LMFDB - Embedded newform 1421.4.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1421,4,Mod(1,1421)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1421, 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("1421.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1421 = 7^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1421.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:	$83.8417141182$
Analytic rank:	$1$
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			1.1
Root			$3.03898$ of defining polynomial
Character	$\chi$	$=$	1421.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.49488 q^{2} +6.46343 q^{3} +22.1937 q^{4} -2.14270 q^{5} -35.5158 q^{6} -77.9928 q^{8} +14.7760 q^{9} +O(q^{10})$	\(q-5.49488 q^{2} +6.46343 q^{3} +22.1937 q^{4} -2.14270 q^{5} -35.5158 q^{6} -77.9928 q^{8} +14.7760 q^{9} +11.7739 q^{10} +52.0703 q^{11} +143.448 q^{12} -7.04574 q^{13} -13.8492 q^{15} +251.011 q^{16} -28.7724 q^{17} -81.1922 q^{18} -76.4208 q^{19} -47.5545 q^{20} -286.120 q^{22} +59.7251 q^{23} -504.101 q^{24} -120.409 q^{25} +38.7155 q^{26} -79.0092 q^{27} -29.0000 q^{29} +76.0998 q^{30} +3.25229 q^{31} -755.335 q^{32} +336.553 q^{33} +158.101 q^{34} +327.934 q^{36} +150.673 q^{37} +419.923 q^{38} -45.5397 q^{39} +167.115 q^{40} +92.3254 q^{41} -100.703 q^{43} +1155.63 q^{44} -31.6605 q^{45} -328.182 q^{46} -324.003 q^{47} +1622.39 q^{48} +661.632 q^{50} -185.969 q^{51} -156.371 q^{52} +374.774 q^{53} +434.146 q^{54} -111.571 q^{55} -493.941 q^{57} +159.352 q^{58} -489.567 q^{59} -307.365 q^{60} -221.508 q^{61} -17.8709 q^{62} +2142.39 q^{64} +15.0969 q^{65} -1849.32 q^{66} -427.538 q^{67} -638.567 q^{68} +386.029 q^{69} -898.999 q^{71} -1152.42 q^{72} +1087.35 q^{73} -827.929 q^{74} -778.254 q^{75} -1696.06 q^{76} +250.235 q^{78} -798.018 q^{79} -537.842 q^{80} -909.622 q^{81} -507.317 q^{82} +436.713 q^{83} +61.6507 q^{85} +553.353 q^{86} -187.440 q^{87} -4061.11 q^{88} -456.763 q^{89} +173.971 q^{90} +1325.52 q^{92} +21.0209 q^{93} +1780.36 q^{94} +163.747 q^{95} -4882.06 q^{96} -803.714 q^{97} +769.390 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 8 q^{3} + 26 q^{4} - 10 q^{5} - 34 q^{6} - 84 q^{8} + 33 q^{9}+O(q^{10}) $ 5 * q - 8 * q^3 + 26 * q^4 - 10 * q^5 - 34 * q^6 - 84 * q^8 + 33 * q^9	\( 5 q - 8 q^{3} + 26 q^{4} - 10 q^{5} - 34 q^{6} - 84 q^{8} + 33 q^{9} + 64 q^{10} + 12 q^{11} + 224 q^{12} - 14 q^{13} - 74 q^{15} + 146 q^{16} - 66 q^{17} - 108 q^{18} - 214 q^{19} - 6 q^{20} - 98 q^{22} + 164 q^{23} - 314 q^{24} + 207 q^{25} - 56 q^{26} - 362 q^{27} - 145 q^{29} - 234 q^{30} - 420 q^{31} - 652 q^{32} + 576 q^{33} - 204 q^{34} - 260 q^{36} + 378 q^{37} + 496 q^{38} - 374 q^{39} + 80 q^{40} + 1158 q^{41} - 204 q^{43} + 784 q^{44} + 1506 q^{45} + 580 q^{46} - 248 q^{47} + 1880 q^{48} + 908 q^{50} + 228 q^{51} - 1482 q^{52} - 554 q^{53} - 918 q^{54} - 546 q^{55} + 44 q^{57} - 440 q^{59} + 636 q^{60} - 618 q^{61} - 1250 q^{62} + 2594 q^{64} - 1656 q^{65} - 2940 q^{66} + 1164 q^{67} - 356 q^{68} + 1968 q^{69} - 692 q^{71} - 2648 q^{72} + 1950 q^{73} - 1832 q^{74} - 3074 q^{75} - 1376 q^{76} - 1302 q^{78} + 272 q^{79} + 890 q^{80} + 1801 q^{81} - 92 q^{82} - 512 q^{83} - 1628 q^{85} + 2446 q^{86} + 232 q^{87} - 6954 q^{88} - 866 q^{89} + 2200 q^{90} + 3468 q^{92} - 40 q^{93} + 5942 q^{94} + 2244 q^{95} - 7386 q^{96} - 1562 q^{97} - 238 q^{99}+O(q^{100}) \) 5 * q - 8 * q^3 + 26 * q^4 - 10 * q^5 - 34 * q^6 - 84 * q^8 + 33 * q^9 + 64 * q^10 + 12 * q^11 + 224 * q^12 - 14 * q^13 - 74 * q^15 + 146 * q^16 - 66 * q^17 - 108 * q^18 - 214 * q^19 - 6 * q^20 - 98 * q^22 + 164 * q^23 - 314 * q^24 + 207 * q^25 - 56 * q^26 - 362 * q^27 - 145 * q^29 - 234 * q^30 - 420 * q^31 - 652 * q^32 + 576 * q^33 - 204 * q^34 - 260 * q^36 + 378 * q^37 + 496 * q^38 - 374 * q^39 + 80 * q^40 + 1158 * q^41 - 204 * q^43 + 784 * q^44 + 1506 * q^45 + 580 * q^46 - 248 * q^47 + 1880 * q^48 + 908 * q^50 + 228 * q^51 - 1482 * q^52 - 554 * q^53 - 918 * q^54 - 546 * q^55 + 44 * q^57 - 440 * q^59 + 636 * q^60 - 618 * q^61 - 1250 * q^62 + 2594 * q^64 - 1656 * q^65 - 2940 * q^66 + 1164 * q^67 - 356 * q^68 + 1968 * q^69 - 692 * q^71 - 2648 * q^72 + 1950 * q^73 - 1832 * q^74 - 3074 * q^75 - 1376 * q^76 - 1302 * q^78 + 272 * q^79 + 890 * q^80 + 1801 * q^81 - 92 * q^82 - 512 * q^83 - 1628 * q^85 + 2446 * q^86 + 232 * q^87 - 6954 * q^88 - 866 * q^89 + 2200 * q^90 + 3468 * q^92 - 40 * q^93 + 5942 * q^94 + 2244 * q^95 - 7386 * q^96 - 1562 * q^97 - 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	$-0.923644\pi$
$2$	−5.49488	−1.94273	−0.971367	+	0.237584i	$0.923644\pi$
