LMFDB - Embedded newform 138.4.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,4,Mod(1,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("138.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	138.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:	$8.14226358079$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	138.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -7.31371 q^{5} -6.00000 q^{6} +17.3137 q^{7} +8.00000 q^{8} +9.00000 q^{9} -14.6274 q^{10} +69.2548 q^{11} -12.0000 q^{12} -3.25483 q^{13} +34.6274 q^{14} +21.9411 q^{15} +16.0000 q^{16} +85.9411 q^{17} +18.0000 q^{18} -19.9411 q^{19} -29.2548 q^{20} -51.9411 q^{21} +138.510 q^{22} +23.0000 q^{23} -24.0000 q^{24} -71.5097 q^{25} -6.50967 q^{26} -27.0000 q^{27} +69.2548 q^{28} -47.1371 q^{29} +43.8823 q^{30} +109.137 q^{31} +32.0000 q^{32} -207.765 q^{33} +171.882 q^{34} -126.627 q^{35} +36.0000 q^{36} +86.9016 q^{37} -39.8823 q^{38} +9.76450 q^{39} -58.5097 q^{40} +65.7645 q^{41} -103.882 q^{42} -398.451 q^{43} +277.019 q^{44} -65.8234 q^{45} +46.0000 q^{46} -164.118 q^{47} -48.0000 q^{48} -43.2355 q^{49} -143.019 q^{50} -257.823 q^{51} -13.0193 q^{52} +631.862 q^{53} -54.0000 q^{54} -506.510 q^{55} +138.510 q^{56} +59.8234 q^{57} -94.2742 q^{58} -665.450 q^{59} +87.7645 q^{60} -490.431 q^{61} +218.274 q^{62} +155.823 q^{63} +64.0000 q^{64} +23.8049 q^{65} -415.529 q^{66} +83.4701 q^{67} +343.765 q^{68} -69.0000 q^{69} -253.255 q^{70} +969.568 q^{71} +72.0000 q^{72} +462.313 q^{73} +173.803 q^{74} +214.529 q^{75} -79.7645 q^{76} +1199.06 q^{77} +19.5290 q^{78} -857.314 q^{79} -117.019 q^{80} +81.0000 q^{81} +131.529 q^{82} -1195.61 q^{83} -207.765 q^{84} -628.548 q^{85} -796.902 q^{86} +141.411 q^{87} +554.039 q^{88} -382.960 q^{89} -131.647 q^{90} -56.3532 q^{91} +92.0000 q^{92} -327.411 q^{93} -328.235 q^{94} +145.844 q^{95} -96.0000 q^{96} -817.724 q^{97} -86.4710 q^{98} +623.294 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} - 6 q^{3} + 8 q^{4} + 8 q^{5} - 12 q^{6} + 12 q^{7} + 16 q^{8} + 18 q^{9} + 16 q^{10} + 48 q^{11} - 24 q^{12} + 84 q^{13} + 24 q^{14} - 24 q^{15} + 32 q^{16} + 104 q^{17} + 36 q^{18} + 28 q^{19}+ \cdots + 432 q^{99}+O(q^{100}) $ 2 * q + 4 * q^2 - 6 * q^3 + 8 * q^4 + 8 * q^5 - 12 * q^6 + 12 * q^7 + 16 * q^8 + 18 * q^9 + 16 * q^10 + 48 * q^11 - 24 * q^12 + 84 * q^13 + 24 * q^14 - 24 * q^15 + 32 * q^16 + 104 * q^17 + 36 * q^18 + 28 * q^19 + 32 * q^20 - 36 * q^21 + 96 * q^22 + 46 * q^23 - 48 * q^24 + 38 * q^25 + 168 * q^26 - 54 * q^27 + 48 * q^28 + 132 * q^29 - 48 * q^30 - 8 * q^31 + 64 * q^32 - 144 * q^33 + 208 * q^34 - 208 * q^35 + 72 * q^36 - 324 * q^37 + 56 * q^38 - 252 * q^39 + 64 * q^40 - 140 * q^41 - 72 * q^42 - 548 * q^43 + 192 * q^44 + 72 * q^45 + 92 * q^46 - 464 * q^47 - 96 * q^48 - 358 * q^49 + 76 * q^50 - 312 * q^51 + 336 * q^52 + 336 * q^53 - 108 * q^54 - 832 * q^55 + 96 * q^56 - 84 * q^57 + 264 * q^58 + 72 * q^59 - 96 * q^60 + 60 * q^61 - 16 * q^62 + 108 * q^63 + 128 * q^64 + 1360 * q^65 - 288 * q^66 - 444 * q^67 + 416 * q^68 - 138 * q^69 - 416 * q^70 + 672 * q^71 + 144 * q^72 - 252 * q^73 - 648 * q^74 - 114 * q^75 + 112 * q^76 + 1312 * q^77 - 504 * q^78 - 1692 * q^79 + 128 * q^80 + 162 * q^81 - 280 * q^82 - 400 * q^83 - 144 * q^84 - 352 * q^85 - 1096 * q^86 - 396 * q^87 + 384 * q^88 - 336 * q^89 + 144 * q^90 - 520 * q^91 + 184 * q^92 + 24 * q^93 - 928 * q^94 + 880 * q^95 - 192 * q^96 + 220 * q^97 - 716 * q^98 + 432 * 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
$5$	−7.31371	−0.654158	−0.327079	−	0.944997i	$-0.606064\pi$
$5$	−7.31371	−0.654158	−0.327079	+	0.944997i	$0.606064\pi$
$6$	−6.00000	−0.408248
$7$	17.3137	0.934852	0.467426	−	0.884032i	$-0.345181\pi$
$7$	17.3137	0.934852	0.467426	+	0.884032i	$0.345181\pi$
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	−14.6274	−0.462560
$11$	69.2548	1.89828	0.949142	−	0.314849i	$-0.101954\pi$
$11$	69.2548	1.89828	0.949142	+	0.314849i	$0.101954\pi$
$12$	−12.0000	−0.288675
$13$	−3.25483	−0.0694407	−0.0347203	−	0.999397i	$-0.511054\pi$
$13$	−3.25483	−0.0694407	−0.0347203	+	0.999397i	$0.511054\pi$
$14$	34.6274	0.661040
$15$	21.9411	0.377678
$16$	16.0000	0.250000
$17$	85.9411	1.22610	0.613052	−	0.790042i	$-0.289941\pi$
$17$	85.9411	1.22610	0.613052	+	0.790042i	$0.289941\pi$
$18$	18.0000	0.235702
$19$	−19.9411	−0.240779	−0.120390	−	0.992727i	$-0.538414\pi$
$19$	−19.9411	−0.240779	−0.120390	+	0.992727i	$0.538414\pi$
$20$	−29.2548	−0.327079
$21$	−51.9411	−0.539737
$22$	138.510	1.34229
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−24.0000	−0.204124
$25$	−71.5097	−0.572077
$26$	−6.50967	−0.0491020
$27$	−27.0000	−0.192450
$28$	69.2548	0.467426
$29$	−47.1371	−0.301832	−0.150916	−	0.988547i	$-0.548222\pi$
$29$	−47.1371	−0.301832	−0.150916	+	0.988547i	$0.548222\pi$
$30$	43.8823	0.267059
$31$	109.137	0.632310	0.316155	−	0.948708i	$-0.397608\pi$
$31$	109.137	0.632310	0.316155	+	0.948708i	$0.397608\pi$
$32$	32.0000	0.176777
$33$	−207.765	−1.09597
$34$	171.882	0.866987
$35$	−126.627	−0.611541
$36$	36.0000	0.166667
$37$	86.9016	0.386123	0.193061	−	0.981187i	$-0.438158\pi$
$37$	86.9016	0.386123	0.193061	+	0.981187i	$0.438158\pi$
$38$	−39.8823	−0.170257
$39$	9.76450	0.0400916
$40$	−58.5097	−0.231280
$41$	65.7645	0.250505	0.125252	−	0.992125i	$-0.460026\pi$
$41$	65.7645	0.250505	0.125252	+	0.992125i	$0.460026\pi$
$42$	−103.882	−0.381652
$43$	−398.451	−1.41310	−0.706549	−	0.707665i	$-0.749749\pi$
$43$	−398.451	−1.41310	−0.706549	+	0.707665i	$0.749749\pi$
$44$	277.019	0.949142
$45$	−65.8234	−0.218053
$46$	46.0000	0.147442
$47$	−164.118	−0.509341	−0.254671	−	0.967028i	$-0.581967\pi$
$47$	−164.118	−0.509341	−0.254671	+	0.967028i	$0.581967\pi$
$48$	−48.0000	−0.144338
$49$	−43.2355	−0.126051
$50$	−143.019	−0.404520
$51$	−257.823	−0.707892
$52$	−13.0193	−0.0347203
$53$	631.862	1.63760	0.818801	−	0.574077i	$-0.194639\pi$
$53$	631.862	1.63760	0.818801	+	0.574077i	$0.194639\pi$
