LMFDB - Embedded newform 289.4.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,4,Mod(1,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, 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("289.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	289.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:	$17.0515519917$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.2555057.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 21x^{2} - 4x + 36 $ x^4 - x^3 - 21x^2 - 4x + 36
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-3.68488$ of defining polynomial
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.68488 q^{2} +9.05894 q^{3} +5.57832 q^{4} -7.08909 q^{5} -33.3811 q^{6} -28.1854 q^{7} +8.92359 q^{8} +55.0643 q^{9} +O(q^{10})$	\(q-3.68488 q^{2} +9.05894 q^{3} +5.57832 q^{4} -7.08909 q^{5} -33.3811 q^{6} -28.1854 q^{7} +8.92359 q^{8} +55.0643 q^{9} +26.1224 q^{10} +15.3047 q^{11} +50.5336 q^{12} +2.51532 q^{13} +103.860 q^{14} -64.2196 q^{15} -77.5089 q^{16} -202.905 q^{18} +14.3453 q^{19} -39.5452 q^{20} -255.330 q^{21} -56.3958 q^{22} -180.191 q^{23} +80.8383 q^{24} -74.7448 q^{25} -9.26864 q^{26} +254.233 q^{27} -157.227 q^{28} -41.2425 q^{29} +236.641 q^{30} -155.242 q^{31} +214.222 q^{32} +138.644 q^{33} +199.809 q^{35} +307.167 q^{36} +225.676 q^{37} -52.8606 q^{38} +22.7861 q^{39} -63.2602 q^{40} -234.306 q^{41} +940.860 q^{42} -321.875 q^{43} +85.3743 q^{44} -390.356 q^{45} +663.983 q^{46} -326.183 q^{47} -702.148 q^{48} +451.418 q^{49} +275.425 q^{50} +14.0313 q^{52} -57.1579 q^{53} -936.818 q^{54} -108.496 q^{55} -251.515 q^{56} +129.953 q^{57} +151.974 q^{58} -241.623 q^{59} -358.238 q^{60} -460.925 q^{61} +572.046 q^{62} -1552.01 q^{63} -169.311 q^{64} -17.8313 q^{65} -510.886 q^{66} +392.696 q^{67} -1632.34 q^{69} -736.272 q^{70} -615.558 q^{71} +491.372 q^{72} +697.452 q^{73} -831.587 q^{74} -677.109 q^{75} +80.0226 q^{76} -431.369 q^{77} -83.9641 q^{78} -991.317 q^{79} +549.468 q^{80} +816.345 q^{81} +863.387 q^{82} -98.9057 q^{83} -1424.31 q^{84} +1186.07 q^{86} -373.613 q^{87} +136.573 q^{88} +698.470 q^{89} +1438.41 q^{90} -70.8954 q^{91} -1005.16 q^{92} -1406.32 q^{93} +1201.94 q^{94} -101.695 q^{95} +1940.62 q^{96} +1428.66 q^{97} -1663.42 q^{98} +842.741 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + 2 q^{3} + 11 q^{4} - 14 q^{5} - 38 q^{6} - 36 q^{7} + 60 q^{8} + 6 q^{9}+O(q^{10}) $ 4 * q + q^2 + 2 * q^3 + 11 * q^4 - 14 * q^5 - 38 * q^6 - 36 * q^7 + 60 * q^8 + 6 * q^9	\( 4 q + q^{2} + 2 q^{3} + 11 q^{4} - 14 q^{5} - 38 q^{6} - 36 q^{7} + 60 q^{8} + 6 q^{9} + 7 q^{10} - 10 q^{11} + 29 q^{12} - 22 q^{13} - 73 q^{14} + 54 q^{15} + 63 q^{16} - 334 q^{18} + 22 q^{19} - 330 q^{20} - 352 q^{21} + 79 q^{22} - 380 q^{23} - 159 q^{24} + 378 q^{25} - 448 q^{26} + 494 q^{27} - 608 q^{28} + 78 q^{29} + 313 q^{30} - 362 q^{31} + 331 q^{32} + 94 q^{33} - 242 q^{35} + 141 q^{36} - 512 q^{37} - 524 q^{38} - 12 q^{39} - 1381 q^{40} - 840 q^{41} + 1455 q^{42} - 114 q^{43} + 1041 q^{44} - 648 q^{45} + 1051 q^{46} + 10 q^{47} - 998 q^{48} + 1006 q^{49} + 805 q^{50} - 1537 q^{52} + 50 q^{53} - 581 q^{54} - 1316 q^{55} - 411 q^{56} - 358 q^{57} + 376 q^{58} + 996 q^{59} - 217 q^{60} - 448 q^{61} + 73 q^{62} - 766 q^{63} - 150 q^{64} + 372 q^{65} - 1090 q^{66} - 868 q^{67} - 1128 q^{69} + 1052 q^{70} - 1116 q^{71} - 39 q^{72} - 540 q^{73} - 1630 q^{74} - 1070 q^{75} - 873 q^{76} - 894 q^{77} + 1245 q^{78} - 940 q^{79} - 307 q^{80} + 1080 q^{81} + 334 q^{82} + 850 q^{83} + 443 q^{84} + 2411 q^{86} - 384 q^{87} + 2252 q^{88} + 784 q^{89} + 2069 q^{90} + 2858 q^{91} + 1566 q^{92} - 1550 q^{93} + 1119 q^{94} - 2494 q^{95} + 2643 q^{96} + 518 q^{97} - 1877 q^{98} + 1406 q^{99}+O(q^{100}) \) 4 * q + q^2 + 2 * q^3 + 11 * q^4 - 14 * q^5 - 38 * q^6 - 36 * q^7 + 60 * q^8 + 6 * q^9 + 7 * q^10 - 10 * q^11 + 29 * q^12 - 22 * q^13 - 73 * q^14 + 54 * q^15 + 63 * q^16 - 334 * q^18 + 22 * q^19 - 330 * q^20 - 352 * q^21 + 79 * q^22 - 380 * q^23 - 159 * q^24 + 378 * q^25 - 448 * q^26 + 494 * q^27 - 608 * q^28 + 78 * q^29 + 313 * q^30 - 362 * q^31 + 331 * q^32 + 94 * q^33 - 242 * q^35 + 141 * q^36 - 512 * q^37 - 524 * q^38 - 12 * q^39 - 1381 * q^40 - 840 * q^41 + 1455 * q^42 - 114 * q^43 + 1041 * q^44 - 648 * q^45 + 1051 * q^46 + 10 * q^47 - 998 * q^48 + 1006 * q^49 + 805 * q^50 - 1537 * q^52 + 50 * q^53 - 581 * q^54 - 1316 * q^55 - 411 * q^56 - 358 * q^57 + 376 * q^58 + 996 * q^59 - 217 * q^60 - 448 * q^61 + 73 * q^62 - 766 * q^63 - 150 * q^64 + 372 * q^65 - 1090 * q^66 - 868 * q^67 - 1128 * q^69 + 1052 * q^70 - 1116 * q^71 - 39 * q^72 - 540 * q^73 - 1630 * q^74 - 1070 * q^75 - 873 * q^76 - 894 * q^77 + 1245 * q^78 - 940 * q^79 - 307 * q^80 + 1080 * q^81 + 334 * q^82 + 850 * q^83 + 443 * q^84 + 2411 * q^86 - 384 * q^87 + 2252 * q^88 + 784 * q^89 + 2069 * q^90 + 2858 * q^91 + 1566 * q^92 - 1550 * q^93 + 1119 * q^94 - 2494 * q^95 + 2643 * q^96 + 518 * q^97 - 1877 * q^98 + 1406 * 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 $

$2$	−3.68488	−1.30280	−0.651400	−	0.758734i	$-0.725818\pi$
$2$	−3.68488	−1.30280	−0.651400	+	0.758734i	$0.725818\pi$
$3$	9.05894	1.74339	0.871697	−	0.490046i	$-0.163020\pi$
$3$	9.05894	1.74339	0.871697	+	0.490046i	$0.163020\pi$
$4$	5.57832	0.697290
$5$	−7.08909	−0.634067	−0.317034	−	0.948414i	$-0.602687\pi$
$5$	−7.08909	−0.634067	−0.317034	+	0.948414i	$0.602687\pi$
$6$	−33.3811	−2.27129
$7$	−28.1854	−1.52187	−0.760935	−	0.648828i	$-0.775259\pi$
$7$	−28.1854	−1.52187	−0.760935	+	0.648828i	$0.775259\pi$
$8$	8.92359	0.394371
$9$	55.0643	2.03942
$10$	26.1224	0.826064
$11$	15.3047	0.419503	0.209751	−	0.977755i	$-0.432735\pi$
$11$	15.3047	0.419503	0.209751	+	0.977755i	$0.432735\pi$
$12$	50.5336	1.21565
$13$	2.51532	0.0536634	0.0268317	−	0.999640i	$-0.491458\pi$
$13$	2.51532	0.0536634	0.0268317	+	0.999640i	$0.491458\pi$
$14$	103.860	1.98269
$15$	−64.2196	−1.10543
$16$	−77.5089	−1.21108
$17$	0	0
$17$	0	0
$18$	−202.905	−2.65696
$19$	14.3453	0.173212	0.0866062	−	0.996243i	$-0.472398\pi$
$19$	14.3453	0.173212	0.0866062	+	0.996243i	$0.472398\pi$
$20$	−39.5452	−0.442129
$21$	−255.330	−2.65322
$22$	−56.3958	−0.546529
