LMFDB - Embedded newform 289.4.a.h.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,4,Mod(1,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	289.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:	$17.0515519917$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 72 x^{10} - 17 x^{9} + 1872 x^{8} + 627 x^{7} - 20922 x^{6} - 5163 x^{5} + 93255 x^{4} - 4607 x^{3} - 117822 x^{2} + 21960 x + 29352 $ x^12 - 72x^10 - 17x^9 + 1872x^8 + 627x^7 - 20922x^6 - 5163x^5 + 93255x^4 - 4607x^3 - 117822x^2 + 21960x + 29352
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3}\cdot 17^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$-4.42326$ of defining polynomial
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.42326 q^{2} -9.44971 q^{3} +11.5652 q^{4} +8.63042 q^{5} -41.7985 q^{6} -12.6513 q^{7} +15.7698 q^{8} +62.2970 q^{9} +O(q^{10})$	\(q+4.42326 q^{2} -9.44971 q^{3} +11.5652 q^{4} +8.63042 q^{5} -41.7985 q^{6} -12.6513 q^{7} +15.7698 q^{8} +62.2970 q^{9} +38.1746 q^{10} -14.5171 q^{11} -109.288 q^{12} -26.6619 q^{13} -55.9602 q^{14} -81.5550 q^{15} -22.7676 q^{16} +275.556 q^{18} -125.285 q^{19} +99.8126 q^{20} +119.552 q^{21} -64.2131 q^{22} +2.31970 q^{23} -149.020 q^{24} -50.5159 q^{25} -117.932 q^{26} -333.547 q^{27} -146.315 q^{28} +21.8015 q^{29} -360.739 q^{30} -323.318 q^{31} -226.866 q^{32} +137.183 q^{33} -109.186 q^{35} +720.478 q^{36} -73.2182 q^{37} -554.167 q^{38} +251.947 q^{39} +136.100 q^{40} +179.916 q^{41} +528.807 q^{42} +186.872 q^{43} -167.894 q^{44} +537.649 q^{45} +10.2606 q^{46} +235.952 q^{47} +215.147 q^{48} -182.944 q^{49} -223.445 q^{50} -308.350 q^{52} +200.645 q^{53} -1475.36 q^{54} -125.289 q^{55} -199.510 q^{56} +1183.90 q^{57} +96.4337 q^{58} -718.203 q^{59} -943.200 q^{60} +727.874 q^{61} -1430.12 q^{62} -788.141 q^{63} -821.345 q^{64} -230.103 q^{65} +606.795 q^{66} +76.9332 q^{67} -21.9205 q^{69} -482.959 q^{70} +923.747 q^{71} +982.414 q^{72} -820.959 q^{73} -323.863 q^{74} +477.361 q^{75} -1448.94 q^{76} +183.661 q^{77} +1114.43 q^{78} -51.0071 q^{79} -196.494 q^{80} +1469.90 q^{81} +795.815 q^{82} +1183.28 q^{83} +1382.64 q^{84} +826.585 q^{86} -206.018 q^{87} -228.933 q^{88} -86.8644 q^{89} +2378.16 q^{90} +337.309 q^{91} +26.8278 q^{92} +3055.26 q^{93} +1043.68 q^{94} -1081.26 q^{95} +2143.82 q^{96} -758.448 q^{97} -809.206 q^{98} -904.375 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 18 q^{3} + 48 q^{4} - 30 q^{5} + 9 q^{6} - 24 q^{7} - 51 q^{8} + 108 q^{9}+O(q^{10}) $ 12 * q - 18 * q^3 + 48 * q^4 - 30 * q^5 + 9 * q^6 - 24 * q^7 - 51 * q^8 + 108 * q^9	\( 12 q - 18 q^{3} + 48 q^{4} - 30 q^{5} + 9 q^{6} - 24 q^{7} - 51 q^{8} + 108 q^{9} - 60 q^{10} - 162 q^{11} - 216 q^{12} - 72 q^{13} - 267 q^{14} - 138 q^{15} + 192 q^{16} + 189 q^{18} - 66 q^{19} - 129 q^{20} + 246 q^{21} - 456 q^{22} - 282 q^{23} - 72 q^{24} + 444 q^{25} + 528 q^{26} - 1092 q^{27} - 120 q^{28} - 648 q^{29} - 1890 q^{30} - 504 q^{31} - 1353 q^{32} + 966 q^{33} - 66 q^{35} - 663 q^{36} + 30 q^{37} - 60 q^{38} - 1758 q^{39} + 450 q^{40} - 318 q^{41} + 804 q^{42} + 486 q^{43} - 2448 q^{44} - 486 q^{45} - 1617 q^{46} - 888 q^{47} - 1257 q^{48} - 570 q^{49} + 435 q^{50} + 225 q^{52} + 1026 q^{53} - 933 q^{54} + 972 q^{55} - 2661 q^{56} + 156 q^{57} - 201 q^{58} - 792 q^{59} + 1458 q^{60} - 1212 q^{61} - 2817 q^{62} - 2112 q^{63} - 1857 q^{64} - 2742 q^{65} - 594 q^{66} + 624 q^{67} - 1506 q^{69} - 1650 q^{70} - 2802 q^{71} + 1455 q^{72} - 726 q^{73} - 270 q^{74} + 264 q^{75} + 675 q^{76} - 1008 q^{77} + 3090 q^{78} + 444 q^{79} + 1143 q^{80} + 2520 q^{81} + 4950 q^{82} + 672 q^{83} - 777 q^{84} + 2778 q^{86} + 726 q^{87} + 3750 q^{88} - 906 q^{89} + 7755 q^{90} - 2280 q^{91} - 87 q^{92} + 132 q^{93} + 735 q^{94} - 966 q^{95} + 5046 q^{96} + 3246 q^{97} + 1911 q^{98} + 282 q^{99}+O(q^{100}) \) 12 * q - 18 * q^3 + 48 * q^4 - 30 * q^5 + 9 * q^6 - 24 * q^7 - 51 * q^8 + 108 * q^9 - 60 * q^10 - 162 * q^11 - 216 * q^12 - 72 * q^13 - 267 * q^14 - 138 * q^15 + 192 * q^16 + 189 * q^18 - 66 * q^19 - 129 * q^20 + 246 * q^21 - 456 * q^22 - 282 * q^23 - 72 * q^24 + 444 * q^25 + 528 * q^26 - 1092 * q^27 - 120 * q^28 - 648 * q^29 - 1890 * q^30 - 504 * q^31 - 1353 * q^32 + 966 * q^33 - 66 * q^35 - 663 * q^36 + 30 * q^37 - 60 * q^38 - 1758 * q^39 + 450 * q^40 - 318 * q^41 + 804 * q^42 + 486 * q^43 - 2448 * q^44 - 486 * q^45 - 1617 * q^46 - 888 * q^47 - 1257 * q^48 - 570 * q^49 + 435 * q^50 + 225 * q^52 + 1026 * q^53 - 933 * q^54 + 972 * q^55 - 2661 * q^56 + 156 * q^57 - 201 * q^58 - 792 * q^59 + 1458 * q^60 - 1212 * q^61 - 2817 * q^62 - 2112 * q^63 - 1857 * q^64 - 2742 * q^65 - 594 * q^66 + 624 * q^67 - 1506 * q^69 - 1650 * q^70 - 2802 * q^71 + 1455 * q^72 - 726 * q^73 - 270 * q^74 + 264 * q^75 + 675 * q^76 - 1008 * q^77 + 3090 * q^78 + 444 * q^79 + 1143 * q^80 + 2520 * q^81 + 4950 * q^82 + 672 * q^83 - 777 * q^84 + 2778 * q^86 + 726 * q^87 + 3750 * q^88 - 906 * q^89 + 7755 * q^90 - 2280 * q^91 - 87 * q^92 + 132 * q^93 + 735 * q^94 - 966 * q^95 + 5046 * q^96 + 3246 * q^97 + 1911 * q^98 + 282 * 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 $

$2$	4.42326	1.56386	0.781929	−	0.623368i	$-0.214236\pi$
$2$	4.42326	1.56386	0.781929	+	0.623368i	$0.214236\pi$
$3$	−9.44971	−1.81860	−0.909299	−	0.416144i	$-0.863381\pi$
$3$	−9.44971	−1.81860	−0.909299	+	0.416144i	$0.863381\pi$
$4$	11.5652	1.44565
$5$	8.63042	0.771928	0.385964	−	0.922514i	$-0.373869\pi$
$5$	8.63042	0.771928	0.385964	+	0.922514i	$0.373869\pi$
$6$	−41.7985	−2.84403
$7$	−12.6513	−0.683108	−0.341554	−	0.939862i	$-0.610953\pi$
$7$	−12.6513	−0.683108	−0.341554	+	0.939862i	$0.610953\pi$
$8$	15.7698	0.696935
$9$	62.2970	2.30730
$10$	38.1746	1.20719
$11$	−14.5171	−0.397917	−0.198958	−	0.980008i	$-0.563756\pi$
$11$	−14.5171	−0.397917	−0.198958	+	0.980008i	$0.563756\pi$
$12$	−109.288	−2.62906
$13$	−26.6619	−0.568822	−0.284411	−	0.958702i	$-0.591798\pi$
$13$	−26.6619	−0.568822	−0.284411	+	0.958702i	$0.591798\pi$
$14$	−55.9602	−1.06828
$15$	−81.5550	−1.40383
$16$	−22.7676	−0.355744
$17$	0	0
$17$	0	0
$18$	275.556	3.60829
$19$	−125.285	−1.51275	−0.756376	−	0.654137i	$-0.773032\pi$