$54$	−54.0000	−0.136083
$55$	−506.510	−1.24178
$56$	138.510	0.330520
$57$	59.8234	0.139014
$58$	−94.2742	−0.213428
$59$	−665.450	−1.46838	−0.734188	−	0.678946i	$-0.762437\pi$
$59$	−665.450	−1.46838	−0.734188	+	0.678946i	$0.762437\pi$
$60$	87.7645	0.188839
$61$	−490.431	−1.02940	−0.514698	−	0.857371i	$-0.672096\pi$
$61$	−490.431	−1.02940	−0.514698	+	0.857371i	$0.672096\pi$
$62$	218.274	0.447110
$63$	155.823	0.311617
$64$	64.0000	0.125000
$65$	23.8049	0.0454252
$66$	−415.529	−0.774971
$67$	83.4701	0.152201	0.0761007	−	0.997100i	$-0.475753\pi$
$67$	83.4701	0.152201	0.0761007	+	0.997100i	$0.475753\pi$
$68$	343.765	0.613052
$69$	−69.0000	−0.120386
$70$	−253.255	−0.432425
$71$	969.568	1.62066	0.810328	−	0.585977i	$-0.199289\pi$
$71$	969.568	1.62066	0.810328	+	0.585977i	$0.199289\pi$
$72$	72.0000	0.117851
$73$	462.313	0.741228	0.370614	−	0.928787i	$-0.379147\pi$
$73$	462.313	0.741228	0.370614	+	0.928787i	$0.379147\pi$
$74$	173.803	0.273030
$75$	214.529	0.330289
$76$	−79.7645	−0.120390
$77$	1199.06	1.77461
$78$	19.5290	0.0283490
$79$	−857.314	−1.22095	−0.610477	−	0.792034i	$-0.709022\pi$
$79$	−857.314	−1.22095	−0.610477	+	0.792034i	$0.709022\pi$
$80$	−117.019	−0.163539
$81$	81.0000	0.111111
$82$	131.529	0.177134
$83$	−1195.61	−1.58114	−0.790571	−	0.612370i	$-0.790216\pi$
$83$	−1195.61	−1.58114	−0.790571	+	0.612370i	$0.790216\pi$
$84$	−207.765	−0.269869
$85$	−628.548	−0.802066
$86$	−796.902	−0.999211
$87$	141.411	0.174263
$88$	554.039	0.671145
$89$	−382.960	−0.456109	−0.228055	−	0.973648i	$-0.573236\pi$
$89$	−382.960	−0.456109	−0.228055	+	0.973648i	$0.573236\pi$
$90$	−131.647	−0.154187
$91$	−56.3532	−0.0649168
$92$	92.0000	0.104257
$93$	−327.411	−0.365064
$94$	−328.235	−0.360159
$95$	145.844	0.157508
$96$	−96.0000	−0.102062
$97$	−817.724	−0.855952	−0.427976	−	0.903790i	$-0.640773\pi$
$97$	−817.724	−0.855952	−0.427976	+	0.903790i	$0.640773\pi$
$98$	−86.4710	−0.0891315
$99$	623.294	0.632761
$100$	−286.039	−0.286039
$101$	530.548	0.522688	0.261344	−	0.965246i	$-0.415834\pi$
$101$	530.548	0.522688	0.261344	+	0.965246i	$0.415834\pi$
$102$	−515.647	−0.500555
$103$	−1427.12	−1.36522	−0.682612	−	0.730781i	$-0.739156\pi$
$103$	−1427.12	−1.36522	−0.682612	+	0.730781i	$0.739156\pi$
$104$	−26.0387	−0.0245510
$105$	379.882	0.353073
$106$	1263.72	1.15796
$107$	1085.49	0.980732	0.490366	−	0.871517i	$-0.336863\pi$
$107$	1085.49	0.980732	0.490366	+	0.871517i	$0.336863\pi$
$108$	−108.000	−0.0962250
$109$	−100.432	−0.0882539	−0.0441269	−	0.999026i	$-0.514051\pi$
$109$	−100.432	−0.0882539	−0.0441269	+	0.999026i	$0.514051\pi$
$110$	−1013.02	−0.878069
$111$	−260.705	−0.222928
$112$	277.019	0.233713
$113$	2289.43	1.90594	0.952971	−	0.303062i	$-0.0980088\pi$
$113$	2289.43	1.90594	0.952971	+	0.303062i	$0.0980088\pi$
$114$	119.647	0.0982978
$115$	−168.215	−0.136401
$116$	−188.548	−0.150916
$117$	−29.2935	−0.0231469
$118$	−1330.90	−1.03830
$119$	1487.96	1.14623
$120$	175.529	0.133529
$121$	3465.23	2.60348
$122$	−980.861	−0.727893
$123$	−197.294	−0.144629
$124$	436.548	0.316155
$125$	1437.21	1.02839
$126$	311.647	0.220347
$127$	313.531	0.219066	0.109533	−	0.993983i	$-0.465065\pi$
$127$	313.531	0.219066	0.109533	+	0.993983i	$0.465065\pi$
$128$	128.000	0.0883883
$129$	1195.35	0.815852
$130$	47.6098	0.0321204
$131$	−517.568	−0.345192	−0.172596	−	0.984993i	$-0.555215\pi$
$131$	−517.568	−0.345192	−0.172596	+	0.984993i	$0.555215\pi$
$132$	−831.058	−0.547987
$133$	−345.255	−0.225093
$134$	166.940	0.107623
$135$	197.470	0.125893
$136$	687.529	0.433494
$137$	−435.038	−0.271298	−0.135649	−	0.990757i	$-0.543312\pi$
$137$	−435.038	−0.271298	−0.135649	+	0.990757i	$0.543312\pi$
$138$	−138.000	−0.0851257
$139$	124.626	0.0760476	0.0380238	−	0.999277i	$-0.487894\pi$
$139$	124.626	0.0760476	0.0380238	+	0.999277i	$0.487894\pi$
$140$	−506.510	−0.305771
$141$	492.353	0.294068
$142$	1939.14	1.14598
$143$	−225.413	−0.131818
$144$	144.000	0.0833333
$145$	344.747	0.197446
$146$	924.626	0.524127
$147$	129.706	0.0727756
$148$	347.606	0.193061
$149$	−2790.29	−1.53416	−0.767079	−	0.641553i	$-0.778291\pi$
$149$	−2790.29	−1.53416	−0.767079	+	0.641553i	$0.778291\pi$
$150$	429.058	0.233550
$151$	2883.14	1.55382	0.776908	−	0.629614i	$-0.216787\pi$
$151$	2883.14	1.55382	0.776908	+	0.629614i	$0.216787\pi$
$152$	−159.529	−0.0851284
$153$	773.470	0.408702
$154$	2398.12	1.25484
$155$	−798.197	−0.413630
$156$	39.0580	0.0200458
$157$	1524.86	0.775142	0.387571	−	0.921840i	$-0.373314\pi$
$157$	1524.86	0.775142	0.387571	+	0.921840i	$0.373314\pi$
$158$	−1714.63	−0.863345
$159$	−1895.59	−0.945470
$160$	−234.039	−0.115640
$161$	398.215	0.194930
$162$	162.000	0.0785674
$163$	−1796.74	−0.863385	−0.431693	−	0.902021i	$-0.642083\pi$
$163$	−1796.74	−0.863385	−0.431693	+	0.902021i	$0.642083\pi$
$164$	263.058	0.125252
$165$	1519.53	0.716940
$166$	−2391.21	−1.11804
$167$	−1339.61	−0.620730	−0.310365	−	0.950618i	$-0.600451\pi$
$167$	−1339.61	−0.620730	−0.310365	+	0.950618i	$0.600451\pi$
$168$	−415.529	−0.190826
$169$	−2186.41	−0.995178
$170$	−1257.10	−0.567147
$171$	−179.470	−0.0802598
$172$	−1593.80	−0.706549
$173$	−1753.65	−0.770678	−0.385339	−	0.922775i	$-0.625915\pi$
$173$	−1753.65	−0.770678	−0.385339	+	0.922775i	$0.625915\pi$
$174$	282.823	0.123223
$175$	−1238.10	−0.534808
$176$	1108.08	0.474571
$177$	1996.35	0.847767
$178$	−765.921	−0.322518
$179$	−4375.18	−1.82690	−0.913452	−	0.406945i	$-0.866594\pi$
$179$	−4375.18	−1.82690	−0.913452	+	0.406945i	$0.866594\pi$
$180$	−263.294	−0.109026
$181$	−3619.02	−1.48619	−0.743093	−	0.669188i	$-0.766642\pi$
$181$	−3619.02	−1.48619	−0.743093	+	0.669188i	$0.766642\pi$
$182$	−112.706	−0.0459031
$183$	1471.29	0.594322
$184$	184.000	0.0737210
$185$	−635.573	−0.252585
$186$	−654.823	−0.258139
$187$	5951.84	2.32749
$188$	−656.471	−0.254671
$189$	−467.470	−0.179912
$190$	291.687	0.111375
$191$	537.369	0.203574	0.101787	−	0.994806i	$-0.467544\pi$
$191$	537.369	0.203574	0.101787	+	0.994806i	$0.467544\pi$
