LMFDB - Embedded newform 2023.4.a.v.1.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2023,4,Mod(1,2023)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2023, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2023.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 2023 = 7 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2023.a (trivial)

Newform invariants

comment:select newform

sage:traces = [56,8,24,240,80,68] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	yes
Analytic conductor:	$119.360863942$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	no (minimal twist has level 119)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	2023.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-4.80359 q^{2} +3.56192 q^{3} +15.0745 q^{4} -13.7155 q^{5} -17.1100 q^{6} +7.00000 q^{7} -33.9829 q^{8} -14.3127 q^{9} +65.8837 q^{10} -19.4335 q^{11} +53.6941 q^{12} -0.895027 q^{13} -33.6251 q^{14} -48.8535 q^{15} +42.6440 q^{16} +68.7525 q^{18} -115.934 q^{19} -206.754 q^{20} +24.9334 q^{21} +93.3505 q^{22} +5.90718 q^{23} -121.044 q^{24} +63.1152 q^{25} +4.29934 q^{26} -147.153 q^{27} +105.521 q^{28} -0.926712 q^{29} +234.672 q^{30} -64.1625 q^{31} +67.0187 q^{32} -69.2205 q^{33} -96.0086 q^{35} -215.757 q^{36} -386.719 q^{37} +556.900 q^{38} -3.18801 q^{39} +466.092 q^{40} +8.77493 q^{41} -119.770 q^{42} -264.301 q^{43} -292.950 q^{44} +196.306 q^{45} -28.3757 q^{46} +615.968 q^{47} +151.894 q^{48} +49.0000 q^{49} -303.179 q^{50} -13.4921 q^{52} -328.843 q^{53} +706.861 q^{54} +266.540 q^{55} -237.880 q^{56} -412.948 q^{57} +4.45154 q^{58} +1.72390 q^{59} -736.441 q^{60} +111.131 q^{61} +308.210 q^{62} -100.189 q^{63} -663.083 q^{64} +12.2758 q^{65} +332.507 q^{66} -986.655 q^{67} +21.0409 q^{69} +461.186 q^{70} -716.935 q^{71} +486.388 q^{72} -116.484 q^{73} +1857.64 q^{74} +224.811 q^{75} -1747.65 q^{76} -136.034 q^{77} +15.3139 q^{78} +73.3432 q^{79} -584.884 q^{80} -137.702 q^{81} -42.1511 q^{82} -176.117 q^{83} +375.858 q^{84} +1269.59 q^{86} -3.30087 q^{87} +660.406 q^{88} -1068.22 q^{89} -942.975 q^{90} -6.26519 q^{91} +89.0477 q^{92} -228.542 q^{93} -2958.86 q^{94} +1590.10 q^{95} +238.715 q^{96} +1135.54 q^{97} -235.376 q^{98} +278.146 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{2} + 24 q^{3} + 240 q^{4} + 80 q^{5} + 68 q^{6} + 392 q^{7} + 96 q^{8} + 576 q^{9} + 80 q^{10} + 176 q^{11} + 288 q^{12} - 96 q^{13} + 56 q^{14} + 192 q^{15} + 1088 q^{16} + 216 q^{18} + 48 q^{19}+ \cdots + 6576 q^{99}+O(q^{100}) $ 56 * q + 8 * q^2 + 24 * q^3 + 240 * q^4 + 80 * q^5 + 68 * q^6 + 392 * q^7 + 96 * q^8 + 576 * q^9 + 80 * q^10 + 176 * q^11 + 288 * q^12 - 96 * q^13 + 56 * q^14 + 192 * q^15 + 1088 * q^16 + 216 * q^18 + 48 * q^19 + 1660 * q^20 + 168 * q^21 + 352 * q^22 + 608 * q^23 + 736 * q^24 + 1792 * q^25 + 864 * q^27 + 1680 * q^28 + 928 * q^29 - 100 * q^30 + 496 * q^31 + 436 * q^32 + 384 * q^33 + 560 * q^35 + 2804 * q^36 + 1392 * q^37 + 624 * q^39 - 1020 * q^40 + 2088 * q^41 + 476 * q^42 + 1312 * q^43 + 2112 * q^44 + 4840 * q^45 + 736 * q^46 + 5228 * q^48 + 2744 * q^49 + 2020 * q^50 - 1536 * q^52 + 1272 * q^53 + 2268 * q^54 - 336 * q^55 + 672 * q^56 + 2448 * q^57 + 1376 * q^58 + 2372 * q^60 + 976 * q^61 + 3776 * q^62 + 4032 * q^63 + 5376 * q^64 + 6080 * q^65 + 976 * q^67 + 1248 * q^69 + 560 * q^70 + 3216 * q^71 + 4532 * q^72 + 4088 * q^73 - 2456 * q^74 - 760 * q^75 - 2640 * q^76 + 1232 * q^77 + 3744 * q^78 + 1792 * q^79 + 13920 * q^80 + 4184 * q^81 + 8204 * q^82 - 2832 * q^83 + 2016 * q^84 + 4908 * q^86 + 832 * q^87 + 2424 * q^88 - 2768 * q^89 + 8660 * q^90 - 672 * q^91 + 6784 * q^92 + 784 * q^93 - 928 * q^94 + 4560 * q^95 + 6656 * q^96 + 9464 * q^97 + 392 * q^98 + 6576 * 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 $

$2$	−4.80359	−1.69833	−0.849163	−	0.528131i	$-0.822893\pi$
$2$	−4.80359	−1.69833	−0.849163	+	0.528131i	$0.822893\pi$
$3$	3.56192	0.685492	0.342746	−	0.939428i	$-0.388643\pi$
$3$	3.56192	0.685492	0.342746	+	0.939428i	$0.388643\pi$
$4$	15.0745	1.88431
$5$	−13.7155	−1.22675	−0.613376	−	0.789791i	$-0.710189\pi$
$5$	−13.7155	−1.22675	−0.613376	+	0.789791i	$0.710189\pi$
$6$	−17.1100	−1.16419
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−33.9829	−1.50185
$9$	−14.3127	−0.530101
$10$	65.8837	2.08342
$11$	−19.4335	−0.532674	−0.266337	−	0.963880i	$-0.585813\pi$
$11$	−19.4335	−0.532674	−0.266337	+	0.963880i	$0.585813\pi$
$12$	53.6941	1.29168
$13$	−0.895027	−0.0190951	−0.00954753	−	0.999954i	$-0.503039\pi$
$13$	−0.895027	−0.0190951	−0.00954753	+	0.999954i	$0.503039\pi$
$14$	−33.6251	−0.641907
$15$	−48.8535	−0.840929
$16$	42.6440	0.666312
$17$	0	0
$17$	0	0
$18$	68.7525	0.900284
$19$	−115.934	−1.39985	−0.699924	−	0.714217i	$-0.746783\pi$
$19$	−115.934	−1.39985	−0.699924	+	0.714217i	$0.746783\pi$
$20$	−206.754	−2.31158
$21$	24.9334	0.259091
$22$	93.3505	0.904654
$23$	5.90718	0.0535536	0.0267768	−	0.999641i	$-0.491476\pi$
$23$	5.90718	0.0535536	0.0267768	+	0.999641i	$0.491476\pi$
$24$	−121.044	−1.02950
$25$	63.1152	0.504922
$26$	4.29934	0.0324296
$27$	−147.153	−1.04887
$28$	105.521	0.712202
$29$	−0.926712	−0.00593400	−0.00296700	−	0.999996i	$-0.500944\pi$
$29$	−0.926712	−0.00593400	−0.00296700	+	0.999996i	$0.500944\pi$
$30$	234.672	1.42817
$31$	−64.1625	−0.371739	−0.185870	−	0.982574i	$-0.559510\pi$
$31$	−64.1625	−0.371739	−0.185870	+	0.982574i	$0.559510\pi$
$32$	67.0187	0.370230
$33$	−69.2205	−0.365144
$34$	0	0
$35$	−96.0086	−0.463669
$36$	−215.757	−0.998875
$37$	−386.719	−1.71828	−0.859138	−	0.511745i	$-0.828999\pi$
$37$	−386.719	−1.71828	−0.859138	+	0.511745i	$0.828999\pi$
$38$	556.900	2.37740
$39$	−3.18801	−0.0130895
$40$	466.092	1.84239
$41$	8.77493	0.0334247	0.0167124	−	0.999860i	$-0.494680\pi$
$41$	8.77493	0.0334247	0.0167124	+	0.999860i	$0.494680\pi$
$42$	−119.770	−0.440022
$43$	−264.301	−0.937337	−0.468669	−	0.883374i	$-0.655266\pi$
