LMFDB - Embedded newform 338.4.e.i.147.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [338,4,Mod(23,338)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("338.23"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(338, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	338.e (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,-18,48,0,0,0,0,-226,72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$19.9426455819$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			147.12
Character	$\chi$	$=$	338.147
Dual form			338.4.e.i.23.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.73205 + 1.00000i) q^{2} +(4.07401 - 7.05638i) q^{3} +(2.00000 + 3.46410i) q^{4} +12.6646i q^{5} +(14.1128 - 8.14801i) q^{6} +(-24.9160 + 14.3853i) q^{7} +8.00000i q^{8} +(-19.6950 - 34.1128i) q^{9} +(-12.6646 + 21.9357i) q^{10} +(45.7613 + 26.4203i) q^{11} +32.5920 q^{12} -57.5411 q^{14} +(89.3664 + 51.5957i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(35.5161 + 61.5158i) q^{17} -78.7801i q^{18} +(-56.9572 + 32.8843i) q^{19} +(-43.8715 + 25.3292i) q^{20} +234.423i q^{21} +(52.8406 + 91.5226i) q^{22} +(-22.2154 + 38.4783i) q^{23} +(56.4511 + 32.5920i) q^{24} -35.3924 q^{25} -100.954 q^{27} +(-99.6641 - 57.5411i) q^{28} +(39.2189 - 67.9292i) q^{29} +(103.191 + 178.733i) q^{30} +195.024i q^{31} +(-27.7128 + 16.0000i) q^{32} +(372.863 - 215.273i) q^{33} +142.065i q^{34} +(-182.184 - 315.552i) q^{35} +(78.7801 - 136.451i) q^{36} +(-201.948 - 116.595i) q^{37} -131.537 q^{38} -101.317 q^{40} +(104.319 + 60.2286i) q^{41} +(-234.423 + 406.032i) q^{42} +(202.551 + 350.829i) q^{43} +211.362i q^{44} +(432.025 - 249.430i) q^{45} +(-76.9566 + 44.4309i) q^{46} -400.779i q^{47} +(65.1841 + 112.902i) q^{48} +(242.372 - 419.800i) q^{49} +(-61.3014 - 35.3924i) q^{50} +578.772 q^{51} +116.566 q^{53} +(-174.858 - 100.954i) q^{54} +(-334.603 + 579.549i) q^{55} +(-115.082 - 199.328i) q^{56} +535.883i q^{57} +(135.858 - 78.4379i) q^{58} +(676.744 - 390.718i) q^{59} +412.765i q^{60} +(-26.2781 - 45.5149i) q^{61} +(-195.024 + 337.792i) q^{62} +(981.444 + 566.637i) q^{63} -64.0000 q^{64} +861.091 q^{66} +(-697.414 - 402.652i) q^{67} +(-142.065 + 246.063i) q^{68} +(181.012 + 313.521i) q^{69} -728.735i q^{70} +(347.771 - 200.786i) q^{71} +(272.902 - 157.560i) q^{72} +323.057i q^{73} +(-233.189 - 403.895i) q^{74} +(-144.189 + 249.742i) q^{75} +(-227.829 - 131.537i) q^{76} -1520.25 q^{77} -794.845 q^{79} +(-175.486 - 101.317i) q^{80} +(120.477 - 208.673i) q^{81} +(120.457 + 208.638i) q^{82} -444.820i q^{83} +(-812.064 + 468.845i) q^{84} +(-779.073 + 449.798i) q^{85} +810.205i q^{86} +(-319.556 - 553.488i) q^{87} +(-211.362 + 366.090i) q^{88} +(-68.5435 - 39.5736i) q^{89} +997.720 q^{90} -177.724 q^{92} +(1376.16 + 794.529i) q^{93} +(400.779 - 694.169i) q^{94} +(-416.467 - 721.341i) q^{95} +260.736i q^{96} +(-3.37434 + 1.94818i) q^{97} +(839.601 - 484.744i) q^{98} -2081.39i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 18 q^{3} + 48 q^{4} - 226 q^{9} + 72 q^{10} - 144 q^{12} + 200 q^{14} - 192 q^{16} + 198 q^{17} - 148 q^{22} + 534 q^{23} - 1472 q^{25} + 2676 q^{27} + 238 q^{29} + 472 q^{30} - 1228 q^{35} + 904 q^{36}+ \cdots - 8186 q^{95}+O(q^{100}) $ 24 * q - 18 * q^3 + 48 * q^4 - 226 * q^9 + 72 * q^10 - 144 * q^12 + 200 * q^14 - 192 * q^16 + 198 * q^17 - 148 * q^22 + 534 * q^23 - 1472 * q^25 + 2676 * q^27 + 238 * q^29 + 472 * q^30 - 1228 * q^35 + 904 * q^36 + 648 * q^38 + 576 * q^40 + 104 * q^42 + 856 * q^43 - 288 * q^48 + 1798 * q^49 - 1156 * q^51 + 356 * q^53 - 2252 * q^55 + 400 * q^56 - 3408 * q^61 - 2500 * q^62 - 1536 * q^64 + 6096 * q^66 - 792 * q^68 + 2336 * q^69 - 1096 * q^74 + 3596 * q^75 - 11160 * q^77 - 3500 * q^79 - 6676 * q^81 + 4560 * q^82 - 3204 * q^87 + 592 * q^88 + 9720 * q^90 + 4272 * q^92 + 3944 * q^94 - 8186 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/338\mathbb{Z}\right)^\times$.

$n$	$171$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.73205	+	1.00000i	0.612372	+	0.353553i
$2$	1.73205	+	1.00000i	0.612372	+	0.353553i
$3$	4.07401	−	7.05638i	0.784043	−	1.35800i	−0.145527	−	0.989354i	$-0.546488\pi$
$3$	4.07401	−	7.05638i	0.784043	−	1.35800i	0.929569	−	0.368647i	$-0.120179\pi$
$4$	2.00000	+	3.46410i	0.250000	+	0.433013i
$5$			12.6646i			1.13276i	0.824145	+	0.566379i	$0.191656\pi$
$5$			12.6646i			1.13276i	−0.824145	+	0.566379i	$0.808344\pi$
$6$	14.1128	−	8.14801i	0.960252	−	0.554402i
$7$	−24.9160	+	14.3853i	−1.34534	+	0.776732i	−0.987585	−	0.157085i	$-0.949790\pi$
$7$	−24.9160	+	14.3853i	−1.34534	+	0.776732i	−0.357753	+	0.933816i	$0.616457\pi$
$8$			8.00000i			0.353553i
$9$	−19.6950	−	34.1128i	−0.729446	−	1.26344i
$10$	−12.6646	+	21.9357i	−0.400490	+	0.693669i
$11$	45.7613	+	26.4203i	1.25432	+	0.724183i	0.971965	−	0.235126i	$-0.0755502\pi$
$11$	45.7613	+	26.4203i	1.25432	+	0.724183i	0.282357	+	0.959309i	$0.408884\pi$
$12$	32.5920			0.784043
$13$		0			0
$13$		0			0
$14$	−57.5411			−1.09846
$15$	89.3664	+	51.5957i	1.53829	+	0.888130i
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	35.5161	+	61.5158i	0.506702	+	0.877633i	0.999970	+	0.00775579i	$0.00246877\pi$
$17$	35.5161	+	61.5158i	0.506702	+	0.877633i	−0.493268	+	0.869877i	$0.664198\pi$
$18$		−	78.7801i		−	1.03159i
$19$	−56.9572	+	32.8843i	−0.687731	+	0.397062i	−0.802761	−	0.596300i	$-0.796637\pi$
$19$	−56.9572	+	32.8843i	−0.687731	+	0.397062i	0.115030	+	0.993362i	$0.463303\pi$
$20$	−43.8715	+	25.3292i	−0.490498	+	0.283189i
$21$			234.423i			2.43596i
$22$	52.8406	+	91.5226i	0.512075	+	0.886940i
$23$	−22.2154	+	38.4783i	−0.201402	+	0.348838i	−0.948980	−	0.315335i	$-0.897883\pi$
$23$	−22.2154	+	38.4783i	−0.201402	+	0.348838i	0.747579	+	0.664173i	$0.231216\pi$
$24$	56.4511	+	32.5920i	0.480126	+	0.277201i
$25$	−35.3924			−0.283139
$26$		0			0
$27$	−100.954			−0.719581
$28$	−99.6641	−	57.5411i	−0.672669	−	0.388366i
$29$	39.2189	−	67.9292i	0.251130	−	0.434970i	−0.712707	−	0.701462i	$-0.752531\pi$
$29$	39.2189	−	67.9292i	0.251130	−	0.434970i	0.963837	+	0.266492i	$0.0858645\pi$
$30$	103.191	+	178.733i	0.628003	+	1.08773i
$31$			195.024i			1.12991i	0.825120	+	0.564957i	$0.191107\pi$
$31$			195.024i			1.12991i	−0.825120	+	0.564957i	$0.808893\pi$
$32$	−27.7128	+	16.0000i	−0.153093	+	0.0883883i
$33$	372.863	−	215.273i	1.96688	−	1.13558i
$34$			142.065i			0.716584i
$35$	−182.184	−	315.552i	−0.879848	−	1.52394i
$36$	78.7801	−	136.451i	0.364723	−	0.631719i
$37$	−201.948	−	116.595i	−0.897297	−	0.518055i	−0.0209750	−	0.999780i	$-0.506677\pi$
$37$	−201.948	−	116.595i	−0.897297	−	0.518055i	−0.876322	+	0.481725i	$0.840010\pi$
$38$	−131.537			−0.561530
$39$		0			0
$40$	−101.317			−0.400490
$41$	104.319	+	60.2286i	0.397363	+	0.229418i	0.685345	−	0.728218i	$-0.259651\pi$
$41$	104.319	+	60.2286i	0.397363	+	0.229418i	−0.287983	+	0.957636i	$0.592985\pi$
$42$	−234.423	+	406.032i	−0.861243	+	1.49172i
$43$	202.551	+	350.829i	0.718344	+	1.24421i	0.961656	+	0.274260i	$0.0884327\pi$
$43$	202.551	+	350.829i	0.718344	+	1.24421i	−0.243312	+	0.969948i	$0.578234\pi$
$44$			211.362i			0.724183i
$45$	432.025	−	249.430i	1.43117	−	0.826285i
$46$	−76.9566	+	44.4309i	−0.246666	+	0.142413i
$47$		−	400.779i		−	1.24382i	−0.783088	−	0.621911i	$-0.786357\pi$
$47$		−	400.779i		−	1.24382i	0.783088	−	0.621911i	$-0.213643\pi$
$48$	65.1841	+	112.902i	0.196011	+	0.339500i
$49$	242.372	−	419.800i	0.706624	−	1.22391i
$50$	−61.3014	−	35.3924i	−0.173386	−	0.100105i
$51$	578.772			1.58910
$52$		0			0
$53$	116.566			0.302105			0.151052	−	0.988526i	$-0.451734\pi$
$53$	116.566			0.302105			0.151052	+	0.988526i	$0.451734\pi$
$54$	−174.858	−	100.954i	−0.440652	−	0.254410i
$55$	−334.603	+	579.549i	−0.820324	+	1.42084i
$56$	−115.082	−	199.328i	−0.274616	−	0.475649i
$57$			535.883i			1.24525i
$58$	135.858	−	78.4379i	0.307570	−	0.177576i
$59$	676.744	−	390.718i	1.49330	−	0.862155i	0.493326	−	0.869844i	$-0.335781\pi$
$59$	676.744	−	390.718i	1.49330	−	0.862155i	0.999970	+	0.00768919i	$0.00244757\pi$
$60$			412.765i			0.888130i
$61$	−26.2781	−	45.5149i	−0.0551567	−	0.0955343i	0.837129	−	0.547006i	$-0.184233\pi$
$61$	−26.2781	−	45.5149i	−0.0551567	−	0.0955343i	−0.892285	+	0.451472i	$0.850899\pi$
$62$	−195.024	+	337.792i	−0.399485	+	0.691929i
$63$	981.444	+	566.637i	1.96270	+	1.13317i
$64$	−64.0000			−0.125000
$65$		0			0
