LMFDB - Embedded newform 510.2.bi.b.37.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [510,2,Mod(37,510)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("510.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(510, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 4, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 510 = 2 \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	510.bi (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [80] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.07237050309$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			37.8
Character	$\chi$	$=$	510.37
Dual form			510.2.bi.b.193.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.923880 - 0.382683i) q^{2} +(0.831470 - 0.555570i) q^{3} +(0.707107 + 0.707107i) q^{4} +(-0.921394 + 2.03741i) q^{5} +(-0.980785 + 0.195090i) q^{6} +(-2.36711 + 0.470848i) q^{7} +(-0.382683 - 0.923880i) q^{8} +(0.382683 - 0.923880i) q^{9} +(1.63094 - 1.52972i) q^{10} +(0.191090 + 0.960674i) q^{11} +(0.980785 + 0.195090i) q^{12} -3.70367 q^{13} +(2.36711 + 0.470848i) q^{14} +(0.365812 + 2.20594i) q^{15} +1.00000i q^{16} +(-2.03747 + 3.58451i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(-2.39279 - 5.77671i) q^{19} +(-2.09219 + 0.789141i) q^{20} +(-1.70659 + 1.70659i) q^{21} +(0.191090 - 0.960674i) q^{22} +(-4.97288 + 7.44244i) q^{23} +(-0.831470 - 0.555570i) q^{24} +(-3.30206 - 3.75451i) q^{25} +(3.42174 + 1.41733i) q^{26} +(-0.195090 - 0.980785i) q^{27} +(-2.00674 - 1.34086i) q^{28} +(-1.49846 - 2.24260i) q^{29} +(0.506212 - 2.17802i) q^{30} +(-0.226744 + 1.13992i) q^{31} +(0.382683 - 0.923880i) q^{32} +(0.692607 + 0.692607i) q^{33} +(3.25411 - 2.53195i) q^{34} +(1.22174 - 5.25661i) q^{35} +(0.923880 - 0.382683i) q^{36} +(2.42091 + 3.62315i) q^{37} +6.25267i q^{38} +(-3.07949 + 2.05765i) q^{39} +(2.23492 + 0.0715751i) q^{40} +(-2.65283 + 3.97024i) q^{41} +(2.22977 - 0.923602i) q^{42} +(4.90635 - 2.03228i) q^{43} +(-0.544178 + 0.814420i) q^{44} +(1.52972 + 1.63094i) q^{45} +(7.44244 - 4.97288i) q^{46} -4.30592i q^{47} +(0.555570 + 0.831470i) q^{48} +(-1.08563 + 0.449683i) q^{49} +(1.61392 + 4.73236i) q^{50} +(0.297350 + 4.11237i) q^{51} +(-2.61889 - 2.61889i) q^{52} +(-4.31375 + 10.4143i) q^{53} +(-0.195090 + 0.980785i) q^{54} +(-2.13335 - 0.495832i) q^{55} +(1.34086 + 2.00674i) q^{56} +(-5.19890 - 3.47380i) q^{57} +(0.526189 + 2.64533i) q^{58} +(13.2442 + 5.48594i) q^{59} +(-1.30117 + 1.81850i) q^{60} +(-0.974664 - 0.651250i) q^{61} +(0.645712 - 0.966376i) q^{62} +(-0.470848 + 2.36711i) q^{63} +(-0.707107 + 0.707107i) q^{64} +(3.41254 - 7.54588i) q^{65} +(-0.374836 - 0.904935i) q^{66} +(-1.11486 + 1.11486i) q^{67} +(-3.97534 + 1.09392i) q^{68} +8.95095i q^{69} +(-3.14035 + 4.38894i) q^{70} +(8.89168 + 1.76867i) q^{71} -1.00000 q^{72} +(-5.41881 - 1.07787i) q^{73} +(-0.850111 - 4.27380i) q^{74} +(-4.83146 - 1.28724i) q^{75} +(2.39279 - 5.77671i) q^{76} +(-0.904663 - 2.18405i) q^{77} +(3.63250 - 0.722550i) q^{78} +(-10.4071 + 2.07011i) q^{79} +(-2.03741 - 0.921394i) q^{80} +(-0.707107 - 0.707107i) q^{81} +(3.97024 - 2.65283i) q^{82} +(-7.10363 - 2.94242i) q^{83} -2.41349 q^{84} +(-5.42579 - 7.45391i) q^{85} -5.31059 q^{86} +(-2.49185 - 1.03216i) q^{87} +(0.814420 - 0.544178i) q^{88} +(-2.19917 - 2.19917i) q^{89} +(-0.789141 - 2.09219i) q^{90} +(8.76700 - 1.74386i) q^{91} +(-8.77896 + 1.74624i) q^{92} +(0.444774 + 1.07378i) q^{93} +(-1.64780 + 3.97815i) q^{94} +(13.9742 + 0.447536i) q^{95} +(-0.195090 - 0.980785i) q^{96} +(13.5461 + 2.69448i) q^{97} +1.17508 q^{98} +(0.960674 + 0.191090i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 48 q^{25} + 16 q^{28} + 32 q^{29} + 16 q^{30} + 16 q^{31} - 16 q^{33} - 32 q^{34} - 32 q^{35} + 48 q^{37} + 32 q^{41} + 32 q^{43} + 16 q^{44} - 64 q^{49} + 48 q^{50} - 32 q^{51} + 16 q^{52} - 32 q^{53}+ \cdots - 144 q^{98}+O(q^{100}) $ 80 * q + 48 * q^25 + 16 * q^28 + 32 * q^29 + 16 * q^30 + 16 * q^31 - 16 * q^33 - 32 * q^34 - 32 * q^35 + 48 * q^37 + 32 * q^41 + 32 * q^43 + 16 * q^44 - 64 * q^49 + 48 * q^50 - 32 * q^51 + 16 * q^52 - 32 * q^53 + 16 * q^55 - 16 * q^56 + 32 * q^57 + 32 * q^58 - 16 * q^60 + 48 * q^61 + 32 * q^62 - 32 * q^65 - 16 * q^67 - 16 * q^70 - 80 * q^72 - 80 * q^73 - 32 * q^74 - 48 * q^77 - 32 * q^78 - 64 * q^79 - 16 * q^80 - 32 * q^82 - 32 * q^83 - 32 * q^85 - 48 * q^87 - 16 * q^88 - 32 * q^89 - 32 * q^92 - 48 * q^93 - 16 * q^94 - 96 * q^95 + 80 * q^97 - 144 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/510\mathbb{Z}\right)^\times$.

$n$	$241$	$307$	$341$
$\chi(n)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−0.923880	−	0.382683i	−0.653281	−	0.270598i
$2$	−0.923880	−	0.382683i	−0.653281	−	0.270598i
$3$	0.831470	−	0.555570i	0.480049	−	0.320759i
$3$	0.831470	−	0.555570i	0.480049	−	0.320759i
$4$	0.707107	+	0.707107i	0.353553	+	0.353553i
$5$	−0.921394	+	2.03741i	−0.412060	+	0.911157i
$5$	−0.921394	+	2.03741i	−0.412060	+	0.911157i
$6$	−0.980785	+	0.195090i	−0.400404	+	0.0796453i
$7$	−2.36711	+	0.470848i	−0.894685	+	0.177964i	−0.620958	−	0.783844i	$-0.713256\pi$
$7$	−2.36711	+	0.470848i	−0.894685	+	0.177964i	−0.273726	+	0.961808i	$0.588256\pi$
$8$	−0.382683	−	0.923880i	−0.135299	−	0.326641i
$9$	0.382683	−	0.923880i	0.127561	−	0.307960i
$10$	1.63094	−	1.52972i	0.515748	−	0.483739i
$11$	0.191090	+	0.960674i	0.0576158	+	0.289654i	0.998841	−	0.0481246i	$-0.0153245\pi$
$11$	0.191090	+	0.960674i	0.0576158	+	0.289654i	−0.941226	+	0.337779i	$0.890324\pi$
$12$	0.980785	+	0.195090i	0.283128	+	0.0563177i
$13$	−3.70367			−1.02721			−0.513606	−	0.858026i	$-0.671691\pi$
$13$	−3.70367			−1.02721			−0.513606	+	0.858026i	$0.671691\pi$
$14$	2.36711	+	0.470848i	0.632638	+	0.125839i
$15$	0.365812	+	2.20594i	0.0944522	+	0.569572i
$16$			1.00000i			0.250000i
$17$	−2.03747	+	3.58451i	−0.494160	+	0.869371i
$17$	−2.03747	+	3.58451i	−0.494160	+	0.869371i
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$	−2.39279	−	5.77671i	−0.548944	−	1.32527i	−0.918265	−	0.395966i	$-0.870410\pi$
$19$	−2.39279	−	5.77671i	−0.548944	−	1.32527i	0.369321	−	0.929302i	$-0.379590\pi$
$20$	−2.09219	+	0.789141i	−0.467828	+	0.176457i
$21$	−1.70659	+	1.70659i	−0.372409	+	0.372409i
$22$	0.191090	−	0.960674i	0.0407405	−	0.204816i
$23$	−4.97288	+	7.44244i	−1.03692	+	1.55186i	−0.219665	+	0.975575i	$0.570496\pi$
$23$	−4.97288	+	7.44244i	−1.03692	+	1.55186i	−0.817252	+	0.576281i	$0.804504\pi$
$24$	−0.831470	−	0.555570i	−0.169723	−	0.113405i
$25$	−3.30206	−	3.75451i	−0.660413	−	0.750903i
$26$	3.42174	+	1.41733i	0.671059	+	0.277962i
$27$	−0.195090	−	0.980785i	−0.0375451	−	0.188752i
$28$	−2.00674	−	1.34086i	−0.379238	−	0.253399i
$29$	−1.49846	−	2.24260i	−0.278257	−	0.416441i	0.665847	−	0.746088i	$-0.268070\pi$
$29$	−1.49846	−	2.24260i	−0.278257	−	0.416441i	−0.944104	+	0.329647i	$0.893070\pi$
$30$	0.506212	−	2.17802i	0.0924212	−	0.397649i
$31$	−0.226744	+	1.13992i	−0.0407244	+	0.204735i	−0.995791	−	0.0916571i	$-0.970784\pi$
$31$	−0.226744	+	1.13992i	−0.0407244	+	0.204735i	0.955066	+	0.296392i	$0.0957836\pi$
$32$	0.382683	−	0.923880i	0.0676495	−	0.163320i
$33$	0.692607	+	0.692607i	0.120567	+	0.120567i
$34$	3.25411	−	2.53195i	0.558076	−	0.434225i
$35$	1.22174	−	5.25661i	0.206511	−	0.888530i
$36$	0.923880	−	0.382683i	0.153980	−	0.0637806i
$37$	2.42091	+	3.62315i	0.397996	+	0.595642i	0.975299	−	0.220887i	$-0.0708952\pi$
$37$	2.42091	+	3.62315i	0.397996	+	0.595642i	−0.577304	+	0.816529i	$0.695895\pi$
$38$			6.25267i			1.01432i
$39$	−3.07949	+	2.05765i	−0.493113	+	0.329487i
$40$	2.23492	+	0.0715751i	0.353372	+	0.0113170i
$41$	−2.65283	+	3.97024i	−0.414302	+	0.620047i	−0.978661	−	0.205482i	$-0.934124\pi$
$41$	−2.65283	+	3.97024i	−0.414302	+	0.620047i	0.564358	+	0.825530i	$0.309124\pi$
$42$	2.22977	−	0.923602i	0.344061	−	0.142515i
$43$	4.90635	−	2.03228i	0.748211	−	0.309919i	0.0241997	−	0.999707i	$-0.492296\pi$
$43$	4.90635	−	2.03228i	0.748211	−	0.309919i	0.724011	+	0.689788i	$0.242296\pi$
$44$	−0.544178	+	0.814420i	−0.0820379	+	0.122778i
$45$	1.52972	+	1.63094i	0.228037	+	0.243126i
$46$	7.44244	−	4.97288i	1.09733	−	0.733211i
$47$		−	4.30592i		−	0.628083i	−0.949409	−	0.314041i	$-0.898317\pi$
$47$		−	4.30592i		−	0.628083i	0.949409	−	0.314041i	$-0.101683\pi$
$48$	0.555570	+	0.831470i	0.0801897	+	0.120012i
$49$	−1.08563	+	0.449683i	−0.155090	+	0.0642405i
$50$	1.61392	+	4.73236i	0.228243	+	0.669257i
$51$	0.297350	+	4.11237i	0.0416373	+	0.575847i
$52$	−2.61889	−	2.61889i	−0.363175	−	0.363175i
$53$	−4.31375	+	10.4143i	−0.592539	+	1.43052i	0.288503	+	0.957479i	$0.406842\pi$
$53$	−4.31375	+	10.4143i	−0.592539	+	1.43052i	−0.881042	+	0.473037i	$0.843158\pi$
$54$	−0.195090	+	0.980785i	−0.0265484	+	0.133468i
$55$	−2.13335	−	0.495832i	−0.287661	−	0.0668579i
$56$	1.34086	+	2.00674i	0.179180	+	0.268162i
$57$	−5.19890	−	3.47380i	−0.688611	−	0.460115i
$58$	0.526189	+	2.64533i	0.0690920	+	0.347349i
$59$	13.2442	+	5.48594i	1.72425	+	0.714209i	0.999687	+	0.0250028i	$0.00795947\pi$
$59$	13.2442	+	5.48594i	1.72425	+	0.714209i	0.724565	+	0.689206i	$0.242041\pi$
$60$	−1.30117	+	1.81850i	−0.167980	+	0.234768i
$61$	−0.974664	−	0.651250i	−0.124793	−	0.0833840i	0.491607	−	0.870817i	$-0.336410\pi$
$61$	−0.974664	−	0.651250i	−0.124793	−	0.0833840i	−0.616400	+	0.787433i	$0.711410\pi$
$62$	0.645712	−	0.966376i	0.0820054	−	0.122730i
$63$	−0.470848	+	2.36711i	−0.0593213	+	0.298228i
$64$	−0.707107	+	0.707107i	−0.0883883	+	0.0883883i