$192$	−192.000	−0.0721688
$193$	−334.784	−0.124861	−0.0624307	−	0.998049i	$-0.519885\pi$
$193$	−334.784	−0.124861	−0.0624307	+	0.998049i	$0.519885\pi$
$194$	−1635.45	−0.605249
$195$	−71.4147	−0.0262262
$196$	−172.942	−0.0630255
$197$	−1674.19	−0.605488	−0.302744	−	0.953072i	$-0.597903\pi$
$197$	−1674.19	−0.605488	−0.302744	+	0.953072i	$0.597903\pi$
$198$	1246.59	0.447430
$199$	767.231	0.273304	0.136652	−	0.990619i	$-0.456366\pi$
$199$	767.231	0.273304	0.136652	+	0.990619i	$0.456366\pi$
$200$	−572.077	−0.202260
$201$	−250.410	−0.0878736
$202$	1061.10	0.369597
$203$	−816.118	−0.282169
$204$	−1031.29	−0.353946
$205$	−480.982	−0.163870
$206$	−2854.23	−0.965359
$207$	207.000	0.0695048
$208$	−52.0773	−0.0173602
$209$	−1381.02	−0.457067
$210$	759.765	0.249661
$211$	−4779.40	−1.55937	−0.779687	−	0.626170i	$-0.784622\pi$
$211$	−4779.40	−1.55937	−0.779687	+	0.626170i	$0.784622\pi$
$212$	2527.45	0.818801
$213$	−2908.70	−0.935686
$214$	2170.98	0.693482
$215$	2914.15	0.924389
$216$	−216.000	−0.0680414
$217$	1889.57	0.591116
$218$	−200.865	−0.0624049
$219$	−1386.94	−0.427948
$220$	−2026.04	−0.620889
$221$	−279.724	−0.0851415
$222$	−521.410	−0.157634
$223$	−797.410	−0.239455	−0.119728	−	0.992807i	$-0.538202\pi$
$223$	−797.410	−0.239455	−0.119728	+	0.992807i	$0.538202\pi$
$224$	554.039	0.165260
$225$	−643.587	−0.190692
$226$	4578.86	1.34770
$227$	−5898.63	−1.72469	−0.862347	−	0.506317i	$-0.831006\pi$
$227$	−5898.63	−1.72469	−0.862347	+	0.506317i	$0.831006\pi$
$228$	239.294	0.0695070
$229$	−168.826	−0.0487176	−0.0243588	−	0.999703i	$-0.507754\pi$
$229$	−168.826	−0.0487176	−0.0243588	+	0.999703i	$0.507754\pi$
$230$	−336.431	−0.0964503
$231$	−3597.17	−1.02457
$232$	−377.097	−0.106714
$233$	4184.67	1.17660	0.588298	−	0.808644i	$-0.299798\pi$
$233$	4184.67	1.17660	0.588298	+	0.808644i	$0.299798\pi$
$234$	−58.5870	−0.0163673
$235$	1200.31	0.333190
$236$	−2661.80	−0.734188
$237$	2571.94	0.704918
$238$	2975.92	0.810505
$239$	2573.96	0.696635	0.348317	−	0.937377i	$-0.386753\pi$
$239$	2573.96	0.696635	0.348317	+	0.937377i	$0.386753\pi$
$240$	351.058	0.0944196
$241$	−1092.40	−0.291981	−0.145990	−	0.989286i	$-0.546637\pi$
$241$	−1092.40	−0.291981	−0.145990	+	0.989286i	$0.546637\pi$
$242$	6930.46	1.84094
$243$	−243.000	−0.0641500
$244$	−1961.72	−0.514698
$245$	316.212	0.0824573
$246$	−394.587	−0.102268
$247$	64.9051	0.0167199
$248$	873.097	0.223555
$249$	3586.82	0.912873
$250$	2874.43	0.727179
$251$	−5504.11	−1.38413	−0.692065	−	0.721836i	$-0.743299\pi$
$251$	−5504.11	−1.38413	−0.692065	+	0.721836i	$0.743299\pi$
$252$	623.294	0.155809
$253$	1592.86	0.395819
$254$	627.061	0.154903
$255$	1885.65	0.463073
$256$	256.000	0.0625000
$257$	3654.39	0.886984	0.443492	−	0.896278i	$-0.353740\pi$
$257$	3654.39	0.886984	0.443492	+	0.896278i	$0.353740\pi$
$258$	2390.70	0.576894
$259$	1504.59	0.360968
$260$	95.2196	0.0227126
$261$	−424.234	−0.100611
$262$	−1035.14	−0.244087
$263$	−5352.43	−1.25492	−0.627462	−	0.778648i	$-0.715906\pi$
$263$	−5352.43	−1.25492	−0.627462	+	0.778648i	$0.715906\pi$
$264$	−1662.12	−0.387485
$265$	−4621.25	−1.07125
$266$	−690.510	−0.159165
$267$	1148.88	0.263335
$268$	333.881	0.0761007
$269$	4423.21	1.00256	0.501279	−	0.865286i	$-0.332863\pi$
$269$	4423.21	1.00256	0.501279	+	0.865286i	$0.332863\pi$
$270$	394.940	0.0890196
$271$	−3179.72	−0.712747	−0.356374	−	0.934344i	$-0.615987\pi$
$271$	−3179.72	−0.712747	−0.356374	+	0.934344i	$0.615987\pi$
$272$	1375.06	0.306526
$273$	169.060	0.0374797
$274$	−870.076	−0.191836
$275$	−4952.39	−1.08596
$276$	−276.000	−0.0601929
$277$	1135.26	0.246249	0.123125	−	0.992391i	$-0.460708\pi$
$277$	1135.26	0.246249	0.123125	+	0.992391i	$0.460708\pi$
$278$	249.251	0.0537738
$279$	982.234	0.210770
$280$	−1013.02	−0.216212
$281$	−2869.86	−0.609257	−0.304629	−	0.952471i	$-0.598532\pi$
$281$	−2869.86	−0.609257	−0.304629	+	0.952471i	$0.598532\pi$
$282$	984.706	0.207938
$283$	857.505	0.180118	0.0900590	−	0.995936i	$-0.471294\pi$
$283$	857.505	0.180118	0.0900590	+	0.995936i	$0.471294\pi$
$284$	3878.27	0.810328
$285$	−437.531	−0.0909371
$286$	−450.826	−0.0932094
$287$	1138.63	0.234185
$288$	288.000	0.0589256
$289$	2472.88	0.503333
$290$	689.494	0.139615
$291$	2453.17	0.494184
$292$	1849.25	0.370614
$293$	8823.46	1.75929	0.879645	−	0.475631i	$-0.157780\pi$
$293$	8823.46	1.75929	0.879645	+	0.475631i	$0.157780\pi$
$294$	259.413	0.0514601
$295$	4866.91	0.960550
$296$	695.213	0.136515
$297$	−1869.88	−0.365325
$298$	−5580.58	−1.08481
$299$	−74.8612	−0.0144794
$300$	858.116	0.165145
$301$	−6898.66	−1.32104
$302$	5766.27	1.09871
$303$	−1591.65	−0.301774
$304$	−319.058	−0.0601948
$305$	3586.87	0.673388
$306$	1546.94	0.288996
$307$	8123.41	1.51019	0.755094	−	0.655617i	$-0.227591\pi$
$307$	8123.41	1.51019	0.755094	+	0.655617i	$0.227591\pi$
$308$	4796.23	0.887307
$309$	4281.35	0.788212
$310$	−1596.39	−0.292481
$311$	3416.66	0.622961	0.311481	−	0.950252i	$-0.399175\pi$
$311$	3416.66	0.622961	0.311481	+	0.950252i	$0.399175\pi$
$312$	78.1160	0.0141745
$313$	5325.14	0.961644	0.480822	−	0.876818i	$-0.340338\pi$
$313$	5325.14	0.961644	0.480822	+	0.876818i	$0.340338\pi$
$314$	3049.73	0.548108
$315$	−1139.65	−0.203847
$316$	−3429.25	−0.610477
$317$	−952.315	−0.168730	−0.0843649	−	0.996435i	$-0.526886\pi$
$317$	−952.315	−0.168730	−0.0843649	+	0.996435i	$0.526886\pi$
$318$	−3791.17	−0.668548
$319$	−3264.47	−0.572963
$320$	−468.077	−0.0817697
$321$	−3256.47	−0.566226
$322$	796.431	0.137836
$323$	−1713.76	−0.295221
$324$	324.000	0.0555556
$325$	232.752	0.0397254
$326$	−3593.49	−0.610506
$327$	301.297	0.0509534
$328$	526.116	0.0885668
$329$	−2841.49	−0.476159
$330$	3039.06	0.506953
$331$	5728.43	0.951248	0.475624	−	0.879649i	$-0.342222\pi$
$331$	5728.43	0.951248	0.475624	+	0.879649i	$0.342222\pi$
$332$	−4782.43	−0.790571
$333$	782.114	0.128708
$334$	−2679.21	−0.438922
$335$	−610.476	−0.0995638
$336$	−831.058	−0.134934