$43$	−264.301	−0.937337	−0.468669	+	0.883374i	$0.655266\pi$
$44$	−292.950	−1.00372
$45$	196.306	0.650303
$46$	−28.3757	−0.0909515
$47$	615.968	1.91166	0.955832	−	0.293914i	$-0.0949581\pi$
$47$	615.968	1.91166	0.955832	+	0.293914i	$0.0949581\pi$
$48$	151.894	0.456752
$49$	49.0000	0.142857
$50$	−303.179	−0.857521
$51$	0	0
$52$	−13.4921	−0.0359810
$53$	−328.843	−0.852264	−0.426132	−	0.904661i	$-0.640124\pi$
$53$	−328.843	−0.852264	−0.426132	+	0.904661i	$0.640124\pi$
$54$	706.861	1.78133
$55$	266.540	0.653459
$56$	−237.880	−0.567644
$57$	−412.948	−0.959584
$58$	4.45154	0.0100779
$59$	1.72390	0.00380394	0.00190197	−	0.999998i	$-0.499395\pi$
$59$	1.72390	0.00380394	0.00190197	+	0.999998i	$0.499395\pi$
$60$	−736.441	−1.58457
$61$	111.131	0.233260	0.116630	−	0.993175i	$-0.462791\pi$
$61$	111.131	0.233260	0.116630	+	0.993175i	$0.462791\pi$
$62$	308.210	0.631335
$63$	−100.189	−0.200359
$64$	−663.083	−1.29508
$65$	12.2758	0.0234249
$66$	332.507	0.620133
$67$	−986.655	−1.79909	−0.899545	−	0.436827i	$-0.856102\pi$
$67$	−986.655	−1.79909	−0.899545	+	0.436827i	$0.856102\pi$
$68$	0	0
$69$	21.0409	0.0367106
$70$	461.186	0.787461
$71$	−716.935	−1.19837	−0.599187	−	0.800609i	$-0.704509\pi$
$71$	−716.935	−1.19837	−0.599187	+	0.800609i	$0.704509\pi$
$72$	486.388	0.796130
$73$	−116.484	−0.186759	−0.0933797	−	0.995631i	$-0.529767\pi$
$73$	−116.484	−0.186759	−0.0933797	+	0.995631i	$0.529767\pi$
$74$	1857.64	2.91819
$75$	224.811	0.346120
$76$	−1747.65	−2.63775
$77$	−136.034	−0.201332
$78$	15.3139	0.0222302
$79$	73.3432	0.104453	0.0522263	−	0.998635i	$-0.483368\pi$
$79$	73.3432	0.104453	0.0522263	+	0.998635i	$0.483368\pi$
$80$	−584.884	−0.817400
$81$	−137.702	−0.188892
$82$	−42.1511	−0.0567660
$83$	−176.117	−0.232907	−0.116454	−	0.993196i	$-0.537153\pi$
$83$	−176.117	−0.232907	−0.116454	+	0.993196i	$0.537153\pi$
$84$	375.858	0.488209
$85$	0	0
$86$	1269.59	1.59190
$87$	−3.30087	−0.00406771
$88$	660.406	0.799994
$89$	−1068.22	−1.27225	−0.636127	−	0.771585i	$-0.719464\pi$
$89$	−1068.22	−1.27225	−0.636127	+	0.771585i	$0.719464\pi$
$90$	−942.975	−1.10443
$91$	−6.26519	−0.00721726
$92$	89.0477	0.100912
$93$	−228.542	−0.254824
$94$	−2958.86	−3.24663
$95$	1590.10	1.71727
$96$	238.715	0.253789
$97$	1135.54	1.18863	0.594313	−	0.804234i	$-0.297424\pi$
$97$	1135.54	1.18863	0.594313	+	0.804234i	$0.297424\pi$
$98$	−235.376	−0.242618
$99$	278.146	0.282371
$100$	951.428	0.951428
$101$	1439.41	1.41809	0.709044	−	0.705165i	$-0.249127\pi$
$101$	1439.41	1.41809	0.709044	+	0.705165i	$0.249127\pi$
$102$	0	0
$103$	684.574	0.654885	0.327442	−	0.944871i	$-0.393813\pi$
$103$	684.574	0.654885	0.327442	+	0.944871i	$0.393813\pi$
$104$	30.4156	0.0286778
$105$	−341.975	−0.317841
$106$	1579.63	1.44742
$107$	−1557.65	−1.40733	−0.703663	−	0.710534i	$-0.748453\pi$
$107$	−1557.65	−1.40733	−0.703663	+	0.710534i	$0.748453\pi$
$108$	−2218.25	−1.97640
$109$	807.009	0.709151	0.354576	−	0.935027i	$-0.384625\pi$
$109$	807.009	0.709151	0.354576	+	0.935027i	$0.384625\pi$
$110$	−1280.35	−1.10979
$111$	−1377.46	−1.17786
$112$	298.508	0.251842
$113$	275.155	0.229065	0.114533	−	0.993419i	$-0.463463\pi$
$113$	275.155	0.229065	0.114533	+	0.993419i	$0.463463\pi$
$114$	1983.63	1.62969
$115$	−81.0200	−0.0656970
$116$	−13.9697	−0.0111815
$117$	12.8103	0.0101223
$118$	−8.28091	−0.00646033
$119$	0	0
$120$	1660.18	1.26294
$121$	−953.340	−0.716258
$122$	−533.827	−0.396151
$123$	31.2556	0.0229124
$124$	−967.216	−0.700472
$125$	848.782	0.607339
$126$	481.267	0.340275
$127$	−1983.10	−1.38560	−0.692801	−	0.721129i	$-0.743623\pi$
$127$	−1983.10	−1.38560	−0.692801	+	0.721129i	$0.743623\pi$
$128$	2649.03	1.82924
$129$	−941.418	−0.642537
$130$	−58.9677	−0.0397831
$131$	1316.05	0.877737	0.438868	−	0.898551i	$-0.355379\pi$
$131$	1316.05	0.877737	0.438868	+	0.898551i	$0.355379\pi$
$132$	−1043.46	−0.688044
$133$	−811.539	−0.529093
$134$	4739.49	3.05544
$135$	2018.27	1.28671
$136$	0	0
$137$	−362.692	−0.226181	−0.113091	−	0.993585i	$-0.536075\pi$
$137$	−362.692	−0.226181	−0.113091	+	0.993585i	$0.536075\pi$
$138$	−101.072	−0.0623465
$139$	−2730.94	−1.66644	−0.833220	−	0.552942i	$-0.813505\pi$
$139$	−2730.94	−1.66644	−0.833220	+	0.552942i	$0.813505\pi$
$140$	−1447.28	−0.873696
$141$	2194.03	1.31043
$142$	3443.86	2.03523
$143$	17.3935	0.0101714
$144$	−610.352	−0.353213
$145$	12.7103	0.00727955
$146$	559.542	0.317178
$147$	174.534	0.0979274
$148$	−5829.58	−3.23776
$149$	3447.97	1.89577	0.947883	−	0.318619i	$-0.103219\pi$
$149$	3447.97	1.89577	0.947883	+	0.318619i	$0.103219\pi$
$150$	−1079.90	−0.587824
$151$	2691.18	1.45037	0.725183	−	0.688556i	$-0.241755\pi$
$151$	2691.18	1.45037	0.725183	+	0.688556i	$0.241755\pi$
$152$	3939.77	2.10235
$153$	0	0
$154$	653.453	0.341927
$155$	880.021	0.456032
$156$	−48.0576	−0.0246647
$157$	−1310.79	−0.666321	−0.333160	−	0.942870i	$-0.608115\pi$
$157$	−1310.79	−0.666321	−0.333160	+	0.942870i	$0.608115\pi$
$158$	−352.311	−0.177394
$159$	−1171.31	−0.584220
$160$	−919.196	−0.454180
$161$	41.3503	0.0202414
$162$	661.464	0.320799
$163$	1525.14	0.732873	0.366436	−	0.930443i	$-0.380578\pi$
$163$	1525.14	0.732873	0.366436	+	0.930443i	$0.380578\pi$
$164$	132.277	0.0629825
$165$	949.394	0.447941
$166$	845.992	0.395553
$167$	−174.188	−0.0807132	−0.0403566	−	0.999185i	$-0.512849\pi$
$167$	−174.188	−0.0807132	−0.0403566	+	0.999185i	$0.512849\pi$
$168$	−847.310	−0.389115
$169$	−2196.20	−0.999635
$170$	0	0
$171$	1659.33	0.742061
$172$	−3984.20	−1.76623
$173$	2944.91	1.29420	0.647101	−	0.762404i	$-0.275981\pi$
$173$	2944.91	1.29420	0.647101	+	0.762404i	$0.275981\pi$
$174$	15.8560	0.00690829
$175$	441.806	0.190842
$176$	−828.721	−0.354927
$177$	6.14039	0.00260757
$178$	5131.27	2.16070
$179$	1622.04	0.677300	0.338650	−	0.940912i	$-0.390030\pi$
$179$	1622.04	0.677300	0.338650	+	0.940912i	$0.390030\pi$
$180$	2959.22	1.22537