$66$	861.091			1.60595
$67$	−697.414	−	402.652i	−1.27168	−	0.734206i	−0.296378	−	0.955071i	$-0.595779\pi$
$67$	−697.414	−	402.652i	−1.27168	−	0.734206i	−0.975305	+	0.220864i	$0.929112\pi$
$68$	−142.065	+	246.063i	−0.253351	+	0.438817i
$69$	181.012	+	313.521i	0.315815	+	0.547008i
$70$		−	728.735i		−	1.24429i
$71$	347.771	−	200.786i	0.581307	−	0.335618i	−0.180345	−	0.983603i	$-0.557722\pi$
$71$	347.771	−	200.786i	0.581307	−	0.335618i	0.761653	+	0.647985i	$0.224388\pi$
$72$	272.902	−	157.560i	0.446692	−	0.257898i
$73$			323.057i			0.517958i	0.965883	+	0.258979i	$0.0833861\pi$
$73$			323.057i			0.517958i	−0.965883	+	0.258979i	$0.916614\pi$
$74$	−233.189	−	403.895i	−0.366320	−	0.634485i
$75$	−144.189	+	249.742i	−0.221993	+	0.384503i
$76$	−227.829	−	131.537i	−0.343865	−	0.198531i
$77$	−1520.25			−2.24998
$78$		0			0
$79$	−794.845			−1.13199			−0.565994	−	0.824409i	$-0.691507\pi$
$79$	−794.845			−1.13199			−0.565994	+	0.824409i	$0.691507\pi$
$80$	−175.486	−	101.317i	−0.245249	−	0.141595i
$81$	120.477	−	208.673i	0.165264	−	0.286245i
$82$	120.457	+	208.638i	0.162223	+	0.280978i
$83$		−	444.820i		−	0.588258i	−0.955766	−	0.294129i	$-0.904971\pi$
$83$		−	444.820i		−	0.588258i	0.955766	−	0.294129i	$-0.0950295\pi$
$84$	−812.064	+	468.845i	−1.05480	+	0.608991i
$85$	−779.073	+	449.798i	−0.994145	+	0.573970i
$86$			810.205i			1.01589i
$87$	−319.556	−	553.488i	−0.393793	−	0.682070i
$88$	−211.362	+	366.090i	−0.256037	+	0.443470i
$89$	−68.5435	−	39.5736i	−0.0816359	−	0.0471325i	0.458626	−	0.888629i	$-0.348342\pi$
$89$	−68.5435	−	39.5736i	−0.0816359	−	0.0471325i	−0.540262	+	0.841497i	$0.681675\pi$
$90$	997.720			1.16854
$91$		0			0
$92$	−177.724			−0.201402
$93$	1376.16	+	794.529i	1.53443	+	0.885901i
$94$	400.779	−	694.169i	0.439757	−	0.761682i
$95$	−416.467	−	721.341i	−0.449774	−	0.779032i
$96$			260.736i			0.277201i
$97$	−3.37434	+	1.94818i	−0.00353209	+	0.00203925i	−0.501765	−	0.865004i	$-0.667316\pi$
$97$	−3.37434	+	1.94818i	−0.00353209	+	0.00203925i	0.498233	+	0.867043i	$0.333982\pi$
$98$	839.601	−	484.744i	0.865434	−	0.499658i
$99$		−	2081.39i		−	2.11301i
$100$	−70.7847	−	122.603i	−0.0707847	−	0.122603i
$101$	−517.657	+	896.609i	−0.509988	+	0.883326i	0.489945	+	0.871754i	$0.337017\pi$
$101$	−517.657	+	896.609i	−0.509988	+	0.883326i	−0.999933	+	0.0115723i	$0.996316\pi$
$102$	1002.46	+	578.772i	0.973123	+	0.561833i
$103$	−1248.51			−1.19436			−0.597181	−	0.802107i	$-0.703713\pi$
$103$	−1248.51			−1.19436			−0.597181	+	0.802107i	$0.703713\pi$
$104$		0			0
$105$	−2968.87			−2.75935
$106$	201.898	+	116.566i	0.185001	+	0.106810i
$107$	581.006	−	1006.33i	0.524934	−	0.909212i	−0.474644	−	0.880178i	$-0.657423\pi$
$107$	581.006	−	1006.33i	0.524934	−	0.909212i	0.999578	−	0.0290348i	$-0.00924335\pi$
$108$	−201.909	−	349.716i	−0.179895	−	0.311588i
$109$			1003.58i			0.881885i	0.897535	+	0.440943i	$0.145356\pi$
$109$			1003.58i			0.881885i	−0.897535	+	0.440943i	$0.854644\pi$
$110$	−1159.10	+	669.205i	−1.00469	+	0.580057i
$111$	−1645.47	+	950.014i	−1.40704	+	0.812354i
$112$		−	460.329i		−	0.388366i
$113$	372.206	+	644.679i	0.309860	+	0.536693i	0.978332	−	0.207045i	$-0.0663845\pi$
$113$	372.206	+	644.679i	0.309860	+	0.536693i	−0.668472	+	0.743738i	$0.733051\pi$
$114$	−535.883	+	928.176i	−0.440263	+	0.762559i
$115$	−487.312	−	281.350i	−0.395149	−	0.228139i
$116$	313.751			0.251130
$117$		0			0
$118$	1562.87			1.21927
$119$	−1769.84	−	1021.82i	−1.36337	−	0.787142i
$120$	−412.765	+	714.931i	−0.314001	+	0.543866i
$121$	730.563	+	1265.37i	0.548883	+	0.950694i
$122$		−	105.112i		−	0.0780034i
$123$	849.992	−	490.743i	0.623099	−	0.359746i
$124$	−675.583	+	390.048i	−0.489267	+	0.282479i
$125$			1134.85i			0.812030i
$126$	1133.27	+	1962.89i	0.801270	+	1.38784i
$127$	841.759	−	1457.97i	0.588142	−	1.01869i	−0.406334	−	0.913725i	$-0.633193\pi$
$127$	841.759	−	1457.97i	0.588142	−	1.01869i	0.994476	−	0.104967i	$-0.0334737\pi$
$128$	−110.851	−	64.0000i	−0.0765466	−	0.0441942i
$129$	3300.78			2.25285
$130$		0			0
$131$	2177.87			1.45253			0.726266	−	0.687414i	$-0.241254\pi$
$131$	2177.87			1.45253			0.726266	+	0.687414i	$0.241254\pi$
$132$	1491.45	+	861.091i	0.983442	+	0.567791i
$133$	946.098	−	1638.69i	0.616821	−	1.06836i
$134$	−805.305	−	1394.83i	−0.519162	−	0.899215i
$135$		−	1278.55i		−	0.815110i
$136$	−492.126	+	284.129i	−0.310290	+	0.179146i
$137$	−1530.84	+	883.829i	−0.954658	+	0.551172i	−0.894525	−	0.447018i	$-0.852486\pi$
$137$	−1530.84	+	883.829i	−0.954658	+	0.551172i	−0.0601334	+	0.998190i	$0.519153\pi$
$138$			724.047i			0.446630i
$139$	−502.768	−	870.819i	−0.306793	−	0.531381i	0.670866	−	0.741579i	$-0.265923\pi$
$139$	−502.768	−	870.819i	−0.306793	−	0.531381i	−0.977659	+	0.210198i	$0.932589\pi$
$140$	728.735	−	1262.21i	0.439924	−	0.761971i
$141$	−2828.05	−	1632.78i	−1.68911	−	0.975209i
$142$	803.143			0.474635
$143$		0			0
$144$	630.241			0.364723
$145$	860.297	+	496.692i	0.492715	+	0.284469i
$146$	−323.057	+	559.551i	−0.183126	+	0.317183i
$147$	−1974.85	−	3420.54i	−1.10805	−	1.91919i
$148$		−	932.757i		−	0.518055i
$149$	118.017	−	68.1369i	0.0648879	−	0.0374631i	−0.467205	−	0.884149i	$-0.654739\pi$
$149$	118.017	−	68.1369i	0.0648879	−	0.0374631i	0.532093	+	0.846686i	$0.321406\pi$
$150$	−499.484	+	288.377i	−0.271885	+	0.156973i
$151$		−	804.394i		−	0.433514i	−0.976226	−	0.216757i	$-0.930452\pi$
$151$		−	804.394i		−	0.433514i	0.976226	−	0.216757i	$-0.0695479\pi$
$152$	−263.074	−	455.658i	−0.140383	−	0.243150i
$153$	1398.98	−	2423.11i	0.739223	−	1.28037i
$154$	−2633.15	−	1520.25i	−1.37783	−	0.795490i
$155$	−2469.90			−1.27992
$156$		0			0
$157$	3730.07			1.89613			0.948064	−	0.318079i	$-0.103038\pi$
$157$	3730.07			1.89613			0.948064	+	0.318079i	$0.103038\pi$
$158$	−1376.71	−	794.845i	−0.693198	−	0.400218i
$159$	474.890	−	822.534i	0.236863	−	0.410259i
$160$	−202.634	−	350.972i	−0.100123	−	0.173417i
$161$		−	1278.30i		−	0.625740i
$162$	417.345	−	240.954i	0.202406	−	0.116859i
$163$	2271.80	−	1311.63i	1.09166	−	0.630273i	0.157646	−	0.987496i	$-0.449610\pi$
$163$	2271.80	−	1311.63i	1.09166	−	0.630273i	0.934019	+	0.357223i	$0.116276\pi$
$164$			481.828i			0.229418i
$165$	2726.35	+	4722.17i	1.28634	+	2.22800i
$166$	444.820	−	770.451i	0.207980	−	0.360233i
$167$	1106.78	+	639.001i	0.512847	+	0.296092i	0.734003	−	0.679146i	$-0.237650\pi$
$167$	1106.78	+	639.001i	0.512847	+	0.296092i	−0.221156	+	0.975238i	$0.570983\pi$
$168$	−1875.38			−0.861243
$169$		0			0
$170$	−1799.19			−0.811716
$171$	2243.55	+	1295.31i	1.00332	+	0.579270i
$172$	−810.205	+	1403.32i	−0.359172	+	0.622104i
$173$	534.991	+	926.631i	0.235113	+	0.407228i	0.959306	−	0.282370i	$-0.0911205\pi$
$173$	534.991	+	926.631i	0.235113	+	0.407228i	−0.724192	+	0.689598i	$0.757787\pi$
$174$		−	1278.22i		−	0.556908i
$175$	881.836	−	509.129i	0.380918	−	0.219923i
$176$	−732.181	+	422.725i	−0.313581	+	0.181046i
$177$		−	6367.15i		−	2.70387i
$178$	−79.1472	−	137.087i	−0.0333277	−	0.0577253i
$179$	368.774	−	638.736i	0.153986	−	0.266712i	−0.778703	−	0.627392i	$-0.784122\pi$
$179$	368.774	−	638.736i	0.153986	−	0.266712i	0.932689	+	0.360681i	$0.117456\pi$
$180$	1728.10	+	997.720i	0.715584	+	0.413142i
$181$	1457.02			0.598338			0.299169	−	0.954200i	$-0.403291\pi$
$181$	1457.02			0.598338			0.299169	+	0.954200i	$0.403291\pi$
$182$		0			0
$183$	−428.228			−0.172981
$184$	−307.826	−	177.724i	−0.123333	−	0.0712063i
$185$	1476.62	−	2557.59i	0.586830	−	1.01642i
$186$	1589.06	+	2752.33i	0.626427	+	1.08500i
$187$			3753.39i			1.46778i
$188$	1388.34	−	801.558i	0.538591	−	0.310955i
$189$	2515.38	−	1452.26i	0.968080	−	0.558921i
$190$		−	1665.87i		−	0.636077i
$191$	−287.715	−	498.337i	−0.108997	−	0.188788i	0.806367	−	0.591415i	$-0.201430\pi$
$191$	−287.715	−	498.337i	−0.108997	−	0.188788i	−0.915364	+	0.402627i	$0.868097\pi$
$192$	−260.736	+	451.609i	−0.0980053	+	0.169750i
$193$	−2112.00	−	1219.36i	−0.787694	−	0.454775i	0.0514564	−	0.998675i	$-0.483614\pi$
$193$	−2112.00	−	1219.36i	−0.787694	−	0.454775i	−0.839150	+	0.543900i	$0.816947\pi$
$194$	−7.79271			−0.00288394
$195$		0			0
$196$	1938.98			0.706624
$197$	3311.27	+	1911.76i	1.19755	+	0.691408i	0.960009	−	0.279969i	$-0.0903242\pi$
$197$	3311.27	+	1911.76i	1.19755	+	0.691408i	0.237544	+	0.971377i	$0.423658\pi$
$198$	2081.39	−	3605.08i	0.747062	−	1.29395i
$199$	−1078.71	−	1868.37i	−0.384258	−	0.665555i	0.607408	−	0.794390i	$-0.292210\pi$
