LMFDB - Embedded newform 867.2.h.m.688.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [867,2,Mod(688,867)] 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("867.688"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(867, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.h (of order $8$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-120] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(16)] == traces)

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

Self dual:	no
Analytic conductor:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			688.12
Character	$\chi$	$=$	867.688
Dual form			867.2.h.m.712.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.48173 - 1.48173i) q^{2} +(0.382683 - 0.923880i) q^{3} -2.39104i q^{4} +(-1.43955 - 0.596279i) q^{5} +(-0.801906 - 1.93597i) q^{6} +(3.82062 - 1.58255i) q^{7} +(-0.579419 - 0.579419i) q^{8} +(-0.707107 - 0.707107i) q^{9} +(-3.01654 + 1.24949i) q^{10} +(-1.69602 - 4.09455i) q^{11} +(-2.20903 - 0.915012i) q^{12} +3.67837i q^{13} +(3.31621 - 8.00605i) q^{14} +(-1.10178 + 1.10178i) q^{15} +3.06500 q^{16} -2.09548 q^{18} +(-0.287454 + 0.287454i) q^{19} +(-1.42573 + 3.44201i) q^{20} -4.13541i q^{21} +(-8.58005 - 3.55397i) q^{22} +(-2.47808 - 5.98262i) q^{23} +(-0.757047 + 0.313579i) q^{24} +(-1.81879 - 1.81879i) q^{25} +(5.45035 + 5.45035i) q^{26} +(-0.923880 + 0.382683i) q^{27} +(-3.78395 - 9.13527i) q^{28} +(4.14501 + 1.71692i) q^{29} +3.26508i q^{30} +(-4.13225 + 9.97614i) q^{31} +(5.70034 - 5.70034i) q^{32} -4.43191 q^{33} -6.44361 q^{35} +(-1.69072 + 1.69072i) q^{36} +(0.273041 - 0.659180i) q^{37} +0.851857i q^{38} +(3.39838 + 1.40765i) q^{39} +(0.488604 + 1.17959i) q^{40} +(-1.85438 + 0.768109i) q^{41} +(-6.12756 - 6.12756i) q^{42} +(2.92181 + 2.92181i) q^{43} +(-9.79024 + 4.05525i) q^{44} +(0.596279 + 1.43955i) q^{45} +(-12.5365 - 5.19278i) q^{46} +8.22412i q^{47} +(1.17293 - 2.83169i) q^{48} +(7.14295 - 7.14295i) q^{49} -5.38991 q^{50} +8.79515 q^{52} +(2.89067 - 2.89067i) q^{53} +(-0.801906 + 1.93597i) q^{54} +6.90559i q^{55} +(-3.13070 - 1.29678i) q^{56} +(0.155569 + 0.375576i) q^{57} +(8.68579 - 3.59777i) q^{58} +(4.32564 + 4.32564i) q^{59} +(2.63440 + 2.63440i) q^{60} +(4.92577 - 2.04032i) q^{61} +(8.65906 + 20.9048i) q^{62} +(-3.82062 - 1.58255i) q^{63} -10.7627i q^{64} +(2.19334 - 5.29519i) q^{65} +(-6.56688 + 6.56688i) q^{66} -6.53830 q^{67} -6.47554 q^{69} +(-9.54768 + 9.54768i) q^{70} +(-0.625392 + 1.50983i) q^{71} +0.819422i q^{72} +(-4.36779 - 1.80920i) q^{73} +(-0.572153 - 1.38130i) q^{74} +(-2.37636 + 0.984322i) q^{75} +(0.687314 + 0.687314i) q^{76} +(-12.9597 - 12.9597i) q^{77} +(7.12123 - 2.94971i) q^{78} +(2.16250 + 5.22074i) q^{79} +(-4.41221 - 1.82760i) q^{80} +1.00000i q^{81} +(-1.60956 + 3.88582i) q^{82} +(8.45025 - 8.45025i) q^{83} -9.88795 q^{84} +8.65866 q^{86} +(3.17245 - 3.17245i) q^{87} +(-1.38975 + 3.35516i) q^{88} -9.33759i q^{89} +(3.01654 + 1.24949i) q^{90} +(5.82123 + 14.0537i) q^{91} +(-14.3047 + 5.92520i) q^{92} +(7.63541 + 7.63541i) q^{93} +(12.1859 + 12.1859i) q^{94} +(0.585206 - 0.242400i) q^{95} +(-3.08500 - 7.44785i) q^{96} +(12.1316 + 5.02506i) q^{97} -21.1678i q^{98} +(-1.69602 + 4.09455i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 120 q^{16} + 24 q^{18} + 72 q^{33} - 96 q^{50} - 144 q^{52} + 48 q^{67} - 72 q^{69} + 120 q^{84} + 48 q^{86}+O(q^{100}) $ 48 * q - 120 * q^16 + 24 * q^18 + 72 * q^33 - 96 * q^50 - 144 * q^52 + 48 * q^67 - 72 * q^69 + 120 * q^84 + 48 * q^86

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$

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 $

$2$	1.48173	−	1.48173i	1.04774	−	1.04774i	0.0489389	−	0.998802i	$-0.484416\pi$
$2$	1.48173	−	1.48173i	1.04774	−	1.04774i	0.998802	−	0.0489389i	$-0.0155840\pi$
$3$	0.382683	−	0.923880i	0.220942	−	0.533402i
$3$	0.382683	−	0.923880i	0.220942	−	0.533402i
$4$		−	2.39104i		−	1.19552i
$5$	−1.43955	−	0.596279i	−0.643785	−	0.266664i	0.0368126	−	0.999322i	$-0.488280\pi$
$5$	−1.43955	−	0.596279i	−0.643785	−	0.266664i	−0.680597	+	0.732658i	$0.738280\pi$
$6$	−0.801906	−	1.93597i	−0.327377	−	0.790357i
$7$	3.82062	−	1.58255i	1.44406	−	0.598149i	0.483282	−	0.875465i	$-0.339445\pi$
$7$	3.82062	−	1.58255i	1.44406	−	0.598149i	0.960779	+	0.277316i	$0.0894448\pi$
$8$	−0.579419	−	0.579419i	−0.204855	−	0.204855i
$9$	−0.707107	−	0.707107i	−0.235702	−	0.235702i
$10$	−3.01654	+	1.24949i	−0.953914	+	0.395124i
$11$	−1.69602	−	4.09455i	−0.511368	−	1.23455i	−0.943088	−	0.332544i	$-0.892093\pi$
$11$	−1.69602	−	4.09455i	−0.511368	−	1.23455i	0.431719	−	0.902008i	$-0.357907\pi$
$12$	−2.20903	−	0.915012i	−0.637693	−	0.264141i
$13$			3.67837i			1.02020i	0.860116	+	0.510099i	$0.170391\pi$
$13$			3.67837i			1.02020i	−0.860116	+	0.510099i	$0.829609\pi$
$14$	3.31621	−	8.00605i	0.886295	−	2.13971i
$15$	−1.10178	+	1.10178i	−0.284479	+	0.284479i
$16$	3.06500			0.766250
$17$		0			0
$17$		0			0
$18$	−2.09548			−0.493910
$19$	−0.287454	+	0.287454i	−0.0659464	+	0.0659464i	−0.739311	−	0.673364i	$-0.764849\pi$
$19$	−0.287454	+	0.287454i	−0.0659464	+	0.0659464i	0.673364	+	0.739311i	$0.264849\pi$
$20$	−1.42573	+	3.44201i	−0.318803	+	0.769658i
$21$		−	4.13541i		−	0.902421i
$22$	−8.58005	−	3.55397i	−1.82927	−	0.757709i
$23$	−2.47808	−	5.98262i	−0.516716	−	1.24746i	−0.939909	−	0.341424i	$-0.889091\pi$
$23$	−2.47808	−	5.98262i	−0.516716	−	1.24746i	0.423193	−	0.906039i	$-0.360909\pi$
$24$	−0.757047	+	0.313579i	−0.154532	+	0.0640091i
$25$	−1.81879	−	1.81879i	−0.363758	−	0.363758i
$26$	5.45035	+	5.45035i	1.06890	+	1.06890i
$27$	−0.923880	+	0.382683i	−0.177801	+	0.0736475i
$28$	−3.78395	−	9.13527i	−0.715100	−	1.72640i
$29$	4.14501	+	1.71692i	0.769709	+	0.318824i	0.732754	−	0.680493i	$-0.238234\pi$
$29$	4.14501	+	1.71692i	0.769709	+	0.318824i	0.0369542	+	0.999317i	$0.488234\pi$
$30$			3.26508i			0.596120i
$31$	−4.13225	+	9.97614i	−0.742175	+	1.79177i	−0.145378	+	0.989376i	$0.546440\pi$
$31$	−4.13225	+	9.97614i	−0.742175	+	1.79177i	−0.596797	+	0.802392i	$0.703560\pi$
$32$	5.70034	−	5.70034i	1.00769	−	1.00769i
$33$	−4.43191			−0.771496
$34$		0			0
$35$	−6.44361			−1.08917
$36$	−1.69072	+	1.69072i	−0.281787	+	0.281787i
$37$	0.273041	−	0.659180i	0.0448877	−	0.108369i	−0.899845	−	0.436209i	$-0.856321\pi$
$37$	0.273041	−	0.659180i	0.0448877	−	0.108369i	0.944733	+	0.327840i	$0.106321\pi$
$38$			0.851857i			0.138190i
$39$	3.39838	+	1.40765i	0.544176	+	0.225405i
$40$	0.488604	+	1.17959i	0.0772551	+	0.186510i
$41$	−1.85438	+	0.768109i	−0.289605	+	0.119958i	−0.522757	−	0.852482i	$-0.675096\pi$
$41$	−1.85438	+	0.768109i	−0.289605	+	0.119958i	0.233151	+	0.972441i	$0.425096\pi$
$42$	−6.12756	−	6.12756i	−0.945504	−	0.945504i
$43$	2.92181	+	2.92181i	0.445572	+	0.445572i	0.893879	−	0.448308i	$-0.147973\pi$
$43$	2.92181	+	2.92181i	0.445572	+	0.445572i	−0.448308	+	0.893879i	$0.647973\pi$
$44$	−9.79024	+	4.05525i	−1.47593	+	0.611352i
$45$	0.596279	+	1.43955i	0.0888881	+	0.214595i
$46$	−12.5365	−	5.19278i	−1.84840	−	0.765633i
$47$			8.22412i			1.19961i	0.800146	+	0.599806i	$0.204756\pi$
$47$			8.22412i			1.19961i	−0.800146	+	0.599806i	$0.795244\pi$
$48$	1.17293	−	2.83169i	0.169297	−	0.408720i
$49$	7.14295	−	7.14295i	1.02042	−	1.02042i
$50$	−5.38991			−0.762248
$51$		0			0
$52$	8.79515			1.21967
$53$	2.89067	−	2.89067i	0.397065	−	0.397065i	−0.480132	−	0.877196i	$-0.659411\pi$
$53$	2.89067	−	2.89067i	0.397065	−	0.397065i	0.877196	+	0.480132i	$0.159411\pi$
$54$	−0.801906	+	1.93597i	−0.109126	+	0.263452i
$55$			6.90559i			0.931149i
$56$	−3.13070	−	1.29678i	−0.418358	−	0.173289i
$57$	0.155569	+	0.375576i	0.0206056	+	0.0497463i
$58$	8.68579	−	3.59777i	1.14050	−	0.472410i
$59$	4.32564	+	4.32564i	0.563150	+	0.563150i	0.930201	−	0.367051i	$-0.119632\pi$
$59$	4.32564	+	4.32564i	0.563150	+	0.563150i	−0.367051	+	0.930201i	$0.619632\pi$
$60$	2.63440	+	2.63440i	0.340100	+	0.340100i
$61$	4.92577	−	2.04032i	0.630680	−	0.261236i	−0.0443618	−	0.999016i	$-0.514125\pi$
$61$	4.92577	−	2.04032i	0.630680	−	0.261236i	0.675042	+	0.737779i	$0.264125\pi$
$62$	8.65906	+	20.9048i	1.09970	+	2.65492i
$63$	−3.82062	−	1.58255i	−0.481353	−	0.199383i
$64$		−	10.7627i		−	1.34534i
$65$	2.19334	−	5.29519i	0.272050	−	0.656787i
$66$	−6.56688	+	6.56688i	−0.808328	+	0.808328i
$67$	−6.53830			−0.798780			−0.399390	−	0.916781i	$-0.630778\pi$
$67$	−6.53830			−0.798780			−0.399390	+	0.916781i	$0.630778\pi$
$68$		0			0
$69$	−6.47554			−0.779564
$70$	−9.54768	+	9.54768i	−1.14117	+	1.14117i
$71$	−0.625392	+	1.50983i	−0.0742204	+	0.179184i	−0.956635	−	0.291288i	$-0.905916\pi$
$71$	−0.625392	+	1.50983i	−0.0742204	+	0.179184i	0.882415	+	0.470472i	$0.155916\pi$
