LMFDB - Embedded newform 483.4.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,4,Mod(1,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, 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("483.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	483.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:	$28.4979225328$
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} - 34x^{5} + 7x^{4} + 295x^{3} + 84x^{2} - 524x - 288 $ x^7 - x^6 - 34x^5 + 7x^4 + 295x^3 + 84x^2 - 524*x - 288
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.37660$ of defining polynomial
Character	$\chi$	$=$	483.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.37660 q^{2} +3.00000 q^{3} -2.35176 q^{4} -18.5873 q^{5} -7.12981 q^{6} +7.00000 q^{7} +24.6020 q^{8} +9.00000 q^{9} +44.1746 q^{10} +29.5947 q^{11} -7.05528 q^{12} -64.1277 q^{13} -16.6362 q^{14} -55.7619 q^{15} -39.6551 q^{16} +57.2759 q^{17} -21.3894 q^{18} +93.4996 q^{19} +43.7129 q^{20} +21.0000 q^{21} -70.3349 q^{22} +23.0000 q^{23} +73.8061 q^{24} +220.488 q^{25} +152.406 q^{26} +27.0000 q^{27} -16.4623 q^{28} -286.528 q^{29} +132.524 q^{30} +229.872 q^{31} -102.572 q^{32} +88.7842 q^{33} -136.122 q^{34} -130.111 q^{35} -21.1658 q^{36} +98.5035 q^{37} -222.211 q^{38} -192.383 q^{39} -457.285 q^{40} -76.2059 q^{41} -49.9087 q^{42} +68.2610 q^{43} -69.5997 q^{44} -167.286 q^{45} -54.6619 q^{46} -561.428 q^{47} -118.965 q^{48} +49.0000 q^{49} -524.011 q^{50} +171.828 q^{51} +150.813 q^{52} -481.176 q^{53} -64.1683 q^{54} -550.086 q^{55} +172.214 q^{56} +280.499 q^{57} +680.962 q^{58} -550.017 q^{59} +131.139 q^{60} +105.356 q^{61} -546.315 q^{62} +63.0000 q^{63} +561.013 q^{64} +1191.96 q^{65} -211.005 q^{66} -870.324 q^{67} -134.699 q^{68} +69.0000 q^{69} +309.222 q^{70} +526.774 q^{71} +221.418 q^{72} +79.3015 q^{73} -234.104 q^{74} +661.463 q^{75} -219.889 q^{76} +207.163 q^{77} +457.218 q^{78} +321.443 q^{79} +737.082 q^{80} +81.0000 q^{81} +181.111 q^{82} -284.623 q^{83} -49.3870 q^{84} -1064.60 q^{85} -162.229 q^{86} -859.583 q^{87} +728.090 q^{88} +1.45559 q^{89} +397.572 q^{90} -448.894 q^{91} -54.0905 q^{92} +689.617 q^{93} +1334.29 q^{94} -1737.90 q^{95} -307.715 q^{96} -97.0465 q^{97} -116.454 q^{98} +266.353 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 6 q^{2} + 21 q^{3} + 18 q^{4} - 41 q^{5} - 18 q^{6} + 49 q^{7} - 33 q^{8} + 63 q^{9} + q^{10} - 126 q^{11} + 54 q^{12} - 87 q^{13} - 42 q^{14} - 123 q^{15} + 2 q^{16} - 204 q^{17} - 54 q^{18} - 286 q^{19}+ \cdots - 1134 q^{99}+O(q^{100}) $ 7 * q - 6 * q^2 + 21 * q^3 + 18 * q^4 - 41 * q^5 - 18 * q^6 + 49 * q^7 - 33 * q^8 + 63 * q^9 + q^10 - 126 * q^11 + 54 * q^12 - 87 * q^13 - 42 * q^14 - 123 * q^15 + 2 * q^16 - 204 * q^17 - 54 * q^18 - 286 * q^19 - 418 * q^20 + 147 * q^21 + 329 * q^22 + 161 * q^23 - 99 * q^24 + 440 * q^25 - 360 * q^26 + 189 * q^27 + 126 * q^28 - 329 * q^29 + 3 * q^30 + 296 * q^31 - 270 * q^32 - 378 * q^33 - 919 * q^34 - 287 * q^35 + 162 * q^36 - 691 * q^37 - 367 * q^38 - 261 * q^39 + 138 * q^40 - 343 * q^41 - 126 * q^42 - 171 * q^43 - 1279 * q^44 - 369 * q^45 - 138 * q^46 - 1403 * q^47 + 6 * q^48 + 343 * q^49 + 230 * q^50 - 612 * q^51 + 2157 * q^52 - 1024 * q^53 - 162 * q^54 - 158 * q^55 - 231 * q^56 - 858 * q^57 + 2608 * q^58 - 1388 * q^59 - 1254 * q^60 - 52 * q^61 - 309 * q^62 + 441 * q^63 - 187 * q^64 - 1067 * q^65 + 987 * q^66 - 1148 * q^67 + 1293 * q^68 + 483 * q^69 + 7 * q^70 - 1590 * q^71 - 297 * q^72 - 802 * q^73 - 878 * q^74 + 1320 * q^75 - 2505 * q^76 - 882 * q^77 - 1080 * q^78 + 618 * q^79 + 195 * q^80 + 567 * q^81 - 1040 * q^82 - 1818 * q^83 + 378 * q^84 - 1526 * q^85 + 1188 * q^86 - 987 * q^87 + 1664 * q^88 - 354 * q^89 + 9 * q^90 - 609 * q^91 + 414 * q^92 + 888 * q^93 + 663 * q^94 + 78 * q^95 - 810 * q^96 - 1575 * q^97 - 294 * q^98 - 1134 * 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 $

$2$	−2.37660	−0.840256	−0.420128	−	0.907465i	$-0.638015\pi$
$2$	−2.37660	−0.840256	−0.420128	+	0.907465i	$0.638015\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−2.35176	−0.293970
$5$	−18.5873	−1.66250	−0.831249	−	0.555900i	$-0.812374\pi$
$5$	−18.5873	−1.66250	−0.831249	+	0.555900i	$0.812374\pi$
$6$	−7.12981	−0.485122
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	24.6020	1.08727
$9$	9.00000	0.333333
$10$	44.1746	1.39692
$11$	29.5947	0.811195	0.405598	−	0.914052i	$-0.367063\pi$
$11$	29.5947	0.811195	0.405598	+	0.914052i	$0.367063\pi$
$12$	−7.05528	−0.169724
$13$	−64.1277	−1.36814	−0.684070	−	0.729416i	$-0.739792\pi$
$13$	−64.1277	−1.36814	−0.684070	+	0.729416i	$0.739792\pi$
$14$	−16.6362	−0.317587
$15$	−55.7619	−0.959844
$16$	−39.6551	−0.619612
$17$	57.2759	0.817144	0.408572	−	0.912726i	$-0.366027\pi$
$17$	57.2759	0.817144	0.408572	+	0.912726i	$0.366027\pi$
$18$	−21.3894	−0.280085
$19$	93.4996	1.12896	0.564481	−	0.825446i	$-0.309076\pi$
$19$	93.4996	1.12896	0.564481	+	0.825446i	$0.309076\pi$
$20$	43.7129	0.488725
$21$	21.0000	0.218218
$22$	−70.3349	−0.681612
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	73.8061	0.627733
$25$	220.488	1.76390
$26$	152.406	1.14959
$27$	27.0000	0.192450
$28$	−16.4623	−0.111110
$29$	−286.528	−1.83472	−0.917359	−	0.398060i	$-0.869684\pi$
$29$	−286.528	−1.83472	−0.917359	+	0.398060i	$0.869684\pi$
$30$	132.524	0.806514
$31$	229.872	1.33182	0.665908	−	0.746034i	$-0.268044\pi$
$31$	229.872	1.33182	0.665908	+	0.746034i	$0.268044\pi$
$32$	−102.572	−0.566634
$33$	88.7842	0.468344
$34$	−136.122	−0.686610
$35$	−130.111	−0.628365
$36$	−21.1658	−0.0979900
$37$	98.5035	0.437672	0.218836	−	0.975762i	$-0.429774\pi$
$37$	98.5035	0.437672	0.218836	+	0.975762i	$0.429774\pi$
$38$	−222.211	−0.948617
$39$	−192.383	−0.789896
$40$	−457.285	−1.80758
$41$	−76.2059	−0.290277	−0.145139	−	0.989411i	$-0.546363\pi$
$41$	−76.2059	−0.290277	−0.145139	+	0.989411i	$0.546363\pi$
$42$	−49.9087	−0.183359
$43$	68.2610	0.242086	0.121043	−	0.992647i	$-0.461376\pi$
$43$	68.2610	0.242086	0.121043	+	0.992647i	$0.461376\pi$
