LMFDB - Embedded newform 435.4.a.j.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [435,4,Mod(1,435)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	435.a (trivial)

Newform invariants

comment:select newform

sage:traces = [7,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$25.6658308525$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 35x^{5} + 18x^{4} + 329x^{3} - 167x^{2} - 767x + 638 $ x^7 - x^6 - 35x^5 + 18x^4 + 329x^3 - 167x^2 - 767*x + 638
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$5.12367$ 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)

$f(q)$	$=$	\(q-5.12367 q^{2} +3.00000 q^{3} +18.2520 q^{4} -5.00000 q^{5} -15.3710 q^{6} -21.7657 q^{7} -52.5281 q^{8} +9.00000 q^{9} +25.6184 q^{10} +57.1430 q^{11} +54.7561 q^{12} -41.2271 q^{13} +111.520 q^{14} -15.0000 q^{15} +123.120 q^{16} +73.0149 q^{17} -46.1131 q^{18} -0.658616 q^{19} -91.2602 q^{20} -65.2970 q^{21} -292.782 q^{22} -96.1672 q^{23} -157.584 q^{24} +25.0000 q^{25} +211.234 q^{26} +27.0000 q^{27} -397.267 q^{28} -29.0000 q^{29} +76.8551 q^{30} -2.01051 q^{31} -210.604 q^{32} +171.429 q^{33} -374.104 q^{34} +108.828 q^{35} +164.268 q^{36} -315.774 q^{37} +3.37453 q^{38} -123.681 q^{39} +262.640 q^{40} +219.873 q^{41} +334.560 q^{42} +81.2960 q^{43} +1042.98 q^{44} -45.0000 q^{45} +492.730 q^{46} +440.820 q^{47} +369.361 q^{48} +130.744 q^{49} -128.092 q^{50} +219.045 q^{51} -752.479 q^{52} +65.8584 q^{53} -138.339 q^{54} -285.715 q^{55} +1143.31 q^{56} -1.97585 q^{57} +148.587 q^{58} -551.520 q^{59} -273.780 q^{60} -149.536 q^{61} +10.3012 q^{62} -195.891 q^{63} +94.1041 q^{64} +206.136 q^{65} -878.346 q^{66} -888.233 q^{67} +1332.67 q^{68} -288.502 q^{69} -557.601 q^{70} -570.702 q^{71} -472.753 q^{72} +664.264 q^{73} +1617.92 q^{74} +75.0000 q^{75} -12.0211 q^{76} -1243.75 q^{77} +633.703 q^{78} +221.956 q^{79} -615.602 q^{80} +81.0000 q^{81} -1126.56 q^{82} -740.432 q^{83} -1191.80 q^{84} -365.074 q^{85} -416.534 q^{86} -87.0000 q^{87} -3001.61 q^{88} -895.415 q^{89} +230.565 q^{90} +897.336 q^{91} -1755.25 q^{92} -6.03152 q^{93} -2258.62 q^{94} +3.29308 q^{95} -631.813 q^{96} -705.666 q^{97} -669.888 q^{98} +514.287 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} + 21 q^{3} + 15 q^{4} - 35 q^{5} - 3 q^{6} - 37 q^{7} - 36 q^{8} + 63 q^{9} + 5 q^{10} - 11 q^{11} + 45 q^{12} - 133 q^{13} - 75 q^{14} - 105 q^{15} - 53 q^{16} + 21 q^{17} - 9 q^{18} - 170 q^{19}+ \cdots - 99 q^{99}+O(q^{100}) $ 7 * q - q^2 + 21 * q^3 + 15 * q^4 - 35 * q^5 - 3 * q^6 - 37 * q^7 - 36 * q^8 + 63 * q^9 + 5 * q^10 - 11 * q^11 + 45 * q^12 - 133 * q^13 - 75 * q^14 - 105 * q^15 - 53 * q^16 + 21 * q^17 - 9 * q^18 - 170 * q^19 - 75 * q^20 - 111 * q^21 - 369 * q^22 - 68 * q^23 - 108 * q^24 + 175 * q^25 + 181 * q^26 + 189 * q^27 - 637 * q^28 - 203 * q^29 + 15 * q^30 - 480 * q^31 - 779 * q^32 - 33 * q^33 - 897 * q^34 + 185 * q^35 + 135 * q^36 - 1032 * q^37 - 194 * q^38 - 399 * q^39 + 180 * q^40 - 638 * q^41 - 225 * q^42 - 512 * q^43 + 625 * q^44 - 315 * q^45 + 16 * q^46 - 111 * q^47 - 159 * q^48 + 178 * q^49 - 25 * q^50 + 63 * q^51 - 1263 * q^52 + 410 * q^53 - 27 * q^54 + 55 * q^55 + 1174 * q^56 - 510 * q^57 + 29 * q^58 - 426 * q^59 - 225 * q^60 - 1192 * q^61 + 460 * q^62 - 333 * q^63 + 390 * q^64 + 665 * q^65 - 1107 * q^66 - 1671 * q^67 + 1509 * q^68 - 204 * q^69 + 375 * q^70 - 1324 * q^71 - 324 * q^72 - 852 * q^73 + 1780 * q^74 + 525 * q^75 - 564 * q^76 - 2107 * q^77 + 543 * q^78 + 366 * q^79 + 265 * q^80 + 567 * q^81 - 318 * q^82 + 470 * q^83 - 1911 * q^84 - 105 * q^85 - 2196 * q^86 - 609 * q^87 - 2518 * q^88 + 51 * q^89 + 45 * q^90 - 1297 * q^91 - 684 * q^92 - 1440 * q^93 - 1837 * q^94 + 850 * q^95 - 2337 * q^96 - 3322 * q^97 + 1068 * q^98 - 99 * 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 $

$2$	−5.12367	−1.81149	−0.905746	−	0.423821i	$-0.860689\pi$
$2$	−5.12367	−1.81149	−0.905746	+	0.423821i	$0.860689\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	18.2520	2.28150
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−15.3710	−1.04587
$7$	−21.7657	−1.17523	−0.587617	−	0.809139i	$-0.699934\pi$
$7$	−21.7657	−1.17523	−0.587617	+	0.809139i	$0.699934\pi$
$8$	−52.5281	−2.32143
$9$	9.00000	0.333333
$10$	25.6184	0.810124
$11$	57.1430	1.56630	0.783148	−	0.621835i	$-0.213613\pi$
$11$	57.1430	1.56630	0.783148	+	0.621835i	$0.213613\pi$
$12$	54.7561	1.31723
$13$	−41.2271	−0.879565	−0.439783	−	0.898104i	$-0.644945\pi$
$13$	−41.2271	−0.879565	−0.439783	+	0.898104i	$0.644945\pi$
$14$	111.520	2.12893
$15$	−15.0000	−0.258199
$16$	123.120	1.92376
$17$	73.0149	1.04169	0.520844	−	0.853652i	$-0.325617\pi$
$17$	73.0149	1.04169	0.520844	+	0.853652i	$0.325617\pi$
$18$	−46.1131	−0.603831
$19$	−0.658616	−0.00795246	−0.00397623	−	0.999992i	$-0.501266\pi$
$19$	−0.658616	−0.00795246	−0.00397623	+	0.999992i	$0.501266\pi$
$20$	−91.2602	−1.02032
$21$	−65.2970	−0.678522
$22$	−292.782	−2.83733
$23$	−96.1672	−0.871837	−0.435919	−	0.899986i	$-0.643576\pi$
$23$	−96.1672	−0.871837	−0.435919	+	0.899986i	$0.643576\pi$
$24$	−157.584	−1.34028
$25$	25.0000	0.200000
$26$	211.234	1.59333
$27$	27.0000	0.192450
$28$	−397.267	−2.68130
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	76.8551	0.467725
$31$	−2.01051	−0.0116483	−0.00582415	−	0.999983i	$-0.501854\pi$
$31$	−2.01051	−0.0116483	−0.00582415	+	0.999983i	$0.501854\pi$
$32$	−210.604	−1.16343
$33$	171.429	0.904301
$34$	−374.104	−1.88701
$35$	108.828	0.525581
$36$	164.268	0.760501
$37$	−315.774	−1.40305	−0.701526	−	0.712644i	$-0.747498\pi$
$37$	−315.774	−1.40305	−0.701526	+	0.712644i	$0.747498\pi$
$38$	3.37453	0.0144058
$39$	−123.681	−0.507817
$40$	262.640	1.03818
$41$	219.873	0.837522	0.418761	−	0.908097i	$-0.362465\pi$
$41$	219.873	0.837522	0.418761	+	0.908097i	$0.362465\pi$
$42$	334.560	1.22914
$43$	81.2960	0.288315	0.144157	−	0.989555i	$-0.453953\pi$
$43$	81.2960	0.288315	0.144157	+	0.989555i	$0.453953\pi$
$44$	1042.98	3.57351
$45$	−45.0000	−0.149071
