LMFDB - Embedded newform 115.4.a.e.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,4,Mod(1,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, 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("115.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	115.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:	$6.78521965066$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 27x^{3} + 7x^{2} + 168x + 92 $ x^5 - x^4 - 27x^3 + 7x^2 + 168*x + 92
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$3.41740$ of defining polynomial
Character	$\chi$	$=$	115.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.41740 q^{2} +7.84147 q^{3} +11.5134 q^{4} -5.00000 q^{5} +34.6389 q^{6} -8.97260 q^{7} +15.5200 q^{8} +34.4886 q^{9} -22.0870 q^{10} -28.9011 q^{11} +90.2818 q^{12} +16.0879 q^{13} -39.6355 q^{14} -39.2073 q^{15} -23.5490 q^{16} +25.1771 q^{17} +152.350 q^{18} -35.6298 q^{19} -57.5669 q^{20} -70.3583 q^{21} -127.668 q^{22} -23.0000 q^{23} +121.700 q^{24} +25.0000 q^{25} +71.0668 q^{26} +58.7218 q^{27} -103.305 q^{28} +138.272 q^{29} -173.194 q^{30} +40.1277 q^{31} -228.186 q^{32} -226.627 q^{33} +111.217 q^{34} +44.8630 q^{35} +397.081 q^{36} +379.745 q^{37} -157.391 q^{38} +126.153 q^{39} -77.6001 q^{40} +412.514 q^{41} -310.801 q^{42} -402.095 q^{43} -332.750 q^{44} -172.443 q^{45} -101.600 q^{46} +110.070 q^{47} -184.659 q^{48} -262.492 q^{49} +110.435 q^{50} +197.426 q^{51} +185.227 q^{52} -421.300 q^{53} +259.397 q^{54} +144.506 q^{55} -139.255 q^{56} -279.390 q^{57} +610.802 q^{58} +755.913 q^{59} -451.409 q^{60} -307.032 q^{61} +177.260 q^{62} -309.453 q^{63} -819.594 q^{64} -80.4396 q^{65} -1001.10 q^{66} +319.974 q^{67} +289.874 q^{68} -180.354 q^{69} +198.178 q^{70} -554.138 q^{71} +535.264 q^{72} -705.131 q^{73} +1677.48 q^{74} +196.037 q^{75} -410.219 q^{76} +259.318 q^{77} +557.268 q^{78} +1170.51 q^{79} +117.745 q^{80} -470.728 q^{81} +1822.24 q^{82} -455.978 q^{83} -810.063 q^{84} -125.886 q^{85} -1776.21 q^{86} +1084.26 q^{87} -448.546 q^{88} -1495.57 q^{89} -761.749 q^{90} -144.351 q^{91} -264.808 q^{92} +314.660 q^{93} +486.222 q^{94} +178.149 q^{95} -1789.31 q^{96} +1041.24 q^{97} -1159.53 q^{98} -996.760 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 6 q^{2} + 4 q^{3} + 22 q^{4} - 25 q^{5} + 19 q^{6} - 3 q^{7} + 138 q^{8} + 77 q^{9} - 30 q^{10} + 23 q^{11} + 47 q^{12} + 132 q^{13} + 93 q^{14} - 20 q^{15} + 282 q^{16} + 23 q^{17} - 15 q^{18} - 161 q^{19}+ \cdots + 2021 q^{99}+O(q^{100}) $ 5 * q + 6 * q^2 + 4 * q^3 + 22 * q^4 - 25 * q^5 + 19 * q^6 - 3 * q^7 + 138 * q^8 + 77 * q^9 - 30 * q^10 + 23 * q^11 + 47 * q^12 + 132 * q^13 + 93 * q^14 - 20 * q^15 + 282 * q^16 + 23 * q^17 - 15 * q^18 - 161 * q^19 - 110 * q^20 - 60 * q^21 + 193 * q^22 - 115 * q^23 + 105 * q^24 + 125 * q^25 - 257 * q^26 + 577 * q^27 + 17 * q^28 + 401 * q^29 - 95 * q^30 + 32 * q^31 + 670 * q^32 + 189 * q^33 - 663 * q^34 + 15 * q^35 - 659 * q^36 - 38 * q^37 - 875 * q^38 + 335 * q^39 - 690 * q^40 - 12 * q^41 - 798 * q^42 - 566 * q^43 + 47 * q^44 - 385 * q^45 - 138 * q^46 + 919 * q^47 - 773 * q^48 - 738 * q^49 + 150 * q^50 - 993 * q^51 - 305 * q^52 + 1156 * q^53 - 8 * q^54 - 115 * q^55 + 343 * q^56 + 114 * q^57 - 1042 * q^58 + 1324 * q^59 - 235 * q^60 - 1673 * q^61 + 565 * q^62 + 270 * q^63 + 2466 * q^64 - 660 * q^65 - 2781 * q^66 + 558 * q^67 - 2267 * q^68 - 92 * q^69 - 465 * q^70 - 108 * q^71 - 789 * q^72 + 1173 * q^73 + 1458 * q^74 + 100 * q^75 - 3477 * q^76 + 2608 * q^77 + 704 * q^78 + 656 * q^79 - 1410 * q^80 - 319 * q^81 + 3505 * q^82 - 82 * q^83 - 718 * q^84 - 115 * q^85 + 112 * q^86 + 2389 * q^87 + 2397 * q^88 + 570 * q^89 + 75 * q^90 - 1589 * q^91 - 506 * q^92 + 911 * q^93 - 948 * q^94 + 805 * q^95 - 5991 * q^96 + 633 * q^97 - 2555 * q^98 + 2021 * q^99

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 $

$2$	4.41740	1.56179	0.780893	−	0.624665i	$-0.214765\pi$
$2$	4.41740	1.56179	0.780893	+	0.624665i	$0.214765\pi$
$3$	7.84147	1.50909	0.754546	−	0.656248i	$-0.227857\pi$
$3$	7.84147	1.50909	0.754546	+	0.656248i	$0.227857\pi$
$4$	11.5134	1.43917
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	34.6389	2.35688
$7$	−8.97260	−0.484475	−0.242237	−	0.970217i	$-0.577881\pi$
$7$	−8.97260	−0.484475	−0.242237	+	0.970217i	$0.577881\pi$
$8$	15.5200	0.685894
$9$	34.4886	1.27736
$10$	−22.0870	−0.698452
$11$	−28.9011	−0.792183	−0.396092	−	0.918211i	$-0.629634\pi$
$11$	−28.9011	−0.792183	−0.396092	+	0.918211i	$0.629634\pi$
$12$	90.2818	2.17184
$13$	16.0879	0.343230	0.171615	−	0.985164i	$-0.445102\pi$
$13$	16.0879	0.343230	0.171615	+	0.985164i	$0.445102\pi$
$14$	−39.6355	−0.756646
$15$	−39.2073	−0.674886
$16$	−23.5490	−0.367954
$17$	25.1771	0.359197	0.179599	−	0.983740i	$-0.442520\pi$
$17$	25.1771	0.359197	0.179599	+	0.983740i	$0.442520\pi$
$18$	152.350	1.99496
$19$	−35.6298	−0.430212	−0.215106	−	0.976591i	$-0.569010\pi$
$19$	−35.6298	−0.430212	−0.215106	+	0.976591i	$0.569010\pi$
$20$	−57.5669	−0.643618
$21$	−70.3583	−0.731117
$22$	−127.668	−1.23722
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	121.700	1.03508
$25$	25.0000	0.200000
$26$	71.0668	0.536051
$27$	58.7218	0.418556
$28$	−103.305	−0.697243
$29$	138.272	0.885395	0.442698	−	0.896671i	$-0.354022\pi$
$29$	138.272	0.885395	0.442698	+	0.896671i	$0.354022\pi$
$30$	−173.194	−1.05403
$31$	40.1277	0.232489	0.116244	−	0.993221i	$-0.462914\pi$
$31$	40.1277	0.232489	0.116244	+	0.993221i	$0.462914\pi$
$32$	−228.186	−1.26056
$33$	−226.627	−1.19548
$34$	111.217	0.560989
$35$	44.8630	0.216664
$36$	397.081	1.83834
$37$	379.745	1.68729	0.843645	−	0.536902i	$-0.180405\pi$
$37$	379.745	1.68729	0.843645	+	0.536902i	$0.180405\pi$
$38$	−157.391	−0.671899
$39$	126.153	0.517965
$40$	−77.6001	−0.306741
$41$	412.514	1.57132	0.785658	−	0.618662i	$-0.212325\pi$
$41$	412.514	1.57132	0.785658	+	0.618662i	$0.212325\pi$
$42$	−310.801	−1.14185
$43$	−402.095	−1.42602	−0.713011	−	0.701153i	$-0.752669\pi$
