LMFDB - Embedded newform 1110.4.a.d.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1110,4,Mod(1,1110)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1110.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1110, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1110.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,4,6,8,10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$65.4921201064$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{61}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 15 $ x^2 - x - 15
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$4.40512$ of defining polynomial
Character	$\chi$	$=$	1110.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} +6.00000 q^{6} -15.0000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +10.0000 q^{10} -26.7846 q^{11} +12.0000 q^{12} -57.0512 q^{13} -30.0000 q^{14} +15.0000 q^{15} +16.0000 q^{16} -12.9744 q^{17} +18.0000 q^{18} +46.6974 q^{19} +20.0000 q^{20} -45.0000 q^{21} -53.5693 q^{22} -165.533 q^{23} +24.0000 q^{24} +25.0000 q^{25} -114.102 q^{26} +27.0000 q^{27} -60.0000 q^{28} +164.851 q^{29} +30.0000 q^{30} -295.533 q^{31} +32.0000 q^{32} -80.3539 q^{33} -25.9488 q^{34} -75.0000 q^{35} +36.0000 q^{36} -37.0000 q^{37} +93.3947 q^{38} -171.154 q^{39} +40.0000 q^{40} -300.271 q^{41} -90.0000 q^{42} +30.4716 q^{43} -107.139 q^{44} +45.0000 q^{45} -331.066 q^{46} -135.482 q^{47} +48.0000 q^{48} -118.000 q^{49} +50.0000 q^{50} -38.9231 q^{51} -228.205 q^{52} +244.615 q^{53} +54.0000 q^{54} -133.923 q^{55} -120.000 q^{56} +140.092 q^{57} +329.702 q^{58} -621.605 q^{59} +60.0000 q^{60} -274.548 q^{61} -591.066 q^{62} -135.000 q^{63} +64.0000 q^{64} -285.256 q^{65} -160.708 q^{66} +358.574 q^{67} -51.8975 q^{68} -496.600 q^{69} -150.000 q^{70} +340.677 q^{71} +72.0000 q^{72} +265.041 q^{73} -74.0000 q^{74} +75.0000 q^{75} +186.789 q^{76} +401.769 q^{77} -342.307 q^{78} +78.9384 q^{79} +80.0000 q^{80} +81.0000 q^{81} -600.543 q^{82} -1198.26 q^{83} -180.000 q^{84} -64.8719 q^{85} +60.9432 q^{86} +494.553 q^{87} -214.277 q^{88} +68.9585 q^{89} +90.0000 q^{90} +855.769 q^{91} -662.133 q^{92} -886.600 q^{93} -270.964 q^{94} +233.487 q^{95} +96.0000 q^{96} +862.211 q^{97} -236.000 q^{98} -241.062 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} + 6 q^{3} + 8 q^{4} + 10 q^{5} + 12 q^{6} - 30 q^{7} + 16 q^{8} + 18 q^{9} + 20 q^{10} - 77 q^{11} + 24 q^{12} - 36 q^{13} - 60 q^{14} + 30 q^{15} + 32 q^{16} - 65 q^{17} + 36 q^{18} - 55 q^{19}+ \cdots - 693 q^{99}+O(q^{100}) $ 2 * q + 4 * q^2 + 6 * q^3 + 8 * q^4 + 10 * q^5 + 12 * q^6 - 30 * q^7 + 16 * q^8 + 18 * q^9 + 20 * q^10 - 77 * q^11 + 24 * q^12 - 36 * q^13 - 60 * q^14 + 30 * q^15 + 32 * q^16 - 65 * q^17 + 36 * q^18 - 55 * q^19 + 40 * q^20 - 90 * q^21 - 154 * q^22 - 128 * q^23 + 48 * q^24 + 50 * q^25 - 72 * q^26 + 54 * q^27 - 120 * q^28 - 53 * q^29 + 60 * q^30 - 388 * q^31 + 64 * q^32 - 231 * q^33 - 130 * q^34 - 150 * q^35 + 72 * q^36 - 74 * q^37 - 110 * q^38 - 108 * q^39 + 80 * q^40 + 118 * q^41 - 180 * q^42 - 353 * q^43 - 308 * q^44 + 90 * q^45 - 256 * q^46 - 146 * q^47 + 96 * q^48 - 236 * q^49 + 100 * q^50 - 195 * q^51 - 144 * q^52 - 448 * q^53 + 108 * q^54 - 385 * q^55 - 240 * q^56 - 165 * q^57 - 106 * q^58 - 17 * q^59 + 120 * q^60 - 18 * q^61 - 776 * q^62 - 270 * q^63 + 128 * q^64 - 180 * q^65 - 462 * q^66 + 147 * q^67 - 260 * q^68 - 384 * q^69 - 300 * q^70 - 45 * q^71 + 144 * q^72 + 163 * q^73 - 148 * q^74 + 150 * q^75 - 220 * q^76 + 1155 * q^77 - 216 * q^78 - 53 * q^79 + 160 * q^80 + 162 * q^81 + 236 * q^82 - 1389 * q^83 - 360 * q^84 - 325 * q^85 - 706 * q^86 - 159 * q^87 - 616 * q^88 - 1018 * q^89 + 180 * q^90 + 540 * q^91 - 512 * q^92 - 1164 * q^93 - 292 * q^94 - 275 * q^95 + 192 * q^96 + 2318 * q^97 - 472 * q^98 - 693 * 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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	4.00000	0.500000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	6.00000	0.408248
$7$	−15.0000	−0.809924	−0.404962	−	0.914334i	$-0.632715\pi$
$7$	−15.0000	−0.809924	−0.404962	+	0.914334i	$0.632715\pi$
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	10.0000	0.316228
$11$	−26.7846	−0.734170	−0.367085	−	0.930187i	$-0.619644\pi$
$11$	−26.7846	−0.734170	−0.367085	+	0.930187i	$0.619644\pi$
$12$	12.0000	0.288675
$13$	−57.0512	−1.21717	−0.608583	−	0.793490i	$-0.708262\pi$
$13$	−57.0512	−1.21717	−0.608583	+	0.793490i	$0.708262\pi$
$14$	−30.0000	−0.572703
$15$	15.0000	0.258199
$16$	16.0000	0.250000
$17$	−12.9744	−0.185103	−0.0925514	−	0.995708i	$-0.529502\pi$
$17$	−12.9744	−0.185103	−0.0925514	+	0.995708i	$0.529502\pi$
$18$	18.0000	0.235702
$19$	46.6974	0.563848	0.281924	−	0.959437i	$-0.409027\pi$
$19$	46.6974	0.563848	0.281924	+	0.959437i	$0.409027\pi$
$20$	20.0000	0.223607
$21$	−45.0000	−0.467610
$22$	−53.5693	−0.519136
$23$	−165.533	−1.50070	−0.750349	−	0.661042i	$-0.770115\pi$
$23$	−165.533	−1.50070	−0.750349	+	0.661042i	$0.770115\pi$
$24$	24.0000	0.204124
$25$	25.0000	0.200000
$26$	−114.102	−0.860667
$27$	27.0000	0.192450
$28$	−60.0000	−0.404962
$29$	164.851	1.05559	0.527795	−	0.849372i	$-0.323019\pi$
$29$	164.851	1.05559	0.527795	+	0.849372i	$0.323019\pi$
$30$	30.0000	0.182574
$31$	−295.533	−1.71224	−0.856118	−	0.516780i	$-0.827131\pi$
$31$	−295.533	−1.71224	−0.856118	+	0.516780i	$0.827131\pi$
$32$	32.0000	0.176777
$33$	−80.3539	−0.423873
$34$	−25.9488	−0.130887
$35$	−75.0000	−0.362209
$36$	36.0000	0.166667
$37$	−37.0000	−0.164399
$37$	−37.0000	−0.164399
$38$	93.3947	0.398701
$39$	−171.154	−0.702732
$40$	40.0000	0.158114
$41$	−300.271	−1.14377	−0.571884	−	0.820334i	$-0.693787\pi$
$41$	−300.271	−1.14377	−0.571884	+	0.820334i	$0.693787\pi$
$42$	−90.0000	−0.330650
$43$	30.4716	0.108067	0.0540335	−	0.998539i	$-0.482792\pi$
$43$	30.4716	0.108067	0.0540335	+	0.998539i	$0.482792\pi$
$44$	−107.139	−0.367085
$45$	45.0000	0.149071
$46$	−331.066	−1.06115
$47$	−135.482	−0.420470	−0.210235	−	0.977651i	$-0.567423\pi$
