LMFDB - Embedded newform 93.2.f.b.4.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [93,2,Mod(4,93)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(93, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("93.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 93 = 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	93.f (of order $5$, degree $4$, 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:	$0.742608738798$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 13 x^{14} - 28 x^{13} + 90 x^{12} - 119 x^{11} + 382 x^{10} - 356 x^{9} + 1869 x^{8} + \cdots + 81 $ x^16 - 3x^15 + 13x^14 - 28x^13 + 90x^12 - 119x^11 + 382x^10 - 356x^9 + 1869x^8 - 2812x^7 + 5846x^6 - 4987x^5 + 4006x^4 - 1014x^3 + 2493x^2 + 729*x + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			4.4
Root			$-0.806001 - 2.48062i$ of defining polynomial
Character	$\chi$	$=$	93.4
Dual form			93.2.f.b.70.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.806001 + 2.48062i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-3.88578 + 2.82319i) q^{4} +0.899861 q^{5} +2.60827 q^{6} +(-1.22800 + 0.892196i) q^{7} +(-5.91490 - 4.29743i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(0.806001 + 2.48062i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-3.88578 + 2.82319i) q^{4} +0.899861 q^{5} +2.60827 q^{6} +(-1.22800 + 0.892196i) q^{7} +(-5.91490 - 4.29743i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(0.725289 + 2.23221i) q^{10} +(4.97831 - 3.61695i) q^{11} +(1.48424 + 4.56801i) q^{12} +(0.226326 - 0.696558i) q^{13} +(-3.20297 - 2.32709i) q^{14} +(0.278072 - 0.855819i) q^{15} +(2.92438 - 9.00032i) q^{16} +(-6.12182 - 4.44776i) q^{17} +(0.806001 - 2.48062i) q^{18} +(0.774344 + 2.38319i) q^{19} +(-3.49666 + 2.54047i) q^{20} +(0.469055 + 1.44360i) q^{21} +(12.9848 + 9.43400i) q^{22} +(4.52838 + 3.29006i) q^{23} +(-5.91490 + 4.29743i) q^{24} -4.19025 q^{25} +1.91031 q^{26} +(-0.809017 + 0.587785i) q^{27} +(2.25292 - 6.93376i) q^{28} +(1.33393 + 4.10541i) q^{29} +2.34708 q^{30} +(-5.25666 + 1.83509i) q^{31} +10.0609 q^{32} +(-1.90154 - 5.85235i) q^{33} +(6.09900 - 18.7708i) q^{34} +(-1.10503 + 0.802853i) q^{35} +4.80309 q^{36} -3.76750 q^{37} +(-5.28765 + 3.84170i) q^{38} +(-0.592528 - 0.430497i) q^{39} +(-5.32259 - 3.86709i) q^{40} +(-0.725289 - 2.23221i) q^{41} +(-3.20297 + 2.32709i) q^{42} +(-0.134532 - 0.414048i) q^{43} +(-9.13329 + 28.1094i) q^{44} +(-0.728003 - 0.528925i) q^{45} +(-4.51150 + 13.8850i) q^{46} +(2.73269 - 8.41035i) q^{47} +(-7.65613 - 5.56250i) q^{48} +(-1.45114 + 4.46616i) q^{49} +(-3.37734 - 10.3944i) q^{50} +(-6.12182 + 4.44776i) q^{51} +(1.08706 + 3.34563i) q^{52} +(-1.19921 - 0.871276i) q^{53} +(-2.11014 - 1.53310i) q^{54} +(4.47979 - 3.25476i) q^{55} +11.0977 q^{56} +2.50583 q^{57} +(-9.10880 + 6.61793i) q^{58} +(-1.21705 + 3.74569i) q^{59} +(1.33561 + 4.11057i) q^{60} +3.67818 q^{61} +(-8.78902 - 11.5607i) q^{62} +1.51790 q^{63} +(2.26035 + 6.95665i) q^{64} +(0.203662 - 0.626806i) q^{65} +(12.9848 - 9.43400i) q^{66} +2.90302 q^{67} +36.3449 q^{68} +(4.52838 - 3.29006i) q^{69} +(-2.88223 - 2.09406i) q^{70} +(10.4065 + 7.56080i) q^{71} +(2.25929 + 6.95339i) q^{72} +(-5.93263 + 4.31031i) q^{73} +(-3.03661 - 9.34571i) q^{74} +(-1.29486 + 3.98516i) q^{75} +(-9.73711 - 7.07442i) q^{76} +(-2.88635 + 8.88326i) q^{77} +(0.590319 - 1.81681i) q^{78} +(6.63830 + 4.82301i) q^{79} +(2.63154 - 8.09903i) q^{80} +(0.309017 + 0.951057i) q^{81} +(4.95267 - 3.59833i) q^{82} +(-1.27676 - 3.92947i) q^{83} +(-5.89821 - 4.28530i) q^{84} +(-5.50879 - 4.00237i) q^{85} +(0.918660 - 0.667446i) q^{86} +4.31669 q^{87} -44.9898 q^{88} +(5.68943 - 4.13361i) q^{89} +(0.725289 - 2.23221i) q^{90} +(0.343538 + 1.05730i) q^{91} -26.8847 q^{92} +(0.120875 + 5.56645i) q^{93} +23.0654 q^{94} +(0.696802 + 2.14454i) q^{95} +(3.10900 - 9.56851i) q^{96} +(3.07965 - 2.23750i) q^{97} -12.2484 q^{98} -6.15353 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} - 4 q^{3} - 9 q^{4} + 6 q^{5} + 2 q^{6} - 7 q^{7} - 2 q^{8} - 4 q^{9}+O(q^{10}) $ 16 * q - 3 * q^2 - 4 * q^3 - 9 * q^4 + 6 * q^5 + 2 * q^6 - 7 * q^7 - 2 * q^8 - 4 * q^9	\( 16 q - 3 q^{2} - 4 q^{3} - 9 q^{4} + 6 q^{5} + 2 q^{6} - 7 q^{7} - 2 q^{8} - 4 q^{9} - 3 q^{10} + 10 q^{11} - 4 q^{12} - 3 q^{13} - 4 q^{14} - 4 q^{15} - 17 q^{16} - q^{17} - 3 q^{18} - 4 q^{19} + 7 q^{20} + 8 q^{21} + 10 q^{22} + 7 q^{23} - 2 q^{24} + 30 q^{25} - 16 q^{26} - 4 q^{27} + 9 q^{28} - 2 q^{29} + 12 q^{30} - 13 q^{31} + 108 q^{32} - 5 q^{33} - 4 q^{34} - 33 q^{35} + 26 q^{36} - 28 q^{37} - 62 q^{38} + 7 q^{39} - 27 q^{40} + 3 q^{41} - 4 q^{42} - 13 q^{43} - 64 q^{44} + q^{45} - q^{46} - 20 q^{47} - 2 q^{48} + q^{49} - 44 q^{50} - q^{51} + 88 q^{52} - 4 q^{53} + 2 q^{54} - 8 q^{55} + 104 q^{56} - 14 q^{57} - 31 q^{58} + 49 q^{59} - 8 q^{60} - 13 q^{62} - 2 q^{63} - 26 q^{64} - q^{65} + 10 q^{66} + 60 q^{67} - 30 q^{68} + 7 q^{69} + 85 q^{70} + 23 q^{71} - 7 q^{72} - 17 q^{73} + 70 q^{74} - 5 q^{75} + 7 q^{76} + 2 q^{77} + 19 q^{78} - 13 q^{79} - 94 q^{80} - 4 q^{81} - 9 q^{82} - 49 q^{83} - 6 q^{84} - 4 q^{85} + 24 q^{86} - 2 q^{87} - 32 q^{88} + 3 q^{89} - 3 q^{90} - 2 q^{91} - 70 q^{92} + 17 q^{93} + 74 q^{94} - 10 q^{95} - 32 q^{96} + 3 q^{97} - 82 q^{98} - 10 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 - 4 * q^3 - 9 * q^4 + 6 * q^5 + 2 * q^6 - 7 * q^7 - 2 * q^8 - 4 * q^9 - 3 * q^10 + 10 * q^11 - 4 * q^12 - 3 * q^13 - 4 * q^14 - 4 * q^15 - 17 * q^16 - q^17 - 3 * q^18 - 4 * q^19 + 7 * q^20 + 8 * q^21 + 10 * q^22 + 7 * q^23 - 2 * q^24 + 30 * q^25 - 16 * q^26 - 4 * q^27 + 9 * q^28 - 2 * q^29 + 12 * q^30 - 13 * q^31 + 108 * q^32 - 5 * q^33 - 4 * q^34 - 33 * q^35 + 26 * q^36 - 28 * q^37 - 62 * q^38 + 7 * q^39 - 27 * q^40 + 3 * q^41 - 4 * q^42 - 13 * q^43 - 64 * q^44 + q^45 - q^46 - 20 * q^47 - 2 * q^48 + q^49 - 44 * q^50 - q^51 + 88 * q^52 - 4 * q^53 + 2 * q^54 - 8 * q^55 + 104 * q^56 - 14 * q^57 - 31 * q^58 + 49 * q^59 - 8 * q^60 - 13 * q^62 - 2 * q^63 - 26 * q^64 - q^65 + 10 * q^66 + 60 * q^67 - 30 * q^68 + 7 * q^69 + 85 * q^70 + 23 * q^71 - 7 * q^72 - 17 * q^73 + 70 * q^74 - 5 * q^75 + 7 * q^76 + 2 * q^77 + 19 * q^78 - 13 * q^79 - 94 * q^80 - 4 * q^81 - 9 * q^82 - 49 * q^83 - 6 * q^84 - 4 * q^85 + 24 * q^86 - 2 * q^87 - 32 * q^88 + 3 * q^89 - 3 * q^90 - 2 * q^91 - 70 * q^92 + 17 * q^93 + 74 * q^94 - 10 * q^95 - 32 * q^96 + 3 * q^97 - 82 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/93\mathbb{Z}\right)^\times$.

