LMFDB - Embedded newform 189.2.be.a.20.21

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [189,2,Mod(20,189)] 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("189.20"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(189, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([7, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.be (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			20.21
Character	$\chi$	$=$	189.20
Dual form			189.2.be.a.104.21

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.924066 + 2.53885i) q^{2} +(-0.795581 - 1.53852i) q^{3} +(-4.05977 + 3.40655i) q^{4} +(0.268129 + 1.52064i) q^{5} +(3.17091 - 3.44156i) q^{6} +(-1.64503 + 2.07217i) q^{7} +(-7.72059 - 4.45748i) q^{8} +(-1.73410 + 2.44804i) q^{9} +(-3.61290 + 2.08591i) q^{10} +(3.67329 + 0.647701i) q^{11} +(8.47094 + 3.53586i) q^{12} +(-0.202039 + 0.555096i) q^{13} +(-6.78104 - 2.26166i) q^{14} +(2.12621 - 1.62231i) q^{15} +(2.34200 - 13.2821i) q^{16} +(-2.21584 - 3.83794i) q^{17} +(-7.81763 - 2.14047i) q^{18} +(5.88065 + 3.39519i) q^{19} +(-6.26867 - 5.26004i) q^{20} +(4.49683 + 0.882332i) q^{21} +(1.74995 + 9.92446i) q^{22} +(1.22335 + 1.45794i) q^{23} +(-0.715581 + 15.4246i) q^{24} +(2.45802 - 0.894647i) q^{25} -1.59600 q^{26} +(5.14598 + 0.720338i) q^{27} +(-0.380517 - 14.0164i) q^{28} +(-0.530750 - 1.45822i) q^{29} +(6.08357 + 3.89901i) q^{30} +(3.97747 + 4.74017i) q^{31} +(18.3265 - 3.23145i) q^{32} +(-1.92590 - 6.16674i) q^{33} +(7.69638 - 9.17219i) q^{34} +(-3.59210 - 1.94588i) q^{35} +(-1.29932 - 15.8458i) q^{36} +(-1.87480 - 3.24725i) q^{37} +(-3.18578 + 18.0675i) q^{38} +(1.01477 - 0.130784i) q^{39} +(4.70810 - 12.9354i) q^{40} +(1.26264 + 0.459562i) q^{41} +(1.91526 + 12.2321i) q^{42} +(-1.06487 + 6.03919i) q^{43} +(-17.1192 + 9.88375i) q^{44} +(-4.18754 - 1.98055i) q^{45} +(-2.57102 + 4.45314i) q^{46} +(-4.70770 - 3.95023i) q^{47} +(-22.2981 + 6.96381i) q^{48} +(-1.58777 - 6.81755i) q^{49} +(4.54275 + 5.41384i) q^{50} +(-4.14188 + 6.46251i) q^{51} +(-1.07073 - 2.94182i) q^{52} -2.96963i q^{53} +(2.92640 + 13.7305i) q^{54} +5.75941i q^{55} +(21.9372 - 8.66568i) q^{56} +(0.545046 - 11.7487i) q^{57} +(3.21176 - 2.69499i) q^{58} +(-0.751711 - 4.26316i) q^{59} +(-3.10545 + 13.8293i) q^{60} +(-6.03545 + 7.19277i) q^{61} +(-8.35913 + 14.4784i) q^{62} +(-2.22011 - 7.62044i) q^{63} +(11.6520 + 20.1818i) q^{64} +(-0.898272 - 0.158390i) q^{65} +(13.8768 - 10.5880i) q^{66} +(4.30322 + 1.56624i) q^{67} +(22.0699 + 8.03280i) q^{68} +(1.26979 - 3.04206i) q^{69} +(1.62096 - 10.9179i) q^{70} +(4.85796 - 2.80474i) q^{71} +(24.3004 - 11.1706i) q^{72} +(-4.50326 - 2.59996i) q^{73} +(6.51183 - 7.76050i) q^{74} +(-3.33199 - 3.06996i) q^{75} +(-35.4400 + 6.24903i) q^{76} +(-7.38481 + 6.54620i) q^{77} +(1.26975 + 2.45549i) q^{78} +(-7.68222 + 2.79610i) q^{79} +20.8253 q^{80} +(-2.98579 - 8.49029i) q^{81} +3.63031i q^{82} +(4.97168 - 1.80954i) q^{83} +(-21.2618 + 11.7366i) q^{84} +(5.24198 - 4.39855i) q^{85} +(-16.3166 + 2.87706i) q^{86} +(-1.82126 + 1.97671i) q^{87} +(-25.4729 - 21.3743i) q^{88} +(2.95330 - 5.11527i) q^{89} +(1.15874 - 12.4617i) q^{90} +(-0.817895 - 1.33181i) q^{91} +(-9.93307 - 1.75147i) q^{92} +(4.12845 - 9.89062i) q^{93} +(5.67881 - 15.6024i) q^{94} +(-3.58608 + 9.85268i) q^{95} +(-19.5519 - 25.6248i) q^{96} +(18.3882 + 3.24234i) q^{97} +(15.8415 - 10.3310i) q^{98} +(-7.95545 + 7.86919i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9} - 18 q^{11} + 3 q^{14} - 24 q^{15} - 24 q^{16} - 12 q^{18} - 12 q^{21} - 12 q^{22} + 12 q^{23} - 12 q^{25} - 12 q^{28} - 48 q^{29} + 42 q^{30}+ \cdots - 192 q^{99}+O(q^{100}) $ 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9 - 18 * q^11 + 3 * q^14 - 24 * q^15 - 24 * q^16 - 12 * q^18 - 12 * q^21 - 12 * q^22 + 12 * q^23 - 12 * q^25 - 12 * q^28 - 48 * q^29 + 42 * q^30 - 6 * q^32 - 36 * q^35 - 36 * q^36 - 6 * q^37 - 18 * q^39 - 12 * q^43 - 18 * q^44 - 6 * q^46 - 24 * q^49 + 18 * q^50 + 24 * q^51 + 57 * q^56 - 12 * q^58 - 6 * q^60 + 21 * q^63 + 18 * q^64 + 78 * q^65 - 12 * q^67 - 69 * q^70 + 18 * q^71 + 114 * q^72 - 6 * q^74 - 57 * q^77 + 12 * q^78 + 24 * q^79 - 42 * q^81 - 48 * q^84 + 54 * q^85 - 42 * q^86 - 72 * q^88 + 6 * q^91 - 120 * q^92 - 60 * q^93 + 126 * q^95 + 126 * q^98 - 192 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$-1$

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 $

$2$	0.924066	+	2.53885i	0.653413	+	1.79524i	0.604740	+	0.796423i	$0.293277\pi$
$2$	0.924066	+	2.53885i	0.653413	+	1.79524i	0.0486735	+	0.998815i	$0.484501\pi$
$3$	−0.795581	−	1.53852i	−0.459329	−	0.888266i
$3$	−0.795581	−	1.53852i	−0.459329	−	0.888266i
$4$	−4.05977	+	3.40655i	−2.02989	+	1.70328i
$5$	0.268129	+	1.52064i	0.119911	+	0.680049i	0.984201	+	0.177055i	$0.0566571\pi$
$5$	0.268129	+	1.52064i	0.119911	+	0.680049i	−0.864290	+	0.502994i	$0.832232\pi$
$6$	3.17091	−	3.44156i	1.29452	−	1.40501i
$7$	−1.64503	+	2.07217i	−0.621762	+	0.783206i
$7$	−1.64503	+	2.07217i	−0.621762	+	0.783206i
$8$	−7.72059	−	4.45748i	−2.72964	−	1.57596i
$9$	−1.73410	+	2.44804i	−0.578034	+	0.816013i
$10$	−3.61290	+	2.08591i	−1.14250	+	0.659622i
$11$	3.67329	+	0.647701i	1.10754	+	0.195289i	0.697364	−	0.716717i	$-0.254356\pi$
$11$	3.67329	+	0.647701i	1.10754	+	0.195289i	0.410176	+	0.912007i	$0.365467\pi$
$12$	8.47094	+	3.53586i	2.44535	+	1.02071i
$13$	−0.202039	+	0.555096i	−0.0560354	+	0.153956i	−0.964552	−	0.263893i	$-0.914994\pi$
$13$	−0.202039	+	0.555096i	−0.0560354	+	0.153956i	0.908517	+	0.417849i	$0.137216\pi$
$14$	−6.78104	−	2.26166i	−1.81231	−	0.604453i
$15$	2.12621	−	1.62231i	0.548986	−	0.418879i
$16$	2.34200	−	13.2821i	0.585500	−	3.32054i
$17$	−2.21584	−	3.83794i	−0.537419	−	0.930838i	−0.999042	−	0.0437613i	$-0.986066\pi$
$17$	−2.21584	−	3.83794i	−0.537419	−	0.930838i	0.461623	−	0.887076i	$-0.347267\pi$
$18$	−7.81763	−	2.14047i	−1.84263	−	0.504514i
$19$	5.88065	+	3.39519i	1.34911	+	0.778911i	0.988124	−	0.153659i	$-0.0491058\pi$
$19$	5.88065	+	3.39519i	1.34911	+	0.778911i	0.360989	+	0.932570i	$0.382439\pi$
$20$	−6.26867	−	5.26004i	−1.40172	−	1.17618i
$21$	4.49683	+	0.882332i	0.981289	+	0.192541i
$22$	1.74995	+	9.92446i	0.373090	+	2.11590i
$23$	1.22335	+	1.45794i	0.255087	+	0.304001i	0.878356	−	0.478006i	$-0.158640\pi$
$23$	1.22335	+	1.45794i	0.255087	+	0.304001i	−0.623269	+	0.782007i	$0.714196\pi$
$24$	−0.715581	+	15.4246i	−0.146067	+	3.14853i
$25$	2.45802	−	0.894647i	0.491604	−	0.178929i
$26$	−1.59600			−0.313002
$27$	5.14598	+	0.720338i	0.990344	+	0.138629i
$28$	−0.380517	−	14.0164i	−0.0719109	−	2.64885i
$29$	−0.530750	−	1.45822i	−0.0985578	−	0.270785i	0.880609	−	0.473844i	$-0.157134\pi$
$29$	−0.530750	−	1.45822i	−0.0985578	−	0.270785i	−0.979167	+	0.203059i	$0.934912\pi$
$30$	6.08357	+	3.89901i	1.11070	+	0.711859i
$31$	3.97747	+	4.74017i	0.714375	+	0.851359i	0.994071	−	0.108729i	$-0.0346782\pi$
$31$	3.97747	+	4.74017i	0.714375	+	0.851359i	−0.279696	+	0.960089i	$0.590234\pi$
$32$	18.3265	−	3.23145i	3.23969	−	0.571245i
$33$	−1.92590	−	6.16674i	−0.335256	−	1.07349i
$34$	7.69638	−	9.17219i	1.31992	−	1.57302i
$35$	−3.59210	−	1.94588i	−0.607175	−	0.328914i
$36$	−1.29932	−	15.8458i	−0.216554	−	2.64096i
$37$	−1.87480	−	3.24725i	−0.308215	−	0.533844i	0.669757	−	0.742580i	$-0.266398\pi$
$37$	−1.87480	−	3.24725i	−0.308215	−	0.533844i	−0.977972	+	0.208736i	$0.933065\pi$
$38$	−3.18578	+	18.0675i	−0.516802	+	2.93093i
$39$	1.01477	−	0.130784i	0.162493	−	0.0209421i
$40$	4.70810	−	12.9354i	0.744416	−	2.04527i
$41$	1.26264	+	0.459562i	0.197191	+	0.0717716i	0.438728	−	0.898620i	$-0.355429\pi$
$41$	1.26264	+	0.459562i	0.197191	+	0.0717716i	−0.241537	+	0.970392i	$0.577651\pi$
$42$	1.91526	+	12.2321i	0.295531	+	1.88746i
$43$	−1.06487	+	6.03919i	−0.162391	+	0.920968i	0.789322	+	0.613980i	$0.210432\pi$
$43$	−1.06487	+	6.03919i	−0.162391	+	0.920968i	−0.951713	+	0.306988i	$0.900679\pi$
$44$	−17.1192	+	9.88375i	−2.58081	+	1.49003i
$45$	−4.18754	−	1.98055i	−0.624242	−	0.295242i
$46$	−2.57102	+	4.45314i	−0.379076	+	0.656580i
$47$	−4.70770	−	3.95023i	−0.686688	−	0.576200i	0.231264	−	0.972891i	$-0.425714\pi$
$47$	−4.70770	−	3.95023i	−0.686688	−	0.576200i	−0.917952	+	0.396691i	$0.870158\pi$
$48$	−22.2981	+	6.96381i	−3.21846	+	1.00514i
$49$	−1.58777	−	6.81755i	−0.226824	−	0.973936i
$50$	4.54275	+	5.41384i	0.642441	+	0.765632i
$51$	−4.14188	+	6.46251i	−0.579979	+	0.904932i
$52$	−1.07073	−	2.94182i	−0.148484	−	0.407957i
$53$		−	2.96963i		−	0.407910i	−0.978980	−	0.203955i	$-0.934620\pi$
$53$		−	2.96963i		−	0.407910i	0.978980	−	0.203955i	$-0.0653796\pi$
$54$	2.92640	+	13.7305i	0.398232	+	1.86849i
$55$			5.75941i			0.776599i
$56$	21.9372	−	8.66568i	2.93149	−	1.15800i
$57$	0.545046	−	11.7487i	0.0721932	−	1.55615i
$58$	3.21176	−	2.69499i	0.421725	−	0.353870i
$59$	−0.751711	−	4.26316i	−0.0978644	−	0.555017i	−0.993832	−	0.110897i	$-0.964628\pi$
$59$	−0.751711	−	4.26316i	−0.0978644	−	0.555017i	0.895967	−	0.444120i	$-0.146484\pi$
$60$	−3.10545	+	13.8293i	−0.400912	+	1.78535i
$61$	−6.03545	+	7.19277i	−0.772760	+	0.920939i	−0.998582	−	0.0532293i	$-0.983049\pi$
$61$	−6.03545	+	7.19277i	−0.772760	+	0.920939i	0.225823	+	0.974168i	$0.427493\pi$
$62$	−8.35913	+	14.4784i	−1.06161	+	1.83876i
$63$	−2.22011	−	7.62044i	−0.279707	−	0.960085i
$64$	11.6520	+	20.1818i	1.45650	+	2.52273i
$65$	−0.898272	−	0.158390i	−0.111417	−	0.0196458i
$66$	13.8768	−	10.5880i	1.70811	−	1.30330i
