LMFDB - Embedded newform 88.4.i.a.81.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [88,4,Mod(9,88)] 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("88.9"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(88, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 6])) N = Newforms(chi, 4, names="a")

Level:	$N$	$=$	$88 = 2^{3} \cdot 11$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	88.i (of order $5$ , degree $4$ , minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.19216808051$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.3
Root			$-1.72876 - 5.32058i$ of defining polynomial
Character	$\chi$	$=$	88.81
Dual form			88.4.i.a.25.3

$q$ -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 $\left(\mathbb{Z}/88\mathbb{Z}\right)^\times$ .

$n$	$23$	$45$	$57$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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	−0.915466	−	0.402396i	$-0.868177\pi$
$3$	0.320520	−	0.986460i	0.0616842	−	0.189844i	0.977150	+	0.212552i	$0.0681774\pi$
$4$		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	$0.0615712\pi$
$7$	5.56367	+	17.1232i	0.300410	+	0.924566i	−0.680941	+	0.732339i	$0.738429\pi$
$8$		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	$0.432954\pi$
$19$	−44.2970	+	136.332i	−0.534864	+	1.64614i	−0.743943	+	0.668244i	$0.767046\pi$
$20$		0			0
$21$	18.6746			0.194054
$22$		0			0
$23$	−45.6230			−0.413611			−0.206806	−	0.978382i	$-0.566307\pi$
$23$	−45.6230			−0.413611			−0.206806	+	0.978382i	$0.566307\pi$
$24$		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	0.623754	−	0.781621i	$-0.285607\pi$
$31$	12.6239	+	9.17179i	0.0731393	+	0.0531388i	−0.550615	+	0.834759i	$0.685607\pi$
$32$		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	$-0.428457\pi$
$43$	125.686			0.445744			0.222872	+	0.974848i	$0.428457\pi$
$44$		0			0
$45$	−247.487			−0.819848
$46$		0			0
$47$	−9.79610	+	30.1493i	−0.0304023	+	0.0935686i	−0.965106	−	0.261859i	$-0.915665\pi$
$47$	−9.79610	+	30.1493i	−0.0304023	+	0.0935686i	0.934704	+	0.355427i	$0.115665\pi$
$48$		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	0.841790	−	0.539806i	$-0.181502\pi$
$59$	−70.9340	−	218.312i	−0.156522	−	0.481726i	−0.998312	+	0.0580796i	$0.981502\pi$
$60$		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	$-0.347615\pi$
$67$	505.264			0.921310			0.460655	+	0.887579i	$0.347615\pi$
$68$		0			0
$69$	−14.6231	+	45.0053i	−0.0255133	+	0.0785218i
$70$		0			0
$71$	689.250	−	500.769i	1.15210	−	0.837048i	0.163339	−	0.986570i	$-0.447774\pi$
$71$	689.250	−	500.769i	1.15210	−	0.837048i	0.988758	+	0.149522i	$0.0477736\pi$
$72$		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	0.923270	−	0.384152i	$-0.125506\pi$
$79$	592.086	+	430.175i	0.843226	+	0.612640i	−0.0800440	+	0.996791i	$0.525506\pi$
$80$		0			0
$81$	198.702	+	611.543i	0.272569	+	0.838880i
$82$		0			0
$83$	−476.872	+	346.468i	−0.630645	+	0.458190i	−0.856624	−	0.515942i	$-0.827442\pi$
$83$	−476.872	+	346.468i	−0.630645	+	0.458190i	0.225979	+	0.974132i	$0.427442\pi$
$84$		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	0.825439	−	0.564492i	$-0.190928\pi$
$103$	−182.051	−	560.295i	−0.174155	−	0.535995i	−0.999594	+	0.0284970i	$0.990928\pi$
$104$		0			0
$105$	−144.230	+	104.790i	−0.134052	+	0.0973944i
$106$		0			0
$107$	173.894	−	535.191i	0.157112	−	0.483540i	−0.841257	−	0.540636i	$-0.818184\pi$
$107$	173.894	−	535.191i	0.157112	−	0.483540i	0.998369	+	0.0570951i	$0.0181838\pi$