$181$	−3451.16	−1.41725	−0.708626	−	0.705584i	$-0.750685\pi$
$181$	−3451.16	−1.41725	−0.708626	+	0.705584i	$0.750685\pi$
$182$	30.0954	0.0122573
$183$	395.839	0.159898
$184$	−200.743	−0.0804292
$185$	5304.04	2.10790
$186$	1097.82	0.432775
$187$	0	0
$188$	9285.40	3.60217
$189$	−1030.07	−0.396436
$190$	−7638.17	−2.91648
$191$	−1324.18	−0.501646	−0.250823	−	0.968033i	$-0.580701\pi$
$191$	−1324.18	−0.501646	−0.250823	+	0.968033i	$0.580701\pi$
$192$	−2361.85	−0.887769
$193$	−3189.66	−1.18962	−0.594810	−	0.803866i	$-0.702773\pi$
$193$	−3189.66	−1.18962	−0.594810	+	0.803866i	$0.702773\pi$
$194$	−5454.67	−2.01867
$195$	43.7252	0.0160576
$196$	738.649	0.269187
$197$	−2003.04	−0.724420	−0.362210	−	0.932097i	$-0.617978\pi$
$197$	−2003.04	−0.724420	−0.362210	+	0.932097i	$0.617978\pi$
$198$	−1336.10	−0.479558
$199$	−487.583	−0.173688	−0.0868438	−	0.996222i	$-0.527678\pi$
$199$	−487.583	−0.173688	−0.0868438	+	0.996222i	$0.527678\pi$
$200$	−2144.84	−0.758314
$201$	−3514.39	−1.23326
$202$	−6914.34	−2.40837
$203$	−6.48698	−0.00224284
$204$	0	0
$205$	−120.353	−0.0410038
$206$	−3288.41	−1.11221
$207$	−84.5480	−0.0283888
$208$	−38.1675	−0.0127233
$209$	2253.00	0.745663
$210$	1642.71	0.539798
$211$	−5602.80	−1.82802	−0.914010	−	0.405691i	$-0.867031\pi$
$211$	−5602.80	−1.82802	−0.914010	+	0.405691i	$0.867031\pi$
$212$	−4957.13	−1.60593
$213$	−2553.67	−0.821476
$214$	7482.32	2.39010
$215$	3625.02	1.14988
$216$	5000.67	1.57524
$217$	−449.137	−0.140504
$218$	−3876.54	−1.20437
$219$	−414.907	−0.128022
$220$	4017.95	1.23132
$221$	0	0
$222$	6616.76	2.00040
$223$	−3118.16	−0.936355	−0.468178	−	0.883634i	$-0.655089\pi$
$223$	−3118.16	−0.936355	−0.468178	+	0.883634i	$0.655089\pi$
$224$	469.131	0.139934
$225$	−903.351	−0.267660
$226$	−1321.73	−0.389027
$227$	−3369.03	−0.985068	−0.492534	−	0.870293i	$-0.663929\pi$
$227$	−3369.03	−0.985068	−0.492534	+	0.870293i	$0.663929\pi$
$228$	−6224.97	−1.80815
$229$	749.837	0.216378	0.108189	−	0.994130i	$-0.465495\pi$
$229$	749.837	0.216378	0.108189	+	0.994130i	$0.465495\pi$
$230$	389.187	0.111575
$231$	−484.544	−0.138011
$232$	31.4923	0.00891195
$233$	−1186.46	−0.333595	−0.166797	−	0.985991i	$-0.553343\pi$
$233$	−1186.46	−0.333595	−0.166797	+	0.985991i	$0.553343\pi$
$234$	−61.5354	−0.0171910
$235$	−8448.32	−2.34514
$236$	25.9869	0.00716780
$237$	261.242	0.0716014
$238$	0	0
$239$	−2775.05	−0.751058	−0.375529	−	0.926811i	$-0.622539\pi$
$239$	−2775.05	−0.751058	−0.375529	+	0.926811i	$0.622539\pi$
$240$	−2083.31	−0.560321
$241$	4788.56	1.27991	0.639955	−	0.768412i	$-0.278953\pi$
$241$	4788.56	1.27991	0.639955	+	0.768412i	$0.278953\pi$
$242$	4579.45	1.21644
$243$	3482.64	0.919388
$244$	1675.24	0.439534
$245$	−672.060	−0.175250
$246$	−150.139	−0.0389126
$247$	103.764	0.0267302
$248$	2180.43	0.558295
$249$	−627.313	−0.159656
$250$	−4077.20	−1.03146
$251$	−4962.40	−1.24790	−0.623952	−	0.781462i	$-0.714474\pi$
$251$	−4962.40	−1.24790	−0.623952	+	0.781462i	$0.714474\pi$
$252$	−1510.30	−0.377539
$253$	−114.797	−0.0285266
$254$	9525.98	2.35320
$255$	0	0
$256$	−7420.18	−1.81157
$257$	−1363.34	−0.330907	−0.165453	−	0.986218i	$-0.552909\pi$
$257$	−1363.34	−0.330907	−0.165453	+	0.986218i	$0.552909\pi$
$258$	4522.19	1.09124
$259$	−2707.03	−0.649447
$260$	185.051	0.0441398
$261$	13.2638	0.00314562
$262$	−6321.75	−1.49068
$263$	−6410.67	−1.50304	−0.751518	−	0.659712i	$-0.770678\pi$
$263$	−6410.67	−1.50304	−0.751518	+	0.659712i	$0.770678\pi$
$264$	2352.31	0.548389
$265$	4510.24	1.04552
$266$	3898.30	0.898572
$267$	−3804.90	−0.872119
$268$	−14873.3	−3.39004
$269$	4539.64	1.02895	0.514473	−	0.857506i	$-0.327987\pi$
$269$	4539.64	1.02895	0.514473	+	0.857506i	$0.327987\pi$
$270$	−9694.96	−2.18525
$271$	5883.15	1.31873	0.659366	−	0.751822i	$-0.270825\pi$
$271$	5883.15	1.31873	0.659366	+	0.751822i	$0.270825\pi$
$272$	0	0
$273$	−22.3161	−0.00494737
$274$	1742.22	0.384130
$275$	−1226.55	−0.268959
$276$	317.181	0.0691740
$277$	8758.75	1.89986	0.949932	−	0.312456i	$-0.101152\pi$
$277$	8758.75	1.89986	0.949932	+	0.312456i	$0.101152\pi$
$278$	13118.3	2.83016
$279$	918.341	0.197060
$280$	3262.65	0.696359
$281$	5635.58	1.19641	0.598204	−	0.801344i	$-0.295881\pi$
$281$	5635.58	1.19641	0.598204	+	0.801344i	$0.295881\pi$
$282$	−10539.2	−2.22554
$283$	−5342.38	−1.12216	−0.561080	−	0.827761i	$-0.689614\pi$
$283$	−5342.38	−1.12216	−0.561080	+	0.827761i	$0.689614\pi$
$284$	−10807.4	−2.25811
$285$	5663.79	1.17717
$286$	−83.5512	−0.0172744
$287$	61.4245	0.0126334
$288$	−959.221	−0.196259
$289$	0	0
$290$	−61.0552	−0.0123630
$291$	4044.71	0.814793
$292$	−1755.94	−0.351912
$293$	−5577.16	−1.11202	−0.556009	−	0.831176i	$-0.687668\pi$
$293$	−5577.16	−1.11202	−0.556009	+	0.831176i	$0.687668\pi$
$294$	−838.390	−0.166313
$295$	−23.6442	−0.00466650
$296$	13141.8	2.58058
$297$	2859.69	0.558707
$298$	−16562.7	−3.21963
$299$	−5.28709	−0.00102261
$300$	3388.91	0.652196
$301$	−1850.11	−0.354280
$302$	−12927.3	−2.46319
$303$	5127.07	0.972087
$304$	−4943.89	−0.932736
$305$	−1524.22	−0.286152
$306$	0	0
$307$	745.927	0.138672	0.0693360	−	0.997593i	$-0.477912\pi$
$307$	745.927	0.138672	0.0693360	+	0.997593i	$0.477912\pi$
$308$	−2050.65	−0.379372
$309$	2438.40	0.448918
$310$	−4227.26	−0.774491
$311$	1020.94	0.186149	0.0930747	−	0.995659i	$-0.470330\pi$
$311$	1020.94	0.186149	0.0930747	+	0.995659i	$0.470330\pi$
$312$	108.338	0.0196584
$313$	3431.96	0.619763	0.309882	−	0.950775i	$-0.399711\pi$
$313$	3431.96	0.619763	0.309882	+	0.950775i	$0.399711\pi$
$314$	6296.49	1.13163
$315$	1374.14	0.245791
$316$	1105.61	0.196821
$317$	5941.66	1.05273	0.526367	−	0.850257i	$-0.323554\pi$
$317$	5941.66	1.05273	0.526367	+	0.850257i	$0.323554\pi$
$318$	5626.50	0.992196
$319$	18.0092	0.00316089
$320$	9094.51	1.58875
$321$	−5548.23	−0.964710
$322$	−198.630	−0.0343764
$323$	0	0
$324$	−2075.78	−0.355930
$325$	−56.4898	−0.00964151
$326$	−7326.15	−1.24466