$19$	−125.285	−1.51275	−0.756376	+	0.654137i	$0.773032\pi$
$20$	99.8126	1.11594
$21$	119.552	1.24230
$22$	−64.2131	−0.622285
$23$	2.31970	0.0210301	0.0105150	−	0.999945i	$-0.496653\pi$
$23$	2.31970	0.0210301	0.0105150	+	0.999945i	$0.496653\pi$
$24$	−149.020	−1.26744
$25$	−50.5159	−0.404127
$26$	−117.932	−0.889556
$27$	−333.547	−2.37745
$28$	−146.315	−0.987536
$29$	21.8015	0.139601	0.0698007	−	0.997561i	$-0.477764\pi$
$29$	21.8015	0.139601	0.0698007	+	0.997561i	$0.477764\pi$
$30$	−360.739	−2.19538
$31$	−323.318	−1.87321	−0.936606	−	0.350383i	$-0.886051\pi$
$31$	−323.318	−1.87321	−0.936606	+	0.350383i	$0.886051\pi$
$32$	−226.866	−1.25327
$33$	137.183	0.723650
$34$	0	0
$35$	−109.186	−0.527310
$36$	720.478	3.33555
$37$	−73.2182	−0.325324	−0.162662	−	0.986682i	$-0.552008\pi$
$37$	−73.2182	−0.325324	−0.162662	+	0.986682i	$0.552008\pi$
$38$	−554.167	−2.36573
$39$	251.947	1.03446
$40$	136.100	0.537983
$41$	179.916	0.685321	0.342661	−	0.939459i	$-0.388672\pi$
$41$	179.916	0.685321	0.342661	+	0.939459i	$0.388672\pi$
$42$	528.807	1.94278
$43$	186.872	0.662739	0.331370	−	0.943501i	$-0.392489\pi$
$43$	186.872	0.662739	0.331370	+	0.943501i	$0.392489\pi$
$44$	−167.894	−0.575249
$45$	537.649	1.78107
$46$	10.2606	0.0328880
$47$	235.952	0.732280	0.366140	−	0.930560i	$-0.380679\pi$
$47$	235.952	0.732280	0.366140	+	0.930560i	$0.380679\pi$
$48$	215.147	0.646956
$49$	−182.944	−0.533363
$50$	−223.445	−0.631997
$51$	0	0
$52$	−308.350	−0.822318
$53$	200.645	0.520014	0.260007	−	0.965607i	$-0.416275\pi$
$53$	200.645	0.520014	0.260007	+	0.965607i	$0.416275\pi$
$54$	−1475.36	−3.71799
$55$	−125.289	−0.307163
$56$	−199.510	−0.476082
$57$	1183.90	2.75109
$58$	96.4337	0.218317
$59$	−718.203	−1.58478	−0.792391	−	0.610014i	$-0.791164\pi$
$59$	−718.203	−1.58478	−0.792391	+	0.610014i	$0.791164\pi$
$60$	−943.200	−2.02944
$61$	727.874	1.52778	0.763891	−	0.645345i	$-0.223286\pi$
$61$	727.874	1.52778	0.763891	+	0.645345i	$0.223286\pi$
$62$	−1430.12	−2.92944
$63$	−788.141	−1.57613
$64$	−821.345	−1.60419
$65$	−230.103	−0.439089
$66$	606.795	1.13169
$67$	76.9332	0.140282	0.0701410	−	0.997537i	$-0.477655\pi$
$67$	76.9332	0.140282	0.0701410	+	0.997537i	$0.477655\pi$
$68$	0	0
$69$	−21.9205	−0.0382452
$70$	−482.959	−0.824639
$71$	923.747	1.54406	0.772032	−	0.635583i	$-0.219240\pi$
$71$	923.747	1.54406	0.772032	+	0.635583i	$0.219240\pi$
$72$	982.414	1.60804
$73$	−820.959	−1.31625	−0.658123	−	0.752910i	$-0.728650\pi$
$73$	−820.959	−1.31625	−0.658123	+	0.752910i	$0.728650\pi$
$74$	−323.863	−0.508761
$75$	477.361	0.734945
$76$	−1448.94	−2.18691
$77$	183.661	0.271820
$78$	1114.43	1.61774
$79$	−51.0071	−0.0726423	−0.0363212	−	0.999340i	$-0.511564\pi$
$79$	−51.0071	−0.0726423	−0.0363212	+	0.999340i	$0.511564\pi$
$80$	−196.494	−0.274609
$81$	1469.90	2.01632
$82$	795.815	1.07174
$83$	1183.28	1.56485	0.782424	−	0.622746i	$-0.213983\pi$
$83$	1183.28	1.56485	0.782424	+	0.622746i	$0.213983\pi$
$84$	1382.64	1.79593
$85$	0	0
$86$	826.585	1.03643
$87$	−206.018	−0.253879
$88$	−228.933	−0.277322
$89$	−86.8644	−0.103456	−0.0517281	−	0.998661i	$-0.516473\pi$
$89$	−86.8644	−0.103456	−0.0517281	+	0.998661i	$0.516473\pi$
$90$	2378.16	2.78534
$91$	337.309	0.388567
$92$	26.8278	0.0304021
$93$	3055.26	3.40662
$94$	1043.68	1.14518
$95$	−1081.26	−1.16774
$96$	2143.82	2.27919
$97$	−758.448	−0.793904	−0.396952	−	0.917839i	$-0.629932\pi$
$97$	−758.448	−0.793904	−0.396952	+	0.917839i	$0.629932\pi$
$98$	−809.206	−0.834104
$99$	−904.375	−0.918112
$100$	−584.227	−0.584227
$101$	991.783	0.977090	0.488545	−	0.872539i	$-0.337528\pi$
$101$	991.783	0.977090	0.488545	+	0.872539i	$0.337528\pi$
$102$	0	0
$103$	−596.460	−0.570592	−0.285296	−	0.958439i	$-0.592092\pi$
$103$	−596.460	−0.570592	−0.285296	+	0.958439i	$0.592092\pi$
$104$	−420.454	−0.396432
$105$	1031.78	0.958966
$106$	887.506	0.813228
$107$	786.005	0.710149	0.355075	−	0.934838i	$-0.384455\pi$
$107$	786.005	0.710149	0.355075	+	0.934838i	$0.384455\pi$
$108$	−3857.54	−3.43696
$109$	489.932	0.430523	0.215261	−	0.976556i	$-0.430940\pi$
$109$	489.932	0.430523	0.215261	+	0.976556i	$0.430940\pi$
$110$	−554.186	−0.480359
$111$	691.891	0.591634
$112$	288.041	0.243012
$113$	−162.976	−0.135677	−0.0678385	−	0.997696i	$-0.521610\pi$
$113$	−162.976	−0.135677	−0.0678385	+	0.997696i	$0.521610\pi$
$114$	5236.72	4.30231
$115$	20.0200	0.0162337
$116$	252.139	0.201815
$117$	−1660.96	−1.31244
$118$	−3176.80	−2.47837
$119$	0	0
$120$	−1286.11	−0.978376
$121$	−1120.25	−0.841662
$122$	3219.57	2.38923
$123$	−1700.15	−1.24632
$124$	−3739.24	−2.70801
$125$	−1514.78	−1.08389
$126$	−3486.15	−2.46485
$127$	−334.191	−0.233501	−0.116751	−	0.993161i	$-0.537248\pi$
$127$	−334.191	−0.233501	−0.116751	+	0.993161i	$0.537248\pi$
$128$	−1818.09	−1.25545
$129$	−1765.89	−1.20526
$130$	−1017.81	−0.686673
$131$	−697.659	−0.465304	−0.232652	−	0.972560i	$-0.574740\pi$
$131$	−697.659	−0.465304	−0.232652	+	0.972560i	$0.574740\pi$
$132$	1586.55	1.04615
$133$	1585.02	1.03337
$134$	340.295	0.219381
$135$	−2878.65	−1.83522
$136$	0	0
$137$	2065.04	1.28780	0.643898	−	0.765111i	$-0.277316\pi$
$137$	2065.04	1.28780	0.643898	+	0.765111i	$0.277316\pi$
$138$	−96.9601	−0.0598101
$139$	−1815.36	−1.10775	−0.553873	−	0.832601i	$-0.686851\pi$
$139$	−1815.36	−1.10775	−0.553873	+	0.832601i	$0.686851\pi$
$140$	−1262.76	−0.762307
$141$	−2229.68	−1.33172
$142$	4085.97	2.41470
$143$	387.055	0.226344
$144$	−1418.36	−0.820808
$145$	188.156	0.107762
$146$	−3631.31	−2.05842
$147$	1728.76	0.969973
$148$	−846.784	−0.470305
$149$	860.952	0.473368	0.236684	−	0.971587i	$-0.423939\pi$
$149$	860.952	0.473368	0.236684	+	0.971587i	$0.423939\pi$
$150$	2111.49	1.14935
$151$	−1008.79	−0.543668	−0.271834	−	0.962344i	$-0.587630\pi$
$151$	−1008.79	−0.543668	−0.271834	+	0.962344i	$0.587630\pi$
$152$	−1975.72	−1.05429
$153$	0	0
$154$	812.382	0.425088
$155$	−2790.37	−1.44599
$156$	2913.82	1.49546
$157$	2083.02	1.05887	0.529436	−	0.848350i	$-0.322404\pi$
$157$	2083.02	1.05887	0.529436	+	0.848350i	$0.322404\pi$
$158$	−225.617	−0.113602
$159$	−1896.04	−0.945697
$160$	−1957.95	−0.967433
$161$	−29.3473	−0.0143658
$162$	6501.75	3.15325
$163$	2555.18	1.22784	0.613918	−	0.789370i	$-0.289592\pi$
