LMFDB - Embedded newform 435.4.a.h.1.4

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			1.4
Root			$2.35472$ 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)

$f(q)$	$=$	\(q+2.35472 q^{2} +3.00000 q^{3} -2.45528 q^{4} -5.00000 q^{5} +7.06417 q^{6} -3.94392 q^{7} -24.6193 q^{8} +9.00000 q^{9} -11.7736 q^{10} +42.8507 q^{11} -7.36583 q^{12} +36.4288 q^{13} -9.28685 q^{14} -15.0000 q^{15} -38.3294 q^{16} +17.8279 q^{17} +21.1925 q^{18} +84.6809 q^{19} +12.2764 q^{20} -11.8318 q^{21} +100.902 q^{22} +93.9097 q^{23} -73.8579 q^{24} +25.0000 q^{25} +85.7797 q^{26} +27.0000 q^{27} +9.68343 q^{28} +29.0000 q^{29} -35.3208 q^{30} +122.782 q^{31} +106.699 q^{32} +128.552 q^{33} +41.9798 q^{34} +19.7196 q^{35} -22.0975 q^{36} -61.2323 q^{37} +199.400 q^{38} +109.286 q^{39} +123.096 q^{40} +13.8437 q^{41} -27.8605 q^{42} +397.388 q^{43} -105.210 q^{44} -45.0000 q^{45} +221.131 q^{46} +235.310 q^{47} -114.988 q^{48} -327.445 q^{49} +58.8681 q^{50} +53.4837 q^{51} -89.4428 q^{52} -50.4554 q^{53} +63.5775 q^{54} -214.253 q^{55} +97.0966 q^{56} +254.043 q^{57} +68.2870 q^{58} -476.712 q^{59} +36.8292 q^{60} -75.4071 q^{61} +289.119 q^{62} -35.4953 q^{63} +557.882 q^{64} -182.144 q^{65} +302.705 q^{66} -698.609 q^{67} -43.7725 q^{68} +281.729 q^{69} +46.4342 q^{70} +44.6799 q^{71} -221.574 q^{72} +669.611 q^{73} -144.185 q^{74} +75.0000 q^{75} -207.915 q^{76} -169.000 q^{77} +257.339 q^{78} +269.236 q^{79} +191.647 q^{80} +81.0000 q^{81} +32.5981 q^{82} +869.721 q^{83} +29.0503 q^{84} -89.1395 q^{85} +935.739 q^{86} +87.0000 q^{87} -1054.95 q^{88} -9.85326 q^{89} -105.963 q^{90} -143.672 q^{91} -230.574 q^{92} +368.347 q^{93} +554.089 q^{94} -423.405 q^{95} +320.098 q^{96} -1524.47 q^{97} -771.043 q^{98} +385.656 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.35472	0.832520	0.416260	−	0.909246i	$-0.363341\pi$
$2$	2.35472	0.832520	0.416260	+	0.909246i	$0.363341\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−2.45528	−0.306910
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	7.06417	0.480656
$7$	−3.94392	−0.212952	−0.106476	−	0.994315i	$-0.533957\pi$
$7$	−3.94392	−0.212952	−0.106476	+	0.994315i	$0.533957\pi$
$8$	−24.6193	−1.08803
$9$	9.00000	0.333333
$10$	−11.7736	−0.372314
$11$	42.8507	1.17454	0.587271	−	0.809390i	$-0.300202\pi$
$11$	42.8507	1.17454	0.587271	+	0.809390i	$0.300202\pi$
$12$	−7.36583	−0.177194
$13$	36.4288	0.777194	0.388597	−	0.921408i	$-0.372960\pi$
$13$	36.4288	0.777194	0.388597	+	0.921408i	$0.372960\pi$
$14$	−9.28685	−0.177287
$15$	−15.0000	−0.258199
$16$	−38.3294	−0.598897
$17$	17.8279	0.254347	0.127174	−	0.991880i	$-0.459409\pi$
$17$	17.8279	0.254347	0.127174	+	0.991880i	$0.459409\pi$
$18$	21.1925	0.277507
$19$	84.6809	1.02248	0.511241	−	0.859438i	$-0.329186\pi$
$19$	84.6809	1.02248	0.511241	+	0.859438i	$0.329186\pi$
$20$	12.2764	0.137254
$21$	−11.8318	−0.122948
$22$	100.902	0.977831
$23$	93.9097	0.851371	0.425685	−	0.904871i	$-0.360033\pi$
$23$	93.9097	0.851371	0.425685	+	0.904871i	$0.360033\pi$
$24$	−73.8579	−0.628174
$25$	25.0000	0.200000
$26$	85.7797	0.647030
$27$	27.0000	0.192450
$28$	9.68343	0.0653570
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	−35.3208	−0.214956
$31$	122.782	0.711367	0.355683	−	0.934607i	$-0.384248\pi$
$31$	122.782	0.711367	0.355683	+	0.934607i	$0.384248\pi$
$32$	106.699	0.589435
$33$	128.552	0.678123
$34$	41.9798	0.211749
$35$	19.7196	0.0952350
$36$	−22.0975	−0.102303
$37$	−61.2323	−0.272069	−0.136034	−	0.990704i	$-0.543436\pi$
$37$	−61.2323	−0.272069	−0.136034	+	0.990704i	$0.543436\pi$
$38$	199.400	0.851236
$39$	109.286	0.448713
$40$	123.096	0.486581
$41$	13.8437	0.0527323	0.0263662	−	0.999652i	$-0.491606\pi$
$41$	13.8437	0.0527323	0.0263662	+	0.999652i	$0.491606\pi$
$42$	−27.8605	−0.102357
$43$	397.388	1.40933	0.704664	−	0.709541i	$-0.251098\pi$
$43$	397.388	1.40933	0.704664	+	0.709541i	$0.251098\pi$
$44$	−105.210	−0.360479
$45$	−45.0000	−0.149071
$46$	221.131	0.708783
$47$	235.310	0.730286	0.365143	−	0.930952i	$-0.381020\pi$
$47$	235.310	0.730286	0.365143	+	0.930952i	$0.381020\pi$
$48$	−114.988	−0.345773
$49$	−327.445	−0.954652
$50$	58.8681	0.166504
$51$	53.4837	0.146847
$52$	−89.4428	−0.238529
$53$	−50.4554	−0.130766	−0.0653829	−	0.997860i	$-0.520827\pi$
$53$	−50.4554	−0.130766	−0.0653829	+	0.997860i	$0.520827\pi$
$54$	63.5775	0.160219
$55$	−214.253	−0.525271
$56$	97.0966	0.231698
$57$	254.043	0.590330
$58$	68.2870	0.154595
$59$	−476.712	−1.05191	−0.525955	−	0.850513i	$-0.676292\pi$
$59$	−476.712	−1.05191	−0.525955	+	0.850513i	$0.676292\pi$
$60$	36.8292	0.0792438
$61$	−75.4071	−0.158277	−0.0791384	−	0.996864i	$-0.525217\pi$
$61$	−75.4071	−0.158277	−0.0791384	+	0.996864i	$0.525217\pi$
$62$	289.119	0.592227
$63$	−35.4953	−0.0709839
$64$	557.882	1.08961
$65$	−182.144	−0.347572
$66$	302.705	0.564551
$67$	−698.609	−1.27386	−0.636931	−	0.770921i	$-0.719796\pi$
$67$	−698.609	−1.27386	−0.636931	+	0.770921i	$0.719796\pi$
$68$	−43.7725	−0.0780616
$69$	281.729	0.491539
$70$	46.4342	0.0792850
$71$	44.6799	0.0746835	0.0373417	−	0.999303i	$-0.488111\pi$
$71$	44.6799	0.0746835	0.0373417	+	0.999303i	$0.488111\pi$
$72$	−221.574	−0.362676
$73$	669.611	1.07359	0.536795	−	0.843713i	$-0.319635\pi$
$73$	669.611	1.07359	0.536795	+	0.843713i	$0.319635\pi$
$74$	−144.185	−0.226503
$75$	75.0000	0.115470
$76$	−207.915	−0.313809
$77$	−169.000	−0.250121
$78$	257.339	0.373563
$79$	269.236	0.383435	0.191718	−	0.981450i	$-0.438594\pi$
$79$	269.236	0.383435	0.191718	+	0.981450i	$0.438594\pi$
$80$	191.647	0.267835
$81$	81.0000	0.111111
$82$	32.5981	0.0439007