$327$	2874.50	0.486117
$328$	−298.197	−0.0501987
$329$	4311.78	0.722541
$330$	−4560.50	−0.760750
$331$	−1816.52	−0.301647	−0.150823	−	0.988561i	$-0.548192\pi$
$331$	−1816.52	−0.301647	−0.150823	+	0.988561i	$0.548192\pi$
$332$	−2654.87	−0.438870
$333$	5535.00	0.910860
$334$	836.730	0.137077
$335$	13532.5	2.20704
$336$	1063.26	0.172636
$337$	5778.60	0.934067	0.467033	−	0.884240i	$-0.345323\pi$
$337$	5778.60	0.934067	0.467033	+	0.884240i	$0.345323\pi$
$338$	10549.6	1.69771
$339$	980.078	0.157022
$340$	0	0
$341$	1246.90	0.198016
$342$	−7970.76	−1.26026
$343$	343.000	0.0539949
$344$	8981.70	1.40774
$345$	−288.587	−0.0450348
$346$	−14146.1	−2.19798
$347$	11109.5	1.71871	0.859353	−	0.511382i	$-0.170866\pi$
$347$	11109.5	1.71871	0.859353	+	0.511382i	$0.170866\pi$
$348$	−49.7589	−0.00766482
$349$	2346.90	0.359962	0.179981	−	0.983670i	$-0.442396\pi$
$349$	2346.90	0.359962	0.179981	+	0.983670i	$0.442396\pi$
$350$	−2122.26	−0.324113
$351$	131.706	0.0200283
$352$	−1302.41	−0.197212
$353$	−6243.67	−0.941408	−0.470704	−	0.882291i	$-0.656000\pi$
$353$	−6243.67	−0.941408	−0.470704	+	0.882291i	$0.656000\pi$
$354$	−29.4959	−0.00442850
$355$	9833.13	1.47011
$356$	−16102.8	−2.39732
$357$	0	0
$358$	−7791.60	−1.15028
$359$	10808.1	1.58894	0.794470	−	0.607303i	$-0.207749\pi$
$359$	10808.1	1.58894	0.794470	+	0.607303i	$0.207749\pi$
$360$	−6671.06	−0.976654
$361$	6581.72	0.959574
$362$	16578.0	2.40696
$363$	−3395.72	−0.490989
$364$	−94.4445	−0.0135995
$365$	1597.64	0.229107
$366$	−1901.45	−0.271558
$367$	4911.56	0.698586	0.349293	−	0.937013i	$-0.386422\pi$
$367$	4911.56	0.698586	0.349293	+	0.937013i	$0.386422\pi$
$368$	251.906	0.0356834
$369$	−125.593	−0.0177185
$370$	−25478.5	−3.57990
$371$	−2301.90	−0.322126
$372$	−3445.14	−0.480168
$373$	−4256.61	−0.590882	−0.295441	−	0.955361i	$-0.595467\pi$
$373$	−4256.61	−0.590882	−0.295441	+	0.955361i	$0.595467\pi$
$374$	0	0
$375$	3023.29	0.416326
$376$	−20932.4	−2.87102
$377$	0.829432	0.000113310 0
$378$	4948.03	0.673278
$379$	8145.30	1.10395	0.551974	−	0.833862i	$-0.313875\pi$
$379$	8145.30	1.10395	0.551974	+	0.833862i	$0.313875\pi$
$380$	23969.9	3.23586
$381$	−7063.63	−0.949818
$382$	6360.82	0.851958
$383$	3961.45	0.528514	0.264257	−	0.964452i	$-0.414873\pi$
$383$	3961.45	0.528514	0.264257	+	0.964452i	$0.414873\pi$
$384$	9435.62	1.25393
$385$	1865.78	0.246984
$386$	15321.8	2.02036
$387$	3782.87	0.496884
$388$	17117.7	2.23974
$389$	−13003.2	−1.69483	−0.847416	−	0.530929i	$-0.821843\pi$
$389$	−13003.2	−1.69483	−0.847416	+	0.530929i	$0.821843\pi$
$390$	−210.038	−0.0272710
$391$	0	0
$392$	−1665.16	−0.214549
$393$	4687.65	0.601681
$394$	9621.78	1.23030
$395$	−1005.94	−0.128137
$396$	4192.91	0.532075
$397$	−7829.03	−0.989743	−0.494871	−	0.868966i	$-0.664785\pi$
$397$	−7829.03	−0.989743	−0.494871	+	0.868966i	$0.664785\pi$
$398$	2342.15	0.294978
$399$	−2890.64	−0.362689
$400$	2691.48	0.336436
$401$	3313.94	0.412694	0.206347	−	0.978479i	$-0.433842\pi$
$401$	3313.94	0.412694	0.206347	+	0.978479i	$0.433842\pi$
$402$	16881.7	2.09448
$403$	57.4272	0.00709839
$404$	21698.4	2.67212
$405$	1888.65	0.231723
$406$	31.1608	0.00380908
$407$	7515.29	0.915281
$408$	0	0
$409$	1704.97	0.206126	0.103063	−	0.994675i	$-0.467136\pi$
$409$	1704.97	0.206126	0.103063	+	0.994675i	$0.467136\pi$
$410$	578.124	0.0696379
$411$	−1291.88	−0.155046
$412$	10319.6	1.23401
$413$	12.0673	0.00143775
$414$	406.134	0.0482135
$415$	2415.53	0.285720
$416$	−59.9836	−0.00706956
$417$	−9727.38	−1.14233
$418$	−10822.5	−1.26638
$419$	−12951.4	−1.51007	−0.755035	−	0.655684i	$-0.772380\pi$
$419$	−12951.4	−1.51007	−0.755035	+	0.655684i	$0.772380\pi$
$420$	−5155.09	−0.598911
$421$	10354.2	1.19865	0.599327	−	0.800504i	$-0.295435\pi$
$421$	10354.2	1.19865	0.599327	+	0.800504i	$0.295435\pi$
$422$	26913.5	3.10457
$423$	−8816.19	−1.01338
$424$	11175.0	1.27997
$425$	0	0
$426$	12266.8	1.39513
$427$	777.917	0.0881640
$428$	−23480.8	−2.65184
$429$	61.9542	0.00697244
$430$	−17413.1	−1.95287
$431$	1178.61	0.131721	0.0658606	−	0.997829i	$-0.479021\pi$
$431$	1178.61	0.131721	0.0658606	+	0.997829i	$0.479021\pi$
$432$	−6275.18	−0.698876
$433$	13300.4	1.47616	0.738082	−	0.674711i	$-0.235732\pi$
$433$	13300.4	1.47616	0.738082	+	0.674711i	$0.235732\pi$
$434$	2157.47	0.238622
$435$	45.2732	0.00499007
$436$	12165.2	1.33626
$437$	−684.844	−0.0749669
$438$	1993.04	0.217423
$439$	10733.2	1.16690	0.583448	−	0.812151i	$-0.301703\pi$
$439$	10733.2	1.16690	0.583448	+	0.812151i	$0.301703\pi$
$440$	−9057.80	−0.981395
$441$	−701.324	−0.0757287
$442$	0	0
$443$	−7564.15	−0.811249	−0.405625	−	0.914040i	$-0.632946\pi$
$443$	−7564.15	−0.811249	−0.405625	+	0.914040i	$0.632946\pi$
$444$	−20764.5	−2.21946
$445$	14651.1	1.56074
$446$	14978.3	1.59024
$447$	12281.4	1.29953
$448$	−4641.58	−0.489495
$449$	13317.3	1.39974	0.699870	−	0.714270i	$-0.253241\pi$
$449$	13317.3	1.39974	0.699870	+	0.714270i	$0.253241\pi$
$450$	4339.33	0.454573
$451$	−170.527	−0.0178045
$452$	4147.81	0.431630
$453$	9585.77	0.994214
$454$	16183.4	1.67297
$455$	85.9303	0.00885379
$456$	14033.2	1.44115
$457$	12203.0	1.24908	0.624541	−	0.780992i	$-0.285286\pi$
$457$	12203.0	1.24908	0.624541	+	0.780992i	$0.285286\pi$
$458$	−3601.91	−0.367481
$459$	0	0
$460$	−1221.33	−0.123794
$461$	11965.0	1.20882	0.604408	−	0.796675i	$-0.293410\pi$
$461$	11965.0	1.20882	0.604408	+	0.796675i	$0.293410\pi$
$462$	2327.55	0.234388
$463$	−1067.81	−0.107182	−0.0535910	−	0.998563i	$-0.517067\pi$
$463$	−1067.81	−0.107182	−0.0535910	+	0.998563i	$0.517067\pi$
$464$	−39.5187	−0.00395390
$465$	3134.56	0.312606
$466$	5699.26	0.566552
$467$	1982.55	0.196449	0.0982244	−	0.995164i	$-0.468684\pi$
$467$	1982.55	0.196449	0.0982244	+	0.995164i	$0.468684\pi$
$468$	193.108	0.0190736
$469$	−6906.58	−0.679992
$470$	40582.2	3.98281
$471$	−4668.93	−0.456757
$472$	−58.5831	−0.00571293
$473$	5136.29	0.499295
$474$	−1254.90	−0.121602