$46$	492.730	1.57933
$47$	440.820	1.36809	0.684044	−	0.729441i	$-0.260220\pi$
$47$	440.820	1.36809	0.684044	+	0.729441i	$0.260220\pi$
$48$	369.361	1.11068
$49$	130.744	0.381177
$50$	−128.092	−0.362298
$51$	219.045	0.601419
$52$	−752.479	−2.00673
$53$	65.8584	0.170686	0.0853429	−	0.996352i	$-0.472801\pi$
$53$	65.8584	0.170686	0.0853429	+	0.996352i	$0.472801\pi$
$54$	−138.339	−0.348622
$55$	−285.715	−0.700469
$56$	1143.31	2.72823
$57$	−1.97585	−0.00459136
$58$	148.587	0.336386
$59$	−551.520	−1.21698	−0.608489	−	0.793562i	$-0.708224\pi$
$59$	−551.520	−1.21698	−0.608489	+	0.793562i	$0.708224\pi$
$60$	−273.780	−0.589082
$61$	−149.536	−0.313871	−0.156936	−	0.987609i	$-0.550161\pi$
$61$	−149.536	−0.313871	−0.156936	+	0.987609i	$0.550161\pi$
$62$	10.3012	0.0211008
$63$	−195.891	−0.391745
$64$	94.1041	0.183797
$65$	206.136	0.393354
$66$	−878.346	−1.63814
$67$	−888.233	−1.61963	−0.809813	−	0.586689i	$-0.800431\pi$
$67$	−888.233	−1.61963	−0.809813	+	0.586689i	$0.800431\pi$
$68$	1332.67	2.37662
$69$	−288.502	−0.503355
$70$	−557.601	−0.952086
$71$	−570.702	−0.953942	−0.476971	−	0.878919i	$-0.658265\pi$
$71$	−570.702	−0.953942	−0.476971	+	0.878919i	$0.658265\pi$
$72$	−472.753	−0.773811
$73$	664.264	1.06502	0.532509	−	0.846425i	$-0.321249\pi$
$73$	664.264	1.06502	0.532509	+	0.846425i	$0.321249\pi$
$74$	1617.92	2.54162
$75$	75.0000	0.115470
$76$	−12.0211	−0.0181436
$77$	−1243.75	−1.84077
$78$	633.703	0.919907
$79$	221.956	0.316102	0.158051	−	0.987431i	$-0.449479\pi$
$79$	221.956	0.316102	0.158051	+	0.987431i	$0.449479\pi$
$80$	−615.602	−0.860330
$81$	81.0000	0.111111
$82$	−1126.56	−1.51716
$83$	−740.432	−0.979192	−0.489596	−	0.871949i	$-0.662856\pi$
$83$	−740.432	−0.979192	−0.489596	+	0.871949i	$0.662856\pi$
$84$	−1191.80	−1.54805
$85$	−365.074	−0.465857
$86$	−416.534	−0.522280
$87$	−87.0000	−0.107211
$88$	−3001.61	−3.63605
$89$	−895.415	−1.06645	−0.533224	−	0.845974i	$-0.679020\pi$
$89$	−895.415	−1.06645	−0.533224	+	0.845974i	$0.679020\pi$
$90$	230.565	0.270041
$91$	897.336	1.03370
$92$	−1755.25	−1.98910
$93$	−6.03152	−0.00672515
$94$	−2258.62	−2.47828
$95$	3.29308	0.00355645
$96$	−631.813	−0.671709
$97$	−705.666	−0.738655	−0.369327	−	0.929299i	$-0.620412\pi$
$97$	−705.666	−0.738655	−0.369327	+	0.929299i	$0.620412\pi$
$98$	−669.888	−0.690499
$99$	514.287	0.522099
$100$	456.301	0.456301
$101$	−1290.41	−1.27129	−0.635647	−	0.771980i	$-0.719266\pi$
$101$	−1290.41	−1.27129	−0.635647	+	0.771980i	$0.719266\pi$
$102$	−1122.31	−1.08947
$103$	897.912	0.858970	0.429485	−	0.903074i	$-0.358695\pi$
$103$	897.912	0.858970	0.429485	+	0.903074i	$0.358695\pi$
$104$	2165.58	2.04185
$105$	326.485	0.303444
$106$	−337.437	−0.309196
$107$	−2080.08	−1.87934	−0.939669	−	0.342086i	$-0.888867\pi$
$107$	−2080.08	−1.87934	−0.939669	+	0.342086i	$0.888867\pi$
$108$	492.805	0.439076
$109$	−1386.38	−1.21827	−0.609133	−	0.793068i	$-0.708482\pi$
$109$	−1386.38	−1.21827	−0.609133	+	0.793068i	$0.708482\pi$
$110$	1463.91	1.26889
$111$	−947.322	−0.810052
$112$	−2679.80	−2.26087
$113$	477.103	0.397187	0.198593	−	0.980082i	$-0.436363\pi$
$113$	477.103	0.397187	0.198593	+	0.980082i	$0.436363\pi$
$114$	10.1236	0.00831721
$115$	480.836	0.389897
$116$	−529.309	−0.423665
$117$	−371.044	−0.293188
$118$	2825.81	2.20455
$119$	−1589.22	−1.22423
$120$	787.921	0.599392
$121$	1934.32	1.45328
$122$	766.174	0.568575
$123$	659.619	0.483543
$124$	−36.6958	−0.0265757
$125$	−125.000	−0.0894427
$126$	1003.68	0.709643
$127$	−1357.50	−0.948495	−0.474247	−	0.880392i	$-0.657280\pi$
$127$	−1357.50	−0.948495	−0.474247	+	0.880392i	$0.657280\pi$
$128$	1202.67	0.830488
$129$	243.888	0.166459
$130$	−1056.17	−0.712557
$131$	2994.84	1.99741	0.998704	−	0.0508962i	$-0.0162078\pi$
$131$	2994.84	1.99741	0.998704	+	0.0508962i	$0.0162078\pi$
$132$	3128.93	2.06317
$133$	14.3352	0.00934601
$134$	4551.01	2.93394
$135$	−135.000	−0.0860663
$136$	−3835.33	−2.41821
$137$	−1067.77	−0.665878	−0.332939	−	0.942948i	$-0.608040\pi$
$137$	−1067.77	−0.665878	−0.332939	+	0.942948i	$0.608040\pi$
$138$	1478.19	0.911824
$139$	−843.314	−0.514597	−0.257298	−	0.966332i	$-0.582832\pi$
$139$	−843.314	−0.514597	−0.257298	+	0.966332i	$0.582832\pi$
$140$	1986.34	1.19912
$141$	1322.46	0.789866
$142$	2924.09	1.72806
$143$	−2355.84	−1.37766
$144$	1108.08	0.641252
$145$	145.000	0.0830455
$146$	−3403.47	−1.92927
$147$	392.231	0.220073
$148$	−5763.52	−3.20107
$149$	1273.71	0.700313	0.350157	−	0.936691i	$-0.386128\pi$
$149$	1273.71	0.700313	0.350157	+	0.936691i	$0.386128\pi$
$150$	−384.276	−0.209173
$151$	−3030.58	−1.63328	−0.816639	−	0.577149i	$-0.804165\pi$
$151$	−3030.58	−1.63328	−0.816639	+	0.577149i	$0.804165\pi$
$152$	34.5958	0.0184611
$153$	657.134	0.347230
$154$	6372.59	3.33453
$155$	10.0525	0.00520928
$156$	−2257.44	−1.15859
$157$	−1513.57	−0.769399	−0.384700	−	0.923042i	$-0.625695\pi$
$157$	−1513.57	−0.769399	−0.384700	+	0.923042i	$0.625695\pi$
$158$	−1137.23	−0.572616
$159$	197.575	0.0985455
$160$	1053.02	0.520304
$161$	2093.14	1.02461
$162$	−415.018	−0.201277
$163$	−3134.88	−1.50640	−0.753200	−	0.657792i	$-0.771491\pi$
$163$	−3134.88	−1.50640	−0.753200	+	0.657792i	$0.771491\pi$
$164$	4013.13	1.91081
$165$	−857.145	−0.404416
$166$	3793.73	1.77380
$167$	703.416	0.325940	0.162970	−	0.986631i	$-0.447893\pi$
$167$	703.416	0.325940	0.162970	+	0.986631i	$0.447893\pi$
$168$	3429.92	1.57514
$169$	−497.323	−0.226365
$170$	1870.52	0.843897
$171$	−5.92754	−0.00265082
$172$	1483.82	0.657791
$173$	−1699.75	−0.746993	−0.373497	−	0.927632i	$-0.621841\pi$
$173$	−1699.75	−0.746993	−0.373497	+	0.927632i	$0.621841\pi$
$174$	445.760	0.194212
$175$	−544.141	−0.235047
$176$	7035.47	3.01317
$177$	−1654.56	−0.702623
$178$	4587.81	1.93186
$179$	−1616.87	−0.675143	−0.337572	−	0.941300i	$-0.609606\pi$
$179$	−1616.87	−0.675143	−0.337572	+	0.941300i	$0.609606\pi$
$180$	−821.341	−0.340107
$181$	790.412	0.324590	0.162295	−	0.986742i	$-0.448110\pi$
$181$	790.412	0.324590	0.162295	+	0.986742i	$0.448110\pi$