$3$	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
$5$	−2.14270	−0.191649	−0.0958246	−	0.995398i	$-0.530549\pi$
$5$	−2.14270	−0.191649	−0.0958246	+	0.995398i	$0.530549\pi$
$6$	−35.5158	−2.41654
$7$	0	0
$7$	0	0
$8$	−77.9928	−3.44683
$9$	14.7760	0.547258
$10$	11.7739	0.372323
$11$	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	$0.523946\pi$
$14$	0	0
$15$	−13.8492	−0.238390
$16$	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	$-0.652643\pi$
$19$	−76.4208	−0.922744	−0.461372	+	0.887207i	$0.652643\pi$
$20$	−47.5545	−0.531676
$21$	0	0
$22$	−286.120	−2.77277
$23$	59.7251	0.541458	0.270729	−	0.962656i	$-0.412735\pi$
$23$	59.7251	0.541458	0.270729	+	0.962656i	$0.412735\pi$
$24$	−504.101	−4.28747
$25$	−120.409	−0.963271
$26$	38.7155	0.292028
$27$	−79.0092	−0.563160
$28$	0	0
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	76.0998	0.463128
$31$	3.25229	0.0188428	0.00942142	−	0.999956i	$-0.497001\pi$
$31$	3.25229	0.0188428	0.00942142	+	0.999956i	$0.497001\pi$
$32$	−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	$-0.391353\pi$
$37$	150.673	0.669471	0.334736	+	0.942312i	$0.391353\pi$
$38$	419.923	1.79265
$39$	−45.5397	−0.186979
$40$	167.115	0.660581
$41$	92.3254	0.351678	0.175839	−	0.984419i	$-0.443736\pi$
$41$	92.3254	0.351678	0.175839	+	0.984419i	$0.443736\pi$
$42$	0	0
$43$	−100.703	−0.357142	−0.178571	−	0.983927i	$-0.557148\pi$
$43$	−100.703	−0.357142	−0.178571	+	0.983927i	$0.557148\pi$
$44$	1155.63	3.95951
$45$	−31.6605	−0.104882
$46$	−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
$49$	0	0
$50$	661.632	1.87138
$51$	−185.969	−0.510604
$52$	−156.371	−0.417015
$53$	374.774	0.971305	0.485653	−	0.874152i	$-0.338582\pi$
$53$	374.774	0.971305	0.485653	+	0.874152i	$0.338582\pi$
$54$	434.146	1.09407
$55$	−111.571	−0.273532
$56$	0	0
$57$	−493.941	−1.14779
$58$	159.352	0.360757
$59$	−489.567	−1.08027	−0.540137	−	0.841577i	$-0.681628\pi$
$59$	−489.567	−1.08027	−0.540137	+	0.841577i	$0.681628\pi$
$60$	−307.365	−0.661345
$61$	−221.508	−0.464937	−0.232468	−	0.972604i	$-0.574680\pi$
$61$	−221.508	−0.464937	−0.232468	+	0.972604i	$0.574680\pi$
$62$	−17.8709	−0.0366066
$63$	0	0
$64$	2142.39	4.18435
$65$	15.0969	0.0288083
$66$	−1849.32	−3.44902
$67$	−427.538	−0.779584	−0.389792	−	0.920903i	$-0.627453\pi$
$67$	−427.538	−0.779584	−0.389792	+	0.920903i	$0.627453\pi$
$68$	−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
$75$	−778.254	−1.19820
$76$	−1696.06	−2.55989
$77$	0	0
$78$	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	$0.692381\pi$
$80$	−537.842	−0.751658
$81$	−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	$0.406754\pi$
$84$	0	0
$85$	61.6507	0.0786701
$86$	553.353	0.693833
$87$	−187.440	−0.230984
$88$	−4061.11	−4.91950
$89$	−456.763	−0.544009	−0.272004	−	0.962296i	$-0.587687\pi$
$89$	−456.763	−0.544009	−0.272004	+	0.962296i	$0.587687\pi$
$90$	173.971	0.203757
$91$	0	0
$92$	1325.52	1.50212
$93$	21.0209	0.0234384
$94$	1780.36	1.95351
$95$	163.747	0.176843
$96$	−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	$0.638196\pi$
$98$	0	0
$99$	769.390	0.781077
$100$	−2672.32	−2.67232
$101$	738.800	0.727855	0.363928	−	0.931427i	$-0.381436\pi$
$101$	738.800	0.727855	0.363928	+	0.931427i	$0.381436\pi$
$102$	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	$-0.244035\pi$
$107$	1594.33	1.44047	0.720233	+	0.693732i	$0.244035\pi$
$108$	−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	$0.532175\pi$
$110$	613.071	0.531400
$111$	973.863	0.832748
$112$	0	0
$113$	−1584.73	−1.31928	−0.659640	−	0.751582i	$-0.729291\pi$
$113$	−1584.73	−1.31928	−0.659640	+	0.751582i	$0.729291\pi$
$114$	2714.15	2.22985
$115$	−127.973	−0.103770
$116$	−643.618	−0.515159
$117$	−104.108	−0.0822629
$118$	2690.11	2.09869
$119$	0	0
$120$	1080.14	0.821689
$121$	1380.32	1.03705
$122$	1217.16	0.903248
$123$	596.739	0.437448
$124$	72.1803	0.0522741
$125$	525.838	0.376259
$126$	0	0
$127$	621.184	0.434025	0.217013	−	0.976169i	$-0.430369\pi$
$127$	621.184	0.434025	0.217013	+	0.976169i	$0.430369\pi$
$128$	−5729.47	−3.95639
$129$	−650.890	−0.444245
$130$	−82.9558	−0.0559669
$131$	1504.34	1.00332	0.501659	−	0.865066i	$-0.332723\pi$
$131$	1504.34	1.00332	0.501659	+	0.865066i	$0.332723\pi$
$132$	7469.36	4.92519
$133$	0	0
$134$	2349.27	1.51452
$135$	169.293	0.107929
$136$	2244.04	1.41489
$137$	−29.3812	−0.0183227	−0.00916135	−	0.999958i	$-0.502916\pi$
$137$	−29.3812	−0.0183227	−0.00916135	+	0.999958i	$0.502916\pi$
$138$	−2121.18	−1.30846
$139$	−1262.60	−0.770450	−0.385225	−	0.922823i	$-0.625876\pi$
$139$	−1262.60	−0.770450	−0.385225	+	0.922823i	$0.625876\pi$
$140$	0	0
