LMFDB - Embedded newform 176.4.m.e.81.2

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)

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")

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);

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 = [16,0,1] 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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 60 x^{14} - 83 x^{13} + 1685 x^{12} - 14618 x^{11} + 106543 x^{10} - 521269 x^{9} + \cdots + 2025 $ x^16 - 4x^15 + 60x^14 - 83x^13 + 1685x^12 - 14618x^11 + 106543x^10 - 521269x^9 + 3907139x^8 - 15948298x^7 + 37290102x^6 - 37052438x^5 + 40742731x^4 + 4262985x^3 + 9787185x^2 + 227475*x + 2025
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.2
Root			$-1.72876 - 5.32058i$ of defining polynomial
Character	$\chi$	$=$	176.81
Dual form			176.4.m.e.113.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.320520 + 0.986460i) q^{3} +(-7.72334 + 5.61133i) q^{5} +(-5.56367 - 17.1232i) q^{7} +(20.9731 + 15.2378i) q^{9} +(-10.0276 - 35.0777i) q^{11} +(-13.3294 - 9.68440i) q^{13} +(-3.05987 - 9.41731i) q^{15} +(64.6073 - 46.9400i) q^{17} +(44.2970 - 136.332i) q^{19} +18.6746 q^{21} +45.6230 q^{23} +(-10.4642 + 32.2056i) q^{25} +(-44.4104 + 32.2661i) q^{27} +(-45.4975 - 140.027i) q^{29} +(-12.6239 - 9.17179i) q^{31} +(37.8168 + 1.35125i) q^{33} +(139.054 + 101.029i) q^{35} +(-89.0157 - 273.962i) q^{37} +(13.8256 - 10.0449i) q^{39} +(92.6741 - 285.221i) q^{41} -125.686 q^{43} -247.487 q^{45} +(9.79610 - 30.1493i) q^{47} +(15.2430 - 11.0747i) q^{49} +(25.5964 + 78.7778i) q^{51} +(421.520 + 306.252i) q^{53} +(274.280 + 214.649i) q^{55} +(120.288 + 87.3943i) q^{57} +(70.9340 + 218.312i) q^{59} +(-600.426 + 436.235i) q^{61} +(144.233 - 443.905i) q^{63} +157.290 q^{65} -505.264 q^{67} +(-14.6231 + 45.0053i) q^{69} +(-689.250 + 500.769i) q^{71} +(74.0022 + 227.755i) q^{73} +(-28.4155 - 20.6451i) q^{75} +(-544.853 + 366.866i) q^{77} +(-592.086 - 430.175i) q^{79} +(198.702 + 611.543i) q^{81} +(476.872 - 346.468i) q^{83} +(-235.588 + 725.067i) q^{85} +152.714 q^{87} +663.369 q^{89} +(-91.6674 + 282.123i) q^{91} +(13.0938 - 9.51322i) q^{93} +(422.884 + 1301.50i) q^{95} +(1103.42 + 801.685i) q^{97} +(324.198 - 888.488i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{3} - q^{5} + 13 q^{7} + 7 q^{9} - 83 q^{11} + 69 q^{13} - 93 q^{15} - 217 q^{17} - 126 q^{19} + 34 q^{21} + 92 q^{23} + 307 q^{25} - 158 q^{27} - 553 q^{29} - 205 q^{31} - 198 q^{33} - 7 q^{35}+ \cdots + 3265 q^{99}+O(q^{100}) $ 16 * q + q^3 - q^5 + 13 * q^7 + 7 * q^9 - 83 * q^11 + 69 * q^13 - 93 * q^15 - 217 * q^17 - 126 * q^19 + 34 * q^21 + 92 * q^23 + 307 * q^25 - 158 * q^27 - 553 * q^29 - 205 * q^31 - 198 * q^33 - 7 * q^35 + 127 * q^37 + 629 * q^39 - 553 * q^41 - 70 * q^43 - 1132 * q^45 - 779 * q^47 + 847 * q^49 + 2176 * q^51 + 1401 * q^53 + 385 * q^55 - 488 * q^57 - 1354 * q^59 - 1623 * q^61 - 256 * q^63 + 1674 * q^65 + 1658 * q^67 + 5470 * q^69 - 1985 * q^71 - 1245 * q^73 - 4114 * q^75 - 2645 * q^77 + 2007 * q^79 + 1966 * q^81 + 2946 * q^83 - 1543 * q^85 + 262 * q^87 - 6410 * q^89 - 3937 * q^91 + 2221 * q^93 + 8359 * q^95 + 6566 * q^97 + 3265 * 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
$3$	−0.320520	+	0.986460i	−0.0616842	+	0.189844i	−0.977150	−	0.212552i	$-0.931823\pi$
$3$	−0.320520	+	0.986460i	−0.0616842	+	0.189844i	0.915466	+	0.402396i	$0.131823\pi$
$4$		0			0
$5$	−7.72334	+	5.61133i	−0.690796	+	0.501893i	−0.876922	−	0.480633i	$-0.840407\pi$
$5$	−7.72334	+	5.61133i	−0.690796	+	0.501893i	0.186125	+	0.982526i	$0.440407\pi$
$6$		0			0
$7$	−5.56367	−	17.1232i	−0.300410	−	0.924566i	−0.981350	−	0.192228i	$-0.938429\pi$
$7$	−5.56367	−	17.1232i	−0.300410	−	0.924566i	0.680941	−	0.732339i	$-0.261571\pi$
$8$		0			0
$9$	20.9731	+	15.2378i	0.776781	+	0.564364i
$10$		0			0
$11$	−10.0276	−	35.0777i	−0.274859	−	0.961485i
$11$	−10.0276	−	35.0777i	−0.274859	−	0.961485i
$12$		0			0
$13$	−13.3294	−	9.68440i	−0.284378	−	0.206613i	0.436447	−	0.899730i	$-0.356237\pi$
$13$	−13.3294	−	9.68440i	−0.284378	−	0.206613i	−0.720825	+	0.693117i	$0.756237\pi$
$14$		0			0
$15$	−3.05987	−	9.41731i	−0.0526703	−	0.162103i
$16$		0			0
$17$	64.6073	−	46.9400i	0.921740	−	0.669683i	−0.0222165	−	0.999753i	$-0.507072\pi$
$17$	64.6073	−	46.9400i	0.921740	−	0.669683i	0.943956	+	0.330070i	$0.107072\pi$
$18$		0			0
$19$	44.2970	−	136.332i	0.534864	−	1.64614i	−0.209079	−	0.977899i	$-0.567046\pi$
$19$	44.2970	−	136.332i	0.534864	−	1.64614i	0.743943	−	0.668244i	$-0.232954\pi$
$20$		0			0
$21$	18.6746			0.194054
$22$		0			0
$23$	45.6230			0.413611			0.206806	−	0.978382i	$-0.433693\pi$
$23$	45.6230			0.413611			0.206806	+	0.978382i	$0.433693\pi$
$24$		0			0
$25$	−10.4642	+	32.2056i	−0.0837139	+	0.257645i
$26$		0			0
$27$	−44.4104	+	32.2661i	−0.316548	+	0.229985i
$28$		0			0
$29$	−45.4975	−	140.027i	−0.291334	−	0.896633i	−0.984428	−	0.175786i	$-0.943753\pi$
$29$	−45.4975	−	140.027i	−0.291334	−	0.896633i	0.693095	−	0.720846i	$-0.256247\pi$
$30$		0			0
$31$	−12.6239	−	9.17179i	−0.0731393	−	0.0531388i	0.550615	−	0.834759i	$-0.314393\pi$
$31$	−12.6239	−	9.17179i	−0.0731393	−	0.0531388i	−0.623754	+	0.781621i	$0.714393\pi$
$32$		0			0
$33$	37.8168	+	1.35125i	0.199487	+	0.00712795i
$34$		0			0
$35$	139.054	+	101.029i	0.671555	+	0.487913i
$36$		0			0
$37$	−89.0157	−	273.962i	−0.395516	−	1.21727i	−0.928559	−	0.371185i	$-0.878952\pi$
$37$	−89.0157	−	273.962i	−0.395516	−	1.21727i	0.533043	−	0.846088i	$-0.321048\pi$
$38$		0			0
$39$	13.8256	−	10.0449i	0.0567659	−	0.0412429i
$40$		0			0
$41$	92.6741	−	285.221i	0.353006	−	1.08644i	−0.604150	−	0.796870i	$-0.706487\pi$
$41$	92.6741	−	285.221i	0.353006	−	1.08644i	0.957157	−	0.289571i	$-0.0935127\pi$
$42$		0			0
$43$	−125.686			−0.445744			−0.222872	−	0.974848i	$-0.571543\pi$
$43$	−125.686			−0.445744			−0.222872	+	0.974848i	$0.571543\pi$
$44$		0			0
$45$	−247.487			−0.819848
$46$		0			0
$47$	9.79610	−	30.1493i	0.0304023	−	0.0935686i	−0.934704	−	0.355427i	$-0.884335\pi$
$47$	9.79610	−	30.1493i	0.0304023	−	0.0935686i	0.965106	+	0.261859i	$0.0843354\pi$
$48$		0			0
$49$	15.2430	−	11.0747i	0.0444403	−	0.0322878i
$50$		0			0
$51$	25.5964	+	78.7778i	0.0702788	+	0.216296i
$52$		0			0
$53$	421.520	+	306.252i	1.09246	+	0.793717i	0.979813	−	0.199919i	$-0.0640678\pi$
$53$	421.520	+	306.252i	1.09246	+	0.793717i	0.112645	+	0.993635i	$0.464068\pi$
$54$		0			0
$55$	274.280	+	214.649i	0.672434	+	0.526240i
$56$		0			0
$57$	120.288	+	87.3943i	0.279518	+	0.203082i
$58$		0			0
$59$	70.9340	+	218.312i	0.156522	+	0.481726i	0.998312	−	0.0580796i	$-0.0184977\pi$
$59$	70.9340	+	218.312i	0.156522	+	0.481726i	−0.841790	+	0.539806i	$0.818498\pi$
$60$		0			0
$61$	−600.426	+	436.235i	−1.26027	+	0.915642i	−0.998771	−	0.0495607i	$-0.984218\pi$