$44$	−69.5997	−0.238467
$45$	−167.286	−0.554166
$46$	−54.6619	−0.175205
$47$	−561.428	−1.74240	−0.871199	−	0.490930i	$-0.836657\pi$
$47$	−561.428	−1.74240	−0.871199	+	0.490930i	$0.836657\pi$
$48$	−118.965	−0.357733
$49$	49.0000	0.142857
$50$	−524.011	−1.48213
$51$	171.828	0.471778
$52$	150.813	0.402192
$53$	−481.176	−1.24707	−0.623534	−	0.781796i	$-0.714304\pi$
$53$	−481.176	−1.24707	−0.623534	+	0.781796i	$0.714304\pi$
$54$	−64.1683	−0.161707
$55$	−550.086	−1.34861
$56$	172.214	0.410948
$57$	280.499	0.651807
$58$	680.962	1.54163
$59$	−550.017	−1.21366	−0.606832	−	0.794830i	$-0.707560\pi$
$59$	−550.017	−1.21366	−0.606832	+	0.794830i	$0.707560\pi$
$60$	131.139	0.282165
$61$	105.356	0.221138	0.110569	−	0.993868i	$-0.464733\pi$
$61$	105.356	0.221138	0.110569	+	0.993868i	$0.464733\pi$
$62$	−546.315	−1.11907
$63$	63.0000	0.125988
$64$	561.013	1.09573
$65$	1191.96	2.27453
$66$	−211.005	−0.393529
$67$	−870.324	−1.58697	−0.793485	−	0.608590i	$-0.791735\pi$
$67$	−870.324	−1.58697	−0.793485	+	0.608590i	$0.791735\pi$
$68$	−134.699	−0.240216
$69$	69.0000	0.120386
$70$	309.222	0.527988
$71$	526.774	0.880515	0.440257	−	0.897872i	$-0.354887\pi$
$71$	526.774	0.880515	0.440257	+	0.897872i	$0.354887\pi$
$72$	221.418	0.362422
$73$	79.3015	0.127144	0.0635722	−	0.997977i	$-0.479751\pi$
$73$	79.3015	0.127144	0.0635722	+	0.997977i	$0.479751\pi$
$74$	−234.104	−0.367757
$75$	661.463	1.01839
$76$	−219.889	−0.331881
$77$	207.163	0.306603
$78$	457.218	0.663715
$79$	321.443	0.457787	0.228894	−	0.973451i	$-0.426489\pi$
$79$	321.443	0.457787	0.228894	+	0.973451i	$0.426489\pi$
$80$	737.082	1.03010
$81$	81.0000	0.111111
$82$	181.111	0.243907
$83$	−284.623	−0.376402	−0.188201	−	0.982131i	$-0.560266\pi$
$83$	−284.623	−0.376402	−0.188201	+	0.982131i	$0.560266\pi$
$84$	−49.3870	−0.0641495
$85$	−1064.60	−1.35850
$86$	−162.229	−0.203414
$87$	−859.583	−1.05928
$88$	728.090	0.881985
$89$	1.45559	0.00173362	0.000866812	−	1.00000i	$-0.499724\pi$
$89$	1.45559	0.00173362	0.000866812		1.00000i	$0.499724\pi$
$90$	397.572	0.465641
$91$	−448.894	−0.517108
$92$	−54.0905	−0.0612970
$93$	689.617	0.768924
$94$	1334.29	1.46406
$95$	−1737.90	−1.87690
$96$	−307.715	−0.327146
$97$	−97.0465	−0.101583	−0.0507916	−	0.998709i	$-0.516174\pi$
$97$	−97.0465	−0.101583	−0.0507916	+	0.998709i	$0.516174\pi$
$98$	−116.454	−0.120037
$99$	266.353	0.270398
$100$	−518.534	−0.518534
$101$	−2000.53	−1.97090	−0.985448	−	0.169975i	$-0.945631\pi$
$101$	−2000.53	−1.97090	−0.985448	+	0.169975i	$0.945631\pi$
$102$	−408.366	−0.396414
$103$	−1594.86	−1.52569	−0.762846	−	0.646580i	$-0.776199\pi$
$103$	−1594.86	−1.52569	−0.762846	+	0.646580i	$0.776199\pi$
$104$	−1577.67	−1.48753
$105$	−390.333	−0.362787
$106$	1143.56	1.04786
$107$	496.921	0.448964	0.224482	−	0.974478i	$-0.427931\pi$
$107$	496.921	0.448964	0.224482	+	0.974478i	$0.427931\pi$
$108$	−63.4975	−0.0565746
$109$	−600.989	−0.528112	−0.264056	−	0.964507i	$-0.585060\pi$
$109$	−600.989	−0.528112	−0.264056	+	0.964507i	$0.585060\pi$
$110$	1307.34	1.13318
$111$	295.510	0.252690
$112$	−277.586	−0.234191
$113$	−1637.25	−1.36300	−0.681501	−	0.731817i	$-0.738673\pi$
$113$	−1637.25	−1.36300	−0.681501	+	0.731817i	$0.738673\pi$
$114$	−666.634	−0.547684
$115$	−427.508	−0.346655
$116$	673.844	0.539352
$117$	−577.149	−0.456047
$118$	1307.17	1.01979
$119$	400.931	0.308851
$120$	−1371.86	−1.04361
$121$	−455.152	−0.341962
$122$	−250.389	−0.185813
$123$	−228.618	−0.167592
$124$	−540.605	−0.391514
$125$	−1774.86	−1.26998
$126$	−149.726	−0.105862
$127$	1102.39	0.770248	0.385124	−	0.922865i	$-0.374159\pi$
$127$	1102.39	0.770248	0.385124	+	0.922865i	$0.374159\pi$
$128$	−512.732	−0.354059
$129$	204.783	0.139769
$130$	−2832.82	−1.91119
$131$	−954.978	−0.636922	−0.318461	−	0.947936i	$-0.603166\pi$
$131$	−954.978	−0.636922	−0.318461	+	0.947936i	$0.603166\pi$
$132$	−208.799	−0.137679
$133$	654.497	0.426708
$134$	2068.41	1.33346
$135$	−501.857	−0.319948
$136$	1409.10	0.888452
$137$	2719.89	1.69617	0.848086	−	0.529859i	$-0.177755\pi$
$137$	2719.89	1.69617	0.848086	+	0.529859i	$0.177755\pi$
$138$	−163.986	−0.101155
$139$	798.932	0.487515	0.243757	−	0.969836i	$-0.421620\pi$
$139$	798.932	0.487515	0.243757	+	0.969836i	$0.421620\pi$
$140$	305.990	0.184721
$141$	−1684.28	−1.00597
$142$	−1251.93	−0.739858
$143$	−1897.84	−1.10983
$144$	−356.896	−0.206537
$145$	5325.77	3.05022
$146$	−188.468	−0.106834
$147$	147.000	0.0824786
$148$	−231.657	−0.128663
$149$	2394.79	1.31671	0.658353	−	0.752710i	$-0.271254\pi$
$149$	2394.79	1.31671	0.658353	+	0.752710i	$0.271254\pi$
$150$	−1572.03	−0.855707
$151$	−2080.55	−1.12128	−0.560639	−	0.828060i	$-0.689445\pi$
$151$	−2080.55	−1.12128	−0.560639	+	0.828060i	$0.689445\pi$
$152$	2300.28	1.22748
$153$	515.483	0.272381
$154$	−492.344	−0.257625
$155$	−4272.71	−2.21414
$156$	452.439	0.232206
$157$	−819.517	−0.416590	−0.208295	−	0.978066i	$-0.566791\pi$
$157$	−819.517	−0.416590	−0.208295	+	0.978066i	$0.566791\pi$
$158$	−763.943	−0.384658
$159$	−1443.53	−0.719995
$160$	1906.53	0.942027
$161$	161.000	0.0788110
$162$	−192.505	−0.0933618
$163$	−243.271	−0.116899	−0.0584493	−	0.998290i	$-0.518616\pi$
$163$	−243.271	−0.116899	−0.0584493	+	0.998290i	$0.518616\pi$
$164$	179.218	0.0853327
$165$	−1650.26	−0.778621
$166$	676.435	0.316274
$167$	−2429.43	−1.12572	−0.562860	−	0.826552i	$-0.690299\pi$
$167$	−2429.43	−1.12572	−0.562860	+	0.826552i	$0.690299\pi$
$168$	516.642	0.237261
$169$	1915.36	0.871808
$170$	2530.14	1.14149
$171$	841.496	0.376321
$172$	−160.534	−0.0711661
$173$	−1244.25	−0.546812	−0.273406	−	0.961899i	$-0.588150\pi$
$173$	−1244.25	−0.546812	−0.273406	+	0.961899i	$0.588150\pi$
$174$	2042.89	0.890062
$175$	1543.41	0.666692
$176$	−1173.58	−0.502626
$177$	−1650.05	−0.700709
$178$	−3.45937	−0.00145669
$179$	−2564.24	−1.07073	−0.535365	−	0.844621i	$-0.679826\pi$
$179$	−2564.24	−1.07073	−0.535365	+	0.844621i	$0.679826\pi$
$180$	393.416	0.162908
