LMFDB - Embedded newform 603.2.t.a.164.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(164,603)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("603.164");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.t (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:	$4.81497924188$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$66$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			164.18
Character	$\chi$	$=$	603.164
Dual form			603.2.t.a.239.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.58257 q^{2} +(-0.843344 - 1.51287i) q^{3} +0.504520 q^{4} +(-1.28815 - 2.23114i) q^{5} +(1.33465 + 2.39422i) q^{6} +(0.0815227 - 0.0470672i) q^{7} +2.36670 q^{8} +(-1.57754 + 2.55174i) q^{9} +O(q^{10})$	\(q-1.58257 q^{2} +(-0.843344 - 1.51287i) q^{3} +0.504520 q^{4} +(-1.28815 - 2.23114i) q^{5} +(1.33465 + 2.39422i) q^{6} +(0.0815227 - 0.0470672i) q^{7} +2.36670 q^{8} +(-1.57754 + 2.55174i) q^{9} +(2.03858 + 3.53093i) q^{10} +(1.89804 + 3.28750i) q^{11} +(-0.425484 - 0.763272i) q^{12} +(4.61845 + 2.66646i) q^{13} +(-0.129015 + 0.0744869i) q^{14} +(-2.28907 + 3.83042i) q^{15} -4.75450 q^{16} +(6.19756 - 3.57817i) q^{17} +(2.49656 - 4.03830i) q^{18} +(2.94986 + 5.10930i) q^{19} +(-0.649897 - 1.12565i) q^{20} +(-0.139958 - 0.0836393i) q^{21} +(-3.00378 - 5.20269i) q^{22} +(-7.87347 - 4.54575i) q^{23} +(-1.99594 - 3.58050i) q^{24} +(-0.818655 + 1.41795i) q^{25} +(-7.30901 - 4.21986i) q^{26} +(5.19085 + 0.234618i) q^{27} +(0.0411298 - 0.0237463i) q^{28} +(3.15434 - 1.82116i) q^{29} +(3.62260 - 6.06190i) q^{30} +3.24009i q^{31} +2.79092 q^{32} +(3.37285 - 5.64398i) q^{33} +(-9.80806 + 5.66269i) q^{34} +(-0.210027 - 0.121259i) q^{35} +(-0.795901 + 1.28740i) q^{36} +(-0.0675779 - 0.117048i) q^{37} +(-4.66835 - 8.08582i) q^{38} +(0.139064 - 9.23585i) q^{39} +(-3.04866 - 5.28043i) q^{40} -4.04698 q^{41} +(0.221493 + 0.132365i) q^{42} +(2.48696 + 1.43585i) q^{43} +(0.957599 + 1.65861i) q^{44} +(7.72539 + 0.232695i) q^{45} +(12.4603 + 7.19396i) q^{46} +(3.65609 - 2.11085i) q^{47} +(4.00968 + 7.19293i) q^{48} +(-3.49557 + 6.05450i) q^{49} +(1.29558 - 2.24400i) q^{50} +(-10.6400 - 6.35847i) q^{51} +(2.33010 + 1.34528i) q^{52} +3.92183 q^{53} +(-8.21488 - 0.371298i) q^{54} +(4.88991 - 8.46958i) q^{55} +(0.192940 - 0.111394i) q^{56} +(5.24196 - 8.77165i) q^{57} +(-4.99195 + 2.88211i) q^{58} +(7.63336 - 4.40712i) q^{59} +(-1.15488 + 1.93252i) q^{60} -10.2574i q^{61} -5.12766i q^{62} +(-0.00850235 + 0.282275i) q^{63} +5.09218 q^{64} -13.7392i q^{65} +(-5.33777 + 8.93198i) q^{66} +(-7.56891 + 3.11634i) q^{67} +(3.12679 - 1.80526i) q^{68} +(-0.237075 + 15.7452i) q^{69} +(0.332381 + 0.191901i) q^{70} +(3.00743 + 1.73634i) q^{71} +(-3.73356 + 6.03919i) q^{72} +(2.23039 + 3.86315i) q^{73} +(0.106947 + 0.185237i) q^{74} +(2.83558 + 0.0426953i) q^{75} +(1.48826 + 2.57774i) q^{76} +(0.309467 + 0.178671i) q^{77} +(-0.220078 + 14.6164i) q^{78} +(10.4173 - 6.01442i) q^{79} +(6.12450 + 10.6080i) q^{80} +(-4.02273 - 8.05094i) q^{81} +6.40462 q^{82} +9.14389i q^{83} +(-0.0706116 - 0.0421977i) q^{84} +(-15.9668 - 9.21842i) q^{85} +(-3.93578 - 2.27233i) q^{86} +(-5.41537 - 3.23624i) q^{87} +(4.49209 + 7.78052i) q^{88} +3.82449i q^{89} +(-12.2260 - 0.368256i) q^{90} +0.502011 q^{91} +(-3.97232 - 2.29342i) q^{92} +(4.90183 - 2.73251i) q^{93} +(-5.78601 + 3.34056i) q^{94} +(7.59971 - 13.1631i) q^{95} +(-2.35371 - 4.22229i) q^{96} -3.36275i q^{97} +(5.53197 - 9.58166i) q^{98} +(-11.3831 - 0.342867i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 6 q^{2} + 3 q^{3} + 126 q^{4} - 3 q^{5} - 2 q^{6} - 6 q^{7} - 12 q^{8} - 7 q^{9}+O(q^{10}) $ 132 * q - 6 * q^2 + 3 * q^3 + 126 * q^4 - 3 * q^5 - 2 * q^6 - 6 * q^7 - 12 * q^8 - 7 * q^9	$ 132 q - 6 q^{2} + 3 q^{3} + 126 q^{4} - 3 q^{5} - 2 q^{6} - 6 q^{7} - 12 q^{8} - 7 q^{9} - 3 q^{11} - 3 q^{12} + 4 q^{15} + 114 q^{16} - 9 q^{17} - 6 q^{18} - 4 q^{19} - 15 q^{20} - 9 q^{21} - 3 q^{23} - 11 q^{24} - 57 q^{25} - 36 q^{26} - 24 q^{28} - 21 q^{29} - 12 q^{30} + 30 q^{32} + 17 q^{33} - 12 q^{34} - 15 q^{35} + 8 q^{36} - 4 q^{37} - 31 q^{39} - 12 q^{40} + 6 q^{41} - 42 q^{42} - 3 q^{43} - 6 q^{44} + 9 q^{45} - 24 q^{46} - 12 q^{47} + 24 q^{48} + 60 q^{49} - 12 q^{50} - 24 q^{51} - 18 q^{52} + 60 q^{53} + 29 q^{54} - 18 q^{56} + 51 q^{57} - 12 q^{58} + 12 q^{59} + 65 q^{60} + 15 q^{63} + 84 q^{64} + 30 q^{66} - 5 q^{67} - 39 q^{68} + 12 q^{69} - 45 q^{70} + 30 q^{71} - 39 q^{72} + 14 q^{73} + 15 q^{74} - 24 q^{75} - 7 q^{76} + 69 q^{77} - 90 q^{78} - 3 q^{79} - 18 q^{80} - 3 q^{81} - 24 q^{82} - 51 q^{84} - 18 q^{85} - 6 q^{86} - 42 q^{87} + 15 q^{88} + 85 q^{90} + 42 q^{91} - 12 q^{92} - q^{93} + 6 q^{94} + 12 q^{95} - 57 q^{96} - 21 q^{98} - 24 q^{99}+O(q^{100}) $ 132 * q - 6 * q^2 + 3 * q^3 + 126 * q^4 - 3 * q^5 - 2 * q^6 - 6 * q^7 - 12 * q^8 - 7 * q^9 - 3 * q^11 - 3 * q^12 + 4 * q^15 + 114 * q^16 - 9 * q^17 - 6 * q^18 - 4 * q^19 - 15 * q^20 - 9 * q^21 - 3 * q^23 - 11 * q^24 - 57 * q^25 - 36 * q^26 - 24 * q^28 - 21 * q^29 - 12 * q^30 + 30 * q^32 + 17 * q^33 - 12 * q^34 - 15 * q^35 + 8 * q^36 - 4 * q^37 - 31 * q^39 - 12 * q^40 + 6 * q^41 - 42 * q^42 - 3 * q^43 - 6 * q^44 + 9 * q^45 - 24 * q^46 - 12 * q^47 + 24 * q^48 + 60 * q^49 - 12 * q^50 - 24 * q^51 - 18 * q^52 + 60 * q^53 + 29 * q^54 - 18 * q^56 + 51 * q^57 - 12 * q^58 + 12 * q^59 + 65 * q^60 + 15 * q^63 + 84 * q^64 + 30 * q^66 - 5 * q^67 - 39 * q^68 + 12 * q^69 - 45 * q^70 + 30 * q^71 - 39 * q^72 + 14 * q^73 + 15 * q^74 - 24 * q^75 - 7 * q^76 + 69 * q^77 - 90 * q^78 - 3 * q^79 - 18 * q^80 - 3 * q^81 - 24 * q^82 - 51 * q^84 - 18 * q^85 - 6 * q^86 - 42 * q^87 + 15 * q^88 + 85 * q^90 + 42 * q^91 - 12 * q^92 - q^93 + 6 * q^94 + 12 * q^95 - 57 * q^96 - 21 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.58257			−1.11904			−0.559522	−	0.828815i	$-0.689015\pi$
$2$	−1.58257			−1.11904			−0.559522	+	0.828815i	$0.689015\pi$
$3$	−0.843344	−	1.51287i	−0.486905	−	0.873455i
$3$	−0.843344	−	1.51287i	−0.486905	−	0.873455i
$4$	0.504520			0.252260
$5$	−1.28815	−	2.23114i	−0.576078	−	0.997796i	−0.995924	−	0.0902004i	$-0.971249\pi$
$5$	−1.28815	−	2.23114i	−0.576078	−	0.997796i	0.419846	−	0.907595i	$-0.362084\pi$
$6$	1.33465	+	2.39422i	0.544868	+	0.977435i
$7$	0.0815227	−	0.0470672i	0.0308127	−	0.0177897i	−0.484515	−	0.874783i	$-0.661004\pi$
$7$	0.0815227	−	0.0470672i	0.0308127	−	0.0177897i	0.515327	+	0.856994i	$0.327670\pi$
$8$	2.36670			0.836754
$9$	−1.57754	+	2.55174i	−0.525847	+	0.850579i
$10$	2.03858	+	3.53093i	0.644656	+	1.11658i
$11$	1.89804	+	3.28750i	0.572280	+	0.991219i	0.996331	+	0.0855804i	$0.0272745\pi$
$11$	1.89804	+	3.28750i	0.572280	+	0.991219i	−0.424051	+	0.905638i	$0.639392\pi$
$12$	−0.425484	−	0.763272i	−0.122827	−	0.220338i
$13$	4.61845	+	2.66646i	1.28093	+	0.739544i	0.977018	−	0.213157i	$-0.0683747\pi$
$13$	4.61845	+	2.66646i	1.28093	+	0.739544i	0.303909	+	0.952701i	$0.401708\pi$
$14$	−0.129015	+	0.0744869i	−0.0344808	+	0.0199075i
$15$	−2.28907	+	3.83042i	−0.591034	+	0.989010i
$16$	−4.75450			−1.18862
$17$	6.19756	−	3.57817i	1.50313	−	0.867833i	0.503137	−	0.864207i	$-0.332179\pi$
$17$	6.19756	−	3.57817i	1.50313	−	0.867833i	0.999993	−	0.00362559i	$-0.00115406\pi$
$18$	2.49656	−	4.03830i	0.588446	−	0.951836i
$19$	2.94986	+	5.10930i	0.676744	+	1.17215i	0.975956	+	0.217968i	$0.0699428\pi$
$19$	2.94986	+	5.10930i	0.676744	+	1.17215i	−0.299212	+	0.954187i	$0.596724\pi$
$20$	−0.649897	−	1.12565i	−0.145321	−	0.251704i
$21$	−0.139958	−	0.0836393i	−0.0305414	−	0.0182516i
$22$	−3.00378	−	5.20269i	−0.640407	−	1.10922i
$23$	−7.87347	−	4.54575i	−1.64173	−	0.947855i	−0.980218	−	0.197923i	$-0.936580\pi$
$23$	−7.87347	−	4.54575i	−1.64173	−	0.947855i	−0.661515	−	0.749932i	$-0.730086\pi$
$24$	−1.99594	−	3.58050i	−0.407420	−	0.730867i
$25$	−0.818655	+	1.41795i	−0.163731	+	0.283590i
$26$	−7.30901	−	4.21986i	−1.43341	−	0.827582i
$27$	5.19085	+	0.234618i	0.998980	+	0.0451522i
$28$	0.0411298	−	0.0237463i	0.00777281	−	0.00448763i
$29$	3.15434	−	1.82116i	0.585746	−	0.338181i	−0.177668	−	0.984091i	$-0.556855\pi$
$29$	3.15434	−	1.82116i	0.585746	−	0.338181i	0.763414	+	0.645910i	$0.223522\pi$
$30$	3.62260	−	6.06190i	0.661394	−	1.10675i
$31$			3.24009i			0.581937i	0.956733	+	0.290968i	$0.0939775\pi$
$31$			3.24009i			0.581937i	−0.956733	+	0.290968i	$0.906023\pi$
$32$	2.79092			0.493370
$33$	3.37285	−	5.64398i	0.587139	−	0.982491i
$34$	−9.80806	+	5.66269i	−1.68207	+	0.971143i
$35$	−0.210027	−	0.121259i	−0.0355010	−	0.0204965i
$36$	−0.795901	+	1.28740i	−0.132650	+	0.214567i
$37$	−0.0675779	−	0.117048i	−0.0111097	−	0.0192426i	0.860417	−	0.509590i	$-0.170203\pi$
$37$	−0.0675779	−	0.117048i	−0.0111097	−	0.0192426i	−0.871527	+	0.490348i	$0.836870\pi$
$38$	−4.66835	−	8.08582i	−0.757306	−	1.31169i
$39$	0.139064	−	9.23585i	0.0222681	−	1.47892i
$40$	−3.04866	−	5.28043i	−0.482035	−	0.834910i
$41$	−4.04698			−0.632032			−0.316016	−	0.948754i	$-0.602345\pi$
$41$	−4.04698			−0.632032			−0.316016	+	0.948754i	$0.602345\pi$
$42$	0.221493	+	0.132365i	0.0341771	+	0.0204243i
$43$	2.48696	+	1.43585i	0.379258	+	0.218965i	0.677495	−	0.735527i	$-0.263065\pi$
$43$	2.48696	+	1.43585i	0.379258	+	0.218965i	−0.298237	+	0.954492i	$0.596399\pi$
$44$	0.957599	+	1.65861i	0.144363	+	0.250045i
$45$	7.72539	+	0.232695i	1.15163	+	0.0346881i
$46$	12.4603	+	7.19396i	1.83717	+	1.06069i
