LMFDB - Embedded newform 504.3.e.c.251.25

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			251.25
Character	$\chi$	$=$	504.251
Dual form			504.3.e.c.251.27

$q$-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	$-0.190790\pi$
$17$	28.0732			1.65137			0.825683	+	0.564135i	$0.190790\pi$
$18$		0			0
$19$		−	29.3568i		−	1.54509i	−0.634958	−	0.772547i	$-0.718983\pi$
$19$		−	29.3568i		−	1.54509i	0.634958	−	0.772547i	$-0.281017\pi$
$20$	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	$-0.552120\pi$
$23$	−7.49845			−0.326020			−0.163010	+	0.986624i	$0.552120\pi$
$24$		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	$-0.600139\pi$
$29$	−17.9470			−0.618862			−0.309431	+	0.950922i	$0.600139\pi$
$30$		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	$0.340004\pi$
$37$			64.8471i			1.75262i	−0.481744	+	0.876312i	$0.659996\pi$
$38$	−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	$-0.712607\pi$
$41$	−50.7873			−1.23871			−0.619357	+	0.785109i	$0.712607\pi$
$42$		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	$-0.339371\pi$
$53$	51.2494			0.966969			0.483485	+	0.875353i	$0.339371\pi$
$54$		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	$-0.574218\pi$
$59$	−27.2645			−0.462110			−0.231055	+	0.972941i	$0.574218\pi$
$60$		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	$-0.723191\pi$
$71$	−91.6063			−1.29023			−0.645115	+	0.764085i	$0.723191\pi$
$72$		0			0
$73$		−	27.5052i		−	0.376783i	−0.982094	−	0.188392i	$-0.939673\pi$
$73$		−	27.5052i		−	0.376783i	0.982094	−	0.188392i	$-0.0603274\pi$
$74$	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	$0.0736803\pi$
$79$			36.2471i			0.458824i	−0.973329	+	0.229412i	$0.926320\pi$
$80$	−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	$-0.248923\pi$
$83$	117.776			1.41899			0.709495	+	0.704711i	$0.248923\pi$
$84$		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	$-0.436566\pi$
$89$	35.2381			0.395933			0.197967	+	0.980209i	$0.436566\pi$
$90$		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	$-0.959296\pi$
$97$		−	24.7402i		−	0.255053i	0.991835	−	0.127527i	$-0.0407038\pi$
$98$	−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	$0.132825\pi$
$109$			88.3506i			0.810556i	−0.914193	+	0.405278i	$0.867175\pi$
$110$	−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	$-0.638464\pi$
$127$		−	230.345i		−	1.81374i	0.421409	−	0.906871i	$-0.361536\pi$
$128$	−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	$-0.419265\pi$
$131$	65.7427			0.501853			0.250926	+	0.968006i	$0.419265\pi$
$132$		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	$-0.936385\pi$
$139$		−	55.1901i		−	0.397051i	0.980096	−	0.198526i	$-0.0636153\pi$
$140$	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	$-0.519247\pi$
$149$	−18.0084			−0.120862			−0.0604308	+	0.998172i	$0.519247\pi$
$150$		0			0
$151$		−	123.390i		−	0.817155i	−0.912724	−	0.408578i	$-0.866025\pi$
$151$		−	123.390i		−	0.817155i	0.912724	−	0.408578i	$-0.133975\pi$
$152$	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	$-0.719735\pi$
$191$	−243.251			−1.27357			−0.636783	+	0.771043i	$0.719735\pi$
$192$		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	$-0.565700\pi$
$197$	−80.7464			−0.409880			−0.204940	+	0.978775i	$0.565700\pi$
$198$		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	$-0.370744\pi$
$227$	179.331			0.790002			0.395001	+	0.918681i	$0.370744\pi$
$228$		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	$-0.597906\pi$
$239$	−144.716			−0.605506			−0.302753	+	0.953069i	$0.597906\pi$
$240$		0			0
$241$			40.5889i			0.168419i	0.996448	+	0.0842093i	$0.0268364\pi$
$241$			40.5889i			0.168419i	−0.996448	+	0.0842093i	$0.973164\pi$
$242$	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	$-0.849151\pi$
$251$	−446.676			−1.77959			−0.889793	+	0.456365i	$0.849151\pi$
$252$		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	$-0.707378\pi$
$257$	−311.679			−1.21276			−0.606379	+	0.795176i	$0.707378\pi$
$258$		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	$-0.339405\pi$
$263$	254.263			0.966781			0.483390	+	0.875405i	$0.339405\pi$
$264$		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	$0.104783\pi$
$277$			179.094i			0.646547i	−0.946306	+	0.323274i	$0.895217\pi$
$278$	−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	$0.0888819\pi$
