LMFDB - Embedded newform 435.4.a.l.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [435,4,Mod(1,435)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(435, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("435.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	435.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:	$25.6658308525$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4 x^{9} - 65 x^{8} + 257 x^{7} + 1374 x^{6} - 5303 x^{5} - 10562 x^{4} + 39282 x^{3} + \cdots + 34560 $ x^10 - 4x^9 - 65x^8 + 257x^7 + 1374x^6 - 5303x^5 - 10562x^4 + 39282x^3 + 22140x^2 - 86080*x + 34560
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{5}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$3.24917$ of defining polynomial
Character	$\chi$	$=$	435.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.24917 q^{2} +3.00000 q^{3} +2.55711 q^{4} +5.00000 q^{5} +9.74751 q^{6} +15.3171 q^{7} -17.6849 q^{8} +9.00000 q^{9} +16.2459 q^{10} +13.1966 q^{11} +7.67133 q^{12} +92.7046 q^{13} +49.7679 q^{14} +15.0000 q^{15} -77.9181 q^{16} -128.287 q^{17} +29.2425 q^{18} +127.704 q^{19} +12.7856 q^{20} +45.9514 q^{21} +42.8782 q^{22} -25.4317 q^{23} -53.0546 q^{24} +25.0000 q^{25} +301.213 q^{26} +27.0000 q^{27} +39.1676 q^{28} -29.0000 q^{29} +48.7376 q^{30} +157.197 q^{31} -111.690 q^{32} +39.5899 q^{33} -416.828 q^{34} +76.5856 q^{35} +23.0140 q^{36} +442.821 q^{37} +414.931 q^{38} +278.114 q^{39} -88.4244 q^{40} +73.3418 q^{41} +149.304 q^{42} -121.058 q^{43} +33.7453 q^{44} +45.0000 q^{45} -82.6321 q^{46} -106.742 q^{47} -233.754 q^{48} -108.386 q^{49} +81.2293 q^{50} -384.862 q^{51} +237.056 q^{52} -634.469 q^{53} +87.7276 q^{54} +65.9832 q^{55} -270.881 q^{56} +383.111 q^{57} -94.2260 q^{58} +420.721 q^{59} +38.3567 q^{60} -404.578 q^{61} +510.761 q^{62} +137.854 q^{63} +260.444 q^{64} +463.523 q^{65} +128.634 q^{66} +760.560 q^{67} -328.045 q^{68} -76.2952 q^{69} +248.840 q^{70} +353.030 q^{71} -159.164 q^{72} -562.959 q^{73} +1438.80 q^{74} +75.0000 q^{75} +326.553 q^{76} +202.135 q^{77} +903.639 q^{78} -1260.71 q^{79} -389.590 q^{80} +81.0000 q^{81} +238.300 q^{82} -1405.98 q^{83} +117.503 q^{84} -641.437 q^{85} -393.338 q^{86} -87.0000 q^{87} -233.381 q^{88} +286.757 q^{89} +146.213 q^{90} +1419.97 q^{91} -65.0318 q^{92} +471.592 q^{93} -346.822 q^{94} +638.519 q^{95} -335.070 q^{96} -565.998 q^{97} -352.164 q^{98} +118.770 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} + 30 q^{3} + 66 q^{4} + 50 q^{5} + 12 q^{6} + 75 q^{7} + 9 q^{8} + 90 q^{9} + 20 q^{10} + 3 q^{11} + 198 q^{12} + 75 q^{13} + 105 q^{14} + 150 q^{15} + 394 q^{16} + 131 q^{17} + 36 q^{18}+ \cdots + 27 q^{99}+O(q^{100}) $ 10 * q + 4 * q^2 + 30 * q^3 + 66 * q^4 + 50 * q^5 + 12 * q^6 + 75 * q^7 + 9 * q^8 + 90 * q^9 + 20 * q^10 + 3 * q^11 + 198 * q^12 + 75 * q^13 + 105 * q^14 + 150 * q^15 + 394 * q^16 + 131 * q^17 + 36 * q^18 + 264 * q^19 + 330 * q^20 + 225 * q^21 + 111 * q^22 + 204 * q^23 + 27 * q^24 + 250 * q^25 + 281 * q^26 + 270 * q^27 + 547 * q^28 - 290 * q^29 + 60 * q^30 + 924 * q^31 - 294 * q^32 + 9 * q^33 - 287 * q^34 + 375 * q^35 + 594 * q^36 + 212 * q^37 - 784 * q^38 + 225 * q^39 + 45 * q^40 - 192 * q^41 + 315 * q^42 + 614 * q^43 - 1247 * q^44 + 450 * q^45 - 94 * q^46 + 173 * q^47 + 1182 * q^48 + 357 * q^49 + 100 * q^50 + 393 * q^51 - 687 * q^52 + 658 * q^53 + 108 * q^54 + 15 * q^55 + 514 * q^56 + 792 * q^57 - 116 * q^58 + 190 * q^59 + 990 * q^60 + 1452 * q^61 - 1420 * q^62 + 675 * q^63 + 2709 * q^64 + 375 * q^65 + 333 * q^66 + 343 * q^67 - 601 * q^68 + 612 * q^69 + 525 * q^70 + 8 * q^71 + 81 * q^72 + 1500 * q^73 - 1570 * q^74 + 750 * q^75 + 2014 * q^76 - 431 * q^77 + 843 * q^78 + 2438 * q^79 + 1970 * q^80 + 810 * q^81 - 518 * q^82 + 1336 * q^83 + 1641 * q^84 + 655 * q^85 - 916 * q^86 - 870 * q^87 + 3242 * q^88 + 1319 * q^89 + 180 * q^90 + 1815 * q^91 - 2950 * q^92 + 2772 * q^93 + 2043 * q^94 + 1320 * q^95 - 882 * q^96 + 2034 * q^97 + 1273 * q^98 + 27 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	3.24917	1.14876	0.574378	−	0.818590i	$-0.305244\pi$
$2$	3.24917	1.14876	0.574378	+	0.818590i	$0.305244\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	2.55711	0.319639
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	9.74751	0.663234
$7$	15.3171	0.827047	0.413523	−	0.910493i	$-0.364298\pi$
$7$	15.3171	0.827047	0.413523	+	0.910493i	$0.364298\pi$
$8$	−17.6849	−0.781568
$9$	9.00000	0.333333
$10$	16.2459	0.513739
$11$	13.1966	0.361722	0.180861	−	0.983509i	$-0.442112\pi$
$11$	13.1966	0.361722	0.180861	+	0.983509i	$0.442112\pi$
$12$	7.67133	0.184544
$13$	92.7046	1.97782	0.988908	−	0.148526i	$-0.0474530\pi$
$13$	92.7046	1.97782	0.988908	+	0.148526i	$0.0474530\pi$
$14$	49.7679	0.950074
$15$	15.0000	0.258199
$16$	−77.9181	−1.21747
$17$	−128.287	−1.83025	−0.915126	−	0.403168i	$-0.867909\pi$
$17$	−128.287	−1.83025	−0.915126	+	0.403168i	$0.867909\pi$
$18$	29.2425	0.382918
$19$	127.704	1.54196	0.770980	−	0.636859i	$-0.219767\pi$
$19$	127.704	1.54196	0.770980	+	0.636859i	$0.219767\pi$
$20$	12.7856	0.142947
$21$	45.9514	0.477496
$22$	42.8782	0.415530
$23$	−25.4317	−0.230560	−0.115280	−	0.993333i	$-0.536777\pi$
$23$	−25.4317	−0.230560	−0.115280	+	0.993333i	$0.536777\pi$
$24$	−53.0546	−0.451239
$25$	25.0000	0.200000
$26$	301.213	2.27203
$27$	27.0000	0.192450
$28$	39.1676	0.264356
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	48.7376	0.296607
$31$	157.197	0.910757	0.455379	−	0.890298i	$-0.349504\pi$
$31$	157.197	0.910757	0.455379	+	0.890298i	$0.349504\pi$
$32$	−111.690	−0.617007
$33$	39.5899	0.208840
$34$	−416.828	−2.10251
$35$	76.5856	0.369867
$36$	23.0140	0.106546
$37$	442.821	1.96755	0.983776	−	0.179403i	$-0.0574167\pi$
$37$	442.821	1.96755	0.983776	+	0.179403i	$0.0574167\pi$
$38$	414.931	1.77134
$39$	278.114	1.14189
$40$	−88.4244	−0.349528
$41$	73.3418	0.279367	0.139684	−	0.990196i	$-0.455391\pi$
$41$	73.3418	0.279367	0.139684	+	0.990196i	$0.455391\pi$
$42$	149.304	0.548526