$47$	3.65609	−	2.11085i	0.533296	−	0.307898i	−0.209062	−	0.977902i	$-0.567041\pi$
$47$	3.65609	−	2.11085i	0.533296	−	0.307898i	0.742358	+	0.670004i	$0.233708\pi$
$48$	4.00968	+	7.19293i	0.578747	+	1.03821i
$49$	−3.49557	+	6.05450i	−0.499367	+	0.864929i
$50$	1.29558	−	2.24400i	0.183222	−	0.317350i
$51$	−10.6400	−	6.35847i	−1.48989	−	0.890364i
$52$	2.33010	+	1.34528i	0.323127	+	0.186557i
$53$	3.92183			0.538705			0.269353	−	0.963042i	$-0.413190\pi$
$53$	3.92183			0.538705			0.269353	+	0.963042i	$0.413190\pi$
$54$	−8.21488	−	0.371298i	−1.11790	−	0.0505273i
$55$	4.88991	−	8.46958i	0.659356	−	1.14204i
$56$	0.192940	−	0.111394i	0.0257826	−	0.0148856i
$57$	5.24196	−	8.77165i	0.694314	−	1.16183i
$58$	−4.99195	+	2.88211i	−0.655476	+	0.378439i
$59$	7.63336	−	4.40712i	0.993779	−	0.573759i	0.0873775	−	0.996175i	$-0.472151\pi$
$59$	7.63336	−	4.40712i	0.993779	−	0.573759i	0.906402	+	0.422417i	$0.138818\pi$
$60$	−1.15488	+	1.93252i	−0.149094	+	0.249488i
$61$		−	10.2574i		−	1.31332i	−0.754185	−	0.656662i	$-0.771968\pi$
$61$		−	10.2574i		−	1.31332i	0.754185	−	0.656662i	$-0.228032\pi$
$62$		−	5.12766i		−	0.651213i
$63$	−0.00850235	+	0.282275i	−0.00107120	+	0.0355633i
$64$	5.09218			0.636523
$65$		−	13.7392i		−	1.70414i
$66$	−5.33777	+	8.93198i	−0.657034	+	1.09945i
$67$	−7.56891	+	3.11634i	−0.924690	+	0.380721i
$67$	−7.56891	+	3.11634i	−0.924690	+	0.380721i
$68$	3.12679	−	1.80526i	0.379179	−	0.218919i
$69$	−0.237075	+	15.7452i	−0.0285404	+	1.89549i
$70$	0.332381	+	0.191901i	0.0397272	+	0.0229365i
$71$	3.00743	+	1.73634i	0.356916	+	0.206065i	0.667727	−	0.744406i	$-0.267267\pi$
$71$	3.00743	+	1.73634i	0.356916	+	0.206065i	−0.310811	+	0.950472i	$0.600601\pi$
$72$	−3.73356	+	6.03919i	−0.440005	+	0.711726i
$73$	2.23039	+	3.86315i	0.261047	+	0.452147i	0.966521	−	0.256589i	$-0.0825988\pi$
$73$	2.23039	+	3.86315i	0.261047	+	0.452147i	−0.705473	+	0.708737i	$0.749265\pi$
$74$	0.106947	+	0.185237i	0.0124323	+	0.0215333i
$75$	2.83558	+	0.0426953i	0.327425	+	0.00493003i
$76$	1.48826	+	2.57774i	0.170715	+	0.295688i
$77$	0.309467	+	0.178671i	0.0352670	+	0.0203614i
$78$	−0.220078	+	14.6164i	−0.0249190	+	1.65498i
$79$	10.4173	−	6.01442i	1.17204	−	0.676676i	0.217878	−	0.975976i	$-0.430087\pi$
$79$	10.4173	−	6.01442i	1.17204	−	0.676676i	0.954159	+	0.299301i	$0.0967533\pi$
$80$	6.12450	+	10.6080i	0.684740	+	1.18600i
$81$	−4.02273	−	8.05094i	−0.446970	−	0.894549i
$82$	6.40462			0.707272
$83$			9.14389i			1.00367i	0.864963	+	0.501836i	$0.167342\pi$
$83$			9.14389i			1.00367i	−0.864963	+	0.501836i	$0.832658\pi$
$84$	−0.0706116	−	0.0421977i	−0.00770436	−	0.00460414i
$85$	−15.9668	−	9.21842i	−1.73184	−	0.999878i
$86$	−3.93578	−	2.27233i	−0.424406	−	0.245031i
$87$	−5.41537	−	3.23624i	−0.580588	−	0.346961i
$88$	4.49209	+	7.78052i	0.478858	+	0.829406i
$89$			3.82449i			0.405395i	0.979241	+	0.202698i	$0.0649708\pi$
$89$			3.82449i			0.405395i	−0.979241	+	0.202698i	$0.935029\pi$
$90$	−12.2260	−	0.368256i	−1.28873	−	0.0388175i
$91$	0.502011			0.0526251
$92$	−3.97232	−	2.29342i	−0.414143	−	0.239106i
$93$	4.90183	−	2.73251i	0.508296	−	0.283348i
$94$	−5.78601	+	3.34056i	−0.596782	+	0.344552i
$95$	7.59971	−	13.1631i	0.779714	−	1.35050i
$96$	−2.35371	−	4.22229i	−0.240224	−	0.430936i
$97$		−	3.36275i		−	0.341435i	−0.985320	−	0.170718i	$-0.945391\pi$
$97$		−	3.36275i		−	0.341435i	0.985320	−	0.170718i	$-0.0546086\pi$
$98$	5.53197	−	9.58166i	0.558814	−	0.967894i
$99$	−11.3831	−	0.342867i	−1.14404	−	0.0344595i
$100$	−0.413028	+	0.715385i	−0.0413028	+	0.0715385i
$101$	−6.15256	−	10.6566i	−0.612203	−	1.06037i	−0.990868	−	0.134833i	$-0.956950\pi$
$101$	−6.15256	−	10.6566i	−0.612203	−	1.06037i	0.378665	−	0.925534i	$-0.376383\pi$
$102$	16.8385	+	10.0627i	1.66726	+	0.996357i
$103$	15.6677			1.54378			0.771891	−	0.635755i	$-0.219311\pi$
$103$	15.6677			1.54378			0.771891	+	0.635755i	$0.219311\pi$
$104$	10.9305	+	6.31071i	1.07182	+	0.618816i
$105$	−0.00632402	+	0.420006i	−0.000617162	+	0.0409884i
$106$	−6.20657			−0.602835
$107$		−	8.22727i		−	0.795360i	−0.917524	−	0.397680i	$-0.869815\pi$
$107$		−	8.22727i		−	0.795360i	0.917524	−	0.397680i	$-0.130185\pi$
$108$	2.61889	+	0.118369i	0.252003	+	0.0113901i
$109$		−	1.19714i		−	0.114666i	−0.998355	−	0.0573328i	$-0.981740\pi$
$109$		−	1.19714i		−	0.114666i	0.998355	−	0.0573328i	$-0.0182596\pi$
$110$	−7.73862	+	13.4037i	−0.737848	+	1.27799i
$111$	−0.120087	+	0.200948i	−0.0113982	+	0.0190732i
$112$	−0.387600	+	0.223781i	−0.0366247	+	0.0211453i
$113$	15.4437			1.45282			0.726409	−	0.687262i	$-0.241188\pi$
$113$	15.4437			1.45282			0.726409	+	0.687262i	$0.241188\pi$
$114$	−8.29575	+	13.8817i	−0.776968	+	1.30014i
$115$			23.4224i			2.18415i
$116$	1.59143	−	0.918810i	0.147760	−	0.0853094i
$117$	−14.0899	+	7.57862i	−1.30261	+	0.700643i
$118$	−12.0803	+	6.97457i	−1.11208	+	0.642061i
$119$	0.336828	−	0.583403i	0.0308770	−	0.0534805i
$120$	−5.41753	+	9.06544i	−0.494551	+	0.827558i
$121$	−1.70511	+	2.95333i	−0.155010	+	0.268485i
$122$			16.2330i			1.46967i
$123$	3.41300	+	6.12255i	0.307740	+	0.552052i
$124$			1.63469i			0.146799i
$125$	−8.66329			−0.774868
$126$	0.0134555	−	0.446719i	0.00119871	−	0.0397969i
$127$	1.11732	−	1.93526i	0.0991465	−	0.171727i	−0.812185	−	0.583400i	$-0.801722\pi$
$127$	1.11732	−	1.93526i	0.0991465	−	0.171727i	0.911332	+	0.411673i	$0.135055\pi$
$128$	−13.6406			−1.20567
$129$	0.0748838	−	4.97336i	0.00659315	−	0.437880i
$130$			21.7432i			1.90701i
$131$	−13.8368	+	7.98865i	−1.20892	+	0.697972i	−0.962524	−	0.271197i	$-0.912581\pi$
$131$	−13.8368	+	7.98865i	−1.20892	+	0.697972i	−0.246399	+	0.969169i	$0.579247\pi$
$132$	1.70167	−	2.84750i	0.148112	−	0.247843i
$133$	0.480961	+	0.277683i	0.0417046	+	0.0240781i
$134$	11.9783	−	4.93182i	1.03477	−	0.426044i
$135$	−6.16313	−	11.8837i	−0.530437	−	1.02279i
$136$	14.6678	−	8.46844i	1.25775	−	0.726162i
$137$	−8.27154	+	14.3267i	−0.706685	+	1.22402i	0.259394	+	0.965771i	$0.416477\pi$
$137$	−8.27154	+	14.3267i	−0.706685	+	1.22402i	−0.966080	+	0.258244i	$0.916856\pi$
$138$	0.375187	−	24.9178i	0.0319380	−	2.12114i
$139$	4.08030	−	2.35576i	0.346086	−	0.199813i	−0.316874	−	0.948468i	$-0.602633\pi$
$139$	4.08030	−	2.35576i	0.346086	−	0.199813i	0.662960	+	0.748655i	$0.269300\pi$
$140$	−0.105963	−	0.0611776i	−0.00895548	−	0.00517045i
$141$	−6.27678	−	3.75102i	−0.528600	−	0.315893i
$142$	−4.75946	−	2.74787i	−0.399405	−	0.230596i
$143$			20.2442i			1.69291i
$144$	7.50042	−	12.1322i	0.625035	−	1.01102i
$145$	−8.12651	−	4.69185i	−0.674870	−	0.389637i
$146$	−3.52974	−	6.11369i	−0.292123	−	0.505973i
$147$	12.1076	+	0.182305i	0.998621	+	0.0150362i
$148$	−0.0340944	−	0.0590532i	−0.00280254	−	0.00485414i
$149$	1.97561	−	1.14062i	0.161848	−	0.0934432i	−0.416888	−	0.908958i	$-0.636879\pi$
$149$	1.97561	−	1.14062i	0.161848	−	0.0934432i	0.578736	+	0.815515i	$0.303546\pi$
$150$	−4.48750	−	0.0675683i	−0.366403	−	0.00551692i
$151$	−6.41207			−0.521807			−0.260904	−	0.965365i	$-0.584020\pi$
$151$	−6.41207			−0.521807			−0.260904	+	0.965365i	$0.584020\pi$
$152$	6.98142	+	12.0922i	0.566268	+	0.980805i
$153$	−0.646370	+	21.4593i	−0.0522559	+	1.73488i
$154$	−0.489752	−	0.282758i	−0.0394653	−	0.0227853i
$155$	7.22909	−	4.17372i	0.580654	−	0.335241i
$156$	0.0701606	−	4.65967i	0.00561734	−	0.373072i
$157$	10.7583	−	18.6340i	0.858608	−	1.48715i	−0.0146497	−	0.999893i	$-0.504663\pi$
$157$	10.7583	−	18.6340i	0.858608	−	1.48715i	0.873257	−	0.487259i	$-0.162003\pi$
$158$	−16.4861	+	9.51823i	−1.31156	+	0.757230i
$159$	−3.30746	−	5.93322i	−0.262298	−	0.470535i
$160$	−3.59512	−	6.22693i	−0.284219	−	0.492282i
$161$	−0.855822			−0.0674482
$162$	6.36624	+	12.7412i	0.500179	+	1.00104i
$163$	−1.69331	+	2.93290i	−0.132630	+	0.229722i	−0.924690	−	0.380722i	$-0.875676\pi$
$163$	−1.69331	+	2.93290i	−0.132630	+	0.229722i	0.792059	+	0.610444i	$0.209009\pi$
$164$	−2.04178			−0.159436
$165$	−16.9372	−	0.255024i	−1.31856	−	0.0198536i
$166$		−	14.4708i		−	1.12315i
$167$			4.75266i			0.367772i	0.982948	+	0.183886i	$0.0588677\pi$
$167$			4.75266i			0.367772i	−0.982948	+	0.183886i	$0.941132\pi$
$168$	−0.331239	−	0.197949i	−0.0255556	−	0.0152721i
$169$	7.72004	+	13.3715i	0.593850	+	1.02858i
$170$	25.2685	+	14.5888i	1.93800	+	1.11891i
$171$	−17.6911	−	0.532871i	−1.35287	−	0.0407497i
$172$	1.25472	+	0.724414i	0.0956716	+	0.0552360i
$173$			14.1021i			1.07216i	0.844167	+	0.536080i	$0.180096\pi$
$173$			14.1021i			1.07216i	−0.844167	+	0.536080i	$0.819904\pi$
$174$	8.57018	+	5.12156i	0.649704	+	0.388264i
$175$			0.154127i			0.0116509i
$176$	−9.02423	−	15.6304i	−0.680227	−	1.17819i
$177$	−13.1050	−	7.83155i	−0.985029	−	0.588655i
$178$		−	6.05251i		−	0.453655i
$179$	−9.67117			−0.722857			−0.361429	−	0.932400i	$-0.617711\pi$
$179$	−9.67117			−0.722857			−0.361429	+	0.932400i	$0.617711\pi$
$180$	3.89761	+	0.117399i	0.290511	+	0.00875042i
$181$	7.35552	−	12.7401i	0.546731	−	0.946966i	−0.451764	−	0.892137i	$-0.649205\pi$
$181$	7.35552	−	12.7401i	0.546731	−	0.946966i	0.998496	−	0.0548291i	$-0.0174614\pi$
$182$	−0.794467			−0.0588898
$183$	−15.5181	+	8.65052i	−1.14713	+	0.639465i
$184$	−18.6341	−	10.7584i	−1.37373	−	0.793121i
$185$	−0.174101	+	0.301551i	−0.0128001	+	0.0221705i
$186$	−7.75747	+	4.32438i	−0.568805	+	0.317079i
$187$	23.5264	+	13.5830i	1.72042	+	0.993287i
$188$	1.84457	−	1.06496i	0.134529	−	0.0776705i
$189$	0.434215	−	0.225192i	0.0315845	−	0.0163803i
$190$	−12.0271	+	20.8315i	−0.872534	+	1.51127i
