LMFDB - Embedded newform 555.2.bb.a.454.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [555,2,Mod(454,555)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(555, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("555.454");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 555 = 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	555.bb (of order $6$, degree $2$, 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:	$4.43169731218$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			454.11
Character	$\chi$	$=$	555.454
Dual form			555.2.bb.a.544.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07810 - 0.622440i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.225137 - 0.389949i) q^{4} +(1.69944 - 1.45324i) q^{5} -1.24488 q^{6} +(-2.38473 + 1.37683i) q^{7} +3.05030i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.07810 - 0.622440i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.225137 - 0.389949i) q^{4} +(1.69944 - 1.45324i) q^{5} -1.24488 q^{6} +(-2.38473 + 1.37683i) q^{7} +3.05030i q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.73671 + 0.508942i) q^{10} -4.69179 q^{11} +(-0.389949 - 0.225137i) q^{12} +(-3.91382 + 2.25964i) q^{13} +3.42797 q^{14} +(0.745132 - 2.10826i) q^{15} +(1.44835 - 2.50862i) q^{16} +(-2.82251 - 1.62958i) q^{17} +(-1.07810 + 0.622440i) q^{18} +(-3.69752 - 6.40430i) q^{19} +(-0.949298 - 0.335514i) q^{20} +(-1.37683 + 2.38473i) q^{21} +(5.05820 + 2.92036i) q^{22} +7.15793i q^{23} +(1.52515 + 2.64163i) q^{24} +(0.776162 - 4.93939i) q^{25} +5.62597 q^{26} -1.00000i q^{27} +(1.07379 + 0.619950i) q^{28} -1.05796 q^{29} +(-2.11559 + 1.80911i) q^{30} +5.45963 q^{31} +(2.16034 - 1.24727i) q^{32} +(-4.06321 + 2.34589i) q^{33} +(2.02863 + 3.51369i) q^{34} +(-2.05184 + 5.80543i) q^{35} -0.450275 q^{36} +(-3.59095 - 4.90969i) q^{37} +9.20595i q^{38} +(-2.25964 + 3.91382i) q^{39} +(4.43283 + 5.18378i) q^{40} +(-2.64635 - 4.58362i) q^{41} +(2.96871 - 1.71398i) q^{42} -6.06345i q^{43} +(1.05630 + 1.82956i) q^{44} +(-0.408829 - 2.19838i) q^{45} +(4.45538 - 7.71695i) q^{46} +5.66058i q^{47} -2.89670i q^{48} +(0.291305 - 0.504554i) q^{49} +(-3.91125 + 4.84203i) q^{50} -3.25915 q^{51} +(1.76229 + 1.01746i) q^{52} +(1.30077 + 0.751001i) q^{53} +(-0.622440 + 1.07810i) q^{54} +(-7.97339 + 6.81831i) q^{55} +(-4.19973 - 7.27415i) q^{56} +(-6.40430 - 3.69752i) q^{57} +(1.14058 + 0.658516i) q^{58} +(-4.19711 + 7.26961i) q^{59} +(-0.989873 + 0.184085i) q^{60} +(-5.20672 - 9.01831i) q^{61} +(-5.88601 - 3.39829i) q^{62} +2.75365i q^{63} -8.89882 q^{64} +(-3.36747 + 9.52785i) q^{65} +5.84071 q^{66} +(8.91716 - 5.14833i) q^{67} +1.46751i q^{68} +(3.57897 + 6.19895i) q^{69} +(5.82561 - 4.98167i) q^{70} +(1.70541 + 2.95386i) q^{71} +(2.64163 + 1.52515i) q^{72} -1.10854i q^{73} +(0.815403 + 7.52828i) q^{74} +(-1.79752 - 4.66572i) q^{75} +(-1.66490 + 2.88369i) q^{76} +(11.1887 - 6.45978i) q^{77} +(4.87223 - 2.81299i) q^{78} +(2.05721 + 3.56319i) q^{79} +(-1.18426 - 6.36805i) q^{80} +(-0.500000 - 0.866025i) q^{81} +6.58878i q^{82} +(1.53105 + 0.883953i) q^{83} +1.23990 q^{84} +(-7.16485 + 1.33244i) q^{85} +(-3.77413 + 6.53699i) q^{86} +(-0.916219 + 0.528979i) q^{87} -14.3113i q^{88} +(1.40172 - 2.42786i) q^{89} +(-0.927600 + 2.62454i) q^{90} +(6.22228 - 10.7773i) q^{91} +(2.79123 - 1.61152i) q^{92} +(4.72818 - 2.72981i) q^{93} +(3.52337 - 6.10266i) q^{94} +(-15.5907 - 5.51029i) q^{95} +(1.24727 - 2.16034i) q^{96} -10.1727i q^{97} +(-0.628109 + 0.362639i) q^{98} +(-2.34589 + 4.06321i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 32 q^{4} - 2 q^{5} + 36 q^{9}+O(q^{10}) $ 72 * q + 32 * q^4 - 2 * q^5 + 36 * q^9	$ 72 q + 32 q^{4} - 2 q^{5} + 36 q^{9} - 8 q^{11} - 16 q^{14} - 24 q^{16} + 4 q^{19} + 4 q^{20} + 12 q^{21} + 10 q^{25} + 24 q^{26} + 16 q^{29} + 12 q^{30} + 24 q^{31} - 44 q^{34} - 2 q^{35} + 64 q^{36} - 8 q^{39} + 46 q^{40} - 48 q^{41} - 8 q^{44} - 4 q^{45} - 64 q^{46} + 32 q^{49} - 46 q^{50} - 8 q^{51} - 12 q^{55} - 72 q^{56} + 32 q^{59} - 68 q^{60} - 8 q^{61} - 136 q^{64} - 42 q^{65} - 32 q^{66} - 4 q^{69} + 4 q^{70} + 12 q^{71} - 96 q^{74} - 8 q^{75} + 8 q^{76} - 8 q^{79} - 44 q^{80} - 36 q^{81} + 136 q^{84} + 4 q^{85} + 8 q^{86} + 8 q^{91} - 28 q^{94} + 18 q^{95} - 20 q^{96} - 4 q^{99}+O(q^{100}) $ 72 * q + 32 * q^4 - 2 * q^5 + 36 * q^9 - 8 * q^11 - 16 * q^14 - 24 * q^16 + 4 * q^19 + 4 * q^20 + 12 * q^21 + 10 * q^25 + 24 * q^26 + 16 * q^29 + 12 * q^30 + 24 * q^31 - 44 * q^34 - 2 * q^35 + 64 * q^36 - 8 * q^39 + 46 * q^40 - 48 * q^41 - 8 * q^44 - 4 * q^45 - 64 * q^46 + 32 * q^49 - 46 * q^50 - 8 * q^51 - 12 * q^55 - 72 * q^56 + 32 * q^59 - 68 * q^60 - 8 * q^61 - 136 * q^64 - 42 * q^65 - 32 * q^66 - 4 * q^69 + 4 * q^70 + 12 * q^71 - 96 * q^74 - 8 * q^75 + 8 * q^76 - 8 * q^79 - 44 * q^80 - 36 * q^81 + 136 * q^84 + 4 * q^85 + 8 * q^86 + 8 * q^91 - 28 * q^94 + 18 * q^95 - 20 * q^96 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/555\mathbb{Z}\right)^\times$.

$n$	$76$	$112$	$371$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

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 $

$2$	−1.07810	−	0.622440i	−0.762330	−	0.440131i	0.0678017	−	0.997699i	$-0.478401\pi$
$2$	−1.07810	−	0.622440i	−0.762330	−	0.440131i	−0.830132	+	0.557567i	$0.811735\pi$
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	−0.225137	−	0.389949i	−0.112569	−	0.194975i
$5$	1.69944	−	1.45324i	0.760011	−	0.649911i
$5$	1.69944	−	1.45324i	0.760011	−	0.649911i
$6$	−1.24488			−0.508220
$7$	−2.38473	+	1.37683i	−0.901345	+	0.520392i	−0.877636	−	0.479327i	$-0.840881\pi$
$7$	−2.38473	+	1.37683i	−0.901345	+	0.520392i	−0.0237085	+	0.999719i	$0.507547\pi$
$8$			3.05030i			1.07844i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−2.73671	+	0.508942i	−0.865425	+	0.160942i
$11$	−4.69179			−1.41463			−0.707314	−	0.706900i	$-0.750093\pi$
$11$	−4.69179			−1.41463			−0.707314	+	0.706900i	$0.750093\pi$
$12$	−0.389949	−	0.225137i	−0.112569	−	0.0649915i
$13$	−3.91382	+	2.25964i	−1.08550	+	0.626713i	−0.932374	−	0.361494i	$-0.882267\pi$
$13$	−3.91382	+	2.25964i	−1.08550	+	0.626713i	−0.153124	+	0.988207i	$0.548933\pi$
$14$	3.42797			0.916163
$15$	0.745132	−	2.10826i	0.192392	−	0.544351i
$16$	1.44835	−	2.50862i	0.362088	−	0.627155i
$17$	−2.82251	−	1.62958i	−0.684559	−	0.395230i	0.117011	−	0.993131i	$-0.462669\pi$
$17$	−2.82251	−	1.62958i	−0.684559	−	0.395230i	−0.801571	+	0.597900i	$0.796002\pi$
$18$	−1.07810	+	0.622440i	−0.254110	+	0.146710i
$19$	−3.69752	−	6.40430i	−0.848270	−	1.46925i	−0.882751	−	0.469842i	$-0.844311\pi$
$19$	−3.69752	−	6.40430i	−0.848270	−	1.46925i	0.0344802	−	0.999405i	$-0.489022\pi$
$20$	−0.949298	−	0.335514i	−0.212269	−	0.0750232i
$21$	−1.37683	+	2.38473i	−0.300448	+	0.520392i
$22$	5.05820	+	2.92036i	1.07841	+	0.622622i
$23$			7.15793i			1.49253i	0.665648	+	0.746266i	$0.268155\pi$
$23$			7.15793i			1.49253i	−0.665648	+	0.746266i	$0.731845\pi$
$24$	1.52515	+	2.64163i	0.311320	+	0.539221i
$25$	0.776162	−	4.93939i	0.155232	−	0.987878i
$26$	5.62597			1.10334
$27$		−	1.00000i		−	0.192450i
$28$	1.07379	+	0.619950i	0.202926	+	0.117160i
$29$	−1.05796			−0.196458			−0.0982290	−	0.995164i	$-0.531318\pi$
$29$	−1.05796			−0.196458			−0.0982290	+	0.995164i	$0.531318\pi$
$30$	−2.11559	+	1.80911i	−0.386253	+	0.330298i
$31$	5.45963			0.980578			0.490289	−	0.871560i	$-0.336891\pi$
$31$	5.45963			0.980578			0.490289	+	0.871560i	$0.336891\pi$
$32$	2.16034	−	1.24727i	0.381898	−	0.220489i
$33$	−4.06321	+	2.34589i	−0.707314	+	0.408368i
$34$	2.02863	+	3.51369i	0.347907	+	0.602592i
$35$	−2.05184	+	5.80543i	−0.346824	+	0.981297i
$36$	−0.450275			−0.0750458
$37$	−3.59095	−	4.90969i	−0.590348	−	0.807149i
$37$	−3.59095	−	4.90969i	−0.590348	−	0.807149i
$38$			9.20595i			1.49340i
$39$	−2.25964	+	3.91382i	−0.361833	+	0.626713i
$40$	4.43283	+	5.18378i	0.700891	+	0.819628i
$41$	−2.64635	−	4.58362i	−0.413291	−	0.715841i	0.581956	−	0.813220i	$-0.302287\pi$
$41$	−2.64635	−	4.58362i	−0.413291	−	0.715841i	−0.995247	+	0.0973791i	$0.968954\pi$
$42$	2.96871	−	1.71398i	0.458081	−	0.264473i
$43$		−	6.06345i		−	0.924668i	−0.886706	−	0.462334i	$-0.847012\pi$
$43$		−	6.06345i		−	0.924668i	0.886706	−	0.462334i	$-0.152988\pi$
$44$	1.05630	+	1.82956i	0.159243	+	0.275816i
$45$	−0.408829	−	2.19838i	−0.0609446	−	0.327715i
$46$	4.45538	−	7.71695i	0.656910	−	1.13780i
$47$			5.66058i			0.825681i	0.910803	+	0.412840i	$0.135463\pi$
$47$			5.66058i			0.825681i	−0.910803	+	0.412840i	$0.864537\pi$
$48$		−	2.89670i		−	0.418103i
$49$	0.291305	−	0.504554i	0.0416149	−	0.0720792i
$50$	−3.91125	+	4.84203i	−0.553135	+	0.684766i
$51$	−3.25915			−0.456373
$52$	1.76229	+	1.01746i	0.244386	+	0.141096i
$53$	1.30077	+	0.751001i	0.178675	+	0.103158i	0.586670	−	0.809826i	$-0.300439\pi$
$53$	1.30077	+	0.751001i	0.178675	+	0.103158i	−0.407995	+	0.912984i	$0.633772\pi$
$54$	−0.622440	+	1.07810i	−0.0847033	+	0.146710i
$55$	−7.97339	+	6.81831i	−1.07513	+	0.919381i
$56$	−4.19973	−	7.27415i	−0.561213	−	0.972049i
$57$	−6.40430	−	3.69752i	−0.848270	−	0.489749i
