LMFDB - Embedded newform 180.2.q.a.11.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,2,Mod(11,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 0]))

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

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

chi := DirichletCharacter("180.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	180.q (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:	$1.43730723638$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.12
Character	$\chi$	$=$	180.11
Dual form			180.2.q.a.131.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.145547 - 1.40670i) q^{2} +(1.30449 - 1.13944i) q^{3} +(-1.95763 + 0.409483i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.79271 - 1.66919i) q^{6} +(-2.51585 - 1.45253i) q^{7} +(0.860949 + 2.69421i) q^{8} +(0.403372 - 2.97276i) q^{9} +O(q^{10})$	\(q+(-0.145547 - 1.40670i) q^{2} +(1.30449 - 1.13944i) q^{3} +(-1.95763 + 0.409483i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.79271 - 1.66919i) q^{6} +(-2.51585 - 1.45253i) q^{7} +(0.860949 + 2.69421i) q^{8} +(0.403372 - 2.97276i) q^{9} +(-0.829399 - 1.14547i) q^{10} +(1.36420 - 2.36286i) q^{11} +(-2.08713 + 2.76476i) q^{12} +(0.923842 + 1.60014i) q^{13} +(-1.67710 + 3.75046i) q^{14} +(0.560001 - 1.63902i) q^{15} +(3.66465 - 1.60323i) q^{16} +6.64799i q^{17} +(-4.24050 - 0.134750i) q^{18} -4.90413i q^{19} +(-1.49062 + 1.33344i) q^{20} +(-4.93695 + 0.971846i) q^{21} +(-3.52240 - 1.57512i) q^{22} +(3.31748 + 5.74605i) q^{23} +(4.19298 + 2.53357i) q^{24} +(0.500000 - 0.866025i) q^{25} +(2.11646 - 1.53247i) q^{26} +(-2.86107 - 4.33754i) q^{27} +(5.51989 + 1.81331i) q^{28} +(4.89787 + 2.82779i) q^{29} +(-2.38713 - 0.549201i) q^{30} +(-4.52751 + 2.61396i) q^{31} +(-2.78865 - 4.92173i) q^{32} +(-0.912750 - 4.63674i) q^{33} +(9.35175 - 0.967594i) q^{34} -2.90505 q^{35} +(0.427639 + 5.98474i) q^{36} -0.280524 q^{37} +(-6.89866 + 0.713781i) q^{38} +(3.02840 + 1.03470i) q^{39} +(2.09271 + 1.90278i) q^{40} +(7.31326 - 4.22231i) q^{41} +(2.08566 + 6.80338i) q^{42} +(6.19728 + 3.57800i) q^{43} +(-1.70305 + 5.18423i) q^{44} +(-1.13705 - 2.77617i) q^{45} +(7.60014 - 5.50304i) q^{46} +(-0.743026 + 1.28696i) q^{47} +(2.95370 - 6.26703i) q^{48} +(0.719659 + 1.24649i) q^{49} +(-1.29101 - 0.577305i) q^{50} +(7.57495 + 8.67221i) q^{51} +(-2.46377 - 2.75419i) q^{52} -4.62498i q^{53} +(-5.68522 + 4.65600i) q^{54} -2.72840i q^{55} +(1.74739 - 8.02877i) q^{56} +(-5.58794 - 6.39738i) q^{57} +(3.26499 - 7.30143i) q^{58} +(2.56148 + 4.43662i) q^{59} +(-0.425124 + 3.43792i) q^{60} +(-5.61584 + 9.72691i) q^{61} +(4.33603 + 5.98842i) q^{62} +(-5.33283 + 6.89310i) q^{63} +(-6.51754 + 4.63915i) q^{64} +(1.60014 + 0.923842i) q^{65} +(-6.38967 + 1.95883i) q^{66} +(-1.48347 + 0.856481i) q^{67} +(-2.72224 - 13.0143i) q^{68} +(10.8749 + 3.71559i) q^{69} +(0.422821 + 4.08655i) q^{70} -5.25318 q^{71} +(8.35652 - 1.47262i) q^{72} -9.36719 q^{73} +(0.0408294 + 0.394614i) q^{74} +(-0.334537 - 1.69944i) q^{75} +(2.00816 + 9.60049i) q^{76} +(-6.86423 + 3.96307i) q^{77} +(1.01475 - 4.41066i) q^{78} +(-7.08892 - 4.09279i) q^{79} +(2.37206 - 3.22076i) q^{80} +(-8.67458 - 2.39826i) q^{81} +(-7.00396 - 9.67304i) q^{82} +(-4.57754 + 7.92854i) q^{83} +(9.26678 - 3.92411i) q^{84} +(3.32399 + 5.75733i) q^{85} +(4.13119 - 9.23851i) q^{86} +(9.61129 - 1.89200i) q^{87} +(7.54055 + 1.64114i) q^{88} -14.8298i q^{89} +(-3.73976 + 2.00355i) q^{90} -5.36761i q^{91} +(-8.84732 - 9.89020i) q^{92} +(-2.92764 + 8.56869i) q^{93} +(1.91852 + 0.857905i) q^{94} +(-2.45207 - 4.24710i) q^{95} +(-9.24576 - 3.24284i) q^{96} +(5.94298 - 10.2935i) q^{97} +(1.64869 - 1.19377i) q^{98} +(-6.47394 - 5.00855i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{6} + 4 q^{9}+O(q^{10}) $ 48 * q + 6 * q^6 + 4 * q^9	$ 48 q + 6 q^{6} + 4 q^{9} - 22 q^{12} - 30 q^{14} - 16 q^{18} - 4 q^{21} - 28 q^{24} + 24 q^{25} - 12 q^{29} + 16 q^{30} - 44 q^{33} - 6 q^{34} + 42 q^{36} + 60 q^{38} - 6 q^{40} - 60 q^{41} - 18 q^{42} - 8 q^{45} - 12 q^{46} - 12 q^{48} + 24 q^{49} - 18 q^{52} - 32 q^{54} - 42 q^{56} - 12 q^{57} - 18 q^{58} + 14 q^{60} - 48 q^{64} + 16 q^{66} + 48 q^{68} + 36 q^{69} + 60 q^{72} - 24 q^{73} + 84 q^{74} + 6 q^{76} + 48 q^{77} + 38 q^{78} - 36 q^{82} + 50 q^{84} - 54 q^{86} - 18 q^{90} + 60 q^{92} - 32 q^{93} + 18 q^{94} - 18 q^{96} - 12 q^{97}+O(q^{100}) $ 48 * q + 6 * q^6 + 4 * q^9 - 22 * q^12 - 30 * q^14 - 16 * q^18 - 4 * q^21 - 28 * q^24 + 24 * q^25 - 12 * q^29 + 16 * q^30 - 44 * q^33 - 6 * q^34 + 42 * q^36 + 60 * q^38 - 6 * q^40 - 60 * q^41 - 18 * q^42 - 8 * q^45 - 12 * q^46 - 12 * q^48 + 24 * q^49 - 18 * q^52 - 32 * q^54 - 42 * q^56 - 12 * q^57 - 18 * q^58 + 14 * q^60 - 48 * q^64 + 16 * q^66 + 48 * q^68 + 36 * q^69 + 60 * q^72 - 24 * q^73 + 84 * q^74 + 6 * q^76 + 48 * q^77 + 38 * q^78 - 36 * q^82 + 50 * q^84 - 54 * q^86 - 18 * q^90 + 60 * q^92 - 32 * q^93 + 18 * q^94 - 18 * q^96 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.145547	−	1.40670i	−0.102917	−	0.994690i
$2$	−0.145547	−	1.40670i	−0.102917	−	0.994690i
$3$	1.30449	−	1.13944i	0.753146	−	0.657854i
$3$	1.30449	−	1.13944i	0.753146	−	0.657854i
$4$	−1.95763	+	0.409483i	−0.978816	+	0.204741i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$	−1.79271	−	1.66919i	−0.731872	−	0.681442i
$7$	−2.51585	−	1.45253i	−0.950901	−	0.549003i	−0.0575403	−	0.998343i	$-0.518326\pi$
$7$	−2.51585	−	1.45253i	−0.950901	−	0.549003i	−0.893361	+	0.449340i	$0.851659\pi$
$8$	0.860949	+	2.69421i	0.304391	+	0.952547i
$9$	0.403372	−	2.97276i	0.134457	−	0.990919i
$10$	−0.829399	−	1.14547i	−0.262279	−	0.362229i
$11$	1.36420	−	2.36286i	0.411322	−	0.712430i	−0.583713	−	0.811960i	$-0.698401\pi$
$11$	1.36420	−	2.36286i	0.411322	−	0.712430i	0.995035	+	0.0995303i	$0.0317340\pi$
$12$	−2.08713	+	2.76476i	−0.602501	+	0.798118i
$13$	0.923842	+	1.60014i	0.256228	+	0.443799i	0.965228	−	0.261409i	$-0.0841870\pi$
$13$	0.923842	+	1.60014i	0.256228	+	0.443799i	−0.709001	+	0.705208i	$0.750854\pi$
$14$	−1.67710	+	3.75046i	−0.448224	+	1.00235i
$15$	0.560001	−	1.63902i	0.144592	−	0.423194i
$16$	3.66465	−	1.60323i	0.916162	−	0.400808i
$17$			6.64799i			1.61237i	0.591661	+	0.806187i	$0.298472\pi$
$17$			6.64799i			1.61237i	−0.591661	+	0.806187i	$0.701528\pi$
$18$	−4.24050	−	0.134750i	−0.999495	−	0.0317608i
$19$		−	4.90413i		−	1.12509i	−0.826768	−	0.562543i	$-0.809823\pi$
$19$		−	4.90413i		−	1.12509i	0.826768	−	0.562543i	$-0.190177\pi$
$20$	−1.49062	+	1.33344i	−0.333312	+	0.298166i
$21$	−4.93695	+	0.971846i	−1.07733	+	0.212074i
$22$	−3.52240	−	1.57512i	−0.750979	−	0.335816i
$23$	3.31748	+	5.74605i	0.691743	+	1.19813i	0.971266	+	0.237995i	$0.0764902\pi$
$23$	3.31748	+	5.74605i	0.691743	+	1.19813i	−0.279523	+	0.960139i	$0.590176\pi$
$24$	4.19298	+	2.53357i	0.855888	+	0.517162i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	2.11646	−	1.53247i	0.415072	−	0.300542i
$27$	−2.86107	−	4.33754i	−0.550614	−	0.834760i
$28$	5.51989	+	1.81331i	1.04316	+	0.342684i
$29$	4.89787	+	2.82779i	0.909512	+	0.525107i	0.880274	−	0.474465i	$-0.157359\pi$
$29$	4.89787	+	2.82779i	0.909512	+	0.525107i	0.0292380	+	0.999572i	$0.490692\pi$
$30$	−2.38713	−	0.549201i	−0.435828	−	0.100270i
$31$	−4.52751	+	2.61396i	−0.813165	+	0.469481i	−0.848054	−	0.529910i	$-0.822226\pi$
$31$	−4.52751	+	2.61396i	−0.813165	+	0.469481i	0.0348886	+	0.999391i	$0.488892\pi$
$32$	−2.78865	−	4.92173i	−0.492969	−	0.870047i
$33$	−0.912750	−	4.63674i	−0.158889	−	0.807153i
$34$	9.35175	−	0.967594i	1.60381	−	0.165941i
$35$	−2.90505			−0.491043
$36$	0.427639	+	5.98474i	0.0712732	+	0.997457i
$37$	−0.280524			−0.0461178			−0.0230589	−	0.999734i	$-0.507341\pi$
$37$	−0.280524			−0.0461178			−0.0230589	+	0.999734i	$0.507341\pi$
$38$	−6.89866	+	0.713781i	−1.11911	+	0.115791i
$39$	3.02840	+	1.03470i	0.484932	+	0.165685i
$40$	2.09271	+	1.90278i	0.330886	+	0.300856i
$41$	7.31326	−	4.22231i	1.14214	−	0.659414i	0.195179	−	0.980768i	$-0.437471\pi$
$41$	7.31326	−	4.22231i	1.14214	−	0.659414i	0.946959	+	0.321354i	$0.104138\pi$
$42$	2.08566	+	6.80338i	0.321824	+	1.04978i
$43$	6.19728	+	3.57800i	0.945076	+	0.545640i	0.891548	−	0.452926i	$-0.149620\pi$
$43$	6.19728	+	3.57800i	0.945076	+	0.545640i	0.0535284	+	0.998566i	$0.482953\pi$
$44$	−1.70305	+	5.18423i	−0.256744	+	0.781552i
$45$	−1.13705	−	2.77617i	−0.169501	−	0.413847i
$46$	7.60014	−	5.50304i	1.12058	−	0.811378i
$47$	−0.743026	+	1.28696i	−0.108381	+	0.187722i	−0.915115	−	0.403194i	$-0.867900\pi$
$47$	−0.743026	+	1.28696i	−0.108381	+	0.187722i	0.806733	+	0.590916i	$0.201233\pi$
$48$	2.95370	−	6.26703i	0.426330	−	0.904568i
$49$	0.719659	+	1.24649i	0.102808	+	0.178069i
$50$	−1.29101	−	0.577305i	−0.182577	−	0.0816432i
$51$	7.57495	+	8.67221i	1.06071	+	1.21435i
$52$	−2.46377	−	2.75419i	−0.341664	−	0.381937i
$53$		−	4.62498i		−	0.635290i	−0.948210	−	0.317645i	$-0.897108\pi$
$53$		−	4.62498i		−	0.635290i	0.948210	−	0.317645i	$-0.102892\pi$
$54$	−5.68522	+	4.65600i	−0.773660	+	0.633601i
$55$		−	2.72840i		−	0.367897i
$56$	1.74739	−	8.02877i	0.233505	−	1.07289i
$57$	−5.58794	−	6.39738i	−0.740141	−	0.847353i
$58$	3.26499	−	7.30143i	0.428714	−	0.958725i
$59$	2.56148	+	4.43662i	0.333477	+	0.577599i	0.983191	−	0.182580i	$-0.0584448\pi$
$59$	2.56148	+	4.43662i	0.333477	+	0.577599i	−0.649714	+	0.760178i	$0.725111\pi$
$60$	−0.425124	+	3.43792i	−0.0548832	+	0.443833i
$61$	−5.61584	+	9.72691i	−0.719034	+	1.24540i	0.242349	+	0.970189i	$0.422082\pi$
$61$	−5.61584	+	9.72691i	−0.719034	+	1.24540i	−0.961383	+	0.275214i	$0.911251\pi$