$83$	869.721	1.15017	0.575086	−	0.818093i	$-0.304969\pi$
$83$	869.721	1.15017	0.575086	+	0.818093i	$0.304969\pi$
$84$	29.0503	0.0377339
$85$	−89.1395	−0.113747
$86$	935.739	1.17329
$87$	87.0000	0.107211
$88$	−1054.95	−1.27794
$89$	−9.85326	−0.0117353	−0.00586766	−	0.999983i	$-0.501868\pi$
$89$	−9.85326	−0.0117353	−0.00586766	+	0.999983i	$0.501868\pi$
$90$	−105.963	−0.124105
$91$	−143.672	−0.165505
$92$	−230.574	−0.261294
$93$	368.347	0.410708
$94$	554.089	0.607978
$95$	−423.405	−0.457267
$96$	320.098	0.340311
$97$	−1524.47	−1.59574	−0.797868	−	0.602832i	$-0.794039\pi$
$97$	−1524.47	−1.59574	−0.797868	+	0.602832i	$0.794039\pi$
$98$	−771.043	−0.794767
$99$	385.656	0.391514
$100$	−61.3820	−0.0613820
$101$	517.330	0.509666	0.254833	−	0.966985i	$-0.417980\pi$
$101$	517.330	0.509666	0.254833	+	0.966985i	$0.417980\pi$
$102$	125.939	0.122253
$103$	−1447.99	−1.38519	−0.692595	−	0.721327i	$-0.743533\pi$
$103$	−1447.99	−1.38519	−0.692595	+	0.721327i	$0.743533\pi$
$104$	−896.851	−0.845610
$105$	59.1588	0.0549839
$106$	−118.809	−0.108865
$107$	−332.747	−0.300634	−0.150317	−	0.988638i	$-0.548029\pi$
$107$	−332.747	−0.300634	−0.150317	+	0.988638i	$0.548029\pi$
$108$	−66.2925	−0.0590648
$109$	890.530	0.782544	0.391272	−	0.920275i	$-0.372035\pi$
$109$	890.530	0.782544	0.391272	+	0.920275i	$0.372035\pi$
$110$	−504.508	−0.437299
$111$	−183.697	−0.157079
$112$	151.168	0.127536
$113$	−936.802	−0.779884	−0.389942	−	0.920839i	$-0.627505\pi$
$113$	−936.802	−0.779884	−0.389942	+	0.920839i	$0.627505\pi$
$114$	598.201	0.491462
$115$	−469.548	−0.380745
$116$	−71.2031	−0.0569917
$117$	327.859	0.259065
$118$	−1122.53	−0.875736
$119$	−70.3119	−0.0541637
$120$	369.289	0.280928
$121$	505.182	0.379551
$122$	−177.563	−0.131769
$123$	41.5312	0.0304450
$124$	−301.465	−0.218325
$125$	−125.000	−0.0894427
$126$	−83.5816	−0.0590956
$127$	2450.72	1.71234	0.856168	−	0.516698i	$-0.172839\pi$
$127$	2450.72	1.71234	0.856168	+	0.516698i	$0.172839\pi$
$128$	460.065	0.317690
$129$	1192.16	0.813676
$130$	−428.898	−0.289361
$131$	546.681	0.364609	0.182304	−	0.983242i	$-0.441644\pi$
$131$	546.681	0.364609	0.182304	+	0.983242i	$0.441644\pi$
$132$	−315.631	−0.208122
$133$	−333.975	−0.217739
$134$	−1645.03	−1.06052
$135$	−135.000	−0.0860663
$136$	−438.910	−0.276737
$137$	−618.064	−0.385436	−0.192718	−	0.981254i	$-0.561730\pi$
$137$	−618.064	−0.385436	−0.192718	+	0.981254i	$0.561730\pi$
$138$	663.394	0.409216
$139$	1285.51	0.784428	0.392214	−	0.919874i	$-0.371709\pi$
$139$	1285.51	0.784428	0.392214	+	0.919874i	$0.371709\pi$
$140$	−48.4171	−0.0292285
$141$	705.929	0.421631
$142$	105.209	0.0621755
$143$	1561.00	0.912848
$144$	−344.964	−0.199632
$145$	−145.000	−0.0830455
$146$	1576.75	0.893786
$147$	−982.336	−0.551168
$148$	150.342	0.0835005
$149$	−125.043	−0.0687512	−0.0343756	−	0.999409i	$-0.510944\pi$
$149$	−125.043	−0.0687512	−0.0343756	+	0.999409i	$0.510944\pi$
$150$	176.604	0.0961312
$151$	1968.65	1.06097	0.530485	−	0.847694i	$-0.322010\pi$
$151$	1968.65	1.06097	0.530485	+	0.847694i	$0.322010\pi$
$152$	−2084.78	−1.11249
$153$	160.451	0.0847824
$154$	−397.948	−0.208231
$155$	−613.912	−0.318133
$156$	−268.328	−0.137715
$157$	1125.84	0.572304	0.286152	−	0.958184i	$-0.407624\pi$
$157$	1125.84	0.572304	0.286152	+	0.958184i	$0.407624\pi$
$158$	633.976	0.319218
$159$	−151.366	−0.0754977
$160$	−533.496	−0.263604
$161$	−370.373	−0.181301
$162$	190.733	0.0925023
$163$	1773.87	0.852394	0.426197	−	0.904630i	$-0.359853\pi$
$163$	1773.87	0.852394	0.426197	+	0.904630i	$0.359853\pi$
$164$	−33.9902	−0.0161841
$165$	−642.760	−0.303266
$166$	2047.95	0.957542
$167$	−1420.91	−0.658403	−0.329201	−	0.944260i	$-0.606779\pi$
$167$	−1420.91	−0.658403	−0.329201	+	0.944260i	$0.606779\pi$
$168$	291.290	0.133771
$169$	−869.944	−0.395969
$170$	−209.899	−0.0946971
$171$	762.129	0.340827
$172$	−975.698	−0.432536
$173$	−339.659	−0.149270	−0.0746352	−	0.997211i	$-0.523779\pi$
$173$	−339.659	−0.149270	−0.0746352	+	0.997211i	$0.523779\pi$
$174$	204.861	0.0892556
$175$	−98.5981	−0.0425904
$176$	−1642.44	−0.703430
$177$	−1430.14	−0.607320
$178$	−23.2017	−0.00976990
$179$	−2593.10	−1.08278	−0.541389	−	0.840772i	$-0.682101\pi$
$179$	−2593.10	−1.08278	−0.541389	+	0.840772i	$0.682101\pi$
$180$	110.488	0.0457514
$181$	−335.225	−0.137663	−0.0688317	−	0.997628i	$-0.521927\pi$
$181$	−335.225	−0.137663	−0.0688317	+	0.997628i	$0.521927\pi$
$182$	−338.309	−0.137786
$183$	−226.221	−0.0913812
$184$	−2311.99	−0.926316
$185$	306.162	0.121673
$186$	867.356	0.341923
$187$	763.938	0.298742
$188$	−577.750	−0.224132
$189$	−106.486	−0.0409826
$190$	−997.001	−0.380685
$191$	927.961	0.351544	0.175772	−	0.984431i	$-0.443758\pi$
$191$	927.961	0.351544	0.175772	+	0.984431i	$0.443758\pi$
$192$	1673.65	0.629089
$193$	2184.47	0.814725	0.407362	−	0.913267i	$-0.366449\pi$
$193$	2184.47	0.814725	0.407362	+	0.913267i	$0.366449\pi$
$194$	−3589.70	−1.32848
$195$	−546.432	−0.200671
$196$	803.970	0.292992
$197$	−3765.55	−1.36185	−0.680924	−	0.732354i	$-0.738422\pi$
$197$	−3765.55	−1.36185	−0.680924	+	0.732354i	$0.738422\pi$
$198$	908.114	0.325944
$199$	−60.0727	−0.0213992	−0.0106996	−	0.999943i	$-0.503406\pi$
$199$	−60.0727	−0.0213992	−0.0106996	+	0.999943i	$0.503406\pi$
$200$	−615.482	−0.217606
$201$	−2095.83	−0.735464
$202$	1218.17	0.424307
$203$	−114.374	−0.0395442
$204$	−131.317	−0.0450689
$205$	−69.2186	−0.0235826
$206$	−3409.61	−1.15320
$207$	845.187	0.283790
$208$	−1396.29	−0.465459
$209$	3628.64	1.20095
$210$	139.303	0.0457752
$211$	−2276.29	−0.742682	−0.371341	−	0.928497i	$-0.621102\pi$
