LMFDB - Embedded newform 1441.4.a.b.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,4,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1441.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1441.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:	$85.0217523183$
Analytic rank:	$1$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.09911 q^{2} +7.59971 q^{3} +8.80270 q^{4} -11.2108 q^{5} -31.1520 q^{6} +21.6950 q^{7} -3.29036 q^{8} +30.7555 q^{9} +O(q^{10})$	\(q-4.09911 q^{2} +7.59971 q^{3} +8.80270 q^{4} -11.2108 q^{5} -31.1520 q^{6} +21.6950 q^{7} -3.29036 q^{8} +30.7555 q^{9} +45.9544 q^{10} +11.0000 q^{11} +66.8979 q^{12} -8.19742 q^{13} -88.9304 q^{14} -85.1989 q^{15} -56.9341 q^{16} +58.8422 q^{17} -126.070 q^{18} +59.6122 q^{19} -98.6855 q^{20} +164.876 q^{21} -45.0902 q^{22} -173.781 q^{23} -25.0058 q^{24} +0.682530 q^{25} +33.6021 q^{26} +28.5408 q^{27} +190.975 q^{28} -171.564 q^{29} +349.240 q^{30} -93.0681 q^{31} +259.702 q^{32} +83.5968 q^{33} -241.201 q^{34} -243.219 q^{35} +270.732 q^{36} -348.564 q^{37} -244.357 q^{38} -62.2980 q^{39} +36.8877 q^{40} -211.209 q^{41} -675.844 q^{42} -221.156 q^{43} +96.8297 q^{44} -344.795 q^{45} +712.347 q^{46} +577.241 q^{47} -432.682 q^{48} +127.675 q^{49} -2.79777 q^{50} +447.183 q^{51} -72.1594 q^{52} -580.189 q^{53} -116.992 q^{54} -123.319 q^{55} -71.3845 q^{56} +453.035 q^{57} +703.261 q^{58} +474.373 q^{59} -749.981 q^{60} +127.704 q^{61} +381.496 q^{62} +667.242 q^{63} -609.074 q^{64} +91.8998 q^{65} -342.672 q^{66} +645.219 q^{67} +517.970 q^{68} -1320.68 q^{69} +996.982 q^{70} -1136.30 q^{71} -101.197 q^{72} +886.775 q^{73} +1428.80 q^{74} +5.18703 q^{75} +524.749 q^{76} +238.645 q^{77} +255.366 q^{78} +831.044 q^{79} +638.278 q^{80} -613.497 q^{81} +865.770 q^{82} -1296.70 q^{83} +1451.35 q^{84} -659.669 q^{85} +906.544 q^{86} -1303.84 q^{87} -36.1940 q^{88} -434.016 q^{89} +1413.35 q^{90} -177.843 q^{91} -1529.74 q^{92} -707.290 q^{93} -2366.18 q^{94} -668.302 q^{95} +1973.66 q^{96} +1312.84 q^{97} -523.353 q^{98} +338.311 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q - 20 q^{2} - 12 q^{3} + 288 q^{4} - 40 q^{5} - 111 q^{6} - 101 q^{7} - 258 q^{8} + 585 q^{9}+O(q^{10}) $ 79 * q - 20 * q^2 - 12 * q^3 + 288 * q^4 - 40 * q^5 - 111 * q^6 - 101 * q^7 - 258 * q^8 + 585 * q^9	\( 79 q - 20 q^{2} - 12 q^{3} + 288 q^{4} - 40 q^{5} - 111 q^{6} - 101 q^{7} - 258 q^{8} + 585 q^{9} - 178 q^{10} + 869 q^{11} - 144 q^{12} - 242 q^{13} - 342 q^{14} - 524 q^{15} + 928 q^{16} - 260 q^{17} - 611 q^{18} - 543 q^{19} - 578 q^{20} - 710 q^{21} - 220 q^{22} - 908 q^{23} - 1322 q^{24} + 1701 q^{25} - 844 q^{26} - 732 q^{27} - 1068 q^{28} - 1747 q^{29} - 973 q^{30} - 1248 q^{31} - 2069 q^{32} - 132 q^{33} - 76 q^{34} - 1630 q^{35} + 2155 q^{36} - 535 q^{37} + 1155 q^{38} - 2514 q^{39} - 298 q^{40} - 2087 q^{41} - 5 q^{42} - 1008 q^{43} + 3168 q^{44} - 1160 q^{45} - 1640 q^{46} - 1960 q^{47} + 3412 q^{48} + 3670 q^{49} - 2394 q^{50} - 2994 q^{51} - 2601 q^{52} - 2466 q^{53} + 1296 q^{54} - 440 q^{55} - 5195 q^{56} - 3776 q^{57} + 1068 q^{58} - 2310 q^{59} + 1599 q^{60} - 3404 q^{61} + 1534 q^{62} - 3409 q^{63} + 2568 q^{64} - 3906 q^{65} - 1221 q^{66} - 2405 q^{67} - 3145 q^{68} - 2420 q^{69} + 455 q^{70} - 8978 q^{71} - 7262 q^{72} - 1868 q^{73} - 2790 q^{74} - 1196 q^{75} - 5483 q^{76} - 1111 q^{77} + 349 q^{78} - 9130 q^{79} - 1697 q^{80} + 4171 q^{81} - 241 q^{82} - 4639 q^{83} - 1659 q^{84} - 7634 q^{85} - 5656 q^{86} - 4412 q^{87} - 2838 q^{88} - 6561 q^{89} - 6756 q^{90} - 2742 q^{91} - 5386 q^{92} - 3234 q^{93} - 5295 q^{94} - 7930 q^{95} - 12593 q^{96} - 4520 q^{97} - 3213 q^{98} + 6435 q^{99}+O(q^{100}) \) 79 * q - 20 * q^2 - 12 * q^3 + 288 * q^4 - 40 * q^5 - 111 * q^6 - 101 * q^7 - 258 * q^8 + 585 * q^9 - 178 * q^10 + 869 * q^11 - 144 * q^12 - 242 * q^13 - 342 * q^14 - 524 * q^15 + 928 * q^16 - 260 * q^17 - 611 * q^18 - 543 * q^19 - 578 * q^20 - 710 * q^21 - 220 * q^22 - 908 * q^23 - 1322 * q^24 + 1701 * q^25 - 844 * q^26 - 732 * q^27 - 1068 * q^28 - 1747 * q^29 - 973 * q^30 - 1248 * q^31 - 2069 * q^32 - 132 * q^33 - 76 * q^34 - 1630 * q^35 + 2155 * q^36 - 535 * q^37 + 1155 * q^38 - 2514 * q^39 - 298 * q^40 - 2087 * q^41 - 5 * q^42 - 1008 * q^43 + 3168 * q^44 - 1160 * q^45 - 1640 * q^46 - 1960 * q^47 + 3412 * q^48 + 3670 * q^49 - 2394 * q^50 - 2994 * q^51 - 2601 * q^52 - 2466 * q^53 + 1296 * q^54 - 440 * q^55 - 5195 * q^56 - 3776 * q^57 + 1068 * q^58 - 2310 * q^59 + 1599 * q^60 - 3404 * q^61 + 1534 * q^62 - 3409 * q^63 + 2568 * q^64 - 3906 * q^65 - 1221 * q^66 - 2405 * q^67 - 3145 * q^68 - 2420 * q^69 + 455 * q^70 - 8978 * q^71 - 7262 * q^72 - 1868 * q^73 - 2790 * q^74 - 1196 * q^75 - 5483 * q^76 - 1111 * q^77 + 349 * q^78 - 9130 * q^79 - 1697 * q^80 + 4171 * q^81 - 241 * q^82 - 4639 * q^83 - 1659 * q^84 - 7634 * q^85 - 5656 * q^86 - 4412 * q^87 - 2838 * q^88 - 6561 * q^89 - 6756 * q^90 - 2742 * q^91 - 5386 * q^92 - 3234 * q^93 - 5295 * q^94 - 7930 * q^95 - 12593 * q^96 - 4520 * q^97 - 3213 * q^98 + 6435 * 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 $

$2$	−4.09911	−1.44925	−0.724627	−	0.689141i	$-0.757988\pi$
$2$	−4.09911	−1.44925	−0.724627	+	0.689141i	$0.757988\pi$
$3$	7.59971	1.46256	0.731282	−	0.682075i	$-0.238922\pi$
$3$	7.59971	1.46256	0.731282	+	0.682075i	$0.238922\pi$
$4$	8.80270	1.10034
$5$	−11.2108	−1.00273	−0.501363	−	0.865237i	$-0.667168\pi$
$5$	−11.2108	−1.00273	−0.501363	+	0.865237i	$0.667168\pi$
$6$	−31.1520	−2.11963
$7$	21.6950	1.17142	0.585711	−	0.810520i	$-0.300815\pi$
$7$	21.6950	1.17142	0.585711	+	0.810520i	$0.300815\pi$
$8$	−3.29036	−0.145415
$9$	30.7555	1.13909
$10$	45.9544	1.45321
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	66.8979	1.60931
$13$	−8.19742	−0.174889	−0.0874444	−	0.996169i	$-0.527870\pi$
$13$	−8.19742	−0.174889	−0.0874444	+	0.996169i	$0.527870\pi$
$14$	−88.9304	−1.69769
$15$	−85.1989	−1.46655
$16$	−56.9341	−0.889595
$17$	58.8422	0.839490	0.419745	−	0.907642i	$-0.362120\pi$
$17$	58.8422	0.839490	0.419745	+	0.907642i	$0.362120\pi$
$18$	−126.070	−1.65084
$19$	59.6122	0.719788	0.359894	−	0.932993i	$-0.382813\pi$
$19$	59.6122	0.719788	0.359894	+	0.932993i	$0.382813\pi$
$20$	−98.6855	−1.10334
$21$	164.876	1.71328
$22$	−45.0902	−0.436967