$182$	−4597.65	−1.87253
$183$	−448.608	−0.181214
$184$	5051.48	2.02391
$185$	1578.87	0.627464
$186$	30.9035	0.0121826
$187$	4172.29	1.63159
$188$	8045.85	3.12130
$189$	−587.673	−0.226174
$190$	−16.8727	−0.00644248
$191$	−2966.34	−1.12375	−0.561877	−	0.827221i	$-0.689921\pi$
$191$	−2966.34	−1.12375	−0.561877	+	0.827221i	$0.689921\pi$
$192$	282.312	0.106115
$193$	−1871.55	−0.698018	−0.349009	−	0.937119i	$-0.613482\pi$
$193$	−1871.55	−0.698018	−0.349009	+	0.937119i	$0.613482\pi$
$194$	3615.60	1.33807
$195$	618.407	0.227103
$196$	2386.34	0.869656
$197$	−1765.75	−0.638603	−0.319301	−	0.947653i	$-0.603448\pi$
$197$	−1765.75	−0.638603	−0.319301	+	0.947653i	$0.603448\pi$
$198$	−2635.04	−0.945778
$199$	−153.070	−0.0545268	−0.0272634	−	0.999628i	$-0.508679\pi$
$199$	−153.070	−0.0545268	−0.0272634	+	0.999628i	$0.508679\pi$
$200$	−1313.20	−0.464287
$201$	−2664.70	−0.935091
$202$	6611.64	2.30294
$203$	631.204	0.218236
$204$	3998.01	1.37214
$205$	−1099.37	−0.374551
$206$	−4600.61	−1.55602
$207$	−865.505	−0.290612
$208$	−5075.90	−1.69207
$209$	−37.6353	−0.0124559
$210$	−1672.80	−0.549687
$211$	5632.85	1.83783	0.918913	−	0.394460i	$-0.129068\pi$
$211$	5632.85	1.83783	0.918913	+	0.394460i	$0.129068\pi$
$212$	1202.05	0.389420
$213$	−1712.11	−0.550758
$214$	10657.7	3.40440
$215$	−406.480	−0.128938
$216$	−1418.26	−0.446760
$217$	43.7600	0.0136895
$218$	7103.35	2.20688
$219$	1992.79	0.614888
$220$	−5214.88	−1.59812
$221$	−3010.19	−0.916233
$222$	4853.77	1.46740
$223$	−2962.89	−0.889730	−0.444865	−	0.895598i	$-0.646748\pi$
$223$	−2962.89	−0.889730	−0.444865	+	0.895598i	$0.646748\pi$
$224$	4583.94	1.36731
$225$	225.000	0.0666667
$226$	−2444.52	−0.719501
$227$	−1006.81	−0.294381	−0.147190	−	0.989108i	$-0.547023\pi$
$227$	−1006.81	−0.294381	−0.147190	+	0.989108i	$0.547023\pi$
$228$	−36.0632	−0.0104752
$229$	−1297.30	−0.374359	−0.187179	−	0.982326i	$-0.559935\pi$
$229$	−1297.30	−0.374359	−0.187179	+	0.982326i	$0.559935\pi$
$230$	−2463.65	−0.706296
$231$	−3731.26	−1.06277
$232$	1523.31	0.431080
$233$	−1649.87	−0.463891	−0.231946	−	0.972729i	$-0.574509\pi$
$233$	−1649.87	−0.463891	−0.231946	+	0.972729i	$0.574509\pi$
$234$	1901.11	0.531109
$235$	−2204.10	−0.611828
$236$	−10066.4	−2.77654
$237$	665.869	0.182501
$238$	8142.63	2.21768
$239$	5704.40	1.54388	0.771939	−	0.635696i	$-0.219287\pi$
$239$	5704.40	1.54388	0.771939	+	0.635696i	$0.219287\pi$
$240$	−1846.81	−0.496712
$241$	7233.99	1.93354	0.966768	−	0.255657i	$-0.0822916\pi$
$241$	7233.99	1.93354	0.966768	+	0.255657i	$0.0822916\pi$
$242$	−9910.83	−2.63261
$243$	243.000	0.0641500
$244$	−2729.34	−0.716098
$245$	−653.718	−0.170467
$246$	−3379.67	−0.875935
$247$	27.1528	0.00699471
$248$	105.608	0.0270408
$249$	−2221.30	−0.565337
$250$	640.459	0.162025
$251$	5887.94	1.48065	0.740326	−	0.672248i	$-0.234671\pi$
$251$	5887.94	1.48065	0.740326	+	0.672248i	$0.234671\pi$
$252$	−3575.41	−0.893768
$253$	−5495.28	−1.36556
$254$	6955.40	1.71819
$255$	−1095.22	−0.268963
$256$	−6914.95	−1.68822
$257$	5751.33	1.39595	0.697973	−	0.716124i	$-0.254086\pi$
$257$	5751.33	1.39595	0.697973	+	0.716124i	$0.254086\pi$
$258$	−1249.60	−0.301538
$259$	6873.03	1.64892
$260$	3762.39	0.897438
$261$	−261.000	−0.0618984
$262$	−15344.6	−3.61829
$263$	5196.53	1.21837	0.609186	−	0.793027i	$-0.291496\pi$
$263$	5196.53	1.21837	0.609186	+	0.793027i	$0.291496\pi$
$264$	−9004.83	−2.09928
$265$	−329.292	−0.0763330
$266$	−73.4489	−0.0169302
$267$	−2686.24	−0.615713
$268$	−16212.1	−3.69518
$269$	−7201.66	−1.63232	−0.816158	−	0.577829i	$-0.803900\pi$
$269$	−7201.66	−1.63232	−0.816158	+	0.577829i	$0.803900\pi$
$270$	691.696	0.155908
$271$	−1510.97	−0.338690	−0.169345	−	0.985557i	$-0.554165\pi$
$271$	−1510.97	−0.338690	−0.169345	+	0.985557i	$0.554165\pi$
$272$	8989.62	2.00396
$273$	2692.01	0.596805
$274$	5470.88	1.20623
$275$	1428.57	0.313259
$276$	−5265.74	−1.14841
$277$	6906.59	1.49811	0.749056	−	0.662507i	$-0.230507\pi$
$277$	6906.59	1.49811	0.749056	+	0.662507i	$0.230507\pi$
$278$	4320.87	0.932188
$279$	−18.0946	−0.00388277
$280$	−5716.54	−1.22010
$281$	−5553.49	−1.17898	−0.589490	−	0.807776i	$-0.700671\pi$
$281$	−5553.49	−1.17898	−0.589490	+	0.807776i	$0.700671\pi$
$282$	−6775.85	−1.43084
$283$	−906.811	−0.190475	−0.0952373	−	0.995455i	$-0.530361\pi$
$283$	−906.811	−0.190475	−0.0952373	+	0.995455i	$0.530361\pi$
$284$	−10416.5	−2.17642
$285$	9.87923	0.00205332
$286$	12070.6	2.49562
$287$	−4785.68	−0.984285
$288$	−1895.44	−0.387812
$289$	418.172	0.0851154
$290$	−742.933	−0.150436
$291$	−2117.00	−0.426462
$292$	12124.2	2.42984
$293$	478.454	0.0953979	0.0476989	−	0.998862i	$-0.484811\pi$
$293$	478.454	0.0953979	0.0476989	+	0.998862i	$0.484811\pi$
$294$	−2009.66	−0.398660
$295$	2757.60	0.544249
$296$	16587.0	3.25709
$297$	1542.86	0.301434
$298$	−6526.09	−1.26861
$299$	3964.70	0.766838
$300$	1368.90	0.263445
$301$	−1769.46	−0.338837
$302$	15527.7	2.95867
$303$	−3871.23	−0.733982
$304$	−81.0890	−0.0152986
$305$	747.680	0.140367
$306$	−3366.94	−0.629004
$307$	−8071.13	−1.50047	−0.750235	−	0.661172i	$-0.770059\pi$
$307$	−8071.13	−1.50047	−0.750235	+	0.661172i	$0.770059\pi$
$308$	−22701.0	−4.19971
$309$	2693.74	0.495926
$310$	−51.5059	−0.00943657
$311$	−2191.99	−0.399667	−0.199834	−	0.979830i	$-0.564040\pi$
$311$	−2191.99	−0.399667	−0.199834	+	0.979830i	$0.564040\pi$
$312$	6496.74	1.17886
$313$	10935.0	1.97471	0.987353	−	0.158535i	$-0.0506771\pi$
$313$	10935.0	1.97471	0.987353	+	0.158535i	$0.0506771\pi$
$314$	7755.02	1.39376
$315$	979.454	0.175194
$316$	4051.15	0.721187
$317$	8640.32	1.53088	0.765440	−	0.643508i	$-0.222522\pi$
$317$	8640.32	1.53088	0.765440	+	0.643508i	$0.222522\pi$
$318$	−1012.31	−0.178514
$319$	−1657.15	−0.290854
$320$	−470.520	−0.0821965
$321$	−6240.25	−1.08504
$322$	−10724.6	−1.85608
$323$	−48.0887	−0.00828399
$324$	1478.41	0.253500
$325$	−1030.68	−0.175913
$326$	16062.1	2.72883
$327$	−4159.14	−0.703366
$328$	−11549.5	−1.94425
