LMFDB - Embedded newform 161.4.a.d.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [161,4,Mod(1,161)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(161, 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("161.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 161 = 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	161.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:	$9.49930751092$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 76 x^{10} + 311 x^{9} + 1979 x^{8} - 8466 x^{7} - 19942 x^{6} + 95647 x^{5} + \cdots - 70656 $ x^12 - 4x^11 - 76x^10 + 311x^9 + 1979x^8 - 8466x^7 - 19942x^6 + 95647x^5 + 50294x^4 - 400320x^3 + 178432x^2 + 227072*x - 70656
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-3.06154$ of defining polynomial
Character	$\chi$	$=$	161.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.06154 q^{2} +5.71887 q^{3} +1.37302 q^{4} +21.1978 q^{5} -17.5086 q^{6} +7.00000 q^{7} +20.2888 q^{8} +5.70552 q^{9} -64.8978 q^{10} +56.8723 q^{11} +7.85212 q^{12} -62.2988 q^{13} -21.4308 q^{14} +121.227 q^{15} -73.0990 q^{16} -8.75386 q^{17} -17.4677 q^{18} -50.6126 q^{19} +29.1049 q^{20} +40.0321 q^{21} -174.117 q^{22} +23.0000 q^{23} +116.029 q^{24} +324.345 q^{25} +190.730 q^{26} -121.780 q^{27} +9.61113 q^{28} +86.9844 q^{29} -371.142 q^{30} -86.3635 q^{31} +61.4852 q^{32} +325.246 q^{33} +26.8003 q^{34} +148.384 q^{35} +7.83379 q^{36} +307.773 q^{37} +154.952 q^{38} -356.279 q^{39} +430.076 q^{40} +361.474 q^{41} -122.560 q^{42} -133.360 q^{43} +78.0868 q^{44} +120.944 q^{45} -70.4154 q^{46} +190.683 q^{47} -418.044 q^{48} +49.0000 q^{49} -992.995 q^{50} -50.0622 q^{51} -85.5375 q^{52} -271.504 q^{53} +372.835 q^{54} +1205.57 q^{55} +142.021 q^{56} -289.447 q^{57} -266.306 q^{58} -789.770 q^{59} +166.447 q^{60} -777.096 q^{61} +264.405 q^{62} +39.9387 q^{63} +396.552 q^{64} -1320.60 q^{65} -995.752 q^{66} -108.415 q^{67} -12.0192 q^{68} +131.534 q^{69} -454.284 q^{70} +536.735 q^{71} +115.758 q^{72} -144.007 q^{73} -942.258 q^{74} +1854.89 q^{75} -69.4921 q^{76} +398.106 q^{77} +1090.76 q^{78} +179.931 q^{79} -1549.53 q^{80} -850.496 q^{81} -1106.67 q^{82} -1064.19 q^{83} +54.9649 q^{84} -185.562 q^{85} +408.287 q^{86} +497.453 q^{87} +1153.87 q^{88} -155.080 q^{89} -370.276 q^{90} -436.092 q^{91} +31.5794 q^{92} -493.902 q^{93} -583.782 q^{94} -1072.87 q^{95} +351.626 q^{96} +183.178 q^{97} -150.015 q^{98} +324.487 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + q^{3} + 72 q^{4} + 16 q^{5} - 15 q^{6} + 84 q^{7} - 21 q^{8} + 203 q^{9} + 106 q^{10} + 50 q^{11} - 139 q^{12} + 21 q^{13} + 28 q^{14} + 192 q^{15} + 516 q^{16} + 26 q^{17} + 251 q^{18}+ \cdots + 2400 q^{99}+O(q^{100}) $ 12 * q + 4 * q^2 + q^3 + 72 * q^4 + 16 * q^5 - 15 * q^6 + 84 * q^7 - 21 * q^8 + 203 * q^9 + 106 * q^10 + 50 * q^11 - 139 * q^12 + 21 * q^13 + 28 * q^14 + 192 * q^15 + 516 * q^16 + 26 * q^17 + 251 * q^18 + 292 * q^19 - 12 * q^20 + 7 * q^21 + 206 * q^22 + 276 * q^23 + 42 * q^24 + 408 * q^25 + 409 * q^26 - 335 * q^27 + 504 * q^28 + 129 * q^29 + 168 * q^30 + 375 * q^31 - 54 * q^32 + 428 * q^33 + 674 * q^34 + 112 * q^35 + 2271 * q^36 + 958 * q^37 - 120 * q^38 + 89 * q^39 + 1424 * q^40 - 347 * q^41 - 105 * q^42 + 392 * q^43 - 1158 * q^44 - 1338 * q^45 + 92 * q^46 + 559 * q^47 - 4767 * q^48 + 588 * q^49 - 888 * q^50 + 204 * q^51 - 1765 * q^52 + 42 * q^53 - 1965 * q^54 + 78 * q^55 - 147 * q^56 + 156 * q^57 - 3695 * q^58 - 620 * q^59 - 1574 * q^60 - 1258 * q^61 + 489 * q^62 + 1421 * q^63 + 4335 * q^64 - 752 * q^65 - 7334 * q^66 + 2024 * q^67 - 5162 * q^68 + 23 * q^69 + 742 * q^70 + 1371 * q^71 - 2483 * q^72 - 1241 * q^73 - 4006 * q^74 + 1357 * q^75 + 4214 * q^76 + 350 * q^77 - 4787 * q^78 + 2660 * q^79 - 5734 * q^80 + 2400 * q^81 - 3551 * q^82 - 1476 * q^83 - 973 * q^84 + 408 * q^85 - 988 * q^86 + 1263 * q^87 + 3324 * q^88 + 1670 * q^89 + 1050 * q^90 + 147 * q^91 + 1656 * q^92 + 135 * q^93 - 3539 * q^94 + 2428 * q^95 - 3973 * q^96 + 1174 * q^97 + 196 * q^98 + 2400 * 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 $

$2$	−3.06154	−1.08242	−0.541209	−	0.840888i	$-0.682033\pi$
$2$	−3.06154	−1.08242	−0.541209	+	0.840888i	$0.682033\pi$
$3$	5.71887	1.10060	0.550299	−	0.834968i	$-0.314514\pi$
$3$	5.71887	1.10060	0.550299	+	0.834968i	$0.314514\pi$
$4$	1.37302	0.171627
$5$	21.1978	1.89599	0.947993	−	0.318292i	$-0.103109\pi$
$5$	21.1978	1.89599	0.947993	+	0.318292i	$0.103109\pi$
$6$	−17.5086	−1.19131
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	20.2888	0.896645
$9$	5.70552	0.211316
$10$	−64.8978	−2.05225
$11$	56.8723	1.55888	0.779439	−	0.626478i	$-0.215504\pi$
$11$	56.8723	1.55888	0.779439	+	0.626478i	$0.215504\pi$
$12$	7.85212	0.188893
$13$	−62.2988	−1.32912	−0.664561	−	0.747234i	$-0.731381\pi$
$13$	−62.2988	−1.32912	−0.664561	+	0.747234i	$0.731381\pi$
$14$	−21.4308	−0.409115
$15$	121.227	2.08672
$16$	−73.0990	−1.14217
$17$	−8.75386	−0.124890	−0.0624448	−	0.998048i	$-0.519890\pi$
$17$	−8.75386	−0.124890	−0.0624448	+	0.998048i	$0.519890\pi$
$18$	−17.4677	−0.228732
$19$	−50.6126	−0.611123	−0.305561	−	0.952172i	$-0.598844\pi$
$19$	−50.6126	−0.611123	−0.305561	+	0.952172i	$0.598844\pi$
$20$	29.1049	0.325403
$21$	40.0321	0.415987
$22$	−174.117	−1.68736
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	116.029	0.986846
$25$	324.345	2.59476
$26$	190.730	1.43866
$27$	−121.780	−0.868024
$28$	9.61113	0.0648690
$29$	86.9844	0.556986	0.278493	−	0.960438i	$-0.410165\pi$
$29$	86.9844	0.556986	0.278493	+	0.960438i	$0.410165\pi$
$30$	−371.142	−2.25870
$31$	−86.3635	−0.500366	−0.250183	−	0.968199i	$-0.580491\pi$
$31$	−86.3635	−0.500366	−0.250183	+	0.968199i	$0.580491\pi$
$32$	61.4852	0.339661
$33$	325.246	1.71570
$34$	26.8003	0.135183
$35$	148.384	0.716615
$36$	7.83379	0.0362676
$37$	307.773	1.36750	0.683751	−	0.729716i	$-0.260348\pi$
$37$	307.773	1.36750	0.683751	+	0.729716i	$0.260348\pi$
$38$	154.952	0.661490
$39$	−356.279	−1.46283
$40$	430.076	1.70003
$41$	361.474	1.37690	0.688449	−	0.725285i	$-0.258292\pi$