$181$	255.483	0.104917	0.0524583	−	0.998623i	$-0.483294\pi$
$181$	255.483	0.104917	0.0524583	+	0.998623i	$0.483294\pi$
$182$	1066.84	0.434503
$183$	316.067	0.127674
$184$	565.846	0.226711
$185$	−1830.91	−0.727629
$186$	−1638.95	−0.646093
$187$	1695.06	0.662863
$188$	1320.34	0.512213
$189$	189.000	0.0727393
$190$	4130.31	1.57707
$191$	3973.57	1.50533	0.752664	−	0.658405i	$-0.228769\pi$
$191$	3973.57	1.50533	0.752664	+	0.658405i	$0.228769\pi$
$192$	1683.04	0.632619
$193$	3401.51	1.26863	0.634316	−	0.773074i	$-0.281282\pi$
$193$	3401.51	1.26863	0.634316	+	0.773074i	$0.281282\pi$
$194$	230.641	0.0853560
$195$	3575.88	1.31320
$196$	−115.236	−0.0419957
$197$	1320.68	0.477638	0.238819	−	0.971064i	$-0.423240\pi$
$197$	1320.68	0.477638	0.238819	+	0.971064i	$0.423240\pi$
$198$	−633.014	−0.227204
$199$	1045.34	0.372373	0.186186	−	0.982514i	$-0.440387\pi$
$199$	1045.34	0.372373	0.186186	+	0.982514i	$0.440387\pi$
$200$	5424.44	1.91783
$201$	−2610.97	−0.916237
$202$	4754.47	1.65606
$203$	−2005.69	−0.693459
$204$	−404.097	−0.138689
$205$	1416.46	0.482585
$206$	3790.35	1.28197
$207$	207.000	0.0695048
$208$	2542.99	0.847716
$209$	2767.10	0.915809
$210$	927.667	0.304834
$211$	−1951.62	−0.636755	−0.318377	−	0.947964i	$-0.603138\pi$
$211$	−1951.62	−0.636755	−0.318377	+	0.947964i	$0.603138\pi$
$212$	1131.61	0.366601
$213$	1580.32	0.508365
$214$	−1180.98	−0.377245
$215$	−1268.79	−0.402468
$216$	664.255	0.209244
$217$	1609.11	0.503379
$218$	1428.31	0.443750
$219$	237.905	0.0734069
$220$	1293.67	0.396451
$221$	−3672.97	−1.11797
$222$	−702.311	−0.212324
$223$	−5170.91	−1.55278	−0.776389	−	0.630254i	$-0.782951\pi$
$223$	−5170.91	−1.55278	−0.776389	+	0.630254i	$0.782951\pi$
$224$	−718.001	−0.214167
$225$	1984.39	0.587967
$226$	3891.09	1.14527
$227$	−1927.93	−0.563706	−0.281853	−	0.959458i	$-0.590949\pi$
$227$	−1927.93	−0.563706	−0.281853	+	0.959458i	$0.590949\pi$
$228$	−659.666	−0.191612
$229$	−1299.40	−0.374964	−0.187482	−	0.982268i	$-0.560033\pi$
$229$	−1299.40	−0.374964	−0.187482	+	0.982268i	$0.560033\pi$
$230$	1016.02	0.291279
$231$	621.489	0.177017
$232$	−7049.16	−1.99483
$233$	1791.31	0.503658	0.251829	−	0.967772i	$-0.418968\pi$
$233$	1791.31	0.503658	0.251829	+	0.967772i	$0.418968\pi$
$234$	1371.65	0.383196
$235$	10435.4	2.89673
$236$	1293.51	0.356781
$237$	964.330	0.264304
$238$	−952.854	−0.259514
$239$	−6811.27	−1.84345	−0.921725	−	0.387843i	$-0.873220\pi$
$239$	−6811.27	−1.84345	−0.921725	+	0.387843i	$0.873220\pi$
$240$	2211.25	0.594730
$241$	4248.35	1.13552	0.567760	−	0.823194i	$-0.307810\pi$
$241$	4248.35	1.13552	0.567760	+	0.823194i	$0.307810\pi$
$242$	1081.71	0.287336
$243$	243.000	0.0641500
$244$	−247.771	−0.0650080
$245$	−910.778	−0.237500
$246$	543.333	0.140820
$247$	−5995.91	−1.54458
$248$	5655.32	1.44804
$249$	−853.868	−0.217316
$250$	4218.13	1.06711
$251$	−4474.69	−1.12526	−0.562630	−	0.826709i	$-0.690210\pi$
$251$	−4474.69	−1.12526	−0.562630	+	0.826709i	$0.690210\pi$
$252$	−148.161	−0.0370367
$253$	680.679	0.169146
$254$	−2619.95	−0.647205
$255$	−3193.81	−0.784330
$256$	−3269.54	−0.798229
$257$	5750.65	1.39578	0.697891	−	0.716204i	$-0.254122\pi$
$257$	5750.65	1.39578	0.697891	+	0.716204i	$0.254122\pi$
$258$	−486.688	−0.117441
$259$	689.524	0.165425
$260$	−2803.21	−0.668644
$261$	−2578.75	−0.611573
$262$	2269.60	0.535178
$263$	3108.60	0.728837	0.364419	−	0.931235i	$-0.381268\pi$
$263$	3108.60	0.728837	0.364419	+	0.931235i	$0.381268\pi$
$264$	2184.27	0.509214
$265$	8943.76	2.07325
$266$	−1555.48	−0.358544
$267$	4.36678	0.00100091
$268$	2046.79	0.466522
$269$	−918.491	−0.208184	−0.104092	−	0.994568i	$-0.533194\pi$
$269$	−918.491	−0.208184	−0.104092	+	0.994568i	$0.533194\pi$
$270$	1192.71	0.268838
$271$	787.124	0.176437	0.0882184	−	0.996101i	$-0.471883\pi$
$271$	787.124	0.176437	0.0882184	+	0.996101i	$0.471883\pi$
$272$	−2271.28	−0.506312
$273$	−1346.68	−0.298553
$274$	−6464.09	−1.42522
$275$	6525.27	1.43087
$276$	−162.271	−0.0353898
$277$	4716.12	1.02298	0.511488	−	0.859290i	$-0.329094\pi$
$277$	4716.12	1.02298	0.511488	+	0.859290i	$0.329094\pi$
$278$	−1898.74	−0.409637
$279$	2068.85	0.443939
$280$	−3201.00	−0.683200
$281$	−7779.18	−1.65148	−0.825742	−	0.564048i	$-0.809243\pi$
$281$	−7779.18	−1.65148	−0.825742	+	0.564048i	$0.809243\pi$
$282$	4002.87	0.845275
$283$	−5264.48	−1.10580	−0.552899	−	0.833248i	$-0.686479\pi$
$283$	−5264.48	−1.10580	−0.552899	+	0.833248i	$0.686479\pi$
$284$	−1238.85	−0.258845
$285$	−5213.71	−1.08363
$286$	4510.42	0.932540
$287$	−533.441	−0.109714
$288$	−923.145	−0.188878
$289$	−1632.47	−0.332276
$290$	−12657.2	−2.56296
$291$	−291.140	−0.0586491
$292$	−186.498	−0.0373766
$293$	−4640.73	−0.925305	−0.462652	−	0.886540i	$-0.653102\pi$
$293$	−4640.73	−0.925305	−0.462652	+	0.886540i	$0.653102\pi$
$294$	−349.361	−0.0693031
$295$	10223.3	2.01771
$296$	2423.38	0.475866
$297$	799.058	0.156115
$298$	−5691.47	−1.10637
$299$	−1474.94	−0.285277
$300$	−1555.60	−0.299376
$301$	477.827	0.0915000
$302$	4944.65	0.942161
$303$	−6001.60	−1.13790
$304$	−3707.74	−0.699518
$305$	−1958.28	−0.367642
$306$	−1225.10	−0.228870
$307$	1594.40	0.296409	0.148204	−	0.988957i	$-0.452651\pi$
$307$	1594.40	0.296409	0.148204	+	0.988957i	$0.452651\pi$
$308$	−487.198	−0.0901321
$309$	−4784.58	−0.880859
$310$	10154.5	1.86045
$311$	−208.917	−0.0380920	−0.0190460	−	0.999819i	$-0.506063\pi$
$311$	−208.917	−0.0380920	−0.0190460	+	0.999819i	$0.506063\pi$
$312$	−4733.01	−0.858827
$313$	777.029	0.140320	0.0701602	−	0.997536i	$-0.477649\pi$
$313$	777.029	0.140320	0.0701602	+	0.997536i	$0.477649\pi$
$314$	1947.67	0.350042
$315$	−1171.00	−0.209455
$316$	−755.957	−0.134576
$317$	8011.54	1.41947	0.709736	−	0.704468i	$-0.248814\pi$
$317$	8011.54	1.41947	0.709736	+	0.704468i	$0.248814\pi$
$318$	3430.69	0.604980
$319$	−8479.71	−1.48832
$320$	−10427.7	−1.82165
$321$	1490.76	0.259210
$322$	−382.633	−0.0662214
$323$	5355.27	0.922524
$324$	−190.493	−0.0326633
$325$	−14139.4	−2.41326
$326$	578.159	0.0982248
$327$	−1802.97	−0.304906