$n$	$32$	$34$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.806001	+	2.48062i	0.569929	+	1.75406i	0.652832	+	0.757502i	$0.273581\pi$
$2$	0.806001	+	2.48062i	0.569929	+	1.75406i	−0.0829038	+	0.996558i	$0.526419\pi$
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$	−3.88578	+	2.82319i	−1.94289	+	1.41159i
$5$	0.899861			0.402430			0.201215	−	0.979547i	$-0.435511\pi$
$5$	0.899861			0.402430			0.201215	+	0.979547i	$0.435511\pi$
$6$	2.60827			1.06482
$7$	−1.22800	+	0.892196i	−0.464141	+	0.337219i	−0.795154	−	0.606408i	$-0.792610\pi$
$7$	−1.22800	+	0.892196i	−0.464141	+	0.337219i	0.331012	+	0.943626i	$0.392610\pi$
$8$	−5.91490	−	4.29743i	−2.09123	−	1.51937i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	0.725289	+	2.23221i	0.229356	+	0.705887i
$11$	4.97831	−	3.61695i	1.50102	−	1.09055i	0.531042	−	0.847345i	$-0.321801\pi$
$11$	4.97831	−	3.61695i	1.50102	−	1.09055i	0.969974	−	0.243207i	$-0.0781995\pi$
$12$	1.48424	+	4.56801i	0.428462	+	1.31867i
$13$	0.226326	−	0.696558i	0.0627714	−	0.193191i	−0.914753	−	0.404014i	$-0.867615\pi$
$13$	0.226326	−	0.696558i	0.0627714	−	0.193191i	0.977524	+	0.210824i	$0.0676146\pi$
$14$	−3.20297	−	2.32709i	−0.856029	−	0.621942i
$15$	0.278072	−	0.855819i	0.0717980	−	0.220971i
$16$	2.92438	−	9.00032i	0.731095	−	2.25008i
$17$	−6.12182	−	4.44776i	−1.48476	−	1.07874i	−0.975984	−	0.217841i	$-0.930098\pi$
$17$	−6.12182	−	4.44776i	−1.48476	−	1.07874i	−0.508775	−	0.860899i	$-0.669902\pi$
$18$	0.806001	−	2.48062i	0.189976	−	0.584687i
$19$	0.774344	+	2.38319i	0.177647	+	0.546740i	0.999744	−	0.0226060i	$-0.00719632\pi$
$19$	0.774344	+	2.38319i	0.177647	+	0.546740i	−0.822098	+	0.569346i	$0.807196\pi$
$20$	−3.49666	+	2.54047i	−0.781878	+	0.568067i
$21$	0.469055	+	1.44360i	0.102356	+	0.315020i
$22$	12.9848	+	9.43400i	2.76837	+	2.01134i
$23$	4.52838	+	3.29006i	0.944232	+	0.686025i	0.949436	−	0.313962i	$-0.101656\pi$
$23$	4.52838	+	3.29006i	0.944232	+	0.686025i	−0.00520348	+	0.999986i	$0.501656\pi$
$24$	−5.91490	+	4.29743i	−1.20737	+	0.877209i
$25$	−4.19025			−0.838050
$26$	1.91031			0.374643
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	2.25292	−	6.93376i	0.425761	−	1.31036i
$29$	1.33393	+	4.10541i	0.247704	+	0.762356i	0.995180	+	0.0980664i	$0.0312658\pi$
$29$	1.33393	+	4.10541i	0.247704	+	0.762356i	−0.747475	+	0.664289i	$0.768734\pi$
$30$	2.34708			0.428517
$31$	−5.25666	+	1.83509i	−0.944124	+	0.329591i
$31$	−5.25666	+	1.83509i	−0.944124	+	0.329591i
$32$	10.0609			1.77854
$33$	−1.90154	−	5.85235i	−0.331016	−	1.01876i
$34$	6.09900	−	18.7708i	1.04597	−	3.21916i
$35$	−1.10503	+	0.802853i	−0.186785	+	0.135707i
$36$	4.80309			0.800515
$37$	−3.76750			−0.619373			−0.309686	−	0.950839i	$-0.600224\pi$
$37$	−3.76750			−0.619373			−0.309686	+	0.950839i	$0.600224\pi$
$38$	−5.28765	+	3.84170i	−0.857770	+	0.623206i
$39$	−0.592528	−	0.430497i	−0.0948804	−	0.0689346i
$40$	−5.32259	−	3.86709i	−0.841576	−	0.611441i
$41$	−0.725289	−	2.23221i	−0.113271	−	0.348613i	0.878311	−	0.478089i	$-0.158670\pi$
$41$	−0.725289	−	2.23221i	−0.113271	−	0.348613i	−0.991583	+	0.129476i	$0.958670\pi$
$42$	−3.20297	+	2.32709i	−0.494229	+	0.359078i
$43$	−0.134532	−	0.414048i	−0.0205160	−	0.0631417i	0.940274	−	0.340418i	$-0.110568\pi$
$43$	−0.134532	−	0.414048i	−0.0205160	−	0.0631417i	−0.960790	+	0.277276i	$0.910568\pi$
$44$	−9.13329	+	28.1094i	−1.37690	+	4.23765i
$45$	−0.728003	−	0.528925i	−0.108524	−	0.0788475i
$46$	−4.51150	+	13.8850i	−0.665184	+	2.04723i
$47$	2.73269	−	8.41035i	0.398604	−	1.22678i	−0.527516	−	0.849545i	$-0.676876\pi$
$47$	2.73269	−	8.41035i	0.398604	−	1.22678i	0.926119	−	0.377231i	$-0.123124\pi$
$48$	−7.65613	−	5.56250i	−1.10507	−	0.802878i
$49$	−1.45114	+	4.46616i	−0.207306	+	0.638022i
$50$	−3.37734	−	10.3944i	−0.477629	−	1.46999i
$51$	−6.12182	+	4.44776i	−0.857226	+	0.622811i
$52$	1.08706	+	3.34563i	0.150748	+	0.463956i
$53$	−1.19921	−	0.871276i	−0.164724	−	0.119679i	0.502369	−	0.864653i	$-0.332462\pi$
$53$	−1.19921	−	0.871276i	−0.164724	−	0.119679i	−0.667093	+	0.744974i	$0.732462\pi$
$54$	−2.11014	−	1.53310i	−0.287153	−	0.208629i
$55$	4.47979	−	3.25476i	0.604054	−	0.438871i
$56$	11.0977			1.48299
$57$	2.50583			0.331905
$58$	−9.10880	+	6.61793i	−1.19604	+	0.868977i
$59$	−1.21705	+	3.74569i	−0.158446	+	0.487647i	−0.998494	−	0.0548655i	$-0.982527\pi$
$59$	−1.21705	+	3.74569i	−0.158446	+	0.487647i	0.840048	+	0.542513i	$0.182527\pi$
$60$	1.33561	+	4.11057i	0.172426	+	0.530673i
$61$	3.67818			0.470943			0.235471	−	0.971881i	$-0.424337\pi$
$61$	3.67818			0.470943			0.235471	+	0.971881i	$0.424337\pi$
$62$	−8.78902	−	11.5607i	−1.11621	−	1.46821i
$63$	1.51790			0.191237
$64$	2.26035	+	6.95665i	0.282544	+	0.869582i
$65$	0.203662	−	0.626806i	0.0252611	−	0.0777457i
$66$	12.9848	−	9.43400i	1.59832	−	1.16125i
$67$	2.90302			0.354660			0.177330	−	0.984151i	$-0.443254\pi$
$67$	2.90302			0.354660			0.177330	+	0.984151i	$0.443254\pi$
$68$	36.3449			4.40747
$69$	4.52838	−	3.29006i	0.545153	−	0.396077i
$70$	−2.88223	−	2.09406i	−0.344492	−	0.250288i
$71$	10.4065	+	7.56080i	1.23503	+	0.897302i	0.997257	−	0.0740188i	$-0.0235825\pi$
$71$	10.4065	+	7.56080i	1.23503	+	0.897302i	0.237773	+	0.971321i	$0.423582\pi$
$72$	2.25929	+	6.95339i	0.266260	+	0.819465i
$73$	−5.93263	+	4.31031i	−0.694362	+	0.504484i	−0.878091	−	0.478493i	$-0.841183\pi$
$73$	−5.93263	+	4.31031i	−0.694362	+	0.504484i	0.183729	+	0.982977i	$0.441183\pi$
$74$	−3.03661	−	9.34571i	−0.352998	−	1.08642i
$75$	−1.29486	+	3.98516i	−0.149517	+	0.460167i
$76$	−9.73711	−	7.07442i	−1.11692	−	0.811492i
$77$	−2.88635	+	8.88326i	−0.328930	+	1.01234i