$58$	1.14058	+	0.658516i	0.149766	+	0.0864674i
$59$	−4.19711	+	7.26961i	−0.546417	+	0.946422i	0.452099	+	0.891968i	$0.350675\pi$
$59$	−4.19711	+	7.26961i	−0.546417	+	0.946422i	−0.998516	+	0.0544547i	$0.982658\pi$
$60$	−0.989873	+	0.184085i	−0.127792	+	0.0237653i
$61$	−5.20672	−	9.01831i	−0.666653	−	1.15468i	−0.978834	−	0.204654i	$-0.934393\pi$
$61$	−5.20672	−	9.01831i	−0.666653	−	1.15468i	0.312182	−	0.950022i	$-0.398940\pi$
$62$	−5.88601	−	3.39829i	−0.747524	−	0.431583i
$63$			2.75365i			0.346928i
$64$	−8.89882			−1.11235
$65$	−3.36747	+	9.52785i	−0.417683	+	1.18178i
$66$	5.84071			0.718942
$67$	8.91716	−	5.14833i	1.08940	−	0.628968i	0.155987	−	0.987759i	$-0.450144\pi$
$67$	8.91716	−	5.14833i	1.08940	−	0.628968i	0.933418	+	0.358791i	$0.116811\pi$
$68$			1.46751i			0.177962i
$69$	3.57897	+	6.19895i	0.430857	+	0.746266i
$70$	5.82561	−	4.98167i	0.696294	−	0.595424i
$71$	1.70541	+	2.95386i	0.202395	+	0.350559i	0.949300	−	0.314372i	$-0.101794\pi$
$71$	1.70541	+	2.95386i	0.202395	+	0.350559i	−0.746904	+	0.664932i	$0.768461\pi$
$72$	2.64163	+	1.52515i	0.311320	+	0.179740i
$73$		−	1.10854i		−	0.129744i	−0.997894	−	0.0648721i	$-0.979336\pi$
$73$		−	1.10854i		−	0.129744i	0.997894	−	0.0648721i	$-0.0206639\pi$
$74$	0.815403	+	7.52828i	0.0947887	+	0.875144i
$75$	−1.79752	−	4.66572i	−0.207560	−	0.538751i
$76$	−1.66490	+	2.88369i	−0.190977	+	0.330782i
$77$	11.1887	−	6.45978i	1.27507	−	0.736160i
$78$	4.87223	−	2.81299i	0.551672	−	0.318508i
$79$	2.05721	+	3.56319i	0.231454	+	0.400890i	0.958236	−	0.285978i	$-0.0923184\pi$
$79$	2.05721	+	3.56319i	0.231454	+	0.400890i	−0.726782	+	0.686868i	$0.758985\pi$
$80$	−1.18426	−	6.36805i	−0.132404	−	0.711969i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$			6.58878i			0.727609i
$83$	1.53105	+	0.883953i	0.168055	+	0.0970264i	0.581668	−	0.813426i	$-0.302400\pi$
$83$	1.53105	+	0.883953i	0.168055	+	0.0970264i	−0.413614	+	0.910453i	$0.635734\pi$
$84$	1.23990			0.135284
$85$	−7.16485	+	1.33244i	−0.777137	+	0.144523i
$86$	−3.77413	+	6.53699i	−0.406975	+	0.704902i
$87$	−0.916219	+	0.528979i	−0.0982290	+	0.0567125i
$88$		−	14.3113i		−	1.52559i
$89$	1.40172	−	2.42786i	0.148582	−	0.257352i	−0.782121	−	0.623126i	$-0.785862\pi$
$89$	1.40172	−	2.42786i	0.148582	−	0.257352i	0.930704	+	0.365774i	$0.119196\pi$
$90$	−0.927600	+	2.62454i	−0.0977776	+	0.276650i
$91$	6.22228	−	10.7773i	0.652272	−	1.12977i
$92$	2.79123	−	1.61152i	0.291006	−	0.168012i
$93$	4.72818	−	2.72981i	0.490289	−	0.283068i
$94$	3.52337	−	6.10266i	0.363408	−	0.629441i
$95$	−15.5907	−	5.51029i	−1.59957	−	0.565344i
$96$	1.24727	−	2.16034i	0.127299	−	0.220489i
$97$		−	10.1727i		−	1.03288i	−0.856322	−	0.516442i	$-0.827256\pi$
$97$		−	10.1727i		−	1.03288i	0.856322	−	0.516442i	$-0.172744\pi$
$98$	−0.628109	+	0.362639i	−0.0634486	+	0.0366321i
$99$	−2.34589	+	4.06321i	−0.235771	+	0.408368i
$100$	−2.10085	+	0.809377i	−0.210085	+	0.0809377i
$101$	10.8659			1.08120			0.540599	−	0.841280i	$-0.318198\pi$
$101$	10.8659			1.08120			0.540599	+	0.841280i	$0.318198\pi$
$102$	3.51369	+	2.02863i	0.347907	+	0.200864i
$103$			18.2722i			1.80042i	0.435459	+	0.900209i	$0.356586\pi$
$103$			18.2722i			1.80042i	−0.435459	+	0.900209i	$0.643414\pi$
$104$	−6.89259	−	11.9383i	−0.675874	−	1.17065i
$105$	1.12577	+	6.05357i	0.109864	+	0.590768i
$106$	−0.934906	−	1.61931i	−0.0908061	−	0.157281i
$107$	−10.8752	+	6.27881i	−1.05135	+	0.606996i	−0.923026	−	0.384737i	$-0.874292\pi$
$107$	−10.8752	+	6.27881i	−1.05135	+	0.606996i	−0.128321	+	0.991733i	$0.540959\pi$
$108$	−0.389949	+	0.225137i	−0.0375229	+	0.0216638i
$109$	2.50085	−	4.33160i	0.239538	−	0.414892i	−0.721044	−	0.692889i	$-0.756337\pi$
$109$	2.50085	−	4.33160i	0.239538	−	0.414892i	0.960582	+	0.277998i	$0.0896707\pi$
$110$	12.8401	−	2.38785i	1.22425	−	0.227673i
$111$	−5.56470	−	2.45645i	−0.528178	−	0.233155i
$112$			7.97652i			0.753710i
$113$	−0.519357	−	0.299851i	−0.0488570	−	0.0282076i	0.475373	−	0.879785i	$-0.342313\pi$
$113$	−0.519357	−	0.299851i	−0.0488570	−	0.0282076i	−0.524230	+	0.851577i	$0.675647\pi$
$114$	4.60297	+	7.97258i	0.431108	+	0.746701i
$115$	10.4022	+	12.1644i	0.970012	+	1.13434i
$116$	0.238186	+	0.412550i	0.0221150	+	0.0383043i
$117$			4.51929i			0.417808i
$118$	9.04979	−	5.22490i	0.833101	−	0.480991i
$119$	8.97458			0.822699
$120$	6.43083	+	2.27287i	0.587052	+	0.207484i
$121$	11.0129			1.00117
$122$			12.9635i			1.17366i
$123$	−4.58362	−	2.64635i	−0.413291	−	0.238614i
$124$	−1.22917	−	2.12898i	−0.110382	−	0.191188i
$125$	−5.85910	−	9.52213i	−0.524054	−	0.851685i
$126$	1.71398	−	2.96871i	0.152694	−	0.264473i
$127$	−8.36188	−	4.82773i	−0.741997	−	0.428392i	0.0807981	−	0.996730i	$-0.474253\pi$
$127$	−8.36188	−	4.82773i	−0.741997	−	0.428392i	−0.822795	+	0.568338i	$0.807586\pi$
$128$	5.27311	+	3.04443i	0.466082	+	0.269092i
$129$	−3.03173	−	5.25110i	−0.266929	−	0.462334i
$130$	9.56097	−	8.17591i	0.838553	−	0.717075i
$131$	1.82153	−	3.15499i	0.159148	−	0.275652i	−0.775414	−	0.631454i	$-0.782459\pi$
$131$	1.82153	−	3.15499i	0.159148	−	0.275652i	0.934562	+	0.355801i	$0.115792\pi$
$132$	1.82956	+	1.05630i	0.159243	+	0.0919388i
$133$	17.6352	+	10.1817i	1.52917	+	0.882866i
$134$	−12.8181			−1.10731
$135$	−1.45324	−	1.69944i	−0.125075	−	0.146264i
$136$	4.97069	−	8.60949i	0.426233	−	0.738258i
$137$		−	21.5699i		−	1.84284i	−0.388568	−	0.921420i	$-0.627030\pi$
$137$		−	21.5699i		−	1.84284i	0.388568	−	0.921420i	$-0.372970\pi$
$138$		−	8.91076i		−	0.758534i
$139$	1.19470	−	2.06929i	0.101333	−	0.175515i	−0.810901	−	0.585184i	$-0.801022\pi$
$139$	1.19470	−	2.06929i	0.101333	−	0.175515i	0.912234	+	0.409669i	$0.134356\pi$
$140$	2.72577	−	0.506907i	0.230369	−	0.0428414i
$141$	2.83029	+	4.90221i	0.238354	+	0.412840i
$142$		−	4.24607i		−	0.356322i
$143$	18.3628	−	10.6018i	1.53558	−	0.886565i
$144$	−1.44835	−	2.50862i	−0.120696	−	0.209052i
$145$	−1.79793	+	1.53747i	−0.149310	+	0.127680i
$146$	−0.689996	+	1.19511i	−0.0571045	+	0.0989079i
$147$		−	0.582609i		−	0.0480528i
$148$	−1.10607	+	2.50564i	−0.0909188	+	0.205963i
$149$	14.3722			1.17742			0.588709	−	0.808345i	$-0.299636\pi$
$149$	14.3722			1.17742			0.588709	+	0.808345i	$0.299636\pi$
$150$	−0.966229	+	6.14895i	−0.0788922	+	0.502059i
$151$	−7.33270	−	12.7006i	−0.596727	−	1.03356i	−0.993301	−	0.115558i	$-0.963134\pi$
$151$	−7.33270	−	12.7006i	−0.596727	−	1.03356i	0.396574	−	0.918003i	$-0.370199\pi$
$152$	19.5350	−	11.2785i	1.58450	−	0.914811i
$153$	−2.82251	+	1.62958i	−0.228186	+	0.131743i
$154$	−16.0833			−1.29603
$155$	9.27828	−	7.93417i	0.745250	−	0.637288i
$156$	2.03492			0.162924
$157$	−0.494190	−	0.285321i	−0.0394407	−	0.0227711i	0.480150	−	0.877186i	$-0.340582\pi$
$157$	−0.494190	−	0.285321i	−0.0394407	−	0.0227711i	−0.519591	+	0.854415i	$0.673916\pi$
$158$		−	5.12195i		−	0.407481i
$159$	1.50200			0.119117
$160$	1.85877	−	5.25916i	0.146948	−	0.415773i
$161$	−9.85523	−	17.0698i	−0.776701	−	1.34529i
$162$			1.24488i			0.0978070i
$163$	−18.0006	−	10.3926i	−1.40991	−	0.814014i	−0.414534	−	0.910034i	$-0.636055\pi$
$163$	−18.0006	−	10.3926i	−1.40991	−	0.814014i	−0.995379	+	0.0960203i	$0.969389\pi$
$164$	−1.19159	+	2.06389i	−0.0930472	+	0.161162i
$165$	−3.49600	+	9.89153i	−0.272163	+	0.770054i
$166$	−1.10042	−	1.90597i	−0.0854088	−	0.147932i
$167$	2.56687	−	1.48198i	0.198630	−	0.114679i	−0.397386	−	0.917652i	$-0.630083\pi$
$167$	2.56687	−	1.48198i	0.198630	−	0.114679i	0.596016	+	0.802972i	$0.296749\pi$
$168$	−7.27415	−	4.19973i	−0.561213	−	0.324016i
$169$	3.71198	−	6.42935i	0.285537	−	0.494565i
$170$	8.55376	+	3.02319i	0.656044	+	0.231868i
$171$	−7.39505			−0.565514
$172$	−2.36444	+	1.36511i	−0.180287	+	0.104089i
$173$	−9.38091	−	5.41607i	−0.713218	−	0.411776i	0.0990336	−	0.995084i	$-0.468425\pi$
$173$	−9.38091	−	5.41607i	−0.713218	−	0.411776i	−0.812251	+	0.583308i	$0.801758\pi$
$174$	1.31703			0.0998439
$175$	4.94974	+	12.8478i	0.374165	+	0.971200i
$176$	−6.79536	+	11.7699i	−0.512220	+	0.887190i
$177$			8.39422i			0.630948i
$178$	−3.02239	+	1.74498i	−0.226538	+	0.130792i
$179$	11.1597			0.834113			0.417056	−	0.908881i	$-0.363062\pi$
$179$	11.1597			0.834113			0.417056	+	0.908881i	$0.363062\pi$
$180$	−0.765213	+	0.654359i	−0.0570356	+	0.0487730i
$181$	6.87592	+	11.9094i	0.511083	+	0.885222i	0.999917	+	0.0128454i	$0.00408895\pi$
$181$	6.87592	+	11.9094i	0.511083	+	0.885222i	−0.488834	+	0.872377i	$0.662578\pi$
$182$	−13.4164	+	7.74599i	−0.994493	+	0.574171i
$183$	−9.01831	−	5.20672i	−0.666653	−	0.384892i
$184$	−21.8338			−1.60961
$185$	−13.2376	−	3.12518i	−0.973245	−	0.229768i
$186$	−6.79658			−0.498349
$187$	13.2426	+	7.64563i	0.968396	+	0.559104i
$188$	2.20734	−	1.27441i	0.160987	−	0.0929458i
$189$	1.37683	+	2.38473i	0.100149	+	0.173464i
$190$	13.3785	+	15.6449i	0.970578	+	1.13500i
$191$	11.3315			0.819920			0.409960	−	0.912103i	$-0.365543\pi$
$191$	11.3315			0.819920			0.409960	+	0.912103i	$0.365543\pi$
$192$	−7.70660	+	4.44941i	−0.556176	+	0.321108i
$193$			11.9813i			0.862436i	0.902248	+	0.431218i	$0.141916\pi$