$47$	−135.482	−0.420470	−0.210235	+	0.977651i	$0.567423\pi$
$48$	48.0000	0.144338
$49$	−118.000	−0.344023
$50$	50.0000	0.141421
$51$	−38.9231	−0.106869
$52$	−228.205	−0.608583
$53$	244.615	0.633971	0.316985	−	0.948430i	$-0.397329\pi$
$53$	244.615	0.633971	0.316985	+	0.948430i	$0.397329\pi$
$54$	54.0000	0.136083
$55$	−133.923	−0.328331
$56$	−120.000	−0.286351
$57$	140.092	0.325538
$58$	329.702	0.746414
$59$	−621.605	−1.37163	−0.685814	−	0.727777i	$-0.740554\pi$
$59$	−621.605	−1.37163	−0.685814	+	0.727777i	$0.740554\pi$
$60$	60.0000	0.129099
$61$	−274.548	−0.576268	−0.288134	−	0.957590i	$-0.593035\pi$
$61$	−274.548	−0.576268	−0.288134	+	0.957590i	$0.593035\pi$
$62$	−591.066	−1.21073
$63$	−135.000	−0.269975
$64$	64.0000	0.125000
$65$	−285.256	−0.544334
$66$	−160.708	−0.299724
$67$	358.574	0.653833	0.326916	−	0.945053i	$-0.393990\pi$
$67$	358.574	0.653833	0.326916	+	0.945053i	$0.393990\pi$
$68$	−51.8975	−0.0925514
$69$	−496.600	−0.866429
$70$	−150.000	−0.256120
$71$	340.677	0.569449	0.284724	−	0.958609i	$-0.408098\pi$
$71$	340.677	0.569449	0.284724	+	0.958609i	$0.408098\pi$
$72$	72.0000	0.117851
$73$	265.041	0.424941	0.212470	−	0.977167i	$-0.431849\pi$
$73$	265.041	0.424941	0.212470	+	0.977167i	$0.431849\pi$
$74$	−74.0000	−0.116248
$75$	75.0000	0.115470
$76$	186.789	0.281924
$77$	401.769	0.594622
$78$	−342.307	−0.496906
$79$	78.9384	0.112421	0.0562105	−	0.998419i	$-0.482098\pi$
$79$	78.9384	0.112421	0.0562105	+	0.998419i	$0.482098\pi$
$80$	80.0000	0.111803
$81$	81.0000	0.111111
$82$	−600.543	−0.808767
$83$	−1198.26	−1.58465	−0.792327	−	0.610097i	$-0.791130\pi$
$83$	−1198.26	−1.58465	−0.792327	+	0.610097i	$0.791130\pi$
$84$	−180.000	−0.233805
$85$	−64.8719	−0.0827805
$86$	60.9432	0.0764149
$87$	494.553	0.609445
$88$	−214.277	−0.259568
$89$	68.9585	0.0821302	0.0410651	−	0.999156i	$-0.486925\pi$
$89$	68.9585	0.0821302	0.0410651	+	0.999156i	$0.486925\pi$
$90$	90.0000	0.105409
$91$	855.769	0.985813
$92$	−662.133	−0.750349
$93$	−886.600	−0.988560
$94$	−270.964	−0.297317
$95$	233.487	0.252160
$96$	96.0000	0.102062
$97$	862.211	0.902518	0.451259	−	0.892393i	$-0.350975\pi$
$97$	862.211	0.902518	0.451259	+	0.892393i	$0.350975\pi$
$98$	−236.000	−0.243261
$99$	−241.062	−0.244723
$100$	100.000	0.100000
$101$	−127.107	−0.125224	−0.0626122	−	0.998038i	$-0.519943\pi$
$101$	−127.107	−0.125224	−0.0626122	+	0.998038i	$0.519943\pi$
$102$	−77.8463	−0.0755679
$103$	608.928	0.582519	0.291260	−	0.956644i	$-0.405926\pi$
$103$	608.928	0.582519	0.291260	+	0.956644i	$0.405926\pi$
$104$	−456.410	−0.430333
$105$	−225.000	−0.209121
$106$	489.230	0.448285
$107$	296.492	0.267878	0.133939	−	0.990990i	$-0.457237\pi$
$107$	296.492	0.267878	0.133939	+	0.990990i	$0.457237\pi$
$108$	108.000	0.0962250
$109$	−136.605	−0.120040	−0.0600199	−	0.998197i	$-0.519116\pi$
$109$	−136.605	−0.120040	−0.0600199	+	0.998197i	$0.519116\pi$
$110$	−267.846	−0.232165
$111$	−111.000	−0.0949158
$112$	−240.000	−0.202481
$113$	267.297	0.222524	0.111262	−	0.993791i	$-0.464511\pi$
$113$	267.297	0.222524	0.111262	+	0.993791i	$0.464511\pi$
$114$	280.184	0.230190
$115$	−827.666	−0.671133
$116$	659.404	0.527795
$117$	−513.461	−0.405722
$118$	−1243.21	−0.969887
$119$	194.616	0.149919
$120$	120.000	0.0912871
$121$	−613.584	−0.460995
$122$	−549.097	−0.407483
$123$	−900.814	−0.660355
$124$	−1182.13	−0.856118
$125$	125.000	0.0894427
$126$	−270.000	−0.190901
$127$	1521.61	1.06316	0.531580	−	0.847008i	$-0.321598\pi$
$127$	1521.61	1.06316	0.531580	+	0.847008i	$0.321598\pi$
$128$	128.000	0.0883883
$129$	91.4148	0.0623925
$130$	−570.512	−0.384902
$131$	−1549.88	−1.03369	−0.516846	−	0.856078i	$-0.672894\pi$
$131$	−1549.88	−1.03369	−0.516846	+	0.856078i	$0.672894\pi$
$132$	−321.416	−0.211937
$133$	−700.461	−0.456674
$134$	717.148	0.462330
$135$	135.000	0.0860663
$136$	−103.795	−0.0654437
$137$	−1591.79	−0.992673	−0.496336	−	0.868130i	$-0.665322\pi$
$137$	−1591.79	−0.992673	−0.496336	+	0.868130i	$0.665322\pi$
$138$	−993.199	−0.612658
$139$	−2311.78	−1.41067	−0.705334	−	0.708875i	$-0.749203\pi$
$139$	−2311.78	−1.41067	−0.705334	+	0.708875i	$0.749203\pi$
$140$	−300.000	−0.181104
$141$	−406.446	−0.242758
$142$	681.353	0.402661
$143$	1528.10	0.893607
$144$	144.000	0.0833333
$145$	824.256	0.472074
$146$	530.082	0.300479
$147$	−354.000	−0.198622
$148$	−148.000	−0.0821995
$149$	1530.68	0.841599	0.420800	−	0.907154i	$-0.361750\pi$
$149$	1530.68	0.841599	0.420800	+	0.907154i	$0.361750\pi$
$150$	150.000	0.0816497
$151$	−787.410	−0.424361	−0.212181	−	0.977230i	$-0.568056\pi$
$151$	−787.410	−0.424361	−0.212181	+	0.977230i	$0.568056\pi$
$152$	373.579	0.199350
$153$	−116.769	−0.0617009
$154$	803.539	0.420461
$155$	−1477.67	−0.765736
$156$	−684.615	−0.351366
$157$	537.965	0.273467	0.136733	−	0.990608i	$-0.456340\pi$
$157$	537.965	0.273467	0.136733	+	0.990608i	$0.456340\pi$
$158$	157.877	0.0794937
$159$	733.845	0.366023
$160$	160.000	0.0790569
$161$	2483.00	1.21545
$162$	162.000	0.0785674
$163$	2494.09	1.19848	0.599240	−	0.800569i	$-0.295470\pi$
$163$	2494.09	1.19848	0.599240	+	0.800569i	$0.295470\pi$
$164$	−1201.09	−0.571884
$165$	−401.769	−0.189562
$166$	−2396.52	−1.12052
$167$	1127.40	0.522402	0.261201	−	0.965284i	$-0.415881\pi$
$167$	1127.40	0.522402	0.261201	+	0.965284i	$0.415881\pi$
$168$	−360.000	−0.165325
$169$	1057.84	0.481495
$170$	−129.744	−0.0585347
$171$	420.276	0.187949
$172$	121.886	0.0540335
$173$	−660.148	−0.290116	−0.145058	−	0.989423i	$-0.546337\pi$
$173$	−660.148	−0.290116	−0.145058	+	0.989423i	$0.546337\pi$
$174$	989.107	0.430942
$175$	−375.000	−0.161985
$176$	−428.554	−0.183542
$177$	−1864.81	−0.791910
$178$	137.917	0.0580748
$179$	−432.744	−0.180697	−0.0903486	−	0.995910i	$-0.528798\pi$
$179$	−432.744	−0.180697	−0.0903486	+	0.995910i	$0.528798\pi$
$180$	180.000	0.0745356
$181$	−397.553	−0.163259	−0.0816296	−	0.996663i	$-0.526012\pi$
$181$	−397.553	−0.163259	−0.0816296	+	0.996663i	$0.526012\pi$
$182$	1711.54	0.697075
