LMFDB - Embedded newform 867.2.h.l.712.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [867,2,Mod(688,867)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			712.4
Character	$\chi$	$=$	867.712
Dual form			867.2.h.l.688.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.952682 + 0.952682i) q^{2} +(0.382683 + 0.923880i) q^{3} -0.184793i q^{4} +(-2.33935 + 0.968988i) q^{5} +(-0.515588 + 1.24474i) q^{6} +(0.170726 + 0.0707170i) q^{7} +(2.08141 - 2.08141i) q^{8} +(-0.707107 + 0.707107i) q^{9} +O(q^{10})$	\(q+(0.952682 + 0.952682i) q^{2} +(0.382683 + 0.923880i) q^{3} -0.184793i q^{4} +(-2.33935 + 0.968988i) q^{5} +(-0.515588 + 1.24474i) q^{6} +(0.170726 + 0.0707170i) q^{7} +(2.08141 - 2.08141i) q^{8} +(-0.707107 + 0.707107i) q^{9} +(-3.15179 - 1.30551i) q^{10} +(-1.36770 + 3.30193i) q^{11} +(0.170726 - 0.0707170i) q^{12} +6.53209i q^{13} +(0.0952768 + 0.230019i) q^{14} +(-1.79046 - 1.79046i) q^{15} +3.59627 q^{16} -1.34730 q^{18} +(-3.27967 - 3.27967i) q^{19} +(0.179062 + 0.432294i) q^{20} +0.184793i q^{21} +(-4.44867 + 1.84270i) q^{22} +(-1.18864 + 2.86963i) q^{23} +(2.71950 + 1.12645i) q^{24} +(0.998063 - 0.998063i) q^{25} +(-6.22301 + 6.22301i) q^{26} +(-0.923880 - 0.382683i) q^{27} +(0.0130680 - 0.0315489i) q^{28} +(-5.87129 + 2.43197i) q^{29} -3.41147i q^{30} +(2.83625 + 6.84731i) q^{31} +(-0.736727 - 0.736727i) q^{32} -3.57398 q^{33} -0.467911 q^{35} +(0.130668 + 0.130668i) q^{36} +(-3.21336 - 7.75775i) q^{37} -6.24897i q^{38} +(-6.03486 + 2.49972i) q^{39} +(-2.85228 + 6.88601i) q^{40} +(6.63788 + 2.74950i) q^{41} +(-0.176049 + 0.176049i) q^{42} +(3.49015 - 3.49015i) q^{43} +(0.610171 + 0.252741i) q^{44} +(0.968988 - 2.33935i) q^{45} +(-3.86624 + 1.60145i) q^{46} +9.04963i q^{47} +(1.37623 + 3.32252i) q^{48} +(-4.92560 - 4.92560i) q^{49} +1.90167 q^{50} +1.20708 q^{52} +(5.41128 + 5.41128i) q^{53} +(-0.515588 - 1.24474i) q^{54} -9.04963i q^{55} +(0.502543 - 0.208160i) q^{56} +(1.77495 - 4.28510i) q^{57} +(-7.91037 - 3.27658i) q^{58} +(-4.63464 + 4.63464i) q^{59} +(-0.330863 + 0.330863i) q^{60} +(-2.75820 - 1.14248i) q^{61} +(-3.82127 + 9.22535i) q^{62} +(-0.170726 + 0.0707170i) q^{63} -8.59627i q^{64} +(-6.32952 - 15.2808i) q^{65} +(-3.40487 - 3.40487i) q^{66} +13.5175 q^{67} -3.10607 q^{69} +(-0.445771 - 0.445771i) q^{70} +(-1.38180 - 3.33596i) q^{71} +2.94356i q^{72} +(7.77119 - 3.21893i) q^{73} +(4.32935 - 10.4520i) q^{74} +(1.30403 + 0.540148i) q^{75} +(-0.606059 + 0.606059i) q^{76} +(-0.467005 + 0.467005i) q^{77} +(-8.13075 - 3.36787i) q^{78} +(2.99371 - 7.22746i) q^{79} +(-8.41291 + 3.48474i) q^{80} -1.00000i q^{81} +(3.70439 + 8.94320i) q^{82} +(1.77660 + 1.77660i) q^{83} +0.0341483 q^{84} +6.65002 q^{86} +(-4.49369 - 4.49369i) q^{87} +(4.02592 + 9.71942i) q^{88} +1.32770i q^{89} +(3.15179 - 1.30551i) q^{90} +(-0.461930 + 1.11520i) q^{91} +(0.530286 + 0.219652i) q^{92} +(-5.24070 + 5.24070i) q^{93} +(-8.62142 + 8.62142i) q^{94} +(10.8502 + 4.49432i) q^{95} +(0.398714 - 0.962580i) q^{96} +(8.09205 - 3.35184i) q^{97} -9.38507i q^{98} +(-1.36770 - 3.30193i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q - 24 q^{16} - 24 q^{18} - 24 q^{33} - 48 q^{35} - 48 q^{50} - 48 q^{52} + 144 q^{67} + 24 q^{69} + 168 q^{84} + 240 q^{86}+O(q^{100}) $ 24 * q - 24 * q^16 - 24 * q^18 - 24 * q^33 - 48 * q^35 - 48 * q^50 - 48 * q^52 + 144 * q^67 + 24 * q^69 + 168 * q^84 + 240 * q^86

Display 100 coefficients 10 coefficients

Character values

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

$n$	$290$	$292$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	0.952682	+	0.952682i	0.673648	+	0.673648i	0.958555	−	0.284907i	$-0.0919627\pi$
$2$	0.952682	+	0.952682i	0.673648	+	0.673648i	−0.284907	+	0.958555i	$0.591963\pi$
$3$	0.382683	+	0.923880i	0.220942	+	0.533402i
$3$	0.382683	+	0.923880i	0.220942	+	0.533402i
$4$		−	0.184793i		−	0.0923963i
$5$	−2.33935	+	0.968988i	−1.04619	+	0.433345i	−0.838529	−	0.544857i	$-0.816584\pi$
$5$	−2.33935	+	0.968988i	−1.04619	+	0.433345i	−0.207658	+	0.978202i	$0.566584\pi$
$6$	−0.515588	+	1.24474i	−0.210488	+	0.508163i
$7$	0.170726	+	0.0707170i	0.0645284	+	0.0267285i	0.414714	−	0.909952i	$-0.363882\pi$
$7$	0.170726	+	0.0707170i	0.0645284	+	0.0267285i	−0.350186	+	0.936680i	$0.613882\pi$
$8$	2.08141	−	2.08141i	0.735891	−	0.735891i
$9$	−0.707107	+	0.707107i	−0.235702	+	0.235702i
$10$	−3.15179	−	1.30551i	−0.996684	−	0.412840i
$11$	−1.36770	+	3.30193i	−0.412378	+	0.995568i	0.572120	+	0.820170i	$0.306121\pi$
$11$	−1.36770	+	3.30193i	−0.412378	+	0.995568i	−0.984498	+	0.175398i	$0.943879\pi$
$12$	0.170726	−	0.0707170i	0.0492844	−	0.0204143i
$13$			6.53209i			1.81168i	0.423625	+	0.905838i	$0.360758\pi$
$13$			6.53209i			1.81168i	−0.423625	+	0.905838i	$0.639242\pi$
$14$	0.0952768	+	0.230019i	0.0254638	+	0.0614750i
$15$	−1.79046	−	1.79046i	−0.462294	−	0.462294i
$16$	3.59627			0.899067
$17$		0			0
$17$		0			0
$18$	−1.34730			−0.317561
$19$	−3.27967	−	3.27967i	−0.752408	−	0.752408i	0.222520	−	0.974928i	$-0.428572\pi$
$19$	−3.27967	−	3.27967i	−0.752408	−	0.752408i	−0.974928	+	0.222520i	$0.928572\pi$
$20$	0.179062	+	0.432294i	0.0400394	+	0.0966638i
$21$			0.184793i			0.0403250i
$22$	−4.44867	+	1.84270i	−0.948460	+	0.392865i
$23$	−1.18864	+	2.86963i	−0.247849	+	0.598360i	−0.998021	−	0.0628829i	$-0.979971\pi$
$23$	−1.18864	+	2.86963i	−0.247849	+	0.598360i	0.750172	+	0.661242i	$0.229971\pi$
$24$	2.71950	+	1.12645i	0.555115	+	0.229936i
$25$	0.998063	−	0.998063i	0.199613	−	0.199613i
$26$	−6.22301	+	6.22301i	−1.22043	+	1.22043i
$27$	−0.923880	−	0.382683i	−0.177801	−	0.0736475i
$28$	0.0130680	−	0.0315489i	0.00246962	−	0.00596218i
$29$	−5.87129	+	2.43197i	−1.09027	+	0.451605i	−0.854101	−	0.520107i	$-0.825892\pi$
$29$	−5.87129	+	2.43197i	−1.09027	+	0.451605i	−0.236170	+	0.971712i	$0.575892\pi$
$30$		−	3.41147i		−	0.622847i
$31$	2.83625	+	6.84731i	0.509405	+	1.22981i	0.944227	+	0.329296i	$0.106812\pi$
$31$	2.83625	+	6.84731i	0.509405	+	1.22981i	−0.434821	+	0.900517i	$0.643188\pi$
$32$	−0.736727	−	0.736727i	−0.130236	−	0.130236i
$33$	−3.57398			−0.622150
$34$		0			0
$35$	−0.467911			−0.0790914
$36$	0.130668	+	0.130668i	0.0217780	+	0.0217780i
$37$	−3.21336	−	7.75775i	−0.528274	−	1.27537i	−0.932653	−	0.360775i	$-0.882512\pi$
$37$	−3.21336	−	7.75775i	−0.528274	−	1.27537i	0.404379	−	0.914591i	$-0.367488\pi$
$38$		−	6.24897i		−	1.01372i
$39$	−6.03486	+	2.49972i	−0.966352	+	0.400276i
$40$	−2.85228	+	6.88601i	−0.450985	+	1.08877i
$41$	6.63788	+	2.74950i	1.03666	+	0.429400i	0.835113	−	0.550078i	$-0.185402\pi$
$41$	6.63788	+	2.74950i	1.03666	+	0.429400i	0.201550	+	0.979478i	$0.435402\pi$
$42$	−0.176049	+	0.176049i	−0.0271649	+	0.0271649i
$43$	3.49015	−	3.49015i	0.532243	−	0.532243i	−0.388996	−	0.921239i	$-0.627178\pi$
$43$	3.49015	−	3.49015i	0.532243	−	0.532243i	0.921239	+	0.388996i	$0.127178\pi$
$44$	0.610171	+	0.252741i	0.0919868	+	0.0381022i
$45$	0.968988	−	2.33935i	0.144448	−	0.348729i
$46$	−3.86624	+	1.60145i	−0.570047	+	0.236121i
$47$			9.04963i			1.32002i	0.751255	+	0.660012i	$0.229449\pi$
$47$			9.04963i			1.32002i	−0.751255	+	0.660012i	$0.770551\pi$
$48$	1.37623	+	3.32252i	0.198642	+	0.479564i
$49$	−4.92560	−	4.92560i	−0.703657	−	0.703657i
$50$	1.90167			0.268937
$51$		0			0
$52$	1.20708			0.167392
$53$	5.41128	+	5.41128i	0.743296	+	0.743296i	0.973211	−	0.229915i	$-0.0738447\pi$
$53$	5.41128	+	5.41128i	0.743296	+	0.743296i	−0.229915	+	0.973211i	$0.573845\pi$
$54$	−0.515588	−	1.24474i	−0.0701626	−	0.169388i
$55$		−	9.04963i		−	1.22025i
$56$	0.502543	−	0.208160i	0.0671551	−	0.0278166i
$57$	1.77495	−	4.28510i	0.235097	−	0.567575i
$58$	−7.91037	−	3.27658i	−1.03868	−	0.430236i
$59$	−4.63464	+	4.63464i	−0.603379	+	0.603379i	−0.941208	−	0.337828i	$-0.890308\pi$
$59$	−4.63464	+	4.63464i	−0.603379	+	0.603379i	0.337828	+	0.941208i	$0.390308\pi$
$60$	−0.330863	+	0.330863i	−0.0427142	+	0.0427142i
$61$	−2.75820	−	1.14248i	−0.353151	−	0.146280i	0.199053	−	0.979989i	$-0.436213\pi$
$61$	−2.75820	−	1.14248i	−0.353151	−	0.146280i	−0.552205	+	0.833709i	$0.686213\pi$
$62$	−3.82127	+	9.22535i	−0.485301	+	1.17162i
$63$	−0.170726	+	0.0707170i	−0.0215095	+	0.00890951i
$64$		−	8.59627i		−	1.07453i
$65$	−6.32952	−	15.2808i	−0.785080	−	1.89535i
$66$	−3.40487	−	3.40487i	−0.419110	−	0.419110i
$67$	13.5175			1.65143			0.825715	−	0.564087i	$-0.190772\pi$
$67$	13.5175			1.65143			0.825715	+	0.564087i	$0.190772\pi$
$68$		0			0
$69$	−3.10607			−0.373927
$70$	−0.445771	−	0.445771i	−0.0532798	−	0.0532798i
$71$	−1.38180	−	3.33596i	−0.163989	−	0.395905i	0.820429	−	0.571749i	$-0.193735\pi$
$71$	−1.38180	−	3.33596i	−0.163989	−	0.395905i	−0.984418	+	0.175843i	$0.943735\pi$
$72$			2.94356i			0.346902i