$65$	3.41254	−	7.54588i	0.423273	−	0.935952i
$66$	−0.374836	−	0.904935i	−0.0461392	−	0.111390i
$67$	−1.11486	+	1.11486i	−0.136202	+	0.136202i	−0.771921	−	0.635719i	$-0.780704\pi$
$67$	−1.11486	+	1.11486i	−0.136202	+	0.136202i	0.635719	+	0.771921i	$0.280704\pi$
$68$	−3.97534	+	1.09392i	−0.482081	+	0.132657i
$69$			8.95095i			1.07757i
$70$	−3.14035	+	4.38894i	−0.375344	+	0.524578i
$71$	8.89168	+	1.76867i	1.05525	+	0.209902i	0.692080	−	0.721821i	$-0.256695\pi$
$71$	8.89168	+	1.76867i	1.05525	+	0.209902i	0.363169	+	0.931723i	$0.381695\pi$
$72$	−1.00000			−0.117851
$73$	−5.41881	−	1.07787i	−0.634223	−	0.126155i	−0.132500	−	0.991183i	$-0.542300\pi$
$73$	−5.41881	−	1.07787i	−0.634223	−	0.126155i	−0.501723	+	0.865028i	$0.667300\pi$
$74$	−0.850111	−	4.27380i	−0.0988235	−	0.496819i
$75$	−4.83146	−	1.28724i	−0.557889	−	0.148637i
$76$	2.39279	−	5.77671i	0.274472	−	0.662634i
$77$	−0.904663	−	2.18405i	−0.103096	−	0.248896i
$78$	3.63250	−	0.722550i	0.411300	−	0.0818127i
$79$	−10.4071	+	2.07011i	−1.17089	+	0.232905i	−0.741968	−	0.670435i	$-0.766107\pi$
$79$	−10.4071	+	2.07011i	−1.17089	+	0.232905i	−0.428925	+	0.903340i	$0.641107\pi$
$80$	−2.03741	−	0.921394i	−0.227789	−	0.103015i
$81$	−0.707107	−	0.707107i	−0.0785674	−	0.0785674i
$82$	3.97024	−	2.65283i	0.438440	−	0.292956i
$83$	−7.10363	−	2.94242i	−0.779725	−	0.322973i	−0.0429204	−	0.999078i	$-0.513666\pi$
$83$	−7.10363	−	2.94242i	−0.779725	−	0.322973i	−0.736804	+	0.676106i	$0.763666\pi$
$84$	−2.41349			−0.263333
$85$	−5.42579	−	7.45391i	−0.588510	−	0.808490i
$86$	−5.31059			−0.572656
$87$	−2.49185	−	1.03216i	−0.267154	−	0.110659i
$88$	0.814420	−	0.544178i	0.0868175	−	0.0580096i
$89$	−2.19917	−	2.19917i	−0.233112	−	0.233112i	0.580878	−	0.813990i	$-0.302709\pi$
$89$	−2.19917	−	2.19917i	−0.233112	−	0.233112i	−0.813990	+	0.580878i	$0.802709\pi$
$90$	−0.789141	−	2.09219i	−0.0831828	−	0.220536i
$91$	8.76700	−	1.74386i	0.919031	−	0.182807i
$92$	−8.77896	+	1.74624i	−0.915269	+	0.182058i
$93$	0.444774	+	1.07378i	0.0461209	+	0.111346i
$94$	−1.64780	+	3.97815i	−0.169958	+	0.410315i
$95$	13.9742	+	0.447536i	1.43373	+	0.0459162i
$96$	−0.195090	−	0.980785i	−0.0199113	−	0.100101i
$97$	13.5461	+	2.69448i	1.37540	+	0.273583i	0.826796	−	0.562502i	$-0.190161\pi$
$97$	13.5461	+	2.69448i	1.37540	+	0.273583i	0.548600	+	0.836085i	$0.315161\pi$
$98$	1.17508			0.118701
$99$	0.960674	+	0.191090i	0.0965514	+	0.0192053i
$100$	0.319930	−	4.98975i	0.0319930	−	0.498975i
$101$		−	7.82631i		−	0.778747i	−0.921080	−	0.389373i	$-0.872692\pi$
$101$		−	7.82631i		−	0.778747i	0.921080	−	0.389373i	$-0.127308\pi$
$102$	1.29902	−	3.91312i	0.128622	−	0.387457i
$103$	3.67375	−	3.67375i	0.361985	−	0.361985i	−0.502558	−	0.864543i	$-0.667608\pi$
$103$	3.67375	−	3.67375i	0.361985	−	0.361985i	0.864543	+	0.502558i	$0.167608\pi$
$104$	1.41733	+	3.42174i	0.138981	+	0.335530i
$105$	−1.90458	−	5.04947i	−0.185868	−	0.492778i
$106$	7.97077	−	7.97077i	0.774190	−	0.774190i
$107$	−0.976348	+	4.90843i	−0.0943871	+	0.474516i	0.904462	+	0.426554i	$0.140273\pi$
$107$	−0.976348	+	4.90843i	−0.0943871	+	0.474516i	−0.998849	+	0.0479620i	$0.984727\pi$
$108$	0.555570	−	0.831470i	0.0534598	−	0.0800082i
$109$	9.97545	+	6.66538i	0.955475	+	0.638428i	0.932447	−	0.361307i	$-0.117669\pi$
$109$	9.97545	+	6.66538i	0.955475	+	0.638428i	0.0230279	+	0.999735i	$0.492669\pi$
$110$	1.78122	+	1.27449i	0.169832	+	0.121518i
$111$	4.02583	+	1.66755i	0.382115	+	0.158277i
$112$	−0.470848	−	2.36711i	−0.0444910	−	0.223671i
$113$	−8.66241	−	5.78804i	−0.814891	−	0.544493i	0.0768478	−	0.997043i	$-0.475514\pi$
$113$	−8.66241	−	5.78804i	−0.814891	−	0.544493i	−0.891739	+	0.452550i	$0.850514\pi$
$114$	3.47380	+	5.19890i	0.325351	+	0.486922i
$115$	−10.5813	−	16.9892i	−0.986712	−	1.58425i
$116$	0.526189	−	2.64533i	0.0488554	−	0.245613i
$117$	−1.41733	+	3.42174i	−0.131032	+	0.316340i
$118$	−10.1367	−	10.1367i	−0.933159	−	0.933159i
$119$	3.13517	−	9.44428i	0.287400	−	0.865756i
$120$	1.89803	−	1.18214i	0.173266	−	0.107914i
$121$	9.27630	−	3.84237i	0.843300	−	0.349306i
$122$	0.651250	+	0.974664i	0.0589614	+	0.0882420i
$123$			4.77497i			0.430544i
$124$	−0.966376	+	0.645712i	−0.0867831	+	0.0579866i
$125$	10.6920	−	3.26827i	0.956320	−	0.292323i
$126$	1.34086	−	2.00674i	0.119453	−	0.178775i
$127$	12.3301	−	5.10729i	1.09412	−	0.453199i	0.238677	−	0.971099i	$-0.423286\pi$
$127$	12.3301	−	5.10729i	1.09412	−	0.453199i	0.855441	+	0.517900i	$0.173286\pi$
$128$	0.923880	−	0.382683i	0.0816602	−	0.0338248i
$129$	2.95041	−	4.41560i	0.259769	−	0.388772i
$130$	−6.04046	+	5.66557i	−0.529783	+	0.496903i
$131$	12.1242	−	8.10115i	1.05930	−	0.707801i	0.101382	−	0.994848i	$-0.467673\pi$
$131$	12.1242	−	8.10115i	1.05930	−	0.707801i	0.957917	+	0.287046i	$0.0926734\pi$
$132$			0.979495i			0.0852541i
$133$	8.38396	+	12.5475i	0.726982	+	1.08800i
$134$	1.45663	−	0.603356i	0.125834	−	0.0521221i
$135$	2.17802	+	0.506212i	0.187454	+	0.0435678i
$136$	4.09136	+	0.510647i	0.350831	+	0.0437876i
$137$	−10.1179	−	10.1179i	−0.864427	−	0.864427i	0.127422	−	0.991849i	$-0.459330\pi$
$137$	−10.1179	−	10.1179i	−0.864427	−	0.864427i	−0.991849	+	0.127422i	$0.959330\pi$
$138$	3.42538	−	8.26960i	0.291588	−	0.703955i
$139$	0.507031	−	2.54902i	0.0430058	−	0.216205i	−0.953307	−	0.302004i	$-0.902344\pi$
$139$	0.507031	−	2.54902i	0.0430058	−	0.216205i	0.996312	+	0.0857992i	$0.0273444\pi$
$140$	4.58088	−	2.85309i	0.387155	−	0.241130i
$141$	−2.39224	−	3.58024i	−0.201463	−	0.301511i
$142$	−7.53801	−	5.03673i	−0.632575	−	0.422673i
$143$	−0.707734	−	3.55802i	−0.0591837	−	0.297536i
$144$	0.923880	+	0.382683i	0.0769900	+	0.0318903i
$145$	5.94977	−	0.986651i	0.494101	−	0.0819369i
$146$	4.59384	+	3.06951i	0.380189	+	0.254034i
$147$	−0.652839	+	0.977042i	−0.0538452	+	0.0805851i
$148$	−0.850111	+	4.27380i	−0.0698787	+	0.351304i
$149$	−13.8822	+	13.8822i	−1.13727	+	1.13727i	−0.148334	+	0.988937i	$0.547391\pi$
$149$	−13.8822	+	13.8822i	−1.13727	+	1.13727i	−0.988937	+	0.148334i	$0.952609\pi$
$150$	3.97109	+	3.03817i	0.324238	+	0.248066i
$151$	3.40501	+	8.22043i	0.277096	+	0.668969i	0.999753	−	0.0222381i	$-0.00707919\pi$
$151$	3.40501	+	8.22043i	0.277096	+	0.668969i	−0.722657	+	0.691207i	$0.757079\pi$
$152$	−4.42130	+	4.42130i	−0.358615	+	0.358615i
$153$	2.53195	+	3.25411i	0.204696	+	0.263079i
$154$			2.36400i			0.190496i
$155$	−2.11356	−	1.51228i	−0.169765	−	0.121470i
$156$	−3.63250	−	0.722550i	−0.290833	−	0.0578503i
$157$	−16.5444			−1.32039			−0.660195	−	0.751094i	$-0.729526\pi$
$157$	−16.5444			−1.32039			−0.660195	+	0.751094i	$0.729526\pi$
$158$	10.4071	+	2.07011i	0.827946	+	0.164689i
$159$	2.19913	+	11.0558i	0.174402	+	0.876780i
$160$	1.52972	+	1.63094i	0.120935	+	0.128937i
$161$	8.26711	−	19.9586i	0.651539	−	1.57296i
$162$	0.382683	+	0.923880i	0.0300665	+	0.0725868i
$163$	−10.9078	+	2.16969i	−0.854361	+	0.169943i	−0.602794	−	0.797897i	$-0.705946\pi$
$163$	−10.9078	+	2.16969i	−0.854361	+	0.169943i	−0.251567	+	0.967840i	$0.580946\pi$
$164$	−4.68322	+	0.931550i	−0.365698	+	0.0727418i
$165$	−2.04929	+	0.772959i	−0.159537	+	0.0601748i
$166$	5.43688	+	5.43688i	0.421984	+	0.421984i
$167$	19.5778	−	13.0815i	1.51498	−	1.01227i	0.528396	−	0.848998i	$-0.322794\pi$
$167$	19.5778	−	13.0815i	1.51498	−	1.01227i	0.986580	−	0.163276i	$-0.0522062\pi$
$168$	2.22977	+	0.923602i	0.172031	+	0.0712574i
$169$	0.717159			0.0551661
$170$	2.16029	+	8.96288i	0.165687	+	0.687421i
$171$	−6.25267			−0.478153
$172$	4.90635	+	2.03228i	0.374106	+	0.154960i
$173$	−9.38527	+	6.27104i	−0.713549	+	0.476778i	−0.858600	−	0.512646i	$-0.828665\pi$
$173$	−9.38527	+	6.27104i	−0.713549	+	0.476778i	0.145051	+	0.989424i	$0.453665\pi$
$174$	1.90718	+	1.90718i	0.144583	+	0.144583i
$175$	9.58416	+	7.33259i	0.724495	+	0.554291i
$176$	−0.960674	+	0.191090i	−0.0724135	+	0.0144039i
$177$	14.0600	−	2.79671i	1.05681	−	0.210214i
$178$	1.19018	+	2.87336i	0.0892080	+	0.215367i
$179$	−0.103360	+	0.249534i	−0.00772552	+	0.0186510i	−0.927695	−	0.373338i	$-0.878213\pi$
$179$	−0.103360	+	0.249534i	−0.00772552	+	0.0186510i	0.919970	+	0.391989i	$0.128213\pi$
$180$	−0.0715751	+	2.23492i	−0.00533490	+	0.166581i
$181$	−0.643620	−	3.23570i	−0.0478399	−	0.240508i	0.949465	−	0.313872i	$-0.101626\pi$
$181$	−0.643620	−	3.23570i	−0.0478399	−	0.240508i	−0.997305	+	0.0733646i	$0.976626\pi$
$182$	−8.76700	−	1.74386i	−0.649853	−	0.129264i
$183$	−1.17222			−0.0866529
$184$	8.77896	+	1.74624i	0.647193	+	0.128735i
$185$	−9.61245	+	1.59404i	−0.706722	+	0.117196i
$186$		−	1.16225i		−	0.0852203i
$187$	−3.83289	−	1.27238i	−0.280288	−	0.0930459i
$188$	3.04474	−	3.04474i	0.222061	−	0.222061i
$189$	0.923602	+	2.22977i	0.0671821	+	0.162192i
$190$	−12.7392	−	5.76117i	−0.924201	−	0.417959i
$191$	−17.3754	+	17.3754i	−1.25724	+	1.25724i	−0.304830	+	0.952407i	$0.598600\pi$
$191$	−17.3754	+	17.3754i	−1.25724	+	1.25724i	−0.952407	+	0.304830i	$0.901400\pi$
$192$	−0.195090	+	0.980785i	−0.0140794	+	0.0707821i
$193$	4.29419	−	6.42672i	0.309103	−	0.462605i	−0.644098	−	0.764943i	$-0.722767\pi$
$193$	4.29419	−	6.42672i	0.309103	−	0.462605i	0.953201	+	0.302338i	$0.0977671\pi$
$194$	−11.4838	−	7.67324i	−0.824490	−	0.550906i
$195$	−1.35485	−	8.17008i	−0.0970225	−	0.585071i
$196$	−1.08563	−	0.449683i	−0.0775451	−	0.0321202i
$197$	−4.77009	−	23.9809i	−0.339855	−	1.70857i	−0.651737	−	0.758445i	$-0.725959\pi$
$197$	−4.77009	−	23.9809i	−0.339855	−	1.70857i	0.311882	−	0.950121i	$-0.399041\pi$
$198$	−0.814420	−	0.544178i	−0.0578783	−	0.0386731i
