LMFDB - Embedded newform 115.4.a.f.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,4,Mod(1,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, 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("115.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	115.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:	$6.78521965066$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 49x^{6} + 31x^{5} + 750x^{4} + 249x^{3} - 2892x^{2} - 620x + 2400 $ x^8 - 2x^7 - 49x^6 + 31x^5 + 750x^4 + 249x^3 - 2892x^2 - 620*x + 2400
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-3.05234$ of defining polynomial
Character	$\chi$	$=$	115.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.05234 q^{2} -8.94300 q^{3} +8.42146 q^{4} +5.00000 q^{5} -36.2401 q^{6} +32.7645 q^{7} +1.70790 q^{8} +52.9772 q^{9} +20.2617 q^{10} +45.7496 q^{11} -75.3131 q^{12} +45.5638 q^{13} +132.773 q^{14} -44.7150 q^{15} -60.4507 q^{16} -76.5649 q^{17} +214.681 q^{18} -32.0225 q^{19} +42.1073 q^{20} -293.013 q^{21} +185.393 q^{22} +23.0000 q^{23} -15.2738 q^{24} +25.0000 q^{25} +184.640 q^{26} -232.314 q^{27} +275.925 q^{28} +287.046 q^{29} -181.200 q^{30} -161.587 q^{31} -258.630 q^{32} -409.139 q^{33} -310.267 q^{34} +163.823 q^{35} +446.145 q^{36} +7.53926 q^{37} -129.766 q^{38} -407.476 q^{39} +8.53952 q^{40} +216.246 q^{41} -1187.39 q^{42} -469.729 q^{43} +385.279 q^{44} +264.886 q^{45} +93.2038 q^{46} -210.315 q^{47} +540.610 q^{48} +730.514 q^{49} +101.309 q^{50} +684.719 q^{51} +383.713 q^{52} +58.7860 q^{53} -941.414 q^{54} +228.748 q^{55} +55.9587 q^{56} +286.377 q^{57} +1163.21 q^{58} -376.609 q^{59} -376.565 q^{60} -52.7319 q^{61} -654.805 q^{62} +1735.77 q^{63} -564.451 q^{64} +227.819 q^{65} -1657.97 q^{66} -16.7678 q^{67} -644.788 q^{68} -205.689 q^{69} +663.865 q^{70} -209.441 q^{71} +90.4800 q^{72} -811.910 q^{73} +30.5516 q^{74} -223.575 q^{75} -269.676 q^{76} +1498.96 q^{77} -1651.23 q^{78} +63.0408 q^{79} -302.253 q^{80} +647.197 q^{81} +876.300 q^{82} -1062.27 q^{83} -2467.60 q^{84} -382.824 q^{85} -1903.50 q^{86} -2567.05 q^{87} +78.1360 q^{88} +436.069 q^{89} +1073.41 q^{90} +1492.87 q^{91} +193.694 q^{92} +1445.07 q^{93} -852.269 q^{94} -160.112 q^{95} +2312.93 q^{96} +655.840 q^{97} +2960.29 q^{98} +2423.68 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{2} + 42 q^{4} + 40 q^{5} + 11 q^{7} + 3 q^{8} + 158 q^{9} + 30 q^{10} + 41 q^{11} + 48 q^{12} + 28 q^{13} + 161 q^{14} + 98 q^{16} + 71 q^{17} + 84 q^{18} + 177 q^{19} + 210 q^{20} + 292 q^{21}+ \cdots + 1319 q^{99}+O(q^{100}) $ 8 * q + 6 * q^2 + 42 * q^4 + 40 * q^5 + 11 * q^7 + 3 * q^8 + 158 * q^9 + 30 * q^10 + 41 * q^11 + 48 * q^12 + 28 * q^13 + 161 * q^14 + 98 * q^16 + 71 * q^17 + 84 * q^18 + 177 * q^19 + 210 * q^20 + 292 * q^21 + 171 * q^22 + 184 * q^23 + 177 * q^24 + 200 * q^25 + 396 * q^26 - 495 * q^27 + 179 * q^28 + 225 * q^29 - 36 * q^31 - 360 * q^32 - 53 * q^33 - 1051 * q^34 + 55 * q^35 - 396 * q^36 - 348 * q^37 - 309 * q^38 - 1077 * q^39 + 15 * q^40 + 620 * q^41 - 2288 * q^42 - 390 * q^43 - 141 * q^44 + 790 * q^45 + 138 * q^46 + 123 * q^47 - 1304 * q^48 + 881 * q^49 + 150 * q^50 + 957 * q^51 - 1890 * q^52 + 1406 * q^53 - 2949 * q^54 + 205 * q^55 + 1031 * q^56 - 1142 * q^57 - 129 * q^58 - 676 * q^59 + 240 * q^60 + 1447 * q^61 - 1556 * q^62 - 58 * q^63 - 2883 * q^64 + 140 * q^65 - 119 * q^66 - 1582 * q^67 + 953 * q^68 + 805 * q^70 + 1396 * q^71 - 1728 * q^72 + 17 * q^73 - 964 * q^74 + 2271 * q^76 + 488 * q^77 - 1919 * q^78 + 708 * q^79 + 490 * q^80 + 4316 * q^81 - 3332 * q^82 + 1486 * q^83 - 3970 * q^84 + 355 * q^85 + 3570 * q^86 - 803 * q^87 - 1031 * q^88 + 1360 * q^89 + 420 * q^90 + 2693 * q^91 + 966 * q^92 + 3833 * q^93 - 3207 * q^94 + 885 * q^95 + 4956 * q^96 - 855 * q^97 + 1817 * q^98 + 1319 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	4.05234	1.43272	0.716359	−	0.697732i	$-0.245807\pi$
$2$	4.05234	1.43272	0.716359	+	0.697732i	$0.245807\pi$
$3$	−8.94300	−1.72108	−0.860540	−	0.509383i	$-0.829874\pi$
$3$	−8.94300	−1.72108	−0.860540	+	0.509383i	$0.829874\pi$
$4$	8.42146	1.05268
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−36.2401	−2.46582
$7$	32.7645	1.76912	0.884559	−	0.466429i	$-0.154460\pi$
$7$	32.7645	1.76912	0.884559	+	0.466429i	$0.154460\pi$
$8$	1.70790	0.0754794
$9$	52.9772	1.96212
$10$	20.2617	0.640731
$11$	45.7496	1.25400	0.627001	−	0.779018i	$-0.284282\pi$
$11$	45.7496	1.25400	0.627001	+	0.779018i	$0.284282\pi$
$12$	−75.3131	−1.81175
$13$	45.5638	0.972086	0.486043	−	0.873935i	$-0.338440\pi$
$13$	45.5638	0.972086	0.486043	+	0.873935i	$0.338440\pi$
$14$	132.773	2.53465
$15$	−44.7150	−0.769690
$16$	−60.4507	−0.944542
$17$	−76.5649	−1.09234	−0.546168	−	0.837676i	$-0.683914\pi$
$17$	−76.5649	−1.09234	−0.546168	+	0.837676i	$0.683914\pi$
$18$	214.681	2.81116
$19$	−32.0225	−0.386656	−0.193328	−	0.981134i	$-0.561928\pi$
$19$	−32.0225	−0.386656	−0.193328	+	0.981134i	$0.561928\pi$
$20$	42.1073	0.470774
$21$	−293.013	−3.04479
$22$	185.393	1.79663
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−15.2738	−0.129906
$25$	25.0000	0.200000
$26$	184.640	1.39273
$27$	−232.314	−1.65588
$28$	275.925	1.86232
$29$	287.046	1.83804	0.919019	−	0.394213i	$-0.128983\pi$
$29$	287.046	1.83804	0.919019	+	0.394213i	$0.128983\pi$
$30$	−181.200	−1.10275
$31$	−161.587	−0.936189	−0.468095	−	0.883678i	$-0.655059\pi$
$31$	−161.587	−0.936189	−0.468095	+	0.883678i	$0.655059\pi$
$32$	−258.630	−1.42874
$33$	−409.139	−2.15824
$34$	−310.267	−1.56501
$35$	163.823	0.791173
$36$	446.145	2.06549
$37$	7.53926	0.0334986	0.0167493	−	0.999860i	$-0.494668\pi$
$37$	7.53926	0.0334986	0.0167493	+	0.999860i	$0.494668\pi$
$38$	−129.766	−0.553969
$39$	−407.476	−1.67304
$40$	8.53952	0.0337554
$41$	216.246	0.823704	0.411852	−	0.911251i	$-0.364882\pi$
$41$	216.246	0.823704	0.411852	+	0.911251i	$0.364882\pi$
$42$	−1187.39	−4.36233
$43$	−469.729	−1.66589	−0.832943	−	0.553359i	$-0.813346\pi$
$43$	−469.729	−1.66589	−0.832943	+	0.553359i	$0.813346\pi$