$61$	−600.426	+	436.235i	−1.26027	+	0.915642i	−0.261502	+	0.965203i	$0.584218\pi$
$62$		0			0
$63$	144.233	−	443.905i	0.288440	−	0.887726i
$64$		0			0
$65$	157.290			0.300145
$66$		0			0
$67$	−505.264			−0.921310			−0.460655	−	0.887579i	$-0.652385\pi$
$67$	−505.264			−0.921310			−0.460655	+	0.887579i	$0.652385\pi$
$68$		0			0
$69$	−14.6231	+	45.0053i	−0.0255133	+	0.0785218i
$70$		0			0
$71$	−689.250	+	500.769i	−1.15210	+	0.837048i	−0.988758	−	0.149522i	$-0.952226\pi$
$71$	−689.250	+	500.769i	−1.15210	+	0.837048i	−0.163339	+	0.986570i	$0.552226\pi$
$72$		0			0
$73$	74.0022	+	227.755i	0.118648	+	0.365161i	0.992690	−	0.120689i	$-0.0385103\pi$
$73$	74.0022	+	227.755i	0.118648	+	0.365161i	−0.874042	+	0.485850i	$0.838510\pi$
$74$		0			0
$75$	−28.4155	−	20.6451i	−0.0437486	−	0.0317852i
$76$		0			0
$77$	−544.853	+	366.866i	−0.806386	+	0.542965i
$78$		0			0
$79$	−592.086	−	430.175i	−0.843226	−	0.612640i	0.0800440	−	0.996791i	$-0.474494\pi$
$79$	−592.086	−	430.175i	−0.843226	−	0.612640i	−0.923270	+	0.384152i	$0.874494\pi$
$80$		0			0
$81$	198.702	+	611.543i	0.272569	+	0.838880i
$82$		0			0
$83$	476.872	−	346.468i	0.630645	−	0.458190i	−0.225979	−	0.974132i	$-0.572558\pi$
$83$	476.872	−	346.468i	0.630645	−	0.458190i	0.856624	+	0.515942i	$0.172558\pi$
$84$		0			0
$85$	−235.588	+	725.067i	−0.300625	+	0.925230i
$86$		0			0
$87$	152.714			0.188191
$88$		0			0
$89$	663.369			0.790078			0.395039	−	0.918664i	$-0.370731\pi$
$89$	663.369			0.790078			0.395039	+	0.918664i	$0.370731\pi$
$90$		0			0
$91$	−91.6674	+	282.123i	−0.105597	+	0.324995i
$92$		0			0
$93$	13.0938	−	9.51322i	0.0145996	−	0.0106073i
$94$		0			0
$95$	422.884	+	1301.50i	0.456705	+	1.40559i
$96$		0			0
$97$	1103.42	+	801.685i	1.15501	+	0.839162i	0.989139	−	0.146986i	$-0.0469571\pi$
$97$	1103.42	+	801.685i	1.15501	+	0.839162i	0.165869	+	0.986148i	$0.446957\pi$
$98$		0			0
$99$	324.198	−	888.488i	0.329122	−	0.901984i
$100$		0			0
$101$	−1217.63	−	884.660i	−1.19959	−	0.871554i	−0.205347	−	0.978689i	$-0.565832\pi$
$101$	−1217.63	−	884.660i	−1.19959	−	0.871554i	−0.994244	+	0.107135i	$0.965832\pi$
$102$		0			0
$103$	182.051	+	560.295i	0.174155	+	0.535995i	0.999594	−	0.0284970i	$-0.00907211\pi$
$103$	182.051	+	560.295i	0.174155	+	0.535995i	−0.825439	+	0.564492i	$0.809072\pi$
$104$		0			0
$105$	−144.230	+	104.790i	−0.134052	+	0.0973944i
$106$		0			0
$107$	−173.894	+	535.191i	−0.157112	+	0.483540i	−0.998369	−	0.0570951i	$-0.981816\pi$
$107$	−173.894	+	535.191i	−0.157112	+	0.483540i	0.841257	+	0.540636i	$0.181816\pi$
$108$		0			0
$109$	163.962			0.144079			0.0720397	−	0.997402i	$-0.477049\pi$
$109$	163.962			0.144079			0.0720397	+	0.997402i	$0.477049\pi$
$110$		0			0
$111$	298.784			0.255489
$112$		0			0
$113$	645.919	−	1987.93i	0.537725	−	1.65495i	−0.199960	−	0.979804i	$-0.564081\pi$
$113$	645.919	−	1987.93i	0.537725	−	1.65495i	0.737686	−	0.675144i	$-0.235919\pi$
$114$		0			0
$115$	−352.362	+	256.006i	−0.285721	+	0.207589i
$116$		0			0
$117$	−131.990	−	406.223i	−0.104295	−	0.320986i
$118$		0			0
$119$	−1163.22	−	845.126i	−0.896066	−	0.651030i
$120$		0			0
$121$	−1129.89	+	703.494i	−0.848905	+	0.528545i
$122$		0			0
$123$	251.656	+	182.838i	0.184480	+	0.134032i
$124$		0			0
$125$	−468.654	−	1442.37i	−0.335342	−	1.03208i
$126$		0			0
$127$	1002.10	−	728.071i	0.700176	−	0.508708i	−0.179814	−	0.983701i	$-0.557549\pi$
$127$	1002.10	−	728.071i	0.700176	−	0.508708i	0.879990	+	0.474993i	$0.157549\pi$
$128$		0			0
$129$	40.2850	−	123.985i	0.0274954	−	0.0846220i
$130$		0			0
$131$	−377.597			−0.251838			−0.125919	−	0.992041i	$-0.540188\pi$
$131$	−377.597			−0.251838			−0.125919	+	0.992041i	$0.540188\pi$
$132$		0			0
$133$	−2580.89			−1.68265
$134$		0			0
$135$	161.941	−	498.403i	0.103242	−	0.317746i
$136$		0			0
$137$	1663.37	−	1208.51i	1.03731	−	0.753649i	0.0675501	−	0.997716i	$-0.478482\pi$
$137$	1663.37	−	1208.51i	1.03731	−	0.753649i	0.969758	+	0.244067i	$0.0784818\pi$
$138$		0			0
$139$	941.224	+	2896.79i	0.574342	+	1.76764i	0.638408	+	0.769698i	$0.279593\pi$
$139$	941.224	+	2896.79i	0.574342	+	1.76764i	−0.0640657	+	0.997946i	$0.520407\pi$
$140$		0			0
$141$	26.6012	+	19.3269i	0.0158881	+	0.0115434i
$142$		0			0
$143$	−206.044	+	564.678i	−0.120491	+	0.330215i
$144$		0			0
$145$	1137.13	+	826.174i	0.651266	+	0.473172i
$146$		0			0
$147$	6.03906	+	18.5863i	0.00338839	+	0.0104284i
$148$		0			0
$149$	668.671	−	485.818i	0.367649	−	0.267112i	−0.388587	−	0.921412i	$-0.627037\pi$
$149$	668.671	−	485.818i	0.367649	−	0.267112i	0.756235	+	0.654300i	$0.227037\pi$
$150$		0			0
$151$	997.185	−	3069.02i	0.537416	−	1.65400i	−0.200955	−	0.979601i	$-0.564404\pi$
$151$	997.185	−	3069.02i	0.537416	−	1.65400i	0.738370	−	0.674395i	$-0.235596\pi$
$152$		0			0
$153$	2070.28			1.09394
$154$		0			0
$155$	148.965			0.0771943
$156$		0			0
$157$	341.555	−	1051.20i	0.173624	−	0.534361i	−0.825944	−	0.563753i	$-0.809357\pi$
$157$	341.555	−	1051.20i	0.173624	−	0.534361i	0.999568	+	0.0293919i	$0.00935708\pi$
$158$		0			0
$159$	−437.211	+	317.653i	−0.218070	+	0.158437i
$160$		0			0
$161$	−253.831	−	781.213i	−0.124253	−	0.382411i
$162$		0			0
$163$	−2542.44	−	1847.19i	−1.22171	−	0.887626i	−0.225471	−	0.974250i	$-0.572392\pi$
$163$	−2542.44	−	1847.19i	−1.22171	−	0.887626i	−0.996241	+	0.0866242i	$0.972392\pi$
$164$		0			0
$165$	−299.654	+	201.767i	−0.141382	+	0.0951971i
$166$		0			0
$167$	109.528	+	79.5766i	0.0507516	+	0.0368732i	0.612872	−	0.790182i	$-0.290014\pi$
$167$	109.528	+	79.5766i	0.0507516	+	0.0368732i	−0.562120	+	0.827056i	$0.690014\pi$
$168$		0			0
$169$	−595.024	−	1831.30i	−0.270835	−	0.833544i
$170$		0			0
$171$	3006.45	−	2184.31i	1.34450	−	0.976834i
$172$		0			0
$173$	−400.668	+	1233.13i	−0.176082	+	0.541925i	−0.999681	−	0.0252471i	$-0.991963\pi$
$173$	−400.668	+	1233.13i	−0.176082	+	0.541925i	0.823599	+	0.567173i	$0.191963\pi$
$174$		0			0
$175$	609.683			0.263358
$176$		0			0
$177$	−238.092			−0.101108
$178$		0			0
$179$	1269.93	−	3908.43i	0.530273	−	1.63201i	−0.223375	−	0.974733i	$-0.571707\pi$
$179$	1269.93	−	3908.43i	0.530273	−	1.63201i	0.753647	−	0.657279i	$-0.228293\pi$
$180$		0			0
$181$	−1284.22	+	933.040i	−0.527377	+	0.383162i	−0.819376	−	0.573257i	$-0.805680\pi$
$181$	−1284.22	+	933.040i	−0.527377	+	0.383162i	0.291998	+	0.956419i	$0.405680\pi$
$182$		0			0
$183$	−237.880	−	732.118i	−0.0960906	−	0.295736i
$184$		0			0
$185$	2224.79	+	1616.41i	0.884162	+	0.642381i
$186$		0			0
$187$	−2294.41	−	1795.58i	−0.897239	−	0.702170i
$188$		0			0
$189$	799.583	+	580.931i	0.307731	+	0.223579i
$190$		0			0
$191$	669.405	+	2060.22i	0.253594	+	0.780482i	0.994103	+	0.108436i	$0.0345842\pi$
$191$	669.405	+	2060.22i	0.253594	+	0.780482i	−0.740510	+	0.672046i	$0.765416\pi$
$192$		0			0
$193$	−1677.50	+	1218.77i	−0.625643	+	0.454556i	−0.854888	−	0.518813i	$-0.826374\pi$
