LMFDB - Embedded newform 867.2.h.i.712.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [867,2,Mod(688,867)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

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

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("867.688"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [16,-8,0,0,0,0,0,32,0,0,0,0,0,0,8,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(16)] == traces)

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

Self dual:	no
Analytic conductor:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8x^{14} + 32x^{12} + 296x^{10} + 1057x^{8} + 1184x^{6} + 512x^{4} - 512x^{2} + 256 $ x^16 - 8x^14 + 32x^12 + 296x^10 + 1057x^8 + 1184x^6 + 512x^4 - 512*x^2 + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			712.1
Root			$-0.602575 + 0.249595i$ of defining polynomial
Character	$\chi$	$=$	867.712
Dual form			867.2.h.i.688.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.46119 - 1.46119i) q^{2} +(-0.382683 - 0.923880i) q^{3} +2.27016i q^{4} +(-0.321304 + 0.133089i) q^{5} +(-0.790791 + 1.90914i) q^{6} +(-4.00649 - 1.65954i) q^{7} +(0.394755 - 0.394755i) q^{8} +(-0.707107 + 0.707107i) q^{9} +(0.663955 + 0.275019i) q^{10} +(0.279298 - 0.674285i) q^{11} +(2.09735 - 0.868752i) q^{12} +5.40303i q^{13} +(3.42934 + 8.27916i) q^{14} +(0.245916 + 0.245916i) q^{15} +3.38669 q^{16} +2.06644 q^{18} +(-2.31235 - 2.31235i) q^{19} +(-0.302132 - 0.729412i) q^{20} +4.33660i q^{21} +(-1.39337 + 0.577151i) q^{22} +(1.36169 - 3.28741i) q^{23} +(-0.515772 - 0.213640i) q^{24} +(-3.45001 + 3.45001i) q^{25} +(7.89486 - 7.89486i) q^{26} +(0.923880 + 0.382683i) q^{27} +(3.76743 - 9.09538i) q^{28} +(4.04850 - 1.67694i) q^{29} -0.718659i q^{30} +(1.26456 + 3.05291i) q^{31} +(-5.73812 - 5.73812i) q^{32} -0.729840 q^{33} +1.50817 q^{35} +(-1.60525 - 1.60525i) q^{36} +(-1.09979 - 2.65513i) q^{37} +6.75758i q^{38} +(4.99175 - 2.06765i) q^{39} +(-0.0742990 + 0.179374i) q^{40} +(10.9474 + 4.53457i) q^{41} +(6.33660 - 6.33660i) q^{42} +(-2.64895 + 2.64895i) q^{43} +(1.53073 + 0.634051i) q^{44} +(0.133089 - 0.321304i) q^{45} +(-6.79323 + 2.81385i) q^{46} -0.476019i q^{47} +(-1.29603 - 3.12890i) q^{48} +(8.34815 + 8.34815i) q^{49} +10.0822 q^{50} -12.2657 q^{52} +(7.16502 + 7.16502i) q^{53} +(-0.790791 - 1.90914i) q^{54} +0.253822i q^{55} +(-2.23669 + 0.926469i) q^{56} +(-1.25144 + 3.02123i) q^{57} +(-8.36597 - 3.46530i) q^{58} +(3.74618 - 3.74618i) q^{59} +(-0.558268 + 0.558268i) q^{60} +(-3.27708 - 1.35741i) q^{61} +(2.61313 - 6.30864i) q^{62} +(4.00649 - 1.65954i) q^{63} +9.99559i q^{64} +(-0.719082 - 1.73602i) q^{65} +(1.06644 + 1.06644i) q^{66} +1.55666 q^{67} -3.55827 q^{69} +(-2.20372 - 2.20372i) q^{70} +(-3.42934 - 8.27916i) q^{71} +0.558268i q^{72} +(-3.78232 + 1.56669i) q^{73} +(-2.27265 + 5.48666i) q^{74} +(4.50766 + 1.86713i) q^{75} +(5.24941 - 5.24941i) q^{76} +(-2.23801 + 2.23801i) q^{77} +(-10.3151 - 4.27267i) q^{78} +(-0.310974 + 0.750758i) q^{79} +(-1.08816 + 0.450730i) q^{80} -1.00000i q^{81} +(-9.37040 - 22.6221i) q^{82} +(5.10072 + 5.10072i) q^{83} -9.84476 q^{84} +7.74124 q^{86} +(-3.09859 - 3.09859i) q^{87} +(-0.155923 - 0.376431i) q^{88} -9.77391i q^{89} +(-0.663955 + 0.275019i) q^{90} +(8.96657 - 21.6472i) q^{91} +(7.46295 + 3.09125i) q^{92} +(2.33660 - 2.33660i) q^{93} +(-0.695554 + 0.695554i) q^{94} +(1.05072 + 0.435221i) q^{95} +(-3.10545 + 7.49721i) q^{96} +(1.63820 - 0.678563i) q^{97} -24.3965i q^{98} +(0.279298 + 0.674285i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} + 32 q^{8} + 8 q^{15} - 24 q^{16} - 8 q^{18} + 32 q^{25} + 40 q^{26} + 16 q^{32} - 24 q^{33} + 16 q^{35} + 48 q^{42} + 48 q^{43} + 32 q^{49} + 120 q^{50} - 32 q^{52} + 16 q^{53} + 56 q^{59}+ \cdots - 48 q^{94}+O(q^{100}) $ 16 * q - 8 * q^2 + 32 * q^8 + 8 * q^15 - 24 * q^16 - 8 * q^18 + 32 * q^25 + 40 * q^26 + 16 * q^32 - 24 * q^33 + 16 * q^35 + 48 * q^42 + 48 * q^43 + 32 * q^49 + 120 * q^50 - 32 * q^52 + 16 * q^53 + 56 * q^59 + 24 * q^60 - 24 * q^66 - 16 * q^67 - 24 * q^69 - 64 * q^70 - 64 * q^76 - 40 * q^77 + 16 * q^83 - 96 * q^84 - 16 * q^86 + 8 * q^87 - 16 * q^93 - 48 * q^94

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 $

$2$	−1.46119	−	1.46119i	−1.03322	−	1.03322i	−0.999429	−	0.0337892i	$-0.989243\pi$
$2$	−1.46119	−	1.46119i	−1.03322	−	1.03322i	−0.0337892	−	0.999429i	$-0.510757\pi$
$3$	−0.382683	−	0.923880i	−0.220942	−	0.533402i
$3$	−0.382683	−	0.923880i	−0.220942	−	0.533402i
$4$			2.27016i			1.13508i
$5$	−0.321304	+	0.133089i	−0.143692	+	0.0595190i	−0.453370	−	0.891322i	$-0.649778\pi$
$5$	−0.321304	+	0.133089i	−0.143692	+	0.0595190i	0.309679	+	0.950841i	$0.399778\pi$
$6$	−0.790791	+	1.90914i	−0.322839	+	0.779402i
$7$	−4.00649	−	1.65954i	−1.51431	−	0.627248i	−0.537870	−	0.843028i	$-0.680771\pi$
$7$	−4.00649	−	1.65954i	−1.51431	−	0.627248i	−0.976442	+	0.215780i	$0.930771\pi$
$8$	0.394755	−	0.394755i	0.139567	−	0.139567i
$9$	−0.707107	+	0.707107i	−0.235702	+	0.235702i
$10$	0.663955	+	0.275019i	0.209961	+	0.0869686i
$11$	0.279298	−	0.674285i	0.0842115	−	0.203304i	−0.876164	−	0.482012i	$-0.839906\pi$
$11$	0.279298	−	0.674285i	0.0842115	−	0.203304i	0.960376	+	0.278708i	$0.0899061\pi$
$12$	2.09735	−	0.868752i	0.605454	−	0.250787i
$13$			5.40303i			1.49853i	0.662269	+	0.749266i	$0.269593\pi$
$13$			5.40303i			1.49853i	−0.662269	+	0.749266i	$0.730407\pi$
$14$	3.42934	+	8.27916i	0.916530	+	2.21270i
$15$	0.245916	+	0.245916i	0.0634951	+	0.0634951i
$16$	3.38669			0.846674
$17$		0			0
$17$		0			0
$18$	2.06644			0.487064
$19$	−2.31235	−	2.31235i	−0.530490	−	0.530490i	0.390228	−	0.920718i	$-0.372396\pi$
$19$	−2.31235	−	2.31235i	−0.530490	−	0.530490i	−0.920718	+	0.390228i	$0.872396\pi$
$20$	−0.302132	−	0.729412i	−0.0675588	−	0.163101i
$21$			4.33660i			0.946323i
$22$	−1.39337	+	0.577151i	−0.297067	+	0.123049i
$23$	1.36169	−	3.28741i	0.283932	−	0.685472i	−0.715988	−	0.698112i	$-0.754024\pi$
$23$	1.36169	−	3.28741i	0.283932	−	0.685472i	0.999920	+	0.0126400i	$0.00402354\pi$
$24$	−0.515772	−	0.213640i	−0.105282	−	0.0436090i
$25$	−3.45001	+	3.45001i	−0.690002	+	0.690002i
$26$	7.89486	−	7.89486i	1.54831	−	1.54831i
$27$	0.923880	+	0.382683i	0.177801	+	0.0736475i
$28$	3.76743	−	9.09538i	0.711977	−	1.71886i
$29$	4.04850	−	1.67694i	0.751787	−	0.311401i	0.0263167	−	0.999654i	$-0.491622\pi$
$29$	4.04850	−	1.67694i	0.751787	−	0.311401i	0.725471	+	0.688253i	$0.241622\pi$
$30$		−	0.718659i		−	0.131209i
$31$	1.26456	+	3.05291i	0.227121	+	0.548319i	0.995825	−	0.0912864i	$-0.0290979\pi$
$31$	1.26456	+	3.05291i	0.227121	+	0.548319i	−0.768704	+	0.639605i	$0.779098\pi$
$32$	−5.73812	−	5.73812i	−1.01437	−	1.01437i
$33$	−0.729840			−0.127049
$34$		0			0
$35$	1.50817			0.254927
$36$	−1.60525	−	1.60525i	−0.267541	−	0.267541i
$37$	−1.09979	−	2.65513i	−0.180805	−	0.436501i	0.807328	−	0.590103i	$-0.200913\pi$
$37$	−1.09979	−	2.65513i	−0.180805	−	0.436501i	−0.988133	+	0.153602i	$0.950913\pi$
$38$			6.75758i			1.09622i
$39$	4.99175	−	2.06765i	0.799320	−	0.331089i
$40$	−0.0742990	+	0.179374i	−0.0117477	+	0.0283615i
$41$	10.9474	+	4.53457i	1.70970	+	0.708180i	0.999993	+	0.00368222i	$0.00117209\pi$
$41$	10.9474	+	4.53457i	1.70970	+	0.708180i	0.709706	+	0.704498i	$0.248828\pi$
$42$	6.33660	−	6.33660i	0.977758	−	0.977758i
$43$	−2.64895	+	2.64895i	−0.403961	+	0.403961i	−0.879626	−	0.475665i	$-0.842207\pi$
$43$	−2.64895	+	2.64895i	−0.403961	+	0.403961i	0.475665	+	0.879626i	$0.342207\pi$
$44$	1.53073	+	0.634051i	0.230767	+	0.0955867i
$45$	0.133089	−	0.321304i	0.0198397	−	0.0478972i
$46$	−6.79323	+	2.81385i	−1.00161	+	0.414879i
$47$		−	0.476019i		−	0.0694345i	−0.999397	−	0.0347172i	$-0.988947\pi$
$47$		−	0.476019i		−	0.0694345i	0.999397	−	0.0347172i	$-0.0110531\pi$
$48$	−1.29603	−	3.12890i	−0.187066	−	0.451618i
$49$	8.34815	+	8.34815i	1.19259	+	1.19259i
$50$	10.0822			1.42585
$51$		0			0
$52$	−12.2657			−1.70095
$53$	7.16502	+	7.16502i	0.984192	+	0.984192i	0.999877	−	0.0156854i	$-0.00499301\pi$
$53$	7.16502	+	7.16502i	0.984192	+	0.984192i	−0.0156854	+	0.999877i	$0.504993\pi$
$54$	−0.790791	−	1.90914i	−0.107613	−	0.259801i
$55$			0.253822i			0.0342253i
$56$	−2.23669	+	0.926469i	−0.298891	+	0.123805i
$57$	−1.25144	+	3.02123i	−0.165757	+	0.400172i
$58$	−8.36597	−	3.46530i	−1.09851	−	0.455016i
$59$	3.74618	−	3.74618i	0.487711	−	0.487711i	−0.419872	−	0.907583i	$-0.637925\pi$
$59$	3.74618	−	3.74618i	0.487711	−	0.487711i	0.907583	+	0.419872i	$0.137925\pi$
$60$	−0.558268	+	0.558268i	−0.0720720	+	0.0720720i
$61$	−3.27708	−	1.35741i	−0.419587	−	0.173799i	0.162893	−	0.986644i	$-0.447918\pi$
$61$	−3.27708	−	1.35741i	−0.419587	−	0.173799i	−0.582480	+	0.812845i	$0.697918\pi$
$62$	2.61313	−	6.30864i	0.331867	−	0.801199i
$63$	4.00649	−	1.65954i	0.504771	−	0.209083i
