LMFDB - Embedded newform 1617.4.a.z.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1617,4,Mod(1,1617)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1617, 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("1617.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1617 = 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1617.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:	$95.4060884793$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4 x^{9} - 45 x^{8} + 168 x^{7} + 651 x^{6} - 2176 x^{5} - 3439 x^{4} + 8716 x^{3} + 7840 x^{2} + \cdots - 4032 $ x^10 - 4x^9 - 45x^8 + 168x^7 + 651x^6 - 2176x^5 - 3439x^4 + 8716x^3 + 7840x^2 - 9216*x - 4032
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 231)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$2.38864$ of defining polynomial
Character	$\chi$	$=$	1617.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.38864 q^{2} +3.00000 q^{3} -2.29442 q^{4} +9.60191 q^{5} +7.16591 q^{6} -24.5896 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.38864 q^{2} +3.00000 q^{3} -2.29442 q^{4} +9.60191 q^{5} +7.16591 q^{6} -24.5896 q^{8} +9.00000 q^{9} +22.9355 q^{10} -11.0000 q^{11} -6.88325 q^{12} -38.2982 q^{13} +28.8057 q^{15} -40.3803 q^{16} +114.205 q^{17} +21.4977 q^{18} +57.0630 q^{19} -22.0308 q^{20} -26.2750 q^{22} -40.1730 q^{23} -73.7689 q^{24} -32.8033 q^{25} -91.4806 q^{26} +27.0000 q^{27} -71.8590 q^{29} +68.8064 q^{30} +220.110 q^{31} +100.263 q^{32} -33.0000 q^{33} +272.795 q^{34} -20.6497 q^{36} +99.1040 q^{37} +136.303 q^{38} -114.895 q^{39} -236.107 q^{40} +452.976 q^{41} +6.92384 q^{43} +25.2386 q^{44} +86.4172 q^{45} -95.9587 q^{46} -74.7978 q^{47} -121.141 q^{48} -78.3552 q^{50} +342.616 q^{51} +87.8721 q^{52} +35.4116 q^{53} +64.4932 q^{54} -105.621 q^{55} +171.189 q^{57} -171.645 q^{58} +115.484 q^{59} -66.0923 q^{60} -3.61161 q^{61} +525.762 q^{62} +562.535 q^{64} -367.736 q^{65} -78.8250 q^{66} +453.304 q^{67} -262.034 q^{68} -120.519 q^{69} +129.937 q^{71} -221.307 q^{72} +315.243 q^{73} +236.723 q^{74} -98.4100 q^{75} -130.926 q^{76} -274.442 q^{78} +491.190 q^{79} -387.728 q^{80} +81.0000 q^{81} +1081.99 q^{82} +851.068 q^{83} +1096.59 q^{85} +16.5385 q^{86} -215.577 q^{87} +270.486 q^{88} +1142.97 q^{89} +206.419 q^{90} +92.1735 q^{92} +660.329 q^{93} -178.665 q^{94} +547.914 q^{95} +300.789 q^{96} -1521.32 q^{97} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} + 30 q^{3} + 26 q^{4} + 20 q^{5} + 12 q^{6} + 36 q^{8} + 90 q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 + 30 * q^3 + 26 * q^4 + 20 * q^5 + 12 * q^6 + 36 * q^8 + 90 * q^9	\( 10 q + 4 q^{2} + 30 q^{3} + 26 q^{4} + 20 q^{5} + 12 q^{6} + 36 q^{8} + 90 q^{9} + 44 q^{10} - 110 q^{11} + 78 q^{12} + 82 q^{13} + 60 q^{15} - 10 q^{16} + 164 q^{17} + 36 q^{18} - 76 q^{19} + 356 q^{20} - 44 q^{22} + 140 q^{23} + 108 q^{24} + 472 q^{25} + 360 q^{26} + 270 q^{27} + 40 q^{29} + 132 q^{30} + 24 q^{31} + 112 q^{32} - 330 q^{33} - 262 q^{34} + 234 q^{36} + 412 q^{37} + 16 q^{38} + 246 q^{39} + 828 q^{40} - 228 q^{41} + 530 q^{43} - 286 q^{44} + 180 q^{45} + 1422 q^{46} + 768 q^{47} - 30 q^{48} + 670 q^{50} + 492 q^{51} + 952 q^{52} + 136 q^{53} + 108 q^{54} - 220 q^{55} - 228 q^{57} + 1708 q^{58} + 608 q^{59} + 1068 q^{60} + 1618 q^{61} + 164 q^{62} - 1238 q^{64} + 2764 q^{65} - 132 q^{66} + 1002 q^{67} + 2816 q^{68} + 420 q^{69} + 812 q^{71} + 324 q^{72} + 134 q^{73} + 342 q^{74} + 1416 q^{75} - 450 q^{76} + 1080 q^{78} + 1262 q^{79} - 1316 q^{80} + 810 q^{81} + 982 q^{82} + 1078 q^{83} - 1402 q^{85} + 1692 q^{86} + 120 q^{87} - 396 q^{88} + 2880 q^{89} + 396 q^{90} + 2364 q^{92} + 72 q^{93} - 2362 q^{94} + 2866 q^{95} + 336 q^{96} - 1030 q^{97} - 990 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 + 30 * q^3 + 26 * q^4 + 20 * q^5 + 12 * q^6 + 36 * q^8 + 90 * q^9 + 44 * q^10 - 110 * q^11 + 78 * q^12 + 82 * q^13 + 60 * q^15 - 10 * q^16 + 164 * q^17 + 36 * q^18 - 76 * q^19 + 356 * q^20 - 44 * q^22 + 140 * q^23 + 108 * q^24 + 472 * q^25 + 360 * q^26 + 270 * q^27 + 40 * q^29 + 132 * q^30 + 24 * q^31 + 112 * q^32 - 330 * q^33 - 262 * q^34 + 234 * q^36 + 412 * q^37 + 16 * q^38 + 246 * q^39 + 828 * q^40 - 228 * q^41 + 530 * q^43 - 286 * q^44 + 180 * q^45 + 1422 * q^46 + 768 * q^47 - 30 * q^48 + 670 * q^50 + 492 * q^51 + 952 * q^52 + 136 * q^53 + 108 * q^54 - 220 * q^55 - 228 * q^57 + 1708 * q^58 + 608 * q^59 + 1068 * q^60 + 1618 * q^61 + 164 * q^62 - 1238 * q^64 + 2764 * q^65 - 132 * q^66 + 1002 * q^67 + 2816 * q^68 + 420 * q^69 + 812 * q^71 + 324 * q^72 + 134 * q^73 + 342 * q^74 + 1416 * q^75 - 450 * q^76 + 1080 * q^78 + 1262 * q^79 - 1316 * q^80 + 810 * q^81 + 982 * q^82 + 1078 * q^83 - 1402 * q^85 + 1692 * q^86 + 120 * q^87 - 396 * q^88 + 2880 * q^89 + 396 * q^90 + 2364 * q^92 + 72 * q^93 - 2362 * q^94 + 2866 * q^95 + 336 * q^96 - 1030 * q^97 - 990 * 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 $

$2$	2.38864	0.844511	0.422255	−	0.906477i	$-0.361239\pi$
$2$	2.38864	0.844511	0.422255	+	0.906477i	$0.361239\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−2.29442	−0.286802
$5$	9.60191	0.858821	0.429410	−	0.903109i	$-0.358721\pi$
$5$	9.60191	0.858821	0.429410	+	0.903109i	$0.358721\pi$
$6$	7.16591	0.487578
$7$	0	0
$7$	0	0
$8$	−24.5896	−1.08672
$9$	9.00000	0.333333
$10$	22.9355	0.725283
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−6.88325	−0.165585
$13$	−38.2982	−0.817079	−0.408539	−	0.912741i	$-0.633962\pi$
$13$	−38.2982	−0.817079	−0.408539	+	0.912741i	$0.633962\pi$
$14$	0	0
$15$	28.8057	0.495840
$16$	−40.3803	−0.630943
$17$	114.205	1.62934	0.814671	−	0.579923i	$-0.196917\pi$
$17$	114.205	1.62934	0.814671	+	0.579923i	$0.196917\pi$
$18$	21.4977	0.281504
$19$	57.0630	0.689008	0.344504	−	0.938785i	$-0.388047\pi$
$19$	57.0630	0.689008	0.344504	+	0.938785i	$0.388047\pi$
$20$	−22.0308	−0.246311
$21$	0	0
$22$	−26.2750	−0.254630
$23$	−40.1730	−0.364202	−0.182101	−	0.983280i	$-0.558290\pi$
