LMFDB - Embedded newform 414.2.e.e.277.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(139,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("414.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.e (of order $3$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 4x^{10} - 3x^{9} + 22x^{8} - 9x^{7} + 69x^{6} - 27x^{5} + 198x^{4} - 81x^{3} + 324x^{2} + 729 $ x^12 + 4x^10 - 3x^9 + 22x^8 - 9x^7 + 69x^6 - 27x^5 + 198x^4 - 81x^3 + 324*x^2 + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.5
Root			$-1.07449 - 1.35848i$ of defining polynomial
Character	$\chi$	$=$	414.277
Dual form			414.2.e.e.139.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(1.07449 + 1.35848i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.11191 + 1.92588i) q^{5} +(1.71372 - 0.251297i) q^{6} +(-0.920971 + 1.59517i) q^{7} -1.00000 q^{8} +(-0.690936 + 2.91935i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(1.07449 + 1.35848i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.11191 + 1.92588i) q^{5} +(1.71372 - 0.251297i) q^{6} +(-0.920971 + 1.59517i) q^{7} -1.00000 q^{8} +(-0.690936 + 2.91935i) q^{9} +2.22381 q^{10} +(0.563838 - 0.976597i) q^{11} +(0.639232 - 1.60978i) q^{12} +(0.510653 + 0.884477i) q^{13} +(0.920971 + 1.59517i) q^{14} +(-1.42153 + 3.57984i) q^{15} +(-0.500000 + 0.866025i) q^{16} -0.618128 q^{17} +(2.18276 + 2.05804i) q^{18} +2.53085 q^{19} +(1.11191 - 1.92588i) q^{20} +(-3.15658 + 0.462874i) q^{21} +(-0.563838 - 0.976597i) q^{22} +(0.500000 + 0.866025i) q^{23} +(-1.07449 - 1.35848i) q^{24} +(0.0273254 - 0.0473289i) q^{25} +1.02131 q^{26} +(-4.70828 + 2.19819i) q^{27} +1.84194 q^{28} +(0.936162 - 1.62148i) q^{29} +(2.38947 + 3.02101i) q^{30} +(-2.78912 - 4.83089i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.93253 - 0.283382i) q^{33} +(-0.309064 + 0.535315i) q^{34} -4.09614 q^{35} +(2.87370 - 0.861307i) q^{36} +8.21587 q^{37} +(1.26543 - 2.19178i) q^{38} +(-0.652852 + 1.64408i) q^{39} +(-1.11191 - 1.92588i) q^{40} +(-1.63379 - 2.82981i) q^{41} +(-1.17743 + 2.96512i) q^{42} +(6.36667 - 11.0274i) q^{43} -1.12768 q^{44} +(-6.39057 + 1.91539i) q^{45} +1.00000 q^{46} +(-1.77134 + 3.06805i) q^{47} +(-1.71372 + 0.251297i) q^{48} +(1.80362 + 3.12397i) q^{49} +(-0.0273254 - 0.0473289i) q^{50} +(-0.664173 - 0.839715i) q^{51} +(0.510653 - 0.884477i) q^{52} -5.09842 q^{53} +(-0.450450 + 5.17659i) q^{54} +2.50774 q^{55} +(0.920971 - 1.59517i) q^{56} +(2.71938 + 3.43812i) q^{57} +(-0.936162 - 1.62148i) q^{58} +(0.660644 + 1.14427i) q^{59} +(3.81100 - 0.558838i) q^{60} +(1.42302 - 2.46474i) q^{61} -5.57824 q^{62} +(-4.02052 - 3.79080i) q^{63} +1.00000 q^{64} +(-1.13560 + 1.96691i) q^{65} +(0.720848 - 1.81531i) q^{66} +(-5.72834 - 9.92178i) q^{67} +(0.309064 + 0.535315i) q^{68} +(-0.639232 + 1.60978i) q^{69} +(-2.04807 + 3.54736i) q^{70} -9.45942 q^{71} +(0.690936 - 2.91935i) q^{72} +8.40706 q^{73} +(4.10793 - 7.11515i) q^{74} +(0.0936563 - 0.0137336i) q^{75} +(-1.26543 - 2.19178i) q^{76} +(1.03856 + 1.79883i) q^{77} +(1.09738 + 1.38742i) q^{78} +(5.68834 - 9.85249i) q^{79} -2.22381 q^{80} +(-8.04522 - 4.03417i) q^{81} -3.26759 q^{82} +(0.993418 - 1.72065i) q^{83} +(1.97915 + 2.50224i) q^{84} +(-0.687301 - 1.19044i) q^{85} +(-6.36667 - 11.0274i) q^{86} +(3.20865 - 0.470509i) q^{87} +(-0.563838 + 0.976597i) q^{88} -12.1601 q^{89} +(-1.53651 + 6.49209i) q^{90} -1.88119 q^{91} +(0.500000 - 0.866025i) q^{92} +(3.56579 - 8.97972i) q^{93} +(1.77134 + 3.06805i) q^{94} +(2.81408 + 4.87412i) q^{95} +(-0.639232 + 1.60978i) q^{96} +(-4.13604 + 7.16383i) q^{97} +3.60725 q^{98} +(2.46145 + 2.32081i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - 6 q^{4} + 5 q^{5} - 3 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) $ 12 * q + 6 * q^2 - 6 * q^4 + 5 * q^5 - 3 * q^7 - 12 * q^8 - 8 * q^9	\( 12 q + 6 q^{2} - 6 q^{4} + 5 q^{5} - 3 q^{7} - 12 q^{8} - 8 q^{9} + 10 q^{10} + 6 q^{11} - 6 q^{13} + 3 q^{14} + 7 q^{15} - 6 q^{16} - 8 q^{17} - 10 q^{18} + 4 q^{19} + 5 q^{20} + 17 q^{21} - 6 q^{22} + 6 q^{23} + q^{25} - 12 q^{26} - 9 q^{27} + 6 q^{28} + 12 q^{29} - q^{30} - 6 q^{31} + 6 q^{32} + 9 q^{33} - 4 q^{34} - 34 q^{35} - 2 q^{36} + 8 q^{37} + 2 q^{38} + 23 q^{39} - 5 q^{40} + 15 q^{41} + 7 q^{42} - 14 q^{43} - 12 q^{44} - 37 q^{45} + 12 q^{46} + 9 q^{47} - 5 q^{49} - q^{50} + 9 q^{51} - 6 q^{52} - 10 q^{53} - 9 q^{54} + 16 q^{55} + 3 q^{56} + 37 q^{57} - 12 q^{58} + 18 q^{59} - 8 q^{60} - 3 q^{61} - 12 q^{62} - 42 q^{63} + 12 q^{64} + 9 q^{65} + 3 q^{66} + 8 q^{67} + 4 q^{68} - 17 q^{70} - 18 q^{71} + 8 q^{72} - 32 q^{73} + 4 q^{74} + 34 q^{75} - 2 q^{76} - q^{77} + 22 q^{78} - 7 q^{79} - 10 q^{80} - 56 q^{81} + 30 q^{82} + 3 q^{83} - 10 q^{84} + 7 q^{85} + 14 q^{86} - 9 q^{87} - 6 q^{88} - 42 q^{89} - 17 q^{90} + 18 q^{91} + 6 q^{92} + 69 q^{93} - 9 q^{94} + 11 q^{95} + 13 q^{97} - 10 q^{98} - 60 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 - 6 * q^4 + 5 * q^5 - 3 * q^7 - 12 * q^8 - 8 * q^9 + 10 * q^10 + 6 * q^11 - 6 * q^13 + 3 * q^14 + 7 * q^15 - 6 * q^16 - 8 * q^17 - 10 * q^18 + 4 * q^19 + 5 * q^20 + 17 * q^21 - 6 * q^22 + 6 * q^23 + q^25 - 12 * q^26 - 9 * q^27 + 6 * q^28 + 12 * q^29 - q^30 - 6 * q^31 + 6 * q^32 + 9 * q^33 - 4 * q^34 - 34 * q^35 - 2 * q^36 + 8 * q^37 + 2 * q^38 + 23 * q^39 - 5 * q^40 + 15 * q^41 + 7 * q^42 - 14 * q^43 - 12 * q^44 - 37 * q^45 + 12 * q^46 + 9 * q^47 - 5 * q^49 - q^50 + 9 * q^51 - 6 * q^52 - 10 * q^53 - 9 * q^54 + 16 * q^55 + 3 * q^56 + 37 * q^57 - 12 * q^58 + 18 * q^59 - 8 * q^60 - 3 * q^61 - 12 * q^62 - 42 * q^63 + 12 * q^64 + 9 * q^65 + 3 * q^66 + 8 * q^67 + 4 * q^68 - 17 * q^70 - 18 * q^71 + 8 * q^72 - 32 * q^73 + 4 * q^74 + 34 * q^75 - 2 * q^76 - q^77 + 22 * q^78 - 7 * q^79 - 10 * q^80 - 56 * q^81 + 30 * q^82 + 3 * q^83 - 10 * q^84 + 7 * q^85 + 14 * q^86 - 9 * q^87 - 6 * q^88 - 42 * q^89 - 17 * q^90 + 18 * q^91 + 6 * q^92 + 69 * q^93 - 9 * q^94 + 11 * q^95 + 13 * q^97 - 10 * q^98 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	1.07449	+	1.35848i	0.620358	+	0.784319i
$3$	1.07449	+	1.35848i	0.620358	+	0.784319i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.11191	+	1.92588i	0.497260	+	0.861280i	0.999995	−	0.00316105i	$-0.00100619\pi$
$5$	1.11191	+	1.92588i	0.497260	+	0.861280i	−0.502735	+	0.864441i	$0.667673\pi$
$6$	1.71372	−	0.251297i	0.699625	−	0.102592i
$7$	−0.920971	+	1.59517i	−0.348094	+	0.602917i	−0.985911	−	0.167271i	$-0.946504\pi$
$7$	−0.920971	+	1.59517i	−0.348094	+	0.602917i	0.637817	+	0.770188i	$0.279838\pi$
$8$	−1.00000			−0.353553
$9$	−0.690936	+	2.91935i	−0.230312	+	0.973117i
$10$	2.22381			0.703232
$11$	0.563838	−	0.976597i	0.170004	−	0.294455i	−0.768417	−	0.639949i	$-0.778955\pi$
$11$	0.563838	−	0.976597i	0.170004	−	0.294455i	0.938421	+	0.345494i	$0.112289\pi$
$12$	0.639232	−	1.60978i	0.184531	−	0.464703i
$13$	0.510653	+	0.884477i	0.141630	+	0.245310i	0.928110	−	0.372305i	$-0.121432\pi$
$13$	0.510653	+	0.884477i	0.141630	+	0.245310i	−0.786481	+	0.617615i	$0.788099\pi$
$14$	0.920971	+	1.59517i	0.246140	+	0.426327i
$15$	−1.42153	+	3.57984i	−0.367039	+	0.924312i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.618128			−0.149918			−0.0749591	−	0.997187i	$-0.523883\pi$
$17$	−0.618128			−0.149918			−0.0749591	+	0.997187i	$0.523883\pi$
$18$	2.18276	+	2.05804i	0.514482	+	0.485085i
$19$	2.53085			0.580618			0.290309	−	0.956933i	$-0.406242\pi$
$19$	2.53085			0.580618			0.290309	+	0.956933i	$0.406242\pi$
$20$	1.11191	−	1.92588i	0.248630	−	0.430640i
$21$	−3.15658	+	0.462874i	−0.688822	+	0.101007i
$22$	−0.563838	−	0.976597i	−0.120211	−	0.208211i
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$24$	−1.07449	−	1.35848i	−0.219330	−	0.277299i
$25$	0.0273254	−	0.0473289i	0.00546508	−	0.00946579i
$26$	1.02131			0.200295
$27$	−4.70828	+	2.19819i	−0.906110	+	0.423043i
$28$	1.84194			0.348094
$29$	0.936162	−	1.62148i	0.173841	−	0.301101i	−0.765919	−	0.642937i	$-0.777716\pi$
$29$	0.936162	−	1.62148i	0.173841	−	0.301101i	0.939760	+	0.341836i	$0.111049\pi$
$30$	2.38947	+	3.02101i	0.436255	+	0.551558i
$31$	−2.78912	−	4.83089i	−0.500940	−	0.867654i	−0.999999	−	0.00108620i	$-0.999654\pi$
$31$	−2.78912	−	4.83089i	−0.500940	−	0.867654i	0.499059	−	0.866568i	$-0.333679\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	1.93253	−	0.283382i	0.336410	−	0.0493304i
$34$	−0.309064	+	0.535315i	−0.0530041	+	0.0918057i
$35$	−4.09614			−0.692374
$36$	2.87370	−	0.861307i	0.478950	−	0.143551i
$37$	8.21587			1.35068			0.675340	−	0.737507i	$-0.263997\pi$
$37$	8.21587			1.35068			0.675340	+	0.737507i	$0.263997\pi$
$38$	1.26543	−	2.19178i	0.205279	−	0.355554i
$39$	−0.652852	+	1.64408i	−0.104540	+	0.263263i
$40$	−1.11191	−	1.92588i	−0.175808	−	0.304508i
$41$	−1.63379	−	2.82981i	−0.255156	−	0.441942i	0.709782	−	0.704421i	$-0.248793\pi$
$41$	−1.63379	−	2.82981i	−0.255156	−	0.441942i	−0.964938	+	0.262479i	$0.915460\pi$
$42$	−1.17743	+	2.96512i	−0.181681	+	0.457527i
$43$	6.36667	−	11.0274i	0.970908	−	1.68166i	0.278082	−	0.960557i	$-0.410301\pi$
$43$	6.36667	−	11.0274i	0.970908	−	1.68166i	0.692826	−	0.721105i	$-0.256365\pi$
$44$	−1.12768			−0.170004
$45$	−6.39057	+	1.91539i	−0.952651	+	0.285529i
$46$	1.00000			0.147442
$47$	−1.77134	+	3.06805i	−0.258377	+	0.447522i	−0.965807	−	0.259261i	$-0.916521\pi$
$47$	−1.77134	+	3.06805i	−0.258377	+	0.447522i	0.707431	+	0.706783i	$0.249854\pi$