$44$	385.279	1.32007
$45$	264.886	0.877485
$46$	93.2038	0.298742
$47$	−210.315	−0.652715	−0.326358	−	0.945246i	$-0.605821\pi$
$47$	−210.315	−0.652715	−0.326358	+	0.945246i	$0.605821\pi$
$48$	540.610	1.62563
$49$	730.514	2.12978
$50$	101.309	0.286544
$51$	684.719	1.88000
$52$	383.713	1.02330
$53$	58.7860	0.152356	0.0761781	−	0.997094i	$-0.475728\pi$
$53$	58.7860	0.152356	0.0761781	+	0.997094i	$0.475728\pi$
$54$	−941.414	−2.37241
$55$	228.748	0.560807
$56$	55.9587	0.133532
$57$	286.377	0.665466
$58$	1163.21	2.63339
$59$	−376.609	−0.831022	−0.415511	−	0.909588i	$-0.636397\pi$
$59$	−376.609	−0.831022	−0.415511	+	0.909588i	$0.636397\pi$
$60$	−376.565	−0.810240
$61$	−52.7319	−0.110682	−0.0553412	−	0.998467i	$-0.517625\pi$
$61$	−52.7319	−0.110682	−0.0553412	+	0.998467i	$0.517625\pi$
$62$	−654.805	−1.34130
$63$	1735.77	3.47122
$64$	−564.451	−1.10244
$65$	227.819	0.434730
$66$	−1657.97	−3.09215
$67$	−16.7678	−0.0305748	−0.0152874	−	0.999883i	$-0.504866\pi$
$67$	−16.7678	−0.0305748	−0.0152874	+	0.999883i	$0.504866\pi$
$68$	−644.788	−1.14988
$69$	−205.689	−0.358870
$70$	663.865	1.13353
$71$	−209.441	−0.350086	−0.175043	−	0.984561i	$-0.556006\pi$
$71$	−209.441	−0.350086	−0.175043	+	0.984561i	$0.556006\pi$
$72$	90.4800	0.148100
$73$	−811.910	−1.30174	−0.650869	−	0.759190i	$-0.725595\pi$
$73$	−811.910	−1.30174	−0.650869	+	0.759190i	$0.725595\pi$
$74$	30.5516	0.0479940
$75$	−223.575	−0.344216
$76$	−269.676	−0.407026
$77$	1498.96	2.21848
$78$	−1651.23	−2.39699
$79$	63.0408	0.0897803	0.0448902	−	0.998992i	$-0.485706\pi$
$79$	63.0408	0.0897803	0.0448902	+	0.998992i	$0.485706\pi$
$80$	−302.253	−0.422412
$81$	647.197	0.887787
$82$	876.300	1.18014
$83$	−1062.27	−1.40481	−0.702404	−	0.711779i	$-0.747890\pi$
$83$	−1062.27	−1.40481	−0.702404	+	0.711779i	$0.747890\pi$
$84$	−2467.60	−3.20520
$85$	−382.824	−0.488508
$86$	−1903.50	−2.38674
$87$	−2567.05	−3.16341
$88$	78.1360	0.0946514
$89$	436.069	0.519362	0.259681	−	0.965694i	$-0.416383\pi$
$89$	436.069	0.519362	0.259681	+	0.965694i	$0.416383\pi$
$90$	1073.41	1.25719
$91$	1492.87	1.71973
$92$	193.694	0.219500
$93$	1445.07	1.61126
$94$	−852.269	−0.935158
$95$	−160.112	−0.172918
$96$	2312.93	2.45898
$97$	655.840	0.686499	0.343250	−	0.939244i	$-0.388472\pi$
$97$	655.840	0.686499	0.343250	+	0.939244i	$0.388472\pi$
$98$	2960.29	3.05137
$99$	2423.68	2.46050
$100$	210.537	0.210537
$101$	831.308	0.818993	0.409496	−	0.912312i	$-0.365704\pi$
$101$	831.308	0.818993	0.409496	+	0.912312i	$0.365704\pi$
$102$	2774.72	2.69351
$103$	−801.275	−0.766524	−0.383262	−	0.923640i	$-0.625199\pi$
$103$	−801.275	−0.766524	−0.383262	+	0.923640i	$0.625199\pi$
$104$	77.8186	0.0733725
$105$	−1465.06	−1.36167
$106$	238.221	0.218284
$107$	901.921	0.814879	0.407439	−	0.913232i	$-0.366422\pi$
$107$	901.921	0.814879	0.407439	+	0.913232i	$0.366422\pi$
$108$	−1956.42	−1.74312
$109$	328.880	0.289000	0.144500	−	0.989505i	$-0.453843\pi$
$109$	328.880	0.289000	0.144500	+	0.989505i	$0.453843\pi$
$110$	926.965	0.803478
$111$	−67.4236	−0.0576537
$112$	−1980.64	−1.67101
$113$	−2209.02	−1.83900	−0.919500	−	0.393090i	$-0.871406\pi$
$113$	−2209.02	−1.83900	−0.919500	+	0.393090i	$0.871406\pi$
$114$	1160.50	0.953426
$115$	115.000	0.0932505
$116$	2417.35	1.93487
$117$	2413.84	1.90735
$118$	−1526.15	−1.19062
$119$	−2508.61	−1.93247
$120$	−76.3689	−0.0580958
$121$	762.027	0.572522
$122$	−213.688	−0.158577
$123$	−1933.88	−1.41766
$124$	−1360.80	−0.985510
$125$	125.000	0.0894427
$126$	7033.94	4.97328
$127$	107.788	0.0753124	0.0376562	−	0.999291i	$-0.488011\pi$
$127$	107.788	0.0753124	0.0376562	+	0.999291i	$0.488011\pi$
$128$	−218.308	−0.150749
$129$	4200.79	2.86712
$130$	923.199	0.622846
$131$	−985.156	−0.657050	−0.328525	−	0.944495i	$-0.606551\pi$
$131$	−985.156	−0.657050	−0.328525	+	0.944495i	$0.606551\pi$
$132$	−3445.54	−2.27194
$133$	−1049.20	−0.684040
$134$	−67.9489	−0.0438051
$135$	−1161.57	−0.740532
$136$	−130.766	−0.0824489
$137$	65.3753	0.0407692	0.0203846	−	0.999792i	$-0.493511\pi$
$137$	65.3753	0.0407692	0.0203846	+	0.999792i	$0.493511\pi$
$138$	−833.521	−0.514160
$139$	−547.498	−0.334088	−0.167044	−	0.985949i	$-0.553422\pi$
$139$	−547.498	−0.334088	−0.167044	+	0.985949i	$0.553422\pi$
$140$	1379.63	0.832855
$141$	1880.85	1.12338
$142$	−848.727	−0.501574
$143$	2084.52	1.21900
$144$	−3202.51	−1.85330
$145$	1435.23	0.821996
$146$	−3290.14	−1.86503
$147$	−6532.98	−3.66552
$148$	63.4916	0.0352633
$149$	3316.98	1.82374	0.911871	−	0.410476i	$-0.134637\pi$
$149$	3316.98	1.82374	0.911871	+	0.410476i	$0.134637\pi$
$150$	−906.001	−0.493165
$151$	−1645.53	−0.886831	−0.443415	−	0.896316i	$-0.646233\pi$
$151$	−1645.53	−0.886831	−0.443415	+	0.896316i	$0.646233\pi$
$152$	−54.6914	−0.0291846
$153$	−4056.19	−2.14329
$154$	6074.31	3.17845
$155$	−807.934	−0.418676
$156$	−3431.55	−1.76118
$157$	−2088.75	−1.06179	−0.530893	−	0.847439i	$-0.678143\pi$
$157$	−2088.75	−1.06179	−0.530893	+	0.847439i	$0.678143\pi$
$158$	255.463	0.128630
$159$	−525.723	−0.262217
$160$	−1293.15	−0.638953
$161$	753.584	0.368887
$162$	2622.66	1.27195
$163$	3160.08	1.51851	0.759253	−	0.650796i	$-0.225565\pi$
$163$	3160.08	1.51851	0.759253	+	0.650796i	$0.225565\pi$
$164$	1821.10	0.867099
$165$	−2045.69	−0.965194
$166$	−4304.67	−2.01269
$167$	−1886.30	−0.874047	−0.437024	−	0.899450i	$-0.643967\pi$
$167$	−1886.30	−0.874047	−0.437024	+	0.899450i	$0.643967\pi$
$168$	−500.438	−0.229819
$169$	−120.944	−0.0550495
$170$	−1551.33	−0.699894
$171$	−1696.46	−0.758664
$172$	−3955.81	−1.75365
$173$	−425.628	−0.187051	−0.0935256	−	0.995617i	$-0.529814\pi$
$173$	−425.628	−0.187051	−0.0935256	+	0.995617i	$0.529814\pi$
$174$	−10402.6	−4.53228
$175$	819.113	0.353824
$176$	−2765.59	−1.18446
$177$	3368.01	1.43026
$178$	1767.10	0.744100
$179$	4680.83	1.95453	0.977266	−	0.212016i	$-0.0680029\pi$
$179$	4680.83	1.95453	0.977266	+	0.212016i	$0.0680029\pi$
$180$	2230.73	0.923714
$181$	−380.264	−0.156159	−0.0780796	−	0.996947i	$-0.524879\pi$
