LMFDB - Embedded newform 126.5.n.a.19.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [126,5,Mod(19,126)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(126, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 5, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("126.19"); S:= CuspForms(chi, 5); N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	126.n (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,-16,-54] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$13.0246153486$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	126.19
Dual form			126.5.n.a.73.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41421 - 2.44949i) q^{2} +(-4.00000 - 6.92820i) q^{4} +(-21.9853 - 12.6932i) q^{5} +(-7.00000 + 48.4974i) q^{7} -22.6274 q^{8} +(-62.1838 + 35.9018i) q^{10} +(21.9853 + 38.0796i) q^{11} +162.507i q^{13} +(108.894 + 85.7321i) q^{14} +(-32.0000 + 55.4256i) q^{16} +(-93.7355 + 54.1182i) q^{17} +(389.338 + 224.784i) q^{19} +203.091i q^{20} +124.368 q^{22} +(-217.911 + 377.433i) q^{23} +(9.73506 + 16.8616i) q^{25} +(398.059 + 229.819i) q^{26} +(364.000 - 145.492i) q^{28} -742.118 q^{29} +(-900.175 + 519.716i) q^{31} +(90.5097 + 156.767i) q^{32} +306.139i q^{34} +(769.485 - 977.377i) q^{35} +(-493.338 + 854.486i) q^{37} +(1101.21 - 635.786i) q^{38} +(497.470 + 287.215i) q^{40} +1143.70i q^{41} +2418.82 q^{43} +(175.882 - 304.637i) q^{44} +(616.346 + 1067.54i) q^{46} +(1165.17 + 672.714i) q^{47} +(-2303.00 - 678.964i) q^{49} +55.0698 q^{50} +(1125.88 - 650.027i) q^{52} +(-1783.10 - 3088.42i) q^{53} -1116.26i q^{55} +(158.392 - 1097.37i) q^{56} +(-1049.51 + 1817.81i) q^{58} +(-3710.93 + 2142.50i) q^{59} +(-1209.57 - 698.345i) q^{61} +2939.96i q^{62} +512.000 q^{64} +(2062.73 - 3572.76i) q^{65} +(-3632.89 - 6292.36i) q^{67} +(749.884 + 432.946i) q^{68} +(-1305.86 - 3267.07i) q^{70} -5987.76 q^{71} +(-500.123 + 288.746i) q^{73} +(1395.37 + 2416.85i) q^{74} -3596.55i q^{76} +(-2000.66 + 799.672i) q^{77} +(1573.12 - 2724.72i) q^{79} +(1407.06 - 812.365i) q^{80} +(2801.47 + 1617.43i) q^{82} +4729.96i q^{83} +2747.74 q^{85} +(3420.73 - 5924.88i) q^{86} +(-497.470 - 861.644i) q^{88} +(725.651 + 418.955i) q^{89} +(-7881.16 - 1137.55i) q^{91} +3486.58 q^{92} +(3295.61 - 1902.72i) q^{94} +(-5706.47 - 9883.89i) q^{95} +5622.23i q^{97} +(-4920.05 + 4680.97i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{4} - 54 q^{5} - 28 q^{7} - 96 q^{10} + 54 q^{11} - 128 q^{16} - 918 q^{17} + 30 q^{19} + 192 q^{22} + 486 q^{23} - 572 q^{25} + 1728 q^{26} + 1456 q^{28} - 3240 q^{29} - 546 q^{31} + 1890 q^{35}+ \cdots - 8910 q^{95}+O(q^{100}) $ 4 * q - 16 * q^4 - 54 * q^5 - 28 * q^7 - 96 * q^10 + 54 * q^11 - 128 * q^16 - 918 * q^17 + 30 * q^19 + 192 * q^22 + 486 * q^23 - 572 * q^25 + 1728 * q^26 + 1456 * q^28 - 3240 * q^29 - 546 * q^31 + 1890 * q^35 - 446 * q^37 + 4320 * q^38 + 768 * q^40 + 2344 * q^43 + 432 * q^44 + 3840 * q^46 - 702 * q^47 - 9212 * q^49 + 3456 * q^50 - 384 * q^52 - 2754 * q^53 + 384 * q^58 - 12366 * q^59 + 7686 * q^61 + 2048 * q^64 + 3024 * q^65 - 5062 * q^67 + 7344 * q^68 - 2016 * q^70 - 18792 * q^71 - 17274 * q^73 + 4320 * q^74 - 4914 * q^77 + 794 * q^79 + 3456 * q^80 + 9984 * q^82 + 10380 * q^85 + 10368 * q^86 - 768 * q^88 + 12474 * q^89 + 2688 * q^91 - 7776 * q^92 + 15168 * q^94 - 8910 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.41421	−	2.44949i	0.353553	−	0.612372i
$2$	1.41421	−	2.44949i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−4.00000	−	6.92820i	−0.250000	−	0.433013i
$5$	−21.9853	−	12.6932i	−0.879411	−	0.507728i	−0.00894701	−	0.999960i	$-0.502848\pi$
$5$	−21.9853	−	12.6932i	−0.879411	−	0.507728i	−0.870464	+	0.492232i	$0.836181\pi$
$6$		0			0
$7$	−7.00000	+	48.4974i	−0.142857	+	0.989743i
$7$	−7.00000	+	48.4974i	−0.142857	+	0.989743i
$8$	−22.6274			−0.353553
$9$		0			0
$10$	−62.1838	+	35.9018i	−0.621838	+	0.359018i
$11$	21.9853	+	38.0796i	0.181697	+	0.314708i	0.942458	−	0.334324i	$-0.108508\pi$
$11$	21.9853	+	38.0796i	0.181697	+	0.314708i	−0.760762	+	0.649031i	$0.775174\pi$
$12$		0			0
$13$			162.507i			0.961579i	0.876836	+	0.480790i	$0.159650\pi$
$13$			162.507i			0.961579i	−0.876836	+	0.480790i	$0.840350\pi$
$14$	108.894	+	85.7321i	0.555584	+	0.437409i
$15$		0			0
$16$	−32.0000	+	55.4256i	−0.125000	+	0.216506i
$17$	−93.7355	+	54.1182i	−0.324344	+	0.187260i	−0.653327	−	0.757076i	$-0.726627\pi$
$17$	−93.7355	+	54.1182i	−0.324344	+	0.187260i	0.328983	+	0.944336i	$0.393294\pi$
$18$		0			0
$19$	389.338	+	224.784i	1.07850	+	0.622671i	0.930491	−	0.366315i	$-0.119381\pi$
$19$	389.338	+	224.784i	1.07850	+	0.622671i	0.148007	+	0.988986i	$0.452714\pi$
$20$			203.091i			0.507728i
$21$		0			0
$22$	124.368			0.256958
$23$	−217.911	+	377.433i	−0.411931	+	0.713485i	−0.995101	−	0.0988653i	$-0.968479\pi$
$23$	−217.911	+	377.433i	−0.411931	+	0.713485i	0.583170	+	0.812350i	$0.301812\pi$
$24$		0			0
$25$	9.73506	+	16.8616i	0.0155761	+	0.0269786i
$26$	398.059	+	229.819i	0.588844	+	0.339970i
$27$		0			0
$28$	364.000	−	145.492i	0.464286	−	0.185577i
$29$	−742.118			−0.882423			−0.441212	−	0.897403i	$-0.645451\pi$
$29$	−742.118			−0.882423			−0.441212	+	0.897403i	$0.645451\pi$
$30$		0			0
$31$	−900.175	+	519.716i	−0.936707	+	0.540808i	−0.888926	−	0.458050i	$-0.848548\pi$
$31$	−900.175	+	519.716i	−0.936707	+	0.540808i	−0.0477804	+	0.998858i	$0.515215\pi$
$32$	90.5097	+	156.767i	0.0883883	+	0.153093i
$33$		0			0
$34$			306.139i			0.264826i
$35$	769.485	−	977.377i	0.628151	−	0.797859i
$36$		0			0
$37$	−493.338	+	854.486i	−0.360364	+	0.624168i	−0.988021	−	0.154322i	$-0.950681\pi$
$37$	−493.338	+	854.486i	−0.360364	+	0.624168i	0.627657	+	0.778490i	$0.284014\pi$
$38$	1101.21	−	635.786i	0.762613	−	0.440295i
$39$		0			0
$40$	497.470	+	287.215i	0.310919	+	0.179509i
$41$			1143.70i			0.680366i	0.940359	+	0.340183i	$0.110489\pi$
$41$			1143.70i			0.680366i	−0.940359	+	0.340183i	$0.889511\pi$
$42$		0			0
$43$	2418.82			1.30818			0.654089	−	0.756418i	$-0.273052\pi$
$43$	2418.82			1.30818			0.654089	+	0.756418i	$0.273052\pi$
$44$	175.882	−	304.637i	0.0908483	−	0.157354i
$45$		0			0
$46$	616.346	+	1067.54i	0.291279	+	0.504510i
$47$	1165.17	+	672.714i	0.527467	+	0.304533i	0.739984	−	0.672624i	$-0.234833\pi$
$47$	1165.17	+	672.714i	0.527467	+	0.304533i	−0.212517	+	0.977157i	$0.568166\pi$
$48$		0			0
$49$	−2303.00	−	678.964i	−0.959184	−	0.282784i
$50$	55.0698			0.0220279
$51$		0			0
$52$	1125.88	−	650.027i	0.416376	−	0.240395i
$53$	−1783.10	−	3088.42i	−0.634782	−	1.09947i	−0.986561	−	0.163391i	$-0.947757\pi$
$53$	−1783.10	−	3088.42i	−0.634782	−	1.09947i	0.351780	−	0.936083i	$-0.385577\pi$
$54$		0			0
$55$		−	1116.26i		−	0.369010i
$56$	158.392	−	1097.37i	0.0505076	−	0.349927i
$57$		0			0
$58$	−1049.51	+	1817.81i	−0.311984	+	0.540372i
$59$	−3710.93	+	2142.50i	−1.06605	+	0.615485i	−0.927100	−	0.374814i	$-0.877707\pi$
$59$	−3710.93	+	2142.50i	−1.06605	+	0.615485i	−0.138952	+	0.990299i	$0.544373\pi$
$60$		0			0
$61$	−1209.57	−	698.345i	−0.325066	−	0.187677i	0.328583	−	0.944475i	$-0.393429\pi$
$61$	−1209.57	−	698.345i	−0.325066	−	0.187677i	−0.653648	+	0.756799i	$0.726762\pi$
$62$			2939.96i			0.764818i
$63$		0			0
$64$	512.000			0.125000
$65$	2062.73	−	3572.76i	0.488221	−	0.845623i
$66$		0			0
$67$	−3632.89	−	6292.36i	−0.809288	−	1.40173i	−0.913358	−	0.407158i	$-0.866520\pi$
$67$	−3632.89	−	6292.36i	−0.809288	−	1.40173i	0.104070	−	0.994570i	$-0.466813\pi$
