924	0.0557899	0.0278949	−	0.999611i	$-0.491120\pi$
$421$	481.924	0.0557899	0.0278949	+	0.999611i	$0.491120\pi$
$422$	13826.8	1.59497
$423$	1426.40	0.163958
$424$	−3818.06	−0.437314
$425$	−25210.4	−2.87737
$426$	9057.42	1.03013
$427$	1787.04	0.202532
$428$	−9816.63	−1.10866
$429$	−2406.64	−0.270848
$430$	−25169.0	−2.82269
$431$	−15555.9	−1.73852	−0.869258	−	0.494359i	$-0.835403\pi$
$431$	−15555.9	−1.73852	−0.869258	+	0.494359i	$0.835403\pi$
$432$	−1252.19	−0.139459
$433$	9166.72	1.01738	0.508689	−	0.860950i	$-0.330130\pi$
$433$	9166.72	1.01738	0.508689	+	0.860950i	$0.330130\pi$
$434$	2608.29	0.288483
$435$	−5297.06	−0.583850
$436$	509.019	0.0559119
$437$	−2855.89	−0.312622
$438$	−14027.6	−1.53028
$439$	8445.55	0.918187	0.459094	−	0.888388i	$-0.348174\pi$
$439$	8445.55	0.918187	0.459094	+	0.888388i	$0.348174\pi$
$440$	5998.89	0.649968
$441$	441.000	0.0476190
$442$	−8141.35	−0.876118
$443$	4370.96	0.468782	0.234391	−	0.972142i	$-0.424690\pi$
$443$	4370.96	0.468782	0.234391	+	0.972142i	$0.424690\pi$
$444$	−6645.66	−0.710336
$445$	−8652.40	−0.921714
$446$	1342.96	0.142581
$447$	6705.02	0.709478
$448$	−4973.59	−0.524509
$449$	454.484	0.0477693	0.0238847	−	0.999715i	$-0.492397\pi$
$449$	454.484	0.0477693	0.0238847	+	0.999715i	$0.492397\pi$
$450$	9877.21	1.03470
$451$	3777.07	0.394357
$452$	14598.4	1.51914
$453$	−8502.50	−0.881859
$454$	−20714.5	−2.14136
$455$	−2735.46	−0.281847
$456$	−2826.41	−0.290260
$457$	5833.13	0.597073	0.298537	−	0.954398i	$-0.403501\pi$
$457$	5833.13	0.597073	0.298537	+	0.954398i	$0.403501\pi$
$458$	8569.25	0.874268
$459$	−2616.63	−0.266087
$460$	−4422.77	−0.448288
$461$	15565.3	1.57256	0.786279	−	0.617871i	$-0.212005\pi$
$461$	15565.3	1.57256	0.786279	+	0.617871i	$0.212005\pi$
$462$	−3569.23	−0.359428
$463$	−19106.6	−1.91784	−0.958918	−	0.283682i	$-0.908444\pi$
$463$	−19106.6	−1.91784	−0.958918	+	0.283682i	$0.908444\pi$
$464$	−4172.67	−0.417481
$465$	−5199.89	−0.518578
$466$	−19985.8	−1.98675
$467$	6876.45	0.681380	0.340690	−	0.940176i	$-0.389339\pi$
$467$	6876.45	0.681380	0.340690	+	0.940176i	$0.389339\pi$
$468$	1756.01	0.173444
$469$	2246.75	0.221205
$470$	−13121.9	−1.28781
$471$	−2745.21	−0.268562
$472$	−6640.68	−0.647589
$473$	−12247.1	−1.19053
$474$	12609.2	1.22186
$475$	−32300.8	−3.12013
$476$	−6647.16	−0.640067
$477$	−4528.82	−0.434718
$478$	−768.226	−0.0735101
$479$	−14775.8	−1.40944	−0.704721	−	0.709485i	$-0.748928\pi$
$479$	−14775.8	−1.40944	−0.704721	+	0.709485i	$0.748928\pi$
$480$	15093.0	1.43521
$481$	−4501.77	−0.426743
$482$	−14772.9	−1.39603
$483$	483.000	0.0455016
$484$	2861.51	0.268737
$485$	−30776.4	−2.88141
$486$	1025.17	0.0956849
$487$	−1976.44	−0.183903	−0.0919516	−	0.995763i	$-0.529310\pi$
$487$	−1976.44	−0.183903	−0.0919516	+	0.995763i	$0.529310\pi$
$488$	1937.03	0.179683
$489$	4231.94	0.391360
$490$	−4056.90	−0.374025
$491$	19477.0	1.79019	0.895095	−	0.445875i	$-0.147107\pi$
$491$	19477.0	1.79019	0.895095	+	0.445875i	$0.147107\pi$
$492$	−2755.95	−0.252536
$493$	−8719.38	−0.796554
$494$	−10431.1	−0.950036
$495$	7115.63	0.646109
$496$	−4096.12	−0.370809
$497$	5009.45	0.452122
$498$	−13234.9	−1.19090
$499$	−11913.4	−1.06878	−0.534388	−	0.845239i	$-0.679458\pi$
$499$	−11913.4	−1.06878	−0.534388	+	0.845239i	$0.679458\pi$