$163$	2555.18	1.22784	0.613918	+	0.789370i	$0.289592\pi$
$164$	2080.77	0.990735
$165$	1183.95	0.558606
$166$	5233.97	2.44720
$167$	−2473.04	−1.14592	−0.572962	−	0.819582i	$-0.694206\pi$
$167$	−2473.04	−1.14592	−0.572962	+	0.819582i	$0.694206\pi$
$168$	1885.31	0.865802
$169$	−1486.14	−0.676442
$170$	0	0
$171$	−7804.87	−3.49037
$172$	2161.22	0.958089
$173$	−1895.93	−0.833206	−0.416603	−	0.909089i	$-0.636779\pi$
$173$	−1895.93	−0.833206	−0.416603	+	0.909089i	$0.636779\pi$
$174$	−911.271	−0.397030
$175$	639.094	0.276063
$176$	330.521	0.141557
$177$	6786.81	2.88208
$178$	−384.224	−0.161791
$179$	−2662.80	−1.11188	−0.555940	−	0.831222i	$-0.687642\pi$
$179$	−2662.80	−1.11188	−0.555940	+	0.831222i	$0.687642\pi$
$180$	6218.03	2.57480
$181$	−1410.66	−0.579303	−0.289651	−	0.957132i	$-0.593539\pi$
$181$	−1410.66	−0.579303	−0.289651	+	0.957132i	$0.593539\pi$
$182$	1492.00	0.607663
$183$	−6878.20	−2.77842
$184$	36.5813	0.0146566
$185$	−631.904	−0.251127
$186$	13514.2	5.32747
$187$	0	0
$188$	2728.84	1.05862
$189$	4219.81	1.62405
$190$	−4782.69	−1.82617
$191$	4025.80	1.52511	0.762557	−	0.646921i	$-0.223944\pi$
$191$	4025.80	1.52511	0.762557	+	0.646921i	$0.223944\pi$
$192$	7761.47	2.91737
$193$	−3819.08	−1.42437	−0.712186	−	0.701991i	$-0.752295\pi$
$193$	−3819.08	−1.42437	−0.712186	+	0.701991i	$0.752295\pi$
$194$	−3354.81	−1.24155
$195$	2174.41	0.798527
$196$	−2115.78	−0.771057
$197$	−657.014	−0.237616	−0.118808	−	0.992917i	$-0.537907\pi$
$197$	−657.014	−0.237616	−0.118808	+	0.992917i	$0.537907\pi$
$198$	−4000.28	−1.43580
$199$	−3078.87	−1.09676	−0.548379	−	0.836230i	$-0.684755\pi$
$199$	−3078.87	−1.09676	−0.548379	+	0.836230i	$0.684755\pi$
$200$	−796.627	−0.281650
$201$	−726.997	−0.255116
$202$	4386.91	1.52803
$203$	−275.818	−0.0953628
$204$	0	0
$205$	1552.75	0.529019
$206$	−2638.30	−0.892325
$207$	144.511	0.0485226
$208$	607.028	0.202355
$209$	1818.78	0.601949
$210$	4563.83	1.49969
$211$	−1405.99	−0.458732	−0.229366	−	0.973340i	$-0.573665\pi$
$211$	−1405.99	−0.458732	−0.229366	+	0.973340i	$0.573665\pi$
$212$	2320.50	0.751759
$213$	−8729.14	−2.80803
$214$	3476.70	1.11057
$215$	1612.79	0.511587
$216$	−5259.98	−1.65693
$217$	4090.40	1.27961
$218$	2167.10	0.673277
$219$	7757.83	2.39372
$220$	−1448.99	−0.444051
$221$	0	0
$222$	3060.41	0.925232
$223$	−3601.84	−1.08160	−0.540800	−	0.841151i	$-0.681879\pi$
$223$	−3601.84	−1.08160	−0.540800	+	0.841151i	$0.681879\pi$
$224$	2870.16	0.856118
$225$	−3146.99	−0.932442
$226$	−720.886	−0.212180
$227$	3977.19	1.16289	0.581443	−	0.813587i	$-0.302488\pi$
$227$	3977.19	1.16289	0.581443	+	0.813587i	$0.302488\pi$
$228$	13692.1	3.97711
$229$	−3018.77	−0.871117	−0.435559	−	0.900160i	$-0.643449\pi$
$229$	−3018.77	−0.871117	−0.435559	+	0.900160i	$0.643449\pi$
$230$	88.5536	0.0253872
$231$	−1735.55	−0.494332
$232$	343.806	0.0972930
$233$	1131.49	0.318138	0.159069	−	0.987267i	$-0.449151\pi$
$233$	1131.49	0.318138	0.159069	+	0.987267i	$0.449151\pi$
$234$	−7346.84	−2.05247
$235$	2036.37	0.565267
$236$	−8306.17	−2.29104
$237$	482.002	0.132107
$238$	0	0
$239$	2866.47	0.775802	0.387901	−	0.921701i	$-0.373200\pi$
$239$	2866.47	0.775802	0.387901	+	0.921701i	$0.373200\pi$
$240$	1856.81	0.499403
$241$	−718.184	−0.191960	−0.0959799	−	0.995383i	$-0.530598\pi$
$241$	−718.184	−0.191960	−0.0959799	+	0.995383i	$0.530598\pi$
$242$	−4955.17	−1.31624
$243$	−4884.37	−1.28944
$244$	8418.01	2.20864
$245$	−1578.88	−0.411718
$246$	−7520.22	−1.94907
$247$	3340.33	0.860486
$248$	−5098.67	−1.30551
$249$	−11181.7	−2.84583
$250$	−6700.24	−1.69504
$251$	−6234.39	−1.56777	−0.783887	−	0.620903i	$-0.786766\pi$
$251$	−6234.39	−1.56777	−0.783887	+	0.620903i	$0.786766\pi$
$252$	−9115.02	−2.27854
$253$	−33.6754	−0.00836821
$254$	−1478.21	−0.365163
$255$	0	0
$256$	−1471.14	−0.359164
$257$	3681.61	0.893590	0.446795	−	0.894636i	$-0.352565\pi$
$257$	3681.61	0.893590	0.446795	+	0.894636i	$0.352565\pi$
$258$	−7810.99	−1.88485
$259$	926.309	0.222232
$260$	−2661.19	−0.634770
$261$	1358.17	0.322102
$262$	−3085.93	−0.727669
$263$	7086.65	1.66153	0.830764	−	0.556625i	$-0.187904\pi$
$263$	7086.65	1.66153	0.830764	+	0.556625i	$0.187904\pi$
$264$	2163.35	0.504337
$265$	1731.65	0.401414
$266$	7010.95	1.61605
$267$	820.843	0.188145
$268$	889.749	0.202799
$269$	584.965	0.132587	0.0662935	−	0.997800i	$-0.478883\pi$
$269$	584.965	0.132587	0.0662935	+	0.997800i	$0.478883\pi$
$270$	−12733.0	−2.87002
$271$	−255.939	−0.0573697	−0.0286849	−	0.999589i	$-0.509132\pi$
$271$	−255.939	−0.0573697	−0.0286849	+	0.999589i	$0.509132\pi$
$272$	0	0
$273$	−3187.47	−0.706647
$274$	9134.19	2.01393
$275$	733.347	0.160809
$276$	−253.515	−0.0552892
$277$	−5483.90	−1.18951	−0.594757	−	0.803905i	$-0.702752\pi$
$277$	−5483.90	−1.18951	−0.594757	+	0.803905i	$0.702752\pi$
$278$	−8029.79	−1.73236
$279$	−20141.7	−4.32206
$280$	−1721.85	−0.367501
$281$	3612.64	0.766946	0.383473	−	0.923552i	$-0.374728\pi$
$281$	3612.64	0.766946	0.383473	+	0.923552i	$0.374728\pi$
$282$	−9862.45	−2.08262
$283$	3778.61	0.793693	0.396846	−	0.917885i	$-0.370105\pi$
$283$	3778.61	0.793693	0.396846	+	0.917885i	$0.370105\pi$
$284$	10683.3	2.23218
$285$	10217.6	2.12364
$286$	1712.04	0.353969
$287$	−2276.18	−0.468149
$288$	−14133.1	−2.89166
$289$	0	0
$290$	832.263	0.168525
$291$	7167.11	1.44379
$292$	−9494.57	−1.90283
$293$	8361.99	1.66728	0.833639	−	0.552309i	$-0.186253\pi$
$293$	8361.99	1.66728	0.833639	+	0.552309i	$0.186253\pi$
$294$	7646.77	1.51690
$295$	−6198.39	−1.22334
$296$	−1154.64	−0.226730
$297$	4842.15	0.946027
$298$	3808.21	0.740281
$299$	−61.8477	−0.0119624
$300$	5520.77	1.06247
$301$	−2364.19	−0.452723
$302$	−4462.12	−0.850219
$303$	−9372.06	−1.77693
$304$	2852.44	0.538153
$305$	6281.86	1.17934
$306$	0	0
$307$	−4070.96	−0.756814	−0.378407	−	0.925639i	$-0.623528\pi$
$307$	−4070.96	−0.756814	−0.378407	+	0.925639i	$0.623528\pi$
$308$	2124.08	0.392957
$309$	5636.38	1.03768
$310$	−12342.5	−2.26132
$311$	−2434.77	−0.443933	−0.221967	−	0.975054i	$-0.571248\pi$
$311$	−2434.77	−0.443933	−0.221967	+	0.975054i	$0.571248\pi$
$312$	3973.17	0.720950
$313$	4352.54	0.786006	0.393003	−	0.919537i	$-0.371436\pi$
$313$	4352.54	0.786006	0.393003	+	0.919537i	$0.371436\pi$
$314$	9213.72	1.65593
