LMFDB - Embedded newform 435.4.a.h.1.6

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:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 49x^{4} + 27x^{3} + 692x^{2} - 82x - 2588 $ x^6 - x^5 - 49x^4 + 27x^3 + 692x^2 - 82x - 2588
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$5.42717$ 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)

$f(q)$	$=$	\(q+5.42717 q^{2} +3.00000 q^{3} +21.4542 q^{4} -5.00000 q^{5} +16.2815 q^{6} -10.2400 q^{7} +73.0180 q^{8} +9.00000 q^{9} -27.1358 q^{10} +12.6318 q^{11} +64.3625 q^{12} +84.2342 q^{13} -55.5740 q^{14} -15.0000 q^{15} +224.647 q^{16} +6.89181 q^{17} +48.8445 q^{18} -79.7045 q^{19} -107.271 q^{20} -30.7199 q^{21} +68.5548 q^{22} -73.8181 q^{23} +219.054 q^{24} +25.0000 q^{25} +457.153 q^{26} +27.0000 q^{27} -219.690 q^{28} +29.0000 q^{29} -81.4075 q^{30} +0.254654 q^{31} +635.056 q^{32} +37.8953 q^{33} +37.4030 q^{34} +51.1998 q^{35} +193.087 q^{36} +40.4065 q^{37} -432.570 q^{38} +252.703 q^{39} -365.090 q^{40} +208.354 q^{41} -166.722 q^{42} -194.427 q^{43} +271.004 q^{44} -45.0000 q^{45} -400.623 q^{46} -522.168 q^{47} +673.942 q^{48} -238.143 q^{49} +135.679 q^{50} +20.6754 q^{51} +1807.17 q^{52} -294.893 q^{53} +146.534 q^{54} -63.1589 q^{55} -747.701 q^{56} -239.114 q^{57} +157.388 q^{58} -196.229 q^{59} -321.812 q^{60} +189.313 q^{61} +1.38205 q^{62} -92.1597 q^{63} +1649.38 q^{64} -421.171 q^{65} +205.664 q^{66} -570.840 q^{67} +147.858 q^{68} -221.454 q^{69} +277.870 q^{70} -1126.87 q^{71} +657.162 q^{72} +581.431 q^{73} +219.293 q^{74} +75.0000 q^{75} -1709.99 q^{76} -129.349 q^{77} +1371.46 q^{78} -255.631 q^{79} -1123.24 q^{80} +81.0000 q^{81} +1130.77 q^{82} -983.081 q^{83} -659.069 q^{84} -34.4591 q^{85} -1055.19 q^{86} +87.0000 q^{87} +922.347 q^{88} +678.642 q^{89} -244.223 q^{90} -862.555 q^{91} -1583.70 q^{92} +0.763963 q^{93} -2833.89 q^{94} +398.523 q^{95} +1905.17 q^{96} -30.8442 q^{97} -1292.44 q^{98} +113.686 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} + 18 q^{3} + 51 q^{4} - 30 q^{5} + 3 q^{6} + 47 q^{7} + 51 q^{8} + 54 q^{9} - 5 q^{10} + 81 q^{11} + 153 q^{12} + 169 q^{13} - 30 q^{14} - 90 q^{15} + 131 q^{16} - q^{17} + 9 q^{18} + 116 q^{19}+ \cdots + 729 q^{99}+O(q^{100}) $ 6 * q + q^2 + 18 * q^3 + 51 * q^4 - 30 * q^5 + 3 * q^6 + 47 * q^7 + 51 * q^8 + 54 * q^9 - 5 * q^10 + 81 * q^11 + 153 * q^12 + 169 * q^13 - 30 * q^14 - 90 * q^15 + 131 * q^16 - q^17 + 9 * q^18 + 116 * q^19 - 255 * q^20 + 141 * q^21 + 90 * q^22 - 52 * q^23 + 153 * q^24 + 150 * q^25 + 294 * q^26 + 162 * q^27 + 344 * q^28 + 174 * q^29 - 15 * q^30 + 340 * q^31 + 499 * q^32 + 243 * q^33 + 920 * q^34 - 235 * q^35 + 459 * q^36 + 332 * q^37 - 378 * q^38 + 507 * q^39 - 255 * q^40 - 616 * q^41 - 90 * q^42 + 334 * q^43 - 52 * q^44 - 270 * q^45 - 158 * q^46 - 85 * q^47 + 393 * q^48 + 879 * q^49 + 25 * q^50 - 3 * q^51 + 2220 * q^52 - 850 * q^53 + 27 * q^54 - 405 * q^55 - 624 * q^56 + 348 * q^57 + 29 * q^58 - 758 * q^59 - 765 * q^60 - 36 * q^61 - 152 * q^62 + 423 * q^63 + 1795 * q^64 - 845 * q^65 + 270 * q^66 + 939 * q^67 - 186 * q^68 - 156 * q^69 + 150 * q^70 - 1388 * q^71 + 459 * q^72 + 1708 * q^73 - 814 * q^74 + 450 * q^75 + 566 * q^76 + 2585 * q^77 + 882 * q^78 + 1250 * q^79 - 655 * q^80 + 486 * q^81 + 1372 * q^82 - 748 * q^83 + 1032 * q^84 + 5 * q^85 - 800 * q^86 + 522 * q^87 + 536 * q^88 + 1099 * q^89 - 45 * q^90 + 539 * q^91 + 1698 * q^92 + 1020 * q^93 - 4542 * q^94 - 580 * q^95 + 1497 * q^96 - 22 * q^97 - 1433 * q^98 + 729 * 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 $

$2$	5.42717	1.91879	0.959397	−	0.282060i	$-0.0910176\pi$
$2$	5.42717	1.91879	0.959397	+	0.282060i	$0.0910176\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	21.4542	2.68177
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	16.2815	1.10782
$7$	−10.2400	−0.552906	−0.276453	−	0.961027i	$-0.589159\pi$
$7$	−10.2400	−0.552906	−0.276453	+	0.961027i	$0.589159\pi$
$8$	73.0180	3.22697
$9$	9.00000	0.333333
$10$	−27.1358	−0.858111
$11$	12.6318	0.346239	0.173119	−	0.984901i	$-0.444615\pi$
$11$	12.6318	0.346239	0.173119	+	0.984901i	$0.444615\pi$
$12$	64.3625	1.54832
$13$	84.2342	1.79710	0.898552	−	0.438866i	$-0.144620\pi$
$13$	84.2342	1.79710	0.898552	+	0.438866i	$0.144620\pi$
$14$	−55.5740	−1.06091
$15$	−15.0000	−0.258199
$16$	224.647	3.51012
$17$	6.89181	0.0983241	0.0491621	−	0.998791i	$-0.484345\pi$
$17$	6.89181	0.0983241	0.0491621	+	0.998791i	$0.484345\pi$
$18$	48.8445	0.639598
$19$	−79.7045	−0.962393	−0.481196	−	0.876613i	$-0.659798\pi$
$19$	−79.7045	−0.962393	−0.481196	+	0.876613i	$0.659798\pi$
$20$	−107.271	−1.19932
$21$	−30.7199	−0.319220
$22$	68.5548	0.664361
$23$	−73.8181	−0.669223	−0.334612	−	0.942356i	$-0.608605\pi$
$23$	−73.8181	−0.669223	−0.334612	+	0.942356i	$0.608605\pi$
$24$	219.054	1.86309
$25$	25.0000	0.200000
$26$	457.153	3.44827
$27$	27.0000	0.192450
$28$	−219.690	−1.48277
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	−81.4075	−0.495430
$31$	0.254654	0.00147540	0.000737698	−	1.00000i	$-0.499765\pi$
$31$	0.254654	0.00147540	0.000737698		1.00000i	$0.499765\pi$
$32$	635.056	3.50822
$33$	37.8953	0.199901
$34$	37.4030	0.188664
$35$	51.1998	0.247267
$36$	193.087	0.893923
$37$	40.4065	0.179535	0.0897674	−	0.995963i	$-0.471388\pi$
$37$	40.4065	0.179535	0.0897674	+	0.995963i	$0.471388\pi$
$38$	−432.570	−1.84663
$39$	252.703	1.03756
$40$	−365.090	−1.44314
$41$	208.354	0.793645	0.396822	−	0.917895i	$-0.370113\pi$
$41$	208.354	0.793645	0.396822	+	0.917895i	$0.370113\pi$
$42$	−166.722	−0.612518
$43$	−194.427	−0.689531	−0.344766	−	0.938689i	$-0.612042\pi$
$43$	−194.427	−0.689531	−0.344766	+	0.938689i	$0.612042\pi$
$44$	271.004	0.928532
$45$	−45.0000	−0.149071
$46$	−400.623	−1.28410
$47$	−522.168	−1.62055	−0.810277	−	0.586047i	$-0.800683\pi$
$47$	−522.168	−1.62055	−0.810277	+	0.586047i	$0.800683\pi$
$48$	673.942	2.02657
$49$	−238.143	−0.694295
$50$	135.679	0.383759
$51$	20.6754	0.0567675