$475$	−7317.20	−0.706813
$476$	0	0
$477$	4706.64	0.451786
$478$	13330.2	1.27554
$479$	6251.24	0.596298	0.298149	−	0.954519i	$-0.403631\pi$
$479$	6251.24	0.596298	0.298149	+	0.954519i	$0.403631\pi$
$480$	−3274.10	−0.311337
$481$	346.124	0.0328106
$482$	−23002.3	−2.17371
$483$	147.286	0.0138753
$484$	−14371.1	−1.34965
$485$	−15574.5	−1.45815
$486$	−16729.2	−1.56142
$487$	8438.97	0.785229	0.392614	−	0.919703i	$-0.371571\pi$
$487$	8438.97	0.785229	0.392614	+	0.919703i	$0.371571\pi$
$488$	−3776.55	−0.350320
$489$	5432.43	0.502378
$490$	3228.30	0.297632
$491$	9668.53	0.888665	0.444333	−	0.895862i	$-0.353441\pi$
$491$	9668.53	0.888665	0.444333	+	0.895862i	$0.353441\pi$
$492$	471.161	0.0431740
$493$	0	0
$494$	−498.441	−0.0453966
$495$	−3814.92	−0.346400
$496$	−2736.15	−0.247695
$497$	−5018.55	−0.452943
$498$	3013.36	0.271148
$499$	−523.551	−0.0469687	−0.0234844	−	0.999724i	$-0.507476\pi$
$499$	−523.551	−0.0469687	−0.0234844	+	0.999724i	$0.507476\pi$
$500$	12794.9	1.14441
$501$	−620.445	−0.0553282
$502$	23837.3	2.11935
$503$	14638.5	1.29761	0.648807	−	0.760953i	$-0.275268\pi$
$503$	14638.5	1.29761	0.648807	+	0.760953i	$0.275268\pi$
$504$	3404.71	0.300909
$505$	−19742.3	−1.73964
$506$	551.439	0.0484475
$507$	−7822.68	−0.685242
$508$	−29894.1	−2.61090
$509$	−10783.1	−0.939004	−0.469502	−	0.882932i	$-0.655566\pi$
$509$	−10783.1	−0.939004	−0.469502	+	0.882932i	$0.655566\pi$
$510$	0	0
$511$	−815.389	−0.0705884
$512$	14451.3	1.24739
$513$	17060.0	1.46826
$514$	6548.94	0.561987
$515$	−9389.28	−0.803381
$516$	−14191.4	−1.21074
$517$	−11970.4	−1.01829
$518$	13003.5	1.10297
$519$	10489.5	0.887165
$520$	−417.165	−0.0351806
$521$	6172.25	0.519024	0.259512	−	0.965740i	$-0.416438\pi$
$521$	6172.25	0.519024	0.259512	+	0.965740i	$0.416438\pi$
$522$	−63.7138	−0.00534229
$523$	8044.42	0.672577	0.336289	−	0.941759i	$-0.390828\pi$
$523$	8044.42	0.672577	0.336289	+	0.941759i	$0.390828\pi$
$524$	19838.7	1.65393
$525$	1573.68	0.130821
$526$	30794.2	2.55264
$527$	0	0
$528$	−2951.84	−0.243300
$529$	−12132.1	−0.997132
$530$	−21665.4	−1.77563
$531$	−24.6737	−0.00201647
$532$	−12233.5	−0.996975
$533$	−7.85380	−0.000638247 0
$534$	18277.2	1.48114
$535$	21364.0	1.72644
$536$	33529.4	2.70196
$537$	5777.56	0.464283
$538$	−21806.6	−1.74749
$539$	−952.241	−0.0760963
$540$	30424.4	2.42455
$541$	−18367.1	−1.45963	−0.729817	−	0.683643i	$-0.760395\pi$
$541$	−18367.1	−1.45963	−0.729817	+	0.683643i	$0.760395\pi$
$542$	−28260.3	−2.23963
$543$	−12292.8	−0.971515
$544$	0	0
$545$	−11068.5	−0.869953
$546$	107.197	0.00840224
$547$	4167.17	0.325732	0.162866	−	0.986648i	$-0.447926\pi$
$547$	4167.17	0.325732	0.162866	+	0.986648i	$0.447926\pi$
$548$	−5467.39	−0.426196
$549$	−1590.59	−0.123651
$550$	5891.83	0.456779
$551$	107.438	0.00830670
$552$	−715.031	−0.0551336
$553$	513.402	0.0394794
$554$	−42073.5	−3.22659
$555$	18892.6	1.44495
$556$	−41167.5	−3.14009
$557$	−9499.84	−0.722659	−0.361329	−	0.932438i	$-0.617677\pi$
$557$	−9499.84	−0.722659	−0.361329	+	0.932438i	$0.617677\pi$
$558$	−4411.33	−0.334671
$559$	236.556	0.0178985
$560$	−4094.19	−0.308948
$561$	0	0
$562$	−27071.0	−2.03189
$563$	13948.4	1.04415	0.522075	−	0.852899i	$-0.325158\pi$
$563$	13948.4	1.04415	0.522075	+	0.852899i	$0.325158\pi$
$564$	33073.8	2.46925
$565$	−3773.88	−0.281006
$566$	25662.6	1.90579
$567$	−963.914	−0.0713943
$568$	24363.5	1.79977
$569$	−10453.6	−0.770193	−0.385096	−	0.922876i	$-0.625832\pi$
$569$	−10453.6	−0.770193	−0.385096	+	0.922876i	$0.625832\pi$
$570$	−27206.5	−1.99922
$571$	23375.9	1.71323	0.856613	−	0.515960i	$-0.172565\pi$
$571$	23375.9	1.71323	0.856613	+	0.515960i	$0.172565\pi$
$572$	262.198	0.0191662
$573$	−4716.63	−0.343874
$574$	−295.058	−0.0214555
$575$	372.833	0.0270404
$576$	9490.52	0.686525
$577$	18975.3	1.36907	0.684534	−	0.728981i	$-0.260006\pi$
$577$	18975.3	1.36907	0.684534	+	0.728981i	$0.260006\pi$
$578$	0	0
$579$	−11361.3	−0.815475
$580$	191.601	0.0137169
$581$	−1232.82	−0.0880307
$582$	−19429.1	−1.38378
$583$	6390.56	0.453979
$584$	3958.46	0.280484
$585$	−175.700	−0.0124176
$586$	26790.4	1.88857
$587$	−28198.5	−1.98275	−0.991377	−	0.131042i	$-0.958168\pi$
$587$	−28198.5	−1.98275	−0.991377	+	0.131042i	$0.958168\pi$
$588$	2631.01	0.184525
$589$	7438.62	0.520379
$590$	113.577	0.00792523
$591$	−7134.67	−0.496584
$592$	−16491.2	−1.14491
$593$	9781.56	0.677370	0.338685	−	0.940900i	$-0.390018\pi$
$593$	9781.56	0.677370	0.338685	+	0.940900i	$0.390018\pi$
$594$	−13736.8	−0.948866
$595$	0	0
$596$	51976.4	3.57221
$597$	−1736.73	−0.119061
$598$	25.3970	0.00173672
$599$	14732.0	1.00490	0.502448	−	0.864607i	$-0.332433\pi$
$599$	14732.0	1.00490	0.502448	+	0.864607i	$0.332433\pi$
$600$	−7639.73	−0.519818
$601$	−22875.8	−1.55262	−0.776311	−	0.630351i	$-0.782911\pi$
$601$	−22875.8	−1.55262	−0.776311	+	0.630351i	$0.782911\pi$
$602$	8887.15	0.601683
$603$	14121.7	0.953700
$604$	40568.1	2.73294
$605$	13075.5	0.878671
$606$	−24628.3	−1.65092
$607$	3140.61	0.210005	0.105003	−	0.994472i	$-0.466515\pi$
$607$	3140.61	0.210005	0.105003	+	0.994472i	$0.466515\pi$
$608$	−7769.76	−0.518265
$609$	−23.1061	−0.00153745
$610$	7321.71	0.485980
$611$	−551.308	−0.0365033
$612$	0	0
$613$	−18951.1	−1.24866	−0.624330	−	0.781160i	$-0.714628\pi$
$613$	−18951.1	−1.24866	−0.624330	+	0.781160i	$0.714628\pi$
$614$	−3583.13	−0.235510
$615$	−428.686	−0.0281078
$616$	4622.84	0.302369
$617$	18435.9	1.20292	0.601459	−	0.798904i	$-0.294586\pi$
$617$	18435.9	1.20292	0.601459	+	0.798904i	$0.294586\pi$
$618$	−11713.1	−0.762409
$619$	8466.61	0.549761	0.274880	−	0.961478i	$-0.411362\pi$
$619$	8466.61	0.549761	0.274880	+	0.961478i	$0.411362\pi$
$620$	13265.9	0.859306
$621$	−869.258	−0.0561709
$622$	−4904.20	−0.316142
$623$	−7477.51	−0.480867
$624$	−135.950	−0.00872170
$625$	−19530.9	−1.24998
$626$	−16485.7	−1.05256
$627$	8025.02	0.511146
$628$	−19759.5	−1.25555
$629$	0	0