$68$	749.884	+	432.946i	0.162172	+	0.0936301i
$69$		0			0
$70$	−1305.86	−	3267.07i	−0.266502	−	0.666748i
$71$	−5987.76			−1.18781			−0.593906	−	0.804534i	$-0.702415\pi$
$71$	−5987.76			−1.18781			−0.593906	+	0.804534i	$0.702415\pi$
$72$		0			0
$73$	−500.123	+	288.746i	−0.0938494	+	0.0541840i	−0.546190	−	0.837661i	$-0.683922\pi$
$73$	−500.123	+	288.746i	−0.0938494	+	0.0541840i	0.452341	+	0.891845i	$0.350589\pi$
$74$	1395.37	+	2416.85i	0.254815	+	0.441353i
$75$		0			0
$76$		−	3596.55i		−	0.622671i
$77$	−2000.66	+	799.672i	−0.337436	+	0.134875i
$78$		0			0
$79$	1573.12	−	2724.72i	0.252061	−	0.436583i	−0.712032	−	0.702147i	$-0.752225\pi$
$79$	1573.12	−	2724.72i	0.252061	−	0.436583i	0.964093	+	0.265564i	$0.0855582\pi$
$80$	1407.06	−	812.365i	0.219853	−	0.126932i
$81$		0			0
$82$	2801.47	+	1617.43i	0.416637	+	0.240546i
$83$			4729.96i			0.686596i	0.939227	+	0.343298i	$0.111544\pi$
$83$			4729.96i			0.686596i	−0.939227	+	0.343298i	$0.888456\pi$
$84$		0			0
$85$	2747.74			0.380309
$86$	3420.73	−	5924.88i	0.462511	−	0.801092i
$87$		0			0
$88$	−497.470	−	861.644i	−0.0642394	−	0.111266i
$89$	725.651	+	418.955i	0.0916110	+	0.0528916i	0.545106	−	0.838367i	$-0.316490\pi$
$89$	725.651	+	418.955i	0.0916110	+	0.0528916i	−0.453495	+	0.891259i	$0.649823\pi$
$90$		0			0
$91$	−7881.16	−	1137.55i	−0.951716	−	0.137368i
$92$	3486.58			0.411931
$93$		0			0
$94$	3295.61	−	1902.72i	0.372975	−	0.215337i
$95$	−5706.47	−	9883.89i	−0.632295	−	1.09517i
$96$		0			0
$97$			5622.23i			0.597537i	0.954326	+	0.298769i	$0.0965759\pi$
$97$			5622.23i			0.597537i	−0.954326	+	0.298769i	$0.903424\pi$
$98$	−4920.05	+	4680.97i	−0.512292	+	0.487398i
$99$		0			0
$100$	77.8805	−	134.893i	0.00778805	−	0.0134893i
$101$	5703.21	−	3292.75i	0.559083	−	0.322787i	−0.193694	−	0.981062i	$-0.562047\pi$
$101$	5703.21	−	3292.75i	0.559083	−	0.322787i	0.752778	+	0.658275i	$0.228714\pi$
$102$		0			0
$103$	1320.25	+	762.249i	0.124447	+	0.0718492i	0.560931	−	0.827863i	$-0.310443\pi$
$103$	1320.25	+	762.249i	0.124447	+	0.0718492i	−0.436484	+	0.899712i	$0.643777\pi$
$104$		−	3677.11i		−	0.339970i
$105$		0			0
$106$	−10086.7			−0.897717
$107$	5303.31	−	9185.61i	0.463212	−	0.802306i	−0.535907	−	0.844277i	$-0.680030\pi$
$107$	5303.31	−	9185.61i	0.463212	−	0.802306i	0.999119	+	0.0419706i	$0.0133636\pi$
$108$		0			0
$109$	6976.13	+	12083.0i	0.587167	+	1.01700i	0.994601	+	0.103769i	$0.0330902\pi$
$109$	6976.13	+	12083.0i	0.587167	+	1.01700i	−0.407434	+	0.913235i	$0.633576\pi$
$110$	−2734.26	−	1578.62i	−0.225972	−	0.130465i
$111$		0			0
$112$	−2464.00	−	1939.90i	−0.196429	−	0.154647i
$113$	8811.30			0.690054			0.345027	−	0.938593i	$-0.387870\pi$
$113$	8811.30			0.690054			0.345027	+	0.938593i	$0.387870\pi$
$114$		0			0
$115$	9581.68	−	5531.99i	0.724513	−	0.418298i
$116$	2968.47	+	5141.54i	0.220606	+	0.382100i
$117$		0			0
$118$			12119.8i			0.870427i
$119$	−1968.45	−	4924.76i	−0.139005	−	0.347769i
$120$		0			0
$121$	6353.79	−	11005.1i	0.433973	−	0.751663i
$122$	−3421.18	+	1975.22i	−0.229856	+	0.132707i
$123$		0			0
$124$	7201.40	+	4157.73i	0.468353	+	0.270404i
$125$			15372.2i			0.983823i
$126$		0			0
$127$	3992.70			0.247548			0.123774	−	0.992310i	$-0.460500\pi$
$127$	3992.70			0.247548			0.123774	+	0.992310i	$0.460500\pi$
$128$	724.077	−	1254.14i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−5834.29	−	10105.3i	−0.345224	−	0.597946i
$131$	17515.4	+	10112.5i	1.02065	+	0.589272i	0.914292	−	0.405056i	$-0.132748\pi$
$131$	17515.4	+	10112.5i	1.02065	+	0.589272i	0.106357	+	0.994328i	$0.466081\pi$
$132$		0			0
$133$	−13626.8	+	17308.4i	−0.770355	+	0.978483i
$134$	−20550.7			−1.14451
$135$		0			0
$136$	2120.99	−	1224.56i	0.114673	−	0.0662065i
$137$	12528.9	+	21700.6i	0.667530	+	1.15620i	0.978593	+	0.205807i	$0.0659818\pi$
$137$	12528.9	+	21700.6i	0.667530	+	1.15620i	−0.311062	+	0.950389i	$0.600685\pi$
$138$		0			0
$139$			20070.1i			1.03877i	0.854541	+	0.519385i	$0.173839\pi$
$139$			20070.1i			1.03877i	−0.854541	+	0.519385i	$0.826161\pi$
$140$	−9849.41	−	1421.64i	−0.502521	−	0.0725326i
$141$		0			0
$142$	−8467.98	+	14667.0i	−0.419955	+	0.727384i
$143$	−6188.20	+	3572.76i	−0.302616	+	0.174716i
$144$		0			0
$145$	16315.7	+	9419.86i	0.776013	+	0.448031i
$146$			1633.40i			0.0766277i
$147$		0			0
$148$	7893.40			0.360364
$149$	−21353.9	+	36986.1i	−0.961846	+	1.66597i	−0.243986	+	0.969779i	$0.578455\pi$
$149$	−21353.9	+	36986.1i	−0.961846	+	1.66597i	−0.717860	+	0.696188i	$0.754878\pi$
$150$		0			0
$151$	−14803.7	−	25640.8i	−0.649258	−	1.12455i	−0.983301	−	0.181989i	$-0.941746\pi$
$151$	−14803.7	−	25640.8i	−0.649258	−	1.12455i	0.334043	−	0.942558i	$-0.391587\pi$
$152$	−8809.71	−	5086.29i	−0.381307	−	0.220147i
$153$		0			0
$154$	−870.573	+	6031.50i	−0.0367082	+	0.254322i
$155$	26387.5			1.09833
$156$		0			0
$157$	10597.6	−	6118.53i	0.429940	−	0.248226i	−0.269381	−	0.963034i	$-0.586819\pi$
$157$	10597.6	−	6118.53i	0.429940	−	0.248226i	0.699321	+	0.714808i	$0.253486\pi$
$158$	−4449.44	−	7706.66i	−0.178234	−	0.308711i
$159$		0			0
$160$		−	4595.43i		−	0.179509i
$161$	−16779.2	−	13210.2i	−0.647319	−	0.509632i
$162$		0			0
$163$	−10765.6	+	18646.5i	−0.405193	+	0.701814i	−0.994344	−	0.106209i	$-0.966129\pi$
$163$	−10765.6	+	18646.5i	−0.405193	+	0.701814i	0.589151	+	0.808023i	$0.299462\pi$
$164$	7923.75	−	4574.78i	0.294607	−	0.170092i
$165$		0			0
$166$	11586.0	+	6689.17i	0.420452	+	0.242748i
$167$		−	16578.9i		−	0.594461i	−0.954806	−	0.297230i	$-0.903937\pi$
$167$		−	16578.9i		−	0.594461i	0.954806	−	0.297230i	$-0.0960629\pi$
$168$		0			0
$169$	2152.52			0.0753658
$170$	3885.88	−	6730.55i	0.134460	−	0.232891i
$171$		0			0
$172$	−9675.28	−	16758.1i	−0.327044	−	0.566458i
$173$	34972.8	+	20191.5i	1.16852	+	0.674648i	0.953332	−	0.301924i	$-0.0976289\pi$
$173$	34972.8	+	20191.5i	1.16852	+	0.674648i	0.215192	+	0.976572i	$0.430962\pi$
$174$		0			0
$175$	−885.891	+	354.094i	−0.0289270	+	0.0115623i
$176$	−2814.12			−0.0908483
$177$		0			0
$178$	2052.45	−	1184.98i	0.0647788	−	0.0374000i
$179$	−26747.2	−	46327.5i	−0.834780	−	1.44588i	−0.894209	−	0.447649i	$-0.852261\pi$
$179$	−26747.2	−	46327.5i	−0.834780	−	1.44588i	0.0594290	−	0.998233i	$-0.481072\pi$
$180$		0			0
$181$			54202.1i			1.65447i	0.561857	+	0.827235i	$0.310087\pi$
$181$			54202.1i			1.65447i	−0.561857	+	0.827235i	$0.689913\pi$
$182$	−13932.1	+	17696.1i	−0.420603	+	0.534238i
$183$		0			0
$184$	4930.77	−	8540.34i	0.145639	−	0.252255i
$185$	21692.3	−	12524.1i	0.633815	−	0.365934i
$186$		0			0
$187$	−4121.60	−	2379.61i	−0.117864	−	0.0680491i
$188$		−	10763.4i		−	0.304533i
$189$		0			0
$190$	−32280.6			−0.894201
$191$	−601.936	+	1042.58i	−0.0165000	+	0.0285788i	−0.874158	−	0.485643i	$-0.838586\pi$
$191$	−601.936	+	1042.58i	−0.0165000	+	0.0285788i	0.857658	+	0.514221i	$0.171919\pi$
$192$		0			0
$193$	−25656.5	−	44438.3i	−0.688783	−	1.19301i	−0.972232	−	0.234019i	$-0.924812\pi$
$193$	−25656.5	−	44438.3i	−0.688783	−	1.19301i	0.283449	−	0.958987i	$-0.408521\pi$
$194$	13771.6	+	7951.03i	0.365915	+	0.211261i
$195$		0			0
$196$	4508.00	+	18671.5i	0.117347	+	0.486035i
$197$	1456.28			0.0375242			0.0187621	−	0.999824i	$-0.494027\pi$
$197$	1456.28			0.0375242			0.0187621	+	0.999824i	$0.494027\pi$
$198$		0			0
$199$	59546.3	−	34379.1i	1.50366	−	0.868137i	0.503667	−	0.863898i	$-0.331984\pi$
$199$	59546.3	−	34379.1i	1.50366	−	0.868137i	0.999991	−	0.00423890i	$-0.00134929\pi$
$200$	−220.279	−	381.535i	−0.00550698	−	0.00953838i