$193$	−1677.50	+	1218.77i	−0.625643	+	0.454556i	0.229245	+	0.973369i	$0.426374\pi$
$194$		0			0
$195$	−50.4147	+	155.160i	−0.0185142	+	0.0569808i
$196$		0			0
$197$	4578.51			1.65587			0.827933	−	0.560828i	$-0.189517\pi$
$197$	4578.51			1.65587			0.827933	+	0.560828i	$0.189517\pi$
$198$		0			0
$199$	−3519.24			−1.25363			−0.626815	−	0.779168i	$-0.715642\pi$
$199$	−3519.24			−1.25363			−0.626815	+	0.779168i	$0.715642\pi$
$200$		0			0
$201$	161.947	−	498.422i	0.0568302	−	0.174905i
$202$		0			0
$203$	−2144.58	+	1558.13i	−0.741477	+	0.538714i
$204$		0			0
$205$	884.720	+	2722.89i	0.301422	+	0.927681i
$206$		0			0
$207$	956.856	+	695.197i	0.321286	+	0.233428i
$208$		0			0
$209$	−5226.41	−	186.747i	−1.72975	−	0.0618065i
$210$		0			0
$211$	1999.73	+	1452.89i	0.652450	+	0.474033i	0.864105	−	0.503312i	$-0.167885\pi$
$211$	1999.73	+	1452.89i	0.652450	+	0.474033i	−0.211655	+	0.977345i	$0.567885\pi$
$212$		0			0
$213$	−273.070	−	840.424i	−0.0878426	−	0.270352i
$214$		0			0
$215$	970.719	−	705.268i	0.307918	−	0.223716i
$216$		0			0
$217$	−86.8154	+	267.190i	−0.0271586	+	0.0835855i
$218$		0			0
$219$	−248.391			−0.0766424
$220$		0			0
$221$	−1315.76			−0.400488
$222$		0			0
$223$	−1522.98	+	4687.24i	−0.457336	+	1.40754i	0.411034	+	0.911620i	$0.365168\pi$
$223$	−1522.98	+	4687.24i	−0.457336	+	1.40754i	−0.868370	+	0.495917i	$0.834832\pi$
$224$		0			0
$225$	−710.211	+	515.999i	−0.210433	+	0.152888i
$226$		0			0
$227$	845.888	+	2603.38i	0.247329	+	0.761199i	0.995245	+	0.0974058i	$0.0310545\pi$
$227$	845.888	+	2603.38i	0.247329	+	0.761199i	−0.747916	+	0.663793i	$0.768946\pi$
$228$		0			0
$229$	1405.81	+	1021.38i	0.405671	+	0.294737i	0.771847	−	0.635809i	$-0.219333\pi$
$229$	1405.81	+	1021.38i	0.405671	+	0.294737i	−0.366176	+	0.930546i	$0.619333\pi$
$230$		0			0
$231$	−187.263	−	655.063i	−0.0533375	−	0.186580i
$232$		0			0
$233$	−827.230	−	601.018i	−0.232591	−	0.168987i	0.465385	−	0.885108i	$-0.345916\pi$
$233$	−827.230	−	601.018i	−0.232591	−	0.168987i	−0.697976	+	0.716121i	$0.745916\pi$
$234$		0			0
$235$	93.5191	+	287.822i	0.0259596	+	0.0798956i
$236$		0			0
$237$	614.126	−	446.189i	0.168320	−	0.122292i
$238$		0			0
$239$	630.391	−	1940.14i	0.170613	−	0.525094i	−0.828793	−	0.559556i	$-0.810972\pi$
$239$	630.391	−	1940.14i	0.170613	−	0.525094i	0.999406	+	0.0344619i	$0.0109717\pi$
$240$		0			0
$241$	−1773.76			−0.474098			−0.237049	−	0.971498i	$-0.576180\pi$
$241$	−1773.76			−0.474098			−0.237049	+	0.971498i	$0.576180\pi$
$242$		0			0
$243$	−2149.10			−0.567344
$244$		0			0
$245$	−55.5832	+	171.068i	−0.0144942	+	0.0446086i
$246$		0			0
$247$	−1910.75	+	1388.24i	−0.492218	+	0.357617i
$248$		0			0
$249$	188.930	+	581.465i	0.0480840	+	0.147987i
$250$		0			0
$251$	4131.15	+	3001.46i	1.03887	+	0.754782i	0.970064	−	0.242848i	$-0.0780817\pi$
$251$	4131.15	+	3001.46i	1.03887	+	0.754782i	0.0688040	+	0.997630i	$0.478082\pi$
$252$		0			0
$253$	−457.492	−	1600.35i	−0.113685	−	0.397681i
$254$		0			0
$255$	−639.738	−	464.797i	−0.157106	−	0.114144i
$256$		0			0
$257$	943.272	+	2903.09i	0.228948	+	0.704630i	0.997867	+	0.0652835i	$0.0207952\pi$
$257$	943.272	+	2903.09i	0.228948	+	0.704630i	−0.768919	+	0.639347i	$0.779205\pi$
$258$		0			0
$259$	−4195.86	+	3048.47i	−1.00663	+	0.731361i
$260$		0			0
$261$	1179.48	−	3630.08i	0.279725	−	0.860906i
$262$		0			0
$263$	6263.62			1.46856			0.734280	−	0.678847i	$-0.237520\pi$
$263$	6263.62			1.46856			0.734280	+	0.678847i	$0.237520\pi$
$264$		0			0
$265$	−4974.03			−1.15303
$266$		0			0
$267$	−212.623	+	654.387i	−0.0487353	+	0.149992i
$268$		0			0
$269$	1464.47	−	1064.00i	0.331934	−	0.241164i	−0.409317	−	0.912392i	$-0.634233\pi$
$269$	1464.47	−	1064.00i	0.331934	−	0.241164i	0.741251	+	0.671228i	$0.234233\pi$
$270$		0			0
$271$	2376.15	+	7313.04i	0.532623	+	1.63925i	0.748730	+	0.662876i	$0.230664\pi$
$271$	2376.15	+	7313.04i	0.532623	+	1.63925i	−0.216106	+	0.976370i	$0.569336\pi$
$272$		0			0
$273$	−248.922	−	180.852i	−0.0551848	−	0.0400941i
$274$		0			0
$275$	1234.63	+	44.1151i	0.270731	+	0.00967361i
$276$		0			0
$277$	−176.099	−	127.943i	−0.0381977	−	0.0277522i	0.568523	−	0.822668i	$-0.307515\pi$
$277$	−176.099	−	127.943i	−0.0381977	−	0.0277522i	−0.606720	+	0.794915i	$0.707515\pi$
$278$		0			0
$279$	−125.004	−	384.722i	−0.0268236	−	0.0825544i
$280$		0			0
$281$	−549.547	+	399.269i	−0.116666	+	0.0847631i	−0.644588	−	0.764530i	$-0.722971\pi$
$281$	−549.547	+	399.269i	−0.116666	+	0.0847631i	0.527922	+	0.849293i	$0.322971\pi$
$282$		0			0
$283$	91.7568	−	282.398i	0.0192734	−	0.0593175i	−0.940957	−	0.338525i	$-0.890072\pi$
$283$	91.7568	−	282.398i	0.0192734	−	0.0593175i	0.960231	+	0.279208i	$0.0900719\pi$
$284$		0			0
$285$	−1419.42			−0.295015
$286$		0			0
$287$	−5399.51			−1.11053
$288$		0			0
$289$	452.546	−	1392.79i	0.0921119	−	0.283491i
$290$		0			0
$291$	−1144.50	+	831.528i	−0.230556	+	0.167509i
$292$		0			0
$293$	1819.59	+	5600.13i	0.362805	+	1.11660i	0.951344	+	0.308130i	$0.0997032\pi$
$293$	1819.59	+	5600.13i	0.362805	+	1.11660i	−0.588539	+	0.808469i	$0.700297\pi$
$294$		0			0
$295$	−1772.87	−	1288.07i	−0.349900	−	0.254217i
$296$		0			0
$297$	1577.15	+	1234.26i	0.308133	+	0.241142i
$298$		0			0
$299$	−608.129	−	441.832i	−0.117622	−	0.0854575i
$300$		0			0
$301$	699.277	+	2152.15i	0.133906	+	0.412120i
$302$		0			0
$303$	1262.96	−	917.592i	0.239455	−	0.173975i
$304$		0			0
$305$	2189.43	−	6738.38i	0.411038	−	1.26504i
$306$		0			0
$307$	1249.08			0.232211			0.116105	−	0.993237i	$-0.462959\pi$
$307$	1249.08			0.232211			0.116105	+	0.993237i	$0.462959\pi$
$308$		0			0
$309$	−611.059			−0.112498
$310$		0			0
$311$	3006.39	−	9252.70i	0.548156	−	1.68705i	−0.165210	−	0.986258i	$-0.552830\pi$
$311$	3006.39	−	9252.70i	0.548156	−	1.68705i	0.713366	−	0.700792i	$-0.247170\pi$
$312$		0			0
$313$	−6806.73	+	4945.38i	−1.22920	+	0.893064i	−0.996830	−	0.0795635i	$-0.974647\pi$
$313$	−6806.73	+	4945.38i	−1.22920	+	0.893064i	−0.232368	+	0.972628i	$0.574647\pi$
$314$		0			0
$315$	1376.93	+	4237.77i	0.246290	+	0.758004i
$316$		0			0
$317$	5795.63	+	4210.77i	1.02686	+	0.746058i	0.967678	−	0.252189i	$-0.0811505\pi$
$317$	5795.63	+	4210.77i	1.02686	+	0.746058i	0.0591829	+	0.998247i	$0.481150\pi$
$318$		0			0
$319$	−4455.59	+	3000.09i	−0.782023	+	0.526560i
$320$		0			0
$321$	−472.208	−	343.079i	−0.0821061	−	0.0596536i
$322$		0			0
$323$	−3537.51	−	10887.3i	−0.609388	−	1.87550i
$324$		0			0
$325$	451.374	−	327.942i	0.0770392	−	0.0559722i
$326$		0			0
$327$	−52.5530	+	161.741i	−0.00888742	+	0.0273527i
$328$		0			0
$329$	−570.755			−0.0956435
$330$		0			0
$331$	3759.76			0.624336			0.312168	−	0.950027i	$-0.398945\pi$
$331$	3759.76			0.624336			0.312168	+	0.950027i	$0.398945\pi$
$332$		0			0
$333$	2307.66	−	7102.24i	0.379756	−	1.16877i
$334$		0			0
$335$	3902.32	−	2835.20i	0.636438	−	0.462399i
$336$		0			0