$211$	−2276.29	−0.742682	−0.371341	+	0.928497i	$0.621102\pi$
$212$	123.882	0.0401333
$213$	134.040	0.0431185
$214$	−783.527	−0.250284
$215$	−1986.94	−0.630271
$216$	−664.721	−0.209391
$217$	−484.244	−0.151487
$218$	2096.95	0.651484
$219$	2008.83	0.619838
$220$	526.052	0.161211
$221$	649.449	0.197677
$222$	−432.556	−0.130771
$223$	3889.04	1.16784	0.583922	−	0.811809i	$-0.301517\pi$
$223$	3889.04	1.16784	0.583922	+	0.811809i	$0.301517\pi$
$224$	−420.813	−0.125521
$225$	225.000	0.0666667
$226$	−2205.91	−0.649269
$227$	−5689.80	−1.66363	−0.831817	−	0.555050i	$-0.812699\pi$
$227$	−5689.80	−1.66363	−0.831817	+	0.555050i	$0.812699\pi$
$228$	−623.746	−0.181178
$229$	−3253.91	−0.938972	−0.469486	−	0.882940i	$-0.655561\pi$
$229$	−3253.91	−0.938972	−0.469486	+	0.882940i	$0.655561\pi$
$230$	−1105.66	−0.316978
$231$	−507.000	−0.144407
$232$	−713.959	−0.202042
$233$	1363.72	0.383436	0.191718	−	0.981450i	$-0.438594\pi$
$233$	1363.72	0.383436	0.191718	+	0.981450i	$0.438594\pi$
$234$	772.017	0.215677
$235$	−1176.55	−0.326594
$236$	1170.46	0.322841
$237$	807.707	0.221376
$238$	−165.565	−0.0450924
$239$	−4788.65	−1.29603	−0.648017	−	0.761626i	$-0.724402\pi$
$239$	−4788.65	−1.29603	−0.648017	+	0.761626i	$0.724402\pi$
$240$	574.941	0.154634
$241$	−632.898	−0.169164	−0.0845820	−	0.996417i	$-0.526956\pi$
$241$	−632.898	−0.169164	−0.0845820	+	0.996417i	$0.526956\pi$
$242$	1189.56	0.315984
$243$	243.000	0.0641500
$244$	185.145	0.0485767
$245$	1637.23	0.426933
$246$	97.7944	0.0253461
$247$	3084.82	0.794667
$248$	−3022.81	−0.773988
$249$	2609.16	0.664052
$250$	−294.340	−0.0744629
$251$	−7413.17	−1.86420	−0.932101	−	0.362198i	$-0.882027\pi$
$251$	−7413.17	−1.86420	−0.932101	+	0.362198i	$0.882027\pi$
$252$	87.1509	0.0217857
$253$	4024.10	0.999971
$254$	5770.78	1.42555
$255$	−267.418	−0.0656721
$256$	−3379.73	−0.825130
$257$	−3920.20	−0.951500	−0.475750	−	0.879581i	$-0.657823\pi$
$257$	−3920.20	−0.951500	−0.475750	+	0.879581i	$0.657823\pi$
$258$	2807.22	0.677402
$259$	241.496	0.0579375
$260$	447.214	0.106673
$261$	261.000	0.0618984
$262$	1287.28	0.303544
$263$	2505.55	0.587448	0.293724	−	0.955890i	$-0.405105\pi$
$263$	2505.55	0.587448	0.293724	+	0.955890i	$0.405105\pi$
$264$	−3164.86	−0.737817
$265$	252.277	0.0584802
$266$	−786.419	−0.181272
$267$	−29.5598	−0.00677539
$268$	1715.28	0.390960
$269$	−3707.17	−0.840261	−0.420131	−	0.907464i	$-0.638016\pi$
$269$	−3707.17	−0.840261	−0.420131	+	0.907464i	$0.638016\pi$
$270$	−317.888	−0.0716519
$271$	4768.39	1.06885	0.534426	−	0.845215i	$-0.320528\pi$
$271$	4768.39	1.06885	0.534426	+	0.845215i	$0.320528\pi$
$272$	−683.332	−0.152328
$273$	−431.017	−0.0955543
$274$	−1455.37	−0.320883
$275$	1071.27	0.234909
$276$	−691.723	−0.150858
$277$	2908.10	0.630798	0.315399	−	0.948959i	$-0.397862\pi$
$277$	2908.10	0.630798	0.315399	+	0.948959i	$0.397862\pi$
$278$	3027.02	0.653053
$279$	1105.04	0.237122
$280$	−485.483	−0.103618
$281$	495.963	0.105291	0.0526454	−	0.998613i	$-0.483235\pi$
$281$	495.963	0.105291	0.0526454	+	0.998613i	$0.483235\pi$
$282$	1662.27	0.351016
$283$	7296.12	1.53254	0.766271	−	0.642517i	$-0.222110\pi$
$283$	7296.12	1.53254	0.766271	+	0.642517i	$0.222110\pi$
$284$	−109.702	−0.0229211
$285$	−1270.21	−0.264003
$286$	3675.72	0.759964
$287$	−54.5986	−0.0112294
$288$	960.293	0.196478
$289$	−4595.17	−0.935308
$290$	−341.435	−0.0691371
$291$	−4573.41	−0.921299
$292$	−1644.08	−0.329495
$293$	853.949	0.170267	0.0851335	−	0.996370i	$-0.472868\pi$
$293$	853.949	0.170267	0.0851335	+	0.996370i	$0.472868\pi$
$294$	−2313.13	−0.458859
$295$	2383.56	0.470428
$296$	1507.50	0.296018
$297$	1156.97	0.226041
$298$	−294.442	−0.0572368
$299$	3421.02	0.661680
$300$	−184.146	−0.0354389
$301$	−1567.27	−0.300119
$302$	4635.63	0.883280
$303$	1551.99	0.294256
$304$	−3245.77	−0.612361
$305$	377.035	0.0707836
$306$	377.818	0.0705831
$307$	−694.287	−0.129072	−0.0645359	−	0.997915i	$-0.520557\pi$
$307$	−694.287	−0.129072	−0.0645359	+	0.997915i	$0.520557\pi$
$308$	414.942	0.0767646
$309$	−4343.96	−0.799740
$310$	−1445.59	−0.264852
$311$	2587.58	0.471794	0.235897	−	0.971778i	$-0.424197\pi$
$311$	2587.58	0.471794	0.235897	+	0.971778i	$0.424197\pi$
$312$	−2690.55	−0.488213
$313$	−3467.68	−0.626214	−0.313107	−	0.949718i	$-0.601370\pi$
$313$	−3467.68	−0.626214	−0.313107	+	0.949718i	$0.601370\pi$
$314$	2651.04	0.476455
$315$	177.477	0.0317450
$316$	−661.048	−0.117680
$317$	−5158.66	−0.914003	−0.457001	−	0.889466i	$-0.651077\pi$
$317$	−5158.66	−0.914003	−0.457001	+	0.889466i	$0.651077\pi$
$318$	−356.426	−0.0628533
$319$	1242.67	0.218107
$320$	−2789.41	−0.487290
$321$	−998.241	−0.173571
$322$	−872.125	−0.150937
$323$	1509.68	0.260065
$324$	−198.878	−0.0341011
$325$	910.720	0.155439
$326$	4176.97	0.709635
$327$	2671.59	0.451802
$328$	−340.822	−0.0573743
$329$	−928.043	−0.155516
$330$	−1513.52	−0.252475
$331$	11056.9	1.83609	0.918043	−	0.396480i	$-0.129768\pi$
$331$	11056.9	1.83609	0.918043	+	0.396480i	$0.129768\pi$
$332$	−2135.41	−0.352999
$333$	−551.091	−0.0906895
$334$	−3345.85	−0.548134
$335$	3493.05	0.569688
$336$	453.504	0.0736330
$337$	6128.18	0.990574	0.495287	−	0.868729i	$-0.335063\pi$
$337$	6128.18	0.990574	0.495287	+	0.868729i	$0.335063\pi$
$338$	−2048.48	−0.329652
$339$	−2810.41	−0.450266
$340$	218.862	0.0349102
$341$	5261.31	0.835531
$342$	1794.60	0.283745
$343$	2644.19	0.416247
$344$	−9783.41	−1.53339
$345$	−1408.65	−0.219823
$346$	−799.803	−0.124271
$347$	−9277.85	−1.43533	−0.717667	−	0.696386i	$-0.754790\pi$
$347$	−9277.85	−1.43533	−0.717667	+	0.696386i	$0.754790\pi$
$348$	−213.609	−0.0329042
$349$	4375.41	0.671090	0.335545	−	0.942024i	$-0.391079\pi$