$199$	−1078.71	−	1868.37i	−0.384258	−	0.665555i	−0.991666	+	0.128835i	$0.958876\pi$
$200$		−	283.139i		−	0.100105i
$201$	−5682.54	+	3280.82i	−1.99411	+	1.15130i
$202$	−1793.22	+	1035.31i	−0.624606	+	0.360616i
$203$			2256.70i			0.780243i
$204$	1157.54	+	2004.92i	0.397276	+	0.688102i
$205$	−762.771	+	1321.16i	−0.259874	+	0.450116i
$206$	−2162.48	−	1248.51i	−0.731394	−	0.422271i
$207$	1750.14			0.587647
$208$		0			0
$209$	−3475.25			−1.15018
$210$	−5142.24	−	2968.87i	−1.68975	−	0.975579i
$211$	−1681.93	+	2913.19i	−0.548762	+	0.950484i	0.449598	+	0.893231i	$0.351567\pi$
$211$	−1681.93	+	2913.19i	−0.548762	+	0.950484i	−0.998360	+	0.0572525i	$0.981766\pi$
$212$	233.132	+	403.796i	0.0755262	+	0.130815i
$213$		−	3272.01i		−	1.05255i
$214$	2012.66	−	1162.01i	0.642910	−	0.371184i
$215$	−4443.11	+	2565.23i	−1.40939	+	0.813709i
$216$		−	807.635i		−	0.254410i
$217$	−2805.47	−	4859.22i	−0.877640	−	1.52012i
$218$	−1003.58	+	1738.25i	−0.311794	+	0.540042i
$219$	2279.61	+	1316.13i	0.703388	+	0.406101i
$220$	−2676.82			−0.820324
$221$		0			0
$222$	−3800.06			−1.14884
$223$	−2852.61	−	1646.95i	−0.856613	−	0.494566i	0.00626360	−	0.999980i	$-0.498006\pi$
$223$	−2852.61	−	1646.95i	−0.856613	−	0.494566i	−0.862877	+	0.505415i	$0.831340\pi$
$224$	460.329	−	797.313i	0.137308	−	0.237824i
$225$	697.054	+	1207.33i	0.206534	+	0.357728i
$226$			1488.82i			0.438208i
$227$	−470.673	+	271.743i	−0.137620	+	0.0794547i	−0.567229	−	0.823560i	$-0.691985\pi$
$227$	−470.673	+	271.743i	−0.137620	+	0.0794547i	0.429609	+	0.903015i	$0.358651\pi$
$228$	−1856.35	+	1071.77i	−0.539210	+	0.311313i
$229$			3071.66i			0.886379i	0.896428	+	0.443189i	$0.146153\pi$
$229$			3071.66i			0.886379i	−0.896428	+	0.443189i	$0.853847\pi$
$230$	−562.700	−	974.625i	−0.161319	−	0.279412i
$231$	−6193.51	+	10727.5i	−1.76408	+	3.05548i
$232$	543.433	+	313.751i	0.153785	+	0.0887879i
$233$	−3383.06			−0.951208			−0.475604	−	0.879660i	$-0.657770\pi$
$233$	−3383.06			−0.951208			−0.475604	+	0.879660i	$0.657770\pi$
$234$		0			0
$235$	5075.71			1.40895
$236$	2706.97	+	1562.87i	0.746648	+	0.431078i
$237$	−3238.20	+	5608.73i	−0.887527	+	1.53724i
$238$	−2043.64	−	3539.68i	−0.556594	−	0.964049i
$239$		−	698.550i		−	0.189060i	−0.995522	−	0.0945302i	$-0.969865\pi$
$239$		−	698.550i		−	0.189060i	0.995522	−	0.0945302i	$-0.0301349\pi$
$240$	−1429.86	+	825.531i	−0.384572	+	0.222032i
$241$	3217.67	−	1857.72i	0.860034	−	0.496541i	−0.00398962	−	0.999992i	$-0.501270\pi$
$241$	3217.67	−	1857.72i	0.860034	−	0.496541i	0.864024	+	0.503451i	$0.167937\pi$
$242$			2922.25i			0.776238i
$243$	−2344.53	−	4060.85i	−0.618938	−	1.07203i
$244$	105.112	−	182.060i	0.0275784	−	0.0477671i
$245$	5316.61	+	3069.55i	1.38639	+	0.800433i
$246$	1962.97			0.508758
$247$		0			0
$248$	−1560.19			−0.399485
$249$	−3138.82	−	1812.20i	−0.798855	−	0.461219i
$250$	−1134.85	+	1965.61i	−0.287096	+	0.497265i
$251$	−1926.42	−	3336.65i	−0.484440	−	0.839074i	0.515400	−	0.856950i	$-0.327643\pi$
$251$	−1926.42	−	3336.65i	−0.484440	−	0.839074i	−0.999840	+	0.0178750i	$0.994310\pi$
$252$			4533.09i			1.13317i
$253$	−2033.21	+	1173.88i	−0.505245	+	0.291704i
$254$	2915.94	−	1683.52i	0.720324	−	0.415879i
$255$			7329.92i			1.80007i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	2288.73	−	3964.19i	0.555513	−	0.962177i	−0.442350	−	0.896842i	$-0.645855\pi$
$257$	2288.73	−	3964.19i	0.555513	−	0.962177i	0.997863	−	0.0653345i	$-0.0208114\pi$
$258$	5717.12	+	3300.78i	1.37958	+	0.796502i
$259$	6708.98			1.60956
$260$		0			0
$261$	−3089.67			−0.732743
$262$	3772.19	+	2177.87i	0.889490	+	0.513547i
$263$	2411.71	−	4177.21i	0.565447	−	0.979383i	−0.431561	−	0.902084i	$-0.642037\pi$
$263$	2411.71	−	4177.21i	0.565447	−	0.979383i	0.997008	−	0.0772990i	$-0.0246296\pi$
$264$	1722.18	+	2982.91i	0.401489	+	0.695399i
$265$			1476.26i			0.342212i
$266$	3277.38	−	1892.20i	0.755448	−	0.436158i
$267$	−558.493	+	322.446i	−0.128012	+	0.0739078i
$268$		−	3221.22i		−	0.734206i
$269$	982.898	+	1702.43i	0.222782	+	0.385870i	0.955652	−	0.294499i	$-0.0951529\pi$
$269$	982.898	+	1702.43i	0.222782	+	0.385870i	−0.732870	+	0.680369i	$0.761820\pi$
$270$	1278.55	−	2214.51i	0.288185	−	0.499151i
$271$	3824.29	+	2207.96i	0.857230	+	0.494922i	0.863084	−	0.505061i	$-0.168530\pi$
$271$	3824.29	+	2207.96i	0.857230	+	0.494922i	−0.00585389	+	0.999983i	$0.501863\pi$
$272$	−1136.52			−0.253351
$273$		0			0
$274$	−3535.32			−0.779475
$275$	−1619.60	−	935.076i	−0.355147	−	0.205044i
$276$	−724.047	+	1254.09i	−0.157908	+	0.273504i
$277$	1806.11	+	3128.28i	0.391765	+	0.678557i	0.992682	−	0.120754i	$-0.0385313\pi$
$277$	1806.11	+	3128.28i	0.391765	+	0.678557i	−0.600917	+	0.799311i	$0.705198\pi$
$278$		−	2011.07i		−	0.433871i
$279$	6652.82	−	3841.01i	1.42758	−	0.824212i
$280$	2524.41	−	1457.47i	0.538795	−	0.311073i
$281$			4095.02i			0.869353i	0.900587	+	0.434676i	$0.143137\pi$
$281$			4095.02i			0.869353i	−0.900587	+	0.434676i	$0.856863\pi$
$282$	−3265.55	−	5656.10i	−0.689577	−	1.19438i
$283$	3363.10	−	5825.05i	0.706415	−	1.22355i	−0.259764	−	0.965672i	$-0.583645\pi$
$283$	3363.10	−	5825.05i	0.706415	−	1.22355i	0.966179	−	0.257874i	$-0.0830219\pi$
$284$	1391.08	+	803.143i	0.290654	+	0.167809i
$285$	−6786.75			−1.41057
$286$		0			0
$287$	−3465.62			−0.712783
$288$	1091.61	+	630.241i	0.223346	+	0.128949i
$289$	−66.2919	+	114.821i	−0.0134932	+	0.0233709i
$290$	993.385	+	1720.59i	0.201150	+	0.348402i
$291$			31.7475i			0.00639544i
$292$	−1119.10	+	646.114i	−0.224282	+	0.129490i
$293$	3900.10	−	2251.72i	0.777632	−	0.448966i	−0.0579584	−	0.998319i	$-0.518459\pi$
$293$	3900.10	−	2251.72i	0.777632	−	0.448966i	0.835590	+	0.549353i	$0.185126\pi$
$294$		−	7899.40i		−	1.56701i
$295$	4948.29	+	8570.69i	0.976613	+	1.69154i
$296$	932.757	−	1615.58i	0.183160	−	0.317243i
$297$	−4619.80	−	2667.24i	−0.902586	−	0.521109i
$298$	272.548			0.0529808
$299$		0			0
$300$	−1153.51			−0.221993
$301$	−10093.5	−	5827.51i	−1.93283	−	1.11592i
$302$	804.394	−	1393.25i	0.153270	−	0.265472i
$303$	4217.88	+	7305.58i	0.799705	+	1.38513i
$304$		−	1052.30i		−	0.198531i
$305$	576.429	−	332.801i	0.108217	−	0.0624792i
$306$	4846.22	−	2797.97i	0.905359	−	0.522709i
$307$		−	1934.75i		−	0.359681i	−0.983696	−	0.179841i	$-0.942442\pi$
$307$		−	1934.75i		−	0.359681i	0.983696	−	0.179841i	$-0.0575582\pi$
$308$	−3040.50	−	5266.31i	−0.562496	−	0.974272i
$309$	−5086.43	+	8809.96i	−0.936431	+	1.62195i
$310$	−4278.00	−	2469.90i	−0.783787	−	0.452520i
$311$	2655.72			0.484219			0.242110	−	0.970249i	$-0.422161\pi$
$311$	2655.72			0.484219			0.242110	+	0.970249i	$0.422161\pi$
$312$		0			0
$313$	6102.36			1.10200			0.550999	−	0.834506i	$-0.314247\pi$
$313$	6102.36			1.10200			0.550999	+	0.834506i	$0.314247\pi$
$314$	6460.67	+	3730.07i	1.16114	+	0.670383i
$315$	−7176.23	+	12429.6i	−1.28360	+	2.22327i
$316$	−1589.69	−	2753.42i	−0.282997	−	0.490165i
$317$		−	1382.99i		−	0.245037i	−0.992466	−	0.122518i	$-0.960903\pi$
$317$		−	1382.99i		−	0.245037i	0.992466	−	0.122518i	$-0.0390971\pi$
$318$	1645.07	−	949.781i	0.290097	−	0.167488i
$319$	3589.42	−	2072.35i	0.629996	−	0.363728i
$320$		−	810.535i		−	0.141595i
$321$	−4734.04	−	8199.60i	−0.823141	−	1.42572i
$322$	1278.30	−	2214.08i	0.221233	−	0.383186i
$323$	−4045.80	−	2335.85i	−0.696949	−	0.402384i
$324$	963.817			0.165264
$325$		0			0
$326$	5246.50			0.891340
$327$	7081.64	+	4088.59i	1.19760	+	0.691436i
$328$	−481.828	+	834.551i	−0.0811114	+	0.140489i
$329$	5765.31	+	9985.81i	0.966115	+	1.67336i
$330$			10905.4i			1.81916i
$331$	8666.02	−	5003.33i	1.43906	−	0.830839i	0.441271	−	0.897374i	$-0.354528\pi$
$331$	8666.02	−	5003.33i	1.43906	−	0.830839i	0.997784	+	0.0665347i	$0.0211943\pi$
$332$	1540.90	−	889.641i	0.254723	−	0.147064i
$333$			9185.34i			1.51157i
$334$	1278.00	+	2213.57i	0.209369	+	0.362637i
$335$	5099.44	−	8832.48i	0.831678	−	1.44051i
$336$	−3248.26	−	1875.38i	−0.527401	−	0.304495i
$337$	−11057.1			−1.78730			−0.893649	−	0.448767i	$-0.851863\pi$
$337$	−11057.1			−1.78730			−0.893649	+	0.448767i	$0.851863\pi$
$338$		0			0
$339$	6065.47			0.971773
$340$	−3116.29	−	1799.19i	−0.497073	−	0.286985i
$341$	−5152.59	+	8924.55i	−0.818266	+	1.41728i
$342$	2590.63	+	4487.10i	0.409606	+	0.709458i
$343$			4078.05i			0.641964i
$344$	−2806.63	+	1620.41i	−0.439894	+	0.253973i