$337$	3120.27	+	9603.20i	0.504368	+	1.55228i	0.801831	+	0.597551i	$0.203859\pi$
$337$	3120.27	+	9603.20i	0.504368	+	1.55228i	−0.297464	+	0.954733i	$0.596141\pi$
$338$		0			0
$339$	1753.99	+	1274.35i	0.281013	+	0.204168i
$340$		0			0
$341$	−195.138	+	534.789i	−0.0309891	+	0.0849280i
$342$		0			0
$343$	−5270.53	−	3829.27i	−0.829686	−	0.602802i
$344$		0			0
$345$	−139.601	−	429.646i	−0.0217851	−	0.0670475i
$346$		0			0
$347$	−5232.66	+	3801.75i	−0.809521	+	0.588151i	−0.913692	−	0.406408i	$-0.866781\pi$
$347$	−5232.66	+	3801.75i	−0.809521	+	0.588151i	0.104171	+	0.994559i	$0.466781\pi$
$348$		0			0
$349$	798.726	−	2458.23i	0.122507	−	0.377037i	−0.870932	−	0.491404i	$-0.836484\pi$
$349$	798.726	−	2458.23i	0.122507	−	0.377037i	0.993439	+	0.114367i	$0.0364839\pi$
$350$		0			0
$351$	904.443			0.137537
$352$		0			0
$353$	−2143.59			−0.323207			−0.161603	−	0.986856i	$-0.551666\pi$
$353$	−2143.59			−0.323207			−0.161603	+	0.986856i	$0.551666\pi$
$354$		0			0
$355$	2513.33	−	7735.22i	0.375756	−	1.15646i
$356$		0			0
$357$	1206.52	−	876.586i	0.178867	−	0.129955i
$358$		0			0
$359$	−3155.05	−	9710.26i	−0.463837	−	1.42754i	−0.860439	−	0.509553i	$-0.829811\pi$
$359$	−3155.05	−	9710.26i	−0.463837	−	1.42754i	0.396603	−	0.917990i	$-0.370189\pi$
$360$		0			0
$361$	−11075.1	−	8046.56i	−1.61469	−	1.17314i
$362$		0			0
$363$	−331.815	−	1340.08i	−0.0479773	−	0.193763i
$364$		0			0
$365$	−1849.56	−	1343.78i	−0.265233	−	0.192703i
$366$		0			0
$367$	1254.50	+	3860.94i	0.178431	+	0.549154i	0.999774	−	0.0212811i	$-0.00677449\pi$
$367$	1254.50	+	3860.94i	0.178431	+	0.549154i	−0.821342	+	0.570435i	$0.806774\pi$
$368$		0			0
$369$	6289.82	−	4569.82i	0.887358	−	0.644703i
$370$		0			0
$371$	2898.82	−	8921.66i	0.405659	−	1.24849i
$372$		0			0
$373$	12702.8			1.76334			0.881671	−	0.471864i	$-0.156419\pi$
$373$	12702.8			1.76334			0.881671	+	0.471864i	$0.156419\pi$
$374$		0			0
$375$	1573.05			0.216619
$376$		0			0
$377$	−749.620	+	2307.09i	−0.102407	+	0.315176i
$378$		0			0
$379$	−3235.73	+	2350.89i	−0.438544	+	0.318621i	−0.785056	−	0.619425i	$-0.787366\pi$
$379$	−3235.73	+	2350.89i	−0.438544	+	0.318621i	0.346512	+	0.938045i	$0.387366\pi$
$380$		0			0
$381$	397.018	+	1221.90i	0.0533855	+	0.164304i
$382$		0			0
$383$	8325.71	+	6048.98i	1.11077	+	0.807020i	0.982784	−	0.184757i	$-0.0591497\pi$
$383$	8325.71	+	6048.98i	1.11077	+	0.807020i	0.127983	+	0.991776i	$0.459150\pi$
$384$		0			0
$385$	2149.47	−	5890.78i	0.284538	−	0.779797i
$386$		0			0
$387$	−2636.03	−	1915.19i	−0.346246	−	0.251562i
$388$		0			0
$389$	−340.972	−	1049.40i	−0.0444420	−	0.136778i	0.926373	−	0.376606i	$-0.122909\pi$
$389$	−340.972	−	1049.40i	−0.0444420	−	0.136778i	−0.970815	+	0.239828i	$0.922909\pi$
$390$		0			0
$391$	2947.58	−	2141.54i	0.381242	−	0.276989i
$392$		0			0
$393$	121.028	−	372.485i	0.0155344	−	0.0478101i
$394$		0			0
$395$	6986.74			0.889977
$396$		0			0
$397$	10352.5			1.30876			0.654379	−	0.756166i	$-0.272930\pi$
$397$	10352.5			1.30876			0.654379	+	0.756166i	$0.272930\pi$
$398$		0			0
$399$	827.229	−	2545.95i	0.103793	−	0.319441i
$400$		0			0
$401$	−9301.20	+	6757.72i	−1.15830	+	0.841557i	−0.989563	−	0.144104i	$-0.953970\pi$
$401$	−9301.20	+	6757.72i	−1.15830	+	0.841557i	−0.168741	+	0.985660i	$0.553970\pi$
$402$		0			0
$403$	79.4460	+	244.510i	0.00982006	+	0.0302230i
$404$		0			0
$405$	−4966.22	−	3608.17i	−0.609317	−	0.442695i
$406$		0			0
$407$	−8717.35	+	5869.66i	−1.06168	+	0.714861i
$408$		0			0
$409$	−6589.14	−	4787.29i	−0.796607	−	0.578769i	0.113310	−	0.993560i	$-0.463855\pi$
$409$	−6589.14	−	4787.29i	−0.796607	−	0.578769i	−0.909917	+	0.414791i	$0.863855\pi$
$410$		0			0
$411$	659.002	+	2028.20i	0.0790904	+	0.243415i
$412$		0			0
$413$	3343.55	−	2429.23i	0.398367	−	0.289430i
$414$		0			0
$415$	−1738.90	+	5351.78i	−0.205685	+	0.633032i
$416$		0			0
$417$	−3159.25			−0.371005
$418$		0			0
$419$	−3940.43			−0.459433			−0.229717	−	0.973258i	$-0.573780\pi$
$419$	−3940.43			−0.459433			−0.229717	+	0.973258i	$0.573780\pi$
$420$		0			0
$421$	18.6265	−	57.3264i	0.00215629	−	0.00663638i	−0.949973	−	0.312333i	$-0.898889\pi$
$421$	18.6265	−	57.3264i	0.00215629	−	0.00663638i	0.952129	+	0.305697i	$0.0988894\pi$
$422$		0			0
$423$	664.864	−	483.052i	0.0764227	−	0.0555244i
$424$		0			0
$425$	835.664	+	2571.91i	0.0953780	+	0.293543i
$426$		0			0
$427$	10810.3	+	7854.15i	1.22517	+	0.890138i
$428$		0			0
$429$	−490.991	−	384.245i	−0.0552570	−	0.0432436i
$430$		0			0
$431$	4228.27	+	3072.02i	0.472549	+	0.343327i	0.798434	−	0.602082i	$-0.205662\pi$
$431$	4228.27	+	3072.02i	0.472549	+	0.343327i	−0.325885	+	0.945410i	$0.605662\pi$
$432$		0			0
$433$	−4432.57	−	13642.0i	−0.491953	−	1.51407i	−0.821652	−	0.569989i	$-0.806947\pi$
$433$	−4432.57	−	13642.0i	−0.491953	−	1.51407i	0.329700	−	0.944086i	$-0.393053\pi$
$434$		0			0
$435$	−1179.46	+	856.928i	−0.130002	+	0.0944519i
$436$		0			0
$437$	2020.96	−	6219.88i	0.221226	−	0.680863i
$438$		0			0
$439$	−3548.07			−0.385741			−0.192871	−	0.981224i	$-0.561780\pi$
$439$	−3548.07			−0.385741			−0.192871	+	0.981224i	$0.561780\pi$
$440$		0			0
$441$	488.448			0.0527425
$442$		0			0
$443$	−2520.57	+	7757.52i	−0.270330	+	0.831989i	0.720088	+	0.693883i	$0.244101\pi$
$443$	−2520.57	+	7757.52i	−0.270330	+	0.831989i	−0.990417	+	0.138106i	$0.955899\pi$
$444$		0			0
$445$	−5123.42	+	3722.38i	−0.545783	+	0.396535i
$446$		0			0
$447$	264.917	+	815.332i	0.0280317	+	0.0862726i
$448$		0			0
$449$	2333.58	+	1695.44i	0.245275	+	0.178203i	0.703630	−	0.710566i	$-0.251561\pi$
$449$	2333.58	+	1695.44i	0.245275	+	0.178203i	−0.458355	+	0.888769i	$0.651561\pi$
$450$		0			0
$451$	−10934.2	−	390.695i	−1.14162	−	0.0407918i
$452$		0			0
$453$	2707.85	+	1967.37i	0.280852	+	0.204051i
$454$		0			0
$455$	−875.110	−	2693.31i	−0.0901665	−	0.277504i
$456$		0			0
$457$	8747.29	−	6355.28i	0.895363	−	0.650519i	−0.0419077	−	0.999121i	$-0.513344\pi$
$457$	8747.29	−	6355.28i	0.895363	−	0.650519i	0.937271	+	0.348602i	$0.113344\pi$
$458$		0			0
$459$	−1354.67	+	4169.25i	−0.137757	+	0.423973i
$460$		0			0
$461$	−14868.7			−1.50218			−0.751091	−	0.660198i	$-0.770472\pi$
$461$	−14868.7			−1.50218			−0.751091	+	0.660198i	$0.770472\pi$
$462$		0			0
$463$	471.604			0.0473376			0.0236688	−	0.999720i	$-0.492465\pi$
$463$	471.604			0.0473376			0.0236688	+	0.999720i	$0.492465\pi$
$464$		0			0
$465$	−47.7462	+	146.948i	−0.00476167	+	0.0146549i
$466$		0			0
$467$	7448.45	−	5411.61i	0.738058	−	0.536231i	−0.154044	−	0.988064i	$-0.549230\pi$
$467$	7448.45	−	5411.61i	0.738058	−	0.536231i	0.892102	+	0.451833i	$0.149230\pi$
$468$		0			0
$469$	2811.12	+	8651.73i	0.276771	+	0.851812i
$470$		0			0
$471$	927.489	+	673.860i	0.0907355	+	0.0659232i
$472$		0			0
$473$	1260.34	+	4408.79i	0.122517	+	0.428576i
$474$		0			0
$475$	3927.12	+	2853.22i	0.379344	+	0.275610i
$476$		0			0