$62$	4.33603	+	5.98842i	0.550677	+	0.760530i
$63$	−5.33283	+	6.89310i	−0.671873	+	0.868449i
$64$	−6.51754	+	4.63915i	−0.814692	+	0.579894i
$65$	1.60014	+	0.923842i	0.198473	+	0.114588i
$66$	−6.38967	+	1.95883i	−0.786514	+	0.241116i
$67$	−1.48347	+	0.856481i	−0.181235	+	0.104636i	−0.587873	−	0.808954i	$-0.700034\pi$
$67$	−1.48347	+	0.856481i	−0.181235	+	0.104636i	0.406638	+	0.913589i	$0.366701\pi$
$68$	−2.72224	−	13.0143i	−0.330120	−	1.57822i
$69$	10.8749	+	3.71559i	1.30918	+	0.447304i
$70$	0.422821	+	4.08655i	0.0505368	+	0.488436i
$71$	−5.25318			−0.623438			−0.311719	−	0.950174i	$-0.600905\pi$
$71$	−5.25318			−0.623438			−0.311719	+	0.950174i	$0.600905\pi$
$72$	8.35652	−	1.47262i	0.984825	−	0.173550i
$73$	−9.36719			−1.09635			−0.548173	−	0.836365i	$-0.684677\pi$
$73$	−9.36719			−1.09635			−0.548173	+	0.836365i	$0.684677\pi$
$74$	0.0408294	+	0.394614i	0.00474632	+	0.0458730i
$75$	−0.334537	−	1.69944i	−0.0386290	−	0.196234i
$76$	2.00816	+	9.60049i	0.230352	+	1.10125i
$77$	−6.86423	+	3.96307i	−0.782252	+	0.451633i
$78$	1.01475	−	4.41066i	0.114898	−	0.499409i
$79$	−7.08892	−	4.09279i	−0.797566	−	0.460475i	0.0450533	−	0.998985i	$-0.485654\pi$
$79$	−7.08892	−	4.09279i	−0.797566	−	0.460475i	−0.842619	+	0.538510i	$0.818988\pi$
$80$	2.37206	−	3.22076i	0.265204	−	0.360092i
$81$	−8.67458	−	2.39826i	−0.963842	−	0.266473i
$82$	−7.00396	−	9.67304i	−0.773458	−	1.06821i
$83$	−4.57754	+	7.92854i	−0.502451	+	0.870270i	0.497545	+	0.867438i	$0.334235\pi$
$83$	−4.57754	+	7.92854i	−0.502451	+	0.870270i	−0.999996	+	0.00283198i	$0.999099\pi$
$84$	9.26678	−	3.92411i	1.01109	−	0.428156i
$85$	3.32399	+	5.75733i	0.360538	+	0.624470i
$86$	4.13119	−	9.23851i	0.445478	−	0.996214i
$87$	9.61129	−	1.89200i	1.03044	−	0.202844i
$88$	7.54055	+	1.64114i	0.803826	+	0.174946i
$89$		−	14.8298i		−	1.57195i	−0.618255	−	0.785977i	$-0.712160\pi$
$89$		−	14.8298i		−	1.57195i	0.618255	−	0.785977i	$-0.287840\pi$
$90$	−3.73976	+	2.00355i	−0.394205	+	0.211193i
$91$		−	5.36761i		−	0.562679i
$92$	−8.84732	−	9.89020i	−0.922397	−	1.03112i
$93$	−2.92764	+	8.56869i	−0.303582	+	0.888532i
$94$	1.91852	+	0.857905i	0.197880	+	0.0884861i
$95$	−2.45207	−	4.24710i	−0.251577	−	0.435744i
$96$	−9.24576	−	3.24284i	−0.943641	−	0.330971i
$97$	5.94298	−	10.2935i	0.603418	−	1.04515i	−0.388881	−	0.921288i	$-0.627138\pi$
$97$	5.94298	−	10.2935i	0.603418	−	1.04515i	0.992299	−	0.123863i	$-0.0395282\pi$
$98$	1.64869	−	1.19377i	0.166543	−	0.120589i
$99$	−6.47394	−	5.00855i	−0.650655	−	0.503378i
$100$	−0.624193	+	1.90010i	−0.0624193	+	0.190010i
$101$	−0.530412	−	0.306234i	−0.0527780	−	0.0304714i	0.473379	−	0.880859i	$-0.343034\pi$
$101$	−0.530412	−	0.306234i	−0.0527780	−	0.0304714i	−0.526157	+	0.850388i	$0.676368\pi$
$102$	11.0967	−	11.9179i	1.09874	−	1.18005i
$103$	−2.65731	+	1.53420i	−0.261833	+	0.151169i	−0.625170	−	0.780488i	$-0.714970\pi$
$103$	−2.65731	+	1.53420i	−0.261833	+	0.151169i	0.363338	+	0.931658i	$0.381637\pi$
$104$	−3.51574	+	3.86666i	−0.344746	+	0.379158i
$105$	−3.78960	+	3.31012i	−0.369827	+	0.323034i
$106$	−6.50598	+	0.673152i	−0.631917	+	0.0653823i
$107$	−7.58586			−0.733352			−0.366676	−	0.930349i	$-0.619504\pi$
$107$	−7.58586			−0.733352			−0.366676	+	0.930349i	$0.619504\pi$
$108$	7.37708	+	7.31975i	0.709860	+	0.704343i
$109$	−14.2287			−1.36286			−0.681430	−	0.731883i	$-0.738642\pi$
$109$	−14.2287			−1.36286			−0.681430	+	0.731883i	$0.738642\pi$
$110$	−3.83805	+	0.397110i	−0.365944	+	0.0378630i
$111$	−0.365940	+	0.319639i	−0.0347335	+	0.0303388i
$112$	−11.5484	−	1.28950i	−1.09122	−	0.121846i
$113$	−8.61053	+	4.97129i	−0.810010	+	0.467660i	−0.846959	−	0.531658i	$-0.821569\pi$
$113$	−8.61053	+	4.97129i	−0.810010	+	0.467660i	0.0369493	+	0.999317i	$0.488236\pi$
$114$	−8.18591	+	8.79170i	−0.766681	+	0.823418i
$115$	5.74605	+	3.31748i	0.535822	+	0.309357i
$116$	−10.7462	−	3.53017i	−0.997756	−	0.327768i
$117$	5.12948	−	2.10091i	0.474221	−	0.194229i
$118$	5.86819	−	4.24898i	0.540211	−	0.391151i
$119$	9.65637	−	16.7253i	0.885198	−	1.53321i
$120$	4.89801	+	0.0976449i	0.447125	+	0.00891372i
$121$	1.77792	+	3.07945i	0.161629	+	0.279950i
$122$	14.5003	+	6.48410i	1.31279	+	0.587042i
$123$	4.72900	−	13.8409i	0.426399	−	1.24799i
$124$	7.79283	−	6.97111i	0.699817	−	0.626024i
$125$		−	1.00000i		−	0.0894427i
$126$	10.4727	+	6.49844i	0.932984	+	0.578927i
$127$			15.7476i			1.39738i	0.715426	+	0.698688i	$0.246233\pi$
$127$			15.7476i			1.39738i	−0.715426	+	0.698688i	$0.753767\pi$
$128$	7.47452	+	8.49303i	0.660661	+	0.750685i
$129$	12.1612	−	2.39395i	1.07073	−	0.210775i
$130$	1.06668	−	2.38539i	0.0935537	−	0.209212i
$131$	6.80703	+	11.7901i	0.594733	+	1.03011i	0.993584	+	0.113093i	$0.0360757\pi$
$131$	6.80703	+	11.7901i	0.594733	+	1.03011i	−0.398851	+	0.917016i	$0.630591\pi$
$132$	3.68549	+	8.70328i	0.320781	+	0.757523i
$133$	−7.12338	+	12.3381i	−0.617675	+	1.06984i
$134$	1.42073	+	1.96214i	0.122732	+	0.169503i
$135$	−4.64653	−	2.32588i	−0.399910	−	0.200180i
$136$	−17.9111	+	5.72357i	−1.53586	+	0.490792i
$137$	9.33516	+	5.38966i	0.797556	+	0.460469i	0.842616	−	0.538515i	$-0.181014\pi$
$137$	9.33516	+	5.38966i	0.797556	+	0.460469i	−0.0450597	+	0.998984i	$0.514348\pi$
$138$	3.64393	−	15.8385i	0.310192	−	1.34826i
$139$	−5.16154	+	2.98002i	−0.437796	+	0.252762i	−0.702662	−	0.711523i	$-0.748006\pi$
$139$	−5.16154	+	2.98002i	−0.437796	+	0.252762i	0.264866	+	0.964285i	$0.414672\pi$
$140$	5.68702	−	1.18957i	0.480641	−	0.100537i
$141$	0.497139	+	2.52545i	0.0418667	+	0.212681i
$142$	0.764585	+	7.38967i	0.0641625	+	0.620128i
$143$	5.04122			0.421568
$144$	−3.28781	−	11.5408i	−0.273984	−	0.961734i
$145$	5.65558			0.469670
$146$	1.36337	+	13.1769i	0.112833	+	1.09053i
$147$	2.35908	+	0.806020i	0.194573	+	0.0664794i
$148$	0.549163	−	0.114870i	0.0451409	−	0.00944223i
$149$	−1.12138	+	0.647431i	−0.0918673	+	0.0530396i	−0.545230	−	0.838287i	$-0.683558\pi$
$149$	−1.12138	+	0.647431i	−0.0918673	+	0.0530396i	0.453363	+	0.891326i	$0.350224\pi$
$150$	−2.34191	+	0.717942i	−0.191216	+	0.0586197i
$151$	6.19704	+	3.57786i	0.504308	+	0.291162i	0.730491	−	0.682923i	$-0.239291\pi$
$151$	6.19704	+	3.57786i	0.504308	+	0.291162i	−0.226183	+	0.974085i	$0.572625\pi$
$152$	13.2128	−	4.22221i	1.07170	−	0.342466i
$153$	19.7629	+	2.68161i	1.59773	+	0.216796i
$154$	6.57393	+	9.07913i	0.529742	+	0.731617i
$155$	−2.61396	+	4.52751i	−0.209958	+	0.363659i
$156$	−6.35218	−	0.785494i	−0.508582	−	0.0628899i
$157$	−7.85293	−	13.6017i	−0.626732	−	1.08553i	−0.988203	−	0.153149i	$-0.951059\pi$
$157$	−7.85293	−	13.6017i	−0.626732	−	1.08553i	0.361471	−	0.932383i	$-0.382275\pi$
$158$	−4.72557	+	10.5677i	−0.375947	+	0.840722i
$159$	−5.26987	−	6.03323i	−0.417928	−	0.478466i
$160$	−4.87591	−	2.86802i	−0.385474	−	0.226737i
$161$		−	19.2749i		−	1.51908i
$162$	−2.11108	+	12.5516i	−0.165862	+	0.986149i
$163$		−	5.63727i		−	0.441545i	−0.975325	−	0.220772i	$-0.929142\pi$
$163$		−	5.63727i		−	0.441545i	0.975325	−	0.220772i	$-0.0708578\pi$
$164$	−12.5877	+	11.2604i	−0.982934	+	0.879288i
$165$	−3.10883	−	3.55916i	−0.242022	−	0.277080i
$166$	11.8194	+	5.28527i	0.917360	+	0.410217i
$167$	0.886283	+	1.53509i	0.0685826	+	0.118789i	0.898278	−	0.439428i	$-0.144819\pi$
$167$	0.886283	+	1.53509i	0.0685826	+	0.118789i	−0.829695	+	0.558217i	$0.811486\pi$
$168$	−6.86882	−	12.4645i	−0.529941	−	0.961655i
$169$	4.79303	−	8.30178i	0.368695	−	0.638598i
$170$	7.61506	−	5.51384i	0.584048	−	0.422892i
$171$	−14.5788	−	1.97819i	−1.11487	−	0.151276i
$172$	−13.5971	−	4.46673i	−1.03677	−	0.340585i
$173$	3.35901	+	1.93932i	0.255380	+	0.147444i	0.622225	−	0.782838i	$-0.286229\pi$
$173$	3.35901	+	1.93932i	0.255380	+	0.147444i	−0.366845	+	0.930282i	$0.619562\pi$
$174$	−4.06038	−	13.2449i	−0.307816	−	1.00409i
$175$	−2.51585	+	1.45253i	−0.190180	+	0.109801i
$176$	1.21109	−	10.8462i	0.0912892	−	0.817562i
$177$	8.39666	+	2.86887i	0.631132	+	0.215637i
$178$	−20.8611	+	2.15843i	−1.56361	+	0.161781i
$179$	−1.59068			−0.118893			−0.0594466	−	0.998231i	$-0.518934\pi$
$179$	−1.59068			−0.118893			−0.0594466	+	0.998231i	$0.518934\pi$
$180$	3.36272	+	4.96912i	0.250642	+	0.370376i
$181$	21.6836			1.61173			0.805866	−	0.592098i	$-0.201700\pi$
$181$	21.6836			1.61173			0.805866	+	0.592098i	$0.201700\pi$
$182$	−7.55064	+	0.781240i	−0.559691	+	0.0579093i
$183$	3.75741	+	19.0875i	0.277756	+	1.41099i
$184$	−12.6249	+	13.8850i	−0.930718	+	1.02362i
$185$	−0.242941	+	0.140262i	−0.0178614	+	0.0103123i
$186$	12.4797	+	2.87118i	0.915057	+	0.210525i
$187$	15.7083	+	9.06918i	1.14870	+	0.663204i
$188$	0.927584	−	2.82365i	0.0676510	−	0.205936i
$189$	0.897636	+	15.0684i	0.0652934	+	1.09606i
$190$	−5.61753	+	4.06748i	−0.407538	+	0.295086i
$191$	9.29721	−	16.1032i	0.672722	−	1.16519i	−0.304407	−	0.952542i	$-0.598458\pi$
$191$	9.29721	−	16.1032i	0.672722	−	1.16519i	0.977129	−	0.212647i	$-0.0682085\pi$
$192$	−3.21602	+	13.4780i	−0.232096	+	0.972693i
$193$	−6.20583	−	10.7488i	−0.446705	−	0.773716i	0.551464	−	0.834199i	$-0.314069\pi$
$193$	−6.20583	−	10.7488i	−0.446705	−	0.773716i	−0.998169	+	0.0604824i	$0.980736\pi$
$194$	−15.3449	−	6.86182i	−1.10170	−	0.492650i
$195$	3.14002	−	0.618118i	0.224862	−	0.0442644i
$196$	−1.91924	−	2.14547i	−0.137089	−	0.153248i
$197$			19.1297i			1.36293i	0.731849	+	0.681467i	$0.238658\pi$
$197$			19.1297i			1.36293i	−0.731849	+	0.681467i	$0.761342\pi$
$198$	−6.10328	+	9.83589i	−0.433741	+	0.699006i
$199$		−	11.9817i		−	0.849361i	−0.905343	−	0.424681i	$-0.860386\pi$
$199$		−	11.9817i		−	0.849361i	0.905343	−	0.424681i	$-0.139614\pi$
$200$	2.76373	+	0.601502i	0.195425	+	0.0425326i