$43$	−402.095	−1.42602	−0.713011	+	0.701153i	$0.752669\pi$
$44$	−332.750	−1.14009
$45$	−172.443	−0.571251
$46$	−101.600	−0.325655
$47$	110.070	0.341603	0.170801	−	0.985305i	$-0.445364\pi$
$47$	110.070	0.341603	0.170801	+	0.985305i	$0.445364\pi$
$48$	−184.659	−0.555276
$49$	−262.492	−0.765284
$50$	110.435	0.312357
$51$	197.426	0.542061
$52$	185.227	0.493967
$53$	−421.300	−1.09189	−0.545943	−	0.837822i	$-0.683829\pi$
$53$	−421.300	−1.09189	−0.545943	+	0.837822i	$0.683829\pi$
$54$	259.397	0.653695
$55$	144.506	0.354275
$56$	−139.255	−0.332298
$57$	−279.390	−0.649229
$58$	610.802	1.38280
$59$	755.913	1.66799	0.833996	−	0.551770i	$-0.186048\pi$
$59$	755.913	1.66799	0.833996	+	0.551770i	$0.186048\pi$
$60$	−451.409	−0.971278
$61$	−307.032	−0.644450	−0.322225	−	0.946663i	$-0.604431\pi$
$61$	−307.032	−0.644450	−0.322225	+	0.946663i	$0.604431\pi$
$62$	177.260	0.363098
$63$	−309.453	−0.618847
$64$	−819.594	−1.60077
$65$	−80.4396	−0.153497
$66$	−1001.10	−1.86708
$67$	319.974	0.583448	0.291724	−	0.956502i	$-0.405771\pi$
$67$	319.974	0.583448	0.291724	+	0.956502i	$0.405771\pi$
$68$	289.874	0.516947
$69$	−180.354	−0.314667
$70$	198.178	0.338382
$71$	−554.138	−0.926254	−0.463127	−	0.886292i	$-0.653273\pi$
$71$	−554.138	−0.926254	−0.463127	+	0.886292i	$0.653273\pi$
$72$	535.264	0.876131
$73$	−705.131	−1.13054	−0.565269	−	0.824907i	$-0.691228\pi$
$73$	−705.131	−1.13054	−0.565269	+	0.824907i	$0.691228\pi$
$74$	1677.48	2.63518
$75$	196.037	0.301818
$76$	−410.219	−0.619149
$77$	259.318	0.383793
$78$	557.268	0.808950
$79$	1170.51	1.66699	0.833495	−	0.552526i	$-0.186336\pi$
$79$	1170.51	1.66699	0.833495	+	0.552526i	$0.186336\pi$
$80$	117.745	0.164554
$81$	−470.728	−0.645717
$82$	1822.24	2.45406
$83$	−455.978	−0.603014	−0.301507	−	0.953464i	$-0.597490\pi$
$83$	−455.978	−0.603014	−0.301507	+	0.953464i	$0.597490\pi$
$84$	−810.063	−1.05220
$85$	−125.886	−0.160638
$86$	−1776.21	−2.22714
$87$	1084.26	1.33614
$88$	−448.546	−0.543354
$89$	−1495.57	−1.78124	−0.890621	−	0.454746i	$-0.849730\pi$
$89$	−1495.57	−1.78124	−0.890621	+	0.454746i	$0.849730\pi$
$90$	−761.749	−0.892172
$91$	−144.351	−0.166286
$92$	−264.808	−0.300088
$93$	314.660	0.350847
$94$	486.222	0.533510
$95$	178.149	0.192397
$96$	−1789.31	−1.90230
$97$	1041.24	1.08992	0.544958	−	0.838463i	$-0.316545\pi$
$97$	1041.24	1.08992	0.544958	+	0.838463i	$0.316545\pi$
$98$	−1159.53	−1.19521
$99$	−996.760	−1.01190
$100$	287.835	0.287835
$101$	1450.22	1.42873	0.714367	−	0.699771i	$-0.246715\pi$
$101$	1450.22	1.42873	0.714367	+	0.699771i	$0.246715\pi$
$102$	872.108	0.846584
$103$	220.283	0.210729	0.105365	−	0.994434i	$-0.466399\pi$
$103$	220.283	0.210729	0.105365	+	0.994434i	$0.466399\pi$
$104$	249.685	0.235419
$105$	351.792	0.326965
$106$	−1861.05	−1.70529
$107$	59.2679	0.0535481	0.0267741	−	0.999642i	$-0.491477\pi$
$107$	59.2679	0.0535481	0.0267741	+	0.999642i	$0.491477\pi$
$108$	676.087	0.602375
$109$	1966.29	1.72786	0.863930	−	0.503612i	$-0.167996\pi$
$109$	1966.29	1.72786	0.863930	+	0.503612i	$0.167996\pi$
$110$	638.339	0.553302
$111$	2977.76	2.54627
$112$	211.296	0.178264
$113$	1819.68	1.51488	0.757439	−	0.652905i	$-0.226450\pi$
$113$	1819.68	1.51488	0.757439	+	0.652905i	$0.226450\pi$
$114$	−1234.17	−1.01396
$115$	115.000	0.0932505
$116$	1591.98	1.27424
$117$	554.851	0.438427
$118$	3339.17	2.60505
$119$	−225.904	−0.174022
$120$	−608.498	−0.462900
$121$	−495.725	−0.372445
$122$	−1356.28	−1.00649
$123$	3234.72	2.37126
$124$	462.006	0.334592
$125$	−125.000	−0.0894427
$126$	−1366.97	−0.966506
$127$	834.517	0.583082	0.291541	−	0.956558i	$-0.405832\pi$
$127$	834.517	0.583082	0.291541	+	0.956558i	$0.405832\pi$
$128$	−1794.98	−1.23950
$129$	−3153.02	−2.15200
$130$	−355.334	−0.239729
$131$	510.293	0.340340	0.170170	−	0.985415i	$-0.445568\pi$
$131$	510.293	0.340340	0.170170	+	0.985415i	$0.445568\pi$
$132$	−2609.25	−1.72050
$133$	319.692	0.208427
$134$	1413.45	0.911221
$135$	−293.609	−0.187184
$136$	390.750	0.246371
$137$	11.2339	0.00700567	0.00350284	−	0.999994i	$-0.498885\pi$
$137$	11.2339	0.00700567	0.00350284	+	0.999994i	$0.498885\pi$
$138$	−796.694	−0.491443
$139$	−1656.81	−1.01100	−0.505501	−	0.862826i	$-0.668692\pi$
$139$	−1656.81	−1.01100	−0.505501	+	0.862826i	$0.668692\pi$
$140$	516.525	0.311817
$141$	863.109	0.515510
$142$	−2447.85	−1.44661
$143$	−464.959	−0.271901
$144$	−812.174	−0.470008
$145$	−691.360	−0.395961
$146$	−3114.84	−1.76566
$147$	−2058.33	−1.15488
$148$	4372.15	2.42830
$149$	−510.206	−0.280522	−0.140261	−	0.990115i	$-0.544794\pi$
$149$	−510.206	−0.280522	−0.140261	+	0.990115i	$0.544794\pi$
$150$	865.972	0.471375
$151$	−2337.38	−1.25969	−0.629846	−	0.776720i	$-0.716882\pi$
$151$	−2337.38	−1.25969	−0.629846	+	0.776720i	$0.716882\pi$
$152$	−552.974	−0.295080
$153$	868.325	0.458823
$154$	1145.51	0.599402
$155$	−200.639	−0.103972
$156$	1452.45	0.745442
$157$	146.592	0.0745178	0.0372589	−	0.999306i	$-0.488137\pi$
$157$	146.592	0.0745178	0.0372589	+	0.999306i	$0.488137\pi$
$158$	5170.59	2.60348
$159$	−3303.61	−1.64776
$160$	1140.93	0.563739
$161$	206.370	0.101020
$162$	−2079.39	−1.00847
$163$	−3278.19	−1.57526	−0.787630	−	0.616149i	$-0.788692\pi$
$163$	−3278.19	−1.57526	−0.787630	+	0.616149i	$0.788692\pi$
$164$	4749.44	2.26139
$165$	1133.14	0.534634
$166$	−2014.24	−0.941778
$167$	−1555.42	−0.720732	−0.360366	−	0.932811i	$-0.617348\pi$
$167$	−1555.42	−0.720732	−0.360366	+	0.932811i	$0.617348\pi$
$168$	−1091.96	−0.501469
$169$	−1938.18	−0.882193
$170$	−556.087	−0.250882
$171$	−1228.82	−0.549534
$172$	−4629.48	−2.05229
$173$	−472.392	−0.207603	−0.103801	−	0.994598i	$-0.533101\pi$
$173$	−472.392	−0.207603	−0.103801	+	0.994598i	$0.533101\pi$
$174$	4789.58	2.08677
$175$	−224.315	−0.0968950
$176$	680.594	0.291487
$177$	5927.47	2.51715
$178$	−6606.54	−2.78192
$179$	2429.45	1.01444	0.507222	−	0.861815i	$-0.330672\pi$
$179$	2429.45	1.01444	0.507222	+	0.861815i	$0.330672\pi$
$180$	−1985.40	−0.822129
$181$	−982.359	−0.403415	−0.201708	−	0.979446i	$-0.564649\pi$