$191$	−17.9889			−1.30163			−0.650817	−	0.759234i	$-0.725574\pi$
$191$	−17.9889			−1.30163			−0.650817	+	0.759234i	$0.725574\pi$
$192$	−4.29446	−	7.70380i	−0.309926	−	0.555974i
$193$	0.481681	+	0.834297i	0.0346722	+	0.0600540i	0.882841	−	0.469672i	$-0.155628\pi$
$193$	0.481681	+	0.834297i	0.0346722	+	0.0600540i	−0.848169	+	0.529726i	$0.822295\pi$
$194$			5.32177i			0.382081i
$195$	−20.7856	+	11.5869i	−1.48849	+	0.829754i
$196$	−1.76358	+	3.05462i	−0.125970	+	0.218187i
$197$	11.4756	−	19.8764i	0.817605	−	1.41613i	−0.0898368	−	0.995956i	$-0.528635\pi$
$197$	11.4756	−	19.8764i	0.817605	−	1.41613i	0.907442	−	0.420177i	$-0.138032\pi$
$198$	18.0145	+	0.542611i	1.28023	+	0.0385617i
$199$	11.7034	+	20.2709i	0.829632	+	1.43697i	0.898327	+	0.439327i	$0.144783\pi$
$199$	11.7034	+	20.2709i	0.829632	+	1.43697i	−0.0686949	+	0.997638i	$0.521883\pi$
$200$	−1.93751	+	3.35586i	−0.137003	+	0.237295i
$201$	11.0978	+	8.82262i	0.782779	+	0.622300i
$202$	9.73685	+	16.8647i	0.685082	+	1.18660i
$203$	0.171433	−	0.296931i	0.0120323	−	0.0208405i
$204$	−5.36808	−	3.20798i	−0.375841	−	0.224603i
$205$	5.21311	+	9.02938i	0.364100	+	0.630639i
$206$	−24.7952			−1.72756
$207$	24.0203	−	12.9199i	1.66953	−	0.897997i
$208$	−21.9584	−	12.6777i	−1.52254	−	0.879040i
$209$	−11.1979	+	19.3953i	−0.774574	+	1.34160i
$210$	0.0100082	−	0.664688i	0.000690631	−	0.0458678i
$211$	10.9576	−	18.9792i	0.754355	−	1.30658i	−0.191339	−	0.981524i	$-0.561283\pi$
$211$	10.9576	−	18.9792i	0.754355	−	1.30658i	0.945694	−	0.325058i	$-0.105384\pi$
$212$	1.97864			0.135894
$213$	0.0905553	−	6.01417i	0.00620475	−	0.412084i
$214$			13.0202i			0.890043i
$215$		−	7.39834i		−	0.504563i
$216$	12.2852	+	0.555269i	0.835901	+	0.0377813i
$217$	0.152502	+	0.264141i	0.0103525	+	0.0179310i
$218$			1.89456i			0.128316i
$219$	3.96345	−	6.63225i	0.267825	−	0.448166i
$220$	2.46706	−	4.27307i	0.166329	−	0.288090i
$221$	38.1642			2.56720
$222$	0.190046	−	0.318014i	0.0127551	−	0.0213437i
$223$	−5.36262	+	9.28834i	−0.359108	+	0.621993i	−0.987812	−	0.155652i	$-0.950252\pi$
$223$	−5.36262	+	9.28834i	−0.359108	+	0.621993i	0.628704	+	0.777645i	$0.283586\pi$
$224$	0.227523	−	0.131361i	0.0152020	−	0.00877690i
$225$	−2.32678	−	4.32587i	−0.155119	−	0.288391i
$226$	−24.4407			−1.62577
$227$	11.0228	−	6.36399i	0.731606	−	0.422393i	−0.0874034	−	0.996173i	$-0.527857\pi$
$227$	11.0228	−	6.36399i	0.731606	−	0.422393i	0.819009	+	0.573780i	$0.194524\pi$
$228$	2.64467	−	4.42547i	0.175148	−	0.293084i
$229$	−11.8556	−	6.84484i	−0.783440	−	0.452319i	0.0542079	−	0.998530i	$-0.482737\pi$
$229$	−11.8556	−	6.84484i	−0.783440	−	0.452319i	−0.837648	+	0.546210i	$0.816070\pi$
$230$		−	37.0676i		−	2.44416i
$231$	0.00931822	−	0.618863i	0.000613094	−	0.0407182i
$232$	7.46537	−	4.31013i	0.490125	−	0.282974i
$233$	7.79537	−	13.5020i	0.510692	−	0.884544i	−0.489232	−	0.872154i	$-0.662723\pi$
$233$	7.79537	−	13.5020i	0.510692	−	0.884544i	0.999923	−	0.0123899i	$-0.00394394\pi$
$234$	22.2982	−	11.9937i	1.45768	−	0.784051i
$235$	−9.41918	−	5.43817i	−0.614440	−	0.354747i
$236$	3.85118	−	2.22348i	0.250691	−	0.144736i
$237$	−17.8844	−	10.6878i	−1.16172	−	0.694244i
$238$	−0.533053	+	0.923275i	−0.0345527	+	0.0598470i
$239$	−15.0389			−0.972783			−0.486392	−	0.873741i	$-0.661687\pi$
$239$	−15.0389			−0.972783			−0.486392	+	0.873741i	$0.661687\pi$
$240$	10.8834	−	18.2117i	0.702518	−	1.17556i
$241$	8.68880	−	15.0494i	0.559695	−	0.969419i	−0.437827	−	0.899059i	$-0.644252\pi$
$241$	8.68880	−	15.0494i	0.559695	−	0.969419i	0.997522	−	0.0703602i	$-0.0224149\pi$
$242$	2.69845	−	4.67385i	0.173463	−	0.300446i
$243$	−8.78746	+	12.8756i	−0.563716	+	0.825969i
$244$		−	5.17506i		−	0.331299i
$245$	18.0113			1.15070
$246$	−5.40130	−	9.68934i	−0.344374	−	0.617770i
$247$			31.4627i			2.00193i
$248$			7.66831i			0.486938i
$249$	13.8335	−	7.71145i	0.876663	−	0.488693i
$250$	13.7102			0.867112
$251$	−7.19124	−	12.4556i	−0.453907	−	0.786190i	0.544717	−	0.838620i	$-0.316637\pi$
$251$	−7.19124	−	12.4556i	−0.453907	−	0.786190i	−0.998625	+	0.0524294i	$0.983304\pi$
$252$	−0.00428960	+	0.142413i	−0.000270220	+	0.00897119i
$253$		−	34.5121i		−	2.16975i
$254$	−1.76824	+	3.06268i	−0.110949	+	0.192170i
$255$	−0.480769	+	31.9299i	−0.0301069	+	1.99953i
$256$	11.4027			0.712671
$257$		−	5.24371i		−	0.327094i	−0.986536	−	0.163547i	$-0.947706\pi$
$257$		−	5.24371i		−	0.327094i	0.986536	−	0.163547i	$-0.0522935\pi$
$258$	−0.118509	+	7.87067i	−0.00737803	+	0.490007i
$259$	−0.0110183	−	0.00636140i	−0.000684641	−	0.000395278i
$260$		−	6.93170i		−	0.429886i
$261$	−0.328979	+	10.9220i	−0.0203633	+	0.676055i
$262$	21.8976	−	12.6426i	1.35284	−	0.781061i
$263$	14.2311	+	8.21633i	0.877527	+	0.506640i	0.869842	−	0.493330i	$-0.164221\pi$
$263$	14.2311	+	8.21633i	0.877527	+	0.506640i	0.00768466	+	0.999970i	$0.497554\pi$
$264$	7.98253	−	13.3576i	0.491291	−	0.822103i
$265$	−5.05190	−	8.75016i	−0.310336	−	0.537518i
$266$	−0.761153	−	0.439452i	−0.0466693	−	0.0269445i
$267$	5.78595	−	3.22536i	0.354094	−	0.197389i
$268$	−3.81867	+	1.57225i	−0.233262	+	0.0960407i
$269$			22.2618i			1.35733i	0.734450	+	0.678663i	$0.237440\pi$
$269$			22.2618i			1.35733i	−0.734450	+	0.678663i	$0.762560\pi$
$270$	9.75356	+	18.8068i	0.593583	+	1.14455i
$271$		−	5.31943i		−	0.323132i	−0.986862	−	0.161566i	$-0.948345\pi$
$271$		−	5.31943i		−	0.323132i	0.986862	−	0.161566i	$-0.0516545\pi$
$272$	−29.4663	+	17.0124i	−1.78666	+	1.03153i
$273$	−0.423368	−	0.759477i	−0.0256234	−	0.0459656i
$274$	13.0903	−	22.6730i	0.790812	−	1.36973i
$275$	−6.21536			−0.374800
$276$	−0.119609	+	7.94375i	−0.00719961	+	0.478157i
$277$	6.25566	−	10.8351i	0.375866	−	0.651019i	−0.614590	−	0.788847i	$-0.710679\pi$
$277$	6.25566	−	10.8351i	0.375866	−	0.651019i	0.990456	+	0.137827i	$0.0440119\pi$
$278$	−6.45735	+	3.72815i	−0.387286	+	0.223600i
$279$	−8.26785	−	5.11137i	−0.494983	−	0.306010i
$280$	−0.497070	−	0.286983i	−0.0297056	−	0.0171505i
$281$	22.8493			1.36307			0.681537	−	0.731783i	$-0.261312\pi$
$281$	22.8493			1.36307			0.681537	+	0.731783i	$0.261312\pi$
$282$	9.93342	+	5.93624i	0.591527	+	0.353498i
$283$	7.55170	+	13.0799i	0.448902	+	0.777521i	0.998315	−	0.0580298i	$-0.0184818\pi$
$283$	7.55170	+	13.0799i	0.448902	+	0.777521i	−0.549413	+	0.835551i	$0.685149\pi$
$284$	1.51731	+	0.876017i	0.0900356	+	0.0519821i
$285$	−26.3232	−	0.396348i	−1.55925	−	0.0234776i
$286$		−	32.0378i		−	1.89444i
$287$	−0.329921	+	0.190480i	−0.0194746	+	0.0112437i
$288$	−4.40279	+	7.12169i	−0.259437	+	0.419650i
$289$	17.1065	−	29.6294i	1.00627	−	1.74290i
$290$	12.8608	+	7.42516i	0.755210	+	0.436021i
$291$	−5.08739	+	2.83595i	−0.298228	+	0.166246i
$292$	1.12528	+	1.94903i	0.0658518	+	0.114059i
$293$	26.8300	−	15.4903i	1.56742	−	0.904952i	0.570954	−	0.820982i	$-0.306573\pi$
$293$	26.8300	−	15.4903i	1.56742	−	0.904952i	0.996468	−	0.0839699i	$-0.0267600\pi$
$294$	−19.1611	−	0.288509i	−1.11750	−	0.0168262i
$295$	−19.6658	−	11.3541i	−1.14499	−	0.661059i
$296$	−0.159936	−	0.277018i	−0.00929612	−	0.0161013i
$297$	9.08114	+	17.5102i	0.526941	+	1.01605i
$298$	−3.12654	+	1.80511i	−0.181115	+	0.104567i
$299$	−24.2422	−	41.9886i	−1.40196	−	2.42827i
$300$	1.43061	+	0.0215406i	0.0825962	+	0.00124365i
$301$	0.270325			0.0155813
$302$	10.1475			0.583925
$303$	−10.9332	+	18.2952i	−0.628098	+	1.05103i
$304$	−14.0251	−	24.2922i	−0.804394	−	1.39325i
$305$	−22.8857	+	13.2131i	−1.31043	+	0.756577i
$306$	1.02292	−	33.9607i	0.0584767	−	1.94141i
$307$	8.98094	+	15.5554i	0.512569	+	0.887796i	0.999894	+	0.0145751i	$0.00463955\pi$
$307$	8.98094	+	15.5554i	0.512569	+	0.887796i	−0.487325	+	0.873221i	$0.662027\pi$
$308$	0.156132	+	0.0901429i	0.00889645	+	0.00513637i
$309$	−13.2133	−	23.7031i	−0.751676	−	1.34842i
$310$	−11.4405	+	6.60519i	−0.649778	+	0.375149i
$311$	6.12785	+	10.6137i	0.347478	+	0.601850i	0.985801	−	0.167919i	$-0.0537047\pi$
$311$	6.12785	+	10.6137i	0.347478	+	0.601850i	−0.638322	+	0.769769i	$0.720371\pi$
$312$	0.329123	−	21.8585i	0.0186329	−	1.23749i
$313$	−15.0152	−	8.66900i	−0.848707	−	0.490001i	0.0115077	−	0.999934i	$-0.496337\pi$
$313$	−15.0152	−	8.66900i	−0.848707	−	0.490001i	−0.860214	+	0.509933i	$0.829670\pi$
$314$	−17.0258	+	29.4895i	−0.960820	+	1.66419i
$315$	0.640747	−	0.344642i	0.0361020	−	0.0194184i
$316$	5.25573	−	3.03440i	0.295658	−	0.170698i
$317$			7.22608i			0.405857i	0.979194	+	0.202928i	$0.0650459\pi$
$317$			7.22608i			0.405857i	−0.979194	+	0.202928i	$0.934954\pi$
$318$	5.23427	+	9.38972i	0.293523	+	0.526549i
$319$	11.9741	+	6.91326i	0.670422	+	0.387068i
$320$	−6.55949	−	11.3614i	−0.366686	−	0.635119i
$321$	−12.4468	+	6.93842i	−0.694711	+	0.387265i
$322$	1.35440			0.0754776
$323$	36.5639	+	21.1102i	2.03447	+	1.17460i
$324$	−2.02955	−	4.06186i	−0.112753	−	0.225659i
$325$	−7.56183	+	4.36582i	−0.419455	+	0.242172i
$326$	2.67978	−	4.64151i	0.148419	−	0.257070i
$327$	−1.81112	+	1.00960i	−0.100155	+	0.0558312i
$328$	−9.57798			−0.528855
$329$	0.198703	−	0.344164i	0.0109549	−	0.0189744i
$330$	26.8043	+	0.403593i	1.47553	+	0.0222170i
$331$	−8.58797	+	4.95827i	−0.472038	+	0.272531i	−0.717092	−	0.696978i	$-0.754527\pi$
$331$	−8.58797	+	4.95827i	−0.472038	+	0.272531i	0.245055	+	0.969509i	$0.421194\pi$
$332$			4.61328i			0.253186i
$333$	0.405283	+	0.0122075i	0.0222094	+	0.000668965i
$334$		−	7.52140i		−	0.411553i
$335$	16.7029	+	12.8730i	0.912575	+	0.703327i
