LMFDB - Embedded newform 825.4.a.bb.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,4,Mod(1,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("825.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	825.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:	$48.6765757547$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 44x^{5} + 118x^{4} + 515x^{3} - 1279x^{2} - 892x + 1840 $ x^7 - 3x^6 - 44x^5 + 118x^4 + 515x^3 - 1279x^2 - 892x + 1840
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 165)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$5.52667$ of defining polynomial
Character	$\chi$	$=$	825.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.52667 q^{2} -3.00000 q^{3} +22.5440 q^{4} +16.5800 q^{6} -22.7119 q^{7} -80.3801 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-5.52667 q^{2} -3.00000 q^{3} +22.5440 q^{4} +16.5800 q^{6} -22.7119 q^{7} -80.3801 q^{8} +9.00000 q^{9} -11.0000 q^{11} -67.6321 q^{12} -25.8814 q^{13} +125.521 q^{14} +263.882 q^{16} +103.221 q^{17} -49.7400 q^{18} -91.5974 q^{19} +68.1358 q^{21} +60.7933 q^{22} +78.7705 q^{23} +241.140 q^{24} +143.038 q^{26} -27.0000 q^{27} -512.019 q^{28} +243.513 q^{29} -177.152 q^{31} -815.345 q^{32} +33.0000 q^{33} -570.470 q^{34} +202.896 q^{36} +71.7571 q^{37} +506.228 q^{38} +77.6442 q^{39} -321.351 q^{41} -376.564 q^{42} +64.4617 q^{43} -247.984 q^{44} -435.338 q^{46} +76.7143 q^{47} -791.645 q^{48} +172.832 q^{49} -309.664 q^{51} -583.471 q^{52} +181.711 q^{53} +149.220 q^{54} +1825.59 q^{56} +274.792 q^{57} -1345.81 q^{58} +623.186 q^{59} -86.9818 q^{61} +979.061 q^{62} -204.407 q^{63} +2395.09 q^{64} -182.380 q^{66} +162.191 q^{67} +2327.03 q^{68} -236.311 q^{69} +326.705 q^{71} -723.421 q^{72} +728.127 q^{73} -396.578 q^{74} -2064.98 q^{76} +249.831 q^{77} -429.113 q^{78} +261.943 q^{79} +81.0000 q^{81} +1776.00 q^{82} -1309.95 q^{83} +1536.06 q^{84} -356.258 q^{86} -730.538 q^{87} +884.181 q^{88} +1223.60 q^{89} +587.816 q^{91} +1775.80 q^{92} +531.456 q^{93} -423.974 q^{94} +2446.03 q^{96} +1300.90 q^{97} -955.184 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 3 q^{2} - 21 q^{3} + 41 q^{4} + 9 q^{6} - 50 q^{7} - 21 q^{8} + 63 q^{9}+O(q^{10}) $ 7 * q - 3 * q^2 - 21 * q^3 + 41 * q^4 + 9 * q^6 - 50 * q^7 - 21 * q^8 + 63 * q^9	\( 7 q - 3 q^{2} - 21 q^{3} + 41 q^{4} + 9 q^{6} - 50 q^{7} - 21 q^{8} + 63 q^{9} - 77 q^{11} - 123 q^{12} - 24 q^{13} + 142 q^{14} + 181 q^{16} - 38 q^{17} - 27 q^{18} + 26 q^{19} + 150 q^{21} + 33 q^{22} - 228 q^{23} + 63 q^{24} + 476 q^{26} - 189 q^{27} - 840 q^{28} + 572 q^{29} - 140 q^{31} - 991 q^{32} + 231 q^{33} - 806 q^{34} + 369 q^{36} + 104 q^{37} - 498 q^{38} + 72 q^{39} + 896 q^{41} - 426 q^{42} - 614 q^{43} - 451 q^{44} - 344 q^{46} - 520 q^{47} - 543 q^{48} + 295 q^{49} + 114 q^{51} + 26 q^{52} - 380 q^{53} + 81 q^{54} + 1522 q^{56} - 78 q^{57} - 1600 q^{58} + 1316 q^{59} - 386 q^{61} - 440 q^{62} - 450 q^{63} + 869 q^{64} - 99 q^{66} - 348 q^{67} - 332 q^{68} + 684 q^{69} + 804 q^{71} - 189 q^{72} - 468 q^{73} - 748 q^{74} - 1698 q^{76} + 550 q^{77} - 1428 q^{78} - 374 q^{79} + 567 q^{81} + 620 q^{82} - 3128 q^{83} + 2520 q^{84} - 2534 q^{86} - 1716 q^{87} + 231 q^{88} + 694 q^{89} - 3376 q^{91} + 1184 q^{92} + 420 q^{93} - 2920 q^{94} + 2973 q^{96} + 8 q^{97} - 4211 q^{98} - 693 q^{99}+O(q^{100}) \) 7 * q - 3 * q^2 - 21 * q^3 + 41 * q^4 + 9 * q^6 - 50 * q^7 - 21 * q^8 + 63 * q^9 - 77 * q^11 - 123 * q^12 - 24 * q^13 + 142 * q^14 + 181 * q^16 - 38 * q^17 - 27 * q^18 + 26 * q^19 + 150 * q^21 + 33 * q^22 - 228 * q^23 + 63 * q^24 + 476 * q^26 - 189 * q^27 - 840 * q^28 + 572 * q^29 - 140 * q^31 - 991 * q^32 + 231 * q^33 - 806 * q^34 + 369 * q^36 + 104 * q^37 - 498 * q^38 + 72 * q^39 + 896 * q^41 - 426 * q^42 - 614 * q^43 - 451 * q^44 - 344 * q^46 - 520 * q^47 - 543 * q^48 + 295 * q^49 + 114 * q^51 + 26 * q^52 - 380 * q^53 + 81 * q^54 + 1522 * q^56 - 78 * q^57 - 1600 * q^58 + 1316 * q^59 - 386 * q^61 - 440 * q^62 - 450 * q^63 + 869 * q^64 - 99 * q^66 - 348 * q^67 - 332 * q^68 + 684 * q^69 + 804 * q^71 - 189 * q^72 - 468 * q^73 - 748 * q^74 - 1698 * q^76 + 550 * q^77 - 1428 * q^78 - 374 * q^79 + 567 * q^81 + 620 * q^82 - 3128 * q^83 + 2520 * q^84 - 2534 * q^86 - 1716 * q^87 + 231 * q^88 + 694 * q^89 - 3376 * q^91 + 1184 * q^92 + 420 * q^93 - 2920 * q^94 + 2973 * q^96 + 8 * q^97 - 4211 * q^98 - 693 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−5.52667	−1.95397	−0.976986	−	0.213304i	$-0.931577\pi$
$2$	−5.52667	−1.95397	−0.976986	+	0.213304i	$0.931577\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	22.5440	2.81801
$5$	0	0
$5$	0	0
$6$	16.5800	1.12813
$7$	−22.7119	−1.22633	−0.613165	−	0.789955i	$-0.710104\pi$
$7$	−22.7119	−1.22633	−0.613165	+	0.789955i	$0.710104\pi$
$8$	−80.3801	−3.55233
$9$	9.00000	0.333333
$10$	0	0
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−67.6321	−1.62698
$13$	−25.8814	−0.552170	−0.276085	−	0.961133i	$-0.589037\pi$
$13$	−25.8814	−0.552170	−0.276085	+	0.961133i	$0.589037\pi$
$14$	125.521	2.39621
$15$	0	0
$16$	263.882	4.12315
$17$	103.221	1.47264	0.736319	−	0.676634i	$-0.236562\pi$
$17$	103.221	1.47264	0.736319	+	0.676634i	$0.236562\pi$
$18$	−49.7400	−0.651324
$19$	−91.5974	−1.10599	−0.552997	−	0.833183i	$-0.686516\pi$
$19$	−91.5974	−1.10599	−0.552997	+	0.833183i	$0.686516\pi$
$20$	0	0
$21$	68.1358	0.708021
$22$	60.7933	0.589145
$23$	78.7705	0.714121	0.357060	−	0.934081i	$-0.383779\pi$
$23$	78.7705	0.714121	0.357060	+	0.934081i	$0.383779\pi$
$24$	241.140	2.05094
$25$	0	0
$26$	143.038	1.07892
$27$	−27.0000	−0.192450
$28$	−512.019	−3.45580
$29$	243.513	1.55928	0.779641	−	0.626227i	$-0.215402\pi$
$29$	243.513	1.55928	0.779641	+	0.626227i	$0.215402\pi$
$30$	0	0
$31$	−177.152	−1.02637	−0.513185	−	0.858278i	$-0.671535\pi$