$315$	−6801.99	−1.21666
$316$	−589.907	−0.105015
$317$	−3770.58	−0.668065	−0.334033	−	0.942561i	$-0.608410\pi$
$317$	−3770.58	−0.668065	−0.334033	+	0.942561i	$0.608410\pi$
$318$	−8386.67	−1.47893
$319$	−316.496	−0.0555497
$320$	−7088.55	−1.23832
$321$	−7427.52	−1.29148
$322$	−129.811	−0.0224661
$323$	0	0
$324$	16999.7	2.91490
$325$	1346.85	0.229876
$326$	11302.2	1.92016
$327$	−4629.72	−0.782948
$328$	2837.25	0.477624
$329$	−2985.11	−0.500227
$330$	5236.89	0.873580
$331$	−9325.54	−1.54857	−0.774287	−	0.632835i	$-0.781891\pi$
$331$	−9325.54	−1.54857	−0.774287	+	0.632835i	$0.781891\pi$
$332$	13684.9	2.26222
$333$	−4561.28	−0.750620
$334$	−10938.9	−1.79206
$335$	663.966	0.108288
$336$	−2721.90	−0.441941
$337$	−1183.38	−0.191284	−0.0956421	−	0.995416i	$-0.530490\pi$
$337$	−1183.38	−0.191284	−0.0956421	+	0.995416i	$0.530490\pi$
$338$	−6573.59	−1.05786
$339$	1540.08	0.246742
$340$	0	0
$341$	4693.65	0.745383
$342$	−34522.9	−5.45844
$343$	6653.89	1.04745
$344$	2946.95	0.461886
$345$	−189.183	−0.0295225
$346$	−8386.17	−1.30302
$347$	4879.95	0.754956	0.377478	−	0.926019i	$-0.376791\pi$
$347$	4879.95	0.754956	0.377478	+	0.926019i	$0.376791\pi$
$348$	−2382.64	−0.367020
$349$	1965.33	0.301438	0.150719	−	0.988577i	$-0.451841\pi$
$349$	1965.33	0.301438	0.150719	+	0.988577i	$0.451841\pi$
$350$	2826.88	0.431723
$351$	8892.99	1.35234
$352$	3293.44	0.498696
$353$	−7433.23	−1.12077	−0.560384	−	0.828233i	$-0.689346\pi$
$353$	−7433.23	−1.12077	−0.560384	+	0.828233i	$0.689346\pi$
$354$	30019.8	4.50716
$355$	7972.32	1.19191
$356$	−1004.60	−0.149562
$357$	0	0
$358$	−11778.2	−1.73882
$359$	−5316.51	−0.781601	−0.390800	−	0.920475i	$-0.627802\pi$
$359$	−5316.51	−0.781601	−0.390800	+	0.920475i	$0.627802\pi$
$360$	8478.64	1.24129
$361$	8837.27	1.28842
$362$	−6239.73	−0.905947
$363$	10586.1	1.53065
$364$	3901.05	0.561732
$365$	−7085.22	−1.01605
$366$	−30424.0	−4.34506
$367$	−413.067	−0.0587518	−0.0293759	−	0.999568i	$-0.509352\pi$
$367$	−413.067	−0.0587518	−0.0293759	+	0.999568i	$0.509352\pi$
$368$	−52.8141	−0.00748132
$369$	11208.2	1.58124
$370$	−2795.07	−0.392727
$371$	−2538.43	−0.355226
$372$	35334.7	4.92478
$373$	5546.88	0.769990	0.384995	−	0.922919i	$-0.374203\pi$
$373$	5546.88	0.769990	0.384995	+	0.922919i	$0.374203\pi$
$374$	0	0
$375$	14314.2	1.97115
$376$	3720.93	0.510351
$377$	−581.270	−0.0794083
$378$	18665.3	2.53979
$379$	13601.4	1.84342	0.921708	−	0.387883i	$-0.126794\pi$
$379$	13601.4	1.84342	0.921708	+	0.387883i	$0.126794\pi$
$380$	−12505.0	−1.68814
$381$	3158.01	0.424645
$382$	17807.2	2.38506
$383$	2571.35	0.343055	0.171527	−	0.985179i	$-0.445130\pi$
$383$	2571.35	0.343055	0.171527	+	0.985179i	$0.445130\pi$
$384$	17180.5	2.28317
$385$	1585.07	0.209826
$386$	−16892.8	−2.22751
$387$	11641.6	1.52914
$388$	−8771.60	−1.14771
$389$	−9976.83	−1.30037	−0.650187	−	0.759775i	$-0.725309\pi$
$389$	−9976.83	−1.30037	−0.650187	+	0.759775i	$0.725309\pi$
$390$	9617.98	1.24878
$391$	0	0
$392$	−2884.99	−0.371719
$393$	6592.68	0.846200
$394$	−2906.14	−0.371597
$395$	−440.212	−0.0560747
$396$	−10459.3	−1.32727
$397$	3477.77	0.439658	0.219829	−	0.975538i	$-0.429450\pi$
$397$	3477.77	0.439658	0.219829	+	0.975538i	$0.429450\pi$
$398$	−13618.6	−1.71517
$399$	−14978.0	−1.87929
$400$	1150.13	0.143766
$401$	10435.4	1.29955	0.649773	−	0.760128i	$-0.274864\pi$
$401$	10435.4	1.29955	0.649773	+	0.760128i	$0.274864\pi$
$402$	−3215.69	−0.398966
$403$	8620.27	1.06552
$404$	11470.2	1.41253
$405$	12685.9	1.55646
$406$	−1220.02	−0.149134
$407$	1062.92	0.129452
$408$	0	0
$409$	−14641.1	−1.77006	−0.885029	−	0.465536i	$-0.845861\pi$
$409$	−14641.1	−1.77006	−0.885029	+	0.465536i	$0.845861\pi$
$410$	6868.22	0.827310
$411$	−19514.0	−2.34198
$412$	−6898.19	−0.824877
$413$	9086.24	1.08258
$414$	639.207	0.0758824
$415$	10212.2	1.20795
$416$	6048.67	0.712886
$417$	17154.6	2.01454
$418$	8044.92	0.941363
$419$	−331.177	−0.0386134	−0.0193067	−	0.999814i	$-0.506146\pi$
$419$	−331.177	−0.0386134	−0.0193067	+	0.999814i	$0.506146\pi$
$420$	11932.7	1.38633
$421$	601.612	0.0696455	0.0348227	−	0.999394i	$-0.488913\pi$
$421$	601.612	0.0696455	0.0348227	+	0.999394i	$0.488913\pi$
$422$	−6219.06	−0.717391
$423$	14699.1	1.68959
$424$	3164.14	0.362416
$425$	0	0
$426$	−38611.2	−4.39136
$427$	−9208.58	−1.04364
$428$	9090.31	1.02663
$429$	−3657.56	−0.411628
$430$	7133.77	0.800049
$431$	−10219.6	−1.14214	−0.571068	−	0.820903i	$-0.693471\pi$
$431$	−10219.6	−1.14214	−0.571068	+	0.820903i	$0.693471\pi$
$432$	7594.07	0.845763
$433$	−1098.15	−0.121879	−0.0609396	−	0.998141i	$-0.519410\pi$
$433$	−1098.15	−0.121879	−0.0609396	+	0.998141i	$0.519410\pi$
$434$	18092.9	2.00112
$435$	−1778.02	−0.195976
$436$	5666.17	0.622386
$437$	−290.623	−0.0318133
$438$	34314.9	3.74344
$439$	1804.38	0.196170	0.0980850	−	0.995178i	$-0.468728\pi$
$439$	1804.38	0.196170	0.0980850	+	0.995178i	$0.468728\pi$
$440$	−1975.79	−0.214073
$441$	−11396.8	−1.23063
$442$	0	0
$443$	−8570.23	−0.919151	−0.459575	−	0.888139i	$-0.651998\pi$
$443$	−8570.23	−0.919151	−0.459575	+	0.888139i	$0.651998\pi$
$444$	8001.86	0.855297
$445$	−749.676	−0.0798608
$446$	−15931.9	−1.69147
$447$	−8135.74	−0.860867
$448$	10391.1	1.09583
$449$	−4142.84	−0.435440	−0.217720	−	0.976011i	$-0.569862\pi$
$449$	−4142.84	−0.435440	−0.217720	+	0.976011i	$0.569862\pi$
$450$	−13919.9	−1.45821
$451$	−2611.87	−0.272701
$452$	−1884.85	−0.196142
$453$	9532.73	0.988713
$454$	17592.1	1.81859
$455$	2911.12	0.299946
$456$	18670.0	1.91733
$457$	−10190.2	−1.04306	−0.521530	−	0.853233i	$-0.674639\pi$
$457$	−10190.2	−1.04306	−0.521530	+	0.853233i	$0.674639\pi$
$458$	−13352.8	−1.36230
$459$	0	0
$460$	231.535	0.0234682
$461$	−10235.7	−1.03411	−0.517055	−	0.855952i	$-0.672972\pi$
$461$	−10235.7	−1.03411	−0.517055	+	0.855952i	$0.672972\pi$
$462$	−7676.77	−0.773064
$463$	−4240.64	−0.425658	−0.212829	−	0.977090i	$-0.568268\pi$
$463$	−4240.64	−0.425658	−0.212829	+	0.977090i	$0.568268\pi$
$464$	−496.369	−0.0496624
$465$	26368.2	2.62967
$466$	5004.86	0.497523
$467$	59.5197	0.00589774	0.00294887	−	0.999996i	$-0.499061\pi$
$467$	59.5197	0.00589774	0.00294887	+	0.999996i	$0.499061\pi$
$468$	−19209.3	−1.89733
$469$	−973.309	−0.0958278