$181$	−982.359	−0.403415	−0.201708	+	0.979446i	$0.564649\pi$
$182$	−637.653	−0.259703
$183$	−2407.58	−0.972533
$184$	−356.960	−0.143019
$185$	−1898.73	−0.754579
$186$	1389.98	0.547947
$187$	−727.648	−0.284550
$188$	1267.28	0.491626
$189$	−526.887	−0.202780
$190$	786.954	0.300482
$191$	1361.14	0.515649	0.257824	−	0.966192i	$-0.416994\pi$
$191$	1361.14	0.515649	0.257824	+	0.966192i	$0.416994\pi$
$192$	−6426.82	−2.41571
$193$	−1456.29	−0.543142	−0.271571	−	0.962418i	$-0.587543\pi$
$193$	−1456.29	−0.543142	−0.271571	+	0.962418i	$0.587543\pi$
$194$	4599.57	1.70222
$195$	−630.765	−0.231641
$196$	−3022.18	−1.10138
$197$	1071.99	0.387695	0.193847	−	0.981032i	$-0.437903\pi$
$197$	1071.99	0.387695	0.193847	+	0.981032i	$0.437903\pi$
$198$	−4403.08	−1.58037
$199$	−2879.31	−1.02567	−0.512836	−	0.858486i	$-0.671405\pi$
$199$	−2879.31	−1.02567	−0.512836	+	0.858486i	$0.671405\pi$
$200$	388.000	0.137179
$201$	2509.07	0.880477
$202$	6406.19	2.23138
$203$	−1240.66	−0.428952
$204$	2273.04	0.780120
$205$	−2062.57	−0.702713
$206$	973.077	0.329114
$207$	−793.238	−0.266347
$208$	−378.855	−0.126293
$209$	1029.74	0.340807
$210$	1554.00	0.510650
$211$	−4746.47	−1.54863	−0.774313	−	0.632802i	$-0.781905\pi$
$211$	−4746.47	−1.54863	−0.774313	+	0.632802i	$0.781905\pi$
$212$	−4850.59	−1.57141
$213$	−4345.25	−1.39780
$214$	261.810	0.0836306
$215$	2010.48	0.637737
$216$	911.363	0.287085
$217$	−360.050	−0.112635
$218$	8685.90	2.69855
$219$	−5529.26	−1.70609
$220$	1663.75	0.509863
$221$	405.048	0.123287
$222$	13153.9	3.97673
$223$	4874.04	1.46363	0.731815	−	0.681503i	$-0.238673\pi$
$223$	4874.04	1.46363	0.731815	+	0.681503i	$0.238673\pi$
$224$	2047.42	0.610709
$225$	862.216	0.255471
$226$	8038.26	2.36592
$227$	−2742.09	−0.801757	−0.400879	−	0.916131i	$-0.631295\pi$
$227$	−2742.09	−0.801757	−0.400879	+	0.916131i	$0.631295\pi$
$228$	−3216.72	−0.934353
$229$	1528.38	0.441041	0.220520	−	0.975382i	$-0.429224\pi$
$229$	1528.38	0.441041	0.220520	+	0.975382i	$0.429224\pi$
$230$	508.001	0.145637
$231$	2033.44	0.579179
$232$	2145.98	0.607287
$233$	5552.78	1.56126	0.780632	−	0.624991i	$-0.214897\pi$
$233$	5552.78	1.56126	0.780632	+	0.624991i	$0.214897\pi$
$234$	2450.99	0.684729
$235$	−550.349	−0.152769
$236$	8703.12	2.40053
$237$	9178.49	2.51564
$238$	−997.909	−0.271785
$239$	2779.63	0.752299	0.376149	−	0.926559i	$-0.377248\pi$
$239$	2779.63	0.752299	0.376149	+	0.926559i	$0.377248\pi$
$240$	923.295	0.248327
$241$	−5568.82	−1.48846	−0.744231	−	0.667922i	$-0.767184\pi$
$241$	−5568.82	−1.48846	−0.744231	+	0.667922i	$0.767184\pi$
$242$	−2189.81	−0.581680
$243$	−5276.68	−1.39300
$244$	−3534.98	−0.927475
$245$	1312.46	0.342245
$246$	14289.0	3.70340
$247$	−573.209	−0.147662
$248$	622.783	0.159463
$249$	−3575.54	−0.910003
$250$	−552.174	−0.139690
$251$	−387.065	−0.0973360	−0.0486680	−	0.998815i	$-0.515498\pi$
$251$	−387.065	−0.0973360	−0.0486680	+	0.998815i	$0.515498\pi$
$252$	−3562.85	−0.890628
$253$	664.726	0.165182
$254$	3686.39	0.910649
$255$	−987.129	−0.242417
$256$	−1372.41	−0.335061
$257$	1476.07	0.358267	0.179133	−	0.983825i	$-0.442671\pi$
$257$	1476.07	0.358267	0.179133	+	0.983825i	$0.442671\pi$
$258$	−13928.1	−3.36096
$259$	−3407.30	−0.817449
$260$	−926.133	−0.220909
$261$	4768.81	1.13097
$262$	2254.17	0.531537
$263$	203.984	0.0478259	0.0239130	−	0.999714i	$-0.492388\pi$
$263$	203.984	0.0478259	0.0239130	+	0.999714i	$0.492388\pi$
$264$	−3517.26	−0.819971
$265$	2106.50	0.488306
$266$	1412.20	0.325518
$267$	−11727.5	−2.68806
$268$	3683.98	0.839683
$269$	−6973.71	−1.58065	−0.790324	−	0.612689i	$-0.790088\pi$
$269$	−6973.71	−1.58065	−0.790324	+	0.612689i	$0.790088\pi$
$270$	−1296.99	−0.292341
$271$	−2164.97	−0.485287	−0.242643	−	0.970116i	$-0.578015\pi$
$271$	−2164.97	−0.485287	−0.242643	+	0.970116i	$0.578015\pi$
$272$	−592.898	−0.132168
$273$	−1131.92	−0.250941
$274$	49.6246	0.0109414
$275$	−722.528	−0.158437
$276$	−2076.48	−0.452861
$277$	1194.00	0.258992	0.129496	−	0.991580i	$-0.458664\pi$
$277$	1194.00	0.258992	0.129496	+	0.991580i	$0.458664\pi$
$278$	−7318.81	−1.57897
$279$	1383.95	0.296971
$280$	696.274	0.148608
$281$	6485.98	1.37694	0.688472	−	0.725263i	$-0.258282\pi$
$281$	6485.98	1.37694	0.688472	+	0.725263i	$0.258282\pi$
$282$	3812.69	0.805116
$283$	−3214.41	−0.675182	−0.337591	−	0.941293i	$-0.609612\pi$
$283$	−3214.41	−0.675182	−0.337591	+	0.941293i	$0.609612\pi$
$284$	−6380.00	−1.33304
$285$	1396.95	0.290344
$286$	−2053.91	−0.424651
$287$	−3701.33	−0.761263
$288$	−7869.81	−1.61018
$289$	−4279.11	−0.870977
$290$	−3054.01	−0.618406
$291$	8164.85	1.64478
$292$	−8118.44	−1.62704
$293$	5585.47	1.11367	0.556837	−	0.830622i	$-0.312015\pi$
$293$	5585.47	1.11367	0.556837	+	0.830622i	$0.312015\pi$
$294$	−9092.44	−1.80368
$295$	−3779.57	−0.745949
$296$	5893.65	1.15730
$297$	−1697.13	−0.331573
$298$	−2253.78	−0.438115
$299$	−370.022	−0.0715684
$300$	2257.05	0.434369
$301$	3607.84	0.690872
$302$	−10325.1	−1.96737
$303$	11371.8	2.15609
$304$	839.047	0.158298
$305$	1535.16	0.288207
$306$	3835.73	0.716583
$307$	2849.51	0.529740	0.264870	−	0.964284i	$-0.414671\pi$
$307$	2849.51	0.529740	0.264870	+	0.964284i	$0.414671\pi$
$308$	2985.63	0.552344
$309$	1727.34	0.318010
$310$	−886.300	−0.162382
$311$	−6617.84	−1.20664	−0.603318	−	0.797501i	$-0.706155\pi$
$311$	−6617.84	−1.20664	−0.603318	+	0.797501i	$0.706155\pi$
$312$	1957.90	0.355269
$313$	−6271.26	−1.13250	−0.566250	−	0.824233i	$-0.691606\pi$
$313$	−6271.26	−1.13250	−0.566250	+	0.824233i	$0.691606\pi$
$314$	647.554	0.116381
$315$	1547.26	0.276757
$316$	13476.5	2.39909
$317$	5650.73	1.00119	0.500594	−	0.865682i	$-0.333115\pi$
$317$	5650.73	1.00119	0.500594	+	0.865682i	$0.333115\pi$
$318$	−14593.3	−2.57344
$319$	−3996.22	−0.701395
$320$	4097.97	0.715885
$321$	464.748	0.0808090
$322$	911.617	0.157772
$323$	−897.055	−0.154531
$324$	−5419.67	−0.929299
$325$	402.198	0.0686460
$326$	−14481.0	−2.46022
$327$	15418.6	2.60750
$328$	6402.23	1.07776
$329$	−987.612	−0.165498