$31$	−177.152	−1.02637	−0.513185	+	0.858278i	$0.671535\pi$
$32$	−815.345	−4.50418
$33$	33.0000	0.174078
$34$	−570.470	−2.87749
$35$	0	0
$36$	202.896	0.939335
$37$	71.7571	0.318832	0.159416	−	0.987211i	$-0.449039\pi$
$37$	71.7571	0.318832	0.159416	+	0.987211i	$0.449039\pi$
$38$	506.228	2.16108
$39$	77.6442	0.318795
$40$	0	0
$41$	−321.351	−1.22406	−0.612032	−	0.790833i	$-0.709648\pi$
$41$	−321.351	−1.22406	−0.612032	+	0.790833i	$0.709648\pi$
$42$	−376.564	−1.38345
$43$	64.4617	0.228612	0.114306	−	0.993446i	$-0.463536\pi$
$43$	64.4617	0.228612	0.114306	+	0.993446i	$0.463536\pi$
$44$	−247.984	−0.849661
$45$	0	0
$46$	−435.338	−1.39537
$47$	76.7143	0.238084	0.119042	−	0.992889i	$-0.462018\pi$
$47$	76.7143	0.238084	0.119042	+	0.992889i	$0.462018\pi$
$48$	−791.645	−2.38050
$49$	172.832	0.503883
$50$	0	0
$51$	−309.664	−0.850228
$52$	−583.471	−1.55602
$53$	181.711	0.470943	0.235471	−	0.971881i	$-0.424337\pi$
$53$	181.711	0.470943	0.235471	+	0.971881i	$0.424337\pi$
$54$	149.220	0.376042
$55$	0	0
$56$	1825.59	4.35633
$57$	274.792	0.638546
$58$	−1345.81	−3.04679
$59$	623.186	1.37512	0.687558	−	0.726129i	$-0.258683\pi$
$59$	623.186	1.37512	0.687558	+	0.726129i	$0.258683\pi$
$60$	0	0
$61$	−86.9818	−0.182572	−0.0912859	−	0.995825i	$-0.529098\pi$
$61$	−86.9818	−0.182572	−0.0912859	+	0.995825i	$0.529098\pi$
$62$	979.061	2.00550
$63$	−204.407	−0.408776
$64$	2395.09	4.67790
$65$	0	0
$66$	−182.380	−0.340143
$67$	162.191	0.295743	0.147871	−	0.989007i	$-0.452758\pi$
$67$	162.191	0.295743	0.147871	+	0.989007i	$0.452758\pi$
$68$	2327.03	4.14990
$69$	−236.311	−0.412298
$70$	0	0
$71$	326.705	0.546096	0.273048	−	0.962000i	$-0.411968\pi$
$71$	326.705	0.546096	0.273048	+	0.962000i	$0.411968\pi$
$72$	−723.421	−1.18411
$73$	728.127	1.16741	0.583704	−	0.811967i	$-0.301603\pi$
$73$	728.127	1.16741	0.583704	+	0.811967i	$0.301603\pi$
$74$	−396.578	−0.622989
$75$	0	0
$76$	−2064.98	−3.11670
$77$	249.831	0.369752
$78$	−429.113	−0.622917
$79$	261.943	0.373049	0.186524	−	0.982450i	$-0.440278\pi$
$79$	261.943	0.373049	0.186524	+	0.982450i	$0.440278\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	1776.00	2.39179
$83$	−1309.95	−1.73236	−0.866179	−	0.499733i	$-0.833431\pi$
$83$	−1309.95	−1.73236	−0.866179	+	0.499733i	$0.833431\pi$
$84$	1536.06	1.99521
$85$	0	0
$86$	−356.258	−0.446701
$87$	−730.538	−0.900252
$88$	884.181	1.07107
$89$	1223.60	1.45731	0.728656	−	0.684879i	$-0.240145\pi$
$89$	1223.60	1.45731	0.728656	+	0.684879i	$0.240145\pi$
$90$	0	0
$91$	587.816	0.677142
$92$	1775.80	2.01240
$93$	531.456	0.592575
$94$	−423.974	−0.465209
$95$	0	0
$96$	2446.03	2.60049
$97$	1300.90	1.36171	0.680857	−	0.732416i	$-0.261607\pi$
$97$	1300.90	1.36171	0.680857	+	0.732416i	$0.261607\pi$
$98$	−955.184	−0.984573
$99$	−99.0000	−0.100504
$100$	0	0
$101$	460.225	0.453407	0.226703	−	0.973964i	$-0.427205\pi$
$101$	460.225	0.453407	0.226703	+	0.973964i	$0.427205\pi$
$102$	1711.41	1.66132
$103$	−247.598	−0.236860	−0.118430	−	0.992962i	$-0.537786\pi$
$103$	−247.598	−0.236860	−0.118430	+	0.992962i	$0.537786\pi$
$104$	2080.35	1.96149
$105$	0	0
$106$	−1004.26	−0.920209
$107$	−805.912	−0.728135	−0.364067	−	0.931373i	$-0.618612\pi$
$107$	−805.912	−0.728135	−0.364067	+	0.931373i	$0.618612\pi$
$108$	−608.689	−0.542325
$109$	−819.958	−0.720530	−0.360265	−	0.932850i	$-0.617314\pi$
$109$	−819.958	−0.720530	−0.360265	+	0.932850i	$0.617314\pi$
$110$	0	0
$111$	−215.271	−0.184078
$112$	−5993.26	−5.05634
$113$	−93.5557	−0.0778848	−0.0389424	−	0.999241i	$-0.512399\pi$
$113$	−93.5557	−0.0778848	−0.0389424	+	0.999241i	$0.512399\pi$
$114$	−1518.68	−1.24770
$115$	0	0
$116$	5489.76	4.39406
$117$	−232.932	−0.184057
$118$	−3444.14	−2.68694
$119$	−2344.36	−1.80594
$120$	0	0
$121$	121.000	0.0909091
$122$	480.719	0.356740
$123$	964.054	0.706714
$124$	−3993.73	−2.89232
$125$	0	0
$126$	1129.69	0.798737
$127$	−398.741	−0.278603	−0.139301	−	0.990250i	$-0.544486\pi$
$127$	−398.741	−0.278603	−0.139301	+	0.990250i	$0.544486\pi$
$128$	−6714.08	−4.63630
$129$	−193.385	−0.131989
$130$	0	0
$131$	−1716.29	−1.14468	−0.572339	−	0.820017i	$-0.693964\pi$
$131$	−1716.29	−1.14468	−0.572339	+	0.820017i	$0.693964\pi$
$132$	743.953	0.490552
$133$	2080.35	1.35631
$134$	−896.374	−0.577873
$135$	0	0
$136$	−8296.94	−5.23130
$137$	−2205.75	−1.37555	−0.687774	−	0.725925i	$-0.741412\pi$
$137$	−2205.75	−1.37555	−0.687774	+	0.725925i	$0.741412\pi$
$138$	1306.01	0.805618
$139$	−812.155	−0.495583	−0.247792	−	0.968813i	$-0.579705\pi$
$139$	−812.155	−0.495583	−0.247792	+	0.968813i	$0.579705\pi$
$140$	0	0
$141$	−230.143	−0.137458
$142$	−1805.59	−1.06706
$143$	284.695	0.166485
$144$	2374.93	1.37438
$145$	0	0
$146$	−4024.11	−2.28108
$147$	−518.496	−0.290917
$148$	1617.70	0.898471
$149$	3123.58	1.71741	0.858703	−	0.512473i	$-0.171271\pi$
$149$	3123.58	1.71741	0.858703	+	0.512473i	$0.171271\pi$
$150$	0	0
$151$	−2322.09	−1.25145	−0.625724	−	0.780045i	$-0.715196\pi$
$151$	−2322.09	−1.25145	−0.625724	+	0.780045i	$0.715196\pi$
$152$	7362.60	3.92886
$153$	928.992	0.490880
$154$	−1380.73	−0.722485
$155$	0	0
$156$	1750.41	0.898367
$157$	−1188.33	−0.604068	−0.302034	−	0.953297i	$-0.597666\pi$
$157$	−1188.33	−0.604068	−0.302034	+	0.953297i	$0.597666\pi$
$158$	−1447.67	−0.728927
$159$	−545.134	−0.271899
$160$	0	0
$161$	−1789.03	−0.875747
$162$	−447.660	−0.217108
$163$	1373.14	0.659834	0.329917	−	0.944010i	$-0.392979\pi$
$163$	1373.14	0.659834	0.329917	+	0.944010i	$0.392979\pi$
$164$	−7244.56	−3.44942
$165$	0	0
$166$	7239.66	3.38498
$167$	1998.75	0.926154	0.463077	−	0.886318i	$-0.346745\pi$
$167$	1998.75	0.926154	0.463077	+	0.886318i	$0.346745\pi$
$168$	−5476.76	−2.51513
$169$	−1527.15	−0.695109
$170$	0	0
$171$	−824.377	−0.368665
$172$	1453.23	0.644230