$349$	4375.41	0.671090	0.335545	+	0.942024i	$0.391079\pi$
$350$	−232.171	−0.0354573
$351$	983.577	0.149571
$352$	4572.13	0.692317
$353$	−3256.89	−0.491067	−0.245534	−	0.969388i	$-0.578963\pi$
$353$	−3256.89	−0.491067	−0.245534	+	0.969388i	$0.578963\pi$
$354$	−3367.58	−0.505606
$355$	−223.399	−0.0333995
$356$	24.1925	0.00360169
$357$	−210.936	−0.0312714
$358$	−6106.03	−0.901435
$359$	−6219.24	−0.914315	−0.457158	−	0.889386i	$-0.651132\pi$
$359$	−6219.24	−0.914315	−0.457158	+	0.889386i	$0.651132\pi$
$360$	1107.87	0.162194
$361$	311.863	0.0454677
$362$	−789.362	−0.114608
$363$	1515.55	0.219134
$364$	352.755	0.0507951
$365$	−3348.06	−0.480124
$366$	−532.688	−0.0760767
$367$	10388.3	1.47756	0.738780	−	0.673947i	$-0.235402\pi$
$367$	10388.3	1.47756	0.738780	+	0.673947i	$0.235402\pi$
$368$	−3599.50	−0.509883
$369$	124.593	0.0175774
$370$	720.926	0.101295
$371$	198.992	0.0278468
$372$	−904.395	−0.126050
$373$	13200.4	1.83241	0.916204	−	0.400712i	$-0.131237\pi$
$373$	13200.4	1.83241	0.916204	+	0.400712i	$0.131237\pi$
$374$	1798.86	0.248708
$375$	−375.000	−0.0516398
$376$	−5793.15	−0.794572
$377$	1056.43	0.144321
$378$	−250.745	−0.0341189
$379$	−5927.59	−0.803376	−0.401688	−	0.915777i	$-0.631576\pi$
$379$	−5927.59	−0.803376	−0.401688	+	0.915777i	$0.631576\pi$
$380$	1039.58	0.140340
$381$	7352.17	0.988617
$382$	2185.09	0.292667
$383$	7463.33	0.995713	0.497857	−	0.867259i	$-0.334121\pi$
$383$	7463.33	0.995713	0.497857	+	0.867259i	$0.334121\pi$
$384$	1380.19	0.183419
$385$	844.999	0.111858
$386$	5143.83	0.678275
$387$	3576.49	0.469776
$388$	3743.00	0.489747
$389$	−409.685	−0.0533981	−0.0266991	−	0.999644i	$-0.508500\pi$
$389$	−409.685	−0.0533981	−0.0266991	+	0.999644i	$0.508500\pi$
$390$	−1286.70	−0.167062
$391$	1674.21	0.216544
$392$	8061.47	1.03869
$393$	1640.04	0.210507
$394$	−8866.82	−1.13377
$395$	−1346.18	−0.171477
$396$	−946.893	−0.120160
$397$	1112.31	0.140618	0.0703091	−	0.997525i	$-0.477601\pi$
$397$	1112.31	0.140618	0.0703091	+	0.997525i	$0.477601\pi$
$398$	−141.455	−0.0178153
$399$	−1001.93	−0.125712
$400$	−958.235	−0.119779
$401$	14999.2	1.86789	0.933947	−	0.357411i	$-0.116340\pi$
$401$	14999.2	1.86789	0.933947	+	0.357411i	$0.116340\pi$
$402$	−4935.09	−0.612289
$403$	4472.81	0.552870
$404$	−1270.19	−0.156421
$405$	−405.000	−0.0496904
$406$	−269.319	−0.0329213
$407$	−2623.85	−0.319556
$408$	−1316.73	−0.159774
$409$	7595.21	0.918238	0.459119	−	0.888375i	$-0.348165\pi$
$409$	7595.21	0.918238	0.459119	+	0.888375i	$0.348165\pi$
$410$	−162.991	−0.0196330
$411$	−1854.19	−0.222532
$412$	3555.21	0.425128
$413$	1880.12	0.224006
$414$	1990.18	0.236261
$415$	−4348.61	−0.514373
$416$	3886.92	0.458106
$417$	3856.53	0.452890
$418$	8544.44	0.999814
$419$	−6501.56	−0.758047	−0.379024	−	0.925387i	$-0.623740\pi$
$419$	−6501.56	−0.758047	−0.379024	+	0.925387i	$0.623740\pi$
$420$	−145.251	−0.0168751
$421$	−4381.60	−0.507235	−0.253617	−	0.967305i	$-0.581620\pi$
$421$	−4381.60	−0.507235	−0.253617	+	0.967305i	$0.581620\pi$
$422$	−5360.02	−0.618298
$423$	2117.79	0.243429
$424$	1242.18	0.142277
$425$	445.697	0.0508694
$426$	315.626	0.0358971
$427$	297.400	0.0337053
$428$	816.986	0.0922676
$429$	4683.00	0.527033
$430$	−4678.69	−0.524713
$431$	−698.269	−0.0780382	−0.0390191	−	0.999238i	$-0.512423\pi$
$431$	−698.269	−0.0780382	−0.0390191	+	0.999238i	$0.512423\pi$
$432$	−1034.89	−0.115258
$433$	−6899.14	−0.765707	−0.382854	−	0.923809i	$-0.625059\pi$
$433$	−6899.14	−0.765707	−0.382854	+	0.923809i	$0.625059\pi$
$434$	−1140.26	−0.126116
$435$	−435.000	−0.0479463
$436$	−2186.50	−0.240170
$437$	7952.36	0.870510
$438$	4730.25	0.516027
$439$	−12502.8	−1.35929	−0.679644	−	0.733542i	$-0.737866\pi$
$439$	−12502.8	−1.35929	−0.679644	+	0.733542i	$0.737866\pi$
$440$	5274.77	0.571511
$441$	−2947.01	−0.318217
$442$	1529.27	0.164570
$443$	7684.41	0.824148	0.412074	−	0.911150i	$-0.364805\pi$
$443$	7684.41	0.824148	0.412074	+	0.911150i	$0.364805\pi$
$444$	451.027	0.0482090
$445$	49.2663	0.00524820
$446$	9157.61	0.972255
$447$	−375.129	−0.0396935
$448$	−2200.24	−0.232035
$449$	6931.63	0.728561	0.364280	−	0.931289i	$-0.381315\pi$
$449$	6931.63	0.728561	0.364280	+	0.931289i	$0.381315\pi$
$450$	529.813	0.0555014
$451$	593.213	0.0619364
$452$	2300.11	0.239354
$453$	5905.95	0.612552
$454$	−13397.9	−1.38501
$455$	718.362	0.0740161
$456$	−6254.35	−0.642296
$457$	−669.132	−0.0684916	−0.0342458	−	0.999413i	$-0.510903\pi$
$457$	−669.132	−0.0684916	−0.0342458	+	0.999413i	$0.510903\pi$
$458$	−7662.06	−0.781713
$459$	481.353	0.0489491
$460$	1152.87	0.116854
$461$	1369.33	0.138343	0.0691715	−	0.997605i	$-0.477964\pi$
$461$	1369.33	0.138343	0.0691715	+	0.997605i	$0.477964\pi$
$462$	−1193.84	−0.120222
$463$	−8213.65	−0.824451	−0.412225	−	0.911082i	$-0.635248\pi$
$463$	−8213.65	−0.824451	−0.412225	+	0.911082i	$0.635248\pi$
$464$	−1111.55	−0.111212
$465$	−1841.74	−0.183674
$466$	3211.19	0.319218
$467$	19762.1	1.95821	0.979103	−	0.203366i	$-0.0651880\pi$
$467$	19762.1	1.95821	0.979103	+	0.203366i	$0.0651880\pi$
$468$	−804.985	−0.0795095
$469$	2755.26	0.271271
$470$	−2770.44	−0.271896
$471$	3377.52	0.330420
$472$	11736.3	1.14451
$473$	17028.3	1.65532
$474$	1901.93	0.184300
$475$	2117.02	0.204496
$476$	172.635	0.0166234
$477$	−454.099	−0.0435886
$478$	−11276.0	−1.07898
$479$	1437.29	0.137101	0.0685506	−	0.997648i	$-0.478163\pi$
$479$	1437.29	0.137101	0.0685506	+	0.997648i	$0.478163\pi$
$480$	−1600.49	−0.152192
$481$	−2230.62	−0.211450
$482$	−1490.30	−0.140833
$483$	−1111.12	−0.104674
$484$	−1240.36	−0.116488
$485$	7622.35	0.713635