$141$	−2094.17	−1.25079
$142$	4939.89	2.91934
$143$	−366.874	−0.214542
$144$	3708.94	2.14637
$145$	62.1384	0.0355883
$146$	−5974.84	−3.38686
$147$	0	0
$148$	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	$0.427036\pi$
$150$	4276.42	2.32779
$151$	−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
$154$	0	0
$155$	−6.96868	−0.00361121
$156$	−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
$160$	1618.46	0.799689
$161$	0	0
$162$	4998.26	2.42408
$163$	−1650.78	−0.793246	−0.396623	−	0.917982i	$-0.629818\pi$
$163$	−1650.78	−0.793246	−0.396623	+	0.917982i	$0.629818\pi$
$164$	2049.04	0.975631
$165$	−721.133	−0.340243
$166$	−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	$0.174422\pi$
$168$	0	0
$169$	−2147.36	−0.977404
$170$	−338.763	−0.152835
$171$	−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	$0.286193\pi$
$180$	−702.664	−0.290964
$181$	−3145.07	−1.29155	−0.645777	−	0.763526i	$-0.723467\pi$
$181$	−3145.07	−1.29155	−0.645777	+	0.763526i	$0.723467\pi$
$182$	0	0
$183$	−1431.70	−0.578329
$184$	−4658.13	−1.86631
$185$	−322.847	−0.128304
$186$	−115.508	−0.0455346
$187$	−1498.19	−0.585874
$188$	−7190.84	−2.78960
$189$	0	0
$190$	−899.771	−0.343559
$191$	−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	$-0.304867\pi$
$193$	3085.29	1.15069	0.575347	+	0.817909i	$0.304867\pi$
$194$	4416.31	1.63440
$195$	97.5779	0.0358344
$196$	0	0
$197$	−2484.45	−0.898526	−0.449263	−	0.893400i	$-0.648313\pi$
$197$	−2484.45	−0.898526	−0.449263	+	0.893400i	$0.648313\pi$
$198$	−4227.70	−1.51742
$199$	−5489.57	−1.95550	−0.977752	−	0.209764i	$-0.932730\pi$
$199$	−5489.57	−1.95550	−0.977752	+	0.209764i	$0.932730\pi$
$200$	9391.02	3.32023
$201$	−2763.37	−0.969715
$202$	−4059.62	−1.41403
$203$	0	0
$204$	−4127.33	−1.41652
$205$	−197.826	−0.0673988
$206$	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
$215$	215.777	0.0684460
$216$	6162.15	1.94112
$217$	0	0
$218$	1262.00	0.392079
$219$	7027.99	2.16853
$220$	−2476.18	−0.758836
$221$	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	$0.214183\pi$
$224$	0	0
$225$	−1779.16	−0.527158
$226$	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	$-0.461033\pi$
$229$	846.348	0.244228	0.122114	+	0.992516i	$0.461033\pi$
$230$	703.197	0.201597
$231$	0	0
$232$	2261.79	0.640060
$233$	823.620	0.231576	0.115788	−	0.993274i	$-0.463061\pi$
$233$	823.620	0.231576	0.115788	+	0.993274i	$0.463061\pi$
$234$	572.059	0.159815
$235$	694.243	0.192712
$236$	−10865.3	−2.99691
$237$	−5157.93	−1.41369
$238$	0	0
$239$	−2471.50	−0.668903	−0.334452	−	0.942413i	$-0.608551\pi$
$239$	−2471.50	−0.668903	−0.334452	+	0.942413i	$0.608551\pi$
$240$	−3476.31	−0.934978
$241$	1148.79	0.307055	0.153527	−	0.988144i	$-0.450937\pi$
$241$	1148.79	0.307055	0.153527	+	0.988144i	$0.450937\pi$
$242$	−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
$250$	−2889.42	−0.730971
$251$	1686.20	0.424032	0.212016	−	0.977266i	$-0.431997\pi$
$251$	1686.20	0.424032	0.212016	+	0.977266i	$0.431997\pi$
$252$	0	0
$253$	3109.91	0.772799
$254$	−3413.33	−0.843195
$255$	398.475	0.0978568
$256$	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
$259$	0	0
$260$	335.057	0.0799205
$261$	−428.503	−0.101623
$262$	−8266.15	−1.94918
$263$	−2321.87	−0.544382	−0.272191	−	0.962243i	$-0.587748\pi$
$263$	−2321.87	−0.544382	−0.272191	+	0.962243i	$0.587748\pi$
$264$	−26248.7	−6.11931
$265$	−803.029	−0.186150
$266$	0	0
$267$	−2952.26	−0.676686
$268$	−9488.66	−2.16273
$269$	−2365.41	−0.536140	−0.268070	−	0.963399i	$-0.586386\pi$
$269$	−2365.41	−0.536140	−0.268070	+	0.963399i	$0.586386\pi$
$270$	−930.246	−0.209678
$271$	−1732.51	−0.388348	−0.194174	−	0.980967i	$-0.562203\pi$
$271$	−1732.51	−0.388348	−0.194174	+	0.980967i	$0.562203\pi$
$272$	−7222.20	−1.60996
$273$	0	0
$274$	161.446	0.0355961
$275$	−6269.73	−1.37483
$276$	8567.42	1.86847
$277$	−688.616	−0.149368	−0.0746839	−	0.997207i	$-0.523795\pi$
$277$	−688.616	−0.149368	−0.0746839	+	0.997207i	$0.523795\pi$
$278$	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
$285$	1058.37	0.219973
$286$	2015.93	0.416798
$287$	0	0
$288$	−11160.8	−2.28353
$289$	−4085.15	−0.831498
$290$	−341.443	−0.0691387
$291$	−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	$0.264561\pi$
$294$	0	0
$295$	1049.00	0.207034
$296$	−11751.4	−2.30755
$297$	−4114.03	−0.803773
$298$	−4541.66	−0.882857
$299$	−420.807	−0.0813910
$300$	−17272.4	−3.32407
$301$	0	0
$302$	14462.7	2.75574
$303$	4775.19	0.905371
$304$	−19182.5	−3.61905
$305$	474.625	0.0891047
$306$	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	$0.808068\pi$
$308$	0	0
$309$	−13131.1	−2.41748
$310$	38.2921	0.00701563
