LMFDB - Embedded newform 1617.4.a.z.1.5

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			1.5
Root			$-0.373481$ 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)

$f(q)$	$=$	$q-0.373481 q^{2} +3.00000 q^{3} -7.86051 q^{4} -15.6838 q^{5} -1.12044 q^{6} +5.92360 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-0.373481 q^{2} +3.00000 q^{3} -7.86051 q^{4} -15.6838 q^{5} -1.12044 q^{6} +5.92360 q^{8} +9.00000 q^{9} +5.85760 q^{10} -11.0000 q^{11} -23.5815 q^{12} -78.6359 q^{13} -47.0514 q^{15} +60.6717 q^{16} -53.5346 q^{17} -3.36133 q^{18} -114.576 q^{19} +123.283 q^{20} +4.10829 q^{22} +25.9410 q^{23} +17.7708 q^{24} +120.982 q^{25} +29.3690 q^{26} +27.0000 q^{27} -269.201 q^{29} +17.5728 q^{30} -279.747 q^{31} -70.0486 q^{32} -33.0000 q^{33} +19.9942 q^{34} -70.7446 q^{36} +60.3231 q^{37} +42.7919 q^{38} -235.908 q^{39} -92.9046 q^{40} -171.202 q^{41} +394.211 q^{43} +86.4656 q^{44} -141.154 q^{45} -9.68846 q^{46} +131.745 q^{47} +182.015 q^{48} -45.1843 q^{50} -160.604 q^{51} +618.119 q^{52} -617.451 q^{53} -10.0840 q^{54} +172.522 q^{55} -343.727 q^{57} +100.542 q^{58} -478.234 q^{59} +369.848 q^{60} +134.787 q^{61} +104.480 q^{62} -459.212 q^{64} +1233.31 q^{65} +12.3249 q^{66} -580.631 q^{67} +420.809 q^{68} +77.8229 q^{69} +317.104 q^{71} +53.3124 q^{72} -282.606 q^{73} -22.5295 q^{74} +362.945 q^{75} +900.624 q^{76} +88.1071 q^{78} -658.919 q^{79} -951.563 q^{80} +81.0000 q^{81} +63.9408 q^{82} -374.689 q^{83} +839.625 q^{85} -147.230 q^{86} -807.604 q^{87} -65.1596 q^{88} +103.941 q^{89} +52.7184 q^{90} -203.909 q^{92} -839.241 q^{93} -49.2041 q^{94} +1796.98 q^{95} -210.146 q^{96} -1409.71 q^{97} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.373481	−0.132046	−0.0660228	−	0.997818i	$-0.521031\pi$
$2$	−0.373481	−0.132046	−0.0660228	+	0.997818i	$0.521031\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−7.86051	−0.982564
$5$	−15.6838	−1.40280	−0.701401	−	0.712767i	$-0.747442\pi$
$5$	−15.6838	−1.40280	−0.701401	+	0.712767i	$0.747442\pi$
$6$	−1.12044	−0.0762365
$7$	0	0
$7$	0	0
$8$	5.92360	0.261789
$9$	9.00000	0.333333
$10$	5.85760	0.185234
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−23.5815	−0.567284
$13$	−78.6359	−1.67767	−0.838834	−	0.544387i	$-0.816762\pi$
$13$	−78.6359	−1.67767	−0.838834	+	0.544387i	$0.816762\pi$
$14$	0	0
$15$	−47.0514	−0.809908
$16$	60.6717	0.947996
$17$	−53.5346	−0.763767	−0.381883	−	0.924210i	$-0.624724\pi$
$17$	−53.5346	−0.763767	−0.381883	+	0.924210i	$0.624724\pi$
$18$	−3.36133	−0.0440152
$19$	−114.576	−1.38345	−0.691723	−	0.722163i	$-0.743148\pi$
$19$	−114.576	−1.38345	−0.691723	+	0.722163i	$0.743148\pi$
$20$	123.283	1.37834
$21$	0	0
$22$	4.10829	0.0398132
$23$	25.9410	0.235177	0.117588	−	0.993062i	$-0.462484\pi$
$23$	25.9410	0.235177	0.117588	+	0.993062i	$0.462484\pi$
$24$	17.7708	0.151144
$25$	120.982	0.967852
$26$	29.3690	0.221529
$27$	27.0000	0.192450
$28$	0	0
$29$	−269.201	−1.72377	−0.861887	−	0.507100i	$-0.830717\pi$
$29$	−269.201	−1.72377	−0.861887	+	0.507100i	$0.830717\pi$
$30$	17.5728	0.106945
$31$	−279.747	−1.62077	−0.810387	−	0.585894i	$-0.800743\pi$
$31$	−279.747	−1.62077	−0.810387	+	0.585894i	$0.800743\pi$
$32$	−70.0486	−0.386967
$33$	−33.0000	−0.174078
$34$	19.9942	0.100852
$35$	0	0
$36$	−70.7446	−0.327521
$37$	60.3231	0.268028	0.134014	−	0.990979i	$-0.457213\pi$
$37$	60.3231	0.268028	0.134014	+	0.990979i	$0.457213\pi$
$38$	42.7919	0.182678
$39$	−235.908	−0.968602
$40$	−92.9046	−0.367238
$41$	−171.202	−0.652129	−0.326064	−	0.945348i	$-0.605723\pi$
$41$	−171.202	−0.652129	−0.326064	+	0.945348i	$0.605723\pi$
$42$	0	0
$43$	394.211	1.39806	0.699030	−	0.715092i	$-0.253615\pi$
$43$	394.211	1.39806	0.699030	+	0.715092i	$0.253615\pi$
$44$	86.4656	0.296254
$45$	−141.154	−0.467601
$46$	−9.68846	−0.0310540
$47$	131.745	0.408871	0.204435	−	0.978880i	$-0.434464\pi$
$47$	131.745	0.408871	0.204435	+	0.978880i	$0.434464\pi$
$48$	182.015	0.547326
$49$	0	0
$50$	−45.1843	−0.127801
$51$	−160.604	−0.440961
$52$	618.119	1.64842
$53$	−617.451	−1.60025	−0.800127	−	0.599831i	$-0.795234\pi$
$53$	−617.451	−1.60025	−0.800127	+	0.599831i	$0.795234\pi$
$54$	−10.0840	−0.0254122
$55$	172.522	0.422961
$56$	0	0
$57$	−343.727	−0.798733
$58$	100.542	0.227617
$59$	−478.234	−1.05527	−0.527634	−	0.849472i	$-0.676921\pi$
$59$	−478.234	−1.05527	−0.527634	+	0.849472i	$0.676921\pi$
$60$	369.848	0.795786
$61$	134.787	0.282914	0.141457	−	0.989944i	$-0.454821\pi$
$61$	134.787	0.282914	0.141457	+	0.989944i	$0.454821\pi$
$62$	104.480	0.214016
$63$	0	0
$64$	−459.212	−0.896899
$65$	1233.31	2.35344
$66$	12.3249	0.0229862
$67$	−580.631	−1.05874	−0.529368	−	0.848392i	$-0.677571\pi$
$67$	−580.631	−1.05874	−0.529368	+	0.848392i	$0.677571\pi$
$68$	420.809	0.750450
$69$	77.8229	0.135779
$70$	0	0
$71$	317.104	0.530047	0.265023	−	0.964242i	$-0.414620\pi$
$71$	317.104	0.530047	0.265023	+	0.964242i	$0.414620\pi$
$72$	53.3124	0.0872629
$73$	−282.606	−0.453103	−0.226551	−	0.973999i	$-0.572745\pi$
$73$	−282.606	−0.453103	−0.226551	+	0.973999i	$0.572745\pi$
$74$	−22.5295	−0.0353920
$75$	362.945	0.558790
$76$	900.624	1.35932
$77$	0	0
$78$	88.1071	0.127900
$79$	−658.919	−0.938407	−0.469203	−	0.883090i	$-0.655459\pi$
$79$	−658.919	−0.938407	−0.469203	+	0.883090i	$0.655459\pi$
