LMFDB - Embedded newform 725.4.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,4,Mod(1,725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(725, 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("725.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	725.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:	$42.7763847542$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.13458092.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 14x^{3} + 18x^{2} + 20x - 8 $ x^5 - x^4 - 14x^3 + 18x^2 + 20*x - 8
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 29)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$3.03898$ of defining polynomial
Character	$\chi$	$=$	725.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.49488 q^{2} +6.46343 q^{3} +22.1937 q^{4} +35.5158 q^{6} -20.3573 q^{7} +77.9928 q^{8} +14.7760 q^{9} +O(q^{10})$	\(q+5.49488 q^{2} +6.46343 q^{3} +22.1937 q^{4} +35.5158 q^{6} -20.3573 q^{7} +77.9928 q^{8} +14.7760 q^{9} +52.0703 q^{11} +143.448 q^{12} -7.04574 q^{13} -111.861 q^{14} +251.011 q^{16} -28.7724 q^{17} +81.1922 q^{18} +76.4208 q^{19} -131.578 q^{21} +286.120 q^{22} -59.7251 q^{23} +504.101 q^{24} -38.7155 q^{26} -79.0092 q^{27} -451.804 q^{28} -29.0000 q^{29} -3.25229 q^{31} +755.335 q^{32} +336.553 q^{33} -158.101 q^{34} +327.934 q^{36} -150.673 q^{37} +419.923 q^{38} -45.5397 q^{39} -92.3254 q^{41} -723.006 q^{42} +100.703 q^{43} +1155.63 q^{44} -328.182 q^{46} -324.003 q^{47} +1622.39 q^{48} +71.4197 q^{49} -185.969 q^{51} -156.371 q^{52} -374.774 q^{53} -434.146 q^{54} -1587.72 q^{56} +493.941 q^{57} -159.352 q^{58} +489.567 q^{59} +221.508 q^{61} -17.8709 q^{62} -300.799 q^{63} +2142.39 q^{64} +1849.32 q^{66} +427.538 q^{67} -638.567 q^{68} -386.029 q^{69} -898.999 q^{71} +1152.42 q^{72} +1087.35 q^{73} -827.929 q^{74} +1696.06 q^{76} -1060.01 q^{77} -250.235 q^{78} -798.018 q^{79} -909.622 q^{81} -507.317 q^{82} +436.713 q^{83} -2920.21 q^{84} +553.353 q^{86} -187.440 q^{87} +4061.11 q^{88} +456.763 q^{89} +143.432 q^{91} -1325.52 q^{92} -21.0209 q^{93} -1780.36 q^{94} +4882.06 q^{96} -803.714 q^{97} +392.442 q^{98} +769.390 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 8 q^{3} + 26 q^{4} + 34 q^{6} - 40 q^{7} + 84 q^{8} + 33 q^{9}+O(q^{10}) $ 5 * q - 8 * q^3 + 26 * q^4 + 34 * q^6 - 40 * q^7 + 84 * q^8 + 33 * q^9	$ 5 q - 8 q^{3} + 26 q^{4} + 34 q^{6} - 40 q^{7} + 84 q^{8} + 33 q^{9} + 12 q^{11} + 224 q^{12} - 14 q^{13} - 192 q^{14} + 146 q^{16} - 66 q^{17} + 108 q^{18} + 214 q^{19} + 98 q^{22} - 164 q^{23} + 314 q^{24} + 56 q^{26} - 362 q^{27} - 540 q^{28} - 145 q^{29} + 420 q^{31} + 652 q^{32} + 576 q^{33} + 204 q^{34} - 260 q^{36} - 378 q^{37} + 496 q^{38} - 374 q^{39} - 1158 q^{41} - 348 q^{42} + 204 q^{43} + 784 q^{44} + 580 q^{46} - 248 q^{47} + 1880 q^{48} - 283 q^{49} + 228 q^{51} - 1482 q^{52} + 554 q^{53} + 918 q^{54} - 608 q^{56} - 44 q^{57} + 440 q^{59} + 618 q^{61} - 1250 q^{62} - 804 q^{63} + 2594 q^{64} + 2940 q^{66} - 1164 q^{67} - 356 q^{68} - 1968 q^{69} - 692 q^{71} + 2648 q^{72} + 1950 q^{73} - 1832 q^{74} + 1376 q^{76} + 1616 q^{77} + 1302 q^{78} + 272 q^{79} + 1801 q^{81} - 92 q^{82} - 512 q^{83} - 3208 q^{84} + 2446 q^{86} + 232 q^{87} + 6954 q^{88} + 866 q^{89} + 2580 q^{91} - 3468 q^{92} + 40 q^{93} - 5942 q^{94} + 7386 q^{96} - 1562 q^{97} + 3408 q^{98} - 238 q^{99}+O(q^{100}) $ 5 * q - 8 * q^3 + 26 * q^4 + 34 * q^6 - 40 * q^7 + 84 * q^8 + 33 * q^9 + 12 * q^11 + 224 * q^12 - 14 * q^13 - 192 * q^14 + 146 * q^16 - 66 * q^17 + 108 * q^18 + 214 * q^19 + 98 * q^22 - 164 * q^23 + 314 * q^24 + 56 * q^26 - 362 * q^27 - 540 * q^28 - 145 * q^29 + 420 * q^31 + 652 * q^32 + 576 * q^33 + 204 * q^34 - 260 * q^36 - 378 * q^37 + 496 * q^38 - 374 * q^39 - 1158 * q^41 - 348 * q^42 + 204 * q^43 + 784 * q^44 + 580 * q^46 - 248 * q^47 + 1880 * q^48 - 283 * q^49 + 228 * q^51 - 1482 * q^52 + 554 * q^53 + 918 * q^54 - 608 * q^56 - 44 * q^57 + 440 * q^59 + 618 * q^61 - 1250 * q^62 - 804 * q^63 + 2594 * q^64 + 2940 * q^66 - 1164 * q^67 - 356 * q^68 - 1968 * q^69 - 692 * q^71 + 2648 * q^72 + 1950 * q^73 - 1832 * q^74 + 1376 * q^76 + 1616 * q^77 + 1302 * q^78 + 272 * q^79 + 1801 * q^81 - 92 * q^82 - 512 * q^83 - 3208 * q^84 + 2446 * q^86 + 232 * q^87 + 6954 * q^88 + 866 * q^89 + 2580 * q^91 - 3468 * q^92 + 40 * q^93 - 5942 * q^94 + 7386 * q^96 - 1562 * q^97 + 3408 * q^98 - 238 * 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 $

$2$	5.49488	1.94273	0.971367	−	0.237584i	$-0.0763557\pi$
$2$	5.49488	1.94273	0.971367	+	0.237584i	$0.0763557\pi$
$3$	6.46343	1.24389	0.621944	−	0.783062i	$-0.286343\pi$
$3$	6.46343	1.24389	0.621944	+	0.783062i	$0.286343\pi$
$4$	22.1937	2.77421
$5$	0	0
$5$	0	0
$6$	35.5158	2.41654
$7$	−20.3573	−1.09919	−0.549595	−	0.835431i	$-0.685218\pi$
$7$	−20.3573	−1.09919	−0.549595	+	0.835431i	$0.685218\pi$
$8$	77.9928	3.44683
$9$	14.7760	0.547258
$10$	0	0
$11$	52.0703	1.42725	0.713627	−	0.700526i	$-0.247051\pi$
$11$	52.0703	1.42725	0.713627	+	0.700526i	$0.247051\pi$
$12$	143.448	3.45081
$13$	−7.04574	−0.150318	−0.0751591	−	0.997172i	$-0.523946\pi$
$13$	−7.04574	−0.150318	−0.0751591	+	0.997172i	$0.523946\pi$
$14$	−111.861	−2.13544
$15$	0	0
$16$	251.011	3.92205
$17$	−28.7724	−0.410490	−0.205245	−	0.978711i	$-0.565799\pi$
$17$	−28.7724	−0.410490	−0.205245	+	0.978711i	$0.565799\pi$
$18$	81.1922	1.06318
$19$	76.4208	0.922744	0.461372	−	0.887207i	$-0.347357\pi$
$19$	76.4208	0.922744	0.461372	+	0.887207i	$0.347357\pi$
$20$	0	0
$21$	−131.578	−1.36727
$22$	286.120	2.77277
$23$	−59.7251	−0.541458	−0.270729	−	0.962656i	$-0.587265\pi$
$23$	−59.7251	−0.541458	−0.270729	+	0.962656i	$0.587265\pi$
$24$	504.101	4.28747
$25$	0	0
$26$	−38.7155	−0.292028
$27$	−79.0092	−0.563160
$28$	−451.804	−3.04939