$330$	5005.51	0.834983
$331$	−6391.40	−1.06134	−0.530669	−	0.847579i	$-0.678059\pi$
$331$	−6391.40	−1.06134	−0.530669	+	0.847579i	$0.678059\pi$
$332$	−5249.86	−0.867841
$333$	13096.9	2.15527
$334$	−6870.92	−1.12563
$335$	−1599.87	−0.260926
$336$	1656.87	0.269017
$337$	4153.87	0.671441	0.335721	−	0.941962i	$-0.391020\pi$
$337$	4153.87	0.671441	0.335721	+	0.941962i	$0.391020\pi$
$338$	−8561.70	−1.37780
$339$	14269.0	2.28609
$340$	−1449.37	−0.231186
$341$	−1159.74	−0.184174
$342$	−5428.19	−0.858254
$343$	5432.84	0.855236
$344$	−6240.52	−0.978100
$345$	901.769	0.140723
$346$	−2086.74	−0.324231
$347$	−3071.86	−0.475234	−0.237617	−	0.971359i	$-0.576366\pi$
$347$	−3071.86	−0.475234	−0.237617	+	0.971359i	$0.576366\pi$
$348$	12483.4	1.92294
$349$	−8358.91	−1.28207	−0.641035	−	0.767512i	$-0.721495\pi$
$349$	−8358.91	−1.28207	−0.641035	+	0.767512i	$0.721495\pi$
$350$	−990.888	−0.151329
$351$	944.712	0.143661
$352$	6594.82	0.998594
$353$	8018.12	1.20896	0.604478	−	0.796622i	$-0.293382\pi$
$353$	8018.12	1.20896	0.604478	+	0.796622i	$0.293382\pi$
$354$	26184.0	3.93125
$355$	2770.69	0.414234
$356$	−17219.1	−2.56352
$357$	−1771.42	−0.262615
$358$	10731.8	1.58434
$359$	2138.46	0.314384	0.157192	−	0.987568i	$-0.449756\pi$
$359$	2138.46	0.314384	0.157192	+	0.987568i	$0.449756\pi$
$360$	−2676.32	−0.391818
$361$	−5589.52	−0.814918
$362$	−4339.47	−0.630048
$363$	−3887.21	−0.562054
$364$	−1661.96	−0.239315
$365$	3525.65	0.505592
$366$	−10635.2	−1.51889
$367$	−4509.96	−0.641467	−0.320733	−	0.947170i	$-0.603929\pi$
$367$	−4509.96	−0.641467	−0.320733	+	0.947170i	$0.603929\pi$
$368$	541.628	0.0767237
$369$	14227.1	2.00713
$370$	−8387.42	−1.17849
$371$	3780.15	0.528991
$372$	3622.80	0.504929
$373$	−3362.09	−0.466709	−0.233355	−	0.972392i	$-0.574970\pi$
$373$	−3362.09	−0.466709	−0.233355	+	0.972392i	$0.574970\pi$
$374$	−3214.31	−0.444406
$375$	−980.184	−0.134977
$376$	1708.29	0.234303
$377$	2224.51	0.303894
$378$	−2327.47	−0.316699
$379$	2107.16	0.285587	0.142793	−	0.989753i	$-0.454392\pi$
$379$	2107.16	0.285587	0.142793	+	0.989753i	$0.454392\pi$
$380$	2051.10	0.276892
$381$	6543.84	0.879924
$382$	6012.71	0.805333
$383$	1373.05	0.183184	0.0915919	−	0.995797i	$-0.470804\pi$
$383$	1373.05	0.183184	0.0915919	+	0.995797i	$0.470804\pi$
$384$	−14075.3	−1.87052
$385$	−1296.59	−0.171637
$386$	−6433.03	−0.848271
$387$	−13867.7	−1.82154
$388$	11988.2	1.56858
$389$	7008.05	0.913425	0.456713	−	0.889614i	$-0.349027\pi$
$389$	7008.05	0.913425	0.456713	+	0.889614i	$0.349027\pi$
$390$	−2786.34	−0.361774
$391$	−579.074	−0.0748978
$392$	−4073.89	−0.524904
$393$	4001.44	0.513604
$394$	4735.39	0.605496
$395$	−5852.53	−0.745501
$396$	−11476.1	−1.45630
$397$	2402.53	0.303727	0.151864	−	0.988401i	$-0.451473\pi$
$397$	2402.53	0.303727	0.151864	+	0.988401i	$0.451473\pi$
$398$	−12719.0	−1.60188
$399$	2506.85	0.314535
$400$	−588.726	−0.0735908
$401$	−11902.0	−1.48218	−0.741091	−	0.671404i	$-0.765691\pi$
$401$	−11902.0	−1.48218	−0.741091	+	0.671404i	$0.765691\pi$
$402$	11083.5	1.37512
$403$	645.572	0.0797971
$404$	16696.9	2.05620
$405$	2353.64	0.288773
$406$	−5480.48	−0.669930
$407$	−10975.1	−1.33664
$408$	3064.05	0.371797
$409$	5277.96	0.638089	0.319044	−	0.947740i	$-0.396638\pi$
$409$	5277.96	0.638089	0.319044	+	0.947740i	$0.396638\pi$
$410$	−9111.20	−1.09749
$411$	88.0903	0.0105722
$412$	2536.20	0.303276
$413$	−6782.51	−0.808100
$414$	−3504.05	−0.415977
$415$	2279.89	0.269676
$416$	−3671.03	−0.432662
$417$	−12991.9	−1.52569
$418$	4548.77	0.532267
$419$	−11196.4	−1.30545	−0.652723	−	0.757597i	$-0.726373\pi$
$419$	−11196.4	−1.30545	−0.652723	+	0.757597i	$0.726373\pi$
$420$	4050.31	0.470560
$421$	5176.82	0.599293	0.299647	−	0.954050i	$-0.403131\pi$
$421$	5176.82	0.599293	0.299647	+	0.954050i	$0.403131\pi$
$422$	−20967.0	−2.41862
$423$	3796.16	0.436349
$424$	−6538.58	−0.748918
$425$	629.428	0.0718394
$426$	−19194.7	−2.18307
$427$	2754.88	0.312220
$428$	682.375	0.0770650
$429$	−3645.96	−0.410324
$430$	8881.07	0.996008
$431$	9348.93	1.04483	0.522415	−	0.852691i	$-0.325031\pi$
$431$	9348.93	1.04483	0.522415	+	0.852691i	$0.325031\pi$
$432$	−1382.84	−0.154009
$433$	4320.91	0.479560	0.239780	−	0.970827i	$-0.422925\pi$
$433$	4320.91	0.479560	0.239780	+	0.970827i	$0.422925\pi$
$434$	−1590.48	−0.175912
$435$	−5421.28	−0.597541
$436$	22638.7	2.48669
$437$	819.484	0.0897054
$438$	−24424.9	−2.66454
$439$	−7016.03	−0.762772	−0.381386	−	0.924416i	$-0.624553\pi$
$439$	−7016.03	−0.762772	−0.381386	+	0.924416i	$0.624553\pi$
$440$	2242.73	0.242995
$441$	−9053.00	−0.977541
$442$	1789.26	0.192548
$443$	12343.6	1.32384	0.661921	−	0.749574i	$-0.269741\pi$
$443$	12343.6	1.32384	0.661921	+	0.749574i	$0.269741\pi$
$444$	34284.1	3.66453
$445$	7477.87	0.796596
$446$	21530.5	2.28588
$447$	−4000.77	−0.423333
$448$	7353.88	0.775532
$449$	18146.9	1.90737	0.953683	−	0.300815i	$-0.0972587\pi$
$449$	18146.9	1.90737	0.953683	+	0.300815i	$0.0972587\pi$
$450$	3808.75	0.398991
$451$	−11922.1	−1.24477
$452$	20950.7	2.18017
$453$	−18328.5	−1.90099
$454$	−12112.9	−1.25217
$455$	721.753	0.0743655
$456$	−4336.13	−0.445302
$457$	5233.82	0.535728	0.267864	−	0.963457i	$-0.413682\pi$
$457$	5233.82	0.535728	0.267864	+	0.963457i	$0.413682\pi$
$458$	6751.47	0.688811
$459$	1478.45	0.150344
$460$	1324.04	0.134204
$461$	−2335.01	−0.235905	−0.117952	−	0.993019i	$-0.537633\pi$
$461$	−2335.01	−0.235905	−0.117952	+	0.993019i	$0.537633\pi$
$462$	8982.49	0.904553
$463$	13644.1	1.36954	0.684769	−	0.728760i	$-0.259903\pi$
$463$	13644.1	1.36954	0.684769	+	0.728760i	$0.259903\pi$
$464$	−3256.17	−0.325784
$465$	−1573.30	−0.156903
$466$	24528.8	2.43836
$467$	−5246.31	−0.519851	−0.259925	−	0.965629i	$-0.583698\pi$
$467$	−5246.31	−0.519851	−0.259925	+	0.965629i	$0.583698\pi$
$468$	6388.21	0.630972
$469$	−2871.00	−0.282666
$470$	−2431.11	−0.238593
$471$	1149.50	0.112454
$472$	11731.8	1.14407
$473$	11621.0	1.12967
$474$	40545.0	3.92889
$475$	−890.744	−0.0860424
$476$	−2600.92	−0.250448