$283$			155.999i			0.551233i	−0.961268	+	0.275616i	$0.911118\pi$
$284$	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	$0.232607\pi$
$307$			409.804i			1.33487i	−0.744670	+	0.667433i	$0.767393\pi$
$308$	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	$-0.790207\pi$
$313$		−	383.358i		−	1.22479i	0.790553	−	0.612393i	$-0.209793\pi$
$314$	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	$-0.350610\pi$
$317$	286.747			0.904566			0.452283	+	0.891874i	$0.350610\pi$
$318$		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	$-0.702053\pi$
$353$	−418.652			−1.18598			−0.592992	+	0.805209i	$0.702053\pi$
$354$		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	$-0.174419\pi$
$359$	612.879			1.70718			0.853592	+	0.520942i	$0.174419\pi$
$360$		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	$-0.738507\pi$
$373$		−	546.200i		−	1.46434i	0.681120	−	0.732171i	$-0.261493\pi$
$374$	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	$-0.488902\pi$
$389$	27.1194			0.0697157			0.0348578	+	0.999392i	$0.488902\pi$
$390$		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	$-0.979795\pi$
$409$		−	51.8874i		−	0.126864i	0.997986	−	0.0634320i	$-0.0202046\pi$
$410$	−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	$-0.333694\pi$
$419$	418.176			0.998034			0.499017	+	0.866592i	$0.333694\pi$
$420$		0			0
$421$			48.3444i			0.114832i	0.998350	+	0.0574161i	$0.0182862\pi$
$421$			48.3444i			0.114832i	−0.998350	+	0.0574161i	$0.981714\pi$
$422$	−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	$-0.539396\pi$
$431$	−106.413			−0.246898			−0.123449	+	0.992351i	$0.539396\pi$
$432$		0			0
$433$		−	261.405i		−	0.603707i	−0.953354	−	0.301854i	$-0.902395\pi$
$433$		−	261.405i		−	0.603707i	0.953354	−	0.301854i	$-0.0976054\pi$
$434$	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	$-0.932612\pi$
$463$		−	194.577i		−	0.420254i	0.977674	−	0.210127i	$-0.0673877\pi$
$464$	−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	$-0.529429\pi$
$467$	−86.2300			−0.184647			−0.0923234	+	0.995729i	$0.529429\pi$
$468$		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	$0.209497\pi$
$487$			595.755i			1.22332i	−0.791122	+	0.611658i	$0.790503\pi$
$488$	−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	$-0.299986\pi$
$521$	612.508			1.17564			0.587820	+	0.808992i	$0.299986\pi$
$522$		0			0
$523$		−	692.859i		−	1.32478i	−0.749160	−	0.662389i	$-0.769542\pi$
$523$		−	692.859i		−	1.32478i	0.749160	−	0.662389i	$-0.230458\pi$
$524$	−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	$-0.800659\pi$
$541$		−	634.171i		−	1.17222i	0.810232	−	0.586110i	$-0.199341\pi$
$542$	−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	$-0.711730\pi$
$557$	−687.553			−1.23439			−0.617193	+	0.786812i	$0.711730\pi$
$558$		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	$-0.825017\pi$
$563$	−960.105			−1.70534			−0.852669	+	0.522452i	$0.825017\pi$
$564$		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	$-0.994164\pi$
$577$		−	21.1560i		−	0.0366654i	0.999832	−	0.0183327i	$-0.00583581\pi$
$578$	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	$-0.390564\pi$
$587$	395.721			0.674141			0.337071	+	0.941479i	$0.390564\pi$
$588$		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	$-0.635001\pi$
$593$	−488.061			−0.823037			−0.411519	+	0.911401i	$0.635001\pi$
$594$		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	$-0.557502\pi$
$599$	−215.241			−0.359334			−0.179667	+	0.983727i	$0.557502\pi$
$600$		0			0
$601$			810.565i			1.34869i	0.738415	+	0.674347i	$0.235575\pi$
$601$			810.565i			1.34869i	−0.738415	+	0.674347i	$0.764425\pi$
$602$	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	$0.209151\pi$
$613$			748.837i			1.22159i	−0.791787	+	0.610797i	$0.790849\pi$
$614$	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	$0.160500\pi$
$619$			598.114i			0.966259i	−0.875549	+	0.483129i	$0.839500\pi$
$620$	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	$0.124384\pi$
$631$			480.690i			0.761791i	−0.924618	+	0.380895i	$0.875616\pi$
$632$	−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	$0.197798\pi$
$643$			748.676i			1.16435i	−0.813064	+	0.582174i	$0.802202\pi$
$644$	−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	$-0.233515\pi$
$653$	970.047			1.48552			0.742762	+	0.669556i	$0.233515\pi$
