LMFDB - Embedded newform 504.3.e.c.251.22

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,3,Mod(251,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.251"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	504.e (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(16)] == traces)

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

Self dual:	no
Analytic conductor:	$13.7330053238$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.22
Character	$\chi$	$=$	504.251
Dual form			504.3.e.c.251.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.540392 - 1.92561i) q^{2} +(-3.41595 + 2.08117i) q^{4} +0.489356i q^{5} +(-5.24868 - 4.63156i) q^{7} +(5.85347 + 5.45315i) q^{8} +(0.942310 - 0.264444i) q^{10} +6.94749i q^{11} +16.5922 q^{13} +(-6.08224 + 12.6098i) q^{14} +(7.33748 - 14.2183i) q^{16} -28.0732 q^{17} +29.3568i q^{19} +(-1.01843 - 1.67162i) q^{20} +(13.3782 - 3.75437i) q^{22} +7.49845 q^{23} +24.7605 q^{25} +(-8.96631 - 31.9502i) q^{26} +(27.5683 + 4.89781i) q^{28} +17.9470 q^{29} +30.8259 q^{31} +(-31.3441 - 6.44566i) q^{32} +(15.1705 + 54.0581i) q^{34} +(2.26648 - 2.56848i) q^{35} -64.8471i q^{37} +(56.5297 - 15.8642i) q^{38} +(-2.66853 + 2.86443i) q^{40} +50.7873 q^{41} +47.5472 q^{43} +(-14.4589 - 23.7323i) q^{44} +(-4.05210 - 14.4391i) q^{46} +65.0090i q^{47} +(6.09730 + 48.6192i) q^{49} +(-13.3804 - 47.6791i) q^{50} +(-56.6783 + 34.5312i) q^{52} -51.2494 q^{53} -3.39980 q^{55} +(-5.46641 - 55.7326i) q^{56} +(-9.69841 - 34.5589i) q^{58} +27.2645 q^{59} +115.375 q^{61} +(-16.6581 - 59.3588i) q^{62} +(4.52627 + 63.8397i) q^{64} +8.11952i q^{65} +7.26829 q^{67} +(95.8968 - 58.4251i) q^{68} +(-6.17067 - 2.97638i) q^{70} +91.6063 q^{71} +27.5052i q^{73} +(-124.870 + 35.0428i) q^{74} +(-61.0964 - 100.281i) q^{76} +(32.1777 - 36.4652i) q^{77} -36.2471i q^{79} +(6.95784 + 3.59064i) q^{80} +(-27.4450 - 97.7966i) q^{82} -117.776 q^{83} -13.7378i q^{85} +(-25.6941 - 91.5574i) q^{86} +(-37.8857 + 40.6669i) q^{88} -35.2381 q^{89} +(-87.0874 - 76.8480i) q^{91} +(-25.6144 + 15.6055i) q^{92} +(125.182 - 35.1303i) q^{94} -14.3659 q^{95} +24.7402i q^{97} +(90.3267 - 38.0144i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 144 q^{22} - 336 q^{25} - 232 q^{28} - 384 q^{43} + 736 q^{46} + 368 q^{49} - 432 q^{58} + 480 q^{64} - 896 q^{67} + 264 q^{70} - 48 q^{88} - 576 q^{91}+O(q^{100}) $ 48 * q + 144 * q^22 - 336 * q^25 - 232 * q^28 - 384 * q^43 + 736 * q^46 + 368 * q^49 - 432 * q^58 + 480 * q^64 - 896 * q^67 + 264 * q^70 - 48 * q^88 - 576 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

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 $

$2$	−0.540392	−	1.92561i	−0.270196	−	0.962805i
$2$	−0.540392	−	1.92561i	−0.270196	−	0.962805i
$3$		0			0
$3$		0			0
$4$	−3.41595	+	2.08117i	−0.853988	+	0.520292i
$5$			0.489356i			0.0978713i	0.998802	+	0.0489356i	$0.0155829\pi$
$5$			0.489356i			0.0978713i	−0.998802	+	0.0489356i	$0.984417\pi$
$6$		0			0
$7$	−5.24868	−	4.63156i	−0.749812	−	0.661651i
$7$	−5.24868	−	4.63156i	−0.749812	−	0.661651i
$8$	5.85347	+	5.45315i	0.731684	+	0.681644i
$9$		0			0
$10$	0.942310	−	0.264444i	0.0942310	−	0.0264444i
$11$			6.94749i			0.631590i	0.948827	+	0.315795i	$0.102271\pi$
$11$			6.94749i			0.631590i	−0.948827	+	0.315795i	$0.897729\pi$
$12$		0			0
$13$	16.5922			1.27633			0.638163	−	0.769901i	$-0.279695\pi$
$13$	16.5922			1.27633			0.638163	+	0.769901i	$0.279695\pi$
$14$	−6.08224	+	12.6098i	−0.434446	+	0.900698i
$15$		0			0
$16$	7.33748	−	14.2183i	0.458593	−	0.888647i
$17$	−28.0732			−1.65137			−0.825683	−	0.564135i	$-0.809210\pi$
$17$	−28.0732			−1.65137			−0.825683	+	0.564135i	$0.809210\pi$
$18$		0			0
$19$			29.3568i			1.54509i	0.634958	+	0.772547i	$0.281017\pi$
$19$			29.3568i			1.54509i	−0.634958	+	0.772547i	$0.718983\pi$
$20$	−1.01843	−	1.67162i	−0.0509216	−	0.0835809i
$21$		0			0
$22$	13.3782	−	3.75437i	0.608098	−	0.170653i
$23$	7.49845			0.326020			0.163010	−	0.986624i	$-0.447880\pi$
$23$	7.49845			0.326020			0.163010	+	0.986624i	$0.447880\pi$
$24$		0			0
$25$	24.7605			0.990421
$26$	−8.96631	−	31.9502i	−0.344858	−	1.22885i
$27$		0			0
$28$	27.5683	+	4.89781i	0.984582	+	0.174922i
$29$	17.9470			0.618862			0.309431	−	0.950922i	$-0.399861\pi$
$29$	17.9470			0.618862			0.309431	+	0.950922i	$0.399861\pi$
$30$		0			0
$31$	30.8259			0.994385			0.497193	−	0.867640i	$-0.334364\pi$
$31$	30.8259			0.994385			0.497193	+	0.867640i	$0.334364\pi$
$32$	−31.3441	−	6.44566i	−0.979504	−	0.201427i
$33$		0			0
$34$	15.1705	+	54.0581i	0.446192	+	1.58994i
$35$	2.26648	−	2.56848i	0.0647567	−	0.0733850i
$36$		0			0
$37$		−	64.8471i		−	1.75262i	−0.481744	−	0.876312i	$-0.659996\pi$
$37$		−	64.8471i		−	1.75262i	0.481744	−	0.876312i	$-0.340004\pi$
$38$	56.5297	−	15.8642i	1.48762	−	0.417478i
$39$		0			0
$40$	−2.66853	+	2.86443i	−0.0667134	+	0.0716108i
$41$	50.7873			1.23871			0.619357	−	0.785109i	$-0.287393\pi$
$41$	50.7873			1.23871			0.619357	+	0.785109i	$0.287393\pi$
$42$		0			0
$43$	47.5472			1.10575			0.552875	−	0.833264i	$-0.313531\pi$
$43$	47.5472			1.10575			0.552875	+	0.833264i	$0.313531\pi$
$44$	−14.4589	−	23.7323i	−0.328611	−	0.539371i
$45$		0			0
$46$	−4.05210	−	14.4391i	−0.0880892	−	0.313894i
$47$			65.0090i			1.38317i	0.722295	+	0.691585i	$0.243087\pi$
$47$			65.0090i			1.38317i	−0.722295	+	0.691585i	$0.756913\pi$
$48$		0			0
$49$	6.09730	+	48.6192i	0.124435	+	0.992228i
$50$	−13.3804	−	47.6791i	−0.267608	−	0.953583i
$51$		0			0
$52$	−56.6783	+	34.5312i	−1.08997	+	0.664062i
$53$	−51.2494			−0.966969			−0.483485	−	0.875353i	$-0.660629\pi$
$53$	−51.2494			−0.966969			−0.483485	+	0.875353i	$0.660629\pi$
$54$		0			0
$55$	−3.39980			−0.0618145
$56$	−5.46641	−	55.7326i	−0.0976144	−	0.995224i
$57$		0			0
$58$	−9.69841	−	34.5589i	−0.167214	−	0.595844i
$59$	27.2645			0.462110			0.231055	−	0.972941i	$-0.425782\pi$
$59$	27.2645			0.462110			0.231055	+	0.972941i	$0.425782\pi$
$60$		0			0
$61$	115.375			1.89140			0.945699	−	0.325043i	$-0.105379\pi$
$61$	115.375			1.89140			0.945699	+	0.325043i	$0.105379\pi$
$62$	−16.6581	−	59.3588i	−0.268679	−	0.957399i
$63$		0			0
$64$	4.52627	+	63.8397i	0.0707230	+	0.997496i
$65$			8.11952i			0.124916i
$66$		0			0
$67$	7.26829			0.108482			0.0542409	−	0.998528i	$-0.482726\pi$
$67$	7.26829			0.108482			0.0542409	+	0.998528i	$0.482726\pi$
$68$	95.8968	−	58.4251i	1.41025	−	0.859192i
$69$		0			0
$70$	−6.17067	−	2.97638i	−0.0881525	−	0.0425197i
$71$	91.6063			1.29023			0.645115	−	0.764085i	$-0.276809\pi$
$71$	91.6063			1.29023			0.645115	+	0.764085i	$0.276809\pi$
$72$		0			0
$73$			27.5052i			0.376783i	0.982094	+	0.188392i	$0.0603274\pi$
$73$			27.5052i			0.376783i	−0.982094	+	0.188392i	$0.939673\pi$
$74$	−124.870	+	35.0428i	−1.68744	+	0.473552i
$75$		0			0