$486$	572.198	0.0534062
$487$	12731.4	1.18463	0.592313	−	0.805708i	$-0.298215\pi$
$487$	12731.4	1.18463	0.592313	+	0.805708i	$0.298215\pi$
$488$	1856.47	0.172210
$489$	5321.61	0.492130
$490$	3855.22	0.355431
$491$	−15590.5	−1.43298	−0.716488	−	0.697600i	$-0.754251\pi$
$491$	−15590.5	−1.43298	−0.716488	+	0.697600i	$0.754251\pi$
$492$	−101.971	−0.00934387
$493$	517.009	0.0472311
$494$	7263.91	0.661576
$495$	−1928.28	−0.175090
$496$	−4706.17	−0.426035
$497$	−176.214	−0.0159040
$498$	6143.86	0.552837
$499$	−7309.53	−0.655750	−0.327875	−	0.944721i	$-0.606333\pi$
$499$	−7309.53	−0.655750	−0.327875	+	0.944721i	$0.606333\pi$
$500$	306.910	0.0274508
$501$	−4262.73	−0.380129
$502$	−17456.0	−1.55199
$503$	11671.8	1.03463	0.517315	−	0.855795i	$-0.326932\pi$
$503$	11671.8	1.03463	0.517315	+	0.855795i	$0.326932\pi$
$504$	873.869	0.0772326
$505$	−2586.65	−0.227930
$506$	9475.63	0.832496
$507$	−2609.83	−0.228613
$508$	−6017.21	−0.525532
$509$	−9056.40	−0.788640	−0.394320	−	0.918973i	$-0.629020\pi$
$509$	−9056.40	−0.788640	−0.394320	+	0.918973i	$0.629020\pi$
$510$	−629.697	−0.0546734
$511$	−2640.90	−0.228623
$512$	−11638.9	−1.00463
$513$	2286.39	0.196777
$514$	−9230.99	−0.792143
$515$	7239.94	0.619476
$516$	−2927.09	−0.249725
$517$	10083.2	0.857752
$518$	568.655	0.0482341
$519$	−1018.98	−0.0861813
$520$	4484.25	0.378168
$521$	−13061.2	−1.09831	−0.549156	−	0.835720i	$-0.685051\pi$
$521$	−13061.2	−1.09831	−0.549156	+	0.835720i	$0.685051\pi$
$522$	614.583	0.0515317
$523$	−12711.3	−1.06277	−0.531383	−	0.847132i	$-0.678328\pi$
$523$	−12711.3	−1.06277	−0.531383	+	0.847132i	$0.678328\pi$
$524$	−1342.25	−0.111902
$525$	−295.794	−0.0245896
$526$	5899.88	0.489063
$527$	2188.95	0.180934
$528$	−4927.32	−0.406125
$529$	−3347.97	−0.275168
$530$	594.043	0.0486860
$531$	−4290.41	−0.350636
$532$	820.002	0.0668263
$533$	504.310	0.0409833
$534$	−69.6051	−0.00564065
$535$	1663.73	0.134448
$536$	17199.3	1.38600
$537$	−7779.30	−0.625143
$538$	−8729.36	−0.699535
$539$	−14031.3	−1.12128
$540$	331.463	0.0264146
$541$	−16338.9	−1.29845	−0.649227	−	0.760595i	$-0.724908\pi$
$541$	−16338.9	−1.29845	−0.649227	+	0.760595i	$0.724908\pi$
$542$	11228.2	0.889841
$543$	−1005.67	−0.0794800
$544$	1902.22	0.149921
$545$	−4452.65	−0.349964
$546$	−1014.93	−0.0795509
$547$	−9583.07	−0.749072	−0.374536	−	0.927212i	$-0.622198\pi$
$547$	−9583.07	−0.749072	−0.374536	+	0.927212i	$0.622198\pi$
$548$	1517.52	0.118294
$549$	−678.664	−0.0527589
$550$	2522.54	0.195566
$551$	2455.75	0.189870
$552$	−6935.97	−0.534809
$553$	−1061.84	−0.0816532
$554$	6847.78	0.525152
$555$	918.485	0.0702478
$556$	−3156.28	−0.240749
$557$	−1288.54	−0.0980198	−0.0490099	−	0.998798i	$-0.515607\pi$
$557$	−1288.54	−0.0980198	−0.0490099	+	0.998798i	$0.515607\pi$
$558$	2602.07	0.197409
$559$	14476.4	1.09532
$560$	−755.841	−0.0570359
$561$	2291.81	0.172479
$562$	1167.86	0.0876567
$563$	−13901.3	−1.04062	−0.520312	−	0.853976i	$-0.674184\pi$
$563$	−13901.3	−1.04062	−0.520312	+	0.853976i	$0.674184\pi$
$564$	−1733.25	−0.129403
$565$	4684.01	0.348775
$566$	17180.4	1.27587
$567$	−319.458	−0.0236613
$568$	−1099.99	−0.0812578
$569$	12631.6	0.930654	0.465327	−	0.885139i	$-0.345937\pi$
$569$	12631.6	0.930654	0.465327	+	0.885139i	$0.345937\pi$
$570$	−2991.00	−0.219788
$571$	836.256	0.0612894	0.0306447	−	0.999530i	$-0.490244\pi$
$571$	836.256	0.0612894	0.0306447	+	0.999530i	$0.490244\pi$
$572$	−3832.69	−0.280162
$573$	2783.88	0.202964
$574$	−128.564	−0.00934874
$575$	2347.74	0.170274
$576$	5020.94	0.363205
$577$	55.7407	0.00402169	0.00201085	−	0.999998i	$-0.499360\pi$
$577$	55.7407	0.00402169	0.00201085	+	0.999998i	$0.499360\pi$
$578$	−10820.3	−0.778663
$579$	6553.42	0.470382
$580$	356.015	0.0254875
$581$	−3430.11	−0.244931
$582$	−10769.1	−0.767000
$583$	−2162.05	−0.153590
$584$	−16485.4	−1.16810
$585$	−1639.30	−0.115857
$586$	2010.81	0.141751
$587$	−24044.3	−1.69065	−0.845327	−	0.534250i	$-0.820594\pi$
$587$	−24044.3	−1.69065	−0.845327	+	0.534250i	$0.820594\pi$
$588$	2411.91	0.169159
$589$	10397.3	0.727359
$590$	5612.63	0.391641
$591$	−11296.6	−0.786264
$592$	2347.00	0.162941
$593$	−15066.0	−1.04332	−0.521659	−	0.853154i	$-0.674687\pi$
$593$	−15066.0	−1.04332	−0.521659	+	0.853154i	$0.674687\pi$
$594$	2724.34	0.188184
$595$	351.559	0.0242227
$596$	307.016	0.0211004
$597$	−180.218	−0.0123548
$598$	8055.55	0.550862
$599$	8354.77	0.569894	0.284947	−	0.958543i	$-0.408024\pi$
$599$	8354.77	0.569894	0.284947	+	0.958543i	$0.408024\pi$
$600$	−1846.45	−0.125635
$601$	5059.15	0.343372	0.171686	−	0.985152i	$-0.445078\pi$
$601$	5059.15	0.343372	0.171686	+	0.985152i	$0.445078\pi$
$602$	−3690.48	−0.249855
$603$	−6287.48	−0.424620
$604$	−4833.59	−0.325622
$605$	−2525.91	−0.169740
$606$	3654.51	0.244974
$607$	15350.8	1.02647	0.513236	−	0.858248i	$-0.328447\pi$
$607$	15350.8	1.02647	0.513236	+	0.858248i	$0.328447\pi$
$608$	9035.39	0.602687
$609$	−343.121	−0.0228308
$610$	887.814	0.0589288
$611$	8572.04	0.567574
$612$	−393.952	−0.0260205
$613$	−17964.0	−1.18362	−0.591811	−	0.806077i	$-0.701587\pi$
$613$	−17964.0	−1.18362	−0.591811	+	0.806077i	$0.701587\pi$
$614$	−1634.85	−0.107455
$615$	−207.656	−0.0136154
$616$	4160.66	0.272139
$617$	14791.0	0.965093	0.482546	−	0.875870i	$-0.339712\pi$
$617$	14791.0	0.965093	0.482546	+	0.875870i	$0.339712\pi$
$618$	−10228.8	−0.665799
$619$	−12870.4	−0.835708	−0.417854	−	0.908514i	$-0.637218\pi$
$619$	−12870.4	−0.835708	−0.417854	+	0.908514i	$0.637218\pi$
$620$	1507.32	0.0976381
$621$	2535.56	0.163846
$622$	6093.03	0.392779
$623$	38.8605	0.00249906
$624$	−4188.88	−0.268733
$625$	625.000	0.0400000