$329$	−9594.72	−1.60782
$330$	4391.73	0.732596
$331$	−10031.0	−1.66571	−0.832857	−	0.553488i	$-0.813297\pi$
$331$	−10031.0	−1.66571	−0.832857	+	0.553488i	$0.813297\pi$
$332$	−13514.4	−2.23403
$333$	−2841.97	−0.467684
$334$	−3604.07	−0.590437
$335$	4441.16	0.724318
$336$	−8039.39	−1.30531
$337$	2538.16	0.410274	0.205137	−	0.978733i	$-0.434236\pi$
$337$	2538.16	0.410274	0.205137	+	0.978733i	$0.434236\pi$
$338$	2548.12	0.410058
$339$	1431.31	0.229316
$340$	−6663.35	−1.06286
$341$	−114.886	−0.0182447
$342$	30.3708	0.00480194
$343$	4619.90	0.727263
$344$	−4270.32	−0.669304
$345$	1442.51	0.225107
$346$	8708.98	1.35317
$347$	8139.07	1.25916	0.629579	−	0.776936i	$-0.283227\pi$
$347$	8139.07	1.25916	0.629579	+	0.776936i	$0.283227\pi$
$348$	−1587.93	−0.244603
$349$	3054.95	0.468561	0.234280	−	0.972169i	$-0.424727\pi$
$349$	3054.95	0.468561	0.234280	+	0.972169i	$0.424727\pi$
$350$	2788.00	0.425786
$351$	−1113.13	−0.169272
$352$	−12034.6	−1.82228
$353$	−4993.98	−0.752982	−0.376491	−	0.926420i	$-0.622869\pi$
$353$	−4993.98	−0.752982	−0.376491	+	0.926420i	$0.622869\pi$
$354$	8477.42	1.27280
$355$	2853.51	0.426616
$356$	−16343.1	−2.43310
$357$	−4767.65	−0.706809
$358$	8284.32	1.22302
$359$	−3701.99	−0.544245	−0.272122	−	0.962263i	$-0.587726\pi$
$359$	−3701.99	−0.544245	−0.272122	+	0.962263i	$0.587726\pi$
$360$	2363.76	0.346059
$361$	−6858.57	−0.999937
$362$	−4049.81	−0.587993
$363$	5802.96	0.839054
$364$	16378.2	2.35838
$365$	−3321.32	−0.476290
$366$	2298.52	0.328267
$367$	−1936.81	−0.275478	−0.137739	−	0.990469i	$-0.543984\pi$
$367$	−1936.81	−0.275478	−0.137739	+	0.990469i	$0.543984\pi$
$368$	−11840.1	−1.67720
$369$	1978.86	0.279174
$370$	−8089.61	−1.13665
$371$	−1433.45	−0.200596
$372$	−110.087	−0.0153435
$373$	12540.1	1.74075	0.870376	−	0.492387i	$-0.163876\pi$
$373$	12540.1	1.74075	0.870376	+	0.492387i	$0.163876\pi$
$374$	−21377.4	−2.95562
$375$	−375.000	−0.0516398
$376$	−23155.4	−3.17593
$377$	1195.59	0.163331
$378$	3011.04	0.409713
$379$	7644.03	1.03601	0.518005	−	0.855378i	$-0.326675\pi$
$379$	7644.03	1.03601	0.518005	+	0.855378i	$0.326675\pi$
$380$	60.1054	0.00811405
$381$	−4072.51	−0.547614
$382$	15198.6	2.03567
$383$	13834.6	1.84574	0.922868	−	0.385115i	$-0.125838\pi$
$383$	13834.6	1.84574	0.922868	+	0.385115i	$0.125838\pi$
$384$	3608.02	0.479482
$385$	6218.77	0.823215
$386$	9589.24	1.26445
$387$	731.664	0.0961049
$388$	−12879.8	−1.68524
$389$	−14818.0	−1.93137	−0.965684	−	0.259719i	$-0.916370\pi$
$389$	−14818.0	−1.93137	−0.965684	+	0.259719i	$0.916370\pi$
$390$	−3168.52	−0.411395
$391$	−7021.64	−0.908183
$392$	−6867.71	−0.884877
$393$	8984.52	1.15320
$394$	9047.14	1.15682
$395$	−1109.78	−0.141365
$396$	9386.78	1.19117
$397$	−2846.02	−0.359792	−0.179896	−	0.983686i	$-0.557576\pi$
$397$	−2846.02	−0.359792	−0.179896	+	0.983686i	$0.557576\pi$
$398$	784.281	0.0987750
$399$	43.0056	0.00539592
$400$	3078.01	0.384751
$401$	7701.88	0.959136	0.479568	−	0.877505i	$-0.340793\pi$
$401$	7701.88	0.959136	0.479568	+	0.877505i	$0.340793\pi$
$402$	13653.0	1.69391
$403$	82.8874	0.0102454
$404$	−23552.6	−2.90046
$405$	−405.000	−0.0496904
$406$	−3234.08	−0.395332
$407$	−18044.3	−2.19759
$408$	−11506.0	−1.39616
$409$	−10969.5	−1.32618	−0.663088	−	0.748541i	$-0.730755\pi$
$409$	−10969.5	−1.32618	−0.663088	+	0.748541i	$0.730755\pi$
$410$	5632.79	0.678497
$411$	−3203.30	−0.384445
$412$	16388.7	1.95974
$413$	12004.2	1.43024
$414$	4434.57	0.526442
$415$	3702.16	0.437908
$416$	8682.61	1.02332
$417$	−2529.94	−0.297103
$418$	192.831	0.0225638
$419$	−10760.9	−1.25467	−0.627335	−	0.778750i	$-0.715854\pi$
$419$	−10760.9	−1.25467	−0.627335	+	0.778750i	$0.715854\pi$
$420$	5959.01	0.692309
$421$	−3562.20	−0.412378	−0.206189	−	0.978512i	$-0.566106\pi$
$421$	−3562.20	−0.412378	−0.206189	+	0.978512i	$0.566106\pi$
$422$	−28860.9	−3.32921
$423$	3967.38	0.456029
$424$	−3459.41	−0.396236
$425$	1825.37	0.208338
$426$	8772.27	0.997695
$427$	3254.75	0.368872
$428$	−37965.7	−4.28772
$429$	−7067.52	−0.795392
$430$	2082.67	0.233571
$431$	−1086.78	−0.121458	−0.0607290	−	0.998154i	$-0.519343\pi$
$431$	−1086.78	−0.121458	−0.0607290	+	0.998154i	$0.519343\pi$
$432$	3324.25	0.370227
$433$	4185.80	0.464565	0.232282	−	0.972648i	$-0.425381\pi$
$433$	4185.80	0.464565	0.232282	+	0.972648i	$0.425381\pi$
$434$	−224.212	−0.0247984
$435$	435.000	0.0479463
$436$	−25304.2	−2.77948
$437$	63.3372	0.00693325
$438$	−10210.4	−1.11386
$439$	3960.69	0.430600	0.215300	−	0.976548i	$-0.430927\pi$
$439$	3960.69	0.430600	0.215300	+	0.976548i	$0.430927\pi$
$440$	15008.1	1.62609
$441$	1176.69	0.127059
$442$	15423.3	1.65975
$443$	1695.58	0.181850	0.0909250	−	0.995858i	$-0.471018\pi$
$443$	1695.58	0.181850	0.0909250	+	0.995858i	$0.471018\pi$
$444$	−17290.5	−1.84814
$445$	4477.07	0.476930
$446$	15180.9	1.61174
$447$	3821.14	0.404326
$448$	−2048.24	−0.216005
$449$	655.044	0.0688495	0.0344248	−	0.999407i	$-0.489040\pi$
$449$	655.044	0.0688495	0.0344248	+	0.999407i	$0.489040\pi$
$450$	−1152.83	−0.120766
$451$	12564.2	1.31181
$452$	8708.11	0.906183
$453$	−9091.73	−0.942973
$454$	5158.58	0.533269
$455$	−4486.68	−0.462283
$456$	103.787	0.0106585
$457$	10691.4	1.09437	0.547183	−	0.837013i	$-0.315700\pi$
$457$	10691.4	1.09437	0.547183	+	0.837013i	$0.315700\pi$
$458$	6646.96	0.678148
$459$	1971.40	0.200473
$460$	8776.24	0.889553
$461$	15258.6	1.54157	0.770783	−	0.637098i	$-0.219865\pi$
$461$	15258.6	1.54157	0.770783	+	0.637098i	$0.219865\pi$
$462$	19117.8	1.92519
$463$	−9359.99	−0.939515	−0.469758	−	0.882795i	$-0.655659\pi$
$463$	−9359.99	−0.939515	−0.469758	+	0.882795i	$0.655659\pi$
$464$	−3570.49	−0.357233
$465$	30.1576	0.00300758
$466$	8453.40	0.840335
$467$	11840.9	1.17330	0.586651	−	0.809840i	$-0.300446\pi$
$467$	11840.9	1.17330	0.586651	+	0.809840i	$0.300446\pi$
$468$	−6772.31	−0.668911
$469$	19333.0	1.90344
$470$	11293.1	1.10832
$471$	−4540.70	−0.444213
$472$	28970.3	2.82514
$473$	4645.50	0.451586
$474$	−3411.70	−0.330600
$475$	−16.4654	−0.00159049