$78$	0.590319	−	1.81681i	0.0668404	−	0.205714i
$79$	6.63830	+	4.82301i	0.746867	+	0.542631i	0.894854	−	0.446359i	$-0.147279\pi$
$79$	6.63830	+	4.82301i	0.746867	+	0.542631i	−0.147987	+	0.988989i	$0.547279\pi$
$80$	2.63154	−	8.09903i	0.294215	−	0.905500i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	4.95267	−	3.59833i	0.546931	−	0.397369i
$83$	−1.27676	−	3.92947i	−0.140143	−	0.431315i	0.856212	−	0.516625i	$-0.172812\pi$
$83$	−1.27676	−	3.92947i	−0.140143	−	0.431315i	−0.996354	+	0.0853100i	$0.972812\pi$
$84$	−5.89821	−	4.28530i	−0.643547	−	0.467564i
$85$	−5.50879	−	4.00237i	−0.597512	−	0.434118i
$86$	0.918660	−	0.667446i	0.0990617	−	0.0719725i
$87$	4.31669			0.462797
$88$	−44.9898			−4.79593
$89$	5.68943	−	4.13361i	0.603078	−	0.438162i	−0.243892	−	0.969802i	$-0.578424\pi$
$89$	5.68943	−	4.13361i	0.603078	−	0.438162i	0.846970	+	0.531640i	$0.178424\pi$
$90$	0.725289	−	2.23221i	0.0764522	−	0.235296i
$91$	0.343538	+	1.05730i	0.0360126	+	0.110835i
$92$	−26.8847			−2.80293
$93$	0.120875	+	5.56645i	0.0125342	+	0.577214i
$94$	23.0654			2.37901
$95$	0.696802	+	2.14454i	0.0714904	+	0.220025i
$96$	3.10900	−	9.56851i	0.317311	−	0.976582i
$97$	3.07965	−	2.23750i	0.312691	−	0.227183i	−0.420359	−	0.907358i	$-0.638096\pi$
$97$	3.07965	−	2.23750i	0.312691	−	0.227183i	0.733050	+	0.680174i	$0.238096\pi$
$98$	−12.2484			−1.23728
$99$	−6.15353			−0.618453
$100$	16.2824	−	11.8299i	1.62824	−	1.18299i
$101$	3.77306	+	2.74129i	0.375433	+	0.272768i	0.759460	−	0.650554i	$-0.225463\pi$
$101$	3.77306	+	2.74129i	0.375433	+	0.272768i	−0.384027	+	0.923322i	$0.625463\pi$
$102$	−15.9674	−	11.6010i	−1.58101	−	1.14867i
$103$	0.632787	+	1.94752i	0.0623504	+	0.191895i	0.977380	−	0.211493i	$-0.0678326\pi$
$103$	0.632787	+	1.94752i	0.0623504	+	0.191895i	−0.915029	+	0.403388i	$0.867833\pi$
$104$	−4.33210	+	3.14746i	−0.424798	+	0.308634i
$105$	0.422085	+	1.29904i	0.0411913	+	0.126774i
$106$	1.19474	−	3.67702i	0.116043	−	0.357144i
$107$	5.48407	+	3.98441i	0.530165	+	0.385187i	0.820419	−	0.571762i	$-0.193740\pi$
$107$	5.48407	+	3.98441i	0.530165	+	0.385187i	−0.290255	+	0.956949i	$0.593740\pi$
$108$	1.48424	−	4.56801i	0.142821	−	0.439557i
$109$	3.64497	−	11.2181i	0.349125	−	1.07450i	−0.610213	−	0.792238i	$-0.708916\pi$
$109$	3.64497	−	11.2181i	0.349125	−	1.07450i	0.959338	−	0.282260i	$-0.0910839\pi$
$110$	11.6845	+	8.48929i	1.11407	+	0.809422i
$111$	−1.16422	+	3.58310i	−0.110503	+	0.340093i
$112$	4.43890	+	13.6615i	0.419437	+	1.29089i
$113$	−0.690866	+	0.501943i	−0.0649912	+	0.0472189i	−0.619807	−	0.784755i	$-0.712789\pi$
$113$	−0.690866	+	0.501943i	−0.0649912	+	0.0472189i	0.554815	+	0.831974i	$0.312789\pi$
$114$	2.01970	+	6.21600i	0.189162	+	0.582182i
$115$	4.07491	+	2.96060i	0.379987	+	0.276077i
$116$	−16.7737	−	12.1868i	−1.55740	−	1.13152i
$117$	−0.592528	+	0.430497i	−0.0547792	+	0.0397994i
$118$	−10.2726			−0.945666
$119$	11.4859			1.05291
$120$	−5.32259	+	3.86709i	−0.485884	+	0.353015i
$121$	8.30202	−	25.5510i	0.754729	−	2.32282i
$122$	2.96462	+	9.12416i	0.268404	+	0.826062i
$123$	−2.34708			−0.211629
$124$	15.2454	−	21.9713i	1.36908	−	1.97308i
$125$	−8.26995			−0.739687
$126$	1.22342	+	3.76531i	0.108991	+	0.335441i
$127$	−4.51633	+	13.8998i	−0.400760	+	1.23341i	0.523625	+	0.851949i	$0.324579\pi$
$127$	−4.51633	+	13.8998i	−0.400760	+	1.23341i	−0.924384	+	0.381462i	$0.875421\pi$
$128$	0.843985	−	0.613191i	0.0745985	−	0.0541989i
$129$	−0.435356			−0.0383309
$130$	1.71902			0.150768
$131$	−12.5074	+	9.08718i	−1.09278	+	0.793950i	−0.979866	−	0.199655i	$-0.936018\pi$
$131$	−12.5074	+	9.08718i	−1.09278	+	0.793950i	−0.112912	+	0.993605i	$0.536018\pi$
$132$	23.9113	+	17.3726i	2.08121	+	1.51209i
$133$	−3.07717	−	2.23569i	−0.266824	−	0.193859i
$134$	2.33983	+	7.20127i	0.202131	+	0.622095i
$135$	−0.728003	+	0.528925i	−0.0626565	+	0.0455226i
$136$	17.0960	+	52.6162i	1.46597	+	4.51180i
$137$	−1.29168	+	3.97539i	−0.110356	+	0.339640i	−0.990950	−	0.134231i	$-0.957144\pi$
$137$	−1.29168	+	3.97539i	−0.110356	+	0.339640i	0.880594	+	0.473871i	$0.157144\pi$
$138$	11.8112	+	8.58137i	1.00544	+	0.730495i
$139$	3.29575	−	10.1433i	0.279542	−	0.860342i	−0.708440	−	0.705771i	$-0.750601\pi$
$139$	3.29575	−	10.1433i	0.279542	−	0.860342i	0.987982	−	0.154571i	$-0.0493994\pi$
$140$	2.02731	−	6.23942i	0.171339	−	0.527327i
$141$	−7.15427	−	5.19788i	−0.602498	−	0.437741i
$142$	−10.3678	+	31.9087i	−0.870042	+	2.67771i
$143$	−1.39270	−	4.28629i	−0.116463	−	0.358438i
$144$	−7.65613	+	5.56250i	−0.638010	+	0.463542i
$145$	1.20035	+	3.69430i	0.0996837	+	0.306795i
$146$	−15.4739	−	11.2425i	−1.28063	−	0.930433i
$147$	3.79914	+	2.76024i	0.313348	+	0.227660i
$148$	14.6397	−	10.6363i	1.20337	−	0.874302i
$149$	−15.7326			−1.28886			−0.644431	−	0.764662i	$-0.722906\pi$
$149$	−15.7326			−1.28886			−0.644431	+	0.764662i	$0.722906\pi$
$150$	−10.9293			−0.892375
$151$	2.44417	−	1.77580i	0.198904	−	0.144512i	−0.483875	−	0.875137i	$-0.660771\pi$
$151$	2.44417	−	1.77580i	0.198904	−	0.144512i	0.682779	+	0.730625i	$0.260771\pi$
$152$	5.66140	−	17.4240i	0.459200	−	1.41327i
$153$	2.33833	+	7.19663i	0.189043	+	0.581813i
$154$	−24.3623			−1.96317
$155$	−4.73026	+	1.65132i	−0.379944	+	0.132638i
$156$	3.51781			0.281650
$157$	−2.75996	−	8.49428i	−0.220269	−	0.677917i	−0.998737	−	0.0502340i	$-0.984003\pi$
$157$	−2.75996	−	8.49428i	−0.220269	−	0.677917i	0.778469	−	0.627683i	$-0.215997\pi$
$158$	−6.61355	+	20.3544i	−0.526146	+	1.61931i
$159$	−1.19921	+	0.871276i	−0.0951034	+	0.0690967i
$160$	9.05343			0.715737
$161$	−8.49624			−0.669598