$108$		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	−0.879990	−	0.474993i	$-0.842451\pi$
$127$	−1002.10	+	728.071i	−0.700176	+	0.508708i	0.179814	+	0.983701i	$0.442451\pi$
$128$		0			0
$129$	40.2850	−	123.985i	0.0274954	−	0.0846220i
$130$		0			0
$131$	377.597			0.251838			0.125919	−	0.992041i	$-0.459812\pi$
$131$	377.597			0.251838			0.125919	+	0.992041i	$0.459812\pi$
$132$		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	$-0.720407\pi$
$139$	−941.224	−	2896.79i	−0.574342	−	1.76764i	0.0640657	−	0.997946i	$-0.479593\pi$
$140$		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	$0.435596\pi$
$151$	−997.185	+	3069.02i	−0.537416	+	1.65400i	−0.738370	+	0.674395i	$0.764404\pi$
$152$		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	0.996241	−	0.0866242i	$-0.0276079\pi$
$163$	2542.44	+	1847.19i	1.22171	+	0.887626i	0.225471	+	0.974250i	$0.427608\pi$
$164$		0			0
$165$	−299.654	+	201.767i	−0.141382	+	0.0951971i
$166$		0			0
$167$	−109.528	−	79.5766i	−0.0507516	−	0.0368732i	0.562120	−	0.827056i	$-0.309986\pi$
$167$	−109.528	−	79.5766i	−0.0507516	−	0.0368732i	−0.612872	+	0.790182i	$0.709986\pi$
$168$		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	$0.428293\pi$
$179$	−1269.93	+	3908.43i	−0.530273	+	1.63201i	−0.753647	+	0.657279i	$0.771707\pi$
$180$		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	$-0.965416\pi$
$191$	−669.405	−	2060.22i	−0.253594	−	0.780482i	0.740510	−	0.672046i	$-0.234584\pi$
$192$		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	$-0.284358\pi$
$199$	3519.24			1.25363			0.626815	+	0.779168i	$0.284358\pi$
$200$		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	0.211655	−	0.977345i	$-0.432115\pi$
$211$	−1999.73	−	1452.89i	−0.652450	−	0.474033i	−0.864105	+	0.503312i	$0.832115\pi$
$212$		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	$-0.634832\pi$
$223$	1522.98	−	4687.24i	0.457336	−	1.40754i	0.868370	−	0.495917i	$-0.165168\pi$
$224$		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	$-0.968946\pi$
$227$	−845.888	−	2603.38i	−0.247329	−	0.761199i	0.747916	−	0.663793i	$-0.231054\pi$
$228$		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	−0.999406	−	0.0344619i	$-0.989028\pi$
$239$	−630.391	+	1940.14i	−0.170613	+	0.525094i	0.828793	+	0.559556i	$0.189028\pi$
$240$		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	−0.0688040	−	0.997630i	$-0.521918\pi$
$251$	−4131.15	−	3001.46i	−1.03887	−	0.754782i	−0.970064	+	0.242848i	$0.921918\pi$
$252$		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	$-0.762480\pi$
$263$	−6263.62			−1.46856			−0.734280	+	0.678847i	$0.762480\pi$
$264$		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	$-0.769336\pi$
$271$	−2376.15	−	7313.04i	−0.532623	−	1.63925i	0.216106	−	0.976370i	$-0.430664\pi$
$272$		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	−0.960231	−	0.279208i	$-0.909928\pi$
$283$	−91.7568	+	282.398i	−0.0192734	+	0.0593175i	0.940957	+	0.338525i	$0.109928\pi$
$284$		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	$-0.537041\pi$
$307$	−1249.08			−0.232211			−0.116105	+	0.993237i	$0.537041\pi$
$308$		0			0
$309$	−611.059			−0.112498
$310$		0			0
$311$	−3006.39	+	9252.70i	−0.548156	+	1.68705i	0.165210	+	0.986258i	$0.447170\pi$
$311$	−3006.39	+	9252.70i	−0.548156	+	1.68705i	−0.713366	+	0.700792i	$0.752830\pi$
$312$		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	$-0.601055\pi$