$345$	−3970.63	+	2292.44i	−0.619627	+	0.357742i
$346$			2139.96i			0.332500i
$347$	4316.98	+	7477.22i	0.667860	+	1.15677i	0.978501	+	0.206240i	$0.0661228\pi$
$347$	4316.98	+	7477.22i	0.667860	+	1.15677i	−0.310642	+	0.950527i	$0.600544\pi$
$348$	1278.22	−	2213.95i	0.196897	−	0.341035i
$349$	−8113.84	−	4684.53i	−1.24448	−	0.718502i	−0.274478	−	0.961593i	$-0.588505\pi$
$349$	−8113.84	−	4684.53i	−1.24448	−	0.718502i	−0.970003	+	0.243092i	$0.921838\pi$
$350$	2036.51			0.311018
$351$		0			0
$352$	−1690.90			−0.256037
$353$	−4345.59	−	2508.93i	−0.655220	−	0.378291i	0.135233	−	0.990814i	$-0.456822\pi$
$353$	−4345.59	−	2508.93i	−0.655220	−	0.378291i	−0.790453	+	0.612522i	$0.790155\pi$
$354$	6367.15	−	11028.2i	0.955961	−	1.65577i
$355$	2542.87	+	4404.38i	0.380174	+	0.658480i
$356$		−	316.589i		−	0.0471325i
$357$	−14420.7	+	8325.79i	−2.13788	+	1.23431i
$358$	1277.47	−	737.549i	0.188594	−	0.108885i
$359$			7268.33i			1.06855i	0.845312	+	0.534273i	$0.179414\pi$
$359$			7268.33i			1.06855i	−0.845312	+	0.534273i	$0.820586\pi$
$360$	1995.44	+	3456.20i	0.292136	+	0.505994i
$361$	−1266.75	+	2194.07i	−0.184684	+	0.319882i
$362$	2523.63	+	1457.02i	0.366406	+	0.211545i
$363$	11905.3			1.72139
$364$		0			0
$365$	−4091.39			−0.586721
$366$	−741.712	−	428.228i	−0.105929	−	0.0611580i
$367$	−5943.72	+	10294.8i	−0.845394	+	1.46427i	0.0398848	+	0.999204i	$0.487301\pi$
$367$	−5943.72	+	10294.8i	−0.845394	+	1.46427i	−0.885279	+	0.465061i	$0.846032\pi$
$368$	−355.447	−	615.652i	−0.0503504	−	0.0872095i
$369$		−	4744.81i		−	0.669391i
$370$	5115.18	−	2953.25i	0.718718	−	0.414952i
$371$	−2904.36	+	1676.83i	−0.406433	+	0.234654i
$372$			6356.23i			0.885901i
$373$	7117.28	+	12327.5i	0.987986	+	1.71124i	0.627830	+	0.778350i	$0.283943\pi$
$373$	7117.28	+	12327.5i	0.987986	+	1.71124i	0.360156	+	0.932892i	$0.382723\pi$
$374$	−3753.39	+	6501.06i	−0.518939	+	0.898828i
$375$	8007.91	+	4623.37i	1.10274	+	0.636666i
$376$	3206.23			0.439757
$377$		0			0
$378$	5809.03			0.790434
$379$	6859.00	+	3960.04i	0.929612	+	0.536712i	0.886689	−	0.462366i	$-0.153000\pi$
$379$	6859.00	+	3960.04i	0.929612	+	0.536712i	0.0429233	+	0.999078i	$0.486333\pi$
$380$	1665.87	−	2885.37i	0.224887	−	0.389516i
$381$	−6858.66	−	11879.5i	−0.922257	−	1.59740i
$382$		−	1150.86i		−	0.154144i
$383$	−9203.20	+	5313.47i	−1.22784	+	0.708892i	−0.966577	−	0.256376i	$-0.917471\pi$
$383$	−9203.20	+	5313.47i	−1.22784	+	0.708892i	−0.261260	+	0.965268i	$0.584138\pi$
$384$	−903.217	+	521.473i	−0.120032	+	0.0693002i
$385$		−	19253.4i		−	2.54869i
$386$	−2438.72	−	4223.99i	−0.321575	−	0.556983i
$387$	7978.51	−	13819.2i	1.04799	−	1.81516i
$388$	−13.4974	−	7.79271i	−0.00176604	−	0.00101963i
$389$	10183.7			1.32733			0.663667	−	0.748028i	$-0.268999\pi$
$389$	10183.7			1.32733			0.663667	+	0.748028i	$0.268999\pi$
$390$		0			0
$391$	−3156.03			−0.408202
$392$	3358.40	+	1938.98i	0.432717	+	0.249829i
$393$	8872.66	−	15367.9i	1.13885	−	1.97254i
$394$	3823.52	+	6622.53i	0.488899	+	0.846798i
$395$		−	10066.4i		−	1.28227i
$396$	7210.16	−	4162.79i	0.914960	−	0.528252i
$397$	3162.78	−	1826.03i	0.399837	−	0.230846i	−0.286577	−	0.958057i	$-0.592517\pi$
$397$	3162.78	−	1826.03i	0.399837	−	0.230846i	0.686414	+	0.727211i	$0.259184\pi$
$398$		−	4314.82i		−	0.543424i
$399$	−7708.82	−	13352.1i	−0.967227	−	1.67529i
$400$	283.139	−	490.411i	0.0353924	−	0.0613014i
$401$	7694.37	+	4442.35i	0.958200	+	0.553217i	0.895619	−	0.444823i	$-0.146733\pi$
$401$	7694.37	+	4442.35i	0.958200	+	0.553217i	0.0625817	+	0.998040i	$0.480067\pi$
$402$	−13123.3			−1.62818
$403$		0			0
$404$	−4141.26			−0.509988
$405$	2642.76	+	1525.80i	0.324246	+	0.187204i
$406$	−2256.70	+	3908.72i	−0.275857	+	0.477799i
$407$	−6160.93	−	10671.0i	−0.750334	−	1.29962i
$408$			4630.17i			0.561833i
$409$	9931.55	−	5733.99i	1.20069	−	0.693221i	0.239984	−	0.970777i	$-0.422858\pi$
$409$	9931.55	−	5733.99i	1.20069	−	0.693221i	0.960709	+	0.277556i	$0.0895244\pi$
$410$	−2642.32	+	1525.54i	−0.318280	+	0.183759i
$411$			14402.9i			1.72857i
$412$	−2497.02	−	4324.96i	−0.298590	−	0.517174i
$413$	−11241.2	+	19470.3i	−1.33933	+	2.31978i
$414$	3031.32	+	1750.14i	0.359859	+	0.207764i
$415$	5633.48			0.666353
$416$		0			0
$417$	−8193.11			−0.962155
$418$	−6019.31	−	3475.25i	−0.704340	−	0.406651i
$419$	7957.04	−	13782.0i	0.927749	−	1.60691i	0.140669	−	0.990057i	$-0.455075\pi$
$419$	7957.04	−	13782.0i	0.927749	−	1.60691i	0.787080	−	0.616851i	$-0.211592\pi$
$420$	−5937.74	−	10284.5i	−0.689839	−	1.19484i
$421$			3091.64i			0.357904i	0.983858	+	0.178952i	$0.0572706\pi$
$421$			3091.64i			0.357904i	−0.983858	+	0.178952i	$0.942729\pi$
$422$	−5826.37	+	3363.86i	−0.672093	+	0.388033i
$423$	−13671.7	+	7893.35i	−1.57149	+	0.907300i
$424$			932.528i			0.106810i
$425$	−1257.00	−	2177.19i	−0.143467	−	0.248492i
$426$	3272.01	−	5667.28i	0.372134	−	0.644556i
$427$	1309.49	+	756.034i	0.148409	+	0.0856840i
$428$	4648.05			0.524934
$429$		0			0
$430$	−10260.9			−1.15076
$431$	4327.26	+	2498.35i	0.483612	+	0.279214i	0.721921	−	0.691976i	$-0.243260\pi$
$431$	4327.26	+	2498.35i	0.483612	+	0.279214i	−0.238308	+	0.971190i	$0.576593\pi$
$432$	807.635	−	1398.87i	0.0899476	−	0.155794i
$433$	−920.918	−	1595.08i	−0.102209	−	0.177031i	0.810386	−	0.585897i	$-0.199258\pi$
$433$	−920.918	−	1595.08i	−0.102209	−	0.177031i	−0.912594	+	0.408866i	$0.865924\pi$
$434$		−	11221.9i		−	1.24117i
$435$	7009.71	−	4047.06i	0.772620	−	0.446072i
$436$	−3476.50	+	2007.16i	−0.381868	+	0.220471i
$437$		−	2922.16i		−	0.319876i
$438$	2632.27	+	4559.23i	0.287157	+	0.497370i
$439$	4981.61	−	8628.40i	0.541593	−	0.938066i	−0.457220	−	0.889354i	$-0.651155\pi$
$439$	4981.61	−	8628.40i	0.541593	−	0.938066i	0.998813	−	0.0487128i	$-0.0155119\pi$
$440$	−4636.39	−	2676.82i	−0.502344	−	0.290028i
$441$	−19094.1			−2.06177
$442$		0			0
$443$	−8480.02			−0.909476			−0.454738	−	0.890625i	$-0.650267\pi$
$443$	−8480.02			−0.909476			−0.454738	+	0.890625i	$0.650267\pi$
$444$	−6581.89	−	3800.06i	−0.703519	−	0.406177i
$445$	501.184	−	868.076i	0.0533897	−	0.0924736i
$446$	−3293.91	−	5705.21i	−0.349711	−	0.605717i
$447$		−	1110.36i		−	0.117491i
$448$	1594.63	−	920.657i	0.168167	−	0.0970914i
$449$	2988.37	−	1725.34i	0.314098	−	0.181344i	−0.334661	−	0.942339i	$-0.608622\pi$
$449$	2988.37	−	1725.34i	0.314098	−	0.181344i	0.648759	+	0.760994i	$0.275288\pi$
$450$			2788.21i			0.292084i
$451$	3182.51	+	5512.27i	0.332281	+	0.575527i
$452$	−1488.82	+	2578.72i	−0.154930	+	0.268347i
$453$	−5676.11	−	3277.10i	−0.588713	−	0.339893i
$454$	−1086.97			−0.112366
$455$		0			0
$456$	−4287.06			−0.440263
$457$	5664.87	+	3270.61i	0.579850	+	0.334776i	0.761074	−	0.648666i	$-0.224673\pi$
$457$	5664.87	+	3270.61i	0.579850	+	0.334776i	−0.181224	+	0.983442i	$0.558006\pi$
$458$	−3071.66	+	5320.27i	−0.313382	+	0.542794i
$459$	−3585.51	−	6210.29i	−0.364613	−	0.631528i
$460$		−	2250.80i		−	0.228139i
$461$	−12656.0	+	7306.92i	−1.27863	+	0.738215i	−0.976596	−	0.215083i	$-0.930998\pi$
$461$	−12656.0	+	7306.92i	−1.27863	+	0.738215i	−0.302030	+	0.953298i	$0.597664\pi$
$462$	−21455.0	+	12387.0i	−2.16055	+	1.24740i
$463$		−	3680.01i		−	0.369383i	−0.982797	−	0.184692i	$-0.940871\pi$
$463$		−	3680.01i		−	0.369383i	0.982797	−	0.184692i	$-0.0591286\pi$
$464$	627.503	+	1086.87i	0.0627825	+	0.108743i
$465$	−10062.4	+	17428.6i	−1.00351	+	1.73813i
$466$	−5859.63	−	3383.06i	−0.582494	−	0.336303i
$467$	−457.544			−0.0453375			−0.0226687	−	0.999743i	$-0.507216\pi$
$467$	−457.544			−0.0453375			−0.0226687	+	0.999743i	$0.507216\pi$
$468$		0			0
$469$	23169.1			2.28112
$470$	8791.39	+	5075.71i	0.862801	+	0.498138i
$471$	15196.3	−	26320.8i	1.48665	−	2.57495i
$472$	3125.74	+	5413.95i	0.304818	+	0.527960i
$473$			21405.9i			2.08085i
$474$	−11217.5	+	6476.40i	−1.08699	+	0.627576i
$475$	2015.85	−	1163.85i	0.194723	−	0.112424i
$476$		−	8174.55i		−	0.787142i
$477$	−2295.77	−	3976.39i	−0.220369	−	0.381691i
$478$	698.550	−	1209.92i	0.0668429	−	0.115775i
$479$	8461.88	+	4885.47i	0.807167	+	0.466018i	0.845971	−	0.533229i	$-0.179021\pi$
$479$	8461.88	+	4885.47i	0.807167	+	0.466018i	−0.0388039	+	0.999247i	$0.512355\pi$
$480$	−3302.12			−0.314001
$481$		0			0
$482$	7430.89			0.702215
$483$	−9020.18	−	5207.80i	−0.849756	−	0.490607i
$484$	−2922.25	+	5061.49i	−0.274442	+	0.475347i
$485$	−24.6729	−	42.7347i	−0.00230998	−	0.00400100i
$486$		−	9378.13i		−	0.875310i