$201$	−0.959261	+	2.80759i	−0.0676610	+	0.198032i
$202$	−0.353580	+	0.790705i	−0.0248778	+	0.0556338i
$203$	−8.21487	−	14.2286i	−0.576571	−	0.998650i
$204$	−18.3801	−	13.8752i	−1.28686	−	0.971457i
$205$	4.22231	−	7.31326i	0.294899	−	0.510780i
$206$	2.54493	+	3.51475i	0.177313	+	0.244884i
$207$	18.4198	−	7.54428i	1.28026	−	0.524363i
$208$	5.95096	+	4.38282i	0.412624	+	0.303894i
$209$	−11.5878	−	6.69021i	−0.801544	−	0.462772i
$210$	5.20792	+	4.84907i	0.359381	+	0.334618i
$211$	17.3170	−	9.99799i	1.19215	−	0.688290i	0.233359	−	0.972391i	$-0.425028\pi$
$211$	17.3170	−	9.99799i	1.19215	−	0.688290i	0.958794	+	0.284101i	$0.0916951\pi$
$212$	1.89385	+	9.05401i	0.130070	+	0.621832i
$213$	−6.85271	+	5.98566i	−0.469540	+	0.410131i
$214$	1.10410	+	10.6711i	0.0754746	+	0.729458i
$215$	7.15600			0.488035
$216$	9.22301	−	11.4427i	0.627546	−	0.778579i
$217$	15.1874			1.03099
$218$	2.07094	+	20.0155i	0.140262	+	1.35562i
$219$	−12.2194	+	10.6733i	−0.825709	+	0.721236i
$220$	1.11723	+	5.34120i	0.0753238	+	0.360104i
$221$	−10.6377	+	6.14169i	−0.715570	+	0.413135i
$222$	0.502899	+	0.468246i	0.0337524	+	0.0314266i
$223$	−19.6991	−	11.3733i	−1.31915	−	0.761611i	−0.335558	−	0.942020i	$-0.608925\pi$
$223$	−19.6991	−	11.3733i	−1.31915	−	0.761611i	−0.983592	+	0.180408i	$0.942258\pi$
$224$	−0.133108	+	16.4329i	−0.00889363	+	1.09797i
$225$	−2.37280	−	1.83571i	−0.158187	−	0.122381i
$226$	8.24637	+	11.3889i	0.548540	+	0.757579i
$227$	3.65981	−	6.33897i	0.242910	−	0.420732i	−0.718632	−	0.695391i	$-0.755231\pi$
$227$	3.65981	−	6.33897i	0.242910	−	0.420732i	0.961542	+	0.274658i	$0.0885647\pi$
$228$	13.5588	+	10.2355i	0.897951	+	0.677865i
$229$	6.19692	+	10.7334i	0.409504	+	0.709282i	0.994834	−	0.101513i	$-0.0323684\pi$
$229$	6.19692	+	10.7334i	0.409504	+	0.709282i	−0.585330	+	0.810795i	$0.699035\pi$
$230$	3.83040	−	8.56584i	0.252569	−	0.564815i
$231$	−4.43864	+	12.9911i	−0.292041	+	0.854753i
$232$	−3.40184	+	15.6305i	−0.223342	+	1.02619i
$233$		−	10.9146i		−	0.715040i	−0.933905	−	0.357520i	$-0.883622\pi$
$233$		−	10.9146i		−	0.715040i	0.933905	−	0.357520i	$-0.116378\pi$
$234$	−3.70193	−	6.90989i	−0.242003	−	0.451713i
$235$			1.48605i			0.0969394i
$236$	−6.83116	−	7.63638i	−0.444671	−	0.497086i
$237$	−13.9109	+	2.73838i	−0.903609	+	0.177877i
$238$	−24.9330	−	11.1493i	−1.61617	−	0.722704i
$239$	−0.162275	−	0.281069i	−0.0104967	−	0.0181808i	0.860729	−	0.509063i	$-0.170008\pi$
$239$	−0.162275	−	0.281069i	−0.0104967	−	0.0181808i	−0.871226	+	0.490882i	$0.836675\pi$
$240$	−0.575532	−	6.90426i	−0.0371504	−	0.445668i
$241$	−4.69812	+	8.13739i	−0.302633	+	0.524175i	−0.976731	−	0.214466i	$-0.931199\pi$
$241$	−4.69812	+	8.13739i	−0.302633	+	0.524175i	0.674099	+	0.738641i	$0.264532\pi$
$242$	4.07310	−	2.94921i	0.261829	−	0.189583i
$243$	−14.0485	+	6.75563i	−0.901214	+	0.433374i
$244$	7.01074	−	21.3413i	0.448816	−	1.36624i
$245$	1.24649	+	0.719659i	0.0796351	+	0.0459773i
$246$	−20.1584	−	4.63779i	−1.28525	−	0.295695i
$247$	7.84730	−	4.53064i	0.499312	−	0.288278i
$248$	−10.9405	−	9.94758i	−0.694723	−	0.631672i
$249$	3.06271	+	15.5585i	0.194092	+	0.985979i
$250$	−1.40670	+	0.145547i	−0.0889678	+	0.00920520i
$251$	−25.1401			−1.58683			−0.793415	−	0.608681i	$-0.791699\pi$
$251$	−25.1401			−1.58683			−0.793415	+	0.608681i	$0.791699\pi$
$252$	7.61711	−	15.6779i	0.479833	−	0.987612i
$253$	18.1028			1.13811
$254$	22.1523	−	2.29202i	1.38996	−	0.143814i
$255$	10.8962	+	3.72288i	0.682347	+	0.233136i
$256$	10.8593	−	11.7506i	0.678705	−	0.734411i
$257$	−21.3978	+	12.3540i	−1.33476	+	0.770624i	−0.986025	−	0.166597i	$-0.946722\pi$
$257$	−21.3978	+	12.3540i	−1.33476	+	0.770624i	−0.348735	+	0.937221i	$0.613389\pi$
$258$	−5.13760	−	16.7587i	−0.319853	−	1.04335i
$259$	0.705755	+	0.407468i	0.0438535	+	0.0253188i
$260$	−3.51079	−	1.15331i	−0.217730	−	0.0715254i
$261$	10.3820	−	13.4195i	0.642630	−	0.830649i
$262$	15.5945	−	11.2915i	0.963430	−	0.697591i
$263$	9.32106	−	16.1446i	0.574761	−	0.995516i	−0.421306	−	0.906918i	$-0.638428\pi$
$263$	9.32106	−	16.1446i	0.574761	−	0.995516i	0.996068	−	0.0885972i	$-0.0282384\pi$
$264$	11.7065	−	6.45113i	0.720487	−	0.397040i
$265$	−2.31249	−	4.00535i	−0.142055	−	0.246047i
$266$	18.3928	+	8.22472i	1.12773	+	0.504290i
$267$	−16.8976	−	19.3453i	−1.03412	−	1.18391i
$268$	2.55337	−	2.28413i	0.155972	−	0.139525i
$269$			5.91652i			0.360736i	0.983599	+	0.180368i	$0.0577289\pi$
$269$			5.91652i			0.360736i	−0.983599	+	0.180368i	$0.942271\pi$
$270$	−2.59554	+	6.87482i	−0.157960	+	0.418388i
$271$		−	1.37246i		−	0.0833710i	−0.999131	−	0.0416855i	$-0.986727\pi$
$271$		−	1.37246i		−	0.0833710i	0.999131	−	0.0416855i	$-0.0132728\pi$
$272$	10.6583	+	24.3625i	0.646253	+	1.47720i
$273$	−6.11605	−	7.00198i	−0.370160	−	0.423779i
$274$	6.22295	−	13.9162i	0.375942	−	0.840711i
$275$	−1.36420	−	2.36286i	−0.0822643	−	0.142486i
$276$	−22.8105	−	2.82068i	−1.37303	−	0.169785i
$277$	15.8596	−	27.4697i	0.952913	−	1.65049i	0.213838	−	0.976869i	$-0.431404\pi$
$277$	15.8596	−	27.4697i	0.952913	−	1.65049i	0.739074	−	0.673624i	$-0.235263\pi$
$278$	4.94325	+	6.82703i	0.296476	+	0.409458i
$279$	5.94440	+	14.5136i	0.355882	+	0.868907i
$280$	−2.50110	−	7.82682i	−0.149469	−	0.467742i
$281$	1.38378	+	0.798927i	0.0825495	+	0.0476600i	0.540707	−	0.841211i	$-0.318157\pi$
$281$	1.38378	+	0.798927i	0.0825495	+	0.0476600i	−0.458157	+	0.888871i	$0.651490\pi$
$282$	3.48021	−	1.06690i	0.207243	−	0.0635329i
$283$	6.61811	−	3.82097i	0.393406	−	0.227133i	−0.290229	−	0.956957i	$-0.593731\pi$
$283$	6.61811	−	3.82097i	0.393406	−	0.227133i	0.683635	+	0.729824i	$0.260398\pi$
$284$	10.2838	−	2.15109i	0.610231	−	0.127644i
$285$	−8.03799	−	2.74632i	−0.476129	−	0.162678i
$286$	−0.733734	−	7.09150i	−0.0433866	−	0.419329i
$287$	−24.5320			−1.44808
$288$	−15.7560	+	6.30470i	−0.928430	+	0.371508i
$289$	−27.1957			−1.59975
$290$	−0.823152	−	7.95572i	−0.0483371	−	0.467176i
$291$	−3.97629	−	20.1994i	−0.233094	−	1.18411i
$292$	18.3375	−	3.83571i	1.07312	−	0.224468i
$293$	3.98314	−	2.29967i	0.232697	−	0.134348i	−0.379118	−	0.925348i	$-0.623773\pi$
$293$	3.98314	−	2.29967i	0.232697	−	0.134348i	0.611816	+	0.791000i	$0.290439\pi$
$294$	0.790475	−	3.43584i	0.0461014	−	0.200382i
$295$	4.43662	+	2.56148i	0.258310	+	0.149135i
$296$	−0.241517	−	0.755790i	−0.0140379	−	0.0439294i
$297$	−14.1521	+	0.843052i	−0.821187	+	0.0489188i
$298$	1.07396	+	1.48322i	0.0622127	+	0.0859208i
$299$	−6.12966	+	10.6169i	−0.354487	+	0.613990i
$300$	1.35079	+	3.18988i	0.0779879	+	0.184168i
$301$	−10.3943	−	18.0034i	−0.599116	−	1.03770i
$302$	4.13103	−	9.23814i	0.237714	−	0.531595i
$303$	−1.04085	+	0.204893i	−0.0597953	+	0.0117708i
$304$	−7.86247	−	17.9719i	−0.450944	−	1.03076i
$305$			11.2317i			0.643124i
$306$	0.895813	−	28.1908i	0.0512102	−	1.61156i
$307$			25.6885i			1.46612i	0.680165	+	0.733059i	$0.261908\pi$
$307$			25.6885i			1.46612i	−0.680165	+	0.733059i	$0.738092\pi$
$308$	11.8148	−	10.5690i	0.673213	−	0.602225i
$309$	−1.71831	+	5.02918i	−0.0977510	+	0.286100i
$310$	6.74932	+	3.01810i	0.383336	+	0.171417i
$311$	2.47952	+	4.29465i	0.140601	+	0.243528i	0.927723	−	0.373269i	$-0.121763\pi$
$311$	2.47952	+	4.29465i	0.140601	+	0.243528i	−0.787122	+	0.616797i	$0.788430\pi$
$312$	−0.180417	+	9.04997i	−0.0102141	+	0.512353i
$313$	11.8798	−	20.5764i	0.671487	−	1.16305i	−0.305996	−	0.952033i	$-0.598989\pi$
$313$	11.8798	−	20.5764i	0.671487	−	1.16305i	0.977483	−	0.211016i	$-0.0676773\pi$
$314$	−17.9906	+	13.0264i	−1.01527	+	0.735124i
$315$	−1.17182	+	8.63601i	−0.0660244	+	0.486584i
$316$	15.5534	+	5.10939i	0.874949	+	0.287425i
$317$	−6.53708	−	3.77418i	−0.367159	−	0.211979i	0.305058	−	0.952334i	$-0.401324\pi$
$317$	−6.53708	−	3.77418i	−0.367159	−	0.211979i	−0.672216	+	0.740355i	$0.734658\pi$
$318$	−7.71995	+	8.29126i	−0.432913	+	0.464951i
$319$	13.3633	−	7.71533i	0.748204	−	0.431976i
$320$	−3.32477	+	7.27639i	−0.185861	+	0.406763i
$321$	−9.89565	+	8.64360i	−0.552321	+	0.482438i
$322$	−27.1141	+	2.80540i	−1.51101	+	0.156339i
$323$	32.6026			1.81406
$324$	17.9637	+	1.14281i	0.997983	+	0.0634895i
$325$	1.84768			0.102491
$326$	−7.92997	+	0.820487i	−0.439200	+	0.0454426i
$327$	−18.5611	+	16.2127i	−1.02643	+	0.896562i
$328$	17.6721	+	16.0683i	0.975780	+	0.887221i
$329$	3.73868	−	2.15853i	0.206120	−	0.119004i
$330$	−4.55420	+	4.89123i	−0.250701	+	0.269254i
$331$	3.57670	+	2.06501i	0.196593	+	0.113503i	0.595065	−	0.803677i	$-0.297126\pi$
$331$	3.57670	+	2.06501i	0.196593	+	0.113503i	−0.398472	+	0.917180i	$0.630459\pi$
$332$	5.71454	−	17.3956i	0.313626	−	0.954707i
$333$	−0.113156	+	0.833930i	−0.00620089	+	0.0456991i
$334$	2.03042	−	1.47016i	0.111099	−	0.0804438i
$335$	−0.856481	+	1.48347i	−0.0467946	+	0.0810506i
$336$	−16.5341	+	11.4766i	−0.902008	+	0.626098i
$337$	16.9915	+	29.4301i	0.925585	+	1.60316i	0.790617	+	0.612311i	$0.209760\pi$
$337$	16.9915	+	29.4301i	0.925585	+	1.60316i	0.134968	+	0.990850i	$0.456907\pi$
$338$	−12.3758	−	5.53408i	−0.673152	−	0.301014i
$339$	−5.56785	+	16.2961i	−0.302404	+	0.885084i
$340$	−8.86468	−	9.90961i	−0.480755	−	0.537424i
$341$			14.2639i			0.772431i
$342$	−0.660830	+	20.7960i	−0.0357336	+	1.12452i
$343$			16.1541i			0.872237i
$344$	−4.30435	+	19.7772i	−0.232075	+	1.06632i
$345$	11.2757	−	2.21964i	0.607063	−	0.119501i
$346$	2.23916	−	5.00739i	0.120378	−	0.269199i
$347$	8.39734	+	14.5446i	0.450793	+	0.780796i	0.998435	−	0.0559162i	$-0.0178080\pi$
$347$	8.39734	+	14.5446i	0.450793	+	0.780796i	−0.547643	+	0.836712i	$0.684475\pi$
$348$	−18.0406	+	7.63950i	−0.967080	+	0.409520i