$67$	4.30322	+	1.56624i	0.525722	+	0.191347i	0.591227	−	0.806505i	$-0.298644\pi$
$67$	4.30322	+	1.56624i	0.525722	+	0.191347i	−0.0655054	+	0.997852i	$0.520866\pi$
$68$	22.0699	+	8.03280i	2.67637	+	0.974121i
$69$	1.26979	−	3.04206i	0.152865	−	0.366221i
$70$	1.62096	−	10.9179i	0.193742	−	1.30494i
$71$	4.85796	−	2.80474i	0.576533	−	0.332862i	−0.183221	−	0.983072i	$-0.558652\pi$
$71$	4.85796	−	2.80474i	0.576533	−	0.332862i	0.759754	+	0.650210i	$0.225319\pi$
$72$	24.3004	−	11.1706i	2.86383	−	1.31647i
$73$	−4.50326	−	2.59996i	−0.527067	−	0.304302i	0.212755	−	0.977106i	$-0.431757\pi$
$73$	−4.50326	−	2.59996i	−0.527067	−	0.304302i	−0.739821	+	0.672804i	$0.765090\pi$
$74$	6.51183	−	7.76050i	0.756985	−	0.902140i
$75$	−3.33199	−	3.06996i	−0.384745	−	0.354488i
$76$	−35.4400	+	6.24903i	−4.06525	+	0.716813i
$77$	−7.38481	+	6.54620i	−0.841577	+	0.746008i
$78$	1.26975	+	2.45549i	0.143771	+	0.278029i
$79$	−7.68222	+	2.79610i	−0.864317	+	0.314586i	−0.735863	−	0.677130i	$-0.763223\pi$
$79$	−7.68222	+	2.79610i	−0.864317	+	0.314586i	−0.128453	+	0.991716i	$0.541001\pi$
$80$	20.8253			2.32834
$81$	−2.98579	−	8.49029i	−0.331755	−	0.943366i
$82$			3.63031i			0.400901i
$83$	4.97168	−	1.80954i	0.545712	−	0.198623i	−0.0544280	−	0.998518i	$-0.517334\pi$
$83$	4.97168	−	1.80954i	0.545712	−	0.198623i	0.600141	+	0.799895i	$0.295111\pi$
$84$	−21.2618	+	11.7366i	−2.31985	+	1.28057i
$85$	5.24198	−	4.39855i	0.568573	−	0.477089i
$86$	−16.3166	+	2.87706i	−1.75946	+	0.310241i
$87$	−1.82126	+	1.97671i	−0.195259	+	0.211925i
$88$	−25.4729	−	21.3743i	−2.71542	−	2.27851i
$89$	2.95330	−	5.11527i	0.313050	−	0.542218i	−0.665971	−	0.745977i	$-0.731983\pi$
$89$	2.95330	−	5.11527i	0.313050	−	0.542218i	0.979021	+	0.203760i	$0.0653161\pi$
$90$	1.15874	−	12.4617i	0.122142	−	1.31358i
$91$	−0.817895	−	1.33181i	−0.0857386	−	0.139611i
$92$	−9.93307	−	1.75147i	−1.03559	−	0.182603i
$93$	4.12845	−	9.89062i	0.428100	−	1.02561i
$94$	5.67881	−	15.6024i	0.585725	−	1.60927i
$95$	−3.58608	+	9.85268i	−0.367924	+	1.01086i
$96$	−19.5519	−	25.6248i	−1.99550	−	2.61532i
$97$	18.3882	+	3.24234i	1.86704	+	0.329209i	0.988828	−	0.149064i	$-0.0476261\pi$
$97$	18.3882	+	3.24234i	1.86704	+	0.329209i	0.878211	+	0.478273i	$0.158737\pi$
$98$	15.8415	−	10.3310i	1.60024	−	1.04359i
$99$	−7.95545	+	7.86919i	−0.799553	+	0.790883i
$100$	−6.93135	+	12.0054i	−0.693135	+	1.20054i
$101$	−2.60176	−	2.18314i	−0.258885	−	0.217230i	0.504102	−	0.863644i	$-0.331824\pi$
$101$	−2.60176	−	2.18314i	−0.258885	−	0.217230i	−0.762987	+	0.646414i	$0.776268\pi$
$102$	−20.2347	−	4.54383i	−2.00353	−	0.449906i
$103$	10.5626	−	1.86248i	1.04077	−	0.183516i	0.372959	−	0.927848i	$-0.378343\pi$
$103$	10.5626	−	1.86248i	1.04077	−	0.183516i	0.667810	+	0.744332i	$0.267232\pi$
$104$	4.03419	−	3.38509i	0.395585	−	0.331935i
$105$	−0.135975	+	7.07462i	−0.0132698	+	0.690413i
$106$	7.53944	−	2.74413i	0.732295	−	0.266534i
$107$		−	16.2364i		−	1.56963i	−0.619731	−	0.784814i	$-0.712758\pi$
$107$		−	16.2364i		−	1.56963i	0.619731	−	0.784814i	$-0.287242\pi$
$108$	−23.3454	+	14.6056i	−2.24641	+	1.40543i
$109$	1.02345			0.0980292			0.0490146	−	0.998798i	$-0.484392\pi$
$109$	1.02345			0.0980292			0.0490146	+	0.998798i	$0.484392\pi$
$110$	−14.6223	+	5.32207i	−1.39418	+	0.507440i
$111$	−3.50441	+	5.46787i	−0.332623	+	0.518987i
$112$	23.6702	+	26.7025i	2.23662	+	2.52315i
$113$	−15.5453	+	2.74106i	−1.46238	+	0.257857i	−0.847513	−	0.530774i	$-0.821901\pi$
$113$	−15.5453	+	2.74106i	−1.46238	+	0.257857i	−0.614866	+	0.788631i	$0.710790\pi$
$114$	30.3317	−	9.47274i	2.84083	−	0.887204i
$115$	−1.88897	+	2.25119i	−0.176148	+	0.209925i
$116$	7.12224	+	4.11203i	0.661284	+	0.381792i
$117$	−1.00854	−	1.45719i	−0.0932398	−	0.134717i
$118$	10.1289	−	5.84793i	0.932441	−	0.538345i
$119$	11.5980	+	1.72193i	1.06318	+	0.157849i
$120$	−23.6471	+	3.04764i	−2.15867	+	0.278211i
$121$	2.73694	+	0.996165i	0.248813	+	0.0905605i
$122$	−23.8385	−	8.67650i	−2.15824	−	0.785534i
$123$	−0.297484	−	2.30821i	−0.0268232	−	0.208125i
$124$	−32.2953	−	5.69453i	−2.90020	−	0.511384i
$125$	5.87974	+	10.1840i	0.525900	+	0.910885i
$126$	17.2956	−	12.6783i	1.54082	−	1.12947i
$127$	2.60535	−	4.51259i	0.231187	−	0.400428i	−0.726971	−	0.686668i	$-0.759072\pi$
$127$	2.60535	−	4.51259i	0.231187	−	0.400428i	0.958158	+	0.286241i	$0.0924057\pi$
$128$	−16.5479	+	19.7211i	−1.46265	+	1.74311i
$129$	10.1386	−	3.16634i	0.892655	−	0.278780i
$130$	−0.427935	−	2.42694i	−0.0375324	−	0.212857i
$131$	9.47971	−	7.95442i	0.828246	−	0.694981i	−0.126641	−	0.991949i	$-0.540420\pi$
$131$	9.47971	−	7.95442i	0.828246	−	0.694981i	0.954888	+	0.296967i	$0.0959753\pi$
$132$	28.8260	+	18.4749i	2.50899	+	1.60803i
$133$	−16.7092	+	6.60051i	−1.44888	+	0.572337i
$134$			12.3725i			1.06882i
$135$	0.284416	+	8.01831i	0.0244786	+	0.690106i
$136$			39.5082i			3.38780i
$137$	4.03432	+	11.0842i	0.344675	+	0.946988i	0.984018	+	0.178066i	$0.0569842\pi$
$137$	4.03432	+	11.0842i	0.344675	+	0.946988i	−0.639343	+	0.768922i	$0.720794\pi$
$138$	8.89671	+	0.412738i	0.757338	+	0.0351346i
$139$	1.99206	+	2.37405i	0.168965	+	0.201364i	0.843882	−	0.536530i	$-0.180265\pi$
$139$	1.99206	+	2.37405i	0.168965	+	0.201364i	−0.674917	+	0.737894i	$0.735821\pi$
$140$	21.2118	−	4.33684i	1.79273	−	0.366530i
$141$	−2.33216	+	10.3856i	−0.196403	+	0.874628i
$142$	11.6099	+	9.74185i	0.974280	+	0.817518i
$143$	−1.10168	+	1.90817i	−0.0921274	+	0.159569i
$144$	28.4539	+	28.7659i	2.37116	+	2.39716i
$145$	2.07512	−	1.19807i	0.172329	−	0.0994943i
$146$	2.43959	−	13.8356i	0.201902	−	1.14504i
$147$	−9.22575	+	7.86673i	−0.760927	+	0.648837i
$148$	18.6732	+	6.79648i	1.53493	+	0.558667i
$149$	2.66884	−	7.33258i	0.218640	−	0.600709i	−0.781078	−	0.624433i	$-0.785330\pi$
$149$	2.66884	−	7.33258i	0.218640	−	0.600709i	0.999719	+	0.0237243i	$0.00755238\pi$
$150$	4.71518	−	11.2963i	0.384993	−	0.922336i
$151$	−3.48892	+	19.7866i	−0.283924	+	1.61021i	0.425180	+	0.905109i	$0.360211\pi$
$151$	−3.48892	+	19.7866i	−0.283924	+	1.61021i	−0.709104	+	0.705104i	$0.750900\pi$
$152$	−30.2680	−	52.4258i	−2.45506	−	4.25229i
$153$	13.2379	+	1.23092i	1.07022	+	0.0995141i
$154$	−23.4439	−	12.6998i	−1.88916	−	1.02338i
$155$	−6.14159	+	7.31927i	−0.493305	+	0.587898i
$156$	−3.67420	+	3.98781i	−0.294171	+	0.319280i
$157$	−19.6633	+	3.46718i	−1.56930	+	0.276711i	−0.889588	−	0.456764i	$-0.849008\pi$
$157$	−19.6633	+	3.46718i	−1.56930	+	0.276711i	−0.679717	+	0.733475i	$0.737897\pi$
$158$	−14.1977	−	16.9202i	−1.12951	−	1.34610i
$159$	−4.56884	+	2.36258i	−0.362332	+	0.187365i
$160$	9.82772	+	27.0014i	0.776950	+	2.13465i
$161$	−5.03354	+	0.136650i	−0.396699	+	0.0107696i
$162$	18.7965	−	15.4261i	1.47679	−	1.21199i
$163$	−2.13227			−0.167012			−0.0835061	−	0.996507i	$-0.526612\pi$
$163$	−2.13227			−0.167012			−0.0835061	+	0.996507i	$0.526612\pi$
$164$	−6.69154	+	2.43552i	−0.522522	+	0.190182i
$165$	8.86098	−	4.58208i	0.689826	−	0.356714i
$166$	9.18831	+	10.9502i	0.713151	+	0.849901i
$167$	−1.82951	−	10.3757i	−0.141572	−	0.802894i	−0.970056	−	0.242881i	$-0.921907\pi$
$167$	−1.82951	−	10.3757i	−0.141572	−	0.802894i	0.828484	−	0.560013i	$-0.189204\pi$
$168$	−30.7852	−	26.8567i	−2.37513	−	2.07204i
$169$	9.69127	+	8.13194i	0.745482	+	0.625534i
$170$	16.0112	+	9.24406i	1.22800	+	0.708987i
$171$	−18.5092	+	8.50845i	−1.41543	+	0.650657i
$172$	−16.2497	−	28.1453i	−1.23903	−	2.14606i
$173$	0.480878	−	2.72719i	0.0365604	−	0.207345i	−0.961055	−	0.276356i	$-0.910873\pi$
$173$	0.480878	−	2.72719i	0.0365604	−	0.207345i	0.997616	+	0.0690110i	$0.0219844\pi$
$174$	−6.70152	−	2.79729i	−0.508041	−	0.212062i
$175$	−2.18965	+	6.56515i	−0.165522	+	0.496279i
$176$	17.2057	−	47.2723i	1.29693	−	3.56328i
$177$	−5.96093	+	4.54822i	−0.448051	+	0.341865i
$178$	15.7160	+	2.77115i	1.17796	+	0.207706i
$179$	−12.2011	+	7.04430i	−0.911951	+	0.526515i	−0.881059	−	0.473007i	$-0.843168\pi$
$179$	−12.2011	+	7.04430i	−0.911951	+	0.526515i	−0.0308929	+	0.999523i	$0.509835\pi$
$180$	23.7473	−	6.22452i	1.77002	−	0.463948i
$181$	−4.88410	−	2.81983i	−0.363032	−	0.209597i	0.307378	−	0.951587i	$-0.400548\pi$
$181$	−4.88410	−	2.81983i	−0.363032	−	0.209597i	−0.670410	+	0.741991i	$0.733882\pi$
$182$	2.62547	−	3.30719i	0.194613	−	0.245145i
$183$	15.8679	+	3.56324i	1.17299	+	0.263402i
$184$	−2.94628	−	16.7092i	−0.217203	−	1.23182i
$185$	4.43519	−	3.72157i	0.326082	−	0.273615i
$186$	28.9258	+	1.34193i	2.12094	+	0.0983951i
$187$	−5.65358	−	15.5331i	−0.413431	−	1.13589i
$188$	32.5688			2.37533
$189$	−9.95794	+	9.47837i	−0.724334	+	0.689450i
$190$	−28.3282			−2.05515
$191$	3.67881	+	10.1075i	0.266190	+	0.731350i	0.998718	+	0.0506138i	$0.0161178\pi$
$191$	3.67881	+	10.1075i	0.266190	+	0.731350i	−0.732529	+	0.680736i	$0.761660\pi$
$192$	21.7801	−	33.9831i	1.57184	−	2.45252i
$193$	19.4039	−	16.2818i	1.39672	−	1.17199i	0.434194	−	0.900819i	$-0.357033\pi$
$193$	19.4039	−	16.2818i	1.39672	−	1.17199i	0.962531	−	0.271172i	$-0.0874112\pi$
$194$	8.76010	+	49.6810i	0.628939	+	3.56689i
$195$	0.470963	+	1.50802i	0.0337263	+	0.107992i
$196$	29.6703	+	22.2689i	2.11931	+	1.59063i
$197$	−11.7268	−	6.77045i	−0.835497	−	0.482375i	0.0202340	−	0.999795i	$-0.493559\pi$
$197$	−11.7268	−	6.77045i	−0.835497	−	0.482375i	−0.855731	+	0.517421i	$0.826892\pi$
$198$	−27.3300	−	12.9261i	−1.94226	−	0.918615i
$199$	1.78988	−	1.03339i	0.126881	−	0.0732548i	−0.435216	−	0.900326i	$-0.643328\pi$