$487$	−17537.2	+	10125.1i	−1.63180	+	0.942118i	−0.648258	+	0.761421i	$0.724502\pi$
$487$	−17537.2	+	10125.1i	−1.63180	+	0.942118i	−0.983539	+	0.180698i	$0.942164\pi$
$488$	364.120	−	210.225i	0.0337765	−	0.0195009i
$489$		−	21374.3i		−	1.97664i
$490$	6139.09	+	10633.2i	0.565992	+	0.980326i
$491$	−8639.72	+	14964.4i	−0.794104	+	1.37543i	0.129303	+	0.991605i	$0.458726\pi$
$491$	−8639.72	+	14964.4i	−0.794104	+	1.37543i	−0.923407	+	0.383823i	$0.874607\pi$
$492$	3399.97	+	1962.97i	0.311549	+	0.179873i
$493$	5571.62			0.508992
$494$		0			0
$495$	26360.0			2.39353
$496$	−2702.33	−	1560.19i	−0.244634	−	0.141239i
$497$	−5776.71	+	10005.6i	−0.521370	+	0.903039i
$498$	−3624.40	−	6277.65i	−0.326131	−	0.564876i
$499$		−	16994.7i		−	1.52462i	−0.647212	−	0.762310i	$-0.724065\pi$
$499$		−	16994.7i		−	1.52462i	0.647212	−	0.762310i	$-0.275935\pi$
$500$	−3931.22	+	2269.69i	−0.351619	+	0.203007i
$501$	9018.08	−	5206.59i	0.804188	−	0.464298i
$502$		−	7705.67i		−	0.685101i
$503$	−1550.97	−	2686.35i	−0.137483	−	0.238128i	0.789060	−	0.614316i	$-0.210568\pi$
$503$	−1550.97	−	2686.35i	−0.137483	−	0.238128i	−0.926543	+	0.376188i	$0.877235\pi$
$504$	−4533.09	+	7851.55i	−0.400635	+	0.693920i
$505$	−11355.2	−	6555.93i	−1.00059	−	0.577693i
$506$	−4695.51			−0.412531
$507$		0			0
$508$	6734.07			0.588142
$509$	−17275.2	−	9973.82i	−1.50434	−	0.868530i	−0.999987	−	0.00503052i	$-0.998399\pi$
$509$	−17275.2	−	9973.82i	−1.50434	−	0.868530i	−0.504350	−	0.863499i	$-0.668268\pi$
$510$	−7329.92	+	12695.8i	−0.636420	+	1.10231i
$511$	−4647.26	−	8049.29i	−0.402314	−	0.696829i
$512$		−	512.000i		−	0.0441942i
$513$	5750.09	−	3319.81i	0.494878	−	0.285718i
$514$	7928.38	−	4577.45i	0.680362	−	0.392807i
$515$		−	15811.9i		−	1.35292i
$516$	6601.56	+	11434.2i	0.563212	+	0.975512i
$517$	10588.7	−	18340.2i	0.900755	−	1.56015i
$518$	11620.3	+	6708.98i	0.985649	+	0.569065i
$519$	8718.22			0.737355
$520$		0			0
$521$	−18106.1			−1.52254			−0.761270	−	0.648436i	$-0.775424\pi$
$521$	−18106.1			−1.52254			−0.761270	+	0.648436i	$0.775424\pi$
$522$	−5351.47	−	3089.67i	−0.448712	−	0.259064i
$523$	427.606	−	740.635i	0.0357512	−	0.0619229i	−0.847596	−	0.530642i	$-0.821951\pi$
$523$	427.606	−	740.635i	0.0357512	−	0.0619229i	0.883347	+	0.468719i	$0.155284\pi$
$524$	4355.74	+	7544.37i	0.363133	+	0.628964i
$525$		−	8296.77i		−	0.689716i
$526$	8354.42	−	4823.42i	0.692528	−	0.399831i
$527$	−11997.1	+	6926.50i	−0.991651	+	0.572530i
$528$			6888.73i			0.567791i
$529$	5096.45	+	8827.31i	0.418875	+	0.725512i
$530$	−1476.26	+	2556.96i	−0.120990	+	0.209561i
$531$	−26657.0	−	15390.4i	−2.17856	−	1.25779i
$532$	7568.79			0.616821
$533$		0			0
$534$	−1289.78			−0.104521
$535$	12744.8	+	7358.21i	1.02992	+	0.594623i
$536$	3221.22	−	5579.32i	0.259581	−	0.449608i
$537$	−3004.78	−	5204.43i	−0.241463	−	0.418226i
$538$			3931.59i			0.315061i
$539$	22182.5	−	12807.1i	1.77267	−	1.02345i
$540$	4429.02	−	2557.10i	0.352953	−	0.203778i
$541$		−	12326.5i		−	0.979592i	−0.871837	−	0.489796i	$-0.837071\pi$
$541$		−	12326.5i		−	0.979592i	0.871837	−	0.489796i	$-0.162929\pi$
$542$	4415.91	+	7648.59i	0.349963	+	0.606153i
$543$	5935.90	−	10281.3i	0.469123	−	0.812544i
$544$	−1968.50	−	1136.52i	−0.155145	−	0.0895730i
$545$	−12709.9			−0.998962
$546$		0			0
$547$	7326.20			0.572661			0.286330	−	0.958131i	$-0.407564\pi$
$547$	7326.20			0.572661			0.286330	+	0.958131i	$0.407564\pi$
$548$	−6123.35	−	3535.32i	−0.477329	−	0.275586i
$549$	−1035.09	+	1792.84i	−0.0804677	+	0.139374i
$550$	−1870.15	−	3239.20i	−0.144988	−	0.251127i
$551$			5158.75i			0.398857i
$552$	−2508.17	+	1448.09i	−0.193396	+	0.111658i
$553$	19804.4	−	11434.1i	1.52291	−	0.879251i
$554$			7224.46i			0.554039i
$555$	−12031.6	−	20839.3i	−0.920200	−	1.59383i
$556$	2011.07	−	3483.28i	0.153396	−	0.265690i
$557$	−505.212	−	291.685i	−0.0384318	−	0.0221886i	0.480661	−	0.876907i	$-0.340397\pi$
$557$	−505.212	−	291.685i	−0.0384318	−	0.0221886i	−0.519093	+	0.854718i	$0.673730\pi$
$558$	15364.0			1.16561
$559$		0			0
$560$	5829.88			0.439924
$561$	26485.3	+	15291.3i	1.99325	+	1.15080i
$562$	−4095.02	+	7092.78i	−0.307363	+	0.532368i
$563$	2719.97	+	4711.13i	0.203611	+	0.352665i	0.949689	−	0.313193i	$-0.101399\pi$
$563$	2719.97	+	4711.13i	0.203611	+	0.352665i	−0.746078	+	0.665858i	$0.768065\pi$
$564$		−	13062.2i		−	0.975209i
$565$	−8164.61	+	4713.84i	−0.607943	+	0.350996i
$566$	11650.1	−	6726.19i	0.865178	−	0.499511i
$567$			6932.39i			0.513462i
$568$	1606.29	+	2782.17i	0.118659	+	0.205523i
$569$	9071.62	−	15712.5i	0.668369	−	1.15765i	−0.309991	−	0.950739i	$-0.600326\pi$
$569$	9071.62	−	15712.5i	0.668369	−	1.15765i	0.978360	−	0.206910i	$-0.0663406\pi$
$570$	−11755.0	−	6786.75i	−0.863794	−	0.498712i
$571$	−12916.3			−0.946634			−0.473317	−	0.880892i	$-0.656944\pi$
$571$	−12916.3			−0.946634			−0.473317	+	0.880892i	$0.656944\pi$
$572$		0			0
$573$	−4688.61			−0.341832
$574$	−6002.62	−	3465.62i	−0.436489	−	0.252007i
$575$	786.257	−	1361.84i	0.0570247	−	0.0987696i
$576$	1260.48	+	2183.22i	0.0911807	+	0.157930i
$577$		−	1345.12i		−	0.0970504i	−0.998822	−	0.0485252i	$-0.984548\pi$
$577$		−	1345.12i		−	0.0970504i	0.998822	−	0.0485252i	$-0.0154521\pi$
$578$	−229.642	+	132.584i	−0.0165257	+	0.00954111i
$579$	−17208.6	+	9935.37i	−1.23517	+	0.713126i
$580$			3973.54i			0.284469i
$581$	6398.86	+	11083.2i	0.456918	+	0.791405i
$582$	−31.7475	+	54.9883i	−0.00226113	+	0.00391639i
$583$	5334.21	+	3079.71i	0.378937	+	0.218779i
$584$	−2584.45			−0.183126
$585$		0			0
$586$	9006.89			0.634934
$587$	−8605.67	−	4968.49i	−0.605100	−	0.349355i	0.165945	−	0.986135i	$-0.446933\pi$
$587$	−8605.67	−	4968.49i	−0.605100	−	0.349355i	−0.771045	+	0.636780i	$0.780266\pi$
$588$	7899.40	−	13682.2i	0.554023	−	0.959596i
$589$	−6413.23	−	11108.0i	−0.448646	−	0.777077i
$590$			19793.2i			1.38114i
$591$	26980.2	−	15577.0i	1.87787	−	1.08419i
$592$	3231.16	−	1865.51i	0.224324	−	0.129514i
$593$		−	15740.8i		−	1.09005i	−0.838420	−	0.545024i	$-0.816520\pi$
$593$		−	15740.8i		−	1.09005i	0.838420	−	0.545024i	$-0.183480\pi$
$594$	−5334.49	−	9239.61i	−0.368479	−	0.638225i
$595$	12940.9	−	22414.4i	0.891641	−	1.54437i
$596$	472.067	+	272.548i	0.0324440	+	0.0187315i
$597$	−17578.6			−1.20510
$598$		0			0
$599$	−6079.68			−0.414706			−0.207353	−	0.978266i	$-0.566485\pi$
$599$	−6079.68			−0.414706			−0.207353	+	0.978266i	$0.566485\pi$
$600$	−1997.94	−	1153.51i	−0.135942	−	0.0784863i
$601$	6882.14	−	11920.2i	0.467102	−	0.809045i	−0.532191	−	0.846624i	$-0.678631\pi$
$601$	6882.14	−	11920.2i	0.467102	−	0.809045i	0.999294	+	0.0375793i	$0.0119647\pi$
$602$	−11655.0	−	20187.1i	−0.789075	−	1.36672i
$603$			31721.0i			2.14225i
$604$	2786.50	−	1608.79i	0.187717	−	0.108379i
$605$	−16025.5	+	9252.30i	−1.07690	+	0.621751i
$606$			16871.5i			1.13095i
$607$	−8132.99	−	14086.8i	−0.543835	−	0.941950i	−0.998679	−	0.0513790i	$-0.983638\pi$
$607$	−8132.99	−	14086.8i	−0.543835	−	0.941950i	0.454844	−	0.890571i	$-0.349695\pi$
$608$	1052.30	−	1822.63i	0.0701913	−	0.121575i
$609$	15924.1	+	9193.81i	1.05957	+	0.611743i
$610$	1331.21			0.0883589
$611$		0			0
$612$	11191.9			0.739223
$613$	−10820.4	−	6247.17i	−0.712940	−	0.411616i	0.0992084	−	0.995067i	$-0.468369\pi$
$613$	−10820.4	−	6247.17i	−0.712940	−	0.411616i	−0.812149	+	0.583450i	$0.801702\pi$
$614$	1934.75	−	3351.09i	0.127167	−	0.220259i
$615$	6215.07	+	10764.8i	0.407505	+	0.705820i
$616$		−	12162.0i		−	0.795490i
$617$	12529.5	−	7233.90i	0.817534	−	0.472003i	−0.0320316	−	0.999487i	$-0.510198\pi$
$617$	12529.5	−	7233.90i	0.817534	−	0.472003i	0.849565	+	0.527484i	$0.176864\pi$
$618$	−17619.9	+	10172.9i	−1.14689	+	0.662156i
$619$			7989.85i			0.518803i	0.965770	+	0.259401i	$0.0835253\pi$
$619$			7989.85i			0.518803i	−0.965770	+	0.259401i	$0.916475\pi$
$620$	−4939.81	−	8556.00i	−0.319980	−	0.554221i
$621$	2242.75	−	3884.55i	0.144925	−	0.251017i
$622$	4599.85	+	2655.72i	0.296523	+	0.171197i
$623$	2277.11			0.146437
$624$		0			0
$625$	−18796.4			−1.20297
$626$	10569.6	+	6102.36i	0.674834	+	0.389615i
$627$	−14158.2	+	24522.7i	−0.901792	+	1.56195i
$628$	7460.14	+	12921.3i	0.474032	+	0.821048i
$629$		−	16564.0i		−	1.05000i
$630$	−24859.2	+	14352.5i	−1.57209	+	0.907644i
$631$	16427.2	−	9484.25i	1.03638	−	0.598355i	0.117575	−	0.993064i	$-0.462488\pi$
$631$	16427.2	−	9484.25i	1.03638	−	0.598355i	0.918806	+	0.394709i	$0.129155\pi$