$477$	−14530.0	−1.39473
$478$	12278.7	1.17493
$479$	12278.3	1.17121	0.585603	−	0.810598i	$-0.300858\pi$
$479$	12278.3	1.17121	0.585603	+	0.810598i	$0.300858\pi$
$480$	8946.55	0.850734
$481$	6109.31	0.579128
$482$	−24599.7	−2.32466
$483$	1618.24	0.152448
$484$	−5707.47	−0.536013
$485$	−5206.20	−0.487426
$486$	−23309.2	−2.17557
$487$	−8945.24	−0.832336	−0.416168	−	0.909288i	$-0.636627\pi$
$487$	−8945.24	−0.832336	−0.416168	+	0.909288i	$0.636627\pi$
$488$	−4765.14	−0.442024
$489$	−25705.8	−2.37721
$490$	5797.67	0.534514
$491$	−7792.94	−0.716274	−0.358137	−	0.933669i	$-0.616588\pi$
$491$	−7792.94	−0.716274	−0.358137	+	0.933669i	$0.616588\pi$
$492$	37242.6	3.41265
$493$	3481.29	0.318031
$494$	−2532.09	−0.230616
$495$	4983.80	0.452536
$496$	−944.970	−0.0855451
$497$	4972.06	0.448747
$498$	−15794.6	−1.42123
$499$	−8577.71	−0.769521	−0.384761	−	0.923016i	$-0.625716\pi$
$499$	−8577.71	−0.769521	−0.384761	+	0.923016i	$0.625716\pi$
$500$	−1439.17	−0.128724
$501$	−12196.8	−1.08765
$502$	−1709.82	−0.152018
$503$	7784.99	0.690091	0.345045	−	0.938586i	$-0.387864\pi$
$503$	7784.99	0.690091	0.345045	+	0.938586i	$0.387864\pi$
$504$	−4802.71	−0.424464
$505$	−7251.09	−0.638949
$506$	2936.36	0.257978
$507$	−15198.2	−1.33131
$508$	9608.12	0.839156
$509$	−11390.4	−0.991891	−0.495946	−	0.868354i	$-0.665178\pi$
$509$	−11390.4	−0.991891	−0.495946	+	0.868354i	$0.665178\pi$
$510$	−4360.54	−0.378604
$511$	6326.85	0.547717
$512$	8297.40	0.716205
$513$	−2092.24	−0.180068
$514$	6520.37	0.559535
$515$	−1101.42	−0.0942411
$516$	−36301.9	−3.09710
$517$	−3181.14	−0.270612
$518$	−15051.4	−1.27668
$519$	−3704.24	−0.313292
$520$	−1248.42	−0.105283
$521$	−12824.5	−1.07841	−0.539206	−	0.842174i	$-0.681276\pi$
$521$	−12824.5	−1.07841	−0.539206	+	0.842174i	$0.681276\pi$
$522$	21065.7	1.76632
$523$	13087.4	1.09421	0.547107	−	0.837063i	$-0.315729\pi$
$523$	13087.4	1.09421	0.547107	+	0.837063i	$0.315729\pi$
$524$	5875.20	0.489808
$525$	−1758.96	−0.146223
$526$	901.080	0.0746938
$527$	1010.30	0.0835093
$528$	5336.86	0.439880
$529$	529.000	0.0434783
$530$	9305.24	0.762630
$531$	26070.4	2.13062
$532$	3680.73	0.299962
$533$	6636.50	0.539322
$534$	−51805.0	−4.19817
$535$	−296.340	−0.0239474
$536$	4966.00	0.400184
$537$	19050.4	1.53089
$538$	−30805.6	−2.46863
$539$	7586.33	0.606245
$540$	−3380.43	−0.269390
$541$	15464.3	1.22895	0.614473	−	0.788938i	$-0.289369\pi$
$541$	15464.3	1.22895	0.614473	+	0.788938i	$0.289369\pi$
$542$	−9563.54	−0.757914
$543$	−7703.14	−0.608791
$544$	−5745.06	−0.452789
$545$	−9831.47	−0.772722
$546$	−5000.14	−0.391916
$547$	6981.32	0.545703	0.272852	−	0.962056i	$-0.412033\pi$
$547$	6981.32	0.545703	0.272852	+	0.962056i	$0.412033\pi$
$548$	129.340	0.0100824
$549$	−10589.1	−0.823192
$550$	−3191.69	−0.247444
$551$	−4926.60	−0.380908
$552$	−2799.09	−0.215828
$553$	−10502.5	−0.807615
$554$	5274.38	0.404489
$555$	−14888.8	−1.13873
$556$	−19075.5	−1.45501
$557$	24964.8	1.89909	0.949543	−	0.313637i	$-0.101547\pi$
$557$	24964.8	1.89909	0.949543	+	0.313637i	$0.101547\pi$
$558$	6113.45	0.463805
$559$	−6468.88	−0.489454
$560$	−1056.48	−0.0797222
$561$	−5705.83	−0.429412
$562$	28651.2	2.15049
$563$	−10820.3	−0.809986	−0.404993	−	0.914320i	$-0.632726\pi$
$563$	−10820.3	−0.809986	−0.404993	+	0.914320i	$0.632726\pi$
$564$	9937.31	0.741908
$565$	−9098.41	−0.677474
$566$	−14199.3	−1.05449
$567$	4223.65	0.312834
$568$	−8600.23	−0.635312
$569$	8438.73	0.621740	0.310870	−	0.950453i	$-0.399380\pi$
$569$	8438.73	0.621740	0.310870	+	0.950453i	$0.399380\pi$
$570$	6170.87	0.453455
$571$	23107.6	1.69356	0.846781	−	0.531942i	$-0.178538\pi$
$571$	23107.6	1.69356	0.846781	+	0.531942i	$0.178538\pi$
$572$	−5353.26	−0.391313
$573$	10673.4	0.778161
$574$	−16350.2	−1.18893
$575$	−575.000	−0.0417029
$576$	−28266.7	−2.04475
$577$	24848.7	1.79283	0.896416	−	0.443215i	$-0.146162\pi$
$577$	24848.7	1.79283	0.896416	+	0.443215i	$0.146162\pi$
$578$	−18902.5	−1.36028
$579$	−11419.5	−0.819651
$580$	−7959.89	−0.569856
$581$	4091.31	0.292145
$582$	36067.4	2.56880
$583$	12176.0	0.864974
$584$	−10943.6	−0.775430
$585$	−2774.25	−0.196070
$586$	24673.2	1.73932
$587$	8663.94	0.609198	0.304599	−	0.952481i	$-0.401478\pi$
$587$	8663.94	0.609198	0.304599	+	0.952481i	$0.401478\pi$
$588$	−23698.3	−1.66208
$589$	−1429.74	−0.100019
$590$	−16695.8	−1.16501
$591$	8405.94	0.585066
$592$	−8942.64	−0.620845
$593$	−24678.9	−1.70901	−0.854503	−	0.519446i	$-0.826138\pi$
$593$	−24678.9	−1.70901	−0.854503	+	0.519446i	$0.826138\pi$
$594$	−7496.88	−0.517846
$595$	1129.52	0.0778250
$596$	−5874.20	−0.403719
$597$	−22578.0	−1.54783
$598$	−1634.54	−0.111774
$599$	19698.4	1.34367	0.671833	−	0.740702i	$-0.265507\pi$
$599$	19698.4	1.34367	0.671833	+	0.740702i	$0.265507\pi$
$600$	3042.49	0.207015
$601$	−18449.1	−1.25217	−0.626086	−	0.779754i	$-0.715344\pi$
$601$	−18449.1	−1.25217	−0.626086	+	0.779754i	$0.715344\pi$
$602$	15937.3	1.07899
$603$	11035.5	0.745272
$604$	−26911.2	−1.81291
$605$	2478.62	0.166563
$606$	50233.9	3.36735
$607$	−11321.0	−0.757012	−0.378506	−	0.925599i	$-0.623562\pi$
$607$	−11321.0	−0.757012	−0.378506	+	0.925599i	$0.623562\pi$
$608$	8130.20	0.542308
$609$	−9728.59	−0.647327
$610$	6781.41	0.450117
$611$	1770.80	0.117248
$612$	9997.36	0.660326
$613$	712.219	0.0469270	0.0234635	−	0.999725i	$-0.492531\pi$
$613$	712.219	0.0469270	0.0234635	+	0.999725i	$0.492531\pi$
$614$	12587.4	0.827341
$615$	−16173.6	−1.06046
$616$	4024.62	0.263241
$617$	3234.25	0.211031	0.105515	−	0.994418i	$-0.466351\pi$
$617$	3234.25	0.211031	0.105515	+	0.994418i	$0.466351\pi$
$618$	7630.36	0.496663
$619$	26905.1	1.74703	0.873513	−	0.486801i	$-0.161836\pi$
$619$	26905.1	1.74703	0.873513	+	0.486801i	$0.161836\pi$
$620$	−2310.03	−0.149634
$621$	−1350.60	−0.0872750
$622$	−29233.6	−1.88451
$623$	13419.2	0.862967
$624$	−2970.78	−0.190587
$625$	625.000	0.0400000
$626$	−27702.6	−1.76872
$627$	8074.68	0.514309
$628$	1687.77	0.107244
$629$	9560.90	0.606070
$630$	6834.87	0.432235