$73$	7.77119	−	3.21893i	0.909549	−	0.376747i	0.121665	−	0.992571i	$-0.461177\pi$
$73$	7.77119	−	3.21893i	0.909549	−	0.376747i	0.787884	+	0.615824i	$0.211177\pi$
$74$	4.32935	−	10.4520i	0.503277	−	1.21502i
$75$	1.30403	+	0.540148i	0.150577	+	0.0623709i
$76$	−0.606059	+	0.606059i	−0.0695197	+	0.0695197i
$77$	−0.467005	+	0.467005i	−0.0532201	+	0.0532201i
$78$	−8.13075	−	3.36787i	−0.920626	−	0.381336i
$79$	2.99371	−	7.22746i	0.336819	−	0.813153i	−0.661198	−	0.750211i	$-0.729952\pi$
$79$	2.99371	−	7.22746i	0.336819	−	0.813153i	0.998017	−	0.0629417i	$-0.0200482\pi$
$80$	−8.41291	+	3.48474i	−0.940592	+	0.389606i
$81$		−	1.00000i		−	0.111111i
$82$	3.70439	+	8.94320i	0.409082	+	0.987611i
$83$	1.77660	+	1.77660i	0.195007	+	0.195007i	0.797856	−	0.602849i	$-0.205968\pi$
$83$	1.77660	+	1.77660i	0.195007	+	0.195007i	−0.602849	+	0.797856i	$0.705968\pi$
$84$	0.0341483			0.00372588
$85$		0			0
$86$	6.65002			0.717090
$87$	−4.49369	−	4.49369i	−0.481774	−	0.481774i
$88$	4.02592	+	9.71942i	0.429164	+	1.03609i
$89$			1.32770i			0.140735i	0.997521	+	0.0703677i	$0.0224173\pi$
$89$			1.32770i			0.140735i	−0.997521	+	0.0703677i	$0.977583\pi$
$90$	3.15179	−	1.30551i	0.332228	−	0.137613i
$91$	−0.461930	+	1.11520i	−0.0484234	+	0.116904i
$92$	0.530286	+	0.219652i	0.0552862	+	0.0229003i
$93$	−5.24070	+	5.24070i	−0.543436	+	0.543436i
$94$	−8.62142	+	8.62142i	−0.889232	+	0.889232i
$95$	10.8502	+	4.49432i	1.11321	+	0.461107i
$96$	0.398714	−	0.962580i	0.0406935	−	0.0982429i
$97$	8.09205	−	3.35184i	0.821623	−	0.340327i	0.0680420	−	0.997682i	$-0.478325\pi$
$97$	8.09205	−	3.35184i	0.821623	−	0.340327i	0.753581	+	0.657355i	$0.228325\pi$
$98$		−	9.38507i		−	0.948035i
$99$	−1.36770	−	3.30193i	−0.137459	−	0.331856i
$100$	−0.184435	−	0.184435i	−0.0184435	−	0.0184435i
$101$	11.0273			1.09726			0.548631	−	0.836065i	$-0.315149\pi$
$101$	11.0273			1.09726			0.548631	+	0.836065i	$0.315149\pi$
$102$		0			0
$103$	6.27126			0.617926			0.308963	−	0.951074i	$-0.400018\pi$
$103$	6.27126			0.617926			0.308963	+	0.951074i	$0.400018\pi$
$104$	13.5960	+	13.5960i	1.33320	+	1.33320i
$105$	−0.179062	−	0.432294i	−0.0174746	−	0.0421875i
$106$			10.3105i			1.00144i
$107$	3.28382	−	1.36020i	0.317459	−	0.131496i	−0.218264	−	0.975890i	$-0.570039\pi$
$107$	3.28382	−	1.36020i	0.317459	−	0.131496i	0.535722	+	0.844394i	$0.320039\pi$
$108$	−0.0707170	+	0.170726i	−0.00680475	+	0.0164281i
$109$	3.32252	+	1.37623i	0.318239	+	0.131819i	0.536085	−	0.844164i	$-0.319903\pi$
$109$	3.32252	+	1.37623i	0.318239	+	0.131819i	−0.217845	+	0.975983i	$0.569903\pi$
$110$	8.62142	−	8.62142i	0.822020	−	0.822020i
$111$	5.93752	−	5.93752i	0.563565	−	0.563565i
$112$	0.613976	+	0.254317i	0.0580153	+	0.0240307i
$113$	−1.80211	+	4.35068i	−0.169528	+	0.409277i	−0.985695	−	0.168539i	$-0.946095\pi$
$113$	−1.80211	+	4.35068i	−0.169528	+	0.409277i	0.816167	+	0.577816i	$0.196095\pi$
$114$	5.77330	−	2.39138i	0.540719	−	0.223973i
$115$		−	7.86484i		−	0.733400i
$116$	0.449409	+	1.08497i	0.0417266	+	0.100737i
$117$	−4.61888	−	4.61888i	−0.427016	−	0.427016i
$118$	−8.83069			−0.812931
$119$		0			0
$120$	−7.45336			−0.680396
$121$	−1.25393	−	1.25393i	−0.113993	−	0.113993i
$122$	−1.53926	−	3.71611i	−0.139358	−	0.336441i
$123$			7.18479i			0.647831i
$124$	1.26533	−	0.524118i	0.113630	−	0.0470671i
$125$	3.47724	−	8.39480i	0.311014	−	0.750854i
$126$	−0.230019	−	0.0952768i	−0.0204917	−	0.00848793i
$127$	−5.49175	+	5.49175i	−0.487314	+	0.487314i	−0.907458	−	0.420143i	$-0.861980\pi$
$127$	−5.49175	+	5.49175i	−0.487314	+	0.487314i	0.420143	+	0.907458i	$0.361980\pi$
$128$	6.71606	−	6.71606i	0.593621	−	0.593621i
$129$	4.56011	+	1.88886i	0.401495	+	0.166305i
$130$	8.52774	−	20.5878i	0.747932	−	1.80567i
$131$	4.57441	−	1.89478i	0.399668	−	0.165548i	−0.173790	−	0.984783i	$-0.555601\pi$
$131$	4.57441	−	1.89478i	0.399668	−	0.165548i	0.573458	+	0.819235i	$0.305601\pi$
$132$			0.660444i			0.0574843i
$133$	−0.327997	−	0.791854i	−0.0284409	−	0.0686624i
$134$	12.8779	+	12.8779i	1.11248	+	1.11248i
$135$	2.53209			0.217928
$136$		0			0
$137$	−11.5885			−0.990075			−0.495037	−	0.868872i	$-0.664846\pi$
$137$	−11.5885			−0.990075			−0.495037	+	0.868872i	$0.664846\pi$
$138$	−2.95910	−	2.95910i	−0.251895	−	0.251895i
$139$	−1.02924	−	2.48481i	−0.0872992	−	0.210759i	0.874200	−	0.485565i	$-0.161386\pi$
$139$	−1.02924	−	2.48481i	−0.0872992	−	0.210759i	−0.961500	+	0.274806i	$0.911386\pi$
$140$			0.0864665i			0.00730775i
$141$	−8.36077	+	3.46314i	−0.704104	+	0.291649i
$142$	1.86169	−	4.49452i	0.156230	−	0.377172i
$143$	−21.5685	−	8.93395i	−1.80365	−	0.747095i
$144$	−2.54294	+	2.54294i	−0.211912	+	0.211912i
$145$	11.3784	−	11.3784i	0.944927	−	0.944927i
$146$	10.4701	+	4.33686i	0.866511	+	0.358921i
$147$	2.66572	−	6.43561i	0.219865	−	0.530800i
$148$	−1.43357	+	0.593806i	−0.117839	+	0.0488105i
$149$			15.9290i			1.30496i	0.757808	+	0.652478i	$0.226270\pi$
$149$			15.9290i			1.30496i	−0.757808	+	0.652478i	$0.773730\pi$
$150$	0.727739	+	1.75692i	0.0594196	+	0.143452i
$151$	0.982302	+	0.982302i	0.0799386	+	0.0799386i	0.745946	−	0.666007i	$-0.231998\pi$
$151$	0.982302	+	0.982302i	0.0799386	+	0.0799386i	−0.666007	+	0.745946i	$0.731998\pi$
$152$	−13.6527			−1.10738
$153$		0			0
$154$	−0.889814			−0.0717033
$155$	−13.2699	−	13.2699i	−1.06587	−	1.06587i
$156$	0.461930	+	1.11520i	0.0369840	+	0.0892873i
$157$			1.78106i			0.142144i	0.997471	+	0.0710720i	$0.0226420\pi$
$157$			1.78106i			0.142144i	−0.997471	+	0.0710720i	$0.977358\pi$
$158$	9.73753	−	4.03342i	0.774677	−	0.320882i
$159$	−2.92856	+	7.07018i	−0.232250	+	0.560701i
$160$	2.43734	+	1.00958i	0.192688	+	0.0798142i
$161$	−0.405864	+	0.405864i	−0.0319865	+	0.0319865i
$162$	0.952682	−	0.952682i	0.0748498	−	0.0748498i
$163$	2.91082	+	1.20570i	0.227993	+	0.0944377i	0.493755	−	0.869601i	$-0.335624\pi$
$163$	2.91082	+	1.20570i	0.227993	+	0.0944377i	−0.265763	+	0.964038i	$0.585624\pi$
$164$	0.508087	−	1.22663i	0.0396749	−	0.0957838i
$165$	8.36077	−	3.46314i	0.650885	−	0.269605i
$166$			3.38507i			0.262732i
$167$	−9.31766	−	22.4948i	−0.721023	−	1.74070i	−0.670418	−	0.741984i	$-0.733885\pi$
$167$	−9.31766	−	22.4948i	−0.721023	−	1.74070i	−0.0506044	−	0.998719i	$-0.516115\pi$
$168$	0.384630	+	0.384630i	0.0296748	+	0.0296748i
$169$	−29.6682			−2.28217
$170$		0			0
$171$	4.63816			0.354689
$172$	−0.644954	−	0.644954i	−0.0491773	−	0.0491773i
$173$	5.76674	+	13.9222i	0.438437	+	1.05848i	0.976489	+	0.215569i	$0.0691608\pi$
$173$	5.76674	+	13.9222i	0.438437	+	1.05848i	−0.538051	+	0.842912i	$0.680839\pi$
$174$		−	8.56212i		−	0.649093i
$175$	0.240975	−	0.0998153i	0.0182160	−	0.00754533i
$176$	−4.91862	+	11.8746i	−0.370755	+	0.895082i
$177$	−6.05546	−	2.50825i	−0.455156	−	0.188532i
$178$	−1.26487	+	1.26487i	−0.0948062	+	0.0948062i
$179$	−11.9513	+	11.9513i	−0.893281	+	0.893281i	−0.994831	−	0.101549i	$-0.967620\pi$
$179$	−11.9513	+	11.9513i	−0.893281	+	0.893281i	0.101549	+	0.994831i	$0.467620\pi$
$180$	−0.432294	−	0.179062i	−0.0322213	−	0.0133465i
$181$	−4.08254	+	9.85612i	−0.303453	+	0.732599i	0.696435	+	0.717620i	$0.254768\pi$
$181$	−4.08254	+	9.85612i	−0.303453	+	0.732599i	−0.999888	+	0.0149798i	$0.995232\pi$
$182$	−1.50250	+	0.622357i	−0.111373	+	0.0461321i
$183$		−	2.98545i		−	0.220691i
$184$	3.49884	+	8.44694i	0.257938	+	0.622717i
$185$	15.0343	+	15.0343i	1.10535	+	1.10535i
$186$	−9.98545			−0.732169
$187$		0			0
$188$	1.67230			0.121965
$189$	−0.130668	−	0.130668i	−0.00950470	−	0.00950470i
$190$	6.05518	+	14.6185i	0.439289	+	1.06054i
$191$			1.77837i			0.128678i	0.997928	+	0.0643392i	$0.0204940\pi$
$191$			1.77837i			0.128678i	−0.997928	+	0.0643392i	$0.979506\pi$
$192$	7.94191	−	3.28965i	0.573158	−	0.237410i
$193$	1.93991	−	4.68336i	0.139638	−	0.337115i	−0.838554	−	0.544818i	$-0.816599\pi$
$193$	1.93991	−	4.68336i	0.139638	−	0.337115i	0.978192	+	0.207703i	$0.0665987\pi$
$194$	10.9024	+	4.51592i	0.782746	+	0.324224i
$195$	11.6954	−	11.6954i	0.837527	−	0.837527i
$196$	−0.910214	+	0.910214i	−0.0650153	+	0.0650153i
$197$	−7.43222	−	3.07853i	−0.529524	−	0.219336i	0.101871	−	0.994798i	$-0.467517\pi$
$197$	−7.43222	−	3.07853i	−0.529524	−	0.219336i	−0.631395	+	0.775462i	$0.717517\pi$
$198$	1.84270	−	4.44867i	0.130955	−	0.316153i
$199$	11.0319	−	4.56957i	0.782033	−	0.323929i	0.0442972	−	0.999018i	$-0.485895\pi$
$199$	11.0319	−	4.56957i	0.782033	−	0.323929i	0.737736	+	0.675090i	$0.235895\pi$
$200$		−	4.15476i		−	0.293786i
$201$	5.17294	+	12.4886i	0.364871	+	0.880876i
$202$	10.5056	+	10.5056i	0.739168	+	0.739168i
$203$	−1.17436			−0.0824242
$204$		0			0
$205$	−18.1925			−1.27062
$206$	5.97452	+	5.97452i	0.416264	+	0.416264i
$207$	−1.18864	−	2.86963i	−0.0826162	−	0.199453i
$208$			23.4911i			1.62882i
$209$	15.3148	−	6.34362i	1.05935	−	0.438797i