$626$	−8165.43	−0.521336
$627$	10885.9	0.693368
$628$	−2764.25	−0.175646
$629$	−1091.64	−0.0691998
$630$	417.908	0.0264283
$631$	−16299.2	−1.02831	−0.514154	−	0.857698i	$-0.671894\pi$
$631$	−16299.2	−1.02831	−0.514154	+	0.857698i	$0.671894\pi$
$632$	−6628.39	−0.417189
$633$	−6828.86	−0.428788
$634$	−12147.2	−0.760926
$635$	−12253.6	−0.765780
$636$	371.646	0.0231710
$637$	−11928.4	−0.741950
$638$	2926.14	0.181579
$639$	402.119	0.0248945
$640$	−2300.32	−0.142075
$641$	−9154.93	−0.564115	−0.282058	−	0.959397i	$-0.591017\pi$
$641$	−9154.93	−0.564115	−0.282058	+	0.959397i	$0.591017\pi$
$642$	−2350.58	−0.144502
$643$	7509.43	0.460564	0.230282	−	0.973124i	$-0.426035\pi$
$643$	7509.43	0.460564	0.230282	+	0.973124i	$0.426035\pi$
$644$	909.368	0.0556430
$645$	−5960.82	−0.363887
$646$	3554.89	0.216510
$647$	−19945.4	−1.21195	−0.605977	−	0.795482i	$-0.707218\pi$
$647$	−19945.4	−1.21195	−0.605977	+	0.795482i	$0.707218\pi$
$648$	−1994.16	−0.120892
$649$	−20427.5	−1.23551
$650$	2144.49	0.129406
$651$	−1452.73	−0.0874610
$652$	−4355.34	−0.261608
$653$	−8028.91	−0.481157	−0.240579	−	0.970630i	$-0.577337\pi$
$653$	−8028.91	−0.481157	−0.240579	+	0.970630i	$0.577337\pi$
$654$	6290.86	0.376134
$655$	−2733.40	−0.163058
$656$	−530.621	−0.0315812
$657$	6026.50	0.357863
$658$	−2185.28	−0.129470
$659$	−2943.00	−0.173965	−0.0869827	−	0.996210i	$-0.527722\pi$
$659$	−2943.00	−0.173965	−0.0869827	+	0.996210i	$0.527722\pi$
$660$	1578.16	0.0930752
$661$	−30286.3	−1.78215	−0.891073	−	0.453859i	$-0.850047\pi$
$661$	−30286.3	−1.78215	−0.891073	+	0.453859i	$0.850047\pi$
$662$	26036.0	1.52858
$663$	1948.35	0.114129
$664$	−21411.9	−1.25142
$665$	1669.88	0.0973759
$666$	−1297.67	−0.0755009
$667$	2723.38	0.158096
$668$	3488.73	0.202070
$669$	11667.1	0.674256
$670$	8225.16	0.474277
$671$	−3231.25	−0.185903
$672$	−1262.44	−0.0724698
$673$	2201.07	0.126070	0.0630348	−	0.998011i	$-0.479922\pi$
$673$	2201.07	0.126070	0.0630348	+	0.998011i	$0.479922\pi$
$674$	14430.2	0.824673
$675$	675.000	0.0384900
$676$	2135.95	0.121527
$677$	22392.9	1.27124	0.635619	−	0.772003i	$-0.280745\pi$
$677$	22392.9	1.27124	0.635619	+	0.772003i	$0.280745\pi$
$678$	−6617.73	−0.374856
$679$	6012.39	0.339815
$680$	2194.55	0.123761
$681$	−17069.4	−0.960500
$682$	12388.9	0.695596
$683$	−31770.8	−1.77991	−0.889953	−	0.456053i	$-0.849263\pi$
$683$	−31770.8	−1.77991	−0.889953	+	0.456053i	$0.849263\pi$
$684$	−1871.24	−0.104603
$685$	3090.32	0.172372
$686$	6226.33	0.346534
$687$	−9761.73	−0.542115
$688$	−15231.6	−0.844042
$689$	−1838.03	−0.101630
$690$	−3316.97	−0.183007
$691$	−19995.8	−1.10084	−0.550418	−	0.834889i	$-0.685532\pi$
$691$	−19995.8	−1.10084	−0.550418	+	0.834889i	$0.685532\pi$
$692$	833.957	0.0458126
$693$	−1521.00	−0.0833737
$694$	−21846.8	−1.19495
$695$	−6427.55	−0.350807
$696$	−2141.88	−0.116649
$697$	246.804	0.0134123
$698$	10302.9	0.558696
$699$	4091.17	0.221377
$700$	242.086	0.0130714
$701$	5940.97	0.320096	0.160048	−	0.987109i	$-0.448835\pi$
$701$	5940.97	0.320096	0.160048	+	0.987109i	$0.448835\pi$
$702$	2316.05	0.124521
$703$	−5185.21	−0.278185
$704$	23905.6	1.27980
$705$	−3529.64	−0.188559
$706$	−7669.08	−0.408824
$707$	−2040.31	−0.108534
$708$	3511.38	0.186393
$709$	−17955.3	−0.951094	−0.475547	−	0.879690i	$-0.657750\pi$
$709$	−17955.3	−0.951094	−0.475547	+	0.879690i	$0.657750\pi$
$710$	−526.044	−0.0278057
$711$	2423.12	0.127812
$712$	242.580	0.0127684
$713$	11530.5	0.605637
$714$	−496.695	−0.0260341
$715$	−7804.99	−0.408238
$716$	6366.78	0.332315
$717$	−14366.0	−0.748266
$718$	−14644.6	−0.761186
$719$	−22809.5	−1.18310	−0.591551	−	0.806268i	$-0.701484\pi$
$719$	−22809.5	−1.18310	−0.591551	+	0.806268i	$0.701484\pi$
$720$	1724.82	0.0892782
$721$	5710.75	0.294979
$722$	734.351	0.0378528
$723$	−1898.69	−0.0976669
$724$	823.070	0.0422502
$725$	725.000	0.0371391
$726$	3568.69	0.182433
$727$	−28267.1	−1.44205	−0.721023	−	0.692911i	$-0.756328\pi$
$727$	−28267.1	−1.44205	−0.721023	+	0.692911i	$0.756328\pi$
$728$	3537.11	0.180074
$729$	729.000	0.0370370
$730$	−7883.75	−0.399713
$731$	7084.59	0.358458
$732$	555.436	0.0280458
$733$	18679.6	0.941264	0.470632	−	0.882330i	$-0.344026\pi$
$733$	18679.6	0.941264	0.470632	+	0.882330i	$0.344026\pi$
$734$	24461.6	1.23010
$735$	4911.68	0.246490
$736$	10020.1	0.501828
$737$	−29935.9	−1.49620
$738$	293.383	0.0146336
$739$	−8577.65	−0.426974	−0.213487	−	0.976946i	$-0.568482\pi$
$739$	−8577.65	−0.426974	−0.213487	+	0.976946i	$0.568482\pi$
$740$	−751.712	−0.0373426
$741$	9254.47	0.458801
$742$	468.572	0.0231830
$743$	12442.0	0.614337	0.307169	−	0.951655i	$-0.400618\pi$
$743$	12442.0	0.614337	0.307169	+	0.951655i	$0.400618\pi$
$744$	−9068.44	−0.446862
$745$	625.216	0.0307465
$746$	31083.2	1.52552
$747$	7827.49	0.383391
$748$	−1875.68	−0.0916867
$749$	1312.33	0.0640206
$750$	−883.021	−0.0429912
$751$	−28327.2	−1.37640	−0.688198	−	0.725523i	$-0.741598\pi$
$751$	−28327.2	−1.37640	−0.688198	+	0.725523i	$0.741598\pi$
$752$	−9019.27	−0.437366
$753$	−22239.5	−1.07630
$754$	2487.61	0.120150
$755$	−9843.26	−0.474480
$756$	261.453	0.0125780
$757$	28073.3	1.34787	0.673937	−	0.738789i	$-0.264602\pi$
$757$	28073.3	1.34787	0.673937	+	0.738789i	$0.264602\pi$
$758$	−13957.8	−0.668827
$759$	12072.3	0.577334
$760$	10423.9	0.497520
$761$	−12715.7	−0.605708	−0.302854	−	0.953037i	$-0.597939\pi$
$761$	−12715.7	−0.605708	−0.302854	+	0.953037i	$0.597939\pi$
$762$	17312.3	0.823044
$763$	−3512.18	−0.166644
$764$	−2278.40	−0.107892
$765$	−802.255	−0.0379158
$766$	17574.1	0.828952
$767$	−17366.0	−0.817538
$768$	−10139.2	−0.476389
