LMFDB - Embedded newform 867.2.h.l.733.4

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			733.4
Character	$\chi$	$=$	867.733
Dual form			867.2.h.l.757.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.952682 - 0.952682i) q^{2} +(0.923880 - 0.382683i) q^{3} -0.184793i q^{4} +(0.968988 + 2.33935i) q^{5} +(-1.24474 - 0.515588i) q^{6} +(-0.0707170 + 0.170726i) q^{7} +(-2.08141 + 2.08141i) q^{8} +(0.707107 - 0.707107i) q^{9} +O(q^{10})$	\(q+(-0.952682 - 0.952682i) q^{2} +(0.923880 - 0.382683i) q^{3} -0.184793i q^{4} +(0.968988 + 2.33935i) q^{5} +(-1.24474 - 0.515588i) q^{6} +(-0.0707170 + 0.170726i) q^{7} +(-2.08141 + 2.08141i) q^{8} +(0.707107 - 0.707107i) q^{9} +(1.30551 - 3.15179i) q^{10} +(-3.30193 - 1.36770i) q^{11} +(-0.0707170 - 0.170726i) q^{12} +6.53209i q^{13} +(0.230019 - 0.0952768i) q^{14} +(1.79046 + 1.79046i) q^{15} +3.59627 q^{16} -1.34730 q^{18} +(3.27967 + 3.27967i) q^{19} +(0.432294 - 0.179062i) q^{20} +0.184793i q^{21} +(1.84270 + 4.44867i) q^{22} +(-2.86963 - 1.18864i) q^{23} +(-1.12645 + 2.71950i) q^{24} +(-0.998063 + 0.998063i) q^{25} +(6.22301 - 6.22301i) q^{26} +(0.382683 - 0.923880i) q^{27} +(0.0315489 + 0.0130680i) q^{28} +(2.43197 + 5.87129i) q^{29} -3.41147i q^{30} +(6.84731 - 2.83625i) q^{31} +(0.736727 + 0.736727i) q^{32} -3.57398 q^{33} -0.467911 q^{35} +(-0.130668 - 0.130668i) q^{36} +(-7.75775 + 3.21336i) q^{37} -6.24897i q^{38} +(2.49972 + 6.03486i) q^{39} +(-6.88601 - 2.85228i) q^{40} +(-2.74950 + 6.63788i) q^{41} +(0.176049 - 0.176049i) q^{42} +(-3.49015 + 3.49015i) q^{43} +(-0.252741 + 0.610171i) q^{44} +(2.33935 + 0.968988i) q^{45} +(1.60145 + 3.86624i) q^{46} +9.04963i q^{47} +(3.32252 - 1.37623i) q^{48} +(4.92560 + 4.92560i) q^{49} +1.90167 q^{50} +1.20708 q^{52} +(-5.41128 - 5.41128i) q^{53} +(-1.24474 + 0.515588i) q^{54} -9.04963i q^{55} +(-0.208160 - 0.502543i) q^{56} +(4.28510 + 1.77495i) q^{57} +(3.27658 - 7.91037i) q^{58} +(4.63464 - 4.63464i) q^{59} +(0.330863 - 0.330863i) q^{60} +(1.14248 - 2.75820i) q^{61} +(-9.22535 - 3.82127i) q^{62} +(0.0707170 + 0.170726i) q^{63} -8.59627i q^{64} +(-15.2808 + 6.32952i) q^{65} +(3.40487 + 3.40487i) q^{66} +13.5175 q^{67} -3.10607 q^{69} +(0.445771 + 0.445771i) q^{70} +(-3.33596 + 1.38180i) q^{71} +2.94356i q^{72} +(-3.21893 - 7.77119i) q^{73} +(10.4520 + 4.32935i) q^{74} +(-0.540148 + 1.30403i) q^{75} +(0.606059 - 0.606059i) q^{76} +(0.467005 - 0.467005i) q^{77} +(3.36787 - 8.13075i) q^{78} +(7.22746 + 2.99371i) q^{79} +(3.48474 + 8.41291i) q^{80} -1.00000i q^{81} +(8.94320 - 3.70439i) q^{82} +(-1.77660 - 1.77660i) q^{83} +0.0341483 q^{84} +6.65002 q^{86} +(4.49369 + 4.49369i) q^{87} +(9.71942 - 4.02592i) q^{88} +1.32770i q^{89} +(-1.30551 - 3.15179i) q^{90} +(-1.11520 - 0.461930i) q^{91} +(-0.219652 + 0.530286i) q^{92} +(5.24070 - 5.24070i) q^{93} +(8.62142 - 8.62142i) q^{94} +(-4.49432 + 10.8502i) q^{95} +(0.962580 + 0.398714i) q^{96} +(-3.35184 - 8.09205i) q^{97} -9.38507i q^{98} +(-3.30193 + 1.36770i) 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 $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$

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	0.284907	−	0.958555i	$-0.408037\pi$
$2$	−0.952682	−	0.952682i	−0.673648	−	0.673648i	−0.958555	+	0.284907i	$0.908037\pi$
$3$	0.923880	−	0.382683i	0.533402	−	0.220942i
$3$	0.923880	−	0.382683i	0.533402	−	0.220942i
$4$		−	0.184793i		−	0.0923963i
$5$	0.968988	+	2.33935i	0.433345	+	1.04619i	0.978202	+	0.207658i	$0.0665840\pi$
$5$	0.968988	+	2.33935i	0.433345	+	1.04619i	−0.544857	+	0.838529i	$0.683416\pi$
$6$	−1.24474	−	0.515588i	−0.508163	−	0.210488i
$7$	−0.0707170	+	0.170726i	−0.0267285	+	0.0645284i	−0.936680	−	0.350186i	$-0.886118\pi$
$7$	−0.0707170	+	0.170726i	−0.0267285	+	0.0645284i	0.909952	+	0.414714i	$0.136118\pi$
$8$	−2.08141	+	2.08141i	−0.735891	+	0.735891i
$9$	0.707107	−	0.707107i	0.235702	−	0.235702i
$10$	1.30551	−	3.15179i	0.412840	−	0.996684i
$11$	−3.30193	−	1.36770i	−0.995568	−	0.412378i	−0.175398	−	0.984498i	$-0.556121\pi$
$11$	−3.30193	−	1.36770i	−0.995568	−	0.412378i	−0.820170	+	0.572120i	$0.806121\pi$
$12$	−0.0707170	−	0.170726i	−0.0204143	−	0.0492844i
$13$			6.53209i			1.81168i	0.423625	+	0.905838i	$0.360758\pi$
$13$			6.53209i			1.81168i	−0.423625	+	0.905838i	$0.639242\pi$
$14$	0.230019	−	0.0952768i	0.0614750	−	0.0254638i
$15$	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	0.974928	−	0.222520i	$-0.0714282\pi$
$19$	3.27967	+	3.27967i	0.752408	+	0.752408i	−0.222520	+	0.974928i	$0.571428\pi$
$20$	0.432294	−	0.179062i	0.0966638	−	0.0400394i
$21$			0.184793i			0.0403250i
$22$	1.84270	+	4.44867i	0.392865	+	0.948460i
$23$	−2.86963	−	1.18864i	−0.598360	−	0.247849i	0.0628829	−	0.998021i	$-0.479971\pi$
$23$	−2.86963	−	1.18864i	−0.598360	−	0.247849i	−0.661242	+	0.750172i	$0.729971\pi$
$24$	−1.12645	+	2.71950i	−0.229936	+	0.555115i
$25$	−0.998063	+	0.998063i	−0.199613	+	0.199613i
$26$	6.22301	−	6.22301i	1.22043	−	1.22043i
$27$	0.382683	−	0.923880i	0.0736475	−	0.177801i
$28$	0.0315489	+	0.0130680i	0.00596218	+	0.00246962i
$29$	2.43197	+	5.87129i	0.451605	+	1.09027i	0.971712	+	0.236170i	$0.0758921\pi$
$29$	2.43197	+	5.87129i	0.451605	+	1.09027i	−0.520107	+	0.854101i	$0.674108\pi$
$30$		−	3.41147i		−	0.622847i
$31$	6.84731	−	2.83625i	1.22981	−	0.509405i	0.329296	−	0.944227i	$-0.393188\pi$
$31$	6.84731	−	2.83625i	1.22981	−	0.509405i	0.900517	+	0.434821i	$0.143188\pi$
$32$	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
$37$	−7.75775	+	3.21336i	−1.27537	+	0.528274i	−0.914591	−	0.404379i	$-0.867488\pi$
$37$	−7.75775	+	3.21336i	−1.27537	+	0.528274i	−0.360775	+	0.932653i	$0.617488\pi$
$38$		−	6.24897i		−	1.01372i
$39$	2.49972	+	6.03486i	0.400276	+	0.966352i
$40$	−6.88601	−	2.85228i	−1.08877	−	0.450985i
$41$	−2.74950	+	6.63788i	−0.429400	+	1.03666i	0.550078	+	0.835113i	$0.314598\pi$
$41$	−2.74950	+	6.63788i	−0.429400	+	1.03666i	−0.979478	+	0.201550i	$0.935402\pi$
$42$	0.176049	−	0.176049i	0.0271649	−	0.0271649i
$43$	−3.49015	+	3.49015i	−0.532243	+	0.532243i	−0.921239	−	0.388996i	$-0.872822\pi$
$43$	−3.49015	+	3.49015i	−0.532243	+	0.532243i	0.388996	+	0.921239i	$0.372822\pi$
$44$	−0.252741	+	0.610171i	−0.0381022	+	0.0919868i
$45$	2.33935	+	0.968988i	0.348729	+	0.144448i
$46$	1.60145	+	3.86624i	0.236121	+	0.570047i
$47$			9.04963i			1.32002i	0.751255	+	0.660012i	$0.229449\pi$
$47$			9.04963i			1.32002i	−0.751255	+	0.660012i	$0.770551\pi$
$48$	3.32252	−	1.37623i	0.479564	−	0.198642i
$49$	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	0.229915	−	0.973211i	$-0.426155\pi$
$53$	−5.41128	−	5.41128i	−0.743296	−	0.743296i	−0.973211	+	0.229915i	$0.926155\pi$
$54$	−1.24474	+	0.515588i	−0.169388	+	0.0701626i
$55$		−	9.04963i		−	1.22025i
$56$	−0.208160	−	0.502543i	−0.0278166	−	0.0671551i
$57$	4.28510	+	1.77495i	0.567575	+	0.235097i
$58$	3.27658	−	7.91037i	0.430236	−	1.03868i
$59$	4.63464	−	4.63464i	0.603379	−	0.603379i	−0.337828	−	0.941208i	$-0.609692\pi$
$59$	4.63464	−	4.63464i	0.603379	−	0.603379i	0.941208	+	0.337828i	$0.109692\pi$
$60$	0.330863	−	0.330863i	0.0427142	−	0.0427142i
$61$	1.14248	−	2.75820i	0.146280	−	0.353151i	−0.833709	−	0.552205i	$-0.813787\pi$
$61$	1.14248	−	2.75820i	0.146280	−	0.353151i	0.979989	+	0.199053i	$0.0637867\pi$
$62$	−9.22535	−	3.82127i	−1.17162	−	0.485301i
$63$	0.0707170	+	0.170726i	0.00890951	+	0.0215095i
$64$		−	8.59627i		−	1.07453i