$64$			9.99559i			1.24945i
$65$	−0.719082	−	1.73602i	−0.0891911	−	0.215326i
$66$	1.06644	+	1.06644i	0.131269	+	0.131269i
$67$	1.55666			0.190176			0.0950880	−	0.995469i	$-0.469687\pi$
$67$	1.55666			0.190176			0.0950880	+	0.995469i	$0.469687\pi$
$68$		0			0
$69$	−3.55827			−0.428365
$70$	−2.20372	−	2.20372i	−0.263395	−	0.263395i
$71$	−3.42934	−	8.27916i	−0.406988	−	0.982556i	−0.985926	−	0.167184i	$-0.946533\pi$
$71$	−3.42934	−	8.27916i	−0.406988	−	0.982556i	0.578938	−	0.815372i	$-0.303467\pi$
$72$			0.558268i			0.0657925i
$73$	−3.78232	+	1.56669i	−0.442687	+	0.183367i	−0.592882	−	0.805289i	$-0.702010\pi$
$73$	−3.78232	+	1.56669i	−0.442687	+	0.183367i	0.150195	+	0.988656i	$0.452010\pi$
$74$	−2.27265	+	5.48666i	−0.264190	+	0.637812i
$75$	4.50766	+	1.86713i	0.520499	+	0.215598i
$76$	5.24941	−	5.24941i	0.602148	−	0.602148i
$77$	−2.23801	+	2.23801i	−0.255045	+	0.255045i
$78$	−10.3151	−	4.27267i	−1.16796	−	0.483785i
$79$	−0.310974	+	0.750758i	−0.0349873	+	0.0844669i	−0.940407	−	0.340050i	$-0.889556\pi$
$79$	−0.310974	+	0.750758i	−0.0349873	+	0.0844669i	0.905420	+	0.424517i	$0.139556\pi$
$80$	−1.08816	+	0.450730i	−0.121660	+	0.0503932i
$81$		−	1.00000i		−	0.111111i
$82$	−9.37040	−	22.6221i	−1.03479	−	2.49820i
$83$	5.10072	+	5.10072i	0.559877	+	0.559877i	0.929272	−	0.369395i	$-0.120435\pi$
$83$	5.10072	+	5.10072i	0.559877	+	0.559877i	−0.369395	+	0.929272i	$0.620435\pi$
$84$	−9.84476			−1.07415
$85$		0			0
$86$	7.74124			0.834759
$87$	−3.09859	−	3.09859i	−0.332203	−	0.332203i
$88$	−0.155923	−	0.376431i	−0.0166214	−	0.0401277i
$89$		−	9.77391i		−	1.03603i	−0.855371	−	0.518016i	$-0.826671\pi$
$89$		−	9.77391i		−	1.03603i	0.855371	−	0.518016i	$-0.173329\pi$
$90$	−0.663955	+	0.275019i	−0.0699870	+	0.0289895i
$91$	8.96657	−	21.6472i	0.939952	−	2.26924i
$92$	7.46295	+	3.09125i	0.778066	+	0.322285i
$93$	2.33660	−	2.33660i	0.242294	−	0.242294i
$94$	−0.695554	+	0.695554i	−0.0717409	+	0.0717409i
$95$	1.05072	+	0.435221i	0.107801	+	0.0446527i
$96$	−3.10545	+	7.49721i	−0.316948	+	0.765181i
$97$	1.63820	−	0.678563i	0.166334	−	0.0688977i	−0.297963	−	0.954577i	$-0.596307\pi$
$97$	1.63820	−	0.678563i	0.166334	−	0.0688977i	0.464297	+	0.885680i	$0.346307\pi$
$98$		−	24.3965i		−	2.46442i
$99$	0.279298	+	0.674285i	0.0280705	+	0.0677682i
$100$	−7.83207	−	7.83207i	−0.783207	−	0.783207i
$101$	14.6089			1.45364			0.726820	−	0.686828i	$-0.240998\pi$
$101$	14.6089			1.45364			0.726820	+	0.686828i	$0.240998\pi$
$102$		0			0
$103$	2.86271			0.282072			0.141036	−	0.990005i	$-0.454957\pi$
$103$	2.86271			0.282072			0.141036	+	0.990005i	$0.454957\pi$
$104$	2.13287	+	2.13287i	0.209145	+	0.209145i
$105$	−0.577151	−	1.39337i	−0.0563242	−	0.135979i
$106$		−	20.9389i		−	2.03377i
$107$	−5.83718	+	2.41784i	−0.564302	+	0.233741i	−0.646552	−	0.762870i	$-0.723789\pi$
$107$	−5.83718	+	2.41784i	−0.564302	+	0.233741i	0.0822497	+	0.996612i	$0.473789\pi$
$108$	−0.868752	+	2.09735i	−0.0835957	+	0.201818i
$109$	−4.34092	−	1.79807i	−0.415784	−	0.172224i	0.164977	−	0.986297i	$-0.447245\pi$
$109$	−4.34092	−	1.79807i	−0.415784	−	0.172224i	−0.580761	+	0.814074i	$0.697245\pi$
$110$	0.370882	−	0.370882i	0.0353622	−	0.0353622i
$111$	−2.03215	+	2.03215i	−0.192883	+	0.192883i
$112$	−13.5688	−	5.62037i	−1.28213	−	0.531075i
$113$	−4.75508	+	11.4798i	−0.447320	+	1.07993i	0.526002	+	0.850483i	$0.323690\pi$
$113$	−4.75508	+	11.4798i	−0.447320	+	1.07993i	−0.973322	+	0.229443i	$0.926310\pi$
$114$	6.24319	−	2.58601i	0.584728	−	0.242202i
$115$			1.23748i			0.115396i
$116$	3.80693	+	9.19074i	0.353464	+	0.853339i
$117$	−3.82052	−	3.82052i	−0.353207	−	0.353207i
$118$	−10.9478			−1.00782
$119$		0			0
$120$	0.194153			0.0177236
$121$	7.40152	+	7.40152i	0.672866	+	0.672866i
$122$	2.80500	+	6.77188i	0.253953	+	0.613097i
$123$		−	11.8494i		−	1.06842i
$124$	−6.93059	+	2.87075i	−0.622386	+	0.257801i
$125$	1.31479	−	3.17418i	0.117598	−	0.283907i
$126$	−8.27916	−	3.42934i	−0.737566	−	0.305510i
$127$	−1.28020	+	1.28020i	−0.113600	+	0.113600i	−0.761622	−	0.648022i	$-0.775596\pi$
$127$	−1.28020	+	1.28020i	−0.113600	+	0.113600i	0.648022	+	0.761622i	$0.275596\pi$
$128$	3.12923	−	3.12923i	0.276587	−	0.276587i
$129$	3.46102	+	1.43360i	0.304726	+	0.126221i
$130$	−1.48594	+	3.58737i	−0.130325	+	0.314633i
$131$	−5.90054	+	2.44408i	−0.515532	+	0.213540i	−0.625253	−	0.780422i	$-0.715004\pi$
$131$	−5.90054	+	2.44408i	−0.515532	+	0.213540i	0.109721	+	0.993962i	$0.465004\pi$
$132$		−	1.65685i		−	0.144211i
$133$	5.42697	+	13.1019i	0.470578	+	1.13608i
$134$	−2.27457	−	2.27457i	−0.196493	−	0.196493i
$135$	−0.347777			−0.0299319
$136$		0			0
$137$	−2.28156			−0.194927			−0.0974633	−	0.995239i	$-0.531073\pi$
$137$	−2.28156			−0.194927			−0.0974633	+	0.995239i	$0.531073\pi$
$138$	5.19931	+	5.19931i	0.442595	+	0.442595i
$139$	6.36200	+	15.3592i	0.539618	+	1.30275i	0.924990	+	0.379991i	$0.124073\pi$
$139$	6.36200	+	15.3592i	0.539618	+	1.30275i	−0.385372	+	0.922761i	$0.625927\pi$
$140$			3.42378i			0.289363i
$141$	−0.439784	+	0.182164i	−0.0370365	+	0.0153410i
$142$	−7.08652	+	17.1084i	−0.594687	+	1.43570i
$143$	3.64318	+	1.50906i	0.304658	+	0.126194i
$144$	−2.39475	+	2.39475i	−0.199563	+	0.199563i
$145$	−1.07762	+	1.07762i	−0.0894913	+	0.0894913i
$146$	7.81593	+	3.23746i	0.646851	+	0.267934i
$147$	4.51799	−	10.9074i	0.372637	−	0.899626i
$148$	6.02757	−	2.49670i	0.495464	−	0.205228i
$149$			12.1814i			0.997936i	0.866620	+	0.498968i	$0.166287\pi$
$149$			12.1814i			0.997936i	−0.866620	+	0.498968i	$0.833713\pi$
$150$	−3.85831	−	9.31478i	−0.315030	−	0.760549i
$151$	13.7053	+	13.7053i	1.11532	+	1.11532i	0.992418	+	0.122907i	$0.0392216\pi$
$151$	13.7053	+	13.7053i	1.11532	+	1.11532i	0.122907	+	0.992418i	$0.460778\pi$
$152$	−1.82562			−0.148078
$153$		0			0
$154$	6.54032			0.527034
$155$	−0.812615	−	0.812615i	−0.0652708	−	0.0652708i
$156$	4.69390	+	11.3321i	0.375813	+	0.907292i
$157$			1.81475i			0.144833i	0.997374	+	0.0724164i	$0.0230711\pi$
$157$			1.81475i			0.144833i	−0.997374	+	0.0724164i	$0.976929\pi$
$158$	1.55139	−	0.642608i	0.123422	−	0.0511232i
$159$	3.87768	−	9.36155i	0.307520	−	0.742420i
$160$	2.60736	+	1.08000i	0.206130	+	0.0853818i
$161$	−10.9112	+	10.9112i	−0.859923	+	0.859923i
$162$	−1.46119	+	1.46119i	−0.114802	+	0.114802i
$163$	13.5894	+	5.62892i	1.06441	+	0.440891i	0.845013	−	0.534745i	$-0.179592\pi$
$163$	13.5894	+	5.62892i	1.06441	+	0.440891i	0.219393	+	0.975637i	$0.429592\pi$
$164$	−10.2942	+	24.8524i	−0.803841	+	1.94064i
$165$	0.234501	−	0.0971334i	0.0182559	−	0.00756182i
$166$		−	14.9063i		−	1.15695i
$167$	−3.07459	−	7.42271i	−0.237919	−	0.574387i	0.759148	−	0.650918i	$-0.225616\pi$
$167$	−3.07459	−	7.42271i	−0.237919	−	0.574387i	−0.997067	+	0.0765308i	$0.975616\pi$
$168$	1.71189	+	1.71189i	0.132075	+	0.132075i
$169$	−16.1928			−1.24560
$170$		0			0
$171$	3.27016			0.250075
$172$	−6.01353	−	6.01353i	−0.458528	−	0.458528i
$173$	−4.60648	−	11.1210i	−0.350224	−	0.845516i	−0.996592	−	0.0824897i	$-0.973713\pi$
$173$	−4.60648	−	11.1210i	−0.350224	−	0.845516i	0.646368	−	0.763026i	$-0.276287\pi$
$174$			9.05526i			0.686477i
$175$	19.5479	−	8.09700i	1.47768	−	0.612075i
$176$	0.945897	−	2.28360i	0.0712996	−	0.172133i
$177$	−4.89462	−	2.02742i	−0.367902	−	0.152390i
$178$	−14.2816	+	14.2816i	−1.07045	+	1.07045i
$179$	6.40090	−	6.40090i	0.478425	−	0.478425i	−0.426202	−	0.904628i	$-0.640149\pi$
$179$	6.40090	−	6.40090i	0.478425	−	0.478425i	0.904628	+	0.426202i	$0.140149\pi$
$180$	0.729412	+	0.302132i	0.0543671	+	0.0225196i
$181$	−3.67457	+	8.87121i	−0.273129	+	0.659392i	−0.999614	−	0.0277909i	$-0.991153\pi$
$181$	−3.67457	+	8.87121i	−0.273129	+	0.659392i	0.726485	+	0.687182i	$0.241153\pi$
$182$	−44.7326	+	18.5288i	−3.31580	+	1.37345i
$183$			3.54709i			0.262208i
$184$	−0.760187	−	1.83525i	−0.0560418	−	0.135297i
$185$	0.706735	+	0.706735i	0.0519602	+	0.0519602i
$186$	−6.82843			−0.500685
$187$		0			0
$188$	1.08064			0.0788136
$189$	−3.06644	−	3.06644i	−0.223050	−	0.223050i
$190$	−0.899356	−	2.17124i	−0.0652461	−	0.157518i
$191$			18.9231i			1.36923i	0.728905	+	0.684615i	$0.240029\pi$
$191$			18.9231i			1.36923i	−0.728905	+	0.684615i	$0.759971\pi$
$192$	9.23472	−	3.82515i	0.666458	−	0.276056i
$193$	−9.50776	+	22.9538i	−0.684384	+	1.65225i	0.0714167	+	0.997447i	$0.477248\pi$
$193$	−9.50776	+	22.9538i	−0.684384	+	1.65225i	−0.755800	+	0.654802i	$0.772752\pi$
$194$	−3.38523	−	1.40221i	−0.243045	−	0.100673i
$195$	−1.32869	+	1.32869i	−0.0951494	+	0.0951494i
$196$	−18.9516	+	18.9516i	−1.35369	+	1.35369i
$197$	10.3255	+	4.27695i	0.735659	+	0.304720i	0.718875	−	0.695139i	$-0.244657\pi$
$197$	10.3255	+	4.27695i	0.735659	+	0.304720i	0.0167839	+	0.999859i	$0.494657\pi$
$198$	0.577151	−	1.39337i	0.0410164	−	0.0990222i
$199$	15.8231	−	6.55416i	1.12167	−	0.464612i	0.256730	−	0.966483i	$-0.417355\pi$