$311$	−4127.77	−0.752619	−0.376309	−	0.926494i	$-0.622807\pi$
$311$	−4127.77	−0.752619	−0.376309	+	0.926494i	$0.622807\pi$
$312$	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	$-0.658118\pi$
$317$	−5379.49	−0.953129	−0.476565	+	0.879139i	$0.658118\pi$
$318$	−13310.4	−2.34720
$319$	−1510.04	−0.265034
$320$	−4590.49	−0.801926
$321$	10304.9	1.79178
$322$	0	0
$323$	2198.81	0.378778
$324$	−20187.9	−3.46157
$325$	848.369	0.144797
$326$	9070.84	1.54106
$327$	−1484.44	−0.251039
$328$	−7200.71	−1.21217
$329$	0	0
$330$	3962.54	0.661002
$331$	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
$335$	916.087	0.149407
$336$	0	0
$337$	−3627.26	−0.586318	−0.293159	−	0.956064i	$-0.594707\pi$
$337$	−3627.26	−0.586318	−0.293159	+	0.956064i	$0.594707\pi$
$338$	11799.5	1.89884
$339$	−10242.8	−1.64104
$340$	1368.26	0.218248
$341$	169.348	0.0268935
$342$	6204.78	0.981041
$343$	0	0
$344$	7854.14	1.23101
$345$	−827.145	−0.129078
$346$	−16889.0	−2.62415
$347$	1172.68	0.181421	0.0907104	−	0.995877i	$-0.471086\pi$
$347$	1172.68	0.181421	0.0907104	+	0.995877i	$0.471086\pi$
$348$	−4159.98	−0.640800
$349$	173.078	0.0265463	0.0132731	−	0.999912i	$-0.495775\pi$
$349$	173.078	0.0265463	0.0132731	+	0.999912i	$0.495775\pi$
$350$	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
$355$	1926.29	0.287991
$356$	−10137.3	−1.50920
$357$	0	0
$358$	−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	$0.607000\pi$
$360$	2469.29	0.361508
$361$	−1018.85	−0.148543
$362$	17281.8	2.50915
$363$	8921.60	1.28998
$364$	0	0
$365$	−2329.86	−0.334111
$366$	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
$370$	1774.00	0.249260
$371$	0	0
$372$	466.533	0.0650231
$373$	−6800.89	−0.944066	−0.472033	−	0.881581i	$-0.656480\pi$
$373$	−6800.89	−0.944066	−0.472033	+	0.881581i	$0.656480\pi$
$374$	8232.37	1.13820
$375$	3398.72	0.468024
$376$	25269.9	3.46595
$377$	204.326	0.0279134
$378$	0	0
$379$	10216.7	1.38468	0.692341	−	0.721571i	$-0.256579\pi$
$379$	10216.7	1.38468	0.692341	+	0.721571i	$0.256579\pi$
$380$	3634.16	0.490601
$381$	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	$0.580699\pi$
$390$	−536.179	−0.0696166
$391$	−1718.43	−0.222263
$392$	0	0
$393$	9723.18	1.24801
$394$	13651.7	1.74560
$395$	1709.91	0.217810
$396$	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
$399$	0	0
$400$	−30224.0	−3.77800
$401$	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
$405$	1949.05	0.239133
$406$	0	0
$407$	7845.58	0.955506
$408$	14504.2	1.75996
$409$	−3357.24	−0.405880	−0.202940	−	0.979191i	$-0.565050\pi$
$409$	−3357.24	−0.405880	−0.202940	+	0.979191i	$0.565050\pi$
$410$	1087.03	0.130938
$411$	−189.904	−0.0227914
$412$	−45088.7	−5.39165
$413$	0	0
$414$	−4849.21	−0.575666
$415$	−935.746	−0.110684
$416$	5321.89	0.627229
$417$	−8160.74	−0.958353
$418$	21865.6	2.55856
$419$	−1652.11	−0.192627	−0.0963134	−	0.995351i	$-0.530705\pi$
$419$	−1652.11	−0.192627	−0.0963134	+	0.995351i	$0.530705\pi$
$420$	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
$425$	3464.45	0.395413
$426$	31928.7	3.63133
$427$	0	0
$428$	35384.2	3.99616
$429$	−2371.27	−0.266867
$430$	−1185.67	−0.132972
$431$	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	$0.249078\pi$
$434$	0	0
$435$	401.627	0.0442679
$436$	−5097.18	−0.559887
$437$	−4564.24	−0.499628
$438$	−38618.0	−4.21287
$439$	3760.84	0.408873	0.204437	−	0.978880i	$-0.434464\pi$
$439$	3760.84	0.408873	0.204437	+	0.978880i	$0.434464\pi$
$440$	8701.75	0.942817
$441$	0	0
$442$	−1113.94	−0.119875
$443$	3713.77	0.398299	0.199149	−	0.979969i	$-0.436182\pi$
$443$	3713.77	0.398299	0.199149	+	0.979969i	$0.436182\pi$
$444$	21613.6	2.31022
$445$	978.707	0.104259
$446$	−28620.1	−3.03856
$447$	5342.20	0.565274
$448$	0	0
$449$	−12043.9	−1.26589	−0.632947	−	0.774195i	$-0.718155\pi$
$449$	−12043.9	−1.26589	−0.632947	+	0.774195i	$0.718155\pi$
$450$	9776.26	1.02413
$451$	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	$-0.731617\pi$
$457$	−12995.7	−1.33023	−0.665113	+	0.746743i	$0.731617\pi$
$458$	−4650.58	−0.474470
$459$	2273.28	0.231172
$460$	−2840.20	−0.287880
$461$	−7874.30	−0.795538	−0.397769	−	0.917486i	$-0.630215\pi$
$461$	−7874.30	−0.795538	−0.397769	+	0.917486i	$0.630215\pi$
$462$	0	0
$463$	−3466.08	−0.347910	−0.173955	−	0.984754i	$-0.555655\pi$
$463$	−3466.08	−0.347910	−0.173955	+	0.984754i	$0.555655\pi$
$464$	−7279.33	−0.728307
$465$	−45.0416	−0.00449195
$466$	−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
$469$	0	0
$470$	−3814.78	−0.374389
$471$	−1515.93	−0.148302
$472$	38182.7	3.72352
$473$	−5243.66	−0.509733
$474$	28342.2	2.74642
$475$	9201.74	0.888853