$41$	361.474	1.37690	0.688449	+	0.725285i	$0.258292\pi$
$42$	−122.560	−0.450271
$43$	−133.360	−0.472959	−0.236479	−	0.971637i	$-0.575994\pi$
$43$	−133.360	−0.472959	−0.236479	+	0.971637i	$0.575994\pi$
$44$	78.0868	0.267546
$45$	120.944	0.400652
$46$	−70.4154	−0.225700
$47$	190.683	0.591785	0.295893	−	0.955221i	$-0.404383\pi$
$47$	190.683	0.591785	0.295893	+	0.955221i	$0.404383\pi$
$48$	−418.044	−1.25707
$49$	49.0000	0.142857
$50$	−992.995	−2.80861
$51$	−50.0622	−0.137453
$52$	−85.5375	−0.228114
$53$	−271.504	−0.703660	−0.351830	−	0.936064i	$-0.614440\pi$
$53$	−271.504	−0.703660	−0.351830	+	0.936064i	$0.614440\pi$
$54$	372.835	0.939565
$55$	1205.57	2.95561
$56$	142.021	0.338900
$57$	−289.447	−0.672600
$58$	−266.306	−0.602892
$59$	−789.770	−1.74270	−0.871350	−	0.490662i	$-0.836755\pi$
$59$	−789.770	−1.74270	−0.871350	+	0.490662i	$0.836755\pi$
$60$	166.447	0.358138
$61$	−777.096	−1.63110	−0.815548	−	0.578689i	$-0.803564\pi$
$61$	−777.096	−1.63110	−0.815548	+	0.578689i	$0.803564\pi$
$62$	264.405	0.541605
$63$	39.9387	0.0798698
$64$	396.552	0.774516
$65$	−1320.60	−2.52000
$66$	−995.752	−1.85710
$67$	−108.415	−0.197687	−0.0988434	−	0.995103i	$-0.531514\pi$
$67$	−108.415	−0.197687	−0.0988434	+	0.995103i	$0.531514\pi$
$68$	−12.0192	−0.0214345
$69$	131.534	0.229491
$70$	−454.284	−0.775677
$71$	536.735	0.897165	0.448583	−	0.893741i	$-0.351929\pi$
$71$	536.735	0.897165	0.448583	+	0.893741i	$0.351929\pi$
$72$	115.758	0.189475
$73$	−144.007	−0.230887	−0.115444	−	0.993314i	$-0.536829\pi$
$73$	−144.007	−0.230887	−0.115444	+	0.993314i	$0.536829\pi$
$74$	−942.258	−1.48021
$75$	1854.89	2.85579
$76$	−69.4921	−0.104885
$77$	398.106	0.589200
$78$	1090.76	1.58339
$79$	179.931	0.256251	0.128126	−	0.991758i	$-0.459104\pi$
$79$	179.931	0.256251	0.128126	+	0.991758i	$0.459104\pi$
$80$	−1549.53	−2.16554
$81$	−850.496	−1.16666
$82$	−1106.67	−1.49038
$83$	−1064.19	−1.40735	−0.703677	−	0.710520i	$-0.748460\pi$
$83$	−1064.19	−1.40735	−0.703677	+	0.710520i	$0.748460\pi$
$84$	54.9649	0.0713947
$85$	−185.562	−0.236789
$86$	408.287	0.511939
$87$	497.453	0.613018
$88$	1153.87	1.39776
$89$	−155.080	−0.184701	−0.0923506	−	0.995727i	$-0.529438\pi$
$89$	−155.080	−0.184701	−0.0923506	+	0.995727i	$0.529438\pi$
$90$	−370.276	−0.433672
$91$	−436.092	−0.502361
$92$	31.5794	0.0357868
$93$	−493.902	−0.550702
$94$	−583.782	−0.640559
$95$	−1072.87	−1.15868
$96$	351.626	0.373830
$97$	183.178	0.191741	0.0958707	−	0.995394i	$-0.469436\pi$
$97$	183.178	0.191741	0.0958707	+	0.995394i	$0.469436\pi$
$98$	−150.015	−0.154631
$99$	324.487	0.329415
$100$	445.332	0.445332
$101$	−232.418	−0.228975	−0.114487	−	0.993425i	$-0.536523\pi$
$101$	−232.418	−0.228975	−0.114487	+	0.993425i	$0.536523\pi$
$102$	153.267	0.148782
$103$	901.072	0.861993	0.430996	−	0.902354i	$-0.358162\pi$
$103$	901.072	0.861993	0.430996	+	0.902354i	$0.358162\pi$
$104$	−1263.97	−1.19175
$105$	848.591	0.788705
$106$	831.221	0.761654
$107$	1131.80	1.02258	0.511288	−	0.859409i	$-0.329168\pi$
$107$	1131.80	1.02258	0.511288	+	0.859409i	$0.329168\pi$
$108$	−167.207	−0.148977
$109$	−2210.57	−1.94252	−0.971258	−	0.238028i	$-0.923499\pi$
$109$	−2210.57	−1.94252	−0.971258	+	0.238028i	$0.923499\pi$
$110$	−3690.89	−3.19920
$111$	1760.11	1.50507
$112$	−511.693	−0.431700
$113$	1091.19	0.908416	0.454208	−	0.890896i	$-0.349922\pi$
$113$	1091.19	0.908416	0.454208	+	0.890896i	$0.349922\pi$
$114$	886.154	0.728034
$115$	487.549	0.395340
$116$	119.431	0.0955941
$117$	−355.447	−0.280864
$118$	2417.91	1.88633
$119$	−61.2770	−0.0472038
$120$	2459.55	1.87104
$121$	1903.46	1.43010
$122$	2379.11	1.76553
$123$	2067.23	1.51541
$124$	−118.579	−0.0858765
$125$	4225.67	3.02365
$126$	−122.274	−0.0864525
$127$	819.946	0.572901	0.286451	−	0.958095i	$-0.407525\pi$
$127$	819.946	0.572901	0.286451	+	0.958095i	$0.407525\pi$
$128$	−1705.94	−1.17801
$129$	−762.670	−0.520537
$130$	4043.05	2.72769
$131$	2086.94	1.39188	0.695940	−	0.718099i	$-0.254988\pi$
$131$	2086.94	1.39188	0.695940	+	0.718099i	$0.254988\pi$
$132$	446.569	0.294461
$133$	−354.288	−0.230983
$134$	331.917	0.213980
$135$	−2581.47	−1.64576
$136$	−177.605	−0.111982
$137$	−1047.08	−0.652981	−0.326491	−	0.945200i	$-0.605866\pi$
$137$	−1047.08	−0.652981	−0.326491	+	0.945200i	$0.605866\pi$
$138$	−402.697	−0.248405
$139$	−1892.78	−1.15499	−0.577496	−	0.816394i	$-0.695970\pi$
$139$	−1892.78	−1.15499	−0.577496	+	0.816394i	$0.695970\pi$
$140$	203.735	0.122991
$141$	1090.49	0.651317
$142$	−1643.23	−0.971107
$143$	−3543.08	−2.07194
$144$	−417.068	−0.241359
$145$	1843.88	1.05604
$146$	440.884	0.249916
$147$	280.225	0.157228
$148$	422.578	0.234701
$149$	−2471.71	−1.35899	−0.679497	−	0.733678i	$-0.737802\pi$
$149$	−2471.71	−1.35899	−0.679497	+	0.733678i	$0.737802\pi$
$150$	−5678.82	−3.09116
$151$	619.505	0.333871	0.166936	−	0.985968i	$-0.446613\pi$
$151$	619.505	0.333871	0.166936	+	0.985968i	$0.446613\pi$
$152$	−1026.87	−0.547960
$153$	−49.9454	−0.0263911
$154$	−1218.82	−0.637761
$155$	−1830.71	−0.948687
$156$	−489.178	−0.251061
$157$	−3298.03	−1.67651	−0.838254	−	0.545280i	$-0.816423\pi$
$157$	−3298.03	−1.67651	−0.838254	+	0.545280i	$0.816423\pi$
$158$	−550.867	−0.277371
$159$	−1552.70	−0.774447
$160$	1303.35	0.643993
$161$	161.000	0.0788110
$162$	2603.83	1.26281
$163$	56.2971	0.0270523	0.0135262	−	0.999909i	$-0.495694\pi$
$163$	56.2971	0.0270523	0.0135262	+	0.999909i	$0.495694\pi$
$164$	496.311	0.236313
$165$	6894.48	3.25294
$166$	3258.07	1.52334
$167$	−3386.93	−1.56939	−0.784695	−	0.619882i	$-0.787180\pi$
$167$	−3386.93	−1.56939	−0.784695	+	0.619882i	$0.787180\pi$
$168$	812.202	0.372993
$169$	1684.14	0.766565
$170$	568.106	0.256304
$171$	−288.771	−0.129140
$172$	−183.106	−0.0811727
$173$	−1838.43	−0.807939	−0.403970	−	0.914772i	$-0.632370\pi$
$173$	−1838.43	−0.807939	−0.403970	+	0.914772i	$0.632370\pi$
$174$	−1522.97	−0.663541
$175$	2270.42	0.980728
$176$	−4157.31	−1.78051
$177$	−4516.60	−1.91801
$178$	474.782	0.199924
$179$	992.872	0.414585	0.207293	−	0.978279i	$-0.433535\pi$