$199$	15.8231	−	6.55416i	1.12167	−	0.464612i	0.864943	+	0.501871i	$0.167355\pi$
$200$			2.72382i			0.192603i
$201$	−0.595707	−	1.43816i	−0.0420179	−	0.101440i
$202$	−21.3464	−	21.3464i	−1.50193	−	1.50193i
$203$	−19.0032			−1.33377
$204$		0			0
$205$	−4.12095			−0.287820
$206$	−4.18297	−	4.18297i	−0.291441	−	0.291441i
$207$	1.36169	+	3.28741i	0.0946440	+	0.228491i
$208$			18.2984i			1.26877i
$209$	−2.20502	+	0.913349i	−0.152524	+	0.0631776i
$210$	−1.19265	+	2.87930i	−0.0823004	+	0.198691i
$211$	4.25411	+	1.76211i	0.292865	+	0.121309i	0.524279	−	0.851547i	$-0.324335\pi$
$211$	4.25411	+	1.76211i	0.292865	+	0.121309i	−0.231413	+	0.972855i	$0.574335\pi$
$212$	−16.2657	+	16.2657i	−1.11714	+	1.11714i
$213$	−6.33660	+	6.33660i	−0.434176	+	0.434176i
$214$	12.0622	+	4.99631i	0.824553	+	0.341541i
$215$	0.498573	−	1.20366i	0.0340024	−	0.0820891i
$216$	0.515772	−	0.213640i	0.0350938	−	0.0145363i
$217$		−	14.3300i		−	0.972787i
$218$	3.71559	+	8.97023i	0.251652	+	0.607541i
$219$	2.89486	+	2.89486i	0.195617	+	0.195617i
$220$	−0.576216			−0.0388485
$221$		0			0
$222$	5.93872			0.398581
$223$	2.85922	+	2.85922i	0.191468	+	0.191468i	0.796330	−	0.604862i	$-0.206772\pi$
$223$	2.85922	+	2.85922i	0.191468	+	0.191468i	−0.604862	+	0.796330i	$0.706772\pi$
$224$	13.4671	+	32.5124i	0.899806	+	2.17232i
$225$		−	4.87905i		−	0.325270i
$226$	23.7222	−	9.82606i	1.57798	−	0.653620i
$227$	−6.64274	+	16.0370i	−0.440894	+	1.06441i	0.534742	+	0.845015i	$0.320409\pi$
$227$	−6.64274	+	16.0370i	−0.440894	+	1.06441i	−0.975636	+	0.219397i	$0.929591\pi$
$228$	−6.85868	−	2.84096i	−0.454227	−	0.188147i
$229$	13.2524	−	13.2524i	0.875745	−	0.875745i	−0.117346	−	0.993091i	$-0.537439\pi$
$229$	13.2524	−	13.2524i	0.875745	−	0.875745i	0.993091	+	0.117346i	$0.0374386\pi$
$230$	1.80820	−	1.80820i	0.119229	−	0.119229i
$231$	2.92410	+	1.21120i	0.192392	+	0.0796912i
$232$	0.936183	−	2.26015i	0.0614634	−	0.148386i
$233$	9.04025	−	3.74459i	0.592246	−	0.245317i	−0.0663703	−	0.997795i	$-0.521142\pi$
$233$	9.04025	−	3.74459i	0.592246	−	0.245317i	0.658617	+	0.752479i	$0.271142\pi$
$234$			11.1650i			0.729880i
$235$	0.0633526	+	0.152947i	0.00413267	+	0.00997715i
$236$	8.50442	+	8.50442i	0.553591	+	0.553591i
$237$	0.812615			0.0527850
$238$		0			0
$239$	−14.2984			−0.924888			−0.462444	−	0.886648i	$-0.653027\pi$
$239$	−14.2984			−0.924888			−0.462444	+	0.886648i	$0.653027\pi$
$240$	0.832841	+	0.832841i	0.0537597	+	0.0537597i
$241$	2.43980	+	5.89021i	0.157162	+	0.379422i	0.982773	−	0.184818i	$-0.0591695\pi$
$241$	2.43980	+	5.89021i	0.157162	+	0.379422i	−0.825611	+	0.564239i	$0.809170\pi$
$242$		−	21.6301i		−	1.39043i
$243$	−0.923880	+	0.382683i	−0.0592669	+	0.0245492i
$244$	3.08154	−	7.43950i	0.197275	−	0.476265i
$245$	−3.79334	−	1.57125i	−0.242347	−	0.100384i
$246$	−17.3142	+	17.3142i	−1.10392	+	1.10392i
$247$	12.4937	−	12.4937i	0.794956	−	0.794956i
$248$	1.70434	+	0.705961i	0.108226	+	0.0448286i
$249$	2.76049	−	6.66442i	0.174939	−	0.422340i
$250$	−6.55924	+	2.71693i	−0.414843	+	0.171834i
$251$			27.4308i			1.73141i	0.500550	+	0.865707i	$0.333131\pi$
$251$			27.4308i			1.73141i	−0.500550	+	0.865707i	$0.666869\pi$
$252$	3.76743	+	9.09538i	0.237326	+	0.572955i
$253$	−1.83633	−	1.83633i	−0.115449	−	0.115449i
$254$	3.74124			0.234746
$255$		0			0
$256$	10.8464			0.677898
$257$	−0.464838	−	0.464838i	−0.0289958	−	0.0289958i	0.692460	−	0.721456i	$-0.256527\pi$
$257$	−0.464838	−	0.464838i	−0.0289958	−	0.0289958i	−0.721456	+	0.692460i	$0.756527\pi$
$258$	−2.96244	−	7.15197i	−0.184434	−	0.445262i
$259$			12.4629i			0.774408i
$260$	3.94104	−	1.63243i	0.244413	−	0.101239i
$261$	−1.67694	+	4.04850i	−0.103800	+	0.250596i
$262$	12.1931	+	5.05054i	0.753291	+	0.312023i
$263$	−6.72329	+	6.72329i	−0.414576	+	0.414576i	−0.883329	−	0.468753i	$-0.844703\pi$
$263$	−6.72329	+	6.72329i	−0.414576	+	0.414576i	0.468753	+	0.883329i	$0.344703\pi$
$264$	−0.288108	+	0.288108i	−0.0177318	+	0.0177318i
$265$	−3.25573	−	1.34857i	−0.199998	−	0.0828420i
$266$	11.2145	−	27.0742i	0.687605	−	1.66002i
$267$	−9.02992	+	3.74032i	−0.552622	+	0.228904i
$268$			3.53386i			0.215865i
$269$	6.61179	+	15.9623i	0.403128	+	0.973238i	0.986902	+	0.161321i	$0.0515755\pi$
$269$	6.61179	+	15.9623i	0.403128	+	0.973238i	−0.583774	+	0.811916i	$0.698424\pi$
$270$	0.508169	+	0.508169i	0.0309262	+	0.0309262i
$271$	−21.2897			−1.29326			−0.646630	−	0.762804i	$-0.723822\pi$
$271$	−21.2897			−1.29326			−0.646630	+	0.762804i	$0.723822\pi$
$272$		0			0
$273$	−23.4308			−1.41809
$274$	3.33379	+	3.33379i	0.201402	+	0.201402i
$275$	1.36271	+	3.28987i	0.0821744	+	0.198387i
$276$		−	8.07784i		−	0.486229i
$277$	−10.4674	+	4.33574i	−0.628925	+	0.260509i	−0.674296	−	0.738461i	$-0.735553\pi$
$277$	−10.4674	+	4.33574i	−0.628925	+	0.260509i	0.0453713	+	0.998970i	$0.485553\pi$
$278$	13.1467	−	31.7389i	0.788485	−	1.90357i
$279$	−3.05291	−	1.26456i	−0.182773	−	0.0757070i
$280$	0.595357	−	0.595357i	0.0355794	−	0.0355794i
$281$	−13.4515	+	13.4515i	−0.802450	+	0.802450i	−0.983478	−	0.181028i	$-0.942058\pi$
$281$	−13.4515	+	13.4515i	−0.802450	+	0.802450i	0.181028	+	0.983478i	$0.442058\pi$
$282$	0.908785	+	0.376431i	0.0541174	+	0.0224162i
$283$	−4.49194	+	10.8445i	−0.267018	+	0.644639i	−0.999340	−	0.0363192i	$-0.988437\pi$
$283$	−4.49194	+	10.8445i	−0.267018	+	0.644639i	0.732322	+	0.680959i	$0.238437\pi$
$284$	18.7950	−	7.78515i	1.11528	−	0.461964i
$285$		−	1.13729i		−	0.0673670i
$286$	−3.11837	−	7.52840i	−0.184393	−	0.445164i
$287$	−36.3354	−	36.3354i	−2.14481	−	2.14481i
$288$	8.11492			0.478177
$289$		0			0
$290$	3.14921			0.184928
$291$	−1.25382	−	1.25382i	−0.0735003	−	0.0735003i
$292$	−3.55663	−	8.58647i	−0.208136	−	0.502485i
$293$		−	20.9548i		−	1.22419i	−0.790784	−	0.612095i	$-0.790327\pi$
$293$		−	20.9548i		−	1.22419i	0.790784	−	0.612095i	$-0.209673\pi$
$294$	−22.5394	+	9.33613i	−1.31453	+	0.544494i
$295$	−0.705089	+	1.70224i	−0.0410519	+	0.0991080i
$296$	−1.48227	−	0.613978i	−0.0861554	−	0.0356868i
$297$	0.516075	−	0.516075i	0.0299457	−	0.0299457i
$298$	17.7993	−	17.7993i	1.03109	−	1.03109i
$299$	17.7620	+	7.35726i	1.02720	+	0.425481i
$300$	−4.23869	+	10.2331i	−0.244721	+	0.590808i
$301$	15.0090	−	6.21695i	0.865106	−	0.358339i
$302$		−	40.0523i		−	2.30475i
$303$	−5.59058	−	13.4969i	−0.321170	−	0.775374i
$304$	−7.83123	−	7.83123i	−0.449152	−	0.449152i
$305$	1.23360			0.0706355
$306$		0			0
$307$	33.4019			1.90634			0.953172	−	0.302428i	$-0.0977971\pi$
$307$	33.4019			1.90634			0.953172	+	0.302428i	$0.0977971\pi$
$308$	−5.08064	−	5.08064i	−0.289496	−	0.289496i
$309$	−1.09551	−	2.64480i	−0.0623216	−	0.150458i
$310$			2.37477i			0.134878i
$311$	−15.0069	+	6.21607i	−0.850965	+	0.352481i	−0.765167	−	0.643831i	$-0.777344\pi$
$311$	−15.0069	+	6.21607i	−0.850965	+	0.352481i	−0.0857975	+	0.996313i	$0.527344\pi$
$312$	1.15430	−	2.78673i	0.0653495	−	0.157768i
$313$	−7.31279	−	3.02906i	−0.413343	−	0.171212i	0.166314	−	0.986073i	$-0.446814\pi$
$313$	−7.31279	−	3.02906i	−0.413343	−	0.171212i	−0.579657	+	0.814860i	$0.696814\pi$
$314$	2.65170	−	2.65170i	0.149644	−	0.149644i
$315$	−1.06644	+	1.06644i	−0.0600869	+	0.0600869i
$316$	−1.70434	−	0.705961i	−0.0958766	−	0.0397134i
$317$	4.13415	−	9.98071i	0.232197	−	0.560573i	−0.764238	−	0.644934i	$-0.776885\pi$
$317$	4.13415	−	9.98071i	0.232197	−	0.560573i	0.996435	+	0.0843612i	$0.0268849\pi$
$318$	−19.3451	+	8.01298i	−1.08482	+	0.449346i
$319$		−	3.19821i		−	0.179065i
$320$	−1.33030	−	3.21162i	−0.0743659	−	0.179535i
$321$	4.46759	+	4.46759i	0.249356	+	0.249356i
$322$	31.8867			1.77698
$323$		0			0
$324$	2.27016			0.126120
$325$	−18.6405	−	18.6405i	−1.03399	−	1.03399i
$326$	−11.6318	−	28.0817i	−0.644227	−	1.55530i
$327$			4.69857i			0.259832i
$328$	6.11159	−	2.53150i	0.337456	−	0.139779i
$329$	−0.789974	+	1.90716i	−0.0435527	+	0.105145i
$330$	−0.484581	−	0.200720i	−0.0266753	−	0.0110493i
$331$	15.8667	−	15.8667i	0.872114	−	0.872114i	−0.120588	−	0.992703i	$-0.538478\pi$
$331$	15.8667	−	15.8667i	0.872114	−	0.872114i	0.992703	+	0.120588i	$0.0384781\pi$
$332$	−11.5795	+	11.5795i	−0.635505	+	0.635505i
$333$	2.65513	+	1.09979i	0.145500	+	0.0602682i
$334$	−6.35344	+	15.3386i	−0.347645	+	0.839289i
$335$	−0.500160	+	0.207173i	−0.0273267	+	0.0113191i
$336$			14.6867i			0.801227i
$337$	6.29980	+	15.2091i	0.343172	+	0.828491i	0.997391	+	0.0721857i	$0.0229974\pi$
$337$	6.29980	+	15.2091i	0.343172	+	0.828491i	−0.654219	+	0.756305i	$0.727003\pi$
$338$	23.6607	+	23.6607i	1.28697	+	1.28697i
$339$	12.4256			0.674867
$340$		0			0
$341$	2.41172			0.130602
$342$	−4.77833	−	4.77833i	−0.258382	−	0.258382i
$343$	−7.97587	−	19.2555i	−0.430657	−	1.03970i
$344$			2.09137i			0.112759i
$345$	1.14329	−	0.473565i	0.0615525	−	0.0254959i
$346$	−9.51899	+	22.9809i	−0.511744	+	1.23546i