$769$	−2730.97	−0.128064	−0.0640320	−	0.997948i	$-0.520396\pi$
$769$	−2730.97	−0.128064	−0.0640320	+	0.997948i	$0.520396\pi$
$770$	1989.74	0.0931237
$771$	−11760.6	−0.549349
$772$	−5363.49	−0.250047
$773$	21816.6	1.01512	0.507561	−	0.861616i	$-0.330547\pi$
$773$	21816.6	1.01512	0.507561	+	0.861616i	$0.330547\pi$
$774$	8421.65	0.391098
$775$	3069.56	0.142273
$776$	37531.3	1.73621
$777$	724.487	0.0334502
$778$	−964.696	−0.0444550
$779$	1172.30	0.0539178
$780$	1341.64	0.0615878
$781$	1914.56	0.0877189
$782$	3942.31	0.180277
$783$	783.000	0.0357371
$784$	12550.8	0.571738
$785$	−5629.20	−0.255942
$786$	3861.85	0.175251
$787$	16740.5	0.758239	0.379119	−	0.925348i	$-0.376227\pi$
$787$	16740.5	0.758239	0.379119	+	0.925348i	$0.376227\pi$
$788$	9245.47	0.417965
$789$	7516.65	0.339163
$790$	−3169.88	−0.142758
$791$	3694.67	0.166078
$792$	−9494.58	−0.425979
$793$	−2746.99	−0.123012
$794$	2619.19	0.117068
$795$	756.831	0.0337636
$796$	147.495	0.00656762
$797$	3731.13	0.165826	0.0829131	−	0.996557i	$-0.473578\pi$
$797$	3731.13	0.165826	0.0829131	+	0.996557i	$0.473578\pi$
$798$	−2359.26	−0.104658
$799$	4195.07	0.185746
$800$	2667.48	0.117887
$801$	−88.6794	−0.00391177
$802$	35319.0	1.55506
$803$	28693.3	1.26098
$804$	5145.84	0.225721
$805$	1851.86	0.0810802
$806$	10532.2	0.460276
$807$	−11121.5	−0.485125
$808$	−12736.3	−0.554531
$809$	−1318.79	−0.0573129	−0.0286564	−	0.999589i	$-0.509123\pi$
$809$	−1318.79	−0.0573129	−0.0286564	+	0.999589i	$0.509123\pi$
$810$	−953.663	−0.0413683
$811$	−6890.79	−0.298358	−0.149179	−	0.988810i	$-0.547663\pi$
$811$	−6890.79	−0.298358	−0.149179	+	0.988810i	$0.547663\pi$
$812$	280.819	0.0121365
$813$	14305.2	0.617102
$814$	−6178.44	−0.266037
$815$	−8869.35	−0.381202
$816$	−2050.00	−0.0879464
$817$	33651.2	1.44101
$818$	17884.6	0.764452
$819$	−1293.05	−0.0551683
$820$	169.951	0.00723773
$821$	25055.7	1.06510	0.532552	−	0.846397i	$-0.321233\pi$
$821$	25055.7	1.06510	0.532552	+	0.846397i	$0.321233\pi$
$822$	−4366.11	−0.185262
$823$	−28476.2	−1.20610	−0.603049	−	0.797704i	$-0.706048\pi$
$823$	−28476.2	−1.20610	−0.603049	+	0.797704i	$0.706048\pi$
$824$	35648.4	1.50713
$825$	3213.80	0.135625
$826$	4427.15	0.186490
$827$	−6404.82	−0.269308	−0.134654	−	0.990893i	$-0.542992\pi$
$827$	−6404.82	−0.269308	−0.134654	+	0.990893i	$0.542992\pi$
$828$	−2075.17	−0.0870980
$829$	42500.5	1.78058	0.890292	−	0.455390i	$-0.150500\pi$
$829$	42500.5	1.78058	0.890292	+	0.455390i	$0.150500\pi$
$830$	−10239.8	−0.428226
$831$	8724.31	0.364191
$832$	20323.0	0.846841
$833$	−5837.66	−0.242813
$834$	9081.06	0.377040
$835$	7104.55	0.294447
$836$	−8909.31	−0.368583
$837$	3315.12	0.136903
$838$	−15309.4	−0.631090
$839$	7738.21	0.318418	0.159209	−	0.987245i	$-0.449106\pi$
$839$	7738.21	0.318418	0.159209	+	0.987245i	$0.449106\pi$
$840$	−1456.45	−0.0598241
$841$	841.000	0.0344828
$842$	−10317.4	−0.422283
$843$	1487.89	0.0607896
$844$	5588.91	0.227936
$845$	4349.72	0.177083
$846$	4986.80	0.202659
$847$	−1992.40	−0.0808260
$848$	1933.93	0.0783152
$849$	21888.4	0.884814
$850$	1049.49	0.0423498
$851$	−5750.31	−0.231631
$852$	−329.105	−0.0132335
$853$	31504.1	1.26457	0.632286	−	0.774735i	$-0.282117\pi$
$853$	31504.1	1.26457	0.632286	+	0.774735i	$0.282117\pi$
$854$	700.294	0.0280604
$855$	−3810.64	−0.152422
$856$	8191.99	0.327099
$857$	−33621.2	−1.34011	−0.670057	−	0.742310i	$-0.733730\pi$
$857$	−33621.2	−1.34011	−0.670057	+	0.742310i	$0.733730\pi$
$858$	11027.2	0.438766
$859$	35655.1	1.41622	0.708111	−	0.706101i	$-0.249547\pi$
$859$	35655.1	1.41622	0.708111	+	0.706101i	$0.249547\pi$
$860$	4878.49	0.193436
$861$	−163.796	−0.00648332
$862$	−1644.23	−0.0649684
$863$	−20500.2	−0.808615	−0.404307	−	0.914623i	$-0.632487\pi$
$863$	−20500.2	−0.808615	−0.404307	+	0.914623i	$0.632487\pi$
$864$	2880.88	0.113437
$865$	1698.29	0.0667558
$866$	−16245.6	−0.637467
$867$	−13785.5	−0.540000
$868$	1188.95	0.0464928
$869$	11536.9	0.450361
$870$	−1024.30	−0.0399163
$871$	−25449.5	−0.990038
$872$	−21924.2	−0.851431
$873$	−13720.2	−0.531912
$874$	18725.6	0.724718
$875$	492.990	0.0190470
$876$	−4932.25	−0.190234
$877$	−15240.7	−0.586822	−0.293411	−	0.955986i	$-0.594790\pi$
$877$	−15240.7	−0.586822	−0.293411	+	0.955986i	$0.594790\pi$
$878$	−29440.7	−1.13164
$879$	2561.85	0.0983036
$880$	8212.20	0.314583
$881$	−17749.3	−0.678761	−0.339381	−	0.940649i	$-0.610217\pi$
$881$	−17749.3	−0.678761	−0.339381	+	0.940649i	$0.610217\pi$
$882$	−6939.39	−0.264922
$883$	−2290.27	−0.0872861	−0.0436431	−	0.999047i	$-0.513896\pi$
$883$	−2290.27	−0.0872861	−0.0436431	+	0.999047i	$0.513896\pi$
$884$	−1594.58	−0.0606690
$885$	7150.69	0.271602
$886$	18094.7	0.686120
$887$	−45630.9	−1.72732	−0.863662	−	0.504072i	$-0.831835\pi$
$887$	−45630.9	−1.72732	−0.863662	+	0.504072i	$0.831835\pi$
$888$	4522.49	0.170906
$889$	−9665.47	−0.364645
$890$	116.009	0.00436923
$891$	3470.91	0.130505
$892$	−9548.68	−0.358423
$893$	19926.2	0.746703
$894$	−883.326	−0.0330457
$895$	12965.5	0.484233
$896$	−1814.46	−0.0676527
$897$	10263.0	0.382021
$898$	16322.1	0.606542
$899$	3560.69	0.132097
$900$	−552.438	−0.0204607
$901$	−899.514	−0.0332599
$902$	1396.85	0.0515633
$903$	−4701.80	−0.173274
$904$	23063.4	0.848537
$905$	1676.12	0.0615649
$906$	13906.9	0.509962
$907$	38959.7	1.42628	0.713140	−	0.701022i	$-0.247272\pi$
$907$	38959.7	1.42628	0.713140	+	0.701022i	$0.247272\pi$
$908$	13970.0	0.510586
$909$	4655.97	0.169889
$910$	1691.54	0.0616199
$911$	34221.7	1.24458	0.622291	−	0.782786i	$-0.286202\pi$
$911$	34221.7	1.24458	0.622291	+	0.782786i	$0.286202\pi$
$912$	−9737.31	−0.353547
$913$	37268.1	1.35093
$914$	−1575.62	−0.0570207
