LMFDB - Embedded newform 624.2.cz.a.379.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,2,Mod(115,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 0, 7]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("624.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.cz (of order $12$, degree $4$, 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:	$4.98266508613$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$56$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			379.20
Character	$\chi$	$=$	624.379
Dual form			624.2.cz.a.163.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.557435 - 1.29972i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(-1.37853 + 1.44902i) q^{4} -3.18768 q^{5} +(1.39971 - 0.202049i) q^{6} +(-1.75583 + 0.470472i) q^{7} +(2.65175 + 0.983971i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.557435 - 1.29972i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(-1.37853 + 1.44902i) q^{4} -3.18768 q^{5} +(1.39971 - 0.202049i) q^{6} +(-1.75583 + 0.470472i) q^{7} +(2.65175 + 0.983971i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(1.77692 + 4.14308i) q^{10} +(2.49175 + 4.31583i) q^{11} +(-1.04285 - 1.70659i) q^{12} +(0.250604 - 3.59683i) q^{13} +(1.59024 + 2.01982i) q^{14} +(0.825031 - 3.07906i) q^{15} +(-0.199297 - 3.99503i) q^{16} +(-0.0307770 - 0.0177691i) q^{17} +(-0.167106 + 1.40431i) q^{18} +(3.25670 - 5.64077i) q^{19} +(4.39432 - 4.61900i) q^{20} -1.81776i q^{21} +(4.22038 - 5.64437i) q^{22} +(-2.42918 + 1.40249i) q^{23} +(-1.63677 + 2.30673i) q^{24} +5.16128 q^{25} +(-4.81456 + 1.67928i) q^{26} +(0.707107 - 0.707107i) q^{27} +(1.73874 - 3.19278i) q^{28} +(-5.57940 - 1.49499i) q^{29} +(-4.46181 + 0.644067i) q^{30} +(-3.84024 - 3.84024i) q^{31} +(-5.08132 + 2.48600i) q^{32} +(-4.81369 + 1.28982i) q^{33} +(-0.00593864 + 0.0499065i) q^{34} +(5.59701 - 1.49971i) q^{35} +(1.91835 - 0.565619i) q^{36} +(7.15487 - 4.13087i) q^{37} +(-9.14681 - 1.08843i) q^{38} +(3.40941 + 1.17299i) q^{39} +(-8.45294 - 3.13658i) q^{40} +(2.83478 - 10.5795i) q^{41} +(-2.36258 + 1.01329i) q^{42} +(12.0489 - 3.22849i) q^{43} +(-9.68867 - 2.33893i) q^{44} +(2.76061 + 1.59384i) q^{45} +(3.17695 + 2.37545i) q^{46} +(4.35547 - 4.35547i) q^{47} +(3.91049 + 0.841485i) q^{48} +(-3.20060 + 1.84787i) q^{49} +(-2.87708 - 6.70821i) q^{50} +(0.0251293 - 0.0251293i) q^{51} +(4.86640 + 5.32148i) q^{52} +(6.42703 + 6.42703i) q^{53} +(-1.31321 - 0.524873i) q^{54} +(-7.94289 - 13.7575i) q^{55} +(-5.11895 - 0.480105i) q^{56} +(4.60567 + 4.60567i) q^{57} +(1.16708 + 8.08500i) q^{58} +(0.00934508 - 0.0161862i) q^{59} +(3.32427 + 5.44007i) q^{60} +(0.759826 + 2.83571i) q^{61} +(-2.85054 + 7.13191i) q^{62} +(1.75583 + 0.470472i) q^{63} +(6.06360 + 5.21850i) q^{64} +(-0.798846 + 11.4655i) q^{65} +(4.35973 + 5.53744i) q^{66} +(-4.23595 - 7.33688i) q^{67} +(0.0681747 - 0.0201011i) q^{68} +(-0.725981 - 2.70940i) q^{69} +(-5.06917 - 6.43854i) q^{70} +(-0.0593426 - 0.221470i) q^{71} +(-1.80450 - 2.17802i) q^{72} +(-6.25663 + 6.25663i) q^{73} +(-9.35734 - 6.99662i) q^{74} +(-1.33584 + 4.98542i) q^{75} +(3.68410 + 12.4950i) q^{76} +(-6.40556 - 6.40556i) q^{77} +(-0.375964 - 5.08514i) q^{78} -3.65771i q^{79} +(0.635293 + 12.7349i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-15.3306 + 2.21299i) q^{82} +11.6463 q^{83} +(2.63397 + 2.50585i) q^{84} +(0.0981070 + 0.0566421i) q^{85} +(-10.9126 - 13.8605i) q^{86} +(2.88811 - 5.00235i) q^{87} +(2.36085 + 13.8963i) q^{88} +(-7.45501 - 1.99756i) q^{89} +(0.532680 - 4.47647i) q^{90} +(1.25219 + 6.43331i) q^{91} +(1.31648 - 5.45330i) q^{92} +(4.70331 - 2.71546i) q^{93} +(-8.08878 - 3.23299i) q^{94} +(-10.3813 + 17.9810i) q^{95} +(-1.08615 - 5.55160i) q^{96} +(1.18978 + 4.44032i) q^{97} +(4.18583 + 3.12981i) q^{98} -4.98350i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q+O(q^{10}) $ 224 * q	$ 224 q + 8 q^{10} - 32 q^{14} + 48 q^{16} - 52 q^{20} + 8 q^{22} - 12 q^{24} + 224 q^{25} + 16 q^{26} - 52 q^{28} - 24 q^{34} + 40 q^{38} - 40 q^{40} + 16 q^{43} - 56 q^{44} + 56 q^{46} + 56 q^{50} - 56 q^{52} - 32 q^{55} + 20 q^{56} + 32 q^{58} - 32 q^{59} + 16 q^{60} - 24 q^{68} - 8 q^{70} + 64 q^{71} + 16 q^{73} - 96 q^{74} + 16 q^{75} - 44 q^{76} - 24 q^{78} - 100 q^{80} + 112 q^{81} + 72 q^{82} - 80 q^{83} - 64 q^{86} - 60 q^{88} + 16 q^{89} + 40 q^{91} - 48 q^{92} - 152 q^{94} - 88 q^{98}+O(q^{100}) $ 224 * q + 8 * q^10 - 32 * q^14 + 48 * q^16 - 52 * q^20 + 8 * q^22 - 12 * q^24 + 224 * q^25 + 16 * q^26 - 52 * q^28 - 24 * q^34 + 40 * q^38 - 40 * q^40 + 16 * q^43 - 56 * q^44 + 56 * q^46 + 56 * q^50 - 56 * q^52 - 32 * q^55 + 20 * q^56 + 32 * q^58 - 32 * q^59 + 16 * q^60 - 24 * q^68 - 8 * q^70 + 64 * q^71 + 16 * q^73 - 96 * q^74 + 16 * q^75 - 44 * q^76 - 24 * q^78 - 100 * q^80 + 112 * q^81 + 72 * q^82 - 80 * q^83 - 64 * q^86 - 60 * q^88 + 16 * q^89 + 40 * q^91 - 48 * q^92 - 152 * q^94 - 88 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$-1$	$e\left(\frac{1}{12}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.557435	−	1.29972i	−0.394166	−	0.919039i
$2$	−0.557435	−	1.29972i	−0.394166	−	0.919039i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$4$	−1.37853	+	1.44902i	−0.689266	+	0.724508i
$5$	−3.18768			−1.42557			−0.712786	−	0.701381i	$-0.752567\pi$
$5$	−3.18768			−1.42557			−0.712786	+	0.701381i	$0.752567\pi$
$6$	1.39971	−	0.202049i	0.571427	−	0.0824862i
$7$	−1.75583	+	0.470472i	−0.663640	+	0.177822i	−0.574888	−	0.818232i	$-0.694954\pi$
$7$	−1.75583	+	0.470472i	−0.663640	+	0.177822i	−0.0887517	+	0.996054i	$0.528288\pi$
$8$	2.65175	+	0.983971i	0.937537	+	0.347886i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	1.77692	+	4.14308i	0.561912	+	1.31016i
$11$	2.49175	+	4.31583i	0.751290	+	1.30127i	0.947198	+	0.320651i	$0.103902\pi$
$11$	2.49175	+	4.31583i	0.751290	+	1.30127i	−0.195907	+	0.980622i	$0.562765\pi$
$12$	−1.04285	−	1.70659i	−0.301045	−	0.492651i
$13$	0.250604	−	3.59683i	0.0695052	−	0.997582i
$13$	0.250604	−	3.59683i	0.0695052	−	0.997582i
$14$	1.59024	+	2.01982i	0.425010	+	0.539820i
$15$	0.825031	−	3.07906i	0.213022	−	0.795010i
$16$	−0.199297	−	3.99503i	−0.0498242	−	0.998758i
$17$	−0.0307770	−	0.0177691i	−0.00746451	−	0.00430964i	0.496263	−	0.868172i	$-0.334705\pi$
$17$	−0.0307770	−	0.0177691i	−0.00746451	−	0.00430964i	−0.503728	+	0.863863i	$0.668038\pi$
$18$	−0.167106	+	1.40431i	−0.0393873	+	0.330998i
$19$	3.25670	−	5.64077i	0.747139	−	1.29408i	−0.202050	−	0.979375i	$-0.564760\pi$
$19$	3.25670	−	5.64077i	0.747139	−	1.29408i	0.949189	−	0.314707i	$-0.101906\pi$
$20$	4.39432	−	4.61900i	0.982599	−	1.03284i
$21$		−	1.81776i		−	0.396669i
$22$	4.22038	−	5.64437i	0.899788	−	1.20338i
$23$	−2.42918	+	1.40249i	−0.506519	+	0.292439i	−0.731402	−	0.681947i	$-0.761133\pi$
$23$	−2.42918	+	1.40249i	−0.506519	+	0.292439i	0.224883	+	0.974386i	$0.427800\pi$
$24$	−1.63677	+	2.30673i	−0.334104	+	0.470859i
$25$	5.16128			1.03226
$26$	−4.81456	+	1.67928i	−0.944213	+	0.329335i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	1.73874	−	3.19278i	0.328591	−	0.603379i
$29$	−5.57940	−	1.49499i	−1.03607	−	0.277614i	−0.299585	−	0.954070i	$-0.596848\pi$
$29$	−5.57940	−	1.49499i	−1.03607	−	0.277614i	−0.736483	+	0.676456i	$0.763515\pi$
$30$	−4.46181	+	0.644067i	−0.814611	+	0.117590i
$31$	−3.84024	−	3.84024i	−0.689727	−	0.689727i	0.272444	−	0.962172i	$-0.412168\pi$
$31$	−3.84024	−	3.84024i	−0.689727	−	0.689727i	−0.962172	+	0.272444i	$0.912168\pi$
$32$	−5.08132	+	2.48600i	−0.898259	+	0.439467i
$33$	−4.81369	+	1.28982i	−0.837956	+	0.224530i
$34$	−0.00593864	+	0.0499065i	−0.00101847	+	0.00855889i
$35$	5.59701	−	1.49971i	0.946067	−	0.253498i
$36$	1.91835	−	0.565619i	0.319725	−	0.0942698i
$37$	7.15487	−	4.13087i	1.17625	−	0.679110i	0.221109	−	0.975249i	$-0.429032\pi$
$37$	7.15487	−	4.13087i	1.17625	−	0.679110i	0.955145	+	0.296139i	$0.0956991\pi$
$38$	−9.14681	−	1.08843i	−1.48381	−	0.176566i
$39$	3.40941	+	1.17299i	0.545943	+	0.187829i
$40$	−8.45294	−	3.13658i	−1.33653	−	0.495937i
$41$	2.83478	−	10.5795i	0.442718	−	1.65225i	−0.279174	−	0.960241i	$-0.590061\pi$
$41$	2.83478	−	10.5795i	0.442718	−	1.65225i	0.721892	−	0.692006i	$-0.243273\pi$
$42$	−2.36258	+	1.01329i	−0.364554	+	0.156353i
$43$	12.0489	−	3.22849i	1.83744	−	0.492340i	0.838796	−	0.544446i	$-0.183260\pi$
$43$	12.0489	−	3.22849i	1.83744	−	0.492340i	0.998642	+	0.0521061i	$0.0165934\pi$
$44$	−9.68867	−	2.33893i	−1.46062	−	0.352608i
$45$	2.76061	+	1.59384i	0.411527	+	0.237595i
$46$	3.17695	+	2.37545i	0.468416	+	0.350241i
$47$	4.35547	−	4.35547i	0.635311	−	0.635311i	−0.314084	−	0.949395i	$-0.601697\pi$
$47$	4.35547	−	4.35547i	0.635311	−	0.635311i	0.949395	+	0.314084i	$0.101697\pi$
$48$	3.91049	+	0.841485i	0.564430	+	0.121458i
$49$	−3.20060	+	1.84787i	−0.457228	+	0.263981i
$50$	−2.87708	−	6.70821i	−0.406880	−	0.948684i
$51$	0.0251293	−	0.0251293i	0.00351880	−	0.00351880i
$52$	4.86640	+	5.32148i	0.674848	+	0.737956i
$53$	6.42703	+	6.42703i	0.882821	+	0.882821i	0.993820	−	0.111000i	$-0.0354053\pi$
$53$	6.42703	+	6.42703i	0.882821	+	0.882821i	−0.111000	+	0.993820i	$0.535405\pi$
$54$	−1.31321	−	0.524873i	−0.178705	−	0.0714262i
$55$	−7.94289	−	13.7575i	−1.07102	−	1.85506i
$56$	−5.11895	−	0.480105i	−0.684049	−	0.0641567i
$57$	4.60567	+	4.60567i	0.610036	+	0.610036i
$58$	1.16708	+	8.08500i	0.153245	+	1.06161i
$59$	0.00934508	−	0.0161862i	0.00121663	−	0.00210726i	−0.865416	−	0.501053i	$-0.832946\pi$
$59$	0.00934508	−	0.0161862i	0.00121663	−	0.00210726i	0.866633	+	0.498946i	$0.166279\pi$
$60$	3.32427	+	5.44007i	0.429162	+	0.702310i