$183$	−823.645	−0.332708
$184$	−1324.27	−0.530577
$185$	−185.000	−0.0735215
$186$	−1773.20	−0.699018
$187$	347.514	0.135897
$188$	−541.928	−0.210235
$189$	−405.000	−0.155870
$190$	466.974	0.178304
$191$	2933.78	1.11142	0.555710	−	0.831376i	$-0.312447\pi$
$191$	2933.78	1.11142	0.555710	+	0.831376i	$0.312447\pi$
$192$	192.000	0.0721688
$193$	1410.17	0.525941	0.262970	−	0.964804i	$-0.415298\pi$
$193$	1410.17	0.525941	0.262970	+	0.964804i	$0.415298\pi$
$194$	1724.42	0.638176
$195$	−855.769	−0.314271
$196$	−472.000	−0.172012
$197$	2820.29	1.01999	0.509994	−	0.860178i	$-0.329648\pi$
$197$	2820.29	1.01999	0.509994	+	0.860178i	$0.329648\pi$
$198$	−482.123	−0.173045
$199$	994.003	0.354085	0.177043	−	0.984203i	$-0.443347\pi$
$199$	994.003	0.354085	0.177043	+	0.984203i	$0.443347\pi$
$200$	200.000	0.0707107
$201$	1075.72	0.377491
$202$	−254.215	−0.0885470
$203$	−2472.77	−0.854947
$204$	−155.693	−0.0534346
$205$	−1501.36	−0.511509
$206$	1217.86	0.411903
$207$	−1489.80	−0.500233
$208$	−912.820	−0.304292
$209$	−1250.77	−0.413960
$210$	−450.000	−0.147871
$211$	−1808.75	−0.590141	−0.295071	−	0.955475i	$-0.595343\pi$
$211$	−1808.75	−0.590141	−0.295071	+	0.955475i	$0.595343\pi$
$212$	978.460	0.316985
$213$	1022.03	0.328772
$214$	592.983	0.189418
$215$	152.358	0.0483290
$216$	216.000	0.0680414
$217$	4433.00	1.38678
$218$	−273.209	−0.0848810
$219$	795.123	0.245340
$220$	−535.693	−0.164165
$221$	740.204	0.225301
$222$	−222.000	−0.0671156
$223$	−1922.28	−0.577245	−0.288622	−	0.957443i	$-0.593197\pi$
$223$	−1922.28	−0.577245	−0.288622	+	0.957443i	$0.593197\pi$
$224$	−480.000	−0.143176
$225$	225.000	0.0666667
$226$	534.594	0.157348
$227$	−5752.35	−1.68192	−0.840962	−	0.541095i	$-0.818010\pi$
$227$	−5752.35	−1.68192	−0.840962	+	0.541095i	$0.818010\pi$
$228$	560.368	0.162769
$229$	−5578.18	−1.60968	−0.804840	−	0.593492i	$-0.797749\pi$
$229$	−5578.18	−1.60968	−0.804840	+	0.593492i	$0.797749\pi$
$230$	−1655.33	−0.474563
$231$	1205.31	0.343305
$232$	1318.81	0.373207
$233$	970.899	0.272986	0.136493	−	0.990641i	$-0.456417\pi$
$233$	970.899	0.272986	0.136493	+	0.990641i	$0.456417\pi$
$234$	−1026.92	−0.286889
$235$	−677.410	−0.188040
$236$	−2486.42	−0.685814
$237$	236.815	0.0649063
$238$	389.231	0.106009
$239$	−2930.18	−0.793044	−0.396522	−	0.918025i	$-0.629783\pi$
$239$	−2930.18	−0.793044	−0.396522	+	0.918025i	$0.629783\pi$
$240$	240.000	0.0645497
$241$	−3231.34	−0.863688	−0.431844	−	0.901948i	$-0.642137\pi$
$241$	−3231.34	−0.863688	−0.431844	+	0.901948i	$0.642137\pi$
$242$	−1227.17	−0.325972
$243$	243.000	0.0641500
$244$	−1098.19	−0.288134
$245$	−590.000	−0.153852
$246$	−1801.63	−0.466942
$247$	−2664.14	−0.686297
$248$	−2364.27	−0.605367
$249$	−3594.78	−0.914900
$250$	250.000	0.0632456
$251$	−3532.50	−0.888324	−0.444162	−	0.895947i	$-0.646499\pi$
$251$	−3532.50	−0.888324	−0.444162	+	0.895947i	$0.646499\pi$
$252$	−540.000	−0.134987
$253$	4433.75	1.10177
$254$	3043.23	0.751768
$255$	−194.616	−0.0477933
$256$	256.000	0.0625000
$257$	763.609	0.185341	0.0926704	−	0.995697i	$-0.470460\pi$
$257$	763.609	0.185341	0.0926704	+	0.995697i	$0.470460\pi$
$258$	182.830	0.0441181
$259$	555.000	0.133151
$260$	−1141.02	−0.272167
$261$	1483.66	0.351863
$262$	−3099.76	−0.730931
$263$	−3670.37	−0.860549	−0.430275	−	0.902698i	$-0.641583\pi$
$263$	−3670.37	−0.860549	−0.430275	+	0.902698i	$0.641583\pi$
$264$	−642.831	−0.149862
$265$	1223.07	0.283520
$266$	−1400.92	−0.322917
$267$	206.875	0.0474179
$268$	1434.30	0.326916
$269$	4925.90	1.11650	0.558248	−	0.829674i	$-0.311474\pi$
$269$	4925.90	1.11650	0.558248	+	0.829674i	$0.311474\pi$
$270$	270.000	0.0608581
$271$	5433.00	1.21783	0.608914	−	0.793236i	$-0.291605\pi$
$271$	5433.00	1.21783	0.608914	+	0.793236i	$0.291605\pi$
$272$	−207.590	−0.0462757
$273$	2567.31	0.569159
$274$	−3183.59	−0.701926
$275$	−669.616	−0.146834
$276$	−1986.40	−0.433214
$277$	330.030	0.0715870	0.0357935	−	0.999359i	$-0.488604\pi$
$277$	330.030	0.0715870	0.0357935	+	0.999359i	$0.488604\pi$
$278$	−4623.57	−0.997493
$279$	−2659.80	−0.570746
$280$	−600.000	−0.128060
$281$	6764.78	1.43613	0.718065	−	0.695976i	$-0.245028\pi$
$281$	6764.78	1.43613	0.718065	+	0.695976i	$0.245028\pi$
$282$	−812.892	−0.171656
$283$	889.783	0.186898	0.0934490	−	0.995624i	$-0.470211\pi$
$283$	889.783	0.186898	0.0934490	+	0.995624i	$0.470211\pi$
$284$	1362.71	0.284724
$285$	700.461	0.145585
$286$	3056.19	0.631876
$287$	4504.07	0.926366
$288$	288.000	0.0589256
$289$	−4744.67	−0.965737
$290$	1648.51	0.333807
$291$	2586.63	0.521069
$292$	1060.16	0.212470
$293$	7552.67	1.50591	0.752955	−	0.658072i	$-0.228628\pi$
$293$	7552.67	1.50591	0.752955	+	0.658072i	$0.228628\pi$
$294$	−708.000	−0.140447
$295$	−3108.02	−0.613410
$296$	−296.000	−0.0581238
$297$	−723.185	−0.141291
$298$	3061.36	0.595101
$299$	9443.88	1.82660
$300$	300.000	0.0577350
$301$	−457.074	−0.0875260
$302$	−1574.82	−0.300069
$303$	−381.322	−0.0722983
$304$	747.158	0.140962
$305$	−1372.74	−0.257715
$306$	−233.539	−0.0436292
$307$	−8377.27	−1.55738	−0.778691	−	0.627408i	$-0.784116\pi$
$307$	−8377.27	−1.55738	−0.778691	+	0.627408i	$0.784116\pi$
$308$	1607.08	0.297311
$309$	1826.78	0.336318
$310$	−2955.33	−0.541457
$311$	7585.96	1.38315	0.691576	−	0.722304i	$-0.256917\pi$
$311$	7585.96	1.38315	0.691576	+	0.722304i	$0.256917\pi$
$312$	−1369.23	−0.248453
$313$	−1313.91	−0.237274	−0.118637	−	0.992938i	$-0.537853\pi$
$313$	−1313.91	−0.237274	−0.118637	+	0.992938i	$0.537853\pi$
$314$	1075.93	0.193370
$315$	−675.000	−0.120736
$316$	315.753	0.0562105
$317$	2869.77	0.508462	0.254231	−	0.967143i	$-0.418178\pi$
$317$	2869.77	0.508462	0.254231	+	0.967143i	$0.418178\pi$
$318$	1467.69	0.258817
$319$	−4415.48	−0.774982
$320$	320.000	0.0559017
$321$	889.475	0.154659
$322$	4966.00	0.859454
$323$	−605.869	−0.104370
$324$	324.000	0.0555556
$325$	−1426.28	−0.243433
$326$	4988.18	0.847453
$327$	−409.814	−0.0693051
$328$	−2402.17	−0.404383
$329$	2032.23	0.340549
$330$	−803.539	−0.134040