$349$	−8.94726	+	15.4971i	−0.478936	+	0.829541i	−0.999708	−	0.0241544i	$-0.992311\pi$
$349$	−8.94726	+	15.4971i	−0.478936	+	0.829541i	0.520772	+	0.853696i	$0.325644\pi$
$350$	2.40945	+	3.32764i	0.128790	+	0.177870i
$351$	4.29750	−	8.58532i	0.229383	−	0.458251i
$352$	−15.4336	−	0.125014i	−0.822616	−	0.00666325i
$353$	0.462966	+	0.267293i	0.0246412	+	0.0142266i	0.512270	−	0.858824i	$-0.328805\pi$
$353$	0.462966	+	0.267293i	0.0246412	+	0.0142266i	−0.487629	+	0.873051i	$0.662138\pi$
$354$	2.81354	−	12.2292i	0.149538	−	0.649973i
$355$	−4.54939	+	2.62659i	−0.241457	+	0.139405i
$356$	6.07255	+	29.0313i	0.321844	+	1.53865i
$357$	−6.46082	−	32.8208i	−0.341943	−	1.73706i
$358$	0.231519	+	2.23762i	0.0122361	+	0.118262i
$359$	21.8779			1.15467			0.577336	−	0.816507i	$-0.304092\pi$
$359$	21.8779			1.15467			0.577336	+	0.816507i	$0.304092\pi$
$360$	6.50065	−	5.45359i	0.342614	−	0.287429i
$361$	−5.05052			−0.265817
$362$	−3.15599	−	30.5025i	−0.165875	−	1.60317i
$363$	5.82811	+	1.99128i	0.305897	+	0.104515i
$364$	2.19795	+	10.5078i	0.115204	+	0.550759i
$365$	−8.11223	+	4.68360i	−0.424613	+	0.245151i
$366$	26.3036	−	8.06369i	1.37491	−	0.421496i
$367$	−20.1984	−	11.6615i	−1.05435	−	0.608728i	−0.130484	−	0.991450i	$-0.541653\pi$
$367$	−20.1984	−	11.6615i	−1.05435	−	0.608728i	−0.923863	+	0.382723i	$0.874987\pi$
$368$	21.3697	+	15.7385i	1.11397	+	0.820428i
$369$	−9.60194	−	23.4437i	−0.499857	−	1.22043i
$370$	0.232666	+	0.321331i	0.0120957	+	0.0167052i
$371$	−6.71790	+	11.6357i	−0.348776	+	0.604098i
$372$	2.22251	−	17.9732i	0.115232	−	0.931865i
$373$	−1.00033	−	1.73262i	−0.0517950	−	0.0897115i	0.838965	−	0.544185i	$-0.183161\pi$
$373$	−1.00033	−	1.73262i	−0.0517950	−	0.0897115i	−0.890760	+	0.454473i	$0.849828\pi$
$374$	10.4714	−	23.4169i	0.541461	−	1.21086i
$375$	−1.13944	−	1.30449i	−0.0588402	−	0.0673634i
$376$	−4.10704	−	0.893863i	−0.211805	−	0.0460975i
$377$			10.4497i			0.538188i
$378$	21.0661	−	3.45586i	1.08352	−	0.177750i
$379$			28.6355i			1.47091i	0.677576	+	0.735453i	$0.263031\pi$
$379$			28.6355i			1.47091i	−0.677576	+	0.735453i	$0.736969\pi$
$380$	6.53936	+	7.31019i	0.335462	+	0.375005i
$381$	17.9434	+	20.5426i	0.919269	+	1.05243i
$382$	−24.0057	−	10.7346i	−1.22824	−	0.549232i
$383$	−10.1979	−	17.6632i	−0.521086	−	0.902548i	−0.999699	−	0.0245219i	$-0.992194\pi$
$383$	−10.1979	−	17.6632i	−0.521086	−	0.902548i	0.478613	−	0.878026i	$-0.341140\pi$
$384$	19.4277	+	2.56231i	0.991414	+	0.130757i
$385$	−3.96307	+	6.86423i	−0.201977	+	0.349834i
$386$	−14.2172	+	10.2942i	−0.723634	+	0.523962i
$387$	13.1363	−	16.9797i	0.667758	−	0.863129i
$388$	−7.41914	+	22.5845i	−0.376650	+	1.14655i
$389$	−17.9895	−	10.3862i	−0.912104	−	0.526604i	−0.0309966	−	0.999519i	$-0.509868\pi$
$389$	−17.9895	−	10.3862i	−0.912104	−	0.526604i	−0.881108	+	0.472916i	$0.843201\pi$
$390$	−1.32653	−	4.32712i	−0.0671715	−	0.219112i
$391$	−38.1996	+	22.0546i	−1.93184	+	1.11535i
$392$	−2.73871	+	3.01207i	−0.138326	+	0.152133i
$393$	22.3138	+	7.62389i	1.12558	+	0.384574i
$394$	26.9098	−	2.78427i	1.35570	−	0.140269i
$395$	−8.18558			−0.411861
$396$	14.7245	+	7.15393i	0.739934	+	0.359498i
$397$	3.48794			0.175054			0.0875272	−	0.996162i	$-0.472104\pi$
$397$	3.48794			0.175054			0.0875272	+	0.996162i	$0.472104\pi$
$398$	−16.8547	+	1.74390i	−0.844851	+	0.0874139i
$399$	4.76606	+	24.2115i	0.238602	+	1.21209i
$400$	0.443883	−	3.97529i	0.0221941	−	0.198765i
$401$	7.88931	−	4.55489i	0.393973	−	0.227460i	−0.289907	−	0.957055i	$-0.593624\pi$
$401$	7.88931	−	4.55489i	0.393973	−	0.227460i	0.683880	+	0.729594i	$0.260291\pi$
$402$	4.08906	+	0.940760i	0.203944	+	0.0469209i
$403$	−8.36541	−	4.82977i	−0.416711	−	0.240588i
$404$	1.16375	+	0.382298i	0.0578987	+	0.0190201i
$405$	−8.71154	+	2.26034i	−0.432880	+	0.112317i
$406$	−18.8197	+	13.6268i	−0.934008	+	0.676287i
$407$	−0.382690	+	0.662839i	−0.0189693	+	0.0328557i
$408$	−16.8431	+	27.8748i	−0.833858	+	1.38001i
$409$	−5.74318	−	9.94748i	−0.283982	−	0.491871i	0.688380	−	0.725350i	$-0.258322\pi$
$409$	−5.74318	−	9.94748i	−0.283982	−	0.491871i	−0.972362	+	0.233479i	$0.924989\pi$
$410$	−10.9021	−	4.87512i	−0.538418	−	0.240765i
$411$	18.3188	−	3.60608i	0.903598	−	0.177875i
$412$	4.57381	−	4.09152i	0.225335	−	0.201575i
$413$		−	14.8825i		−	0.732319i
$414$	−13.2935	−	24.8131i	−0.653340	−	1.21950i
$415$			9.15508i			0.449405i
$416$	5.29918	−	9.00914i	0.259814	−	0.441709i
$417$	−3.33762	+	9.76864i	−0.163444	+	0.478372i
$418$	−7.72458	+	17.2743i	−0.377822	+	0.844915i
$419$	16.5760	+	28.7104i	0.809790	+	1.40260i	0.913009	+	0.407938i	$0.133752\pi$
$419$	16.5760	+	28.7104i	0.809790	+	1.40260i	−0.103220	+	0.994659i	$0.532914\pi$
$420$	6.06321	−	8.03177i	0.295854	−	0.391910i
$421$	−1.32245	+	2.29056i	−0.0644525	+	0.111635i	−0.896451	−	0.443143i	$-0.853863\pi$
$421$	−1.32245	+	2.29056i	−0.0644525	+	0.111635i	0.831999	+	0.554778i	$0.187197\pi$
$422$	−16.5846	−	22.9047i	−0.807328	−	1.11499i
$423$	3.52610	+	2.72796i	0.171445	+	0.132638i
$424$	12.4607	−	3.98187i	0.605144	−	0.193377i
$425$	5.75733	+	3.32399i	0.279271	+	0.161237i
$426$	9.41745	+	8.76854i	0.456277	+	0.424837i
$427$	28.2572	−	16.3143i	1.36746	−	0.789504i
$428$	14.8503	−	3.10628i	0.717817	−	0.150148i
$429$	6.57620	−	5.74414i	0.317502	−	0.277330i
$430$	−1.04153	−	10.0664i	−0.0502272	−	0.485444i
$431$	21.3143			1.02668			0.513338	−	0.858187i	$-0.328409\pi$
$431$	21.3143			1.02668			0.513338	+	0.858187i	$0.328409\pi$
$432$	−17.4389	−	11.3086i	−0.839030	−	0.544085i
$433$	−8.37576			−0.402513			−0.201257	−	0.979539i	$-0.564503\pi$
$433$	−8.37576			−0.402513			−0.201257	+	0.979539i	$0.564503\pi$
$434$	−2.21048	−	21.3641i	−0.106106	−	1.02551i
$435$	7.37763	−	6.44417i	0.353730	−	0.308974i
$436$	27.8545	−	5.82640i	1.33399	−	0.279034i
$437$	28.1794	−	16.2694i	1.34800	−	0.778270i
$438$	16.7927	+	15.6356i	0.802386	+	0.747097i
$439$	−20.3968	−	11.7761i	−0.973487	−	0.562043i	−0.0731896	−	0.997318i	$-0.523318\pi$
$439$	−20.3968	−	11.7761i	−0.973487	−	0.562043i	−0.900298	+	0.435275i	$0.856651\pi$
$440$	7.35088	−	2.34901i	0.350439	−	0.111985i
$441$	3.99579	−	1.63657i	0.190276	−	0.0779321i
$442$	10.1878	+	14.0702i	0.484585	+	0.669252i
$443$	−8.66888	+	15.0149i	−0.411871	+	0.713381i	−0.995094	−	0.0989307i	$-0.968458\pi$
$443$	−8.66888	+	15.0149i	−0.411871	+	0.713381i	0.583224	+	0.812312i	$0.301791\pi$
$444$	0.585489	−	0.775582i	0.0277861	−	0.0368075i
$445$	−7.41490	−	12.8430i	−0.351500	−	0.608815i
$446$	−13.1317	+	29.3662i	−0.621804	+	1.39053i
$447$	−0.725124	+	2.12231i	−0.0342972	+	0.100382i
$448$	23.1356	−	2.20452i	1.09305	−	0.104154i
$449$		−	9.70770i		−	0.458135i	−0.973411	−	0.229067i	$-0.926432\pi$
$449$		−	9.70770i		−	0.458135i	0.973411	−	0.229067i	$-0.0735676\pi$
$450$	−2.23695	+	3.60501i	−0.105451	+	0.169942i
$451$		−	23.0403i		−	1.08492i
$452$	14.8206	−	13.2578i	0.697102	−	0.623595i
$453$	12.1607	−	2.39385i	0.571359	−	0.112473i
$454$	−9.44973	−	4.22565i	−0.443498	−	0.198319i
$455$	−2.68381	−	4.64849i	−0.125819	−	0.217925i
$456$	12.4249	−	20.5629i	0.581851	−	0.962946i
$457$	−10.5863	+	18.3361i	−0.495208	+	0.857726i	−0.999985	−	0.00552412i	$-0.998242\pi$
$457$	−10.5863	+	18.3361i	−0.495208	+	0.857726i	0.504776	+	0.863250i	$0.331575\pi$
$458$	14.1968	−	10.2794i	0.663371	−	0.480327i
$459$	28.8359	−	19.0204i	1.34595	−	0.887795i
$460$	−12.6071	−	4.14150i	−0.587809	−	0.193099i
$461$	−8.83216	−	5.09925i	−0.411355	−	0.237496i	0.280017	−	0.959995i	$-0.409660\pi$
$461$	−8.83216	−	5.09925i	−0.411355	−	0.237496i	−0.691372	+	0.722499i	$0.742993\pi$
$462$	18.9207	+	4.35304i	0.880270	+	0.202522i
$463$	5.44361	−	3.14287i	0.252986	−	0.146062i	−0.368145	−	0.929769i	$-0.620007\pi$
$463$	5.44361	−	3.14287i	0.252986	−	0.146062i	0.621131	+	0.783707i	$0.286674\pi$
$464$	22.4826	+	2.51041i	1.04373	+	0.116543i
$465$	1.74893	+	8.88452i	0.0811048	+	0.412010i
$466$	−15.3536	+	1.58859i	−0.711243	+	0.0735899i
$467$	−20.7682			−0.961037			−0.480519	−	0.876984i	$-0.659552\pi$
$467$	−20.7682			−0.961037			−0.480519	+	0.876984i	$0.659552\pi$
$468$	−9.18136	+	6.21324i	−0.424408	+	0.287207i
$469$	4.97624			0.229782
$470$	2.09044	−	0.216290i	0.0964246	−	0.00997673i
$471$	−25.7423	−	8.79530i	−1.18614	−	0.405266i
$472$	−9.74788	+	10.7209i	−0.448682	+	0.493468i
$473$	16.9086	−	9.76221i	0.777460	−	0.448867i
$474$	5.87677	+	19.1699i	0.269929	+	0.880504i
$475$	−4.24710	−	2.45207i	−0.194870	−	0.112509i
$476$	−12.0549	+	36.6961i	−0.552535	+	1.68196i
$477$	−13.7490	−	1.86559i	−0.629521	−	0.0854195i
$478$	−0.371762	+	0.269182i	−0.0170040	+	0.0123121i
$479$	−11.7444	+	20.3418i	−0.536614	+	0.929443i	0.462469	+	0.886635i	$0.346964\pi$
$479$	−11.7444	+	20.3418i	−0.536614	+	0.929443i	−0.999083	+	0.0428075i	$0.986370\pi$
$480$	−9.62848	+	1.81450i	−0.439478	+	0.0828201i
$481$	−0.259160	−	0.448878i	−0.0118167	−	0.0204671i
$482$	12.1307	+	5.42450i	0.552538	+	0.247079i
$483$	−21.9625	−	25.1439i	−0.999329	−	1.14409i
$484$	−4.74150	−	5.30040i	−0.215523	−	0.240927i
$485$		−	11.8860i		−	0.539713i
$486$	11.5479	+	18.7789i	0.523823	+	0.851827i
$487$		−	23.1434i		−	1.04873i	−0.851495	−	0.524363i	$-0.824304\pi$
$487$		−	23.1434i		−	1.04873i	0.851495	−	0.524363i	$-0.175696\pi$
$488$	−31.0413	−	6.75587i	−1.40517	−	0.305824i
$489$	−6.42330	−	7.35374i	−0.290472	−	0.332548i
$490$	0.830925	−	1.85818i	0.0375374	−	0.0839441i
$491$	−6.51941	−	11.2920i	−0.294217	−	0.509599i	0.680585	−	0.732669i	$-0.261726\pi$
$491$	−6.51941	−	11.2920i	−0.294217	−	0.509599i	−0.974802	+	0.223070i	$0.928392\pi$
$492$	−3.59001	+	29.0319i	−0.161850	+	1.30886i