$199$	1.78988	−	1.03339i	0.126881	−	0.0732548i	0.562097	+	0.827071i	$0.309995\pi$
$200$	−22.9653	−	4.04939i	−1.62389	−	0.286335i
$201$	−1.01386	−	7.86667i	−0.0715122	−	0.554872i
$202$	3.13846	−	8.62285i	0.220821	−	0.606702i
$203$	3.89479	+	1.29902i	0.273360	+	0.0911730i
$204$	−5.19979	−	40.3459i	−0.364058	−	2.82477i
$205$	−0.360277	+	2.04323i	−0.0251629	+	0.142706i
$206$	14.4891	+	25.0959i	1.00951	+	1.74852i
$207$	−5.69050	+	0.466610i	−0.395517	+	0.0324316i
$208$	6.89970	+	3.98354i	0.478408	+	0.276209i
$209$	19.4023	+	16.2804i	1.34208	+	1.12614i
$210$	−18.0871	+	6.19220i	−1.24813	+	0.427302i
$211$	−0.325203	−	1.84432i	−0.0223879	−	0.126968i	0.971565	−	0.236771i	$-0.0760891\pi$
$211$	−0.325203	−	1.84432i	−0.0223879	−	0.126968i	−0.993953	+	0.109803i	$0.964978\pi$
$212$	10.1162	+	12.0560i	0.694783	+	0.828010i
$213$	−8.18006	−	5.24267i	−0.560488	−	0.359222i
$214$	41.2217	−	15.0035i	2.81786	−	1.02562i
$215$	−9.46893			−0.645776
$216$	−36.5191	−	28.4996i	−2.48481	−	1.93915i
$217$	−16.3655	+	0.444289i	−1.11096	+	0.0301603i
$218$	0.945739	+	2.59840i	0.0640536	+	0.175986i
$219$	−0.417383	+	8.99684i	−0.0282042	+	0.607950i
$220$	−19.6197	−	23.3819i	−1.32276	−	1.57641i
$221$	2.57811	−	0.454591i	0.173423	−	0.0305791i
$222$	−17.1204	−	3.84449i	−1.14905	−	0.258025i
$223$	−4.19171	+	4.99548i	−0.280697	+	0.334522i	−0.887910	−	0.460017i	$-0.847843\pi$
$223$	−4.19171	+	4.99548i	−0.280697	+	0.334522i	0.607213	+	0.794539i	$0.292288\pi$
$224$	−23.4514	+	43.2914i	−1.56691	+	2.89253i
$225$	−2.07233	+	7.56874i	−0.138155	+	0.504583i
$226$	−21.3240	−	36.9343i	−1.41845	−	2.45683i
$227$	0.904207	−	5.12801i	0.0600143	−	0.340358i	−0.939985	−	0.341215i	$-0.889162\pi$
$227$	0.904207	−	5.12801i	0.0600143	−	0.340358i	1.00000		0.000856752i	$0.000272713\pi$
$228$	37.8097	+	49.5536i	2.50401	+	3.28177i
$229$	1.95355	−	5.36734i	0.129094	−	0.354683i	−0.858260	−	0.513216i	$-0.828454\pi$
$229$	1.95355	−	5.36734i	0.129094	−	0.354683i	0.987354	+	0.158532i	$0.0506762\pi$
$230$	−7.46097	−	2.71557i	−0.491962	−	0.179060i
$231$	15.9467	+	6.15366i	1.04922	+	0.404881i
$232$	−2.40231	+	13.6242i	−0.157719	+	0.894470i
$233$	18.1292	−	10.4669i	1.18768	−	0.685709i	0.229904	−	0.973213i	$-0.426159\pi$
$233$	18.1292	−	10.4669i	1.18768	−	0.685709i	0.957779	+	0.287504i	$0.0928255\pi$
$234$	2.76763	−	3.90708i	0.180926	−	0.255414i
$235$	4.74459	−	8.21787i	0.309503	−	0.536075i
$236$	17.5745	+	14.7467i	1.14400	+	0.959931i
$237$	10.4137	+	9.59474i	0.676442	+	0.623245i
$238$	6.34557	+	31.0367i	0.411322	+	2.01181i
$239$	11.8604	+	14.1346i	0.767182	+	0.914292i	0.998279	−	0.0586383i	$-0.0186759\pi$
$239$	11.8604	+	14.1346i	0.767182	+	0.914292i	−0.231097	+	0.972931i	$0.574231\pi$
$240$	−16.5682	−	32.0401i	−1.06947	−	2.06818i
$241$	−6.31746	−	17.3571i	−0.406944	−	1.11807i	−0.958788	−	0.284122i	$-0.908298\pi$
$241$	−6.31746	−	17.3571i	−0.406944	−	1.11807i	0.551845	−	0.833947i	$-0.313924\pi$
$242$			7.86920i			0.505852i
$243$	−10.6871	+	11.3484i	−0.685575	+	0.728002i
$244$		−	49.7611i		−	3.18563i
$245$	9.94129	−	4.24240i	0.635126	−	0.271037i
$246$	5.58532	−	2.88821i	0.356107	−	0.184145i
$247$	−3.07278	+	2.57837i	−0.195516	+	0.164058i
$248$	−9.57921	−	54.3264i	−0.608281	−	3.44973i
$249$	−6.73940	−	6.20940i	−0.427092	−	0.393505i
$250$	−20.4224	+	24.3385i	−1.29163	+	1.53930i
$251$	10.9656	−	18.9930i	0.692145	−	1.19883i	−0.278989	−	0.960294i	$-0.589999\pi$
$251$	10.9656	−	18.9930i	0.692145	−	1.19883i	0.971134	−	0.238536i	$-0.0766675\pi$
$252$	34.9726	+	23.3743i	2.20306	+	1.47245i
$253$	3.54943	+	6.14779i	0.223151	+	0.386508i
$254$	13.8643	+	2.44465i	0.869924	+	0.153391i
$255$	−10.9377	−	4.56551i	−0.684944	−	0.285903i
$256$	−21.5631	−	7.84831i	−1.34769	−	0.490520i
$257$	7.41388	+	2.69843i	0.462465	+	0.168324i	0.562736	−	0.826637i	$-0.309749\pi$
$257$	7.41388	+	2.69843i	0.462465	+	0.168324i	−0.100271	+	0.994960i	$0.531971\pi$
$258$	17.4076	+	22.8145i	1.08375	+	1.42037i
$259$	9.81294	+	1.45691i	0.609746	+	0.0905280i
$260$	4.18634	−	2.41699i	0.259626	−	0.149895i
$261$	4.49016	+	1.22941i	0.277934	+	0.0760986i
$262$	28.9550	+	16.7172i	1.78884	+	1.03279i
$263$	−18.4770	+	22.0201i	−1.13934	+	1.35781i	−0.214835	+	0.976650i	$0.568921\pi$
$263$	−18.4770	+	22.0201i	−1.13934	+	1.35781i	−0.924507	+	0.381165i	$0.875523\pi$
$264$	−12.6191	+	56.1955i	−0.776649	+	3.45860i
$265$	4.51572	−	0.796244i	0.277399	−	0.0489129i
$266$	−32.1981	−	36.3230i	−1.97419	−	2.22710i
$267$	−10.2196	−	0.474108i	−0.625426	−	0.0290149i
$268$	−22.8056	+	8.30055i	−1.39307	+	0.507037i
$269$	15.1159			0.921632			0.460816	−	0.887496i	$-0.347557\pi$
$269$	15.1159			0.921632			0.460816	+	0.887496i	$0.347557\pi$
$270$	−20.0945	+	8.13153i	−1.22291	+	0.494869i
$271$		−	20.2306i		−	1.22892i	−0.788948	−	0.614460i	$-0.789374\pi$
$271$		−	20.2306i		−	1.22892i	0.788948	−	0.614460i	$-0.210626\pi$
$272$	−56.1656	+	20.4426i	−3.40554	+	1.23951i
$273$	−1.39831	+	2.31791i	−0.0846297	+	0.140286i
$274$	−24.4132	+	20.4851i	−1.47485	+	1.23755i
$275$	9.60849	−	1.69424i	0.579414	−	0.102166i
$276$	5.20790	+	16.6757i	0.313478	+	1.00376i
$277$	−12.6623	−	10.6250i	−0.760806	−	0.638392i	0.177531	−	0.984115i	$-0.443189\pi$
$277$	−12.6623	−	10.6250i	−0.760806	−	0.638392i	−0.938336	+	0.345723i	$0.887634\pi$
$278$	−4.18656	+	7.25133i	−0.251093	+	0.434906i
$279$	−18.5015	+	1.51708i	−1.10765	+	0.0908253i
$280$	19.0594	+	31.0351i	1.13901	+	1.85470i
$281$	13.9997	+	2.46852i	0.835151	+	0.147260i	0.574841	−	0.818265i	$-0.305064\pi$
$281$	13.9997	+	2.46852i	0.835151	+	0.147260i	0.260310	+	0.965525i	$0.416175\pi$
$282$	−28.5226	+	3.67601i	−1.69850	+	0.218903i
$283$	1.50970	−	4.14787i	0.0897424	−	0.246565i	−0.886699	−	0.462347i	$-0.847008\pi$
$283$	1.50970	−	4.14787i	0.0897424	−	0.246565i	0.976442	+	0.215781i	$0.0692298\pi$
$284$	−10.1677	+	27.9355i	−0.603341	+	1.65767i
$285$	18.0116	−	2.32134i	1.06691	−	0.137504i
$286$	−5.86259	−	1.03373i	−0.346662	−	0.0611259i
$287$	−3.02936	+	1.86040i	−0.178818	+	0.109816i
$288$	−23.8692	+	50.4676i	−1.40651	+	2.97383i
$289$	−1.31987	+	2.28608i	−0.0776392	+	0.134475i
$290$	4.95927	+	4.16132i	0.291218	+	0.244361i
$291$	−9.64090	−	30.8702i	−0.565160	−	1.80964i
$292$	27.1391	−	4.78536i	1.58820	−	0.280042i
$293$	−20.2510	+	16.9926i	−1.18308	+	0.992719i	−0.183123	+	0.983090i	$0.558621\pi$
$293$	−20.2510	+	16.9926i	−1.18308	+	0.992719i	−0.999954	+	0.00962952i	$0.996935\pi$
$294$	−28.4977	−	16.1534i	−1.66202	−	0.942087i
$295$	6.28117	−	2.28616i	0.365704	−	0.133105i
$296$			33.4275i			1.94294i
$297$	18.4361	+	5.97906i	1.06977	+	0.346941i
$298$	21.0825			1.22128
$299$	−1.05646	+	0.384520i	−0.0610967	+	0.0222374i
$300$	23.9851	+	1.11272i	1.38478	+	0.0642430i
$301$	−10.7625	−	12.1412i	−0.620339	−	0.699809i
$302$	−53.4592	+	9.42631i	−3.07623	+	0.542423i
$303$	−1.28889	+	5.73974i	−0.0740450	+	0.329739i
$304$	58.8679	−	70.1561i	3.37631	−	4.02373i
$305$	−12.5559	−	7.24913i	−0.718946	−	0.415084i
$306$	9.10758	+	34.7465i	0.520646	+	1.98633i
$307$	−15.3405	+	8.85684i	−0.875529	+	0.505487i	−0.869181	−	0.494493i	$-0.835354\pi$
$307$	−15.3405	+	8.85684i	−0.875529	+	0.505487i	−0.00634703	+	0.999980i	$0.502020\pi$
$308$	7.68069	−	51.7328i	0.437648	−	2.94775i
$309$	−11.2689	−	14.7691i	−0.641066	−	0.840185i
$310$	−24.2578	−	8.82910i	−1.37775	−	0.501459i
$311$	22.1660	+	8.06778i	1.25692	+	0.457482i	0.882735	−	0.469872i	$-0.155700\pi$
$311$	22.1660	+	8.06778i	1.25692	+	0.457482i	0.374186	+	0.927354i	$0.377922\pi$
$312$	−8.41756	−	3.51358i	−0.476551	−	0.198917i
$313$	−13.1258	−	2.31444i	−0.741916	−	0.130820i	−0.210100	−	0.977680i	$-0.567379\pi$
$313$	−13.1258	−	2.31444i	−0.741916	−	0.130820i	−0.531816	+	0.846860i	$0.678490\pi$
$314$	−26.9729	−	46.7183i	−1.52217	−	2.63647i
$315$	10.9926	−	5.41924i	0.619365	−	0.305340i
$316$	21.6630	−	37.5214i	1.21864	−	2.11074i
$317$	13.2017	−	15.7332i	0.741484	−	0.883666i	−0.255044	−	0.966930i	$-0.582090\pi$
$317$	13.2017	−	15.7332i	0.741484	−	0.883666i	0.996528	+	0.0832635i	$0.0265343\pi$
$318$	−10.2201	−	9.41641i	−0.573117	−	0.528046i
$319$	−1.00511	−	5.70025i	−0.0562752	−	0.319153i
$320$	−27.5650	+	23.1298i	−1.54093	+	1.29299i
$321$	−24.9800	+	12.9173i	−1.39425	+	0.720976i
$322$	−4.99826	−	12.6531i	−0.278542	−	0.705131i
$323$		−	30.0928i		−	1.67441i
$324$	41.0443	+	24.2974i	2.28024	+	1.34986i
$325$			1.54519i			0.0857118i
$326$	−1.97036	−	5.41351i	−0.109128	−	0.299827i
$327$	−0.814242	−	1.57461i	−0.0450277	−	0.0870760i
$328$	−7.69981	−	9.17628i	−0.425151	−	0.506675i
$329$	15.9298	−	3.25691i	0.878240	−	0.179559i
$330$	19.8213	+	18.2626i	1.09113	+	1.00532i
$331$	0.871850	+	0.731569i	0.0479212	+	0.0402107i	0.666434	−	0.745564i	$-0.267820\pi$
$331$	0.871850	+	0.731569i	0.0479212	+	0.0402107i	−0.618512	+	0.785775i	$0.712264\pi$
$332$	−14.0196	+	24.2826i	−0.769424	+	1.33268i
$333$	11.2005	+	1.04147i	0.613782	+	0.0570723i
$334$	24.6517	−	14.2327i	1.34888	−	0.778777i
$335$	−1.22787	+	6.96358i	−0.0670856	+	0.380461i
$336$	22.2508	−	57.6611i	1.21388	−	3.14567i
$337$	−3.57167	−	1.29998i	−0.194561	−	0.0708145i	0.242902	−	0.970051i	$-0.421901\pi$
$337$	−3.57167	−	1.29998i	−0.194561	−	0.0708145i	−0.437463	+	0.899236i	$0.644123\pi$
$338$	−11.6904	+	32.1191i	−0.635874	+	1.74705i
$339$	16.5847	+	21.7361i	0.900759	+	1.18054i
$340$	−6.29738	+	35.7142i	−0.341523	+	1.93687i
$341$	11.5402	+	19.9882i	0.624937	+	1.08242i
$342$	−38.7054	−	39.1297i	−2.09295	−	2.11589i
$343$	16.7390	+	7.92493i	0.903823	+	0.427906i