$76$	−61.0964	−	100.281i	−0.803900	−	1.31949i
$77$	32.1777	−	36.4652i	0.417892	−	0.473574i
$78$		0			0
$79$		−	36.2471i		−	0.458824i	−0.973329	−	0.229412i	$-0.926320\pi$
$79$		−	36.2471i		−	0.458824i	0.973329	−	0.229412i	$-0.0736803\pi$
$80$	6.95784	+	3.59064i	0.0869730	+	0.0448830i
$81$		0			0
$82$	−27.4450	−	97.7966i	−0.334695	−	1.19264i
$83$	−117.776			−1.41899			−0.709495	−	0.704711i	$-0.751077\pi$
$83$	−117.776			−1.41899			−0.709495	+	0.704711i	$0.751077\pi$
$84$		0			0
$85$		−	13.7378i		−	0.161621i
$86$	−25.6941	−	91.5574i	−0.298769	−	1.06462i
$87$		0			0
$88$	−37.8857	+	40.6669i	−0.430520	+	0.462124i
$89$	−35.2381			−0.395933			−0.197967	−	0.980209i	$-0.563434\pi$
$89$	−35.2381			−0.395933			−0.197967	+	0.980209i	$0.563434\pi$
$90$		0			0
$91$	−87.0874	−	76.8480i	−0.957004	−	0.844483i
$92$	−25.6144	+	15.6055i	−0.278417	+	0.169625i
$93$		0			0
$94$	125.182	−	35.1303i	1.33172	−	0.373727i
$95$	−14.3659			−0.151220
$96$		0			0
$97$			24.7402i			0.255053i	0.991835	+	0.127527i	$0.0407038\pi$
$97$			24.7402i			0.255053i	−0.991835	+	0.127527i	$0.959296\pi$
$98$	90.3267	−	38.0144i	0.921701	−	0.387902i
$99$		0			0
$100$	−84.5808	+	51.5308i	−0.845808	+	0.515308i
$101$			54.1213i			0.535854i	0.963439	+	0.267927i	$0.0863387\pi$
$101$			54.1213i			0.535854i	−0.963439	+	0.267927i	$0.913661\pi$
$102$		0			0
$103$	−118.143			−1.14701			−0.573507	−	0.819200i	$-0.694418\pi$
$103$	−118.143			−1.14701			−0.573507	+	0.819200i	$0.694418\pi$
$104$	97.1222	+	90.4800i	0.933868	+	0.870000i
$105$		0			0
$106$	27.6947	+	98.6863i	0.261271	+	0.931003i
$107$			85.2840i			0.797046i	0.917158	+	0.398523i	$0.130477\pi$
$107$			85.2840i			0.797046i	−0.917158	+	0.398523i	$0.869523\pi$
$108$		0			0
$109$		−	88.3506i		−	0.810556i	−0.914193	−	0.405278i	$-0.867175\pi$
$109$		−	88.3506i		−	0.810556i	0.914193	−	0.405278i	$-0.132825\pi$
$110$	1.83722	+	6.54669i	0.0167020	+	0.0595154i
$111$		0			0
$112$	−104.365	+	40.6436i	−0.931832	+	0.362889i
$113$		−	113.657i		−	1.00581i	−0.864341	−	0.502907i	$-0.832264\pi$
$113$		−	113.657i		−	1.00581i	0.864341	−	0.502907i	$-0.167736\pi$
$114$		0			0
$115$			3.66942i			0.0319080i
$116$	−61.3061	+	37.3507i	−0.528501	+	0.321989i
$117$		0			0
$118$	−14.7335	−	52.5007i	−0.124860	−	0.444922i
$119$	147.347	+	130.023i	1.23821	+	1.09263i
$120$		0			0
$121$	72.7324			0.601094
$122$	−62.3478	−	222.168i	−0.511048	−	1.82105i
$123$		0			0
$124$	−105.300	+	64.1540i	−0.849194	+	0.517371i
$125$			24.3506i			0.194805i
$126$		0			0
$127$			230.345i			1.81374i	0.421409	+	0.906871i	$0.361536\pi$
$127$			230.345i			1.81374i	−0.421409	+	0.906871i	$0.638464\pi$
$128$	120.485	−	43.2143i	0.941285	−	0.337612i
$129$		0			0
$130$	15.6350	−	4.38772i	0.120269	−	0.0337517i
$131$	−65.7427			−0.501853			−0.250926	−	0.968006i	$-0.580735\pi$
$131$	−65.7427			−0.501853			−0.250926	+	0.968006i	$0.580735\pi$
$132$		0			0
$133$	135.968	−	154.084i	1.02231	−	1.15853i
$134$	−3.92772	−	13.9959i	−0.0293113	−	0.104447i
$135$		0			0
$136$	−164.326	−	153.087i	−1.20828	−	1.12564i
$137$			251.938i			1.83896i	0.393131	+	0.919482i	$0.371392\pi$
$137$			251.938i			1.83896i	−0.393131	+	0.919482i	$0.628608\pi$
$138$		0			0
$139$			55.1901i			0.397051i	0.980096	+	0.198526i	$0.0636153\pi$
$139$			55.1901i			0.397051i	−0.980096	+	0.198526i	$0.936385\pi$
$140$	−2.39677	+	13.4907i	−0.0171198	+	0.0963623i
$141$		0			0
$142$	−49.5033	−	176.398i	−0.348615	−	1.24224i
$143$			115.274i			0.806115i
$144$		0			0
$145$			8.78248i			0.0605688i
$146$	52.9643	−	14.8636i	0.362769	−	0.101805i
$147$		0			0
$148$	134.958	+	221.515i	0.911876	+	1.49672i
$149$	18.0084			0.120862			0.0604308	−	0.998172i	$-0.480753\pi$
$149$	18.0084			0.120862			0.0604308	+	0.998172i	$0.480753\pi$
$150$		0			0
$151$			123.390i			0.817155i	0.912724	+	0.408578i	$0.133975\pi$
$151$			123.390i			0.817155i	−0.912724	+	0.408578i	$0.866025\pi$
$152$	−160.087	+	171.839i	−1.05320	+	1.13052i
$153$		0			0
$154$	−87.6063	−	42.2563i	−0.568872	−	0.274392i
$155$			15.0849i			0.0973217i
$156$		0			0
$157$	39.5283			0.251773			0.125886	−	0.992045i	$-0.459823\pi$
$157$	39.5283			0.251773			0.125886	+	0.992045i	$0.459823\pi$
$158$	−69.7978	+	19.5876i	−0.441758	+	0.123972i
$159$		0			0
$160$	3.15422	−	15.3384i	0.0197139	−	0.0958653i
$161$	−39.3570	−	34.7295i	−0.244453	−	0.215711i
$162$		0			0
$163$	−5.42728			−0.0332962			−0.0166481	−	0.999861i	$-0.505300\pi$
$163$	−5.42728			−0.0332962			−0.0166481	+	0.999861i	$0.505300\pi$
$164$	−173.487	+	105.697i	−1.05785	+	0.644493i
$165$		0			0
$166$	63.6452	+	226.791i	0.383405	+	1.36621i
$167$			156.148i			0.935019i	0.883988	+	0.467509i	$0.154849\pi$
$167$			156.148i			0.935019i	−0.883988	+	0.467509i	$0.845151\pi$
$168$		0			0
$169$	106.302			0.629009
$170$	−26.4537	+	7.42379i	−0.155610	+	0.0436694i
$171$		0			0
$172$	−162.419	+	98.9538i	−0.944297	+	0.575313i
$173$		−	148.083i		−	0.855970i	−0.903786	−	0.427985i	$-0.859224\pi$
$173$		−	148.083i		−	0.855970i	0.903786	−	0.427985i	$-0.140776\pi$
$174$		0			0
$175$	−129.960	−	114.680i	−0.742629	−	0.655314i
$176$	98.7818	+	50.9771i	0.561260	+	0.289642i
$177$		0			0
$178$	19.0424	+	67.8548i	0.106980	+	0.381207i
$179$			146.484i			0.818348i	0.912456	+	0.409174i	$0.134183\pi$
$179$			146.484i			0.818348i	−0.912456	+	0.409174i	$0.865817\pi$
$180$		0			0
$181$	150.952			0.833987			0.416993	−	0.908910i	$-0.363084\pi$
$181$	150.952			0.833987			0.416993	+	0.908910i	$0.363084\pi$
$182$	−100.918	+	209.224i	−0.554494	+	1.14958i
$183$		0			0
$184$	43.8920	+	40.8902i	0.238543	+	0.222229i
$185$	31.7333			0.171532
$186$		0			0
$187$		−	195.038i		−	1.04299i
$188$	−135.295	−	222.068i	−0.719653	−	1.18121i
$189$		0			0
$190$	7.76323	+	27.6632i	0.0408591	+	0.145596i
$191$	243.251			1.27357			0.636783	−	0.771043i	$-0.280265\pi$
$191$	243.251			1.27357			0.636783	+	0.771043i	$0.280265\pi$
$192$		0			0
$193$	−138.025			−0.715158			−0.357579	−	0.933883i	$-0.616398\pi$
$193$	−138.025			−0.715158			−0.357579	+	0.933883i	$0.616398\pi$
$194$	47.6399	−	13.3694i	0.245567	−	0.0689143i
$195$		0			0
$196$	−122.013	−	153.391i	−0.622514	−	0.782609i
$197$	80.7464			0.409880			0.204940	−	0.978775i	$-0.434300\pi$
$197$	80.7464			0.409880			0.204940	+	0.978775i	$0.434300\pi$
$198$		0			0
$199$	−230.552			−1.15855			−0.579276	−	0.815131i	$-0.696665\pi$
$199$	−230.552			−1.15855			−0.579276	+	0.815131i	$0.696665\pi$
$200$	144.935	+	135.023i	0.724675	+	0.675115i
$201$		0			0
$202$	104.217	−	29.2467i	0.515923	−	0.144786i
$203$	−94.1981	−	83.1226i	−0.464030	−	0.409471i
$204$		0			0
$205$			24.8531i			0.121235i
$206$	63.8432	+	227.497i	0.309919	+	1.10435i
$207$		0			0
$208$	121.745	−	235.914i	0.585314	−	1.13420i
$209$	−203.956			−0.975866
$210$		0			0