$331$	1761.70	0.292544	0.146272	−	0.989244i	$-0.453273\pi$
$331$	1761.70	0.292544	0.146272	+	0.989244i	$0.453273\pi$
$332$	−4793.04	−0.792327
$333$	−333.000	−0.0547997
$334$	2254.81	0.369394
$335$	1792.87	0.292403
$336$	−720.000	−0.116902
$337$	2211.28	0.357437	0.178718	−	0.983900i	$-0.442805\pi$
$337$	2211.28	0.357437	0.178718	+	0.983900i	$0.442805\pi$
$338$	2115.69	0.340469
$339$	801.891	0.128474
$340$	−259.488	−0.0413903
$341$	7915.75	1.25707
$342$	840.553	0.132900
$343$	6915.00	1.08856
$344$	243.773	0.0382074
$345$	−2483.00	−0.387479
$346$	−1320.30	−0.205143
$347$	−8171.18	−1.26413	−0.632063	−	0.774917i	$-0.717792\pi$
$347$	−8171.18	−1.26413	−0.632063	+	0.774917i	$0.717792\pi$
$348$	1978.21	0.304722
$349$	4176.79	0.640626	0.320313	−	0.947312i	$-0.396212\pi$
$349$	4176.79	0.640626	0.320313	+	0.947312i	$0.396212\pi$
$350$	−750.000	−0.114541
$351$	−1540.38	−0.234244
$352$	−857.108	−0.129784
$353$	1495.33	0.225463	0.112731	−	0.993626i	$-0.464040\pi$
$353$	1495.33	0.225463	0.112731	+	0.993626i	$0.464040\pi$
$354$	−3729.63	−0.559965
$355$	1703.38	0.254665
$356$	275.834	0.0410651
$357$	583.847	0.0865559
$358$	−865.488	−0.127772
$359$	1103.46	0.162224	0.0811120	−	0.996705i	$-0.474153\pi$
$359$	1103.46	0.162224	0.0811120	+	0.996705i	$0.474153\pi$
$360$	360.000	0.0527046
$361$	−4678.36	−0.682075
$362$	−795.107	−0.115442
$363$	−1840.75	−0.266155
$364$	3423.07	0.492906
$365$	1325.20	0.190039
$366$	−1647.29	−0.235260
$367$	−4983.52	−0.708821	−0.354411	−	0.935090i	$-0.615319\pi$
$367$	−4983.52	−0.708821	−0.354411	+	0.935090i	$0.615319\pi$
$368$	−2648.53	−0.375175
$369$	−2702.44	−0.381256
$370$	−370.000	−0.0519875
$371$	−3669.22	−0.513468
$372$	−3546.40	−0.494280
$373$	−1391.91	−0.193219	−0.0966093	−	0.995322i	$-0.530800\pi$
$373$	−1391.91	−0.193219	−0.0966093	+	0.995322i	$0.530800\pi$
$374$	695.028	0.0960936
$375$	375.000	0.0516398
$376$	−1083.86	−0.148659
$377$	−9404.96	−1.28483
$378$	−810.000	−0.110217
$379$	6168.03	0.835964	0.417982	−	0.908455i	$-0.362738\pi$
$379$	6168.03	0.835964	0.417982	+	0.908455i	$0.362738\pi$
$380$	933.947	0.126080
$381$	4564.84	0.613816
$382$	5867.57	0.785892
$383$	3021.56	0.403119	0.201559	−	0.979476i	$-0.435399\pi$
$383$	3021.56	0.403119	0.201559	+	0.979476i	$0.435399\pi$
$384$	384.000	0.0510310
$385$	2008.85	0.265923
$386$	2820.35	0.371896
$387$	274.245	0.0360223
$388$	3448.84	0.451259
$389$	−1304.45	−0.170021	−0.0850107	−	0.996380i	$-0.527092\pi$
$389$	−1304.45	−0.170021	−0.0850107	+	0.996380i	$0.527092\pi$
$390$	−1711.54	−0.222223
$391$	2147.69	0.277784
$392$	−944.000	−0.121631
$393$	−4649.64	−0.596803
$394$	5640.58	0.721240
$395$	394.692	0.0502762
$396$	−964.247	−0.122362
$397$	−581.119	−0.0734648	−0.0367324	−	0.999325i	$-0.511695\pi$
$397$	−581.119	−0.0734648	−0.0367324	+	0.999325i	$0.511695\pi$
$398$	1988.01	0.250376
$399$	−2101.38	−0.263661
$400$	400.000	0.0500000
$401$	−280.212	−0.0348956	−0.0174478	−	0.999848i	$-0.505554\pi$
$401$	−280.212	−0.0348956	−0.0174478	+	0.999848i	$0.505554\pi$
$402$	2151.44	0.266926
$403$	16860.5	2.08408
$404$	−508.429	−0.0626122
$405$	405.000	0.0496904
$406$	−4945.53	−0.604539
$407$	991.031	0.120697
$408$	−311.385	−0.0377840
$409$	4398.97	0.531822	0.265911	−	0.963998i	$-0.414327\pi$
$409$	4398.97	0.531822	0.265911	+	0.963998i	$0.414327\pi$
$410$	−3002.71	−0.361692
$411$	−4775.38	−0.573120
$412$	2435.71	0.291260
$413$	9324.07	1.11091
$414$	−2979.60	−0.353718
$415$	−5991.31	−0.708679
$416$	−1825.64	−0.215167
$417$	−6935.35	−0.814450
$418$	−2501.54	−0.292714
$419$	−1105.83	−0.128934	−0.0644669	−	0.997920i	$-0.520535\pi$
$419$	−1105.83	−0.128934	−0.0644669	+	0.997920i	$0.520535\pi$
$420$	−900.000	−0.104561
$421$	−97.9803	−0.0113427	−0.00567134	−	0.999984i	$-0.501805\pi$
$421$	−97.9803	−0.0113427	−0.00567134	+	0.999984i	$0.501805\pi$
$422$	−3617.51	−0.417293
$423$	−1219.34	−0.140157
$424$	1956.92	0.224143
$425$	−324.359	−0.0370206
$426$	2044.06	0.232477
$427$	4118.23	0.466733
$428$	1185.97	0.133939
$429$	4584.29	0.515924
$430$	304.716	0.0341738
$431$	−7923.81	−0.885560	−0.442780	−	0.896630i	$-0.646008\pi$
$431$	−7923.81	−0.885560	−0.442780	+	0.896630i	$0.646008\pi$
$432$	432.000	0.0481125
$433$	−3310.70	−0.367442	−0.183721	−	0.982978i	$-0.558814\pi$
$433$	−3310.70	−0.367442	−0.183721	+	0.982978i	$0.558814\pi$
$434$	8866.00	0.980603
$435$	2472.77	0.272552
$436$	−546.418	−0.0600199
$437$	−7729.97	−0.846166
$438$	1590.25	0.173481
$439$	14667.0	1.59458	0.797289	−	0.603598i	$-0.206267\pi$
$439$	14667.0	1.59458	0.797289	+	0.603598i	$0.206267\pi$
$440$	−1071.39	−0.116082
$441$	−1062.00	−0.114674
$442$	1480.41	0.159312
$443$	10521.6	1.12844	0.564219	−	0.825625i	$-0.309177\pi$
$443$	10521.6	1.12844	0.564219	+	0.825625i	$0.309177\pi$
$444$	−444.000	−0.0474579
$445$	344.792	0.0367297
$446$	−3844.57	−0.408174
$447$	4592.04	0.485898
$448$	−960.000	−0.101240
$449$	−8576.96	−0.901496	−0.450748	−	0.892651i	$-0.648843\pi$
$449$	−8576.96	−0.901496	−0.450748	+	0.892651i	$0.648843\pi$
$450$	450.000	0.0471405
$451$	8042.66	0.839721
$452$	1069.19	0.111262
$453$	−2362.23	−0.245005
$454$	−11504.7	−1.18930
$455$	4278.84	0.440869
$456$	1120.74	0.115095
$457$	−6264.65	−0.641243	−0.320622	−	0.947207i	$-0.603892\pi$
$457$	−6264.65	−0.641243	−0.320622	+	0.947207i	$0.603892\pi$
$458$	−11156.4	−1.13822
$459$	−350.308	−0.0356231
$460$	−3310.66	−0.335566
$461$	1440.59	0.145542	0.0727709	−	0.997349i	$-0.476816\pi$
$461$	1440.59	0.145542	0.0727709	+	0.997349i	$0.476816\pi$
$462$	2410.62	0.242753
$463$	241.973	0.0242882	0.0121441	−	0.999926i	$-0.496134\pi$
$463$	241.973	0.0242882	0.0121441	+	0.999926i	$0.496134\pi$
$464$	2637.62	0.263897
$465$	−4433.00	−0.442098
$466$	1941.80	0.193030
$467$	7604.45	0.753516	0.376758	−	0.926312i	$-0.377039\pi$
$467$	7604.45	0.753516	0.376758	+	0.926312i	$0.377039\pi$
$468$	−2053.84	−0.202861
$469$	−5378.61	−0.529555
$470$	−1354.82	−0.132964
$471$	1613.90	0.157886
$472$	−4972.84	−0.484944
$473$	−816.171	−0.0793395
$474$	473.630	0.0458957