$23$	−173.781	−1.57547	−0.787735	−	0.616014i	$-0.788746\pi$
$23$	−173.781	−1.57547	−0.787735	+	0.616014i	$0.788746\pi$
$24$	−25.0058	−0.212678
$25$	0.682530	0.00546024
$26$	33.6021	0.253458
$27$	28.5408	0.203433
$28$	190.975	1.28896
$29$	−171.564	−1.09858	−0.549288	−	0.835633i	$-0.685101\pi$
$29$	−171.564	−1.09858	−0.549288	+	0.835633i	$0.685101\pi$
$30$	349.240	2.12541
$31$	−93.0681	−0.539210	−0.269605	−	0.962971i	$-0.586893\pi$
$31$	−93.0681	−0.539210	−0.269605	+	0.962971i	$0.586893\pi$
$32$	259.702	1.43466
$33$	83.5968	0.440980
$34$	−241.201	−1.21663
$35$	−243.219	−1.17462
$36$	270.732	1.25339
$37$	−348.564	−1.54875	−0.774373	−	0.632729i	$-0.781935\pi$
$37$	−348.564	−1.54875	−0.774373	+	0.632729i	$0.781935\pi$
$38$	−244.357	−1.04316
$39$	−62.2980	−0.255786
$40$	36.8877	0.145811
$41$	−211.209	−0.804520	−0.402260	−	0.915525i	$-0.631775\pi$
$41$	−211.209	−0.804520	−0.402260	+	0.915525i	$0.631775\pi$
$42$	−675.844	−2.48298
$43$	−221.156	−0.784326	−0.392163	−	0.919896i	$-0.628273\pi$
$43$	−221.156	−0.784326	−0.392163	+	0.919896i	$0.628273\pi$
$44$	96.8297	0.331764
$45$	−344.795	−1.14220
$46$	712.347	2.28326
$47$	577.241	1.79147	0.895737	−	0.444584i	$-0.146648\pi$
$47$	577.241	1.79147	0.895737	+	0.444584i	$0.146648\pi$
$48$	−432.682	−1.30109
$49$	127.675	0.372230
$50$	−2.79777	−0.00791328
$51$	447.183	1.22781
$52$	−72.1594	−0.192437
$53$	−580.189	−1.50368	−0.751841	−	0.659345i	$-0.770834\pi$
$53$	−580.189	−1.50368	−0.751841	+	0.659345i	$0.770834\pi$
$54$	−116.992	−0.294826
$55$	−123.319	−0.302333
$56$	−71.3845	−0.170342
$57$	453.035	1.05274
$58$	703.261	1.59212
$59$	474.373	1.04675	0.523373	−	0.852103i	$-0.324673\pi$
$59$	474.373	1.04675	0.523373	+	0.852103i	$0.324673\pi$
$60$	−749.981	−1.61370
$61$	127.704	0.268046	0.134023	−	0.990978i	$-0.457210\pi$
$61$	127.704	0.268046	0.134023	+	0.990978i	$0.457210\pi$
$62$	381.496	0.781453
$63$	667.242	1.33436
$64$	−609.074	−1.18960
$65$	91.8998	0.175366
$66$	−342.672	−0.639092
$67$	645.219	1.17651	0.588254	−	0.808676i	$-0.299816\pi$
$67$	645.219	1.17651	0.588254	+	0.808676i	$0.299816\pi$
$68$	517.970	0.923722
$69$	−1320.68	−2.30423
$70$	996.982	1.70232
$71$	−1136.30	−1.89935	−0.949677	−	0.313232i	$-0.898588\pi$
$71$	−1136.30	−1.89935	−0.949677	+	0.313232i	$0.898588\pi$
$72$	−101.197	−0.165641
$73$	886.775	1.42177	0.710885	−	0.703309i	$-0.248295\pi$
$73$	886.775	1.42177	0.710885	+	0.703309i	$0.248295\pi$
$74$	1428.80	2.24453
$75$	5.18703	0.00798595
$76$	524.749	0.792010
$77$	238.645	0.353197
$78$	255.366	0.370699
$79$	831.044	1.18354	0.591770	−	0.806107i	$-0.298429\pi$
$79$	831.044	1.18354	0.591770	+	0.806107i	$0.298429\pi$
$80$	638.278	0.892020
$81$	−613.497	−0.841560
$82$	865.770	1.16595
$83$	−1296.70	−1.71484	−0.857420	−	0.514617i	$-0.827934\pi$
$83$	−1296.70	−1.71484	−0.857420	+	0.514617i	$0.827934\pi$
$84$	1451.35	1.88519
$85$	−659.669	−0.841778
$86$	906.544	1.13669
$87$	−1303.84	−1.60674
$88$	−36.1940	−0.0438442
$89$	−434.016	−0.516917	−0.258459	−	0.966022i	$-0.583215\pi$
$89$	−434.016	−0.516917	−0.258459	+	0.966022i	$0.583215\pi$
$90$	1413.35	1.65534
$91$	−177.843	−0.204869
$92$	−1529.74	−1.73355
$93$	−707.290	−0.788630
$94$	−2366.18	−2.59630
$95$	−668.302	−0.721751
$96$	1973.66	2.09829
$97$	1312.84	1.37421	0.687107	−	0.726556i	$-0.258880\pi$
$97$	1312.84	1.37421	0.687107	+	0.726556i	$0.258880\pi$
$98$	−523.353	−0.539455
$99$	338.311	0.343450
$100$	6.00811	0.00600811
$101$	−1372.27	−1.35194	−0.675971	−	0.736928i	$-0.736276\pi$
$101$	−1372.27	−1.35194	−0.675971	+	0.736928i	$0.736276\pi$
$102$	−1833.05	−1.77940
$103$	−1390.79	−1.33047	−0.665235	−	0.746634i	$-0.731669\pi$
$103$	−1390.79	−1.33047	−0.665235	+	0.746634i	$0.731669\pi$
$104$	26.9725	0.0254314
$105$	−1848.39	−1.71795
$106$	2378.26	2.17922
$107$	−756.466	−0.683461	−0.341730	−	0.939798i	$-0.611013\pi$
$107$	−756.466	−0.683461	−0.341730	+	0.939798i	$0.611013\pi$
$108$	251.237	0.223845
$109$	−1253.07	−1.10112	−0.550562	−	0.834794i	$-0.685587\pi$
$109$	−1253.07	−1.10112	−0.550562	+	0.834794i	$0.685587\pi$
$110$	505.498	0.438158
$111$	−2648.99	−2.26514
$112$	−1235.19	−1.04209
$113$	1212.70	1.00957	0.504785	−	0.863245i	$-0.331572\pi$
$113$	1212.70	1.00957	0.504785	+	0.863245i	$0.331572\pi$
$114$	−1857.04	−1.52568
$115$	1948.23	1.57977
$116$	−1510.23	−1.20880
$117$	−252.116	−0.199215
$118$	−1944.51	−1.51700
$119$	1276.58	0.983397
$120$	280.335	0.213258
$121$	121.000	0.0909091
$122$	−523.472	−0.388466
$123$	−1605.13	−1.17666
$124$	−819.251	−0.593313
$125$	1393.70	0.997251
$126$	−2735.10	−1.93383
$127$	−717.517	−0.501333	−0.250667	−	0.968073i	$-0.580650\pi$
$127$	−717.517	−0.501333	−0.250667	+	0.968073i	$0.580650\pi$
$128$	419.046	0.289366
$129$	−1680.72	−1.14713
$130$	−376.707	−0.254149
$131$	−131.000	−0.0873704
$131$	−131.000	−0.0873704
$132$	735.877	0.485227
$133$	1293.29	0.843176
$134$	−2644.82	−1.70506
$135$	−319.966	−0.203988
$136$	−193.612	−0.122074
$137$	930.099	0.580027	0.290014	−	0.957023i	$-0.406340\pi$
$137$	930.099	0.580027	0.290014	+	0.957023i	$0.406340\pi$
$138$	5413.62	3.33941
$139$	570.222	0.347954	0.173977	−	0.984750i	$-0.444338\pi$
$139$	570.222	0.347954	0.173977	+	0.984750i	$0.444338\pi$
$140$	−2140.99	−1.29247
$141$	4386.86	2.62015
$142$	4657.82	2.75265
$143$	−90.1716	−0.0527310
$144$	−1751.04	−1.01333
$145$	1923.38	1.10157
$146$	−3634.99	−2.06051
$147$	970.291	0.544410
$148$	−3068.31	−1.70414
$149$	104.467	0.0574381	0.0287190	−	0.999588i	$-0.490857\pi$
$149$	104.467	0.0574381	0.0287190	+	0.999588i	$0.490857\pi$
$150$	−21.2622	−0.0115737
$151$	1719.69	0.926800	0.463400	−	0.886149i	$-0.346629\pi$
$151$	1719.69	0.926800	0.463400	+	0.886149i	$0.346629\pi$
$152$	−196.146	−0.104668
$153$	1809.72	0.956257
$154$	−978.234	−0.511872
$155$	1043.37	0.540680
$156$	−548.390	−0.281451
$157$	2144.52	1.09014	0.545069	−	0.838391i	$-0.316504\pi$
$157$	2144.52	1.09014	0.545069	+	0.838391i	$0.316504\pi$
$158$	−3406.54	−1.71525
$159$	−4409.27	−2.19923
$160$	−2911.47	−1.43858
$161$	−3770.18	−1.84554
$162$	2514.79	1.21963
$163$	31.5337	0.0151528	0.00757642	−	0.999971i	$-0.497588\pi$
$163$	31.5337	0.0151528	0.00757642	+	0.999971i	$0.497588\pi$
$164$	−1859.21	−0.885244
$165$	−937.188	−0.442182
$166$	5315.33	2.48524
$167$	−2540.01	−1.17696	−0.588479	−	0.808513i	$-0.700273\pi$