$48$	−1.71372	+	0.251297i	−0.247355	+	0.0362716i
$49$	1.80362	+	3.12397i	0.257661	+	0.446281i
$50$	−0.0273254	−	0.0473289i	−0.00386439	−	0.00669332i
$51$	−0.664173	−	0.839715i	−0.0930029	−	0.117584i
$52$	0.510653	−	0.884477i	0.0708148	−	0.122655i
$53$	−5.09842			−0.700322			−0.350161	−	0.936690i	$-0.613873\pi$
$53$	−5.09842			−0.700322			−0.350161	+	0.936690i	$0.613873\pi$
$54$	−0.450450	+	5.17659i	−0.0612984	+	0.704445i
$55$	2.50774			0.338144
$56$	0.920971	−	1.59517i	0.123070	−	0.213163i
$57$	2.71938	+	3.43812i	0.360191	+	0.455390i
$58$	−0.936162	−	1.62148i	−0.122924	−	0.212911i
$59$	0.660644	+	1.14427i	0.0860085	+	0.148971i	0.905821	−	0.423662i	$-0.139255\pi$
$59$	0.660644	+	1.14427i	0.0860085	+	0.148971i	−0.819812	+	0.572633i	$0.805922\pi$
$60$	3.81100	−	0.558838i	0.491998	−	0.0721456i
$61$	1.42302	−	2.46474i	0.182199	−	0.315577i	−0.760430	−	0.649419i	$-0.775012\pi$
$61$	1.42302	−	2.46474i	0.182199	−	0.315577i	0.942629	+	0.333842i	$0.108345\pi$
$62$	−5.57824			−0.708437
$63$	−4.02052	−	3.79080i	−0.506539	−	0.477596i
$64$	1.00000			0.125000
$65$	−1.13560	+	1.96691i	−0.140854	+	0.243966i
$66$	0.720848	−	1.81531i	0.0887302	−	0.223449i
$67$	−5.72834	−	9.92178i	−0.699828	−	1.21214i	−0.968526	−	0.248913i	$-0.919927\pi$
$67$	−5.72834	−	9.92178i	−0.699828	−	1.21214i	0.268698	−	0.963225i	$-0.413407\pi$
$68$	0.309064	+	0.535315i	0.0374795	+	0.0649164i
$69$	−0.639232	+	1.60978i	−0.0769545	+	0.193794i
$70$	−2.04807	+	3.54736i	−0.244791	+	0.423990i
$71$	−9.45942			−1.12263			−0.561313	−	0.827603i	$-0.689704\pi$
$71$	−9.45942			−1.12263			−0.561313	+	0.827603i	$0.689704\pi$
$72$	0.690936	−	2.91935i	0.0814276	−	0.344049i
$73$	8.40706			0.983972			0.491986	−	0.870603i	$-0.336271\pi$
$73$	8.40706			0.983972			0.491986	+	0.870603i	$0.336271\pi$
$74$	4.10793	−	7.11515i	0.477537	−	0.827119i
$75$	0.0936563	−	0.0137336i	0.0108145	−	0.00158582i
$76$	−1.26543	−	2.19178i	−0.145154	−	0.251415i
$77$	1.03856	+	1.79883i	0.118355	+	0.204996i
$78$	1.09738	+	1.38742i	0.124254	+	0.157095i
$79$	5.68834	−	9.85249i	0.639988	−	1.10849i	−0.345447	−	0.938438i	$-0.612273\pi$
$79$	5.68834	−	9.85249i	0.639988	−	1.10849i	0.985435	−	0.170053i	$-0.0543940\pi$
$80$	−2.22381			−0.248630
$81$	−8.04522	−	4.03417i	−0.893913	−	0.448241i
$82$	−3.26759			−0.360844
$83$	0.993418	−	1.72065i	0.109042	−	0.188866i	−0.806341	−	0.591452i	$-0.798555\pi$
$83$	0.993418	−	1.72065i	0.109042	−	0.188866i	0.915382	+	0.402586i	$0.131888\pi$
$84$	1.97915	+	2.50224i	0.215943	+	0.273017i
$85$	−0.687301	−	1.19044i	−0.0745483	−	0.129121i
$86$	−6.36667	−	11.0274i	−0.686536	−	1.18911i
$87$	3.20865	−	0.470509i	0.344003	−	0.0504439i
$88$	−0.563838	+	0.976597i	−0.0601054	+	0.104106i
$89$	−12.1601			−1.28897			−0.644486	−	0.764616i	$-0.722928\pi$
$89$	−12.1601			−1.28897			−0.644486	+	0.764616i	$0.722928\pi$
$90$	−1.53651	+	6.49209i	−0.161963	+	0.684327i
$91$	−1.88119			−0.197202
$92$	0.500000	−	0.866025i	0.0521286	−	0.0902894i
$93$	3.56579	−	8.97972i	0.369755	−	0.931153i
$94$	1.77134	+	3.06805i	0.182700	+	0.316446i
$95$	2.81408	+	4.87412i	0.288718	+	0.500074i
$96$	−0.639232	+	1.60978i	−0.0652414	+	0.164297i
$97$	−4.13604	+	7.16383i	−0.419951	+	0.727377i	−0.995934	−	0.0900850i	$-0.971286\pi$
$97$	−4.13604	+	7.16383i	−0.419951	+	0.727377i	0.575983	+	0.817462i	$0.304619\pi$
$98$	3.60725			0.364387
$99$	2.46145	+	2.32081i	0.247385	+	0.233250i
$100$	−0.0546508			−0.00546508
$101$	−7.67597	+	13.2952i	−0.763787	+	1.32292i	0.177098	+	0.984193i	$0.443329\pi$
$101$	−7.67597	+	13.2952i	−0.763787	+	1.32292i	−0.940885	+	0.338725i	$0.890004\pi$
$102$	−1.05930	+	0.155334i	−0.104886	+	0.0153803i
$103$	3.17685	+	5.50247i	0.313024	+	0.542174i	0.979016	−	0.203786i	$-0.0653245\pi$
$103$	3.17685	+	5.50247i	0.313024	+	0.542174i	−0.665991	+	0.745960i	$0.731991\pi$
$104$	−0.510653	−	0.884477i	−0.0500737	−	0.0867301i
$105$	−4.40126	−	5.56452i	−0.429519	−	0.543042i
$106$	−2.54921	+	4.41536i	−0.247601	+	0.428858i
$107$	−0.788014			−0.0761801			−0.0380901	−	0.999274i	$-0.512127\pi$
$107$	−0.788014			−0.0761801			−0.0380901	+	0.999274i	$0.512127\pi$
$108$	4.25783	+	2.97840i	0.409710	+	0.286596i
$109$	−5.24332			−0.502219			−0.251109	−	0.967959i	$-0.580795\pi$
$109$	−5.24332			−0.502219			−0.251109	+	0.967959i	$0.580795\pi$
$110$	1.25387	−	2.17177i	0.119552	−	0.207070i
$111$	8.82788	+	11.1611i	0.837905	+	1.05936i
$112$	−0.920971	−	1.59517i	−0.0870236	−	0.150729i
$113$	−0.0313964	−	0.0543802i	−0.00295352	−	0.00511565i	0.864545	−	0.502556i	$-0.167607\pi$
$113$	−0.0313964	−	0.0543802i	−0.00295352	−	0.00511565i	−0.867498	+	0.497440i	$0.834273\pi$
$114$	4.33719	−	0.635996i	0.406215	−	0.0595665i
$115$	−1.11191	+	1.92588i	−0.103686	+	0.179589i
$116$	−1.87232			−0.173841
$117$	−2.93493	+	0.879658i	−0.271334	+	0.0813245i
$118$	1.32129			0.121634
$119$	0.569278	−	0.986019i	0.0521856	−	0.0903882i
$120$	1.42153	−	3.57984i	0.129768	−	0.326794i
$121$	4.86417	+	8.42499i	0.442198	+	0.765909i
$122$	−1.42302	−	2.46474i	−0.128834	−	0.223147i
$123$	2.08875	−	5.26008i	0.188336	−	0.474286i
$124$	−2.78912	+	4.83089i	−0.250470	+	0.433827i
$125$	11.2406			1.00539
$126$	−5.29319	+	1.58648i	−0.471555	+	0.141335i
$127$	−21.2474			−1.88541			−0.942703	−	0.333633i	$-0.891725\pi$
$127$	−21.2474			−1.88541			−0.942703	+	0.333633i	$0.891725\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	21.8214	−	3.19985i	1.92127	−	0.281731i
$130$	1.13560	+	1.96691i	0.0995985	+	0.172510i
$131$	−8.44197	−	14.6219i	−0.737579	−	1.27752i	−0.953583	−	0.301131i	$-0.902636\pi$
$131$	−8.44197	−	14.6219i	−0.737579	−	1.27752i	0.216004	−	0.976393i	$-0.430698\pi$
$132$	−1.21168	−	1.53193i	−0.105463	−	0.133337i
$133$	−2.33084	+	4.03714i	−0.202110	+	0.350065i
$134$	−11.4567			−0.989706
$135$	−9.46863	−	6.62340i	−0.814930	−	0.570051i
$136$	0.618128			0.0530041
$137$	3.97610	−	6.88680i	0.339701	−	0.588379i	−0.644676	−	0.764456i	$-0.723008\pi$
$137$	3.97610	−	6.88680i	0.339701	−	0.588379i	0.984376	+	0.176077i	$0.0563409\pi$
$138$	1.07449	+	1.35848i	0.0914668	+	0.115641i
$139$	−2.53346	−	4.38808i	−0.214885	−	0.372192i	0.738352	−	0.674416i	$-0.235604\pi$
$139$	−2.53346	−	4.38808i	−0.214885	−	0.372192i	−0.953237	+	0.302224i	$0.902271\pi$
$140$	2.04807	+	3.54736i	0.173093	+	0.299807i
$141$	−6.07118	+	0.890265i	−0.511286	+	0.0749739i
$142$	−4.72971	+	8.19210i	−0.396909	+	0.687466i
$143$	1.15170			0.0963103
$144$	−2.18276	−	2.05804i	−0.181897	−	0.171504i
$145$	4.16370			0.345776
$146$	4.20353	−	7.28072i	0.347886	−	0.602557i
$147$	−2.30587	+	5.80687i	−0.190185	+	0.478942i
$148$	−4.10793	−	7.11515i	−0.337670	−	0.584862i
$149$	2.97269	+	5.14885i	0.243532	+	0.421810i	0.961718	−	0.274041i	$-0.0883605\pi$
$149$	2.97269	+	5.14885i	0.243532	+	0.421810i	−0.718186	+	0.695852i	$0.755027\pi$
$150$	0.0349345	−	0.0879755i	0.00285239	−	0.00718317i
$151$	−1.01521	+	1.75840i	−0.0826168	+	0.143096i	−0.904373	−	0.426742i	$-0.859661\pi$
$151$	−1.01521	+	1.75840i	−0.0826168	+	0.143096i	0.821756	+	0.569839i	$0.192994\pi$
$152$	−2.53085			−0.205279
$153$	0.427087	−	1.80453i	0.0345279	−	0.145888i
$154$	2.07712			0.167379
$155$	6.20248	−	10.7430i	0.498195	−	0.862899i
$156$	1.75024	−	0.256651i	0.140131	−	0.0205485i
$157$	8.22657	+	14.2488i	0.656552	+	1.13718i	0.981502	+	0.191450i	$0.0613189\pi$
$157$	8.22657	+	14.2488i	0.656552	+	1.13718i	−0.324951	+	0.945731i	$0.605348\pi$
$158$	−5.68834	−	9.85249i	−0.452540	−	0.783822i
$159$	−5.47821	−	6.92610i	−0.434450	−	0.549276i
$160$	−1.11191	+	1.92588i	−0.0879040	+	0.152254i
$161$	−1.84194			−0.145165
$162$	−7.51630	+	4.95028i	−0.590536	+	0.388930i
$163$	1.48687			0.116460			0.0582302	−	0.998303i	$-0.481454\pi$
$163$	1.48687			0.116460			0.0582302	+	0.998303i	$0.481454\pi$
$164$	−1.63379	+	2.82981i	−0.127578	+	0.220971i
$165$	2.69455	+	3.40672i	0.209770	+	0.265213i
$166$	−0.993418	−	1.72065i	−0.0771042	−	0.133548i
$167$	8.12382	+	14.0709i	0.628640	+	1.08884i	0.987825	+	0.155570i	$0.0497213\pi$
$167$	8.12382	+	14.0709i	0.628640	+	1.08884i	−0.359185	+	0.933266i	$0.616945\pi$
$168$	3.15658	−	0.462874i	0.243535	−	0.0357115i
$169$	5.97847	−	10.3550i	0.459882	−	0.796539i
$170$	−1.37460			−0.105427
$171$	−1.74866	+	7.38845i	−0.133723	+	0.565009i
$172$	−12.7333			−0.970908
$173$	0.709632	−	1.22912i	0.0539523	−	0.0934481i	−0.837788	−	0.545996i	$-0.816151\pi$
$173$	0.709632	−	1.22912i	0.0539523	−	0.0934481i	0.891740	+	0.452548i	$0.149485\pi$
$174$	1.19685	−	3.01402i	0.0907329	−	0.228492i
$175$	0.0503318	+	0.0871772i	0.00380472	+	0.00658998i
$176$	0.563838	+	0.976597i	0.0425009	+	0.0736138i
$177$	−0.844610	+	2.12698i	−0.0634848	+	0.159874i
$178$	−6.08007	+	10.5310i	−0.455720	+	0.789331i
$179$	−12.3925			−0.926258			−0.463129	−	0.886291i	$-0.653273\pi$
$179$	−12.3925			−0.926258			−0.463129	+	0.886291i	$0.653273\pi$
$180$	4.85406	+	4.57671i	0.361800	+	0.341128i
$181$	10.0398			0.746250			0.373125	−	0.927781i	$-0.378286\pi$
$181$	10.0398			0.746250			0.373125	+	0.927781i	$0.378286\pi$
$182$	−0.940594	+	1.62916i	−0.0697214	+	0.120761i
$183$	4.87731	−	0.715199i	0.360541	−	0.0528690i
$184$	−0.500000	−	0.866025i	−0.0368605	−	0.0638442i
$185$	9.13528	+	15.8228i	0.671639	+	1.16331i
$186$	−5.99377	−	7.57792i	−0.439484	−	0.555640i
$187$	−0.348524	+	0.603662i	−0.0254866	+	0.0441441i
$188$	3.54268			0.258377
$189$	0.829702	−	9.53498i	0.0603519	−	0.693568i