$72$			0.819422i			0.0965698i
$73$	−4.36779	−	1.80920i	−0.511211	−	0.211750i	0.112140	−	0.993692i	$-0.464229\pi$
$73$	−4.36779	−	1.80920i	−0.511211	−	0.211750i	−0.623351	+	0.781942i	$0.714229\pi$
$74$	−0.572153	−	1.38130i	−0.0665114	−	0.160573i
$75$	−2.37636	+	0.984322i	−0.274399	+	0.113660i
$76$	0.687314	+	0.687314i	0.0788403	+	0.0788403i
$77$	−12.9597	−	12.9597i	−1.47689	−	1.47689i
$78$	7.12123	−	2.94971i	0.806321	−	0.333989i
$79$	2.16250	+	5.22074i	0.243301	+	0.587380i	0.997607	−	0.0691433i	$-0.0220266\pi$
$79$	2.16250	+	5.22074i	0.243301	+	0.587380i	−0.754306	+	0.656523i	$0.772027\pi$
$80$	−4.41221	−	1.82760i	−0.493300	−	0.204332i
$81$			1.00000i			0.111111i
$82$	−1.60956	+	3.88582i	−0.177746	+	0.429117i
$83$	8.45025	−	8.45025i	0.927535	−	0.927535i	−0.0700108	−	0.997546i	$-0.522303\pi$
$83$	8.45025	−	8.45025i	0.927535	−	0.927535i	0.997546	+	0.0700108i	$0.0223034\pi$
$84$	−9.88795			−1.07886
$85$		0			0
$86$	8.65866			0.933687
$87$	3.17245	−	3.17245i	0.340122	−	0.340122i
$88$	−1.38975	+	3.35516i	−0.148148	+	0.357661i
$89$		−	9.33759i		−	0.989783i	−0.868955	−	0.494892i	$-0.835208\pi$
$89$		−	9.33759i		−	0.989783i	0.868955	−	0.494892i	$-0.164792\pi$
$90$	3.01654	+	1.24949i	0.317971	+	0.131708i
$91$	5.82123	+	14.0537i	0.610231	+	1.47323i
$92$	−14.3047	+	5.92520i	−1.49137	+	0.617745i
$93$	7.63541	+	7.63541i	0.791755	+	0.791755i
$94$	12.1859	+	12.1859i	1.25688	+	1.25688i
$95$	0.585206	−	0.242400i	0.0600408	−	0.0248697i
$96$	−3.08500	−	7.44785i	−0.314862	−	0.760143i
$97$	12.1316	+	5.02506i	1.23177	+	0.510217i	0.901134	−	0.433540i	$-0.142736\pi$
$97$	12.1316	+	5.02506i	1.23177	+	0.510217i	0.330639	+	0.943757i	$0.392736\pi$
$98$		−	21.1678i		−	2.13827i
$99$	−1.69602	+	4.09455i	−0.170456	+	0.411517i
$100$	−4.34881	+	4.34881i	−0.434881	+	0.434881i
$101$	−2.75389			−0.274022			−0.137011	−	0.990570i	$-0.543750\pi$
$101$	−2.75389			−0.274022			−0.137011	+	0.990570i	$0.543750\pi$
$102$		0			0
$103$	10.7754			1.06173			0.530865	−	0.847456i	$-0.321867\pi$
$103$	10.7754			1.06173			0.530865	+	0.847456i	$0.321867\pi$
$104$	2.13132	−	2.13132i	0.208993	−	0.208993i
$105$	−2.46586	+	5.95312i	−0.240644	+	0.580965i
$106$		−	8.56639i		−	0.832041i
$107$	−2.90282	−	1.20239i	−0.280627	−	0.116239i	0.237931	−	0.971282i	$-0.423531\pi$
$107$	−2.90282	−	1.20239i	−0.280627	−	0.116239i	−0.518558	+	0.855043i	$0.673531\pi$
$108$	0.915012	+	2.20903i	0.0880471	+	0.212564i
$109$	1.86390	−	0.772053i	0.178529	−	0.0739493i	−0.291628	−	0.956532i	$-0.594197\pi$
$109$	1.86390	−	0.772053i	0.178529	−	0.0739493i	0.470158	+	0.882582i	$0.344197\pi$
$110$	10.2322	+	10.2322i	0.975603	+	0.975603i
$111$	−0.504515	−	0.504515i	−0.0478864	−	0.0478864i
$112$	11.7102	−	4.85053i	1.10651	−	0.458332i
$113$	3.01099	+	7.26916i	0.283250	+	0.683825i	0.999908	−	0.0135998i	$-0.00432907\pi$
$113$	3.01099	+	7.26916i	0.283250	+	0.683825i	−0.716658	+	0.697425i	$0.754329\pi$
$114$	0.787014	+	0.325992i	0.0737106	+	0.0305319i
$115$			10.0899i			0.940887i
$116$	4.10522	−	9.91089i	0.381160	−	0.920203i
$117$	2.60100	−	2.60100i	0.240463	−	0.240463i
$118$	12.8188			1.18007
$119$		0			0
$120$	1.27678			0.116554
$121$	−6.11067	+	6.11067i	−0.555515	+	0.555515i
$122$	4.27546	−	10.3219i	0.387082	−	0.934497i
$123$			2.00717i			0.180980i
$124$	23.8534	+	9.88039i	2.14210	+	0.887286i
$125$	4.51512	+	10.9005i	0.403845	+	0.974968i
$126$	−8.00605	+	3.31621i	−0.713235	+	0.295432i
$127$	14.1941	+	14.1941i	1.25952	+	1.25952i	0.951321	+	0.308201i	$0.0997269\pi$
$127$	14.1941	+	14.1941i	1.25952	+	1.25952i	0.308201	+	0.951321i	$0.400273\pi$
$128$	−4.54675	−	4.54675i	−0.401879	−	0.401879i
$129$	3.81753	−	1.58127i	0.336115	−	0.139223i
$130$	−4.59610	−	11.0960i	−0.403105	−	0.973181i
$131$	0.405612	+	0.168010i	0.0354385	+	0.0146791i	0.400332	−	0.916370i	$-0.368895\pi$
$131$	0.405612	+	0.168010i	0.0354385	+	0.0146791i	−0.364894	+	0.931049i	$0.618895\pi$
$132$			10.5969i			0.922340i
$133$	−0.643342	+	1.55316i	−0.0557848	+	0.134676i
$134$	−9.68798	+	9.68798i	−0.836914	+	0.836914i
$135$	1.55815			0.134104
$136$		0			0
$137$	2.64760			0.226200			0.113100	−	0.993584i	$-0.463922\pi$
$137$	2.64760			0.226200			0.113100	+	0.993584i	$0.463922\pi$
$138$	−9.59500	+	9.59500i	−0.816781	+	0.816781i
$139$	3.59100	−	8.66945i	0.304585	−	0.735333i	−0.695277	−	0.718742i	$-0.744718\pi$
$139$	3.59100	−	8.66945i	0.304585	−	0.735333i	0.999862	−	0.0165916i	$-0.00528153\pi$
$140$			15.4069i			1.30212i
$141$	7.59810	+	3.14724i	0.639875	+	0.265045i
$142$	1.31050	+	3.16382i	0.109974	+	0.265502i
$143$	15.0613	−	6.23859i	1.25949	−	0.521697i
$144$	−2.16728	−	2.16728i	−0.180607	−	0.180607i
$145$	−4.94317	−	4.94317i	−0.410508	−	0.410508i
$146$	−9.15262	+	3.79114i	−0.757476	+	0.313757i
$147$	−3.86573	−	9.33271i	−0.318840	−	0.769749i
$148$	−1.57613	−	0.652853i	−0.129557	−	0.0536642i
$149$		−	7.90923i		−	0.647950i	−0.946066	−	0.323975i	$-0.894981\pi$
$149$		−	7.90923i		−	0.647950i	0.946066	−	0.323975i	$-0.105019\pi$
$150$	−2.06263	+	4.97963i	−0.168413	+	0.406585i
$151$	−9.82971	+	9.82971i	−0.799931	+	0.799931i	−0.983084	−	0.183154i	$-0.941369\pi$
$151$	−9.82971	+	9.82971i	−0.799931	+	0.799931i	0.183154	+	0.983084i	$0.441369\pi$
$152$	0.333112			0.0270190
$153$		0			0
$154$	−38.4055			−3.09480
$155$	11.8971	−	11.8971i	0.955601	−	0.955601i
$156$	3.36576	−	8.12566i	0.269476	−	0.650573i
$157$			2.42647i			0.193653i	0.995301	+	0.0968265i	$0.0308692\pi$
$157$			2.42647i			0.193653i	−0.995301	+	0.0968265i	$0.969131\pi$
$158$	10.9400	+	4.53148i	0.870337	+	0.360506i
$159$	−1.56442	−	3.77685i	−0.124067	−	0.299523i
$160$	−11.6049	+	4.80690i	−0.917448	+	0.380019i
$161$	−18.9357	−	18.9357i	−1.49234	−	1.49234i
$162$	1.48173	+	1.48173i	0.116416	+	0.116416i
$163$	0.522249	−	0.216323i	0.0409057	−	0.0169437i	−0.362137	−	0.932125i	$-0.617953\pi$
$163$	0.522249	−	0.216323i	0.0409057	−	0.0169437i	0.403043	+	0.915181i	$0.367953\pi$
$164$	1.83658	+	4.43390i	0.143413	+	0.346229i
$165$	6.37993	+	2.64265i	0.496677	+	0.205730i
$166$		−	25.0420i		−	1.94363i
$167$	−4.65170	+	11.2302i	−0.359960	+	0.869019i	0.635345	+	0.772228i	$0.280858\pi$
$167$	−4.65170	+	11.2302i	−0.359960	+	0.869019i	−0.995305	+	0.0967911i	$0.969142\pi$
$168$	−2.39614	+	2.39614i	−0.184866	+	0.184866i
$169$	−0.530441			−0.0408032
$170$		0			0
$171$	0.406521			0.0310874
$172$	6.98617	−	6.98617i	0.532690	−	0.532690i
$173$	−5.63030	+	13.5927i	−0.428064	+	1.03344i	0.551837	+	0.833952i	$0.313927\pi$
$173$	−5.63030	+	13.5927i	−0.428064	+	1.03344i	−0.979901	+	0.199485i	$0.936073\pi$
$174$		−	9.40143i		−	0.712720i
$175$	−9.82725	−	4.07058i	−0.742870	−	0.307707i
$176$	−5.19830	−	12.5498i	−0.391836	−	0.945976i
$177$	5.65172	−	2.34102i	0.424809	−	0.175962i
$178$	−13.8358	−	13.8358i	−1.03704	−	1.03704i
$179$	−14.9737	−	14.9737i	−1.11918	−	1.11918i	−0.991861	−	0.127322i	$-0.959362\pi$
$179$	−14.9737	−	14.9737i	−1.11918	−	1.11918i	−0.127322	−	0.991861i	$-0.540638\pi$
$180$	3.44201	−	1.42573i	0.256553	−	0.106268i
$181$	1.49493	+	3.60909i	0.111117	+	0.268261i	0.969650	−	0.244498i	$-0.0786232\pi$
$181$	1.49493	+	3.60909i	0.111117	+	0.268261i	−0.858532	+	0.512760i	$0.828623\pi$
$182$	29.4492	+	12.1983i	2.18292	+	0.904196i
$183$		−	5.33162i		−	0.394124i
$184$	−2.03060	+	4.90229i	−0.149697	+	0.361402i
$185$	−0.786111	+	0.786111i	−0.0577960	+	0.0577960i
$186$	22.6272			1.65911
$187$		0			0
$188$	19.6642			1.43416
$189$	−2.92418	+	2.92418i	−0.212703	+	0.212703i
$190$	0.507945	−	1.22629i	0.0368502	−	0.0889643i
$191$			13.4653i			0.974316i	0.873314	+	0.487158i	$0.161966\pi$
$191$			13.4653i			0.974316i	−0.873314	+	0.487158i	$0.838034\pi$
$192$	−9.94345	−	4.11871i	−0.717607	−	0.297242i
$193$	−9.26042	−	22.3566i	−0.666579	−	1.60926i	−0.787294	−	0.616578i	$-0.788519\pi$
$193$	−9.26042	−	22.3566i	−0.666579	−	1.60926i	0.120715	−	0.992687i	$-0.461481\pi$
$194$	25.4215	−	10.5299i	1.82515	−	0.756004i
$195$	−4.05276	−	4.05276i	−0.290224	−	0.290224i
$196$	−17.0791	−	17.0791i	−1.21993	−	1.21993i
$197$	−0.0462665	+	0.0191642i	−0.00329635	+	0.00136539i	−0.384331	−	0.923195i	$-0.625568\pi$
$197$	−0.0462665	+	0.0191642i	−0.00329635	+	0.00136539i	0.381035	+	0.924561i	$0.375568\pi$
$198$	3.55397	+	8.58005i	0.252570	+	0.609757i
$199$	−7.56868	−	3.13505i	−0.536530	−	0.222238i	0.0979308	−	0.995193i	$-0.468778\pi$
$199$	−7.56868	−	3.13505i	−0.536530	−	0.222238i	−0.634460	+	0.772955i	$0.718778\pi$
$200$			2.10768i			0.149036i
$201$	−2.50210	+	6.04060i	−0.176484	+	0.426071i
$202$	−4.08051	+	4.08051i	−0.287104	+	0.287104i
$203$	18.5536			1.30221
$204$		0			0
$205$	3.12747			0.218432
$206$	15.9662	−	15.9662i	1.11242	−	1.11242i