$167$	−2540.01	−1.17696	−0.588479	+	0.808513i	$0.700273\pi$
$168$	−542.501	−0.249136
$169$	−2129.80	−0.969414
$170$	2704.06	1.21995
$171$	1833.40	0.819906
$172$	−1946.77	−0.863023
$173$	−1226.08	−0.538829	−0.269414	−	0.963024i	$-0.586830\pi$
$173$	−1226.08	−0.538829	−0.269414	+	0.963024i	$0.586830\pi$
$174$	5344.58	2.32857
$175$	14.8075	0.00639625
$176$	−626.275	−0.268223
$177$	3605.09	1.53093
$178$	1779.08	0.749145
$179$	−1501.30	−0.626886	−0.313443	−	0.949607i	$-0.601482\pi$
$179$	−1501.30	−0.626886	−0.313443	+	0.949607i	$0.601482\pi$
$180$	−3035.12	−1.25680
$181$	1854.98	0.761767	0.380884	−	0.924623i	$-0.375620\pi$
$181$	1854.98	0.761767	0.380884	+	0.924623i	$0.375620\pi$
$182$	728.999	0.296907
$183$	970.511	0.392034
$184$	571.802	0.229097
$185$	3907.69	1.55297
$186$	2899.26	1.14292
$187$	647.264	0.253116
$188$	5081.28	1.97123
$189$	619.195	0.238306
$190$	2739.44	1.04600
$191$	−495.220	−0.187606	−0.0938032	−	0.995591i	$-0.529902\pi$
$191$	−495.220	−0.187606	−0.0938032	+	0.995591i	$0.529902\pi$
$192$	−4628.78	−1.73986
$193$	561.066	0.209256	0.104628	−	0.994511i	$-0.466635\pi$
$193$	561.066	0.209256	0.104628	+	0.994511i	$0.466635\pi$
$194$	−5381.48	−1.99159
$195$	698.411	0.256483
$196$	1123.88	0.409578
$197$	−2159.59	−0.781039	−0.390520	−	0.920595i	$-0.627705\pi$
$197$	−2159.59	−0.781039	−0.390520	+	0.920595i	$0.627705\pi$
$198$	−1386.77	−0.497746
$199$	−5019.66	−1.78811	−0.894056	−	0.447955i	$-0.852152\pi$
$199$	−5019.66	−1.78811	−0.894056	+	0.447955i	$0.852152\pi$
$200$	−2.24577	−0.000794000 0
$201$	4903.47	1.72072
$202$	5625.10	1.95931
$203$	−3722.10	−1.28690
$204$	3936.42	1.35100
$205$	2367.83	0.806714
$206$	5700.99	1.92819
$207$	−5344.72	−1.79461
$208$	466.712	0.155580
$209$	655.734	0.217024
$210$	7576.77	2.48975
$211$	5939.00	1.93771	0.968857	−	0.247622i	$-0.0796492\pi$
$211$	5939.00	1.93771	0.968857	+	0.247622i	$0.0796492\pi$
$212$	−5107.23	−1.65456
$213$	−8635.55	−2.77793
$214$	3100.84	0.990508
$215$	2479.34	0.786464
$216$	−93.9097	−0.0295822
$217$	−2019.12	−0.631643
$218$	5136.48	1.59581
$219$	6739.23	2.07943
$220$	−1085.54	−0.332669
$221$	−482.354	−0.146817
$222$	10858.5	3.28277
$223$	−3235.05	−0.971458	−0.485729	−	0.874109i	$-0.661446\pi$
$223$	−3235.05	−0.971458	−0.485729	+	0.874109i	$0.661446\pi$
$224$	5634.24	1.68060
$225$	20.9916	0.00621973
$226$	−4971.00	−1.46312
$227$	−991.042	−0.289770	−0.144885	−	0.989449i	$-0.546281\pi$
$227$	−991.042	−0.289770	−0.144885	+	0.989449i	$0.546281\pi$
$228$	3987.93	1.15837
$229$	4838.24	1.39616	0.698079	−	0.716021i	$-0.254038\pi$
$229$	4838.24	1.39616	0.698079	+	0.716021i	$0.254038\pi$
$230$	−7985.99	−2.28948
$231$	1813.64	0.516573
$232$	564.509	0.159749
$233$	2458.73	0.691317	0.345658	−	0.938360i	$-0.387656\pi$
$233$	2458.73	0.691317	0.345658	+	0.938360i	$0.387656\pi$
$234$	1033.45	0.288713
$235$	−6471.35	−1.79636
$236$	4175.76	1.15177
$237$	6315.69	1.73100
$238$	−5232.86	−1.42519
$239$	−140.137	−0.0379276	−0.0189638	−	0.999820i	$-0.506037\pi$
$239$	−140.137	−0.0379276	−0.0189638	+	0.999820i	$0.506037\pi$
$240$	4850.72	1.30464
$241$	1929.24	0.515657	0.257829	−	0.966191i	$-0.416993\pi$
$241$	1929.24	0.515657	0.257829	+	0.966191i	$0.416993\pi$
$242$	−495.992	−0.131750
$243$	−5433.00	−1.43427
$244$	1124.14	0.294941
$245$	−1431.34	−0.373245
$246$	6579.59	1.70528
$247$	−488.666	−0.125883
$248$	306.228	0.0784092
$249$	−9854.57	−2.50806
$250$	−5712.93	−1.44527
$251$	−2262.16	−0.568870	−0.284435	−	0.958695i	$-0.591806\pi$
$251$	−2262.16	−0.568870	−0.284435	+	0.958695i	$0.591806\pi$
$252$	5873.53	1.46825
$253$	−1911.59	−0.475022
$254$	2941.18	0.726559
$255$	−5013.29	−1.23115
$256$	3154.88	0.770233
$257$	−7410.98	−1.79877	−0.899386	−	0.437156i	$-0.855986\pi$
$257$	−7410.98	−1.79877	−0.899386	+	0.437156i	$0.855986\pi$
$258$	6889.46	1.66248
$259$	−7562.12	−1.81424
$260$	808.966	0.192961
$261$	−5276.55	−1.25138
$262$	536.983	0.126622
$263$	−4317.07	−1.01218	−0.506088	−	0.862482i	$-0.668909\pi$
$263$	−4317.07	−1.01218	−0.506088	+	0.862482i	$0.668909\pi$
$264$	−275.064	−0.0641250
$265$	6504.40	1.50778
$266$	−5301.34	−1.22198
$267$	−3298.40	−0.756025
$268$	5679.67	1.29456
$269$	8356.64	1.89410	0.947051	−	0.321083i	$-0.104047\pi$
$269$	8356.64	1.89410	0.947051	+	0.321083i	$0.104047\pi$
$270$	1311.58	0.295630
$271$	3401.73	0.762511	0.381256	−	0.924470i	$-0.375492\pi$
$271$	3401.73	0.762511	0.381256	+	0.924470i	$0.375492\pi$
$272$	−3350.12	−0.746806
$273$	−1351.56	−0.299633
$274$	−3812.58	−0.840607
$275$	7.50783	0.00164632
$276$	−11625.6	−2.53543
$277$	−6650.71	−1.44261	−0.721304	−	0.692618i	$-0.756457\pi$
$277$	−6650.71	−1.44261	−0.721304	+	0.692618i	$0.756457\pi$
$278$	−2337.40	−0.504274
$279$	−2862.36	−0.614211
$280$	800.279	0.170807
$281$	−5068.54	−1.07603	−0.538014	−	0.842936i	$-0.680825\pi$
$281$	−5068.54	−1.07603	−0.538014	+	0.842936i	$0.680825\pi$
$282$	−17982.2	−3.79726
$283$	5090.81	1.06932	0.534659	−	0.845068i	$-0.320440\pi$
$283$	5090.81	1.06932	0.534659	+	0.845068i	$0.320440\pi$
$284$	−10002.5	−2.08993
$285$	−5078.90	−1.05561
$286$	369.623	0.0764206
$287$	−4582.19	−0.942433
$288$	7987.27	1.63422
$289$	−1450.60	−0.295257
$290$	−7884.14	−1.59646
$291$	9977.21	2.00988
$292$	7806.02	1.56443
$293$	−8713.98	−1.73746	−0.868731	−	0.495284i	$-0.835064\pi$
$293$	−8713.98	−1.73746	−0.868731	+	0.495284i	$0.835064\pi$
$294$	−3977.33	−0.788988
$295$	−5318.11	−1.04960
$296$	1146.90	0.225211
$297$	313.949	0.0613373
$298$	−428.222	−0.0832423
$299$	1424.55	0.275532
$300$	45.6599	0.00878725
$301$	−4797.99	−0.918776
$302$	−7049.22	−1.34317
$303$	−10428.9	−1.97730
$304$	−3393.97	−0.640320
$305$	−1431.66	−0.268776
$306$	−7418.25	−1.38586
$307$	4758.42	0.884616	0.442308	−	0.896863i	$-0.354160\pi$
$307$	4758.42	0.884616	0.442308	+	0.896863i	$0.354160\pi$
$308$	2100.72	0.388636
$309$	−10569.6	−1.94590
$310$	−4276.89	−0.783583
$311$	3572.34	0.651346	0.325673	−	0.945482i	$-0.394409\pi$
$311$	3572.34	0.651346	0.325673	+	0.945482i	$0.394409\pi$
$312$	204.983	0.0371951
$313$	−6565.96	−1.18572	−0.592860	−	0.805306i	$-0.702001\pi$
$313$	−6565.96	−1.18572	−0.592860	+	0.805306i	$0.702001\pi$
$314$	−8790.64	−1.57989
$315$	−7480.33	−1.33800
$316$	7315.43	1.30229
$317$	6227.95	1.10346	0.551729	−	0.834023i	$-0.313968\pi$