$52$	1807.17	4.81942
$53$	−294.893	−0.764276	−0.382138	−	0.924105i	$-0.624812\pi$
$53$	−294.893	−0.764276	−0.382138	+	0.924105i	$0.624812\pi$
$54$	146.534	0.369272
$55$	−63.1589	−0.154843
$56$	−747.701	−1.78421
$57$	−239.114	−0.555638
$58$	157.388	0.356311
$59$	−196.229	−0.432997	−0.216498	−	0.976283i	$-0.569464\pi$
$59$	−196.229	−0.432997	−0.216498	+	0.976283i	$0.569464\pi$
$60$	−321.812	−0.692430
$61$	189.313	0.397360	0.198680	−	0.980064i	$-0.436334\pi$
$61$	189.313	0.397360	0.198680	+	0.980064i	$0.436334\pi$
$62$	1.38205	0.00283098
$63$	−92.1597	−0.184302
$64$	1649.38	3.22144
$65$	−421.171	−0.803690
$66$	205.664	0.383569
$67$	−570.840	−1.04088	−0.520442	−	0.853897i	$-0.674233\pi$
$67$	−570.840	−1.04088	−0.520442	+	0.853897i	$0.674233\pi$
$68$	147.858	0.263683
$69$	−221.454	−0.386376
$70$	277.870	0.474454
$71$	−1126.87	−1.88358	−0.941792	−	0.336196i	$-0.890859\pi$
$71$	−1126.87	−1.88358	−0.941792	+	0.336196i	$0.890859\pi$
$72$	657.162	1.07566
$73$	581.431	0.932210	0.466105	−	0.884729i	$-0.345657\pi$
$73$	581.431	0.932210	0.466105	+	0.884729i	$0.345657\pi$
$74$	219.293	0.344490
$75$	75.0000	0.115470
$76$	−1709.99	−2.58092
$77$	−129.349	−0.191437
$78$	1371.46	1.99086
$79$	−255.631	−0.364060	−0.182030	−	0.983293i	$-0.558267\pi$
$79$	−255.631	−0.364060	−0.182030	+	0.983293i	$0.558267\pi$
$80$	−1123.24	−1.56977
$81$	81.0000	0.111111
$82$	1130.77	1.52284
$83$	−983.081	−1.30009	−0.650043	−	0.759897i	$-0.725249\pi$
$83$	−983.081	−1.30009	−0.650043	+	0.759897i	$0.725249\pi$
$84$	−659.069	−0.856075
$85$	−34.4591	−0.0439719
$86$	−1055.19	−1.32307
$87$	87.0000	0.107211
$88$	922.347	1.11730
$89$	678.642	0.808268	0.404134	−	0.914700i	$-0.367573\pi$
$89$	678.642	0.808268	0.404134	+	0.914700i	$0.367573\pi$
$90$	−244.223	−0.286037
$91$	−862.555	−0.993630
$92$	−1583.70	−1.79470
$93$	0.763963	0.000851820 0
$94$	−2833.89	−3.10951
$95$	398.523	0.430395
$96$	1905.17	2.02547
$97$	−30.8442	−0.0322861	−0.0161431	−	0.999870i	$-0.505139\pi$
$97$	−30.8442	−0.0322861	−0.0161431	+	0.999870i	$0.505139\pi$
$98$	−1292.44	−1.33221
$99$	113.686	0.115413
$100$	536.354	0.536354
$101$	1749.78	1.72386	0.861930	−	0.507028i	$-0.169256\pi$
$101$	1749.78	1.72386	0.861930	+	0.507028i	$0.169256\pi$
$102$	112.209	0.108925
$103$	1912.26	1.82933	0.914663	−	0.404217i	$-0.132456\pi$
$103$	1912.26	1.82933	0.914663	+	0.404217i	$0.132456\pi$
$104$	6150.61	5.79920
$105$	153.599	0.142760
$106$	−1600.43	−1.46649
$107$	1719.25	1.55333	0.776663	−	0.629916i	$-0.216911\pi$
$107$	1719.25	1.55333	0.776663	+	0.629916i	$0.216911\pi$
$108$	579.262	0.516107
$109$	−779.425	−0.684911	−0.342456	−	0.939534i	$-0.611259\pi$
$109$	−779.425	−0.684911	−0.342456	+	0.939534i	$0.611259\pi$
$110$	−342.774	−0.297111
$111$	121.220	0.103654
$112$	−2300.38	−1.94076
$113$	766.529	0.638132	0.319066	−	0.947732i	$-0.396631\pi$
$113$	766.529	0.638132	0.319066	+	0.947732i	$0.396631\pi$
$114$	−1297.71	−1.06615
$115$	369.090	0.299286
$116$	622.170	0.497992
$117$	758.108	0.599035
$118$	−1064.97	−0.830831
$119$	−70.5719	−0.0543640
$120$	−1095.27	−0.833200
$121$	−1171.44	−0.880119
$122$	1027.43	0.762453
$123$	625.062	0.458211
$124$	5.46339	0.00395667
$125$	−125.000	−0.0894427
$126$	−500.166	−0.353637
$127$	−1363.54	−0.952715	−0.476358	−	0.879252i	$-0.658043\pi$
$127$	−1363.54	−0.952715	−0.476358	+	0.879252i	$0.658043\pi$
$128$	3870.99	2.67305
$129$	−583.281	−0.398101
$130$	−2285.77	−1.54211
$131$	−1346.83	−0.898269	−0.449134	−	0.893464i	$-0.648268\pi$
$131$	−1346.83	−0.898269	−0.449134	+	0.893464i	$0.648268\pi$
$132$	813.013	0.536088
$133$	816.171	0.532113
$134$	−3098.05	−1.99724
$135$	−135.000	−0.0860663
$136$	503.226	0.317289
$137$	−2508.42	−1.56430	−0.782148	−	0.623093i	$-0.785876\pi$
$137$	−2508.42	−1.56430	−0.782148	+	0.623093i	$0.785876\pi$
$138$	−1201.87	−0.741376
$139$	1363.95	0.832292	0.416146	−	0.909298i	$-0.363380\pi$
$139$	1363.95	0.832292	0.416146	+	0.909298i	$0.363380\pi$
$140$	1098.45	0.663113
$141$	−1566.50	−0.935628
$142$	−6115.69	−3.61421
$143$	1064.03	0.622227
$144$	2021.83	1.17004
$145$	−145.000	−0.0830455
$146$	3155.52	1.78872
$147$	−714.430	−0.400851
$148$	866.887	0.481471
$149$	2792.25	1.53523	0.767617	−	0.640909i	$-0.221442\pi$
$149$	2792.25	1.53523	0.767617	+	0.640909i	$0.221442\pi$
$150$	407.038	0.221563
$151$	306.493	0.165179	0.0825897	−	0.996584i	$-0.473681\pi$
$151$	306.493	0.165179	0.0825897	+	0.996584i	$0.473681\pi$
$152$	−5819.86	−3.10561
$153$	62.0263	0.0327747
$154$	−701.999	−0.367329
$155$	−1.27327	−0.000659817 0
$156$	5421.52	2.78249
$157$	−1828.15	−0.929315	−0.464657	−	0.885491i	$-0.653822\pi$
$157$	−1828.15	−0.929315	−0.464657	+	0.885491i	$0.653822\pi$
$158$	−1387.35	−0.698556
$159$	−884.678	−0.441255
$160$	−3175.28	−1.56892
$161$	755.894	0.370018
$162$	439.601	0.213199
$163$	2101.15	1.00966	0.504830	−	0.863219i	$-0.331555\pi$
$163$	2101.15	1.00966	0.504830	+	0.863219i	$0.331555\pi$
$164$	4470.06	2.12837
$165$	−189.477	−0.0893984
$166$	−5335.35	−2.49460
$167$	1564.53	0.724950	0.362475	−	0.931994i	$-0.381932\pi$
$167$	1564.53	0.724950	0.362475	+	0.931994i	$0.381932\pi$
$168$	−2243.10	−1.03011
$169$	4898.40	2.22959
$170$	−187.015	−0.0843730
$171$	−717.341	−0.320798
$172$	−4171.27	−1.84916
$173$	−2695.23	−1.18448	−0.592239	−	0.805762i	$-0.701756\pi$
$173$	−2695.23	−1.18448	−0.592239	+	0.805762i	$0.701756\pi$
$174$	472.164	0.205716
$175$	−255.999	−0.110581
$176$	2837.70	1.21534
$177$	−588.686	−0.249991
$178$	3683.10	1.55090
$179$	−3604.16	−1.50496	−0.752480	−	0.658615i	$-0.771143\pi$
$179$	−3604.16	−1.50496	−0.752480	+	0.658615i	$0.771143\pi$
$180$	−965.437	−0.399775
$181$	−2658.32	−1.09166	−0.545832	−	0.837894i	$-0.683786\pi$
$181$	−2658.32	−1.09166	−0.545832	+	0.837894i	$0.683786\pi$
$182$	−4681.23	−1.90657
$183$	567.938	0.229416
$184$	−5390.05	−2.15956
$185$	−202.033	−0.0802904
$186$	4.14615	0.00163447
$187$	87.0559	0.0340436
$188$	−11202.7	−4.34595
$189$	−276.479	−0.106407