$493$	−18.7991	+	32.5610i	−0.846669	+	1.46647i
$494$	−7.51542	−	10.3794i	−0.338135	−	0.466992i
$495$	−8.11087	−	1.10056i	−0.364556	−	0.0494665i
$496$	−12.4009	+	16.8379i	−0.556819	+	0.756044i
$497$	13.2162	+	7.63038i	0.592828	+	0.342269i
$498$	21.4404	−	6.57282i	0.960768	−	0.294535i
$499$	18.7528	−	10.8269i	0.839489	−	0.484679i	−0.0176013	−	0.999845i	$-0.505603\pi$
$499$	18.7528	−	10.8269i	0.839489	−	0.484679i	0.857091	+	0.515166i	$0.172270\pi$
$500$	0.409483	+	1.95763i	0.0183126	+	0.0875480i
$501$	2.90528	+	0.992638i	0.129798	+	0.0443478i
$502$	3.65907	+	35.3647i	0.163312	+	1.57840i
$503$	−7.47335			−0.333220			−0.166610	−	0.986023i	$-0.553282\pi$
$503$	−7.47335			−0.333220			−0.166610	+	0.986023i	$0.553282\pi$
$504$	−23.1627	−	8.43316i	−1.03175	−	0.375643i
$505$	−0.612468			−0.0272544
$506$	−2.63481	−	25.4653i	−0.117132	−	1.13207i
$507$	−3.20689	−	16.2909i	−0.142423	−	0.723505i
$508$	−6.44839	−	30.8281i	−0.286101	−	1.36777i
$509$	17.9618	−	10.3703i	0.796144	−	0.459654i	−0.0459770	−	0.998942i	$-0.514640\pi$
$509$	17.9618	−	10.3703i	0.796144	−	0.459654i	0.842121	+	0.539289i	$0.181307\pi$
$510$	3.65108	−	15.8696i	0.161672	−	0.702717i
$511$	23.5664	+	13.6061i	1.04252	+	0.601898i
$512$	−18.1101	−	13.5655i	−0.800362	−	0.599518i
$513$	−21.2719	+	14.0311i	−0.939176	+	0.619487i
$514$	20.4929	+	28.3023i	0.903902	+	1.24836i
$515$	−1.53420	+	2.65731i	−0.0676049	+	0.117095i
$516$	−22.8268	+	9.66626i	−1.00489	+	0.425533i
$517$	2.02727	+	3.51134i	0.0891593	+	0.154428i
$518$	0.470466	−	1.05209i	0.0206711	−	0.0462264i
$519$	6.59151	−	1.29755i	0.289335	−	0.0569561i
$520$	−1.11138	+	5.10650i	−0.0487374	+	0.223935i
$521$			25.8070i			1.13063i	0.824877	+	0.565313i	$0.191245\pi$
$521$			25.8070i			1.13063i	−0.824877	+	0.565313i	$0.808755\pi$
$522$	−20.3884	−	12.6512i	−0.892376	−	0.553729i
$523$		−	23.3489i		−	1.02098i	−0.859885	−	0.510488i	$-0.829465\pi$
$523$		−	23.3489i		−	1.02098i	0.859885	−	0.510488i	$-0.170535\pi$
$524$	−18.1535	−	20.2934i	−0.793040	−	0.886520i
$525$	−1.62683	+	4.76145i	−0.0710007	+	0.207807i
$526$	−24.0673	−	10.7622i	−1.04938	−	0.469253i
$527$	−17.3776	−	30.0988i	−0.756979	−	1.31113i
$528$	−10.7787	−	15.5287i	−0.469082	−	0.675798i
$529$	−10.5114	+	18.2062i	−0.457016	+	0.791576i
$530$	−5.29777	+	3.83596i	−0.230120	+	0.166623i
$531$	14.2222	−	5.82506i	0.617192	−	0.252786i
$532$	8.89273	−	27.0703i	0.385549	−	1.17364i
$533$	13.5126	+	7.80149i	0.585295	+	0.337920i
$534$	−24.7537	+	26.5856i	−1.07120	+	1.15047i
$535$	−6.56954	+	3.79293i	−0.284026	+	0.163983i
$536$	−3.58473	−	3.25939i	−0.154837	−	0.140784i
$537$	−2.07502	+	1.81248i	−0.0895439	+	0.0782143i
$538$	8.32279	−	0.861131i	0.358821	−	0.0371260i
$539$	3.92703			0.169149
$540$	10.0486	+	2.65055i	0.432423	+	0.114062i
$541$	−19.1224			−0.822135			−0.411068	−	0.911605i	$-0.634844\pi$
$541$	−19.1224			−0.822135			−0.411068	+	0.911605i	$0.634844\pi$
$542$	−1.93065	+	0.199757i	−0.0829283	+	0.00858031i
$543$	28.2860	−	24.7071i	1.21387	−	1.06028i
$544$	32.7196	−	18.5389i	1.40284	−	0.794850i
$545$	−12.3224	+	7.11434i	−0.527833	+	0.304745i
$546$	−8.95954	+	9.62259i	−0.383433	+	0.411809i
$547$	−10.9567	−	6.32587i	−0.468476	−	0.270475i	0.247125	−	0.968984i	$-0.420514\pi$
$547$	−10.9567	−	6.32587i	−0.468476	−	0.270475i	−0.715602	+	0.698509i	$0.753847\pi$
$548$	−20.4818	−	6.72838i	−0.874938	−	0.287422i
$549$	26.6505	+	20.6181i	1.13742	+	0.879959i
$550$	−3.12529	+	2.26293i	−0.133263	+	0.0964917i
$551$	13.8679	−	24.0198i	0.590790	−	1.02328i
$552$	−0.647871	+	32.4981i	−0.0275752	+	1.38321i
$553$	11.8898	+	20.5937i	0.505604	+	0.875732i
$554$	−40.9500	−	18.3117i	−1.73980	−	0.777988i
$555$	−0.157094	+	0.459785i	−0.00666825	+	0.0195168i
$556$	8.88413	−	7.94734i	0.376771	−	0.337042i
$557$		−	35.4783i		−	1.50327i	−0.659582	−	0.751633i	$-0.729267\pi$
$557$		−	35.4783i		−	1.50327i	0.659582	−	0.751633i	$-0.270733\pi$
$558$	19.5511	−	10.4744i	0.827666	−	0.443418i
$559$			13.2220i			0.559232i
$560$	−10.6460	+	4.65748i	−0.449875	+	0.196814i
$561$	30.8250	−	6.06795i	1.30143	−	0.256189i
$562$	0.922449	−	2.06285i	0.0389112	−	0.0870162i
$563$	0.308450	+	0.534252i	0.0129996	+	0.0225160i	0.872452	−	0.488700i	$-0.162529\pi$
$563$	0.308450	+	0.534252i	0.0129996	+	0.0225160i	−0.859452	+	0.511216i	$0.829195\pi$
$564$	−2.00734	−	4.74034i	−0.0845245	−	0.199604i
$565$	−4.97129	+	8.61053i	−0.209144	+	0.362248i
$566$	−6.33821	−	8.75359i	−0.266415	−	0.367941i
$567$	18.3404	+	18.6337i	0.770224	+	0.782542i
$568$	−4.52272	−	14.1532i	−0.189769	−	0.593854i
$569$	11.0982	+	6.40754i	0.465260	+	0.268618i	0.714253	−	0.699887i	$-0.246766\pi$
$569$	11.0982	+	6.40754i	0.465260	+	0.268618i	−0.248993	+	0.968505i	$0.580100\pi$
$570$	−2.69335	+	11.7068i	−0.112812	+	0.490344i
$571$	−17.7603	+	10.2539i	−0.743243	+	0.429112i	−0.823247	−	0.567683i	$-0.807840\pi$
$571$	−17.7603	+	10.2539i	−0.743243	+	0.429112i	0.0800040	+	0.996795i	$0.474507\pi$
$572$	−9.86885	+	2.06429i	−0.412637	+	0.0863124i
$573$	−6.22052	−	31.6000i	−0.259866	−	1.32011i
$574$	3.57056	+	34.5093i	0.149032	+	1.44039i
$575$	6.63496			0.276697
$576$	11.1621	+	21.2464i	0.465087	+	0.885265i
$577$	−20.2930			−0.844811			−0.422405	−	0.906407i	$-0.638814\pi$
$577$	−20.2930			−0.844811			−0.422405	+	0.906407i	$0.638814\pi$
$578$	3.95825	+	38.2563i	0.164642	+	1.59125i
$579$	−20.3430	−	6.95054i	−0.845426	−	0.288855i
$580$	−11.0715	+	2.31586i	−0.459721	+	0.0961609i
$581$	23.0328	−	13.2980i	0.955561	−	0.551694i
$582$	−27.8359	+	8.53343i	−1.15383	+	0.353722i
$583$	−10.9282	−	6.30940i	−0.452600	−	0.261308i
$584$	−8.06467	−	25.2372i	−0.333718	−	1.04432i
$585$	3.39181	−	4.38418i	0.140234	−	0.181264i
$586$	−3.81468	−	5.26839i	−0.157583	−	0.217635i
$587$	−1.58094	+	2.73827i	−0.0652524	+	0.113020i	−0.896806	−	0.442424i	$-0.854119\pi$
$587$	−1.58094	+	2.73827i	−0.0652524	+	0.113020i	0.831554	+	0.555445i	$0.187452\pi$
$588$	−4.94826	−	0.611888i	−0.204063	−	0.0252338i
$589$	12.8192	+	22.2035i	0.528206	+	0.914880i
$590$	2.95751	−	6.61383i	0.121759	−	0.272287i
$591$	21.7970	+	24.9544i	0.896611	+	1.02649i
$592$	−1.02802	+	0.449745i	−0.0422514	+	0.0184844i
$593$			25.3926i			1.04275i	0.853328	+	0.521374i	$0.174581\pi$
$593$			25.3926i			1.04275i	−0.853328	+	0.521374i	$0.825419\pi$
$594$	3.24572	+	19.7851i	0.133173	+	0.811792i
$595$		−	19.3127i		−	0.791745i
$596$	1.93014	−	1.72662i	0.0790618	−	0.0707251i
$597$	−13.6524	−	15.6300i	−0.558755	−	0.639693i
$598$	15.8270	+	7.07736i	0.647213	+	0.289415i
$599$	−10.5125	−	18.2082i	−0.429529	−	0.743965i	0.567303	−	0.823509i	$-0.307987\pi$
$599$	−10.5125	−	18.2082i	−0.429529	−	0.743965i	−0.996831	+	0.0795440i	$0.974654\pi$
$600$	4.29062	−	2.36444i	0.175164	−	0.0965279i
$601$	10.4037	−	18.0197i	0.424374	−	0.735038i	−0.571987	−	0.820262i	$-0.693827\pi$
$601$	10.4037	−	18.0197i	0.424374	−	0.735038i	0.996362	+	0.0852243i	$0.0271607\pi$
$602$	−23.8126	+	17.2420i	−0.970530	+	0.702732i
$603$	1.94772	+	4.75548i	0.0793173	+	0.193658i
$604$	−13.5966	−	4.46656i	−0.553238	−	0.181742i
$605$	3.07945	+	1.77792i	0.125197	+	0.0722828i
$606$	0.439716	+	1.43435i	0.0178623	+	0.0582663i
$607$	−5.00469	+	2.88946i	−0.203134	+	0.117280i	−0.598117	−	0.801409i	$-0.704084\pi$
$607$	−5.00469	+	2.88946i	−0.203134	+	0.117280i	0.394982	+	0.918689i	$0.370751\pi$
$608$	−24.1368	+	13.6759i	−0.978877	+	0.554632i
$609$	−26.9287	−	9.20067i	−1.09121	−	0.372830i
$610$	15.7996	−	1.63474i	0.639709	−	0.0661885i
$611$	−2.74575			−0.111081
$612$	−39.7865	+	2.84294i	−1.60827	+	0.114919i
$613$	3.50597			0.141605			0.0708025	−	0.997490i	$-0.477444\pi$
$613$	3.50597			0.141605			0.0708025	+	0.997490i	$0.477444\pi$
$614$	36.1361	−	3.73888i	1.45833	−	0.150889i
$615$	−2.82504	−	14.3511i	−0.113916	−	0.578692i
$616$	−16.5871	−	15.0817i	−0.668313	−	0.607659i
$617$	22.3161	−	12.8842i	0.898411	−	0.518698i	0.0217270	−	0.999764i	$-0.493084\pi$
$617$	22.3161	−	12.8842i	0.898411	−	0.518698i	0.876684	+	0.481066i	$0.159750\pi$
$618$	7.32466	+	1.68517i	0.294641	+	0.0677873i
$619$	20.9296	+	12.0837i	0.841230	+	0.485685i	0.857682	−	0.514180i	$-0.171904\pi$
$619$	20.9296	+	12.0837i	0.841230	+	0.485685i	−0.0164519	+	0.999865i	$0.505237\pi$
$620$	3.26323	−	9.93358i	0.131055	−	0.398942i
$621$	15.4322	−	30.8296i	0.619271	−	1.23715i
$622$	5.68042	−	4.11302i	0.227764	−	0.164917i
$623$	−21.5406	+	37.3095i	−0.863008	+	1.49477i
$624$	12.7569	−	1.06340i	0.510684	−	0.0425701i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−30.6740	−	13.7165i	−1.22598	−	0.548223i
$627$	−22.7392	+	4.47625i	−0.908116	+	0.178764i
$628$	20.9428	+	23.4114i	0.835709	+	0.934218i
$629$		−	1.86492i		−	0.0743592i
$630$	12.3189	+	0.391454i	0.490795	+	0.0155959i
$631$		−	31.4403i		−	1.25162i	−0.779976	−	0.625809i	$-0.784769\pi$
$631$		−	31.4403i		−	1.25162i	0.779976	−	0.625809i	$-0.215231\pi$
$632$	4.92364	−	22.6227i	0.195852	−	0.899884i
$633$	11.1978	−	32.7739i	0.445071	−	1.30264i
$634$	−4.35771	+	9.74505i	−0.173067	+	0.387025i
$635$	7.87382	+	13.6378i	0.312463	+	0.541202i
$636$	12.7870	+	9.65292i	0.507036	+	0.382763i
$637$	−1.32970	+	2.30311i	−0.0526847	+	0.0912526i
$638$	−12.7982	−	17.6753i	−0.506685	−	0.699773i
$639$	−2.11899	+	15.6164i	−0.0838259	+	0.617777i
$640$	10.7196	+	3.61792i	0.423731	+	0.143011i
$641$	−7.46326	−	4.30892i	−0.294781	−	0.170192i	0.345315	−	0.938487i	$-0.387772\pi$
$641$	−7.46326	−	4.30892i	−0.294781	−	0.170192i	−0.640096	+	0.768295i	$0.721105\pi$
$642$	13.5993	+	12.6622i	0.536720	+	0.499737i
$643$	5.43130	−	3.13576i	0.214189	−	0.123662i	−0.389067	−	0.921209i	$-0.627203\pi$
$643$	5.43130	−	3.13576i	0.214189	−	0.123662i	0.603257	+	0.797547i	$0.293869\pi$