$190$	5.62815			0.408309
$191$	7.56965	−	13.1110i	0.547720	−	0.948680i	−0.450710	−	0.892671i	$-0.648829\pi$
$191$	7.56965	−	13.1110i	0.547720	−	0.948680i	0.998430	−	0.0560091i	$-0.0178376\pi$
$192$	1.07449	+	1.35848i	0.0775447	+	0.0980399i
$193$	5.00671	+	8.67188i	0.360391	+	0.624215i	0.988025	−	0.154293i	$-0.0493100\pi$
$193$	5.00671	+	8.67188i	0.360391	+	0.624215i	−0.627634	+	0.778508i	$0.715977\pi$
$194$	4.13604	+	7.16383i	0.296950	+	0.514333i
$195$	−3.89220	+	0.570744i	−0.278726	+	0.0408719i
$196$	1.80362	−	3.12397i	0.128830	−	0.223141i
$197$	9.84084			0.701131			0.350565	−	0.936538i	$-0.385989\pi$
$197$	9.84084			0.701131			0.350565	+	0.936538i	$0.385989\pi$
$198$	3.24060	−	0.971276i	0.230300	−	0.0690256i
$199$	8.48844			0.601729			0.300865	−	0.953667i	$-0.402725\pi$
$199$	8.48844			0.601729			0.300865	+	0.953667i	$0.402725\pi$
$200$	−0.0273254	+	0.0473289i	−0.00193220	+	0.00334666i
$201$	7.32348	−	18.4427i	0.516559	−	1.30085i
$202$	7.67597	+	13.2952i	0.540079	+	0.935445i
$203$	1.72436	+	2.98667i	0.121026	+	0.209623i
$204$	−0.395128	+	0.995049i	−0.0276645	+	0.0696673i
$205$	3.63325	−	6.29298i	0.253757	−	0.439520i
$206$	6.35370			0.442683
$207$	−2.87370	+	0.861307i	−0.199736	+	0.0598650i
$208$	−1.02131			−0.0708148
$209$	1.42699	−	2.47162i	0.0987072	−	0.170966i
$210$	−7.01965	+	1.02935i	−0.484402	+	0.0710317i
$211$	0.956140	+	1.65608i	0.0658234	+	0.114009i	0.897059	−	0.441911i	$-0.145699\pi$
$211$	0.956140	+	1.65608i	0.0658234	+	0.114009i	−0.831236	+	0.555920i	$0.812366\pi$
$212$	2.54921	+	4.41536i	0.175081	+	0.303248i
$213$	−10.1641	−	12.8504i	−0.696431	−	0.880497i
$214$	−0.394007	+	0.682440i	−0.0269337	+	0.0466506i
$215$	28.3166			1.93117
$216$	4.70828	−	2.19819i	0.320358	−	0.149568i
$217$	10.2748			0.697498
$218$	−2.62166	+	4.54084i	−0.177561	+	0.307545i
$219$	9.03331	+	11.4208i	0.610415	+	0.771747i
$220$	−1.25387	−	2.17177i	−0.0845360	−	0.146421i
$221$	−0.315649	−	0.546720i	−0.0212329	−	0.0367764i
$222$	14.0797	−	2.06462i	0.944969	−	0.138568i
$223$	7.13206	−	12.3531i	0.477598	−	0.827224i	−0.522072	−	0.852901i	$-0.674841\pi$
$223$	7.13206	−	12.3531i	0.477598	−	0.827224i	0.999670	+	0.0256772i	$0.00817421\pi$
$224$	−1.84194			−0.123070
$225$	0.119290	+	0.112474i	0.00795265	+	0.00749824i
$226$	−0.0627928			−0.00417691
$227$	−1.62900	+	2.82152i	−0.108121	+	0.187271i	−0.915009	−	0.403433i	$-0.867817\pi$
$227$	−1.62900	+	2.82152i	−0.108121	+	0.187271i	0.806888	+	0.590704i	$0.201150\pi$
$228$	1.61780	−	4.07411i	0.107142	−	0.269815i
$229$	1.46882	+	2.54407i	0.0970625	+	0.168117i	0.910468	−	0.413581i	$-0.135722\pi$
$229$	1.46882	+	2.54407i	0.0970625	+	0.168117i	−0.813405	+	0.581698i	$0.802389\pi$
$230$	1.11191	+	1.92588i	0.0733170	+	0.126989i
$231$	−1.32776	+	3.34369i	−0.0873602	+	0.219999i
$232$	−0.936162	+	1.62148i	−0.0614620	+	0.106455i
$233$	13.2649			0.869011			0.434505	−	0.900669i	$-0.356923\pi$
$233$	13.2649			0.869011			0.434505	+	0.900669i	$0.356923\pi$
$234$	−0.705657	+	2.98155i	−0.0461303	+	0.194910i
$235$	−7.87827			−0.513921
$236$	0.660644	−	1.14427i	0.0430043	−	0.0744856i
$237$	19.4965	−	2.85892i	1.26643	−	0.185707i
$238$	−0.569278	−	0.986019i	−0.0369008	−	0.0639141i
$239$	9.22601	+	15.9799i	0.596781	+	1.03365i	0.993293	+	0.115625i	$0.0368872\pi$
$239$	9.22601	+	15.9799i	0.596781	+	1.03365i	−0.396512	+	0.918030i	$0.629779\pi$
$240$	−2.38947	−	3.02101i	−0.154240	−	0.195005i
$241$	1.66180	−	2.87832i	0.107046	−	0.185409i	−0.807526	−	0.589831i	$-0.799194\pi$
$241$	1.66180	−	2.87832i	0.107046	−	0.185409i	0.914572	+	0.404423i	$0.132528\pi$
$242$	9.72835			0.625362
$243$	−3.16418	−	15.2639i	−0.202982	−	0.979182i
$244$	−2.84603			−0.182199
$245$	−4.01093	+	6.94713i	−0.256249	+	0.443836i
$246$	−3.51099	−	4.43895i	−0.223853	−	0.283017i
$247$	1.29239	+	2.23848i	0.0822327	+	0.142431i
$248$	2.78912	+	4.83089i	0.177109	+	0.306762i
$249$	3.40489	−	0.499286i	0.215776	−	0.0316410i
$250$	5.62030	−	9.73465i	0.355459	−	0.615673i
$251$	−18.7472			−1.18331			−0.591656	−	0.806191i	$-0.701526\pi$
$251$	−18.7472			−1.18331			−0.591656	+	0.806191i	$0.701526\pi$
$252$	−1.27266	+	5.37728i	−0.0801703	+	0.338737i
$253$	1.12768			0.0708964
$254$	−10.6237	+	18.4008i	−0.666592	+	1.15457i
$255$	0.878690	−	2.21280i	0.0550257	−	0.138571i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	11.5310	+	19.9724i	0.719287	+	1.24584i	0.961283	+	0.275564i	$0.0888646\pi$
$257$	11.5310	+	19.9724i	0.719287	+	1.24584i	−0.241996	+	0.970277i	$0.577802\pi$
$258$	8.13956	−	20.4978i	0.506747	−	1.27614i
$259$	−7.56658	+	13.1057i	−0.470164	+	0.814348i
$260$	2.27120			0.140854
$261$	4.08684	+	3.85332i	0.252969	+	0.238515i
$262$	−16.8839			−1.04309
$263$	4.32917	−	7.49835i	0.266948	−	0.462368i	−0.701124	−	0.713039i	$-0.747318\pi$
$263$	4.32917	−	7.49835i	0.266948	−	0.462368i	0.968072	+	0.250671i	$0.0806514\pi$
$264$	−1.93253	+	0.283382i	−0.118939	+	0.0174409i
$265$	−5.66897	−	9.81895i	−0.348242	−	0.603173i
$266$	2.33084	+	4.03714i	0.142913	+	0.247533i
$267$	−13.0660	−	16.5193i	−0.799624	−	1.01096i
$268$	−5.72834	+	9.92178i	−0.349914	+	0.606069i
$269$	−11.2893			−0.688323			−0.344162	−	0.938910i	$-0.611837\pi$
$269$	−11.2893			−0.688323			−0.344162	+	0.938910i	$0.611837\pi$
$270$	−10.4703	+	4.88838i	−0.637205	+	0.297497i
$271$	−22.7798			−1.38378			−0.691888	−	0.722005i	$-0.743221\pi$
$271$	−22.7798			−1.38378			−0.691888	+	0.722005i	$0.743221\pi$
$272$	0.309064	−	0.535315i	0.0187398	−	0.0324582i
$273$	−2.02132	−	2.55556i	−0.122336	−	0.154669i
$274$	−3.97610	−	6.88680i	−0.240205	−	0.416047i
$275$	−0.0308142	−	0.0533718i	−0.00185817	−	0.00321844i
$276$	1.71372	−	0.251297i	0.103154	−	0.0151263i
$277$	−9.10849	+	15.7764i	−0.547276	+	0.947911i	0.451183	+	0.892431i	$0.351002\pi$
$277$	−9.10849	+	15.7764i	−0.547276	+	0.947911i	−0.998460	+	0.0554793i	$0.982331\pi$
$278$	−5.06692			−0.303893
$279$	16.0302	−	4.80457i	0.959701	−	0.287642i
$280$	4.09614			0.244791
$281$	8.01371	−	13.8802i	0.478058	−	0.828021i	−0.521626	−	0.853175i	$-0.674674\pi$
$281$	8.01371	−	13.8802i	0.478058	−	0.828021i	0.999684	+	0.0251537i	$0.00800751\pi$
$282$	−2.26460	+	5.70293i	−0.134855	+	0.339604i
$283$	−2.39616	−	4.15027i	−0.142437	−	0.246708i	0.785977	−	0.618256i	$-0.212160\pi$
$283$	−2.39616	−	4.15027i	−0.142437	−	0.246708i	−0.928414	+	0.371548i	$0.878827\pi$
$284$	4.72971	+	8.19210i	0.280657	+	0.486112i
$285$	−3.59770	+	9.06007i	−0.213109	+	0.536672i
$286$	0.575852	−	0.997404i	0.0340508	−	0.0589778i
$287$	6.01870			0.355273
$288$	−2.87370	+	0.861307i	−0.169334	+	0.0507530i
$289$	−16.6179			−0.977525
$290$	2.08185	−	3.60587i	0.122250	−	0.211744i
$291$	−14.1761	+	2.07875i	−0.831015	+	0.121858i
$292$	−4.20353	−	7.28072i	−0.245993	−	0.426072i
$293$	0.932969	+	1.61595i	0.0545046	+	0.0944047i	0.891990	−	0.452054i	$-0.149309\pi$
$293$	0.932969	+	1.61595i	0.0545046	+	0.0944047i	−0.837486	+	0.546459i	$0.815975\pi$
$294$	3.87596	+	4.90038i	0.226050	+	0.285796i
$295$	−1.46915	+	2.54464i	−0.0855372	+	0.148155i
$296$	−8.21587			−0.477537
$297$	−0.507961	+	5.83752i	−0.0294749	+	0.338727i
$298$	5.94538			0.344407
$299$	−0.510653	+	0.884477i	−0.0295318	+	0.0511506i
$300$	−0.0587218	−	0.0742420i	−0.00339030	−	0.00428636i
$301$	11.7270	+	20.3118i	0.675935	+	1.17075i
$302$	1.01521	+	1.75840i	0.0584189	+	0.101184i
$303$	−26.3090	+	3.85789i	−1.51141	+	0.221630i
$304$	−1.26543	+	2.19178i	−0.0725772	+	0.125707i
$305$	6.32905			0.362400
$306$	−1.34923	−	1.27213i	−0.0771302	−	0.0727231i
$307$	−4.12277			−0.235299			−0.117649	−	0.993055i	$-0.537536\pi$
$307$	−4.12277			−0.235299			−0.117649	+	0.993055i	$0.537536\pi$
$308$	1.03856	−	1.79883i	0.0591773	−	0.102498i
$309$	−4.06149	+	10.2280i	−0.231050	+	0.581853i
$310$	−6.20248	−	10.7430i	−0.352277	−	0.610162i
$311$	15.8693	+	27.4864i	0.899865	+	1.55861i	0.827665	+	0.561222i	$0.189669\pi$
$311$	15.8693	+	27.4864i	0.899865	+	1.55861i	0.0722001	+	0.997390i	$0.476998\pi$
$312$	0.652852	−	1.64408i	0.0369605	−	0.0930774i
$313$	11.6970	−	20.2599i	0.661156	−	1.14516i	−0.319157	−	0.947702i	$-0.603400\pi$
$313$	11.6970	−	20.2599i	0.661156	−	1.14516i	0.980312	−	0.197453i	$-0.0632671\pi$
$314$	16.4531			0.928504
$315$	2.83017	−	11.9581i	0.159462	−	0.673760i
$316$	−11.3767			−0.639988
$317$	−13.6539	+	23.6492i	−0.766878	+	1.32827i	0.172370	+	0.985032i	$0.444857\pi$
$317$	−13.6539	+	23.6492i	−0.766878	+	1.32827i	−0.939248	+	0.343239i	$0.888476\pi$
$318$	−8.73729	+	1.28122i	−0.489963	+	0.0718471i
$319$	−1.05569	−	1.82850i	−0.0591072	−	0.102377i
$320$	1.11191	+	1.92588i	0.0621575	+	0.107660i
$321$	−0.846714	−	1.07050i	−0.0472590	−	0.0597495i
$322$	−0.920971	+	1.59517i	−0.0513237	+	0.0888953i
$323$	−1.56439			−0.0870451
$324$	0.528915	+	8.98444i	0.0293842	+	0.499136i
$325$	0.0558152			0.00309607
$326$	0.743434	−	1.28766i	0.0411750	−	0.0713172i
$327$	−5.63390	−	7.12294i	−0.311555	−	0.393899i
$328$	1.63379	+	2.82981i	0.0902111	+	0.156250i
$329$	−3.26271	−	5.65118i	−0.179879	−	0.311559i
$330$	4.29758	−	0.630188i	0.236574	−	0.0346907i
$331$	−14.1660	+	24.5362i	−0.778634	+	1.34863i	0.154095	+	0.988056i	$0.450754\pi$
$331$	−14.1660	+	24.5362i	−0.778634	+	1.34863i	−0.932729	+	0.360578i	$0.882580\pi$
$332$	−1.98684			−0.109042
$333$	−5.67664	+	23.9850i	−0.311078	+	1.31437i
$334$	16.2476			0.889031
$335$	12.7388	−	22.0642i	0.695993	−	1.20550i