$470$	9007.37	0.883998
$471$	−19683.9	−1.92566
$472$	−11325.9	−1.10449
$473$	−2712.85	−0.263715
$474$	2132.02	0.206597
$475$	6328.87	0.611344
$476$	0	0
$477$	12499.6	1.19983
$478$	12679.2	1.21324
$479$	−14778.8	−1.40973	−0.704865	−	0.709341i	$-0.748993\pi$
$479$	−14778.8	−1.40973	−0.704865	+	0.709341i	$0.748993\pi$
$480$	18502.0	1.75937
$481$	1952.14	0.185052
$482$	−3176.71	−0.300198
$483$	277.324	0.0261256
$484$	−12956.0	−1.21675
$485$	−6545.72	−0.612837
$486$	−21604.8	−2.01649
$487$	−3920.93	−0.364834	−0.182417	−	0.983221i	$-0.558392\pi$
$487$	−3920.93	−0.364834	−0.182417	+	0.983221i	$0.558392\pi$
$488$	11478.5	1.06476
$489$	−24145.7	−2.23294
$490$	−6983.79	−0.643868
$491$	1593.61	0.146473	0.0732367	−	0.997315i	$-0.476667\pi$
$491$	1593.61	0.146473	0.0732367	+	0.997315i	$0.476667\pi$
$492$	−19662.6	−1.80175
$493$	0	0
$494$	14775.1	1.34568
$495$	−7805.13	−0.708717
$496$	7361.18	0.666385
$497$	−11686.6	−1.05476
$498$	−49459.5	−4.45047
$499$	−297.390	−0.0266794	−0.0133397	−	0.999911i	$-0.504246\pi$
$499$	−297.390	−0.0266794	−0.0133397	+	0.999911i	$0.504246\pi$
$500$	−17518.7	−1.56692
$501$	23369.5	2.08398
$502$	−27576.3	−2.45178
$503$	−15738.5	−1.39512	−0.697561	−	0.716525i	$-0.745732\pi$
$503$	−15738.5	−1.39512	−0.697561	+	0.716525i	$0.745732\pi$
$504$	−12428.9	−1.09846
$505$	8559.50	0.754243
$506$	−148.955	−0.0130867
$507$	14043.6	1.23018
$508$	−3864.99	−0.337561
$509$	−19131.6	−1.66599	−0.832997	−	0.553277i	$-0.813377\pi$
$509$	−19131.6	−1.66599	−0.832997	+	0.553277i	$0.813377\pi$
$510$	0	0
$511$	10386.2	0.899139
$512$	8037.53	0.693773
$513$	41788.3	3.59649
$514$	16284.7	1.39745
$515$	−5147.70	−0.440456
$516$	−20422.9	−1.74238
$517$	−3425.35	−0.291386
$518$	4097.30	0.347539
$519$	17916.0	1.51527
$520$	−3628.69	−0.306017
$521$	−16429.7	−1.38157	−0.690787	−	0.723058i	$-0.742736\pi$
$521$	−16429.7	−1.38157	−0.690787	+	0.723058i	$0.742736\pi$
$522$	6007.53	0.503722
$523$	3606.66	0.301546	0.150773	−	0.988568i	$-0.451824\pi$
$523$	3606.66	0.301546	0.150773	+	0.988568i	$0.451824\pi$
$524$	−8068.58	−0.672667
$525$	−6039.25	−0.502047
$526$	31346.1	2.59839
$527$	0	0
$528$	−3123.33	−0.257434
$529$	−12161.6	−0.999558
$530$	7659.55	0.627754
$531$	−44741.9	−3.65656
$532$	18331.1	1.49390
$533$	−4796.90	−0.389826
$534$	3630.80	0.294232
$535$	6783.55	0.548184
$536$	1213.22	0.0977674
$537$	25162.6	2.02206
$538$	2587.45	0.207347
$539$	2655.82	0.212234
$540$	−33292.2	−2.65309
$541$	24648.2	1.95880	0.979400	−	0.201931i	$-0.0647217\pi$
$541$	24648.2	1.95880	0.979400	+	0.201931i	$0.0647217\pi$
$542$	−1132.08	−0.0897181
$543$	13330.4	1.05352
$544$	0	0
$545$	4228.32	0.332333
$546$	−14099.0	−1.10509
$547$	6616.10	0.517156	0.258578	−	0.965990i	$-0.416746\pi$
$547$	6616.10	0.517156	0.258578	+	0.965990i	$0.416746\pi$
$548$	23882.6	1.86170
$549$	45344.4	3.52505
$550$	3243.78	0.251482
$551$	−2731.40	−0.211182
$552$	−345.683	−0.0266544
$553$	645.308	0.0496226
$554$	−24256.7	−1.86023
$555$	5971.31	0.456699
$556$	−20995.0	−1.60141
$557$	6856.99	0.521616	0.260808	−	0.965391i	$-0.416011\pi$
$557$	6856.99	0.521616	0.260808	+	0.965391i	$0.416011\pi$
$558$	−89092.1	−6.75909
$559$	−4982.38	−0.376980
$560$	2485.91	0.187588
$561$	0	0
$562$	15979.6	1.19939
$563$	20537.2	1.53737	0.768684	−	0.639629i	$-0.220912\pi$
$563$	20537.2	1.53737	0.768684	+	0.639629i	$0.220912\pi$
$564$	−25786.7	−1.92521
$565$	−1406.55	−0.104733
$566$	16713.8	1.24122
$567$	−18596.2	−1.37737
$568$	14567.3	1.07611
$569$	−12241.2	−0.901891	−0.450945	−	0.892552i	$-0.648913\pi$
$569$	−12241.2	−0.901891	−0.450945	+	0.892552i	$0.648913\pi$
$570$	45195.0	3.32107
$571$	−5037.80	−0.369221	−0.184611	−	0.982812i	$-0.559102\pi$
$571$	−5037.80	−0.369221	−0.184611	+	0.982812i	$0.559102\pi$
$572$	4476.37	0.327214
$573$	−38042.7	−2.77357
$574$	−10068.1	−0.732118
$575$	−117.182	−0.00849882
$576$	−51167.3	−3.70134
$577$	−6963.10	−0.502388	−0.251194	−	0.967937i	$-0.580823\pi$
$577$	−6963.10	−0.502388	−0.251194	+	0.967937i	$0.580823\pi$
$578$	0	0
$579$	36089.2	2.59036
$580$	2176.07	0.155787
$581$	−14970.1	−1.06896
$582$	31702.0	2.25789
$583$	−2912.80	−0.206922
$584$	−12946.4	−0.917338
$585$	−14334.8	−1.01311
$586$	36987.2	2.60739
$587$	4148.82	0.291721	0.145860	−	0.989305i	$-0.453405\pi$
$587$	4148.82	0.291721	0.145860	+	0.989305i	$0.453405\pi$
$588$	19993.5	1.40224
$589$	40506.8	2.83371
$590$	−27417.1	−1.91313
$591$	6208.59	0.432127
$592$	1667.01	0.115732
$593$	11579.9	0.801903	0.400951	−	0.916099i	$-0.368680\pi$
$593$	11579.9	0.801903	0.400951	+	0.916099i	$0.368680\pi$
$594$	21418.1	1.47945
$595$	0	0
$596$	9957.08	0.684326
$597$	29094.4	1.99456
$598$	−273.568	−0.0187074
$599$	−4270.75	−0.291316	−0.145658	−	0.989335i	$-0.546530\pi$
$599$	−4270.75	−0.291316	−0.145658	+	0.989335i	$0.546530\pi$
$600$	7527.90	0.512208
$601$	−8584.45	−0.582640	−0.291320	−	0.956626i	$-0.594094\pi$
$601$	−8584.45	−0.582640	−0.291320	+	0.956626i	$0.594094\pi$
$602$	−10457.4	−0.707994
$603$	4792.71	0.323672
$604$	−11666.8	−0.785954
$605$	−9668.25	−0.649703
$606$	−41455.0	−2.77887
$607$	27576.2	1.84396	0.921979	−	0.387241i	$-0.126572\pi$
$607$	27576.2	1.84396	0.921979	+	0.387241i	$0.126572\pi$
$608$	28422.8	1.89588
$609$	2606.40	0.173427
$610$	27786.3	1.84432
$611$	−6290.93	−0.416537
$612$	0	0
$613$	−4036.96	−0.265989	−0.132995	−	0.991117i	$-0.542459\pi$
$613$	−4036.96	−0.265989	−0.132995	+	0.991117i	$0.542459\pi$
$614$	−18006.9	−1.18355
$615$	−14673.0	−0.962072
$616$	2896.31	0.189441
$617$	−9008.21	−0.587775	−0.293887	−	0.955840i	$-0.594949\pi$
$617$	−9008.21	−0.587775	−0.293887	+	0.955840i	$0.594949\pi$
$618$	24931.1	1.62278
$619$	5131.94	0.333231	0.166616	−	0.986022i	$-0.446716\pi$
$619$	5131.94	0.333231	0.166616	+	0.986022i	$0.446716\pi$
$620$	−32271.2	−2.09039
$621$	−773.729	−0.0499979
$622$	−10769.6	−0.694249
$623$	1098.95	0.0706718
$624$	−5736.24	−0.368002
$625$	−6758.66	−0.432554
$626$	19252.4	1.22920
$627$	−17186.9	−1.09470
$628$	24090.5	1.53076
$629$	0	0
$630$	−30086.9	−1.90269
$631$	−14562.4	−0.918734	−0.459367	−	0.888247i	$-0.651924\pi$
$631$	−14562.4	−0.918734	−0.459367	+	0.888247i	$0.651924\pi$
$632$	−804.373	−0.0506270
$633$	13286.2	0.834248
$634$	−16678.2	−1.04476
