LMFDB - Embedded newform 176.4.m.d.81.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [176,4,Mod(49,176)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("176.49"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(176, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 176 = 2^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	176.m (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$10.3843361610$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 70 x^{10} - 84 x^{9} + 2459 x^{8} - 8514 x^{7} + 54995 x^{6} - 432951 x^{5} + \cdots + 40896025 $ x^12 - x^11 + 70x^10 - 84x^9 + 2459x^8 - 8514x^7 + 54995x^6 - 432951x^5 + 3635141x^4 - 13377765x^3 + 34447885x^2 - 51287900x + 40896025
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 44)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.1
Root			$-5.22867 - 3.79885i$ of defining polynomial
Character	$\chi$	$=$	176.81
Dual form			176.4.m.d.113.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.99717 + 6.14667i) q^{3} +(0.0709832 - 0.0515723i) q^{5} +(7.55109 + 23.2399i) q^{7} +(-11.9494 - 8.68176i) q^{9} +(-36.2742 - 3.89603i) q^{11} +(26.7042 + 19.4017i) q^{13} +(0.175232 + 0.539309i) q^{15} +(-39.3680 + 28.6025i) q^{17} +(33.2359 - 102.290i) q^{19} -157.929 q^{21} -141.967 q^{23} +(-38.6247 + 118.875i) q^{25} +(-63.9451 + 46.4589i) q^{27} +(-37.9483 - 116.793i) q^{29} +(-100.904 - 73.3112i) q^{31} +(96.3936 - 215.185i) q^{33} +(1.73453 + 1.26021i) q^{35} +(-60.0493 - 184.813i) q^{37} +(-172.589 + 125.393i) q^{39} +(-49.0925 + 151.091i) q^{41} +451.693 q^{43} -1.29595 q^{45} +(-188.225 + 579.298i) q^{47} +(-205.580 + 149.362i) q^{49} +(-97.1855 - 299.106i) q^{51} +(281.895 + 204.809i) q^{53} +(-2.77579 + 1.59419i) q^{55} +(562.362 + 408.580i) q^{57} +(28.8437 + 88.7718i) q^{59} +(-371.255 + 269.733i) q^{61} +(111.532 - 343.260i) q^{63} +2.89614 q^{65} +768.836 q^{67} +(283.532 - 872.622i) q^{69} +(900.219 - 654.047i) q^{71} +(326.904 + 1006.11i) q^{73} +(-653.544 - 474.827i) q^{75} +(-183.367 - 872.428i) q^{77} +(-39.6700 - 28.8219i) q^{79} +(-281.093 - 865.116i) q^{81} +(-810.103 + 588.574i) q^{83} +(-1.31937 + 4.06059i) q^{85} +793.677 q^{87} +948.854 q^{89} +(-249.248 + 767.105i) q^{91} +(652.143 - 473.810i) q^{93} +(-2.91612 - 8.97488i) q^{95} +(331.040 + 240.515i) q^{97} +(399.632 + 361.480i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{3} - 4 q^{5} - 6 q^{7} + 47 q^{9} - 39 q^{11} - 10 q^{13} - 74 q^{15} - 56 q^{17} + 141 q^{19} - 304 q^{21} + 388 q^{23} - 203 q^{25} + 331 q^{27} + 772 q^{29} - 882 q^{31} + 981 q^{33} - 412 q^{35}+ \cdots - 3563 q^{99}+O(q^{100}) $ 12 * q + 4 * q^3 - 4 * q^5 - 6 * q^7 + 47 * q^9 - 39 * q^11 - 10 * q^13 - 74 * q^15 - 56 * q^17 + 141 * q^19 - 304 * q^21 + 388 * q^23 - 203 * q^25 + 331 * q^27 + 772 * q^29 - 882 * q^31 + 981 * q^33 - 412 * q^35 - 192 * q^37 + 154 * q^39 - 180 * q^41 + 2330 * q^43 - 1340 * q^45 - 196 * q^47 - 973 * q^49 - 2969 * q^51 + 2246 * q^53 - 2672 * q^55 + 431 * q^57 + 1099 * q^59 - 470 * q^61 + 2008 * q^63 - 3892 * q^65 + 4394 * q^67 - 1394 * q^69 + 2084 * q^71 + 2824 * q^73 - 4623 * q^75 + 3654 * q^77 - 838 * q^79 + 1518 * q^81 - 789 * q^83 - 2632 * q^85 + 3036 * q^87 - 954 * q^89 - 2460 * q^91 - 808 * q^93 - 4362 * q^95 + 2651 * q^97 - 3563 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/176\mathbb{Z}\right)^\times$.

$n$	$111$	$133$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.99717	+	6.14667i	−0.384357	+	1.18293i	0.552590	+	0.833454i	$0.313640\pi$
$3$	−1.99717	+	6.14667i	−0.384357	+	1.18293i	−0.936946	+	0.349474i	$0.886360\pi$
$4$		0			0
$5$	0.0709832	−	0.0515723i	0.00634893	−	0.00461277i	−0.584606	−	0.811317i	$-0.698751\pi$
$5$	0.0709832	−	0.0515723i	0.00634893	−	0.00461277i	0.590955	+	0.806704i	$0.298751\pi$
$6$		0			0
$7$	7.55109	+	23.2399i	0.407721	+	1.25483i	0.918602	+	0.395184i	$0.129319\pi$
$7$	7.55109	+	23.2399i	0.407721	+	1.25483i	−0.510882	+	0.859651i	$0.670681\pi$
$8$		0			0
$9$	−11.9494	−	8.68176i	−0.442571	−	0.321547i
$10$		0			0
$11$	−36.2742	−	3.89603i	−0.994282	−	0.106791i
$11$	−36.2742	−	3.89603i	−0.994282	−	0.106791i
$12$		0			0
$13$	26.7042	+	19.4017i	0.569723	+	0.413928i	0.835005	−	0.550243i	$-0.185465\pi$
$13$	26.7042	+	19.4017i	0.569723	+	0.413928i	−0.265281	+	0.964171i	$0.585465\pi$
$14$		0			0
$15$	0.175232	+	0.539309i	0.00301632	+	0.00928327i
$16$		0			0
$17$	−39.3680	+	28.6025i	−0.561655	+	0.408066i	−0.832064	−	0.554679i	$-0.812841\pi$
$17$	−39.3680	+	28.6025i	−0.561655	+	0.408066i	0.270409	+	0.962745i	$0.412841\pi$
$18$		0			0
$19$	33.2359	−	102.290i	0.401307	−	1.23510i	−0.522633	−	0.852558i	$-0.675050\pi$
$19$	33.2359	−	102.290i	0.401307	−	1.23510i	0.923940	−	0.382538i	$-0.124950\pi$
$20$		0			0
$21$	−157.929			−1.64109
$22$		0			0
$23$	−141.967			−1.28705			−0.643523	−	0.765427i	$-0.722528\pi$
$23$	−141.967			−1.28705			−0.643523	+	0.765427i	$0.722528\pi$
$24$		0			0
$25$	−38.6247	+	118.875i	−0.308998	+	0.950998i
$26$		0			0
$27$	−63.9451	+	46.4589i	−0.455787	+	0.331149i
$28$		0			0
$29$	−37.9483	−	116.793i	−0.242994	−	0.747858i	−0.995960	−	0.0897989i	$-0.971378\pi$
$29$	−37.9483	−	116.793i	−0.242994	−	0.747858i	0.752966	−	0.658059i	$-0.228622\pi$
$30$		0			0
$31$	−100.904	−	73.3112i	−0.584611	−	0.424744i	0.255773	−	0.966737i	$-0.417670\pi$
$31$	−100.904	−	73.3112i	−0.584611	−	0.424744i	−0.840383	+	0.541993i	$0.817670\pi$
$32$		0			0
$33$	96.3936	−	215.185i	0.508484	−	1.13512i
$34$		0			0
$35$	1.73453	+	1.26021i	0.00837685	+	0.00608613i
$36$		0			0
$37$	−60.0493	−	184.813i	−0.266812	−	0.821164i	−0.991270	−	0.131845i	$-0.957910\pi$
$37$	−60.0493	−	184.813i	−0.266812	−	0.821164i	0.724458	−	0.689319i	$-0.242090\pi$
$38$		0			0
$39$	−172.589	+	125.393i	−0.708624	+	0.514846i
$40$		0			0
$41$	−49.0925	+	151.091i	−0.186999	+	0.575524i	−0.999977	−	0.00677054i	$-0.997845\pi$
$41$	−49.0925	+	151.091i	−0.186999	+	0.575524i	0.812978	+	0.582294i	$0.197845\pi$
$42$		0			0
$43$	451.693			1.60192			0.800960	−	0.598718i	$-0.204323\pi$
$43$	451.693			1.60192			0.800960	+	0.598718i	$0.204323\pi$
$44$		0			0
$45$	−1.29595			−0.00429307
$46$		0			0
$47$	−188.225	+	579.298i	−0.584159	+	1.79786i	0.0184617	+	0.999830i	$0.494123\pi$
$47$	−188.225	+	579.298i	−0.584159	+	1.79786i	−0.602621	+	0.798028i	$0.705877\pi$
$48$		0			0
$49$	−205.580	+	149.362i	−0.599357	+	0.435459i
$50$		0			0
$51$	−97.1855	−	299.106i	−0.266837	−	0.821240i
$52$		0			0
$53$	281.895	+	204.809i	0.730590	+	0.530805i	0.889750	−	0.456448i	$-0.150879\pi$
$53$	281.895	+	204.809i	0.730590	+	0.530805i	−0.159160	+	0.987253i	$0.550879\pi$
$54$		0			0
$55$	−2.77579	+	1.59419i	−0.00680522	+	0.00390838i
$56$		0			0
$57$	562.362	+	408.580i	1.30678	+	0.949435i
$58$		0			0
$59$	28.8437	+	88.7718i	0.0636463	+	0.195883i	0.977823	−	0.209432i	$-0.0671616\pi$
$59$	28.8437	+	88.7718i	0.0636463	+	0.195883i	−0.914177	+	0.405316i	$0.867162\pi$