$193$			11.9813i			0.862436i	−0.902248	+	0.431218i	$0.858084\pi$
$194$	−6.33191	+	10.9672i	−0.454604	+	0.787398i
$195$	1.84761	+	9.93510i	0.132310	+	0.711467i
$196$	−0.262334			−0.0187382
$197$	−23.3359	−	13.4730i	−1.66261	−	0.959909i	−0.971462	−	0.237197i	$-0.923771\pi$
$197$	−23.3359	−	13.4730i	−1.66261	−	0.959909i	−0.691149	−	0.722712i	$-0.742895\pi$
$198$	5.05820	−	2.92036i	0.359471	−	0.207541i
$199$	8.21510			0.582353			0.291176	−	0.956669i	$-0.405953\pi$
$199$	8.21510			0.582353			0.291176	+	0.956669i	$0.405953\pi$
$200$	15.0666	+	2.36753i	1.06537	+	0.167409i
$201$	5.14833	−	8.91716i	0.363135	−	0.628968i
$202$	−11.7145	−	6.76337i	−0.824230	−	0.475869i
$203$	2.52295	−	1.45663i	0.177076	−	0.102235i
$204$	0.733757	+	1.27090i	0.0513733	+	0.0889811i
$205$	−11.1584	−	3.94377i	−0.779338	−	0.275445i
$206$	11.3734	−	19.6993i	0.792420	−	1.37251i
$207$	6.19895	+	3.57897i	0.430857	+	0.248755i
$208$			13.0910i			0.907700i
$209$	17.3480	+	30.0476i	1.19999	+	2.07844i
$210$	2.55429	−	7.22706i	0.176263	−	0.498715i
$211$	−21.6299			−1.48906			−0.744530	−	0.667589i	$-0.767326\pi$
$211$	−21.6299			−1.48906			−0.744530	+	0.667589i	$0.767326\pi$
$212$		−	0.676314i		−	0.0464494i
$213$	2.95386	+	1.70541i	0.202395	+	0.116853i
$214$	15.6327			1.06863
$215$	−8.81168	−	10.3044i	−0.600951	−	0.702757i
$216$	3.05030			0.207546
$217$	−13.0198	+	7.51696i	−0.883839	+	0.510285i
$218$	−5.39232	+	3.11326i	−0.365214	+	0.210856i
$219$	−0.554268	−	0.960020i	−0.0374539	−	0.0648721i
$220$	4.45390	+	1.57416i	0.300282	+	0.106130i
$221$	14.7291			0.990784
$222$	4.47030	+	6.11198i	0.300027	+	0.410209i
$223$		−	2.58880i		−	0.173359i	−0.996236	−	0.0866794i	$-0.972374\pi$
$223$		−	2.58880i		−	0.173359i	0.996236	−	0.0866794i	$-0.0276256\pi$
$224$	−3.43456	+	5.94883i	−0.229481	+	0.397473i
$225$	−3.88956	−	3.14187i	−0.259304	−	0.209458i
$226$	0.373278	+	0.646537i	0.0248301	+	0.0430070i
$227$	−3.74041	+	2.15953i	−0.248260	+	0.143333i	−0.618967	−	0.785417i	$-0.712449\pi$
$227$	−3.74041	+	2.15953i	−0.248260	+	0.143333i	0.370707	+	0.928750i	$0.379115\pi$
$228$			3.32980i			0.220522i
$229$	−12.8166	−	22.1989i	−0.846943	−	1.46695i	−0.883923	−	0.467632i	$-0.845107\pi$
$229$	−12.8166	−	22.1989i	−0.846943	−	1.46695i	0.0369809	−	0.999316i	$-0.488226\pi$
$230$	−3.64297	−	19.5892i	−0.240211	−	1.29167i
$231$	6.45978	−	11.1887i	0.425022	−	0.736160i
$232$		−	3.22709i		−	0.211869i
$233$			18.6977i			1.22492i	0.790500	+	0.612462i	$0.209821\pi$
$233$			18.6977i			1.22492i	−0.790500	+	0.612462i	$0.790179\pi$
$234$	2.81299	−	4.87223i	0.183891	−	0.318508i
$235$	8.22621	+	9.61980i	0.536619	+	0.627526i
$236$	3.77970			0.246038
$237$	3.56319	+	2.05721i	0.231454	+	0.133630i
$238$	−9.67547	−	5.58614i	−0.627168	−	0.362095i
$239$	−1.84451	+	3.19478i	−0.119311	+	0.206653i	−0.919495	−	0.393102i	$-0.871402\pi$
$239$	−1.84451	+	3.19478i	−0.119311	+	0.206653i	0.800184	+	0.599755i	$0.204735\pi$
$240$	−4.20962	−	4.92276i	−0.271730	−	0.317763i
$241$	13.1652	+	22.8029i	0.848047	+	1.46886i	0.882948	+	0.469470i	$0.155555\pi$
$241$	13.1652	+	22.8029i	0.848047	+	1.46886i	−0.0349009	+	0.999391i	$0.511112\pi$
$242$	−11.8730	−	6.85485i	−0.763222	−	0.440647i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−2.34445	+	4.06071i	−0.150088	+	0.259961i
$245$	−0.238187	−	1.28079i	−0.0152172	−	0.0818270i
$246$	3.29439	+	5.70605i	0.210043	+	0.363805i
$247$	28.9429	+	16.7102i	1.84159	+	1.06324i
$248$			16.6535i			1.05750i
$249$	1.76791			0.112036
$250$	0.389731	+	13.9127i	0.0246487	+	0.879918i
$251$	−23.8258			−1.50387			−0.751936	−	0.659236i	$-0.770880\pi$
$251$	−23.8258			−1.50387			−0.751936	+	0.659236i	$0.770880\pi$
$252$	1.07379	−	0.619950i	0.0676421	−	0.0390532i
$253$		−	33.5835i		−	2.11138i
$254$	6.00995	+	10.4095i	0.377098	+	0.653152i
$255$	−5.53872	+	4.73635i	−0.346848	+	0.296602i
$256$	5.10887	+	8.84882i	0.319304	+	0.553051i
$257$	7.45837	+	4.30609i	0.465241	+	0.268607i	0.714245	−	0.699896i	$-0.246770\pi$
$257$	7.45837	+	4.30609i	0.465241	+	0.268607i	−0.249005	+	0.968502i	$0.580103\pi$
$258$			7.54827i			0.469935i
$259$	15.3233	+	6.76420i	0.952141	+	0.420307i
$260$	4.47352	−	0.831934i	0.277436	−	0.0515943i
$261$	−0.528979	+	0.916219i	−0.0327430	+	0.0567125i
$262$	−3.92758	+	2.26759i	−0.242647	+	0.140092i
$263$	−10.0690	+	5.81334i	−0.620881	+	0.358466i	−0.777212	−	0.629239i	$-0.783367\pi$
$263$	−10.0690	+	5.81334i	−0.620881	+	0.358466i	0.156331	+	0.987705i	$0.450033\pi$
$264$	−7.15567	−	12.3940i	−0.440401	−	0.762797i
$265$	3.30197	−	0.614062i	0.202838	−	0.0377215i
$266$	−12.6750	−	21.9537i	−0.777154	−	1.34607i
$267$		−	2.80345i		−	0.171568i
$268$	−4.01517	−	2.31816i	−0.245266	−	0.141604i
$269$	−18.0601			−1.10114			−0.550572	−	0.834788i	$-0.685590\pi$
$269$	−18.0601			−1.10114			−0.550572	+	0.834788i	$0.685590\pi$
$270$	0.508942	+	2.73671i	0.0309733	+	0.166551i
$271$	−1.55980	+	2.70166i	−0.0947513	+	0.164114i	−0.909505	−	0.415693i	$-0.863539\pi$
$271$	−1.55980	+	2.70166i	−0.0947513	+	0.164114i	0.814753	+	0.579808i	$0.196872\pi$
$272$	−8.17598	+	4.72040i	−0.495741	+	0.286216i
$273$		−	12.4446i		−	0.753179i
$274$	−13.4260	+	23.2544i	−0.811092	+	1.40485i
$275$	−3.64159	+	23.1746i	−0.219596	+	1.39748i
$276$	1.61152	−	2.79123i	0.0970019	−	0.168012i
$277$	−6.80156	+	3.92688i	−0.408666	+	0.235944i	−0.690217	−	0.723603i	$-0.742485\pi$
$277$	−6.80156	+	3.92688i	−0.408666	+	0.235944i	0.281550	+	0.959547i	$0.409151\pi$
$278$	−2.57601	+	1.48726i	−0.154499	+	0.0892000i
$279$	2.72981	−	4.72818i	0.163430	−	0.283068i
$280$	−17.7083	−	6.25871i	−1.05827	−	0.374029i
$281$	−3.95088	+	6.84313i	−0.235690	+	0.408227i	−0.959473	−	0.281801i	$-0.909068\pi$
$281$	−3.95088	+	6.84313i	−0.235690	+	0.408227i	0.723783	+	0.690028i	$0.242402\pi$
$282$		−	7.04675i		−	0.419628i
$283$	10.9144	−	6.30145i	0.648795	−	0.374582i	−0.139199	−	0.990264i	$-0.544453\pi$
$283$	10.9144	−	6.30145i	0.648795	−	0.374582i	0.787995	+	0.615682i	$0.211120\pi$
$284$	0.767905	−	1.33005i	0.0455668	−	0.0789240i
$285$	−16.2571	+	3.02331i	−0.962988	+	0.179085i
$286$	−26.3959			−1.56082
$287$	12.6217	+	7.28714i	0.745035	+	0.430146i
$288$		−	2.49455i		−	0.146993i
$289$	−3.18896	−	5.52344i	−0.187586	−	0.324908i
$290$	2.89533	−	0.538440i	0.170020	−	0.0316183i
$291$	−5.08636	−	8.80984i	−0.298168	−	0.516442i
$292$	−0.432272	+	0.249573i	−0.0252968	+	0.0146051i
$293$	−8.70877	+	5.02801i	−0.508772	+	0.293739i	−0.732329	−	0.680951i	$-0.761566\pi$
$293$	−8.70877	+	5.02801i	−0.508772	+	0.293739i	0.223557	+	0.974691i	$0.428233\pi$
$294$	−0.362639	+	0.628109i	−0.0211495	+	0.0366321i
$295$	3.43180	+	18.4537i	0.199807	+	1.07441i
$296$	14.9760	−	10.9535i	0.870464	−	0.636657i
$297$			4.69179i			0.272245i
$298$	−15.4947	−	8.94584i	−0.897581	−	0.518219i
$299$	−16.1744	−	28.0148i	−0.935388	−	1.62014i
$300$	−1.41470	+	1.75137i	−0.0816780	+	0.101115i
$301$	8.34832	+	14.4597i	0.481189	+	0.833444i
$302$			18.2567i			1.05055i
$303$	9.41015	−	5.43295i	0.540599	−	0.312115i
$304$	−21.4213			−1.22859
$305$	−21.9543	−	7.75939i	−1.25710	−	0.444302i
$306$	4.05725			0.231938
$307$			23.0011i			1.31274i	0.754437	+	0.656372i	$0.227910\pi$
$307$			23.0011i			1.31274i	−0.754437	+	0.656372i	$0.772090\pi$
$308$	−5.03797	−	2.90867i	−0.287065	−	0.165737i
$309$	9.13612	+	15.8242i	0.519736	+	0.900209i
$310$	−14.9414	+	2.77864i	−0.848617	+	0.157816i
$311$	10.7819	−	18.6748i	0.611384	−	1.05895i	−0.379623	−	0.925141i	$-0.623946\pi$
$311$	10.7819	−	18.6748i	0.611384	−	1.05895i	0.991007	−	0.133807i	$-0.0427202\pi$
$312$	−11.9383	−	6.89259i	−0.675874	−	0.390216i
$313$	−22.3377	−	12.8967i	−1.26260	−	0.728964i	−0.289026	−	0.957321i	$-0.593331\pi$
$313$	−22.3377	−	12.8967i	−1.26260	−	0.728964i	−0.973578	+	0.228357i	$0.926665\pi$
$314$	0.355190	+	0.615207i	0.0200445	+	0.0347182i
$315$	4.00173	+	4.67966i	0.225472	+	0.263669i
$316$	0.926308	−	1.60441i	0.0521089	−	0.0902553i
$317$	−12.9776	−	7.49262i	−0.728895	−	0.420828i	0.0891230	−	0.996021i	$-0.471594\pi$
$317$	−12.9776	−	7.49262i	−0.728895	−	0.420828i	−0.818018	+	0.575193i	$0.804927\pi$
$318$	−1.61931	−	0.934906i	−0.0908061	−	0.0524269i
$319$	4.96372			0.277915
$320$	−15.1230	+	12.9322i	−0.845400	+	0.722929i
$321$	−6.27881	+	10.8752i	−0.350449	+	0.606996i
$322$			24.5372i			1.36740i
$323$			24.1016i			1.34105i
$324$	−0.225137	+	0.389949i	−0.0125076	+	0.0216638i
$325$	8.12351	+	21.0857i	0.450611	+	1.16963i
$326$	12.9376	+	22.4085i	0.716546	+	1.24109i
$327$		−	5.00170i		−	0.276595i
$328$	13.9814	−	8.07216i	0.771993	−	0.445711i
$329$	−7.79364	−	13.4990i	−0.429677	−	0.744223i
$330$	9.92591	−	8.48798i	0.546404	−	0.467248i
$331$	−3.76096	+	6.51418i	−0.206721	+	0.358051i	−0.950680	−	0.310174i	$-0.899613\pi$
$331$	−3.76096	+	6.51418i	−0.206721	+	0.358051i	0.743959	+	0.668226i	$0.232946\pi$
$332$		−	0.796043i		−	0.0436885i
$333$	−6.04739	+	0.655006i	−0.331395	+	0.0358941i
$334$	−3.68978			−0.201896
$335$	7.67237	−	21.7081i	0.419186	−	1.18604i
$336$	3.98826	+	6.90787i	0.217577	+	0.376855i
$337$	17.5329	−	10.1226i	0.955076	−	0.551414i	0.0604221	−	0.998173i	$-0.480755\pi$