$347$	−19.6581	−	8.14267i	−1.05530	−	0.437121i	−0.213522	−	0.976938i	$-0.568493\pi$
$347$	−19.6581	−	8.14267i	−1.05530	−	0.437121i	−0.841782	+	0.539817i	$0.818493\pi$
$348$	7.03429	−	7.03429i	0.377077	−	0.377077i
$349$	−4.53844	+	4.53844i	−0.242937	+	0.242937i	−0.818064	−	0.575127i	$-0.804953\pi$
$349$	−4.53844	+	4.53844i	−0.242937	+	0.242937i	0.575127	+	0.818064i	$0.304953\pi$
$350$	−40.3945	−	16.7319i	−2.15917	−	0.894359i
$351$	−2.06765	+	4.99175i	−0.110363	+	0.266440i
$352$	−5.47177	+	2.26648i	−0.291646	+	0.120804i
$353$			10.0201i			0.533315i	0.963791	+	0.266658i	$0.0859193\pi$
$353$			10.0201i			0.533315i	−0.963791	+	0.266658i	$0.914081\pi$
$354$	4.18953	+	10.1144i	0.222671	+	0.537575i
$355$	2.20372	+	2.20372i	0.116961	+	0.116961i
$356$	22.1883			1.17598
$357$		0			0
$358$	−18.7059			−0.988636
$359$	21.3098	+	21.3098i	1.12469	+	1.12469i	0.991027	+	0.133662i	$0.0426738\pi$
$359$	21.3098	+	21.3098i	1.12469	+	1.12469i	0.133662	+	0.991027i	$0.457326\pi$
$360$	−0.0742990	−	0.179374i	−0.00391590	−	0.00945382i
$361$		−	8.30606i		−	0.437161i
$362$	18.3318	−	7.59327i	0.963497	−	0.399094i
$363$	4.00567	−	9.67055i	0.210243	−	0.507572i
$364$	49.1426	+	20.3555i	2.57577	+	1.06692i
$365$	1.00677	−	1.00677i	0.0526966	−	0.0526966i
$366$	5.18297	−	5.18297i	0.270918	−	0.270918i
$367$	−22.9459	−	9.50450i	−1.19777	−	0.496131i	−0.307490	−	0.951551i	$-0.599489\pi$
$367$	−22.9459	−	9.50450i	−1.19777	−	0.496131i	−0.890277	+	0.455420i	$0.849489\pi$
$368$	4.61163	−	11.1335i	0.240398	−	0.580372i
$369$	−10.9474	+	4.53457i	−0.569900	+	0.236060i
$370$		−	2.06535i		−	0.107372i
$371$	−16.8159	−	40.5973i	−0.873040	−	2.10771i
$372$	5.30445	+	5.30445i	0.275023	+	0.275023i
$373$	6.09593			0.315635			0.157818	−	0.987468i	$-0.449554\pi$
$373$	6.09593			0.315635			0.157818	+	0.987468i	$0.449554\pi$
$374$		0			0
$375$	−3.43571			−0.177419
$376$	−0.187911	−	0.187911i	−0.00969075	−	0.00969075i
$377$	9.06058	+	21.8742i	0.466643	+	1.12658i
$378$			8.96130i			0.460920i
$379$	−25.8338	+	10.7007i	−1.32699	+	0.549658i	−0.929796	−	0.368076i	$-0.880017\pi$
$379$	−25.8338	+	10.7007i	−1.32699	+	0.549658i	−0.397196	+	0.917734i	$0.630017\pi$
$380$	−0.988021	+	2.38529i	−0.0506844	+	0.122363i
$381$	1.67266	+	0.692840i	0.0856932	+	0.0354953i
$382$	27.6503	−	27.6503i	1.41471	−	1.41471i
$383$	25.5375	−	25.5375i	1.30491	−	1.30491i	0.379864	−	0.925043i	$-0.375971\pi$
$383$	25.5375	−	25.5375i	1.30491	−	1.30491i	0.925043	−	0.379864i	$-0.124029\pi$
$384$	−4.08853	−	1.69353i	−0.208642	−	0.0864223i
$385$	0.421228	−	1.01694i	0.0214678	−	0.0518278i
$386$	47.4325	−	19.6472i	2.41425	−	1.00002i
$387$		−	3.74618i		−	0.190429i
$388$	1.54045	+	3.71897i	0.0782044	+	0.188802i
$389$	16.3515	+	16.3515i	0.829056	+	0.829056i	0.987386	−	0.158330i	$-0.0506110\pi$
$389$	16.3515	+	16.3515i	0.829056	+	0.829056i	−0.158330	+	0.987386i	$0.550611\pi$
$390$	3.88294			0.196620
$391$		0			0
$392$	6.59094			0.332893
$393$	4.51608	+	4.51608i	0.227806	+	0.227806i
$394$	−8.83804	−	21.3369i	−0.445254	−	1.07494i
$395$		−	0.282609i		−	0.0142196i
$396$	−1.53073	+	0.634051i	−0.0769223	+	0.0318622i
$397$	−1.61236	+	3.89258i	−0.0809219	+	0.195363i	−0.959162	−	0.282857i	$-0.908718\pi$
$397$	−1.61236	+	3.89258i	−0.0809219	+	0.195363i	0.878240	+	0.478220i	$0.158718\pi$
$398$	−32.6975	−	13.5438i	−1.63898	−	0.678887i
$399$	10.0277	−	10.0277i	0.502015	−	0.502015i
$400$	−11.6841	+	11.6841i	−0.584207	+	0.584207i
$401$	−5.72116	−	2.36978i	−0.285701	−	0.118341i	0.235231	−	0.971940i	$-0.424415\pi$
$401$	−5.72116	−	2.36978i	−0.285701	−	0.118341i	−0.520932	+	0.853598i	$0.674415\pi$
$402$	−1.23099	+	2.97187i	−0.0613962	+	0.148224i
$403$	−16.4950	+	6.83244i	−0.821673	+	0.340348i
$404$			33.1645i			1.65000i
$405$	0.133089	+	0.321304i	0.00661322	+	0.0159657i
$406$	27.7674	+	27.7674i	1.37807	+	1.37807i
$407$	−2.09748			−0.103968
$408$		0			0
$409$	−34.6034			−1.71103			−0.855515	−	0.517778i	$-0.826759\pi$
$409$	−34.6034			−1.71103			−0.855515	+	0.517778i	$0.826759\pi$
$410$	6.02149	+	6.02149i	0.297380	+	0.297380i
$411$	0.873115	+	2.10788i	0.0430676	+	0.103974i
$412$			6.49882i			0.320174i
$413$	−21.2260	+	8.79209i	−1.04446	+	0.432630i
$414$	2.81385	−	6.79323i	0.138293	−	0.333869i
$415$	−2.31773	−	0.960036i	−0.113773	−	0.0471263i
$416$	31.0032	−	31.0032i	1.52006	−	1.52006i
$417$	11.7554	−	11.7554i	0.575666	−	0.575666i
$418$	4.55653	+	1.88738i	0.222867	+	0.0923146i
$419$	2.23315	−	5.39130i	0.109097	−	0.263382i	−0.859897	−	0.510467i	$-0.829473\pi$
$419$	2.23315	−	5.39130i	0.109097	−	0.263382i	0.968994	+	0.247085i	$0.0794726\pi$
$420$	3.16316	−	1.31023i	0.154347	−	0.0639325i
$421$		−	27.0152i		−	1.31664i	−0.752739	−	0.658319i	$-0.771268\pi$
$421$		−	27.0152i		−	1.31664i	0.752739	−	0.658319i	$-0.228732\pi$
$422$	−3.64129	−	8.79086i	−0.177255	−	0.427932i
$423$	0.336596	+	0.336596i	0.0163659	+	0.0163659i
$424$	5.65685			0.274721
$425$		0			0
$426$	18.5180			0.897198
$427$	10.8769	+	10.8769i	0.526371	+	0.526371i
$428$	−5.48888	−	13.2513i	−0.265315	−	0.640528i
$429$		−	3.94335i		−	0.190387i
$430$	−2.48729	+	1.03027i	−0.119948	+	0.0496840i
$431$	6.63463	−	16.0174i	0.319579	−	0.771532i	−0.679697	−	0.733493i	$-0.737889\pi$
$431$	6.63463	−	16.0174i	0.319579	−	0.771532i	0.999276	−	0.0380389i	$-0.0121111\pi$
$432$	3.12890	+	1.29603i	0.150539	+	0.0623554i
$433$	2.81148	−	2.81148i	0.135111	−	0.135111i	−0.636317	−	0.771428i	$-0.719543\pi$
$433$	2.81148	−	2.81148i	0.135111	−	0.135111i	0.771428	+	0.636317i	$0.219543\pi$
$434$	−20.9389	+	20.9389i	−1.00510	+	1.00510i
$435$	1.40798	+	0.583202i	0.0675072	+	0.0279624i
$436$	4.08190	−	9.85457i	0.195487	−	0.471949i
$437$	−10.7504	+	4.45294i	−0.514259	+	0.213013i
$438$		−	8.45990i		−	0.404230i
$439$	−1.07029	−	2.58391i	−0.0510821	−	0.123323i	0.896278	−	0.443492i	$-0.146260\pi$
$439$	−1.07029	−	2.58391i	−0.0510821	−	0.123323i	−0.947361	+	0.320169i	$0.896260\pi$
$440$	0.100197	+	0.100197i	0.00477672	+	0.00477672i
$441$	−11.8061			−0.562194
$442$		0			0
$443$	9.88565			0.469682			0.234841	−	0.972034i	$-0.424543\pi$
$443$	9.88565			0.469682			0.234841	+	0.972034i	$0.424543\pi$
$444$	−4.61331	−	4.61331i	−0.218938	−	0.218938i
$445$	1.30080	+	3.14040i	0.0616636	+	0.148869i
$446$		−	8.35574i		−	0.395656i
$447$	11.2541	−	4.66160i	0.532301	−	0.220486i
$448$	16.5881	−	40.0472i	0.783715	−	1.89205i
$449$	37.0007	+	15.3262i	1.74617	+	0.723287i	0.998227	+	0.0595234i	$0.0189581\pi$
$449$	37.0007	+	15.3262i	1.74617	+	0.723287i	0.747942	+	0.663764i	$0.231042\pi$
$450$	−7.12923	+	7.12923i	−0.336075	+	0.336075i
$451$	6.11518	−	6.11518i	0.287953	−	0.287953i
$452$	−26.0609	−	10.7948i	−1.22580	−	0.507744i
$453$	7.41728	−	17.9069i	0.348494	−	0.841339i
$454$	33.1394	−	13.7268i	1.55531	−	0.644230i
$455$			8.14869i			0.382016i
$456$	0.698636	+	1.68666i	0.0327166	+	0.0789849i
$457$	−0.319645	−	0.319645i	−0.0149523	−	0.0149523i	0.699591	−	0.714543i	$-0.253366\pi$
$457$	−0.319645	−	0.319645i	−0.0149523	−	0.0149523i	−0.714543	+	0.699591i	$0.753366\pi$
$458$	−38.7287			−1.80967
$459$		0			0
$460$	−2.80929			−0.130984
$461$	−8.15362	−	8.15362i	−0.379752	−	0.379752i	0.491261	−	0.871013i	$-0.336536\pi$
$461$	−8.15362	−	8.15362i	−0.379752	−	0.379752i	−0.871013	+	0.491261i	$0.836536\pi$
$462$	−2.50287	−	6.04247i	−0.116444	−	0.281121i
$463$			4.41067i			0.204981i	0.994734	+	0.102491i	$0.0326811\pi$
$463$			4.41067i			0.204981i	−0.994734	+	0.102491i	$0.967319\pi$
$464$	13.7110	−	5.67929i	0.636519	−	0.263655i
$465$	−0.439784	+	1.06173i	−0.0203945	+	0.0492367i
$466$	−18.6811	−	7.73797i	−0.865385	−	0.358454i
$467$	5.90141	−	5.90141i	0.273085	−	0.273085i	−0.557256	−	0.830341i	$-0.688146\pi$
$467$	5.90141	−	5.90141i	0.273085	−	0.273085i	0.830341	+	0.557256i	$0.188146\pi$
$468$	8.67319	−	8.67319i	0.400918	−	0.400918i
$469$	−6.23673	−	2.58334i	−0.287986	−	0.119288i
$470$	0.130914	−	0.316055i	0.00603862	−	0.0145785i
$471$	1.67661	−	0.694475i	0.0772542	−	0.0319997i
$472$		−	2.95764i		−	0.136137i
$473$	1.04630	+	2.52599i	0.0481089	+	0.116145i
$474$	−1.18739	−	1.18739i	−0.0545384	−	0.0545384i
$475$	15.9553			0.732078
$476$		0			0
$477$	−10.1329			−0.463952
$478$	20.8927	+	20.8927i	0.955611	+	0.955611i
$479$	−4.88417	−	11.7914i	−0.223163	−	0.538764i	0.772153	−	0.635437i	$-0.219180\pi$
$479$	−4.88417	−	11.7914i	−0.223163	−	0.538764i	−0.995316	+	0.0966727i	$0.969180\pi$
$480$		−	2.82219i		−	0.128815i
$481$	14.3458	−	5.94221i	0.654111	−	0.270941i
$482$	5.04170	−	12.1717i	0.229643	−	0.554407i
$483$	14.2562	+	5.90510i	0.648678	+	0.268691i
$484$	−16.8026	+	16.8026i	−0.763756	+	0.763756i
$485$	−0.436051	+	0.436051i	−0.0198000	+	0.0198000i
$486$	1.90914	+	0.790791i	0.0866003	+	0.0358710i
$487$	4.91528	−	11.8665i	0.222732	−	0.537724i	−0.772527	−	0.634982i	$-0.781007\pi$
$487$	4.91528	−	11.8665i	0.222732	−	0.537724i	0.995259	+	0.0972585i	$0.0310074\pi$