$181$	−380.264	−0.156159	−0.0780796	+	0.996947i	$0.524879\pi$
$182$	6049.64	2.46389
$183$	471.581	0.190493
$184$	39.2818	0.0157386
$185$	37.6963	0.0149810
$186$	5855.92	2.30848
$187$	−3502.81	−1.36979
$188$	−1771.16	−0.687102
$189$	−7611.64	−2.92945
$190$	−648.830	−0.247743
$191$	1466.03	0.555383	0.277691	−	0.960670i	$-0.410431\pi$
$191$	1466.03	0.555383	0.277691	+	0.960670i	$0.410431\pi$
$192$	5047.88	1.89739
$193$	−2129.58	−0.794253	−0.397126	−	0.917764i	$-0.629993\pi$
$193$	−2129.58	−0.794253	−0.397126	+	0.917764i	$0.629993\pi$
$194$	2657.69	0.983561
$195$	−2037.38	−0.748205
$196$	6151.99	2.24198
$197$	−1146.95	−0.414807	−0.207403	−	0.978256i	$-0.566501\pi$
$197$	−1146.95	−0.414807	−0.207403	+	0.978256i	$0.566501\pi$
$198$	9821.59	3.52520
$199$	−3857.88	−1.37426	−0.687130	−	0.726535i	$-0.741130\pi$
$199$	−3857.88	−1.37426	−0.687130	+	0.726535i	$0.741130\pi$
$200$	42.6976	0.0150959
$201$	149.954	0.0526217
$202$	3368.74	1.17339
$203$	9404.93	3.25171
$204$	5766.34	1.97904
$205$	1081.23	0.368372
$206$	−3247.04	−1.09821
$207$	1218.47	0.409130
$208$	−2754.36	−0.918176
$209$	−1465.02	−0.484868
$210$	−5936.94	−1.95089
$211$	1880.22	0.613458	0.306729	−	0.951797i	$-0.400765\pi$
$211$	1880.22	0.613458	0.306729	+	0.951797i	$0.400765\pi$
$212$	495.064	0.160383
$213$	1873.03	0.602526
$214$	3654.89	1.16749
$215$	−2348.65	−0.745007
$216$	−396.770	−0.124985
$217$	−5294.32	−1.65623
$218$	1332.73	0.414056
$219$	7260.91	2.24040
$220$	1926.39	0.590352
$221$	−3488.58	−1.06184
$222$	−273.223	−0.0826015
$223$	−3181.06	−0.955246	−0.477623	−	0.878565i	$-0.658501\pi$
$223$	−3181.06	−0.955246	−0.477623	+	0.878565i	$0.658501\pi$
$224$	−8473.89	−2.52761
$225$	1324.43	0.392423
$226$	−8951.70	−2.63477
$227$	4817.24	1.40851	0.704255	−	0.709947i	$-0.251281\pi$
$227$	4817.24	1.40851	0.704255	+	0.709947i	$0.251281\pi$
$228$	2411.71	0.700525
$229$	−1440.61	−0.415714	−0.207857	−	0.978159i	$-0.566649\pi$
$229$	−1440.61	−0.415714	−0.207857	+	0.978159i	$0.566649\pi$
$230$	466.019	0.133602
$231$	−13405.2	−3.81818
$232$	490.247	0.138734
$233$	2313.68	0.650533	0.325266	−	0.945622i	$-0.394546\pi$
$233$	2313.68	0.650533	0.325266	+	0.945622i	$0.394546\pi$
$234$	9781.70	2.73269
$235$	−1051.58	−0.291903
$236$	−3171.60	−0.874803
$237$	−563.774	−0.154519
$238$	−10165.7	−2.76869
$239$	−2798.09	−0.757293	−0.378647	−	0.925541i	$-0.623610\pi$
$239$	−2798.09	−0.757293	−0.378647	+	0.925541i	$0.623610\pi$
$240$	2703.05	0.727005
$241$	−1809.31	−0.483600	−0.241800	−	0.970326i	$-0.577738\pi$
$241$	−1809.31	−0.483600	−0.241800	+	0.970326i	$0.577738\pi$
$242$	3087.99	0.820263
$243$	484.593	0.127929
$244$	−444.080	−0.116514
$245$	3652.57	0.952465
$246$	−7836.75	−2.03111
$247$	−1459.07	−0.375863
$248$	−275.975	−0.0706630
$249$	9499.86	2.41779
$250$	506.543	0.128146
$251$	5814.80	1.46226	0.731129	−	0.682239i	$-0.238994\pi$
$251$	5814.80	1.46226	0.731129	+	0.682239i	$0.238994\pi$
$252$	14617.7	3.65409
$253$	1052.24	0.261478
$254$	436.795	0.107901
$255$	3423.60	0.840761
$256$	3630.95	0.886462
$257$	1886.38	0.457856	0.228928	−	0.973443i	$-0.426478\pi$
$257$	1886.38	0.457856	0.228928	+	0.973443i	$0.426478\pi$
$258$	17023.0	4.10778
$259$	247.020	0.0592629
$260$	1918.57	0.457633
$261$	15206.9	3.60645
$262$	−3992.19	−0.941367
$263$	−6017.91	−1.41095	−0.705476	−	0.708734i	$-0.749267\pi$
$263$	−6017.91	−1.41095	−0.705476	+	0.708734i	$0.749267\pi$
$264$	−698.770	−0.162903
$265$	293.930	0.0681358
$266$	−4251.72	−0.980037
$267$	−3899.77	−0.893864
$268$	−141.209	−0.0321856
$269$	−3189.16	−0.722848	−0.361424	−	0.932401i	$-0.617709\pi$
$269$	−3189.16	−0.722848	−0.361424	+	0.932401i	$0.617709\pi$
$270$	−4707.07	−1.06097
$271$	1167.43	0.261683	0.130841	−	0.991403i	$-0.458232\pi$
$271$	1167.43	0.261683	0.130841	+	0.991403i	$0.458232\pi$
$272$	4628.40	1.03176
$273$	−13350.8	−2.95980
$274$	264.923	0.0584109
$275$	1143.74	0.250800
$276$	−1732.20	−0.377776
$277$	−4164.36	−0.903293	−0.451646	−	0.892197i	$-0.649163\pi$
$277$	−4164.36	−0.903293	−0.451646	+	0.892197i	$0.649163\pi$
$278$	−2218.65	−0.478654
$279$	−8560.42	−1.83691
$280$	279.793	0.0597173
$281$	4958.59	1.05269	0.526343	−	0.850273i	$-0.323563\pi$
$281$	4958.59	1.05269	0.526343	+	0.850273i	$0.323563\pi$
$282$	7621.84	1.60948
$283$	2171.54	0.456129	0.228065	−	0.973646i	$-0.426760\pi$
$283$	2171.54	0.456129	0.228065	+	0.973646i	$0.426760\pi$
$284$	−1763.80	−0.368529
$285$	1431.89	0.297605
$286$	8447.20	1.74648
$287$	7085.18	1.45723
$288$	−13701.5	−2.80336
$289$	949.183	0.193198
$290$	5816.04	1.17769
$291$	−5865.17	−1.18152
$292$	−6837.47	−1.37032
$293$	5170.00	1.03083	0.515417	−	0.856939i	$-0.327637\pi$
$293$	5170.00	1.03083	0.515417	+	0.856939i	$0.327637\pi$
$294$	−26473.9	−5.25166
$295$	−1883.04	−0.371644
$296$	12.8763	0.00252845
$297$	−10628.3	−2.07648
$298$	13441.5	2.61291
$299$	1047.97	0.202694
$300$	−1882.83	−0.362350
$301$	−15390.5	−2.94715
$302$	−6668.25	−1.27058
$303$	−7434.39	−1.40955
$304$	1935.78	0.365213
$305$	−263.660	−0.0494987
$306$	−16437.1	−3.07073
$307$	9189.38	1.70836	0.854178	−	0.519980i	$-0.174061\pi$
$307$	9189.38	1.70836	0.854178	+	0.519980i	$0.174061\pi$
$308$	12623.5	2.33535
$309$	7165.80	1.31925
$310$	−3274.03	−0.599846
$311$	2264.59	0.412903	0.206452	−	0.978457i	$-0.433808\pi$
$311$	2264.59	0.412903	0.206452	+	0.978457i	$0.433808\pi$
$312$	−695.931	−0.126280
$313$	2467.42	0.445581	0.222791	−	0.974866i	$-0.428483\pi$
$313$	2467.42	0.445581	0.222791	+	0.974866i	$0.428483\pi$
$314$	−8464.32	−1.52124
$315$	8678.86	1.55238
$316$	530.896	0.0945102
$317$	7178.08	1.27180	0.635901	−	0.771771i	$-0.280629\pi$
$317$	7178.08	1.27180	0.635901	+	0.771771i	$0.280629\pi$
$318$	−2130.41	−0.375684
$319$	13132.2	2.30490
$320$	−2822.26	−0.493028
$321$	−8065.88	−1.40247
$322$	3053.78	0.528511
$323$	2451.80	0.422358
$324$	5450.34	0.934558
$325$	1139.09	0.194417
$326$	12805.7	2.17559
$327$	−2941.17	−0.497392
$328$	369.327	0.0621727
$329$	−6890.88	−1.15473