$210$	0.241249	−	0.582427i	0.0166478	−	0.0401913i
$211$	−2.35279	−	0.974556i	−0.161972	−	0.0670912i	0.300224	−	0.953869i	$-0.402939\pi$
$211$	−2.35279	−	0.974556i	−0.161972	−	0.0670912i	−0.462197	+	0.886778i	$0.652939\pi$
$212$	0.999964	−	0.999964i	0.0686778	−	0.0686778i
$213$	2.55323	−	2.55323i	0.174945	−	0.174945i
$214$	4.42427	+	1.83259i	0.302437	+	0.125274i
$215$	−4.78275	+	11.5466i	−0.326181	+	0.787471i
$216$	−2.71950	+	1.12645i	−0.185038	+	0.0766454i
$217$			1.36959i			0.0929735i
$218$	1.85419	+	4.47642i	0.125582	+	0.303181i
$219$	5.94781	+	5.94781i	0.401916	+	0.401916i
$220$	−1.67230			−0.112747
$221$		0			0
$222$	11.3131			0.759289
$223$	−3.14353	−	3.14353i	−0.210506	−	0.210506i	0.593976	−	0.804483i	$-0.297557\pi$
$223$	−3.14353	−	3.14353i	−0.210506	−	0.210506i	−0.804483	+	0.593976i	$0.797557\pi$
$224$	−0.0736793	−	0.177878i	−0.00492291	−	0.0118849i
$225$			1.41147i			0.0940983i
$226$	−5.86165	+	2.42798i	−0.389911	+	0.161507i
$227$	−2.87787	+	6.94779i	−0.191011	+	0.461141i	−0.990151	−	0.140004i	$-0.955288\pi$
$227$	−2.87787	+	6.94779i	−0.191011	+	0.461141i	0.799140	+	0.601145i	$0.205288\pi$
$228$	−0.791854	−	0.327997i	−0.0524418	−	0.0217221i
$229$	9.71382	−	9.71382i	0.641907	−	0.641907i	−0.309117	−	0.951024i	$-0.600033\pi$
$229$	9.71382	−	9.71382i	0.641907	−	0.641907i	0.951024	+	0.309117i	$0.100033\pi$
$230$	7.49269	−	7.49269i	0.494053	−	0.494053i
$231$	−0.610171	−	0.252741i	−0.0401463	−	0.0166291i
$232$	−7.15865	+	17.2825i	−0.469988	+	1.13465i
$233$	18.9629	−	7.85469i	1.24230	−	0.514578i	0.337867	−	0.941194i	$-0.390294\pi$
$233$	18.9629	−	7.85469i	1.24230	−	0.514578i	0.904433	+	0.426616i	$0.140294\pi$
$234$		−	8.80066i		−	0.575317i
$235$	−8.76899	−	21.1702i	−0.572026	−	1.38099i
$236$	0.856448	+	0.856448i	0.0557500	+	0.0557500i
$237$	7.82295			0.508155
$238$		0			0
$239$	25.9145			1.67627			0.838134	−	0.545465i	$-0.183647\pi$
$239$	25.9145			1.67627			0.838134	+	0.545465i	$0.183647\pi$
$240$	−6.43896	−	6.43896i	−0.415633	−	0.415633i
$241$	−4.35391	−	10.5113i	−0.280460	−	0.677091i	0.719386	−	0.694610i	$-0.244423\pi$
$241$	−4.35391	−	10.5113i	−0.280460	−	0.677091i	−0.999847	+	0.0175193i	$0.994423\pi$
$242$		−	2.38919i		−	0.153583i
$243$	0.923880	−	0.382683i	0.0592669	−	0.0245492i
$244$	−0.211122	+	0.509694i	−0.0135157	+	0.0326298i
$245$	16.2955	+	6.74983i	1.04108	+	0.431231i
$246$	−6.84483	+	6.84483i	−0.436410	+	0.436410i
$247$	21.4231	−	21.4231i	1.36312	−	1.36312i
$248$	20.1555	+	8.34868i	1.27987	+	0.530141i
$249$	−0.961488	+	2.32124i	−0.0609318	+	0.147102i
$250$	11.3103	−	4.68487i	0.715325	−	0.296297i
$251$			0.859785i			0.0542691i	0.999632	+	0.0271346i	$0.00863826\pi$
$251$			0.859785i			0.0542691i	−0.999632	+	0.0271346i	$0.991362\pi$
$252$	0.0130680	+	0.0315489i	0.000823205	+	0.00198739i
$253$	−7.84960	−	7.84960i	−0.493500	−	0.493500i
$254$	−10.4638			−0.656557
$255$		0			0
$256$	−4.39599			−0.274750
$257$	−0.0212341	−	0.0212341i	−0.00132454	−	0.00132454i	0.706444	−	0.707769i	$-0.250298\pi$
$257$	−0.0212341	−	0.0212341i	−0.00132454	−	0.00132454i	−0.707769	+	0.706444i	$0.750298\pi$
$258$	2.54485	+	6.14381i	0.158435	+	0.382497i
$259$		−	1.55169i		−	0.0964173i
$260$	−2.82378	+	1.16965i	−0.175123	+	0.0725385i
$261$	2.43197	−	5.87129i	0.150535	−	0.363424i
$262$	6.16308	+	2.55283i	0.380757	+	0.157715i
$263$	8.65652	−	8.65652i	0.533784	−	0.533784i	−0.387913	−	0.921696i	$-0.626804\pi$
$263$	8.65652	−	8.65652i	0.533784	−	0.533784i	0.921696	+	0.387913i	$0.126804\pi$
$264$	−7.43893	+	7.43893i	−0.457834	+	0.457834i
$265$	−17.9023	−	7.41538i	−1.09973	−	0.455523i
$266$	0.441909	−	1.06686i	0.0270952	−	0.0654135i
$267$	−1.22663	+	0.508087i	−0.0750686	+	0.0310944i
$268$		−	2.49794i		−	0.152586i
$269$	8.25340	+	19.9255i	0.503219	+	1.21488i	0.947721	+	0.319100i	$0.103380\pi$
$269$	8.25340	+	19.9255i	0.503219	+	1.21488i	−0.444503	+	0.895778i	$0.646620\pi$
$270$	2.41228	+	2.41228i	0.146806	+	0.146806i
$271$	−3.39693			−0.206349			−0.103174	−	0.994663i	$-0.532900\pi$
$271$	−3.39693			−0.206349			−0.103174	+	0.994663i	$0.532900\pi$
$272$		0			0
$273$	−1.20708			−0.0730559
$274$	−11.0402	−	11.0402i	−0.666962	−	0.666962i
$275$	1.93048	+	4.66058i	0.116412	+	0.281044i
$276$			0.573978i			0.0345494i
$277$	−14.7055	+	6.09123i	−0.883570	+	0.365987i	−0.777880	−	0.628413i	$-0.783705\pi$
$277$	−14.7055	+	6.09123i	−0.883570	+	0.365987i	−0.105690	+	0.994399i	$0.533705\pi$
$278$	1.38669	−	3.34778i	0.0831684	−	0.200786i
$279$	−6.84731	−	2.83625i	−0.409938	−	0.169802i
$280$	−0.973916	+	0.973916i	−0.0582026	+	0.0582026i
$281$	11.3247	−	11.3247i	0.675572	−	0.675572i	−0.283423	−	0.958995i	$-0.591470\pi$
$281$	11.3247	−	11.3247i	0.675572	−	0.675572i	0.958995	+	0.283423i	$0.0914700\pi$
$282$	−11.2644	−	4.66588i	−0.670787	−	0.277849i
$283$	−10.2696	+	24.7930i	−0.610464	+	1.47379i	0.252028	+	0.967720i	$0.418902\pi$
$283$	−10.2696	+	24.7930i	−0.610464	+	1.47379i	−0.862492	+	0.506071i	$0.831098\pi$
$284$	−0.616460	+	0.255346i	−0.0365802	+	0.0151520i
$285$			11.7442i			0.695668i
$286$	−12.0367	−	29.0591i	−0.711744	−	1.71830i
$287$	0.938823	+	0.938823i	0.0554170	+	0.0554170i
$288$	1.04189			0.0613939
$289$		0			0
$290$	21.6800			1.27310
$291$	6.19339	+	6.19339i	0.363063	+	0.363063i
$292$	−0.594835	−	1.43606i	−0.0348101	−	0.0840389i
$293$			2.40879i			0.140723i	0.997522	+	0.0703614i	$0.0224152\pi$
$293$			2.40879i			0.140723i	−0.997522	+	0.0703614i	$0.977585\pi$
$294$	8.67067	−	3.59151i	0.505684	−	0.209461i
$295$	6.35112	−	15.3330i	0.369776	−	0.892719i
$296$	−22.8354	−	9.45874i	−1.32728	−	0.549778i
$297$	2.52718	−	2.52718i	0.146642	−	0.146642i
$298$	−15.1753	+	15.1753i	−0.879081	+	0.879081i
$299$	−18.7447	−	7.76430i	−1.08403	−	0.449021i
$300$	0.0998153	−	0.240975i	0.00576284	−	0.0139127i
$301$	0.842673	−	0.349047i	0.0485709	−	0.0201187i
$302$			1.87164i			0.107701i
$303$	4.21998	+	10.1879i	0.242432	+	0.585282i
$304$	−11.7946	−	11.7946i	−0.676465	−	0.676465i
$305$	7.55943			0.432852
$306$		0			0
$307$	−6.41921			−0.366364			−0.183182	−	0.983079i	$-0.558640\pi$
$307$	−6.41921			−0.366364			−0.183182	+	0.983079i	$0.558640\pi$
$308$	0.0862990	+	0.0862990i	0.00491734	+	0.00491734i
$309$	2.39991	+	5.79389i	0.136526	+	0.329603i
$310$		−	25.2841i		−	1.43604i
$311$	0.502543	−	0.208160i	0.0284966	−	0.0118037i	−0.368390	−	0.929671i	$-0.620091\pi$
$311$	0.502543	−	0.208160i	0.0284966	−	0.0118037i	0.396886	+	0.917868i	$0.370091\pi$
$312$	−7.35809	+	17.7640i	−0.416570	+	1.00569i
$313$	15.3535	+	6.35965i	0.867834	+	0.359468i	0.771766	−	0.635906i	$-0.219374\pi$
$313$	15.3535	+	6.35965i	0.867834	+	0.359468i	0.0960674	+	0.995375i	$0.469374\pi$
$314$	−1.69678	+	1.69678i	−0.0957550	+	0.0957550i
$315$	0.330863	−	0.330863i	0.0186420	−	0.0186420i
$316$	−1.33558	−	0.553216i	−0.0751323	−	0.0311208i
$317$	9.97172	−	24.0739i	0.560068	−	1.35212i	−0.349644	−	0.936883i	$-0.613697\pi$
$317$	9.97172	−	24.0739i	0.560068	−	1.35212i	0.909712	−	0.415241i	$-0.136303\pi$
$318$	−9.52562	+	3.94564i	−0.534170	+	0.221261i
$319$		−	22.7128i		−	1.27167i
$320$	8.32968	+	20.1096i	0.465643	+	1.12416i
$321$	2.51332	+	2.51332i	0.140280	+	0.140280i
$322$	−0.773318			−0.0430953
$323$		0			0
$324$	−0.184793			−0.0102663
$325$	6.51944	+	6.51944i	0.361633	+	0.361633i
$326$	1.62443	+	3.92173i	0.0899691	+	0.217205i
$327$			3.59627i			0.198874i
$328$	19.5390	−	8.09333i	1.07886	−	0.446879i
$329$	−0.639963	+	1.54501i	−0.0352823	+	0.0851790i
$330$	11.2644	+	4.66588i	0.620087	+	0.256848i
$331$	−15.9175	+	15.9175i	−0.874905	+	0.874905i	−0.993002	−	0.118097i	$-0.962320\pi$
$331$	−15.9175	+	15.9175i	−0.874905	+	0.874905i	0.118097	+	0.993002i	$0.462320\pi$
$332$	0.328302	−	0.328302i	0.0180179	−	0.0180179i
$333$	7.75775	+	3.21336i	0.425122	+	0.176091i
$334$	12.5537	−	30.3072i	0.686905	−	1.65834i
$335$	−31.6222	+	13.0983i	−1.72770	+	0.715639i
$336$			0.664563i			0.0362549i
$337$	−0.190196	−	0.459175i	−0.0103607	−	0.0250128i	0.918615	−	0.395155i	$-0.129309\pi$
$337$	−0.190196	−	0.459175i	−0.0103607	−	0.0250128i	−0.928975	+	0.370142i	$0.879309\pi$
$338$	−28.2644	−	28.2644i	−1.53738	−	1.53738i
$339$	−4.70914			−0.255765
$340$		0			0
$341$	−26.4884			−1.43443
$342$	4.41869	+	4.41869i	0.238935	+	0.238935i
$343$	−0.987624	−	2.38433i	−0.0533267	−	0.128742i
$344$		−	14.5289i		−	0.783346i
$345$	7.26616	−	3.00974i	0.391197	−	0.162039i
$346$	−7.76951	+	18.7573i	−0.417692	+	1.00840i
$347$	−12.8094	−	5.30584i	−0.687647	−	0.284833i	0.0113726	−	0.999935i	$-0.496380\pi$
$347$	−12.8094	−	5.30584i	−0.687647	−	0.284833i	−0.699019	+	0.715103i	$0.746380\pi$
$348$	−0.830400	+	0.830400i	−0.0445141	+	0.0445141i
$349$	−19.1257	+	19.1257i	−1.02378	+	1.02378i	−0.0240668	+	0.999710i	$0.507661\pi$