$207$	−2.47808	+	5.98262i	−0.172239	+	0.415821i
$208$			11.2742i			0.781727i
$209$	1.66452	+	0.689467i	0.115137	+	0.0476914i
$210$	5.16717	+	12.4746i	0.356569	+	0.860833i
$211$	−25.2796	+	10.4711i	−1.74032	+	0.720863i	−0.741568	+	0.670878i	$0.765918\pi$
$211$	−25.2796	+	10.4711i	−1.74032	+	0.720863i	−0.998750	+	0.0499857i	$0.984082\pi$
$212$	−6.91172	−	6.91172i	−0.474699	−	0.474699i
$213$	1.15557	+	1.15557i	0.0791786	+	0.0791786i
$214$	−6.08282	+	2.51958i	−0.415813	+	0.172235i
$215$	−2.46386	−	5.94829i	−0.168034	−	0.405670i
$216$	0.757047	+	0.313579i	0.0515105	+	0.0213364i
$217$			44.6546i			3.03135i
$218$	1.61782	−	3.90577i	0.109573	−	0.264532i
$219$	−3.34296	+	3.34296i	−0.225896	+	0.225896i
$220$	16.5116			1.11321
$221$		0			0
$222$	−1.49511			−0.100345
$223$	7.30920	−	7.30920i	0.489460	−	0.489460i	−0.418676	−	0.908136i	$-0.637506\pi$
$223$	7.30920	−	7.30920i	0.489460	−	0.489460i	0.908136	+	0.418676i	$0.137506\pi$
$224$	12.7578	−	30.8000i	0.852414	−	2.05791i
$225$			2.57216i			0.171477i
$226$	15.2324	+	6.30946i	1.01324	+	0.419699i
$227$	4.04631	+	9.76865i	0.268563	+	0.648368i	0.999416	−	0.0341663i	$-0.0108776\pi$
$227$	4.04631	+	9.76865i	0.268563	+	0.648368i	−0.730853	+	0.682535i	$0.760878\pi$
$228$	0.898019	−	0.371972i	0.0594728	−	0.0246344i
$229$	−15.2891	−	15.2891i	−1.01033	−	1.01033i	−0.999946	−	0.0103875i	$-0.996693\pi$
$229$	−15.2891	−	15.2891i	−1.01033	−	1.01033i	−0.0103875	−	0.999946i	$-0.503307\pi$
$230$	14.9505	+	14.9505i	0.985806	+	0.985806i
$231$	−16.9326	+	7.01373i	−1.11409	+	0.461470i
$232$	−1.40688	−	3.39651i	−0.0923662	−	0.222992i
$233$	−6.05733	−	2.50903i	−0.396829	−	0.164372i	0.175340	−	0.984508i	$-0.443898\pi$
$233$	−6.05733	−	2.50903i	−0.396829	−	0.164372i	−0.572169	+	0.820136i	$0.693898\pi$
$234$		−	7.70797i		−	0.503885i
$235$	4.90388	−	11.8390i	0.319894	−	0.772291i
$236$	10.3428	−	10.3428i	0.673258	−	0.673258i
$237$	5.65089			0.367065
$238$		0			0
$239$	−20.4618			−1.32356			−0.661781	−	0.749697i	$-0.730199\pi$
$239$	−20.4618			−1.32356			−0.661781	+	0.749697i	$0.730199\pi$
$240$	−3.37696	+	3.37696i	−0.217982	+	0.217982i
$241$	−2.53278	+	6.11468i	−0.163151	+	0.393881i	−0.984220	−	0.176947i	$-0.943378\pi$
$241$	−2.53278	+	6.11468i	−0.163151	+	0.393881i	0.821069	+	0.570828i	$0.193378\pi$
$242$			18.1087i			1.16407i
$243$	0.923880	+	0.382683i	0.0592669	+	0.0245492i
$244$	−4.87849	−	11.7777i	−0.312314	−	0.753992i
$245$	−14.5418	+	6.02341i	−0.929041	+	0.384821i
$246$	2.97408	+	2.97408i	0.189620	+	0.189620i
$247$	−1.05736	−	1.05736i	−0.0672784	−	0.0672784i
$248$	8.17467	−	3.38606i	0.519092	−	0.215015i
$249$	−4.57324	−	11.0408i	−0.289817	−	0.699681i
$250$	22.8417	+	9.46135i	1.44464	+	0.598389i
$251$		−	6.15242i		−	0.388337i	−0.980968	−	0.194169i	$-0.937799\pi$
$251$		−	6.15242i		−	0.388337i	0.980968	−	0.194169i	$-0.0622009\pi$
$252$	−3.78395	+	9.13527i	−0.238367	+	0.575468i
$253$	−20.2933	+	20.2933i	−1.27583	+	1.27583i
$254$	42.0636			2.63931
$255$		0			0
$256$	8.05133			0.503208
$257$	−0.954212	+	0.954212i	−0.0595221	+	0.0595221i	−0.736241	−	0.676719i	$-0.763401\pi$
$257$	−0.954212	+	0.954212i	−0.0595221	+	0.0595221i	0.676719	+	0.736241i	$0.263401\pi$
$258$	3.31352	−	7.99956i	0.206291	−	0.498031i
$259$		−	2.95058i		−	0.183340i
$260$	−12.6610	−	5.24437i	−0.785203	−	0.325242i
$261$	−1.71692	−	4.14501i	−0.106275	−	0.256570i
$262$	0.849953	−	0.352062i	0.0525103	−	0.0217505i
$263$	19.3807	+	19.3807i	1.19507	+	1.19507i	0.975625	+	0.219443i	$0.0704239\pi$
$263$	19.3807	+	19.3807i	1.19507	+	1.19507i	0.219443	+	0.975625i	$0.429576\pi$
$264$	2.56793	+	2.56793i	0.158045	+	0.158045i
$265$	−5.88491	+	2.43761i	−0.361507	+	0.149741i
$266$	1.34811	+	3.25463i	0.0826580	+	0.199554i
$267$	−8.62681	−	3.57334i	−0.527952	−	0.218685i
$268$			15.6333i			0.954958i
$269$	0.336362	−	0.812051i	0.0205084	−	0.0495116i	−0.913294	−	0.407302i	$-0.866470\pi$
$269$	0.336362	−	0.812051i	0.0205084	−	0.0495116i	0.933802	+	0.357790i	$0.116470\pi$
$270$	2.30876	−	2.30876i	0.140507	−	0.140507i
$271$	−14.8751			−0.903595			−0.451798	−	0.892120i	$-0.649217\pi$
$271$	−14.8751			−0.903595			−0.451798	+	0.892120i	$0.649217\pi$
$272$		0			0
$273$	15.2116			0.920648
$274$	3.92303	−	3.92303i	0.236999	−	0.236999i
$275$	−4.36242	+	10.5318i	−0.263064	+	0.635093i
$276$			15.4833i			0.931985i
$277$	15.0769	+	6.24508i	0.905886	+	0.375230i	0.786480	−	0.617615i	$-0.211901\pi$
$277$	15.0769	+	6.24508i	0.905886	+	0.375230i	0.119406	+	0.992846i	$0.461901\pi$
$278$	−7.52488	−	18.1667i	−0.451312	−	1.08956i
$279$	9.97614	−	4.13225i	0.597256	−	0.247392i
$280$	3.73355	+	3.73355i	0.223122	+	0.223122i
$281$	21.5722	+	21.5722i	1.28689	+	1.28689i	0.936666	+	0.350225i	$0.113895\pi$
$281$	21.5722	+	21.5722i	1.28689	+	1.28689i	0.350225	+	0.936666i	$0.386105\pi$
$282$	15.9217	−	6.59497i	0.948122	−	0.392725i
$283$	0.0901640	+	0.217675i	0.00535970	+	0.0129395i	0.926537	−	0.376204i	$-0.122771\pi$
$283$	0.0901640	+	0.217675i	0.00535970	+	0.0129395i	−0.921177	+	0.389144i	$0.872771\pi$
$284$	3.61007	+	1.49534i	0.214218	+	0.0887320i
$285$		−	0.633422i		−	0.0375207i
$286$	13.0728	−	31.5606i	0.773013	−	1.86622i
$287$	−5.86931	+	5.86931i	−0.346455	+	0.346455i
$288$	−8.06150			−0.475028
$289$		0			0
$290$	−14.6489			−0.860211
$291$	9.28509	−	9.28509i	0.544302	−	0.544302i
$292$	−4.32587	+	10.4436i	−0.253152	+	0.611163i
$293$		−	24.7566i		−	1.44630i	−0.690692	−	0.723149i	$-0.742694\pi$
$293$		−	24.7566i		−	1.44630i	0.690692	−	0.723149i	$-0.257306\pi$
$294$	−19.5565	−	8.10058i	−1.14056	−	0.472435i
$295$	−3.64767	−	8.80624i	−0.212375	−	0.512719i
$296$	−0.540146	+	0.223736i	−0.0313954	+	0.0130044i
$297$	3.13383	+	3.13383i	0.181843	+	0.181843i
$298$	−11.7193	−	11.7193i	−0.678883	−	0.678883i
$299$	22.0063	−	9.11532i	1.27266	−	0.527153i
$300$	2.35356	+	5.68199i	0.135883	+	0.328050i
$301$	15.7871	+	6.53921i	0.909951	+	0.376914i
$302$			29.1299i			1.67624i
$303$	−1.05387	+	2.54426i	−0.0605431	+	0.146164i
$304$	−0.881046	+	0.881046i	−0.0505315	+	0.0505315i
$305$	−8.30748			−0.475685
$306$		0			0
$307$	4.52959			0.258517			0.129259	−	0.991611i	$-0.458740\pi$
$307$	4.52959			0.258517			0.129259	+	0.991611i	$0.458740\pi$
$308$	−30.9872	+	30.9872i	−1.76566	+	1.76566i
$309$	4.12356	−	9.95516i	0.234581	−	0.566329i
$310$		−	35.2567i		−	2.00244i
$311$	−25.9860	−	10.7638i	−1.47353	−	0.610357i	−0.505870	−	0.862610i	$-0.668829\pi$
$311$	−25.9860	−	10.7638i	−1.47353	−	0.610357i	−0.967661	+	0.252253i	$0.918829\pi$
$312$	−1.15346	−	2.78470i	−0.0653019	−	0.157653i
$313$	−11.5528	+	4.78533i	−0.653004	+	0.270483i	−0.684491	−	0.729021i	$-0.739976\pi$
$313$	−11.5528	+	4.78533i	−0.653004	+	0.270483i	0.0314873	+	0.999504i	$0.489976\pi$
$314$	3.59536	+	3.59536i	0.202898	+	0.202898i
$315$	4.55632	+	4.55632i	0.256720	+	0.256720i
$316$	12.4830	−	5.17064i	0.702225	−	0.290871i
$317$	−11.7640	−	28.4007i	−0.660729	−	1.59514i	−0.796663	−	0.604424i	$-0.793403\pi$
$317$	−11.7640	−	28.4007i	−0.660729	−	1.59514i	0.135934	−	0.990718i	$-0.456597\pi$
$318$	−7.91431	−	3.27822i	−0.443813	−	0.183833i
$319$		−	19.8839i		−	1.11328i
$320$	−6.41758	+	15.4934i	−0.358754	+	0.866109i
$321$	−2.22173	+	2.22173i	−0.124005	+	0.124005i
$322$	−56.1150			−3.12717
$323$		0			0
$324$	2.39104			0.132836
$325$	6.69019	−	6.69019i	0.371105	−	0.371105i
$326$	0.453300	−	1.09436i	0.0251060	−	0.0606112i
$327$		−	2.01747i		−	0.111566i
$328$	1.51952	+	0.629405i	0.0839014	+	0.0347531i
$329$	13.0151	+	31.4213i	0.717547	+	1.73231i
$330$	13.3690	−	5.53763i	0.735941	−	0.304837i
$331$	−8.39287	−	8.39287i	−0.461314	−	0.461314i	0.437772	−	0.899086i	$-0.355768\pi$
$331$	−8.39287	−	8.39287i	−0.461314	−	0.461314i	−0.899086	+	0.437772i	$0.855768\pi$
$332$	−20.2049	−	20.2049i	−1.10889	−	1.10889i
$333$	−0.659180	+	0.273041i	−0.0361228	+	0.0149626i
$334$	9.74756	+	23.5327i	0.533363	+	1.28765i
$335$	9.41218	+	3.89865i	0.514242	+	0.213006i
$336$		−	12.6751i		−	0.691481i
$337$	−10.5360	+	25.4361i	−0.573931	+	1.38559i	0.324253	+	0.945971i	$0.394887\pi$
$337$	−10.5360	+	25.4361i	−0.573931	+	1.38559i	−0.898183	+	0.439621i	$0.855113\pi$
$338$	−0.785970	+	0.785970i	−0.0427512	+	0.0427512i
$339$	7.86808			0.427336
$340$		0			0
$341$	47.8562			2.59156
$342$	0.602354	−	0.602354i	0.0325716	−	0.0325716i
$343$	4.90853	−	11.8502i	0.265036	−	0.639853i
$344$		−	3.38590i		−	0.182556i
$345$	9.32184	+	3.86123i	0.501871	+	0.207882i
$346$	11.7982	+	28.4833i	0.634274	+	1.53127i
$347$	−13.6281	+	5.64495i	−0.731596	+	0.303037i	−0.717208	−	0.696860i	$-0.754580\pi$
$347$	−13.6281	+	5.64495i	−0.731596	+	0.303037i	−0.0143883	+	0.999896i	$0.504580\pi$
$348$	−7.58546	−	7.58546i	−0.406624	−	0.406624i