$336$	1.17743	−	2.96512i	0.0642340	−	0.161760i
$337$	−15.7110	−	27.2123i	−0.855833	−	1.48235i	−0.875870	−	0.482547i	$-0.839712\pi$
$337$	−15.7110	−	27.2123i	−0.855833	−	1.48235i	0.0200373	−	0.999799i	$-0.493622\pi$
$338$	−5.97847	−	10.3550i	−0.325186	−	0.563238i
$339$	0.0401392	−	0.101082i	0.00218006	−	0.00549004i
$340$	−0.687301	+	1.19044i	−0.0372741	+	0.0645607i
$341$	−6.29045			−0.340647
$342$	5.52426	+	5.20861i	0.298718	+	0.281649i
$343$	−19.5379			−1.05495
$344$	−6.36667	+	11.0274i	−0.343268	+	0.594557i
$345$	−3.81100	+	0.558838i	−0.205178	+	0.0300868i
$346$	−0.709632	−	1.22912i	−0.0381500	−	0.0660778i
$347$	−14.9415	−	25.8795i	−0.802102	−	1.38928i	−0.918230	−	0.396048i	$-0.870381\pi$
$347$	−14.9415	−	25.8795i	−0.802102	−	1.38928i	0.116128	−	0.993234i	$-0.462952\pi$
$348$	−2.01180	−	2.54351i	−0.107844	−	0.136347i
$349$	13.1752	−	22.8201i	0.705252	−	1.22153i	−0.261349	−	0.965244i	$-0.584167\pi$
$349$	13.1752	−	22.8201i	0.705252	−	1.22153i	0.966601	−	0.256288i	$-0.0824994\pi$
$350$	0.100664			0.00538069
$351$	−4.34855	−	3.04185i	−0.232109	−	0.162362i
$352$	1.12768			0.0601054
$353$	−1.77314	+	3.07117i	−0.0943747	+	0.163462i	−0.909347	−	0.416038i	$-0.863418\pi$
$353$	−1.77314	+	3.07117i	−0.0943747	+	0.163462i	0.814973	+	0.579499i	$0.196752\pi$
$354$	1.41971	+	1.79494i	0.0754569	+	0.0954002i
$355$	−10.5180	−	18.2177i	−0.558237	−	0.966896i
$356$	6.08007	+	10.5310i	0.322243	+	0.558141i
$357$	1.95117	−	0.286116i	0.103267	−	0.0151429i
$358$	−6.19624	+	10.7322i	−0.327482	+	0.567215i
$359$	−27.7114			−1.46255			−0.731276	−	0.682081i	$-0.761075\pi$
$359$	−27.7114			−1.46255			−0.731276	+	0.682081i	$0.761075\pi$
$360$	6.39057	−	1.91539i	0.336813	−	0.100950i
$361$	−12.5948			−0.662883
$362$	5.01988	−	8.69469i	0.263839	−	0.456983i
$363$	−6.21867	+	15.6605i	−0.326396	+	0.821961i
$364$	0.940594	+	1.62916i	0.0493005	+	0.0853910i
$365$	9.34787	+	16.1910i	0.489290	+	0.847475i
$366$	1.81928	−	4.58148i	0.0950951	−	0.239478i
$367$	−3.83429	+	6.64119i	−0.200148	+	0.346667i	−0.948576	−	0.316549i	$-0.897476\pi$
$367$	−3.83429	+	6.64119i	−0.200148	+	0.346667i	0.748428	+	0.663216i	$0.230809\pi$
$368$	−1.00000			−0.0521286
$369$	9.39006	−	2.81439i	0.488827	−	0.146512i
$370$	18.2706			0.949841
$371$	4.69550	−	8.13284i	0.243778	−	0.422236i
$372$	−9.55956	+	1.40179i	−0.495640	+	0.0726796i
$373$	17.6201	+	30.5189i	0.912334	+	1.58021i	0.810759	+	0.585381i	$0.199055\pi$
$373$	17.6201	+	30.5189i	0.912334	+	1.58021i	0.101575	+	0.994828i	$0.467612\pi$
$374$	0.348524	+	0.603662i	0.0180218	+	0.0312146i
$375$	12.0779	+	15.2701i	0.623702	+	0.788546i
$376$	1.77134	−	3.06805i	0.0913499	−	0.158223i
$377$	1.91222			0.0984841
$378$	−7.84269	−	5.48603i	−0.403384	−	0.282171i
$379$	−8.25013			−0.423781			−0.211890	−	0.977293i	$-0.567962\pi$
$379$	−8.25013			−0.423781			−0.211890	+	0.977293i	$0.567962\pi$
$380$	2.81408	−	4.87412i	0.144359	−	0.250037i
$381$	−22.8302	−	28.8642i	−1.16963	−	1.47876i
$382$	−7.56965	−	13.1110i	−0.387297	−	0.670818i
$383$	−8.59435	−	14.8859i	−0.439151	−	0.760632i	0.558473	−	0.829523i	$-0.311387\pi$
$383$	−8.59435	−	14.8859i	−0.439151	−	0.760632i	−0.997624	+	0.0688908i	$0.978054\pi$
$384$	1.71372	−	0.251297i	0.0874531	−	0.0128239i
$385$	−2.30956	+	4.00027i	−0.117706	+	0.203873i
$386$	10.0134			0.509670
$387$	27.7939	+	26.2058i	1.41284	+	1.33211i
$388$	8.27208			0.419951
$389$	−0.230741	+	0.399655i	−0.0116990	+	0.0202633i	−0.871816	−	0.489834i	$-0.837057\pi$
$389$	−0.230741	+	0.399655i	−0.0116990	+	0.0202633i	0.860117	+	0.510097i	$0.170391\pi$
$390$	−1.45182	+	3.65612i	−0.0735158	+	0.185135i
$391$	−0.309064	−	0.535315i	−0.0156300	−	0.0270720i
$392$	−1.80362	−	3.12397i	−0.0910968	−	0.157784i
$393$	10.7928	−	27.1794i	0.544423	−	1.37102i
$394$	4.92042	−	8.52241i	0.247887	−	0.429353i
$395$	25.2996			1.27296
$396$	0.779152	−	3.29208i	0.0391539	−	0.165433i
$397$	−21.3731			−1.07268			−0.536342	−	0.844001i	$-0.680194\pi$
$397$	−21.3731			−1.07268			−0.536342	+	0.844001i	$0.680194\pi$
$398$	4.24422	−	7.35120i	0.212743	−	0.368482i
$399$	−7.98885	+	1.17147i	−0.399943	+	0.0586468i
$400$	0.0273254	+	0.0473289i	0.00136627	+	0.00236645i
$401$	−18.7989	−	32.5606i	−0.938771	−	1.62600i	−0.767767	−	0.640729i	$-0.778632\pi$
$401$	−18.7989	−	32.5606i	−0.938771	−	1.62600i	−0.171004	−	0.985270i	$-0.554701\pi$
$402$	−12.3101	−	15.5637i	−0.613972	−	0.776245i
$403$	2.84854	−	4.93382i	0.141896	−	0.245771i
$404$	15.3519			0.763787
$405$	−1.17621	−	19.9797i	−0.0584463	−	0.992801i
$406$	3.44871			0.171157
$407$	4.63242	−	8.02359i	0.229621	−	0.397714i
$408$	0.664173	+	0.839715i	0.0328815	+	0.0415721i
$409$	15.1950	+	26.3185i	0.751345	+	1.30137i	0.947171	+	0.320729i	$0.103928\pi$
$409$	15.1950	+	26.3185i	0.751345	+	1.30137i	−0.195826	+	0.980639i	$0.562739\pi$
$410$	−3.63325	−	6.29298i	−0.179433	−	0.310788i
$411$	13.6279	−	1.99836i	0.672213	−	0.0985719i
$412$	3.17685	−	5.50247i	0.156512	−	0.271087i
$413$	−2.43374			−0.119756
$414$	−0.690936	+	2.91935i	−0.0339576	+	0.143478i
$415$	4.41835			0.216888
$416$	−0.510653	+	0.884477i	−0.0250368	+	0.0433651i
$417$	3.23894	−	8.15660i	0.158611	−	0.399431i
$418$	−1.42699	−	2.47162i	−0.0697965	−	0.120891i
$419$	−3.98972	−	6.91040i	−0.194911	−	0.337595i	0.751961	−	0.659208i	$-0.229108\pi$
$419$	−3.98972	−	6.91040i	−0.194911	−	0.337595i	−0.946871	+	0.321613i	$0.895775\pi$
$420$	−2.61838	+	6.59387i	−0.127764	+	0.321748i
$421$	−3.86156	+	6.68843i	−0.188201	+	0.325974i	−0.944651	−	0.328078i	$-0.893599\pi$
$421$	−3.86156	+	6.68843i	−0.188201	+	0.325974i	0.756449	+	0.654052i	$0.226932\pi$
$422$	1.91228			0.0930883
$423$	−7.73284	−	7.29099i	−0.375983	−	0.354500i
$424$	5.09842			0.247601
$425$	−0.0168906	+	0.0292554i	−0.000819314	+	0.00141909i
$426$	−16.2108	+	2.37712i	−0.785418	+	0.115172i
$427$	2.62111	+	4.53990i	0.126845	+	0.219701i
$428$	0.394007	+	0.682440i	0.0190450	+	0.0329870i
$429$	1.23750	+	1.56457i	0.0597468	+	0.0755380i
$430$	14.1583	−	24.5229i	0.682773	−	1.18260i
$431$	35.2560			1.69822			0.849111	−	0.528215i	$-0.177138\pi$
$431$	35.2560			1.69822			0.849111	+	0.528215i	$0.177138\pi$
$432$	0.450450	−	5.17659i	0.0216723	−	0.249059i
$433$	−10.3442			−0.497110			−0.248555	−	0.968618i	$-0.579956\pi$
$433$	−10.3442			−0.497110			−0.248555	+	0.968618i	$0.579956\pi$
$434$	5.13739	−	8.89823i	0.246603	−	0.427129i
$435$	4.47386	+	5.65630i	0.214505	+	0.271199i
$436$	2.62166	+	4.54084i	0.125555	+	0.217467i
$437$	1.26543	+	2.19178i	0.0605336	+	0.104847i
$438$	14.4074	−	2.11267i	0.688411	−	0.100947i
$439$	−14.3541	+	24.8621i	−0.685084	+	1.18660i	0.288326	+	0.957532i	$0.406901\pi$
$439$	−14.3541	+	24.8621i	−0.685084	+	1.18660i	−0.973410	+	0.229069i	$0.926432\pi$
$440$	−2.50774			−0.119552
$441$	−10.3661	+	3.10695i	−0.493626	+	0.147950i
$442$	−0.631298			−0.0300278
$443$	10.2742	−	17.7954i	0.488141	−	0.845485i	−0.511766	−	0.859125i	$-0.671008\pi$
$443$	10.2742	−	17.7954i	0.488141	−	0.845485i	0.999907	+	0.0136397i	$0.00434178\pi$
$444$	5.25185	−	13.2257i	0.249242	−	0.627664i
$445$	−13.5209	−	23.4189i	−0.640954	−	1.11016i
$446$	−7.13206	−	12.3531i	−0.337713	−	0.584936i
$447$	−3.80048	+	9.57074i	−0.179757	+	0.452680i
$448$	−0.920971	+	1.59517i	−0.0435118	+	0.0753646i
$449$	−20.9787			−0.990046			−0.495023	−	0.868880i	$-0.664840\pi$
$449$	−20.9787			−0.990046			−0.495023	+	0.868880i	$0.664840\pi$
$450$	0.157050	−	0.0470711i	0.00740340	−	0.00221895i
$451$	−3.68478			−0.173510
$452$	−0.0313964	+	0.0543802i	−0.00147676	+	0.00255783i
$453$	−3.47959	+	0.510239i	−0.163485	+	0.0239731i
$454$	1.62900	+	2.82152i	0.0764530	+	0.132420i
$455$	−2.09171	−	3.62294i	−0.0980607	−	0.169846i
$456$	−2.71938	−	3.43812i	−0.127347	−	0.161005i
$457$	13.2097	−	22.8799i	0.617925	−	1.07028i	−0.371938	−	0.928257i	$-0.621307\pi$
$457$	13.2097	−	22.8799i	0.617925	−	1.07028i	0.989864	−	0.142021i	$-0.0453599\pi$
$458$	2.93764			0.137267
$459$	2.91032	−	1.35877i	0.135842	−	0.0634218i
$460$	2.22381			0.103686
$461$	−17.7521	+	30.7475i	−0.826795	+	1.43205i	0.0737439	+	0.997277i	$0.476505\pi$
$461$	−17.7521	+	30.7475i	−0.826795	+	1.43205i	−0.900539	+	0.434775i	$0.856828\pi$
$462$	2.23184	+	2.82172i	0.103835	+	0.131278i
$463$	−11.7069	−	20.2769i	−0.544064	−	0.942346i	−0.998665	−	0.0516513i	$-0.983552\pi$
$463$	−11.7069	−	20.2769i	−0.544064	−	0.942346i	0.454601	−	0.890695i	$-0.349782\pi$
$464$	0.936162	+	1.62148i	0.0434602	+	0.0752753i
$465$	21.2587	−	3.11733i	0.985848	−	0.144563i
$466$	6.63244	−	11.4877i	0.307242	−	0.532158i
$467$	−31.1747			−1.44259			−0.721296	−	0.692627i	$-0.756453\pi$
$467$	−31.1747			−1.44259			−0.721296	+	0.692627i	$0.756453\pi$
$468$	2.22927	+	2.10189i	0.103048	+	0.0971600i
$469$	21.1025			0.974425
$470$	−3.93913	+	6.82278i	−0.181699	+	0.314711i
$471$	−10.5174	+	26.4859i	−0.484615	+	1.22040i
$472$	−0.660644	−	1.14427i	−0.0304086	−	0.0526692i
$473$	−7.17955	−	12.4353i	−0.330116	−	0.571777i
$474$	7.27234	−	18.3139i	0.334030	−	0.841186i
$475$	0.0691566	−	0.119783i	0.00317312	−	0.00549601i
$476$	−1.13856			−0.0521856
$477$	3.52268	−	14.8841i	0.161293	−	0.681495i
$478$	18.4520			0.843976
$479$	−12.6288	+	21.8737i	−0.577025	+	0.999436i	0.418794	+	0.908081i	$0.362453\pi$
$479$	−12.6288	+	21.8737i	−0.577025	+	0.999436i	−0.995818	+	0.0913549i	$0.970880\pi$
$480$	−3.81100	+	0.558838i	−0.173948	+	0.0255073i
$481$	4.19546	+	7.26675i	0.191296	+	0.331335i