$476$	0	0
$477$	5537.65	0.531555
$478$	13580.6	1.29950
$479$	−8119.86	−0.774542	−0.387271	−	0.921966i	$-0.626582\pi$
$479$	−8119.86	−0.774542	−0.387271	+	0.921966i	$0.626582\pi$
$480$	10460.8	0.994724
$481$	−1061.60	−0.100634
$482$	−6312.48	−0.596526
$483$	0	0
$484$	30634.4	2.87701
$485$	1722.12	0.161232
$486$	20584.0	1.92121
$487$	9698.92	0.902464	0.451232	−	0.892407i	$-0.350985\pi$
$487$	9698.92	0.902464	0.451232	+	0.892407i	$0.350985\pi$
$488$	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
$495$	−1648.57	−0.149693
$496$	816.361	0.0739026
$497$	0	0
$498$	−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	$0.814228\pi$
$500$	11670.3	1.04382
$501$	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	$0.656075\pi$
$504$	0	0
$505$	−1583.03	−0.139493
$506$	−17088.6	−1.50134
$507$	−13879.3	−1.21578
$508$	13786.4	1.20408
$509$	7931.22	0.690658	0.345329	−	0.938482i	$-0.387767\pi$
$509$	7931.22	0.690658	0.345329	+	0.938482i	$0.387767\pi$
$510$	−2189.57	−0.190110
$511$	0	0
$512$	−32981.1	−2.84682
$513$	6037.95	0.519653
$514$	19748.4	1.69468
$515$	4353.10	0.372467
$516$	−14445.7	−1.23243
$517$	−16871.0	−1.43517
$518$	0	0
$519$	19865.9	1.68018
$520$	−1177.45	−0.0992974
$521$	−13771.1	−1.15801	−0.579005	−	0.815324i	$-0.696559\pi$
$521$	−13771.1	−1.15801	−0.579005	+	0.815324i	$0.696559\pi$
$522$	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
$530$	4412.55	0.361640
$531$	−7233.83	−0.591189
$532$	0	0
$533$	−650.501	−0.0528636
$534$	16222.3	1.31462
$535$	−3416.18	−0.276064
$536$	33344.9	2.68709
$537$	19265.6	1.54817
$538$	12997.7	1.04158
$539$	0	0
$540$	3757.24	0.299419
$541$	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
$545$	492.110	0.0386783
$546$	0	0
$547$	−9079.06	−0.709676	−0.354838	−	0.934928i	$-0.615464\pi$
$547$	−9079.06	−0.709676	−0.354838	+	0.934928i	$0.615464\pi$
$548$	−652.079	−0.0508311
$549$	−3272.99	−0.254440
$550$	34451.4	2.67093
$551$	2216.20	0.171349
$552$	−30107.5	−2.32148
$553$	0	0
$554$	3783.86	0.290182
$555$	−2086.70	−0.159595
$556$	−28021.8	−2.13739
$557$	−5982.38	−0.455084	−0.227542	−	0.973768i	$-0.573069\pi$
$557$	−5982.38	−0.455084	−0.227542	+	0.973768i	$0.573069\pi$
$558$	−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
$565$	3395.60	0.252839
$566$	27680.6	2.05566
$567$	0	0
$568$	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	$0.379669\pi$
$570$	−5815.61	−0.427349
$571$	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
$574$	0	0
$575$	−7191.43	−0.521571
$576$	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
$580$	1379.08	0.0987297
$581$	0	0
$582$	28544.6	2.03301
$583$	19514.6	1.38630
$584$	−84805.2	−6.00901
$585$	223.072	0.0157656
$586$	−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	$0.384203\pi$
$588$	0	0
$589$	−248.543	−0.0173871
$590$	−5764.11	−0.402211
$591$	−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	$0.587829\pi$
$600$	60698.2	4.12999
$601$	−2646.60	−0.179629	−0.0898147	−	0.995958i	$-0.528627\pi$
$601$	−2646.60	−0.179629	−0.0898147	+	0.995958i	$0.528627\pi$
$602$	0	0
$603$	−6317.29	−0.426634
$604$	−58414.5	−3.93518
$605$	−2957.61	−0.198751
$606$	−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
$609$	0	0
$610$	−2608.01	−0.173107
$611$	2282.84	0.151152
$612$	−9435.44	−0.623211
$613$	−9721.86	−0.640558	−0.320279	−	0.947323i	$-0.603777\pi$
$613$	−9721.86	−0.640558	−0.320279	+	0.947323i	$0.603777\pi$
$614$	48690.1	3.20028
$615$	−1278.63	−0.0838366
$616$	0	0
$617$	−14150.2	−0.923282	−0.461641	−	0.887067i	$-0.652739\pi$
$617$	−14150.2	−0.923282	−0.461641	+	0.887067i	$0.652739\pi$
$618$	72153.7	4.69652
$619$	10804.4	0.701560	0.350780	−	0.936458i	$-0.385917\pi$
$619$	10804.4	0.701560	0.350780	+	0.936458i	$0.385917\pi$
$620$	−154.661	−0.0100183
$621$	−4718.83	−0.304928
$622$	22681.6	1.46214
$623$	0	0
$624$	−11431.0	−0.733341
$625$	13924.4	0.891161
$626$	−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
$635$	−1331.01	−0.0831805
$636$	53760.5	3.35179
$637$	0	0
$638$	8297.49	0.514891
$639$	−13283.6	−0.822364
$640$	12276.6	0.758239
$641$	−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	$0.608602\pi$
$644$	0	0
$645$	1394.66	0.0851392
$646$	−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
$650$	−4661.69	−0.281302
$651$	0	0
$652$	−36636.9	−2.20063
$653$	20205.6	1.21088	0.605441	−	0.795890i	$-0.292997\pi$
$653$	20205.6	1.21088	0.605441	+	0.795890i	$0.292997\pi$
$654$	8156.84	0.487703
$655$	−3223.35	−0.192285
$656$	23174.7	1.37930
$657$	16066.6	0.954061
$658$	0	0
$659$	−9268.73	−0.547888	−0.273944	−	0.961746i	$-0.588328\pi$
$659$	−9268.73	−0.547888	−0.273944	+	0.961746i	$0.588328\pi$