$631$	16199.5	1.02202	0.511008	−	0.859576i	$-0.329272\pi$
$631$	16199.5	1.02202	0.511008	+	0.859576i	$0.329272\pi$
$632$	18166.3	1.14338
$633$	−37219.3	−2.33702
$634$	24961.5	1.56364
$635$	−4172.59	−0.260762
$636$	−38035.7	−2.37141
$637$	−4222.96	−0.262668
$638$	−17652.9	−1.09543
$639$	−19111.5	−1.18316
$640$	8974.92	0.554320
$641$	19943.5	1.22889	0.614446	−	0.788959i	$-0.289380\pi$
$641$	19943.5	1.22889	0.614446	+	0.788959i	$0.289380\pi$
$642$	2052.97	0.126206
$643$	−27691.0	−1.69833	−0.849164	−	0.528129i	$-0.822894\pi$
$643$	−27691.0	−1.69833	−0.849164	+	0.528129i	$0.822894\pi$
$644$	2376.01	0.145385
$645$	15765.1	0.962403
$646$	−3962.65	−0.241344
$647$	−23560.3	−1.43161	−0.715805	−	0.698300i	$-0.753940\pi$
$647$	−23560.3	−1.43161	−0.715805	+	0.698300i	$0.753940\pi$
$648$	−7305.70	−0.442893
$649$	−21846.7	−1.32136
$650$	1776.67	0.107210
$651$	−2823.32	−0.169976
$652$	−37743.0	−2.26707
$653$	5571.58	0.333894	0.166947	−	0.985966i	$-0.446609\pi$
$653$	5571.58	0.333894	0.166947	+	0.985966i	$0.446609\pi$
$654$	68110.2	4.07235
$655$	−2551.46	−0.152205
$656$	−9714.32	−0.578171
$657$	−24319.0	−1.44410
$658$	−4362.68	−0.258472
$659$	10177.4	0.601602	0.300801	−	0.953687i	$-0.402746\pi$
$659$	10177.4	0.601602	0.300801	+	0.953687i	$0.402746\pi$
$660$	13046.2	0.769430
$661$	−27413.8	−1.61312	−0.806561	−	0.591151i	$-0.798674\pi$
$661$	−27413.8	−1.61312	−0.806561	+	0.591151i	$0.798674\pi$
$662$	−28233.3	−1.65758
$663$	3176.17	0.186052
$664$	−7076.79	−0.413604
$665$	−1598.46	−0.0932113
$666$	57854.1	3.36607
$667$	−3180.25	−0.184618
$668$	−17908.2	−1.03726
$669$	38219.6	2.20875
$670$	−7067.26	−0.407511
$671$	8873.57	0.510522
$672$	16054.8	0.921616
$673$	12767.5	0.731277	0.365639	−	0.930757i	$-0.380851\pi$
$673$	12767.5	0.731277	0.365639	+	0.930757i	$0.380851\pi$
$674$	18349.3	1.04865
$675$	1468.05	0.0837112
$676$	−22315.0	−1.26963
$677$	17036.9	0.967180	0.483590	−	0.875295i	$-0.339333\pi$
$677$	17036.9	0.967180	0.483590	+	0.875295i	$0.339333\pi$
$678$	63031.7	3.57038
$679$	−9342.63	−0.528037
$680$	−1953.75	−0.110181
$681$	−21502.0	−1.20993
$682$	−5123.02	−0.287640
$683$	−510.213	−0.0285838	−0.0142919	−	0.999898i	$-0.504549\pi$
$683$	−510.213	−0.0285838	−0.0142919	+	0.999898i	$0.504549\pi$
$684$	−14147.9	−0.790875
$685$	−56.1695	−0.00313303
$686$	23999.0	1.33569
$687$	11984.8	0.665570
$688$	9468.96	0.524710
$689$	−6777.84	−0.374768
$690$	3983.47	0.219780
$691$	22793.1	1.25483	0.627416	−	0.778684i	$-0.284112\pi$
$691$	22793.1	1.25483	0.627416	+	0.778684i	$0.284112\pi$
$692$	−5438.83	−0.298776
$693$	8943.53	0.490240
$694$	−13569.6	−0.742213
$695$	8284.07	0.452134
$696$	16827.7	0.916452
$697$	10385.9	0.564412
$698$	−36924.6	−2.00232
$699$	43541.9	2.35609
$700$	−2582.62	−0.139449
$701$	26324.3	1.41834	0.709168	−	0.705039i	$-0.249071\pi$
$701$	26324.3	1.41834	0.709168	+	0.705039i	$0.249071\pi$
$702$	4173.17	0.224368
$703$	−13530.2	−0.725892
$704$	23687.2	1.26810
$705$	−4315.55	−0.230543
$706$	35419.2	1.88813
$707$	−13012.2	−0.692185
$708$	68245.2	3.62262
$709$	−10961.3	−0.580620	−0.290310	−	0.956933i	$-0.593758\pi$
$709$	−10961.3	−0.580620	−0.290310	+	0.956933i	$0.593758\pi$
$710$	12239.2	0.646944
$711$	40369.2	2.12934
$712$	−23211.3	−1.22174
$713$	−922.938	−0.0484773
$714$	−7825.07	−0.410148
$715$	2324.80	0.121598
$716$	27971.2	1.45996
$717$	21796.4	1.13529
$718$	9446.44	0.491000
$719$	−1304.68	−0.0676723	−0.0338362	−	0.999427i	$-0.510772\pi$
$719$	−1304.68	−0.0676723	−0.0338362	+	0.999427i	$0.510772\pi$
$720$	4060.87	0.210194
$721$	−1976.51	−0.102093
$722$	−24691.1	−1.27273
$723$	−43667.7	−2.24622
$724$	−11310.3	−0.580585
$725$	3456.80	0.177079
$726$	−17171.3	−0.877808
$727$	1583.59	0.0807869	0.0403934	−	0.999184i	$-0.487139\pi$
$727$	1583.59	0.0807869	0.0403934	+	0.999184i	$0.487139\pi$
$728$	−2240.32	−0.114055
$729$	−28667.3	−1.45645
$730$	15574.2	0.789626
$731$	−10123.6	−0.512223
$732$	−27719.4	−1.39964
$733$	−34351.2	−1.73095	−0.865477	−	0.500948i	$-0.832985\pi$
$733$	−34351.2	−1.73095	−0.865477	+	0.500948i	$0.832985\pi$
$734$	−19922.3	−1.00183
$735$	10291.6	0.516480
$736$	5248.27	0.262845
$737$	−9247.61	−0.462198
$738$	62846.5	3.13471
$739$	14996.6	0.746494	0.373247	−	0.927732i	$-0.378244\pi$
$739$	14996.6	0.746494	0.373247	+	0.927732i	$0.378244\pi$
$740$	−21860.8	−1.08597
$741$	−4494.80	−0.222835
$742$	16698.4	0.826171
$743$	−32781.7	−1.61863	−0.809317	−	0.587372i	$-0.800162\pi$
$743$	−32781.7	−1.61863	−0.809317	+	0.587372i	$0.800162\pi$
$744$	4883.53	0.240644
$745$	2551.03	0.125453
$746$	−14851.7	−0.728899
$747$	−15726.1	−0.770263
$748$	−8377.69	−0.409517
$749$	−531.787	−0.0259427
$750$	−4329.86	−0.210805
$751$	−24044.4	−1.16830	−0.584149	−	0.811647i	$-0.698571\pi$
$751$	−24044.4	−1.16830	−0.584149	+	0.811647i	$0.698571\pi$
$752$	−2592.04	−0.125694
$753$	−3035.16	−0.146889
$754$	9826.54	0.474617
$755$	11686.9	0.563351
$756$	−6066.26	−0.291835
$757$	−21680.9	−1.04096	−0.520479	−	0.853874i	$-0.674247\pi$
$757$	−21680.9	−1.04096	−0.520479	+	0.853874i	$0.674247\pi$
$758$	9308.15	0.446025
$759$	5212.43	0.249274
$760$	2764.87	0.131964
$761$	−10299.1	−0.490594	−0.245297	−	0.969448i	$-0.578885\pi$
$761$	−10299.1	−0.490594	−0.245297	+	0.969448i	$0.578885\pi$
$762$	28906.7	1.37425
$763$	−17642.8	−0.837105
$764$	15671.4	0.742108
$765$	−4341.62	−0.205192
$766$	6065.29	0.286094
$767$	12161.1	0.572505
$768$	−10761.7	−0.505637
$769$	28377.9	1.33073	0.665365	−	0.746518i	$-0.268276\pi$
$769$	28377.9	1.33073	0.665365	+	0.746518i	$0.268276\pi$
$770$	−5727.56	−0.268061
$771$	11574.5	0.540657
$772$	−16766.9	−0.781675
$773$	35409.5	1.64759	0.823797	−	0.566885i	$-0.191852\pi$
$773$	35409.5	1.64759	0.823797	+	0.566885i	$0.191852\pi$
$774$	−61259.2	−2.84485
$775$	1003.19	0.0464978
$776$	16160.1	0.747568
$777$	−26718.2	−1.23361
$778$	30957.3	1.42657
$779$	−14697.8	−0.675999
$780$	−7262.24	−0.333372
$781$	16015.2	0.733763
$782$	−2558.00	−0.116974
$783$	8119.58	0.370588
$784$	6181.45	0.281589
$785$	−732.959	−0.0333254