$337$	17.5329	−	10.1226i	0.955076	−	0.551414i	0.894654	+	0.446759i	$0.147422\pi$
$338$	−8.00376	+	4.62097i	−0.435347	+	0.251348i
$339$	−0.599702			−0.0325713
$340$	2.13266	+	2.49395i	0.115660	+	0.135253i
$341$	−25.6154			−1.38715
$342$	7.97258	+	4.60297i	0.431108	+	0.248900i
$343$		−	17.6713i		−	0.954159i
$344$	18.4953			0.997201
$345$	15.0908	+	5.33360i	0.812462	+	0.287152i
$346$	6.74236	+	11.6781i	0.362471	+	0.627819i
$347$			4.63916i			0.249043i	0.992217	+	0.124521i	$0.0397396\pi$
$347$			4.63916i			0.249043i	−0.992217	+	0.124521i	$0.960260\pi$
$348$	0.412550	+	0.238186i	0.0221150	+	0.0127681i
$349$	−0.0245391	+	0.0425030i	−0.00131355	+	0.00227514i	−0.866681	−	0.498862i	$-0.833751\pi$
$349$	−0.0245391	+	0.0425030i	−0.00131355	+	0.00227514i	0.865368	+	0.501137i	$0.167085\pi$
$350$	2.66066	−	16.9321i	0.142218	−	0.905057i
$351$	2.25964	+	3.91382i	0.120611	+	0.208904i
$352$	−10.1359	+	5.85194i	−0.540243	+	0.311910i
$353$	8.38555	+	4.84140i	0.446318	+	0.257682i	0.706274	−	0.707939i	$-0.250375\pi$
$353$	8.38555	+	4.84140i	0.446318	+	0.257682i	−0.259956	+	0.965620i	$0.583708\pi$
$354$	5.22490	−	9.04979i	0.277700	−	0.480991i
$355$	7.19093	+	2.54152i	0.381655	+	0.134890i
$356$	−1.26232			−0.0669029
$357$	7.77222	−	4.48729i	0.411349	−	0.237493i
$358$	−12.0312	−	6.94622i	−0.635869	−	0.367119i
$359$	−13.0274			−0.687559			−0.343779	−	0.939050i	$-0.611707\pi$
$359$	−13.0274			−0.687559			−0.343779	+	0.939050i	$0.611707\pi$
$360$	6.70570	−	1.24705i	0.353421	−	0.0657252i
$361$	−17.8434	+	30.9056i	−0.939125	+	1.62661i
$362$		−	17.1194i		−	0.899775i
$363$	9.53743	−	5.50644i	0.500585	−	0.289013i
$364$	−5.60347			−0.293701
$365$	−1.61097	−	1.88388i	−0.0843221	−	0.0986070i
$366$	6.48174	+	11.2267i	0.338806	+	0.586829i
$367$	−30.0004	+	17.3207i	−1.56601	+	0.904135i	−0.569381	+	0.822074i	$0.692817\pi$
$367$	−30.0004	+	17.3207i	−1.56601	+	0.904135i	−0.996627	+	0.0820618i	$0.973850\pi$
$368$	17.9565	+	10.3672i	0.936048	+	0.540428i
$369$	−5.29271			−0.275527
$370$	12.3262	+	11.6088i	0.640806	+	0.603515i
$371$	−4.13599			−0.214730
$372$	−2.12898	−	1.22917i	−0.110382	−	0.0637293i
$373$	17.1299	−	9.88996i	0.886954	−	0.512083i	0.0140088	−	0.999902i	$-0.495541\pi$
$373$	17.1299	−	9.88996i	0.886954	−	0.512083i	0.872945	+	0.487819i	$0.162207\pi$
$374$	−9.51789	−	16.4855i	−0.492158	−	0.852443i
$375$	−9.83520	−	5.31685i	−0.507887	−	0.274561i
$376$	−17.2665			−0.890450
$377$	4.14066	−	2.39061i	0.213255	−	0.123123i
$378$		−	3.42797i		−	0.176316i
$379$	18.3193	−	31.7299i	0.940997	−	1.62985i	0.177422	−	0.984135i	$-0.443224\pi$
$379$	18.3193	−	31.7299i	0.940997	−	1.62985i	0.763575	−	0.645720i	$-0.223442\pi$
$380$	1.36132	+	7.32016i	0.0698342	+	0.375516i
$381$	−9.65547			−0.494664
$382$	−12.2165	−	7.05319i	−0.625050	−	0.360873i
$383$	20.3033	−	11.7221i	1.03745	−	0.598972i	0.118340	−	0.992973i	$-0.462243\pi$
$383$	20.3033	−	11.7221i	1.03745	−	0.598972i	0.919110	+	0.394001i	$0.128909\pi$
$384$	6.08886			0.310721
$385$	9.62678	−	27.2378i	0.490626	−	1.38817i
$386$	7.45767	−	12.9171i	0.379585	−	0.657461i
$387$	−5.25110	−	3.03173i	−0.266929	−	0.154111i
$388$	−3.96684	+	2.29026i	−0.201386	+	0.116270i
$389$	12.1468	+	21.0390i	0.615870	+	1.06672i	0.990231	+	0.139435i	$0.0445285\pi$
$389$	12.1468	+	21.0390i	0.615870	+	1.06672i	−0.374362	+	0.927283i	$0.622138\pi$
$390$	4.19209	−	11.8610i	0.212275	−	0.600607i
$391$	11.6644	−	20.2033i	0.589894	−	1.02173i
$392$	1.53904	+	0.888566i	0.0777333	+	0.0448793i
$393$		−	3.64306i		−	0.183768i
$394$	16.7722	+	29.0503i	0.844972	+	1.46353i
$395$	8.67427	+	3.06578i	0.436450	+	0.154256i
$396$	2.11259			0.106162
$397$		−	24.3022i		−	1.21969i	−0.792520	−	0.609846i	$-0.791231\pi$
$397$		−	24.3022i		−	1.21969i	0.792520	−	0.609846i	$-0.208769\pi$
$398$	−8.85668	−	5.11341i	−0.443945	−	0.256312i
$399$	20.3634			1.01945
$400$	−11.2669	−	9.10107i	−0.563345	−	0.455054i
$401$	27.6288			1.37972			0.689858	−	0.723945i	$-0.257673\pi$
$401$	27.6288			1.37972			0.689858	+	0.723945i	$0.257673\pi$
$402$	−11.1008	+	6.40905i	−0.553657	+	0.319654i
$403$	−21.3680	+	12.3368i	−1.06442	+	0.614541i
$404$	−2.44632	−	4.23715i	−0.121709	−	0.210806i
$405$	−2.10826	−	0.745132i	−0.104760	−	0.0370259i
$406$	−3.62665			−0.179988
$407$	16.8480	+	23.0352i	0.835123	+	1.14181i
$408$		−	9.94139i		−	0.492172i
$409$	7.17148	−	12.4214i	0.354607	−	0.614197i	−0.632444	−	0.774606i	$-0.717948\pi$
$409$	7.17148	−	12.4214i	0.354607	−	0.614197i	0.987051	+	0.160409i	$0.0512813\pi$
$410$	9.57511	+	11.1972i	0.472881	+	0.552991i
$411$	−10.7849	−	18.6801i	−0.531982	−	0.921420i
$412$	7.12524	−	4.11376i	0.351036	−	0.202670i
$413$		−	23.1148i		−	1.13740i
$414$	−4.45538	−	7.71695i	−0.218970	−	0.379267i
$415$	3.88652	−	0.722771i	0.190782	−	0.0354794i
$416$	−5.63679	+	9.76320i	−0.276366	+	0.478680i
$417$		−	2.38941i		−	0.117010i
$418$		−	43.1923i		−	2.11261i
$419$	13.2669	−	22.9789i	0.648130	−	1.12259i	−0.335439	−	0.942062i	$-0.608885\pi$
$419$	13.2669	−	22.9789i	0.648130	−	1.12259i	0.983569	−	0.180532i	$-0.0577821\pi$
$420$	2.10713	−	1.80188i	0.102817	−	0.0879226i
$421$	−15.8372			−0.771858			−0.385929	−	0.922528i	$-0.626119\pi$
$421$	−15.8372			−0.771858			−0.385929	+	0.922528i	$0.626119\pi$
$422$	23.3191	+	13.4633i	1.13516	+	0.655382i
$423$	4.90221	+	2.83029i	0.238354	+	0.137613i
$424$	−2.29078	+	3.96774i	−0.111250	+	0.192691i
$425$	−10.2398	+	12.6767i	−0.496705	+	0.614908i
$426$	−2.12304	−	3.67721i	−0.102861	−	0.178161i
$427$	24.8333	+	14.3375i	1.20177	+	0.693841i
$428$	4.89683	+	2.82719i	0.236697	+	0.136657i
$429$	10.6018	−	18.3628i	0.511858	−	0.886565i
$430$	3.08595	+	16.5939i	0.148818	+	0.800230i
$431$	4.06347	+	7.03813i	0.195730	+	0.339015i	0.947140	−	0.320821i	$-0.103959\pi$
$431$	4.06347	+	7.03813i	0.195730	+	0.339015i	−0.751409	+	0.659836i	$0.770626\pi$
$432$	−2.50862	−	1.44835i	−0.120696	−	0.0696839i
$433$			16.9157i			0.812915i	0.913670	+	0.406457i	$0.133236\pi$
$433$			16.9157i			0.812915i	−0.913670	+	0.406457i	$0.866764\pi$
$434$	18.7154			0.898369
$435$	−0.788319	+	2.23046i	−0.0377970	+	0.106942i
$436$	−2.25214			−0.107858
$437$	45.8415	−	26.4666i	2.19290	−	1.26607i
$438$			1.37999i			0.0659386i
$439$	6.41209	+	11.1061i	0.306033	+	0.530064i	0.977491	−	0.210979i	$-0.0676650\pi$
$439$	6.41209	+	11.1061i	0.306033	+	0.530064i	−0.671458	+	0.741043i	$0.734332\pi$
$440$	−20.7979	−	24.3212i	−0.991500	−	1.15947i
$441$	−0.291305	−	0.504554i	−0.0138716	−	0.0240264i
$442$	−15.8794	−	9.16795i	−0.755304	−	0.436075i
$443$			24.8452i			1.18043i	0.807246	+	0.590215i	$0.200957\pi$
$443$			24.8452i			1.18043i	−0.807246	+	0.590215i	$0.799043\pi$
$444$	0.294932	+	2.72299i	0.0139969	+	0.129227i
$445$	−1.14613	−	6.16303i	−0.0543318	−	0.292156i
$446$	−1.61137	+	2.79098i	−0.0763007	+	0.132157i
$447$	12.4467	−	7.18611i	0.588709	−	0.339891i
$448$	21.2213	−	12.2521i	1.00261	−	0.578859i
$449$	15.6204	+	27.0554i	0.737174	+	1.27682i	0.953763	+	0.300560i	$0.0971736\pi$
$449$	15.6204	+	27.0554i	0.737174	+	1.27682i	−0.216589	+	0.976263i	$0.569493\pi$
$450$	2.23769	+	5.80826i	0.105486	+	0.273804i
$451$	12.4161	+	21.5054i	0.584653	+	1.01265i
$452$			0.270030i			0.0127012i
$453$	−12.7006	−	7.33270i	−0.596727	−	0.344520i
$454$	5.37671			0.252341
$455$	−5.08769	−	27.3578i	−0.238515	−	1.28255i
$456$	11.2785	−	19.5350i	0.528166	−	0.914811i
$457$	24.6272	−	14.2185i	1.15201	−	0.665114i	0.202634	−	0.979254i	$-0.435050\pi$
$457$	24.6272	−	14.2185i	1.15201	−	0.665114i	0.949376	+	0.314141i	$0.101716\pi$
$458$			31.9102i			1.49106i
$459$	−1.62958	+	2.82251i	−0.0760621	+	0.131743i
$460$	2.40159	−	6.79501i	0.111975	−	0.316819i
$461$	4.01396	−	6.95238i	0.186949	−	0.323805i	−0.757283	−	0.653087i	$-0.773473\pi$
$461$	4.01396	−	6.95238i	0.186949	−	0.323805i	0.944231	+	0.329282i	$0.106807\pi$
$462$	−13.9285	+	8.04165i	−0.648015	+	0.374131i
$463$	−15.8966	+	9.17790i	−0.738777	+	0.426533i	−0.821625	−	0.570029i	$-0.806932\pi$
$463$	−15.8966	+	9.17790i	−0.738777	+	0.426533i	0.0828473	+	0.996562i	$0.473599\pi$
$464$	−1.53230	+	2.65402i	−0.0711351	+	0.123210i
$465$	4.06814	−	11.5103i	0.188656	−	0.533779i
$466$	11.6382	−	20.1579i	0.539128	−	0.933796i
$467$			25.6952i			1.18903i	0.804083	+	0.594517i	$0.202657\pi$
$467$			25.6952i			1.18903i	−0.804083	+	0.594517i	$0.797343\pi$
$468$	1.76229	−	1.01746i	0.0814620	−	0.0470321i
$469$	−14.1767	+	24.5548i	−0.654619	+	1.13383i
$470$	−2.88091	−	15.4914i	−0.132887	−	0.714565i
$471$	−0.570642			−0.0262938
$472$	−22.1745	−	12.8024i	−1.02066	−	0.589280i
$473$			28.4484i			1.30806i
$474$	−2.56098	−	4.43574i	−0.117630	−	0.203740i
$475$	−34.5032	+	13.2927i	−1.58312	+	0.609913i
$476$	−2.02051	−	3.49963i	−0.0926101	−	0.160405i
$477$	1.30077	−	0.751001i	0.0595583	−	0.0343860i
$478$	3.97712	−	2.29619i	0.181909	−	0.105025i
$479$	−11.9500	+	20.6980i	−0.546010	+	0.945717i	0.452532	+	0.891748i	$0.350521\pi$
$479$	−11.9500	+	20.6980i	−0.546010	+	0.945717i	−0.998543	+	0.0539695i	$0.982813\pi$
$480$	−1.01984	−	5.48395i	−0.0465492	−	0.250307i