$336$	0.665431	+	0.397663i	0.0363022	+	0.0216943i
$337$	2.56771	+	1.48247i	0.139872	+	0.0807551i	0.568303	−	0.822819i	$-0.307600\pi$
$337$	2.56771	+	1.48247i	0.139872	+	0.0807551i	−0.428431	+	0.903574i	$0.640934\pi$
$338$	−12.2175	−	21.1613i	−0.664544	−	1.15102i
$339$	−13.0243	−	23.3642i	−0.707385	−	1.26897i
$340$	−8.05555	−	4.65088i	−0.436874	−	0.252229i
$341$	−10.6518	+	6.14981i	−0.576827	+	0.333031i
$342$	27.9974	+	0.843304i	1.51393	+	0.0456007i
$343$			1.31705i			0.0711138i
$344$	5.88589	+	3.39822i	0.317346	+	0.183220i
$345$	35.4350	−	19.7532i	1.90776	−	1.06347i
$346$		−	22.3175i		−	1.19979i
$347$	−2.60602			−0.139899			−0.0699494	−	0.997551i	$-0.522284\pi$
$347$	−2.60602			−0.139899			−0.0699494	+	0.997551i	$0.522284\pi$
$348$	−2.73216	−	1.63274i	−0.146459	−	0.0875243i
$349$	7.11325	−	12.3205i	0.380763	−	0.659501i	−0.610408	−	0.792087i	$-0.708995\pi$
$349$	7.11325	−	12.3205i	0.380763	−	0.659501i	0.991172	+	0.132586i	$0.0423279\pi$
$350$		−	0.243916i		−	0.0130379i
$351$	23.3481	+	14.9248i	1.24623	+	0.796626i
$352$	5.29728	+	9.17515i	0.282346	+	0.489037i
$353$	−8.31858			−0.442754			−0.221377	−	0.975188i	$-0.571055\pi$
$353$	−8.31858			−0.442754			−0.221377	+	0.975188i	$0.571055\pi$
$354$	20.7395	+	12.3940i	1.10229	+	0.658731i
$355$		−	8.94665i		−	0.474839i
$356$			1.92953i			0.102265i
$357$	−1.16667	−	0.0175666i	−0.0617470	−	0.000929723i
$358$	15.3053			0.808909
$359$			20.3603i			1.07458i	0.843398	+	0.537289i	$0.180551\pi$
$359$			20.3603i			1.07458i	−0.843398	+	0.537289i	$0.819449\pi$
$360$	18.2837	+	0.550719i	0.963634	+	0.0290254i
$361$	−7.90331	+	13.6889i	−0.415964	+	0.720471i
$362$	−11.6406	+	20.1621i	−0.611816	+	1.05970i
$363$	5.90600	+	0.0889266i	0.309984	+	0.00466743i
$364$	0.253275			0.0132752
$365$	5.74615	−	9.95262i	0.300767	−	0.520944i
$366$	24.5584	−	13.6900i	1.28369	−	0.715589i
$367$	−2.54549	+	1.46964i	−0.132874	+	0.0767147i	−0.564963	−	0.825116i	$-0.691110\pi$
$367$	−2.54549	+	1.46964i	−0.132874	+	0.0767147i	0.432090	+	0.901831i	$0.357776\pi$
$368$	37.4344	+	21.6128i	1.95140	+	1.12664i
$369$	6.38428	−	10.3268i	0.332352	−	0.537593i
$370$	0.275526	−	0.477225i	0.0143239	−	0.0248098i
$371$	0.319718	−	0.184590i	0.0165990	−	0.00958341i
$372$	2.47307	−	1.37861i	0.128223	−	0.0714774i
$373$			20.9727i			1.08593i	0.839756	+	0.542963i	$0.182698\pi$
$373$			20.9727i			1.08593i	−0.839756	+	0.542963i	$0.817302\pi$
$374$	−37.2322	−	21.4960i	−1.92523	−	1.11153i
$375$	7.30614	+	13.1064i	0.377287	+	0.676813i
$376$	8.65287	−	4.99574i	0.446238	−	0.257635i
$377$	19.4242			1.00040
$378$	−0.687175	+	0.356382i	−0.0353445	+	0.0183303i
$379$	−23.6352	+	13.6458i	−1.21406	+	0.700938i	−0.963641	−	0.267200i	$-0.913902\pi$
$379$	−23.6352	+	13.6458i	−1.21406	+	0.700938i	−0.250418	+	0.968138i	$0.580568\pi$
$380$	3.83420	−	6.64104i	0.196691	−	0.340678i
$381$	−3.87009	−	0.0582719i	−0.198271	−	0.00298536i
$382$	28.4687			1.45659
$383$	−2.24646	+	3.89098i	−0.114789	+	0.198820i	−0.917695	−	0.397285i	$-0.869952\pi$
$383$	−2.24646	+	3.89098i	−0.114789	+	0.198820i	0.802907	+	0.596105i	$0.203286\pi$
$384$	11.5037	+	20.6364i	0.587045	+	1.05310i
$385$		−	0.920617i		−	0.0469190i
$386$	−0.762293	−	1.32033i	−0.0387997	−	0.0672031i
$387$	−7.58719	+	4.08096i	−0.385678	+	0.207447i
$388$		−	1.69657i		−	0.0861304i
$389$			18.6206i			0.944104i	0.881571	+	0.472052i	$0.156487\pi$
$389$			18.6206i			0.944104i	−0.881571	+	0.472052i	$0.843513\pi$
$390$	32.8946	−	18.3370i	1.66568	−	0.928531i
$391$	−65.0618			−3.29032
$392$	−8.27296	+	14.3292i	−0.417847	+	0.723733i
$393$	23.7549	+	14.1960i	1.19828	+	0.716093i
$394$	−18.1610	+	31.4557i	−0.914936	+	1.58472i
$395$	−26.8380	−	15.4949i	−1.35037	−	0.779635i
$396$	−5.74299	−	0.172983i	−0.288596	−	0.00869274i
$397$	−15.7072			−0.788323			−0.394161	−	0.919041i	$-0.628965\pi$
$397$	−15.7072			−0.788323			−0.394161	+	0.919041i	$0.628965\pi$
$398$	−18.5214	−	32.0800i	−0.928395	−	1.60803i
$399$	0.0144820	−	0.961812i	0.000725007	−	0.0481508i
$400$	3.89229	−	6.74165i	0.194615	−	0.337083i
$401$	13.0778	+	22.6513i	0.653072	+	1.13115i	0.982373	+	0.186929i	$0.0598535\pi$
$401$	13.0778	+	22.6513i	0.653072	+	1.13115i	−0.329301	+	0.944225i	$0.606813\pi$
$402$	−17.5630	−	13.9624i	−0.875964	−	0.696381i
$403$	−8.63957	+	14.9642i	−0.430368	+	0.745419i
$404$	−3.10409	−	5.37644i	−0.154434	−	0.267488i
$405$	−12.7809	+	19.3461i	−0.635088	+	0.961315i
$406$	−0.271305	+	0.469914i	−0.0134646	+	0.0233214i
$407$	0.256531	−	0.444325i	0.0127158	−	0.0220244i
$408$	−25.1816	−	15.0486i	−1.24668	−	0.745016i
$409$			0.160951i			0.00795849i	0.999992	+	0.00397925i	$0.00126664\pi$
$409$			0.160951i			0.00795849i	−0.999992	+	0.00397925i	$0.998733\pi$
$410$	−8.25010	−	14.2896i	−0.407444	−	0.705713i
$411$	28.6502	+	0.431386i	1.41321	+	0.0212787i
$412$	7.90466			0.389434
$413$	0.414862	−	0.718561i	0.0204140	−	0.0353581i
$414$	−38.0137	+	20.4467i	−1.86827	+	1.00490i
$415$	20.4013	−	11.7787i	1.00146	−	0.578193i
$416$	12.8897	+	7.44188i	0.631970	+	0.364868i
$417$	−7.00505	−	4.18624i	−0.343039	−	0.205001i
$418$	17.7214	−	30.6944i	0.866783	−	1.50131i
$419$	−9.59841	−	5.54165i	−0.468913	−	0.270727i	0.246872	−	0.969048i	$-0.420597\pi$
$419$	−9.59841	−	5.54165i	−0.468913	−	0.270727i	−0.715785	+	0.698321i	$0.753931\pi$
$420$	−0.00319060	+	0.211901i	−0.000155685	+	0.0103397i
$421$	−15.0745			−0.734687			−0.367343	−	0.930085i	$-0.619733\pi$
$421$	−15.0745			−0.734687			−0.367343	+	0.930085i	$0.619733\pi$
$422$	−17.3412	+	30.0359i	−0.844157	+	1.46212i
$423$	−0.381309	+	12.6593i	−0.0185399	+	0.615518i
$424$	9.28180			0.450764
$425$			11.7171i			0.568364i
$426$	−0.143310	+	9.51783i	−0.00694339	+	0.461141i
$427$	−0.482786	−	0.836211i	−0.0233637	−	0.0404671i
$428$		−	4.15082i		−	0.200637i
$429$	30.6268	−	17.0728i	1.47868	−	0.824284i
$430$			11.7084i			0.564628i
$431$	29.1762	+	16.8449i	1.40537	+	0.811390i	0.994937	−	0.100502i	$-0.0320448\pi$
$431$	29.1762	+	16.8449i	1.40537	+	0.811390i	0.410431	+	0.911891i	$0.365378\pi$
$432$	−24.6799	−	1.11549i	−1.18741	−	0.0536690i
$433$	0.254740	+	0.147074i	0.0122420	+	0.00706795i	0.506109	−	0.862470i	$-0.331084\pi$
$433$	0.254740	+	0.147074i	0.0122420	+	0.00706795i	−0.493866	+	0.869538i	$0.664417\pi$
$434$	−0.241344	−	0.418020i	−0.0115849	−	0.0200656i
$435$	−0.244694	+	16.2512i	−0.0117322	+	0.779185i
$436$		−	0.603983i		−	0.0289255i
$437$		−	53.6373i		−	2.56582i
$438$	−6.27242	+	10.4960i	−0.299708	+	0.501517i
$439$	−14.8710			−0.709756			−0.354878	−	0.934913i	$-0.615478\pi$
$439$	−14.8710			−0.709756			−0.354878	+	0.934913i	$0.615478\pi$
$440$	11.5730	−	20.0449i	0.551719	−	0.955605i
$441$	−9.93510	−	18.4710i	−0.473100	−	0.879572i
$442$	−60.3974			−2.87281
$443$	−18.1780	−	31.4852i	−0.863662	−	1.49591i	−0.868369	−	0.495918i	$-0.834832\pi$
$443$	−18.1780	−	31.4852i	−0.863662	−	1.49591i	0.00470681	−	0.999989i	$-0.498502\pi$
$444$	−0.0605864	+	0.101382i	−0.00287530	+	0.00481140i
$445$	8.53297	−	4.92651i	0.404501	−	0.233539i
$446$	8.48671	−	14.6994i	0.401858	−	0.696038i
$447$	−3.39173	−	2.02690i	−0.160423	−	0.0958693i
$448$	0.415128	−	0.239674i	0.0196130	−	0.0113236i
$449$	−25.3658	−	14.6450i	−1.19709	−	0.691139i	−0.237183	−	0.971465i	$-0.576224\pi$
$449$	−25.3658	−	14.6450i	−1.19709	−	0.691139i	−0.959905	+	0.280326i	$0.909557\pi$
$450$	3.68229	+	6.84598i	0.173585	+	0.322723i
$451$	−7.68133	−	13.3044i	−0.361700	−	0.626482i
$452$	7.79164			0.366488
$453$	5.40758	+	9.70062i	0.254070	+	0.455775i
$454$	−17.4443	+	10.0714i	−0.818700	+	0.472676i
$455$	−0.646665	−	1.12006i	−0.0303161	−	0.0525091i
$456$	12.4061	−	20.7598i	0.580970	−	0.972169i
$457$	3.15654	+	5.46728i	0.147657	+	0.255749i	0.930361	−	0.366645i	$-0.119494\pi$
$457$	3.15654	+	5.46728i	0.147657	+	0.255749i	−0.782704	+	0.622394i	$0.786160\pi$
$458$	18.7623	+	10.8324i	0.876704	+	0.506165i
$459$	33.0101	−	17.1197i	1.54078	−	0.799078i
$460$			11.8171i			0.550974i
$461$	−26.9384	−	15.5529i	−1.25464	−	0.724370i	−0.282617	−	0.959233i	$-0.591202\pi$
$461$	−26.9384	−	15.5529i	−1.25464	−	0.724370i	−0.972028	+	0.234863i	$0.924536\pi$
$462$	−0.0147467	+	0.979393i	−0.000686079	+	0.0455655i
$463$	−0.926892	−	0.535141i	−0.0430763	−	0.0248701i	0.478307	−	0.878193i	$-0.341251\pi$
$463$	−0.926892	−	0.535141i	−0.0430763	−	0.0248701i	−0.521383	+	0.853322i	$0.674584\pi$
$464$	−14.9973	+	8.65870i	−0.696232	+	0.401970i
$465$	−12.4109	−	7.41678i	−0.575541	−	0.343945i
$466$	−12.3367	+	21.3678i	−0.571486	+	0.989844i
$467$	−30.3349	+	17.5139i	−1.40373	+	0.810445i	−0.994773	−	0.102107i	$-0.967442\pi$
$467$	−30.3349	+	17.5139i	−1.40373	+	0.810445i	−0.408959	+	0.912553i	$0.634108\pi$
$468$	−7.10864	+	3.82356i	−0.328597	+	0.176744i
$469$	−0.470361	+	0.610299i	−0.0217193	+	0.0281810i
$470$	14.9065	+	8.60627i	0.687585	+	0.396977i
$471$	−37.2637	−	0.561079i	−1.71702	−	0.0258532i
$472$	18.0659	−	10.4303i	0.831549	−	0.480095i
$473$			10.9012i			0.501237i
$474$	28.3033	+	16.9141i	1.30001	+	0.776890i
$475$	−9.65966			−0.443216
$476$	0.169936	−	0.294339i	0.00778902	−	0.0134910i
$477$	−6.18685	+	10.0075i	−0.283276	+	0.458211i
$478$	23.8000			1.08859
$479$			15.3036i			0.699237i	0.936892	+	0.349619i	$0.113689\pi$
$479$			15.3036i			0.699237i	−0.936892	+	0.349619i	$0.886311\pi$
$480$	−6.38860	+	10.6904i	−0.291598	+	0.487947i
$481$		−	0.720775i		−	0.0328645i
$482$	−13.7506	+	23.8167i	−0.626323	+	1.08482i
$483$	0.721753	+	1.29475i	0.0328409	+	0.0589130i