$635$	−2884.21	−0.180246
$636$	−21928.1	−1.36715
$637$	4877.62	0.303388
$638$	−1399.94	−0.0868718
$639$	57546.7	3.56262
$640$	−15690.9	−0.969121
$641$	−19333.1	−1.19128	−0.595640	−	0.803252i	$-0.703101\pi$
$641$	−19333.1	−1.19128	−0.595640	+	0.803252i	$0.703101\pi$
$642$	−32853.8	−2.01968
$643$	−19912.0	−1.22123	−0.610615	−	0.791928i	$-0.709078\pi$
$643$	−19912.0	−1.22123	−0.610615	+	0.791928i	$0.709078\pi$
$644$	−339.408	−0.0207679
$645$	−15240.4	−0.930371
$646$	0	0
$647$	7742.24	0.470447	0.235223	−	0.971941i	$-0.424418\pi$
$647$	7742.24	0.470447	0.235223	+	0.971941i	$0.424418\pi$
$648$	23180.1	1.40525
$649$	10426.3	0.630611
$650$	5957.46	0.359494
$651$	−38653.1	−2.32709
$652$	29551.2	1.77502
$653$	10554.3	0.632498	0.316249	−	0.948676i	$-0.397577\pi$
$653$	10554.3	0.632498	0.316249	+	0.948676i	$0.397577\pi$
$654$	−20478.4	−1.22442
$655$	−6021.09	−0.359181
$656$	−4096.26	−0.243799
$657$	−51143.3	−3.03697
$658$	−13203.9	−0.782283
$659$	−21754.7	−1.28595	−0.642977	−	0.765885i	$-0.722301\pi$
$659$	−21754.7	−1.28595	−0.642977	+	0.765885i	$0.722301\pi$
$660$	13692.6	0.807549
$661$	24822.0	1.46061	0.730306	−	0.683120i	$-0.239377\pi$
$661$	24822.0	1.46061	0.730306	+	0.683120i	$0.239377\pi$
$662$	−41249.2	−2.42175
$663$	0	0
$664$	18660.2	1.09060
$665$	13679.4	0.797690
$666$	−20175.7	−1.17386
$667$	50.5730	0.00293582
$668$	−28601.2	−1.65661
$669$	34036.3	1.96700
$670$	2936.89	0.169346
$671$	−10566.7	−0.607930
$672$	−27122.1	−1.55693
$673$	−23576.4	−1.35038	−0.675189	−	0.737645i	$-0.735938\pi$
$673$	−23576.4	−1.35038	−0.675189	+	0.737645i	$0.735938\pi$
$674$	−5234.39	−0.299141
$675$	16849.4	0.960791
$676$	−17187.6	−0.977899
$677$	5217.93	0.296221	0.148110	−	0.988971i	$-0.452681\pi$
$677$	5217.93	0.296221	0.148110	+	0.988971i	$0.452681\pi$
$678$	6812.16	0.385869
$679$	9595.38	0.542322
$680$	0	0
$681$	−37583.3	−2.11482
$682$	20761.2	1.16567
$683$	−13939.9	−0.780958	−0.390479	−	0.920612i	$-0.627691\pi$
$683$	−13939.9	−0.780958	−0.390479	+	0.920612i	$0.627691\pi$
$684$	−90264.9	−5.04586
$685$	17822.1	0.994086
$686$	29431.9	1.63807
$687$	28526.5	1.58421
$688$	−4254.64	−0.235766
$689$	−5349.59	−0.295795
$690$	−836.806	−0.0461691
$691$	14140.0	0.778455	0.389228	−	0.921142i	$-0.372742\pi$
$691$	14140.0	0.778455	0.389228	+	0.921142i	$0.372742\pi$
$692$	−21926.8	−1.20452
$693$	11441.6	0.627170
$694$	21585.3	1.18064
$695$	−15667.3	−0.855100
$696$	−3248.87	−0.176937
$697$	0	0
$698$	8693.18	0.471406
$699$	−10692.2	−0.578565
$700$	7391.25	0.399090
$701$	23850.7	1.28506	0.642532	−	0.766259i	$-0.277884\pi$
$701$	23850.7	1.28506	0.642532	+	0.766259i	$0.277884\pi$
$702$	39336.0	2.11487
$703$	9173.13	0.492135
$704$	11923.6	0.638334
$705$	−19243.1	−1.02799
$706$	−32879.1	−1.75272
$707$	−12547.4	−0.667458
$708$	78490.9	4.16648
$709$	28474.5	1.50830	0.754149	−	0.656703i	$-0.228049\pi$
$709$	28474.5	1.50830	0.754149	+	0.656703i	$0.228049\pi$
$710$	35263.6	1.86397
$711$	−3177.59	−0.167607
$712$	−1369.84	−0.0721023
$713$	−750.001	−0.0393938
$714$	0	0
$715$	3340.44	0.174721
$716$	−30795.8	−1.60739
$717$	−27087.4	−1.41087
$718$	−23516.3	−1.22231
$719$	−5053.95	−0.262143	−0.131071	−	0.991373i	$-0.541842\pi$
$719$	−5053.95	−0.262143	−0.131071	+	0.991373i	$0.541842\pi$
$720$	−12241.0	−0.633604
$721$	7546.02	0.389776
$722$	39089.5	2.01490
$723$	6786.63	0.349098
$724$	−16314.6	−0.837470
$725$	−1101.32	−0.0564167
$726$	46824.9	2.39371
$727$	20929.6	1.06773	0.533863	−	0.845571i	$-0.320740\pi$
$727$	20929.6	1.06773	0.533863	+	0.845571i	$0.320740\pi$
$728$	5319.31	0.270806
$729$	6468.60	0.328639
$730$	−31339.8	−1.58895
$731$	0	0
$732$	−79547.8	−4.01663
$733$	−20140.2	−1.01487	−0.507433	−	0.861691i	$-0.669406\pi$
$733$	−20140.2	−1.01487	−0.507433	+	0.861691i	$0.669406\pi$
$734$	−1827.10	−0.0918795
$735$	14919.9	0.748749
$736$	−526.261	−0.0263563
$737$	−1116.85	−0.0558205
$738$	49576.9	2.47283
$739$	5481.57	0.272859	0.136430	−	0.990650i	$-0.456437\pi$
$739$	5481.57	0.272859	0.136430	+	0.990650i	$0.456437\pi$
$740$	−7308.10	−0.363042
$741$	−31565.2	−1.56488
$742$	−11228.1	−0.555523
$743$	32587.9	1.60906	0.804531	−	0.593911i	$-0.202417\pi$
$743$	32587.9	1.60906	0.804531	+	0.593911i	$0.202417\pi$
$744$	48180.9	2.37419
$745$	7430.37	0.365406
$746$	24535.3	1.20415
$747$	73715.1	3.61057
$748$	0	0
$749$	−9944.02	−0.485109
$750$	63315.4	3.08260
$751$	−3824.32	−0.185821	−0.0929104	−	0.995674i	$-0.529617\pi$
$751$	−3824.32	−0.185821	−0.0929104	+	0.995674i	$0.529617\pi$
$752$	−5372.07	−0.260504
$753$	58913.2	2.85115
$754$	−2571.11	−0.124183
$755$	−8706.24	−0.419672
$756$	48803.0	2.34782
$757$	−16870.1	−0.809980	−0.404990	−	0.914321i	$-0.632725\pi$
$757$	−16870.1	−0.809980	−0.404990	+	0.914321i	$0.632725\pi$
$758$	60162.3	2.88284
$759$	318.223	0.0152184
$760$	−17051.3	−0.813836
$761$	−19951.4	−0.950378	−0.475189	−	0.879884i	$-0.657620\pi$
$761$	−19951.4	−0.950378	−0.475189	+	0.879884i	$0.657620\pi$
$762$	13968.7	0.664084
$763$	−6198.30	−0.294094
$764$	46559.2	2.20478
$765$	0	0
$766$	11373.8	0.536489
$767$	19148.7	0.901458
$768$	13901.8	0.653175
$769$	−19560.4	−0.917249	−0.458625	−	0.888630i	$-0.651658\pi$
$769$	−19560.4	−0.917249	−0.458625	+	0.888630i	$0.651658\pi$
$770$	7011.19	0.328137
$771$	−34790.2	−1.62508
$772$	−44168.5	−2.05914
$773$	−29989.8	−1.39542	−0.697710	−	0.716381i	$-0.745797\pi$
$773$	−29989.8	−1.39542	−0.697710	+	0.716381i	$0.745797\pi$
$774$	51493.8	2.39135
$775$	16332.7	0.757016
$776$	−11960.6	−0.553299
$777$	−8753.35	−0.404150
$778$	−44130.1	−2.03360
$779$	−22540.7	−1.03672
$780$	25147.5	1.15439
$781$	−13410.2	−0.614409
$782$	0	0
$783$	−7271.82	−0.331895
$784$	4165.19	0.189741
$785$	17977.3	0.817373
$786$	29161.1	1.32334
$787$	−36288.4	−1.64364	−0.821819	−	0.569749i	$-0.807040\pi$
$787$	−36288.4	−1.64364	−0.821819	+	0.569749i	$0.807040\pi$
$788$	−7598.50	−0.343509
$789$	−66966.8	−3.02165
$790$	−1947.17	−0.0876928
$791$	2061.87	0.0926822
$792$	−14261.8	−0.639864
$793$	−19406.5	−0.869036
$794$	15383.1	0.687563
$795$	−16363.6	−0.730010
$796$	−35607.7	−1.58553
$797$	−29090.7	−1.29291	−0.646453	−	0.762954i	$-0.723748\pi$
$797$	−29090.7	−1.29291	−0.646453	+	0.762954i	$0.723748\pi$
$798$	−66251.5	−2.93894