$23$	−40.1730	−0.364202	−0.182101	+	0.983280i	$0.558290\pi$
$24$	−73.7689	−0.627417
$25$	−32.8033	−0.262427
$26$	−91.4806	−0.690032
$27$	27.0000	0.192450
$28$	0	0
$29$	−71.8590	−0.460134	−0.230067	−	0.973175i	$-0.573895\pi$
$29$	−71.8590	−0.460134	−0.230067	+	0.973175i	$0.573895\pi$
$30$	68.8064	0.418743
$31$	220.110	1.27525	0.637627	−	0.770345i	$-0.279916\pi$
$31$	220.110	1.27525	0.637627	+	0.770345i	$0.279916\pi$
$32$	100.263	0.553880
$33$	−33.0000	−0.174078
$34$	272.795	1.37600
$35$	0	0
$36$	−20.6497	−0.0956006
$37$	99.1040	0.440340	0.220170	−	0.975461i	$-0.429339\pi$
$37$	99.1040	0.440340	0.220170	+	0.975461i	$0.429339\pi$
$38$	136.303	0.581875
$39$	−114.895	−0.471741
$40$	−236.107	−0.933296
$41$	452.976	1.72544	0.862718	−	0.505685i	$-0.168760\pi$
$41$	452.976	1.72544	0.862718	+	0.505685i	$0.168760\pi$
$42$	0	0
$43$	6.92384	0.0245553	0.0122776	−	0.999925i	$-0.496092\pi$
$43$	6.92384	0.0245553	0.0122776	+	0.999925i	$0.496092\pi$
$44$	25.2386	0.0864740
$45$	86.4172	0.286274
$46$	−95.9587	−0.307573
$47$	−74.7978	−0.232136	−0.116068	−	0.993241i	$-0.537029\pi$
$47$	−74.7978	−0.232136	−0.116068	+	0.993241i	$0.537029\pi$
$48$	−121.141	−0.364275
$49$	0	0
$50$	−78.3552	−0.221622
$51$	342.616	0.940701
$52$	87.8721	0.234340
$53$	35.4116	0.0917764	0.0458882	−	0.998947i	$-0.485388\pi$
$53$	35.4116	0.0917764	0.0458882	+	0.998947i	$0.485388\pi$
$54$	64.4932	0.162526
$55$	−105.621	−0.258944
$56$	0	0
$57$	171.189	0.397799
$58$	−171.645	−0.388588
$59$	115.484	0.254826	0.127413	−	0.991850i	$-0.459333\pi$
$59$	115.484	0.254826	0.127413	+	0.991850i	$0.459333\pi$
$60$	−66.0923	−0.142208
$61$	−3.61161	−0.00758064	−0.00379032	−	0.999993i	$-0.501206\pi$
$61$	−3.61161	−0.00758064	−0.00379032	+	0.999993i	$0.501206\pi$
$62$	525.762	1.07697
$63$	0	0
$64$	562.535	1.09870
$65$	−367.736	−0.701724
$66$	−78.8250	−0.147010
$67$	453.304	0.826565	0.413283	−	0.910603i	$-0.364382\pi$
$67$	453.304	0.826565	0.413283	+	0.910603i	$0.364382\pi$
$68$	−262.034	−0.467299
$69$	−120.519	−0.210272
$70$	0	0
$71$	129.937	0.217192	0.108596	−	0.994086i	$-0.465365\pi$
$71$	129.937	0.217192	0.108596	+	0.994086i	$0.465365\pi$
$72$	−221.307	−0.362239
$73$	315.243	0.505430	0.252715	−	0.967541i	$-0.418677\pi$
$73$	315.243	0.505430	0.252715	+	0.967541i	$0.418677\pi$
$74$	236.723	0.371872
$75$	−98.4100	−0.151512
$76$	−130.926	−0.197609
$77$	0	0
$78$	−274.442	−0.398390
$79$	491.190	0.699534	0.349767	−	0.936837i	$-0.386261\pi$
$79$	491.190	0.699534	0.349767	+	0.936837i	$0.386261\pi$
$80$	−387.728	−0.541867
$81$	81.0000	0.111111
$82$	1081.99	1.45715
$83$	851.068	1.12550	0.562752	−	0.826626i	$-0.309742\pi$
$83$	851.068	1.12550	0.562752	+	0.826626i	$0.309742\pi$
$84$	0	0
$85$	1096.59	1.39931
$86$	16.5385	0.0207372
$87$	−215.577	−0.265658
$88$	270.486	0.327658
$89$	1142.97	1.36128	0.680641	−	0.732617i	$-0.261701\pi$
$89$	1142.97	1.36128	0.680641	+	0.732617i	$0.261701\pi$
$90$	206.419	0.241761
$91$	0	0
$92$	92.1735	0.104454
$93$	660.329	0.736268
$94$	−178.665	−0.196041
$95$	547.914	0.591735
$96$	300.789	0.319783
$97$	−1521.32	−1.59244	−0.796219	−	0.605008i	$-0.793170\pi$
$97$	−1521.32	−1.59244	−0.796219	+	0.605008i	$0.793170\pi$
$98$	0	0
$99$	−99.0000	−0.100504
$100$	75.2645	0.0752645
$101$	−1362.01	−1.34183	−0.670914	−	0.741535i	$-0.734098\pi$
$101$	−1362.01	−1.34183	−0.670914	+	0.741535i	$0.734098\pi$
$102$	818.384	0.794432
$103$	897.736	0.858802	0.429401	−	0.903114i	$-0.358725\pi$
$103$	897.736	0.858802	0.429401	+	0.903114i	$0.358725\pi$
$104$	941.739	0.887934
$105$	0	0
$106$	84.5853	0.0775062
$107$	−927.854	−0.838308	−0.419154	−	0.907915i	$-0.637673\pi$
$107$	−927.854	−0.838308	−0.419154	+	0.907915i	$0.637673\pi$
$108$	−61.9492	−0.0551951
$109$	1707.88	1.50079	0.750393	−	0.660992i	$-0.229864\pi$
$109$	1707.88	1.50079	0.750393	+	0.660992i	$0.229864\pi$
$110$	−252.290	−0.218681
$111$	297.312	0.254231
$112$	0	0
$113$	1973.95	1.64331	0.821655	−	0.569986i	$-0.193051\pi$
$113$	1973.95	1.64331	0.821655	+	0.569986i	$0.193051\pi$
$114$	408.908	0.335946
$115$	−385.737	−0.312784
$116$	164.874	0.131967
$117$	−344.684	−0.272360
$118$	275.850	0.215204
$119$	0	0
$120$	−708.322	−0.538839
$121$	121.000	0.0909091
$122$	−8.62682	−0.00640193
$123$	1358.93	0.996181
$124$	−505.023	−0.365745
$125$	−1515.21	−1.08420
$126$	0	0
$127$	−42.0915	−0.0294096	−0.0147048	−	0.999892i	$-0.504681\pi$
$127$	−42.0915	−0.0294096	−0.0147048	+	0.999892i	$0.504681\pi$
$128$	541.587	0.373984
$129$	20.7715	0.0141770
$130$	−878.388	−0.592614
$131$	−1617.72	−1.07894	−0.539470	−	0.842005i	$-0.681375\pi$
$131$	−1617.72	−1.07894	−0.539470	+	0.842005i	$0.681375\pi$
$132$	75.7157	0.0499258
$133$	0	0
$134$	1082.78	0.698043
$135$	259.252	0.165280
$136$	−2808.26	−1.77064
$137$	−46.1015	−0.0287498	−0.0143749	−	0.999897i	$-0.504576\pi$
$137$	−46.1015	−0.0287498	−0.0143749	+	0.999897i	$0.504576\pi$
$138$	−287.876	−0.177577
$139$	−1850.74	−1.12933	−0.564667	−	0.825319i	$-0.690995\pi$
$139$	−1850.74	−1.12933	−0.564667	+	0.825319i	$0.690995\pi$
$140$	0	0
$141$	−224.394	−0.134024
$142$	310.371	0.183421
$143$	421.281	0.246359
$144$	−363.423	−0.210314
$145$	−689.984	−0.395173
$146$	753.000	0.426841
$147$	0	0
$148$	−227.386	−0.126290
$149$	5.14696	0.00282990	0.00141495	−	0.999999i	$-0.499550\pi$
$149$	5.14696	0.00282990	0.00141495	+	0.999999i	$0.499550\pi$
$150$	−235.066	−0.127954
$151$	−611.383	−0.329494	−0.164747	−	0.986336i	$-0.552681\pi$
$151$	−611.383	−0.329494	−0.164747	+	0.986336i	$0.552681\pi$
$152$	−1403.16	−0.748757
$153$	1027.85	0.543114
$154$	0	0
$155$	2113.47	1.09522
$156$	263.616	0.135296
$157$	−49.2908	−0.0250563	−0.0125281	−	0.999922i	$-0.503988\pi$
$157$	−49.2908	−0.0250563	−0.0125281	+	0.999922i	$0.503988\pi$
$158$	1173.27	0.590764
$159$	106.235	0.0529871
$160$	962.716	0.475684
$161$	0	0
$162$	193.480	0.0938345
$163$	1112.98	0.534817	0.267408	−	0.963583i	$-0.413833\pi$
$163$	1112.98	0.534817	0.267408	+	0.963583i	$0.413833\pi$
$164$	−1039.31	−0.494859
$165$	−316.863	−0.149502