$330$	−8289.84	−1.38285
$331$	−10304.2	−1.71109	−0.855545	−	0.517728i	$-0.826778\pi$
$331$	−10304.2	−1.71109	−0.855545	+	0.517728i	$0.826778\pi$
$332$	−8945.85	−1.47882
$333$	399.409	0.0657281
$334$	−7643.91	−1.25226
$335$	−83.8390	−0.0136735
$336$	17712.8	2.87593
$337$	−1582.19	−0.255749	−0.127874	−	0.991790i	$-0.540815\pi$
$337$	−1582.19	−0.255749	−0.127874	+	0.991790i	$0.540815\pi$
$338$	−490.105	−0.0788705
$339$	19755.2	3.16507
$340$	−3223.94	−0.514243
$341$	−7392.54	−1.17398
$342$	−6874.64	−1.08695
$343$	12696.7	1.99871
$344$	−802.253	−0.125740
$345$	−1028.44	−0.160492
$346$	−1724.79	−0.267992
$347$	2566.92	0.397117	0.198559	−	0.980089i	$-0.436374\pi$
$347$	2566.92	0.397117	0.198559	+	0.980089i	$0.436374\pi$
$348$	−21618.3	−3.33007
$349$	−215.226	−0.0330108	−0.0165054	−	0.999864i	$-0.505254\pi$
$349$	−215.226	−0.0330108	−0.0165054	+	0.999864i	$0.505254\pi$
$350$	3319.32	0.506930
$351$	−10585.1	−1.60966
$352$	−11832.2	−1.79165
$353$	−5111.32	−0.770675	−0.385338	−	0.922776i	$-0.625915\pi$
$353$	−5111.32	−0.770675	−0.385338	+	0.922776i	$0.625915\pi$
$354$	13648.3	2.04915
$355$	−1047.21	−0.156563
$356$	3672.34	0.546724
$357$	22434.5	3.32594
$358$	18968.3	2.80029
$359$	−4317.14	−0.634680	−0.317340	−	0.948312i	$-0.602790\pi$
$359$	−4317.14	−0.634680	−0.317340	+	0.948312i	$0.602790\pi$
$360$	452.400	0.0662321
$361$	−5833.56	−0.850497
$362$	−1540.96	−0.223732
$363$	−6814.80	−0.985356
$364$	12572.2	1.81033
$365$	−4059.55	−0.582155
$366$	1911.01	0.272923
$367$	−7628.24	−1.08499	−0.542495	−	0.840059i	$-0.682520\pi$
$367$	−7628.24	−1.08499	−0.542495	+	0.840059i	$0.682520\pi$
$368$	−1390.37	−0.196951
$369$	11456.1	1.61620
$370$	152.758	0.0214636
$371$	1926.10	0.269536
$372$	12169.6	1.69614
$373$	8487.60	1.17821	0.589104	−	0.808057i	$-0.299481\pi$
$373$	8487.60	1.17821	0.589104	+	0.808057i	$0.299481\pi$
$374$	−14194.6	−1.96253
$375$	−1117.87	−0.153938
$376$	−359.198	−0.0492666
$377$	13078.9	1.78673
$378$	−30845.0	−4.19707
$379$	−1227.48	−0.166363	−0.0831815	−	0.996534i	$-0.526508\pi$
$379$	−1227.48	−0.166363	−0.0831815	+	0.996534i	$0.526508\pi$
$380$	−1348.38	−0.182028
$381$	−963.951	−0.129619
$382$	5940.85	0.795707
$383$	−4106.30	−0.547838	−0.273919	−	0.961753i	$-0.588320\pi$
$383$	−4106.30	−0.547838	−0.273919	+	0.961753i	$0.588320\pi$
$384$	1952.33	0.259452
$385$	7494.82	0.992133
$386$	−8629.80	−1.13794
$387$	−24884.9	−3.26866
$388$	5523.13	0.722666
$389$	−11206.6	−1.46066	−0.730328	−	0.683097i	$-0.760633\pi$
$389$	−11206.6	−1.46066	−0.730328	+	0.683097i	$0.760633\pi$
$390$	−8256.17	−1.07197
$391$	−1760.99	−0.227768
$392$	1247.65	0.160754
$393$	8810.25	1.13084
$394$	−4647.84	−0.594301
$395$	315.204	0.0401510
$396$	20411.0	2.59013
$397$	7629.81	0.964557	0.482278	−	0.876018i	$-0.339809\pi$
$397$	7629.81	0.964557	0.482278	+	0.876018i	$0.339809\pi$
$398$	−15633.4	−1.96893
$399$	9383.01	1.17729
$400$	−1511.27	−0.188908
$401$	1221.46	0.152112	0.0760560	−	0.997104i	$-0.475767\pi$
$401$	1221.46	0.152112	0.0760560	+	0.997104i	$0.475767\pi$
$402$	607.666	0.0753921
$403$	−7362.51	−0.910056
$404$	7000.83	0.862140
$405$	3235.98	0.397030
$406$	38112.0	4.65878
$407$	344.918	0.0420073
$408$	1169.44	0.141901
$409$	16112.2	1.94791	0.973957	−	0.226731i	$-0.0728038\pi$
$409$	16112.2	1.94791	0.973957	+	0.226731i	$0.0728038\pi$
$410$	4381.50	0.527773
$411$	−584.651	−0.0701672
$412$	−6747.91	−0.806907
$413$	−12339.4	−1.47018
$414$	4937.67	0.586168
$415$	−5311.34	−0.628249
$416$	−11784.2	−1.38886
$417$	4896.27	0.574992
$418$	−5936.75	−0.694679
$419$	1997.98	0.232954	0.116477	−	0.993193i	$-0.462840\pi$
$419$	1997.98	0.232954	0.116477	+	0.993193i	$0.462840\pi$
$420$	−12338.0	−1.43341
$421$	−4849.75	−0.561431	−0.280715	−	0.959791i	$-0.590572\pi$
$421$	−4849.75	−0.561431	−0.280715	+	0.959791i	$0.590572\pi$
$422$	7619.29	0.878913
$423$	−11141.9	−1.28070
$424$	100.401	0.0114998
$425$	−1914.12	−0.218467
$426$	7590.16	0.863250
$427$	−1727.74	−0.195810
$428$	7595.49	0.857809
$429$	−18641.9	−2.09799
$430$	−9517.52	−1.06738
$431$	13262.3	1.48219	0.741094	−	0.671402i	$-0.234307\pi$
$431$	13262.3	1.48219	0.741094	+	0.671402i	$0.234307\pi$
$432$	14043.5	1.56405
$433$	13656.0	1.51562	0.757812	−	0.652473i	$-0.226269\pi$
$433$	13656.0	1.51562	0.757812	+	0.652473i	$0.226269\pi$
$434$	−21454.4	−2.37291
$435$	−12835.3	−1.41472
$436$	2769.65	0.304225
$437$	−736.517	−0.0806234
$438$	29423.7	3.20986
$439$	−1132.68	−0.123143	−0.0615717	−	0.998103i	$-0.519611\pi$
$439$	−1132.68	−0.123143	−0.0615717	+	0.998103i	$0.519611\pi$
$440$	390.680	0.0423294
$441$	38700.5	4.17887
$442$	−14136.9	−1.52132
$443$	6583.81	0.706109	0.353054	−	0.935603i	$-0.385143\pi$
$443$	6583.81	0.706109	0.353054	+	0.935603i	$0.385143\pi$
$444$	−567.805	−0.0606910
$445$	2180.35	0.232266
$446$	−12890.8	−1.36860
$447$	−29663.7	−3.13881
$448$	−18494.0	−1.95035
$449$	−12407.9	−1.30416	−0.652078	−	0.758152i	$-0.726103\pi$
$449$	−12407.9	−1.30416	−0.652078	+	0.758152i	$0.726103\pi$
$450$	5367.04	0.562232
$451$	9893.15	1.03293
$452$	−18603.2	−1.93588
$453$	14716.0	1.52631
$454$	19521.1	2.01800
$455$	7464.37	0.769088
$456$	489.105	0.0502290
$457$	17336.1	1.77450	0.887251	−	0.461286i	$-0.152612\pi$
$457$	17336.1	1.77450	0.887251	+	0.461286i	$0.152612\pi$
$458$	−5837.86	−0.595601
$459$	17787.1	1.80878
$460$	968.468	0.0981632
$461$	9940.64	1.00430	0.502150	−	0.864781i	$-0.332543\pi$
$461$	9940.64	1.00430	0.502150	+	0.864781i	$0.332543\pi$
$462$	−54322.5	−5.47037
$463$	6459.56	0.648383	0.324191	−	0.945991i	$-0.394908\pi$
$463$	6459.56	0.648383	0.324191	+	0.945991i	$0.394908\pi$
$464$	−17352.1	−1.73610
$465$	7225.35	0.720576
$466$	9375.82	0.932031
$467$	8151.66	0.807739	0.403869	−	0.914817i	$-0.367665\pi$
$467$	8151.66	0.807739	0.403869	+	0.914817i	$0.367665\pi$
$468$	20328.1	2.00783
$469$	−549.389	−0.0540905
$470$	−4261.34	−0.418215
$471$	18679.7	1.82742
$472$	−643.212	−0.0627251
$473$	−21489.9	−2.08902
$474$	−2284.60	−0.221382
$475$	−800.562	−0.0773312