$500$	−25985.9	−2.32425
$501$	−9826.59	−0.876286
$502$	8070.89	0.717572
$503$	9898.33	0.877425	0.438712	−	0.898628i	$-0.355435\pi$
$503$	9898.33	0.877425	0.438712	+	0.898628i	$0.355435\pi$
$504$	478.014	0.0422469
$505$	−6999.09	−0.616743
$506$	−3909.16	−0.343445
$507$	−5401.48	−0.473152
$508$	4861.79	0.424621
$509$	−17204.8	−1.49821	−0.749104	−	0.662452i	$-0.769516\pi$
$509$	−17204.8	−1.49821	−0.749104	+	0.662452i	$0.769516\pi$
$510$	24071.3	2.08999
$511$	−7758.32	−0.671640
$512$	14704.4	1.26924
$513$	−3352.56	−0.288537
$514$	22154.8	1.90118
$515$	9996.32	0.855322
$516$	8936.11	0.762384
$517$	−6385.04	−0.543160
$518$	−6676.48	−0.566308
$519$	3348.98	0.283245
$520$	−2965.06	−0.250051
$521$	−7123.84	−0.599042	−0.299521	−	0.954090i	$-0.596827\pi$
$521$	−7123.84	−0.599042	−0.299521	+	0.954090i	$0.596827\pi$
$522$	3416.18	0.286441
$523$	−1675.23	−0.140063	−0.0700315	−	0.997545i	$-0.522310\pi$
$523$	−1675.23	−0.140063	−0.0700315	+	0.997545i	$0.522310\pi$
$524$	17714.0	1.47679
$525$	5462.85	0.454130
$526$	18067.2	1.49766
$527$	−8559.42	−0.707503
$528$	5605.22	0.462000
$529$	529.000	0.0434783
$530$	41662.1	3.41450
$531$	−7876.89	−0.643744
$532$	−8516.68	−0.694070
$533$	−1866.88	−0.151714
$534$	5580.10	0.452200
$535$	19661.2	1.58884
$536$	2435.32	0.196250
$537$	−8942.86	−0.718646
$538$	−23253.3	−1.86342
$539$	−1974.06	−0.157753
$540$	−5191.94	−0.413751
$541$	−11416.0	−0.907229	−0.453614	−	0.891198i	$-0.649866\pi$
$541$	−11416.0	−0.907229	−0.453614	+	0.891198i	$0.649866\pi$
$542$	−10927.3	−0.865989
$543$	−12454.1	−0.984264
$544$	24844.3	1.95807
$545$	−1019.49	−0.0801285
$546$	1764.15	0.138276
$547$	−11367.2	−0.888532	−0.444266	−	0.895895i	$-0.646536\pi$
$547$	−11367.2	−0.888532	−0.444266	+	0.895895i	$0.646536\pi$
$548$	15274.5	1.19068
$549$	2297.63	0.178616
$550$	−44213.6	−3.42777
$551$	−11171.7	−0.863759
$552$	523.539	0.0403683
$553$	6973.86	0.536273
$554$	−15950.8	−1.22325
$555$	13310.2	1.01800
$556$	−18505.9	−1.41155
$557$	4522.58	0.344036	0.172018	−	0.985094i	$-0.444971\pi$
$557$	4522.58	0.344036	0.172018	+	0.985094i	$0.444971\pi$
$558$	3353.51	0.254418
$559$	6053.32	0.458011
$560$	6371.07	0.480762
$561$	11712.9	0.881495
$562$	1729.05	0.129778
$563$	19087.9	1.42888	0.714441	−	0.699696i	$-0.246681\pi$
$563$	19087.9	1.42888	0.714441	+	0.699696i	$0.246681\pi$
$564$	4658.86	0.347826
$565$	−29238.4	−2.17711
$566$	5922.70	0.439841
$567$	567.000	0.0419961
$568$	5429.90	0.401115
$569$	20243.2	1.49146	0.745729	−	0.666249i	$-0.232101\pi$
$569$	20243.2	1.49146	0.745729	+	0.666249i	$0.232101\pi$
$570$	30841.3	2.26632
$571$	17982.8	1.31797	0.658983	−	0.752158i	$-0.270987\pi$
$571$	17982.8	1.31797	0.658983	+	0.752158i	$0.270987\pi$
$572$	−7860.48	−0.574586
$573$	−12196.2	−0.889184
$574$	−2768.73	−0.201332
$575$	5983.13	0.433937
$576$	−6394.62	−0.462574
$577$	−15741.8	−1.13577	−0.567885	−	0.823108i	$-0.692238\pi$
$577$	−15741.8	−1.13577	−0.567885	+	0.823108i	$0.692238\pi$
$578$	18896.1	1.35982
$579$	7724.58	0.554443
$580$	−17301.1	−1.23860
$581$	−7319.90	−0.522686
$582$	19848.3	1.41364
$583$	20272.5	1.44014
$584$	−8409.49	−0.595869
$585$	−3517.02	−0.248566
$586$	2585.50	0.182263
$587$	13251.9	0.931793	0.465896	−	0.884839i	$-0.345732\pi$