$481$	25.1485	+	11.1014i	1.14667	+	0.506180i
$482$		−	32.7783i		−	1.49301i
$483$	−17.0698	−	9.85523i	−0.776701	−	0.448429i
$484$	−2.47941	−	4.29446i	−0.112700	−	0.195203i
$485$	−14.7834	−	17.2879i	−0.671282	−	0.785002i
$486$	0.622440	+	1.07810i	0.0282344	+	0.0489035i
$487$		−	29.9073i		−	1.35523i	−0.735417	−	0.677615i	$-0.763014\pi$
$487$		−	29.9073i		−	1.35523i	0.735417	−	0.677615i	$-0.236986\pi$
$488$	27.5085	−	15.8821i	1.24525	−	0.718947i
$489$	−20.7853			−0.939942
$490$	−0.540428	+	1.52908i	−0.0244141	+	0.0690767i
$491$	−43.8865			−1.98057			−0.990286	−	0.139045i	$-0.955597\pi$
$491$	−43.8865			−1.98057			−0.990286	+	0.139045i	$0.955597\pi$
$492$			2.38317i			0.107442i
$493$	2.98610	+	1.72403i	0.134487	+	0.0776462i
$494$	−20.8022	−	36.0304i	−0.935934	−	1.62108i
$495$	1.91814	+	10.3143i	0.0862139	+	0.463594i
$496$	7.90746	−	13.6961i	0.355055	−	0.614974i
$497$	−8.13392	−	4.69612i	−0.364856	−	0.210650i
$498$	−1.90597	−	1.10042i	−0.0854088	−	0.0493108i
$499$	19.4599	+	33.7055i	0.871143	+	1.50886i	0.860815	+	0.508918i	$0.169954\pi$
$499$	19.4599	+	33.7055i	0.871143	+	1.50886i	0.0103282	+	0.999947i	$0.496712\pi$
$500$	−2.39404	+	4.42854i	−0.107065	+	0.198050i
$501$	1.48198	−	2.56687i	0.0662101	−	0.114679i
$502$	25.6865	+	14.8301i	1.14645	+	0.661901i
$503$	13.6662	+	7.89020i	0.609347	+	0.351807i	0.772710	−	0.634759i	$-0.218901\pi$
$503$	13.6662	+	7.89020i	0.609347	+	0.351807i	−0.163363	+	0.986566i	$0.552234\pi$
$504$	−8.39946			−0.374142
$505$	18.4659	−	15.7908i	0.821722	−	0.702682i
$506$	−20.9037	+	36.2063i	−0.929283	+	1.60957i
$507$		−	7.42397i		−	0.329710i
$508$			4.34761i			0.192894i
$509$	16.9747	−	29.4010i	0.752388	−	1.30317i	−0.194274	−	0.980947i	$-0.562235\pi$
$509$	16.9747	−	29.4010i	0.752388	−	1.30317i	0.946662	−	0.322228i	$-0.104432\pi$
$510$	8.91937	−	1.65872i	0.394956	−	0.0734494i
$511$	1.52626	+	2.64356i	0.0675178	+	0.116944i
$512$		−	24.8976i		−	1.10033i
$513$	−6.40430	+	3.69752i	−0.282757	+	0.163250i
$514$	−5.36057	−	9.28478i	−0.236445	−	0.409534i
$515$	26.5540	+	31.0525i	1.17011	+	1.36834i
$516$	−1.36511	+	2.36444i	−0.0600956	+	0.104089i
$517$		−	26.5583i		−	1.16803i
$518$	−12.3097	−	16.8303i	−0.540855	−	0.739480i
$519$	−10.8321			−0.475478
$520$	−29.0628	−	10.2718i	−1.27449	−	0.450447i
$521$	8.73403	+	15.1278i	0.382645	+	0.662761i	0.991439	−	0.130567i	$-0.0416799\pi$
$521$	8.73403	+	15.1278i	0.382645	+	0.662761i	−0.608794	+	0.793328i	$0.708347\pi$
$522$	1.14058	−	0.658516i	0.0499219	−	0.0288225i
$523$	13.9246	−	8.03936i	0.608880	−	0.351537i	−0.163647	−	0.986519i	$-0.552326\pi$
$523$	13.9246	−	8.03936i	0.608880	−	0.351537i	0.772527	+	0.634982i	$0.218993\pi$
$524$	−1.64038			−0.0716603
$525$	10.7105	+	8.65163i	0.467444	+	0.377588i
$526$	14.4738			0.631089
$527$	−15.4099	−	8.89688i	−0.671264	−	0.387554i
$528$			13.5907i			0.591460i
$529$	−28.2360			−1.22765
$530$	−3.94206	−	1.39326i	−0.171232	−	0.0605192i
$531$	4.19711	+	7.26961i	0.182139	+	0.315474i
$532$		−	9.16912i		−	0.397532i
$533$	20.7147	+	11.9596i	0.897253	+	0.518029i
$534$	−1.74498	+	3.02239i	−0.0755126	+	0.130792i
$535$	−9.35709	+	26.4748i	−0.404542	+	1.14460i
$536$	15.7039	+	27.2000i	0.678306	+	1.17486i
$537$	9.66455	−	5.57983i	0.417056	−	0.240788i
$538$	19.4705	+	11.2413i	0.839435	+	0.484648i
$539$	−1.36674	+	2.36726i	−0.0588696	+	0.101965i
$540$	−0.335514	+	0.949298i	−0.0144382	+	0.0408513i
$541$	−19.6837			−0.846270			−0.423135	−	0.906067i	$-0.639070\pi$
$541$	−19.6837			−0.846270			−0.423135	+	0.906067i	$0.639070\pi$
$542$	3.36324	−	1.94177i	0.144463	−	0.0834060i
$543$	11.9094	+	6.87592i	0.511083	+	0.295074i
$544$	−8.13011			−0.348576
$545$	−2.04484	−	10.9956i	−0.0875912	−	0.471000i
$546$	−7.74599	+	13.4164i	−0.331498	+	0.574171i
$547$		−	11.5293i		−	0.492958i	−0.969148	−	0.246479i	$-0.920726\pi$
$547$		−	11.5293i		−	0.492958i	0.969148	−	0.246479i	$-0.0792736\pi$
$548$	−8.41116	+	4.85619i	−0.359307	+	0.207446i
$549$	−10.4134			−0.444435
$550$	18.3508	−	22.7178i	0.782479	−	0.968689i
$551$	3.91183	+	6.77549i	0.166650	+	0.288645i
$552$	−18.9086	+	10.9169i	−0.804805	+	0.464654i
$553$	−9.81179	−	5.66484i	−0.417240	−	0.240893i
$554$	9.77700			0.415385
$555$	−13.0267	+	3.91230i	−0.552951	+	0.166068i
$556$	−1.07589			−0.0456278
$557$	18.5837	+	10.7293i	0.787415	+	0.454614i	0.839052	−	0.544052i	$-0.183110\pi$
$557$	18.5837	+	10.7293i	0.787415	+	0.454614i	−0.0516366	+	0.998666i	$0.516444\pi$
$558$	−5.88601	+	3.39829i	−0.249175	+	0.143861i
$559$	13.7012	+	23.7312i	0.579501	+	1.00372i
$560$	11.5918	+	13.5556i	0.489844	+	0.572828i
$561$	15.2913			0.645597
$562$	8.51887	−	4.91837i	0.359347	−	0.207469i
$563$			4.27470i			0.180157i	0.995935	+	0.0900785i	$0.0287118\pi$
$563$			4.27470i			0.180157i	−0.995935	+	0.0900785i	$0.971288\pi$
$564$	1.27441	−	2.20734i	0.0536623	−	0.0929458i
$565$	−1.31837	+	0.245175i	−0.0554643	+	0.0103146i
$566$	−15.6891			−0.659461
$567$	2.38473	+	1.37683i	0.100149	+	0.0578213i
$568$	−9.01016	+	5.20202i	−0.378058	+	0.218272i
$569$	6.93563			0.290757			0.145378	−	0.989376i	$-0.453560\pi$
$569$	6.93563			0.290757			0.145378	+	0.989376i	$0.453560\pi$
$570$	19.4086	+	6.85965i	0.812935	+	0.287319i
$571$	−15.1928	+	26.3148i	−0.635800	+	1.10124i	0.350545	+	0.936546i	$0.385996\pi$
$571$	−15.1928	+	26.3148i	−0.635800	+	1.10124i	−0.986345	+	0.164692i	$0.947337\pi$
$572$	−8.26831	−	4.77371i	−0.345715	−	0.199599i
$573$	9.81339	−	5.66576i	0.409960	−	0.236691i
$574$	−9.07161	−	15.7125i	−0.378642	−	0.655827i
$575$	35.3558	+	5.55572i	1.47444	+	0.231689i
$576$	−4.44941	+	7.70660i	−0.185392	+	0.321108i
$577$	−11.5986	−	6.69646i	−0.482856	−	0.278777i	0.238750	−	0.971081i	$-0.423262\pi$
$577$	−11.5986	−	6.69646i	−0.482856	−	0.278777i	−0.721606	+	0.692304i	$0.756596\pi$
$578$			7.93974i			0.330250i
$579$	5.99067	+	10.3761i	0.248964	+	0.431218i
$580$	1.00432	+	0.354960i	0.0417020	+	0.0147389i
$581$	−4.86820			−0.201967
$582$			12.6638i			0.524932i
$583$	−6.10295	−	3.52354i	−0.252758	−	0.145930i
$584$	3.38136			0.139922
$585$	6.56763	+	7.68024i	0.271538	+	0.317539i
$586$	12.5185			0.517136
$587$	−40.4158	+	23.3341i	−1.66814	+	0.963100i	−0.699497	+	0.714635i	$0.746593\pi$
$587$	−40.4158	+	23.3341i	−1.66814	+	0.963100i	−0.968641	+	0.248465i	$0.920074\pi$
$588$	−0.227188	+	0.131167i	−0.00936908	+	0.00540924i
$589$	−20.1871	−	34.9651i	−0.831795	−	1.44071i
$590$	7.78648	−	22.0309i	0.320564	−	0.906999i
$591$	−26.9459			−1.10841
$592$	−17.5175	+	1.89736i	−0.719965	+	0.0779809i
$593$		−	19.1772i		−	0.787512i	−0.919215	−	0.393756i	$-0.871176\pi$
$593$		−	19.1772i		−	0.787512i	0.919215	−	0.393756i	$-0.128824\pi$
$594$	2.92036	−	5.05820i	0.119824	−	0.207541i
$595$	15.2517	−	13.0423i	0.625260	−	0.534680i
$596$	−3.23572	−	5.60444i	−0.132540	−	0.229567i
$597$	7.11449	−	4.10755i	0.291176	−	0.168111i
$598$			40.2703i			1.64678i
$599$	−17.9516	−	31.0932i	−0.733484	−	1.27043i	−0.955385	−	0.295363i	$-0.904560\pi$
$599$	−17.9516	−	31.0932i	−0.733484	−	1.27043i	0.221901	−	0.975069i	$-0.428774\pi$
$600$	14.2318	−	5.48297i	0.581012	−	0.223841i
$601$	19.0487	−	32.9934i	0.777014	−	1.34583i	−0.156642	−	0.987655i	$-0.550067\pi$
$601$	19.0487	−	32.9934i	0.777014	−	1.34583i	0.933656	−	0.358172i	$-0.116600\pi$
$602$		−	20.7853i		−	0.847146i
$603$		−	10.2967i		−	0.419312i
$604$	−3.30173	+	5.71876i	−0.134345	+	0.232693i
$605$	18.7157	−	16.0044i	0.760900	−	0.650671i
$606$	−13.5267			−0.549486
$607$	23.3310	+	13.4701i	0.946975	+	0.546736i	0.892140	−	0.451759i	$-0.149203\pi$
$607$	23.3310	+	13.4701i	0.946975	+	0.546736i	0.0548352	+	0.998495i	$0.482537\pi$
$608$	−15.9758	−	9.22365i	−0.647905	−	0.374068i
$609$	1.45663	−	2.52295i	0.0590255	−	0.102235i
$610$	18.8391	+	22.0306i	0.762773	+	0.891993i
$611$	−12.7909	−	22.1545i	−0.517465	−	0.896275i
$612$	1.27090	+	0.733757i	0.0513733	+	0.0296604i
$613$	9.79530	+	5.65532i	0.395628	+	0.228416i	0.684596	−	0.728923i	$-0.259979\pi$
$613$	9.79530	+	5.65532i	0.395628	+	0.228416i	−0.288968	+	0.957339i	$0.593312\pi$
$614$	14.3168	−	24.7975i	0.577780	−	1.00074i
$615$	−11.6354	+	2.16381i	−0.469183	+	0.0872532i
$616$	19.7042	+	34.1288i	0.793907	+	1.37509i
$617$	−27.4017	−	15.8204i	−1.10315	−	0.636905i	−0.166104	−	0.986108i	$-0.553119\pi$
$617$	−27.4017	−	15.8204i	−1.10315	−	0.636905i	−0.937047	+	0.349204i	$0.886452\pi$
$618$		−	22.7467i		−	0.915008i
$619$	−3.47900			−0.139833			−0.0699163	−	0.997553i	$-0.522273\pi$
$619$	−3.47900			−0.139833			−0.0699163	+	0.997553i	$0.522273\pi$
$620$	−5.18281	−	1.83178i	−0.208147	−	0.0735661i
$621$	7.15793			0.287238
$622$	−23.2478	+	13.4221i	−0.932153	+	0.538179i
$623$			7.71973i			0.309284i
$624$	6.54552	+	11.3372i	0.262031	+	0.453850i
$625$	−23.7951	−	7.66754i	−0.951806	−	0.306701i
$626$	16.0548	+	27.8078i	0.641680	+	1.11142i
$627$	30.0476	+	17.3480i	1.19999	+	0.692812i
$628$			0.256945i			0.0102532i
$629$	2.13476	+	19.7094i	0.0851186	+	0.785865i
$630$	−1.40145	−	7.53596i	−0.0558352	−	0.300240i
$631$	−19.8159	+	34.3222i	−0.788859	+	1.36634i	0.137808	+	0.990459i	$0.455994\pi$