$344$	35.1410	−	41.8794i	1.89468	−	2.25799i
$345$	4.96634	+	1.11522i	0.267379	+	0.0600415i
$346$	7.36829	−	1.29923i	0.396122	−	0.0698470i
$347$	−3.58267	−	4.26966i	−0.192328	−	0.229208i	0.661259	−	0.750157i	$-0.270022\pi$
$347$	−3.58267	−	4.26966i	−0.192328	−	0.229208i	−0.853587	+	0.520950i	$0.825578\pi$
$348$	0.660123	−	14.2292i	0.0353863	−	0.762764i
$349$	−4.68587	−	12.8743i	−0.250829	−	0.689147i	−0.999652	−	0.0263773i	$-0.991603\pi$
$349$	−4.68587	−	12.8743i	−0.250829	−	0.689147i	0.748823	−	0.662770i	$-0.230619\pi$
$350$	−18.6913	+	0.507431i	−0.999093	+	0.0271233i
$351$	−1.43954	+	2.71098i	−0.0768371	+	0.144701i
$352$	69.4115			3.69964
$353$	−31.1015	+	11.3200i	−1.65537	+	0.602504i	−0.989625	−	0.143677i	$-0.954107\pi$
$353$	−31.1015	+	11.3200i	−1.65537	+	0.602504i	−0.665742	+	0.746182i	$0.731885\pi$
$354$	−17.0555	−	10.9310i	−0.906491	−	0.580978i
$355$	5.56755	+	6.63515i	0.295495	+	0.352157i
$356$	5.43571	+	30.8274i	0.288092	+	1.63385i
$357$	−6.57790	−	19.2137i	−0.348140	−	1.01690i
$358$	−29.1590	−	24.4673i	−1.54110	−	1.29314i
$359$	−11.9268	−	6.88593i	−0.629472	−	0.363426i	0.151076	−	0.988522i	$-0.451726\pi$
$359$	−11.9268	−	6.88593i	−0.629472	−	0.363426i	−0.780547	+	0.625097i	$0.785060\pi$
$360$	23.5020	+	33.9569i	1.23867	+	1.78968i
$361$	13.5547	+	23.4774i	0.713404	+	1.23565i
$362$	2.64591	−	15.0057i	0.139066	−	0.788682i
$363$	−0.644837	−	5.00337i	−0.0338452	−	0.262609i
$364$	7.85734	+	2.62063i	0.411836	+	0.137358i
$365$	2.74613	−	7.54494i	0.143739	−	0.394920i
$366$	5.61647	+	43.5789i	0.293578	+	2.27791i
$367$	19.2168	+	3.38845i	1.00311	+	0.176875i	0.650996	−	0.759081i	$-0.274352\pi$
$367$	19.2168	+	3.38845i	1.00311	+	0.176875i	0.352115	+	0.935957i	$0.385463\pi$
$368$	22.2296	−	12.8343i	1.15880	−	0.669033i
$369$	−3.31457	+	2.29406i	−0.172549	+	0.119424i
$370$	13.5469	+	7.82131i	0.704271	+	0.406611i
$371$	6.15357	+	4.88512i	0.319477	+	0.253623i
$372$	16.9324	+	54.2174i	0.877902	+	2.81104i
$373$	−0.191635	−	1.08681i	−0.00992246	−	0.0562731i	0.979445	−	0.201714i	$-0.0646511\pi$
$373$	−0.191635	−	1.08681i	−0.00992246	−	0.0562731i	−0.989367	+	0.145441i	$0.953540\pi$
$374$	34.2119	−	28.7072i	1.76905	−	1.48441i
$375$	10.9905	−	17.1483i	0.567547	−	0.885535i
$376$	18.7381	+	51.4826i	0.966345	+	2.65501i
$377$	0.916687			0.0472118
$378$	−33.2659	−	16.5231i	−1.71102	−	0.849856i
$379$	1.32497			0.0680590			0.0340295	−	0.999421i	$-0.489166\pi$
$379$	1.32497			0.0680590			0.0340295	+	0.999421i	$0.489166\pi$
$380$	−19.0050	−	52.2158i	−0.974936	−	2.67861i
$381$	−9.01548	−	0.418248i	−0.461877	−	0.0214275i
$382$	−22.2619	+	18.6799i	−1.13902	+	0.955747i
$383$	−4.08890	−	23.1893i	−0.208933	−	1.18492i	−0.891130	−	0.453749i	$-0.850086\pi$
$383$	−4.08890	−	23.1893i	−0.208933	−	1.18492i	0.682197	−	0.731169i	$-0.261025\pi$
$384$	43.5065	+	9.76966i	2.22018	+	0.498556i
$385$	−11.9345	−	9.47439i	−0.608237	−	0.482859i
$386$	59.2676	+	34.2182i	3.01664	+	1.74166i
$387$	−12.9376	−	13.0794i	−0.657654	−	0.664864i
$388$	−85.6971	+	49.4772i	−4.35061	+	2.51183i
$389$	−11.4440	−	2.01789i	−0.580234	−	0.102311i	−0.124175	−	0.992260i	$-0.539628\pi$
$389$	−11.4440	−	2.01789i	−0.580234	−	0.102311i	−0.456059	+	0.889949i	$0.650739\pi$
$390$	−3.39344	+	2.58922i	−0.171834	+	0.131110i
$391$	2.88472	−	7.92571i	0.145887	−	0.400820i
$392$	−18.1306	+	59.7130i	−0.915735	+	3.01596i
$393$	−19.7799	−	8.25636i	−0.997766	−	0.416478i
$394$	6.35285	−	36.0288i	0.320052	−	1.81511i
$395$	−6.31167	−	10.9321i	−0.317575	−	0.550056i
$396$	5.49053	−	59.0478i	0.275910	−	2.96726i
$397$	−17.0000	−	9.81498i	−0.853208	−	0.492600i	0.00852412	−	0.999964i	$-0.497287\pi$
$397$	−17.0000	−	9.81498i	−0.853208	−	0.492600i	−0.861732	+	0.507364i	$0.830620\pi$
$398$	4.27758	+	3.58931i	0.214416	+	0.179916i
$399$	23.4486	+	20.4563i	1.17390	+	1.02410i
$400$	−6.12614	−	34.7431i	−0.306307	−	1.73715i
$401$	−6.30065	−	7.50882i	−0.314640	−	0.374973i	0.585427	−	0.810725i	$-0.300927\pi$
$401$	−6.30065	−	7.50882i	−0.314640	−	0.374973i	−0.900067	+	0.435752i	$0.856482\pi$
$402$	19.0354	−	9.84336i	0.949400	−	0.490942i
$403$	−3.43485	+	1.25018i	−0.171102	+	0.0622761i
$404$	17.9996			0.895511
$405$	12.1101	−	6.81680i	0.601754	−	0.338729i
$406$	0.301034	+	11.0887i	0.0149401	+	0.550321i
$407$	−4.78344	−	13.1424i	−0.237106	−	0.651444i
$408$	60.7843	−	31.4320i	3.00927	−	1.55612i
$409$	−6.29242	−	7.49902i	−0.311140	−	0.370803i	0.587700	−	0.809079i	$-0.300034\pi$
$409$	−6.29242	−	7.49902i	−0.311140	−	0.370803i	−0.898840	+	0.438276i	$0.855589\pi$
$410$	−5.52038	+	0.973393i	−0.272632	+	0.0480724i
$411$	13.8437	−	15.0253i	0.682858	−	0.741143i
$412$	−36.5373	+	43.5435i	−1.80006	+	2.14523i
$413$	10.0706	+	5.45535i	0.495541	+	0.268440i
$414$	−6.44305	−	14.0162i	−0.316659	−	0.688856i
$415$	4.08471	+	7.07492i	0.200510	+	0.347294i
$416$	−1.90889	+	10.8258i	−0.0935909	+	0.530780i
$417$	2.06768	−	4.95358i	0.101255	−	0.242578i
$418$	−23.4046	+	64.3036i	−1.14476	+	3.14519i
$419$	−14.3025	−	5.20569i	−0.698724	−	0.254315i	−0.0318580	−	0.999492i	$-0.510142\pi$
$419$	−14.3025	−	5.20569i	−0.698724	−	0.254315i	−0.666866	+	0.745178i	$0.732365\pi$
$420$	−23.5481	−	29.1846i	−1.14903	−	1.42406i
$421$	0.990993	−	5.62020i	0.0482981	−	0.273912i	−0.951089	−	0.308917i	$-0.900034\pi$
$421$	0.990993	−	5.62020i	0.0482981	−	0.273912i	0.999387	+	0.0350049i	$0.0111447\pi$
$422$	4.38193	−	2.52991i	0.213309	−	0.123154i
$423$	17.8339	−	4.67454i	0.867116	−	0.227284i
$424$	−13.2371	+	22.9273i	−0.642849	+	1.11345i
$425$	−8.88018	−	7.45135i	−0.430752	−	0.361444i
$426$	5.75145	−	25.6125i	0.278658	−	1.24093i
$427$	−4.97615	−	24.3388i	−0.240813	−	1.17784i
$428$	55.3100	+	65.9159i	2.67351	+	3.18617i
$429$	3.81224	+	0.176858i	0.184057	+	0.00853880i
$430$	−8.74992	−	24.0402i	−0.421958	−	1.15932i
$431$			19.8527i			0.956271i	0.878286	+	0.478135i	$0.158687\pi$
$431$			19.8527i			0.956271i	−0.878286	+	0.478135i	$0.841313\pi$
$432$	21.6195	−	66.6626i	1.04017	−	3.20731i
$433$			16.3842i			0.787374i	0.919244	+	0.393687i	$0.128801\pi$
$433$			16.3842i			0.787374i	−0.919244	+	0.393687i	$0.871199\pi$
$434$	−16.2508	−	41.1389i	−0.780062	−	1.97473i
$435$	−3.49418	−	2.23945i	−0.167533	−	0.107374i
$436$	−4.15499	+	3.48645i	−0.198988	+	0.166971i
$437$	2.24414	+	12.7271i	0.107352	+	0.608821i
$438$	−23.2273	+	7.25400i	−1.10984	+	0.346609i
$439$	−16.4078	+	19.5541i	−0.783104	+	0.933267i	−0.999069	−	0.0431343i	$-0.986266\pi$
$439$	−16.4078	+	19.5541i	−0.783104	+	0.933267i	0.215966	+	0.976401i	$0.430710\pi$
$440$	25.6725	−	44.4660i	1.22389	−	2.11984i
$441$	19.4430	+	7.93540i	0.925856	+	0.377876i
$442$	3.53648	+	6.12537i	0.168213	+	0.291354i
$443$	−22.6046	−	3.98580i	−1.07398	−	0.189371i	−0.391426	−	0.920210i	$-0.628018\pi$
$443$	−22.6046	−	3.98580i	−1.07398	−	0.189371i	−0.682550	+	0.730838i	$0.739129\pi$
$444$	−4.39950	−	34.1362i	−0.208791	−	1.62003i
$445$	8.57033	+	3.11935i	0.406273	+	0.147871i
$446$	−16.5562	−	6.02596i	−0.783958	−	0.285338i
$447$	−13.4046	+	1.72759i	−0.634017	+	0.0817124i
$448$	−60.9880	−	9.05479i	−2.88141	−	0.427799i
$449$	−12.1267	+	7.00134i	−0.572293	+	0.330414i	−0.758065	−	0.652179i	$-0.773855\pi$
$449$	−12.1267	+	7.00134i	−0.572293	+	0.330414i	0.185771	+	0.982593i	$0.440522\pi$
$450$	−21.1309	+	1.73269i	−0.996118	+	0.0816797i
$451$	4.34038	+	2.50592i	0.204380	+	0.117999i
$452$	53.7728	−	64.0840i	2.52926	−	3.01426i
$453$	33.2179	−	10.3741i	1.56071	−	0.487417i
$454$	13.8548	−	2.44298i	0.650238	−	0.114655i
$455$	1.80589	−	1.60082i	0.0846616	−	0.0750474i
$456$	−56.5776	+	88.2771i	−2.64949	+	4.13395i
$457$	−19.2648	+	7.01181i	−0.901169	+	0.327999i	−0.750721	−	0.660619i	$-0.770294\pi$
$457$	−19.2648	+	7.01181i	−0.901169	+	0.327999i	−0.150448	+	0.988618i	$0.548072\pi$
$458$	15.4321			0.721093
$459$	−8.63804	−	21.3461i	−0.403189	−	0.996352i
$460$		−	15.5742i		−	0.726151i
$461$	−4.74427	+	1.72677i	−0.220963	+	0.0804238i	−0.450129	−	0.892963i	$-0.648622\pi$
$461$	−4.74427	+	1.72677i	−0.220963	+	0.0804238i	0.229167	+	0.973387i	$0.426400\pi$
$462$	−0.887441	+	46.1726i	−0.0412875	+	2.14815i
$463$	20.9354	−	17.5669i	0.972950	−	0.816402i	−0.0100609	−	0.999949i	$-0.503203\pi$
$463$	20.9354	−	17.5669i	0.972950	−	0.816402i	0.983011	+	0.183547i	$0.0587581\pi$
$464$	−20.6114	+	3.63434i	−0.956858	+	0.168720i
$465$	16.1470	+	3.62591i	0.748799	+	0.168147i
$466$	43.3265	+	36.3552i	2.00706	+	1.68412i
$467$	−15.8795	+	27.5042i	−0.734818	+	1.27274i	0.219986	+	0.975503i	$0.429399\pi$
$467$	−15.8795	+	27.5042i	−0.734818	+	1.27274i	−0.954803	+	0.297238i	$0.903934\pi$
$468$	9.05845	+	2.48021i	0.418727	+	0.114648i
$469$	−10.3244	+	6.34048i	−0.476738	+	0.292776i
$470$	25.2482	+	4.45195i	1.16461	+	0.205353i
$471$	20.9781	+	27.4941i	0.966620	+	1.26686i
$472$	−13.1993	+	36.2649i	−0.607549	+	1.66923i
$473$	−7.82317	+	21.4940i	−0.359710	+	0.988294i
$474$	−14.7367	+	35.3050i	−0.676877	+	1.62161i
$475$	17.4923	+	3.08436i	0.802600	+	0.141520i
$476$	−52.9510	+	32.5185i	−2.42701	+	1.49048i
$477$	7.26976	+	5.14963i	0.332860	+	0.235785i
$478$	−24.9259	+	43.1730i	−1.14009	+	1.97469i
$479$	−13.9459	−	11.7020i	−0.637206	−	0.534679i	0.265953	−	0.963986i	$-0.414313\pi$
$479$	−13.9459	−	11.7020i	−0.637206	−	0.534679i	−0.903159	+	0.429307i	$0.858758\pi$
$480$	33.7236	−	36.6020i	1.53926	−	1.67065i
$481$	2.18132	−	0.384625i	0.0994595	−	0.0175374i
$482$	38.2293	−	32.0782i	1.74130	−	1.46112i
$483$	4.21483	+	7.63550i	0.191781	+	0.347427i