$60$		0			0
$61$	−371.255	+	269.733i	−0.779252	+	0.566160i	−0.904754	−	0.425934i	$-0.859946\pi$
$61$	−371.255	+	269.733i	−0.779252	+	0.566160i	0.125503	+	0.992093i	$0.459946\pi$
$62$		0			0
$63$	111.532	−	343.260i	0.223043	−	0.686455i
$64$		0			0
$65$	2.89614			0.00552649
$66$		0			0
$67$	768.836			1.40191			0.700957	−	0.713204i	$-0.252757\pi$
$67$	768.836			1.40191			0.700957	+	0.713204i	$0.252757\pi$
$68$		0			0
$69$	283.532	−	872.622i	0.494685	−	1.52248i
$70$		0			0
$71$	900.219	−	654.047i	1.50474	−	1.09326i	0.536291	−	0.844033i	$-0.319825\pi$
$71$	900.219	−	654.047i	1.50474	−	1.09326i	0.968446	−	0.249223i	$-0.0801751\pi$
$72$		0			0
$73$	326.904	+	1006.11i	0.524127	+	1.61310i	0.766037	+	0.642797i	$0.222226\pi$
$73$	326.904	+	1006.11i	0.524127	+	1.61310i	−0.241910	+	0.970299i	$0.577774\pi$
$74$		0			0
$75$	−653.544	−	474.827i	−1.00620	−	0.731044i
$76$		0			0
$77$	−183.367	−	872.428i	−0.271384	−	1.29120i
$78$		0			0
$79$	−39.6700	−	28.8219i	−0.0564965	−	0.0410471i	0.559179	−	0.829047i	$-0.311117\pi$
$79$	−39.6700	−	28.8219i	−0.0564965	−	0.0410471i	−0.615675	+	0.788000i	$0.711117\pi$
$80$		0			0
$81$	−281.093	−	865.116i	−0.385587	−	1.18672i
$82$		0			0
$83$	−810.103	+	588.574i	−1.07133	+	0.778366i	−0.976151	−	0.217094i	$-0.930342\pi$
$83$	−810.103	+	588.574i	−1.07133	+	0.778366i	−0.0951784	+	0.995460i	$0.530342\pi$
$84$		0			0
$85$	−1.31937	+	4.06059i	−0.00168359	+	0.00518157i
$86$		0			0
$87$	793.677			0.978059
$88$		0			0
$89$	948.854			1.13009			0.565047	−	0.825059i	$-0.308858\pi$
$89$	948.854			1.13009			0.565047	+	0.825059i	$0.308858\pi$
$90$		0			0
$91$	−249.248	+	767.105i	−0.287124	+	0.883676i
$92$		0			0
$93$	652.143	−	473.810i	0.727141	−	0.528299i
$94$		0			0
$95$	−2.91612	−	8.97488i	−0.00314934	−	0.00969267i
$96$		0			0
$97$	331.040	+	240.515i	0.346516	+	0.251759i	0.747406	−	0.664368i	$-0.231299\pi$
$97$	331.040	+	240.515i	0.346516	+	0.251759i	−0.400890	+	0.916126i	$0.631299\pi$
$98$		0			0
$99$	399.632	+	361.480i	0.405702	+	0.366970i
$100$		0			0
$101$	−239.170	−	173.767i	−0.235627	−	0.171193i	0.463706	−	0.885989i	$-0.346519\pi$
$101$	−239.170	−	173.767i	−0.235627	−	0.171193i	−0.699333	+	0.714796i	$0.746519\pi$
$102$		0			0
$103$	−14.6196	−	44.9945i	−0.0139855	−	0.0430431i	0.943820	−	0.330459i	$-0.107204\pi$
$103$	−14.6196	−	44.9945i	−0.0139855	−	0.0430431i	−0.957806	+	0.287416i	$0.907204\pi$
$104$		0			0
$105$	−11.2103	+	8.14474i	−0.0104192	+	0.00756996i
$106$		0			0
$107$	−40.9037	+	125.889i	−0.0369562	+	0.113739i	−0.967833	−	0.251594i	$-0.919045\pi$
$107$	−40.9037	+	125.889i	−0.0369562	+	0.113739i	0.930877	+	0.365334i	$0.119045\pi$
$108$		0			0
$109$	−1326.34			−1.16551			−0.582756	−	0.812647i	$-0.698026\pi$
$109$	−1326.34			−1.16551			−0.582756	+	0.812647i	$0.698026\pi$
$110$		0			0
$111$	1255.91			1.07393
$112$		0			0
$113$	−406.632	+	1251.48i	−0.338519	+	1.04186i	0.626443	+	0.779467i	$0.284510\pi$
$113$	−406.632	+	1251.48i	−0.338519	+	1.04186i	−0.964962	+	0.262388i	$0.915490\pi$
$114$		0			0
$115$	−10.0772	+	7.32154i	−0.00817136	+	0.00593684i
$116$		0			0
$117$	−150.658	−	463.678i	−0.119046	−	0.366385i
$118$		0			0
$119$	−961.990	−	698.926i	−0.741054	−	0.538407i
$120$		0			0
$121$	1300.64	+	282.651i	0.977191	+	0.212360i
$122$		0			0
$123$	−830.662	−	603.511i	−0.608929	−	0.442413i
$124$		0			0
$125$	6.77808	+	20.8608i	0.00485000	+	0.0149268i
$126$		0			0
$127$	279.263	−	202.896i	0.195123	−	0.141765i	−0.485934	−	0.873995i	$-0.661521\pi$
$127$	279.263	−	202.896i	0.195123	−	0.141765i	0.681057	+	0.732230i	$0.261521\pi$
$128$		0			0
$129$	−902.110	+	2776.41i	−0.615708	+	1.89495i
$130$		0			0
$131$	−31.6857			−0.0211328			−0.0105664	−	0.999944i	$-0.503363\pi$
$131$	−31.6857			−0.0211328			−0.0105664	+	0.999944i	$0.503363\pi$
$132$		0			0
$133$	2628.16			1.71346
$134$		0			0
$135$	−2.14304	+	6.59559i	−0.00136625	+	0.00420488i
$136$		0			0
$137$	−772.582	+	561.314i	−0.481797	+	0.350046i	−0.802021	−	0.597296i	$-0.796242\pi$
$137$	−772.582	+	561.314i	−0.481797	+	0.350046i	0.320224	+	0.947342i	$0.396242\pi$
$138$		0			0
$139$	428.463	+	1318.67i	0.261452	+	0.804666i	0.992490	+	0.122329i	$0.0390362\pi$
$139$	428.463	+	1318.67i	0.261452	+	0.804666i	−0.731038	+	0.682337i	$0.760964\pi$
$140$		0			0
$141$	−3184.84	−	2313.92i	−1.90221	−	1.38204i
$142$		0			0
$143$	−893.084	−	807.823i	−0.522262	−	0.472402i
$144$		0			0
$145$	−8.71696	−	6.33325i	−0.00499244	−	0.00362722i
$146$		0			0
$147$	−507.503	−	1561.93i	−0.284749	−	0.876368i
$148$		0			0
$149$	−2145.20	+	1558.58i	−1.17947	+	0.856938i	−0.992112	−	0.125353i	$-0.959994\pi$
$149$	−2145.20	+	1558.58i	−1.17947	+	0.856938i	−0.187362	+	0.982291i	$0.559994\pi$
$150$		0			0
$151$	−624.070	+	1920.69i	−0.336332	+	1.03512i	0.629731	+	0.776814i	$0.283165\pi$
$151$	−624.070	+	1920.69i	−0.336332	+	1.03512i	−0.966062	+	0.258309i	$0.916835\pi$
$152$		0			0
$153$	718.745			0.379785
$154$		0			0
$155$	−10.9433			−0.00567090
$156$		0			0
$157$	−249.783	+	768.754i	−0.126974	+	0.390785i	−0.994256	−	0.107033i	$-0.965865\pi$
$157$	−249.783	+	768.754i	−0.126974	+	0.390785i	0.867282	+	0.497817i	$0.165865\pi$
$158$		0			0
$159$	−1821.89	+	1323.68i	−0.908711	+	0.660217i
$160$		0			0
$161$	−1072.00	−	3299.28i	−0.524755	−	1.61503i
$162$		0			0
$163$	74.5331	+	54.1514i	0.0358152	+	0.0260213i	0.605549	−	0.795808i	$-0.292954\pi$
$163$	74.5331	+	54.1514i	0.0358152	+	0.0260213i	−0.569734	+	0.821829i	$0.692954\pi$
$164$		0			0
$165$	−4.25525	−	20.2457i	−0.00200770	−	0.00955230i
$166$		0			0
$167$	513.234	+	372.887i	0.237816	+	0.172783i	0.700310	−	0.713839i	$-0.253045\pi$
$167$	513.234	+	372.887i	0.237816	+	0.172783i	−0.462494	+	0.886623i	$0.653045\pi$
$168$		0			0
$169$	−342.224	−	1053.26i	−0.155769	−	0.479407i
$170$		0			0
$171$	−1285.20	+	933.754i	−0.574748	+	0.417579i
$172$		0			0
$173$	643.360	−	1980.06i	0.282738	−	0.870179i	−0.704329	−	0.709874i	$-0.748752\pi$
$173$	643.360	−	1980.06i	0.282738	−	0.870179i	0.987067	−	0.160305i	$-0.0512479\pi$
$174$		0			0
$175$	−3054.29			−1.31933
$176$		0			0
$177$	−603.257			−0.256179
$178$		0			0
$179$	323.277	−	994.945i	0.134988	−	0.415451i	−0.860600	−	0.509282i	$-0.829911\pi$
$179$	323.277	−	994.945i	0.134988	−	0.415451i	0.995588	+	0.0938306i	$0.0299112\pi$
$180$		0			0
$181$	2067.25	−	1501.94i	0.848936	−	0.616788i	−0.0759166	−	0.997114i	$-0.524188\pi$
$181$	2067.25	−	1501.94i	0.848936	−	0.616788i	0.924852	+	0.380326i	$0.124188\pi$
$182$		0			0
$183$	−916.497	−	2820.69i	−0.370215	−	1.13941i
$184$		0			0
$185$	−13.7937	−	10.0217i	−0.00548181	−	0.00398277i
$186$		0			0
$187$	1539.48	−	884.156i	0.602021	−	0.345753i
$188$		0			0
$189$	−1562.55	−	1135.26i	−0.601370	−	0.436921i
$190$		0			0
$191$	147.758	+	454.753i	0.0559760	+	0.172276i	0.975136	−	0.221609i	$-0.0711308\pi$
$191$	147.758	+	454.753i	0.0559760	+	0.172276i	−0.919160	+	0.393885i	$0.871131\pi$
$192$		0			0