$631$	−19.8159	+	34.3222i	−0.788859	+	1.36634i	−0.926667	+	0.375884i	$0.877339\pi$
$632$	−10.8688	+	6.27509i	−0.432337	+	0.249610i
$633$	−18.7320	+	10.8149i	−0.744530	+	0.429855i
$634$	9.32741	+	16.1556i	0.370439	+	0.641619i
$635$	−21.2263	+	3.94743i	−0.842342	+	0.156649i
$636$	−0.338157	−	0.585705i	−0.0134088	−	0.0232247i
$637$			2.63298i			0.104322i
$638$	−5.35137	−	3.08962i	−0.211863	−	0.122319i
$639$	3.41083			0.134930
$640$	13.3856	−	2.48930i	0.529113	−	0.0983983i
$641$	−10.6654	+	18.4731i	−0.421259	+	0.729642i	−0.996063	−	0.0886490i	$-0.971745\pi$
$641$	−10.6654	+	18.4731i	−0.421259	+	0.729642i	0.574804	+	0.818291i	$0.305078\pi$
$642$	13.5383	−	7.81636i	0.534316	−	0.308487i
$643$		−	17.3563i		−	0.684467i	−0.939615	−	0.342234i	$-0.888817\pi$
$643$		−	17.3563i		−	0.684467i	0.939615	−	0.342234i	$-0.111183\pi$
$644$	−4.43756	+	7.68608i	−0.174864	+	0.302874i
$645$	−12.7834	−	4.51807i	−0.503344	−	0.177899i
$646$	15.0018	−	25.9839i	0.590238	−	1.02232i
$647$	22.6217	−	13.0606i	0.889350	−	0.513466i	0.0156200	−	0.999878i	$-0.495028\pi$
$647$	22.6217	−	13.0606i	0.889350	−	0.513466i	0.873730	+	0.486412i	$0.161694\pi$
$648$	2.64163	−	1.52515i	0.103773	−	0.0599135i
$649$	19.6920	−	34.1075i	0.772977	−	1.33884i
$650$	4.36667	−	27.7889i	0.171275	−	1.08997i
$651$	−7.51696	+	13.0198i	−0.294613	+	0.510285i
$652$			9.35907i			0.366530i
$653$	4.20583	−	2.42824i	0.164587	−	0.0950242i	−0.415444	−	0.909619i	$-0.636374\pi$
$653$	4.20583	−	2.42824i	0.164587	−	0.0950242i	0.580031	+	0.814595i	$0.303040\pi$
$654$	−3.11326	+	5.39232i	−0.121738	+	0.210856i
$655$	−1.48939	−	8.00883i	−0.0581952	−	0.312931i
$656$	−15.3314			−0.598591
$657$	−0.960020	−	0.554268i	−0.0374539	−	0.0216240i
$658$			19.4043i			0.756458i
$659$	−19.2263	−	33.3009i	−0.748950	−	1.29722i	−0.948326	−	0.317296i	$-0.897225\pi$
$659$	−19.2263	−	33.3009i	−0.748950	−	1.29722i	0.199377	−	0.979923i	$-0.436108\pi$
$660$	4.64427	−	0.863688i	0.180778	−	0.0336190i
$661$	6.26706	+	10.8549i	0.243760	+	0.422206i	0.961782	−	0.273815i	$-0.0882856\pi$
$661$	6.26706	+	10.8549i	0.243760	+	0.422206i	−0.718022	+	0.696020i	$0.754952\pi$
$662$	8.10937	−	4.68194i	0.315179	−	0.181969i
$663$	12.7557	−	7.36453i	0.495392	−	0.286015i
$664$	−2.69632	+	4.67016i	−0.104637	+	0.181237i
$665$	44.7664	−	8.32514i	1.73597	−	0.322835i
$666$	6.92738	+	3.05798i	0.268431	+	0.118494i
$667$		−	7.57280i		−	0.293220i
$668$	−1.15580	−	0.667299i	−0.0447191	−	0.0258186i
$669$	−1.29440	−	2.24197i	−0.0500444	−	0.0866794i
$670$	−21.7835	+	18.6278i	−0.841571	+	0.719655i
$671$	24.4288	+	42.3120i	0.943065	+	1.63344i
$672$			6.86912i			0.264982i
$673$	−1.20977	+	0.698459i	−0.0466331	+	0.0269236i	−0.523135	−	0.852250i	$-0.675238\pi$
$673$	−1.20977	+	0.698459i	−0.0466331	+	0.0269236i	0.476502	+	0.879173i	$0.341904\pi$
$674$	−25.2029			−0.970778
$675$	−4.93939	−	0.776162i	−0.190117	−	0.0298745i
$676$	−3.34282			−0.128570
$677$			3.08442i			0.118544i	0.998242	+	0.0592720i	$0.0188779\pi$
$677$			3.08442i			0.118544i	−0.998242	+	0.0592720i	$0.981122\pi$
$678$	0.646537	+	0.373278i	0.0248301	+	0.0143357i
$679$	14.0061	+	24.2592i	0.537504	+	0.930984i
$680$	−4.06432	−	21.8549i	−0.155860	−	0.838098i
$681$	−2.15953	+	3.74041i	−0.0827533	+	0.143333i
$682$	27.6159	+	15.9441i	1.05747	+	0.610529i
$683$	−24.9831	−	14.4240i	−0.955953	−	0.551920i	−0.0610281	−	0.998136i	$-0.519438\pi$
$683$	−24.9831	−	14.4240i	−0.955953	−	0.551920i	−0.894925	+	0.446216i	$0.852771\pi$
$684$	1.66490	+	2.88369i	0.0636591	+	0.110261i
$685$	−31.3463	−	36.6566i	−1.19768	−	1.40058i
$686$	−10.9993	+	19.0514i	−0.419955	+	0.727384i
$687$	−22.1989	−	12.8166i	−0.846943	−	0.488983i
$688$	−15.2109	−	8.78201i	−0.579910	−	0.334811i
$689$	−6.78798			−0.258602
$690$	−12.9495	−	15.1433i	−0.492980	−	0.576494i
$691$	−3.25335	+	5.63497i	−0.123763	+	0.214365i	−0.921249	−	0.388974i	$-0.872830\pi$
$691$	−3.25335	+	5.63497i	−0.123763	+	0.214365i	0.797485	+	0.603338i	$0.206163\pi$
$692$			4.87744i			0.185412i
$693$		−	12.9196i		−	0.490773i
$694$	2.88760	−	5.00146i	0.109612	−	0.189853i
$695$	−0.976857	−	5.25281i	−0.0370543	−	0.199251i
$696$	−1.61354	−	2.79474i	−0.0611612	−	0.105934i
$697$			17.2497i			0.653381i
$698$	0.0529112	−	0.0305483i	0.00200272	−	0.00115627i
$699$	9.34883	+	16.1926i	0.353605	+	0.612462i
$700$	3.89561	−	4.82266i	0.147240	−	0.182279i
$701$	−22.7247	+	39.3603i	−0.858300	+	1.48662i	0.0152499	+	0.999884i	$0.495146\pi$
$701$	−22.7247	+	39.3603i	−0.858300	+	1.48662i	−0.873550	+	0.486735i	$0.838188\pi$
$702$		−	5.62597i		−	0.212339i
$703$	−18.1655	+	41.1512i	−0.685126	+	1.55205i
$704$	41.7514			1.57356
$705$	11.9340	+	4.21788i	0.449461	+	0.158855i
$706$	−6.02696	−	10.4390i	−0.226828	−	0.392877i
$707$	−25.9123	+	14.9605i	−0.974532	+	0.562646i
$708$	3.27332	−	1.88985i	0.123019	−	0.0710250i
$709$	14.5758			0.547405			0.273702	−	0.961814i	$-0.411752\pi$
$709$	14.5758			0.547405			0.273702	+	0.961814i	$0.411752\pi$
$710$	−6.17058	−	7.21593i	−0.231578	−	0.270809i
$711$	4.11441			0.154303
$712$	7.40569	+	4.27567i	0.277540	+	0.160238i
$713$			39.0796i			1.46354i
$714$	−11.1723			−0.418112
$715$	15.7994	−	44.7027i	0.590866	−	1.67179i
$716$	−2.51246	−	4.35170i	−0.0938949	−	0.162631i
$717$			3.68901i			0.137769i
$718$	14.0448	+	8.10876i	0.524147	+	0.302616i
$719$	−12.6433	+	21.8988i	−0.471515	+	0.816687i	−0.999469	−	0.0325854i	$-0.989626\pi$
$719$	−12.6433	+	21.8988i	−0.471515	+	0.816687i	0.527954	+	0.849273i	$0.322959\pi$
$720$	−6.10702	−	2.15843i	−0.227595	−	0.0804398i
$721$	−25.1577	−	43.5744i	−0.936922	−	1.62280i
$722$	38.4738	−	22.2129i	1.43185	−	0.826677i
$723$	22.8029	+	13.1652i	0.848047	+	0.489620i
$724$	3.09605	−	5.36252i	0.115064	−	0.199296i
$725$	−0.821148	+	5.22567i	−0.0304967	+	0.194077i
$726$	−13.7097			−0.508815
$727$	8.71158	−	5.02963i	0.323095	−	0.186539i	−0.329677	−	0.944094i	$-0.606940\pi$
$727$	8.71158	−	5.02963i	0.323095	−	0.186539i	0.652771	+	0.757555i	$0.273606\pi$
$728$	32.8740	+	18.9798i	1.21839	+	0.703438i
$729$	−1.00000			−0.0370370
$730$	0.564181	+	3.03374i	0.0208813	+	0.112284i
$731$	−9.88086	+	17.1142i	−0.365457	+	0.632990i
$732$			4.68891i			0.173307i
$733$	9.36954	−	5.40951i	0.346072	−	0.199805i	−0.316882	−	0.948465i	$-0.602636\pi$
$733$	9.36954	−	5.40951i	0.346072	−	0.199805i	0.662954	+	0.748660i	$0.269303\pi$
$734$	43.1245			1.59175
$735$	−0.846673	−	0.990107i	−0.0312300	−	0.0365206i
$736$	8.92790	+	15.4636i	0.329087	+	0.569995i
$737$	−41.8374	+	24.1549i	−1.54110	+	0.889755i
$738$	5.70605	+	3.29439i	0.210043	+	0.121268i
$739$	19.8210			0.729126			0.364563	−	0.931179i	$-0.381218\pi$
$739$	19.8210			0.729126			0.364563	+	0.931179i	$0.381218\pi$
$740$	1.76161	+	5.86557i	0.0647580	+	0.215623i
$741$	33.4204			1.22773
$742$	4.45901	+	2.57441i	0.163695	+	0.0945095i
$743$	7.56535	−	4.36786i	0.277546	−	0.160241i	−0.354766	−	0.934955i	$-0.615439\pi$
$743$	7.56535	−	4.36786i	0.277546	−	0.160241i	0.632312	+	0.774714i	$0.282106\pi$
$744$	8.32674	+	14.4223i	0.305273	+	0.528749i
$745$	24.4247	−	20.8863i	0.894850	−	0.765217i
$746$	−24.6236			−0.901535
$747$	1.53105	−	0.883953i	0.0560182	−	0.0323421i
$748$		−	6.88526i		−	0.251750i
$749$	17.2897	−	29.9466i	0.631751	−	1.09422i
$750$	7.29388	+	11.8539i	0.266335	+	0.432843i
$751$	17.7192			0.646583			0.323292	−	0.946299i	$-0.395211\pi$
$751$	17.7192			0.646583			0.323292	+	0.946299i	$0.395211\pi$
$752$	14.2002	+	8.19852i	0.517830	+	0.298969i
$753$	−20.6338	+	11.9129i	−0.751936	+	0.434130i
$754$	−5.95205			−0.216761
$755$	−30.9185	−	10.9277i	−1.12524	−	0.397698i
$756$	0.619950	−	1.07379i	0.0225474	−	0.0390532i
$757$	2.37392	+	1.37059i	0.0862817	+	0.0498148i	0.542520	−	0.840043i	$-0.317470\pi$
$757$	2.37392	+	1.37059i	0.0862817	+	0.0498148i	−0.456238	+	0.889858i	$0.650804\pi$
$758$	−39.4999	+	22.8053i	−1.43470	+	0.828325i
$759$	−16.7917	−	29.0842i	−0.609502	−	1.05569i
$760$	16.8080	−	47.5563i	0.609691	−	1.72505i
$761$	12.4659	−	21.5915i	0.451887	−	0.782691i	−0.546617	−	0.837383i	$-0.684084\pi$
$761$	12.4659	−	21.5915i	0.451887	−	0.782691i	0.998503	+	0.0546922i	$0.0174178\pi$
$762$	10.4095	+	6.00995i	0.377098	+	0.217717i
$763$			13.7729i			0.498614i
$764$	−2.55115	−	4.41872i	−0.0922973	−	0.159864i
$765$	−2.42850	+	6.87116i	−0.0878026	+	0.248427i
$766$	−29.1852			−1.05451
$767$		−	37.9359i		−	1.36979i
$768$	8.84882	+	5.10887i	0.319304	+	0.184350i
$769$	13.9415			0.502744			0.251372	−	0.967891i	$-0.419118\pi$
$769$	13.9415			0.502744			0.251372	+	0.967891i	$0.419118\pi$
$770$	−27.3325	+	23.3730i	−0.984996	+	0.842303i
$771$	8.61219			0.310160
$772$	4.67212	−	2.69745i	0.168153	−	0.0970832i
$773$	3.35550	−	1.93730i	0.120689	−	0.0696798i	−0.438440	−	0.898760i	$-0.644469\pi$
$773$	3.35550	−	1.93730i	0.120689	−	0.0696798i	0.559129	+	0.829081i	$0.311136\pi$
$774$	3.77413	+	6.53699i	0.135658	+	0.234967i
$775$	4.23756	−	26.9672i	0.152218	−	0.968691i
$776$	31.0298			1.11391
$777$	16.6524	−	1.80366i	0.597403	−	0.0647059i
$778$		−	30.2427i		−	1.08425i
$779$	−19.5699	+	33.8961i	−0.701165	+	1.21445i
$780$	3.45822	−	2.95724i	0.123824	−	0.105886i