$65$	−15.2808	+	6.32952i	−1.89535	+	0.785080i
$66$	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
$71$	−3.33596	+	1.38180i	−0.395905	+	0.163989i	−0.571749	−	0.820429i	$-0.693735\pi$
$71$	−3.33596	+	1.38180i	−0.395905	+	0.163989i	0.175843	+	0.984418i	$0.443735\pi$
$72$			2.94356i			0.346902i
$73$	−3.21893	−	7.77119i	−0.376747	−	0.909549i	−0.992571	−	0.121665i	$-0.961177\pi$
$73$	−3.21893	−	7.77119i	−0.376747	−	0.909549i	0.615824	−	0.787884i	$-0.288823\pi$
$74$	10.4520	+	4.32935i	1.21502	+	0.503277i
$75$	−0.540148	+	1.30403i	−0.0623709	+	0.150577i
$76$	0.606059	−	0.606059i	0.0695197	−	0.0695197i
$77$	0.467005	−	0.467005i	0.0532201	−	0.0532201i
$78$	3.36787	−	8.13075i	0.381336	−	0.920626i
$79$	7.22746	+	2.99371i	0.813153	+	0.336819i	0.750211	−	0.661198i	$-0.229952\pi$
$79$	7.22746	+	2.99371i	0.813153	+	0.336819i	0.0629417	+	0.998017i	$0.479952\pi$
$80$	3.48474	+	8.41291i	0.389606	+	0.940592i
$81$		−	1.00000i		−	0.111111i
$82$	8.94320	−	3.70439i	0.987611	−	0.409082i
$83$	−1.77660	−	1.77660i	−0.195007	−	0.195007i	0.602849	−	0.797856i	$-0.294032\pi$
$83$	−1.77660	−	1.77660i	−0.195007	−	0.195007i	−0.797856	+	0.602849i	$0.794032\pi$
$84$	0.0341483			0.00372588
$85$		0			0
$86$	6.65002			0.717090
$87$	4.49369	+	4.49369i	0.481774	+	0.481774i
$88$	9.71942	−	4.02592i	1.03609	−	0.429164i
$89$			1.32770i			0.140735i	0.997521	+	0.0703677i	$0.0224173\pi$
$89$			1.32770i			0.140735i	−0.997521	+	0.0703677i	$0.977583\pi$
$90$	−1.30551	−	3.15179i	−0.137613	−	0.332228i
$91$	−1.11520	−	0.461930i	−0.116904	−	0.0484234i
$92$	−0.219652	+	0.530286i	−0.0229003	+	0.0552862i
$93$	5.24070	−	5.24070i	0.543436	−	0.543436i
$94$	8.62142	−	8.62142i	0.889232	−	0.889232i
$95$	−4.49432	+	10.8502i	−0.461107	+	1.11321i
$96$	0.962580	+	0.398714i	0.0982429	+	0.0406935i
$97$	−3.35184	−	8.09205i	−0.340327	−	0.821623i	−0.997682	−	0.0680420i	$-0.978325\pi$
$97$	−3.35184	−	8.09205i	−0.340327	−	0.821623i	0.657355	−	0.753581i	$-0.271675\pi$
$98$		−	9.38507i		−	0.948035i
$99$	−3.30193	+	1.36770i	−0.331856	+	0.137459i
$100$	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
$105$	−0.432294	+	0.179062i	−0.0421875	+	0.0174746i
$106$			10.3105i			1.00144i
$107$	−1.36020	−	3.28382i	−0.131496	−	0.317459i	0.844394	−	0.535722i	$-0.179961\pi$
$107$	−1.36020	−	3.28382i	−0.131496	−	0.317459i	−0.975890	+	0.218264i	$0.929961\pi$
$108$	−0.170726	−	0.0707170i	−0.0164281	−	0.00680475i
$109$	−1.37623	+	3.32252i	−0.131819	+	0.318239i	−0.975983	−	0.217845i	$-0.930097\pi$
$109$	−1.37623	+	3.32252i	−0.131819	+	0.318239i	0.844164	+	0.536085i	$0.180097\pi$
$110$	−8.62142	+	8.62142i	−0.822020	+	0.822020i
$111$	−5.93752	+	5.93752i	−0.563565	+	0.563565i
$112$	−0.254317	+	0.613976i	−0.0240307	+	0.0580153i
$113$	−4.35068	−	1.80211i	−0.409277	−	0.169528i	0.168539	−	0.985695i	$-0.446095\pi$
$113$	−4.35068	−	1.80211i	−0.409277	−	0.169528i	−0.577816	+	0.816167i	$0.696095\pi$
$114$	−2.39138	−	5.77330i	−0.223973	−	0.540719i
$115$		−	7.86484i		−	0.733400i
$116$	1.08497	−	0.449409i	0.100737	−	0.0417266i
$117$	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
$122$	−3.71611	+	1.53926i	−0.336441	+	0.139358i
$123$			7.18479i			0.647831i
$124$	−0.524118	−	1.26533i	−0.0470671	−	0.113630i
$125$	8.39480	+	3.47724i	0.750854	+	0.311014i
$126$	0.0952768	−	0.230019i	0.00848793	−	0.0204917i
$127$	5.49175	−	5.49175i	0.487314	−	0.487314i	−0.420143	−	0.907458i	$-0.638020\pi$
$127$	5.49175	−	5.49175i	0.487314	−	0.487314i	0.907458	+	0.420143i	$0.138020\pi$
$128$	−6.71606	+	6.71606i	−0.593621	+	0.593621i
$129$	−1.88886	+	4.56011i	−0.166305	+	0.401495i
$130$	20.5878	+	8.52774i	1.80567	+	0.747932i
$131$	−1.89478	−	4.57441i	−0.165548	−	0.399668i	0.819235	−	0.573458i	$-0.194399\pi$
$131$	−1.89478	−	4.57441i	−0.165548	−	0.399668i	−0.984783	+	0.173790i	$0.944399\pi$
$132$			0.660444i			0.0574843i
$133$	−0.791854	+	0.327997i	−0.0686624	+	0.0284409i
$134$	−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
$139$	−2.48481	+	1.02924i	−0.210759	+	0.0872992i	−0.485565	−	0.874200i	$-0.661386\pi$
$139$	−2.48481	+	1.02924i	−0.210759	+	0.0872992i	0.274806	+	0.961500i	$0.411386\pi$
$140$			0.0864665i			0.00730775i
$141$	3.46314	+	8.36077i	0.291649	+	0.704104i
$142$	4.49452	+	1.86169i	0.377172	+	0.156230i
$143$	8.93395	−	21.5685i	0.747095	−	1.80365i
$144$	2.54294	−	2.54294i	0.211912	−	0.211912i
$145$	−11.3784	+	11.3784i	−0.944927	+	0.944927i
$146$	−4.33686	+	10.4701i	−0.358921	+	0.866511i
$147$	6.43561	+	2.66572i	0.530800	+	0.219865i
$148$	0.593806	+	1.43357i	0.0488105	+	0.117839i
$149$			15.9290i			1.30496i	0.757808	+	0.652478i	$0.226270\pi$
$149$			15.9290i			1.30496i	−0.757808	+	0.652478i	$0.773730\pi$
$150$	1.75692	−	0.727739i	0.143452	−	0.0594196i
$151$	−0.982302	−	0.982302i	−0.0799386	−	0.0799386i	0.666007	−	0.745946i	$-0.268002\pi$
$151$	−0.982302	−	0.982302i	−0.0799386	−	0.0799386i	−0.745946	+	0.666007i	$0.768002\pi$
$152$	−13.6527			−1.10738
$153$		0			0
$154$	−0.889814			−0.0717033
$155$	13.2699	+	13.2699i	1.06587	+	1.06587i
$156$	1.11520	−	0.461930i	0.0892873	−	0.0369840i
$157$			1.78106i			0.142144i	0.997471	+	0.0710720i	$0.0226420\pi$
$157$			1.78106i			0.142144i	−0.997471	+	0.0710720i	$0.977358\pi$
$158$	−4.03342	−	9.73753i	−0.320882	−	0.774677i
$159$	−7.07018	−	2.92856i	−0.560701	−	0.232250i
$160$	−1.00958	+	2.43734i	−0.0798142	+	0.192688i
$161$	0.405864	−	0.405864i	0.0319865	−	0.0319865i
$162$	−0.952682	+	0.952682i	−0.0748498	+	0.0748498i
$163$	−1.20570	+	2.91082i	−0.0944377	+	0.227993i	−0.964038	−	0.265763i	$-0.914376\pi$
$163$	−1.20570	+	2.91082i	−0.0944377	+	0.227993i	0.869601	+	0.493755i	$0.164376\pi$
$164$	1.22663	+	0.508087i	0.0957838	+	0.0396749i
$165$	−3.46314	−	8.36077i	−0.269605	−	0.650885i
$166$			3.38507i			0.262732i
$167$	−22.4948	+	9.31766i	−1.74070	+	0.721023i	−0.741984	+	0.670418i	$0.766115\pi$
$167$	−22.4948	+	9.31766i	−1.74070	+	0.721023i	−0.998719	+	0.0506044i	$0.983885\pi$
$168$	−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
$173$	13.9222	−	5.76674i	1.05848	−	0.438437i	0.215569	−	0.976489i	$-0.430839\pi$
$173$	13.9222	−	5.76674i	1.05848	−	0.438437i	0.842912	+	0.538051i	$0.180839\pi$
$174$		−	8.56212i		−	0.649093i
$175$	−0.0998153	−	0.240975i	−0.00754533	−	0.0182160i
$176$	−11.8746	−	4.91862i	−0.895082	−	0.370755i
$177$	2.50825	−	6.05546i	0.188532	−	0.455156i
$178$	1.26487	−	1.26487i	0.0948062	−	0.0948062i
$179$	11.9513	−	11.9513i	0.893281	−	0.893281i	−0.101549	−	0.994831i	$-0.532380\pi$
$179$	11.9513	−	11.9513i	0.893281	−	0.893281i	0.994831	+	0.101549i	$0.0323800\pi$
$180$	0.179062	−	0.432294i	0.0133465	−	0.0322213i
$181$	−9.85612	−	4.08254i	−0.732599	−	0.303453i	−0.0149798	−	0.999888i	$-0.504768\pi$
$181$	−9.85612	−	4.08254i	−0.732599	−	0.303453i	−0.717620	+	0.696435i	$0.754768\pi$
$182$	0.622357	+	1.50250i	0.0461321	+	0.111373i
$183$		−	2.98545i		−	0.220691i
$184$	8.44694	−	3.49884i	0.622717	−	0.257938i
$185$	−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
$190$	14.6185	−	6.05518i	1.06054	−	0.439289i
$191$			1.77837i			0.128678i	0.997928	+	0.0643392i	$0.0204940\pi$
$191$			1.77837i			0.128678i	−0.997928	+	0.0643392i	$0.979506\pi$
$192$	−3.28965	−	7.94191i	−0.237410	−	0.573158i
$193$	4.68336	+	1.93991i	0.337115	+	0.139638i	0.544818	−	0.838554i	$-0.316599\pi$
$193$	4.68336	+	1.93991i	0.337115	+	0.139638i	−0.207703	+	0.978192i	$0.566599\pi$
$194$	−4.51592	+	10.9024i	−0.324224	+	0.782746i