$632$		−	6358.76i		−	0.400218i
$633$	13704.4	+	23736.7i	0.860506	+	1.49044i
$634$	1382.99	−	2395.42i	0.0866336	−	0.150054i
$635$	18464.6	+	10660.5i	1.15393	+	0.666222i
$636$	3799.12			0.236863
$637$		0			0
$638$	8289.40			0.514390
$639$	−13698.7	−	7908.96i	−0.848064	−	0.489630i
$640$	810.535	−	1403.89i	0.0500613	−	0.0867087i
$641$	12260.2	+	21235.3i	0.755459	+	1.30849i	0.945146	+	0.326649i	$0.105919\pi$
$641$	12260.2	+	21235.3i	0.755459	+	1.30849i	−0.189687	+	0.981845i	$0.560747\pi$
$642$		−	18936.2i		−	1.16410i
$643$	−10198.0	+	5887.83i	−0.625460	+	0.361110i	−0.778992	−	0.627034i	$-0.784269\pi$
$643$	−10198.0	+	5887.83i	−0.625460	+	0.361110i	0.153532	+	0.988144i	$0.450935\pi$
$644$	4428.16	−	2556.60i	0.270954	−	0.156435i
$645$			41803.1i			2.55193i
$646$	−4671.69	−	8091.61i	−0.284528	−	0.492817i
$647$	−10917.4	+	18909.5i	−0.663382	+	1.14901i	0.316340	+	0.948646i	$0.397546\pi$
$647$	−10917.4	+	18909.5i	−0.663382	+	1.14901i	−0.979721	+	0.200365i	$0.935787\pi$
$648$	1669.38	+	963.817i	0.101203	+	0.0584295i
$649$	41291.5			2.49743
$650$		0			0
$651$	−45718.1			−2.75243
$652$	9087.21	+	5246.50i	0.545832	+	0.315136i
$653$	−3663.85	+	6345.98i	−0.219567	+	0.380302i	−0.954676	−	0.297648i	$-0.903798\pi$
$653$	−3663.85	+	6345.98i	−0.219567	+	0.380302i	0.735108	+	0.677950i	$0.237131\pi$
$654$	8177.18	+	14163.3i	0.488919	+	0.846832i
$655$			27581.9i			1.64537i
$656$	−1669.10	+	963.657i	−0.0993407	+	0.0573544i
$657$	11020.4	−	6362.61i	0.654407	−	0.377822i
$658$			23061.2i			1.36629i
$659$	4184.17	+	7247.20i	0.247333	+	0.428393i	0.962785	−	0.270269i	$-0.0871126\pi$
$659$	4184.17	+	7247.20i	0.247333	+	0.428393i	−0.715452	+	0.698662i	$0.753779\pi$
$660$	−10905.4	+	18888.7i	−0.643169	+	1.11400i
$661$	−13148.1	−	7591.06i	−0.773679	−	0.446684i	0.0605065	−	0.998168i	$-0.480728\pi$
$661$	−13148.1	−	7591.06i	−0.773679	−	0.446684i	−0.834185	+	0.551484i	$0.814062\pi$
$662$	20013.3			1.17498
$663$		0			0
$664$	3558.56			0.207980
$665$	20753.4	+	11982.0i	1.21020	+	0.698708i
$666$	−9185.34	+	15909.5i	−0.534421	+	0.925645i
$667$	1742.53	+	3018.15i	0.101156	+	0.175207i
$668$			5112.01i			0.296092i
$669$	−23243.1	+	13419.4i	−1.34324	+	0.775521i
$670$	17665.0	−	10198.9i	1.01859	−	0.588085i
$671$		−	2777.10i		−	0.159774i
$672$	−3750.76	−	6496.51i	−0.215311	−	0.372929i
$673$	−9952.15	+	17237.6i	−0.570026	+	0.987314i	0.426537	+	0.904470i	$0.359733\pi$
$673$	−9952.15	+	17237.6i	−0.570026	+	0.987314i	−0.996563	+	0.0828434i	$0.973600\pi$
$674$	−19151.5	−	11057.1i	−1.09449	−	0.631905i
$675$	3573.01			0.203741
$676$		0			0
$677$	−10760.9			−0.610896			−0.305448	−	0.952209i	$-0.598806\pi$
$677$	−10760.9			−0.610896			−0.305448	+	0.952209i	$0.598806\pi$
$678$	10505.7	+	6065.47i	0.595087	+	0.343574i
$679$	56.0501	−	97.0816i	0.00316790	−	0.00548697i
$680$	−3598.38	−	6232.58i	−0.202929	−	0.351483i
$681$			4428.33i			0.249183i
$682$	−17849.1	+	10305.2i	−1.00217	+	0.578601i
$683$	−20073.0	+	11589.1i	−1.12456	+	0.649262i	−0.942560	−	0.334037i	$-0.891589\pi$
$683$	−20073.0	+	11589.1i	−1.12456	+	0.649262i	−0.181995	+	0.983299i	$0.558256\pi$
$684$			10362.5i			0.579270i
$685$	−11193.3	−	19387.4i	−0.624344	−	1.08140i
$686$	−4078.05	+	7063.38i	−0.226969	+	0.393121i
$687$	21674.8	+	12513.9i	1.20370	+	0.694959i
$688$	−6481.64			−0.359172
$689$		0			0
$690$	−9169.77			−0.505923
$691$	15026.3	+	8675.41i	0.827244	+	0.477610i	0.852908	−	0.522061i	$-0.174837\pi$
$691$	15026.3	+	8675.41i	0.827244	+	0.477610i	−0.0256641	+	0.999671i	$0.508170\pi$
$692$	−2139.96	+	3706.53i	−0.117557	+	0.203614i
$693$	29941.4	+	51860.1i	1.64124	+	2.84271i
$694$			17267.9i			0.944497i
$695$	11028.6	−	6367.36i	0.601925	−	0.347522i
$696$	4427.90	−	2556.45i	0.241148	−	0.139227i
$697$			8556.34i			0.464985i
$698$	−9369.06	−	16227.7i	−0.508057	−	0.879981i
$699$	−13782.6	+	23872.2i	−0.745788	+	1.29174i
$700$	3527.35	+	2036.51i	0.190459	+	0.109961i
$701$	−50.2552			−0.00270772			−0.00135386	−	0.999999i	$-0.500431\pi$
$701$	−50.2552			−0.00270772			−0.00135386	+	0.999999i	$0.500431\pi$
$702$		0			0
$703$	15336.5			0.822799
$704$	−2928.72	−	1690.90i	−0.156790	−	0.0905229i
$705$	20678.5	−	35816.1i	1.10468	−	1.91335i
$706$	−5017.86	−	8691.19i	−0.267492	−	0.463311i
$707$		−	29786.6i		−	1.58450i
$708$	22056.5	−	12734.3i	1.17081	−	0.675966i
$709$	−22044.2	+	12727.2i	−1.16768	+	0.674163i	−0.953133	−	0.302550i	$-0.902162\pi$
$709$	−22044.2	+	12727.2i	−1.16768	+	0.674163i	−0.214550	+	0.976713i	$0.568829\pi$
$710$			10171.5i			0.537647i
$711$	15654.5	+	27114.4i	0.825724	+	1.43020i
$712$	316.589	−	548.348i	0.0166639	−	0.0288626i
$713$	−7504.19	−	4332.55i	−0.394157	−	0.227567i
$714$	−33303.1			−1.74557
$715$		0			0
$716$	2950.20			0.153986
$717$	−4929.24	−	2845.90i	−0.256744	−	0.148231i
$718$	−7268.33	+	12589.1i	−0.377788	+	0.654348i
$719$	3742.99	+	6483.06i	0.194145	+	0.336269i	0.946620	−	0.322352i	$-0.104473\pi$
$719$	3742.99	+	6483.06i	0.194145	+	0.336269i	−0.752475	+	0.658621i	$0.771140\pi$
$720$			7981.76i			0.413142i
$721$	31107.9	−	17960.1i	1.60682	−	0.927698i
$722$	−4388.14	+	2533.50i	−0.226191	+	0.130591i
$723$		−	30273.5i		−	1.55724i
$724$	2914.03	+	5047.26i	0.149585	+	0.259088i
$725$	−1388.05	+	2404.17i	−0.0711047	+	0.123157i
$726$	20620.5	+	11905.3i	1.05413	+	0.608604i
$727$	−19443.6			−0.991919			−0.495959	−	0.868346i	$-0.665183\pi$
$727$	−19443.6			−0.991919			−0.495959	+	0.868346i	$0.665183\pi$
$728$		0			0
$729$	−31700.8			−1.61057
$730$	−7086.49	−	4091.39i	−0.359292	−	0.207437i
$731$	−14387.7	+	24920.2i	−0.727972	+	1.26088i
$732$	−856.456	−	1483.42i	−0.0432452	−	0.0749030i
$733$		−	24222.3i		−	1.22056i	−0.792186	−	0.610280i	$-0.791057\pi$
$733$		−	24222.3i		−	1.22056i	0.792186	−	0.610280i	$-0.208943\pi$
$734$	−20589.6	+	11887.4i	−1.03539	+	0.597784i
$735$	43319.8	−	25010.7i	2.17398	−	1.25515i
$736$		−	1421.79i		−	0.0712063i
$737$	−21276.4	−	36851.8i	−1.06340	−	1.84186i
$738$	4744.81	−	8218.26i	0.236665	−	0.409916i
$739$	−3126.92	−	1805.33i	−0.155650	−	0.0898647i	0.420152	−	0.907454i	$-0.361977\pi$
$739$	−3126.92	−	1805.33i	−0.155650	−	0.0898647i	−0.575802	+	0.817589i	$0.695310\pi$
$740$	11813.0			0.586830
$741$		0			0
$742$	−6707.33			−0.331852
$743$	−22672.2	−	13089.8i	−1.11947	−	0.646324i	−0.178201	−	0.983994i	$-0.557028\pi$
$743$	−22672.2	−	13089.8i	−1.11947	−	0.646324i	−0.941264	+	0.337670i	$0.890361\pi$
$744$	−6356.23	+	11009.3i	−0.313213	+	0.542502i
$745$	862.928	+	1494.63i	0.0424365	+	0.0735022i
$746$			28469.1i			1.39722i
$747$	−15174.1	+	8760.75i	−0.743226	+	0.429102i
$748$	−13002.1	+	7506.77i	−0.635567	+	0.366945i
$749$			33431.7i			1.63093i
$750$	9246.74	+	16015.8i	0.450191	+	0.779753i
$751$	6379.01	−	11048.8i	0.309951	−	0.536851i	−0.668400	−	0.743802i	$-0.733021\pi$
$751$	6379.01	−	11048.8i	0.309951	−	0.536851i	0.978351	+	0.206950i	$0.0663539\pi$
$752$	5553.36	+	3206.23i	0.269295	+	0.155478i
$753$	−31392.9			−1.51929
$754$		0			0
$755$	10187.3			0.491066
$756$	10061.5	+	5809.03i	0.484040	+	0.279461i
$757$	−39.2371	+	67.9606i	−0.00188388	+	0.00326297i	−0.866966	−	0.498368i	$-0.833933\pi$
$757$	−39.2371	+	67.9606i	−0.00188388	+	0.00326297i	0.865082	+	0.501631i	$0.167266\pi$
$758$	7920.09	+	13718.0i	0.379513	+	0.657335i
$759$			19129.5i			0.914832i
$760$	5770.73	−	3331.73i	0.275429	−	0.159019i
$761$	−14703.1	+	8488.84i	−0.700377	+	0.404363i	−0.807488	−	0.589884i	$-0.799173\pi$
$761$	−14703.1	+	8488.84i	−0.700377	+	0.404363i	0.107111	+	0.994247i	$0.465840\pi$
$762$		−	27434.6i		−	1.30427i
$763$	−14436.8	−	25005.2i	−0.684988	−	1.18643i
$764$	1150.86	−	1993.35i	0.0544983	−	0.0943938i
$765$	30687.7	+	17717.6i	1.45035	+	0.837360i
$766$	−21253.9			−1.00252
$767$		0			0
$768$	−2085.89			−0.0980053
$769$	−19909.4	−	11494.7i	−0.933616	−	0.539024i	−0.0456629	−	0.998957i	$-0.514540\pi$
$769$	−19909.4	−	11494.7i	−0.933616	−	0.539024i	−0.887954	+	0.459933i	$0.847873\pi$
$770$	19253.4	−	33347.9i	0.901096	−	1.56074i
$771$	−18648.6	−	32300.3i	−0.871092	−	1.50878i
$772$		−	9754.90i		−	0.454775i
$773$	5225.10	−	3016.71i	0.243123	−	0.140367i	−0.373488	−	0.927635i	$-0.621838\pi$
$773$	5225.10	−	3016.71i	0.243123	−	0.140367i	0.616611	+	0.787268i	$0.288505\pi$
$774$	27638.4	−	15957.0i	1.28351	−	0.741038i
$775$		−	6902.36i		−	0.319923i
$776$	−15.5854	−	26.9947i	−0.000720984	−	0.00124878i
$777$	27332.4	−	47341.1i	1.26196	−	2.18578i