$587$	13251.9	0.931793	0.465896	+	0.884839i	$0.345732\pi$
$588$	1440.38	0.101021
$589$	−10966.8	−0.767195
$590$	72462.1	5.05630
$591$	−9917.12	−0.690247
$592$	10484.9	0.727918
$593$	7940.53	0.549880	0.274940	−	0.961461i	$-0.411342\pi$
$593$	7940.53	0.549880	0.274940	+	0.961461i	$0.411342\pi$
$594$	−4589.01	−0.316986
$595$	13313.2	0.917294
$596$	21899.7	1.50511
$597$	3736.58	0.256161
$598$	1932.17	0.132128
$599$	14136.9	0.964305	0.482152	−	0.876087i	$-0.339855\pi$
$599$	14136.9	0.964305	0.482152	+	0.876087i	$0.339855\pi$
$600$	5921.36	0.402898
$601$	22357.1	1.51741	0.758705	−	0.651434i	$-0.225832\pi$
$601$	22357.1	1.51741	0.758705	+	0.651434i	$0.225832\pi$
$602$	8977.55	0.607803
$603$	2888.68	0.195085
$604$	−27770.5	−1.87081
$605$	−5731.17	−0.385132
$606$	4513.85	0.302579
$607$	17602.7	1.17705	0.588525	−	0.808479i	$-0.299709\pi$
$607$	17602.7	1.17705	0.588525	+	0.808479i	$0.299709\pi$
$608$	31831.8	2.12327
$609$	1889.41	0.125719
$610$	−21136.6	−1.40294
$611$	3155.91	0.208960
$612$	−8546.35	−0.564486
$613$	−13152.8	−0.866615	−0.433307	−	0.901246i	$-0.642654\pi$
$613$	−13152.8	−0.866615	−0.433307	+	0.901246i	$0.642654\pi$
$614$	−18342.4	−1.20560
$615$	5519.74	0.361915
$616$	−2139.75	−0.139956
$617$	−10128.5	−0.660870	−0.330435	−	0.943829i	$-0.607196\pi$
$617$	−10128.5	−0.660870	−0.330435	+	0.943829i	$0.607196\pi$
$618$	−6446.83	−0.419627
$619$	2493.66	0.161920	0.0809600	−	0.996717i	$-0.474201\pi$
$619$	2493.66	0.161920	0.0809600	+	0.996717i	$0.474201\pi$
$620$	−16983.7	−1.10013
$621$	621.000	0.0401286
$622$	−24981.9	−1.61042
$623$	3086.22	0.198470
$624$	−2770.47	−0.177737
$625$	19528.7	1.24984
$626$	−24390.8	−1.55727
$627$	15007.2	0.955867
$628$	−8966.31	−0.569737
$629$	21909.7	1.38887
$630$	−5216.02	−0.329859
$631$	14021.4	0.884601	0.442301	−	0.896867i	$-0.354162\pi$
$631$	14021.4	0.884601	0.442301	+	0.896867i	$0.354162\pi$
$632$	7559.19	0.475773
$633$	9832.21	0.617370
$634$	−4263.78	−0.267092
$635$	−9737.43	−0.608532
$636$	−14791.9	−0.922226
$637$	975.712	0.0606894
$638$	−15291.9	−0.948923
$639$	6440.72	0.398734
$640$	18578.1	1.14744
$641$	815.452	0.0502472	0.0251236	−	0.999684i	$-0.492002\pi$
$641$	815.452	0.0502472	0.0251236	+	0.999684i	$0.492002\pi$
$642$	−12679.9	−0.779495
$643$	−7116.65	−0.436475	−0.218237	−	0.975896i	$-0.570031\pi$
$643$	−7116.65	−0.436475	−0.218237	+	0.975896i	$0.570031\pi$
$644$	1577.56	0.0965287
$645$	−17897.7	−1.09259
$646$	50767.3	3.09197
$647$	21304.6	1.29454	0.647272	−	0.762259i	$-0.275910\pi$
$647$	21304.6	1.29454	0.647272	+	0.762259i	$0.275910\pi$
$648$	614.589	0.0372583
$649$	35259.5	2.13260
$650$	21853.3	1.31870
$651$	1854.75	0.111664
$652$	13822.2	0.830244
$653$	−11961.5	−0.716830	−0.358415	−	0.933562i	$-0.616683\pi$
$653$	−11961.5	−0.716830	−0.358415	+	0.933562i	$0.616683\pi$
$654$	657.488	0.0393116
$655$	−35478.4	−2.11642
$656$	4348.08	0.258787
$657$	−9974.98	−0.592331
$658$	4680.47	0.277300
$659$	2599.95	0.153687	0.0768434	−	0.997043i	$-0.475516\pi$
$659$	2599.95	0.153687	0.0768434	+	0.997043i	$0.475516\pi$
$660$	23240.8	1.37068
$661$	1245.18	0.0732708	0.0366354	−	0.999329i	$-0.488336\pi$
$661$	1245.18	0.0732708	0.0366354	+	0.999329i	$0.488336\pi$
$662$	−17512.4	−1.02815
$663$	−5789.30	−0.339122
$664$	−7934.28	−0.463719
$665$	17057.6	0.994686