$190$	2162.85	0.825840
$191$	−145.942	−0.0552877	−0.0276439	−	0.999618i	$-0.508800\pi$
$191$	−145.942	−0.0552877	−0.0276439	+	0.999618i	$0.508800\pi$
$192$	4948.13	1.85990
$193$	1151.46	0.429451	0.214725	−	0.976674i	$-0.431114\pi$
$193$	1151.46	0.429451	0.214725	+	0.976674i	$0.431114\pi$
$194$	−167.397	−0.0619504
$195$	−1263.51	−0.464011
$196$	−5109.16	−1.86194
$197$	4328.08	1.56529	0.782647	−	0.622466i	$-0.213869\pi$
$197$	4328.08	1.56529	0.782647	+	0.622466i	$0.213869\pi$
$198$	616.993	0.221454
$199$	1532.72	0.545988	0.272994	−	0.962016i	$-0.411986\pi$
$199$	1532.72	0.545988	0.272994	+	0.962016i	$0.411986\pi$
$200$	1825.45	0.645394
$201$	−1712.52	−0.600955
$202$	9496.36	3.30773
$203$	−296.959	−0.102672
$204$	443.574	0.152237
$205$	−1041.77	−0.354929
$206$	10378.2	3.51010
$207$	−664.363	−0.223074
$208$	18923.0	6.30805
$209$	−1006.81	−0.333218
$210$	833.610	0.273926
$211$	5345.39	1.74404	0.872019	−	0.489472i	$-0.162810\pi$
$211$	5345.39	1.74404	0.872019	+	0.489472i	$0.162810\pi$
$212$	−6326.67	−2.04961
$213$	−3380.60	−1.08749
$214$	9330.65	2.98051
$215$	972.135	0.308368
$216$	1971.48	0.621030
$217$	−2.60765	−0.000815755 0
$218$	−4230.07	−1.31420
$219$	1744.29	0.538212
$220$	−1355.02	−0.415252
$221$	580.526	0.176699
$222$	657.879	0.198892
$223$	3783.05	1.13602	0.568008	−	0.823023i	$-0.307714\pi$
$223$	3783.05	1.13602	0.568008	+	0.823023i	$0.307714\pi$
$224$	−6502.95	−1.93972
$225$	225.000	0.0666667
$226$	4160.08	1.22444
$227$	−4348.46	−1.27144	−0.635721	−	0.771919i	$-0.719297\pi$
$227$	−4348.46	−1.27144	−0.635721	+	0.771919i	$0.719297\pi$
$228$	−5129.98	−1.49009
$229$	−3068.67	−0.885517	−0.442759	−	0.896641i	$-0.646000\pi$
$229$	−3068.67	−0.885517	−0.442759	+	0.896641i	$0.646000\pi$
$230$	2003.12	0.574268
$231$	−388.047	−0.110526
$232$	2117.52	0.599233
$233$	−275.696	−0.0775170	−0.0387585	−	0.999249i	$-0.512340\pi$
$233$	−275.696	−0.0775170	−0.0387585	+	0.999249i	$0.512340\pi$
$234$	4114.38	1.14942
$235$	2610.84	0.724734
$236$	−4209.92	−1.16120
$237$	−766.894	−0.210190
$238$	−383.006	−0.104313
$239$	3132.87	0.847901	0.423950	−	0.905685i	$-0.360643\pi$
$239$	3132.87	0.847901	0.423950	+	0.905685i	$0.360643\pi$
$240$	−3369.71	−0.906308
$241$	5699.61	1.52342	0.761710	−	0.647918i	$-0.224360\pi$
$241$	5699.61	1.52342	0.761710	+	0.647918i	$0.224360\pi$
$242$	−6357.59	−1.68877
$243$	243.000	0.0641500
$244$	4061.54	1.06563
$245$	1190.72	0.310498
$246$	3392.32	0.879212
$247$	−6713.85	−1.72952
$248$	18.5943	0.00476105
$249$	−2949.24	−0.750605
$250$	−678.396	−0.171622
$251$	1714.12	0.431054	0.215527	−	0.976498i	$-0.430853\pi$
$251$	1714.12	0.431054	0.215527	+	0.976498i	$0.430853\pi$
$252$	−1977.21	−0.494255
$253$	−932.454	−0.231711
$254$	−7400.17	−1.82806
$255$	−103.377	−0.0253872
$256$	7813.52	1.90760
$257$	−803.085	−0.194922	−0.0974612	−	0.995239i	$-0.531072\pi$
$257$	−803.085	−0.194922	−0.0974612	+	0.995239i	$0.531072\pi$
$258$	−3165.56	−0.763874
$259$	−413.761	−0.0992659
$260$	−9035.87	−2.15531
$261$	261.000	0.0618984
$262$	−7309.48	−1.72359
$263$	−1694.24	−0.397230	−0.198615	−	0.980078i	$-0.563644\pi$
$263$	−1694.24	−0.397230	−0.198615	+	0.980078i	$0.563644\pi$
$264$	2767.04	0.645074
$265$	1474.46	0.341794
$266$	4429.50	1.02101
$267$	2035.92	0.466654
$268$	−12246.9	−2.79141
$269$	3364.95	0.762693	0.381347	−	0.924432i	$-0.375460\pi$
$269$	3364.95	0.762693	0.381347	+	0.924432i	$0.375460\pi$
$270$	−732.668	−0.165143
$271$	8044.10	1.80312	0.901558	−	0.432658i	$-0.142424\pi$
$271$	8044.10	1.80312	0.901558	+	0.432658i	$0.142424\pi$
$272$	1548.23	0.345129
$273$	−2587.66	−0.573673
$274$	−13613.6	−3.00156
$275$	315.795	0.0692477
$276$	−4751.11	−1.03617
$277$	−6971.54	−1.51220	−0.756100	−	0.654456i	$-0.772898\pi$
$277$	−6971.54	−1.51220	−0.756100	+	0.654456i	$0.772898\pi$
$278$	7402.38	1.59700
$279$	2.29189	0.000491798 0
$280$	3738.51	0.797923
$281$	−1916.94	−0.406957	−0.203478	−	0.979079i	$-0.565225\pi$
$281$	−1916.94	−0.406957	−0.203478	+	0.979079i	$0.565225\pi$
$282$	−8501.68	−1.79528
$283$	2036.63	0.427792	0.213896	−	0.976856i	$-0.431385\pi$
$283$	2036.63	0.427792	0.213896	+	0.976856i	$0.431385\pi$
$284$	−24176.0	−5.05134
$285$	1195.57	0.248489
$286$	5774.66	1.19393
$287$	−2133.54	−0.438811
$288$	5715.50	1.16941
$289$	−4865.50	−0.990332
$290$	−786.939	−0.159347
$291$	−92.5325	−0.0186404
$292$	12474.1	2.49997
$293$	−1754.55	−0.349836	−0.174918	−	0.984583i	$-0.555966\pi$
$293$	−1754.55	−0.349836	−0.174918	+	0.984583i	$0.555966\pi$
$294$	−3877.33	−0.769151
$295$	981.143	0.193642
$296$	2950.40	0.579353
$297$	341.058	0.0666337
$298$	15154.0	2.94580
$299$	−6218.01	−1.20266
$300$	1609.06	0.309664
$301$	1990.92	0.381246
$302$	1663.39	0.316945
$303$	5249.35	0.995271
$304$	−17905.4	−3.37811
$305$	−946.563	−0.177705
$306$	336.627	0.0628879
$307$	8909.41	1.65631	0.828154	−	0.560500i	$-0.189391\pi$
$307$	8909.41	1.65631	0.828154	+	0.560500i	$0.189391\pi$
$308$	−2775.07	−0.513391
$309$	5736.78	1.05616
$310$	−6.91026	−0.00126605
$311$	−7422.88	−1.35342	−0.676709	−	0.736251i	$-0.736595\pi$
$311$	−7422.88	−1.35342	−0.676709	+	0.736251i	$0.736595\pi$
$312$	18451.8	3.34817
$313$	−1453.62	−0.262504	−0.131252	−	0.991349i	$-0.541900\pi$
$313$	−1453.62	−0.262504	−0.131252	+	0.991349i	$0.541900\pi$
$314$	−9921.69	−1.78316
$315$	460.798	0.0824224
$316$	−5484.35	−0.976326
$317$	5203.30	0.921912	0.460956	−	0.887423i	$-0.347507\pi$
$317$	5203.30	0.921912	0.460956	+	0.887423i	$0.347507\pi$
$318$	−4801.29	−0.846677
$319$	366.322	0.0642949
$320$	−8246.88	−1.44067
$321$	5157.74	0.896813
$322$	4102.37	0.709987
$323$	−549.309	−0.0946264
$324$	1737.79	0.297974
$325$	2105.86	0.359421
$326$	11403.3	1.93733
$327$	−2338.27	−0.395434
$328$	15213.6	2.56107
$329$	5346.98	0.896014
$330$	−1028.32	−0.171537
$331$	−10985.0	−1.82414	−0.912070	−	0.410035i	$-0.865516\pi$
$331$	−10985.0	−1.82414	−0.912070	+	0.410035i	$0.865516\pi$
$332$	−21091.2	−3.48653
$333$	363.659	0.0598449