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	0	0
$31$	−3.25229	−0.0188428	−0.00942142	−	0.999956i	$-0.502999\pi$
$31$	−3.25229	−0.0188428	−0.00942142	+	0.999956i	$0.502999\pi$
$32$	755.335	4.17268
$33$	336.553	1.77534
$34$	−158.101	−0.797473
$35$	0	0
$36$	327.934	1.51821
$37$	−150.673	−0.669471	−0.334736	−	0.942312i	$-0.608647\pi$
$37$	−150.673	−0.669471	−0.334736	+	0.942312i	$0.608647\pi$
$38$	419.923	1.79265
$39$	−45.5397	−0.186979
$40$	0	0
$41$	−92.3254	−0.351678	−0.175839	−	0.984419i	$-0.556264\pi$
$41$	−92.3254	−0.351678	−0.175839	+	0.984419i	$0.556264\pi$
$42$	−723.006	−2.65624
$43$	100.703	0.357142	0.178571	−	0.983927i	$-0.442852\pi$
$43$	100.703	0.357142	0.178571	+	0.983927i	$0.442852\pi$
$44$	1155.63	3.95951
$45$	0	0
$46$	−328.182	−1.05191
$47$	−324.003	−1.00555	−0.502774	−	0.864418i	$-0.667687\pi$
$47$	−324.003	−1.00555	−0.502774	+	0.864418i	$0.667687\pi$
$48$	1622.39	4.87859
$49$	71.4197	0.208221
$50$	0	0
$51$	−185.969	−0.510604
$52$	−156.371	−0.417015
$53$	−374.774	−0.971305	−0.485653	−	0.874152i	$-0.661418\pi$
$53$	−374.774	−0.971305	−0.485653	+	0.874152i	$0.661418\pi$
$54$	−434.146	−1.09407
$55$	0	0
$56$	−1587.72	−3.78872
$57$	493.941	1.14779
$58$	−159.352	−0.360757
$59$	489.567	1.08027	0.540137	−	0.841577i	$-0.318372\pi$
$59$	489.567	1.08027	0.540137	+	0.841577i	$0.318372\pi$
$60$	0	0
$61$	221.508	0.464937	0.232468	−	0.972604i	$-0.425320\pi$
$61$	221.508	0.464937	0.232468	+	0.972604i	$0.425320\pi$
$62$	−17.8709	−0.0366066
$63$	−300.799	−0.601541
$64$	2142.39	4.18435
$65$	0	0
$66$	1849.32	3.44902
$67$	427.538	0.779584	0.389792	−	0.920903i	$-0.372547\pi$
$67$	427.538	0.779584	0.389792	+	0.920903i	$0.372547\pi$
$68$	−638.567	−1.13879
$69$	−386.029	−0.673514
$70$	0	0
$71$	−898.999	−1.50270	−0.751349	−	0.659905i	$-0.770596\pi$
$71$	−898.999	−1.50270	−0.751349	+	0.659905i	$0.770596\pi$
$72$	1152.42	1.88630
$73$	1087.35	1.74335	0.871673	−	0.490087i	$-0.163035\pi$
$73$	1087.35	1.74335	0.871673	+	0.490087i	$0.163035\pi$
$74$	−827.929	−1.30060
$75$	0	0
$76$	1696.06	2.55989
$77$	−1060.01	−1.56882
$78$	−250.235	−0.363250
$79$	−798.018	−1.13651	−0.568253	−	0.822854i	$-0.692381\pi$
$79$	−798.018	−1.13651	−0.568253	+	0.822854i	$0.692381\pi$
$80$	0	0
$81$	−909.622	−1.24777
$82$	−507.317	−0.683217
$83$	436.713	0.577536	0.288768	−	0.957399i	$-0.406754\pi$
$83$	436.713	0.577536	0.288768	+	0.957399i	$0.406754\pi$
$84$	−2920.21	−3.79310
$85$	0	0
$86$	553.353	0.693833
$87$	−187.440	−0.230984
$88$	4061.11	4.91950
$89$	456.763	0.544009	0.272004	−	0.962296i	$-0.412313\pi$
$89$	456.763	0.544009	0.272004	+	0.962296i	$0.412313\pi$
$90$	0	0
$91$	143.432	0.165228
$92$	−1325.52	−1.50212
$93$	−21.0209	−0.0234384
$94$	−1780.36	−1.95351
$95$	0	0
$96$	4882.06	5.19034
$97$	−803.714	−0.841287	−0.420643	−	0.907226i	$-0.638196\pi$
$97$	−803.714	−0.841287	−0.420643	+	0.907226i	$0.638196\pi$
$98$	392.442	0.404517
$99$	769.390	0.781077
$100$	0	0
$101$	−738.800	−0.727855	−0.363928	−	0.931427i	$-0.618564\pi$
$101$	−738.800	−0.727855	−0.363928	+	0.931427i	$0.618564\pi$
$102$	−1021.87	−0.991967
$103$	−2031.60	−1.94349	−0.971743	−	0.236042i	$-0.924150\pi$
$103$	−2031.60	−1.94349	−0.971743	+	0.236042i	$0.924150\pi$
$104$	−549.517	−0.518121
$105$	0	0
$106$	−2059.34	−1.88699
$107$	−1594.33	−1.44047	−0.720233	−	0.693732i	$-0.755965\pi$
$107$	−1594.33	−1.44047	−0.720233	+	0.693732i	$0.755965\pi$
$108$	−1753.51	−1.56233
$109$	−229.668	−0.201818	−0.100909	−	0.994896i	$-0.532175\pi$
$109$	−229.668	−0.201818	−0.100909	+	0.994896i	$0.532175\pi$
$110$	0	0
$111$	−973.863	−0.832748
$112$	−5109.91	−4.31108
$113$	1584.73	1.31928	0.659640	−	0.751582i	$-0.270709\pi$
$113$	1584.73	1.31928	0.659640	+	0.751582i	$0.270709\pi$
$114$	2714.15	2.22985
$115$	0	0
$116$	−643.618	−0.515159
$117$	−104.108	−0.0822629
$118$	2690.11	2.09869
$119$	585.728	0.451207
$120$	0	0
$121$	1380.32	1.03705
$122$	1217.16	0.903248
$123$	−596.739	−0.437448
$124$	−72.1803	−0.0522741
$125$	0	0
$126$	−1652.85	−1.16863
$127$	−621.184	−0.434025	−0.217013	−	0.976169i	$-0.569631\pi$
$127$	−621.184	−0.434025	−0.217013	+	0.976169i	$0.569631\pi$
$128$	5729.47	3.95639
$129$	650.890	0.444245
$130$	0	0
$131$	−1504.34	−1.00332	−0.501659	−	0.865066i	$-0.667277\pi$
$131$	−1504.34	−1.00332	−0.501659	+	0.865066i	$0.667277\pi$
$132$	7469.36	4.92519
$133$	−1555.72	−1.01427
$134$	2349.27	1.51452
$135$	0	0
$136$	−2244.04	−1.41489
$137$	29.3812	0.0183227	0.00916135	−	0.999958i	$-0.497084\pi$
$137$	29.3812	0.0183227	0.00916135	+	0.999958i	$0.497084\pi$
$138$	−2121.18	−1.30846
$139$	1262.60	0.770450	0.385225	−	0.922823i	$-0.374124\pi$
$139$	1262.60	0.770450	0.385225	+	0.922823i	$0.374124\pi$
$140$	0	0
$141$	−2094.17	−1.25079
$142$	−4939.89	−2.91934
$143$	−366.874	−0.214542
$144$	3708.94	2.14637
$145$	0	0
$146$	5974.84	3.38686
$147$	461.616	0.259003
$148$	−3343.99	−1.85726
$149$	826.526	0.454441	0.227220	−	0.973843i	$-0.427036\pi$
$149$	826.526	0.454441	0.227220	+	0.973843i	$0.427036\pi$
$150$	0	0
$151$	−2632.03	−1.41849	−0.709243	−	0.704964i	$-0.750963\pi$
$151$	−2632.03	−1.41849	−0.709243	+	0.704964i	$0.750963\pi$
$152$	5960.27	3.18054
$153$	−425.140	−0.224644
$154$	−5824.64	−3.04781
$155$	0	0
$156$	−1010.69	−0.518720
$157$	−234.540	−0.119225	−0.0596124	−	0.998222i	$-0.518986\pi$
$157$	−234.540	−0.119225	−0.0596124	+	0.998222i	$0.518986\pi$
$158$	−4385.01	−2.20793
$159$	−2422.33	−1.20820
$160$	0	0
$161$	1215.84	0.595166
$162$	−4998.26	−2.42408
$163$	1650.78	0.793246	0.396623	−	0.917982i	$-0.370182\pi$
$163$	1650.78	0.793246	0.396623	+	0.917982i	$0.370182\pi$
$164$	−2049.04	−0.975631
$165$	0	0
$166$	2399.69	1.12200
$167$	3684.28	1.70717	0.853587	−	0.520950i	$-0.174422\pi$
$167$	3684.28	1.70717	0.853587	+	0.520950i	$0.174422\pi$
$168$	−10262.1	−4.71274
$169$	−2147.36	−0.977404