$476$	−29006.4	−2.79308
$477$	592.725	0.0568953
$478$	−29227.5	−2.79672
$479$	581.072	0.0554277	0.0277139	−	0.999616i	$-0.491177\pi$
$479$	581.072	0.0554277	0.0277139	+	0.999616i	$0.491177\pi$
$480$	3159.06	0.300398
$481$	13018.5	1.23408
$482$	−37064.6	−3.50258
$483$	6279.43	0.591561
$484$	35305.3	3.31567
$485$	3528.33	0.330336
$486$	−1245.05	−0.116207
$487$	−5996.94	−0.558003	−0.279001	−	0.960291i	$-0.590003\pi$
$487$	−5996.94	−0.558003	−0.279001	+	0.960291i	$0.590003\pi$
$488$	7854.84	0.728631
$489$	−9404.65	−0.869720
$490$	3349.44	0.308800
$491$	18570.0	1.70683	0.853414	−	0.521234i	$-0.174528\pi$
$491$	18570.0	1.70683	0.853414	+	0.521234i	$0.174528\pi$
$492$	12039.4	1.10321
$493$	−2117.43	−0.193437
$494$	−139.122	−0.0126709
$495$	−2571.43	−0.233490
$496$	−247.534	−0.0224085
$497$	12421.7	1.12111
$498$	11381.2	1.02410
$499$	3462.43	0.310621	0.155310	−	0.987866i	$-0.450362\pi$
$499$	3462.43	0.310621	0.155310	+	0.987866i	$0.450362\pi$
$500$	−2281.50	−0.204064
$501$	2110.25	0.188181
$502$	−30167.9	−2.68219
$503$	−2437.40	−0.216060	−0.108030	−	0.994148i	$-0.534454\pi$
$503$	−2437.40	−0.216060	−0.108030	+	0.994148i	$0.534454\pi$
$504$	10289.8	0.909410
$505$	6452.05	0.568540
$506$	28156.0	2.47369
$507$	−1491.97	−0.130692
$508$	−24777.2	−2.16399
$509$	−17387.0	−1.51407	−0.757037	−	0.653372i	$-0.773354\pi$
$509$	−17387.0	−1.51407	−0.757037	+	0.653372i	$0.773354\pi$
$510$	5611.57	0.487224
$511$	−14458.1	−1.25165
$512$	25808.5	2.22771
$513$	−17.7826	−0.00153045
$514$	−29467.9	−2.52874
$515$	−4489.56	−0.384143
$516$	4451.45	0.379776
$517$	25189.7	2.14283
$518$	−35215.1	−2.98700
$519$	−5099.26	−0.431277
$520$	−10827.9	−0.913145
$521$	−13912.4	−1.16989	−0.584945	−	0.811073i	$-0.698884\pi$
$521$	−13912.4	−1.16989	−0.584945	+	0.811073i	$0.698884\pi$
$522$	1337.28	0.112129
$523$	4178.69	0.349371	0.174686	−	0.984624i	$-0.444109\pi$
$523$	4178.69	0.349371	0.174686	+	0.984624i	$0.444109\pi$
$524$	54661.9	4.55709
$525$	−1632.42	−0.135704
$526$	−26625.3	−2.20707
$527$	−146.797	−0.0121339
$528$	21106.4	1.73966
$529$	−2918.86	−0.239900
$530$	1687.18	0.138277
$531$	−4963.68	−0.405659
$532$	261.647	0.0213230
$533$	−9064.73	−0.736655
$534$	13763.4	1.11536
$535$	10400.4	0.840465
$536$	46657.1	3.75985
$537$	−4850.61	−0.389794
$538$	36899.0	2.95693
$539$	7471.08	0.597036
$540$	−2464.02	−0.196361
$541$	15727.3	1.24985	0.624927	−	0.780683i	$-0.285129\pi$
$541$	15727.3	1.24985	0.624927	+	0.780683i	$0.285129\pi$
$542$	7741.72	0.613534
$543$	2371.24	0.187402
$544$	−15377.2	−1.21194
$545$	6931.89	0.544825
$546$	−13793.0	−1.08111
$547$	−17384.0	−1.35884	−0.679420	−	0.733750i	$-0.737769\pi$
$547$	−17384.0	−1.35884	−0.679420	+	0.733750i	$0.737769\pi$
$548$	−19488.9	−1.51920
$549$	−1345.82	−0.104624
$550$	−7319.55	−0.567467
$551$	19.0999	0.00147674
$552$	15154.4	1.16851
$553$	−4831.02	−0.371494
$554$	−35387.1	−2.71382
$555$	4736.61	0.362266
$556$	−15392.2	−1.17405
$557$	−18853.0	−1.43416	−0.717080	−	0.696991i	$-0.754522\pi$
$557$	−18853.0	−1.43416	−0.717080	+	0.696991i	$0.754522\pi$
$558$	92.7106	0.00703360
$559$	−3351.60	−0.253592
$560$	13399.0	1.01109
$561$	12516.9	0.942001
$562$	28454.3	2.13571
$563$	6897.37	0.516323	0.258161	−	0.966102i	$-0.416883\pi$
$563$	6897.37	0.516323	0.258161	+	0.966102i	$0.416883\pi$
$564$	24137.6	1.80208
$565$	−2385.52	−0.177627
$566$	4646.20	0.345043
$567$	−1763.02	−0.130582
$568$	29977.9	2.21451
$569$	4008.52	0.295336	0.147668	−	0.989037i	$-0.452823\pi$
$569$	4008.52	0.295336	0.147668	+	0.989037i	$0.452823\pi$
$570$	−50.6180	−0.00371957
$571$	−6259.59	−0.458766	−0.229383	−	0.973336i	$-0.573671\pi$
$571$	−6259.59	−0.458766	−0.229383	+	0.973336i	$0.573671\pi$
$572$	−42998.9	−3.14314
$573$	−8899.02	−0.648799
$574$	24520.3	1.78302
$575$	−2404.18	−0.174367
$576$	846.937	0.0612657
$577$	−12282.9	−0.886208	−0.443104	−	0.896470i	$-0.646123\pi$
$577$	−12282.9	−0.886208	−0.443104	+	0.896470i	$0.646123\pi$
$578$	−2142.58	−0.154186
$579$	−5614.66	−0.403001
$580$	2646.54	0.189469
$581$	16116.0	1.15078
$582$	10846.8	0.772533
$583$	3763.34	0.267344
$584$	−34892.5	−2.47237
$585$	1855.22	0.131118
$586$	−2451.44	−0.172813
$587$	−3526.91	−0.247992	−0.123996	−	0.992283i	$-0.539571\pi$
$587$	−3526.91	−0.247992	−0.123996	+	0.992283i	$0.539571\pi$
$588$	7159.01	0.502096
$589$	1.32415	9.26327e−5 0
$590$	−14129.0	−0.985903
$591$	−5297.26	−0.368697
$592$	−38878.2	−2.69913
$593$	−14783.4	−1.02375	−0.511875	−	0.859060i	$-0.671049\pi$
$593$	−14783.4	−1.02375	−0.511875	+	0.859060i	$0.671049\pi$
$594$	−7905.11	−0.546045
$595$	7946.08	0.547492
$596$	23247.9	1.59777
$597$	−459.210	−0.0314811
$598$	−20313.8	−1.38912
$599$	23249.3	1.58588	0.792940	−	0.609300i	$-0.208549\pi$
$599$	23249.3	1.58588	0.792940	+	0.609300i	$0.208549\pi$
$600$	−3939.60	−0.268056
$601$	−15134.4	−1.02720	−0.513599	−	0.858031i	$-0.671688\pi$
$601$	−15134.4	−1.02720	−0.513599	+	0.858031i	$0.671688\pi$
$602$	9066.14	0.613801
$603$	−7994.09	−0.539875
$604$	−55314.2	−3.72633
$605$	−9671.60	−0.649928
$606$	19834.9	1.32960
$607$	−26346.6	−1.76174	−0.880870	−	0.473358i	$-0.843042\pi$
$607$	−26346.6	−1.76174	−0.880870	+	0.473358i	$0.843042\pi$
$608$	138.707	0.00925217
$609$	1893.61	0.125998
$610$	−3830.87	−0.254274
$611$	−18173.7	−1.20332
$612$	11994.0	0.792206
$613$	3259.35	0.214754	0.107377	−	0.994218i	$-0.465755\pi$
$613$	3259.35	0.214754	0.107377	+	0.994218i	$0.465755\pi$
$614$	41353.9	2.71809
$615$	−3298.10	−0.216247
$616$	65332.0	4.27322
$617$	−6482.74	−0.422990	−0.211495	−	0.977379i	$-0.567833\pi$
$617$	−6482.74	−0.422990	−0.211495	+	0.977379i	$0.567833\pi$
$618$	−13801.8	−0.898367
$619$	−3720.63	−0.241591	−0.120796	−	0.992677i	$-0.538545\pi$
$619$	−3720.63	−0.241591	−0.120796	+	0.992677i	$0.538545\pi$
$620$	183.479	0.0118850
$621$	−2596.52	−0.167785
$622$	11231.1	0.723994
$623$	19489.3	1.25333
$624$	−15227.7	−0.976917
$625$	625.000	0.0400000
$626$	−56027.4	−3.57717
$627$	−112.906	−0.00719142
$628$	−27625.6	−1.75539