$166$	2032.89	0.950501
$167$	2306.20	1.06862	0.534309	−	0.845289i	$-0.320572\pi$
$167$	2306.20	1.06862	0.534309	+	0.845289i	$0.320572\pi$
$168$	0	0
$169$	−730.244	−0.332382
$170$	2619.35	1.18173
$171$	513.567	0.229669
$172$	−15.8862	−0.00704249
$173$	65.0302	0.0285789	0.0142895	−	0.999898i	$-0.495451\pi$
$173$	65.0302	0.0285789	0.0142895	+	0.999898i	$0.495451\pi$
$174$	−514.935	−0.224351
$175$	0	0
$176$	444.184	0.190236
$177$	346.452	0.147124
$178$	2730.13	1.14962
$179$	−274.984	−0.114823	−0.0574114	−	0.998351i	$-0.518285\pi$
$179$	−274.984	−0.114823	−0.0574114	+	0.998351i	$0.518285\pi$
$180$	−198.277	−0.0821038
$181$	3424.08	1.40613	0.703066	−	0.711124i	$-0.251814\pi$
$181$	3424.08	1.40613	0.703066	+	0.711124i	$0.251814\pi$
$182$	0	0
$183$	−10.8348	−0.00437669
$184$	987.839	0.395785
$185$	951.587	0.378173
$186$	1577.29	0.621787
$187$	−1256.26	−0.491265
$188$	171.617	0.0665770
$189$	0	0
$190$	1308.77	0.499726
$191$	1727.69	0.654509	0.327255	−	0.944936i	$-0.393876\pi$
$191$	1727.69	0.654509	0.327255	+	0.944936i	$0.393876\pi$
$192$	1687.60	0.634335
$193$	1663.89	0.620568	0.310284	−	0.950644i	$-0.399576\pi$
$193$	1663.89	0.620568	0.310284	+	0.950644i	$0.399576\pi$
$194$	−3633.88	−1.34483
$195$	−1103.21	−0.405141
$196$	0	0
$197$	−4142.37	−1.49813	−0.749065	−	0.662497i	$-0.769497\pi$
$197$	−4142.37	−1.49813	−0.749065	+	0.662497i	$0.769497\pi$
$198$	−236.475	−0.0848765
$199$	−1236.73	−0.440552	−0.220276	−	0.975438i	$-0.570696\pi$
$199$	−1236.73	−0.440552	−0.220276	+	0.975438i	$0.570696\pi$
$200$	806.621	0.285184
$201$	1359.91	0.477218
$202$	−3253.34	−1.13319
$203$	0	0
$204$	−786.102	−0.269795
$205$	4349.43	1.48184
$206$	2144.37	0.725267
$207$	−361.557	−0.121401
$208$	1546.50	0.515530
$209$	−627.693	−0.207744
$210$	0	0
$211$	5307.98	1.73183	0.865915	−	0.500191i	$-0.166737\pi$
$211$	5307.98	1.73183	0.865915	+	0.500191i	$0.166737\pi$
$212$	−81.2488	−0.0263217
$213$	389.810	0.125396
$214$	−2216.31	−0.707960
$215$	66.4821	0.0210886
$216$	−663.920	−0.209139
$217$	0	0
$218$	4079.51	1.26743
$219$	945.728	0.291810
$220$	242.338	0.0742657
$221$	−4373.86	−1.33130
$222$	710.170	0.214700
$223$	5542.34	1.66432	0.832158	−	0.554538i	$-0.187105\pi$
$223$	5542.34	1.66432	0.832158	+	0.554538i	$0.187105\pi$
$224$	0	0
$225$	−295.230	−0.0874756
$226$	4715.06	1.38779
$227$	−5711.96	−1.67011	−0.835057	−	0.550163i	$-0.814565\pi$
$227$	−5711.96	−1.67011	−0.835057	+	0.550163i	$0.814565\pi$
$228$	−392.779	−0.114090
$229$	4898.92	1.41367	0.706833	−	0.707381i	$-0.250123\pi$
$229$	4898.92	1.41367	0.706833	+	0.707381i	$0.250123\pi$
$230$	−921.387	−0.264150
$231$	0	0
$232$	1766.99	0.500036
$233$	−5894.61	−1.65738	−0.828689	−	0.559709i	$-0.810913\pi$
$233$	−5894.61	−1.65738	−0.828689	+	0.559709i	$0.810913\pi$
$234$	−823.325	−0.230011
$235$	−718.202	−0.199363
$236$	−264.969	−0.0730847
$237$	1473.57	0.403876
$238$	0	0
$239$	4259.24	1.15275	0.576376	−	0.817185i	$-0.304467\pi$
$239$	4259.24	1.15275	0.576376	+	0.817185i	$0.304467\pi$
$240$	−1163.19	−0.312847
$241$	−6325.42	−1.69069	−0.845344	−	0.534222i	$-0.820605\pi$
$241$	−6325.42	−1.69069	−0.845344	+	0.534222i	$0.820605\pi$
$242$	289.025	0.0767737
$243$	243.000	0.0641500
$244$	8.28653	0.00217414
$245$	0	0
$246$	3245.98	0.841286
$247$	−2185.41	−0.562974
$248$	−5412.42	−1.38584
$249$	2553.20	0.649810
$250$	−3619.29	−0.915617
$251$	−3403.85	−0.855974	−0.427987	−	0.903785i	$-0.640777\pi$
$251$	−3403.85	−0.855974	−0.427987	+	0.903785i	$0.640777\pi$
$252$	0	0
$253$	441.903	0.109811
$254$	−100.541	−0.0248367
$255$	3289.76	0.807894
$256$	−3206.62	−0.782867
$257$	1644.38	0.399118	0.199559	−	0.979886i	$-0.436049\pi$
$257$	1644.38	0.399118	0.199559	+	0.979886i	$0.436049\pi$
$258$	49.6156	0.0119726
$259$	0	0
$260$	843.740	0.201256
$261$	−646.731	−0.153378
$262$	−3864.15	−0.911176
$263$	−5283.74	−1.23882	−0.619410	−	0.785068i	$-0.712628\pi$
$263$	−5283.74	−1.23882	−0.619410	+	0.785068i	$0.712628\pi$
$264$	811.457	0.189173
$265$	340.019	0.0788195
$266$	0	0
$267$	3428.90	0.785937
$268$	−1040.07	−0.237061
$269$	−591.216	−0.134004	−0.0670020	−	0.997753i	$-0.521343\pi$
$269$	−591.216	−0.134004	−0.0670020	+	0.997753i	$0.521343\pi$
$270$	619.258	0.139581
$271$	−2304.35	−0.516529	−0.258265	−	0.966074i	$-0.583151\pi$
$271$	−2304.35	−0.516529	−0.258265	+	0.966074i	$0.583151\pi$
$272$	−4611.64	−1.02802
$273$	0	0
$274$	−110.120	−0.0242795
$275$	360.837	0.0791246
$276$	276.521	0.0603065
$277$	7444.83	1.61486	0.807431	−	0.589963i	$-0.200858\pi$
$277$	7444.83	1.61486	0.807431	+	0.589963i	$0.200858\pi$
$278$	−4420.74	−0.953735
$279$	1980.99	0.425085
$280$	0	0
$281$	4155.68	0.882231	0.441115	−	0.897450i	$-0.354583\pi$
$281$	4155.68	0.882231	0.441115	+	0.897450i	$0.354583\pi$
$282$	−535.995	−0.113184
$283$	510.658	0.107263	0.0536316	−	0.998561i	$-0.482920\pi$
$283$	510.658	0.107263	0.0536316	+	0.998561i	$0.482920\pi$
$284$	−298.128	−0.0622911
$285$	1643.74	0.341638
$286$	1006.29	0.208052
$287$	0	0
$288$	902.367	0.184627
$289$	8129.82	1.65476
$290$	−1648.12	−0.333727
$291$	−4563.96	−0.919395
$292$	−723.298	−0.144958
$293$	5588.57	1.11429	0.557146	−	0.830414i	$-0.311896\pi$
$293$	5588.57	1.11429	0.557146	+	0.830414i	$0.311896\pi$
$294$	0	0
$295$	1108.87	0.218850
$296$	−2436.93	−0.478526
$297$	−297.000	−0.0580259
$298$	12.2942	0.00238988
$299$	1538.56	0.297582
$300$	225.793	0.0434540
$301$	0	0
$302$	−1460.37	−0.278262
$303$	−4086.02	−0.774705
$304$	−2304.22	−0.434725
$305$	−34.6783	−0.00651041
$306$	2455.15	0.458666
$307$	8959.15	1.66556	0.832778	−	0.553607i	$-0.186749\pi$
$307$	8959.15	1.66556	0.832778	+	0.553607i	$0.186749\pi$
$308$	0	0
$309$	2693.21	0.495829
$310$	5048.32	0.924921
$311$	−366.676	−0.0668563	−0.0334281	−	0.999441i	$-0.510642\pi$
$311$	−366.676	−0.0668563	−0.0334281	+	0.999441i	$0.510642\pi$
$312$	2825.22	0.512649
$313$	6850.56	1.23711	0.618556	−	0.785740i	$-0.287718\pi$
$313$	6850.56	1.23711	0.618556	+	0.785740i	$0.287718\pi$
$314$	−117.738	−0.0211603
$315$	0	0
$316$	−1126.99	−0.200628