$630$	−6600.83	−0.417434
$631$	17128.8	1.08065	0.540323	−	0.841458i	$-0.318302\pi$
$631$	17128.8	1.08065	0.540323	+	0.841458i	$0.318302\pi$
$632$	−2492.41	−0.156872
$633$	−19956.7	−1.25309
$634$	−28541.3	−1.78789
$635$	27199.2	1.69979
$636$	−17656.9	−1.10085
$637$	−43.8563	−0.00272787
$638$	−86.5090	−0.00536822
$639$	10261.3	0.635260
$640$	−36332.7	−2.24403
$641$	27652.1	1.70389	0.851945	−	0.523631i	$-0.175423\pi$
$641$	27652.1	1.70389	0.851945	+	0.523631i	$0.175423\pi$
$642$	26651.4	1.63839
$643$	−31040.9	−1.90379	−0.951894	−	0.306428i	$-0.900866\pi$
$643$	−31040.9	−1.90379	−0.951894	+	0.306428i	$0.900866\pi$
$644$	623.334	0.0381410
$645$	12912.0	0.788234
$646$	0	0
$647$	−5099.85	−0.309885	−0.154943	−	0.987923i	$-0.549519\pi$
$647$	−5099.85	−0.309885	−0.154943	+	0.987923i	$0.549519\pi$
$648$	4679.51	0.283686
$649$	−33.5014	−0.00202626
$650$	271.354	0.0163744
$651$	−1599.79	−0.0963145
$652$	22990.7	1.38096
$653$	12448.9	0.746040	0.373020	−	0.927823i	$-0.378322\pi$
$653$	12448.9	0.746040	0.373020	+	0.927823i	$0.378322\pi$
$654$	−13807.9	−0.825585
$655$	−18050.2	−1.07677
$656$	374.198	0.0222713
$657$	1667.21	0.0990013
$658$	−20712.0	−1.22711
$659$	1249.87	0.0738816	0.0369408	−	0.999317i	$-0.488239\pi$
$659$	1249.87	0.0738816	0.0369408	+	0.999317i	$0.488239\pi$
$660$	14311.6	0.844059
$661$	−24709.2	−1.45397	−0.726986	−	0.686653i	$-0.759079\pi$
$661$	−24709.2	−1.45397	−0.726986	+	0.686653i	$0.759079\pi$
$662$	8725.83	0.512294
$663$	0	0
$664$	5984.95	0.349791
$665$	11130.7	0.649066
$666$	−26587.9	−1.54694
$667$	−5.47426	−0.000317787 0
$668$	−2625.80	−0.152089
$669$	−11106.6	−0.641864
$670$	−65004.5	−3.74827
$671$	−2159.66	−0.124252
$672$	1671.01	0.0959234
$673$	7866.74	0.450580	0.225290	−	0.974292i	$-0.427667\pi$
$673$	7866.74	0.450580	0.225290	+	0.974292i	$0.427667\pi$
$674$	−27758.0	−1.58635
$675$	−9287.57	−0.529598
$676$	−33106.5	−1.88362
$677$	8378.80	0.475662	0.237831	−	0.971307i	$-0.423564\pi$
$677$	8378.80	0.475662	0.237831	+	0.971307i	$0.423564\pi$
$678$	−4707.89	−0.266675
$679$	7948.79	0.449258
$680$	0	0
$681$	−12000.2	−0.675256
$682$	−5989.60	−0.336296
$683$	18176.6	1.01831	0.509156	−	0.860674i	$-0.329958\pi$
$683$	18176.6	1.01831	0.509156	+	0.860674i	$0.329958\pi$
$684$	25013.6	1.39827
$685$	4974.50	0.277469
$686$	−1647.63	−0.0917010
$687$	2670.86	0.148326
$688$	−11270.8	−0.624559
$689$	294.323	0.0162740
$690$	1386.25	0.0764837
$691$	21913.5	1.20641	0.603203	−	0.797587i	$-0.293891\pi$
$691$	21913.5	1.20641	0.603203	+	0.797587i	$0.293891\pi$
$692$	44392.9	2.43868
$693$	1947.02	0.106726
$694$	−53365.7	−2.91892
$695$	37456.2	2.04431
$696$	112.173	0.00610907
$697$	0	0
$698$	−11273.5	−0.611332
$699$	−4226.07	−0.228676
$700$	6660.00	0.359606
$701$	−27012.0	−1.45539	−0.727696	−	0.685900i	$-0.759409\pi$
$701$	−27012.0	−1.45539	−0.727696	+	0.685900i	$0.759409\pi$
$702$	−632.660	−0.0340145
$703$	44833.9	2.40532
$704$	12886.0	0.689857
$705$	−30092.2	−1.60757
$706$	29992.0	1.59882
$707$	10075.9	0.535987
$708$	92.5632	0.00491347
$709$	−18035.8	−0.955357	−0.477678	−	0.878535i	$-0.658522\pi$
$709$	−18035.8	−0.955357	−0.477678	+	0.878535i	$0.658522\pi$
$710$	−47234.3	−2.49672
$711$	−1049.74	−0.0553704
$712$	36301.0	1.91073
$713$	−379.020	−0.0199080
$714$	0	0
$715$	−238.561	−0.0124779
$716$	24451.3	1.27624
$717$	−9884.49	−0.514844
$718$	−51917.7	−2.69854
$719$	9212.47	0.477840	0.238920	−	0.971039i	$-0.423207\pi$
$719$	9212.47	0.477840	0.238920	+	0.971039i	$0.423207\pi$
$720$	8371.29	0.433305
$721$	4792.02	0.247523
$722$	−31615.9	−1.62967
$723$	17056.5	0.877368
$724$	−52024.4	−2.67054
$725$	−58.4896	−0.00299621
$726$	16311.6	0.833859
$727$	−18531.0	−0.945359	−0.472680	−	0.881234i	$-0.656713\pi$
$727$	−18531.0	−0.945359	−0.472680	+	0.881234i	$0.656713\pi$
$728$	212.909	0.0108392
$729$	16122.8	0.819124
$730$	−7674.40	−0.389099
$731$	0	0
$732$	5967.07	0.301297
$733$	10291.4	0.518582	0.259291	−	0.965799i	$-0.416511\pi$
$733$	10291.4	0.518582	0.259291	+	0.965799i	$0.416511\pi$
$734$	−23593.1	−1.18643
$735$	−2393.82	−0.120133
$736$	395.892	0.0198271
$737$	19174.1	0.958329
$738$	603.298	0.0300917
$739$	8231.80	0.409759	0.204879	−	0.978787i	$-0.434320\pi$
$739$	8231.80	0.409759	0.204879	+	0.978787i	$0.434320\pi$
$740$	79955.7	3.97193
$741$	369.600	0.0183233
$742$	11057.4	0.547074
$743$	25362.2	1.25229	0.626144	−	0.779707i	$-0.284632\pi$
$743$	25362.2	1.25229	0.626144	+	0.779707i	$0.284632\pi$
$744$	7766.50	0.382707
$745$	−47290.7	−2.32564
$746$	20447.0	1.00351
$747$	2520.71	0.123465
$748$	0	0
$749$	−10903.6	−0.531919
$750$	−14522.7	−0.707056
$751$	−10647.3	−0.517345	−0.258673	−	0.965965i	$-0.583285\pi$
$751$	−10647.3	−0.517345	−0.258673	+	0.965965i	$0.583285\pi$
$752$	26267.3	1.27377
$753$	−17675.7	−0.855428
$754$	−3.98425	−0.000192438 0
$755$	−36910.9	−1.77924
$756$	−15527.7	−0.747008
$757$	8774.07	0.421267	0.210633	−	0.977565i	$-0.432447\pi$
$757$	8774.07	0.421267	0.210633	+	0.977565i	$0.432447\pi$
$758$	−39126.7	−1.87486
$759$	−408.898	−0.0195548
$760$	−54036.0	−2.57907
$761$	26991.0	1.28571	0.642853	−	0.765990i	$-0.277751\pi$
$761$	26991.0	1.28571	0.642853	+	0.765990i	$0.277751\pi$
$762$	33930.8	1.61310
$763$	5649.07	0.268034
$764$	−19961.3	−0.945256
$765$	0	0
$766$	−19029.2	−0.897589
$767$	−1.54294	−7.26365e−5 0
$768$	−26430.1	−1.24181
$769$	−29762.8	−1.39567	−0.697837	−	0.716257i	$-0.745854\pi$
$769$	−29762.8	−1.39567	−0.697837	+	0.716257i	$0.745854\pi$
$770$	−8962.45	−0.419460
$771$	−4856.12	−0.226834
$772$	−48082.4	−2.24161
$773$	−39045.3	−1.81677	−0.908384	−	0.418136i	$-0.862684\pi$
$773$	−39045.3	−1.81677	−0.908384	+	0.418136i	$0.862684\pi$
$774$	−18171.3	−0.843870
$775$	−4049.63	−0.187699
$776$	−38588.9	−1.78513
$777$	−9642.23	−0.445190
$778$	62462.2	2.87838
$779$	−1017.31	−0.0467895
$780$	659.135	0.0302575
$781$	13932.6	0.638343
$782$	0	0
$783$	136.368	0.00622401
$784$	2089.56	0.0951875