$475$	1167.43	0.112770
$476$	778.463	0.0749596
$477$	2201.53	0.211324
$478$	−5860.36	−0.560767
$479$	15776.1	1.50486	0.752430	−	0.658672i	$-0.228882\pi$
$479$	15776.1	1.50486	0.752430	+	0.658672i	$0.228882\pi$
$480$	480.000	0.0456435
$481$	2110.90	0.200101
$482$	−6462.67	−0.610719
$483$	7449.00	0.701741
$484$	−2454.34	−0.230497
$485$	4311.05	0.403618
$486$	486.000	0.0453609
$487$	−12752.9	−1.18663	−0.593316	−	0.804970i	$-0.702181\pi$
$487$	−12752.9	−1.18663	−0.593316	+	0.804970i	$0.702181\pi$
$488$	−2196.39	−0.203741
$489$	7482.27	0.691943
$490$	−1180.00	−0.108790
$491$	1135.95	0.104409	0.0522046	−	0.998636i	$-0.483375\pi$
$491$	1135.95	0.104409	0.0522046	+	0.998636i	$0.483375\pi$
$492$	−3603.26	−0.330178
$493$	−2138.84	−0.195393
$494$	−5328.29	−0.485285
$495$	−1205.31	−0.109444
$496$	−4728.53	−0.428059
$497$	−5110.15	−0.461210
$498$	−7189.57	−0.646932
$499$	−5259.34	−0.471825	−0.235912	−	0.971774i	$-0.575808\pi$
$499$	−5259.34	−0.471825	−0.235912	+	0.971774i	$0.575808\pi$
$500$	500.000	0.0447214
$501$	3382.21	0.301609
$502$	−7065.00	−0.628140
$503$	22139.7	1.96255	0.981275	−	0.192614i	$-0.0616964\pi$
$503$	22139.7	1.96255	0.981275	+	0.192614i	$0.0616964\pi$
$504$	−1080.00	−0.0954504
$505$	−635.537	−0.0560020
$506$	8867.49	0.779067
$507$	3173.53	0.277991
$508$	6086.46	0.531580
$509$	−13693.7	−1.19246	−0.596228	−	0.802815i	$-0.703335\pi$
$509$	−13693.7	−1.19246	−0.596228	+	0.802815i	$0.703335\pi$
$510$	−389.231	−0.0337950
$511$	−3975.61	−0.344170
$512$	512.000	0.0441942
$513$	1260.83	0.108513
$514$	1527.22	0.131056
$515$	3044.64	0.260510
$516$	365.659	0.0311962
$517$	3628.83	0.308696
$518$	1110.00	0.0941517
$519$	−1980.44	−0.167499
$520$	−2282.05	−0.192451
$521$	13384.4	1.12549	0.562746	−	0.826630i	$-0.309745\pi$
$521$	13384.4	1.12549	0.562746	+	0.826630i	$0.309745\pi$
$522$	2967.32	0.248805
$523$	−11324.1	−0.946781	−0.473391	−	0.880853i	$-0.656970\pi$
$523$	−11324.1	−0.946781	−0.473391	+	0.880853i	$0.656970\pi$
$524$	−6199.52	−0.516846
$525$	−1125.00	−0.0935220
$526$	−7340.73	−0.608500
$527$	3834.36	0.316940
$528$	−1285.66	−0.105968
$529$	15234.3	1.25210
$530$	2446.15	0.200479
$531$	−5594.44	−0.457209
$532$	−2801.84	−0.228337
$533$	17130.9	1.39216
$534$	413.751	0.0335295
$535$	1482.46	0.119799
$536$	2868.59	0.231165
$537$	−1298.23	−0.104326
$538$	9851.80	0.789482
$539$	3160.59	0.252572
$540$	540.000	0.0430331
$541$	−8718.79	−0.692884	−0.346442	−	0.938071i	$-0.612610\pi$
$541$	−8718.79	−0.692884	−0.346442	+	0.938071i	$0.612610\pi$
$542$	10866.0	0.861134
$543$	−1192.66	−0.0942577
$544$	−415.180	−0.0327219
$545$	−683.023	−0.0536835
$546$	5134.61	0.402456
$547$	16618.2	1.29898	0.649490	−	0.760370i	$-0.274982\pi$
$547$	16618.2	1.29898	0.649490	+	0.760370i	$0.274982\pi$
$548$	−6367.18	−0.496336
$549$	−2470.94	−0.192089
$550$	−1339.23	−0.103827
$551$	7698.11	0.595192
$552$	−3972.80	−0.306329
$553$	−1184.08	−0.0910525
$554$	660.061	0.0506197
$555$	−555.000	−0.0424476
$556$	−9247.13	−0.705334
$557$	−3006.33	−0.228693	−0.114347	−	0.993441i	$-0.536477\pi$
$557$	−3006.33	−0.228693	−0.114347	+	0.993441i	$0.536477\pi$
$558$	−5319.60	−0.403578
$559$	−1738.44	−0.131535
$560$	−1200.00	−0.0905522
$561$	1042.54	0.0784601
$562$	13529.6	1.01550
$563$	13739.2	1.02849	0.514245	−	0.857643i	$-0.328072\pi$
$563$	13739.2	1.02849	0.514245	+	0.857643i	$0.328072\pi$
$564$	−1625.78	−0.121379
$565$	1336.49	0.0995157
$566$	1779.57	0.132157
$567$	−1215.00	−0.0899915
$568$	2725.41	0.201331
$569$	−15449.8	−1.13829	−0.569146	−	0.822236i	$-0.692726\pi$
$569$	−15449.8	−1.13829	−0.569146	+	0.822236i	$0.692726\pi$
$570$	1400.92	0.102944
$571$	17518.4	1.28393	0.641963	−	0.766735i	$-0.278120\pi$
$571$	17518.4	1.28393	0.641963	+	0.766735i	$0.278120\pi$
$572$	6112.39	0.446804
$573$	8801.35	0.641678
$574$	9008.14	0.655040
$575$	−4138.33	−0.300140
$576$	576.000	0.0416667
$577$	−2617.70	−0.188867	−0.0944337	−	0.995531i	$-0.530104\pi$
$577$	−2617.70	−0.188867	−0.0944337	+	0.995531i	$0.530104\pi$
$578$	−9489.33	−0.682879
$579$	4230.52	0.303652
$580$	3297.02	0.236037
$581$	17973.9	1.28345
$582$	5173.26	0.368451
$583$	−6551.92	−0.465442
$584$	2120.33	0.150239
$585$	−2567.31	−0.181445
$586$	15105.3	1.06484
$587$	6984.06	0.491078	0.245539	−	0.969387i	$-0.421035\pi$
$587$	6984.06	0.491078	0.245539	+	0.969387i	$0.421035\pi$
$588$	−1416.00	−0.0993110
$589$	−13800.6	−0.965441
$590$	−6216.05	−0.433747
$591$	8460.88	0.588890
$592$	−592.000	−0.0410997
$593$	9635.18	0.667234	0.333617	−	0.942709i	$-0.391731\pi$
$593$	9635.18	0.667234	0.333617	+	0.942709i	$0.391731\pi$
$594$	−1446.37	−0.0999079
$595$	973.078	0.0670459
$596$	6122.73	0.420800
$597$	2982.01	0.204431
$598$	18887.8	1.29160
$599$	−9031.78	−0.616074	−0.308037	−	0.951374i	$-0.599672\pi$
$599$	−9031.78	−0.616074	−0.308037	+	0.951374i	$0.599672\pi$
$600$	600.000	0.0408248
$601$	−13888.4	−0.942631	−0.471315	−	0.881965i	$-0.656221\pi$
$601$	−13888.4	−0.942631	−0.471315	+	0.881965i	$0.656221\pi$
$602$	−914.148	−0.0618902
$603$	3227.17	0.217944
$604$	−3149.64	−0.212181
$605$	−3067.92	−0.206163
$606$	−762.644	−0.0511226
$607$	−25762.8	−1.72270	−0.861350	−	0.508012i	$-0.830381\pi$
$607$	−25762.8	−1.72270	−0.861350	+	0.508012i	$0.830381\pi$
$608$	1494.32	0.0996752
$609$	−7418.30	−0.493604
$610$	−2745.48	−0.182232
$611$	7729.42	0.511782
$612$	−467.078	−0.0308505
$613$	−3581.26	−0.235964	−0.117982	−	0.993016i	$-0.537642\pi$
$613$	−3581.26	−0.235964	−0.117982	+	0.993016i	$0.537642\pi$
$614$	−16754.5	−1.10123
$615$	−4504.07	−0.295320
$616$	3214.16	0.210231
$617$	21318.3	1.39099	0.695496	−	0.718530i	$-0.255185\pi$
$617$	21318.3	1.39099	0.695496	+	0.718530i	$0.255185\pi$
$618$	3653.57	0.237812
$619$	−18295.6	−1.18798	−0.593992	−	0.804471i	$-0.702449\pi$
$619$	−18295.6	−1.18798	−0.593992	+	0.804471i	$0.702449\pi$
$620$	−5910.66	−0.382868
$621$	−4469.40	−0.288810
$622$	15171.9	0.978036
$623$	−1034.38	−0.0665192
$624$	−2738.46	−0.175683
$625$	625.000	0.0400000
$626$	−2627.83	−0.167778