$317$	−4117.31	−0.729500	−0.364750	−	0.931106i	$-0.618845\pi$
$317$	−4117.31	−0.729500	−0.364750	+	0.931106i	$0.618845\pi$
$318$	253.756	0.0447482
$319$	790.449	0.138736
$320$	5401.41	0.943587
$321$	−2783.56	−0.483998
$322$	0	0
$323$	6516.89	1.12263
$324$	−185.848	−0.0318669
$325$	1256.31	0.214423
$326$	2658.50	0.451658
$327$	5123.65	0.866479
$328$	−11138.5	−1.87506
$329$	0	0
$330$	−756.871	−0.126256
$331$	−8623.49	−1.43199	−0.715996	−	0.698104i	$-0.754027\pi$
$331$	−8623.49	−1.43199	−0.715996	+	0.698104i	$0.754027\pi$
$332$	−1952.70	−0.322797
$333$	891.936	0.146780
$334$	5508.68	0.902459
$335$	4352.58	0.709872
$336$	0	0
$337$	−11987.4	−1.93766	−0.968832	−	0.247719i	$-0.920319\pi$
$337$	−11987.4	−1.93766	−0.968832	+	0.247719i	$0.920319\pi$
$338$	−1744.29	−0.280700
$339$	5921.86	0.948765
$340$	−2516.03	−0.401326
$341$	−2421.21	−0.384504
$342$	1226.73	0.193958
$343$	0	0
$344$	−170.255	−0.0266846
$345$	−1157.21	−0.180586
$346$	155.334	0.0241352
$347$	8405.36	1.30036	0.650178	−	0.759782i	$-0.274694\pi$
$347$	8405.36	1.30036	0.650178	+	0.759782i	$0.274694\pi$
$348$	494.623	0.0761913
$349$	5629.44	0.863429	0.431715	−	0.902010i	$-0.357909\pi$
$349$	5629.44	0.863429	0.431715	+	0.902010i	$0.357909\pi$
$350$	0	0
$351$	−1034.05	−0.157247
$352$	−1102.89	−0.167001
$353$	−8137.26	−1.22692	−0.613460	−	0.789726i	$-0.710223\pi$
$353$	−8137.26	−1.22692	−0.613460	+	0.789726i	$0.710223\pi$
$354$	827.549	0.124248
$355$	1247.64	0.186529
$356$	−2622.44	−0.390418
$357$	0	0
$358$	−656.837	−0.0969690
$359$	7687.62	1.13019	0.565094	−	0.825027i	$-0.308840\pi$
$359$	7687.62	1.13019	0.565094	+	0.825027i	$0.308840\pi$
$360$	−2124.97	−0.311099
$361$	−3602.81	−0.525268
$362$	8178.89	1.18749
$363$	363.000	0.0524864
$364$	0	0
$365$	3026.93	0.434074
$366$	−25.8805	−0.00369616
$367$	−5157.50	−0.733568	−0.366784	−	0.930306i	$-0.619541\pi$
$367$	−5157.50	−0.733568	−0.366784	+	0.930306i	$0.619541\pi$
$368$	1622.20	0.229791
$369$	4076.78	0.575146
$370$	2273.00	0.319371
$371$	0	0
$372$	−1515.07	−0.211163
$373$	9586.16	1.33070	0.665352	−	0.746530i	$-0.268282\pi$
$373$	9586.16	1.33070	0.665352	+	0.746530i	$0.268282\pi$
$374$	−3000.74	−0.414879
$375$	−4545.64	−0.625962
$376$	1839.25	0.252266
$377$	2752.07	0.375966
$378$	0	0
$379$	−10706.5	−1.45107	−0.725536	−	0.688184i	$-0.758408\pi$
$379$	−10706.5	−1.45107	−0.725536	+	0.688184i	$0.758408\pi$
$380$	−1257.14	−0.169711
$381$	−126.274	−0.0169796
$382$	4126.83	0.552740
$383$	2976.64	0.397126	0.198563	−	0.980088i	$-0.436373\pi$
$383$	2976.64	0.397126	0.198563	+	0.980088i	$0.436373\pi$
$384$	1624.76	0.215920
$385$	0	0
$386$	3974.44	0.524076
$387$	62.3146	0.00818508
$388$	3490.54	0.456714
$389$	−10873.8	−1.41728	−0.708641	−	0.705569i	$-0.750691\pi$
$389$	−10873.8	−1.41728	−0.708641	+	0.705569i	$0.750691\pi$
$390$	−2635.17	−0.342146
$391$	−4587.96	−0.593410
$392$	0	0
$393$	−4853.17	−0.622926
$394$	−9894.61	−1.26519
$395$	4716.36	0.600774
$396$	227.147	0.0288247
$397$	−14782.4	−1.86878	−0.934391	−	0.356250i	$-0.884055\pi$
$397$	−14782.4	−1.86878	−0.934391	+	0.356250i	$0.884055\pi$
$398$	−2954.11	−0.372050
$399$	0	0
$400$	1324.61	0.165576
$401$	3110.58	0.387369	0.193685	−	0.981064i	$-0.437956\pi$
$401$	3110.58	0.387369	0.193685	+	0.981064i	$0.437956\pi$
$402$	3248.33	0.403015
$403$	−8429.82	−1.04198
$404$	3125.01	0.384839
$405$	777.755	0.0954245
$406$	0	0
$407$	−1090.14	−0.132768
$408$	−8424.78	−1.02228
$409$	−6755.76	−0.816750	−0.408375	−	0.912814i	$-0.633904\pi$
$409$	−6755.76	−0.816750	−0.408375	+	0.912814i	$0.633904\pi$
$410$	10389.2	1.25143
$411$	−138.305	−0.0165987
$412$	−2059.78	−0.246306
$413$	0	0
$414$	−863.628	−0.102524
$415$	8171.88	0.966607
$416$	−3839.90	−0.452564
$417$	−5552.21	−0.652021
$418$	−1499.33	−0.175442
$419$	−7282.40	−0.849089	−0.424545	−	0.905407i	$-0.639566\pi$
$419$	−7282.40	−0.849089	−0.424545	+	0.905407i	$0.639566\pi$
$420$	0	0
$421$	−1247.18	−0.144379	−0.0721895	−	0.997391i	$-0.522999\pi$
$421$	−1247.18	−0.144379	−0.0721895	+	0.997391i	$0.522999\pi$
$422$	12678.8	1.46255
$423$	−673.181	−0.0773786
$424$	−870.757	−0.0997351
$425$	−3746.31	−0.427583
$426$	931.114	0.105898
$427$	0	0
$428$	2128.88	0.240428
$429$	1263.84	0.142235
$430$	158.802	0.0178095
$431$	−14612.9	−1.63313	−0.816566	−	0.577252i	$-0.804125\pi$
$431$	−14612.9	−1.63313	−0.816566	+	0.577252i	$0.804125\pi$
$432$	−1090.27	−0.121425
$433$	−4439.78	−0.492753	−0.246377	−	0.969174i	$-0.579240\pi$
$433$	−4439.78	−0.492753	−0.246377	+	0.969174i	$0.579240\pi$
$434$	0	0
$435$	−2069.95	−0.228153
$436$	−3918.59	−0.430428
$437$	−2292.39	−0.250938
$438$	2259.00	0.246437
$439$	4249.70	0.462021	0.231010	−	0.972951i	$-0.425797\pi$
$439$	4249.70	0.462021	0.231010	+	0.972951i	$0.425797\pi$
$440$	2597.18	0.281399
$441$	0	0
$442$	−10447.6	−1.12430
$443$	−13565.3	−1.45486	−0.727432	−	0.686180i	$-0.759286\pi$
$443$	−13565.3	−1.45486	−0.727432	+	0.686180i	$0.759286\pi$
$444$	−682.157	−0.0729138
$445$	10974.7	1.16910
$446$	13238.6	1.40553
$447$	15.4409	0.00163385
$448$	0	0
$449$	2642.37	0.277731	0.138865	−	0.990311i	$-0.455654\pi$
$449$	2642.37	0.277731	0.138865	+	0.990311i	$0.455654\pi$
$450$	−705.197	−0.0738740
$451$	−4982.73	−0.520239
$452$	−4529.07	−0.471304
$453$	−1834.15	−0.190234
$454$	−13643.8	−1.41043
$455$	0	0
$456$	−4209.47	−0.432295
$457$	3989.20	0.408330	0.204165	−	0.978936i	$-0.434552\pi$
$457$	3989.20	0.408330	0.204165	+	0.978936i	$0.434552\pi$
$458$	11701.7	1.19386
$459$	3083.54	0.313567
$460$	885.042	0.0897072
$461$	−4592.18	−0.463946	−0.231973	−	0.972722i	$-0.574518\pi$
$461$	−4592.18	−0.463946	−0.231973	+	0.972722i	$0.574518\pi$
$462$	0	0
$463$	6872.37	0.689819	0.344910	−	0.938636i	$-0.387910\pi$
$463$	6872.37	0.689819	0.344910	+	0.938636i	$0.387910\pi$
$464$	2901.69	0.290318
$465$	6340.42	0.632323
$466$	−14080.1	−1.39967
$467$	−13883.2	−1.37567	−0.687834	−	0.725868i	$-0.741438\pi$
$467$	−13883.2	−1.37567	−0.687834	+	0.725868i	$0.741438\pi$
$468$	790.849	0.0781132
$469$	0	0