$170$	0	0
$171$	1129.19	0.504979
$172$	2234.98	0.990790
$173$	3073.58	1.35075	0.675375	−	0.737474i	$-0.263982\pi$
$173$	3073.58	1.35075	0.675375	+	0.737474i	$0.263982\pi$
$174$	−1029.96	−0.448741
$175$	0	0
$176$	13070.2	5.59776
$177$	3164.28	1.34374
$178$	2509.86	1.05686
$179$	2980.70	1.24463	0.622313	−	0.782769i	$-0.286193\pi$
$179$	2980.70	1.24463	0.622313	+	0.782769i	$0.286193\pi$
$180$	0	0
$181$	3145.07	1.29155	0.645777	−	0.763526i	$-0.276533\pi$
$181$	3145.07	1.29155	0.645777	+	0.763526i	$0.276533\pi$
$182$	788.143	0.320995
$183$	1431.70	0.578329
$184$	−4658.13	−1.86631
$185$	0	0
$186$	−115.508	−0.0455346
$187$	−1498.19	−0.585874
$188$	−7190.84	−2.78960
$189$	1608.41	0.619021
$190$	0	0
$191$	−2125.56	−0.805236	−0.402618	−	0.915368i	$-0.631900\pi$
$191$	−2125.56	−0.805236	−0.402618	+	0.915368i	$0.631900\pi$
$192$	13847.2	5.20486
$193$	−3085.29	−1.15069	−0.575347	−	0.817909i	$-0.695133\pi$
$193$	−3085.29	−1.15069	−0.575347	+	0.817909i	$0.695133\pi$
$194$	−4416.31	−1.63440
$195$	0	0
$196$	1585.07	0.577649
$197$	2484.45	0.898526	0.449263	−	0.893400i	$-0.351687\pi$
$197$	2484.45	0.898526	0.449263	+	0.893400i	$0.351687\pi$
$198$	4227.70	1.51742
$199$	5489.57	1.95550	0.977752	−	0.209764i	$-0.0672696\pi$
$199$	5489.57	1.95550	0.977752	+	0.209764i	$0.0672696\pi$
$200$	0	0
$201$	2763.37	0.969715
$202$	−4059.62	−1.41403
$203$	590.362	0.204115
$204$	−4127.33	−1.41652
$205$	0	0
$206$	−11163.4	−3.77568
$207$	−882.496	−0.296318
$208$	−1768.56	−0.589556
$209$	3979.26	1.31699
$210$	0	0
$211$	−1884.64	−0.614902	−0.307451	−	0.951564i	$-0.599476\pi$
$211$	−1884.64	−0.614902	−0.307451	+	0.951564i	$0.599476\pi$
$212$	−8317.63	−2.69461
$213$	−5810.62	−1.86919
$214$	−8760.67	−2.79844
$215$	0	0
$216$	−6162.15	−1.94112
$217$	66.2078	0.0207119
$218$	−1262.00	−0.392079
$219$	7027.99	2.16853
$220$	0	0
$221$	202.723	0.0617041
$222$	−5351.26	−1.61781
$223$	5208.50	1.56407	0.782033	−	0.623237i	$-0.214183\pi$
$223$	5208.50	1.56407	0.782033	+	0.623237i	$0.214183\pi$
$224$	−15376.6	−4.58657
$225$	0	0
$226$	8707.89	2.56301
$227$	5243.29	1.53308	0.766540	−	0.642196i	$-0.221977\pi$
$227$	5243.29	1.53308	0.766540	+	0.642196i	$0.221977\pi$
$228$	10962.4	3.18422
$229$	−846.348	−0.244228	−0.122114	−	0.992516i	$-0.538967\pi$
$229$	−846.348	−0.244228	−0.122114	+	0.992516i	$0.538967\pi$
$230$	0	0
$231$	−6851.31	−1.95144
$232$	−2261.79	−0.640060
$233$	−823.620	−0.231576	−0.115788	−	0.993274i	$-0.536939\pi$
$233$	−823.620	−0.231576	−0.115788	+	0.993274i	$0.536939\pi$
$234$	−572.059	−0.159815
$235$	0	0
$236$	10865.3	2.99691
$237$	−5157.93	−1.41369
$238$	3218.51	0.876575
$239$	−2471.50	−0.668903	−0.334452	−	0.942413i	$-0.608551\pi$
$239$	−2471.50	−0.668903	−0.334452	+	0.942413i	$0.608551\pi$
$240$	0	0
$241$	−1148.79	−0.307055	−0.153527	−	0.988144i	$-0.549063\pi$
$241$	−1148.79	−0.307055	−0.153527	+	0.988144i	$0.549063\pi$
$242$	7584.69	2.01472
$243$	−3746.03	−0.988922
$244$	4916.08	1.28983
$245$	0	0
$246$	−3279.01	−0.849846
$247$	−538.441	−0.138705
$248$	−253.655	−0.0649480
$249$	2822.67	0.718391
$250$	0	0
$251$	−1686.20	−0.424032	−0.212016	−	0.977266i	$-0.568003\pi$
$251$	−1686.20	−0.424032	−0.212016	+	0.977266i	$0.568003\pi$
$252$	−6675.84	−1.66880
$253$	−3109.91	−0.772799
$254$	−3413.33	−0.843195
$255$	0	0
$256$	14343.7	3.50188
$257$	−3593.97	−0.872318	−0.436159	−	0.899870i	$-0.643662\pi$
$257$	−3593.97	−0.872318	−0.436159	+	0.899870i	$0.643662\pi$
$258$	3576.56	0.863051
$259$	3067.29	0.735877
$260$	0	0
$261$	−428.503	−0.101623
$262$	−8266.15	−1.94918
$263$	2321.87	0.544382	0.272191	−	0.962243i	$-0.412252\pi$
$263$	2321.87	0.544382	0.272191	+	0.962243i	$0.412252\pi$
$264$	26248.7	6.11931
$265$	0	0
$266$	−8548.51	−1.97046
$267$	2952.26	0.676686
$268$	9488.66	2.16273
$269$	2365.41	0.536140	0.268070	−	0.963399i	$-0.413614\pi$
$269$	2365.41	0.536140	0.268070	+	0.963399i	$0.413614\pi$
$270$	0	0
$271$	1732.51	0.388348	0.194174	−	0.980967i	$-0.437797\pi$
$271$	1732.51	0.388348	0.194174	+	0.980967i	$0.437797\pi$
$272$	−7222.20	−1.60996
$273$	927.065	0.205526
$274$	161.446	0.0355961
$275$	0	0
$276$	−8567.42	−1.86847
$277$	688.616	0.149368	0.0746839	−	0.997207i	$-0.476205\pi$
$277$	688.616	0.149368	0.0746839	+	0.997207i	$0.476205\pi$
$278$	6937.85	1.49678
$279$	−48.0557	−0.0103119
$280$	0	0
$281$	2224.44	0.472238	0.236119	−	0.971724i	$-0.424125\pi$
$281$	2224.44	0.472238	0.236119	+	0.971724i	$0.424125\pi$
$282$	−11507.2	−2.42995
$283$	−5037.52	−1.05813	−0.529063	−	0.848582i	$-0.677457\pi$
$283$	−5037.52	−1.05813	−0.529063	+	0.848582i	$0.677457\pi$
$284$	−19952.1	−4.16881
$285$	0	0
$286$	−2015.93	−0.416798
$287$	1879.50	0.386561
$288$	11160.8	2.28353
$289$	−4085.15	−0.831498
$290$	0	0
$291$	−5194.75	−1.04647
$292$	24132.3	4.83642
$293$	6761.01	1.34806	0.674032	−	0.738702i	$-0.264561\pi$
$293$	6761.01	1.34806	0.674032	+	0.738702i	$0.264561\pi$
$294$	2536.53	0.503174
$295$	0	0
$296$	−11751.4	−2.30755
$297$	−4114.03	−0.803773
$298$	4541.66	0.882857
$299$	420.807	0.0813910
$300$	0	0
$301$	−2050.05	−0.392568
$302$	−14462.7	−2.75574
$303$	−4775.19	−0.905371
$304$	19182.5	3.61905
$305$	0	0
$306$	−2336.09	−0.436424
$307$	−8860.99	−1.64731	−0.823653	−	0.567093i	$-0.808068\pi$
$307$	−8860.99	−1.64731	−0.823653	+	0.567093i	$0.808068\pi$
$308$	−23525.6	−4.35226
$309$	−13131.1	−2.41748
$310$	0	0
$311$	4127.77	0.752619	0.376309	−	0.926494i	$-0.377193\pi$
$311$	4127.77	0.752619	0.376309	+	0.926494i	$0.377193\pi$
$312$	−3551.76	−0.644484
$313$	5384.53	0.972369	0.486184	−	0.873856i	$-0.338388\pi$
$313$	5384.53	0.972369	0.486184	+	0.873856i	$0.338388\pi$
$314$	−1288.77	−0.231622
$315$	0	0
$316$	−17711.0	−3.15291
$317$	5379.49	0.953129	0.476565	−	0.879139i	$-0.341882\pi$
$317$	5379.49	0.953129	0.476565	+	0.879139i	$0.341882\pi$