$179$	992.872	0.414585	0.207293	+	0.978279i	$0.433535\pi$
$180$	166.059	0.0687628
$181$	214.433	0.0880589	0.0440294	−	0.999030i	$-0.485980\pi$
$181$	214.433	0.0880589	0.0440294	+	0.999030i	$0.485980\pi$
$182$	1335.11	0.543764
$183$	−4444.11	−1.79518
$184$	466.641	0.186963
$185$	6524.10	2.59276
$186$	1512.10	0.596089
$187$	−497.853	−0.194688
$188$	261.811	0.101567
$189$	−852.463	−0.328082
$190$	3284.65	1.25418
$191$	921.929	0.349259	0.174629	−	0.984634i	$-0.444127\pi$
$191$	921.929	0.349259	0.174629	+	0.984634i	$0.444127\pi$
$192$	2267.83	0.852431
$193$	−2662.22	−0.992906	−0.496453	−	0.868064i	$-0.665364\pi$
$193$	−2662.22	−0.992906	−0.496453	+	0.868064i	$0.665364\pi$
$194$	−560.807	−0.207544
$195$	−7552.32	−2.77350
$196$	67.2779	0.0245182
$197$	−4372.22	−1.58126	−0.790629	−	0.612295i	$-0.790246\pi$
$197$	−4372.22	−1.58126	−0.790629	+	0.612295i	$0.790246\pi$
$198$	−993.428	−0.356565
$199$	−72.5491	−0.0258436	−0.0129218	−	0.999917i	$-0.504113\pi$
$199$	−72.5491	−0.0258436	−0.0129218	+	0.999917i	$0.504113\pi$
$200$	6580.56	2.32658
$201$	−620.012	−0.217574
$202$	711.556	0.247846
$203$	608.891	0.210521
$204$	−68.7364	−0.0235907
$205$	7662.45	2.61058
$206$	−2758.67	−0.933036
$207$	131.227	0.0440624
$208$	4553.98	1.51808
$209$	−2878.46	−0.952666
$210$	−2598.00	−0.853708
$211$	3142.17	1.02519	0.512596	−	0.858630i	$-0.328684\pi$
$211$	3142.17	1.02519	0.512596	+	0.858630i	$0.328684\pi$
$212$	−372.781	−0.120767
$213$	3069.52	0.987418
$214$	−3465.06	−1.10685
$215$	−2826.94	−0.896723
$216$	−2470.77	−0.778310
$217$	−604.545	−0.189121
$218$	6767.75	2.10261
$219$	−823.559	−0.254114
$220$	1655.27	0.507264
$221$	545.355	0.165993
$222$	−5388.66	−1.62911
$223$	3516.93	1.05610	0.528051	−	0.849212i	$-0.322923\pi$
$223$	3516.93	1.05610	0.528051	+	0.849212i	$0.322923\pi$
$224$	430.397	0.128380
$225$	1850.56	0.548314
$226$	−3340.73	−0.983285
$227$	3098.37	0.905929	0.452965	−	0.891528i	$-0.350366\pi$
$227$	3098.37	0.905929	0.452965	+	0.891528i	$0.350366\pi$
$228$	−397.416	−0.115437
$229$	−931.461	−0.268789	−0.134395	−	0.990928i	$-0.542909\pi$
$229$	−931.461	−0.268789	−0.134395	+	0.990928i	$0.542909\pi$
$230$	−1492.65	−0.427923
$231$	2276.72	0.648473
$232$	1764.81	0.499419
$233$	−3884.24	−1.09212	−0.546062	−	0.837745i	$-0.683874\pi$
$233$	−3884.24	−1.09212	−0.546062	+	0.837745i	$0.683874\pi$
$234$	1088.22	0.304012
$235$	4042.04	1.12202
$236$	−1084.37	−0.299095
$237$	1029.00	0.282030
$238$	187.602	0.0510942
$239$	2848.69	0.770990	0.385495	−	0.922710i	$-0.374031\pi$
$239$	2848.69	0.770990	0.385495	+	0.922710i	$0.374031\pi$
$240$	−8861.59	−2.38339
$241$	−2775.83	−0.741937	−0.370969	−	0.928645i	$-0.620974\pi$
$241$	−2775.83	−0.741937	−0.370969	+	0.928645i	$0.620974\pi$
$242$	−5827.53	−1.54797
$243$	−1575.81	−0.416001
$244$	−1066.97	−0.279941
$245$	1038.69	0.270855
$246$	−6328.89	−1.64031
$247$	3153.11	0.812256
$248$	−1752.21	−0.448651
$249$	−6085.99	−1.54893
$250$	−12937.1	−3.27285
$251$	4062.77	1.02167	0.510836	−	0.859678i	$-0.329336\pi$
$251$	4062.77	1.02167	0.510836	+	0.859678i	$0.329336\pi$
$252$	54.8365	0.0137078
$253$	1308.06	0.325048
$254$	−2510.30	−0.620118
$255$	−1061.21	−0.260609
$256$	2050.39	0.500583
$257$	−1242.38	−0.301548	−0.150774	−	0.988568i	$-0.548177\pi$
$257$	−1242.38	−0.301548	−0.150774	+	0.988568i	$0.548177\pi$
$258$	2334.94	0.563439
$259$	2154.41	0.516867
$260$	−1813.20	−0.432500
$261$	496.292	0.117700
$262$	−6389.23	−1.50660
$263$	−3728.47	−0.874172	−0.437086	−	0.899420i	$-0.643989\pi$
$263$	−3728.47	−0.874172	−0.437086	+	0.899420i	$0.643989\pi$
$264$	6598.83	1.53837
$265$	−5755.28	−1.33413
$266$	1084.67	0.250020
$267$	−886.881	−0.203282
$268$	−148.856	−0.0339285
$269$	7100.46	1.60938	0.804689	−	0.593697i	$-0.202332\pi$
$269$	7100.46	1.60938	0.804689	+	0.593697i	$0.202332\pi$
$270$	7903.28	1.78140
$271$	−4062.52	−0.910629	−0.455315	−	0.890331i	$-0.650473\pi$
$271$	−4062.52	−0.910629	−0.455315	+	0.890331i	$0.650473\pi$
$272$	639.898	0.142645
$273$	−2493.95	−0.552897
$274$	3205.69	0.706798
$275$	18446.3	4.04492
$276$	180.599	0.0393869
$277$	5515.22	1.19631	0.598154	−	0.801381i	$-0.295901\pi$
$277$	5515.22	1.19631	0.598154	+	0.801381i	$0.295901\pi$
$278$	5794.83	1.25018
$279$	−492.749	−0.105735
$280$	3010.53	0.642549
$281$	6383.34	1.35515	0.677577	−	0.735452i	$-0.263030\pi$
$281$	6383.34	1.35515	0.677577	+	0.735452i	$0.263030\pi$
$282$	−3338.58	−0.704997
$283$	−7953.95	−1.67072	−0.835359	−	0.549704i	$-0.814740\pi$
$283$	−7953.95	−1.67072	−0.835359	+	0.549704i	$0.814740\pi$
$284$	736.947	0.153978
$285$	−6135.63	−1.27524
$286$	10847.3	2.24270
$287$	2530.32	0.520418
$288$	350.806	0.0717758
$289$	−4836.37	−0.984403
$290$	−5645.10	−1.14307
$291$	1047.57	0.211030
$292$	−197.725	−0.0396266
$293$	2925.22	0.583254	0.291627	−	0.956532i	$-0.405803\pi$
$293$	2925.22	0.583254	0.291627	+	0.956532i	$0.405803\pi$
$294$	−857.919	−0.170187
$295$	−16741.4	−3.30413
$296$	6244.33	1.22616
$297$	−6925.94	−1.35314
$298$	7567.23	1.47100
$299$	−1432.87	−0.277141
$300$	2546.80	0.490132
$301$	−933.521	−0.178762
$302$	−1896.64	−0.361388
$303$	−1329.17	−0.252009
$304$	3699.73	0.698007
$305$	−16472.7	−3.09254
$306$	152.910	0.0285662
$307$	−7493.31	−1.39305	−0.696524	−	0.717533i	$-0.745271\pi$
$307$	−7493.31	−1.39305	−0.696524	+	0.717533i	$0.745271\pi$
$308$	546.608	0.101123
$309$	5153.12	0.948707
$310$	5604.80	1.02688
$311$	6544.21	1.19321	0.596605	−	0.802535i	$-0.296516\pi$
$311$	6544.21	1.19321	0.596605	+	0.802535i	$0.296516\pi$
$312$	−7228.46	−1.31164
$313$	−1640.74	−0.296294	−0.148147	−	0.988965i	$-0.547331\pi$
$313$	−1640.74	−0.296294	−0.148147	+	0.988965i	$0.547331\pi$
$314$	10097.1	1.81468
$315$	846.610	0.151432
$316$	247.049	0.0439797
$317$	−1099.90	−0.194879	−0.0974396	−	0.995241i	$-0.531065\pi$
$317$	−1099.90	−0.194879	−0.0974396	+	0.995241i	$0.531065\pi$
$318$	4753.65	0.838275
$319$	4947.01	0.868274
$320$	8406.02	1.46847
$321$	6472.65	1.12545
$322$	−492.908	−0.0853064
$323$	443.056	0.0763229