$476$	−21126.2	−2.03428
$477$	3114.32	0.298941
$478$	−11338.8	−1.08499
$479$	−214.878	−0.0204969	−0.0102485	−	0.999947i	$-0.503262\pi$
$479$	−214.878	−0.0204969	−0.0102485	+	0.999947i	$0.503262\pi$
$480$	11564.6	1.09969
$481$	343.517	0.0325635
$482$	−7331.92	−0.692863
$483$	−6739.30	−0.634883
$484$	6417.38	0.602684
$485$	3279.20	0.307012
$486$	1963.74	0.183286
$487$	6216.61	0.578442	0.289221	−	0.957262i	$-0.406604\pi$
$487$	6216.61	0.578442	0.289221	+	0.957262i	$0.406604\pi$
$488$	−90.0611	−0.00835425
$489$	−28260.6	−2.61347
$490$	14801.4	1.36461
$491$	−17480.8	−1.60671	−0.803356	−	0.595499i	$-0.796954\pi$
$491$	−17480.8	−1.60671	−0.803356	+	0.595499i	$0.796954\pi$
$492$	−16286.1	−1.49235
$493$	−21977.7	−2.00776
$494$	−5912.63	−0.538506
$495$	12118.4	1.10037
$496$	9768.04	0.884270
$497$	−6862.24	−0.619343
$498$	38496.7	3.46401
$499$	−17884.0	−1.60440	−0.802200	−	0.597055i	$-0.796337\pi$
$499$	−17884.0	−1.60440	−0.802200	+	0.597055i	$0.796337\pi$
$500$	1052.68	0.0941548
$501$	16869.1	1.50431
$502$	23563.5	2.09501
$503$	3215.45	0.285029	0.142515	−	0.989793i	$-0.454481\pi$
$503$	3215.45	0.285029	0.142515	+	0.989793i	$0.454481\pi$
$504$	2964.53	0.262005
$505$	4156.54	0.366265
$506$	4264.04	0.374624
$507$	1081.60	0.0947446
$508$	907.736	0.0792801
$509$	6737.65	0.586721	0.293360	−	0.956002i	$-0.405226\pi$
$509$	6737.65	0.586721	0.293360	+	0.956002i	$0.405226\pi$
$510$	13873.6	1.20457
$511$	−26601.9	−2.30293
$512$	16460.3	1.42080
$513$	7439.26	0.640256
$514$	7644.24	0.655979
$515$	−4006.38	−0.342800
$516$	35376.8	3.01817
$517$	−9621.84	−0.818507
$518$	1001.01	0.0849070
$519$	3806.39	0.321930
$520$	389.093	0.0328132
$521$	13464.5	1.13223	0.566114	−	0.824327i	$-0.308446\pi$
$521$	13464.5	1.13223	0.566114	+	0.824327i	$0.308446\pi$
$522$	61623.5	5.16702
$523$	−21370.5	−1.78674	−0.893372	−	0.449317i	$-0.851667\pi$
$523$	−21370.5	−1.78674	−0.893372	+	0.449317i	$0.851667\pi$
$524$	−8296.46	−0.691665
$525$	−7325.32	−0.608959
$526$	−24386.6	−2.02150
$527$	12371.9	1.02263
$528$	24732.7	2.03855
$529$	529.000	0.0434783
$530$	1191.11	0.0976194
$531$	−19951.7	−1.63056
$532$	−8835.81	−0.720077
$533$	9852.96	0.800711
$534$	−15803.2	−1.28066
$535$	4509.61	0.364425
$536$	−28.6378	−0.00230777
$537$	−41860.6	−3.36391
$538$	−12923.5	−1.03564
$539$	33420.7	2.67075
$540$	−9782.10	−0.779546
$541$	−14485.2	−1.15114	−0.575572	−	0.817751i	$-0.695221\pi$
$541$	−14485.2	−1.15114	−0.575572	+	0.817751i	$0.695221\pi$
$542$	4730.81	0.374918
$543$	3400.70	0.268763
$544$	19802.0	1.56067
$545$	1644.40	0.129245
$546$	−54101.9	−4.24056
$547$	−18926.7	−1.47943	−0.739714	−	0.672922i	$-0.765039\pi$
$547$	−18926.7	−1.47943	−0.739714	+	0.672922i	$0.765039\pi$
$548$	550.555	0.0429171
$549$	−2793.59	−0.217172
$550$	4634.82	0.359327
$551$	−9191.93	−0.710689
$552$	−351.297	−0.0270873
$553$	2065.50	0.158832
$554$	−16875.4	−1.29416
$555$	−337.118	−0.0257835
$556$	−4610.73	−0.351688
$557$	2146.15	0.163259	0.0816294	−	0.996663i	$-0.473988\pi$
$557$	2146.15	0.163259	0.0816294	+	0.996663i	$0.473988\pi$
$558$	−34689.7	−2.63178
$559$	−21402.6	−1.61938
$560$	−9903.19	−0.747296
$561$	31325.6	2.35752
$562$	20093.9	1.50820
$563$	−14066.3	−1.05297	−0.526487	−	0.850183i	$-0.676491\pi$
$563$	−14066.3	−1.05297	−0.526487	+	0.850183i	$0.676491\pi$
$564$	15839.5	1.18256
$565$	−11045.1	−0.822426
$566$	8799.81	0.653505
$567$	21205.1	1.57060
$568$	−357.706	−0.0264243
$569$	−1253.22	−0.0923337	−0.0461668	−	0.998934i	$-0.514701\pi$
$569$	−1253.22	−0.0923337	−0.0461668	+	0.998934i	$0.514701\pi$
$570$	5802.49	0.426385
$571$	12499.6	0.916097	0.458048	−	0.888927i	$-0.348549\pi$
$571$	12499.6	0.916097	0.458048	+	0.888927i	$0.348549\pi$
$572$	17554.7	1.28322
$573$	−13110.7	−0.955858
$574$	28711.6	2.08780
$575$	575.000	0.0417029
$576$	−29903.0	−2.16312
$577$	−7260.56	−0.523849	−0.261925	−	0.965088i	$-0.584357\pi$
$577$	−7260.56	−0.523849	−0.261925	+	0.965088i	$0.584357\pi$
$578$	3846.41	0.276799
$579$	19044.9	1.36697
$580$	12086.7	0.865301
$581$	−34804.7	−2.48527
$582$	−23767.7	−1.69279
$583$	2689.44	0.191055
$584$	−1386.67	−0.0982545
$585$	12069.2	0.852991
$586$	20950.6	1.47690
$587$	14411.6	1.01334	0.506671	−	0.862139i	$-0.330876\pi$
$587$	14411.6	1.01334	0.506671	+	0.862139i	$0.330876\pi$
$588$	−55017.2	−3.85863
$589$	5174.42	0.361983
$590$	−7630.74	−0.532462
$591$	10257.2	0.713916
$592$	−455.753	−0.0316408
$593$	21665.4	1.50032	0.750160	−	0.661256i	$-0.229976\pi$
$593$	21665.4	1.50032	0.750160	+	0.661256i	$0.229976\pi$
$594$	−43069.3	−2.97501
$595$	−12543.1	−0.864227
$596$	27933.8	1.91982
$597$	34501.0	2.36521
$598$	4246.72	0.290403
$599$	−23174.4	−1.58077	−0.790384	−	0.612612i	$-0.790119\pi$
$599$	−23174.4	−1.58077	−0.790384	+	0.612612i	$0.790119\pi$
$600$	−381.845	−0.0259812
$601$	−22969.1	−1.55895	−0.779475	−	0.626433i	$-0.784514\pi$
$601$	−22969.1	−1.55895	−0.779475	+	0.626433i	$0.784514\pi$
$602$	−62367.4	−4.22243
$603$	−888.311	−0.0599914
$604$	−13857.8	−0.933551
$605$	3810.13	0.256040
$606$	−30126.7	−2.01949
$607$	−4606.78	−0.308045	−0.154023	−	0.988067i	$-0.549223\pi$
$607$	−4606.78	−0.308045	−0.154023	+	0.988067i	$0.549223\pi$
$608$	8281.98	0.552432
$609$	−84108.2	−5.59645
$610$	−1068.44	−0.0709177
$611$	−9582.75	−0.634495
$612$	−34159.1	−2.25621
$613$	7780.72	0.512660	0.256330	−	0.966589i	$-0.417487\pi$
$613$	7780.72	0.512660	0.256330	+	0.966589i	$0.417487\pi$
$614$	37238.5	2.44759
$615$	−9669.41	−0.633997
$616$	2560.09	0.167449
$617$	2438.43	0.159105	0.0795523	−	0.996831i	$-0.474651\pi$
$617$	2438.43	0.159105	0.0795523	+	0.996831i	$0.474651\pi$
$618$	29038.3	1.89011
$619$	6821.13	0.442915	0.221458	−	0.975170i	$-0.428919\pi$
$619$	6821.13	0.442915	0.221458	+	0.975170i	$0.428919\pi$
$620$	−6803.99	−0.440733
$621$	−5343.21	−0.345275
$622$	9176.88	0.591574
$623$	14287.6	0.918813
$624$	24632.2	1.58025
$625$	625.000	0.0400000
$626$	9998.83	0.638393
$627$	13101.6	0.834496
$628$	−17590.3	−1.11772
$629$	−577.242	−0.0365917
$630$	35169.7	2.22412