$43$	−121.058	−0.429330	−0.214665	−	0.976688i	$-0.568866\pi$
$43$	−121.058	−0.429330	−0.214665	+	0.976688i	$0.568866\pi$
$44$	33.7453	0.115620
$45$	45.0000	0.149071
$46$	−82.6321	−0.264857
$47$	−106.742	−0.331274	−0.165637	−	0.986187i	$-0.552968\pi$
$47$	−106.742	−0.331274	−0.165637	+	0.986187i	$0.552968\pi$
$48$	−233.754	−0.702907
$49$	−108.386	−0.315994
$50$	81.2293	0.229751
$51$	−384.862	−1.05670
$52$	237.056	0.632187
$53$	−634.469	−1.64436	−0.822180	−	0.569228i	$-0.807242\pi$
$53$	−634.469	−1.64436	−0.822180	+	0.569228i	$0.807242\pi$
$54$	87.7276	0.221078
$55$	65.9832	0.161767
$56$	−270.881	−0.646394
$57$	383.111	0.890251
$58$	−94.2260	−0.213319
$59$	420.721	0.928360	0.464180	−	0.885741i	$-0.346349\pi$
$59$	420.721	0.928360	0.464180	+	0.885741i	$0.346349\pi$
$60$	38.3567	0.0825304
$61$	−404.578	−0.849195	−0.424598	−	0.905382i	$-0.639584\pi$
$61$	−404.578	−0.849195	−0.424598	+	0.905382i	$0.639584\pi$
$62$	510.761	1.04624
$63$	137.854	0.275682
$64$	260.444	0.508680
$65$	463.523	0.884507
$66$	128.634	0.239906
$67$	760.560	1.38682	0.693412	−	0.720542i	$-0.256107\pi$
$67$	760.560	1.38682	0.693412	+	0.720542i	$0.256107\pi$
$68$	−328.045	−0.585020
$69$	−76.2952	−0.133114
$70$	248.840	0.424886
$71$	353.030	0.590097	0.295049	−	0.955482i	$-0.404664\pi$
$71$	353.030	0.590097	0.295049	+	0.955482i	$0.404664\pi$
$72$	−159.164	−0.260523
$73$	−562.959	−0.902595	−0.451297	−	0.892374i	$-0.649039\pi$
$73$	−562.959	−0.902595	−0.451297	+	0.892374i	$0.649039\pi$
$74$	1438.80	2.26024
$75$	75.0000	0.115470
$76$	326.553	0.492870
$77$	202.135	0.299161
$78$	903.639	1.31176
$79$	−1260.71	−1.79546	−0.897730	−	0.440547i	$-0.854785\pi$
$79$	−1260.71	−1.79546	−0.897730	+	0.440547i	$0.854785\pi$
$80$	−389.590	−0.544469
$81$	81.0000	0.111111
$82$	238.300	0.320925
$83$	−1405.98	−1.85935	−0.929677	−	0.368377i	$-0.879914\pi$
$83$	−1405.98	−1.85935	−0.929677	+	0.368377i	$0.879914\pi$
$84$	117.503	0.152626
$85$	−641.437	−0.818514
$86$	−393.338	−0.493195
$87$	−87.0000	−0.107211
$88$	−233.381	−0.282710
$89$	286.757	0.341530	0.170765	−	0.985312i	$-0.445376\pi$
$89$	286.757	0.341530	0.170765	+	0.985312i	$0.445376\pi$
$90$	146.213	0.171246
$91$	1419.97	1.63575
$92$	−65.0318	−0.0736960
$93$	471.592	0.525826
$94$	−346.822	−0.380553
$95$	638.519	0.689586
$96$	−335.070	−0.356229
$97$	−565.998	−0.592457	−0.296229	−	0.955117i	$-0.595729\pi$
$97$	−565.998	−0.592457	−0.296229	+	0.955117i	$0.595729\pi$
$98$	−352.164	−0.362999
$99$	118.770	0.120574
$100$	63.9278	0.0639278
$101$	8.66755	0.00853914	0.00426957	−	0.999991i	$-0.498641\pi$
$101$	8.66755	0.00853914	0.00426957	+	0.999991i	$0.498641\pi$
$102$	−1250.48	−1.21389
$103$	22.2219	0.0212581	0.0106291	−	0.999944i	$-0.496617\pi$
$103$	22.2219	0.0212581	0.0106291	+	0.999944i	$0.496617\pi$
$104$	−1639.47	−1.54580
$105$	229.757	0.213543
$106$	−2061.50	−1.88897
$107$	−382.081	−0.345207	−0.172604	−	0.984991i	$-0.555218\pi$
$107$	−382.081	−0.345207	−0.172604	+	0.984991i	$0.555218\pi$
$108$	69.0420	0.0615145
$109$	−1458.66	−1.28179	−0.640893	−	0.767630i	$-0.721436\pi$
$109$	−1458.66	−1.28179	−0.640893	+	0.767630i	$0.721436\pi$
$110$	214.391	0.185831
$111$	1328.46	1.13597
$112$	−1193.48	−1.00690
$113$	863.401	0.718778	0.359389	−	0.933188i	$-0.382985\pi$
$113$	863.401	0.718778	0.359389	+	0.933188i	$0.382985\pi$
$114$	1244.79	1.02268
$115$	−127.159	−0.103110
$116$	−74.1562	−0.0593555
$117$	834.341	0.659272
$118$	1367.00	1.06646
$119$	−1965.00	−1.51370
$120$	−265.273	−0.201800
$121$	−1156.85	−0.869157
$122$	−1314.54	−0.975518
$123$	220.025	0.161293
$124$	401.971	0.291113
$125$	125.000	0.0894427
$126$	447.911	0.316691
$127$	145.667	0.101779	0.0508893	−	0.998704i	$-0.483794\pi$
$127$	145.667	0.101779	0.0508893	+	0.998704i	$0.483794\pi$
$128$	1739.75	1.20136
$129$	−363.174	−0.247874
$130$	1506.06	1.01608
$131$	−2700.11	−1.80084	−0.900420	−	0.435021i	$-0.856741\pi$
$131$	−2700.11	−1.80084	−0.900420	+	0.435021i	$0.856741\pi$
$132$	101.236	0.0667534
$133$	1956.05	1.27527
$134$	2471.19	1.59312
$135$	135.000	0.0860663
$136$	2268.75	1.43047
$137$	2853.11	1.77926	0.889628	−	0.456686i	$-0.150964\pi$
$137$	2853.11	1.77926	0.889628	+	0.456686i	$0.150964\pi$
$138$	−247.896	−0.152915
$139$	227.123	0.138592	0.0692960	−	0.997596i	$-0.477925\pi$
$139$	227.123	0.138592	0.0692960	+	0.997596i	$0.477925\pi$
$140$	195.838	0.118224
$141$	−320.225	−0.191261
$142$	1147.05	0.677877
$143$	1223.39	0.715419
$144$	−701.263	−0.405823
$145$	−145.000	−0.0830455
$146$	−1829.15	−1.03686
$147$	−325.157	−0.182439
$148$	1132.34	0.628906
$149$	−2969.86	−1.63289	−0.816444	−	0.577425i	$-0.804058\pi$
$149$	−2969.86	−1.63289	−0.816444	+	0.577425i	$0.804058\pi$
$150$	243.688	0.132647
$151$	−1346.91	−0.725892	−0.362946	−	0.931810i	$-0.618229\pi$
$151$	−1346.91	−0.725892	−0.362946	+	0.931810i	$0.618229\pi$
$152$	−2258.42	−1.20515
$153$	−1154.59	−0.610084
$154$	656.770	0.343662
$155$	785.987	0.407303
$156$	711.168	0.364993
$157$	−667.920	−0.339527	−0.169764	−	0.985485i	$-0.554300\pi$
$157$	−667.920	−0.339527	−0.169764	+	0.985485i	$0.554300\pi$
$158$	−4096.27	−2.06254
$159$	−1903.41	−0.949371
$160$	−558.451	−0.275934
$161$	−389.541	−0.190684
$162$	263.183	0.127639
$163$	−685.566	−0.329434	−0.164717	−	0.986341i	$-0.552671\pi$
$163$	−685.566	−0.329434	−0.164717	+	0.986341i	$0.552671\pi$
$164$	187.543	0.0892967
$165$	197.950	0.0933961
$166$	−4568.27	−2.13594
$167$	1234.27	0.571922	0.285961	−	0.958241i	$-0.407687\pi$
$167$	1234.27	0.571922	0.285961	+	0.958241i	$0.407687\pi$
$168$	−812.644	−0.373196
$169$	6397.14	2.91176
$170$	−2084.14	−0.940272
$171$	1149.33	0.513987
$172$	−309.559	−0.137231
$173$	−2489.30	−1.09398	−0.546988	−	0.837140i	$-0.684226\pi$
$173$	−2489.30	−1.09398	−0.546988	+	0.837140i	$0.684226\pi$
$174$	−282.678	−0.123160
$175$	382.928	0.165409
$176$	−1028.26	−0.440385
$177$	1262.16	0.535989
$178$	931.721	0.392334
$179$	655.747	0.273815	0.136907	−	0.990584i	$-0.456284\pi$
$179$	655.747	0.273815	0.136907	+	0.990584i	$0.456284\pi$
$180$	115.070	0.0476490