$778$	17638.6	+	10183.7i	0.812823	+	0.469283i
$779$	−7922.29			−0.364372
$780$		0			0
$781$	21219.3			0.972196
$782$	−5466.40	−	3156.03i	−0.249972	−	0.144321i
$783$	−3959.32	+	6857.75i	−0.180708	+	0.312996i
$784$	3877.95	+	6716.81i	0.176656	+	0.305977i
$785$			47239.9i			2.14785i
$786$	30735.8	−	17745.3i	1.39480	−	0.805286i
$787$	32610.9	−	18827.9i	1.47707	−	0.852786i	0.477404	−	0.878684i	$-0.341578\pi$
$787$	32610.9	−	18827.9i	1.47707	−	0.852786i	0.999665	+	0.0258980i	$0.00824452\pi$
$788$			15294.1i			0.691408i
$789$	−19650.7	−	34035.9i	−0.886669	−	1.53576i
$790$	10066.4	−	17435.5i	0.453350	−	0.785225i
$791$	−18547.8	−	10708.6i	−0.833733	−	0.481356i
$792$	16651.2			0.747062
$793$		0			0
$794$	7304.13			0.326466
$795$	10417.1	+	6014.30i	0.464724	+	0.268308i
$796$	4314.82	−	7473.49i	0.192129	−	0.332778i
$797$	12114.0	+	20982.1i	0.538395	+	0.932527i	0.998991	+	0.0449170i	$0.0143023\pi$
$797$	12114.0	+	20982.1i	0.538395	+	0.932527i	−0.460596	+	0.887610i	$0.652364\pi$
$798$		−	30835.3i		−	1.36787i
$799$	24654.2	−	14234.1i	1.09162	−	0.630246i
$800$	980.822	−	566.278i	0.0433466	−	0.0250262i
$801$			3117.61i			0.137522i
$802$	8884.69	+	15388.7i	0.391184	+	0.677550i
$803$	−8535.25	+	14783.5i	−0.375097	+	0.649686i
$804$	−22730.2	−	13123.3i	−0.997053	−	0.575649i
$805$	16189.2			0.708812
$806$		0			0
$807$	16017.3			0.698682
$808$	−7172.87	−	4141.26i	−0.312303	−	0.180308i
$809$	−19987.2	+	34618.9i	−0.868621	+	1.50450i	−0.00521394	+	0.999986i	$0.501660\pi$
$809$	−19987.2	+	34618.9i	−0.868621	+	1.50450i	−0.863407	+	0.504509i	$0.831674\pi$
$810$	3051.59	+	5285.51i	0.132373	+	0.229277i
$811$		−	13394.4i		−	0.579953i	−0.957034	−	0.289977i	$-0.906352\pi$
$811$		−	13394.4i		−	0.579953i	0.957034	−	0.289977i	$-0.0936475\pi$
$812$	−7817.44	+	4513.40i	−0.337855	+	0.195061i
$813$	31160.4	−	17990.5i	1.34421	−	0.776080i
$814$		−	24643.7i		−	1.06113i
$815$	16611.2	+	28771.5i	0.713946	+	1.23659i
$816$	−4630.17	+	8019.70i	−0.198638	+	0.344051i
$817$	−23073.5	−	13321.5i	−0.988054	−	0.570453i
$818$	22935.9			0.980362
$819$		0			0
$820$	−6102.17			−0.259874
$821$	27313.8	+	15769.6i	1.16109	+	0.670358i	0.951566	−	0.307445i	$-0.0994741\pi$
$821$	27313.8	+	15769.6i	1.16109	+	0.670358i	0.209528	+	0.977803i	$0.432807\pi$
$822$	−14402.9	+	24946.5i	−0.611142	+	1.05853i
$823$	−13443.2	−	23284.2i	−0.569379	−	0.986193i	−0.996627	−	0.0820590i	$-0.973850\pi$
$823$	−13443.2	−	23284.2i	−0.569379	−	0.986193i	0.427249	−	0.904134i	$-0.359483\pi$
$824$		−	9988.07i		−	0.422271i
$825$	−13196.5	+	7619.01i	−0.556901	+	0.321527i
$826$	−38940.5	+	22482.3i	−1.64033	+	0.947047i
$827$			16064.3i			0.675466i	0.941242	+	0.337733i	$0.109660\pi$
$827$			16064.3i			0.675466i	−0.941242	+	0.337733i	$0.890340\pi$
$828$	3500.27	+	6062.65i	0.146912	+	0.254458i
$829$	3927.65	−	6802.90i	0.164551	−	0.285011i	−0.771945	−	0.635690i	$-0.780716\pi$
$829$	3927.65	−	6802.90i	0.164551	−	0.285011i	0.936496	+	0.350679i	$0.114049\pi$
$830$	9757.47	+	5633.48i	0.408056	+	0.235591i
$831$	29432.5			1.22864
$832$		0			0
$833$	34432.5			1.43219
$834$	−14190.9	−	8193.11i	−0.589197	−	0.340173i
$835$	−8092.70	+	14017.0i	−0.335401	+	0.580931i
$836$	−6950.50	−	12038.6i	−0.287545	−	0.498043i
$837$		−	19688.5i		−	0.813065i
$838$	27564.0	−	15914.1i	1.13626	−	0.656017i
$839$	4508.98	−	2603.26i	0.185539	−	0.107121i	−0.404354	−	0.914603i	$-0.632503\pi$
$839$	4508.98	−	2603.26i	0.185539	−	0.107121i	0.589892	+	0.807482i	$0.299170\pi$
$840$		−	23751.0i		−	0.975579i
$841$	9118.25	+	15793.3i	0.373867	+	0.647557i
$842$	−3091.64	+	5354.88i	−0.126538	+	0.219170i
$843$	28896.0	+	16683.1i	1.18058	+	0.681610i
$844$	−13455.4			−0.548762
$845$		0			0
$846$	−31573.4			−1.28312
$847$	−36405.5	−	21018.7i	−1.47687	−	0.852670i
$848$	−932.528	+	1615.19i	−0.0377631	+	0.0654077i
$849$	−27402.5	−	47462.6i	−1.10772	−	1.91862i
$850$		−	5028.00i		−	0.202893i
$851$	8972.72	−	5180.40i	0.361435	−	0.208674i
$852$	11334.6	−	6544.01i	0.455770	−	0.263139i
$853$		−	11007.6i		−	0.441842i	−0.975292	−	0.220921i	$-0.929094\pi$
$853$		−	11007.6i		−	0.441842i	0.975292	−	0.220921i	$-0.0709064\pi$
$854$	1512.07	+	2618.98i	0.0605877	+	0.104941i
$855$	−16404.6	+	28413.7i	−0.656172	+	1.13652i
$856$	8050.65	+	4648.05i	0.321455	+	0.185592i
$857$	15769.9			0.628576			0.314288	−	0.949328i	$-0.398234\pi$
$857$	15769.9			0.628576			0.314288	+	0.949328i	$0.398234\pi$
$858$		0			0
$859$	13386.6			0.531716			0.265858	−	0.964012i	$-0.414345\pi$
$859$	13386.6			0.531716			0.265858	+	0.964012i	$0.414345\pi$
$860$	−17772.5	−	10260.9i	−0.704693	−	0.406854i
$861$	−14118.9	+	24454.7i	−0.558853	+	0.967961i
$862$	4996.69	+	8654.52i	0.197434	+	0.341965i
$863$		−	13233.1i		−	0.521968i	−0.965343	−	0.260984i	$-0.915953\pi$
$863$		−	13233.1i		−	0.521968i	0.965343	−	0.260984i	$-0.0840471\pi$
$864$	2797.73	−	1615.27i	0.110163	−	0.0636026i
$865$	−11735.4	+	6775.45i	−0.461291	+	0.266326i
$866$		−	3683.67i		−	0.144545i
$867$	540.147	+	935.563i	0.0211584	+	0.0366475i
$868$	11221.9	−	19436.9i	0.438820	−	0.760059i
$869$	−36373.1	−	21000.0i	−1.41988	−	0.819767i
$870$	16188.2			0.630841
$871$		0			0
$872$	−8028.64			−0.311794
$873$	132.916	+	76.7388i	0.00515293	+	0.00297505i
$874$	2922.16	−	5061.32i	0.113093	−	0.195883i
$875$	−16325.1	−	28275.8i	−0.630729	−	1.09245i
$876$			10529.1i			0.406101i
$877$	−30934.9	+	17860.3i	−1.19110	+	0.687684i	−0.958557	−	0.284901i	$-0.908039\pi$
$877$	−30934.9	+	17860.3i	−1.19110	+	0.687684i	−0.232547	+	0.972585i	$0.574706\pi$
$878$	17256.8	−	9963.22i	0.663313	−	0.382964i
$879$		−	36694.1i		−	1.40803i
$880$	−5353.64	−	9272.78i	−0.205081	−	0.355211i
$881$	263.170	−	455.824i	0.0100641	−	0.0174315i	−0.860950	−	0.508690i	$-0.830130\pi$
$881$	263.170	−	455.824i	0.0100641	−	0.0174315i	0.871014	+	0.491259i	$0.163463\pi$
$882$	−33071.9	−	19094.1i	−1.26257	−	0.728947i
$883$	−39626.2			−1.51022			−0.755112	−	0.655596i	$-0.772417\pi$
$883$	−39626.2			−1.51022			−0.755112	+	0.655596i	$0.772417\pi$
$884$		0			0
$885$	80637.5			3.06282
$886$	−14687.8	−	8480.02i	−0.556938	−	0.321548i
$887$	18332.2	−	31752.3i	0.693951	−	1.20196i	−0.276582	−	0.960990i	$-0.589202\pi$
$887$	18332.2	−	31752.3i	0.693951	−	1.20196i	0.970533	−	0.240968i	$-0.0774650\pi$
$888$	−7600.11	−	13163.8i	−0.287211	−	0.497463i
$889$			48435.7i			1.82731i
$890$	1736.15	−	1002.37i	0.0653887	−	0.0377522i
$891$	11026.4	−	6366.08i	0.414588	−	0.239362i
$892$		−	13175.6i		−	0.494566i
$893$	13179.3	+	22827.3i	0.493874	+	0.855415i
$894$	1110.36	−	1923.20i	0.0415392	−	0.0719480i
$895$	8089.34	+	4670.38i	0.302119	+	0.174429i
$896$	3682.63			0.137308
$897$		0			0
$898$	6901.34			0.256460
$899$	13247.8	+	7648.64i	0.491479	+	0.283756i
$900$	−2788.21	+	4829.33i	−0.103267	+	0.178864i
$901$	4139.97	+	7170.64i	0.153077	+	0.265137i
$902$			12730.0i			0.469916i
$903$	−82242.3	+	47482.6i	−3.03084	+	1.74986i
$904$	−5157.43	+	2977.65i	−0.189750	+	0.109552i
$905$			18452.6i			0.677772i
$906$	−6554.21	−	11352.2i	−0.240341	−	0.416283i
$907$	−17715.0	+	30683.3i	−0.648530	+	1.12329i	0.334944	+	0.942238i	$0.391283\pi$
$907$	−17715.0	+	30683.3i	−0.648530	+	1.12329i	−0.983474	+	0.181049i	$0.942051\pi$
$908$	−1882.69	−	1086.97i	−0.0688098	−	0.0397273i
$909$	40781.1			1.48804
$910$		0			0
$911$	−1970.18			−0.0716521			−0.0358261	−	0.999358i	$-0.511406\pi$
$911$	−1970.18			−0.0716521			−0.0358261	+	0.999358i	$0.511406\pi$
$912$	−7425.41	−	4287.06i	−0.269605	−	0.155657i
$913$	11752.3	−	20355.6i	0.426006	−	0.737865i
$914$	6541.22	+	11329.7i	0.236723	+	0.410016i
$915$		−	5423.34i		−	0.195945i
$916$	−10640.5	+	6143.31i	−0.383813	+	0.221595i
$917$	−54263.9	+	31329.3i	−1.95415	+	1.12823i
$918$		−	14342.0i		−	0.515640i
$919$	−3499.62	−	6061.52i	−0.125617	−	0.217575i	0.796357	−	0.604827i	$-0.206758\pi$
$919$	−3499.62	−	6061.52i	−0.125617	−	0.217575i	−0.921974	+	0.387252i	$0.873424\pi$
$920$	2250.80	−	3898.50i	0.0806594	−	0.139706i
$921$	−13652.4	−	7882.19i	−0.488448	−	0.282005i
$922$	−29227.7			−1.04399
$923$		0			0
$924$	−49548.1			−1.76408
$925$	7147.41	+	4126.56i	0.254060	+	0.146681i
$926$	3680.01	−	6373.96i	0.130597	−	0.226200i
$927$	24589.4	+	42590.1i	0.871222	+	1.50900i
$928$			2510.01i			0.0887879i
$929$	−20466.4	+	11816.3i	−0.722801	+	0.417309i	−0.815783	−	0.578358i	$-0.803694\pi$
$929$	−20466.4	+	11816.3i	−0.722801	+	0.417309i	0.0929817	+	0.995668i	$0.470360\pi$