$23$	−180.191	−1.63359	−0.816793	−	0.576931i	$-0.804250\pi$
$23$	−180.191	−1.63359	−0.816793	+	0.576931i	$0.804250\pi$
$24$	80.8383	0.687544
$25$	−74.7448	−0.597958
$26$	−9.26864	−0.0699127
$27$	254.233	1.81212
$28$	−157.227	−1.06118
$29$	−41.2425	−0.264088	−0.132044	−	0.991244i	$-0.542154\pi$
$29$	−41.2425	−0.264088	−0.132044	+	0.991244i	$0.542154\pi$
$30$	236.641	1.44015
$31$	−155.242	−0.899426	−0.449713	−	0.893173i	$-0.648474\pi$
$31$	−155.242	−0.899426	−0.449713	+	0.893173i	$0.648474\pi$
$32$	214.222	1.18342
$33$	138.644	0.731358
$34$	0	0
$35$	199.809	0.964968
$36$	307.167	1.42207
$37$	225.676	1.00273	0.501363	−	0.865237i	$-0.332832\pi$
$37$	225.676	1.00273	0.501363	+	0.865237i	$0.332832\pi$
$38$	−52.8606	−0.225661
$39$	22.7861	0.0935564
$40$	−63.2602	−0.250058
$41$	−234.306	−0.892497	−0.446249	−	0.894909i	$-0.647240\pi$
$41$	−234.306	−0.892497	−0.446249	+	0.894909i	$0.647240\pi$
$42$	940.860	3.45661
$43$	−321.875	−1.14152	−0.570761	−	0.821117i	$-0.693352\pi$
$43$	−321.875	−1.14152	−0.570761	+	0.821117i	$0.693352\pi$
$44$	85.3743	0.292515
$45$	−390.356	−1.29313
$46$	663.983	2.12824
$47$	−326.183	−1.01231	−0.506156	−	0.862442i	$-0.668934\pi$
$47$	−326.183	−1.01231	−0.506156	+	0.862442i	$0.668934\pi$
$48$	−702.148	−2.11138
$49$	451.418	1.31609
$50$	275.425	0.779021
$51$	0	0
$52$	14.0313	0.0374189
$53$	−57.1579	−0.148137	−0.0740683	−	0.997253i	$-0.523598\pi$
$53$	−57.1579	−0.148137	−0.0740683	+	0.997253i	$0.523598\pi$
$54$	−936.818	−2.36083
$55$	−108.496	−0.265993
$56$	−251.515	−0.600181
$57$	129.953	0.301977
$58$	151.974	0.344054
$59$	−241.623	−0.533164	−0.266582	−	0.963812i	$-0.585894\pi$
$59$	−241.623	−0.533164	−0.266582	+	0.963812i	$0.585894\pi$
$60$	−358.238	−0.770805
$61$	−460.925	−0.967465	−0.483732	−	0.875216i	$-0.660719\pi$
$61$	−460.925	−0.967465	−0.483732	+	0.875216i	$0.660719\pi$
$62$	572.046	1.17177
$63$	−1552.01	−3.10373
$64$	−169.311	−0.330685
$65$	−17.8313	−0.0340262
$66$	−510.886	−0.952814
$67$	392.696	0.716052	0.358026	−	0.933712i	$-0.383450\pi$
$67$	392.696	0.716052	0.358026	+	0.933712i	$0.383450\pi$
$68$	0	0
$69$	−1632.34	−2.84798
$70$	−736.272	−1.25716
$71$	−615.558	−1.02892	−0.514460	−	0.857515i	$-0.672007\pi$
$71$	−615.558	−1.02892	−0.514460	+	0.857515i	$0.672007\pi$
$72$	491.372	0.804288
$73$	697.452	1.11823	0.559114	−	0.829091i	$-0.311142\pi$
$73$	697.452	1.11823	0.559114	+	0.829091i	$0.311142\pi$
$74$	−831.587	−1.30635
$75$	−677.109	−1.04248
$76$	80.0226	0.120779
$77$	−431.369	−0.638429
$78$	−83.9641	−0.121885
$79$	−991.317	−1.41180	−0.705898	−	0.708313i	$-0.749456\pi$
$79$	−991.317	−1.41180	−0.705898	+	0.708313i	$0.749456\pi$
$80$	549.468	0.767904
$81$	816.345	1.11981
$82$	863.387	1.16275
$83$	−98.9057	−0.130799	−0.0653995	−	0.997859i	$-0.520832\pi$
$83$	−98.9057	−0.130799	−0.0653995	+	0.997859i	$0.520832\pi$
$84$	−1424.31	−1.85006
$85$	0	0
$86$	1186.07	1.48717
$87$	−373.613	−0.460409
$88$	136.573	0.165440
$89$	698.470	0.831884	0.415942	−	0.909391i	$-0.363452\pi$
$89$	698.470	0.831884	0.415942	+	0.909391i	$0.363452\pi$
$90$	1438.41	1.68469
$91$	−70.8954	−0.0816687
$92$	−1005.16	−1.13908
$93$	−1406.32	−1.56805
$94$	1201.94	1.31884
$95$	−101.695	−0.109828
$96$	1940.62	2.06317
$97$	1428.66	1.49545	0.747725	−	0.664009i	$-0.231146\pi$
$97$	1428.66	1.49545	0.747725	+	0.664009i	$0.231146\pi$
$98$	−1663.42	−1.71460
$99$	842.741	0.855542
$100$	−416.950	−0.416950
$101$	408.671	0.402617	0.201308	−	0.979528i	$-0.435481\pi$
$101$	408.671	0.402617	0.201308	+	0.979528i	$0.435481\pi$
$102$	0	0
$103$	1649.55	1.57801	0.789007	−	0.614384i	$-0.210596\pi$
$103$	1649.55	1.57801	0.789007	+	0.614384i	$0.210596\pi$
$104$	22.4457	0.0211633
$105$	1810.06	1.68232
$106$	210.620	0.192993
$107$	−2055.01	−1.85668	−0.928340	−	0.371731i	$-0.878764\pi$
$107$	−2055.01	−1.85668	−0.928340	+	0.371731i	$0.878764\pi$
$108$	1418.19	1.26357
$109$	445.064	0.391095	0.195548	−	0.980694i	$-0.437352\pi$
$109$	445.064	0.391095	0.195548	+	0.980694i	$0.437352\pi$
$110$	399.795	0.346536
$111$	2044.38	1.74814
$112$	2184.62	1.84310
$113$	−1226.02	−1.02066	−0.510330	−	0.859979i	$-0.670477\pi$
$113$	−1226.02	−1.02066	−0.510330	+	0.859979i	$0.670477\pi$
$114$	−478.861	−0.393416
$115$	1277.39	1.03580
$116$	−230.064	−0.184146
$117$	138.504	0.109442
$118$	890.352	0.694607
$119$	0	0
$120$	−573.070	−0.435949
$121$	−1096.77	−0.824017
$122$	1698.45	1.26041
$123$	−2122.56	−1.55597
$124$	−865.987	−0.627161
$125$	1416.01	1.01321
$126$	5718.97	4.04354
$127$	−591.124	−0.413022	−0.206511	−	0.978444i	$-0.566211\pi$
$127$	−591.124	−0.413022	−0.206511	+	0.978444i	$0.566211\pi$
$128$	−1089.89	−0.752604
$129$	−2915.84	−1.99012
$130$	65.7063	0.0443294
$131$	−2025.27	−1.35075	−0.675375	−	0.737474i	$-0.736018\pi$
$131$	−2025.27	−1.35075	−0.675375	+	0.737474i	$0.736018\pi$
$132$	773.401	0.509969
$133$	−404.328	−0.263607
$134$	−1447.04	−0.932873
$135$	−1802.28	−1.14901
$136$	0	0
$137$	623.919	0.389087	0.194544	−	0.980894i	$-0.437677\pi$
$137$	623.919	0.389087	0.194544	+	0.980894i	$0.437677\pi$
$138$	6014.98	3.71036
$139$	1033.14	0.630429	0.315214	−	0.949020i	$-0.397924\pi$
$139$	1033.14	0.630429	0.315214	+	0.949020i	$0.397924\pi$
$140$	1114.60	0.672863
$141$	−2954.87	−1.76486
$142$	2268.25	1.34048
$143$	38.4961	0.0225119
$144$	−4267.98	−2.46989
$145$	292.372	0.167449
$146$	−2570.02	−1.45683
$147$	4089.37	2.29446
$148$	1258.89	0.699190
$149$	−284.476	−0.156411	−0.0782054	−	0.996937i	$-0.524919\pi$
$149$	−284.476	−0.156411	−0.0782054	+	0.996937i	$0.524919\pi$
$150$	2495.06	1.35814
$151$	3153.25	1.69939	0.849696	−	0.527273i	$-0.176786\pi$
$151$	3153.25	1.69939	0.849696	+	0.527273i	$0.176786\pi$
$152$	128.012	0.0683099
$153$	0	0
$154$	1589.54	0.831745
$155$	1100.52	0.570297
$156$	127.108	0.0652359
$157$	−482.335	−0.245188	−0.122594	−	0.992457i	$-0.539121\pi$
$157$	−482.335	−0.245188	−0.122594	+	0.992457i	$0.539121\pi$
$158$	3652.88	1.83929
$159$	−517.790	−0.258261
$160$	−1518.64	−0.750369
$161$	5078.77	2.48611
$162$	−3008.13	−1.45890
$163$	3717.39	1.78631	0.893155	−	0.449749i	$-0.148487\pi$
$163$	3717.39	1.78631	0.893155	+	0.449749i	$0.148487\pi$
$164$	−1307.03	−0.622329
$165$	−982.860	−0.463731
$166$	364.455	0.170405