$80$	−951.563	−1.32985
$81$	81.0000	0.111111
$82$	63.9408	0.0861107
$83$	−374.689	−0.495511	−0.247756	−	0.968823i	$-0.579693\pi$
$83$	−374.689	−0.495511	−0.247756	+	0.968823i	$0.579693\pi$
$84$	0	0
$85$	839.625	1.07141
$86$	−147.230	−0.184608
$87$	−807.604	−0.995222
$88$	−65.1596	−0.0789323
$89$	103.941	0.123794	0.0618971	−	0.998083i	$-0.480285\pi$
$89$	103.941	0.123794	0.0618971	+	0.998083i	$0.480285\pi$
$90$	52.7184	0.0617446
$91$	0	0
$92$	−203.909	−0.231076
$93$	−839.241	−0.935755
$94$	−49.2041	−0.0539896
$95$	1796.98	1.94070
$96$	−210.146	−0.223416
$97$	−1409.71	−1.47561	−0.737806	−	0.675012i	$-0.764138\pi$
$97$	−1409.71	−1.47561	−0.737806	+	0.675012i	$0.764138\pi$
$98$	0	0
$99$	−99.0000	−0.100504
$100$	−950.977	−0.950977
$101$	1346.24	1.32630	0.663149	−	0.748488i	$-0.269220\pi$
$101$	1346.24	1.32630	0.663149	+	0.748488i	$0.269220\pi$
$102$	59.9825	0.0582269
$103$	169.086	0.161753	0.0808764	−	0.996724i	$-0.474228\pi$
$103$	169.086	0.161753	0.0808764	+	0.996724i	$0.474228\pi$
$104$	−465.808	−0.439195
$105$	0	0
$106$	230.606	0.211306
$107$	−1151.59	−1.04045	−0.520225	−	0.854029i	$-0.674152\pi$
$107$	−1151.59	−1.04045	−0.520225	+	0.854029i	$0.674152\pi$
$108$	−212.234	−0.189095
$109$	−1432.64	−1.25892	−0.629458	−	0.777034i	$-0.716723\pi$
$109$	−1432.64	−1.25892	−0.629458	+	0.777034i	$0.716723\pi$
$110$	−64.4336	−0.0558501
$111$	180.969	0.154746
$112$	0	0
$113$	−901.099	−0.750162	−0.375081	−	0.926992i	$-0.622385\pi$
$113$	−901.099	−0.750162	−0.375081	+	0.926992i	$0.622385\pi$
$114$	128.376	0.105469
$115$	−406.853	−0.329906
$116$	2116.06	1.69372
$117$	−707.723	−0.559223
$118$	178.612	0.139343
$119$	0	0
$120$	−278.714	−0.212025
$121$	121.000	0.0909091
$122$	−50.3405	−0.0373575
$123$	−513.606	−0.376507
$124$	2198.95	1.59251
$125$	63.0251	0.0450971
$126$	0	0
$127$	1583.30	1.10626	0.553132	−	0.833093i	$-0.313432\pi$
$127$	1583.30	1.10626	0.553132	+	0.833093i	$0.313432\pi$
$128$	731.896	0.505399
$129$	1182.63	0.807170
$130$	−460.618	−0.310761
$131$	429.920	0.286735	0.143368	−	0.989669i	$-0.454207\pi$
$131$	429.920	0.286735	0.143368	+	0.989669i	$0.454207\pi$
$132$	259.397	0.171042
$133$	0	0
$134$	216.855	0.139801
$135$	−423.463	−0.269969
$136$	−317.117	−0.199946
$137$	2048.65	1.27758	0.638789	−	0.769382i	$-0.279436\pi$
$137$	2048.65	1.27758	0.638789	+	0.769382i	$0.279436\pi$
$138$	−29.0654	−0.0179291
$139$	1847.91	1.12761	0.563804	−	0.825909i	$-0.309337\pi$
$139$	1847.91	1.12761	0.563804	+	0.825909i	$0.309337\pi$
$140$	0	0
$141$	395.234	0.236062
$142$	−118.432	−0.0699903
$143$	864.995	0.505836
$144$	546.046	0.315999
$145$	4222.10	2.41811
$146$	105.548	0.0598302
$147$	0	0
$148$	−474.170	−0.263355
$149$	2757.83	1.51631	0.758154	−	0.652075i	$-0.226101\pi$
$149$	2757.83	1.51631	0.758154	+	0.652075i	$0.226101\pi$
$150$	−135.553	−0.0737857
$151$	1112.81	0.599729	0.299865	−	0.953982i	$-0.403059\pi$
$151$	1112.81	0.599729	0.299865	+	0.953982i	$0.403059\pi$
$152$	−678.701	−0.362171
$153$	−481.811	−0.254589
$154$	0	0
$155$	4387.49	2.27363
$156$	1854.36	0.951713
$157$	−1648.17	−0.837822	−0.418911	−	0.908027i	$-0.637588\pi$
$157$	−1648.17	−0.837822	−0.418911	+	0.908027i	$0.637588\pi$
$158$	246.094	0.123912
$159$	−1852.35	−0.923907
$160$	1098.63	0.542838
$161$	0	0
$162$	−30.2520	−0.0146717
$163$	2028.25	0.974629	0.487315	−	0.873226i	$-0.337976\pi$
$163$	2028.25	0.974629	0.487315	+	0.873226i	$0.337976\pi$
$164$	1345.74	0.640758
$165$	517.565	0.244196
$166$	139.939	0.0654301
$167$	354.033	0.164047	0.0820237	−	0.996630i	$-0.473862\pi$
$167$	354.033	0.164047	0.0820237	+	0.996630i	$0.473862\pi$
$168$	0	0
$169$	3986.61	1.81457
$170$	−313.584	−0.141475
$171$	−1031.18	−0.461149
$172$	−3098.70	−1.37368
$173$	2439.05	1.07189	0.535946	−	0.844252i	$-0.319955\pi$
$173$	2439.05	1.07189	0.535946	+	0.844252i	$0.319955\pi$
$174$	301.625	0.131415
$175$	0	0
$176$	−667.389	−0.285832
$177$	−1434.70	−0.609259
$178$	−38.8198	−0.0163465
$179$	−3485.36	−1.45535	−0.727677	−	0.685920i	$-0.759400\pi$
$179$	−3485.36	−1.45535	−0.727677	+	0.685920i	$0.759400\pi$
$180$	1109.54	0.459447
$181$	1289.03	0.529352	0.264676	−	0.964337i	$-0.414735\pi$
$181$	1289.03	0.529352	0.264676	+	0.964337i	$0.414735\pi$
$182$	0	0
$183$	404.361	0.163340
$184$	153.664	0.0615666
$185$	−946.095	−0.375991
$186$	313.441	0.123562
$187$	588.880	0.230284
$188$	−1035.58	−0.401742
$189$	0	0
$190$	−671.139	−0.256261
$191$	2834.69	1.07388	0.536940	−	0.843621i	$-0.319580\pi$
$191$	2834.69	1.07388	0.536940	+	0.843621i	$0.319580\pi$
$192$	−1377.64	−0.517825
$193$	−593.155	−0.221224	−0.110612	−	0.993864i	$-0.535281\pi$
$193$	−593.155	−0.221224	−0.110612	+	0.993864i	$0.535281\pi$
$194$	526.501	0.194848
$195$	3699.93	1.35876
$196$	0	0
$197$	1832.40	0.662705	0.331353	−	0.943507i	$-0.392495\pi$
$197$	1832.40	0.662705	0.331353	+	0.943507i	$0.392495\pi$
$198$	36.9746	0.0132711
$199$	2165.87	0.771528	0.385764	−	0.922597i	$-0.373938\pi$
$199$	2165.87	0.771528	0.385764	+	0.922597i	$0.373938\pi$
$200$	716.646	0.253373
$201$	−1741.89	−0.611262
$202$	−502.796	−0.175132
$203$	0	0
$204$	1262.43	0.433272
$205$	2685.10	0.914807
$206$	−63.1504	−0.0213587
$207$	233.469	0.0783922
$208$	−4770.98	−1.59042
$209$	1260.33	0.417125
$210$	0	0
$211$	63.4979	0.0207174	0.0103587	−	0.999946i	$-0.496703\pi$