$482$	−1.66180	−	2.87832i	−0.0756928	−	0.131104i
$483$	−1.97915	−	2.50224i	−0.0900545	−	0.113856i
$484$	4.86417	−	8.42499i	0.221099	−	0.382954i
$485$	−18.3956			−0.835300
$486$	−14.8011	−	4.89171i	−0.671389	−	0.221893i
$487$	−20.1864			−0.914732			−0.457366	−	0.889278i	$-0.651207\pi$
$487$	−20.1864			−0.914732			−0.457366	+	0.889278i	$0.651207\pi$
$488$	−1.42302	+	2.46474i	−0.0644169	+	0.111573i
$489$	1.59763	+	2.01988i	0.0722472	+	0.0913421i
$490$	4.01093	+	6.94713i	0.181195	+	0.313839i
$491$	9.36872	+	16.2271i	0.422804	+	0.732319i	0.996213	−	0.0869512i	$-0.0277124\pi$
$491$	9.36872	+	16.2271i	0.422804	+	0.732319i	−0.573408	+	0.819270i	$0.694379\pi$
$492$	−5.59974	+	0.821134i	−0.252456	+	0.0370196i
$493$	−0.578668	+	1.00228i	−0.0260619	+	0.0451405i
$494$	2.58478			0.116295
$495$	−1.73269	+	7.32098i	−0.0778786	+	0.329054i
$496$	5.57824			0.250470
$497$	8.71186	−	15.0894i	0.390780	−	0.676851i
$498$	1.27005	−	3.19836i	0.0569123	−	0.143322i
$499$	3.68302	+	6.37918i	0.164875	+	0.285571i	0.936611	−	0.350372i	$-0.113945\pi$
$499$	3.68302	+	6.37918i	0.164875	+	0.285571i	−0.771736	+	0.635943i	$0.780611\pi$
$500$	−5.62030	−	9.73465i	−0.251348	−	0.435347i
$501$	−10.3860	+	26.1551i	−0.464013	+	1.16852i
$502$	−9.37359	+	16.2355i	−0.418364	+	0.724628i
$503$	36.9598			1.64796			0.823978	−	0.566622i	$-0.191750\pi$
$503$	36.9598			1.64796			0.823978	+	0.566622i	$0.191750\pi$
$504$	4.02052	+	3.79080i	0.179088	+	0.168856i
$505$	−34.1399			−1.51920
$506$	0.563838	−	0.976597i	0.0250657	−	0.0434150i
$507$	20.4909	−	3.00474i	0.910032	−	0.133445i
$508$	10.6237	+	18.4008i	0.471351	+	0.816405i
$509$	−8.53970	−	14.7912i	−0.378515	−	0.655608i	0.612331	−	0.790601i	$-0.290232\pi$
$509$	−8.53970	−	14.7912i	−0.378515	−	0.655608i	−0.990846	+	0.134994i	$0.956899\pi$
$510$	−1.47700	−	1.86737i	−0.0654026	−	0.0826885i
$511$	−7.74266	+	13.4107i	−0.342515	+	0.593253i
$512$	−1.00000			−0.0441942
$513$	−11.9160	+	5.56331i	−0.526104	+	0.245626i
$514$	23.0621			1.01723
$515$	−7.06472	+	12.2365i	−0.311309	+	0.539203i
$516$	−13.6819	−	17.2980i	−0.602311	−	0.761501i
$517$	1.99750	+	3.45977i	0.0878500	+	0.152161i
$518$	7.56658	+	13.1057i	0.332456	+	0.575831i
$519$	2.43223	−	0.356656i	0.106763	−	0.0156555i
$520$	1.13560	−	1.96691i	0.0497993	−	0.0862548i
$521$	−43.3203			−1.89790			−0.948948	−	0.315433i	$-0.897850\pi$
$521$	−43.3203			−1.89790			−0.948948	+	0.315433i	$0.897850\pi$
$522$	5.38049	−	1.61265i	0.235498	−	0.0705836i
$523$	17.0660			0.746246			0.373123	−	0.927782i	$-0.378287\pi$
$523$	17.0660			0.746246			0.373123	+	0.927782i	$0.378287\pi$
$524$	−8.44197	+	14.6219i	−0.368789	+	0.638762i
$525$	−0.0643474	+	0.162046i	−0.00280835	+	0.00707226i
$526$	−4.32917	−	7.49835i	−0.188761	−	0.326944i
$527$	1.72403	+	2.98611i	0.0751000	+	0.130077i
$528$	−0.720848	+	1.81531i	−0.0313709	+	0.0790011i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	−11.3379			−0.492489
$531$	−3.79698	+	1.13803i	−0.164775	+	0.0493865i
$532$	4.66169			0.202110
$533$	1.66860	−	2.89010i	0.0722752	−	0.125184i
$534$	−20.8391	+	3.05580i	−0.901796	+	0.132238i
$535$	−0.876198	−	1.51762i	−0.0378813	−	0.0656124i
$536$	5.72834	+	9.92178i	0.247427	+	0.428555i
$537$	−13.3156	−	16.8349i	−0.574611	−	0.726481i
$538$	−5.64467	+	9.77685i	−0.243359	+	0.421510i
$539$	4.06781			0.175213
$540$	−1.00172	+	11.5118i	−0.0431070	+	0.495388i
$541$	−8.42741			−0.362323			−0.181161	−	0.983453i	$-0.557986\pi$
$541$	−8.42741			−0.362323			−0.181161	+	0.983453i	$0.557986\pi$
$542$	−11.3899	+	19.7279i	−0.489239	+	0.847386i
$543$	10.7876	+	13.6388i	0.462942	+	0.585298i
$544$	−0.309064	−	0.535315i	−0.0132510	−	0.0229514i
$545$	−5.83008	−	10.0980i	−0.249733	−	0.432551i
$546$	−3.22384	+	0.472737i	−0.137967	+	0.0202313i
$547$	5.59233	−	9.68620i	0.239111	−	0.414152i	−0.721349	−	0.692572i	$-0.756477\pi$
$547$	5.59233	−	9.68620i	0.239111	−	0.414152i	0.960459	+	0.278420i	$0.0898108\pi$
$548$	−7.95219			−0.339701
$549$	6.21222	+	5.85726i	0.265131	+	0.249982i
$550$	−0.0616284			−0.00262784
$551$	2.36929	−	4.10373i	0.100935	−	0.174825i
$552$	0.639232	−	1.60978i	0.0272075	−	0.0685167i
$553$	10.4776	+	18.1477i	0.445552	+	0.771720i
$554$	9.10849	+	15.7764i	0.386983	+	0.670274i
$555$	−11.6791	+	29.4115i	−0.495752	+	1.24845i
$556$	−2.53346	+	4.38808i	−0.107443	+	0.186096i
$557$	−16.1370			−0.683748			−0.341874	−	0.939746i	$-0.611062\pi$
$557$	−16.1370			−0.683748			−0.341874	+	0.939746i	$0.611062\pi$
$558$	3.85420	−	16.2848i	0.163161	−	0.689392i
$559$	13.0046			0.550038
$560$	2.04807	−	3.54736i	0.0865467	−	0.149903i
$561$	−1.19455	+	0.175166i	−0.0504339	+	0.00739552i
$562$	−8.01371	−	13.8802i	−0.338038	−	0.585499i
$563$	15.3046	+	26.5084i	0.645013	+	1.11720i	0.984298	+	0.176512i	$0.0564815\pi$
$563$	15.3046	+	26.5084i	0.645013	+	1.11720i	−0.339285	+	0.940684i	$0.610185\pi$
$564$	3.80658	+	4.81266i	0.160286	+	0.202650i
$565$	0.0698198	−	0.120931i	0.00293734	−	0.00508762i
$566$	−4.79232			−0.201436
$567$	13.8446	−	9.11812i	0.581418	−	0.382925i
$568$	9.45942			0.396909
$569$	−6.53027	+	11.3108i	−0.273763	+	0.474172i	−0.969822	−	0.243813i	$-0.921602\pi$
$569$	−6.53027	+	11.3108i	−0.273763	+	0.474172i	0.696059	+	0.717985i	$0.254935\pi$
$570$	6.04740	+	7.64573i	0.253298	+	0.320244i
$571$	17.1807	+	29.7579i	0.718991	+	1.24533i	0.961400	+	0.275155i	$0.0887293\pi$
$571$	17.1807	+	29.7579i	0.718991	+	1.24533i	−0.242408	+	0.970174i	$0.577937\pi$
$572$	−0.575852	−	0.997404i	−0.0240776	−	0.0417036i
$573$	25.9446	−	3.80446i	1.08385	−	0.158934i
$574$	3.00935	−	5.21235i	0.125608	−	0.217559i
$575$	0.0546508			0.00227909
$576$	−0.690936	+	2.91935i	−0.0287890	+	0.121640i
$577$	3.04560			0.126790			0.0633950	−	0.997989i	$-0.479807\pi$
$577$	3.04560			0.126790			0.0633950	+	0.997989i	$0.479807\pi$
$578$	−8.30896	+	14.3915i	−0.345607	+	0.598609i
$579$	−6.40090	+	16.1194i	−0.266012	+	0.669898i
$580$	−2.08185	−	3.60587i	−0.0864441	−	0.149726i
$581$	1.82982	+	3.16934i	0.0759137	+	0.131486i
$582$	−5.28778	+	13.3162i	−0.219186	+	0.551974i
$583$	−2.87469	+	4.97910i	−0.119057	+	0.206213i
$584$	−8.40706			−0.347886
$585$	−4.95748	−	4.67422i	−0.204967	−	0.193255i
$586$	1.86594			0.0770812
$587$	19.0794	−	33.0465i	0.787491	−	1.36397i	−0.140009	−	0.990150i	$-0.544713\pi$
$587$	19.0794	−	33.0465i	0.787491	−	1.36397i	0.927500	−	0.373823i	$-0.121953\pi$
$588$	6.18183	−	0.906491i	0.254934	−	0.0373830i
$589$	−7.05885	−	12.2263i	−0.290855	−	0.503776i
$590$	1.46915	+	2.54464i	0.0604839	+	0.104761i
$591$	10.5739	+	13.3686i	0.434952	+	0.549910i
$592$	−4.10793	+	7.11515i	−0.168835	+	0.292431i
$593$	16.4895			0.677142			0.338571	−	0.940941i	$-0.390056\pi$
$593$	16.4895			0.677142			0.338571	+	0.940941i	$0.390056\pi$
$594$	4.80146	+	3.35867i	0.197006	+	0.137808i
$595$	2.53194			0.103799
$596$	2.97269	−	5.14885i	0.121766	−	0.210905i
$597$	9.12075	+	11.5314i	0.373288	+	0.471948i
$598$	0.510653	+	0.884477i	0.0208822	+	0.0361690i
$599$	−9.65185	−	16.7175i	−0.394364	−	0.683058i	0.598656	−	0.801006i	$-0.295702\pi$
$599$	−9.65185	−	16.7175i	−0.394364	−	0.683058i	−0.993020	+	0.117948i	$0.962368\pi$
$600$	−0.0936563	+	0.0137336i	−0.00382350	+	0.000560671i
$601$	15.5478	−	26.9297i	0.634210	−	1.09848i	−0.352472	−	0.935822i	$-0.614659\pi$
$601$	15.5478	−	26.9297i	0.634210	−	1.09848i	0.986682	−	0.162661i	$-0.0520078\pi$
$602$	23.4541			0.955917
$603$	32.9231	−	9.86772i	1.34073	−	0.401845i
$604$	2.03042			0.0826168
$605$	−10.8170	+	18.7356i	−0.439774	+	0.761711i
$606$	−9.81346	+	24.7132i	−0.398644	+	1.00390i
$607$	−1.31870	−	2.28405i	−0.0535243	−	0.0927068i	0.838022	−	0.545637i	$-0.183712\pi$
$607$	−1.31870	−	2.28405i	−0.0535243	−	0.0927068i	−0.891546	+	0.452930i	$0.850379\pi$
$608$	1.26543	+	2.19178i	0.0513199	+	0.0888886i
$609$	−2.20453	+	5.55166i	−0.0893320	+	0.224964i
$610$	3.16452	−	5.48111i	0.128128	−	0.221924i
$611$	−3.61816			−0.146375
$612$	−1.77631	+	0.532398i	−0.0718033	+	0.0215209i
$613$	−8.14467			−0.328960			−0.164480	−	0.986380i	$-0.552595\pi$
$613$	−8.14467			−0.328960			−0.164480	+	0.986380i	$0.552595\pi$
$614$	−2.06138	+	3.57042i	−0.0831907	+	0.144090i
$615$	12.4528	−	1.82605i	0.502145	−	0.0736334i
$616$	−1.03856	−	1.79883i	−0.0418447	−	0.0724771i
$617$	−23.0753	−	39.9676i	−0.928976	−	1.60903i	−0.785038	−	0.619447i	$-0.787357\pi$
$617$	−23.0753	−	39.9676i	−0.928976	−	1.60903i	−0.143938	−	0.989587i	$-0.545977\pi$
$618$	6.82700	+	8.63137i	0.274622	+	0.347205i
$619$	23.1803	−	40.1495i	0.931695	−	1.61374i	0.151271	−	0.988492i	$-0.451663\pi$
$619$	23.1803	−	40.1495i	0.931695	−	1.61374i	0.780424	−	0.625251i	$-0.215003\pi$
$620$	−12.4050			−0.498195
$621$	−4.25783	−	2.97840i	−0.170861	−	0.119519i
$622$	31.7386			1.27260
$623$	11.1991	−	19.3975i	0.448684	−	0.777143i
$624$	−1.09738	−	1.38742i	−0.0439306	−	0.0555414i
$625$	12.3619	+	21.4114i	0.494475	+	0.856456i
$626$	−11.6970	−	20.2599i	−0.467508	−	0.809747i
$627$	4.89094	−	0.717198i	0.195326	−	0.0286421i
$628$	8.22657	−	14.2488i	0.328276	−	0.568590i
$629$	−5.07846			−0.202491
$630$	−8.94090	−	8.43003i	−0.356214	−	0.335860i
$631$	29.2909			1.16605			0.583025	−	0.812454i	$-0.301869\pi$
$631$	29.2909			1.16605			0.583025	+	0.812454i	$0.301869\pi$
$632$	−5.68834	+	9.85249i	−0.226270	+	0.391911i
$633$	−1.22239	+	3.07834i	−0.0485857	+	0.122353i
$634$	13.6539	+	23.6492i	0.542265	+	0.939230i
$635$	−23.6252	−	40.9200i	−0.937537	−	1.62386i