$328$	−1874.82	−0.315608
$329$	−3930.00	−0.658564
$330$	3922.01	0.654241
$331$	7646.13	1.26970	0.634848	−	0.772637i	$-0.281063\pi$
$331$	7646.13	1.26970	0.634848	+	0.772637i	$0.281063\pi$
$332$	669.364	0.110651
$333$	886.531	0.145891
$334$	5773.80	0.945893
$335$	16177.0	2.63833
$336$	−832.758	−0.135210
$337$	−8932.53	−1.44387	−0.721937	−	0.691958i	$-0.756748\pi$
$337$	−8932.53	−1.44387	−0.721937	+	0.691958i	$0.756748\pi$
$338$	−4552.06	−0.732542
$339$	−4911.74	−0.786930
$340$	2503.69	0.399358
$341$	6803.01	1.08036
$342$	−1999.90	−0.316206
$343$	343.000	0.0539949
$344$	1679.36	0.263212
$345$	−1282.52	−0.200141
$346$	2957.09	0.459462
$347$	9425.54	1.45818	0.729092	−	0.684416i	$-0.239943\pi$
$347$	9425.54	1.45818	0.729092	+	0.684416i	$0.239943\pi$
$348$	2021.53	0.311395
$349$	3578.33	0.548835	0.274418	−	0.961611i	$-0.411515\pi$
$349$	3578.33	0.548835	0.274418	+	0.961611i	$0.411515\pi$
$350$	−3668.08	−0.560192
$351$	−1731.45	−0.263299
$352$	−3035.58	−0.459651
$353$	2353.40	0.354840	0.177420	−	0.984135i	$-0.443225\pi$
$353$	2353.40	0.354840	0.177420	+	0.984135i	$0.443225\pi$
$354$	3921.52	0.588775
$355$	−9791.30	−1.46385
$356$	−3.42321	−0.000509634 0
$357$	1202.79	0.178315
$358$	6094.19	0.899687
$359$	−11659.0	−1.71404	−0.857020	−	0.515282i	$-0.827687\pi$
$359$	−11659.0	−1.71404	−0.857020	+	0.515282i	$0.827687\pi$
$360$	−4115.57	−0.602526
$361$	1883.18	0.274555
$362$	−607.182	−0.0881568
$363$	−1365.45	−0.197432
$364$	1055.69	0.152014
$365$	−1474.00	−0.211377
$366$	−751.166	−0.107279
$367$	−5341.21	−0.759697	−0.379848	−	0.925049i	$-0.624024\pi$
$367$	−5341.21	−0.759697	−0.379848	+	0.925049i	$0.624024\pi$
$368$	−912.068	−0.129198
$369$	−685.853	−0.0967590
$370$	4351.35	0.611395
$371$	−3368.23	−0.471347
$372$	−1621.81	−0.226041
$373$	5390.36	0.748264	0.374132	−	0.927376i	$-0.377941\pi$
$373$	5390.36	0.748264	0.374132	+	0.927376i	$0.377941\pi$
$374$	−4028.50	−0.556975
$375$	−5324.57	−0.733225
$376$	−13812.3	−1.89445
$377$	18374.4	2.51015
$378$	−449.178	−0.0611196
$379$	−3452.43	−0.467914	−0.233957	−	0.972247i	$-0.575168\pi$
$379$	−3452.43	−0.467914	−0.233957	+	0.972247i	$0.575168\pi$
$380$	4087.14	0.551752
$381$	3307.18	0.444703
$382$	−9443.60	−1.26486
$383$	−1627.75	−0.217165	−0.108583	−	0.994087i	$-0.534631\pi$
$383$	−1627.75	−0.217165	−0.108583	+	0.994087i	$0.534631\pi$
$384$	−1538.20	−0.204416
$385$	−3850.60	−0.509727
$386$	−8084.04	−1.06598
$387$	614.349	0.0806954
$388$	228.230	0.0298624
$389$	−14813.6	−1.93080	−0.965400	−	0.260774i	$-0.916022\pi$
$389$	−14813.6	−1.93080	−0.965400	+	0.260774i	$0.916022\pi$
$390$	−8498.45	−1.10342
$391$	1317.35	0.170386
$392$	1205.50	0.155324
$393$	−2864.93	−0.367727
$394$	−3138.73	−0.401338
$395$	−5974.76	−0.761070
$396$	−626.397	−0.0794890
$397$	−11703.4	−1.47954	−0.739772	−	0.672858i	$-0.765067\pi$
$397$	−11703.4	−1.47954	−0.739772	+	0.672858i	$0.765067\pi$
$398$	−2484.36	−0.312888
$399$	1963.49	0.246360
$400$	−8743.47	−1.09293
$401$	9223.26	1.14860	0.574299	−	0.818646i	$-0.305275\pi$
$401$	9223.26	1.14860	0.574299	+	0.818646i	$0.305275\pi$
$402$	6205.24	0.769874
$403$	−14741.2	−1.82211
$404$	4704.78	0.579385
$405$	−1505.57	−0.184722
$406$	4766.74	0.582683
$407$	2915.18	0.355038
$408$	4227.31	0.512948
$409$	−5792.20	−0.700259	−0.350129	−	0.936701i	$-0.613862\pi$
$409$	−5792.20	−0.700259	−0.350129	+	0.936701i	$0.613862\pi$
$410$	−3366.37	−0.405495
$411$	8159.66	0.979285
$412$	3750.73	0.448508
$413$	−3850.12	−0.458722
$414$	−491.957	−0.0584018
$415$	5290.36	0.625768
$416$	6577.68	0.775234
$417$	2396.80	0.281467
$418$	−6576.29	−0.769514
$419$	6695.49	0.780659	0.390330	−	0.920675i	$-0.372361\pi$
$419$	6695.49	0.780659	0.390330	+	0.920675i	$0.372361\pi$
$420$	917.970	0.106648
$421$	2517.43	0.291431	0.145715	−	0.989327i	$-0.453452\pi$
$421$	2517.43	0.291431	0.145715	+	0.989327i	$0.453452\pi$
$422$	4638.23	0.535037
$423$	−5052.85	−0.580799
$424$	−11837.9	−1.35589
$425$	12628.6	1.44136
$426$	−3755.79	−0.427157
$427$	737.490	0.0835823
$428$	−1168.64	−0.131982
$429$	−5693.53	−0.640760
$430$	3015.41	0.338176
$431$	13834.6	1.54615	0.773075	−	0.634315i	$-0.218718\pi$
$431$	13834.6	1.54615	0.773075	+	0.634315i	$0.218718\pi$
$432$	−1070.69	−0.119244
$433$	2784.73	0.309066	0.154533	−	0.987988i	$-0.450613\pi$
$433$	2784.73	0.309066	0.154533	+	0.987988i	$0.450613\pi$
$434$	−3824.21	−0.422967
$435$	15977.3	1.76104
$436$	1413.38	0.155249
$437$	2150.49	0.235405
$438$	−565.405	−0.0616806
$439$	−4686.37	−0.509495	−0.254747	−	0.967008i	$-0.581992\pi$
$439$	−4686.37	−0.509495	−0.254747	+	0.967008i	$0.581992\pi$
$440$	−13533.2	−1.46630
$441$	441.000	0.0476190
$442$	8729.19	0.939379
$443$	−13064.7	−1.40118	−0.700589	−	0.713565i	$-0.747079\pi$
$443$	−13064.7	−1.40118	−0.700589	+	0.713565i	$0.747079\pi$
$444$	−694.970	−0.0742833
$445$	−27.0555	−0.00288215
$446$	12289.2	1.30473
$447$	7184.38	0.760200
$448$	3927.09	0.414147
$449$	5232.49	0.549970	0.274985	−	0.961449i	$-0.411327\pi$
$449$	5232.49	0.549970	0.274985	+	0.961449i	$0.411327\pi$
$450$	−4716.10	−0.494043
$451$	−2255.29	−0.235471
$452$	3850.41	0.400682
$453$	−6241.66	−0.647371
$454$	4581.92	0.473657
$455$	8343.72	0.859692
$456$	6900.84	0.708687
$457$	−14800.6	−1.51497	−0.757487	−	0.652850i	$-0.773573\pi$
$457$	−14800.6	−1.51497	−0.757487	+	0.652850i	$0.773573\pi$
$458$	3088.16	0.315066
$459$	1546.45	0.157259
$460$	1005.40	0.101906
$461$	−9727.75	−0.982790	−0.491395	−	0.870937i	$-0.663513\pi$
$461$	−9727.75	−0.982790	−0.491395	+	0.870937i	$0.663513\pi$
$462$	−1477.03	−0.148740
$463$	−6159.07	−0.618221	−0.309111	−	0.951026i	$-0.600031\pi$
$463$	−6159.07	−0.618221	−0.309111	+	0.951026i	$0.600031\pi$
$464$	11362.3	1.13681
$465$	−12818.1	−1.27834
$466$	−4257.22	−0.423202
$467$	−10062.4	−0.997069	−0.498534	−	0.866870i	$-0.666128\pi$
$467$	−10062.4	−0.997069	−0.498534	+	0.866870i	$0.666128\pi$
$468$	1357.32	0.134064
$469$	−6092.27	−0.599818
$470$	−24800.9	−2.43400
$471$	−2458.55	−0.240518