$930$	−34857.2	+	20124.8i	−1.22905	+	0.709590i
$931$			31880.9i			1.12229i
$932$	−6766.11	−	11719.3i	−0.237802	−	0.411885i
$933$	10819.4	−	18739.8i	0.379649	−	0.657571i
$934$	−792.489	−	457.544i	−0.0277634	−	0.0160292i
$935$	−47535.2			−1.66264
$936$		0			0
$937$	−30872.4			−1.07637			−0.538183	−	0.842828i	$-0.680889\pi$
$937$	−30872.4			−1.07637			−0.538183	+	0.842828i	$0.680889\pi$
$938$	40130.0	+	23169.1i	1.39690	+	0.806499i
$939$	24861.0	−	43060.6i	0.864014	−	1.49652i
$940$	10151.4	+	17582.8i	0.352237	+	0.610092i
$941$			6690.77i			0.231788i	0.993262	+	0.115894i	$0.0369733\pi$
$941$			6690.77i			0.231788i	−0.993262	+	0.115894i	$0.963027\pi$
$942$	52641.6	−	30392.7i	1.82076	−	1.05122i
$943$	−4634.98	+	2676.01i	−0.160059	+	0.0924102i
$944$			12503.0i			0.431078i
$945$	18392.3	+	31856.3i	0.633122	+	1.09660i
$946$	−21405.9	+	37076.0i	−0.735692	+	1.27426i
$947$	−18599.7	−	10738.6i	−0.638237	−	0.368486i	0.145698	−	0.989329i	$-0.453457\pi$
$947$	−18599.7	−	10738.6i	−0.638237	−	0.368486i	−0.783935	+	0.620843i	$0.786791\pi$
$948$	−25905.6			−0.887527
$949$		0			0
$950$	4655.41			0.158991
$951$	−9758.94	−	5634.33i	−0.332761	−	0.192119i
$952$	8174.55	−	14158.7i	0.278297	−	0.482024i
$953$	−3925.25	−	6798.73i	−0.133422	−	0.231094i	0.791571	−	0.611077i	$-0.209263\pi$
$953$	−3925.25	−	6798.73i	−0.133422	−	0.231094i	−0.924994	+	0.379983i	$0.875930\pi$
$954$		−	9183.08i		−	0.311649i
$955$	6311.25	−	3643.80i	0.213851	−	0.123467i
$956$	2419.85	−	1397.10i	0.0818656	−	0.0472651i
$957$		−	33771.1i		−	1.14071i
$958$	9770.94	+	16923.8i	0.329525	+	0.570753i
$959$	25428.2	−	44043.0i	0.856226	−	1.48303i
$960$	−5719.45	−	3302.12i	−0.192286	−	0.111016i
$961$	−8243.39			−0.276707
$962$		0			0
$963$	−45771.7			−1.53164
$964$	12870.7	+	7430.89i	0.430017	+	0.248270i
$965$	15442.7	−	26747.6i	0.515150	−	0.892266i
$966$	−10415.6	−	18040.4i	−0.346912	−	0.600869i
$967$		−	44143.2i		−	1.46799i	−0.679152	−	0.733997i	$-0.737652\pi$
$967$		−	44143.2i		−	1.46799i	0.679152	−	0.733997i	$-0.262348\pi$
$968$	−10123.0	+	5844.51i	−0.336121	+	0.194060i
$969$	−32965.2	+	19032.5i	−1.09288	+	0.630972i
$970$		−	98.6916i		−	0.00326680i
$971$	−14315.9	−	24795.8i	−0.473139	−	0.819500i	0.526389	−	0.850244i	$-0.323546\pi$
$971$	−14315.9	−	24795.8i	−0.473139	−	0.819500i	−0.999527	+	0.0307439i	$0.990212\pi$
$972$	9378.13	−	16243.4i	0.309469	−	0.536016i
$973$	25053.9	+	14464.9i	0.825481	+	0.476591i
$974$	−40500.4			−1.33236
$975$		0			0
$976$	840.898			0.0275784
$977$	−8058.88	−	4652.80i	−0.263896	−	0.152360i	0.362215	−	0.932095i	$-0.382021\pi$
$977$	−8058.88	−	4652.80i	−0.263896	−	0.152360i	−0.626110	+	0.779734i	$0.715354\pi$
$978$	21374.3	−	37021.3i	0.698849	−	1.21044i
$979$	−2091.09	−	3621.88i	−0.0682651	−	0.118239i
$980$			24556.4i			0.800433i
$981$	34234.9	−	19765.5i	1.11421	−	0.643287i
$982$	−29928.9	+	17279.4i	−0.972574	+	0.561516i
$983$		−	28467.2i		−	0.923666i	−0.886967	−	0.461833i	$-0.847192\pi$
$983$		−	28467.2i		−	0.923666i	0.886967	−	0.461833i	$-0.152808\pi$
$984$	3925.94	+	6799.93i	0.127190	+	0.220299i
$985$	−24211.7	+	41935.9i	−0.783197	+	1.35654i
$986$	9650.33	+	5571.62i	0.311693	+	0.179956i
$987$	93951.6			3.02990
$988$		0			0
$989$	−17999.1			−0.578703
$990$	45656.9	+	26360.0i	1.46573	+	0.846240i
$991$	−7749.06	+	13421.8i	−0.248393	+	0.430229i	−0.963080	−	0.269215i	$-0.913236\pi$
$991$	−7749.06	+	13421.8i	−0.248393	+	0.430229i	0.714687	+	0.699444i	$0.246569\pi$
$992$	−3120.39	−	5404.67i	−0.0998713	−	0.172982i
$993$		−	81534.3i		−	2.60565i
$994$	−20011.1	+	11553.4i	−0.638545	+	0.368664i
$995$	23662.2	−	13661.4i	0.753912	−	0.435272i
$996$		−	14497.6i		−	0.461219i
$997$	−630.399	−	1091.88i	−0.0200250	−	0.0346844i	0.855839	−	0.517242i	$-0.173041\pi$
$997$	−630.399	−	1091.88i	−0.0200250	−	0.0346844i	−0.875864	+	0.482558i	$0.839708\pi$
$998$	16994.7	−	29435.6i	0.539035	−	0.933636i
$999$	20387.5	+	11770.7i	0.645678	+	0.372782i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.4.e.i.147.12		24
13.2	odd	12		338.4.c.p.315.6		12
13.3	even	3	inner	338.4.e.i.23.5		24
13.4	even	6		338.4.b.h.337.7		12
13.5	odd	4		338.4.c.p.191.6		12
13.6	odd	12		338.4.a.n.1.1	✓	6
13.7	odd	12		338.4.a.o.1.1	yes	6
13.8	odd	4		338.4.c.o.191.6		12
13.9	even	3		338.4.b.h.337.1		12
13.10	even	6	inner	338.4.e.i.23.12		24
13.11	odd	12		338.4.c.o.315.6		12
13.12	even	2	inner	338.4.e.i.147.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
338.4.a.n.1.1	✓	6	13.6	odd	12
338.4.a.o.1.1	yes	6	13.7	odd	12
338.4.b.h.337.1		12	13.9	even	3
338.4.b.h.337.7		12	13.4	even	6
338.4.c.o.191.6		12	13.8	odd	4
338.4.c.o.315.6		12	13.11	odd	12
338.4.c.p.191.6		12	13.5	odd	4
338.4.c.p.315.6		12	13.2	odd	12
338.4.e.i.23.5		24	13.3	even	3	inner
338.4.e.i.23.12		24	13.10	even	6	inner
338.4.e.i.147.5		24	13.12	even	2	inner
338.4.e.i.147.12		24	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:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	338.e (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 + 1.00000i) q^{2} +(4.07401 - 7.05638i) q^{3} +(2.00000 + 3.46410i) q^{4} +12.6646i q^{5} +(14.1128 - 8.14801i) q^{6} +(-24.9160 + 14.3853i) q^{7} +8.00000i q^{8} +(-19.6950 - 34.1128i) q^{9} +(-12.6646 + 21.9357i) q^{10} +(45.7613 + 26.4203i) q^{11} +32.5920 q^{12} -57.5411 q^{14} +(89.3664 + 51.5957i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(35.5161 + 61.5158i) q^{17} -78.7801i q^{18} +(-56.9572 + 32.8843i) q^{19} +(-43.8715 + 25.3292i) q^{20} +234.423i q^{21} +(52.8406 + 91.5226i) q^{22} +(-22.2154 + 38.4783i) q^{23} +(56.4511 + 32.5920i) q^{24} -35.3924 q^{25} -100.954 q^{27} +(-99.6641 - 57.5411i) q^{28} +(39.2189 - 67.9292i) q^{29} +(103.191 + 178.733i) q^{30} +195.024i q^{31} +(-27.7128 + 16.0000i) q^{32} +(372.863 - 215.273i) q^{33} +142.065i q^{34} +(-182.184 - 315.552i) q^{35} +(78.7801 - 136.451i) q^{36} +(-201.948 - 116.595i) q^{37} -131.537 q^{38} -101.317 q^{40} +(104.319 + 60.2286i) q^{41} +(-234.423 + 406.032i) q^{42} +(202.551 + 350.829i) q^{43} +211.362i q^{44} +(432.025 - 249.430i) q^{45} +(-76.9566 + 44.4309i) q^{46} -400.779i q^{47} +(65.1841 + 112.902i) q^{48} +(242.372 - 419.800i) q^{49} +(-61.3014 - 35.3924i) q^{50} +578.772 q^{51} +116.566 q^{53} +(-174.858 - 100.954i) q^{54} +(-334.603 + 579.549i) q^{55} +(-115.082 - 199.328i) q^{56} +535.883i q^{57} +(135.858 - 78.4379i) q^{58} +(676.744 - 390.718i) q^{59} +412.765i q^{60} +(-26.2781 - 45.5149i) q^{61} +(-195.024 + 337.792i) q^{62} +(981.444 + 566.637i) q^{63} -64.0000 q^{64} +861.091 q^{66} +(-697.414 - 402.652i) q^{67} +(-142.065 + 246.063i) q^{68} +(181.012 + 313.521i) q^{69} -728.735i q^{70} +(347.771 - 200.786i) q^{71} +(272.902 - 157.560i) q^{72} +323.057i q^{73} +(-233.189 - 403.895i) q^{74} +(-144.189 + 249.742i) q^{75} +(-227.829 - 131.537i) q^{76} -1520.25 q^{77} -794.845 q^{79} +(-175.486 - 101.317i) q^{80} +(120.477 - 208.673i) q^{81} +(120.457 + 208.638i) q^{82} -444.820i q^{83} +(-812.064 + 468.845i) q^{84} +(-779.073 + 449.798i) q^{85} +810.205i q^{86} +(-319.556 - 553.488i) q^{87} +(-211.362 + 366.090i) q^{88} +(-68.5435 - 39.5736i) q^{89} +997.720 q^{90} -177.724 q^{92} +(1376.16 + 794.529i) q^{93} +(400.779 - 694.169i) q^{94} +(-416.467 - 721.341i) q^{95} +260.736i q^{96} +(-3.37434 + 1.94818i) q^{97} +(839.601 - 484.744i) q^{98} -2081.39i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 18 q^{3} + 48 q^{4} - 226 q^{9} + 72 q^{10} - 144 q^{12} + 200 q^{14} - 192 q^{16} + 198 q^{17} - 148 q^{22} + 534 q^{23} - 1472 q^{25} + 2676 q^{27} + 238 q^{29} + 472 q^{30} - 1228 q^{35} + 904 q^{36}+ \cdots - 8186 q^{95}+O(q^{100}) \) 24 * q - 18 * q^3 + 48 * q^4 - 226 * q^9 + 72 * q^10 - 144 * q^12 + 200 * q^14 - 192 * q^16 + 198 * q^17 - 148 * q^22 + 534 * q^23 - 1472 * q^25 + 2676 * q^27 + 238 * q^29 + 472 * q^30 - 1228 * q^35 + 904 * q^36 + 648 * q^38 + 576 * q^40 + 104 * q^42 + 856 * q^43 - 288 * q^48 + 1798 * q^49 - 1156 * q^51 + 356 * q^53 - 2252 * q^55 + 400 * q^56 - 3408 * q^61 - 2500 * q^62 - 1536 * q^64 + 6096 * q^66 - 792 * q^68 + 2336 * q^69 - 1096 * q^74 + 3596 * q^75 - 11160 * q^77 - 3500 * q^79 - 6676 * q^81 + 4560 * q^82 - 3204 * q^87 + 592 * q^88 + 9720 * q^90 + 4272 * q^92 + 3944 * q^94 - 8186 * q^95

Introduction

L-functions

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