$317$	6227.95	1.10346	0.551729	+	0.834023i	$0.313968\pi$
$318$	18074.1	3.18724
$319$	−1887.21	−0.331233
$320$	6828.22	1.19284
$321$	−5748.92	−0.999605
$322$	15454.4	2.67466
$323$	3507.71	0.604255
$324$	−5400.43	−0.926000
$325$	−5.59499	−0.000954935 0
$326$	−129.260	−0.0219603
$327$	−9522.98	−1.61047
$328$	694.955	0.116989
$329$	12523.3	2.09857
$330$	3841.64	0.640834
$331$	1355.34	0.225063	0.112532	−	0.993648i	$-0.464104\pi$
$331$	1355.34	0.225063	0.112532	+	0.993648i	$0.464104\pi$
$332$	−11414.5	−1.88690
$333$	−10720.3	−1.76417
$334$	10411.8	1.70571
$335$	−7233.43	−1.17972
$336$	−9387.05	−1.52412
$337$	−8033.58	−1.29857	−0.649284	−	0.760546i	$-0.724931\pi$
$337$	−8033.58	−1.29857	−0.649284	+	0.760546i	$0.724931\pi$
$338$	8730.29	1.40493
$339$	9216.18	1.47656
$340$	−5806.87	−0.926241
$341$	−1023.75	−0.162578
$342$	−7515.33	−1.18825
$343$	−4671.49	−0.735384
$344$	727.684	0.114053
$345$	14805.9	2.31051
$346$	5025.85	0.780900
$347$	8081.07	1.25019	0.625093	−	0.780550i	$-0.285061\pi$
$347$	8081.07	1.25019	0.625093	+	0.780550i	$0.285061\pi$
$348$	−11477.3	−1.76795
$349$	−4020.88	−0.616712	−0.308356	−	0.951271i	$-0.599779\pi$
$349$	−4020.88	−0.616712	−0.308356	+	0.951271i	$0.599779\pi$
$350$	−60.6977	−0.00926979
$351$	−233.961	−0.0355781
$352$	2856.72	0.432567
$353$	−10020.3	−1.51083	−0.755417	−	0.655244i	$-0.772566\pi$
$353$	−10020.3	−1.51083	−0.755417	+	0.655244i	$0.772566\pi$
$354$	−14777.7	−2.21871
$355$	12738.9	1.90453
$356$	−3820.52	−0.568784
$357$	9701.66	1.43828
$358$	6154.00	0.908517
$359$	−3968.56	−0.583434	−0.291717	−	0.956505i	$-0.594227\pi$
$359$	−3968.56	−0.583434	−0.291717	+	0.956505i	$0.594227\pi$
$360$	1134.50	0.166093
$361$	−3305.38	−0.481905
$362$	−7603.78	−1.10399
$363$	919.564	0.132960
$364$	−1565.50	−0.225425
$365$	−9941.48	−1.42565
$366$	−3978.23	−0.568157
$367$	−8620.36	−1.22610	−0.613050	−	0.790044i	$-0.710058\pi$
$367$	−8620.36	−1.22610	−0.613050	+	0.790044i	$0.710058\pi$
$368$	9894.05	1.40153
$369$	−6495.85	−0.916424
$370$	−16018.1	−2.25065
$371$	−12587.2	−1.76145
$372$	−6226.06	−0.867759
$373$	4884.59	0.678055	0.339028	−	0.940776i	$-0.389902\pi$
$373$	4884.59	0.678055	0.339028	+	0.940776i	$0.389902\pi$
$374$	−2653.21	−0.366829
$375$	10591.7	1.45854
$376$	−1899.33	−0.260507
$377$	1406.38	0.192129
$378$	−2538.15	−0.345366
$379$	5489.85	0.744050	0.372025	−	0.928223i	$-0.378664\pi$
$379$	5489.85	0.744050	0.372025	+	0.928223i	$0.378664\pi$
$380$	−5882.86	−0.794170
$381$	−5452.92	−0.733232
$382$	2029.96	0.271889
$383$	8028.64	1.07113	0.535567	−	0.844493i	$-0.320098\pi$
$383$	8028.64	1.07113	0.535567	+	0.844493i	$0.320098\pi$
$384$	3184.63	0.423216
$385$	−2675.41	−0.354160
$386$	−2299.87	−0.303265
$387$	−6801.77	−0.893420
$388$	11556.6	1.51210
$389$	−8488.94	−1.10644	−0.553222	−	0.833034i	$-0.686602\pi$
$389$	−8488.94	−1.10644	−0.553222	+	0.833034i	$0.686602\pi$
$390$	−2862.86	−0.371710
$391$	−10225.6	−1.32259
$392$	−420.096	−0.0541277
$393$	−995.561	−0.127785
$394$	8852.42	1.13192
$395$	−9316.68	−1.18677
$396$	2978.05	0.377911
$397$	6929.15	0.875980	0.437990	−	0.898980i	$-0.355691\pi$
$397$	6929.15	0.875980	0.437990	+	0.898980i	$0.355691\pi$
$398$	20576.1	2.59143
$399$	9828.62	1.23320
$400$	−38.8592	−0.00485740
$401$	−7644.29	−0.951965	−0.475982	−	0.879455i	$-0.657907\pi$
$401$	−7644.29	−0.951965	−0.475982	+	0.879455i	$0.657907\pi$
$402$	−20099.9	−2.49376
$403$	762.918	0.0943019
$404$	−12079.7	−1.48759
$405$	6877.81	0.843854
$406$	15257.3	1.86504
$407$	−3834.21	−0.466965
$408$	−1471.39	−0.178541
$409$	−10871.9	−1.31438	−0.657189	−	0.753726i	$-0.728255\pi$
$409$	−10871.9	−1.31438	−0.657189	+	0.753726i	$0.728255\pi$
$410$	−9705.99	−1.16913
$411$	7068.48	0.848327
$412$	−12242.7	−1.46397
$413$	10291.5	1.22618
$414$	21908.6	2.60084
$415$	14537.1	1.71952
$416$	−2128.88	−0.250907
$417$	4333.52	0.508905
$418$	−2687.93	−0.314524
$419$	10889.7	1.26968	0.634840	−	0.772643i	$-0.281066\pi$
$419$	10889.7	1.26968	0.634840	+	0.772643i	$0.281066\pi$
$420$	−16270.9	−1.89033
$421$	−936.289	−0.108389	−0.0541947	−	0.998530i	$-0.517259\pi$
$421$	−936.289	−0.108389	−0.0541947	+	0.998530i	$0.517259\pi$
$422$	−24344.6	−2.80824
$423$	17753.4	2.04066
$424$	1909.03	0.218658
$425$	40.1616	0.00458382
$426$	35398.1	4.02592
$427$	2770.54	0.313995
$428$	−6658.94	−0.752038
$429$	−685.278	−0.0771224
$430$	−10163.1	−1.13979
$431$	2834.15	0.316743	0.158371	−	0.987380i	$-0.449376\pi$
$431$	2834.15	0.316743	0.158371	+	0.987380i	$0.449376\pi$
$432$	−1624.95	−0.180973
$433$	−15550.0	−1.72583	−0.862914	−	0.505351i	$-0.831363\pi$
$433$	−15550.0	−1.72583	−0.862914	+	0.505351i	$0.831363\pi$
$434$	8276.58	0.915411
$435$	14617.1	1.61112
$436$	−11030.4	−1.21161
$437$	−10359.5	−1.13400
$438$	−27624.8	−3.01362
$439$	−1382.55	−0.150308	−0.0751542	−	0.997172i	$-0.523945\pi$
$439$	−1382.55	−0.150308	−0.0751542	+	0.997172i	$0.523945\pi$
$440$	405.764	0.0439638
$441$	3926.70	0.424004
$442$	1977.22	0.212776
$443$	−16372.4	−1.75593	−0.877965	−	0.478725i	$-0.841099\pi$
$443$	−16372.4	−1.75593	−0.877965	+	0.478725i	$0.841099\pi$
$444$	−23318.2	−2.49242
$445$	4865.68	0.518327
$446$	13260.8	1.40789
$447$	793.918	0.0840068
$448$	−13213.9	−1.39352
$449$	−9732.26	−1.02293	−0.511463	−	0.859305i	$-0.670896\pi$
$449$	−9732.26	−1.02293	−0.511463	+	0.859305i	$0.670896\pi$
$450$	−86.0468	−0.00901396
$451$	−2323.30	−0.242572
$452$	10675.1	1.11087
$453$	13069.2	1.35550
$454$	4062.39	0.419950
$455$	1993.77	0.205427
$456$	−1490.65	−0.153084
$457$	−3939.25	−0.403217	−0.201609	−	0.979466i	$-0.564617\pi$
$457$	−3939.25	−0.403217	−0.201609	+	0.979466i	$0.564617\pi$
$458$	−19832.5	−2.02339
$459$	1679.41	0.170780
$460$	17149.6	1.73828
$461$	−17381.0	−1.75599	−0.877995	−	0.478669i	$-0.841119\pi$
$461$	−17381.0	−1.75599	−0.877995	+	0.478669i	$0.841119\pi$
$462$	−7434.29	−0.748646
$463$	14800.1	1.48557	0.742786	−	0.669529i	$-0.233504\pi$
$463$	14800.1	1.48557	0.742786	+	0.669529i	$0.233504\pi$
$464$	9767.86	0.977287
$465$	7929.30	0.790780
$466$	−10078.6	−1.00189
$467$	17024.2	1.68691	0.843453	−	0.537203i	$-0.180519\pi$
$467$	17024.2	1.68691	0.843453	+	0.537203i	$0.180519\pi$
$468$	−2219.30	−0.219203
$469$	13998.1	1.37819
$470$	26526.8	2.60338
$471$	16297.7	1.59440
$472$	−1560.86	−0.152212
$473$	−2432.72	−0.236483
$474$	−25888.7	−2.50866