$211$	−10.9675			−0.0519789			−0.0259894	−	0.999662i	$-0.508274\pi$
$211$	−10.9675			−0.0519789			−0.0259894	+	0.999662i	$0.508274\pi$
$212$	175.065	−	106.659i	0.825780	−	0.503106i
$213$		0			0
$214$	164.224	−	46.0867i	0.767401	−	0.215359i
$215$			23.2675i			0.108221i
$216$		0			0
$217$	−161.796	−	142.772i	−0.745602	−	0.657936i
$218$	−170.129	+	47.7439i	−0.780408	+	0.219009i
$219$		0			0
$220$	11.6136	−	7.07555i	0.0527889	−	0.0321616i
$221$	−465.797			−2.10768
$222$		0			0
$223$	−150.911			−0.676730			−0.338365	−	0.941015i	$-0.609874\pi$
$223$	−150.911			−0.676730			−0.338365	+	0.941015i	$0.609874\pi$
$224$	134.662	+	179.003i	0.601169	+	0.799122i
$225$		0			0
$226$	−218.859	+	61.4193i	−0.968403	+	0.271767i
$227$	−179.331			−0.790002			−0.395001	−	0.918681i	$-0.629256\pi$
$227$	−179.331			−0.790002			−0.395001	+	0.918681i	$0.629256\pi$
$228$		0			0
$229$	−12.7967			−0.0558808			−0.0279404	−	0.999610i	$-0.508895\pi$
$229$	−12.7967			−0.0558808			−0.0279404	+	0.999610i	$0.508895\pi$
$230$	7.06587	−	1.98292i	0.0307212	−	0.00862140i
$231$		0			0
$232$	105.052	+	97.8677i	0.452812	+	0.421844i
$233$		−	88.7566i		−	0.380930i	−0.981694	−	0.190465i	$-0.939000\pi$
$233$		−	88.7566i		−	0.380930i	0.981694	−	0.190465i	$-0.0609995\pi$
$234$		0			0
$235$	−31.8126			−0.135373
$236$	−93.1342	+	56.7419i	−0.394636	+	0.240432i
$237$		0			0
$238$	170.748	−	353.997i	0.717428	−	1.48738i
$239$	144.716			0.605506			0.302753	−	0.953069i	$-0.402094\pi$
$239$	144.716			0.605506			0.302753	+	0.953069i	$0.402094\pi$
$240$		0			0
$241$		−	40.5889i		−	0.168419i	−0.996448	−	0.0842093i	$-0.973164\pi$
$241$		−	40.5889i		−	0.168419i	0.996448	−	0.0842093i	$-0.0268364\pi$
$242$	−39.3040	−	140.054i	−0.162413	−	0.578737i
$243$		0			0
$244$	−394.117	+	240.115i	−1.61523	+	0.984079i
$245$	−23.7921	+	2.98375i	−0.0971106	+	0.0121786i
$246$		0			0
$247$			487.095i			1.97204i
$248$	180.439	+	168.099i	0.727576	+	0.677817i
$249$		0			0
$250$	46.8898	−	13.1589i	0.187559	−	0.0526355i
$251$	446.676			1.77959			0.889793	−	0.456365i	$-0.150849\pi$
$251$	446.676			1.77959			0.889793	+	0.456365i	$0.150849\pi$
$252$		0			0
$253$			52.0954i			0.205911i
$254$	443.555	−	124.477i	1.74628	−	0.490065i
$255$		0			0
$256$	−148.323	−	208.654i	−0.579386	−	0.815053i
$257$	311.679			1.21276			0.606379	−	0.795176i	$-0.292622\pi$
$257$	311.679			1.21276			0.606379	+	0.795176i	$0.292622\pi$
$258$		0			0
$259$	−300.343	+	340.362i	−1.15963	+	1.31414i
$260$	−16.8981	−	27.7359i	−0.0649926	−	0.106677i
$261$		0			0
$262$	35.5268	+	126.595i	0.135598	+	0.483186i
$263$	−254.263			−0.966781			−0.483390	−	0.875405i	$-0.660595\pi$
$263$	−254.263			−0.966781			−0.483390	+	0.875405i	$0.660595\pi$
$264$		0			0
$265$		−	25.0792i		−	0.0946385i
$266$	−370.182	−	178.555i	−1.39166	−	0.671259i
$267$		0			0
$268$	−24.8281	+	15.1265i	−0.0926423	+	0.0564422i
$269$		−	381.909i		−	1.41974i	−0.704335	−	0.709868i	$-0.748755\pi$
$269$		−	381.909i		−	1.41974i	0.704335	−	0.709868i	$-0.251245\pi$
$270$		0			0
$271$	−108.365			−0.399870			−0.199935	−	0.979809i	$-0.564073\pi$
$271$	−108.365			−0.399870			−0.199935	+	0.979809i	$0.564073\pi$
$272$	−205.987	+	399.155i	−0.757304	+	1.46748i
$273$		0			0
$274$	485.135	−	136.145i	1.77057	−	0.496881i
$275$			172.024i			0.625540i
$276$		0			0
$277$		−	179.094i		−	0.646547i	−0.946306	−	0.323274i	$-0.895217\pi$
$277$		−	179.094i		−	0.646547i	0.946306	−	0.323274i	$-0.104783\pi$
$278$	106.275	−	29.8243i	0.382283	−	0.107282i
$279$		0			0
$280$	27.2731	−	2.67502i	0.0974039	−	0.00955365i
$281$		−	347.268i		−	1.23583i	−0.786245	−	0.617915i	$-0.787977\pi$
$281$		−	347.268i		−	1.23583i	0.786245	−	0.617915i	$-0.212023\pi$
$282$		0			0
$283$		−	155.999i		−	0.551233i	−0.961268	−	0.275616i	$-0.911118\pi$
$283$		−	155.999i		−	0.551233i	0.961268	−	0.275616i	$-0.0888819\pi$
$284$	−312.923	+	190.648i	−1.10184	+	0.671296i
$285$		0			0
$286$	221.974	−	62.2933i	0.776132	−	0.217809i
$287$	−266.566	−	235.224i	−0.928802	−	0.819597i
$288$		0			0
$289$	499.105			1.72701
$290$	16.9116	−	4.74598i	0.0583160	−	0.0163654i
$291$		0			0
$292$	−57.2429	−	93.9564i	−0.196037	−	0.321769i
$293$		−	479.808i		−	1.63757i	−0.574101	−	0.818785i	$-0.694648\pi$
$293$		−	479.808i		−	1.63757i	0.574101	−	0.818785i	$-0.305352\pi$
$294$		0			0
$295$			13.3420i			0.0452272i
$296$	353.621	−	379.581i	1.19467	−	1.28237i
$297$		0			0
$298$	−9.73158	−	34.6771i	−0.0326563	−	0.116366i
$299$	124.416			0.416108
$300$		0			0
$301$	−249.560	−	220.218i	−0.829104	−	0.731621i
$302$	237.602	−	66.6792i	0.786762	−	0.220792i
$303$		0			0
$304$	417.405	+	215.405i	1.37304	+	0.708568i
$305$			56.4596i			0.185114i
$306$		0			0
$307$		−	409.804i		−	1.33487i	−0.744670	−	0.667433i	$-0.767393\pi$
$307$		−	409.804i		−	1.33487i	0.744670	−	0.667433i	$-0.232607\pi$
$308$	−34.0275	+	191.531i	−0.110479	+	0.621852i
$309$		0			0
$310$	29.0476	−	8.15174i	0.0937019	−	0.0262959i
$311$		−	229.581i		−	0.738202i	−0.929389	−	0.369101i	$-0.879666\pi$
$311$		−	229.581i		−	0.738202i	0.929389	−	0.369101i	$-0.120334\pi$
$312$		0			0
$313$			383.358i			1.22479i	0.790553	+	0.612393i	$0.209793\pi$
$313$			383.358i			1.22479i	−0.790553	+	0.612393i	$0.790207\pi$
$314$	−21.3608	−	76.1161i	−0.0680279	−	0.242408i
$315$		0			0
$316$	75.4363	+	123.818i	0.238722	+	0.391830i
$317$	−286.747			−0.904566			−0.452283	−	0.891874i	$-0.649390\pi$
$317$	−286.747			−0.904566			−0.452283	+	0.891874i	$0.649390\pi$
$318$		0			0
$319$			124.687i			0.390867i
$320$	−31.2404	+	2.21496i	−0.0976262	+	0.00692175i
$321$		0			0
$322$	−45.6074	+	94.5538i	−0.141638	+	0.293645i
$323$		−	824.139i		−	2.55151i
$324$		0			0
$325$	410.833			1.26410
$326$	2.93286	+	10.4508i	0.00899650	+	0.0320578i
$327$		0			0
$328$	297.282	+	276.951i	0.906348	+	0.844362i
$329$	301.093	−	341.212i	0.915177	−	1.03712i
$330$		0			0
$331$	145.600			0.439880			0.219940	−	0.975513i	$-0.429414\pi$
$331$	145.600			0.439880			0.219940	+	0.975513i	$0.429414\pi$
$332$	402.318	−	245.112i	1.21180	−	0.738289i
$333$		0			0
$334$	300.680	−	84.3811i	0.900241	−	0.252638i
$335$			3.55678i			0.0106173i
$336$		0			0
$337$	−115.312			−0.342172			−0.171086	−	0.985256i	$-0.554728\pi$
$337$	−115.312			−0.342172			−0.171086	+	0.985256i	$0.554728\pi$
$338$	−57.4450	−	204.697i	−0.169956	−	0.605613i
$339$		0			0
$340$	28.5907	+	46.9277i	0.0840902	+	0.138023i
$341$			214.163i			0.628044i
$342$		0			0
$343$	193.180	−	283.426i	0.563206	−	0.826316i
$344$	278.316	+	259.282i	0.809059	+	0.753727i
$345$		0			0
$346$	−285.150	+	80.0227i	−0.824132	+	0.231279i
$347$		−	166.848i		−	0.480831i	−0.970670	−	0.240416i	$-0.922716\pi$
$347$		−	166.848i		−	0.480831i	0.970670	−	0.240416i	$-0.0772838\pi$
$348$		0			0
$349$	−65.9305			−0.188913			−0.0944563	−	0.995529i	$-0.530111\pi$