$181$	−1121.86	−0.460704	−0.230352	−	0.973107i	$-0.573988\pi$
$181$	−1121.86	−0.460704	−0.230352	+	0.973107i	$0.573988\pi$
$182$	4613.72	1.87907
$183$	−1213.73	−0.490283
$184$	449.757	0.180199
$185$	2214.11	0.879916
$186$	1532.28	0.604045
$187$	−1692.96	−0.662042
$188$	−272.950	−0.105888
$189$	413.562	0.159165
$190$	2074.66	0.792165
$191$	928.723	0.351832	0.175916	−	0.984405i	$-0.443711\pi$
$191$	928.723	0.351832	0.175916	+	0.984405i	$0.443711\pi$
$192$	781.333	0.293687
$193$	−1909.34	−0.712109	−0.356054	−	0.934465i	$-0.615878\pi$
$193$	−1909.34	−0.712109	−0.356054	+	0.934465i	$0.615878\pi$
$194$	−1839.02	−0.680588
$195$	1390.57	0.510670
$196$	−277.155	−0.101004
$197$	1882.11	0.680685	0.340342	−	0.940302i	$-0.389457\pi$
$197$	1882.11	0.680685	0.340342	+	0.940302i	$0.389457\pi$
$198$	385.903	0.138510
$199$	−859.913	−0.306320	−0.153160	−	0.988201i	$-0.548945\pi$
$199$	−859.913	−0.306320	−0.153160	+	0.988201i	$0.548945\pi$
$200$	−442.122	−0.156314
$201$	2281.68	0.800683
$202$	28.1623	0.00980938
$203$	−444.197	−0.153579
$204$	−984.136	−0.337761
$205$	366.709	0.124937
$206$	72.2027	0.0244204
$207$	−228.886	−0.0768534
$208$	−7223.36	−2.40793
$209$	1685.26	0.557760
$210$	746.519	0.245308
$211$	3021.13	0.985701	0.492850	−	0.870114i	$-0.335955\pi$
$211$	3021.13	0.985701	0.492850	+	0.870114i	$0.335955\pi$
$212$	−1622.41	−0.525601
$213$	1059.09	0.340693
$214$	−1241.45	−0.396559
$215$	−605.290	−0.192002
$216$	−477.492	−0.150413
$217$	2407.81	0.753239
$218$	−4739.45	−1.47246
$219$	−1688.88	−0.521113
$220$	168.726	0.0517070
$221$	−11892.8	−3.61990
$222$	4316.41	1.30495
$223$	−2426.93	−0.728787	−0.364394	−	0.931245i	$-0.618724\pi$
$223$	−2426.93	−0.728787	−0.364394	+	0.931245i	$0.618724\pi$
$224$	−1710.77	−0.510293
$225$	225.000	0.0666667
$226$	2805.34	0.825700
$227$	−688.137	−0.201204	−0.100602	−	0.994927i	$-0.532077\pi$
$227$	−688.137	−0.201204	−0.100602	+	0.994927i	$0.532077\pi$
$228$	979.658	0.284559
$229$	−2876.74	−0.830132	−0.415066	−	0.909791i	$-0.636241\pi$
$229$	−2876.74	−0.830132	−0.415066	+	0.909791i	$0.636241\pi$
$230$	−413.160	−0.118448
$231$	606.404	0.172721
$232$	512.861	0.145134
$233$	3643.42	1.02441	0.512207	−	0.858862i	$-0.328828\pi$
$233$	3643.42	1.02441	0.512207	+	0.858862i	$0.328828\pi$
$234$	2710.92	0.757343
$235$	−533.708	−0.148150
$236$	1075.83	0.296740
$237$	−3782.14	−1.03661
$238$	−6384.60	−1.73888
$239$	39.6875	0.0107413	0.00537066	−	0.999986i	$-0.498290\pi$
$239$	39.6875	0.0107413	0.00537066	+	0.999986i	$0.498290\pi$
$240$	−1168.77	−0.314349
$241$	1360.67	0.363688	0.181844	−	0.983327i	$-0.441793\pi$
$241$	1360.67	0.363688	0.181844	+	0.983327i	$0.441793\pi$
$242$	−3758.80	−0.998449
$243$	243.000	0.0641500
$244$	−1034.55	−0.271436
$245$	−541.929	−0.141317
$246$	714.900	0.185286
$247$	11838.7	3.04971
$248$	−2780.02	−0.711819
$249$	−4217.94	−1.07350
$250$	406.146	0.102748
$251$	−4520.37	−1.13675	−0.568373	−	0.822771i	$-0.692427\pi$
$251$	−4520.37	−1.13675	−0.568373	+	0.822771i	$0.692427\pi$
$252$	352.508	0.0881188
$253$	−335.614	−0.0833986
$254$	473.298	0.116919
$255$	−1924.31	−0.472569
$256$	3569.19	0.871384
$257$	−2843.13	−0.690077	−0.345038	−	0.938589i	$-0.612134\pi$
$257$	−2843.13	−0.690077	−0.345038	+	0.938589i	$0.612134\pi$
$258$	−1180.02	−0.284746
$259$	6782.75	1.62726
$260$	1185.28	0.282723
$261$	−261.000	−0.0618984
$262$	−8773.13	−2.06872
$263$	−3664.30	−0.859127	−0.429563	−	0.903037i	$-0.641333\pi$
$263$	−3664.30	−0.859127	−0.429563	+	0.903037i	$0.641333\pi$
$264$	−700.143	−0.163223
$265$	−3172.35	−0.735380
$266$	6355.55	1.46498
$267$	860.270	0.197182
$268$	1944.84	0.443283
$269$	3948.22	0.894896	0.447448	−	0.894310i	$-0.352333\pi$
$269$	3948.22	0.894896	0.447448	+	0.894310i	$0.352333\pi$
$270$	438.638	0.0988691
$271$	8099.47	1.81553	0.907763	−	0.419484i	$-0.137789\pi$
$271$	8099.47	1.81553	0.907763	+	0.419484i	$0.137789\pi$
$272$	9995.91	2.22828
$273$	4259.90	0.944399
$274$	9270.26	2.04393
$275$	329.916	0.0723443
$276$	−195.095	−0.0425484
$277$	−4316.21	−0.936230	−0.468115	−	0.883668i	$-0.655067\pi$
$277$	−4316.21	−0.936230	−0.468115	+	0.883668i	$0.655067\pi$
$278$	737.961	0.159208
$279$	1414.78	0.303586
$280$	−1354.41	−0.289076
$281$	−5441.20	−1.15514	−0.577571	−	0.816341i	$-0.695999\pi$
$281$	−5441.20	−1.15514	−0.577571	+	0.816341i	$0.695999\pi$
$282$	−1040.47	−0.219712
$283$	−1488.06	−0.312565	−0.156282	−	0.987712i	$-0.549951\pi$
$283$	−1488.06	−0.312565	−0.156282	+	0.987712i	$0.549951\pi$
$284$	902.736	0.188618
$285$	1915.56	0.398132
$286$	3975.00	0.821842
$287$	1123.39	0.231050
$288$	−1005.21	−0.205669
$289$	11544.7	2.34982
$290$	−471.130	−0.0953989
$291$	−1697.99	−0.342055
$292$	−1439.55	−0.288504
$293$	−1329.28	−0.265042	−0.132521	−	0.991180i	$-0.542307\pi$
$293$	−1329.28	−0.265042	−0.132521	+	0.991180i	$0.542307\pi$
$294$	−1056.49	−0.209578
$295$	2103.61	0.415175
$296$	−7831.24	−1.53778
$297$	356.309	0.0696134
$298$	−9649.58	−1.87579
$299$	−2357.64	−0.456006
$300$	191.783	0.0369087
$301$	−1854.26	−0.355076
$302$	−4376.33	−0.833873
$303$	26.0026	0.00493007
$304$	−9950.43	−1.87729
$305$	−2022.89	−0.379772
$306$	−3751.45	−0.700837
$307$	3273.11	0.608489	0.304245	−	0.952594i	$-0.401596\pi$
$307$	3273.11	0.608489	0.304245	+	0.952594i	$0.401596\pi$
$308$	516.881	0.0956234
$309$	66.6657	0.0122734
$310$	2553.80	0.467892
$311$	6819.97	1.24349	0.621744	−	0.783220i	$-0.286424\pi$
$311$	6819.97	1.24349	0.621744	+	0.783220i	$0.286424\pi$
$312$	−4918.41	−0.892468
$313$	6086.97	1.09922	0.549610	−	0.835421i	$-0.314776\pi$
$313$	6086.97	1.09922	0.549610	+	0.835421i	$0.314776\pi$
$314$	−2170.19	−0.390034
$315$	689.270	0.123289
$316$	−3223.78	−0.573899
$317$	528.192	0.0935844	0.0467922	−	0.998905i	$-0.485100\pi$
$317$	528.192	0.0935844	0.0467922	+	0.998905i	$0.485100\pi$
$318$	−6184.50	−1.09060
$319$	−382.703	−0.0671700
$320$	1302.22	0.227489
$321$	−1146.24	−0.199305
$322$	−1265.69	−0.219049
$323$	−16382.8	−2.82218
$324$	207.126	0.0355154
$325$	2317.61	0.395563
$326$	−2227.52	−0.378439
$327$	−4375.99	−0.740039