$334$	8490.94	1.39103
$335$	2854.20	0.465498
$336$	−6901.14	−1.12050
$337$	2295.27	0.371013	0.185507	−	0.982643i	$-0.440607\pi$
$337$	2295.27	0.371013	0.185507	+	0.982643i	$0.440607\pi$
$338$	26584.4	4.27812
$339$	2299.59	0.368426
$340$	−739.290	−0.117922
$341$	3.21674	0.000510839 0
$342$	−3893.13	−0.615545
$343$	5950.88	0.936786
$344$	−14196.7	−2.22510
$345$	1107.27	0.172793
$346$	−14627.5	−2.27277
$347$	−5313.01	−0.821952	−0.410976	−	0.911646i	$-0.634812\pi$
$347$	−5313.01	−0.821952	−0.410976	+	0.911646i	$0.634812\pi$
$348$	1866.51	0.287516
$349$	2086.08	0.319958	0.159979	−	0.987120i	$-0.448857\pi$
$349$	2086.08	0.319958	0.159979	+	0.987120i	$0.448857\pi$
$350$	−1389.35	−0.212182
$351$	2274.32	0.345853
$352$	8021.89	1.21468
$353$	5382.37	0.811543	0.405772	−	0.913975i	$-0.367003\pi$
$353$	5382.37	0.811543	0.405772	+	0.913975i	$0.367003\pi$
$354$	−3194.90	−0.479681
$355$	5634.33	0.842364
$356$	14559.7	2.16759
$357$	−211.716	−0.0313871
$358$	−19560.4	−2.88771
$359$	−7990.36	−1.17469	−0.587347	−	0.809335i	$-0.699827\pi$
$359$	−7990.36	−1.17469	−0.587347	+	0.809335i	$0.699827\pi$
$360$	−3285.81	−0.481048
$361$	−506.193	−0.0737998
$362$	−14427.1	−2.09468
$363$	−3514.31	−0.508137
$364$	−18505.4	−2.66469
$365$	−2907.16	−0.416897
$366$	3082.29	0.440202
$367$	−429.201	−0.0610466	−0.0305233	−	0.999534i	$-0.509717\pi$
$367$	−429.201	−0.0610466	−0.0305233	+	0.999534i	$0.509717\pi$
$368$	−16583.0	−2.34905
$369$	1875.19	0.264548
$370$	−1096.46	−0.154061
$371$	3019.69	0.422572
$372$	16.3902	0.00228438
$373$	6270.80	0.870482	0.435241	−	0.900314i	$-0.356663\pi$
$373$	6270.80	0.870482	0.435241	+	0.900314i	$0.356663\pi$
$374$	472.467	0.0653227
$375$	−375.000	−0.0516398
$376$	−38127.7	−5.22948
$377$	2442.79	0.333714
$378$	−1500.50	−0.204173
$379$	10417.0	1.41183	0.705917	−	0.708294i	$-0.250535\pi$
$379$	10417.0	1.41183	0.705917	+	0.708294i	$0.250535\pi$
$380$	8549.96	1.15422
$381$	−4090.63	−0.550050
$382$	−792.049	−0.106086
$383$	10769.3	1.43677	0.718387	−	0.695644i	$-0.244881\pi$
$383$	10769.3	1.43677	0.718387	+	0.695644i	$0.244881\pi$
$384$	11613.0	1.54329
$385$	646.745	0.0856134
$386$	6249.18	0.824028
$387$	−1749.84	−0.229844
$388$	−661.736	−0.0865839
$389$	−11121.7	−1.44960	−0.724798	−	0.688961i	$-0.758067\pi$
$389$	−11121.7	−1.44960	−0.724798	+	0.688961i	$0.758067\pi$
$390$	−6857.30	−0.890340
$391$	−508.740	−0.0658008
$392$	−17388.7	−2.24047
$393$	−4040.49	−0.518616
$394$	23489.2	3.00348
$395$	1278.16	0.162813
$396$	2439.04	0.309511
$397$	11286.7	1.42686	0.713432	−	0.700724i	$-0.247140\pi$
$397$	11286.7	1.42686	0.713432	+	0.700724i	$0.247140\pi$
$398$	8318.33	1.04764
$399$	2448.51	0.307215
$400$	5616.19	0.702023
$401$	−15418.0	−1.92005	−0.960023	−	0.279922i	$-0.909691\pi$
$401$	−15418.0	−1.92005	−0.960023	+	0.279922i	$0.909691\pi$
$402$	−9294.14	−1.15311
$403$	21.4506	0.00265144
$404$	37540.1	4.62299
$405$	−405.000	−0.0496904
$406$	−1611.65	−0.197006
$407$	510.406	0.0621619
$408$	1509.68	0.183187
$409$	13849.5	1.67437	0.837183	−	0.546922i	$-0.184201\pi$
$409$	13849.5	1.67437	0.837183	+	0.546922i	$0.184201\pi$
$410$	−5653.86	−0.681035
$411$	−7525.25	−0.903147
$412$	41025.9	4.90583
$413$	2009.37	0.239406
$414$	−3605.61	−0.428034
$415$	4915.40	0.581416
$416$	53493.4	6.30464
$417$	4091.85	0.480524
$418$	−5464.13	−0.639376
$419$	−2793.33	−0.325688	−0.162844	−	0.986652i	$-0.552067\pi$
$419$	−2793.33	−0.325688	−0.162844	+	0.986652i	$0.552067\pi$
$420$	3295.35	0.382849
$421$	−3643.79	−0.421823	−0.210911	−	0.977505i	$-0.567643\pi$
$421$	−3643.79	−0.421823	−0.210911	+	0.977505i	$0.567643\pi$
$422$	29010.4	3.34645
$423$	−4699.51	−0.540185
$424$	−21532.4	−2.46629
$425$	172.295	0.0196648
$426$	−18347.1	−2.08666
$427$	−1938.55	−0.219703
$428$	36885.0	4.16566
$429$	3192.08	0.359243
$430$	5275.94	0.591694
$431$	5834.03	0.652007	0.326004	−	0.945369i	$-0.394298\pi$
$431$	5834.03	0.652007	0.326004	+	0.945369i	$0.394298\pi$
$432$	6065.48	0.675522
$433$	7919.15	0.878915	0.439457	−	0.898263i	$-0.355171\pi$
$433$	7919.15	0.878915	0.439457	+	0.898263i	$0.355171\pi$
$434$	−14.1522	−0.00156527
$435$	−435.000	−0.0479463
$436$	−16721.9	−1.83677
$437$	5883.63	0.644056
$438$	9466.57	1.03272
$439$	11696.0	1.27158	0.635788	−	0.771864i	$-0.280675\pi$
$439$	11696.0	1.27158	0.635788	+	0.771864i	$0.280675\pi$
$440$	−4611.73	−0.499672
$441$	−2143.29	−0.231432
$442$	3150.61	0.339049
$443$	−2786.16	−0.298814	−0.149407	−	0.988776i	$-0.547736\pi$
$443$	−2786.16	−0.298814	−0.149407	+	0.988776i	$0.547736\pi$
$444$	2600.66	0.277977
$445$	−3393.21	−0.361468
$446$	20531.2	2.17978
$447$	8376.74	0.886368
$448$	−16889.5	−1.78115
$449$	11013.8	1.15762	0.578811	−	0.815462i	$-0.303517\pi$
$449$	11013.8	1.15762	0.578811	+	0.815462i	$0.303517\pi$
$450$	1221.11	0.127920
$451$	2631.88	0.274790
$452$	16445.2	1.71132
$453$	919.480	0.0953663
$454$	−23599.8	−2.43963
$455$	4312.77	0.444365
$456$	−17459.6	−1.79303
$457$	12773.5	1.30748	0.653739	−	0.756720i	$-0.273199\pi$
$457$	12773.5	1.30748	0.653739	+	0.756720i	$0.273199\pi$
$458$	−16654.2	−1.69912
$459$	186.079	0.0189225
$460$	7918.52	0.802615
$461$	−13343.4	−1.34808	−0.674039	−	0.738696i	$-0.735442\pi$
$461$	−13343.4	−1.34808	−0.674039	+	0.738696i	$0.735442\pi$
$462$	−2106.00	−0.212077
$463$	17265.4	1.73303	0.866514	−	0.499153i	$-0.166355\pi$
$463$	17265.4	1.73303	0.866514	+	0.499153i	$0.166355\pi$
$464$	6514.78	0.651812
$465$	−3.81981	−0.000380945 0
$466$	−1496.25	−0.148739
$467$	−16016.7	−1.58708	−0.793538	−	0.608521i	$-0.791763\pi$
$467$	−16016.7	−1.58708	−0.793538	+	0.608521i	$0.791763\pi$
$468$	16264.6	1.60647
$469$	5845.38	0.575511
$470$	14169.5	1.39062
$471$	−5484.46	−0.536540
$472$	−14328.2	−1.39727
$473$	−2455.96	−0.238742
$474$	−4162.06	−0.403312
$475$	−1992.61	−0.192479
$476$	−1514.06	−0.145792
$477$	−2654.03	−0.254759
$478$	17002.6	1.62695
$479$	−5847.01	−0.557738	−0.278869	−	0.960329i	$-0.589960\pi$
$479$	−5847.01	−0.557738	−0.278869	+	0.960329i	$0.589960\pi$