$167$	−2128.93	−0.986475	−0.493237	−	0.869895i	$-0.664187\pi$
$167$	−2128.93	−0.986475	−0.493237	+	0.869895i	$0.664187\pi$
$168$	−2278.46	−1.04635
$169$	−2190.67	−0.997120
$170$	0	0
$171$	789.914	0.353253
$172$	−1795.52	−0.795971
$173$	1197.86	0.526426	0.263213	−	0.964738i	$-0.415218\pi$
$173$	1197.86	0.526426	0.263213	+	0.964738i	$0.415218\pi$
$174$	1376.72	0.599821
$175$	2106.71	0.910015
$176$	−1186.25	−0.508050
$177$	−2188.85	−0.929515
$178$	−2573.78	−1.08378
$179$	4095.63	1.71018	0.855089	−	0.518482i	$-0.173503\pi$
$179$	4095.63	1.71018	0.855089	+	0.518482i	$0.173503\pi$
$180$	−2177.53	−0.901687
$181$	−1297.08	−0.532660	−0.266330	−	0.963882i	$-0.585811\pi$
$181$	−1297.08	−0.532660	−0.266330	+	0.963882i	$0.585811\pi$
$182$	261.241	0.106398
$183$	−4175.49	−1.68667
$184$	−1607.95	−0.644239
$185$	−1599.83	−0.635795
$186$	5182.13	2.04286
$187$	0	0
$188$	−1819.55	−0.705876
$189$	−7165.67	−2.75781
$190$	374.734	0.143084
$191$	4381.72	1.65995	0.829974	−	0.557803i	$-0.188355\pi$
$191$	4381.72	1.65995	0.829974	+	0.557803i	$0.188355\pi$
$192$	−1533.77	−0.576514
$193$	1022.20	0.381240	0.190620	−	0.981664i	$-0.438950\pi$
$193$	1022.20	0.381240	0.190620	+	0.981664i	$0.438950\pi$
$194$	−5264.44	−1.94827
$195$	−161.533	−0.0593211
$196$	2518.15	0.917695
$197$	−2202.50	−0.796555	−0.398278	−	0.917265i	$-0.630392\pi$
$197$	−2202.50	−0.796555	−0.398278	+	0.917265i	$0.630392\pi$
$198$	−3105.40	−1.11460
$199$	−76.0165	−0.0270787	−0.0135394	−	0.999908i	$-0.504310\pi$
$199$	−76.0165	−0.0270787	−0.0135394	+	0.999908i	$0.504310\pi$
$200$	−666.992	−0.235817
$201$	3557.41	1.24836
$202$	−1505.90	−0.524529
$203$	1162.44	0.401907
$204$	0	0
$205$	1661.01	0.565904
$206$	−6078.40	−2.05584
$207$	−9922.12	−3.33157
$208$	−194.960	−0.0649905
$209$	219.550	0.0726631
$210$	−6669.84	−2.19173
$211$	1972.63	0.643609	0.321804	−	0.946806i	$-0.395711\pi$
$211$	1972.63	0.643609	0.321804	+	0.946806i	$0.395711\pi$
$212$	−318.845	−0.103294
$213$	−5576.30	−1.79381
$214$	7572.44	2.41889
$215$	2281.80	0.723801
$216$	2268.67	0.714647
$217$	4375.55	1.36881
$218$	−1640.01	−0.509520
$219$	6318.17	1.94951
$220$	−605.226	−0.185474
$221$	0	0
$222$	−7533.29	−2.27748
$223$	1177.47	0.353584	0.176792	−	0.984248i	$-0.443428\pi$
$223$	1177.47	0.353584	0.176792	+	0.984248i	$0.443428\pi$
$224$	−6037.94	−1.80101
$225$	−4115.77	−1.21949
$226$	4517.75	1.32972
$227$	2845.44	0.831976	0.415988	−	0.909370i	$-0.363436\pi$
$227$	2845.44	0.831976	0.415988	+	0.909370i	$0.363436\pi$
$228$	724.920	0.210566
$229$	3605.93	1.04055	0.520277	−	0.853998i	$-0.325829\pi$
$229$	3605.93	1.04055	0.520277	+	0.853998i	$0.325829\pi$
$230$	−4707.03	−1.34945
$231$	−3907.74	−1.11303
$232$	−368.032	−0.104149
$233$	−835.204	−0.234833	−0.117416	−	0.993083i	$-0.537461\pi$
$233$	−835.204	−0.234833	−0.117416	+	0.993083i	$0.537461\pi$
$234$	−510.372	−0.142581
$235$	2312.34	0.641875
$236$	−1347.85	−0.371770
$237$	−8980.28	−2.46132
$238$	0	0
$239$	−4057.52	−1.09816	−0.549078	−	0.835771i	$-0.685021\pi$
$239$	−4057.52	−1.09816	−0.549078	+	0.835771i	$0.685021\pi$
$240$	4977.59	1.33876
$241$	−2130.64	−0.569487	−0.284743	−	0.958604i	$-0.591908\pi$
$241$	−2130.64	−0.569487	−0.284743	+	0.958604i	$0.591908\pi$
$242$	4041.45	1.07353
$243$	530.923	0.140159
$244$	−2571.19	−0.674604
$245$	−3200.14	−0.834489
$246$	7821.37	2.02712
$247$	36.0830	0.00929516
$248$	−1385.31	−0.354708
$249$	−895.981	−0.228034
$250$	−5217.82	−1.32002
$251$	2164.17	0.544227	0.272113	−	0.962265i	$-0.412277\pi$
$251$	2164.17	0.544227	0.272113	+	0.962265i	$0.412277\pi$
$252$	−8657.62	−2.16420
$253$	−2757.77	−0.685294
$254$	2178.22	0.538085
$255$	0	0
$256$	5370.59	1.31118
$257$	6991.31	1.69691	0.848456	−	0.529267i	$-0.177533\pi$
$257$	6991.31	1.69691	0.848456	+	0.529267i	$0.177533\pi$
$258$	10744.5	2.59273
$259$	−6360.76	−1.52602
$260$	−99.4688	−0.0237261
$261$	−2270.99	−0.538586
$262$	7462.85	1.75976
$263$	−2985.57	−0.699993	−0.349996	−	0.936751i	$-0.613817\pi$
$263$	−2985.57	−0.699993	−0.349996	+	0.936751i	$0.613817\pi$
$264$	1237.20	0.288426
$265$	405.198	0.0939287
$266$	1489.90	0.343427
$267$	6327.40	1.45030
$268$	2190.58	0.499296
$269$	−4063.25	−0.920969	−0.460484	−	0.887668i	$-0.652324\pi$
$269$	−4063.25	−0.920969	−0.460484	+	0.887668i	$0.652324\pi$
$270$	6641.19	1.49693
$271$	6295.85	1.41124	0.705619	−	0.708591i	$-0.250669\pi$
$271$	6295.85	1.41124	0.705619	+	0.708591i	$0.250669\pi$
$272$	0	0
$273$	−642.237	−0.142381
$274$	−2299.06	−0.506903
$275$	−1143.94	−0.250845
$276$	−9105.72	−1.98587
$277$	−4710.13	−1.02168	−0.510838	−	0.859677i	$-0.670665\pi$
$277$	−4710.13	−1.02168	−0.510838	+	0.859677i	$0.670665\pi$
$278$	−3806.99	−0.821323
$279$	−8548.28	−1.83431
$280$	1783.01	0.380555
$281$	−2458.26	−0.521878	−0.260939	−	0.965355i	$-0.584032\pi$
$281$	−2458.26	−0.521878	−0.260939	+	0.965355i	$0.584032\pi$
$282$	10888.3	2.29926
$283$	−9204.70	−1.93344	−0.966718	−	0.255843i	$-0.917647\pi$
$283$	−9204.70	−1.93344	−0.966718	+	0.255843i	$0.917647\pi$
$284$	−3433.78	−0.717455
$285$	−921.249	−0.191474
$286$	−141.854	−0.0293286
$287$	6604.00	1.35826
$288$	11796.0	2.41349
$289$	0	0
$290$	−1077.35	−0.218153
$291$	12942.2	2.60716
$292$	3890.61	0.779729
$293$	423.010	0.0843431	0.0421716	−	0.999110i	$-0.486572\pi$
$293$	423.010	0.0843431	0.0421716	+	0.999110i	$0.486572\pi$
$294$	−15068.8	−2.98922
$295$	1712.89	0.338062
$296$	2013.84	0.395446
$297$	3890.95	0.760189
$298$	1048.26	0.203772
$299$	−453.239	−0.0876638
$300$	−3777.13	−0.726909
$301$	9072.17	1.73725
$302$	−11619.4	−2.21397
$303$	3702.12	0.701919
$304$	−1111.89	−0.209773
$305$	3267.54	0.613438
$306$	0	0
$307$	632.590	0.117602	0.0588010	−	0.998270i	$-0.481272\pi$
$307$	632.590	0.117602	0.0588010	+	0.998270i	$0.481272\pi$
$308$	−2406.31	−0.445170
$309$	14943.2	2.75110
$310$	−4055.29	−0.742983
$311$	5293.07	0.965089	0.482544	−	0.875872i	$-0.339713\pi$
$311$	5293.07	0.965089	0.482544	+	0.875872i	$0.339713\pi$
$312$	203.334	0.0368959
$313$	3817.93	0.689464	0.344732	−	0.938701i	$-0.387970\pi$
$313$	3817.93	0.689464	0.344732	+	0.938701i	$0.387970\pi$
$314$	1777.35	0.319431
$315$	11002.4	1.96798
$316$	−5529.88	−0.984431
$317$	1389.54	0.246197	0.123098	−	0.992394i	$-0.460717\pi$