$470$	−1715.52	−0.168364
$471$	−147.872	−0.0144662
$472$	−2839.71	−0.276924
$473$	−76.1623	−0.00740369
$474$	3519.82	0.341078
$475$	−1871.86	−0.180814
$476$	0	0
$477$	318.704	0.0305921
$478$	10173.8	0.973511
$479$	14049.1	1.34012	0.670061	−	0.742306i	$-0.266268\pi$
$479$	14049.1	1.34012	0.670061	+	0.742306i	$0.266268\pi$
$480$	2888.15	0.274636
$481$	−3795.51	−0.359793
$482$	−15109.1	−1.42780
$483$	0	0
$484$	−277.624	−0.0260729
$485$	−14607.6	−1.36762
$486$	580.439	0.0541754
$487$	−2789.43	−0.259550	−0.129775	−	0.991543i	$-0.541426\pi$
$487$	−2789.43	−0.259550	−0.129775	+	0.991543i	$0.541426\pi$
$488$	88.8081	0.00823802
$489$	3338.93	0.308777
$490$	0	0
$491$	15981.9	1.46895	0.734473	−	0.678638i	$-0.237429\pi$
$491$	15981.9	1.46895	0.734473	+	0.678638i	$0.237429\pi$
$492$	−3117.94	−0.285707
$493$	−8206.67	−0.749716
$494$	−5220.16	−0.475437
$495$	−950.589	−0.0863147
$496$	−8888.11	−0.804613
$497$	0	0
$498$	6098.68	0.548772
$499$	5127.36	0.459984	0.229992	−	0.973193i	$-0.426130\pi$
$499$	5127.36	0.459984	0.229992	+	0.973193i	$0.426130\pi$
$500$	3476.53	0.310950
$501$	6918.60	0.616967
$502$	−8130.57	−0.722879
$503$	10543.1	0.934583	0.467292	−	0.884103i	$-0.345230\pi$
$503$	10543.1	0.934583	0.467292	+	0.884103i	$0.345230\pi$
$504$	0	0
$505$	−13077.9	−1.15239
$506$	1055.55	0.0927366
$507$	−2190.73	−0.191901
$508$	96.5754	0.00843472
$509$	−19230.7	−1.67463	−0.837315	−	0.546720i	$-0.815876\pi$
$509$	−19230.7	−1.67463	−0.837315	+	0.546720i	$0.815876\pi$
$510$	7858.05	0.682275
$511$	0	0
$512$	−11992.1	−1.03512
$513$	1540.70	0.132600
$514$	3927.81	0.337059
$515$	8619.98	0.737557
$516$	−47.6585	−0.00406599
$517$	822.776	0.0699916
$518$	0	0
$519$	195.091	0.0165001
$520$	9042.50	0.762576
$521$	17493.7	1.47104	0.735521	−	0.677502i	$-0.236938\pi$
$521$	17493.7	1.47104	0.735521	+	0.677502i	$0.236938\pi$
$522$	−1544.81	−0.129529
$523$	−11254.8	−0.940989	−0.470495	−	0.882403i	$-0.655925\pi$
$523$	−11254.8	−0.940989	−0.470495	+	0.882403i	$0.655925\pi$
$524$	3711.73	0.309442
$525$	0	0
$526$	−12620.9	−1.04620
$527$	25137.7	2.07783
$528$	1332.55	0.109833
$529$	−10553.1	−0.867357
$530$	812.181	0.0665639
$531$	1039.36	0.0849421
$532$	0	0
$533$	−17348.2	−1.40982
$534$	8190.39	0.663732
$535$	−8909.17	−0.719957
$536$	−11146.6	−0.898243
$537$	−824.952	−0.0662929
$538$	−1412.20	−0.113168
$539$	0	0
$540$	−594.831	−0.0474027
$541$	−21234.9	−1.68754	−0.843771	−	0.536703i	$-0.819670\pi$
$541$	−21234.9	−1.68754	−0.843771	+	0.536703i	$0.819670\pi$
$542$	−5504.26	−0.436214
$543$	10272.2	0.811831
$544$	11450.6	0.902460
$545$	16398.9	1.28891
$546$	0	0
$547$	−9244.31	−0.722593	−0.361296	−	0.932451i	$-0.617666\pi$
$547$	−9244.31	−0.722593	−0.361296	+	0.932451i	$0.617666\pi$
$548$	105.776	0.00824549
$549$	−32.5045	−0.00252688
$550$	861.908	0.0668216
$551$	−4100.49	−0.317036
$552$	2963.52	0.228507
$553$	0	0
$554$	17783.0	1.36377
$555$	2854.76	0.218339
$556$	4246.36	0.323895
$557$	6169.39	0.469310	0.234655	−	0.972079i	$-0.424604\pi$
$557$	6169.39	0.469310	0.234655	+	0.972079i	$0.424604\pi$
$558$	4731.86	0.358989
$559$	−265.171	−0.0200636
$560$	0	0
$561$	−3768.77	−0.283632
$562$	9926.40	0.745053
$563$	21363.3	1.59921	0.799606	−	0.600525i	$-0.205042\pi$
$563$	21363.3	1.59921	0.799606	+	0.600525i	$0.205042\pi$
$564$	514.852	0.0384383
$565$	18953.7	1.41131
$566$	1219.78	0.0905849
$567$	0	0
$568$	−3195.09	−0.236026
$569$	−16147.0	−1.18966	−0.594830	−	0.803851i	$-0.702781\pi$
$569$	−16147.0	−1.18966	−0.594830	+	0.803851i	$0.702781\pi$
$570$	3926.30	0.288517
$571$	−15157.4	−1.11089	−0.555445	−	0.831553i	$-0.687452\pi$
$571$	−15157.4	−1.11089	−0.555445	+	0.831553i	$0.687452\pi$
$572$	−966.593	−0.0706561
$573$	5183.07	0.377881
$574$	0	0
$575$	1317.81	0.0955763
$576$	5062.81	0.366233
$577$	−20053.6	−1.44687	−0.723434	−	0.690393i	$-0.757438\pi$
$577$	−20053.6	−1.44687	−0.723434	+	0.690393i	$0.757438\pi$
$578$	19419.2	1.39746
$579$	4991.68	0.358285
$580$	1583.11	0.113336
$581$	0	0
$582$	−10901.6	−0.776438
$583$	−389.527	−0.0276716
$584$	−7751.70	−0.549260
$585$	−3309.63	−0.233908
$586$	13349.1	0.941032
$587$	2514.57	0.176810	0.0884049	−	0.996085i	$-0.471823\pi$
$587$	2514.57	0.176810	0.0884049	+	0.996085i	$0.471823\pi$
$588$	0	0
$589$	12560.1	0.878661
$590$	2648.68	0.184821
$591$	−12427.1	−0.864946
$592$	−4001.85	−0.277829
$593$	−13803.2	−0.955864	−0.477932	−	0.878397i	$-0.658614\pi$
$593$	−13803.2	−0.955864	−0.477932	+	0.878397i	$0.658614\pi$
$594$	−709.425	−0.0490035
$595$	0	0
$596$	−11.8093	−0.000811622 0
$597$	−3710.20	−0.254353
$598$	3675.05	0.251311
$599$	14780.3	1.00819	0.504097	−	0.863647i	$-0.331825\pi$
$599$	14780.3	1.00819	0.504097	+	0.863647i	$0.331825\pi$
$600$	2419.86	0.164651
$601$	−2674.39	−0.181515	−0.0907577	−	0.995873i	$-0.528929\pi$
$601$	−2674.39	−0.181515	−0.0907577	+	0.995873i	$0.528929\pi$
$602$	0	0
$603$	4079.73	0.275522
$604$	1402.77	0.0944996
$605$	1161.83	0.0780746
$606$	−9760.01	−0.654247
$607$	13250.3	0.886021	0.443010	−	0.896516i	$-0.353910\pi$
$607$	13250.3	0.886021	0.443010	+	0.896516i	$0.353910\pi$
$608$	5721.31	0.381628
$609$	0	0
$610$	−82.8340	−0.00549811
$611$	2864.63	0.189673
$612$	−2358.31	−0.155766
$613$	28214.5	1.85901	0.929504	−	0.368812i	$-0.120235\pi$
$613$	28214.5	1.85901	0.929504	+	0.368812i	$0.120235\pi$
$614$	21400.1	1.40658
$615$	13048.3	0.855541
$616$	0	0
$617$	−7689.81	−0.501751	−0.250875	−	0.968019i	$-0.580718\pi$
$617$	−7689.81	−0.501751	−0.250875	+	0.968019i	$0.580718\pi$
$618$	6433.10	0.418733
$619$	5066.24	0.328965	0.164483	−	0.986380i	$-0.447405\pi$
$619$	5066.24	0.328965	0.164483	+	0.986380i	$0.447405\pi$
$620$	−4849.19	−0.314110
$621$	−1084.67	−0.0700907
$622$	−875.856	−0.0564608
$623$	0	0
$624$	4639.49	0.297641
$625$	−10448.5	−0.668706
$626$	16363.5	1.04475
$627$	−1883.08	−0.119941
$628$	113.094	0.00718618
$629$	11318.2	0.717465
$630$	0	0
$631$	−10423.0	−0.657577	−0.328789	−	0.944403i	$-0.606640\pi$
$631$	−10423.0	−0.657577	−0.328789	+	0.944403i	$0.606640\pi$