$337$	−6304.39	−1.01906	−0.509528	−	0.860454i	$-0.670180\pi$
$337$	−6304.39	−1.01906	−0.509528	+	0.860454i	$0.670180\pi$
$338$	−4372.81	−0.703697
$339$	−6868.29	−1.10040
$340$	−2514.19	−0.401033
$341$	7558.27	1.20030
$342$	−358.940	−0.0567522
$343$	−6687.17	−1.05269
$344$	−3187.61	−0.499605
$345$	504.646	0.0787514
$346$	−3507.29	−0.544952
$347$	9338.30	1.44469	0.722344	−	0.691534i	$-0.243065\pi$
$347$	9338.30	1.44469	0.722344	+	0.691534i	$0.243065\pi$
$348$	565.645	0.0871315
$349$	4224.27	0.647908	0.323954	−	0.946073i	$-0.394988\pi$
$349$	4224.27	0.647908	0.323954	+	0.946073i	$0.394988\pi$
$350$	−2476.20	−0.378166
$351$	87.8805	0.0133639
$352$	2216.15	0.335572
$353$	−6291.13	−0.948564	−0.474282	−	0.880373i	$-0.657292\pi$
$353$	−6291.13	−0.948564	−0.474282	+	0.880373i	$0.657292\pi$
$354$	3992.70	0.599462
$355$	−7091.14	−1.06016
$356$	−1531.84	−0.228055
$357$	−4463.88	−0.661775
$358$	−8750.35	−1.29182
$359$	12068.0	1.77416	0.887079	−	0.461618i	$-0.152731\pi$
$359$	12068.0	1.77416	0.887079	+	0.461618i	$0.152731\pi$
$360$	−526.587	−0.0770933
$361$	−6461.35	−0.942025
$362$	−7238.04	−1.05089
$363$	−10395.7	−1.50312
$364$	−225.413	−0.0324584
$365$	−3381.22	−0.484880
$366$	2942.58	0.420249
$367$	8119.00	1.15479	0.577395	−	0.816465i	$-0.304069\pi$
$367$	8119.00	1.15479	0.577395	+	0.816465i	$0.304069\pi$
$368$	368.000	0.0521286
$369$	591.881	0.0835015
$370$	−1271.15	−0.178605
$371$	10939.9	1.53092
$372$	−1309.65	−0.182532
$373$	5256.30	0.729654	0.364827	−	0.931075i	$-0.381128\pi$
$373$	5256.30	0.729654	0.364827	+	0.931075i	$0.381128\pi$
$374$	11903.7	1.64579
$375$	−4311.64	−0.593739
$376$	−1312.94	−0.180079
$377$	153.423	0.0209594
$378$	−934.940	−0.127217
$379$	3375.35	0.457467	0.228734	−	0.973489i	$-0.426542\pi$
$379$	3375.35	0.457467	0.228734	+	0.973489i	$0.426542\pi$
$380$	583.374	0.0787539
$381$	−940.592	−0.126478
$382$	1074.74	0.143949
$383$	−8034.61	−1.07193	−0.535966	−	0.844240i	$-0.680052\pi$
$383$	−8034.61	−1.07193	−0.535966	+	0.844240i	$0.680052\pi$
$384$	−384.000	−0.0510310
$385$	−8769.56	−1.16088
$386$	−669.568	−0.0882904
$387$	−3586.06	−0.471032
$388$	−3270.90	−0.427976
$389$	26.5264	0.00345743	0.00172872	−	0.999999i	$-0.499450\pi$
$389$	26.5264	0.00345743	0.00172872	+	0.999999i	$0.499450\pi$
$390$	−142.829	−0.0185447
$391$	1976.65	0.255661
$392$	−345.884	−0.0445658
$393$	1552.70	0.199296
$394$	−3348.38	−0.428145
$395$	6270.14	0.798696
$396$	2493.17	0.316381
$397$	9160.19	1.15803	0.579014	−	0.815318i	$-0.303438\pi$
$397$	9160.19	1.15803	0.579014	+	0.815318i	$0.303438\pi$
$398$	1534.46	0.193255
$399$	1035.76	0.129958
$400$	−1144.15	−0.143019
$401$	4494.80	0.559750	0.279875	−	0.960036i	$-0.409707\pi$
$401$	4494.80	0.559750	0.279875	+	0.960036i	$0.409707\pi$
$402$	−500.821	−0.0621360
$403$	−355.223	−0.0439080
$404$	2122.19	0.261344
$405$	−592.410	−0.0726842
$406$	−1632.24	−0.199523
$407$	6018.35	0.732970
$408$	−2062.59	−0.250278
$409$	−7988.04	−0.965729	−0.482864	−	0.875695i	$-0.660404\pi$
$409$	−7988.04	−0.965729	−0.482864	+	0.875695i	$0.660404\pi$
$410$	−961.965	−0.115873
$411$	1305.11	0.156634
$412$	−5708.47	−0.682612
$413$	−11521.4	−1.37272
$414$	414.000	0.0491473
$415$	8744.32	1.03432
$416$	−104.155	−0.0122755
$417$	−373.877	−0.0439061
$418$	−2762.04	−0.323196
$419$	−12558.9	−1.46430	−0.732150	−	0.681143i	$-0.761483\pi$
$419$	−12558.9	−1.46430	−0.732150	+	0.681143i	$0.761483\pi$
$420$	1519.53	0.176537
$421$	−12609.7	−1.45976	−0.729879	−	0.683577i	$-0.760423\pi$
$421$	−12609.7	−1.45976	−0.729879	+	0.683577i	$0.760423\pi$
$422$	−9558.81	−1.10264
$423$	−1477.06	−0.169780
$424$	5054.90	0.578980
$425$	−6145.62	−0.701427
$426$	−5817.41	−0.661630
$427$	−8491.17	−0.962334
$428$	4341.96	0.490366
$429$	676.239	0.0761052
$430$	5828.31	0.653642
$431$	−1715.05	−0.191673	−0.0958364	−	0.995397i	$-0.530553\pi$
$431$	−1715.05	−0.191673	−0.0958364	+	0.995397i	$0.530553\pi$
$432$	−432.000	−0.0481125
$433$	16686.2	1.85194	0.925969	−	0.377601i	$-0.123251\pi$
$433$	16686.2	1.85194	0.925969	+	0.377601i	$0.123251\pi$
$434$	3779.14	0.417982
$435$	−1034.24	−0.113996
$436$	−401.729	−0.0441269
$437$	−458.646	−0.0502060
$438$	−2773.88	−0.302605
$439$	11447.0	1.24450	0.622249	−	0.782819i	$-0.286219\pi$
$439$	11447.0	1.24450	0.622249	+	0.782819i	$0.286219\pi$
$440$	−4052.08	−0.439035
$441$	−389.119	−0.0420170
$442$	−559.448	−0.0602042
$443$	12008.1	1.28786	0.643932	−	0.765082i	$-0.277302\pi$
$443$	12008.1	1.28786	0.643932	+	0.765082i	$0.277302\pi$
$444$	−1042.82	−0.111464
$445$	2800.86	0.298368
$446$	−1594.82	−0.169320
$447$	8370.87	0.885747
$448$	1108.08	0.116857
$449$	3225.83	0.339057	0.169528	−	0.985525i	$-0.445776\pi$
$449$	3225.83	0.339057	0.169528	+	0.985525i	$0.445776\pi$
$450$	−1287.17	−0.134840
$451$	4554.51	0.475529
$452$	9157.72	0.952971
$453$	−8649.41	−0.897096
$454$	−11797.3	−1.21954
$455$	412.151	0.0424658
$456$	478.587	0.0491489
$457$	1318.20	0.134929	0.0674645	−	0.997722i	$-0.478509\pi$
$457$	1318.20	0.134929	0.0674645	+	0.997722i	$0.478509\pi$
$458$	−337.652	−0.0344486
$459$	−2320.41	−0.235964
$460$	−672.861	−0.0682007
$461$	−7837.18	−0.791787	−0.395894	−	0.918296i	$-0.629565\pi$
$461$	−7837.18	−0.791787	−0.395894	+	0.918296i	$0.629565\pi$
$462$	−7194.35	−0.724483
$463$	15812.5	1.58719	0.793594	−	0.608448i	$-0.208208\pi$
$463$	15812.5	1.58719	0.793594	+	0.608448i	$0.208208\pi$
$464$	−754.193	−0.0754581
$465$	2394.59	0.238810
$466$	8369.34	0.831979
$467$	−8142.16	−0.806797	−0.403399	−	0.915024i	$-0.632171\pi$
$467$	−8142.16	−0.806797	−0.403399	+	0.915024i	$0.632171\pi$
$468$	−117.174	−0.0115734
$469$	1445.18	0.142286
$470$	2400.62	0.235601
$471$	−4574.59	−0.447528
$472$	−5323.60	−0.519149
$473$	−27594.6	−2.68246
$474$	5143.88	0.498452
$475$	1425.98	0.137744
$476$	5951.84	0.573114
$477$	5686.76	0.545867
$478$	5147.92	0.492595
$479$	−2216.85	−0.211463	−0.105731	−	0.994395i	$-0.533718\pi$
$479$	−2216.85	−0.211463	−0.105731	+	0.994395i	$0.533718\pi$
$480$	702.116	0.0667647