$666$	−8584.04	−0.499437
$667$	2069.35	0.120128
$668$	−32095.2	−1.85899
$669$	954.980	0.0551893
$670$	−26573.9	−1.53230
$671$	−10284.9	−0.591721
$672$	−5383.53	−0.309039
$673$	2226.81	0.127544	0.0637722	−	0.997964i	$-0.479687\pi$
$673$	2226.81	0.127544	0.0637722	+	0.997964i	$0.479687\pi$
$674$	−41583.0	−2.37644
$675$	7023.67	0.400505
$676$	−17642.1	−1.00376
$677$	−16559.7	−0.940092	−0.470046	−	0.882642i	$-0.655763\pi$
$677$	−16559.7	−0.940092	−0.470046	+	0.882642i	$0.655763\pi$
$678$	18856.4	1.06811
$679$	10977.6	0.620447
$680$	14430.7	0.813809
$681$	−14730.0	−0.828864
$682$	−15011.4	−0.842839
$683$	17260.9	0.967015	0.483507	−	0.875340i	$-0.339363\pi$
$683$	17260.9	0.967015	0.483507	+	0.875340i	$0.339363\pi$
$684$	−10950.0	−0.612112
$685$	−30592.5	−1.70639
$686$	1447.06	0.0805378
$687$	6093.58	0.338405
$688$	−14098.6	−0.781255
$689$	−10020.0	−0.554038
$690$	−5712.78	−0.315191
$691$	−10249.2	−0.564254	−0.282127	−	0.959377i	$-0.591040\pi$
$691$	−10249.2	−0.564254	−0.282127	+	0.959377i	$0.591040\pi$
$692$	10938.3	0.600886
$693$	−2538.08	−0.139125
$694$	6490.80	0.355025
$695$	37064.5	2.02293
$696$	2047.99	0.111536
$697$	9085.93	0.493765
$698$	45232.4	2.45282
$699$	−14211.9	−0.769018
$700$	17842.6	0.963409
$701$	6339.59	0.341574	0.170787	−	0.985308i	$-0.445369\pi$
$701$	6339.59	0.341574	0.170787	+	0.985308i	$0.445369\pi$
$702$	2268.20	0.121948
$703$	28071.9	1.50605
$704$	28624.4	1.53242
$705$	−9330.99	−0.498476
$706$	5960.19	0.317726
$707$	2496.50	0.132802
$708$	−25727.2	−1.36566
$709$	−3640.88	−0.192858	−0.0964290	−	0.995340i	$-0.530742\pi$
$709$	−3640.88	−0.192858	−0.0964290	+	0.995340i	$0.530742\pi$
$710$	−59250.3	−3.13186
$711$	8966.39	0.472948
$712$	3345.26	0.176080
$713$	2031.39	0.106699
$714$	−8585.98	−0.450031
$715$	15743.3	0.823451
$716$	−29208.8	−1.52456
$717$	−546.284	−0.0284538
$718$	18597.7	0.966660
$719$	−20060.8	−1.04053	−0.520265	−	0.854005i	$-0.674167\pi$
$719$	−20060.8	−1.04053	−0.520265	+	0.854005i	$0.674167\pi$
$720$	8191.37	0.423992
$721$	−3565.59	−0.184174
$722$	36108.7	1.86126
$723$	−10505.0	−0.540367
$724$	−40677.0	−2.08805
$725$	23404.9	1.19895
$726$	3696.14	0.188949
$727$	16892.6	0.861778	0.430889	−	0.902405i	$-0.358200\pi$
$727$	16892.6	0.861778	0.430889	+	0.902405i	$0.358200\pi$
$728$	1057.61	0.0538427
$729$	729.000	0.0370370
$730$	91763.2	4.65247
$731$	−29461.0	−1.49063
$732$	7504.42	0.378923
$733$	11694.5	0.589288	0.294644	−	0.955607i	$-0.404799\pi$
$733$	11694.5	0.589288	0.294644	+	0.955607i	$0.404799\pi$
$734$	−2450.45	−0.123226
$735$	−2884.86	−0.144775
$736$	−5896.25	−0.295297
$737$	−12930.7	−0.646278
$738$	−3559.79	−0.177558
$739$	20095.0	1.00028	0.500140	−	0.865945i	$-0.333282\pi$
$739$	20095.0	1.00028	0.500140	+	0.865945i	$0.333282\pi$
$740$	43473.4	2.15962
$741$	−7417.55	−0.367733
$742$	−14860.5	−0.735235
$743$	16963.4	0.837588	0.418794	−	0.908081i	$-0.362453\pi$
$743$	16963.4	0.837588	0.418794	+	0.908081i	$0.362453\pi$
$744$	2010.42	0.0990667
$745$	−43861.7	−2.15701
$746$	−5858.42	−0.287523
$747$	−9411.30	−0.460966
$748$	38256.2	1.87004
$749$	−7012.96	−0.342120
$750$	−33565.3	−1.63418
$751$	−2164.61	−0.105177	−0.0525883	−	0.998616i	$-0.516747\pi$
$751$	−2164.61	−0.105177	−0.0525883	+	0.998616i	$0.516747\pi$