$173$	3535.61	1.55380	0.776901	−	0.629623i	$-0.216791\pi$
$173$	3535.61	1.55380	0.776901	+	0.629623i	$0.216791\pi$
$174$	4037.44	1.75907
$175$	0	0
$176$	−2902.70	−1.24318
$177$	−1869.56	−0.793924
$178$	−6762.40	−2.84755
$179$	1088.82	0.454650	0.227325	−	0.973819i	$-0.427002\pi$
$179$	1088.82	0.454650	0.227325	+	0.973819i	$0.427002\pi$
$180$	0	0
$181$	−1478.22	−0.607047	−0.303524	−	0.952824i	$-0.598163\pi$
$181$	−1478.22	−0.607047	−0.303524	+	0.952824i	$0.598163\pi$
$182$	−3248.66	−1.32312
$183$	260.945	0.105408
$184$	−6331.57	−2.53679
$185$	0	0
$186$	−2937.18	−1.15787
$187$	−1135.43	−0.444017
$188$	1729.45	0.670921
$189$	613.222	0.236007
$190$	0	0
$191$	−2024.38	−0.766907	−0.383453	−	0.923560i	$-0.625265\pi$
$191$	−2024.38	−0.766907	−0.383453	+	0.923560i	$0.625265\pi$
$192$	−7185.26	−2.70079
$193$	−2645.53	−0.986680	−0.493340	−	0.869836i	$-0.664224\pi$
$193$	−2645.53	−0.986680	−0.493340	+	0.869836i	$0.664224\pi$
$194$	−7189.64	−2.66075
$195$	0	0
$196$	3896.33	1.41995
$197$	−4172.00	−1.50885	−0.754424	−	0.656388i	$-0.772084\pi$
$197$	−4172.00	−1.50885	−0.754424	+	0.656388i	$0.772084\pi$
$198$	547.140	0.196382
$199$	−1439.79	−0.512884	−0.256442	−	0.966560i	$-0.582550\pi$
$199$	−1439.79	−0.512884	−0.256442	+	0.966560i	$0.582550\pi$
$200$	0	0
$201$	−486.572	−0.170747
$202$	−2543.51	−0.885944
$203$	−5530.64	−1.91219
$204$	−6981.08	−2.39595
$205$	0	0
$206$	1368.39	0.462817
$207$	708.934	0.238040
$208$	−6829.62	−2.27668
$209$	1007.57	0.333470
$210$	0	0
$211$	3283.75	1.07139	0.535694	−	0.844412i	$-0.320050\pi$
$211$	3283.75	1.07139	0.535694	+	0.844412i	$0.320050\pi$
$212$	4096.51	1.32712
$213$	−980.116	−0.315288
$214$	4454.01	1.42275
$215$	0	0
$216$	2170.26	0.683646
$217$	4023.47	1.25867
$218$	4531.63	1.40789
$219$	−2184.38	−0.674003
$220$	0	0
$221$	−2671.51	−0.813146
$222$	1189.73	0.359683
$223$	500.566	0.150316	0.0751578	−	0.997172i	$-0.476054\pi$
$223$	500.566	0.150316	0.0751578	+	0.997172i	$0.476054\pi$
$224$	18518.1	5.52361
$225$	0	0
$226$	517.051	0.152185
$227$	2617.76	0.765406	0.382703	−	0.923872i	$-0.374993\pi$
$227$	2617.76	0.765406	0.382703	+	0.923872i	$0.374993\pi$
$228$	6194.93	1.79943
$229$	−1700.58	−0.490732	−0.245366	−	0.969430i	$-0.578908\pi$
$229$	−1700.58	−0.490732	−0.245366	+	0.969430i	$0.578908\pi$
$230$	0	0
$231$	−749.494	−0.213476
$232$	−19573.6	−5.53908
$233$	−269.221	−0.0756965	−0.0378482	−	0.999283i	$-0.512050\pi$
$233$	−269.221	−0.0756965	−0.0378482	+	0.999283i	$0.512050\pi$
$234$	1287.34	0.359641
$235$	0	0
$236$	14049.1	3.87509
$237$	−785.828	−0.215380
$238$	12956.5	3.52875
$239$	−4919.00	−1.33131	−0.665656	−	0.746258i	$-0.731848\pi$
$239$	−4919.00	−1.33131	−0.665656	+	0.746258i	$0.731848\pi$
$240$	0	0
$241$	−1461.81	−0.390721	−0.195360	−	0.980732i	$-0.562588\pi$
$241$	−1461.81	−0.390721	−0.195360	+	0.980732i	$0.562588\pi$
$242$	−668.727	−0.177634
$243$	−243.000	−0.0641500
$244$	−1960.92	−0.514488
$245$	0	0
$246$	−5328.01	−1.38090
$247$	2370.67	0.610696
$248$	14239.5	3.64601
$249$	3929.85	1.00018
$250$	0	0
$251$	−675.343	−0.169830	−0.0849149	−	0.996388i	$-0.527062\pi$
$251$	−675.343	−0.169830	−0.0849149	+	0.996388i	$0.527062\pi$
$252$	−4608.17	−1.15193
$253$	−866.475	−0.215315
$254$	2203.71	0.544382
$255$	0	0
$256$	17945.8	4.38130
$257$	−919.202	−0.223106	−0.111553	−	0.993758i	$-0.535582\pi$
$257$	−919.202	−0.223106	−0.111553	+	0.993758i	$0.535582\pi$
$258$	1068.77	0.257903
$259$	−1629.74	−0.390993
$260$	0	0
$261$	2191.61	0.519761
$262$	9485.35	2.23667
$263$	−4.19206	−0.000982864 0	−0.000491432	−	1.00000i	$-0.500156\pi$
$263$	−4.19206	−0.000982864 0	−0.000491432		1.00000i	$0.500156\pi$
$264$	−2652.54	−0.618381
$265$	0	0
$266$	−11497.4	−2.65020
$267$	−3670.79	−0.841380
$268$	3656.43	0.833404
$269$	−780.938	−0.177006	−0.0885030	−	0.996076i	$-0.528208\pi$
$269$	−780.938	−0.177006	−0.0885030	+	0.996076i	$0.528208\pi$
$270$	0	0
$271$	140.696	0.0315375	0.0157688	−	0.999876i	$-0.494980\pi$
$271$	140.696	0.0315375	0.0157688	+	0.999876i	$0.494980\pi$
$272$	27238.2	6.07191
$273$	−1763.45	−0.390948
$274$	12190.4	2.68778
$275$	0	0
$276$	−5327.41	−1.16186
$277$	−5498.79	−1.19274	−0.596372	−	0.802708i	$-0.703392\pi$
$277$	−5498.79	−1.19274	−0.596372	+	0.802708i	$0.703392\pi$
$278$	4488.51	0.968356
$279$	−1594.37	−0.342123
$280$	0	0
$281$	−8998.47	−1.91033	−0.955166	−	0.296069i	$-0.904324\pi$
$281$	−8998.47	−1.91033	−0.955166	+	0.296069i	$0.904324\pi$
$282$	1271.92	0.268588
$283$	−2401.12	−0.504353	−0.252177	−	0.967681i	$-0.581146\pi$
$283$	−2401.12	−0.504353	−0.252177	+	0.967681i	$0.581146\pi$
$284$	7365.26	1.53890
$285$	0	0
$286$	−1573.42	−0.325308
$287$	7298.51	1.50111
$288$	−7338.10	−1.50139
$289$	5741.65	1.16866
$290$	0	0
$291$	−3902.70	−0.786186
$292$	16414.9	3.28976
$293$	−436.888	−0.0871101	−0.0435550	−	0.999051i	$-0.513868\pi$
$293$	−436.888	−0.0871101	−0.0435550	+	0.999051i	$0.513868\pi$
$294$	2865.55	0.568444
$295$	0	0
$296$	−5767.84	−1.13260
$297$	297.000	0.0580259
$298$	−17263.0	−3.35576
$299$	−2038.69	−0.394316
$300$	0	0
$301$	−1464.05	−0.280353
$302$	12833.4	2.44529
$303$	−1380.68	−0.261775
$304$	−24170.9	−4.56018
$305$	0	0
$306$	−5134.23	−0.959165
$307$	−4525.10	−0.841241	−0.420620	−	0.907237i	$-0.638188\pi$
$307$	−4525.10	−0.841241	−0.420620	+	0.907237i	$0.638188\pi$
$308$	5632.21	1.04196
$309$	742.793	0.136751
$310$	0	0
$311$	4072.50	0.742541	0.371270	−	0.928525i	$-0.378922\pi$
$311$	4072.50	0.742541	0.371270	+	0.928525i	$0.378922\pi$
$312$	−6241.04	−1.13247
$313$	−6956.74	−1.25629	−0.628144	−	0.778097i	$-0.716185\pi$
$313$	−6956.74	−1.25629	−0.628144	+	0.778097i	$0.716185\pi$
$314$	6567.48	1.18033
$315$	0	0
$316$	5905.25	1.05125
$317$	3469.83	0.614779	0.307390	−	0.951584i	$-0.400545\pi$
$317$	3469.83	0.614779	0.307390	+	0.951584i	$0.400545\pi$
$318$	3012.77	0.531283