$318$	−13310.4	−2.34720
$319$	−1510.04	−0.265034
$320$	0	0
$321$	−10304.9	−1.79178
$322$	6680.90	1.15625
$323$	−2198.81	−0.378778
$324$	−20187.9	−3.46157
$325$	0	0
$326$	9070.84	1.54106
$327$	−1484.44	−0.251039
$328$	−7200.71	−1.21217
$329$	6595.83	1.10529
$330$	0	0
$331$	5825.09	0.967298	0.483649	−	0.875262i	$-0.339311\pi$
$331$	5825.09	0.967298	0.483649	+	0.875262i	$0.339311\pi$
$332$	9692.29	1.60221
$333$	−2226.34	−0.366374
$334$	20244.7	3.31658
$335$	0	0
$336$	−33027.6	−5.36251
$337$	3627.26	0.586318	0.293159	−	0.956064i	$-0.405293\pi$
$337$	3627.26	0.586318	0.293159	+	0.956064i	$0.405293\pi$
$338$	−11799.5	−1.89884
$339$	10242.8	1.64104
$340$	0	0
$341$	−169.348	−0.0268935
$342$	6204.78	0.981041
$343$	5528.64	0.870317
$344$	7854.14	1.23101
$345$	0	0
$346$	16889.0	2.62415
$347$	−1172.68	−0.181421	−0.0907104	−	0.995877i	$-0.528914\pi$
$347$	−1172.68	−0.181421	−0.0907104	+	0.995877i	$0.528914\pi$
$348$	−4159.98	−0.640800
$349$	−173.078	−0.0265463	−0.0132731	−	0.999912i	$-0.504225\pi$
$349$	−173.078	−0.0265463	−0.0132731	+	0.999912i	$0.504225\pi$
$350$	0	0
$351$	556.678	0.0846532
$352$	39330.5	5.95547
$353$	−13008.4	−1.96137	−0.980687	−	0.195582i	$-0.937340\pi$
$353$	−13008.4	−1.96137	−0.980687	+	0.195582i	$0.937340\pi$
$354$	17387.4	2.61053
$355$	0	0
$356$	10137.3	1.50920
$357$	3785.82	0.561251
$358$	16378.6	2.41798
$359$	−4487.40	−0.659710	−0.329855	−	0.944032i	$-0.607000\pi$
$359$	−4487.40	−0.659710	−0.329855	+	0.944032i	$0.607000\pi$
$360$	0	0
$361$	−1018.85	−0.148543
$362$	17281.8	2.50915
$363$	8921.60	1.28998
$364$	3183.29	0.458379
$365$	0	0
$366$	7867.02	1.12354
$367$	−1674.11	−0.238114	−0.119057	−	0.992887i	$-0.537987\pi$
$367$	−1674.11	−0.238114	−0.119057	+	0.992887i	$0.537987\pi$
$368$	−14991.7	−2.12363
$369$	−1364.20	−0.192459
$370$	0	0
$371$	7629.39	1.06765
$372$	−466.533	−0.0650231
$373$	6800.89	0.944066	0.472033	−	0.881581i	$-0.343520\pi$
$373$	6800.89	0.944066	0.472033	+	0.881581i	$0.343520\pi$
$374$	−8232.37	−1.13820
$375$	0	0
$376$	−25269.9	−3.46595
$377$	204.326	0.0279134
$378$	8838.04	1.20259
$379$	10216.7	1.38468	0.692341	−	0.721571i	$-0.256579\pi$
$379$	10216.7	1.38468	0.692341	+	0.721571i	$0.256579\pi$
$380$	0	0
$381$	−4014.98	−0.539879
$382$	−11679.7	−1.56436
$383$	7184.47	0.958509	0.479255	−	0.877676i	$-0.340907\pi$
$383$	7184.47	0.958509	0.479255	+	0.877676i	$0.340907\pi$
$384$	37032.1	4.92131
$385$	0	0
$386$	−16953.3	−2.23549
$387$	1487.99	0.195449
$388$	−17837.4	−2.33391
$389$	−3848.67	−0.501633	−0.250817	−	0.968035i	$-0.580699\pi$
$389$	−3848.67	−0.501633	−0.250817	+	0.968035i	$0.580699\pi$
$390$	0	0
$391$	1718.43	0.222263
$392$	5570.22	0.717700
$393$	−9723.18	−1.24801
$394$	13651.7	1.74560
$395$	0	0
$396$	17075.6	2.16687
$397$	1622.51	0.205117	0.102559	−	0.994727i	$-0.467297\pi$
$397$	1622.51	0.205117	0.102559	+	0.994727i	$0.467297\pi$
$398$	30164.5	3.79902
$399$	−10055.3	−1.26164
$400$	0	0
$401$	13842.9	1.72389	0.861947	−	0.506999i	$-0.169245\pi$
$401$	13842.9	1.72389	0.861947	+	0.506999i	$0.169245\pi$
$402$	15184.4	1.88390
$403$	22.9148	0.00283242
$404$	−16396.7	−2.01923
$405$	0	0
$406$	3243.97	0.396540
$407$	−7845.58	−0.955506
$408$	−14504.2	−1.75996
$409$	3357.24	0.405880	0.202940	−	0.979191i	$-0.434950\pi$
$409$	3357.24	0.405880	0.202940	+	0.979191i	$0.434950\pi$
$410$	0	0
$411$	189.904	0.0227914
$412$	−45088.7	−5.39165
$413$	−9966.26	−1.18743
$414$	−4849.21	−0.575666
$415$	0	0
$416$	−5321.89	−0.627229
$417$	8160.74	0.958353
$418$	21865.6	2.55856
$419$	1652.11	0.192627	0.0963134	−	0.995351i	$-0.469295\pi$
$419$	1652.11	0.192627	0.0963134	+	0.995351i	$0.469295\pi$
$420$	0	0
$421$	−6405.13	−0.741490	−0.370745	−	0.928735i	$-0.620898\pi$
$421$	−6405.13	−0.741490	−0.370745	+	0.928735i	$0.620898\pi$
$422$	−10355.9	−1.19459
$423$	−4787.46	−0.550294
$424$	−29229.7	−3.34792
$425$	0	0
$426$	−31928.7	−3.63133
$427$	−4509.30	−0.511054
$428$	−35384.2	−3.99616
$429$	−2371.27	−0.266867
$430$	0	0
$431$	252.536	0.0282233	0.0141116	−	0.999900i	$-0.495508\pi$
$431$	252.536	0.0282233	0.0141116	+	0.999900i	$0.495508\pi$
$432$	−19832.2	−2.20874
$433$	12779.1	1.41831	0.709153	−	0.705055i	$-0.249078\pi$
$433$	12779.1	1.41831	0.709153	+	0.705055i	$0.249078\pi$
$434$	363.804	0.0402377
$435$	0	0
$436$	−5097.18	−0.559887
$437$	−4564.24	−0.499628
$438$	38618.0	4.21287
$439$	−3760.84	−0.408873	−0.204437	−	0.978880i	$-0.565536\pi$
$439$	−3760.84	−0.408873	−0.204437	+	0.978880i	$0.565536\pi$
$440$	0	0
$441$	1055.29	0.113950
$442$	1113.94	0.119875
$443$	−3713.77	−0.398299	−0.199149	−	0.979969i	$-0.563818\pi$
$443$	−3713.77	−0.398299	−0.199149	+	0.979969i	$0.563818\pi$
$444$	−21613.6	−2.31022
$445$	0	0
$446$	28620.1	3.03856
$447$	5342.20	0.565274
$448$	−43613.2	−4.59939
$449$	−12043.9	−1.26589	−0.632947	−	0.774195i	$-0.718155\pi$
$449$	−12043.9	−1.26589	−0.632947	+	0.774195i	$0.718155\pi$
$450$	0	0
$451$	−4807.41	−0.501934
$452$	35171.0	3.65997
$453$	−17011.9	−1.76444
$454$	28811.2	2.97837
$455$	0	0
$456$	38523.8	3.95624
$457$	12995.7	1.33023	0.665113	−	0.746743i	$-0.268383\pi$
$457$	12995.7	1.33023	0.665113	+	0.746743i	$0.268383\pi$
$458$	−4650.58	−0.474470
$459$	2273.28	0.231172
$460$	0	0
$461$	7874.30	0.795538	0.397769	−	0.917486i	$-0.369785\pi$
$461$	7874.30	0.795538	0.397769	+	0.917486i	$0.369785\pi$
$462$	−37647.1	−3.79113
$463$	3466.08	0.347910	0.173955	−	0.984754i	$-0.444345\pi$
$463$	3466.08	0.347910	0.173955	+	0.984754i	$0.444345\pi$
$464$	−7279.33	−0.728307
$465$	0	0
$466$	−4525.69	−0.449890
$467$	−14835.9	−1.47007	−0.735034	−	0.678030i	$-0.762834\pi$
$467$	−14835.9	−1.47007	−0.735034	+	0.678030i	$0.762834\pi$
$468$	−2310.54	−0.228215
$469$	−8703.53	−0.856912
$470$	0	0
$471$	−1515.93	−0.148302
$472$	38182.7	3.72352
$473$	5243.66	0.509733