$752$	−7350.33	−0.356435
$753$	5739.19	0.277753
$754$	7558.30	0.365062
$755$	55620.2	2.68109
$756$	1851.91	0.0890919
$757$	815.620	0.0391601	0.0195801	−	0.999808i	$-0.493767\pi$
$757$	815.620	0.0391601	0.0195801	+	0.999808i	$0.493767\pi$
$758$	17744.6	0.850281
$759$	−2779.80	−0.132938
$760$	18489.3	0.882470
$761$	9078.39	0.432446	0.216223	−	0.976344i	$-0.430626\pi$
$761$	9078.39	0.432446	0.216223	+	0.976344i	$0.430626\pi$
$762$	6279.86	0.298550
$763$	363.641	0.0172539
$764$	−39834.7	−1.88635
$765$	17117.0	0.808977
$766$	−50166.2	−2.36629
$767$	−17427.6	−0.820436
$768$	5070.92	0.238257
$769$	39849.4	1.86867	0.934334	−	0.356398i	$-0.115995\pi$
$769$	39849.4	1.86867	0.934334	+	0.356398i	$0.115995\pi$
$770$	23348.6	1.09276
$771$	15754.2	0.735894
$772$	25229.7	1.17622
$773$	−15379.0	−0.715579	−0.357789	−	0.933802i	$-0.616469\pi$
$773$	−15379.0	−0.715579	−0.357789	+	0.933802i	$0.616469\pi$
$774$	11542.6	0.536032
$775$	22975.6	1.06491
$776$	11899.0	0.550451
$777$	−4747.63	−0.219203
$778$	−14737.1	−0.679112
$779$	11641.4	0.535424
$780$	−11487.2	−0.527316
$781$	−28830.7	−1.32093
$782$	−9403.69	−0.430020
$783$	2429.24	0.110873
$784$	−2272.50	−0.103521
$785$	17958.1	0.816501
$786$	22880.7	1.03833
$787$	10286.7	0.465923	0.232961	−	0.972486i	$-0.425158\pi$
$787$	10286.7	0.465923	0.232961	+	0.972486i	$0.425158\pi$
$788$	−32390.9	−1.46431
$789$	12847.6	0.579703
$790$	−82484.8	−3.71478
$791$	10429.1	0.468792
$792$	−2751.10	−0.123429
$793$	5083.49	0.227642
$794$	39368.1	1.75960
$795$	29625.8	1.32166
$796$	12204.3	0.543429
$797$	12956.7	0.575847	0.287924	−	0.957653i	$-0.407035\pi$
$797$	12956.7	0.575847	0.287924	+	0.957653i	$0.407035\pi$
$798$	−11000.8	−0.488000
$799$	−15359.5	−0.680077
$800$	−66688.1	−2.94723
$801$	3968.00	0.175034
$802$	−12262.0	−0.539881
$803$	44651.3	1.96228
$804$	9434.90	0.413860
$805$	−3159.61	−0.138337
$806$	7419.64	0.324250
$807$	−16535.3	−0.721279
$808$	2706.04	0.117820
$809$	−5061.38	−0.219961	−0.109981	−	0.993934i	$-0.535079\pi$
$809$	−5061.38	−0.219961	−0.109981	+	0.993934i	$0.535079\pi$
$810$	−6706.31	−0.290908
$811$	13283.9	0.575169	0.287584	−	0.957755i	$-0.407148\pi$
$811$	13283.9	0.575169	0.287584	+	0.957755i	$0.407148\pi$
$812$	6171.12	0.266704
$813$	−7770.36	−0.335201
$814$	38425.0	1.65454
$815$	−27683.8	−1.18984
$816$	13483.6	0.578458
$817$	−37746.9	−1.61640
$818$	−23986.4	−1.02526
$819$	1254.49	0.0535230
$820$	18028.4	0.767778
$821$	−43569.2	−1.85210	−0.926050	−	0.377400i	$-0.876818\pi$
$821$	−43569.2	−1.85210	−0.926050	+	0.377400i	$0.876818\pi$
$822$	19729.7	0.837168
$823$	44730.6	1.89455	0.947273	−	0.320429i	$-0.103827\pi$
$823$	44730.6	1.89455	0.947273	+	0.320429i	$0.103827\pi$
$824$	−3864.86	−0.163396
$825$	−31440.2	−1.32680
$826$	−25846.5	−1.08876
$827$	−28295.2	−1.18974	−0.594872	−	0.803820i	$-0.702797\pi$
$827$	−28295.2	−1.18974	−0.594872	+	0.803820i	$0.702797\pi$
$828$	2028.29	0.0851303
$829$	20807.8	0.871756	0.435878	−	0.900006i	$-0.356438\pi$
$829$	20807.8	0.871756	0.435878	+	0.900006i	$0.356438\pi$
$830$	86577.7	3.62067
$831$	−11342.6	−0.473489
$832$	−14148.1	−0.589539
$833$	−4748.70	−0.197518
$834$	−23903.6	−0.992463
$835$	64281.9	2.66415
$836$	49015.9	2.02781
$837$	2384.68	0.0984785
$838$	−63072.9	−2.60002