$201$		0			0
$202$		−	18626.6i		−	0.456490i
$203$	5194.82	−	35990.8i	0.126060	−	0.873372i
$204$		0			0
$205$	14517.2	−	25144.5i	0.345441	−	0.598322i
$206$	3734.24	−	2155.96i	0.0879970	−	0.0508051i
$207$		0			0
$208$	−9007.04	−	5200.22i	−0.208188	−	0.120197i
$209$			19767.8i			0.452549i
$210$		0			0
$211$	−622.821			−0.0139894			−0.00699469	−	0.999976i	$-0.502226\pi$
$211$	−622.821			−0.0139894			−0.00699469	+	0.999976i	$0.502226\pi$
$212$	−14264.8	+	24707.4i	−0.317391	+	0.549737i
$213$		0			0
$214$	−15000.0	−	25980.8i	−0.327540	−	0.567316i
$215$	−53178.5	−	30702.6i	−1.15043	−	0.664199i
$216$		0			0
$217$	−18903.7	−	47294.2i	−0.401446	−	1.00436i
$218$	39463.0			0.830380
$219$		0			0
$220$	−7733.64	+	4465.02i	−0.159786	+	0.0922525i
$221$	−8794.58	−	15232.7i	−0.180066	−	0.311883i
$222$		0			0
$223$			11509.7i			0.231449i	0.993281	+	0.115725i	$0.0369190\pi$
$223$			11509.7i			0.231449i	−0.993281	+	0.115725i	$0.963081\pi$
$224$	−8236.38	+	3292.11i	−0.164150	+	0.0656113i
$225$		0			0
$226$	12461.1	−	21583.2i	0.243971	−	0.422570i
$227$	48815.4	−	28183.6i	0.947339	−	0.546946i	0.0550855	−	0.998482i	$-0.482457\pi$
$227$	48815.4	−	28183.6i	0.947339	−	0.546946i	0.892253	+	0.451535i	$0.149124\pi$
$228$		0			0
$229$	−36484.4	−	21064.3i	−0.695722	−	0.401675i	0.110030	−	0.993928i	$-0.464905\pi$
$229$	−36484.4	−	21064.3i	−0.695722	−	0.401675i	−0.805752	+	0.592253i	$0.798239\pi$
$230$		−	31293.6i		−	0.591562i
$231$		0			0
$232$	16792.2			0.311984
$233$	−27550.9	+	47719.6i	−0.507486	+	0.878992i	0.492476	+	0.870326i	$0.336092\pi$
$233$	−27550.9	+	47719.6i	−0.507486	+	0.878992i	−0.999962	+	0.00866633i	$0.997241\pi$
$234$		0			0
$235$	−17077.8	−	29579.6i	−0.309240	−	0.535620i
$236$	29687.4	+	17140.0i	0.533026	+	0.307743i
$237$		0			0
$238$	−14846.9	−	2142.97i	−0.262110	−	0.0378323i
$239$	−23082.5			−0.404098			−0.202049	−	0.979375i	$-0.564760\pi$
$239$	−23082.5			−0.404098			−0.202049	+	0.979375i	$0.564760\pi$
$240$		0			0
$241$	70643.9	−	40786.3i	1.21630	−	0.702231i	0.252175	−	0.967682i	$-0.418854\pi$
$241$	70643.9	−	40786.3i	1.21630	−	0.702231i	0.964124	+	0.265451i	$0.0855209\pi$
$242$	−17971.2	−	31127.1i	−0.306865	−	0.531506i
$243$		0			0
$244$			11173.5i			0.187677i
$245$	42013.9	+	44159.7i	0.699940	+	0.735688i
$246$		0			0
$247$	−36529.0	+	63270.0i	−0.598747	+	1.03706i
$248$	20368.6	−	11759.8i	0.331176	−	0.191204i
$249$		0			0
$250$	37654.1	+	21739.6i	0.602466	+	0.347834i
$251$			27207.6i			0.431859i	0.976409	+	0.215930i	$0.0692782\pi$
$251$			27207.6i			0.431859i	−0.976409	+	0.215930i	$0.930722\pi$
$252$		0			0
$253$	−19163.4			−0.299385
$254$	5646.53	−	9780.08i	0.0875214	−	0.151592i
$255$		0			0
$256$	−2048.00	−	3547.24i	−0.0312500	−	0.0541266i
$257$	−93469.3	−	53964.5i	−1.41515	−	0.817038i	−0.419283	−	0.907856i	$-0.637719\pi$
$257$	−93469.3	−	53964.5i	−1.41515	−	0.817038i	−0.995868	+	0.0908179i	$0.971052\pi$
$258$		0			0
$259$	−37987.0	−	29907.0i	−0.566286	−	0.445834i
$260$	−33003.7			−0.488221
$261$		0			0
$262$	49540.9	−	28602.5i	0.721708	−	0.416678i
$263$	−20072.0	−	34765.8i	−0.290188	−	0.502621i	0.683666	−	0.729795i	$-0.260385\pi$
$263$	−20072.0	−	34765.8i	−0.290188	−	0.502621i	−0.973854	+	0.227174i	$0.927051\pi$
$264$		0			0
$265$			90533.1i			1.28919i
$266$	23125.5	+	57856.5i	0.326834	+	0.817690i
$267$		0			0
$268$	−29063.1	+	50338.8i	−0.404644	+	0.700864i
$269$	−91239.0	+	52676.9i	−1.26089	+	0.727973i	−0.973246	−	0.229765i	$-0.926204\pi$
$269$	−91239.0	+	52676.9i	−1.26089	+	0.727973i	−0.287641	+	0.957738i	$0.592871\pi$
$270$		0			0
$271$	−13189.3	−	7614.84i	−0.179590	−	0.103687i	0.407510	−	0.913201i	$-0.366397\pi$
$271$	−13189.3	−	7614.84i	−0.179590	−	0.103687i	−0.587100	+	0.809514i	$0.699731\pi$
$272$		−	6927.13i		−	0.0936301i
$273$		0			0
$274$	70874.0			0.944030
$275$	−428.056	+	741.415i	−0.00566025	+	0.00980384i
$276$		0			0
$277$	4935.81	+	8549.07i	0.0643278	+	0.111419i	0.896396	−	0.443255i	$-0.146176\pi$
$277$	4935.81	+	8549.07i	0.0643278	+	0.111419i	−0.832068	+	0.554674i	$0.812843\pi$
$278$	49161.4	+	28383.4i	0.636114	+	0.367260i
$279$		0			0
$280$	−17411.5	+	22115.5i	−0.222085	+	0.282086i
$281$	155117.			1.96448			0.982240	−	0.187631i	$-0.0600810\pi$
$281$	155117.			1.96448			0.982240	+	0.187631i	$0.0600810\pi$
$282$		0			0
$283$	−94970.0	+	54831.0i	−1.18581	+	0.684626i	−0.957351	−	0.288929i	$-0.906701\pi$
$283$	−94970.0	+	54831.0i	−1.18581	+	0.684626i	−0.228456	+	0.973554i	$0.573368\pi$
$284$	23951.1	+	41484.4i	0.296953	+	0.514338i
$285$		0			0
$286$			20210.6i			0.247085i
$287$	−55466.3	−	8005.87i	−0.673388	−	0.0971952i
$288$		0			0
$289$	−35902.9	+	62185.7i	−0.429867	+	0.744552i
$290$	46147.7	−	26643.4i	0.548724	−	0.316806i
$291$		0			0
$292$	4000.99	+	2309.97i	0.0469247	+	0.0270920i
$293$			89912.4i			1.04733i	0.851924	+	0.523666i	$0.175436\pi$
$293$			89912.4i			1.04733i	−0.851924	+	0.523666i	$0.824564\pi$
$294$		0			0
$295$	108781.			1.25000
$296$	11163.0	−	19334.8i	0.127408	−	0.220677i
$297$		0			0
$298$	60398.1	+	104613.i	0.680128	+	1.17802i
$299$	−61335.5	−	35412.1i	−0.686072	−	0.396104i
$300$		0			0
$301$	−16931.7	+	117307.i	−0.186883	+	1.29476i
$302$	−83742.5			−0.918189
$303$		0			0
$304$	−24917.6	+	14386.2i	−0.269624	+	0.155668i
$305$	17728.5	+	30706.6i	0.190578	+	0.330090i
$306$		0			0
$307$		−	141681.i		−	1.50327i	−0.659582	−	0.751633i	$-0.729267\pi$
$307$		−	141681.i		−	1.50327i	0.659582	−	0.751633i	$-0.270733\pi$
$308$	13542.9	+	10662.3i	0.142762	+	0.112396i
$309$		0			0
$310$	37317.5	−	64635.9i	0.388320	−	0.672590i
$311$	74171.3	−	42822.8i	0.766858	−	0.442746i	−0.0648948	−	0.997892i	$-0.520671\pi$
$311$	74171.3	−	42822.8i	0.766858	−	0.442746i	0.831753	+	0.555147i	$0.187338\pi$
$312$		0			0
$313$	15442.6	+	8915.78i	0.157627	+	0.0910061i	0.576739	−	0.816929i	$-0.304325\pi$
$313$	15442.6	+	8915.78i	0.157627	+	0.0910061i	−0.419112	+	0.907935i	$0.637658\pi$
$314$		−	34611.6i		−	0.351045i
$315$		0			0
$316$	−25169.8			−0.252061
$317$	40402.6	−	69979.4i	0.402060	−	0.696388i	−0.591914	−	0.806001i	$-0.701628\pi$
$317$	40402.6	−	69979.4i	0.402060	−	0.696388i	0.993974	+	0.109613i	$0.0349610\pi$
$318$		0			0
$319$	−16315.7	−	28259.6i	−0.160333	−	0.277705i
$320$	−11256.5	−	6498.92i	−0.109926	−	0.0634660i
$321$		0			0
$322$	−56087.5	+	22418.4i	−0.540946	+	0.216218i
$323$	−48659.7			−0.466406
$324$		0			0
$325$	−2740.13	+	1582.01i	−0.0259421	+	0.0149777i
$326$	30449.6	+	52740.3i	0.286514	+	0.496258i
$327$		0			0
$328$		−	25878.9i		−	0.240546i
$329$	−40781.1	+	51799.0i	−0.376762	+	0.478552i
$330$		0			0
$331$	−36402.1	+	63050.3i	−0.332254	+	0.575482i	−0.982954	−	0.183854i	$-0.941143\pi$
$331$	−36402.1	+	63050.3i	−0.332254	+	0.575482i	0.650699	+	0.759336i	$0.274476\pi$
$332$	32770.1	−	18919.8i	0.297305	−	0.171649i
$333$		0			0
$334$	−40609.9	−	23446.1i	−0.364031	−	0.210174i
$335$			184452.i			1.64359i
$336$		0			0
$337$	126538.			1.11419			0.557095	−	0.830449i	$-0.311916\pi$
$337$	126538.			1.11419			0.557095	+	0.830449i	$0.311916\pi$
$338$	3044.13	−	5272.58i	0.0266458	−	0.0461519i
$339$		0			0
$340$	−10990.9	−	19036.9i	−0.0950773	−	0.164679i
$341$	−39581.2	−	22852.2i	−0.340393	−	0.196526i
$342$		0			0
$343$	49049.0	−	106937.i	0.416910	−	0.908948i
$344$	−54731.7			−0.462511
$345$		0			0
$346$	98917.9	−	57110.3i	0.826271	−	0.477048i
$347$	−33474.6	−	57979.8i	−0.278008	−	0.481524i	0.692882	−	0.721051i	$-0.256341\pi$
$347$	−33474.6	−	57979.8i	−0.278008	−	0.481524i	−0.970890	+	0.239528i	$0.923007\pi$