$654$		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	$0.152671\pi$
$691$			637.724i			0.922901i	−0.887166	+	0.461450i	$0.847329\pi$
$692$	−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	$-0.726463\pi$
$701$	−915.416			−1.30587			−0.652936	+	0.757413i	$0.726463\pi$
$702$		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	$0.00600809\pi$
$709$			26.7631i			0.0377477i	−0.999822	+	0.0188739i	$0.993992\pi$
$710$	−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	$-0.548852\pi$
$743$	−227.166			−0.305741			−0.152870	+	0.988246i	$0.548852\pi$
$744$		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	$-0.995828\pi$
$751$		−	19.6849i		−	0.0262116i	0.999914	−	0.0131058i	$-0.00417182\pi$
$752$	−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	$0.252000\pi$
$757$			1077.26i			1.42307i	−0.702650	+	0.711535i	$0.748000\pi$
$758$	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	$-0.479325\pi$
$761$	98.7893			0.129815			0.0649075	+	0.997891i	$0.479325\pi$
$762$		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	$-0.930733\pi$
$769$		−	332.048i		−	0.431792i	0.976416	−	0.215896i	$-0.0692672\pi$
$770$	−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	$-0.808858\pi$
$787$		−	889.382i		−	1.13009i	0.825059	−	0.565046i	$-0.191142\pi$
$788$	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	$-0.684203\pi$
$811$		−	1357.90i		−	1.67436i	0.546929	−	0.837179i	$-0.315797\pi$
$812$	−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	$-0.693103\pi$
$821$	−936.137			−1.14024			−0.570120	+	0.821561i	$0.693103\pi$
$822$		0			0
$823$		−	129.080i		−	0.156841i	−0.996920	−	0.0784207i	$-0.975012\pi$
$823$		−	129.080i		−	0.156841i	0.996920	−	0.0784207i	$-0.0249877\pi$
$824$	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	$-0.689792\pi$
$857$	−962.482			−1.12308			−0.561542	+	0.827449i	$0.689792\pi$
$858$		0			0
$859$		−	160.713i		−	0.187093i	−0.995615	−	0.0935466i	$-0.970180\pi$
$859$		−	160.713i		−	0.187093i	0.995615	−	0.0935466i	$-0.0298204\pi$
$860$	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	$-0.235353\pi$
$863$	1275.31			1.47777			0.738884	+	0.673832i	$0.235353\pi$
$864$		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	$-0.772705\pi$
$877$		−	1148.72i		−	1.30983i	0.755704	−	0.654913i	$-0.227295\pi$
$878$	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	$-0.142217\pi$
$881$	1589.04			1.80368			0.901840	+	0.432070i	$0.142217\pi$
$882$		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	$-0.491402\pi$
$911$	49.2079			0.0540152			0.0270076	+	0.999635i	$0.491402\pi$
$912$		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	$0.121732\pi$
$919$			685.900i			0.746355i	−0.927760	+	0.373177i	$0.878268\pi$
$920$	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	$-0.533305\pi$
$929$	−194.049			−0.208880			−0.104440	+	0.994531i	$0.533305\pi$
$930$		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	$-0.909841\pi$
$937$		−	523.728i		−	0.558942i	0.960154	−	0.279471i	$-0.0901590\pi$
$938$	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	$-0.822778\pi$
$967$		−	1022.00i		−	1.05687i	0.848973	−	0.528437i	$-0.177222\pi$
$968$	−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	$-0.480104\pi$
$971$	121.308			0.124931			0.0624654	+	0.998047i	$0.480104\pi$
$972$		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	$-0.888554\pi$
$991$		−	679.844i		−	0.686019i	0.939332	−	0.343009i	$-0.111446\pi$
$992$	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.251.25	yes	48
3.2	odd	2	inner	504.3.e.c.251.24	yes	48
4.3	odd	2		2016.3.e.c.1007.14		48
7.6	odd	2	inner	504.3.e.c.251.26	yes	48
8.3	odd	2	inner	504.3.e.c.251.21	✓	48
8.5	even	2		2016.3.e.c.1007.45		48
12.11	even	2		2016.3.e.c.1007.47		48
21.20	even	2	inner	504.3.e.c.251.23	yes	48
24.5	odd	2		2016.3.e.c.1007.20		48
24.11	even	2	inner	504.3.e.c.251.28	yes	48
28.27	even	2		2016.3.e.c.1007.19		48
56.13	odd	2		2016.3.e.c.1007.48		48
56.27	even	2	inner	504.3.e.c.251.22	yes	48
84.83	odd	2		2016.3.e.c.1007.46		48
168.83	odd	2	inner	504.3.e.c.251.27	yes	48
168.125	even	2		2016.3.e.c.1007.13		48

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

Varieties

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Representations

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Database

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