$644$	7.89274	+	37.7332i	0.311018	+	1.48690i
$645$	9.33491	−	8.15381i	0.367562	−	0.321056i
$646$	−4.74521	−	45.8622i	−0.186698	−	1.80442i
$647$	29.1559			1.14624			0.573119	−	0.819472i	$-0.305733\pi$
$647$	29.1559			1.14624			0.573119	+	0.819472i	$0.305733\pi$
$648$	−1.00696	−	25.4359i	−0.0395572	−	0.999217i
$649$	13.9775			0.548665
$650$	−0.268925	−	2.59914i	−0.0105481	−	0.101947i
$651$	19.8117	−	17.3050i	0.776483	−	0.678238i
$652$	2.30836	+	11.0357i	0.0904025	+	0.432191i
$653$	0.967175	−	0.558399i	0.0378485	−	0.0218518i	−0.480956	−	0.876745i	$-0.659710\pi$
$653$	0.967175	−	0.558399i	0.0378485	−	0.0218518i	0.518805	+	0.854893i	$0.326377\pi$
$654$	25.5079	+	23.7503i	0.997439	+	0.928710i
$655$	11.7901	+	6.80703i	0.460678	+	0.265973i
$656$	20.0312	−	27.1981i	0.782085	−	1.06191i
$657$	−3.77847	+	27.8464i	−0.147412	+	1.08639i
$658$	−3.58056	−	4.94505i	−0.139585	−	0.192778i
$659$	14.5949	−	25.2791i	0.568536	−	0.984734i	−0.428175	−	0.903696i	$-0.640843\pi$
$659$	14.5949	−	25.2791i	0.568536	−	0.984734i	0.996711	−	0.0810377i	$-0.0258234\pi$
$660$	7.54337	+	5.69451i	0.293625	+	0.221659i
$661$	−21.6093	−	37.4284i	−0.840504	−	1.45580i	−0.889469	−	0.456996i	$-0.848925\pi$
$661$	−21.6093	−	37.4284i	−0.840504	−	1.45580i	0.0489644	−	0.998801i	$-0.484408\pi$
$662$	2.38428	−	5.33191i	0.0926675	−	0.207231i
$663$	−6.87870	+	20.1327i	−0.267147	+	0.781891i
$664$	−25.3022	−	5.50680i	−0.981915	−	0.213705i
$665$			14.2468i			0.552465i
$666$	1.18956	+	0.0378005i	0.0460946	+	0.00146474i
$667$			37.5246i			1.45296i
$668$	−2.36361	−	2.64222i	−0.0914507	−	0.102230i
$669$	−38.6563	+	7.60956i	−1.49454	+	0.294203i
$670$	2.21146	+	0.988901i	0.0854362	+	0.0382046i
$671$	15.3222	+	26.5389i	0.591508	+	1.02452i
$672$	18.5506	+	21.5882i	0.715605	+	0.832782i
$673$	−2.45420	+	4.25080i	−0.0946025	+	0.163856i	−0.909443	−	0.415829i	$-0.863491\pi$
$673$	−2.45420	+	4.25080i	−0.0946025	+	0.163856i	0.814840	+	0.579686i	$0.196825\pi$
$674$	38.9264	−	28.1855i	1.49939	−	1.08566i
$675$	−5.18696	+	0.308991i	−0.199646	+	0.0118931i
$676$	−5.98356	+	18.2145i	−0.230137	+	0.700557i
$677$	−12.4723	−	7.20089i	−0.479349	−	0.276753i	0.240796	−	0.970576i	$-0.422592\pi$
$677$	−12.4723	−	7.20089i	−0.479349	−	0.276753i	−0.720145	+	0.693823i	$0.755925\pi$
$678$	23.7342	+	5.46047i	0.911507	+	0.209708i
$679$	−29.9032	+	17.2646i	−1.14758	+	0.662556i
$680$	−12.6497	+	13.9123i	−0.485092	+	0.533512i
$681$	−2.44868	−	12.4392i	−0.0938336	−	0.476672i
$682$	20.0650	−	2.07606i	0.768329	−	0.0794964i
$683$	−4.73033			−0.181001			−0.0905006	−	0.995896i	$-0.528847\pi$
$683$	−4.73033			−0.181001			−0.0905006	+	0.995896i	$0.528847\pi$
$684$	29.3500	−	2.09720i	1.12222	−	0.0801884i
$685$	10.7793			0.411856
$686$	22.7240	−	2.35117i	0.867606	−	0.0897682i
$687$	20.3138	+	6.94057i	0.775020	+	0.264799i
$688$	28.4472	+	3.17642i	1.08454	+	0.121100i
$689$	7.40062	−	4.27275i	0.281941	−	0.162779i
$690$	−4.76352	−	15.5385i	−0.181344	−	0.591541i
$691$	−1.24667	−	0.719766i	−0.0474256	−	0.0273812i	0.476100	−	0.879391i	$-0.342050\pi$
$691$	−1.24667	−	0.719766i	−0.0474256	−	0.0273812i	−0.523525	+	0.852010i	$0.675383\pi$
$692$	−7.36982	−	2.42103i	−0.280158	−	0.0920336i
$693$	9.01240	+	22.0043i	0.342353	+	0.835874i
$694$	19.2378	−	13.9295i	0.730256	−	0.528757i
$695$	−2.98002	+	5.16154i	−0.113038	+	0.195788i
$696$	13.3723	+	24.2659i	0.506875	+	0.919798i
$697$	28.0699	+	48.6184i	1.06322	+	1.84155i
$698$	23.1021	+	10.3306i	0.874427	+	0.391019i
$699$	−12.4365	−	14.2380i	−0.470392	−	0.538530i
$700$	4.33032	−	3.87371i	0.163671	−	0.146412i
$701$			22.0819i			0.834023i	0.908901	+	0.417012i	$0.136923\pi$
$701$			22.0819i			0.834023i	−0.908901	+	0.417012i	$0.863077\pi$
$702$	−12.7025	−	4.79574i	−0.479425	−	0.181004i
$703$			1.37573i			0.0518865i
$704$	2.07046	+	21.7288i	0.0780335	+	0.818934i
$705$	1.69326	+	1.93854i	0.0637719	+	0.0730095i
$706$	0.308619	−	0.690160i	0.0116150	−	0.0259745i
$707$	0.889625	+	1.54088i	0.0334578	+	0.0579506i
$708$	−17.6123	−	2.17789i	−0.661912	−	0.0818503i
$709$	7.51444	−	13.0154i	0.282211	−	0.488803i	−0.689718	−	0.724078i	$-0.742266\pi$
$709$	7.51444	−	13.0154i	0.282211	−	0.488803i	0.971929	+	0.235275i	$0.0755990\pi$
$710$	4.35699	+	6.01735i	0.163515	+	0.225827i
$711$	−15.0264	+	19.4227i	−0.563532	+	0.728409i
$712$	39.9546	−	12.7677i	1.49736	−	0.478489i
$713$	−30.0399	−	17.3435i	−1.12500	−	0.649521i
$714$	−45.2288	+	13.8654i	−1.69264	+	0.518901i
$715$	4.36582	−	2.52061i	0.163272	−	0.0942654i
$716$	3.11397	−	0.651357i	0.116374	−	0.0243423i
$717$	−0.531945	−	0.181748i	−0.0198659	−	0.00678751i
$718$	−3.18426	−	30.7757i	−0.118836	−	1.14854i
$719$	−9.57708			−0.357165			−0.178582	−	0.983925i	$-0.557151\pi$
$719$	−9.57708			−0.357165			−0.178582	+	0.983925i	$0.557151\pi$
$720$	−8.61773	−	8.35073i	−0.321164	−	0.311213i
$721$	8.91385			0.331969
$722$	0.735088	+	7.10459i	0.0273571	+	0.264405i
$723$	3.14339	+	15.9683i	0.116904	+	0.593868i
$724$	−42.4486	+	8.87908i	−1.57759	+	0.329988i
$725$	4.89787	−	2.82779i	0.181902	−	0.105021i
$726$	1.95287	−	8.48825i	0.0724779	−	0.315029i
$727$	−17.1265	−	9.88800i	−0.635188	−	0.366726i	0.147571	−	0.989052i	$-0.452855\pi$
$727$	−17.1265	−	9.88800i	−0.635188	−	0.366726i	−0.782758	+	0.622326i	$0.786188\pi$
$728$	14.4615	−	4.62124i	0.535978	−	0.171275i
$729$	−10.6285	+	24.8200i	−0.393649	+	0.919261i
$730$	7.76914	+	10.7298i	0.287549	+	0.397128i
$731$	−23.7865	+	41.1994i	−0.879776	+	1.52382i
$732$	−15.1716	−	35.8277i	−0.560760	−	1.32423i
$733$	−8.78392	−	15.2142i	−0.324441	−	0.561949i	0.656958	−	0.753927i	$-0.271843\pi$
$733$	−8.78392	−	15.2142i	−0.324441	−	0.561949i	−0.981399	+	0.191978i	$0.938510\pi$
$734$	−13.4645	+	30.1105i	−0.496985	+	1.11140i
$735$	2.44603	−	0.481505i	0.0902232	−	0.0177606i
$736$	19.0292	−	32.3515i	0.701425	−	1.19249i
$737$			4.67364i			0.172156i
$738$	−31.5808	+	16.9192i	−1.16251	+	0.622806i
$739$		−	22.3060i		−	0.820538i	−0.911965	−	0.410269i	$-0.865435\pi$
$739$		−	22.3060i		−	0.820538i	0.911965	−	0.410269i	$-0.134565\pi$
$740$	0.418154	−	0.374061i	0.0153716	−	0.0137508i
$741$	5.07433	−	14.8517i	0.186410	−	0.545590i
$742$	17.3458	+	7.75655i	0.636785	+	0.284752i
$743$	−0.727251	−	1.25964i	−0.0266803	−	0.0462116i	0.852377	−	0.522928i	$-0.175160\pi$
$743$	−0.727251	−	1.25964i	−0.0266803	−	0.0462116i	−0.879057	+	0.476716i	$0.841827\pi$
$744$	−25.6064	−	0.510480i	−0.938776	−	0.0187151i
$745$	−0.647431	+	1.12138i	−0.0237200	+	0.0410843i
$746$	−2.29168	+	1.65934i	−0.0839045	+	0.0607528i
$747$	21.7232	+	16.8061i	0.794809	+	0.614902i
$748$	−34.4647	−	11.3218i	−1.26015	−	0.413968i
$749$	19.0849	+	11.0186i	0.697345	+	0.402613i
$750$	−1.66919	+	1.79271i	−0.0609500	+	0.0654606i
$751$	−28.4405	+	16.4201i	−1.03781	+	0.599178i	−0.919211	−	0.393764i	$-0.871173\pi$
$751$	−28.4405	+	16.4201i	−1.03781	+	0.599178i	−0.118596	+	0.992943i	$0.537839\pi$
$752$	−0.659633	+	5.90750i	−0.0240543	+	0.215424i
$753$	−32.7949	+	28.6455i	−1.19511	+	1.04390i
$754$	14.6997	−	1.52092i	0.535330	−	0.0553888i
$755$	7.15572			0.260423
$756$	−7.92748	−	29.1308i	−0.288320	−	1.05948i
$757$	−19.4550			−0.707105			−0.353552	−	0.935415i	$-0.615026\pi$
$757$	−19.4550			−0.707105			−0.353552	+	0.935415i	$0.615026\pi$
$758$	40.2817	−	4.16781i	1.46310	−	0.151382i
$759$	23.6149	−	20.6270i	0.857167	−	0.748713i
$760$	9.33149	−	10.2629i	0.338489	−	0.372275i
$761$	−43.9863	+	25.3955i	−1.59450	+	0.920587i	−0.601983	+	0.798509i	$0.705622\pi$
$761$	−43.9863	+	25.3955i	−1.59450	+	0.920587i	−0.992521	+	0.122078i	$0.961044\pi$
$762$	26.2857	−	28.2310i	0.952231	−	1.02270i
$763$	35.7972	+	20.6675i	1.29594	+	0.748214i
$764$	−11.6065	+	35.3313i	−0.419909	+	1.27824i
$765$	18.4559	−	7.55908i	0.667276	−	0.273299i
$766$	−23.3626	+	16.9162i	−0.844127	+	0.611207i
$767$	−4.73281	+	8.19747i	−0.170892	+	0.295993i
$768$	0.776769	−	27.7019i	0.0280292	−	0.999607i
$769$	−3.70970	−	6.42540i	−0.133775	−	0.231706i	0.791354	−	0.611359i	$-0.209377\pi$
$769$	−3.70970	−	6.42540i	−0.133775	−	0.231706i	−0.925129	+	0.379653i	$0.876043\pi$
$770$	10.2328	+	4.57579i	0.368763	+	0.164900i
$771$	−13.8366	+	40.4971i	−0.498311	+	1.45847i
$772$	16.5502	+	18.5010i	0.595654	+	0.665867i
$773$			8.44881i			0.303882i	0.988390	+	0.151941i	$0.0485525\pi$
$773$			8.44881i			0.303882i	−0.988390	+	0.151941i	$0.951448\pi$
$774$	−25.7974	−	16.0076i	−0.927270	−	0.575381i
$775$			5.22792i			0.187792i
$776$	32.8496	+	7.14942i	1.17923	+	0.256649i
$777$	1.38493	−	0.272626i	0.0496842	−	0.00978041i
$778$	−11.9921	+	26.8176i	−0.429936	+	0.961457i
$779$	−20.7068	−	35.8652i	−0.741897	−	1.28500i
$780$	−5.89390	+	2.49583i	−0.211035	+	0.0893652i
$781$	−7.16639	+	12.4125i	−0.256433	+	0.444156i
$782$	36.5841	+	50.5256i	1.30824	+	1.80679i
$783$	−1.74752	−	29.3352i	−0.0624514	−	1.04836i
$784$	4.63571	+	3.41415i	0.165561	+	0.121934i
$785$	−13.6017	−	7.85293i	−0.485465	−	0.280283i
$786$	7.47685	−	32.4985i	0.266691	−	1.15918i
$787$	−19.6951	+	11.3710i	−0.702053	+	0.405331i	−0.808112	−	0.589029i	$-0.799510\pi$
$787$	−19.6951	+	11.3710i	−0.702053	+	0.405331i	0.106058	+	0.994360i	$0.466177\pi$
$788$	−7.83328	−	37.4489i	−0.279049	−	1.33406i
$789$	−6.23648	−	31.6811i	−0.222024	−	1.12788i
$790$	1.19139	+	11.5147i	0.0423876	+	0.409674i
$791$	28.8837			1.02699
$792$	7.92035	−	21.7542i	0.281437	−	0.773004i
$793$	−20.7526			−0.736946
$794$	−0.507658	−	4.90649i	−0.0180161	−	0.174125i
$795$	−7.58045	−	2.58999i	−0.268851	−	0.0918576i
$796$	4.90631	+	23.4558i	0.173899	+	0.831368i
$797$	−16.9439	+	9.78254i	−0.600182	+	0.346515i	−0.769113	−	0.639112i	$-0.779302\pi$