$331$	−3759.76			−0.624336			−0.312168	+	0.950027i	$0.601055\pi$
$332$		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	−0.104171	−	0.994559i	$-0.533219\pi$
$347$	5232.66	−	3801.75i	0.809521	−	0.588151i	0.913692	+	0.406408i	$0.133219\pi$
$348$		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	$0.170189\pi$
$359$	3155.05	+	9710.26i	0.463837	+	1.42754i	−0.396603	+	0.917990i	$0.629811\pi$
$360$		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	0.821342	−	0.570435i	$-0.193226\pi$
$367$	−1254.50	−	3860.94i	−0.178431	−	0.549154i	−0.999774	+	0.0212811i	$0.993226\pi$
$368$		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	−0.346512	−	0.938045i	$-0.612634\pi$
$379$	3235.73	−	2350.89i	0.438544	−	0.318621i	0.785056	+	0.619425i	$0.212634\pi$
$380$		0			0
$381$	397.018	+	1221.90i	0.0533855	+	0.164304i
$382$		0			0
$383$	−8325.71	−	6048.98i	−1.11077	−	0.807020i	−0.127983	−	0.991776i	$-0.540850\pi$
$383$	−8325.71	−	6048.98i	−1.11077	−	0.807020i	−0.982784	+	0.184757i	$0.940850\pi$
$384$		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	$-0.426220\pi$
$419$	3940.43			0.459433			0.229717	+	0.973258i	$0.426220\pi$
$420$		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	0.325885	−	0.945410i	$-0.394338\pi$
$431$	−4228.27	−	3072.02i	−0.472549	−	0.343327i	−0.798434	+	0.602082i	$0.794338\pi$
$432$		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	$-0.438220\pi$
$439$	3548.07			0.385741			0.192871	+	0.981224i	$0.438220\pi$
$440$		0			0
$441$	488.448			0.0527425
$442$		0			0
$443$	2520.57	−	7757.52i	0.270330	−	0.831989i	−0.720088	−	0.693883i	$-0.755899\pi$
$443$	2520.57	−	7757.52i	0.270330	−	0.831989i	0.990417	−	0.138106i	$-0.0441015\pi$
$444$		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	$-0.507535\pi$
$463$	−471.604			−0.0473376			−0.0236688	+	0.999720i	$0.507535\pi$
$464$		0			0
$465$	−47.7462	+	146.948i	−0.00476167	+	0.0146549i
$466$		0			0
$467$	−7448.45	+	5411.61i	−0.738058	+	0.536231i	−0.892102	−	0.451833i	$-0.850770\pi$
$467$	−7448.45	+	5411.61i	−0.738058	+	0.536231i	0.154044	+	0.988064i	$0.450770\pi$
$468$		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	−0.637385	−	0.770546i	$-0.719984\pi$
$479$	−1064.22	+	773.203i	−0.101515	+	0.0737548i	0.535870	+	0.844301i	$0.319984\pi$
$480$		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	$0.207353\pi$
$487$	−2197.89	+	6764.40i	−0.204509	+	0.629414i	−0.999733	+	0.0230983i	$0.992647\pi$
$488$		0			0
$489$	2637.08	−	1915.95i	0.243871	−	0.177183i
$490$		0			0
$491$	−521.486	−	1604.97i	−0.0479314	−	0.147518i	0.924226	−	0.381845i	$-0.124711\pi$
$491$	−521.486	−	1604.97i	−0.0479314	−	0.147518i	−0.972158	+	0.234327i	$0.924711\pi$
$492$		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	$0.0995511\pi$
$499$	4041.45	+	12438.3i	0.362566	+	1.11586i	−0.588926	+	0.808187i	$0.700449\pi$
$500$		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	$-0.710501\pi$
$503$	3909.83	−	12033.2i	0.346581	−	1.06667i	0.960732	−	0.277479i	$-0.0894989\pi$
$504$		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	0.303521	−	0.952825i	$-0.401838\pi$
$523$	15590.7	−	11327.3i	1.30350	−	0.947052i	0.999983	+	0.00577306i	$0.00183763\pi$
$524$		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	−0.972889	−	0.231273i	$-0.925711\pi$
$547$	−637.955	+	1963.42i	−0.0498665	+	0.153473i	0.923022	+	0.384746i	$0.125711\pi$
$548$		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	0.743209	−	0.669059i	$-0.233303\pi$