$660$	−16004.6	−0.943908
$661$	18209.9	1.07153	0.535765	−	0.844367i	$-0.320023\pi$
$661$	18209.9	1.07153	0.535765	+	0.844367i	$0.320023\pi$
$662$	−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
$670$	−5033.79	−0.290257
$671$	−11534.0	−0.663583
$672$	0	0
$673$	−63.9154	−0.00366086	−0.00183043	−	0.999998i	$-0.500583\pi$
$673$	−63.9154	−0.00366086	−0.00183043	+	0.999998i	$0.500583\pi$
$674$	19931.3	1.13906
$675$	9513.40	0.542476
$676$	−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
$679$	0	0
$680$	−4808.31	−0.271162
$681$	33889.6	1.90698
$682$	−930.545	−0.0522470
$683$	−22719.5	−1.27282	−0.636410	−	0.771351i	$-0.719581\pi$
$683$	−22719.5	−1.27282	−0.636410	+	0.771351i	$0.719581\pi$
$684$	−25061.0	−1.40092
$685$	62.9553	0.00351153
$686$	0	0
$687$	5470.31	0.303793
$688$	−25277.7	−1.40073
$689$	−2640.56	−0.146005
$690$	4545.07	0.250765
$691$	−10495.0	−0.577783	−0.288891	−	0.957362i	$-0.593287\pi$
$691$	−10495.0	−0.577783	−0.288891	+	0.957362i	$0.593287\pi$
$692$	68214.1	3.74727
$693$	0	0
$694$	−6443.76	−0.352452
$695$	2705.38	0.147656
$696$	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
$705$	4487.19	0.239713
$706$	71479.4	3.81043
$707$	0	0
$708$	−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	$0.644877\pi$
$710$	−10584.7	−0.559489
$711$	−11791.5	−0.621962
$712$	35624.2	1.87510
$713$	194.243	0.0102026
$714$	0	0
$715$	786.102	0.0411168
$716$	66152.8	3.45286
$717$	−15974.4	−0.832041
$718$	24657.7	1.28164
$719$	−6525.25	−0.338457	−0.169229	−	0.985577i	$-0.554128\pi$
$719$	−6525.25	−0.338457	−0.169229	+	0.985577i	$0.554128\pi$
$720$	−7947.14	−0.411351
$721$	0	0
$722$	5598.48	0.288579
$723$	7425.14	0.381942
$724$	−69800.8	−3.58305
$725$	3491.86	0.178875
$726$	−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	$0.508663\pi$
$728$	0	0
$729$	347.561	0.0176579
$730$	12802.3	0.649088
$731$	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	$0.216648\pi$
$740$	−7165.17	−0.355942
$741$	3480.18	0.172534
$742$	0	0
$743$	−30790.4	−1.52031	−0.760156	−	0.649741i	$-0.774877\pi$
$743$	−30790.4	−1.52031	−0.760156	+	0.649741i	$0.774877\pi$
$744$	−1639.48	−0.0807881
$745$	−1771.00	−0.0870932
$746$	37370.1	1.83407
$747$	6452.86	0.316061
$748$	−33250.4	−1.62534
$749$	0	0
$750$	−18675.6	−0.909247
$751$	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
$755$	5639.65	0.271852
$756$	0	0
$757$	−7197.74	−0.345583	−0.172792	−	0.984958i	$-0.555279\pi$
$757$	−7197.74	−0.345583	−0.172792	+	0.984958i	$0.555279\pi$
$758$	−56139.3	−2.69007
$759$	20100.7	0.961275
$760$	−12771.1	−0.609548
$761$	−9185.20	−0.437534	−0.218767	−	0.975777i	$-0.570203\pi$
$761$	−9185.20	−0.437534	−0.218767	+	0.975777i	$0.570203\pi$
$762$	−22061.9	−1.04884
$763$	0	0
$764$	−47174.1	−2.23390
$765$	910.949	0.0430528
$766$	−39477.8	−1.86213
$767$	3449.36	0.162385
$768$	92709.4	4.35594
$769$	−32791.1	−1.53768	−0.768840	−	0.639441i	$-0.779166\pi$
$769$	−32791.1	−1.53768	−0.768840	+	0.639441i	$0.779166\pi$
$770$	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
$775$	−391.604	−0.0181508
$776$	62683.9	2.89977
$777$	0	0
$778$	21148.0	0.974540
$779$	−7055.58	−0.324509
$780$	2165.62	0.0994122
$781$	−46811.2	−2.14473
$782$	9442.59	0.431798
$783$	2291.27	0.104576
$784$	0	0
$785$	502.548	0.0228493
$786$	−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
$790$	−9395.77	−0.423148
$791$	0	0
$792$	−60006.8	−2.69224
$793$	1560.68	0.0698884
$794$	−8915.52	−0.398489
$795$	−5190.33	−0.231550
$796$	−121834.	−5.42499
$797$	1248.33	0.0554807	0.0277404	−	0.999615i	$-0.491169\pi$
$797$	1248.33	0.0554807	0.0277404	+	0.999615i	$0.491169\pi$
$798$	0	0
$799$	9322.35	0.412767
$800$	90949.0	4.01942
$801$	−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	$0.670693\pi$
$810$	−10709.8	−0.464572
$811$	−23248.4	−1.00661	−0.503306	−	0.864108i	$-0.667883\pi$
$811$	−23248.4	−1.00661	−0.503306	+	0.864108i	$0.667883\pi$
$812$	0	0
$813$	−11197.9	−0.483062
$814$	−43110.5	−1.85629
$815$	3537.13	0.152025
$816$	−46680.2	−2.00261
$817$	7695.84	0.329551
$818$	18447.6	0.788516
$819$	0	0
$820$	−4390.49	−0.186979
$821$	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	$-0.415262\pi$
$823$	12422.7	0.526158	0.263079	+	0.964774i	$0.415262\pi$
$824$	158450.	6.69886
$825$	−40524.0	−1.71014
$826$	0	0
$827$	−4915.14	−0.206670	−0.103335	−	0.994647i	$-0.532951\pi$
$827$	−4915.14	−0.206670	−0.103335	+	0.994647i	$0.532951\pi$
$828$	19585.9	0.822048
$829$	45226.4	1.89478	0.947392	−	0.320074i	$-0.103708\pi$
$829$	45226.4	1.89478	0.947392	+	0.320074i	$0.103708\pi$
$830$	5141.81	0.215030
$831$	−4450.82	−0.185797