$636$	−3.25908	+	8.20732i	−0.129231	+	0.325441i
$637$	−1.84205	+	3.19053i	−0.0729848	+	0.126413i
$638$	−2.11138			−0.0835902
$639$	6.53586	−	27.6154i	0.258554	−	1.09245i
$640$	2.22381			0.0879040
$641$	−12.6046	+	21.8317i	−0.497850	+	0.862301i	−0.999997	−	0.00248092i	$-0.999210\pi$
$641$	−12.6046	+	21.8317i	−0.497850	+	0.862301i	0.502147	+	0.864782i	$0.332544\pi$
$642$	−1.35044	+	0.198025i	−0.0532975	+	0.00781544i
$643$	13.1378	+	22.7553i	0.518104	+	0.897382i	0.999779	+	0.0210319i	$0.00669514\pi$
$643$	13.1378	+	22.7553i	0.518104	+	0.897382i	−0.481675	+	0.876350i	$0.659972\pi$
$644$	0.920971	+	1.59517i	0.0362913	+	0.0628585i
$645$	30.4259	+	38.4675i	1.19802	+	1.51466i
$646$	−0.782196	+	1.35480i	−0.0307751	+	0.0533040i
$647$	38.0255			1.49494			0.747468	−	0.664298i	$-0.231269\pi$
$647$	38.0255			1.49494			0.747468	+	0.664298i	$0.231269\pi$
$648$	8.04522	+	4.03417i	0.316046	+	0.158477i
$649$	1.48999			0.0584871
$650$	0.0279076	−	0.0483373i	0.00109463	−	0.00189595i
$651$	11.0402	+	13.9581i	0.432699	+	0.547061i
$652$	−0.743434	−	1.28766i	−0.0291151	−	0.0504288i
$653$	−3.46606	−	6.00338i	−0.135637	−	0.234931i	0.790203	−	0.612845i	$-0.209975\pi$
$653$	−3.46606	−	6.00338i	−0.135637	−	0.234931i	−0.925841	+	0.377914i	$0.876641\pi$
$654$	−8.98560	+	1.31763i	−0.351365	+	0.0515234i
$655$	18.7734	−	32.5165i	0.733537	−	1.27052i
$656$	3.26759			0.127578
$657$	−5.80874	+	24.5431i	−0.226620	+	0.957519i
$658$	−6.52542			−0.254387
$659$	−10.4160	+	18.0411i	−0.405750	+	0.702780i	−0.994408	−	0.105602i	$-0.966323\pi$
$659$	−10.4160	+	18.0411i	−0.405750	+	0.702780i	0.588658	+	0.808382i	$0.299656\pi$
$660$	1.60303	−	4.03691i	0.0623979	−	0.157136i
$661$	10.6693	+	18.4797i	0.414986	+	0.718777i	0.995427	−	0.0955254i	$-0.0304531\pi$
$661$	10.6693	+	18.4797i	0.414986	+	0.718777i	−0.580441	+	0.814302i	$0.697120\pi$
$662$	14.1660	+	24.5362i	0.550577	+	0.953628i
$663$	0.403546	−	1.01625i	0.0156724	−	0.0394679i
$664$	−0.993418	+	1.72065i	−0.0385521	+	0.0667742i
$665$	−10.3667			−0.402005
$666$	17.9333	+	16.9086i	0.694901	+	0.655195i
$667$	1.87232			0.0724966
$668$	8.12382	−	14.0709i	0.314320	−	0.544418i
$669$	24.4448	−	3.58453i	0.945089	−	0.138586i
$670$	−12.7388	−	22.0642i	−0.492141	−	0.852414i
$671$	−1.60470	−	2.77943i	−0.0619488	−	0.107299i
$672$	−1.97915	−	2.50224i	−0.0763474	−	0.0965261i
$673$	2.33117	−	4.03771i	0.0898602	−	0.155642i	−0.817592	−	0.575798i	$-0.804691\pi$
$673$	2.33117	−	4.03771i	0.0898602	−	0.155642i	0.907452	+	0.420156i	$0.138025\pi$
$674$	−31.4220			−1.21033
$675$	−0.0246174	+	0.282905i	−0.000947525	+	0.0108890i
$676$	−11.9569			−0.459882
$677$	10.2692	−	17.7868i	0.394678	−	0.683602i	−0.598382	−	0.801211i	$-0.704190\pi$
$677$	10.2692	−	17.7868i	0.394678	−	0.683602i	0.993060	+	0.117609i	$0.0375229\pi$
$678$	−0.0674703	−	0.0853028i	−0.00259118	−	0.00327603i
$679$	−7.61835	−	13.1954i	−0.292365	−	0.506392i
$680$	0.687301	+	1.19044i	0.0263568	+	0.0456513i
$681$	−5.58333	+	0.818728i	−0.213954	+	0.0313737i
$682$	−3.14522	+	5.44769i	−0.120437	+	0.208603i
$683$	22.7309			0.869773			0.434887	−	0.900485i	$-0.356788\pi$
$683$	22.7309			0.869773			0.434887	+	0.900485i	$0.356788\pi$
$684$	7.27292	−	2.17984i	0.278087	−	0.0833484i
$685$	17.6842			0.675678
$686$	−9.76897	+	16.9204i	−0.372981	+	0.646022i
$687$	−1.87784	+	4.72895i	−0.0716439	+	0.180421i
$688$	6.36667	+	11.0274i	0.242727	+	0.420416i
$689$	−2.60353	−	4.50944i	−0.0991864	−	0.171796i
$690$	−1.42153	+	3.57984i	−0.0541169	+	0.136282i
$691$	−16.3526	+	28.3235i	−0.622082	+	1.07748i	0.367015	+	0.930215i	$0.380380\pi$
$691$	−16.3526	+	28.3235i	−0.622082	+	1.07748i	−0.989097	+	0.147263i	$0.952954\pi$
$692$	−1.41926			−0.0539523
$693$	−5.96901	+	1.78903i	−0.226744	+	0.0679598i
$694$	−29.8830			−1.13434
$695$	5.63394	−	9.75827i	0.213707	−	0.370152i
$696$	−3.20865	+	0.470509i	−0.121623	+	0.0178346i
$697$	1.00989	+	1.74919i	0.0382524	+	0.0662552i
$698$	−13.1752	−	22.8201i	−0.498688	−	0.863754i
$699$	14.2530	+	18.0201i	0.539098	+	0.681581i
$700$	0.0503318	−	0.0871772i	0.00190236	−	0.00329499i
$701$	22.2770			0.841390			0.420695	−	0.907202i	$-0.361786\pi$
$701$	22.2770			0.841390			0.420695	+	0.907202i	$0.361786\pi$
$702$	−4.80860	+	2.24503i	−0.181489	+	0.0847332i
$703$	20.7932			0.784229
$704$	0.563838	−	0.976597i	0.0212505	−	0.0368069i
$705$	−8.46513	−	10.7025i	−0.318815	−	0.403078i
$706$	1.77314	+	3.07117i	0.0667330	+	0.115585i
$707$	−14.1387	−	24.4889i	−0.531740	−	0.921001i
$708$	2.26432	−	0.332036i	0.0850985	−	0.0124787i
$709$	−11.8831	+	20.5822i	−0.446281	+	0.772981i	−0.998140	−	0.0609561i	$-0.980585\pi$
$709$	−11.8831	+	20.5822i	−0.446281	+	0.772981i	0.551860	+	0.833937i	$0.313918\pi$
$710$	−21.0360			−0.789467
$711$	24.8326	+	23.4137i	0.931295	+	0.878082i
$712$	12.1601			0.455720
$713$	2.78912	−	4.83089i	0.104453	−	0.180918i
$714$	0.727802	−	1.83282i	0.0272373	−	0.0685916i
$715$	1.28059	+	2.21804i	0.0478912	+	0.0829501i
$716$	6.19624	+	10.7322i	0.231564	+	0.401081i
$717$	−11.7951	+	29.7036i	−0.440497	+	1.10930i
$718$	−13.8557	+	23.9988i	−0.517090	+	0.895627i
$719$	−21.9474			−0.818498			−0.409249	−	0.912423i	$-0.634209\pi$
$719$	−21.9474			−0.818498			−0.409249	+	0.912423i	$0.634209\pi$
$720$	1.53651	−	6.49209i	0.0572625	−	0.241946i
$721$	−11.7031			−0.435848
$722$	−6.29739	+	10.9074i	−0.234364	+	0.405931i
$723$	5.69573	−	0.835209i	0.211826	−	0.0310618i
$724$	−5.01988	−	8.69469i	−0.186562	−	0.323136i
$725$	−0.0511619	−	0.0886151i	−0.00190011	−	0.00329108i
$726$	10.4530	+	13.2158i	0.387948	+	0.490483i
$727$	11.8633	−	20.5479i	0.439986	−	0.762078i	−0.557702	−	0.830041i	$-0.688317\pi$
$727$	11.8633	−	20.5479i	0.439986	−	0.762078i	0.997688	+	0.0679634i	$0.0216501\pi$
$728$	1.88119			0.0697214
$729$	17.3359	−	20.6995i	0.642070	−	0.766646i
$730$	18.6957			0.691960
$731$	−3.93542	+	6.81634i	−0.145557	+	0.252112i
$732$	−3.05804	−	3.86628i	−0.113028	−	0.142902i
$733$	12.3876	+	21.4560i	0.457548	+	0.792497i	0.998831	−	0.0483440i	$-0.0153944\pi$
$733$	12.3876	+	21.4560i	0.457548	+	0.792497i	−0.541283	+	0.840841i	$0.682061\pi$
$734$	3.83429	+	6.64119i	0.141526	+	0.245131i
$735$	−13.7472	+	2.01587i	−0.507074	+	0.0743564i
$736$	−0.500000	+	0.866025i	−0.0184302	+	0.0319221i
$737$	−12.9194			−0.475893
$738$	2.25769	−	9.53923i	0.0831068	−	0.351144i
$739$	0.731473			0.0269077			0.0134538	−	0.999909i	$-0.495717\pi$
$739$	0.731473			0.0269077			0.0134538	+	0.999909i	$0.495717\pi$
$740$	9.13528	−	15.8228i	0.335820	−	0.581656i
$741$	−1.65227	+	4.16092i	−0.0606978	+	0.152855i
$742$	−4.69550	−	8.13284i	−0.172377	−	0.298566i
$743$	8.99989	+	15.5883i	0.330174	+	0.571878i	0.982546	−	0.186021i	$-0.0595592\pi$
$743$	8.99989	+	15.5883i	0.330174	+	0.571878i	−0.652372	+	0.757899i	$0.726226\pi$
$744$	−3.56579	+	8.97972i	−0.130728	+	0.329212i
$745$	−6.61071	+	11.4501i	−0.242198	+	0.419499i
$746$	35.2402			1.29023
$747$	4.33679	+	4.08899i	0.158675	+	0.149608i
$748$	0.697049			0.0254866
$749$	0.725738	−	1.25701i	0.0265179	−	0.0459303i
$750$	19.2633	−	2.82473i	0.703396	−	0.103145i
$751$	−3.01031	−	5.21401i	−0.109848	−	0.190262i	0.805861	−	0.592105i	$-0.201703\pi$
$751$	−3.01031	−	5.21401i	−0.109848	−	0.190262i	−0.915708	+	0.401843i	$0.868370\pi$
$752$	−1.77134	−	3.06805i	−0.0645942	−	0.111880i
$753$	−20.1437	−	25.4677i	−0.734077	−	0.928094i
$754$	0.956108	−	1.65603i	0.0348194	−	0.0603089i
$755$	−4.51529			−0.164328
$756$	−8.67239	+	4.04895i	−0.315412	+	0.147259i
$757$	8.88580			0.322960			0.161480	−	0.986876i	$-0.448373\pi$
$757$	8.88580			0.322960			0.161480	+	0.986876i	$0.448373\pi$
$758$	−4.12507	+	7.14482i	−0.149829	+	0.259512i
$759$	1.21168	+	1.53193i	0.0439812	+	0.0556054i
$760$	−2.81408	−	4.87412i	−0.102077	−	0.176803i
$761$	−16.3942	−	28.3956i	−0.594290	−	1.02934i	−0.993647	−	0.112545i	$-0.964100\pi$
$761$	−16.3942	−	28.3956i	−0.594290	−	1.02934i	0.399357	−	0.916796i	$-0.369234\pi$
$762$	−36.4123	+	5.33942i	−1.31908	+	0.193427i
$763$	4.82894	−	8.36397i	0.174819	−	0.302796i
$764$	−15.1393			−0.547720
$765$	3.95019	−	1.18395i	0.142820	−	0.0428060i
$766$	−17.1887			−0.621053
$767$	−0.674720	+	1.16865i	−0.0243627	+	0.0421975i
$768$	0.639232	−	1.60978i	0.0230663	−	0.0580878i
$769$	−21.7865	−	37.7353i	−0.785641	−	1.36077i	−0.928616	−	0.371043i	$-0.879000\pi$
$769$	−21.7865	−	37.7353i	−0.785641	−	1.36077i	0.142975	−	0.989726i	$-0.454333\pi$
$770$	2.30956	+	4.00027i	0.0832307	+	0.144160i
$771$	−14.7420	+	37.1248i	−0.530921	+	1.33702i
$772$	5.00671	−	8.67188i	0.180195	−	0.312108i
$773$	−19.8015			−0.712210			−0.356105	−	0.934446i	$-0.615895\pi$
$773$	−19.8015			−0.712210			−0.356105	+	0.934446i	$0.615895\pi$
$774$	36.5918	−	10.9673i	1.31526	−	0.394212i
$775$	−0.304855			−0.0109507
$776$	4.13604	−	7.16383i	0.148475	−	0.257167i
$777$	−25.9340	+	3.80291i	−0.930379	+	0.136429i
$778$	0.230741	+	0.399655i	0.00827246	+	0.0143283i
$779$	−4.13489	−	7.16184i	−0.148148	−	0.256600i
$780$	2.44038	+	3.08537i	0.0873796	+	0.110474i
$781$	−5.33359	+	9.23804i	−0.190851	+	0.330563i
$782$	−0.618128			−0.0221042
$783$	−0.843387	+	9.69225i	−0.0301402	+	0.346373i
$784$	−3.60725			−0.128830
$785$	−18.2944	+	31.6868i	−0.652954	+	1.13095i
$786$	−18.1417	−	22.9365i	−0.647092	−	0.818118i
$787$	17.8745	+	30.9595i	0.637156	+	1.10359i	0.986054	+	0.166425i	$0.0532224\pi$
$787$	17.8745	+	30.9595i	0.637156	+	1.10359i	−0.348899	+	0.937160i	$0.613444\pi$