$631$	−15698.7	−0.990420	−0.495210	−	0.868773i	$-0.664909\pi$
$631$	−15698.7	−0.990420	−0.495210	+	0.868773i	$0.664909\pi$
$632$	107.668	0.00677657
$633$	−16814.8	−1.05581
$634$	29088.0	1.82213
$635$	538.942	0.0336807
$636$	−4427.36	−0.276032
$637$	33284.9	2.07033
$638$	53216.3	3.30228
$639$	−11095.6	−0.686909
$640$	−1091.54	−0.0674172
$641$	15360.1	0.946472	0.473236	−	0.880936i	$-0.343086\pi$
$641$	15360.1	0.946472	0.473236	+	0.880936i	$0.343086\pi$
$642$	−32685.7	−2.00935
$643$	−14107.3	−0.865221	−0.432610	−	0.901581i	$-0.642407\pi$
$643$	−14107.3	−0.865221	−0.432610	+	0.901581i	$0.642407\pi$
$644$	6346.28	0.388320
$645$	21003.9	1.28222
$646$	9935.52	0.605121
$647$	8107.22	0.492624	0.246312	−	0.969191i	$-0.420781\pi$
$647$	8107.22	0.492624	0.246312	+	0.969191i	$0.420781\pi$
$648$	1105.35	0.0670097
$649$	−17229.7	−1.04210
$650$	4616.00	0.278545
$651$	47347.0	2.85050
$652$	26612.5	1.59850
$653$	−25123.5	−1.50560	−0.752802	−	0.658247i	$-0.771298\pi$
$653$	−25123.5	−1.50560	−0.752802	+	0.658247i	$0.771298\pi$
$654$	−11918.6	−0.712623
$655$	−4925.78	−0.293842
$656$	−13072.2	−0.778023
$657$	−43012.7	−2.55416
$658$	−27924.2	−1.65440
$659$	−809.773	−0.0478669	−0.0239334	−	0.999714i	$-0.507619\pi$
$659$	−809.773	−0.0478669	−0.0239334	+	0.999714i	$0.507619\pi$
$660$	−17227.7	−1.01604
$661$	4086.36	0.240455	0.120228	−	0.992746i	$-0.461638\pi$
$661$	4086.36	0.240455	0.120228	+	0.992746i	$0.461638\pi$
$662$	−41756.2	−2.45151
$663$	31198.4	1.82752
$664$	−1814.25	−0.106034
$665$	−5246.01	−0.305912
$666$	1618.54	0.0941699
$667$	6602.06	0.383258
$668$	−15885.4	−0.920095
$669$	28448.2	1.64405
$670$	−339.744	−0.0195902
$671$	−2412.47	−0.138796
$672$	75781.9	4.35022
$673$	−8985.56	−0.514662	−0.257331	−	0.966323i	$-0.582843\pi$
$673$	−8985.56	−0.514662	−0.257331	+	0.966323i	$0.582843\pi$
$674$	−6411.56	−0.366416
$675$	−5807.84	−0.331176
$676$	−1018.52	−0.0579497
$677$	10328.0	0.586316	0.293158	−	0.956064i	$-0.405294\pi$
$677$	10328.0	0.586316	0.293158	+	0.956064i	$0.405294\pi$
$678$	80055.0	4.53465
$679$	21488.3	1.21450
$680$	−653.828	−0.0368723
$681$	−43080.6	−2.42416
$682$	−29957.1	−1.68199
$683$	4516.74	0.253043	0.126521	−	0.991964i	$-0.459619\pi$
$683$	4516.74	0.253043	0.126521	+	0.991964i	$0.459619\pi$
$684$	−14286.7	−0.798633
$685$	326.876	0.0182326
$686$	51451.3	2.86359
$687$	12883.4	0.715476
$688$	28395.5	1.57350
$689$	2678.51	0.148103
$690$	−4167.61	−0.229939
$691$	7957.06	0.438062	0.219031	−	0.975718i	$-0.429710\pi$
$691$	7957.06	0.438062	0.219031	+	0.975718i	$0.429710\pi$
$692$	−3584.41	−0.196906
$693$	79410.9	4.35291
$694$	10402.0	0.568957
$695$	−2737.49	−0.149409
$696$	−4384.28	−0.238773
$697$	−16556.8	−0.899762
$698$	−872.167	−0.0472951
$699$	−20691.2	−1.11962
$700$	6898.13	0.372464
$701$	7970.58	0.429450	0.214725	−	0.976675i	$-0.431114\pi$
$701$	7970.58	0.429450	0.214725	+	0.976675i	$0.431114\pi$
$702$	−42894.4	−2.30619
$703$	−241.426	−0.0129524
$704$	−25823.4	−1.38247
$705$	9404.24	0.502389
$706$	−20712.8	−1.10416
$707$	27237.4	1.44889
$708$	28363.6	1.50561
$709$	2079.18	0.110134	0.0550672	−	0.998483i	$-0.482463\pi$
$709$	2079.18	0.110134	0.0550672	+	0.998483i	$0.482463\pi$
$710$	−4243.63	−0.224311
$711$	3339.72	0.176159
$712$	744.765	0.0392012
$713$	−3716.50	−0.195209
$714$	90912.2	4.76513
$715$	10422.6	0.545152
$716$	39419.4	2.05750
$717$	25023.3	1.30336
$718$	−17494.5	−0.909318
$719$	29046.5	1.50661	0.753305	−	0.657671i	$-0.228458\pi$
$719$	29046.5	1.50661	0.753305	+	0.657671i	$0.228458\pi$
$720$	−16012.5	−0.828822
$721$	−26253.4	−1.35607
$722$	−23639.6	−1.21852
$723$	16180.6	0.832315
$724$	−3202.38	−0.164386
$725$	7176.15	0.367608
$726$	−27615.9	−1.41174
$727$	14037.7	0.716133	0.358067	−	0.933696i	$-0.383436\pi$
$727$	14037.7	0.716133	0.358067	+	0.933696i	$0.383436\pi$
$728$	2549.69	0.129805
$729$	−21808.0	−1.10796
$730$	−16450.7	−0.834065
$731$	35964.8	1.81971
$732$	3971.40	0.200529
$733$	10862.5	0.547358	0.273679	−	0.961821i	$-0.411759\pi$
$733$	10862.5	0.547358	0.273679	+	0.961821i	$0.411759\pi$
$734$	−30912.2	−1.55448
$735$	−32664.9	−1.63927
$736$	−5948.49	−0.297913
$737$	−767.121	−0.0383409
$738$	46423.9	2.31557
$739$	−8660.65	−0.431106	−0.215553	−	0.976492i	$-0.569155\pi$
$739$	−8660.65	−0.431106	−0.215553	+	0.976492i	$0.569155\pi$
$740$	317.458	0.0157702
$741$	13048.4	0.646890
$742$	7805.20	0.386170
$743$	−33484.3	−1.65332	−0.826661	−	0.562700i	$-0.809762\pi$
$743$	−33484.3	−1.65332	−0.826661	+	0.562700i	$0.809762\pi$
$744$	2468.04	0.121617
$745$	16584.9	0.815603
$746$	34394.7	1.68804
$747$	−56275.9	−2.75640
$748$	−29498.8	−1.44196
$749$	29551.0	1.44162
$750$	−4530.01	−0.220550
$751$	29209.3	1.41926	0.709628	−	0.704577i	$-0.248863\pi$
$751$	29209.3	1.41926	0.709628	+	0.704577i	$0.248863\pi$
$752$	12713.7	0.616517
$753$	−52001.7	−2.51666
$754$	53000.1	2.55988
$755$	−8227.66	−0.396603
$756$	−64101.2	−3.08378
$757$	3283.09	0.157630	0.0788151	−	0.996889i	$-0.474886\pi$
$757$	3283.09	0.157630	0.0788151	+	0.996889i	$0.474886\pi$
$758$	−4974.18	−0.238351
$759$	−9410.19	−0.450024
$760$	−273.457	−0.0130517
$761$	22957.1	1.09355	0.546776	−	0.837279i	$-0.315855\pi$
$761$	22957.1	1.09355	0.546776	+	0.837279i	$0.315855\pi$
$762$	−3906.26	−0.185707
$763$	10775.6	0.511275
$764$	12346.1	0.584642
$765$	−20281.0	−0.958509
$766$	−16640.1	−0.784898
$767$	−17159.7	−0.807825
$768$	−32471.6	−1.52567
$769$	−2510.87	−0.117743	−0.0588714	−	0.998266i	$-0.518750\pi$
$769$	−2510.87	−0.117743	−0.0588714	+	0.998266i	$0.518750\pi$
$770$	30371.6	1.42145
$771$	−16869.9	−0.788007
$772$	−17934.2	−0.836096
$773$	−11566.1	−0.538167	−0.269084	−	0.963117i	$-0.586721\pi$
$773$	−11566.1	−0.538167	−0.269084	+	0.963117i	$0.586721\pi$
$774$	−100842.	−4.68307
$775$	−4039.67	−0.187238
$776$	1120.11	0.0518166
$777$	−2209.10	−0.101996
$778$	−45412.8	−2.09271
$779$	−6924.72	−0.318490
$780$	−17157.7	−0.787623
$781$	−9581.85	−0.439008
$782$	−7136.14	−0.326327
$783$	−66684.7	−3.04357
$784$	−44160.0	−2.01166