$839$	−4447.15	−0.182995	−0.0914974	−	0.995805i	$-0.529165\pi$
$839$	−4447.15	−0.182995	−0.0914974	+	0.995805i	$0.529165\pi$
$840$	−3126.99	−0.128442
$841$	−16294.1	−0.668091
$842$	2033.15	0.0832151
$843$	1229.52	0.0502336
$844$	32113.6	1.30971
$845$	35334.4	1.43851
$846$	6017.74	0.244556
$847$	2044.25	0.0829295
$848$	23337.2	0.945052
$849$	4211.62	0.170250
$850$	−106358.	−4.29183
$851$	−5199.79	−0.209455
$852$	21036.4	0.845888
$853$	29357.2	1.17840	0.589199	−	0.807988i	$-0.299444\pi$
$853$	29357.2	1.17840	0.589199	+	0.807988i	$0.299444\pi$
$854$	7539.22	0.302092
$855$	21931.2	0.877230
$856$	−7601.57	−0.303524
$857$	31964.4	1.27408	0.637038	−	0.770832i	$-0.280159\pi$
$857$	31964.4	1.27408	0.637038	+	0.770832i	$0.280159\pi$
$858$	−10153.2	−0.403991
$859$	−29455.0	−1.16996	−0.584979	−	0.811049i	$-0.698897\pi$
$859$	−29455.0	−1.16996	−0.584979	+	0.811049i	$0.698897\pi$
$860$	−58456.7	−2.31786
$861$	−1968.84	−0.0779301
$862$	−65627.5	−2.59313
$863$	1565.48	0.0617493	0.0308746	−	0.999523i	$-0.490171\pi$
$863$	1565.48	0.0617493	0.0308746	+	0.999523i	$0.490171\pi$
$864$	−6921.69	−0.272547
$865$	−21907.8	−0.861142
$866$	38672.8	1.51750
$867$	13437.0	0.526348
$868$	6057.91	0.236888
$869$	−40136.5	−1.56679
$870$	−22347.4	−0.870858
$871$	6391.20	0.248631
$872$	394.162	0.0153074
$873$	14114.1	0.547182
$874$	−12048.5	−0.466300
$875$	−18564.2	−0.717239
$876$	−32579.9	−1.25659
$877$	−22776.8	−0.876986	−0.438493	−	0.898735i	$-0.644488\pi$
$877$	−22776.8	−0.876986	−0.438493	+	0.898735i	$0.644488\pi$
$878$	35630.3	1.36955
$879$	1838.55	0.0705491
$880$	−36667.2	−1.40461
$881$	31559.9	1.20690	0.603451	−	0.797400i	$-0.293792\pi$
$881$	31559.9	1.20690	0.603451	+	0.797400i	$0.293792\pi$
$882$	1860.50	0.0710276
$883$	28686.9	1.09331	0.546655	−	0.837358i	$-0.315901\pi$
$883$	28686.9	1.09331	0.546655	+	0.837358i	$0.315901\pi$
$884$	−18908.8	−0.719425
$885$	51527.7	1.95716
$886$	18440.3	0.699227
$887$	21387.2	0.809597	0.404799	−	0.914406i	$-0.367342\pi$
$887$	21387.2	0.809597	0.404799	+	0.914406i	$0.367342\pi$
$888$	−5146.11	−0.194473
$889$	3473.24	0.131034
$890$	−36502.9	−1.37481
$891$	−3263.24	−0.122697
$892$	3119.12	0.117081
$893$	−19679.4	−0.737455
$894$	28287.3	1.05824
$895$	58500.8	2.18488
$896$	−6626.63	−0.247076
$897$	1373.96	0.0511430
$898$	1917.39	0.0712517
$899$	7946.43	0.294803
$900$	22940.5	0.849647
$901$	48766.5	1.80316
$902$	15934.8	0.588215
$903$	6383.92	0.235264
$904$	11304.4	0.415905
$905$	81469.9	2.99243
$906$	−35870.5	−1.31536
$907$	419.350	0.0153520	0.00767602	−	0.999971i	$-0.497557\pi$
$907$	419.350	0.0153520	0.00767602	+	0.999971i	$0.497557\pi$
$908$	−48110.7	−1.75838
$909$	3209.79	0.117120
$910$	−11540.4	−0.420398
$911$	−37537.8	−1.36519	−0.682593	−	0.730799i	$-0.739148\pi$
$911$	−37537.8	−1.36519	−0.682593	+	0.730799i	$0.739148\pi$
$912$	17275.9	0.627263
$913$	42128.1	1.52709
$914$	24609.0	0.890583
$915$	−15030.2	−0.543042
$916$	19902.6	0.717905
$917$	12654.8	0.455723
$918$	−11039.1	−0.396890
$919$	−36170.4	−1.29831	−0.649157	−	0.760654i	$-0.724878\pi$
$919$	−36170.4	−1.29831	−0.649157	+	0.760654i	$0.724878\pi$
$920$	−3424.80	−0.122731
$921$	−13043.2	−0.466654
$922$	65667.4	2.34560
$923$	14250.1	0.508177
$924$	−8289.77	−0.295144
$925$	−58810.9	−2.09048
$926$	−80607.4	−2.86061