$481$	−282.850	−0.0268126
$482$	−2184.79	−0.206462
$483$	−1194.65	−0.112543
$484$	13860.9	1.30174
$485$	5980.60	0.559928
$486$	−486.000	−0.0453609
$487$	−85.0055	−0.00790958	−0.00395479	−	0.999992i	$-0.501259\pi$
$487$	−85.0055	−0.00790958	−0.00395479	+	0.999992i	$0.501259\pi$
$488$	−3923.44	−0.363947
$489$	5390.23	0.498476
$490$	632.424	0.0583061
$491$	−1200.29	−0.110322	−0.0551611	−	0.998477i	$-0.517567\pi$
$491$	−1200.29	−0.110322	−0.0551611	+	0.998477i	$0.517567\pi$
$492$	−789.174	−0.0723145
$493$	−4051.01	−0.370078
$494$	129.810	0.0118227
$495$	−4558.59	−0.413926
$496$	1746.19	0.158077
$497$	16786.8	1.51507
$498$	7173.64	0.645499
$499$	−18846.0	−1.69071	−0.845353	−	0.534208i	$-0.820610\pi$
$499$	−18846.0	−1.69071	−0.845353	+	0.534208i	$0.820610\pi$
$500$	5748.86	0.514193
$501$	4018.82	0.358378
$502$	−11008.2	−0.978727
$503$	−8489.56	−0.752546	−0.376273	−	0.926509i	$-0.622795\pi$
$503$	−8489.56	−0.752546	−0.376273	+	0.926509i	$0.622795\pi$
$504$	1246.59	0.110173
$505$	−3880.28	−0.341921
$506$	3185.72	0.279887
$507$	6559.22	0.574566
$508$	1254.12	0.109533
$509$	7158.36	0.623357	0.311679	−	0.950188i	$-0.399109\pi$
$509$	7158.36	0.623357	0.311679	+	0.950188i	$0.399109\pi$
$510$	3771.29	0.327442
$511$	8004.35	0.692939
$512$	512.000	0.0441942
$513$	538.410	0.0463380
$514$	7308.79	0.627192
$515$	10437.5	0.893072
$516$	4781.41	0.407926
$517$	−11365.9	−0.966874
$518$	3009.18	0.255243
$519$	5260.94	0.444951
$520$	190.439	0.0160602
$521$	−4283.35	−0.360186	−0.180093	−	0.983650i	$-0.557640\pi$
$521$	−4283.35	−0.360186	−0.180093	+	0.983650i	$0.557640\pi$
$522$	−848.468	−0.0711426
$523$	19831.0	1.65803	0.829014	−	0.559228i	$-0.188902\pi$
$523$	19831.0	1.65803	0.829014	+	0.559228i	$0.188902\pi$
$524$	−2070.27	−0.172596
$525$	3714.29	0.308771
$526$	−10704.9	−0.887365
$527$	9379.36	0.775278
$528$	−3324.23	−0.273994
$529$	529.000	0.0434783
$530$	−9242.51	−0.757489
$531$	−5989.05	−0.489459
$532$	−1381.02	−0.112547
$533$	−214.053	−0.0173952
$534$	2297.76	0.186206
$535$	−7938.96	−0.641554
$536$	667.761	0.0538114
$537$	13125.5	1.05476
$538$	8846.43	0.708916
$539$	−2994.27	−0.239281
$540$	789.881	0.0629464
$541$	−15713.7	−1.24877	−0.624384	−	0.781117i	$-0.714650\pi$
$541$	−15713.7	−1.24877	−0.624384	+	0.781117i	$0.714650\pi$
$542$	−6359.45	−0.503988
$543$	10857.1	0.858050
$544$	2750.12	0.216747
$545$	734.533	0.0577320
$546$	338.119	0.0265022
$547$	21143.1	1.65267	0.826337	−	0.563176i	$-0.190421\pi$
$547$	21143.1	1.65267	0.826337	+	0.563176i	$0.190421\pi$
$548$	−1740.15	−0.135649
$549$	−4413.88	−0.343132
$550$	−9904.78	−0.767893
$551$	939.967	0.0726750
$552$	−552.000	−0.0425628
$553$	−14843.3	−1.14141
$554$	2270.52	0.174125
$555$	1906.72	0.145830
$556$	498.503	0.0380238
$557$	3746.75	0.285018	0.142509	−	0.989794i	$-0.454483\pi$
$557$	3746.75	0.285018	0.142509	+	0.989794i	$0.454483\pi$
$558$	1964.47	0.149037
$559$	1296.89	0.0981264
$560$	−2026.04	−0.152885
$561$	−17855.5	−1.34378
$562$	−5739.71	−0.430810
$563$	−16060.2	−1.20223	−0.601116	−	0.799162i	$-0.705277\pi$
$563$	−16060.2	−1.20223	−0.601116	+	0.799162i	$0.705277\pi$
$564$	1969.41	0.147034
$565$	−16744.2	−1.24679
$566$	1715.01	0.127363
$567$	1402.41	0.103872
$568$	7756.54	0.572988
$569$	17547.1	1.29282	0.646409	−	0.762991i	$-0.276270\pi$
$569$	17547.1	1.29282	0.646409	+	0.762991i	$0.276270\pi$
$570$	−875.061	−0.0643023
$571$	−5551.81	−0.406893	−0.203446	−	0.979086i	$-0.565214\pi$
$571$	−5551.81	−0.406893	−0.203446	+	0.979086i	$0.565214\pi$
$572$	−901.652	−0.0659090
$573$	−1612.11	−0.117534
$574$	2277.25	0.165594
$575$	−1644.72	−0.119286
$576$	576.000	0.0416667
$577$	1394.14	0.100587	0.0502937	−	0.998734i	$-0.483984\pi$
$577$	1394.14	0.100587	0.0502937	+	0.998734i	$0.483984\pi$
$578$	4945.75	0.355910
$579$	1004.35	0.0720888
$580$	1378.99	0.0987230
$581$	−20700.4	−1.47814
$582$	4906.34	0.349441
$583$	43759.5	3.10863
$584$	3698.50	0.262064
$585$	214.244	0.0151417
$586$	17646.9	1.24401
$587$	−26307.6	−1.84980	−0.924900	−	0.380210i	$-0.875852\pi$
$587$	−26307.6	−1.84980	−0.924900	+	0.380210i	$0.875852\pi$
$588$	518.826	0.0363878
$589$	−2176.32	−0.152247
$590$	9733.81	0.679211
$591$	5022.57	0.349579
$592$	1390.43	0.0965306
$593$	10657.9	0.738056	0.369028	−	0.929418i	$-0.379691\pi$
$593$	10657.9	0.738056	0.369028	+	0.929418i	$0.379691\pi$
$594$	−3739.76	−0.258324
$595$	−10882.5	−0.749814
$596$	−11161.2	−0.767079
$597$	−2301.69	−0.157792
$598$	−149.722	−0.0102385
$599$	5018.67	0.342333	0.171166	−	0.985242i	$-0.445246\pi$
$599$	5018.67	0.342333	0.171166	+	0.985242i	$0.445246\pi$
$600$	1716.23	0.116775
$601$	7715.55	0.523667	0.261833	−	0.965113i	$-0.415673\pi$
$601$	7715.55	0.523667	0.261833	+	0.965113i	$0.415673\pi$
$602$	−13797.3	−0.934114
$603$	751.231	0.0507338
$604$	11532.5	0.776908
$605$	−25343.7	−1.70309
$606$	−3183.29	−0.213387
$607$	26998.5	1.80533	0.902664	−	0.430346i	$-0.141608\pi$
$607$	26998.5	1.80533	0.902664	+	0.430346i	$0.141608\pi$
$608$	−638.116	−0.0425642
$609$	2448.35	0.162910
$610$	7173.73	0.476157
$611$	534.176	0.0353690
$612$	3093.88	0.204351
$613$	3756.96	0.247540	0.123770	−	0.992311i	$-0.460501\pi$
$613$	3756.96	0.247540	0.123770	+	0.992311i	$0.460501\pi$
$614$	16246.8	1.06786
$615$	1442.95	0.0946102
$616$	9592.46	0.627421
$617$	14186.2	0.925632	0.462816	−	0.886454i	$-0.346839\pi$
$617$	14186.2	0.925632	0.462816	+	0.886454i	$0.346839\pi$
$618$	8562.70	0.557350
$619$	−25670.2	−1.66684	−0.833418	−	0.552643i	$-0.813619\pi$
$619$	−25670.2	−1.66684	−0.833418	+	0.552643i	$0.813619\pi$
$620$	−3192.79	−0.206815
$621$	−621.000	−0.0401286
$622$	6833.32	0.440500
$623$	−6630.47	−0.426395
$624$	156.232	0.0100229
$625$	−1572.66	−0.100650
$626$	10650.3	0.679985
$627$	4143.06	0.263888
$628$	6099.45	0.387571
$629$	7468.42	0.473427
$630$	−2279.29	−0.144142
$631$	−948.530	−0.0598421	−0.0299211	−	0.999552i	$-0.509526\pi$
$631$	−948.530	−0.0598421	−0.0299211	+	0.999552i	$0.509526\pi$
$632$	−6858.51	−0.431672