$193$	1431.61	−	1040.13i	0.533936	−	0.387927i	−0.287892	−	0.957663i	$-0.592954\pi$
$193$	1431.61	−	1040.13i	0.533936	−	0.387927i	0.821828	+	0.569736i	$0.192954\pi$
$194$		0			0
$195$	−5.78409	+	17.8016i	−0.00212414	+	0.00653743i
$196$		0			0
$197$	−524.670			−0.189752			−0.0948761	−	0.995489i	$-0.530245\pi$
$197$	−524.670			−0.189752			−0.0948761	+	0.995489i	$0.530245\pi$
$198$		0			0
$199$	1061.88			0.378264			0.189132	−	0.981952i	$-0.439433\pi$
$199$	1061.88			0.378264			0.189132	+	0.981952i	$0.439433\pi$
$200$		0			0
$201$	−1535.50	+	4725.78i	−0.538835	+	1.65836i
$202$		0			0
$203$	2427.70	−	1763.83i	0.839365	−	0.609834i
$204$		0			0
$205$	4.30738	+	13.2567i	0.00146751	+	0.00451654i
$206$		0			0
$207$	1696.42	+	1232.52i	0.569609	+	0.413845i
$208$		0			0
$209$	−1604.13	+	3580.99i	−0.530909	+	1.18518i
$210$		0			0
$211$	4347.67	+	3158.77i	1.41851	+	1.03061i	0.992015	+	0.126120i	$0.0402523\pi$
$211$	4347.67	+	3158.77i	1.41851	+	1.03061i	0.426496	+	0.904489i	$0.359748\pi$
$212$		0			0
$213$	2222.32	+	6839.60i	0.714887	+	2.20020i
$214$		0			0
$215$	32.0626	−	23.2948i	0.0101705	−	0.00738928i
$216$		0			0
$217$	941.805	−	2898.58i	0.294626	−	0.906767i
$218$		0			0
$219$	−6837.10			−2.10963
$220$		0			0
$221$	−1606.23			−0.488898
$222$		0			0
$223$	−356.495	+	1097.18i	−0.107052	+	0.329474i	−0.990207	−	0.139609i	$-0.955415\pi$
$223$	−356.495	+	1097.18i	−0.107052	+	0.329474i	0.883154	+	0.469083i	$0.155415\pi$
$224$		0			0
$225$	1493.59	−	1085.15i	0.442544	−	0.321527i
$226$		0			0
$227$	−1876.95	−	5776.66i	−0.548800	−	1.68903i	−0.711779	−	0.702404i	$-0.752110\pi$
$227$	−1876.95	−	5776.66i	−0.548800	−	1.68903i	0.162979	−	0.986630i	$-0.447890\pi$
$228$		0			0
$229$	2227.05	+	1618.05i	0.642653	+	0.466915i	0.860761	−	0.509010i	$-0.169988\pi$
$229$	2227.05	+	1618.05i	0.642653	+	0.466915i	−0.218107	+	0.975925i	$0.569988\pi$
$230$		0			0
$231$	5728.74	+	615.295i	1.63170	+	0.175253i
$232$		0			0
$233$	2389.72	+	1736.23i	0.671914	+	0.488174i	0.870665	−	0.491876i	$-0.163689\pi$
$233$	2389.72	+	1736.23i	0.671914	+	0.488174i	−0.198752	+	0.980050i	$0.563689\pi$
$234$		0			0
$235$	16.5149	+	50.8276i	0.00458431	+	0.0141091i
$236$		0			0
$237$	256.387	−	186.276i	0.0702706	−	0.0510545i
$238$		0			0
$239$	−1697.65	+	5224.84i	−0.459465	+	1.41409i	0.406347	+	0.913719i	$0.366802\pi$
$239$	−1697.65	+	5224.84i	−0.459465	+	1.41409i	−0.865812	+	0.500369i	$0.833198\pi$
$240$		0			0
$241$	4038.21			1.07935			0.539676	−	0.841873i	$-0.318547\pi$
$241$	4038.21			1.07935			0.539676	+	0.841873i	$0.318547\pi$
$242$		0			0
$243$	3744.88			0.988618
$244$		0			0
$245$	−6.88973	+	21.2044i	−0.00179661	+	0.00552939i
$246$		0			0
$247$	2872.13	−	2086.72i	0.739875	−	0.537551i
$248$		0			0
$249$	−1999.86	−	6154.92i	−0.508979	−	1.56647i
$250$		0			0
$251$	3615.77	+	2627.01i	0.909265	+	0.660620i	0.940829	−	0.338882i	$-0.110049\pi$
$251$	3615.77	+	2627.01i	0.909265	+	0.660620i	−0.0315640	+	0.999502i	$0.510049\pi$
$252$		0			0
$253$	5149.73	+	553.106i	1.27969	+	0.137445i
$254$		0			0
$255$	−22.3241	−	16.2194i	−0.00548232	−	0.00398314i
$256$		0			0
$257$	−1464.18	−	4506.29i	−0.355382	−	1.09375i	−0.955788	−	0.294058i	$-0.904994\pi$
$257$	−1464.18	−	4506.29i	−0.355382	−	1.09375i	0.600406	−	0.799695i	$-0.295006\pi$
$258$		0			0
$259$	3841.59	−	2791.08i	0.921640	−	0.669611i
$260$		0			0
$261$	−560.507	+	1725.06i	−0.132929	+	0.409114i
$262$		0			0
$263$	−3942.64			−0.924386			−0.462193	−	0.886779i	$-0.652937\pi$
$263$	−3942.64			−0.924386			−0.462193	+	0.886779i	$0.652937\pi$
$264$		0			0
$265$	30.5723			0.00708694
$266$		0			0
$267$	−1895.03	+	5832.29i	−0.434359	+	1.33682i
$268$		0			0
$269$	2752.65	−	1999.92i	0.623910	−	0.453297i	−0.230375	−	0.973102i	$-0.573995\pi$
$269$	2752.65	−	1999.92i	0.623910	−	0.453297i	0.854285	+	0.519805i	$0.173995\pi$
$270$		0			0
$271$	−1231.13	−	3789.03i	−0.275962	−	0.849325i	−0.988963	−	0.148162i	$-0.952664\pi$
$271$	−1231.13	−	3789.03i	−0.275962	−	0.849325i	0.713001	−	0.701163i	$-0.247336\pi$
$272$		0			0
$273$	−4217.35	−	3064.09i	−0.934967	−	0.679293i
$274$		0			0
$275$	1864.22	−	4161.61i	0.408789	−	0.912562i
$276$		0			0
$277$	−2861.55	−	2079.04i	−0.620700	−	0.450965i	0.232466	−	0.972605i	$-0.425321\pi$
$277$	−2861.55	−	2079.04i	−0.620700	−	0.450965i	−0.853166	+	0.521640i	$0.825321\pi$
$278$		0			0
$279$	569.276	+	1752.05i	0.122157	+	0.375959i
$280$		0			0
$281$	3541.62	−	2573.14i	0.751870	−	0.546265i	−0.144536	−	0.989500i	$-0.546169\pi$
$281$	3541.62	−	2573.14i	0.751870	−	0.546265i	0.896406	+	0.443234i	$0.146169\pi$
$282$		0			0
$283$	−766.922	+	2360.34i	−0.161091	+	0.495787i	−0.998727	−	0.0504415i	$-0.983937\pi$
$283$	−766.922	+	2360.34i	−0.161091	+	0.495787i	0.837636	+	0.546229i	$0.183937\pi$
$284$		0			0
$285$	60.9897			0.0126762
$286$		0			0
$287$	−3882.04			−0.798431
$288$		0			0
$289$	−786.466	+	2420.49i	−0.160079	+	0.492671i
$290$		0			0
$291$	−2139.51	+	1554.45i	−0.430998	+	0.313138i
$292$		0			0
$293$	−1380.78	−	4249.60i	−0.275311	−	0.847319i	−0.989137	−	0.146996i	$-0.953039\pi$
$293$	−1380.78	−	4249.60i	−0.275311	−	0.847319i	0.713826	−	0.700323i	$-0.246961\pi$
$294$		0			0
$295$	6.62558	+	4.81377i	0.00130765	+	0.000950063i
$296$		0			0
$297$	2500.57	−	1436.13i	0.488544	−	0.280581i
$298$		0			0
$299$	−3791.10	−	2754.39i	−0.733260	−	0.532745i
$300$		0			0
$301$	3410.77	+	10497.3i	0.653135	+	2.01014i
$302$		0			0
$303$	1545.75	−	1123.05i	0.293073	−	0.212930i
$304$		0			0
$305$	−12.4421	+	38.2930i	−0.00233585	+	0.00718901i
$306$		0			0
$307$	3630.47			0.674925			0.337462	−	0.941339i	$-0.390431\pi$
$307$	3630.47			0.674925			0.337462	+	0.941339i	$0.390431\pi$
$308$		0			0
$309$	305.764			0.0562923
$310$		0			0
$311$	2711.74	−	8345.89i	0.494434	−	1.52171i	−0.323404	−	0.946261i	$-0.604827\pi$
$311$	2711.74	−	8345.89i	0.494434	−	1.52171i	0.817837	−	0.575449i	$-0.195173\pi$
$312$		0			0
$313$	−2727.32	+	1981.51i	−0.492515	+	0.357833i	−0.806151	−	0.591710i	$-0.798453\pi$
$313$	−2727.32	+	1981.51i	−0.492515	+	0.357833i	0.313636	+	0.949543i	$0.398453\pi$
$314$		0			0
$315$	−9.78580	−	30.1176i	−0.00175037	−	0.00538709i
$316$		0			0
$317$	3651.95	+	2653.29i	0.647047	+	0.470107i	0.862264	−	0.506459i	$-0.169046\pi$
$317$	3651.95	+	2653.29i	0.647047	+	0.470107i	−0.215217	+	0.976566i	$0.569046\pi$
$318$		0			0
$319$	921.517	+	4384.42i	0.161740	+	0.769531i
$320$		0			0
$321$	−692.104	−	502.843i	−0.120341	−	0.0874329i
$322$		0			0
$323$	1617.31	+	4977.56i	0.278605	+	0.857458i
$324$		0			0
$325$	−3337.82	+	2425.06i	−0.569688	+	0.413903i
$326$		0			0
$327$	2648.94	−	8152.61i	0.447972	−	1.37872i
$328$		0			0
$329$	−14884.1			−2.49419
$330$		0			0
$331$	−575.331			−0.0955379			−0.0477690	−	0.998858i	$-0.515211\pi$
$331$	−575.331			−0.0955379			−0.0477690	+	0.998858i	$0.515211\pi$
$332$		0			0
$333$	−886.946	+	2729.74i	−0.145959	+	0.449216i
$334$		0			0
$335$	54.5744	−	39.6506i	0.00890065	−	0.00646670i