$349$	18.3356	+	18.3356i	0.981483	+	0.981483i	0.999832	−	0.0183484i	$-0.00584081\pi$
$349$	18.3356	+	18.3356i	0.981483	+	0.981483i	−0.0183484	+	0.999832i	$0.505841\pi$
$350$	−20.5928	+	8.52983i	−1.10073	+	0.455938i
$351$	−1.40765	−	3.39838i	−0.0751350	−	0.181392i
$352$	−33.0082	−	13.6724i	−1.75934	−	0.728743i
$353$		−	21.2680i		−	1.13198i	−0.824411	−	0.565991i	$-0.808494\pi$
$353$		−	21.2680i		−	1.13198i	0.824411	−	0.565991i	$-0.191506\pi$
$354$	4.90556	−	11.8431i	0.260728	−	0.629452i
$355$	1.80056	−	1.80056i	0.0955638	−	0.0955638i
$356$	−22.3266			−1.18331
$357$		0			0
$358$	−44.3738			−2.34523
$359$	−24.6575	+	24.6575i	−1.30137	+	1.30137i	−0.373902	+	0.927468i	$0.621981\pi$
$359$	−24.6575	+	24.6575i	−1.30137	+	1.30137i	−0.927468	+	0.373902i	$0.878019\pi$
$360$	0.488604	−	1.17959i	0.0257517	−	0.0621701i
$361$			18.8347i			0.991302i
$362$	7.56277	+	3.13260i	0.397491	+	0.164646i
$363$	3.30707	+	7.98397i	0.173576	+	0.419050i
$364$	33.6030	−	13.9188i	1.76127	−	0.729544i
$365$	5.20884	+	5.20884i	0.272643	+	0.272643i
$366$	−7.90001	−	7.90001i	−0.412940	−	0.412940i
$367$	−8.97236	+	3.71647i	−0.468353	+	0.193998i	−0.604363	−	0.796709i	$-0.706572\pi$
$367$	−8.97236	+	3.71647i	−0.468353	+	0.193998i	0.136009	+	0.990708i	$0.456572\pi$
$368$	−7.59533	−	18.3368i	−0.395934	−	0.955869i
$369$	1.85438	+	0.768109i	0.0965351	+	0.0399862i
$370$			2.32961i			0.121110i
$371$	6.46953	−	15.6188i	0.335881	−	0.810889i
$372$	18.2566	−	18.2566i	0.946560	−	0.946560i
$373$	−14.4620			−0.748813			−0.374407	−	0.927265i	$-0.622154\pi$
$373$	−14.4620			−0.748813			−0.374407	+	0.927265i	$0.622154\pi$
$374$		0			0
$375$	11.7986			0.609276
$376$	4.76521	−	4.76521i	0.245747	−	0.245747i
$377$	−6.31547	+	15.2469i	−0.325263	+	0.785255i
$378$			8.66568i			0.445715i
$379$	−15.4763	−	6.41051i	−0.794966	−	0.329286i	−0.0520279	−	0.998646i	$-0.516568\pi$
$379$	−15.4763	−	6.41051i	−0.794966	−	0.329286i	−0.742938	+	0.669360i	$0.766568\pi$
$380$	−0.579589	−	1.39925i	−0.0297323	−	0.0717801i
$381$	18.5455	−	7.68179i	0.950114	−	0.393550i
$382$	19.9519	+	19.9519i	1.02083	+	1.02083i
$383$	−8.77307	−	8.77307i	−0.448283	−	0.448283i	0.446500	−	0.894783i	$-0.352670\pi$
$383$	−8.77307	−	8.77307i	−0.448283	−	0.448283i	−0.894783	+	0.446500i	$0.852670\pi$
$384$	−5.94061	+	2.46068i	−0.303156	+	0.125571i
$385$	10.9285	+	26.3837i	0.556966	+	1.34464i
$386$	−46.8479	−	19.4050i	−2.38449	−	0.987690i
$387$		−	4.13206i		−	0.210044i
$388$	12.0151	−	29.0071i	0.609975	−	1.47261i
$389$	12.7970	−	12.7970i	0.648833	−	0.648833i	−0.303878	−	0.952711i	$-0.598281\pi$
$389$	12.7970	−	12.7970i	0.648833	−	0.648833i	0.952711	+	0.303878i	$0.0982814\pi$
$390$	−12.0102			−0.608160
$391$		0			0
$392$	−8.27751			−0.418077
$393$	0.310442	−	0.310442i	0.0156597	−	0.0156597i
$394$	−0.0401583	+	0.0969506i	−0.00202314	+	0.00488430i
$395$		−	8.80496i		−	0.443025i
$396$	9.79024	+	4.05525i	0.491978	+	0.203784i
$397$	2.69853	+	6.51484i	0.135436	+	0.326970i	0.977017	−	0.213159i	$-0.0683753\pi$
$397$	2.69853	+	6.51484i	0.135436	+	0.326970i	−0.841582	+	0.540129i	$0.818375\pi$
$398$	−15.8600	+	6.56944i	−0.794992	+	0.329296i
$399$	1.18874	+	1.18874i	0.0595115	+	0.0595115i
$400$	−5.57460	−	5.57460i	−0.278730	−	0.278730i
$401$	−21.7020	+	8.98927i	−1.08375	+	0.448903i	−0.851822	−	0.523831i	$-0.824502\pi$
$401$	−21.7020	+	8.98927i	−1.08375	+	0.448903i	−0.231925	+	0.972734i	$0.574502\pi$
$402$	5.24310	+	12.6580i	0.261502	+	0.631322i
$403$	−36.6960	−	15.2000i	−1.82796	−	0.757165i
$404$			6.58466i			0.327599i
$405$	0.596279	−	1.43955i	0.0296294	−	0.0715316i
$406$	27.4915	−	27.4915i	1.36438	−	1.36438i
$407$	−3.16213			−0.156741
$408$		0			0
$409$	4.90401			0.242488			0.121244	−	0.992623i	$-0.461312\pi$
$409$	4.90401			0.242488			0.121244	+	0.992623i	$0.461312\pi$
$410$	4.63407	−	4.63407i	0.228860	−	0.228860i
$411$	1.01319	−	2.44606i	0.0499771	−	0.120655i
$412$		−	25.7644i		−	1.26932i
$413$	23.3722	+	9.68108i	1.15007	+	0.476375i
$414$	5.19278	+	12.5365i	0.255211	+	0.616134i
$415$	−17.2032	+	7.12581i	−0.844473	+	0.349792i
$416$	20.9680	+	20.9680i	1.02804	+	1.02804i
$417$	−6.63531	−	6.63531i	−0.324933	−	0.324933i
$418$	3.48797	−	1.44476i	0.170602	−	0.0706657i
$419$	11.4579	+	27.6619i	0.559756	+	1.35137i	0.909960	+	0.414697i	$0.136112\pi$
$419$	11.4579	+	27.6619i	0.559756	+	1.35137i	−0.350204	+	0.936673i	$0.613888\pi$
$420$	14.2342	+	5.89598i	0.694556	+	0.287694i
$421$		−	27.0945i		−	1.32051i	−0.751043	−	0.660254i	$-0.770449\pi$
$421$		−	27.0945i		−	1.32051i	0.751043	−	0.660254i	$-0.229551\pi$
$422$	−21.9421	+	52.9729i	−1.06812	+	2.57868i
$423$	5.81533	−	5.81533i	0.282751	−	0.282751i
$424$	−3.34982			−0.162682
$425$		0			0
$426$	3.42449			0.165917
$427$	15.5906	−	15.5906i	0.754482	−	0.754482i
$428$	−2.87496	+	6.94078i	−0.138967	+	0.335495i
$429$		−	16.3022i		−	0.787078i
$430$	−12.4645	−	5.16298i	−0.601093	−	0.248981i
$431$	−1.83627	−	4.43315i	−0.0884500	−	0.213537i	0.873464	−	0.486888i	$-0.161868\pi$
$431$	−1.83627	−	4.43315i	−0.0884500	−	0.213537i	−0.961914	+	0.273351i	$0.911868\pi$
$432$	−2.83169	+	1.17293i	−0.136240	+	0.0564324i
$433$	−0.627750	−	0.627750i	−0.0301678	−	0.0301678i	0.691862	−	0.722030i	$-0.256791\pi$
$433$	−0.627750	−	0.627750i	−0.0301678	−	0.0301678i	−0.722030	+	0.691862i	$0.756791\pi$
$434$	66.1661	+	66.1661i	3.17607	+	3.17607i
$435$	−6.45856	+	2.67522i	−0.309664	+	0.128267i
$436$	−1.84601	−	4.45667i	−0.0884079	−	0.213436i
$437$	2.43206	+	1.00739i	0.116341	+	0.0481902i
$438$			9.90672i			0.473361i
$439$	6.82052	−	16.4662i	0.325526	−	0.785889i	−0.673388	−	0.739289i	$-0.735162\pi$
$439$	6.82052	−	16.4662i	0.325526	−	0.785889i	0.998914	−	0.0465993i	$-0.0148384\pi$
$440$	4.00123	−	4.00123i	0.190751	−	0.190751i
$441$	−10.1017			−0.481031
$442$		0			0
$443$	−28.0844			−1.33433			−0.667164	−	0.744911i	$-0.732492\pi$
$443$	−28.0844			−1.33433			−0.667164	+	0.744911i	$0.732492\pi$
$444$	−1.20632	+	1.20632i	−0.0572492	+	0.0572492i
$445$	−5.56782	+	13.4419i	−0.263940	+	0.637207i
$446$		−	21.6605i		−	1.02565i
$447$	−7.30718	−	3.02673i	−0.345618	−	0.143160i
$448$	−17.0326	−	41.1203i	−0.804714	−	1.94275i
$449$	5.79810	−	2.40165i	0.273629	−	0.113341i	−0.241650	−	0.970364i	$-0.577688\pi$
$449$	5.79810	−	2.40165i	0.273629	−	0.113341i	0.515279	+	0.857023i	$0.327688\pi$
$450$	3.81124	+	3.81124i	0.179664	+	0.179664i
$451$	6.29012	+	6.29012i	0.296190	+	0.296190i
$452$	17.3809	−	7.19939i	0.817527	−	0.338631i
$453$	5.31980	+	12.8431i	0.249946	+	0.603423i
$454$	20.4700	+	8.47897i	0.960706	+	0.397938i
$455$		−	23.7020i		−	1.11117i
$456$	0.127476	−	0.307755i	0.00596963	−	0.0144120i
$457$	13.8807	−	13.8807i	0.649313	−	0.649313i	−0.303514	−	0.952827i	$-0.598160\pi$
$457$	13.8807	−	13.8807i	0.649313	−	0.649313i	0.952827	+	0.303514i	$0.0981599\pi$
$458$	−45.3087			−2.11714
$459$		0			0
$460$	24.1254			1.12485
$461$	−24.1549	+	24.1549i	−1.12501	+	1.12501i	−0.134028	+	0.990978i	$0.542791\pi$
$461$	−24.1549	+	24.1549i	−1.12501	+	1.12501i	−0.990978	+	0.134028i	$0.957209\pi$
$462$	−14.6971	+	35.4821i	−0.683773	+	1.65077i
$463$			32.4372i			1.50748i	0.657170	+	0.753742i	$0.271753\pi$
$463$			32.4372i			1.50748i	−0.657170	+	0.753742i	$0.728247\pi$
$464$	12.7045	+	5.26236i	0.589789	+	0.244299i
$465$	−6.43869	−	15.5444i	−0.298587	−	0.720853i
$466$	−12.6930	+	5.25762i	−0.587993	+	0.243555i
$467$	−25.4243	−	25.4243i	−1.17649	−	1.17649i	−0.980631	−	0.195863i	$-0.937249\pi$
$467$	−25.4243	−	25.4243i	−1.17649	−	1.17649i	−0.195863	−	0.980631i	$-0.562751\pi$
$468$	−6.21911	−	6.21911i	−0.287478	−	0.287478i
$469$	−24.9804	+	10.3472i	−1.15349	+	0.477790i
$470$	−10.2760	−	24.8084i	−0.473996	−	1.14433i
$471$	2.24176	+	0.928568i	0.103295	+	0.0427862i
$472$		−	5.01271i		−	0.230729i
$473$	7.00805	−	16.9189i	0.322230	−	0.777933i
$474$	8.37309	−	8.37309i	0.384589	−	0.384589i
$475$	1.04564			0.0479771
$476$		0			0
$477$	−4.08803			−0.187178
$478$	−30.3188	+	30.3188i	−1.38675	+	1.38675i
$479$	−11.0805	+	26.7507i	−0.506280	+	1.22227i	0.439729	+	0.898130i	$0.355074\pi$
$479$	−11.0805	+	26.7507i	−0.506280	+	1.22227i	−0.946010	+	0.324139i	$0.894926\pi$
$480$			12.5610i			0.573331i
$481$	2.42471	+	1.00435i	0.110557	+	0.0457943i
$482$	5.30740	+	12.8132i	0.241746	+	0.583626i
$483$	−24.7406	+	10.2479i	−1.12574	+	0.466296i
$484$	14.6109	+	14.6109i	0.664130	+	0.664130i
$485$	−14.4676	−	14.4676i	−0.656940	−	0.656940i
$486$	1.93597	−	0.801906i	0.0878175	−	0.0363752i
$487$	−5.35420	−	12.9262i	−0.242622	−	0.585741i	0.754920	−	0.655817i	$-0.227676\pi$
$487$	−5.35420	−	12.9262i	−0.242622	−	0.585741i	−0.997542	+	0.0700761i	$0.977676\pi$