$799$	0	0
$800$	11460.3	0.506480
$801$	−5411.39	−0.238704
$802$	46158.4	2.03231
$803$	11918.0	0.523757
$804$	−8407.87	−0.368809
$805$	−253.280	−0.0110894
$806$	38129.7	1.66633
$807$	−5527.75	−0.241123
$808$	15640.3	0.680968
$809$	3569.56	0.155129	0.0775644	−	0.996987i	$-0.475286\pi$
$809$	3569.56	0.155129	0.0775644	+	0.996987i	$0.475286\pi$
$810$	56112.8	2.43408
$811$	24700.0	1.06946	0.534732	−	0.845022i	$-0.320413\pi$
$811$	24700.0	1.06946	0.534732	+	0.845022i	$0.320413\pi$
$812$	−3189.90	−0.137861
$813$	2418.55	0.104332
$814$	4701.57	0.202445
$815$	22052.3	0.947801
$816$	0	0
$817$	−23412.3	−1.00256
$818$	−64761.2	−2.76812
$819$	21013.3	0.896539
$820$	17957.9	0.764776
$821$	−6655.21	−0.282909	−0.141455	−	0.989945i	$-0.545178\pi$
$821$	−6655.21	−0.282909	−0.141455	+	0.989945i	$0.545178\pi$
$822$	−86315.5	−3.66253
$823$	4887.46	0.207006	0.103503	−	0.994629i	$-0.466995\pi$
$823$	4887.46	0.207006	0.103503	+	0.994629i	$0.466995\pi$
$824$	−9406.08	−0.397665
$825$	−6929.91	−0.292447
$826$	40190.8	1.69300
$827$	−21935.8	−0.922347	−0.461174	−	0.887310i	$-0.652571\pi$
$827$	−21935.8	−0.922347	−0.461174	+	0.887310i	$0.652571\pi$
$828$	1671.29	0.0701467
$829$	41942.6	1.75721	0.878605	−	0.477550i	$-0.158475\pi$
$829$	41942.6	1.75721	0.878605	+	0.477550i	$0.158475\pi$
$830$	45171.4	1.88906
$831$	51821.3	2.16325
$832$	21898.6	0.912497
$833$	0	0
$834$	75879.2	3.15046
$835$	−21343.3	−0.884571
$836$	21034.5	0.870209
$837$	107842.	4.45347
$838$	−1464.88	−0.0603859
$839$	42161.2	1.73488	0.867441	−	0.497540i	$-0.165763\pi$
$839$	42161.2	1.73488	0.867441	+	0.497540i	$0.165763\pi$
$840$	16271.0	0.668336
$841$	−23913.7	−0.980511
$842$	2661.08	0.108916
$843$	−34138.4	−1.39477
$844$	−16260.6	−0.663166
$845$	−12826.0	−0.522164
$846$	65018.0	2.64227
$847$	14172.7	0.574947
$848$	−4568.22	−0.184992
$849$	−35706.8	−1.44341
$850$	0	0
$851$	−169.844	−0.00684159
$852$	−100954.	−4.05943
$853$	8674.96	0.348212	0.174106	−	0.984727i	$-0.444296\pi$
$853$	8674.96	0.348212	0.174106	+	0.984727i	$0.444296\pi$
$854$	−40731.9	−1.63211
$855$	−67359.3	−2.69431
$856$	12395.2	0.494928
$857$	−26939.7	−1.07380	−0.536898	−	0.843647i	$-0.680404\pi$
$857$	−26939.7	−1.07380	−0.536898	+	0.843647i	$0.680404\pi$
$858$	−16178.3	−0.643728
$859$	3089.68	0.122722	0.0613611	−	0.998116i	$-0.480456\pi$
$859$	3089.68	0.122722	0.0613611	+	0.998116i	$0.480456\pi$
$860$	18652.2	0.739576
$861$	21509.2	0.851374
$862$	−45203.9	−1.78614
$863$	−10012.6	−0.394939	−0.197469	−	0.980309i	$-0.563272\pi$
$863$	−10012.6	−0.394939	−0.197469	+	0.980309i	$0.563272\pi$
$864$	75670.3	2.97958
$865$	−16362.6	−0.643175
$866$	−4857.40	−0.190602
$867$	0	0
$868$	47306.4	1.84987
$869$	740.477	0.0289056
$870$	−7864.65	−0.306479
$871$	−2051.19	−0.0797954
$872$	7726.15	0.300046
$873$	−47249.0	−1.83177
$874$	−1285.50	−0.0497514
$875$	19163.9	0.740411
$876$	89720.9	3.46049
$877$	−17171.8	−0.661177	−0.330588	−	0.943775i	$-0.607247\pi$
$877$	−17171.8	−0.661177	−0.330588	+	0.943775i	$0.607247\pi$
$878$	7981.26	0.306782
$879$	−79018.4	−3.03211
$880$	2852.53	0.109271
$881$	−46614.5	−1.78261	−0.891307	−	0.453400i	$-0.850211\pi$
$881$	−46614.5	−1.78261	−0.891307	+	0.453400i	$0.850211\pi$
$882$	−50411.2	−1.92453
$883$	−48461.9	−1.84697	−0.923484	−	0.383637i	$-0.874671\pi$
$883$	−48461.9	−1.84697	−0.923484	+	0.383637i	$0.874671\pi$
$884$	0	0
$885$	58573.0	2.22476
$886$	−37908.3	−1.43742
$887$	−7302.52	−0.276431	−0.138216	−	0.990402i	$-0.544137\pi$
$887$	−7302.52	−0.276431	−0.138216	+	0.990402i	$0.544137\pi$
$888$	10911.0	0.412330
$889$	4227.96	0.159507
$890$	−3316.01	−0.124891
$891$	−21338.8	−0.802329
$892$	−41656.0	−1.56362
$893$	−29561.2	−1.10776
$894$	−35986.5	−1.34627
$895$	−22981.0	−0.858292
$896$	23001.3	0.857612
$897$	584.443	0.0217547
$898$	−18324.8	−0.680966
$899$	−7048.82	−0.261503
$900$	−36395.6	−1.34799
$901$	0	0
$902$	−11553.0	−0.426465
$903$	22340.9	0.823320
$904$	−2570.11	−0.0945581
$905$	−12174.6	−0.447180
$906$	42165.7	1.54621
$907$	−30995.0	−1.13470	−0.567349	−	0.823478i	$-0.692031\pi$
$907$	−30995.0	−1.13470	−0.567349	+	0.823478i	$0.692031\pi$
$908$	45997.0	1.68113
$909$	61785.1	2.25444
$910$	12876.6	0.469072
$911$	29080.3	1.05760	0.528801	−	0.848746i	$-0.322642\pi$
$911$	29080.3	1.05760	0.528801	+	0.848746i	$0.322642\pi$
$912$	−26954.7	−0.978683
$913$	−17177.9	−0.622679
$914$	−45074.0	−1.63120
$915$	−59361.7	−2.14474
$916$	−34912.7	−1.25933
$917$	8826.33	0.317853
$918$	0	0
$919$	−52815.9	−1.89579	−0.947897	−	0.318577i	$-0.896795\pi$
$919$	−52815.9	−1.89579	−0.947897	+	0.318577i	$0.896795\pi$
$920$	315.712	0.0113138
$921$	38469.4	1.37634
$922$	−45275.2	−1.61720
$923$	−24628.8	−0.878297
$924$	−20072.0	−0.714631
$925$	3698.68	0.131472
$926$	−18757.5	−0.665668
$927$	−37157.7	−1.31653
$928$	−4946.02	−0.174958
$929$	37249.7	1.31553	0.657763	−	0.753225i	$-0.271503\pi$
$929$	37249.7	1.31553	0.657763	+	0.753225i	$0.271503\pi$
$930$	116633.	4.11242
$931$	22920.0	0.806846
$932$	13085.9	0.459917
$933$	23007.9	0.807336
$934$	263.271	0.00922323
$935$	0	0
$936$	−26193.0	−0.914686
$937$	48587.8	1.69402	0.847009	−	0.531579i	$-0.178401\pi$
$937$	48587.8	1.69402	0.847009	+	0.531579i	$0.178401\pi$
$938$	−4305.19	−0.149861
$939$	−41130.2	−1.42943
$940$	23551.0	0.817179
$941$	17402.8	0.602886	0.301443	−	0.953484i	$-0.402532\pi$
$941$	17402.8	0.602886	0.301443	+	0.953484i	$0.402532\pi$
$942$	−87067.0	−3.01146
$943$	417.352	0.0144123
$944$	16351.8	0.563777
$945$	36418.8	1.25365
$946$	−11999.7	−0.412413
$947$	40669.1	1.39553	0.697766	−	0.716325i	$-0.254177\pi$
$947$	40669.1	1.39553	0.697766	+	0.716325i	$0.254177\pi$
$948$	5574.46	0.190981
$949$	21888.3	0.748710
$950$	27994.2	0.956055
$951$	35630.9	1.21494
$952$	0	0
$953$	−46549.9	−1.58227	−0.791133	−	0.611645i	$-0.790508\pi$
$953$	−46549.9	−1.58227	−0.791133	+	0.611645i	$0.790508\pi$
$954$	55289.0	1.87636
$955$	34744.3	1.17728
$956$	33151.4	1.12154
$957$	2990.79	0.101023
$958$	−65370.5	−2.20462
$959$	−26125.5	−0.879704
$960$	66984.7	2.25200
$961$	74743.4	2.50893
$962$	8634.81	0.289394
$963$	48965.8	1.63853
$964$	−8305.95	−0.277507
$965$	−32960.3	−1.09951
$966$	1226.68	0.0408568
$967$	41120.0	1.36746	0.683728	−	0.729737i	$-0.260357\pi$