$349$	−65.9305			−0.188913			−0.0944563	+	0.995529i	$0.530111\pi$
$350$	−150.599	+	312.225i	−0.430284	+	0.892070i
$351$		0			0
$352$	44.7811	−	217.763i	0.127219	−	0.618645i
$353$	418.652			1.18598			0.592992	−	0.805209i	$-0.297947\pi$
$353$	418.652			1.18598			0.592992	+	0.805209i	$0.297947\pi$
$354$		0			0
$355$			44.8281i			0.126276i
$356$	120.372	−	73.3363i	0.338122	−	0.206001i
$357$		0			0
$358$	282.072	−	79.1589i	0.787910	−	0.221114i
$359$	−612.879			−1.70718			−0.853592	−	0.520942i	$-0.825581\pi$
$359$	−612.879			−1.70718			−0.853592	+	0.520942i	$0.825581\pi$
$360$		0			0
$361$	−500.820			−1.38731
$362$	−81.5730	−	290.674i	−0.225340	−	0.802967i
$363$		0			0
$364$	457.420	+	81.2656i	1.25665	+	0.223257i
$365$	−13.4598			−0.0368763
$366$		0			0
$367$	−114.767			−0.312716			−0.156358	−	0.987700i	$-0.549975\pi$
$367$	−114.767			−0.312716			−0.156358	+	0.987700i	$0.549975\pi$
$368$	55.0198	−	106.616i	0.149510	−	0.289716i
$369$		0			0
$370$	−17.1484	−	61.1061i	−0.0463471	−	0.165152i
$371$	268.992	+	237.364i	0.725045	+	0.639796i
$372$		0			0
$373$			546.200i			1.46434i	0.681120	+	0.732171i	$0.261493\pi$
$373$			546.200i			1.46434i	−0.681120	+	0.732171i	$0.738507\pi$
$374$	−375.568	+	105.397i	−1.00419	+	0.281810i
$375$		0			0
$376$	−354.504	+	380.528i	−0.942830	+	1.01204i
$377$	297.781			0.789870
$378$		0			0
$379$	250.576			0.661150			0.330575	−	0.943780i	$-0.392757\pi$
$379$	250.576			0.661150			0.330575	+	0.943780i	$0.392757\pi$
$380$	49.0733	−	29.8979i	0.129140	−	0.0786787i
$381$		0			0
$382$	−131.451	−	468.407i	−0.344112	−	1.22620i
$383$		−	423.702i		−	1.10627i	−0.833092	−	0.553135i	$-0.813431\pi$
$383$		−	423.702i		−	1.10627i	0.833092	−	0.553135i	$-0.186569\pi$
$384$		0			0
$385$	17.8445	+	15.7464i	0.0463492	+	0.0408997i
$386$	74.5878	+	265.783i	0.193233	+	0.688558i
$387$		0			0
$388$	−51.4884	−	84.5113i	−0.132702	−	0.217813i
$389$	−27.1194			−0.0697157			−0.0348578	−	0.999392i	$-0.511098\pi$
$389$	−27.1194			−0.0697157			−0.0348578	+	0.999392i	$0.511098\pi$
$390$		0			0
$391$	−210.506			−0.538378
$392$	−229.437	+	317.840i	−0.585299	+	0.810817i
$393$		0			0
$394$	−43.6347	−	155.486i	−0.110748	−	0.394635i
$395$	17.7377			0.0449057
$396$		0			0
$397$	−215.658			−0.543220			−0.271610	−	0.962407i	$-0.587556\pi$
$397$	−215.658			−0.543220			−0.271610	+	0.962407i	$0.587556\pi$
$398$	124.588	+	443.953i	0.313036	+	1.11546i
$399$		0			0
$400$	181.680	−	352.054i	0.454200	−	0.880135i
$401$			423.953i			1.05724i	0.848859	+	0.528620i	$0.177290\pi$
$401$			423.953i			1.05724i	−0.848859	+	0.528620i	$0.822710\pi$
$402$		0			0
$403$	511.471			1.26916
$404$	−112.635	−	184.876i	−0.278801	−	0.457613i
$405$		0			0
$406$	−109.158	+	226.308i	−0.268862	+	0.557408i
$407$	450.525			1.10694
$408$		0			0
$409$			51.8874i			0.126864i	0.997986	+	0.0634320i	$0.0202046\pi$
$409$			51.8874i			0.126864i	−0.997986	+	0.0634320i	$0.979795\pi$
$410$	47.8574	−	13.4304i	0.116725	−	0.0327571i
$411$		0			0
$412$	403.569	−	245.874i	0.979537	−	0.596783i
$413$	−143.102	−	126.277i	−0.346495	−	0.305755i
$414$		0			0
$415$		−	57.6345i		−	0.138878i
$416$	−520.069	−	106.948i	−1.25017	−	0.257086i
$417$		0			0
$418$	110.216	+	392.740i	0.263675	+	0.939569i
$419$	−418.176			−0.998034			−0.499017	−	0.866592i	$-0.666306\pi$
$419$	−418.176			−0.998034			−0.499017	+	0.866592i	$0.666306\pi$
$420$		0			0
$421$		−	48.3444i		−	0.114832i	−0.998350	−	0.0574161i	$-0.981714\pi$
$421$		−	48.3444i		−	0.114832i	0.998350	−	0.0574161i	$-0.0182862\pi$
$422$	5.92677	+	21.1192i	0.0140445	+	0.0500456i
$423$		0			0
$424$	−299.987	−	279.471i	−0.707516	−	0.659129i
$425$	−695.107			−1.63555
$426$		0			0
$427$	−605.568	−	534.368i	−1.41819	−	1.25145i
$428$	−177.490	−	291.326i	−0.414697	−	0.680668i
$429$		0			0
$430$	44.8042	−	12.5736i	0.104196	−	0.0292409i
$431$	106.413			0.246898			0.123449	−	0.992351i	$-0.460604\pi$
$431$	106.413			0.246898			0.123449	+	0.992351i	$0.460604\pi$
$432$		0			0
$433$			261.405i			0.603707i	0.953354	+	0.301854i	$0.0976054\pi$
$433$			261.405i			0.603707i	−0.953354	+	0.301854i	$0.902395\pi$
$434$	−187.491	+	388.708i	−0.432006	+	0.895641i
$435$		0			0
$436$	183.872	+	301.802i	0.421726	+	0.692205i
$437$			220.130i			0.503731i
$438$		0			0
$439$	611.541			1.39303			0.696517	−	0.717541i	$-0.254732\pi$
$439$	611.541			1.39303			0.696517	+	0.717541i	$0.254732\pi$
$440$	−19.9006	−	18.5396i	−0.0452287	−	0.0421355i
$441$		0			0
$442$	251.713	+	896.944i	0.569486	+	2.02929i
$443$			695.830i			1.57072i	0.619038	+	0.785361i	$0.287523\pi$
$443$			695.830i			1.57072i	−0.619038	+	0.785361i	$0.712477\pi$
$444$		0			0
$445$		−	17.2440i		−	0.0387505i
$446$	81.5509	+	290.595i	0.182849	+	0.651559i
$447$		0			0
$448$	271.921	−	356.038i	0.606966	−	0.794728i
$449$		−	45.4904i		−	0.101315i	−0.998716	−	0.0506574i	$-0.983868\pi$
$449$		−	45.4904i		−	0.101315i	0.998716	−	0.0506574i	$-0.0161317\pi$
$450$		0			0
$451$			352.844i			0.782360i
$452$	236.539	+	388.247i	0.523317	+	0.858953i
$453$		0			0
$454$	96.9087	+	345.321i	0.213455	+	0.760619i
$455$	37.6060	−	42.6168i	0.0826506	−	0.0936632i
$456$		0			0
$457$	567.174			1.24108			0.620540	−	0.784175i	$-0.286913\pi$
$457$	567.174			1.24108			0.620540	+	0.784175i	$0.286913\pi$
$458$	6.91523	+	24.6415i	0.0150988	+	0.0538023i
$459$		0			0
$460$	−7.63667	−	12.5346i	−0.0166015	−	0.0272490i
$461$			166.006i			0.360099i	0.983658	+	0.180050i	$0.0576258\pi$
$461$			166.006i			0.360099i	−0.983658	+	0.180050i	$0.942374\pi$
$462$		0			0
$463$			194.577i			0.420254i	0.977674	+	0.210127i	$0.0673877\pi$
$463$			194.577i			0.420254i	−0.977674	+	0.210127i	$0.932612\pi$
$464$	131.686	−	255.177i	0.283806	−	0.549950i
$465$		0			0
$466$	−170.911	+	47.9633i	−0.366761	+	0.102926i
$467$	86.2300			0.184647			0.0923234	−	0.995729i	$-0.470571\pi$
$467$	86.2300			0.184647			0.0923234	+	0.995729i	$0.470571\pi$
$468$		0			0
$469$	−38.1489	−	33.6635i	−0.0813410	−	0.0717772i
$470$	17.1912	+	61.2586i	0.0365771	+	0.130338i
$471$		0			0
$472$	159.592	+	148.677i	0.338118	+	0.314994i
$473$			330.334i			0.698380i
$474$		0			0
$475$			726.889i			1.53029i
$476$	−773.931	−	137.497i	−1.62590	−	0.288860i
$477$		0			0
$478$	−78.2033	−	278.667i	−0.163605	−	0.582984i
$479$			574.253i			1.19886i	0.800428	+	0.599429i	$0.204606\pi$
$479$			574.253i			1.19886i	−0.800428	+	0.599429i	$0.795394\pi$
$480$		0			0
$481$		−	1075.96i		−	2.23692i
$482$	−78.1584	+	21.9339i	−0.162154	+	0.0455060i
$483$		0			0
$484$	−248.450	+	151.368i	−0.513327	+	0.312744i
$485$	−12.1068			−0.0249624
$486$		0			0
$487$		−	595.755i		−	1.22332i	−0.791122	−	0.611658i	$-0.790503\pi$
$487$		−	595.755i		−	1.22332i	0.791122	−	0.611658i	$-0.209497\pi$
$488$	675.346	+	629.159i	1.38391	+	1.28926i
$489$		0			0