$195$	−11.6954	+	11.6954i	−0.837527	+	0.837527i
$196$	0.910214	−	0.910214i	0.0650153	−	0.0650153i
$197$	3.07853	−	7.43222i	0.219336	−	0.529524i	−0.775462	−	0.631395i	$-0.782483\pi$
$197$	3.07853	−	7.43222i	0.219336	−	0.529524i	0.994798	+	0.101871i	$0.0324828\pi$
$198$	4.44867	+	1.84270i	0.316153	+	0.130955i
$199$	−4.56957	−	11.0319i	−0.323929	−	0.782033i	−0.999018	−	0.0442972i	$-0.985895\pi$
$199$	−4.56957	−	11.0319i	−0.323929	−	0.782033i	0.675090	−	0.737736i	$-0.264105\pi$
$200$		−	4.15476i		−	0.293786i
$201$	12.4886	−	5.17294i	0.880876	−	0.364871i
$202$	−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
$207$	−2.86963	+	1.18864i	−0.199453	+	0.0826162i
$208$			23.4911i			1.62882i
$209$	−6.34362	−	15.3148i	−0.438797	−	1.05935i
$210$	0.582427	+	0.241249i	0.0401913	+	0.0166478i
$211$	0.974556	−	2.35279i	0.0670912	−	0.161972i	−0.886778	−	0.462197i	$-0.847061\pi$
$211$	0.974556	−	2.35279i	0.0670912	−	0.161972i	0.953869	+	0.300224i	$0.0970615\pi$
$212$	−0.999964	+	0.999964i	−0.0686778	+	0.0686778i
$213$	−2.55323	+	2.55323i	−0.174945	+	0.174945i
$214$	−1.83259	+	4.42427i	−0.125274	+	0.302437i
$215$	−11.5466	−	4.78275i	−0.787471	−	0.326181i
$216$	1.12645	+	2.71950i	0.0766454	+	0.185038i
$217$			1.36959i			0.0929735i
$218$	4.47642	−	1.85419i	0.303181	−	0.125582i
$219$	−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	0.804483	−	0.593976i	$-0.202443\pi$
$223$	3.14353	+	3.14353i	0.210506	+	0.210506i	−0.593976	+	0.804483i	$0.702443\pi$
$224$	−0.177878	+	0.0736793i	−0.0118849	+	0.00492291i
$225$			1.41147i			0.0940983i
$226$	2.42798	+	5.86165i	0.161507	+	0.389911i
$227$	−6.94779	−	2.87787i	−0.461141	−	0.191011i	0.140004	−	0.990151i	$-0.455288\pi$
$227$	−6.94779	−	2.87787i	−0.461141	−	0.191011i	−0.601145	+	0.799140i	$0.705288\pi$
$228$	0.327997	−	0.791854i	0.0217221	−	0.0524418i
$229$	−9.71382	+	9.71382i	−0.641907	+	0.641907i	−0.951024	−	0.309117i	$-0.899967\pi$
$229$	−9.71382	+	9.71382i	−0.641907	+	0.641907i	0.309117	+	0.951024i	$0.399967\pi$
$230$	−7.49269	+	7.49269i	−0.494053	+	0.494053i
$231$	0.252741	−	0.610171i	0.0166291	−	0.0401463i
$232$	−17.2825	−	7.15865i	−1.13465	−	0.469988i
$233$	−7.85469	−	18.9629i	−0.514578	−	1.24230i	−0.941194	−	0.337867i	$-0.890294\pi$
$233$	−7.85469	−	18.9629i	−0.514578	−	1.24230i	0.426616	−	0.904433i	$-0.359706\pi$
$234$		−	8.80066i		−	0.575317i
$235$	−21.1702	+	8.76899i	−1.38099	+	0.572026i
$236$	−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
$241$	−10.5113	+	4.35391i	−0.677091	+	0.280460i	−0.694610	−	0.719386i	$-0.744423\pi$
$241$	−10.5113	+	4.35391i	−0.677091	+	0.280460i	0.0175193	+	0.999847i	$0.494423\pi$
$242$		−	2.38919i		−	0.153583i
$243$	−0.382683	−	0.923880i	−0.0245492	−	0.0592669i
$244$	−0.509694	−	0.211122i	−0.0326298	−	0.0135157i
$245$	−6.74983	+	16.2955i	−0.431231	+	1.04108i
$246$	6.84483	−	6.84483i	0.436410	−	0.436410i
$247$	−21.4231	+	21.4231i	−1.36312	+	1.36312i
$248$	−8.34868	+	20.1555i	−0.530141	+	1.27987i
$249$	−2.32124	−	0.961488i	−0.147102	−	0.0609318i
$250$	−4.68487	−	11.3103i	−0.296297	−	0.715325i
$251$			0.859785i			0.0542691i	0.999632	+	0.0271346i	$0.00863826\pi$
$251$			0.859785i			0.0542691i	−0.999632	+	0.0271346i	$0.991362\pi$
$252$	0.0315489	−	0.0130680i	0.00198739	−	0.000823205i
$253$	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	0.707769	−	0.706444i	$-0.249702\pi$
$257$	0.0212341	+	0.0212341i	0.00132454	+	0.00132454i	−0.706444	+	0.707769i	$0.749702\pi$
$258$	6.14381	−	2.54485i	0.382497	−	0.158435i
$259$		−	1.55169i		−	0.0964173i
$260$	1.16965	+	2.82378i	0.0725385	+	0.175123i
$261$	5.87129	+	2.43197i	0.363424	+	0.150535i
$262$	−2.55283	+	6.16308i	−0.157715	+	0.380757i
$263$	−8.65652	+	8.65652i	−0.533784	+	0.533784i	−0.921696	−	0.387913i	$-0.873196\pi$
$263$	−8.65652	+	8.65652i	−0.533784	+	0.533784i	0.387913	+	0.921696i	$0.373196\pi$
$264$	7.43893	−	7.43893i	0.457834	−	0.457834i
$265$	7.41538	−	17.9023i	0.455523	−	1.09973i
$266$	1.06686	+	0.441909i	0.0654135	+	0.0270952i
$267$	0.508087	+	1.22663i	0.0310944	+	0.0750686i
$268$		−	2.49794i		−	0.152586i
$269$	19.9255	−	8.25340i	1.21488	−	0.503219i	0.319100	−	0.947721i	$-0.396620\pi$
$269$	19.9255	−	8.25340i	1.21488	−	0.503219i	0.895778	+	0.444503i	$0.146620\pi$
$270$	−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
$275$	4.66058	−	1.93048i	0.281044	−	0.116412i
$276$			0.573978i			0.0345494i
$277$	6.09123	+	14.7055i	0.365987	+	0.883570i	0.994399	+	0.105690i	$0.0337050\pi$
$277$	6.09123	+	14.7055i	0.365987	+	0.883570i	−0.628413	+	0.777880i	$0.716295\pi$
$278$	3.34778	+	1.38669i	0.200786	+	0.0831684i
$279$	2.83625	−	6.84731i	0.169802	−	0.409938i
$280$	0.973916	−	0.973916i	0.0582026	−	0.0582026i
$281$	−11.3247	+	11.3247i	−0.675572	+	0.675572i	−0.958995	−	0.283423i	$-0.908530\pi$
$281$	−11.3247	+	11.3247i	−0.675572	+	0.675572i	0.283423	+	0.958995i	$0.408530\pi$
$282$	4.66588	−	11.2644i	0.277849	−	0.670787i
$283$	−24.7930	−	10.2696i	−1.47379	−	0.610464i	−0.506071	−	0.862492i	$-0.668902\pi$
$283$	−24.7930	−	10.2696i	−1.47379	−	0.610464i	−0.967720	+	0.252028i	$0.918902\pi$
$284$	0.255346	+	0.616460i	0.0151520	+	0.0365802i
$285$			11.7442i			0.695668i
$286$	−29.0591	+	12.0367i	−1.71830	+	0.711744i
$287$	−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
$292$	−1.43606	+	0.594835i	−0.0840389	+	0.0348101i
$293$			2.40879i			0.140723i	0.997522	+	0.0703614i	$0.0224152\pi$
$293$			2.40879i			0.140723i	−0.997522	+	0.0703614i	$0.977585\pi$
$294$	−3.59151	−	8.67067i	−0.209461	−	0.505684i
$295$	15.3330	+	6.35112i	0.892719	+	0.369776i
$296$	9.45874	−	22.8354i	0.549778	−	1.32728i
$297$	−2.52718	+	2.52718i	−0.146642	+	0.146642i
$298$	15.1753	−	15.1753i	0.879081	−	0.879081i
$299$	7.76430	−	18.7447i	0.449021	−	1.08403i
$300$	0.240975	+	0.0998153i	0.0139127	+	0.00576284i
$301$	−0.349047	−	0.842673i	−0.0201187	−	0.0485709i
$302$			1.87164i			0.107701i
$303$	10.1879	−	4.21998i	0.585282	−	0.242432i
$304$	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
$309$	5.79389	−	2.39991i	0.329603	−	0.136526i
$310$		−	25.2841i		−	1.43604i
$311$	−0.208160	−	0.502543i	−0.0118037	−	0.0284966i	0.917868	−	0.396886i	$-0.129909\pi$
$311$	−0.208160	−	0.502543i	−0.0118037	−	0.0284966i	−0.929671	+	0.368390i	$0.879909\pi$
$312$	−17.7640	−	7.35809i	−1.00569	−	0.416570i
$313$	−6.35965	+	15.3535i	−0.359468	+	0.867834i	0.635906	+	0.771766i	$0.280626\pi$
$313$	−6.35965	+	15.3535i	−0.359468	+	0.867834i	−0.995375	+	0.0960674i	$0.969374\pi$
$314$	1.69678	−	1.69678i	0.0957550	−	0.0957550i
$315$	−0.330863	+	0.330863i	−0.0186420	+	0.0186420i
$316$	0.553216	−	1.33558i	0.0311208	−	0.0751323i
$317$	24.0739	+	9.97172i	1.35212	+	0.560068i	0.936883	−	0.349644i	$-0.113697\pi$
$317$	24.0739	+	9.97172i	1.35212	+	0.560068i	0.415241	+	0.909712i	$0.363697\pi$
$318$	3.94564	+	9.52562i	0.221261	+	0.534170i
$319$		−	22.7128i		−	1.27167i
$320$	20.1096	−	8.32968i	1.12416	−	0.465643i
$321$	−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
$326$	3.92173	−	1.62443i	0.217205	−	0.0899691i
$327$			3.59627i			0.198874i
$328$	−8.09333	−	19.5390i	−0.446879	−	1.07886i
$329$	−1.54501	−	0.639963i	−0.0851790	−	0.0352823i
$330$	−4.66588	+	11.2644i	−0.256848	+	0.620087i
$331$	15.9175	−	15.9175i	0.874905	−	0.874905i	−0.118097	−	0.993002i	$-0.537680\pi$
$331$	15.9175	−	15.9175i	0.874905	−	0.874905i	0.993002	+	0.118097i	$0.0376795\pi$
$332$	−0.328302	+	0.328302i	−0.0180179	+	0.0180179i