$211$	63.4979	0.0207174	0.0103587	+	0.999946i	$0.496703\pi$
$212$	4853.48	1.57235
$213$	951.312	0.306023
$214$	430.097	0.137387
$215$	−6182.72	−1.96120
$216$	159.937	0.0503813
$217$	0	0
$218$	535.064	0.166234
$219$	−847.817	−0.261599
$220$	−1356.11	−0.415586
$221$	4209.74	1.28135
$222$	−67.5886	−0.0204336
$223$	−3792.09	−1.13873	−0.569366	−	0.822084i	$-0.692811\pi$
$223$	−3792.09	−1.13873	−0.569366	+	0.822084i	$0.692811\pi$
$224$	0	0
$225$	1088.83	0.322617
$226$	336.544	0.0990555
$227$	−606.076	−0.177210	−0.0886050	−	0.996067i	$-0.528241\pi$
$227$	−606.076	−0.177210	−0.0886050	+	0.996067i	$0.528241\pi$
$228$	2701.87	0.784806
$229$	−2038.61	−0.588275	−0.294137	−	0.955763i	$-0.595032\pi$
$229$	−2038.61	−0.588275	−0.294137	+	0.955763i	$0.595032\pi$
$230$	151.952	0.0435627
$231$	0	0
$232$	−1594.64	−0.451265
$233$	−3415.09	−0.960214	−0.480107	−	0.877210i	$-0.659402\pi$
$233$	−3415.09	−0.960214	−0.480107	+	0.877210i	$0.659402\pi$
$234$	264.321	0.0738429
$235$	−2066.26	−0.573564
$236$	3759.17	1.03687
$237$	−1976.76	−0.541789
$238$	0	0
$239$	6414.94	1.73618	0.868092	−	0.496403i	$-0.165346\pi$
$239$	6414.94	1.73618	0.868092	+	0.496403i	$0.165346\pi$
$240$	−2854.69	−0.767789
$241$	−6503.59	−1.73831	−0.869156	−	0.494539i	$-0.835337\pi$
$241$	−6503.59	−1.73831	−0.869156	+	0.494539i	$0.835337\pi$
$242$	−45.1912	−0.0120041
$243$	243.000	0.0641500
$244$	−1059.50	−0.277981
$245$	0	0
$246$	191.822	0.0497160
$247$	9009.77	2.32096
$248$	−1657.11	−0.424301
$249$	−1124.07	−0.286084
$250$	−23.5387	−0.00595487
$251$	−7281.36	−1.83106	−0.915529	−	0.402252i	$-0.868228\pi$
$251$	−7281.36	−1.83106	−0.915529	+	0.402252i	$0.868228\pi$
$252$	0	0
$253$	−285.351	−0.0709084
$254$	−591.335	−0.146077
$255$	2518.88	0.618581
$256$	3400.35	0.830163
$257$	3369.28	0.817781	0.408890	−	0.912583i	$-0.365916\pi$
$257$	3369.28	0.817781	0.408890	+	0.912583i	$0.365916\pi$
$258$	−441.691	−0.106583
$259$	0	0
$260$	−9694.45	−2.31240
$261$	−2422.81	−0.574591
$262$	−160.567	−0.0378621
$263$	2598.76	0.609302	0.304651	−	0.952464i	$-0.401460\pi$
$263$	2598.76	0.609302	0.304651	+	0.952464i	$0.401460\pi$
$264$	−195.479	−0.0455716
$265$	9683.98	2.24484
$266$	0	0
$267$	311.822	0.0714726
$268$	4564.06	1.04028
$269$	−5083.20	−1.15215	−0.576074	−	0.817397i	$-0.695416\pi$
$269$	−5083.20	−1.15215	−0.576074	+	0.817397i	$0.695416\pi$
$270$	158.155	0.0356482
$271$	488.084	0.109406	0.0547029	−	0.998503i	$-0.482579\pi$
$271$	488.084	0.109406	0.0547029	+	0.998503i	$0.482579\pi$
$272$	−3248.03	−0.724048
$273$	0	0
$274$	−765.133	−0.168698
$275$	−1330.80	−0.291818
$276$	−611.728	−0.133412
$277$	−2062.77	−0.447436	−0.223718	−	0.974654i	$-0.571819\pi$
$277$	−2062.77	−0.447436	−0.223718	+	0.974654i	$0.571819\pi$
$278$	−690.159	−0.148896
$279$	−2517.72	−0.540258
$280$	0	0
$281$	5093.51	1.08133	0.540664	−	0.841239i	$-0.318173\pi$
$281$	5093.51	1.08133	0.540664	+	0.841239i	$0.318173\pi$
$282$	−147.612	−0.0311709
$283$	−4289.53	−0.901012	−0.450506	−	0.892773i	$-0.648756\pi$
$283$	−4289.53	−0.901012	−0.450506	+	0.892773i	$0.648756\pi$
$284$	−2492.60	−0.520805
$285$	5390.95	1.12046
$286$	−323.059	−0.0667934
$287$	0	0
$288$	−630.437	−0.128989
$289$	−2047.05	−0.416660
$290$	−1576.88	−0.319301
$291$	−4229.13	−0.851945
$292$	2221.43	0.445203
$293$	2402.81	0.479091	0.239545	−	0.970885i	$-0.423002\pi$
$293$	2402.81	0.479091	0.239545	+	0.970885i	$0.423002\pi$
$294$	0	0
$295$	7500.53	1.48033
$296$	357.330	0.0701668
$297$	−297.000	−0.0580259
$298$	−1030.00	−0.200222
$299$	−2039.89	−0.394548
$300$	−2852.93	−0.549047
$301$	0	0
$302$	−415.613	−0.0791916
$303$	4038.72	0.765738
$304$	−6951.51	−1.31150
$305$	−2113.97	−0.396872
$306$	179.947	0.0336173
$307$	2122.18	0.394525	0.197262	−	0.980351i	$-0.436795\pi$
$307$	2122.18	0.394525	0.197262	+	0.980351i	$0.436795\pi$
$308$	0	0
$309$	507.258	0.0933880
$310$	−1638.65	−0.300222
$311$	−8197.92	−1.49473	−0.747366	−	0.664413i	$-0.768682\pi$
$311$	−8197.92	−1.49473	−0.747366	+	0.664413i	$0.768682\pi$
$312$	−1397.42	−0.253569
$313$	−6335.22	−1.14405	−0.572025	−	0.820236i	$-0.693842\pi$
$313$	−6335.22	−1.14405	−0.572025	+	0.820236i	$0.693842\pi$
$314$	615.560	0.110631
$315$	0	0
$316$	5179.44	0.922045
$317$	−4721.31	−0.836515	−0.418258	−	0.908328i	$-0.637359\pi$
$317$	−4721.31	−0.836515	−0.418258	+	0.908328i	$0.637359\pi$
$318$	691.819	0.121998
$319$	2961.22	0.519738
$320$	7202.19	1.25817
$321$	−3454.76	−0.600705
$322$	0	0
$323$	6133.76	1.05663
$324$	−636.701	−0.109174
$325$	−9513.49	−1.62373
$326$	−757.512	−0.128695
$327$	−4297.92	−0.726836
$328$	−1014.13	−0.170720
$329$	0	0
$330$	−193.301	−0.0322450
$331$	6162.15	1.02327	0.511635	−	0.859203i	$-0.329040\pi$
$331$	6162.15	1.02327	0.511635	+	0.859203i	$0.329040\pi$
$332$	2945.25	0.486872
$333$	542.907	0.0893428
$334$	−132.225	−0.0216617
$335$	9106.50	1.48520
$336$	0	0
$337$	−7705.65	−1.24556	−0.622779	−	0.782397i	$-0.713997\pi$
$337$	−7705.65	−1.24556	−0.622779	+	0.782397i	$0.713997\pi$
$338$	−1488.92	−0.239606
$339$	−2703.30	−0.433106
$340$	−6599.88	−1.05273
$341$	3077.22	0.488682
$342$	385.127	0.0608926
$343$	0	0
$344$	2335.15	0.365996
$345$	−1220.56	−0.190471
$346$	−910.938	−0.141539
$347$	−6625.71	−1.02503	−0.512517	−	0.858677i	$-0.671287\pi$
$347$	−6625.71	−1.02503	−0.512517	+	0.858677i	$0.671287\pi$
$348$	6348.18	0.977869