$627$	−3752.31	−0.239000
$628$	2151.86	0.136733
$629$	480.052	0.0304307
$630$	−1350.00	−0.0853735
$631$	−23436.2	−1.47858	−0.739288	−	0.673389i	$-0.764838\pi$
$631$	−23436.2	−1.47858	−0.739288	+	0.673389i	$0.764838\pi$
$632$	631.507	0.0397468
$633$	−5426.26	−0.340718
$634$	5739.55	0.359537
$635$	7608.07	0.475460
$636$	2935.38	0.183012
$637$	6732.05	0.418734
$638$	−8830.95	−0.547995
$639$	3066.09	0.189816
$640$	640.000	0.0395285
$641$	25842.2	1.59236	0.796181	−	0.605059i	$-0.206850\pi$
$641$	25842.2	1.59236	0.796181	+	0.605059i	$0.206850\pi$
$642$	1778.95	0.109361
$643$	−16165.6	−0.991459	−0.495730	−	0.868477i	$-0.665099\pi$
$643$	−16165.6	−0.991459	−0.495730	+	0.868477i	$0.665099\pi$
$644$	9931.99	0.607726
$645$	457.074	0.0279028
$646$	−1211.74	−0.0738006
$647$	19181.1	1.16551	0.582757	−	0.812646i	$-0.301974\pi$
$647$	19181.1	1.16551	0.582757	+	0.812646i	$0.301974\pi$
$648$	648.000	0.0392837
$649$	16649.4	1.00701
$650$	−2852.56	−0.172133
$651$	13299.0	0.800659
$652$	9976.36	0.599240
$653$	15846.6	0.949656	0.474828	−	0.880079i	$-0.342510\pi$
$653$	15846.6	0.949656	0.474828	+	0.880079i	$0.342510\pi$
$654$	−819.628	−0.0490061
$655$	−7749.40	−0.462281
$656$	−4804.34	−0.285942
$657$	2385.37	0.141647
$658$	4064.46	0.240804
$659$	8331.36	0.492479	0.246240	−	0.969209i	$-0.420805\pi$
$659$	8331.36	0.492479	0.246240	+	0.969209i	$0.420805\pi$
$660$	−1607.08	−0.0947809
$661$	23218.8	1.36627	0.683136	−	0.730291i	$-0.260615\pi$
$661$	23218.8	1.36627	0.683136	+	0.730291i	$0.260615\pi$
$662$	3523.41	0.206860
$663$	2220.61	0.130078
$664$	−9586.09	−0.560260
$665$	−3502.30	−0.204231
$666$	−666.000	−0.0387492
$667$	−27288.3	−1.58412
$668$	4509.62	0.261201
$669$	−5766.85	−0.333272
$670$	3585.74	0.206760
$671$	7353.68	0.423078
$672$	−1440.00	−0.0826625
$673$	−1004.45	−0.0575313	−0.0287656	−	0.999586i	$-0.509158\pi$
$673$	−1004.45	−0.0575313	−0.0287656	+	0.999586i	$0.509158\pi$
$674$	4422.57	0.252746
$675$	675.000	0.0384900
$676$	4231.38	0.240748
$677$	−2250.83	−0.127779	−0.0638895	−	0.997957i	$-0.520351\pi$
$677$	−2250.83	−0.127779	−0.0638895	+	0.997957i	$0.520351\pi$
$678$	1603.78	0.0908450
$679$	−12933.2	−0.730971
$680$	−518.975	−0.0292673
$681$	−17257.0	−0.971059
$682$	15831.5	0.888885
$683$	−14575.9	−0.816592	−0.408296	−	0.912850i	$-0.633877\pi$
$683$	−14575.9	−0.816592	−0.408296	+	0.912850i	$0.633877\pi$
$684$	1681.11	0.0939747
$685$	−7958.97	−0.443937
$686$	13830.0	0.769726
$687$	−16734.6	−0.929349
$688$	487.546	0.0270167
$689$	−13955.6	−0.771648
$690$	−4966.00	−0.273989
$691$	−14486.8	−0.797545	−0.398772	−	0.917050i	$-0.630564\pi$
$691$	−14486.8	−0.797545	−0.398772	+	0.917050i	$0.630564\pi$
$692$	−2640.59	−0.145058
$693$	3615.92	0.198207
$694$	−16342.4	−0.893872
$695$	−11558.9	−0.630870
$696$	3956.43	0.215471
$697$	3895.84	0.211715
$698$	8353.58	0.452991
$699$	2912.70	0.157608
$700$	−1500.00	−0.0809924
$701$	12920.4	0.696141	0.348071	−	0.937468i	$-0.386837\pi$
$701$	12920.4	0.696141	0.348071	+	0.937468i	$0.386837\pi$
$702$	−3080.77	−0.165635
$703$	−1727.80	−0.0926960
$704$	−1714.22	−0.0917712
$705$	−2032.23	−0.108565
$706$	2990.66	0.159426
$707$	1906.61	0.101422
$708$	−7459.26	−0.395955
$709$	−6570.90	−0.348061	−0.174031	−	0.984740i	$-0.555679\pi$
$709$	−6570.90	−0.348061	−0.174031	+	0.984740i	$0.555679\pi$
$710$	3406.77	0.180076
$711$	710.445	0.0374737
$712$	551.668	0.0290374
$713$	48920.6	2.56955
$714$	1167.69	0.0612043
$715$	7640.48	0.399633
$716$	−1730.98	−0.0903486
$717$	−8790.54	−0.457864
$718$	2206.92	0.114710
$719$	−9874.49	−0.512179	−0.256089	−	0.966653i	$-0.582434\pi$
$719$	−9874.49	−0.512179	−0.256089	+	0.966653i	$0.582434\pi$
$720$	720.000	0.0372678
$721$	−9133.92	−0.471796
$722$	−9356.71	−0.482300
$723$	−9694.01	−0.498650
$724$	−1590.21	−0.0816296
$725$	4121.28	0.211118
$726$	−3681.50	−0.188200
$727$	26800.8	1.36725	0.683623	−	0.729835i	$-0.260403\pi$
$727$	26800.8	1.36725	0.683623	+	0.729835i	$0.260403\pi$
$728$	6846.15	0.348537
$729$	729.000	0.0370370
$730$	2650.41	0.134378
$731$	−395.350	−0.0200035
$732$	−3294.58	−0.166354
$733$	−6828.40	−0.344083	−0.172041	−	0.985090i	$-0.555036\pi$
$733$	−6828.40	−0.344083	−0.172041	+	0.985090i	$0.555036\pi$
$734$	−9967.03	−0.501212
$735$	−1770.00	−0.0888264
$736$	−5297.06	−0.265289
$737$	−9604.27	−0.480024
$738$	−5404.89	−0.269589
$739$	−1380.58	−0.0687219	−0.0343609	−	0.999409i	$-0.510940\pi$
$739$	−1380.58	−0.0687219	−0.0343609	+	0.999409i	$0.510940\pi$
$740$	−740.000	−0.0367607
$741$	−7992.43	−0.396234
$742$	−7338.45	−0.363077
$743$	30950.1	1.52820	0.764098	−	0.645100i	$-0.223184\pi$
$743$	30950.1	1.52820	0.764098	+	0.645100i	$0.223184\pi$
$744$	−7092.80	−0.349509
$745$	7653.41	0.376375
$746$	−2783.83	−0.136626
$747$	−10784.3	−0.528218
$748$	1390.06	0.0679485
$749$	−4447.38	−0.216961
$750$	750.000	0.0365148
$751$	−27718.1	−1.34680	−0.673401	−	0.739277i	$-0.735167\pi$
$751$	−27718.1	−1.34680	−0.673401	+	0.739277i	$0.735167\pi$
$752$	−2167.71	−0.105117
$753$	−10597.5	−0.512874
$754$	−18809.9	−0.908511
$755$	−3937.05	−0.189780
$756$	−1620.00	−0.0779350
$757$	21897.4	1.05136	0.525678	−	0.850684i	$-0.323812\pi$
$757$	21897.4	1.05136	0.525678	+	0.850684i	$0.323812\pi$
$758$	12336.1	0.591116
$759$	13301.2	0.636106
$760$	1867.89	0.0891522
$761$	24294.7	1.15727	0.578635	−	0.815587i	$-0.303586\pi$
$761$	24294.7	1.15727	0.578635	+	0.815587i	$0.303586\pi$
$762$	9129.69	0.434034
$763$	2049.07	0.0972232
$764$	11735.1	0.555710
$765$	−583.847	−0.0275935
$766$	6043.12	0.285048
$767$	35463.3	1.66950
$768$	768.000	0.0360844
$769$	−37156.2	−1.74238	−0.871189	−	0.490948i	$-0.836650\pi$
$769$	−37156.2	−1.74238	−0.871189	+	0.490948i	$0.836650\pi$
$770$	4017.69	0.188036
$771$	2290.83	0.107007
$772$	5640.70	0.262970
$773$	−22294.5	−1.03736	−0.518680	−	0.854969i	$-0.673576\pi$
$773$	−22294.5	−1.03736	−0.518680	+	0.854969i	$0.673576\pi$
$774$	548.489	0.0254716
$775$	−7388.33	−0.342447
$776$	6897.68	0.319088
$777$	1665.00	0.0768746