$480$	−9525.84	−0.905819
$481$	3403.61	0.322643
$482$	30932.7	2.92313
$483$	2267.68	0.213630
$484$	−25132.2	−2.36028
$485$	154.221	0.0144388
$486$	1318.80	0.123091
$487$	−342.662	−0.0318840	−0.0159420	−	0.999873i	$-0.505075\pi$
$487$	−342.662	−0.0318840	−0.0159420	+	0.999873i	$0.505075\pi$
$488$	13823.2	1.28227
$489$	6303.44	0.582927
$490$	6462.22	0.595782
$491$	−1673.48	−0.153815	−0.0769073	−	0.997038i	$-0.524505\pi$
$491$	−1673.48	−0.153815	−0.0769073	+	0.997038i	$0.524505\pi$
$492$	13410.2	1.22882
$493$	199.863	0.0182583
$494$	−36437.2	−3.31859
$495$	−568.430	−0.0516142
$496$	57.2074	0.00517881
$497$	11539.1	1.04144
$498$	−16006.0	−1.44026
$499$	10918.2	0.979487	0.489743	−	0.871867i	$-0.337090\pi$
$499$	10918.2	0.979487	0.489743	+	0.871867i	$0.337090\pi$
$500$	−2681.77	−0.239865
$501$	4693.58	0.418550
$502$	9302.84	0.827103
$503$	16957.6	1.50319	0.751595	−	0.659625i	$-0.229285\pi$
$503$	16957.6	1.50319	0.751595	+	0.659625i	$0.229285\pi$
$504$	−6729.31	−0.594737
$505$	−8748.91	−0.770933
$506$	−5060.58	−0.444606
$507$	14695.2	1.28725
$508$	−29253.6	−2.55496
$509$	−226.179	−0.0196959	−0.00984795	−	0.999952i	$-0.503135\pi$
$509$	−226.179	−0.0196959	−0.00984795	+	0.999952i	$0.503135\pi$
$510$	−561.045	−0.0487128
$511$	−5953.83	−0.515425
$512$	11437.3	0.987234
$513$	−2152.02	−0.185213
$514$	−4358.48	−0.374016
$515$	−9561.30	−0.818100
$516$	−12513.8	−1.06762
$517$	−6595.91	−0.561099
$518$	−2245.55	−0.190471
$519$	−8085.70	−0.683859
$520$	−30753.0	−2.59348
$521$	−2051.24	−0.172489	−0.0862443	−	0.996274i	$-0.527487\pi$
$521$	−2051.24	−0.172489	−0.0862443	+	0.996274i	$0.527487\pi$
$522$	1416.49	0.118770
$523$	−11922.9	−0.996852	−0.498426	−	0.866932i	$-0.666088\pi$
$523$	−11922.9	−0.996852	−0.498426	+	0.866932i	$0.666088\pi$
$524$	−28895.1	−2.40895
$525$	−767.997	−0.0638441
$526$	−9194.94	−0.762203
$527$	1.75503	0.000145067 0
$528$	8513.09	0.701676
$529$	−6717.89	−0.552140
$530$	8002.16	0.655833
$531$	−1766.06	−0.144332
$532$	17510.3	1.42700
$533$	17550.5	1.42626
$534$	11049.3	0.895412
$535$	−8596.24	−0.694669
$536$	−41681.6	−3.35890
$537$	−10812.5	−0.868889
$538$	18262.1	1.46345
$539$	−3008.17	−0.240392
$540$	−2896.31	−0.230810
$541$	12876.2	1.02327	0.511635	−	0.859203i	$-0.329040\pi$
$541$	12876.2	1.02327	0.511635	+	0.859203i	$0.329040\pi$
$542$	43656.7	3.45981
$543$	−7974.96	−0.630273
$544$	4376.69	0.344943
$545$	3897.12	0.306302
$546$	−14043.7	−1.10076
$547$	9065.39	0.708607	0.354304	−	0.935130i	$-0.384718\pi$
$547$	9065.39	0.708607	0.354304	+	0.935130i	$0.384718\pi$
$548$	−53816.0	−4.19508
$549$	1703.81	0.132453
$550$	1713.87	0.132872
$551$	−2311.43	−0.178712
$552$	−16170.1	−1.24682
$553$	2617.65	0.201291
$554$	−37835.7	−2.90160
$555$	−606.098	−0.0463557
$556$	29262.4	2.23202
$557$	−19520.2	−1.48492	−0.742458	−	0.669893i	$-0.766340\pi$
$557$	−19520.2	−1.48492	−0.742458	+	0.669893i	$0.766340\pi$
$558$	12.4385	0.000943660 0
$559$	−16377.4	−1.23916
$560$	11501.9	0.867936
$561$	261.168	0.0196551
$562$	−10403.5	−0.780866
$563$	9786.46	0.732593	0.366297	−	0.930498i	$-0.380626\pi$
$563$	9786.46	0.732593	0.366297	+	0.930498i	$0.380626\pi$
$564$	−33608.0	−2.50914
$565$	−3832.64	−0.285381
$566$	11053.1	0.820844
$567$	−829.437	−0.0614340
$568$	−82281.5	−6.07826
$569$	13236.9	0.975257	0.487628	−	0.873051i	$-0.337862\pi$
$569$	13236.9	0.975257	0.487628	+	0.873051i	$0.337862\pi$
$570$	6488.55	0.476799
$571$	−21385.2	−1.56733	−0.783663	−	0.621186i	$-0.786651\pi$
$571$	−21385.2	−1.56733	−0.783663	+	0.621186i	$0.786651\pi$
$572$	22827.8	1.66867
$573$	−437.825	−0.0319204
$574$	−11579.1	−0.841987
$575$	−1845.45	−0.133845
$576$	14844.4	1.07381
$577$	1531.13	0.110471	0.0552356	−	0.998473i	$-0.482409\pi$
$577$	1531.13	0.110471	0.0552356	+	0.998473i	$0.482409\pi$
$578$	−26405.9	−1.90024
$579$	3454.39	0.247944
$580$	−3110.85	−0.222709
$581$	10066.7	0.718825
$582$	−502.190	−0.0357671
$583$	−3725.02	−0.264622
$584$	42454.9	3.00821
$585$	−3790.54	−0.267897
$586$	−9522.25	−0.671263
$587$	2742.12	0.192810	0.0964050	−	0.995342i	$-0.469266\pi$
$587$	2742.12	0.192810	0.0964050	+	0.995342i	$0.469266\pi$
$588$	−15327.5	−1.07499
$589$	−20.2971	−0.00141991
$590$	5324.83	0.371559
$591$	12984.2	0.903723
$592$	9077.22	0.630188
$593$	−8476.47	−0.586993	−0.293497	−	0.955960i	$-0.594819\pi$
$593$	−8476.47	−0.586993	−0.293497	+	0.955960i	$0.594819\pi$
$594$	1850.98	0.127856
$595$	352.859	0.0243123
$596$	59905.3	4.11714
$597$	4598.16	0.315226
$598$	−33746.2	−2.30767
$599$	−14839.1	−1.01220	−0.506100	−	0.862475i	$-0.668913\pi$
$599$	−14839.1	−1.01220	−0.506100	+	0.862475i	$0.668913\pi$
$600$	5476.35	0.372618
$601$	−13198.6	−0.895814	−0.447907	−	0.894080i	$-0.647830\pi$
$601$	−13198.6	−0.895814	−0.447907	+	0.894080i	$0.647830\pi$
$602$	10805.1	0.731532
$603$	−5137.56	−0.346961
$604$	6575.56	0.442973
$605$	5857.19	0.393601
$606$	28489.1	1.90972
$607$	2310.67	0.154509	0.0772547	−	0.997011i	$-0.475385\pi$
$607$	2310.67	0.154509	0.0772547	+	0.997011i	$0.475385\pi$
$608$	−50616.8	−3.37629
$609$	−890.877	−0.0592777
$610$	−5137.15	−0.340979
$611$	−43984.4	−2.91231
$612$	1330.72	0.0878942
$613$	−3944.92	−0.259925	−0.129962	−	0.991519i	$-0.541486\pi$
$613$	−3944.92	−0.259925	−0.129962	+	0.991519i	$0.541486\pi$
$614$	48352.9	3.17811
$615$	−3125.31	−0.204918
$616$	−9444.80	−0.617762
$617$	−26587.7	−1.73482	−0.867408	−	0.497598i	$-0.834216\pi$
$617$	−26587.7	−1.73482	−0.867408	+	0.497598i	$0.834216\pi$
$618$	31134.5	2.02656
$619$	8691.35	0.564353	0.282177	−	0.959362i	$-0.408944\pi$
$619$	8691.35	0.564353	0.282177	+	0.959362i	$0.408944\pi$
$620$	−27.3170	−0.00176948
$621$	−1993.09	−0.128792
$622$	−40285.2	−2.59693
$623$	−6949.26	−0.446896
$624$	56769.0	3.64195
$625$	625.000	0.0400000
$626$	−7889.06	−0.503690
$627$	−3020.43	−0.192383
$628$	−39221.5	−2.49221
$629$	278.474	0.0176526
$630$	2500.83	0.158151
$631$	−19396.9	−1.22374	−0.611869	−	0.790959i	$-0.709582\pi$