$328$	−1297.04	−0.218345
$329$	−1634.97	−0.273979
$330$	643.172	0.107289
$331$	−4640.42	−0.770576	−0.385288	−	0.922796i	$-0.625898\pi$
$331$	−4640.42	−0.770576	−0.385288	+	0.922796i	$0.625898\pi$
$332$	−3595.25	−0.594322
$333$	3985.39	0.655850
$334$	4010.37	0.656998
$335$	3802.80	0.620206
$336$	−3580.44	−0.581337
$337$	2733.84	0.441904	0.220952	−	0.975285i	$-0.429084\pi$
$337$	2733.84	0.441904	0.220952	+	0.975285i	$0.429084\pi$
$338$	20785.4	3.34490
$339$	2590.20	0.414987
$340$	−1640.23	−0.261629
$341$	2074.48	0.329441
$342$	3734.38	0.590445
$343$	−6913.93	−1.08839
$344$	2140.90	0.335551
$345$	−381.476	−0.0595304
$346$	−8088.16	−1.25671
$347$	11957.0	1.84982	0.924910	−	0.380187i	$-0.124140\pi$
$347$	11957.0	1.84982	0.924910	+	0.380187i	$0.124140\pi$
$348$	−222.469	−0.0342689
$349$	5552.21	0.851584	0.425792	−	0.904821i	$-0.359996\pi$
$349$	5552.21	0.851584	0.425792	+	0.904821i	$0.359996\pi$
$350$	1244.20	0.190015
$351$	2503.02	0.380631
$352$	−1473.93	−0.223185
$353$	−3044.14	−0.458990	−0.229495	−	0.973310i	$-0.573707\pi$
$353$	−3044.14	−0.458990	−0.229495	+	0.973310i	$0.573707\pi$
$354$	4100.99	0.615720
$355$	1765.15	0.263899
$356$	733.268	0.109166
$357$	−5894.99	−0.873938
$358$	2130.63	0.314546
$359$	−5.90514	−0.000868138 0	−0.000434069	−	1.00000i	$-0.500138\pi$
$359$	−5.90514	−0.000868138 0	−0.000434069		1.00000i	$0.500138\pi$
$360$	−795.819	−0.116509
$361$	9449.24	1.37764
$362$	−3645.13	−0.529236
$363$	−3470.55	−0.501808
$364$	3631.01	0.522848
$365$	−2814.80	−0.403653
$366$	−3943.63	−0.563215
$367$	13082.6	1.86078	0.930390	−	0.366572i	$-0.119469\pi$
$367$	13082.6	1.86078	0.930390	+	0.366572i	$0.119469\pi$
$368$	1981.59	0.280700
$369$	660.076	0.0931225
$370$	7194.01	1.01081
$371$	−9718.24	−1.35996
$372$	1205.91	0.168074
$373$	4362.30	0.605553	0.302777	−	0.953062i	$-0.402086\pi$
$373$	4362.30	0.605553	0.302777	+	0.953062i	$0.402086\pi$
$374$	−5500.73	−0.760524
$375$	375.000	0.0516398
$376$	1887.71	0.258913
$377$	−2688.43	−0.367271
$378$	1343.73	0.182842
$379$	9062.62	1.22827	0.614136	−	0.789200i	$-0.289504\pi$
$379$	9062.62	1.22827	0.614136	+	0.789200i	$0.289504\pi$
$380$	1632.76	0.220418
$381$	437.002	0.0587619
$382$	3017.58	0.404169
$383$	−10642.7	−1.41989	−0.709946	−	0.704256i	$-0.751281\pi$
$383$	−10642.7	−1.41989	−0.709946	+	0.704256i	$0.751281\pi$
$384$	5219.25	0.693603
$385$	1010.67	0.133789
$386$	−6203.76	−0.818039
$387$	−1089.52	−0.143110
$388$	−1447.32	−0.189372
$389$	7071.75	0.921728	0.460864	−	0.887471i	$-0.347540\pi$
$389$	7071.75	0.921728	0.460864	+	0.887471i	$0.347540\pi$
$390$	4518.19	0.586635
$391$	3262.57	0.421983
$392$	1916.79	0.246971
$393$	−8100.34	−1.03972
$394$	6115.30	0.781940
$395$	−6303.57	−0.802954
$396$	303.708	0.0385401
$397$	−14393.7	−1.81964	−0.909821	−	0.415001i	$-0.863781\pi$
$397$	−14393.7	−1.81964	−0.909821	+	0.415001i	$0.863781\pi$
$398$	−2794.01	−0.351886
$399$	5868.16	0.736279
$400$	−1947.95	−0.243494
$401$	6410.03	0.798258	0.399129	−	0.916895i	$-0.369313\pi$
$401$	6410.03	0.798258	0.399129	+	0.916895i	$0.369313\pi$
$402$	7413.57	0.919789
$403$	14572.9	1.80131
$404$	22.1639	0.00272944
$405$	405.000	0.0496904
$406$	−1443.27	−0.176424
$407$	5843.76	0.711706
$408$	6806.25	0.825881
$409$	−1504.93	−0.181941	−0.0909704	−	0.995854i	$-0.528997\pi$
$409$	−1504.93	−0.181941	−0.0909704	+	0.995854i	$0.528997\pi$
$410$	1191.50	0.143522
$411$	8559.34	1.02725
$412$	56.8238	0.00679493
$413$	6444.24	0.767797
$414$	−743.689	−0.0882858
$415$	−7029.90	−0.831528
$416$	−10354.2	−1.22033
$417$	681.368	0.0800162
$418$	5475.70	0.640730
$419$	9086.25	1.05941	0.529705	−	0.848182i	$-0.322303\pi$
$419$	9086.25	1.05941	0.529705	+	0.848182i	$0.322303\pi$
$420$	587.514	0.0682565
$421$	3629.83	0.420207	0.210104	−	0.977679i	$-0.432620\pi$
$421$	3629.83	0.420207	0.210104	+	0.977679i	$0.432620\pi$
$422$	9816.15	1.13233
$423$	−960.675	−0.110425
$424$	11220.5	1.28518
$425$	−3207.19	−0.366050
$426$	3441.16	0.391373
$427$	−6196.97	−0.702324
$428$	−977.023	−0.110342
$429$	3670.17	0.413047
$430$	−1966.69	−0.220563
$431$	13184.1	1.47344	0.736722	−	0.676196i	$-0.236373\pi$
$431$	13184.1	1.47344	0.736722	+	0.676196i	$0.236373\pi$
$432$	−2103.79	−0.234302
$433$	1537.65	0.170658	0.0853290	−	0.996353i	$-0.472806\pi$
$433$	1537.65	0.170658	0.0853290	+	0.996353i	$0.472806\pi$
$434$	7823.39	0.865287
$435$	−435.000	−0.0479463
$436$	−3729.96	−0.409708
$437$	−3247.73	−0.355515
$438$	−5487.45	−0.598632
$439$	−11087.1	−1.20537	−0.602684	−	0.797980i	$-0.705902\pi$
$439$	−11087.1	−1.20537	−0.602684	+	0.797980i	$0.705902\pi$
$440$	−1166.91	−0.126432
$441$	−975.472	−0.105331
$442$	−38641.9	−4.15838
$443$	−55.7328	−0.00597731	−0.00298865	−	0.999996i	$-0.500951\pi$
$443$	−55.7328	−0.00597731	−0.00298865	+	0.999996i	$0.500951\pi$
$444$	3397.03	0.363099
$445$	1433.78	0.152737
$446$	−7885.52	−0.837198
$447$	−8909.57	−0.942748
$448$	3989.26	0.420702
$449$	14054.7	1.47725	0.738623	−	0.674119i	$-0.235477\pi$
$449$	14054.7	1.47725	0.738623	+	0.674119i	$0.235477\pi$
$450$	731.063	0.0765837
$451$	967.865	0.101053
$452$	2207.81	0.229749
$453$	−4040.72	−0.419094
$454$	−2235.88	−0.231134
$455$	7099.84	0.731528
$456$	−6775.27	−0.695792
$457$	−14171.3	−1.45056	−0.725280	−	0.688454i	$-0.758289\pi$
$457$	−14171.3	−1.45056	−0.725280	+	0.688454i	$0.758289\pi$
$458$	−9347.01	−0.953618
$459$	−3463.76	−0.352232
$460$	−325.159	−0.0329579
$461$	13504.2	1.36432	0.682161	−	0.731202i	$-0.261041\pi$
$461$	13504.2	1.36432	0.682161	+	0.731202i	$0.261041\pi$
$462$	1970.31	0.198414
$463$	4288.75	0.430486	0.215243	−	0.976561i	$-0.430946\pi$
$463$	4288.75	0.430486	0.215243	+	0.976561i	$0.430946\pi$
$464$	2259.62	0.226078
$465$	2357.96	0.235157
$466$	11838.1	1.17680
$467$	2434.86	0.241268	0.120634	−	0.992697i	$-0.461507\pi$
$467$	2434.86	0.241268	0.120634	+	0.992697i	$0.461507\pi$
$468$	2133.50	0.210729
$469$	11649.6	1.14697
$470$	−1734.11	−0.170188
$471$	−2003.76	−0.196026
$472$	−7440.41	−0.725577
$473$	−1597.56	−0.155298
$474$	−12288.8	−1.19081