$61$	0.759826	+	2.83571i	0.0972858	+	0.363076i	0.997356	−	0.0726691i	$-0.0231517\pi$
$61$	0.759826	+	2.83571i	0.0972858	+	0.363076i	−0.900070	+	0.435745i	$0.856485\pi$
$62$	−2.85054	+	7.13191i	−0.362019	+	0.905753i
$63$	1.75583	+	0.470472i	0.221213	+	0.0592739i
$64$	6.06360	+	5.21850i	0.757950	+	0.652312i
$65$	−0.798846	+	11.4655i	−0.0990847	+	1.42212i
$66$	4.35973	+	5.53744i	0.536645	+	0.681612i
$67$	−4.23595	−	7.33688i	−0.517503	−	0.896342i	−0.999793	−	0.0203304i	$-0.993528\pi$
$67$	−4.23595	−	7.33688i	−0.517503	−	0.896342i	0.482290	−	0.876012i	$-0.339805\pi$
$68$	0.0681747	−	0.0201011i	0.00826740	−	0.00243761i
$69$	−0.725981	−	2.70940i	−0.0873979	−	0.326173i
$70$	−5.06917	−	6.43854i	−0.605882	−	0.769552i
$71$	−0.0593426	−	0.221470i	−0.00704267	−	0.0262836i	0.962315	−	0.271937i	$-0.0876642\pi$
$71$	−0.0593426	−	0.221470i	−0.00704267	−	0.0262836i	−0.969358	+	0.245653i	$0.920998\pi$
$72$	−1.80450	−	2.17802i	−0.212663	−	0.256682i
$73$	−6.25663	+	6.25663i	−0.732283	+	0.732283i	−0.971072	−	0.238788i	$-0.923250\pi$
$73$	−6.25663	+	6.25663i	−0.732283	+	0.732283i	0.238788	+	0.971072i	$0.423250\pi$
$74$	−9.35734	−	6.99662i	−1.08777	−	0.813341i
$75$	−1.33584	+	4.98542i	−0.154249	+	0.575666i
$76$	3.68410	+	12.4950i	0.422596	+	1.43328i
$77$	−6.40556	−	6.40556i	−0.729981	−	0.729981i
$78$	−0.375964	−	5.08514i	−0.0425696	−	0.575779i
$79$		−	3.65771i		−	0.411524i	−0.978602	−	0.205762i	$-0.934033\pi$
$79$		−	3.65771i		−	0.411524i	0.978602	−	0.205762i	$-0.0659673\pi$
$80$	0.635293	+	12.7349i	0.0710280	+	1.42380i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−15.3306	+	2.21299i	−1.69298	+	0.244384i
$83$	11.6463			1.27835			0.639173	−	0.769063i	$-0.279277\pi$
$83$	11.6463			1.27835			0.639173	+	0.769063i	$0.279277\pi$
$84$	2.63397	+	2.50585i	0.287390	+	0.273410i
$85$	0.0981070	+	0.0566421i	0.0106412	+	0.00614370i
$86$	−10.9126	−	13.8605i	−1.17674	−	1.49461i
$87$	2.88811	−	5.00235i	0.309638	−	0.536308i
$88$	2.36085	+	13.8963i	0.251667	+	1.48135i
$89$	−7.45501	−	1.99756i	−0.790229	−	0.211741i	−0.158940	−	0.987288i	$-0.550807\pi$
$89$	−7.45501	−	1.99756i	−0.790229	−	0.211741i	−0.631290	+	0.775547i	$0.717474\pi$
$90$	0.532680	−	4.47647i	0.0561494	−	0.471862i
$91$	1.25219	+	6.43331i	0.131265	+	0.674394i
$92$	1.31648	−	5.45330i	0.137252	−	0.568546i
$93$	4.70331	−	2.71546i	0.487711	−	0.281580i
$94$	−8.08878	−	3.23299i	−0.834294	−	0.333458i
$95$	−10.3813	+	17.9810i	−1.06510	+	1.84481i
$96$	−1.08615	−	5.55160i	−0.110855	−	0.566608i
$97$	1.18978	+	4.44032i	0.120804	+	0.450846i	0.999655	−	0.0262490i	$-0.00835627\pi$
$97$	1.18978	+	4.44032i	0.120804	+	0.450846i	−0.878851	+	0.477095i	$0.841690\pi$
$98$	4.18583	+	3.12981i	0.422832	+	0.316158i
$99$		−	4.98350i		−	0.500860i
$100$	−7.11500	+	7.47878i	−0.711500	+	0.747878i
$101$	−4.56450	−	1.22305i	−0.454185	−	0.121699i	0.0244719	−	0.999701i	$-0.492210\pi$
$101$	−4.56450	−	1.22305i	−0.454185	−	0.121699i	−0.478657	+	0.878002i	$0.658876\pi$
$102$	−0.0466689	−	0.0186530i	−0.00462091	−	0.00184693i
$103$			0.445876i			0.0439334i	0.999759	+	0.0219667i	$0.00699279\pi$
$103$			0.445876i			0.0439334i	−0.999759	+	0.0219667i	$0.993007\pi$
$104$	4.20372	−	9.29133i	0.412208	−	0.911090i
$105$			5.79445i			0.565480i
$106$	4.77067	−	11.9360i	0.463369	−	1.15932i
$107$	3.02629	+	0.810891i	0.292562	+	0.0783918i	0.402115	−	0.915589i	$-0.368275\pi$
$107$	3.02629	+	0.810891i	0.292562	+	0.0783918i	−0.109553	+	0.993981i	$0.534942\pi$
$108$	0.0498397	+	1.99938i	0.00479582	+	0.192390i
$109$		−	8.59498i		−	0.823249i	−0.911353	−	0.411625i	$-0.864961\pi$
$109$		−	8.59498i		−	0.823249i	0.911353	−	0.411625i	$-0.135039\pi$
$110$	−13.4532	+	17.9924i	−1.28271	+	1.71551i
$111$	2.13829	+	7.98022i	0.202958	+	0.757449i
$112$	2.22948	+	6.92082i	0.210666	+	0.653956i
$113$	−8.94857	+	15.4994i	−0.841811	+	1.45806i	0.0465515	+	0.998916i	$0.485177\pi$
$113$	−8.94857	+	15.4994i	−0.841811	+	1.45806i	−0.888362	+	0.459143i	$0.848157\pi$
$114$	3.41871	−	8.55344i	0.320192	−	0.801103i
$115$	7.74344	−	4.47068i	0.722080	−	0.416893i
$116$	9.85765	−	6.02374i	0.915260	−	0.559290i
$117$	−2.01545	+	2.98965i	−0.186328	+	0.276393i
$118$	−0.0262467	−	0.00312324i	−0.00241620	−	0.000287517i
$119$	0.0623988	+	0.0167197i	0.00572009	+	0.00153269i
$120$	5.21748	−	7.35310i	0.476289	−	0.671243i
$121$	−6.91762	+	11.9817i	−0.628874	+	1.08924i
$122$	3.26207	−	2.56828i	0.295334	−	0.232522i
$123$	9.48536	+	5.47637i	0.855266	+	0.493788i
$124$	10.8585	−	0.270675i	0.975119	−	0.0243073i
$125$	−0.514117			−0.0459840
$126$	−0.367278	−	2.54434i	−0.0327197	−	0.226667i
$127$	−4.52242	−	7.83306i	−0.401300	−	0.695072i	0.592583	−	0.805509i	$-0.298108\pi$
$127$	−4.52242	−	7.83306i	−0.401300	−	0.695072i	−0.993883	+	0.110437i	$0.964775\pi$
$128$	3.40251	−	10.7899i	0.300742	−	0.953706i
$129$			12.4739i			1.09827i
$130$	15.3473	−	5.35302i	1.34604	−	0.469491i
$131$	−1.36764	−	1.36764i	−0.119491	−	0.119491i	0.644833	−	0.764324i	$-0.276927\pi$
$131$	−1.36764	−	1.36764i	−0.119491	−	0.119491i	−0.764324	+	0.644833i	$0.776927\pi$
$132$	4.76685	−	8.75318i	0.414901	−	0.761866i
$133$	−3.06438	+	11.4364i	−0.265715	+	0.991662i
$134$	−7.17460	+	9.59537i	−0.619791	+	0.828913i
$135$	−2.25403	+	2.25403i	−0.193996	+	0.193996i
$136$	−0.0641287	−	0.0774029i	−0.00549899	−	0.00663724i
$137$	−5.57846	−	20.8191i	−0.476600	−	1.77869i	−0.615227	−	0.788350i	$-0.710935\pi$
$137$	−5.57846	−	20.8191i	−0.476600	−	1.77869i	0.138627	−	0.990345i	$-0.455731\pi$
$138$	−3.11677	+	2.45388i	−0.265317	+	0.208889i
$139$	−5.67838	−	21.1920i	−0.481634	−	1.79748i	−0.594762	−	0.803902i	$-0.702754\pi$
$139$	−5.67838	−	21.1920i	−0.481634	−	1.79748i	0.113128	−	0.993580i	$-0.463913\pi$
$140$	−5.54255	+	10.1776i	−0.468431	+	0.860161i
$141$	3.07978	+	5.33434i	0.259365	+	0.449233i
$142$	−0.254768	+	0.200584i	−0.0213797	+	0.0168326i
$143$	16.1478	−	7.88083i	1.35034	−	0.659028i
$144$	−1.82492	+	3.55945i	−0.152077	+	0.296621i
$145$	17.7853	+	4.76556i	1.47699	+	0.395758i
$146$	11.6195	+	4.64419i	0.961638	+	0.384356i
$147$	−0.956525	−	3.56980i	−0.0788929	−	0.294432i
$148$	−3.87753	+	16.0621i	−0.318731	+	1.32029i
$149$	−3.82247	+	6.62072i	−0.313149	+	0.542391i	−0.979042	−	0.203657i	$-0.934717\pi$
$149$	−3.82247	+	6.62072i	−0.313149	+	0.542391i	0.665893	+	0.746047i	$0.268051\pi$
$150$	7.22428	−	1.04283i	0.589860	−	0.0851469i
$151$	7.53040	+	7.53040i	0.612815	+	0.612815i	0.943679	−	0.330863i	$-0.107340\pi$
$151$	7.53040	+	7.53040i	0.612815	+	0.612815i	−0.330863	+	0.943679i	$0.607340\pi$
$152$	14.1863	−	11.7534i	1.15066	−	0.953330i
$153$	0.0177691	+	0.0307770i	0.00143655	+	0.00248817i
$154$	−4.75473	+	11.8961i	−0.383147	+	0.958615i
$155$	12.2414	+	12.2414i	0.983256	+	0.983256i
$156$	−6.39967	+	3.32328i	−0.512384	+	0.266076i
$157$	5.30467	−	5.30467i	0.423359	−	0.423359i	−0.463000	−	0.886358i	$-0.653227\pi$
$157$	5.30467	−	5.30467i	0.423359	−	0.423359i	0.886358	+	0.463000i	$0.153227\pi$
$158$	−4.75399	+	2.03893i	−0.378207	+	0.162209i
$159$	−7.87147	+	4.54460i	−0.624248	+	0.360410i
$160$	16.1976	−	7.92456i	1.28053	−	0.626492i
$161$	3.60539	−	3.60539i	0.284144	−	0.284144i
$162$	0.846871	−	1.13261i	0.0665365	−	0.0889864i
$163$	12.4883	+	7.21011i	0.978157	+	0.564739i	0.901713	−	0.432335i	$-0.142310\pi$
$163$	12.4883	+	7.21011i	0.978157	+	0.564739i	0.0764437	+	0.997074i	$0.475643\pi$
$164$	11.4221	+	18.6919i	0.891915	+	1.45959i
$165$	15.3445	−	4.11154i	1.19457	−	0.320083i
$166$	−6.49204	−	15.1369i	−0.503880	−	1.17485i
$167$	5.59887	−	20.8953i	0.433253	−	1.61692i	−0.311959	−	0.950096i	$-0.600985\pi$
$167$	5.59887	−	20.8953i	0.433253	−	1.61692i	0.745212	−	0.666828i	$-0.232348\pi$
$168$	1.78863	−	4.82027i	0.137996	−	0.371892i
$169$	−12.8744	−	1.80276i	−0.990338	−	0.138674i
$170$	0.0189305	−	0.159086i	0.00145190	−	0.0122013i
$171$	−5.64077	+	3.25670i	−0.431361	+	0.249046i
$172$	−11.9316	+	21.9096i	−0.909779	+	1.67059i
$173$	−6.07993	+	1.62911i	−0.462249	+	0.123859i	−0.482425	−	0.875937i	$-0.660244\pi$
$173$	−6.07993	+	1.62911i	−0.462249	+	0.123859i	0.0201764	+	0.999796i	$0.493577\pi$
$174$	−8.11157	−	0.965240i	−0.614937	−	0.0731747i
$175$	−9.06231	+	2.42824i	−0.685047	+	0.183558i
$176$	16.7453	−	10.8147i	1.26222	−	0.815192i
$177$	0.0132159	+	0.0132159i	0.000993371	+	0.000993371i
$178$	1.55941	+	10.8029i	0.116883	+	0.809713i
$179$	−17.6054	−	4.71734i	−1.31589	−	0.352591i	−0.468451	−	0.883489i	$-0.655188\pi$
$179$	−17.6054	−	4.71734i	−1.31589	−	0.352591i	−0.847435	+	0.530899i	$0.821854\pi$
$180$	−6.11509	+	1.80301i	−0.455792	+	0.134388i
$181$	−6.07786	+	6.07786i	−0.451763	+	0.451763i	−0.895940	−	0.444176i	$-0.853496\pi$
$181$	−6.07786	+	6.07786i	−0.451763	+	0.451763i	0.444176	+	0.895940i	$0.353496\pi$
$182$	7.66348	−	5.21365i	0.568055	−	0.386461i
$183$	−2.93574			−0.217016
$184$	−7.82160	+	1.32881i	−0.576616	+	0.0979613i
$185$	−22.8074	+	13.1679i	−1.67683	+	0.968121i
$186$	−6.15112	−	4.59929i	−0.451022	−	0.337236i
$187$		−	0.177104i		−	0.0129512i
$188$	0.306991	+	12.3153i	0.0223896	+	0.898186i
$189$	−0.908882	+	1.57423i	−0.0661115	+	0.114508i
$190$	29.1571	+	3.46956i	2.11528	+	0.251708i
$191$	−8.65619	−	4.99765i	−0.626340	−	0.361617i	0.152993	−	0.988227i	$-0.451109\pi$
$191$	−8.65619	−	4.99765i	−0.626340	−	0.361617i	−0.779333	+	0.626610i	$0.784442\pi$
$192$	−6.61006	+	4.50634i	−0.477040	+	0.325217i
$193$	4.01976	−	15.0019i	0.289348	−	1.07986i	−0.656255	−	0.754540i	$-0.727860\pi$
$193$	4.01976	−	15.0019i	0.289348	−	1.07986i	0.945603	−	0.325323i	$-0.105473\pi$
$194$	5.10794	−	4.02157i	0.366729	−	0.288732i
$195$	−10.8681	−	3.73913i	−0.778281	−	0.267764i