$488$	−1.82949	+	0.757799i	−0.0828170	+	0.0343039i
$489$		−	14.7091i		−	0.665168i
$490$	3.24689	+	7.83869i	0.146680	+	0.354116i
$491$	−14.4695	−	14.4695i	−0.652998	−	0.652998i	0.300716	−	0.953714i	$-0.402774\pi$
$491$	−14.4695	−	14.4695i	−0.652998	−	0.652998i	−0.953714	+	0.300716i	$0.902774\pi$
$492$	26.9000			1.21275
$493$		0			0
$494$	−36.5114			−1.64273
$495$	−0.179479	−	0.179479i	−0.00806699	−	0.00806699i
$496$	4.28267	+	10.3393i	0.192297	+	0.464247i
$497$			38.8615i			1.74318i
$498$	−13.7716	+	5.70438i	−0.617120	+	0.255619i
$499$	2.71128	−	6.54560i	0.121373	−	0.293021i	−0.851502	−	0.524352i	$-0.824308\pi$
$499$	2.71128	−	6.54560i	0.121373	−	0.293021i	0.972875	+	0.231330i	$0.0743078\pi$
$500$	7.20590	+	2.98478i	0.322257	+	0.133483i
$501$	−5.68110	+	5.68110i	−0.253813	+	0.253813i
$502$	40.0816	−	40.0816i	1.78893	−	1.78893i
$503$	−16.9323	−	7.01359i	−0.754974	−	0.312720i	−0.0282046	−	0.999602i	$-0.508979\pi$
$503$	−16.9323	−	7.01359i	−0.754974	−	0.312720i	−0.726769	+	0.686882i	$0.758979\pi$
$504$	0.926469	−	2.23669i	0.0412682	−	0.0996303i
$505$	−4.69390	+	1.94428i	−0.208876	+	0.0865192i
$506$			5.36647i			0.238569i
$507$	6.19670	+	14.9602i	0.275205	+	0.664404i
$508$	−2.90626	−	2.90626i	−0.128945	−	0.128945i
$509$	−9.62950			−0.426820			−0.213410	−	0.976963i	$-0.568457\pi$
$509$	−9.62950			−0.426820			−0.213410	+	0.976963i	$0.568457\pi$
$510$		0			0
$511$	17.7538			0.785383
$512$	−22.1071	−	22.1071i	−0.977004	−	0.977004i
$513$	−1.25144	−	3.02123i	−0.0552522	−	0.133391i
$514$			1.35843i			0.0599179i
$515$	−0.919802	+	0.380994i	−0.0405313	+	0.0167886i
$516$	−3.25450	+	7.85706i	−0.143271	+	0.345888i
$517$	−0.320972	−	0.132951i	−0.0141163	−	0.00584718i
$518$	18.2107	−	18.2107i	0.800133	−	0.800133i
$519$	−8.51166	+	8.51166i	−0.373620	+	0.373620i
$520$	−0.969162	−	0.401440i	−0.0425006	−	0.0176043i
$521$	1.24172	−	2.99778i	0.0544008	−	0.131335i	−0.894342	−	0.447383i	$-0.852356\pi$
$521$	1.24172	−	2.99778i	0.0544008	−	0.131335i	0.948743	+	0.316048i	$0.102356\pi$
$522$	8.36597	−	3.46530i	0.366168	−	0.151672i
$523$			6.77444i			0.296226i	0.988970	+	0.148113i	$0.0473199\pi$
$523$			6.77444i			0.296226i	−0.988970	+	0.148113i	$0.952680\pi$
$524$	−5.54846	−	13.3952i	−0.242385	−	0.585170i
$525$	−14.9613	−	14.9613i	−0.652965	−	0.652965i
$526$	19.6480			0.856695
$527$		0			0
$528$	−2.47175			−0.107569
$529$	7.31059	+	7.31059i	0.317852	+	0.317852i
$530$	2.78673	+	6.72777i	0.121048	+	0.292236i
$531$			5.29790i			0.229909i
$532$	−29.7433	+	12.3201i	−1.28954	+	0.534144i
$533$	−24.5004	+	59.1492i	−1.06123	+	2.56204i
$534$	18.6598	+	7.72912i	0.807487	+	0.334472i
$535$	1.55372	−	1.55372i	0.0671734	−	0.0671734i
$536$	0.614498	−	0.614498i	0.0265423	−	0.0265423i
$537$	−8.36317	−	3.46414i	−0.360898	−	0.149489i
$538$	13.6629	−	32.9850i	0.589047	−	1.42209i
$539$	7.96065	−	3.29741i	0.342889	−	0.142029i
$540$		−	0.789510i		−	0.0339751i
$541$	9.42462	+	22.7531i	0.405196	+	0.978230i	0.986384	+	0.164460i	$0.0525883\pi$
$541$	9.42462	+	22.7531i	0.405196	+	0.978230i	−0.581188	+	0.813770i	$0.697412\pi$
$542$	31.1084	+	31.1084i	1.33622	+	1.33622i
$543$	9.60212			0.412067
$544$		0			0
$545$	1.63406			0.0699953
$546$	34.2368	+	34.2368i	1.46520	+	1.46520i
$547$	12.2978	+	29.6894i	0.525814	+	1.26943i	0.934243	+	0.356637i	$0.116077\pi$
$547$	12.2978	+	29.6894i	0.525814	+	1.26943i	−0.408429	+	0.912790i	$0.633923\pi$
$548$		−	5.17950i		−	0.221257i
$549$	3.27708	−	1.35741i	0.139862	−	0.0579329i
$550$	2.81595	−	6.79831i	0.120073	−	0.289881i
$551$	−13.2392	−	5.48387i	−0.564010	−	0.233621i
$552$	−1.40464	+	1.40464i	−0.0597856	+	0.0597856i
$553$	2.49183	−	2.49183i	0.105963	−	0.105963i
$554$	21.6302	+	8.95953i	0.918980	+	0.380654i
$555$	0.382482	−	0.923394i	0.0162355	−	0.0391959i
$556$	−34.8679	+	14.4428i	−1.47873	+	0.612509i
$557$		−	43.4415i		−	1.84068i	−0.391124	−	0.920338i	$-0.627914\pi$
$557$		−	43.4415i		−	1.84068i	0.391124	−	0.920338i	$-0.372086\pi$
$558$	2.61313	+	6.30864i	0.110622	+	0.267066i
$559$	−14.3124	−	14.3124i	−0.605348	−	0.605348i
$560$	5.10771			0.215840
$561$		0			0
$562$	39.3105			1.65821
$563$	−10.1814	−	10.1814i	−0.429093	−	0.429093i	0.459226	−	0.888319i	$-0.348127\pi$
$563$	−10.1814	−	10.1814i	−0.429093	−	0.429093i	−0.888319	+	0.459226i	$0.848127\pi$
$564$	−0.413542	−	0.998380i	−0.0174133	−	0.0420394i
$565$		−	4.32134i		−	0.181800i
$566$	22.4095	−	9.28232i	0.941942	−	0.390165i
$567$	−1.65954	+	4.00649i	−0.0696943	+	0.168257i
$568$	−4.62199	−	1.91449i	−0.193934	−	0.0803302i
$569$	11.8867	−	11.8867i	0.498317	−	0.498317i	−0.412597	−	0.910914i	$-0.635378\pi$
$569$	11.8867	−	11.8867i	0.498317	−	0.498317i	0.910914	+	0.412597i	$0.135378\pi$
$570$	−1.66179	+	1.66179i	−0.0696049	+	0.0696049i
$571$	20.9654	+	8.68415i	0.877374	+	0.363420i	0.775478	−	0.631375i	$-0.217509\pi$
$571$	20.9654	+	8.68415i	0.877374	+	0.363420i	0.101896	+	0.994795i	$0.467509\pi$
$572$	−3.42580	+	8.27060i	−0.143240	+	0.345811i
$573$	17.4827	−	7.24157i	0.730350	−	0.302521i
$574$			106.186i			4.43212i
$575$	6.64376	+	16.0394i	0.277064	+	0.668891i
$576$	−7.06795	−	7.06795i	−0.294498	−	0.294498i
$577$	20.5881			0.857095			0.428548	−	0.903519i	$-0.359025\pi$
$577$	20.5881			0.857095			0.428548	+	0.903519i	$0.359025\pi$
$578$		0			0
$579$	24.8450			1.03252
$580$	−2.44636	−	2.44636i	−0.101580	−	0.101580i
$581$	−11.9711	−	28.9009i	−0.496646	−	1.19901i
$582$			3.66415i			0.151884i
$583$	6.83244	−	2.83009i	0.282971	−	0.117210i
$584$	−0.874632	+	2.11155i	−0.0361925	+	0.0873765i
$585$	1.73602	+	0.719082i	0.0717755	+	0.0297304i
$586$	−30.6189	+	30.6189i	−1.26485	+	1.26485i
$587$	−7.43305	+	7.43305i	−0.306795	+	0.306795i	−0.843665	−	0.536870i	$-0.819606\pi$
$587$	−7.43305	+	7.43305i	−0.306795	+	0.306795i	0.536870	+	0.843665i	$0.319606\pi$
$588$	24.7615	+	10.2565i	1.02115	+	0.422973i
$589$	4.13530	−	9.98350i	0.170392	−	0.411363i
$590$	3.51756	−	1.45702i	0.144816	−	0.0599847i
$591$		−	11.1762i		−	0.459728i
$592$	−3.72466	−	8.99212i	−0.153083	−	0.369574i
$593$	5.51139	+	5.51139i	0.226326	+	0.226326i	0.811156	−	0.584830i	$-0.198839\pi$
$593$	5.51139	+	5.51139i	0.226326	+	0.226326i	−0.584830	+	0.811156i	$0.698839\pi$
$594$	−1.50817			−0.0618809
$595$		0			0
$596$	−27.6536			−1.13274
$597$	−12.1105	−	12.1105i	−0.495650	−	0.495650i
$598$	−15.2033	−	36.7040i	−0.621709	−	1.50094i
$599$			16.8503i			0.688484i	0.938881	+	0.344242i	$0.111864\pi$
$599$			16.8503i			0.688484i	−0.938881	+	0.344242i	$0.888136\pi$
$600$	2.51648	−	1.04236i	0.102735	−	0.0425541i
$601$	11.6206	−	28.0547i	0.474016	−	1.14437i	−0.488358	−	0.872644i	$-0.662404\pi$
$601$	11.6206	−	28.0547i	0.474016	−	1.14437i	0.962373	−	0.271731i	$-0.0875961\pi$
$602$	−31.0152	−	12.8469i	−1.26409	−	0.523601i
$603$	−1.10072	+	1.10072i	−0.0448249	+	0.0448249i
$604$	−31.1133	+	31.1133i	−1.26598	+	1.26598i
$605$	−3.36320	−	1.39308i	−0.136733	−	0.0566368i
$606$	−11.5526	+	27.8904i	−0.469291	+	1.13297i
$607$	−23.1402	+	9.58497i	−0.939230	+	0.389042i	−0.799173	−	0.601101i	$-0.794729\pi$
$607$	−23.1402	+	9.58497i	−0.939230	+	0.389042i	−0.140058	+	0.990143i	$0.544729\pi$
$608$			26.5371i			1.07622i
$609$	7.27222	+	17.5567i	0.294685	+	0.711434i
$610$	−1.80252	−	1.80252i	−0.0729819	−	0.0729819i
$611$	2.57194			0.104050
$612$		0			0
$613$	−31.5000			−1.27227			−0.636137	−	0.771576i	$-0.719469\pi$
$613$	−31.5000			−1.27227			−0.636137	+	0.771576i	$0.719469\pi$
$614$	−48.8065	−	48.8065i	−1.96967	−	1.96967i
$615$	1.57702	+	3.80726i	0.0635915	+	0.153524i
$616$			1.76693i			0.0711916i
$617$	10.6751	−	4.42179i	0.429765	−	0.178014i	−0.157306	−	0.987550i	$-0.550281\pi$
$617$	10.6751	−	4.42179i	0.429765	−	0.178014i	0.587071	+	0.809535i	$0.300281\pi$
$618$	−2.26381	+	5.46532i	−0.0910637	+	0.219847i
$619$	−21.9190	−	9.07913i	−0.880998	−	0.364921i	−0.104114	−	0.994565i	$-0.533201\pi$
$619$	−21.9190	−	9.07913i	−0.880998	−	0.364921i	−0.776884	+	0.629644i	$0.783201\pi$
$620$	1.84476	−	1.84476i	0.0740875	−	0.0740875i
$621$	2.51608	−	2.51608i	0.100967	−	0.100967i
$622$	31.0109	+	12.8451i	1.24342	+	0.515042i
$623$	−16.2202	+	39.1591i	−0.649850	+	1.56888i
$624$	16.9055	−	7.00250i	0.676763	−	0.280324i
$625$		−	23.2004i		−	0.928016i
$626$	6.25935	+	15.1114i	0.250174	+	0.603974i
$627$	1.68765	+	1.68765i	0.0673982	+	0.0673982i
$628$	−4.11977			−0.164397
$629$		0			0
$630$	3.11654			0.124166
$631$	−26.0280	−	26.0280i	−1.03616	−	1.03616i	−0.999321	−	0.0368373i	$-0.988272\pi$
$631$	−26.0280	−	26.0280i	−1.03616	−	1.03616i	−0.0368373	−	0.999321i	$-0.511728\pi$
$632$	0.173607	+	0.419124i	0.00690571	+	0.0166719i
$633$		−	4.60462i		−	0.183017i
$634$	−20.6245	+	8.54295i	−0.819104	+	0.339284i
$635$	0.240954	−	0.581714i	0.00956197	−	0.0230846i
$636$	21.2522	+	8.80296i	0.842705	+	0.349060i
$637$	−45.1053	+	45.1053i	−1.78714	+	1.78714i