$475$	3192.59	0.308392
$476$	−5024.71	−0.483839
$477$	−5710.22	−0.548120
$478$	128.952	0.0123391
$479$	5102.67	0.486737	0.243369	−	0.969934i	$-0.421748\pi$
$479$	5102.67	0.486737	0.243369	+	0.969934i	$0.421748\pi$
$480$	−1675.35	−0.159310
$481$	41051.6	3.89146
$482$	4421.07	0.417788
$483$	−1168.62	−0.110092
$484$	−2958.19	−0.277817
$485$	−2829.99	−0.264955
$486$	789.549	0.0736927
$487$	−16.0388	−0.00149237	−0.000746187	−	1.00000i	$-0.500238\pi$
$487$	−16.0388	−0.00149237	−0.000746187		1.00000i	$0.500238\pi$
$488$	7154.91	0.663704
$489$	−2056.70	−0.190199
$490$	−1760.82	−0.162338
$491$	8830.31	0.811622	0.405811	−	0.913957i	$-0.366989\pi$
$491$	8830.31	0.811622	0.405811	+	0.913957i	$0.366989\pi$
$492$	562.629	0.0515555
$493$	3720.34	0.339869
$494$	38466.0	3.50338
$495$	593.849	0.0539223
$496$	−12248.5	−1.10882
$497$	5407.40	0.488038
$498$	−13704.8	−1.23319
$499$	−18025.8	−1.61712	−0.808562	−	0.588411i	$-0.799754\pi$
$499$	−18025.8	−1.61712	−0.808562	+	0.588411i	$0.799754\pi$
$500$	319.639	0.0285894
$501$	3702.82	0.330199
$502$	−14687.5	−1.30584
$503$	−10613.5	−0.940823	−0.470412	−	0.882447i	$-0.655895\pi$
$503$	−10613.5	−0.940823	−0.470412	+	0.882447i	$0.655895\pi$
$504$	−2437.93	−0.215465
$505$	43.3377	0.00381882
$506$	−1090.47	−0.0958046
$507$	19191.4	1.68111
$508$	372.487	0.0325324
$509$	21672.1	1.88723	0.943615	−	0.331045i	$-0.107401\pi$
$509$	21672.1	1.88723	0.943615	+	0.331045i	$0.107401\pi$
$510$	−6252.42	−0.542866
$511$	−8622.92	−0.746488
$512$	−2321.09	−0.200349
$513$	3448.00	0.296750
$514$	−9237.83	−0.792730
$515$	111.109	0.00950693
$516$	−928.677	−0.0792301
$517$	−1408.63	−0.119829
$518$	22038.3	1.86932
$519$	−7467.90	−0.631608
$520$	−8197.34	−0.691302
$521$	5074.30	0.426697	0.213348	−	0.976976i	$-0.431563\pi$
$521$	5074.30	0.426697	0.213348	+	0.976976i	$0.431563\pi$
$522$	−848.034	−0.0711062
$523$	−2270.14	−0.189802	−0.0949009	−	0.995487i	$-0.530253\pi$
$523$	−2270.14	−0.189802	−0.0949009	+	0.995487i	$0.530253\pi$
$524$	−6904.49	−0.575619
$525$	1148.78	0.0954991
$526$	−11905.9	−0.986927
$527$	−20166.5	−1.66692
$528$	−3084.77	−0.254257
$529$	−11520.2	−0.946842
$530$	−10307.5	−0.844772
$531$	3786.49	0.309453
$532$	5001.85	0.407627
$533$	6799.12	0.552538
$534$	2795.16	0.226514
$535$	−1910.40	−0.154381
$536$	−13450.4	−1.08390
$537$	1967.24	0.158087
$538$	12828.4	1.02802
$539$	−1430.33	−0.114302
$540$	345.210	0.0275101
$541$	−16931.4	−1.34554	−0.672771	−	0.739850i	$-0.734896\pi$
$541$	−16931.4	−1.34554	−0.672771	+	0.739850i	$0.734896\pi$
$542$	26316.5	2.08560
$543$	−3365.59	−0.265988
$544$	14328.4	1.12928
$545$	−7293.32	−0.573232
$546$	13841.1	1.08488
$547$	−19277.9	−1.50688	−0.753439	−	0.657518i	$-0.771607\pi$
$547$	−19277.9	−1.50688	−0.753439	+	0.657518i	$0.771607\pi$
$548$	7295.73	0.568719
$549$	−3641.20	−0.283065
$550$	1071.95	0.0831059
$551$	−3703.41	−0.286335
$552$	1349.27	0.104038
$553$	−19310.5	−1.48493
$554$	−14024.1	−1.07550
$555$	6642.32	0.508020
$556$	580.778	0.0442994
$557$	22405.6	1.70441	0.852205	−	0.523208i	$-0.175265\pi$
$557$	22405.6	1.70441	0.852205	+	0.523208i	$0.175265\pi$
$558$	4596.85	0.348746
$559$	−11222.6	−0.849136
$560$	−5967.40	−0.450301
$561$	−5078.89	−0.382230
$562$	−17679.4	−1.32698
$563$	−5383.32	−0.402984	−0.201492	−	0.979490i	$-0.564579\pi$
$563$	−5383.32	−0.402984	−0.201492	+	0.979490i	$0.564579\pi$
$564$	−818.851	−0.0611345
$565$	4317.00	0.321447
$566$	−4834.96	−0.359061
$567$	1240.69	0.0918941
$568$	−6243.28	−0.461201
$569$	11142.9	0.820977	0.410489	−	0.911866i	$-0.365358\pi$
$569$	11142.9	0.820977	0.410489	+	0.911866i	$0.365358\pi$
$570$	6223.97	0.457357
$571$	19658.2	1.44075	0.720377	−	0.693583i	$-0.243969\pi$
$571$	19658.2	1.44075	0.720377	+	0.693583i	$0.243969\pi$
$572$	3128.34	0.228676
$573$	2786.17	0.203131
$574$	3650.07	0.265420
$575$	−635.794	−0.0461120
$576$	2344.00	0.169560
$577$	11106.1	0.801305	0.400652	−	0.916230i	$-0.368784\pi$
$577$	11106.1	0.801305	0.400652	+	0.916230i	$0.368784\pi$
$578$	37510.6	2.69937
$579$	−5728.01	−0.411136
$580$	−370.781	−0.0265446
$581$	−21535.6	−1.53777
$582$	−5517.07	−0.392938
$583$	−8372.86	−0.594800
$584$	9955.87	0.705439
$585$	4171.71	0.294836
$586$	−4319.05	−0.304468
$587$	3384.91	0.238007	0.119003	−	0.992894i	$-0.462030\pi$
$587$	3384.91	0.238007	0.119003	+	0.992894i	$0.462030\pi$
$588$	−831.464	−0.0583146
$589$	20074.7	1.40435
$590$	6834.98	0.476935
$591$	5646.33	0.392993
$592$	−34503.8	−2.39543
$593$	−14326.2	−0.992087	−0.496044	−	0.868298i	$-0.665214\pi$
$593$	−14326.2	−0.992087	−0.496044	+	0.868298i	$0.665214\pi$
$594$	1157.71	0.0799687
$595$	−9824.98	−0.676949
$596$	−7594.26	−0.521934
$597$	−2579.74	−0.176854
$598$	−7660.37	−0.523839
$599$	−9809.62	−0.669132	−0.334566	−	0.942372i	$-0.608590\pi$
$599$	−9809.62	−0.669132	−0.334566	+	0.942372i	$0.608590\pi$
$600$	−1326.37	−0.0902478
$601$	21136.6	1.43457	0.717287	−	0.696778i	$-0.245384\pi$
$601$	21136.6	1.43457	0.717287	+	0.696778i	$0.245384\pi$
$602$	−6024.81	−0.407895
$603$	6845.04	0.462275
$604$	−3444.19	−0.232023
$605$	−5784.24	−0.388699
$606$	84.4870	0.00566345
$607$	−14745.5	−0.986002	−0.493001	−	0.870029i	$-0.664100\pi$
$607$	−14745.5	−0.986002	−0.493001	+	0.870029i	$0.664100\pi$
$608$	−14263.2	−0.951400
$609$	−1332.59	−0.0886687
$610$	−6572.72	−0.436265
$611$	−9895.44	−0.655199
$612$	−2952.41	−0.195007
$613$	−5291.00	−0.348616	−0.174308	−	0.984691i	$-0.555769\pi$
$613$	−5291.00	−0.348616	−0.174308	+	0.984691i	$0.555769\pi$
$614$	10634.9	0.699005
$615$	1100.13	0.0721323
$616$	−3574.73	−0.233815
$617$	−11432.8	−0.745977	−0.372988	−	0.927836i	$-0.621667\pi$
$617$	−11432.8	−0.745977	−0.372988	+	0.927836i	$0.621667\pi$
$618$	216.608	0.0140991
$619$	−28040.9	−1.82077	−0.910387	−	0.413759i	$-0.864216\pi$
$619$	−28040.9	−1.82077	−0.910387	+	0.413759i	$0.864216\pi$
$620$	2009.86	0.130190
$621$	−686.657	−0.0443713
$622$	22159.2	1.42846
$623$	4392.28	0.282461
$624$	−21670.1	−1.39022
$625$	625.000	0.0400000
$626$	19777.6	1.26274
$627$	5055.78	0.322023