$484$	−14.5048	+	5.27933i	−0.659311	+	0.239970i
$485$			28.8311i			1.30915i
$486$	−38.6875	−	16.6462i	−1.75490	−	0.755085i
$487$	25.8036			1.16927			0.584637	−	0.811295i	$-0.301237\pi$
$487$	25.8036			1.16927			0.584637	+	0.811295i	$0.301237\pi$
$488$	78.6588	−	28.6295i	3.56072	−	1.29600i
$489$	1.69639	+	3.28054i	0.0767136	+	0.148351i
$490$	19.9572	+	21.3192i	0.901576	+	0.963102i
$491$	28.9536	−	5.10530i	1.30666	−	0.230399i	0.523394	−	0.852090i	$-0.324665\pi$
$491$	28.9536	−	5.10530i	1.30666	−	0.230399i	0.783262	+	0.621692i	$0.213554\pi$
$492$	9.07077	+	8.35743i	0.408942	+	0.376782i
$493$	−4.42052	+	5.26818i	−0.199090	+	0.237267i
$494$	−9.38553	−	5.41874i	−0.422275	−	0.243801i
$495$	−14.0993	−	9.98739i	−0.633715	−	0.448900i
$496$	72.2748	−	41.7279i	3.24524	−	1.87364i
$497$	−2.17957	+	14.6804i	−0.0977672	+	0.658505i
$498$	9.53708	−	22.8482i	0.427367	−	1.02385i
$499$	−16.0431	−	5.83922i	−0.718189	−	0.261399i	−0.0430323	−	0.999074i	$-0.513702\pi$
$499$	−16.0431	−	5.83922i	−0.718189	−	0.261399i	−0.675157	+	0.737674i	$0.735924\pi$
$500$	−58.5627	−	21.3151i	−2.61900	−	0.953240i
$501$	−14.5077	+	11.0694i	−0.648155	+	0.494546i
$502$	58.3535	+	10.2893i	2.60444	+	0.459233i
$503$	−9.54837	−	16.5383i	−0.425741	−	0.737405i	0.570748	−	0.821125i	$-0.306653\pi$
$503$	−9.54837	−	16.5383i	−0.425741	−	0.737405i	−0.996489	+	0.0837201i	$0.973320\pi$
$504$	−16.8275	+	68.7304i	−0.749555	+	3.06150i
$505$	2.62215	−	4.54170i	0.116684	−	0.202103i
$506$	−12.3284	+	14.6924i	−0.548065	+	0.653158i
$507$	4.80097	−	21.3798i	0.213219	−	0.949512i
$508$	4.79527	+	27.1953i	0.212756	+	1.20660i
$509$	−8.04301	+	6.74889i	−0.356500	+	0.299139i	−0.803394	−	0.595448i	$-0.796975\pi$
$509$	−8.04301	+	6.74889i	−0.356500	+	0.299139i	0.446894	+	0.894587i	$0.352530\pi$
$510$	1.48399	−	31.9880i	0.0657123	−	1.41645i
$511$	12.7955	−	5.05451i	0.566041	−	0.223598i
$512$		−	10.5097i		−	0.464467i
$513$	27.8160	+	21.7077i	1.22811	+	0.958416i
$514$			21.3163i			0.940220i
$515$	5.66431	+	15.5626i	0.249599	+	0.685768i
$516$	−30.3742	+	47.3923i	−1.33715	+	2.08633i
$517$	−14.7342	−	17.5595i	−0.648009	−	0.772267i
$518$	5.36892	+	26.2599i	0.235897	+	1.15379i
$519$	−4.57842	+	1.42986i	−0.200970	+	0.0627640i
$520$	6.22917	+	5.22690i	0.273167	+	0.229215i
$521$	−4.56525	+	7.90725i	−0.200007	+	0.346423i	−0.948530	−	0.316686i	$-0.897430\pi$
$521$	−4.56525	+	7.90725i	−0.200007	+	0.346423i	0.748523	+	0.663109i	$0.230763\pi$
$522$	1.02792	+	12.5359i	0.0449908	+	0.548682i
$523$	23.7892	−	13.7347i	1.04023	−	0.600575i	0.120329	−	0.992734i	$-0.461605\pi$
$523$	23.7892	−	13.7347i	1.04023	−	0.600575i	0.919898	+	0.392159i	$0.128272\pi$
$524$	−11.3883	+	64.5863i	−0.497500	+	2.82146i
$525$	11.8427	−	1.85428i	0.516857	−	0.0809276i
$526$	−72.9796	−	26.5624i	−3.18206	−	1.15818i
$527$	9.37906	−	25.7687i	0.408558	−	1.12250i
$528$	−86.4180	+	11.1376i	−3.76086	+	0.484701i
$529$	3.36492	−	19.0834i	0.146301	−	0.829715i
$530$	6.19437	+	10.7290i	0.269066	+	0.466036i
$531$	11.7399	+	5.55254i	0.509470	+	0.240960i
$532$	45.3507	−	83.7175i	1.96620	−	3.62961i
$533$	−0.510203	+	0.608036i	−0.0220993	+	0.0263370i
$534$	−8.23985	−	26.3840i	−0.356573	−	1.14175i
$535$	24.6896	−	4.35344i	1.06742	−	0.188216i
$536$	−26.2419	−	31.2738i	−1.13348	−	1.35082i
$537$	20.5448	+	13.1673i	0.886572	+	0.568212i
$538$	13.9681	+	38.3770i	0.602206	+	1.65455i
$539$	−1.41661	−	26.0713i	−0.0610175	−	1.12297i
$540$	−28.4695	−	31.5836i	−1.22513	−	1.35914i
$541$	19.0517			0.819099			0.409549	−	0.912288i	$-0.365686\pi$
$541$	19.0517			0.819099			0.409549	+	0.912288i	$0.365686\pi$
$542$	51.3624	−	18.6944i	2.20620	−	0.802992i
$543$	−0.452681	+	9.75770i	−0.0194264	+	0.418743i
$544$	−53.0106	−	63.1756i	−2.27281	−	2.70863i
$545$	0.274418	+	1.55630i	0.0117548	+	0.0666647i
$546$	−7.17696	−	1.40821i	−0.307145	−	0.0602656i
$547$	5.27460	+	4.42591i	0.225526	+	0.189238i	0.748548	−	0.663080i	$-0.230751\pi$
$547$	5.27460	+	4.42591i	0.225526	+	0.189238i	−0.523023	+	0.852319i	$0.675196\pi$
$548$	−54.1374	−	31.2562i	−2.31263	−	1.33520i
$549$	−7.14210	−	27.2480i	−0.304817	−	1.16292i
$550$	13.1803	+	22.8289i	0.562010	+	0.973429i
$551$	1.82980	−	10.3773i	0.0779520	−	0.442088i
$552$	−23.3635	+	17.8265i	−0.994416	+	0.758745i
$553$	6.84347	−	20.5185i	0.291014	−	0.872536i
$554$	15.2743	−	41.9659i	0.648945	−	1.78296i
$555$	−9.25427	−	3.86283i	−0.392822	−	0.163968i
$556$	−16.1746	−	2.85203i	−0.685958	−	0.120953i
$557$	−5.66374	+	3.26996i	−0.239980	+	0.138553i	−0.615168	−	0.788396i	$-0.710912\pi$
$557$	−5.66374	+	3.26996i	−0.239980	+	0.138553i	0.375187	+	0.926949i	$0.377578\pi$
$558$	−20.9482	−	45.5705i	−0.886808	−	1.92915i
$559$	−3.13719	−	1.81126i	−0.132689	−	0.0766079i
$560$	−34.2581	+	43.1535i	−1.44767	+	1.82357i
$561$	−19.4001	+	21.0560i	−0.819073	+	0.888984i
$562$	6.66942	+	37.8242i	0.281333	+	1.59552i
$563$	−25.1194	+	21.0777i	−1.05866	+	0.888320i	−0.993977	−	0.109586i	$-0.965047\pi$
$563$	−25.1194	+	21.0777i	−1.05866	+	0.888320i	−0.0646809	+	0.997906i	$0.520603\pi$
$564$	−25.9112	−	50.1079i	−1.09106	−	2.10992i
$565$	−8.33630	−	22.9038i	−0.350711	−	0.963570i
$566$	11.9259			0.501282
$567$	22.5050	+	7.77970i	0.945122	+	0.326717i
$568$	−50.0084			−2.09831
$569$	3.57085	+	9.81082i	0.149698	+	0.411291i	0.991763	−	0.128084i	$-0.0408828\pi$
$569$	3.57085	+	9.81082i	0.149698	+	0.411291i	−0.842066	+	0.539375i	$0.818661\pi$
$570$	22.5374	+	43.5836i	0.943989	+	1.82552i
$571$	−32.6363	+	27.3851i	−1.36579	+	1.14603i	−0.391640	+	0.920118i	$0.628092\pi$
$571$	−32.6363	+	27.3851i	−1.36579	+	1.14603i	−0.974147	+	0.225914i	$0.927463\pi$
$572$	−2.02770	−	11.4997i	−0.0847826	−	0.480826i
$573$	12.6238	−	13.7012i	0.527365	−	0.572378i
$574$	−7.52262	−	5.97196i	−0.313988	−	0.249265i
$575$	4.31137	+	2.48917i	0.179796	+	0.103806i
$576$	−69.6116	−	6.47281i	−2.90048	−	0.269700i
$577$	27.4313	−	15.8374i	1.14198	−	0.659321i	0.195059	−	0.980792i	$-0.437510\pi$
$577$	27.4313	−	15.8374i	1.14198	−	0.659321i	0.946920	+	0.321470i	$0.104177\pi$
$578$	−7.02365	−	1.23846i	−0.292145	−	0.0515131i
$579$	−40.4873	−	16.8998i	−1.68260	−	0.702334i
$580$	−4.34322	+	11.9329i	−0.180342	+	0.495487i
$581$	−4.42887	+	13.2789i	−0.183740	+	0.550902i
$582$	69.4659	−	53.0029i	2.87946	−	2.19704i
$583$	1.92343	−	10.9083i	0.0796603	−	0.451776i
$584$	23.1785	+	40.1464i	0.959135	+	1.66127i
$585$	1.94544	−	1.92434i	0.0804340	−	0.0795618i
$586$	−61.8550	−	35.7120i	−2.55521	−	1.47525i
$587$	−22.4457	−	18.8342i	−0.926432	−	0.777369i	0.0487411	−	0.998811i	$-0.484479\pi$
$587$	−22.4457	−	18.8342i	−0.926432	−	0.777369i	−0.975173	+	0.221442i	$0.928924\pi$
$588$	10.6560	−	63.3652i	0.439446	−	2.61314i
$589$	7.29633	+	41.3795i	0.300640	+	1.70501i
$590$	11.6084	+	13.8344i	0.477911	+	0.569552i
$591$	−1.08689	+	23.4283i	−0.0447088	+	0.963713i
$592$	−47.5212	+	17.2963i	−1.95311	+	0.710873i
$593$	−39.3635			−1.61647			−0.808234	−	0.588862i	$-0.799576\pi$
$593$	−39.3635			−1.61647			−0.808234	+	0.588862i	$0.799576\pi$
$594$	1.85625	+	52.3316i	0.0761627	+	2.14719i
$595$	0.491324	+	18.0980i	0.0201423	+	0.741946i
$596$	14.1439	+	38.8602i	0.579359	+	1.59177i
$597$	−3.01388	−	1.93162i	−0.123350	−	0.0790561i
$598$	−1.95248	−	2.32687i	−0.0798427	−	0.0951528i
$599$	19.7367	−	3.48012i	0.806422	−	0.142194i	0.244785	−	0.969578i	$-0.421283\pi$
$599$	19.7367	−	3.48012i	0.806422	−	0.142194i	0.561637	+	0.827384i	$0.310172\pi$
$600$	12.0406	+	38.5542i	0.491557	+	1.57397i
$601$	−4.00429	+	4.77213i	−0.163338	+	0.194659i	−0.841505	−	0.540249i	$-0.818330\pi$
$601$	−4.00429	+	4.77213i	−0.163338	+	0.194659i	0.678167	+	0.734908i	$0.262775\pi$
$602$	20.8795	−	38.5436i	0.850985	−	1.57092i
$603$	−11.2964	+	7.81842i	−0.460026	+	0.318391i
$604$	−53.2400	−	92.2143i	−2.16630	−	3.75215i
$605$	−0.780951	+	4.42899i	−0.0317502	+	0.180064i
$606$	−15.7634	+	2.03159i	−0.640342	+	0.0825276i
$607$	−8.90150	+	24.4567i	−0.361301	+	0.992665i	0.617269	+	0.786752i	$0.288239\pi$
$607$	−8.90150	+	24.4567i	−0.361301	+	0.992665i	−0.978570	+	0.205914i	$0.933983\pi$
$608$	118.743	+	43.2189i	4.81566	+	1.75276i
$609$	−1.10006	−	7.02569i	−0.0445765	−	0.284695i
$610$	6.80201	−	38.5761i	0.275405	−	1.56190i
$611$	3.14389	−	1.81513i	0.127188	−	0.0734322i
$612$	−57.9361	+	40.0984i	−2.34193	+	1.62088i
$613$	−13.5782	+	23.5181i	−0.548417	+	0.949886i	0.449966	+	0.893046i	$0.351436\pi$
$613$	−13.5782	+	23.5181i	−0.548417	+	0.949886i	−0.998383	+	0.0568405i	$0.981897\pi$
$614$	−36.6618	−	30.7629i	−1.47955	−	1.24149i
$615$	3.43019	−	1.07126i	0.138319	−	0.0431976i
$616$	86.1947	−	17.6228i	3.47288	−	0.710043i
$617$	−8.14874	−	9.71129i	−0.328056	−	0.390962i	0.576655	−	0.816988i	$-0.304358\pi$
$617$	−8.14874	−	9.71129i	−0.328056	−	0.390962i	−0.904711	+	0.426026i	$0.859913\pi$
$618$	27.0833	−	42.2577i	1.08945	−	1.69985i
$619$	9.37859	+	25.7675i	0.376957	+	1.03568i	0.972611	+	0.232440i	$0.0746709\pi$
$619$	9.37859	+	25.7675i	0.376957	+	1.03568i	−0.595654	+	0.803241i	$0.703107\pi$
$620$		−	50.6362i		−	2.03360i
$621$	5.24515	+	8.38374i	0.210481	+	0.336428i
$622$			63.7314i			2.55540i
$623$	5.74144	+	14.5345i	0.230026	+	0.582313i
$624$	0.639497	−	13.7846i	0.0256004	−	0.551824i
$625$	−3.89065	+	3.26464i	−0.155626	+	0.130586i
$626$	−6.25313	−	35.4632i	−0.249925	−	1.41740i
$627$	9.61173	−	42.8032i	0.383855	−	1.70940i
$628$	68.0175	−	81.0601i	2.71419	−	3.23465i
$629$	−8.30850	+	14.3907i	−0.331281	+	0.573796i