$199$	3.83877	+	5.74512i	0.272123	+	0.407261i	0.942211	−	0.335021i	$-0.108743\pi$
$199$	3.83877	+	5.74512i	0.272123	+	0.407261i	−0.670087	+	0.742282i	$0.733743\pi$
$200$	−2.20507	+	4.48750i	−0.155922	+	0.317314i
$201$	−0.307588	+	1.54635i	−0.0216956	+	0.109071i
$202$	−2.99500	+	7.23056i	−0.210727	+	0.508741i
$203$	4.60295	+	4.60295i	0.323064	+	0.323064i
$204$	−2.69763	+	3.11814i	−0.188872	+	0.218314i
$205$	−5.64470	−	9.06306i	−0.394243	−	0.632991i
$206$	−4.79998	+	1.98822i	−0.334431	+	0.138526i
$207$	4.97288	+	7.44244i	0.345639	+	0.517285i
$208$		−	3.70367i		−	0.256803i
$209$	5.09230	−	3.40256i	0.352242	−	0.235360i
$210$	−0.172746	+	5.39396i	−0.0119206	+	0.372218i
$211$	−13.2365	+	19.8099i	−0.911240	+	1.36377i	0.0201706	+	0.999797i	$0.493579\pi$
$211$	−13.2365	+	19.8099i	−0.911240	+	1.36377i	−0.931411	+	0.363970i	$0.881421\pi$
$212$	−10.4143	+	4.31375i	−0.715258	+	0.296270i
$213$	8.37578	−	3.46936i	0.573899	−	0.237717i
$214$	2.78040	−	4.16117i	0.190065	−	0.284452i
$215$	−0.380106	+	11.8688i	−0.0259230	+	0.809443i
$216$	−0.831470	+	0.555570i	−0.0565743	+	0.0378018i
$217$		−	2.80508i		−	0.190421i
$218$	−6.66538	−	9.97545i	−0.451437	−	0.675623i
$219$	−5.10441	+	2.11431i	−0.344924	+	0.142872i
$220$	−1.15790	−	1.85912i	−0.0780658	−	0.125342i
$221$	7.54612	−	13.2758i	0.507607	−	0.893029i
$222$	−3.08124	−	3.08124i	−0.206799	−	0.206799i
$223$	2.53896	−	6.12960i	0.170022	−	0.410468i	−0.815785	−	0.578356i	$-0.803695\pi$
$223$	2.53896	−	6.12960i	0.170022	−	0.410468i	0.985806	+	0.167887i	$0.0536945\pi$
$224$	−0.470848	+	2.36711i	−0.0314599	+	0.158159i
$225$	−4.73236	+	1.61392i	−0.315491	+	0.107595i
$226$	5.78804	+	8.66241i	0.385015	+	0.576215i
$227$	9.46121	+	6.32178i	0.627963	+	0.419591i	0.828417	−	0.560112i	$-0.189242\pi$
$227$	9.46121	+	6.32178i	0.627963	+	0.419591i	−0.200454	+	0.979703i	$0.564242\pi$
$228$	−1.21983	−	6.13252i	−0.0807855	−	0.406136i
$229$	16.7933	+	6.95600i	1.10973	+	0.459666i	0.860845	−	0.508867i	$-0.169936\pi$
$229$	16.7933	+	6.95600i	1.10973	+	0.459666i	0.248886	+	0.968533i	$0.419936\pi$
$230$	3.27436	+	19.7453i	0.215905	+	1.30196i
$231$	−1.96559	−	1.31337i	−0.129326	−	0.0864132i
$232$	−1.49846	+	2.24260i	−0.0983787	+	0.147234i
$233$	−3.67016	+	18.4511i	−0.240440	+	1.20877i	0.652216	+	0.758033i	$0.273840\pi$
$233$	−3.67016	+	18.4511i	−0.240440	+	1.20877i	−0.892656	+	0.450739i	$0.851160\pi$
$234$	2.61889	−	2.61889i	0.171202	−	0.171202i
$235$	8.77292	+	3.96745i	0.572282	+	0.258808i
$236$	5.48594	+	13.2442i	0.357104	+	0.862126i
$237$	−7.50312	+	7.50312i	−0.487380	+	0.487380i
$238$	−6.51069	+	7.52560i	−0.422025	+	0.487812i
$239$			0.567062i			0.0366802i	0.999832	+	0.0183401i	$0.00583816\pi$
$239$			0.567062i			0.0366802i	−0.999832	+	0.0183401i	$0.994162\pi$
$240$	−2.20594	+	0.365812i	−0.142393	+	0.0236131i
$241$	−26.7068	−	5.31231i	−1.72033	−	0.342196i	−0.766435	−	0.642322i	$-0.777971\pi$
$241$	−26.7068	−	5.31231i	−1.72033	−	0.342196i	−0.953900	+	0.300126i	$0.902971\pi$
$242$	−10.0406			−0.645434
$243$	−0.980785	−	0.195090i	−0.0629174	−	0.0125150i
$244$	−0.228689	−	1.14969i	−0.0146403	−	0.0736017i
$245$	0.0841064	−	2.62621i	0.00537336	−	0.167782i
$246$	1.82730	−	4.41150i	0.116504	−	0.281267i
$247$	8.86211	+	21.3950i	0.563882	+	1.36133i
$248$	1.13992	−	0.226744i	0.0723848	−	0.0143982i
$249$	−7.54118	+	1.50003i	−0.477903	+	0.0950607i
$250$	−11.1288	−	1.07216i	−0.703848	−	0.0678094i
$251$	17.6881	+	17.6881i	1.11646	+	1.11646i	0.992256	+	0.124206i	$0.0396383\pi$
$251$	17.6881	+	17.6881i	1.11646	+	1.11646i	0.124206	+	0.992256i	$0.460362\pi$
$252$	−2.00674	+	1.34086i	−0.126413	+	0.0844663i
$253$	−8.10002	−	3.35514i	−0.509244	−	0.210936i
$254$	−13.3460			−0.837402
$255$	−8.65255	−	3.18329i	−0.541844	−	0.199345i
$256$	−1.00000			−0.0625000
$257$	−6.48984	−	2.68818i	−0.404825	−	0.167684i	0.170973	−	0.985276i	$-0.445309\pi$
$257$	−6.48984	−	2.68818i	−0.404825	−	0.167684i	−0.575799	+	0.817592i	$0.695309\pi$
$258$	−4.41560	+	2.95041i	−0.274903	+	0.183684i
$259$	−7.43653	−	7.43653i	−0.462083	−	0.462083i
$260$	7.74878	−	2.92272i	0.480559	−	0.181259i
$261$	−2.64533	+	0.526189i	−0.163742	+	0.0325703i
$262$	−14.3015	+	2.84475i	−0.883550	+	0.175749i
$263$	0.0186097	+	0.0449278i	0.00114752	+	0.00277037i	0.924452	−	0.381298i	$-0.124523\pi$
$263$	0.0186097	+	0.0449278i	0.00114752	+	0.00277037i	−0.923305	+	0.384068i	$0.874523\pi$
$264$	0.374836	−	0.904935i	0.0230696	−	0.0556949i
$265$	−17.2435	−	18.3846i	−1.05926	−	1.12935i
$266$	−2.94406	−	14.8008i	−0.180512	−	0.907493i
$267$	−3.05034	−	0.606750i	−0.186678	−	0.0371325i
$268$	−1.57665			−0.0963090
$269$	−17.1885	−	3.41900i	−1.04800	−	0.208460i	−0.359086	−	0.933304i	$-0.616912\pi$
$269$	−17.1885	−	3.41900i	−1.04800	−	0.208460i	−0.688913	+	0.724844i	$0.741912\pi$
$270$	−1.81850	−	1.30117i	−0.110671	−	0.0791866i
$271$			14.5013i			0.880890i	0.897780	+	0.440445i	$0.145179\pi$
$271$			14.5013i			0.880890i	−0.897780	+	0.440445i	$0.854821\pi$
$272$	−3.58451	−	2.03747i	−0.217343	−	0.123540i
$273$	6.32066	−	6.32066i	0.382543	−	0.382543i
$274$	5.47575	+	13.2196i	0.330802	+	0.798627i
$275$	2.97587	−	3.88966i	0.179452	−	0.234555i
$276$	−6.32927	+	6.32927i	−0.380978	+	0.380978i
$277$	−4.98176	+	25.0450i	−0.299325	+	1.50481i	0.479485	+	0.877550i	$0.340823\pi$
$277$	−4.98176	+	25.0450i	−0.299325	+	1.50481i	−0.778810	+	0.627259i	$0.784177\pi$
$278$	−1.44390	+	2.16095i	−0.0865995	+	0.129605i
$279$	0.966376	+	0.645712i	0.0578554	+	0.0386577i
$280$	−5.32401	+	0.882882i	−0.318171	+	0.0527623i
$281$	−5.65510	−	2.34242i	−0.337355	−	0.139737i	0.207574	−	0.978219i	$-0.433443\pi$
$281$	−5.65510	−	2.34242i	−0.337355	−	0.139737i	−0.544929	+	0.838482i	$0.683443\pi$
$282$	0.840043	+	4.22318i	0.0500238	+	0.251487i
$283$	17.8628	+	11.9355i	1.06183	+	0.709495i	0.958483	−	0.285150i	$-0.0920435\pi$
$283$	17.8628	+	11.9355i	1.06183	+	0.709495i	0.103351	+	0.994645i	$0.467044\pi$
$284$	5.03673	+	7.53801i	0.298875	+	0.447298i
$285$	11.8678	−	7.39155i	0.702987	−	0.437838i
$286$	−0.707734	+	3.55802i	−0.0418492	+	0.210390i
$287$	4.41017	−	10.6471i	0.260324	−	0.628478i
$288$	−0.707107	−	0.707107i	−0.0416667	−	0.0416667i
$289$	−8.69741	−	14.6067i	−0.511612	−	0.859216i
$290$	−5.87445	−	1.36533i	−0.344959	−	0.0801750i
$291$	12.7601	−	5.28542i	0.748012	−	0.309837i
$292$	−3.06951	−	4.59384i	−0.179629	−	0.268834i
$293$			12.7924i			0.747337i	0.927562	+	0.373669i	$0.121900\pi$
$293$			12.7924i			0.747337i	−0.927562	+	0.373669i	$0.878100\pi$
$294$	0.977042	−	0.652839i	0.0569823	−	0.0380743i
$295$	−23.3803	+	21.9292i	−1.36125	+	1.27677i
$296$	2.42091	−	3.62315i	0.140713	−	0.210591i
$297$	0.904935	−	0.374836i	0.0525097	−	0.0217502i
$298$	18.1379	−	7.51298i	1.05070	−	0.435215i
$299$	18.4179	−	27.5643i	1.06513	−	1.59409i
$300$	−2.50615	−	4.32657i	−0.144692	−	0.249795i
$301$	−10.6570	+	7.12077i	−0.614259	+	0.410434i
$302$		−	8.89773i		−	0.512007i
$303$	−4.34806	−	6.50734i	−0.249790	−	0.373837i
$304$	5.77671	−	2.39279i	0.331317	−	0.137236i
$305$	2.22491	−	1.38573i	0.127398	−	0.0793467i
$306$	−1.09392	−	3.97534i	−0.0625353	−	0.227255i
$307$	10.6477	+	10.6477i	0.607699	+	0.607699i	0.942344	−	0.334645i	$-0.108617\pi$
$307$	10.6477	+	10.6477i	0.607699	+	0.607699i	−0.334645	+	0.942344i	$0.608617\pi$
$308$	0.904663	−	2.18405i	0.0515480	−	0.124448i
$309$	1.01358	−	5.09563i	0.0576608	−	0.289881i
$310$	1.37395	+	2.20599i	0.0780349	+	0.125292i
$311$	2.26195	+	3.38525i	0.128263	+	0.191960i	0.890043	−	0.455876i	$-0.150674\pi$
$311$	2.26195	+	3.38525i	0.128263	+	0.191960i	−0.761780	+	0.647836i	$0.775674\pi$
$312$	3.07949	+	2.05765i	0.174342	+	0.116491i
$313$	2.66967	+	13.4213i	0.150898	+	0.758618i	0.979918	+	0.199399i	$0.0638989\pi$
$313$	2.66967	+	13.4213i	0.150898	+	0.758618i	−0.829020	+	0.559219i	$0.811101\pi$
$314$	15.2851	+	6.33128i	0.862586	+	0.357295i
$315$	−4.38894	−	3.14035i	−0.247289	−	0.176939i
$316$	−8.82273	−	5.89516i	−0.496318	−	0.331629i
$317$	−10.6041	+	15.8702i	−0.595588	+	0.891361i	−0.999728	−	0.0233364i	$-0.992571\pi$
$317$	−10.6041	+	15.8702i	−0.595588	+	0.891361i	0.404139	+	0.914697i	$0.367571\pi$
$318$	2.19913	−	11.0558i	0.123321	−	0.619977i
$319$	1.86807	−	1.86807i	0.104592	−	0.104592i
$320$	−0.789141	−	2.09219i	−0.0441143	−	0.116957i
$321$	1.91518	+	4.62364i	0.106895	+	0.258067i
$322$	−15.2756	+	15.2756i	−0.851277	+	0.851277i
$323$	25.5819	+	3.19290i	1.42342	+	0.177658i
$324$		−	1.00000i		−	0.0555556i
$325$	12.2298	+	13.9055i	0.678385	+	0.771337i
$326$	10.9078	+	2.16969i	0.604124	+	0.120168i
$327$	11.9974			0.663456
$328$	4.68322	+	0.931550i	0.258587	+	0.0514362i
$329$	2.02743	+	10.1926i	0.111776	+	0.561936i
$330$	2.18909	+	0.0701075i	0.120506	+	0.00385929i
$331$	−3.24686	+	7.83860i	−0.178463	+	0.430849i	−0.987645	−	0.156710i	$-0.949911\pi$
$331$	−3.24686	+	7.83860i	−0.178463	+	0.430849i	0.809181	+	0.587559i	$0.199911\pi$
$332$	−2.94242	−	7.10363i	−0.161486	−	0.389862i
$333$	4.27380	−	0.850111i	0.234203	−	0.0465858i
$334$	−23.0936	+	4.59360i	−1.26363	+	0.251351i
$335$	−1.24420	−	3.29864i	−0.0679777	−	0.180224i
$336$	−1.70659	−	1.70659i	−0.0931023	−	0.0931023i
$337$	3.33573	−	2.22887i	0.181709	−	0.121414i	−0.461389	−	0.887198i	$-0.652649\pi$
$337$	3.33573	−	2.22887i	0.181709	−	0.121414i	0.643098	+	0.765784i	$0.277649\pi$
$338$	−0.662568	−	0.274445i	−0.0360390	−	0.0149278i
$339$	−10.4182			−0.565839
$340$	1.43410	−	9.10733i	0.0777748	−	0.493914i
$341$	−1.13842			−0.0616488
$342$	5.77671	+	2.39279i	0.312369	+	0.129387i