$628$	−1707.94	−0.108526
$629$	−56808.5	−3.60112
$630$	2239.56	0.141629
$631$	−11034.1	−0.696132	−0.348066	−	0.937470i	$-0.613161\pi$
$631$	−11034.1	−0.696132	−0.348066	+	0.937470i	$0.613161\pi$
$632$	22295.6	1.40327
$633$	9063.38	0.569095
$634$	1716.19	0.107506
$635$	728.336	0.0455167
$636$	−4867.22	−0.303456
$637$	−10047.9	−0.624977
$638$	−1243.47	−0.0771619
$639$	3177.27	0.196699
$640$	8698.74	0.537263
$641$	−13944.7	−0.859256	−0.429628	−	0.903006i	$-0.641355\pi$
$641$	−13944.7	−0.859256	−0.429628	+	0.903006i	$0.641355\pi$
$642$	−3724.34	−0.228953
$643$	−19721.2	−1.20953	−0.604766	−	0.796403i	$-0.706733\pi$
$643$	−19721.2	−1.20953	−0.604766	+	0.796403i	$0.706733\pi$
$644$	−996.100	−0.0609501
$645$	−1815.87	−0.110852
$646$	−53230.5	−3.24199
$647$	−17085.3	−1.03816	−0.519082	−	0.854724i	$-0.673726\pi$
$647$	−17085.3	−1.03816	−0.519082	+	0.854724i	$0.673726\pi$
$648$	−1432.47	−0.0868409
$649$	5552.11	0.335808
$650$	7530.32	0.454406
$651$	7223.43	0.434883
$652$	−1753.07	−0.105300
$653$	3094.80	0.185465	0.0927327	−	0.995691i	$-0.470440\pi$
$653$	3094.80	0.185465	0.0927327	+	0.995691i	$0.470440\pi$
$654$	−14218.3	−0.850124
$655$	−13500.6	−0.805360
$656$	−5714.65	−0.340121
$657$	−5066.63	−0.300865
$658$	−5312.31	−0.314735
$659$	−7435.85	−0.439544	−0.219772	−	0.975551i	$-0.570531\pi$
$659$	−7435.85	−0.439544	−0.219772	+	0.975551i	$0.570531\pi$
$660$	506.179	0.0298530
$661$	21337.1	1.25555	0.627775	−	0.778395i	$-0.283966\pi$
$661$	21337.1	1.25555	0.627775	+	0.778395i	$0.283966\pi$
$662$	−15077.5	−0.885204
$663$	−35678.5	−2.08995
$664$	24864.6	1.45321
$665$	9780.27	0.570320
$666$	12949.2	0.753412
$667$	737.521	0.0428140
$668$	3156.17	0.182808
$669$	−7280.80	−0.420765
$670$	12355.9	0.712465
$671$	−5339.07	−0.307172
$672$	−5132.31	−0.294618
$673$	−4392.84	−0.251607	−0.125804	−	0.992055i	$-0.540151\pi$
$673$	−4392.84	−0.251607	−0.125804	+	0.992055i	$0.540151\pi$
$674$	8882.70	0.507639
$675$	675.000	0.0384900
$676$	16358.2	0.930712
$677$	21663.4	1.22983	0.614913	−	0.788595i	$-0.289191\pi$
$677$	21663.4	1.22983	0.614913	+	0.788595i	$0.289191\pi$
$678$	8416.01	0.476718
$679$	−8669.46	−0.489990
$680$	11343.7	0.639724
$681$	−2064.41	−0.116165
$682$	6740.33	0.378447
$683$	8116.08	0.454690	0.227345	−	0.973814i	$-0.426996\pi$
$683$	8116.08	0.454690	0.227345	+	0.973814i	$0.426996\pi$
$684$	2938.97	0.164290
$685$	14265.6	0.795707
$686$	−22464.5	−1.25029
$687$	−8630.21	−0.479277
$688$	9432.61	0.522696
$689$	−58818.2	−3.25224
$690$	−1239.48	−0.0683859
$691$	−26418.5	−1.45442	−0.727212	−	0.686413i	$-0.759184\pi$
$691$	−26418.5	−1.45442	−0.727212	+	0.686413i	$0.759184\pi$
$692$	−6365.42	−0.349677
$693$	1819.21	0.0997202
$694$	38850.5	2.12499
$695$	1135.61	0.0619803
$696$	1538.58	0.0837929
$697$	−9408.83	−0.511313
$698$	18040.1	0.978262
$699$	10930.3	0.591445
$700$	979.190	0.0528713
$701$	−18824.8	−1.01427	−0.507134	−	0.861867i	$-0.669295\pi$
$701$	−18824.8	−1.01427	−0.507134	+	0.861867i	$0.669295\pi$
$702$	8132.75	0.437252
$703$	56549.9	3.03389
$704$	3436.99	0.184001
$705$	−1601.12	−0.0855345
$706$	−9890.94	−0.527267
$707$	132.762	0.00706227
$708$	3227.49	0.171323
$709$	−18712.6	−0.991210	−0.495605	−	0.868548i	$-0.665054\pi$
$709$	−18712.6	−0.991210	−0.495605	+	0.868548i	$0.665054\pi$
$710$	5735.27	0.303156
$711$	−11346.4	−0.598487
$712$	−5071.25	−0.266929
$713$	−3997.80	−0.209984
$714$	−19153.8	−1.00394
$715$	6116.95	0.319945
$716$	1676.82	0.0875218
$717$	119.063	0.00620150
$718$	−19.1868	−0.000997278 0
$719$	4139.21	0.214696	0.107348	−	0.994222i	$-0.465764\pi$
$719$	4139.21	0.214696	0.107348	+	0.994222i	$0.465764\pi$
$720$	−3506.31	−0.181490
$721$	340.375	0.0175815
$722$	30702.2	1.58257
$723$	4082.02	0.209975
$724$	−2868.73	−0.147259
$725$	−725.000	−0.0371391
$726$	−11276.4	−0.576455
$727$	−20932.3	−1.06786	−0.533931	−	0.845528i	$-0.679286\pi$
$727$	−20932.3	−1.06786	−0.533931	+	0.845528i	$0.679286\pi$
$728$	−25111.9	−1.27845
$729$	729.000	0.0370370
$730$	−9145.76	−0.463698
$731$	15530.2	0.785782
$732$	−3103.65	−0.156714
$733$	9244.31	0.465821	0.232910	−	0.972498i	$-0.425175\pi$
$733$	9244.31	0.465821	0.232910	+	0.972498i	$0.425175\pi$
$734$	42507.6	2.13758
$735$	−1625.79	−0.0815892
$736$	2840.47	0.142257
$737$	10036.8	0.501644
$738$	2144.70	0.106975
$739$	18604.3	0.926075	0.463038	−	0.886339i	$-0.346759\pi$
$739$	18604.3	0.926075	0.463038	+	0.886339i	$0.346759\pi$
$740$	5661.72	0.281255
$741$	35516.2	1.76075
$742$	−31576.2	−1.56226
$743$	−25455.8	−1.25691	−0.628453	−	0.777848i	$-0.716312\pi$
$743$	−25455.8	−1.25691	−0.628453	+	0.777848i	$0.716312\pi$
$744$	−8340.05	−0.410969
$745$	−14849.3	−0.730249
$746$	14173.9	0.695632
$747$	−12653.8	−0.619784
$748$	−4329.10	−0.211614
$749$	−5852.38	−0.285502
$750$	1218.44	0.0593215
$751$	−30977.0	−1.50515	−0.752574	−	0.658508i	$-0.771188\pi$
$751$	−30977.0	−1.50515	−0.752574	+	0.658508i	$0.771188\pi$
$752$	8317.10	0.403316
$753$	−13561.1	−0.656301
$754$	−8735.18	−0.421905
$755$	−6734.53	−0.324629
$756$	1057.52	0.0508754
$757$	10166.1	0.488102	0.244051	−	0.969762i	$-0.421524\pi$
$757$	10166.1	0.488102	0.244051	+	0.969762i	$0.421524\pi$
$758$	29446.0	1.41098
$759$	−1006.84	−0.0481502
$760$	−11292.1	−0.538958
$761$	5617.56	0.267591	0.133795	−	0.991009i	$-0.457284\pi$
$761$	5617.56	0.267591	0.133795	+	0.991009i	$0.457284\pi$
$762$	1419.89	0.0675030
$763$	−22342.5	−1.06010
$764$	2374.85	0.112459
$765$	−5772.94	−0.272838
$766$	−34580.1	−1.63111
$767$	39002.8	1.83613
$768$	10707.6	0.503094
$769$	25596.5	1.20030	0.600152	−	0.799886i	$-0.295107\pi$
$769$	25596.5	1.20030	0.600152	+	0.799886i	$0.295107\pi$
$770$	3283.85	0.153691
$771$	−8529.40	−0.398416
$772$	−4882.39	−0.227618
$773$	−16425.4	−0.764269	−0.382134	−	0.924107i	$-0.624811\pi$
$773$	−16425.4	−0.764269	−0.382134	+	0.924107i	$0.624811\pi$
$774$	−3540.05	−0.164398
$775$	3929.93	0.182151
$776$	10009.6	0.463046
$777$	20348.2	0.939497
$778$	22977.3	1.05884
$779$	9366.02	0.430773
$780$	3555.84	0.163230
$781$	4658.81	0.213451