$488$	−4.03628	−	1.67188i	−0.182714	−	0.0756826i
$489$		−	0.565279i		−	0.0255628i
$490$	−12.6219	+	30.4721i	−0.570201	+	1.37659i
$491$	−0.112813	+	0.112813i	−0.00509119	+	0.00509119i	−0.709648	−	0.704557i	$-0.751146\pi$
$491$	−0.112813	+	0.112813i	−0.00509119	+	0.00509119i	0.704557	+	0.709648i	$0.251146\pi$
$492$	4.79922			0.216365
$493$		0			0
$494$	−3.13345			−0.140981
$495$	4.88299	−	4.88299i	0.219474	−	0.219474i
$496$	−12.6654	+	30.5769i	−0.568692	+	1.37294i
$497$			6.75821i			0.303147i
$498$	−23.1358	−	9.58314i	−1.03674	−	0.429431i
$499$	2.43821	+	5.88636i	0.109149	+	0.263510i	0.969011	−	0.247017i	$-0.0794504\pi$
$499$	2.43821	+	5.88636i	0.109149	+	0.263510i	−0.859862	+	0.510527i	$0.829450\pi$
$500$	26.0635	−	10.7958i	1.16559	−	0.482805i
$501$	8.59523	+	8.59523i	0.384006	+	0.384006i
$502$	−9.11622	−	9.11622i	−0.406877	−	0.406877i
$503$	22.1515	−	9.17545i	0.987686	−	0.409113i	0.170419	−	0.985372i	$-0.445488\pi$
$503$	22.1515	−	9.17545i	0.987686	−	0.409113i	0.817267	+	0.576259i	$0.195488\pi$
$504$	1.29678	+	3.13070i	0.0577631	+	0.139453i
$505$	3.96435	+	1.64209i	0.176411	+	0.0730719i
$506$			60.1382i			2.67347i
$507$	−0.202991	+	0.490064i	−0.00901515	+	0.0217645i
$508$	33.9387	−	33.9387i	1.50579	−	1.50579i
$509$	5.68783			0.252108			0.126054	−	0.992023i	$-0.459769\pi$
$509$	5.68783			0.252108			0.126054	+	0.992023i	$0.459769\pi$
$510$		0			0
$511$	−19.5508			−0.864878
$512$	21.0234	−	21.0234i	0.929111	−	0.929111i
$513$	0.155569	−	0.375576i	0.00686853	−	0.0165821i
$514$			2.82777i			0.124727i
$515$	−15.5117	−	6.42514i	−0.683526	−	0.283126i
$516$	−3.78089	−	9.12787i	−0.166444	−	0.401832i
$517$	33.6741	−	13.9483i	1.48098	−	0.613443i
$518$	−4.37196	−	4.37196i	−0.192093	−	0.192093i
$519$	10.4034	+	10.4034i	0.456660	+	0.456660i
$520$	−4.33899	+	1.79727i	−0.190277	+	0.0788155i
$521$	2.65458	+	6.40871i	0.116299	+	0.280771i	0.971301	−	0.237854i	$-0.0764441\pi$
$521$	2.65458	+	6.40871i	0.116299	+	0.280771i	−0.855002	+	0.518625i	$0.826444\pi$
$522$	−8.68579	−	3.59777i	−0.380167	−	0.157470i
$523$		−	2.86550i		−	0.125299i	−0.998036	−	0.0626497i	$-0.980045\pi$
$523$		−	2.86550i		−	0.125299i	0.998036	−	0.0626497i	$-0.0199551\pi$
$524$	0.401719	−	0.969836i	0.0175492	−	0.0423675i
$525$	−7.52145	+	7.52145i	−0.328263	+	0.328263i
$526$	57.4340			2.50424
$527$		0			0
$528$	−13.5838			−0.591159
$529$	−13.3874	+	13.3874i	−0.582062	+	0.582062i
$530$	−5.10796	+	12.3317i	−0.221876	+	0.535655i
$531$		−	6.11738i		−	0.265472i
$532$	3.71368	+	1.53826i	0.161009	+	0.0666919i
$533$	−2.82539	−	6.82110i	−0.122381	−	0.295455i
$534$	−18.0773	+	7.48787i	−0.782282	+	0.324032i
$535$	3.46179	+	3.46179i	0.149666	+	0.149666i
$536$	3.78841	+	3.78841i	0.163634	+	0.163634i
$537$	−19.5640	+	8.10368i	−0.844250	+	0.349700i
$538$	−0.704841	−	1.70164i	−0.0303879	−	0.0733628i
$539$	−41.3617	−	17.1326i	−1.78157	−	0.737952i
$540$		−	3.72561i		−	0.160325i
$541$	11.4378	−	27.6133i	0.491750	−	1.18719i	−0.462079	−	0.886839i	$-0.652896\pi$
$541$	11.4378	−	27.6133i	0.491750	−	1.18719i	0.953829	−	0.300351i	$-0.0971037\pi$
$542$	−22.0408	+	22.0408i	−0.946733	+	0.946733i
$543$	3.90645			0.167642
$544$		0			0
$545$	−3.14353			−0.134654
$546$	22.5395	−	22.5395i	0.964601	−	0.964601i
$547$	4.56191	−	11.0134i	0.195053	−	0.470900i	−0.795847	−	0.605498i	$-0.792974\pi$
$547$	4.56191	−	11.0134i	0.195053	−	0.470900i	0.990900	+	0.134597i	$0.0429741\pi$
$548$		−	6.33053i		−	0.270427i
$549$	−4.92577	−	2.04032i	−0.210227	−	0.0870788i
$550$	9.14138	+	22.0692i	0.389790	+	0.941036i
$551$	−1.68503	+	0.697963i	−0.0717848	+	0.0297342i
$552$	3.75205	+	3.75205i	0.159698	+	0.159698i
$553$	16.5242	+	16.5242i	0.702681	+	0.702681i
$554$	31.5935	−	13.0864i	1.34228	−	0.555990i
$555$	0.425440	+	1.02710i	0.0180589	+	0.0435981i
$556$	−20.7290	−	8.58624i	−0.879106	−	0.364138i
$557$			21.2677i			0.901142i	0.892741	+	0.450571i	$0.148780\pi$
$557$			21.2677i			0.901142i	−0.892741	+	0.450571i	$0.851220\pi$
$558$	8.65906	−	20.9048i	0.366567	−	0.884972i
$559$	−10.7475	+	10.7475i	−0.454571	+	0.454571i
$560$	−19.7497			−0.834576
$561$		0			0
$562$	63.9284			2.69665
$563$	14.0253	−	14.0253i	0.591095	−	0.591095i	−0.346832	−	0.937927i	$-0.612743\pi$
$563$	14.0253	−	14.0253i	0.591095	−	0.591095i	0.937927	+	0.346832i	$0.112743\pi$
$564$	7.52517	−	18.1674i	0.316867	−	0.764984i
$565$		−	12.2597i		−	0.515769i
$566$	0.456134	+	0.188937i	0.0191728	+	0.00794162i
$567$	1.58255	+	3.82062i	0.0664610	+	0.160451i
$568$	1.23719	−	0.512460i	0.0519112	−	0.0215023i
$569$	−25.8167	−	25.8167i	−1.08229	−	1.08229i	−0.996295	−	0.0859961i	$-0.972593\pi$
$569$	−25.8167	−	25.8167i	−1.08229	−	1.08229i	−0.0859961	−	0.996295i	$-0.527407\pi$
$570$	−0.938560	−	0.938560i	−0.0393120	−	0.0393120i
$571$	15.0132	−	6.21868i	0.628284	−	0.260244i	−0.0457400	−	0.998953i	$-0.514565\pi$
$571$	15.0132	−	6.21868i	0.628284	−	0.260244i	0.674024	+	0.738710i	$0.264565\pi$
$572$	−14.9167	−	36.0122i	−0.623700	−	1.50574i
$573$	12.4403	+	5.15295i	0.519702	+	0.215268i
$574$			17.3935i			0.725989i
$575$	−6.37402	+	15.3883i	−0.265815	+	0.641735i
$576$	−7.61039	+	7.61039i	−0.317099	+	0.317099i
$577$	12.9656			0.539764			0.269882	−	0.962893i	$-0.413015\pi$
$577$	12.9656			0.539764			0.269882	+	0.962893i	$0.413015\pi$
$578$		0			0
$579$	−24.1986			−1.00566
$580$	−11.8193	+	11.8193i	−0.490770	+	0.490770i
$581$	18.9123	−	45.6582i	0.784612	−	1.89422i
$582$		−	27.5160i		−	1.14057i
$583$	−16.7386	−	6.93337i	−0.693243	−	0.287151i
$584$	1.48249	+	3.57906i	0.0613461	+	0.148103i
$585$	−5.29519	+	2.19334i	−0.218929	+	0.0906834i
$586$	−36.6826	−	36.6826i	−1.51534	−	1.51534i
$587$	−16.8979	−	16.8979i	−0.697453	−	0.697453i	0.266408	−	0.963860i	$-0.414163\pi$
$587$	−16.8979	−	16.8979i	−0.697453	−	0.697453i	−0.963860	+	0.266408i	$0.914163\pi$
$588$	−22.3149	+	9.24313i	−0.920251	+	0.381180i
$589$	−1.67985	−	4.05551i	−0.0692169	−	0.167104i
$590$	−18.4533	−	7.64362i	−0.759711	−	0.314683i
$591$			0.0500785i			0.00205995i
$592$	0.836872	−	2.02039i	0.0343952	−	0.0830374i
$593$	−15.1140	+	15.1140i	−0.620658	+	0.620658i	−0.945700	−	0.325041i	$-0.894622\pi$
$593$	−15.1140	+	15.1140i	−0.620658	+	0.620658i	0.325041	+	0.945700i	$0.394622\pi$
$594$	9.28698			0.381049
$595$		0			0
$596$	−18.9113			−0.774637
$597$	−5.79282	+	5.79282i	−0.237084	+	0.237084i
$598$	19.1010	−	46.1139i	0.781097	−	1.88574i
$599$			2.23714i			0.0914070i	0.998955	+	0.0457035i	$0.0145529\pi$
$599$			2.23714i			0.0914070i	−0.998955	+	0.0457035i	$0.985447\pi$
$600$	1.94724	+	0.806575i	0.0794959	+	0.0329283i
$601$	−4.34177	−	10.4820i	−0.177105	−	0.427568i	0.810252	−	0.586081i	$-0.199330\pi$
$601$	−4.34177	−	10.4820i	−0.177105	−	0.427568i	−0.987357	+	0.158513i	$0.949330\pi$
$602$	33.0815	−	13.7028i	1.34830	−	0.558484i
$603$	4.62327	+	4.62327i	0.188274	+	0.188274i
$604$	23.5033	+	23.5033i	0.956334	+	0.956334i
$605$	12.4403	−	5.15292i	0.505768	−	0.209496i
$606$	2.20836	+	5.33145i	0.0897084	+	0.216575i
$607$	17.8110	+	7.37755i	0.722925	+	0.299445i	0.713641	−	0.700511i	$-0.247045\pi$
$607$	17.8110	+	7.37755i	0.722925	+	0.299445i	0.00928405	+	0.999957i	$0.497045\pi$
$608$			3.27717i			0.132907i
$609$	7.10017	−	17.1413i	0.287713	−	0.694601i
$610$	−12.3094	+	12.3094i	−0.498394	+	0.498394i
$611$	−30.2514			−1.22384
$612$		0			0
$613$	35.8715			1.44884			0.724418	−	0.689361i	$-0.242109\pi$
$613$	35.8715			1.44884			0.724418	+	0.689361i	$0.242109\pi$
$614$	6.71162	−	6.71162i	0.270859	−	0.270859i
$615$	1.19683	−	2.88941i	0.0482609	−	0.116512i
$616$			15.0182i			0.605099i
$617$	−8.03525	−	3.32831i	−0.323487	−	0.133993i	0.215030	−	0.976607i	$-0.431015\pi$
$617$	−8.03525	−	3.32831i	−0.323487	−	0.133993i	−0.538517	+	0.842615i	$0.681015\pi$
$618$	−8.64085	−	20.8609i	−0.347586	−	0.839147i
$619$	2.01659	−	0.835300i	0.0810537	−	0.0335735i	−0.341788	−	0.939777i	$-0.611033\pi$
$619$	2.01659	−	0.835300i	0.0810537	−	0.0335735i	0.422842	+	0.906203i	$0.361033\pi$
$620$	−28.4466	−	28.4466i	−1.14244	−	1.14244i
$621$	4.57890	+	4.57890i	0.183745	+	0.183745i
$622$	−54.4532	+	22.5553i	−2.18337	+	0.904383i
$623$	−14.7773	−	35.6754i	−0.592038	−	1.42931i
$624$	10.4160	+	4.31446i	0.416975	+	0.172717i
$625$		−	5.52321i		−	0.220928i
$626$	−10.0276	+	24.2087i	−0.400783	+	0.967575i
$627$	1.27397	−	1.27397i	0.0508774	−	0.0508774i
$628$	5.80178			0.231516
$629$		0			0
$630$	13.5025			0.537951
$631$	2.97410	−	2.97410i	0.118397	−	0.118397i	−0.645426	−	0.763823i	$-0.723320\pi$
$631$	2.97410	−	2.97410i	0.118397	−	0.118397i	0.763823	+	0.645426i	$0.223320\pi$
$632$	1.77200	−	4.27799i	0.0704864	−	0.170169i
$633$			27.3624i			1.08756i
$634$	−59.5131	−	24.6511i	−2.36357	−	0.979022i