$632$	−12078.2	−0.760196
$633$	15923.9	0.999873
$634$	−9834.77	−0.616070
$635$	−404.159	−0.0252576
$636$	−243.746	−0.0151968
$637$	0	0
$638$	1888.10	0.117164
$639$	1169.43	0.0723973
$640$	5200.27	0.321185
$641$	26501.7	1.63300	0.816500	−	0.577345i	$-0.195911\pi$
$641$	26501.7	1.63300	0.816500	+	0.577345i	$0.195911\pi$
$642$	−6648.92	−0.408741
$643$	−24778.0	−1.51967	−0.759835	−	0.650116i	$-0.774720\pi$
$643$	−24778.0	−1.51967	−0.759835	+	0.650116i	$0.774720\pi$
$644$	0	0
$645$	199.446	0.0121755
$646$	15566.5	0.948073
$647$	15748.6	0.956944	0.478472	−	0.878103i	$-0.341191\pi$
$647$	15748.6	0.956944	0.478472	+	0.878103i	$0.341191\pi$
$648$	−1991.76	−0.120746
$649$	−1270.33	−0.0768330
$650$	3000.87	0.181083
$651$	0	0
$652$	−2553.63	−0.153386
$653$	−22036.4	−1.32060	−0.660299	−	0.751003i	$-0.729571\pi$
$653$	−22036.4	−1.32060	−0.660299	+	0.751003i	$0.729571\pi$
$654$	12238.5	0.731751
$655$	−15533.2	−0.926616
$656$	−18291.3	−1.08865
$657$	2837.19	0.168477
$658$	0	0
$659$	15557.4	0.919620	0.459810	−	0.888017i	$-0.347917\pi$
$659$	15557.4	0.919620	0.459810	+	0.888017i	$0.347917\pi$
$660$	727.015	0.0428773
$661$	−603.263	−0.0354980	−0.0177490	−	0.999842i	$-0.505650\pi$
$661$	−603.263	−0.0354980	−0.0177490	+	0.999842i	$0.505650\pi$
$662$	−20598.4	−1.20933
$663$	−13121.6	−0.768627
$664$	−20927.4	−1.22311
$665$	0	0
$666$	2130.51	0.123957
$667$	2886.79	0.167582
$668$	−5291.38	−0.306482
$669$	16627.0	0.960894
$670$	10396.7	0.599494
$671$	39.7277	0.00228565
$672$	0	0
$673$	27846.4	1.59495	0.797474	−	0.603353i	$-0.206169\pi$
$673$	27846.4	1.59495	0.797474	+	0.603353i	$0.206169\pi$
$674$	−28633.4	−1.63638
$675$	−885.690	−0.0505040
$676$	1675.48	0.0953279
$677$	−1722.35	−0.0977776	−0.0488888	−	0.998804i	$-0.515568\pi$
$677$	−1722.35	−0.0977776	−0.0488888	+	0.998804i	$0.515568\pi$
$678$	14145.2	0.801242
$679$	0	0
$680$	−26964.7	−1.52066
$681$	−17135.9	−0.964241
$682$	−5783.39	−0.324717
$683$	−2076.95	−0.116357	−0.0581787	−	0.998306i	$-0.518529\pi$
$683$	−2076.95	−0.116357	−0.0581787	+	0.998306i	$0.518529\pi$
$684$	−1178.34	−0.0658696
$685$	−442.663	−0.0246909
$686$	0	0
$687$	14696.7	0.816180
$688$	−279.587	−0.0154930
$689$	−1356.20	−0.0749886
$690$	−2764.16	−0.152507
$691$	−26984.1	−1.48556	−0.742780	−	0.669536i	$-0.766493\pi$
$691$	−26984.1	−1.48556	−0.742780	+	0.669536i	$0.766493\pi$
$692$	−149.206	−0.00819649
$693$	0	0
$694$	20077.4	1.09816
$695$	−17770.6	−0.969896
$696$	5300.96	0.288696
$697$	51732.2	2.81133
$698$	13446.7	0.729175
$699$	−17683.8	−0.956888
$700$	0	0
$701$	−13198.7	−0.711138	−0.355569	−	0.934650i	$-0.615713\pi$
$701$	−13198.7	−0.711138	−0.355569	+	0.934650i	$0.615713\pi$
$702$	−2469.98	−0.132797
$703$	5655.17	0.303398
$704$	−6187.88	−0.331271
$705$	−2154.61	−0.115102
$706$	−19437.0	−1.03615
$707$	0	0
$708$	−794.906	−0.0421955
$709$	−23208.7	−1.22937	−0.614683	−	0.788774i	$-0.710716\pi$
$709$	−23208.7	−1.22937	−0.614683	+	0.788774i	$0.710716\pi$
$710$	2980.16	0.157526
$711$	4420.71	0.233178
$712$	−28105.1	−1.47933
$713$	−8842.47	−0.464450
$714$	0	0
$715$	4045.10	0.211578
$716$	630.928	0.0329314
$717$	12777.7	0.665541
$718$	18362.9	0.954455
$719$	−6835.21	−0.354535	−0.177267	−	0.984163i	$-0.556726\pi$
$719$	−6835.21	−0.354535	−0.177267	+	0.984163i	$0.556726\pi$
$720$	−3489.56	−0.180622
$721$	0	0
$722$	−8605.81	−0.443594
$723$	−18976.3	−0.976120
$724$	−7856.26	−0.403281
$725$	2357.22	0.120751
$726$	867.075	0.0443253
$727$	22574.3	1.15163	0.575815	−	0.817580i	$-0.304685\pi$
$727$	22574.3	1.15163	0.575815	+	0.817580i	$0.304685\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	7230.24	0.366580
$731$	790.738	0.0400089
$732$	24.8596	0.00125524
$733$	−35201.9	−1.77382	−0.886912	−	0.461939i	$-0.847154\pi$
$733$	−35201.9	−1.77382	−0.886912	+	0.461939i	$0.847154\pi$
$734$	−12319.4	−0.619506
$735$	0	0
$736$	−4027.86	−0.201724
$737$	−4986.34	−0.249219
$738$	9737.95	0.485717
$739$	−16782.4	−0.835388	−0.417694	−	0.908588i	$-0.637162\pi$
$739$	−16782.4	−0.835388	−0.417694	+	0.908588i	$0.637162\pi$
$740$	−2183.34	−0.108461
$741$	−6556.24	−0.325033
$742$	0	0
$743$	9395.63	0.463920	0.231960	−	0.972725i	$-0.425486\pi$
$743$	9395.63	0.463920	0.231960	+	0.972725i	$0.425486\pi$
$744$	−16237.2	−0.800116
$745$	49.4207	0.00243038
$746$	22897.8	1.12379
$747$	7659.61	0.375168
$748$	2882.37	0.140896
$749$	0	0
$750$	−10857.9	−0.528632
$751$	13478.3	0.654901	0.327450	−	0.944868i	$-0.393811\pi$
$751$	13478.3	0.654901	0.327450	+	0.944868i	$0.393811\pi$
$752$	3020.36	0.146464
$753$	−10211.6	−0.494197
$754$	6573.71	0.317507
$755$	−5870.45	−0.282977
$756$	0	0
$757$	24393.2	1.17118	0.585591	−	0.810607i	$-0.300863\pi$
$757$	24393.2	1.17118	0.585591	+	0.810607i	$0.300863\pi$
$758$	−25574.0	−1.22545
$759$	1325.71	0.0633994
$760$	−13473.0	−0.643049
$761$	−11196.6	−0.533348	−0.266674	−	0.963787i	$-0.585925\pi$
$761$	−11196.6	−0.533348	−0.266674	+	0.963787i	$0.585925\pi$
$762$	−301.624	−0.0143395
$763$	0	0
$764$	−3964.04	−0.187715
$765$	9869.29	0.466438
$766$	7110.11	0.335377
$767$	−4422.84	−0.208213
$768$	−9619.87	−0.451988
$769$	−13930.6	−0.653249	−0.326625	−	0.945154i	$-0.605911\pi$
$769$	−13930.6	−0.653249	−0.326625	+	0.945154i	$0.605911\pi$
$770$	0	0
$771$	4933.13	0.230431
$772$	−3817.66	−0.177980
$773$	5064.94	0.235670	0.117835	−	0.993033i	$-0.462405\pi$
$773$	5064.94	0.235670	0.117835	+	0.993033i	$0.462405\pi$
$774$	148.847	0.00691239
$775$	−7220.33	−0.334661
$776$	37408.6	1.73053
$777$	0	0
$778$	−25973.5	−1.19691
$779$	25848.2	1.18884
$780$	2531.22	0.116195
$781$	−1429.30	−0.0654859
$782$	−10959.0	−0.501141
$783$	−1940.19	−0.0885528
$784$	0	0
$785$	−473.286	−0.0215188
$786$	−11592.5	−0.526068
$787$	1566.21	0.0709397	0.0354698	−	0.999371i	$-0.488707\pi$
$787$	1566.21	0.0709397	0.0354698	+	0.999371i	$0.488707\pi$
$788$	9504.31	0.429666
$789$	−15851.2	−0.715233
$790$	11265.7	0.507360
$791$	0	0
$792$	2434.37	0.109219
$793$	138.318	0.00619398
$794$	−35309.7	−1.57821
$795$	1020.06	0.0455065
$796$	2837.58	0.126351