$317$	1389.54	0.246197	0.123098	+	0.992394i	$0.460717\pi$
$318$	1907.99	0.336462
$319$	−631.203	−0.110786
$320$	1200.26	0.209677
$321$	−18616.2	−3.23692
$322$	−18714.6	−3.23890
$323$	0	0
$324$	4553.83	0.780836
$325$	−188.007	−0.0320885
$326$	−13698.1	−2.32721
$327$	4031.81	0.681833
$328$	−2090.85	−0.351975
$329$	9193.61	1.54061
$330$	3621.72	0.604149
$331$	−5736.36	−0.952565	−0.476282	−	0.879292i	$-0.658016\pi$
$331$	−5736.36	−0.952565	−0.476282	+	0.879292i	$0.658016\pi$
$332$	−551.728	−0.0912048
$333$	12426.7	2.04498
$334$	7844.83	1.28518
$335$	−2783.86	−0.454025
$336$	19790.3	3.21325
$337$	3997.46	0.646159	0.323080	−	0.946372i	$-0.395282\pi$
$337$	3997.46	0.646159	0.323080	+	0.946372i	$0.395282\pi$
$338$	8072.36	1.29905
$339$	−11106.5	−1.77941
$340$	0	0
$341$	−2375.92	−0.377312
$342$	−2910.74	−0.460218
$343$	−3055.81	−0.481045
$344$	−2872.28	−0.450183
$345$	11571.8	1.80581
$346$	−4413.97	−0.685828
$347$	2485.37	0.384500	0.192250	−	0.981346i	$-0.438422\pi$
$347$	2485.37	0.384500	0.192250	+	0.981346i	$0.438422\pi$
$348$	−2084.14	−0.321038
$349$	−9518.10	−1.45986	−0.729932	−	0.683520i	$-0.760448\pi$
$349$	−9518.10	−1.45986	−0.729932	+	0.683520i	$0.760448\pi$
$350$	−7762.98	−1.18557
$351$	639.478	0.0972444
$352$	3278.60	0.496448
$353$	174.509	0.0263121	0.0131561	−	0.999913i	$-0.495812\pi$
$353$	174.509	0.0263121	0.0131561	+	0.999913i	$0.495812\pi$
$354$	8065.65	1.21097
$355$	4363.74	0.652404
$356$	3896.29	0.580065
$357$	0	0
$358$	−15091.9	−2.22802
$359$	−8112.87	−1.19270	−0.596352	−	0.802723i	$-0.703384\pi$
$359$	−8112.87	−1.19270	−0.596352	+	0.802723i	$0.703384\pi$
$360$	−3483.38	−0.509973
$361$	−6653.21	−0.969997
$362$	4779.59	0.693949
$363$	−9935.55	−1.43659
$364$	−395.477	−0.0569468
$365$	−4944.30	−0.709031
$366$	15386.2	2.19740
$367$	−41.1424	−0.00585181	−0.00292591	−	0.999996i	$-0.500931\pi$
$367$	−41.1424	−0.00585181	−0.00292591	+	0.999996i	$0.500931\pi$
$368$	13966.4	1.97840
$369$	−12901.9	−1.82018
$370$	5895.19	0.828315
$371$	1611.02	0.225445
$372$	−7844.93	−1.09339
$373$	1275.50	0.177059	0.0885296	−	0.996074i	$-0.471783\pi$
$373$	1275.50	0.177059	0.0885296	+	0.996074i	$0.471783\pi$
$374$	0	0
$375$	12827.5	1.76643
$376$	−2910.73	−0.399227
$377$	−103.738	−0.0141718
$378$	26404.6	3.59288
$379$	−4101.12	−0.555832	−0.277916	−	0.960605i	$-0.589644\pi$
$379$	−4101.12	−0.555832	−0.277916	+	0.960605i	$0.589644\pi$
$380$	−567.287	−0.0765822
$381$	−5354.95	−0.720059
$382$	−16146.1	−2.16258
$383$	−10390.1	−1.38619	−0.693094	−	0.720848i	$-0.743753\pi$
$383$	−10390.1	−1.38619	−0.693094	+	0.720848i	$0.743753\pi$
$384$	−9873.22	−1.31209
$385$	3058.01	0.404807
$386$	−3766.67	−0.496679
$387$	−17723.8	−2.32804
$388$	7969.53	1.04276
$389$	6213.37	0.809846	0.404923	−	0.914351i	$-0.367298\pi$
$389$	6213.37	0.809846	0.404923	+	0.914351i	$0.367298\pi$
$390$	595.229	0.0772835
$391$	0	0
$392$	4028.27	0.519027
$393$	−18346.8	−2.35489
$394$	8115.93	1.03775
$395$	7027.54	0.895174
$396$	4701.08	0.596561
$397$	−171.318	−0.0216580	−0.0108290	−	0.999941i	$-0.503447\pi$
$397$	−171.318	−0.0216580	−0.0108290	+	0.999941i	$0.503447\pi$
$398$	280.111	0.0352782
$399$	−3662.78	−0.459570
$400$	5793.39	0.724174
$401$	−9328.60	−1.16172	−0.580858	−	0.814005i	$-0.697283\pi$
$401$	−9328.60	−1.16172	−0.580858	+	0.814005i	$0.697283\pi$
$402$	−13108.6	−1.62636
$403$	−390.482	−0.0482663
$404$	2279.70	0.280741
$405$	−5787.14	−0.710038
$406$	−4283.44	−0.523605
$407$	3453.89	0.420646
$408$	0	0
$409$	−6370.74	−0.770202	−0.385101	−	0.922874i	$-0.625833\pi$
$409$	−6370.74	−0.770202	−0.385101	+	0.922874i	$0.625833\pi$
$410$	−6120.63	−0.737260
$411$	5652.04	0.678332
$412$	9201.74	1.10033
$413$	6810.26	0.811406
$414$	36561.8	4.34037
$415$	701.152	0.0829354
$416$	538.837	0.0635064
$417$	9359.13	1.09909
$418$	−809.014	−0.0946655
$419$	−8067.75	−0.940657	−0.470329	−	0.882491i	$-0.655865\pi$
$419$	−8067.75	−0.940657	−0.470329	+	0.882491i	$0.655865\pi$
$420$	10097.1	1.17306
$421$	−6254.81	−0.724088	−0.362044	−	0.932161i	$-0.617921\pi$
$421$	−6254.81	−0.724088	−0.362044	+	0.932161i	$0.617921\pi$
$422$	−7268.90	−0.838494
$423$	−17961.1	−2.06453
$424$	−510.054	−0.0584208
$425$	0	0
$426$	20548.0	2.33698
$427$	12991.4	1.47236
$428$	−11463.5	−1.29464
$429$	348.734	0.0392472
$430$	−8408.14	−0.942969
$431$	−5910.99	−0.660609	−0.330305	−	0.943874i	$-0.607151\pi$
$431$	−5910.99	−0.660609	−0.330305	+	0.943874i	$0.607151\pi$
$432$	−19705.3	−2.19461
$433$	11833.5	1.31335	0.656677	−	0.754172i	$-0.271962\pi$
$433$	11833.5	1.31335	0.656677	+	0.754172i	$0.271962\pi$
$434$	−16123.4	−1.78329
$435$	2648.58	0.291930
$436$	2482.71	0.272707
$437$	−2584.90	−0.282957
$438$	−23281.7	−2.53982
$439$	−7520.94	−0.817665	−0.408833	−	0.912609i	$-0.634064\pi$
$439$	−7520.94	−0.817665	−0.408833	+	0.912609i	$0.634064\pi$
$440$	−968.176	−0.104900
$441$	24857.0	2.68406
$442$	0	0
$443$	8478.34	0.909296	0.454648	−	0.890671i	$-0.349765\pi$
$443$	8478.34	0.909296	0.454648	+	0.890671i	$0.349765\pi$
$444$	11404.2	1.21896
$445$	−4951.52	−0.527471
$446$	−4338.83	−0.460649
$447$	−2577.05	−0.272685
$448$	4772.09	0.503259
$449$	1078.67	0.113375	0.0566877	−	0.998392i	$-0.481946\pi$
$449$	1078.67	0.113375	0.0566877	+	0.998392i	$0.481946\pi$
$450$	15166.1	1.58875
$451$	−3585.97	−0.374405
$452$	−6839.15	−0.711696
$453$	28565.1	2.96271
$454$	−10485.1	−1.08390
$455$	502.584	0.0517835
$456$	1159.65	0.119091
$457$	5664.74	0.579837	0.289918	−	0.957051i	$-0.406372\pi$
$457$	5664.74	0.579837	0.289918	+	0.957051i	$0.406372\pi$
$458$	−13287.4	−1.35563
$459$	0	0
$460$	7125.70	0.722256
$461$	710.717	0.0718034	0.0359017	−	0.999355i	$-0.488570\pi$
$461$	710.717	0.0718034	0.0359017	+	0.999355i	$0.488570\pi$
$462$	14399.5	1.45006
$463$	8328.23	0.835952	0.417976	−	0.908458i	$-0.362740\pi$
$463$	8328.23	0.835952	0.417976	+	0.908458i	$0.362740\pi$
$464$	3196.66	0.319831
$465$	9969.56	0.994252
$466$	3077.62	0.305940
$467$	−14132.8	−1.40040	−0.700201	−	0.713946i	$-0.746906\pi$
$467$	−14132.8	−1.40040	−0.700201	+	0.713946i	$0.746906\pi$
$468$	772.622	0.0763130
$469$	−11068.3	−1.08974
$470$	−8520.69	−0.836235
$471$	−4369.44	−0.427459
$472$	−2156.15	−0.210264