$324$	−1167.75	−0.200231
$325$	−20206.3	−3.44875
$326$	−172.356	−0.0292819
$327$	−12642.0	−2.13793
$328$	7333.86	1.23459
$329$	1334.78	0.223674
$330$	−21107.7	−3.52104
$331$	10120.4	1.68056	0.840279	−	0.542154i	$-0.182391\pi$
$331$	10120.4	1.68056	0.840279	+	0.542154i	$0.182391\pi$
$332$	−1461.16	−0.241540
$333$	1756.01	0.288974
$334$	10369.2	1.69874
$335$	−2298.16	−0.374811
$336$	−2926.31	−0.475128
$337$	551.690	0.0891765	0.0445882	−	0.999005i	$-0.485802\pi$
$337$	551.690	0.0891765	0.0445882	+	0.999005i	$0.485802\pi$
$338$	−5156.07	−0.829743
$339$	6240.41	0.999800
$340$	−254.780	−0.0406394
$341$	−4911.70	−0.780010
$342$	884.085	0.139783
$343$	343.000	0.0539949
$344$	−2705.71	−0.424076
$345$	2788.23	0.435111
$346$	5628.43	0.874527
$347$	−6732.36	−1.04153	−0.520767	−	0.853699i	$-0.674354\pi$
$347$	−6732.36	−1.04153	−0.520767	+	0.853699i	$0.674354\pi$
$348$	683.012	0.105211
$349$	5616.35	0.861422	0.430711	−	0.902490i	$-0.358263\pi$
$349$	5616.35	0.861422	0.430711	+	0.902490i	$0.358263\pi$
$350$	−6950.97	−1.06156
$351$	7586.78	1.15371
$352$	3496.81	0.529490
$353$	−1184.60	−0.178612	−0.0893060	−	0.996004i	$-0.528465\pi$
$353$	−1184.60	−0.178612	−0.0893060	+	0.996004i	$0.528465\pi$
$354$	13827.7	2.07609
$355$	11377.6	1.70101
$356$	−212.927	−0.0316998
$357$	−350.436	−0.0519524
$358$	−3039.72	−0.448754
$359$	8883.20	1.30595	0.652977	−	0.757378i	$-0.273520\pi$
$359$	8883.20	1.30595	0.652977	+	0.757378i	$0.273520\pi$
$360$	2453.81	0.359242
$361$	−4297.36	−0.626529
$362$	−656.494	−0.0953165
$363$	10885.7	1.57397
$364$	−598.762	−0.0862189
$365$	−3052.63	−0.437759
$366$	13605.8	1.94314
$367$	−3695.88	−0.525677	−0.262838	−	0.964840i	$-0.584659\pi$
$367$	−3695.88	−0.525677	−0.262838	+	0.964840i	$0.584659\pi$
$368$	−1681.28	−0.238159
$369$	2062.40	0.290960
$370$	−19973.8	−2.80645
$371$	−1900.53	−0.265959
$372$	−678.137	−0.0945155
$373$	7051.40	0.978841	0.489421	−	0.872048i	$-0.337208\pi$
$373$	7051.40	0.978841	0.489421	+	0.872048i	$0.337208\pi$
$374$	1524.19	0.210733
$375$	24166.1	3.32782
$376$	3868.71	0.530621
$377$	−5419.03	−0.740303
$378$	2609.85	0.355122
$379$	−12273.2	−1.66341	−0.831706	−	0.555216i	$-0.812636\pi$
$379$	−12273.2	−1.66341	−0.831706	+	0.555216i	$0.812636\pi$
$380$	−1473.08	−0.198861
$381$	4689.17	0.630534
$382$	−2822.52	−0.378044
$383$	2311.87	0.308436	0.154218	−	0.988037i	$-0.450714\pi$
$383$	2311.87	0.308436	0.154218	+	0.988037i	$0.450714\pi$
$384$	−9756.07	−1.29652
$385$	8438.97	1.11712
$386$	8150.49	1.07474
$387$	−760.889	−0.0999436
$388$	251.507	0.0329081
$389$	−13783.7	−1.79656	−0.898278	−	0.439428i	$-0.855181\pi$
$389$	−13783.7	−1.79656	−0.898278	+	0.439428i	$0.855181\pi$
$390$	23121.7	3.00209
$391$	−201.339	−0.0260413
$392$	994.149	0.128092
$393$	11934.9	1.53190
$394$	13385.7	1.71158
$395$	3814.14	0.485849
$396$	445.526	0.0565367
$397$	−12201.3	−1.54248	−0.771242	−	0.636542i	$-0.780364\pi$
$397$	−12201.3	−1.54248	−0.771242	+	0.636542i	$0.780364\pi$
$398$	222.112	0.0279735
$399$	−2026.13	−0.254219
$400$	−23709.3	−2.96366
$401$	−25.3570	−0.00315777	−0.00157889	−	0.999999i	$-0.500503\pi$
$401$	−25.3570	−0.00315777	−0.00157889	+	0.999999i	$0.500503\pi$
$402$	1898.19	0.235505
$403$	5380.35	0.665048
$404$	−319.114	−0.0392983
$405$	−18028.6	−2.21197
$406$	−1864.14	−0.227872
$407$	17503.8	2.13177
$408$	−1015.70	−0.123247
$409$	11668.3	1.41066	0.705329	−	0.708880i	$-0.250799\pi$
$409$	11668.3	1.41066	0.705329	+	0.708880i	$0.250799\pi$
$410$	−23458.9	−2.82573
$411$	−5988.14	−0.718670
$412$	1237.19	0.147942
$413$	−5528.39	−0.658679
$414$	−401.757	−0.0476939
$415$	−22558.5	−2.66832
$416$	−3830.46	−0.451451
$417$	−10824.6	−1.27118
$418$	8812.51	1.03118
$419$	1468.66	0.171238	0.0856189	−	0.996328i	$-0.472713\pi$
$419$	1468.66	0.171238	0.0856189	+	0.996328i	$0.472713\pi$
$420$	1165.13	0.135363
$421$	12222.2	1.41490	0.707450	−	0.706763i	$-0.249845\pi$
$421$	12222.2	1.41490	0.707450	+	0.706763i	$0.249845\pi$
$422$	−9619.86	−1.10969
$423$	1087.94	0.125053
$424$	−5508.49	−0.630933
$425$	−2839.27	−0.324059
$426$	−9397.45	−1.06880
$427$	−5439.67	−0.616497
$428$	1553.99	0.175502
$429$	−20262.4	−2.28037
$430$	8654.77	0.970629
$431$	−3102.58	−0.346742	−0.173371	−	0.984857i	$-0.555466\pi$
$431$	−3102.58	−0.346742	−0.173371	+	0.984857i	$0.555466\pi$
$432$	8902.02	0.991432
$433$	−1743.58	−0.193513	−0.0967564	−	0.995308i	$-0.530847\pi$
$433$	−1743.58	−0.193513	−0.0967564	+	0.995308i	$0.530847\pi$
$434$	1850.84	0.204707
$435$	10544.9	1.16227
$436$	−3035.16	−0.333389
$437$	−1164.09	−0.127428
$438$	2521.36	0.275057
$439$	11386.2	1.23789	0.618944	−	0.785435i	$-0.287561\pi$
$439$	11386.2	1.23789	0.618944	+	0.785435i	$0.287561\pi$
$440$	24459.4	2.65013
$441$	279.571	0.0301880
$442$	−1669.63	−0.179674
$443$	−2893.26	−0.310300	−0.155150	−	0.987891i	$-0.549586\pi$
$443$	−2893.26	−0.310300	−0.155150	+	0.987891i	$0.549586\pi$
$444$	2416.67	0.258311
$445$	−3287.34	−0.350191
$446$	−10767.2	−1.14314
$447$	−14135.4	−1.49571
$448$	2775.87	0.292740
$449$	−13992.4	−1.47069	−0.735345	−	0.677693i	$-0.762980\pi$
$449$	−13992.4	−1.47069	−0.735345	+	0.677693i	$0.762980\pi$
$450$	−5665.56	−0.593504
$451$	20557.9	2.14642
$452$	1498.23	0.155909
$453$	3542.87	0.367458
$454$	−9485.78	−0.980594
$455$	−9244.17	−0.952469
$456$	−5872.52	−0.603084
$457$	14375.9	1.47150	0.735752	−	0.677251i	$-0.236829\pi$
$457$	14375.9	1.47150	0.735752	+	0.677251i	$0.236829\pi$
$458$	2851.70	0.290942
$459$	1066.05	0.108407
$460$	669.413	0.0678512
$461$	10075.8	1.01795	0.508977	−	0.860780i	$-0.330024\pi$
$461$	10075.8	1.01795	0.508977	+	0.860780i	$0.330024\pi$
$462$	−6970.27	−0.701918
$463$	4599.21	0.461649	0.230825	−	0.972995i	$-0.425858\pi$
$463$	4599.21	0.461649	0.230825	+	0.972995i	$0.425858\pi$
$464$	−6358.47	−0.636174
$465$	−10469.6	−1.04412
$466$	11891.7	1.18213
$467$	15054.9	1.49177	0.745886	−	0.666074i	$-0.232026\pi$
$467$	15054.9	1.49177	0.745886	+	0.666074i	$0.232026\pi$
$468$	−488.036	−0.0482040
$469$	−758.906	−0.0747186
$470$	−12374.9	−1.21449