$778$	−2608.90	−0.120223
$779$	−14021.9	−0.644912
$780$	−3423.07	−0.157136
$781$	−9124.90	−0.418072
$782$	4295.38	0.196423
$783$	4450.98	0.203148
$784$	−1888.00	−0.0860058
$785$	2689.83	0.122298
$786$	−9299.29	−0.422003
$787$	−43500.5	−1.97030	−0.985149	−	0.171699i	$-0.945074\pi$
$787$	−43500.5	−1.97030	−0.985149	+	0.171699i	$0.945074\pi$
$788$	11281.2	0.509994
$789$	−11011.1	−0.496838
$790$	789.384	0.0355506
$791$	−4009.46	−0.180227
$792$	−1928.49	−0.0865227
$793$	15663.3	0.701414
$794$	−1162.24	−0.0519474
$795$	3669.22	0.163691
$796$	3976.01	0.177043
$797$	−36522.4	−1.62320	−0.811599	−	0.584215i	$-0.801403\pi$
$797$	−36522.4	−1.62320	−0.811599	+	0.584215i	$0.801403\pi$
$798$	−4202.76	−0.186436
$799$	1757.79	0.0778302
$800$	800.000	0.0353553
$801$	620.626	0.0273767
$802$	−560.424	−0.0246749
$803$	−7099.02	−0.311979
$804$	4302.89	0.188745
$805$	12415.0	0.543566
$806$	33721.1	1.47367
$807$	14777.7	0.644609
$808$	−1016.86	−0.0442735
$809$	−14247.0	−0.619155	−0.309577	−	0.950874i	$-0.600188\pi$
$809$	−14247.0	−0.619155	−0.309577	+	0.950874i	$0.600188\pi$
$810$	810.000	0.0351364
$811$	−39964.8	−1.73040	−0.865200	−	0.501427i	$-0.832808\pi$
$811$	−39964.8	−1.73040	−0.865200	+	0.501427i	$0.832808\pi$
$812$	−9891.07	−0.427473
$813$	16299.0	0.703113
$814$	1982.06	0.0853455
$815$	12470.5	0.535976
$816$	−622.770	−0.0267173
$817$	1422.94	0.0609333
$818$	8797.95	0.376055
$819$	7701.92	0.328604
$820$	−6005.43	−0.255755
$821$	4118.14	0.175060	0.0875299	−	0.996162i	$-0.472103\pi$
$821$	4118.14	0.175060	0.0875299	+	0.996162i	$0.472103\pi$
$822$	−9550.77	−0.405257
$823$	−8340.10	−0.353241	−0.176621	−	0.984279i	$-0.556517\pi$
$823$	−8340.10	−0.353241	−0.176621	+	0.984279i	$0.556517\pi$
$824$	4871.42	0.205952
$825$	−2008.85	−0.0847746
$826$	18648.1	0.785535
$827$	21269.1	0.894315	0.447158	−	0.894455i	$-0.352436\pi$
$827$	21269.1	0.894315	0.447158	+	0.894455i	$0.352436\pi$
$828$	−5959.20	−0.250116
$829$	−33984.8	−1.42381	−0.711906	−	0.702275i	$-0.752168\pi$
$829$	−33984.8	−1.42381	−0.711906	+	0.702275i	$0.752168\pi$
$830$	−11982.6	−0.501111
$831$	990.091	0.0413308
$832$	−3651.28	−0.152146
$833$	1530.98	0.0636797
$834$	−13870.7	−0.575903
$835$	5637.02	0.233625
$836$	−5003.09	−0.206980
$837$	−7979.40	−0.329520
$838$	−2211.66	−0.0911700
$839$	−27279.6	−1.12252	−0.561262	−	0.827638i	$-0.689684\pi$
$839$	−27279.6	−1.12252	−0.561262	+	0.827638i	$0.689684\pi$
$840$	−1800.00	−0.0739356
$841$	2786.89	0.114268
$842$	−195.961	−0.00802048
$843$	20294.3	0.829150
$844$	−7235.02	−0.295071
$845$	5289.22	0.215331
$846$	−2438.68	−0.0991057
$847$	9203.76	0.373371
$848$	3913.84	0.158493
$849$	2669.35	0.107906
$850$	−648.719	−0.0261775
$851$	6124.73	0.246713
$852$	4088.12	0.164386
$853$	24831.6	0.996738	0.498369	−	0.866965i	$-0.333932\pi$
$853$	24831.6	0.996738	0.498369	+	0.866965i	$0.333932\pi$
$854$	8236.45	0.330030
$855$	2101.38	0.0840535
$856$	2371.93	0.0947091
$857$	−31072.0	−1.23851	−0.619253	−	0.785191i	$-0.712565\pi$
$857$	−31072.0	−1.23851	−0.619253	+	0.785191i	$0.712565\pi$
$858$	9168.58	0.364814
$859$	−9614.51	−0.381889	−0.190945	−	0.981601i	$-0.561155\pi$
$859$	−9614.51	−0.381889	−0.190945	+	0.981601i	$0.561155\pi$
$860$	609.432	0.0241645
$861$	13512.2	0.534838
$862$	−15847.6	−0.626186
$863$	−9045.39	−0.356789	−0.178394	−	0.983959i	$-0.557090\pi$
$863$	−9045.39	−0.356789	−0.178394	+	0.983959i	$0.557090\pi$
$864$	864.000	0.0340207
$865$	−3300.74	−0.129744
$866$	−6621.41	−0.259820
$867$	−14234.0	−0.557568
$868$	17732.0	0.693391
$869$	−2114.33	−0.0825361
$870$	4945.53	0.192723
$871$	−20457.1	−0.795824
$872$	−1092.84	−0.0424405
$873$	7759.89	0.300839
$874$	−15459.9	−0.598330
$875$	−1875.00	−0.0724418
$876$	3180.49	0.122670
$877$	−10014.0	−0.385574	−0.192787	−	0.981241i	$-0.561753\pi$
$877$	−10014.0	−0.385574	−0.192787	+	0.981241i	$0.561753\pi$
$878$	29334.1	1.12754
$879$	22658.0	0.869437
$880$	−2142.77	−0.0820827
$881$	32799.0	1.25429	0.627143	−	0.778904i	$-0.284224\pi$
$881$	32799.0	1.25429	0.627143	+	0.778904i	$0.284224\pi$
$882$	−2124.00	−0.0810871
$883$	7981.54	0.304191	0.152095	−	0.988366i	$-0.451398\pi$
$883$	7981.54	0.304191	0.152095	+	0.988366i	$0.451398\pi$
$884$	2960.82	0.112651
$885$	−9324.07	−0.354153
$886$	21043.3	0.797926
$887$	−35304.2	−1.33641	−0.668206	−	0.743976i	$-0.732938\pi$
$887$	−35304.2	−1.33641	−0.668206	+	0.743976i	$0.732938\pi$
$888$	−888.000	−0.0335578
$889$	−22824.2	−0.861079
$890$	689.585	0.0259718
$891$	−2169.55	−0.0815744
$892$	−7689.13	−0.288622
$893$	−6326.65	−0.237081
$894$	9184.09	0.343582
$895$	−2163.72	−0.0808102
$896$	−1920.00	−0.0715878
$897$	28331.6	1.05459
$898$	−17153.9	−0.637454
$899$	−48719.0	−1.80742
$900$	900.000	0.0333333
$901$	−3173.73	−0.117350
$902$	16085.3	0.593772
$903$	−1371.22	−0.0505332
$904$	2138.38	0.0786741
$905$	−1987.77	−0.0730117
$906$	−4724.46	−0.173245
$907$	−6843.62	−0.250539	−0.125269	−	0.992123i	$-0.539980\pi$
$907$	−6843.62	−0.250539	−0.125269	+	0.992123i	$0.539980\pi$
$908$	−23009.4	−0.840962
$909$	−1143.97	−0.0417414
$910$	8557.69	0.311741
$911$	−18795.3	−0.683552	−0.341776	−	0.939781i	$-0.611028\pi$
$911$	−18795.3	−0.683552	−0.341776	+	0.939781i	$0.611028\pi$
$912$	2241.47	0.0813844
$913$	32095.0	1.16340
$914$	−12529.3	−0.453427
$915$	−4118.23	−0.148792
$916$	−22312.7	−0.804840
$917$	23248.2	0.837212
$918$	−700.616	−0.0251893
$919$	−44917.0	−1.61227	−0.806134	−	0.591734i	$-0.798444\pi$
$919$	−44917.0	−1.61227	−0.806134	+	0.591734i	$0.798444\pi$
$920$	−6621.33	−0.237281
$921$	−25131.8	−0.899154
$922$	2881.17	0.102914
$923$	−19436.0	−0.693114
$924$	4821.23	0.171652
$925$	−925.000	−0.0328798
$926$	483.945	0.0171743
$927$	5480.35	0.194173
$928$	5275.24	0.186604
$929$	−1382.40	−0.0488213	−0.0244107	−	0.999702i	$-0.507771\pi$
$929$	−1382.40	−0.0488213	−0.0244107	+	0.999702i	$0.507771\pi$
$930$	−8866.00	−0.312610
$931$	−5510.29	−0.193977
$932$	3883.60	0.136493
$933$	22757.9	0.798563
$934$	15208.9	0.532816
$935$	1737.57	0.0607750
$936$	−4107.69	−0.143444