$336$		0			0
$337$	−2119.29	−	6522.51i	−0.342567	−	1.05431i	−0.962873	−	0.269954i	$-0.912991\pi$
$337$	−2119.29	−	6522.51i	−0.342567	−	1.05431i	0.620306	−	0.784360i	$-0.287009\pi$
$338$		0			0
$339$	−6880.35	−	4998.86i	−1.10233	−	0.800888i
$340$		0			0
$341$	3374.60	+	3052.43i	0.535909	+	0.484746i
$342$		0			0
$343$	1757.26	+	1276.73i	0.276627	+	0.200982i
$344$		0			0
$345$	−24.8771	−	76.5638i	−0.00388214	−	0.0119480i
$346$		0			0
$347$	−5848.41	+	4249.12i	−0.904782	+	0.657362i	−0.939690	−	0.342028i	$-0.888886\pi$
$347$	−5848.41	+	4249.12i	−0.904782	+	0.657362i	0.0349081	+	0.999391i	$0.488886\pi$
$348$		0			0
$349$	−3965.03	+	12203.1i	−0.608147	+	1.87169i	−0.134642	+	0.990894i	$0.542988\pi$
$349$	−3965.03	+	12203.1i	−0.608147	+	1.87169i	−0.473505	+	0.880791i	$0.657012\pi$
$350$		0			0
$351$	−2608.98			−0.396744
$352$		0			0
$353$	9780.78			1.47473			0.737363	−	0.675497i	$-0.236071\pi$
$353$	9780.78			1.47473			0.737363	+	0.675497i	$0.236071\pi$
$354$		0			0
$355$	30.1697	−	92.8527i	0.00451054	−	0.0138820i
$356$		0			0
$357$	6217.33	−	4517.16i	0.921726	−	0.669673i
$358$		0			0
$359$	−170.527	−	524.830i	−0.0250699	−	0.0771572i	0.937739	−	0.347341i	$-0.112915\pi$
$359$	−170.527	−	524.830i	−0.0250699	−	0.0771572i	−0.962809	+	0.270184i	$0.912915\pi$
$360$		0			0
$361$	−3809.48	−	2767.75i	−0.555398	−	0.403521i
$362$		0			0
$363$	−4334.97	+	7430.12i	−0.626797	+	1.07432i
$364$		0			0
$365$	75.0919	+	54.5575i	0.0107685	+	0.00782375i
$366$		0			0
$367$	1379.05	+	4244.29i	0.196147	+	0.603680i	0.999961	+	0.00879870i	$0.00280075\pi$
$367$	1379.05	+	4244.29i	0.196147	+	0.603680i	−0.803814	+	0.594881i	$0.797199\pi$
$368$		0			0
$369$	1898.36	−	1379.24i	0.267818	−	0.194581i
$370$		0			0
$371$	−2631.11	+	8097.74i	−0.368196	+	1.13319i
$372$		0			0
$373$	−10086.8			−1.40020			−0.700102	−	0.714043i	$-0.746862\pi$
$373$	−10086.8			−1.40020			−0.700102	+	0.714043i	$0.746862\pi$
$374$		0			0
$375$	−141.761			−0.0195214
$376$		0			0
$377$	1252.60	−	3855.12i	0.171120	−	0.526654i
$378$		0			0
$379$	−386.794	+	281.022i	−0.0524229	+	0.0380875i	−0.613688	−	0.789549i	$-0.710315\pi$
$379$	−386.794	+	281.022i	−0.0524229	+	0.0380875i	0.561265	+	0.827636i	$0.310315\pi$
$380$		0			0
$381$	689.400	+	2121.76i	0.0927009	+	0.285304i
$382$		0			0
$383$	−14.1316	−	10.2672i	−0.00188536	−	0.00136979i	0.586842	−	0.809701i	$-0.300371\pi$
$383$	−14.1316	−	10.2672i	−0.00188536	−	0.00136979i	−0.588728	+	0.808332i	$0.700371\pi$
$384$		0			0
$385$	−58.0091	−	52.4710i	−0.00767900	−	0.00694590i
$386$		0			0
$387$	−5397.47	−	3921.49i	−0.708963	−	0.515092i
$388$		0			0
$389$	−3569.92	−	10987.1i	−0.465301	−	1.43205i	−0.858603	−	0.512641i	$-0.828667\pi$
$389$	−3569.92	−	10987.1i	−0.465301	−	1.43205i	0.393302	−	0.919409i	$-0.371333\pi$
$390$		0			0
$391$	5588.93	−	4060.60i	0.722876	−	0.525200i
$392$		0			0
$393$	63.2819	−	194.762i	0.00812252	−	0.0249985i
$394$		0			0
$395$	−4.30231			−0.000548033
$396$		0			0
$397$	−1357.56			−0.171622			−0.0858109	−	0.996311i	$-0.527348\pi$
$397$	−1357.56			−0.171622			−0.0858109	+	0.996311i	$0.527348\pi$
$398$		0			0
$399$	−5248.90	+	16154.5i	−0.658581	+	2.02690i
$400$		0			0
$401$	−7159.39	+	5201.60i	−0.891578	+	0.647769i	−0.936289	−	0.351231i	$-0.885763\pi$
$401$	−7159.39	+	5201.60i	−0.891578	+	0.647769i	0.0447109	+	0.999000i	$0.485763\pi$
$402$		0			0
$403$	−1272.20	−	3915.43i	−0.157253	−	0.483974i
$404$		0			0
$405$	−64.5689	−	46.9120i	−0.00792210	−	0.00575575i
$406$		0			0
$407$	1458.21	+	6937.90i	0.177594	+	0.844961i
$408$		0			0
$409$	6881.53	+	4999.72i	0.831955	+	0.604451i	0.920112	−	0.391656i	$-0.128098\pi$
$409$	6881.53	+	4999.72i	0.831955	+	0.604451i	−0.0881567	+	0.996107i	$0.528098\pi$
$410$		0			0
$411$	−1907.23	−	5869.85i	−0.228897	−	0.704473i
$412$		0			0
$413$	−1845.24	+	1340.65i	−0.219851	+	0.159731i
$414$		0			0
$415$	−27.1495	+	83.5577i	−0.00321137	+	0.00988358i
$416$		0			0
$417$	−8961.18			−1.05235
$418$		0			0
$419$	8675.96			1.01157			0.505786	−	0.862659i	$-0.331203\pi$
$419$	8675.96			1.01157			0.505786	+	0.862659i	$0.331203\pi$
$420$		0			0
$421$	2803.81	−	8629.23i	0.324582	−	0.998961i	−0.647047	−	0.762450i	$-0.723996\pi$
$421$	2803.81	−	8629.23i	0.324582	−	0.998961i	0.971629	−	0.236511i	$-0.0760039\pi$
$422$		0			0
$423$	7278.51	−	5288.15i	0.836627	−	0.607845i
$424$		0			0
$425$	−1879.54	−	5784.62i	−0.214520	−	0.660225i
$426$		0			0
$427$	−9071.93	−	6591.15i	−1.02815	−	0.746997i
$428$		0			0
$429$	6749.07	−	3876.13i	0.759553	−	0.436227i
$430$		0			0
$431$	−12180.9	−	8849.92i	−1.36133	−	0.989062i	−0.998359	−	0.0572603i	$-0.981763\pi$
$431$	−12180.9	−	8849.92i	−1.36133	−	0.989062i	−0.362968	−	0.931802i	$-0.618237\pi$
$432$		0			0
$433$	−1399.62	−	4307.59i	−0.155338	−	0.478082i	0.842857	−	0.538138i	$-0.180872\pi$
$433$	−1399.62	−	4307.59i	−0.155338	−	0.478082i	−0.998195	+	0.0600559i	$0.980872\pi$
$434$		0			0
$435$	56.3377	−	40.9317i	0.00620962	−	0.00451155i
$436$		0			0
$437$	−4718.38	+	14521.7i	−0.516501	+	1.58963i
$438$		0			0
$439$	−1061.24			−0.115376			−0.0576881	−	0.998335i	$-0.518373\pi$
$439$	−1061.24			−0.115376			−0.0576881	+	0.998335i	$0.518373\pi$
$440$		0			0
$441$	3753.28			0.405278
$442$		0			0
$443$	−1758.82	+	5413.09i	−0.188632	+	0.580550i	−0.999992	−	0.00399685i	$-0.998728\pi$
$443$	−1758.82	+	5413.09i	−0.188632	+	0.580550i	0.811360	+	0.584547i	$0.198728\pi$
$444$		0			0
$445$	67.3526	−	48.9346i	0.00717488	−	0.00521285i
$446$		0			0
$447$	−5295.74	−	16298.6i	−0.560357	−	1.72460i
$448$		0			0
$449$	6525.44	+	4741.01i	0.685867	+	0.498312i	0.875299	−	0.483582i	$-0.160665\pi$
$449$	6525.44	+	4741.01i	0.685867	+	0.498312i	−0.189432	+	0.981894i	$0.560665\pi$
$450$		0			0
$451$	2369.45	−	5289.45i	0.247390	−	0.552263i
$452$		0			0
$453$	−10559.5	−	7671.91i	−1.09520	−	0.795712i
$454$		0			0
$455$	21.8690	+	67.3058i	0.00225326	+	0.00693483i
$456$		0			0
$457$	2613.10	−	1898.53i	0.267474	−	0.194332i	−0.445961	−	0.895052i	$-0.647138\pi$
$457$	2613.10	−	1898.53i	0.267474	−	0.194332i	0.713436	+	0.700721i	$0.247138\pi$
$458$		0			0
$459$	1188.55	−	3657.98i	0.120864	−	0.371983i
$460$		0			0
$461$	14797.9			1.49503			0.747515	−	0.664245i	$-0.231247\pi$
$461$	14797.9			1.49503			0.747515	+	0.664245i	$0.231247\pi$
$462$		0			0
$463$	11153.9			1.11958			0.559792	−	0.828633i	$-0.310881\pi$
$463$	11153.9			1.11958			0.559792	+	0.828633i	$0.310881\pi$
$464$		0			0
$465$	21.8557	−	67.2650i	0.00217965	−	0.00670826i
$466$		0			0
$467$	15388.0	−	11180.1i	1.52478	−	1.10782i	0.565731	−	0.824590i	$-0.308594\pi$
$467$	15388.0	−	11180.1i	1.52478	−	1.10782i	0.959052	−	0.283230i	$-0.0914058\pi$
$468$		0			0
$469$	5805.55	+	17867.6i	0.571589	+	1.75917i
$470$		0			0
$471$	−4226.42	−	3070.67i	−0.413467	−	0.300401i
$472$		0			0
$473$	−16384.8	−	1759.81i	−1.59276	−	0.171070i
$474$		0			0
$475$	10875.9	+	7901.81i	1.05057	+	0.763284i
$476$		0			0