$343$	16.4053	−	10.9617i	0.885801	−	0.591873i
$344$	−3.75516	−	3.75516i	−0.202464	−	0.202464i
$345$	−18.2367	−	8.24735i	−0.981833	−	0.444023i
$346$	11.0707	−	2.20210i	0.595163	−	0.118385i
$347$	7.43437	−	1.47879i	0.399098	−	0.0793855i	0.00853925	−	0.999964i	$-0.497282\pi$
$347$	7.43437	−	1.47879i	0.399098	−	0.0793855i	0.390559	+	0.920578i	$0.372282\pi$
$348$	−1.03216	−	2.49185i	−0.0553294	−	0.133577i
$349$	−4.37887	+	10.5715i	−0.234395	+	0.565880i	−0.996685	−	0.0813555i	$-0.974075\pi$
$349$	−4.37887	+	10.5715i	−0.234395	+	0.565880i	0.762290	+	0.647236i	$0.224075\pi$
$350$	−6.04855	−	10.4421i	−0.323309	−	0.558155i
$351$	0.722550	+	3.63250i	0.0385669	+	0.193889i
$352$	0.960674	+	0.191090i	0.0512041	+	0.0101851i
$353$	19.0151			1.01207			0.506035	−	0.862513i	$-0.331111\pi$
$353$	19.0151			1.01207			0.506035	+	0.862513i	$0.331111\pi$
$354$	−14.0600	−	2.79671i	−0.747281	−	0.148643i
$355$	−11.7962	+	16.4864i	−0.626080	+	0.875005i
$356$		−	3.11010i		−	0.164835i
$357$	−2.64016	−	9.59444i	−0.139732	−	0.507791i
$358$	0.190985	−	0.190985i	0.0100939	−	0.0100939i
$359$	−0.488011	−	1.17816i	−0.0257562	−	0.0621811i	0.910478	−	0.413557i	$-0.135714\pi$
$359$	−0.488011	−	1.17816i	−0.0257562	−	0.0621811i	−0.936234	+	0.351376i	$0.885714\pi$
$360$	0.921394	−	2.03741i	0.0485618	−	0.107381i
$361$	−14.2099	+	14.2099i	−0.747890	+	0.747890i
$362$	−0.643620	+	3.23570i	−0.0338279	+	0.170065i
$363$	5.57825	−	8.34845i	0.292782	−	0.438180i
$364$	7.43230	+	4.96611i	0.389559	+	0.260295i
$365$	7.18892	−	10.0472i	0.376285	−	0.525894i
$366$	1.08299	+	0.448589i	0.0566087	+	0.0234481i
$367$	−1.23708	−	6.21924i	−0.0645753	−	0.324642i	0.934972	−	0.354721i	$-0.115424\pi$
$367$	−1.23708	−	6.21924i	−0.0645753	−	0.324642i	−0.999548	+	0.0300790i	$0.990424\pi$
$368$	−7.44244	−	4.97288i	−0.387964	−	0.259229i
$369$	2.65283	+	3.97024i	0.138101	+	0.206682i
$370$	9.49076	+	2.20583i	0.493401	+	0.114676i
$371$	5.30757	−	26.6830i	0.275556	−	1.38531i
$372$	−0.444774	+	1.07378i	−0.0230604	+	0.0556728i
$373$	−14.9410	−	14.9410i	−0.773618	−	0.773618i	0.205119	−	0.978737i	$-0.434242\pi$
$373$	−14.9410	−	14.9410i	−0.773618	−	0.773618i	−0.978737	+	0.205119i	$0.934242\pi$
$374$	3.05420	+	2.64231i	0.157929	+	0.136631i
$375$	7.07431	−	8.65761i	0.365316	−	0.447077i
$376$	−3.97815	+	1.64780i	−0.205157	+	0.0849790i
$377$	5.54980	+	8.30586i	0.285829	+	0.427773i
$378$		−	2.41349i		−	0.124136i
$379$	8.81958	−	5.89305i	0.453031	−	0.302706i	−0.308041	−	0.951373i	$-0.599673\pi$
$379$	8.81958	−	5.89305i	0.453031	−	0.302706i	0.761072	+	0.648667i	$0.224673\pi$
$380$	9.56481	+	10.1977i	0.490665	+	0.523132i
$381$	7.41464	−	11.0968i	0.379863	−	0.568506i
$382$	22.7020	−	9.40348i	1.16154	−	0.481124i
$383$	−20.8005	+	8.61586i	−1.06286	+	0.440250i	−0.844465	−	0.535611i	$-0.820081\pi$
$383$	−20.8005	+	8.61586i	−1.06286	+	0.440250i	−0.218393	+	0.975861i	$0.570081\pi$
$384$	0.555570	−	0.831470i	0.0283513	−	0.0424308i
$385$	5.28335	+	0.169204i	0.269265	+	0.00862341i
$386$	−6.42672	+	4.29419i	−0.327111	+	0.218569i
$387$		−	5.31059i		−	0.269953i
$388$	7.67324	+	11.4838i	0.389550	+	0.583002i
$389$	−22.7695	+	9.43144i	−1.15446	+	0.478193i	−0.876027	−	0.482262i	$-0.839815\pi$
$389$	−22.7695	+	9.43144i	−1.15446	+	0.478193i	−0.278434	+	0.960455i	$0.589815\pi$
$390$	−1.87484	+	8.06665i	−0.0949362	+	0.408470i
$391$	−16.5454	−	32.9891i	−0.836736	−	1.66833i
$392$	0.830906	+	0.830906i	0.0419671	+	0.0419671i
$393$	5.58017	−	13.4717i	0.281482	−	0.679559i
$394$	−4.77009	+	23.9809i	−0.240314	+	1.20814i
$395$	5.37142	−	23.1109i	0.270265	−	1.16284i
$396$	0.544178	+	0.814420i	0.0273460	+	0.0409261i
$397$	25.1008	+	16.7718i	1.25977	+	0.841753i	0.992545	−	0.121880i	$-0.0388924\pi$
$397$	25.1008	+	16.7718i	1.25977	+	0.841753i	0.267228	+	0.963633i	$0.413892\pi$
$398$	−1.34800	−	6.77684i	−0.0675690	−	0.339692i
$399$	13.9420	+	5.77497i	0.697974	+	0.289110i
$400$	3.75451	−	3.30206i	0.187726	−	0.165103i
$401$	−8.23108	−	5.49983i	−0.411040	−	0.274648i	0.332811	−	0.942994i	$-0.392003\pi$
$401$	−8.23108	−	5.49983i	−0.411040	−	0.274648i	−0.743851	+	0.668345i	$0.767003\pi$
$402$	0.875938	−	1.31093i	0.0436878	−	0.0653834i
$403$	0.839784	−	4.22188i	0.0418326	−	0.210307i
$404$	5.53403	−	5.53403i	0.275328	−	0.275328i
$405$	2.09219	−	0.789141i	0.103962	−	0.0392127i
$406$	−2.49110	−	6.01404i	−0.123631	−	0.298472i
$407$	−3.01806	+	3.01806i	−0.149599	+	0.149599i
$408$	3.68554	−	1.84845i	0.182462	−	0.0915120i
$409$		−	26.3313i		−	1.30200i	−0.759078	−	0.651000i	$-0.774350\pi$
$409$		−	26.3313i		−	1.30200i	0.759078	−	0.651000i	$-0.225650\pi$
$410$	1.74674	+	10.5333i	0.0862653	+	0.520203i
$411$	−14.0339	−	2.79151i	−0.692240	−	0.137695i
$412$	5.19546			0.255962
$413$	−33.9336	−	6.74982i	−1.66977	−	0.332137i
$414$	−1.74624	−	8.77896i	−0.0858232	−	0.431462i
$415$	12.5402	−	11.7619i	0.615572	−	0.577367i
$416$	−1.41733	+	3.42174i	−0.0694904	+	0.167765i
$417$	−0.994578	−	2.40112i	−0.0487047	−	0.117583i
$418$	−6.00677	+	1.19482i	−0.293801	+	0.0584406i
$419$	9.36373	−	1.86256i	0.457448	−	0.0909921i	0.0390128	−	0.999239i	$-0.487579\pi$
$419$	9.36373	−	1.86256i	0.457448	−	0.0909921i	0.418435	+	0.908247i	$0.362579\pi$
$420$	2.22377	−	4.91726i	0.108509	−	0.239938i
$421$	3.27742	+	3.27742i	0.159732	+	0.159732i	0.782448	−	0.622716i	$-0.213971\pi$
$421$	3.27742	+	3.27742i	0.159732	+	0.159732i	−0.622716	+	0.782448i	$0.713971\pi$
$422$	19.8099	−	13.2365i	0.964329	−	0.644344i
$423$	−3.97815	−	1.64780i	−0.193424	−	0.0801190i
$424$	11.2724			0.547435
$425$	20.1860	−	4.18656i	0.979163	−	0.203078i
$426$	−9.06588			−0.439243
$427$	2.61378	+	1.08266i	0.126490	+	0.0523937i
$428$	−4.16117	+	2.78040i	−0.201138	+	0.134396i
$429$	−2.56519	−	2.56519i	−0.123848	−	0.123848i
$430$	4.89315	−	10.8198i	0.235969	−	0.521779i
$431$	−24.5722	+	4.88771i	−1.18360	+	0.235433i	−0.747373	−	0.664404i	$-0.768685\pi$
$431$	−24.5722	+	4.88771i	−1.18360	+	0.235433i	−0.436226	+	0.899837i	$0.643685\pi$
$432$	0.980785	−	0.195090i	0.0471881	−	0.00938629i
$433$	12.7610	+	30.8077i	0.613253	+	1.48052i	0.859406	+	0.511293i	$0.170833\pi$
$433$	12.7610	+	30.8077i	0.613253	+	1.48052i	−0.246153	+	0.969231i	$0.579167\pi$
$434$	−1.07346	+	2.59155i	−0.0515275	+	0.124398i
$435$	4.39890	−	4.12589i	0.210911	−	0.197821i
$436$	2.34057	+	11.7668i	0.112093	+	0.563530i
$437$	54.8919	+	10.9187i	2.62583	+	0.522311i
$438$	5.52497			0.263993
$439$	−6.57992	−	1.30883i	−0.314043	−	0.0624670i	0.0355526	−	0.999368i	$-0.488681\pi$
$439$	−6.57992	−	1.30883i	−0.314043	−	0.0624670i	−0.349595	+	0.936901i	$0.613681\pi$
$440$	0.358311	+	2.16071i	0.0170818	+	0.103008i
$441$			1.17508i			0.0559561i
$442$	−12.0521	+	9.37749i	−0.573262	+	0.446042i
$443$	−7.53010	+	7.53010i	−0.357766	+	0.357766i	−0.862989	−	0.505223i	$-0.831410\pi$
$443$	−7.53010	+	7.53010i	−0.357766	+	0.357766i	0.505223	+	0.862989i	$0.331410\pi$
$444$	1.66755	+	4.02583i	0.0791386	+	0.191057i
$445$	6.50692	−	2.45431i	0.308457	−	0.116345i
$446$	−4.69139	+	4.69139i	−0.222144	+	0.222144i
$447$	−3.83008	+	19.2551i	−0.181157	+	0.910736i
$448$	1.34086	−	2.00674i	0.0633498	−	0.0948096i
$449$	−16.4824	−	11.0132i	−0.777852	−	0.519744i	0.102119	−	0.994772i	$-0.467438\pi$
$449$	−16.4824	−	11.0132i	−0.777852	−	0.519744i	−0.879970	+	0.475028i	$0.842438\pi$
$450$	4.98975	+	0.319930i	0.235219	+	0.0150816i
$451$	−4.32104	−	1.78983i	−0.203470	−	0.0842799i
$452$	−2.03249	−	10.2180i	−0.0956002	−	0.480615i
$453$	7.39819	+	4.94331i	0.347597	+	0.232257i
$454$	−6.32178	−	9.46121i	−0.296696	−	0.444037i
$455$	−4.52490	+	19.4687i	−0.212131	+	0.912709i
$456$	−1.21983	+	6.13252i	−0.0571240	+	0.287182i
$457$	12.0550	−	29.1034i	0.563910	−	1.36140i	−0.342706	−	0.939443i	$-0.611344\pi$
$457$	12.0550	−	29.1034i	0.563910	−	1.36140i	0.906616	−	0.421956i	$-0.138656\pi$
$458$	−12.8530	−	12.8530i	−0.600582	−	0.600582i
$459$	3.91312	+	1.29902i	0.182649	+	0.0606331i
$460$	4.53107	−	19.4953i	0.211262	−	0.908973i
$461$	−1.86542	+	0.772681i	−0.0868811	+	0.0359873i	−0.425701	−	0.904864i	$-0.639972\pi$
$461$	−1.86542	+	0.772681i	−0.0868811	+	0.0359873i	0.338820	+	0.940851i	$0.389972\pi$
$462$	1.31337	+	1.96559i	0.0611034	+	0.0914476i
$463$		−	35.0831i		−	1.63045i	−0.579144	−	0.815226i	$-0.696613\pi$
$463$		−	35.0831i		−	1.63045i	0.579144	−	0.815226i	$-0.303387\pi$
$464$	2.24260	−	1.49846i	0.104110	−	0.0695642i
$465$	−2.59754	−	0.0831882i	−0.120458	−	0.00385776i
$466$	10.4517	−	15.6421i	0.484166	−	0.724606i
$467$	−32.7475	+	13.5644i	−1.51537	+	0.627688i	−0.976658	−	0.214801i	$-0.931090\pi$
$467$	−32.7475	+	13.5644i	−1.51537	+	0.627688i	−0.538715	+	0.842488i	$0.681090\pi$
$468$	−3.42174	+	1.41733i	−0.158170	+	0.0655162i
$469$	2.11406	−	3.16392i	0.0976184	−	0.146096i
$470$	−6.58684	−	7.02270i	−0.303828	−	0.323933i
$471$	−13.7562	+	9.19160i	−0.633852	+	0.423526i
$472$		−	14.3355i		−	0.659843i
$473$	2.88991	+	4.32505i	0.132878	+	0.198866i
$474$	9.80330	−	4.06066i	0.450280	−	0.186512i
$475$	−13.7876	+	28.0588i	−0.632618	+	1.28743i
$476$	8.89501	−	4.46121i	0.407702	−	0.204479i
$477$	7.97077	+	7.97077i	0.364957	+	0.364957i
$478$	0.217005	−	0.523897i	0.00992558	−	0.0239625i
$479$	6.63601	−	33.3615i	0.303207	−	1.52432i	−0.465688	−	0.884949i	$-0.654193\pi$
$479$	6.63601	−	33.3615i	0.303207	−	1.52432i	0.768895	−	0.639375i	$-0.220807\pi$
$480$	2.17802	+	0.506212i	0.0994123	+	0.0231053i
$481$	−8.96626	−	13.4190i	−0.408826	−	0.611852i
$482$	22.6409	+	15.1282i	1.03127	+	0.689069i