$797$	22740.4	1.01067	0.505337	−	0.862922i	$-0.331368\pi$
$797$	22740.4	1.01067	0.505337	+	0.862922i	$0.331368\pi$
$798$	0	0
$799$	−8542.30	−0.378229
$800$	−3288.96	−0.145353
$801$	10286.7	0.453761
$802$	7430.05	0.327137
$803$	−3467.67	−0.152393
$804$	−3120.20	−0.136867
$805$	0	0
$806$	−20135.8	−0.879966
$807$	−1773.65	−0.0773673
$808$	33491.2	1.45819
$809$	−18093.4	−0.786316	−0.393158	−	0.919471i	$-0.628617\pi$
$809$	−18093.4	−0.786316	−0.393158	+	0.919471i	$0.628617\pi$
$810$	1857.77	0.0805870
$811$	−20196.5	−0.874470	−0.437235	−	0.899347i	$-0.644042\pi$
$811$	−20196.5	−0.874470	−0.437235	+	0.899347i	$0.644042\pi$
$812$	0	0
$813$	−6913.06	−0.298218
$814$	−2603.96	−0.112124
$815$	10686.7	0.459312
$816$	−13834.9	−0.593529
$817$	395.095	0.0169188
$818$	−16137.0	−0.689754
$819$	0	0
$820$	−9979.40	−0.424995
$821$	−4885.95	−0.207699	−0.103849	−	0.994593i	$-0.533116\pi$
$821$	−4885.95	−0.207699	−0.103849	+	0.994593i	$0.533116\pi$
$822$	−330.359	−0.0140178
$823$	5151.90	0.218206	0.109103	−	0.994030i	$-0.465202\pi$
$823$	5151.90	0.218206	0.109103	+	0.994030i	$0.465202\pi$
$824$	−22075.0	−0.933275
$825$	1082.51	0.0456826
$826$	0	0
$827$	−32692.2	−1.37463	−0.687314	−	0.726360i	$-0.741211\pi$
$827$	−32692.2	−1.37463	−0.687314	+	0.726360i	$0.741211\pi$
$828$	829.562	0.0348180
$829$	−13415.8	−0.562064	−0.281032	−	0.959698i	$-0.590677\pi$
$829$	−13415.8	−0.562064	−0.281032	+	0.959698i	$0.590677\pi$
$830$	19519.7	0.816310
$831$	22334.5	0.932340
$832$	−21544.1	−0.897725
$833$	0	0
$834$	−13262.2	−0.550639
$835$	22143.9	0.917751
$836$	1440.19	0.0595813
$837$	5942.96	0.245423
$838$	−17395.0	−0.717065
$839$	−26986.1	−1.11045	−0.555224	−	0.831701i	$-0.687367\pi$
$839$	−26986.1	−1.11045	−0.555224	+	0.831701i	$0.687367\pi$
$840$	0	0
$841$	−19225.3	−0.788277
$842$	−2979.05	−0.121930
$843$	12467.0	0.509356
$844$	−12178.7	−0.496692
$845$	−7011.74	−0.285457
$846$	−1607.98	−0.0653471
$847$	0	0
$848$	−1429.93	−0.0579057
$849$	1531.97	0.0619284
$850$	−8948.57	−0.361098
$851$	−3981.30	−0.160373
$852$	−894.385	−0.0359638
$853$	5991.15	0.240484	0.120242	−	0.992745i	$-0.461633\pi$
$853$	5991.15	0.240484	0.120242	+	0.992745i	$0.461633\pi$
$854$	0	0
$855$	4931.23	0.197245
$856$	22815.6	0.911005
$857$	40157.8	1.60066	0.800330	−	0.599560i	$-0.204658\pi$
$857$	40157.8	1.60066	0.800330	+	0.599560i	$0.204658\pi$
$858$	3018.86	0.120119
$859$	−49267.2	−1.95690	−0.978449	−	0.206488i	$-0.933797\pi$
$859$	−49267.2	−1.95690	−0.978449	+	0.206488i	$0.933797\pi$
$860$	−152.538	−0.00604824
$861$	0	0
$862$	−34905.0	−1.37920
$863$	−2488.72	−0.0981657	−0.0490828	−	0.998795i	$-0.515630\pi$
$863$	−2488.72	−0.0981657	−0.0490828	+	0.998795i	$0.515630\pi$
$864$	2707.10	0.106594
$865$	624.414	0.0245442
$866$	−10605.0	−0.416136
$867$	24389.5	0.955374
$868$	0	0
$869$	−5403.09	−0.210917
$870$	−4944.36	−0.192678
$871$	−17360.7	−0.675369
$872$	−41996.2	−1.63093
$873$	−13691.9	−0.530813
$874$	−5475.69	−0.211920
$875$	0	0
$876$	−2169.89	−0.0836917
$877$	−49164.1	−1.89299	−0.946495	−	0.322718i	$-0.895403\pi$
$877$	−49164.1	−1.89299	−0.946495	+	0.322718i	$0.895403\pi$
$878$	10151.0	0.390182
$879$	16765.7	0.643337
$880$	4265.01	0.163379
$881$	43780.7	1.67424	0.837122	−	0.547016i	$-0.184236\pi$
$881$	43780.7	1.67424	0.837122	+	0.547016i	$0.184236\pi$
$882$	0	0
$883$	17001.0	0.647940	0.323970	−	0.946067i	$-0.394982\pi$
$883$	17001.0	0.647940	0.323970	+	0.946067i	$0.394982\pi$
$884$	10035.4	0.381820
$885$	3326.60	0.126353
$886$	−32402.5	−1.22865
$887$	32643.7	1.23570	0.617852	−	0.786294i	$-0.288003\pi$
$887$	32643.7	1.23570	0.617852	+	0.786294i	$0.288003\pi$
$888$	−7310.78	−0.276277
$889$	0	0
$890$	26214.5	0.987316
$891$	−891.000	−0.0335013
$892$	−12716.4	−0.477329
$893$	−4268.19	−0.159944
$894$	36.8827	0.00137980
$895$	−2640.37	−0.0986122
$896$	0	0
$897$	4615.67	0.171809
$898$	6311.66	0.234547
$899$	−15816.9	−0.586788
$900$	677.380	0.0250882
$901$	4044.18	0.149535
$902$	−11901.9	−0.439347
$903$	0	0
$904$	−48538.8	−1.78581
$905$	32877.7	1.20762
$906$	−4381.12	−0.160654
$907$	−38139.6	−1.39626	−0.698129	−	0.715972i	$-0.745984\pi$
$907$	−38139.6	−1.39626	−0.698129	+	0.715972i	$0.745984\pi$
$908$	13105.6	0.478992
$909$	−12258.1	−0.447276
$910$	0	0
$911$	−3723.85	−0.135430	−0.0677150	−	0.997705i	$-0.521571\pi$
$911$	−3723.85	−0.135430	−0.0677150	+	0.997705i	$0.521571\pi$
$912$	−6912.67	−0.250988
$913$	−9361.75	−0.339352
$914$	9528.75	0.344839
$915$	−104.035	−0.00375879
$916$	−11240.1	−0.405442
$917$	0	0
$918$	7365.46	0.264811
$919$	30670.9	1.10091	0.550457	−	0.834864i	$-0.314454\pi$
$919$	30670.9	1.10091	0.550457	+	0.834864i	$0.314454\pi$
$920$	9485.14	0.339908
$921$	26877.4	0.961609
$922$	−10969.0	−0.391807
$923$	−4976.34	−0.177463
$924$	0	0
$925$	−3250.94	−0.115557
$926$	16415.6	0.582560
$927$	8079.62	0.286267
$928$	−7204.80	−0.254859
$929$	19395.7	0.684986	0.342493	−	0.939520i	$-0.388729\pi$
$929$	19395.7	0.684986	0.342493	+	0.939520i	$0.388729\pi$
$930$	15145.0	0.534003
$931$	0	0
$932$	13524.7	0.475339
$933$	−1100.03	−0.0385995
$934$	−33161.9	−1.16177
$935$	−12062.5	−0.421909
$936$	8475.65	0.295978
$937$	34603.5	1.20645	0.603227	−	0.797569i	$-0.293881\pi$
$937$	34603.5	1.20645	0.603227	+	0.797569i	$0.293881\pi$
$938$	0	0
$939$	20551.7	0.714247
$940$	1647.85	0.0571777
$941$	−961.888	−0.0333227	−0.0166614	−	0.999861i	$-0.505304\pi$
$941$	−961.888	−0.0333227	−0.0166614	+	0.999861i	$0.505304\pi$
$942$	−353.213	−0.0122169
$943$	−18197.4	−0.628408
$944$	−4663.29	−0.160781
$945$	0	0
$946$	−181.924	−0.00625249
$947$	−2283.60	−0.0783602	−0.0391801	−	0.999232i	$-0.512475\pi$
$947$	−2283.60	−0.0783602	−0.0391801	+	0.999232i	$0.512475\pi$
$948$	−3380.98	−0.115832
$949$	−12073.2	−0.412976
$950$	−4471.19	−0.152699
$951$	−12351.9	−0.421177
$952$	0	0
$953$	42787.7	1.45438	0.727192	−	0.686434i	$-0.240825\pi$
$953$	42787.7	1.45438	0.727192	+	0.686434i	$0.240825\pi$
$954$	761.268	0.0258354
$955$	16589.1	0.562106
$956$	−9772.47	−0.330611