$333$	−3.21336	+	7.75775i	−0.176091	+	0.425122i
$334$	30.3072	+	12.5537i	1.65834	+	0.686905i
$335$	13.0983	+	31.6222i	0.715639	+	1.72770i
$336$			0.664563i			0.0362549i
$337$	−0.459175	+	0.190196i	−0.0250128	+	0.0103607i	−0.395155	−	0.918615i	$-0.629309\pi$
$337$	−0.459175	+	0.190196i	−0.0250128	+	0.0103607i	0.370142	+	0.928975i	$0.379309\pi$
$338$	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
$343$	−2.38433	+	0.987624i	−0.128742	+	0.0533267i
$344$		−	14.5289i		−	0.783346i
$345$	−3.00974	−	7.26616i	−0.162039	−	0.391197i
$346$	−18.7573	−	7.76951i	−1.00840	−	0.417692i
$347$	5.30584	−	12.8094i	0.284833	−	0.687647i	−0.715103	−	0.699019i	$-0.753620\pi$
$347$	5.30584	−	12.8094i	0.284833	−	0.687647i	0.999935	+	0.0113726i	$0.00362010\pi$
$348$	0.830400	−	0.830400i	0.0445141	−	0.0445141i
$349$	19.1257	−	19.1257i	1.02378	−	1.02378i	0.0240668	−	0.999710i	$-0.492339\pi$
$349$	19.1257	−	19.1257i	1.02378	−	1.02378i	0.999710	−	0.0240668i	$-0.00766145\pi$
$350$	−0.134481	+	0.324665i	−0.00718830	+	0.0173541i
$351$	6.03486	+	2.49972i	0.322117	+	0.133425i
$352$	−1.42499	−	3.44024i	−0.0759524	−	0.183365i
$353$		−	8.96997i		−	0.477423i	−0.971090	−	0.238712i	$-0.923275\pi$
$353$		−	8.96997i		−	0.477423i	0.971090	−	0.238712i	$-0.0767251\pi$
$354$	−8.15849	+	3.37936i	−0.433619	+	0.179611i
$355$	−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	0.812111	−	0.583503i	$-0.198318\pi$
$359$	4.33150	+	4.33150i	0.228608	+	0.228608i	−0.583503	+	0.812111i	$0.698318\pi$
$360$	−6.88601	+	2.85228i	−0.362925	+	0.150328i
$361$			2.51249i			0.132236i
$362$	5.50039	+	13.2791i	0.289094	+	0.697935i
$363$	1.63833	+	0.678620i	0.0859902	+	0.0356183i
$364$	−0.0853612	+	0.206080i	−0.00447414	+	0.0108015i
$365$	15.0604	−	15.0604i	0.788297	−	0.788297i
$366$	−2.84419	+	2.84419i	−0.148668	+	0.148668i
$367$	−6.85817	+	16.5571i	−0.357994	+	0.864274i	0.637588	+	0.770377i	$0.279932\pi$
$367$	−6.85817	+	16.5571i	−0.357994	+	0.864274i	−0.995582	+	0.0938961i	$0.970068\pi$
$368$	−10.3200	−	4.27467i	−0.537965	−	0.222832i
$369$	2.74950	+	6.63788i	0.143133	+	0.345554i
$370$			28.6459i			1.48923i
$371$	1.30652	−	0.541177i	0.0678309	−	0.0280965i
$372$	−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
$377$	−38.3518	+	15.8858i	−1.97522	+	0.818162i
$378$		−	0.248970i		−	0.0128057i
$379$	14.5453	+	35.1154i	0.747141	+	1.80376i	0.573988	+	0.818864i	$0.305396\pi$
$379$	14.5453	+	35.1154i	0.747141	+	1.80376i	0.173154	+	0.984895i	$0.444604\pi$
$380$	2.00504	+	0.830517i	0.102857	+	0.0426046i
$381$	2.97212	−	7.17532i	0.152266	−	0.367603i
$382$	1.69422	−	1.69422i	0.0866840	−	0.0866840i
$383$	15.0392	−	15.0392i	0.768465	−	0.768465i	−0.209371	−	0.977836i	$-0.567142\pi$
$383$	15.0392	−	15.0392i	0.768465	−	0.768465i	0.977836	+	0.209371i	$0.0671418\pi$
$384$	−3.63470	+	8.77495i	−0.185483	+	0.447795i
$385$	1.54501	+	0.639963i	0.0787409	+	0.0326155i
$386$	−2.61363	−	6.30987i	−0.133030	−	0.321164i
$387$			4.93582i			0.250902i
$388$	−1.49535	+	0.619394i	−0.0759149	+	0.0314450i
$389$	−9.75920	−	9.75920i	−0.494811	−	0.494811i	0.415007	−	0.909818i	$-0.363779\pi$
$389$	−9.75920	−	9.75920i	−0.494811	−	0.494811i	−0.909818	+	0.415007i	$0.863779\pi$
$390$	22.2841			1.12840
$391$		0			0
$392$	−20.5044			−1.03563
$393$	−3.50110	−	3.50110i	−0.176607	−	0.176607i
$394$	−10.0134	+	4.14769i	−0.504468	+	0.208957i
$395$			19.8084i			0.996669i
$396$	0.252741	+	0.610171i	0.0127007	+	0.0306623i
$397$	26.3880	+	10.9302i	1.32437	+	0.548573i	0.929045	−	0.369966i	$-0.120631\pi$
$397$	26.3880	+	10.9302i	1.32437	+	0.548573i	0.395328	+	0.918540i	$0.370631\pi$
$398$	−6.15657	+	14.8633i	−0.308601	+	0.745029i
$399$	−0.606059	+	0.606059i	−0.0303409	+	0.0303409i
$400$	−3.58930	+	3.58930i	−0.179465	+	0.179465i
$401$	10.2470	−	24.7384i	0.511709	−	1.23538i	−0.431179	−	0.902266i	$-0.641902\pi$
$401$	10.2470	−	24.7384i	0.511709	−	1.23538i	0.942888	−	0.333109i	$-0.108098\pi$
$402$	−16.8258	−	6.96948i	−0.839196	−	0.347606i
$403$	18.5266	+	44.7272i	0.922877	+	2.22802i
$404$		−	2.03777i		−	0.101383i
$405$	2.33935	−	0.968988i	0.116243	−	0.0481494i
$406$	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
$411$	−10.7064	+	4.43474i	−0.528108	+	0.218749i
$412$		−	1.15888i		−	0.0570940i
$413$	0.463506	+	1.11900i	0.0228076	+	0.0550625i
$414$	3.86624	+	1.60145i	0.190016	+	0.0787070i
$415$	2.43457	−	5.87758i	0.119508	−	0.288519i
$416$	−4.81237	+	4.81237i	−0.235946	+	0.235946i
$417$	−1.90179	+	1.90179i	−0.0931312	+	0.0931312i
$418$	−8.54673	+	20.6336i	−0.418034	+	1.00922i
$419$	17.5861	+	7.28441i	0.859138	+	0.355867i	0.768370	−	0.640005i	$-0.221068\pi$
$419$	17.5861	+	7.28441i	0.859138	+	0.355867i	0.0907678	+	0.995872i	$0.471068\pi$
$420$	0.0330893	+	0.0798846i	0.00161459	+	0.00389797i
$421$		−	6.41653i		−	0.312722i	−0.987700	−	0.156361i	$-0.950024\pi$
$421$		−	6.41653i		−	0.312722i	0.987700	−	0.156361i	$-0.0499764\pi$
$422$	−3.16990	+	1.31302i	−0.154308	+	0.0639166i
$423$	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
$428$	−0.606825	+	0.251355i	−0.0293320	+	0.0121497i
$429$		−	23.3455i		−	1.12713i
$430$	6.44379	+	15.5567i	0.310747	+	0.750210i
$431$	−7.99243	−	3.31057i	−0.384982	−	0.159465i	0.181794	−	0.983337i	$-0.441810\pi$
$431$	−7.99243	−	3.31057i	−0.384982	−	0.159465i	−0.566776	+	0.823872i	$0.691810\pi$
$432$	1.37623	−	3.32252i	0.0662140	−	0.159855i
$433$	−16.4885	+	16.4885i	−0.792385	+	0.792385i	−0.981881	−	0.189497i	$-0.939314\pi$
$433$	−16.4885	+	16.4885i	−0.792385	+	0.792385i	0.189497	+	0.981881i	$0.439314\pi$
$434$	1.30478	−	1.30478i	0.0626314	−	0.0626314i
$435$	−6.15796	+	14.8666i	−0.295251	+	0.712800i
$436$	0.613976	+	0.254317i	0.0294041	+	0.0121796i
$437$	−5.51310	−	13.3098i	−0.263727	−	0.636694i
$438$			11.3327i			0.541500i
$439$	12.1946	−	5.05117i	0.582017	−	0.241079i	−0.0721953	−	0.997391i	$-0.523000\pi$
$439$	12.1946	−	5.05117i	0.582017	−	0.241079i	0.654212	+	0.756311i	$0.273000\pi$
$440$	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
$445$	−3.10594	+	1.28652i	−0.147236	+	0.0609870i
$446$		−	5.98957i		−	0.283614i
$447$	6.09577	+	14.7165i	0.288320	+	0.696066i
$448$	1.46761	+	0.607903i	0.0693379	+	0.0287207i
$449$	1.03777	−	2.50540i	0.0489755	−	0.118237i	−0.897498	−	0.441018i	$-0.854618\pi$
$449$	1.03777	−	2.50540i	0.0489755	−	0.118237i	0.946474	+	0.322781i	$0.104618\pi$
$450$	1.34469	−	1.34469i	0.0633891	−	0.0633891i
$451$	18.1573	−	18.1573i	0.854994	−	0.854994i
$452$	−0.333016	+	0.803973i	−0.0156638	+	0.0378157i
$453$	−1.28344	−	0.531618i	−0.0603013	−	0.0249776i
$454$	3.87734	+	9.36073i	0.181973	+	0.439321i
$455$		−	3.05644i		−	0.143288i
$456$	−12.6135	+	5.22466i	−0.590679	+	0.244667i
$457$	18.5734	+	18.5734i	0.868829	+	0.868829i	0.992343	−	0.123514i	$-0.0394163\pi$
$457$	18.5734	+	18.5734i	0.868829	+	0.868829i	−0.123514	+	0.992343i	$0.539416\pi$
$458$	18.5084			0.864839
$459$		0			0
$460$	−1.45336			−0.0677634
$461$	−18.0455	−	18.0455i	−0.840464	−	0.840464i	0.148455	−	0.988919i	$-0.452570\pi$
$461$	−18.0455	−	18.0455i	−0.840464	−	0.840464i	−0.988919	+	0.148455i	$0.952570\pi$
$462$	−0.822081	+	0.340517i	−0.0382467	+	0.0158423i
$463$		−	2.82564i		−	0.131318i	−0.997842	−	0.0656592i	$-0.979085\pi$
$463$		−	2.82564i		−	0.131318i	0.997842	−	0.0656592i	$-0.0209150\pi$
$464$	8.74600	+	21.1147i	0.406023	+	0.980226i
$465$	17.3380	+	7.18163i	0.804030	+	0.333040i
$466$	−10.5826	+	25.5486i	−0.490229	+	1.18352i