$477$	4173.95	+	12846.1i	0.400655	+	1.23309i
$478$		0			0
$479$	1064.22	−	773.203i	0.101515	−	0.0737548i	−0.535870	−	0.844301i	$-0.680016\pi$
$479$	1064.22	−	773.203i	0.101515	−	0.0737548i	0.637385	+	0.770546i	$0.280016\pi$
$480$		0			0
$481$	−1466.63	+	4513.82i	−0.139028	+	0.427885i
$482$		0			0
$483$	851.993			0.0802630
$484$		0			0
$485$	−13020.6			−1.21904
$486$		0			0
$487$	2197.89	−	6764.40i	0.204509	−	0.629414i	−0.795224	−	0.606315i	$-0.792647\pi$
$487$	2197.89	−	6764.40i	0.204509	−	0.629414i	0.999733	−	0.0230983i	$-0.00735306\pi$
$488$		0			0
$489$	2637.08	−	1915.95i	0.243871	−	0.177183i
$490$		0			0
$491$	521.486	+	1604.97i	0.0479314	+	0.147518i	0.972158	−	0.234327i	$-0.0752888\pi$
$491$	521.486	+	1604.97i	0.0479314	+	0.147518i	−0.924226	+	0.381845i	$0.875289\pi$
$492$		0			0
$493$	−9512.33	−	6911.11i	−0.868994	−	0.631361i
$494$		0			0
$495$	2481.71	+	8681.28i	0.225343	+	0.788271i
$496$		0			0
$497$	12409.5	+	9016.05i	1.12001	+	0.813733i
$498$		0			0
$499$	−4041.45	−	12438.3i	−0.362566	−	1.11586i	−0.951491	−	0.307675i	$-0.900449\pi$
$499$	−4041.45	−	12438.3i	−0.362566	−	1.11586i	0.588926	−	0.808187i	$-0.299551\pi$
$500$		0			0
$501$	−113.605	+	82.5389i	−0.0101307	+	0.00736041i
$502$		0			0
$503$	−3909.83	+	12033.2i	−0.346581	+	1.06667i	0.614150	+	0.789189i	$0.289499\pi$
$503$	−3909.83	+	12033.2i	−0.346581	+	1.06667i	−0.960732	+	0.277479i	$0.910501\pi$
$504$		0			0
$505$	14368.3			1.26610
$506$		0			0
$507$	1997.22			0.174950
$508$		0			0
$509$	−338.874	+	1042.95i	−0.0295095	+	0.0908209i	−0.964727	−	0.263254i	$-0.915204\pi$
$509$	−338.874	+	1042.95i	−0.0295095	+	0.0908209i	0.935217	+	0.354075i	$0.115204\pi$
$510$		0			0
$511$	3488.18	−	2534.31i	0.301973	−	0.219396i
$512$		0			0
$513$	2431.65	+	7483.85i	0.209279	+	0.644093i
$514$		0			0
$515$	−4550.04	−	3305.80i	−0.389318	−	0.282856i
$516$		0			0
$517$	−1155.80	−	41.2984i	−0.0983211	−	0.00351315i
$518$		0			0
$519$	−1088.01	−	790.486i	−0.0920200	−	0.0668564i
$520$		0			0
$521$	5106.48	+	15716.1i	0.429403	+	1.32157i	0.898715	+	0.438533i	$0.144502\pi$
$521$	5106.48	+	15716.1i	0.429403	+	1.32157i	−0.469312	+	0.883032i	$0.655498\pi$
$522$		0			0
$523$	−15590.7	+	11327.3i	−1.30350	+	0.947052i	−0.999983	−	0.00577306i	$-0.998162\pi$
$523$	−15590.7	+	11327.3i	−1.30350	+	0.947052i	−0.303521	+	0.952825i	$0.598162\pi$
$524$		0			0
$525$	−195.416	+	601.427i	−0.0162450	+	0.0499970i
$526$		0			0
$527$	−1246.12			−0.103002
$528$		0			0
$529$	−10085.5			−0.828926
$530$		0			0
$531$	−1838.90	+	5659.56i	−0.150286	+	0.462531i
$532$		0			0
$533$	−3997.49	+	2904.35i	−0.324860	+	0.236025i
$534$		0			0
$535$	−1660.09	−	5109.24i	−0.134153	−	0.412881i
$536$		0			0
$537$	3448.48	+	2505.46i	0.277119	+	0.201339i
$538$		0			0
$539$	−541.327	−	423.638i	−0.0432590	−	0.0338541i
$540$		0			0
$541$	7103.29	+	5160.84i	0.564500	+	0.410133i	0.833103	−	0.553118i	$-0.186562\pi$
$541$	7103.29	+	5160.84i	0.564500	+	0.410133i	−0.268603	+	0.963251i	$0.586562\pi$
$542$		0			0
$543$	−508.789	−	1565.89i	−0.0402103	−	0.123755i
$544$		0			0
$545$	−1266.33	+	920.043i	−0.0995296	+	0.0723125i
$546$		0			0
$547$	637.955	−	1963.42i	0.0498665	−	0.153473i	−0.923022	−	0.384746i	$-0.874289\pi$
$547$	637.955	−	1963.42i	0.0498665	−	0.153473i	0.972889	+	0.231273i	$0.0742890\pi$
$548$		0			0
$549$	−19240.1			−1.49571
$550$		0			0
$551$	−21105.6			−1.63181
$552$		0			0
$553$	−4071.82	+	12531.8i	−0.313112	+	0.963661i
$554$		0			0
$555$	−2307.61	+	1676.58i	−0.176491	+	0.128228i
$556$		0			0
$557$	−2401.56	−	7391.25i	−0.182688	−	0.562257i	0.817212	−	0.576337i	$-0.195518\pi$
$557$	−2401.56	−	7391.25i	−0.182688	−	0.562257i	−0.999901	+	0.0140793i	$0.995518\pi$
$558$		0			0
$559$	1675.33	+	1217.20i	0.126760	+	0.0920965i
$560$		0			0
$561$	2506.67	−	1687.82i	0.188648	−	0.127023i
$562$		0			0
$563$	−4495.98	−	3266.52i	−0.336560	−	0.244525i	0.406649	−	0.913584i	$-0.366697\pi$
$563$	−4495.98	−	3266.52i	−0.336560	−	0.244525i	−0.743209	+	0.669059i	$0.766697\pi$
$564$		0			0
$565$	6166.31	+	18978.0i	0.459148	+	1.41311i
$566$		0			0
$567$	9366.07	−	6804.85i	0.693718	−	0.504015i
$568$		0			0
$569$	41.3080	−	127.133i	0.00304345	−	0.00936677i	−0.949523	−	0.313697i	$-0.898433\pi$
$569$	41.3080	−	127.133i	0.00304345	−	0.00936677i	0.952567	+	0.304330i	$0.0984325\pi$
$570$		0			0
$571$	16220.9			1.18884			0.594418	−	0.804156i	$-0.297382\pi$
$571$	16220.9			1.18884			0.594418	+	0.804156i	$0.297382\pi$
$572$		0			0
$573$	−2246.88			−0.163813
$574$		0			0
$575$	−477.410	+	1469.32i	−0.0346250	+	0.106565i
$576$		0			0
$577$	6236.86	−	4531.34i	0.449989	−	0.326936i	−0.339602	−	0.940569i	$-0.610292\pi$
$577$	6236.86	−	4531.34i	0.449989	−	0.326936i	0.789592	+	0.613633i	$0.210292\pi$
$578$		0			0
$579$	−664.600	−	2045.43i	−0.0477026	−	0.146814i
$580$		0			0
$581$	−8585.80	−	6237.95i	−0.613079	−	0.445428i
$582$		0			0
$583$	6515.78	−	17857.0i	0.462875	−	1.26854i
$584$		0			0
$585$	3298.86	+	2396.76i	0.233147	+	0.169391i
$586$		0			0
$587$	2077.18	+	6392.91i	0.146055	+	0.449512i	0.997145	−	0.0755079i	$-0.0240578\pi$
$587$	2077.18	+	6392.91i	0.146055	+	0.449512i	−0.851090	+	0.525020i	$0.824058\pi$
$588$		0			0
$589$	−1809.61	+	1314.76i	−0.126594	+	0.0919756i
$590$		0			0
$591$	−1467.51	+	4516.52i	−0.102141	+	0.314357i
$592$		0			0
$593$	6418.85			0.444503			0.222252	−	0.974989i	$-0.428659\pi$
$593$	6418.85			0.444503			0.222252	+	0.974989i	$0.428659\pi$
$594$		0			0
$595$	13726.2			0.945747
$596$		0			0
$597$	1127.99	−	3471.59i	0.0773292	−	0.237995i
$598$		0			0
$599$	−6957.04	+	5054.59i	−0.474553	+	0.344783i	−0.799213	−	0.601048i	$-0.794750\pi$
$599$	−6957.04	+	5054.59i	−0.474553	+	0.344783i	0.324660	+	0.945831i	$0.394750\pi$
$600$		0			0
$601$	−6410.06	−	19728.1i	−0.435061	−	1.33898i	−0.893024	−	0.450009i	$-0.851421\pi$
$601$	−6410.06	−	19728.1i	−0.435061	−	1.33898i	0.457963	−	0.888971i	$-0.348579\pi$
$602$		0			0
$603$	−10596.9	−	7699.13i	−0.715656	−	0.519955i
$604$		0			0
$605$	4779.00	−	11773.5i	0.321147	−	0.791177i
$606$		0			0
$607$	12997.0	+	9442.86i	0.869079	+	0.631423i	0.930340	−	0.366699i	$-0.119512\pi$
$607$	12997.0	+	9442.86i	0.869079	+	0.631423i	−0.0612604	+	0.998122i	$0.519512\pi$
$608$		0			0
$609$	−849.649	−	2614.95i	−0.0565345	−	0.173995i
$610$		0			0
$611$	−422.554	+	307.003i	−0.0279782	+	0.0203274i
$612$		0			0
$613$	1959.29	−	6030.07i	0.129095	−	0.397312i	−0.865530	−	0.500857i	$-0.833018\pi$
$613$	1959.29	−	6030.07i	0.129095	−	0.397312i	0.994625	+	0.103544i	$0.0330184\pi$
$614$		0			0
$615$	−2969.59			−0.194708
$616$		0			0
$617$	19097.9			1.24611			0.623057	−	0.782177i	$-0.285891\pi$
$617$	19097.9			1.24611			0.623057	+	0.782177i	$0.285891\pi$
$618$		0			0
$619$	−175.300	+	539.518i	−0.0113827	+	0.0350324i	−0.956587	−	0.291448i	$-0.905863\pi$
$619$	−175.300	+	539.518i	−0.0113827	+	0.0350324i	0.945204	+	0.326481i	$0.105863\pi$