$927$	−4584.33	−0.162426
$928$	−23065.1	−0.815892
$929$	2432.90	0.0859212	0.0429606	−	0.999077i	$-0.486321\pi$
$929$	2432.90	0.0859212	0.0429606	+	0.999077i	$0.486321\pi$
$930$	−21937.4	−0.773501
$931$	−6084.28	−0.214183
$932$	−46418.4	−1.63142
$933$	−17764.6	−0.623351
$934$	29010.6	1.01633
$935$	−76621.4	−2.67999
$936$	1359.78	0.0474848
$937$	7084.56	0.247004	0.123502	−	0.992344i	$-0.460588\pi$
$937$	7084.56	0.247004	0.123502	+	0.992344i	$0.460588\pi$
$938$	9478.65	0.329945
$939$	−17344.2	−0.602778
$940$	−30476.6	−1.05748
$941$	23135.7	0.801492	0.400746	−	0.916189i	$-0.368751\pi$
$941$	23135.7	0.801492	0.400746	+	0.916189i	$0.368751\pi$
$942$	−11581.6	−0.400582
$943$	−2156.35	−0.0744647
$944$	40590.0	1.39946
$945$	−3709.10	−0.127679
$946$	−51668.2	−1.77577
$947$	−47327.3	−1.62400	−0.812002	−	0.583655i	$-0.801622\pi$
$947$	−47327.3	−1.62400	−0.812002	+	0.583655i	$0.801622\pi$
$948$	29285.7	1.00333
$949$	−22069.6	−0.754912
$950$	−136272.	−4.65393
$951$	−3031.97	−0.103384
$952$	−5147.27	−0.175235
$953$	53557.9	1.82047	0.910236	−	0.414090i	$-0.135900\pi$
$953$	53557.9	1.82047	0.910236	+	0.414090i	$0.135900\pi$
$954$	−19106.3	−0.648416
$955$	79782.8	2.70336
$956$	−1784.25	−0.0603629
$957$	−10874.1	−0.367303
$958$	−62336.4	−2.10229
$959$	10912.0	0.367432
$960$	41831.2	1.40635
$961$	−21990.3	−0.738154
$962$	−18992.2	−0.636521
$963$	−9016.66	−0.301721
$964$	−34311.1	−1.14635
$965$	−50531.3	−1.68566
$966$	2037.69	0.0678692
$967$	−49840.7	−1.65746	−0.828732	−	0.559645i	$-0.810937\pi$
$967$	−49840.7	−1.65746	−0.828732	+	0.559645i	$0.810937\pi$
$968$	2215.83	0.0735738
$969$	36100.5	1.19682
$970$	−129840.	−4.29786
$971$	−34691.4	−1.14655	−0.573274	−	0.819363i	$-0.694327\pi$
$971$	−34691.4	−1.14655	−0.573274	+	0.819363i	$0.694327\pi$
$972$	2381.03	0.0785717
$973$	−13220.5	−0.435591
$974$	−8338.24	−0.274306
$975$	15539.9	0.510435
$976$	−11839.8	−0.388302
$977$	50521.5	1.65438	0.827188	−	0.561926i	$-0.189939\pi$
$977$	50521.5	1.65438	0.827188	+	0.561926i	$0.189939\pi$
$978$	17853.8	0.583744
$979$	−17762.1	−0.579855
$980$	−9422.42	−0.307131
$981$	467.538	0.0152165
$982$	82170.0	2.67021
$983$	42125.1	1.36682	0.683409	−	0.730036i	$-0.260497\pi$
$983$	42125.1	1.36682	0.683409	+	0.730036i	$0.260497\pi$
$984$	−2134.09	−0.0691384
$985$	64874.1	2.09854
$986$	−36785.5	−1.18812
$987$	3328.27	0.107335
$988$	−24226.9	−0.780123
$989$	6991.91	0.224803
$990$	30019.6	0.963723
$991$	−9172.16	−0.294009	−0.147005	−	0.989136i	$-0.546963\pi$
$991$	−9172.16	−0.294009	−0.147005	+	0.989136i	$0.546963\pi$
$992$	−22641.9	−0.724680
$993$	−12453.0	−0.397970
$994$	21134.0	0.674376
$995$	−24443.3	−0.778800
$996$	−30738.9	−0.977910
$997$	−49474.9	−1.57160	−0.785800	−	0.618481i	$-0.787748\pi$
$997$	−49474.9	−1.57160	−0.785800	+	0.618481i	$0.787748\pi$
$998$	−50260.7	−1.59416
$999$	−6104.10	−0.193318

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.4.a.c.1.7	✓	7
3.2	odd	2		1449.4.a.h.1.1		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.4.a.c.1.7	✓	7	1.1	even	1	trivial
1449.4.a.h.1.1		7	3.2	odd	2

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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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	483.a (trivial)