$563$	4495.98	+	3266.52i	0.336560	+	0.244525i	−0.406649	+	0.913584i	$0.633303\pi$
$564$		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	$-0.702618\pi$
$571$	−16220.9			−1.18884			−0.594418	+	0.804156i	$0.702618\pi$
$572$		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	0.851090	−	0.525020i	$-0.175942\pi$
$587$	−2077.18	−	6392.91i	−0.146055	−	0.449512i	−0.997145	+	0.0755079i	$0.975942\pi$
$588$		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	−0.324660	−	0.945831i	$-0.605250\pi$
$599$	6957.04	−	5054.59i	0.474553	−	0.344783i	0.799213	+	0.601048i	$0.205250\pi$
$600$		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	0.0612604	−	0.998122i	$-0.480488\pi$
$607$	−12997.0	−	9442.86i	−0.869079	−	0.631423i	−0.930340	+	0.366699i	$0.880488\pi$
$608$		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	−0.945204	−	0.326481i	$-0.894137\pi$
$619$	175.300	−	539.518i	0.0113827	−	0.0350324i	0.956587	+	0.291448i	$0.0941372\pi$
$620$		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	$-0.850649\pi$
$631$	−6912.81	−	21275.4i	−0.436125	−	1.34225i	0.455805	−	0.890080i	$-0.349351\pi$
$632$		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	$0.607941\pi$
$643$	−21723.5	+	15783.0i	−1.33233	+	0.967996i	−0.999689	+	0.0249433i	$0.992059\pi$
$644$		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	$-0.934375\pi$
$647$	−24290.6	−	17648.2i	−1.47598	−	1.07237i	−0.497162	−	0.867658i	$-0.665625\pi$
$648$		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	$-0.475839\pi$
$659$	2565.72			0.151664			0.0758319	+	0.997121i	$0.475839\pi$
$660$		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	$-0.698577\pi$
$683$	−20854.2			−1.16832			−0.584162	+	0.811637i	$0.698577\pi$
$684$		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	$0.0587220\pi$
$691$	26542.7	+	19284.4i	1.46126	+	1.06167i	0.478231	+	0.878234i	$0.341278\pi$
$692$		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	0.953844	−	0.300301i	$-0.0970873\pi$
$719$	109.031	+	335.564i	0.00565533	+	0.0174053i	−0.948189	+	0.317707i	$0.897087\pi$
$720$		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	$-0.761918\pi$
$727$	−28739.8			−1.46616			−0.733081	+	0.680141i	$0.761918\pi$
$728$		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	0.199654	−	0.979866i	$-0.436018\pi$
$739$	−13471.1	−	9787.31i	−0.670557	−	0.487188i	−0.870212	+	0.492678i	$0.836018\pi$
$740$		0			0
$741$	−757.009	−	2329.83i	−0.0375296	−	0.115504i
$742$		0			0
$743$	−16074.2	+	11678.6i	−0.793681	+	0.576643i	−0.909054	−	0.416679i	$-0.863194\pi$
$743$	−16074.2	+	11678.6i	−0.793681	+	0.576643i	0.115372	+	0.993322i	$0.463194\pi$
$744$		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	$0.337693\pi$
$751$	−8639.71	+	26590.3i	−0.419797	+	1.29200i	−0.907889	+	0.419211i	$0.862307\pi$
$752$		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	−0.359332	−	0.933210i	$-0.616995\pi$
$787$	9210.19	−	6691.59i	0.417164	−	0.303087i	0.776496	+	0.630123i	$0.216995\pi$
$788$		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	−0.998537	−	0.0540728i	$-0.982780\pi$
$811$	−3670.38	+	11296.3i	−0.158920	+	0.489107i	0.839617	+	0.543180i	$0.182780\pi$
$812$		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	0.829459	−	0.558568i	$-0.188649\pi$
$823$	13092.9	+	9512.58i	0.554546	+	0.402901i	−0.274913	+	0.961469i	$0.588649\pi$
$824$		0			0
$825$	−439.242	+	1203.77i	−0.0185363	+	0.0508000i
$826$		0			0