$797$	−16.9439	+	9.78254i	−0.600182	+	0.346515i	0.168931	+	0.985628i	$0.445968\pi$
$798$	33.3647	−	10.2283i	1.18110	−	0.362079i
$799$	−8.55569	−	4.93963i	−0.302678	−	0.174751i
$800$	−5.65667	−	0.0458194i	−0.199993	−	0.00161996i
$801$	−44.0854	−	5.98193i	−1.55768	−	0.211361i
$802$	−7.55565	−	10.4350i	−0.266799	−	0.368471i
$803$	−12.7787	+	22.1334i	−0.450951	+	0.781070i
$804$	0.728221	−	5.88902i	0.0256824	−	0.207690i
$805$	−9.63745	−	16.6926i	−0.339676	−	0.588335i
$806$	−5.57650	+	12.4706i	−0.196424	+	0.439259i
$807$	6.74149	+	7.71802i	0.237312	+	0.271687i
$808$	0.368400	−	1.69269i	0.0129603	−	0.0595488i
$809$			6.76733i			0.237927i	0.992899	+	0.118963i	$0.0379571\pi$
$809$			6.76733i			0.237927i	−0.992899	+	0.118963i	$0.962043\pi$
$810$	4.44757	+	11.9256i	0.156272	+	0.419022i
$811$		−	17.7744i		−	0.624144i	−0.950059	−	0.312072i	$-0.898977\pi$
$811$		−	17.7744i		−	0.624144i	0.950059	−	0.312072i	$-0.101023\pi$
$812$	21.9080	+	24.4905i	0.768822	+	0.859447i
$813$	−1.56383	−	1.79036i	−0.0548459	−	0.0627905i
$814$	0.988118	+	0.441858i	0.0346335	+	0.0154871i
$815$	−2.81863	−	4.88202i	−0.0987324	−	0.171010i
$816$	41.6631	+	19.6362i	1.45850	+	0.687404i
$817$	17.5470	−	30.3923i	0.613892	−	1.06329i
$818$	−13.1573	+	9.52678i	−0.460033	+	0.333096i
$819$	−15.9566	−	2.16515i	−0.557569	−	0.0756564i
$820$	−5.27108	+	16.0456i	−0.184074	+	0.560338i
$821$	10.1110	+	5.83759i	0.352876	+	0.203733i	0.665951	−	0.745995i	$-0.268026\pi$
$821$	10.1110	+	5.83759i	0.352876	+	0.203733i	−0.313075	+	0.949728i	$0.601359\pi$
$822$	−7.73892	−	25.2442i	−0.269926	−	0.880493i
$823$	8.05124	−	4.64839i	0.280649	−	0.162033i	−0.353068	−	0.935598i	$-0.614862\pi$
$823$	8.05124	−	4.64839i	0.280649	−	0.162033i	0.633717	+	0.773565i	$0.281528\pi$
$824$	−6.42126	−	5.83849i	−0.223695	−	0.203393i
$825$	−4.47191	−	1.52791i	−0.155692	−	0.0531948i
$826$	−20.9352	+	2.16610i	−0.728430	+	0.0753682i
$827$	52.8269			1.83697			0.918485	−	0.395456i	$-0.129413\pi$
$827$	52.8269			1.83697			0.918485	+	0.395456i	$0.129413\pi$
$828$	−32.9699	+	22.3115i	−1.14578	+	0.775378i
$829$	29.7034			1.03164			0.515821	−	0.856696i	$-0.327487\pi$
$829$	29.7034			1.03164			0.515821	+	0.856696i	$0.327487\pi$
$830$	12.8785	−	1.33249i	0.447019	−	0.0462516i
$831$	−10.6113	−	53.9049i	−0.368100	−	1.86994i
$832$	−13.4445	−	6.14313i	−0.466103	−	0.212975i
$833$	−8.28662	+	4.78428i	−0.287114	+	0.165766i
$834$	14.2274	+	3.27325i	0.492653	+	0.113344i
$835$	1.53509	+	0.886283i	0.0531239	+	0.0306711i
$836$	25.4242	+	8.35198i	0.879313	+	0.288859i
$837$	24.2917	+	12.1595i	0.839644	+	0.420295i
$838$	37.9745	−	27.4962i	1.31181	−	0.949841i
$839$	−11.9629	+	20.7203i	−0.413005	+	0.715345i	−0.995217	−	0.0976920i	$-0.968854\pi$
$839$	−11.9629	+	20.7203i	−0.413005	+	0.715345i	0.582212	+	0.813037i	$0.302187\pi$
$840$	−12.1808	−	7.36014i	−0.420278	−	0.253949i
$841$	1.49277	+	2.58556i	0.0514750	+	0.0891573i
$842$	3.41462	+	1.52692i	0.117675	+	0.0526211i
$843$	2.71545	−	0.534541i	0.0935251	−	0.0184106i
$844$	−29.8064	+	26.6634i	−1.02598	+	0.917792i
$845$		−	9.58606i		−	0.329771i
$846$	3.32422	−	5.35723i	0.114289	−	0.184185i
$847$		−	10.3299i		−	0.354940i
$848$	−7.41493	−	16.9489i	−0.254630	−	0.582029i
$849$	4.27949	−	12.5253i	0.146872	−	0.429868i
$850$	3.83791	−	8.58265i	0.131639	−	0.294382i
$851$	−0.930633	−	1.61190i	−0.0319017	−	0.0552553i
$852$	10.9641	−	14.5238i	0.375622	−	0.497577i
$853$	20.6307	−	35.7334i	0.706382	−	1.22349i	−0.259808	−	0.965660i	$-0.583659\pi$
$853$	20.6307	−	35.7334i	0.706382	−	1.22349i	0.966190	−	0.257830i	$-0.0830073\pi$
$854$	−27.0621	−	37.3750i	−0.926047	−	1.27895i
$855$	−13.6147	+	5.57624i	−0.465613	+	0.190703i
$856$	−6.53103	−	20.4379i	−0.223226	−	0.698553i
$857$	21.3024	+	12.2989i	0.727676	+	0.420124i	0.817571	−	0.575827i	$-0.195320\pi$
$857$	21.3024	+	12.2989i	0.727676	+	0.420124i	−0.0898956	+	0.995951i	$0.528653\pi$
$858$	−9.03745	−	8.41473i	−0.308534	−	0.287274i
$859$	8.14291	−	4.70131i	0.277832	−	0.160407i	−0.354609	−	0.935015i	$-0.615386\pi$
$859$	8.14291	−	4.70131i	0.277832	−	0.160407i	0.632442	+	0.774608i	$0.282053\pi$
$860$	−14.0088	+	2.93026i	−0.477697	+	0.0999211i
$861$	−32.0017	+	27.9527i	−1.09062	+	0.952625i
$862$	−3.10224	−	29.9830i	−0.105663	−	1.02122i
$863$	14.4801			0.492909			0.246455	−	0.969154i	$-0.420734\pi$
$863$	14.4801			0.492909			0.246455	+	0.969154i	$0.420734\pi$
$864$	−13.3697	+	26.1773i	−0.454845	+	0.890571i
$865$	3.87865			0.131878
$866$	1.21907	+	11.7822i	0.0414255	+	0.400376i
$867$	−35.4765	+	30.9878i	−1.20484	+	1.05240i
$868$	−29.7313	+	6.21897i	−1.00915	+	0.211086i
$869$	−19.3414	+	11.1668i	−0.656112	+	0.378807i
$870$	−10.1388	−	9.44021i	−0.343738	−	0.320053i
$871$	−2.74098	−	1.58251i	−0.0928746	−	0.0536212i
$872$	−12.2502	−	38.3350i	−0.414843	−	1.29819i
$873$	−28.2030	−	21.8192i	−0.954526	−	0.738467i
$874$	−26.9876	−	37.2721i	−0.912870	−	1.26075i
$875$	−1.45253	+	2.51585i	−0.0491043	+	0.0850512i
$876$	19.5505	−	25.8981i	0.660551	−	0.875014i
$877$	−13.6148	−	23.5816i	−0.459740	−	0.796293i	0.539207	−	0.842173i	$-0.318724\pi$
$877$	−13.6148	−	23.5816i	−0.459740	−	0.796293i	−0.998947	+	0.0458800i	$0.985391\pi$
$878$	−13.5968	+	30.4063i	−0.458870	+	1.02616i
$879$	2.57563	−	7.53842i	0.0868739	−	0.254264i
$880$	−4.37426	−	9.99862i	−0.147456	−	0.337053i
$881$			24.9990i			0.842236i	0.907006	+	0.421118i	$0.138362\pi$
$881$			24.9990i			0.842236i	−0.907006	+	0.421118i	$0.861638\pi$
$882$	−2.88375	−	5.38270i	−0.0971010	−	0.181245i
$883$			50.7029i			1.70629i	0.521676	+	0.853143i	$0.325307\pi$
$883$			50.7029i			1.70629i	−0.521676	+	0.853143i	$0.674693\pi$
$884$	18.3098	−	16.3791i	0.615826	−	0.550890i
$885$	8.70616	−	1.71382i	0.292654	−	0.0576095i
$886$	22.3833	+	10.0092i	0.751981	+	0.336264i
$887$	13.4181	+	23.2409i	0.450537	+	0.780353i	0.998419	−	0.0562024i	$-0.0178992\pi$
$887$	13.4181	+	23.2409i	0.450537	+	0.780353i	−0.547882	+	0.836555i	$0.684566\pi$
$888$	−1.17623	−	0.710726i	−0.0394717	−	0.0238504i
$889$	22.8738	−	39.6186i	0.767164	−	1.32877i
$890$	−16.9871	+	12.2998i	−0.569407	+	0.412291i
$891$	−17.5006	+	17.2251i	−0.586292	+	0.577064i
$892$	43.2208	+	14.1983i	1.44714	+	0.475393i
$893$	6.31142	+	3.64390i	0.211204	+	0.121938i
$894$	3.09100	+	0.711139i	0.103379	+	0.0237841i
$895$	−1.37757	+	0.795341i	−0.0460471	+	0.0265853i
$896$	−6.46842	−	32.2241i	−0.216095	−	1.07653i
$897$	4.10119	+	20.8339i	0.136935	+	0.695625i
$898$	−13.6559	+	1.41293i	−0.455702	+	0.0471500i
$899$	−29.5669			−0.986112
$900$	5.39676	+	2.62202i	0.179892	+	0.0874008i
$901$	30.7468			1.02432
$902$	−32.4109	+	3.35344i	−1.07916	+	0.111657i
$903$	−34.0729	−	11.6416i	−1.13388	−	0.387408i
$904$	−20.8069	−	18.9185i	−0.692028	−	0.629221i
$905$	18.7786	−	10.8418i	0.624221	−	0.360394i
$906$	−5.13739	−	16.7581i	−0.170678	−	0.556750i
$907$	−2.50386	−	1.44560i	−0.0831392	−	0.0480004i	0.457854	−	0.889027i	$-0.348618\pi$
$907$	−2.50386	−	1.44560i	−0.0831392	−	0.0480004i	−0.540993	+	0.841027i	$0.681952\pi$
$908$	−4.56885	+	13.9080i	−0.151623	+	0.461553i
$909$	−1.12431	+	1.45326i	−0.0372911	+	0.0482017i
$910$	−6.14843	+	4.45190i	−0.203818	+	0.147579i
$911$	29.6254	−	51.3127i	0.981534	−	1.70007i	0.325108	−	0.945677i	$-0.394599\pi$
$911$	29.6254	−	51.3127i	0.981534	−	1.70007i	0.656427	−	0.754390i	$-0.272067\pi$
$912$	−30.7343	−	14.4854i	−1.01772	−	0.479658i
$913$	12.4894	+	21.6322i	0.413337	+	0.715921i
$914$	27.3343	+	12.2231i	0.904137	+	0.404304i
$915$	12.7978	+	14.6516i	0.423081	+	0.484366i
$916$	−16.5264	−	18.4745i	−0.546049	−	0.610414i
$917$		−	39.5496i		−	1.30604i
$918$	−30.9530	−	37.7952i	−1.02160	−	1.24743i
$919$		−	21.5957i		−	0.712378i	−0.934414	−	0.356189i	$-0.884076\pi$
$919$		−	21.5957i		−	0.712378i	0.934414	−	0.356189i	$-0.115924\pi$
$920$	−3.99094	+	18.3372i	−0.131577	+	0.604561i
$921$	29.2704	+	33.5103i	0.964491	+	1.10420i
$922$	−5.88764	+	13.1664i	−0.193899	+	0.433613i
$923$	−4.85311	−	8.40583i	−0.159742	−	0.276681i
$924$	3.36959	−	27.2494i	0.110851	−	0.896439i
$925$	−0.140262	+	0.242941i	−0.00461178	+	0.00798784i
$926$	−5.21339	−	7.20012i	−0.171323	−	0.236611i
$927$	3.48892	+	8.51839i	0.114591	+	0.279781i
$928$	0.259135	−	31.9917i	0.00850653	−	1.05018i
$929$	−13.9584	−	8.05890i	−0.457961	−	0.264404i	0.253225	−	0.967407i	$-0.418509\pi$
$929$	−13.9584	−	8.05890i	−0.457961	−	0.264404i	−0.711187	+	0.703003i	$0.751842\pi$
$930$	12.2433	−	3.75335i	0.401475	−	0.123077i
$931$	6.11293	−	3.52930i	0.200343	−	0.115668i
$932$	4.46935	+	21.3668i	0.146398	+	0.699893i
$933$	8.12798	+	2.77707i	0.266098	+	0.0909171i
$934$	3.02275	+	29.2147i	0.0989073	+	0.955934i
$935$	18.1384			0.593188
$936$	10.0765	+	12.0111i	0.329361	+	0.392596i
$937$	−49.1241			−1.60481			−0.802407	−	0.596778i	$-0.796447\pi$
$937$	−49.1241			−1.60481			−0.802407	+	0.596778i	$0.796447\pi$
$938$	−0.724277	−	7.00010i	−0.0236485	−	0.228561i
$939$	−7.94847	−	40.3780i	−0.259389	−	1.31769i
$940$	−0.608513	−	2.90914i	−0.0198475	−	0.0948858i
$941$	−12.0397	+	6.95114i	−0.392484	+	0.226601i	−0.683236	−	0.730198i	$-0.739428\pi$
$941$	−12.0397	+	6.95114i	−0.392484	+	0.226601i	0.290752	+	0.956798i	$0.406095\pi$
$942$	−8.62567	+	37.4919i	−0.281040	+	1.22155i
$943$	48.5232	+	28.0149i	1.58013	+	0.912290i
$944$	16.4999	+	12.1520i	0.537025	+	0.395514i
$945$	8.31156	+	12.6008i	0.270375	+	0.409903i
$946$	−16.1935	−	22.3646i	−0.526498	−	0.727136i
$947$	8.27310	−	14.3294i	0.268840	−	0.465644i	−0.699723	−	0.714414i	$-0.746693\pi$
$947$	8.27310	−	14.3294i	0.268840	−	0.465644i	0.968562	+	0.248771i	$0.0800265\pi$