$781$	−8.00144	−	13.8589i	−0.286314	−	0.495911i
$782$	−25.1507	+	14.5208i	−0.899388	+	0.519262i
$783$			1.05796i			0.0378084i
$784$	−0.843823	−	1.46154i	−0.0301365	−	0.0521980i
$785$	−1.25449	+	0.233295i	−0.0447745	+	0.00832665i
$786$	−2.26759	+	3.92758i	−0.0808822	+	0.140092i
$787$			2.40768i			0.0858246i	0.999079	+	0.0429123i	$0.0136636\pi$
$787$			2.40768i			0.0858246i	−0.999079	+	0.0429123i	$0.986336\pi$
$788$			12.1331i			0.432223i
$789$	−5.81334	+	10.0690i	−0.206960	+	0.358466i
$790$	−7.44345	−	8.70443i	−0.264826	−	0.309690i
$791$	1.65137			0.0587160
$792$	−12.3940	−	7.15567i	−0.440401	−	0.254266i
$793$	40.7563	+	23.5307i	1.44730	+	0.835599i
$794$	−15.1266	+	26.2001i	−0.536825	+	0.929807i
$795$	2.55256	−	2.18278i	0.0905298	−	0.0774151i
$796$	−1.84953	−	3.20347i	−0.0655547	−	0.113544i
$797$	−20.8434	−	12.0339i	−0.738311	−	0.426264i	0.0831441	−	0.996538i	$-0.473504\pi$
$797$	−20.8434	−	12.0339i	−0.738311	−	0.426264i	−0.821455	+	0.570274i	$0.806837\pi$
$798$	−21.9537	−	12.6750i	−0.777154	−	0.448690i
$799$	9.22436	−	15.9771i	0.326334	−	0.565228i
$800$	−4.48399	−	11.6389i	−0.158533	−	0.411496i
$801$	−1.40172	−	2.42786i	−0.0495275	−	0.0857841i
$802$	−29.7865	−	17.1973i	−1.05180	−	0.607256i
$803$			5.20101i			0.183540i
$804$	−4.63632			−0.163510
$805$	−41.5549	−	14.6869i	−1.46462	−	0.517645i
$806$	30.7157			1.08191
$807$	−15.6405	+	9.03005i	−0.550572	+	0.317873i
$808$			33.1442i			1.16601i
$809$	−11.3725	−	19.6977i	−0.399836	−	0.692536i	0.593870	−	0.804561i	$-0.297600\pi$
$809$	−11.3725	−	19.6977i	−0.399836	−	0.692536i	−0.993705	+	0.112025i	$0.964266\pi$
$810$	1.80911	+	2.11559i	0.0635658	+	0.0743344i
$811$	−5.59282	−	9.68705i	−0.196391	−	0.340158i	0.750965	−	0.660342i	$-0.229589\pi$
$811$	−5.59282	−	9.68705i	−0.196391	−	0.340158i	−0.947355	+	0.320184i	$0.896255\pi$
$812$	−1.13602	−	0.655882i	−0.0398665	−	0.0230169i
$813$			3.11961i			0.109409i
$814$	−3.82570	−	35.3211i	−0.134091	−	1.23800i
$815$	−45.6938	+	8.49761i	−1.60059	+	0.297658i
$816$	−4.72040	+	8.17598i	−0.165247	+	0.286216i
$817$	−38.8322	+	22.4198i	−1.35857	+	0.784368i
$818$	−15.4631	+	8.92763i	−0.540655	+	0.312147i
$819$	−6.22228	−	10.7773i	−0.217424	−	0.376589i
$820$	0.974309	+	5.23911i	0.0340243	+	0.182958i
$821$	18.6607	+	32.3212i	0.651262	+	1.12802i	0.982817	+	0.184583i	$0.0590933\pi$
$821$	18.6607	+	32.3212i	0.651262	+	1.12802i	−0.331555	+	0.943436i	$0.607573\pi$
$822$			26.8519i			0.936568i
$823$	−3.60256	−	2.07994i	−0.125577	−	0.0725022i	0.435895	−	0.899997i	$-0.356432\pi$
$823$	−3.60256	−	2.07994i	−0.125577	−	0.0725022i	−0.561473	+	0.827495i	$0.689765\pi$
$824$	−55.7358			−1.94165
$825$	8.43358	+	21.8906i	0.293619	+	0.762132i
$826$	−14.3876	+	24.9200i	−0.500607	+	0.867077i
$827$	28.0287	−	16.1824i	0.974652	−	0.562716i	0.0740007	−	0.997258i	$-0.476423\pi$
$827$	28.0287	−	16.1824i	0.974652	−	0.562716i	0.900651	+	0.434543i	$0.143090\pi$
$828$		−	3.22303i		−	0.112008i
$829$	−1.32601	+	2.29672i	−0.0460542	+	0.0797683i	−0.888134	−	0.459585i	$-0.847998\pi$
$829$	−1.32601	+	2.29672i	−0.0460542	+	0.0797683i	0.842079	+	0.539354i	$0.181331\pi$
$830$	−4.63993	−	1.63991i	−0.161054	−	0.0569221i
$831$	−3.92688	+	6.80156i	−0.136222	+	0.235944i
$832$	34.8284	−	20.1082i	1.20746	−	0.697125i
$833$	−1.64442	+	0.949407i	−0.0569758	+	0.0328950i
$834$	−1.48726	+	2.57601i	−0.0514996	+	0.0892000i
$835$	2.20855	−	6.24882i	0.0764299	−	0.216249i
$836$	7.81136	−	13.5297i	0.270162	−	0.467934i
$837$		−	5.45963i		−	0.188712i
$838$	−28.6060	+	16.5157i	−0.988178	+	0.570525i
$839$	17.5469	−	30.3921i	0.605785	−	1.04925i	−0.386142	−	0.922439i	$-0.626192\pi$
$839$	17.5469	−	30.3921i	0.605785	−	1.04925i	0.991927	−	0.126811i	$-0.0404742\pi$
$840$	−18.4652	+	3.43394i	−0.637109	+	0.118482i
$841$	−27.8807			−0.961404
$842$	17.0741	+	9.85771i	0.588411	+	0.339719i
$843$			7.90176i			0.272151i
$844$	4.86969	+	8.43454i	0.167622	+	0.290329i
$845$	−3.03513	−	16.3207i	−0.104412	−	0.561448i
$846$	−3.52337	−	6.10266i	−0.121136	−	0.209814i
$847$	−26.2628	+	15.1628i	−0.902400	+	0.521001i
$848$	3.76795	−	2.17543i	0.129392	−	0.0747045i
$849$	6.30145	−	10.9144i	0.216265	−	0.374582i
$850$	18.9300	−	7.29299i	0.649294	−	0.250148i
$851$	35.1432	−	25.7038i	1.20469	−	0.881114i
$852$		−	1.53581i		−	0.0526160i
$853$	25.9391	+	14.9759i	0.888137	+	0.512766i	0.873333	−	0.487124i	$-0.161954\pi$
$853$	25.9391	+	14.9759i	0.888137	+	0.512766i	0.0148042	+	0.999890i	$0.495288\pi$
$854$	−17.8485	−	30.9145i	−0.610762	−	1.05787i
$855$	−12.5674	+	10.7468i	−0.429796	+	0.367533i
$856$	−19.1522	−	33.1726i	−0.654610	−	1.13382i
$857$			44.2267i			1.51075i	0.655290	+	0.755377i	$0.272546\pi$
$857$			44.2267i			1.51075i	−0.655290	+	0.755377i	$0.727454\pi$
$858$	−22.8595	+	13.1979i	−0.780410	+	0.450570i
$859$	27.9205			0.952634			0.476317	−	0.879274i	$-0.341971\pi$
$859$	27.9205			0.952634			0.476317	+	0.879274i	$0.341971\pi$
$860$	−2.03437	+	5.75602i	−0.0693716	+	0.196279i
$861$	14.5743			0.496690
$862$		−	10.1171i		−	0.344588i
$863$	−6.32793	−	3.65343i	−0.215405	−	0.124364i	0.388416	−	0.921484i	$-0.373022\pi$
$863$	−6.32793	−	3.65343i	−0.215405	−	0.124364i	−0.603821	+	0.797120i	$0.706356\pi$
$864$	−1.24727	−	2.16034i	−0.0424331	−	0.0734963i
$865$	−23.8131	+	4.42849i	−0.809671	+	0.150573i
$866$	10.5290	−	18.2367i	0.357789	−	0.619709i
$867$	−5.52344	−	3.18896i	−0.187586	−	0.108303i
$868$	5.86247	+	3.38470i	0.198985	+	0.114884i
$869$	−9.65198	−	16.7177i	−0.327421	−	0.567110i
$870$	2.23821	−	1.91397i	0.0758824	−	0.0648896i
$871$	−23.2668	+	40.2992i	−0.788364	+	1.36549i
$872$	13.2127	+	7.62833i	0.447437	+	0.258328i
$873$	−8.80984	−	5.08636i	−0.298168	−	0.172147i
$874$	−65.8955			−2.22895
$875$	27.0827	+	14.6408i	0.915563	+	0.494949i
$876$	−0.249573	+	0.432272i	−0.00843228	+	0.0146051i
$877$			44.0347i			1.48695i	0.668765	+	0.743474i	$0.266823\pi$
$877$			44.0347i			1.48695i	−0.668765	+	0.743474i	$0.733177\pi$
$878$		−	15.9646i		−	0.538778i
$879$	−5.02801	+	8.70877i	−0.169591	+	0.293739i
$880$	5.55628	+	29.8775i	0.187302	+	1.00717i
$881$	−28.1374	−	48.7354i	−0.947973	−	1.64194i	−0.749687	−	0.661793i	$-0.769796\pi$
$881$	−28.1374	−	48.7354i	−0.947973	−	1.64194i	−0.198286	−	0.980144i	$-0.563537\pi$
$882$			0.725278i			0.0244214i
$883$	−18.5028	+	10.6826i	−0.622669	+	0.359498i	−0.777907	−	0.628379i	$-0.783719\pi$
$883$	−18.5028	+	10.6826i	−0.622669	+	0.359498i	0.155239	+	0.987877i	$0.450385\pi$
$884$	−3.31606	−	5.74358i	−0.111531	−	0.193178i
$885$	12.1989	+	14.2654i	0.410060	+	0.479527i
$886$	15.4646	−	26.7855i	0.519544	−	0.899877i
$887$			24.2359i			0.813762i	0.913481	+	0.406881i	$0.133384\pi$
$887$			24.2359i			0.813762i	−0.913481	+	0.406881i	$0.866616\pi$
$888$	7.49289	−	16.9740i	0.251445	−	0.569610i
$889$	26.5878			0.891726
$890$	−2.60048	+	7.35775i	−0.0871682	+	0.246632i
$891$	2.34589	+	4.06321i	0.0785904	+	0.136123i
$892$	−1.00950	+	0.582835i	−0.0338006	+	0.0195148i
$893$	36.2521	−	20.9301i	1.21313	−	0.700401i
$894$	−17.8917			−0.598388
$895$	18.9651	−	16.2177i	0.633934	−	0.542099i
$896$	−16.7666			−0.560134
$897$	−28.0148	−	16.1744i	−0.935388	−	0.540047i
$898$		−	38.8911i		−	1.29781i
$899$	−5.77606			−0.192642
$900$	−0.349486	+	2.22408i	−0.0116495	+	0.0741361i
$901$	−2.44763	−	4.23942i	−0.0815423	−	0.141235i
$902$		−	30.9132i		−	1.02930i
$903$	14.4597	+	8.34832i	0.481189	+	0.277815i
$904$	0.914634	−	1.58419i	0.0304203	−	0.0526895i
$905$	28.9925	+	10.2469i	0.963744	+	0.340620i
$906$	9.12833	+	15.8107i	0.303269	+	0.525276i
$907$	6.75150	−	3.89798i	0.224180	−	0.129430i	−0.383704	−	0.923456i	$-0.625352\pi$
$907$	6.75150	−	3.89798i	0.224180	−	0.129430i	0.607884	+	0.794026i	$0.292018\pi$
$908$	1.68421	+	0.972381i	0.0558926	+	0.0322696i
$909$	5.43295	−	9.41015i	0.180200	−	0.312115i
$910$	−11.5436	+	32.6612i	−0.382666	+	1.08271i
$911$	2.61073			0.0864973			0.0432486	−	0.999064i	$-0.486229\pi$
$911$	2.61073			0.0864973			0.0432486	+	0.999064i	$0.486229\pi$
$912$	−18.5514	+	10.7106i	−0.614297	+	0.354665i
$913$	−7.18337	−	4.14732i	−0.237735	−	0.137256i
$914$	−35.4007			−1.17095
$915$	−22.8927	+	4.25731i	−0.756808	+	0.140742i
$916$	−5.77097	+	9.99562i	−0.190678	+	0.330265i
$917$			10.0317i			0.331277i
$918$	3.51369	−	2.02863i	0.115969	−	0.0669547i
$919$	50.7688			1.67471			0.837354	−	0.546661i	$-0.184101\pi$
$919$	50.7688			1.67471			0.837354	+	0.546661i	$0.184101\pi$
$920$	−37.1052	+	31.7299i	−1.22332	+	1.04610i
$921$	11.5006	+	19.9196i	0.378957	+	0.656372i
$922$	−8.65488	+	4.99690i	−0.285033	+	0.164564i
$923$	−13.3494	−	7.70726i	−0.439400	−	0.253688i
$924$	−5.81735			−0.191377
$925$	−27.0380	+	13.9264i	−0.889006	+	0.457896i
$926$	22.8508			0.750923
$927$	15.8242	+	9.13612i	0.519736	+	0.300070i
$928$	−2.28555	+	1.31956i	−0.0750269	+	0.0433168i
$929$	5.89656	+	10.2131i	0.193460	+	0.335082i	0.946395	−	0.323013i	$-0.104696\pi$
$929$	5.89656	+	10.2131i	0.193460	+	0.335082i	−0.752935	+	0.658095i	$0.771362\pi$
$930$	−11.5503	+	9.87709i	−0.378751	+	0.323883i
$931$	−4.30842			−0.141203