$349$	−19.1257	+	19.1257i	−1.02378	+	1.02378i	−0.999710	+	0.0240668i	$0.992339\pi$
$350$	0.324665	+	0.134481i	0.0173541	+	0.00718830i
$351$	2.49972	−	6.03486i	0.133425	−	0.322117i
$352$	3.44024	−	1.42499i	0.183365	−	0.0759524i
$353$		−	8.96997i		−	0.477423i	−0.971090	−	0.238712i	$-0.923275\pi$
$353$		−	8.96997i		−	0.477423i	0.971090	−	0.238712i	$-0.0767251\pi$
$354$	−3.37936	−	8.15849i	−0.179611	−	0.433619i
$355$	6.46501	+	6.46501i	0.343127	+	0.343127i
$356$	0.245348			0.0130034
$357$		0			0
$358$	−22.7716			−1.20351
$359$	−4.33150	−	4.33150i	−0.228608	−	0.228608i	0.583503	−	0.812111i	$-0.301682\pi$
$359$	−4.33150	−	4.33150i	−0.228608	−	0.228608i	−0.812111	+	0.583503i	$0.801682\pi$
$360$	−2.85228	−	6.88601i	−0.150328	−	0.362925i
$361$			2.51249i			0.132236i
$362$	−13.2791	+	5.50039i	−0.697935	+	0.289094i
$363$	0.678620	−	1.63833i	0.0356183	−	0.0859902i
$364$	0.206080	+	0.0853612i	0.0108015	+	0.00447414i
$365$	−15.0604	+	15.0604i	−0.788297	+	0.788297i
$366$	2.84419	−	2.84419i	0.148668	−	0.148668i
$367$	16.5571	+	6.85817i	0.864274	+	0.357994i	0.770377	−	0.637588i	$-0.220068\pi$
$367$	16.5571	+	6.85817i	0.864274	+	0.357994i	0.0938961	+	0.995582i	$0.470068\pi$
$368$	−4.27467	+	10.3200i	−0.222832	+	0.537965i
$369$	−6.63788	+	2.74950i	−0.345554	+	0.143133i
$370$			28.6459i			1.48923i
$371$	0.541177	+	1.30652i	0.0280965	+	0.0678309i
$372$	0.968443	+	0.968443i	0.0502114	+	0.0502114i
$373$	15.5389			0.804574			0.402287	−	0.915514i	$-0.368215\pi$
$373$	15.5389			0.804574			0.402287	+	0.915514i	$0.368215\pi$
$374$		0			0
$375$	9.08647			0.469223
$376$	18.8360	+	18.8360i	0.971394	+	0.971394i
$377$	−15.8858	−	38.3518i	−0.818162	−	1.97522i
$378$		−	0.248970i		−	0.0128057i
$379$	−35.1154	+	14.5453i	−1.80376	+	0.747141i	−0.818864	+	0.573988i	$0.805396\pi$
$379$	−35.1154	+	14.5453i	−1.80376	+	0.747141i	−0.984895	+	0.173154i	$0.944604\pi$
$380$	0.830517	−	2.00504i	0.0426046	−	0.102857i
$381$	−7.17532	−	2.97212i	−0.367603	−	0.152266i
$382$	−1.69422	+	1.69422i	−0.0866840	+	0.0866840i
$383$	−15.0392	+	15.0392i	−0.768465	+	0.768465i	−0.977836	−	0.209371i	$-0.932858\pi$
$383$	−15.0392	+	15.0392i	−0.768465	+	0.768465i	0.209371	+	0.977836i	$0.432858\pi$
$384$	8.77495	+	3.63470i	0.447795	+	0.185483i
$385$	0.639963	−	1.54501i	0.0326155	−	0.0787409i
$386$	6.30987	−	2.61363i	0.321164	−	0.133030i
$387$			4.93582i			0.250902i
$388$	−0.619394	−	1.49535i	−0.0314450	−	0.0759149i
$389$	9.75920	+	9.75920i	0.494811	+	0.494811i	0.909818	−	0.415007i	$-0.136221\pi$
$389$	9.75920	+	9.75920i	0.494811	+	0.494811i	−0.415007	+	0.909818i	$0.636221\pi$
$390$	22.2841			1.12840
$391$		0			0
$392$	−20.5044			−1.03563
$393$	3.50110	+	3.50110i	0.176607	+	0.176607i
$394$	−4.14769	−	10.0134i	−0.208957	−	0.504468i
$395$			19.8084i			0.996669i
$396$	−0.610171	+	0.252741i	−0.0306623	+	0.0127007i
$397$	10.9302	−	26.3880i	0.548573	−	1.32437i	−0.369966	−	0.929045i	$-0.620631\pi$
$397$	10.9302	−	26.3880i	0.548573	−	1.32437i	0.918540	−	0.395328i	$-0.129369\pi$
$398$	14.8633	+	6.15657i	0.745029	+	0.308601i
$399$	0.606059	−	0.606059i	0.0303409	−	0.0303409i
$400$	3.58930	−	3.58930i	0.179465	−	0.179465i
$401$	−24.7384	−	10.2470i	−1.23538	−	0.511709i	−0.333109	−	0.942888i	$-0.608098\pi$
$401$	−24.7384	−	10.2470i	−1.23538	−	0.511709i	−0.902266	+	0.431179i	$0.858098\pi$
$402$	−6.96948	+	16.8258i	−0.347606	+	0.839196i
$403$	−44.7272	+	18.5266i	−2.22802	+	0.922877i
$404$		−	2.03777i		−	0.101383i
$405$	0.968988	+	2.33935i	0.0481494	+	0.116243i
$406$	−1.11880	−	1.11880i	−0.0555249	−	0.0555249i
$407$	30.0104			1.48756
$408$		0			0
$409$	38.8357			1.92030			0.960152	−	0.279479i	$-0.0901616\pi$
$409$	38.8357			1.92030			0.960152	+	0.279479i	$0.0901616\pi$
$410$	−17.3317	−	17.3317i	−0.855952	−	0.855952i
$411$	−4.43474	−	10.7064i	−0.218749	−	0.528108i
$412$		−	1.15888i		−	0.0570940i
$413$	−1.11900	+	0.463506i	−0.0550625	+	0.0228076i
$414$	1.60145	−	3.86624i	0.0787070	−	0.190016i
$415$	−5.87758	−	2.43457i	−0.288519	−	0.119508i
$416$	4.81237	−	4.81237i	0.235946	−	0.235946i
$417$	1.90179	−	1.90179i	0.0931312	−	0.0931312i
$418$	20.6336	+	8.54673i	1.00922	+	0.418034i
$419$	7.28441	−	17.5861i	0.355867	−	0.859138i	−0.640005	−	0.768370i	$-0.721068\pi$
$419$	7.28441	−	17.5861i	0.355867	−	0.859138i	0.995872	−	0.0907678i	$-0.0289321\pi$
$420$	−0.0798846	+	0.0330893i	−0.00389797	+	0.00161459i
$421$		−	6.41653i		−	0.312722i	−0.987700	−	0.156361i	$-0.950024\pi$
$421$		−	6.41653i		−	0.312722i	0.987700	−	0.156361i	$-0.0499764\pi$
$422$	−1.31302	−	3.16990i	−0.0639166	−	0.154308i
$423$	−6.39905	−	6.39905i	−0.311133	−	0.311133i
$424$	22.5262			1.09397
$425$		0			0
$426$	4.86484			0.235702
$427$	−0.390103	−	0.390103i	−0.0188784	−	0.0188784i
$428$	−0.251355	−	0.606825i	−0.0121497	−	0.0293320i
$429$		−	23.3455i		−	1.12713i
$430$	−15.5567	+	6.44379i	−0.750210	+	0.310747i
$431$	−3.31057	+	7.99243i	−0.159465	+	0.384982i	−0.983337	−	0.181794i	$-0.941810\pi$
$431$	−3.31057	+	7.99243i	−0.159465	+	0.384982i	0.823872	+	0.566776i	$0.191810\pi$
$432$	−3.32252	−	1.37623i	−0.159855	−	0.0662140i
$433$	16.4885	−	16.4885i	0.792385	−	0.792385i	−0.189497	−	0.981881i	$-0.560686\pi$
$433$	16.4885	−	16.4885i	0.792385	−	0.792385i	0.981881	+	0.189497i	$0.0606856\pi$
$434$	−1.30478	+	1.30478i	−0.0626314	+	0.0626314i
$435$	14.8666	+	6.15796i	0.712800	+	0.295251i
$436$	0.254317	−	0.613976i	0.0121796	−	0.0294041i
$437$	13.3098	−	5.51310i	0.636694	−	0.263727i
$438$			11.3327i			0.541500i
$439$	5.05117	+	12.1946i	0.241079	+	0.582017i	0.997391	−	0.0721953i	$-0.0230005\pi$
$439$	5.05117	+	12.1946i	0.241079	+	0.582017i	−0.756311	+	0.654212i	$0.773000\pi$
$440$	−18.8360	−	18.8360i	−0.897972	−	0.897972i
$441$	6.96585			0.331707
$442$		0			0
$443$	−30.5235			−1.45022			−0.725108	−	0.688635i	$-0.758210\pi$
$443$	−30.5235			−1.45022			−0.725108	+	0.688635i	$0.758210\pi$
$444$	−1.09721	−	1.09721i	−0.0520713	−	0.0520713i
$445$	−1.28652	−	3.10594i	−0.0609870	−	0.147236i
$446$		−	5.98957i		−	0.283614i
$447$	−14.7165	+	6.09577i	−0.696066	+	0.288320i
$448$	0.607903	−	1.46761i	0.0287207	−	0.0693379i
$449$	−2.50540	−	1.03777i	−0.118237	−	0.0489755i	0.322781	−	0.946474i	$-0.395382\pi$
$449$	−2.50540	−	1.03777i	−0.118237	−	0.0489755i	−0.441018	+	0.897498i	$0.645382\pi$
$450$	−1.34469	+	1.34469i	−0.0633891	+	0.0633891i
$451$	−18.1573	+	18.1573i	−0.854994	+	0.854994i
$452$	0.803973	+	0.333016i	0.0378157	+	0.0156638i
$453$	−0.531618	+	1.28344i	−0.0249776	+	0.0603013i
$454$	−9.36073	+	3.87734i	−0.439321	+	0.181973i
$455$		−	3.05644i		−	0.143288i
$456$	−5.22466	−	12.6135i	−0.244667	−	0.590679i
$457$	−18.5734	−	18.5734i	−0.868829	−	0.868829i	0.123514	−	0.992343i	$-0.460584\pi$
$457$	−18.5734	−	18.5734i	−0.868829	−	0.868829i	−0.992343	+	0.123514i	$0.960584\pi$
$458$	18.5084			0.864839
$459$		0			0
$460$	−1.45336			−0.0677634
$461$	18.0455	+	18.0455i	0.840464	+	0.840464i	0.988919	−	0.148455i	$-0.0474301\pi$
$461$	18.0455	+	18.0455i	0.840464	+	0.840464i	−0.148455	+	0.988919i	$0.547430\pi$
$462$	−0.340517	−	0.822081i	−0.0158423	−	0.0382467i
$463$		−	2.82564i		−	0.131318i	−0.997842	−	0.0656592i	$-0.979085\pi$
$463$		−	2.82564i		−	0.131318i	0.997842	−	0.0656592i	$-0.0209150\pi$
$464$	−21.1147	+	8.74600i	−0.980226	+	0.406023i
$465$	7.18163	−	17.3380i	0.333040	−	0.804030i
$466$	25.5486	+	10.5826i	1.18352	+	0.490229i
$467$	−23.3339	+	23.3339i	−1.07977	+	1.07977i	−0.0832363	+	0.996530i	$0.526526\pi$
$467$	−23.3339	+	23.3339i	−1.07977	+	1.07977i	−0.996530	+	0.0832363i	$0.973474\pi$
$468$	−0.853535	+	0.853535i	−0.0394547	+	0.0394547i
$469$	2.30780	+	0.955920i	0.106564	+	0.0441403i
$470$	11.8144	−	28.5225i	0.544959	−	1.31565i
$471$	−1.64548	+	0.681582i	−0.0758199	+	0.0314056i
$472$			19.2932i			0.888043i
$473$	6.75073	+	16.2977i	0.310399	+	0.749370i
$474$	7.45279	+	7.45279i	0.342318	+	0.342318i
$475$	−6.54664			−0.300380
$476$		0			0
$477$	−7.65270			−0.350393
$478$	24.6883	+	24.6883i	1.12921	+	1.12921i
$479$	13.3246	+	32.1684i	0.608816	+	1.46981i	0.864289	+	0.502996i	$0.167769\pi$
$479$	13.3246	+	32.1684i	0.608816	+	1.46981i	−0.255473	+	0.966816i	$0.582231\pi$
$480$			2.63816i			0.120415i
$481$	50.6743	−	20.9900i	2.31055	−	0.957061i
$482$	5.86601	−	14.1618i	0.267190	−	0.645053i
$483$	−0.530286	−	0.219652i	−0.0241289	−	0.00999451i
$484$	−0.231716	+	0.231716i	−0.0105325	+	0.0105325i
$485$	−15.6822	+	15.6822i	−0.712092	+	0.712092i
$486$	1.24474	+	0.515588i	0.0564625	+	0.0233875i
$487$	−8.25932	+	19.9398i	−0.374266	+	0.903557i	0.618751	+	0.785587i	$0.287639\pi$
$487$	−8.25932	+	19.9398i	−0.374266	+	0.903557i	−0.993017	+	0.117970i	$0.962361\pi$
$488$	−8.11893	+	3.36297i	−0.367527	+	0.152235i
$489$			3.15064i			0.142477i
$490$	9.09402	+	21.9549i	0.410826	+	0.991822i