$475$	40.6871	0.00393022
$476$	11237.4	1.08207
$477$	−17844.0	−1.71283
$478$	574.436	0.0549667
$479$	−197.935	−0.0188807	−0.00944036	−	0.999955i	$-0.503005\pi$
$479$	−197.935	−0.0188807	−0.00944036	+	0.999955i	$0.503005\pi$
$480$	−22126.3	−2.10401
$481$	2857.33	0.270859
$482$	−7908.18	−0.747319
$483$	−28652.3	−2.69922
$484$	1065.13	0.100031
$485$	−14718.0	−1.37796
$486$	22270.5	2.07862
$487$	6596.42	0.613783	0.306891	−	0.951745i	$-0.400711\pi$
$487$	6596.42	0.613783	0.306891	+	0.951745i	$0.400711\pi$
$488$	−420.191	−0.0389778
$489$	239.647	0.0221620
$490$	5867.22	0.540926
$491$	9228.68	0.848237	0.424119	−	0.905607i	$-0.360584\pi$
$491$	9228.68	0.848237	0.424119	+	0.905607i	$0.360584\pi$
$492$	−14129.5	−1.29473
$493$	−10095.2	−0.922243
$494$	2003.10	0.182436
$495$	−3792.74	−0.344386
$496$	5298.74	0.479679
$497$	−24652.1	−2.22494
$498$	40395.0	3.63482
$499$	−12287.7	−1.10235	−0.551176	−	0.834389i	$-0.685821\pi$
$499$	−12287.7	−1.10235	−0.551176	+	0.834389i	$0.685821\pi$
$500$	12268.3	1.09731
$501$	−19303.3	−1.72138
$502$	9272.85	0.824437
$503$	1998.54	0.177158	0.0885789	−	0.996069i	$-0.471767\pi$
$503$	1998.54	0.177158	0.0885789	+	0.996069i	$0.471767\pi$
$504$	−2195.47	−0.194036
$505$	15384.3	1.35563
$506$	7835.81	0.688428
$507$	−16185.9	−1.41783
$508$	−6316.09	−0.551636
$509$	3721.69	0.324089	0.162044	−	0.986783i	$-0.448191\pi$
$509$	3721.69	0.324089	0.162044	+	0.986783i	$0.448191\pi$
$510$	20550.0	1.78426
$511$	19238.6	1.66549
$512$	−16284.5	−1.40563
$513$	1701.38	0.146429
$514$	30378.4	2.60688
$515$	15591.9	1.33410
$516$	−14794.9	−1.26223
$517$	6349.65	0.540150
$518$	30998.0	2.62929
$519$	−9317.87	−0.788071
$520$	−302.384	−0.0255008
$521$	−1171.09	−0.0984767	−0.0492383	−	0.998787i	$-0.515679\pi$
$521$	−1171.09	−0.0984767	−0.0492383	+	0.998787i	$0.515679\pi$
$522$	21629.2	1.81357
$523$	11715.7	0.979522	0.489761	−	0.871857i	$-0.337084\pi$
$523$	11715.7	0.979522	0.489761	+	0.871857i	$0.337084\pi$
$524$	−1153.15	−0.0961370
$525$	112.533	0.00935492
$526$	17696.2	1.46690
$527$	−5476.33	−0.452662
$528$	−4759.50	−0.392293
$529$	18032.8	1.48210
$530$	−26662.2	−2.18516
$531$	14589.6	1.19234
$532$	11384.4	0.927778
$533$	1731.37	0.140702
$534$	13520.5	1.09567
$535$	8480.60	0.685324
$536$	−2123.00	−0.171082
$537$	−11409.5	−0.916861
$538$	−34254.8	−2.74504
$539$	1404.42	0.112231
$540$	−2816.57	−0.224455
$541$	20042.0	1.59274	0.796371	−	0.604808i	$-0.206750\pi$
$541$	20042.0	1.59274	0.796371	+	0.604808i	$0.206750\pi$
$542$	−13944.1	−1.10507
$543$	14097.3	1.11413
$544$	15281.4	1.20439
$545$	14048.0	1.10413
$546$	5540.18	0.434245
$547$	−10156.9	−0.793923	−0.396962	−	0.917835i	$-0.629935\pi$
$547$	−10156.9	−0.793923	−0.396962	+	0.917835i	$0.629935\pi$
$548$	8187.39	0.638226
$549$	3927.59	0.305329
$550$	−30.7754	−0.00238594
$551$	−10227.3	−0.790742
$552$	4345.52	0.335069
$553$	18029.5	1.38643
$554$	27262.0	2.09071
$555$	29697.3	2.27132
$556$	5019.50	0.382867
$557$	−9755.95	−0.742142	−0.371071	−	0.928605i	$-0.621009\pi$
$557$	−9755.95	−0.742142	−0.371071	+	0.928605i	$0.621009\pi$
$558$	11733.1	0.890148
$559$	1812.91	0.137170
$560$	13847.5	1.04493
$561$	4919.02	0.370198
$562$	20776.5	1.55944
$563$	−25344.1	−1.89721	−0.948604	−	0.316466i	$-0.897504\pi$
$563$	−25344.1	−1.89721	−0.948604	+	0.316466i	$0.897504\pi$
$564$	38616.3	2.88305
$565$	−13595.4	−1.01232
$566$	−20867.8	−1.54971
$567$	−13309.8	−0.985822
$568$	3738.84	0.276194
$569$	17194.3	1.26683	0.633413	−	0.773814i	$-0.281653\pi$
$569$	17194.3	1.26683	0.633413	+	0.773814i	$0.281653\pi$
$570$	20819.0	1.52984
$571$	18827.6	1.37988	0.689939	−	0.723868i	$-0.257637\pi$
$571$	18827.6	1.37988	0.689939	+	0.723868i	$0.257637\pi$
$572$	−793.754	−0.0580219
$573$	−3763.52	−0.274386
$574$	18782.9	1.36582
$575$	−118.611	−0.00860245
$576$	−18732.4	−1.35506
$577$	−6300.84	−0.454606	−0.227303	−	0.973824i	$-0.572991\pi$
$577$	−6300.84	−0.454606	−0.227303	+	0.973824i	$0.572991\pi$
$578$	5946.16	0.427903
$579$	4263.94	0.306050
$580$	16930.9	1.21210
$581$	−28132.0	−2.00880
$582$	−40897.7	−2.91282
$583$	−6382.08	−0.453377
$584$	−2917.81	−0.206746
$585$	2826.43	0.199758
$586$	35719.6	2.51802
$587$	−18185.7	−1.27871	−0.639355	−	0.768912i	$-0.720799\pi$
$587$	−18185.7	−1.27871	−0.639355	+	0.768912i	$0.720799\pi$
$588$	8541.18	0.599035
$589$	−5548.00	−0.388117
$590$	21799.5	1.52114
$591$	−16412.3	−1.14232
$592$	19845.2	1.37776
$593$	12931.0	0.895469	0.447734	−	0.894167i	$-0.352231\pi$
$593$	12931.0	0.895469	0.447734	+	0.894167i	$0.352231\pi$
$594$	−1286.91	−0.0888934
$595$	−14311.5	−0.986078
$596$	919.592	0.0632013
$597$	−38147.9	−2.61523
$598$	−5839.40	−0.399316
$599$	12861.7	0.877322	0.438661	−	0.898653i	$-0.355453\pi$
$599$	12861.7	0.877322	0.438661	+	0.898653i	$0.355453\pi$
$600$	−17.0672	−0.00116128
$601$	−25648.9	−1.74083	−0.870416	−	0.492316i	$-0.836150\pi$
$601$	−25648.9	−1.74083	−0.870416	+	0.492316i	$0.836150\pi$
$602$	19667.5	1.33154
$603$	19844.0	1.34015
$604$	15138.0	1.01979
$605$	−1356.51	−0.0911569
$606$	42749.1	2.86561
$607$	−18477.7	−1.23556	−0.617782	−	0.786350i	$-0.711968\pi$
$607$	−18477.7	−1.23556	−0.617782	+	0.786350i	$0.711968\pi$
$608$	15481.4	1.03265
$609$	−28286.8	−1.88217
$610$	5868.55	0.389525
$611$	−4731.89	−0.313309
$612$	15930.4	1.05221
$613$	6077.95	0.400467	0.200233	−	0.979748i	$-0.435830\pi$
$613$	6077.95	0.400467	0.200233	+	0.979748i	$0.435830\pi$
$614$	−19505.3	−1.28203
$615$	17994.8	1.17987
$616$	−785.230	−0.0513601
$617$	3372.11	0.220026	0.110013	−	0.993930i	$-0.464911\pi$
$617$	3372.11	0.220026	0.110013	+	0.993930i	$0.464911\pi$
$618$	43325.9	2.82010
$619$	4980.18	0.323377	0.161688	−	0.986842i	$-0.448306\pi$
$619$	4980.18	0.323377	0.161688	+	0.986842i	$0.448306\pi$
$620$	9184.47	0.594931
$621$	−4959.85	−0.320502
$622$	−14643.4	−0.943966
$623$	−9416.00	−0.605529
$624$	3546.88	0.227546
$625$	−15709.9	−1.00543
$626$	26914.6	1.71841
$627$	4983.39	0.317412
$628$	18877.6	1.19952
$629$	−20510.3	−1.30016
$630$	30662.7	1.93910
$631$	23246.5	1.46660	0.733302	−	0.679903i	$-0.237978\pi$
$631$	23246.5	1.46660	0.733302	+	0.679903i	$0.237978\pi$
$632$	−2734.43	−0.172104
$633$	45134.6	2.83403
$634$	−25529.0	−1.59919
$635$	8043.95	0.502700
$636$	−38813.5	−2.41990
$637$	−1046.60	−0.0650988
$638$	7735.87	0.480041
$639$	−34947.5	−2.16354