$349$	−713.696	−0.109465	−0.0547325	−	0.998501i	$-0.517431\pi$
$349$	−713.696	−0.109465	−0.0547325	+	0.998501i	$0.517431\pi$
$350$	0	0
$351$	−2123.17	−0.322867
$352$	770.534	0.116675
$353$	9996.47	1.50725	0.753624	−	0.657306i	$-0.228304\pi$
$353$	9996.47	1.50725	0.753624	+	0.657306i	$0.228304\pi$
$354$	535.835	0.0804500
$355$	−4973.40	−0.743551
$356$	−817.026	−0.121636
$357$	0	0
$358$	1301.72	0.192173
$359$	5044.14	0.741558	0.370779	−	0.928721i	$-0.379091\pi$
$359$	5044.14	0.741558	0.370779	+	0.928721i	$0.379091\pi$
$360$	−836.141	−0.122413
$361$	6268.60	0.913924
$362$	−481.428	−0.0698985
$363$	363.000	0.0524864
$364$	0	0
$365$	4432.33	0.635613
$366$	−151.021	−0.0215683
$367$	−11275.1	−1.60370	−0.801850	−	0.597525i	$-0.796151\pi$
$367$	−11275.1	−1.60370	−0.801850	+	0.597525i	$0.796151\pi$
$368$	1573.88	0.222947
$369$	−1540.82	−0.217376
$370$	353.349	0.0496479
$371$	0	0
$372$	6596.86	0.919439
$373$	−10449.4	−1.45054	−0.725268	−	0.688466i	$-0.758284\pi$
$373$	−10449.4	−1.45054	−0.725268	+	0.688466i	$0.758284\pi$
$374$	−219.936	−0.0304080
$375$	189.075	0.0260368
$376$	780.403	0.107038
$377$	21168.9	2.89192
$378$	0	0
$379$	−9998.31	−1.35509	−0.677545	−	0.735482i	$-0.736956\pi$
$379$	−9998.31	−1.35509	−0.677545	+	0.735482i	$0.736956\pi$
$380$	−14125.2	−1.90686
$381$	4749.91	0.638702
$382$	−1058.70	−0.141801
$383$	7488.44	0.999064	0.499532	−	0.866295i	$-0.333505\pi$
$383$	7488.44	0.999064	0.499532	+	0.866295i	$0.333505\pi$
$384$	2195.69	0.291792
$385$	0	0
$386$	221.532	0.0292117
$387$	3547.90	0.466020
$388$	11081.0	1.44988
$389$	6329.28	0.824954	0.412477	−	0.910968i	$-0.364664\pi$
$389$	6329.28	0.824954	0.412477	+	0.910968i	$0.364664\pi$
$390$	−1381.85	−0.179418
$391$	−1388.74	−0.179620
$392$	0	0
$393$	1289.76	0.165547
$394$	−684.366	−0.0875073
$395$	10334.3	1.31640
$396$	778.191	0.0987514
$397$	13703.4	1.73237	0.866187	−	0.499719i	$-0.166564\pi$
$397$	13703.4	1.73237	0.866187	+	0.499719i	$0.166564\pi$
$398$	−808.910	−0.101877
$399$	0	0
$400$	7340.16	0.917520
$401$	244.844	0.0304911	0.0152455	−	0.999884i	$-0.495147\pi$
$401$	244.844	0.0304911	0.0152455	+	0.999884i	$0.495147\pi$
$402$	650.564	0.0807144
$403$	21998.2	2.71912
$404$	−10582.1	−1.30317
$405$	−1270.39	−0.155867
$406$	0	0
$407$	−663.554	−0.0808136
$408$	−951.352	−0.115439
$409$	−563.042	−0.0680700	−0.0340350	−	0.999421i	$-0.510836\pi$
$409$	−563.042	−0.0680700	−0.0340350	+	0.999421i	$0.510836\pi$
$410$	−1002.83	−0.120796
$411$	6145.96	0.737610
$412$	−1329.10	−0.158932
$413$	0	0
$414$	−87.1962	−0.0103513
$415$	5876.54	0.695104
$416$	5508.34	0.649203
$417$	5543.72	0.651025
$418$	−470.711	−0.0550795
$419$	−7190.47	−0.838371	−0.419185	−	0.907901i	$-0.637684\pi$
$419$	−7190.47	−0.838371	−0.419185	+	0.907901i	$0.637684\pi$
$420$	0	0
$421$	−3991.94	−0.462126	−0.231063	−	0.972939i	$-0.574220\pi$
$421$	−3991.94	−0.462126	−0.231063	+	0.972939i	$0.574220\pi$
$422$	−23.7153	−0.00273564
$423$	1185.70	0.136290
$424$	−3657.54	−0.418928
$425$	−6476.69	−0.739213
$426$	−355.297	−0.0404089
$427$	0	0
$428$	9052.07	1.02231
$429$	2594.99	0.292044
$430$	2309.13	0.258968
$431$	−12799.0	−1.43041	−0.715203	−	0.698917i	$-0.753666\pi$
$431$	−12799.0	−1.43041	−0.715203	+	0.698917i	$0.753666\pi$
$432$	1638.14	0.182442
$433$	933.425	0.103597	0.0517986	−	0.998658i	$-0.483505\pi$
$433$	933.425	0.103597	0.0517986	+	0.998658i	$0.483505\pi$
$434$	0	0
$435$	12666.3	1.39610
$436$	11261.3	1.23697
$437$	−2972.21	−0.325354
$438$	316.644	0.0345430
$439$	−11409.2	−1.24039	−0.620193	−	0.784450i	$-0.712946\pi$
$439$	−11409.2	−1.24039	−0.620193	+	0.784450i	$0.712946\pi$
$440$	1021.95	0.110726
$441$	0	0
$442$	−1572.26	−0.169196
$443$	−13651.1	−1.46407	−0.732036	−	0.681266i	$-0.761430\pi$
$443$	−13651.1	−1.46407	−0.732036	+	0.681266i	$0.761430\pi$
$444$	−1422.51	−0.152048
$445$	−1630.18	−0.173659
$446$	1416.28	0.150365
$447$	8273.48	0.875441
$448$	0	0
$449$	−10354.5	−1.08833	−0.544165	−	0.838978i	$-0.683154\pi$
$449$	−10354.5	−1.08833	−0.544165	+	0.838978i	$0.683154\pi$
$450$	−406.659	−0.0426002
$451$	1883.22	0.196624
$452$	7083.10	0.737082
$453$	3338.43	0.346254
$454$	226.358	0.0233998
$455$	0	0
$456$	−2036.10	−0.209099
$457$	4971.25	0.508852	0.254426	−	0.967092i	$-0.418113\pi$
$457$	4971.25	0.508852	0.254426	+	0.967092i	$0.418113\pi$
$458$	761.381	0.0776790
$459$	−1445.43	−0.146987
$460$	3198.07	0.324154
$461$	13126.8	1.32619	0.663096	−	0.748534i	$-0.269242\pi$
$461$	13126.8	1.32619	0.663096	+	0.748534i	$0.269242\pi$
$462$	0	0
$463$	−6489.16	−0.651354	−0.325677	−	0.945481i	$-0.605592\pi$
$463$	−6489.16	−0.651354	−0.325677	+	0.945481i	$0.605592\pi$
$464$	−16332.9	−1.63413
$465$	13162.5	1.31268
$466$	1275.47	0.126792
$467$	−12172.3	−1.20614	−0.603071	−	0.797687i	$-0.706057\pi$
$467$	−12172.3	−1.20614	−0.603071	+	0.797687i	$0.706057\pi$
$468$	5563.07	0.549472
$469$	0	0
$470$	771.708	0.0757366
$471$	−4944.50	−0.483717
$472$	−2832.87	−0.276257
$473$	−4336.32	−0.421531
$474$	738.281	0.0715409
$475$	−13861.5	−1.33897
$476$	0	0
$477$	−5557.06	−0.533418
$478$	−2395.86	−0.229255
$479$	−10879.7	−1.03780	−0.518899	−	0.854836i	$-0.673658\pi$
$479$	−10879.7	−1.03780	−0.518899	+	0.854836i	$0.673658\pi$
$480$	3295.88	0.313408
$481$	−4743.56	−0.449663
$482$	2428.97	0.229536
$483$	0	0