$471$	−18861.0	−1.84516
$472$	−16023.5	−1.56258
$473$	−7584.50	−0.737285
$474$	−3150.34	−0.305274
$475$	−16416.0	−1.58572
$476$	−84.1345	−0.00810147
$477$	−1549.07	−0.148694
$478$	−8721.39	−0.834533
$479$	10087.1	0.962195	0.481097	−	0.876667i	$-0.340238\pi$
$479$	10087.1	0.962195	0.481097	+	0.876667i	$0.340238\pi$
$480$	7453.69	0.708777
$481$	−19173.9	−1.81758
$482$	8498.31	0.803086
$483$	920.739	0.0867393
$484$	2613.49	0.245444
$485$	3882.97	0.363539
$486$	4824.40	0.450286
$487$	15351.3	1.42840	0.714202	−	0.699940i	$-0.246790\pi$
$487$	15351.3	1.42840	0.714202	+	0.699940i	$0.246790\pi$
$488$	−15766.3	−1.46251
$489$	321.956	0.0297737
$490$	−3179.99	−0.293178
$491$	−1685.47	−0.154917	−0.0774584	−	0.996996i	$-0.524680\pi$
$491$	−1685.47	−0.154917	−0.0774584	+	0.996996i	$0.524680\pi$
$492$	2838.34	0.260086
$493$	−761.449	−0.0695618
$494$	−9653.36	−0.879201
$495$	6878.39	0.624567
$496$	6313.09	0.571504
$497$	3757.14	0.339097
$498$	18632.5	1.67659
$499$	18.1350	0.00162693	0.000813463	−	1.00000i	$-0.499741\pi$
$499$	18.1350	0.00162693	0.000813463		1.00000i	$0.499741\pi$
$500$	5801.93	0.518940
$501$	−19369.4	−1.72727
$502$	−12438.3	−1.10588
$503$	−2444.63	−0.216701	−0.108351	−	0.994113i	$-0.534557\pi$
$503$	−2444.63	−0.216701	−0.108351	+	0.994113i	$0.534557\pi$
$504$	810.306	0.0716149
$505$	−4926.74	−0.434133
$506$	−4004.69	−0.351838
$507$	9631.40	0.843680
$508$	1125.80	0.0983255
$509$	16064.8	1.39894	0.699469	−	0.714663i	$-0.253420\pi$
$509$	16064.8	1.39894	0.699469	+	0.714663i	$0.253420\pi$
$510$	3248.93	0.282088
$511$	−1008.05	−0.0872672
$512$	7370.19	0.636171
$513$	6163.63	0.530469
$514$	3803.61	0.326401
$515$	19100.7	1.63433
$516$	−1047.16	−0.0893385
$517$	10844.6	0.922521
$518$	−6595.81	−0.559466
$519$	−10513.8	−0.889216
$520$	−26793.2	−2.25954
$521$	8377.95	0.704501	0.352250	−	0.935906i	$-0.385417\pi$
$521$	8377.95	0.704501	0.352250	+	0.935906i	$0.385417\pi$
$522$	−1519.42	−0.127400
$523$	8809.80	0.736569	0.368284	−	0.929713i	$-0.379945\pi$
$523$	8809.80	0.736569	0.368284	+	0.929713i	$0.379945\pi$
$524$	2865.40	0.238885
$525$	12984.2	1.07939
$526$	11414.8	0.946219
$527$	756.014	0.0624905
$528$	−23775.1	−1.95962
$529$	529.000	0.0434783
$530$	17620.0	1.44408
$531$	−4506.05	−0.368260
$532$	−486.445	−0.0396429
$533$	−22519.4	−1.83006
$534$	2715.22	0.220036
$535$	23991.7	1.93879
$536$	−2199.61	−0.177255
$537$	5678.11	0.456291
$538$	−21738.3	−1.74202
$539$	2786.74	0.222697
$540$	−3544.41	−0.282458
$541$	−7434.32	−0.590806	−0.295403	−	0.955373i	$-0.595454\pi$
$541$	−7434.32	−0.590806	−0.295403	+	0.955373i	$0.595454\pi$
$542$	12437.6	0.985681
$543$	1226.31	0.0969174
$544$	−538.233	−0.0424202
$545$	−46859.2	−3.68298
$546$	7635.34	0.598466
$547$	455.940	0.0356391	0.0178196	−	0.999841i	$-0.494328\pi$
$547$	455.940	0.0356391	0.0178196	+	0.999841i	$0.494328\pi$
$548$	−1437.67	−0.112069
$549$	−4433.74	−0.344676
$550$	−56474.0	−4.37829
$551$	−4402.51	−0.340387
$552$	2668.66	0.205772
$553$	1259.52	0.0968539
$554$	−16885.0	−1.29490
$555$	37310.5	2.85359
$556$	−2598.83	−0.198228
$557$	1594.04	0.121260	0.0606299	−	0.998160i	$-0.480689\pi$
$557$	1594.04	0.121260	0.0606299	+	0.998160i	$0.480689\pi$
$558$	1508.57	0.114450
$559$	8308.18	0.628620
$560$	−10846.7	−0.818497
$561$	−2847.16	−0.214273
$562$	−19542.8	−1.46684
$563$	−296.715	−0.0222115	−0.0111057	−	0.999938i	$-0.503535\pi$
$563$	−296.715	−0.0222115	−0.0111057	+	0.999938i	$0.503535\pi$
$564$	1497.26	0.111784
$565$	23130.9	1.72234
$566$	24351.3	1.80841
$567$	−5953.47	−0.440957
$568$	10889.7	0.804439
$569$	9664.74	0.712069	0.356034	−	0.934473i	$-0.384129\pi$
$569$	9664.74	0.712069	0.356034	+	0.934473i	$0.384129\pi$
$570$	18784.5	1.38034
$571$	−16310.5	−1.19540	−0.597701	−	0.801719i	$-0.703919\pi$
$571$	−16310.5	−1.19540	−0.597701	+	0.801719i	$0.703919\pi$
$572$	−4864.72	−0.355601
$573$	5272.39	0.384393
$574$	−7746.67	−0.563310
$575$	7459.94	0.541045
$576$	2262.54	0.163667
$577$	−8762.32	−0.632201	−0.316101	−	0.948726i	$-0.602374\pi$
$577$	−8762.32	−0.632201	−0.316101	+	0.948726i	$0.602374\pi$
$578$	14806.7	1.06553
$579$	−15224.9	−1.09279
$580$	2531.68	0.181245
$581$	−7449.35	−0.531930
$582$	−3207.18	−0.228423
$583$	−15441.1	−1.09692
$584$	−2921.73	−0.207024
$585$	−7534.69	−0.532515
$586$	−8955.68	−0.631324
$587$	−6530.50	−0.459187	−0.229593	−	0.973287i	$-0.573740\pi$
$587$	−6530.50	−0.459187	−0.229593	+	0.973287i	$0.573740\pi$
$588$	384.754	0.0269847
$589$	4371.08	0.305785
$590$	51254.3	3.57645
$591$	−25004.2	−1.74033
$592$	−22497.9	−1.56192
$593$	−22582.6	−1.56384	−0.781919	−	0.623380i	$-0.785759\pi$
$593$	−22582.6	−1.56384	−0.781919	+	0.623380i	$0.785759\pi$
$594$	21204.0	1.46467
$595$	−1298.94	−0.0894978
$596$	−3393.70	−0.233241
$597$	−414.899	−0.0284434
$598$	4386.80	0.299982
$599$	22629.5	1.54360	0.771800	−	0.635866i	$-0.219357\pi$
$599$	22629.5	1.54360	0.771800	+	0.635866i	$0.219357\pi$
$600$	37633.4	2.56063
$601$	−2348.12	−0.159370	−0.0796852	−	0.996820i	$-0.525392\pi$
$601$	−2348.12	−0.159370	−0.0796852	+	0.996820i	$0.525392\pi$
$602$	2858.01	0.193495
$603$	−618.565	−0.0417743
$604$	850.591	0.0573015
$605$	40349.2	2.71145
$606$	4069.30	0.272779
$607$	18556.6	1.24084	0.620420	−	0.784270i	$-0.286962\pi$
$607$	18556.6	1.24084	0.620420	+	0.784270i	$0.286962\pi$
$608$	−3111.93	−0.207575
$609$	3482.17	0.231699
$610$	50431.8	3.34741
$611$	−11879.3	−0.786555
$612$	−68.5759	−0.00452944
$613$	4231.12	0.278782	0.139391	−	0.990237i	$-0.455486\pi$
$613$	4231.12	0.278782	0.139391	+	0.990237i	$0.455486\pi$
$614$	22941.1	1.50786
$615$	43820.6	2.87320
$616$	8077.08	0.528304
$617$	10492.4	0.684615	0.342308	−	0.939588i	$-0.388792\pi$
$617$	10492.4	0.684615	0.342308	+	0.939588i	$0.388792\pi$
$618$	−15776.5	−1.02690
$619$	−216.464	−0.0140556	−0.00702779	−	0.999975i	$-0.502237\pi$
$619$	−216.464	−0.0140556	−0.00702779	+	0.999975i	$0.502237\pi$
$620$	−2513.60	−0.162821
$621$	−2800.95	−0.180996
$622$	−20035.4	−1.29155
$623$	−1085.56	−0.0698105
$624$	26043.6	1.67080
$625$	49031.7	3.13803