$640$	−4697.85	−0.290155
$641$	21921.7	1.35079	0.675395	−	0.737456i	$-0.263973\pi$
$641$	21921.7	1.35079	0.675395	+	0.737456i	$0.263973\pi$
$642$	23565.4	1.44868
$643$	−23092.5	−1.41630	−0.708149	−	0.706063i	$-0.750470\pi$
$643$	−23092.5	−1.41630	−0.708149	+	0.706063i	$0.750470\pi$
$644$	−33187.8	−2.03072
$645$	18842.3	1.15025
$646$	−14378.5	−0.875719
$647$	19724.1	1.19851	0.599255	−	0.800558i	$-0.295464\pi$
$647$	19724.1	1.19851	0.599255	+	0.800558i	$0.295464\pi$
$648$	2018.63	0.122375
$649$	5218.10	0.315606
$650$	22.9345	0.00138394
$651$	−15344.7	−0.923818
$652$	277.582	0.0166732
$653$	10875.8	0.651767	0.325883	−	0.945410i	$-0.394338\pi$
$653$	10875.8	0.651767	0.325883	+	0.945410i	$0.394338\pi$
$654$	39035.7	2.33397
$655$	1468.62	0.0876086
$656$	12025.0	0.715697
$657$	27273.2	1.61953
$658$	−51334.3	−3.04137
$659$	6779.28	0.400733	0.200367	−	0.979721i	$-0.435787\pi$
$659$	6779.28	0.400733	0.200367	+	0.979721i	$0.435787\pi$
$660$	−8249.79	−0.486549
$661$	−4338.46	−0.255290	−0.127645	−	0.991820i	$-0.540742\pi$
$661$	−4338.46	−0.255290	−0.127645	+	0.991820i	$0.540742\pi$
$662$	−5555.67	−0.326174
$663$	−3665.75	−0.214730
$664$	4266.63	0.249363
$665$	−14498.8	−0.845475
$666$	43943.6	2.55673
$667$	29814.6	1.73077
$668$	−22359.0	−1.29505
$669$	−24585.5	−1.42082
$670$	29650.6	1.70971
$671$	1404.74	0.0808188
$672$	42818.6	2.45798
$673$	31513.5	1.80499	0.902493	−	0.430704i	$-0.141735\pi$
$673$	31513.5	1.80499	0.902493	+	0.430704i	$0.141735\pi$
$674$	32930.5	1.88195
$675$	19.4800	0.00111079
$676$	−18748.0	−1.06668
$677$	−16061.9	−0.911832	−0.455916	−	0.890023i	$-0.650688\pi$
$677$	−16061.9	−0.911832	−0.455916	+	0.890023i	$0.650688\pi$
$678$	−37778.1	−2.13991
$679$	28482.1	1.60979
$680$	2170.55	0.122407
$681$	−7531.63	−0.423807
$682$	4196.46	0.235617
$683$	21785.6	1.22050	0.610252	−	0.792208i	$-0.291068\pi$
$683$	21785.6	1.22050	0.610252	+	0.792208i	$0.291068\pi$
$684$	16138.9	0.902174
$685$	−10427.2	−0.581609
$686$	19148.9	1.06576
$687$	36769.2	2.04197
$688$	12591.3	0.697732
$689$	4756.05	0.262977
$690$	−60691.2	−3.34851
$691$	−23049.5	−1.26895	−0.634474	−	0.772944i	$-0.718783\pi$
$691$	−23049.5	−1.26895	−0.634474	+	0.772944i	$0.718783\pi$
$692$	−10792.8	−0.592893
$693$	7339.66	0.402324
$694$	−33125.2	−1.81184
$695$	−6392.66	−0.348903
$696$	4290.10	0.233643
$697$	−12428.0	−0.675386
$698$	16482.0	0.893773
$699$	18685.6	1.01110
$700$	130.346	0.00703803
$701$	−4508.92	−0.242938	−0.121469	−	0.992595i	$-0.538760\pi$
$701$	−4508.92	−0.242938	−0.121469	+	0.992595i	$0.538760\pi$
$702$	959.033	0.0515618
$703$	−20778.7	−1.11477
$704$	−6699.81	−0.358677
$705$	−49180.3	−2.62729
$706$	41074.1	2.18958
$707$	−29771.5	−1.58370
$708$	31734.6	1.68454
$709$	10744.3	0.569128	0.284564	−	0.958657i	$-0.408151\pi$
$709$	10744.3	0.569128	0.284564	+	0.958657i	$0.408151\pi$
$710$	−52218.0	−2.76015
$711$	25559.2	1.34816
$712$	1428.07	0.0751675
$713$	16173.4	0.849510
$714$	−39768.2	−2.08443
$715$	1010.90	0.0528747
$716$	−13215.5	−0.689786
$717$	−1065.00	−0.0554716
$718$	16267.6	0.845544
$719$	13480.2	0.699205	0.349603	−	0.936898i	$-0.386317\pi$
$719$	13480.2	0.699205	0.349603	+	0.936898i	$0.386317\pi$
$720$	19630.6	1.01609
$721$	−30173.2	−1.55854
$722$	13549.1	0.698402
$723$	14661.7	0.754182
$724$	16328.9	0.838201
$725$	−117.098	−0.00599849
$726$	−3769.40	−0.192693
$727$	10114.5	0.515991	0.257996	−	0.966146i	$-0.416938\pi$
$727$	10114.5	0.515991	0.257996	+	0.966146i	$0.416938\pi$
$728$	585.169	0.0297909
$729$	−24724.8	−1.25615
$730$	40751.2	2.06612
$731$	−13013.3	−0.658433
$732$	8543.11	0.431370
$733$	−19499.5	−0.982579	−0.491290	−	0.870996i	$-0.663474\pi$
$733$	−19499.5	−0.982579	−0.491290	+	0.870996i	$0.663474\pi$
$734$	35335.8	1.77693
$735$	−10877.8	−0.545894
$736$	−45131.2	−2.26027
$737$	7097.41	0.354731
$738$	26627.2	1.32813
$739$	−4025.13	−0.200361	−0.100181	−	0.994969i	$-0.531942\pi$
$739$	−4025.13	−0.200361	−0.100181	+	0.994969i	$0.531942\pi$
$740$	34398.3	1.70879
$741$	−3713.72	−0.184112
$742$	51596.4	2.55278
$743$	−15660.6	−0.773259	−0.386629	−	0.922235i	$-0.626361\pi$
$743$	−15660.6	−0.773259	−0.386629	+	0.922235i	$0.626361\pi$
$744$	2327.24	0.114678
$745$	−1171.16	−0.0575947
$746$	−20022.5	−0.982674
$747$	−39880.8	−1.95336
$748$	5697.67	0.278513
$749$	−16411.6	−0.800621
$750$	−43416.6	−2.11380
$751$	−29523.3	−1.43452	−0.717258	−	0.696808i	$-0.754603\pi$
$751$	−29523.3	−1.43452	−0.717258	+	0.696808i	$0.754603\pi$
$752$	−32864.7	−1.59369
$753$	−17191.8	−0.832008
$754$	−5764.93	−0.278443
$755$	−19279.2	−0.929327
$756$	5450.59	0.262217
$757$	17894.6	0.859170	0.429585	−	0.903026i	$-0.358660\pi$
$757$	17894.6	0.859170	0.429585	+	0.903026i	$0.358660\pi$
$758$	−22503.5	−1.07832
$759$	−14527.5	−0.694750
$760$	2198.96	0.104953
$761$	26989.9	1.28566	0.642828	−	0.766011i	$-0.277761\pi$
$761$	26989.9	1.28566	0.642828	+	0.766011i	$0.277761\pi$
$762$	22352.1	1.06264
$763$	−27185.5	−1.28988
$764$	−4359.27	−0.206430
$765$	−20288.5	−0.958864
$766$	−32910.3	−1.55235
$767$	−3888.63	−0.183064
$768$	23976.1	1.12652
$769$	17468.3	0.819147	0.409573	−	0.912277i	$-0.365678\pi$
$769$	17468.3	0.819147	0.409573	+	0.912277i	$0.365678\pi$
$770$	10966.8	0.513268
$771$	−56321.3	−2.63082
$772$	4938.90	0.230252
$773$	5847.61	0.272088	0.136044	−	0.990703i	$-0.456561\pi$
$773$	5847.61	0.272088	0.136044	+	0.990703i	$0.456561\pi$
$774$	27881.2	1.29479
$775$	−63.5218	−0.00294422
$776$	−4319.72	−0.199831
$777$	−57469.9	−2.65344
$778$	34797.1	1.60352
$779$	−12590.6	−0.579084
$780$	6147.91	0.282218
$781$	−12499.3	−0.572677
$782$	41916.0	1.91677
$783$	−4896.59	−0.223487
$784$	−7269.04	−0.331134
$785$	−24041.9	−1.09311
$786$	4080.92	0.185193
$787$	16717.4	0.757195	0.378597	−	0.925561i	$-0.376407\pi$
$787$	16717.4	0.757195	0.378597	+	0.925561i	$0.376407\pi$
$788$	−19010.3	−0.859407
$789$	−32808.5	−1.48037
$790$	38190.1	1.71993
$791$	26309.6	1.18263
$792$	−1113.16	−0.0499427
$793$	−1046.84	−0.0468782
$794$	−28403.3	−1.26952
$795$	49431.5	2.20523
$796$	−44186.6	−1.96753
$797$	22847.4	1.01543	0.507714	−	0.861525i	$-0.330490\pi$
$797$	22847.4	1.01543	0.507714	+	0.861525i	$0.330490\pi$
$798$	−40288.6	−1.78722
$799$	33966.1	1.50392
$800$	177.254	0.00783361
$801$	−13348.4	−0.588817
$802$	31334.8	1.37964
$803$	9754.53	0.428680