$474$	−28342.2	−2.74642
$475$	0	0
$476$	12999.5	1.25175
$477$	−5537.65	−0.531555
$478$	−13580.6	−1.29950
$479$	8119.86	0.774542	0.387271	−	0.921966i	$-0.373418\pi$
$479$	8119.86	0.774542	0.387271	+	0.921966i	$0.373418\pi$
$480$	0	0
$481$	1061.60	0.100634
$482$	−6312.48	−0.596526
$483$	7858.51	0.740320
$484$	30634.4	2.87701
$485$	0	0
$486$	−20584.0	−1.92121
$487$	−9698.92	−0.902464	−0.451232	−	0.892407i	$-0.649015\pi$
$487$	−9698.92	−0.902464	−0.451232	+	0.892407i	$0.649015\pi$
$488$	17276.0	1.60256
$489$	10669.7	0.986709
$490$	0	0
$491$	−6844.25	−0.629076	−0.314538	−	0.949245i	$-0.601850\pi$
$491$	−6844.25	−0.629076	−0.314538	+	0.949245i	$0.601850\pi$
$492$	−13243.9	−1.21358
$493$	834.400	0.0762261
$494$	−2958.67	−0.269467
$495$	0	0
$496$	−816.361	−0.0739026
$497$	18301.2	1.65175
$498$	15510.2	1.39564
$499$	−18603.4	−1.66895	−0.834473	−	0.551049i	$-0.814228\pi$
$499$	−18603.4	−1.66895	−0.834473	+	0.551049i	$0.814228\pi$
$500$	0	0
$501$	23813.1	2.12353
$502$	−9265.47	−0.823781
$503$	−10624.8	−0.941822	−0.470911	−	0.882181i	$-0.656075\pi$
$503$	−10624.8	−0.941822	−0.470911	+	0.882181i	$0.656075\pi$
$504$	−23460.1	−2.07341
$505$	0	0
$506$	−17088.6	−1.50134
$507$	−13879.3	−1.21578
$508$	−13786.4	−1.20408
$509$	−7931.22	−0.690658	−0.345329	−	0.938482i	$-0.612233\pi$
$509$	−7931.22	−0.690658	−0.345329	+	0.938482i	$0.612233\pi$
$510$	0	0
$511$	−22135.4	−1.91627
$512$	32981.1	2.84682
$513$	−6037.95	−0.519653
$514$	−19748.4	−1.69468
$515$	0	0
$516$	14445.7	1.23243
$517$	−16871.0	−1.43517
$518$	16854.4	1.42961
$519$	19865.9	1.68018
$520$	0	0
$521$	13771.1	1.15801	0.579005	−	0.815324i	$-0.303441\pi$
$521$	13771.1	1.15801	0.579005	+	0.815324i	$0.303441\pi$
$522$	−2354.57	−0.197427
$523$	−20397.1	−1.70536	−0.852680	−	0.522433i	$-0.825024\pi$
$523$	−20397.1	−1.70536	−0.852680	+	0.522433i	$0.825024\pi$
$524$	−33386.8	−2.78342
$525$	0	0
$526$	12758.4	1.05759
$527$	93.5761	0.00773480
$528$	84478.6	6.96299
$529$	−8599.91	−0.706823
$530$	0	0
$531$	7233.83	0.591189
$532$	−34527.3	−2.81381
$533$	650.501	0.0528636
$534$	16222.3	1.31462
$535$	0	0
$536$	33344.9	2.68709
$537$	19265.6	1.54817
$538$	12997.7	1.04158
$539$	3718.85	0.297184
$540$	0	0
$541$	1883.72	0.149699	0.0748496	−	0.997195i	$-0.476152\pi$
$541$	1883.72	0.149699	0.0748496	+	0.997195i	$0.476152\pi$
$542$	9519.92	0.754457
$543$	20328.0	1.60655
$544$	−21732.8	−1.71284
$545$	0	0
$546$	5094.11	0.399282
$547$	9079.06	0.709676	0.354838	−	0.934928i	$-0.384536\pi$
$547$	9079.06	0.709676	0.354838	+	0.934928i	$0.384536\pi$
$548$	652.079	0.0508311
$549$	3272.99	0.254440
$550$	0	0
$551$	−2216.20	−0.171349
$552$	−30107.5	−2.32148
$553$	16245.5	1.24924
$554$	3783.86	0.290182
$555$	0	0
$556$	28021.8	2.13739
$557$	5982.38	0.455084	0.227542	−	0.973768i	$-0.426931\pi$
$557$	5982.38	0.455084	0.227542	+	0.973768i	$0.426931\pi$
$558$	−264.060	−0.0200333
$559$	−709.530	−0.0536850
$560$	0	0
$561$	−9683.44	−0.728762
$562$	12223.0	0.917432
$563$	7837.88	0.586727	0.293363	−	0.956001i	$-0.405225\pi$
$563$	7837.88	0.586727	0.293363	+	0.956001i	$0.405225\pi$
$564$	−46477.5	−3.46996
$565$	0	0
$566$	−27680.6	−2.05566
$567$	18517.4	1.37153
$568$	−70115.4	−5.17954
$569$	10019.2	0.738182	0.369091	−	0.929393i	$-0.379669\pi$
$569$	10019.2	0.738182	0.369091	+	0.929393i	$0.379669\pi$
$570$	0	0
$571$	8832.38	0.647327	0.323663	−	0.946172i	$-0.395085\pi$
$571$	8832.38	0.647327	0.323663	+	0.946172i	$0.395085\pi$
$572$	−8142.30	−0.595186
$573$	−13738.4	−1.00162
$574$	10327.6	0.750986
$575$	0	0
$576$	31655.8	2.28992
$577$	17583.3	1.26863	0.634317	−	0.773073i	$-0.281281\pi$
$577$	17583.3	1.26863	0.634317	+	0.773073i	$0.281281\pi$
$578$	−22447.4	−1.61538
$579$	−19941.6	−1.43133
$580$	0	0
$581$	−8890.30	−0.634823
$582$	−28544.6	−2.03301
$583$	−19514.6	−1.38630
$584$	84805.2	6.00901
$585$	0	0
$586$	37151.0	2.61893
$587$	10120.7	0.711630	0.355815	−	0.934556i	$-0.384203\pi$
$587$	10120.7	0.711630	0.355815	+	0.934556i	$0.384203\pi$
$588$	10245.0	0.718530
$589$	−248.543	−0.0173871
$590$	0	0
$591$	16058.1	1.11767
$592$	−37820.6	−2.62570
$593$	−3597.06	−0.249095	−0.124548	−	0.992214i	$-0.539748\pi$
$593$	−3597.06	−0.249095	−0.124548	+	0.992214i	$0.539748\pi$
$594$	−22606.1	−1.56152
$595$	0	0
$596$	18343.7	1.26072
$597$	35481.5	2.43243
$598$	2312.29	0.158121
$599$	−7987.90	−0.544870	−0.272435	−	0.962174i	$-0.587829\pi$
$599$	−7987.90	−0.544870	−0.272435	+	0.962174i	$0.587829\pi$
$600$	0	0
$601$	2646.60	0.179629	0.0898147	−	0.995958i	$-0.471373\pi$
$601$	2646.60	0.179629	0.0898147	+	0.995958i	$0.471373\pi$
$602$	−11264.8	−0.762655
$603$	6317.29	0.426634
$604$	−58414.5	−3.93518
$605$	0	0
$606$	−26239.1	−1.75889
$607$	15181.8	1.01517	0.507587	−	0.861600i	$-0.330537\pi$
$607$	15181.8	1.01517	0.507587	+	0.861600i	$0.330537\pi$
$608$	57723.3	3.85031
$609$	3815.76	0.253896
$610$	0	0
$611$	2282.84	0.151152
$612$	−9435.44	−0.623211
$613$	9721.86	0.640558	0.320279	−	0.947323i	$-0.396223\pi$
$613$	9721.86	0.640558	0.320279	+	0.947323i	$0.396223\pi$
$614$	−48690.1	−3.20028
$615$	0	0
$616$	−82673.2	−5.40747
$617$	14150.2	0.923282	0.461641	−	0.887067i	$-0.347261\pi$
$617$	14150.2	0.923282	0.461641	+	0.887067i	$0.347261\pi$
$618$	−72153.7	−4.69652
$619$	−10804.4	−0.701560	−0.350780	−	0.936458i	$-0.614083\pi$
$619$	−10804.4	−0.701560	−0.350780	+	0.936458i	$0.614083\pi$
$620$	0	0
$621$	4718.83	0.304928
$622$	22681.6	1.46214
$623$	−9298.46	−0.597970
$624$	−11431.0	−0.733341
$625$	0	0
$626$	29587.3	1.88905
$627$	25719.7	1.63819
$628$	−5205.30	−0.330755
$629$	4335.22	0.274811
$630$	0	0
$631$	20692.1	1.30545	0.652725	−	0.757595i	$-0.273626\pi$
$631$	20692.1	1.30545	0.652725	+	0.757595i	$0.273626\pi$
$632$	−62239.6	−3.91734
$633$	−12181.3	−0.764869
$634$	29559.6	1.85168
$635$	0	0
$636$	−53760.5	−3.35179