$484$	−951.122	−0.0893240
$485$	22109.6	2.06999
$486$	−90.7559	−0.00847073
$487$	385.967	0.0359134	0.0179567	−	0.999839i	$-0.494284\pi$
$487$	385.967	0.0359134	0.0179567	+	0.999839i	$0.494284\pi$
$488$	798.426	0.0740636
$489$	6084.74	0.562703
$490$	0	0
$491$	−17786.7	−1.63483	−0.817415	−	0.576049i	$-0.804594\pi$
$491$	−17786.7	−1.63483	−0.817415	+	0.576049i	$0.804594\pi$
$492$	4037.21	0.369942
$493$	14411.6	1.31656
$494$	−3364.98	−0.306473
$495$	1552.70	0.140987
$496$	−16972.7	−1.53649
$497$	0	0
$498$	419.818	0.0377761
$499$	−2954.27	−0.265033	−0.132516	−	0.991181i	$-0.542306\pi$
$499$	−2954.27	−0.265033	−0.132516	+	0.991181i	$0.542306\pi$
$500$	−495.410	−0.0443108
$501$	1062.10	0.0947128
$502$	2719.45	0.241783
$503$	−3898.60	−0.345587	−0.172793	−	0.984958i	$-0.555279\pi$
$503$	−3898.60	−0.345587	−0.172793	+	0.984958i	$0.555279\pi$
$504$	0	0
$505$	−21114.2	−1.86053
$506$	106.573	0.00936315
$507$	11959.8	1.04764
$508$	−12445.6	−1.08698
$509$	16161.2	1.40734	0.703668	−	0.710529i	$-0.251544\pi$
$509$	16161.2	1.40734	0.703668	+	0.710529i	$0.251544\pi$
$510$	−940.753	−0.0816808
$511$	0	0
$512$	−7125.13	−0.615018
$513$	−3093.55	−0.266244
$514$	−1258.36	−0.107984
$515$	−2651.91	−0.226907
$516$	−9296.09	−0.793096
$517$	−1449.19	−0.123279
$518$	0	0
$519$	7317.14	0.618857
$520$	7305.64	0.616103
$521$	10751.0	0.904046	0.452023	−	0.892006i	$-0.350703\pi$
$521$	10751.0	0.904046	0.452023	+	0.892006i	$0.350703\pi$
$522$	904.875	0.0758722
$523$	−10205.6	−0.853271	−0.426636	−	0.904424i	$-0.640301\pi$
$523$	−10205.6	−0.853271	−0.426636	+	0.904424i	$0.640301\pi$
$524$	−3379.39	−0.281736
$525$	0	0
$526$	−970.589	−0.0804557
$527$	14976.1	1.23789
$528$	−2002.17	−0.165025
$529$	−11494.1	−0.944692
$530$	−3616.78	−0.296421
$531$	−4304.11	−0.351756
$532$	0	0
$533$	13462.6	1.09406
$534$	−116.460	−0.00943763
$535$	18061.3	1.45955
$536$	−3439.43	−0.277165
$537$	−10456.1	−0.840249
$538$	1898.48	0.152136
$539$	0	0
$540$	3328.63	0.265262
$541$	17763.6	1.41168	0.705839	−	0.708372i	$-0.250570\pi$
$541$	17763.6	1.41168	0.705839	+	0.708372i	$0.250570\pi$
$542$	−182.290	−0.0144466
$543$	3867.08	0.305621
$544$	3750.02	0.295553
$545$	22469.2	1.76601
$546$	0	0
$547$	−7938.12	−0.620493	−0.310246	−	0.950656i	$-0.600412\pi$
$547$	−7938.12	−0.620493	−0.310246	+	0.950656i	$0.600412\pi$
$548$	−16103.5	−1.25530
$549$	1213.08	0.0943045
$550$	497.028	0.0385333
$551$	30844.0	2.38475
$552$	460.992	0.0355455
$553$	0	0
$554$	770.406	0.0590820
$555$	−2838.28	−0.217078
$556$	−14525.5	−1.10795
$557$	19202.6	1.46075	0.730376	−	0.683046i	$-0.239345\pi$
$557$	19202.6	1.46075	0.730376	+	0.683046i	$0.239345\pi$
$558$	940.322	0.0713387
$559$	−30999.1	−2.34548
$560$	0	0
$561$	1766.64	0.132955
$562$	−1902.33	−0.142785
$563$	3737.83	0.279806	0.139903	−	0.990165i	$-0.455321\pi$
$563$	3737.83	0.279806	0.139903	+	0.990165i	$0.455321\pi$
$564$	−3106.74	−0.231946
$565$	14132.7	1.05233
$566$	1602.06	0.118975
$567$	0	0
$568$	1878.40	0.138760
$569$	708.018	0.0521646	0.0260823	−	0.999660i	$-0.491697\pi$
$569$	708.018	0.0521646	0.0260823	+	0.999660i	$0.491697\pi$
$570$	−2013.42	−0.147952
$571$	1538.54	0.112760	0.0563798	−	0.998409i	$-0.482044\pi$
$571$	1538.54	0.112760	0.0563798	+	0.998409i	$0.482044\pi$
$572$	−6799.31	−0.497016
$573$	8504.07	0.620005
$574$	0	0
$575$	3138.38	0.227616
$576$	−4132.91	−0.298966
$577$	−21613.6	−1.55942	−0.779710	−	0.626141i	$-0.784633\pi$
$577$	−21613.6	−1.55942	−0.779710	+	0.626141i	$0.784633\pi$
$578$	764.535	0.0550181
$579$	−1779.47	−0.127724
$580$	−33187.9	−2.37595
$581$	0	0
$582$	1579.50	0.112496
$583$	6791.96	0.482495
$584$	−1674.04	−0.118617
$585$	11099.8	0.784478
$586$	−897.404	−0.0632618
$587$	−6569.63	−0.461938	−0.230969	−	0.972961i	$-0.574190\pi$
$587$	−6569.63	−0.461938	−0.230969	+	0.972961i	$0.574190\pi$
$588$	0	0
$589$	32052.2	2.24225
$590$	−2801.31	−0.195471
$591$	5497.19	0.382613
$592$	3659.90	0.254090
$593$	−7630.15	−0.528386	−0.264193	−	0.964470i	$-0.585106\pi$
$593$	−7630.15	−0.528386	−0.264193	+	0.964470i	$0.585106\pi$
$594$	110.924	0.00766206
$595$	0	0
$596$	−21677.9	−1.48987
$597$	6497.60	0.445442
$598$	761.861	0.0520984
$599$	19367.2	1.32107	0.660537	−	0.750794i	$-0.270329\pi$
$599$	19367.2	1.32107	0.660537	+	0.750794i	$0.270329\pi$
$600$	2149.94	0.146285
$601$	12187.5	0.827187	0.413593	−	0.910462i	$-0.364274\pi$
$601$	12187.5	0.827187	0.413593	+	0.910462i	$0.364274\pi$
$602$	0	0
$603$	−5225.68	−0.352912
$604$	−8747.25	−0.589272
$605$	−1897.74	−0.127527
$606$	−1508.39	−0.101112
$607$	−11736.6	−0.784804	−0.392402	−	0.919794i	$-0.628356\pi$
$607$	−11736.6	−0.784804	−0.392402	+	0.919794i	$0.628356\pi$
$608$	8025.87	0.535349
$609$	0	0
$610$	789.530	0.0524051
$611$	−10359.9	−0.685949
$612$	3787.28	0.250150
$613$	3769.29	0.248353	0.124176	−	0.992260i	$-0.460371\pi$
$613$	3769.29	0.248353	0.124176	+	0.992260i	$0.460371\pi$
$614$	−792.594	−0.0520953
$615$	8055.30	0.528164
$616$	0	0
$617$	−14739.4	−0.961725	−0.480862	−	0.876796i	$-0.659676\pi$
$617$	−14739.4	−0.961725	−0.480862	+	0.876796i	$0.659676\pi$
$618$	−189.451	−0.0123315
$619$	16715.0	1.08535	0.542677	−	0.839941i	$-0.317411\pi$
$619$	16715.0	1.08535	0.542677	+	0.839941i	$0.317411\pi$
$620$	−34487.9	−2.23398
$621$	700.406	0.0452598
$622$	3061.77	0.197373
$623$	0	0
$624$	−14312.9	−0.918231