$633$	14338.2	0.900305
$634$	−1904.63	−0.119310
$635$	−2293.07	−0.143304
$636$	−7582.34	−0.472735
$637$	140.724	0.00875307
$638$	−6528.94	−0.405146
$639$	8726.11	0.540218
$640$	−936.155	−0.0578199
$641$	−28678.3	−1.76712	−0.883560	−	0.468318i	$-0.844860\pi$
$641$	−28678.3	−1.76712	−0.883560	+	0.468318i	$0.844860\pi$
$642$	−6512.94	−0.400382
$643$	7606.41	0.466513	0.233256	−	0.972415i	$-0.425062\pi$
$643$	7606.41	0.466513	0.233256	+	0.972415i	$0.425062\pi$
$644$	1592.86	0.0974651
$645$	−8742.46	−0.533696
$646$	−3427.53	−0.208753
$647$	546.880	0.0332304	0.0166152	−	0.999862i	$-0.494711\pi$
$647$	546.880	0.0332304	0.0166152	+	0.999862i	$0.494711\pi$
$648$	648.000	0.0392837
$649$	−46085.6	−2.78739
$650$	465.504	0.0280901
$651$	−5668.70	−0.341281
$652$	−7186.97	−0.431693
$653$	2615.66	0.156751	0.0783756	−	0.996924i	$-0.475027\pi$
$653$	2615.66	0.156751	0.0783756	+	0.996924i	$0.475027\pi$
$654$	602.594	0.0360295
$655$	3785.34	0.225810
$656$	1052.23	0.0626262
$657$	4160.82	0.247076
$658$	−5682.97	−0.336695
$659$	5101.12	0.301535	0.150767	−	0.988569i	$-0.451826\pi$
$659$	5101.12	0.301535	0.150767	+	0.988569i	$0.451826\pi$
$660$	6078.12	0.358470
$661$	−33184.1	−1.95267	−0.976334	−	0.216268i	$-0.930611\pi$
$661$	−33184.1	−1.95267	−0.976334	+	0.216268i	$0.930611\pi$
$662$	11456.9	0.672634
$663$	839.172	0.0491565
$664$	−9564.85	−0.559018
$665$	2525.09	0.147246
$666$	1564.23	0.0910099
$667$	−1084.15	−0.0629364
$668$	−5358.43	−0.310365
$669$	2392.23	0.138249
$670$	−1220.95	−0.0704022
$671$	−33964.7	−1.95409
$672$	−1662.12	−0.0954130
$673$	−22540.9	−1.29107	−0.645533	−	0.763733i	$-0.723365\pi$
$673$	−22540.9	−1.29107	−0.645533	+	0.763733i	$0.723365\pi$
$674$	−12608.8	−0.720582
$675$	1930.76	0.110096
$676$	−8745.62	−0.497589
$677$	30165.0	1.71246	0.856229	−	0.516596i	$-0.172801\pi$
$677$	30165.0	1.71246	0.856229	+	0.516596i	$0.172801\pi$
$678$	−13736.6	−0.778098
$679$	−14157.8	−0.800188
$680$	−5028.39	−0.283573
$681$	17695.9	0.995753
$682$	15116.5	0.848742
$683$	417.726	0.0234024	0.0117012	−	0.999932i	$-0.496275\pi$
$683$	417.726	0.0234024	0.0117012	+	0.999932i	$0.496275\pi$
$684$	−717.881	−0.0401299
$685$	3181.74	0.177472
$686$	−13374.3	−0.744365
$687$	506.478	0.0281271
$688$	−6375.21	−0.353274
$689$	−2056.61	−0.113716
$690$	1009.29	0.0556856
$691$	−5421.98	−0.298498	−0.149249	−	0.988800i	$-0.547686\pi$
$691$	−5421.98	−0.298498	−0.149249	+	0.988800i	$0.547686\pi$
$692$	−7014.59	−0.385339
$693$	10791.5	0.591538
$694$	18676.6	1.02155
$695$	−911.476	−0.0497471
$696$	1131.29	0.0616113
$697$	5651.88	0.307145
$698$	8448.54	0.458140
$699$	−12554.0	−0.679308
$700$	−4952.39	−0.267404
$701$	14840.0	0.799572	0.399786	−	0.916608i	$-0.369084\pi$
$701$	14840.0	0.799572	0.399786	+	0.916608i	$0.369084\pi$
$702$	175.761	0.00944968
$703$	−1732.92	−0.0929703
$704$	4432.31	0.237285
$705$	−3600.93	−0.192367
$706$	−12582.3	−0.670736
$707$	9185.76	0.488637
$708$	7985.40	0.423884
$709$	15302.4	0.810569	0.405284	−	0.914191i	$-0.367173\pi$
$709$	15302.4	0.810569	0.405284	+	0.914191i	$0.367173\pi$
$710$	−14182.3	−0.749649
$711$	−7715.82	−0.406985
$712$	−3063.68	−0.161259
$713$	2510.15	0.131846
$714$	−8927.76	−0.467945
$715$	1648.60	0.0862298
$716$	−17500.7	−0.913452
$717$	−7721.88	−0.402202
$718$	24135.9	1.25452
$719$	26125.2	1.35508	0.677542	−	0.735484i	$-0.263045\pi$
$719$	26125.2	1.35508	0.677542	+	0.735484i	$0.263045\pi$
$720$	−1053.17	−0.0545132
$721$	−24708.7	−1.27628
$722$	−12922.7	−0.666112
$723$	3277.19	0.168575
$724$	−14476.1	−0.743093
$725$	3370.76	0.172671
$726$	−20791.4	−1.06287
$727$	−4928.32	−0.251419	−0.125709	−	0.992067i	$-0.540121\pi$
$727$	−4928.32	−0.251419	−0.125709	+	0.992067i	$0.540121\pi$
$728$	−450.826	−0.0229515
$729$	729.000	0.0370370
$730$	−6762.44	−0.342862
$731$	−34243.3	−1.73261
$732$	5885.17	0.297161
$733$	16142.2	0.813405	0.406703	−	0.913561i	$-0.366679\pi$
$733$	16142.2	0.813405	0.406703	+	0.913561i	$0.366679\pi$
$734$	16238.0	0.816560
$735$	−948.635	−0.0476067
$736$	736.000	0.0368605
$737$	5780.71	0.288922
$738$	1183.76	0.0590445
$739$	−1612.09	−0.0802457	−0.0401229	−	0.999195i	$-0.512775\pi$
$739$	−1612.09	−0.0802457	−0.0401229	+	0.999195i	$0.512775\pi$
$740$	−2542.29	−0.126293
$741$	−194.715	−0.00965323
$742$	21879.8	1.08252
$743$	−33768.1	−1.66734	−0.833668	−	0.552265i	$-0.813764\pi$
$743$	−33768.1	−1.66734	−0.833668	+	0.552265i	$0.813764\pi$
$744$	−2619.29	−0.129070
$745$	20407.4	1.00358
$746$	10512.6	0.515943
$747$	−10760.5	−0.527048
$748$	23807.4	1.16375
$749$	18793.9	0.916840
$750$	−8623.29	−0.419837
$751$	−12656.6	−0.614977	−0.307488	−	0.951552i	$-0.599489\pi$
$751$	−12656.6	−0.614977	−0.307488	+	0.951552i	$0.599489\pi$
$752$	−2625.88	−0.127335
$753$	16512.3	0.799127
$754$	306.847	0.0148206
$755$	−21086.4	−1.01644
$756$	−1869.88	−0.0899562
$757$	−35451.3	−1.70211	−0.851056	−	0.525075i	$-0.824037\pi$
$757$	−35451.3	−1.70211	−0.851056	+	0.525075i	$0.824037\pi$
$758$	6750.70	0.323478
$759$	−4778.58	−0.228526
$760$	1166.75	0.0556874
$761$	4234.99	0.201732	0.100866	−	0.994900i	$-0.467839\pi$
$761$	4234.99	0.201732	0.100866	+	0.994900i	$0.467839\pi$
$762$	−1881.18	−0.0894332
$763$	−1738.86	−0.0825043
$764$	2149.48	0.101787
$765$	−5656.94	−0.267355
$766$	−16069.2	−0.757970
$767$	2165.93	0.101965
$768$	−768.000	−0.0360844
$769$	23381.4	1.09643	0.548216	−	0.836337i	$-0.315307\pi$
$769$	23381.4	1.09643	0.548216	+	0.836337i	$0.315307\pi$
$770$	−17539.1	−0.820865
$771$	−10963.2	−0.512100
$772$	−1339.14	−0.0624307
$773$	8976.44	0.417672	0.208836	−	0.977951i	$-0.433033\pi$
$773$	8976.44	0.417672	0.208836	+	0.977951i	$0.433033\pi$
$774$	−7172.11	−0.333070
$775$	−7804.36	−0.361730
$776$	−6541.79	−0.302625
$777$	−4513.77	−0.208405
$778$	53.0528	0.00244478
$779$	−1311.42	−0.0603163
$780$	−285.659	−0.0131131
$781$	67147.2	3.07646
$782$	3953.29	0.180779
$783$	1272.70	0.0580877
$784$	−691.768	−0.0315128
$785$	−11152.4	−0.507065
$786$	3105.41	0.140924