$631$	−19396.9	−1.22374	−0.611869	+	0.790959i	$0.709582\pi$
$632$	−18665.7	−1.17481
$633$	16036.2	1.00692
$634$	28239.2	1.76896
$635$	6817.71	0.426067
$636$	−18980.0	−1.18334
$637$	−20059.8	−1.24772
$638$	1988.09	0.123369
$639$	−10141.8	−0.627861
$640$	−19355.0	−1.19543
$641$	−11088.7	−0.683273	−0.341636	−	0.939832i	$-0.610981\pi$
$641$	−11088.7	−0.683273	−0.341636	+	0.939832i	$0.610981\pi$
$642$	27991.9	1.72080
$643$	−3896.33	−0.238968	−0.119484	−	0.992836i	$-0.538124\pi$
$643$	−3896.33	−0.238968	−0.119484	+	0.992836i	$0.538124\pi$
$644$	16217.1	0.992302
$645$	2916.41	0.178036
$646$	−2981.19	−0.181569
$647$	14565.2	0.885034	0.442517	−	0.896760i	$-0.354086\pi$
$647$	14565.2	0.885034	0.442517	+	0.896760i	$0.354086\pi$
$648$	5914.45	0.358552
$649$	−2478.72	−0.149920
$650$	11428.8	0.689655
$651$	−7.82295	−0.000470976 0
$652$	45078.3	2.70767
$653$	27443.4	1.64463	0.822314	−	0.569034i	$-0.192683\pi$
$653$	27443.4	1.64463	0.822314	+	0.569034i	$0.192683\pi$
$654$	−12690.2	−0.758756
$655$	6734.16	0.401718
$656$	46806.2	2.78579
$657$	5232.88	0.310737
$658$	29019.0	1.71927
$659$	10355.6	0.612135	0.306068	−	0.952010i	$-0.400987\pi$
$659$	10355.6	0.612135	0.306068	+	0.952010i	$0.400987\pi$
$660$	−4065.06	−0.239746
$661$	9704.01	0.571017	0.285508	−	0.958376i	$-0.407838\pi$
$661$	9704.01	0.571017	0.285508	+	0.958376i	$0.407838\pi$
$662$	−59617.4	−3.50015
$663$	1741.58	0.102017
$664$	−71782.6	−4.19534
$665$	−4080.85	−0.237968
$666$	1973.64	0.114830
$667$	−2140.72	−0.124272
$668$	33565.6	1.94415
$669$	11349.1	0.655879
$670$	15490.2	0.893194
$671$	2391.35	0.137582
$672$	−19508.8	−1.11990
$673$	16876.5	0.966629	0.483315	−	0.875447i	$-0.339433\pi$
$673$	16876.5	0.966629	0.483315	+	0.875447i	$0.339433\pi$
$674$	12456.8	0.711898
$675$	675.000	0.0384900
$676$	105091.	5.97924
$677$	−1095.44	−0.0621880	−0.0310940	−	0.999516i	$-0.509899\pi$
$677$	−1095.44	−0.0621880	−0.0310940	+	0.999516i	$0.509899\pi$
$678$	12480.2	0.706933
$679$	315.843	0.0178512
$680$	−2516.13	−0.141896
$681$	−13045.4	−0.734067
$682$	17.4578	0.000980195 0
$683$	−23004.5	−1.28879	−0.644394	−	0.764693i	$-0.722890\pi$
$683$	−23004.5	−1.28879	−0.644394	+	0.764693i	$0.722890\pi$
$684$	−15389.9	−0.860305
$685$	12542.1	0.699574
$686$	32296.4	1.79750
$687$	−9206.01	−0.511254
$688$	−43677.5	−2.42034
$689$	−24840.0	−1.37348
$690$	6009.35	0.331554
$691$	4973.91	0.273830	0.136915	−	0.990583i	$-0.456281\pi$
$691$	4973.91	0.273830	0.136915	+	0.990583i	$0.456281\pi$
$692$	−57824.0	−3.17650
$693$	−1164.14	−0.0638125
$694$	−28834.6	−1.57716
$695$	−6819.75	−0.372212
$696$	6352.56	0.345967
$697$	1435.94	0.0780344
$698$	11321.5	0.613933
$699$	−827.089	−0.0447545
$700$	−5492.24	−0.296553
$701$	19281.6	1.03888	0.519440	−	0.854507i	$-0.326141\pi$
$701$	19281.6	1.03888	0.519440	+	0.854507i	$0.326141\pi$
$702$	12343.1	0.663621
$703$	−3220.58	−0.172783
$704$	20834.6	1.11539
$705$	7832.52	0.418425
$706$	29211.0	1.55718
$707$	−17917.7	−0.953132
$708$	−12629.8	−0.670417
$709$	35391.4	1.87468	0.937342	−	0.348412i	$-0.113279\pi$
$709$	35391.4	1.87468	0.937342	+	0.348412i	$0.113279\pi$
$710$	30578.5	1.61632
$711$	−2300.68	−0.121353
$712$	49553.0	2.60826
$713$	−18.7981	−0.000987369 0
$714$	−1149.02	−0.0602253
$715$	−5320.14	−0.278268
$716$	−77324.3	−4.03596
$717$	9398.60	0.489536
$718$	−43365.0	−2.25399
$719$	−19325.0	−1.00237	−0.501183	−	0.865341i	$-0.667102\pi$
$719$	−19325.0	−1.00237	−0.501183	+	0.865341i	$0.667102\pi$
$720$	−10109.1	−0.523257
$721$	−19581.5	−1.01145
$722$	−2747.19	−0.141607
$723$	17098.8	0.879547
$724$	−57032.0	−2.92759
$725$	725.000	0.0371391
$726$	−19072.8	−0.975010
$727$	16887.9	0.861537	0.430768	−	0.902462i	$-0.358243\pi$
$727$	16887.9	0.861537	0.430768	+	0.902462i	$0.358243\pi$
$728$	−62982.0	−3.20641
$729$	729.000	0.0370370
$730$	−15777.6	−0.799940
$731$	−1339.95	−0.0677975
$732$	12184.6	0.615241
$733$	6698.16	0.337520	0.168760	−	0.985657i	$-0.446024\pi$
$733$	6698.16	0.337520	0.168760	+	0.985657i	$0.446024\pi$
$734$	−2329.35	−0.117136
$735$	3572.15	0.179266
$736$	−46878.6	−2.34778
$737$	−7210.73	−0.360394
$738$	10176.9	0.507613
$739$	4934.50	0.245627	0.122814	−	0.992430i	$-0.460808\pi$
$739$	4934.50	0.245627	0.122814	+	0.992430i	$0.460808\pi$
$740$	−4334.44	−0.215320
$741$	−20141.5	−0.998540
$742$	16388.4	0.810829
$743$	−5140.65	−0.253825	−0.126913	−	0.991914i	$-0.540507\pi$
$743$	−5140.65	−0.253825	−0.126913	+	0.991914i	$0.540507\pi$
$744$	55.7830	0.00274880
$745$	−13961.2	−0.686578
$746$	34032.7	1.67027
$747$	−8847.73	−0.433362
$748$	1867.71	0.0912971
$749$	−17605.0	−0.858843
$750$	−2035.19	−0.0990861
$751$	9625.37	0.467690	0.233845	−	0.972274i	$-0.424869\pi$
$751$	9625.37	0.467690	0.233845	+	0.972274i	$0.424869\pi$
$752$	−117304.	−5.68834
$753$	5142.37	0.248869
$754$	13257.4	0.640328
$755$	−1532.47	−0.0738704
$756$	−5931.62	−0.285358
$757$	−5128.83	−0.246249	−0.123125	−	0.992391i	$-0.539291\pi$
$757$	−5128.83	−0.246249	−0.123125	+	0.992391i	$0.539291\pi$
$758$	56534.8	2.70902
$759$	−2797.36	−0.133778
$760$	29099.3	1.38887
$761$	−25024.7	−1.19204	−0.596022	−	0.802968i	$-0.703253\pi$
$761$	−25024.7	−1.19204	−0.596022	+	0.802968i	$0.703253\pi$
$762$	−22200.5	−1.05543
$763$	7981.28	0.378692
$764$	−3131.05	−0.148269
$765$	−310.132	−0.0146573
$766$	58446.7	2.75687
$767$	−16529.2	−0.778140
$768$	23440.6	1.10135
$769$	−26474.8	−1.24149	−0.620746	−	0.784012i	$-0.713170\pi$
$769$	−26474.8	−1.24149	−0.620746	+	0.784012i	$0.713170\pi$
$770$	3509.99	0.164274
$771$	−2409.26	−0.112539
$772$	24703.6	1.15169
$773$	−24685.1	−1.14859	−0.574295	−	0.818648i	$-0.694724\pi$
$773$	−24685.1	−1.14859	−0.574295	+	0.818648i	$0.694724\pi$
$774$	−9496.69	−0.441023
$775$	6.36636	0.000295079 0
$776$	−2252.18	−0.104186
$777$	−1241.28	−0.0573112
$778$	−60359.4	−2.78148
$779$	−16606.8	−0.763798
$780$	−27107.6	−1.24437
$781$	−14234.3	−0.652170
$782$	−2761.02	−0.126258
$783$	783.000	0.0357371
$784$	−53498.3	−2.43706
$785$	9140.76	0.415602