$319$	−2678.64	−0.470141
$320$	0	0
$321$	2417.74	0.420389
$322$	9887.37	1.71118
$323$	−9454.81	−1.62873
$324$	1826.07	0.313112
$325$	0	0
$326$	−7588.91	−1.28930
$327$	2459.87	0.415998
$328$	25830.3	4.34828
$329$	−1742.33	−0.291969
$330$	0	0
$331$	−6125.51	−1.01719	−0.508593	−	0.861007i	$-0.669834\pi$
$331$	−6125.51	−1.01719	−0.508593	+	0.861007i	$0.669834\pi$
$332$	−29531.6	−4.88180
$333$	645.814	0.106277
$334$	−11046.4	−1.80968
$335$	0	0
$336$	17979.8	2.91928
$337$	−393.612	−0.0636244	−0.0318122	−	0.999494i	$-0.510128\pi$
$337$	−393.612	−0.0636244	−0.0318122	+	0.999494i	$0.510128\pi$
$338$	8440.07	1.35822
$339$	280.667	0.0449668
$340$	0	0
$341$	1948.67	0.309462
$342$	4556.05	0.720360
$343$	3864.85	0.608403
$344$	−5181.43	−0.812105
$345$	0	0
$346$	−19540.2	−3.03608
$347$	−11157.7	−1.72616	−0.863081	−	0.505066i	$-0.831468\pi$
$347$	−11157.7	−1.72616	−0.863081	+	0.505066i	$0.831468\pi$
$348$	−16469.3	−2.53691
$349$	10724.4	1.64488	0.822442	−	0.568849i	$-0.192611\pi$
$349$	10724.4	1.64488	0.822442	+	0.568849i	$0.192611\pi$
$350$	0	0
$351$	698.797	0.106265
$352$	8968.79	1.35806
$353$	−11941.0	−1.80044	−0.900221	−	0.435434i	$-0.856595\pi$
$353$	−11941.0	−1.80044	−0.900221	+	0.435434i	$0.856595\pi$
$354$	10332.4	1.55130
$355$	0	0
$356$	27584.8	4.10672
$357$	7033.07	1.04266
$358$	−6017.55	−0.888373
$359$	−6203.49	−0.912000	−0.456000	−	0.889980i	$-0.650718\pi$
$359$	−6203.49	−0.912000	−0.456000	+	0.889980i	$0.650718\pi$
$360$	0	0
$361$	1531.08	0.223222
$362$	8169.65	1.18615
$363$	−363.000	−0.0524864
$364$	13251.8	1.90819
$365$	0	0
$366$	−1442.16	−0.205964
$367$	−8213.93	−1.16829	−0.584147	−	0.811648i	$-0.698571\pi$
$367$	−8213.93	−1.16829	−0.584147	+	0.811648i	$0.698571\pi$
$368$	20786.1	2.94443
$369$	−2892.16	−0.408022
$370$	0	0
$371$	−4127.01	−0.577531
$372$	11981.2	1.66988
$373$	9943.74	1.38034	0.690171	−	0.723647i	$-0.257535\pi$
$373$	9943.74	1.38034	0.690171	+	0.723647i	$0.257535\pi$
$374$	6275.17	0.867597
$375$	0	0
$376$	−6166.30	−0.845752
$377$	−6302.44	−0.860988
$378$	−3389.07	−0.461151
$379$	157.475	0.0213429	0.0106715	−	0.999943i	$-0.496603\pi$
$379$	157.475	0.0213429	0.0106715	+	0.999943i	$0.496603\pi$
$380$	0	0
$381$	1196.22	0.160852
$382$	11188.1	1.49851
$383$	−1458.87	−0.194634	−0.0973170	−	0.995253i	$-0.531026\pi$
$383$	−1458.87	−0.194634	−0.0973170	+	0.995253i	$0.531026\pi$
$384$	20142.2	2.67677
$385$	0	0
$386$	14621.0	1.92795
$387$	580.155	0.0762040
$388$	29327.5	3.83732
$389$	−10673.1	−1.39112	−0.695561	−	0.718467i	$-0.744844\pi$
$389$	−10673.1	−1.39112	−0.695561	+	0.718467i	$0.744844\pi$
$390$	0	0
$391$	8130.79	1.05164
$392$	−13892.2	−1.78996
$393$	5148.86	0.660880
$394$	23057.3	2.94825
$395$	0	0
$396$	−2231.86	−0.283220
$397$	−11133.2	−1.40746	−0.703729	−	0.710469i	$-0.748483\pi$
$397$	−11133.2	−1.40746	−0.703729	+	0.710469i	$0.748483\pi$
$398$	7957.24	1.00216
$399$	−6241.06	−0.783067
$400$	0	0
$401$	−4774.47	−0.594578	−0.297289	−	0.954788i	$-0.596082\pi$
$401$	−4774.47	−0.594578	−0.297289	+	0.954788i	$0.596082\pi$
$402$	2689.12	0.333635
$403$	4584.94	0.566730
$404$	10375.3	1.27770
$405$	0	0
$406$	30566.0	3.73637
$407$	−789.328	−0.0961316
$408$	24890.8	3.02029
$409$	10071.6	1.21762	0.608811	−	0.793315i	$-0.291647\pi$
$409$	10071.6	1.21762	0.608811	+	0.793315i	$0.291647\pi$
$410$	0	0
$411$	6617.25	0.794172
$412$	−5581.86	−0.667472
$413$	−14153.8	−1.68635
$414$	−3918.04	−0.465124
$415$	0	0
$416$	21102.2	2.48707
$417$	2436.46	0.286125
$418$	−5568.51	−0.651590
$419$	9562.75	1.11497	0.557483	−	0.830188i	$-0.311767\pi$
$419$	9562.75	1.11497	0.557483	+	0.830188i	$0.311767\pi$
$420$	0	0
$421$	−5260.86	−0.609022	−0.304511	−	0.952509i	$-0.598493\pi$
$421$	−5260.86	−0.609022	−0.304511	+	0.952509i	$0.598493\pi$
$422$	−18148.2	−2.09346
$423$	690.429	0.0793612
$424$	−14606.0	−1.67294
$425$	0	0
$426$	5416.77	0.616065
$427$	1975.52	0.223893
$428$	−18168.5	−2.05189
$429$	−854.086	−0.0961204
$430$	0	0
$431$	−8124.33	−0.907971	−0.453985	−	0.891009i	$-0.649998\pi$
$431$	−8124.33	−0.907971	−0.453985	+	0.891009i	$0.649998\pi$
$432$	−7124.80	−0.793500
$433$	13122.3	1.45639	0.728194	−	0.685371i	$-0.240360\pi$
$433$	13122.3	1.45639	0.728194	+	0.685371i	$0.240360\pi$
$434$	−22236.4	−2.45940
$435$	0	0
$436$	−18485.2	−2.03046
$437$	−7215.17	−0.789813
$438$	12072.3	1.31698
$439$	−12317.7	−1.33916	−0.669579	−	0.742741i	$-0.733526\pi$
$439$	−12317.7	−1.33916	−0.669579	+	0.742741i	$0.733526\pi$
$440$	0	0
$441$	1555.49	0.167961
$442$	14764.6	1.58886
$443$	−17206.2	−1.84535	−0.922674	−	0.385582i	$-0.874001\pi$
$443$	−17206.2	−1.84535	−0.922674	+	0.385582i	$0.874001\pi$
$444$	−4853.09	−0.518733
$445$	0	0
$446$	−2766.46	−0.293712
$447$	−9370.74	−0.991545
$448$	−54397.0	−5.73665
$449$	477.868	0.0502271	0.0251136	−	0.999685i	$-0.492005\pi$
$449$	477.868	0.0502271	0.0251136	+	0.999685i	$0.492005\pi$
$450$	0	0
$451$	3534.87	0.369069
$452$	−2109.12	−0.219480
$453$	6966.26	0.722524
$454$	−14467.5	−1.49558
$455$	0	0
$456$	−22087.8	−2.26833
$457$	−1386.92	−0.141963	−0.0709816	−	0.997478i	$-0.522613\pi$
$457$	−1386.92	−0.141963	−0.0709816	+	0.997478i	$0.522613\pi$
$458$	9398.56	0.958877
$459$	−2786.98	−0.283409
$460$	0	0
$461$	12143.7	1.22688	0.613439	−	0.789742i	$-0.289786\pi$
$461$	12143.7	1.22688	0.613439	+	0.789742i	$0.289786\pi$
$462$	4142.20	0.417127
$463$	−13979.7	−1.40322	−0.701612	−	0.712559i	$-0.747536\pi$
$463$	−13979.7	−1.40322	−0.701612	+	0.712559i	$0.747536\pi$
$464$	64258.5	6.42915
$465$	0	0
$466$	1487.90	0.147909
$467$	17218.5	1.70616	0.853082	−	0.521777i	$-0.174731\pi$
$467$	17218.5	1.70616	0.853082	+	0.521777i	$0.174731\pi$
$468$	−5251.24	−0.518672
$469$	−3683.67	−0.362678
$470$	0	0
$471$	3564.98	0.348759
$472$	−50091.7	−4.88487
$473$	−709.078	−0.0689291
$474$	4343.01	0.420846
$475$	0	0