$787$	−33632.8	−1.52335	−0.761677	−	0.647957i	$-0.775624\pi$
$787$	−33632.8	−1.52335	−0.761677	+	0.647957i	$0.775624\pi$
$788$	−6696.77	−0.302744
$789$	16057.3	0.724530
$790$	12540.3	0.564764
$791$	39638.5	1.78177
$792$	4986.35	0.223715
$793$	1596.27	0.0714820
$794$	18320.4	0.818849
$795$	13863.8	0.618487
$796$	3068.92	0.136652
$797$	38371.3	1.70537	0.852686	−	0.522424i	$-0.174972\pi$
$797$	38371.3	1.70537	0.852686	+	0.522424i	$0.174972\pi$
$798$	2071.53	0.0918939
$799$	−14104.5	−0.624506
$800$	−2288.31	−0.101130
$801$	−3446.64	−0.152036
$802$	8989.60	0.395803
$803$	32017.4	1.40706
$804$	−1001.64	−0.0439368
$805$	−2912.43	−0.127515
$806$	−710.446	−0.0310476
$807$	−13269.6	−0.578827
$808$	4244.39	0.184798
$809$	−15249.5	−0.662722	−0.331361	−	0.943504i	$-0.607508\pi$
$809$	−15249.5	−0.662722	−0.331361	+	0.943504i	$0.607508\pi$
$810$	−1184.82	−0.0513955
$811$	9708.02	0.420339	0.210169	−	0.977665i	$-0.432598\pi$
$811$	9708.02	0.420339	0.210169	+	0.977665i	$0.432598\pi$
$812$	−3264.47	−0.141084
$813$	9539.17	0.411505
$814$	12036.7	0.518288
$815$	13140.9	0.564790
$816$	−4125.17	−0.176973
$817$	7945.56	0.340245
$818$	−15976.1	−0.682873
$819$	−507.179	−0.0216389
$820$	−1923.93	−0.0819348
$821$	9028.52	0.383797	0.191899	−	0.981415i	$-0.438536\pi$
$821$	9028.52	0.383797	0.191899	+	0.981415i	$0.438536\pi$
$822$	2610.23	0.110757
$823$	42539.1	1.80172	0.900862	−	0.434105i	$-0.142935\pi$
$823$	42539.1	1.80172	0.900862	+	0.434105i	$0.142935\pi$
$824$	−11416.9	−0.482679
$825$	14857.2	0.626982
$826$	−23042.8	−0.970656
$827$	21526.4	0.905134	0.452567	−	0.891730i	$-0.350508\pi$
$827$	21526.4	0.905134	0.452567	+	0.891730i	$0.350508\pi$
$828$	828.000	0.0347524
$829$	38550.4	1.61509	0.807546	−	0.589804i	$-0.200795\pi$
$829$	38550.4	1.61509	0.807546	+	0.589804i	$0.200795\pi$
$830$	17488.6	0.731373
$831$	−3405.77	−0.142172
$832$	−208.309	−0.00868008
$833$	−3715.71	−0.154552
$834$	−747.754	−0.0310463
$835$	9797.49	0.406055
$836$	−5524.08	−0.228534
$837$	−2946.70	−0.121688
$838$	−25117.8	−1.03542
$839$	30566.4	1.25777	0.628884	−	0.777499i	$-0.283512\pi$
$839$	30566.4	1.25777	0.628884	+	0.777499i	$0.283512\pi$
$840$	3039.06	0.124830
$841$	−22167.1	−0.908897
$842$	−25219.3	−1.03220
$843$	8609.57	0.351755
$844$	−19117.6	−0.779687
$845$	15990.7	0.651004
$846$	−2954.12	−0.120053
$847$	59996.0	2.43387
$848$	10109.8	0.409401
$849$	−2572.52	−0.103991
$850$	−12291.2	−0.495984
$851$	1998.74	0.0805121
$852$	−11634.8	−0.467843
$853$	20617.3	0.827576	0.413788	−	0.910373i	$-0.364205\pi$
$853$	20617.3	0.827576	0.413788	+	0.910373i	$0.364205\pi$
$854$	−16982.3	−0.680473
$855$	1312.59	0.0525026
$856$	8683.92	0.346741
$857$	1553.09	0.0619048	0.0309524	−	0.999521i	$-0.490146\pi$
$857$	1553.09	0.0619048	0.0309524	+	0.999521i	$0.490146\pi$
$858$	1352.48	0.0538145
$859$	−34732.9	−1.37959	−0.689797	−	0.724003i	$-0.742300\pi$
$859$	−34732.9	−1.37959	−0.689797	+	0.724003i	$0.742300\pi$
$860$	11656.6	0.462194
$861$	−3415.88	−0.135207
$862$	−3430.10	−0.135533
$863$	9162.01	0.361389	0.180694	−	0.983539i	$-0.442166\pi$
$863$	9162.01	0.361389	0.180694	+	0.983539i	$0.442166\pi$
$864$	−864.000	−0.0340207
$865$	12825.7	0.504145
$866$	33372.5	1.30952
$867$	−7418.63	−0.290600
$868$	7558.27	0.295558
$869$	−59373.1	−2.31772
$870$	−2068.48	−0.0806070
$871$	−271.681	−0.0105690
$872$	−803.459	−0.0312025
$873$	−7359.52	−0.285317
$874$	−917.292	−0.0355010
$875$	24883.5	0.961390
$876$	−5547.75	−0.213974
$877$	−5772.11	−0.222247	−0.111123	−	0.993807i	$-0.535445\pi$
$877$	−5772.11	−0.222247	−0.111123	+	0.993807i	$0.535445\pi$
$878$	22894.0	0.879993
$879$	−26470.4	−1.01573
$880$	−8104.15	−0.310444
$881$	9412.65	0.359955	0.179977	−	0.983671i	$-0.442398\pi$
$881$	9412.65	0.359955	0.179977	+	0.983671i	$0.442398\pi$
$882$	−778.239	−0.0297105
$883$	−45232.2	−1.72388	−0.861940	−	0.507011i	$-0.830750\pi$
$883$	−45232.2	−1.72388	−0.861940	+	0.507011i	$0.830750\pi$
$884$	−1118.90	−0.0425708
$885$	−14600.7	−0.554574
$886$	24016.3	0.910658
$887$	31353.8	1.18687	0.593437	−	0.804880i	$-0.297771\pi$
$887$	31353.8	1.18687	0.593437	+	0.804880i	$0.297771\pi$
$888$	−2085.64	−0.0788169
$889$	5428.38	0.204794
$890$	5601.72	0.210978
$891$	5609.64	0.210920
$892$	−3189.64	−0.119728
$893$	3272.69	0.122639
$894$	16741.7	0.626317
$895$	31998.8	1.19508
$896$	2216.15	0.0826301
$897$	224.584	0.00835967
$898$	6451.66	0.239749
$899$	−5144.40	−0.190851
$900$	−2574.35	−0.0953462
$901$	54302.9	2.00787
$902$	9109.02	0.336250
$903$	20696.0	0.762701
$904$	18315.4	0.673852
$905$	26468.5	0.972200
$906$	−17298.8	−0.634343
$907$	−8652.83	−0.316772	−0.158386	−	0.987377i	$-0.550629\pi$
$907$	−8652.83	−0.316772	−0.158386	+	0.987377i	$0.550629\pi$
$908$	−23594.5	−0.862347
$909$	4774.94	0.174229
$910$	824.302	0.0300279
$911$	23107.3	0.840370	0.420185	−	0.907438i	$-0.361965\pi$
$911$	23107.3	0.840370	0.420185	+	0.907438i	$0.361965\pi$
$912$	957.174	0.0347535
$913$	−82801.5	−3.00146
$914$	2636.39	0.0954092
$915$	−10760.6	−0.388781
$916$	−675.304	−0.0243588
$917$	−8961.02	−0.322703
$918$	−4640.82	−0.166852
$919$	−42056.1	−1.50958	−0.754790	−	0.655966i	$-0.772261\pi$
$919$	−42056.1	−1.50958	−0.754790	+	0.655966i	$0.772261\pi$
$920$	−1345.72	−0.0482252
$921$	−24370.2	−0.871907
$922$	−15674.4	−0.559878
$923$	−3155.78	−0.112539
$924$	−14388.7	−0.512287
$925$	−6214.30	−0.220892
$926$	31624.9	1.12231
$927$	−12844.1	−0.455074
$928$	−1508.39	−0.0533569
$929$	1263.92	0.0446369	0.0223185	−	0.999751i	$-0.492895\pi$
$929$	1263.92	0.0446369	0.0223185	+	0.999751i	$0.492895\pi$
$930$	4789.18	0.168864
$931$	862.164	0.0303505
$932$	16738.7	0.588298
$933$	−10250.0	−0.359667
$934$	−16284.3	−0.570492
$935$	−43530.0	−1.52255
$936$	−234.348	−0.00818366
$937$	−27756.8	−0.967743	−0.483871	−	0.875139i	$-0.660770\pi$
$937$	−27756.8	−0.967743	−0.483871	+	0.875139i	$0.660770\pi$
$938$	2890.35	0.100611
$939$	−15975.4	−0.555205
$940$	4801.24	0.166595