$473$	−4926.18	−0.478871
$474$	33091.2	3.20660
$475$	−1072.24	−0.103574
$476$	0	0
$477$	−3147.36	−0.302113
$478$	14951.5	1.43068
$479$	−6522.89	−0.622210	−0.311105	−	0.950376i	$-0.600699\pi$
$479$	−6522.89	−0.622210	−0.311105	+	0.950376i	$0.600699\pi$
$480$	−13757.3	−1.30819
$481$	567.646	0.0538096
$482$	7851.13	0.741928
$483$	46008.3	4.33426
$484$	−6118.12	−0.574579
$485$	−10127.9	−0.948216
$486$	−1956.39	−0.182600
$487$	2178.49	0.202704	0.101352	−	0.994851i	$-0.467683\pi$
$487$	2178.49	0.202704	0.101352	+	0.994851i	$0.467683\pi$
$488$	−4113.11	−0.381540
$489$	33675.6	3.11424
$490$	11792.1	1.08717
$491$	−12618.8	−1.15983	−0.579915	−	0.814677i	$-0.696914\pi$
$491$	−12618.8	−1.15983	−0.579915	+	0.814677i	$0.696914\pi$
$492$	−11840.3	−1.08496
$493$	0	0
$494$	−132.961	−0.0121097
$495$	−5974.27	−0.542472
$496$	12032.6	1.08927
$497$	17349.8	1.56588
$498$	3301.58	0.297083
$499$	−13762.8	−1.23469	−0.617343	−	0.786694i	$-0.711791\pi$
$499$	−13762.8	−1.23469	−0.617343	+	0.786694i	$0.711791\pi$
$500$	7898.95	0.706504
$501$	−19285.8	−1.71981
$502$	−7974.69	−0.709019
$503$	−491.671	−0.0435836	−0.0217918	−	0.999763i	$-0.506937\pi$
$503$	−491.671	−0.0435836	−0.0217918	+	0.999763i	$0.506937\pi$
$504$	−13849.5	−1.22402
$505$	−2897.11	−0.255286
$506$	10162.0	0.892802
$507$	−19845.2	−1.73837
$508$	−3297.48	−0.287996
$509$	576.514	0.0502034	0.0251017	−	0.999685i	$-0.492009\pi$
$509$	576.514	0.0502034	0.0251017	+	0.999685i	$0.492009\pi$
$510$	0	0
$511$	−19658.0	−1.70180
$512$	−11070.9	−0.955600
$513$	3647.05	0.313881
$514$	−25762.1	−2.21074
$515$	−11693.8	−1.00057
$516$	−16265.5	−1.38769
$517$	−4992.12	−0.424668
$518$	23438.6	1.98810
$519$	10851.4	0.917768
$520$	−159.120	−0.0134189
$521$	−6102.95	−0.513196	−0.256598	−	0.966518i	$-0.582602\pi$
$521$	−6102.95	−0.513196	−0.256598	+	0.966518i	$0.582602\pi$
$522$	8368.33	0.701670
$523$	13593.3	1.13651	0.568255	−	0.822853i	$-0.307619\pi$
$523$	13593.3	1.13651	0.568255	+	0.822853i	$0.307619\pi$
$524$	−11297.6	−0.941864
$525$	19084.6	1.58651
$526$	11001.5	0.911951
$527$	0	0
$528$	−10746.1	−0.885731
$529$	20301.9	1.66860
$530$	−1493.10	−0.122370
$531$	−13304.8	−1.08735
$532$	−2255.47	−0.183810
$533$	−589.354	−0.0478944
$534$	−23315.7	−1.88945
$535$	14568.1	1.17726
$536$	3504.26	0.282390
$537$	37102.1	2.98151
$538$	14972.6	1.19984
$539$	6908.80	0.552103
$540$	−10053.7	−0.801190
$541$	20360.3	1.61803	0.809017	−	0.587786i	$-0.200000\pi$
$541$	20360.3	1.61803	0.809017	+	0.587786i	$0.200000\pi$
$542$	−23199.4	−1.83856
$543$	−11750.2	−0.928635
$544$	0	0
$545$	−3155.10	−0.247981
$546$	2366.56	0.185494
$547$	253.860	0.0198433	0.00992164	−	0.999951i	$-0.496842\pi$
$547$	253.860	0.0198433	0.00992164	+	0.999951i	$0.496842\pi$
$548$	3480.42	0.271307
$549$	−25380.5	−1.97307
$550$	4215.29	0.326801
$551$	−591.636	−0.0457433
$552$	−14566.4	−1.12316
$553$	27940.7	2.14857
$554$	17356.2	1.33104
$555$	−14492.8	−1.10844
$556$	5763.17	0.439592
$557$	1519.94	0.115623	0.0578116	−	0.998328i	$-0.481588\pi$
$557$	1519.94	0.115623	0.0578116	+	0.998328i	$0.481588\pi$
$558$	31499.4	2.38974
$559$	−809.617	−0.0612579
$560$	−15487.0	−1.16865
$561$	0	0
$562$	9058.40	0.679903
$563$	−25112.9	−1.87990	−0.939948	−	0.341317i	$-0.889127\pi$
$563$	−25112.9	−1.87990	−0.939948	+	0.341317i	$0.889127\pi$
$564$	−16483.2	−1.23062
$565$	8691.39	0.647168
$566$	33918.2	2.51888
$567$	−23009.0	−1.70421
$568$	−5492.99	−0.405776
$569$	3649.16	0.268859	0.134430	−	0.990923i	$-0.457080\pi$
$569$	3649.16	0.268859	0.134430	+	0.990923i	$0.457080\pi$
$570$	3394.69	0.249452
$571$	−4111.91	−0.301362	−0.150681	−	0.988582i	$-0.548147\pi$
$571$	−4111.91	−0.301362	−0.150681	+	0.988582i	$0.548147\pi$
$572$	214.744	0.0156974
$573$	39693.7	2.89394
$574$	−24334.9	−1.76955
$575$	13468.4	0.976817
$576$	−9322.98	−0.674405
$577$	25307.1	1.82591	0.912954	−	0.408062i	$-0.133795\pi$
$577$	25307.1	1.82591	0.912954	+	0.408062i	$0.133795\pi$
$578$	0	0
$579$	9260.01	0.664651
$580$	1630.94	0.116761
$581$	2787.70	0.199059
$582$	−47690.3	−3.39661
$583$	−874.783	−0.0621438
$584$	6223.78	0.440996
$585$	−981.870	−0.0693938
$586$	−1558.74	−0.109882
$587$	6734.14	0.473506	0.236753	−	0.971570i	$-0.423917\pi$
$587$	6734.14	0.473506	0.236753	+	0.971570i	$0.423917\pi$
$588$	22811.8	1.59990
$589$	−2226.99	−0.155792
$590$	−6311.79	−0.440427
$591$	−19952.3	−1.38871
$592$	−17491.9	−1.21438
$593$	885.596	0.0613273	0.0306636	−	0.999530i	$-0.490238\pi$
$593$	885.596	0.0613273	0.0306636	+	0.999530i	$0.490238\pi$
$594$	−14337.7	−0.990374
$595$	0	0
$596$	−1586.90	−0.109064
$597$	−688.629	−0.0472089
$598$	1670.13	0.114208
$599$	7411.88	0.505578	0.252789	−	0.967521i	$-0.418652\pi$
$599$	7411.88	0.505578	0.252789	+	0.967521i	$0.418652\pi$
$600$	−6042.24	−0.411123
$601$	−19232.0	−1.30531	−0.652653	−	0.757657i	$-0.726344\pi$
$601$	−19232.0	−1.30531	−0.652653	+	0.757657i	$0.726344\pi$
$602$	−33429.8	−2.26329
$603$	21623.6	1.46033
$604$	17589.9	1.18497
$605$	7775.08	0.522483
$606$	−13641.9	−0.914461
$607$	3485.07	0.233039	0.116519	−	0.993188i	$-0.462826\pi$
$607$	3485.07	0.233039	0.116519	+	0.993188i	$0.462826\pi$
$608$	3073.08	0.204983
$609$	10530.5	0.700682
$610$	−12040.5	−0.799188
$611$	−820.455	−0.0543241
$612$	0	0
$613$	−27347.9	−1.80191	−0.900954	−	0.433915i	$-0.857132\pi$
$613$	−27347.9	−1.80191	−0.900954	+	0.433915i	$0.857132\pi$
$614$	−2331.02	−0.153212
$615$	15047.0	0.986592
$616$	−3849.36	−0.251778
$617$	−12625.9	−0.823822	−0.411911	−	0.911224i	$-0.635139\pi$
$617$	−12625.9	−0.823822	−0.411911	+	0.911224i	$0.635139\pi$
$618$	−55063.9	−3.58413
$619$	−16469.8	−1.06943	−0.534714	−	0.845033i	$-0.679581\pi$
$619$	−16469.8	−1.06943	−0.534714	+	0.845033i	$0.679581\pi$
$620$	6139.06	0.397662
$621$	−45810.6	−2.96025
$622$	−19504.3	−1.25732
$623$	−19686.7	−1.26602
$624$	−1766.13	−0.113304
$625$	−695.113	−0.0444872
$626$	−14068.6	−0.898235
$627$	1988.89	0.126680
$628$	−2690.62	−0.170967
$629$	0	0
$630$	−40542.3	−2.56388
$631$	6691.13	0.422139	0.211069	−	0.977471i	$-0.432305\pi$
$631$	6691.13	0.422139	0.211069	+	0.977471i	$0.432305\pi$
$632$	−8846.11	−0.556771
$633$	17869.9	1.12206
$634$	−5120.28	−0.320745
$635$	4190.53	0.261884
$636$	−2888.40	−0.180082