$629$	−23056.2	−1.46154
$630$	−5018.40	−0.317362
$631$	−13113.6	−0.827328	−0.413664	−	0.910430i	$-0.635751\pi$
$631$	−13113.6	−0.827328	−0.413664	+	0.910430i	$0.635751\pi$
$632$	−11658.9	−0.733809
$633$	16898.6	1.06107
$634$	−44270.2	−2.77318
$635$	6787.51	0.424180
$636$	3606.15	0.224832
$637$	−5390.19	−0.335270
$638$	8490.68	0.526880
$639$	−5136.32	−0.317981
$640$	−6013.37	−0.371405
$641$	25815.2	1.59070	0.795352	−	0.606148i	$-0.207286\pi$
$641$	25815.2	1.59070	0.795352	+	0.606148i	$0.207286\pi$
$642$	31973.0	1.96553
$643$	9425.88	0.578103	0.289052	−	0.957313i	$-0.406660\pi$
$643$	9425.88	0.578103	0.289052	+	0.957313i	$0.406660\pi$
$644$	38204.1	2.33766
$645$	−1219.44	−0.0744425
$646$	246.391	0.0150064
$647$	2734.65	0.166167	0.0830836	−	0.996543i	$-0.473523\pi$
$647$	2734.65	0.166167	0.0830836	+	0.996543i	$0.473523\pi$
$648$	−4254.77	−0.257937
$649$	−31515.5	−1.90615
$650$	5280.86	0.318665
$651$	131.280	0.00790363
$652$	−57218.0	−3.43686
$653$	602.998	0.0361365	0.0180683	−	0.999837i	$-0.494248\pi$
$653$	602.998	0.0361365	0.0180683	+	0.999837i	$0.494248\pi$
$654$	21310.1	1.27414
$655$	−14974.2	−0.893268
$656$	27070.9	1.61119
$657$	5978.38	0.355006
$658$	49160.2	2.91256
$659$	−23932.8	−1.41470	−0.707352	−	0.706862i	$-0.750110\pi$
$659$	−23932.8	−1.41470	−0.707352	+	0.706862i	$0.750110\pi$
$660$	−15644.6	−0.922676
$661$	−12965.0	−0.762905	−0.381452	−	0.924388i	$-0.624576\pi$
$661$	−12965.0	−0.762905	−0.381452	+	0.924388i	$0.624576\pi$
$662$	51395.4	3.01743
$663$	−9030.58	−0.528988
$664$	38893.4	2.27313
$665$	−71.6760	−0.00417966
$666$	14561.3	0.847206
$667$	2788.85	0.161896
$668$	12838.8	0.743633
$669$	−8888.67	−0.513686
$670$	−22755.1	−1.31210
$671$	−8544.94	−0.491615
$672$	13751.8	0.789416
$673$	−4523.17	−0.259072	−0.129536	−	0.991575i	$-0.541349\pi$
$673$	−4523.17	−0.259072	−0.129536	+	0.991575i	$0.541349\pi$
$674$	−13004.7	−0.743208
$675$	675.000	0.0384900
$676$	−9077.16	−0.516452
$677$	−17685.7	−1.00401	−0.502007	−	0.864863i	$-0.667405\pi$
$677$	−17685.7	−1.00401	−0.502007	+	0.864863i	$0.667405\pi$
$678$	−7333.57	−0.415404
$679$	15359.3	0.868093
$680$	19176.6	1.08146
$681$	−3020.44	−0.169961
$682$	588.640	0.0330501
$683$	31140.8	1.74461	0.872307	−	0.488958i	$-0.162623\pi$
$683$	31140.8	1.74461	0.872307	+	0.488958i	$0.162623\pi$
$684$	−108.190	−0.00604786
$685$	5338.83	0.297790
$686$	−23670.8	−1.31743
$687$	−3891.91	−0.216136
$688$	10009.2	0.554647
$689$	−2715.15	−0.150129
$690$	−7390.94	−0.407780
$691$	−18166.3	−1.00012	−0.500058	−	0.865992i	$-0.666688\pi$
$691$	−18166.3	−1.00012	−0.500058	+	0.865992i	$0.666688\pi$
$692$	−31024.0	−1.70427
$693$	−11193.8	−0.613589
$694$	−41701.9	−2.28096
$695$	4216.57	0.230135
$696$	4569.94	0.248884
$697$	16054.0	0.872437
$698$	−15652.6	−0.848794
$699$	−4949.61	−0.267828
$700$	−9931.68	−0.536261
$701$	−11583.6	−0.624120	−0.312060	−	0.950062i	$-0.601019\pi$
$701$	−11583.6	−0.624120	−0.312060	+	0.950062i	$0.601019\pi$
$702$	5703.33	0.306636
$703$	207.974	0.0111577
$704$	5377.39	0.287881
$705$	−6612.29	−0.353239
$706$	25587.5	1.36402
$707$	28086.6	1.49407
$708$	−30199.1	−1.60304
$709$	−20232.9	−1.07174	−0.535869	−	0.844301i	$-0.680016\pi$
$709$	−20232.9	−1.07174	−0.535869	+	0.844301i	$0.680016\pi$
$710$	−14620.5	−0.772811
$711$	1997.61	0.105367
$712$	47034.4	2.47569
$713$	193.345	0.0101554
$714$	24427.9	1.28038
$715$	11779.2	0.616108
$716$	−29511.2	−1.54034
$717$	17113.2	0.891359
$718$	18967.8	0.985895
$719$	16489.7	0.855304	0.427652	−	0.903943i	$-0.359341\pi$
$719$	16489.7	0.855304	0.427652	+	0.903943i	$0.359341\pi$
$720$	−5540.42	−0.286777
$721$	−19543.6	−1.00949
$722$	35141.1	1.81138
$723$	21702.0	1.11633
$724$	14426.6	0.740554
$725$	−725.000	−0.0371391
$726$	−29732.5	−1.51994
$727$	27239.4	1.38962	0.694810	−	0.719194i	$-0.255489\pi$
$727$	27239.4	1.38962	0.694810	+	0.719194i	$0.255489\pi$
$728$	−47135.3	−2.39966
$729$	729.000	0.0370370
$730$	17017.4	0.862796
$731$	5935.82	0.300334
$732$	−8188.01	−0.413439
$733$	−8145.16	−0.410434	−0.205217	−	0.978716i	$-0.565790\pi$
$733$	−8145.16	−0.410434	−0.205217	+	0.978716i	$0.565790\pi$
$734$	9923.57	0.499027
$735$	−1961.15	−0.0984194
$736$	20253.2	1.01433
$737$	−50756.3	−2.53681
$738$	−10139.0	−0.505721
$739$	23926.8	1.19102	0.595508	−	0.803349i	$-0.296951\pi$
$739$	23926.8	1.19102	0.595508	+	0.803349i	$0.296951\pi$
$740$	28817.6	1.43156
$741$	81.4585	0.00403840
$742$	7344.53	0.363378
$743$	−2938.74	−0.145103	−0.0725517	−	0.997365i	$-0.523114\pi$
$743$	−2938.74	−0.145103	−0.0725517	+	0.997365i	$0.523114\pi$
$744$	316.824	0.0156120
$745$	−6368.57	−0.313190
$746$	−64251.3	−3.15336
$747$	−6663.89	−0.326397
$748$	76152.7	3.72249
$749$	45274.3	2.20866
$750$	1921.38	0.0935451
$751$	7625.31	0.370508	0.185254	−	0.982691i	$-0.440689\pi$
$751$	7625.31	0.370508	0.185254	+	0.982691i	$0.440689\pi$
$752$	54273.9	2.63187
$753$	17663.8	0.854855
$754$	−6125.80	−0.295873
$755$	15152.9	0.730424
$756$	−10726.2	−0.516017
$757$	−1641.02	−0.0787898	−0.0393949	−	0.999224i	$-0.512543\pi$
$757$	−1641.02	−0.0787898	−0.0393949	+	0.999224i	$0.512543\pi$
$758$	−39165.5	−1.87672
$759$	−16485.8	−0.788404
$760$	−172.979	−0.00825606
$761$	−18376.8	−0.875374	−0.437687	−	0.899127i	$-0.644202\pi$
$761$	−18376.8	−0.875374	−0.437687	+	0.899127i	$0.644202\pi$
$762$	20866.2	0.991998
$763$	30175.4	1.43175
$764$	−54141.8	−2.56385
$765$	−3285.67	−0.155286
$766$	−70884.2	−3.34354
$767$	22737.6	1.07041
$768$	−20744.8	−0.974694
$769$	−16315.5	−0.765085	−0.382543	−	0.923938i	$-0.624951\pi$
$769$	−16315.5	−0.765085	−0.382543	+	0.923938i	$0.624951\pi$
$770$	−31863.0	−1.49125
$771$	17254.0	0.805950
$772$	−34159.7	−1.59253
$773$	−1255.81	−0.0584325	−0.0292163	−	0.999573i	$-0.509301\pi$
$773$	−1255.81	−0.0584325	−0.0292163	+	0.999573i	$0.509301\pi$
$774$	−3748.81	−0.174093
$775$	−50.2626	−0.00232966
$776$	37067.3	1.71474
$777$	20619.1	0.952002
$778$	75922.6	3.49866
$779$	−144.812	−0.00666036
$780$	11287.2	0.518136
$781$	−32611.6	−1.49415