$620$		0			0
$621$	−2026.14	+	1472.08i	−0.130928	+	0.0951246i
$622$		0			0
$623$	−3690.76	−	11359.0i	−0.237347	−	0.730479i
$624$		0			0
$625$	8288.73	+	6022.11i	0.530478	+	0.385415i
$626$		0			0
$627$	1859.39	−	5095.79i	0.118432	−	0.324571i
$628$		0			0
$629$	−18610.8	−	13521.6i	−1.17975	−	0.857139i
$630$		0			0
$631$	6912.81	+	21275.4i	0.436125	+	1.34225i	0.891930	+	0.452174i	$0.149351\pi$
$631$	6912.81	+	21275.4i	0.436125	+	1.34225i	−0.455805	+	0.890080i	$0.650649\pi$
$632$		0			0
$633$	−2074.17	+	1506.97i	−0.130238	+	0.0946237i
$634$		0			0
$635$	−3654.14	+	11246.3i	−0.228362	+	0.702827i
$636$		0			0
$637$	−310.433			−0.0193089
$638$		0			0
$639$	−22086.3			−1.36733
$640$		0			0
$641$	6830.28	−	21021.5i	0.420874	−	1.29532i	−0.486017	−	0.873949i	$-0.661551\pi$
$641$	6830.28	−	21021.5i	0.420874	−	1.29532i	0.906890	−	0.421367i	$-0.138449\pi$
$642$		0			0
$643$	21723.5	−	15783.0i	1.33233	−	0.967996i	0.332643	−	0.943053i	$-0.392059\pi$
$643$	21723.5	−	15783.0i	1.33233	−	0.967996i	0.999689	−	0.0249433i	$-0.00794053\pi$
$644$		0			0
$645$	384.584	+	1183.63i	0.0234775	+	0.0722563i
$646$		0			0
$647$	24290.6	+	17648.2i	1.47598	+	1.07237i	0.978823	+	0.204708i	$0.0656245\pi$
$647$	24290.6	+	17648.2i	1.47598	+	1.07237i	0.497162	+	0.867658i	$0.334375\pi$
$648$		0			0
$649$	6946.60	−	4677.36i	0.420151	−	0.282901i
$650$		0			0
$651$	−235.746	−	171.280i	−0.0141930	−	0.0103118i
$652$		0			0
$653$	−6407.37	−	19719.8i	−0.383981	−	1.18177i	−0.937217	−	0.348747i	$-0.886607\pi$
$653$	−6407.37	−	19719.8i	−0.383981	−	1.18177i	0.553236	−	0.833025i	$-0.313393\pi$
$654$		0			0
$655$	2916.31	−	2118.82i	0.173969	−	0.126396i
$656$		0			0
$657$	−1918.45	+	5904.37i	−0.113920	+	0.350611i
$658$		0			0
$659$	−2565.72			−0.151664			−0.0758319	−	0.997121i	$-0.524161\pi$
$659$	−2565.72			−0.151664			−0.0758319	+	0.997121i	$0.524161\pi$
$660$		0			0
$661$	4419.10			0.260035			0.130017	−	0.991512i	$-0.458497\pi$
$661$	4419.10			0.260035			0.130017	+	0.991512i	$0.458497\pi$
$662$		0			0
$663$	421.729	−	1297.95i	0.0247038	−	0.0760304i
$664$		0			0
$665$	19933.1	−	14482.3i	1.16237	−	0.844508i
$666$		0			0
$667$	−2075.73	−	6388.45i	−0.120499	−	0.370858i
$668$		0			0
$669$	−4135.63	−	3004.71i	−0.239002	−	0.173645i
$670$		0			0
$671$	21323.0	+	16687.2i	1.22677	+	0.960061i
$672$		0			0
$673$	−9292.42	−	6751.34i	−0.532238	−	0.386694i	0.288956	−	0.957342i	$-0.406692\pi$
$673$	−9292.42	−	6751.34i	−0.532238	−	0.386694i	−0.821194	+	0.570649i	$0.806692\pi$
$674$		0			0
$675$	−574.427	−	1767.90i	−0.0327551	−	0.100810i
$676$		0			0
$677$	−4870.99	+	3538.98i	−0.276525	+	0.200907i	−0.717400	−	0.696661i	$-0.754668\pi$
$677$	−4870.99	+	3538.98i	−0.276525	+	0.200907i	0.440875	+	0.897568i	$0.354668\pi$
$678$		0			0
$679$	7588.33	−	23354.5i	0.428885	−	1.31997i
$680$		0			0
$681$	−2839.25			−0.159766
$682$		0			0
$683$	20854.2			1.16832			0.584162	−	0.811637i	$-0.301423\pi$
$683$	20854.2			1.16832			0.584162	+	0.811637i	$0.301423\pi$
$684$		0			0
$685$	−6065.42	+	18667.4i	−0.338318	+	1.04124i
$686$		0			0
$687$	−1458.14	+	1059.40i	−0.0809776	+	0.0588337i
$688$		0			0
$689$	−2652.75	−	8164.33i	−0.146679	−	0.451432i
$690$		0			0
$691$	−26542.7	−	19284.4i	−1.46126	−	1.06167i	−0.983032	−	0.183436i	$-0.941278\pi$
$691$	−26542.7	−	19284.4i	−1.46126	−	1.06167i	−0.478231	−	0.878234i	$-0.658722\pi$
$692$		0			0
$693$	−17017.5	−	608.059i	−0.932815	−	0.0333308i
$694$		0			0
$695$	−23524.2	−	17091.4i	−1.28392	−	0.932824i
$696$		0			0
$697$	−7400.86	−	22777.5i	−0.402192	−	1.23782i
$698$		0			0
$699$	858.024	−	623.391i	0.0464284	−	0.0337322i
$700$		0			0
$701$	−5177.08	+	15933.4i	−0.278938	+	0.858484i	0.709212	+	0.704995i	$0.249051\pi$
$701$	−5177.08	+	15933.4i	−0.278938	+	0.858484i	−0.988150	+	0.153489i	$0.950949\pi$
$702$		0			0
$703$	−41292.9			−2.21535
$704$		0			0
$705$	−313.900			−0.0167690
$706$		0			0
$707$	−8373.73	+	25771.7i	−0.445441	+	1.37093i
$708$		0			0
$709$	15984.8	−	11613.6i	0.846716	−	0.615175i	−0.0775226	−	0.996991i	$-0.524701\pi$
$709$	15984.8	−	11613.6i	0.846716	−	0.615175i	0.924239	+	0.381815i	$0.124701\pi$
$710$		0			0
$711$	−5862.92	−	18044.2i	−0.309250	−	0.951774i
$712$		0			0
$713$	−575.940	−	418.445i	−0.0302512	−	0.0219788i
$714$		0			0
$715$	−1577.25	−	5517.38i	−0.0824976	−	0.288585i
$716$		0			0
$717$	1711.82	+	1243.71i	0.0891620	+	0.0647800i
$718$		0			0
$719$	−109.031	−	335.564i	−0.00565533	−	0.0174053i	0.948189	−	0.317707i	$-0.102913\pi$
$719$	−109.031	−	335.564i	−0.00565533	−	0.0174053i	−0.953844	+	0.300301i	$0.902913\pi$
$720$		0			0
$721$	8581.17	−	6234.59i	0.443245	−	0.322036i
$722$		0			0
$723$	568.525	−	1749.74i	0.0292444	−	0.0900049i
$724$		0			0
$725$	4985.75			0.255401
$726$		0			0
$727$	28739.8			1.46616			0.733081	−	0.680141i	$-0.238082\pi$
$727$	28739.8			1.46616			0.733081	+	0.680141i	$0.238082\pi$
$728$		0			0
$729$	−4676.14	+	14391.7i	−0.237572	+	0.731173i
$730$		0			0
$731$	−8120.26	+	5899.72i	−0.410860	+	0.298507i
$732$		0			0
$733$	−3810.12	−	11726.3i	−0.191992	−	0.590890i	−0.999999	−	0.00171673i	$-0.999454\pi$
$733$	−3810.12	−	11726.3i	−0.191992	−	0.590890i	0.808007	−	0.589173i	$-0.200546\pi$
$734$		0			0
$735$	−150.936	−	109.661i	−0.00757462	−	0.00550329i
$736$		0			0
$737$	5066.60	+	17723.5i	0.253230	+	0.885825i
$738$		0			0
$739$	13471.1	+	9787.31i	0.670557	+	0.487188i	0.870212	−	0.492678i	$-0.163982\pi$
$739$	13471.1	+	9787.31i	0.670557	+	0.487188i	−0.199654	+	0.979866i	$0.563982\pi$
$740$		0			0
$741$	−757.009	−	2329.83i	−0.0375296	−	0.115504i
$742$		0			0
$743$	16074.2	−	11678.6i	0.793681	−	0.576643i	−0.115372	−	0.993322i	$-0.536806\pi$
$743$	16074.2	−	11678.6i	0.793681	−	0.576643i	0.909054	+	0.416679i	$0.136806\pi$
$744$		0			0
$745$	−2438.29	+	7504.27i	−0.119909	+	0.369041i
$746$		0			0
$747$	15280.9			0.748459
$748$		0			0
$749$	10131.7			0.494263
$750$		0			0
$751$	8639.71	−	26590.3i	0.419797	−	1.29200i	−0.488092	−	0.872792i	$-0.662307\pi$
$751$	8639.71	−	26590.3i	0.419797	−	1.29200i	0.907889	−	0.419211i	$-0.137693\pi$
$752$		0			0
$753$	−4284.93	+	3113.19i	−0.207373	+	0.150665i
$754$		0			0
$755$	9519.70	+	29298.6i	0.458884	+	1.41230i
$756$		0			0
$757$	20285.0	+	14737.9i	0.973939	+	0.707608i	0.956346	−	0.292237i	$-0.0943996\pi$
$757$	20285.0	+	14737.9i	0.973939	+	0.707608i	0.0175931	+	0.999845i	$0.494400\pi$
$758$		0			0
$759$	1725.32	+	61.6481i	0.0825100	+	0.00294820i
$760$		0			0
$761$	6838.51	+	4968.47i	0.325750	+	0.236671i	0.738625	−	0.674116i	$-0.235475\pi$
$761$	6838.51	+	4968.47i	0.325750	+	0.236671i	−0.412875	+	0.910788i	$0.635475\pi$
$762$		0			0
$763$	−912.227	−	2807.55i	−0.0432829	−	0.133211i
$764$		0			0
$765$	−15989.5	+	11617.0i	−0.755687	+	0.549039i
$766$		0			0
$767$	1168.71	−	3596.93i	0.0550193	−	0.169332i
$768$		0			0