$196$	1.73454	−	7.18506i	0.123896	−	0.513218i
$197$	2.96445	+	5.13458i	0.211208	+	0.365824i	0.952093	−	0.305809i	$-0.0989268\pi$
$197$	2.96445	+	5.13458i	0.211208	+	0.365824i	−0.740885	+	0.671632i	$0.765593\pi$
$198$	−6.47714	+	2.77798i	−0.460310	+	0.197422i
$199$	18.4968	+	10.6792i	1.31121	+	0.757025i	0.982296	−	0.187336i	$-0.0599855\pi$
$199$	18.4968	+	10.6792i	1.31121	+	0.757025i	0.328910	+	0.944361i	$0.393319\pi$
$200$	13.6865	+	5.07855i	0.967778	+	0.359108i
$201$	8.18322	−	2.19269i	0.577200	−	0.154660i
$202$	0.954788	+	6.61434i	0.0671786	+	0.465383i
$203$	10.4998			0.736942
$204$	0.00177121	+	0.0710543i	0.000124010	+	0.00497479i
$205$	−9.03636	+	33.7242i	−0.631127	+	2.35540i
$206$	0.579513	−	0.248547i	0.0403766	−	0.0173171i
$207$	2.80498			0.194959
$208$	−14.4194	−	0.284336i	−0.999806	−	0.0197152i
$209$	32.4595			2.24527
$210$	7.53115	−	3.23003i	0.519698	−	0.222893i
$211$	2.76101	−	10.3042i	0.190076	−	0.709372i	−0.803411	−	0.595425i	$-0.796984\pi$
$211$	2.76101	−	10.3042i	0.190076	−	0.709372i	0.993487	−	0.113947i	$-0.0363495\pi$
$212$	−18.1727	+	0.453002i	−1.24811	+	0.0311123i
$213$	0.229282			0.0157102
$214$	−0.633029	−	4.38534i	−0.0432730	−	0.299776i
$215$	−38.4079	+	10.2914i	−2.61940	+	0.701866i
$216$	2.57085	−	1.17930i	0.174924	−	0.0802413i
$217$	8.54952	+	4.93607i	0.580379	+	0.335082i
$218$	−11.1710	+	4.79114i	−0.756598	+	0.324497i
$219$	−4.42411	−	7.66278i	−0.298953	−	0.517803i
$220$	30.8843	+	7.45577i	2.08222	+	0.502668i
$221$	−0.0716252	+	0.106247i	−0.00481804	+	0.00714691i
$222$	9.18008	−	7.22763i	0.616126	−	0.485087i
$223$	−2.39905	+	8.95337i	−0.160652	+	0.599562i	0.837903	+	0.545820i	$0.183782\pi$
$223$	−2.39905	+	8.95337i	−0.160652	+	0.599562i	−0.998555	+	0.0537424i	$0.982885\pi$
$224$	7.75232	−	6.75560i	0.517974	−	0.451378i
$225$	−4.46980	−	2.58064i	−0.297987	−	0.172043i
$226$	25.1331	+	2.99072i	1.67183	+	0.198940i
$227$	7.26504	−	12.5834i	0.482198	−	0.835191i	−0.517593	−	0.855627i	$-0.673172\pi$
$227$	7.26504	−	12.5834i	0.482198	−	0.835191i	0.999791	+	0.0204356i	$0.00650532\pi$
$228$	−13.0228	+	0.324626i	−0.862453	+	0.0214989i
$229$		−	20.8705i		−	1.37916i	−0.724209	−	0.689580i	$-0.757795\pi$
$229$		−	20.8705i		−	1.37916i	0.724209	−	0.689580i	$-0.242205\pi$
$230$	−10.1271	−	7.57218i	−0.667760	−	0.499295i
$231$	7.84517	−	4.52941i	0.516174	−	0.298013i
$232$	−13.3242	−	9.45432i	−0.874774	−	0.620706i
$233$	9.41358			0.616704			0.308352	−	0.951272i	$-0.400222\pi$
$233$	9.41358			0.616704			0.308352	+	0.951272i	$0.400222\pi$
$234$	5.00917	+	0.952978i	0.327460	+	0.0622981i
$235$	−13.8838	+	13.8838i	−0.905682	+	0.905682i
$236$	0.0105715	+	0.0358543i	0.000688146	+	0.00233392i
$237$	3.53308	+	0.946685i	0.229498	+	0.0614938i
$238$	−0.0130524	−	0.0904210i	−0.000846060	−	0.00586113i
$239$	0.353989	+	0.353989i	0.0228976	+	0.0228976i	0.718463	−	0.695565i	$-0.244846\pi$
$239$	0.353989	+	0.353989i	0.0228976	+	0.0228976i	−0.695565	+	0.718463i	$0.744846\pi$
$240$	−12.4654	−	2.68238i	−0.804636	−	0.173147i
$241$	13.5202	−	3.62272i	0.870911	−	0.233360i	0.204429	−	0.978881i	$-0.434466\pi$
$241$	13.5202	−	3.62272i	0.870911	−	0.233360i	0.666482	+	0.745521i	$0.267799\pi$
$242$	19.4289	+	2.31195i	1.24894	+	0.148618i
$243$	−0.965926	+	0.258819i	−0.0619642	+	0.0166032i
$244$	−5.15644	−	2.80812i	−0.330107	−	0.179771i
$245$	10.2025	−	5.89040i	0.651812	−	0.376324i
$246$	1.83027	−	15.3810i	0.116694	−	0.980657i
$247$	−19.4728	−	13.1274i	−1.23902	−	0.835277i
$248$	−6.40469	−	13.9621i	−0.406698	−	0.886591i
$249$	−3.01428	+	11.2494i	−0.191022	+	0.712904i
$250$	0.286587	+	0.668206i	0.0181253	+	0.0422611i
$251$	−2.66540	+	0.714193i	−0.168239	+	0.0450794i	−0.341955	−	0.939716i	$-0.611089\pi$
$251$	−2.66540	+	0.714193i	−0.168239	+	0.0450794i	0.173716	+	0.984796i	$0.444422\pi$
$252$	−3.10219	+	1.89566i	−0.195419	+	0.119415i
$253$	−12.1058	−	6.98929i	−0.761086	−	0.439413i
$254$	−7.65982	+	10.2443i	−0.480620	+	0.642784i
$255$	−0.0801040	+	0.0801040i	−0.00501631	+	0.00501631i
$256$	−15.9206	+	1.59239i	−0.995035	+	0.0995246i
$257$	−14.8089	+	8.54994i	−0.923756	+	0.533331i	−0.884831	−	0.465911i	$-0.845727\pi$
$257$	−14.8089	+	8.54994i	−0.923756	+	0.533331i	−0.0389247	+	0.999242i	$0.512393\pi$
$258$	16.2126	−	6.95340i	1.00935	−	0.432900i
$259$	−10.6193	+	10.6193i	−0.659848	+	0.659848i
$260$	−15.5125	−	16.9632i	−0.962045	−	1.05201i
$261$	4.08440	+	4.08440i	0.252818	+	0.252818i
$262$	−1.01517	+	2.53991i	−0.0627176	+	0.156916i
$263$	−4.64381	−	8.04331i	−0.286349	−	0.495972i	0.686586	−	0.727048i	$-0.259108\pi$
$263$	−4.64381	−	8.04331i	−0.286349	−	0.495972i	−0.972936	+	0.231077i	$0.925775\pi$
$264$	−14.0339	−	1.31623i	−0.863725	−	0.0810084i
$265$	−20.4873	−	20.4873i	−1.25852	−	1.25852i
$266$	16.5723	−	2.39223i	1.01611	−	0.146677i
$267$	3.85900	−	6.68398i	0.236167	−	0.409053i
$268$	16.4706	+	3.97616i	1.00610	+	0.242883i
$269$	1.76482	+	6.58639i	0.107603	+	0.401579i	0.998627	−	0.0523758i	$-0.0166794\pi$
$269$	1.76482	+	6.58639i	0.107603	+	0.401579i	−0.891025	+	0.453955i	$0.850013\pi$
$270$	4.18607	+	1.67313i	0.254756	+	0.101823i
$271$	−22.2302	−	5.95655i	−1.35039	−	0.361835i	−0.490109	−	0.871661i	$-0.663043\pi$
$271$	−22.2302	−	5.95655i	−1.35039	−	0.361835i	−0.860277	+	0.509826i	$0.829710\pi$
$272$	−0.0648543	+	0.126496i	−0.00393237	+	0.00766996i
$273$	−6.53819	−	0.455540i	−0.395710	−	0.0275705i
$274$	−23.9493	+	18.8557i	−1.44683	+	1.13912i
$275$	12.8606	+	22.2752i	0.775524	+	1.34325i
$276$	4.92675	+	2.68304i	0.296556	+	0.161500i
$277$	−1.79074	−	6.68314i	−0.107595	−	0.401551i	0.891031	−	0.453942i	$-0.149983\pi$
$277$	−1.79074	−	6.68314i	−0.107595	−	0.401551i	−0.998627	+	0.0523907i	$0.983316\pi$
$278$	−24.3783	+	19.1935i	−1.46211	+	1.15115i
$279$	1.40562	+	5.24586i	0.0841525	+	0.314062i
$280$	16.3176	+	1.53042i	0.975161	+	0.0914600i
$281$	−0.873160	+	0.873160i	−0.0520884	+	0.0520884i	−0.732671	−	0.680583i	$-0.761727\pi$
$281$	−0.873160	+	0.873160i	−0.0520884	+	0.0520884i	0.680583	+	0.732671i	$0.261727\pi$
$282$	5.21636	−	6.97640i	0.310630	−	0.415438i
$283$	−2.48737	+	9.28299i	−0.147859	+	0.551816i	0.851753	+	0.523944i	$0.175540\pi$
$283$	−2.48737	+	9.28299i	−0.147859	+	0.551816i	−0.999611	+	0.0278725i	$0.991127\pi$
$284$	0.402719	+	0.219315i	0.0238970	+	0.0130139i
$285$	−14.6814	−	14.6814i	−0.869651	−	0.869651i
$286$	−19.2442	−	16.5945i	−1.13793	−	0.981253i
$287$			19.9095i			1.17522i
$288$	5.64355	+	0.387720i	0.332549	+	0.0228466i
$289$	−8.49937	−	14.7213i	−0.499963	−	0.865961i
$290$	−3.72027	−	25.7724i	−0.218462	−	1.51341i
$291$	−4.59696			−0.269479
$292$	−0.440992	−	17.6909i	−0.0258071	−	1.03528i
$293$	−6.68930	−	3.86207i	−0.390793	−	0.225625i	0.291711	−	0.956507i	$-0.405776\pi$
$293$	−6.68930	−	3.86207i	−0.390793	−	0.225625i	−0.682504	+	0.730882i	$0.739109\pi$
$294$	−4.10653	+	3.23315i	−0.239498	+	0.188561i
$295$	−0.0297891	+	0.0515962i	−0.00173439	+	0.00300405i
$296$	23.0376	−	3.91386i	1.33903	−	0.227489i
$297$	4.81369	+	1.28982i	0.279319	+	0.0748432i
$298$	10.7358	+	1.27752i	0.621911	+	0.0740046i
$299$	4.43575	+	9.08882i	0.256526	+	0.525620i
$300$	−5.38245	−	8.80821i	−0.310756	−	0.508542i
$301$	−19.6368	+	11.3373i	−1.13185	+	0.653473i
$302$	5.58969	−	13.9851i	0.321650	−	0.804752i
$303$	2.36276	−	4.09242i	0.135737	−	0.235103i
$304$	−23.1841	−	11.8864i	−1.32970	−	0.681734i
$305$	−2.42208	−	9.03933i	−0.138688	−	0.517591i
$306$	0.0300962	−	0.0402509i	0.00172049	−	0.00230099i
$307$			7.45875i			0.425693i	0.977086	+	0.212847i	$0.0682735\pi$
$307$			7.45875i			0.425693i	−0.977086	+	0.212847i	$0.931727\pi$
$308$	18.1120	−	0.451489i	1.03203	−	0.0257260i
$309$	−0.430683	−	0.115401i	−0.0245007	−	0.00656494i
$310$	9.08661	−	22.7342i	0.516085	−	1.29122i
$311$		−	7.23255i		−	0.410120i	−0.978749	−	0.205060i	$-0.934261\pi$
$311$		−	7.23255i		−	0.410120i	0.978749	−	0.205060i	$-0.0657390\pi$
$312$	7.88673	+	6.46525i	0.446498	+	0.366023i
$313$		−	5.55779i		−	0.314145i	−0.987587	−	0.157072i	$-0.949794\pi$
$313$		−	5.55779i		−	0.314145i	0.987587	−	0.157072i	$-0.0502056\pi$
$314$	−9.85158	−	3.93756i	−0.555957	−	0.222210i
$315$	−5.59701	−	1.49971i	−0.315356	−	0.0844993i
$316$	5.30008	+	5.04227i	0.298153	+	0.283650i
$317$		−	25.3320i		−	1.42279i	−0.702794	−	0.711393i	$-0.748065\pi$
$317$		−	25.3320i		−	1.42279i	0.702794	−	0.711393i	$-0.251935\pi$
$318$	10.2945	+	7.69738i	0.577289	+	0.431647i
$319$	−7.45030	−	27.8049i	−0.417137	−	1.55678i
$320$	−19.3288	−	16.6349i	−1.08051	−	0.929918i
$321$	−1.56652	+	2.71330i	−0.0874347	+	0.151441i
$322$	−6.69575	−	2.67622i	−0.373140	−	0.149140i
$323$	−0.200463	+	0.115737i	−0.0111540	+	0.00643979i
$324$	−1.94415	−	0.469336i	−0.108008	−	0.0260742i
$325$	1.29344	−	18.5643i	0.0717472	−	1.02976i
$326$	2.40970	−	20.2504i	0.133461	−	1.12157i
$327$	8.30211	+	2.22454i	0.459108	+	0.123018i
$328$	17.9271	−	25.2650i	0.989858	−	1.39503i
$329$	−5.59832	+	9.69658i	−0.308646	+	0.534590i
$330$	−13.8974	−	17.6516i	−0.765026	−	0.971687i
$331$	12.0671	+	6.96693i	0.663266	+	0.382937i	0.793520	−	0.608544i	$-0.208246\pi$
$331$	12.0671	+	6.96693i	0.663266	+	0.382937i	−0.130254	+	0.991481i	$0.541579\pi$
$332$	−16.0548	+	16.8756i	−0.881120	+	0.926172i
$333$	−8.26173			−0.452740
$334$	−30.2789	+	4.37080i	−1.65679	+	0.239160i
$335$	13.5028	+	23.3876i	0.737738	+	1.27780i
$336$	−7.26203	+	0.362275i	−0.396176	+	0.0197637i
$337$			32.5338i			1.77223i	0.463465	+	0.886115i	$0.346606\pi$
$337$			32.5338i			1.77223i	−0.463465	+	0.886115i	$0.653394\pi$
$338$	4.83355	+	17.7380i	0.262911	+	0.964820i
$339$	−12.6552	−	12.6552i	−0.687336	−	0.687336i
$340$	−0.217319	+	0.0640757i	−0.0117858	+	0.00347499i