$941$	−7081.47	−0.245323	−0.122662	−	0.992449i	$-0.539143\pi$
$941$	−7081.47	−0.245323	−0.122662	+	0.992449i	$0.539143\pi$
$942$	−9149.18	−0.316450
$943$	1512.58	0.0522338
$944$	−10647.2	−0.367094
$945$	3418.94	0.117691
$946$	−55189.3	−1.89678
$947$	−34048.7	−1.16836	−0.584179	−	0.811625i	$-0.698583\pi$
$947$	−34048.7	−1.16836	−0.584179	+	0.811625i	$0.698583\pi$
$948$	10287.8	0.352459
$949$	−1504.75	−0.0514713
$950$	2851.97	0.0974000
$951$	2856.94	0.0974161
$952$	11903.7	0.405252
$953$	−10453.3	−0.355314	−0.177657	−	0.984092i	$-0.556852\pi$
$953$	−10453.3	−0.355314	−0.177657	+	0.984092i	$0.556852\pi$
$954$	11373.5	0.385987
$955$	−3930.16	−0.133170
$956$	10295.8	0.348317
$957$	9793.41	0.330801
$958$	−4433.71	−0.149527
$959$	−7532.12	−0.253623
$960$	1404.23	0.0472098
$961$	−17880.1	−0.600185
$962$	−565.700	−0.0189594
$963$	9769.41	0.326911
$964$	−4369.58	−0.145990
$965$	2448.51	0.0816791
$966$	−2389.29	−0.0795799
$967$	−22280.5	−0.740945	−0.370473	−	0.928843i	$-0.620804\pi$
$967$	−22280.5	−0.740945	−0.370473	+	0.928843i	$0.620804\pi$
$968$	27721.9	0.920469
$969$	5141.29	0.170446
$970$	11961.2	0.395929
$971$	−39430.9	−1.30319	−0.651595	−	0.758567i	$-0.725900\pi$
$971$	−39430.9	−1.30319	−0.651595	+	0.758567i	$0.725900\pi$
$972$	−972.000	−0.0320750
$973$	2157.73	0.0710933
$974$	−170.011	−0.00559292
$975$	−698.256	−0.0229355
$976$	−7846.89	−0.257349
$977$	56586.0	1.85297	0.926483	−	0.376337i	$-0.122817\pi$
$977$	56586.0	1.85297	0.926483	+	0.376337i	$0.122817\pi$
$978$	10780.5	0.352476
$979$	−26521.9	−0.865825
$980$	1264.85	0.0412286
$981$	−903.891	−0.0294180
$982$	−2400.57	−0.0780095
$983$	42422.5	1.37647	0.688235	−	0.725488i	$-0.258386\pi$
$983$	42422.5	1.37647	0.688235	+	0.725488i	$0.258386\pi$
$984$	−1578.35	−0.0511340
$985$	12244.5	0.396085
$986$	−8102.03	−0.261685
$987$	8524.46	0.274910
$988$	259.620	0.00835994
$989$	−9164.37	−0.294651
$990$	−9117.17	−0.292690
$991$	−23798.6	−0.762853	−0.381426	−	0.924399i	$-0.624567\pi$
$991$	−23798.6	−0.762853	−0.381426	+	0.924399i	$0.624567\pi$
$992$	3492.39	0.111778
$993$	−17185.3	−0.549203
$994$	33573.6	1.07132
$995$	−5611.31	−0.178784
$996$	14347.3	0.456437
$997$	−35708.9	−1.13431	−0.567157	−	0.823610i	$-0.691957\pi$
$997$	−35708.9	−1.13431	−0.567157	+	0.823610i	$0.691957\pi$
$998$	−37692.0	−1.19551
$999$	−2346.34	−0.0743093

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.4.a.e.1.1	✓	2
3.2	odd	2		414.4.a.g.1.2		2
4.3	odd	2		1104.4.a.p.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.4.a.e.1.1	✓	2	1.1	even	1	trivial
414.4.a.g.1.2		2	3.2	odd	2
1104.4.a.p.1.1		2	4.3	odd	2

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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	138.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -7.31371 q^{5} -6.00000 q^{6} +17.3137 q^{7} +8.00000 q^{8} +9.00000 q^{9} -14.6274 q^{10} +69.2548 q^{11} -12.0000 q^{12} -3.25483 q^{13} +34.6274 q^{14} +21.9411 q^{15} +16.0000 q^{16} +85.9411 q^{17} +18.0000 q^{18} -19.9411 q^{19} -29.2548 q^{20} -51.9411 q^{21} +138.510 q^{22} +23.0000 q^{23} -24.0000 q^{24} -71.5097 q^{25} -6.50967 q^{26} -27.0000 q^{27} +69.2548 q^{28} -47.1371 q^{29} +43.8823 q^{30} +109.137 q^{31} +32.0000 q^{32} -207.765 q^{33} +171.882 q^{34} -126.627 q^{35} +36.0000 q^{36} +86.9016 q^{37} -39.8823 q^{38} +9.76450 q^{39} -58.5097 q^{40} +65.7645 q^{41} -103.882 q^{42} -398.451 q^{43} +277.019 q^{44} -65.8234 q^{45} +46.0000 q^{46} -164.118 q^{47} -48.0000 q^{48} -43.2355 q^{49} -143.019 q^{50} -257.823 q^{51} -13.0193 q^{52} +631.862 q^{53} -54.0000 q^{54} -506.510 q^{55} +138.510 q^{56} +59.8234 q^{57} -94.2742 q^{58} -665.450 q^{59} +87.7645 q^{60} -490.431 q^{61} +218.274 q^{62} +155.823 q^{63} +64.0000 q^{64} +23.8049 q^{65} -415.529 q^{66} +83.4701 q^{67} +343.765 q^{68} -69.0000 q^{69} -253.255 q^{70} +969.568 q^{71} +72.0000 q^{72} +462.313 q^{73} +173.803 q^{74} +214.529 q^{75} -79.7645 q^{76} +1199.06 q^{77} +19.5290 q^{78} -857.314 q^{79} -117.019 q^{80} +81.0000 q^{81} +131.529 q^{82} -1195.61 q^{83} -207.765 q^{84} -628.548 q^{85} -796.902 q^{86} +141.411 q^{87} +554.039 q^{88} -382.960 q^{89} -131.647 q^{90} -56.3532 q^{91} +92.0000 q^{92} -327.411 q^{93} -328.235 q^{94} +145.844 q^{95} -96.0000 q^{96} -817.724 q^{97} -86.4710 q^{98} +623.294 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} - 6 q^{3} + 8 q^{4} + 8 q^{5} - 12 q^{6} + 12 q^{7} + 16 q^{8} + 18 q^{9} + 16 q^{10} + 48 q^{11} - 24 q^{12} + 84 q^{13} + 24 q^{14} - 24 q^{15} + 32 q^{16} + 104 q^{17} + 36 q^{18} + 28 q^{19}+ \cdots + 432 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 - 6 * q^3 + 8 * q^4 + 8 * q^5 - 12 * q^6 + 12 * q^7 + 16 * q^8 + 18 * q^9 + 16 * q^10 + 48 * q^11 - 24 * q^12 + 84 * q^13 + 24 * q^14 - 24 * q^15 + 32 * q^16 + 104 * q^17 + 36 * q^18 + 28 * q^19 + 32 * q^20 - 36 * q^21 + 96 * q^22 + 46 * q^23 - 48 * q^24 + 38 * q^25 + 168 * q^26 - 54 * q^27 + 48 * q^28 + 132 * q^29 - 48 * q^30 - 8 * q^31 + 64 * q^32 - 144 * q^33 + 208 * q^34 - 208 * q^35 + 72 * q^36 - 324 * q^37 + 56 * q^38 - 252 * q^39 + 64 * q^40 - 140 * q^41 - 72 * q^42 - 548 * q^43 + 192 * q^44 + 72 * q^45 + 92 * q^46 - 464 * q^47 - 96 * q^48 - 358 * q^49 + 76 * q^50 - 312 * q^51 + 336 * q^52 + 336 * q^53 - 108 * q^54 - 832 * q^55 + 96 * q^56 - 84 * q^57 + 264 * q^58 + 72 * q^59 - 96 * q^60 + 60 * q^61 - 16 * q^62 + 108 * q^63 + 128 * q^64 + 1360 * q^65 - 288 * q^66 - 444 * q^67 + 416 * q^68 - 138 * q^69 - 416 * q^70 + 672 * q^71 + 144 * q^72 - 252 * q^73 - 648 * q^74 - 114 * q^75 + 112 * q^76 + 1312 * q^77 - 504 * q^78 - 1692 * q^79 + 128 * q^80 + 162 * q^81 - 280 * q^82 - 400 * q^83 - 144 * q^84 - 352 * q^85 - 1096 * q^86 - 396 * q^87 + 384 * q^88 - 336 * q^89 + 144 * q^90 - 520 * q^91 + 184 * q^92 + 24 * q^93 - 928 * q^94 + 880 * q^95 - 192 * q^96 + 220 * q^97 - 716 * q^98 + 432 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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