$637$	1135.46	0.0706258
$638$	2325.91	0.144332
$639$	−33895.3	−2.09840
$640$	7726.31	0.477202
$641$	−14335.5	−0.883335	−0.441668	−	0.897179i	$-0.645613\pi$
$641$	−14335.5	−0.883335	−0.441668	+	0.897179i	$0.645613\pi$
$642$	68598.3	4.21707
$643$	−30421.9	−1.86582	−0.932910	−	0.360109i	$-0.882740\pi$
$643$	−30421.9	−1.86582	−0.932910	+	0.360109i	$0.882740\pi$
$644$	28331.0	1.73354
$645$	20670.7	1.26187
$646$	0	0
$647$	−9221.00	−0.560301	−0.280151	−	0.959956i	$-0.590384\pi$
$647$	−9221.00	−0.560301	−0.280151	+	0.959956i	$0.590384\pi$
$648$	7284.73	0.441622
$649$	−3697.96	−0.223664
$650$	692.783	0.0418049
$651$	39637.8	2.38637
$652$	20736.8	1.24558
$653$	24958.5	1.49572	0.747858	−	0.663859i	$-0.231082\pi$
$653$	24958.5	1.49572	0.747858	+	0.663859i	$0.231082\pi$
$654$	−14856.7	−0.888293
$655$	14357.3	0.856467
$656$	18160.8	1.08088
$657$	38404.7	2.28054
$658$	−33877.3	−2.00711
$659$	−3367.32	−0.199047	−0.0995236	−	0.995035i	$-0.531732\pi$
$659$	−3367.32	−0.199047	−0.0995236	+	0.995035i	$0.531732\pi$
$660$	−5482.71	−0.323355
$661$	−6389.67	−0.375990	−0.187995	−	0.982170i	$-0.560199\pi$
$661$	−6389.67	−0.375990	−0.187995	+	0.982170i	$0.560199\pi$
$662$	21137.8	1.24100
$663$	0	0
$664$	−882.595	−0.0515833
$665$	2866.32	0.167144
$666$	−45790.8	−2.66420
$667$	7431.55	0.431410
$668$	−11875.8	−0.687859
$669$	10666.6	0.616436
$670$	10258.2	0.591504
$671$	−7054.30	−0.405854
$672$	−54697.3	−3.13987
$673$	27441.4	1.57175	0.785877	−	0.618383i	$-0.212212\pi$
$673$	27441.4	1.57175	0.785877	+	0.618383i	$0.212212\pi$
$674$	−14730.2	−0.841817
$675$	−19002.6	−1.08357
$676$	−12220.3	−0.695282
$677$	16931.5	0.961194	0.480597	−	0.876941i	$-0.340420\pi$
$677$	16931.5	0.961194	0.480597	+	0.876941i	$0.340420\pi$
$678$	40926.0	2.31822
$679$	−40267.4	−2.27588
$680$	0	0
$681$	25776.7	1.45046
$682$	8754.98	0.491562
$683$	−69.2829	−0.00388146	−0.00194073	−	0.999998i	$-0.500618\pi$
$683$	−69.2829	−0.00388146	−0.00194073	+	0.999998i	$0.500618\pi$
$684$	4406.39	0.246320
$685$	−4423.01	−0.246708
$686$	11260.3	0.626705
$687$	32665.9	1.81409
$688$	24948.1	1.38247
$689$	−143.770	−0.00794952
$690$	−42640.7	−2.35262
$691$	1509.96	0.0831282	0.0415641	−	0.999136i	$-0.486766\pi$
$691$	1509.96	0.0831282	0.0415641	+	0.999136i	$0.486766\pi$
$692$	6682.05	0.367072
$693$	−23753.0	−1.30202
$694$	−9158.27	−0.500927
$695$	−7324.01	−0.399734
$696$	−3333.98	−0.181572
$697$	0	0
$698$	35073.0	1.90191
$699$	−7566.06	−0.409406
$700$	11751.9	0.634544
$701$	−16452.5	−0.886449	−0.443224	−	0.896411i	$-0.646165\pi$
$701$	−16452.5	−0.886449	−0.443224	+	0.896411i	$0.646165\pi$
$702$	−2356.40	−0.126690
$703$	3237.38	0.173684
$704$	−2591.24	−0.138723
$705$	20947.4	1.11904
$706$	−643.045	−0.0342795
$707$	−11518.6	−0.612730
$708$	−12210.1	−0.648141
$709$	4602.45	0.243792	0.121896	−	0.992543i	$-0.461103\pi$
$709$	4602.45	0.243792	0.121896	+	0.992543i	$0.461103\pi$
$710$	−16079.9	−0.849953
$711$	−54586.2	−2.87925
$712$	6232.87	0.328071
$713$	27973.2	1.46929
$714$	0	0
$715$	−272.903	−0.0142741
$716$	22846.7	1.19249
$717$	−36756.8	−1.91452
$718$	29894.9	1.55386
$719$	23515.7	1.21973	0.609865	−	0.792505i	$-0.291224\pi$
$719$	23515.7	1.21973	0.609865	+	0.792505i	$0.291224\pi$
$720$	30256.1	1.56608
$721$	−46493.4	−2.40153
$722$	24516.3	1.26371
$723$	−19301.3	−0.992839
$724$	−7235.54	−0.371418
$725$	3082.66	0.157914
$726$	36611.3	1.87159
$727$	−8389.04	−0.427968	−0.213984	−	0.976837i	$-0.568644\pi$
$727$	−8389.04	−0.427968	−0.213984	+	0.976837i	$0.568644\pi$
$728$	−632.641	−0.0322078
$729$	−17231.7	−0.875462
$730$	18219.1	0.923727
$731$	0	0
$732$	−23292.2	−1.17610
$733$	−7677.37	−0.386863	−0.193431	−	0.981114i	$-0.561962\pi$
$733$	−7677.37	−0.386863	−0.193431	+	0.981114i	$0.561962\pi$
$734$	151.605	0.00762374
$735$	−28989.9	−1.45484
$736$	−38601.0	−1.93322
$737$	6010.08	0.300386
$738$	47541.9	2.37133
$739$	26617.3	1.32494	0.662472	−	0.749087i	$-0.269507\pi$
$739$	26617.3	1.32494	0.662472	+	0.749087i	$0.269507\pi$
$740$	−8924.39	−0.443334
$741$	326.873	0.0162051
$742$	−5936.41	−0.293710
$743$	20951.6	1.03451	0.517253	−	0.855832i	$-0.326954\pi$
$743$	20951.6	1.03451	0.517253	+	0.855832i	$0.326954\pi$
$744$	−12549.5	−0.618395
$745$	2016.68	0.0991750
$746$	−4700.07	−0.230673
$747$	−5446.18	−0.266754
$748$	0	0
$749$	57921.2	2.82563
$750$	−47267.9	−2.30131
$751$	8252.35	0.400975	0.200488	−	0.979696i	$-0.435747\pi$
$751$	8252.35	0.400975	0.200488	+	0.979696i	$0.435747\pi$
$752$	25282.1	1.22599
$753$	19605.0	0.948801
$754$	382.262	0.0184631
$755$	−22353.7	−1.07753
$756$	−39972.4	−1.92299
$757$	−21203.1	−1.01802	−0.509010	−	0.860760i	$-0.669988\pi$
$757$	−21203.1	−1.01802	−0.509010	+	0.860760i	$0.669988\pi$
$758$	15112.1	0.724139
$759$	−24982.4	−1.19474
$760$	−907.485	−0.0433131
$761$	29378.2	1.39942	0.699711	−	0.714426i	$-0.253312\pi$
$761$	29378.2	1.39942	0.699711	+	0.714426i	$0.253312\pi$
$762$	19732.3	0.938094
$763$	−12544.3	−0.595196
$764$	24442.6	1.15746
$765$	0	0
$766$	38286.3	1.80593
$767$	−607.760	−0.0286114
$768$	48651.8	2.28590
$769$	−16559.6	−0.776532	−0.388266	−	0.921547i	$-0.626926\pi$
$769$	−16559.6	−0.776532	−0.388266	+	0.921547i	$0.626926\pi$
$770$	−11268.4	−0.527383
$771$	63333.9	2.95838
$772$	5702.13	0.265835
$773$	−39537.3	−1.83966	−0.919830	−	0.392317i	$-0.871673\pi$
$773$	−39537.3	−1.83966	−0.919830	+	0.392317i	$0.871673\pi$
$774$	65310.1	3.03297
$775$	11603.5	0.537820
$776$	12748.8	0.589762
$777$	−57621.7	−2.66045
$778$	−22895.5	−1.05507
$779$	−3361.18	−0.154592
$780$	−901.082	−0.0413640
$781$	−9420.91	−0.431634
$782$	0	0
$783$	−10485.2	−0.478558
$784$	−34988.9	−1.59388
$785$	3419.32	0.155466
$786$	67605.5	3.06795
$787$	17801.2	0.806280	0.403140	−	0.915138i	$-0.367919\pi$
$787$	17801.2	0.806280	0.403140	+	0.915138i	$0.367919\pi$
$788$	−12286.2	−0.555430
$789$	−27046.1	−1.22036
$790$	−25895.6	−1.16623
$791$	34556.0	1.55331
$792$	7520.28	0.337401
$793$	−1159.37	−0.0519175
$794$	631.287	0.0282161
$795$	3670.66	0.163755
$796$	−424.044	−0.0188817
$797$	34006.4	1.51138	0.755688	−	0.654932i	$-0.227303\pi$
$797$	34006.4	1.51138	0.755688	+	0.654932i	$0.227303\pi$
$798$	13496.9	0.598728
$799$	0	0
$800$	−16012.0	−0.707636