$162$	−2.11014	+	1.53310i	−0.165788	+	0.120452i
$163$	0.964013	+	0.700397i	0.0755074	+	0.0548593i	0.624899	−	0.780706i	$-0.285140\pi$
$163$	0.964013	+	0.700397i	0.0755074	+	0.0548593i	−0.549391	+	0.835565i	$0.685140\pi$
$164$	9.12025	+	6.62625i	0.712172	+	0.517423i
$165$	−1.71113	−	5.26631i	−0.133211	−	0.409981i
$166$	8.71843	−	6.33431i	0.676681	−	0.491638i
$167$	−4.09630	−	12.6071i	−0.316982	−	0.975569i	−0.974931	−	0.222507i	$-0.928576\pi$
$167$	−4.09630	−	12.6071i	−0.316982	−	0.975569i	0.657950	−	0.753062i	$-0.271424\pi$
$168$	3.42937	−	10.5545i	0.264582	−	0.814298i
$169$	10.0833	+	7.32591i	0.775635	+	0.563532i
$170$	5.48825	−	16.8911i	0.420930	−	1.29549i
$171$	0.774344	−	2.38319i	0.0592156	−	0.182247i
$172$	1.69170	+	1.22909i	0.128991	+	0.0937172i
$173$	−0.585372	+	1.80159i	−0.0445050	+	0.136972i	−0.970840	−	0.239729i	$-0.922942\pi$
$173$	−0.585372	+	1.80159i	−0.0445050	+	0.136972i	0.926335	+	0.376701i	$0.122942\pi$
$174$	3.47925	+	10.7080i	0.263761	+	0.811774i
$175$	5.14564	−	3.73853i	0.388974	−	0.282606i
$176$	−17.9953	−	55.3837i	−1.35644	−	4.17470i
$177$	3.18627	+	2.31496i	0.239495	+	0.174003i
$178$	14.8396	+	10.7816i	1.11227	+	0.808114i
$179$	18.5084	−	13.4471i	1.38338	−	1.00508i	0.386824	−	0.922154i	$-0.373572\pi$
$179$	18.5084	−	13.4471i	1.38338	−	1.00508i	0.996555	−	0.0829304i	$-0.0264279\pi$
$180$	4.32211			0.322151
$181$	13.3096			0.989296			0.494648	−	0.869093i	$-0.335297\pi$
$181$	13.3096			0.989296			0.494648	+	0.869093i	$0.335297\pi$
$182$	−2.34587	+	1.70437i	−0.173887	+	0.126337i
$183$	1.13662	−	3.49816i	0.0840214	−	0.258591i
$184$	−12.6461	−	38.9208i	−0.932285	−	2.86928i
$185$	−3.39022			−0.249254
$186$	−13.7108	+	4.78641i	−1.00532	+	0.350957i
$187$	−46.5637			−3.40507
$188$	13.1253	+	40.3957i	0.957264	+	2.94616i
$189$	0.469055	−	1.44360i	0.0341188	−	0.105007i
$190$	−4.75815	+	3.45700i	−0.345192	+	0.250797i
$191$	2.94257			0.212917			0.106458	−	0.994317i	$-0.466049\pi$
$191$	2.94257			0.212917			0.106458	+	0.994317i	$0.466049\pi$
$192$	7.31466			0.527890
$193$	−17.4775	+	12.6982i	−1.25806	+	0.914035i	−0.998661	−	0.0517353i	$-0.983525\pi$
$193$	−17.4775	+	12.6982i	−1.25806	+	0.914035i	−0.259400	+	0.965770i	$0.583525\pi$
$194$	8.03257	+	5.83600i	0.576705	+	0.419000i
$195$	−0.533193	−	0.387387i	−0.0381827	−	0.0277414i
$196$	−6.96997	−	21.4513i	−0.497855	−	1.53224i
$197$	−12.6299	+	9.17619i	−0.899846	+	0.653776i	−0.938426	−	0.345479i	$-0.887716\pi$
$197$	−12.6299	+	9.17619i	−0.899846	+	0.653776i	0.0385806	+	0.999255i	$0.487716\pi$
$198$	−4.95975	−	15.2645i	−0.352474	−	1.08480i
$199$	3.28772	−	10.1186i	0.233060	−	0.717286i	−0.764312	−	0.644846i	$-0.776921\pi$
$199$	3.28772	−	10.1186i	0.233060	−	0.717286i	0.997373	−	0.0724398i	$-0.0230785\pi$
$200$	24.7849	+	18.0073i	1.75256	+	1.27331i
$201$	0.897082	−	2.76093i	0.0632753	−	0.194741i
$202$	−3.75899	+	11.5690i	−0.264482	+	0.813991i
$203$	−5.30090	−	3.85133i	−0.372050	−	0.270310i
$204$	11.2312	−	34.5661i	0.786341	−	2.42011i
$205$	−0.652659	−	2.00868i	−0.0455837	−	0.140292i
$206$	−4.32102	+	3.13940i	−0.301060	+	0.218733i
$207$	−1.72969	−	5.32343i	−0.120222	−	0.370004i
$208$	−5.60738	−	4.07400i	−0.388802	−	0.282481i
$209$	12.4748	+	9.06347i	0.862900	+	0.626933i
$210$	−2.88223	+	2.09406i	−0.198892	+	0.144504i
$211$	−18.9518			−1.30470			−0.652348	−	0.757920i	$-0.726216\pi$
$211$	−18.9518			−1.30470			−0.652348	+	0.757920i	$0.726216\pi$
$212$	7.11963			0.488978
$213$	10.4065	−	7.56080i	0.713045	−	0.518057i
$214$	−5.46362	+	16.8153i	−0.373485	+	1.14947i
$215$	−0.121060	−	0.372586i	−0.00825625	−	0.0254101i
$216$	7.31122			0.497466
$217$	4.81793	−	6.94346i	0.327063	−	0.471353i
$218$	30.7656			2.08371
$219$	2.26606	+	6.97423i	0.153126	+	0.471275i
$220$	−8.21869	+	25.2945i	−0.554104	+	1.70536i
$221$	−4.48365	+	3.25756i	−0.301603	+	0.219127i
$222$	−9.82666			−0.659522
$223$	11.5171			0.771242			0.385621	−	0.922657i	$-0.373987\pi$
$223$	11.5171			0.771242			0.385621	+	0.922657i	$0.373987\pi$
$224$	−12.3548	+	8.97632i	−0.825493	+	0.599756i
$225$	3.38998	+	2.46297i	0.225999	+	0.164198i
$226$	−1.80197	−	1.30921i	−0.119865	−	0.0870871i
$227$	−5.37724	−	16.5494i	−0.356900	−	1.09842i	−0.954900	−	0.296928i	$-0.904038\pi$
$227$	−5.37724	−	16.5494i	−0.356900	−	1.09842i	0.598000	−	0.801496i	$-0.295962\pi$
$228$	−9.73711	+	7.07442i	−0.644856	+	0.468515i
$229$	7.32163	+	22.5337i	0.483827	+	1.48907i	0.833672	+	0.552259i	$0.186234\pi$
$229$	7.32163	+	22.5337i	0.483827	+	1.48907i	−0.349845	+	0.936808i	$0.613766\pi$
$230$	−4.05972	+	12.4945i	−0.267690	+	0.823865i
$231$	7.55655	+	5.49016i	0.497185	+	0.361226i
$232$	9.75266	−	30.0156i	0.640293	−	1.97062i
$233$	1.64939	−	5.07631i	0.108055	−	0.332560i	−0.882380	−	0.470538i	$-0.844060\pi$
$233$	1.64939	−	5.07631i	0.108055	−	0.332560i	0.990435	+	0.137977i	$0.0440600\pi$
$234$	−1.54547	−	1.12285i	−0.101031	−	0.0734032i
$235$	2.45904	−	7.56815i	0.160410	−	0.493692i
$236$	−5.84559	−	17.9909i	−0.380516	−	1.17111i
$237$	6.63830	−	4.82301i	0.431204	−	0.313288i
$238$	9.25764	+	28.4921i	0.600083	+	1.84687i
$239$	−2.46672	−	1.79218i	−0.159559	−	0.115926i	0.505141	−	0.863037i	$-0.331441\pi$
$239$	−2.46672	−	1.79218i	−0.159559	−	0.115926i	−0.664700	+	0.747111i	$0.731441\pi$
$240$	−6.88945	−	5.00548i	−0.444712	−	0.323102i
$241$	1.40209	−	1.01868i	0.0903167	−	0.0656189i	−0.541710	−	0.840565i	$-0.682223\pi$
$241$	1.40209	−	1.01868i	0.0903167	−	0.0656189i	0.632027	+	0.774946i	$0.282223\pi$
$242$	70.0736			4.50450
$243$	1.00000			0.0641500
$244$	−14.2926	+	10.3842i	−0.914991	+	0.664780i
$245$	−1.30583	+	4.01892i	−0.0834262	+	0.256759i