$348$		0			0
$349$			25527.5i			0.209583i	0.994494	+	0.104792i	$0.0334176\pi$
$349$			25527.5i			0.209583i	−0.994494	+	0.104792i	$0.966582\pi$
$350$	−385.489	+	2670.75i	−0.00314685	+	0.0218020i
$351$		0			0
$352$	−3979.76	+	6893.15i	−0.0321197	+	0.0556330i
$353$	48995.9	−	28287.8i	0.393197	−	0.227013i	−0.290347	−	0.956921i	$-0.593771\pi$
$353$	48995.9	−	28287.8i	0.393197	−	0.227013i	0.683545	+	0.729909i	$0.260437\pi$
$354$		0			0
$355$	131643.	+	76003.9i	1.04458	+	0.603086i
$356$		−	6703.27i		−	0.0528916i
$357$		0			0
$358$	−151305.			−1.18056
$359$	18902.4	−	32739.9i	0.146665	−	0.254032i	−0.783328	−	0.621609i	$-0.786479\pi$
$359$	18902.4	−	32739.9i	0.146665	−	0.254032i	0.929993	+	0.367577i	$0.119813\pi$
$360$		0			0
$361$	35895.4	+	62172.6i	0.275438	+	0.477073i
$362$	132767.	+	76653.3i	1.01315	+	0.584943i
$363$		0			0
$364$	23643.5	+	59152.5i	0.178447	+	0.446447i
$365$	14660.5			0.110043
$366$		0			0
$367$	9367.27	−	5408.20i	0.0695474	−	0.0401532i	−0.464823	−	0.885404i	$-0.653882\pi$
$367$	9367.27	−	5408.20i	0.0695474	−	0.0401532i	0.534370	+	0.845250i	$0.320549\pi$
$368$	−13946.3	−	24155.7i	−0.102983	−	0.178371i
$369$		0			0
$370$		−	70846.9i		−	0.517508i
$371$	162262.	−	64856.9i	1.17888	−	0.471203i
$372$		0			0
$373$	15511.7	−	26867.0i	0.111491	−	0.193109i	−0.804880	−	0.593437i	$-0.797771\pi$
$373$	15511.7	−	26867.0i	0.111491	−	0.193109i	0.916372	+	0.400328i	$0.131104\pi$
$374$	−11657.7	+	6730.55i	−0.0833428	+	0.0481180i
$375$		0			0
$376$	−26364.9	−	15221.8i	−0.186488	−	0.107669i
$377$		−	120599.i		−	0.848519i
$378$		0			0
$379$	−98527.5			−0.685929			−0.342964	−	0.939348i	$-0.611431\pi$
$379$	−98527.5			−0.685929			−0.342964	+	0.939348i	$0.611431\pi$
$380$	−45651.7	+	79071.1i	−0.316148	+	0.547584i
$381$		0			0
$382$	1702.53	+	2948.87i	0.0116673	+	0.0202083i
$383$	4454.26	+	2571.67i	0.0303653	+	0.0175314i	0.515106	−	0.857127i	$-0.327753\pi$
$383$	4454.26	+	2571.67i	0.0303653	+	0.0175314i	−0.484741	+	0.874658i	$0.661086\pi$
$384$		0			0
$385$	54135.5	+	7813.79i	0.365225	+	0.0527157i
$386$	−145135.			−0.974086
$387$		0			0
$388$	38951.9	−	22488.9i	0.258741	−	0.149384i
$389$	43141.0	+	74722.4i	0.285096	+	0.493801i	0.972632	−	0.232349i	$-0.0746412\pi$
$389$	43141.0	+	74722.4i	0.285096	+	0.493801i	−0.687537	+	0.726150i	$0.741308\pi$
$390$		0			0
$391$		−	47171.9i		−	0.308553i
$392$	52110.9	+	15363.2i	0.339123	+	0.0999792i
$393$		0			0
$394$	2059.48	−	3567.13i	0.0132668	−	0.0229788i
$395$	−69170.8	+	39935.8i	−0.443331	+	0.255957i
$396$		0			0
$397$	−135036.	−	77963.1i	−0.856778	−	0.494661i	0.00615368	−	0.999981i	$-0.498041\pi$
$397$	−135036.	−	77963.1i	−0.856778	−	0.494661i	−0.862932	+	0.505320i	$0.831375\pi$
$398$		−	194478.i		−	1.22773i
$399$		0			0
$400$	−1246.09			−0.00778805
$401$	17307.2	−	29977.0i	0.107631	−	0.186423i	−0.807179	−	0.590307i	$-0.799007\pi$
$401$	17307.2	−	29977.0i	0.107631	−	0.186423i	0.914810	+	0.403884i	$0.132340\pi$
$402$		0			0
$403$	−84457.5	−	146285.i	−0.520030	−	0.900718i
$404$	−45625.7	−	26342.0i	−0.279542	−	0.161393i
$405$		0			0
$406$	−80812.5	−	63623.3i	−0.490260	−	0.385980i
$407$	−43384.7			−0.261907
$408$		0			0
$409$	−271749.	+	156894.i	−1.62450	+	0.937907i	−0.638809	+	0.769366i	$0.720572\pi$
$409$	−271749.	+	156894.i	−1.62450	+	0.937907i	−0.985695	+	0.168542i	$0.946094\pi$
$410$	−41060.7	−	71119.3i	−0.244264	−	0.423077i
$411$		0			0
$412$		−	12196.0i		−	0.0718492i
$413$	−77929.4	−	194968.i	−0.456879	−	1.14304i
$414$		0			0
$415$	60038.3	−	103989.i	0.348604	−	0.603800i
$416$	−25475.8	+	14708.4i	−0.147211	+	0.0849924i
$417$		0			0
$418$	48421.0	+	27955.9i	0.277128	+	0.160000i
$419$			7324.74i			0.0417219i	0.999782	+	0.0208609i	$0.00664073\pi$
$419$			7324.74i			0.0417219i	−0.999782	+	0.0208609i	$0.993359\pi$
$420$		0			0
$421$	−25178.3			−0.142057			−0.0710285	−	0.997474i	$-0.522628\pi$
$421$	−25178.3			−0.142057			−0.0710285	+	0.997474i	$0.522628\pi$
$422$	−880.802	+	1525.59i	−0.00494599	+	0.00856671i
$423$		0			0
$424$	40347.0	+	69883.0i	0.224429	+	0.388723i
$425$	−1825.04	−	1053.69i	−0.0101040	−	0.00583357i
$426$		0			0
$427$	42334.9	−	53772.6i	0.232190	−	0.294920i
$428$	−84853.0			−0.463212
$429$		0			0
$430$	−150411.	+	86840.1i	−0.813474	+	0.469660i
$431$	6913.59	+	11974.7i	0.0372176	+	0.0644629i	0.884034	−	0.467422i	$-0.154817\pi$
$431$	6913.59	+	11974.7i	0.0372176	+	0.0644629i	−0.846817	+	0.531885i	$0.821484\pi$
$432$		0			0
$433$		−	47438.8i		−	0.253022i	−0.991965	−	0.126511i	$-0.959622\pi$
$433$		−	47438.8i		−	0.253022i	0.991965	−	0.126511i	$-0.0403779\pi$
$434$	−142580.	−	20579.7i	−0.756973	−	0.109260i
$435$		0			0
$436$	55809.1	−	96664.1i	0.293584	−	0.508502i
$437$	−169682.	+	97966.0i	−0.888532	+	0.512994i
$438$		0			0
$439$	95101.7	+	54907.0i	0.493469	+	0.284904i	0.726012	−	0.687682i	$-0.241372\pi$
$439$	95101.7	+	54907.0i	0.493469	+	0.284904i	−0.232544	+	0.972586i	$0.574705\pi$
$440$			25258.0i			0.130465i
$441$		0			0
$442$	−49749.7			−0.254651
$443$	−41280.4	+	71499.7i	−0.210347	+	0.364331i	−0.951823	−	0.306648i	$-0.900793\pi$
$443$	−41280.4	+	71499.7i	−0.210347	+	0.364331i	0.741476	+	0.670979i	$0.234126\pi$
$444$		0			0
$445$	−10635.8	−	18421.7i	−0.0537092	−	0.0930270i
$446$	28193.0	+	16277.2i	0.141733	+	0.0818297i
$447$		0			0
$448$	−3584.00	+	24830.7i	−0.0178571	+	0.123718i
$449$	330438.			1.63907			0.819534	−	0.573030i	$-0.194232\pi$
$449$	330438.			1.63907			0.819534	+	0.573030i	$0.194232\pi$
$450$		0			0
$451$	−43551.5	+	25144.5i	−0.214116	+	0.123620i
$452$	−35245.2	−	61046.4i	−0.172513	−	0.298802i
$453$		0			0
$454$		−	159430.i		−	0.773499i
$455$	158830.	+	125047.i	0.767204	+	0.604017i
$456$		0			0
$457$	186644.	−	323276.i	0.893677	−	1.54789i	0.0582431	−	0.998302i	$-0.481450\pi$
$457$	186644.	−	323276.i	0.893677	−	1.54789i	0.835434	−	0.549591i	$-0.185217\pi$
$458$	−103193.	+	59578.7i	−0.491950	+	0.284027i
$459$		0			0
$460$	−76653.4	−	44255.9i	−0.362256	−	0.209149i
$461$			20355.2i			0.0957798i	0.998853	+	0.0478899i	$0.0152497\pi$
$461$			20355.2i			0.0957798i	−0.998853	+	0.0478899i	$0.984750\pi$
$462$		0			0
$463$	−31552.7			−0.147189			−0.0735944	−	0.997288i	$-0.523447\pi$
$463$	−31552.7			−0.147189			−0.0735944	+	0.997288i	$0.523447\pi$
$464$	23747.8	−	41132.3i	0.110303	−	0.191050i
$465$		0			0
$466$	77925.8	+	134971.i	0.358847	+	0.621541i
$467$	209452.	+	120927.i	0.960397	+	0.554486i	0.896295	−	0.443458i	$-0.146248\pi$
$467$	209452.	+	120927.i	0.960397	+	0.554486i	0.0641019	+	0.997943i	$0.479582\pi$
$468$		0			0
$469$	330593.	−	132139.i	1.50296	−	0.600740i
$470$	−96606.6			−0.437332
$471$		0			0
$472$	83968.7	−	48479.3i	0.376906	−	0.217607i
$473$	53178.5	+	92107.8i	0.237691	+	0.411694i
$474$		0			0
$475$			8753.16i			0.0387951i
$476$	−26245.9	+	33336.8i	−0.115837	+	0.147133i
$477$		0			0
$478$	−32643.5	+	56540.3i	−0.142870	+	0.247458i
$479$	−235631.	+	136042.i	−1.02698	+	0.592926i	−0.916117	−	0.400910i	$-0.868694\pi$
$479$	−235631.	+	136042.i	−1.02698	+	0.592926i	−0.110861	+	0.993836i	$0.535361\pi$
$480$		0			0
$481$	−138860.	−	80170.8i	−0.600187	−	0.346518i
$482$		−	230722.i		−	0.993104i
$483$		0			0
$484$	−101661.			−0.433973
$485$	71364.1	−	123606.i	0.303387	−	0.525481i
$486$		0			0
$487$	203873.	+	353119.i	0.859611	+	1.48889i	0.872300	+	0.488971i	$0.162628\pi$
$487$	203873.	+	353119.i	0.859611	+	1.48889i	−0.0126891	+	0.999919i	$0.504039\pi$