$472$	−13531.5	−1.31958
$473$	2020.17	0.196379
$474$	−2291.83	−0.222083
$475$	20615.5	1.99138
$476$	−942.894	−0.0907930
$477$	−4330.58	−0.415689
$478$	16187.7	1.54897
$479$	−10456.7	−0.997447	−0.498724	−	0.866761i	$-0.666198\pi$
$479$	−10456.7	−0.997447	−0.498724	+	0.866761i	$0.666198\pi$
$480$	5719.59	0.543880
$481$	−6316.80	−0.598797
$482$	−10096.6	−0.954128
$483$	483.000	0.0455016
$484$	1070.41	0.100527
$485$	1803.83	0.168882
$486$	−577.514	−0.0539024
$487$	13730.9	1.27763	0.638814	−	0.769362i	$-0.279426\pi$
$487$	13730.9	1.27763	0.638814	+	0.769362i	$0.279426\pi$
$488$	2591.96	0.240436
$489$	−729.814	−0.0674915
$490$	2164.56	0.199561
$491$	598.232	0.0549854	0.0274927	−	0.999622i	$-0.491248\pi$
$491$	598.232	0.0549854	0.0274927	+	0.999622i	$0.491248\pi$
$492$	537.654	0.0492669
$493$	−16411.1	−1.49923
$494$	14249.9	1.29784
$495$	−4950.78	−0.449537
$496$	−9115.62	−0.825209
$497$	3687.42	0.332803
$498$	2029.30	0.182601
$499$	21351.5	1.91548	0.957740	−	0.287637i	$-0.0928695\pi$
$499$	21351.5	1.91548	0.957740	+	0.287637i	$0.0928695\pi$
$500$	4174.03	0.373337
$501$	−7288.30	−0.649934
$502$	10634.6	0.945506
$503$	−17641.6	−1.56382	−0.781909	−	0.623393i	$-0.785754\pi$
$503$	−17641.6	−1.56382	−0.781909	+	0.623393i	$0.785754\pi$
$504$	1549.93	0.136983
$505$	37184.5	3.27661
$506$	−1617.70	−0.142126
$507$	5746.09	0.503339
$508$	−2592.56	−0.226430
$509$	17861.4	1.55539	0.777694	−	0.628643i	$-0.216389\pi$
$509$	17861.4	1.55539	0.777694	+	0.628643i	$0.216389\pi$
$510$	7590.42	0.659038
$511$	555.111	0.0480561
$512$	11872.3	1.02478
$513$	2524.49	0.217269
$514$	−13667.0	−1.17281
$515$	29644.2	2.53646
$516$	−481.601	−0.0410878
$517$	−16615.3	−1.41342
$518$	−1638.73	−0.138999
$519$	−3732.75	−0.315702
$520$	29324.6	2.47302
$521$	−5121.32	−0.430651	−0.215326	−	0.976542i	$-0.569081\pi$
$521$	−5121.32	−0.430651	−0.215326	+	0.976542i	$0.569081\pi$
$522$	6128.66	0.513878
$523$	−20247.4	−1.69284	−0.846421	−	0.532514i	$-0.821247\pi$
$523$	−20247.4	−1.69284	−0.846421	+	0.532514i	$0.821247\pi$
$524$	2245.88	0.187236
$525$	4630.24	0.384915
$526$	−7387.90	−0.612410
$527$	13166.1	1.08829
$528$	−3520.75	−0.290191
$529$	529.000	0.0434783
$530$	−21255.8	−1.74206
$531$	−4950.16	−0.404555
$532$	−1539.22	−0.125439
$533$	4886.91	0.397140
$534$	−10.3781	−0.000841019 0
$535$	−9236.42	−0.746402
$536$	−21411.7	−1.72546
$537$	−7692.73	−0.618186
$538$	2182.89	0.174928
$539$	1450.14	0.115885
$540$	1180.25	0.0940551
$541$	−11955.7	−0.950117	−0.475059	−	0.879954i	$-0.657573\pi$
$541$	−11955.7	−0.950117	−0.475059	+	0.879954i	$0.657573\pi$
$542$	−1870.68	−0.148252
$543$	766.449	0.0605736
$544$	−5874.88	−0.463021
$545$	11170.8	0.877986
$546$	3200.53	0.250861
$547$	−687.068	−0.0537055	−0.0268527	−	0.999639i	$-0.508549\pi$
$547$	−687.068	−0.0537055	−0.0268527	+	0.999639i	$0.508549\pi$
$548$	−6396.52	−0.498624
$549$	948.202	0.0737127
$550$	−15508.0	−1.20230
$551$	−26790.2	−2.07133
$552$	1697.54	0.130891
$553$	2250.10	0.173027
$554$	−11208.4	−0.859562
$555$	−5492.74	−0.420097
$556$	−1878.90	−0.143315
$557$	−9513.77	−0.723719	−0.361859	−	0.932233i	$-0.617858\pi$
$557$	−9513.77	−0.723719	−0.361859	+	0.932233i	$0.617858\pi$
$558$	−4916.84	−0.373022
$559$	−4377.42	−0.331208
$560$	5159.57	0.389342
$561$	5085.19	0.382704
$562$	18488.0	1.38767
$563$	−962.909	−0.0720813	−0.0360407	−	0.999350i	$-0.511475\pi$
$563$	−962.909	−0.0720813	−0.0360407	+	0.999350i	$0.511475\pi$
$564$	3961.03	0.295726
$565$	30432.0	2.26599
$566$	12511.6	0.929154
$567$	567.000	0.0419961
$568$	12959.7	0.957353
$569$	−2959.75	−0.218065	−0.109033	−	0.994038i	$-0.534775\pi$
$569$	−2959.75	−0.218065	−0.109033	+	0.994038i	$0.534775\pi$
$570$	12390.9	0.910524
$571$	12950.8	0.949170	0.474585	−	0.880210i	$-0.342598\pi$
$571$	12950.8	0.949170	0.474585	+	0.880210i	$0.342598\pi$
$572$	4463.27	0.326256
$573$	11920.7	0.869101
$574$	1267.78	0.0921882
$575$	5071.21	0.367799
$576$	5049.12	0.365243
$577$	−3672.12	−0.264944	−0.132472	−	0.991187i	$-0.542291\pi$
$577$	−3672.12	−0.264944	−0.132472	+	0.991187i	$0.542291\pi$
$578$	3879.74	0.279197
$579$	10204.5	0.732445
$580$	−12524.9	−0.896672
$581$	−1992.36	−0.142267
$582$	691.923	0.0492803
$583$	−14240.3	−1.01162
$584$	1950.98	0.138240
$585$	10727.6	0.758177
$586$	11029.2	0.777493
$587$	−25387.4	−1.78509	−0.892545	−	0.450958i	$-0.851082\pi$
$587$	−25387.4	−1.78509	−0.892545	+	0.450958i	$0.851082\pi$
$588$	−345.709	−0.0242462
$589$	21493.0	1.50357
$590$	−24296.8	−1.69540
$591$	3962.04	0.275764
$592$	−3906.17	−0.271187
$593$	−20575.1	−1.42482	−0.712409	−	0.701764i	$-0.752396\pi$
$593$	−20575.1	−1.42482	−0.712409	+	0.701764i	$0.752396\pi$
$594$	−1899.04	−0.131176
$595$	−7452.23	−0.513465
$596$	−5631.98	−0.387072
$597$	3136.02	0.214990
$598$	3505.34	0.239706
$599$	−8494.19	−0.579404	−0.289702	−	0.957117i	$-0.593556\pi$
$599$	−8494.19	−0.579404	−0.289702	+	0.957117i	$0.593556\pi$
$600$	16273.3	1.10726
$601$	−20361.3	−1.38195	−0.690977	−	0.722877i	$-0.742819\pi$
$601$	−20361.3	−1.38195	−0.690977	+	0.722877i	$0.742819\pi$
$602$	−1135.61	−0.0768834
$603$	−7832.91	−0.528990
$604$	4892.96	0.329622
$605$	8460.04	0.568511
$606$	14263.4	0.956125
$607$	15203.9	1.01665	0.508324	−	0.861166i	$-0.330265\pi$
$607$	15203.9	1.01665	0.508324	+	0.861166i	$0.330265\pi$
$608$	−9590.41	−0.639708
$609$	−6017.08	−0.400368
$610$	4654.05	0.308913
$611$	36003.1	2.38384
$612$	−1212.29	−0.0800719
$613$	−8351.51	−0.550268	−0.275134	−	0.961406i	$-0.588722\pi$
$613$	−8351.51	−0.550268	−0.275134	+	0.961406i	$0.588722\pi$
$614$	−3789.27	−0.249059
$615$	4249.38	0.278621
$616$	5096.63	0.333359
$617$	−4627.21	−0.301920	−0.150960	−	0.988540i	$-0.548236\pi$
$617$	−4627.21	−0.301920	−0.150960	+	0.988540i	$0.548236\pi$
$618$	11371.1	0.740147
$619$	916.391	0.0595038	0.0297519	−	0.999557i	$-0.490528\pi$
$619$	916.391	0.0595038	0.0297519	+	0.999557i	$0.490528\pi$
$620$	10048.4	0.650891
$621$	621.000	0.0401286
$622$	496.513	0.0320070
$623$	10.1892	0.000655248 0