$626$	5023.18	0.320713
$627$	−16461.5	−1.04850
$628$	−4528.26	−0.287735
$629$	−2694.20	−0.170787
$630$	−2591.93	−0.163913
$631$	5295.63	0.334098	0.167049	−	0.985949i	$-0.446576\pi$
$631$	5295.63	0.334098	0.167049	+	0.985949i	$0.446576\pi$
$632$	3650.58	0.229766
$633$	17969.6	1.12832
$634$	3367.40	0.210941
$635$	17381.0	1.08621
$636$	−2131.88	−0.132916
$637$	−3052.64	−0.189875
$638$	−15145.5	−0.939834
$639$	3062.35	0.189585
$640$	−36162.2	−2.23349
$641$	−5076.56	−0.312811	−0.156406	−	0.987693i	$-0.549991\pi$
$641$	−5076.56	−0.312811	−0.156406	+	0.987693i	$0.549991\pi$
$642$	−19816.3	−1.21820
$643$	−7101.58	−0.435550	−0.217775	−	0.975999i	$-0.569880\pi$
$643$	−7101.58	−0.435550	−0.217775	+	0.975999i	$0.569880\pi$
$644$	221.056	0.0135261
$645$	−16166.9	−0.986931
$646$	−1356.43	−0.0826132
$647$	−6858.76	−0.416763	−0.208382	−	0.978048i	$-0.566820\pi$
$647$	−6858.76	−0.416763	−0.208382	+	0.978048i	$0.566820\pi$
$648$	−17255.5	−1.04608
$649$	−44916.1	−2.71666
$650$	61862.4	3.73299
$651$	−3457.32	−0.208146
$652$	77.2970	0.00464292
$653$	20913.4	1.25330	0.626648	−	0.779302i	$-0.284426\pi$
$653$	20913.4	1.25330	0.626648	+	0.779302i	$0.284426\pi$
$654$	38703.9	2.31413
$655$	44238.4	2.63899
$656$	−26423.4	−1.57265
$657$	−821.637	−0.0487901
$658$	−4086.47	−0.242108
$659$	−980.066	−0.0579331	−0.0289666	−	0.999580i	$-0.509222\pi$
$659$	−980.066	−0.0579331	−0.0289666	+	0.999580i	$0.509222\pi$
$660$	9466.26	0.558293
$661$	−4993.21	−0.293817	−0.146909	−	0.989150i	$-0.546932\pi$
$661$	−4993.21	−0.293817	−0.146909	+	0.989150i	$0.546932\pi$
$662$	−30983.9	−1.81907
$663$	3118.82	0.182692
$664$	−21591.2	−1.26190
$665$	−7510.12	−0.437940
$666$	−5376.08	−0.312791
$667$	2000.64	0.116140
$668$	−4650.31	−0.269350
$669$	20112.9	1.16234
$670$	7035.90	0.405702
$671$	−44195.2	−2.54268
$672$	2461.38	0.141295
$673$	27668.7	1.58477	0.792386	−	0.610020i	$-0.208839\pi$
$673$	27668.7	1.58477	0.792386	+	0.610020i	$0.208839\pi$
$674$	−1689.02	−0.0965262
$675$	−39498.9	−2.25232
$676$	2312.36	0.131564
$677$	−14247.5	−0.808824	−0.404412	−	0.914577i	$-0.632524\pi$
$677$	−14247.5	−0.808824	−0.404412	+	0.914577i	$0.632524\pi$
$678$	−19105.2	−1.08220
$679$	1282.25	0.0724715
$680$	−3764.83	−0.212316
$681$	17719.2	0.997064
$682$	15037.3	0.844296
$683$	15657.6	0.877193	0.438597	−	0.898684i	$-0.355476\pi$
$683$	15657.6	0.877193	0.438597	+	0.898684i	$0.355476\pi$
$684$	−396.489	−0.0221639
$685$	−22195.8	−1.23804
$686$	−1050.11	−0.0584450
$687$	−5326.91	−0.295829
$688$	9748.49	0.540200
$689$	16914.4	0.935250
$690$	−8536.27	−0.470971
$691$	12906.9	0.710565	0.355282	−	0.934759i	$-0.384385\pi$
$691$	12906.9	0.710565	0.355282	+	0.934759i	$0.384385\pi$
$692$	−2524.20	−0.138664
$693$	2271.41	0.124507
$694$	20611.4	1.12737
$695$	−40122.8	−2.18985
$696$	10092.7	0.549659
$697$	−3164.30	−0.171960
$698$	−17194.7	−0.932419
$699$	−22213.5	−1.20199
$700$	3117.32	0.168320
$701$	9069.94	0.488683	0.244342	−	0.969689i	$-0.421428\pi$
$701$	9069.94	0.488683	0.244342	+	0.969689i	$0.421428\pi$
$702$	−23227.2	−1.24880
$703$	−15577.2	−0.835711
$704$	22552.9	1.20738
$705$	23115.9	1.23489
$706$	3626.71	0.193333
$707$	−1626.93	−0.0865443
$708$	−6201.37	−0.329183
$709$	19970.6	1.05785	0.528923	−	0.848670i	$-0.322596\pi$
$709$	19970.6	1.05785	0.528923	+	0.848670i	$0.322596\pi$
$710$	−34832.9	−1.84120
$711$	1026.60	0.0541499
$712$	−3146.37	−0.165611
$713$	−1986.36	−0.104334
$714$	1072.87	0.0562342
$715$	−75105.4	−3.92837
$716$	1363.23	0.0711541
$717$	16291.3	0.848550
$718$	−27196.3	−1.41359
$719$	−11009.5	−0.571049	−0.285524	−	0.958371i	$-0.592168\pi$
$719$	−11009.5	−0.571049	−0.285524	+	0.958371i	$0.592168\pi$
$720$	−8840.91	−0.457613
$721$	6307.50	0.325803
$722$	13156.5	0.678166
$723$	−15874.6	−0.816575
$724$	294.420	0.0151133
$725$	28213.0	1.44525
$726$	−33326.9	−1.70369
$727$	30078.9	1.53448	0.767239	−	0.641362i	$-0.221630\pi$
$727$	30078.9	1.53448	0.767239	+	0.641362i	$0.221630\pi$
$728$	−8847.76	−0.450439
$729$	13951.5	0.708812
$730$	9345.75	0.473838
$731$	1167.42	0.0590676
$732$	−6101.85	−0.308102
$733$	−5414.09	−0.272816	−0.136408	−	0.990653i	$-0.543556\pi$
$733$	−5414.09	−0.272816	−0.136408	+	0.990653i	$0.543556\pi$
$734$	11315.1	0.569001
$735$	5940.14	0.298103
$736$	1414.16	0.0708243
$737$	−6165.82	−0.308170
$738$	−6314.12	−0.314940
$739$	10013.7	0.498456	0.249228	−	0.968445i	$-0.419823\pi$
$739$	10013.7	0.498456	0.249228	+	0.968445i	$0.419823\pi$
$740$	8957.71	0.444989
$741$	18032.2	0.893968
$742$	5818.55	0.287878
$743$	−25510.3	−1.25960	−0.629799	−	0.776758i	$-0.716863\pi$
$743$	−25510.3	−1.25960	−0.629799	+	0.776758i	$0.716863\pi$
$744$	−10020.7	−0.493784
$745$	−52394.7	−2.57663
$746$	−21588.1	−1.05951
$747$	−6071.78	−0.297396
$748$	−683.561	−0.0334137
$749$	7922.63	0.386498
$750$	−73985.4	−3.60209
$751$	39363.4	1.91264	0.956319	−	0.292324i	$-0.0944286\pi$
$751$	39363.4	1.91264	0.956319	+	0.292324i	$0.0944286\pi$
$752$	−13938.7	−0.675920
$753$	23234.5	1.12445
$754$	16590.6	0.801316
$755$	13132.1	0.633015
$756$	−1170.45	−0.0563079
$757$	−28780.6	−1.38183	−0.690917	−	0.722934i	$-0.742793\pi$
$757$	−28780.6	−1.38183	−0.690917	+	0.722934i	$0.742793\pi$
$758$	37575.0	1.80051
$759$	7480.65	0.357748
$760$	−21767.3	−1.03892
$761$	−29195.9	−1.39074	−0.695369	−	0.718653i	$-0.744759\pi$
$761$	−29195.9	−1.39074	−0.695369	+	0.718653i	$0.744759\pi$
$762$	−14356.1	−0.682501
$763$	−15474.0	−0.734202
$764$	1265.83	0.0599423
$765$	−1058.73	−0.0500372
$766$	−7077.88	−0.333857
$767$	49201.8	2.31626
$768$	11725.9	0.550941
$769$	31566.9	1.48028	0.740139	−	0.672454i	$-0.234760\pi$
$769$	31566.9	1.48028	0.740139	+	0.672454i	$0.234760\pi$
$770$	−25836.2	−1.20919
$771$	−7105.04	−0.331883
$772$	−3655.28	−0.170410
$773$	20763.4	0.966114	0.483057	−	0.875589i	$-0.339526\pi$
$773$	20763.4	0.966114	0.483057	+	0.875589i	$0.339526\pi$
$774$	2329.49	0.108181
$775$	−28011.6	−1.29833
$776$	3716.46	0.171924
$777$	12320.8	0.568863
$778$	42199.3	1.94462
$779$	−18295.2	−0.841453
$780$	−10369.5	−0.476009