$635$	−11.9694	−	28.8967i	−0.474991	−	1.14673i
$636$	−9.03060	+	3.74060i	−0.358087	+	0.148324i
$637$	26.2744	+	26.2744i	1.04103	+	1.04103i
$638$	−29.4625	−	29.4625i	−1.16643	−	1.16643i
$639$	1.50983	−	0.625392i	0.0597279	−	0.0247401i
$640$	3.83412	+	9.25638i	0.151557	+	0.365891i
$641$	23.4008	+	9.69295i	0.924278	+	0.382848i	0.793505	−	0.608564i	$-0.208254\pi$
$641$	23.4008	+	9.69295i	0.924278	+	0.382848i	0.130773	+	0.991412i	$0.458254\pi$
$642$			6.58399i			0.259849i
$643$	−8.01041	+	19.3389i	−0.315900	+	0.762650i	0.683563	+	0.729891i	$0.260429\pi$
$643$	−8.01041	+	19.3389i	−0.315900	+	0.762650i	−0.999463	+	0.0327587i	$0.989571\pi$
$644$	−45.2760	+	45.2760i	−1.78412	+	1.78412i
$645$	−6.43838			−0.253511
$646$		0			0
$647$	−36.9349			−1.45206			−0.726030	−	0.687663i	$-0.758636\pi$
$647$	−36.9349			−1.45206			−0.726030	+	0.687663i	$0.758636\pi$
$648$	0.579419	−	0.579419i	0.0227617	−	0.0227617i
$649$	10.3752	−	25.0479i	0.407261	−	0.983216i
$650$		−	19.8261i		−	0.777644i
$651$	41.2555	+	17.0886i	1.61693	+	0.669754i
$652$	−0.517237	−	1.24872i	−0.0202566	−	0.0489037i
$653$	5.33933	−	2.21162i	0.208944	−	0.0865475i	−0.275757	−	0.961227i	$-0.588928\pi$
$653$	5.33933	−	2.21162i	0.208944	−	0.0865475i	0.484701	+	0.874680i	$0.338928\pi$
$654$	−2.98935	−	2.98935i	−0.116893	−	0.116893i
$655$	−0.483717	−	0.483717i	−0.0189004	−	0.0189004i
$656$	−5.68368	+	2.35426i	−0.221910	+	0.0919182i
$657$	1.80920	+	4.36779i	0.0705835	+	0.170404i
$658$	65.8427	+	27.2729i	2.56682	+	1.06321i
$659$		−	1.17066i		−	0.0456024i	−0.999740	−	0.0228012i	$-0.992742\pi$
$659$		−	1.17066i		−	0.0456024i	0.999740	−	0.0228012i	$-0.00725847\pi$
$660$	6.31870	−	15.2547i	0.245955	−	0.593788i
$661$	10.9823	−	10.9823i	0.427161	−	0.427161i	−0.460499	−	0.887660i	$-0.652330\pi$
$661$	10.9823	−	10.9823i	0.427161	−	0.427161i	0.887660	+	0.460499i	$0.152330\pi$
$662$	−24.8719			−0.966675
$663$		0			0
$664$	−9.79246			−0.380021
$665$	1.85224	−	1.85224i	0.0718268	−	0.0718268i
$666$	−0.572153	+	1.38130i	−0.0221705	+	0.0535243i
$667$		−	29.0527i		−	1.12492i
$668$	26.8519	+	11.1224i	1.03893	+	0.430339i
$669$	−3.95571	−	9.54993i	−0.152937	−	0.369222i
$670$	19.7230	−	8.16955i	0.761968	−	0.315617i
$671$	−16.7084	−	16.7084i	−0.645020	−	0.645020i
$672$	−23.5733	−	23.5733i	−0.909358	−	0.909358i
$673$	9.97409	−	4.13140i	0.384473	−	0.159254i	−0.182071	−	0.983285i	$-0.558280\pi$
$673$	9.97409	−	4.13140i	0.384473	−	0.159254i	0.566544	+	0.824032i	$0.308280\pi$
$674$	22.0779	+	53.3008i	0.850410	+	2.05307i
$675$	2.37636	+	0.984322i	0.0914663	+	0.0378866i
$676$			1.26831i			0.0487811i
$677$	17.0046	−	41.0526i	0.653538	−	1.57778i	−0.154070	−	0.988060i	$-0.549238\pi$
$677$	17.0046	−	41.0526i	0.653538	−	1.57778i	0.807608	−	0.589720i	$-0.200762\pi$
$678$	11.6584	−	11.6584i	0.447737	−	0.447737i
$679$	54.3026			2.08394
$680$		0			0
$681$	10.5735			0.405178
$682$	70.9099	−	70.9099i	2.71528	−	2.71528i
$683$	15.9576	−	38.5252i	0.610602	−	1.47412i	−0.251738	−	0.967795i	$-0.581002\pi$
$683$	15.9576	−	38.5252i	0.610602	−	1.47412i	0.862341	−	0.506329i	$-0.168998\pi$
$684$		−	0.972009i		−	0.0371657i
$685$	−3.81134	−	1.57871i	−0.145624	−	0.0603194i
$686$	−10.2857	−	24.8320i	−0.392711	−	0.948089i
$687$	−19.9762	+	8.27441i	−0.762140	+	0.315689i
$688$	8.95535	+	8.95535i	0.341419	+	0.341419i
$689$	10.6330	+	10.6330i	0.405084	+	0.405084i
$690$	19.5338	−	8.09114i	0.743637	−	0.308025i
$691$	−17.7607	−	42.8782i	−0.675649	−	1.63116i	−0.771854	−	0.635800i	$-0.780670\pi$
$691$	−17.7607	−	42.8782i	−0.675649	−	1.63116i	0.0962041	−	0.995362i	$-0.469330\pi$
$692$	32.5008	+	13.4623i	1.23550	+	0.511759i
$693$			18.3278i			0.696214i
$694$	−11.8289	+	28.5575i	−0.449019	+	1.08403i
$695$	−10.3388	+	10.3388i	−0.392174	+	0.392174i
$696$	−3.67635			−0.139352
$697$		0			0
$698$	54.3368			2.05668
$699$	−4.63608	+	4.63608i	−0.175353	+	0.175353i
$700$	−9.73293	+	23.4974i	−0.367870	+	0.888117i
$701$		−	14.9568i		−	0.564910i	−0.959280	−	0.282455i	$-0.908851\pi$
$701$		−	14.9568i		−	0.564910i	0.959280	−	0.282455i	$-0.0911489\pi$
$702$	−7.12123	−	2.94971i	−0.268774	−	0.111330i
$703$	0.110997	+	0.267971i	0.00418633	+	0.0101067i
$704$	−44.0684	+	18.2537i	−1.66089	+	0.687964i
$705$	−9.06118	−	9.06118i	−0.341264	−	0.341264i
$706$	−31.5134	−	31.5134i	−1.18602	−	1.18602i
$707$	−10.5216	+	4.35818i	−0.395704	+	0.163906i
$708$	−5.59747	−	13.5135i	−0.210366	−	0.507868i
$709$	5.85105	+	2.42358i	0.219741	+	0.0910196i	0.489838	−	0.871813i	$-0.337056\pi$
$709$	5.85105	+	2.42358i	0.219741	+	0.0910196i	−0.270097	+	0.962833i	$0.587056\pi$
$710$		−	5.33589i		−	0.200252i
$711$	2.16250	−	5.22074i	0.0811002	−	0.195793i
$712$	−5.41038	+	5.41038i	−0.202762	+	0.202762i
$713$	69.9236			2.61866
$714$		0			0
$715$	−25.4013			−0.949956
$716$	−35.8026	+	35.8026i	−1.33801	+	1.33801i
$717$	−7.83038	+	18.9042i	−0.292431	+	0.705991i
$718$			73.0713i			2.72700i
$719$	−4.63434	−	1.91961i	−0.172832	−	0.0715893i	0.294590	−	0.955624i	$-0.404817\pi$
$719$	−4.63434	−	1.91961i	−0.172832	−	0.0715893i	−0.467422	+	0.884035i	$0.654817\pi$
$720$	1.82760	+	4.41221i	0.0681105	+	0.164433i
$721$	41.1687	−	17.0526i	1.53320	−	0.635074i
$722$	27.9080	+	27.9080i	1.03863	+	1.03863i
$723$	4.67998	+	4.67998i	0.174050	+	0.174050i
$724$	8.62948	−	3.57445i	0.320712	−	0.132843i
$725$	−4.41619	−	10.6616i	−0.164013	−	0.395962i
$726$	16.7303	+	6.92990i	0.620919	+	0.257193i
$727$		−	5.81340i		−	0.215607i	−0.994172	−	0.107804i	$-0.965618\pi$
$727$		−	5.81340i		−	0.215607i	0.994172	−	0.107804i	$-0.0343818\pi$
$728$	4.77004	−	11.5159i	0.176789	−	0.426808i
$729$	0.707107	−	0.707107i	0.0261891	−	0.0261891i
$730$	15.4362			0.571319
$731$		0			0
$732$	−12.7481			−0.471184
$733$	−30.7775	+	30.7775i	−1.13679	+	1.13679i	−0.147772	+	0.989021i	$0.547210\pi$
$733$	−30.7775	+	30.7775i	−1.13679	+	1.13679i	−0.989021	+	0.147772i	$0.952790\pi$
$734$	−7.78780	+	18.8014i	−0.287453	+	0.693973i
$735$			15.7399i			0.580576i
$736$	−48.2289	−	19.9771i	−1.77774	−	0.736364i
$737$	11.0891	+	26.7714i	0.408471	+	0.986136i
$738$	3.88582	−	1.60956i	0.143039	−	0.0592487i
$739$	22.4838	+	22.4838i	0.827078	+	0.827078i	0.987112	−	0.160033i	$-0.0511602\pi$
$739$	22.4838	+	22.4838i	0.827078	+	0.827078i	−0.160033	+	0.987112i	$0.551160\pi$
$740$	1.87962	+	1.87962i	0.0690964	+	0.0690964i
$741$	−1.38151	+	0.572241i	−0.0507511	+	0.0210218i
$742$	−13.5568	−	32.7290i	−0.497685	−	1.20152i
$743$	−32.5506	−	13.4829i	−1.19417	−	0.494640i	−0.305057	−	0.952334i	$-0.598675\pi$
$743$	−32.5506	−	13.4829i	−1.19417	−	0.494640i	−0.889110	+	0.457694i	$0.848675\pi$
$744$		−	8.84820i		−	0.324391i
$745$	−4.71611	+	11.3857i	−0.172785	+	0.417140i
$746$	−21.4287	+	21.4287i	−0.784562	+	0.784562i
$747$	−11.9505			−0.437244
$748$		0			0
$749$	−12.9935			−0.474770
$750$	17.4823	−	17.4823i	0.638363	−	0.638363i
$751$	8.36995	−	20.2068i	0.305424	−	0.737358i	−0.694418	−	0.719572i	$-0.744338\pi$
$751$	8.36995	−	20.2068i	0.305424	−	0.737358i	0.999842	−	0.0177862i	$-0.00566183\pi$
$752$			25.2070i			0.919203i
$753$	−5.68410	−	2.35443i	−0.207140	−	0.0858002i
$754$	13.2339	+	31.9496i	0.481952	+	1.16353i
$755$	20.0116	−	8.28907i	0.728296	−	0.301670i
$756$	6.99184	+	6.99184i	0.254291	+	0.254291i
$757$	−7.27668	−	7.27668i	−0.264475	−	0.264475i	0.562394	−	0.826869i	$-0.309880\pi$
$757$	−7.27668	−	7.27668i	−0.264475	−	0.264475i	−0.826869	+	0.562394i	$0.809880\pi$
$758$	−32.4304	+	13.4331i	−1.17792	+	0.487912i
$759$	10.9826	+	26.5144i	0.398644	+	0.962413i
$760$	−0.479530	−	0.198628i	−0.0173944	−	0.00720499i
$761$			41.0310i			1.48737i	0.668528	+	0.743687i	$0.266925\pi$
$761$			41.0310i			1.48737i	−0.668528	+	0.743687i	$0.733075\pi$
$762$	16.0970	−	38.8617i	0.583134	−	1.40781i
$763$	5.89945	−	5.89945i	0.213574	−	0.213574i
$764$	32.1961			1.16482
$765$		0			0
$766$	−25.9986			−0.939369
$767$	−15.9113	+	15.9113i	−0.574524	+	0.574524i
$768$	3.08111	−	7.43846i	0.111180	−	0.268412i
$769$			19.1855i			0.691847i	0.938263	+	0.345924i	$0.112434\pi$
$769$			19.1855i			0.691847i	−0.938263	+	0.345924i	$0.887566\pi$
$770$	55.2865	+	22.9004i	1.99239	+	0.825273i
$771$	0.516416	+	1.24674i	0.0185983	+	0.0449002i
$772$	−53.4556	+	22.1420i	−1.92391	+	0.796910i
$773$	−16.0187	−	16.0187i	−0.576152	−	0.576152i	0.357689	−	0.933841i	$-0.383565\pi$
$773$	−16.0187	−	16.0187i	−0.576152	−	0.576152i	−0.933841	+	0.357689i	$0.883565\pi$
$774$	−6.12260	−	6.12260i	−0.220072	−	0.220072i
$775$	25.6602	−	10.6288i	0.921742	−	0.381798i
$776$	−4.11764	−	9.94086i	−0.147815	−	0.356856i
$777$	−2.72598	−	1.12914i	−0.0977941	−	0.0405076i
$778$		−	37.9234i		−	1.35962i
$779$	0.312253	−	0.753844i	0.0111876	−	0.0270093i