$484$	−0.860261	+	1.49002i	−0.0391028	+	0.0677280i
$485$	−7.50275	+	4.33172i	−0.340682	+	0.196693i
$486$	13.9068	−	20.3765i	0.630823	−	0.924295i
$487$	−5.81408	+	3.35676i	−0.263461	+	0.152109i	−0.625912	−	0.779893i	$-0.715273\pi$
$487$	−5.81408	+	3.35676i	−0.263461	+	0.152109i	0.362451	+	0.932003i	$0.381940\pi$
$488$		−	24.2762i		−	1.09893i
$489$	5.86513	+	0.0883113i	0.265231	+	0.00399357i
$490$	−28.5040			−1.28768
$491$	21.8781	−	12.6313i	0.987346	−	0.570044i	0.0828661	−	0.996561i	$-0.473593\pi$
$491$	21.8781	−	12.6313i	0.987346	−	0.570044i	0.904480	+	0.426516i	$0.140259\pi$
$492$	1.72192	+	3.08895i	0.0776304	+	0.139260i
$493$	13.0328	−	22.5735i	0.586968	−	1.01666i
$494$		−	49.7919i		−	2.24024i
$495$	13.8981	+	25.8389i	0.624674	+	1.16137i
$496$		−	15.4050i		−	0.691705i
$497$	0.326898			0.0146634
$498$	−21.8925	+	12.2039i	−0.981025	+	0.546869i
$499$	32.9725	+	19.0367i	1.47605	+	0.852199i	0.999635	−	0.0270211i	$-0.00860214\pi$
$499$	32.9725	+	19.0367i	1.47605	+	0.852199i	0.476416	+	0.879220i	$0.341935\pi$
$500$	−4.37080			−0.195468
$501$	7.19015	−	4.00813i	0.321232	−	0.179070i
$502$	11.3806	+	19.7118i	0.507942	+	0.879782i
$503$	−5.29644	+	9.17371i	−0.236157	+	0.409036i	−0.959608	−	0.281340i	$-0.909221\pi$
$503$	−5.29644	+	9.17371i	−0.236157	+	0.409036i	0.723451	+	0.690375i	$0.242555\pi$
$504$	−0.0201225	+	0.668059i	−0.000896327	+	0.0297577i
$505$	−15.8508	+	27.4544i	−0.705353	+	1.22171i
$506$			54.6177i			2.42805i
$507$	13.7187	−	22.9562i	0.609268	−	1.01952i
$508$	0.563713	−	0.976379i	0.0250107	−	0.0433198i
$509$	−28.9481	+	16.7132i	−1.28310	+	0.740801i	−0.977415	−	0.211331i	$-0.932220\pi$
$509$	−28.9481	+	16.7132i	−1.28310	+	0.740801i	−0.305690	+	0.952131i	$0.598887\pi$
$510$	0.760849	−	50.5313i	0.0336909	−	2.23756i
$511$	0.363655	+	0.209956i	0.0160871	+	0.00928791i
$512$	9.23551			0.408156
$513$	14.1135	+	27.2137i	0.623128	+	1.20152i
$514$			8.29853i			0.366032i
$515$	−20.1823	−	34.9568i	−0.889339	−	1.54038i
$516$	0.0377804	−	2.50916i	0.00166319	−	0.110460i
$517$	13.8788	+	8.01294i	0.610390	+	0.352409i
$518$	0.0174371	+	0.0100673i	0.000766144	+	0.000442333i
$519$	21.3346	−	11.8929i	0.936484	−	0.522040i
$520$		−	32.5165i		−	1.42594i
$521$	−34.2697			−1.50138			−0.750690	−	0.660654i	$-0.770279\pi$
$521$	−34.2697			−1.50138			−0.750690	+	0.660654i	$0.770279\pi$
$522$	0.520632	−	17.2848i	0.0227874	−	0.756535i
$523$	5.07468	+	8.78960i	0.221900	+	0.384342i	0.955385	−	0.295363i	$-0.0954407\pi$
$523$	5.07468	+	8.78960i	0.221900	+	0.384342i	−0.733485	+	0.679706i	$0.762107\pi$
$524$	−6.98092	+	4.03043i	−0.304963	+	0.176070i
$525$	0.233174	−	0.129982i	0.0101765	−	0.00567289i
$526$	−22.5217	−	13.0029i	−0.981991	−	0.566953i
$527$	11.5936	+	20.0807i	0.505024	+	0.874727i
$528$	−16.0362	+	26.8343i	−0.697888	+	1.16781i
$529$	29.8277	+	51.6631i	1.29686	+	2.24622i
$530$	7.99498	+	13.8477i	0.347280	+	0.601506i
$531$	−0.796116	+	26.4308i	−0.0345485	+	1.14700i
$532$	0.242654	+	0.140096i	0.0105204	+	0.00607395i
$533$	−18.6908	−	10.7911i	−0.809587	−	0.467415i
$534$	−9.15665	+	5.10435i	−0.396247	+	0.220887i
$535$	−18.3562	+	10.5979i	−0.793607	+	0.458189i
$536$	−17.9133	+	7.37543i	−0.773738	+	0.318570i
$537$	8.15613	+	14.6312i	0.351963	+	0.631383i
$538$		−	35.2308i		−	1.51891i
$539$	−26.5389			−1.14311
$540$	−3.10942	−	5.99558i	−0.133808	−	0.258009i
$541$			16.2538i			0.698805i	0.936973	+	0.349403i	$0.113615\pi$
$541$			16.2538i			0.698805i	−0.936973	+	0.349403i	$0.886385\pi$
$542$			8.41836i			0.361600i
$543$	−25.4774	−	0.383613i	−1.09334	−	0.0164624i
$544$	17.2969	−	9.98637i	0.741599	−	0.428162i
$545$	−2.67099	+	1.54210i	−0.114413	+	0.0660563i
$546$	0.670009	+	1.20192i	0.0286737	+	0.0514376i
$547$	−22.6619	+	13.0838i	−0.968951	+	0.559424i	−0.898916	−	0.438121i	$-0.855644\pi$
$547$	−22.6619	+	13.0838i	−0.968951	+	0.559424i	−0.0700346	+	0.997545i	$0.522311\pi$
$548$	−4.17316	+	7.22812i	−0.178268	+	0.308770i
$549$	26.1742	+	16.1815i	1.11709	+	0.690608i
$550$	9.83622			0.419418
$551$	18.6097	+	10.7443i	0.792800	+	0.457723i
$552$	−0.561084	+	37.2640i	−0.0238813	+	1.58606i
$553$	0.566164	−	0.980624i	0.0240757	−	0.0417004i
$554$	−9.90000	+	17.1473i	−0.420611	+	0.728519i
$555$	0.603034	+	0.00907988i	0.0255974	+	0.000385419i
$556$	2.05859	−	1.18853i	0.0873037	−	0.0504048i
$557$	−22.6100	−	13.0539i	−0.958017	−	0.553112i	−0.0624550	−	0.998048i	$-0.519893\pi$
$557$	−22.6100	−	13.0539i	−0.958017	−	0.553112i	−0.895562	+	0.444936i	$0.853226\pi$
$558$	13.0844	+	8.08909i	0.553908	+	0.342438i
$559$	7.65727	+	13.2628i	0.323868	+	0.560956i
$560$	0.998572	+	0.576526i	0.0421974	+	0.0243627i
$561$	0.708395	−	47.0475i	0.0299084	−	1.98635i
$562$	−36.1605			−1.52534
$563$	−3.54455	−	6.13935i	−0.149385	−	0.258743i	0.781615	−	0.623761i	$-0.214396\pi$
$563$	−3.54455	−	6.13935i	−0.149385	−	0.258743i	−0.931000	+	0.365018i	$0.881063\pi$
$564$	−3.16676	−	1.89246i	−0.133345	−	0.0796870i
$565$	−19.8937	−	34.4570i	−0.836936	−	1.44962i
$566$	−11.9511	−	20.6999i	−0.502341	−	0.870081i
$567$	−0.706879	−	0.466996i	−0.0296861	−	0.0196120i
$568$	7.11767	+	4.10939i	0.298651	+	0.172426i
$569$	22.3924	−	12.9283i	0.938740	−	0.541982i	0.0491749	−	0.998790i	$-0.484341\pi$
$569$	22.3924	−	12.9283i	0.938740	−	0.541982i	0.889565	+	0.456808i	$0.151008\pi$
$570$	41.6582	+	0.627247i	1.74487	+	0.0262725i
$571$	28.0088			1.17213			0.586066	−	0.810263i	$-0.300676\pi$
$571$	28.0088			1.17213			0.586066	+	0.810263i	$0.300676\pi$
$572$			10.2136i			0.427052i
$573$	15.1709	+	27.2149i	0.633773	+	1.13692i
$574$	0.522122	−	0.301447i	0.0217929	−	0.0125822i
$575$	12.8913	−	7.44280i	0.537605	−	0.310386i
$576$	−8.03312	+	12.9939i	−0.334713	+	0.541413i
$577$	−30.8061	−	17.7859i	−1.28247	−	0.740436i	−0.305173	−	0.952297i	$-0.598714\pi$
$577$	−30.8061	−	17.7859i	−1.28247	−	0.740436i	−0.977300	+	0.211861i	$0.932048\pi$
$578$	−27.0722	+	46.8905i	−1.12606	+	1.95039i
$579$	0.855958	−	1.43232i	0.0355724	−	0.0595252i
$580$	−4.09999	−	2.36713i	−0.170243	−	0.0982897i
$581$	0.430377	+	0.745435i	0.0178550	+	0.0309259i
$582$	8.05114	−	4.48809i	0.333730	−	0.186037i
$583$	7.44379	+	12.8930i	0.308290	+	0.533975i
$584$	5.27866	+	9.14290i	0.218432	+	0.378336i
$585$	35.0588	+	21.6742i	1.44950	+	0.896116i
$586$	−42.4602	+	24.5144i	−1.75402	+	1.01268i
$587$	38.2229			1.57763			0.788814	−	0.614632i	$-0.210696\pi$
$587$	38.2229			1.57763			0.788814	+	0.614632i	$0.210696\pi$
$588$	6.10854	+	0.0919763i	0.251912	+	0.00379304i
$589$	−16.5546	+	9.55780i	−0.682120	+	0.393822i
$590$	31.1225	+	17.9686i	1.28129	+	0.739754i
$591$	−39.7483	−	0.598489i	−1.63503	−	0.0246186i
$592$	0.321299	+	0.556506i	0.0132053	+	0.0228723i
$593$	0.222996	+	0.386240i	0.00915733	+	0.0158610i	0.870568	−	0.492049i	$-0.163752\pi$
$593$	0.222996	+	0.386240i	0.00915733	+	0.0158610i	−0.861410	+	0.507910i	$0.830418\pi$
$594$	−14.3715	−	27.7111i	−0.589670	−	1.13700i
$595$	−1.73554			−0.0711502
$596$	0.996735	−	0.575465i	0.0408279	−	0.0235720i
$597$	20.7972	−	34.8010i	0.851172	−	1.42431i
$598$	38.3648	+	66.4499i	1.56886	+	2.71734i
$599$	11.7608			0.480532			0.240266	−	0.970707i	$-0.422765\pi$
$599$	11.7608			0.480532			0.240266	+	0.970707i	$0.422765\pi$
$600$	6.71097	+	0.101047i	0.273974	+	0.00412523i
$601$	2.02538			0.0826171			0.0413086	−	0.999146i	$-0.486847\pi$
$601$	2.02538			0.0826171			0.0413086	+	0.999146i	$0.486847\pi$
$602$	−0.427808			−0.0174361
$603$	3.98819	−	24.2300i	0.162412	−	0.986723i
$604$	−3.23502			−0.131631
$605$	8.78573			0.357191
$606$	17.3026	−	28.9533i	0.702869	−	1.17615i
$607$	34.4303			1.39748			0.698741	−	0.715375i	$-0.253744\pi$
$607$	34.4303			1.39748			0.698741	+	0.715375i	$0.253744\pi$
$608$	8.23281	+	14.2597i	0.333885	+	0.578305i
$609$	−0.593796	−	0.00894078i	−0.0240618	−	0.000362298i
$610$	36.2181	−	20.9105i	1.46643	−	0.846643i
$611$	22.5140			0.910817
$612$	−0.326107	+	10.8266i	−0.0131821	+	0.437640i
$613$	−7.86653	−	13.6252i	−0.317726	−	0.550318i	0.662287	−	0.749250i	$-0.269586\pi$
$613$	−7.86653	−	13.6252i	−0.317726	−	0.550318i	−0.980013	+	0.198932i	$0.936253\pi$
$614$	−14.2129	−	24.6175i	−0.573588	−	0.993483i
$615$	9.26381	−	15.5016i	0.373553	−	0.625086i
$616$	0.732414	+	0.422859i	0.0295098	+	0.0170375i
$617$	−29.6985	+	17.1465i	−1.19562	+	0.690291i	−0.959575	−	0.281452i	$-0.909184\pi$
$617$	−29.6985	+	17.1465i	−1.19562	+	0.690291i	−0.236043	+	0.971743i	$0.575851\pi$
$618$	20.9109	+	37.5118i	0.841158	+	1.50895i
$619$	22.2957			0.896140			0.448070	−	0.893998i	$-0.352111\pi$
$619$	22.2957			0.896140			0.448070	+	0.893998i	$0.352111\pi$
$620$	3.64722	−	2.10572i	0.146476	−	0.0845678i
$621$	−39.8035	−	25.4436i	−1.59726	−	1.02102i
$622$	−9.69773	−	16.7970i	−0.388844	−	0.673497i
$623$	0.180008	+	0.311783i	0.00721186	+	0.0124913i
$624$	−0.661180	+	43.9118i	−0.0264684	+	1.75788i
$625$	15.2529	+	26.4188i	0.610115	+	1.05675i
$626$	23.7625	+	13.7193i	0.949740	+	0.548333i
$627$	38.7862	+	0.584004i	1.54897	+	0.0233229i
$628$	5.42779	−	9.40120i	0.216592	−	0.375149i
$629$	−0.837636	−	0.483610i	−0.0333987	−	0.0192828i
$630$	−1.01403	+	0.545419i	−0.0403997	+	0.0217300i
$631$	9.20245	−	5.31304i	0.366344	−	0.211509i	−0.305516	−	0.952187i	$-0.598829\pi$
$631$	9.20245	−	5.31304i	0.366344	−	0.211509i	0.671860	+	0.740678i	$0.265496\pi$
$632$	24.6546	−	14.2343i	0.980706	−	0.566211i
$633$	−37.9541	−	0.571474i	−1.50854	−	0.0227141i
$634$		−	11.4358i		−	0.454172i