\(f(q)\)	\(=\)	\(q+4.21883 q^{2} +3.00000 q^{3} +9.79849 q^{4} -19.6249 q^{5} +12.6565 q^{6} +7.00000 q^{7} +7.58752 q^{8} +9.00000 q^{9} -82.7940 q^{10} -40.2869 q^{11} +29.3955 q^{12} +19.9125 q^{13} +29.5318 q^{14} -58.8746 q^{15} -46.3775 q^{16} -96.9123 q^{17} +37.9694 q^{18} -124.169 q^{19} -192.294 q^{20} +21.0000 q^{21} -169.963 q^{22} +23.0000 q^{23} +22.7626 q^{24} +260.136 q^{25} +84.0074 q^{26} +27.0000 q^{27} +68.5894 q^{28} +89.9718 q^{29} -248.382 q^{30} +88.3213 q^{31} -256.359 q^{32} -120.861 q^{33} -408.856 q^{34} -137.374 q^{35} +88.1864 q^{36} -226.078 q^{37} -523.848 q^{38} +59.7375 q^{39} -148.904 q^{40} -93.7541 q^{41} +88.5953 q^{42} +303.996 q^{43} -394.751 q^{44} -176.624 q^{45} +97.0330 q^{46} +158.489 q^{47} -139.132 q^{48} +49.0000 q^{49} +1097.47 q^{50} -290.737 q^{51} +195.112 q^{52} -503.202 q^{53} +113.908 q^{54} +790.626 q^{55} +53.1127 q^{56} -372.507 q^{57} +379.575 q^{58} -875.210 q^{59} -576.883 q^{60} +255.292 q^{61} +372.612 q^{62} +63.0000 q^{63} -710.513 q^{64} -390.780 q^{65} -509.890 q^{66} +320.964 q^{67} -949.594 q^{68} +69.0000 q^{69} -579.558 q^{70} +715.635 q^{71} +68.2877 q^{72} -1108.33 q^{73} -953.783 q^{74} +780.408 q^{75} -1216.67 q^{76} -282.008 q^{77} +252.022 q^{78} +996.266 q^{79} +910.153 q^{80} +81.0000 q^{81} -395.532 q^{82} -1045.70 q^{83} +205.768 q^{84} +1901.89 q^{85} +1282.51 q^{86} +269.915 q^{87} -305.678 q^{88} +440.889 q^{89} -745.146 q^{90} +139.387 q^{91} +225.365 q^{92} +264.964 q^{93} +668.638 q^{94} +2436.80 q^{95} -769.076 q^{96} +1568.23 q^{97} +206.722 q^{98} -362.582 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 6 q^{2} + 21 q^{3} + 18 q^{4} - 41 q^{5} - 18 q^{6} + 49 q^{7} - 33 q^{8} + 63 q^{9} + q^{10} - 126 q^{11} + 54 q^{12} - 87 q^{13} - 42 q^{14} - 123 q^{15} + 2 q^{16} - 204 q^{17} - 54 q^{18} - 286 q^{19}+ \cdots - 1134 q^{99}+O(q^{100}) \) 7 * q - 6 * q^2 + 21 * q^3 + 18 * q^4 - 41 * q^5 - 18 * q^6 + 49 * q^7 - 33 * q^8 + 63 * q^9 + q^10 - 126 * q^11 + 54 * q^12 - 87 * q^13 - 42 * q^14 - 123 * q^15 + 2 * q^16 - 204 * q^17 - 54 * q^18 - 286 * q^19 - 418 * q^20 + 147 * q^21 + 329 * q^22 + 161 * q^23 - 99 * q^24 + 440 * q^25 - 360 * q^26 + 189 * q^27 + 126 * q^28 - 329 * q^29 + 3 * q^30 + 296 * q^31 - 270 * q^32 - 378 * q^33 - 919 * q^34 - 287 * q^35 + 162 * q^36 - 691 * q^37 - 367 * q^38 - 261 * q^39 + 138 * q^40 - 343 * q^41 - 126 * q^42 - 171 * q^43 - 1279 * q^44 - 369 * q^45 - 138 * q^46 - 1403 * q^47 + 6 * q^48 + 343 * q^49 + 230 * q^50 - 612 * q^51 + 2157 * q^52 - 1024 * q^53 - 162 * q^54 - 158 * q^55 - 231 * q^56 - 858 * q^57 + 2608 * q^58 - 1388 * q^59 - 1254 * q^60 - 52 * q^61 - 309 * q^62 + 441 * q^63 - 187 * q^64 - 1067 * q^65 + 987 * q^66 - 1148 * q^67 + 1293 * q^68 + 483 * q^69 + 7 * q^70 - 1590 * q^71 - 297 * q^72 - 802 * q^73 - 878 * q^74 + 1320 * q^75 - 2505 * q^76 - 882 * q^77 - 1080 * q^78 + 618 * q^79 + 195 * q^80 + 567 * q^81 - 1040 * q^82 - 1818 * q^83 + 378 * q^84 - 1526 * q^85 + 1188 * q^86 - 987 * q^87 + 1664 * q^88 - 354 * q^89 + 9 * q^90 - 609 * q^91 + 414 * q^92 + 888 * q^93 + 663 * q^94 + 78 * q^95 - 810 * q^96 - 1575 * q^97 - 294 * q^98 - 1134 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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