$782$	10600.7	0.484756
$783$	−783.000	−0.0357371
$784$	8445.21	0.384713
$785$	−3339.60	−0.151841
$786$	−26319.4	−1.19438
$787$	35122.2	1.59081	0.795407	−	0.606076i	$-0.207257\pi$
$787$	35122.2	1.59081	0.795407	+	0.606076i	$0.207257\pi$
$788$	4812.77	0.217573
$789$	−10992.9	−0.496017
$790$	−20481.4	−0.922398
$791$	13224.8	0.594463
$792$	−2100.43	−0.0942367
$793$	−37506.2	−1.67955
$794$	−46767.5	−2.09032
$795$	−9517.04	−0.424572
$796$	−2198.89	−0.0979117
$797$	−15617.2	−0.694092	−0.347046	−	0.937848i	$-0.612815\pi$
$797$	−15617.2	−0.694092	−0.347046	+	0.937848i	$0.612815\pi$
$798$	19066.7	0.845805
$799$	13693.6	0.606315
$800$	−2792.25	−0.123401
$801$	2580.81	0.113843
$802$	20827.3	0.917003
$803$	−7429.17	−0.326488
$804$	5834.51	0.255929
$805$	−1947.71	−0.0852765
$806$	47349.9	2.06927
$807$	11844.6	0.516668
$808$	−153.284	−0.00667392
$809$	38122.1	1.65674	0.828370	−	0.560182i	$-0.189269\pi$
$809$	38122.1	1.65674	0.828370	+	0.560182i	$0.189269\pi$
$810$	1315.91	0.0570821
$811$	14593.9	0.631887	0.315943	−	0.948778i	$-0.397679\pi$
$811$	14593.9	0.631887	0.315943	+	0.948778i	$0.397679\pi$
$812$	−1135.86	−0.0490897
$813$	24298.4	1.04819
$814$	18987.4	0.817576
$815$	−3427.83	−0.147327
$816$	29987.7	1.28650
$817$	−15459.6	−0.662009
$818$	−4889.76	−0.209005
$819$	12779.7	0.545249
$820$	937.716	0.0399347
$821$	−33424.2	−1.42085	−0.710423	−	0.703775i	$-0.751496\pi$
$821$	−33424.2	−1.42085	−0.710423	+	0.703775i	$0.751496\pi$
$822$	27810.8	1.18006
$823$	39376.7	1.66778	0.833892	−	0.551928i	$-0.186108\pi$
$823$	39376.7	1.66778	0.833892	+	0.551928i	$0.186108\pi$
$824$	−392.991	−0.0166147
$825$	989.748	0.0417680
$826$	20938.4	0.882011
$827$	−8360.01	−0.351519	−0.175759	−	0.984433i	$-0.556238\pi$
$827$	−8360.01	−0.351519	−0.175759	+	0.984433i	$0.556238\pi$
$828$	−585.286	−0.0245653
$829$	6309.82	0.264353	0.132177	−	0.991226i	$-0.457803\pi$
$829$	6309.82	0.264353	0.132177	+	0.991226i	$0.457803\pi$
$830$	−22841.3	−0.955222
$831$	−12948.6	−0.540533
$832$	24144.4	1.00608
$833$	13904.5	0.578348
$834$	2213.88	0.0919190
$835$	6171.37	0.255771
$836$	4309.40	0.178282
$837$	4244.33	0.175275
$838$	29522.8	1.21700
$839$	−17336.1	−0.713360	−0.356680	−	0.934227i	$-0.616091\pi$
$839$	−17336.1	−0.713360	−0.356680	+	0.934227i	$0.616091\pi$
$840$	−4063.22	−0.166898
$841$	841.000	0.0344828
$842$	11793.9	0.482715
$843$	−16323.6	−0.666921
$844$	7725.35	0.315068
$845$	31985.7	1.30218
$846$	−3121.40	−0.126851
$847$	−17719.6	−0.718834
$848$	49436.6	2.00196
$849$	−4464.17	−0.180459
$850$	−10420.7	−0.420502
$851$	−11261.7	−0.453639
$852$	2708.21	0.108899
$853$	−2482.79	−0.0996591	−0.0498295	−	0.998758i	$-0.515868\pi$
$853$	−2482.79	−0.0996591	−0.0498295	+	0.998758i	$0.515868\pi$
$854$	−20135.0	−0.806799
$855$	5746.67	0.229862
$856$	6757.05	0.269803
$857$	−41167.3	−1.64090	−0.820448	−	0.571721i	$-0.806276\pi$
$857$	−41167.3	−1.64090	−0.820448	+	0.571721i	$0.806276\pi$
$858$	11925.0	0.474490
$859$	−31282.9	−1.24256	−0.621279	−	0.783589i	$-0.713387\pi$
$859$	−31282.9	−1.24256	−0.621279	+	0.783589i	$0.713387\pi$
$860$	−1547.79	−0.0613714
$861$	3370.16	0.133397
$862$	42837.3	1.69263
$863$	−18016.6	−0.710652	−0.355326	−	0.934742i	$-0.615630\pi$
$863$	−18016.6	−0.710652	−0.355326	+	0.934742i	$0.615630\pi$
$864$	−3015.63	−0.118743
$865$	−12446.5	−0.489241
$866$	4996.10	0.196044
$867$	34634.0	1.35667
$868$	6157.04	0.240764
$869$	−16637.2	−0.649457
$870$	−1413.39	−0.0550786
$871$	70507.4	2.74288
$872$	25796.3	1.00180
$873$	−5093.98	−0.197486
$874$	−10552.4	−0.408399
$875$	1914.64	0.0739733
$876$	−4318.65	−0.166568
$877$	13691.7	0.527181	0.263590	−	0.964635i	$-0.415093\pi$
$877$	13691.7	0.527181	0.263590	+	0.964635i	$0.415093\pi$
$878$	−36023.7	−1.38467
$879$	−3987.84	−0.153022
$880$	−5141.29	−0.196946
$881$	−30275.0	−1.15776	−0.578882	−	0.815412i	$-0.696511\pi$
$881$	−30275.0	−1.15776	−0.578882	+	0.815412i	$0.696511\pi$
$882$	−3169.48	−0.121000
$883$	26094.1	0.994491	0.497246	−	0.867610i	$-0.334345\pi$
$883$	26094.1	0.994491	0.497246	+	0.867610i	$0.334345\pi$
$884$	−30411.3	−1.15706
$885$	6310.82	0.239702
$886$	−181.086	−0.00686646
$887$	−7825.04	−0.296211	−0.148106	−	0.988972i	$-0.547318\pi$
$887$	−7825.04	−0.296211	−0.148106	+	0.988972i	$0.547318\pi$
$888$	−23493.7	−0.887835
$889$	2231.20	0.0841756
$890$	4658.60	0.175457
$891$	1068.93	0.0401913
$892$	−6205.94	−0.232949
$893$	−13631.3	−0.510811
$894$	−28948.7	−1.08299
$895$	3278.74	0.122454
$896$	26647.9	0.993577
$897$	−7072.92	−0.263275
$898$	45666.2	1.69699
$899$	−4558.72	−0.169123
$900$	575.350	0.0213093
$901$	81394.5	3.00959
$902$	3144.76	0.116085
$903$	−5562.78	−0.205003
$904$	−15269.1	−0.561774
$905$	−5609.32	−0.206033
$906$	−13129.0	−0.481437
$907$	−21608.8	−0.791080	−0.395540	−	0.918449i	$-0.629443\pi$
$907$	−21608.8	−0.791080	−0.395540	+	0.918449i	$0.629443\pi$
$908$	−1759.64	−0.0643126
$909$	78.0079	0.00284638
$910$	23068.6	0.840347
$911$	30884.1	1.12320	0.561601	−	0.827409i	$-0.310186\pi$
$911$	30884.1	1.12320	0.561601	+	0.827409i	$0.310186\pi$
$912$	−29851.3	−1.08385
$913$	−18554.2	−0.672568
$914$	−46045.0	−1.66634
$915$	−6068.67	−0.219261
$916$	−7356.14	−0.265342
$917$	−41358.0	−1.48938
$918$	−11254.4	−0.404629
$919$	2004.36	0.0719453	0.0359726	−	0.999353i	$-0.488547\pi$
$919$	2004.36	0.0719453	0.0359726	+	0.999353i	$0.488547\pi$
$920$	2248.79	0.0805873
$921$	9819.33	0.351311
$922$	43877.4	1.56727
$923$	32727.5	1.16710
$924$	1550.64	0.0552082
$925$	11070.5	0.393510
$926$	13934.9	0.494523
$927$	199.997	0.00708605
$928$	3239.01	0.114575
$929$	35337.2	1.24798	0.623991	−	0.781431i	$-0.285510\pi$
$929$	35337.2	1.24798	0.623991	+	0.781431i	$0.285510\pi$
$930$	7661.41	0.270137
$931$	−13841.3	−0.487249
$932$	9316.62	0.327442
$933$	20459.9	0.717929
$934$	7911.29	0.277158
$935$	−8464.82	−0.296074
$936$	−14755.2	−0.515266
$937$	−5564.16	−0.193995	−0.0969974	−	0.995285i	$-0.530924\pi$
$937$	−5564.16	−0.193995	−0.0969974	+	0.995285i	$0.530924\pi$
$938$	37851.5	1.31759
$939$	18260.9	0.634635
$940$	−1364.75	−0.0473545