$467$	23.3339	−	23.3339i	1.07977	−	1.07977i	0.0832363	−	0.996530i	$-0.473474\pi$
$467$	23.3339	−	23.3339i	1.07977	−	1.07977i	0.996530	−	0.0832363i	$-0.0265256\pi$
$468$	0.853535	−	0.853535i	0.0394547	−	0.0394547i
$469$	−0.955920	+	2.30780i	−0.0441403	+	0.106564i
$470$	28.5225	+	11.8144i	1.31565	+	0.544959i
$471$	0.681582	+	1.64548i	0.0314056	+	0.0758199i
$472$			19.2932i			0.888043i
$473$	16.2977	−	6.75073i	0.749370	−	0.310399i
$474$	−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
$479$	32.1684	−	13.3246i	1.46981	−	0.608816i	0.502996	−	0.864289i	$-0.332231\pi$
$479$	32.1684	−	13.3246i	1.46981	−	0.608816i	0.966816	+	0.255473i	$0.0822312\pi$
$480$			2.63816i			0.120415i
$481$	−20.9900	−	50.6743i	−0.957061	−	2.31055i
$482$	14.1618	+	5.86601i	0.645053	+	0.267190i
$483$	0.219652	−	0.530286i	0.00999451	−	0.0241289i
$484$	0.231716	−	0.231716i	0.0105325	−	0.0105325i
$485$	15.6822	−	15.6822i	0.712092	−	0.712092i
$486$	−0.515588	+	1.24474i	−0.0233875	+	0.0564625i
$487$	−19.9398	−	8.25932i	−0.903557	−	0.374266i	−0.117970	−	0.993017i	$-0.537639\pi$
$487$	−19.9398	−	8.25932i	−0.903557	−	0.374266i	−0.785587	+	0.618751i	$0.787639\pi$
$488$	3.36297	+	8.11893i	0.152235	+	0.367527i
$489$			3.15064i			0.142477i
$490$	21.9549	−	9.09402i	0.991822	−	0.410826i
$491$	24.2685	+	24.2685i	1.09522	+	1.09522i	0.994961	+	0.100263i	$0.0319683\pi$
$491$	24.2685	+	24.2685i	1.09522	+	1.09522i	0.100263	+	0.994961i	$0.468032\pi$
$492$	1.32770			0.0598572
$493$		0			0
$494$	40.8188			1.83653
$495$	−6.39905	−	6.39905i	−0.287616	−	0.287616i
$496$	24.6247	−	10.1999i	1.10568	−	0.457989i
$497$		−	0.667252i		−	0.0299303i
$498$	1.29541	+	3.12739i	0.0580487	+	0.140142i
$499$	−16.7649	−	6.94425i	−0.750500	−	0.310867i	−0.0255545	−	0.999673i	$-0.508135\pi$
$499$	−16.7649	−	6.94425i	−0.750500	−	0.310867i	−0.724946	+	0.688806i	$0.758135\pi$
$500$	0.642568	−	1.55130i	0.0287365	−	0.0693761i
$501$	−17.2168	+	17.2168i	−0.769190	+	0.769190i
$502$	0.819102	−	0.819102i	0.0365583	−	0.0365583i
$503$	9.64929	−	23.2955i	0.430241	−	1.03869i	−0.548969	−	0.835843i	$-0.684979\pi$
$503$	9.64929	−	23.2955i	0.430241	−	1.03869i	0.979210	−	0.202850i	$-0.0650205\pi$
$504$	−0.502543	−	0.208160i	−0.0223850	−	0.00927219i
$505$	10.6854	+	25.7968i	0.475493	+	1.14794i
$506$		−	14.9564i		−	0.664891i
$507$	−27.4098	+	11.3535i	−1.21731	+	0.504228i
$508$	−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
$513$	4.28510	−	1.77495i	0.189192	−	0.0783658i
$514$		−	0.0404586i		−	0.00178455i
$515$	6.07678	+	14.6706i	0.267775	+	0.646466i
$516$	0.842673	+	0.349047i	0.0370966	+	0.0153659i
$517$	12.3772	−	29.8812i	0.544349	−	1.31417i
$518$	−1.47827	+	1.47827i	−0.0649513	+	0.0649513i
$519$	10.6556	−	10.6556i	0.467727	−	0.467727i
$520$	18.6313	−	44.9800i	0.817038	−	1.97250i
$521$	−0.972215	−	0.402705i	−0.0425935	−	0.0176428i	0.361285	−	0.932455i	$-0.382338\pi$
$521$	−0.972215	−	0.402705i	−0.0425935	−	0.0176428i	−0.403879	+	0.914813i	$0.632338\pi$
$522$	−3.27658	−	7.91037i	−0.143412	−	0.346227i
$523$		−	15.0915i		−	0.659906i	−0.943997	−	0.329953i	$-0.892967\pi$
$523$		−	15.0915i		−	0.659906i	0.943997	−	0.329953i	$-0.107033\pi$
$524$	−0.845316	+	0.350142i	−0.0369278	+	0.0152960i
$525$	−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
$530$	−24.1197	+	9.99072i	−1.04769	+	0.433969i
$531$		−	6.55438i		−	0.284436i
$532$	0.0606113	+	0.146329i	0.00262783	+	0.00634415i
$533$	−43.3592	−	17.9600i	−1.87810	−	0.777933i
$534$	0.684544	−	1.65264i	0.0296231	−	0.0715165i
$535$	6.36396	−	6.36396i	0.275138	−	0.275138i
$536$	−28.1356	+	28.1356i	−1.21527	+	1.21527i
$537$	6.46799	−	15.6151i	0.279114	−	0.673842i
$538$	−26.8455	−	11.1198i	−1.15739	−	0.479408i
$539$	−9.52721	−	23.0007i	−0.410366	−	0.990711i
$540$		−	0.467911i		−	0.0201357i
$541$	17.8477	−	7.39276i	0.767332	−	0.317839i	0.0355409	−	0.999368i	$-0.488685\pi$
$541$	17.8477	−	7.39276i	0.767332	−	0.317839i	0.731791	+	0.681529i	$0.238685\pi$
$542$	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
$547$	15.4675	−	6.40683i	0.661341	−	0.273936i	−0.0266618	−	0.999645i	$-0.508488\pi$
$547$	15.4675	−	6.40683i	0.661341	−	0.273936i	0.688003	+	0.725708i	$0.258488\pi$
$548$			2.14147i			0.0914792i
$549$	−1.14248	−	2.75820i	−0.0487600	−	0.117717i
$550$	−6.27918	−	2.60092i	−0.267745	−	0.110904i
$551$	−11.2798	+	27.2320i	−0.480537	+	1.16012i
$552$	6.46501	−	6.46501i	0.275169	−	0.275169i
$553$	−1.02221	+	1.02221i	−0.0434688	+	0.0434688i
$554$	8.20669	−	19.8127i	0.348669	−	0.841761i
$555$	−19.6433	−	8.13652i	−0.833812	−	0.345376i
$556$	0.190196	+	0.459175i	0.00806612	+	0.0194733i
$557$			19.8084i			0.839309i	0.907684	+	0.419654i	$0.137849\pi$
$557$			19.8084i			0.839309i	−0.907684	+	0.419654i	$0.862151\pi$
$558$	−9.22535	+	3.82127i	−0.390540	+	0.161767i
$559$	−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	$0.0180318\pi$
$563$	25.0330	+	25.0330i	1.05501	+	1.05501i	0.0566184	+	0.998396i	$0.481968\pi$
$564$	1.54501	−	0.639963i	0.0650565	−	0.0269473i
$565$		−	11.9240i		−	0.501645i
$566$	13.8362	+	33.4035i	0.581578	+	1.40405i
$567$	0.170726	+	0.0707170i	0.00716982	+	0.00296984i
$568$	4.06741	−	9.81960i	0.170665	−	0.412021i
$569$	−12.7322	+	12.7322i	−0.533760	+	0.533760i	−0.921689	−	0.387929i	$-0.873190\pi$
$569$	−12.7322	+	12.7322i	−0.533760	+	0.533760i	0.387929	+	0.921689i	$0.373190\pi$
$570$	11.1885	−	11.1885i	0.468635	−	0.468635i
$571$	−5.31631	+	12.8347i	−0.222481	+	0.537115i	−0.995226	−	0.0976010i	$-0.968883\pi$
$571$	−5.31631	+	12.8347i	−0.222481	+	0.537115i	0.772745	+	0.634716i	$0.218883\pi$
$572$	−3.98569	−	1.65093i	−0.166650	−	0.0690288i
$573$	0.680553	+	1.64300i	0.0284305	+	0.0686373i
$574$			1.78880i			0.0746631i
$575$	4.05041	−	1.67774i	0.168914	−	0.0699664i
$576$	−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
$581$	0.428947	−	0.177676i	0.0177957	−	0.00737123i
$582$			11.8007i			0.489153i
$583$	10.4666	+	25.2687i	0.433483	+	1.04652i
$584$	22.8750	+	9.47513i	0.946574	+	0.392084i
$585$	−6.32952	+	15.2808i	−0.261693	+	0.631784i
$586$	2.29481	−	2.29481i	0.0947976	−	0.0947976i
$587$	−18.3382	+	18.3382i	−0.756897	+	0.756897i	−0.975756	−	0.218860i	$-0.929766\pi$
$587$	−18.3382	+	18.3382i	−0.756897	+	0.756897i	0.218860	+	0.975756i	$0.429766\pi$
$588$	0.492604	−	1.18925i	0.0203147	−	0.0490439i
$589$	31.7589	+	13.1550i	1.30860	+	0.542041i
$590$	−8.55684	−	20.6580i	−0.352279	−	0.850478i
$591$		−	8.04458i		−	0.330910i
$592$	−27.8989	+	11.5561i	−1.14664	+	0.474953i
$593$	26.6197	+	26.6197i	1.09314	+	1.09314i	0.995192	+	0.0979472i	$0.0312276\pi$
$593$	26.6197	+	26.6197i	1.09314	+	1.09314i	0.0979472	+	0.995192i	$0.468772\pi$
$594$	4.81521			0.197570
$595$		0			0
$596$	2.94356			0.120573
$597$	−8.44347	−	8.44347i	−0.345568	−	0.345568i
$598$	−25.2547	+	10.4608i	−1.03274	+	0.427775i
$599$		−	9.59720i		−	0.392131i	−0.980591	−	0.196065i	$-0.937183\pi$
$599$		−	9.59720i		−	0.392131i	0.980591	−	0.196065i	$-0.0628165\pi$
$600$	−1.58996	−	3.83850i	−0.0649098	−	0.156706i
$601$	−26.0188	−	10.7773i	−1.06133	−	0.439616i	−0.217405	−	0.976081i	$-0.569759\pi$
$601$	−26.0188	−	10.7773i	−1.06133	−	0.439616i	−0.843922	+	0.536465i	$0.819759\pi$
$602$	−0.470269	+	1.13533i	−0.0191667	+	0.0462726i
$603$	9.55834	−	9.55834i	0.389246	−	0.389246i
$604$	−0.181522	+	0.181522i	−0.00738603	+	0.00738603i
$605$	−1.71833	+	4.14840i	−0.0698598	+	0.168657i
$606$	−13.7262	−	5.68556i	−0.557587	−	0.230960i