$624$	7628.98	0.489429
$625$	5428.82	0.347445
$626$	−1846.69	−0.117905
$627$	8301.29	0.528742
$628$	1927.31	0.122465
$629$	5641.87	0.357641
$630$	2783.00	0.175996
$631$	21323.5	1.34528	0.672642	−	0.739968i	$-0.265159\pi$
$631$	21323.5	1.34528	0.672642	+	0.739968i	$0.265159\pi$
$632$	7908.15	0.497736
$633$	−5854.87	−0.367631
$634$	−19040.2	−1.19272
$635$	−20490.5	−1.28054
$636$	3394.83	0.211657
$637$	−3142.26	−0.195449
$638$	20152.9	1.25057
$639$	4740.96	0.293505
$640$	9530.31	0.588623
$641$	−19671.2	−1.21211	−0.606056	−	0.795422i	$-0.707249\pi$
$641$	−19671.2	−1.21211	−0.606056	+	0.795422i	$0.707249\pi$
$642$	−3542.95	−0.217802
$643$	−24462.0	−1.50029	−0.750147	−	0.661271i	$-0.770017\pi$
$643$	−24462.0	−1.50029	−0.750147	+	0.661271i	$0.770017\pi$
$644$	−378.633	−0.0231681
$645$	−3806.36	−0.232365
$646$	−12727.4	−0.775156
$647$	−17951.0	−1.09076	−0.545382	−	0.838187i	$-0.683616\pi$
$647$	−17951.0	−1.09076	−0.545382	+	0.838187i	$0.683616\pi$
$648$	1992.76	0.120807
$649$	−16277.6	−0.984518
$650$	33603.6	2.02776
$651$	4827.32	0.290626
$652$	572.116	0.0343647
$653$	3335.36	0.199882	0.0999408	−	0.994993i	$-0.468135\pi$
$653$	3335.36	0.199882	0.0999408	+	0.994993i	$0.468135\pi$
$654$	4284.93	0.256199
$655$	17750.5	1.05888
$656$	3021.96	0.179859
$657$	713.714	0.0423815
$658$	9340.04	0.553363
$659$	16147.3	0.954490	0.477245	−	0.878770i	$-0.341635\pi$
$659$	16147.3	0.954490	0.477245	+	0.878770i	$0.341635\pi$
$660$	3881.01	0.228891
$661$	13069.7	0.769068	0.384534	−	0.923111i	$-0.374362\pi$
$661$	13069.7	0.769068	0.384534	+	0.923111i	$0.374362\pi$
$662$	−18171.8	−1.06687
$663$	−11018.9	−0.645459
$664$	−7002.29	−0.409249
$665$	−12165.3	−0.709401
$666$	−2106.93	−0.122586
$667$	−6590.14	−0.382565
$668$	5713.44	0.330928
$669$	−15512.7	−0.896497
$670$	−38446.2	−2.21688
$671$	3117.98	0.179386
$672$	−2154.00	−0.123650
$673$	21038.9	1.20504	0.602518	−	0.798106i	$-0.294164\pi$
$673$	21038.9	1.20504	0.602518	+	0.798106i	$0.294164\pi$
$674$	21229.1	1.21322
$675$	5953.16	0.339463
$676$	−4504.47	−0.256285
$677$	24992.0	1.41879	0.709395	−	0.704811i	$-0.248968\pi$
$677$	24992.0	1.41879	0.709395	+	0.704811i	$0.248968\pi$
$678$	11673.3	0.661222
$679$	−679.326	−0.0383949
$680$	−26191.4	−1.47705
$681$	−5783.79	−0.325456
$682$	−16168.1	−0.907781
$683$	−9824.16	−0.550382	−0.275191	−	0.961390i	$-0.588741\pi$
$683$	−9824.16	−0.550382	−0.275191	+	0.961390i	$0.588741\pi$
$684$	−1979.00	−0.110627
$685$	−50555.3	−2.81988
$686$	−815.175	−0.0453696
$687$	−3898.20	−0.216486
$688$	−2706.90	−0.149999
$689$	30856.7	1.70616
$690$	3048.05	0.168170
$691$	30416.5	1.67452	0.837262	−	0.546801i	$-0.184155\pi$
$691$	30416.5	1.67452	0.837262	+	0.546801i	$0.184155\pi$
$692$	2926.18	0.160746
$693$	1864.47	0.102201
$694$	−22400.8	−1.22525
$695$	−14850.0	−0.810492
$696$	−21147.5	−1.15171
$697$	−4364.76	−0.237198
$698$	−8504.26	−0.461162
$699$	5373.92	0.290787
$700$	−3629.74	−0.195987
$701$	6099.82	0.328655	0.164327	−	0.986406i	$-0.447455\pi$
$701$	6099.82	0.328655	0.164327	+	0.986406i	$0.447455\pi$
$702$	4114.96	0.221238
$703$	9210.04	0.494115
$704$	16603.0	0.888850
$705$	31306.3	1.67243
$706$	−5593.09	−0.298157
$707$	−14003.7	−0.744929
$708$	3880.53	0.205987
$709$	−19268.1	−1.02063	−0.510317	−	0.859987i	$-0.670472\pi$
$709$	−19268.1	−1.02063	−0.510317	+	0.859987i	$0.670472\pi$
$710$	23270.0	1.23001
$711$	2892.99	0.152596
$712$	35.8105	0.00188491
$713$	5287.06	0.277703
$714$	−2858.56	−0.149831
$715$	35275.8	1.84509
$716$	6030.49	0.314762
$717$	−20433.8	−1.06432
$718$	27708.9	1.44023
$719$	3936.73	0.204194	0.102097	−	0.994774i	$-0.467445\pi$
$719$	3936.73	0.204194	0.102097	+	0.994774i	$0.467445\pi$
$720$	6633.74	0.343368
$721$	−11164.0	−0.576658
$722$	−4475.56	−0.230697
$723$	12745.1	0.655593
$724$	−600.835	−0.0308423
$725$	−63175.8	−3.23626
$726$	3245.14	0.165893
$727$	23397.7	1.19363	0.596817	−	0.802377i	$-0.296432\pi$
$727$	23397.7	1.19363	0.596817	+	0.802377i	$0.296432\pi$
$728$	−11043.7	−0.562234
$729$	729.000	0.0370370
$730$	3503.11	0.177611
$731$	3909.71	0.197819
$732$	−743.314	−0.0375324
$733$	−14923.0	−0.751970	−0.375985	−	0.926626i	$-0.622696\pi$
$733$	−14923.0	−0.751970	−0.375985	+	0.926626i	$0.622696\pi$
$734$	12693.9	0.638340
$735$	−2732.33	−0.137121
$736$	−2359.15	−0.118151
$737$	−25757.0	−1.28734
$738$	1630.00	0.0813023
$739$	−5991.46	−0.298240	−0.149120	−	0.988819i	$-0.547644\pi$
$739$	−5991.46	−0.298240	−0.149120	+	0.988819i	$0.547644\pi$
$740$	4305.87	0.213901
$741$	−17987.7	−0.891763
$742$	8004.95	0.396052
$743$	−16198.5	−0.799817	−0.399908	−	0.916555i	$-0.630958\pi$
$743$	−16198.5	−0.799817	−0.399908	+	0.916555i	$0.630958\pi$
$744$	16966.0	0.836025
$745$	−44512.7	−2.18902
$746$	−12810.7	−0.628733
$747$	−2561.60	−0.125467
$748$	−3986.39	−0.194862
$749$	3478.45	0.169693
$750$	12654.4	0.616097
$751$	23436.0	1.13874	0.569368	−	0.822082i	$-0.307188\pi$
$751$	23436.0	1.13874	0.569368	+	0.822082i	$0.307188\pi$
$752$	22263.5	1.07961
$753$	−13424.1	−0.649669
$754$	−43668.5	−2.10917
$755$	38671.9	1.86412
$756$	−444.483	−0.0213832
$757$	−9638.94	−0.462792	−0.231396	−	0.972860i	$-0.574329\pi$
$757$	−9638.94	−0.462792	−0.231396	+	0.972860i	$0.574329\pi$
$758$	8205.06	0.393168
$759$	2042.04	0.0976564
$760$	−42756.0	−2.04069
$761$	21695.5	1.03346	0.516729	−	0.856149i	$-0.327150\pi$
$761$	21695.5	1.03346	0.516729	+	0.856149i	$0.327150\pi$
$762$	−7859.84	−0.373664
$763$	−4206.92	−0.199608
$764$	−9344.89	−0.442521
$765$	−9581.43	−0.452833
$766$	3868.52	0.182474
$767$	35271.3	1.66046
$768$	−9808.63	−0.460858
$769$	−25127.8	−1.17832	−0.589162	−	0.808015i	$-0.700542\pi$
$769$	−25127.8	−1.17832	−0.589162	+	0.808015i	$0.700542\pi$
$770$	9151.35	0.428301
$771$	17252.0	0.805855
$772$	−7999.54	−0.372940
$773$	36061.5	1.67793	0.838967	−	0.544182i	$-0.183160\pi$
$773$	36061.5	1.67793	0.838967	+	0.544182i	$0.183160\pi$
$774$	−1460.06	−0.0678048
$775$	50684.0	2.34919
$776$	−2387.54	−0.110448
$777$	2068.57	0.0955079