$635$	−5.75712			−0.228464
$636$	−1.66868	−	2.99343i	−0.0661673	−	0.118697i
$637$	−32.2882	+	18.6416i	−1.27931	+	0.738607i
$638$	−18.9498	−	10.9407i	−0.750232	−	0.433146i
$639$	−9.17502	+	4.93502i	−0.362958	+	0.195226i
$640$	17.5711	+	30.4340i	0.694557	+	1.20301i
$641$	4.00589	+	6.93841i	0.158223	+	0.274051i	0.934228	−	0.356676i	$-0.116090\pi$
$641$	4.00589	+	6.93841i	0.158223	+	0.274051i	−0.776005	+	0.630727i	$0.782757\pi$
$642$	19.6979	−	10.9805i	0.777412	−	0.433366i
$643$	9.49717	+	16.4496i	0.374532	+	0.648708i	0.990257	−	0.139253i	$-0.0444701\pi$
$643$	9.49717	+	16.4496i	0.374532	+	0.648708i	−0.615725	+	0.787961i	$0.711137\pi$
$644$	−0.431779			−0.0170145
$645$	−11.1927	+	6.23935i	−0.440713	+	0.245674i
$646$	−57.8648	−	33.4082i	−2.27666	−	1.31443i
$647$	−2.49215	−	4.31653i	−0.0979764	−	0.169700i	0.812871	−	0.582444i	$-0.197904\pi$
$647$	−2.49215	−	4.31653i	−0.0979764	−	0.169700i	−0.910847	+	0.412744i	$0.864570\pi$
$648$	−9.52059	−	19.0541i	−0.374004	−	0.748518i
$649$	28.9769	+	16.7298i	1.13744	+	0.656702i
$650$	11.9671	−	6.90921i	0.469389	−	0.271002i
$651$	0.270999	−	0.453477i	0.0106213	−	0.0177731i
$652$	−0.854309	+	1.47971i	−0.0334573	+	0.0579498i
$653$	10.1649	−	17.6061i	0.397782	−	0.688978i	−0.595670	−	0.803229i	$-0.703113\pi$
$653$	10.1649	−	17.6061i	0.397782	−	0.688978i	0.993452	+	0.114251i	$0.0364468\pi$
$654$	2.86622	−	1.59777i	0.112078	−	0.0624776i
$655$	35.6476	+	20.5811i	1.39287	+	0.804172i
$656$	19.2414			0.751249
$657$	−13.3763	−	0.402904i	−0.521858	−	0.0157188i
$658$	−0.314461	+	0.544662i	−0.0122590	+	0.0212331i
$659$	−35.8124	+	20.6763i	−1.39505	+	0.805434i	−0.993869	−	0.110563i	$-0.964735\pi$
$659$	−35.8124	+	20.6763i	−1.39505	+	0.805434i	−0.401184	+	0.915997i	$0.631401\pi$
$660$	−8.54517	−	0.128665i	−0.332620	−	0.00500826i
$661$	−10.8021	+	6.23661i	−0.420154	+	0.242576i	−0.695143	−	0.718871i	$-0.744659\pi$
$661$	−10.8021	+	6.23661i	−0.420154	+	0.242576i	0.274989	+	0.961447i	$0.411326\pi$
$662$	13.5910	−	7.84679i	0.528231	−	0.304974i
$663$	−32.1855	−	57.7374i	−1.24998	−	2.24233i
$664$			21.6408i			0.839827i
$665$		−	1.43079i		−	0.0554835i
$666$	−0.641388	−	0.0193191i	−0.0248533	−	0.000748601i
$667$	−33.1141			−1.28218
$668$			2.39781i			0.0927741i
$669$	18.5746	+	0.279677i	0.718134	+	0.0108129i
$670$	−26.4334	−	20.3724i	−1.02121	−	0.787054i
$671$	33.7212	−	19.4689i	1.30179	−	0.751590i
$672$	−0.390612	−	0.233431i	−0.0150682	−	0.00900478i
$673$	14.8224	+	8.55771i	0.571361	+	0.329876i	0.757693	−	0.652611i	$-0.226327\pi$
$673$	14.8224	+	8.55771i	0.571361	+	0.329876i	−0.186332	+	0.982487i	$0.559660\pi$
$674$	−4.06357	−	2.34610i	−0.156523	−	0.0903685i
$675$	−4.58219	+	7.16831i	−0.176369	+	0.275908i
$676$	3.89492	+	6.74619i	0.149804	+	0.259469i
$677$	−14.2984	−	24.7656i	−0.549532	−	0.951818i	−0.998307	−	0.0581727i	$-0.981473\pi$
$677$	−14.2984	−	24.7656i	−0.549532	−	0.951818i	0.448774	−	0.893645i	$-0.351861\pi$
$678$	20.6119	+	36.9755i	0.791595	+	1.42004i
$679$	−0.158275	−	0.274140i	−0.00607403	−	0.0105205i
$680$	−37.7885	−	21.8172i	−1.44912	−	0.836652i
$681$	−18.9239	−	11.3089i	−0.725164	−	0.433360i
$682$	16.8572	−	9.73250i	0.645495	−	0.372677i
$683$	0.575117	+	0.996132i	0.0220062	+	0.0381159i	0.876819	−	0.480821i	$-0.159661\pi$
$683$	0.575117	+	0.996132i	0.0220062	+	0.0381159i	−0.854813	+	0.518937i	$0.826328\pi$
$684$	−8.92552	−	0.268844i	−0.341276	−	0.0102795i
$685$	42.6199			1.62842
$686$		−	2.08431i		−	0.0795795i
$687$	−0.356979	+	23.7085i	−0.0136196	+	0.904536i
$688$	−11.8243	−	6.82674i	−0.450795	−	0.260267i
$689$	18.1128	+	10.4574i	0.690042	+	0.398396i
$690$	−56.0783	+	31.2607i	−2.13487	+	1.19008i
$691$	−13.2440	−	22.9392i	−0.503825	−	0.872650i	−0.999990	−	0.00442194i	$-0.998592\pi$
$691$	−13.2440	−	22.9392i	−0.503825	−	0.872650i	0.496166	−	0.868228i	$-0.334741\pi$
$692$			7.11477i			0.270463i
$693$	−0.944117	+	0.507817i	−0.0358640	+	0.0192904i
$694$	4.12421			0.156553
$695$	−10.5121	−	6.06914i	−0.398745	−	0.230216i
$696$	−12.8165	−	7.65919i	−0.485810	−	0.290321i
$697$	−25.0814	+	14.4808i	−0.950026	+	0.548498i
$698$	−11.2572	+	19.4980i	−0.426091	+	0.738011i
$699$	−27.0009	−	0.406552i	−1.02127	−	0.0153772i
$700$			0.0777601i			0.00293906i
$701$	5.78393	−	10.0181i	0.218456	−	0.378377i	−0.735880	−	0.677112i	$-0.763231\pi$
$701$	5.78393	−	10.0181i	0.218456	−	0.378377i	0.954336	+	0.298735i	$0.0965647\pi$
$702$	−36.9499	−	23.6195i	−1.39458	−	0.891460i
$703$	0.398690	−	0.690551i	0.0150369	−	0.0260446i
$704$	9.66516	+	16.7405i	0.364269	+	0.630933i
$705$	−0.283617	+	18.8362i	−0.0106816	+	0.709413i
$706$	13.1647			0.495461
$707$	−1.00315	−	0.579167i	−0.0377272	−	0.0217818i
$708$	−6.61171	−	3.95117i	−0.248483	−	0.148494i
$709$	41.7200			1.56683			0.783414	−	0.621501i	$-0.213477\pi$
$709$	41.7200			1.56683			0.783414	+	0.621501i	$0.213477\pi$
$710$			14.1587i			0.531366i
$711$	−1.08646	+	36.0702i	−0.0407456	+	1.35274i
$712$			9.05141i			0.339216i
$713$	14.7286	−	25.5107i	0.551592	−	0.955385i
$714$	1.84634	+	0.0278003i	0.0690976	+	0.00104040i
$715$	45.1676	−	26.0775i	1.68917	−	0.975245i
$716$	−4.87930			−0.182348
$717$	12.6829	+	22.7518i	0.473653	+	0.849682i
$718$		−	32.2216i		−	1.20250i
$719$	24.4199	−	14.0988i	0.910709	−	0.525798i	0.0300496	−	0.999548i	$-0.490433\pi$
$719$	24.4199	−	14.0988i	0.910709	−	0.525798i	0.880659	+	0.473750i	$0.157100\pi$
$720$	−36.7304	−	1.10635i	−1.36886	−	0.0412312i
$721$	1.27727	−	0.737433i	0.0475681	−	0.0274634i
$722$	12.5075	−	21.6637i	0.465482	−	0.806238i
$723$	−30.0955	−	0.453147i	−1.11926	−	0.0168527i
$724$	3.71100	−	6.42765i	0.137918	−	0.238882i
$725$			5.96360i			0.221483i
$726$	−9.34664	−	0.140732i	−0.346886	−	0.00522306i
$727$		−	21.6875i		−	0.804343i	−0.915564	−	0.402172i	$-0.868255\pi$
$727$		−	21.6875i		−	0.804343i	0.915564	−	0.402172i	$-0.131745\pi$
$728$	1.18811			0.0440342
$729$	26.8899	+	2.43573i	0.995923	+	0.0902123i
$730$	−9.09366	+	15.7507i	−0.336572	+	0.582959i
$731$	20.5508			0.760099
$732$	−7.82918	+	4.36436i	−0.289375	+	0.161311i
$733$		−	31.7950i		−	1.17438i	−0.809451	−	0.587188i	$-0.800235\pi$
$733$		−	31.7950i		−	1.17438i	0.809451	−	0.587188i	$-0.199765\pi$
$734$	4.02842	−	2.32581i	0.148692	−	0.0858471i
$735$	−15.1897	−	27.2487i	−0.560280	−	1.00508i
$736$	−21.9742	−	12.6868i	−0.809981	−	0.467643i
$737$	−24.6111	−	18.9679i	−0.906560	−	0.698691i
$738$	−10.1035	+	16.3429i	−0.371917	+	0.601591i
$739$	−18.2978	+	10.5643i	−0.673097	+	0.388613i	−0.797249	−	0.603650i	$-0.793712\pi$
$739$	−18.2978	+	10.5643i	−0.673097	+	0.388613i	0.124152	+	0.992263i	$0.460379\pi$
$740$	−0.0878373	+	0.152139i	−0.00322896	+	0.00559273i
$741$	47.5990	−	26.5339i	1.74859	−	0.974748i
$742$	−0.505976	+	0.292125i	−0.0185750	+	0.0107243i
$743$	−20.6853	−	11.9426i	−0.758868	−	0.438133i	0.0700210	−	0.997546i	$-0.477693\pi$
$743$	−20.6853	−	11.9426i	−0.758868	−	0.438133i	−0.828889	+	0.559413i	$0.811027\pi$
$744$	11.6011	−	6.46703i	0.425319	−	0.237093i
$745$	−5.08976	−	2.93858i	−0.186474	−	0.107661i
$746$		−	33.1908i		−	1.21520i
$747$	−23.3328	−	14.4249i	−0.853703	−	0.527778i
$748$	11.8696	+	6.85289i	0.433994	+	0.250567i
$749$	−0.387234	−	0.670709i	−0.0141492	−	0.0245072i
$750$	−11.5625	−	20.7418i	−0.422201	−	0.757383i
$751$	−6.28550	−	10.8868i	−0.229361	−	0.397265i	0.728258	−	0.685303i	$-0.240330\pi$
$751$	−6.28550	−	10.8868i	−0.229361	−	0.397265i	−0.957619	+	0.288038i	$0.906997\pi$
$752$	−17.3829	+	10.0360i	−0.633889	+	0.365976i
$753$	−12.7790	+	21.3838i	−0.465692	+	0.779267i
$754$	−30.7401			−1.11949
$755$	8.25970	+	14.3062i	0.300601	+	0.520657i
$756$	0.219070	−	0.113614i	0.00796750	−	0.00413210i
$757$	−13.9386	−	8.04744i	−0.506606	−	0.292489i	0.224831	−	0.974398i	$-0.427817\pi$
$757$	−13.9386	−	8.04744i	−0.506606	−	0.292489i	−0.731438	+	0.681908i	$0.761150\pi$
$758$	37.4043	−	21.5954i	1.35859	−	0.784380i
$759$	−52.2122	+	29.1056i	−1.89518	+	1.05646i
$760$	17.9862	−	31.1530i	0.652429	−	1.13004i
$761$	−8.98979	+	5.19026i	−0.325880	+	0.188147i	−0.654010	−	0.756486i	$-0.726915\pi$
$761$	−8.98979	+	5.19026i	−0.325880	+	0.188147i	0.328131	+	0.944632i	$0.393581\pi$
$762$	6.12468	+	0.0922192i	0.221874	+	0.00334075i
$763$	−0.0563461	−	0.0975944i	−0.00203987	−	0.00353315i
$764$	−9.07578			−0.328350
$765$	48.7112	−	26.2006i	1.76116	−	0.947284i
$766$	3.55518	−	6.15774i	0.128454	−	0.222488i
$767$	47.0057			1.69728
$768$	−9.61644	−	17.2508i	−0.347003	−	0.622486i
$769$			40.2701i			1.45218i	0.687602	+	0.726088i	$0.258664\pi$
$769$			40.2701i			1.45218i	−0.687602	+	0.726088i	$0.741336\pi$
$770$			1.45694i			0.0525044i
$771$	−7.93305	+	4.42225i	−0.285702	+	0.159264i
$772$	0.243018	+	0.420919i	0.00874640	+	0.0151492i
$773$	9.80643	+	5.66174i	0.352713	+	0.203639i	0.665879	−	0.746059i	$-0.268057\pi$
$773$	9.80643	+	5.66174i	0.352713	+	0.203639i	−0.313167	+	0.949698i	$0.601390\pi$
$774$	12.0072	−	6.45840i	0.431591	−	0.232142i
$775$	−4.59429	−	2.65251i	−0.165032	−	0.0952811i
$776$		−	7.95860i		−	0.285697i
$777$	−0.000331766		0.0220340i	−1.19020e−5		0.000790466i
$778$		−	29.4684i		−	1.05649i
$779$	−11.9380	−	20.6772i	−0.427724	−	0.740839i
$780$	−10.4867	+	5.84581i	−0.375486	+	0.209314i
$781$			13.1826i			0.471709i
$782$	102.965			3.68201
$783$	16.8010	−	8.71330i	0.600418	−	0.311388i
$784$	16.6197	−	28.7861i	0.593560	−	1.02808i
$785$	−55.4333			−1.97850
$786$	−37.5938	−	22.4661i	−1.34093	−	0.801340i