$491$	−24.2685	−	24.2685i	−1.09522	−	1.09522i	−0.994961	−	0.100263i	$-0.968032\pi$
$491$	−24.2685	−	24.2685i	−1.09522	−	1.09522i	−0.100263	−	0.994961i	$-0.531968\pi$
$492$	1.32770			0.0598572
$493$		0			0
$494$	40.8188			1.83653
$495$	6.39905	+	6.39905i	0.287616	+	0.287616i
$496$	10.1999	+	24.6247i	0.457989	+	1.10568i
$497$		−	0.667252i		−	0.0299303i
$498$	−3.12739	+	1.29541i	−0.140142	+	0.0580487i
$499$	−6.94425	+	16.7649i	−0.310867	+	0.750500i	0.688806	+	0.724946i	$0.258135\pi$
$499$	−6.94425	+	16.7649i	−0.310867	+	0.750500i	−0.999673	+	0.0255545i	$0.991865\pi$
$500$	−1.55130	−	0.642568i	−0.0693761	−	0.0287365i
$501$	17.2168	−	17.2168i	0.769190	−	0.769190i
$502$	−0.819102	+	0.819102i	−0.0365583	+	0.0365583i
$503$	−23.2955	−	9.64929i	−1.03869	−	0.430241i	−0.202850	−	0.979210i	$-0.565021\pi$
$503$	−23.2955	−	9.64929i	−1.03869	−	0.430241i	−0.835843	+	0.548969i	$0.815021\pi$
$504$	−0.208160	+	0.502543i	−0.00927219	+	0.0223850i
$505$	−25.7968	+	10.6854i	−1.14794	+	0.475493i
$506$		−	14.9564i		−	0.664891i
$507$	−11.3535	−	27.4098i	−0.504228	−	1.21731i
$508$	1.01483	+	1.01483i	0.0450260	+	0.0450260i
$509$	2.82026			0.125006			0.0625029	−	0.998045i	$-0.480092\pi$
$509$	2.82026			0.125006			0.0625029	+	0.998045i	$0.480092\pi$
$510$		0			0
$511$	1.55438			0.0687616
$512$	−17.6201	−	17.6201i	−0.778706	−	0.778706i
$513$	1.77495	+	4.28510i	0.0783658	+	0.189192i
$514$		−	0.0404586i		−	0.00178455i
$515$	−14.6706	+	6.07678i	−0.646466	+	0.267775i
$516$	0.349047	−	0.842673i	0.0153659	−	0.0370966i
$517$	−29.8812	−	12.3772i	−1.31417	−	0.544349i
$518$	1.47827	−	1.47827i	0.0649513	−	0.0649513i
$519$	−10.6556	+	10.6556i	−0.467727	+	0.467727i
$520$	−44.9800	−	18.6313i	−1.97250	−	0.817038i
$521$	−0.402705	+	0.972215i	−0.0176428	+	0.0425935i	−0.932455	−	0.361285i	$-0.882338\pi$
$521$	−0.402705	+	0.972215i	−0.0176428	+	0.0425935i	0.914813	+	0.403879i	$0.132338\pi$
$522$	7.91037	−	3.27658i	0.346227	−	0.143412i
$523$		−	15.0915i		−	0.659906i	−0.943997	−	0.329953i	$-0.892967\pi$
$523$		−	15.0915i		−	0.659906i	0.943997	−	0.329953i	$-0.107033\pi$
$524$	−0.350142	−	0.845316i	−0.0152960	−	0.0369278i
$525$	0.184435	+	0.184435i	0.00804938	+	0.00804938i
$526$	16.4938			0.719165
$527$		0			0
$528$	−12.8530			−0.559354
$529$	9.44154	+	9.44154i	0.410502	+	0.410502i
$530$	−9.99072	−	24.1197i	−0.433969	−	1.04769i
$531$		−	6.55438i		−	0.284436i
$532$	−0.146329	+	0.0606113i	−0.00634415	+	0.00262783i
$533$	−17.9600	+	43.3592i	−0.777933	+	1.87810i
$534$	−1.65264	−	0.684544i	−0.0715165	−	0.0296231i
$535$	−6.36396	+	6.36396i	−0.275138	+	0.275138i
$536$	28.1356	−	28.1356i	1.21527	−	1.21527i
$537$	−15.6151	−	6.46799i	−0.673842	−	0.279114i
$538$	−11.1198	+	26.8455i	−0.479408	+	1.15739i
$539$	23.0007	−	9.52721i	0.990711	−	0.410366i
$540$		−	0.467911i		−	0.0201357i
$541$	7.39276	+	17.8477i	0.317839	+	0.767332i	0.999368	+	0.0355409i	$0.0113154\pi$
$541$	7.39276	+	17.8477i	0.317839	+	0.767332i	−0.681529	+	0.731791i	$0.738685\pi$
$542$	−3.23619	−	3.23619i	−0.139006	−	0.139006i
$543$	−10.6682			−0.457816
$544$		0			0
$545$	−9.10607			−0.390061
$546$	−1.14997	−	1.14997i	−0.0492140	−	0.0492140i
$547$	6.40683	+	15.4675i	0.273936	+	0.661341i	0.999645	−	0.0266618i	$-0.00848772\pi$
$547$	6.40683	+	15.4675i	0.273936	+	0.661341i	−0.725708	+	0.688003i	$0.758488\pi$
$548$			2.14147i			0.0914792i
$549$	2.75820	−	1.14248i	0.117717	−	0.0487600i
$550$	−2.60092	+	6.27918i	−0.110904	+	0.267745i
$551$	27.2320	+	11.2798i	1.16012	+	0.480537i
$552$	−6.46501	+	6.46501i	−0.275169	+	0.275169i
$553$	1.02221	−	1.02221i	0.0434688	−	0.0434688i
$554$	−19.8127	−	8.20669i	−0.841761	−	0.348669i
$555$	−8.13652	+	19.6433i	−0.345376	+	0.833812i
$556$	−0.459175	+	0.190196i	−0.0194733	+	0.00806612i
$557$			19.8084i			0.839309i	0.907684	+	0.419654i	$0.137849\pi$
$557$			19.8084i			0.839309i	−0.907684	+	0.419654i	$0.862151\pi$
$558$	−3.82127	−	9.22535i	−0.161767	−	0.390540i
$559$	22.7980	+	22.7980i	0.964252	+	0.964252i
$560$	−1.68273			−0.0711085
$561$		0			0
$562$	21.5776			0.910196
$563$	−25.0330	−	25.0330i	−1.05501	−	1.05501i	−0.998396	−	0.0566184i	$-0.981968\pi$
$563$	−25.0330	−	25.0330i	−1.05501	−	1.05501i	−0.0566184	−	0.998396i	$-0.518032\pi$
$564$	0.639963	+	1.54501i	0.0269473	+	0.0650565i
$565$		−	11.9240i		−	0.501645i
$566$	−33.4035	+	13.8362i	−1.40405	+	0.581578i
$567$	0.0707170	−	0.170726i	0.00296984	−	0.00716982i
$568$	−9.81960	−	4.06741i	−0.412021	−	0.170665i
$569$	12.7322	−	12.7322i	0.533760	−	0.533760i	−0.387929	−	0.921689i	$-0.626810\pi$
$569$	12.7322	−	12.7322i	0.533760	−	0.533760i	0.921689	+	0.387929i	$0.126810\pi$
$570$	−11.1885	+	11.1885i	−0.468635	+	0.468635i
$571$	12.8347	+	5.31631i	0.537115	+	0.222481i	0.634716	−	0.772745i	$-0.281117\pi$
$571$	12.8347	+	5.31631i	0.537115	+	0.222481i	−0.0976010	+	0.995226i	$0.531117\pi$
$572$	−1.65093	+	3.98569i	−0.0690288	+	0.166650i
$573$	−1.64300	+	0.680553i	−0.0686373	+	0.0284305i
$574$			1.78880i			0.0746631i
$575$	1.67774	+	4.05041i	0.0699664	+	0.168914i
$576$	6.07848	+	6.07848i	0.253270	+	0.253270i
$577$	4.15570			0.173004			0.0865020	−	0.996252i	$-0.472431\pi$
$577$	4.15570			0.173004			0.0865020	+	0.996252i	$0.472431\pi$
$578$		0			0
$579$	5.06923			0.210670
$580$	−2.10265	−	2.10265i	−0.0873077	−	0.0873077i
$581$	0.177676	+	0.428947i	0.00737123	+	0.0177957i
$582$			11.8007i			0.489153i
$583$	−25.2687	+	10.4666i	−1.04652	+	0.433483i
$584$	9.47513	−	22.8750i	0.392084	−	0.946574i
$585$	15.2808	+	6.32952i	0.631784	+	0.261693i
$586$	−2.29481	+	2.29481i	−0.0947976	+	0.0947976i
$587$	18.3382	−	18.3382i	0.756897	−	0.756897i	−0.218860	−	0.975756i	$-0.570234\pi$
$587$	18.3382	−	18.3382i	0.756897	−	0.756897i	0.975756	+	0.218860i	$0.0702337\pi$
$588$	−1.18925	−	0.492604i	−0.0490439	−	0.0203147i
$589$	13.1550	−	31.7589i	0.542041	−	1.30860i
$590$	20.6580	−	8.55684i	0.850478	−	0.352279i
$591$		−	8.04458i		−	0.330910i
$592$	−11.5561	−	27.8989i	−0.474953	−	1.14664i
$593$	−26.6197	−	26.6197i	−1.09314	−	1.09314i	−0.995192	−	0.0979472i	$-0.968772\pi$
$593$	−26.6197	−	26.6197i	−1.09314	−	1.09314i	−0.0979472	−	0.995192i	$-0.531228\pi$
$594$	4.81521			0.197570
$595$		0			0
$596$	2.94356			0.120573
$597$	8.44347	+	8.44347i	0.345568	+	0.345568i
$598$	−10.4608	−	25.2547i	−0.427775	−	1.03274i
$599$		−	9.59720i		−	0.392131i	−0.980591	−	0.196065i	$-0.937183\pi$
$599$		−	9.59720i		−	0.392131i	0.980591	−	0.196065i	$-0.0628165\pi$
$600$	3.83850	−	1.58996i	0.156706	−	0.0649098i
$601$	−10.7773	+	26.0188i	−0.439616	+	1.06133i	0.536465	+	0.843922i	$0.319759\pi$
$601$	−10.7773	+	26.0188i	−0.439616	+	1.06133i	−0.976081	+	0.217405i	$0.930241\pi$
$602$	1.13533	+	0.470269i	0.0462726	+	0.0191667i
$603$	−9.55834	+	9.55834i	−0.389246	+	0.389246i
$604$	0.181522	−	0.181522i	0.00738603	−	0.00738603i
$605$	4.14840	+	1.71833i	0.168657	+	0.0698598i
$606$	−5.68556	+	13.7262i	−0.230960	+	0.557587i
$607$	15.0302	−	6.22571i	0.610057	−	0.252694i	−0.0561959	−	0.998420i	$-0.517897\pi$
$607$	15.0302	−	6.22571i	0.610057	−	0.252694i	0.666253	+	0.745726i	$0.267897\pi$
$608$			4.83244i			0.195981i
$609$	−0.449409	−	1.08497i	−0.0182110	−	0.0439652i
$610$	7.20174	+	7.20174i	0.291590	+	0.291590i
$611$	−59.1130			−2.39146
$612$		0			0
$613$	−4.12330			−0.166539			−0.0832693	−	0.996527i	$-0.526536\pi$
$613$	−4.12330			−0.166539			−0.0832693	+	0.996527i	$0.526536\pi$
$614$	−6.11547	−	6.11547i	−0.246800	−	0.246800i
$615$	−6.96198	−	16.8077i	−0.280734	−	0.677752i
$616$			1.94406i			0.0783284i
$617$	11.7267	−	4.85734i	0.472097	−	0.195549i	−0.133933	−	0.990990i	$-0.542761\pi$
$617$	11.7267	−	4.85734i	0.472097	−	0.195549i	0.606031	+	0.795441i	$0.292761\pi$
$618$	−3.23339	+	7.80608i	−0.130066	+	0.314007i
$619$	23.9506	+	9.92067i	0.962657	+	0.398745i	0.807974	−	0.589219i	$-0.200564\pi$
$619$	23.9506	+	9.92067i	0.962657	+	0.398745i	0.154683	+	0.987964i	$0.450564\pi$
$620$	−2.45218	+	2.45218i	−0.0984821	+	0.0984821i
$621$	2.19632	−	2.19632i	0.0881353	−	0.0881353i
$622$	0.677074	+	0.280453i	0.0271482	+	0.0112452i
$623$	−0.0938907	+	0.226672i	−0.00376165	+	0.00908143i
$624$	−21.7030	+	8.98967i	−0.868814	+	0.359875i
$625$			30.0651i			1.20260i
$626$	8.56833	+	20.6858i	0.342459	+	0.826770i
$627$	11.7215	+	11.7215i	0.468111	+	0.468111i
$628$	0.329126			0.0131336
$629$		0			0
$630$	0.630415			0.0251163
$631$	−21.3130	−	21.3130i	−0.848458	−	0.848458i	0.141483	−	0.989941i	$-0.454813\pi$
$631$	−21.3130	−	21.3130i	−0.848458	−	0.848458i	−0.989941	+	0.141483i	$0.954813\pi$
$632$	−8.81218	−	21.2745i	−0.350530	−	0.846254i
$633$		−	2.54664i		−	0.101220i
$634$	32.4346	−	13.4349i	1.28814	−	0.533567i
$635$	7.52566	−	18.1686i	0.298647	−	0.720997i
$636$	1.30652	+	0.541177i	0.0518067	+	0.0214590i