$341$	7.00493	−	26.1427i	0.379338	−	1.41571i
$342$	7.37716	+	5.51601i	0.398911	+	0.298272i
$343$	13.7478	−	13.7478i	0.742311	−	0.742311i
$344$	35.1274	+	3.29459i	1.89394	+	0.177632i
$345$	2.31419	+	8.63669i	0.124592	+	0.464984i
$346$	5.50655	+	6.99407i	0.296034	+	0.376003i
$347$	2.71226	+	10.1223i	0.145602	+	0.543393i	0.999728	+	0.0233269i	$0.00742586\pi$
$347$	2.71226	+	10.1223i	0.145602	+	0.543393i	−0.854126	+	0.520066i	$0.825907\pi$
$348$	3.26714	+	11.0808i	0.175137	+	0.593994i
$349$	−4.60204	−	7.97097i	−0.246342	−	0.426676i	0.716166	−	0.697930i	$-0.245895\pi$
$349$	−4.60204	−	7.97097i	−0.246342	−	0.426676i	−0.962508	+	0.271254i	$0.912562\pi$
$350$	8.20768	+	10.4249i	0.438719	+	0.557232i
$351$	−2.36614	−	2.72055i	−0.126295	−	0.145212i
$352$	−23.3905	−	15.7356i	−1.24672	−	0.838713i
$353$	−14.4709	−	3.87748i	−0.770211	−	0.206377i	−0.147746	−	0.989025i	$-0.547202\pi$
$353$	−14.4709	−	3.87748i	−0.770211	−	0.206377i	−0.622465	+	0.782648i	$0.713869\pi$
$354$	0.00980996	−	0.0245440i	0.000521394	−	0.00130450i
$355$	0.189165	+	0.705974i	0.0100398	+	0.0374692i
$356$	13.1715	−	8.04872i	0.698087	−	0.426581i
$357$	−0.0323000	+	0.0559453i	−0.00170950	+	0.00296094i
$358$	3.68263	+	25.5116i	0.194633	+	1.34833i
$359$	18.4558	+	18.4558i	0.974057	+	0.974057i	0.999672	−	0.0256146i	$-0.00815428\pi$
$359$	18.4558	+	18.4558i	0.974057	+	0.974057i	−0.0256146	+	0.999672i	$0.508154\pi$
$360$	5.75217	+	6.94283i	0.303166	+	0.365919i
$361$	−11.7122	−	20.2861i	−0.616432	−	1.06769i
$362$	11.2875	+	4.51149i	0.593258	+	0.237119i
$363$	−9.78299	−	9.78299i	−0.513474	−	0.513474i
$364$	−11.0482	−	7.05409i	−0.579081	−	0.369735i
$365$	19.9441	−	19.9441i	1.04392	−	1.04392i
$366$	1.63649	+	3.81564i	0.0855405	+	0.199447i
$367$	−14.1660	+	8.17872i	−0.739457	+	0.426926i	−0.821872	−	0.569672i	$-0.807070\pi$
$367$	−14.1660	+	8.17872i	−0.739457	+	0.426926i	0.0824146	+	0.996598i	$0.473737\pi$
$368$	6.08711	+	9.42514i	0.317313	+	0.491320i
$369$	−7.74476	+	7.74476i	−0.403176	+	0.403176i
$370$	29.8282	+	22.3030i	1.55069	+	1.15948i
$371$	−14.3085	−	8.26101i	−0.742860	−	0.428890i
$372$	−2.54892	+	10.5585i	−0.132156	+	0.547434i
$373$	16.5649	−	4.43854i	0.857696	−	0.229819i	0.196936	−	0.980416i	$-0.436901\pi$
$373$	16.5649	−	4.43854i	0.857696	−	0.229819i	0.660760	+	0.750598i	$0.270234\pi$
$374$	−0.230186	+	0.0987242i	−0.0119026	+	0.00510490i
$375$	0.133063	−	0.496598i	0.00687135	−	0.0256442i
$376$	15.8353	−	7.26399i	0.816643	−	0.374611i
$377$	−6.77546	+	19.6935i	−0.348954	+	1.01427i
$378$	2.55270	+	0.303759i	0.131297	+	0.0156237i
$379$	−25.9556	+	14.9855i	−1.33325	+	0.769753i	−0.985797	−	0.167943i	$-0.946287\pi$
$379$	−25.9556	+	14.9855i	−1.33325	+	0.769753i	−0.347455	+	0.937697i	$0.612954\pi$
$380$	−11.7437	−	39.8300i	−0.602441	−	2.04324i
$381$	8.73665	−	2.34098i	0.447592	−	0.119932i
$382$	−1.67028	+	14.0365i	−0.0854587	+	0.718168i
$383$	15.4591	−	4.14226i	0.789924	−	0.211660i	0.158769	−	0.987316i	$-0.449248\pi$
$383$	15.4591	−	4.14226i	0.789924	−	0.211660i	0.631156	+	0.775656i	$0.282581\pi$
$384$	9.54165	+	6.07921i	0.486920	+	0.310229i
$385$	20.4188	+	20.4188i	1.04064	+	1.04064i
$386$	−21.7390	+	3.13805i	−1.10649	+	0.159723i
$387$	−12.0489	−	3.22849i	−0.612479	−	0.164113i
$388$	−8.07425	−	4.39712i	−0.409908	−	0.223230i
$389$	19.7241	−	19.7241i	1.00005	−	1.00005i	5.12196e−5	−	1.00000i	$-0.499984\pi$
$389$	19.7241	−	19.7241i	1.00005	−	1.00005i	1.00000		5.12196e-5i	$-1.63037e-5\pi$
$390$	1.19845	+	16.2098i	0.0606860	+	0.820814i
$391$	0.0996837			0.00504122
$392$	−10.3054	+	1.75079i	−0.520503	+	0.0884284i
$393$	1.67501	−	0.967066i	0.0844929	−	0.0487820i
$394$	5.02101	−	6.71514i	0.252955	−	0.338304i
$395$			11.6596i			0.586658i
$396$	7.22117	+	6.86991i	0.362877	+	0.345226i
$397$	−1.86883	+	3.23692i	−0.0937941	+	0.162456i	−0.909105	−	0.416568i	$-0.863233\pi$
$397$	−1.86883	+	3.23692i	−0.0937941	+	0.162456i	0.815311	+	0.579024i	$0.196566\pi$
$398$	3.56910	−	29.9936i	0.178903	−	1.50344i
$399$	−10.2536	−	5.91992i	−0.513322	−	0.296367i
$400$	−1.02863	−	20.6195i	−0.0514313	−	1.03097i
$401$	−1.45746	+	5.43931i	−0.0727820	+	0.271626i	−0.992721	−	0.120435i	$-0.961571\pi$
$401$	−1.45746	+	5.43931i	−0.0727820	+	0.271626i	0.919939	+	0.392061i	$0.128238\pi$
$402$	−7.41149	−	9.41360i	−0.369651	−	0.469508i
$403$	−14.7751	+	12.8503i	−0.735999	+	0.640119i
$404$	8.06454	−	4.92802i	0.401226	−	0.245178i
$405$	−1.59384	−	2.76061i	−0.0791985	−	0.137176i
$406$	−5.85296	−	13.6468i	−0.290477	−	0.677278i
$407$	35.6563	+	20.5862i	1.76742	+	1.02042i
$408$	0.0913632	−	0.0419102i	0.00452315	−	0.00207486i
$409$	35.0012	−	9.37855i	1.73070	−	0.463739i	0.750355	−	0.661035i	$-0.229883\pi$
$409$	35.0012	−	9.37855i	1.73070	−	0.463739i	0.980344	+	0.197296i	$0.0632161\pi$
$410$	48.8691	−	7.05431i	2.41347	−	0.348387i
$411$	21.5535			1.06316
$412$	−0.646081	−	0.614654i	−0.0318301	−	0.0302818i
$413$	−0.00879320	+	0.0328167i	−0.000432685	+	0.00161480i
$414$	−1.56359	−	3.64568i	−0.0768463	−	0.179175i
$415$	−37.1246			−1.82237
$416$	7.66832	+	18.8997i	0.375970	+	0.926632i
$417$	21.9396			1.07439
$418$	−18.0941	−	42.1882i	−0.885010	−	2.06349i
$419$	−5.97317	+	22.2922i	−0.291809	+	1.08904i	0.651910	+	0.758296i	$0.273968\pi$
$419$	−5.97317	+	22.2922i	−0.291809	+	1.08904i	−0.943719	+	0.330749i	$0.892699\pi$
$420$	−8.39625	−	7.98783i	−0.409695	−	0.389766i
$421$	−39.3934			−1.91992			−0.959960	−	0.280139i	$-0.909620\pi$
$421$	−39.3934			−1.91992			−0.959960	+	0.280139i	$0.909620\pi$
$422$	−14.9317	+	2.15540i	−0.726862	+	0.104923i
$423$	−5.94968	+	1.59421i	−0.289284	+	0.0775133i
$424$	10.7189	+	23.3669i	0.520556	+	1.13480i
$425$	−0.158849	−	0.0917113i	−0.00770529	−	0.00444865i
$426$	−0.127810	−	0.298002i	−0.00619241	−	0.0144383i
$427$	−2.66825	−	4.62154i	−0.129125	−	0.223652i
$428$	−5.34683	+	3.26730i	−0.258449	+	0.157931i
$429$	3.43295	+	17.6373i	0.165744	+	0.851535i
$430$	34.7858	+	44.1827i	1.67752	+	2.13068i
$431$	−1.91987	+	7.16506i	−0.0924769	+	0.345129i	−0.996625	−	0.0820909i	$-0.973840\pi$
$431$	−1.91987	+	7.16506i	−0.0924769	+	0.345129i	0.904148	+	0.427220i	$0.140507\pi$
$432$	−2.96584	−	2.68399i	−0.142694	−	0.129134i
$433$	−12.9794	−	7.49364i	−0.623748	−	0.360121i	0.154579	−	0.987980i	$-0.450598\pi$
$433$	−12.9794	−	7.49364i	−0.623748	−	0.360121i	−0.778327	+	0.627859i	$0.783931\pi$
$434$	1.64969	−	13.8635i	0.0791878	−	0.665469i
$435$	−9.20635	+	15.9459i	−0.441411	+	0.764546i
$436$	12.4543	+	11.8485i	0.596451	+	0.567438i
$437$			18.2699i			0.873970i
$438$	−7.49330	+	10.0216i	−0.358044	+	0.478850i
$439$	7.22187	−	4.16955i	0.344681	−	0.199002i	−0.317659	−	0.948205i	$-0.602897\pi$
$439$	7.22187	−	4.16955i	0.344681	−	0.199002i	0.662340	+	0.749203i	$0.269563\pi$
$440$	−7.52563	−	44.2970i	−0.358770	−	2.11178i
$441$	3.69573			0.175987
$442$	0.178017	+	0.0338671i	0.00846740	+	0.00161089i
$443$	−15.1308	+	15.1308i	−0.718888	+	0.718888i	−0.968377	−	0.249490i	$-0.919737\pi$
$443$	−15.1308	+	15.1308i	−0.718888	+	0.718888i	0.249490	+	0.968377i	$0.419737\pi$
$444$	−14.5112	−	7.90257i	−0.688670	−	0.375039i
$445$	23.7642	+	6.36759i	1.12653	+	0.301853i
$446$	12.9742	−	1.87284i	0.614345	−	0.0886814i
$447$	−5.40580	−	5.40580i	−0.255685	−	0.255685i
$448$	−13.1018	−	6.31002i	−0.619001	−	0.298120i
$449$	−23.1971	+	6.21566i	−1.09474	+	0.293335i	−0.760621	−	0.649196i	$-0.775106\pi$
$449$	−23.1971	+	6.21566i	−1.09474	+	0.293335i	−0.334120	+	0.942531i	$0.608439\pi$
$450$	−0.862481	+	7.24802i	−0.0406578	+	0.341675i
$451$	52.7231	−	14.1271i	2.48263	−	0.665220i
$452$	−10.1230	−	34.3330i	−0.476144	−	1.61489i
$453$	−9.22282	+	5.32480i	−0.433326	+	0.250181i
$454$	−20.4047	−	2.42806i	−0.957639	−	0.113955i
$455$	−3.99158	−	20.5073i	−0.187128	−	0.961398i
$456$	7.68127	+	16.7450i	0.359708	+	0.784154i
$457$	−0.995083	+	3.71370i	−0.0465480	+	0.173720i	−0.985287	−	0.170911i	$-0.945329\pi$
$457$	−0.995083	+	3.71370i	−0.0465480	+	0.173720i	0.938739	+	0.344630i	$0.111996\pi$
$458$	−27.1257	+	11.6339i	−1.26750	+	0.543618i
$459$	−0.0343272	+	0.00919796i	−0.00160226	+	0.000429324i
$460$	−4.19650	+	17.3833i	−0.195663	+	0.810503i
$461$	−12.7701	−	7.37285i	−0.594765	−	0.343388i	0.172214	−	0.985059i	$-0.444908\pi$
$461$	−12.7701	−	7.37285i	−0.594765	−	0.343388i	−0.766979	+	0.641672i	$0.778241\pi$
$462$	−10.2601	−	7.67166i	−0.477345	−	0.356918i
$463$	−10.0377	+	10.0377i	−0.466490	+	0.466490i	−0.900776	−	0.434285i	$-0.857001\pi$
$463$	−10.0377	+	10.0377i	−0.466490	+	0.466490i	0.434285	+	0.900776i	$0.357001\pi$
$464$	−4.86060	+	22.5878i	−0.225647	+	1.04861i
$465$	−14.9926	+	8.65600i	−0.695267	+	0.401413i
$466$	−5.24746	−	12.2350i	−0.243084	−	0.566775i
$467$	20.7092	−	20.7092i	0.958308	−	0.958308i	−0.0408570	−	0.999165i	$-0.513009\pi$
$467$	20.7092	−	20.7092i	0.958308	−	0.958308i	0.999165	+	0.0408570i	$0.0130088\pi$
$468$	−1.55369	−	7.04174i	−0.0718192	−	0.325504i
$469$	10.8894	+	10.8894i	0.502825	+	0.502825i
$470$	25.7844	+	10.3057i	1.18935	+	0.475368i
$471$	3.75097	+	6.49686i	0.172835	+	0.299360i
$472$	0.0407076	−	0.0337264i	0.00187372	−	0.00155238i
$473$	43.9564	+	43.9564i	2.02112	+	2.02112i
$474$	−0.739037	−	5.11972i	−0.0339451	−	0.235156i
$475$	16.8088	−	29.1136i	0.771239	−	1.33582i
$476$	−0.110246	+	0.0673683i	−0.00505312	+	0.00308782i
$477$	−2.35246	−	8.77949i	−0.107712	−	0.401985i
$478$	0.262760	−	0.657412i	0.0120184	−	0.0300693i
$479$	5.87281	+	1.57361i	0.268336	+	0.0719003i	0.390478	−	0.920612i	$-0.372310\pi$
$479$	5.87281	+	1.57361i	0.268336	+	0.0719003i	−0.122142	+	0.992513i	$0.538976\pi$
$480$	3.46229	+	17.6967i	0.158031	+	0.807741i