$630$	23.9166	+	22.9009i	0.952859	+	0.912395i
$631$	6.73167	+	11.6596i	0.267983	+	0.464161i	0.968341	−	0.249631i	$-0.0803094\pi$
$631$	6.73167	+	11.6596i	0.267983	+	0.464161i	−0.700358	+	0.713792i	$0.746976\pi$
$632$	71.7748	+	12.6558i	2.85505	+	0.503422i
$633$	−2.57879	+	1.96763i	−0.102498	+	0.0782064i
$634$	52.1436	+	18.9787i	2.07089	+	0.753741i
$635$	7.56058	+	2.75183i	0.300032	+	0.109203i
$636$	10.5002	−	25.1555i	0.416359	−	0.997481i
$637$	4.10519	+	0.496044i	0.162653	+	0.0196540i
$638$	13.5433	−	7.81923i	0.536184	−	0.309566i
$639$	−1.55807	+	16.7562i	−0.0616361	+	0.662864i
$640$	−34.4256	−	19.8756i	−1.36079	−	0.785652i
$641$	−2.24686	+	2.67770i	−0.0887456	+	0.105763i	−0.808590	−	0.588373i	$-0.799769\pi$
$641$	−2.24686	+	2.67770i	−0.0887456	+	0.105763i	0.719844	+	0.694136i	$0.244213\pi$
$642$	−55.8784	−	51.4840i	−2.20534	−	2.03191i
$643$	−13.5707	+	2.39288i	−0.535176	+	0.0943660i	−0.434703	−	0.900574i	$-0.643147\pi$
$643$	−13.5707	+	2.39288i	−0.535176	+	0.0943660i	−0.100473	+	0.994940i	$0.532036\pi$
$644$	19.9695	−	17.7018i	0.786909	−	0.697548i
$645$	7.53331	+	14.5682i	0.296624	+	0.573621i
$646$	76.4011	−	27.8077i	3.00596	−	1.09408i
$647$	33.5335			1.31834			0.659170	−	0.751994i	$-0.270908\pi$
$647$	33.5335			1.31834			0.659170	+	0.751994i	$0.270908\pi$
$648$	−14.7933	+	78.8592i	−0.581135	+	3.09788i
$649$		−	16.1467i		−	0.633815i
$650$	−3.92301	+	1.42786i	−0.153873	+	0.0560052i
$651$	13.7036	+	24.8252i	0.537087	+	0.972976i
$652$	8.65653	−	7.26369i	0.339016	−	0.284468i
$653$	8.49895	−	1.49859i	0.332589	−	0.0586445i	−0.00485985	−	0.999988i	$-0.501547\pi$
$653$	8.49895	−	1.49859i	0.332589	−	0.0586445i	0.337449	+	0.941344i	$0.390436\pi$
$654$	3.24528	−	3.52228i	0.126900	−	0.137732i
$655$	14.6376	+	12.2824i	0.571937	+	0.479912i
$656$	9.06107	−	15.6942i	0.353775	−	0.612757i
$657$	14.1739	−	6.51557i	0.552977	−	0.254196i
$658$	22.9890	+	37.4339i	0.896206	+	1.45932i
$659$	−45.2808	−	7.98422i	−1.76389	−	0.311021i	−0.804677	−	0.593713i	$-0.797662\pi$
$659$	−45.2808	−	7.98422i	−1.76389	−	0.311021i	−0.959211	+	0.282691i	$0.908773\pi$
$660$	−20.3645	+	48.7876i	−0.792685	+	1.89905i
$661$	−11.1294	+	30.5776i	−0.432882	+	1.18933i	0.511154	+	0.859489i	$0.329218\pi$
$661$	−11.1294	+	30.5776i	−0.432882	+	1.18933i	−0.944036	+	0.329843i	$0.893004\pi$
$662$	−1.05170	+	2.88951i	−0.0408754	+	0.112304i
$663$	−2.75050	−	3.60482i	−0.106820	−	0.140000i
$664$	−46.4503	−	8.19044i	−1.80262	−	0.317851i
$665$	−14.5172	−	23.6389i	−0.562953	−	0.916677i
$666$	7.70584	+	29.3987i	0.298595	+	1.13918i
$667$	1.47670	−	2.55772i	0.0571782	−	0.0990355i
$668$	42.7727	+	35.8906i	1.65493	+	1.38865i
$669$	11.0205	+	2.47472i	0.426077	+	0.0956783i
$670$	−18.8141	+	3.31744i	−0.726853	+	0.128164i
$671$	−26.8287	+	22.5120i	−1.03571	+	0.869065i
$672$	85.2622	+	1.63875i	3.28906	+	0.0632160i
$673$	5.75164	−	2.09342i	0.221709	−	0.0806956i	−0.228777	−	0.973479i	$-0.573473\pi$
$673$	5.75164	−	2.09342i	0.221709	−	0.0806956i	0.450487	+	0.892783i	$0.351251\pi$
$674$		−	10.2692i		−	0.395555i
$675$	13.2934	−	2.83323i	0.511662	−	0.109051i
$676$	−67.0462			−2.57870
$677$	3.75793	−	1.36778i	0.144429	−	0.0525679i	−0.268794	−	0.963198i	$-0.586625\pi$
$677$	3.75793	−	1.36778i	0.144429	−	0.0525679i	0.413223	+	0.910630i	$0.364403\pi$
$678$	−39.8592	+	62.1917i	−1.53078	+	2.38846i
$679$	−36.9678	+	32.7697i	−1.41869	+	1.25759i
$680$	−60.0777	+	10.5933i	−2.30387	+	0.406235i
$681$	−8.60893	+	2.68861i	−0.329895	+	0.103028i
$682$	−40.0832	+	47.7693i	−1.53487	+	1.82918i
$683$	18.1293	+	10.4670i	0.693699	+	0.400507i	0.804996	−	0.593280i	$-0.202167\pi$
$683$	18.1293	+	10.4670i	0.693699	+	0.400507i	−0.111297	+	0.993787i	$0.535501\pi$
$684$	46.1587	−	97.5949i	1.76492	−	3.73164i
$685$	−15.7733	+	9.10674i	−0.602668	+	0.347951i
$686$	−4.65225	+	49.8211i	−0.177624	+	1.90218i
$687$	−9.81197	+	1.26457i	−0.374350	+	0.0482464i
$688$	77.7194	+	28.2876i	2.96303	+	1.07845i
$689$	1.64843	+	0.599979i	0.0628002	+	0.0228574i
$690$	1.75784	+	13.6393i	0.0669200	+	0.519240i
$691$	5.21218	+	0.919049i	0.198281	+	0.0349623i	0.271906	−	0.962324i	$-0.412346\pi$
$691$	5.21218	+	0.919049i	0.198281	+	0.0349623i	−0.0736256	+	0.997286i	$0.523457\pi$
$692$	7.33807	+	12.7099i	0.278952	+	0.483158i
$693$	−3.21934	−	29.4301i	−0.122293	−	1.11796i
$694$	7.52941	−	13.0413i	0.285812	−	0.495042i
$695$	−3.07593	+	3.66576i	−0.116677	+	0.139050i
$696$	22.8723	−	7.14313i	0.866973	−	0.270760i
$697$	−1.03402	−	5.86424i	−0.0391665	−	0.222124i
$698$	28.3559	−	23.7935i	1.07329	−	0.900596i
$699$	−30.5268	−	19.5649i	−1.15463	−	0.740013i
$700$	−13.4751	−	34.1122i	−0.509309	−	1.28932i
$701$			11.0468i			0.417232i	0.977998	+	0.208616i	$0.0668959\pi$
$701$			11.0468i			0.417232i	−0.977998	+	0.208616i	$0.933104\pi$
$702$	−8.21300	−	1.14966i	−0.309980	−	0.0433912i
$703$		−	25.4612i		−	0.960288i
$704$	29.7294	+	81.6808i	1.12047	+	3.07846i
$705$	−16.4181	−	0.761671i	−0.618341	−	0.0286862i
$706$	−57.4797	−	68.5016i	−2.16328	−	2.57809i
$707$	8.80381	−	1.79997i	0.331101	−	0.0676949i
$708$	8.70625	−	38.7709i	0.327201	−	1.45710i
$709$	−32.6424	−	27.3902i	−1.22591	−	1.02866i	−0.998494	−	0.0548636i	$-0.982528\pi$
$709$	−32.6424	−	27.3902i	−1.22591	−	1.02866i	−0.227417	−	0.973798i	$-0.573028\pi$
$710$	−11.7009	+	20.2665i	−0.439126	+	0.760588i
$711$	6.47678	−	23.6551i	0.242898	−	0.887135i
$712$	−45.6025	+	26.3286i	−1.70903	+	0.986706i
$713$	−2.04501	+	11.5978i	−0.0765861	+	0.434341i
$714$	42.7022	−	34.4550i	1.59809	−	1.28945i
$715$	−3.19703	−	1.16362i	−0.119562	−	0.0435170i
$716$	25.5368	−	70.1619i	0.954356	−	2.62207i
$717$	12.3105	−	29.4927i	0.459746	−	1.10142i
$718$	6.46122	−	36.6434i	0.241130	−	1.36752i
$719$	21.3837	+	37.0377i	0.797479	+	1.38127i	0.921253	+	0.388963i	$0.127167\pi$
$719$	21.3837	+	37.0377i	0.797479	+	1.38127i	−0.123775	+	0.992310i	$0.539500\pi$
$720$	−36.1131	+	50.9811i	−1.34586	+	1.89995i
$721$	−13.5165	+	24.9514i	−0.503380	+	0.929239i
$722$	−47.0802	+	56.1080i	−1.75214	+	2.08812i
$723$	−21.6782	+	23.5285i	−0.806221	+	0.875036i
$724$	29.4342	−	5.19005i	1.09391	−	0.192887i
$725$	−2.60919	−	3.10951i	−0.0969029	−	0.115484i
$726$	12.1069	−	6.26059i	0.449331	−	0.232352i
$727$	−16.5881	−	45.5755i	−0.615219	−	1.69030i	−0.718393	−	0.695638i	$-0.755122\pi$
$727$	−16.5881	−	45.5755i	−0.615219	−	1.69030i	0.103173	−	0.994663i	$-0.467100\pi$
$728$	0.378119	+	13.9281i	0.0140140	+	0.516209i
$729$	25.9622	+	7.41369i	0.961564	+	0.274581i
$730$	21.6931			0.802897
$731$	25.5376	−	9.29494i	0.944544	−	0.343786i
$732$	−76.5585	+	39.5890i	−2.82968	+	1.46325i
$733$	33.7990	+	40.2800i	1.24839	+	1.48778i	0.807100	+	0.590414i	$0.201036\pi$
$733$	33.7990	+	40.2800i	1.24839	+	1.48778i	0.441293	+	0.897363i	$0.354520\pi$
$734$	9.15486	+	51.9198i	0.337912	+	1.91639i
$735$	−14.4361	−	11.9197i	−0.532485	−	0.439665i
$736$	27.1310	+	22.7656i	1.00006	+	0.839152i
$737$	14.7925	+	8.54046i	0.544889	+	0.314592i
$738$	−8.88715	−	6.29533i	−0.327140	−	0.231734i
$739$	−18.2526	−	31.6144i	−0.671431	−	1.16295i	−0.977498	−	0.210943i	$-0.932347\pi$
$739$	−18.2526	−	31.6144i	−0.671431	−	1.16295i	0.306067	−	0.952010i	$-0.400987\pi$
$740$	−5.32815	+	30.2174i	−0.195867	+	1.11082i
$741$	6.41152	+	2.67624i	0.235533	+	0.0983140i
$742$	−6.71628	+	20.1372i	−0.246562	+	0.739258i
$743$	9.45684	−	25.9825i	0.346938	−	0.953204i	−0.636391	−	0.771367i	$-0.719573\pi$
$743$	9.45684	−	25.9825i	0.346938	−	0.953204i	0.983329	−	0.181837i	$-0.0582044\pi$
$744$	−75.9613	+	57.9589i	−2.78488	+	2.12488i
$745$	11.8658	+	2.09226i	0.434729	+	0.0766544i
$746$	2.58217	−	1.49082i	0.0945401	−	0.0545827i
$747$	−4.19156	+	15.3088i	−0.153361	+	0.560119i
$748$	75.8665	+	43.8016i	2.77395	+	1.60154i
$749$	33.6445	+	26.7093i	1.22934	+	0.975935i
$750$	53.6929	+	12.0571i	1.96059	+	0.440262i
$751$	−4.50550	−	25.5520i	−0.164408	−	0.932404i	−0.949673	−	0.313244i	$-0.898584\pi$
$751$	−4.50550	−	25.5520i	−0.164408	−	0.932404i	0.785265	−	0.619160i	$-0.212527\pi$
$752$	−63.4929	+	53.2769i	−2.31535	+	1.94281i
$753$	−37.9453	−	1.76037i	−1.38280	−	0.0641513i
$754$	0.847079	+	2.32733i	0.0308488	+	0.0847564i
$755$	−31.0237			−1.12907
$756$	8.13841	−	72.4023i	0.295991	−	2.63324i
$757$	20.1349			0.731816			0.365908	−	0.930651i	$-0.380758\pi$
$757$	20.1349			0.731816			0.365908	+	0.930651i	$0.380758\pi$
$758$	1.22436	+	3.36389i	0.0444707	+	0.122182i
$759$	6.63465	−	10.3519i	0.240823	−	0.375752i
$760$	71.6048	−	60.0836i	2.59738	−	2.17946i
$761$	−7.31335	−	41.4761i	−0.265109	−	1.50351i	−0.768725	−	0.639579i	$-0.779109\pi$
$761$	−7.31335	−	41.4761i	−0.265109	−	1.50351i	0.503616	−	0.863928i	$-0.332003\pi$
$762$	−7.26903	−	23.2754i	−0.263329	−	0.843181i
$763$	−1.68361	+	2.12077i	−0.0609508	+	0.0767771i
$764$	−49.3667	−	28.5019i	−1.78603	−	1.03116i
$765$	1.67769	+	20.4601i	0.0606569	+	0.739737i
$766$	55.0957	−	31.8095i	1.99069	−	1.14933i
$767$	2.51834	+	0.444052i	0.0909321	+	0.0160338i
$768$	5.08037	+	39.4192i	0.183322	+	1.42242i
$769$	−1.83007	+	5.02807i	−0.0659939	+	0.181317i	−0.968306	−	0.249766i	$-0.919646\pi$
$769$	−1.83007	+	5.02807i	−0.0659939	+	0.181317i	0.902312	+	0.431083i	$0.141868\pi$
$770$	13.0258	−	39.0548i	0.469418	−	1.40744i
$771$	−1.74675	−	13.5532i	−0.0629076	−	0.488108i
$772$	−23.3106	+	132.201i	−0.838967	+	4.75802i
$773$	−1.71685	−	2.97367i	−0.0617508	−	0.106956i	0.833497	−	0.552524i	$-0.186335\pi$
$773$	−1.71685	−	2.97367i	−0.0617508	−	0.106956i	−0.895248	+	0.445568i	$0.853002\pi$