$625$	−16111.2	−1.03111
$626$	2366.08	0.151067
$627$	3781.00	0.240827
$628$	12955.4	0.823214
$629$	−3229.37	−0.204711
$630$	0	0
$631$	2264.65	0.142875	0.0714376	−	0.997445i	$-0.477241\pi$
$631$	2264.65	0.142875	0.0714376	+	0.997445i	$0.477241\pi$
$632$	−3903.17	−0.245664
$633$	190.494	0.0119612
$634$	1763.32	0.110458
$635$	−24832.2	−1.55187
$636$	14560.4	0.907797
$637$	0	0
$638$	−1105.96	−0.0686290
$639$	2853.94	0.176682
$640$	−11478.9	−0.708974
$641$	16691.9	1.02853	0.514267	−	0.857630i	$-0.328064\pi$
$641$	16691.9	1.02853	0.514267	+	0.857630i	$0.328064\pi$
$642$	1290.29	0.0793204
$643$	−17787.1	−1.09091	−0.545455	−	0.838140i	$-0.683643\pi$
$643$	−17787.1	−1.09091	−0.545455	+	0.838140i	$0.683643\pi$
$644$	0	0
$645$	−18548.2	−1.13230
$646$	−2290.85	−0.139523
$647$	27898.7	1.69523	0.847613	−	0.530615i	$-0.178039\pi$
$647$	27898.7	1.69523	0.847613	+	0.530615i	$0.178039\pi$
$648$	479.812	0.0290876
$649$	5260.58	0.318175
$650$	3553.11	0.214407
$651$	0	0
$652$	−15943.1	−0.957636
$653$	5740.41	0.344012	0.172006	−	0.985096i	$-0.444975\pi$
$653$	5740.41	0.344012	0.172006	+	0.985096i	$0.444975\pi$
$654$	1605.19	0.0959754
$655$	−6742.79	−0.402233
$656$	−10387.1	−0.618216
$657$	−2543.45	−0.151034
$658$	0	0
$659$	15716.3	0.929015	0.464507	−	0.885569i	$-0.346231\pi$
$659$	15716.3	0.929015	0.464507	+	0.885569i	$0.346231\pi$
$660$	−4068.33	−0.239939
$661$	−24849.8	−1.46225	−0.731125	−	0.682244i	$-0.761004\pi$
$661$	−24849.8	−1.46225	−0.731125	+	0.682244i	$0.761004\pi$
$662$	−2301.45	−0.135118
$663$	12629.2	0.739786
$664$	−2219.51	−0.129719
$665$	0	0
$666$	−202.766	−0.0117973
$667$	−6983.35	−0.405392
$668$	−2782.88	−0.161187
$669$	−11376.3	−0.657448
$670$	−3401.11	−0.196114
$671$	−1482.66	−0.0853016
$672$	0	0
$673$	−13008.8	−0.745101	−0.372550	−	0.928012i	$-0.621517\pi$
$673$	−13008.8	−0.745101	−0.372550	+	0.928012i	$0.621517\pi$
$674$	2877.91	0.164471
$675$	3266.50	0.186263
$676$	−31336.8	−1.78293
$677$	915.461	0.0519705	0.0259853	−	0.999662i	$-0.491728\pi$
$677$	915.461	0.0519705	0.0259853	+	0.999662i	$0.491728\pi$
$678$	1009.63	0.0571897
$679$	0	0
$680$	4973.61	0.280484
$681$	−1818.23	−0.102312
$682$	−1149.28	−0.0645283
$683$	15271.7	0.855573	0.427787	−	0.903880i	$-0.359293\pi$
$683$	15271.7	0.855573	0.427787	+	0.903880i	$0.359293\pi$
$684$	8105.62	0.453108
$685$	−32130.6	−1.79219
$686$	0	0
$687$	−6115.82	−0.339641
$688$	23917.5	1.32536
$689$	48553.8	2.68469
$690$	455.856	0.0251509
$691$	−23206.7	−1.27760	−0.638802	−	0.769371i	$-0.720570\pi$
$691$	−23206.7	−1.27760	−0.638802	+	0.769371i	$0.720570\pi$
$692$	−19172.2	−1.05320
$693$	0	0
$694$	2474.58	0.135351
$695$	−28982.2	−1.58181
$696$	−4783.93	−0.260538
$697$	9165.23	0.498074
$698$	266.552	0.0144544
$699$	−10245.3	−0.554380
$700$	0	0
$701$	−5128.94	−0.276344	−0.138172	−	0.990408i	$-0.544123\pi$
$701$	−5128.94	−0.276344	−0.138172	+	0.990408i	$0.544123\pi$
$702$	792.964	0.0426332
$703$	−6911.56	−0.370803
$704$	5051.33	0.270425
$705$	−6198.77	−0.331148
$706$	−3733.49	−0.199025
$707$	0	0
$708$	11277.5	0.598636
$709$	−24020.8	−1.27238	−0.636191	−	0.771531i	$-0.719491\pi$
$709$	−24020.8	−1.27238	−0.636191	+	0.771531i	$0.719491\pi$
$710$	1857.47	0.0981826
$711$	−5930.27	−0.312802
$712$	615.703	0.0324079
$713$	−7256.90	−0.381168
$714$	0	0
$715$	−13566.4	−0.709587
$716$	27396.7	1.42998
$717$	19244.8	1.00239
$718$	−1883.89	−0.0979195
$719$	14157.6	0.734338	0.367169	−	0.930154i	$-0.380327\pi$
$719$	14157.6	0.734338	0.367169	+	0.930154i	$0.380327\pi$
$720$	−8564.07	−0.443283
$721$	0	0
$722$	−2341.21	−0.120680
$723$	−19510.8	−1.00361
$724$	−10132.4	−0.520122
$725$	−32568.4	−1.66836
$726$	−135.574	−0.00693059
$727$	5101.93	0.260275	0.130138	−	0.991496i	$-0.458458\pi$
$727$	5101.93	0.260275	0.130138	+	0.991496i	$0.458458\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	−1655.39	−0.0839299
$731$	−21103.9	−1.06779
$732$	−3178.49	−0.160492
$733$	13254.7	0.667903	0.333952	−	0.942590i	$-0.391618\pi$
$733$	13254.7	0.667903	0.333952	+	0.942590i	$0.391618\pi$
$734$	4211.06	0.211761
$735$	0	0
$736$	−1817.13	−0.0910057
$737$	6386.94	0.319221
$738$	575.467	0.0287036
$739$	−1203.25	−0.0598947	−0.0299473	−	0.999551i	$-0.509534\pi$
$739$	−1203.25	−0.0598947	−0.0299473	+	0.999551i	$0.509534\pi$
$740$	7436.79	0.369435
$741$	27029.3	1.34001
$742$	0	0
$743$	20578.1	1.01607	0.508034	−	0.861337i	$-0.330372\pi$
$743$	20578.1	1.01607	0.508034	+	0.861337i	$0.330372\pi$
$744$	−4971.33	−0.244970
$745$	−43253.2	−2.12708
$746$	3902.66	0.191537
$747$	−3372.20	−0.165170
$748$	−4628.90	−0.226269
$749$	0	0
$750$	−70.6161	−0.00343805
$751$	−5888.84	−0.286134	−0.143067	−	0.989713i	$-0.545696\pi$
$751$	−5888.84	−0.286134	−0.143067	+	0.989713i	$0.545696\pi$
$752$	7993.17	0.387608
$753$	−21844.1	−1.05716
$754$	−7906.19	−0.381865
$755$	−17453.1	−0.841301
$756$	0	0
$757$	−35225.6	−1.69128	−0.845638	−	0.533757i	$-0.820780\pi$
$757$	−35225.6	−1.69128	−0.845638	+	0.533757i	$0.820780\pi$
$758$	3734.18	0.178933
$759$	−856.052	−0.0409390
$760$	10644.6	0.508054
$761$	7279.88	0.346775	0.173387	−	0.984854i	$-0.444529\pi$
$761$	7279.88	0.346775	0.173387	+	0.984854i	$0.444529\pi$
$762$	−1774.00	−0.0843378
$763$	0	0
$764$	−22282.1	−1.05516
$765$	7556.63	0.357138
$766$	−2796.79	−0.131922
$767$	37606.4	1.77039