$481$	−13.0650	−	26.7701i	−0.595712	−	1.22061i
$482$	−12.2451	−	15.5530i	−0.557750	−	0.708419i
$483$	2.54939	+	4.41568i	0.116001	+	0.200920i
$484$	−7.82547	−	26.5409i	−0.355703	−	1.20640i
$485$	−3.79264	−	14.1543i	−0.172215	−	0.642714i
$486$	0.874833	+	1.11116i	0.0396832	+	0.0504031i
$487$	4.84213	+	18.0711i	0.219418	+	0.818879i	0.984564	+	0.175023i	$0.0559999\pi$
$487$	4.84213	+	18.0711i	0.219418	+	0.818879i	−0.765146	+	0.643856i	$0.777333\pi$
$488$	−0.775383	+	8.26726i	−0.0350999	+	0.374241i
$489$	−10.1966	+	10.1966i	−0.461108	+	0.461108i
$490$	−13.3431	−	9.97681i	−0.602778	−	0.450706i
$491$	4.40004	−	16.4212i	0.198571	−	0.741078i	−0.792742	−	0.609557i	$-0.791347\pi$
$491$	4.40004	−	16.4212i	0.198571	−	0.741078i	0.991313	−	0.131521i	$-0.0419860\pi$
$492$	−21.0112	+	6.19508i	−0.947259	+	0.279296i
$493$	0.145152	+	0.145152i	0.00653732	+	0.00653732i
$494$	−6.20713	+	32.6268i	−0.279272	+	1.46795i
$495$			15.8858i			0.714013i
$496$	−14.5765	+	16.1072i	−0.654505	+	0.723236i
$497$	0.208391	+	0.360943i	0.00934760	+	0.0161905i
$498$	16.3014	−	2.35312i	0.730482	−	0.105446i
$499$	27.9690			1.25206			0.626032	−	0.779797i	$-0.284678\pi$
$499$	27.9690			1.25206			0.626032	+	0.779797i	$0.284678\pi$
$500$	0.708726	−	0.744963i	0.0316952	−	0.0333158i
$501$	18.7342	+	10.8162i	0.836981	+	0.483231i
$502$	2.41404	+	3.06616i	0.107744	+	0.136849i
$503$	14.7779	−	25.5961i	0.658915	−	1.14127i	−0.321983	−	0.946746i	$-0.604349\pi$
$503$	14.7779	−	25.5961i	0.658915	−	1.14127i	0.980897	−	0.194528i	$-0.0623174\pi$
$504$	4.19309	+	2.97526i	0.186775	+	0.132529i
$505$	14.5502	+	3.89870i	0.647474	+	0.173490i
$506$	−2.33591	+	19.6302i	−0.103844	+	0.872670i
$507$	5.07348	−	11.9691i	0.225321	−	0.531567i
$508$	17.5845	+	4.24507i	0.780188	+	0.188345i
$509$	6.80051	−	3.92627i	0.301427	−	0.174029i	−0.341657	−	0.939825i	$-0.610988\pi$
$509$	6.80051	−	3.92627i	0.301427	−	0.174029i	0.643084	+	0.765796i	$0.277655\pi$
$510$	0.148765	+	0.0594598i	0.00658744	+	0.00263293i
$511$	8.04199	−	13.9291i	0.355757	−	0.616188i
$512$	10.9443	+	19.8046i	0.483676	+	0.875247i
$513$	−1.68579	−	6.29146i	−0.0744296	−	0.277775i
$514$	19.3675	+	14.4814i	0.854265	+	0.638747i
$515$		−	1.42131i		−	0.0626303i
$516$	−18.0749	−	17.1957i	−0.795704	−	0.756999i
$517$	29.6502	+	7.94476i	1.30402	+	0.349410i
$518$	19.7216	+	7.88249i	0.866516	+	0.346337i
$519$		−	6.29441i		−	0.276294i
$520$	−13.4001	+	29.6177i	−0.587633	+	1.29882i
$521$		−	14.8286i		−	0.649653i	−0.945774	−	0.324826i	$-0.894694\pi$
$521$		−	14.8286i		−	0.649653i	0.945774	−	0.324826i	$-0.105306\pi$
$522$	3.03178	−	7.58536i	0.132697	−	0.332002i
$523$	32.4062	+	8.68322i	1.41703	+	0.379691i	0.884428	−	0.466677i	$-0.154549\pi$
$523$	32.4062	+	8.68322i	1.41703	+	0.379691i	0.532598	+	0.846368i	$0.321216\pi$
$524$	3.86706	−	0.0963964i	0.168933	−	0.00421110i
$525$		−	9.38200i		−	0.409464i
$526$	−7.86541	+	10.5193i	−0.342948	+	0.458661i
$527$	0.0499533	+	0.186428i	0.00217600	+	0.00812095i
$528$	6.11224	+	18.9738i	0.266001	+	0.825728i
$529$	−7.56605	+	13.1048i	−0.328959	+	0.569774i
$530$	−15.2074	+	38.0480i	−0.660566	+	1.65270i
$531$	−0.0161862	+	0.00934508i	−0.000702419	+	0.000405542i
$532$	−12.3472	−	20.2058i	−0.535319	−	0.876032i
$533$	−37.3424	−	12.8475i	−1.61748	−	0.556487i
$534$	−10.8384	−	1.28972i	−0.469024	−	0.0558118i
$535$	−9.64683	−	2.58486i	−0.417069	−	0.111753i
$536$	−4.01342	−	23.6236i	−0.173353	−	1.02039i
$537$	9.11320	−	15.7845i	0.393264	−	0.681153i
$538$	7.57667	−	5.96525i	0.326654	−	0.257180i
$539$	−15.9502	−	9.20883i	−0.687022	−	0.396652i
$540$	−0.158873	−	6.37337i	−0.00683679	−	0.274266i
$541$	20.6953			0.889762			0.444881	−	0.895590i	$-0.353246\pi$
$541$	20.6953			0.889762			0.444881	+	0.895590i	$0.353246\pi$
$542$	4.65003	+	32.2133i	0.199736	+	1.38368i
$543$	−4.29769	−	7.44382i	−0.184432	−	0.319445i
$544$	0.200561	+	0.0137789i	0.00859900	+	0.000590764i
$545$			27.3980i			1.17360i
$546$	3.05254	+	8.75174i	0.130637	+	0.374540i
$547$	18.5223	+	18.5223i	0.791956	+	0.791956i	0.981812	−	0.189856i	$-0.0608022\pi$
$547$	18.5223	+	18.5223i	0.791956	+	0.791956i	−0.189856	+	0.981812i	$0.560802\pi$
$548$	37.8573	+	20.6165i	1.61718	+	0.880694i
$549$	0.759826	−	2.83571i	0.0324286	−	0.121025i
$550$	21.7826	−	29.1322i	0.928812	−	1.24220i
$551$	−26.6034	+	26.6034i	−1.13334	+	1.13334i
$552$	0.740845	−	7.89900i	0.0315325	−	0.336204i
$553$	1.72085	+	6.42230i	0.0731780	+	0.273104i
$554$	−7.68797	+	6.05287i	−0.326631	+	0.257162i
$555$	−6.81619	−	25.4384i	−0.289331	−	1.07980i
$556$	38.5354	+	20.9858i	1.63426	+	0.889996i
$557$	−0.847657	−	1.46818i	−0.0359164	−	0.0622090i	0.847508	−	0.530782i	$-0.178102\pi$
$557$	−0.847657	−	1.46818i	−0.0359164	−	0.0622090i	−0.883425	+	0.468573i	$0.844768\pi$
$558$	6.03460	−	4.75114i	0.255465	−	0.201132i
$559$	−8.59283	−	44.1469i	−0.363438	−	1.86721i
$560$	−7.10687	−	22.0613i	−0.300320	−	0.932261i
$561$	0.171070	+	0.0458380i	0.00722257	+	0.00193528i
$562$	1.62159	+	0.648132i	0.0684027	+	0.0273398i
$563$	−0.665562	−	2.48391i	−0.0280501	−	0.104684i	0.950482	−	0.310781i	$-0.100591\pi$
$563$	−0.665562	−	2.48391i	−0.0280501	−	0.104684i	−0.978532	+	0.206097i	$0.933924\pi$
$564$	−11.9751	−	2.89091i	−0.504244	−	0.121729i
$565$	28.5252	−	49.4070i	1.20006	−	2.07857i
$566$	13.4518	−	1.94178i	0.565422	−	0.0816193i
$567$	−1.28535	−	1.28535i	−0.0539798	−	0.0539798i
$568$	0.0605576	−	0.645674i	0.00254094	−	0.0270919i
$569$	−17.4308	−	30.1910i	−0.730736	−	1.26567i	−0.956569	−	0.291507i	$-0.905843\pi$
$569$	−17.4308	−	30.1910i	−0.730736	−	1.26567i	0.225832	−	0.974166i	$-0.427490\pi$
$570$	−10.8977	+	27.2656i	−0.456456	+	1.14203i
$571$	−1.28971	−	1.28971i	−0.0539726	−	0.0539726i	0.679605	−	0.733578i	$-0.262151\pi$
$571$	−1.28971	−	1.28971i	−0.0539726	−	0.0539726i	−0.733578	+	0.679605i	$0.762151\pi$
$572$	−10.8408	+	34.2624i	−0.453276	+	1.43258i
$573$	7.06775	−	7.06775i	0.295259	−	0.295259i
$574$	25.8768	−	11.0983i	1.08007	−	0.463232i
$575$	−12.5377	+	7.23864i	−0.522858	+	0.301872i
$576$	−2.64199	−	7.55115i	−0.110083	−	0.314631i
$577$	19.4306	−	19.4306i	0.808905	−	0.808905i	−0.175563	−	0.984468i	$-0.556175\pi$
$577$	19.4306	−	19.4306i	0.808905	−	0.808905i	0.984468	+	0.175563i	$0.0561747\pi$
$578$	−14.3957	+	19.2530i	−0.598784	+	0.800818i
$579$	13.4504	+	7.76557i	0.558978	+	0.322726i
$580$	−31.4230	+	19.2017i	−1.30477	+	0.797308i
$581$	−20.4488	+	5.47925i	−0.848361	+	0.227318i
$582$	2.56251	+	5.97475i	0.106219	+	0.247661i
$583$	−11.7235	+	43.7525i	−0.485536	+	1.81205i
$584$	−22.7474	+	10.4347i	−0.941294	+	0.431791i
$585$	6.42459	−	9.53002i	0.265624	−	0.394018i
$586$	−1.29075	+	10.8471i	−0.0533204	+	0.448088i
$587$	4.14214	−	2.39147i	0.170965	−	0.0987064i	−0.412076	−	0.911149i	$-0.635196\pi$
$587$	4.14214	−	2.39147i	0.170965	−	0.0987064i	0.583041	+	0.812443i	$0.301863\pi$
$588$	6.49130	+	3.53507i	0.267697	+	0.145784i
$589$	−34.1684	+	9.15540i	−1.40789	+	0.377242i
$590$	0.0836660	+	0.00995587i	0.00344447	+	0.000409877i
$591$	−5.72688	+	1.53451i	−0.235572	+	0.0631214i
$592$	−17.9289	−	27.7607i	−0.736873	−	1.14096i
$593$	−11.0287	−	11.0287i	−0.452895	−	0.452895i	0.443419	−	0.896314i	$-0.353765\pi$
$593$	−11.0287	−	11.0287i	−0.452895	−	0.452895i	−0.896314	+	0.443419i	$0.853765\pi$
$594$	−1.00691	−	6.97543i	−0.0413141	−	0.286205i
$595$	−0.198907	−	0.0532971i	−0.00815441	−	0.00218497i
$596$	−4.32413	−	14.6657i	−0.177123	−	0.600731i
$597$	−15.1026	+	15.1026i	−0.618108	+	0.618108i
$598$	9.34026	−	10.8317i	0.381952	−	0.442939i
$599$	27.5123			1.12412			0.562060	−	0.827096i	$-0.310009\pi$
$599$	27.5123			1.12412			0.562060	+	0.827096i	$0.310009\pi$
$600$	−8.44782	+	11.9057i	−0.344881	+	0.486047i
$601$	−2.91298	+	1.68181i	−0.118823	+	0.0686025i	−0.558234	−	0.829684i	$-0.688521\pi$
$601$	−2.91298	+	1.68181i	−0.118823	+	0.0686025i	0.439411	+	0.898286i	$0.355187\pi$
$602$	25.6816	+	19.2025i	1.04670	+	0.782636i
$603$			8.47189i			0.345002i
$604$	−21.2926	+	0.530772i	−0.866383	+	0.0215968i
$605$	22.0511	−	38.1937i	0.896506	−	1.55279i
$606$	−6.63608	−	0.789663i	−0.269572	−	0.0320779i
$607$	23.8626	+	13.7771i	0.968554	+	0.559195i	0.898795	−	0.438369i	$-0.144444\pi$
$607$	23.8626	+	13.7771i	0.968554	+	0.559195i	0.0697588	+	0.997564i	$0.477777\pi$
$608$	−2.52538	+	36.7587i	−0.102418	+	1.49076i
$609$	−2.71755	+	10.1420i	−0.110121	+	0.410976i
$610$	−10.3984	+	8.18686i	−0.421020	+	0.331476i
$611$	−14.5744	−	16.7574i	−0.589617	−	0.677932i
$612$	−0.0690916	−	0.0166793i	−0.00279286	−	0.000674222i
$613$	11.9386	+	20.6782i	0.482194	+	0.835184i	0.999791	−	0.0204400i	$-0.00650671\pi$
$613$	11.9386	+	20.6782i	0.482194	+	0.835184i	−0.517597	+	0.855624i	$0.673173\pi$
$614$	9.69427	−	4.15777i	0.391229	−	0.167794i
$615$	−30.2362	−	17.4569i	−1.21924	−	0.703930i
$616$	−10.6831	−	23.2888i	−0.430434	−	0.938334i
$617$	2.56287	−	0.686719i	0.103177	−	0.0276463i	−0.206861	−	0.978370i	$-0.566325\pi$
$617$	2.56287	−	0.686719i	0.103177	−	0.0276463i	0.310038	+	0.950724i	$0.399658\pi$
$618$	0.0900888	+	0.624095i	0.00362390	+	0.0251048i
$619$	2.01051			0.0808091			0.0404046	−	0.999183i	$-0.487135\pi$
$619$	2.01051			0.0808091			0.0404046	+	0.999183i	$0.487135\pi$
$620$	−34.6133	+	0.862824i	−1.39010	+	0.0346519i
$621$	−0.725981	+	2.70940i	−0.0291326	+	0.108724i
$622$	−9.40027	+	4.03168i	−0.376917	+	0.161656i
$623$	14.0295			0.562080
$624$	4.00666	−	13.8545i	0.160395	−	0.554623i
$625$	−24.1676			−0.966703
$626$	−7.22356	+	3.09811i	−0.288711	+	0.123825i
$627$	−8.40114	+	31.3535i	−0.335509	+	1.25214i
$628$	0.373894	+	14.9992i	0.0149200	+	0.598534i
$629$	−0.293607			−0.0117069