$637$	32.1745	−	32.1745i	1.27480	−	1.27480i
$638$	21.6380	−	21.6380i	0.856659	−	0.856659i
$639$	3.33596	+	1.38180i	0.131968	+	0.0546631i
$640$	−9.20339	+	22.2190i	−0.363796	+	0.878282i
$641$	0.552500	−	0.228853i	0.0218224	−	0.00903914i	−0.371746	−	0.928335i	$-0.621241\pi$
$641$	0.552500	−	0.228853i	0.0218224	−	0.00903914i	0.393568	+	0.919296i	$0.371241\pi$
$642$			4.78880i			0.188999i
$643$	12.4688	+	30.1024i	0.491723	+	1.18712i	0.953843	+	0.300307i	$0.0970891\pi$
$643$	12.4688	+	30.1024i	0.491723	+	1.18712i	−0.462120	+	0.886818i	$0.652911\pi$
$644$	0.0750006	+	0.0750006i	0.00295544	+	0.00295544i
$645$	−12.4979			−0.492106
$646$		0			0
$647$	−13.8648			−0.545083			−0.272542	−	0.962144i	$-0.587864\pi$
$647$	−13.8648			−0.545083			−0.272542	+	0.962144i	$0.587864\pi$
$648$	−2.08141	−	2.08141i	−0.0817656	−	0.0817656i
$649$	−8.96444	−	21.6421i	−0.351885	−	0.849525i
$650$			12.4219i			0.487227i
$651$	−1.26533	+	0.524118i	−0.0495923	+	0.0205418i
$652$	0.222804	−	0.537897i	0.00872569	−	0.0210657i
$653$	1.38230	+	0.572566i	0.0540934	+	0.0224062i	0.409566	−	0.912280i	$-0.365680\pi$
$653$	1.38230	+	0.572566i	0.0540934	+	0.0224062i	−0.355473	+	0.934687i	$0.615680\pi$
$654$	−3.42610	+	3.42610i	−0.133971	+	0.133971i
$655$	−8.86510	+	8.86510i	−0.346388	+	0.346388i
$656$	23.8716	+	9.88794i	0.932029	+	0.386059i
$657$	−3.21893	+	7.77119i	−0.125582	+	0.303183i
$658$	−2.08158	+	0.862220i	−0.0811485	+	0.0336128i
$659$		−	49.3441i		−	1.92217i	−0.276246	−	0.961087i	$-0.589091\pi$
$659$		−	49.3441i		−	1.92217i	0.276246	−	0.961087i	$-0.410909\pi$
$660$	−0.639963	−	1.54501i	−0.0249105	−	0.0601393i
$661$	32.4616	+	32.4616i	1.26261	+	1.26261i	0.949823	+	0.312787i	$0.101263\pi$
$661$	32.4616	+	32.4616i	1.26261	+	1.26261i	0.312787	+	0.949823i	$0.398737\pi$
$662$	−30.3286			−1.17876
$663$		0			0
$664$	7.39567			0.287008
$665$	1.53459	+	1.53459i	0.0595090	+	0.0595090i
$666$	4.32935	+	10.4520i	0.167759	+	0.405006i
$667$		−	19.7392i		−	0.764304i
$668$	−4.15688	+	1.72183i	−0.160834	+	0.0666198i
$669$	1.70127	−	4.10722i	0.0657747	−	0.158794i
$670$	−42.6045	−	17.6473i	−1.64595	−	0.681777i
$671$	7.54479	−	7.54479i	0.291263	−	0.291263i
$672$	0.136142	−	0.136142i	0.00525178	−	0.00525178i
$673$	32.1478	+	13.3161i	1.23921	+	0.513296i	0.903467	−	0.428658i	$-0.141014\pi$
$673$	32.1478	+	13.3161i	1.23921	+	0.513296i	0.335740	+	0.941955i	$0.391014\pi$
$674$	0.256251	−	0.618644i	0.00987041	−	0.0238293i
$675$	−1.30403	+	0.540148i	−0.0501922	+	0.0207903i
$676$			5.48246i			0.210864i
$677$	5.42931	+	13.1075i	0.208665	+	0.503763i	0.993214	−	0.116305i	$-0.0371050\pi$
$677$	5.42931	+	13.1075i	0.208665	+	0.503763i	−0.784548	+	0.620068i	$0.787105\pi$
$678$	−4.48632	−	4.48632i	−0.172296	−	0.172296i
$679$	1.61856			0.0621145
$680$		0			0
$681$	−7.52023			−0.288176
$682$	−25.2351	−	25.2351i	−0.966301	−	0.966301i
$683$	17.0405	+	41.1393i	0.652036	+	1.57415i	0.809819	+	0.586679i	$0.199565\pi$
$683$	17.0405	+	41.1393i	0.652036	+	1.57415i	−0.157784	+	0.987474i	$0.550435\pi$
$684$		−	0.857097i		−	0.0327719i
$685$	27.1096	−	11.2291i	1.03580	−	0.429044i
$686$	1.33062	−	3.21241i	0.0508034	−	0.122650i
$687$	12.6917	+	5.25708i	0.484219	+	0.200570i
$688$	12.5515	−	12.5515i	0.478522	−	0.478522i
$689$	−35.3470	+	35.3470i	−1.34661	+	1.34661i
$690$	9.78967	+	4.05502i	0.372687	+	0.154372i
$691$	−2.29144	+	5.53202i	−0.0871704	+	0.210448i	−0.961453	−	0.274969i	$-0.911332\pi$
$691$	−2.29144	+	5.53202i	−0.0871704	+	0.210448i	0.874283	+	0.485417i	$0.161332\pi$
$692$	2.57271	−	1.06565i	0.0977998	−	0.0405100i
$693$		−	0.660444i		−	0.0250882i
$694$	−7.14854	−	17.2581i	−0.271355	−	0.655109i
$695$	4.81551	+	4.81551i	0.182663	+	0.182663i
$696$	−18.7065			−0.709066
$697$		0			0
$698$	−36.4415			−1.37933
$699$	14.5136	+	14.5136i	0.548953	+	0.548953i
$700$	−0.0184451	−	0.0445305i	−0.000697160	−	0.00168309i
$701$			15.4739i			0.584441i	0.956351	+	0.292221i	$0.0943941\pi$
$701$			15.4739i			0.584441i	−0.956351	+	0.292221i	$0.905606\pi$
$702$	8.13075	−	3.36787i	0.306875	−	0.127112i
$703$	−14.9041	+	35.9816i	−0.562118	+	1.35707i
$704$	28.3842	+	11.7571i	1.06977	+	0.443114i
$705$	16.2030	−	16.2030i	0.610239	−	0.610239i
$706$	8.54553	−	8.54553i	0.321615	−	0.321615i
$707$	1.88265	+	0.779821i	0.0708045	+	0.0293282i
$708$	−0.463506	+	1.11900i	−0.0174196	+	0.0420547i
$709$	29.5625	−	12.2452i	1.11024	−	0.459878i	0.249222	−	0.968446i	$-0.419825\pi$
$709$	29.5625	−	12.2452i	1.11024	−	0.459878i	0.861022	+	0.508568i	$0.169825\pi$
$710$			12.3182i			0.462294i
$711$	2.99371	+	7.22746i	0.112273	+	0.271051i
$712$	2.76348	+	2.76348i	0.103566	+	0.103566i
$713$	−23.0205			−0.862126
$714$		0			0
$715$	59.1130			2.21070
$716$	2.20851	+	2.20851i	0.0825358	+	0.0825358i
$717$	9.91704	+	23.9418i	0.370359	+	0.894125i
$718$		−	8.25309i		−	0.308003i
$719$	21.5600	−	8.93044i	0.804052	−	0.333049i	0.0574740	−	0.998347i	$-0.481695\pi$
$719$	21.5600	−	8.93044i	0.804052	−	0.333049i	0.746578	+	0.665298i	$0.231695\pi$
$720$	3.48474	−	8.41291i	0.129869	−	0.313531i
$721$	1.07067	+	0.443485i	0.0398737	+	0.0165162i
$722$	−2.39360	+	2.39360i	−0.0890807	+	0.0890807i
$723$	8.04498	−	8.04498i	0.299196	−	0.299196i
$724$	1.82134	+	0.754422i	0.0676895	+	0.0280379i
$725$	−3.43266	+	8.28717i	−0.127486	+	0.307778i
$726$	2.20732	−	0.914302i	0.0819213	−	0.0339329i
$727$			4.75372i			0.176306i	0.996107	+	0.0881528i	$0.0280964\pi$
$727$			4.75372i			0.176306i	−0.996107	+	0.0881528i	$0.971904\pi$
$728$	1.35972	+	3.28265i	0.0503946	+	0.121663i
$729$	0.707107	+	0.707107i	0.0261891	+	0.0261891i
$730$	−28.6955			−1.06207
$731$		0			0
$732$	−0.551689			−0.0203910
$733$	0.694919	+	0.694919i	0.0256674	+	0.0256674i	0.719824	−	0.694157i	$-0.244222\pi$
$733$	0.694919	+	0.694919i	0.0256674	+	0.0256674i	−0.694157	+	0.719824i	$0.744222\pi$
$734$	9.23999	+	22.3073i	0.341054	+	0.823378i
$735$			17.6382i			0.650593i
$736$	2.98984	−	1.23843i	0.110207	−	0.0456492i
$737$	−18.4880	+	44.6339i	−0.681013	+	1.64411i
$738$	−8.94320	−	3.70439i	−0.329204	−	0.136361i
$739$	−7.04021	+	7.04021i	−0.258978	+	0.258978i	−0.824638	−	0.565660i	$-0.808621\pi$
$739$	−7.04021	+	7.04021i	−0.258978	+	0.258978i	0.565660	+	0.824638i	$0.308621\pi$
$740$	2.77823	−	2.77823i	0.102130	−	0.102130i
$741$	27.9906	+	11.5941i	1.02826	+	0.425920i
$742$	−0.729125	+	1.76026i	−0.0267670	+	0.0646213i
$743$	−42.9846	+	17.8048i	−1.57695	+	0.653195i	−0.987927	−	0.154919i	$-0.950488\pi$
$743$	−42.9846	+	17.8048i	−1.57695	+	0.653195i	−0.589026	+	0.808114i	$0.700488\pi$
$744$			21.8161i			0.799819i
$745$	−15.4350	−	37.2635i	−0.565496	−	1.36523i
$746$	14.8036	+	14.8036i	0.541999	+	0.541999i
$747$	−2.51249			−0.0919271
$748$		0			0
$749$	0.656822			0.0239998
$750$	8.65652	+	8.65652i	0.316091	+	0.316091i
$751$	5.09563	+	12.3019i	0.185942	+	0.448904i	0.989171	−	0.146766i	$-0.0468866\pi$
$751$	5.09563	+	12.3019i	0.185942	+	0.448904i	−0.803229	+	0.595670i	$0.796887\pi$
$752$			32.5449i			1.18679i
$753$	−0.794338	+	0.329025i	−0.0289473	+	0.0119904i
$754$	21.4029	−	51.6712i	0.779448	−	1.88175i
$755$	−3.24978	−	1.34610i	−0.118272	−	0.0489898i
$756$	−0.0241465	+	0.0241465i	−0.000878199	+	0.000878199i
$757$	31.8816	−	31.8816i	1.15876	−	1.15876i	0.174013	−	0.984743i	$-0.444326\pi$
$757$	31.8816	−	31.8816i	1.15876	−	1.15876i	0.984743	−	0.174013i	$-0.0556736\pi$
$758$	−47.3109	−	19.5968i	−1.71841	−	0.711788i
$759$	4.24817	−	10.2560i	0.154199	−	0.372269i
$760$	31.9384	−	13.2293i	1.15853	−	0.479878i
$761$		−	24.0036i		−	0.870131i	−0.900399	−	0.435065i	$-0.856725\pi$
$761$		−	24.0036i		−	0.870131i	0.900399	−	0.435065i	$-0.143275\pi$
$762$	−4.00432	−	9.66728i	−0.145061	−	0.350209i
$763$	0.469917	+	0.469917i	0.0170121	+	0.0170121i
$764$	0.328630			0.0118894
$765$		0			0
$766$	−28.6551			−1.03535
$767$	−30.2739	−	30.2739i	−1.09313	−	1.09313i
$768$	−1.68227	−	4.06137i	−0.0607038	−	0.146552i
$769$		−	30.5773i		−	1.10264i	−0.834292	−	0.551322i	$-0.814123\pi$
$769$		−	30.5773i		−	1.10264i	0.834292	−	0.551322i	$-0.185877\pi$
$770$	2.08158	−	0.862220i	0.0750150	−	0.0310722i
$771$	0.0114918	−	0.0277436i	0.000413867	−	0.000999163i
$772$	−0.865450	−	0.358481i	−0.0311482	−	0.0129020i
$773$	−32.0564	+	32.0564i	−1.15299	+	1.15299i	−0.167039	+	0.985950i	$0.553421\pi$
$773$	−32.0564	+	32.0564i	−1.15299	+	1.15299i	−0.985950	+	0.167039i	$0.946579\pi$
$774$	−4.70227	+	4.70227i	−0.169020	+	0.169020i
$775$	9.66480	+	4.00329i	0.347170	+	0.143802i
$776$	9.86634	−	23.8195i	0.354181	−	0.855069i
$777$	1.43357	−	0.593806i	0.0514292	−	0.0213027i
$778$			18.5948i			0.666657i
$779$	−12.7526	−	30.7875i	−0.456910	−	1.10308i
$780$	−2.16123	−	2.16123i	−0.0773844	−	0.0773844i
$781$	12.9050			0.461776
$782$		0			0
$783$	6.35504			0.227110