$787$	−18.5803	−	10.7273i	−0.662316	−	0.382389i	0.130843	−	0.991403i	$-0.458232\pi$
$787$	−18.5803	−	10.7273i	−0.662316	−	0.382389i	−0.793159	+	0.609015i	$0.791565\pi$
$788$	5.78969	−	10.0280i	0.206249	−	0.357234i
$789$	0.428506	−	28.4590i	0.0152552	−	1.01317i
$790$	42.4730	+	24.5218i	1.51112	+	0.872446i
$791$	1.25901	−	0.726890i	0.0447652	−	0.0258452i
$792$	−26.9403	−	0.811464i	−0.957282	−	0.0288341i
$793$	27.3510	−	47.3733i	0.971261	−	1.68227i
$794$	24.8577			0.882168
$795$	−8.97734	+	15.0223i	−0.318393	+	0.532785i
$796$	5.90460	+	10.2271i	0.209283	+	0.362489i
$797$			14.6284i			0.518163i	0.965855	+	0.259082i	$0.0834199\pi$
$797$			14.6284i			0.518163i	−0.965855	+	0.259082i	$0.916580\pi$
$798$	−0.0229187	+	1.52213i	−0.000811315	+	0.0538829i
$799$	15.1059	−	26.1642i	0.534409	−	0.925623i
$800$	−2.28480	+	3.95739i	−0.0807799	+	0.139915i
$801$	−9.75909	−	6.03329i	−0.344821	−	0.213176i
$802$	−20.6964	−	35.8473i	−0.730817	−	1.26581i
$803$	−8.46673	+	14.6648i	−0.298785	+	0.517510i
$804$	5.59906	+	4.45119i	0.197464	+	0.156981i
$805$	1.10243	+	1.90946i	0.0388554	+	0.0672996i
$806$	13.6727	−	23.6818i	0.481601	−	0.834157i
$807$	33.6792	−	18.7744i	1.18556	−	0.660889i
$808$	−14.5613	−	25.2208i	−0.512263	−	0.887266i
$809$	−2.38402			−0.0838177			−0.0419088	−	0.999121i	$-0.513344\pi$
$809$	−2.38402			−0.0838177			−0.0419088	+	0.999121i	$0.513344\pi$
$810$	20.2266	−	30.6165i	0.710691	−	1.07575i
$811$	−25.4522	−	14.6948i	−0.893747	−	0.516005i	−0.0185806	−	0.999827i	$-0.505915\pi$
$811$	−25.4522	−	14.6948i	−0.893747	−	0.516005i	−0.875166	+	0.483822i	$0.839248\pi$
$812$	0.0864916	−	0.149808i	0.00303526	−	0.00525722i
$813$	−8.04760	+	4.48611i	−0.282242	+	0.157335i
$814$	−0.405977	+	0.703174i	−0.0142295	+	0.0246462i
$815$	8.72494			0.305621
$816$	50.5877	+	30.2314i	1.77093	+	1.05831i
$817$			16.9422i			0.592732i
$818$		−	0.254715i		−	0.00890591i
$819$	−0.791943	+	1.28100i	−0.0276727	+	0.0447618i
$820$	2.63012	+	4.55550i	0.0918477	+	0.159085i
$821$			26.5338i			0.926036i	0.886349	+	0.463018i	$0.153233\pi$
$821$			26.5338i			0.926036i	−0.886349	+	0.463018i	$0.846767\pi$
$822$	−45.3409	−	0.682697i	−1.58145	−	0.0238118i
$823$	−2.67621	+	4.63533i	−0.0932867	+	0.161577i	−0.908892	−	0.417031i	$-0.863071\pi$
$823$	−2.67621	+	4.63533i	−0.0932867	+	0.161577i	0.815606	+	0.578608i	$0.196404\pi$
$824$	37.0807			1.29177
$825$	5.24169	+	9.40302i	0.182492	+	0.327371i
$826$	−0.656546	+	1.13717i	−0.0228442	+	0.0395673i
$827$	−32.7839	+	18.9278i	−1.14001	+	0.658184i	−0.946433	−	0.322901i	$-0.895342\pi$
$827$	−32.7839	+	18.9278i	−1.14001	+	0.658184i	−0.193576	+	0.981085i	$0.562009\pi$
$828$	12.1187	−	6.51836i	0.421154	−	0.226529i
$829$	−11.3673			−0.394801			−0.197400	−	0.980323i	$-0.563250\pi$
$829$	−11.3673			−0.394801			−0.197400	+	0.980323i	$0.563250\pi$
$830$	−32.2864	+	18.6406i	−1.12068	+	0.647024i
$831$	−21.6678	−	0.326252i	−0.751647	−	0.0113175i
$832$	23.5180	+	13.5781i	0.815339	+	0.470736i
$833$			50.0309i			1.73347i
$834$	11.0860	+	6.62500i	0.383876	+	0.229405i
$835$	10.6038	−	6.12213i	0.366961	−	0.211865i
$836$	−5.64956	+	9.78532i	−0.195394	+	0.338432i
$837$	−0.760182	+	16.8188i	−0.0262757	+	0.581343i
$838$	15.1901	+	8.77003i	0.524734	+	0.302956i
$839$	2.46904	−	1.42550i	0.0852409	−	0.0492138i	−0.456774	−	0.889583i	$-0.650995\pi$
$839$	2.46904	−	1.42550i	0.0852409	−	0.0492138i	0.542015	+	0.840369i	$0.317662\pi$
$840$	−0.0149671	+	0.994027i	−0.000516413	+	0.0342972i
$841$	−7.86677	+	13.6256i	−0.271268	+	0.469850i
$842$	23.8564			0.822147
$843$	−19.2698	−	34.5680i	−0.663688	−	1.19058i
$844$	5.52835	−	9.57538i	0.190294	−	0.329598i
$845$	19.8891	−	34.4490i	0.684207	−	1.18508i
$846$	0.603448	−	20.0342i	0.0207470	−	0.688792i
$847$			0.321018i			0.0110303i
$848$	−18.6464			−0.640318
$849$	13.4195	−	22.4556i	0.460557	−	0.770675i
$850$		−	18.5431i		−	0.636025i
$851$			1.22877i			0.0421217i
$852$	0.0456870	−	3.03427i	0.00156521	−	0.103952i
$853$	−8.09542			−0.277182			−0.138591	−	0.990350i	$-0.544257\pi$
$853$	−8.09542			−0.277182			−0.138591	+	0.990350i	$0.544257\pi$
$854$	0.764042	+	1.32336i	0.0261450	+	0.0452844i
$855$	21.5999	+	40.1578i	0.738700	+	1.37337i
$856$		−	19.4715i		−	0.665521i
$857$	−17.7125	+	30.6790i	−0.605049	+	1.04798i	0.386995	+	0.922082i	$0.373513\pi$
$857$	−17.7125	+	30.6790i	−0.605049	+	1.04798i	−0.992044	+	0.125894i	$0.959820\pi$
$858$	−48.4690	+	27.0189i	−1.65470	+	0.922410i
$859$	−50.3268			−1.71713			−0.858564	−	0.512706i	$-0.828643\pi$
$859$	−50.3268			−1.71713			−0.858564	+	0.512706i	$0.828643\pi$
$860$		−	3.73261i		−	0.127281i
$861$	0.566408	+	0.338487i	0.0193031	+	0.0115356i
$862$	−46.1733	−	26.6582i	−1.57267	−	0.907981i
$863$		−	16.2172i		−	0.552041i	−0.961152	−	0.276021i	$-0.910984\pi$
$863$		−	16.2172i		−	0.552041i	0.961152	−	0.276021i	$-0.0890158\pi$
$864$	14.4873	+	0.654799i	0.492866	+	0.0222767i
$865$	31.4637	−	18.1656i	1.06980	−	0.617648i
$866$	−0.403144	−	0.232755i	−0.0136994	−	0.00790935i
$867$	−59.2520	−	0.892158i	−2.01230	−	0.0302993i
$868$	0.0769401	+	0.133264i	0.00261152	+	0.00452328i
$869$	39.5448	+	22.8312i	1.34147	+	0.774496i
$870$	0.387245	−	25.7186i	0.0131288	−	0.871942i
$871$	−43.2662	−	5.78957i	−1.46602	−	0.196172i
$872$		−	2.83328i		−	0.0959469i
$873$	8.58084	+	5.30487i	0.290418	+	0.179543i
$874$			84.8846i			2.87126i
$875$	−0.706255	+	0.407756i	−0.0238758	+	0.0137847i
$876$	1.99964	−	3.34610i	0.0675615	−	0.113054i
$877$	15.3852	−	26.6480i	0.519522	−	0.899839i	−0.480221	−	0.877148i	$-0.659443\pi$
$877$	15.3852	−	26.6480i	0.519522	−	0.899839i	0.999743	−	0.0226907i	$-0.00722331\pi$
$878$	23.5344			0.794248
$879$	−46.0616	−	27.5265i	−1.55362	−	0.928447i
$880$	−23.2491	+	40.2686i	−0.783727	+	1.35745i
$881$	45.1236	−	26.0521i	1.52025	−	0.877718i	0.520537	−	0.853839i	$-0.325732\pi$
$881$	45.1236	−	26.0521i	1.52025	−	0.877718i	0.999715	−	0.0238790i	$-0.00760163\pi$
$882$	15.7230	+	29.2316i	0.529420	+	0.984279i
$883$	−6.37993	−	3.68346i	−0.214702	−	0.123958i	0.388793	−	0.921325i	$-0.372892\pi$
$883$	−6.37993	−	3.68346i	−0.214702	−	0.123958i	−0.603495	+	0.797367i	$0.706226\pi$
$884$	19.2546			0.647602
$885$	−0.592149	+	39.3272i	−0.0199049	+	1.32197i
$886$	28.7679	+	49.8275i	0.966476	+	1.67399i
$887$	−24.8208	−	14.3303i	−0.833402	−	0.481165i	0.0216142	−	0.999766i	$-0.493119\pi$
$887$	−24.8208	−	14.3303i	−0.833402	−	0.481165i	−0.855016	+	0.518602i	$0.826453\pi$
$888$	−0.284210	+	0.475584i	−0.00953747	+	0.0159596i
$889$		−	0.210357i		−	0.00705515i
$890$	−13.5040	+	7.79654i	−0.452655	+	0.261341i
$891$	18.8322	−	28.5057i	0.630901	−	0.954978i
$892$	−2.70555	+	4.68615i	−0.0905885	+	0.156904i
$893$	21.5699	+	12.4534i	0.721809	+	0.416737i
$894$	5.36764	+	3.20771i	0.179521	+	0.107282i
$895$	12.4579	+	21.5777i	0.416422	+	0.721264i
$896$	−1.11202	+	0.642022i	−0.0371498	+	0.0214485i
$897$	−43.0788	+	72.0861i	−1.43836	+	2.40688i
$898$	40.1432	+	23.1767i	1.33959	+	0.773415i
$899$	5.90071	+	10.2203i	0.196800	+	0.340867i
$900$	−1.17391	−	2.18249i	−0.0391302	−	0.0727496i
$901$	24.3058	−	14.0330i	0.809744	−	0.467506i
$902$	12.1562	+	21.0552i	0.404758	+	0.701061i
$903$	−0.227977	−	0.408966i	−0.00758660	−	0.0136095i
$904$	36.5505			1.21565
$905$	−37.9000			−1.25984
$906$	−8.55787	−	15.3519i	−0.284316	−	0.510032i
$907$	6.31128	+	10.9315i	0.209563	+	0.362973i	0.951577	−	0.307411i	$-0.0994627\pi$
$907$	6.31128	+	10.9315i	0.209563	+	0.362973i	−0.742014	+	0.670384i	$0.766129\pi$
$908$	5.56120	−	3.21076i	0.184555	−	0.106553i
$909$	36.8986	+	1.11142i	1.22385	+	0.0368634i
$910$	1.02339	+	1.77257i	0.0339251	+	0.0587600i
$911$	−31.5429	−	18.2113i	−1.04506	−	0.603367i	−0.123799	−	0.992307i	$-0.539508\pi$
$911$	−31.5429	−	18.2113i	−1.04506	−	0.603367i	−0.921263	+	0.388941i	$0.872841\pi$
$912$	−24.9229	+	41.7048i	−0.825279	+	1.38098i
$913$	−30.0606	+	17.3555i	−0.994859	+	0.574382i
$914$	−4.99543	−	8.65235i	−0.165234	−	0.286194i
$915$	39.2901	+	23.4799i	1.29889	+	0.776220i
$916$	−5.98139	−	3.45336i	−0.197631	−	0.114102i
$917$	−0.752006	+	1.30251i	−0.0248334	+	0.0430128i
$918$	−52.2408	+	27.0930i	−1.72420	+	0.894203i
$919$	−20.9296	+	12.0837i	−0.690403	+	0.398604i	−0.803763	−	0.594950i	$-0.797172\pi$
$919$	−20.9296	+	12.0837i	−0.690403	+	0.398604i	0.113360	+	0.993554i	$0.463839\pi$
$920$			55.4338i			1.82760i
$921$	15.9593	−	26.7056i	0.525877	−	0.879979i
$922$	42.6318	+	24.6135i	1.40400	+	0.810602i
$923$	9.25976	+	16.0384i	0.304789	+	0.527910i
$924$	0.00470122	−	0.312229i	0.000154659	−	0.0102716i
$925$	0.221292			0.00727603
$926$	1.46687	+	0.846897i	0.0482043	+	0.0278308i
$927$	−24.7164	+	39.9798i	−0.811793	+	1.31311i
$928$	8.80350	−	5.08271i	0.288989	−	0.166848i
$929$	23.4901	−	40.6861i	0.770686	−	1.33487i	−0.166502	−	0.986041i	$-0.553247\pi$
$929$	23.4901	−	40.6861i	0.770686	−	1.33487i	0.937188	−	0.348825i	$-0.113419\pi$
$930$	19.6411	+	11.7376i	0.644056	+	0.384889i
$931$	−41.2457			−1.35177
$932$	3.93292	−	6.81201i	0.128827	−	0.223135i
$933$	10.8893	−	18.2217i	0.356500	−	0.596550i
$934$	48.0071	−	27.7169i	1.57084	−	0.906924i
$935$		−	69.9877i		−	2.28884i
$936$	−33.3465	+	17.9363i	−1.08997	+	0.586266i
$937$			19.8290i			0.647785i	0.946094	+	0.323893i	$0.104992\pi$
$937$			19.8290i			0.647785i	−0.946094	+	0.323893i	$0.895008\pi$
$938$	0.744378	−	0.965840i	0.0243048	−	0.0315358i
$939$	−0.452115	+	30.0269i	−0.0147542	+	0.979891i
$940$	−4.75216	−	2.74366i	−0.154999	−	0.0894884i