$630$	1.17076	+	8.11052i	0.0466443	+	0.323131i
$631$	−41.1790	+	11.0339i	−1.63931	+	0.439252i	−0.956592	−	0.291429i	$-0.905869\pi$
$631$	−41.1790	+	11.0339i	−1.63931	+	0.439252i	−0.682719	+	0.730681i	$0.739202\pi$
$632$	3.59908	−	9.69934i	0.143164	−	0.385819i
$633$	9.23851	+	5.33386i	0.367198	+	0.212002i
$634$	−32.9244	+	14.1209i	−1.30760	+	0.560814i
$635$	14.4160	+	24.9693i	0.572082	+	0.990875i
$636$	4.26589	−	17.6708i	0.169153	−	0.700692i
$637$	5.84438	+	11.9751i	0.231563	+	0.474470i
$638$	−31.9855	+	25.1827i	−1.26632	+	0.996993i
$639$	−0.0593426	+	0.221470i	−0.00234756	+	0.00876120i
$640$	−10.8461	+	34.3949i	−0.428730	+	1.35958i
$641$	2.27134	+	1.31136i	0.0897124	+	0.0517955i	0.544185	−	0.838965i	$-0.316839\pi$
$641$	2.27134	+	1.31136i	0.0897124	+	0.0517955i	−0.454473	+	0.890761i	$0.650172\pi$
$642$	4.39975	+	0.523550i	0.173644	+	0.0206629i
$643$	−10.7333	+	18.5906i	−0.423279	+	0.733142i	−0.996258	−	0.0864288i	$-0.972454\pi$
$643$	−10.7333	+	18.5906i	−0.423279	+	0.733142i	0.572979	+	0.819570i	$0.305788\pi$
$644$	0.254122	+	10.1944i	0.0100138	+	0.401716i
$645$		−	39.7628i		−	1.56566i
$646$	0.262171	+	0.196029i	0.0103150	+	0.00771266i
$647$	−7.00712	+	4.04556i	−0.275478	+	0.159047i	−0.631375	−	0.775478i	$-0.717509\pi$
$647$	−7.00712	+	4.04556i	−0.275478	+	0.159047i	0.355896	+	0.934525i	$0.384176\pi$
$648$	0.473734	+	2.78847i	0.0186100	+	0.109542i
$649$	0.0931423			0.00365616
$650$	−24.8493	+	8.66726i	−0.974670	+	0.339958i
$651$	−6.98065	+	6.98065i	−0.273593	+	0.273593i
$652$	−27.6630	+	8.15634i	−1.08337	+	0.319427i
$653$	20.5629	+	5.50982i	0.804690	+	0.215616i	0.637642	−	0.770333i	$-0.279910\pi$
$653$	20.5629	+	5.50982i	0.804690	+	0.215616i	0.167048	+	0.985949i	$0.446577\pi$
$654$	−1.73661	−	12.0304i	−0.0679067	−	0.470427i
$655$	4.35959	+	4.35959i	0.170343	+	0.170343i
$656$	−42.8306	−	9.21657i	−1.67225	−	0.359846i
$657$	8.54672	−	2.29009i	0.333439	−	0.0893448i
$658$	15.7235	+	1.87103i	0.612967	+	0.0729402i
$659$	5.01691	−	1.34428i	0.195431	−	0.0523656i	−0.159776	−	0.987153i	$-0.551077\pi$
$659$	5.01691	−	1.34428i	0.195431	−	0.0523656i	0.355207	+	0.934788i	$0.384410\pi$
$660$	−15.1952	+	27.9023i	−0.591471	+	1.08610i
$661$	−7.57253	+	4.37200i	−0.294537	+	0.170051i	−0.639986	−	0.768386i	$-0.721060\pi$
$661$	−7.57253	+	4.37200i	−0.294537	+	0.170051i	0.345449	+	0.938438i	$0.387727\pi$
$662$	2.32843	−	19.5674i	0.0904970	−	0.760508i
$663$	−0.0840883	−	0.0966833i	−0.00326572	−	0.00375487i
$664$	30.8831	+	11.4596i	1.19850	+	0.444719i
$665$	9.76824	−	36.4556i	0.378796	−	1.41369i
$666$	4.60538	+	10.7379i	0.178455	+	0.416086i
$667$	15.6501	−	4.19342i	0.605973	−	0.162370i
$668$	22.5593	+	36.9176i	0.872847	+	1.42839i
$669$	−8.02737	−	4.63461i	−0.310356	−	0.179184i
$670$	22.8703	−	30.5869i	0.883557	−	1.18168i
$671$	−10.3452	+	10.3452i	−0.399371	+	0.399371i
$672$	4.51896	+	9.23664i	0.174323	+	0.356311i
$673$	28.5632	−	16.4910i	1.10103	−	0.635681i	0.164540	−	0.986370i	$-0.447386\pi$
$673$	28.5632	−	16.4910i	1.10103	−	0.635681i	0.936492	+	0.350689i	$0.114053\pi$
$674$	42.2848	−	18.1355i	1.62875	−	0.698553i
$675$	3.64958	−	3.64958i	0.140472	−	0.140472i
$676$	20.3600	−	16.1700i	0.783077	−	0.621925i
$677$	27.8722	+	27.8722i	1.07121	+	1.07121i	0.997262	+	0.0739526i	$0.0235614\pi$
$677$	27.8722	+	27.8722i	1.07121	+	1.07121i	0.0739526	+	0.997262i	$0.476439\pi$
$678$	−9.39373	+	23.5026i	−0.360764	+	0.902613i
$679$	−4.17810	−	7.23668i	−0.160341	−	0.277718i
$680$	0.204421	+	0.246735i	0.00783921	+	0.00946187i
$681$	10.2743	+	10.2743i	0.393713	+	0.393713i
$682$	−37.8830	+	5.46845i	−1.45061	+	0.209398i
$683$	−3.49764	+	6.05809i	−0.133833	+	0.231806i	−0.925151	−	0.379599i	$-0.876062\pi$
$683$	−3.49764	+	6.05809i	−0.133833	+	0.231806i	0.791318	+	0.611405i	$0.209395\pi$
$684$	3.05697	−	12.6630i	0.116886	−	0.484183i
$685$	17.7823	+	66.3645i	0.679428	+	2.53566i
$686$	−25.5318	−	10.2048i	−0.974807	−	0.389619i
$687$	20.1593	+	5.40168i	0.769127	+	0.206087i
$688$	−15.2992	−	47.4922i	−0.583277	−	1.81062i
$689$	24.7276	−	21.5063i	0.942046	−	0.819325i
$690$	9.93524	−	7.82219i	0.378228	−	0.297786i
$691$	−6.71250	−	11.6264i	−0.255355	−	0.442288i	0.709637	−	0.704568i	$-0.248859\pi$
$691$	−6.71250	−	11.6264i	−0.255355	−	0.442288i	−0.964992	+	0.262279i	$0.915526\pi$
$692$	6.02077	−	11.0557i	0.228875	−	0.420275i
$693$	2.34460	+	8.75015i	0.0890639	+	0.332391i
$694$	11.6442	−	9.16768i	0.442008	−	0.348000i
$695$	18.1008	+	67.5533i	0.686604	+	2.56244i
$696$	12.5807	−	10.4232i	0.476871	−	0.395090i
$697$	−0.275235	+	0.275235i	−0.0104253	+	0.0104253i
$698$	−7.79467	+	10.4246i	−0.295033	+	0.394579i
$699$	−2.43641	+	9.09282i	−0.0921537	+	0.343922i
$700$	8.97414	−	16.4788i	0.339190	−	0.622842i
$701$	−28.0148	−	28.0148i	−1.05810	−	1.05810i	−0.998204	−	0.0598996i	$-0.980922\pi$
$701$	−28.0148	−	28.0148i	−1.05810	−	1.05810i	−0.0598996	−	0.998204i	$-0.519078\pi$
$702$	−2.21698	+	4.59184i	−0.0836743	+	0.173308i
$703$		−	53.8120i		−	2.02956i
$704$	−7.41320	+	39.1727i	−0.279395	+	1.47638i
$705$	−9.81735	−	17.0042i	−0.369743	−	0.640414i
$706$	3.02698	+	20.9696i	0.113922	+	0.789201i
$707$	8.58989			0.323056
$708$	−0.0373687		0.000931511i	−0.00140440		3.50083e-5i
$709$	−12.6729	−	7.31672i	−0.475942	−	0.274785i	0.242782	−	0.970081i	$-0.421940\pi$
$709$	−12.6729	−	7.31672i	−0.475942	−	0.274785i	−0.718724	+	0.695296i	$0.755273\pi$
$710$	0.812119	−	0.639396i	0.0304783	−	0.0239961i
$711$	−1.82885	+	3.16767i	−0.0685874	+	0.118797i
$712$	−17.8033	−	12.6326i	−0.667207	−	0.473425i
$713$	14.7145	+	3.94274i	0.551063	+	0.147657i
$714$	0.0907182	+	0.0107951i	0.00339504	+	0.000403995i
$715$	−51.4739	+	25.1215i	−1.92501	+	0.939492i
$716$	31.1051	−	19.0074i	1.16245	−	0.710342i
$717$	−0.433546	+	0.250308i	−0.0161911	+	0.00934792i
$718$	13.6994	−	34.2751i	0.511257	−	1.27914i
$719$	1.68519	−	2.91883i	0.0628469	−	0.108854i	−0.832890	−	0.553439i	$-0.813315\pi$
$719$	1.68519	−	2.91883i	0.0628469	−	0.108854i	0.895737	+	0.444585i	$0.146649\pi$
$720$	5.81725	−	11.3464i	0.216796	−	0.422854i
$721$	−0.209772	−	0.782880i	−0.00781232	−	0.0291560i
$722$	−19.8375	+	26.5308i	−0.738274	+	0.987373i
$723$			13.9971i			0.520558i
$724$	−0.428391	−	17.1854i	−0.0159210	−	0.638692i
$725$	−28.7968	−	7.71609i	−1.06949	−	0.286568i
$726$	−7.26174	+	18.1685i	−0.269509	+	0.674297i
$727$			36.1085i			1.33919i	0.742726	+	0.669596i	$0.233533\pi$
$727$			36.1085i			1.33919i	−0.742726	+	0.669596i	$0.766467\pi$
$728$	−3.00969	+	18.2917i	−0.111546	+	0.677935i
$729$		−	1.00000i		−	0.0370370i
$730$	−37.0393	−	14.8042i	−1.37089	−	0.547927i
$731$	−0.428195	−	0.114735i	−0.0158374	−	0.00424361i
$732$	4.04702	−	4.25394i	0.149582	−	0.157230i
$733$			49.1832i			1.81662i	0.418296	+	0.908311i	$0.362628\pi$
$733$			49.1832i			1.81662i	−0.418296	+	0.908311i	$0.637372\pi$
$734$	18.5266	+	13.8527i	0.683831	+	0.511311i
$735$	3.04909	+	11.3794i	0.112468	+	0.419734i
$736$	8.85686	−	13.1654i	0.326468	−	0.485284i
$737$	21.1098	−	36.5633i	0.777590	−	1.34683i
$738$	14.3832	+	5.74880i	0.529453	+	0.211616i
$739$	−21.5026	+	12.4146i	−0.790987	+	0.456677i	−0.840310	−	0.542106i	$-0.817627\pi$
$739$	−21.5026	+	12.4146i	−0.790987	+	0.456677i	0.0493227	+	0.998783i	$0.484294\pi$
$740$	12.3603	−	51.2007i	0.454374	−	1.88217i
$741$	17.7200	−	15.4116i	0.650961	−	0.566160i
$742$	−2.76093	+	23.2020i	−0.101357	+	0.851771i
$743$	17.0362	+	4.56483i	0.624997	+	0.167468i	0.557399	−	0.830245i	$-0.311800\pi$
$743$	17.0362	+	4.56483i	0.624997	+	0.167468i	0.0675988	+	0.997713i	$0.478466\pi$
$744$	15.1440	−	2.57281i	0.555205	−	0.0943237i
$745$	12.1848	−	21.1047i	0.446417	−	0.773217i
$746$	−15.0027	−	19.0554i	−0.549287	−	0.697669i
$747$	−10.0860	−	5.82314i	−0.369026	−	0.213058i
$748$	0.256627	+	0.244144i	0.00938322	+	0.00892679i
$749$	−5.69514			−0.208096
$750$	−0.719612	+	0.103877i	−0.0262765	+	0.00379304i
$751$	10.1795	+	17.6315i	0.371456	+	0.643381i	0.989790	−	0.142535i	$-0.0455252\pi$
$751$	10.1795	+	17.6315i	0.371456	+	0.643381i	−0.618334	+	0.785916i	$0.712192\pi$
$752$	−18.2683	−	16.5322i	−0.666176	−	0.602868i
$753$		−	2.75943i		−	0.100559i
$754$	29.3729	−	2.17165i	1.06970	−	0.0790868i
$755$	−24.0045	−	24.0045i	−0.873613	−	0.873613i
$756$	−1.02816	−	3.48711i	−0.0373939	−	0.126825i
$757$	−6.57962	+	24.5555i	−0.239140	+	0.892484i	0.737098	+	0.675786i	$0.236195\pi$
$757$	−6.57962	+	24.5555i	−0.239140	+	0.892484i	−0.976239	+	0.216698i	$0.930471\pi$
$758$	33.9455	+	25.3816i	1.23296	+	0.921900i
$759$	9.88435	−	9.88435i	0.358779	−	0.358779i
$760$	−45.2214	+	37.4662i	−1.64035	+	1.35904i
$761$	−3.64805	−	13.6147i	−0.132242	−	0.493532i	0.867752	−	0.496997i	$-0.165564\pi$
$761$	−3.64805	−	13.6147i	−0.132242	−	0.493532i	−0.999994	+	0.00346439i	$0.998897\pi$
$762$	−7.91272	−	10.0502i	−0.286648	−	0.364082i
$763$	4.04370	+	15.0913i	0.146392	+	0.546341i
$764$	19.1745	−	5.65353i	0.693710	−	0.204538i
$765$	−0.0566421	−	0.0981070i	−0.00204790	−	0.00354707i
$766$	−14.0012	−	17.7835i	−0.505885	−	0.642543i
$767$	−0.0558769	−	0.0376690i	−0.00201760	−	0.00136015i
$768$	2.58241	−	15.7902i	0.0931847	−	0.569781i
$769$	−5.85253	−	1.56818i	−0.211048	−	0.0565500i	0.151746	−	0.988419i	$-0.451510\pi$
$769$	−5.85253	−	1.56818i	−0.211048	−	0.0565500i	−0.362794	+	0.931869i	$0.618177\pi$
$770$	15.1566	−	37.9209i	0.546204	−	1.36657i
$771$	−4.42578	−	16.5172i	−0.159390	−	0.594853i
$772$	16.1967	+	26.5053i	0.582931	+	0.953948i
$773$	25.5055	−	44.1768i	0.917368	−	1.58893i	0.113972	−	0.993484i	$-0.463642\pi$
$773$	25.5055	−	44.1768i	0.917368	−	1.58893i	0.803396	−	0.595445i	$-0.203024\pi$
$774$	2.52035	+	17.4598i	0.0905919	+	0.627580i