$804$	43163.8	1.89337
$805$	42266.8	1.85057
$806$	−3127.28	−0.136667
$807$	63508.0	2.77025
$808$	4515.27	0.196593
$809$	−23307.6	−1.01292	−0.506459	−	0.862264i	$-0.669046\pi$
$809$	−23307.6	−1.01292	−0.506459	+	0.862264i	$0.669046\pi$
$810$	−28192.9	−1.22296
$811$	−12451.6	−0.539131	−0.269565	−	0.962982i	$-0.586880\pi$
$811$	−12451.6	−0.539131	−0.269565	+	0.962982i	$0.586880\pi$
$812$	−32764.5	−1.41602
$813$	25852.2	1.11522
$814$	15716.8	0.676751
$815$	−353.519	−0.0151941
$816$	−25460.0	−1.09225
$817$	−13183.6	−0.564549
$818$	44565.1	1.90487
$819$	−5469.66	−0.233364
$820$	20843.3	0.887658
$821$	37654.9	1.60069	0.800344	−	0.599541i	$-0.204650\pi$
$821$	37654.9	1.60069	0.800344	+	0.599541i	$0.204650\pi$
$822$	−28974.5	−1.22944
$823$	−2142.32	−0.0907371	−0.0453686	−	0.998970i	$-0.514446\pi$
$823$	−2142.32	−0.0907371	−0.0453686	+	0.998970i	$0.514446\pi$
$824$	4576.20	0.193470
$825$	57.0573	0.00240786
$826$	−42186.1	−1.77705
$827$	32636.2	1.37228	0.686138	−	0.727472i	$-0.259305\pi$
$827$	32636.2	1.37228	0.686138	+	0.727472i	$0.259305\pi$
$828$	−47048.0	−1.97467
$829$	−26213.8	−1.09824	−0.549120	−	0.835743i	$-0.685037\pi$
$829$	−26213.8	−1.09824	−0.549120	+	0.835743i	$0.685037\pi$
$830$	−59589.2	−2.49202
$831$	−50543.5	−2.10991
$832$	4992.83	0.208047
$833$	7512.66	0.312483
$834$	−17763.6	−0.737533
$835$	28475.6	1.18017
$836$	5772.23	0.238800
$837$	−2656.24	−0.109693
$838$	−44638.0	−1.84009
$839$	42842.3	1.76291	0.881455	−	0.472267i	$-0.156564\pi$
$839$	42842.3	1.76291	0.881455	+	0.472267i	$0.156564\pi$
$840$	6081.89	0.249816
$841$	5045.34	0.206869
$842$	3837.95	0.157084
$843$	−38519.4	−1.57376
$844$	52279.2	2.13214
$845$	23876.8	0.972057
$846$	−72773.0	−2.95743
$847$	2625.10	0.106493
$848$	33032.5	1.33767
$849$	38688.6	1.56395
$850$	−164.627	−0.00664312
$851$	60573.8	2.44000
$852$	−76016.2	−3.05666
$853$	−20450.0	−0.820862	−0.410431	−	0.911892i	$-0.634622\pi$
$853$	−20450.0	−0.820862	−0.410431	+	0.911892i	$0.634622\pi$
$854$	−11356.7	−0.455058
$855$	−20554.0	−0.822142
$856$	2489.05	0.0993853
$857$	−25967.7	−1.03505	−0.517526	−	0.855667i	$-0.673147\pi$
$857$	−25967.7	−1.03505	−0.517526	+	0.855667i	$0.673147\pi$
$858$	2809.03	0.111770
$859$	40349.7	1.60269	0.801347	−	0.598200i	$-0.204117\pi$
$859$	40349.7	1.60269	0.801347	+	0.598200i	$0.204117\pi$
$860$	21824.9	0.865376
$861$	−34823.3	−1.37837
$862$	−11617.5	−0.459041
$863$	−24356.3	−0.960717	−0.480358	−	0.877072i	$-0.659493\pi$
$863$	−24356.3	−0.960717	−0.480358	+	0.877072i	$0.659493\pi$
$864$	7412.11	0.291858
$865$	13745.4	0.540298
$866$	63741.0	2.50116
$867$	−11024.1	−0.431832
$868$	−17773.7	−0.695020
$869$	9141.48	0.356851
$870$	−59917.1	−2.33492
$871$	−5289.13	−0.205758
$872$	4123.06	0.160120
$873$	40377.1	1.56536
$874$	42464.6	1.64346
$875$	30236.4	1.16820
$876$	59323.4	2.28807
$877$	−4343.04	−0.167223	−0.0836113	−	0.996498i	$-0.526645\pi$
$877$	−4343.04	−0.167223	−0.0836113	+	0.996498i	$0.526645\pi$
$878$	5667.21	0.217835
$879$	−66223.7	−2.54115
$880$	7021.05	0.268954
$881$	22220.4	0.849743	0.424872	−	0.905254i	$-0.360319\pi$
$881$	22220.4	0.849743	0.424872	+	0.905254i	$0.360319\pi$
$882$	−16096.0	−0.614490
$883$	48580.6	1.85149	0.925746	−	0.378147i	$-0.123439\pi$
$883$	48580.6	1.85149	0.925746	+	0.378147i	$0.123439\pi$
$884$	−4246.02	−0.161549
$885$	−40416.0	−1.53511
$886$	67112.3	2.54479
$887$	9263.41	0.350659	0.175330	−	0.984510i	$-0.443901\pi$
$887$	9263.41	0.350659	0.175330	+	0.984510i	$0.443901\pi$
$888$	8716.13	0.329385
$889$	−15566.6	−0.587273
$890$	−19945.0	−0.751187
$891$	−6748.47	−0.253740
$892$	−28477.2	−1.06893
$893$	34410.6	1.28948
$894$	−3254.36	−0.121747
$895$	16830.8	0.628595
$896$	9091.23	0.338969
$897$	10826.2	0.402983
$898$	39893.6	1.48248
$899$	15967.2	0.592364
$900$	184.783	0.00684380
$901$	−34139.6	−1.26233
$902$	9523.47	0.351548
$903$	−36463.3	−1.34377
$904$	−3990.23	−0.146806
$905$	−20795.9	−0.763844
$906$	−53572.0	−1.96447
$907$	−44035.1	−1.61208	−0.806042	−	0.591858i	$-0.798395\pi$
$907$	−44035.1	−1.61208	−0.806042	+	0.591858i	$0.798395\pi$
$908$	−8723.85	−0.318845
$909$	−42205.0	−1.53999
$910$	−8172.68	−0.297716
$911$	6761.46	0.245903	0.122951	−	0.992413i	$-0.460764\pi$
$911$	6761.46	0.245903	0.122951	+	0.992413i	$0.460764\pi$
$912$	−25793.1	−0.936509
$913$	−14263.7	−0.517044
$914$	16147.4	0.584364
$915$	−10880.2	−0.393103
$916$	42589.6	1.53625
$917$	−2842.05	−0.102348
$918$	−6884.07	−0.247503
$919$	43069.7	1.54596	0.772980	−	0.634430i	$-0.218765\pi$
$919$	43069.7	1.54596	0.772980	+	0.634430i	$0.218765\pi$
$920$	−6410.37	−0.229721
$921$	36162.6	1.29381
$922$	71246.4	2.54488
$923$	9314.73	0.332176
$924$	15964.9	0.568405
$925$	−237.906	−0.00845653
$926$	−60667.3	−2.15297
$927$	−42774.4	−1.51553
$928$	−44555.6	−1.57609
$929$	9885.66	0.349126	0.174563	−	0.984646i	$-0.444149\pi$
$929$	9885.66	0.349126	0.174563	+	0.984646i	$0.444149\pi$
$930$	−32503.1	−1.14604
$931$	7610.98	0.267927
$932$	21643.5	0.760682
$933$	27148.7	0.952635
$934$	−69784.0	−2.44476
$935$	−7256.36	−0.253806
$936$	829.552	0.0289688
$937$	−42561.1	−1.48390	−0.741948	−	0.670457i	$-0.766098\pi$
$937$	−42561.1	−1.48390	−0.741948	+	0.670457i	$0.766098\pi$
$938$	−57379.5	−1.99734
$939$	−49899.4	−1.73419
$940$	−56965.4	−1.97660
$941$	−42953.7	−1.48805	−0.744023	−	0.668154i	$-0.767085\pi$
$941$	−42953.7	−1.48805	−0.744023	+	0.668154i	$0.767085\pi$
$942$	−66806.2	−2.31068
$943$	36704.1	1.26750
$944$	−27008.0	−0.931180
$945$	−6941.68	−0.238956
$946$	9971.98	0.342724
$947$	20350.5	0.698312	0.349156	−	0.937065i	$-0.386468\pi$
$947$	20350.5	0.698312	0.349156	+	0.937065i	$0.386468\pi$
$948$	55595.1	1.90469
$949$	−7269.27	−0.248652
$950$	−166.781	−0.00569589
$951$	47330.6	1.61388
$952$	−4200.42	−0.143000
$953$	12988.0	0.441472	0.220736	−	0.975334i	$-0.429154\pi$
$953$	12988.0	0.441472	0.220736	+	0.975334i	$0.429154\pi$
$954$	73144.6	2.48233
$955$	5551.82	0.188118
$956$	−1233.58	−0.0417332
$957$	−14342.2	−0.484450
$958$	811.356	0.0273630
$959$	20178.5	0.679457
$960$	51892.5	1.74461
$961$	−21129.3	−0.709252
$962$	−11712.5	−0.392543
$963$	−23265.5	−0.778525
$964$	16982.5	0.567397
$965$	−6290.01	−0.209826
$966$	117449.	3.91186
$967$	18301.6	0.608626	0.304313	−	0.952572i	$-0.401573\pi$
$967$	18301.6	0.608626	0.304313	+	0.952572i	$0.401573\pi$