$786$	−21928.4	−0.995116
$787$	−35383.4	−1.60265	−0.801323	−	0.598232i	$-0.795870\pi$
$787$	−35383.4	−1.60265	−0.801323	+	0.598232i	$0.795870\pi$
$788$	92855.3	4.19776
$789$	−5082.73	−0.229341
$790$	6936.77	0.312404
$791$	−7849.22	−0.352827
$792$	8301.12	0.372434
$793$	15946.6	0.714098
$794$	61255.0	2.73786
$795$	4423.39	0.197335
$796$	32883.2	1.46421
$797$	−24869.4	−1.10529	−0.552647	−	0.833415i	$-0.686382\pi$
$797$	−24869.4	−1.10529	−0.552647	+	0.833415i	$0.686382\pi$
$798$	13288.5	0.589483
$799$	−3598.69	−0.159340
$800$	15876.4	0.701644
$801$	6107.77	0.269423
$802$	−83676.1	−3.68417
$803$	7344.51	0.322767
$804$	−36740.7	−1.61162
$805$	−3779.47	−0.165477
$806$	116.416	0.00508757
$807$	10094.8	0.440341
$808$	127765.	5.56284
$809$	834.568	0.0362693	0.0181346	−	0.999836i	$-0.494227\pi$
$809$	834.568	0.0362693	0.0181346	+	0.999836i	$0.494227\pi$
$810$	−2198.00	−0.0953456
$811$	−17419.5	−0.754232	−0.377116	−	0.926166i	$-0.623084\pi$
$811$	−17419.5	−0.754232	−0.377116	+	0.926166i	$0.623084\pi$
$812$	−6371.00	−0.275343
$813$	24132.3	1.04103
$814$	2770.06	0.119276
$815$	−10505.7	−0.451533
$816$	4644.69	0.199260
$817$	15496.7	0.663600
$818$	75163.8	3.21276
$819$	−7762.99	−0.331210
$820$	−22350.3	−0.951837
$821$	20163.7	0.857148	0.428574	−	0.903507i	$-0.359016\pi$
$821$	20163.7	0.857148	0.428574	+	0.903507i	$0.359016\pi$
$822$	−40840.8	−1.73295
$823$	10456.9	0.442898	0.221449	−	0.975172i	$-0.428921\pi$
$823$	10456.9	0.442898	0.221449	+	0.975172i	$0.428921\pi$
$824$	139629.	5.90318
$825$	947.384	0.0399802
$826$	10905.2	0.459371
$827$	−10943.6	−0.460154	−0.230077	−	0.973172i	$-0.573898\pi$
$827$	−10943.6	−0.460154	−0.230077	+	0.973172i	$0.573898\pi$
$828$	−14253.3	−0.598234
$829$	−33775.8	−1.41506	−0.707528	−	0.706685i	$-0.750190\pi$
$829$	−33775.8	−1.41506	−0.707528	+	0.706685i	$0.750190\pi$
$830$	26676.7	1.11562
$831$	−20914.6	−0.873069
$832$	138934.	5.78926
$833$	−1641.24	−0.0682660
$834$	22207.1	0.922027
$835$	−7822.63	−0.324207
$836$	−21600.3	−0.893613
$837$	6.87567	0.000283940 0
$838$	−15159.9	−0.624927
$839$	39087.3	1.60840	0.804198	−	0.594361i	$-0.202595\pi$
$839$	39087.3	1.60840	0.804198	+	0.594361i	$0.202595\pi$
$840$	11215.5	0.460681
$841$	841.000	0.0344828
$842$	−19775.4	−0.809391
$843$	−5750.81	−0.234957
$844$	114681.	4.67711
$845$	−24492.0	−0.997101
$846$	−25505.1	−1.03650
$847$	11995.5	0.486623
$848$	−66246.9	−2.68270
$849$	6109.89	0.246986
$850$	935.076	0.0377327
$851$	−2982.73	−0.120149
$852$	−72527.9	−2.91639
$853$	47274.9	1.89761	0.948806	−	0.315859i	$-0.102293\pi$
$853$	47274.9	1.89761	0.948806	+	0.315859i	$0.102293\pi$
$854$	−10520.9	−0.421565
$855$	3586.70	0.143465
$856$	125536.	5.01254
$857$	15482.0	0.617099	0.308550	−	0.951208i	$-0.400156\pi$
$857$	15482.0	0.617099	0.308550	+	0.951208i	$0.400156\pi$
$858$	17324.0	0.689313
$859$	−32719.1	−1.29960	−0.649802	−	0.760103i	$-0.725148\pi$
$859$	−32719.1	−1.29960	−0.649802	+	0.760103i	$0.725148\pi$
$860$	20856.3	0.826971
$861$	−6400.61	−0.253348
$862$	31662.2	1.25107
$863$	−1741.34	−0.0686858	−0.0343429	−	0.999410i	$-0.510934\pi$
$863$	−1741.34	−0.0686858	−0.0343429	+	0.999410i	$0.510934\pi$
$864$	17146.5	0.675158
$865$	13476.2	0.529715
$866$	42978.6	1.68646
$867$	−14596.5	−0.571769
$868$	−55.9449	−0.00218767
$869$	−3229.08	−0.126052
$870$	−2360.82	−0.0919991
$871$	−48084.3	−1.87058
$872$	−56912.0	−2.21019
$873$	−277.598	−0.0107620
$874$	31931.5	1.23581
$875$	1280.00	0.0494534
$876$	37422.3	1.44336
$877$	11848.6	0.456213	0.228106	−	0.973636i	$-0.426747\pi$
$877$	11848.6	0.456213	0.228106	+	0.973636i	$0.426747\pi$
$878$	63476.4	2.43989
$879$	−5263.65	−0.201978
$880$	−14188.5	−0.543516
$881$	−29332.3	−1.12171	−0.560857	−	0.827913i	$-0.689528\pi$
$881$	−29332.3	−1.12171	−0.560857	+	0.827913i	$0.689528\pi$
$882$	−11632.0	−0.444070
$883$	−25723.3	−0.980360	−0.490180	−	0.871621i	$-0.663069\pi$
$883$	−25723.3	−0.980360	−0.490180	+	0.871621i	$0.663069\pi$
$884$	12454.7	0.473865
$885$	2943.43	0.111799
$886$	−15121.0	−0.573362
$887$	10959.8	0.414875	0.207437	−	0.978248i	$-0.433488\pi$
$887$	10959.8	0.414875	0.207437	+	0.978248i	$0.433488\pi$
$888$	8851.20	0.334490
$889$	13962.6	0.526762
$890$	−18415.5	−0.693583
$891$	1023.17	0.0384710
$892$	81162.1	3.04653
$893$	41619.2	1.55961
$894$	45462.0	1.70076
$895$	18020.8	0.673039
$896$	−39638.8	−1.47795
$897$	−18654.0	−0.694359
$898$	59773.6	2.22124
$899$	7.38497	0.000273974 0
$900$	4827.18	0.178785
$901$	−2032.34	−0.0751467
$902$	14283.7	0.527266
$903$	5972.77	0.220112
$904$	55970.3	2.05923
$905$	13291.6	0.488207
$906$	4990.17	0.182988
$907$	−3053.42	−0.111783	−0.0558915	−	0.998437i	$-0.517800\pi$
$907$	−3053.42	−0.111783	−0.0558915	+	0.998437i	$0.517800\pi$
$908$	−93292.4	−3.40971
$909$	15748.0	0.574620
$910$	23406.2	0.852644
$911$	−32880.5	−1.19581	−0.597903	−	0.801568i	$-0.703999\pi$
$911$	−32880.5	−1.19581	−0.597903	+	0.801568i	$0.703999\pi$
$912$	−53716.2	−1.95035
$913$	−12418.1	−0.450140
$914$	69323.8	2.50878
$915$	−2839.69	−0.102598
$916$	−65835.7	−2.37475
$917$	13791.5	0.496658
$918$	1009.88	0.0363083
$919$	−49962.9	−1.79339	−0.896694	−	0.442650i	$-0.854038\pi$
$919$	−49962.9	−1.79339	−0.896694	+	0.442650i	$0.854038\pi$
$920$	26950.2	0.965786
$921$	26728.2	0.956270
$922$	−72416.8	−2.58668
$923$	−94920.7	−3.38500
$924$	−8325.22	−0.296406
$925$	1010.16	0.0359070
$926$	93702.3	3.32532
$927$	17210.3	0.609775
$928$	18416.6	0.651460
$929$	−48163.6	−1.70096	−0.850482	−	0.526004i	$-0.823690\pi$
$929$	−48163.6	−1.70096	−0.850482	+	0.526004i	$0.823690\pi$
$930$	−20.7308	−0.000730956 0
$931$	18981.1	0.668185
$932$	−5914.83	−0.207883
$933$	−22268.6	−0.781396
$934$	−86925.3	−3.04527
$935$	−435.279	−0.0152248
$936$	55355.5	1.93307
$937$	32244.1	1.12419	0.562097	−	0.827071i	$-0.309995\pi$
$937$	32244.1	1.12419	0.562097	+	0.827071i	$0.309995\pi$
$938$	31723.9	1.10429
$939$	−4360.87	−0.151557
$940$	56013.4	1.94357