$769$	1122.88			0.0526556			0.0263278	−	0.999653i	$-0.491619\pi$
$769$	1122.88			0.0526556			0.0263278	+	0.999653i	$0.491619\pi$
$770$		0			0
$771$	−3166.12			−0.147893
$772$		0			0
$773$	−24.7372	+	76.1332i	−0.00115101	+	0.00354246i	−0.951630	−	0.307245i	$-0.900593\pi$
$773$	−24.7372	+	76.1332i	−0.00115101	+	0.00354246i	0.950479	+	0.310788i	$0.100593\pi$
$774$		0			0
$775$	427.482	−	310.584i	0.0198137	−	0.0143955i
$776$		0			0
$777$	−1662.33	−	5116.14i	−0.0767515	−	0.236217i
$778$		0			0
$779$	−34779.6	−	25268.9i	−1.59963	−	1.16220i
$780$		0			0
$781$	24477.4	+	19155.8i	1.12147	+	0.877654i
$782$		0			0
$783$	6538.68	+	4750.63i	0.298433	+	0.216825i
$784$		0			0
$785$	3260.68	+	10035.3i	0.148253	+	0.456275i
$786$		0			0
$787$	−9210.19	+	6691.59i	−0.417164	+	0.303087i	−0.776496	−	0.630123i	$-0.783005\pi$
$787$	−9210.19	+	6691.59i	−0.417164	+	0.303087i	0.359332	+	0.933210i	$0.383005\pi$
$788$		0			0
$789$	−2007.62	+	6178.81i	−0.0905868	+	0.278798i
$790$		0			0
$791$	−37633.5			−1.69165
$792$		0			0
$793$	12228.0			0.547578
$794$		0			0
$795$	1594.28	−	4906.68i	0.0711235	−	0.218896i
$796$		0			0
$797$	−2453.26	+	1782.40i	−0.109033	+	0.0792168i	−0.640965	−	0.767570i	$-0.721466\pi$
$797$	−2453.26	+	1782.40i	−0.109033	+	0.0792168i	0.531933	+	0.846786i	$0.321466\pi$
$798$		0			0
$799$	−782.307	−	2407.69i	−0.0346383	−	0.106606i
$800$		0			0
$801$	13912.9	+	10108.3i	0.613718	+	0.445892i
$802$		0			0
$803$	7247.07	−	4879.68i	0.318485	−	0.214446i
$804$		0			0
$805$	6344.07	+	4609.24i	0.277763	+	0.201807i
$806$		0			0
$807$	580.200	+	1785.67i	0.0253085	+	0.0778917i
$808$		0			0
$809$	−26835.1	+	19496.8i	−1.16622	+	0.847308i	−0.990551	−	0.137142i	$-0.956208\pi$
$809$	−26835.1	+	19496.8i	−1.16622	+	0.847308i	−0.175668	+	0.984450i	$0.556208\pi$
$810$		0			0
$811$	3670.38	−	11296.3i	0.158920	−	0.489107i	−0.839617	−	0.543180i	$-0.817220\pi$
$811$	3670.38	−	11296.3i	0.158920	−	0.489107i	0.998537	+	0.0540728i	$0.0172203\pi$
$812$		0			0
$813$	−7975.62			−0.344056
$814$		0			0
$815$	30001.3			1.28945
$816$		0			0
$817$	−5567.53	+	17135.1i	−0.238413	+	0.733758i
$818$		0			0
$819$	−6221.50	+	4520.18i	−0.265442	+	0.192855i
$820$		0			0
$821$	−10457.9	−	32186.1i	−0.444560	−	1.36821i	−0.882966	−	0.469437i	$-0.844457\pi$
$821$	−10457.9	−	32186.1i	−0.444560	−	1.36821i	0.438406	−	0.898777i	$-0.355543\pi$
$822$		0			0
$823$	−13092.9	−	9512.58i	−0.554546	−	0.402901i	0.274913	−	0.961469i	$-0.411351\pi$
$823$	−13092.9	−	9512.58i	−0.554546	−	0.402901i	−0.829459	+	0.558568i	$0.811351\pi$
$824$		0			0
$825$	−439.242	+	1203.77i	−0.0185363	+	0.0508000i
$826$		0			0
$827$	−2633.83	−	1913.59i	−0.110747	−	0.0804621i	0.531034	−	0.847351i	$-0.321804\pi$
$827$	−2633.83	−	1913.59i	−0.110747	−	0.0804621i	−0.641780	+	0.766889i	$0.721804\pi$
$828$		0			0
$829$	−12870.8	−	39612.4i	−0.539231	−	1.65958i	−0.734324	−	0.678799i	$-0.762501\pi$
$829$	−12870.8	−	39612.4i	−0.539231	−	1.65958i	0.195093	−	0.980785i	$-0.437499\pi$
$830$		0			0
$831$	182.654	−	132.706i	0.00762480	−	0.00553974i
$832$		0			0
$833$	464.965	−	1431.02i	0.0193398	−	0.0595219i
$834$		0			0
$835$	−1292.45			−0.0535654
$836$		0			0
$837$	856.570			0.0353732
$838$		0			0
$839$	−12128.9	+	37329.0i	−0.499091	+	1.53604i	0.311393	+	0.950281i	$0.399205\pi$
$839$	−12128.9	+	37329.0i	−0.499091	+	1.53604i	−0.810483	+	0.585762i	$0.800795\pi$
$840$		0			0
$841$	2193.60	−	1593.74i	0.0899421	−	0.0653468i
$842$		0			0
$843$	−217.722	−	670.080i	−0.00889532	−	0.0273770i
$844$		0			0
$845$	14871.6	+	10804.8i	0.605442	+	0.439879i
$846$		0			0
$847$	18332.4	+	15433.4i	0.743695	+	0.626089i
$848$		0			0
$849$	249.165	+	181.029i	0.0100722	+	0.00731789i
$850$		0			0
$851$	−4061.17	−	12499.0i	−0.163590	−	0.503478i
$852$		0			0
$853$	−7157.60	+	5200.30i	−0.287306	+	0.208740i	−0.722098	−	0.691791i	$-0.756822\pi$
$853$	−7157.60	+	5200.30i	−0.287306	+	0.208740i	0.434792	+	0.900531i	$0.356822\pi$
$854$		0			0
$855$	−10962.9	+	33740.4i	−0.438507	+	1.34959i
$856$		0			0
$857$	−42923.0			−1.71088			−0.855439	−	0.517903i	$-0.826713\pi$
$857$	−42923.0			−1.71088			−0.855439	+	0.517903i	$0.826713\pi$
$858$		0			0
$859$	36820.6			1.46252			0.731259	−	0.682100i	$-0.238933\pi$
$859$	36820.6			1.46252			0.731259	+	0.682100i	$0.238933\pi$
$860$		0			0
$861$	1730.65	−	5326.40i	0.0685023	−	0.210828i
$862$		0			0
$863$	−32803.2	+	23832.9i	−1.29390	+	0.940073i	−0.999876	−	0.0157257i	$-0.994994\pi$
$863$	−32803.2	+	23832.9i	−1.29390	+	0.940073i	−0.294023	+	0.955798i	$0.594994\pi$
$864$		0			0
$865$	−3825.01	−	11772.2i	−0.150352	−	0.462735i
$866$		0			0
$867$	1228.88	+	892.836i	0.0481373	+	0.0349738i
$868$		0			0
$869$	−9152.35	+	25082.7i	−0.357275	+	0.979138i
$870$		0			0
$871$	6734.87	+	4893.17i	0.262001	+	0.190355i
$872$		0			0
$873$	10926.3	+	33627.6i	0.423595	+	1.30369i
$874$		0			0
$875$	−22090.5	+	16049.7i	−0.853482	+	0.620091i
$876$		0			0
$877$	−13922.4	+	42848.7i	−0.536061	+	1.64982i	0.205286	+	0.978702i	$0.434188\pi$
$877$	−13922.4	+	42848.7i	−0.536061	+	1.64982i	−0.741346	+	0.671123i	$0.765812\pi$
$878$		0			0
$879$	−6107.53			−0.234359
$880$		0			0
$881$	26845.7			1.02662			0.513312	−	0.858202i	$-0.328418\pi$
$881$	26845.7			1.02662			0.513312	+	0.858202i	$0.328418\pi$
$882$		0			0
$883$	−13997.0	+	43078.2i	−0.533448	+	1.64179i	0.213529	+	0.976937i	$0.431504\pi$
$883$	−13997.0	+	43078.2i	−0.533448	+	1.64179i	−0.746978	+	0.664849i	$0.768496\pi$
$884$		0			0
$885$	1838.87	−	1336.01i	0.0698450	−	0.0507453i
$886$		0			0
$887$	−690.979	−	2126.62i	−0.0261565	−	0.0805014i	0.937126	−	0.348991i	$-0.113476\pi$
$887$	−690.979	−	2126.62i	−0.0261565	−	0.0805014i	−0.963283	+	0.268489i	$0.913476\pi$
$888$		0			0
$889$	−18042.3	−	13108.5i	−0.680674	−	0.494538i
$890$		0			0
$891$	19459.0	−	13102.4i	0.731652	−	0.492644i
$892$		0			0
$893$	−3676.38	−	2671.04i	−0.137766	−	0.100093i
$894$		0			0
$895$	12123.5	+	37312.1i	0.452785	+	1.39353i
$896$		0			0
$897$	630.767	−	458.279i	0.0234790	−	0.0170585i
$898$		0			0
$899$	−709.943	+	2184.98i	−0.0263381	+	0.0810602i
$900$		0			0
$901$	41608.8			1.53850
$902$		0			0
$903$	−2347.15			−0.0864985
$904$		0			0
$905$	4682.86	−	14412.4i	0.172004	−	0.529374i
$906$		0			0
$907$	−4374.73	+	3178.42i	−0.160155	+	0.116359i	−0.664976	−	0.746865i	$-0.731558\pi$
$907$	−4374.73	+	3178.42i	−0.160155	+	0.116359i	0.504821	+	0.863224i	$0.331558\pi$
$908$		0			0
$909$	−12057.2	−	37108.1i	−0.439946	−	1.35401i
$910$		0			0
$911$	−3590.08	−	2608.35i	−0.130565	−	0.0948610i	0.520586	−	0.853809i	$-0.325714\pi$
$911$	−3590.08	−	2608.35i	−0.130565	−	0.0948610i	−0.651151	+	0.758948i	$0.725714\pi$
$912$		0			0
$913$	−16935.2	−	13253.3i	−0.613881	−	0.480418i
$914$		0			0
$915$	5945.39	+	4319.58i	0.214807	+	0.156066i
$916$		0			0
$917$	2100.83	+	6465.67i	0.0756547	+	0.232841i
$918$		0			0