$488$	27369.4	+	15801.7i	0.114928	+	0.0663537i
$489$		0			0
$490$	167585.	−	40461.3i	0.697981	−	0.168519i
$491$	286772.			1.18953			0.594763	−	0.803901i	$-0.297246\pi$
$491$	286772.			1.18953			0.594763	+	0.803901i	$0.297246\pi$
$492$		0			0
$493$	69562.8	−	40162.1i	0.286209	−	0.165243i
$494$	103320.	+	178955.i	0.423378	+	0.733313i
$495$		0			0
$496$		−	66523.7i		−	0.270404i
$497$	41914.3	−	290391.i	0.169687	−	1.17563i
$498$		0			0
$499$	−175718.	+	304352.i	−0.705690	+	1.22229i	0.260751	+	0.965406i	$0.416030\pi$
$499$	−175718.	+	304352.i	−0.705690	+	1.22229i	−0.966442	+	0.256886i	$0.917304\pi$
$500$	106502.	−	61488.9i	0.426008	−	0.245956i
$501$		0			0
$502$	66644.7	+	38477.3i	0.264459	+	0.152685i
$503$			116045.i			0.458660i	0.973349	+	0.229330i	$0.0736535\pi$
$503$			116045.i			0.458660i	−0.973349	+	0.229330i	$0.926347\pi$
$504$		0			0
$505$	−167182.			−0.655552
$506$	−27101.1	+	46940.5i	−0.105849	+	0.183335i
$507$		0			0
$508$	−15970.8	−	27662.2i	−0.0618870	−	0.107191i
$509$	−72030.7	−	41586.9i	−0.278024	−	0.160517i	0.354505	−	0.935054i	$-0.384649\pi$
$509$	−72030.7	−	41586.9i	−0.278024	−	0.160517i	−0.632528	+	0.774537i	$0.717983\pi$
$510$		0			0
$511$	−10502.6	−	26275.9i	−0.0402212	−	0.100627i
$512$	−11585.2			−0.0441942
$513$		0			0
$514$	−264371.	+	152635.i	−1.00066	+	0.577733i
$515$	−19350.8	−	33516.5i	−0.0729598	−	0.126370i
$516$		0			0
$517$			59159.2i			0.221330i
$518$	−126979.	+	50753.9i	−0.473229	+	0.189151i
$519$		0			0
$520$	−46674.3	+	80842.3i	−0.172612	+	0.298973i
$521$	−174948.	+	101006.i	−0.644517	+	0.372112i	−0.786352	−	0.617778i	$-0.788033\pi$
$521$	−174948.	+	101006.i	−0.644517	+	0.372112i	0.141835	+	0.989890i	$0.454700\pi$
$522$		0			0
$523$	−24134.0	−	13933.8i	−0.0882321	−	0.0509408i	0.455235	−	0.890371i	$-0.349555\pi$
$523$	−24134.0	−	13933.8i	−0.0882321	−	0.0509408i	−0.543467	+	0.839431i	$0.682889\pi$
$524$		−	161800.i		−	0.589272i
$525$		0			0
$526$	−113545.			−0.410389
$527$	56252.3	−	97431.8i	0.202544	−	0.350816i
$528$		0			0
$529$	44949.9	+	77855.5i	0.160626	+	0.278213i
$530$	221760.	+	128033.i	0.789462	+	0.455796i
$531$		0			0
$532$	174423.	+	25175.8i	0.616284	+	0.0889530i
$533$	−185858.			−0.654226
$534$		0			0
$535$	−233190.	+	134632.i	−0.814707	+	0.470372i
$536$	82203.0	+	142380.i	0.286126	+	0.495586i
$537$		0			0
$538$			297985.i			1.02951i
$539$	−24777.4	−	102625.i	−0.0852861	−	0.353243i
$540$		0			0
$541$	18996.8	−	32903.4i	0.0649062	−	0.112421i	−0.831746	−	0.555156i	$-0.812659\pi$
$541$	18996.8	−	32903.4i	0.0649062	−	0.112421i	0.896652	+	0.442735i	$0.145992\pi$
$542$	−37305.0	+	21538.0i	−0.126990	+	0.0733175i
$543$		0			0
$544$	−16967.9	−	9796.44i	−0.0573365	−	0.0331032i
$545$		−	354198.i		−	1.19249i
$546$		0			0
$547$	360160.			1.20371			0.601854	−	0.798606i	$-0.294429\pi$
$547$	360160.			1.20371			0.601854	+	0.798606i	$0.294429\pi$
$548$	100231.	−	173605.i	0.333765	−	0.578098i
$549$		0			0
$550$	1210.73	+	2097.04i	0.00400240	+	0.00693236i
$551$	−288934.	−	166816.i	−0.951691	−	0.549459i
$552$		0			0
$553$	121130.	+	95365.1i	0.396097	+	0.311845i
$554$	27921.1			0.0909732
$555$		0			0
$556$	139049.	−	80280.2i	0.449800	−	0.259692i
$557$	155272.	+	268938.i	0.500474	+	0.866847i	1.00000		0.000547960i	$0.000174421\pi$
$557$	155272.	+	268938.i	0.500474	+	0.866847i	−0.499525	+	0.866299i	$0.666492\pi$
$558$		0			0
$559$			393075.i			1.25792i
$560$	29548.2	+	73925.2i	0.0942226	+	0.235731i
$561$		0			0
$562$	219369.	−	379958.i	0.694548	−	1.20299i
$563$	−14453.4	+	8344.68i	−0.0455988	+	0.0263265i	−0.522626	−	0.852562i	$-0.675048\pi$
$563$	−14453.4	+	8344.68i	−0.0455988	+	0.0263265i	0.477027	+	0.878888i	$0.341714\pi$
$564$		0			0
$565$	−193719.	−	111844.i	−0.606841	−	0.350360i
$566$			310171.i			0.968207i
$567$		0			0
$568$	135488.			0.419955
$569$	−65131.1	+	112810.i	−0.201170	+	0.348437i	−0.948906	−	0.315560i	$-0.897808\pi$
$569$	−65131.1	+	112810.i	−0.201170	+	0.348437i	0.747736	+	0.663997i	$0.231141\pi$
$570$		0			0
$571$	249119.	+	431487.i	0.764073	+	1.32341i	0.940735	+	0.339142i	$0.110137\pi$
$571$	249119.	+	431487.i	0.764073	+	1.32341i	−0.176662	+	0.984272i	$0.556530\pi$
$572$	49505.6	+	28582.1i	0.151308	+	0.0873578i
$573$		0			0
$574$	−98051.5	+	124542.i	−0.297598	+	0.378000i
$575$	−8485.52			−0.0256651
$576$		0			0
$577$	−29199.1	+	16858.1i	−0.0877035	+	0.0506357i	−0.543210	−	0.839597i	$-0.682791\pi$
$577$	−29199.1	+	16858.1i	−0.0877035	+	0.0506357i	0.455507	+	0.890232i	$0.349458\pi$
$578$	101549.	+	175888.i	0.303962	+	0.526478i
$579$		0			0
$580$		−	150718.i		−	0.448031i
$581$	−229391.	−	33109.7i	−0.679554	−	0.0980851i
$582$		0			0
$583$	78404.0	−	135800.i	0.230675	−	0.399541i
$584$	11316.5	−	6533.58i	0.0331808	−	0.0191569i
$585$		0			0
$586$	220240.	+	127155.i	0.641357	+	0.370288i
$587$			356809.i			1.03552i	0.855525	+	0.517762i	$0.173235\pi$
$587$			356809.i			1.03552i	−0.855525	+	0.517762i	$0.826765\pi$
$588$		0			0
$589$	−467296.			−1.34698
$590$	153840.	−	266458.i	0.441941	−	0.765464i
$591$		0			0
$592$	−31573.6	−	54687.1i	−0.0900909	−	0.156042i
$593$	28872.6	+	16669.6i	0.0821063	+	0.0474041i	0.540491	−	0.841350i	$-0.318238\pi$
$593$	28872.6	+	16669.6i	0.0821063	+	0.0474041i	−0.458385	+	0.888754i	$0.651572\pi$
$594$		0			0
$595$	−19234.1	+	133258.i	−0.0543299	+	0.376409i
$596$	341663.			0.961846
$597$		0			0
$598$	−173483.	+	100160.i	−0.485126	+	0.280088i
$599$	162165.	+	280878.i	0.451963	+	0.782824i	0.998508	−	0.0546064i	$-0.0173904\pi$
$599$	162165.	+	280878.i	0.451963	+	0.782824i	−0.546545	+	0.837430i	$0.684057\pi$
$600$		0			0
$601$		−	66322.0i		−	0.183615i	−0.995777	−	0.0918076i	$-0.970736\pi$
$601$		−	66322.0i		−	0.183615i	0.995777	−	0.0918076i	$-0.0292645\pi$
$602$	263396.	+	207371.i	0.726803	+	0.572209i
$603$		0			0
$604$	−118430.	+	205126.i	−0.324629	+	0.562274i
$605$	−279380.	+	161300.i	−0.763281	+	0.440680i
$606$		0			0
$607$	−422322.	−	243828.i	−1.14622	−	0.661768i	−0.198253	−	0.980151i	$-0.563527\pi$
$607$	−422322.	−	243828.i	−1.14622	−	0.661768i	−0.947962	+	0.318383i	$0.896860\pi$
$608$			81380.6i			0.220147i
$609$		0			0
$610$	100287.			0.269517
$611$	−109321.	+	189349.i	−0.292833	+	0.507201i
$612$		0			0
$613$	170755.	+	295757.i	0.454415	+	0.787070i	0.998654	−	0.0518597i	$-0.0165149\pi$
$613$	170755.	+	295757.i	0.454415	+	0.787070i	−0.544239	+	0.838930i	$0.683182\pi$
$614$	−347047.	−	200368.i	−0.920558	−	0.531484i
$615$		0			0
$616$	45269.8	−	18094.5i	0.119302	−	0.0476854i
$617$	−240873.			−0.632728			−0.316364	−	0.948638i	$-0.602462\pi$
$617$	−240873.			−0.632728			−0.316364	+	0.948638i	$0.602462\pi$
$618$		0			0
$619$	−133658.	+	77167.4i	−0.348830	+	0.201397i	−0.664170	−	0.747582i	$-0.731215\pi$
$619$	−133658.	+	77167.4i	−0.348830	+	0.201397i	0.315340	+	0.948979i	$0.397881\pi$
$620$	−105550.	−	182818.i	−0.274584	−	0.475593i
$621$		0			0
$622$		−	242242.i		−	0.626137i
$623$	−25397.8	+	32259.5i	−0.0654364	+	0.0831154i
$624$		0			0
$625$	201207.	−	348501.i	0.515091	−	0.892164i
$626$	43678.2	−	25217.6i	0.111459	−	0.0643510i
$627$		0			0
$628$	−84780.8	−	48948.2i	−0.214970	−	0.124113i
$629$		−	106794.i		−	0.269927i
$630$		0			0
$631$	220248.			0.553164			0.276582	−	0.960990i	$-0.410798\pi$
$631$	220248.			0.553164			0.276582	+	0.960990i	$0.410798\pi$
$632$	−35595.5	+	61653.3i	−0.0891172	+	0.154355i
$633$		0			0
$634$	−114276.	−	197932.i	−0.284299	−	0.492421i
$635$	−87780.7	−	50680.2i	−0.217696	−	0.125687i
$636$		0			0