$483$	−4.21454	−	21.1879i	−0.191768	−	0.964083i
$484$	9.27630	+	3.84237i	0.421650	+	0.174653i
$485$	−17.9710	+	25.1162i	−0.816023	+	1.14047i
$486$	0.831470	+	0.555570i	0.0377162	+	0.0252012i
$487$	7.82374	−	11.7091i	0.354528	−	0.530588i	−0.610747	−	0.791826i	$-0.709131\pi$
$487$	7.82374	−	11.7091i	0.354528	−	0.530588i	0.965274	+	0.261238i	$0.0841307\pi$
$488$	−0.228689	+	1.14969i	−0.0103522	+	0.0520442i
$489$	−7.86405	+	7.86405i	−0.355625	+	0.355625i
$490$	−1.08271	+	2.39412i	−0.0489119	+	0.108155i
$491$	6.91700	+	16.6991i	0.312160	+	0.753620i	0.999624	+	0.0274024i	$0.00872356\pi$
$491$	6.91700	+	16.6991i	0.312160	+	0.753620i	−0.687465	+	0.726218i	$0.741276\pi$
$492$	−3.37641	+	3.37641i	−0.152220	+	0.152220i
$493$	11.0917	−	0.802000i	0.499545	−	0.0361202i
$494$		−	23.1578i		−	1.04192i
$495$	−1.27449	+	1.78122i	−0.0572840	+	0.0800597i
$496$	−1.13992	−	0.226744i	−0.0511838	−	0.0101811i
$497$	−21.8804			−0.981470
$498$	7.54118	+	1.50003i	0.337928	+	0.0672181i
$499$	3.79833	+	19.0955i	0.170036	+	0.854831i	0.967773	+	0.251825i	$0.0810306\pi$
$499$	3.79833	+	19.0955i	0.170036	+	0.854831i	−0.797736	+	0.603006i	$0.793969\pi$
$500$	9.87138	+	5.24936i	0.441462	+	0.234758i
$501$	9.01067	−	21.7537i	0.402567	−	0.971883i
$502$	−9.57272	−	23.1106i	−0.427252	−	1.03148i
$503$	−24.9108	+	4.95507i	−1.11072	+	0.220935i	−0.716160	−	0.697936i	$-0.754102\pi$
$503$	−24.9108	+	4.95507i	−1.11072	+	0.220935i	−0.394557	+	0.918871i	$0.629102\pi$
$504$	2.36711	−	0.470848i	0.105440	−	0.0209732i
$505$	15.9454	+	7.21112i	0.709560	+	0.320890i
$506$	6.19949	+	6.19949i	0.275601	+	0.275601i
$507$	0.596296	−	0.398432i	0.0264824	−	0.0176950i
$508$	12.3301	+	5.10729i	0.547059	+	0.226599i
$509$	21.6155			0.958090			0.479045	−	0.877790i	$-0.340983\pi$
$509$	21.6155			0.958090			0.479045	+	0.877790i	$0.340983\pi$
$510$	6.77572	+	6.25217i	0.300034	+	0.276851i
$511$	13.3344			0.589881
$512$	0.923880	+	0.382683i	0.0408301	+	0.0169124i
$513$	−5.19890	+	3.47380i	−0.229537	+	0.153372i
$514$	4.96711	+	4.96711i	0.219090	+	0.219090i
$515$	4.09995	+	10.8699i	0.180665	+	0.478985i
$516$	5.20855	−	1.03605i	0.229294	−	0.0456094i
$517$	4.13658	−	0.822818i	0.181927	−	0.0361875i
$518$	4.02462	+	9.71629i	0.176832	+	0.426909i
$519$	−4.31957	+	10.4284i	−0.189608	+	0.457754i
$520$	−8.27741	−	0.265091i	−0.362988	−	0.0116250i
$521$	4.22491	+	21.2400i	0.185096	+	0.930543i	0.955950	+	0.293530i	$0.0948301\pi$
$521$	4.22491	+	21.2400i	0.185096	+	0.930543i	−0.770853	+	0.637013i	$0.780170\pi$
$522$	2.64533	+	0.526189i	0.115783	+	0.0230307i
$523$	−32.8082			−1.43460			−0.717301	−	0.696763i	$-0.754623\pi$
$523$	−32.8082			−1.43460			−0.717301	+	0.696763i	$0.754623\pi$
$524$	14.3015	+	2.84475i	0.624764	+	0.124273i
$525$	12.0427	+	0.772146i	0.525587	+	0.0336992i
$526$		−	0.0486295i		−	0.00212035i
$527$	−3.62406	−	3.13532i	−0.157867	−	0.136577i
$528$	−0.692607	+	0.692607i	−0.0301419	+	0.0301419i
$529$	−21.8587	−	52.7715i	−0.950376	−	2.29441i
$530$	8.89549	+	23.5839i	0.386395	+	1.02442i
$531$	10.1367	−	10.1367i	0.439895	−	0.439895i
$532$	−2.94406	+	14.8008i	−0.127641	+	0.641695i
$533$	9.82520	−	14.7045i	0.425577	−	0.636921i
$534$	2.58595	+	1.72788i	0.111905	+	0.0747726i
$535$	−9.10088	−	6.51182i	−0.393465	−	0.281531i
$536$	1.45663	+	0.603356i	0.0629169	+	0.0260610i
$537$	0.0526927	+	0.264904i	0.00227386	+	0.0114314i
$538$	14.5717	+	9.73648i	0.628230	+	0.419770i
$539$	−0.639452	−	0.957008i	−0.0275432	−	0.0412212i
$540$	1.18214	+	1.89803i	0.0508714	+	0.0816784i
$541$	−6.48868	+	32.6208i	−0.278970	+	1.40248i	0.546229	+	0.837636i	$0.316063\pi$
$541$	−6.48868	+	32.6208i	−0.278970	+	1.40248i	−0.825199	+	0.564842i	$0.808937\pi$
$542$	5.54940	−	13.3974i	0.238367	−	0.575469i
$543$	−2.33281	−	2.33281i	−0.100110	−	0.100110i
$544$	2.53195	+	3.25411i	0.108556	+	0.139519i
$545$	−22.7714	+	14.1826i	−0.975421	+	0.607517i
$546$	−8.25833	+	3.42071i	−0.353424	+	0.146393i
$547$	−0.242859	−	0.363464i	−0.0103839	−	0.0155406i	0.826241	−	0.563316i	$-0.190475\pi$
$547$	−0.242859	−	0.363464i	−0.0103839	−	0.0155406i	−0.836625	+	0.547776i	$0.815475\pi$
$548$		−	14.3088i		−	0.611242i
$549$	−0.974664	+	0.651250i	−0.0415977	+	0.0277947i
$550$	−4.23785	+	2.45476i	−0.180703	+	0.104671i
$551$	−9.36937	+	14.0222i	−0.399148	+	0.597368i
$552$	8.26960	−	3.42538i	0.351977	−	0.145794i
$553$	23.6601	−	9.80035i	1.00613	−	0.416753i
$554$	14.1869	−	21.2321i	0.602742	−	0.902067i
$555$	−7.10687	+	6.66579i	−0.301670	+	0.282947i
$556$	2.16095	−	1.44390i	0.0916448	−	0.0612351i
$557$		−	8.04450i		−	0.340856i	−0.985370	−	0.170428i	$-0.945485\pi$
$557$		−	8.04450i		−	0.340856i	0.985370	−	0.170428i	$-0.0545151\pi$
$558$	−0.645712	−	0.966376i	−0.0273351	−	0.0409099i
$559$	−18.1715	+	7.52688i	−0.768572	+	0.318353i
$560$	5.25661	+	1.22174i	0.222132	+	0.0516277i
$561$	−3.89383	+	1.07149i	−0.164397	+	0.0452383i
$562$	4.32823	+	4.32823i	0.182575	+	0.182575i
$563$	12.9258	−	31.2056i	0.544757	−	1.31516i	−0.376576	−	0.926386i	$-0.622899\pi$
$563$	12.9258	−	31.2056i	0.544757	−	1.31516i	0.921333	−	0.388774i	$-0.127101\pi$
$564$	0.840043	−	4.22318i	0.0353722	−	0.177828i
$565$	19.7741	−	12.3158i	0.831903	−	0.518130i
$566$	−11.9355	−	17.8628i	−0.501688	−	0.750830i
$567$	2.00674	+	1.34086i	0.0842752	+	0.0563109i
$568$	−1.76867	−	8.89168i	−0.0742116	−	0.373087i
$569$	−13.7309	−	5.68752i	−0.575628	−	0.238433i	0.0758258	−	0.997121i	$-0.475841\pi$
$569$	−13.7309	−	5.68752i	−0.575628	−	0.238433i	−0.651454	+	0.758688i	$0.725841\pi$
$570$	−13.7930	+	2.28730i	−0.577726	+	0.0958044i
$571$	−23.5858	−	15.7595i	−0.987036	−	0.659516i	−0.0463964	−	0.998923i	$-0.514774\pi$
$571$	−23.5858	−	15.7595i	−0.987036	−	0.659516i	−0.940640	+	0.339407i	$0.889774\pi$
$572$	2.01546	−	3.01634i	0.0842704	−	0.126120i
$573$	−4.79385	+	24.1003i	−0.200266	+	1.00681i
$574$	−8.14893	+	8.14893i	−0.340130	+	0.340130i
$575$	44.3635	−	5.90467i	1.85009	−	0.246242i
$576$	0.382683	+	0.923880i	0.0159451	+	0.0384950i
$577$	−27.9349	+	27.9349i	−1.16294	+	1.16294i	−0.179117	+	0.983828i	$0.557324\pi$
$577$	−27.9349	+	27.9349i	−1.16294	+	1.16294i	−0.983828	+	0.179117i	$0.942676\pi$
$578$	2.44563	+	16.8232i	0.101725	+	0.699751i
$579$		−	7.72935i		−	0.321221i
$580$	4.90479	+	3.50945i	0.203660	+	0.145722i
$581$	18.2005	+	3.62031i	0.755085	+	0.150196i
$582$	−13.8115			−0.572504
$583$	−10.8291	−	2.15404i	−0.448494	−	0.0892111i
$584$	1.07787	+	5.41881i	0.0446025	+	0.224232i
$585$	−5.66557	−	6.04046i	−0.234242	−	0.249742i
$586$	4.89542	−	11.8186i	0.202228	−	0.488222i
$587$	−9.10429	−	21.9797i	−0.375774	−	0.907199i	−0.992748	−	0.120215i	$-0.961642\pi$
$587$	−9.10429	−	21.9797i	−0.375774	−	0.907199i	0.616974	−	0.786984i	$-0.288358\pi$
$588$	−1.15250	+	0.229247i	−0.0475283	+	0.00945397i
$589$	7.12753	−	1.41775i	0.293685	−	0.0584175i
$590$	29.9925	−	11.3127i	1.23477	−	0.465736i
$591$	−17.2892	−	17.2892i	−0.711184	−	0.711184i
$592$	−3.62315	+	2.42091i	−0.148911	+	0.0994989i
$593$	−4.05787	−	1.68082i	−0.166637	−	0.0690232i	0.297806	−	0.954626i	$-0.403745\pi$
$593$	−4.05787	−	1.68082i	−0.166637	−	0.0690232i	−0.464442	+	0.885603i	$0.653745\pi$
$594$	−0.979495			−0.0401892
$595$	16.3531	+	15.0895i	0.670413	+	0.618610i
$596$	−19.6324			−0.804172
$597$	6.38364	+	2.64419i	0.261265	+	0.108220i
$598$	−27.5643	+	18.4179i	−1.12719	+	0.753164i
$599$	−1.74369	−	1.74369i	−0.0712451	−	0.0712451i	0.670586	−	0.741831i	$-0.266043\pi$
$599$	−1.74369	−	1.74369i	−0.0712451	−	0.0712451i	−0.741831	+	0.670586i	$0.766043\pi$
$600$	0.659670	+	4.95629i	0.0269309	+	0.202340i
$601$	−14.7228	+	2.92855i	−0.600556	+	0.119458i	−0.486000	−	0.873959i	$-0.661545\pi$
$601$	−14.7228	+	2.92855i	−0.600556	+	0.119458i	−0.114556	+	0.993417i	$0.536545\pi$
$602$	12.5708	−	2.50048i	0.512346	−	0.101912i
$603$	0.603356	+	1.45663i	0.0245706	+	0.0593186i
$604$	−3.40501	+	8.22043i	−0.138548	+	0.334485i
$605$	−0.718657	+	22.4399i	−0.0292176	+	0.912313i
$606$	1.52684	+	7.67593i	0.0620235	+	0.311813i
$607$	23.2283	+	4.62040i	0.942809	+	0.187536i	0.642483	−	0.766300i	$-0.277904\pi$
$607$	23.2283	+	4.62040i	0.942809	+	0.187536i	0.300326	+	0.953837i	$0.402904\pi$
$608$	−6.25267			−0.253579
$609$	6.38447	+	1.26995i	0.258712	+	0.0514610i
$610$	−2.58585	+	0.428811i	−0.104698	+	0.0173621i
$611$			15.9477i			0.645175i
$612$	−0.510647	+	4.09136i	−0.0206417	+	0.165383i
$613$	1.20998	−	1.20998i	0.0488706	−	0.0488706i	−0.682249	−	0.731120i	$-0.738998\pi$
$613$	1.20998	−	1.20998i	0.0488706	−	0.0488706i	0.731120	+	0.682249i	$0.238998\pi$
$614$	−5.76252	−	13.9119i	−0.232556	−	0.561440i
$615$	−9.72856	−	4.39963i	−0.392293	−	0.177410i
$616$	−1.67160	+	1.67160i	−0.0673506	+	0.0673506i
$617$	−3.21867	+	16.1814i	−0.129579	+	0.651437i	0.860331	+	0.509737i	$0.170257\pi$
$617$	−3.21867	+	16.1814i	−0.129579	+	0.651437i	−0.989910	+	0.141701i	$0.954743\pi$
$618$	−2.88644	+	4.31987i	−0.116110	+	0.173771i
$619$	25.3077	+	16.9100i	1.01720	+	0.679672i	0.948111	−	0.317939i	$-0.102991\pi$
$619$	25.3077	+	16.9100i	1.01720	+	0.679672i	0.0690894	+	0.997610i	$0.477991\pi$
$620$	−0.425165	−	2.56386i	−0.0170750	−	0.102967i
$621$	8.26960	+	3.42538i	0.331847	+	0.137456i
$622$	−0.794291	−	3.99317i	−0.0318482	−	0.160112i
$623$	6.24116	+	4.17021i	0.250047	+	0.167076i
$624$	−2.05765	−	3.07949i	−0.0823718	−	0.123278i
$625$	−3.19274	+	24.7953i	−0.127710	+	0.991812i
$626$	2.66967	−	13.4213i	0.106701	−	0.536424i
$627$	2.34373	−	5.65826i	0.0935994	−	0.225969i
$628$	−11.6987	−	11.6987i	−0.466828	−	0.466828i