$915$	1131.11	0.0408669
$916$	7989.26	0.288180
$917$	−2156.07	−0.0776441
$918$	1133.45	0.0407511
$919$	519.522	0.0186479	0.00932396	−	0.999957i	$-0.497032\pi$
$919$	519.522	0.0186479	0.00932396	+	0.999957i	$0.497032\pi$
$920$	11559.9	0.414261
$921$	−2082.86	−0.0745197
$922$	3224.40	0.115173
$923$	1627.63	0.0580436
$924$	1244.82	0.0443201
$925$	−1530.81	−0.0544137
$926$	−19340.9	−0.686372
$927$	−13031.9	−0.461730
$928$	3094.28	0.109455
$929$	36926.5	1.30411	0.652056	−	0.758171i	$-0.273907\pi$
$929$	36926.5	1.30411	0.652056	+	0.758171i	$0.273907\pi$
$930$	−4336.78	−0.152912
$931$	−27728.4	−0.976113
$932$	−3348.32	−0.117680
$933$	7762.73	0.272391
$934$	46534.3	1.63025
$935$	−3819.69	−0.133601
$936$	−8071.66	−0.281870
$937$	24916.0	0.868697	0.434348	−	0.900745i	$-0.356979\pi$
$937$	24916.0	0.868697	0.434348	+	0.900745i	$0.356979\pi$
$938$	6487.88	0.225839
$939$	−10403.0	−0.361545
$940$	2888.75	0.100235
$941$	−41585.1	−1.44063	−0.720317	−	0.693645i	$-0.756004\pi$
$941$	−41585.1	−1.44063	−0.720317	+	0.693645i	$0.756004\pi$
$942$	7953.12	0.275081
$943$	1300.06	0.0448948
$944$	18272.1	0.629985
$945$	532.430	0.0183280
$946$	40097.1	1.37808
$947$	173.666	0.00595923	0.00297962	−	0.999996i	$-0.499052\pi$
$947$	173.666	0.00595923	0.00297962	+	0.999996i	$0.499052\pi$
$948$	−1983.15	−0.0679426
$949$	24393.1	0.834388
$950$	4985.01	0.170247
$951$	−15476.0	−0.527700
$952$	1731.03	0.0589317
$953$	−22394.5	−0.761207	−0.380603	−	0.924738i	$-0.624284\pi$
$953$	−22394.5	−0.761207	−0.380603	+	0.924738i	$0.624284\pi$
$954$	−1069.28	−0.0362884
$955$	−4639.80	−0.157215
$956$	11757.5	0.397766
$957$	3728.01	0.125924
$958$	3384.42	0.114140
$959$	2437.60	0.0820793
$960$	−8368.23	−0.281337
$961$	−14715.5	−0.493957
$962$	−5252.49	−0.176037
$963$	−2994.72	−0.100211
$964$	1553.94	0.0519181
$965$	−10922.4	−0.364356
$966$	−2616.38	−0.0871434
$967$	35240.6	1.17194	0.585968	−	0.810334i	$-0.300715\pi$
$967$	35240.6	1.17194	0.585968	+	0.810334i	$0.300715\pi$
$968$	−12437.2	−0.412962
$969$	4529.05	0.150149
$970$	17948.5	0.594116
$971$	−23385.4	−0.772888	−0.386444	−	0.922313i	$-0.626297\pi$
$971$	−23385.4	−0.772888	−0.386444	+	0.922313i	$0.626297\pi$
$972$	−596.633	−0.0196883
$973$	−5069.95	−0.167045
$974$	29978.8	0.986226
$975$	2732.16	0.0897427
$976$	2890.31	0.0947915
$977$	37442.2	1.22608	0.613041	−	0.790051i	$-0.289946\pi$
$977$	37442.2	1.22608	0.613041	+	0.790051i	$0.289946\pi$
$978$	12530.9	0.409708
$979$	−422.219	−0.0137836
$980$	−4019.85	−0.131030
$981$	8014.77	0.260848
$982$	−36711.4	−1.19298
$983$	−35213.6	−1.14256	−0.571282	−	0.820754i	$-0.693554\pi$
$983$	−35213.6	−1.14256	−0.571282	+	0.820754i	$0.693554\pi$
$984$	−1022.47	−0.0331251
$985$	18827.7	0.609037
$986$	1217.41	0.0393208
$987$	−2784.13	−0.0897870
$988$	−7574.10	−0.243891
$989$	37318.6	1.19986
$990$	−4540.57	−0.145766
$991$	−43883.0	−1.40665	−0.703324	−	0.710869i	$-0.748302\pi$
$991$	−43883.0	−1.40665	−0.703324	+	0.710869i	$0.748302\pi$
$992$	13100.8	0.419305
$993$	33170.8	1.06007
$994$	−414.935	−0.0132404
$995$	300.363	0.00957001
$996$	−6406.22	−0.203804
$997$	−8968.04	−0.284875	−0.142438	−	0.989804i	$-0.545494\pi$
$997$	−8968.04	−0.284875	−0.142438	+	0.989804i	$0.545494\pi$
$998$	−17211.9	−0.545925
$999$	−1653.27	−0.0523596

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.4.a.h.1.4	✓	6
3.2	odd	2		1305.4.a.h.1.3		6
5.4	even	2		2175.4.a.k.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.4.a.h.1.4	✓	6	1.1	even	1	trivial
1305.4.a.h.1.3		6	3.2	odd	2
2175.4.a.k.1.3		6	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)

\(f(q)\)	\(=\)	\(q+2.35472 q^{2} +3.00000 q^{3} -2.45528 q^{4} -5.00000 q^{5} +7.06417 q^{6} -3.94392 q^{7} -24.6193 q^{8} +9.00000 q^{9} -11.7736 q^{10} +42.8507 q^{11} -7.36583 q^{12} +36.4288 q^{13} -9.28685 q^{14} -15.0000 q^{15} -38.3294 q^{16} +17.8279 q^{17} +21.1925 q^{18} +84.6809 q^{19} +12.2764 q^{20} -11.8318 q^{21} +100.902 q^{22} +93.9097 q^{23} -73.8579 q^{24} +25.0000 q^{25} +85.7797 q^{26} +27.0000 q^{27} +9.68343 q^{28} +29.0000 q^{29} -35.3208 q^{30} +122.782 q^{31} +106.699 q^{32} +128.552 q^{33} +41.9798 q^{34} +19.7196 q^{35} -22.0975 q^{36} -61.2323 q^{37} +199.400 q^{38} +109.286 q^{39} +123.096 q^{40} +13.8437 q^{41} -27.8605 q^{42} +397.388 q^{43} -105.210 q^{44} -45.0000 q^{45} +221.131 q^{46} +235.310 q^{47} -114.988 q^{48} -327.445 q^{49} +58.8681 q^{50} +53.4837 q^{51} -89.4428 q^{52} -50.4554 q^{53} +63.5775 q^{54} -214.253 q^{55} +97.0966 q^{56} +254.043 q^{57} +68.2870 q^{58} -476.712 q^{59} +36.8292 q^{60} -75.4071 q^{61} +289.119 q^{62} -35.4953 q^{63} +557.882 q^{64} -182.144 q^{65} +302.705 q^{66} -698.609 q^{67} -43.7725 q^{68} +281.729 q^{69} +46.4342 q^{70} +44.6799 q^{71} -221.574 q^{72} +669.611 q^{73} -144.185 q^{74} +75.0000 q^{75} -207.915 q^{76} -169.000 q^{77} +257.339 q^{78} +269.236 q^{79} +191.647 q^{80} +81.0000 q^{81} +32.5981 q^{82} +869.721 q^{83} +29.0503 q^{84} -89.1395 q^{85} +935.739 q^{86} +87.0000 q^{87} -1054.95 q^{88} -9.85326 q^{89} -105.963 q^{90} -143.672 q^{91} -230.574 q^{92} +368.347 q^{93} +554.089 q^{94} -423.405 q^{95} +320.098 q^{96} -1524.47 q^{97} -771.043 q^{98} +385.656 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} + 18 q^{3} + 51 q^{4} - 30 q^{5} + 3 q^{6} + 47 q^{7} + 51 q^{8} + 54 q^{9} - 5 q^{10} + 81 q^{11} + 153 q^{12} + 169 q^{13} - 30 q^{14} - 90 q^{15} + 131 q^{16} - q^{17} + 9 q^{18} + 116 q^{19}+ \cdots + 729 q^{99}+O(q^{100}) \) 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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