$788$	−4.92042	−	8.52241i	−0.175283	−	0.303598i
$789$	14.8380	−	2.17582i	0.528247	−	0.0774611i
$790$	12.6498	−	21.9101i	0.450060	−	0.779527i
$791$	0.115661			0.00411242
$792$	−2.46145	−	2.32081i	−0.0874639	−	0.0824663i
$793$	2.90667			0.103219
$794$	−10.6865	+	18.5096i	−0.379251	+	0.656882i
$795$	7.24758	−	18.2516i	0.257045	−	0.647316i
$796$	−4.24422	−	7.35120i	−0.150432	−	0.260556i
$797$	−23.6241	−	40.9181i	−0.836807	−	1.44939i	−0.892551	−	0.450947i	$-0.851086\pi$
$797$	−23.6241	−	40.9181i	−0.836807	−	1.44939i	0.0557433	−	0.998445i	$-0.482247\pi$
$798$	−2.97990	+	7.50428i	−0.105487	+	0.265649i
$799$	1.09492	−	1.89645i	0.0387353	−	0.0670916i
$800$	0.0546508			0.00193220
$801$	8.40187	−	35.4997i	0.296866	−	1.25432i
$802$	−37.5978			−1.32762
$803$	4.74022	−	8.21030i	0.167279	−	0.289735i
$804$	−19.6336	+	2.87903i	−0.692423	+	0.101536i
$805$	−2.04807	−	3.54736i	−0.0721849	−	0.125028i
$806$	−2.84854	−	4.93382i	−0.100336	−	0.173786i
$807$	−12.1303	−	15.3363i	−0.427007	−	0.539865i
$808$	7.67597	−	13.2952i	0.270040	−	0.467722i
$809$	−0.468245			−0.0164626			−0.00823131	−	0.999966i	$-0.502620\pi$
$809$	−0.468245			−0.0164626			−0.00823131	+	0.999966i	$0.502620\pi$
$810$	−17.8911	−	8.97124i	−0.628628	−	0.315217i
$811$	−3.13642			−0.110135			−0.0550673	−	0.998483i	$-0.517537\pi$
$811$	−3.13642			−0.110135			−0.0550673	+	0.998483i	$0.517537\pi$
$812$	1.72436	−	2.98667i	0.0605130	−	0.104812i
$813$	−24.4767	−	30.9459i	−0.858436	−	1.08532i
$814$	−4.63242	−	8.02359i	−0.162366	−	0.281227i
$815$	1.65326	+	2.86353i	0.0579111	+	0.100305i
$816$	1.05930	−	0.155334i	0.0370830	−	0.00543777i
$817$	16.1131	−	27.9087i	0.563727	−	0.976403i
$818$	30.3900			1.06256
$819$	1.29978	−	5.49184i	0.0454180	−	0.191901i
$820$	−7.26650			−0.253757
$821$	−5.79060	+	10.0296i	−0.202093	+	0.350036i	−0.949203	−	0.314665i	$-0.898108\pi$
$821$	−5.79060	+	10.0296i	−0.202093	+	0.350036i	0.747109	+	0.664701i	$0.231441\pi$
$822$	5.08330	−	12.8013i	0.177300	−	0.446495i
$823$	−21.6672	−	37.5287i	−0.755271	−	1.30817i	−0.945239	−	0.326378i	$-0.894172\pi$
$823$	−21.6672	−	37.5287i	−0.755271	−	1.30817i	0.189968	−	0.981790i	$-0.439162\pi$
$824$	−3.17685	−	5.50247i	−0.110671	−	0.191687i
$825$	0.0393949	−	0.0992080i	0.00137155	−	0.00345398i
$826$	−1.21687	+	2.10768i	−0.0423403	+	0.0733355i
$827$	36.5494			1.27095			0.635473	−	0.772123i	$-0.280805\pi$
$827$	36.5494			1.27095			0.635473	+	0.772123i	$0.280805\pi$
$828$	2.18276	+	2.05804i	0.0758563	+	0.0715219i
$829$	−1.57598			−0.0547362			−0.0273681	−	0.999625i	$-0.508713\pi$
$829$	−1.57598			−0.0547362			−0.0273681	+	0.999625i	$0.508713\pi$
$830$	2.20918	−	3.82641i	0.0766816	−	0.132817i
$831$	−31.2189	+	4.57787i	−1.08297	+	0.158805i
$832$	0.510653	+	0.884477i	0.0177037	+	0.0306637i
$833$	−1.11487	−	1.93101i	−0.0386280	−	0.0669056i
$834$	−5.44436	−	6.88330i	−0.188523	−	0.238349i
$835$	−18.0659	+	31.2910i	−0.625195	+	1.08287i
$836$	−2.85399			−0.0987072
$837$	23.7512	+	16.6142i	0.820962	+	0.574271i
$838$	−7.97944			−0.275645
$839$	−15.0145	+	26.0059i	−0.518359	+	0.897824i	0.481414	+	0.876494i	$0.340124\pi$
$839$	−15.0145	+	26.0059i	−0.518359	+	0.897824i	−0.999772	+	0.0213304i	$0.993210\pi$
$840$	4.40126	+	5.56452i	0.151858	+	0.191994i
$841$	12.7472	+	22.0788i	0.439559	+	0.761338i
$842$	3.86156	+	6.68843i	0.133078	+	0.230498i
$843$	27.4666	−	4.02764i	0.945999	−	0.138719i
$844$	0.956140	−	1.65608i	0.0329117	−	0.0570047i
$845$	26.5900			0.914724
$846$	−10.1806	+	3.05134i	−0.350016	+	0.104907i
$847$	−17.9191			−0.615706
$848$	2.54921	−	4.41536i	0.0875403	−	0.151624i
$849$	3.06341	−	7.71457i	0.105136	−	0.264763i
$850$	0.0168906	+	0.0292554i	0.000579342	+	0.00100345i
$851$	4.10793	+	7.11515i	0.140818	+	0.243904i
$852$	−6.04677	+	15.2276i	−0.207159	+	0.521688i
$853$	−22.3544	+	38.7189i	−0.765398	+	1.32571i	0.174637	+	0.984633i	$0.444125\pi$
$853$	−22.3544	+	38.7189i	−0.765398	+	1.32571i	−0.940036	+	0.341076i	$0.889209\pi$
$854$	5.24223			0.179385
$855$	−16.1736	+	4.84757i	−0.553126	+	0.165783i
$856$	0.788014			0.0269337
$857$	20.6061	−	35.6907i	0.703889	−	1.21917i	−0.263201	−	0.964741i	$-0.584778\pi$
$857$	20.6061	−	35.6907i	0.703889	−	1.21917i	0.967091	−	0.254431i	$-0.0818883\pi$
$858$	1.97370	−	0.289420i	0.0673811	−	0.00988062i
$859$	−28.8538	−	49.9763i	−0.984479	−	1.70517i	−0.644229	−	0.764833i	$-0.722822\pi$
$859$	−28.8538	−	49.9763i	−0.984479	−	1.70517i	−0.340250	−	0.940335i	$-0.610512\pi$
$860$	−14.1583	−	24.5229i	−0.482794	−	0.836223i
$861$	6.46705	+	8.17629i	0.220396	+	0.278647i
$862$	17.6280	−	30.5326i	0.600412	−	1.03994i
$863$	50.2682			1.71115			0.855575	−	0.517679i	$-0.173204\pi$
$863$	50.2682			1.71115			0.855575	+	0.517679i	$0.173204\pi$
$864$	−4.25783	−	2.97840i	−0.144854	−	0.101327i
$865$	3.15618			0.107313
$866$	−5.17210	+	8.95834i	−0.175755	+	0.304417i
$867$	−17.8558	−	22.5751i	−0.606415	−	0.766691i
$868$	−5.13739	−	8.89823i	−0.174375	−	0.302026i
$869$	−6.41461	−	11.1104i	−0.217601	−	0.376895i
$870$	7.13543	−	1.04632i	0.241914	−	0.0354737i
$871$	5.85039	−	10.1332i	0.198233	−	0.343349i
$872$	5.24332			0.177561
$873$	−18.0560	−	17.0243i	−0.611103	−	0.576185i
$874$	2.53085			0.0856074
$875$	−10.3523	+	17.9307i	−0.349971	+	0.606167i
$876$	5.37406	−	13.5335i	0.181573	−	0.457254i
$877$	−19.9486	−	34.5520i	−0.673616	−	1.16674i	−0.976871	−	0.213828i	$-0.931407\pi$
$877$	−19.9486	−	34.5520i	−0.673616	−	1.16674i	0.303255	−	0.952909i	$-0.401927\pi$
$878$	14.3541	+	24.8621i	0.484428	+	0.839054i
$879$	−1.19277	+	3.00374i	−0.0402311	+	0.101314i
$880$	−1.25387	+	2.17177i	−0.0422680	+	0.0732103i
$881$	−13.0748			−0.440500			−0.220250	−	0.975443i	$-0.570687\pi$
$881$	−13.0748			−0.440500			−0.220250	+	0.975443i	$0.570687\pi$
$882$	−2.49238	+	10.5308i	−0.0839227	+	0.354591i
$883$	42.4567			1.42878			0.714390	−	0.699747i	$-0.246704\pi$
$883$	42.4567			1.42878			0.714390	+	0.699747i	$0.246704\pi$
$884$	−0.315649	+	0.546720i	−0.0106164	+	0.0183882i
$885$	−5.03543	+	0.738386i	−0.169264	+	0.0248206i
$886$	−10.2742	−	17.7954i	−0.345168	−	0.597848i
$887$	−7.95225	−	13.7737i	−0.267010	−	0.462476i	0.701078	−	0.713085i	$-0.252702\pi$
$887$	−7.95225	−	13.7737i	−0.267010	−	0.462476i	−0.968088	+	0.250609i	$0.919369\pi$
$888$	−8.82788	−	11.1611i	−0.296244	−	0.374542i
$889$	19.5683	−	33.8933i	0.656299	−	1.13674i
$890$	−27.0419			−0.906446
$891$	−8.47596	+	5.58231i	−0.283955	+	0.187014i
$892$	−14.2641			−0.477598
$893$	−4.48301	+	7.76480i	−0.150018	+	0.259839i
$894$	6.38826	+	8.07668i	0.213655	+	0.270125i
$895$	−13.7793	−	23.8664i	−0.460591	−	0.797767i
$896$	0.920971	+	1.59517i	0.0307675	+	0.0532909i
$897$	−1.75024	+	0.256651i	−0.0584387	+	0.00856933i
$898$	−10.4894	+	18.1681i	−0.350034	+	0.606277i
$899$	−10.4443			−0.348336
$900$	0.0377602	−	0.159545i	0.00125867	−	0.00531816i
$901$	3.15148			0.104991
$902$	−1.84239	+	3.19111i	−0.0613449	+	0.106252i
$903$	−14.9926	+	37.7558i	−0.498923	+	1.25644i
$904$	0.0313964	+	0.0543802i	0.00104423	+	0.00180866i
$905$	11.1633	+	19.3354i	0.371080	+	0.642730i
$906$	−1.29791	+	3.26853i	−0.0431203	+	0.108590i
$907$	−13.3645	+	23.1479i	−0.443760	+	0.768615i	−0.997965	−	0.0637653i	$-0.979689\pi$
$907$	−13.3645	+	23.1479i	−0.443760	+	0.768615i	0.554205	+	0.832380i	$0.313022\pi$
$908$	3.25801			0.108121
$909$	−33.5097	−	31.5949i	−1.11144	−	1.04794i
$910$	−4.18341			−0.138679
$911$	−16.0956	+	27.8783i	−0.533270	+	0.923650i	0.465975	+	0.884798i	$0.345704\pi$
$911$	−16.0956	+	27.8783i	−0.533270	+	0.923650i	−0.999245	+	0.0388523i	$0.987630\pi$
$912$	−4.33719	+	0.635996i	−0.143619	+	0.0210599i
$913$	−1.12025	−	1.94034i	−0.0370750	−	0.0642158i
$914$	−13.2097	−	22.8799i	−0.436939	−	0.756801i
$915$	6.80051	+	8.59788i	0.224818	+	0.284237i
$916$	1.46882	−	2.54407i	0.0485312	−	0.0840586i
$917$	31.0993			1.02699
$918$	0.278436	−	3.19980i	0.00918974	−	0.105609i
$919$	15.6491			0.516216			0.258108	−	0.966116i	$-0.416901\pi$
$919$	15.6491			0.516216			0.258108	+	0.966116i	$0.416901\pi$
$920$	1.11191	−	1.92588i	0.0366585	−	0.0634944i
$921$	−4.42988	−	5.60070i	−0.145969	−	0.184549i
$922$	17.7521	+	30.7475i	0.584633	+	1.01261i
$923$	−4.83048	−	8.36664i	−0.158997	−	0.275391i
$924$	3.55960	−	0.521973i	0.117102	−	0.0171716i
$925$	0.224502	−	0.388848i	0.00738157	−	0.0127853i
$926$	−23.4137			−0.769423
$927$	−18.2586	+	5.47249i	−0.599692	+	0.179740i
$928$	1.87232			0.0614620
$929$	14.2479	−	24.6781i	0.467459	−	0.809664i	−0.531849	−	0.846839i	$-0.678503\pi$
$929$	14.2479	−	24.6781i	0.467459	−	0.809664i	0.999309	+	0.0371754i	$0.0118360\pi$
$930$	7.92965	−	19.9692i	0.260024	−	0.654816i
$931$	4.56471	+	7.90631i	0.149602	+	0.259119i
$932$	−6.63244	−	11.4877i	−0.217253	−	0.376293i
$933$	−20.2883	+	51.0921i	−0.664210	+	1.67268i
$934$	−15.5873	+	26.9980i	−0.510033	+	0.883403i
$935$	−1.55011			−0.0506939
$936$	2.93493	−	0.879658i	0.0959311	−	0.0287525i
$937$	13.7041			0.447694			0.223847	−	0.974624i	$-0.428138\pi$
$937$	13.7041			0.447694			0.223847	+	0.974624i	$0.428138\pi$
$938$	10.5513	−	18.2753i	0.344511	−	0.596711i
$939$	40.0910	−	5.87886i	1.30832	−	0.191849i
$940$	3.93913	+	6.82278i	0.128480	+	0.222535i
$941$	14.7300	+	25.5131i	0.480183	+	0.831702i	0.999742	−	0.0227331i	$-0.00723679\pi$
$941$	14.7300	+	25.5131i	0.480183	+	0.831702i	−0.519558	+	0.854435i	$0.673903\pi$
$942$	17.6788	+	22.3513i	0.576005	+	0.728243i