$937$	−33890.0	−1.18158	−0.590789	−	0.806826i	$-0.701184\pi$
$937$	−33890.0	−1.18158	−0.590789	+	0.806826i	$0.701184\pi$
$938$	−10757.2	−0.374452
$939$	−3941.74	−0.136990
$940$	−2709.64	−0.0940199
$941$	−28444.7	−0.985411	−0.492706	−	0.870196i	$-0.663992\pi$
$941$	−28444.7	−0.985411	−0.492706	+	0.870196i	$0.663992\pi$
$942$	3227.79	0.111642
$943$	49704.9	1.71645
$944$	−9945.67	−0.342907
$945$	−2025.00	−0.0697071
$946$	−1632.34	−0.0561015
$947$	−48462.6	−1.66296	−0.831480	−	0.555555i	$-0.812506\pi$
$947$	−48462.6	−1.66296	−0.831480	+	0.555555i	$0.812506\pi$
$948$	947.260	0.0324532
$949$	−15120.9	−0.517224
$950$	2334.87	0.0797401
$951$	8609.32	0.293561
$952$	1556.93	0.0530044
$953$	52813.5	1.79517	0.897586	−	0.440840i	$-0.145320\pi$
$953$	52813.5	1.79517	0.897586	+	0.440840i	$0.145320\pi$
$954$	4403.07	0.149428
$955$	14668.9	0.497042
$956$	−11720.7	−0.396522
$957$	−13246.4	−0.447436
$958$	31552.2	1.06410
$959$	23876.9	0.803989
$960$	960.000	0.0322749
$961$	57548.9	1.93175
$962$	4221.79	0.141493
$963$	2668.43	0.0892926
$964$	−12925.3	−0.431844
$965$	7050.87	0.235208
$966$	14898.0	0.496206
$967$	−4569.66	−0.151965	−0.0759825	−	0.997109i	$-0.524209\pi$
$967$	−4569.66	−0.151965	−0.0759825	+	0.997109i	$0.524209\pi$
$968$	−4908.67	−0.162986
$969$	−1817.61	−0.0602580
$970$	8622.11	0.285401
$971$	9889.14	0.326836	0.163418	−	0.986557i	$-0.447748\pi$
$971$	9889.14	0.326836	0.163418	+	0.986557i	$0.447748\pi$
$972$	972.000	0.0320750
$973$	34676.7	1.14253
$974$	−25505.8	−0.839075
$975$	−4278.84	−0.140546
$976$	−4392.78	−0.144067
$977$	12036.7	0.394153	0.197077	−	0.980388i	$-0.436855\pi$
$977$	12036.7	0.394153	0.197077	+	0.980388i	$0.436855\pi$
$978$	14964.5	0.489277
$979$	−1847.03	−0.0602975
$980$	−2360.00	−0.0769260
$981$	−1229.44	−0.0400133
$982$	2271.91	0.0738284
$983$	−48079.3	−1.56001	−0.780005	−	0.625773i	$-0.784784\pi$
$983$	−48079.3	−1.56001	−0.780005	+	0.625773i	$0.784784\pi$
$984$	−7206.52	−0.233471
$985$	14101.5	0.456152
$986$	−4277.68	−0.138163
$987$	6096.69	0.196616
$988$	−10656.6	−0.343149
$989$	−5044.07	−0.162176
$990$	−2410.62	−0.0773883
$991$	−31042.7	−0.995059	−0.497530	−	0.867447i	$-0.665759\pi$
$991$	−31042.7	−0.995059	−0.497530	+	0.867447i	$0.665759\pi$
$992$	−9457.06	−0.302684
$993$	5285.11	0.168900
$994$	−10220.3	−0.326125
$995$	4970.01	0.158352
$996$	−14379.1	−0.457450
$997$	54044.7	1.71676	0.858382	−	0.513011i	$-0.171470\pi$
$997$	54044.7	1.71676	0.858382	+	0.513011i	$0.171470\pi$
$998$	−10518.7	−0.333630
$999$	−999.000	−0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.4.a.d.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.4.a.d.1.2	✓	2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1110.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} +6.00000 q^{6} -15.0000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +10.0000 q^{10} -26.7846 q^{11} +12.0000 q^{12} -57.0512 q^{13} -30.0000 q^{14} +15.0000 q^{15} +16.0000 q^{16} -12.9744 q^{17} +18.0000 q^{18} +46.6974 q^{19} +20.0000 q^{20} -45.0000 q^{21} -53.5693 q^{22} -165.533 q^{23} +24.0000 q^{24} +25.0000 q^{25} -114.102 q^{26} +27.0000 q^{27} -60.0000 q^{28} +164.851 q^{29} +30.0000 q^{30} -295.533 q^{31} +32.0000 q^{32} -80.3539 q^{33} -25.9488 q^{34} -75.0000 q^{35} +36.0000 q^{36} -37.0000 q^{37} +93.3947 q^{38} -171.154 q^{39} +40.0000 q^{40} -300.271 q^{41} -90.0000 q^{42} +30.4716 q^{43} -107.139 q^{44} +45.0000 q^{45} -331.066 q^{46} -135.482 q^{47} +48.0000 q^{48} -118.000 q^{49} +50.0000 q^{50} -38.9231 q^{51} -228.205 q^{52} +244.615 q^{53} +54.0000 q^{54} -133.923 q^{55} -120.000 q^{56} +140.092 q^{57} +329.702 q^{58} -621.605 q^{59} +60.0000 q^{60} -274.548 q^{61} -591.066 q^{62} -135.000 q^{63} +64.0000 q^{64} -285.256 q^{65} -160.708 q^{66} +358.574 q^{67} -51.8975 q^{68} -496.600 q^{69} -150.000 q^{70} +340.677 q^{71} +72.0000 q^{72} +265.041 q^{73} -74.0000 q^{74} +75.0000 q^{75} +186.789 q^{76} +401.769 q^{77} -342.307 q^{78} +78.9384 q^{79} +80.0000 q^{80} +81.0000 q^{81} -600.543 q^{82} -1198.26 q^{83} -180.000 q^{84} -64.8719 q^{85} +60.9432 q^{86} +494.553 q^{87} -214.277 q^{88} +68.9585 q^{89} +90.0000 q^{90} +855.769 q^{91} -662.133 q^{92} -886.600 q^{93} -270.964 q^{94} +233.487 q^{95} +96.0000 q^{96} +862.211 q^{97} -236.000 q^{98} -241.062 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} + 6 q^{3} + 8 q^{4} + 10 q^{5} + 12 q^{6} - 30 q^{7} + 16 q^{8} + 18 q^{9} + 20 q^{10} - 77 q^{11} + 24 q^{12} - 36 q^{13} - 60 q^{14} + 30 q^{15} + 32 q^{16} - 65 q^{17} + 36 q^{18} - 55 q^{19}+ \cdots - 693 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 + 6 * q^3 + 8 * q^4 + 10 * q^5 + 12 * q^6 - 30 * q^7 + 16 * q^8 + 18 * q^9 + 20 * q^10 - 77 * q^11 + 24 * q^12 - 36 * q^13 - 60 * q^14 + 30 * q^15 + 32 * q^16 - 65 * q^17 + 36 * q^18 - 55 * q^19 + 40 * q^20 - 90 * q^21 - 154 * q^22 - 128 * q^23 + 48 * q^24 + 50 * q^25 - 72 * q^26 + 54 * q^27 - 120 * q^28 - 53 * q^29 + 60 * q^30 - 388 * q^31 + 64 * q^32 - 231 * q^33 - 130 * q^34 - 150 * q^35 + 72 * q^36 - 74 * q^37 - 110 * q^38 - 108 * q^39 + 80 * q^40 + 118 * q^41 - 180 * q^42 - 353 * q^43 - 308 * q^44 + 90 * q^45 - 256 * q^46 - 146 * q^47 + 96 * q^48 - 236 * q^49 + 100 * q^50 - 195 * q^51 - 144 * q^52 - 448 * q^53 + 108 * q^54 - 385 * q^55 - 240 * q^56 - 165 * q^57 - 106 * q^58 - 17 * q^59 + 120 * q^60 - 18 * q^61 - 776 * q^62 - 270 * q^63 + 128 * q^64 - 180 * q^65 - 462 * q^66 + 147 * q^67 - 260 * q^68 - 384 * q^69 - 300 * q^70 - 45 * q^71 + 144 * q^72 + 163 * q^73 - 148 * q^74 + 150 * q^75 - 220 * q^76 + 1155 * q^77 - 216 * q^78 - 53 * q^79 + 160 * q^80 + 162 * q^81 + 236 * q^82 - 1389 * q^83 - 360 * q^84 - 325 * q^85 - 706 * q^86 - 159 * q^87 - 616 * q^88 - 1018 * q^89 + 180 * q^90 + 540 * q^91 - 512 * q^92 - 1164 * q^93 - 292 * q^94 - 275 * q^95 + 192 * q^96 + 2318 * q^97 - 472 * q^98 - 693 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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