$774$	21.2515	−	44.9328i	0.763869	−	1.61508i
$775$	14.0175	+	8.09300i	0.503523	+	0.290709i
$776$	−127.515	−	106.998i	−4.57752	−	3.84100i
$777$	−5.56550	−	16.2565i	−0.199661	−	0.583199i
$778$	−5.45190	−	30.9193i	−0.195460	−	1.10851i
$779$	5.86482	+	6.98942i	0.210129	+	0.250422i
$780$	−7.04916	−	4.51787i	−0.252401	−	0.161766i
$781$	19.6613	−	7.15614i	0.703538	−	0.256067i
$782$	22.7879			0.814892
$783$	−1.68082	−	7.88631i	−0.0600675	−	0.281834i
$784$	−94.2702	+	5.12226i	−3.36679	+	0.182938i
$785$	−10.5446	−	28.9711i	−0.376354	−	1.03402i
$786$	2.68368	−	57.8477i	0.0957238	−	2.06336i
$787$	6.66979	+	7.94875i	0.237752	+	0.283342i	0.871706	−	0.490028i	$-0.163014\pi$
$787$	6.66979	+	7.94875i	0.237752	+	0.283342i	−0.633954	+	0.773371i	$0.718569\pi$
$788$	70.6719	−	12.4614i	2.51758	−	0.443918i
$789$	48.5783	+	10.9086i	1.72943	+	0.388355i
$790$	21.9227	−	26.1264i	0.779973	−	0.929536i
$791$	19.8925	−	36.7216i	0.707297	−	1.30567i
$792$	96.4976	−	25.2934i	3.42889	−	0.898763i
$793$	−2.77329	−	4.80347i	−0.0984822	−	0.170576i
$794$	9.20960	−	52.2302i	0.326837	−	1.85358i
$795$	−4.81766	−	6.31406i	−0.170865	−	0.223937i
$796$	−3.74621	+	10.2926i	−0.132781	+	0.364812i
$797$	26.1222	+	9.50770i	0.925296	+	0.336780i	0.760343	−	0.649522i	$-0.225031\pi$
$797$	26.1222	+	9.50770i	0.925296	+	0.336780i	0.164952	+	0.986302i	$0.447253\pi$
$798$	−30.2674	+	78.4354i	−1.07146	+	2.77658i
$799$	−4.72926	+	26.8209i	−0.167309	+	0.948857i
$800$	42.1558	−	24.3387i	1.49043	−	0.860503i
$801$	7.40106	+	16.1002i	0.261504	+	0.568872i
$802$	13.2416	−	22.9351i	0.467576	−	0.809865i
$803$	−14.8578	−	12.4672i	−0.524320	−	0.439957i
$804$	30.9143	+	28.4831i	1.09026	+	1.00452i
$805$	−1.55743	−	7.61755i	−0.0548924	−	0.268483i
$806$	−6.34806	−	7.56532i	−0.223601	−	0.266477i
$807$	−12.0259	−	23.2561i	−0.423332	−	0.818654i
$808$	10.3558	+	28.4525i	0.364317	+	1.00095i
$809$			46.1025i			1.62088i	0.585823	+	0.810439i	$0.300771\pi$
$809$			46.1025i			1.62088i	−0.585823	+	0.810439i	$0.699229\pi$
$810$	28.4973	+	24.4465i	1.00129	+	0.858962i
$811$			15.6581i			0.549830i	0.961468	+	0.274915i	$0.0886498\pi$
$811$			15.6581i			0.549830i	−0.961468	+	0.274915i	$0.911350\pi$
$812$	−20.2371	+	7.99409i	−0.710183	+	0.280538i
$813$	−31.1252	+	16.0951i	−1.09161	+	0.564479i
$814$	28.9464	−	24.2889i	1.01457	−	0.851325i
$815$	−0.571724	−	3.24241i	−0.0200266	−	0.113577i
$816$	76.1357	+	70.1482i	2.66528	+	2.45568i
$817$	−26.7664	+	31.8989i	−0.936436	+	1.11600i
$818$	13.2243	−	22.9051i	0.462376	−	0.800858i
$819$	4.67863	+	0.307249i	0.163484	+	0.0107362i
$820$	−5.49774	−	9.52237i	−0.191989	−	0.332536i
$821$	−1.44801	−	0.255324i	−0.0505360	−	0.00891087i	0.148323	−	0.988939i	$-0.452612\pi$
$821$	−1.44801	−	0.255324i	−0.0505360	−	0.00891087i	−0.198859	+	0.980028i	$0.563724\pi$
$822$	50.9394	+	21.2627i	1.77672	+	0.741620i
$823$	−36.3320	−	13.2238i	−1.26645	−	0.460952i	−0.380524	−	0.924771i	$-0.624257\pi$
$823$	−36.3320	−	13.2238i	−1.26645	−	0.460952i	−0.885930	+	0.463819i	$0.846479\pi$
$824$	−89.8518	−	32.7034i	−3.13014	−	1.13928i
$825$	−10.2510	−	13.4350i	−0.356893	−	0.467746i
$826$	−4.54444	+	30.6088i	−0.158121	+	1.06502i
$827$	−20.8625	+	12.0449i	−0.725459	+	0.418844i	−0.816759	−	0.576980i	$-0.804231\pi$
$827$	−20.8625	+	12.0449i	−0.725459	+	0.418844i	0.0912997	+	0.995823i	$0.470898\pi$
$828$	21.5126	−	21.2793i	0.747615	−	0.739508i
$829$	−36.2761	−	20.9440i	−1.25992	−	0.727416i	−0.286863	−	0.957972i	$-0.592612\pi$
$829$	−36.2761	−	20.9440i	−1.25992	−	0.727416i	−0.973059	+	0.230556i	$0.925946\pi$
$830$	−14.1876	+	16.9082i	−0.492460	+	0.586891i
$831$	−6.27282	+	27.9343i	−0.217602	+	0.969030i
$832$	−13.5570	+	2.39047i	−0.470005	+	0.0828746i
$833$	−22.6471	+	21.2003i	−0.784676	+	0.734548i
$834$	14.4871	+	0.672087i	0.501646	+	0.0232725i
$835$	15.2871	−	5.56404i	0.529031	−	0.192552i
$836$	−134.229			−4.64241
$837$	17.0535	+	27.2579i	0.589454	+	0.942172i
$838$		−	41.1224i		−	1.42055i
$839$	15.9125	−	5.79166i	0.549359	−	0.199950i	−0.0524025	−	0.998626i	$-0.516688\pi$
$839$	15.9125	−	5.79166i	0.549359	−	0.199950i	0.601762	+	0.798676i	$0.294466\pi$
$840$	32.5848	−	54.0142i	1.12428	−	1.86367i
$841$	20.3706	−	17.0929i	0.702433	−	0.589412i
$842$	15.1846	−	2.67745i	0.523296	−	0.0922711i
$843$	−7.34001	−	23.5027i	−0.252803	−	0.809477i
$844$	7.60301	+	6.37968i	0.261706	+	0.219598i
$845$	−9.76721	+	16.9173i	−0.336002	+	0.581973i
$846$	28.3477	+	40.9581i	0.974613	+	1.40817i
$847$	−6.56657	+	4.03268i	−0.225630	+	0.138565i
$848$	−39.4430	−	6.95487i	−1.35448	−	0.238831i
$849$	−7.58268	+	0.977259i	−0.260237	+	0.0335394i
$850$	10.7120	−	29.4310i	0.367419	−	1.00947i
$851$	2.44074	−	6.70587i	0.0836674	−	0.229874i
$852$	51.0686	−	6.58175i	1.74958	−	0.225487i
$853$	25.5559	+	4.50619i	0.875017	+	0.154289i	0.593080	−	0.805144i	$-0.297912\pi$
$853$	25.5559	+	4.50619i	0.875017	+	0.154289i	0.281937	+	0.959433i	$0.409023\pi$
$854$	57.1942	−	35.1243i	1.95714	−	1.20193i
$855$	−17.9011	−	25.8644i	−0.612205	−	0.884544i
$856$	−72.3733	+	125.354i	−2.47367	+	4.28452i
$857$	−10.0030	−	8.39351i	−0.341696	−	0.286717i	0.455750	−	0.890108i	$-0.349371\pi$
$857$	−10.0030	−	8.39351i	−0.341696	−	0.286717i	−0.797445	+	0.603391i	$0.793816\pi$
$858$	3.07375	+	9.84214i	0.104936	+	0.336005i
$859$	−10.8516	+	1.91344i	−0.370253	+	0.0652856i	−0.355679	−	0.934608i	$-0.615750\pi$
$859$	−10.8516	+	1.91344i	−0.370253	+	0.0652856i	−0.0145741	+	0.999894i	$0.504639\pi$
$860$	38.4417	−	32.2564i	1.31085	−	1.09993i
$861$	5.27238	+	3.18064i	0.179682	+	0.108396i
$862$	−50.4030	+	18.3452i	−1.71673	+	0.624840i
$863$		−	4.80238i		−	0.163475i	−0.996654	−	0.0817375i	$-0.973953\pi$
$863$		−	4.80238i		−	0.163475i	0.996654	−	0.0817375i	$-0.0260469\pi$
$864$	96.6354	−	3.42774i	3.28760	−	0.116614i
$865$	4.27601			0.145389
$866$	−41.5970	+	15.1401i	−1.41352	+	0.514481i
$867$	4.56724	+	0.211884i	0.155112	+	0.00719597i
$868$	64.9266	−	57.5536i	2.20375	−	1.95350i
$869$	−30.0301	+	5.29511i	−1.01870	+	0.179624i
$870$	2.45678	−	10.9406i	0.0832927	−	0.370921i
$871$	−1.73883	+	2.07226i	−0.0589181	+	0.0702158i
$872$	−7.90167	−	4.56203i	−0.267584	−	0.154490i
$873$	−39.8243	+	39.3925i	−1.34785	+	1.33323i
$874$	−30.2385	+	17.4582i	−1.02283	+	0.590534i
$875$	−30.7753	−	4.56916i	−1.04040	−	0.154466i
$876$	−28.9537	−	37.9470i	−0.978256	−	1.28211i
$877$	−2.77444	−	1.00981i	−0.0936861	−	0.0340989i	0.294752	−	0.955574i	$-0.404763\pi$
$877$	−2.77444	−	1.00981i	−0.0936861	−	0.0340989i	−0.388438	+	0.921475i	$0.626985\pi$
$878$	−64.8069	−	23.5878i	−2.18713	−	0.796049i
$879$	42.2549	+	17.6376i	1.42522	+	0.594902i
$880$	76.4973	+	13.4885i	2.57872	+	0.454698i
$881$	−12.1716	−	21.0818i	−0.410071	−	0.710264i	0.584826	−	0.811159i	$-0.301163\pi$
$881$	−12.1716	−	21.0818i	−0.410071	−	0.710264i	−0.994897	+	0.100895i	$0.967829\pi$
$882$	−2.18019	+	56.6956i	−0.0734110	+	1.90904i
$883$	−5.42908	+	9.40345i	−0.182703	+	0.316451i	−0.942800	−	0.333358i	$-0.891818\pi$
$883$	−5.42908	+	9.40345i	−0.182703	+	0.316451i	0.760097	+	0.649810i	$0.225151\pi$
$884$	−8.91796	+	10.6280i	−0.299944	+	0.357459i
$885$	−8.51448	−	7.84489i	−0.286211	−	0.263703i
$886$	−10.7688	−	61.0728i	−0.361784	−	2.05178i
$887$	24.6997	−	20.7255i	0.829336	−	0.695896i	−0.125802	−	0.992055i	$-0.540150\pi$
$887$	24.6997	−	20.7255i	0.829336	−	0.695896i	0.955138	+	0.296160i	$0.0957060\pi$
$888$	51.4290	−	26.5943i	1.72584	−	0.892447i
$889$	5.06498	+	12.8221i	0.169874	+	0.430038i
$890$			24.6413i			0.825977i
$891$	−5.46852	−	33.1212i	−0.183202	−	1.10960i
$892$		−	34.5598i		−	1.15715i
$893$	−14.2725	−	39.2135i	−0.477612	−	1.31223i
$894$	−16.7729	−	32.4359i	−0.560968	−	1.08482i
$895$	−13.9833	−	16.6646i	−0.467409	−	0.557037i
$896$	−13.6436	−	66.7318i	−0.455799	−	2.22935i
$897$	1.43209	+	1.31947i	0.0478162	+	0.0440558i
$898$	−28.9812	−	24.3181i	−0.967115	−	0.811506i
$899$	4.80118	−	8.31589i	0.160128	−	0.277351i
$900$	−17.3701	−	37.7868i	−0.579005	−	1.25956i
$901$	−11.3973	+	6.58021i	−0.379698	+	0.219219i
$902$	−2.35136	+	13.3352i	−0.0782916	+	0.444014i
$903$	−10.1171	+	26.2176i	−0.336677	+	0.872468i
$904$	132.237	+	48.1304i	4.39814	+	1.60079i
$905$	2.97837	−	8.18301i	0.0990045	−	0.272013i
$906$	57.0338	+	74.7488i	1.89482	+	2.48336i
$907$	8.73599	−	49.5443i	0.290074	−	1.64509i	−0.396503	−	0.918033i	$-0.629776\pi$
$907$	8.73599	−	49.5443i	0.290074	−	1.64509i	0.686577	−	0.727057i	$-0.259113\pi$
$908$	13.7980	+	23.8988i	0.457902	+	0.793109i
$909$	9.85613	−	2.58344i	0.326907	−	0.0856872i
$910$	5.73300	+	3.10563i	0.190047	+	0.102951i
$911$	19.0150	−	22.6612i	0.629995	−	0.750799i	−0.352759	−	0.935714i	$-0.614756\pi$
$911$	19.0150	−	22.6612i	0.629995	−	0.750799i	0.982755	+	0.184915i	$0.0592009\pi$
$912$	−154.771	−	34.7547i	−5.12498	−	1.15084i
$913$	19.4345	−	3.42682i	0.643187	−	0.113411i
$914$	−35.6039	−	42.4311i	−1.17767	−	1.40349i
$915$	−1.16374	+	25.0847i	−0.0384720	+	0.829276i
$916$	10.3531	+	28.4450i	0.342078	+	0.939850i
$917$	0.888520	+	32.7288i	0.0293415	+	1.08080i
$918$	46.2125	−	41.6559i	1.52524	−	1.37485i
$919$	38.0493			1.25513			0.627566	−	0.778564i	$-0.284051\pi$
$919$	38.0493			1.25513			0.627566	+	0.778564i	$0.284051\pi$
$920$	24.6186	−	8.96045i	0.811653	−	0.295417i
$921$	25.8311	+	16.5554i	0.851162	+	0.545518i
$922$	−8.76803	−	10.4493i	−0.288760	−	0.344131i
$923$	0.575408	+	3.26330i	0.0189398	+	0.107413i
$924$	−85.7027	+	29.3408i	−2.81941	+	0.965240i