$801$	38460.8	1.69656
$802$	34374.7	1.51348
$803$	10674.3	0.469099
$804$	19844.4	0.870469
$805$	−36003.8	−1.57636
$806$	1438.88	0.0628813
$807$	−36808.7	−1.60561
$808$	3646.81	0.158780
$809$	−7943.98	−0.345235	−0.172618	−	0.984989i	$-0.555223\pi$
$809$	−7943.98	−0.345235	−0.172618	+	0.984989i	$0.555223\pi$
$810$	21324.9	0.925038
$811$	29182.7	1.26355	0.631777	−	0.775150i	$-0.282326\pi$
$811$	29182.7	1.26355	0.631777	+	0.775150i	$0.282326\pi$
$812$	6484.45	0.280246
$813$	57033.7	2.46034
$814$	−12727.2	−0.548018
$815$	−26352.9	−1.13264
$816$	0	0
$817$	−4617.38	−0.197726
$818$	23475.4	1.00342
$819$	−3903.81	−0.166557
$820$	9265.66	0.394599
$821$	−29589.4	−1.25783	−0.628913	−	0.777475i	$-0.716500\pi$
$821$	−29589.4	−1.25783	−0.628913	+	0.777475i	$0.716500\pi$
$822$	−20827.1	−0.883732
$823$	11121.5	0.471046	0.235523	−	0.971869i	$-0.424320\pi$
$823$	11121.5	0.471046	0.235523	+	0.971869i	$0.424320\pi$
$824$	14720.0	0.622323
$825$	−10362.9	−0.437322
$826$	−25095.0	−1.05710
$827$	12401.7	0.521461	0.260730	−	0.965412i	$-0.416037\pi$
$827$	12401.7	0.521461	0.260730	+	0.965412i	$0.416037\pi$
$828$	−55348.7	−2.32307
$829$	−6224.06	−0.260761	−0.130380	−	0.991464i	$-0.541620\pi$
$829$	−6224.06	−0.260761	−0.130380	+	0.991464i	$0.541620\pi$
$830$	−2583.66	−0.108048
$831$	−42668.8	−1.78118
$832$	−425.870	−0.0177457
$833$	0	0
$834$	−34487.3	−1.43189
$835$	15092.1	0.625491
$836$	1224.72	0.0506672
$837$	−39467.6	−1.62987
$838$	29728.7	1.22549
$839$	−36811.6	−1.51475	−0.757377	−	0.652978i	$-0.773519\pi$
$839$	−36811.6	−1.51475	−0.757377	+	0.652978i	$0.773519\pi$
$840$	16152.2	0.663458
$841$	−22688.1	−0.930258
$842$	23048.2	0.943342
$843$	−22269.3	−0.909839
$844$	11004.0	0.448782
$845$	15529.9	0.632241
$846$	66184.3	2.68967
$847$	30912.8	1.25405
$848$	4430.25	0.179405
$849$	−83384.8	−3.37074
$850$	0	0
$851$	−40664.8	−1.63804
$852$	−31106.4	−1.25081
$853$	−3319.10	−0.133228	−0.0666141	−	0.997779i	$-0.521220\pi$
$853$	−3319.10	−0.133228	−0.0666141	+	0.997779i	$0.521220\pi$
$854$	−47871.6	−1.91819
$855$	−5599.77	−0.223986
$856$	−18338.0	−0.732221
$857$	8084.66	0.322248	0.161124	−	0.986934i	$-0.448488\pi$
$857$	8084.66	0.322248	0.161124	+	0.986934i	$0.448488\pi$
$858$	−1285.04	−0.0511313
$859$	−23619.8	−0.938181	−0.469091	−	0.883150i	$-0.655418\pi$
$859$	−23619.8	−0.938181	−0.469091	+	0.883150i	$0.655418\pi$
$860$	12728.6	0.504699
$861$	59825.3	2.36799
$862$	21781.3	0.860642
$863$	−34938.3	−1.37812	−0.689058	−	0.724706i	$-0.741975\pi$
$863$	−34938.3	−1.37812	−0.689058	+	0.724706i	$0.741975\pi$
$864$	54462.4	2.14450
$865$	−8491.75	−0.333790
$866$	−43605.0	−1.71104
$867$	0	0
$868$	24408.2	0.954457
$869$	−15171.8	−0.592252
$870$	−9759.69	−0.380327
$871$	987.756	0.0384258
$872$	3971.57	0.154237
$873$	78668.3	3.04985
$874$	9525.02	0.368637
$875$	−39910.8	−1.54198
$876$	35244.8	1.35937
$877$	−20700.0	−0.797022	−0.398511	−	0.917164i	$-0.630473\pi$
$877$	−20700.0	−0.797022	−0.398511	+	0.917164i	$0.630473\pi$
$878$	27713.8	1.06525
$879$	3832.02	0.147043
$880$	8409.42	0.322138
$881$	5183.11	0.198211	0.0991053	−	0.995077i	$-0.468402\pi$
$881$	5183.11	0.198211	0.0991053	+	0.995077i	$0.468402\pi$
$882$	−91595.2	−3.49679
$883$	7357.34	0.280401	0.140201	−	0.990123i	$-0.455225\pi$
$883$	7357.34	0.280401	0.140201	+	0.990123i	$0.455225\pi$
$884$	0	0
$885$	15517.0	0.589375
$886$	−31241.6	−1.18463
$887$	35702.2	1.35148	0.675740	−	0.737140i	$-0.263824\pi$
$887$	35702.2	1.35148	0.675740	+	0.737140i	$0.263824\pi$
$888$	18243.2	0.689417
$889$	16661.1	0.628565
$890$	18245.7	0.687189
$891$	12493.9	0.469765
$892$	6568.30	0.246550
$893$	−4679.19	−0.175345
$894$	9496.12	0.355255
$895$	−29034.3	−1.08437
$896$	30718.9	1.14537
$897$	−4105.86	−0.152832
$898$	−3974.77	−0.147706
$899$	6402.56	0.237528
$900$	−22959.1	−0.850337
$901$	0	0
$902$	13213.9	0.487775
$903$	82184.2	3.02870
$904$	−10940.5	−0.402519
$905$	9195.14	0.337742
$906$	−105259.	−3.85982
$907$	5660.56	0.207228	0.103614	−	0.994618i	$-0.466959\pi$
$907$	5660.56	0.207228	0.103614	+	0.994618i	$0.466959\pi$
$908$	15872.8	0.580128
$909$	22503.2	0.821105
$910$	−1851.96	−0.0674636
$911$	11754.9	0.427506	0.213753	−	0.976888i	$-0.431431\pi$
$911$	11754.9	0.427506	0.213753	+	0.976888i	$0.431431\pi$
$912$	−10072.5	−0.365718
$913$	−1513.72	−0.0548705
$914$	−20873.9	−0.755412
$915$	29600.4	1.06946
$916$	20115.0	0.725567
$917$	57083.0	2.05567
$918$	0	0
$919$	4513.88	0.162023	0.0810116	−	0.996713i	$-0.474185\pi$
$919$	4513.88	0.162023	0.0810116	+	0.996713i	$0.474185\pi$
$920$	11398.9	0.408491
$921$	5730.59	0.205027
$922$	−2618.90	−0.0935455
$923$	−1548.32	−0.0552153
$924$	−21798.6	−0.776106
$925$	−16868.1	−0.599588
$926$	−30688.5	−1.08908
$927$	90831.6	3.21823
$928$	−8835.06	−0.312527
$929$	15124.4	0.534138	0.267069	−	0.963677i	$-0.413945\pi$
$929$	15124.4	0.534138	0.267069	+	0.963677i	$0.413945\pi$
$930$	−36736.6	−1.29531
$931$	6475.72	0.227963
$932$	−4659.03	−0.163746
$933$	47949.6	1.68253
$934$	52077.6	1.82444
$935$	0	0
$936$	1235.96	0.0431608
$937$	−19918.8	−0.694470	−0.347235	−	0.937778i	$-0.612879\pi$
$937$	−19918.8	−0.694470	−0.347235	+	0.937778i	$0.612879\pi$
$938$	40785.4	1.41971
$939$	34586.4	1.20201
$940$	12899.0	0.447573
$941$	−2072.11	−0.0717843	−0.0358921	−	0.999356i	$-0.511427\pi$
$941$	−2072.11	−0.0717843	−0.0358921	+	0.999356i	$0.511427\pi$
$942$	16100.9	0.556894
$943$	42219.8	1.45797
$944$	18728.0	0.645703
$945$	50798.1	1.74864
$946$	18152.4	0.623874
$947$	5522.83	0.189512	0.0947560	−	0.995501i	$-0.469793\pi$
$947$	5522.83	0.189512	0.0947560	+	0.995501i	$0.469793\pi$
$948$	−50094.9	−1.71625
$949$	1754.31	0.0600079
$950$	3951.06	0.134936
$951$	12587.8	0.429217
$952$	0	0
$953$	−39192.3	−1.33218	−0.666089	−	0.745873i	$-0.732033\pi$
$953$	−39192.3	−1.33218	−0.666089	+	0.745873i	$0.732033\pi$
$954$	11597.6	0.393593
$955$	−31062.4	−1.05252
$956$	−22634.1	−0.765733
$957$	−5718.03	−0.193143
$958$	24036.1	0.810616
$959$	−17585.4	−0.592140
$960$	10873.1	0.365549
$961$	−5691.04	−0.191032
$962$	−2091.71	−0.0701033
$963$	−113158.	−3.78655
$964$	−11885.4	−0.397097
$965$	−7246.44	−0.241732
$966$	−169535.	−5.64668
$967$	53414.4	1.77631	0.888155	−	0.459543i	$-0.151987\pi$