$490$	18.6026	+	44.2019i	0.0379645	+	0.0902080i
$491$		−	571.410i		−	1.16377i	−0.813272	−	0.581883i	$-0.802316\pi$
$491$		−	571.410i		−	1.16377i	0.813272	−	0.581883i	$-0.197684\pi$
$492$		0			0
$493$	−503.830			−1.02197
$494$	937.955	−	263.222i	1.89869	−	0.532838i
$495$		0			0
$496$	226.185	−	438.294i	0.456018	−	0.883657i
$497$	−480.812	−	424.280i	−0.967429	−	0.853683i
$498$		0			0
$499$	−22.8477			−0.0457870			−0.0228935	−	0.999738i	$-0.507288\pi$
$499$	−22.8477			−0.0457870			−0.0228935	+	0.999738i	$0.507288\pi$
$500$	−50.6778	−	83.1806i	−0.101356	−	0.166361i
$501$		0			0
$502$	−241.380	−	860.124i	−0.480837	−	1.71339i
$503$		−	688.951i		−	1.36968i	−0.728692	−	0.684842i	$-0.759871\pi$
$503$		−	688.951i		−	1.36968i	0.728692	−	0.684842i	$-0.240129\pi$
$504$		0			0
$505$	−26.4846			−0.0524447
$506$	100.316	−	28.1519i	0.198252	−	0.0556362i
$507$		0			0
$508$	−479.387	−	786.848i	−0.943675	−	1.54891i
$509$		−	62.9269i		−	0.123628i	−0.998088	−	0.0618142i	$-0.980311\pi$
$509$		−	62.9269i		−	0.123628i	0.998088	−	0.0618142i	$-0.0196886\pi$
$510$		0			0
$511$	127.392	−	144.366i	0.249299	−	0.282516i
$512$	−321.633	+	398.367i	−0.628190	+	0.778060i
$513$		0			0
$514$	−168.429	−	600.172i	−0.327682	−	1.16765i
$515$		−	57.8138i		−	0.112260i
$516$		0			0
$517$	−451.650			−0.873597
$518$	817.707	+	394.416i	1.57859	+	0.761420i
$519$		0			0
$520$	−44.2770	+	47.5274i	−0.0851480	+	0.0913988i
$521$	−612.508			−1.17564			−0.587820	−	0.808992i	$-0.700014\pi$
$521$	−612.508			−1.17564			−0.587820	+	0.808992i	$0.700014\pi$
$522$		0			0
$523$			692.859i			1.32478i	0.749160	+	0.662389i	$0.230458\pi$
$523$			692.859i			1.32478i	−0.749160	+	0.662389i	$0.769542\pi$
$524$	224.574	−	136.822i	0.428576	−	0.261110i
$525$		0			0
$526$	137.402	+	489.612i	0.261220	+	0.930822i
$527$	−865.383			−1.64209
$528$		0			0
$529$	−472.773			−0.893711
$530$	−48.2928	+	13.5526i	−0.0911184	+	0.0255709i
$531$		0			0
$532$	−143.784	+	809.317i	−0.270270	+	1.52127i
$533$	842.675			1.58100
$534$		0			0
$535$	−41.7343			−0.0780079
$536$	42.5447	+	39.6351i	0.0793745	+	0.0739460i
$537$		0			0
$538$	−735.408	+	206.380i	−1.36693	+	0.383607i
$539$	−337.781	+	42.3609i	−0.626681	+	0.0785917i
$540$		0			0
$541$			634.171i			1.17222i	0.810232	+	0.586110i	$0.199341\pi$
$541$			634.171i			1.17222i	−0.810232	+	0.586110i	$0.800659\pi$
$542$	58.5594	+	208.668i	0.108043	+	0.384997i
$543$		0			0
$544$	879.930	+	180.950i	1.61752	+	0.332629i
$545$	43.2349			0.0793301
$546$		0			0
$547$	−361.551			−0.660971			−0.330486	−	0.943811i	$-0.607213\pi$
$547$	−361.551			−0.660971			−0.330486	+	0.943811i	$0.607213\pi$
$548$	−524.326	−	860.609i	−0.956799	−	1.57045i
$549$		0			0
$550$	331.250	−	92.9601i	0.602273	−	0.169018i
$551$			526.866i			0.956200i
$552$		0			0
$553$	−167.881	+	190.249i	−0.303581	+	0.344031i
$554$	−344.865	+	96.7807i	−0.622499	+	0.174694i
$555$		0			0
$556$	−114.860	−	188.527i	−0.206583	−	0.339077i
$557$	687.553			1.23439			0.617193	−	0.786812i	$-0.288270\pi$
$557$	687.553			1.23439			0.617193	+	0.786812i	$0.288270\pi$
$558$		0			0
$559$	788.915			1.41130
$560$	−19.8892	−	51.0718i	−0.0355164	−	0.0911996i
$561$		0			0
$562$	−668.704	+	187.661i	−1.18986	+	0.333916i
$563$	960.105			1.70534			0.852669	−	0.522452i	$-0.174983\pi$
$563$	960.105			1.70534			0.852669	+	0.522452i	$0.174983\pi$
$564$		0			0
$565$	55.6187			0.0984403
$566$	−300.393	+	84.3005i	−0.530730	+	0.148941i
$567$		0			0
$568$	536.215	+	499.543i	0.944041	+	0.879478i
$569$			569.590i			1.00104i	0.865726	+	0.500518i	$0.166857\pi$
$569$			569.590i			1.00104i	−0.865726	+	0.500518i	$0.833143\pi$
$570$		0			0
$571$	413.155			0.723564			0.361782	−	0.932263i	$-0.382168\pi$
$571$	413.155			0.723564			0.361782	+	0.932263i	$0.382168\pi$
$572$	−239.905	−	393.772i	−0.419415	−	0.688413i
$573$		0			0
$574$	−308.900	+	640.416i	−0.538154	+	1.11571i
$575$	185.666			0.322897
$576$		0			0
$577$			21.1560i			0.0366654i	0.999832	+	0.0183327i	$0.00583581\pi$
$577$			21.1560i			0.0366654i	−0.999832	+	0.0183327i	$0.994164\pi$
$578$	−269.712	−	961.082i	−0.466630	−	1.66277i
$579$		0			0
$580$	−18.2778	−	30.0005i	−0.0315135	−	0.0517251i
$581$	618.169	+	545.487i	1.06397	+	0.938876i
$582$		0			0
$583$		−	356.054i		−	0.610728i
$584$	−149.990	+	161.001i	−0.256832	+	0.275686i
$585$		0			0
$586$	−923.923	+	259.284i	−1.57666	+	0.442464i
$587$	−395.721			−0.674141			−0.337071	−	0.941479i	$-0.609436\pi$
$587$	−395.721			−0.674141			−0.337071	+	0.941479i	$0.609436\pi$
$588$		0			0
$589$			904.950i			1.53642i
$590$	25.6916	−	7.20993i	0.0435450	−	0.0122202i
$591$		0			0
$592$	−922.019	−	475.814i	−1.55746	−	0.803740i
$593$	488.061			0.823037			0.411519	−	0.911401i	$-0.364999\pi$
$593$	488.061			0.823037			0.411519	+	0.911401i	$0.364999\pi$
$594$		0			0
$595$	−63.6275	+	72.1053i	−0.106937	+	0.121185i
$596$	−61.5158	+	37.4785i	−0.103214	+	0.0628833i
$597$		0			0
$598$	−67.2335	−	239.577i	−0.112431	−	0.400631i
$599$	215.241			0.359334			0.179667	−	0.983727i	$-0.442498\pi$
$599$	215.241			0.359334			0.179667	+	0.983727i	$0.442498\pi$
$600$		0			0
$601$		−	810.565i		−	1.34869i	−0.738415	−	0.674347i	$-0.764425\pi$
$601$		−	810.565i		−	1.34869i	0.738415	−	0.674347i	$-0.235575\pi$
$602$	−289.194	+	599.560i	−0.480388	+	0.995946i
$603$		0			0
$604$	−256.796	−	421.496i	−0.425159	−	0.697841i
$605$			35.5920i			0.0588298i
$606$		0			0
$607$	−621.412			−1.02374			−0.511872	−	0.859062i	$-0.671048\pi$
$607$	−621.412			−1.02374			−0.511872	+	0.859062i	$0.671048\pi$
$608$	189.224	−	920.162i	0.311223	−	1.51342i
$609$		0			0
$610$	108.719	−	30.5103i	0.178228	−	0.0500169i
$611$			1078.65i			1.76538i
$612$		0			0
$613$		−	748.837i		−	1.22159i	−0.791787	−	0.610797i	$-0.790849\pi$
$613$		−	748.837i		−	1.22159i	0.791787	−	0.610797i	$-0.209151\pi$
$614$	−789.123	+	221.455i	−1.28522	+	0.360675i
$615$		0			0
$616$	387.201	−	37.9778i	0.628574	−	0.0616523i
$617$		−	439.740i		−	0.712707i	−0.934351	−	0.356353i	$-0.884020\pi$
$617$		−	439.740i		−	0.712707i	0.934351	−	0.356353i	$-0.115980\pi$
$618$		0			0
$619$		−	598.114i		−	0.966259i	−0.875549	−	0.483129i	$-0.839500\pi$
$619$		−	598.114i		−	0.966259i	0.875549	−	0.483129i	$-0.160500\pi$
$620$	−31.3941	−	51.5292i	−0.0506357	−	0.0831116i
$621$		0			0
$622$	−442.083	+	124.064i	−0.710745	+	0.199459i
$623$	184.953	+	163.207i	0.296875	+	0.261970i
$624$		0			0
$625$	607.097			0.971355
$626$	738.199	−	207.164i	1.17923	−	0.330932i
$627$		0			0
$628$	−135.027	+	82.2650i	−0.215011	+	0.130995i
$629$			1820.47i			2.89422i
$630$		0			0
$631$		−	480.690i		−	0.761791i	−0.924618	−	0.380895i	$-0.875616\pi$
$631$		−	480.690i		−	0.761791i	0.924618	−	0.380895i	$-0.124384\pi$
$632$	197.661	−	212.171i	0.312755	−	0.335714i
$633$		0			0
$634$	154.956	+	552.164i	0.244410	+	0.870921i