$785$	17978.1	0.817411
$786$	−22517.6	−1.02185
$787$	38300.6	1.73478	0.867389	−	0.497631i	$-0.165796\pi$
$787$	38300.6	1.73478	0.867389	+	0.497631i	$0.165796\pi$
$788$	−30194.8	−1.36503
$789$	−22834.3	−1.03032
$790$	4832.12	0.217619
$791$	1926.08	0.0865785
$792$	−9452.21	−0.424078
$793$	−99.4652	−0.00445411
$794$	37607.5	1.68091
$795$	16065.1	0.716693
$796$	−7350.05	−0.327281
$797$	17159.1	0.762618	0.381309	−	0.924448i	$-0.375473\pi$
$797$	17159.1	0.762618	0.381309	+	0.924448i	$0.375473\pi$
$798$	13885.4	0.615963
$799$	0	0
$800$	4229.90	0.186937
$801$	15289.1	0.674423
$802$	−15918.8	−0.700890
$803$	2263.69	0.0994819
$804$	−52977.5	−2.32385
$805$	−567.140	−0.0248311
$806$	−275.857	−0.0120554
$807$	16169.8	0.705334
$808$	−48915.4	−2.12975
$809$	−23686.7	−1.02939	−0.514697	−	0.857372i	$-0.672095\pi$
$809$	−23686.7	−1.02939	−0.514697	+	0.857372i	$0.672095\pi$
$810$	−9072.31	−0.393541
$811$	11042.5	0.478119	0.239059	−	0.971005i	$-0.423161\pi$
$811$	11042.5	0.478119	0.239059	+	0.971005i	$0.423161\pi$
$812$	−97.7879	−0.00422621
$813$	20955.3	0.903979
$814$	−36100.4	−1.55444
$815$	−20918.1	−0.899054
$816$	0	0
$817$	30641.5	1.31213
$818$	−8189.98	−0.350068
$819$	89.6720	0.00382588
$820$	−1814.25	−0.0772639
$821$	1003.64	0.0426640	0.0213320	−	0.999772i	$-0.493209\pi$
$821$	1003.64	0.0426640	0.0213320	+	0.999772i	$0.493209\pi$
$822$	6205.66	0.263318
$823$	24050.8	1.01866	0.509330	−	0.860571i	$-0.329893\pi$
$823$	24050.8	1.01866	0.509330	+	0.860571i	$0.329893\pi$
$824$	−23263.8	−0.983535
$825$	−4368.87	−0.184369
$826$	−57.9663	−0.00244178
$827$	−26326.9	−1.10698	−0.553492	−	0.832855i	$-0.686705\pi$
$827$	−26326.9	−1.10698	−0.553492	+	0.832855i	$0.686705\pi$
$828$	−1274.52	−0.0534933
$829$	−2486.61	−0.104178	−0.0520889	−	0.998642i	$-0.516588\pi$
$829$	−2486.61	−0.104178	−0.0520889	+	0.998642i	$0.516588\pi$
$830$	−11603.2	−0.485245
$831$	31198.0	1.30234
$832$	593.477	0.0247297
$833$	0	0
$834$	46726.4	1.94005
$835$	2389.08	0.0990151
$836$	33962.9	1.40506
$837$	9441.68	0.389907
$838$	62213.5	2.56459
$839$	−9048.11	−0.372319	−0.186159	−	0.982520i	$-0.559604\pi$
$839$	−9048.11	−0.372319	−0.186159	+	0.982520i	$0.559604\pi$
$840$	11621.3	0.477348
$841$	−24388.1	−0.999965
$842$	−49737.4	−2.03570
$843$	20073.5	0.820128
$844$	−84459.2	−3.44456
$845$	30122.0	1.22631
$846$	42349.3	1.72104
$847$	−6673.38	−0.270720
$848$	−14023.2	−0.567874
$849$	−19029.1	−0.769232
$850$	0	0
$851$	−2284.42	−0.0920198
$852$	−38495.2	−1.54791
$853$	33090.7	1.32826	0.664129	−	0.747618i	$-0.268803\pi$
$853$	33090.7	1.32826	0.664129	+	0.747618i	$0.268803\pi$
$854$	−3736.79	−0.149731
$855$	−22758.6	−0.910325
$856$	52933.5	2.11359
$857$	−11080.5	−0.441662	−0.220831	−	0.975312i	$-0.570877\pi$
$857$	−11080.5	−0.441662	−0.220831	+	0.975312i	$0.570877\pi$
$858$	−297.603	−0.0118415
$859$	−20817.4	−0.826868	−0.413434	−	0.910534i	$-0.635671\pi$
$859$	−20817.4	−0.826868	−0.413434	+	0.910534i	$0.635671\pi$
$860$	54645.3	2.16673
$861$	218.789	0.00866006
$862$	−5661.58	−0.223706
$863$	−23732.9	−0.936127	−0.468064	−	0.883695i	$-0.655048\pi$
$863$	−23732.9	−0.936127	−0.468064	+	0.883695i	$0.655048\pi$
$864$	−9861.98	−0.388323
$865$	−40390.9	−1.58767
$866$	−63889.9	−2.50701
$867$	0	0
$868$	−6770.51	−0.264754
$869$	−1425.31	−0.0556392
$870$	−217.474	−0.00847477
$871$	883.083	0.0343538
$872$	−27424.5	−1.06504
$873$	−16252.7	−0.630092
$874$	3289.71	0.127318
$875$	5941.47	0.229552
$876$	−6254.50	−0.241233
$877$	−6269.19	−0.241386	−0.120693	−	0.992690i	$-0.538512\pi$
$877$	−6269.19	−0.241386	−0.120693	+	0.992690i	$0.538512\pi$
$878$	−51557.9	−1.98177
$879$	−19865.4	−0.762279
$880$	11366.3	0.435408
$881$	−12382.8	−0.473537	−0.236768	−	0.971566i	$-0.576088\pi$
$881$	−12382.8	−0.473537	−0.236768	+	0.971566i	$0.576088\pi$
$882$	3368.87	0.128612
$883$	−680.599	−0.0259388	−0.0129694	−	0.999916i	$-0.504128\pi$
$883$	−680.599	−0.0259388	−0.0129694	+	0.999916i	$0.504128\pi$
$884$	0	0
$885$	−84.2186	−0.00319884
$886$	36335.1	1.37777
$887$	−20733.5	−0.784850	−0.392425	−	0.919784i	$-0.628364\pi$
$887$	−20733.5	−0.784850	−0.392425	+	0.919784i	$0.628364\pi$
$888$	46810.1	1.76897
$889$	−13881.7	−0.523708
$890$	−70377.9	−2.65064
$891$	2676.03	0.100618
$892$	−47004.6	−1.76438
$893$	−71411.7	−2.67604
$894$	−58994.8	−2.20703
$895$	−22247.0	−0.830879
$896$	18543.2	0.691389
$897$	−18.8322	−0.000700991 0
$898$	−63970.9	−2.37721
$899$	59.4601	0.00220590
$900$	−13617.5	−0.504353
$901$	0	0
$902$	819.144	0.0302378
$903$	−6589.93	−0.242856
$904$	−9350.54	−0.344020
$905$	47334.4	1.73862
$906$	−46046.1	−1.68850
$907$	6731.38	0.246430	0.123215	−	0.992380i	$-0.460680\pi$
$907$	6731.38	0.246430	0.123215	+	0.992380i	$0.460680\pi$
$908$	−50786.4	−1.85617
$909$	−20601.9	−0.751730
$910$	−412.774	−0.0150366
$911$	−12538.5	−0.456004	−0.228002	−	0.973661i	$-0.573219\pi$
$911$	−12538.5	−0.456004	−0.228002	+	0.973661i	$0.573219\pi$
$912$	−17609.8	−0.639383
$913$	3422.56	0.124064
$914$	−58618.0	−2.12135
$915$	−5429.14	−0.196155
$916$	11303.4	0.407724
$917$	9212.33	0.331753
$918$	0	0
$919$	−12538.3	−0.450055	−0.225028	−	0.974352i	$-0.572247\pi$
$919$	−12538.3	−0.450055	−0.225028	+	0.974352i	$0.572247\pi$
$920$	2753.29	0.0986668
$921$	2656.93	0.0950585
$922$	−57474.8	−2.05296
$923$	641.677	0.0228830
$924$	−7304.24	−0.260056
$925$	−24407.8	−0.867594
$926$	5129.32	0.182030
$927$	−9798.13	−0.347155
$928$	−62.1071	−0.00219694
$929$	−10142.9	−0.358211	−0.179106	−	0.983830i	$-0.557320\pi$
$929$	−10142.9	−0.358211	−0.179106	+	0.983830i	$0.557320\pi$
$930$	−15057.2	−0.530907
$931$	−5680.77	−0.199978
$932$	−17885.2	−0.628595
$933$	3636.52	0.127604
$934$	−9523.37	−0.333634
$935$	0	0
$936$	−435.330	−0.0152022
$937$	−49990.5	−1.74292	−0.871462	−	0.490463i	$-0.836828\pi$
$937$	−49990.5	−1.74292	−0.871462	+	0.490463i	$0.836828\pi$
$938$	33176.4	1.15485
$939$	12224.4	0.424843
$940$	−127354.	−4.41897