$778$	35206.1	1.62237
$779$	−7125.22	−0.327712
$780$	−8409.62	−0.386042
$781$	15589.7	0.714269
$782$	−3130.81	−0.143168
$783$	−7736.25	−0.353092
$784$	−1943.10	−0.0885159
$785$	15232.6	0.692580
$786$	6808.81	0.308985
$787$	41719.2	1.88962	0.944809	−	0.327621i	$-0.106247\pi$
$787$	41719.2	1.88962	0.944809	+	0.327621i	$0.106247\pi$
$788$	−3105.92	−0.140411
$789$	9325.79	0.420794
$790$	14199.6	0.639494
$791$	−11460.7	−0.515166
$792$	6552.81	0.293995
$793$	−6756.22	−0.302548
$794$	27814.4	1.24320
$795$	26831.3	1.19699
$796$	−2458.39	−0.109466
$797$	16934.5	0.752636	0.376318	−	0.926491i	$-0.377190\pi$
$797$	16934.5	0.752636	0.376318	+	0.926491i	$0.377190\pi$
$798$	−4666.44	−0.207005
$799$	−32156.3	−1.42379
$800$	−22615.8	−0.999485
$801$	13.1003	0.000577875 0
$802$	−21920.0	−0.965115
$803$	2346.91	0.103139
$804$	6140.38	0.269346
$805$	−2992.55	−0.131023
$806$	35033.9	1.53104
$807$	−2755.47	−0.120195
$808$	−49217.2	−2.14289
$809$	15655.1	0.680351	0.340175	−	0.940362i	$-0.389514\pi$
$809$	15655.1	0.680351	0.340175	+	0.940362i	$0.389514\pi$
$810$	3578.14	0.155214
$811$	−4507.36	−0.195160	−0.0975800	−	0.995228i	$-0.531110\pi$
$811$	−4507.36	−0.195160	−0.0975800	+	0.995228i	$0.531110\pi$
$812$	4716.91	0.203856
$813$	2361.37	0.101866
$814$	−6928.23	−0.298322
$815$	4521.76	0.194344
$816$	−6813.85	−0.292319
$817$	6382.38	0.273306
$818$	13765.8	0.588396
$819$	−4040.05	−0.172369
$820$	−3331.18	−0.141866
$821$	26463.0	1.12493	0.562464	−	0.826822i	$-0.309853\pi$
$821$	26463.0	1.12493	0.562464	+	0.826822i	$0.309853\pi$
$822$	−19392.3	−0.822850
$823$	31394.3	1.32969	0.664846	−	0.746980i	$-0.268497\pi$
$823$	31394.3	1.32969	0.664846	+	0.746980i	$0.268497\pi$
$824$	−39236.8	−1.65883
$825$	19575.8	0.826112
$826$	9150.21	0.385444
$827$	−42198.0	−1.77433	−0.887164	−	0.461454i	$-0.847328\pi$
$827$	−42198.0	−1.77433	−0.887164	+	0.461454i	$0.847328\pi$
$828$	−486.814	−0.0204323
$829$	14110.6	0.591171	0.295586	−	0.955316i	$-0.404485\pi$
$829$	14110.6	0.591171	0.295586	+	0.955316i	$0.404485\pi$
$830$	−12573.1	−0.525805
$831$	14148.4	0.590616
$832$	−35976.5	−1.49911
$833$	2806.52	0.116735
$834$	−5696.23	−0.236504
$835$	45156.6	1.87151
$836$	−6507.55	−0.269220
$837$	6206.55	0.256308
$838$	−15912.5	−0.655954
$839$	36515.0	1.50255	0.751273	−	0.659991i	$-0.229440\pi$
$839$	36515.0	1.50255	0.751273	+	0.659991i	$0.229440\pi$
$840$	−9602.99	−0.394446
$841$	57709.1	2.36619
$842$	−5982.94	−0.244876
$843$	−23337.5	−0.953485
$844$	4589.75	0.187187
$845$	−35601.4	−1.44938
$846$	12008.6	0.488020
$847$	−3186.06	−0.129250
$848$	19081.1	0.772698
$849$	−15793.4	−0.638433
$850$	−30013.2	−1.21111
$851$	2265.58	0.0912610
$852$	−3716.54	−0.149444
$853$	−34620.8	−1.38968	−0.694839	−	0.719166i	$-0.744524\pi$
$853$	−34620.8	−1.38968	−0.694839	+	0.719166i	$0.744524\pi$
$854$	−1752.72	−0.0702306
$855$	−15641.1	−0.625633
$856$	12225.3	0.488144
$857$	22011.4	0.877358	0.438679	−	0.898644i	$-0.355446\pi$
$857$	22011.4	0.877358	0.438679	+	0.898644i	$0.355446\pi$
$858$	13531.3	0.538402
$859$	23608.0	0.937714	0.468857	−	0.883274i	$-0.344666\pi$
$859$	23608.0	0.937714	0.468857	+	0.883274i	$0.344666\pi$
$860$	2983.89	0.118314
$861$	−1600.32	−0.0633436
$862$	−32879.4	−1.29916
$863$	50504.8	1.99212	0.996062	−	0.0886545i	$-0.0282567\pi$
$863$	50504.8	1.99212	0.996062	+	0.0886545i	$0.0282567\pi$
$864$	−2769.43	−0.109049
$865$	23127.2	0.909075
$866$	−6618.21	−0.259695
$867$	−4897.42	−0.191840
$868$	−3784.23	−0.147978
$869$	9513.03	0.371355
$870$	−37971.7	−1.47973
$871$	55811.9	2.17120
$872$	−14785.5	−0.574199
$873$	−873.419	−0.0338611
$874$	−5110.86	−0.197800
$875$	−12424.0	−0.480009
$876$	−559.495	−0.0215794
$877$	−17449.5	−0.671866	−0.335933	−	0.941886i	$-0.609052\pi$
$877$	−17449.5	−0.671866	−0.335933	+	0.941886i	$0.609052\pi$
$878$	11137.6	0.428106
$879$	−13922.2	−0.534225
$880$	21813.7	0.835615
$881$	5971.54	0.228361	0.114181	−	0.993460i	$-0.463576\pi$
$881$	5971.54	0.228361	0.114181	+	0.993460i	$0.463576\pi$
$882$	−1048.08	−0.0400122
$883$	−18867.4	−0.719069	−0.359535	−	0.933132i	$-0.617065\pi$
$883$	−18867.4	−0.719069	−0.359535	+	0.933132i	$0.617065\pi$
$884$	8637.95	0.328649
$885$	30670.0	1.16493
$886$	31049.6	1.17735
$887$	25810.7	0.977043	0.488521	−	0.872552i	$-0.337536\pi$
$887$	25810.7	0.977043	0.488521	+	0.872552i	$0.337536\pi$
$888$	7270.15	0.274741
$889$	7716.75	0.291126
$890$	64.3003	0.00242174
$891$	2397.17	0.0901328
$892$	12160.7	0.456470
$893$	−52493.3	−1.96710
$894$	−17074.4	−0.638763
$895$	47662.4	1.78009
$896$	−3589.13	−0.133822
$897$	−4424.81	−0.164705
$898$	−12435.5	−0.462115
$899$	−65864.8	−2.44351
$900$	−4666.80	−0.172845
$901$	−27559.8	−1.01903
$902$	5359.94	0.197856
$903$	1433.48	0.0528276
$904$	−40279.6	−1.48195
$905$	−4748.74	−0.174424
$906$	14834.0	0.543957
$907$	−14754.3	−0.540140	−0.270070	−	0.962841i	$-0.587047\pi$
$907$	−14754.3	−0.540140	−0.270070	+	0.962841i	$0.587047\pi$
$908$	4534.03	0.165713
$909$	−18004.8	−0.656966
$910$	−19829.7	−0.722361
$911$	31500.1	1.14561	0.572803	−	0.819693i	$-0.305856\pi$
$911$	31500.1	1.14561	0.572803	+	0.819693i	$0.305856\pi$
$912$	−11123.2	−0.403867
$913$	−8423.33	−0.305336
$914$	35175.2	1.27297
$915$	−5874.84	−0.212258
$916$	3055.88	0.110228
$917$	−6684.85	−0.240734
$918$	−3675.29	−0.132138
$919$	−4521.21	−0.162286	−0.0811431	−	0.996702i	$-0.525857\pi$
$919$	−4521.21	−0.162286	−0.0811431	+	0.996702i	$0.525857\pi$
$920$	−10517.6	−0.376906
$921$	4783.21	0.171132
$922$	23119.0	0.825795
$923$	−33780.8	−1.20467
$924$	−1461.59	−0.0520378
$925$	21718.8	0.772010
$926$	14637.7	0.519464
$927$	−14353.8	−0.508564
$928$	29389.6	1.03961
$929$	−33508.2	−1.18339	−0.591695	−	0.806162i	$-0.701541\pi$
$929$	−33508.2	−1.18339	−0.591695	+	0.806162i	$0.701541\pi$
$930$	30463.6	1.07413
$931$	4581.48	0.161280
$932$	−4212.72	−0.148060
$933$	−626.751	−0.0219924
$934$	23914.3	0.837793
$935$	−31506.7	−1.10201
$936$	−14199.0	−0.495844
$937$	6766.87	0.235927	0.117964	−	0.993018i	$-0.462363\pi$