$607$	−6.22571	−	15.0302i	−0.252694	−	0.610057i	0.745726	−	0.666253i	$-0.232103\pi$
$607$	−6.22571	−	15.0302i	−0.252694	−	0.610057i	−0.998420	+	0.0561959i	$0.982103\pi$
$608$			4.83244i			0.195981i
$609$	−1.08497	+	0.449409i	−0.0439652	+	0.0182110i
$610$	−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
$615$	−16.8077	+	6.96198i	−0.677752	+	0.280734i
$616$			1.94406i			0.0783284i
$617$	−4.85734	−	11.7267i	−0.195549	−	0.472097i	0.795441	−	0.606031i	$-0.207239\pi$
$617$	−4.85734	−	11.7267i	−0.195549	−	0.472097i	−0.990990	+	0.133933i	$0.957239\pi$
$618$	−7.80608	−	3.23339i	−0.314007	−	0.130066i
$619$	−9.92067	+	23.9506i	−0.398745	+	0.962657i	0.589219	+	0.807974i	$0.299436\pi$
$619$	−9.92067	+	23.9506i	−0.398745	+	0.962657i	−0.987964	+	0.154683i	$0.950564\pi$
$620$	2.45218	−	2.45218i	0.0984821	−	0.0984821i
$621$	−2.19632	+	2.19632i	−0.0881353	+	0.0881353i
$622$	−0.280453	+	0.677074i	−0.0112452	+	0.0271482i
$623$	−0.226672	−	0.0938907i	−0.00908143	−	0.00376165i
$624$	8.98967	+	21.7030i	0.359875	+	0.868814i
$625$			30.0651i			1.20260i
$626$	20.6858	−	8.56833i	0.826770	−	0.342459i
$627$	−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	0.989941	−	0.141483i	$-0.0451871\pi$
$631$	21.3130	+	21.3130i	0.848458	+	0.848458i	−0.141483	+	0.989941i	$0.545187\pi$
$632$	−21.2745	+	8.81218i	−0.846254	+	0.350530i
$633$		−	2.54664i		−	0.101220i
$634$	−13.4349	−	32.4346i	−0.533567	−	1.28814i
$635$	18.1686	+	7.52566i	0.720997	+	0.298647i
$636$	−0.541177	+	1.30652i	−0.0214590	+	0.0518067i
$637$	−32.1745	+	32.1745i	−1.27480	+	1.27480i
$638$	−21.6380	+	21.6380i	−0.856659	+	0.856659i
$639$	−1.38180	+	3.33596i	−0.0546631	+	0.131968i
$640$	−22.2190	−	9.20339i	−0.878282	−	0.363796i
$641$	−0.228853	−	0.552500i	−0.00903914	−	0.0218224i	0.919296	−	0.393568i	$-0.128759\pi$
$641$	−0.228853	−	0.552500i	−0.00903914	−	0.0218224i	−0.928335	+	0.371746i	$0.878759\pi$
$642$			4.78880i			0.188999i
$643$	30.1024	−	12.4688i	1.18712	−	0.491723i	0.300307	−	0.953843i	$-0.402911\pi$
$643$	30.1024	−	12.4688i	1.18712	−	0.491723i	0.886818	+	0.462120i	$0.152911\pi$
$644$	−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
$649$	−21.6421	+	8.96444i	−0.849525	+	0.351885i
$650$			12.4219i			0.487227i
$651$	0.524118	+	1.26533i	0.0205418	+	0.0495923i
$652$	0.537897	+	0.222804i	0.0210657	+	0.00872569i
$653$	−0.572566	+	1.38230i	−0.0224062	+	0.0540934i	−0.934687	−	0.355473i	$-0.884320\pi$
$653$	−0.572566	+	1.38230i	−0.0224062	+	0.0540934i	0.912280	+	0.409566i	$0.134320\pi$
$654$	3.42610	−	3.42610i	0.133971	−	0.133971i
$655$	8.86510	−	8.86510i	0.346388	−	0.346388i
$656$	−9.88794	+	23.8716i	−0.386059	+	0.932029i
$657$	−7.77119	−	3.21893i	−0.303183	−	0.125582i
$658$	0.862220	+	2.08158i	0.0336128	+	0.0811485i
$659$		−	49.3441i		−	1.92217i	−0.276246	−	0.961087i	$-0.589091\pi$
$659$		−	49.3441i		−	1.92217i	0.276246	−	0.961087i	$-0.410909\pi$
$660$	−1.54501	+	0.639963i	−0.0601393	+	0.0249105i
$661$	−32.4616	−	32.4616i	−1.26261	−	1.26261i	−0.949823	−	0.312787i	$-0.898737\pi$
$661$	−32.4616	−	32.4616i	−1.26261	−	1.26261i	−0.312787	−	0.949823i	$-0.601263\pi$
$662$	−30.3286			−1.17876
$663$		0			0
$664$	7.39567			0.287008
$665$	−1.53459	−	1.53459i	−0.0595090	−	0.0595090i
$666$	10.4520	−	4.32935i	0.405006	−	0.167759i
$667$		−	19.7392i		−	0.764304i
$668$	1.72183	+	4.15688i	0.0666198	+	0.160834i
$669$	4.10722	+	1.70127i	0.158794	+	0.0657747i
$670$	17.6473	−	42.6045i	0.681777	−	1.64595i
$671$	−7.54479	+	7.54479i	−0.291263	+	0.291263i
$672$	−0.136142	+	0.136142i	−0.00525178	+	0.00525178i
$673$	−13.3161	+	32.1478i	−0.513296	+	1.23921i	0.428658	+	0.903467i	$0.358986\pi$
$673$	−13.3161	+	32.1478i	−0.513296	+	1.23921i	−0.941955	+	0.335740i	$0.891014\pi$
$674$	0.618644	+	0.256251i	0.0238293	+	0.00987041i
$675$	0.540148	+	1.30403i	0.0207903	+	0.0501922i
$676$			5.48246i			0.210864i
$677$	13.1075	−	5.42931i	0.503763	−	0.208665i	−0.116305	−	0.993214i	$-0.537105\pi$
$677$	13.1075	−	5.42931i	0.503763	−	0.208665i	0.620068	+	0.784548i	$0.287105\pi$
$678$	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
$683$	41.1393	−	17.0405i	1.57415	−	0.652036i	0.586679	−	0.809819i	$-0.300435\pi$
$683$	41.1393	−	17.0405i	1.57415	−	0.652036i	0.987474	+	0.157784i	$0.0504348\pi$
$684$		−	0.857097i		−	0.0327719i
$685$	−11.2291	−	27.1096i	−0.429044	−	1.03580i
$686$	3.21241	+	1.33062i	0.122650	+	0.0508034i
$687$	−5.25708	+	12.6917i	−0.200570	+	0.484219i
$688$	−12.5515	+	12.5515i	−0.478522	+	0.478522i
$689$	35.3470	−	35.3470i	1.34661	−	1.34661i
$690$	−4.05502	+	9.78967i	−0.154372	+	0.372687i
$691$	−5.53202	−	2.29144i	−0.210448	−	0.0871704i	0.274969	−	0.961453i	$-0.411332\pi$
$691$	−5.53202	−	2.29144i	−0.210448	−	0.0871704i	−0.485417	+	0.874283i	$0.661332\pi$
$692$	−1.06565	−	2.57271i	−0.0405100	−	0.0977998i
$693$		−	0.660444i		−	0.0250882i
$694$	−17.2581	+	7.14854i	−0.655109	+	0.271355i
$695$	−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
$700$	−0.0445305	+	0.0184451i	−0.00168309	+	0.000697160i
$701$			15.4739i			0.584441i	0.956351	+	0.292221i	$0.0943941\pi$
$701$			15.4739i			0.584441i	−0.956351	+	0.292221i	$0.905606\pi$
$702$	−3.36787	−	8.13075i	−0.127112	−	0.306875i
$703$	−35.9816	−	14.9041i	−1.35707	−	0.562118i
$704$	−11.7571	+	28.3842i	−0.443114	+	1.06977i
$705$	−16.2030	+	16.2030i	−0.610239	+	0.610239i
$706$	−8.54553	+	8.54553i	−0.321615	+	0.321615i
$707$	−0.779821	+	1.88265i	−0.0293282	+	0.0708045i
$708$	−1.11900	−	0.463506i	−0.0420547	−	0.0174196i
$709$	−12.2452	−	29.5625i	−0.459878	−	1.11024i	−0.968446	−	0.249222i	$-0.919825\pi$
$709$	−12.2452	−	29.5625i	−0.459878	−	1.11024i	0.508568	−	0.861022i	$-0.330175\pi$
$710$			12.3182i			0.462294i
$711$	7.22746	−	2.99371i	0.271051	−	0.112273i
$712$	−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
$717$	23.9418	−	9.91704i	0.894125	−	0.370359i
$718$		−	8.25309i		−	0.308003i
$719$	−8.93044	−	21.5600i	−0.333049	−	0.804052i	−0.998347	−	0.0574740i	$-0.981695\pi$
$719$	−8.93044	−	21.5600i	−0.333049	−	0.804052i	0.665298	−	0.746578i	$-0.268305\pi$
$720$	8.41291	+	3.48474i	0.313531	+	0.129869i
$721$	−0.443485	+	1.07067i	−0.0165162	+	0.0398737i
$722$	2.39360	−	2.39360i	0.0890807	−	0.0890807i
$723$	−8.04498	+	8.04498i	−0.299196	+	0.299196i
$724$	−0.754422	+	1.82134i	−0.0280379	+	0.0676895i
$725$	−8.28717	−	3.43266i	−0.307778	−	0.127486i
$726$	−0.914302	−	2.20732i	−0.0339329	−	0.0819213i
$727$			4.75372i			0.176306i	0.996107	+	0.0881528i	$0.0280964\pi$
$727$			4.75372i			0.176306i	−0.996107	+	0.0881528i	$0.971904\pi$
$728$	3.28265	−	1.35972i	0.121663	−	0.0503946i
$729$	−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	0.694157	−	0.719824i	$-0.255778\pi$
$733$	−0.694919	−	0.694919i	−0.0256674	−	0.0256674i	−0.719824	+	0.694157i	$0.755778\pi$
$734$	22.3073	−	9.23999i	0.823378	−	0.341054i
$735$			17.6382i			0.650593i
$736$	−1.23843	−	2.98984i	−0.0456492	−	0.110207i
$737$	−44.6339	−	18.4880i	−1.64411	−	0.681013i
$738$	3.70439	−	8.94320i	0.136361	−	0.329204i
$739$	7.04021	−	7.04021i	0.258978	−	0.258978i	−0.565660	−	0.824638i	$-0.691379\pi$
$739$	7.04021	−	7.04021i	0.258978	−	0.258978i	0.824638	+	0.565660i	$0.191379\pi$
$740$	−2.77823	+	2.77823i	−0.102130	+	0.102130i
$741$	−11.5941	+	27.9906i	−0.425920	+	1.02826i
$742$	−1.76026	−	0.729125i	−0.0646213	−	0.0267670i
$743$	17.8048	+	42.9846i	0.653195	+	1.57695i	0.808114	+	0.589026i	$0.200488\pi$
$743$	17.8048	+	42.9846i	0.653195	+	1.57695i	−0.154919	+	0.987927i	$0.549512\pi$