$780$	−9.69033	+	9.69033i	−0.346969	+	0.346969i
$781$	7.24274			0.259166
$782$		0			0
$783$	−4.48652			−0.160335
$784$	21.8931	−	21.8931i	0.781898	−	0.781898i
$785$	1.44685	−	3.49301i	0.0516403	−	0.124671i
$786$		−	0.919982i		−	0.0328147i
$787$	29.6970	+	12.3009i	1.05858	+	0.438479i	0.842948	−	0.537995i	$-0.180818\pi$
$787$	29.6970	+	12.3009i	1.05858	+	0.438479i	0.215634	+	0.976474i	$0.430818\pi$
$788$	0.0458225	+	0.110625i	0.00163236	+	0.00394086i
$789$	25.3222	−	10.4888i	0.901493	−	0.373411i
$790$	−13.0466	−	13.0466i	−0.464176	−	0.464176i
$791$	23.0077	+	23.0077i	0.818059	+	0.818059i
$792$	3.35516	−	1.38975i	0.119220	−	0.0493827i
$793$	7.50507	+	18.1188i	0.266513	+	0.643419i
$794$	13.6517	+	5.65473i	0.484481	+	0.200679i
$795$			6.36978i			0.225913i
$796$	−7.49604	+	18.0970i	−0.265690	+	0.641432i
$797$	26.9602	−	26.9602i	0.954980	−	0.954980i	−0.0440490	−	0.999029i	$-0.514026\pi$
$797$	26.9602	−	26.9602i	0.954980	−	0.954980i	0.999029	+	0.0440490i	$0.0140258\pi$
$798$	3.52278			0.124705
$799$		0			0
$800$	−20.7354			−0.733109
$801$	−6.60268	+	6.60268i	−0.233294	+	0.233294i
$802$	−18.8369	+	45.4762i	−0.665153	+	1.60582i
$803$			20.9525i			0.739399i
$804$	14.4433	+	5.98262i	0.509377	+	0.210991i
$805$	15.9678	+	38.5497i	0.562791	+	1.35870i
$806$	−76.8958	+	31.8513i	−2.70854	+	1.12191i
$807$	−0.621517	−	0.621517i	−0.0218784	−	0.0218784i
$808$	1.59565	+	1.59565i	0.0561349	+	0.0561349i
$809$	24.2088	−	10.0276i	0.851136	−	0.352552i	0.0859013	−	0.996304i	$-0.472623\pi$
$809$	24.2088	−	10.0276i	0.851136	−	0.352552i	0.765234	+	0.643752i	$0.222623\pi$
$810$	−1.24949	−	3.01654i	−0.0439027	−	0.105990i
$811$	21.9733	+	9.10165i	0.771588	+	0.319602i	0.733516	−	0.679673i	$-0.237878\pi$
$811$	21.9733	+	9.10165i	0.771588	+	0.319602i	0.0380726	+	0.999275i	$0.487878\pi$
$812$		−	44.3625i		−	1.55682i
$813$	−5.69244	+	13.7428i	−0.199642	+	0.481980i
$814$	−4.68541	+	4.68541i	−0.164224	+	0.164224i
$815$	−0.880791			−0.0308528
$816$		0			0
$817$	−1.67977			−0.0587677
$818$	7.26641	−	7.26641i	0.254064	−	0.254064i
$819$	5.82123	−	14.0537i	0.203410	−	0.491076i
$820$		−	7.47792i		−	0.261140i
$821$	26.5187	+	10.9844i	0.925508	+	0.383358i	0.793973	−	0.607953i	$-0.208009\pi$
$821$	26.5187	+	10.9844i	0.925508	+	0.383358i	0.131536	+	0.991311i	$0.458009\pi$
$822$	−2.12313	−	5.12568i	−0.0740526	−	0.178779i
$823$	25.5047	−	10.5644i	0.889037	−	0.368251i	0.109042	−	0.994037i	$-0.465222\pi$
$823$	25.5047	−	10.5644i	0.889037	−	0.368251i	0.779995	+	0.625786i	$0.215222\pi$
$824$	−6.24346	−	6.24346i	−0.217501	−	0.217501i
$825$	8.06071	+	8.06071i	0.280638	+	0.280638i
$826$	48.9760	−	20.2865i	1.70409	−	0.705859i
$827$	9.57318	+	23.1117i	0.332892	+	0.803673i	0.998360	+	0.0572464i	$0.0182320\pi$
$827$	9.57318	+	23.1117i	0.332892	+	0.803673i	−0.665468	+	0.746426i	$0.731768\pi$
$828$	14.3047	+	5.92520i	0.497123	+	0.205915i
$829$		−	26.6547i		−	0.925757i	−0.886422	−	0.462878i	$-0.846817\pi$
$829$		−	26.6547i		−	0.925757i	0.886422	−	0.462878i	$-0.153183\pi$
$830$	−14.9320	+	36.0491i	−0.518298	+	1.25128i
$831$	11.5394	−	11.5394i	0.400297	−	0.400297i
$832$	39.5893			1.37251
$833$		0			0
$834$	−19.6635			−0.680890
$835$	13.3927	−	13.3927i	0.463473	−	0.463473i
$836$	1.64854	−	3.97994i	0.0570161	−	0.137649i
$837$		−	10.7981i		−	0.373237i
$838$	57.9649	+	24.0098i	2.00236	+	0.829406i
$839$	−9.24754	−	22.3255i	−0.319260	−	0.770763i	−0.999294	−	0.0375814i	$-0.988035\pi$
$839$	−9.24754	−	22.3255i	−0.319260	−	0.770763i	0.680033	−	0.733181i	$-0.261965\pi$
$840$	4.87811	−	2.02058i	0.168311	−	0.0697167i
$841$	−6.27282	−	6.27282i	−0.216304	−	0.216304i
$842$	−40.1468	−	40.1468i	−1.38355	−	1.38355i
$843$	28.1855	−	11.6748i	0.970759	−	0.402101i
$844$	25.0369	+	60.4445i	0.861807	+	2.08059i
$845$	0.763595	+	0.316291i	0.0262685	+	0.0108808i
$846$		−	17.2335i		−	0.592500i
$847$	−13.6761	+	33.0170i	−0.469917	+	1.13448i
$848$	8.85992	−	8.85992i	0.304251	−	0.304251i
$849$	0.235610			0.00808611
$850$		0			0
$851$	−4.62024			−0.158380
$852$	2.76303	−	2.76303i	0.0946597	−	0.0946597i
$853$	−5.50422	+	13.2884i	−0.188461	+	0.454985i	−0.989664	−	0.143408i	$-0.954194\pi$
$853$	−5.50422	+	13.2884i	−0.188461	+	0.454985i	0.801203	+	0.598393i	$0.204194\pi$
$854$		−	46.2021i		−	1.58100i
$855$	−0.585206	−	0.242400i	−0.0200136	−	0.00828991i
$856$	0.985264	+	2.37864i	0.0336756	+	0.0813001i
$857$	−41.0116	+	16.9876i	−1.40093	+	0.580284i	−0.949993	−	0.312273i	$-0.898910\pi$
$857$	−41.0116	+	16.9876i	−1.40093	+	0.580284i	−0.450936	+	0.892556i	$0.648910\pi$
$858$	−24.1555	−	24.1555i	−0.824654	−	0.824654i
$859$	20.9393	+	20.9393i	0.714438	+	0.714438i	0.967460	−	0.253022i	$-0.0814246\pi$
$859$	20.9393	+	20.9393i	0.714438	+	0.714438i	−0.253022	+	0.967460i	$0.581425\pi$
$860$	−14.2226	+	5.89120i	−0.484987	+	0.200888i
$861$	3.17645	+	7.66863i	0.108253	+	0.261346i
$862$	−9.28958	−	3.84787i	−0.316404	−	0.131059i
$863$		−	17.1407i		−	0.583477i	−0.956498	−	0.291739i	$-0.905766\pi$
$863$		−	17.1407i		−	0.583477i	0.956498	−	0.291739i	$-0.0942337\pi$
$864$	−3.08500	+	7.44785i	−0.104954	+	0.253381i
$865$	16.2101	−	16.2101i	0.551161	−	0.551161i
$866$	−1.86031			−0.0632160
$867$		0			0
$868$	106.771			3.62405
$869$	17.7089	−	17.7089i	0.600735	−	0.600735i
$870$	−5.60588	+	13.5338i	−0.190057	+	0.458838i
$871$		−	24.0503i		−	0.814913i
$872$	−1.52732	−	0.632637i	−0.0517216	−	0.0214238i
$873$	−5.02506	−	12.1316i	−0.170072	−	0.410591i
$874$	5.09634	−	2.11097i	0.172386	−	0.0714048i
$875$	34.5012	+	34.5012i	1.16635	+	1.16635i
$876$	7.99316	+	7.99316i	0.270064	+	0.270064i
$877$	−33.0727	+	13.6992i	−1.11679	+	0.462588i	−0.863269	−	0.504743i	$-0.831587\pi$
$877$	−33.0727	+	13.6992i	−1.11679	+	0.462588i	−0.253516	+	0.967331i	$0.581587\pi$
$878$	−14.2923	−	34.5046i	−0.482341	−	1.16447i
$879$	−22.8721	−	9.47395i	−0.771458	−	0.319548i
$880$			21.1656i			0.713494i
$881$	−16.4973	+	39.8281i	−0.555809	+	1.34184i	0.357248	+	0.934010i	$0.383715\pi$
$881$	−16.4973	+	39.8281i	−0.555809	+	1.34184i	−0.913057	+	0.407832i	$0.866285\pi$
$882$	−14.9679	+	14.9679i	−0.503996	+	0.503996i
$883$	−40.9100			−1.37673			−0.688366	−	0.725363i	$-0.741672\pi$
$883$	−40.9100			−1.37673			−0.688366	+	0.725363i	$0.741672\pi$
$884$		0			0
$885$	−9.53181			−0.320408
$886$	−41.6134	+	41.6134i	−1.39803	+	1.39803i
$887$	−9.04474	+	21.8359i	−0.303693	+	0.733179i	0.696190	+	0.717858i	$0.254877\pi$
$887$	−9.04474	+	21.8359i	−0.303693	+	0.733179i	−0.999883	+	0.0153215i	$0.995123\pi$
$888$			0.584650i			0.0196196i
$889$	76.6932	+	31.7674i	2.57221	+	1.06544i
$890$	11.6673	+	28.1672i	0.391087	+	0.944168i
$891$	4.09455	−	1.69602i	0.137172	−	0.0568187i
$892$	−17.4766	−	17.4766i	−0.585160	−	0.585160i
$893$	−2.36406	−	2.36406i	−0.0791101	−	0.0791101i
$894$	−15.3121	+	6.34246i	−0.512112	+	0.212124i
$895$	12.6268	+	30.4837i	0.422067	+	1.01896i
$896$	−24.5669	−	10.1759i	−0.820722	−	0.339954i
$897$		−	23.8195i		−	0.795309i
$898$	5.03261	−	12.1498i	0.167940	−	0.405444i
$899$	−34.2564	+	34.2564i	−1.14252	+	1.14252i
$900$	6.15014			0.205005
$901$		0			0
$902$	18.6405			0.620661
$903$	12.0829	−	12.0829i	0.402093	−	0.402093i
$904$	2.46727	−	5.95651i	0.0820600	−	0.198110i
$905$		−	6.08684i		−	0.202334i
$906$	26.9126	+	11.1475i	0.894110	+	0.370352i
$907$	−19.7976	−	47.7956i	−0.657369	−	1.58703i	−0.801853	−	0.597521i	$-0.796152\pi$
$907$	−19.7976	−	47.7956i	−0.657369	−	1.58703i	0.144484	−	0.989507i	$-0.453848\pi$
$908$	23.3573	−	9.67490i	0.775138	−	0.321073i
$909$	1.94729	+	1.94729i	0.0645876	+	0.0645876i
$910$	−35.1200	−	35.1200i	−1.16422	−	1.16422i
$911$	30.6063	−	12.6775i	1.01403	−	0.420025i	0.187107	−	0.982339i	$-0.440089\pi$
$911$	30.6063	−	12.6775i	1.01403	−	0.420025i	0.826924	+	0.562314i	$0.190089\pi$
$912$	0.476819	+	1.15114i	0.0157891	+	0.0381181i
$913$	−48.9317	−	20.2682i	−1.61940	−	0.670779i
$914$		−	41.1349i		−	1.36062i
$915$	−3.17913	+	7.67511i	−0.105099	+	0.253731i
$916$	−36.5569	+	36.5569i	−1.20788	+	1.20788i
$917$	1.81558			0.0599556
$918$		0			0
$919$	11.3691			0.375033			0.187517	−	0.982261i	$-0.439956\pi$
$919$	11.3691			0.375033			0.187517	+	0.982261i	$0.439956\pi$
$920$	5.84627	−	5.84627i	0.192746	−	0.192746i
$921$	1.73340	−	4.18479i	0.0571174	−	0.137894i
$922$			71.5820i			2.35743i
$923$	−5.55372	−	2.30043i	−0.182803	−	0.0757194i
$924$	16.7701	+	40.4867i	0.551697	+	1.33191i
$925$	−1.69552	+	0.702305i	−0.0557482	+	0.0230917i
$926$	48.0631	+	48.0631i	1.57945	+	1.57945i
$927$	−7.61935	−	7.61935i	−0.250252	−	0.250252i
$928$	33.4150	−	13.8409i	1.09690	−	0.454351i
$929$	19.7375	+	47.6505i	0.647566	+	1.56336i	0.816254	+	0.577693i	$0.196047\pi$