$967$	53414.4	1.77631	0.888155	+	0.459543i	$0.151987\pi$
$968$	−9787.11	−0.324968
$969$	0	0
$970$	37320.1	1.23534
$971$	−39644.8	−1.31026	−0.655130	−	0.755516i	$-0.727386\pi$
$971$	−39644.8	−1.31026	−0.655130	+	0.755516i	$0.727386\pi$
$972$	2961.66	0.0977317
$973$	−29119.4	−0.959431
$974$	−8027.47	−0.264083
$975$	−1703.14	−0.0559428
$976$	35725.8	1.17167
$977$	40232.8	1.31746	0.658732	−	0.752378i	$-0.271093\pi$
$977$	40232.8	1.31746	0.658732	+	0.752378i	$0.271093\pi$
$978$	−124090.	−4.05723
$979$	10689.9	0.348978
$980$	−17851.4	−0.581880
$981$	24507.2	0.797608
$982$	46498.6	1.51103
$983$	40449.2	1.31244	0.656220	−	0.754569i	$-0.272154\pi$
$983$	40449.2	1.31244	0.656220	+	0.754569i	$0.272154\pi$
$984$	−18940.9	−0.613631
$985$	15613.7	0.505070
$986$	0	0
$987$	83284.3	2.68589
$988$	201.282	0.00648142
$989$	57999.0	1.86477
$990$	22014.5	0.706733
$991$	−41635.0	−1.33459	−0.667296	−	0.744793i	$-0.732548\pi$
$991$	−41635.0	−1.33459	−0.667296	+	0.744793i	$0.732548\pi$
$992$	−33256.2	−1.06440
$993$	−51965.4	−1.66070
$994$	−63931.7	−2.04003
$995$	538.888	0.0171697
$996$	−4998.07	−0.159006
$997$	−33986.6	−1.07960	−0.539802	−	0.841792i	$-0.681501\pi$
$997$	−33986.6	−1.07960	−0.539802	+	0.841792i	$0.681501\pi$
$998$	50714.3	1.60855
$999$	57374.2	1.81706

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.4.a.d.1.1	yes	4
17.4	even	4		289.4.b.d.288.7		8
17.13	even	4		289.4.b.d.288.8		8
17.16	even	2		289.4.a.c.1.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.4.a.c.1.1	✓	4	17.16	even	2
289.4.a.d.1.1	yes	4	1.1	even	1	trivial
289.4.b.d.288.7		8	17.4	even	4
289.4.b.d.288.8		8	17.13	even	4

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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q-3.68488 q^{2} +9.05894 q^{3} +5.57832 q^{4} -7.08909 q^{5} -33.3811 q^{6} -28.1854 q^{7} +8.92359 q^{8} +55.0643 q^{9} +O(q^{10})\)	\(q-3.68488 q^{2} +9.05894 q^{3} +5.57832 q^{4} -7.08909 q^{5} -33.3811 q^{6} -28.1854 q^{7} +8.92359 q^{8} +55.0643 q^{9} +26.1224 q^{10} +15.3047 q^{11} +50.5336 q^{12} +2.51532 q^{13} +103.860 q^{14} -64.2196 q^{15} -77.5089 q^{16} -202.905 q^{18} +14.3453 q^{19} -39.5452 q^{20} -255.330 q^{21} -56.3958 q^{22} -180.191 q^{23} +80.8383 q^{24} -74.7448 q^{25} -9.26864 q^{26} +254.233 q^{27} -157.227 q^{28} -41.2425 q^{29} +236.641 q^{30} -155.242 q^{31} +214.222 q^{32} +138.644 q^{33} +199.809 q^{35} +307.167 q^{36} +225.676 q^{37} -52.8606 q^{38} +22.7861 q^{39} -63.2602 q^{40} -234.306 q^{41} +940.860 q^{42} -321.875 q^{43} +85.3743 q^{44} -390.356 q^{45} +663.983 q^{46} -326.183 q^{47} -702.148 q^{48} +451.418 q^{49} +275.425 q^{50} +14.0313 q^{52} -57.1579 q^{53} -936.818 q^{54} -108.496 q^{55} -251.515 q^{56} +129.953 q^{57} +151.974 q^{58} -241.623 q^{59} -358.238 q^{60} -460.925 q^{61} +572.046 q^{62} -1552.01 q^{63} -169.311 q^{64} -17.8313 q^{65} -510.886 q^{66} +392.696 q^{67} -1632.34 q^{69} -736.272 q^{70} -615.558 q^{71} +491.372 q^{72} +697.452 q^{73} -831.587 q^{74} -677.109 q^{75} +80.0226 q^{76} -431.369 q^{77} -83.9641 q^{78} -991.317 q^{79} +549.468 q^{80} +816.345 q^{81} +863.387 q^{82} -98.9057 q^{83} -1424.31 q^{84} +1186.07 q^{86} -373.613 q^{87} +136.573 q^{88} +698.470 q^{89} +1438.41 q^{90} -70.8954 q^{91} -1005.16 q^{92} -1406.32 q^{93} +1201.94 q^{94} -101.695 q^{95} +1940.62 q^{96} +1428.66 q^{97} -1663.42 q^{98} +842.741 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + 2 q^{3} + 11 q^{4} - 14 q^{5} - 38 q^{6} - 36 q^{7} + 60 q^{8} + 6 q^{9}+O(q^{10}) \) 4 * q + q^2 + 2 * q^3 + 11 * q^4 - 14 * q^5 - 38 * q^6 - 36 * q^7 + 60 * q^8 + 6 * q^9	\( 4 q + q^{2} + 2 q^{3} + 11 q^{4} - 14 q^{5} - 38 q^{6} - 36 q^{7} + 60 q^{8} + 6 q^{9} + 7 q^{10} - 10 q^{11} + 29 q^{12} - 22 q^{13} - 73 q^{14} + 54 q^{15} + 63 q^{16} - 334 q^{18} + 22 q^{19} - 330 q^{20} - 352 q^{21} + 79 q^{22} - 380 q^{23} - 159 q^{24} + 378 q^{25} - 448 q^{26} + 494 q^{27} - 608 q^{28} + 78 q^{29} + 313 q^{30} - 362 q^{31} + 331 q^{32} + 94 q^{33} - 242 q^{35} + 141 q^{36} - 512 q^{37} - 524 q^{38} - 12 q^{39} - 1381 q^{40} - 840 q^{41} + 1455 q^{42} - 114 q^{43} + 1041 q^{44} - 648 q^{45} + 1051 q^{46} + 10 q^{47} - 998 q^{48} + 1006 q^{49} + 805 q^{50} - 1537 q^{52} + 50 q^{53} - 581 q^{54} - 1316 q^{55} - 411 q^{56} - 358 q^{57} + 376 q^{58} + 996 q^{59} - 217 q^{60} - 448 q^{61} + 73 q^{62} - 766 q^{63} - 150 q^{64} + 372 q^{65} - 1090 q^{66} - 868 q^{67} - 1128 q^{69} + 1052 q^{70} - 1116 q^{71} - 39 q^{72} - 540 q^{73} - 1630 q^{74} - 1070 q^{75} - 873 q^{76} - 894 q^{77} + 1245 q^{78} - 940 q^{79} - 307 q^{80} + 1080 q^{81} + 334 q^{82} + 850 q^{83} + 443 q^{84} + 2411 q^{86} - 384 q^{87} + 2252 q^{88} + 784 q^{89} + 2069 q^{90} + 2858 q^{91} + 1566 q^{92} - 1550 q^{93} + 1119 q^{94} - 2494 q^{95} + 2643 q^{96} + 518 q^{97} - 1877 q^{98} + 1406 q^{99}+O(q^{100}) \) 4 * q + q^2 + 2 * q^3 + 11 * q^4 - 14 * q^5 - 38 * q^6 - 36 * q^7 + 60 * q^8 + 6 * q^9 + 7 * q^10 - 10 * q^11 + 29 * q^12 - 22 * q^13 - 73 * q^14 + 54 * q^15 + 63 * q^16 - 334 * q^18 + 22 * q^19 - 330 * q^20 - 352 * q^21 + 79 * q^22 - 380 * q^23 - 159 * q^24 + 378 * q^25 - 448 * q^26 + 494 * q^27 - 608 * q^28 + 78 * q^29 + 313 * q^30 - 362 * q^31 + 331 * q^32 + 94 * q^33 - 242 * q^35 + 141 * q^36 - 512 * q^37 - 524 * q^38 - 12 * q^39 - 1381 * q^40 - 840 * q^41 + 1455 * q^42 - 114 * q^43 + 1041 * q^44 - 648 * q^45 + 1051 * q^46 + 10 * q^47 - 998 * q^48 + 1006 * q^49 + 805 * q^50 - 1537 * q^52 + 50 * q^53 - 581 * q^54 - 1316 * q^55 - 411 * q^56 - 358 * q^57 + 376 * q^58 + 996 * q^59 - 217 * q^60 - 448 * q^61 + 73 * q^62 - 766 * q^63 - 150 * q^64 + 372 * q^65 - 1090 * q^66 - 868 * q^67 - 1128 * q^69 + 1052 * q^70 - 1116 * q^71 - 39 * q^72 - 540 * q^73 - 1630 * q^74 - 1070 * q^75 - 873 * q^76 - 894 * q^77 + 1245 * q^78 - 940 * q^79 - 307 * q^80 + 1080 * q^81 + 334 * q^82 + 850 * q^83 + 443 * q^84 + 2411 * q^86 - 384 * q^87 + 2252 * q^88 + 784 * q^89 + 2069 * q^90 + 2858 * q^91 + 1566 * q^92 - 1550 * q^93 + 1119 * q^94 - 2494 * q^95 + 2643 * q^96 + 518 * q^97 - 1877 * q^98 + 1406 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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