$637$	−503.204	−0.0312993
$638$	−8297.49	−0.514891
$639$	−13283.6	−0.822364
$640$	0	0
$641$	−1995.59	−0.122966	−0.0614828	−	0.998108i	$-0.519583\pi$
$641$	−1995.59	−0.122966	−0.0614828	+	0.998108i	$0.519583\pi$
$642$	−56624.0	−3.48095
$643$	−10911.2	−0.669203	−0.334602	−	0.942360i	$-0.608602\pi$
$643$	−10911.2	−0.669203	−0.334602	+	0.942360i	$0.608602\pi$
$644$	26984.0	1.65112
$645$	0	0
$646$	−12082.2	−0.735864
$647$	−20046.3	−1.21808	−0.609042	−	0.793138i	$-0.708446\pi$
$647$	−20046.3	−1.21808	−0.609042	+	0.793138i	$0.708446\pi$
$648$	−70943.9	−4.30083
$649$	25491.9	1.54183
$650$	0	0
$651$	427.930	0.0257633
$652$	36636.9	2.20063
$653$	−20205.6	−1.21088	−0.605441	−	0.795890i	$-0.707003\pi$
$653$	−20205.6	−1.21088	−0.605441	+	0.795890i	$0.707003\pi$
$654$	−8156.84	−0.487703
$655$	0	0
$656$	−23174.7	−1.37930
$657$	16066.6	0.954061
$658$	36243.3	2.14728
$659$	−9268.73	−0.547888	−0.273944	−	0.961746i	$-0.588328\pi$
$659$	−9268.73	−0.547888	−0.273944	+	0.961746i	$0.588328\pi$
$660$	0	0
$661$	−18209.9	−1.07153	−0.535765	−	0.844367i	$-0.679977\pi$
$661$	−18209.9	−1.07153	−0.535765	+	0.844367i	$0.679977\pi$
$662$	32008.1	1.87920
$663$	1310.29	0.0767531
$664$	34060.5	1.99067
$665$	0	0
$666$	−12233.4	−0.711767
$667$	1732.03	0.100546
$668$	81767.8	4.73607
$669$	33664.8	1.94552
$670$	0	0
$671$	11534.0	0.663583
$672$	−99385.5	−5.70518
$673$	63.9154	0.00366086	0.00183043	−	0.999998i	$-0.499417\pi$
$673$	63.9154	0.00366086	0.00183043	+	0.999998i	$0.499417\pi$
$674$	19931.3	1.13906
$675$	0	0
$676$	−47657.8	−2.71153
$677$	−11436.2	−0.649231	−0.324616	−	0.945846i	$-0.605235\pi$
$677$	−11436.2	−0.649231	−0.324616	+	0.945846i	$0.605235\pi$
$678$	56282.9	3.18810
$679$	16361.5	0.924735
$680$	0	0
$681$	33889.6	1.90698
$682$	−930.545	−0.0522470
$683$	22719.5	1.27282	0.636410	−	0.771351i	$-0.280419\pi$
$683$	22719.5	1.27282	0.636410	+	0.771351i	$0.280419\pi$
$684$	25061.0	1.40092
$685$	0	0
$686$	30379.2	1.69079
$687$	−5470.31	−0.303793
$688$	25277.7	1.40073
$689$	2640.56	0.146005
$690$	0	0
$691$	10495.0	0.577783	0.288891	−	0.957362i	$-0.406713\pi$
$691$	10495.0	0.577783	0.288891	+	0.957362i	$0.406713\pi$
$692$	68214.1	3.74727
$693$	−15662.7	−0.858552
$694$	−6443.76	−0.352452
$695$	0	0
$696$	−14618.9	−0.796163
$697$	2656.42	0.144360
$698$	−951.043	−0.0515723
$699$	−5323.41	−0.288054
$700$	0	0
$701$	−6530.49	−0.351859	−0.175930	−	0.984403i	$-0.556293\pi$
$701$	−6530.49	−0.351859	−0.175930	+	0.984403i	$0.556293\pi$
$702$	3058.88	0.164459
$703$	−11514.5	−0.617751
$704$	111555.	5.97212
$705$	0	0
$706$	−71479.4	−3.81043
$707$	15040.0	0.800052
$708$	70227.2	3.72782
$709$	−16597.7	−0.879183	−0.439591	−	0.898198i	$-0.644877\pi$
$709$	−16597.7	−0.879183	−0.439591	+	0.898198i	$0.644877\pi$
$710$	0	0
$711$	−11791.5	−0.621962
$712$	35624.2	1.87510
$713$	194.243	0.0102026
$714$	20802.6	1.09036
$715$	0	0
$716$	66152.8	3.45286
$717$	−15974.4	−0.832041
$718$	−24657.7	−1.28164
$719$	6525.25	0.338457	0.169229	−	0.985577i	$-0.445872\pi$
$719$	6525.25	0.338457	0.169229	+	0.985577i	$0.445872\pi$
$720$	0	0
$721$	41357.8	2.13626
$722$	−5598.48	−0.288579
$723$	−7425.14	−0.381942
$724$	69800.8	3.58305
$725$	0	0
$726$	49023.1	2.50609
$727$	−1066.84	−0.0544249	−0.0272125	−	0.999630i	$-0.508663\pi$
$727$	−1066.84	−0.0544249	−0.0272125	+	0.999630i	$0.508663\pi$
$728$	11186.7	0.569514
$729$	347.561	0.0176579
$730$	0	0
$731$	−2897.48	−0.146603
$732$	31774.7	1.60441
$733$	6226.75	0.313765	0.156883	−	0.987617i	$-0.449856\pi$
$733$	6226.75	0.313765	0.156883	+	0.987617i	$0.449856\pi$
$734$	−9199.02	−0.462592
$735$	0	0
$736$	−45112.4	−2.25933
$737$	22262.1	1.11266
$738$	−7496.10	−0.373896
$739$	31226.3	1.55437	0.777183	−	0.629274i	$-0.216648\pi$
$739$	31226.3	1.55437	0.777183	+	0.629274i	$0.216648\pi$
$740$	0	0
$741$	−3480.18	−0.172534
$742$	41922.6	2.07416
$743$	30790.4	1.52031	0.760156	−	0.649741i	$-0.225123\pi$
$743$	30790.4	1.52031	0.760156	+	0.649741i	$0.225123\pi$
$744$	−1639.48	−0.0807881
$745$	0	0
$746$	37370.1	1.83407
$747$	6452.86	0.316061
$748$	−33250.4	−1.62534
$749$	32456.3	1.58335
$750$	0	0
$751$	11908.0	0.578598	0.289299	−	0.957239i	$-0.406578\pi$
$751$	11908.0	0.578598	0.289299	+	0.957239i	$0.406578\pi$
$752$	−81328.5	−3.94381
$753$	−10898.6	−0.527448
$754$	1122.75	0.0542283
$755$	0	0
$756$	35696.7	1.71730
$757$	7197.74	0.345583	0.172792	−	0.984958i	$-0.444721\pi$
$757$	7197.74	0.345583	0.172792	+	0.984958i	$0.444721\pi$
$758$	56139.3	2.69007
$759$	−20100.7	−0.961275
$760$	0	0
$761$	9185.20	0.437534	0.218767	−	0.975777i	$-0.429797\pi$
$761$	9185.20	0.437534	0.218767	+	0.975777i	$0.429797\pi$
$762$	−22061.9	−1.04884
$763$	4675.42	0.221837
$764$	−47174.1	−2.23390
$765$	0	0
$766$	39477.8	1.86213
$767$	−3449.36	−0.162385
$768$	92709.4	4.35594
$769$	32791.1	1.53768	0.768840	−	0.639441i	$-0.220834\pi$
$769$	32791.1	1.53768	0.768840	+	0.639441i	$0.220834\pi$
$770$	0	0
$771$	−23229.4	−1.08507
$772$	−68474.0	−3.19227
$773$	28237.1	1.31386	0.656932	−	0.753950i	$-0.271854\pi$
$773$	28237.1	1.31386	0.656932	+	0.753950i	$0.271854\pi$
$774$	8176.33	0.379706
$775$	0	0
$776$	−62683.9	−2.89977
$777$	19825.2	0.915349
$778$	−21148.0	−0.974540
$779$	−7055.58	−0.324509
$780$	0	0
$781$	−46811.2	−2.14473
$782$	9442.59	0.431798
$783$	2291.27	0.104576
$784$	17927.1	0.816652
$785$	0	0
$786$	−53427.7	−2.42456
$787$	−12082.3	−0.547254	−0.273627	−	0.961836i	$-0.588223\pi$
$787$	−12082.3	−0.547254	−0.273627	+	0.961836i	$0.588223\pi$
$788$	55139.1	2.49270
$789$	15007.2	0.677151
$790$	0	0
$791$	−32260.8	−1.45014
$792$	60006.8	2.69224
$793$	−1560.68	−0.0698884
$794$	8915.52	0.398489
$795$	0	0
$796$	121834.	5.42499
$797$	1248.33	0.0554807	0.0277404	−	0.999615i	$-0.491169\pi$
$797$	1248.33	0.0554807	0.0277404	+	0.999615i	$0.491169\pi$
$798$	−55252.7	−2.45103