$781$	30525.4	1.39857
$782$	616.406	0.0281875
$783$	−10593.0	−0.483478
$784$	−3581.85	−0.163167
$785$	−69910.9	−3.17863
$786$	−36539.2	−1.65816
$787$	−17154.2	−0.776976	−0.388488	−	0.921454i	$-0.627002\pi$
$787$	−17154.2	−0.776976	−0.388488	+	0.921454i	$0.627002\pi$
$788$	−6003.14	−0.271387
$789$	−21322.6	−0.962111
$790$	−11677.1	−0.525891
$791$	7638.36	0.343349
$792$	6583.43	0.295369
$793$	48412.1	2.16793
$794$	37354.8	1.66961
$795$	−32913.7	−1.46834
$796$	−99.6112	−0.00443546
$797$	−16711.1	−0.742705	−0.371353	−	0.928492i	$-0.621106\pi$
$797$	−16711.1	−0.742705	−0.371353	+	0.928492i	$0.621106\pi$
$798$	6203.08	0.275171
$799$	−1669.21	−0.0739078
$800$	19942.4	0.881340
$801$	−884.810	−0.0390303
$802$	77.6313	0.00341803
$803$	−8190.03	−0.359925
$804$	−851.289	−0.0373416
$805$	3412.84	0.149425
$806$	−16472.1	−0.719859
$807$	40606.6	1.77128
$808$	−4715.47	−0.205309
$809$	3984.12	0.173145	0.0865725	−	0.996246i	$-0.472409\pi$
$809$	3984.12	0.173145	0.0865725	+	0.996246i	$0.472409\pi$
$810$	55195.3	2.39428
$811$	−25313.9	−1.09604	−0.548022	−	0.836464i	$-0.684619\pi$
$811$	−25313.9	−1.09604	−0.548022	+	0.836464i	$0.684619\pi$
$812$	836.019	0.0361312
$813$	−23233.0	−1.00224
$814$	−53588.4	−2.30746
$815$	1193.37	0.0512908
$816$	3659.50	0.156995
$817$	6749.70	0.289036
$818$	−35722.9	−1.52692
$819$	−2488.13	−0.106157
$820$	10520.7	0.448047
$821$	5818.48	0.247340	0.123670	−	0.992323i	$-0.460534\pi$
$821$	5818.48	0.247340	0.123670	+	0.992323i	$0.460534\pi$
$822$	18332.9	0.777901
$823$	−23291.9	−0.986519	−0.493260	−	0.869882i	$-0.664195\pi$
$823$	−23291.9	−0.986519	−0.493260	+	0.869882i	$0.664195\pi$
$824$	18281.6	0.772902
$825$	105492.	4.45183
$826$	16925.4	0.712965
$827$	−31308.3	−1.31644	−0.658219	−	0.752826i	$-0.728690\pi$
$827$	−31308.3	−1.31644	−0.658219	+	0.752826i	$0.728690\pi$
$828$	180.177	0.00756231
$829$	35657.8	1.49390	0.746952	−	0.664878i	$-0.231517\pi$
$829$	35657.8	1.49390	0.746952	+	0.664878i	$0.231517\pi$
$830$	69063.7	2.88824
$831$	31540.8	1.31665
$832$	−24704.7	−1.02943
$833$	−428.939	−0.0178414
$834$	33139.9	1.37595
$835$	−71795.2	−2.97554
$836$	−3952.18	−0.163503
$837$	10517.4	0.434330
$838$	−4496.35	−0.185351
$839$	34137.4	1.40471	0.702356	−	0.711826i	$-0.252131\pi$
$839$	34137.4	1.40471	0.702356	+	0.711826i	$0.252131\pi$
$840$	17216.9	0.707189
$841$	−16822.7	−0.689766
$842$	−37418.7	−1.53151
$843$	36505.5	1.49148
$844$	4314.25	0.175951
$845$	35700.1	1.45340
$846$	−3330.78	−0.135360
$847$	13324.2	0.540527
$848$	19846.7	0.803700
$849$	−45487.7	−1.83879
$850$	8692.54	0.350767
$851$	7078.78	0.285144
$852$	4214.51	0.169468
$853$	24323.4	0.976338	0.488169	−	0.872749i	$-0.337665\pi$
$853$	24323.4	0.976338	0.488169	+	0.872749i	$0.337665\pi$
$854$	16653.8	0.667307
$855$	−6121.31	−0.244847
$856$	22962.9	0.916888
$857$	−21362.8	−0.851504	−0.425752	−	0.904840i	$-0.639990\pi$
$857$	−21362.8	−0.851504	−0.425752	+	0.904840i	$0.639990\pi$
$858$	62034.2	2.46831
$859$	10647.2	0.422909	0.211455	−	0.977388i	$-0.432180\pi$
$859$	10647.2	0.422909	0.211455	+	0.977388i	$0.432180\pi$
$860$	−3881.44	−0.153902
$861$	14470.6	0.572771
$862$	9498.67	0.375320
$863$	−5325.96	−0.210079	−0.105039	−	0.994468i	$-0.533497\pi$
$863$	−5325.96	−0.210079	−0.105039	+	0.994468i	$0.533497\pi$
$864$	−7487.70	−0.294834
$865$	−38970.7	−1.53184
$866$	5338.04	0.209462
$867$	−27658.6	−1.08343
$868$	−830.051	−0.0324583
$869$	10233.1	0.399464
$870$	−32283.6	−1.25806
$871$	6754.13	0.262750
$872$	−44849.7	−1.74175
$873$	1045.13	0.0405180
$874$	3563.91	0.137930
$875$	29579.7	1.14283
$876$	−1130.76	−0.0436129
$877$	11646.0	0.448412	0.224206	−	0.974542i	$-0.428021\pi$
$877$	11646.0	0.448412	0.224206	+	0.974542i	$0.428021\pi$
$878$	−34859.2	−1.33991
$879$	16729.0	0.641928
$880$	−88125.7	−3.37581
$881$	−13691.1	−0.523568	−0.261784	−	0.965126i	$-0.584311\pi$
$881$	−13691.1	−0.523568	−0.261784	+	0.965126i	$0.584311\pi$
$882$	−855.916	−0.0326760
$883$	30201.4	1.15103	0.575515	−	0.817791i	$-0.304802\pi$
$883$	30201.4	1.15103	0.575515	+	0.817791i	$0.304802\pi$
$884$	748.783	0.0284890
$885$	−95741.7	−3.63652
$886$	8857.83	0.335874
$887$	−3125.48	−0.118313	−0.0591564	−	0.998249i	$-0.518841\pi$
$887$	−3125.48	−0.118313	−0.0591564	+	0.998249i	$0.518841\pi$
$888$	35710.5	1.34951
$889$	5739.62	0.216536
$890$	10064.3	0.379053
$891$	−48369.7	−1.81868
$892$	4828.81	0.181256
$893$	−9650.94	−0.361653
$894$	43276.0	1.61898
$895$	21046.7	0.786047
$896$	−11941.6	−0.445246
$897$	−8194.42	−0.305021
$898$	42838.1	1.59190
$899$	−7512.28	−0.278697
$900$	2540.85	0.0941057
$901$	2376.71	0.0878798
$902$	−62938.8	−2.32332
$903$	−5338.69	−0.196745
$904$	22139.0	0.814526
$905$	4545.49	0.166958
$906$	−10846.6	−0.397743
$907$	−11972.1	−0.438286	−0.219143	−	0.975693i	$-0.570326\pi$
$907$	−11972.1	−0.438286	−0.219143	+	0.975693i	$0.570326\pi$
$908$	4254.12	0.155482
$909$	−1326.07	−0.0483859
$910$	28301.4	1.03097
$911$	12197.1	0.443588	0.221794	−	0.975094i	$-0.428809\pi$
$911$	12197.1	0.443588	0.221794	+	0.975094i	$0.428809\pi$
$912$	21158.3	0.768225
$913$	−60523.1	−2.19389
$914$	−44012.4	−1.59278
$915$	−94205.2	−3.40364
$916$	−1278.91	−0.0461315
$917$	14608.5	0.526082
$918$	−3263.75	−0.117342
$919$	4088.46	0.146753	0.0733764	−	0.997304i	$-0.476623\pi$
$919$	4088.46	0.146753	0.0733764	+	0.997304i	$0.476623\pi$
$920$	9891.76	0.354480
$921$	−42853.3	−1.53319
$922$	−30847.5	−1.10185
$923$	−33438.0	−1.19244
$924$	3125.98	0.111296
$925$	99824.6	3.54834
$926$	−14080.7	−0.499697
$927$	5141.09	0.182153
$928$	5348.26	0.189187
$929$	−15266.0	−0.539139	−0.269569	−	0.962981i	$-0.586881\pi$
$929$	−15266.0	−0.539139	−0.269569	+	0.962981i	$0.586881\pi$
$930$	32053.2	1.13018
$931$	−2480.02	−0.0873032
$932$	−5333.13	−0.187438
$933$	37425.5	1.31324
$934$	−46091.1	−1.61472
$935$	−10553.4	−0.369125
$936$	−7211.59	−0.251836
$937$	24862.2	0.866824	0.433412	−	0.901196i	$-0.357309\pi$
$937$	24862.2	0.866824	0.433412	+	0.901196i	$0.357309\pi$
$938$	2323.42	0.0808767
$939$	−9383.16	−0.326100
$940$	5549.80	0.192569