$775$	−19.8206	−	19.8206i	−0.711975	−	0.711975i
$776$	−1.21414	+	12.9454i	−0.0435851	+	0.464711i
$777$	−7.50895	−	13.0059i	−0.269382	−	0.466583i
$778$	−36.6307	−	14.6409i	−1.31327	−	0.524900i
$779$	−50.4448	−	50.4448i	−1.80737	−	1.80737i
$780$	20.4001	−	10.5936i	0.730440	−	0.379310i
$781$	0.807959	−	0.807959i	0.0289111	−	0.0289111i
$782$	−0.0555672	−	0.129561i	−0.00198708	−	0.00463308i
$783$	−5.00235	+	2.88811i	−0.178769	+	0.103213i
$784$	8.02015	+	12.4182i	0.286434	+	0.443508i
$785$	−16.9096	+	16.9096i	−0.603528	+	0.603528i
$786$	−2.19062	−	1.63796i	−0.0781368	−	0.0584241i
$787$	−23.8262	−	13.7560i	−0.849311	−	0.490350i	0.0111076	−	0.999938i	$-0.496464\pi$
$787$	−23.8262	−	13.7560i	−0.849311	−	0.490350i	−0.860418	+	0.509589i	$0.829798\pi$
$788$	−11.5267	−	2.78265i	−0.410621	−	0.0991277i
$789$	8.97114	−	2.40381i	0.319381	−	0.0855779i
$790$	15.1542	−	6.49946i	0.539161	−	0.231241i
$791$	8.42011	−	31.4243i	0.299385	−	1.11732i
$792$	4.90361	−	13.2150i	0.174242	−	0.469575i
$793$	10.3900	−	2.02233i	0.368959	−	0.0718149i
$794$	5.24883	+	0.624587i	0.186274	+	0.0221658i
$795$	25.0917	−	14.4867i	0.889911	−	0.513791i
$796$	−40.9727	+	12.0807i	−1.45224	+	0.428187i
$797$	17.0462	−	4.56750i	0.603806	−	0.161789i	0.0560506	−	0.998428i	$-0.482149\pi$
$797$	17.0462	−	4.56750i	0.603806	−	0.161789i	0.547755	+	0.836639i	$0.315483\pi$
$798$	−1.97851	+	16.6268i	−0.0700384	+	0.588581i
$799$	−0.211441	+	0.0566554i	−0.00748024	+	0.00200432i
$800$	−26.2261	+	12.8309i	−0.927233	+	0.453643i
$801$	5.45745	+	5.45745i	0.192829	+	0.192829i
$802$	7.88200	−	1.13778i	0.278323	−	0.0401763i
$803$	−42.5925	−	11.4126i	−1.50306	−	0.402743i
$804$	−8.10360	+	14.8803i	−0.285792	+	0.524788i
$805$	−11.4928	+	11.4928i	−0.405068	+	0.405068i
$806$	24.9379	+	12.0402i	0.878401	+	0.424098i
$807$	−6.81873			−0.240031
$808$	−10.9005	−	7.73458i	−0.383478	−	0.272102i
$809$	−22.4118	+	12.9395i	−0.787959	+	0.454928i	−0.839243	−	0.543756i	$-0.817002\pi$
$809$	−22.4118	+	12.9395i	−0.787959	+	0.454928i	0.0512848	+	0.998684i	$0.483668\pi$
$810$	−2.69955	+	3.61040i	−0.0948526	+	0.126857i
$811$			11.3837i			0.399736i	0.979823	+	0.199868i	$0.0640514\pi$
$811$			11.3837i			0.399736i	−0.979823	+	0.199868i	$0.935949\pi$
$812$	−14.4743	+	15.2144i	−0.507949	+	0.533920i
$813$	11.5072	−	19.9310i	0.403574	−	0.699011i
$814$	6.88014	−	57.8185i	0.241149	−	2.02654i
$815$	−39.8086	−	22.9835i	−1.39443	−	0.805077i
$816$	−0.105400	−	0.0953841i	−0.00368975	−	0.00333911i
$817$	21.0284	−	78.4792i	0.735692	−	2.74564i
$818$	−31.7004	−	40.2638i	−1.10838	−	1.40779i
$819$	2.13223	−	6.19751i	0.0745060	−	0.216558i
$820$	−36.4099	−	59.5837i	−1.27149	−	2.08075i
$821$	4.73709	+	8.20488i	0.165326	+	0.286352i	0.936771	−	0.349943i	$-0.113799\pi$
$821$	4.73709	+	8.20488i	0.165326	+	0.286352i	−0.771445	+	0.636296i	$0.780466\pi$
$822$	−12.0147	−	28.0135i	−0.419060	−	0.977082i
$823$	−8.95746	−	5.17159i	−0.312237	−	0.180270i	0.335690	−	0.941973i	$-0.391031\pi$
$823$	−8.95746	−	5.17159i	−0.312237	−	0.180270i	−0.647927	+	0.761702i	$0.724364\pi$
$824$	−0.438729	+	1.18235i	−0.0152838	+	0.0411892i
$825$	−24.8448	+	6.65715i	−0.864985	+	0.231772i
$826$	0.0475540	−	0.00686448i	0.00165462	−	0.000238846i
$827$	2.90291			0.100944			0.0504720	−	0.998725i	$-0.483927\pi$
$827$	2.90291			0.100944			0.0504720	+	0.998725i	$0.483927\pi$
$828$	−3.86675	+	4.06446i	−0.134379	+	0.141250i
$829$	−10.5541	+	39.3883i	−0.366558	+	1.36801i	0.498738	+	0.866753i	$0.333797\pi$
$829$	−10.5541	+	39.3883i	−0.366558	+	1.36801i	−0.865296	+	0.501261i	$0.832870\pi$
$830$	20.6945	+	48.2515i	0.718318	+	1.67483i
$831$	6.91890			0.240014
$832$	20.2896	−	20.5020i	0.703416	−	0.710778i
$833$	0.131339			0.00455064
$834$	−12.2299	−	28.5153i	−0.423486	−	0.987403i
$835$	−17.8474	+	66.6073i	−0.617634	+	2.30504i
$836$	−44.7465	+	47.0344i	−1.54759	+	1.62672i
$837$	−5.43092			−0.187720
$838$	32.3032	−	4.66301i	1.11590	−	0.161081i
$839$	37.8412	−	10.1395i	1.30642	−	0.350055i	0.462548	−	0.886594i	$-0.346935\pi$
$839$	37.8412	−	10.1395i	1.30642	−	0.350055i	0.843876	+	0.536539i	$0.180269\pi$
$840$	−5.70157	+	15.3655i	−0.196723	+	0.530158i
$841$	3.77991	+	2.18233i	0.130342	+	0.0752528i
$842$	21.9593	+	51.2004i	0.756767	+	1.76448i
$843$	−0.617418	−	1.06940i	−0.0212650	−	0.0368320i
$844$	11.1248	+	18.2054i	0.382933	+	0.626657i
$845$	41.0394	+	5.74663i	1.41180	+	0.197690i
$846$	5.38859	+	6.84424i	0.185264	+	0.235310i
$847$	6.50909	−	24.2923i	0.223655	−	0.834692i
$848$	24.3953	−	26.9571i	0.837738	−	0.925710i
$849$	−8.32290	−	4.80523i	−0.285641	−	0.164915i
$850$	−0.0306510	+	0.257581i	−0.00105132	+	0.00883497i
$851$	−11.5870	+	20.0692i	−0.397197	+	0.687965i
$852$	−0.316073	+	0.332234i	−0.0108285	+	0.0113821i
$853$			47.9176i			1.64067i	0.571885	+	0.820334i	$0.306212\pi$
$853$			47.9176i			1.64067i	−0.571885	+	0.820334i	$0.693788\pi$
$854$	−4.51932	+	6.04417i	−0.154648	+	0.206827i
$855$	17.9810	−	10.3813i	0.614936	−	0.355033i
$856$	7.22708	+	5.12806i	0.247016	+	0.175274i
$857$	−1.85735			−0.0634458			−0.0317229	−	0.999497i	$-0.510099\pi$
$857$	−1.85735			−0.0634458			−0.0317229	+	0.999497i	$0.510099\pi$
$858$	21.0098	−	14.2935i	0.717263	−	0.487972i
$859$	25.3741	−	25.3741i	0.865755	−	0.865755i	−0.126244	−	0.991999i	$-0.540292\pi$
$859$	25.3741	−	25.3741i	0.865755	−	0.865755i	0.991999	+	0.126244i	$0.0402924\pi$
$860$	38.0342	−	69.8407i	1.29696	−	2.38155i
$861$	−19.2311	−	5.15296i	−0.655395	−	0.175612i
$862$	10.3828	−	1.49876i	0.353638	−	0.0510481i
$863$	25.6251	+	25.6251i	0.872290	+	0.872290i	0.992722	−	0.120432i	$-0.0384279\pi$
$863$	25.6251	+	25.6251i	0.872290	+	0.872290i	−0.120432	+	0.992722i	$0.538428\pi$
$864$	−1.83517	+	5.35090i	−0.0624337	+	0.182041i
$865$	19.3809	−	5.19308i	0.658969	−	0.176570i
$866$	−2.50446	+	21.0467i	−0.0851051	+	0.715196i
$867$	16.4195	−	4.39960i	0.557636	−	0.149418i
$868$	−18.9382	+	5.58386i	−0.642805	+	0.189529i
$869$	15.7861	−	9.11409i	0.535506	−	0.309174i
$870$	25.8571	+	3.07687i	0.876637	+	0.104316i
$871$	−27.4511	+	13.3973i	−0.930143	+	0.453951i
$872$	8.45720	−	22.7918i	0.286397	−	0.771827i
$873$	1.18978	−	4.44032i	0.0402680	−	0.150282i
$874$	23.7458	−	10.1843i	0.803213	−	0.344489i
$875$	0.902699	−	0.241878i	0.0305168	−	0.00817695i
$876$	17.2023	+	4.15278i	0.581211	+	0.140310i
$877$	−15.0580	−	8.69372i	−0.508471	−	0.293566i	0.223734	−	0.974650i	$-0.428175\pi$
$877$	−15.0580	−	8.69372i	−0.508471	−	0.293566i	−0.732205	+	0.681084i	$0.761509\pi$
$878$	−9.44496	−	7.06214i	−0.318752	−	0.238336i
$879$	5.46179	−	5.46179i	0.184222	−	0.184222i
$880$	−53.3786	+	34.4739i	−1.79939	+	1.16212i
$881$	−3.63799	+	2.10039i	−0.122567	+	0.0707641i	−0.560030	−	0.828472i	$-0.689210\pi$
$881$	−3.63799	+	2.10039i	−0.122567	+	0.0707641i	0.437463	+	0.899236i	$0.355877\pi$
$882$	−2.06013	−	4.80341i	−0.0693682	−	0.161739i
$883$	35.5020	−	35.5020i	1.19474	−	1.19474i	0.219016	−	0.975721i	$-0.429715\pi$
$883$	35.5020	−	35.5020i	1.19474	−	1.19474i	0.975721	−	0.219016i	$-0.0702847\pi$
$884$	−0.0552152	−	0.250250i	−0.00185709	−	0.00841683i
$885$	−0.0421281	−	0.0421281i	−0.00141612	−	0.00141612i
$886$	28.1003	+	11.2314i	0.944047	+	0.377325i
$887$	−12.9917	−	22.5024i	−0.436220	−	0.755555i	0.561174	−	0.827698i	$-0.310350\pi$
$887$	−12.9917	−	22.5024i	−0.436220	−	0.755555i	−0.997394	+	0.0721423i	$0.977016\pi$
$888$	−2.18207	+	23.2656i	−0.0732256	+	0.780743i
$889$	11.6258	+	11.6258i	0.389918	+	0.389918i
$890$	−4.97091	−	34.4362i	−0.166625	−	1.15430i
$891$	−2.49175	+	4.31583i	−0.0834767	+	0.144586i
$892$	−9.66642	−	15.8188i	−0.323656	−	0.529652i
$893$	−10.3838	−	38.7527i	−0.347479	−	1.29681i
$894$	−4.01263	+	10.0394i	−0.134202	+	0.335767i
$895$	56.1202	+	15.0374i	1.87589	+	0.502644i
$896$	−0.897843	+	20.5461i	−0.0299948	+	0.686396i
$897$	−9.92719	+	1.93224i	−0.331459	+	0.0645158i
$898$	21.0095	+	26.6849i	0.701096	+	0.890487i
$899$	15.6851	+	27.1673i	0.523126	+	0.906082i
$900$	9.90116	−	2.91932i	0.330039	−	0.0973106i
$901$	−0.0836020	−	0.312007i	−0.00278519	−	0.0103945i
$902$	−47.7510	−	60.6502i	−1.58993	−	2.01943i
$903$	−5.86863	−	21.9020i	−0.195296	−	0.728854i
$904$	−38.9803	+	32.2954i	−1.29647	+	1.07413i
$905$	19.3742	−	19.3742i	0.644022	−	0.644022i
$906$	12.0619	+	9.01883i	0.400728	+	0.299631i
$907$	2.31414	−	8.63648i	0.0768397	−	0.286770i	−0.916804	−	0.399336i	$-0.869241\pi$
$907$	2.31414	−	8.63648i	0.0768397	−	0.286770i	0.993644	+	0.112567i	$0.0359072\pi$
$908$	8.21849	+	27.8738i	0.272740	+	0.925025i
$909$	3.34145	+	3.34145i	0.110829	+	0.110829i
$910$	−24.4287	+	16.6194i	−0.809803	+	0.550929i
$911$			3.20976i			0.106344i	0.998585	+	0.0531721i	$0.0169332\pi$
$911$			3.20976i			0.106344i	−0.998585	+	0.0531721i	$0.983067\pi$
$912$	17.4819	−	19.3177i	0.578884	−	0.639673i
$913$	29.0196	+	50.2634i	0.960408	+	1.66348i
$914$	5.38146	−	0.776819i	0.178003	−	0.0256949i
$915$	9.35820			0.309373
$916$	30.2417	+	28.7706i	0.999213	+	0.950609i
$917$	3.04477	+	1.75790i	0.100547	+	0.0580509i
$918$	0.0310899	+	0.0394885i	0.00102612	+	0.00130331i
$919$	9.09272	−	15.7491i	0.299941	−	0.519513i	−0.676181	−	0.736735i	$-0.736366\pi$
$919$	9.09272	−	15.7491i	0.299941	−	0.519513i	0.976122	+	0.217222i	$0.0696996\pi$
$920$	24.9327	−	4.23582i	0.822008	−	0.139651i
$921$	−7.20460	−	1.93047i	−0.237400	−	0.0636110i
$922$	−2.46409	+	20.7075i	−0.0811506	+	0.681964i
$923$	−0.811461	+	0.157944i	−0.0267095	+	0.00519879i
$924$	−4.25163	+	17.6117i	−0.139868	+	0.579383i
$925$	36.9283	−	21.3206i	1.21420	−	0.701016i
$926$	18.6415	+	7.45080i	0.612598	+	0.244848i
$927$	0.222938	−	0.386140i	0.00732224	−	0.0126825i