$957$	2371.35	0.0800990
$958$	33558.1	1.13175
$959$	0	0
$960$	16204.2	0.544780
$961$	18657.3	0.626274
$962$	−9066.09	−0.303849
$963$	−8350.68	−0.279436
$964$	14513.1	0.484893
$965$	15976.6	0.532957
$966$	0	0
$967$	−27952.2	−0.929557	−0.464779	−	0.885427i	$-0.653866\pi$
$967$	−27952.2	−0.929557	−0.464779	+	0.885427i	$0.653866\pi$
$968$	−2975.34	−0.0987925
$969$	19550.7	0.648151
$970$	−34892.2	−1.15497
$971$	11137.5	0.368094	0.184047	−	0.982917i	$-0.441080\pi$
$971$	11137.5	0.368094	0.184047	+	0.982917i	$0.441080\pi$
$972$	−557.543	−0.0183984
$973$	0	0
$974$	−6662.93	−0.219193
$975$	3768.93	0.123797
$976$	145.838	0.00478295
$977$	−49391.4	−1.61737	−0.808685	−	0.588242i	$-0.799820\pi$
$977$	−49391.4	−1.61737	−0.808685	+	0.588242i	$0.799820\pi$
$978$	7975.50	0.260765
$979$	−12572.6	−0.410442
$980$	0	0
$981$	15371.0	0.500262
$982$	38174.9	1.24054
$983$	−8979.63	−0.291359	−0.145679	−	0.989332i	$-0.546537\pi$
$983$	−8979.63	−0.291359	−0.145679	+	0.989332i	$0.546537\pi$
$984$	−33415.5	−1.08257
$985$	−39774.6	−1.28663
$986$	−19602.8	−0.633143
$987$	0	0
$988$	5014.25	0.161462
$989$	−278.151	−0.00894308
$990$	−2270.61	−0.0728937
$991$	4264.67	0.136702	0.0683510	−	0.997661i	$-0.478226\pi$
$991$	4264.67	0.136702	0.0683510	+	0.997661i	$0.478226\pi$
$992$	22068.9	0.706338
$993$	−25870.5	−0.826761
$994$	0	0
$995$	−11875.0	−0.378355
$996$	−5858.11	−0.186367
$997$	26153.1	0.830769	0.415385	−	0.909646i	$-0.363647\pi$
$997$	26153.1	0.830769	0.415385	+	0.909646i	$0.363647\pi$
$998$	12247.4	0.388461
$999$	2675.81	0.0847435

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.4.a.z.1.7		10
7.3	odd	6		231.4.i.b.100.4	yes	20
7.5	odd	6		231.4.i.b.67.4	✓	20
7.6	odd	2		1617.4.a.y.1.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.4.i.b.67.4	✓	20	7.5	odd	6
231.4.i.b.100.4	yes	20	7.3	odd	6
1617.4.a.y.1.7		10	7.6	odd	2
1617.4.a.z.1.7		10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1617.a (trivial)

\(f(q)\)	\(=\)	\(q+2.38864 q^{2} +3.00000 q^{3} -2.29442 q^{4} +9.60191 q^{5} +7.16591 q^{6} -24.5896 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.38864 q^{2} +3.00000 q^{3} -2.29442 q^{4} +9.60191 q^{5} +7.16591 q^{6} -24.5896 q^{8} +9.00000 q^{9} +22.9355 q^{10} -11.0000 q^{11} -6.88325 q^{12} -38.2982 q^{13} +28.8057 q^{15} -40.3803 q^{16} +114.205 q^{17} +21.4977 q^{18} +57.0630 q^{19} -22.0308 q^{20} -26.2750 q^{22} -40.1730 q^{23} -73.7689 q^{24} -32.8033 q^{25} -91.4806 q^{26} +27.0000 q^{27} -71.8590 q^{29} +68.8064 q^{30} +220.110 q^{31} +100.263 q^{32} -33.0000 q^{33} +272.795 q^{34} -20.6497 q^{36} +99.1040 q^{37} +136.303 q^{38} -114.895 q^{39} -236.107 q^{40} +452.976 q^{41} +6.92384 q^{43} +25.2386 q^{44} +86.4172 q^{45} -95.9587 q^{46} -74.7978 q^{47} -121.141 q^{48} -78.3552 q^{50} +342.616 q^{51} +87.8721 q^{52} +35.4116 q^{53} +64.4932 q^{54} -105.621 q^{55} +171.189 q^{57} -171.645 q^{58} +115.484 q^{59} -66.0923 q^{60} -3.61161 q^{61} +525.762 q^{62} +562.535 q^{64} -367.736 q^{65} -78.8250 q^{66} +453.304 q^{67} -262.034 q^{68} -120.519 q^{69} +129.937 q^{71} -221.307 q^{72} +315.243 q^{73} +236.723 q^{74} -98.4100 q^{75} -130.926 q^{76} -274.442 q^{78} +491.190 q^{79} -387.728 q^{80} +81.0000 q^{81} +1081.99 q^{82} +851.068 q^{83} +1096.59 q^{85} +16.5385 q^{86} -215.577 q^{87} +270.486 q^{88} +1142.97 q^{89} +206.419 q^{90} +92.1735 q^{92} +660.329 q^{93} -178.665 q^{94} +547.914 q^{95} +300.789 q^{96} -1521.32 q^{97} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + 30 q^{3} + 26 q^{4} + 20 q^{5} + 12 q^{6} + 36 q^{8} + 90 q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 + 30 * q^3 + 26 * q^4 + 20 * q^5 + 12 * q^6 + 36 * q^8 + 90 * q^9	\( 10 q + 4 q^{2} + 30 q^{3} + 26 q^{4} + 20 q^{5} + 12 q^{6} + 36 q^{8} + 90 q^{9} + 44 q^{10} - 110 q^{11} + 78 q^{12} + 82 q^{13} + 60 q^{15} - 10 q^{16} + 164 q^{17} + 36 q^{18} - 76 q^{19} + 356 q^{20} - 44 q^{22} + 140 q^{23} + 108 q^{24} + 472 q^{25} + 360 q^{26} + 270 q^{27} + 40 q^{29} + 132 q^{30} + 24 q^{31} + 112 q^{32} - 330 q^{33} - 262 q^{34} + 234 q^{36} + 412 q^{37} + 16 q^{38} + 246 q^{39} + 828 q^{40} - 228 q^{41} + 530 q^{43} - 286 q^{44} + 180 q^{45} + 1422 q^{46} + 768 q^{47} - 30 q^{48} + 670 q^{50} + 492 q^{51} + 952 q^{52} + 136 q^{53} + 108 q^{54} - 220 q^{55} - 228 q^{57} + 1708 q^{58} + 608 q^{59} + 1068 q^{60} + 1618 q^{61} + 164 q^{62} - 1238 q^{64} + 2764 q^{65} - 132 q^{66} + 1002 q^{67} + 2816 q^{68} + 420 q^{69} + 812 q^{71} + 324 q^{72} + 134 q^{73} + 342 q^{74} + 1416 q^{75} - 450 q^{76} + 1080 q^{78} + 1262 q^{79} - 1316 q^{80} + 810 q^{81} + 982 q^{82} + 1078 q^{83} - 1402 q^{85} + 1692 q^{86} + 120 q^{87} - 396 q^{88} + 2880 q^{89} + 396 q^{90} + 2364 q^{92} + 72 q^{93} - 2362 q^{94} + 2866 q^{95} + 336 q^{96} - 1030 q^{97} - 990 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 + 30 * q^3 + 26 * q^4 + 20 * q^5 + 12 * q^6 + 36 * q^8 + 90 * q^9 + 44 * q^10 - 110 * q^11 + 78 * q^12 + 82 * q^13 + 60 * q^15 - 10 * q^16 + 164 * q^17 + 36 * q^18 - 76 * q^19 + 356 * q^20 - 44 * q^22 + 140 * q^23 + 108 * q^24 + 472 * q^25 + 360 * q^26 + 270 * q^27 + 40 * q^29 + 132 * q^30 + 24 * q^31 + 112 * q^32 - 330 * q^33 - 262 * q^34 + 234 * q^36 + 412 * q^37 + 16 * q^38 + 246 * q^39 + 828 * q^40 - 228 * q^41 + 530 * q^43 - 286 * q^44 + 180 * q^45 + 1422 * q^46 + 768 * q^47 - 30 * q^48 + 670 * q^50 + 492 * q^51 + 952 * q^52 + 136 * q^53 + 108 * q^54 - 220 * q^55 - 228 * q^57 + 1708 * q^58 + 608 * q^59 + 1068 * q^60 + 1618 * q^61 + 164 * q^62 - 1238 * q^64 + 2764 * q^65 - 132 * q^66 + 1002 * q^67 + 2816 * q^68 + 420 * q^69 + 812 * q^71 + 324 * q^72 + 134 * q^73 + 342 * q^74 + 1416 * q^75 - 450 * q^76 + 1080 * q^78 + 1262 * q^79 - 1316 * q^80 + 810 * q^81 + 982 * q^82 + 1078 * q^83 - 1402 * q^85 + 1692 * q^86 + 120 * q^87 - 396 * q^88 + 2880 * q^89 + 396 * q^90 + 2364 * q^92 + 72 * q^93 - 2362 * q^94 + 2866 * q^95 + 336 * q^96 - 1030 * q^97 - 990 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more