$782$	35976.6	1.64517
$783$	−783.000	−0.0357371
$784$	16097.2	0.733291
$785$	7567.83	0.344086
$786$	−46033.8	−2.08902
$787$	−18667.8	−0.845534	−0.422767	−	0.906238i	$-0.638941\pi$
$787$	−18667.8	−0.845534	−0.422767	+	0.906238i	$0.638941\pi$
$788$	−32228.6	−1.45697
$789$	15589.6	0.703428
$790$	5686.16	0.256082
$791$	−10384.5	−0.466788
$792$	−27014.5	−1.21202
$793$	6164.94	0.276070
$794$	14582.1	0.651761
$795$	−987.876	−0.0440709
$796$	−2793.84	−0.124403
$797$	−7280.08	−0.323556	−0.161778	−	0.986827i	$-0.551723\pi$
$797$	−7280.08	−0.323556	−0.161778	+	0.986827i	$0.551723\pi$
$798$	−220.347	−0.00977467
$799$	32186.4	1.42512
$800$	−5265.11	−0.232687
$801$	−8058.73	−0.355482
$802$	−39461.9	−1.73747
$803$	37958.1	1.66813
$804$	−48636.2	−2.13341
$805$	−10465.7	−0.458221
$806$	−424.688	−0.0185595
$807$	−21605.0	−0.942418
$808$	67782.8	2.95122
$809$	44097.9	1.91644	0.958221	−	0.286030i	$-0.0923356\pi$
$809$	44097.9	1.91644	0.958221	+	0.286030i	$0.0923356\pi$
$810$	2075.09	0.0900138
$811$	−17249.1	−0.746854	−0.373427	−	0.927660i	$-0.621817\pi$
$811$	−17249.1	−0.746854	−0.373427	+	0.927660i	$0.621817\pi$
$812$	11520.8	0.497905
$813$	−4532.91	−0.195543
$814$	92452.9	3.98093
$815$	15674.4	0.673682
$816$	26968.9	1.15698
$817$	−53.5428	−0.00229281
$818$	56204.1	2.40236
$819$	8076.02	0.344565
$820$	−20065.6	−0.854540
$821$	11201.7	0.476177	0.238088	−	0.971244i	$-0.423479\pi$
$821$	11201.7	0.476177	0.238088	+	0.971244i	$0.423479\pi$
$822$	16412.6	0.696419
$823$	12114.8	0.513118	0.256559	−	0.966529i	$-0.417411\pi$
$823$	12114.8	0.513118	0.256559	+	0.966529i	$0.417411\pi$
$824$	−47165.6	−1.99404
$825$	4285.72	0.180860
$826$	−61505.5	−2.59086
$827$	37074.2	1.55888	0.779442	−	0.626474i	$-0.215502\pi$
$827$	37074.2	1.55888	0.779442	+	0.626474i	$0.215502\pi$
$828$	−15797.2	−0.663033
$829$	611.209	0.0256069	0.0128035	−	0.999918i	$-0.495924\pi$
$829$	611.209	0.0256069	0.0128035	+	0.999918i	$0.495924\pi$
$830$	−18968.7	−0.793267
$831$	20719.8	0.864935
$832$	−3879.64	−0.161662
$833$	9546.23	0.397068
$834$	12962.6	0.538199
$835$	−3517.08	−0.145765
$836$	−686.920	−0.0284182
$837$	−54.2837	−0.00224172
$838$	55135.6	2.27282
$839$	−43306.8	−1.78202	−0.891010	−	0.453983i	$-0.850003\pi$
$839$	−43306.8	−1.78202	−0.891010	+	0.453983i	$0.850003\pi$
$840$	−17149.6	−0.704426
$841$	841.000	0.0344828
$842$	18251.6	0.747020
$843$	−16660.5	−0.680685
$844$	102811.	4.19301
$845$	2486.62	0.101233
$846$	−20327.5	−0.826094
$847$	−42101.7	−1.70795
$848$	8108.51	0.328358
$849$	−2720.43	−0.109971
$850$	−9352.61	−0.377402
$851$	30367.1	1.22323
$852$	−31249.4	−1.25656
$853$	−3447.15	−0.138368	−0.0691842	−	0.997604i	$-0.522040\pi$
$853$	−3447.15	−0.138368	−0.0691842	+	0.997604i	$0.522040\pi$
$854$	−16676.3	−0.668209
$855$	29.6377	0.00118548
$856$	109263.	4.36276
$857$	−42416.7	−1.69069	−0.845347	−	0.534217i	$-0.820607\pi$
$857$	−42416.7	−1.69069	−0.845347	+	0.534217i	$0.820607\pi$
$858$	36211.7	1.44085
$859$	29061.5	1.15433	0.577163	−	0.816629i	$-0.304160\pi$
$859$	29061.5	1.15433	0.577163	+	0.816629i	$0.304160\pi$
$860$	−7419.09	−0.294173
$861$	−14357.0	−0.568277
$862$	5568.31	0.220020
$863$	20744.0	0.818232	0.409116	−	0.912482i	$-0.365837\pi$
$863$	20744.0	0.818232	0.409116	+	0.912482i	$0.365837\pi$
$864$	−5686.31	−0.223903
$865$	8498.77	0.334066
$866$	−21446.7	−0.841556
$867$	1254.52	0.0491414
$868$	798.708	0.0312326
$869$	12683.2	0.495109
$870$	−2228.80	−0.0868544
$871$	36619.3	1.42457
$872$	72823.8	2.82812
$873$	−6350.99	−0.246218
$874$	−324.519	−0.0125595
$875$	2720.71	0.105116
$876$	36372.5	1.40287
$877$	−26329.7	−1.01379	−0.506893	−	0.862009i	$-0.669206\pi$
$877$	−26329.7	−1.01379	−0.506893	+	0.862009i	$0.669206\pi$
$878$	−20293.3	−0.780028
$879$	1435.36	0.0550780
$880$	−35177.3	−1.34753
$881$	−7199.40	−0.275317	−0.137658	−	0.990480i	$-0.543958\pi$
$881$	−7199.40	−0.275317	−0.137658	+	0.990480i	$0.543958\pi$
$882$	−6028.99	−0.230166
$883$	64.9911	0.00247693	0.00123846	−	0.999999i	$-0.499606\pi$
$883$	64.9911	0.00247693	0.00123846	+	0.999999i	$0.499606\pi$
$884$	−54942.2	−2.09039
$885$	8272.79	0.314222
$886$	−8687.61	−0.329420
$887$	12243.2	0.463456	0.231728	−	0.972781i	$-0.425562\pi$
$887$	12243.2	0.463456	0.231728	+	0.972781i	$0.425562\pi$
$888$	49761.0	1.88048
$889$	29546.9	1.11470
$890$	−22939.1	−0.863954
$891$	4628.58	0.174033
$892$	−54078.8	−2.02992
$893$	−290.331	−0.0108797
$894$	−19578.3	−0.732433
$895$	8084.36	0.301933
$896$	−26177.0	−0.976018
$897$	11894.1	0.442734
$898$	−3356.23	−0.124720
$899$	58.3047	0.00216304
$900$	4106.71	0.152100
$901$	4808.64	0.177801
$902$	−64374.9	−2.37633
$903$	−5308.38	−0.195628
$904$	−25061.3	−0.922043
$905$	−3952.06	−0.145161
$906$	46583.1	1.70819
$907$	30619.9	1.12097	0.560483	−	0.828166i	$-0.310616\pi$
$907$	30619.9	1.12097	0.560483	+	0.828166i	$0.310616\pi$
$908$	−18376.4	−0.671631
$909$	−11613.7	−0.423764
$910$	22988.3	0.837422
$911$	3062.05	0.111362	0.0556808	−	0.998449i	$-0.482267\pi$
$911$	3062.05	0.111362	0.0556808	+	0.998449i	$0.482267\pi$
$912$	−243.267	−0.00883265
$913$	−42310.5	−1.53370
$914$	−54779.5	−1.98243
$915$	2243.04	0.0810412
$916$	−23678.4	−0.854101
$917$	−65184.7	−2.34742
$918$	−10100.8	−0.363155
$919$	−1527.71	−0.0548361	−0.0274180	−	0.999624i	$-0.508729\pi$
$919$	−1527.71	−0.0548361	−0.0274180	+	0.999624i	$0.508729\pi$
$920$	−25257.4	−0.905121
$921$	−24213.4	−0.866296
$922$	−78179.9	−2.79253
$923$	23528.4	0.839054
$924$	−68103.1	−2.42471
$925$	−7894.35	−0.280610
$926$	47957.5	1.70192
$927$	8081.21	0.286323
$928$	6107.52	0.216044
$929$	−968.476	−0.0342031	−0.0171015	−	0.999854i	$-0.505444\pi$
$929$	−968.476	−0.0342031	−0.0171015	+	0.999854i	$0.505444\pi$
$930$	−154.518	−0.00544821
$931$	−86.1098	−0.00303129
$932$	−30113.5	−1.05837
$933$	−6575.98	−0.230748
$934$	−60669.0	−2.12543
$935$	−20861.4	−0.729671
$936$	19490.2	0.680618
$937$	−47051.9	−1.64047	−0.820234	−	0.572029i	$-0.806157\pi$
$937$	−47051.9	−1.64047	−0.820234	+	0.572029i	$0.806157\pi$