$941$	37391.5	1.29535	0.647677	−	0.761915i	$-0.275740\pi$
$941$	37391.5	1.29535	0.647677	+	0.761915i	$0.275740\pi$
$942$	−29765.1	−1.02951
$943$	−15380.3	−0.531125
$944$	−44082.3	−1.51987
$945$	1382.39	0.0475866
$946$	−13328.9	−0.458097
$947$	17887.8	0.613807	0.306903	−	0.951741i	$-0.400707\pi$
$947$	17887.8	0.613807	0.306903	+	0.951741i	$0.400707\pi$
$948$	−16453.1	−0.563682
$949$	48976.4	1.67528
$950$	−10814.2	−0.369327
$951$	15609.9	0.532266
$952$	−5153.02	−0.175431
$953$	20302.3	0.690090	0.345045	−	0.938586i	$-0.387864\pi$
$953$	20302.3	0.690090	0.345045	+	0.938586i	$0.387864\pi$
$954$	−14403.9	−0.488829
$955$	729.708	0.0247254
$956$	67213.0	2.27387
$957$	1098.97	0.0371207
$958$	−31732.7	−1.07018
$959$	25686.1	0.864908
$960$	−24740.6	−0.831772
$961$	−29790.9	−0.999998
$962$	18472.0	0.619085
$963$	15473.2	0.517776
$964$	122280.	4.08546
$965$	−5757.31	−0.192056
$966$	12307.1	0.409911
$967$	−19313.4	−0.642273	−0.321137	−	0.947033i	$-0.604065\pi$
$967$	−19313.4	−0.642273	−0.321137	+	0.947033i	$0.604065\pi$
$968$	−85536.0	−2.84012
$969$	−1647.93	−0.0546326
$970$	836.983	0.0277050
$971$	−25297.3	−0.836077	−0.418038	−	0.908429i	$-0.637282\pi$
$971$	−25297.3	−0.836077	−0.418038	+	0.908429i	$0.637282\pi$
$972$	5213.36	0.172036
$973$	−13966.8	−0.460179
$974$	−1859.68	−0.0611787
$975$	6317.57	0.207512
$976$	42528.6	1.39478
$977$	21461.4	0.702776	0.351388	−	0.936230i	$-0.385710\pi$
$977$	21461.4	0.702776	0.351388	+	0.936230i	$0.385710\pi$
$978$	34209.8	1.11852
$979$	8572.45	0.279854
$980$	25545.8	0.832684
$981$	−7014.82	−0.228304
$982$	−9082.24	−0.295138
$983$	14059.8	0.456193	0.228096	−	0.973639i	$-0.426750\pi$
$983$	14059.8	0.456193	0.228096	+	0.973639i	$0.426750\pi$
$984$	45640.7	1.47863
$985$	−21640.4	−0.700021
$986$	1084.69	0.0350340
$987$	16040.9	0.517314
$988$	−144040.	−4.63818
$989$	14352.2	0.461450
$990$	−3084.97	−0.0990370
$991$	−60932.3	−1.95316	−0.976578	−	0.215162i	$-0.930972\pi$
$991$	−60932.3	−1.95316	−0.976578	+	0.215162i	$0.930972\pi$
$992$	161.720	0.00517601
$993$	−32955.0	−1.05317
$994$	62624.5	1.99832
$995$	−7663.60	−0.244173
$996$	−63273.5	−2.01295
$997$	−4183.32	−0.132886	−0.0664428	−	0.997790i	$-0.521165\pi$
$997$	−4183.32	−0.132886	−0.0664428	+	0.997790i	$0.521165\pi$
$998$	59254.7	1.87943
$999$	1090.98	0.0345515

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.4.a.h.1.6	✓	6
3.2	odd	2		1305.4.a.h.1.1		6
5.4	even	2		2175.4.a.k.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.4.a.h.1.6	✓	6	1.1	even	1	trivial
1305.4.a.h.1.1		6	3.2	odd	2
2175.4.a.k.1.1		6	5.4	even	2

Overview	Random
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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)

\(f(q)\)	\(=\)	\(q+5.42717 q^{2} +3.00000 q^{3} +21.4542 q^{4} -5.00000 q^{5} +16.2815 q^{6} -10.2400 q^{7} +73.0180 q^{8} +9.00000 q^{9} -27.1358 q^{10} +12.6318 q^{11} +64.3625 q^{12} +84.2342 q^{13} -55.5740 q^{14} -15.0000 q^{15} +224.647 q^{16} +6.89181 q^{17} +48.8445 q^{18} -79.7045 q^{19} -107.271 q^{20} -30.7199 q^{21} +68.5548 q^{22} -73.8181 q^{23} +219.054 q^{24} +25.0000 q^{25} +457.153 q^{26} +27.0000 q^{27} -219.690 q^{28} +29.0000 q^{29} -81.4075 q^{30} +0.254654 q^{31} +635.056 q^{32} +37.8953 q^{33} +37.4030 q^{34} +51.1998 q^{35} +193.087 q^{36} +40.4065 q^{37} -432.570 q^{38} +252.703 q^{39} -365.090 q^{40} +208.354 q^{41} -166.722 q^{42} -194.427 q^{43} +271.004 q^{44} -45.0000 q^{45} -400.623 q^{46} -522.168 q^{47} +673.942 q^{48} -238.143 q^{49} +135.679 q^{50} +20.6754 q^{51} +1807.17 q^{52} -294.893 q^{53} +146.534 q^{54} -63.1589 q^{55} -747.701 q^{56} -239.114 q^{57} +157.388 q^{58} -196.229 q^{59} -321.812 q^{60} +189.313 q^{61} +1.38205 q^{62} -92.1597 q^{63} +1649.38 q^{64} -421.171 q^{65} +205.664 q^{66} -570.840 q^{67} +147.858 q^{68} -221.454 q^{69} +277.870 q^{70} -1126.87 q^{71} +657.162 q^{72} +581.431 q^{73} +219.293 q^{74} +75.0000 q^{75} -1709.99 q^{76} -129.349 q^{77} +1371.46 q^{78} -255.631 q^{79} -1123.24 q^{80} +81.0000 q^{81} +1130.77 q^{82} -983.081 q^{83} -659.069 q^{84} -34.4591 q^{85} -1055.19 q^{86} +87.0000 q^{87} +922.347 q^{88} +678.642 q^{89} -244.223 q^{90} -862.555 q^{91} -1583.70 q^{92} +0.763963 q^{93} -2833.89 q^{94} +398.523 q^{95} +1905.17 q^{96} -30.8442 q^{97} -1292.44 q^{98} +113.686 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} + 18 q^{3} + 51 q^{4} - 30 q^{5} + 3 q^{6} + 47 q^{7} + 51 q^{8} + 54 q^{9} - 5 q^{10} + 81 q^{11} + 153 q^{12} + 169 q^{13} - 30 q^{14} - 90 q^{15} + 131 q^{16} - q^{17} + 9 q^{18} + 116 q^{19}+ \cdots + 729 q^{99}+O(q^{100}) \) 6 * q + q^2 + 18 * q^3 + 51 * q^4 - 30 * q^5 + 3 * q^6 + 47 * q^7 + 51 * q^8 + 54 * q^9 - 5 * q^10 + 81 * q^11 + 153 * q^12 + 169 * q^13 - 30 * q^14 - 90 * q^15 + 131 * q^16 - q^17 + 9 * q^18 + 116 * q^19 - 255 * q^20 + 141 * q^21 + 90 * q^22 - 52 * q^23 + 153 * q^24 + 150 * q^25 + 294 * q^26 + 162 * q^27 + 344 * q^28 + 174 * q^29 - 15 * q^30 + 340 * q^31 + 499 * q^32 + 243 * q^33 + 920 * q^34 - 235 * q^35 + 459 * q^36 + 332 * q^37 - 378 * q^38 + 507 * q^39 - 255 * q^40 - 616 * q^41 - 90 * q^42 + 334 * q^43 - 52 * q^44 - 270 * q^45 - 158 * q^46 - 85 * q^47 + 393 * q^48 + 879 * q^49 + 25 * q^50 - 3 * q^51 + 2220 * q^52 - 850 * q^53 + 27 * q^54 - 405 * q^55 - 624 * q^56 + 348 * q^57 + 29 * q^58 - 758 * q^59 - 765 * q^60 - 36 * q^61 - 152 * q^62 + 423 * q^63 + 1795 * q^64 - 845 * q^65 + 270 * q^66 + 939 * q^67 - 186 * q^68 - 156 * q^69 + 150 * q^70 - 1388 * q^71 + 459 * q^72 + 1708 * q^73 - 814 * q^74 + 450 * q^75 + 566 * q^76 + 2585 * q^77 + 882 * q^78 + 1250 * q^79 - 655 * q^80 + 486 * q^81 + 1372 * q^82 - 748 * q^83 + 1032 * q^84 + 5 * q^85 - 800 * q^86 + 522 * q^87 + 536 * q^88 + 1099 * q^89 - 45 * q^90 + 539 * q^91 + 1698 * q^92 + 1020 * q^93 - 4542 * q^94 - 580 * q^95 + 1497 * q^96 - 22 * q^97 - 1433 * q^98 + 729 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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