$919$	27843.2	−	20229.3i	0.999416	−	0.726118i	0.0374533	−	0.999298i	$-0.488075\pi$
$919$	27843.2	−	20229.3i	0.999416	−	0.726118i	0.961963	+	0.273180i	$0.0880754\pi$
$920$		0			0
$921$	−400.355	+	1232.17i	−0.0143237	+	0.0440839i
$922$		0			0
$923$	14037.0			0.500576
$924$		0			0
$925$	9754.59			0.346734
$926$		0			0
$927$	−4719.51	+	14525.2i	−0.167216	+	0.514638i
$928$		0			0
$929$	−18848.0	+	13693.9i	−0.665645	+	0.483619i	−0.868565	−	0.495576i	$-0.834957\pi$
$929$	−18848.0	+	13693.9i	−0.665645	+	0.483619i	0.202920	+	0.979195i	$0.434957\pi$
$930$		0			0
$931$	−834.618	−	2568.69i	−0.0293808	−	0.0904247i
$932$		0			0
$933$	8163.81	+	5931.36i	0.286464	+	0.208129i
$934$		0			0
$935$	27796.1	+	993.194i	0.972224	+	0.0347389i
$936$		0			0
$937$	−16473.0	−	11968.4i	−0.574334	−	0.417278i	0.262343	−	0.964975i	$-0.415505\pi$
$937$	−16473.0	−	11968.4i	−0.574334	−	0.417278i	−0.836677	+	0.547697i	$0.815505\pi$
$938$		0			0
$939$	−2696.72	−	8299.66i	−0.0937212	−	0.288444i
$940$		0			0
$941$	−4302.50	+	3125.95i	−0.149051	+	0.108292i	−0.659812	−	0.751431i	$-0.729364\pi$
$941$	−4302.50	+	3125.95i	−0.149051	+	0.108292i	0.510760	+	0.859723i	$0.329364\pi$
$942$		0			0
$943$	4228.07	−	13012.7i	0.146007	−	0.449365i
$944$		0			0
$945$	−9435.25			−0.324792
$946$		0			0
$947$	11908.6			0.408636			0.204318	−	0.978905i	$-0.434502\pi$
$947$	11908.6			0.408636			0.204318	+	0.978905i	$0.434502\pi$
$948$		0			0
$949$	1219.27	−	3752.52i	0.0417061	−	0.128358i
$950$		0			0
$951$	−6011.37	+	4367.52i	−0.204976	+	0.148924i
$952$		0			0
$953$	−5024.32	−	15463.3i	−0.170780	−	0.525607i	0.828635	−	0.559789i	$-0.189118\pi$
$953$	−5024.32	−	15463.3i	−0.170780	−	0.525607i	−0.999416	+	0.0341812i	$0.989118\pi$
$954$		0			0
$955$	−16730.6	−	12155.5i	−0.566900	−	0.411877i
$956$		0			0
$957$	−1531.36	−	5356.85i	−0.0517261	−	0.180943i
$958$		0			0
$959$	−29948.0	−	21758.5i	−1.00842	−	0.732657i
$960$		0			0
$961$	−9130.68	−	28101.4i	−0.306491	−	0.943283i
$962$		0			0
$963$	−11802.2	+	8574.83i	−0.394935	+	0.286937i
$964$		0			0
$965$	6116.94	−	18826.0i	0.204053	−	0.628011i
$966$		0			0
$967$	−11751.0			−0.390783			−0.195392	−	0.980725i	$-0.562598\pi$
$967$	−11751.0			−0.390783			−0.195392	+	0.980725i	$0.562598\pi$
$968$		0			0
$969$	11873.8			0.393644
$970$		0			0
$971$	−6673.15	+	20537.8i	−0.220547	+	0.678775i	0.778166	+	0.628059i	$0.216150\pi$
$971$	−6673.15	+	20537.8i	−0.220547	+	0.678775i	−0.998713	+	0.0507160i	$0.983850\pi$
$972$		0			0
$973$	44365.7	−	32233.5i	1.46177	−	1.06203i
$974$		0			0
$975$	178.828	+	550.375i	0.00587391	+	0.0180780i
$976$		0			0
$977$	−18970.3	−	13782.7i	−0.621201	−	0.451329i	0.232140	−	0.972682i	$-0.425427\pi$
$977$	−18970.3	−	13782.7i	−0.621201	−	0.451329i	−0.853341	+	0.521354i	$0.825427\pi$
$978$		0			0
$979$	−6652.03	−	23269.5i	−0.217160	−	0.759648i
$980$		0			0
$981$	3438.78	+	2498.42i	0.111918	+	0.0813133i
$982$		0			0
$983$	3980.21	+	12249.8i	0.129144	+	0.397465i	0.994633	−	0.103462i	$-0.0329922\pi$
$983$	3980.21	+	12249.8i	0.129144	+	0.397465i	−0.865489	+	0.500928i	$0.832992\pi$
$984$		0			0
$985$	−35361.4	+	25691.6i	−1.14387	+	0.831067i
$986$		0			0
$987$	182.938	−	563.027i	0.00589969	−	0.0181574i
$988$		0			0
$989$	−5734.20			−0.184365
$990$		0			0
$991$	−54990.5			−1.76270			−0.881348	−	0.472468i	$-0.843363\pi$
$991$	−54990.5			−1.76270			−0.881348	+	0.472468i	$0.843363\pi$
$992$		0			0
$993$	−1205.08	+	3708.85i	−0.0385116	+	0.118527i
$994$		0			0
$995$	27180.3	−	19747.6i	0.866004	−	0.629188i
$996$		0			0
$997$	8792.29	+	27059.9i	0.279293	+	0.859574i	0.988052	+	0.154123i	$0.0492553\pi$
$997$	8792.29	+	27059.9i	0.279293	+	0.859574i	−0.708759	+	0.705451i	$0.750745\pi$
$998$		0			0
$999$	12792.9	+	9294.58i	0.405155	+	0.294362i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	176.4.m.e.81.2		16
4.3	odd	2		88.4.i.a.81.3	yes	16
11.3	even	5	inner	176.4.m.e.113.2		16
11.5	even	5		1936.4.a.bw.1.4		8
11.6	odd	10		1936.4.a.bv.1.4		8
44.3	odd	10		88.4.i.a.25.3	✓	16
44.27	odd	10		968.4.a.n.1.5		8
44.39	even	10		968.4.a.o.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.4.i.a.25.3	✓	16	44.3	odd	10
88.4.i.a.81.3	yes	16	4.3	odd	2
176.4.m.e.81.2		16	1.1	even	1	trivial
176.4.m.e.113.2		16	11.3	even	5	inner
968.4.a.n.1.5		8	44.27	odd	10
968.4.a.o.1.5		8	44.39	even	10
1936.4.a.bv.1.4		8	11.6	odd	10
1936.4.a.bw.1.4		8	11.5	even	5

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)

\(f(q)\)	\(=\)	\(q+(-0.320520 + 0.986460i) q^{3} +(-7.72334 + 5.61133i) q^{5} +(-5.56367 - 17.1232i) q^{7} +(20.9731 + 15.2378i) q^{9} +(-10.0276 - 35.0777i) q^{11} +(-13.3294 - 9.68440i) q^{13} +(-3.05987 - 9.41731i) q^{15} +(64.6073 - 46.9400i) q^{17} +(44.2970 - 136.332i) q^{19} +18.6746 q^{21} +45.6230 q^{23} +(-10.4642 + 32.2056i) q^{25} +(-44.4104 + 32.2661i) q^{27} +(-45.4975 - 140.027i) q^{29} +(-12.6239 - 9.17179i) q^{31} +(37.8168 + 1.35125i) q^{33} +(139.054 + 101.029i) q^{35} +(-89.0157 - 273.962i) q^{37} +(13.8256 - 10.0449i) q^{39} +(92.6741 - 285.221i) q^{41} -125.686 q^{43} -247.487 q^{45} +(9.79610 - 30.1493i) q^{47} +(15.2430 - 11.0747i) q^{49} +(25.5964 + 78.7778i) q^{51} +(421.520 + 306.252i) q^{53} +(274.280 + 214.649i) q^{55} +(120.288 + 87.3943i) q^{57} +(70.9340 + 218.312i) q^{59} +(-600.426 + 436.235i) q^{61} +(144.233 - 443.905i) q^{63} +157.290 q^{65} -505.264 q^{67} +(-14.6231 + 45.0053i) q^{69} +(-689.250 + 500.769i) q^{71} +(74.0022 + 227.755i) q^{73} +(-28.4155 - 20.6451i) q^{75} +(-544.853 + 366.866i) q^{77} +(-592.086 - 430.175i) q^{79} +(198.702 + 611.543i) q^{81} +(476.872 - 346.468i) q^{83} +(-235.588 + 725.067i) q^{85} +152.714 q^{87} +663.369 q^{89} +(-91.6674 + 282.123i) q^{91} +(13.0938 - 9.51322i) q^{93} +(422.884 + 1301.50i) q^{95} +(1103.42 + 801.685i) q^{97} +(324.198 - 888.488i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{3} - q^{5} + 13 q^{7} + 7 q^{9} - 83 q^{11} + 69 q^{13} - 93 q^{15} - 217 q^{17} - 126 q^{19} + 34 q^{21} + 92 q^{23} + 307 q^{25} - 158 q^{27} - 553 q^{29} - 205 q^{31} - 198 q^{33} - 7 q^{35}+ \cdots + 3265 q^{99}+O(q^{100}) \) 16 * q + q^3 - q^5 + 13 * q^7 + 7 * q^9 - 83 * q^11 + 69 * q^13 - 93 * q^15 - 217 * q^17 - 126 * q^19 + 34 * q^21 + 92 * q^23 + 307 * q^25 - 158 * q^27 - 553 * q^29 - 205 * q^31 - 198 * q^33 - 7 * q^35 + 127 * q^37 + 629 * q^39 - 553 * q^41 - 70 * q^43 - 1132 * q^45 - 779 * q^47 + 847 * q^49 + 2176 * q^51 + 1401 * q^53 + 385 * q^55 - 488 * q^57 - 1354 * q^59 - 1623 * q^61 - 256 * q^63 + 1674 * q^65 + 1658 * q^67 + 5470 * q^69 - 1985 * q^71 - 1245 * q^73 - 4114 * q^75 - 2645 * q^77 + 2007 * q^79 + 1966 * q^81 + 2946 * q^83 - 1543 * q^85 + 262 * q^87 - 6410 * q^89 - 3937 * q^91 + 2221 * q^93 + 8359 * q^95 + 6566 * q^97 + 3265 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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