$638$	−4.67319	+	4.67319i	−0.185013	+	0.185013i
$639$	8.27916	+	3.42934i	0.327519	+	0.135663i
$640$	−0.588969	+	1.42190i	−0.0232811	+	0.0562054i
$641$	−33.0736	+	13.6995i	−1.30633	+	0.541099i	−0.923811	−	0.382848i	$-0.874943\pi$
$641$	−33.0736	+	13.6995i	−1.30633	+	0.541099i	−0.382518	+	0.923948i	$0.624943\pi$
$642$		−	13.0560i		−	0.515279i
$643$	−6.38557	−	15.4161i	−0.251822	−	0.607953i	0.746529	−	0.665353i	$-0.231719\pi$
$643$	−6.38557	−	15.4161i	−0.251822	−	0.607953i	−0.998351	+	0.0574003i	$0.981719\pi$
$644$	−24.7702	−	24.7702i	−0.976081	−	0.976081i
$645$	−1.30284			−0.0512991
$646$		0			0
$647$	19.2205			0.755636			0.377818	−	0.925880i	$-0.376675\pi$
$647$	19.2205			0.755636			0.377818	+	0.925880i	$0.376675\pi$
$648$	−0.394755	−	0.394755i	−0.0155074	−	0.0155074i
$649$	−1.47969	−	3.57229i	−0.0580829	−	0.140225i
$650$			54.4747i			2.13667i
$651$	−13.2392	+	5.48387i	−0.518887	+	0.214930i
$652$	−12.7786	+	30.8502i	−0.500447	+	1.20819i
$653$	−25.9238	−	10.7380i	−1.01447	−	0.420209i	−0.187390	−	0.982286i	$-0.560003\pi$
$653$	−25.9238	−	10.7380i	−1.01447	−	0.420209i	−0.827085	+	0.562076i	$0.810003\pi$
$654$	6.86552	−	6.86552i	0.268463	−	0.268463i
$655$	1.57059	−	1.57059i	0.0613679	−	0.0613679i
$656$	37.0756	+	15.3572i	1.44756	+	0.599598i
$657$	1.56669	−	3.78232i	0.0611224	−	0.147562i
$658$	3.94104	−	1.63243i	0.153638	−	0.0636388i
$659$			27.6727i			1.07797i	0.842314	+	0.538987i	$0.181193\pi$
$659$			27.6727i			1.07797i	−0.842314	+	0.538987i	$0.818807\pi$
$660$	0.220508	+	0.532354i	0.00858327	+	0.0207219i
$661$	−9.76776	−	9.76776i	−0.379922	−	0.379922i	0.491152	−	0.871074i	$-0.336576\pi$
$661$	−9.76776	−	9.76776i	−0.379922	−	0.379922i	−0.871074	+	0.491152i	$0.836576\pi$
$662$	−46.3687			−1.80217
$663$		0			0
$664$	4.02707			0.156281
$665$	−3.48742	−	3.48742i	−0.135236	−	0.135236i
$666$	−2.27265	−	5.48666i	−0.0880634	−	0.212604i
$667$		−	15.5926i		−	0.603746i
$668$	16.8507	−	6.97981i	0.651975	−	0.270057i
$669$	1.54740	−	3.73575i	0.0598259	−	0.144433i
$670$	1.03355	+	0.428110i	0.0399295	+	0.0165393i
$671$	−1.83056	+	1.83056i	−0.0706681	+	0.0706681i
$672$	24.8839	−	24.8839i	0.959917	−	0.959917i
$673$	18.0747	+	7.48680i	0.696730	+	0.288595i	0.702801	−	0.711387i	$-0.251933\pi$
$673$	18.0747	+	7.48680i	0.696730	+	0.288595i	−0.00607110	+	0.999982i	$0.501933\pi$
$674$	13.0181	−	31.4286i	0.501440	−	1.21058i
$675$	−4.50766	+	1.86713i	−0.173500	+	0.0718659i
$676$		−	36.7601i		−	1.41385i
$677$	−13.0257	−	31.4468i	−0.500618	−	1.20860i	−0.949148	−	0.314830i	$-0.898052\pi$
$677$	−13.0257	−	31.4468i	−0.500618	−	1.20860i	0.448530	−	0.893768i	$-0.351948\pi$
$678$	−18.1562	−	18.1562i	−0.697284	−	0.697284i
$679$	−7.68953			−0.295097
$680$		0			0
$681$	17.3583			0.665172
$682$	−3.52398	−	3.52398i	−0.134940	−	0.134940i
$683$	−2.55788	−	6.17527i	−0.0978746	−	0.236290i	0.867357	−	0.497687i	$-0.165817\pi$
$683$	−2.55788	−	6.17527i	−0.0978746	−	0.236290i	−0.965232	+	0.261396i	$0.915817\pi$
$684$			7.42378i			0.283855i
$685$	0.733074	−	0.303649i	0.0280093	−	0.0116018i
$686$	−16.4816	+	39.7902i	−0.629272	+	1.51920i
$687$	−17.3151	−	7.17216i	−0.660614	−	0.273635i
$688$	−8.97118	+	8.97118i	−0.342023	+	0.342023i
$689$	−38.7129	+	38.7129i	−1.47484	+	1.47484i
$690$	−2.36253	−	0.978591i	−0.0899399	−	0.0372543i
$691$	13.4152	−	32.3870i	0.510337	−	1.23206i	−0.433352	−	0.901225i	$-0.642669\pi$
$691$	13.4152	−	32.3870i	0.510337	−	1.23206i	0.943688	−	0.330836i	$-0.107331\pi$
$692$	25.2465	−	10.4574i	0.959728	−	0.397532i
$693$		−	3.16502i		−	0.120229i
$694$	16.8263	+	40.6223i	0.638718	+	1.54200i
$695$	−4.08827	−	4.08827i	−0.155077	−	0.155077i
$696$	−2.44636			−0.0927292
$697$		0			0
$698$	13.2630			0.502014
$699$	−6.91911	−	6.91911i	−0.261705	−	0.261705i
$700$	18.3815	+	44.3768i	0.694754	+	1.67729i
$701$		−	39.3006i		−	1.48436i	−0.670199	−	0.742182i	$-0.733791\pi$
$701$		−	39.3006i		−	1.48436i	0.670199	−	0.742182i	$-0.266209\pi$
$702$	10.3151	−	4.27267i	0.389320	−	0.161262i
$703$	−3.59649	+	8.68271i	−0.135644	+	0.327474i
$704$	6.73987	+	2.79175i	0.254018	+	0.105218i
$705$	0.117060	−	0.117060i	0.00440875	−	0.00440875i
$706$	14.6413	−	14.6413i	0.551031	−	0.551031i
$707$	−58.5304	−	24.2441i	−2.20126	−	0.911793i
$708$	4.60256	−	11.1116i	0.172975	−	0.417598i
$709$	−11.2801	+	4.67236i	−0.423632	+	0.175474i	−0.584306	−	0.811533i	$-0.698633\pi$
$709$	−11.2801	+	4.67236i	−0.423632	+	0.175474i	0.160674	+	0.987008i	$0.448633\pi$
$710$		−	6.44012i		−	0.241693i
$711$	−0.310974	−	0.750758i	−0.0116624	−	0.0281556i
$712$	−3.85830	−	3.85830i	−0.144596	−	0.144596i
$713$	11.7581			0.440344
$714$		0			0
$715$	−1.37141			−0.0512877
$716$	14.5311	+	14.5311i	0.543051	+	0.543051i
$717$	5.47177	+	13.2100i	0.204347	+	0.493337i
$718$		−	62.2754i		−	2.32410i
$719$	28.8601	−	11.9542i	1.07630	−	0.445818i	0.227090	−	0.973874i	$-0.427079\pi$
$719$	28.8601	−	11.9542i	1.07630	−	0.445818i	0.849209	+	0.528056i	$0.177079\pi$
$720$	0.450730	−	1.08816i	0.0167977	−	0.0405533i
$721$	−11.4694	−	4.75080i	−0.427144	−	0.176929i
$722$	−12.1367	+	12.1367i	−0.451683	+	0.451683i
$723$	4.50817	−	4.50817i	0.167661	−	0.167661i
$724$	−20.1391	−	8.34187i	−0.748462	−	0.310023i
$725$	−8.18189	+	19.7528i	−0.303868	+	0.733602i
$726$	−19.9836	+	8.27747i	−0.741660	+	0.307206i
$727$			36.9344i			1.36982i	0.728627	+	0.684910i	$0.240159\pi$
$727$			36.9344i			1.36982i	−0.728627	+	0.684910i	$0.759841\pi$
$728$	−5.00574	−	12.0849i	−0.185525	−	0.447897i
$729$	0.707107	+	0.707107i	0.0261891	+	0.0261891i
$730$	−2.94216			−0.108894
$731$		0			0
$732$	−8.05245			−0.297627
$733$	−5.86713	−	5.86713i	−0.216707	−	0.216707i	0.590402	−	0.807109i	$-0.298969\pi$
$733$	−5.86713	−	5.86713i	−0.216707	−	0.216707i	−0.807109	+	0.590402i	$0.798969\pi$
$734$	19.6405	+	47.4162i	0.724942	+	1.75017i
$735$			4.10588i			0.151448i
$736$	−26.6771	+	11.0500i	−0.983331	+	0.407309i
$737$	0.434771	−	1.04963i	0.0160150	−	0.0386636i
$738$	22.6221	+	9.37040i	0.832732	+	0.344929i
$739$	−15.0340	+	15.0340i	−0.553036	+	0.553036i	−0.927316	−	0.374280i	$-0.877890\pi$
$739$	−15.0340	+	15.0340i	−0.553036	+	0.553036i	0.374280	+	0.927316i	$0.377890\pi$
$740$	−1.60440	+	1.60440i	−0.0589790	+	0.0589790i
$741$	−16.3238	−	6.76155i	−0.599671	−	0.248392i
$742$	−34.7491	+	83.8917i	−1.27568	+	3.07976i
$743$	44.6998	−	18.5153i	1.63988	−	0.679259i	0.643592	−	0.765369i	$-0.277444\pi$
$743$	44.6998	−	18.5153i	1.63988	−	0.679259i	0.996286	+	0.0861097i	$0.0274436\pi$
$744$		−	1.84476i		−	0.0676324i
$745$	−1.62120	−	3.91392i	−0.0593962	−	0.143395i
$746$	−8.90731	−	8.90731i	−0.326120	−	0.326120i
$747$	−7.21351			−0.263929
$748$		0			0
$749$	27.3991			1.00114
$750$	5.02023	+	5.02023i	0.183313	+	0.183313i
$751$	11.1847	+	27.0023i	0.408136	+	0.985327i	0.985628	+	0.168931i	$0.0540314\pi$
$751$	11.1847	+	27.0023i	0.408136	+	0.985327i	−0.577492	+	0.816396i	$0.695969\pi$
$752$		−	1.61213i		−	0.0587883i
$753$	25.3427	−	10.4973i	0.923540	−	0.382543i
$754$	18.7231	−	45.2016i	0.681855	−	1.64614i
$755$	−6.22761	−	2.57956i	−0.226646	−	0.0938798i
$756$	6.96130	−	6.96130i	0.253180	−	0.253180i
$757$	−29.9765	+	29.9765i	−1.08951	+	1.08951i	−0.0939362	+	0.995578i	$0.529945\pi$
$757$	−29.9765	+	29.9765i	−1.08951	+	1.08951i	−0.995578	+	0.0939362i	$0.970055\pi$
$758$	53.3838	+	22.1123i	1.93899	+	0.803155i
$759$	−0.993816	+	2.39929i	−0.0360733	+	0.0870885i
$760$	0.586581	−	0.242970i	0.0212775	−	0.00881344i
$761$			15.1503i			0.549197i	0.961559	+	0.274598i	$0.0885449\pi$
$761$			15.1503i			0.549197i	−0.961559	+	0.274598i	$0.911455\pi$
$762$	−1.43171	−	3.45645i	−0.0518654	−	0.125214i
$763$	14.4079	+	14.4079i	0.521600	+	0.521600i
$764$	−42.9585			−1.55418
$765$		0			0
$766$	−74.6304			−2.69651
$767$	20.2407	+	20.2407i	0.730850	+	0.730850i
$768$	−4.15073	−	10.0207i	−0.149777	−	0.361592i
$769$			28.3540i			1.02247i	0.859440	+	0.511236i	$0.170812\pi$
$769$			28.3540i			1.02247i	−0.859440	+	0.511236i	$0.829188\pi$
$770$	−2.10143	+	0.870442i	−0.0757303	+	0.0313685i
$771$	−0.251568	+	0.607339i	−0.00906001	+	0.0218728i
$772$	−52.1087	−	21.5841i	−1.87543	−	0.776830i
$773$	−14.9910	+	14.9910i	−0.539187	+	0.539187i	−0.923290	−	0.384103i	$-0.874511\pi$
$773$	−14.9910	+	14.9910i	−0.539187	+	0.539187i	0.384103	+	0.923290i	$0.374511\pi$
$774$	−5.47388	+	5.47388i	−0.196755	+	0.196755i
$775$	−14.8953	−	6.16984i	−0.535055	−	0.221627i
$776$	0.378820	−	0.914552i	0.0135988	−	0.0328305i
$777$	11.5142	−	4.76935i	0.413071	−	0.171100i
$778$		−	47.7855i		−	1.71319i
$779$	−14.8288	−	35.7998i	−0.531295	−	1.28266i
$780$	−3.01634	−	3.01634i	−0.108002	−	0.108002i
$781$	−6.54032			−0.234031
$782$		0			0
$783$	4.38206			0.156602
$784$	28.2726	+	28.2726i	1.00974	+	1.00974i
$785$	−0.241523	−	0.583087i	−0.00862031	−	0.0208113i
$786$		−	13.1977i		−	0.470746i