$799$	9322.35	0.412767
$800$	0	0
$801$	6749.12	0.297713
$802$	76065.1	3.34907
$803$	56618.5	2.48820
$804$	61329.4	2.69020
$805$	0	0
$806$	125.914	0.00550264
$807$	15288.7	0.666898
$808$	−57621.1	−2.50879
$809$	−23512.6	−1.02183	−0.510914	−	0.859632i	$-0.670693\pi$
$809$	−23512.6	−1.02183	−0.510914	+	0.859632i	$0.670693\pi$
$810$	0	0
$811$	23248.4	1.00661	0.503306	−	0.864108i	$-0.332117\pi$
$811$	23248.4	1.00661	0.503306	+	0.864108i	$0.332117\pi$
$812$	13102.3	0.566258
$813$	11197.9	0.483062
$814$	−43110.5	−1.85629
$815$	0	0
$816$	−46680.2	−2.00261
$817$	7695.84	0.329551
$818$	18447.6	0.788516
$819$	2119.35	0.0904226
$820$	0	0
$821$	26898.0	1.14342	0.571708	−	0.820457i	$-0.306281\pi$
$821$	26898.0	1.14342	0.571708	+	0.820457i	$0.306281\pi$
$822$	1043.50	0.0442776
$823$	−12422.7	−0.526158	−0.263079	−	0.964774i	$-0.584738\pi$
$823$	−12422.7	−0.526158	−0.263079	+	0.964774i	$0.584738\pi$
$824$	−158450.	−6.69886
$825$	0	0
$826$	−54763.4	−2.30686
$827$	4915.14	0.206670	0.103335	−	0.994647i	$-0.467049\pi$
$827$	4915.14	0.206670	0.103335	+	0.994647i	$0.467049\pi$
$828$	−19585.9	−0.822048
$829$	−45226.4	−1.89478	−0.947392	−	0.320074i	$-0.896292\pi$
$829$	−45226.4	−1.89478	−0.947392	+	0.320074i	$0.896292\pi$
$830$	0	0
$831$	4450.82	0.185797
$832$	−15094.7	−0.628983
$833$	−2054.92	−0.0854725
$834$	44842.3	1.86183
$835$	0	0
$836$	88314.5	3.65362
$837$	256.961	0.0106115
$838$	9078.13	0.374223
$839$	3982.56	0.163877	0.0819387	−	0.996637i	$-0.473889\pi$
$839$	3982.56	0.163877	0.0819387	+	0.996637i	$0.473889\pi$
$840$	0	0
$841$	841.000	0.0344828
$842$	−35195.5	−1.44052
$843$	14377.5	0.587411
$844$	−41827.3	−1.70587
$845$	0	0
$846$	−26306.5	−1.06907
$847$	−28099.6	−1.13992
$848$	−94072.5	−3.80951
$849$	−32559.7	−1.31619
$850$	0	0
$851$	8998.94	0.362491
$852$	−128959.	−5.18553
$853$	37142.6	1.49090	0.745450	−	0.666562i	$-0.232235\pi$
$853$	37142.6	1.49090	0.745450	+	0.666562i	$0.232235\pi$
$854$	−24778.0	−0.992842
$855$	0	0
$856$	−124346.	−4.96504
$857$	−18690.5	−0.744990	−0.372495	−	0.928034i	$-0.621498\pi$
$857$	−18690.5	−0.744990	−0.372495	+	0.928034i	$0.621498\pi$
$858$	−13029.8	−0.518451
$859$	−22852.1	−0.907687	−0.453843	−	0.891081i	$-0.649947\pi$
$859$	−22852.1	−0.907687	−0.453843	+	0.891081i	$0.649947\pi$
$860$	0	0
$861$	12148.0	0.480839
$862$	1387.65	0.0548303
$863$	−41976.4	−1.65573	−0.827865	−	0.560928i	$-0.810445\pi$
$863$	−41976.4	−1.65573	−0.827865	+	0.560928i	$0.810445\pi$
$864$	−59678.4	−2.34988
$865$	0	0
$866$	70219.9	2.75539
$867$	−26404.1	−1.03429
$868$	1469.40	0.0574592
$869$	−41553.0	−1.62208
$870$	0	0
$871$	−3012.32	−0.117186
$872$	−17912.4	−0.695633
$873$	−11875.7	−0.460401
$874$	−25080.0	−0.970644
$875$	0	0
$876$	155977.	6.01596
$877$	−44394.0	−1.70932	−0.854662	−	0.519184i	$-0.826236\pi$
$877$	−44394.0	−1.70932	−0.854662	+	0.519184i	$0.826236\pi$
$878$	−20665.4	−0.794331
$879$	43699.4	1.67684
$880$	0	0
$881$	−6337.13	−0.242342	−0.121171	−	0.992632i	$-0.538665\pi$
$881$	−6337.13	−0.242342	−0.121171	+	0.992632i	$0.538665\pi$
$882$	5798.72	0.221375
$883$	2834.24	0.108018	0.0540090	−	0.998540i	$-0.482800\pi$
$883$	2834.24	0.108018	0.0540090	+	0.998540i	$0.482800\pi$
$884$	4499.17	0.171181
$885$	0	0
$886$	−20406.7	−0.773788
$887$	−76.3532	−0.00289029	−0.00144515	−	0.999999i	$-0.500460\pi$
$887$	−76.3532	−0.00289029	−0.00144515	+	0.999999i	$0.500460\pi$
$888$	−75954.3	−2.87034
$889$	12645.6	0.477077
$890$	0	0
$891$	−47364.3	−1.78088
$892$	115596.	4.33905
$893$	−24760.6	−0.927863
$894$	29354.7	1.09818
$895$	0	0
$896$	−116637.	−4.34883
$897$	2719.86	0.101241
$898$	−66179.7	−2.45929
$899$	94.3163	0.00349903
$900$	0	0
$901$	10783.2	0.398711
$902$	−26416.2	−0.975124
$903$	−13250.4	−0.488310
$904$	123597.	4.54733
$905$	0	0
$906$	−93478.6	−3.42783
$907$	−18209.7	−0.666641	−0.333320	−	0.942814i	$-0.608169\pi$
$907$	−18209.7	−0.666641	−0.333320	+	0.942814i	$0.608169\pi$
$908$	116368.	4.25309
$909$	−10916.5	−0.398325
$910$	0	0
$911$	33348.8	1.21284	0.606419	−	0.795145i	$-0.292605\pi$
$911$	33348.8	1.21284	0.606419	+	0.795145i	$0.292605\pi$
$912$	123985.	4.50170
$913$	22739.8	0.824291
$914$	71409.8	2.58427
$915$	0	0
$916$	−18783.6	−0.677541
$917$	30624.2	1.10284
$918$	12491.4	0.449105
$919$	20190.6	0.724730	0.362365	−	0.932036i	$-0.381969\pi$
$919$	20190.6	0.724730	0.362365	+	0.932036i	$0.381969\pi$
$920$	0	0
$921$	−57272.4	−2.04907
$922$	43268.4	1.54552
$923$	6334.11	0.225883
$924$	−152056.	−5.41372
$925$	0	0
$926$	19045.7	0.675897
$927$	−30018.8	−1.06359
$928$	−21904.7	−0.774846
$929$	9089.58	0.321011	0.160506	−	0.987035i	$-0.448688\pi$
$929$	9089.58	0.321011	0.160506	+	0.987035i	$0.448688\pi$
$930$	0	0
$931$	5457.95	0.192134
$932$	−18279.2	−0.642440
$933$	26679.6	0.936173
$934$	−81521.3	−2.85595
$935$	0	0
$936$	−8119.64	−0.283546
$937$	−39646.5	−1.38228	−0.691140	−	0.722721i	$-0.742891\pi$
$937$	−39646.5	−1.38228	−0.691140	+	0.722721i	$0.742891\pi$
$938$	−47824.8	−1.66475
$939$	34802.5	1.20952
$940$	0	0
$941$	−51013.4	−1.76726	−0.883629	−	0.468188i	$-0.844907\pi$
$941$	−51013.4	−1.76726	−0.883629	+	0.468188i	$0.844907\pi$
$942$	−8329.86	−0.288112
$943$	5514.14	0.190419
$944$	122887.	4.23689
$945$	0	0
$946$	28813.3	0.990276
$947$	−43867.1	−1.50527	−0.752634	−	0.658439i	$-0.771217\pi$
$947$	−43867.1	−1.50527	−0.752634	+	0.658439i	$0.771217\pi$
$948$	−114474.	−3.92187
$949$	−7661.16	−0.262057
$950$	0	0
$951$	34769.9	1.18559
$952$	45682.6	1.55523
$953$	4167.10	0.141643	0.0708214	−	0.997489i	$-0.477438\pi$
$953$	4167.10	0.141643	0.0708214	+	0.997489i	$0.477438\pi$
$954$	−30428.7	−1.03267
$955$	0	0
$956$	−54851.7	−1.85568
$957$	−9760.04	−0.329673
$958$	44617.6	1.50473
$959$	−598.123	−0.0201401
$960$	0	0
$961$	−29780.4	−0.999645
$962$	5833.37	0.195505
$963$	−23557.8	−0.788307