$784$	−17.7138	−	17.7138i	−0.632635	−	0.632635i
$785$	−1.72583	−	4.16651i	−0.0615974	−	0.148709i
$786$			6.67087i			0.237942i
$787$	−17.3174	+	7.17310i	−0.617299	+	0.255694i	−0.669346	−	0.742951i	$-0.733425\pi$
$787$	−17.3174	+	7.17310i	−0.617299	+	0.255694i	0.0520469	+	0.998645i	$0.483425\pi$
$788$	−0.568889	+	1.37342i	−0.0202658	+	0.0489260i
$789$	11.3103	+	4.68487i	0.402657	+	0.166786i
$790$	−18.8711	+	18.8711i	−0.671404	+	0.671404i
$791$	−0.615334	+	0.615334i	−0.0218788	+	0.0218788i
$792$	−9.71942	−	4.02592i	−0.345365	−	0.143055i
$793$	7.46280	−	18.0168i	0.265012	−	0.639795i
$794$	35.5524	−	14.7263i	1.26171	−	0.522616i
$795$		−	19.3773i		−	0.687243i
$796$	−0.844423	−	2.03862i	−0.0299298	−	0.0722569i
$797$	31.5144	+	31.5144i	1.11630	+	1.11630i	0.992280	+	0.124018i	$0.0395779\pi$
$797$	31.5144	+	31.5144i	1.11630	+	1.11630i	0.124018	+	0.992280i	$0.460422\pi$
$798$	1.15476			0.0408782
$799$		0			0
$800$	−1.47060			−0.0519935
$801$	−0.938823	−	0.938823i	−0.0331717	−	0.0331717i
$802$	−13.8057	−	33.3299i	−0.487496	−	1.17692i
$803$			30.0624i			1.06088i
$804$	2.30780	−	0.955920i	0.0813897	−	0.0337127i
$805$	0.556178	−	1.34273i	0.0196027	−	0.0473251i
$806$	−60.2608	−	24.9609i	−2.12260	−	0.879209i
$807$	−15.2503	+	15.2503i	−0.536836	+	0.536836i
$808$	22.9525	−	22.9525i	0.807465	−	0.807465i
$809$	−7.82085	−	3.23950i	−0.274966	−	0.113895i	0.240939	−	0.970540i	$-0.422545\pi$
$809$	−7.82085	−	3.23950i	−0.274966	−	0.113895i	−0.515906	+	0.856645i	$0.672545\pi$
$810$	−1.30551	+	3.15179i	−0.0458711	+	0.110743i
$811$	10.0993	−	4.18326i	0.354634	−	0.146894i	−0.198252	−	0.980151i	$-0.563527\pi$
$811$	10.0993	−	4.18326i	0.354634	−	0.146894i	0.552886	+	0.833257i	$0.313527\pi$
$812$			0.217014i			0.00761568i
$813$	−1.29995	−	3.13835i	−0.0455911	−	0.110067i
$814$	28.5904	+	28.5904i	1.00209	+	1.00209i
$815$	−7.97771			−0.279447
$816$		0			0
$817$	−22.8931			−0.800929
$818$	36.9981	+	36.9981i	1.29361	+	1.29361i
$819$	−0.461930	−	1.11520i	−0.0161411	−	0.0389682i
$820$			3.36184i			0.117401i
$821$	11.6113	−	4.80956i	0.405238	−	0.167855i	−0.170748	−	0.985315i	$-0.554618\pi$
$821$	11.6113	−	4.80956i	0.405238	−	0.167855i	0.575986	+	0.817460i	$0.304618\pi$
$822$	5.97490	−	14.4247i	0.208399	−	0.503119i
$823$	−47.3668	−	19.6200i	−1.65110	−	0.683910i	−0.653757	−	0.756704i	$-0.726808\pi$
$823$	−47.3668	−	19.6200i	−1.65110	−	0.683910i	−0.997347	+	0.0727943i	$0.976808\pi$
$824$	13.0531	−	13.0531i	0.454726	−	0.454726i
$825$	−3.56705	+	3.56705i	−0.124189	+	0.124189i
$826$	−1.50763	−	0.624480i	−0.0524571	−	0.0217284i
$827$	10.9240	−	26.3729i	0.379865	−	0.917075i	−0.612125	−	0.790761i	$-0.709685\pi$
$827$	10.9240	−	26.3729i	0.379865	−	0.917075i	0.991990	−	0.126315i	$-0.0403149\pi$
$828$	−0.530286	+	0.219652i	−0.0184287	+	0.00763343i
$829$		−	4.09865i		−	0.142352i	−0.997464	−	0.0711760i	$-0.977325\pi$
$829$		−	4.09865i		−	0.142352i	0.997464	−	0.0711760i	$-0.0226752\pi$
$830$	−3.28009	−	7.91884i	−0.113854	−	0.274867i
$831$	−11.2551	−	11.2551i	−0.390436	−	0.390436i
$832$	56.1516			1.94671
$833$		0			0
$834$	3.62361			0.125475
$835$	43.5945	+	43.5945i	1.50865	+	1.50865i
$836$	−1.17225	−	2.83007i	−0.0405432	−	0.0978800i
$837$		−	7.41147i		−	0.256178i
$838$	23.6937	−	9.81426i	0.818486	−	0.339028i
$839$	14.3112	−	34.5503i	0.494077	−	1.19281i	−0.458551	−	0.888668i	$-0.651631\pi$
$839$	14.3112	−	34.5503i	0.494077	−	1.19281i	0.952628	−	0.304139i	$-0.0983687\pi$
$840$	−1.27248	−	0.527080i	−0.0439048	−	0.0181860i
$841$	8.05147	−	8.05147i	0.277637	−	0.277637i
$842$	6.11291	−	6.11291i	0.210665	−	0.210665i
$843$	14.7964	+	6.12886i	0.509614	+	0.211089i
$844$	−0.180091	+	0.434777i	−0.00619897	+	0.0149656i
$845$	69.4041	−	28.7481i	2.38757	−	0.988966i
$846$		−	12.1925i		−	0.419188i
$847$	−0.125404	−	0.302752i	−0.00430893	−	0.0104027i
$848$	19.4604	+	19.4604i	0.668273	+	0.668273i
$849$	−26.8357			−0.921000
$850$		0			0
$851$	26.0814			0.894059
$852$	−0.471818	−	0.471818i	−0.0161642	−	0.0161642i
$853$	21.5292	+	51.9761i	0.737147	+	1.77963i	0.617135	+	0.786857i	$0.288293\pi$
$853$	21.5292	+	51.9761i	0.737147	+	1.77963i	0.120011	+	0.992773i	$0.461707\pi$
$854$		−	0.743289i		−	0.0254348i
$855$	−10.8502	+	4.49432i	−0.371071	+	0.153702i
$856$	4.00384	−	9.66612i	0.136848	−	0.330381i
$857$	16.4638	+	6.81952i	0.562392	+	0.232950i	0.645723	−	0.763572i	$-0.276556\pi$
$857$	16.4638	+	6.81952i	0.562392	+	0.232950i	−0.0833314	+	0.996522i	$0.526556\pi$
$858$	22.2409	−	22.2409i	0.759291	−	0.759291i
$859$	3.86034	−	3.86034i	0.131713	−	0.131713i	−0.638177	−	0.769890i	$-0.720311\pi$
$859$	3.86034	−	3.86034i	0.131713	−	0.131713i	0.769890	+	0.638177i	$0.220311\pi$
$860$	2.13372	+	0.883817i	0.0727594	+	0.0301379i
$861$	−0.508087	+	1.22663i	−0.0173156	+	0.0418035i
$862$	−10.7682	+	4.46033i	−0.366766	+	0.151919i
$863$		−	8.23947i		−	0.280475i	−0.990118	−	0.140237i	$-0.955213\pi$
$863$		−	8.23947i		−	0.280475i	0.990118	−	0.140237i	$-0.0447866\pi$
$864$	0.398714	+	0.962580i	0.0135645	+	0.0327476i
$865$	−26.9808	−	26.9808i	−0.917375	−	0.917375i
$866$	31.4165			1.06758
$867$		0			0
$868$	0.253089			0.00859040
$869$	19.7700	+	19.7700i	0.670652	+	0.670652i
$870$	8.29659	+	20.0297i	0.281281	+	0.679072i
$871$			88.2978i			2.99186i
$872$	9.78004	−	4.05102i	0.331194	−	0.137185i
$873$	−3.35184	+	8.09205i	−0.113442	+	0.273874i
$874$	17.9322	+	7.42778i	0.606567	+	0.251248i
$875$	1.18731	−	1.18731i	0.0401384	−	0.0401384i
$876$	1.09911	−	1.09911i	0.0371355	−	0.0371355i
$877$	7.52991	+	3.11899i	0.254267	+	0.105321i	0.506176	−	0.862430i	$-0.331058\pi$
$877$	7.52991	+	3.11899i	0.254267	+	0.105321i	−0.251909	+	0.967751i	$0.581058\pi$
$878$	−6.80542	+	16.4297i	−0.229672	+	0.554477i
$879$	−2.22543	+	0.921802i	−0.0750618	+	0.0310916i
$880$		−	32.5449i		−	1.09709i
$881$	7.21563	+	17.4201i	0.243101	+	0.586897i	0.997588	−	0.0694181i	$-0.0221143\pi$
$881$	7.21563	+	17.4201i	0.243101	+	0.586897i	−0.754487	+	0.656315i	$0.772114\pi$
$882$	6.63624	+	6.63624i	0.223454	+	0.223454i
$883$	−17.2189			−0.579463			−0.289732	−	0.957108i	$-0.593566\pi$
$883$	−17.2189			−0.579463			−0.289732	+	0.957108i	$0.593566\pi$
$884$		0			0
$885$	16.5963			0.557877
$886$	−29.0792	−	29.0792i	−0.976936	−	0.976936i
$887$	4.28217	+	10.3381i	0.143781	+	0.347118i	0.979321	−	0.202311i	$-0.0648452\pi$
$887$	4.28217	+	10.3381i	0.143781	+	0.347118i	−0.835540	+	0.549429i	$0.814845\pi$
$888$		−	24.7169i		−	0.829444i
$889$	−1.32595	+	0.549225i	−0.0444708	+	0.0184204i
$890$	1.73333	−	4.18462i	0.0581012	−	0.140269i
$891$	3.30193	+	1.36770i	0.110619	+	0.0458197i
$892$	−0.580901	+	0.580901i	−0.0194500	+	0.0194500i
$893$	29.6798	−	29.6798i	0.993197	−	0.993197i
$894$	−19.8275	−	8.21281i	−0.663130	−	0.274677i
$895$	16.3775	−	39.5388i	0.547440	−	1.32164i
$896$	1.62155	−	0.671666i	0.0541720	−	0.0224388i
$897$		−	20.2891i		−	0.677433i
$898$	−1.39819	−	3.37552i	−0.0466581	−	0.112643i
$899$	−33.3049	−	33.3049i	−1.11078	−	1.11078i
$900$	0.260830			0.00869433
$901$		0			0
$902$	−34.5963			−1.15193
$903$	0.644954	+	0.644954i	0.0214627	+	0.0214627i
$904$	5.30462	+	12.8065i	0.176429	+	0.425938i
$905$		−	27.0128i		−	0.897936i
$906$	−1.72917	+	0.716247i	−0.0574480	+	0.0237957i
$907$	15.7205	−	37.9527i	0.521991	−	1.26020i	−0.414674	−	0.909970i	$-0.636104\pi$
$907$	15.7205	−	37.9527i	0.521991	−	1.26020i	0.936665	−	0.350227i	$-0.113896\pi$
$908$	1.28390	+	0.531808i	0.0426077	+	0.0176487i
$909$	−7.79751	+	7.79751i	−0.258627	+	0.258627i
$910$	2.91181	−	2.91181i	0.0965257	−	0.0965257i
$911$	35.4481	+	14.6831i	1.17445	+	0.486472i	0.882661	−	0.470011i	$-0.155750\pi$
$911$	35.4481	+	14.6831i	1.17445	+	0.486472i	0.291788	+	0.956483i	$0.405750\pi$
$912$	6.38318	−	15.4104i	0.211368	−	0.510288i
$913$	−8.29605	+	3.43634i	−0.274559	+	0.113726i
$914$		−	35.3892i		−	1.17057i
$915$	2.89287	+	6.98400i	0.0956353	+	0.230884i
$916$	−1.79504	−	1.79504i	−0.0593098	−	0.0593098i
$917$	0.914964			0.0302148
$918$		0			0
$919$	22.7110			0.749167			0.374584	−	0.927193i	$-0.377786\pi$
$919$	22.7110			0.749167			0.374584	+	0.927193i	$0.377786\pi$
$920$	−16.3700	−	16.3700i	−0.539702	−	0.539702i
$921$	−2.45653	−	5.93058i	−0.0809453	−	0.195419i
$922$			34.3833i			1.13235i
$923$	21.7908	−	9.02603i	0.717252	−	0.297096i
$924$	−0.0467047	+	0.112755i	−0.00153647	+	0.00370937i
$925$	−10.9499	−	4.53558i	−0.360029	−	0.149129i
$926$	2.69193	−	2.69193i	0.0884624	−	0.0884624i
$927$	−4.43445	+	4.43445i	−0.145646	+	0.145646i
$928$	6.11723	+	2.53384i	0.200808	+	0.0831774i
$929$	8.24451	−	19.9040i	0.270494	−	0.653029i	−0.729011	−	0.684502i	$-0.760020\pi$
$929$	8.24451	−	19.9040i	0.270494	−	0.653029i	0.999505	+	0.0314726i	$0.0100197\pi$
$930$	23.3594	−	9.67579i	0.765986	−	0.317282i
$931$			32.3087i			1.05888i