$476$	−52851.3	−5.08915
$477$	1635.40	0.156981
$478$	27185.7	2.60135
$479$	−4584.03	−0.437264	−0.218632	−	0.975807i	$-0.570159\pi$
$479$	−4584.03	−0.437264	−0.218632	+	0.975807i	$0.570159\pi$
$480$	0	0
$481$	−1857.17	−0.176049
$482$	8078.96	0.763457
$483$	5367.09	0.505613
$484$	2727.83	0.256182
$485$	0	0
$486$	1342.98	0.125347
$487$	11313.4	1.05269	0.526345	−	0.850271i	$-0.323562\pi$
$487$	11313.4	1.05269	0.526345	+	0.850271i	$0.323562\pi$
$488$	6991.60	0.648555
$489$	−4119.43	−0.380955
$490$	0	0
$491$	11275.3	1.03634	0.518172	−	0.855276i	$-0.326613\pi$
$491$	11275.3	1.03634	0.518172	+	0.855276i	$0.326613\pi$
$492$	21733.7	1.99152
$493$	25135.7	2.29626
$494$	−13101.9	−1.19328
$495$	0	0
$496$	−46747.2	−4.23188
$497$	−7420.11	−0.669693
$498$	−21719.0	−1.95432
$499$	12723.2	1.14142	0.570711	−	0.821151i	$-0.306668\pi$
$499$	12723.2	1.14142	0.570711	+	0.821151i	$0.306668\pi$
$500$	0	0
$501$	−5996.24	−0.534715
$502$	3732.40	0.331843
$503$	−6292.26	−0.557770	−0.278885	−	0.960325i	$-0.589965\pi$
$503$	−6292.26	−0.557770	−0.278885	+	0.960325i	$0.589965\pi$
$504$	16430.3	1.45211
$505$	0	0
$506$	4788.72	0.420720
$507$	4581.46	0.401321
$508$	−8989.24	−0.785105
$509$	10774.4	0.938243	0.469121	−	0.883134i	$-0.344571\pi$
$509$	10774.4	0.938243	0.469121	+	0.883134i	$0.344571\pi$
$510$	0	0
$511$	−16537.2	−1.43163
$512$	−45467.8	−3.92464
$513$	2473.13	0.212849
$514$	5080.12	0.435943
$515$	0	0
$516$	−4359.68	−0.371946
$517$	−843.858	−0.0717849
$518$	9007.04	0.763990
$519$	−10606.8	−0.897088
$520$	0	0
$521$	19639.0	1.65144	0.825720	−	0.564081i	$-0.190769\pi$
$521$	19639.0	1.65144	0.825720	+	0.564081i	$0.190769\pi$
$522$	−12112.3	−1.01560
$523$	10687.7	0.893573	0.446787	−	0.894641i	$-0.352568\pi$
$523$	10687.7	0.893573	0.446787	+	0.894641i	$0.352568\pi$
$524$	−38692.1	−3.22571
$525$	0	0
$526$	23.1681	0.00192049
$527$	−18285.9	−1.51147
$528$	8708.09	0.717748
$529$	−5962.22	−0.490032
$530$	0	0
$531$	5608.67	0.458372
$532$	46899.6	3.82210
$533$	8317.02	0.675891
$534$	20287.2	1.64403
$535$	0	0
$536$	−13036.9	−1.05058
$537$	−3266.46	−0.262492
$538$	4315.98	0.345865
$539$	−1901.15	−0.151926
$540$	0	0
$541$	−16445.8	−1.30695	−0.653474	−	0.756949i	$-0.726689\pi$
$541$	−16445.8	−1.30695	−0.653474	+	0.756949i	$0.726689\pi$
$542$	−777.579	−0.0616234
$543$	4434.67	0.350479
$544$	−84161.0	−6.63304
$545$	0	0
$546$	9745.99	0.763901
$547$	−12260.5	−0.958358	−0.479179	−	0.877717i	$-0.659065\pi$
$547$	−12260.5	−0.958358	−0.479179	+	0.877717i	$0.659065\pi$
$548$	−49726.5	−3.87630
$549$	−782.836	−0.0608572
$550$	0	0
$551$	−22305.1	−1.72456
$552$	18994.7	1.46462
$553$	−5949.22	−0.457480
$554$	30390.0	2.33059
$555$	0	0
$556$	−18309.3	−1.39656
$557$	−1323.07	−0.100647	−0.0503233	−	0.998733i	$-0.516025\pi$
$557$	−1323.07	−0.100647	−0.0503233	+	0.998733i	$0.516025\pi$
$558$	8811.55	0.668499
$559$	−1668.36	−0.126233
$560$	0	0
$561$	3406.30	0.256353
$562$	49731.5	3.73274
$563$	9015.48	0.674880	0.337440	−	0.941347i	$-0.390439\pi$
$563$	9015.48	0.674880	0.337440	+	0.941347i	$0.390439\pi$
$564$	−5188.35	−0.387356
$565$	0	0
$566$	13270.2	0.985492
$567$	−1839.67	−0.136259
$568$	−26260.6	−1.93991
$569$	−4443.29	−0.327368	−0.163684	−	0.986513i	$-0.552338\pi$
$569$	−4443.29	−0.327368	−0.163684	+	0.986513i	$0.552338\pi$
$570$	0	0
$571$	465.028	0.0340820	0.0170410	−	0.999855i	$-0.494575\pi$
$571$	465.028	0.0340820	0.0170410	+	0.999855i	$0.494575\pi$
$572$	6418.18	0.469157
$573$	6073.15	0.442774
$574$	−40336.4	−2.93312
$575$	0	0
$576$	21555.8	1.55930
$577$	5973.81	0.431010	0.215505	−	0.976503i	$-0.430860\pi$
$577$	5973.81	0.431010	0.215505	+	0.976503i	$0.430860\pi$
$578$	−31732.2	−2.28354
$579$	7936.59	0.569660
$580$	0	0
$581$	29751.5	2.12444
$582$	21568.9	1.53619
$583$	−1998.82	−0.141995
$584$	−58526.9	−4.14702
$585$	0	0
$586$	2414.53	0.170211
$587$	−11025.2	−0.775228	−0.387614	−	0.921822i	$-0.626701\pi$
$587$	−11025.2	−0.775228	−0.387614	+	0.921822i	$0.626701\pi$
$588$	−11689.0	−0.819806
$589$	16226.7	1.13516
$590$	0	0
$591$	12516.0	0.871134
$592$	18935.4	1.31459
$593$	25114.5	1.73917	0.869586	−	0.493781i	$-0.164386\pi$
$593$	25114.5	1.73917	0.869586	+	0.493781i	$0.164386\pi$
$594$	−1641.42	−0.113381
$595$	0	0
$596$	70418.1	4.83966
$597$	4319.37	0.296114
$598$	11267.2	0.770482
$599$	25219.1	1.72024	0.860121	−	0.510091i	$-0.170388\pi$
$599$	25219.1	1.72024	0.860121	+	0.510091i	$0.170388\pi$
$600$	0	0
$601$	7581.22	0.514550	0.257275	−	0.966338i	$-0.417175\pi$
$601$	7581.22	0.514550	0.257275	+	0.966338i	$0.417175\pi$
$602$	8091.31	0.547803
$603$	1459.72	0.0985809
$604$	−52349.2	−3.52659
$605$	0	0
$606$	7630.53	0.511500
$607$	−9575.56	−0.640297	−0.320148	−	0.947367i	$-0.603733\pi$
$607$	−9575.56	−0.640297	−0.320148	+	0.947367i	$0.603733\pi$
$608$	74683.4	4.98160
$609$	16591.9	1.10400
$610$	0	0
$611$	−1985.47	−0.131463
$612$	20943.2	1.38330
$613$	−18041.1	−1.18870	−0.594349	−	0.804207i	$-0.702590\pi$
$613$	−18041.1	−1.18870	−0.594349	+	0.804207i	$0.702590\pi$
$614$	25008.7	1.64376
$615$	0	0
$616$	−20081.5	−1.31348
$617$	−11684.9	−0.762427	−0.381214	−	0.924487i	$-0.624494\pi$
$617$	−11684.9	−0.762427	−0.381214	+	0.924487i	$0.624494\pi$
$618$	−4105.17	−0.267207
$619$	−6501.70	−0.422174	−0.211087	−	0.977467i	$-0.567700\pi$
$619$	−6501.70	−0.422174	−0.211087	+	0.977467i	$0.567700\pi$
$620$	0	0
$621$	−2126.80	−0.137433
$622$	−22507.3	−1.45090
$623$	−27790.2	−1.78715
$624$	20488.9	1.31444
$625$	0	0
$626$	38447.6	2.45475
$627$	−3022.71	−0.192529
$628$	−26789.7	−1.70227
$629$	7406.87	0.469525
$630$	0	0
$631$	16323.9	1.02986	0.514931	−	0.857232i	$-0.327818\pi$
$631$	16323.9	1.02986	0.514931	+	0.857232i	$0.327818\pi$
$632$	−21055.0	−1.32519
$633$	−9851.26	−0.618566
$634$	−19176.6	−1.20126
$635$	0	0
$636$	−12289.5	−0.766213