$768$	10201.0	0.479295
$769$	−9375.88	−0.439666	−0.219833	−	0.975538i	$-0.570551\pi$
$769$	−9375.88	−0.439666	−0.219833	+	0.975538i	$0.570551\pi$
$770$	0	0
$771$	10107.8	0.472146
$772$	4662.50	0.217367
$773$	−13793.4	−0.641804	−0.320902	−	0.947112i	$-0.603986\pi$
$773$	−13793.4	−0.641804	−0.320902	+	0.947112i	$0.603986\pi$
$774$	−1325.07	−0.0615359
$775$	−33844.2	−1.56867
$776$	−8350.57	−0.386299
$777$	0	0
$778$	−2363.87	−0.108932
$779$	19615.6	0.902185
$780$	−29083.3	−1.33507
$781$	−3488.15	−0.159815
$782$	518.668	0.0237180
$783$	−7268.44	−0.331741
$784$	0	0
$785$	25849.5	1.17530
$786$	−481.702	−0.0218597
$787$	13468.0	0.610016	0.305008	−	0.952350i	$-0.401341\pi$
$787$	13468.0	0.610016	0.305008	+	0.952350i	$0.401341\pi$
$788$	−14403.6	−0.651150
$789$	7796.29	0.351781
$790$	−3859.68	−0.173825
$791$	0	0
$792$	−586.437	−0.0263108
$793$	−10599.1	−0.474635
$794$	−5117.95	−0.228752
$795$	29051.9	1.29606
$796$	−17024.8	−0.758076
$797$	−19932.4	−0.885873	−0.442937	−	0.896553i	$-0.646063\pi$
$797$	−19932.4	−0.885873	−0.442937	+	0.896553i	$0.646063\pi$
$798$	0	0
$799$	−7052.89	−0.312282
$800$	−8474.58	−0.374527
$801$	935.465	0.0412647
$802$	−91.4447	−0.00402621
$803$	3108.66	0.136616
$804$	13692.2	0.600604
$805$	0	0
$806$	−8215.90	−0.359048
$807$	−15249.6	−0.665193
$808$	7974.60	0.347210
$809$	−3693.25	−0.160504	−0.0802519	−	0.996775i	$-0.525572\pi$
$809$	−3693.25	−0.160504	−0.0802519	+	0.996775i	$0.525572\pi$
$810$	474.466	0.0205815
$811$	17967.5	0.777959	0.388980	−	0.921246i	$-0.372828\pi$
$811$	17967.5	0.777959	0.388980	+	0.921246i	$0.372828\pi$
$812$	0	0
$813$	1464.25	0.0631655
$814$	247.825	0.0106711
$815$	−31810.6	−1.36721
$816$	−9744.10	−0.418029
$817$	−45167.0	−1.93414
$818$	210.285	0.00898834
$819$	0	0
$820$	−21106.3	−0.898857
$821$	−26741.7	−1.13677	−0.568387	−	0.822761i	$-0.692432\pi$
$821$	−26741.7	−1.13677	−0.568387	+	0.822761i	$0.692432\pi$
$822$	−2295.40	−0.0973981
$823$	−12340.4	−0.522670	−0.261335	−	0.965248i	$-0.584163\pi$
$823$	−12340.4	−0.522670	−0.261335	+	0.965248i	$0.584163\pi$
$824$	1001.60	0.0423451
$825$	−3992.39	−0.168481
$826$	0	0
$827$	−36993.6	−1.55549	−0.777747	−	0.628578i	$-0.783637\pi$
$827$	−36993.6	−1.55549	−0.777747	+	0.628578i	$0.783637\pi$
$828$	−1835.18	−0.0770254
$829$	−14452.7	−0.605504	−0.302752	−	0.953069i	$-0.597905\pi$
$829$	−14452.7	−0.605504	−0.302752	+	0.953069i	$0.597905\pi$
$830$	−2194.78	−0.0917854
$831$	−6188.31	−0.258327
$832$	36110.6	1.50470
$833$	0	0
$834$	−2070.48	−0.0859649
$835$	−5552.58	−0.230126
$836$	−9906.86	−0.409852
$837$	−7553.16	−0.311918
$838$	2685.50	0.110703
$839$	−7474.56	−0.307569	−0.153785	−	0.988104i	$-0.549146\pi$
$839$	−7474.56	−0.307569	−0.153785	+	0.988104i	$0.549146\pi$
$840$	0	0
$841$	48080.4	1.97140
$842$	1490.91	0.0610217
$843$	15280.5	0.624305
$844$	−499.126	−0.0203562
$845$	−62525.2	−2.54548
$846$	−442.837	−0.0179965
$847$	0	0
$848$	−37461.8	−1.51703
$849$	−12868.6	−0.520199
$850$	2418.92	0.0976098
$851$	1564.84	0.0630340
$852$	−7477.80	−0.300687
$853$	−9581.18	−0.384588	−0.192294	−	0.981337i	$-0.561593\pi$
$853$	−9581.18	−0.384588	−0.192294	+	0.981337i	$0.561593\pi$
$854$	0	0
$855$	16172.8	0.646900
$856$	−6821.55	−0.272378
$857$	35869.9	1.42975	0.714873	−	0.699254i	$-0.246485\pi$
$857$	35869.9	1.42975	0.714873	+	0.699254i	$0.246485\pi$
$858$	−969.178	−0.0385632
$859$	−29593.1	−1.17544	−0.587720	−	0.809064i	$-0.699974\pi$
$859$	−29593.1	−1.17544	−0.587720	+	0.809064i	$0.699974\pi$
$860$	48599.4	1.92700
$861$	0	0
$862$	4780.18	0.188879
$863$	−18759.8	−0.739967	−0.369983	−	0.929038i	$-0.620637\pi$
$863$	−18759.8	−0.739967	−0.369983	+	0.929038i	$0.620637\pi$
$864$	−1891.31	−0.0744719
$865$	−38253.5	−1.50365
$866$	−348.617	−0.0136795
$867$	−6141.15	−0.240559
$868$	0	0
$869$	7248.10	0.282940
$870$	−4730.63	−0.184349
$871$	45658.5	1.77621
$872$	−8486.38	−0.329570
$873$	−12687.4	−0.491871
$874$	1110.06	0.0429616
$875$	0	0
$876$	6664.28	0.257038
$877$	21532.9	0.829093	0.414546	−	0.910028i	$-0.363940\pi$
$877$	21532.9	0.829093	0.414546	+	0.910028i	$0.363940\pi$
$878$	4261.10	0.163787
$879$	7208.42	0.276603
$880$	10467.2	0.400965
$881$	8511.21	0.325483	0.162741	−	0.986669i	$-0.447966\pi$
$881$	8511.21	0.325483	0.162741	+	0.986669i	$0.447966\pi$
$882$	0	0
$883$	−30172.1	−1.14991	−0.574955	−	0.818185i	$-0.694981\pi$
$883$	−30172.1	−1.14991	−0.574955	+	0.818185i	$0.694981\pi$
$884$	−33090.7	−1.25901
$885$	22501.6	0.854670
$886$	5098.44	0.193324
$887$	1403.28	0.0531201	0.0265601	−	0.999647i	$-0.491545\pi$
$887$	1403.28	0.0531201	0.0265601	+	0.999647i	$0.491545\pi$
$888$	1071.99	0.0405108
$889$	0	0
$890$	608.843	0.0229308
$891$	−891.000	−0.0335013
$892$	29807.8	1.11888
$893$	−15094.7	−0.565651
$894$	−3089.99	−0.115598
$895$	54663.7	2.04157
$896$	0	0
$897$	−6119.68	−0.227793
$898$	3867.22	0.143709
$899$	75308.3	2.79385
$900$	−8558.79	−0.316992
$901$	33055.0	1.22222
$902$	−703.349	−0.0259634
$903$	0	0
$904$	−5337.75	−0.196384
$905$	−20216.8	−0.742575
$906$	−1246.84	−0.0457213
$907$	−29507.2	−1.08023	−0.540116	−	0.841591i	$-0.681620\pi$
$907$	−29507.2	−1.08023	−0.540116	+	0.841591i	$0.681620\pi$
$908$	4764.07	0.174120
$909$	12116.2	0.442099
$910$	0	0
$911$	31186.9	1.13421	0.567106	−	0.823645i	$-0.308063\pi$
$911$	31186.9	1.13421	0.567106	+	0.823645i	$0.308063\pi$