$832$	−15094.7	−0.628983
$833$	0	0
$834$	44842.3	1.86183
$835$	−7894.31	−0.327178
$836$	−88314.5	−3.65362
$837$	−256.961	−0.0106115
$838$	9078.13	0.374223
$839$	−3982.56	−0.163877	−0.0819387	−	0.996637i	$-0.526111\pi$
$839$	−3982.56	−0.163877	−0.0819387	+	0.996637i	$0.526111\pi$
$840$	0	0
$841$	841.000	0.0344828
$842$	35195.5	1.44052
$843$	14377.5	0.587411
$844$	−41827.3	−1.70587
$845$	4601.15	0.187319
$846$	26306.5	1.06907
$847$	0	0
$848$	94072.5	3.80951
$849$	−32559.7	−1.31619
$850$	−19036.7	−0.768182
$851$	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	$0.232235\pi$
$854$	0	0
$855$	2419.52	0.0967789
$856$	−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	$-0.350053\pi$
$859$	22852.1	0.907687	0.453843	+	0.891081i	$0.350053\pi$
$860$	4788.90	0.189884
$861$	0	0
$862$	−1387.65	−0.0548303
$863$	41976.4	1.65573	0.827865	−	0.560928i	$-0.189555\pi$
$863$	41976.4	1.65573	0.827865	+	0.560928i	$0.189555\pi$
$864$	59678.4	2.34988
$865$	−6585.77	−0.258870
$866$	−70219.9	−2.75539
$867$	−26404.1	−1.03429
$868$	0	0
$869$	−41553.0	−1.62208
$870$	−2206.89	−0.0860008
$871$	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	$-0.173764\pi$
$877$	44394.0	1.70932	0.854662	+	0.519184i	$0.173764\pi$
$878$	−20665.4	−0.794331
$879$	43699.4	1.67684
$880$	−28005.6	−1.07281
$881$	6337.13	0.242342	0.121171	−	0.992632i	$-0.461335\pi$
$881$	6337.13	0.242342	0.121171	+	0.992632i	$0.461335\pi$
$882$	0	0
$883$	−2834.24	−0.108018	−0.0540090	−	0.998540i	$-0.517200\pi$
$883$	−2834.24	−0.108018	−0.0540090	+	0.998540i	$0.517200\pi$
$884$	4499.17	0.171181
$885$	6780.12	0.257527
$886$	−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
$889$	0	0
$890$	−5377.88	−0.202547
$891$	−47364.3	−1.78088
$892$	115596.	4.33905
$893$	24760.6	0.927863
$894$	−29354.7	−1.09818
$895$	−6386.75	−0.238531
$896$	0	0
$897$	−2719.86	−0.101241
$898$	66179.7	2.45929
$899$	−94.3163	−0.00349903
$900$	−39486.1	−1.46245
$901$	−10783.2	−0.398711
$902$	−26416.2	−0.975124
$903$	0	0
$904$	123597.	4.54733
$905$	6738.95	0.247525
$906$	93478.6	3.42783
$907$	18209.7	0.666641	0.333320	−	0.942814i	$-0.391831\pi$
$907$	18209.7	0.666641	0.333320	+	0.942814i	$0.391831\pi$
$908$	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
$915$	3067.71	0.110836
$916$	18783.6	0.677541
$917$	0	0
$918$	−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	$0.381969\pi$
$920$	9980.98	0.357677
$921$	−57272.4	−2.04907
$922$	43268.4	1.54552
$923$	6334.11	0.225883
$924$	0	0
$925$	−18142.3	−0.644882
$926$	19045.7	0.675897
$927$	−30018.8	−1.06359
$928$	21904.7	0.774846
$929$	−9089.58	−0.321011	−0.160506	−	0.987035i	$-0.551312\pi$
$929$	−9089.58	−0.321011	−0.160506	+	0.987035i	$0.551312\pi$
$930$	247.498	0.00872666
$931$	0	0
$932$	18279.2	0.642440
$933$	−26679.6	−0.936173
$934$	81521.3	2.85595
$935$	3210.17	0.112282
$936$	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	$0.742891\pi$
$938$	0	0
$939$	34802.5	1.20952
$940$	15407.8	0.534625
$941$	51013.4	1.76726	0.883629	−	0.468188i	$-0.155093\pi$
$941$	51013.4	1.76726	0.883629	+	0.468188i	$0.155093\pi$
$942$	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	$-0.228783\pi$
$947$	43867.1	1.50527	0.752634	+	0.658439i	$0.228783\pi$
$948$	−114474.	−3.92187
$949$	−7661.16	−0.262057
$950$	−50562.5	−1.72680
$951$	−34769.9	−1.18559
$952$	0	0
$953$	−4167.10	−0.141643	−0.0708214	−	0.997489i	$-0.522562\pi$
$953$	−4167.10	−0.141643	−0.0708214	+	0.997489i	$0.522562\pi$
$954$	−30428.7	−1.03267
$955$	4554.44	0.154323
$956$	−54851.7	−1.85568
$957$	−9760.04	−0.329673
$958$	44617.6	1.50473
$959$	0	0
$960$	−29670.3	−0.997507
$961$	−29780.4	−0.999645
$962$	5833.37	0.195505
$963$	23557.8	0.788307
$964$	25496.0	0.851836
$965$	−6610.85	−0.220529
$966$	0	0
$967$	−21935.0	−0.729454	−0.364727	−	0.931115i	$-0.618838\pi$
$967$	−21935.0	−0.729454	−0.364727	+	0.931115i	$0.618838\pi$
$968$	−107655.	−3.57455
$969$	14211.9	0.471157
$970$	−9462.85	−0.313231
$971$	24169.6	0.798805	0.399403	−	0.916776i	$-0.369218\pi$
$971$	24169.6	0.798805	0.399403	+	0.916776i	$0.369218\pi$
$972$	−83138.4	−2.74348
$973$	0	0
$974$	−53294.4	−1.75325
$975$	5483.38	0.180111
$976$	−55600.9	−1.82351
$977$	16106.2	0.527415	0.263707	−	0.964603i	$-0.415055\pi$
$977$	16106.2	0.527415	0.263707	+	0.964603i	$0.415055\pi$
$978$	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
$985$	5323.43	0.172202
$986$	−4584.93	−0.148087
$987$	0	0
$988$	11950.0	0.384798
$989$	−6014.52	−0.193378
$990$	9058.71	0.290813
$991$	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
$994$	0	0
$995$	11762.5	0.374771
$996$	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	1421.4.a.e.1.1		5