$938$	−99055.8	−3.44807
$939$	32805.0	1.14010
$940$	−40229.3	−1.39589
$941$	−31285.3	−1.08382	−0.541908	−	0.840438i	$-0.682298\pi$
$941$	−31285.3	−1.08382	−0.541908	+	0.840438i	$0.682298\pi$
$942$	23265.0	0.804688
$943$	−21144.6	−0.730183
$944$	−67903.3	−2.34117
$945$	2938.36	0.101148
$946$	−23802.0	−0.818045
$947$	−1155.25	−0.0396416	−0.0198208	−	0.999804i	$-0.506310\pi$
$947$	−1155.25	−0.0396416	−0.0198208	+	0.999804i	$0.506310\pi$
$948$	12153.5	0.416378
$949$	−27385.7	−0.936752
$950$	84.3633	0.00288116
$951$	25921.0	0.883853
$952$	83478.5	2.84197
$953$	8073.69	0.274431	0.137215	−	0.990541i	$-0.456185\pi$
$953$	8073.69	0.274431	0.137215	+	0.990541i	$0.456185\pi$
$954$	−3036.93	−0.103065
$955$	14831.7	0.502558
$956$	104117.	3.52236
$957$	−4971.44	−0.167925
$958$	−2977.22	−0.100407
$959$	23240.6	0.782563
$960$	−1411.56	−0.0474562
$961$	−29787.0	−0.999864
$962$	−66702.3	−2.23552
$963$	−18720.7	−0.626446
$964$	132035.	4.41137
$965$	9357.77	0.312163
$966$	−32173.7	−1.07161
$967$	30587.8	1.01721	0.508603	−	0.861001i	$-0.330162\pi$
$967$	30587.8	1.01721	0.508603	+	0.861001i	$0.330162\pi$
$968$	−101606.	−3.37370
$969$	−144.266	−0.00478276
$970$	−18078.0	−0.598402
$971$	−37585.6	−1.24220	−0.621101	−	0.783730i	$-0.713314\pi$
$971$	−37585.6	−1.24220	−0.621101	+	0.783730i	$0.713314\pi$
$972$	4435.24	0.146359
$973$	18355.3	0.604772
$974$	30726.4	1.01082
$975$	−3092.04	−0.101563
$976$	−18410.9	−0.603811
$977$	605.357	0.0198230	0.00991151	−	0.999951i	$-0.496845\pi$
$977$	605.357	0.0198230	0.00991151	+	0.999951i	$0.496845\pi$
$978$	48186.4	1.57549
$979$	−51166.7	−1.67037
$980$	−11931.7	−0.388922
$981$	−12477.4	−0.406089
$982$	−95146.6	−3.09190
$983$	24370.9	0.790755	0.395378	−	0.918519i	$-0.370614\pi$
$983$	24370.9	0.790755	0.395378	+	0.918519i	$0.370614\pi$
$984$	−34648.5	−1.12251
$985$	8828.77	0.285592
$986$	10849.0	0.350409
$987$	−28784.2	−0.928278
$988$	495.594	0.0159585
$989$	−7818.02	−0.251363
$990$	13175.2	0.422965
$991$	53287.8	1.70812	0.854058	−	0.520178i	$-0.174134\pi$
$991$	53287.8	1.70812	0.854058	+	0.520178i	$0.174134\pi$
$992$	423.421	0.0135520
$993$	−30092.9	−0.961701
$994$	−63644.7	−2.03087
$995$	765.350	0.0243851
$996$	−40543.1	−1.28982
$997$	880.741	0.0279773	0.0139886	−	0.999902i	$-0.495547\pi$
$997$	880.741	0.0279773	0.0139886	+	0.999902i	$0.495547\pi$
$998$	−17740.4	−0.562687
$999$	−8525.90	−0.270017

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.4.a.j.1.1	✓	7
3.2	odd	2		1305.4.a.m.1.7		7
5.4	even	2		2175.4.a.m.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.4.a.j.1.1	✓	7	1.1	even	1	trivial
1305.4.a.m.1.7		7	3.2	odd	2
2175.4.a.m.1.7		7	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	435.a (trivial)

\(f(q)\)	\(=\)	\(q-5.12367 q^{2} +3.00000 q^{3} +18.2520 q^{4} -5.00000 q^{5} -15.3710 q^{6} -21.7657 q^{7} -52.5281 q^{8} +9.00000 q^{9} +25.6184 q^{10} +57.1430 q^{11} +54.7561 q^{12} -41.2271 q^{13} +111.520 q^{14} -15.0000 q^{15} +123.120 q^{16} +73.0149 q^{17} -46.1131 q^{18} -0.658616 q^{19} -91.2602 q^{20} -65.2970 q^{21} -292.782 q^{22} -96.1672 q^{23} -157.584 q^{24} +25.0000 q^{25} +211.234 q^{26} +27.0000 q^{27} -397.267 q^{28} -29.0000 q^{29} +76.8551 q^{30} -2.01051 q^{31} -210.604 q^{32} +171.429 q^{33} -374.104 q^{34} +108.828 q^{35} +164.268 q^{36} -315.774 q^{37} +3.37453 q^{38} -123.681 q^{39} +262.640 q^{40} +219.873 q^{41} +334.560 q^{42} +81.2960 q^{43} +1042.98 q^{44} -45.0000 q^{45} +492.730 q^{46} +440.820 q^{47} +369.361 q^{48} +130.744 q^{49} -128.092 q^{50} +219.045 q^{51} -752.479 q^{52} +65.8584 q^{53} -138.339 q^{54} -285.715 q^{55} +1143.31 q^{56} -1.97585 q^{57} +148.587 q^{58} -551.520 q^{59} -273.780 q^{60} -149.536 q^{61} +10.3012 q^{62} -195.891 q^{63} +94.1041 q^{64} +206.136 q^{65} -878.346 q^{66} -888.233 q^{67} +1332.67 q^{68} -288.502 q^{69} -557.601 q^{70} -570.702 q^{71} -472.753 q^{72} +664.264 q^{73} +1617.92 q^{74} +75.0000 q^{75} -12.0211 q^{76} -1243.75 q^{77} +633.703 q^{78} +221.956 q^{79} -615.602 q^{80} +81.0000 q^{81} -1126.56 q^{82} -740.432 q^{83} -1191.80 q^{84} -365.074 q^{85} -416.534 q^{86} -87.0000 q^{87} -3001.61 q^{88} -895.415 q^{89} +230.565 q^{90} +897.336 q^{91} -1755.25 q^{92} -6.03152 q^{93} -2258.62 q^{94} +3.29308 q^{95} -631.813 q^{96} -705.666 q^{97} -669.888 q^{98} +514.287 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} + 21 q^{3} + 15 q^{4} - 35 q^{5} - 3 q^{6} - 37 q^{7} - 36 q^{8} + 63 q^{9} + 5 q^{10} - 11 q^{11} + 45 q^{12} - 133 q^{13} - 75 q^{14} - 105 q^{15} - 53 q^{16} + 21 q^{17} - 9 q^{18} - 170 q^{19}+ \cdots - 99 q^{99}+O(q^{100}) \) 7 * q - q^2 + 21 * q^3 + 15 * q^4 - 35 * q^5 - 3 * q^6 - 37 * q^7 - 36 * q^8 + 63 * q^9 + 5 * q^10 - 11 * q^11 + 45 * q^12 - 133 * q^13 - 75 * q^14 - 105 * q^15 - 53 * q^16 + 21 * q^17 - 9 * q^18 - 170 * q^19 - 75 * q^20 - 111 * q^21 - 369 * q^22 - 68 * q^23 - 108 * q^24 + 175 * q^25 + 181 * q^26 + 189 * q^27 - 637 * q^28 - 203 * q^29 + 15 * q^30 - 480 * q^31 - 779 * q^32 - 33 * q^33 - 897 * q^34 + 185 * q^35 + 135 * q^36 - 1032 * q^37 - 194 * q^38 - 399 * q^39 + 180 * q^40 - 638 * q^41 - 225 * q^42 - 512 * q^43 + 625 * q^44 - 315 * q^45 + 16 * q^46 - 111 * q^47 - 159 * q^48 + 178 * q^49 - 25 * q^50 + 63 * q^51 - 1263 * q^52 + 410 * q^53 - 27 * q^54 + 55 * q^55 + 1174 * q^56 - 510 * q^57 + 29 * q^58 - 426 * q^59 - 225 * q^60 - 1192 * q^61 + 460 * q^62 - 333 * q^63 + 390 * q^64 + 665 * q^65 - 1107 * q^66 - 1671 * q^67 + 1509 * q^68 - 204 * q^69 + 375 * q^70 - 1324 * q^71 - 324 * q^72 - 852 * q^73 + 1780 * q^74 + 525 * q^75 - 564 * q^76 - 2107 * q^77 + 543 * q^78 + 366 * q^79 + 265 * q^80 + 567 * q^81 - 318 * q^82 + 470 * q^83 - 1911 * q^84 - 105 * q^85 - 2196 * q^86 - 609 * q^87 - 2518 * q^88 + 51 * q^89 + 45 * q^90 - 1297 * q^91 - 684 * q^92 - 1440 * q^93 - 1837 * q^94 + 850 * q^95 - 2337 * q^96 - 3322 * q^97 + 1068 * q^98 - 99 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more