$246$	−1.89175	−	5.82221i	−0.120614	−	0.371211i
$247$	1.83528			0.116776
$248$	38.9788	+	11.7358i	2.47516	+	0.745221i
$249$	−4.13169			−0.261835
$250$	−6.66559	−	20.5146i	−0.421569	−	1.29745i
$251$	2.29835	−	7.07359i	0.145070	−	0.446481i	−0.851950	−	0.523624i	$-0.824580\pi$
$251$	2.29835	−	7.07359i	0.145070	−	0.446481i	0.997020	+	0.0771428i	$0.0245798\pi$
$252$	−5.89821	+	4.28530i	−0.371552	+	0.269948i
$253$	34.4437			2.16545
$254$	−38.1203			−2.39188
$255$	−5.50879	+	4.00237i	−0.344974	+	0.250638i
$256$	14.0367	+	10.1983i	0.877294	+	0.637392i
$257$	−19.2571	−	13.9911i	−1.20123	−	0.872742i	−0.206821	−	0.978379i	$-0.566312\pi$
$257$	−19.2571	−	13.9911i	−1.20123	−	0.872742i	−0.994405	+	0.105637i	$0.966312\pi$
$258$	−0.350897	−	1.07995i	−0.0218459	−	0.0672347i
$259$	4.62650	−	3.36135i	0.287477	−	0.208864i
$260$	0.978205	+	3.01060i	0.0606657	+	0.186710i
$261$	1.33393	−	4.10541i	0.0825681	−	0.254119i
$262$	−32.6228	−	23.7018i	−2.01544	−	1.46430i
$263$	3.92843	−	12.0905i	0.242238	−	0.745530i	−0.753841	−	0.657057i	$-0.771801\pi$
$263$	3.92843	−	12.0905i	0.242238	−	0.745530i	0.996079	−	0.0884735i	$-0.0281989\pi$
$264$	−13.9026	+	42.7879i	−0.855647	+	2.63341i
$265$	−1.07912	−	0.784027i	−0.0662899	−	0.0481624i
$266$	3.06569	−	9.43524i	0.187970	−	0.578512i
$267$	−2.17317	−	6.68833i	−0.132996	−	0.409319i
$268$	−11.2805	+	8.19576i	−0.689066	+	0.500636i
$269$	2.48078	+	7.63506i	0.151256	+	0.465518i	0.997762	−	0.0668608i	$-0.0212983\pi$
$269$	2.48078	+	7.63506i	0.151256	+	0.465518i	−0.846506	+	0.532378i	$0.821298\pi$
$270$	−1.89883	−	1.37958i	−0.115559	−	0.0839586i
$271$	−1.52793	−	1.11011i	−0.0928152	−	0.0674342i	0.540410	−	0.841402i	$-0.318269\pi$
$271$	−1.52793	−	1.11011i	−0.0928152	−	0.0674342i	−0.633225	+	0.773968i	$0.718269\pi$
$272$	−57.9338	+	42.0914i	−3.51275	+	2.55216i
$273$	1.11171			0.0672840
$274$	−10.9025			−0.658645
$275$	−20.8604	+	15.1559i	−1.25793	+	0.913937i
$276$	−8.30784	+	25.5689i	−0.500073	+	1.53907i
$277$	1.42714	+	4.39228i	0.0857484	+	0.263906i	0.984732	−	0.174075i	$-0.0556936\pi$
$277$	1.42714	+	4.39228i	0.0857484	+	0.263906i	−0.898984	+	0.437981i	$0.855694\pi$
$278$	27.8180			1.66841
$279$	5.33136	+	1.60517i	0.319180	+	0.0960990i
$280$	9.98636			0.596799
$281$	−2.98533	−	9.18789i	−0.178090	−	0.548104i	0.821671	−	0.569961i	$-0.193042\pi$
$281$	−2.98533	−	9.18789i	−0.178090	−	0.548104i	−0.999761	+	0.0218578i	$0.993042\pi$
$282$	7.12760	−	21.9365i	0.424442	−	1.30630i
$283$	−14.5227	+	10.5513i	−0.863284	+	0.627212i	−0.928776	−	0.370641i	$-0.879138\pi$
$283$	−14.5227	+	10.5513i	−0.863284	+	0.627212i	0.0654927	+	0.997853i	$0.479138\pi$
$284$	−61.7831			−3.66615
$285$	2.25490			0.133569
$286$	9.51012	−	6.90951i	0.562345	−	0.408568i
$287$	2.88223	+	2.09406i	0.170132	+	0.123608i
$288$	−8.13946	−	5.91366i	−0.479622	−	0.348466i
$289$	12.4408	+	38.2888i	0.731812	+	2.25228i
$290$	−8.19665	+	5.95522i	−0.481324	+	0.349702i
$291$	−1.17632	−	3.62034i	−0.0689572	−	0.212228i
$292$	10.8841	−	33.4978i	0.636944	−	1.96031i
$293$	17.7613	+	12.9044i	1.03763	+	0.753881i	0.969821	−	0.243817i	$-0.0783997\pi$
$293$	17.7613	+	12.9044i	1.03763	+	0.753881i	0.0678073	+	0.997698i	$0.478400\pi$
$294$	−3.78498	+	11.6490i	−0.220744	+	0.679381i
$295$	−1.09517	+	3.37060i	−0.0637635	+	0.196244i
$296$	22.2844	+	16.1906i	1.29525	+	0.941057i
$297$	−1.90154	+	5.85235i	−0.110339	+	0.339588i
$298$	−12.6805	−	39.0264i	−0.734559	−	2.26074i
$299$	3.31661	−	2.40966i	0.191804	−	0.139354i
$300$	−6.21932	−	19.1411i	−0.359073	−	1.10511i
$301$	0.534618	+	0.388423i	0.0308149	+	0.0223883i
$302$	6.37507	+	4.63176i	0.366844	+	0.266528i
$303$	3.77306	−	2.74129i	0.216757	−	0.157483i
$304$	23.7139			1.36009
$305$	3.30985			0.189522
$306$	−15.9674	+	11.6010i	−0.912794	+	0.663184i
$307$	−7.95316	+	24.4773i	−0.453911	+	1.39699i	0.418498	+	0.908218i	$0.362557\pi$
$307$	−7.95316	+	24.4773i	−0.453911	+	1.39699i	−0.872409	+	0.488777i	$0.837443\pi$
$308$	−13.8634	−	42.6671i	−0.789939	−	2.43118i
$309$	2.04774			0.116492
$310$	−7.90889	−	10.4030i	−0.449195	−	0.590850i
$311$	14.7362			0.835613			0.417806	−	0.908536i	$-0.362799\pi$
$311$	14.7362			0.835613			0.417806	+	0.908536i	$0.362799\pi$
$312$	1.65472	+	5.09269i	0.0936799	+	0.288317i
$313$	7.74154	−	23.8260i	0.437578	−	1.34673i	−0.452844	−	0.891590i	$-0.649590\pi$
$313$	7.74154	−	23.8260i	0.437578	−	1.34673i	0.890422	−	0.455137i	$-0.150410\pi$
$314$	18.8465	−	13.6928i	1.06357	−	0.772729i
$315$	1.36589			0.0769595
$316$	−39.4112			−2.21705
$317$	15.3783	−	11.1730i	0.863732	−	0.627538i	−0.0651658	−	0.997874i	$-0.520758\pi$
$317$	15.3783	−	11.1730i	0.863732	−	0.627538i	0.928898	+	0.370337i	$0.120758\pi$
$318$	−3.12786	−	2.27253i	−0.175402	−	0.127437i
$319$	21.4898	+	15.6132i	1.20320	+	0.874174i
$320$	2.03400	+	6.26002i	0.113704	+	0.349946i
$321$	5.48407	−	3.98441i	0.306091	−	0.222388i
$322$	−6.84798	−	21.0759i	−0.381623	−	1.17451i
$323$	5.85945	−	18.0335i	0.326029	−	1.00341i
$324$	−3.88578	−	2.82319i	−0.215877	−	0.156844i
$325$	−0.948360	+	2.91875i	−0.0526056	+	0.161903i
$326$	−0.960419	+	2.95587i	−0.0531927	+	0.163710i
$327$	−9.54267	−	6.93315i	−0.527711	−	0.383404i
$328$	−5.30275	+	16.3202i	−0.292795	+	0.901131i
$329$	4.14793	+	12.7660i	0.228683	+	0.703814i
$330$	11.6845	−	8.48929i	0.643211	−	0.467320i
$331$	0.816905	+	2.51418i	0.0449012	+	0.138192i	0.970994	−	0.239105i	$-0.0768539\pi$
$331$	0.816905	+	2.51418i	0.0449012	+	0.138192i	−0.926093	+	0.377296i	$0.876854\pi$
$332$	16.0548	+	11.6645i	0.881124	+	0.640174i
$333$	3.04797	+	2.21448i	0.167028	+	0.121353i