$477$	−1590.38	−	4894.69i	−0.152660	−	0.469838i
$478$		0			0
$479$	−8605.87	+	6252.53i	−0.820902	+	0.596420i	−0.916971	−	0.398954i	$-0.869373\pi$
$479$	−8605.87	+	6252.53i	−0.820902	+	0.596420i	0.0960686	+	0.995375i	$0.469373\pi$
$480$		0			0
$481$	1982.12	−	6100.34i	0.187894	−	0.578277i
$482$		0			0
$483$	22420.6			2.11216
$484$		0			0
$485$	35.9022			0.00336131
$486$		0			0
$487$	−2394.26	+	7368.77i	−0.222781	+	0.685648i	0.775729	+	0.631067i	$0.217383\pi$
$487$	−2394.26	+	7368.77i	−0.222781	+	0.685648i	−0.998509	+	0.0545818i	$0.982617\pi$
$488$		0			0
$489$	−481.707	+	349.980i	−0.0445471	+	0.0323654i
$490$		0			0
$491$	3106.85	+	9561.91i	0.285561	+	0.878865i	0.986230	+	0.165379i	$0.0528848\pi$
$491$	3106.85	+	9561.91i	0.285561	+	0.878865i	−0.700669	+	0.713486i	$0.747115\pi$
$492$		0			0
$493$	4834.52	+	3512.48i	0.441655	+	0.320881i
$494$		0			0
$495$	47.0094	+	5.04905i	0.00426852	+	0.000458460i
$496$		0			0
$497$	21997.6	+	15982.2i	1.98537	+	1.44245i
$498$		0			0
$499$	−1354.32	−	4168.18i	−0.121499	−	0.373935i	0.871748	−	0.489954i	$-0.162987\pi$
$499$	−1354.32	−	4168.18i	−0.121499	−	0.373935i	−0.993247	+	0.116019i	$0.962987\pi$
$500$		0			0
$501$	−3317.03	+	2409.96i	−0.295796	+	0.214909i
$502$		0			0
$503$	−1618.23	+	4980.40i	−0.143446	+	0.441482i	−0.996808	−	0.0798375i	$-0.974560\pi$
$503$	−1618.23	+	4980.40i	−0.143446	+	0.441482i	0.853362	+	0.521319i	$0.174560\pi$
$504$		0			0
$505$	−25.9386			−0.00228565
$506$		0			0
$507$	7157.51			0.626975
$508$		0			0
$509$	−1167.14	+	3592.10i	−0.101636	+	0.312804i	−0.988926	−	0.148408i	$-0.952585\pi$
$509$	−1167.14	+	3592.10i	−0.101636	+	0.312804i	0.887290	+	0.461212i	$0.152585\pi$
$510$		0			0
$511$	−20913.3	+	15194.4i	−1.81047	+	1.31538i
$512$		0			0
$513$	2626.98	+	8085.02i	0.226090	+	0.695833i
$514$		0			0
$515$	−3.35821	−	2.43988i	−0.000287341	−	0.000208765i
$516$		0			0
$517$	9084.69	−	20280.3i	0.772813	−	1.72519i
$518$		0			0
$519$	10885.9	+	7909.04i	0.920686	+	0.668918i
$520$		0			0
$521$	−25.1807	−	77.4982i	−0.00211744	−	0.00651681i	0.949992	−	0.312274i	$-0.101091\pi$
$521$	−25.1807	−	77.4982i	−0.00211744	−	0.00651681i	−0.952110	+	0.305757i	$0.901091\pi$
$522$		0			0
$523$	−12856.3	+	9340.68i	−1.07489	+	0.780955i	−0.976785	−	0.214221i	$-0.931279\pi$
$523$	−12856.3	+	9340.68i	−1.07489	+	0.780955i	−0.0981071	+	0.995176i	$0.531279\pi$
$524$		0			0
$525$	6099.96	−	18773.7i	0.507093	−	1.56067i
$526$		0			0
$527$	6069.28			0.501673
$528$		0			0
$529$	7987.49			0.656488
$530$		0			0
$531$	426.030	−	1311.19i	0.0348176	−	0.107157i
$532$		0			0
$533$	−4242.40	+	3082.29i	−0.344763	+	0.250485i
$534$		0			0
$535$	3.58889	+	11.0455i	0.000290021	+	0.000892593i
$536$		0			0
$537$	5469.96	+	3974.16i	0.439565	+	0.319363i
$538$		0			0
$539$	8039.16	−	4617.06i	0.642433	−	0.368963i
$540$		0			0
$541$	−5879.62	−	4271.79i	−0.467254	−	0.339480i	0.329116	−	0.944290i	$-0.393249\pi$
$541$	−5879.62	−	4271.79i	−0.467254	−	0.339480i	−0.796370	+	0.604809i	$0.793249\pi$
$542$		0			0
$543$	5103.30	+	15706.3i	0.403322	+	1.24130i
$544$		0			0
$545$	−94.1481	+	68.4026i	−0.00739975	+	0.00537623i
$546$		0			0
$547$	5387.74	−	16581.8i	0.421139	−	1.29613i	−0.485504	−	0.874234i	$-0.661364\pi$
$547$	5387.74	−	16581.8i	0.421139	−	1.29613i	0.906643	−	0.421898i	$-0.138636\pi$
$548$		0			0
$549$	6778.04			0.526921
$550$		0			0
$551$	−13207.9			−1.02119
$552$		0			0
$553$	370.266	−	1139.56i	0.0284726	−	0.0876295i
$554$		0			0
$555$	89.1487	−	64.7703i	0.00681829	−	0.00495378i
$556$		0			0
$557$	−3873.73	−	11922.1i	−0.294677	−	0.906922i	−0.983330	−	0.181831i	$-0.941798\pi$
$557$	−3873.73	−	11922.1i	−0.294677	−	0.906922i	0.688653	−	0.725091i	$-0.258202\pi$
$558$		0			0
$559$	12062.1	+	8763.62i	0.912651	+	0.663080i
$560$		0			0
$561$	2360.00	+	11228.5i	0.177610	+	0.845040i
$562$		0			0
$563$	3598.62	+	2614.55i	0.269385	+	0.195720i	0.714274	−	0.699866i	$-0.246757\pi$
$563$	3598.62	+	2614.55i	0.269385	+	0.195720i	−0.444889	+	0.895586i	$0.646757\pi$
$564$		0			0
$565$	35.6779	+	109.805i	0.00265660	+	0.00817618i
$566$		0			0
$567$	17982.6	−	13065.1i	1.33192	−	0.967697i
$568$		0			0
$569$	−2032.67	+	6255.91i	−0.149761	+	0.460916i	−0.997592	−	0.0693493i	$-0.977908\pi$
$569$	−2032.67	+	6255.91i	−0.149761	+	0.460916i	0.847832	+	0.530265i	$0.177908\pi$
$570$		0			0
$571$	−17109.0			−1.25392			−0.626962	−	0.779050i	$-0.715702\pi$
$571$	−17109.0			−1.25392			−0.626962	+	0.779050i	$0.715702\pi$
$572$		0			0
$573$	−3090.32			−0.225305
$574$		0			0
$575$	5483.42	−	16876.2i	0.397695	−	1.22398i
$576$		0			0
$577$	8517.64	−	6188.43i	0.614548	−	0.446495i	−0.236465	−	0.971640i	$-0.575989\pi$
$577$	8517.64	−	6188.43i	0.614548	−	0.446495i	0.851013	+	0.525145i	$0.175989\pi$
$578$		0			0
$579$	3534.14	+	10877.0i	0.253668	+	0.780709i
$580$		0			0
$581$	−19795.5	−	14382.3i	−1.41352	−	1.02699i
$582$		0			0
$583$	−9427.59	−	8527.56i	−0.669727	−	0.605790i
$584$		0			0
$585$	−34.6071	−	25.1436i	−0.00244586	−	0.00177702i
$586$		0			0
$587$	−4496.79	−	13839.7i	−0.316188	−	0.973127i	−0.975263	−	0.221049i	$-0.929052\pi$
$587$	−4496.79	−	13839.7i	−0.316188	−	0.973127i	0.659075	−	0.752078i	$-0.270948\pi$
$588$		0			0
$589$	−10852.6	+	7884.88i	−0.759209	+	0.551597i
$590$		0			0
$591$	1047.86	−	3224.97i	0.0729325	−	0.224463i
$592$		0			0
$593$	4585.83			0.317568			0.158784	−	0.987313i	$-0.449243\pi$
$593$	4585.83			0.317568			0.158784	+	0.987313i	$0.449243\pi$
$594$		0			0
$595$	−104.330			−0.00718845
$596$		0			0
$597$	−2120.76	+	6527.02i	−0.145388	+	0.447459i
$598$		0			0
$599$	19009.3	−	13811.0i	1.29666	−	0.942076i	0.296740	−	0.954958i	$-0.404101\pi$
$599$	19009.3	−	13811.0i	1.29666	−	0.942076i	0.999917	+	0.0128821i	$0.00410060\pi$
$600$		0			0
$601$	−1161.42	−	3574.49i	−0.0788276	−	0.242607i	0.903875	−	0.427796i	$-0.140710\pi$
$601$	−1161.42	−	3574.49i	−0.0788276	−	0.242607i	−0.982703	+	0.185190i	$0.940710\pi$
$602$		0			0
$603$	−9187.14	−	6674.85i	−0.620446	−	0.450781i
$604$		0			0
$605$	106.901	−	47.0136i	0.00718368	−	0.00315930i
$606$		0			0
$607$	−12705.8	−	9231.31i	−0.849610	−	0.617278i	0.0754287	−	0.997151i	$-0.475967\pi$
$607$	−12705.8	−	9231.31i	−0.849610	−	0.617278i	−0.925038	+	0.379874i	$0.875967\pi$
$608$		0			0
$609$	5993.13	+	18444.9i	0.398775	+	1.22730i
$610$		0			0
$611$	−16265.8	+	11817.8i	−1.07699	+	0.782481i
$612$		0			0
$613$	844.131	−	2597.97i	0.0556185	−	0.171176i	−0.919388	−	0.393351i	$-0.871316\pi$
$613$	844.131	−	2597.97i	0.0556185	−	0.171176i	0.975007	+	0.222175i	$0.0713157\pi$
$614$		0			0
$615$	−90.0874			−0.00590679
$616$		0			0
$617$	3140.17			0.204892			0.102446	−	0.994739i	$-0.467333\pi$
$617$	3140.17			0.204892			0.102446	+	0.994739i	$0.467333\pi$
$618$		0			0
$619$	−1608.42	+	4950.20i	−0.104439	+	0.321430i	−0.989598	−	0.143858i	$-0.954049\pi$
$619$	−1608.42	+	4950.20i	−0.104439	+	0.321430i	0.885159	+	0.465288i	$0.154049\pi$
$620$		0			0