$941$	−2.25804	−	3.91104i	−0.0736100	−	0.127496i	0.826871	−	0.562392i	$-0.190119\pi$
$941$	−2.25804	−	3.91104i	−0.0736100	−	0.127496i	−0.900481	+	0.434895i	$0.856785\pi$
$942$	58.9723	+	0.887946i	1.92142	+	0.0289308i
$943$	31.8638	+	18.3966i	1.03763	+	0.599075i
$944$	−36.2928	+	20.9537i	−1.18123	+	0.681984i
$945$	−1.06177	−	0.678714i	−0.0345393	−	0.0220786i
$946$		−	17.2519i		−	0.560906i
$947$	−0.859093	−	0.495997i	−0.0279168	−	0.0161178i	0.485977	−	0.873972i	$-0.338464\pi$
$947$	−0.859093	−	0.495997i	−0.0279168	−	0.0161178i	−0.513893	+	0.857854i	$0.671797\pi$
$948$	−9.02303	−	5.39218i	−0.293054	−	0.175130i
$949$			23.7890i			0.772223i
$950$	15.2871			0.495978
$951$	10.9321	−	6.09407i	0.354498	−	0.197614i
$952$	0.797170	−	1.38074i	0.0258364	−	0.0447500i
$953$		−	14.9187i		−	0.483263i	−0.970368	−	0.241631i	$-0.922318\pi$
$953$		−	14.9187i		−	0.483263i	0.970368	−	0.241631i	$-0.0776825\pi$
$954$	9.79111	−	15.8375i	0.316999	−	0.512759i
$955$	23.1724	+	40.1359i	0.749843	+	1.29877i
$956$	−7.58741			−0.245394
$957$	0.360548	−	23.9455i	0.0116548	−	0.774049i
$958$		−	24.2189i		−	0.782477i
$959$			1.55727i			0.0502869i
$960$	−11.6563	+	19.5052i	−0.376207	+	0.629527i
$961$	20.5018			0.661349
$962$			1.14068i			0.0367769i
$963$	20.9938	+	12.9789i	0.676517	+	0.418238i
$964$	4.38367	−	7.59274i	0.141188	−	0.244546i
$965$	1.24095	−	2.14940i	0.0399477	−	0.0691915i
$966$	−1.14222	−	2.04902i	−0.0367504	−	0.0659263i
$967$	29.4622			0.947439			0.473719	−	0.880676i	$-0.342911\pi$
$967$	29.4622			0.947439			0.473719	+	0.880676i	$0.342911\pi$
$968$	−4.03548	+	6.98965i	−0.129705	+	0.224656i
$969$	1.10096	−	73.1194i	0.0353679	−	2.34893i
$970$	11.8736	−	6.85523i	0.381239	−	0.220108i
$971$	−40.7728	−	23.5402i	−1.30846	−	0.755441i	−0.326622	−	0.945155i	$-0.605910\pi$
$971$	−40.7728	−	23.5402i	−1.30846	−	0.755441i	−0.981839	+	0.189714i	$0.939244\pi$
$972$	−4.43345	+	6.49598i	−0.142203	+	0.208359i
$973$	0.221758	−	0.384096i	0.00710923	−	0.0123136i
$974$	9.20117	−	5.31230i	0.294824	−	0.170217i
$975$	12.9821	+	7.75816i	0.415761	+	0.248460i
$976$			48.7688i			1.56105i
$977$	2.16454	+	1.24970i	0.0692498	+	0.0399814i	0.534225	−	0.845342i	$-0.320603\pi$
$977$	2.16454	+	1.24970i	0.0692498	+	0.0399814i	−0.464975	+	0.885324i	$0.653937\pi$
$978$	−9.28197	−	0.139759i	−0.296805	−	0.00446899i
$979$	−12.5730	+	7.25903i	−0.401835	+	0.232000i
$980$	9.08704			0.290275
$981$	3.05480	+	1.88854i	0.0975321	+	0.0602965i
$982$	−34.6236	+	19.9900i	−1.10488	+	0.637905i
$983$	21.9519	−	38.0218i	0.700157	−	1.21271i	−0.268254	−	0.963348i	$-0.586447\pi$
$983$	21.9519	−	38.0218i	0.700157	−	1.21271i	0.968411	−	0.249359i	$-0.0802199\pi$
$984$	8.07754	+	14.4902i	0.257502	+	0.461931i
$985$	−59.1293			−1.88402
$986$	−20.6253	+	35.7241i	−0.656843	+	1.13769i
$987$	−0.688249	−	0.0103630i	−0.0219072	−	0.000329857i
$988$			15.8736i			0.505006i
$989$	−13.0540	−	22.6102i	−0.415093	−	0.718963i
$990$	−21.9947	−	40.8918i	−0.699037	−	1.29963i
$991$		−	28.3582i		−	0.900828i	−0.892820	−	0.450414i	$-0.851276\pi$
$991$		−	28.3582i		−	0.900828i	0.892820	−	0.450414i	$-0.148724\pi$
$992$			9.04282i			0.287110i
$993$	14.7438	+	8.81094i	0.467881	+	0.279607i
$994$	−0.517338			−0.0164090
$995$	30.1514	−	52.2238i	0.955865	−	1.65561i
$996$	6.97928	−	3.89058i	0.221147	−	0.123278i
$997$	12.9418	−	22.4158i	0.409870	−	0.709916i	−0.585005	−	0.811030i	$-0.698907\pi$
$997$	12.9418	−	22.4158i	0.409870	−	0.709916i	0.994875	+	0.101114i	$0.0322407\pi$
$998$	−52.1812	−	30.1268i	−1.65177	−	0.953648i
$999$	−0.323325	−	0.623435i	−0.0102296	−	0.0197246i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.t.a.164.18	yes	132
9.5	odd	6		603.2.k.a.365.18	yes	132
67.38	odd	6		603.2.k.a.38.18	✓	132
603.239	even	6	inner	603.2.t.a.239.18	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
603.2.k.a.38.18	✓	132	67.38	odd	6
603.2.k.a.365.18	yes	132	9.5	odd	6
603.2.t.a.164.18	yes	132	1.1	even	1	trivial
603.2.t.a.239.18	yes	132	603.239	even	6	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:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.58257 q^{2} +(-0.843344 - 1.51287i) q^{3} +0.504520 q^{4} +(-1.28815 - 2.23114i) q^{5} +(1.33465 + 2.39422i) q^{6} +(0.0815227 - 0.0470672i) q^{7} +2.36670 q^{8} +(-1.57754 + 2.55174i) q^{9} +O(q^{10})\)	\(q-1.58257 q^{2} +(-0.843344 - 1.51287i) q^{3} +0.504520 q^{4} +(-1.28815 - 2.23114i) q^{5} +(1.33465 + 2.39422i) q^{6} +(0.0815227 - 0.0470672i) q^{7} +2.36670 q^{8} +(-1.57754 + 2.55174i) q^{9} +(2.03858 + 3.53093i) q^{10} +(1.89804 + 3.28750i) q^{11} +(-0.425484 - 0.763272i) q^{12} +(4.61845 + 2.66646i) q^{13} +(-0.129015 + 0.0744869i) q^{14} +(-2.28907 + 3.83042i) q^{15} -4.75450 q^{16} +(6.19756 - 3.57817i) q^{17} +(2.49656 - 4.03830i) q^{18} +(2.94986 + 5.10930i) q^{19} +(-0.649897 - 1.12565i) q^{20} +(-0.139958 - 0.0836393i) q^{21} +(-3.00378 - 5.20269i) q^{22} +(-7.87347 - 4.54575i) q^{23} +(-1.99594 - 3.58050i) q^{24} +(-0.818655 + 1.41795i) q^{25} +(-7.30901 - 4.21986i) q^{26} +(5.19085 + 0.234618i) q^{27} +(0.0411298 - 0.0237463i) q^{28} +(3.15434 - 1.82116i) q^{29} +(3.62260 - 6.06190i) q^{30} +3.24009i q^{31} +2.79092 q^{32} +(3.37285 - 5.64398i) q^{33} +(-9.80806 + 5.66269i) q^{34} +(-0.210027 - 0.121259i) q^{35} +(-0.795901 + 1.28740i) q^{36} +(-0.0675779 - 0.117048i) q^{37} +(-4.66835 - 8.08582i) q^{38} +(0.139064 - 9.23585i) q^{39} +(-3.04866 - 5.28043i) q^{40} -4.04698 q^{41} +(0.221493 + 0.132365i) q^{42} +(2.48696 + 1.43585i) q^{43} +(0.957599 + 1.65861i) q^{44} +(7.72539 + 0.232695i) q^{45} +(12.4603 + 7.19396i) q^{46} +(3.65609 - 2.11085i) q^{47} +(4.00968 + 7.19293i) q^{48} +(-3.49557 + 6.05450i) q^{49} +(1.29558 - 2.24400i) q^{50} +(-10.6400 - 6.35847i) q^{51} +(2.33010 + 1.34528i) q^{52} +3.92183 q^{53} +(-8.21488 - 0.371298i) q^{54} +(4.88991 - 8.46958i) q^{55} +(0.192940 - 0.111394i) q^{56} +(5.24196 - 8.77165i) q^{57} +(-4.99195 + 2.88211i) q^{58} +(7.63336 - 4.40712i) q^{59} +(-1.15488 + 1.93252i) q^{60} -10.2574i q^{61} -5.12766i q^{62} +(-0.00850235 + 0.282275i) q^{63} +5.09218 q^{64} -13.7392i q^{65} +(-5.33777 + 8.93198i) q^{66} +(-7.56891 + 3.11634i) q^{67} +(3.12679 - 1.80526i) q^{68} +(-0.237075 + 15.7452i) q^{69} +(0.332381 + 0.191901i) q^{70} +(3.00743 + 1.73634i) q^{71} +(-3.73356 + 6.03919i) q^{72} +(2.23039 + 3.86315i) q^{73} +(0.106947 + 0.185237i) q^{74} +(2.83558 + 0.0426953i) q^{75} +(1.48826 + 2.57774i) q^{76} +(0.309467 + 0.178671i) q^{77} +(-0.220078 + 14.6164i) q^{78} +(10.4173 - 6.01442i) q^{79} +(6.12450 + 10.6080i) q^{80} +(-4.02273 - 8.05094i) q^{81} +6.40462 q^{82} +9.14389i q^{83} +(-0.0706116 - 0.0421977i) q^{84} +(-15.9668 - 9.21842i) q^{85} +(-3.93578 - 2.27233i) q^{86} +(-5.41537 - 3.23624i) q^{87} +(4.49209 + 7.78052i) q^{88} +3.82449i q^{89} +(-12.2260 - 0.368256i) q^{90} +0.502011 q^{91} +(-3.97232 - 2.29342i) q^{92} +(4.90183 - 2.73251i) q^{93} +(-5.78601 + 3.34056i) q^{94} +(7.59971 - 13.1631i) q^{95} +(-2.35371 - 4.22229i) q^{96} -3.36275i q^{97} +(5.53197 - 9.58166i) q^{98} +(-11.3831 - 0.342867i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 6 q^{2} + 3 q^{3} + 126 q^{4} - 3 q^{5} - 2 q^{6} - 6 q^{7} - 12 q^{8} - 7 q^{9}+O(q^{10}) \) 132 * q - 6 * q^2 + 3 * q^3 + 126 * q^4 - 3 * q^5 - 2 * q^6 - 6 * q^7 - 12 * q^8 - 7 * q^9	\( 132 q - 6 q^{2} + 3 q^{3} + 126 q^{4} - 3 q^{5} - 2 q^{6} - 6 q^{7} - 12 q^{8} - 7 q^{9} - 3 q^{11} - 3 q^{12} + 4 q^{15} + 114 q^{16} - 9 q^{17} - 6 q^{18} - 4 q^{19} - 15 q^{20} - 9 q^{21} - 3 q^{23} - 11 q^{24} - 57 q^{25} - 36 q^{26} - 24 q^{28} - 21 q^{29} - 12 q^{30} + 30 q^{32} + 17 q^{33} - 12 q^{34} - 15 q^{35} + 8 q^{36} - 4 q^{37} - 31 q^{39} - 12 q^{40} + 6 q^{41} - 42 q^{42} - 3 q^{43} - 6 q^{44} + 9 q^{45} - 24 q^{46} - 12 q^{47} + 24 q^{48} + 60 q^{49} - 12 q^{50} - 24 q^{51} - 18 q^{52} + 60 q^{53} + 29 q^{54} - 18 q^{56} + 51 q^{57} - 12 q^{58} + 12 q^{59} + 65 q^{60} + 15 q^{63} + 84 q^{64} + 30 q^{66} - 5 q^{67} - 39 q^{68} + 12 q^{69} - 45 q^{70} + 30 q^{71} - 39 q^{72} + 14 q^{73} + 15 q^{74} - 24 q^{75} - 7 q^{76} + 69 q^{77} - 90 q^{78} - 3 q^{79} - 18 q^{80} - 3 q^{81} - 24 q^{82} - 51 q^{84} - 18 q^{85} - 6 q^{86} - 42 q^{87} + 15 q^{88} + 85 q^{90} + 42 q^{91} - 12 q^{92} - q^{93} + 6 q^{94} + 12 q^{95} - 57 q^{96} - 21 q^{98} - 24 q^{99}+O(q^{100}) \) 132 * q - 6 * q^2 + 3 * q^3 + 126 * q^4 - 3 * q^5 - 2 * q^6 - 6 * q^7 - 12 * q^8 - 7 * q^9 - 3 * q^11 - 3 * q^12 + 4 * q^15 + 114 * q^16 - 9 * q^17 - 6 * q^18 - 4 * q^19 - 15 * q^20 - 9 * q^21 - 3 * q^23 - 11 * q^24 - 57 * q^25 - 36 * q^26 - 24 * q^28 - 21 * q^29 - 12 * q^30 + 30 * q^32 + 17 * q^33 - 12 * q^34 - 15 * q^35 + 8 * q^36 - 4 * q^37 - 31 * q^39 - 12 * q^40 + 6 * q^41 - 42 * q^42 - 3 * q^43 - 6 * q^44 + 9 * q^45 - 24 * q^46 - 12 * q^47 + 24 * q^48 + 60 * q^49 - 12 * q^50 - 24 * q^51 - 18 * q^52 + 60 * q^53 + 29 * q^54 - 18 * q^56 + 51 * q^57 - 12 * q^58 + 12 * q^59 + 65 * q^60 + 15 * q^63 + 84 * q^64 + 30 * q^66 - 5 * q^67 - 39 * q^68 + 12 * q^69 - 45 * q^70 + 30 * q^71 - 39 * q^72 + 14 * q^73 + 15 * q^74 - 24 * q^75 - 7 * q^76 + 69 * q^77 - 90 * q^78 - 3 * q^79 - 18 * q^80 - 3 * q^81 - 24 * q^82 - 51 * q^84 - 18 * q^85 - 6 * q^86 - 42 * q^87 + 15 * q^88 + 85 * q^90 + 42 * q^91 - 12 * q^92 - q^93 + 6 * q^94 + 12 * q^95 - 57 * q^96 - 21 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more