$334$	27.9718	−	20.3227i	1.53055	−	1.11201i
$335$	2.61231			0.142726
$336$	14.3646			0.783653
$337$	−15.5136	+	11.2713i	−0.845077	+	0.613985i	−0.923784	−	0.382913i	$-0.874921\pi$
$337$	−15.5136	+	11.2713i	−0.845077	+	0.613985i	0.0787070	+	0.996898i	$0.474921\pi$
$338$	−10.0457	+	30.9174i	−0.546412	+	1.68168i
$339$	0.263887	+	0.812162i	0.0143324	+	0.0441106i
$340$	32.7054			1.77370
$341$	−19.5318	+	28.1487i	−1.05771	+	1.52434i
$342$	6.53589			0.353420
$343$	−5.48607	−	16.8844i	−0.296220	−	0.911671i
$344$	−0.983596	+	3.02720i	−0.0530319	+	0.163215i
$345$	4.07491	−	2.96060i	0.219386	−	0.159393i
$346$	−4.94086			−0.265622
$347$	−17.5600			−0.942668			−0.471334	−	0.881955i	$-0.656227\pi$
$347$	−17.5600			−0.942668			−0.471334	+	0.881955i	$0.656227\pi$
$348$	−16.7737	+	12.1868i	−0.899164	+	0.653281i
$349$	−20.7527	−	15.0777i	−1.11087	−	0.807091i	−0.128066	−	0.991766i	$-0.540877\pi$
$349$	−20.7527	−	15.0777i	−1.11087	−	0.807091i	−0.982800	+	0.184674i	$0.940877\pi$
$350$	13.4212	+	9.75110i	0.717395	+	0.521218i
$351$	0.226326	+	0.696558i	0.0120804	+	0.0371795i
$352$	50.0864	−	36.3899i	2.66961	−	1.93959i
$353$	−2.40003	−	7.38655i	−0.127741	−	0.393146i	0.866650	−	0.498917i	$-0.166269\pi$
$353$	−2.40003	−	7.38655i	−0.127741	−	0.393146i	−0.994390	+	0.105771i	$0.966269\pi$
$354$	−3.17439	+	9.76978i	−0.168717	+	0.519258i
$355$	9.36445	+	6.80367i	0.497013	+	0.361101i
$356$	−10.4379	+	32.1246i	−0.553209	+	1.70260i
$357$	3.54934	−	10.9237i	0.187851	−	0.578145i
$358$	48.2748	+	35.0737i	2.55141	+	1.85370i
$359$	−5.68233	+	17.4884i	−0.299902	+	0.923004i	0.681628	+	0.731698i	$0.261272\pi$
$359$	−5.68233	+	17.4884i	−0.299902	+	0.923004i	−0.981531	+	0.191305i	$0.938728\pi$
$360$	2.03305	+	6.25708i	0.107151	+	0.329777i
$361$	10.2914	−	7.47711i	0.541650	−	0.393532i
$362$	10.7276	+	33.0160i	0.563828	+	1.73528i
$363$	−21.7350	−	15.7914i	−1.14079	−	0.828833i
$364$	−4.31988	−	3.13857i	−0.226423	−	0.164506i
$365$	−5.33854	+	3.87868i	−0.279432	+	0.203019i
$366$	9.59370			0.501471
$367$	27.5561			1.43841			0.719207	−	0.694796i	$-0.244505\pi$
$367$	27.5561			1.43841			0.719207	+	0.694796i	$0.244505\pi$
$368$	42.8543	−	31.1355i	2.23393	−	1.62305i
$369$	−0.725289	+	2.23221i	−0.0377570	+	0.116204i
$370$	−2.73252	−	8.40984i	−0.142057	−	0.437207i
$371$	2.24998			0.116813
$372$	−16.1848	−	21.2888i	−0.839144	−	1.10377i
$373$	−10.1248			−0.524242			−0.262121	−	0.965035i	$-0.584422\pi$
$373$	−10.1248			−0.524242			−0.262121	+	0.965035i	$0.584422\pi$
$374$	−37.5303	−	115.507i	−1.94065	−	5.97270i
$375$	−2.55555	+	7.86519i	−0.131968	+	0.406157i
$376$	−52.3065	+	38.0029i	−2.69750	+	1.95985i
$377$	3.16156			0.162829
$378$	3.95909			0.203633
$379$	−19.9738	+	14.5118i	−1.02598	+	0.745421i	−0.967501	−	0.252868i	$-0.918626\pi$
$379$	−19.9738	+	14.5118i	−1.02598	+	0.745421i	−0.0584825	+	0.998288i	$0.518626\pi$
$380$	−8.76205	−	6.36600i	−0.449483	−	0.326569i
$381$	11.8239	+	8.59057i	0.605757	+	0.440108i
$382$	2.37171	+	7.29938i	0.121347	+	0.373469i
$383$	4.12861	−	2.99961i	0.210962	−	0.153273i	−0.477287	−	0.878748i	$-0.658380\pi$
$383$	4.12861	−	2.99961i	0.210962	−	0.153273i	0.688249	+	0.725475i	$0.258380\pi$
$384$	−0.322374	−	0.992164i	−0.0164511	−	0.0506312i
$385$	−2.59731	+	7.99370i	−0.132371	+	0.407397i
$386$	−45.5862	−	33.1203i	−2.32028	−	1.68578i
$387$	−0.134532	+	0.414048i	−0.00683866	+	0.0210472i
$388$	−5.64998	+	17.3888i	−0.286834	+	0.882784i
$389$	−8.54070	−	6.20518i	−0.433031	−	0.314615i	0.349829	−	0.936814i	$-0.386240\pi$
$389$	−8.54070	−	6.20518i	−0.433031	−	0.314615i	−0.782860	+	0.622198i	$0.786240\pi$
$390$	0.531205	−	1.63488i	0.0268986	−	0.0827854i
$391$	−13.0885	−	40.2823i	−0.661915	−	2.03716i
$392$	27.7764	−	20.1807i	1.40292	−	1.01928i
$393$	4.77741	+	14.7034i	0.240989	+	0.741686i
$394$	−32.9423	−	23.9340i	−1.65961	−	1.20578i
$395$	5.97355	+	4.34004i	0.300562	+	0.218371i
$396$	23.9113	−	17.3726i	1.20159	−	0.873004i
$397$	8.46114			0.424652			0.212326	−	0.977199i	$-0.431896\pi$
$397$	8.46114			0.424652			0.212326	+	0.977199i	$0.431896\pi$
$398$	27.7502			1.39099
$399$	−3.07717	+	2.23569i	−0.154051	+	0.111925i
$400$	−12.2539	+	37.7136i	−0.612694	+	1.88568i
$401$	4.56822	+	14.0595i	0.228126	+	0.702100i	0.997959	+	0.0638546i	$0.0203394\pi$
$401$	4.56822	+	14.0595i	0.228126	+	0.702100i	−0.769833	+	0.638245i	$0.779661\pi$
$402$	7.57187			0.377650
$403$	0.0885297	+	4.07690i	0.00440998	+	0.203085i
$404$	−22.4004			−1.11446
$405$	0.278072	+	0.855819i	0.0138175	+	0.0425260i
$406$	5.28114	−	16.2537i	0.262099	−	0.806656i
$407$	−18.7558	+	13.6269i	−0.929689	+	0.675458i
$408$	55.3239			2.73894
$409$	0.379662			0.0187731			0.00938654	−	0.999956i	$-0.497012\pi$
$409$	0.379662			0.0187731			0.00938654	+	0.999956i	$0.497012\pi$
$410$	4.45671	−	3.23799i	0.220101	−	0.159913i
$411$	3.38167	+	2.45693i	0.166805	+	0.121191i
$412$	−7.95708	−	5.78116i	−0.392017	−	0.284817i
$413$	−1.84735	−	5.68556i	−0.0909022	−	0.279768i
$414$	11.8112	−	8.58137i	0.580491	−	0.421752i
$415$	−1.14891	−	3.53598i	−0.0563977	−	0.173574i
$416$	2.27704	−	7.00802i	0.111641	−	0.343596i
$417$	−8.62839	−	6.26889i	−0.422534	−	0.306989i
$418$	−12.4283	+	38.2503i	−0.607887	+	1.87089i
$419$	1.98694	−	6.11517i	0.0970684	−	0.298746i	−0.890719	−	0.454555i	$-0.849798\pi$
$419$	1.98694	−	6.11517i	0.0970684	−	0.298746i	0.987787	+	0.155809i	$0.0497984\pi$
$420$	−5.30757	−	3.85617i	−0.258983	−	0.188162i
$421$	−2.73153	+	8.40679i	−0.133127	+	0.409722i	−0.995294	−	0.0969019i	$-0.969107\pi$
$421$	−2.73153	+	8.40679i	−0.133127	+	0.409722i	0.862167	+	0.506624i	$0.169107\pi$