$787$	33.2768	−	13.7837i	1.18619	−	0.491336i	0.299677	−	0.954041i	$-0.403121\pi$
$787$	33.2768	−	13.7837i	1.18619	−	0.491336i	0.886512	+	0.462705i	$0.153121\pi$
$788$	−9.70935	+	23.4405i	−0.345881	+	0.835032i
$789$	8.78440	+	3.63862i	0.312733	+	0.129538i
$790$	−0.412945	+	0.412945i	−0.0146919	+	0.0146919i
$791$	38.1024	−	38.1024i	1.35476	−	1.35476i
$792$	0.376431	+	0.155923i	0.0133759	+	0.00554048i
$793$	7.33414	−	17.7062i	0.260443	−	0.628765i
$794$	8.04376	−	3.33183i	0.285462	−	0.118242i
$795$			3.52398i			0.124983i
$796$	14.8790	+	35.9211i	0.527372	+	1.27319i
$797$	−0.379043	−	0.379043i	−0.0134264	−	0.0134264i	0.700362	−	0.713788i	$-0.253022\pi$
$797$	−0.379043	−	0.379043i	−0.0134264	−	0.0134264i	−0.713788	+	0.700362i	$0.753022\pi$
$798$	−29.3049			−1.03738
$799$		0			0
$800$	39.5931			1.39983
$801$	6.91120	+	6.91120i	0.244195	+	0.244195i
$802$	4.89701	+	11.8224i	0.172919	+	0.417464i
$803$			2.98793i			0.105442i
$804$	3.26486	−	1.35235i	0.115143	−	0.0476937i
$805$	2.05366	−	4.95797i	0.0723820	−	0.174745i
$806$	34.0858	+	14.1188i	1.20062	+	0.497314i
$807$	12.2170	−	12.2170i	0.430059	−	0.430059i
$808$	5.76693	−	5.76693i	0.202880	−	0.202880i
$809$	4.58398	+	1.89874i	0.161164	+	0.0667563i	0.461807	−	0.886980i	$-0.347201\pi$
$809$	4.58398	+	1.89874i	0.161164	+	0.0667563i	−0.300643	+	0.953737i	$0.597201\pi$
$810$	0.275019	−	0.663955i	0.00966318	−	0.0233290i
$811$	−42.9855	+	17.8052i	−1.50943	+	0.625225i	−0.975439	−	0.220268i	$-0.929307\pi$
$811$	−42.9855	+	17.8052i	−1.50943	+	0.625225i	−0.533987	+	0.845493i	$0.679307\pi$
$812$		−	43.1404i		−	1.51393i
$813$	8.14723	+	19.6692i	0.285736	+	0.689827i
$814$	3.06483	+	3.06483i	0.107422	+	0.107422i
$815$	−5.11548			−0.179188
$816$		0			0
$817$	12.2506			0.428594
$818$	50.5622	+	50.5622i	1.76787	+	1.76787i
$819$	8.96657	+	21.6472i	0.313317	+	0.756415i
$820$		−	9.35521i		−	0.326698i
$821$	−28.9219	+	11.9798i	−1.00938	+	0.418099i	−0.825229	−	0.564799i	$-0.808954\pi$
$821$	−28.9219	+	11.9798i	−1.00938	+	0.418099i	−0.184152	+	0.982898i	$0.558954\pi$
$822$	1.80424	−	4.35581i	0.0629299	−	0.151926i
$823$	42.1814	+	17.4721i	1.47035	+	0.609039i	0.966939	−	0.255008i	$-0.0820782\pi$
$823$	42.1814	+	17.4721i	1.47035	+	0.609039i	0.503411	+	0.864047i	$0.332078\pi$
$824$	1.13007	−	1.13007i	0.0393678	−	0.0393678i
$825$	2.51796	−	2.51796i	0.0876640	−	0.0876640i
$826$	43.8621	+	18.1683i	1.52616	+	0.632156i
$827$	−0.279298	+	0.674285i	−0.00971214	+	0.0234472i	−0.928661	−	0.370929i	$-0.879039\pi$
$827$	−0.279298	+	0.674285i	−0.00971214	+	0.0234472i	0.918949	+	0.394376i	$0.129039\pi$
$828$	−7.46295	+	3.09125i	−0.259355	+	0.107428i
$829$			24.0881i			0.836616i	0.908305	+	0.418308i	$0.137377\pi$
$829$			24.0881i			0.836616i	−0.908305	+	0.418308i	$0.862623\pi$
$830$	1.98385	+	4.78944i	0.0688605	+	0.166244i
$831$	8.01140	+	8.01140i	0.277912	+	0.277912i
$832$	−54.0065			−1.87234
$833$		0			0
$834$	−34.3539			−1.18958
$835$	1.97576	+	1.97576i	0.0683739	+	0.0683739i
$836$	−2.07345	−	5.00574i	−0.0717117	−	0.173127i
$837$			3.30445i			0.114218i
$838$	−11.1408	+	4.61466i	−0.384852	+	0.159411i
$839$	12.4886	−	30.1502i	0.431155	−	1.04090i	−0.547760	−	0.836635i	$-0.684519\pi$
$839$	12.4886	−	30.1502i	0.431155	−	1.04090i	0.978916	−	0.204265i	$-0.0654806\pi$
$840$	−0.777871	−	0.322205i	−0.0268391	−	0.0111171i
$841$	−6.92789	+	6.92789i	−0.238893	+	0.238893i
$842$	−39.4743	+	39.4743i	−1.36037	+	1.36037i
$843$	17.5753	+	7.27991i	0.605324	+	0.250733i
$844$	−4.00027	+	9.65752i	−0.137695	+	0.332425i
$845$	5.20280	−	2.15507i	0.178982	−	0.0741367i
$846$		−	0.983662i		−	0.0338190i
$847$	−17.3710	−	41.9373i	−0.596874	−	1.44098i
$848$	24.2657	+	24.2657i	0.833289	+	0.833289i
$849$	11.7380			0.402848
$850$		0			0
$851$	−10.2261			−0.350546
$852$	−14.3851	−	14.3851i	−0.492825	−	0.492825i
$853$	−9.10191	−	21.9739i	−0.311643	−	0.752374i	−0.999644	−	0.0266640i	$-0.991512\pi$
$853$	−9.10191	−	21.9739i	−0.311643	−	0.752374i	0.688001	−	0.725710i	$-0.258488\pi$
$854$		−	31.7865i		−	1.08771i
$855$	−1.05072	+	0.435221i	−0.0359337	+	0.0148842i
$856$	−1.34980	+	3.25871i	−0.0461353	+	0.111380i
$857$	39.7356	+	16.4590i	1.35734	+	0.562229i	0.938327	−	0.345750i	$-0.112376\pi$
$857$	39.7356	+	16.4590i	1.35734	+	0.562229i	0.419015	+	0.907979i	$0.362376\pi$
$858$	−5.76199	+	5.76199i	−0.196711	+	0.196711i
$859$	−4.23962	+	4.23962i	−0.144654	+	0.144654i	−0.775725	−	0.631071i	$-0.782616\pi$
$859$	−4.23962	+	4.23962i	−0.144654	+	0.144654i	0.631071	+	0.775725i	$0.282616\pi$
$860$	2.73251	+	1.13184i	0.0931777	+	0.0385955i
$861$	−19.6646	+	47.4745i	−0.670167	+	1.61793i
$862$	−33.0990	+	13.7100i	−1.12736	+	0.466966i
$863$		−	54.1552i		−	1.84346i	−0.387828	−	0.921732i	$-0.626775\pi$
$863$		−	54.1552i		−	1.84346i	0.387828	−	0.921732i	$-0.373225\pi$
$864$	−3.10545	−	7.49721i	−0.105649	−	0.255060i
$865$	2.96016	+	2.96016i	0.100648	+	0.100648i
$866$	−8.21621			−0.279198
$867$		0			0
$868$	32.5315			1.10419
$869$	0.419370	+	0.419370i	0.0142262	+	0.0142262i
$870$	−1.20515	−	2.90949i	−0.0408584	−	0.0986410i
$871$			8.41067i			0.284985i
$872$	−2.42339	+	1.00380i	−0.0820665	+	0.0339930i
$873$	−0.678563	+	1.63820i	−0.0229659	+	0.0554446i
$874$	22.2149	+	9.20173i	0.751431	+	0.311253i
$875$	−10.5354	+	10.5354i	−0.356161	+	0.356161i
$876$	−6.57180	+	6.57180i	−0.222041	+	0.222041i
$877$	−24.6822	−	10.2237i	−0.833460	−	0.345231i	−0.0751887	−	0.997169i	$-0.523956\pi$
$877$	−24.6822	−	10.2237i	−0.833460	−	0.345231i	−0.758272	+	0.651939i	$0.773956\pi$
$878$	−2.21169	+	5.33948i	−0.0746408	+	0.180199i
$879$	−19.3597	+	8.01904i	−0.652985	+	0.270475i
$880$			0.859617i			0.0289777i
$881$	−4.63852	−	11.1984i	−0.156276	−	0.377283i	0.826278	−	0.563263i	$-0.190454\pi$
$881$	−4.63852	−	11.1984i	−0.156276	−	0.377283i	−0.982554	+	0.185980i	$0.940454\pi$
$882$	17.2509	+	17.2509i	0.580869	+	0.580869i
$883$	44.5718			1.49996			0.749981	−	0.661460i	$-0.230063\pi$
$883$	44.5718			1.49996			0.749981	+	0.661460i	$0.230063\pi$
$884$		0			0
$885$	1.84249			0.0619345
$886$	−14.4448	−	14.4448i	−0.485284	−	0.485284i
$887$	8.41668	+	20.3197i	0.282604	+	0.682267i	0.999895	−	0.0145071i	$-0.00461792\pi$
$887$	8.41668	+	20.3197i	0.282604	+	0.682267i	−0.717290	+	0.696774i	$0.754618\pi$
$888$			1.60440i			0.0538402i
$889$	7.25367	−	3.00457i	0.243280	−	0.100770i
$890$	2.68801	−	6.48944i	0.0901024	−	0.217526i
$891$	−0.674285	−	0.279298i	−0.0225894	−	0.00935683i
$892$	−6.49089	+	6.49089i	−0.217331	+	0.217331i
$893$	−1.10072	+	1.10072i	−0.0368343	+	0.0368343i
$894$	−23.2559	−	9.63291i	−0.777794	−	0.322173i
$895$	−1.20475	+	2.90852i	−0.0402703	+	0.0972211i
$896$	−17.7303	+	7.34413i	−0.592328	+	0.245350i
$897$		−	19.2254i		−	0.641919i
$898$	−31.6706	−	76.4595i	−1.05686	−	2.55149i
$899$	10.2391	+	10.2391i	0.341493	+	0.341493i
$900$	11.0762			0.369207
$901$		0			0
$902$	−17.8709			−0.595036
$903$	−11.4874	−	11.4874i	−0.382277	−	0.382277i
$904$	2.65460	+	6.40878i	0.0882908	+	0.213153i
$905$		−	3.33940i		−	0.111005i
$906$	−37.0035	+	15.3273i	−1.22936	+	0.509217i
$907$	6.11147	−	14.7544i	0.202928	−	0.489912i	−0.789350	−	0.613943i	$-0.789582\pi$
$907$	6.11147	−	14.7544i	0.202928	−	0.489912i	0.992278	+	0.124032i	$0.0395824\pi$
$908$	−36.4065	−	15.0801i	−1.20819	−	0.500450i
$909$	−10.3300	+	10.3300i	−0.342626	+	0.342626i
$910$	11.9068	−	11.9068i	0.394706	−	0.394706i
$911$	−35.1451	−	14.5576i	−1.16441	−	0.482314i	−0.285068	−	0.958507i	$-0.592016\pi$
$911$	−35.1451	−	14.5576i	−1.16441	−	0.482314i	−0.879341	+	0.476193i	$0.842016\pi$
$912$	−4.23823	+	10.2320i	−0.140342	+	0.338815i
$913$	4.86396	−	2.01472i	0.160974	−	0.0666774i
$914$			0.934124i			0.0308981i
$915$	−0.472077	−	1.13969i	−0.0156064	−	0.0376771i
$916$	30.0851	+	30.0851i	0.994041	+	0.994041i
$917$	27.6965			0.914619
$918$		0			0
$919$	7.23321			0.238602			0.119301	−	0.992858i	$-0.461935\pi$
$919$	7.23321			0.238602			0.119301	+	0.992858i	$0.461935\pi$
$920$	0.488503	+	0.488503i	0.0161055	+	0.0161055i
$921$	−12.7823	−	30.8593i	−0.421192	−	1.01685i
$922$			23.8280i			0.784734i
$923$	44.7326	−	18.5288i	1.47239	−	0.609884i
$924$	−2.74962	+	6.63817i	−0.0904559	+	0.218380i
$925$	12.9545	+	5.36594i	0.425942	+	0.176431i
$926$	6.44483	−	6.44483i	0.211790	−	0.211790i
$927$	−2.02424	+	2.02424i	−0.0664849	+	0.0664849i
$928$	−32.8533	−	13.6083i	−1.07846	−	0.446713i
$929$	−16.9119	+	40.8290i	−0.554862	+	1.33956i	0.358927	+	0.933366i	$0.383143\pi$
$929$	−16.9119	+	40.8290i	−0.554862	+	1.33956i	−0.913789	+	0.406190i	$0.866857\pi$
$930$	2.19400	−	0.908785i	0.0719442	−	0.0298002i
$931$		−	38.6077i		−	1.26532i
$932$	8.50083	+	20.5228i	0.278454	+	0.672247i
$933$	11.4858	+	11.4858i	0.376028	+	0.376028i
$934$	−17.2462			−0.564312
$935$		0			0
$936$	−3.01634			−0.0985921
$937$	15.9199	+	15.9199i	0.520080	+	0.520080i	0.917595	−	0.397515i	$-0.130127\pi$