$964$	−25496.0	−0.851836
$965$	0	0
$966$	43181.6	1.43824
$967$	21935.0	0.729454	0.364727	−	0.931115i	$-0.381162\pi$
$967$	21935.0	0.729454	0.364727	+	0.931115i	$0.381162\pi$
$968$	107655.	3.57455
$969$	−14211.9	−0.471157
$970$	0	0
$971$	−24169.6	−0.798805	−0.399403	−	0.916776i	$-0.630782\pi$
$971$	−24169.6	−0.798805	−0.399403	+	0.916776i	$0.630782\pi$
$972$	−83138.4	−2.74348
$973$	−25703.2	−0.846871
$974$	−53294.4	−1.75325
$975$	0	0
$976$	55600.9	1.82351
$977$	−16106.2	−0.527415	−0.263707	−	0.964603i	$-0.584945\pi$
$977$	−16106.2	−0.527415	−0.263707	+	0.964603i	$0.584945\pi$
$978$	58628.7	1.91691
$979$	23783.8	0.776439
$980$	0	0
$981$	−3393.57	−0.110447
$982$	−37608.3	−1.22213
$983$	22527.2	0.730933	0.365466	−	0.930825i	$-0.380910\pi$
$983$	22527.2	0.730933	0.365466	+	0.930825i	$0.380910\pi$
$984$	−46541.3	−1.50781
$985$	0	0
$986$	4584.93	0.148087
$987$	42631.7	1.37486
$988$	−11950.0	−0.384798
$989$	−6014.52	−0.193378
$990$	0	0
$991$	8337.94	0.267269	0.133634	−	0.991031i	$-0.457335\pi$
$991$	8337.94	0.267269	0.133634	+	0.991031i	$0.457335\pi$
$992$	−2456.57	−0.0786251
$993$	37650.1	1.20321
$994$	100563.	3.20891
$995$	0	0
$996$	62645.5	1.99297
$997$	18827.2	0.598058	0.299029	−	0.954244i	$-0.403337\pi$
$997$	18827.2	0.598058	0.299029	+	0.954244i	$0.403337\pi$
$998$	−102224.	−3.24232
$999$	11904.5	0.377020

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.4.a.c.1.5		5
5.4	even	2		29.4.a.b.1.1	✓	5
15.14	odd	2		261.4.a.f.1.5		5
20.19	odd	2		464.4.a.l.1.5		5
35.34	odd	2		1421.4.a.e.1.1		5
40.19	odd	2		1856.4.a.bb.1.1		5
40.29	even	2		1856.4.a.y.1.5		5
145.144	even	2		841.4.a.b.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.4.a.b.1.1	✓	5	5.4	even	2
261.4.a.f.1.5		5	15.14	odd	2
464.4.a.l.1.5		5	20.19	odd	2
725.4.a.c.1.5		5	1.1	even	1	trivial
841.4.a.b.1.5		5	145.144	even	2
1421.4.a.e.1.1		5	35.34	odd	2
1856.4.a.y.1.5		5	40.29	even	2
1856.4.a.bb.1.1		5	40.19	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:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	725.a (trivial)

\(f(q)\)	\(=\)	\(q+5.49488 q^{2} +6.46343 q^{3} +22.1937 q^{4} +35.5158 q^{6} -20.3573 q^{7} +77.9928 q^{8} +14.7760 q^{9} +O(q^{10})\)	\(q+5.49488 q^{2} +6.46343 q^{3} +22.1937 q^{4} +35.5158 q^{6} -20.3573 q^{7} +77.9928 q^{8} +14.7760 q^{9} +52.0703 q^{11} +143.448 q^{12} -7.04574 q^{13} -111.861 q^{14} +251.011 q^{16} -28.7724 q^{17} +81.1922 q^{18} +76.4208 q^{19} -131.578 q^{21} +286.120 q^{22} -59.7251 q^{23} +504.101 q^{24} -38.7155 q^{26} -79.0092 q^{27} -451.804 q^{28} -29.0000 q^{29} -3.25229 q^{31} +755.335 q^{32} +336.553 q^{33} -158.101 q^{34} +327.934 q^{36} -150.673 q^{37} +419.923 q^{38} -45.5397 q^{39} -92.3254 q^{41} -723.006 q^{42} +100.703 q^{43} +1155.63 q^{44} -328.182 q^{46} -324.003 q^{47} +1622.39 q^{48} +71.4197 q^{49} -185.969 q^{51} -156.371 q^{52} -374.774 q^{53} -434.146 q^{54} -1587.72 q^{56} +493.941 q^{57} -159.352 q^{58} +489.567 q^{59} +221.508 q^{61} -17.8709 q^{62} -300.799 q^{63} +2142.39 q^{64} +1849.32 q^{66} +427.538 q^{67} -638.567 q^{68} -386.029 q^{69} -898.999 q^{71} +1152.42 q^{72} +1087.35 q^{73} -827.929 q^{74} +1696.06 q^{76} -1060.01 q^{77} -250.235 q^{78} -798.018 q^{79} -909.622 q^{81} -507.317 q^{82} +436.713 q^{83} -2920.21 q^{84} +553.353 q^{86} -187.440 q^{87} +4061.11 q^{88} +456.763 q^{89} +143.432 q^{91} -1325.52 q^{92} -21.0209 q^{93} -1780.36 q^{94} +4882.06 q^{96} -803.714 q^{97} +392.442 q^{98} +769.390 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 8 q^{3} + 26 q^{4} + 34 q^{6} - 40 q^{7} + 84 q^{8} + 33 q^{9}+O(q^{10}) \) 5 * q - 8 * q^3 + 26 * q^4 + 34 * q^6 - 40 * q^7 + 84 * q^8 + 33 * q^9	\( 5 q - 8 q^{3} + 26 q^{4} + 34 q^{6} - 40 q^{7} + 84 q^{8} + 33 q^{9} + 12 q^{11} + 224 q^{12} - 14 q^{13} - 192 q^{14} + 146 q^{16} - 66 q^{17} + 108 q^{18} + 214 q^{19} + 98 q^{22} - 164 q^{23} + 314 q^{24} + 56 q^{26} - 362 q^{27} - 540 q^{28} - 145 q^{29} + 420 q^{31} + 652 q^{32} + 576 q^{33} + 204 q^{34} - 260 q^{36} - 378 q^{37} + 496 q^{38} - 374 q^{39} - 1158 q^{41} - 348 q^{42} + 204 q^{43} + 784 q^{44} + 580 q^{46} - 248 q^{47} + 1880 q^{48} - 283 q^{49} + 228 q^{51} - 1482 q^{52} + 554 q^{53} + 918 q^{54} - 608 q^{56} - 44 q^{57} + 440 q^{59} + 618 q^{61} - 1250 q^{62} - 804 q^{63} + 2594 q^{64} + 2940 q^{66} - 1164 q^{67} - 356 q^{68} - 1968 q^{69} - 692 q^{71} + 2648 q^{72} + 1950 q^{73} - 1832 q^{74} + 1376 q^{76} + 1616 q^{77} + 1302 q^{78} + 272 q^{79} + 1801 q^{81} - 92 q^{82} - 512 q^{83} - 3208 q^{84} + 2446 q^{86} + 232 q^{87} + 6954 q^{88} + 866 q^{89} + 2580 q^{91} - 3468 q^{92} + 40 q^{93} - 5942 q^{94} + 7386 q^{96} - 1562 q^{97} + 3408 q^{98} - 238 q^{99}+O(q^{100}) \) 5 * q - 8 * q^3 + 26 * q^4 + 34 * q^6 - 40 * q^7 + 84 * q^8 + 33 * q^9 + 12 * q^11 + 224 * q^12 - 14 * q^13 - 192 * q^14 + 146 * q^16 - 66 * q^17 + 108 * q^18 + 214 * q^19 + 98 * q^22 - 164 * q^23 + 314 * q^24 + 56 * q^26 - 362 * q^27 - 540 * q^28 - 145 * q^29 + 420 * q^31 + 652 * q^32 + 576 * q^33 + 204 * q^34 - 260 * q^36 - 378 * q^37 + 496 * q^38 - 374 * q^39 - 1158 * q^41 - 348 * q^42 + 204 * q^43 + 784 * q^44 + 580 * q^46 - 248 * q^47 + 1880 * q^48 - 283 * q^49 + 228 * q^51 - 1482 * q^52 + 554 * q^53 + 918 * q^54 - 608 * q^56 - 44 * q^57 + 440 * q^59 + 618 * q^61 - 1250 * q^62 - 804 * q^63 + 2594 * q^64 + 2940 * q^66 - 1164 * q^67 - 356 * q^68 - 1968 * q^69 - 692 * q^71 + 2648 * q^72 + 1950 * q^73 - 1832 * q^74 + 1376 * q^76 + 1616 * q^77 + 1302 * q^78 + 272 * q^79 + 1801 * q^81 - 92 * q^82 - 512 * q^83 - 3208 * q^84 + 2446 * q^86 + 232 * q^87 + 6954 * q^88 + 866 * q^89 + 2580 * q^91 - 3468 * q^92 + 40 * q^93 - 5942 * q^94 + 7386 * q^96 - 1562 * q^97 + 3408 * q^98 - 238 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more