$968$	−398.134	−0.0132195
$969$	26657.6	0.883762
$970$	60330.8	1.99702
$971$	−36446.0	−1.20454	−0.602270	−	0.798292i	$-0.705737\pi$
$971$	−36446.0	−1.20454	−0.602270	+	0.798292i	$0.705737\pi$
$972$	−47825.1	−1.57818
$973$	12371.0	0.407601
$974$	−27039.4	−0.889527
$975$	−42.5202	−0.00139665
$976$	−7270.69	−0.238452
$977$	13262.8	0.434305	0.217152	−	0.976138i	$-0.430323\pi$
$977$	13262.8	0.434305	0.217152	+	0.976138i	$0.430323\pi$
$978$	−982.339	−0.0321184
$979$	−4774.18	−0.155856
$980$	−12599.7	−0.410695
$981$	−38538.9	−1.25428
$982$	−37829.4	−1.22931
$983$	−5968.42	−0.193655	−0.0968276	−	0.995301i	$-0.530870\pi$
$983$	−5968.42	−0.193655	−0.0968276	+	0.995301i	$0.530870\pi$
$984$	5281.45	0.171104
$985$	24210.8	0.783169
$986$	41381.4	1.33656
$987$	95173.2	3.06930
$988$	−4301.58	−0.138514
$989$	38432.7	1.23568
$990$	15546.9	0.499103
$991$	−12668.2	−0.406072	−0.203036	−	0.979171i	$-0.565081\pi$
$991$	−12668.2	−0.406072	−0.203036	+	0.979171i	$0.565081\pi$
$992$	−24170.0	−0.773585
$993$	10300.2	0.329170
$994$	101052.	3.22451
$995$	56274.5	1.79299
$996$	−86746.8	−2.75972
$997$	−24993.5	−0.793932	−0.396966	−	0.917833i	$-0.629937\pi$
$997$	−24993.5	−0.793932	−0.396966	+	0.917833i	$0.629937\pi$
$998$	50368.7	1.59759
$999$	−9948.32	−0.315066

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.4.a.b.1.14	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.4.a.b.1.14	✓	79	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:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q-4.09911 q^{2} +7.59971 q^{3} +8.80270 q^{4} -11.2108 q^{5} -31.1520 q^{6} +21.6950 q^{7} -3.29036 q^{8} +30.7555 q^{9} +O(q^{10})\)	\(q-4.09911 q^{2} +7.59971 q^{3} +8.80270 q^{4} -11.2108 q^{5} -31.1520 q^{6} +21.6950 q^{7} -3.29036 q^{8} +30.7555 q^{9} +45.9544 q^{10} +11.0000 q^{11} +66.8979 q^{12} -8.19742 q^{13} -88.9304 q^{14} -85.1989 q^{15} -56.9341 q^{16} +58.8422 q^{17} -126.070 q^{18} +59.6122 q^{19} -98.6855 q^{20} +164.876 q^{21} -45.0902 q^{22} -173.781 q^{23} -25.0058 q^{24} +0.682530 q^{25} +33.6021 q^{26} +28.5408 q^{27} +190.975 q^{28} -171.564 q^{29} +349.240 q^{30} -93.0681 q^{31} +259.702 q^{32} +83.5968 q^{33} -241.201 q^{34} -243.219 q^{35} +270.732 q^{36} -348.564 q^{37} -244.357 q^{38} -62.2980 q^{39} +36.8877 q^{40} -211.209 q^{41} -675.844 q^{42} -221.156 q^{43} +96.8297 q^{44} -344.795 q^{45} +712.347 q^{46} +577.241 q^{47} -432.682 q^{48} +127.675 q^{49} -2.79777 q^{50} +447.183 q^{51} -72.1594 q^{52} -580.189 q^{53} -116.992 q^{54} -123.319 q^{55} -71.3845 q^{56} +453.035 q^{57} +703.261 q^{58} +474.373 q^{59} -749.981 q^{60} +127.704 q^{61} +381.496 q^{62} +667.242 q^{63} -609.074 q^{64} +91.8998 q^{65} -342.672 q^{66} +645.219 q^{67} +517.970 q^{68} -1320.68 q^{69} +996.982 q^{70} -1136.30 q^{71} -101.197 q^{72} +886.775 q^{73} +1428.80 q^{74} +5.18703 q^{75} +524.749 q^{76} +238.645 q^{77} +255.366 q^{78} +831.044 q^{79} +638.278 q^{80} -613.497 q^{81} +865.770 q^{82} -1296.70 q^{83} +1451.35 q^{84} -659.669 q^{85} +906.544 q^{86} -1303.84 q^{87} -36.1940 q^{88} -434.016 q^{89} +1413.35 q^{90} -177.843 q^{91} -1529.74 q^{92} -707.290 q^{93} -2366.18 q^{94} -668.302 q^{95} +1973.66 q^{96} +1312.84 q^{97} -523.353 q^{98} +338.311 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 20 q^{2} - 12 q^{3} + 288 q^{4} - 40 q^{5} - 111 q^{6} - 101 q^{7} - 258 q^{8} + 585 q^{9}+O(q^{10}) \) 79 * q - 20 * q^2 - 12 * q^3 + 288 * q^4 - 40 * q^5 - 111 * q^6 - 101 * q^7 - 258 * q^8 + 585 * q^9	\( 79 q - 20 q^{2} - 12 q^{3} + 288 q^{4} - 40 q^{5} - 111 q^{6} - 101 q^{7} - 258 q^{8} + 585 q^{9} - 178 q^{10} + 869 q^{11} - 144 q^{12} - 242 q^{13} - 342 q^{14} - 524 q^{15} + 928 q^{16} - 260 q^{17} - 611 q^{18} - 543 q^{19} - 578 q^{20} - 710 q^{21} - 220 q^{22} - 908 q^{23} - 1322 q^{24} + 1701 q^{25} - 844 q^{26} - 732 q^{27} - 1068 q^{28} - 1747 q^{29} - 973 q^{30} - 1248 q^{31} - 2069 q^{32} - 132 q^{33} - 76 q^{34} - 1630 q^{35} + 2155 q^{36} - 535 q^{37} + 1155 q^{38} - 2514 q^{39} - 298 q^{40} - 2087 q^{41} - 5 q^{42} - 1008 q^{43} + 3168 q^{44} - 1160 q^{45} - 1640 q^{46} - 1960 q^{47} + 3412 q^{48} + 3670 q^{49} - 2394 q^{50} - 2994 q^{51} - 2601 q^{52} - 2466 q^{53} + 1296 q^{54} - 440 q^{55} - 5195 q^{56} - 3776 q^{57} + 1068 q^{58} - 2310 q^{59} + 1599 q^{60} - 3404 q^{61} + 1534 q^{62} - 3409 q^{63} + 2568 q^{64} - 3906 q^{65} - 1221 q^{66} - 2405 q^{67} - 3145 q^{68} - 2420 q^{69} + 455 q^{70} - 8978 q^{71} - 7262 q^{72} - 1868 q^{73} - 2790 q^{74} - 1196 q^{75} - 5483 q^{76} - 1111 q^{77} + 349 q^{78} - 9130 q^{79} - 1697 q^{80} + 4171 q^{81} - 241 q^{82} - 4639 q^{83} - 1659 q^{84} - 7634 q^{85} - 5656 q^{86} - 4412 q^{87} - 2838 q^{88} - 6561 q^{89} - 6756 q^{90} - 2742 q^{91} - 5386 q^{92} - 3234 q^{93} - 5295 q^{94} - 7930 q^{95} - 12593 q^{96} - 4520 q^{97} - 3213 q^{98} + 6435 q^{99}+O(q^{100}) \) 79 * q - 20 * q^2 - 12 * q^3 + 288 * q^4 - 40 * q^5 - 111 * q^6 - 101 * q^7 - 258 * q^8 + 585 * q^9 - 178 * q^10 + 869 * q^11 - 144 * q^12 - 242 * q^13 - 342 * q^14 - 524 * q^15 + 928 * q^16 - 260 * q^17 - 611 * q^18 - 543 * q^19 - 578 * q^20 - 710 * q^21 - 220 * q^22 - 908 * q^23 - 1322 * q^24 + 1701 * q^25 - 844 * q^26 - 732 * q^27 - 1068 * q^28 - 1747 * q^29 - 973 * q^30 - 1248 * q^31 - 2069 * q^32 - 132 * q^33 - 76 * q^34 - 1630 * q^35 + 2155 * q^36 - 535 * q^37 + 1155 * q^38 - 2514 * q^39 - 298 * q^40 - 2087 * q^41 - 5 * q^42 - 1008 * q^43 + 3168 * q^44 - 1160 * q^45 - 1640 * q^46 - 1960 * q^47 + 3412 * q^48 + 3670 * q^49 - 2394 * q^50 - 2994 * q^51 - 2601 * q^52 - 2466 * q^53 + 1296 * q^54 - 440 * q^55 - 5195 * q^56 - 3776 * q^57 + 1068 * q^58 - 2310 * q^59 + 1599 * q^60 - 3404 * q^61 + 1534 * q^62 - 3409 * q^63 + 2568 * q^64 - 3906 * q^65 - 1221 * q^66 - 2405 * q^67 - 3145 * q^68 - 2420 * q^69 + 455 * q^70 - 8978 * q^71 - 7262 * q^72 - 1868 * q^73 - 2790 * q^74 - 1196 * q^75 - 5483 * q^76 - 1111 * q^77 + 349 * q^78 - 9130 * q^79 - 1697 * q^80 + 4171 * q^81 - 241 * q^82 - 4639 * q^83 - 1659 * q^84 - 7634 * q^85 - 5656 * q^86 - 4412 * q^87 - 2838 * q^88 - 6561 * q^89 - 6756 * q^90 - 2742 * q^91 - 5386 * q^92 - 3234 * q^93 - 5295 * q^94 - 7930 * q^95 - 12593 * q^96 - 4520 * q^97 - 3213 * q^98 + 6435 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more