$948$	26.1111	−	11.0570i	0.848048	−	0.359115i
$949$	−8.65380	−	14.9888i	−0.280914	−	0.486558i
$950$	−2.83118	+	6.33131i	−0.0918556	+	0.205415i
$951$	−12.8280	+	2.52521i	−0.415975	+	0.0818854i
$952$	53.3752	+	11.6166i	1.72990	+	0.376498i
$953$		−	4.44099i		−	0.143858i	−0.997410	−	0.0719288i	$-0.977085\pi$
$953$		−	4.44099i		−	0.143858i	0.997410	−	0.0719288i	$-0.0229155\pi$
$954$	−0.623214	+	19.6122i	−0.0201773	+	0.634970i
$955$		−	18.5944i		−	0.601701i
$956$	0.432768	+	0.483780i	0.0139967	+	0.0156466i
$957$	8.64119	−	25.2912i	0.279330	−	0.817549i
$958$	30.3243	+	13.5602i	0.979734	+	0.438109i
$959$	−15.6572	−	27.1191i	−0.505598	−	0.875721i
$960$	3.95386	+	13.2803i	0.127610	+	0.428621i
$961$	−1.83442	+	3.17731i	−0.0591748	+	0.102494i
$962$	−0.593718	+	0.429894i	−0.0191422	+	0.0138603i
$963$	−3.05992	+	22.5509i	−0.0986047	+	0.726693i
$964$	5.86507	−	17.8538i	0.188901	−	0.575032i
$965$	−10.7488	−	6.20583i	−0.346016	−	0.199773i
$966$	−32.1734	+	34.5544i	−1.03516	+	1.11177i
$967$	48.9198	−	28.2439i	1.57316	−	0.908262i	0.577377	−	0.816478i	$-0.304076\pi$
$967$	48.9198	−	28.2439i	1.57316	−	0.908262i	0.995779	−	0.0917837i	$-0.0292568\pi$
$968$	−6.76599	+	7.44134i	−0.217467	+	0.239174i
$969$	42.5297	−	37.1486i	1.36625	−	1.19338i
$970$	−16.7200	+	1.72996i	−0.536847	+	0.0555458i
$971$	−23.7664			−0.762699			−0.381350	−	0.924431i	$-0.624541\pi$
$971$	−23.7664			−0.762699			−0.381350	+	0.924431i	$0.624541\pi$
$972$	24.7356	−	18.9777i	0.793393	−	0.608709i
$973$	17.3142			0.555068
$974$	−32.5559	+	3.36845i	−1.04316	+	0.107932i
$975$	2.41028	−	2.10532i	0.0771907	−	0.0674241i
$976$	−4.98554	+	44.6492i	−0.159583	+	1.42919i
$977$	22.5361	−	13.0112i	0.720994	−	0.416266i	−0.0941246	−	0.995560i	$-0.530005\pi$
$977$	22.5361	−	13.0112i	0.720994	−	0.416266i	0.815118	+	0.579295i	$0.196672\pi$
$978$	−9.40965	+	10.1060i	−0.300887	+	0.323154i
$979$	−35.0408	−	20.2308i	−1.11991	−	0.646579i
$980$	−2.73485	−	0.898413i	−0.0873616	−	0.0286988i
$981$	−5.73945	+	42.2984i	−0.183247	+	1.35048i
$982$	−14.9356	+	10.8144i	−0.476613	+	0.345101i
$983$	18.3976	−	31.8656i	0.586793	−	1.01636i	−0.407856	−	0.913046i	$-0.633724\pi$
$983$	18.3976	−	31.8656i	0.586793	−	1.01636i	0.994649	−	0.103309i	$-0.0329431\pi$
$984$	41.3618	+	0.824574i	1.31857	+	0.0262865i
$985$	9.56484	+	16.5668i	0.304761	+	0.527862i
$986$	48.5398	+	21.7056i	1.54582	+	0.691248i
$987$	2.41756	−	7.07576i	0.0769516	−	0.225224i
$988$	−13.5069	+	12.0827i	−0.429712	+	0.384401i
$989$			47.4798i			1.50977i
$990$	−0.367651	+	11.5698i	−0.0116847	+	0.367712i
$991$			52.7208i			1.67473i	0.546644	+	0.837365i	$0.315905\pi$
$991$			52.7208i			1.67473i	−0.546644	+	0.837365i	$0.684095\pi$
$992$	25.4909	+	14.9938i	0.809336	+	0.476052i
$993$	7.01870	−	1.38164i	0.222732	−	0.0438451i
$994$	8.81011	−	19.7019i	0.279440	−	0.624905i
$995$	−5.99086	−	10.3765i	−0.189923	−	0.328956i
$996$	−12.3666	−	29.2037i	−0.391851	−	0.925354i
$997$	−15.7894	+	27.3481i	−0.500057	+	0.866124i	0.499943	+	0.866058i	$0.333354\pi$
$997$	−15.7894	+	27.3481i	−0.500057	+	0.866124i	−1.00000		6.55936e-5i	$0.999979\pi$
$998$	−17.9597	−	24.8038i	−0.568504	−	0.785150i
$999$	0.802599	+	1.21678i	0.0253931	+	0.0384973i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.2.q.a.11.12	yes	48
3.2	odd	2		540.2.q.a.251.13		48
4.3	odd	2	inner	180.2.q.a.11.4	✓	48
5.2	odd	4		900.2.o.b.299.23		48
5.3	odd	4		900.2.o.c.299.2		48
5.4	even	2		900.2.r.f.551.13		48
9.2	odd	6		1620.2.e.b.971.39		48
9.4	even	3		540.2.q.a.71.21		48
9.5	odd	6	inner	180.2.q.a.131.4	yes	48
9.7	even	3		1620.2.e.b.971.10		48
12.11	even	2		540.2.q.a.251.21		48
20.3	even	4		900.2.o.c.299.16		48
20.7	even	4		900.2.o.b.299.9		48
20.19	odd	2		900.2.r.f.551.21		48
36.7	odd	6		1620.2.e.b.971.40		48
36.11	even	6		1620.2.e.b.971.9		48
36.23	even	6	inner	180.2.q.a.131.12	yes	48
36.31	odd	6		540.2.q.a.71.13		48
45.14	odd	6		900.2.r.f.851.21		48
45.23	even	12		900.2.o.b.599.9		48
45.32	even	12		900.2.o.c.599.16		48
180.23	odd	12		900.2.o.b.599.23		48
180.59	even	6		900.2.r.f.851.13		48
180.167	odd	12		900.2.o.c.599.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.q.a.11.4	✓	48	4.3	odd	2	inner
180.2.q.a.11.12	yes	48	1.1	even	1	trivial
180.2.q.a.131.4	yes	48	9.5	odd	6	inner
180.2.q.a.131.12	yes	48	36.23	even	6	inner
540.2.q.a.71.13		48	36.31	odd	6
540.2.q.a.71.21		48	9.4	even	3
540.2.q.a.251.13		48	3.2	odd	2
540.2.q.a.251.21		48	12.11	even	2
900.2.o.b.299.9		48	20.7	even	4
900.2.o.b.299.23		48	5.2	odd	4
900.2.o.b.599.9		48	45.23	even	12
900.2.o.b.599.23		48	180.23	odd	12
900.2.o.c.299.2		48	5.3	odd	4
900.2.o.c.299.16		48	20.3	even	4
900.2.o.c.599.2		48	180.167	odd	12
900.2.o.c.599.16		48	45.32	even	12
900.2.r.f.551.13		48	5.4	even	2
900.2.r.f.551.21		48	20.19	odd	2
900.2.r.f.851.13		48	180.59	even	6
900.2.r.f.851.21		48	45.14	odd	6
1620.2.e.b.971.9		48	36.11	even	6
1620.2.e.b.971.10		48	9.7	even	3
1620.2.e.b.971.39		48	9.2	odd	6
1620.2.e.b.971.40		48	36.7	odd	6

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:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	180.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.145547 - 1.40670i) q^{2} +(1.30449 - 1.13944i) q^{3} +(-1.95763 + 0.409483i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.79271 - 1.66919i) q^{6} +(-2.51585 - 1.45253i) q^{7} +(0.860949 + 2.69421i) q^{8} +(0.403372 - 2.97276i) q^{9} +O(q^{10})\)	\(q+(-0.145547 - 1.40670i) q^{2} +(1.30449 - 1.13944i) q^{3} +(-1.95763 + 0.409483i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.79271 - 1.66919i) q^{6} +(-2.51585 - 1.45253i) q^{7} +(0.860949 + 2.69421i) q^{8} +(0.403372 - 2.97276i) q^{9} +(-0.829399 - 1.14547i) q^{10} +(1.36420 - 2.36286i) q^{11} +(-2.08713 + 2.76476i) q^{12} +(0.923842 + 1.60014i) q^{13} +(-1.67710 + 3.75046i) q^{14} +(0.560001 - 1.63902i) q^{15} +(3.66465 - 1.60323i) q^{16} +6.64799i q^{17} +(-4.24050 - 0.134750i) q^{18} -4.90413i q^{19} +(-1.49062 + 1.33344i) q^{20} +(-4.93695 + 0.971846i) q^{21} +(-3.52240 - 1.57512i) q^{22} +(3.31748 + 5.74605i) q^{23} +(4.19298 + 2.53357i) q^{24} +(0.500000 - 0.866025i) q^{25} +(2.11646 - 1.53247i) q^{26} +(-2.86107 - 4.33754i) q^{27} +(5.51989 + 1.81331i) q^{28} +(4.89787 + 2.82779i) q^{29} +(-2.38713 - 0.549201i) q^{30} +(-4.52751 + 2.61396i) q^{31} +(-2.78865 - 4.92173i) q^{32} +(-0.912750 - 4.63674i) q^{33} +(9.35175 - 0.967594i) q^{34} -2.90505 q^{35} +(0.427639 + 5.98474i) q^{36} -0.280524 q^{37} +(-6.89866 + 0.713781i) q^{38} +(3.02840 + 1.03470i) q^{39} +(2.09271 + 1.90278i) q^{40} +(7.31326 - 4.22231i) q^{41} +(2.08566 + 6.80338i) q^{42} +(6.19728 + 3.57800i) q^{43} +(-1.70305 + 5.18423i) q^{44} +(-1.13705 - 2.77617i) q^{45} +(7.60014 - 5.50304i) q^{46} +(-0.743026 + 1.28696i) q^{47} +(2.95370 - 6.26703i) q^{48} +(0.719659 + 1.24649i) q^{49} +(-1.29101 - 0.577305i) q^{50} +(7.57495 + 8.67221i) q^{51} +(-2.46377 - 2.75419i) q^{52} -4.62498i q^{53} +(-5.68522 + 4.65600i) q^{54} -2.72840i q^{55} +(1.74739 - 8.02877i) q^{56} +(-5.58794 - 6.39738i) q^{57} +(3.26499 - 7.30143i) q^{58} +(2.56148 + 4.43662i) q^{59} +(-0.425124 + 3.43792i) q^{60} +(-5.61584 + 9.72691i) q^{61} +(4.33603 + 5.98842i) q^{62} +(-5.33283 + 6.89310i) q^{63} +(-6.51754 + 4.63915i) q^{64} +(1.60014 + 0.923842i) q^{65} +(-6.38967 + 1.95883i) q^{66} +(-1.48347 + 0.856481i) q^{67} +(-2.72224 - 13.0143i) q^{68} +(10.8749 + 3.71559i) q^{69} +(0.422821 + 4.08655i) q^{70} -5.25318 q^{71} +(8.35652 - 1.47262i) q^{72} -9.36719 q^{73} +(0.0408294 + 0.394614i) q^{74} +(-0.334537 - 1.69944i) q^{75} +(2.00816 + 9.60049i) q^{76} +(-6.86423 + 3.96307i) q^{77} +(1.01475 - 4.41066i) q^{78} +(-7.08892 - 4.09279i) q^{79} +(2.37206 - 3.22076i) q^{80} +(-8.67458 - 2.39826i) q^{81} +(-7.00396 - 9.67304i) q^{82} +(-4.57754 + 7.92854i) q^{83} +(9.26678 - 3.92411i) q^{84} +(3.32399 + 5.75733i) q^{85} +(4.13119 - 9.23851i) q^{86} +(9.61129 - 1.89200i) q^{87} +(7.54055 + 1.64114i) q^{88} -14.8298i q^{89} +(-3.73976 + 2.00355i) q^{90} -5.36761i q^{91} +(-8.84732 - 9.89020i) q^{92} +(-2.92764 + 8.56869i) q^{93} +(1.91852 + 0.857905i) q^{94} +(-2.45207 - 4.24710i) q^{95} +(-9.24576 - 3.24284i) q^{96} +(5.94298 - 10.2935i) q^{97} +(1.64869 - 1.19377i) q^{98} +(-6.47394 - 5.00855i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{6} + 4 q^{9}+O(q^{10}) \) 48 * q + 6 * q^6 + 4 * q^9	\( 48 q + 6 q^{6} + 4 q^{9} - 22 q^{12} - 30 q^{14} - 16 q^{18} - 4 q^{21} - 28 q^{24} + 24 q^{25} - 12 q^{29} + 16 q^{30} - 44 q^{33} - 6 q^{34} + 42 q^{36} + 60 q^{38} - 6 q^{40} - 60 q^{41} - 18 q^{42} - 8 q^{45} - 12 q^{46} - 12 q^{48} + 24 q^{49} - 18 q^{52} - 32 q^{54} - 42 q^{56} - 12 q^{57} - 18 q^{58} + 14 q^{60} - 48 q^{64} + 16 q^{66} + 48 q^{68} + 36 q^{69} + 60 q^{72} - 24 q^{73} + 84 q^{74} + 6 q^{76} + 48 q^{77} + 38 q^{78} - 36 q^{82} + 50 q^{84} - 54 q^{86} - 18 q^{90} + 60 q^{92} - 32 q^{93} + 18 q^{94} - 18 q^{96} - 12 q^{97}+O(q^{100}) \) 48 * q + 6 * q^6 + 4 * q^9 - 22 * q^12 - 30 * q^14 - 16 * q^18 - 4 * q^21 - 28 * q^24 + 24 * q^25 - 12 * q^29 + 16 * q^30 - 44 * q^33 - 6 * q^34 + 42 * q^36 + 60 * q^38 - 6 * q^40 - 60 * q^41 - 18 * q^42 - 8 * q^45 - 12 * q^46 - 12 * q^48 + 24 * q^49 - 18 * q^52 - 32 * q^54 - 42 * q^56 - 12 * q^57 - 18 * q^58 + 14 * q^60 - 48 * q^64 + 16 * q^66 + 48 * q^68 + 36 * q^69 + 60 * q^72 - 24 * q^73 + 84 * q^74 + 6 * q^76 + 48 * q^77 + 38 * q^78 - 36 * q^82 + 50 * q^84 - 54 * q^86 - 18 * q^90 + 60 * q^92 - 32 * q^93 + 18 * q^94 - 18 * q^96 - 12 * q^97

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