$629$	−17.9198	+	1.29571i	−0.714508	+	0.0516634i
$630$	2.85309	+	4.58088i	0.113670	+	0.182507i
$631$	−18.3185	+	7.58777i	−0.729248	+	0.302064i	−0.716243	−	0.697851i	$-0.754140\pi$
$631$	−18.3185	+	7.58777i	−0.729248	+	0.302064i	−0.0130051	+	0.999915i	$0.504140\pi$
$632$	5.89516	+	8.82273i	0.234497	+	0.350950i
$633$			23.8251i			0.946963i
$634$	15.8702	−	10.6041i	0.630287	−	0.421145i
$635$	−0.955241	+	29.8273i	−0.0379076	+	1.18366i
$636$	−6.26259	+	9.37263i	−0.248328	+	0.371649i
$637$	4.02082	−	1.66548i	0.159311	−	0.0659886i
$638$	−2.44075	+	1.01099i	−0.0966302	+	0.0400256i
$639$	5.03673	−	7.53801i	0.199250	−	0.298199i
$640$	−0.0715751	+	2.23492i	−0.00282926	+	0.0883431i
$641$	1.82997	−	1.22275i	0.0722794	−	0.0482955i	−0.518906	−	0.854832i	$-0.673660\pi$
$641$	1.82997	−	1.22275i	0.0722794	−	0.0482955i	0.591185	+	0.806536i	$0.298660\pi$
$642$		−	5.00460i		−	0.197516i
$643$	−13.7474	−	20.5745i	−0.542145	−	0.811377i	0.454709	−	0.890640i	$-0.349743\pi$
$643$	−13.7474	−	20.5745i	−0.542145	−	0.811377i	−0.996854	+	0.0792630i	$0.974743\pi$
$644$	19.9586	−	8.26711i	0.786478	−	0.325770i
$645$	6.27788	+	10.0797i	0.247191	+	0.396887i
$646$	−22.4127	−	12.7396i	−0.881817	−	0.501234i
$647$	−33.5681	−	33.5681i	−1.31970	−	1.31970i	−0.914013	−	0.405685i	$-0.867033\pi$
$647$	−33.5681	−	33.5681i	−1.31970	−	1.31970i	−0.405685	−	0.914013i	$-0.632967\pi$
$648$	−0.382683	+	0.923880i	−0.0150332	+	0.0362934i
$649$	−2.73936	+	13.7717i	−0.107529	+	0.540587i
$650$	−5.97742	−	17.5271i	−0.234454	−	0.687470i
$651$	−1.55842	−	2.33234i	−0.0610792	−	0.0914114i
$652$	−9.24714	−	6.17874i	−0.362146	−	0.241978i
$653$	7.48777	+	37.6436i	0.293019	+	1.47311i	0.794143	+	0.607731i	$0.207920\pi$
$653$	7.48777	+	37.6436i	0.293019	+	1.47311i	−0.501124	+	0.865376i	$0.667080\pi$
$654$	−11.0841	−	4.59120i	−0.433424	−	0.179530i
$655$	5.33415	+	32.1664i	0.208423	+	1.25684i
$656$	−3.97024	−	2.65283i	−0.155012	−	0.103576i
$657$	−3.06951	+	4.59384i	−0.119753	+	0.179223i
$658$	2.02743	−	10.1926i	0.0790376	−	0.397349i
$659$	−27.0017	+	27.0017i	−1.05184	+	1.05184i	−0.0532569	+	0.998581i	$0.516960\pi$
$659$	−27.0017	+	27.0017i	−1.05184	+	1.05184i	−0.998581	+	0.0532569i	$0.983040\pi$
$660$	−1.99563	−	0.902501i	−0.0776798	−	0.0351298i
$661$	−6.98374	−	16.8602i	−0.271636	−	0.655787i	0.727918	−	0.685665i	$-0.240488\pi$
$661$	−6.98374	−	16.8602i	−0.271636	−	0.655787i	−0.999554	+	0.0298775i	$0.990488\pi$
$662$	5.99941	−	5.99941i	0.233174	−	0.233174i
$663$	−1.10129	−	15.2309i	−0.0427704	−	0.591517i
$664$			7.68892i			0.298388i
$665$	−33.2893	+	5.52037i	−1.29090	+	0.214071i
$666$	−4.27380	−	0.850111i	−0.165606	−	0.0329412i
$667$	24.1421			0.934786
$668$	23.0936	+	4.59360i	0.893518	+	0.177732i
$669$	−1.29435	−	6.50715i	−0.0500426	−	0.251581i
$670$	−0.112849	+	3.52368i	−0.00435973	+	0.136132i
$671$	0.439390	−	1.06078i	0.0169625	−	0.0409510i
$672$	0.923602	+	2.22977i	0.0356287	+	0.0860153i
$673$	36.3402	−	7.22852i	1.40081	−	0.278639i	0.563840	−	0.825884i	$-0.309323\pi$
$673$	36.3402	−	7.22852i	1.40081	−	0.278639i	0.836972	+	0.547245i	$0.184323\pi$
$674$	−3.93477	+	0.782674i	−0.151562	+	0.0301475i
$675$	−3.03817	+	3.97109i	−0.116939	+	0.152847i
$676$	0.507108	+	0.507108i	0.0195041	+	0.0195041i
$677$	−15.0905	+	10.0832i	−0.579976	+	0.387528i	−0.810674	−	0.585498i	$-0.800899\pi$
$677$	−15.0905	+	10.0832i	−0.579976	+	0.387528i	0.230698	+	0.973025i	$0.425899\pi$
$678$	9.62516	+	3.98687i	0.369652	+	0.153115i
$679$	−33.3338			−1.27923
$680$	−4.81015	+	7.86527i	−0.184461	+	0.301619i
$681$	11.3789			0.436040
$682$	1.05176	+	0.435654i	0.0402740	+	0.0166820i
$683$	4.31980	−	2.88640i	0.165293	−	0.110445i	−0.470173	−	0.882574i	$-0.655808\pi$
$683$	4.31980	−	2.88640i	0.165293	−	0.110445i	0.635465	+	0.772129i	$0.280808\pi$
$684$	−4.42130	−	4.42130i	−0.169053	−	0.169053i
$685$	29.9368	−	11.2917i	1.14382	−	0.431433i
$686$	−19.3513	+	3.84922i	−0.738837	+	0.146964i
$687$	17.8276	−	3.54614i	0.680167	−	0.135294i
$688$	2.03228	+	4.90635i	0.0774798	+	0.187053i
$689$	15.9767	−	38.5712i	0.608664	−	1.46944i
$690$	13.6924	+	14.5985i	0.521261	+	0.555754i
$691$	−4.33514	−	21.7942i	−0.164916	−	0.829090i	−0.971329	−	0.237738i	$-0.923594\pi$
$691$	−4.33514	−	21.7942i	−0.164916	−	0.829090i	0.806413	−	0.591353i	$-0.201406\pi$
$692$	−11.0707	−	2.20210i	−0.420844	−	0.0837111i
$693$	−2.36400			−0.0898009
$694$	−7.43437	−	1.47879i	−0.282205	−	0.0561340i
$695$	4.72622	+	3.38168i	0.179276	+	0.128274i
$696$			2.69716i			0.102235i
$697$	−8.82630	−	17.5984i	−0.334320	−	0.666585i
$698$	8.09109	−	8.09109i	0.306252	−	0.306252i
$699$	7.19927	+	17.3806i	0.272301	+	0.657394i
$700$	1.59211	+	11.9619i	0.0601759	+	0.452119i
$701$	10.0061	−	10.0061i	0.377924	−	0.377924i	−0.492429	−	0.870353i	$-0.663891\pi$
$701$	10.0061	−	10.0061i	0.377924	−	0.377924i	0.870353	+	0.492429i	$0.163891\pi$
$702$	0.722550	−	3.63250i	0.0272709	−	0.137100i
$703$	15.1372	−	22.6544i	0.570909	−	0.854425i
$704$	−0.814420	−	0.544178i	−0.0306946	−	0.0205095i
$705$	9.49861	−	1.57516i	0.357738	−	0.0593238i
$706$	−17.5676	−	7.27675i	−0.661166	−	0.273864i
$707$	3.68500	+	18.5257i	0.138589	+	0.696733i
$708$	11.9195	+	7.96435i	0.447962	+	0.299319i
$709$	4.72582	+	7.07269i	0.177482	+	0.265620i	0.909535	−	0.415627i	$-0.136438\pi$
$709$	4.72582	+	7.07269i	0.177482	+	0.265620i	−0.732053	+	0.681247i	$0.761438\pi$
$710$	17.2074	−	10.7172i	0.645781	−	0.402208i
$711$	−2.07011	+	10.4071i	−0.0776350	+	0.390298i
$712$	−1.19018	+	2.87336i	−0.0446040	+	0.107684i
$713$	−7.35620	−	7.35620i	−0.275492	−	0.275492i
$714$	−1.23244	+	9.87445i	−0.0461229	+	0.369542i
$715$	7.90124	+	1.83640i	0.295489	+	0.0686773i
$716$	−0.249534	+	0.103360i	−0.00932552	+	0.00386276i
$717$	0.315043	+	0.471495i	0.0117655	+	0.0176083i
$718$			1.27523i			0.0475913i
$719$	15.3239	−	10.2391i	0.571486	−	0.381855i	−0.235990	−	0.971756i	$-0.575833\pi$
$719$	15.3239	−	10.2391i	0.571486	−	0.381855i	0.807476	+	0.589901i	$0.200833\pi$
$720$	−1.63094	+	1.52972i	−0.0607815	+	0.0570092i
$721$	−6.96640	+	10.4260i	−0.259442	+	0.388283i
$722$	18.5661	−	7.69034i	0.690960	−	0.286205i
$723$	−25.1572	+	10.4205i	−0.935608	+	0.387541i
$724$	1.83288	−	2.74309i	0.0681183	−	0.101946i
$725$	−3.47187	+	13.0312i	−0.128942	+	0.483967i
$726$	−8.34845	+	5.57825i	−0.309840	+	0.207028i
$727$		−	42.1800i		−	1.56437i	−0.623047	−	0.782184i	$-0.714106\pi$
$727$		−	42.1800i		−	1.56437i	0.623047	−	0.782184i	$-0.285894\pi$
$728$	−4.96611	−	7.43230i	−0.184056	−	0.275460i
$729$	−0.923880	+	0.382683i	−0.0342178	+	0.0141735i
$730$	−10.4866	+	6.53131i	−0.388126	+	0.241734i
$731$	−2.71184	+	21.7276i	−0.100301	+	0.803623i
$732$	−0.828884	−	0.828884i	−0.0306364	−	0.0306364i
$733$	8.25540	−	19.9303i	0.304920	−	0.736142i	−0.694934	−	0.719073i	$-0.744567\pi$
$733$	8.25540	−	19.9303i	0.304920	−	0.736142i	0.999854	−	0.0170688i	$-0.00543344\pi$
$734$	−1.23708	+	6.21924i	−0.0456616	+	0.229556i
$735$	−1.38911	−	2.23034i	−0.0512382	−	0.0822674i
$736$	4.97288	+	7.44244i	0.183303	+	0.274332i
$737$	−1.28405	−	0.857976i	−0.0472987	−	0.0316040i
$738$	−0.931550	−	4.68322i	−0.0342908	−	0.172392i
$739$	−13.6466	−	5.65259i	−0.501997	−	0.207934i	0.117291	−	0.993098i	$-0.462579\pi$
$739$	−13.6466	−	5.65259i	−0.501997	−	0.207934i	−0.619288	+	0.785164i	$0.712579\pi$
$740$	−7.92419	−	5.66988i	−0.291299	−	0.208429i
$741$	19.2550	+	12.8658i	0.707350	+	0.472636i
$742$	−15.1147	+	22.6207i	−0.554878	+	0.830433i
$743$	−3.66654	+	18.4329i	−0.134512	+	0.676238i	0.853404	+	0.521250i	$0.174534\pi$
$743$	−3.66654	+	18.4329i	−0.134512	+	0.676238i	−0.987916	+	0.154988i	$0.950466\pi$
$744$	0.821835	−	0.821835i	0.0301299	−	0.0301299i
$745$	−15.4927	−	41.0746i	−0.567608	−	1.50486i
$746$	8.08603	+	19.5214i	0.296051	+	0.714730i
$747$	−5.43688	+	5.43688i	−0.198925	+	0.198925i
$748$	−1.81055	−	3.60997i	−0.0662002	−	0.131994i
$749$		−	12.0785i		−	0.441340i
$750$	−9.84893	+	5.29137i	−0.359632	+	0.193213i
$751$	27.4160	+	5.45339i	1.00043	+	0.198997i	0.668023	−	0.744141i	$-0.267141\pi$
$751$	27.4160	+	5.45339i	1.00043	+	0.198997i	0.332402	+	0.943138i	$0.392141\pi$
$752$	4.30592			0.157021
$753$	24.5341	+	4.88013i	0.894072	+	0.177842i
$754$	−1.94883	−	9.79743i	−0.0709722	−	0.356801i
$755$	−19.8857	−	0.636856i	−0.723716	−	0.0231776i
$756$	−0.923602	+	2.22977i	−0.0335911	+	0.0810960i
$757$	3.73255	+	9.01117i	0.135662	+	0.327516i	0.977081	−	0.212866i	$-0.0682797\pi$
$757$	3.73255	+	9.01117i	0.135662	+	0.327516i	−0.841420	+	0.540382i	$0.818280\pi$
$758$	−10.4034	+	2.06937i	−0.377869	+	0.0751627i
$759$	−8.59894	+	1.71044i	−0.312122	+	0.0620849i
$760$	−4.93423	−	13.0818i	−0.178984	−	0.474525i
$761$	29.8260	+	29.8260i	1.08119	+	1.08119i	0.996399	+	0.0847921i	$0.0270226\pi$
$761$	29.8260	+	29.8260i	1.08119	+	1.08119i	0.0847921	+	0.996399i	$0.472977\pi$
$762$	−11.0968	+	7.41464i	−0.401994	+	0.268604i
$763$	−26.7514	−	11.0808i	−0.968466	−	0.401152i
$764$	−24.5725			−0.889001
$765$	−8.96288	+	2.16029i	−0.324053	+	0.0781055i
$766$	22.5143			0.813476
$767$	−49.0523	−	20.3181i	−1.77117	−	0.733644i
$768$	−0.831470	+	0.555570i	−0.0300031	+	0.0200474i
$769$	−8.63482	−	8.63482i	−0.311380	−	0.311380i	0.534064	−	0.845444i	$-0.320664\pi$
$769$	−8.63482	−	8.63482i	−0.311380	−	0.311380i	−0.845444	+	0.534064i	$0.820664\pi$
$770$	−4.81643	−	2.17817i	−0.173572	−	0.0784960i
$771$	−6.88958	+	1.37042i	−0.248122	+	0.0493546i
$772$	7.58083	−	1.50792i	0.272840	−	0.0542713i
$773$	6.52898	+	15.7624i	0.234831	+	0.566933i	0.996734	−	0.0807590i	$-0.0257344\pi$