$621$	9078.07	−	6595.60i	0.586619	−	0.426204i
$622$		0			0
$623$	7164.88	+	22051.2i	0.460762	+	1.41808i
$624$		0			0
$625$	−12638.6	−	9182.45i	−0.808868	−	0.587677i
$626$		0			0
$627$	−18807.4	−	17011.9i	−1.19792	−	1.08356i
$628$		0			0
$629$	7650.13	+	5558.15i	0.484946	+	0.352334i
$630$		0			0
$631$	−6703.88	−	20632.4i	−0.422943	−	1.30169i	−0.904950	−	0.425518i	$-0.860092\pi$
$631$	−6703.88	−	20632.4i	−0.422943	−	1.30169i	0.482007	−	0.876168i	$-0.339908\pi$
$632$		0			0
$633$	−28099.0	+	20415.1i	−1.76435	+	1.28188i
$634$		0			0
$635$	9.35913	−	28.8044i	0.000584891	−	0.00180011i
$636$		0			0
$637$	−8387.71			−0.521716
$638$		0			0
$639$	−16435.4			−1.01749
$640$		0			0
$641$	−8989.68	+	27667.4i	−0.553933	+	1.70483i	0.144813	+	0.989459i	$0.453742\pi$
$641$	−8989.68	+	27667.4i	−0.553933	+	1.70483i	−0.698745	+	0.715371i	$0.746258\pi$
$642$		0			0
$643$	−19584.2	+	14228.7i	−1.20113	+	0.872670i	−0.994395	−	0.105728i	$-0.966283\pi$
$643$	−19584.2	+	14228.7i	−1.20113	+	0.872670i	−0.206732	+	0.978398i	$0.566283\pi$
$644$		0			0
$645$	79.1511	+	243.602i	0.00483190	+	0.0148710i
$646$		0			0
$647$	10682.0	+	7760.90i	0.649075	+	0.471580i	0.862956	−	0.505279i	$-0.168611\pi$
$647$	10682.0	+	7760.90i	0.649075	+	0.471580i	−0.213881	+	0.976860i	$0.568611\pi$
$648$		0			0
$649$	−700.426	−	3332.51i	−0.0423638	−	0.201560i
$650$		0			0
$651$	15935.7	+	11577.9i	0.959398	+	0.697043i
$652$		0			0
$653$	−5960.77	−	18345.4i	−0.357217	−	1.09940i	−0.954713	−	0.297529i	$-0.903837\pi$
$653$	−5960.77	−	18345.4i	−0.357217	−	1.09940i	0.597495	−	0.801872i	$-0.296163\pi$
$654$		0			0
$655$	−2.24915	+	1.63410i	−0.000134170	+	9.74805e-5i
$656$		0			0
$657$	4828.47	−	14860.5i	0.286722	−	0.882440i
$658$		0			0
$659$	7086.80			0.418911			0.209456	−	0.977818i	$-0.432831\pi$
$659$	7086.80			0.418911			0.209456	+	0.977818i	$0.432831\pi$
$660$		0			0
$661$	−23077.2			−1.35794			−0.678969	−	0.734167i	$-0.737573\pi$
$661$	−23077.2			−1.35794			−0.678969	+	0.734167i	$0.737573\pi$
$662$		0			0
$663$	3207.92	−	9872.95i	0.187911	−	0.578331i
$664$		0			0
$665$	186.555	−	135.540i	0.0108786	−	0.00790380i
$666$		0			0
$667$	5387.39	+	16580.7i	0.312744	+	0.962528i
$668$		0			0
$669$	−6032.02	−	4382.52i	−0.348597	−	0.253271i
$670$		0			0
$671$	14517.9	−	8337.93i	0.835256	−	0.479705i
$672$		0			0
$673$	−18632.1	−	13537.0i	−1.06718	−	0.775355i	−0.0917806	−	0.995779i	$-0.529256\pi$
$673$	−18632.1	−	13537.0i	−1.06718	−	0.775355i	−0.975404	+	0.220424i	$0.929256\pi$
$674$		0			0
$675$	−3052.92	−	9395.92i	−0.174084	−	0.535777i
$676$		0			0
$677$	23003.6	−	16713.1i	1.30591	−	0.948798i	0.305913	−	0.952059i	$-0.401038\pi$
$677$	23003.6	−	16713.1i	1.30591	−	0.948798i	0.999995	+	0.00326149i	$0.00103817\pi$
$678$		0			0
$679$	−3089.82	+	9509.48i	−0.174634	+	0.537467i
$680$		0			0
$681$	39255.9			2.20894
$682$		0			0
$683$	−11600.3			−0.649887			−0.324943	−	0.945733i	$-0.605345\pi$
$683$	−11600.3			−0.649887			−0.324943	+	0.945733i	$0.605345\pi$
$684$		0			0
$685$	−25.8921	+	79.6877i	−0.00144421	+	0.00444483i
$686$		0			0
$687$	−14393.4	+	10457.4i	−0.799334	+	0.580751i
$688$		0			0
$689$	3554.13	+	10938.5i	0.196519	+	0.604824i
$690$		0			0
$691$	14094.9	+	10240.5i	0.775967	+	0.563773i	0.903766	−	0.428027i	$-0.140791\pi$
$691$	14094.9	+	10240.5i	0.775967	+	0.563773i	−0.127799	+	0.991800i	$0.540791\pi$
$692$		0			0
$693$	−5383.08	+	12017.0i	−0.295074	+	0.658710i
$694$		0			0
$695$	98.4207	+	71.5069i	0.00537167	+	0.00390275i
$696$		0			0
$697$	−2388.91	−	7352.32i	−0.129823	−	0.399554i
$698$		0			0
$699$	−15444.8	+	11221.3i	−0.835729	+	0.607192i
$700$		0			0
$701$	397.990	−	1224.89i	0.0214435	−	0.0659963i	−0.939762	−	0.341829i	$-0.888954\pi$
$701$	397.990	−	1224.89i	0.0214435	−	0.0659963i	0.961206	+	0.275833i	$0.0889536\pi$
$702$		0			0
$703$	−20900.2			−1.12129
$704$		0			0
$705$	−345.404			−0.0184520
$706$		0			0
$707$	2232.33	−	6870.40i	0.118749	−	0.365471i
$708$		0			0
$709$	−2497.89	+	1814.82i	−0.132313	+	0.0961313i	−0.651973	−	0.758242i	$-0.726059\pi$
$709$	−2497.89	+	1814.82i	−0.132313	+	0.0961313i	0.519660	+	0.854373i	$0.326059\pi$
$710$		0			0
$711$	223.808	+	688.811i	0.0118052	+	0.0363325i
$712$		0			0
$713$	14325.0	+	10407.7i	0.752421	+	0.546666i
$714$		0			0
$715$	−105.055	−	11.2834i	−0.00549488	−	0.000590177i
$716$		0			0
$717$	−28724.9	−	20869.9i	−1.49617	−	1.08703i
$718$		0			0
$719$	5534.31	+	17032.9i	0.287058	+	0.883475i	0.985774	+	0.168075i	$0.0537552\pi$
$719$	5534.31	+	17032.9i	0.287058	+	0.883475i	−0.698716	+	0.715399i	$0.746245\pi$
$720$		0			0
$721$	935.272	−	679.515i	0.0483098	−	0.0350991i
$722$		0			0
$723$	−8065.00	+	24821.5i	−0.414856	+	1.27679i
$724$		0			0
$725$	15349.5			0.786296
$726$		0			0
$727$	−5694.09			−0.290484			−0.145242	−	0.989396i	$-0.546396\pi$
$727$	−5694.09			−0.290484			−0.145242	+	0.989396i	$0.546396\pi$
$728$		0			0
$729$	110.333	−	339.570i	0.00560549	−	0.0172519i
$730$		0			0
$731$	−17782.2	+	12919.6i	−0.899726	+	0.653689i
$732$		0			0
$733$	3107.21	+	9563.00i	0.156572	+	0.481879i	0.998317	−	0.0579964i	$-0.0184712\pi$
$733$	3107.21	+	9563.00i	0.156572	+	0.481879i	−0.841745	+	0.539876i	$0.818471\pi$
$734$		0			0
$735$	−116.577	−	84.6978i	−0.00585033	−	0.00425051i
$736$		0			0
$737$	−27888.9	−	2995.41i	−1.39390	−	0.149711i
$738$		0			0
$739$	−7036.60	−	5112.39i	−0.350264	−	0.254482i	0.398716	−	0.917075i	$-0.369456\pi$
$739$	−7036.60	−	5112.39i	−0.350264	−	0.254482i	−0.748980	+	0.662593i	$0.769456\pi$
$740$		0			0
$741$	7090.26	+	21821.6i	0.351508	+	1.08183i
$742$		0			0
$743$	21819.4	−	15852.7i	1.07736	−	0.782747i	0.100138	−	0.994974i	$-0.468072\pi$
$743$	21819.4	−	15852.7i	1.07736	−	0.782747i	0.977220	+	0.212227i	$0.0680716\pi$
$744$		0			0
$745$	−71.8936	+	221.266i	−0.00353554	+	0.0108813i
$746$		0			0
$747$	14790.1			0.724420
$748$		0			0
$749$	−3234.50			−0.157792
$750$		0			0
$751$	11956.7	−	36799.0i	0.580968	−	1.78804i	−0.0339219	−	0.999424i	$-0.510800\pi$
$751$	11956.7	−	36799.0i	0.580968	−	1.78804i	0.614890	−	0.788613i	$-0.289200\pi$
$752$		0			0
$753$	−23368.7	+	16978.4i	−1.13095	+	0.821681i
$754$		0			0
$755$	54.7559	+	168.521i	0.00263943	+	0.00812334i
$756$		0			0
$757$	10367.6	+	7532.50i	0.497776	+	0.361656i	0.808167	−	0.588953i	$-0.200460\pi$
$757$	10367.6	+	7532.50i	0.497776	+	0.361656i	−0.310391	+	0.950609i	$0.600460\pi$
$758$		0			0
$759$	−13684.7	+	30549.0i	−0.654443	+	1.46095i
$760$		0			0
$761$	13486.3	+	9798.38i	0.642416	+	0.466742i	0.860679	−	0.509147i	$-0.170039\pi$
$761$	13486.3	+	9798.38i	0.642416	+	0.466742i	−0.218263	+	0.975890i	$0.570039\pi$
$762$		0			0
$763$	−10015.3	−	30824.1i	−0.475203	−	1.46252i
$764$		0			0
$765$	51.0188	−	37.0673i	0.00241122	−	0.00175186i
$766$		0			0
$767$	−952.078	+	2930.20i	−0.0448208	+	0.137944i
$768$		0			0
$769$	3634.44			0.170431			0.0852154	−	0.996363i	$-0.472842\pi$
$769$	3634.44			0.170431			0.0852154	+	0.996363i	$0.472842\pi$