$635$	−112.721			−0.177513
$636$		0			0
$637$	101.168	+	806.701i	0.158819	+	1.26641i
$638$	240.098	−	67.3796i	0.376329	−	0.105611i
$639$		0			0
$640$	21.1472	+	58.9599i	0.0330425	+	0.0921248i
$641$			890.272i			1.38888i	0.719551	+	0.694440i	$0.244348\pi$
$641$			890.272i			1.38888i	−0.719551	+	0.694440i	$0.755652\pi$
$642$		0			0
$643$		−	748.676i		−	1.16435i	−0.813064	−	0.582174i	$-0.802202\pi$
$643$		−	748.676i		−	1.16435i	0.813064	−	0.582174i	$-0.197798\pi$
$644$	206.720	+	36.7260i	0.320993	+	0.0570279i
$645$		0			0
$646$	−1586.97	+	445.358i	−2.45661	+	0.689408i
$647$		−	1011.64i		−	1.56359i	−0.623535	−	0.781795i	$-0.714304\pi$
$647$		−	1011.64i		−	1.56359i	0.623535	−	0.781795i	$-0.285696\pi$
$648$		0			0
$649$			189.420i			0.291864i
$650$	−222.011	−	791.104i	−0.341555	−	1.21708i
$651$		0			0
$652$	18.5393	−	11.2951i	0.0284346	−	0.0173237i
$653$	−970.047			−1.48552			−0.742762	−	0.669556i	$-0.766485\pi$
$653$	−970.047			−1.48552			−0.742762	+	0.669556i	$0.766485\pi$
$654$		0			0
$655$		−	32.1716i		−	0.0491170i
$656$	372.651	−	722.111i	0.568065	−	1.10078i
$657$		0			0
$658$	−819.749	−	395.400i	−1.24582	−	0.600912i
$659$		−	122.648i		−	0.186112i	−0.995661	−	0.0930562i	$-0.970336\pi$
$659$		−	122.648i		−	0.186112i	0.995661	−	0.0930562i	$-0.0296636\pi$
$660$		0			0
$661$	−550.866			−0.833382			−0.416691	−	0.909048i	$-0.636810\pi$
$661$	−550.866			−0.833382			−0.416691	+	0.909048i	$0.636810\pi$
$662$	−78.6812	−	280.370i	−0.118854	−	0.423519i
$663$		0			0
$664$	−689.399	−	642.251i	−1.03825	−	0.967245i
$665$	75.4022	+	66.5366i	0.113387	+	0.100055i
$666$		0			0
$667$	134.575			0.201761
$668$	−324.970	−	533.395i	−0.486483	−	0.798495i
$669$		0			0
$670$	6.84898	−	1.92206i	0.0102224	−	0.00286874i
$671$			801.569i			1.19459i
$672$		0			0
$673$	−929.335			−1.38088			−0.690442	−	0.723387i	$-0.742584\pi$
$673$	−929.335			−1.38088			−0.690442	+	0.723387i	$0.742584\pi$
$674$	62.3136	+	222.046i	0.0924535	+	0.329445i
$675$		0			0
$676$	−363.124	+	221.233i	−0.537166	+	0.327268i
$677$			426.954i			0.630656i	0.948983	+	0.315328i	$0.102115\pi$
$677$			426.954i			0.630656i	−0.948983	+	0.315328i	$0.897885\pi$
$678$		0			0
$679$	114.586	−	129.853i	0.168756	−	0.191242i
$680$	74.9143	−	80.4138i	0.110168	−	0.118256i
$681$		0			0
$682$	412.394	−	115.732i	0.604684	−	0.169695i
$683$		−	1012.14i		−	1.48190i	−0.671558	−	0.740952i	$-0.734375\pi$
$683$		−	1012.14i		−	1.48190i	0.671558	−	0.740952i	$-0.265625\pi$
$684$		0			0
$685$	−123.288			−0.179982
$686$	−650.162	−	218.828i	−0.947758	−	0.318991i
$687$		0			0
$688$	348.877	−	676.043i	0.507088	−	0.982620i
$689$	−850.342			−1.23417
$690$		0			0
$691$		−	637.724i		−	0.922901i	−0.887166	−	0.461450i	$-0.847329\pi$
$691$		−	637.724i		−	0.922901i	0.887166	−	0.461450i	$-0.152671\pi$
$692$	308.185	+	505.844i	0.445354	+	0.730988i
$693$		0			0
$694$	−321.285	+	90.1635i	−0.462947	+	0.129919i
$695$	−27.0076			−0.0388599
$696$		0			0
$697$	−1425.76			−2.04557
$698$	35.6283	+	126.956i	0.0510434	+	0.181886i
$699$		0			0
$700$	682.606	+	121.272i	0.975151	+	0.173246i
$701$	915.416			1.30587			0.652936	−	0.757413i	$-0.273537\pi$
$701$	915.416			1.30587			0.652936	+	0.757413i	$0.273537\pi$
$702$		0			0
$703$	1903.70			2.70797
$704$	−443.526	+	31.4462i	−0.630009	+	0.0446680i
$705$		0			0
$706$	−226.236	−	806.161i	−0.320448	−	1.14187i
$707$	250.666	−	284.065i	0.354549	−	0.401790i
$708$		0			0
$709$		−	26.7631i		−	0.0377477i	−0.999822	−	0.0188739i	$-0.993992\pi$
$709$		−	26.7631i		−	0.0377477i	0.999822	−	0.0188739i	$-0.00600809\pi$
$710$	86.3216	−	24.2248i	0.121580	−	0.0341194i
$711$		0			0
$712$	−206.265	−	192.158i	−0.289698	−	0.269886i
$713$	231.147			0.324189
$714$		0			0
$715$	−56.4103			−0.0788955
$716$	−304.859	−	500.384i	−0.425780	−	0.698860i
$717$		0			0
$718$	331.195	+	1180.17i	0.461274	+	1.64369i
$719$		−	812.958i		−	1.13068i	−0.824859	−	0.565339i	$-0.808745\pi$
$719$		−	812.958i		−	1.13068i	0.824859	−	0.565339i	$-0.191255\pi$
$720$		0			0
$721$	620.092	+	547.184i	0.860045	+	0.758924i
$722$	270.639	+	964.385i	0.374847	+	1.33571i
$723$		0			0
$724$	−515.644	+	314.156i	−0.712215	+	0.433917i
$725$	444.377			0.612934
$726$		0			0
$727$	402.292			0.553359			0.276679	−	0.960962i	$-0.410766\pi$
$727$	402.292			0.553359			0.276679	+	0.960962i	$0.410766\pi$
$728$	−90.6999	−	924.728i	−0.124588	−	1.27023i
$729$		0			0
$730$	7.27358	+	25.9184i	0.00996381	+	0.0355047i
$731$	−1334.80			−1.82600
$732$		0			0
$733$	−707.087			−0.964648			−0.482324	−	0.875993i	$-0.660207\pi$
$733$	−707.087			−0.964648			−0.482324	+	0.875993i	$0.660207\pi$
$734$	62.0190	+	220.996i	0.0844946	+	0.301085i
$735$		0			0
$736$	−235.032	−	48.3325i	−0.319338	−	0.0656691i
$737$			50.4963i			0.0685161i
$738$		0			0
$739$	1178.59			1.59484			0.797420	−	0.603425i	$-0.206198\pi$
$739$	1178.59			1.59484			0.797420	+	0.603425i	$0.206198\pi$
$740$	−108.400	+	66.0424i	−0.146486	+	0.0892465i
$741$		0			0
$742$	311.711	−	646.243i	0.420095	−	0.870947i
$743$	227.166			0.305741			0.152870	−	0.988246i	$-0.451148\pi$
$743$	227.166			0.305741			0.152870	+	0.988246i	$0.451148\pi$
$744$		0			0
$745$			8.81251i			0.0118289i
$746$	1051.77	−	295.162i	1.40988	−	0.395659i
$747$		0			0
$748$	405.908	+	666.242i	0.542657	+	0.890698i
$749$	394.998	−	447.628i	0.527367	−	0.597635i
$750$		0			0
$751$			19.6849i			0.0262116i	0.999914	+	0.0131058i	$0.00417182\pi$
$751$			19.6849i			0.0262116i	−0.999914	+	0.0131058i	$0.995828\pi$
$752$	924.321	+	477.002i	1.22915	+	0.634312i
$753$		0			0
$754$	−160.918	−	573.410i	−0.213420	−	0.760491i
$755$	−60.3819			−0.0799760
$756$		0			0
$757$		−	1077.26i		−	1.42307i	−0.702650	−	0.711535i	$-0.748000\pi$
$757$		−	1077.26i		−	1.42307i	0.702650	−	0.711535i	$-0.252000\pi$
$758$	−135.409	−	482.512i	−0.178640	−	0.636559i
$759$		0			0
$760$	−84.0905	−	78.3396i	−0.110645	−	0.103078i
$761$	−98.7893			−0.129815			−0.0649075	−	0.997891i	$-0.520675\pi$
$761$	−98.7893			−0.129815			−0.0649075	+	0.997891i	$0.520675\pi$
$762$		0			0
$763$	−409.201	+	463.724i	−0.536306	+	0.607764i
$764$	−830.934	+	506.246i	−1.08761	+	0.662626i
$765$		0			0
$766$	−815.884	+	228.965i	−1.06512	+	0.298910i
$767$	452.379			0.589803
$768$		0			0
$769$			332.048i			0.431792i	0.976416	+	0.215896i	$0.0692672\pi$
$769$			332.048i			0.431792i	−0.976416	+	0.215896i	$0.930733\pi$
$770$	20.6784	−	42.8707i	0.0268550	−	0.0556762i
$771$		0			0
$772$	471.489	−	287.254i	0.610737	−	0.372091i
$773$			1460.93i			1.88995i	0.327149	+	0.944973i	$0.393912\pi$
$773$			1460.93i			1.88995i	−0.327149	+	0.944973i	$0.606088\pi$
$774$		0			0
$775$	763.267			0.984860
$776$	−134.912	+	144.816i	−0.173856	+	0.186618i
$777$		0			0
$778$	14.6551	+	52.2214i	0.0188369	+	0.0671226i