$929$	19.7375	+	47.6505i	0.647566	+	1.56336i	−0.168688	+	0.985669i	$0.553953\pi$
$930$	−32.5729	−	13.4921i	−1.06811	−	0.442425i
$931$			4.10653i			0.134586i
$932$	−5.99919	+	14.4833i	−0.196510	+	0.474417i
$933$	−19.8888	+	19.8888i	−0.651131	+	0.651131i
$934$	−75.3437			−2.46532
$935$		0			0
$936$	−3.01414			−0.0985202
$937$	−32.8390	+	32.8390i	−1.07280	+	1.07280i	−0.0756695	+	0.997133i	$0.524109\pi$
$937$	−32.8390	+	32.8390i	−1.07280	+	1.07280i	−0.997133	+	0.0756695i	$0.975891\pi$
$938$	−21.6824	+	52.3459i	−0.707955	+	1.70915i
$939$			12.5047i			0.408075i
$940$	−28.3076	−	11.7254i	−0.923291	−	0.382440i
$941$	0.309417	+	0.746999i	0.0100867	+	0.0243515i	0.928843	−	0.370474i	$-0.120805\pi$
$941$	0.309417	+	0.746999i	0.0100867	+	0.0243515i	−0.918756	+	0.394826i	$0.870805\pi$
$942$	4.69757	−	1.94580i	0.153055	−	0.0633975i
$943$	9.19061	+	9.19061i	0.299288	+	0.299288i
$944$	13.2581	+	13.2581i	0.431514	+	0.431514i
$945$	5.95312	−	2.46586i	0.193655	−	0.0802145i
$946$	−14.6852	−	35.4533i	−0.477458	−	1.15269i
$947$	48.2977	+	20.0056i	1.56946	+	0.650093i	0.986701	−	0.162549i	$-0.0519714\pi$
$947$	48.2977	+	20.0056i	1.56946	+	0.650093i	0.582763	+	0.812642i	$0.301971\pi$
$948$		−	13.5115i		−	0.438834i
$949$	6.65490	−	16.0664i	0.216027	−	0.521536i
$950$	1.54935	−	1.54935i	0.0502676	−	0.0502676i
$951$	−30.7407			−0.996835
$952$		0			0
$953$	−48.1209			−1.55879			−0.779395	−	0.626533i	$-0.784473\pi$
$953$	−48.1209			−1.55879			−0.779395	+	0.626533i	$0.784473\pi$
$954$	−6.05735	+	6.05735i	−0.196114	+	0.196114i
$955$	8.02909	−	19.3839i	0.259815	−	0.627249i
$956$			48.9250i			1.58235i
$957$	−18.3703	−	7.60922i	−0.593827	−	0.245971i
$958$	23.2190	+	56.0555i	0.750171	+	1.81107i
$959$	10.1155	−	4.18997i	0.326646	−	0.135301i
$960$	11.8582	+	11.8582i	0.382720	+	0.382720i
$961$	−60.5276	−	60.5276i	−1.95250	−	1.95250i
$962$	5.08094	−	2.10459i	0.163816	−	0.0678548i
$963$	1.20239	+	2.90282i	0.0387465	+	0.0935422i
$964$	14.6205	+	6.05600i	0.470894	+	0.195050i
$965$			37.7052i			1.21377i
$966$	−21.4743	+	51.8435i	−0.690924	+	1.66804i
$967$	9.06046	−	9.06046i	0.291365	−	0.291365i	−0.546254	−	0.837619i	$-0.683947\pi$
$967$	9.06046	−	9.06046i	0.291365	−	0.291365i	0.837619	+	0.546254i	$0.183947\pi$
$968$	7.08127			0.227601
$969$		0			0
$970$	−42.8741			−1.37661
$971$	−13.3838	+	13.3838i	−0.429507	+	0.429507i	−0.888460	−	0.458954i	$-0.848224\pi$
$971$	−13.3838	+	13.3838i	−0.429507	+	0.429507i	0.458954	+	0.888460i	$0.348224\pi$
$972$	0.915012	−	2.20903i	0.0293490	−	0.0708548i
$973$		−	38.8057i		−	1.24405i
$974$	−27.0866	−	11.2196i	−0.867909	−	0.359500i
$975$	−3.62071	−	8.74116i	−0.115955	−	0.279941i
$976$	15.0975	−	6.25359i	0.483259	−	0.200172i
$977$	−3.39027	−	3.39027i	−0.108464	−	0.108464i	0.650792	−	0.759256i	$-0.274437\pi$
$977$	−3.39027	−	3.39027i	−0.108464	−	0.108464i	−0.759256	+	0.650792i	$0.774437\pi$
$978$	−0.837590	−	0.837590i	−0.0267832	−	0.0267832i
$979$	−38.2332	+	15.8367i	−1.22194	+	0.506144i
$980$	14.4022	+	34.7700i	0.460062	+	1.11069i
$981$	−1.86390	−	0.772053i	−0.0595098	−	0.0246498i
$982$			0.334317i			0.0106685i
$983$	5.66907	−	13.6863i	0.180815	−	0.436527i	−0.807320	−	0.590114i	$-0.799083\pi$
$983$	5.66907	−	13.6863i	0.180815	−	0.436527i	0.988135	+	0.153588i	$0.0490827\pi$
$984$	1.16299	−	1.16299i	0.0370747	−	0.0370747i
$985$	0.0780300			0.00248624
$986$		0			0
$987$	34.0102			1.08256
$988$	−2.52820	+	2.52820i	−0.0804327	+	0.0804327i
$989$	10.2396	−	24.7206i	0.325600	−	0.786068i
$990$		−	14.4705i		−	0.459904i
$991$	14.1641	+	5.86695i	0.449936	+	0.186370i	0.596133	−	0.802886i	$-0.296703\pi$
$991$	14.1641	+	5.86695i	0.449936	+	0.186370i	−0.146197	+	0.989256i	$0.546703\pi$
$992$	33.3122	+	80.4227i	1.05766	+	2.55342i
$993$	−10.9658	+	4.54219i	−0.347990	+	0.144142i
$994$	10.0138	+	10.0138i	0.317620	+	0.317620i
$995$	9.02610	+	9.02610i	0.286147	+	0.286147i
$996$	−26.3990	+	10.9348i	−0.836484	+	0.346483i
$997$	0.735037	+	1.77454i	0.0232788	+	0.0562001i	0.935092	−	0.354406i	$-0.115317\pi$
$997$	0.735037	+	1.77454i	0.0232788	+	0.0562001i	−0.911813	+	0.410606i	$0.865317\pi$
$998$	12.3348	+	5.10923i	0.390450	+	0.161730i
$999$			0.713491i			0.0225739i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.h.m.688.12		48
17.2	even	8	inner	867.2.h.m.712.11		48
17.3	odd	16		867.2.e.k.616.2		24
17.4	even	4	inner	867.2.h.m.757.1		48
17.5	odd	16		867.2.e.k.829.12		24
17.6	odd	16		867.2.d.g.577.11		12
17.7	odd	16		867.2.a.o.1.1	✓	6
17.8	even	8	inner	867.2.h.m.733.1		48
17.9	even	8	inner	867.2.h.m.733.2		48
17.10	odd	16		867.2.a.p.1.1	yes	6
17.11	odd	16		867.2.d.g.577.12		12
17.12	odd	16		867.2.e.k.829.11		24
17.13	even	4	inner	867.2.h.m.757.2		48
17.14	odd	16		867.2.e.k.616.1		24
17.15	even	8	inner	867.2.h.m.712.12		48
17.16	even	2	inner	867.2.h.m.688.11		48
51.41	even	16		2601.2.a.bh.1.6		6
51.44	even	16		2601.2.a.bi.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
867.2.a.o.1.1	✓	6	17.7	odd	16
867.2.a.p.1.1	yes	6	17.10	odd	16
867.2.d.g.577.11		12	17.6	odd	16
867.2.d.g.577.12		12	17.11	odd	16
867.2.e.k.616.1		24	17.14	odd	16
867.2.e.k.616.2		24	17.3	odd	16
867.2.e.k.829.11		24	17.12	odd	16
867.2.e.k.829.12		24	17.5	odd	16
867.2.h.m.688.11		48	17.16	even	2	inner
867.2.h.m.688.12		48	1.1	even	1	trivial
867.2.h.m.712.11		48	17.2	even	8	inner
867.2.h.m.712.12		48	17.15	even	8	inner
867.2.h.m.733.1		48	17.8	even	8	inner
867.2.h.m.733.2		48	17.9	even	8	inner
867.2.h.m.757.1		48	17.4	even	4	inner
867.2.h.m.757.2		48	17.13	even	4	inner
2601.2.a.bh.1.6		6	51.41	even	16
2601.2.a.bi.1.6		6	51.44	even	16

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:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.h (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.48173 - 1.48173i) q^{2} +(0.382683 - 0.923880i) q^{3} -2.39104i q^{4} +(-1.43955 - 0.596279i) q^{5} +(-0.801906 - 1.93597i) q^{6} +(3.82062 - 1.58255i) q^{7} +(-0.579419 - 0.579419i) q^{8} +(-0.707107 - 0.707107i) q^{9} +(-3.01654 + 1.24949i) q^{10} +(-1.69602 - 4.09455i) q^{11} +(-2.20903 - 0.915012i) q^{12} +3.67837i q^{13} +(3.31621 - 8.00605i) q^{14} +(-1.10178 + 1.10178i) q^{15} +3.06500 q^{16} -2.09548 q^{18} +(-0.287454 + 0.287454i) q^{19} +(-1.42573 + 3.44201i) q^{20} -4.13541i q^{21} +(-8.58005 - 3.55397i) q^{22} +(-2.47808 - 5.98262i) q^{23} +(-0.757047 + 0.313579i) q^{24} +(-1.81879 - 1.81879i) q^{25} +(5.45035 + 5.45035i) q^{26} +(-0.923880 + 0.382683i) q^{27} +(-3.78395 - 9.13527i) q^{28} +(4.14501 + 1.71692i) q^{29} +3.26508i q^{30} +(-4.13225 + 9.97614i) q^{31} +(5.70034 - 5.70034i) q^{32} -4.43191 q^{33} -6.44361 q^{35} +(-1.69072 + 1.69072i) q^{36} +(0.273041 - 0.659180i) q^{37} +0.851857i q^{38} +(3.39838 + 1.40765i) q^{39} +(0.488604 + 1.17959i) q^{40} +(-1.85438 + 0.768109i) q^{41} +(-6.12756 - 6.12756i) q^{42} +(2.92181 + 2.92181i) q^{43} +(-9.79024 + 4.05525i) q^{44} +(0.596279 + 1.43955i) q^{45} +(-12.5365 - 5.19278i) q^{46} +8.22412i q^{47} +(1.17293 - 2.83169i) q^{48} +(7.14295 - 7.14295i) q^{49} -5.38991 q^{50} +8.79515 q^{52} +(2.89067 - 2.89067i) q^{53} +(-0.801906 + 1.93597i) q^{54} +6.90559i q^{55} +(-3.13070 - 1.29678i) q^{56} +(0.155569 + 0.375576i) q^{57} +(8.68579 - 3.59777i) q^{58} +(4.32564 + 4.32564i) q^{59} +(2.63440 + 2.63440i) q^{60} +(4.92577 - 2.04032i) q^{61} +(8.65906 + 20.9048i) q^{62} +(-3.82062 - 1.58255i) q^{63} -10.7627i q^{64} +(2.19334 - 5.29519i) q^{65} +(-6.56688 + 6.56688i) q^{66} -6.53830 q^{67} -6.47554 q^{69} +(-9.54768 + 9.54768i) q^{70} +(-0.625392 + 1.50983i) q^{71} +0.819422i q^{72} +(-4.36779 - 1.80920i) q^{73} +(-0.572153 - 1.38130i) q^{74} +(-2.37636 + 0.984322i) q^{75} +(0.687314 + 0.687314i) q^{76} +(-12.9597 - 12.9597i) q^{77} +(7.12123 - 2.94971i) q^{78} +(2.16250 + 5.22074i) q^{79} +(-4.41221 - 1.82760i) q^{80} +1.00000i q^{81} +(-1.60956 + 3.88582i) q^{82} +(8.45025 - 8.45025i) q^{83} -9.88795 q^{84} +8.65866 q^{86} +(3.17245 - 3.17245i) q^{87} +(-1.38975 + 3.35516i) q^{88} -9.33759i q^{89} +(3.01654 + 1.24949i) q^{90} +(5.82123 + 14.0537i) q^{91} +(-14.3047 + 5.92520i) q^{92} +(7.63541 + 7.63541i) q^{93} +(12.1859 + 12.1859i) q^{94} +(0.585206 - 0.242400i) q^{95} +(-3.08500 - 7.44785i) q^{96} +(12.1316 + 5.02506i) q^{97} -21.1678i q^{98} +(-1.69602 + 4.09455i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 120 q^{16} + 24 q^{18} + 72 q^{33} - 96 q^{50} - 144 q^{52} + 48 q^{67} - 72 q^{69} + 120 q^{84} + 48 q^{86}+O(q^{100}) \) 48 * q - 120 * q^16 + 24 * q^18 + 72 * q^33 - 96 * q^50 - 144 * q^52 + 48 * q^67 - 72 * q^69 + 120 * q^84 + 48 * q^86

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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