$770$		0			0
$771$	30622.9			1.43042
$772$		0			0
$773$	7622.28	−	23459.0i	0.354663	−	1.09154i	−0.601542	−	0.798841i	$-0.705447\pi$
$773$	7622.28	−	23459.0i	0.354663	−	1.09154i	0.956205	−	0.292699i	$-0.0945533\pi$
$774$		0			0
$775$	12612.2	−	9163.33i	0.584575	−	0.424718i
$776$		0			0
$777$	9483.52	+	29187.3i	0.437863	+	1.34760i
$778$		0			0
$779$	13823.4	+	10043.3i	0.635783	+	0.461924i
$780$		0			0
$781$	−35203.0	+	20217.8i	−1.61288	+	0.926312i
$782$		0			0
$783$	7852.67	+	5705.30i	0.358406	+	0.260397i
$784$		0			0
$785$	21.9160	+	67.4505i	0.000996452	+	0.00306676i
$786$		0			0
$787$	13567.4	−	9857.28i	0.614517	−	0.446473i	−0.236485	−	0.971635i	$-0.575995\pi$
$787$	13567.4	−	9857.28i	0.614517	−	0.446473i	0.851002	+	0.525162i	$0.175995\pi$
$788$		0			0
$789$	7874.14	−	24234.1i	0.355294	−	1.09348i
$790$		0			0
$791$	−32154.8			−1.44538
$792$		0			0
$793$	−15147.3			−0.678307
$794$		0			0
$795$	−61.0582	+	187.918i	−0.00272391	+	0.00838334i
$796$		0			0
$797$	−7743.18	+	5625.75i	−0.344137	+	0.250031i	−0.746405	−	0.665491i	$-0.768222\pi$
$797$	−7743.18	+	5625.75i	−0.344137	+	0.250031i	0.402268	+	0.915522i	$0.368222\pi$
$798$		0			0
$799$	−9159.33	−	28189.5i	−0.405549	−	1.24815i
$800$		0			0
$801$	−11338.2	−	8237.72i	−0.500147	−	0.363378i
$802$		0			0
$803$	−7938.37	−	37769.4i	−0.348866	−	1.65984i
$804$		0			0
$805$	−246.246	−	178.908i	−0.0107814	−	0.00783314i
$806$		0			0
$807$	6795.31	+	20913.8i	0.296414	+	0.912269i
$808$		0			0
$809$	35581.6	−	25851.5i	1.54633	−	1.12348i	0.600127	−	0.799905i	$-0.295117\pi$
$809$	35581.6	−	25851.5i	1.54633	−	1.12348i	0.946204	−	0.323570i	$-0.104883\pi$
$810$		0			0
$811$	9261.50	−	28504.0i	0.401005	−	1.23417i	−0.523180	−	0.852222i	$-0.675255\pi$
$811$	9261.50	−	28504.0i	0.401005	−	1.23417i	0.924185	−	0.381945i	$-0.124745\pi$
$812$		0			0
$813$	25748.7			1.11076
$814$		0			0
$815$	8.08330			0.000347418
$816$		0			0
$817$	15012.4	−	46203.5i	0.642862	−	1.97852i
$818$		0			0
$819$	9638.19	−	7002.55i	0.411216	−	0.298766i
$820$		0			0
$821$	−375.536	−	1155.78i	−0.0159638	−	0.0491315i	0.942757	−	0.333480i	$-0.108223\pi$
$821$	−375.536	−	1155.78i	−0.0159638	−	0.0491315i	−0.958721	+	0.284348i	$0.908223\pi$
$822$		0			0
$823$	−7685.49	−	5583.83i	−0.325515	−	0.236501i	0.413010	−	0.910727i	$-0.364477\pi$
$823$	−7685.49	−	5583.83i	−0.325515	−	0.236501i	−0.738525	+	0.674226i	$0.764477\pi$
$824$		0			0
$825$	21856.9	+	19770.2i	0.922374	+	0.834316i
$826$		0			0
$827$	−23256.2	−	16896.6i	−0.977867	−	0.710462i	−0.0206363	−	0.999787i	$-0.506569\pi$
$827$	−23256.2	−	16896.6i	−0.977867	−	0.710462i	−0.957231	+	0.289325i	$0.906569\pi$
$828$		0			0
$829$	3821.03	+	11759.9i	0.160084	+	0.492688i	0.998640	−	0.0521265i	$-0.0165999\pi$
$829$	3821.03	+	11759.9i	0.160084	+	0.492688i	−0.838556	+	0.544815i	$0.816600\pi$
$830$		0			0
$831$	18494.2	−	13436.8i	0.772029	−	0.560912i
$832$		0			0
$833$	3821.11	−	11760.2i	0.158936	−	0.489155i
$834$		0			0
$835$	55.6616			0.00230689
$836$		0			0
$837$	9858.29			0.407111
$838$		0			0
$839$	987.035	−	3037.78i	0.0406153	−	0.125001i	−0.928693	−	0.370850i	$-0.879067\pi$
$839$	987.035	−	3037.78i	0.0406153	−	0.125001i	0.969308	+	0.245848i	$0.0790666\pi$
$840$		0			0
$841$	7530.62	−	5471.31i	0.308771	−	0.224335i
$842$		0			0
$843$	8743.00	+	26908.2i	0.357206	+	1.09937i
$844$		0			0
$845$	−78.6111	−	57.1143i	−0.00320036	−	0.00232520i
$846$		0			0
$847$	3252.49	+	32361.1i	0.131944	+	1.31280i
$848$		0			0
$849$	−12976.6	−	9428.04i	−0.524564	−	0.381118i
$850$		0			0
$851$	8525.00	+	26237.2i	0.343400	+	1.05688i
$852$		0			0
$853$	−4823.75	+	3504.66i	−0.193625	+	0.140677i	−0.680374	−	0.732865i	$-0.738183\pi$
$853$	−4823.75	+	3504.66i	−0.193625	+	0.140677i	0.486749	+	0.873542i	$0.338183\pi$
$854$		0			0
$855$	−43.0719	+	132.562i	−0.00172284	+	0.00530235i
$856$		0			0
$857$	−17358.2			−0.691886			−0.345943	−	0.938256i	$-0.612441\pi$
$857$	−17358.2			−0.691886			−0.345943	+	0.938256i	$0.612441\pi$
$858$		0			0
$859$	22138.3			0.879337			0.439669	−	0.898160i	$-0.355096\pi$
$859$	22138.3			0.879337			0.439669	+	0.898160i	$0.355096\pi$
$860$		0			0
$861$	7753.11	−	23861.6i	0.306882	−	0.944486i
$862$		0			0
$863$	−9045.97	+	6572.28i	−0.356811	+	0.259239i	−0.751721	−	0.659481i	$-0.770776\pi$
$863$	−9045.97	+	6572.28i	−0.356811	+	0.259239i	0.394910	+	0.918720i	$0.370776\pi$
$864$		0			0
$865$	−56.4484	−	173.730i	−0.00221885	−	0.00682891i
$866$		0			0
$867$	−13307.3	−	9668.30i	−0.521267	−	0.378723i
$868$		0			0
$869$	1326.71	+	1200.05i	0.0517900	+	0.0468457i
$870$		0			0
$871$	20531.1	+	14916.7i	0.798703	+	0.580292i
$872$		0			0
$873$	−1867.65	−	5748.02i	−0.0724058	−	0.222842i
$874$		0			0
$875$	−433.620	+	315.043i	−0.0167532	+	0.0121719i
$876$		0			0
$877$	−3444.19	+	10600.1i	−0.132614	+	0.408143i	−0.995211	−	0.0977480i	$-0.968836\pi$
$877$	−3444.19	+	10600.1i	−0.132614	+	0.408143i	0.862598	+	0.505891i	$0.168836\pi$
$878$		0			0
$879$	28878.6			1.10813
$880$		0			0
$881$	−35280.1			−1.34917			−0.674584	−	0.738198i	$-0.735677\pi$
$881$	−35280.1			−1.34917			−0.674584	+	0.738198i	$0.735677\pi$
$882$		0			0
$883$	−227.794	+	701.077i	−0.00868162	+	0.0267193i	−0.955303	−	0.295627i	$-0.904471\pi$
$883$	−227.794	+	701.077i	−0.00868162	+	0.0267193i	0.946622	+	0.322346i	$0.104471\pi$
$884$		0			0
$885$	−42.8211	+	31.1114i	−0.00162646	+	0.00118169i
$886$		0			0
$887$	5692.40	+	17519.4i	0.215481	+	0.663184i	0.999119	+	0.0419654i	$0.0133619\pi$
$887$	5692.40	+	17519.4i	0.215481	+	0.663184i	−0.783638	+	0.621218i	$0.786638\pi$
$888$		0			0
$889$	6824.02	+	4957.94i	0.257447	+	0.187046i
$890$		0			0
$891$	6825.92	+	32476.6i	0.256652	+	1.22111i
$892$		0			0
$893$	53000.3	+	38507.0i	1.98610	+	1.44299i
$894$		0			0
$895$	−28.3644	−	87.2965i	−0.00105935	−	0.00326034i
$896$		0			0
$897$	24501.8	−	17801.6i	0.912032	−	0.662630i
$898$		0			0
$899$	−4733.08	+	14566.9i	−0.175592	+	0.540416i
$900$		0			0
$901$	−16955.7			−0.626943
$902$		0			0
$903$	−71335.3			−2.62889
$904$		0			0
$905$	69.2811	−	213.225i	0.00254473	−	0.00783188i
$906$		0			0
$907$	7557.11	−	5490.56i	0.276659	−	0.201005i	−0.440800	−	0.897605i	$-0.645305\pi$
$907$	7557.11	−	5490.56i	0.276659	−	0.201005i	0.717459	+	0.696601i	$0.245305\pi$
$908$		0			0
$909$	1349.34	+	4152.83i	0.0492350	+	0.151530i
$910$		0			0
$911$	24562.2	+	17845.5i	0.893286	+	0.649010i	0.936733	−	0.350046i	$-0.113834\pi$
$911$	24562.2	+	17845.5i	0.893286	+	0.649010i	−0.0434471	+	0.999056i	$0.513834\pi$
$912$		0			0
$913$	31679.0	−	18193.9i	1.14833	−	0.659507i
$914$		0			0
$915$	−210.525	−	152.955i	−0.00760628	−	0.00552629i
$916$		0			0
$917$	−239.262	−	736.371i	−0.00861626	−	0.0265181i
$918$		0			0
$919$	23333.6	−	16952.9i	0.837547	−	0.608514i	−0.0841370	−	0.996454i	$-0.526813\pi$
$919$	23333.6	−	16952.9i	0.837547	−	0.608514i	0.921684	+	0.387940i	$0.126813\pi$
$920$		0			0
$921$	−7250.69	+	22315.3i	−0.259412	+	0.798387i