$637$	110336.	−	374253.i	0.271919	−	0.922331i
$638$	−92295.4			−0.226745
$639$		0			0
$640$	−31838.1	+	18381.7i	−0.0777297	+	0.0448773i
$641$	−340604.	−	589943.i	−0.828960	−	1.43580i	−0.898855	−	0.438247i	$-0.855600\pi$
$641$	−340604.	−	589943.i	−0.828960	−	1.43580i	0.0698947	−	0.997554i	$-0.477734\pi$
$642$		0			0
$643$		−	572102.i		−	1.38373i	−0.722027	−	0.691865i	$-0.756789\pi$
$643$		−	572102.i		−	1.38373i	0.722027	−	0.691865i	$-0.243211\pi$
$644$	−24406.1	+	169090.i	−0.0588472	+	0.407705i
$645$		0			0
$646$	−68815.2	+	119191.i	−0.164899	+	0.285614i
$647$	525915.	−	303637.i	1.25634	−	0.725348i	0.283979	−	0.958830i	$-0.408345\pi$
$647$	525915.	−	303637.i	1.25634	−	0.725348i	0.972361	+	0.233482i	$0.0750120\pi$
$648$		0			0
$649$	−163171.	−	94207.1i	−0.387396	−	0.223663i
$650$			8949.23i			0.0211816i
$651$		0			0
$652$	172249.			0.405193
$653$	−242335.	+	419737.i	−0.568316	+	0.984353i	0.428416	+	0.903581i	$0.359072\pi$
$653$	−242335.	+	419737.i	−0.568316	+	0.984353i	−0.996733	+	0.0807713i	$0.974262\pi$
$654$		0			0
$655$	−256720.	−	444652.i	−0.598380	−	1.03642i
$656$	−63390.0	−	36598.3i	−0.147304	−	0.0850458i
$657$		0			0
$658$	69207.8	+	173148.i	0.159847	+	0.399912i
$659$	−329627.			−0.759017			−0.379509	−	0.925188i	$-0.623907\pi$
$659$	−329627.			−0.759017			−0.379509	+	0.925188i	$0.623907\pi$
$660$		0			0
$661$	−182392.	+	105304.i	−0.417449	+	0.241014i	−0.693985	−	0.719989i	$-0.744147\pi$
$661$	−182392.	+	105304.i	−0.417449	+	0.241014i	0.276536	+	0.961003i	$0.410813\pi$
$662$	102961.	+	178333.i	0.234939	+	0.406927i
$663$		0			0
$664$		−	107027.i		−	0.242748i
$665$	519288.	−	207562.i	1.17426	−	0.469358i
$666$		0			0
$667$	161716.	−	280100.i	0.363497	−	0.629595i
$668$	−114862.	+	66315.7i	−0.257409	+	0.148615i
$669$		0			0
$670$	451814.	+	260855.i	1.00649	+	0.581098i
$671$		−	61413.2i		−	0.136401i
$672$		0			0
$673$	94709.8			0.209105			0.104553	−	0.994519i	$-0.466659\pi$
$673$	94709.8			0.209105			0.104553	+	0.994519i	$0.466659\pi$
$674$	178951.	−	309952.i	0.393926	−	0.682300i
$675$		0			0
$676$	−8610.09	−	14913.1i	−0.0188414	−	0.0326343i
$677$	−466400.	−	269276.i	−1.01761	−	0.587517i	−0.104199	−	0.994556i	$-0.533228\pi$
$677$	−466400.	−	269276.i	−1.01761	−	0.587517i	−0.913411	+	0.407039i	$0.866561\pi$
$678$		0			0
$679$	−272664.	−	39355.6i	−0.591408	−	0.0853625i
$680$	−62174.1			−0.134460
$681$		0			0
$682$	−111953.	+	64635.9i	−0.240694	+	0.138965i
$683$	−64535.9	−	111779.i	−0.138344	−	0.239618i	0.788526	−	0.615001i	$-0.210845\pi$
$683$	−64535.9	−	111779.i	−0.138344	−	0.239618i	−0.926870	+	0.375383i	$0.877511\pi$
$684$		0			0
$685$		−	636126.i		−	1.35570i
$686$	−192575.	−	271377.i	−0.409215	−	0.576666i
$687$		0			0
$688$	−77402.3	+	134065.i	−0.163522	+	0.283229i
$689$	501890.	−	289766.i	1.05723	−	0.610393i
$690$		0			0
$691$	113201.	+	65356.6i	0.237079	+	0.136878i	0.613834	−	0.789435i	$-0.289627\pi$
$691$	113201.	+	65356.6i	0.237079	+	0.136878i	−0.376754	+	0.926313i	$0.622960\pi$
$692$		−	323064.i		−	0.674648i
$693$		0			0
$694$	−189361.			−0.393162
$695$	254753.	−	441246.i	0.527413	−	0.913505i
$696$		0			0
$697$	−61894.8	−	107205.i	−0.127406	−	0.220673i
$698$	62529.3	+	36101.3i	0.128343	+	0.0740989i
$699$		0			0
$700$	5996.80	+	4721.26i	0.0122384	+	0.00963522i
$701$	182501.			0.371389			0.185694	−	0.982608i	$-0.440547\pi$
$701$	182501.			0.371389			0.185694	+	0.982608i	$0.440547\pi$
$702$		0			0
$703$	−384150.	+	221789.i	−0.777302	+	0.448776i
$704$	11256.5	+	19496.8i	0.0227121	+	0.0393385i
$705$		0			0
$706$		−	160020.i		−	0.321044i
$707$	119767.	+	299640.i	0.239607	+	0.599462i
$708$		0			0
$709$	−406899.	+	704770.i	−0.809458	+	1.40202i	0.103783	+	0.994600i	$0.466905\pi$
$709$	−406899.	+	704770.i	−0.809458	+	1.40202i	−0.913240	+	0.407422i	$0.866428\pi$
$710$	372342.	−	214972.i	0.738627	−	0.426446i
$711$		0			0
$712$	−16419.6	−	9479.86i	−0.0323894	−	0.0187000i
$713$		−	453008.i		−	0.891101i
$714$		0			0
$715$	181399.			0.354832
$716$	−213978.	+	370620.i	−0.417390	+	0.722941i
$717$		0			0
$718$	−53464.0	−	92602.4i	−0.103708	−	0.179628i
$719$	364222.	+	210283.i	0.704544	+	0.406769i	0.809038	−	0.587757i	$-0.199989\pi$
$719$	364222.	+	210283.i	0.704544	+	0.406769i	−0.104494	+	0.994526i	$0.533322\pi$
$720$		0			0
$721$	−46208.9	+	58693.1i	−0.0888904	+	0.112906i
$722$	203055.			0.389528
$723$		0			0
$724$	375523.	−	216808.i	0.716406	−	0.413617i
$725$	−7224.56	−	12513.3i	−0.0137447	−	0.0238065i
$726$		0			0
$727$		−	172948.i		−	0.327225i	−0.986525	−	0.163613i	$-0.947685\pi$
$727$		−	172948.i		−	0.327225i	0.986525	−	0.163613i	$-0.0523147\pi$
$728$	178330.	+	25739.8i	0.336483	+	0.0485671i
$729$		0			0
$730$	20733.0	−	35910.7i	0.0389061	−	0.0673873i
$731$	−226729.	+	130902.i	−0.424300	+	0.244970i
$732$		0			0
$733$	113936.	+	65780.9i	0.212057	+	0.122431i	0.602267	−	0.798295i	$-0.294264\pi$
$733$	113936.	+	65780.9i	0.212057	+	0.122431i	−0.390210	+	0.920726i	$0.627598\pi$
$734$		−	30593.4i		−	0.0567852i
$735$		0			0
$736$	−78892.3			−0.145639
$737$	159740.	−	276678.i	0.294090	−	0.509378i
$738$		0			0
$739$	244884.	+	424151.i	0.448406	+	0.776662i	0.998282	−	0.0585842i	$-0.0186586\pi$
$739$	244884.	+	424151.i	0.448406	+	0.776662i	−0.549877	+	0.835246i	$0.685325\pi$
$740$	−173539.	−	100193.i	−0.316908	−	0.182967i
$741$		0			0
$742$	70607.2	−	489181.i	0.128245	−	0.888509i
$743$	−580258.			−1.05110			−0.525549	−	0.850763i	$-0.676140\pi$
$743$	−580258.			−1.05110			−0.525549	+	0.850763i	$0.676140\pi$
$744$		0			0
$745$	938945.	−	542100.i	1.69172	−	0.976713i
$746$	−43873.7	−	75991.5i	−0.0788364	−	0.136549i
$747$		0			0
$748$			38073.7i			0.0680491i
$749$	408355.	+	321496.i	0.727904	+	0.573076i
$750$		0			0
$751$	−218698.	+	378797.i	−0.387763	+	0.671624i	−0.992148	−	0.125067i	$-0.960085\pi$
$751$	−218698.	+	378797.i	−0.387763	+	0.671624i	0.604386	+	0.796692i	$0.293419\pi$
$752$	−74571.2	+	43053.7i	−0.131867	+	0.0761333i
$753$		0			0
$754$	−295407.	−	170553.i	−0.519610	−	0.299997i
$755$			751627.i			1.31859i
$756$		0			0
$757$	−24171.7			−0.0421809			−0.0210905	−	0.999778i	$-0.506714\pi$
$757$	−24171.7			−0.0421809			−0.0210905	+	0.999778i	$0.506714\pi$
$758$	−139339.	+	241342.i	−0.242512	+	0.420044i
$759$		0			0
$760$	129123.	+	223647.i	0.223550	+	0.387200i
$761$	561376.	+	324111.i	0.969359	+	0.559659i	0.899041	−	0.437865i	$-0.144265\pi$
$761$	561376.	+	324111.i	0.969359	+	0.559659i	0.0703180	+	0.997525i	$0.477599\pi$
$762$		0			0
$763$	−634828.	+	253743.i	−1.09045	+	0.435859i
$764$	9630.98			0.0165000
$765$		0			0
$766$	12598.5	−	7273.77i	0.0214715	−	0.0123966i
$767$	−348172.	−	603051.i	−0.591838	−	1.02509i
$768$		0			0
$769$			179564.i			0.303646i	0.988408	+	0.151823i	$0.0485143\pi$
$769$			179564.i			0.303646i	−0.988408	+	0.151823i	$0.951486\pi$
$770$	95698.9	−	121554.i	0.161408	−	0.205016i
$771$		0			0
$772$	−205252.	+	355506.i	−0.344391	+	0.596503i
$773$	−529068.	+	305457.i	−0.885426	+	0.511201i	−0.872444	−	0.488715i	$-0.837466\pi$
$773$	−529068.	+	305457.i	−0.885426	+	0.511201i	−0.0129823	+	0.999916i	$0.504133\pi$
$774$		0			0
$775$	−17526.5	−	10118.9i	−0.0291805	−	0.0168474i
$776$		−	127216.i		−	0.211261i
$777$		0			0
$778$	244042.			0.403186
$779$	−257085.	+	445284.i	−0.423644	+	0.733773i
$780$		0			0
$781$	−131643.	−	228012.i	−0.215821	−	0.373814i
$782$	−115547.	−	66711.1i	−0.188949	−	0.109090i
$783$		0			0
$784$	111328.	−	105918.i	0.181122	−	0.172321i
$785$	−310655.			−0.504126
$786$		0			0