$779$			1490.95i			1.91393i
$780$		0			0
$781$			636.434i			0.814897i
$782$	113.755	+	405.352i	0.145467	+	0.518353i
$783$		0			0
$784$	736.023	+	270.049i	0.938805	+	0.344450i
$785$			19.3434i			0.0246413i
$786$		0			0
$787$			889.382i			1.13009i	0.825059	+	0.565046i	$0.191142\pi$
$787$			889.382i			1.13009i	−0.825059	+	0.565046i	$0.808858\pi$
$788$	−275.826	+	168.047i	−0.350033	+	0.213257i
$789$		0			0
$790$	−9.58533	−	34.1560i	−0.0121333	−	0.0432354i
$791$	−526.409	+	596.549i	−0.665498	+	0.754171i
$792$		0			0
$793$	1914.33			2.41404
$794$	116.540	+	415.274i	0.146776	+	0.523015i
$795$		0			0
$796$	787.555	−	479.817i	0.989390	−	0.602785i
$797$		−	1370.49i		−	1.71956i	−0.510662	−	0.859782i	$-0.670600\pi$
$797$		−	1370.49i		−	1.71956i	0.510662	−	0.859782i	$-0.329400\pi$
$798$		0			0
$799$		−	1825.01i		−	2.28412i
$800$	−776.097	−	159.598i	−0.970121	−	0.199497i
$801$		0			0
$802$	816.369	−	229.101i	1.01792	−	0.285662i
$803$	−191.092			−0.237973
$804$		0			0
$805$	16.9951	−	19.2596i	0.0211120	−	0.0239250i
$806$	−276.395	−	984.895i	−0.342922	−	1.22195i
$807$		0			0
$808$	−295.132	+	316.797i	−0.365262	+	0.392076i
$809$			1096.60i			1.35550i	0.735291	+	0.677751i	$0.237045\pi$
$809$			1096.60i			1.35550i	−0.735291	+	0.677751i	$0.762955\pi$
$810$		0			0
$811$			1357.90i			1.67436i	0.546929	+	0.837179i	$0.315797\pi$
$811$			1357.90i			1.67436i	−0.546929	+	0.837179i	$0.684203\pi$
$812$	494.769	+	87.9010i	0.609321	+	0.108252i
$813$		0			0
$814$	−243.460	−	867.535i	−0.299091	−	1.06577i
$815$		−	2.65587i		−	0.00325874i
$816$		0			0
$817$			1395.83i			1.70849i
$818$	99.9149	−	28.0395i	0.122145	−	0.0342781i
$819$		0			0
$820$	−51.7234	−	84.8970i	−0.0630774	−	0.103533i
$821$	936.137			1.14024			0.570120	−	0.821561i	$-0.306897\pi$
$821$	936.137			1.14024			0.570120	+	0.821561i	$0.306897\pi$
$822$		0			0
$823$			129.080i			0.156841i	0.996920	+	0.0784207i	$0.0249877\pi$
$823$			129.080i			0.156841i	−0.996920	+	0.0784207i	$0.975012\pi$
$824$	−691.544	−	644.249i	−0.839252	−	0.781856i
$825$		0			0
$826$	−165.829	+	343.799i	−0.200761	+	0.416221i
$827$		−	22.8284i		−	0.0276039i	−0.999905	−	0.0138020i	$-0.995607\pi$
$827$		−	22.8284i		−	0.0276039i	0.999905	−	0.0138020i	$-0.00439344\pi$
$828$		0			0
$829$	−630.043			−0.760004			−0.380002	−	0.924986i	$-0.624077\pi$
$829$	−630.043			−0.760004			−0.380002	+	0.924986i	$0.624077\pi$
$830$	−110.982	+	31.1452i	−0.133713	+	0.0375243i
$831$		0			0
$832$	75.1010	+	1059.24i	0.0902656	+	1.27313i
$833$	−171.171	−	1364.90i	−0.205487	−	1.63853i
$834$		0			0
$835$	−76.4121			−0.0915115
$836$	696.704	−	424.467i	0.833378	−	0.507735i
$837$		0			0
$838$	225.979	+	805.245i	0.269665	+	0.960913i
$839$		−	265.666i		−	0.316647i	−0.987387	−	0.158323i	$-0.949391\pi$
$839$		−	265.666i		−	0.316647i	0.987387	−	0.158323i	$-0.0506088\pi$
$840$		0			0
$841$	−518.905			−0.617010
$842$	−93.0924	+	26.1249i	−0.110561	+	0.0310272i
$843$		0			0
$844$	37.4646	−	22.8253i	0.0443894	−	0.0270442i
$845$			52.0198i			0.0615619i
$846$		0			0
$847$	−381.749	−	336.864i	−0.450707	−	0.397715i
$848$	−376.041	+	728.681i	−0.443445	+	0.859294i
$849$		0			0
$850$	375.630	+	1338.51i	0.441918	+	1.57471i
$851$		−	486.253i		−	0.571390i
$852$		0			0
$853$	760.591			0.891665			0.445833	−	0.895116i	$-0.352908\pi$
$853$	760.591			0.891665			0.445833	+	0.895116i	$0.352908\pi$
$854$	−701.740	+	1454.86i	−0.821710	+	1.70358i
$855$		0			0
$856$	−465.066	+	499.207i	−0.543302	+	0.583186i
$857$	962.482			1.12308			0.561542	−	0.827449i	$-0.310208\pi$
$857$	962.482			1.12308			0.561542	+	0.827449i	$0.310208\pi$
$858$		0			0
$859$			160.713i			0.187093i	0.995615	+	0.0935466i	$0.0298204\pi$
$859$			160.713i			0.187093i	−0.995615	+	0.0935466i	$0.970180\pi$
$860$	−48.4236	−	79.4808i	−0.0563066	−	0.0924196i
$861$		0			0
$862$	−57.5047	−	204.910i	−0.0667108	−	0.237715i
$863$	−1275.31			−1.47777			−0.738884	−	0.673832i	$-0.764647\pi$
$863$	−1275.31			−1.47777			−0.738884	+	0.673832i	$0.764647\pi$
$864$		0			0
$865$	72.4652			0.0837748
$866$	503.365	−	141.261i	0.581253	−	0.163119i
$867$		0			0
$868$	849.819	+	150.980i	0.979054	+	0.173940i
$869$	251.826			0.289789
$870$		0			0
$871$	120.597			0.138458
$872$	481.789	−	517.158i	0.552511	−	0.593071i
$873$		0			0
$874$	423.886	−	118.957i	0.484995	−	0.136106i
$875$	112.781	−	127.809i	0.128893	−	0.146067i
$876$		0			0
$877$			1148.72i			1.30983i	0.755704	+	0.654913i	$0.227295\pi$
$877$			1148.72i			1.30983i	−0.755704	+	0.654913i	$0.772705\pi$
$878$	−330.472	−	1177.59i	−0.376392	−	1.34122i
$879$		0			0
$880$	−24.9460	+	48.3395i	−0.0283477	+	0.0549313i
$881$	−1589.04			−1.80368			−0.901840	−	0.432070i	$-0.857783\pi$
$881$	−1589.04			−1.80368			−0.901840	+	0.432070i	$0.857783\pi$
$882$		0			0
$883$	523.232			0.592561			0.296281	−	0.955101i	$-0.404254\pi$
$883$	523.232			0.592561			0.296281	+	0.955101i	$0.404254\pi$
$884$	1591.14	−	969.403i	1.79993	−	1.09661i
$885$		0			0
$886$	1339.90	−	376.021i	1.51230	−	0.424403i
$887$			1190.80i			1.34250i	0.741231	+	0.671250i	$0.234242\pi$
$887$			1190.80i			1.34250i	−0.741231	+	0.671250i	$0.765758\pi$
$888$		0			0
$889$	1066.86	−	1209.01i	1.20006	−	1.35996i
$890$	−33.2052	+	9.31850i	−0.0373092	+	0.0104702i
$891$		0			0
$892$	515.504	−	314.070i	0.577919	−	0.352097i
$893$	−1908.46			−2.13713
$894$		0			0
$895$	−71.6831			−0.0800928
$896$	−832.535	−	331.213i	−0.929168	−	0.369658i
$897$		0			0
$898$	−87.5967	+	24.5826i	−0.0975465	+	0.0273748i
$899$	553.233			0.615387
$900$		0			0
$901$	1438.73			1.59682
$902$	679.441	−	190.674i	0.753260	−	0.211390i
$903$		0			0
$904$	619.789	−	665.288i	0.685607	−	0.735938i
$905$			73.8691i			0.0816233i
$906$		0			0
$907$	1762.93			1.94369			0.971845	−	0.235623i	$-0.0757129\pi$
$907$	1762.93			1.94369			0.971845	+	0.235623i	$0.0757129\pi$
$908$	612.585	−	373.217i	0.674653	−	0.411032i
$909$		0			0
$910$	−102.385	−	49.3848i	−0.112511	−	0.0542691i
$911$	−49.2079			−0.0540152			−0.0270076	−	0.999635i	$-0.508598\pi$
$911$	−49.2079			−0.0540152			−0.0270076	+	0.999635i	$0.508598\pi$
$912$		0			0
$913$		−	818.248i		−	0.896219i
$914$	−306.496	−	1092.16i	−0.335335	−	1.19492i
$915$		0			0
$916$	43.7129	−	26.6321i	0.0477216	−	0.0290743i
$917$	345.062	+	304.491i	0.376295	+	0.332052i
$918$		0			0
$919$		−	685.900i		−	0.746355i	−0.927760	−	0.373177i	$-0.878268\pi$
$919$		−	685.900i		−	0.746355i	0.927760	−	0.373177i	$-0.121732\pi$
$920$	−20.0099	+	21.4788i	−0.0217499	+	0.0233465i
$921$		0			0
$922$	319.662	−	89.7081i	0.346705	−	0.0972973i
$923$	1519.95			1.64675
$924$		0			0
$925$		−	1605.65i		−	1.73584i
$926$	374.680	−	105.148i	0.404623	−	0.113551i
$927$		0			0
$928$	−562.533	−	115.680i	−0.606178	−	0.124655i
$929$	194.049			0.208880			0.104440	−	0.994531i	$-0.466695\pi$