$967$	41120.0	1.36746	0.683728	+	0.729737i	$0.260357\pi$
$968$	−17666.2	−0.586584
$969$	0	0
$970$	−28953.4	−0.958389
$971$	25706.4	0.849595	0.424798	−	0.905288i	$-0.360345\pi$
$971$	25706.4	0.849595	0.424798	+	0.905288i	$0.360345\pi$
$972$	−56488.8	−1.86407
$973$	22966.7	0.756710
$974$	−17343.3	−0.570549
$975$	−12727.3	−0.418052
$976$	−16572.0	−0.543500
$977$	32403.0	1.06107	0.530533	−	0.847664i	$-0.321992\pi$
$977$	32403.0	1.06107	0.530533	+	0.847664i	$0.321992\pi$
$978$	−106803.	−3.49200
$979$	1261.02	0.0411670
$980$	−18260.1	−0.595200
$981$	30521.3	0.993345
$982$	7048.93	0.229063
$983$	29111.3	0.944563	0.472282	−	0.881448i	$-0.343431\pi$
$983$	29111.3	0.944563	0.472282	+	0.881448i	$0.343431\pi$
$984$	−26811.2	−0.868606
$985$	−5670.30	−0.183422
$986$	0	0
$987$	28208.4	0.909711
$988$	38631.6	1.24396
$989$	433.488	0.0139374
$990$	−34524.1	−1.10833
$991$	31298.2	1.00325	0.501624	−	0.865086i	$-0.332736\pi$
$991$	31298.2	1.00325	0.501624	+	0.865086i	$0.332736\pi$
$992$	73349.7	2.34764
$993$	88123.6	2.81623
$994$	−51693.0	−1.64950
$995$	−26571.9	−0.846619
$996$	−129319.	−4.11408
$997$	11418.1	0.362702	0.181351	−	0.983418i	$-0.441953\pi$
$997$	11418.1	0.362702	0.181351	+	0.983418i	$0.441953\pi$
$998$	−1315.43	−0.0417228
$999$	24421.7	0.773442

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.4.a.h.1.11	✓	12
17.4	even	4		289.4.b.f.288.3		24
17.13	even	4		289.4.b.f.288.4		24
17.16	even	2		289.4.a.i.1.11	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.4.a.h.1.11	✓	12	1.1	even	1	trivial
289.4.a.i.1.11	yes	12	17.16	even	2
289.4.b.f.288.3		24	17.4	even	4
289.4.b.f.288.4		24	17.13	even	4

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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q+4.42326 q^{2} -9.44971 q^{3} +11.5652 q^{4} +8.63042 q^{5} -41.7985 q^{6} -12.6513 q^{7} +15.7698 q^{8} +62.2970 q^{9} +O(q^{10})\)	\(q+4.42326 q^{2} -9.44971 q^{3} +11.5652 q^{4} +8.63042 q^{5} -41.7985 q^{6} -12.6513 q^{7} +15.7698 q^{8} +62.2970 q^{9} +38.1746 q^{10} -14.5171 q^{11} -109.288 q^{12} -26.6619 q^{13} -55.9602 q^{14} -81.5550 q^{15} -22.7676 q^{16} +275.556 q^{18} -125.285 q^{19} +99.8126 q^{20} +119.552 q^{21} -64.2131 q^{22} +2.31970 q^{23} -149.020 q^{24} -50.5159 q^{25} -117.932 q^{26} -333.547 q^{27} -146.315 q^{28} +21.8015 q^{29} -360.739 q^{30} -323.318 q^{31} -226.866 q^{32} +137.183 q^{33} -109.186 q^{35} +720.478 q^{36} -73.2182 q^{37} -554.167 q^{38} +251.947 q^{39} +136.100 q^{40} +179.916 q^{41} +528.807 q^{42} +186.872 q^{43} -167.894 q^{44} +537.649 q^{45} +10.2606 q^{46} +235.952 q^{47} +215.147 q^{48} -182.944 q^{49} -223.445 q^{50} -308.350 q^{52} +200.645 q^{53} -1475.36 q^{54} -125.289 q^{55} -199.510 q^{56} +1183.90 q^{57} +96.4337 q^{58} -718.203 q^{59} -943.200 q^{60} +727.874 q^{61} -1430.12 q^{62} -788.141 q^{63} -821.345 q^{64} -230.103 q^{65} +606.795 q^{66} +76.9332 q^{67} -21.9205 q^{69} -482.959 q^{70} +923.747 q^{71} +982.414 q^{72} -820.959 q^{73} -323.863 q^{74} +477.361 q^{75} -1448.94 q^{76} +183.661 q^{77} +1114.43 q^{78} -51.0071 q^{79} -196.494 q^{80} +1469.90 q^{81} +795.815 q^{82} +1183.28 q^{83} +1382.64 q^{84} +826.585 q^{86} -206.018 q^{87} -228.933 q^{88} -86.8644 q^{89} +2378.16 q^{90} +337.309 q^{91} +26.8278 q^{92} +3055.26 q^{93} +1043.68 q^{94} -1081.26 q^{95} +2143.82 q^{96} -758.448 q^{97} -809.206 q^{98} -904.375 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 18 q^{3} + 48 q^{4} - 30 q^{5} + 9 q^{6} - 24 q^{7} - 51 q^{8} + 108 q^{9}+O(q^{10}) \) 12 * q - 18 * q^3 + 48 * q^4 - 30 * q^5 + 9 * q^6 - 24 * q^7 - 51 * q^8 + 108 * q^9	\( 12 q - 18 q^{3} + 48 q^{4} - 30 q^{5} + 9 q^{6} - 24 q^{7} - 51 q^{8} + 108 q^{9} - 60 q^{10} - 162 q^{11} - 216 q^{12} - 72 q^{13} - 267 q^{14} - 138 q^{15} + 192 q^{16} + 189 q^{18} - 66 q^{19} - 129 q^{20} + 246 q^{21} - 456 q^{22} - 282 q^{23} - 72 q^{24} + 444 q^{25} + 528 q^{26} - 1092 q^{27} - 120 q^{28} - 648 q^{29} - 1890 q^{30} - 504 q^{31} - 1353 q^{32} + 966 q^{33} - 66 q^{35} - 663 q^{36} + 30 q^{37} - 60 q^{38} - 1758 q^{39} + 450 q^{40} - 318 q^{41} + 804 q^{42} + 486 q^{43} - 2448 q^{44} - 486 q^{45} - 1617 q^{46} - 888 q^{47} - 1257 q^{48} - 570 q^{49} + 435 q^{50} + 225 q^{52} + 1026 q^{53} - 933 q^{54} + 972 q^{55} - 2661 q^{56} + 156 q^{57} - 201 q^{58} - 792 q^{59} + 1458 q^{60} - 1212 q^{61} - 2817 q^{62} - 2112 q^{63} - 1857 q^{64} - 2742 q^{65} - 594 q^{66} + 624 q^{67} - 1506 q^{69} - 1650 q^{70} - 2802 q^{71} + 1455 q^{72} - 726 q^{73} - 270 q^{74} + 264 q^{75} + 675 q^{76} - 1008 q^{77} + 3090 q^{78} + 444 q^{79} + 1143 q^{80} + 2520 q^{81} + 4950 q^{82} + 672 q^{83} - 777 q^{84} + 2778 q^{86} + 726 q^{87} + 3750 q^{88} - 906 q^{89} + 7755 q^{90} - 2280 q^{91} - 87 q^{92} + 132 q^{93} + 735 q^{94} - 966 q^{95} + 5046 q^{96} + 3246 q^{97} + 1911 q^{98} + 282 q^{99}+O(q^{100}) \) 12 * q - 18 * q^3 + 48 * q^4 - 30 * q^5 + 9 * q^6 - 24 * q^7 - 51 * q^8 + 108 * q^9 - 60 * q^10 - 162 * q^11 - 216 * q^12 - 72 * q^13 - 267 * q^14 - 138 * q^15 + 192 * q^16 + 189 * q^18 - 66 * q^19 - 129 * q^20 + 246 * q^21 - 456 * q^22 - 282 * q^23 - 72 * q^24 + 444 * q^25 + 528 * q^26 - 1092 * q^27 - 120 * q^28 - 648 * q^29 - 1890 * q^30 - 504 * q^31 - 1353 * q^32 + 966 * q^33 - 66 * q^35 - 663 * q^36 + 30 * q^37 - 60 * q^38 - 1758 * q^39 + 450 * q^40 - 318 * q^41 + 804 * q^42 + 486 * q^43 - 2448 * q^44 - 486 * q^45 - 1617 * q^46 - 888 * q^47 - 1257 * q^48 - 570 * q^49 + 435 * q^50 + 225 * q^52 + 1026 * q^53 - 933 * q^54 + 972 * q^55 - 2661 * q^56 + 156 * q^57 - 201 * q^58 - 792 * q^59 + 1458 * q^60 - 1212 * q^61 - 2817 * q^62 - 2112 * q^63 - 1857 * q^64 - 2742 * q^65 - 594 * q^66 + 624 * q^67 - 1506 * q^69 - 1650 * q^70 - 2802 * q^71 + 1455 * q^72 - 726 * q^73 - 270 * q^74 + 264 * q^75 + 675 * q^76 - 1008 * q^77 + 3090 * q^78 + 444 * q^79 + 1143 * q^80 + 2520 * q^81 + 4950 * q^82 + 672 * q^83 - 777 * q^84 + 2778 * q^86 + 726 * q^87 + 3750 * q^88 - 906 * q^89 + 7755 * q^90 - 2280 * q^91 - 87 * q^92 + 132 * q^93 + 735 * q^94 - 966 * q^95 + 5046 * q^96 + 3246 * q^97 + 1911 * q^98 + 282 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more