$941$	37095.1	1.28509	0.642543	−	0.766250i	$-0.277879\pi$
$941$	37095.1	1.28509	0.642543	+	0.766250i	$0.277879\pi$
$942$	57743.8	1.99723
$943$	8313.91	0.287103
$944$	57731.4	1.99046
$945$	−18070.3	−0.622039
$946$	23220.2	0.798050
$947$	3646.99	0.125144	0.0625720	−	0.998040i	$-0.480070\pi$
$947$	3646.99	0.125144	0.0625720	+	0.998040i	$0.480070\pi$
$948$	1412.84	0.0484040
$949$	8971.48	0.306877
$950$	50258.1	1.71641
$951$	−6290.21	−0.214484
$952$	−1243.23	−0.0423251
$953$	−3581.74	−0.121746	−0.0608731	−	0.998146i	$-0.519388\pi$
$953$	−3581.74	−0.121746	−0.0608731	+	0.998146i	$0.519388\pi$
$954$	4742.55	0.160949
$955$	19542.8	0.662189
$956$	3911.31	0.132323
$957$	28291.3	0.955620
$958$	−30882.0	−1.04150
$959$	−7329.59	−0.246804
$960$	48073.0	1.61620
$961$	−22332.3	−0.749634
$962$	58701.6	1.96738
$963$	6457.54	0.216086
$964$	−3811.27	−0.127337
$965$	−56433.1	−1.88253
$966$	−2818.88	−0.0938881
$967$	32887.3	1.09368	0.546838	−	0.837238i	$-0.315831\pi$
$967$	32887.3	1.09368	0.546838	+	0.837238i	$0.315831\pi$
$968$	38618.9	1.28229
$969$	2533.78	0.0840008
$970$	−11887.9	−0.393501
$971$	45749.8	1.51203	0.756016	−	0.654554i	$-0.227143\pi$
$971$	45749.8	1.51203	0.756016	+	0.654554i	$0.227143\pi$
$972$	−2163.62	−0.0713971
$973$	−13249.5	−0.436546
$974$	−46998.5	−1.54613
$975$	−115557.	−3.79569
$976$	56804.9	1.86299
$977$	2323.42	0.0760827	0.0380413	−	0.999276i	$-0.487888\pi$
$977$	2323.42	0.0760827	0.0380413	+	0.999276i	$0.487888\pi$
$978$	−985.681	−0.0322276
$979$	−8819.74	−0.287927
$980$	1426.14	0.0464861
$981$	−12612.5	−0.410484
$982$	5160.13	0.167685
$983$	−32361.0	−1.05001	−0.525003	−	0.851100i	$-0.675936\pi$
$983$	−32361.0	−1.05001	−0.525003	+	0.851100i	$0.675936\pi$
$984$	41941.5	1.35879
$985$	−92681.3	−2.99804
$986$	2331.21	0.0752949
$987$	7633.42	0.246175
$988$	4329.27	0.139405
$989$	−3067.28	−0.0986187
$990$	−21058.5	−0.676042
$991$	−6747.66	−0.216293	−0.108147	−	0.994135i	$-0.534492\pi$
$991$	−6747.66	−0.216293	−0.108147	+	0.994135i	$0.534492\pi$
$992$	−5310.08	−0.169955
$993$	57877.0	1.84962
$994$	−11502.6	−0.367044
$995$	−1537.88	−0.0489990
$996$	−8356.17	−0.265839
$997$	−26396.0	−0.838485	−0.419242	−	0.907874i	$-0.637704\pi$
$997$	−26396.0	−0.838485	−0.419242	+	0.907874i	$0.637704\pi$
$998$	−55.5211	−0.00176101
$999$	−37480.7	−1.18702

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.4.a.d.1.4	✓	12
3.2	odd	2		1449.4.a.o.1.9		12
7.6	odd	2		1127.4.a.h.1.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.4.a.d.1.4	✓	12	1.1	even	1	trivial
1127.4.a.h.1.4		12	7.6	odd	2
1449.4.a.o.1.9		12	3.2	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:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	161.a (trivial)

\(f(q)\)	\(=\)	\(q-3.06154 q^{2} +5.71887 q^{3} +1.37302 q^{4} +21.1978 q^{5} -17.5086 q^{6} +7.00000 q^{7} +20.2888 q^{8} +5.70552 q^{9} -64.8978 q^{10} +56.8723 q^{11} +7.85212 q^{12} -62.2988 q^{13} -21.4308 q^{14} +121.227 q^{15} -73.0990 q^{16} -8.75386 q^{17} -17.4677 q^{18} -50.6126 q^{19} +29.1049 q^{20} +40.0321 q^{21} -174.117 q^{22} +23.0000 q^{23} +116.029 q^{24} +324.345 q^{25} +190.730 q^{26} -121.780 q^{27} +9.61113 q^{28} +86.9844 q^{29} -371.142 q^{30} -86.3635 q^{31} +61.4852 q^{32} +325.246 q^{33} +26.8003 q^{34} +148.384 q^{35} +7.83379 q^{36} +307.773 q^{37} +154.952 q^{38} -356.279 q^{39} +430.076 q^{40} +361.474 q^{41} -122.560 q^{42} -133.360 q^{43} +78.0868 q^{44} +120.944 q^{45} -70.4154 q^{46} +190.683 q^{47} -418.044 q^{48} +49.0000 q^{49} -992.995 q^{50} -50.0622 q^{51} -85.5375 q^{52} -271.504 q^{53} +372.835 q^{54} +1205.57 q^{55} +142.021 q^{56} -289.447 q^{57} -266.306 q^{58} -789.770 q^{59} +166.447 q^{60} -777.096 q^{61} +264.405 q^{62} +39.9387 q^{63} +396.552 q^{64} -1320.60 q^{65} -995.752 q^{66} -108.415 q^{67} -12.0192 q^{68} +131.534 q^{69} -454.284 q^{70} +536.735 q^{71} +115.758 q^{72} -144.007 q^{73} -942.258 q^{74} +1854.89 q^{75} -69.4921 q^{76} +398.106 q^{77} +1090.76 q^{78} +179.931 q^{79} -1549.53 q^{80} -850.496 q^{81} -1106.67 q^{82} -1064.19 q^{83} +54.9649 q^{84} -185.562 q^{85} +408.287 q^{86} +497.453 q^{87} +1153.87 q^{88} -155.080 q^{89} -370.276 q^{90} -436.092 q^{91} +31.5794 q^{92} -493.902 q^{93} -583.782 q^{94} -1072.87 q^{95} +351.626 q^{96} +183.178 q^{97} -150.015 q^{98} +324.487 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + q^{3} + 72 q^{4} + 16 q^{5} - 15 q^{6} + 84 q^{7} - 21 q^{8} + 203 q^{9} + 106 q^{10} + 50 q^{11} - 139 q^{12} + 21 q^{13} + 28 q^{14} + 192 q^{15} + 516 q^{16} + 26 q^{17} + 251 q^{18}+ \cdots + 2400 q^{99}+O(q^{100}) \) 12 * q + 4 * q^2 + q^3 + 72 * q^4 + 16 * q^5 - 15 * q^6 + 84 * q^7 - 21 * q^8 + 203 * q^9 + 106 * q^10 + 50 * q^11 - 139 * q^12 + 21 * q^13 + 28 * q^14 + 192 * q^15 + 516 * q^16 + 26 * q^17 + 251 * q^18 + 292 * q^19 - 12 * q^20 + 7 * q^21 + 206 * q^22 + 276 * q^23 + 42 * q^24 + 408 * q^25 + 409 * q^26 - 335 * q^27 + 504 * q^28 + 129 * q^29 + 168 * q^30 + 375 * q^31 - 54 * q^32 + 428 * q^33 + 674 * q^34 + 112 * q^35 + 2271 * q^36 + 958 * q^37 - 120 * q^38 + 89 * q^39 + 1424 * q^40 - 347 * q^41 - 105 * q^42 + 392 * q^43 - 1158 * q^44 - 1338 * q^45 + 92 * q^46 + 559 * q^47 - 4767 * q^48 + 588 * q^49 - 888 * q^50 + 204 * q^51 - 1765 * q^52 + 42 * q^53 - 1965 * q^54 + 78 * q^55 - 147 * q^56 + 156 * q^57 - 3695 * q^58 - 620 * q^59 - 1574 * q^60 - 1258 * q^61 + 489 * q^62 + 1421 * q^63 + 4335 * q^64 - 752 * q^65 - 7334 * q^66 + 2024 * q^67 - 5162 * q^68 + 23 * q^69 + 742 * q^70 + 1371 * q^71 - 2483 * q^72 - 1241 * q^73 - 4006 * q^74 + 1357 * q^75 + 4214 * q^76 + 350 * q^77 - 4787 * q^78 + 2660 * q^79 - 5734 * q^80 + 2400 * q^81 - 3551 * q^82 - 1476 * q^83 - 973 * q^84 + 408 * q^85 - 988 * q^86 + 1263 * q^87 + 3324 * q^88 + 1670 * q^89 + 1050 * q^90 + 147 * q^91 + 1656 * q^92 + 135 * q^93 - 3539 * q^94 + 2428 * q^95 - 3973 * q^96 + 1174 * q^97 + 196 * q^98 + 2400 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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