$637$	−4473.13	−0.278229
$638$	14803.9	0.918642
$639$	2940.35	0.182032
$640$	0	0
$641$	−5751.02	−0.354370	−0.177185	−	0.984178i	$-0.556699\pi$
$641$	−5751.02	−0.354370	−0.177185	+	0.984178i	$0.556699\pi$
$642$	−13362.0	−0.821428
$643$	−9790.94	−0.600493	−0.300247	−	0.953862i	$-0.597069\pi$
$643$	−9790.94	−0.600493	−0.300247	+	0.953862i	$0.597069\pi$
$644$	−40332.0	−2.46786
$645$	0	0
$646$	52253.6	3.18249
$647$	15216.4	0.924601	0.462300	−	0.886723i	$-0.347024\pi$
$647$	15216.4	0.924601	0.462300	+	0.886723i	$0.347024\pi$
$648$	−6510.79	−0.394703
$649$	−6855.04	−0.414613
$650$	0	0
$651$	−12070.4	−0.726692
$652$	30956.2	1.85942
$653$	−3813.10	−0.228512	−0.114256	−	0.993451i	$-0.536448\pi$
$653$	−3813.10	−0.228512	−0.114256	+	0.993451i	$0.536448\pi$
$654$	−13594.9	−0.812848
$655$	0	0
$656$	−84798.7	−5.04700
$657$	6553.14	0.389136
$658$	9629.28	0.570499
$659$	4906.77	0.290046	0.145023	−	0.989428i	$-0.453674\pi$
$659$	4906.77	0.290046	0.145023	+	0.989428i	$0.453674\pi$
$660$	0	0
$661$	−14073.3	−0.828121	−0.414061	−	0.910249i	$-0.635890\pi$
$661$	−14073.3	−0.828121	−0.414061	+	0.910249i	$0.635890\pi$
$662$	33853.6	1.98755
$663$	8014.53	0.469470
$664$	105294.	6.15391
$665$	0	0
$666$	−3569.20	−0.207663
$667$	19181.6	1.11352
$668$	45059.8	2.60991
$669$	−1501.70	−0.0867847
$670$	0	0
$671$	956.800	0.0550475
$672$	−55554.2	−3.18906
$673$	−22075.7	−1.26442	−0.632211	−	0.774797i	$-0.717852\pi$
$673$	−22075.7	−1.26442	−0.632211	+	0.774797i	$0.717852\pi$
$674$	2175.36	0.124320
$675$	0	0
$676$	−34428.2	−1.95882
$677$	915.678	0.0519828	0.0259914	−	0.999662i	$-0.491726\pi$
$677$	915.678	0.0519828	0.0259914	+	0.999662i	$0.491726\pi$
$678$	−1551.15	−0.0878639
$679$	−29545.9	−1.66991
$680$	0	0
$681$	−7853.29	−0.441907
$682$	−10769.7	−0.604680
$683$	13167.9	0.737712	0.368856	−	0.929487i	$-0.379750\pi$
$683$	13167.9	0.737712	0.368856	+	0.929487i	$0.379750\pi$
$684$	−18584.8	−1.03890
$685$	0	0
$686$	−21359.7	−1.18880
$687$	5101.75	0.283325
$688$	17010.2	0.942601
$689$	−4702.94	−0.260040
$690$	0	0
$691$	−10122.2	−0.557261	−0.278631	−	0.960398i	$-0.589881\pi$
$691$	−10122.2	−0.557261	−0.278631	+	0.960398i	$0.589881\pi$
$692$	79707.0	4.37862
$693$	2248.48	0.123251
$694$	61665.0	3.37287
$695$	0	0
$696$	58720.7	3.19799
$697$	−33170.3	−1.80261
$698$	−59270.3	−3.21406
$699$	807.664	0.0437034
$700$	0	0
$701$	−24245.5	−1.30633	−0.653166	−	0.757215i	$-0.726560\pi$
$701$	−24245.5	−1.30633	−0.653166	+	0.757215i	$0.726560\pi$
$702$	−3862.02	−0.207639
$703$	−6572.76	−0.352627
$704$	−26345.9	−1.41044
$705$	0	0
$706$	65994.0	3.51801
$707$	−10452.6	−0.556026
$708$	−42147.4	−2.23728
$709$	−11430.7	−0.605484	−0.302742	−	0.953073i	$-0.597902\pi$
$709$	−11430.7	−0.605484	−0.302742	+	0.953073i	$0.597902\pi$
$710$	0	0
$711$	2357.48	0.124350
$712$	−98352.7	−5.17686
$713$	−13954.4	−0.732952
$714$	−38869.4	−2.03733
$715$	0	0
$716$	24546.4	1.28121
$717$	14757.0	0.768634
$718$	34284.6	1.78202
$719$	−21262.0	−1.10284	−0.551418	−	0.834229i	$-0.685913\pi$
$719$	−21262.0	−1.10284	−0.551418	+	0.834229i	$0.685913\pi$
$720$	0	0
$721$	5623.42	0.290468
$722$	−8461.78	−0.436170
$723$	4385.44	0.225583
$724$	−33325.1	−1.71066
$725$	0	0
$726$	2006.18	0.102557
$727$	23601.1	1.20401	0.602005	−	0.798492i	$-0.294369\pi$
$727$	23601.1	1.20401	0.602005	+	0.798492i	$0.294369\pi$
$728$	−47248.7	−2.40543
$729$	729.000	0.0370370
$730$	0	0
$731$	6653.82	0.336663
$732$	5882.76	0.297040
$733$	26625.6	1.34167	0.670833	−	0.741609i	$-0.265937\pi$
$733$	26625.6	1.34167	0.670833	+	0.741609i	$0.265937\pi$
$734$	45395.7	2.28281
$735$	0	0
$736$	−64225.1	−3.21653
$737$	−1784.10	−0.0891697
$738$	15984.0	0.797263
$739$	21193.4	1.05496	0.527478	−	0.849568i	$-0.323138\pi$
$739$	21193.4	1.05496	0.527478	+	0.849568i	$0.323138\pi$
$740$	0	0
$741$	−7112.00	−0.352586
$742$	22808.6	1.12848
$743$	−7823.72	−0.386305	−0.193152	−	0.981169i	$-0.561871\pi$
$743$	−7823.72	−0.386305	−0.193152	+	0.981169i	$0.561871\pi$
$744$	−42718.5	−2.10502
$745$	0	0
$746$	−54955.7	−2.69715
$747$	−11789.6	−0.577453
$748$	−25597.3	−1.25124
$749$	18303.8	0.892933
$750$	0	0
$751$	−12583.0	−0.611400	−0.305700	−	0.952128i	$-0.598890\pi$
$751$	−12583.0	−0.611400	−0.305700	+	0.952128i	$0.598890\pi$
$752$	20243.5	0.981655
$753$	2026.03	0.0980513
$754$	34831.5	1.68235
$755$	0	0
$756$	13824.5	0.665069
$757$	6361.62	0.305439	0.152719	−	0.988270i	$-0.451197\pi$
$757$	6361.62	0.305439	0.152719	+	0.988270i	$0.451197\pi$
$758$	−870.313	−0.0417034
$759$	2599.42	0.124312
$760$	0	0
$761$	27923.1	1.33011	0.665053	−	0.746796i	$-0.268409\pi$
$761$	27923.1	1.33011	0.665053	+	0.746796i	$0.268409\pi$
$762$	−6611.13	−0.314299
$763$	18622.8	0.883606
$764$	−45637.8	−2.16115
$765$	0	0
$766$	8062.69	0.380309
$767$	−16128.9	−0.759297
$768$	−53837.4	−2.52954
$769$	32729.8	1.53481	0.767404	−	0.641164i	$-0.221548\pi$
$769$	32729.8	1.53481	0.767404	+	0.641164i	$0.221548\pi$
$770$	0	0
$771$	2757.61	0.128810
$772$	−59640.9	−2.78047
$773$	−27519.7	−1.28049	−0.640243	−	0.768173i	$-0.721166\pi$
$773$	−27519.7	−1.28049	−0.640243	+	0.768173i	$0.721166\pi$
$774$	−3206.32	−0.148900
$775$	0	0
$776$	−104566.	−4.83726
$777$	4889.23	0.225740
$778$	58986.5	2.71821
$779$	29435.0	1.35381
$780$	0	0
$781$	−3593.76	−0.164654
$782$	−44936.2	−2.05488
$783$	−6574.84	−0.300084
$784$	45607.1	2.07758
$785$	0	0
$786$	−28456.0	−1.29134
$787$	15918.4	0.721005	0.360503	−	0.932758i	$-0.382605\pi$
$787$	15918.4	0.721005	0.360503	+	0.932758i	$0.382605\pi$
$788$	−94053.8	−4.25194
$789$	12.5762	0.000567457 0
$790$	0	0
$791$	2124.83	0.0955124
$792$	7957.63	0.357023
$793$	2251.21	0.100811
$794$	61529.6	2.75013
$795$	0	0
$796$	−32458.7	−1.44531
$797$	−22354.3	−0.993514	−0.496757	−	0.867890i	$-0.665476\pi$
$797$	−22354.3	−0.993514	−0.496757	+	0.867890i	$0.665476\pi$