$422$	−15.2752	−	47.0121i	−0.743583	−	2.28851i
$423$	−7.15427	+	5.19788i	−0.347853	+	0.252730i
$424$	3.34896	+	10.3070i	0.162640	+	0.500553i
$425$	25.6520	+	18.6372i	1.24430	+	0.904039i
$426$	27.1431	+	19.7206i	1.31509	+	0.955468i
$427$	−4.51682	+	3.28166i	−0.218584	+	0.158811i
$428$	−32.5586			−1.57378
$429$	−4.50687			−0.217594
$430$	0.826667	−	0.600608i	0.0398654	−	0.0289639i
$431$	10.2308	−	31.4871i	0.492799	−	1.51668i	−0.327560	−	0.944830i	$-0.606226\pi$
$431$	10.2308	−	31.4871i	0.492799	−	1.51668i	0.820359	−	0.571849i	$-0.193774\pi$
$432$	2.92438	+	9.00032i	0.140699	+	0.433028i
$433$	−27.9847			−1.34486			−0.672430	−	0.740160i	$-0.734750\pi$
$433$	−27.9847			−1.34486			−0.672430	+	0.740160i	$0.734750\pi$
$434$	21.1073	+	6.35500i	1.01318	+	0.305050i
$435$	3.88442			0.186244
$436$	17.5071	+	53.8814i	0.838440	+	2.58045i
$437$	−4.33430	+	13.3396i	−0.207338	+	0.638120i
$438$	−15.4739	+	11.2425i	−0.739373	+	0.537186i
$439$	−35.3042			−1.68498			−0.842488	−	0.538716i	$-0.818910\pi$
$439$	−35.3042			−1.68498			−0.842488	+	0.538716i	$0.818910\pi$
$440$	−40.4846			−1.93003
$441$	3.79914	−	2.76024i	0.180911	−	0.131440i
$442$	−11.6946	−	8.49661i	−0.556255	−	0.404143i
$443$	−26.2422	−	19.0661i	−1.24680	−	0.905856i	−0.248772	−	0.968562i	$-0.580027\pi$
$443$	−26.2422	−	19.0661i	−1.24680	−	0.905856i	−0.998032	+	0.0627061i	$0.980027\pi$
$444$	−5.59186	−	17.2100i	−0.265378	−	0.816749i
$445$	5.11970	−	3.71968i	0.242697	−	0.176330i
$446$	9.28279	+	28.5695i	0.439553	+	1.35280i
$447$	−4.86163	+	14.9626i	−0.229947	+	0.707705i
$448$	−8.98242	−	6.52611i	−0.424379	−	0.308330i
$449$	10.3254	−	31.7783i	0.487286	−	1.49971i	−0.341357	−	0.939934i	$-0.610887\pi$
$449$	10.3254	−	31.7783i	0.487286	−	1.49971i	0.828643	−	0.559777i	$-0.189113\pi$
$450$	−3.37734	+	10.3944i	−0.159210	+	0.489997i
$451$	−11.6845	−	8.48929i	−0.550202	−	0.399745i
$452$	1.26747	−	3.90089i	0.0596170	−	0.183482i
$453$	−0.933591	−	2.87330i	−0.0438639	−	0.134999i
$454$	36.7187	−	26.6777i	1.72329	−	1.25205i
$455$	0.309137	+	0.951425i	0.0144926	+	0.0446035i
$456$	−14.8217	−	10.7686i	−0.694092	−	0.504287i
$457$	26.7113	+	19.4069i	1.24950	+	0.907815i	0.998193	−	0.0600929i	$-0.0191397\pi$
$457$	26.7113	+	19.4069i	1.24950	+	0.907815i	0.251307	+	0.967907i	$0.419140\pi$
$458$	−49.9961	+	36.3243i	−2.33617	+	1.69732i
$459$	7.56699			0.353197
$460$	−24.1925			−1.12798
$461$	19.1565	−	13.9180i	0.892209	−	0.648228i	−0.0442441	−	0.999021i	$-0.514088\pi$
$461$	19.1565	−	13.9180i	0.892209	−	0.648228i	0.936453	+	0.350793i	$0.114088\pi$
$462$	−7.52838	+	23.1700i	−0.350252	+	1.07796i
$463$	3.27074	+	10.0663i	0.152004	+	0.467821i	0.997845	−	0.0656145i	$-0.0209008\pi$
$463$	3.27074	+	10.0663i	0.152004	+	0.467821i	−0.845841	+	0.533435i	$0.820901\pi$
$464$	40.8509			1.89646
$465$	0.108771	+	5.00903i	0.00504414	+	0.232288i
$466$	13.9218			0.644915
$467$	5.75001	+	17.6967i	0.266079	+	0.818906i	0.991443	+	0.130540i	$0.0416713\pi$
$467$	5.75001	+	17.6967i	0.266079	+	0.818906i	−0.725364	+	0.688365i	$0.758329\pi$
$468$	1.08706	−	3.34563i	0.0502494	−	0.154652i
$469$	−3.56492	+	2.59006i	−0.164612	+	0.119598i
$470$	20.7557			0.957387
$471$	−8.93141			−0.411538
$472$	23.2956	−	16.9252i	1.07227	−	0.779046i
$473$	−2.16733	−	1.57466i	−0.0996542	−	0.0724030i
$474$	17.3145	+	12.5797i	0.795281	+	0.577806i
$475$	−3.24470	−	9.98615i	−0.148877	−	0.458196i
$476$	−44.6317	+	32.4268i	−2.04569	+	1.48628i
$477$	0.458057	+	1.40975i	0.0209730	+	0.0645482i
$478$	2.45752	−	7.56347i	0.112404	−	0.345945i
$479$	22.8126	+	16.5743i	1.04233	+	0.757299i	0.970740	−	0.240135i	$-0.0771917\pi$
$479$	22.8126	+	16.5743i	1.04233	+	0.757299i	0.0715932	+	0.997434i	$0.477192\pi$
$480$	2.79767	−	8.61033i	0.127695	−	0.393006i
$481$	−0.852681	+	2.62428i	−0.0388789	+	0.119657i
$482$	3.65704	+	2.65700i	0.166574	+	0.121023i
$483$	−2.62548	+	8.08041i	−0.119464	+	0.367671i
$484$	39.8754	+	122.724i	1.81252	+	5.57835i
$485$	2.77126	−	2.01344i	0.125836	−	0.0914254i
$486$	0.806001	+	2.48062i	0.0365609	+	0.112523i
$487$	29.5137	+	21.4429i	1.33739	+	0.971673i	0.999536	+	0.0304752i	$0.00970205\pi$
$487$	29.5137	+	21.4429i	1.33739	+	0.971673i	0.337857	+	0.941197i	$0.390298\pi$
$488$	−21.7561	−	15.8067i	−0.984852	−	0.715537i
$489$	0.964013	−	0.700397i	0.0435942	−	0.0316730i
$490$	−11.0219			−0.497918
$491$	−15.5194			−0.700381			−0.350191	−	0.936678i	$-0.613883\pi$
$491$	−15.5194			−0.700381			−0.350191	+	0.936678i	$0.613883\pi$
$492$	9.12025	−	6.62625i	0.411173	−	0.298735i
$493$	10.0938	−	31.0656i	0.454603	−	1.39912i
$494$	1.47924	+	4.55263i	0.0665541	+	0.204832i
$495$	−5.53732			−0.248884
$496$	1.14390	+	52.6781i	0.0513628	+	2.36532i
$497$	−19.5250			−0.875816
$498$	−3.33014	−	10.2491i	−0.149227	−	0.459275i
$499$	6.15592	−	18.9460i	0.275577	−	0.848138i	−0.713489	−	0.700666i	$-0.752886\pi$
$499$	6.15592	−	18.9460i	0.275577	−	0.848138i	0.989066	−	0.147472i	$-0.0471137\pi$
$500$	32.1352	−	23.3476i	1.43713	−	1.04414i
$501$	−13.2559			−0.592231
$502$	19.3993			0.865834
$503$	−14.0844	+	10.2329i	−0.627992	+	0.456263i	−0.855704	−	0.517466i	$-0.826876\pi$
$503$	−14.0844	+	10.2329i	−0.627992	+	0.456263i	0.227712	+	0.973729i	$0.426876\pi$
$504$	−8.97820	−	6.52305i	−0.399921	−	0.290560i
$505$	3.39523	+	2.46678i	0.151086	+	0.109770i
$506$	27.7616	+	85.4415i	1.23415	+	3.79834i
$507$	10.0833	−	7.32591i	0.447813	−	0.325355i
$508$	−21.6923	−	66.7622i	−0.962442	−	2.96209i
$509$	−3.32981	+	10.2481i	−0.147591	+	0.454239i	−0.997335	−	0.0729565i	$-0.976757\pi$
$509$	−3.32981	+	10.2481i	−0.147591	+	0.454239i	0.849744	+	0.527196i	$0.176757\pi$