$785$	−10443.7	−0.474845
$786$	35702.1	1.62017
$787$	−751.934	−0.0340579	−0.0170289	−	0.999855i	$-0.505421\pi$
$787$	−751.934	−0.0340579	−0.0170289	+	0.999855i	$0.505421\pi$
$788$	−9659.01	−0.436660
$789$	53818.1	2.42836
$790$	1277.31	0.0575250
$791$	−72377.4	−3.25341
$792$	4139.42	0.185717
$793$	−2402.66	−0.107593
$794$	30918.6	1.38194
$795$	−2628.62	−0.117267
$796$	−32489.0	−1.44666
$797$	−15898.3	−0.706585	−0.353292	−	0.935513i	$-0.614938\pi$
$797$	−15898.3	−0.706585	−0.353292	+	0.935513i	$0.614938\pi$
$798$	38023.1	1.68672
$799$	16102.8	0.712985
$800$	−6465.75	−0.285748
$801$	23101.7	1.01905
$802$	4949.78	0.217934
$803$	−37144.6	−1.63238
$804$	1262.84	0.0553940
$805$	3767.92	0.164971
$806$	−29835.4	−1.30385
$807$	28520.6	1.24408
$808$	1419.80	0.0618171
$809$	−30018.9	−1.30458	−0.652292	−	0.757967i	$-0.726193\pi$
$809$	−30018.9	−1.30458	−0.652292	+	0.757967i	$0.726193\pi$
$810$	13113.3	0.568833
$811$	5012.47	0.217030	0.108515	−	0.994095i	$-0.465390\pi$
$811$	5012.47	0.217030	0.108515	+	0.994095i	$0.465390\pi$
$812$	79203.2	3.42301
$813$	−10440.3	−0.450377
$814$	1397.73	0.0601846
$815$	15800.4	0.679096
$816$	−41391.8	−1.77574
$817$	15041.9	0.644125
$818$	65292.1	2.79081
$819$	79088.3	3.37432
$820$	9105.52	0.387779
$821$	−2707.44	−0.115092	−0.0575459	−	0.998343i	$-0.518328\pi$
$821$	−2707.44	−0.115092	−0.0575459	+	0.998343i	$0.518328\pi$
$822$	−2369.20	−0.100530
$823$	15781.8	0.668431	0.334215	−	0.942497i	$-0.391529\pi$
$823$	15781.8	0.668431	0.334215	+	0.942497i	$0.391529\pi$
$824$	−1368.50	−0.0578568
$825$	−10228.5	−0.431648
$826$	−50003.5	−2.10635
$827$	−21176.8	−0.890435	−0.445218	−	0.895422i	$-0.646874\pi$
$827$	−21176.8	−0.890435	−0.445218	+	0.895422i	$0.646874\pi$
$828$	10261.3	0.430684
$829$	20905.6	0.875852	0.437926	−	0.899011i	$-0.355713\pi$
$829$	20905.6	0.875852	0.437926	+	0.899011i	$0.355713\pi$
$830$	−21523.4	−0.900104
$831$	37241.8	1.55464
$832$	−25718.5	−1.07167
$833$	−55931.7	−2.32643
$834$	19841.4	0.823801
$835$	−9431.48	−0.390886
$836$	−12337.6	−0.510412
$837$	37538.8	1.55022
$838$	8096.51	0.333758
$839$	28724.8	1.18199	0.590995	−	0.806675i	$-0.298735\pi$
$839$	28724.8	1.18199	0.590995	+	0.806675i	$0.298735\pi$
$840$	−2502.19	−0.102778
$841$	58006.4	2.37839
$842$	−19652.8	−0.804372
$843$	−44344.6	−1.81176
$844$	15834.2	0.645777
$845$	−604.719	−0.0246189
$846$	−45150.8	−1.83489
$847$	24967.4	1.01286
$848$	−3553.66	−0.143907
$849$	−19420.1	−0.785035
$850$	−7756.67	−0.313002
$851$	173.403	0.00698493
$852$	15773.7	0.634268
$853$	−37511.5	−1.50571	−0.752854	−	0.658188i	$-0.771323\pi$
$853$	−37511.5	−1.50571	−0.752854	+	0.658188i	$0.771323\pi$
$854$	−7001.37	−0.280541
$855$	−8482.31	−0.339285
$856$	1540.40	0.0615066
$857$	26541.3	1.05792	0.528958	−	0.848648i	$-0.322583\pi$
$857$	26541.3	1.05792	0.528958	+	0.848648i	$0.322583\pi$
$858$	−75543.3	−3.00583
$859$	20535.4	0.815667	0.407833	−	0.913056i	$-0.366284\pi$
$859$	20535.4	0.815667	0.407833	+	0.913056i	$0.366284\pi$
$860$	−19779.0	−0.784256
$861$	−63362.7	−2.50801
$862$	53743.4	2.12356
$863$	21337.9	0.841660	0.420830	−	0.907140i	$-0.361739\pi$
$863$	21337.9	0.841660	0.420830	+	0.907140i	$0.361739\pi$
$864$	60083.3	2.36583
$865$	−2128.14	−0.0836519
$866$	55338.7	2.17146
$867$	−8488.54	−0.332510
$868$	−44585.9	−1.74348
$869$	2884.09	0.112585
$870$	−52012.8	−2.02690
$871$	−764.004	−0.0297214
$872$	561.696	0.0218136
$873$	34744.5	1.34699
$874$	−2984.62	−0.115511
$875$	4095.56	0.158235
$876$	61147.5	2.35843
$877$	−42216.5	−1.62548	−0.812742	−	0.582624i	$-0.802026\pi$
$877$	−42216.5	−1.62548	−0.812742	+	0.582624i	$0.802026\pi$
$878$	−4590.01	−0.176430
$879$	−46235.3	−1.77415
$880$	−13828.0	−0.529706
$881$	−33457.6	−1.27947	−0.639737	−	0.768594i	$-0.720957\pi$
$881$	−33457.6	−1.27947	−0.639737	+	0.768594i	$0.720957\pi$
$882$	156828.	5.98715
$883$	22192.2	0.845785	0.422893	−	0.906180i	$-0.361015\pi$
$883$	22192.2	0.845785	0.422893	+	0.906180i	$0.361015\pi$
$884$	−29379.0	−1.11779
$885$	16840.1	0.639630
$886$	26679.8	1.01165
$887$	17904.9	0.677777	0.338889	−	0.940826i	$-0.389949\pi$
$887$	17904.9	0.677777	0.338889	+	0.940826i	$0.389949\pi$
$888$	−115.153	−0.00435167
$889$	3531.64	0.133237
$890$	8835.50	0.332772
$891$	29609.0	1.11329
$892$	−26789.2	−1.00557
$893$	6734.82	0.252376
$894$	−120208.	−4.49703
$895$	23404.1	0.874093
$896$	−7152.77	−0.266693
$897$	−9371.96	−0.348852
$898$	−50281.1	−1.86849
$899$	−46382.9	−1.72075
$900$	11153.6	0.413097
$901$	−4500.95	−0.166424
$902$	40090.4	1.47989
$903$	137637.	5.07228
$904$	−3772.79	−0.138807
$905$	−1901.32	−0.0698365
$906$	59634.1	2.18677
$907$	9482.20	0.347135	0.173567	−	0.984822i	$-0.444471\pi$
$907$	9482.20	0.347135	0.173567	+	0.984822i	$0.444471\pi$
$908$	40568.2	1.48271
$909$	44040.4	1.60696
$910$	30248.2	1.10189
$911$	24018.2	0.873499	0.436750	−	0.899583i	$-0.356130\pi$
$911$	24018.2	0.873499	0.436750	+	0.899583i	$0.356130\pi$
$912$	−17311.7	−0.628561
$913$	−48598.3	−1.76163
$914$	70251.7	2.54236
$915$	2357.91	0.0851913
$916$	−12132.1	−0.437615
$917$	−32278.2	−1.16240
$918$	72079.3	2.59147
$919$	−39263.9	−1.40935	−0.704677	−	0.709528i	$-0.748908\pi$
$919$	−39263.9	−1.40935	−0.704677	+	0.709528i	$0.748908\pi$
$920$	196.409	0.00703849
$921$	−82180.5	−2.94022
$922$	40282.9	1.43888
$923$	−9542.92	−0.340313
$924$	−112892.	−4.01933
$925$	188.481	0.00669971
$926$	26176.3	0.928950
$927$	−42449.3	−1.50401
$928$	−74238.7	−2.62608
$929$	30536.7	1.07845	0.539223	−	0.842163i	$-0.318718\pi$
$929$	30536.7	1.07845	0.539223	+	0.842163i	$0.318718\pi$
$930$	29279.6	1.03238
$931$	−23392.9	−0.823491
$932$	19484.6	0.684805
$933$	−20252.2	−0.710640
$934$	33033.3	1.15726
$935$	−17514.1	−0.612590
$936$	4122.61	0.143965
$937$	−37724.9	−1.31528	−0.657640	−	0.753332i	$-0.728445\pi$
$937$	−37724.9	−1.31528	−0.657640	+	0.753332i	$0.728445\pi$
$938$	−2226.31	−0.0774964
$939$	−22066.1	−0.766881
$940$	−8855.81	−0.307281
$941$	33414.9	1.15759	0.578797	−	0.815472i	$-0.303522\pi$