$798$	34492.3	1.53009
$799$	7918.56	0.350611
$800$	0	0
$801$	11012.4	0.485771
$802$	26386.9	1.16179
$803$	−8009.39	−0.351987
$804$	−10969.3	−0.481166
$805$	0	0
$806$	−25339.5	−1.10737
$807$	2342.81	0.102194
$808$	−36992.9	−1.61065
$809$	−10807.7	−0.469687	−0.234844	−	0.972033i	$-0.575458\pi$
$809$	−10807.7	−0.469687	−0.234844	+	0.972033i	$0.575458\pi$
$810$	0	0
$811$	28002.3	1.21245	0.606224	−	0.795294i	$-0.292684\pi$
$811$	28002.3	1.21245	0.606224	+	0.795294i	$0.292684\pi$
$812$	−124683.	−5.38857
$813$	−422.088	−0.0182082
$814$	4362.35	0.187838
$815$	0	0
$816$	−81714.6	−3.50562
$817$	−5904.52	−0.252843
$818$	−55662.2	−2.37920
$819$	5290.35	0.225714
$820$	0	0
$821$	22914.0	0.974062	0.487031	−	0.873385i	$-0.338080\pi$
$821$	22914.0	0.974062	0.487031	+	0.873385i	$0.338080\pi$
$822$	−36571.3	−1.55179
$823$	−41418.7	−1.75427	−0.877137	−	0.480241i	$-0.840549\pi$
$823$	−41418.7	−1.75427	−0.877137	+	0.480241i	$0.840549\pi$
$824$	19901.9	0.841404
$825$	0	0
$826$	78223.1	3.29507
$827$	−32040.6	−1.34723	−0.673616	−	0.739081i	$-0.735260\pi$
$827$	−32040.6	−1.34723	−0.673616	+	0.739081i	$0.735260\pi$
$828$	15982.2	0.670799
$829$	−30398.3	−1.27355	−0.636777	−	0.771048i	$-0.719733\pi$
$829$	−30398.3	−1.27355	−0.636777	+	0.771048i	$0.719733\pi$
$830$	0	0
$831$	16496.4	0.688631
$832$	−61988.1	−2.58299
$833$	17839.9	0.742038
$834$	−13465.5	−0.559080
$835$	0	0
$836$	22714.7	0.939719
$837$	4783.11	0.197525
$838$	−52850.1	−2.17861
$839$	1882.20	0.0774503	0.0387252	−	0.999250i	$-0.487670\pi$
$839$	1882.20	0.0774503	0.0387252	+	0.999250i	$0.487670\pi$
$840$	0	0
$841$	34909.4	1.43136
$842$	29075.0	1.19001
$843$	26995.4	1.10293
$844$	74029.1	3.01918
$845$	0	0
$846$	−3815.77	−0.155070
$847$	−2748.14	−0.111484
$848$	47950.3	1.94177
$849$	7203.37	0.291189
$850$	0	0
$851$	5652.34	0.227685
$852$	−22095.8	−0.888484
$853$	55.3222	0.00222063	0.00111031	−	0.999999i	$-0.499647\pi$
$853$	55.3222	0.00222063	0.00111031	+	0.999999i	$0.499647\pi$
$854$	−10918.1	−0.437481
$855$	0	0
$856$	64779.3	2.58658
$857$	−14804.2	−0.590084	−0.295042	−	0.955484i	$-0.595334\pi$
$857$	−14804.2	−0.590084	−0.295042	+	0.955484i	$0.595334\pi$
$858$	4720.25	0.187817
$859$	−27076.1	−1.07546	−0.537732	−	0.843116i	$-0.680719\pi$
$859$	−27076.1	−1.07546	−0.537732	+	0.843116i	$0.680719\pi$
$860$	0	0
$861$	−21895.5	−0.866664
$862$	44900.5	1.77415
$863$	−19420.1	−0.766012	−0.383006	−	0.923746i	$-0.625111\pi$
$863$	−19420.1	−0.766012	−0.383006	+	0.923746i	$0.625111\pi$
$864$	22014.3	0.866831
$865$	0	0
$866$	−72522.4	−2.84574
$867$	−17224.9	−0.674729
$868$	90705.2	3.54693
$869$	−2881.37	−0.112478
$870$	0	0
$871$	−4197.72	−0.163300
$872$	65908.3	2.55956
$873$	11708.1	0.453905
$874$	39875.8	1.54327
$875$	0	0
$876$	−49244.8	−1.89934
$877$	11594.4	0.446424	0.223212	−	0.974770i	$-0.428346\pi$
$877$	11594.4	0.446424	0.223212	+	0.974770i	$0.428346\pi$
$878$	68075.7	2.61668
$879$	1310.66	0.0502930
$880$	0	0
$881$	37326.6	1.42743	0.713715	−	0.700436i	$-0.247011\pi$
$881$	37326.6	1.42743	0.713715	+	0.700436i	$0.247011\pi$
$882$	−8596.66	−0.328191
$883$	5523.51	0.210511	0.105255	−	0.994445i	$-0.466434\pi$
$883$	5523.51	0.210511	0.105255	+	0.994445i	$0.466434\pi$
$884$	−60226.7	−2.29145
$885$	0	0
$886$	95092.7	3.60576
$887$	−23588.7	−0.892931	−0.446466	−	0.894801i	$-0.647318\pi$
$887$	−23588.7	−0.892931	−0.446466	+	0.894801i	$0.647318\pi$
$888$	17303.5	0.653906
$889$	9056.19	0.341659
$890$	0	0
$891$	−891.000	−0.0335013
$892$	11284.8	0.423590
$893$	−7026.83	−0.263319
$894$	51788.9	1.93745
$895$	0	0
$896$	152490.	5.68563
$897$	6116.07	0.227658
$898$	−2641.02	−0.0981424
$899$	−43138.8	−1.60040
$900$	0	0
$901$	18756.5	0.693529
$902$	−19536.0	−0.721151
$903$	4392.15	0.161862
$904$	7520.02	0.276673
$905$	0	0
$906$	−38500.2	−1.41179
$907$	4838.37	0.177128	0.0885641	−	0.996070i	$-0.471772\pi$
$907$	4838.37	0.177128	0.0885641	+	0.996070i	$0.471772\pi$
$908$	59015.0	2.15692
$909$	4142.03	0.151136
$910$	0	0
$911$	51548.7	1.87474	0.937368	−	0.348340i	$-0.113254\pi$
$911$	51548.7	1.87474	0.937368	+	0.348340i	$0.113254\pi$
$912$	72512.6	2.63282
$913$	14409.5	0.522326
$914$	7665.02	0.277392
$915$	0	0
$916$	−38338.0	−1.38289
$917$	38980.2	1.40375
$918$	15402.7	0.553774
$919$	42013.4	1.50804	0.754022	−	0.656849i	$-0.228111\pi$
$919$	42013.4	1.50804	0.754022	+	0.656849i	$0.228111\pi$
$920$	0	0
$921$	13575.3	0.485690
$922$	−67114.4	−2.39728
$923$	−8455.58	−0.301537
$924$	−16896.6	−0.601578
$925$	0	0
$926$	77261.3	2.74186
$927$	−2228.38	−0.0789532
$928$	−198547.	−7.02329
$929$	−25281.9	−0.892867	−0.446434	−	0.894817i	$-0.647306\pi$
$929$	−25281.9	−0.892867	−0.446434	+	0.894817i	$0.647306\pi$
$930$	0	0
$931$	−15830.9	−0.557292
$932$	−6069.34	−0.213313
$933$	−12217.5	−0.428706
$934$	−95161.1	−3.33380
$935$	0	0
$936$	18723.1	0.653830
$937$	−2911.37	−0.101505	−0.0507526	−	0.998711i	$-0.516162\pi$
$937$	−2911.37	−0.101505	−0.0507526	+	0.998711i	$0.516162\pi$
$938$	20358.4	0.708662
$939$	20870.2	0.725318
$940$	0	0
$941$	6587.58	0.228214	0.114107	−	0.993468i	$-0.463599\pi$
$941$	6587.58	0.228214	0.114107	+	0.993468i	$0.463599\pi$
$942$	−19702.4	−0.681465
$943$	−25313.0	−0.874130
$944$	164447.	5.66981
$945$	0	0
$946$	3918.84	0.134685
$947$	24055.4	0.825445	0.412723	−	0.910857i	$-0.364578\pi$
$947$	24055.4	0.825445	0.412723	+	0.910857i	$0.364578\pi$
$948$	−17715.7	−0.606941
$949$	−18844.9	−0.644607
$950$	0	0
$951$	−10409.5	−0.354943
$952$	188440.	6.41529
$953$	35573.5	1.20917	0.604584	−	0.796541i	$-0.293339\pi$
$953$	35573.5	1.20917	0.604584	+	0.796541i	$0.293339\pi$
$954$	−9038.32	−0.306736
$955$	0	0
$956$	−110894.	−3.75165
$957$	8035.92	0.271436
$958$	25334.4	0.854402
$959$	50096.8	1.68687
$960$	0	0
$961$	1591.89	0.0534353
$962$	10264.0	0.343996
$963$	−7253.21	−0.242712