$928$	32.0672	−	6.27383i	1.05266	−	0.205949i
$929$	−9.45146	−	35.2733i	−0.310092	−	1.15728i	−0.928472	−	0.371401i	$-0.878877\pi$
$929$	−9.45146	−	35.2733i	−0.310092	−	1.15728i	0.618380	−	0.785879i	$-0.287789\pi$
$930$	19.6078	+	14.6610i	0.642965	+	0.480754i
$931$			24.0718i			0.788921i
$932$	−12.9769	+	13.6404i	−0.425073	+	0.446807i
$933$	6.98611	+	1.87192i	0.228715	+	0.0612840i
$934$	−38.4602	−	15.3721i	−1.25846	−	0.502990i
$935$			0.564551i			0.0184628i
$936$	−8.28619	+	5.94467i	−0.270843	+	0.194307i
$937$		−	15.4434i		−	0.504514i	−0.967660	−	0.252257i	$-0.918827\pi$
$937$		−	15.4434i		−	0.504514i	0.967660	−	0.252257i	$-0.0811729\pi$
$938$	8.08300	−	20.2232i	0.263919	−	0.660312i
$939$	5.36841	+	1.43846i	0.175192	+	0.0469424i
$940$	−0.978587	−	39.2572i	−0.0319180	−	1.28043i
$941$			56.4116i			1.83897i	0.393129	+	0.919483i	$0.371392\pi$
$941$			56.4116i			1.83897i	−0.393129	+	0.919483i	$0.628608\pi$
$942$	6.35317	−	8.49678i	0.206997	−	0.276840i
$943$	7.95149	+	29.6754i	0.258936	+	0.966362i
$944$	−0.0665266	−	0.0341080i	−0.00216526	−	0.00111012i
$945$	2.89722	−	5.01814i	0.0942467	−	0.163240i
$946$	32.6281	−	81.6338i	1.06083	−	2.65414i
$947$	−32.1084	+	18.5378i	−1.04338	+	0.602397i	−0.920790	−	0.390060i	$-0.872454\pi$
$947$	−32.1084	+	18.5378i	−1.04338	+	0.602397i	−0.122593	+	0.992457i	$0.539121\pi$
$948$	−6.24222	+	3.81445i	−0.202738	+	0.123888i
$949$	20.9361	+	24.0720i	0.679615	+	0.781410i
$950$	−47.2093	−	5.61769i	−1.53167	−	0.182262i
$951$	24.4688	+	6.55640i	0.793456	+	0.212606i
$952$	0.149015	+	0.105735i	0.00482959	+	0.00342690i
$953$	−11.5623	+	20.0265i	−0.374540	+	0.648723i	−0.990258	−	0.139244i	$-0.955533\pi$
$953$	−11.5623	+	20.0265i	−0.374540	+	0.648723i	0.615718	+	0.787967i	$0.288866\pi$
$954$	−10.0995	+	7.95152i	−0.326984	+	0.257440i
$955$	27.5931	+	15.9309i	0.892893	+	0.515512i
$956$	−1.00092	+	0.0249505i	−0.0323721	+	0.000806958i
$957$	28.7857			0.930511
$958$	−1.22845	−	8.51018i	−0.0396896	−	0.274952i
$959$	19.5896	+	33.9302i	0.632581	+	1.09566i
$960$	21.0707	−	14.3648i	0.680055	−	0.463621i
$961$		−	1.50514i		−	0.0485530i
$962$	−27.5107	+	31.9034i	−0.886980	+	1.02861i
$963$	−2.21540	−	2.21540i	−0.0713902	−	0.0713902i
$964$	−13.3886	+	24.5850i	−0.431218	+	0.791829i
$965$	−12.8137	+	47.8213i	−0.412487	+	1.53942i
$966$	4.31802	−	5.77495i	0.138930	−	0.185806i
$967$	−16.1592	+	16.1592i	−0.519644	+	0.519644i	−0.917464	−	0.397819i	$-0.869767\pi$
$967$	−16.1592	+	16.1592i	−0.519644	+	0.519644i	0.397819	+	0.917464i	$0.369767\pi$
$968$	−30.1334	+	24.9657i	−0.968525	+	0.802428i
$969$	−0.0599100	−	0.223587i	−0.00192459	−	0.00718265i
$970$	−16.2825	+	12.8195i	−0.522798	+	0.411608i
$971$	−4.43290	−	16.5438i	−0.142258	−	0.530916i	−0.999862	−	0.0166047i	$-0.994714\pi$
$971$	−4.43290	−	16.5438i	−0.142258	−	0.530916i	0.857604	−	0.514311i	$-0.171952\pi$
$972$	0.956527	−	1.75643i	0.0306806	−	0.0563376i
$973$	19.9405	+	34.5380i	0.639263	+	1.10724i
$974$	20.7881	−	16.3669i	0.666095	−	0.524428i
$975$	17.5969	+	6.05415i	0.563553	+	0.193888i
$976$	11.1773	−	3.60068i	0.357777	−	0.115255i
$977$	−46.6024	−	12.4871i	−1.49094	−	0.399497i	−0.580887	−	0.813984i	$-0.697294\pi$
$977$	−46.6024	−	12.4871i	−1.49094	−	0.399497i	−0.910055	+	0.414488i	$0.863961\pi$
$978$	18.9367	+	7.56878i	0.605529	+	0.242023i
$979$	−9.95485	−	37.1520i	−0.318158	−	1.18738i
$980$	−5.52915	+	22.9036i	−0.176622	+	0.731630i
$981$	−4.29749	+	7.44347i	−0.137208	+	0.237652i
$982$	−23.7956	+	3.43493i	−0.759350	+	0.109613i
$983$	−33.1104	−	33.1104i	−1.05606	−	1.05606i	−0.998333	−	0.0577248i	$-0.981615\pi$
$983$	−33.1104	−	33.1104i	−1.05606	−	1.05606i	−0.0577248	−	0.998333i	$-0.518385\pi$
$984$	19.7642	+	23.8553i	0.630061	+	0.760479i
$985$	−9.44971	−	16.3674i	−0.301093	−	0.521508i
$986$	0.107744	−	0.269570i	0.00343127	−	0.00858485i
$987$	−7.91722	−	7.91722i	−0.252008	−	0.252008i
$988$	45.8657	−	10.1198i	1.45918	−	0.321954i
$989$	−24.7410	+	24.7410i	−0.786718	+	0.786718i
$990$	20.6470	−	8.85529i	0.656206	−	0.281440i
$991$	22.4493	−	12.9611i	0.713126	−	0.411723i	−0.0990915	−	0.995078i	$-0.531594\pi$
$991$	22.4493	−	12.9611i	0.713126	−	0.411723i	0.812217	+	0.583355i	$0.198260\pi$
$992$	29.0603	+	9.96664i	0.922666	+	0.316441i
$993$	−9.85272	+	9.85272i	−0.312667	+	0.312667i
$994$	0.352960	−	0.472051i	0.0111952	−	0.0149726i
$995$	−58.9619	−	34.0417i	−1.86922	−	1.07919i
$996$	−12.1453	−	19.8755i	−0.384840	−	0.629778i
$997$	9.15243	−	2.45239i	0.289860	−	0.0776679i	−0.110959	−	0.993825i	$-0.535392\pi$
$997$	9.15243	−	2.45239i	0.289860	−	0.0776679i	0.400819	+	0.916157i	$0.368726\pi$
$998$	−15.5909	−	36.3518i	−0.493521	−	1.15070i
$999$	2.13829	−	7.98022i	0.0676526	−	0.252483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.cz.a.379.20	yes	224
13.7	odd	12		624.2.ch.a.475.13	yes	224
16.3	odd	4		624.2.ch.a.67.13	✓	224
208.163	even	12	inner	624.2.cz.a.163.20	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
624.2.ch.a.67.13	✓	224	16.3	odd	4
624.2.ch.a.475.13	yes	224	13.7	odd	12
624.2.cz.a.163.20	yes	224	208.163	even	12	inner
624.2.cz.a.379.20	yes	224	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.cz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.557435 - 1.29972i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(-1.37853 + 1.44902i) q^{4} -3.18768 q^{5} +(1.39971 - 0.202049i) q^{6} +(-1.75583 + 0.470472i) q^{7} +(2.65175 + 0.983971i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.557435 - 1.29972i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(-1.37853 + 1.44902i) q^{4} -3.18768 q^{5} +(1.39971 - 0.202049i) q^{6} +(-1.75583 + 0.470472i) q^{7} +(2.65175 + 0.983971i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(1.77692 + 4.14308i) q^{10} +(2.49175 + 4.31583i) q^{11} +(-1.04285 - 1.70659i) q^{12} +(0.250604 - 3.59683i) q^{13} +(1.59024 + 2.01982i) q^{14} +(0.825031 - 3.07906i) q^{15} +(-0.199297 - 3.99503i) q^{16} +(-0.0307770 - 0.0177691i) q^{17} +(-0.167106 + 1.40431i) q^{18} +(3.25670 - 5.64077i) q^{19} +(4.39432 - 4.61900i) q^{20} -1.81776i q^{21} +(4.22038 - 5.64437i) q^{22} +(-2.42918 + 1.40249i) q^{23} +(-1.63677 + 2.30673i) q^{24} +5.16128 q^{25} +(-4.81456 + 1.67928i) q^{26} +(0.707107 - 0.707107i) q^{27} +(1.73874 - 3.19278i) q^{28} +(-5.57940 - 1.49499i) q^{29} +(-4.46181 + 0.644067i) q^{30} +(-3.84024 - 3.84024i) q^{31} +(-5.08132 + 2.48600i) q^{32} +(-4.81369 + 1.28982i) q^{33} +(-0.00593864 + 0.0499065i) q^{34} +(5.59701 - 1.49971i) q^{35} +(1.91835 - 0.565619i) q^{36} +(7.15487 - 4.13087i) q^{37} +(-9.14681 - 1.08843i) q^{38} +(3.40941 + 1.17299i) q^{39} +(-8.45294 - 3.13658i) q^{40} +(2.83478 - 10.5795i) q^{41} +(-2.36258 + 1.01329i) q^{42} +(12.0489 - 3.22849i) q^{43} +(-9.68867 - 2.33893i) q^{44} +(2.76061 + 1.59384i) q^{45} +(3.17695 + 2.37545i) q^{46} +(4.35547 - 4.35547i) q^{47} +(3.91049 + 0.841485i) q^{48} +(-3.20060 + 1.84787i) q^{49} +(-2.87708 - 6.70821i) q^{50} +(0.0251293 - 0.0251293i) q^{51} +(4.86640 + 5.32148i) q^{52} +(6.42703 + 6.42703i) q^{53} +(-1.31321 - 0.524873i) q^{54} +(-7.94289 - 13.7575i) q^{55} +(-5.11895 - 0.480105i) q^{56} +(4.60567 + 4.60567i) q^{57} +(1.16708 + 8.08500i) q^{58} +(0.00934508 - 0.0161862i) q^{59} +(3.32427 + 5.44007i) q^{60} +(0.759826 + 2.83571i) q^{61} +(-2.85054 + 7.13191i) q^{62} +(1.75583 + 0.470472i) q^{63} +(6.06360 + 5.21850i) q^{64} +(-0.798846 + 11.4655i) q^{65} +(4.35973 + 5.53744i) q^{66} +(-4.23595 - 7.33688i) q^{67} +(0.0681747 - 0.0201011i) q^{68} +(-0.725981 - 2.70940i) q^{69} +(-5.06917 - 6.43854i) q^{70} +(-0.0593426 - 0.221470i) q^{71} +(-1.80450 - 2.17802i) q^{72} +(-6.25663 + 6.25663i) q^{73} +(-9.35734 - 6.99662i) q^{74} +(-1.33584 + 4.98542i) q^{75} +(3.68410 + 12.4950i) q^{76} +(-6.40556 - 6.40556i) q^{77} +(-0.375964 - 5.08514i) q^{78} -3.65771i q^{79} +(0.635293 + 12.7349i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-15.3306 + 2.21299i) q^{82} +11.6463 q^{83} +(2.63397 + 2.50585i) q^{84} +(0.0981070 + 0.0566421i) q^{85} +(-10.9126 - 13.8605i) q^{86} +(2.88811 - 5.00235i) q^{87} +(2.36085 + 13.8963i) q^{88} +(-7.45501 - 1.99756i) q^{89} +(0.532680 - 4.47647i) q^{90} +(1.25219 + 6.43331i) q^{91} +(1.31648 - 5.45330i) q^{92} +(4.70331 - 2.71546i) q^{93} +(-8.08878 - 3.23299i) q^{94} +(-10.3813 + 17.9810i) q^{95} +(-1.08615 - 5.55160i) q^{96} +(1.18978 + 4.44032i) q^{97} +(4.18583 + 3.12981i) q^{98} -4.98350i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q+O(q^{10}) \) 224 * q	\( 224 q + 8 q^{10} - 32 q^{14} + 48 q^{16} - 52 q^{20} + 8 q^{22} - 12 q^{24} + 224 q^{25} + 16 q^{26} - 52 q^{28} - 24 q^{34} + 40 q^{38} - 40 q^{40} + 16 q^{43} - 56 q^{44} + 56 q^{46} + 56 q^{50} - 56 q^{52} - 32 q^{55} + 20 q^{56} + 32 q^{58} - 32 q^{59} + 16 q^{60} - 24 q^{68} - 8 q^{70} + 64 q^{71} + 16 q^{73} - 96 q^{74} + 16 q^{75} - 44 q^{76} - 24 q^{78} - 100 q^{80} + 112 q^{81} + 72 q^{82} - 80 q^{83} - 64 q^{86} - 60 q^{88} + 16 q^{89} + 40 q^{91} - 48 q^{92} - 152 q^{94} - 88 q^{98}+O(q^{100}) \) 224 * q + 8 * q^10 - 32 * q^14 + 48 * q^16 - 52 * q^20 + 8 * q^22 - 12 * q^24 + 224 * q^25 + 16 * q^26 - 52 * q^28 - 24 * q^34 + 40 * q^38 - 40 * q^40 + 16 * q^43 - 56 * q^44 + 56 * q^46 + 56 * q^50 - 56 * q^52 - 32 * q^55 + 20 * q^56 + 32 * q^58 - 32 * q^59 + 16 * q^60 - 24 * q^68 - 8 * q^70 + 64 * q^71 + 16 * q^73 - 96 * q^74 + 16 * q^75 - 44 * q^76 - 24 * q^78 - 100 * q^80 + 112 * q^81 + 72 * q^82 - 80 * q^83 - 64 * q^86 - 60 * q^88 + 16 * q^89 + 40 * q^91 - 48 * q^92 - 152 * q^94 - 88 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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