$941$	33414.9	1.15759	0.578797	+	0.815472i	$0.303522\pi$
$942$	75696.4	2.61817
$943$	4973.65	0.171754
$944$	22766.3	0.784935
$945$	−38058.2	−1.31009
$946$	−87084.5	−2.99298
$947$	−11604.7	−0.398205	−0.199103	−	0.979979i	$-0.563803\pi$
$947$	−11604.7	−0.398205	−0.199103	+	0.979979i	$0.563803\pi$
$948$	−4747.80	−0.162660
$949$	−36993.7	−1.26540
$950$	−3244.15	−0.110794
$951$	−64193.5	−2.18887
$952$	−4284.47	−0.145862
$953$	33381.8	1.13467	0.567336	−	0.823487i	$-0.307974\pi$
$953$	33381.8	1.13467	0.567336	+	0.823487i	$0.307974\pi$
$954$	12620.3	0.428298
$955$	7330.14	0.248375
$956$	−23564.0	−0.797190
$957$	−117442.	−3.96693
$958$	−870.758	−0.0293663
$959$	2141.99	0.0721256
$960$	25239.4	0.848540
$961$	−3680.68	−0.123550
$962$	1392.05	0.0466543
$963$	47781.2	1.59889
$964$	−15237.0	−0.509078
$965$	−10647.9	−0.355201
$966$	−27309.9	−0.909609
$967$	44013.3	1.46367	0.731837	−	0.681479i	$-0.238663\pi$
$967$	44013.3	1.46367	0.731837	+	0.681479i	$0.238663\pi$
$968$	1301.47	0.0432136
$969$	−21926.4	−0.726913
$970$	13288.4	0.439862
$971$	54941.3	1.81581	0.907905	−	0.419176i	$-0.137681\pi$
$971$	54941.3	1.81581	0.907905	+	0.419176i	$0.137681\pi$
$972$	4080.98	0.134668
$973$	−17938.5	−0.591040
$974$	25191.8	0.828745
$975$	−10186.9	−0.334607
$976$	3187.68	0.104544
$977$	52377.7	1.71516	0.857580	−	0.514351i	$-0.171967\pi$
$977$	52377.7	1.71516	0.857580	+	0.514351i	$0.171967\pi$
$978$	−114521.	−3.74437
$979$	19950.0	0.651282
$980$	30760.0	1.00264
$981$	17423.1	0.567052
$982$	−70838.0	−2.30197
$983$	−18746.9	−0.608275	−0.304137	−	0.952628i	$-0.598368\pi$
$983$	−18746.9	−0.608275	−0.304137	+	0.952628i	$0.598368\pi$
$984$	−3302.89	−0.107004
$985$	−5734.76	−0.185507
$986$	−89060.9	−2.87655
$987$	61625.1	1.98738
$988$	−12287.5	−0.395664
$989$	−10803.8	−0.347361
$990$	49108.0	1.57652
$991$	51116.6	1.63852	0.819260	−	0.573423i	$-0.194385\pi$
$991$	51116.6	1.63852	0.819260	+	0.573423i	$0.194385\pi$
$992$	41791.2	1.33757
$993$	92150.5	2.94492
$994$	−27808.1	−0.887344
$995$	−19289.4	−0.614587
$996$	80002.7	2.54516
$997$	−36176.5	−1.14917	−0.574584	−	0.818445i	$-0.694836\pi$
$997$	−36176.5	−1.14917	−0.574584	+	0.818445i	$0.694836\pi$
$998$	−72471.9	−2.29865
$999$	−1751.47	−0.0554696

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.4.a.f.1.6	✓	8
3.2	odd	2		1035.4.a.r.1.3		8
4.3	odd	2		1840.4.a.v.1.7		8
5.2	odd	4		575.4.b.k.24.13		16
5.3	odd	4		575.4.b.k.24.4		16
5.4	even	2		575.4.a.n.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.4.a.f.1.6	✓	8	1.1	even	1	trivial
575.4.a.n.1.3		8	5.4	even	2
575.4.b.k.24.4		16	5.3	odd	4
575.4.b.k.24.13		16	5.2	odd	4
1035.4.a.r.1.3		8	3.2	odd	2
1840.4.a.v.1.7		8	4.3	odd	2

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	115.a (trivial)

\(f(q)\)	\(=\)	\(q+4.05234 q^{2} -8.94300 q^{3} +8.42146 q^{4} +5.00000 q^{5} -36.2401 q^{6} +32.7645 q^{7} +1.70790 q^{8} +52.9772 q^{9} +20.2617 q^{10} +45.7496 q^{11} -75.3131 q^{12} +45.5638 q^{13} +132.773 q^{14} -44.7150 q^{15} -60.4507 q^{16} -76.5649 q^{17} +214.681 q^{18} -32.0225 q^{19} +42.1073 q^{20} -293.013 q^{21} +185.393 q^{22} +23.0000 q^{23} -15.2738 q^{24} +25.0000 q^{25} +184.640 q^{26} -232.314 q^{27} +275.925 q^{28} +287.046 q^{29} -181.200 q^{30} -161.587 q^{31} -258.630 q^{32} -409.139 q^{33} -310.267 q^{34} +163.823 q^{35} +446.145 q^{36} +7.53926 q^{37} -129.766 q^{38} -407.476 q^{39} +8.53952 q^{40} +216.246 q^{41} -1187.39 q^{42} -469.729 q^{43} +385.279 q^{44} +264.886 q^{45} +93.2038 q^{46} -210.315 q^{47} +540.610 q^{48} +730.514 q^{49} +101.309 q^{50} +684.719 q^{51} +383.713 q^{52} +58.7860 q^{53} -941.414 q^{54} +228.748 q^{55} +55.9587 q^{56} +286.377 q^{57} +1163.21 q^{58} -376.609 q^{59} -376.565 q^{60} -52.7319 q^{61} -654.805 q^{62} +1735.77 q^{63} -564.451 q^{64} +227.819 q^{65} -1657.97 q^{66} -16.7678 q^{67} -644.788 q^{68} -205.689 q^{69} +663.865 q^{70} -209.441 q^{71} +90.4800 q^{72} -811.910 q^{73} +30.5516 q^{74} -223.575 q^{75} -269.676 q^{76} +1498.96 q^{77} -1651.23 q^{78} +63.0408 q^{79} -302.253 q^{80} +647.197 q^{81} +876.300 q^{82} -1062.27 q^{83} -2467.60 q^{84} -382.824 q^{85} -1903.50 q^{86} -2567.05 q^{87} +78.1360 q^{88} +436.069 q^{89} +1073.41 q^{90} +1492.87 q^{91} +193.694 q^{92} +1445.07 q^{93} -852.269 q^{94} -160.112 q^{95} +2312.93 q^{96} +655.840 q^{97} +2960.29 q^{98} +2423.68 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{2} + 42 q^{4} + 40 q^{5} + 11 q^{7} + 3 q^{8} + 158 q^{9} + 30 q^{10} + 41 q^{11} + 48 q^{12} + 28 q^{13} + 161 q^{14} + 98 q^{16} + 71 q^{17} + 84 q^{18} + 177 q^{19} + 210 q^{20} + 292 q^{21}+ \cdots + 1319 q^{99}+O(q^{100}) \) 8 * q + 6 * q^2 + 42 * q^4 + 40 * q^5 + 11 * q^7 + 3 * q^8 + 158 * q^9 + 30 * q^10 + 41 * q^11 + 48 * q^12 + 28 * q^13 + 161 * q^14 + 98 * q^16 + 71 * q^17 + 84 * q^18 + 177 * q^19 + 210 * q^20 + 292 * q^21 + 171 * q^22 + 184 * q^23 + 177 * q^24 + 200 * q^25 + 396 * q^26 - 495 * q^27 + 179 * q^28 + 225 * q^29 - 36 * q^31 - 360 * q^32 - 53 * q^33 - 1051 * q^34 + 55 * q^35 - 396 * q^36 - 348 * q^37 - 309 * q^38 - 1077 * q^39 + 15 * q^40 + 620 * q^41 - 2288 * q^42 - 390 * q^43 - 141 * q^44 + 790 * q^45 + 138 * q^46 + 123 * q^47 - 1304 * q^48 + 881 * q^49 + 150 * q^50 + 957 * q^51 - 1890 * q^52 + 1406 * q^53 - 2949 * q^54 + 205 * q^55 + 1031 * q^56 - 1142 * q^57 - 129 * q^58 - 676 * q^59 + 240 * q^60 + 1447 * q^61 - 1556 * q^62 - 58 * q^63 - 2883 * q^64 + 140 * q^65 - 119 * q^66 - 1582 * q^67 + 953 * q^68 + 805 * q^70 + 1396 * q^71 - 1728 * q^72 + 17 * q^73 - 964 * q^74 + 2271 * q^76 + 488 * q^77 - 1919 * q^78 + 708 * q^79 + 490 * q^80 + 4316 * q^81 - 3332 * q^82 + 1486 * q^83 - 3970 * q^84 + 355 * q^85 + 3570 * q^86 - 803 * q^87 - 1031 * q^88 + 1360 * q^89 + 420 * q^90 + 2693 * q^91 + 966 * q^92 + 3833 * q^93 - 3207 * q^94 + 885 * q^95 + 4956 * q^96 - 855 * q^97 + 1817 * q^98 + 1319 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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