$744$			21.8161i			0.799819i
$745$	−37.2635	+	15.4350i	−1.36523	+	0.565496i
$746$	−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
$751$	12.3019	−	5.09563i	0.448904	−	0.185942i	−0.146766	−	0.989171i	$-0.546887\pi$
$751$	12.3019	−	5.09563i	0.448904	−	0.185942i	0.595670	+	0.803229i	$0.296887\pi$
$752$			32.5449i			1.18679i
$753$	0.329025	+	0.794338i	0.0119904	+	0.0289473i
$754$	51.6712	+	21.4029i	1.88175	+	0.779448i
$755$	1.34610	−	3.24978i	0.0489898	−	0.118272i
$756$	0.0241465	−	0.0241465i	0.000878199	−	0.000878199i
$757$	−31.8816	+	31.8816i	−1.15876	+	1.15876i	−0.174013	+	0.984743i	$0.555674\pi$
$757$	−31.8816	+	31.8816i	−1.15876	+	1.15876i	−0.984743	+	0.174013i	$0.944326\pi$
$758$	19.5968	−	47.3109i	0.711788	−	1.71841i
$759$	10.2560	+	4.24817i	0.372269	+	0.154199i
$760$	−13.2293	−	31.9384i	−0.479878	−	1.15853i
$761$		−	24.0036i		−	0.870131i	−0.900399	−	0.435065i	$-0.856725\pi$
$761$		−	24.0036i		−	0.870131i	0.900399	−	0.435065i	$-0.143275\pi$
$762$	−9.66728	+	4.00432i	−0.350209	+	0.145061i
$763$	−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
$768$	−4.06137	+	1.68227i	−0.146552	+	0.0607038i
$769$		−	30.5773i		−	1.10264i	−0.834292	−	0.551322i	$-0.814123\pi$
$769$		−	30.5773i		−	1.10264i	0.834292	−	0.551322i	$-0.185877\pi$
$770$	−0.862220	−	2.08158i	−0.0310722	−	0.0750150i
$771$	0.0277436	+	0.0114918i	0.000999163	+	0.000413867i
$772$	0.358481	−	0.865450i	0.0129020	−	0.0311482i
$773$	32.0564	−	32.0564i	1.15299	−	1.15299i	0.167039	−	0.985950i	$-0.446579\pi$
$773$	32.0564	−	32.0564i	1.15299	−	1.15299i	0.985950	−	0.167039i	$-0.0534205\pi$
$774$	4.70227	−	4.70227i	0.169020	−	0.169020i
$775$	−4.00329	+	9.66480i	−0.143802	+	0.347170i
$776$	23.8195	+	9.86634i	0.855069	+	0.354181i
$777$	−0.593806	−	1.43357i	−0.0213027	−	0.0514292i
$778$			18.5948i			0.666657i
$779$	−30.7875	+	12.7526i	−1.10308	+	0.456910i
$780$	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
$785$	−4.16651	+	1.72583i	−0.148709	+	0.0615974i
$786$			6.67087i			0.237942i
$787$	7.17310	+	17.3174i	0.255694	+	0.617299i	0.998645	−	0.0520469i	$-0.0165745\pi$
$787$	7.17310	+	17.3174i	0.255694	+	0.617299i	−0.742951	+	0.669346i	$0.766575\pi$
$788$	−1.37342	−	0.568889i	−0.0489260	−	0.0202658i
$789$	−4.68487	+	11.3103i	−0.166786	+	0.402657i
$790$	18.8711	−	18.8711i	0.671404	−	0.671404i
$791$	0.615334	−	0.615334i	0.0218788	−	0.0218788i
$792$	4.02592	−	9.71942i	0.143055	−	0.345365i
$793$	18.0168	+	7.46280i	0.639795	+	0.265012i
$794$	−14.7263	−	35.5524i	−0.522616	−	1.26171i
$795$		−	19.3773i		−	0.687243i
$796$	−2.03862	+	0.844423i	−0.0722569	+	0.0299298i
$797$	−31.5144	−	31.5144i	−1.11630	−	1.11630i	−0.992280	−	0.124018i	$-0.960422\pi$
$797$	−31.5144	−	31.5144i	−1.11630	−	1.11630i	−0.124018	−	0.992280i	$-0.539578\pi$
$798$	1.15476			0.0408782
$799$		0			0
$800$	−1.47060			−0.0519935
$801$	0.938823	+	0.938823i	0.0331717	+	0.0331717i
$802$	−33.3299	+	13.8057i	−1.17692	+	0.487496i
$803$			30.0624i			1.06088i
$804$	−0.955920	−	2.30780i	−0.0337127	−	0.0813897i
$805$	1.34273	+	0.556178i	0.0473251	+	0.0196027i
$806$	24.9609	−	60.2608i	0.879209	−	2.12260i
$807$	15.2503	−	15.2503i	0.536836	−	0.536836i
$808$	−22.9525	+	22.9525i	−0.807465	+	0.807465i
$809$	3.23950	−	7.82085i	0.113895	−	0.274966i	−0.856645	−	0.515906i	$-0.827455\pi$
$809$	3.23950	−	7.82085i	0.113895	−	0.274966i	0.970540	+	0.240939i	$0.0774555\pi$
$810$	−3.15179	−	1.30551i	−0.110743	−	0.0458711i
$811$	−4.18326	−	10.0993i	−0.146894	−	0.354634i	0.833257	−	0.552886i	$-0.186473\pi$
$811$	−4.18326	−	10.0993i	−0.146894	−	0.354634i	−0.980151	+	0.198252i	$0.936473\pi$
$812$			0.217014i			0.00761568i
$813$	−3.13835	+	1.29995i	−0.110067	+	0.0455911i
$814$	−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
$819$	−1.11520	+	0.461930i	−0.0389682	+	0.0161411i
$820$			3.36184i			0.117401i
$821$	−4.80956	−	11.6113i	−0.167855	−	0.405238i	0.817460	−	0.575986i	$-0.195382\pi$
$821$	−4.80956	−	11.6113i	−0.167855	−	0.405238i	−0.985315	+	0.170748i	$0.945382\pi$
$822$	14.4247	+	5.97490i	0.503119	+	0.208399i
$823$	19.6200	−	47.3668i	0.683910	−	1.65110i	−0.0727943	−	0.997347i	$-0.523192\pi$
$823$	19.6200	−	47.3668i	0.683910	−	1.65110i	0.756704	−	0.653757i	$-0.226808\pi$
$824$	−13.0531	+	13.0531i	−0.454726	+	0.454726i
$825$	3.56705	−	3.56705i	0.124189	−	0.124189i
$826$	0.624480	−	1.50763i	0.0217284	−	0.0524571i
$827$	26.3729	+	10.9240i	0.917075	+	0.379865i	0.790761	−	0.612125i	$-0.209685\pi$
$827$	26.3729	+	10.9240i	0.917075	+	0.379865i	0.126315	+	0.991990i	$0.459685\pi$
$828$	0.219652	+	0.530286i	0.00763343	+	0.0184287i
$829$		−	4.09865i		−	0.142352i	−0.997464	−	0.0711760i	$-0.977325\pi$
$829$		−	4.09865i		−	0.142352i	0.997464	−	0.0711760i	$-0.0226752\pi$
$830$	−7.91884	+	3.28009i	−0.274867	+	0.113854i
$831$	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
$836$	−2.83007	+	1.17225i	−0.0978800	+	0.0405432i
$837$		−	7.41147i		−	0.256178i
$838$	−9.81426	−	23.6937i	−0.339028	−	0.818486i
$839$	34.5503	+	14.3112i	1.19281	+	0.494077i	0.888668	−	0.458551i	$-0.151631\pi$
$839$	34.5503	+	14.3112i	1.19281	+	0.494077i	0.304139	+	0.952628i	$0.401631\pi$
$840$	0.527080	−	1.27248i	0.0181860	−	0.0439048i
$841$	−8.05147	+	8.05147i	−0.277637	+	0.277637i
$842$	−6.11291	+	6.11291i	−0.210665	+	0.210665i
$843$	−6.12886	+	14.7964i	−0.211089	+	0.509614i
$844$	−0.434777	−	0.180091i	−0.0149656	−	0.00619897i
$845$	−28.7481	−	69.4041i	−0.988966	−	2.38757i
$846$		−	12.1925i		−	0.419188i
$847$	−0.302752	+	0.125404i	−0.0104027	+	0.00430893i
$848$	−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
$853$	51.9761	−	21.5292i	1.77963	−	0.737147i	0.786857	−	0.617135i	$-0.211707\pi$
$853$	51.9761	−	21.5292i	1.77963	−	0.737147i	0.992773	−	0.120011i	$-0.0382930\pi$
$854$		−	0.743289i		−	0.0254348i
$855$	4.49432	+	10.8502i	0.153702	+	0.371071i
$856$	9.66612	+	4.00384i	0.330381	+	0.136848i
$857$	−6.81952	+	16.4638i	−0.232950	+	0.562392i	−0.996522	−	0.0833314i	$-0.973444\pi$
$857$	−6.81952	+	16.4638i	−0.232950	+	0.562392i	0.763572	+	0.645723i	$0.223444\pi$
$858$	−22.2409	+	22.2409i	−0.759291	+	0.759291i
$859$	−3.86034	+	3.86034i	−0.131713	+	0.131713i	−0.769890	−	0.638177i	$-0.779689\pi$
$859$	−3.86034	+	3.86034i	−0.131713	+	0.131713i	0.638177	+	0.769890i	$0.279689\pi$
$860$	−0.883817	+	2.13372i	−0.0301379	+	0.0727594i
$861$	−1.22663	−	0.508087i	−0.0418035	−	0.0173156i
$862$	4.46033	+	10.7682i	0.151919	+	0.366766i
$863$		−	8.23947i		−	0.280475i	−0.990118	−	0.140237i	$-0.955213\pi$
$863$		−	8.23947i		−	0.280475i	0.990118	−	0.140237i	$-0.0447866\pi$
$864$	0.962580	−	0.398714i	0.0327476	−	0.0135645i
$865$	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
$870$	20.0297	−	8.29659i	0.679072	−	0.281281i
$871$			88.2978i			2.99186i
$872$	−4.05102	−	9.78004i	−0.137185	−	0.331194i
$873$	−8.09205	−	3.35184i	−0.273874	−	0.113442i
$874$	−7.42778	+	17.9322i	−0.251248	+	0.606567i
$875$	−1.18731	+	1.18731i	−0.0401384	+	0.0401384i
$876$	−1.09911	+	1.09911i	−0.0371355	+	0.0371355i
$877$	−3.11899	+	7.52991i	−0.105321	+	0.254267i	−0.967751	−	0.251909i	$-0.918942\pi$
$877$	−3.11899	+	7.52991i	−0.105321	+	0.254267i	0.862430	+	0.506176i	$0.168942\pi$
$878$	−16.4297	−	6.80542i	−0.554477	−	0.229672i
$879$	0.921802	+	2.22543i	0.0310916	+	0.0750618i
$880$		−	32.5449i		−	1.09709i
$881$	17.4201	−	7.21563i	0.586897	−	0.243101i	−0.0694181	−	0.997588i	$-0.522114\pi$