$922$		0			0
$923$	36729.2			1.30981
$924$		0			0
$925$	24289.0			0.863369
$926$		0			0
$927$	−215.936	+	664.581i	−0.00765076	+	0.0235466i
$928$		0			0
$929$	239.373	−	173.914i	0.00845378	−	0.00614203i	−0.583550	−	0.812077i	$-0.698337\pi$
$929$	239.373	−	173.914i	0.00845378	−	0.00614203i	0.592004	+	0.805935i	$0.298337\pi$
$930$		0			0
$931$	8445.58	+	25992.8i	0.297307	+	0.915016i
$932$		0			0
$933$	45883.6	+	33336.4i	1.61003	+	1.16976i
$934$		0			0
$935$	63.6792	−	142.155i	0.00222731	−	0.00497214i
$936$		0			0
$937$	−40061.2	−	29106.2i	−1.39674	−	1.01479i	−0.995088	−	0.0989944i	$-0.968437\pi$
$937$	−40061.2	−	29106.2i	−1.39674	−	1.01479i	−0.401648	−	0.915794i	$-0.631563\pi$
$938$		0			0
$939$	−6732.78	−	20721.4i	−0.233989	−	0.720145i
$940$		0			0
$941$	17130.7	−	12446.2i	0.593457	−	0.431172i	−0.250093	−	0.968222i	$-0.580461\pi$
$941$	17130.7	−	12446.2i	0.593457	−	0.431172i	0.843551	+	0.537050i	$0.180461\pi$
$942$		0			0
$943$	6969.49	−	21449.9i	0.240676	−	0.740726i
$944$		0			0
$945$	−169.463			−0.00583347
$946$		0			0
$947$	−26386.2			−0.905425			−0.452713	−	0.891656i	$-0.649544\pi$
$947$	−26386.2			−0.905425			−0.452713	+	0.891656i	$0.649544\pi$
$948$		0			0
$949$	−10790.5	+	33209.8i	−0.369099	+	1.13597i
$950$		0			0
$951$	−23602.5	+	17148.2i	−0.804799	+	0.584721i
$952$		0			0
$953$	7402.76	+	22783.4i	0.251625	+	0.774423i	0.994476	+	0.104966i	$0.0334733\pi$
$953$	7402.76	+	22783.4i	0.251625	+	0.774423i	−0.742850	+	0.669457i	$0.766527\pi$
$954$		0			0
$955$	33.9410	+	24.6596i	0.00115006	+	0.000835566i
$956$		0			0
$957$	−28790.0	−	3092.19i	−0.972466	−	0.104448i
$958$		0			0
$959$	−18878.7	−	13716.2i	−0.635688	−	0.461854i
$960$		0			0
$961$	−4398.80	−	13538.1i	−0.147655	−	0.454436i
$962$		0			0
$963$	1581.71	−	1149.18i	0.0529282	−	0.0384546i
$964$		0			0
$965$	47.9786	−	147.663i	0.00160050	−	0.00492584i
$966$		0			0
$967$	18414.5			0.612380			0.306190	−	0.951970i	$-0.400946\pi$
$967$	18414.5			0.612380			0.306190	+	0.951970i	$0.400946\pi$
$968$		0			0
$969$	−33825.5			−1.12139
$970$		0			0
$971$	10283.3	−	31648.7i	0.339863	−	1.04599i	−0.624414	−	0.781094i	$-0.714662\pi$
$971$	10283.3	−	31648.7i	0.339863	−	1.04599i	0.964277	−	0.264897i	$-0.0853379\pi$
$972$		0			0
$973$	−27410.5	+	19914.9i	−0.903123	+	0.656157i
$974$		0			0
$975$	−8239.88	−	25359.7i	−0.270654	−	0.832986i
$976$		0			0
$977$	6788.12	+	4931.86i	0.222284	+	0.161499i	0.693354	−	0.720597i	$-0.256132\pi$
$977$	6788.12	+	4931.86i	0.222284	+	0.161499i	−0.471070	+	0.882096i	$0.656132\pi$
$978$		0			0
$979$	−34419.0	−	3696.76i	−1.12363	−	0.120683i
$980$		0			0
$981$	15849.0	+	11515.0i	0.515822	+	0.374766i
$982$		0			0
$983$	16958.8	+	52193.7i	0.550255	+	1.69351i	0.708157	+	0.706055i	$0.249527\pi$
$983$	16958.8	+	52193.7i	0.550255	+	1.69351i	−0.157902	+	0.987455i	$0.550473\pi$
$984$		0			0
$985$	−37.2427	+	27.0584i	−0.00120472	+	0.000875282i
$986$		0			0
$987$	29726.2	−	91487.8i	0.958657	−	2.95044i
$988$		0			0
$989$	−64125.3			−2.06174
$990$		0			0
$991$	−45505.7			−1.45866			−0.729332	−	0.684160i	$-0.760169\pi$
$991$	−45505.7			−1.45866			−0.729332	+	0.684160i	$0.760169\pi$
$992$		0			0
$993$	1149.04	−	3536.37i	0.0367206	−	0.113014i
$994$		0			0
$995$	75.3755	−	54.7635i	0.00240157	−	0.00174484i
$996$		0			0
$997$	1010.97	+	3111.44i	0.0321141	+	0.0988369i	0.965829	−	0.259181i	$-0.0834526\pi$
$997$	1010.97	+	3111.44i	0.0321141	+	0.0988369i	−0.933715	+	0.358018i	$0.883453\pi$
$998$		0			0
$999$	12426.1	+	9028.06i	0.393537	+	0.285921i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	176.4.m.d.81.1		12
4.3	odd	2		44.4.e.a.37.3	yes	12
11.3	even	5	inner	176.4.m.d.113.1		12
11.5	even	5		1936.4.a.br.1.2		6
11.6	odd	10		1936.4.a.bs.1.2		6
12.11	even	2		396.4.j.d.37.2		12
44.3	odd	10		44.4.e.a.25.3	✓	12
44.27	odd	10		484.4.a.i.1.5		6
44.39	even	10		484.4.a.h.1.5		6
132.47	even	10		396.4.j.d.289.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.4.e.a.25.3	✓	12	44.3	odd	10
44.4.e.a.37.3	yes	12	4.3	odd	2
176.4.m.d.81.1		12	1.1	even	1	trivial
176.4.m.d.113.1		12	11.3	even	5	inner
396.4.j.d.37.2		12	12.11	even	2
396.4.j.d.289.2		12	132.47	even	10
484.4.a.h.1.5		6	44.39	even	10
484.4.a.i.1.5		6	44.27	odd	10
1936.4.a.br.1.2		6	11.5	even	5
1936.4.a.bs.1.2		6	11.6	odd	10

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:	\( N \)	\(=\)	\( 176 = 2^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	176.m (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.99717 + 6.14667i) q^{3} +(0.0709832 - 0.0515723i) q^{5} +(7.55109 + 23.2399i) q^{7} +(-11.9494 - 8.68176i) q^{9} +(-36.2742 - 3.89603i) q^{11} +(26.7042 + 19.4017i) q^{13} +(0.175232 + 0.539309i) q^{15} +(-39.3680 + 28.6025i) q^{17} +(33.2359 - 102.290i) q^{19} -157.929 q^{21} -141.967 q^{23} +(-38.6247 + 118.875i) q^{25} +(-63.9451 + 46.4589i) q^{27} +(-37.9483 - 116.793i) q^{29} +(-100.904 - 73.3112i) q^{31} +(96.3936 - 215.185i) q^{33} +(1.73453 + 1.26021i) q^{35} +(-60.0493 - 184.813i) q^{37} +(-172.589 + 125.393i) q^{39} +(-49.0925 + 151.091i) q^{41} +451.693 q^{43} -1.29595 q^{45} +(-188.225 + 579.298i) q^{47} +(-205.580 + 149.362i) q^{49} +(-97.1855 - 299.106i) q^{51} +(281.895 + 204.809i) q^{53} +(-2.77579 + 1.59419i) q^{55} +(562.362 + 408.580i) q^{57} +(28.8437 + 88.7718i) q^{59} +(-371.255 + 269.733i) q^{61} +(111.532 - 343.260i) q^{63} +2.89614 q^{65} +768.836 q^{67} +(283.532 - 872.622i) q^{69} +(900.219 - 654.047i) q^{71} +(326.904 + 1006.11i) q^{73} +(-653.544 - 474.827i) q^{75} +(-183.367 - 872.428i) q^{77} +(-39.6700 - 28.8219i) q^{79} +(-281.093 - 865.116i) q^{81} +(-810.103 + 588.574i) q^{83} +(-1.31937 + 4.06059i) q^{85} +793.677 q^{87} +948.854 q^{89} +(-249.248 + 767.105i) q^{91} +(652.143 - 473.810i) q^{93} +(-2.91612 - 8.97488i) q^{95} +(331.040 + 240.515i) q^{97} +(399.632 + 361.480i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} - 4 q^{5} - 6 q^{7} + 47 q^{9} - 39 q^{11} - 10 q^{13} - 74 q^{15} - 56 q^{17} + 141 q^{19} - 304 q^{21} + 388 q^{23} - 203 q^{25} + 331 q^{27} + 772 q^{29} - 882 q^{31} + 981 q^{33} - 412 q^{35}+ \cdots - 3563 q^{99}+O(q^{100}) \) 12 * q + 4 * q^3 - 4 * q^5 - 6 * q^7 + 47 * q^9 - 39 * q^11 - 10 * q^13 - 74 * q^15 - 56 * q^17 + 141 * q^19 - 304 * q^21 + 388 * q^23 - 203 * q^25 + 331 * q^27 + 772 * q^29 - 882 * q^31 + 981 * q^33 - 412 * q^35 - 192 * q^37 + 154 * q^39 - 180 * q^41 + 2330 * q^43 - 1340 * q^45 - 196 * q^47 - 973 * q^49 - 2969 * q^51 + 2246 * q^53 - 2672 * q^55 + 431 * q^57 + 1099 * q^59 - 470 * q^61 + 2008 * q^63 - 3892 * q^65 + 4394 * q^67 - 1394 * q^69 + 2084 * q^71 + 2824 * q^73 - 4623 * q^75 + 3654 * q^77 - 838 * q^79 + 1518 * q^81 - 789 * q^83 - 2632 * q^85 + 3036 * q^87 - 954 * q^89 - 2460 * q^91 - 808 * q^93 - 4362 * q^95 + 2651 * q^97 - 3563 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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