$925$	−7.51343	−	6.30452i	−0.247040	−	0.207291i
$926$	63.9453	+	36.9189i	2.10137	+	1.21323i
$927$	−13.7573	+	29.0875i	−0.451848	+	0.955359i
$928$	−14.4390	−	25.0090i	−0.473982	−	0.820961i
$929$	6.90932	−	39.1847i	0.226688	−	1.28561i	−0.632745	−	0.774360i	$-0.718072\pi$
$929$	6.90932	−	39.1847i	0.226688	−	1.28561i	0.859433	−	0.511249i	$-0.170817\pi$
$930$	5.71525	+	44.3454i	0.187411	+	1.45414i
$931$	13.8098	−	45.4824i	0.452598	−	1.49063i
$932$	−37.9444	+	104.251i	−1.24291	+	3.41486i
$933$	−5.22243	−	40.5215i	−0.170975	−	1.32662i
$934$	−84.5027	−	14.9001i	−2.76501	−	0.487546i
$935$	22.1043	−	12.7619i	0.722887	−	0.417359i
$936$	1.29114	+	15.7459i	0.0422021	+	0.514672i
$937$	20.6367	+	11.9146i	0.674170	+	0.389232i	0.797655	−	0.603114i	$-0.206074\pi$
$937$	20.6367	+	11.9146i	0.674170	+	0.389232i	−0.123485	+	0.992346i	$0.539407\pi$
$938$	−25.6380	−	20.3532i	−0.837110	−	0.664554i
$939$	6.88186	+	22.0357i	0.224581	+	0.719109i
$940$	8.73266	+	49.5254i	0.284828	+	1.61534i
$941$	16.7484	−	14.0535i	0.545981	−	0.458132i	−0.327596	−	0.944818i	$-0.606239\pi$
$941$	16.7484	−	14.0535i	0.545981	−	0.458132i	0.873577	+	0.486685i	$0.161794\pi$
$942$	−50.4181	+	78.6666i	−1.64271	+	2.56310i
$943$	0.874639	+	2.40305i	0.0284822	+	0.0782541i
$944$	−58.3845			−1.90025
$945$	−17.0832	−	12.6010i	−0.555715	−	0.409910i
$946$	−61.7991			−2.00926
$947$	−10.2309	−	28.1093i	−0.332461	−	0.913430i	−0.987470	−	0.157808i	$-0.949557\pi$
$947$	−10.2309	−	28.1093i	−0.332461	−	0.913430i	0.655009	−	0.755621i	$-0.272665\pi$
$948$	−74.9622	−	3.47766i	−2.43466	−	0.112949i
$949$	2.35306	−	1.97445i	0.0763835	−	0.0640934i
$950$	8.33328	+	47.2604i	0.270367	+	1.53333i
$951$	−34.7090	−	7.79411i	−1.12552	−	0.252741i
$952$	−81.8677	−	64.9921i	−2.65335	−	2.10641i
$953$	12.7773	+	7.37698i	0.413898	+	0.238964i	0.692463	−	0.721453i	$-0.256526\pi$
$953$	12.7773	+	7.37698i	0.413898	+	0.238964i	−0.278565	+	0.960417i	$0.589859\pi$
$954$	−6.35640	+	23.2154i	−0.205796	+	0.751627i
$955$	−14.3834	+	8.30424i	−0.465435	+	0.268719i
$956$	−96.3007	−	16.9804i	−3.11459	−	0.549186i
$957$	−7.97032	+	6.08139i	−0.257644	+	0.196584i
$958$	16.8227	−	46.2201i	0.543518	−	1.49330i
$959$	−29.6049	−	9.87404i	−0.955993	−	0.318849i
$960$	57.5159	+	24.0077i	1.85632	+	0.774846i
$961$	−1.26581	+	7.17874i	−0.0408324	+	0.231572i
$962$	2.99219	+	5.18262i	0.0964719	+	0.167094i
$963$	39.7472	+	28.1555i	1.28084	+	0.907298i
$964$	84.7753	+	48.9451i	2.73043	+	1.57641i
$965$	29.9615	+	25.1407i	0.964495	+	0.809307i
$966$	−15.4906	+	17.7565i	−0.498402	+	0.571307i
$967$	2.25593	+	12.7940i	0.0725459	+	0.411428i	0.999356	+	0.0358968i	$0.0114288\pi$
$967$	2.25593	+	12.7940i	0.0725459	+	0.411428i	−0.926810	+	0.375532i	$0.877460\pi$
$968$	−16.6904	−	19.8909i	−0.536450	−	0.639316i
$969$	−46.2984	+	23.9413i	−1.48732	+	0.769104i
$970$	−73.1979	+	26.6419i	−2.35024	+	0.855418i
$971$	29.7033			0.953225			0.476613	−	0.879113i	$-0.341864\pi$
$971$	29.7033			0.953225			0.476613	+	0.879113i	$0.341864\pi$
$972$	4.72803	−	82.4781i	0.151652	−	2.64548i
$973$	−8.19643	+	0.222516i	−0.262765	+	0.00713354i
$974$	23.8443	+	65.5115i	0.764019	+	2.09913i
$975$	2.37731	−	1.22933i	0.0761349	−	0.0393699i
$976$	81.4003	+	97.0091i	2.60556	+	3.10519i
$977$	−37.2441	+	6.56715i	−1.19155	+	0.210102i	−0.734041	−	0.679105i	$-0.762368\pi$
$977$	−37.2441	+	6.56715i	−1.19155	+	0.210102i	−0.457505	+	0.889207i	$0.651257\pi$
$978$	−6.76123	+	7.33833i	−0.216200	+	0.234654i
$979$	14.1615	−	16.8770i	0.452604	−	0.539392i
$980$	−25.9074	+	51.0887i	−0.827581	+	1.63197i
$981$	−1.77477	+	2.50546i	−0.0566642	+	0.0799931i
$982$	39.7166	+	68.7911i	1.26741	+	2.19521i
$983$	−7.18185	+	40.7303i	−0.229065	+	1.29909i	0.625694	+	0.780069i	$0.284816\pi$
$983$	−7.18185	+	40.7303i	−0.229065	+	1.29909i	−0.854759	+	0.519025i	$0.826295\pi$
$984$	−7.99208	+	19.1468i	−0.254778	+	0.610378i
$985$	7.15110	−	19.6475i	0.227853	−	0.626021i
$986$	−17.4600	−	6.35491i	−0.556038	−	0.202381i
$987$	−17.6843	−	21.9173i	−0.562898	−	0.697634i
$988$	3.69143	−	20.9352i	0.117440	−	0.666036i
$989$	−10.1075	+	5.83555i	−0.321399	+	0.185560i
$990$	12.3279	−	45.0249i	0.391805	−	1.43099i
$991$	7.82595	−	13.5549i	0.248599	−	0.430587i	−0.714538	−	0.699597i	$-0.753363\pi$
$991$	7.82595	−	13.5549i	0.248599	−	0.430587i	0.963137	+	0.269010i	$0.0866964\pi$
$992$	88.2106	+	74.0175i	2.80069	+	2.35006i
$993$	0.431908	−	1.92338i	0.0137062	−	0.0610367i
$994$	−39.2854	+	8.03203i	−1.24606	+	0.254761i
$995$	2.05132	+	2.44467i	0.0650313	+	0.0775013i
$996$	48.5131	+	2.25063i	1.53719	+	0.0713139i
$997$	−9.65589	−	26.5294i	−0.305805	−	0.840193i	−0.993463	−	0.114158i	$-0.963583\pi$
$997$	−9.65589	−	26.5294i	−0.305805	−	0.840193i	0.687657	−	0.726035i	$-0.258639\pi$
$998$		−	46.1269i		−	1.46012i
$999$	−7.30856	−	18.0608i	−0.231233	−	0.571417i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.be.a.20.21	✓	132
3.2	odd	2		567.2.be.a.62.1		132
7.6	odd	2	inner	189.2.be.a.20.22	yes	132
21.20	even	2		567.2.be.a.62.2		132
27.4	even	9		567.2.be.a.503.2		132
27.23	odd	18	inner	189.2.be.a.104.22	yes	132
189.104	even	18	inner	189.2.be.a.104.21	yes	132
189.139	odd	18		567.2.be.a.503.1		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.20.21	✓	132	1.1	even	1	trivial
189.2.be.a.20.22	yes	132	7.6	odd	2	inner
189.2.be.a.104.21	yes	132	189.104	even	18	inner
189.2.be.a.104.22	yes	132	27.23	odd	18	inner
567.2.be.a.62.1		132	3.2	odd	2
567.2.be.a.62.2		132	21.20	even	2
567.2.be.a.503.1		132	189.139	odd	18
567.2.be.a.503.2		132	27.4	even	9

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.924066 + 2.53885i) q^{2} +(-0.795581 - 1.53852i) q^{3} +(-4.05977 + 3.40655i) q^{4} +(0.268129 + 1.52064i) q^{5} +(3.17091 - 3.44156i) q^{6} +(-1.64503 + 2.07217i) q^{7} +(-7.72059 - 4.45748i) q^{8} +(-1.73410 + 2.44804i) q^{9} +(-3.61290 + 2.08591i) q^{10} +(3.67329 + 0.647701i) q^{11} +(8.47094 + 3.53586i) q^{12} +(-0.202039 + 0.555096i) q^{13} +(-6.78104 - 2.26166i) q^{14} +(2.12621 - 1.62231i) q^{15} +(2.34200 - 13.2821i) q^{16} +(-2.21584 - 3.83794i) q^{17} +(-7.81763 - 2.14047i) q^{18} +(5.88065 + 3.39519i) q^{19} +(-6.26867 - 5.26004i) q^{20} +(4.49683 + 0.882332i) q^{21} +(1.74995 + 9.92446i) q^{22} +(1.22335 + 1.45794i) q^{23} +(-0.715581 + 15.4246i) q^{24} +(2.45802 - 0.894647i) q^{25} -1.59600 q^{26} +(5.14598 + 0.720338i) q^{27} +(-0.380517 - 14.0164i) q^{28} +(-0.530750 - 1.45822i) q^{29} +(6.08357 + 3.89901i) q^{30} +(3.97747 + 4.74017i) q^{31} +(18.3265 - 3.23145i) q^{32} +(-1.92590 - 6.16674i) q^{33} +(7.69638 - 9.17219i) q^{34} +(-3.59210 - 1.94588i) q^{35} +(-1.29932 - 15.8458i) q^{36} +(-1.87480 - 3.24725i) q^{37} +(-3.18578 + 18.0675i) q^{38} +(1.01477 - 0.130784i) q^{39} +(4.70810 - 12.9354i) q^{40} +(1.26264 + 0.459562i) q^{41} +(1.91526 + 12.2321i) q^{42} +(-1.06487 + 6.03919i) q^{43} +(-17.1192 + 9.88375i) q^{44} +(-4.18754 - 1.98055i) q^{45} +(-2.57102 + 4.45314i) q^{46} +(-4.70770 - 3.95023i) q^{47} +(-22.2981 + 6.96381i) q^{48} +(-1.58777 - 6.81755i) q^{49} +(4.54275 + 5.41384i) q^{50} +(-4.14188 + 6.46251i) q^{51} +(-1.07073 - 2.94182i) q^{52} -2.96963i q^{53} +(2.92640 + 13.7305i) q^{54} +5.75941i q^{55} +(21.9372 - 8.66568i) q^{56} +(0.545046 - 11.7487i) q^{57} +(3.21176 - 2.69499i) q^{58} +(-0.751711 - 4.26316i) q^{59} +(-3.10545 + 13.8293i) q^{60} +(-6.03545 + 7.19277i) q^{61} +(-8.35913 + 14.4784i) q^{62} +(-2.22011 - 7.62044i) q^{63} +(11.6520 + 20.1818i) q^{64} +(-0.898272 - 0.158390i) q^{65} +(13.8768 - 10.5880i) q^{66} +(4.30322 + 1.56624i) q^{67} +(22.0699 + 8.03280i) q^{68} +(1.26979 - 3.04206i) q^{69} +(1.62096 - 10.9179i) q^{70} +(4.85796 - 2.80474i) q^{71} +(24.3004 - 11.1706i) q^{72} +(-4.50326 - 2.59996i) q^{73} +(6.51183 - 7.76050i) q^{74} +(-3.33199 - 3.06996i) q^{75} +(-35.4400 + 6.24903i) q^{76} +(-7.38481 + 6.54620i) q^{77} +(1.26975 + 2.45549i) q^{78} +(-7.68222 + 2.79610i) q^{79} +20.8253 q^{80} +(-2.98579 - 8.49029i) q^{81} +3.63031i q^{82} +(4.97168 - 1.80954i) q^{83} +(-21.2618 + 11.7366i) q^{84} +(5.24198 - 4.39855i) q^{85} +(-16.3166 + 2.87706i) q^{86} +(-1.82126 + 1.97671i) q^{87} +(-25.4729 - 21.3743i) q^{88} +(2.95330 - 5.11527i) q^{89} +(1.15874 - 12.4617i) q^{90} +(-0.817895 - 1.33181i) q^{91} +(-9.93307 - 1.75147i) q^{92} +(4.12845 - 9.89062i) q^{93} +(5.67881 - 15.6024i) q^{94} +(-3.58608 + 9.85268i) q^{95} +(-19.5519 - 25.6248i) q^{96} +(18.3882 + 3.24234i) q^{97} +(15.8415 - 10.3310i) q^{98} +(-7.95545 + 7.86919i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9} - 18 q^{11} + 3 q^{14} - 24 q^{15} - 24 q^{16} - 12 q^{18} - 12 q^{21} - 12 q^{22} + 12 q^{23} - 12 q^{25} - 12 q^{28} - 48 q^{29} + 42 q^{30}+ \cdots - 192 q^{99}+O(q^{100}) \) 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9 - 18 * q^11 + 3 * q^14 - 24 * q^15 - 24 * q^16 - 12 * q^18 - 12 * q^21 - 12 * q^22 + 12 * q^23 - 12 * q^25 - 12 * q^28 - 48 * q^29 + 42 * q^30 - 6 * q^32 - 36 * q^35 - 36 * q^36 - 6 * q^37 - 18 * q^39 - 12 * q^43 - 18 * q^44 - 6 * q^46 - 24 * q^49 + 18 * q^50 + 24 * q^51 + 57 * q^56 - 12 * q^58 - 6 * q^60 + 21 * q^63 + 18 * q^64 + 78 * q^65 - 12 * q^67 - 69 * q^70 + 18 * q^71 + 114 * q^72 - 6 * q^74 - 57 * q^77 + 12 * q^78 + 24 * q^79 - 42 * q^81 - 48 * q^84 + 54 * q^85 - 42 * q^86 - 72 * q^88 + 6 * q^91 - 120 * q^92 - 60 * q^93 + 126 * q^95 + 126 * q^98 - 192 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more