$937$	6766.87	0.235927	0.117964	+	0.993018i	$0.462363\pi$
$938$	14478.9	0.504001
$939$	2331.09	0.0810140
$940$	−24541.6	−0.851553
$941$	33988.9	1.17748	0.588739	−	0.808323i	$-0.299625\pi$
$941$	33988.9	1.17748	0.588739	+	0.808323i	$0.299625\pi$
$942$	5843.00	0.202097
$943$	−1752.74	−0.0605269
$944$	21811.0	0.752000
$945$	−3513.00	−0.120929
$946$	−4801.14	−0.165009
$947$	11421.6	0.391923	0.195962	−	0.980612i	$-0.437217\pi$
$947$	11421.6	0.391923	0.195962	+	0.980612i	$0.437217\pi$
$948$	−2267.87	−0.0776973
$949$	−5085.43	−0.173951
$950$	−48994.9	−1.67327
$951$	24034.6	0.819533
$952$	9863.72	0.335803
$953$	44873.3	1.52528	0.762638	−	0.646825i	$-0.223904\pi$
$953$	44873.3	1.52528	0.762638	+	0.646825i	$0.223904\pi$
$954$	10292.1	0.349285
$955$	−73858.0	−2.50260
$956$	16018.5	0.541919
$957$	−25439.1	−0.859279
$958$	24851.3	0.838111
$959$	19039.2	0.641093
$960$	−31283.2	−1.05173
$961$	23050.3	0.773734
$962$	15012.5	0.503143
$963$	4472.29	0.149655
$964$	−9991.11	−0.333809
$965$	−63224.9	−2.10910
$966$	−1147.90	−0.0382330
$967$	17375.3	0.577820	0.288910	−	0.957356i	$-0.406707\pi$
$967$	17375.3	0.577820	0.288910	+	0.957356i	$0.406707\pi$
$968$	−11197.6	−0.371804
$969$	16065.8	0.532620
$970$	−4286.99	−0.141904
$971$	−30059.6	−0.993469	−0.496734	−	0.867903i	$-0.665468\pi$
$971$	−30059.6	−0.993469	−0.496734	+	0.867903i	$0.665468\pi$
$972$	−571.478	−0.0188582
$973$	5592.53	0.184263
$974$	−32632.8	−1.07353
$975$	−42418.1	−1.39330
$976$	−4177.90	−0.137020
$977$	−46546.4	−1.52421	−0.762105	−	0.647454i	$-0.775834\pi$
$977$	−46546.4	−1.52421	−0.762105	+	0.647454i	$0.775834\pi$
$978$	1734.48	0.0567101
$979$	43.0779	0.00140631
$980$	2141.93	0.0698178
$981$	−5408.90	−0.176037
$982$	−1421.76	−0.0462018
$983$	40574.4	1.31650	0.658251	−	0.752799i	$-0.271297\pi$
$983$	40574.4	1.31650	0.658251	+	0.752799i	$0.271297\pi$
$984$	−5624.46	−0.182217
$985$	−24547.9	−0.794072
$986$	39002.7	1.25974
$987$	−11790.0	−0.380222
$988$	14101.0	0.454060
$989$	1570.00	0.0504785
$990$	11766.0	0.377726
$991$	26374.9	0.845435	0.422717	−	0.906262i	$-0.361076\pi$
$991$	26374.9	0.845435	0.422717	+	0.906262i	$0.361076\pi$
$992$	−23578.4	−0.754652
$993$	22938.4	0.733059
$994$	−8763.52	−0.279640
$995$	−19430.0	−0.619069
$996$	2008.09	0.0638844
$997$	−20286.4	−0.644411	−0.322205	−	0.946670i	$-0.604424\pi$
$997$	−20286.4	−0.644411	−0.322205	+	0.946670i	$0.604424\pi$
$998$	−50744.0	−1.60949
$999$	2659.59	0.0842301

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.4.a.c.1.3	✓	7
3.2	odd	2		1449.4.a.h.1.5		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.4.a.c.1.3	✓	7	1.1	even	1	trivial
1449.4.a.h.1.5		7	3.2	odd	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	483.a (trivial)

\(f(q)\)	\(=\)	\(q-2.37660 q^{2} +3.00000 q^{3} -2.35176 q^{4} -18.5873 q^{5} -7.12981 q^{6} +7.00000 q^{7} +24.6020 q^{8} +9.00000 q^{9} +44.1746 q^{10} +29.5947 q^{11} -7.05528 q^{12} -64.1277 q^{13} -16.6362 q^{14} -55.7619 q^{15} -39.6551 q^{16} +57.2759 q^{17} -21.3894 q^{18} +93.4996 q^{19} +43.7129 q^{20} +21.0000 q^{21} -70.3349 q^{22} +23.0000 q^{23} +73.8061 q^{24} +220.488 q^{25} +152.406 q^{26} +27.0000 q^{27} -16.4623 q^{28} -286.528 q^{29} +132.524 q^{30} +229.872 q^{31} -102.572 q^{32} +88.7842 q^{33} -136.122 q^{34} -130.111 q^{35} -21.1658 q^{36} +98.5035 q^{37} -222.211 q^{38} -192.383 q^{39} -457.285 q^{40} -76.2059 q^{41} -49.9087 q^{42} +68.2610 q^{43} -69.5997 q^{44} -167.286 q^{45} -54.6619 q^{46} -561.428 q^{47} -118.965 q^{48} +49.0000 q^{49} -524.011 q^{50} +171.828 q^{51} +150.813 q^{52} -481.176 q^{53} -64.1683 q^{54} -550.086 q^{55} +172.214 q^{56} +280.499 q^{57} +680.962 q^{58} -550.017 q^{59} +131.139 q^{60} +105.356 q^{61} -546.315 q^{62} +63.0000 q^{63} +561.013 q^{64} +1191.96 q^{65} -211.005 q^{66} -870.324 q^{67} -134.699 q^{68} +69.0000 q^{69} +309.222 q^{70} +526.774 q^{71} +221.418 q^{72} +79.3015 q^{73} -234.104 q^{74} +661.463 q^{75} -219.889 q^{76} +207.163 q^{77} +457.218 q^{78} +321.443 q^{79} +737.082 q^{80} +81.0000 q^{81} +181.111 q^{82} -284.623 q^{83} -49.3870 q^{84} -1064.60 q^{85} -162.229 q^{86} -859.583 q^{87} +728.090 q^{88} +1.45559 q^{89} +397.572 q^{90} -448.894 q^{91} -54.0905 q^{92} +689.617 q^{93} +1334.29 q^{94} -1737.90 q^{95} -307.715 q^{96} -97.0465 q^{97} -116.454 q^{98} +266.353 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 6 q^{2} + 21 q^{3} + 18 q^{4} - 41 q^{5} - 18 q^{6} + 49 q^{7} - 33 q^{8} + 63 q^{9} + q^{10} - 126 q^{11} + 54 q^{12} - 87 q^{13} - 42 q^{14} - 123 q^{15} + 2 q^{16} - 204 q^{17} - 54 q^{18} - 286 q^{19}+ \cdots - 1134 q^{99}+O(q^{100}) \) 7 * q - 6 * q^2 + 21 * q^3 + 18 * q^4 - 41 * q^5 - 18 * q^6 + 49 * q^7 - 33 * q^8 + 63 * q^9 + q^10 - 126 * q^11 + 54 * q^12 - 87 * q^13 - 42 * q^14 - 123 * q^15 + 2 * q^16 - 204 * q^17 - 54 * q^18 - 286 * q^19 - 418 * q^20 + 147 * q^21 + 329 * q^22 + 161 * q^23 - 99 * q^24 + 440 * q^25 - 360 * q^26 + 189 * q^27 + 126 * q^28 - 329 * q^29 + 3 * q^30 + 296 * q^31 - 270 * q^32 - 378 * q^33 - 919 * q^34 - 287 * q^35 + 162 * q^36 - 691 * q^37 - 367 * q^38 - 261 * q^39 + 138 * q^40 - 343 * q^41 - 126 * q^42 - 171 * q^43 - 1279 * q^44 - 369 * q^45 - 138 * q^46 - 1403 * q^47 + 6 * q^48 + 343 * q^49 + 230 * q^50 - 612 * q^51 + 2157 * q^52 - 1024 * q^53 - 162 * q^54 - 158 * q^55 - 231 * q^56 - 858 * q^57 + 2608 * q^58 - 1388 * q^59 - 1254 * q^60 - 52 * q^61 - 309 * q^62 + 441 * q^63 - 187 * q^64 - 1067 * q^65 + 987 * q^66 - 1148 * q^67 + 1293 * q^68 + 483 * q^69 + 7 * q^70 - 1590 * q^71 - 297 * q^72 - 802 * q^73 - 878 * q^74 + 1320 * q^75 - 2505 * q^76 - 882 * q^77 - 1080 * q^78 + 618 * q^79 + 195 * q^80 + 567 * q^81 - 1040 * q^82 - 1818 * q^83 + 378 * q^84 - 1526 * q^85 + 1188 * q^86 - 987 * q^87 + 1664 * q^88 - 354 * q^89 + 9 * q^90 - 609 * q^91 + 414 * q^92 + 888 * q^93 + 663 * q^94 + 78 * q^95 - 810 * q^96 - 1575 * q^97 - 294 * q^98 - 1134 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more