$912$	−20854.5	−0.757196
$913$	4121.58	0.149402
$914$	−1856.67	−0.0671916
$915$	−6341.92	−0.229134
$916$	16024.5	0.578017
$917$	0	0
$918$	539.842	0.0194090
$919$	15101.4	0.542055	0.271028	−	0.962572i	$-0.412637\pi$
$919$	15101.4	0.542055	0.271028	+	0.962572i	$0.412637\pi$
$920$	−2410.03	−0.0863657
$921$	6366.54	0.227779
$922$	−4902.60	−0.175118
$923$	−24935.8	−0.889243
$924$	0	0
$925$	7297.97	0.259412
$926$	2423.58	0.0860084
$927$	1521.77	0.0539176
$928$	18857.2	0.667045
$929$	47842.3	1.68962	0.844809	−	0.535068i	$-0.179714\pi$
$929$	47842.3	1.68962	0.844809	+	0.535068i	$0.179714\pi$
$930$	−4915.94	−0.173333
$931$	0	0
$932$	26844.3	0.943472
$933$	−24593.8	−0.862984
$934$	4546.14	0.159266
$935$	−9235.88	−0.323043
$936$	−4192.27	−0.146398
$937$	30585.9	1.06638	0.533190	−	0.845995i	$-0.320993\pi$
$937$	30585.9	1.06638	0.533190	+	0.845995i	$0.320993\pi$
$938$	0	0
$939$	−19005.7	−0.660518
$940$	16241.8	0.563564
$941$	19754.8	0.684366	0.342183	−	0.939633i	$-0.388834\pi$
$941$	19754.8	0.684366	0.342183	+	0.939633i	$0.388834\pi$
$942$	1846.68	0.0638727
$943$	−4441.15	−0.153366
$944$	−29015.3	−1.00039
$945$	0	0
$946$	1619.53	0.0556613
$947$	5614.30	0.192651	0.0963253	−	0.995350i	$-0.469291\pi$
$947$	5614.30	0.192651	0.0963253	+	0.995350i	$0.469291\pi$
$948$	15538.3	0.532343
$949$	22223.0	0.760156
$950$	5177.03	0.176805
$951$	−14163.9	−0.482962
$952$	0	0
$953$	26400.8	0.897383	0.448692	−	0.893687i	$-0.351890\pi$
$953$	26400.8	0.897383	0.448692	+	0.893687i	$0.351890\pi$
$954$	2075.46	0.0704354
$955$	−44458.7	−1.50644
$956$	−50424.7	−1.70591
$957$	8883.65	0.300071
$958$	4063.36	0.137037
$959$	0	0
$960$	21606.6	0.726405
$961$	48467.3	1.62691
$962$	1771.63	0.0593759
$963$	−10364.3	−0.346817
$964$	51121.5	1.70800
$965$	9302.93	0.310334
$966$	0	0
$967$	−38787.7	−1.28990	−0.644948	−	0.764227i	$-0.723121\pi$
$967$	−38787.7	−1.28990	−0.644948	+	0.764227i	$0.723121\pi$
$968$	716.756	0.0237990
$969$	18401.3	0.610046
$970$	−8257.53	−0.273333
$971$	−7871.68	−0.260159	−0.130079	−	0.991504i	$-0.541523\pi$
$971$	−7871.68	−0.260159	−0.130079	+	0.991504i	$0.541523\pi$
$972$	−1910.10	−0.0630315
$973$	0	0
$974$	−144.151	−0.00474220
$975$	−28540.5	−0.937464
$976$	8177.77	0.268201
$977$	52588.0	1.72205	0.861023	−	0.508565i	$-0.169824\pi$
$977$	52588.0	1.72205	0.861023	+	0.508565i	$0.169824\pi$
$978$	−2272.54	−0.0743024
$979$	−1143.35	−0.0373253
$980$	0	0
$981$	−12893.7	−0.419639
$982$	6642.99	0.215872
$983$	5989.62	0.194343	0.0971715	−	0.995268i	$-0.469020\pi$
$983$	5989.62	0.194343	0.0971715	+	0.995268i	$0.469020\pi$
$984$	−3042.40	−0.0985652
$985$	−28739.0	−0.929644
$986$	−5382.46	−0.173846
$987$	0	0
$988$	−70821.4	−2.28050
$989$	10226.2	0.328791
$990$	−579.903	−0.0186167
$991$	−34134.0	−1.09415	−0.547074	−	0.837084i	$-0.684259\pi$
$991$	−34134.0	−1.09415	−0.547074	+	0.837084i	$0.684259\pi$
$992$	19595.9	0.627187
$993$	18486.5	0.590786
$994$	0	0
$995$	−33969.0	−1.08230
$996$	8835.74	0.281095
$997$	−23179.8	−0.736321	−0.368160	−	0.929762i	$-0.620012\pi$
$997$	−23179.8	−0.736321	−0.368160	+	0.929762i	$0.620012\pi$
$998$	1103.36	0.0349964
$999$	1628.72	0.0515821

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.4.a.z.1.5		10
7.3	odd	6		231.4.i.b.100.6	yes	20
7.5	odd	6		231.4.i.b.67.6	✓	20
7.6	odd	2		1617.4.a.y.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.4.i.b.67.6	✓	20	7.5	odd	6
231.4.i.b.100.6	yes	20	7.3	odd	6
1617.4.a.y.1.5		10	7.6	odd	2
1617.4.a.z.1.5		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)

\(f(q)\)	\(=\)	\(q-0.373481 q^{2} +3.00000 q^{3} -7.86051 q^{4} -15.6838 q^{5} -1.12044 q^{6} +5.92360 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-0.373481 q^{2} +3.00000 q^{3} -7.86051 q^{4} -15.6838 q^{5} -1.12044 q^{6} +5.92360 q^{8} +9.00000 q^{9} +5.85760 q^{10} -11.0000 q^{11} -23.5815 q^{12} -78.6359 q^{13} -47.0514 q^{15} +60.6717 q^{16} -53.5346 q^{17} -3.36133 q^{18} -114.576 q^{19} +123.283 q^{20} +4.10829 q^{22} +25.9410 q^{23} +17.7708 q^{24} +120.982 q^{25} +29.3690 q^{26} +27.0000 q^{27} -269.201 q^{29} +17.5728 q^{30} -279.747 q^{31} -70.0486 q^{32} -33.0000 q^{33} +19.9942 q^{34} -70.7446 q^{36} +60.3231 q^{37} +42.7919 q^{38} -235.908 q^{39} -92.9046 q^{40} -171.202 q^{41} +394.211 q^{43} +86.4656 q^{44} -141.154 q^{45} -9.68846 q^{46} +131.745 q^{47} +182.015 q^{48} -45.1843 q^{50} -160.604 q^{51} +618.119 q^{52} -617.451 q^{53} -10.0840 q^{54} +172.522 q^{55} -343.727 q^{57} +100.542 q^{58} -478.234 q^{59} +369.848 q^{60} +134.787 q^{61} +104.480 q^{62} -459.212 q^{64} +1233.31 q^{65} +12.3249 q^{66} -580.631 q^{67} +420.809 q^{68} +77.8229 q^{69} +317.104 q^{71} +53.3124 q^{72} -282.606 q^{73} -22.5295 q^{74} +362.945 q^{75} +900.624 q^{76} +88.1071 q^{78} -658.919 q^{79} -951.563 q^{80} +81.0000 q^{81} +63.9408 q^{82} -374.689 q^{83} +839.625 q^{85} -147.230 q^{86} -807.604 q^{87} -65.1596 q^{88} +103.941 q^{89} +52.7184 q^{90} -203.909 q^{92} -839.241 q^{93} -49.2041 q^{94} +1796.98 q^{95} -210.146 q^{96} -1409.71 q^{97} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + 30 q^{3} + 26 q^{4} + 20 q^{5} + 12 q^{6} + 36 q^{8} + 90 q^{9}+O(q^{10}) \) 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

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