$827$	2633.83	+	1913.59i	0.110747	+	0.0804621i	0.641780	−	0.766889i	$-0.278196\pi$
$827$	2633.83	+	1913.59i	0.110747	+	0.0804621i	−0.531034	+	0.847351i	$0.678196\pi$
$828$		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	$-0.600795\pi$
$839$	12128.9	−	37329.0i	0.499091	−	1.53604i	0.810483	−	0.585762i	$-0.199205\pi$
$840$		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	$-0.761067\pi$
$859$	−36820.6			−1.46252			−0.731259	+	0.682100i	$0.761067\pi$
$860$		0			0
$861$	1730.65	−	5326.40i	0.0685023	−	0.210828i
$862$		0			0
$863$	32803.2	−	23832.9i	1.29390	−	0.940073i	0.294023	−	0.955798i	$-0.405006\pi$
$863$	32803.2	−	23832.9i	1.29390	−	0.940073i	0.999876	+	0.0157257i	$0.00500586\pi$
$864$		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	$-0.568496\pi$
$883$	13997.0	−	43078.2i	0.533448	−	1.64179i	0.746978	−	0.664849i	$-0.231504\pi$
$884$		0			0
$885$	1838.87	−	1336.01i	0.0698450	−	0.0507453i
$886$		0			0
$887$	690.979	+	2126.62i	0.0261565	+	0.0805014i	0.963283	−	0.268489i	$-0.0865244\pi$
$887$	690.979	+	2126.62i	0.0261565	+	0.0805014i	−0.937126	+	0.348991i	$0.886524\pi$
$888$		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	−0.504821	−	0.863224i	$-0.668442\pi$
$907$	4374.73	−	3178.42i	0.160155	−	0.116359i	0.664976	+	0.746865i	$0.268442\pi$
$908$		0			0
$909$	−12057.2	−	37108.1i	−0.439946	−	1.35401i
$910$		0			0
$911$	3590.08	+	2608.35i	0.130565	+	0.0948610i	0.651151	−	0.758948i	$-0.274286\pi$
$911$	3590.08	+	2608.35i	0.130565	+	0.0948610i	−0.520586	+	0.853809i	$0.674286\pi$
$912$		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	−0.961963	−	0.273180i	$-0.911925\pi$
$919$	−27843.2	+	20229.3i	−0.999416	+	0.726118i	−0.0374533	+	0.999298i	$0.511925\pi$
$920$		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	$-0.565498\pi$
$947$	−11908.6			−0.408636			−0.204318	+	0.978905i	$0.565498\pi$
$948$		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	$-0.437402\pi$
$967$	11751.0			0.390783			0.195392	+	0.980725i	$0.437402\pi$
$968$		0			0
$969$	11873.8			0.393644
$970$		0			0
$971$	6673.15	−	20537.8i	0.220547	−	0.678775i	−0.778166	−	0.628059i	$-0.783850\pi$
$971$	6673.15	−	20537.8i	0.220547	−	0.678775i	0.998713	−	0.0507160i	$-0.0161503\pi$
$972$		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	0.865489	−	0.500928i	$-0.167008\pi$
$983$	−3980.21	−	12249.8i	−0.129144	−	0.397465i	−0.994633	+	0.103462i	$0.967008\pi$
$984$		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	$-0.156637\pi$
$991$	54990.5			1.76270			0.881348	+	0.472468i	$0.156637\pi$
$992$		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

Display

a_p

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p

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a_n

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a_n

instead) (See

a_n

instead) Display

a_n

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a_p

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Twists

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

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

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

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Modular forms

Varieties

Fields

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Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	88.4.i.a.81.3

Level	$88$
Weight	$4$
Character	88.81
Analytic conductor	$5.192$
Analytic rank	$0$
Dimension	$16$
Inner twists	$2$