$786$	17676.0	0.802138
$787$	6117.56	0.277087	0.138544	−	0.990356i	$-0.455758\pi$
$787$	6117.56	0.277087	0.138544	+	0.990356i	$0.455758\pi$
$788$	12342.2	0.557960
$789$	1599.54	0.0721737
$790$	−25853.0	−1.16431
$791$	−16327.3	−0.733921
$792$	−15469.7	−0.694057
$793$	−4939.51	−0.221194
$794$	10612.9	0.474357
$795$	16518.0	0.736899
$796$	−33150.6	−1.47612
$797$	4099.46	0.182196	0.0910980	−	0.995842i	$-0.470962\pi$
$797$	4099.46	0.182196	0.0910980	+	0.995842i	$0.470962\pi$
$798$	11073.8	0.491236
$799$	2771.24	0.122703
$800$	−5704.64	−0.252112
$801$	−51580.3	−2.27528
$802$	−52575.6	−2.31485
$803$	20379.1	0.895594
$804$	28887.8	1.26716
$805$	−1031.85	−0.0451775
$806$	2851.75	0.124626
$807$	−54684.1	−2.38534
$808$	22507.4	0.979960
$809$	21358.6	0.928216	0.464108	−	0.885779i	$-0.346375\pi$
$809$	21358.6	0.928216	0.464108	+	0.885779i	$0.346375\pi$
$810$	10397.0	0.451002
$811$	13967.7	0.604776	0.302388	−	0.953185i	$-0.402216\pi$
$811$	13967.7	0.604776	0.302388	+	0.953185i	$0.402216\pi$
$812$	−14284.2	−0.617336
$813$	−16976.6	−0.732342
$814$	−48481.2	−2.08755
$815$	16390.9	0.704478
$816$	−4649.19	−0.199454
$817$	14326.6	0.613492
$818$	23314.8	0.996557
$819$	−4978.45	−0.212407
$820$	−23747.2	−1.01133
$821$	−22387.6	−0.951684	−0.475842	−	0.879531i	$-0.657857\pi$
$821$	−22387.6	−0.951684	−0.475842	+	0.879531i	$0.657857\pi$
$822$	389.130	0.0165115
$823$	−22615.7	−0.957877	−0.478939	−	0.877848i	$-0.658978\pi$
$823$	−22615.7	−0.957877	−0.478939	+	0.877848i	$0.658978\pi$
$824$	3418.80	0.144538
$825$	−5665.68	−0.239095
$826$	−29961.0	−1.26208
$827$	10878.0	0.457394	0.228697	−	0.973498i	$-0.426554\pi$
$827$	10878.0	0.457394	0.228697	+	0.973498i	$0.426554\pi$
$828$	−9132.86	−0.383320
$829$	27382.3	1.14720	0.573600	−	0.819136i	$-0.305547\pi$
$829$	27382.3	1.14720	0.573600	+	0.819136i	$0.305547\pi$
$830$	10071.2	0.421176
$831$	9362.74	0.390842
$832$	−13185.6	−0.549432
$833$	−6608.81	−0.274888
$834$	−57390.2	−2.38281
$835$	7777.12	0.322321
$836$	11855.8	0.490480
$837$	2356.37	0.0973096
$838$	−49459.1	−2.03883
$839$	−31799.7	−1.30852	−0.654260	−	0.756270i	$-0.727020\pi$
$839$	−31799.7	−1.30852	−0.654260	+	0.756270i	$0.727020\pi$
$840$	5459.81	0.224264
$841$	−5269.87	−0.216076
$842$	22868.0	0.935968
$843$	50859.6	2.07793
$844$	−54647.9	−2.22874
$845$	9690.89	0.394529
$846$	16769.1	0.681483
$847$	4447.94	0.180440
$848$	9921.21	0.401764
$849$	−25205.7	−1.01891
$850$	2780.43	0.112198
$851$	−8734.14	−0.351824
$852$	−50028.6	−2.01168
$853$	32016.4	1.28514	0.642568	−	0.766229i	$-0.277869\pi$
$853$	32016.4	1.28514	0.642568	+	0.766229i	$0.277869\pi$
$854$	12169.4	0.487620
$855$	6144.11	0.245759
$856$	919.839	0.0367283
$857$	25280.1	1.00764	0.503822	−	0.863807i	$-0.331927\pi$
$857$	25280.1	1.00764	0.503822	+	0.863807i	$0.331927\pi$
$858$	−16105.7	−0.640837
$859$	−22313.5	−0.886296	−0.443148	−	0.896448i	$-0.646138\pi$
$859$	−22313.5	−0.886296	−0.443148	+	0.896448i	$0.646138\pi$
$860$	23147.4	0.917813
$861$	−29023.8	−1.14881
$862$	41297.9	1.63180
$863$	−1478.28	−0.0583096	−0.0291548	−	0.999575i	$-0.509282\pi$
$863$	−1478.28	−0.0583096	−0.0291548	+	0.999575i	$0.509282\pi$
$864$	−13399.5	−0.527615
$865$	2361.96	0.0928428
$866$	19087.2	0.748970
$867$	−33554.5	−1.31438
$868$	−4145.39	−0.162101
$869$	−33829.0	−1.32056
$870$	−23947.9	−0.933230
$871$	5147.72	0.200257
$872$	30516.9	1.18513
$873$	35910.9	1.39221
$874$	3619.99	0.140101
$875$	1121.57	0.0433327
$876$	−63660.5	−2.45535
$877$	32974.6	1.26964	0.634819	−	0.772661i	$-0.281075\pi$
$877$	32974.6	1.26964	0.634819	+	0.772661i	$0.281075\pi$
$878$	−30992.6	−1.19129
$879$	43798.3	1.68064
$880$	−3402.97	−0.130357
$881$	−32000.7	−1.22376	−0.611879	−	0.790951i	$-0.709586\pi$
$881$	−32000.7	−1.22376	−0.611879	+	0.790951i	$0.709586\pi$
$882$	−39990.7	−1.52671
$883$	−44218.6	−1.68525	−0.842623	−	0.538503i	$-0.818990\pi$
$883$	−44218.6	−1.68525	−0.842623	+	0.538503i	$0.818990\pi$
$884$	4663.47	0.177432
$885$	−29637.4	−1.12570
$886$	54526.6	2.06756
$887$	27374.8	1.03625	0.518126	−	0.855304i	$-0.326630\pi$
$887$	27374.8	1.03625	0.518126	+	0.855304i	$0.326630\pi$
$888$	46214.9	1.74647
$889$	−7487.79	−0.282489
$890$	33032.7	1.24411
$891$	13604.6	0.511526
$892$	56116.7	2.10642
$893$	−3921.76	−0.146962
$894$	−17673.0	−0.661155
$895$	−12147.2	−0.453673
$896$	16105.7	0.600505
$897$	−2901.52	−0.108003
$898$	80162.2	2.97889
$899$	5548.54	0.205844
$900$	9927.02	0.367667
$901$	−10607.1	−0.392203
$902$	−52664.8	−1.94406
$903$	28290.8	1.04259
$904$	28241.5	1.03905
$905$	4911.80	0.180413
$906$	−80964.3	−2.96894
$907$	7835.16	0.286838	0.143419	−	0.989662i	$-0.454190\pi$
$907$	7835.16	0.286838	0.143419	+	0.989662i	$0.454190\pi$
$908$	−31570.7	−1.15387
$909$	50016.0	1.82500
$910$	3188.27	0.116143
$911$	−36528.6	−1.32848	−0.664241	−	0.747519i	$-0.731245\pi$
$911$	−36528.6	−1.32848	−0.664241	+	0.747519i	$0.731245\pi$
$912$	6579.36	0.238886
$913$	13178.3	0.477698
$914$	23119.8	0.836692
$915$	12037.9	0.434930
$916$	17596.8	0.634734
$917$	−4578.65	−0.164886
$918$	6530.89	0.234805
$919$	−15741.5	−0.565030	−0.282515	−	0.959263i	$-0.591169\pi$
$919$	−15741.5	−0.565030	−0.282515	+	0.959263i	$0.591169\pi$
$920$	1784.80	0.0639600
$921$	22344.4	0.799427
$922$	−10314.7	−0.368433
$923$	−8914.93	−0.317918
$924$	23411.7	0.833538
$925$	9493.63	0.337458
$926$	60271.5	2.13892
$927$	7597.26	0.269177
$928$	−31551.7	−1.11609
$929$	47428.9	1.67502	0.837510	−	0.546422i	$-0.184011\pi$
$929$	47428.9	1.67502	0.837510	+	0.546422i	$0.184011\pi$
$930$	−6949.89	−0.245049
$931$	9352.54	0.329234
$932$	63931.3	2.24693
$933$	−51893.6	−1.82092
$934$	−23175.0	−0.811895
$935$	3638.24	0.127255
$936$	8611.29	0.300714
$937$	−34978.0	−1.21951	−0.609756	−	0.792589i	$-0.708733\pi$
$937$	−34978.0	−1.21951	−0.609756	+	0.792589i	$0.708733\pi$
$938$	−12682.3	−0.441464
$939$	−49175.9	−1.70905
$940$	−6336.38	−0.219862
$941$	45144.0	1.56392	0.781962	−	0.623326i	$-0.214219\pi$
$941$	45144.0	1.56392	0.781962	+	0.623326i	$0.214219\pi$