$932$	−1.45149	−	3.50420i	−0.0475450	−	0.114784i
$933$	0.384630	+	0.384630i	0.0125922	+	0.0125922i
$934$	−44.4597			−1.45476
$935$		0			0
$936$	−19.2276			−0.628474
$937$	26.5501	+	26.5501i	0.867355	+	0.867355i	0.992179	−	0.124824i	$-0.0398365\pi$
$937$	26.5501	+	26.5501i	0.867355	+	0.867355i	−0.124824	+	0.992179i	$0.539837\pi$
$938$	1.28791	+	3.10929i	0.0420517	+	0.101522i
$939$			16.6186i			0.542326i
$940$	−3.91210	+	1.62044i	−0.127599	+	0.0528530i
$941$	14.8762	−	35.9144i	0.484952	−	1.17078i	−0.472278	−	0.881450i	$-0.656568\pi$
$941$	14.8762	−	35.9144i	0.484952	−	1.17078i	0.957230	−	0.289328i	$-0.0934318\pi$
$942$	−2.21695	−	0.918293i	−0.0722323	−	0.0299196i
$943$	−15.7801	+	15.7801i	−0.513871	+	0.513871i
$944$	−16.6674	+	16.6674i	−0.542478	+	0.542478i
$945$	0.432294	+	0.179062i	0.0140625	+	0.00582488i
$946$	−9.09524	+	21.9579i	−0.295712	+	0.713911i
$947$	−43.9132	+	18.1894i	−1.42699	+	0.591077i	−0.956605	−	0.291387i	$-0.905883\pi$
$947$	−43.9132	+	18.1894i	−1.42699	+	0.591077i	−0.470381	+	0.882464i	$0.655883\pi$
$948$		−	1.44562i		−	0.0469516i
$949$	21.0263	+	50.7621i	0.682544	+	1.64781i
$950$	−6.23687	−	6.23687i	−0.202351	−	0.202351i
$951$	26.0574			0.844968
$952$		0			0
$953$	48.6332			1.57538			0.787692	−	0.616069i	$-0.211276\pi$
$953$	48.6332			1.57538			0.787692	+	0.616069i	$0.211276\pi$
$954$	−7.29060	−	7.29060i	−0.236042	−	0.236042i
$955$	−1.72322	−	4.16022i	−0.0557621	−	0.134622i
$956$		−	4.78880i		−	0.154881i
$957$	20.9839	−	8.69180i	0.678312	−	0.280966i
$958$	−17.9522	+	43.3404i	−0.580008	+	1.40026i
$959$	−1.97846	−	0.819506i	−0.0638879	−	0.0264632i
$960$	−15.3912	+	15.3912i	−0.496750	+	0.496750i
$961$	−16.9210	+	16.9210i	−0.545840	+	0.545840i
$962$	68.2733	+	28.2797i	2.20122	+	0.911775i
$963$	−1.36020	+	3.28382i	−0.0438319	+	0.105820i
$964$	−1.94241	+	0.804571i	−0.0625607	+	0.0259135i
$965$			12.8357i			0.413197i
$966$	−0.295936	−	0.714453i	−0.00952159	−	0.0229871i
$967$	0.984864	+	0.984864i	0.0316711	+	0.0316711i	0.722765	−	0.691094i	$-0.242871\pi$
$967$	0.984864	+	0.984864i	0.0316711	+	0.0316711i	−0.691094	+	0.722765i	$0.742871\pi$
$968$	−5.21987			−0.167773
$969$		0			0
$970$	−29.8803			−0.959399
$971$	−9.25543	−	9.25543i	−0.297021	−	0.297021i	0.542825	−	0.839846i	$-0.317355\pi$
$971$	−9.25543	−	9.25543i	−0.297021	−	0.297021i	−0.839846	+	0.542825i	$0.817355\pi$
$972$	−0.0707170	−	0.170726i	−0.00226825	−	0.00547604i
$973$		−	0.497007i		−	0.0159333i
$974$	−26.8648	+	11.1278i	−0.860803	+	0.356556i
$975$	−3.52829	+	8.51805i	−0.112996	+	0.272796i
$976$	−9.91922	−	4.10867i	−0.317506	−	0.131515i
$977$	2.40579	−	2.40579i	0.0769681	−	0.0769681i	−0.667575	−	0.744543i	$-0.732668\pi$
$977$	2.40579	−	2.40579i	0.0769681	−	0.0769681i	0.744543	+	0.667575i	$0.232668\pi$
$978$	−3.00156	+	3.00156i	−0.0959794	+	0.0959794i
$979$	−4.38395	−	1.81589i	−0.140112	−	0.0580362i
$980$	1.24732	−	3.01129i	0.0398441	−	0.0961922i
$981$	−3.32252	+	1.37623i	−0.106080	+	0.0439397i
$982$		−	46.2404i		−	1.47559i
$983$	−5.61098	−	13.5461i	−0.178962	−	0.432054i	0.808787	−	0.588102i	$-0.200125\pi$
$983$	−5.61098	−	13.5461i	−0.178962	−	0.432054i	−0.987749	+	0.156048i	$0.950125\pi$
$984$	14.9545	+	14.9545i	0.476733	+	0.476733i
$985$	20.3696			0.649029
$986$		0			0
$987$	−1.67230			−0.0532300
$988$	−3.95883	−	3.95883i	−0.125947	−	0.125947i
$989$	5.86692	+	14.1640i	0.186557	+	0.450389i
$990$			12.1925i			0.387504i
$991$	43.1150	−	17.8588i	1.36959	−	0.567304i	0.427916	−	0.903819i	$-0.359248\pi$
$991$	43.1150	−	17.8588i	1.36959	−	0.567304i	0.941678	+	0.336514i	$0.109248\pi$
$992$	2.95506	−	7.13414i	0.0938231	−	0.226509i
$993$	−20.7972	−	8.61448i	−0.659979	−	0.273372i
$994$	0.635679	−	0.635679i	0.0201625	−	0.0201625i
$995$	−21.3796	+	21.3796i	−0.677780	+	0.677780i
$996$	0.428947	+	0.177676i	0.0135917	+	0.00562987i
$997$	0.593134	−	1.43195i	0.0187848	−	0.0453504i	−0.914209	−	0.405243i	$-0.867187\pi$
$997$	0.593134	−	1.43195i	0.0187848	−	0.0453504i	0.932994	+	0.359893i	$0.117187\pi$
$998$	−22.5873	+	9.35596i	−0.714988	+	0.296158i
$999$			8.39693i			0.265667i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.h.l.712.4		24
17.2	even	8	inner	867.2.h.l.757.4		24
17.3	odd	16		867.2.d.d.577.4		6
17.4	even	4	inner	867.2.h.l.733.4		24
17.5	odd	16		867.2.a.i.1.2	✓	3
17.6	odd	16		867.2.e.j.829.4		12
17.7	odd	16		867.2.e.j.616.4		12
17.8	even	8	inner	867.2.h.l.688.4		24
17.9	even	8	inner	867.2.h.l.688.3		24
17.10	odd	16		867.2.e.j.616.3		12
17.11	odd	16		867.2.e.j.829.3		12
17.12	odd	16		867.2.a.j.1.2	yes	3
17.13	even	4	inner	867.2.h.l.733.3		24
17.14	odd	16		867.2.d.d.577.3		6
17.15	even	8	inner	867.2.h.l.757.3		24
17.16	even	2	inner	867.2.h.l.712.3		24
51.5	even	16		2601.2.a.y.1.2		3
51.29	even	16		2601.2.a.z.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
867.2.a.i.1.2	✓	3	17.5	odd	16
867.2.a.j.1.2	yes	3	17.12	odd	16
867.2.d.d.577.3		6	17.14	odd	16
867.2.d.d.577.4		6	17.3	odd	16
867.2.e.j.616.3		12	17.10	odd	16
867.2.e.j.616.4		12	17.7	odd	16
867.2.e.j.829.3		12	17.11	odd	16
867.2.e.j.829.4		12	17.6	odd	16
867.2.h.l.688.3		24	17.9	even	8	inner
867.2.h.l.688.4		24	17.8	even	8	inner
867.2.h.l.712.3		24	17.16	even	2	inner
867.2.h.l.712.4		24	1.1	even	1	trivial
867.2.h.l.733.3		24	17.13	even	4	inner
867.2.h.l.733.4		24	17.4	even	4	inner
867.2.h.l.757.3		24	17.15	even	8	inner
867.2.h.l.757.4		24	17.2	even	8	inner
2601.2.a.y.1.2		3	51.5	even	16
2601.2.a.z.1.2		3	51.29	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.952682 + 0.952682i) q^{2} +(0.382683 + 0.923880i) q^{3} -0.184793i q^{4} +(-2.33935 + 0.968988i) q^{5} +(-0.515588 + 1.24474i) q^{6} +(0.170726 + 0.0707170i) q^{7} +(2.08141 - 2.08141i) q^{8} +(-0.707107 + 0.707107i) q^{9} +O(q^{10})\)	\(q+(0.952682 + 0.952682i) q^{2} +(0.382683 + 0.923880i) q^{3} -0.184793i q^{4} +(-2.33935 + 0.968988i) q^{5} +(-0.515588 + 1.24474i) q^{6} +(0.170726 + 0.0707170i) q^{7} +(2.08141 - 2.08141i) q^{8} +(-0.707107 + 0.707107i) q^{9} +(-3.15179 - 1.30551i) q^{10} +(-1.36770 + 3.30193i) q^{11} +(0.170726 - 0.0707170i) q^{12} +6.53209i q^{13} +(0.0952768 + 0.230019i) q^{14} +(-1.79046 - 1.79046i) q^{15} +3.59627 q^{16} -1.34730 q^{18} +(-3.27967 - 3.27967i) q^{19} +(0.179062 + 0.432294i) q^{20} +0.184793i q^{21} +(-4.44867 + 1.84270i) q^{22} +(-1.18864 + 2.86963i) q^{23} +(2.71950 + 1.12645i) q^{24} +(0.998063 - 0.998063i) q^{25} +(-6.22301 + 6.22301i) q^{26} +(-0.923880 - 0.382683i) q^{27} +(0.0130680 - 0.0315489i) q^{28} +(-5.87129 + 2.43197i) q^{29} -3.41147i q^{30} +(2.83625 + 6.84731i) q^{31} +(-0.736727 - 0.736727i) q^{32} -3.57398 q^{33} -0.467911 q^{35} +(0.130668 + 0.130668i) q^{36} +(-3.21336 - 7.75775i) q^{37} -6.24897i q^{38} +(-6.03486 + 2.49972i) q^{39} +(-2.85228 + 6.88601i) q^{40} +(6.63788 + 2.74950i) q^{41} +(-0.176049 + 0.176049i) q^{42} +(3.49015 - 3.49015i) q^{43} +(0.610171 + 0.252741i) q^{44} +(0.968988 - 2.33935i) q^{45} +(-3.86624 + 1.60145i) q^{46} +9.04963i q^{47} +(1.37623 + 3.32252i) q^{48} +(-4.92560 - 4.92560i) q^{49} +1.90167 q^{50} +1.20708 q^{52} +(5.41128 + 5.41128i) q^{53} +(-0.515588 - 1.24474i) q^{54} -9.04963i q^{55} +(0.502543 - 0.208160i) q^{56} +(1.77495 - 4.28510i) q^{57} +(-7.91037 - 3.27658i) q^{58} +(-4.63464 + 4.63464i) q^{59} +(-0.330863 + 0.330863i) q^{60} +(-2.75820 - 1.14248i) q^{61} +(-3.82127 + 9.22535i) q^{62} +(-0.170726 + 0.0707170i) q^{63} -8.59627i q^{64} +(-6.32952 - 15.2808i) q^{65} +(-3.40487 - 3.40487i) q^{66} +13.5175 q^{67} -3.10607 q^{69} +(-0.445771 - 0.445771i) q^{70} +(-1.38180 - 3.33596i) q^{71} +2.94356i q^{72} +(7.77119 - 3.21893i) q^{73} +(4.32935 - 10.4520i) q^{74} +(1.30403 + 0.540148i) q^{75} +(-0.606059 + 0.606059i) q^{76} +(-0.467005 + 0.467005i) q^{77} +(-8.13075 - 3.36787i) q^{78} +(2.99371 - 7.22746i) q^{79} +(-8.41291 + 3.48474i) q^{80} -1.00000i q^{81} +(3.70439 + 8.94320i) q^{82} +(1.77660 + 1.77660i) q^{83} +0.0341483 q^{84} +6.65002 q^{86} +(-4.49369 - 4.49369i) q^{87} +(4.02592 + 9.71942i) q^{88} +1.32770i q^{89} +(3.15179 - 1.30551i) q^{90} +(-0.461930 + 1.11520i) q^{91} +(0.530286 + 0.219652i) q^{92} +(-5.24070 + 5.24070i) q^{93} +(-8.62142 + 8.62142i) q^{94} +(10.8502 + 4.49432i) q^{95} +(0.398714 - 0.962580i) q^{96} +(8.09205 - 3.35184i) q^{97} -9.38507i q^{98} +(-1.36770 - 3.30193i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q - 24 q^{16} - 24 q^{18} - 24 q^{33} - 48 q^{35} - 48 q^{50} - 48 q^{52} + 144 q^{67} + 24 q^{69} + 168 q^{84} + 240 q^{86}+O(q^{100}) \) 24 * q - 24 * q^16 - 24 * q^18 - 24 * q^33 - 48 * q^35 - 48 * q^50 - 48 * q^52 + 144 * q^67 + 24 * q^69 + 168 * q^84 + 240 * q^86

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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