$787$	1.03191e6	−	595774.i	1.66607	−	0.961905i	0.696342	−	0.717710i	$-0.254810\pi$
$787$	1.03191e6	−	595774.i	1.66607	−	0.961905i	0.969726	−	0.244195i	$-0.0785236\pi$
$788$	−5825.10	−	10089.4i	−0.00938104	−	0.0162484i
$789$		0			0
$790$			225911.i			0.361979i
$791$	−61679.1	+	427325.i	−0.0985791	+	0.682976i
$792$		0			0
$793$	113486.	−	196563.i	0.180466	−	0.312576i
$794$	−381939.	+	220513.i	−0.605834	+	0.349778i
$795$		0			0
$796$	−476371.	−	275033.i	−0.751829	−	0.434069i
$797$		−	900495.i		−	1.41764i	−0.705392	−	0.708818i	$-0.749229\pi$
$797$		−	900495.i		−	1.41764i	0.705392	−	0.708818i	$-0.250771\pi$
$798$		0			0
$799$	−145624.			−0.228108
$800$	−1762.23	+	3052.28i	−0.00275349	+	0.00476919i
$801$		0			0
$802$	−48952.2	−	84787.8i	−0.0761069	−	0.131821i
$803$	−21990.7	−	12696.3i	−0.0341042	−	0.0196901i
$804$		0			0
$805$	201215.	+	503411.i	0.310505	+	0.776838i
$806$	−477764.			−0.735433
$807$		0			0
$808$	−129049.	+	74506.4i	−0.197666	+	0.114122i
$809$	277882.	+	481306.i	0.424584	+	0.735401i	0.996381	−	0.0849939i	$-0.0270871\pi$
$809$	277882.	+	481306.i	0.424584	+	0.735401i	−0.571798	+	0.820395i	$0.693754\pi$
$810$		0			0
$811$		−	70954.2i		−	0.107879i	−0.998544	−	0.0539395i	$-0.982822\pi$
$811$		−	70954.2i		−	0.107879i	0.998544	−	0.0539395i	$-0.0171778\pi$
$812$	−270131.	+	107972.i	−0.409696	+	0.163757i
$813$		0			0
$814$	−61355.2	+	106270.i	−0.0925982	+	0.160385i
$815$	473368.	−	273299.i	0.712662	−	0.411455i
$816$		0			0
$817$	941738.	+	543713.i	1.41087	+	0.814564i
$818$			887527.i			1.32640i
$819$		0			0
$820$	−232275.			−0.345441
$821$	−312356.	+	541016.i	−0.463408	+	0.802646i	−0.999128	−	0.0417495i	$-0.986707\pi$
$821$	−312356.	+	541016.i	−0.463408	+	0.802646i	0.535720	+	0.844396i	$0.320040\pi$
$822$		0			0
$823$	105029.	+	181916.i	0.155064	+	0.268579i	0.933082	−	0.359663i	$-0.117108\pi$
$823$	105029.	+	181916.i	0.155064	+	0.268579i	−0.778018	+	0.628242i	$0.783775\pi$
$824$	−29873.9	−	17247.7i	−0.0439985	−	0.0254025i
$825$		0			0
$826$	−587781.	−	84838.8i	−0.861500	−	0.124347i
$827$	880910.			1.28801			0.644007	−	0.765020i	$-0.277271\pi$
$827$	880910.			1.28801			0.644007	+	0.765020i	$0.277271\pi$
$828$		0			0
$829$	−1.11951e6	+	646349.i	−1.62899	+	0.940498i	−0.644595	+	0.764524i	$0.722974\pi$
$829$	−1.11951e6	+	646349.i	−1.62899	+	0.940498i	−0.984395	+	0.175974i	$0.943692\pi$
$830$	−169814.	−	294127.i	−0.246500	−	0.426951i
$831$		0			0
$832$			83203.5i			0.120197i
$833$	252617.	−	60991.2i	0.364060	−	0.0878977i
$834$		0			0
$835$	−210440.	+	364492.i	−0.301825	+	0.522775i
$836$	136955.	−	79071.1i	0.195959	−	0.113137i
$837$		0			0
$838$	17941.9	+	10358.7i	0.0255493	+	0.0147509i
$839$			1.11586e6i			1.58520i	0.609741	+	0.792601i	$0.291274\pi$
$839$			1.11586e6i			1.58520i	−0.609741	+	0.792601i	$0.708726\pi$
$840$		0			0
$841$	−156542.			−0.221330
$842$	−35607.5	+	61674.1i	−0.0502247	+	0.0869918i
$843$		0			0
$844$	2491.28	+	4315.03i	0.00349734	+	0.00605758i
$845$	−47323.8	−	27322.4i	−0.0662775	−	0.0382653i
$846$		0			0
$847$	489242.	+	385178.i	0.681957	+	0.536902i
$848$	228237.			0.317391
$849$		0			0
$850$	−5162.00	+	2980.28i	−0.00714464	+	0.00412496i
$851$	−215008.	−	372404.i	−0.296889	−	0.514228i
$852$		0			0
$853$			1.28959e6i			1.77236i	0.463341	+	0.886180i	$0.346650\pi$
$853$			1.28959e6i			1.77236i	−0.463341	+	0.886180i	$0.653350\pi$
$854$	−71844.7	−	179745.i	−0.0985097	−	0.246457i
$855$		0			0
$856$	−120000.	+	207847.i	−0.163770	+	0.283658i
$857$	566854.	−	327273.i	0.771809	−	0.445604i	−0.0617109	−	0.998094i	$-0.519656\pi$
$857$	566854.	−	327273.i	0.771809	−	0.445604i	0.833519	+	0.552490i	$0.186322\pi$
$858$		0			0
$859$	211796.	+	122281.i	0.287033	+	0.165718i	0.636603	−	0.771192i	$-0.280339\pi$
$859$	211796.	+	122281.i	0.287033	+	0.165718i	−0.349570	+	0.936910i	$0.613672\pi$
$860$			491242.i			0.664199i
$861$		0			0
$862$	39109.2			0.0526337
$863$	−232638.	+	402942.i	−0.312363	+	0.541029i	−0.978873	−	0.204467i	$-0.934454\pi$
$863$	−232638.	+	402942.i	−0.312363	+	0.541029i	0.666510	+	0.745496i	$0.267787\pi$
$864$		0			0
$865$	−512591.	−	887833.i	−0.685075	−	1.18659i
$866$	−116201.	−	67088.6i	−0.154944	−	0.0894567i
$867$		0			0
$868$	−252049.	+	320145.i	−0.334538	+	0.424921i
$869$	138342.			0.183195
$870$		0			0
$871$	1.02255e6	−	590370.i	1.34787	−	0.778194i
$872$	−157852.	−	273407.i	−0.207595	−	0.359565i
$873$		0			0
$874$			554179.i			0.725484i
$875$	−745514.	−	107606.i	−0.973732	−	0.140546i
$876$		0			0
$877$	−152086.	+	263420.i	−0.197738	+	0.342492i	−0.947795	−	0.318882i	$-0.896693\pi$
$877$	−152086.	+	263420.i	−0.197738	+	0.342492i	0.750057	+	0.661373i	$0.230026\pi$
$878$	268988.	−	155301.i	0.348935	−	0.201458i
$879$		0			0
$880$	61869.1	+	35720.2i	0.0798930	+	0.0461262i
$881$		−	697876.i		−	0.899138i	−0.893246	−	0.449569i	$-0.851578\pi$
$881$		−	697876.i		−	0.899138i	0.893246	−	0.449569i	$-0.148422\pi$
$882$		0			0
$883$	891773.			1.14375			0.571877	−	0.820339i	$-0.306215\pi$
$883$	891773.			1.14375			0.571877	+	0.820339i	$0.306215\pi$
$884$	−70356.6	+	121861.i	−0.0900328	+	0.155941i
$885$		0			0
$886$	116758.	+	202232.i	0.148738	+	0.257621i
$887$	1.09340e6	+	631278.i	1.38974	+	0.802367i	0.993286	−	0.115687i	$-0.0369070\pi$
$887$	1.09340e6	+	631278.i	1.38974	+	0.802367i	0.396455	+	0.918054i	$0.370240\pi$
$888$		0			0
$889$	−27948.9	+	193636.i	−0.0353640	+	0.245009i
$890$	−60164.9			−0.0759562
$891$		0			0
$892$	79741.8	−	46039.0i	0.100220	−	0.0578623i
$893$	302431.	+	523826.i	0.379248	+	0.656877i
$894$		0			0
$895$			1.35803e6i			1.69537i
$896$	55754.0	+	43894.9i	0.0694480	+	0.0546761i
$897$		0			0
$898$	467310.	−	809404.i	0.579498	−	1.00372i
$899$	668036.	−	385691.i	0.826572	−	0.477221i
$900$		0			0
$901$	334280.	+	192997.i	0.411776	+	0.237739i
$902$			142239.i			0.174825i
$903$		0			0
$904$	−199377.			−0.243971
$905$	687998.	−	1.19165e6i	0.840021	−	1.45496i
$906$		0			0
$907$	−475990.	−	824439.i	−0.578607	−	1.00218i	−0.995639	−	0.0932848i	$-0.970263\pi$
$907$	−475990.	−	824439.i	−0.578607	−	1.00218i	0.417033	−	0.908891i	$-0.363070\pi$
$908$	−390523.	−	225469.i	−0.473669	−	0.273473i
$909$		0			0
$910$	530920.	−	212211.i	0.641131	−	0.256263i
$911$	743243.			0.895559			0.447779	−	0.894144i	$-0.352215\pi$
$911$	743243.			0.895559			0.447779	+	0.894144i	$0.352215\pi$
$912$		0			0
$913$	−180115.	+	103989.i	−0.216077	+	0.124752i
$914$	−527908.	−	914363.i	−0.631925	−	1.09453i
$915$		0			0
$916$			337028.i			0.401675i
$917$	−613038.	+	778662.i	−0.729035	+	0.925999i
$918$		0			0
$919$	262150.	−	454057.i	0.310398	−	0.537625i	−0.668050	−	0.744116i	$-0.732871\pi$
$919$	262150.	−	454057.i	0.310398	−	0.537625i	0.978449	+	0.206491i	$0.0662043\pi$
$920$	−216809.	+	125175.i	−0.256154	+	0.147891i
$921$		0			0
$922$	49859.9	+	28786.6i	0.0586529	+	0.0338633i
$923$		−	973052.i		−	1.14218i
$924$		0			0
$925$	−19210.7			−0.0224522
$926$	−44622.3	+	77288.1i	−0.0520391	+	0.0901344i
$927$		0			0
$928$	−67168.8	−	116340.i	−0.0779959	−	0.135093i
$929$	−848178.	−	489696.i	−0.982779	−	0.567408i	−0.0796709	−	0.996821i	$-0.525387\pi$
$929$	−848178.	−	489696.i	−0.982779	−	0.567408i	−0.903108	+	0.429414i	$0.858720\pi$
$930$		0			0
$931$	−744024.	−	782024.i	−0.858396	−	0.902237i
$932$	440815.			0.507486
$933$		0			0
$934$	592420.	−	342034.i	0.679103	−	0.392081i
$935$	60409.7	+	104633.i	0.0691009	+	0.119686i
$936$		0			0
$937$		−	1.13988e6i		−	1.29831i	−0.760656	−	0.649155i	$-0.775123\pi$