$929$	194.049			0.208880			0.104440	+	0.994531i	$0.466695\pi$
$930$		0			0
$931$	−1427.30	+	178.997i	−1.53308	+	0.192263i
$932$	184.717	+	303.189i	0.198195	+	0.325310i
$933$		0			0
$934$	−46.5980	−	166.045i	−0.0498908	−	0.177779i
$935$	95.4432			0.102078
$936$		0			0
$937$			523.728i			0.558942i	0.960154	+	0.279471i	$0.0901590\pi$
$937$			523.728i			0.558942i	−0.960154	+	0.279471i	$0.909841\pi$
$938$	−44.2075	+	91.6514i	−0.0471295	+	0.0977094i
$939$		0			0
$940$	108.670	−	66.2073i	0.115607	−	0.0704333i
$941$		−	144.646i		−	0.153716i	−0.997042	−	0.0768578i	$-0.975511\pi$
$941$		−	144.646i		−	0.153716i	0.997042	−	0.0768578i	$-0.0244887\pi$
$942$		0			0
$943$	380.826			0.403845
$944$	200.052	−	387.656i	0.211920	−	0.410652i
$945$		0			0
$946$	636.095	−	178.510i	0.672404	−	0.188699i
$947$			177.497i			0.187431i	0.995599	+	0.0937155i	$0.0298744\pi$
$947$			177.497i			0.187431i	−0.995599	+	0.0937155i	$0.970126\pi$
$948$		0			0
$949$			456.373i			0.480898i
$950$	1399.71	−	392.805i	1.47337	−	0.413479i
$951$		0			0
$952$	153.460	+	1564.59i	0.161197	+	1.64348i
$953$		−	59.3443i		−	0.0622710i	−0.999515	−	0.0311355i	$-0.990088\pi$
$953$		−	59.3443i		−	0.0622710i	0.999515	−	0.0311355i	$-0.00991234\pi$
$954$		0			0
$955$			119.036i			0.124645i
$956$	−494.343	+	301.178i	−0.517095	+	0.315040i
$957$		0			0
$958$	1105.79	−	310.322i	1.15427	−	0.323926i
$959$	1166.87	−	1322.34i	1.21675	−	1.37888i
$960$		0			0
$961$	−10.7613			−0.0111980
$962$	−2071.88	+	581.439i	−2.15372	+	0.604407i
$963$		0			0
$964$	84.4723	+	138.650i	0.0876269	+	0.143828i
$965$		−	67.5436i		−	0.0699934i
$966$		0			0
$967$			1022.00i			1.05687i	0.848973	+	0.528437i	$0.177222\pi$
$967$			1022.00i			1.05687i	−0.848973	+	0.528437i	$0.822778\pi$
$968$	425.737	+	396.621i	0.439811	+	0.409732i
$969$		0			0
$970$	6.54239	+	23.3129i	0.00674473	+	0.0240339i
$971$	−121.308			−0.124931			−0.0624654	−	0.998047i	$-0.519896\pi$
$971$	−121.308			−0.124931			−0.0624654	+	0.998047i	$0.519896\pi$
$972$		0			0
$973$	255.616	−	289.675i	0.262710	−	0.297714i
$974$	−1147.19	+	321.941i	−1.17782	+	0.330535i
$975$		0			0
$976$	846.564	−	1640.45i	0.867381	−	1.68078i
$977$			485.885i			0.497323i	0.968590	+	0.248662i	$0.0799907\pi$
$977$			485.885i			0.497323i	−0.968590	+	0.248662i	$0.920009\pi$
$978$		0			0
$979$		−	244.816i		−	0.250068i
$980$	75.0630	−	59.7077i	0.0765949	−	0.0609262i
$981$		0			0
$982$	−1100.31	+	308.785i	−1.12048	+	0.314445i
$983$		−	258.044i		−	0.262507i	−0.991349	−	0.131253i	$-0.958100\pi$
$983$		−	258.044i		−	0.262507i	0.991349	−	0.131253i	$-0.0419001\pi$
$984$		0			0
$985$			39.5138i			0.0401155i
$986$	272.265	+	970.180i	0.276131	+	0.983956i
$987$		0			0
$988$	−1013.73	−	1663.89i	−1.02604	−	1.68410i
$989$	356.531			0.360496
$990$		0			0
$991$			679.844i			0.686019i	0.939332	+	0.343009i	$0.111446\pi$
$991$			679.844i			0.686019i	−0.939332	+	0.343009i	$0.888554\pi$
$992$	−966.212	−	198.693i	−0.974004	−	0.200296i
$993$		0			0
$994$	−557.172	+	1155.14i	−0.560535	+	1.16211i
$995$		−	112.822i		−	0.113389i
$996$		0			0
$997$	982.612			0.985569			0.492784	−	0.870152i	$-0.335979\pi$
$997$	982.612			0.985569			0.492784	+	0.870152i	$0.335979\pi$
$998$	12.3467	+	43.9958i	0.0123715	+	0.0440840i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.3.e.c.251.22	yes	48
3.2	odd	2	inner	504.3.e.c.251.27	yes	48
4.3	odd	2		2016.3.e.c.1007.48		48
7.6	odd	2	inner	504.3.e.c.251.21	✓	48
8.3	odd	2	inner	504.3.e.c.251.26	yes	48
8.5	even	2		2016.3.e.c.1007.19		48
12.11	even	2		2016.3.e.c.1007.13		48
21.20	even	2	inner	504.3.e.c.251.28	yes	48
24.5	odd	2		2016.3.e.c.1007.46		48
24.11	even	2	inner	504.3.e.c.251.23	yes	48
28.27	even	2		2016.3.e.c.1007.45		48
56.13	odd	2		2016.3.e.c.1007.14		48
56.27	even	2	inner	504.3.e.c.251.25	yes	48
84.83	odd	2		2016.3.e.c.1007.20		48
168.83	odd	2	inner	504.3.e.c.251.24	yes	48
168.125	even	2		2016.3.e.c.1007.47		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.3.e.c.251.21	✓	48	7.6	odd	2	inner
504.3.e.c.251.22	yes	48	1.1	even	1	trivial
504.3.e.c.251.23	yes	48	24.11	even	2	inner
504.3.e.c.251.24	yes	48	168.83	odd	2	inner
504.3.e.c.251.25	yes	48	56.27	even	2	inner
504.3.e.c.251.26	yes	48	8.3	odd	2	inner
504.3.e.c.251.27	yes	48	3.2	odd	2	inner
504.3.e.c.251.28	yes	48	21.20	even	2	inner
2016.3.e.c.1007.13		48	12.11	even	2
2016.3.e.c.1007.14		48	56.13	odd	2
2016.3.e.c.1007.19		48	8.5	even	2
2016.3.e.c.1007.20		48	84.83	odd	2
2016.3.e.c.1007.45		48	28.27	even	2
2016.3.e.c.1007.46		48	24.5	odd	2
2016.3.e.c.1007.47		48	168.125	even	2
2016.3.e.c.1007.48		48	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	504.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.540392 - 1.92561i) q^{2} +(-3.41595 + 2.08117i) q^{4} +0.489356i q^{5} +(-5.24868 - 4.63156i) q^{7} +(5.85347 + 5.45315i) q^{8} +(0.942310 - 0.264444i) q^{10} +6.94749i q^{11} +16.5922 q^{13} +(-6.08224 + 12.6098i) q^{14} +(7.33748 - 14.2183i) q^{16} -28.0732 q^{17} +29.3568i q^{19} +(-1.01843 - 1.67162i) q^{20} +(13.3782 - 3.75437i) q^{22} +7.49845 q^{23} +24.7605 q^{25} +(-8.96631 - 31.9502i) q^{26} +(27.5683 + 4.89781i) q^{28} +17.9470 q^{29} +30.8259 q^{31} +(-31.3441 - 6.44566i) q^{32} +(15.1705 + 54.0581i) q^{34} +(2.26648 - 2.56848i) q^{35} -64.8471i q^{37} +(56.5297 - 15.8642i) q^{38} +(-2.66853 + 2.86443i) q^{40} +50.7873 q^{41} +47.5472 q^{43} +(-14.4589 - 23.7323i) q^{44} +(-4.05210 - 14.4391i) q^{46} +65.0090i q^{47} +(6.09730 + 48.6192i) q^{49} +(-13.3804 - 47.6791i) q^{50} +(-56.6783 + 34.5312i) q^{52} -51.2494 q^{53} -3.39980 q^{55} +(-5.46641 - 55.7326i) q^{56} +(-9.69841 - 34.5589i) q^{58} +27.2645 q^{59} +115.375 q^{61} +(-16.6581 - 59.3588i) q^{62} +(4.52627 + 63.8397i) q^{64} +8.11952i q^{65} +7.26829 q^{67} +(95.8968 - 58.4251i) q^{68} +(-6.17067 - 2.97638i) q^{70} +91.6063 q^{71} +27.5052i q^{73} +(-124.870 + 35.0428i) q^{74} +(-61.0964 - 100.281i) q^{76} +(32.1777 - 36.4652i) q^{77} -36.2471i q^{79} +(6.95784 + 3.59064i) q^{80} +(-27.4450 - 97.7966i) q^{82} -117.776 q^{83} -13.7378i q^{85} +(-25.6941 - 91.5574i) q^{86} +(-37.8857 + 40.6669i) q^{88} -35.2381 q^{89} +(-87.0874 - 76.8480i) q^{91} +(-25.6144 + 15.6055i) q^{92} +(125.182 - 35.1303i) q^{94} -14.3659 q^{95} +24.7402i q^{97} +(90.3267 - 38.0144i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 144 q^{22} - 336 q^{25} - 232 q^{28} - 384 q^{43} + 736 q^{46} + 368 q^{49} - 432 q^{58} + 480 q^{64} - 896 q^{67} + 264 q^{70} - 48 q^{88} - 576 q^{91}+O(q^{100}) \) 48 * q + 144 * q^22 - 336 * q^25 - 232 * q^28 - 384 * q^43 + 736 * q^46 + 368 * q^49 - 432 * q^58 + 480 * q^64 - 896 * q^67 + 264 * q^70 - 48 * q^88 - 576 * q^91

Introduction

L-functions

Modular forms

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