$964$	−32955.2	−1.10105
$965$	0	0
$966$	−29662.1	−0.987953
$967$	9704.79	0.322735	0.161368	−	0.986894i	$-0.448410\pi$
$967$	9704.79	0.322735	0.161368	+	0.986894i	$0.448410\pi$
$968$	−9725.99	−0.322939
$969$	28364.4	0.940347
$970$	0	0
$971$	38920.4	1.28632	0.643159	−	0.765732i	$-0.277623\pi$
$971$	38920.4	1.28632	0.643159	+	0.765732i	$0.277623\pi$
$972$	−5478.20	−0.180775
$973$	18445.6	0.607748
$974$	−62525.5	−2.05693
$975$	0	0
$976$	−22952.9	−0.752770
$977$	26937.4	0.882090	0.441045	−	0.897485i	$-0.354608\pi$
$977$	26937.4	0.882090	0.441045	+	0.897485i	$0.354608\pi$
$978$	22766.7	0.744376
$979$	−13459.5	−0.439396
$980$	0	0
$981$	−7379.62	−0.240177
$982$	−62314.5	−2.02499
$983$	15996.4	0.519030	0.259515	−	0.965739i	$-0.416437\pi$
$983$	15996.4	0.519030	0.259515	+	0.965739i	$0.416437\pi$
$984$	−77490.8	−2.51048
$985$	0	0
$986$	−138917.	−4.48682
$987$	5226.99	0.168568
$988$	53444.4	1.72094
$989$	5077.67	0.163256
$990$	0	0
$991$	11038.3	0.353826	0.176913	−	0.984226i	$-0.443389\pi$
$991$	11038.3	0.353826	0.176913	+	0.984226i	$0.443389\pi$
$992$	144440.	4.62296
$993$	18376.5	0.587272
$994$	41008.5	1.30856
$995$	0	0
$996$	88594.8	2.81851
$997$	14083.6	0.447376	0.223688	−	0.974661i	$-0.428190\pi$
$997$	14083.6	0.447376	0.223688	+	0.974661i	$0.428190\pi$
$998$	−70316.9	−2.23030
$999$	−1937.44	−0.0613593

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.4.a.bb.1.1		7
3.2	odd	2		2475.4.a.br.1.7		7
5.2	odd	4		165.4.c.a.34.1	✓	14
5.3	odd	4		165.4.c.a.34.14	yes	14
5.4	even	2		825.4.a.bc.1.7		7
15.2	even	4		495.4.c.c.199.14		14
15.8	even	4		495.4.c.c.199.1		14
15.14	odd	2		2475.4.a.bq.1.1		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.c.a.34.1	✓	14	5.2	odd	4
165.4.c.a.34.14	yes	14	5.3	odd	4
495.4.c.c.199.1		14	15.8	even	4
495.4.c.c.199.14		14	15.2	even	4
825.4.a.bb.1.1		7	1.1	even	1	trivial
825.4.a.bc.1.7		7	5.4	even	2
2475.4.a.bq.1.1		7	15.14	odd	2
2475.4.a.br.1.7		7	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	825.a (trivial)

\(f(q)\)	\(=\)	\(q-5.52667 q^{2} -3.00000 q^{3} +22.5440 q^{4} +16.5800 q^{6} -22.7119 q^{7} -80.3801 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-5.52667 q^{2} -3.00000 q^{3} +22.5440 q^{4} +16.5800 q^{6} -22.7119 q^{7} -80.3801 q^{8} +9.00000 q^{9} -11.0000 q^{11} -67.6321 q^{12} -25.8814 q^{13} +125.521 q^{14} +263.882 q^{16} +103.221 q^{17} -49.7400 q^{18} -91.5974 q^{19} +68.1358 q^{21} +60.7933 q^{22} +78.7705 q^{23} +241.140 q^{24} +143.038 q^{26} -27.0000 q^{27} -512.019 q^{28} +243.513 q^{29} -177.152 q^{31} -815.345 q^{32} +33.0000 q^{33} -570.470 q^{34} +202.896 q^{36} +71.7571 q^{37} +506.228 q^{38} +77.6442 q^{39} -321.351 q^{41} -376.564 q^{42} +64.4617 q^{43} -247.984 q^{44} -435.338 q^{46} +76.7143 q^{47} -791.645 q^{48} +172.832 q^{49} -309.664 q^{51} -583.471 q^{52} +181.711 q^{53} +149.220 q^{54} +1825.59 q^{56} +274.792 q^{57} -1345.81 q^{58} +623.186 q^{59} -86.9818 q^{61} +979.061 q^{62} -204.407 q^{63} +2395.09 q^{64} -182.380 q^{66} +162.191 q^{67} +2327.03 q^{68} -236.311 q^{69} +326.705 q^{71} -723.421 q^{72} +728.127 q^{73} -396.578 q^{74} -2064.98 q^{76} +249.831 q^{77} -429.113 q^{78} +261.943 q^{79} +81.0000 q^{81} +1776.00 q^{82} -1309.95 q^{83} +1536.06 q^{84} -356.258 q^{86} -730.538 q^{87} +884.181 q^{88} +1223.60 q^{89} +587.816 q^{91} +1775.80 q^{92} +531.456 q^{93} -423.974 q^{94} +2446.03 q^{96} +1300.90 q^{97} -955.184 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 3 q^{2} - 21 q^{3} + 41 q^{4} + 9 q^{6} - 50 q^{7} - 21 q^{8} + 63 q^{9}+O(q^{10}) \) 7 * q - 3 * q^2 - 21 * q^3 + 41 * q^4 + 9 * q^6 - 50 * q^7 - 21 * q^8 + 63 * q^9	\( 7 q - 3 q^{2} - 21 q^{3} + 41 q^{4} + 9 q^{6} - 50 q^{7} - 21 q^{8} + 63 q^{9} - 77 q^{11} - 123 q^{12} - 24 q^{13} + 142 q^{14} + 181 q^{16} - 38 q^{17} - 27 q^{18} + 26 q^{19} + 150 q^{21} + 33 q^{22} - 228 q^{23} + 63 q^{24} + 476 q^{26} - 189 q^{27} - 840 q^{28} + 572 q^{29} - 140 q^{31} - 991 q^{32} + 231 q^{33} - 806 q^{34} + 369 q^{36} + 104 q^{37} - 498 q^{38} + 72 q^{39} + 896 q^{41} - 426 q^{42} - 614 q^{43} - 451 q^{44} - 344 q^{46} - 520 q^{47} - 543 q^{48} + 295 q^{49} + 114 q^{51} + 26 q^{52} - 380 q^{53} + 81 q^{54} + 1522 q^{56} - 78 q^{57} - 1600 q^{58} + 1316 q^{59} - 386 q^{61} - 440 q^{62} - 450 q^{63} + 869 q^{64} - 99 q^{66} - 348 q^{67} - 332 q^{68} + 684 q^{69} + 804 q^{71} - 189 q^{72} - 468 q^{73} - 748 q^{74} - 1698 q^{76} + 550 q^{77} - 1428 q^{78} - 374 q^{79} + 567 q^{81} + 620 q^{82} - 3128 q^{83} + 2520 q^{84} - 2534 q^{86} - 1716 q^{87} + 231 q^{88} + 694 q^{89} - 3376 q^{91} + 1184 q^{92} + 420 q^{93} - 2920 q^{94} + 2973 q^{96} + 8 q^{97} - 4211 q^{98} - 693 q^{99}+O(q^{100}) \) 7 * q - 3 * q^2 - 21 * q^3 + 41 * q^4 + 9 * q^6 - 50 * q^7 - 21 * q^8 + 63 * q^9 - 77 * q^11 - 123 * q^12 - 24 * q^13 + 142 * q^14 + 181 * q^16 - 38 * q^17 - 27 * q^18 + 26 * q^19 + 150 * q^21 + 33 * q^22 - 228 * q^23 + 63 * q^24 + 476 * q^26 - 189 * q^27 - 840 * q^28 + 572 * q^29 - 140 * q^31 - 991 * q^32 + 231 * q^33 - 806 * q^34 + 369 * q^36 + 104 * q^37 - 498 * q^38 + 72 * q^39 + 896 * q^41 - 426 * q^42 - 614 * q^43 - 451 * q^44 - 344 * q^46 - 520 * q^47 - 543 * q^48 + 295 * q^49 + 114 * q^51 + 26 * q^52 - 380 * q^53 + 81 * q^54 + 1522 * q^56 - 78 * q^57 - 1600 * q^58 + 1316 * q^59 - 386 * q^61 - 440 * q^62 - 450 * q^63 + 869 * q^64 - 99 * q^66 - 348 * q^67 - 332 * q^68 + 684 * q^69 + 804 * q^71 - 189 * q^72 - 468 * q^73 - 748 * q^74 - 1698 * q^76 + 550 * q^77 - 1428 * q^78 - 374 * q^79 + 567 * q^81 + 620 * q^82 - 3128 * q^83 + 2520 * q^84 - 2534 * q^86 - 1716 * q^87 + 231 * q^88 + 694 * q^89 - 3376 * q^91 + 1184 * q^92 + 420 * q^93 - 2920 * q^94 + 2973 * q^96 + 8 * q^97 - 4211 * q^98 - 693 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more