$881$	17.4201	−	7.21563i	0.586897	−	0.243101i	0.656315	+	0.754487i	$0.272114\pi$
$882$	−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
$887$	10.3381	−	4.28217i	0.347118	−	0.143781i	−0.202311	−	0.979321i	$-0.564845\pi$
$887$	10.3381	−	4.28217i	0.347118	−	0.143781i	0.549429	+	0.835540i	$0.314845\pi$
$888$		−	24.7169i		−	0.829444i
$889$	0.549225	+	1.32595i	0.0184204	+	0.0444708i
$890$	4.18462	+	1.73333i	0.140269	+	0.0581012i
$891$	−1.36770	+	3.30193i	−0.0458197	+	0.110619i
$892$	0.580901	−	0.580901i	0.0194500	−	0.0194500i
$893$	−29.6798	+	29.6798i	−0.993197	+	0.993197i
$894$	8.21281	−	19.8275i	0.274677	−	0.663130i
$895$	39.5388	+	16.3775i	1.32164	+	0.547440i
$896$	−0.671666	−	1.62155i	−0.0224388	−	0.0541720i
$897$		−	20.2891i		−	0.677433i
$898$	−3.37552	+	1.39819i	−0.112643	+	0.0466581i
$899$	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
$904$	12.8065	−	5.30462i	0.425938	−	0.176429i
$905$		−	27.0128i		−	0.897936i
$906$	0.716247	+	1.72917i	0.0237957	+	0.0574480i
$907$	37.9527	+	15.7205i	1.26020	+	0.521991i	0.909970	−	0.414674i	$-0.136104\pi$
$907$	37.9527	+	15.7205i	1.26020	+	0.521991i	0.350227	+	0.936665i	$0.386104\pi$
$908$	−0.531808	+	1.28390i	−0.0176487	+	0.0426077i
$909$	7.79751	−	7.79751i	0.258627	−	0.258627i
$910$	−2.91181	+	2.91181i	−0.0965257	+	0.0965257i
$911$	−14.6831	+	35.4481i	−0.486472	+	1.17445i	0.470011	+	0.882661i	$0.344250\pi$
$911$	−14.6831	+	35.4481i	−0.486472	+	1.17445i	−0.956483	+	0.291788i	$0.905750\pi$
$912$	15.4104	+	6.38318i	0.510288	+	0.211368i
$913$	3.43634	+	8.29605i	0.113726	+	0.274559i
$914$		−	35.3892i		−	1.17057i
$915$	6.98400	−	2.89287i	0.230884	−	0.0956353i
$916$	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
$921$	−5.93058	+	2.45653i	−0.195419	+	0.0809453i
$922$			34.3833i			1.13235i
$923$	−9.02603	−	21.7908i	−0.297096	−	0.717252i
$924$	−0.112755	−	0.0467047i	−0.00370937	−	0.00153647i
$925$	4.53558	−	10.9499i	0.149129	−	0.360029i
$926$	−2.69193	+	2.69193i	−0.0884624	+	0.0884624i
$927$	4.43445	−	4.43445i	0.145646	−	0.145646i
$928$	−2.53384	+	6.11723i	−0.0831774	+	0.200808i
$929$	19.9040	+	8.24451i	0.653029	+	0.270494i	0.684502	−	0.729011i	$-0.260020\pi$
$929$	19.9040	+	8.24451i	0.653029	+	0.270494i	−0.0314726	+	0.999505i	$0.510020\pi$
$930$	−9.67579	−	23.3594i	−0.317282	−	0.765986i
$931$			32.3087i			1.05888i
$932$	−3.50420	+	1.45149i	−0.114784	+	0.0475450i
$933$	−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	0.124824	−	0.992179i	$-0.460163\pi$
$937$	−26.5501	−	26.5501i	−0.867355	−	0.867355i	−0.992179	+	0.124824i	$0.960163\pi$
$938$	3.10929	−	1.28791i	0.101522	−	0.0420517i
$939$			16.6186i			0.542326i
$940$	1.62044	+	3.91210i	0.0528530	+	0.127599i
$941$	35.9144	+	14.8762i	1.17078	+	0.484952i	0.881450	−	0.472278i	$-0.156568\pi$
$941$	35.9144	+	14.8762i	1.17078	+	0.484952i	0.289328	+	0.957230i	$0.406568\pi$
$942$	0.918293	−	2.21695i	0.0299196	−	0.0722323i
$943$	15.7801	−	15.7801i	0.513871	−	0.513871i
$944$	16.6674	−	16.6674i	0.542478	−	0.542478i
$945$	−0.179062	+	0.432294i	−0.00582488	+	0.0140625i
$946$	−21.9579	−	9.09524i	−0.713911	−	0.295712i
$947$	18.1894	+	43.9132i	0.591077	+	1.42699i	0.882464	+	0.470381i	$0.155883\pi$
$947$	18.1894	+	43.9132i	0.591077	+	1.42699i	−0.291387	+	0.956605i	$0.594117\pi$
$948$		−	1.44562i		−	0.0469516i
$949$	50.7621	−	21.0263i	1.64781	−	0.682544i
$950$	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
$955$	−4.16022	+	1.72322i	−0.134622	+	0.0557621i
$956$		−	4.78880i		−	0.154881i
$957$	−8.69180	−	20.9839i	−0.280966	−	0.678312i
$958$	−43.3404	−	17.9522i	−1.40026	−	0.580008i
$959$	0.819506	−	1.97846i	0.0264632	−	0.0638879i
$960$	15.3912	−	15.3912i	0.496750	−	0.496750i
$961$	16.9210	−	16.9210i	0.545840	−	0.545840i
$962$	−28.2797	+	68.2733i	−0.911775	+	2.20122i
$963$	−3.28382	−	1.36020i	−0.105820	−	0.0438319i
$964$	0.804571	+	1.94241i	0.0259135	+	0.0625607i
$965$			12.8357i			0.413197i
$966$	−0.714453	+	0.295936i	−0.0229871	+	0.00952159i
$967$	−0.984864	−	0.984864i	−0.0316711	−	0.0316711i	0.691094	−	0.722765i	$-0.257129\pi$
$967$	−0.984864	−	0.984864i	−0.0316711	−	0.0316711i	−0.722765	+	0.691094i	$0.757129\pi$
$968$	−5.21987			−0.167773
$969$		0			0
$970$	−29.8803			−0.959399
$971$	9.25543	+	9.25543i	0.297021	+	0.297021i	0.839846	−	0.542825i	$-0.182645\pi$
$971$	9.25543	+	9.25543i	0.297021	+	0.297021i	−0.542825	+	0.839846i	$0.682645\pi$
$972$	−0.170726	+	0.0707170i	−0.00547604	+	0.00226825i
$973$		−	0.497007i		−	0.0159333i
$974$	11.1278	+	26.8648i	0.356556	+	0.860803i
$975$	−8.51805	−	3.52829i	−0.272796	−	0.112996i
$976$	4.10867	−	9.91922i	0.131515	−	0.317506i
$977$	−2.40579	+	2.40579i	−0.0769681	+	0.0769681i	−0.744543	−	0.667575i	$-0.767332\pi$
$977$	−2.40579	+	2.40579i	−0.0769681	+	0.0769681i	0.667575	+	0.744543i	$0.267332\pi$
$978$	3.00156	−	3.00156i	0.0959794	−	0.0959794i
$979$	1.81589	−	4.38395i	0.0580362	−	0.140112i
$980$	3.01129	+	1.24732i	0.0961922	+	0.0398441i
$981$	1.37623	+	3.32252i	0.0439397	+	0.106080i
$982$		−	46.2404i		−	1.47559i
$983$	−13.5461	+	5.61098i	−0.432054	+	0.178962i	−0.588102	−	0.808787i	$-0.700125\pi$
$983$	−13.5461	+	5.61098i	−0.432054	+	0.178962i	0.156048	+	0.987749i	$0.450125\pi$
$984$	−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
$989$	14.1640	−	5.86692i	0.450389	−	0.186557i
$990$			12.1925i			0.387504i
$991$	−17.8588	−	43.1150i	−0.567304	−	1.36959i	−0.903819	−	0.427916i	$-0.859248\pi$
$991$	−17.8588	−	43.1150i	−0.567304	−	1.36959i	0.336514	−	0.941678i	$-0.390752\pi$
$992$	7.13414	+	2.95506i	0.226509	+	0.0938231i
$993$	8.61448	−	20.7972i	0.273372	−	0.659979i
$994$	−0.635679	+	0.635679i	−0.0201625	+	0.0201625i
$995$	21.3796	−	21.3796i	0.677780	−	0.677780i
$996$	−0.177676	+	0.428947i	−0.00562987	+	0.0135917i
$997$	1.43195	+	0.593134i	0.0453504	+	0.0187848i	0.405243	−	0.914209i	$-0.367187\pi$
$997$	1.43195	+	0.593134i	0.0453504	+	0.0187848i	−0.359893	+	0.932994i	$0.617187\pi$
$998$	9.35596	+	22.5873i	0.296158	+	0.714988i
$999$			8.39693i			0.265667i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.h.l.733.4		24
17.2	even	8	inner	867.2.h.l.688.4		24
17.3	odd	16		867.2.a.j.1.2	yes	3
17.4	even	4	inner	867.2.h.l.712.3		24
17.5	odd	16		867.2.d.d.577.4		6
17.6	odd	16		867.2.e.j.616.4		12
17.7	odd	16		867.2.e.j.829.3		12
17.8	even	8	inner	867.2.h.l.757.3		24
17.9	even	8	inner	867.2.h.l.757.4		24
17.10	odd	16		867.2.e.j.829.4		12
17.11	odd	16		867.2.e.j.616.3		12
17.12	odd	16		867.2.d.d.577.3		6
17.13	even	4	inner	867.2.h.l.712.4		24
17.14	odd	16		867.2.a.i.1.2	✓	3
17.15	even	8	inner	867.2.h.l.688.3		24
17.16	even	2	inner	867.2.h.l.733.3		24
51.14	even	16		2601.2.a.y.1.2		3
51.20	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	17.14	odd	16
867.2.a.j.1.2	yes	3	17.3	odd	16
867.2.d.d.577.3		6	17.12	odd	16
867.2.d.d.577.4		6	17.5	odd	16
867.2.e.j.616.3		12	17.11	odd	16
867.2.e.j.616.4		12	17.6	odd	16
867.2.e.j.829.3		12	17.7	odd	16
867.2.e.j.829.4		12	17.10	odd	16
867.2.h.l.688.3		24	17.15	even	8	inner
867.2.h.l.688.4		24	17.2	even	8	inner
867.2.h.l.712.3		24	17.4	even	4	inner
867.2.h.l.712.4		24	17.13	even	4	inner
867.2.h.l.733.3		24	17.16	even	2	inner
867.2.h.l.733.4		24	1.1	even	1	trivial
867.2.h.l.757.3		24	17.8	even	8	inner
867.2.h.l.757.4		24	17.9	even	8	inner
2601.2.a.y.1.2		3	51.14	even	16
2601.2.a.z.1.2		3	51.20	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)

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