$937$	15.9199	+	15.9199i	0.520080	+	0.520080i	−0.397515	+	0.917595i	$0.630127\pi$
$938$	5.33831	+	12.8878i	0.174302	+	0.420802i
$939$			7.91531i			0.258306i
$940$	−0.347214	+	0.143821i	−0.0113249	+	0.00469091i
$941$	−0.853914	+	2.06153i	−0.0278368	+	0.0672040i	−0.937187	−	0.348828i	$-0.886580\pi$
$941$	−0.853914	+	2.06153i	−0.0278368	+	0.0672040i	0.909350	+	0.416032i	$0.136580\pi$
$942$	−3.46461	−	1.43509i	−0.112883	−	0.0467577i
$943$	29.8140	−	29.8140i	0.970876	−	0.970876i
$944$	12.6872	−	12.6872i	0.412932	−	0.412932i
$945$	1.39337	+	0.577151i	0.0453262	+	0.0187747i
$946$	2.16211	−	5.21980i	0.0702963	−	0.169710i
$947$	−12.7581	+	5.28459i	−0.414584	+	0.171726i	−0.580218	−	0.814461i	$-0.697033\pi$
$947$	−12.7581	+	5.28459i	−0.414584	+	0.171726i	0.165635	+	0.986187i	$0.447033\pi$
$948$			1.84476i			0.0599152i
$949$	−8.46487	−	20.4360i	−0.274781	−	0.663381i
$950$	−23.3137	−	23.3137i	−0.756397	−	0.756397i
$951$	−10.8030			−0.350313
$952$		0			0
$953$	−7.23736			−0.234441			−0.117221	−	0.993106i	$-0.537398\pi$
$953$	−7.23736			−0.234441			−0.117221	+	0.993106i	$0.537398\pi$
$954$	14.8061	+	14.8061i	0.479364	+	0.479364i
$955$	−2.51845	−	6.08008i	−0.0814952	−	0.196747i
$956$		−	32.4597i		−	1.04982i
$957$	−2.95476	+	1.22390i	−0.0955138	+	0.0395631i
$958$	−10.0928	+	24.3662i	−0.326084	+	0.787237i
$959$	9.14105	+	3.78635i	0.295180	+	0.122267i
$960$	−2.45807	+	2.45807i	−0.0793339	+	0.0793339i
$961$	14.1992	−	14.1992i	0.458037	−	0.458037i
$962$	−29.6446	−	12.2792i	−0.955781	−	0.395897i
$963$	2.41784	−	5.83718i	0.0779138	−	0.188101i
$964$	−13.3717	+	5.53874i	−0.430674	+	0.178391i
$965$		−	8.64052i		−	0.278148i
$966$	−12.2025	−	29.4595i	−0.392609	−	0.947843i
$967$	−7.51233	−	7.51233i	−0.241580	−	0.241580i	0.575923	−	0.817504i	$-0.304643\pi$
$967$	−7.51233	−	7.51233i	−0.241580	−	0.241580i	−0.817504	+	0.575923i	$0.804643\pi$
$968$	5.84357			0.187820
$969$		0			0
$970$	1.27431			0.0409155
$971$	18.1366	+	18.1366i	0.582032	+	0.582032i	0.935461	−	0.353429i	$-0.114984\pi$
$971$	18.1366	+	18.1366i	0.582032	+	0.582032i	−0.353429	+	0.935461i	$0.614984\pi$
$972$	−0.868752	−	2.09735i	−0.0278652	−	0.0672727i
$973$		−	72.0946i		−	2.31125i
$974$	−24.5214	+	10.1571i	−0.785717	+	0.325455i
$975$	−10.0882	+	24.3550i	−0.323080	+	0.779985i
$976$	−11.0985	−	4.59714i	−0.355253	−	0.147151i
$977$	12.2091	−	12.2091i	0.390604	−	0.390604i	−0.484299	−	0.874903i	$-0.660925\pi$
$977$	12.2091	−	12.2091i	0.390604	−	0.390604i	0.874903	+	0.484299i	$0.160925\pi$
$978$	−21.4928	+	21.4928i	−0.687264	+	0.687264i
$979$	−6.59040	−	2.72983i	−0.210630	−	0.0872459i
$980$	3.56699	−	8.61148i	0.113943	−	0.275084i
$981$	4.34092	−	1.79807i	0.138595	−	0.0574079i
$982$			42.2853i			1.34938i
$983$	13.3924	+	32.3321i	0.427151	+	1.03123i	0.980187	+	0.198076i	$0.0634694\pi$
$983$	13.3924	+	32.3321i	0.427151	+	1.03123i	−0.553035	+	0.833158i	$0.686531\pi$
$984$	−4.67761	−	4.67761i	−0.149117	−	0.149117i
$985$	−3.88683			−0.123845
$986$		0			0
$987$	2.06430			0.0657074
$988$	28.3627	+	28.3627i	0.902338	+	0.902338i
$989$	5.10113	+	12.3152i	0.162207	+	0.391601i
$990$			0.524507i			0.0166699i
$991$	21.1761	−	8.77143i	0.672681	−	0.278634i	−0.0200826	−	0.999798i	$-0.506393\pi$
$991$	21.1761	−	8.77143i	0.672681	−	0.278634i	0.692764	+	0.721165i	$0.256393\pi$
$992$	10.2618	−	24.7741i	0.325812	−	0.786579i
$993$	−20.7309	−	8.58701i	−0.657875	−	0.272501i
$994$	56.7841	−	56.7841i	1.80108	−	1.80108i
$995$	−4.21176	+	4.21176i	−0.133522	+	0.133522i
$996$	15.1293	+	6.26676i	0.479390	+	0.198570i
$997$	−22.8935	+	55.2698i	−0.725044	+	1.75041i	−0.0666028	+	0.997780i	$0.521216\pi$
$997$	−22.8935	+	55.2698i	−0.725044	+	1.75041i	−0.658441	+	0.752632i	$0.728784\pi$
$998$	−13.5261	+	5.60268i	−0.428160	+	0.177350i
$999$		−	2.87389i		−	0.0909260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.h.i.712.1		16
17.2	even	8		867.2.h.k.757.3		16
17.3	odd	16		867.2.d.f.577.1		8
17.4	even	4		867.2.h.k.733.3		16
17.5	odd	16		867.2.a.l.1.4		4
17.6	odd	16		867.2.e.g.829.1		8
17.7	odd	16		867.2.e.g.616.4		8
17.8	even	8	inner	867.2.h.i.688.1		16
17.9	even	8	inner	867.2.h.i.688.2		16
17.10	odd	16		51.2.e.a.4.4	✓	8
17.11	odd	16		51.2.e.a.13.1	yes	8
17.12	odd	16		867.2.a.k.1.4		4
17.13	even	4		867.2.h.k.733.4		16
17.14	odd	16		867.2.d.f.577.2		8
17.15	even	8		867.2.h.k.757.4		16
17.16	even	2	inner	867.2.h.i.712.2		16
51.5	even	16		2601.2.a.be.1.1		4
51.11	even	16		153.2.f.b.64.4		8
51.29	even	16		2601.2.a.bf.1.1		4
51.44	even	16		153.2.f.b.55.1		8
68.11	even	16		816.2.bd.e.625.2		8
68.27	even	16		816.2.bd.e.769.2		8
204.11	odd	16		2448.2.be.x.1441.2		8
204.95	odd	16		2448.2.be.x.1585.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.e.a.4.4	✓	8	17.10	odd	16
51.2.e.a.13.1	yes	8	17.11	odd	16
153.2.f.b.55.1		8	51.44	even	16
153.2.f.b.64.4		8	51.11	even	16
816.2.bd.e.625.2		8	68.11	even	16
816.2.bd.e.769.2		8	68.27	even	16
867.2.a.k.1.4		4	17.12	odd	16
867.2.a.l.1.4		4	17.5	odd	16
867.2.d.f.577.1		8	17.3	odd	16
867.2.d.f.577.2		8	17.14	odd	16
867.2.e.g.616.4		8	17.7	odd	16
867.2.e.g.829.1		8	17.6	odd	16
867.2.h.i.688.1		16	17.8	even	8	inner
867.2.h.i.688.2		16	17.9	even	8	inner
867.2.h.i.712.1		16	1.1	even	1	trivial
867.2.h.i.712.2		16	17.16	even	2	inner
867.2.h.k.733.3		16	17.4	even	4
867.2.h.k.733.4		16	17.13	even	4
867.2.h.k.757.3		16	17.2	even	8
867.2.h.k.757.4		16	17.15	even	8
2448.2.be.x.1441.2		8	204.11	odd	16
2448.2.be.x.1585.2		8	204.95	odd	16
2601.2.a.be.1.1		4	51.5	even	16
2601.2.a.bf.1.1		4	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-1.46119 - 1.46119i) q^{2} +(-0.382683 - 0.923880i) q^{3} +2.27016i q^{4} +(-0.321304 + 0.133089i) q^{5} +(-0.790791 + 1.90914i) q^{6} +(-4.00649 - 1.65954i) q^{7} +(0.394755 - 0.394755i) q^{8} +(-0.707107 + 0.707107i) q^{9} +(0.663955 + 0.275019i) q^{10} +(0.279298 - 0.674285i) q^{11} +(2.09735 - 0.868752i) q^{12} +5.40303i q^{13} +(3.42934 + 8.27916i) q^{14} +(0.245916 + 0.245916i) q^{15} +3.38669 q^{16} +2.06644 q^{18} +(-2.31235 - 2.31235i) q^{19} +(-0.302132 - 0.729412i) q^{20} +4.33660i q^{21} +(-1.39337 + 0.577151i) q^{22} +(1.36169 - 3.28741i) q^{23} +(-0.515772 - 0.213640i) q^{24} +(-3.45001 + 3.45001i) q^{25} +(7.89486 - 7.89486i) q^{26} +(0.923880 + 0.382683i) q^{27} +(3.76743 - 9.09538i) q^{28} +(4.04850 - 1.67694i) q^{29} -0.718659i q^{30} +(1.26456 + 3.05291i) q^{31} +(-5.73812 - 5.73812i) q^{32} -0.729840 q^{33} +1.50817 q^{35} +(-1.60525 - 1.60525i) q^{36} +(-1.09979 - 2.65513i) q^{37} +6.75758i q^{38} +(4.99175 - 2.06765i) q^{39} +(-0.0742990 + 0.179374i) q^{40} +(10.9474 + 4.53457i) q^{41} +(6.33660 - 6.33660i) q^{42} +(-2.64895 + 2.64895i) q^{43} +(1.53073 + 0.634051i) q^{44} +(0.133089 - 0.321304i) q^{45} +(-6.79323 + 2.81385i) q^{46} -0.476019i q^{47} +(-1.29603 - 3.12890i) q^{48} +(8.34815 + 8.34815i) q^{49} +10.0822 q^{50} -12.2657 q^{52} +(7.16502 + 7.16502i) q^{53} +(-0.790791 - 1.90914i) q^{54} +0.253822i q^{55} +(-2.23669 + 0.926469i) q^{56} +(-1.25144 + 3.02123i) q^{57} +(-8.36597 - 3.46530i) q^{58} +(3.74618 - 3.74618i) q^{59} +(-0.558268 + 0.558268i) q^{60} +(-3.27708 - 1.35741i) q^{61} +(2.61313 - 6.30864i) q^{62} +(4.00649 - 1.65954i) q^{63} +9.99559i q^{64} +(-0.719082 - 1.73602i) q^{65} +(1.06644 + 1.06644i) q^{66} +1.55666 q^{67} -3.55827 q^{69} +(-2.20372 - 2.20372i) q^{70} +(-3.42934 - 8.27916i) q^{71} +0.558268i q^{72} +(-3.78232 + 1.56669i) q^{73} +(-2.27265 + 5.48666i) q^{74} +(4.50766 + 1.86713i) q^{75} +(5.24941 - 5.24941i) q^{76} +(-2.23801 + 2.23801i) q^{77} +(-10.3151 - 4.27267i) q^{78} +(-0.310974 + 0.750758i) q^{79} +(-1.08816 + 0.450730i) q^{80} -1.00000i q^{81} +(-9.37040 - 22.6221i) q^{82} +(5.10072 + 5.10072i) q^{83} -9.84476 q^{84} +7.74124 q^{86} +(-3.09859 - 3.09859i) q^{87} +(-0.155923 - 0.376431i) q^{88} -9.77391i q^{89} +(-0.663955 + 0.275019i) q^{90} +(8.96657 - 21.6472i) q^{91} +(7.46295 + 3.09125i) q^{92} +(2.33660 - 2.33660i) q^{93} +(-0.695554 + 0.695554i) q^{94} +(1.05072 + 0.435221i) q^{95} +(-3.10545 + 7.49721i) q^{96} +(1.63820 - 0.678563i) q^{97} -24.3965i q^{98} +(0.279298 + 0.674285i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} + 32 q^{8} + 8 q^{15} - 24 q^{16} - 8 q^{18} + 32 q^{25} + 40 q^{26} + 16 q^{32} - 24 q^{33} + 16 q^{35} + 48 q^{42} + 48 q^{43} + 32 q^{49} + 120 q^{50} - 32 q^{52} + 16 q^{53} + 56 q^{59}+ \cdots - 48 q^{94}+O(q^{100}) \) 16 * q - 8 * q^2 + 32 * q^8 + 8 * q^15 - 24 * q^16 - 8 * q^18 + 32 * q^25 + 40 * q^26 + 16 * q^32 - 24 * q^33 + 16 * q^35 + 48 * q^42 + 48 * q^43 + 32 * q^49 + 120 * q^50 - 32 * q^52 + 16 * q^53 + 56 * q^59 + 24 * q^60 - 24 * q^66 - 16 * q^67 - 24 * q^69 - 64 * q^70 - 64 * q^76 - 40 * q^77 + 16 * q^83 - 96 * q^84 - 16 * q^86 + 8 * q^87 - 16 * q^93 - 48 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more