$773$	6.52898	+	15.7624i	0.234831	+	0.566933i	−0.761902	+	0.647692i	$0.775734\pi$
$774$	−2.03228	+	4.90635i	−0.0730487	+	0.176355i
$775$	5.02856	−	2.91277i	0.180631	−	0.104630i
$776$	−2.69448	−	13.5461i	−0.0967263	−	0.486276i
$777$	−10.3148	−	2.05173i	−0.370040	−	0.0736055i
$778$	24.6456			0.883586
$779$	29.2826	+	5.82467i	1.04916	+	0.208691i
$780$	4.81910	−	6.73514i	0.172551	−	0.241157i
$781$			8.87998i			0.317751i
$782$	2.66156	+	36.8096i	0.0951774	+	1.31631i
$783$	−1.90718	+	1.90718i	−0.0681569	+	0.0681569i
$784$	−0.449683	−	1.08563i	−0.0160601	−	0.0387725i
$785$	15.2440	−	33.7078i	0.544080	−	1.20308i
$786$	−10.3108	+	10.3108i	−0.367774	+	0.367774i
$787$	2.20133	−	11.0668i	0.0784690	−	0.394490i	−0.921512	−	0.388349i	$-0.873045\pi$
$787$	2.20133	−	11.0668i	0.0784690	−	0.394490i	0.999981	−	0.00614066i	$-0.00195465\pi$
$788$	13.5841	−	20.3300i	0.483912	−	0.724226i
$789$	0.0404339	+	0.0270171i	0.00143949	+	0.000961834i
$790$	−13.8067	+	19.2962i	−0.491221	+	0.686527i
$791$	23.2302	+	9.62226i	0.825971	+	0.342128i
$792$	−0.191090	−	0.960674i	−0.00679009	−	0.0341361i
$793$	3.60983	+	2.41201i	0.128189	+	0.0856531i
$794$	−16.7718	−	25.1008i	−0.595209	−	0.890794i
$795$	−24.5514	−	5.70620i	−0.870748	−	0.202378i
$796$	−1.34800	+	6.77684i	−0.0477785	+	0.240199i
$797$	−17.1124	+	41.3131i	−0.606154	+	1.46338i	0.260997	+	0.965340i	$0.415949\pi$
$797$	−17.1124	+	41.3131i	−0.606154	+	1.46338i	−0.867151	+	0.498045i	$0.834051\pi$
$798$	−10.6708	−	10.6708i	−0.377741	−	0.377741i
$799$	15.4346	+	8.77319i	0.546037	+	0.310373i
$800$	−4.73236	+	1.61392i	−0.167314	+	0.0570607i
$801$	−2.87336	+	1.19018i	−0.101525	+	0.0420531i
$802$	5.49983	+	8.23108i	0.194206	+	0.290649i
$803$		−	5.41168i		−	0.190974i
$804$	−1.31093	+	0.875938i	−0.0462331	+	0.0308919i
$805$	33.0465	+	35.2332i	1.16474	+	1.24181i
$806$	−2.39150	+	3.57913i	−0.0842370	+	0.126070i
$807$	−16.1912	+	6.70661i	−0.569957	+	0.236084i
$808$	−7.23056	+	2.99500i	−0.254370	+	0.105364i
$809$	3.90374	−	5.84236i	0.137248	−	0.205406i	−0.756478	−	0.654019i	$-0.773082\pi$
$809$	3.90374	−	5.84236i	0.137248	−	0.205406i	0.893726	+	0.448612i	$0.148082\pi$
$810$	−2.23492	−	0.0715751i	−0.0785272	−	0.00251489i
$811$	−8.09005	+	5.40560i	−0.284080	+	0.189816i	−0.689444	−	0.724339i	$-0.742145\pi$
$811$	−8.09005	+	5.40560i	−0.284080	+	0.189816i	0.405364	+	0.914156i	$0.367145\pi$
$812$			6.50955i			0.228440i
$813$	8.05648	+	12.0574i	0.282553	+	0.422870i
$814$	3.94328	−	1.63336i	0.138212	−	0.0572492i
$815$	5.62980	−	24.2227i	0.197203	−	0.848483i
$816$	−4.11237	+	0.297350i	−0.143962	+	0.0104093i
$817$	−23.4797	−	23.4797i	−0.821452	−	0.821452i
$818$	−10.0766	+	24.3270i	−0.352319	+	0.850573i
$819$	1.74386	−	8.76700i	0.0609356	−	0.306344i
$820$	2.41714	−	10.4000i	0.0844103	−	0.363182i
$821$	−21.5762	−	32.2911i	−0.753015	−	1.12697i	−0.987923	−	0.154948i	$-0.950479\pi$
$821$	−21.5762	−	32.2911i	−0.753015	−	1.12697i	0.234908	−	0.972018i	$-0.424521\pi$
$822$	11.8973	+	7.94955i	0.414968	+	0.277272i
$823$	0.0730959	+	0.367478i	0.00254796	+	0.0128095i	0.982038	−	0.188681i	$-0.0604214\pi$
$823$	0.0730959	+	0.367478i	0.00254796	+	0.0128095i	−0.979490	+	0.201491i	$0.935421\pi$
$824$	−4.79998	−	1.98822i	−0.167215	−	0.0692628i
$825$	0.313370	−	4.88744i	0.0109101	−	0.170159i
$826$	28.7676	+	19.2219i	1.00095	+	0.668814i
$827$	20.9460	−	31.3478i	0.728362	−	1.09007i	−0.263734	−	0.964595i	$-0.584954\pi$
$827$	20.9460	−	31.3478i	0.728362	−	1.09007i	0.992097	−	0.125476i	$-0.0400458\pi$
$828$	−1.74624	+	8.77896i	−0.0606861	+	0.305090i
$829$	23.2442	−	23.2442i	0.807304	−	0.807304i	−0.176921	−	0.984225i	$-0.556614\pi$
$829$	23.2442	−	23.2442i	0.807304	−	0.807304i	0.984225	+	0.176921i	$0.0566138\pi$
$830$	−16.0867	+	6.06764i	−0.558376	+	0.210611i
$831$	9.77208	+	23.5919i	0.338990	+	0.818394i
$832$	2.61889	−	2.61889i	0.0907936	−	0.0907936i
$833$	0.600050	−	4.80767i	0.0207905	−	0.166576i
$834$			2.59896i			0.0899945i
$835$	8.61341	+	51.9412i	0.298079	+	1.79750i
$836$	6.00677	+	1.19482i	0.207749	+	0.0413238i
$837$	1.16225			0.0401732
$838$	−9.36373	−	1.86256i	−0.323465	−	0.0643411i
$839$	4.00396	+	20.1293i	0.138232	+	0.694940i	0.986288	+	0.165033i	$0.0527731\pi$
$839$	4.00396	+	20.1293i	0.138232	+	0.694940i	−0.848056	+	0.529907i	$0.822227\pi$
$840$	−3.93625	+	3.69195i	−0.135814	+	0.127384i
$841$	8.31393	−	20.0716i	0.286687	−	0.692124i
$842$	−1.77373	−	4.28216i	−0.0611267	−	0.147573i
$843$	−6.00342	+	1.19415i	−0.206769	+	0.0411289i
$844$	−23.3673	+	4.64805i	−0.804336	+	0.159992i
$845$	−0.660786	+	1.46115i	−0.0227317	+	0.0502649i
$846$	3.04474	+	3.04474i	0.104680	+	0.104680i
$847$	−20.1489	+	13.4630i	−0.692323	+	0.462596i
$848$	−10.4143	−	4.31375i	−0.357629	−	0.148135i
$849$	21.4834			0.737309
$850$	−20.2515	−	3.85695i	−0.694621	−	0.132292i
$851$	−39.0040			−1.33704
$852$	8.37578	+	3.46936i	0.286950	+	0.118858i
$853$	31.9991	−	21.3811i	1.09563	−	0.732076i	0.129874	−	0.991530i	$-0.458543\pi$
$853$	31.9991	−	21.3811i	1.09563	−	0.732076i	0.965755	+	0.259454i	$0.0835427\pi$
$854$	−2.00050	−	2.00050i	−0.0684557	−	0.0684557i
$855$	5.76117	−	12.7392i	0.197028	−	0.435673i
$856$	4.90843	−	0.976348i	0.167767	−	0.0333709i
$857$	−41.2298	+	8.20111i	−1.40838	+	0.280145i	−0.839985	−	0.542610i	$-0.817436\pi$
$857$	−41.2298	+	8.20111i	−1.40838	+	0.280145i	−0.568397	+	0.822754i	$0.692436\pi$
$858$	1.38827	+	3.35158i	0.0473947	+	0.114421i
$859$	−5.72021	+	13.8098i	−0.195171	+	0.471184i	−0.990922	−	0.134440i	$-0.957076\pi$
$859$	−5.72021	+	13.8098i	−0.195171	+	0.471184i	0.795751	+	0.605624i	$0.207076\pi$
$860$	−8.66126	+	8.12371i	−0.295346	+	0.277016i
$861$	−2.24828	−	11.3029i	−0.0766213	−	0.385201i
$862$	24.5722	+	4.88771i	0.836931	+	0.166476i
$863$	15.4801			0.526949			0.263475	−	0.964666i	$-0.415132\pi$
$863$	15.4801			0.526949			0.263475	+	0.964666i	$0.415132\pi$
$864$	−0.980785	−	0.195090i	−0.0333670	−	0.00663711i
$865$	−4.12913	−	24.8997i	−0.140394	−	0.846616i
$866$		−	33.3460i		−	1.13314i
$867$	−15.3467	−	7.31299i	−0.521200	−	0.248362i
$868$	1.98349	−	1.98349i	0.0673240	−	0.0673240i
$869$	−3.97739	−	9.60228i	−0.134924	−	0.325735i
$870$	−5.64296	+	2.12844i	−0.191314	+	0.0721607i
$871$	4.12906	−	4.12906i	0.139908	−	0.139908i
$872$	2.34057	−	11.7668i	0.0792617	−	0.398476i
$873$	7.67324	−	11.4838i	0.259700	−	0.388668i
$874$	−46.5351	−	31.0938i	−1.57407	−	1.05176i
$875$	−23.7703	+	12.7707i	−0.803582	+	0.431727i
$876$	−5.10441	−	2.11431i	−0.172462	−	0.0714360i
$877$	4.68842	+	23.5703i	0.158317	+	0.795912i	0.975579	+	0.219647i	$0.0704906\pi$
$877$	4.68842	+	23.5703i	0.158317	+	0.795912i	−0.817263	+	0.576265i	$0.804509\pi$
$878$	5.57819	+	3.72723i	0.188255	+	0.125788i
$879$	7.10705	+	10.6365i	0.239715	+	0.358759i
$880$	0.495832	−	2.13335i	0.0167145	−	0.0719154i
$881$	−1.30625	+	6.56695i	−0.0440086	+	0.221246i	−0.996531	−	0.0832223i	$-0.973479\pi$
$881$	−1.30625	+	6.56695i	−0.0440086	+	0.221246i	0.952522	+	0.304469i	$0.0984788\pi$
$882$	0.449683	−	1.08563i	0.0151416	−	0.0365551i
$883$	1.16713	+	1.16713i	0.0392770	+	0.0392770i	0.726473	−	0.687196i	$-0.241158\pi$
$883$	1.16713	+	1.16713i	0.0392770	+	0.0392770i	−0.687196	+	0.726473i	$0.741158\pi$
$884$	14.7233	−	4.05152i	0.495200	−	0.136267i
$885$	−7.25677	+	31.2228i	−0.243934	+	1.04954i
$886$	9.83855	−	4.07526i	0.330533	−	0.136911i
$887$	19.4018	+	29.0369i	0.651450	+	0.974963i	0.999300	+	0.0374133i	$0.0119118\pi$
$887$	19.4018	+	29.0369i	0.651450	+	0.974963i	−0.347850	+	0.937550i	$0.613088\pi$
$888$		−	4.35753i		−	0.146229i
$889$	−26.7820	+	17.8951i	−0.898238	+	0.600183i
$890$	−6.95083	−	0.222606i	−0.232992	−	0.00746176i
$891$	0.544178	−	0.814420i	0.0182307	−	0.0272841i
$892$	6.12960	−	2.53896i	0.205234	−	0.0850108i
$893$	−24.8741	+	10.3032i	−0.832378	+	0.344782i
$894$	10.9072	−	16.3237i	0.364790	−	0.545946i
$895$	−0.413167	−	0.440506i	−0.0138106	−	0.0147245i
$896$	−2.00674	+	1.34086i	−0.0670405	+	0.0447950i
$897$		−	33.1513i		−	1.10689i
$898$	11.0132	+	16.4824i	0.367514	+	0.550024i
$899$	2.89615	−	1.19962i	0.0965920	−	0.0400097i
$900$	−4.48750	−	2.20507i	−0.149583	−	0.0735024i
$901$	−28.5411	−	36.6816i	−0.950840	−	1.22204i
$902$	3.30718	+	3.30718i	0.110117	+	0.110117i
$903$	−4.90487	+	11.8414i	−0.163224	+	0.394057i
$904$	−2.03249	+	10.2180i	−0.0675996	+	0.339846i
$905$	7.18547	+	1.67004i	0.238853	+	0.0555139i
$906$	−4.94331	−	7.39819i	−0.164231	−	0.245788i
$907$	−41.7848	−	27.9197i	−1.38744	−	0.927059i	−0.999987	−	0.00516989i	$-0.998354\pi$
$907$	−41.7848	−	27.9197i	−1.38744	−	0.927059i	−0.387455	−	0.921889i	$-0.626646\pi$
$908$	2.21991	+	11.1603i	0.0736704	+	0.370366i
$909$	−7.23056	−	2.99500i	−0.239823	−	0.0993378i
$910$	11.6308	−	16.2552i	0.385558	−	0.538854i
$911$	−25.9675	−	17.3510i	−0.860343	−	0.574863i	0.0452665	−	0.998975i	$-0.485586\pi$
$911$	−25.9675	−	17.3510i	−0.860343	−	0.574863i	−0.905610	+	0.424112i	$0.860586\pi$
$912$	3.47380	−	5.19890i	0.115029	−	0.172153i
$913$	1.46927	−	7.38654i	0.0486259	−	0.244459i
$914$	−22.2748	+	22.2748i	−0.736784	+	0.736784i
$915$	1.08008	−	2.38829i	0.0357062	−	0.0789544i
$916$	6.95600	+	16.7933i	0.229833	+	0.554865i
$917$	−24.8850	+	24.8850i	−0.821776	+	0.821776i
$918$	−3.11814	−	2.69763i	−0.102914	−	0.0890349i
$919$			34.1051i			1.12502i	0.826789	+	0.562512i	$0.190165\pi$
$919$			34.1051i			1.12502i	−0.826789	+	0.562512i	$0.809835\pi$
$920$	−11.6467	+	16.2773i	−0.383980	+	0.536648i
$921$	14.7688	+	2.93771i	0.486650	+	0.0968007i