$932$	7.29114	−	4.20954i	0.238829	−	0.137888i
$933$		−	21.5637i		−	0.705965i
$934$	15.9937	−	27.7020i	0.523331	−	0.906436i
$935$	33.6159	−	6.25150i	1.09936	−	0.204446i
$936$	−13.7852			−0.450582
$937$	−14.6640	−	8.46625i	−0.479051	−	0.276580i	0.240970	−	0.970533i	$-0.422534\pi$
$937$	−14.6640	−	8.46625i	−0.479051	−	0.276580i	−0.720021	+	0.693952i	$0.755868\pi$
$938$	30.5677	−	17.6483i	0.998072	−	0.576237i
$939$	−25.7934			−0.841736
$940$	1.89921	−	5.37358i	0.0619453	−	0.175267i
$941$	11.7981	−	20.4350i	0.384608	−	0.666161i	−0.607107	−	0.794620i	$-0.707670\pi$
$941$	11.7981	−	20.4350i	0.384608	−	0.666161i	0.991715	+	0.128460i	$0.0410033\pi$
$942$	0.615207	+	0.355190i	0.0200445	+	0.0115727i
$943$	32.8092	−	18.9424i	1.06842	−	0.616850i
$944$	12.1578	+	21.0579i	0.395702	+	0.685376i
$945$	5.80543	+	2.05184i	0.188851	+	0.0667462i
$946$	17.7074	−	30.6702i	0.575718	−	0.997173i
$947$	−45.8673	−	26.4815i	−1.49049	−	0.860533i	−0.490547	−	0.871415i	$-0.663203\pi$
$947$	−45.8673	−	26.4815i	−1.49049	−	0.860533i	−0.999941	+	0.0108817i	$0.996536\pi$
$948$		−	1.85262i		−	0.0601702i
$949$	2.50489	+	4.33861i	0.0813123	+	0.140837i
$950$	45.4718	+	7.14531i	1.47530	+	0.231824i
$951$	−14.9852			−0.485930
$952$			27.3751i			0.887233i
$953$	−33.4718	−	19.3249i	−1.08426	−	0.625996i	−0.152216	−	0.988347i	$-0.548641\pi$
$953$	−33.4718	−	19.3249i	−1.08426	−	0.625996i	−0.932042	+	0.362351i	$0.881974\pi$
$954$	−1.86981			−0.0605374
$955$	19.2572	−	16.4675i	0.623148	−	0.532875i
$956$	1.66107			0.0537228
$957$	4.29871	−	2.48186i	0.138957	−	0.0802271i
$958$	25.7666	−	14.8763i	0.832480	−	0.480633i
$959$	29.6980	+	51.4385i	0.958999	+	1.66103i
$960$	−6.63080	+	18.7611i	−0.214008	+	0.605511i
$961$	−1.19247			−0.0384668
$962$	−20.2026	−	27.6218i	−0.651357	−	0.890562i
$963$			12.5576i			0.404664i
$964$	5.92797	−	10.2675i	0.190927	−	0.330695i
$965$	17.4118	+	20.3615i	0.560506	+	0.655461i
$966$	12.2686	+	21.2498i	0.394735	+	0.683701i
$967$	−27.1560	+	15.6785i	−0.873278	+	0.504187i	−0.868436	−	0.495801i	$-0.834874\pi$
$967$	−27.1560	+	15.6785i	−0.873278	+	0.504187i	−0.00484164	+	0.999988i	$0.501541\pi$
$968$			33.5925i			1.07971i
$969$	12.0508	+	20.8726i	0.387128	+	0.670525i
$970$	5.17733	+	27.8398i	0.166234	+	0.893883i
$971$	−12.9070	+	22.3557i	−0.414207	+	0.717427i	−0.995345	−	0.0963779i	$-0.969274\pi$
$971$	−12.9070	+	22.3557i	−0.414207	+	0.717427i	0.581138	+	0.813805i	$0.302608\pi$
$972$			0.450275i			0.0144426i
$973$			6.57960i			0.210932i
$974$	−18.6155	+	32.2430i	−0.596480	+	1.03313i
$975$	17.5780	+	14.1990i	0.562947	+	0.454733i
$976$	−30.1647			−0.965547
$977$	−14.9485	−	8.63053i	−0.478245	−	0.276115i	0.241440	−	0.970416i	$-0.422380\pi$
$977$	−14.9485	−	8.63053i	−0.478245	−	0.276115i	−0.719685	+	0.694301i	$0.755714\pi$
$978$	22.4085	+	12.9376i	0.716546	+	0.413698i
$979$	−6.57659	+	11.3910i	−0.210189	+	0.364058i
$980$	−0.445820	+	0.381236i	−0.0142412	+	0.0121781i
$981$	−2.50085	−	4.33160i	−0.0798460	−	0.138297i
$982$	47.3140	+	27.3167i	1.50985	+	0.871712i
$983$	−30.8364	−	17.8034i	−0.983529	−	0.567841i	−0.0801954	−	0.996779i	$-0.525554\pi$
$983$	−30.8364	−	17.8034i	−0.983529	−	0.567841i	−0.903334	+	0.428938i	$0.858888\pi$
$984$	8.07216	−	13.9814i	0.257331	−	0.445711i
$985$	−59.2373	+	11.0163i	−1.88746	+	0.351007i
$986$	−2.14620	−	3.71733i	−0.0683491	−	0.118384i
$987$	−13.4990	−	7.79364i	−0.429677	−	0.248074i
$988$		−	15.0483i		−	0.478751i
$989$	43.4018			1.38010
$990$	4.35210	−	12.3138i	0.138319	−	0.391357i
$991$	51.9640			1.65069			0.825345	−	0.564628i	$-0.190980\pi$
$991$	51.9640			1.65069			0.825345	+	0.564628i	$0.190980\pi$
$992$	11.7947	−	6.80965i	0.374481	−	0.216207i
$993$			7.52192i			0.238701i
$994$	5.84611	+	10.1258i	0.185427	+	0.321169i
$995$	13.9610	−	11.9385i	0.442594	−	0.378477i
$996$	−0.398022	−	0.689393i	−0.0126118	−	0.0218443i
$997$	−9.48801	−	5.47791i	−0.300488	−	0.173487i	0.342174	−	0.939637i	$-0.388837\pi$
$997$	−9.48801	−	5.47791i	−0.300488	−	0.173487i	−0.642662	+	0.766150i	$0.722170\pi$
$998$		−	48.4504i		−	1.53367i
$999$	−4.90969	+	3.59095i	−0.155336	+	0.113613i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	555.2.bb.a.454.11	✓	72
5.4	even	2	inner	555.2.bb.a.454.26	yes	72
37.26	even	3	inner	555.2.bb.a.544.26	yes	72
185.174	even	6	inner	555.2.bb.a.544.11	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
555.2.bb.a.454.11	✓	72	1.1	even	1	trivial
555.2.bb.a.454.26	yes	72	5.4	even	2	inner
555.2.bb.a.544.11	yes	72	185.174	even	6	inner
555.2.bb.a.544.26	yes	72	37.26	even	3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 555 = 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	555.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07810 - 0.622440i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.225137 - 0.389949i) q^{4} +(1.69944 - 1.45324i) q^{5} -1.24488 q^{6} +(-2.38473 + 1.37683i) q^{7} +3.05030i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.07810 - 0.622440i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.225137 - 0.389949i) q^{4} +(1.69944 - 1.45324i) q^{5} -1.24488 q^{6} +(-2.38473 + 1.37683i) q^{7} +3.05030i q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.73671 + 0.508942i) q^{10} -4.69179 q^{11} +(-0.389949 - 0.225137i) q^{12} +(-3.91382 + 2.25964i) q^{13} +3.42797 q^{14} +(0.745132 - 2.10826i) q^{15} +(1.44835 - 2.50862i) q^{16} +(-2.82251 - 1.62958i) q^{17} +(-1.07810 + 0.622440i) q^{18} +(-3.69752 - 6.40430i) q^{19} +(-0.949298 - 0.335514i) q^{20} +(-1.37683 + 2.38473i) q^{21} +(5.05820 + 2.92036i) q^{22} +7.15793i q^{23} +(1.52515 + 2.64163i) q^{24} +(0.776162 - 4.93939i) q^{25} +5.62597 q^{26} -1.00000i q^{27} +(1.07379 + 0.619950i) q^{28} -1.05796 q^{29} +(-2.11559 + 1.80911i) q^{30} +5.45963 q^{31} +(2.16034 - 1.24727i) q^{32} +(-4.06321 + 2.34589i) q^{33} +(2.02863 + 3.51369i) q^{34} +(-2.05184 + 5.80543i) q^{35} -0.450275 q^{36} +(-3.59095 - 4.90969i) q^{37} +9.20595i q^{38} +(-2.25964 + 3.91382i) q^{39} +(4.43283 + 5.18378i) q^{40} +(-2.64635 - 4.58362i) q^{41} +(2.96871 - 1.71398i) q^{42} -6.06345i q^{43} +(1.05630 + 1.82956i) q^{44} +(-0.408829 - 2.19838i) q^{45} +(4.45538 - 7.71695i) q^{46} +5.66058i q^{47} -2.89670i q^{48} +(0.291305 - 0.504554i) q^{49} +(-3.91125 + 4.84203i) q^{50} -3.25915 q^{51} +(1.76229 + 1.01746i) q^{52} +(1.30077 + 0.751001i) q^{53} +(-0.622440 + 1.07810i) q^{54} +(-7.97339 + 6.81831i) q^{55} +(-4.19973 - 7.27415i) q^{56} +(-6.40430 - 3.69752i) q^{57} +(1.14058 + 0.658516i) q^{58} +(-4.19711 + 7.26961i) q^{59} +(-0.989873 + 0.184085i) q^{60} +(-5.20672 - 9.01831i) q^{61} +(-5.88601 - 3.39829i) q^{62} +2.75365i q^{63} -8.89882 q^{64} +(-3.36747 + 9.52785i) q^{65} +5.84071 q^{66} +(8.91716 - 5.14833i) q^{67} +1.46751i q^{68} +(3.57897 + 6.19895i) q^{69} +(5.82561 - 4.98167i) q^{70} +(1.70541 + 2.95386i) q^{71} +(2.64163 + 1.52515i) q^{72} -1.10854i q^{73} +(0.815403 + 7.52828i) q^{74} +(-1.79752 - 4.66572i) q^{75} +(-1.66490 + 2.88369i) q^{76} +(11.1887 - 6.45978i) q^{77} +(4.87223 - 2.81299i) q^{78} +(2.05721 + 3.56319i) q^{79} +(-1.18426 - 6.36805i) q^{80} +(-0.500000 - 0.866025i) q^{81} +6.58878i q^{82} +(1.53105 + 0.883953i) q^{83} +1.23990 q^{84} +(-7.16485 + 1.33244i) q^{85} +(-3.77413 + 6.53699i) q^{86} +(-0.916219 + 0.528979i) q^{87} -14.3113i q^{88} +(1.40172 - 2.42786i) q^{89} +(-0.927600 + 2.62454i) q^{90} +(6.22228 - 10.7773i) q^{91} +(2.79123 - 1.61152i) q^{92} +(4.72818 - 2.72981i) q^{93} +(3.52337 - 6.10266i) q^{94} +(-15.5907 - 5.51029i) q^{95} +(1.24727 - 2.16034i) q^{96} -10.1727i q^{97} +(-0.628109 + 0.362639i) q^{98} +(-2.34589 + 4.06321i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 32 q^{4} - 2 q^{5} + 36 q^{9}+O(q^{10}) \) 72 * q + 32 * q^4 - 2 * q^5 + 36 * q^9	\( 72 q + 32 q^{4} - 2 q^{5} + 36 q^{9} - 8 q^{11} - 16 q^{14} - 24 q^{16} + 4 q^{19} + 4 q^{20} + 12 q^{21} + 10 q^{25} + 24 q^{26} + 16 q^{29} + 12 q^{30} + 24 q^{31} - 44 q^{34} - 2 q^{35} + 64 q^{36} - 8 q^{39} + 46 q^{40} - 48 q^{41} - 8 q^{44} - 4 q^{45} - 64 q^{46} + 32 q^{49} - 46 q^{50} - 8 q^{51} - 12 q^{55} - 72 q^{56} + 32 q^{59} - 68 q^{60} - 8 q^{61} - 136 q^{64} - 42 q^{65} - 32 q^{66} - 4 q^{69} + 4 q^{70} + 12 q^{71} - 96 q^{74} - 8 q^{75} + 8 q^{76} - 8 q^{79} - 44 q^{80} - 36 q^{81} + 136 q^{84} + 4 q^{85} + 8 q^{86} + 8 q^{91} - 28 q^{94} + 18 q^{95} - 20 q^{96} - 4 q^{99}+O(q^{100}) \) 72 * q + 32 * q^4 - 2 * q^5 + 36 * q^9 - 8 * q^11 - 16 * q^14 - 24 * q^16 + 4 * q^19 + 4 * q^20 + 12 * q^21 + 10 * q^25 + 24 * q^26 + 16 * q^29 + 12 * q^30 + 24 * q^31 - 44 * q^34 - 2 * q^35 + 64 * q^36 - 8 * q^39 + 46 * q^40 - 48 * q^41 - 8 * q^44 - 4 * q^45 - 64 * q^46 + 32 * q^49 - 46 * q^50 - 8 * q^51 - 12 * q^55 - 72 * q^56 + 32 * q^59 - 68 * q^60 - 8 * q^61 - 136 * q^64 - 42 * q^65 - 32 * q^66 - 4 * q^69 + 4 * q^70 + 12 * q^71 - 96 * q^74 - 8 * q^75 + 8 * q^76 - 8 * q^79 - 44 * q^80 - 36 * q^81 + 136 * q^84 + 4 * q^85 + 8 * q^86 + 8 * q^91 - 28 * q^94 + 18 * q^95 - 20 * q^96 - 4 * q^99

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