$942$	5077.78	0.175629
$943$	−9487.83	−0.327642
$944$	−17801.0	−0.613744
$945$	2634.44	0.0906859
$946$	51334.6	1.76430
$947$	26123.6	0.896413	0.448207	−	0.893930i	$-0.352063\pi$
$947$	26123.6	0.896413	0.448207	+	0.893930i	$0.352063\pi$
$948$	105675.	3.62044
$949$	−11344.1	−0.388035
$950$	−3934.77	−0.134380
$951$	44310.0	1.51088
$952$	−3506.04	−0.119361
$953$	−22143.5	−0.752673	−0.376336	−	0.926483i	$-0.622816\pi$
$953$	−22143.5	−0.752673	−0.376336	+	0.926483i	$0.622816\pi$
$954$	−64185.0	−2.17827
$955$	−6805.72	−0.230605
$956$	32003.0	1.08269
$957$	−31336.2	−1.05847
$958$	54237.9	1.82917
$959$	−100.797	−0.00339407
$960$	32134.1	1.08034
$961$	−28180.8	−0.945949
$962$	26987.3	0.904474
$963$	2044.07	0.0684000
$964$	−64116.0	−2.14215
$965$	7281.47	0.242900
$966$	7148.42	0.238092
$967$	44869.8	1.49216	0.746078	−	0.665858i	$-0.231934\pi$
$967$	44869.8	1.49216	0.746078	+	0.665858i	$0.231934\pi$
$968$	−7693.65	−0.255458
$969$	−7034.23	−0.233201
$970$	−22997.9	−0.761254
$971$	−25048.3	−0.827845	−0.413923	−	0.910312i	$-0.635842\pi$
$971$	−25048.3	−0.827845	−0.413923	+	0.910312i	$0.635842\pi$
$972$	−60752.5	−2.00477
$973$	14865.9	0.489805
$974$	−39514.7	−1.29993
$975$	3153.82	0.103593
$976$	7230.31	0.237128
$977$	37320.7	1.22210	0.611052	−	0.791590i	$-0.290747\pi$
$977$	37320.7	1.22210	0.611052	+	0.791590i	$0.290747\pi$
$978$	−113553.	−3.71269
$979$	43223.8	1.41107
$980$	15110.9	0.492551
$981$	67814.7	2.20709
$982$	−34424.5	−1.11867
$983$	−17189.4	−0.557737	−0.278869	−	0.960329i	$-0.589959\pi$
$983$	−17189.4	−0.557737	−0.278869	+	0.960329i	$0.589959\pi$
$984$	50202.9	1.62643
$985$	−5359.93	−0.173382
$986$	15378.2	0.496697
$987$	−7744.33	−0.249752
$988$	−6599.58	−0.212511
$989$	9248.19	0.297346
$990$	22015.4	0.706764
$991$	−57797.1	−1.85266	−0.926330	−	0.376712i	$-0.877055\pi$
$991$	−57797.1	−1.85266	−0.926330	+	0.376712i	$0.877055\pi$
$992$	−9156.57	−0.293066
$993$	−50117.9	−1.60166
$994$	21963.5	0.700846
$995$	14396.5	0.458695
$996$	−41166.6	−1.30965
$997$	46801.0	1.48666	0.743331	−	0.668923i	$-0.233245\pi$
$997$	46801.0	1.48666	0.743331	+	0.668923i	$0.233245\pi$
$998$	−37891.2	−1.20183
$999$	22299.3	0.706226

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.4.a.e.1.4	✓	5
3.2	odd	2		1035.4.a.k.1.2		5
4.3	odd	2		1840.4.a.n.1.2		5
5.2	odd	4		575.4.b.i.24.9		10
5.3	odd	4		575.4.b.i.24.2		10
5.4	even	2		575.4.a.j.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.4.a.e.1.4	✓	5	1.1	even	1	trivial
575.4.a.j.1.2		5	5.4	even	2
575.4.b.i.24.2		10	5.3	odd	4
575.4.b.i.24.9		10	5.2	odd	4
1035.4.a.k.1.2		5	3.2	odd	2
1840.4.a.n.1.2		5	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	115.a (trivial)

\(f(q)\)	\(=\)	\(q+4.41740 q^{2} +7.84147 q^{3} +11.5134 q^{4} -5.00000 q^{5} +34.6389 q^{6} -8.97260 q^{7} +15.5200 q^{8} +34.4886 q^{9} -22.0870 q^{10} -28.9011 q^{11} +90.2818 q^{12} +16.0879 q^{13} -39.6355 q^{14} -39.2073 q^{15} -23.5490 q^{16} +25.1771 q^{17} +152.350 q^{18} -35.6298 q^{19} -57.5669 q^{20} -70.3583 q^{21} -127.668 q^{22} -23.0000 q^{23} +121.700 q^{24} +25.0000 q^{25} +71.0668 q^{26} +58.7218 q^{27} -103.305 q^{28} +138.272 q^{29} -173.194 q^{30} +40.1277 q^{31} -228.186 q^{32} -226.627 q^{33} +111.217 q^{34} +44.8630 q^{35} +397.081 q^{36} +379.745 q^{37} -157.391 q^{38} +126.153 q^{39} -77.6001 q^{40} +412.514 q^{41} -310.801 q^{42} -402.095 q^{43} -332.750 q^{44} -172.443 q^{45} -101.600 q^{46} +110.070 q^{47} -184.659 q^{48} -262.492 q^{49} +110.435 q^{50} +197.426 q^{51} +185.227 q^{52} -421.300 q^{53} +259.397 q^{54} +144.506 q^{55} -139.255 q^{56} -279.390 q^{57} +610.802 q^{58} +755.913 q^{59} -451.409 q^{60} -307.032 q^{61} +177.260 q^{62} -309.453 q^{63} -819.594 q^{64} -80.4396 q^{65} -1001.10 q^{66} +319.974 q^{67} +289.874 q^{68} -180.354 q^{69} +198.178 q^{70} -554.138 q^{71} +535.264 q^{72} -705.131 q^{73} +1677.48 q^{74} +196.037 q^{75} -410.219 q^{76} +259.318 q^{77} +557.268 q^{78} +1170.51 q^{79} +117.745 q^{80} -470.728 q^{81} +1822.24 q^{82} -455.978 q^{83} -810.063 q^{84} -125.886 q^{85} -1776.21 q^{86} +1084.26 q^{87} -448.546 q^{88} -1495.57 q^{89} -761.749 q^{90} -144.351 q^{91} -264.808 q^{92} +314.660 q^{93} +486.222 q^{94} +178.149 q^{95} -1789.31 q^{96} +1041.24 q^{97} -1159.53 q^{98} -996.760 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 6 q^{2} + 4 q^{3} + 22 q^{4} - 25 q^{5} + 19 q^{6} - 3 q^{7} + 138 q^{8} + 77 q^{9} - 30 q^{10} + 23 q^{11} + 47 q^{12} + 132 q^{13} + 93 q^{14} - 20 q^{15} + 282 q^{16} + 23 q^{17} - 15 q^{18} - 161 q^{19}+ \cdots + 2021 q^{99}+O(q^{100}) \) 5 * q + 6 * q^2 + 4 * q^3 + 22 * q^4 - 25 * q^5 + 19 * q^6 - 3 * q^7 + 138 * q^8 + 77 * q^9 - 30 * q^10 + 23 * q^11 + 47 * q^12 + 132 * q^13 + 93 * q^14 - 20 * q^15 + 282 * q^16 + 23 * q^17 - 15 * q^18 - 161 * q^19 - 110 * q^20 - 60 * q^21 + 193 * q^22 - 115 * q^23 + 105 * q^24 + 125 * q^25 - 257 * q^26 + 577 * q^27 + 17 * q^28 + 401 * q^29 - 95 * q^30 + 32 * q^31 + 670 * q^32 + 189 * q^33 - 663 * q^34 + 15 * q^35 - 659 * q^36 - 38 * q^37 - 875 * q^38 + 335 * q^39 - 690 * q^40 - 12 * q^41 - 798 * q^42 - 566 * q^43 + 47 * q^44 - 385 * q^45 - 138 * q^46 + 919 * q^47 - 773 * q^48 - 738 * q^49 + 150 * q^50 - 993 * q^51 - 305 * q^52 + 1156 * q^53 - 8 * q^54 - 115 * q^55 + 343 * q^56 + 114 * q^57 - 1042 * q^58 + 1324 * q^59 - 235 * q^60 - 1673 * q^61 + 565 * q^62 + 270 * q^63 + 2466 * q^64 - 660 * q^65 - 2781 * q^66 + 558 * q^67 - 2267 * q^68 - 92 * q^69 - 465 * q^70 - 108 * q^71 - 789 * q^72 + 1173 * q^73 + 1458 * q^74 + 100 * q^75 - 3477 * q^76 + 2608 * q^77 + 704 * q^78 + 656 * q^79 - 1410 * q^80 - 319 * q^81 + 3505 * q^82 - 82 * q^83 - 718 * q^84 - 115 * q^85 + 112 * q^86 + 2389 * q^87 + 2397 * q^88 + 570 * q^89 + 75 * q^90 - 1589 * q^91 - 506 * q^92 + 911 * q^93 - 948 * q^94 + 805 * q^95 - 5991 * q^96 + 633 * q^97 - 2555 * q^98 + 2021 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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