$922$	2.01911			0.0664959
$923$	−32.9319	−	6.55055i	−1.08397	−	0.215614i
$924$	−0.461193	−	2.31857i	−0.0151721	−	0.0762755i
$925$	5.60916	−	21.0532i	0.184428	−	0.692226i
$926$	−13.4257	+	32.4126i	−0.441197	+	1.06514i
$927$	−1.98822	−	4.79998i	−0.0653016	−	0.157652i
$928$	−2.64533	+	0.526189i	−0.0868372	+	0.0172730i
$929$	6.82534	−	1.35764i	0.223932	−	0.0445429i	−0.0818488	−	0.996645i	$-0.526082\pi$
$929$	6.82534	−	1.35764i	0.223932	−	0.0445429i	0.305781	+	0.952102i	$0.401082\pi$
$930$	2.36798	+	1.07089i	0.0776490	+	0.0351159i
$931$	5.19538	+	5.19538i	0.170272	+	0.170272i
$932$	−15.6421	+	10.4517i	−0.512374	+	0.342357i
$933$	3.76148	+	1.55806i	0.123145	+	0.0510085i
$934$	35.4456			1.15982
$935$	6.12396	−	6.63678i	0.200275	−	0.217046i
$936$	3.70367			0.121058
$937$	−16.2628	−	6.73628i	−0.531283	−	0.220065i	0.100882	−	0.994898i	$-0.467834\pi$
$937$	−16.2628	−	6.73628i	−0.531283	−	0.220065i	−0.632165	+	0.774834i	$0.717834\pi$
$938$	−3.16392	+	2.11406i	−0.103306	+	0.0690267i
$939$	9.67623	+	9.67623i	0.315772	+	0.315772i
$940$	3.39798	+	9.00880i	0.110830	+	0.293835i
$941$	33.9720	−	6.75746i	1.10746	−	0.220287i	0.392704	−	0.919665i	$-0.371540\pi$
$941$	33.9720	−	6.75746i	1.10746	−	0.220287i	0.714752	+	0.699378i	$0.246540\pi$
$942$	16.2265	−	3.22766i	0.528689	−	0.105163i
$943$	−16.3561	−	39.4871i	−0.532627	−	1.28588i
$944$	−5.48594	+	13.2442i	−0.178552	+	0.431063i
$945$	−5.39396	−	0.172746i	−0.175465	−	0.00561942i
$946$	−1.01480	−	5.10175i	−0.0329940	−	0.165872i
$947$	32.2996	+	6.42478i	1.04959	+	0.208777i	0.689610	−	0.724181i	$-0.257782\pi$
$947$	32.2996	+	6.42478i	1.04959	+	0.208777i	0.359984	+	0.932958i	$0.382782\pi$
$948$	−10.6110			−0.344630
$949$	20.0695	+	3.99207i	0.651482	+	0.129588i
$950$	23.4757	−	20.6467i	0.761653	−	0.669868i
$951$			19.0870i			0.618937i
$952$	−9.92515	+	0.717651i	−0.321676	+	0.0232592i
$953$	−21.6714	+	21.6714i	−0.702005	+	0.702005i	−0.964841	−	0.262835i	$-0.915342\pi$
$953$	−21.6714	+	21.6714i	−0.702005	+	0.702005i	0.262835	+	0.964841i	$0.415342\pi$
$954$	−4.31375	−	10.4143i	−0.139663	−	0.337176i
$955$	−19.3911	−	51.4103i	−0.627483	−	1.66360i
$956$	−0.400973	+	0.400973i	−0.0129684	+	0.0129684i
$957$	0.515399	−	2.59109i	0.0166605	−	0.0837580i
$958$	−18.8977	+	28.2825i	−0.610558	+	0.913765i
$959$	28.7141	+	19.1861i	0.927226	+	0.619553i
$960$	−1.81850	−	1.30117i	−0.0586920	−	0.0419950i
$961$	27.3923	+	11.3462i	0.883621	+	0.366008i
$962$	3.14853	+	15.8287i	0.101513	+	0.510339i
$963$	4.16117	+	2.78040i	0.134092	+	0.0895973i
$964$	−15.1282	−	22.6409i	−0.487246	−	0.729215i
$965$	9.13720	+	14.6706i	0.294137	+	0.472262i
$966$	−4.21454	+	21.1879i	−0.135600	+	0.681709i
$967$	−9.45741	+	22.8322i	−0.304130	+	0.734235i	0.695743	+	0.718291i	$0.255075\pi$
$967$	−9.45741	+	22.8322i	−0.304130	+	0.734235i	−0.999873	+	0.0159437i	$0.994925\pi$
$968$	−7.09977	−	7.09977i	−0.228195	−	0.228195i
$969$	23.0445	−	11.5578i	0.740295	−	0.371288i
$970$	26.2146	−	16.3271i	0.841701	−	0.524233i
$971$	13.6030	−	5.63456i	0.436542	−	0.180822i	−0.153579	−	0.988136i	$-0.549080\pi$
$971$	13.6030	−	5.63456i	0.436542	−	0.180822i	0.590121	+	0.807315i	$0.299080\pi$
$972$	−0.555570	−	0.831470i	−0.0178199	−	0.0266694i
$973$			6.27255i			0.201089i
$974$	−11.7091	+	7.82374i	−0.375182	+	0.250689i
$975$	17.8941	+	4.76749i	0.573071	+	0.152682i
$976$	0.651250	−	0.974664i	0.0208460	−	0.0311982i
$977$	3.53798	−	1.46548i	0.113190	−	0.0468848i	−0.325370	−	0.945587i	$-0.605489\pi$
$977$	3.53798	−	1.46548i	0.113190	−	0.0468848i	0.438560	+	0.898702i	$0.355489\pi$
$978$	10.2749	−	4.25599i	0.328554	−	0.136092i
$979$	1.69245	−	2.53293i	0.0540909	−	0.0809527i
$980$	1.91648	−	1.79754i	0.0612198	−	0.0574203i
$981$	9.97545	−	6.66538i	0.318492	−	0.212809i
$982$		−	18.0750i		−	0.576796i
$983$	−1.84479	−	2.76092i	−0.0588395	−	0.0880596i	0.800883	−	0.598821i	$-0.204364\pi$
$983$	−1.84479	−	2.76092i	−0.0588395	−	0.0880596i	−0.859723	+	0.510761i	$0.829364\pi$
$984$	4.41150	−	1.82730i	0.140633	−	0.0582522i
$985$	53.2540	+	12.3772i	1.69681	+	0.394371i
$986$	−10.5543	−	3.50366i	−0.336118	−	0.111579i
$987$	7.34845	+	7.34845i	0.233904	+	0.233904i
$988$	−8.86211	+	21.3950i	−0.281941	+	0.680666i
$989$	−9.27359	+	46.6215i	−0.294883	+	1.48248i
$990$	1.85912	−	1.15790i	0.0590866	−	0.0368006i
$991$	−19.8726	−	29.7414i	−0.631273	−	0.944767i	−0.999885	−	0.0151834i	$-0.995167\pi$
$991$	−19.8726	−	29.7414i	−0.631273	−	0.944767i	0.368612	−	0.929583i	$-0.379833\pi$
$992$	0.966376	+	0.645712i	0.0306825	+	0.0205014i
$993$	1.65523	+	8.32142i	0.0525272	+	0.264072i
$994$	20.2148	+	8.37326i	0.641176	+	0.265584i
$995$	−15.2422	+	2.52761i	−0.483210	+	0.0801308i
$996$	−6.39310	−	4.27173i	−0.202573	−	0.135355i
$997$	−9.89605	+	14.8105i	−0.313411	+	0.469053i	−0.954414	−	0.298486i	$-0.903519\pi$
$997$	−9.89605	+	14.8105i	−0.313411	+	0.469053i	0.641003	+	0.767538i	$0.278519\pi$
$998$	3.79833	−	19.0955i	0.120234	−	0.604457i
$999$	3.08124	−	3.08124i	0.0974860	−	0.0974860i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	510.2.bi.b.37.8	yes	80
5.3	odd	4		510.2.bd.b.343.10	✓	80
17.6	odd	16		510.2.bd.b.397.10	yes	80
85.23	even	16	inner	510.2.bi.b.193.8	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.bd.b.343.10	✓	80	5.3	odd	4
510.2.bd.b.397.10	yes	80	17.6	odd	16
510.2.bi.b.37.8	yes	80	1.1	even	1	trivial
510.2.bi.b.193.8	yes	80	85.23	even	16	inner

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:	\( N \)	\(=\)	\( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	510.bi (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.923880 - 0.382683i) q^{2} +(0.831470 - 0.555570i) q^{3} +(0.707107 + 0.707107i) q^{4} +(-0.921394 + 2.03741i) q^{5} +(-0.980785 + 0.195090i) q^{6} +(-2.36711 + 0.470848i) q^{7} +(-0.382683 - 0.923880i) q^{8} +(0.382683 - 0.923880i) q^{9} +(1.63094 - 1.52972i) q^{10} +(0.191090 + 0.960674i) q^{11} +(0.980785 + 0.195090i) q^{12} -3.70367 q^{13} +(2.36711 + 0.470848i) q^{14} +(0.365812 + 2.20594i) q^{15} +1.00000i q^{16} +(-2.03747 + 3.58451i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(-2.39279 - 5.77671i) q^{19} +(-2.09219 + 0.789141i) q^{20} +(-1.70659 + 1.70659i) q^{21} +(0.191090 - 0.960674i) q^{22} +(-4.97288 + 7.44244i) q^{23} +(-0.831470 - 0.555570i) q^{24} +(-3.30206 - 3.75451i) q^{25} +(3.42174 + 1.41733i) q^{26} +(-0.195090 - 0.980785i) q^{27} +(-2.00674 - 1.34086i) q^{28} +(-1.49846 - 2.24260i) q^{29} +(0.506212 - 2.17802i) q^{30} +(-0.226744 + 1.13992i) q^{31} +(0.382683 - 0.923880i) q^{32} +(0.692607 + 0.692607i) q^{33} +(3.25411 - 2.53195i) q^{34} +(1.22174 - 5.25661i) q^{35} +(0.923880 - 0.382683i) q^{36} +(2.42091 + 3.62315i) q^{37} +6.25267i q^{38} +(-3.07949 + 2.05765i) q^{39} +(2.23492 + 0.0715751i) q^{40} +(-2.65283 + 3.97024i) q^{41} +(2.22977 - 0.923602i) q^{42} +(4.90635 - 2.03228i) q^{43} +(-0.544178 + 0.814420i) q^{44} +(1.52972 + 1.63094i) q^{45} +(7.44244 - 4.97288i) q^{46} -4.30592i q^{47} +(0.555570 + 0.831470i) q^{48} +(-1.08563 + 0.449683i) q^{49} +(1.61392 + 4.73236i) q^{50} +(0.297350 + 4.11237i) q^{51} +(-2.61889 - 2.61889i) q^{52} +(-4.31375 + 10.4143i) q^{53} +(-0.195090 + 0.980785i) q^{54} +(-2.13335 - 0.495832i) q^{55} +(1.34086 + 2.00674i) q^{56} +(-5.19890 - 3.47380i) q^{57} +(0.526189 + 2.64533i) q^{58} +(13.2442 + 5.48594i) q^{59} +(-1.30117 + 1.81850i) q^{60} +(-0.974664 - 0.651250i) q^{61} +(0.645712 - 0.966376i) q^{62} +(-0.470848 + 2.36711i) q^{63} +(-0.707107 + 0.707107i) q^{64} +(3.41254 - 7.54588i) q^{65} +(-0.374836 - 0.904935i) q^{66} +(-1.11486 + 1.11486i) q^{67} +(-3.97534 + 1.09392i) q^{68} +8.95095i q^{69} +(-3.14035 + 4.38894i) q^{70} +(8.89168 + 1.76867i) q^{71} -1.00000 q^{72} +(-5.41881 - 1.07787i) q^{73} +(-0.850111 - 4.27380i) q^{74} +(-4.83146 - 1.28724i) q^{75} +(2.39279 - 5.77671i) q^{76} +(-0.904663 - 2.18405i) q^{77} +(3.63250 - 0.722550i) q^{78} +(-10.4071 + 2.07011i) q^{79} +(-2.03741 - 0.921394i) q^{80} +(-0.707107 - 0.707107i) q^{81} +(3.97024 - 2.65283i) q^{82} +(-7.10363 - 2.94242i) q^{83} -2.41349 q^{84} +(-5.42579 - 7.45391i) q^{85} -5.31059 q^{86} +(-2.49185 - 1.03216i) q^{87} +(0.814420 - 0.544178i) q^{88} +(-2.19917 - 2.19917i) q^{89} +(-0.789141 - 2.09219i) q^{90} +(8.76700 - 1.74386i) q^{91} +(-8.77896 + 1.74624i) q^{92} +(0.444774 + 1.07378i) q^{93} +(-1.64780 + 3.97815i) q^{94} +(13.9742 + 0.447536i) q^{95} +(-0.195090 - 0.980785i) q^{96} +(13.5461 + 2.69448i) q^{97} +1.17508 q^{98} +(0.960674 + 0.191090i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 48 q^{25} + 16 q^{28} + 32 q^{29} + 16 q^{30} + 16 q^{31} - 16 q^{33} - 32 q^{34} - 32 q^{35} + 48 q^{37} + 32 q^{41} + 32 q^{43} + 16 q^{44} - 64 q^{49} + 48 q^{50} - 32 q^{51} + 16 q^{52} - 32 q^{53}+ \cdots - 144 q^{98}+O(q^{100}) \) 80 * q + 48 * q^25 + 16 * q^28 + 32 * q^29 + 16 * q^30 + 16 * q^31 - 16 * q^33 - 32 * q^34 - 32 * q^35 + 48 * q^37 + 32 * q^41 + 32 * q^43 + 16 * q^44 - 64 * q^49 + 48 * q^50 - 32 * q^51 + 16 * q^52 - 32 * q^53 + 16 * q^55 - 16 * q^56 + 32 * q^57 + 32 * q^58 - 16 * q^60 + 48 * q^61 + 32 * q^62 - 32 * q^65 - 16 * q^67 - 16 * q^70 - 80 * q^72 - 80 * q^73 - 32 * q^74 - 48 * q^77 - 32 * q^78 - 64 * q^79 - 16 * q^80 - 32 * q^82 - 32 * q^83 - 32 * q^85 - 48 * q^87 - 16 * q^88 - 32 * q^89 - 32 * q^92 - 48 * q^93 - 16 * q^94 - 96 * q^95 + 80 * q^97 - 144 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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