$937$		−	1.13988e6i		−	1.29831i	0.760656	−	0.649155i	$-0.224877\pi$
$938$	143855.	−	996658.i	0.163501	−	1.13277i
$939$		0			0
$940$	−136622.	+	236637.i	−0.154620	+	0.267810i
$941$	−693791.	+	400561.i	−0.783519	+	0.452365i	−0.837676	−	0.546167i	$-0.816086\pi$
$941$	−693791.	+	400561.i	−0.783519	+	0.452365i	0.0541569	+	0.998532i	$0.482753\pi$
$942$		0			0
$943$	−431669.	−	249224.i	−0.485431	−	0.280264i
$944$		−	274240.i		−	0.307743i
$945$		0			0
$946$	300823.			0.336146
$947$	340143.	−	589145.i	0.379282	−	0.656935i	−0.611676	−	0.791108i	$-0.709504\pi$
$947$	340143.	−	589145.i	0.379282	−	0.656935i	0.990958	+	0.134173i	$0.0428378\pi$
$948$		0			0
$949$	−46923.3	−	81273.5i	−0.0521022	−	0.0902436i
$950$	21440.8	+	12378.8i	0.0237571	+	0.0137162i
$951$		0			0
$952$	44540.8	+	111435.i	0.0491456	+	0.122955i
$953$	394774.			0.434673			0.217337	−	0.976097i	$-0.430263\pi$
$953$	394774.			0.434673			0.217337	+	0.976097i	$0.430263\pi$
$954$		0			0
$955$	26467.5	−	15281.0i	0.0290206	−	0.0167550i
$956$	92329.9	+	159920.i	0.101024	+	0.174979i
$957$		0			0
$958$			769567.i			0.838524i
$959$	−1.14013e6	+	455714.i	−1.23970	+	0.495513i
$960$		0			0
$961$	78449.9	−	135879.i	0.0849465	−	0.147132i
$962$	−392755.	+	226757.i	−0.424396	+	0.245025i
$963$		0			0
$964$	−565151.	−	326290.i	−0.608150	−	0.351115i
$965$			1.30265e6i			1.39886i
$966$		0			0
$967$	−604328.			−0.646279			−0.323140	−	0.946351i	$-0.604738\pi$
$967$	−604328.			−0.646279			−0.323140	+	0.946351i	$0.604738\pi$
$968$	−143770.	+	249017.i	−0.153433	+	0.265753i
$969$		0			0
$970$	−201848.	−	349611.i	−0.214527	−	0.371571i
$971$	−657301.	−	379493.i	−0.697149	−	0.402499i	0.109136	−	0.994027i	$-0.465192\pi$
$971$	−657301.	−	379493.i	−0.697149	−	0.402499i	−0.806285	+	0.591528i	$0.798525\pi$
$972$		0			0
$973$	−973346.	−	140490.i	−1.02811	−	0.148396i
$974$	1.15328e6			1.21567
$975$		0			0
$976$	77412.4	−	44694.1i	0.0812664	−	0.0469192i
$977$	612591.	+	1.06104e6i	0.641773	+	1.11158i	0.985037	+	0.172345i	$0.0551344\pi$
$977$	612591.	+	1.06104e6i	0.641773	+	1.11158i	−0.343263	+	0.939239i	$0.611532\pi$
$978$		0			0
$979$			36843.3i			0.0384409i
$980$	137892.	−	467719.i	0.143577	−	0.487005i
$981$		0			0
$982$	405557.	−	702446.i	0.420561	−	0.728434i
$983$	1.03964e6	−	600236.i	1.07591	−	0.621177i	0.146120	−	0.989267i	$-0.453322\pi$
$983$	1.03964e6	−	600236.i	1.07591	−	0.621177i	0.929790	+	0.368090i	$0.119988\pi$
$984$		0			0
$985$	−32016.6	−	18484.8i	−0.0329992	−	0.0190521i
$986$		−	227191.i		−	0.233689i
$987$		0			0
$988$	584464.			0.598747
$989$	−527088.	+	912944.i	−0.538878	+	0.933365i
$990$		0			0
$991$	−904963.	−	1.56744e6i	−0.921475	−	1.59604i	−0.797134	−	0.603802i	$-0.793652\pi$
$991$	−904963.	−	1.56744e6i	−0.921475	−	1.59604i	−0.124340	−	0.992240i	$-0.539682\pi$
$992$	−162949.	−	94078.7i	−0.165588	−	0.0956022i
$993$		0			0
$994$	−652034.	−	513344.i	−0.659929	−	0.519560i
$995$	−1.74552e6			−1.76311
$996$		0			0
$997$	648903.	−	374644.i	0.652814	−	0.376902i	−0.136719	−	0.990610i	$-0.543656\pi$
$997$	648903.	−	374644.i	0.652814	−	0.376902i	0.789534	+	0.613707i	$0.210323\pi$
$998$	497004.	+	860837.i	0.498998	+	0.864291i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.5.n.a.19.2		4
3.2	odd	2		14.5.d.a.5.1	yes	4
7.2	even	3		882.5.c.b.685.2		4
7.3	odd	6	inner	126.5.n.a.73.2		4
7.5	odd	6		882.5.c.b.685.1		4
12.11	even	2		112.5.s.b.33.2		4
15.2	even	4		350.5.i.a.299.2		8
15.8	even	4		350.5.i.a.299.3		8
15.14	odd	2		350.5.k.a.201.2		4
21.2	odd	6		98.5.b.b.97.3		4
21.5	even	6		98.5.b.b.97.4		4
21.11	odd	6		98.5.d.a.31.1		4
21.17	even	6		14.5.d.a.3.1	✓	4
21.20	even	2		98.5.d.a.19.1		4
84.23	even	6		784.5.c.b.97.4		4
84.47	odd	6		784.5.c.b.97.1		4
84.59	odd	6		112.5.s.b.17.2		4
105.17	odd	12		350.5.i.a.199.3		8
105.38	odd	12		350.5.i.a.199.2		8
105.59	even	6		350.5.k.a.101.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.5.d.a.3.1	✓	4	21.17	even	6
14.5.d.a.5.1	yes	4	3.2	odd	2
98.5.b.b.97.3		4	21.2	odd	6
98.5.b.b.97.4		4	21.5	even	6
98.5.d.a.19.1		4	21.20	even	2
98.5.d.a.31.1		4	21.11	odd	6
112.5.s.b.17.2		4	84.59	odd	6
112.5.s.b.33.2		4	12.11	even	2
126.5.n.a.19.2		4	1.1	even	1	trivial
126.5.n.a.73.2		4	7.3	odd	6	inner
350.5.i.a.199.2		8	105.38	odd	12
350.5.i.a.199.3		8	105.17	odd	12
350.5.i.a.299.2		8	15.2	even	4
350.5.i.a.299.3		8	15.8	even	4
350.5.k.a.101.2		4	105.59	even	6
350.5.k.a.201.2		4	15.14	odd	2
784.5.c.b.97.1		4	84.47	odd	6
784.5.c.b.97.4		4	84.23	even	6
882.5.c.b.685.1		4	7.5	odd	6
882.5.c.b.685.2		4	7.2	even	3

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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	126.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41421 - 2.44949i) q^{2} +(-4.00000 - 6.92820i) q^{4} +(-21.9853 - 12.6932i) q^{5} +(-7.00000 + 48.4974i) q^{7} -22.6274 q^{8} +(-62.1838 + 35.9018i) q^{10} +(21.9853 + 38.0796i) q^{11} +162.507i q^{13} +(108.894 + 85.7321i) q^{14} +(-32.0000 + 55.4256i) q^{16} +(-93.7355 + 54.1182i) q^{17} +(389.338 + 224.784i) q^{19} +203.091i q^{20} +124.368 q^{22} +(-217.911 + 377.433i) q^{23} +(9.73506 + 16.8616i) q^{25} +(398.059 + 229.819i) q^{26} +(364.000 - 145.492i) q^{28} -742.118 q^{29} +(-900.175 + 519.716i) q^{31} +(90.5097 + 156.767i) q^{32} +306.139i q^{34} +(769.485 - 977.377i) q^{35} +(-493.338 + 854.486i) q^{37} +(1101.21 - 635.786i) q^{38} +(497.470 + 287.215i) q^{40} +1143.70i q^{41} +2418.82 q^{43} +(175.882 - 304.637i) q^{44} +(616.346 + 1067.54i) q^{46} +(1165.17 + 672.714i) q^{47} +(-2303.00 - 678.964i) q^{49} +55.0698 q^{50} +(1125.88 - 650.027i) q^{52} +(-1783.10 - 3088.42i) q^{53} -1116.26i q^{55} +(158.392 - 1097.37i) q^{56} +(-1049.51 + 1817.81i) q^{58} +(-3710.93 + 2142.50i) q^{59} +(-1209.57 - 698.345i) q^{61} +2939.96i q^{62} +512.000 q^{64} +(2062.73 - 3572.76i) q^{65} +(-3632.89 - 6292.36i) q^{67} +(749.884 + 432.946i) q^{68} +(-1305.86 - 3267.07i) q^{70} -5987.76 q^{71} +(-500.123 + 288.746i) q^{73} +(1395.37 + 2416.85i) q^{74} -3596.55i q^{76} +(-2000.66 + 799.672i) q^{77} +(1573.12 - 2724.72i) q^{79} +(1407.06 - 812.365i) q^{80} +(2801.47 + 1617.43i) q^{82} +4729.96i q^{83} +2747.74 q^{85} +(3420.73 - 5924.88i) q^{86} +(-497.470 - 861.644i) q^{88} +(725.651 + 418.955i) q^{89} +(-7881.16 - 1137.55i) q^{91} +3486.58 q^{92} +(3295.61 - 1902.72i) q^{94} +(-5706.47 - 9883.89i) q^{95} +5622.23i q^{97} +(-4920.05 + 4680.97i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{4} - 54 q^{5} - 28 q^{7} - 96 q^{10} + 54 q^{11} - 128 q^{16} - 918 q^{17} + 30 q^{19} + 192 q^{22} + 486 q^{23} - 572 q^{25} + 1728 q^{26} + 1456 q^{28} - 3240 q^{29} - 546 q^{31} + 1890 q^{35}+ \cdots - 8910 q^{95}+O(q^{100}) \) 4 * q - 16 * q^4 - 54 * q^5 - 28 * q^7 - 96 * q^10 + 54 * q^11 - 128 * q^16 - 918 * q^17 + 30 * q^19 + 192 * q^22 + 486 * q^23 - 572 * q^25 + 1728 * q^26 + 1456 * q^28 - 3240 * q^29 - 546 * q^31 + 1890 * q^35 - 446 * q^37 + 4320 * q^38 + 768 * q^40 + 2344 * q^43 + 432 * q^44 + 3840 * q^46 - 702 * q^47 - 9212 * q^49 + 3456 * q^50 - 384 * q^52 - 2754 * q^53 + 384 * q^58 - 12366 * q^59 + 7686 * q^61 + 2048 * q^64 + 3024 * q^65 - 5062 * q^67 + 7344 * q^68 - 2016 * q^70 - 18792 * q^71 - 17274 * q^73 + 4320 * q^74 - 4914 * q^77 + 794 * q^79 + 3456 * q^80 + 9984 * q^82 + 10380 * q^85 + 10368 * q^86 - 768 * q^88 + 12474 * q^89 + 2688 * q^91 - 7776 * q^92 + 15168 * q^94 - 8910 * q^95

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