$941$	35384.3	1.22582	0.612909	−	0.790154i	$-0.289999\pi$
$941$	35384.3	1.22582	0.612909	+	0.790154i	$0.289999\pi$
$942$	−6510.56	−0.225186
$943$	−1865.21	−0.0644110
$944$	−32781.8	−1.13025
$945$	2067.81	0.0711809
$946$	−5190.75	−0.178399
$947$	8856.56	0.303906	0.151953	−	0.988388i	$-0.451444\pi$
$947$	8856.56	0.303906	0.151953	+	0.988388i	$0.451444\pi$
$948$	−9671.35	−0.331341
$949$	−52188.9	−1.78517
$950$	10373.3	0.354267
$951$	1584.58	0.0540310
$952$	34750.7	1.18306
$953$	−26016.5	−0.884320	−0.442160	−	0.896936i	$-0.645788\pi$
$953$	−26016.5	−0.884320	−0.442160	+	0.896936i	$0.645788\pi$
$954$	−18553.5	−0.629656
$955$	4643.61	0.157344
$956$	101.485	0.00343334
$957$	−1148.11	−0.0387806
$958$	16579.5	0.559142
$959$	43701.5	1.47153
$960$	3906.66	0.131341
$961$	−5080.00	−0.170521
$962$	133384.	4.47033
$963$	−3438.73	−0.115069
$964$	3479.40	0.116249
$965$	−9546.68	−0.318465
$966$	−3797.06	−0.126468
$967$	−11223.4	−0.373239	−0.186619	−	0.982432i	$-0.559753\pi$
$967$	−11223.4	−0.373239	−0.186619	+	0.982432i	$0.559753\pi$
$968$	20458.7	0.679306
$969$	−49148.4	−1.62938
$970$	−9195.12	−0.304368
$971$	−33787.2	−1.11667	−0.558333	−	0.829617i	$-0.688559\pi$
$971$	−33787.2	−1.11667	−0.558333	+	0.829617i	$0.688559\pi$
$972$	621.378	0.0205048
$973$	3478.87	0.114622
$974$	−52.1127	−0.00171437
$975$	6952.84	0.228379
$976$	31523.9	1.03387
$977$	39082.5	1.27980	0.639898	−	0.768460i	$-0.278977\pi$
$977$	39082.5	1.27980	0.639898	+	0.768460i	$0.278977\pi$
$978$	−6682.57	−0.218492
$979$	3784.22	0.123539
$980$	−1385.77	−0.0451703
$981$	−13128.0	−0.427262
$982$	28691.2	0.932355
$983$	−17510.6	−0.568162	−0.284081	−	0.958800i	$-0.591688\pi$
$983$	−17510.6	−0.568162	−0.284081	+	0.958800i	$0.591688\pi$
$984$	−3891.12	−0.126061
$985$	9410.56	0.304411
$986$	12088.0	0.390427
$987$	−4904.92	−0.158182
$988$	30272.9	0.974808
$989$	3078.72	0.0989864
$990$	1929.52	0.0619435
$991$	−47916.0	−1.53592	−0.767962	−	0.640495i	$-0.778729\pi$
$991$	−47916.0	−1.53592	−0.767962	+	0.640495i	$0.778729\pi$
$992$	−17557.4	−0.561943
$993$	−13921.3	−0.444892
$994$	17569.6	0.560636
$995$	−4299.57	−0.136990
$996$	−10785.7	−0.343132
$997$	39414.7	1.25203	0.626016	−	0.779810i	$-0.284684\pi$
$997$	39414.7	1.25203	0.626016	+	0.779810i	$0.284684\pi$
$998$	−58568.8	−1.85768
$999$	11956.2	0.378655

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.4.a.l.1.7	✓	10
3.2	odd	2		1305.4.a.q.1.4		10
5.4	even	2		2175.4.a.p.1.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.4.a.l.1.7	✓	10	1.1	even	1	trivial
1305.4.a.q.1.4		10	3.2	odd	2
2175.4.a.p.1.4		10	5.4	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:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	435.a (trivial)

\(f(q)\)	\(=\)	\(q+3.24917 q^{2} +3.00000 q^{3} +2.55711 q^{4} +5.00000 q^{5} +9.74751 q^{6} +15.3171 q^{7} -17.6849 q^{8} +9.00000 q^{9} +16.2459 q^{10} +13.1966 q^{11} +7.67133 q^{12} +92.7046 q^{13} +49.7679 q^{14} +15.0000 q^{15} -77.9181 q^{16} -128.287 q^{17} +29.2425 q^{18} +127.704 q^{19} +12.7856 q^{20} +45.9514 q^{21} +42.8782 q^{22} -25.4317 q^{23} -53.0546 q^{24} +25.0000 q^{25} +301.213 q^{26} +27.0000 q^{27} +39.1676 q^{28} -29.0000 q^{29} +48.7376 q^{30} +157.197 q^{31} -111.690 q^{32} +39.5899 q^{33} -416.828 q^{34} +76.5856 q^{35} +23.0140 q^{36} +442.821 q^{37} +414.931 q^{38} +278.114 q^{39} -88.4244 q^{40} +73.3418 q^{41} +149.304 q^{42} -121.058 q^{43} +33.7453 q^{44} +45.0000 q^{45} -82.6321 q^{46} -106.742 q^{47} -233.754 q^{48} -108.386 q^{49} +81.2293 q^{50} -384.862 q^{51} +237.056 q^{52} -634.469 q^{53} +87.7276 q^{54} +65.9832 q^{55} -270.881 q^{56} +383.111 q^{57} -94.2260 q^{58} +420.721 q^{59} +38.3567 q^{60} -404.578 q^{61} +510.761 q^{62} +137.854 q^{63} +260.444 q^{64} +463.523 q^{65} +128.634 q^{66} +760.560 q^{67} -328.045 q^{68} -76.2952 q^{69} +248.840 q^{70} +353.030 q^{71} -159.164 q^{72} -562.959 q^{73} +1438.80 q^{74} +75.0000 q^{75} +326.553 q^{76} +202.135 q^{77} +903.639 q^{78} -1260.71 q^{79} -389.590 q^{80} +81.0000 q^{81} +238.300 q^{82} -1405.98 q^{83} +117.503 q^{84} -641.437 q^{85} -393.338 q^{86} -87.0000 q^{87} -233.381 q^{88} +286.757 q^{89} +146.213 q^{90} +1419.97 q^{91} -65.0318 q^{92} +471.592 q^{93} -346.822 q^{94} +638.519 q^{95} -335.070 q^{96} -565.998 q^{97} -352.164 q^{98} +118.770 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + 30 q^{3} + 66 q^{4} + 50 q^{5} + 12 q^{6} + 75 q^{7} + 9 q^{8} + 90 q^{9} + 20 q^{10} + 3 q^{11} + 198 q^{12} + 75 q^{13} + 105 q^{14} + 150 q^{15} + 394 q^{16} + 131 q^{17} + 36 q^{18}+ \cdots + 27 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 + 30 * q^3 + 66 * q^4 + 50 * q^5 + 12 * q^6 + 75 * q^7 + 9 * q^8 + 90 * q^9 + 20 * q^10 + 3 * q^11 + 198 * q^12 + 75 * q^13 + 105 * q^14 + 150 * q^15 + 394 * q^16 + 131 * q^17 + 36 * q^18 + 264 * q^19 + 330 * q^20 + 225 * q^21 + 111 * q^22 + 204 * q^23 + 27 * q^24 + 250 * q^25 + 281 * q^26 + 270 * q^27 + 547 * q^28 - 290 * q^29 + 60 * q^30 + 924 * q^31 - 294 * q^32 + 9 * q^33 - 287 * q^34 + 375 * q^35 + 594 * q^36 + 212 * q^37 - 784 * q^38 + 225 * q^39 + 45 * q^40 - 192 * q^41 + 315 * q^42 + 614 * q^43 - 1247 * q^44 + 450 * q^45 - 94 * q^46 + 173 * q^47 + 1182 * q^48 + 357 * q^49 + 100 * q^50 + 393 * q^51 - 687 * q^52 + 658 * q^53 + 108 * q^54 + 15 * q^55 + 514 * q^56 + 792 * q^57 - 116 * q^58 + 190 * q^59 + 990 * q^60 + 1452 * q^61 - 1420 * q^62 + 675 * q^63 + 2709 * q^64 + 375 * q^65 + 333 * q^66 + 343 * q^67 - 601 * q^68 + 612 * q^69 + 525 * q^70 + 8 * q^71 + 81 * q^72 + 1500 * q^73 - 1570 * q^74 + 750 * q^75 + 2014 * q^76 - 431 * q^77 + 843 * q^78 + 2438 * q^79 + 1970 * q^80 + 810 * q^81 - 518 * q^82 + 1336 * q^83 + 1641 * q^84 + 655 * q^85 - 916 * q^86 - 870 * q^87 + 3242 * q^88 + 1319 * q^89 + 180 * q^90 + 1815 * q^91 - 2950 * q^92 + 2772 * q^93 + 2043 * q^94 + 1320 * q^95 - 882 * q^96 + 2034 * q^97 + 1273 * q^98 + 27 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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