$943$	1.63379	−	2.82981i	0.0532036	−	0.0921514i
$944$	−1.32129			−0.0430043
$945$	19.2858	−	9.00411i	0.627366	−	0.292904i
$946$	−14.3591			−0.466854
$947$	−13.0712	+	22.6399i	−0.424756	+	0.735699i	−0.996398	−	0.0848046i	$-0.972973\pi$
$947$	−13.0712	+	22.6399i	−0.424756	+	0.735699i	0.571642	+	0.820503i	$0.306307\pi$
$948$	−12.2241	−	15.4550i	−0.397022	−	0.501955i
$949$	4.29309	+	7.43585i	0.139360	+	0.241378i
$950$	−0.0691566	−	0.119783i	−0.00224374	−	0.00388626i
$951$	−46.7979	+	6.86235i	−1.51753	+	0.222527i
$952$	−0.569278	+	0.986019i	−0.0184504	+	0.0319571i
$953$	42.2500			1.36861			0.684306	−	0.729195i	$-0.260105\pi$
$953$	42.2500			1.36861			0.684306	+	0.729195i	$0.260105\pi$
$954$	−11.1287	−	10.4928i	−0.360303	−	0.339716i
$955$	33.6670			1.08944
$956$	9.22601	−	15.9799i	0.298390	−	0.516827i
$957$	1.34966	−	3.39884i	0.0436283	−	0.109869i
$958$	12.6288	+	21.8737i	0.408018	+	0.706708i
$959$	7.32374	+	12.6851i	0.236496	+	0.409623i
$960$	−1.42153	+	3.57984i	−0.0458798	+	0.115539i
$961$	−0.0583585	+	0.101080i	−0.00188253	+	0.00326064i
$962$	8.39091			0.270534
$963$	0.544467	−	2.30049i	0.0175452	−	0.0741322i
$964$	−3.32360			−0.107046
$965$	−11.1340	+	19.2846i	−0.358416	+	0.620795i
$966$	−3.15658	+	0.462874i	−0.101561	+	0.0148927i
$967$	−24.6375	−	42.6735i	−0.792290	−	1.37229i	−0.924546	−	0.381070i	$-0.875556\pi$
$967$	−24.6375	−	42.6735i	−0.792290	−	1.37229i	0.132256	−	0.991216i	$-0.457778\pi$
$968$	−4.86417	−	8.42499i	−0.156340	−	0.270790i
$969$	−1.68093	−	2.12520i	−0.0539991	−	0.0682711i
$970$	−9.19778	+	15.9310i	−0.295323	+	0.511514i
$971$	−13.6418			−0.437786			−0.218893	−	0.975749i	$-0.570245\pi$
$971$	−13.6418			−0.437786			−0.218893	+	0.975749i	$0.570245\pi$
$972$	−11.6369	+	10.3722i	−0.373253	+	0.332689i
$973$	9.33297			0.299201
$974$	−10.0932	+	17.4819i	−0.323407	+	0.560157i
$975$	0.0599729	+	0.0758238i	0.00192067	+	0.00242830i
$976$	1.42302	+	2.46474i	0.0455496	+	0.0788943i
$977$	27.8935	+	48.3130i	0.892392	+	1.54567i	0.836999	+	0.547205i	$0.184308\pi$
$977$	27.8935	+	48.3130i	0.892392	+	1.54567i	0.0553936	+	0.998465i	$0.482359\pi$
$978$	2.54808	−	0.373645i	0.0814786	−	0.0119479i
$979$	−6.85635	+	11.8755i	−0.219130	+	0.379544i
$980$	8.02185			0.256249
$981$	3.62279	−	15.3071i	0.115667	−	0.488717i
$982$	18.7374			0.597936
$983$	−4.38490	+	7.59488i	−0.139857	+	0.242239i	−0.927442	−	0.373966i	$-0.877998\pi$
$983$	−4.38490	+	7.59488i	−0.139857	+	0.242239i	0.787586	+	0.616205i	$0.211331\pi$
$984$	−2.08875	+	5.26008i	−0.0665868	+	0.167685i
$985$	10.9421	+	18.9523i	0.348644	+	0.603869i
$986$	0.578668	+	1.00228i	0.0184285	+	0.0319192i
$987$	4.17126	−	10.5045i	0.132773	−	0.334361i
$988$	1.29239	−	2.23848i	0.0411164	−	0.0712156i
$989$	12.7333			0.404897
$990$	5.47381	+	5.16104i	0.173969	+	0.164029i
$991$	−44.4166			−1.41094			−0.705469	−	0.708740i	$-0.749264\pi$
$991$	−44.4166			−1.41094			−0.705469	+	0.708740i	$0.749264\pi$
$992$	2.78912	−	4.83089i	0.0885546	−	0.153381i
$993$	−48.5533	+	7.11975i	−1.54079	+	0.225938i
$994$	−8.71186	−	15.0894i	−0.276323	−	0.478606i
$995$	9.43835	+	16.3477i	0.299216	+	0.518257i
$996$	−2.13484	−	2.69908i	−0.0676449	−	0.0855235i
$997$	6.76209	−	11.7123i	0.214157	−	0.370931i	−0.738854	−	0.673865i	$-0.764633\pi$
$997$	6.76209	−	11.7123i	0.214157	−	0.370931i	0.953012	+	0.302934i	$0.0979661\pi$
$998$	7.36604			0.233168
$999$	−38.6826	+	18.0601i	−1.22386	+	0.571395i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.e.e.277.5	yes	12
3.2	odd	2		1242.2.e.e.829.3		12
9.2	odd	6		3726.2.a.x.1.4		6
9.4	even	3	inner	414.2.e.e.139.5	✓	12
9.5	odd	6		1242.2.e.e.415.3		12
9.7	even	3		3726.2.a.w.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.e.e.139.5	✓	12	9.4	even	3	inner
414.2.e.e.277.5	yes	12	1.1	even	1	trivial
1242.2.e.e.415.3		12	9.5	odd	6
1242.2.e.e.829.3		12	3.2	odd	2
3726.2.a.w.1.3		6	9.7	even	3
3726.2.a.x.1.4		6	9.2	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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.07449 + 1.35848i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.11191 + 1.92588i) q^{5} +(1.71372 - 0.251297i) q^{6} +(-0.920971 + 1.59517i) q^{7} -1.00000 q^{8} +(-0.690936 + 2.91935i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.07449 + 1.35848i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.11191 + 1.92588i) q^{5} +(1.71372 - 0.251297i) q^{6} +(-0.920971 + 1.59517i) q^{7} -1.00000 q^{8} +(-0.690936 + 2.91935i) q^{9} +2.22381 q^{10} +(0.563838 - 0.976597i) q^{11} +(0.639232 - 1.60978i) q^{12} +(0.510653 + 0.884477i) q^{13} +(0.920971 + 1.59517i) q^{14} +(-1.42153 + 3.57984i) q^{15} +(-0.500000 + 0.866025i) q^{16} -0.618128 q^{17} +(2.18276 + 2.05804i) q^{18} +2.53085 q^{19} +(1.11191 - 1.92588i) q^{20} +(-3.15658 + 0.462874i) q^{21} +(-0.563838 - 0.976597i) q^{22} +(0.500000 + 0.866025i) q^{23} +(-1.07449 - 1.35848i) q^{24} +(0.0273254 - 0.0473289i) q^{25} +1.02131 q^{26} +(-4.70828 + 2.19819i) q^{27} +1.84194 q^{28} +(0.936162 - 1.62148i) q^{29} +(2.38947 + 3.02101i) q^{30} +(-2.78912 - 4.83089i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.93253 - 0.283382i) q^{33} +(-0.309064 + 0.535315i) q^{34} -4.09614 q^{35} +(2.87370 - 0.861307i) q^{36} +8.21587 q^{37} +(1.26543 - 2.19178i) q^{38} +(-0.652852 + 1.64408i) q^{39} +(-1.11191 - 1.92588i) q^{40} +(-1.63379 - 2.82981i) q^{41} +(-1.17743 + 2.96512i) q^{42} +(6.36667 - 11.0274i) q^{43} -1.12768 q^{44} +(-6.39057 + 1.91539i) q^{45} +1.00000 q^{46} +(-1.77134 + 3.06805i) q^{47} +(-1.71372 + 0.251297i) q^{48} +(1.80362 + 3.12397i) q^{49} +(-0.0273254 - 0.0473289i) q^{50} +(-0.664173 - 0.839715i) q^{51} +(0.510653 - 0.884477i) q^{52} -5.09842 q^{53} +(-0.450450 + 5.17659i) q^{54} +2.50774 q^{55} +(0.920971 - 1.59517i) q^{56} +(2.71938 + 3.43812i) q^{57} +(-0.936162 - 1.62148i) q^{58} +(0.660644 + 1.14427i) q^{59} +(3.81100 - 0.558838i) q^{60} +(1.42302 - 2.46474i) q^{61} -5.57824 q^{62} +(-4.02052 - 3.79080i) q^{63} +1.00000 q^{64} +(-1.13560 + 1.96691i) q^{65} +(0.720848 - 1.81531i) q^{66} +(-5.72834 - 9.92178i) q^{67} +(0.309064 + 0.535315i) q^{68} +(-0.639232 + 1.60978i) q^{69} +(-2.04807 + 3.54736i) q^{70} -9.45942 q^{71} +(0.690936 - 2.91935i) q^{72} +8.40706 q^{73} +(4.10793 - 7.11515i) q^{74} +(0.0936563 - 0.0137336i) q^{75} +(-1.26543 - 2.19178i) q^{76} +(1.03856 + 1.79883i) q^{77} +(1.09738 + 1.38742i) q^{78} +(5.68834 - 9.85249i) q^{79} -2.22381 q^{80} +(-8.04522 - 4.03417i) q^{81} -3.26759 q^{82} +(0.993418 - 1.72065i) q^{83} +(1.97915 + 2.50224i) q^{84} +(-0.687301 - 1.19044i) q^{85} +(-6.36667 - 11.0274i) q^{86} +(3.20865 - 0.470509i) q^{87} +(-0.563838 + 0.976597i) q^{88} -12.1601 q^{89} +(-1.53651 + 6.49209i) q^{90} -1.88119 q^{91} +(0.500000 - 0.866025i) q^{92} +(3.56579 - 8.97972i) q^{93} +(1.77134 + 3.06805i) q^{94} +(2.81408 + 4.87412i) q^{95} +(-0.639232 + 1.60978i) q^{96} +(-4.13604 + 7.16383i) q^{97} +3.60725 q^{98} +(2.46145 + 2.32081i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 6 q^{4} + 5 q^{5} - 3 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) \) 12 * q + 6 * q^2 - 6 * q^4 + 5 * q^5 - 3 * q^7 - 12 * q^8 - 8 * q^9	\( 12 q + 6 q^{2} - 6 q^{4} + 5 q^{5} - 3 q^{7} - 12 q^{8} - 8 q^{9} + 10 q^{10} + 6 q^{11} - 6 q^{13} + 3 q^{14} + 7 q^{15} - 6 q^{16} - 8 q^{17} - 10 q^{18} + 4 q^{19} + 5 q^{20} + 17 q^{21} - 6 q^{22} + 6 q^{23} + q^{25} - 12 q^{26} - 9 q^{27} + 6 q^{28} + 12 q^{29} - q^{30} - 6 q^{31} + 6 q^{32} + 9 q^{33} - 4 q^{34} - 34 q^{35} - 2 q^{36} + 8 q^{37} + 2 q^{38} + 23 q^{39} - 5 q^{40} + 15 q^{41} + 7 q^{42} - 14 q^{43} - 12 q^{44} - 37 q^{45} + 12 q^{46} + 9 q^{47} - 5 q^{49} - q^{50} + 9 q^{51} - 6 q^{52} - 10 q^{53} - 9 q^{54} + 16 q^{55} + 3 q^{56} + 37 q^{57} - 12 q^{58} + 18 q^{59} - 8 q^{60} - 3 q^{61} - 12 q^{62} - 42 q^{63} + 12 q^{64} + 9 q^{65} + 3 q^{66} + 8 q^{67} + 4 q^{68} - 17 q^{70} - 18 q^{71} + 8 q^{72} - 32 q^{73} + 4 q^{74} + 34 q^{75} - 2 q^{76} - q^{77} + 22 q^{78} - 7 q^{79} - 10 q^{80} - 56 q^{81} + 30 q^{82} + 3 q^{83} - 10 q^{84} + 7 q^{85} + 14 q^{86} - 9 q^{87} - 6 q^{88} - 42 q^{89} - 17 q^{90} + 18 q^{91} + 6 q^{92} + 69 q^{93} - 9 q^{94} + 11 q^{95} + 13 q^{97} - 10 q^{98} - 60 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 - 6 * q^4 + 5 * q^5 - 3 * q^7 - 12 * q^8 - 8 * q^9 + 10 * q^10 + 6 * q^11 - 6 * q^13 + 3 * q^14 + 7 * q^15 - 6 * q^16 - 8 * q^17 - 10 * q^18 + 4 * q^19 + 5 * q^20 + 17 * q^21 - 6 * q^22 + 6 * q^23 + q^25 - 12 * q^26 - 9 * q^27 + 6 * q^28 + 12 * q^29 - q^30 - 6 * q^31 + 6 * q^32 + 9 * q^33 - 4 * q^34 - 34 * q^35 - 2 * q^36 + 8 * q^37 + 2 * q^38 + 23 * q^39 - 5 * q^40 + 15 * q^41 + 7 * q^42 - 14 * q^43 - 12 * q^44 - 37 * q^45 + 12 * q^46 + 9 * q^47 - 5 * q^49 - q^50 + 9 * q^51 - 6 * q^52 - 10 * q^53 - 9 * q^54 + 16 * q^55 + 3 * q^56 + 37 * q^57 - 12 * q^58 + 18 * q^59 - 8 * q^60 - 3 * q^61 - 12 * q^62 - 42 * q^63 + 12 * q^64 + 9 * q^65 + 3 * q^66 + 8 * q^67 + 4 * q^68 - 17 * q^70 - 18 * q^71 + 8 * q^72 - 32 * q^73 + 4 * q^74 + 34 * q^75 - 2 * q^76 - q^77 + 22 * q^78 - 7 * q^79 - 10 * q^80 - 56 * q^81 + 30 * q^82 + 3 * q^83 - 10 * q^84 + 7 * q^85 + 14 * q^86 - 9 * q^87 - 6 * q^88 - 42 * q^89 - 17 * q^90 + 18 * q^91 + 6 * q^92 + 69 * q^93 - 9 * q^94 + 11 * q^95 + 13 * q^97 - 10 * q^98 - 60 * q^99

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