7.6	odd	2		29.4.a.b.1.1	✓	5
21.20	even	2		261.4.a.f.1.5		5
28.27	even	2		464.4.a.l.1.5		5
35.34	odd	2		725.4.a.c.1.5		5
56.13	odd	2		1856.4.a.y.1.5		5
56.27	even	2		1856.4.a.bb.1.1		5
203.202	odd	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	7.6	odd	2
261.4.a.f.1.5		5	21.20	even	2
464.4.a.l.1.5		5	28.27	even	2
725.4.a.c.1.5		5	35.34	odd	2
841.4.a.b.1.5		5	203.202	odd	2
1421.4.a.e.1.1		5	1.1	even	1	trivial
1856.4.a.y.1.5		5	56.13	odd	2
1856.4.a.bb.1.1		5	56.27	even	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:	\( N \)	\(=\)	\( 1421 = 7^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1421.a (trivial)

\(f(q)\)	\(=\)	\(q-5.49488 q^{2} +6.46343 q^{3} +22.1937 q^{4} -2.14270 q^{5} -35.5158 q^{6} -77.9928 q^{8} +14.7760 q^{9} +O(q^{10})\)	\(q-5.49488 q^{2} +6.46343 q^{3} +22.1937 q^{4} -2.14270 q^{5} -35.5158 q^{6} -77.9928 q^{8} +14.7760 q^{9} +11.7739 q^{10} +52.0703 q^{11} +143.448 q^{12} -7.04574 q^{13} -13.8492 q^{15} +251.011 q^{16} -28.7724 q^{17} -81.1922 q^{18} -76.4208 q^{19} -47.5545 q^{20} -286.120 q^{22} +59.7251 q^{23} -504.101 q^{24} -120.409 q^{25} +38.7155 q^{26} -79.0092 q^{27} -29.0000 q^{29} +76.0998 q^{30} +3.25229 q^{31} -755.335 q^{32} +336.553 q^{33} +158.101 q^{34} +327.934 q^{36} +150.673 q^{37} +419.923 q^{38} -45.5397 q^{39} +167.115 q^{40} +92.3254 q^{41} -100.703 q^{43} +1155.63 q^{44} -31.6605 q^{45} -328.182 q^{46} -324.003 q^{47} +1622.39 q^{48} +661.632 q^{50} -185.969 q^{51} -156.371 q^{52} +374.774 q^{53} +434.146 q^{54} -111.571 q^{55} -493.941 q^{57} +159.352 q^{58} -489.567 q^{59} -307.365 q^{60} -221.508 q^{61} -17.8709 q^{62} +2142.39 q^{64} +15.0969 q^{65} -1849.32 q^{66} -427.538 q^{67} -638.567 q^{68} +386.029 q^{69} -898.999 q^{71} -1152.42 q^{72} +1087.35 q^{73} -827.929 q^{74} -778.254 q^{75} -1696.06 q^{76} +250.235 q^{78} -798.018 q^{79} -537.842 q^{80} -909.622 q^{81} -507.317 q^{82} +436.713 q^{83} +61.6507 q^{85} +553.353 q^{86} -187.440 q^{87} -4061.11 q^{88} -456.763 q^{89} +173.971 q^{90} +1325.52 q^{92} +21.0209 q^{93} +1780.36 q^{94} +163.747 q^{95} -4882.06 q^{96} -803.714 q^{97} +769.390 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 8 q^{3} + 26 q^{4} - 10 q^{5} - 34 q^{6} - 84 q^{8} + 33 q^{9}+O(q^{10}) \) 5 * q - 8 * q^3 + 26 * q^4 - 10 * q^5 - 34 * q^6 - 84 * q^8 + 33 * q^9	\( 5 q - 8 q^{3} + 26 q^{4} - 10 q^{5} - 34 q^{6} - 84 q^{8} + 33 q^{9} + 64 q^{10} + 12 q^{11} + 224 q^{12} - 14 q^{13} - 74 q^{15} + 146 q^{16} - 66 q^{17} - 108 q^{18} - 214 q^{19} - 6 q^{20} - 98 q^{22} + 164 q^{23} - 314 q^{24} + 207 q^{25} - 56 q^{26} - 362 q^{27} - 145 q^{29} - 234 q^{30} - 420 q^{31} - 652 q^{32} + 576 q^{33} - 204 q^{34} - 260 q^{36} + 378 q^{37} + 496 q^{38} - 374 q^{39} + 80 q^{40} + 1158 q^{41} - 204 q^{43} + 784 q^{44} + 1506 q^{45} + 580 q^{46} - 248 q^{47} + 1880 q^{48} + 908 q^{50} + 228 q^{51} - 1482 q^{52} - 554 q^{53} - 918 q^{54} - 546 q^{55} + 44 q^{57} - 440 q^{59} + 636 q^{60} - 618 q^{61} - 1250 q^{62} + 2594 q^{64} - 1656 q^{65} - 2940 q^{66} + 1164 q^{67} - 356 q^{68} + 1968 q^{69} - 692 q^{71} - 2648 q^{72} + 1950 q^{73} - 1832 q^{74} - 3074 q^{75} - 1376 q^{76} - 1302 q^{78} + 272 q^{79} + 890 q^{80} + 1801 q^{81} - 92 q^{82} - 512 q^{83} - 1628 q^{85} + 2446 q^{86} + 232 q^{87} - 6954 q^{88} - 866 q^{89} + 2200 q^{90} + 3468 q^{92} - 40 q^{93} + 5942 q^{94} + 2244 q^{95} - 7386 q^{96} - 1562 q^{97} - 238 q^{99}+O(q^{100}) \) 5 * q - 8 * q^3 + 26 * q^4 - 10 * q^5 - 34 * q^6 - 84 * q^8 + 33 * q^9 + 64 * q^10 + 12 * q^11 + 224 * q^12 - 14 * q^13 - 74 * q^15 + 146 * q^16 - 66 * q^17 - 108 * q^18 - 214 * q^19 - 6 * q^20 - 98 * q^22 + 164 * q^23 - 314 * q^24 + 207 * q^25 - 56 * q^26 - 362 * q^27 - 145 * q^29 - 234 * q^30 - 420 * q^31 - 652 * q^32 + 576 * q^33 - 204 * q^34 - 260 * q^36 + 378 * q^37 + 496 * q^38 - 374 * q^39 + 80 * q^40 + 1158 * q^41 - 204 * q^43 + 784 * q^44 + 1506 * q^45 + 580 * q^46 - 248 * q^47 + 1880 * q^48 + 908 * q^50 + 228 * q^51 - 1482 * q^52 - 554 * q^53 - 918 * q^54 - 546 * q^55 + 44 * q^57 - 440 * q^59 + 636 * q^60 - 618 * q^61 - 1250 * q^62 + 2594 * q^64 - 1656 * q^65 - 2940 * q^66 + 1164 * q^67 - 356 * q^68 + 1968 * q^69 - 692 * q^71 - 2648 * q^72 + 1950 * q^73 - 1832 * q^74 - 3074 * q^75 - 1376 * q^76 - 1302 * q^78 + 272 * q^79 + 890 * q^80 + 1801 * q^81 - 92 * q^82 - 512 * q^83 - 1628 * q^85 + 2446 * q^86 + 232 * q^87 - 6954 * q^88 - 866 * q^89 + 2200 * q^90 + 3468 * q^92 - 40 * q^93 + 5942 * q^94 + 2244 * q^95 - 7386 * q^96 - 1562 * q^97 - 238 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more