$941$	10771.0	0.373141	0.186571	−	0.982442i	$-0.440263\pi$
$941$	10771.0	0.373141	0.186571	+	0.982442i	$0.440263\pi$
$942$	22427.6	0.775723
$943$	51.8351	0.00179001
$944$	73.5140	0.00253461
$945$	14127.9	0.486329
$946$	−24672.6	−0.847966
$947$	−48958.4	−1.67997	−0.839986	−	0.542608i	$-0.817437\pi$
$947$	−48958.4	−1.67997	−0.839986	+	0.542608i	$0.817437\pi$
$948$	3938.09	0.134919
$949$	104.256	0.00356618
$950$	35148.8	1.20040
$951$	21163.7	0.721641
$952$	0	0
$953$	−23048.5	−0.783435	−0.391718	−	0.920086i	$-0.628119\pi$
$953$	−23048.5	−0.783435	−0.391718	+	0.920086i	$0.628119\pi$
$954$	−22608.7	−0.767280
$955$	18161.8	0.615396
$956$	−41832.4	−1.41523
$957$	64.1475	0.00216676
$958$	−30028.4	−1.01271
$959$	−2538.84	−0.0854886
$960$	32393.9	1.08907
$961$	−25674.2	−0.861810
$962$	−1662.64	−0.0557230
$963$	22294.2	0.746025
$964$	72185.1	2.41175
$965$	43747.8	1.45937
$966$	−707.503	−0.0235648
$967$	31563.1	1.04964	0.524819	−	0.851214i	$-0.324133\pi$
$967$	31563.1	1.04964	0.524819	+	0.851214i	$0.324133\pi$
$968$	32397.2	1.07571
$969$	0	0
$970$	74813.6	2.47641
$971$	−25889.0	−0.855632	−0.427816	−	0.903866i	$-0.640717\pi$
$971$	−25889.0	−0.855632	−0.427816	+	0.903866i	$0.640717\pi$
$972$	52498.9	1.73241
$973$	−19116.6	−0.629855
$974$	−40537.4	−1.33357
$975$	−201.212	−0.00660918
$976$	4739.07	0.155424
$977$	25831.7	0.845883	0.422942	−	0.906157i	$-0.360998\pi$
$977$	25831.7	0.845883	0.422942	+	0.906157i	$0.360998\pi$
$978$	−26095.2	−0.853202
$979$	20759.1	0.677697
$980$	−10131.0	−0.330226
$981$	−11550.5	−0.375922
$982$	−46443.6	−1.50924
$983$	50248.9	1.63041	0.815203	−	0.579175i	$-0.196625\pi$
$983$	50248.9	1.63041	0.815203	+	0.579175i	$0.196625\pi$
$984$	−1062.15	−0.0344108
$985$	27472.7	0.888684
$986$	0	0
$987$	15358.2	0.495296
$988$	1564.19	0.0503680
$989$	−1561.27	−0.0501978
$990$	18325.3	0.588299
$991$	−25790.5	−0.826703	−0.413351	−	0.910572i	$-0.635642\pi$
$991$	−25790.5	−0.826703	−0.413351	+	0.910572i	$0.635642\pi$
$992$	−4300.09	−0.137629
$993$	−6470.30	−0.206776
$994$	24107.0	0.769245
$995$	6687.44	0.213072
$996$	−9456.42	−0.300842
$997$	12867.3	0.408738	0.204369	−	0.978894i	$-0.434486\pi$
$997$	12867.3	0.408738	0.204369	+	0.978894i	$0.434486\pi$
$998$	2514.93	0.0797681
$999$	56906.7	1.80225

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2023.4.a.v.1.6		56
17.10	odd	16		119.4.k.a.15.25	yes	112
17.12	odd	16		119.4.k.a.8.25	✓	112
17.16	even	2		2023.4.a.u.1.6		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.4.k.a.8.25	✓	112	17.12	odd	16
119.4.k.a.15.25	yes	112	17.10	odd	16
2023.4.a.u.1.6		56	17.16	even	2
2023.4.a.v.1.6		56	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2023 = 7 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2023.a (trivial)

\(f(q)\)	\(=\)	\(q-4.80359 q^{2} +3.56192 q^{3} +15.0745 q^{4} -13.7155 q^{5} -17.1100 q^{6} +7.00000 q^{7} -33.9829 q^{8} -14.3127 q^{9} +65.8837 q^{10} -19.4335 q^{11} +53.6941 q^{12} -0.895027 q^{13} -33.6251 q^{14} -48.8535 q^{15} +42.6440 q^{16} +68.7525 q^{18} -115.934 q^{19} -206.754 q^{20} +24.9334 q^{21} +93.3505 q^{22} +5.90718 q^{23} -121.044 q^{24} +63.1152 q^{25} +4.29934 q^{26} -147.153 q^{27} +105.521 q^{28} -0.926712 q^{29} +234.672 q^{30} -64.1625 q^{31} +67.0187 q^{32} -69.2205 q^{33} -96.0086 q^{35} -215.757 q^{36} -386.719 q^{37} +556.900 q^{38} -3.18801 q^{39} +466.092 q^{40} +8.77493 q^{41} -119.770 q^{42} -264.301 q^{43} -292.950 q^{44} +196.306 q^{45} -28.3757 q^{46} +615.968 q^{47} +151.894 q^{48} +49.0000 q^{49} -303.179 q^{50} -13.4921 q^{52} -328.843 q^{53} +706.861 q^{54} +266.540 q^{55} -237.880 q^{56} -412.948 q^{57} +4.45154 q^{58} +1.72390 q^{59} -736.441 q^{60} +111.131 q^{61} +308.210 q^{62} -100.189 q^{63} -663.083 q^{64} +12.2758 q^{65} +332.507 q^{66} -986.655 q^{67} +21.0409 q^{69} +461.186 q^{70} -716.935 q^{71} +486.388 q^{72} -116.484 q^{73} +1857.64 q^{74} +224.811 q^{75} -1747.65 q^{76} -136.034 q^{77} +15.3139 q^{78} +73.3432 q^{79} -584.884 q^{80} -137.702 q^{81} -42.1511 q^{82} -176.117 q^{83} +375.858 q^{84} +1269.59 q^{86} -3.30087 q^{87} +660.406 q^{88} -1068.22 q^{89} -942.975 q^{90} -6.26519 q^{91} +89.0477 q^{92} -228.542 q^{93} -2958.86 q^{94} +1590.10 q^{95} +238.715 q^{96} +1135.54 q^{97} -235.376 q^{98} +278.146 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{2} + 24 q^{3} + 240 q^{4} + 80 q^{5} + 68 q^{6} + 392 q^{7} + 96 q^{8} + 576 q^{9} + 80 q^{10} + 176 q^{11} + 288 q^{12} - 96 q^{13} + 56 q^{14} + 192 q^{15} + 1088 q^{16} + 216 q^{18} + 48 q^{19}+ \cdots + 6576 q^{99}+O(q^{100}) \) 56 * q + 8 * q^2 + 24 * q^3 + 240 * q^4 + 80 * q^5 + 68 * q^6 + 392 * q^7 + 96 * q^8 + 576 * q^9 + 80 * q^10 + 176 * q^11 + 288 * q^12 - 96 * q^13 + 56 * q^14 + 192 * q^15 + 1088 * q^16 + 216 * q^18 + 48 * q^19 + 1660 * q^20 + 168 * q^21 + 352 * q^22 + 608 * q^23 + 736 * q^24 + 1792 * q^25 + 864 * q^27 + 1680 * q^28 + 928 * q^29 - 100 * q^30 + 496 * q^31 + 436 * q^32 + 384 * q^33 + 560 * q^35 + 2804 * q^36 + 1392 * q^37 + 624 * q^39 - 1020 * q^40 + 2088 * q^41 + 476 * q^42 + 1312 * q^43 + 2112 * q^44 + 4840 * q^45 + 736 * q^46 + 5228 * q^48 + 2744 * q^49 + 2020 * q^50 - 1536 * q^52 + 1272 * q^53 + 2268 * q^54 - 336 * q^55 + 672 * q^56 + 2448 * q^57 + 1376 * q^58 + 2372 * q^60 + 976 * q^61 + 3776 * q^62 + 4032 * q^63 + 5376 * q^64 + 6080 * q^65 + 976 * q^67 + 1248 * q^69 + 560 * q^70 + 3216 * q^71 + 4532 * q^72 + 4088 * q^73 - 2456 * q^74 - 760 * q^75 - 2640 * q^76 + 1232 * q^77 + 3744 * q^78 + 1792 * q^79 + 13920 * q^80 + 4184 * q^81 + 8204 * q^82 - 2832 * q^83 + 2016 * q^84 + 4908 * q^86 + 832 * q^87 + 2424 * q^88 - 2768 * q^89 + 8660 * q^90 - 672 * q^91 + 6784 * q^92 + 784 * q^93 - 928 * q^94 + 4560 * q^95 + 6656 * q^96 + 9464 * q^97 + 392 * q^98 + 6576 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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