$510$	−14.3684	−	10.4393i	−0.636245	−	0.462259i
$511$	3.43965	−	10.5861i	0.152161	−	0.468303i
$512$	−13.3396	+	41.0552i	−0.589534	+	1.81440i
$513$	−2.02726	−	1.47289i	−0.0895057	−	0.0650297i
$514$	19.1853	−	59.0463i	0.846228	−	2.60442i
$515$	0.569421	+	1.75250i	0.0250917	+	0.0772242i
$516$	1.69170	−	1.22909i	0.0744728	−	0.0541077i
$517$	−16.8157	−	51.7533i	−0.739553	−	2.27611i
$518$	12.0672	+	8.76731i	0.530201	+	0.385214i
$519$	1.53252	+	1.11344i	0.0672703	+	0.0488747i
$520$	−3.89829	+	2.83228i	−0.170951	+	0.124203i
$521$	3.67361			0.160944			0.0804718	−	0.996757i	$-0.474357\pi$
$521$	3.67361			0.160944			0.0804718	+	0.996757i	$0.474357\pi$
$522$	11.2591			0.492797
$523$	28.9125	−	21.0062i	1.26426	−	0.918536i	0.265298	−	0.964166i	$-0.414530\pi$
$523$	28.9125	−	21.0062i	1.26426	−	0.918536i	0.998958	+	0.0456299i	$0.0145295\pi$
$524$	22.9463	−	70.6216i	1.00242	−	3.08512i
$525$	−1.96546	−	6.04906i	−0.0857797	−	0.264003i
$526$	33.1581			1.44576
$527$	40.3423	+	12.1463i	1.75734	+	0.529101i
$528$	−58.2339			−2.53430
$529$	2.57433	+	7.92297i	0.111927	+	0.344477i
$530$	1.07510	−	3.30881i	0.0466993	−	0.143726i
$531$	3.18627	−	2.31496i	0.138273	−	0.100461i
$532$	18.2690			0.792060
$533$	−1.71902			−0.0744588
$534$	14.8396	−	10.7816i	0.642172	−	0.466565i
$535$	4.93490	+	3.58541i	0.213354	+	0.155011i
$536$	−17.1711	−	12.4755i	−0.741678	−	0.538860i
$537$	−7.06956	−	21.7579i	−0.305074	−	0.938922i
$538$	−16.9401	+	12.3077i	−0.730341	+	0.530624i
$539$	8.92964	+	27.4826i	0.384627	+	1.18376i
$540$	1.33561	−	4.11057i	0.0574754	−	0.176891i
$541$	−3.37448	−	2.45170i	−0.145080	−	0.105407i	0.512878	−	0.858462i	$-0.328579\pi$
$541$	−3.37448	−	2.45170i	−0.145080	−	0.105407i	−0.657958	+	0.753055i	$0.728579\pi$
$542$	1.52223	−	4.68496i	0.0653856	−	0.201236i
$543$	4.11290	−	12.6582i	0.176501	−	0.543215i
$544$	−61.5912	−	44.7486i	−2.64070	−	1.91858i
$545$	3.27997	−	10.0947i	0.140499	−	0.432410i
$546$	0.896042	+	2.75773i	0.0383471	+	0.118020i
$547$	−2.42174	+	1.75949i	−0.103546	+	0.0752306i	−0.638353	−	0.769743i	$-0.720384\pi$
$547$	−2.42174	+	1.75949i	−0.103546	+	0.0752306i	0.534807	+	0.844974i	$0.320384\pi$
$548$	−6.20407	−	19.0942i	−0.265025	−	0.815662i
$549$	−2.97571	−	2.16198i	−0.127000	−	0.0922711i
$550$	−54.4095	−	39.5308i	−2.32003	−	1.68560i
$551$	−8.75104	+	6.35800i	−0.372807	+	0.270860i
$552$	−40.9237			−1.74183
$553$	−12.4549			−0.529637
$554$	−9.74528	+	7.08036i	−0.414037	+	0.300816i
$555$	−1.04764	+	3.22430i	−0.0444697	+	0.136864i
$556$	15.8298	+	48.7191i	0.671333	+	2.06615i
$557$	−9.54939			−0.404621			−0.202310	−	0.979321i	$-0.564845\pi$
$557$	−9.54939			−0.404621			−0.202310	+	0.979321i	$0.564845\pi$
$558$	0.315276	+	14.5188i	0.0133467	+	0.614631i
$559$	−0.318857			−0.0134862
$560$	3.99440	+	12.2935i	0.168794	+	0.519495i
$561$	−14.3890	+	44.2847i	−0.607502	+	1.86970i
$562$	20.3854	−	14.8109i	0.859908	−	0.624760i
$563$	9.95166			0.419413			0.209706	−	0.977764i	$-0.432749\pi$
$563$	9.95166			0.419413			0.209706	+	0.977764i	$0.432749\pi$
$564$	42.4745			1.78850
$565$	−0.621683	+	0.451679i	−0.0261544	+	0.0190023i
$566$	−37.8791	−	27.5208i	−1.59218	−	1.15678i
$567$	−1.22800	−	0.892196i	−0.0515713	−	0.0374687i
$568$	−29.0617	−	89.4428i	−1.21940	−	3.75294i
$569$	16.9699	−	12.3294i	0.711417	−	0.516875i	−0.172213	−	0.985060i	$-0.555092\pi$
$569$	16.9699	−	12.3294i	0.711417	−	0.516875i	0.883631	+	0.468185i	$0.155092\pi$
$570$	1.81745	+	5.59354i	0.0761246	+	0.234288i
$571$	6.22455	−	19.1572i	0.260489	−	0.801704i	−0.732209	−	0.681080i	$-0.761510\pi$
$571$	6.22455	−	19.1572i	0.260489	−	0.801704i	0.992698	−	0.120624i	$-0.0384895\pi$
$572$	17.5127	+	12.7237i	0.732244	+	0.532006i
$573$	0.909304	−	2.79855i	0.0379867	−	0.116911i
$574$	−2.87148	+	8.83751i	−0.119853	+	0.368870i
$575$	−18.9750	−	13.7862i	−0.791314	−	0.574923i
$576$	2.26035	−	6.95665i	0.0941814	−	0.289861i
$577$	2.22449	+	6.84629i	0.0926069	+	0.285015i	0.986623	−	0.163021i	$-0.0521238\pi$
$577$	2.22449	+	6.84629i	0.0926069	+	0.285015i	−0.894016	+	0.448036i	$0.852124\pi$
$578$	−84.9526	+	61.7217i	−3.53356	+	2.56728i
$579$	6.67583	+	20.5461i	0.277438	+	0.853866i
$580$	−15.0940	−	10.9664i	−0.626744	−	0.455356i
$581$	5.07373	+	3.68628i	0.210494	+	0.152933i
$582$	8.03257	−	5.83600i	0.332961	−	0.241910i
$583$	−9.12139			−0.377769
$584$	53.6142			2.21857
$585$	−0.533193	+	0.387387i	−0.0220448	+	0.0160165i
$586$	−17.6951	+	54.4600i	−0.730979	+	2.24972i
$587$	0.597894	+	1.84013i	0.0246777	+	0.0759503i	0.962637	−	0.270795i	$-0.0872867\pi$
$587$	0.597894	+	1.84013i	0.0246777	+	0.0759503i	−0.937959	+	0.346746i	$0.887287\pi$
$588$	−22.5553			−0.930164
$589$	−8.44382	−	11.1066i	−0.347921	−	0.457640i
$590$	−9.24387			−0.380564
$591$	4.82421	+	14.8474i	0.198441	+	0.610740i
$592$	−11.0176	+	33.9087i	−0.452820	+	1.39364i
$593$	12.6902	−	9.22000i	0.521126	−	0.378620i	−0.295902	−	0.955218i	$-0.595620\pi$
$593$	12.6902	−	9.22000i	0.521126	−	0.378620i	0.817028	+	0.576598i	$0.195620\pi$
$594$	−16.0501			−0.658543
$595$	10.3357			0.423723
$596$	61.1333	−	44.4159i	2.50412	−	1.81935i
$597$	−8.60736	−	6.25362i	−0.352276	−	0.255943i
$598$	8.65061	+	6.28504i	0.353750	+	0.257014i
$599$	−5.87845	−	18.0920i	−0.240187	−	0.739220i	−0.996391	−	0.0848836i	$-0.972948\pi$
$599$	−5.87845	−	18.0920i	−0.240187	−	0.739220i	0.756204	−	0.654336i	$-0.227052\pi$
$600$	24.7849	−	18.0073i	1.01184	−	0.735145i
$601$	−4.17652	−	12.8540i	−0.170364	−	0.524326i	0.829027	−	0.559208i	$-0.188895\pi$
$601$	−4.17652	−	12.8540i	−0.170364	−	0.524326i	−0.999391	+	0.0348815i	$0.988895\pi$
$602$	−0.532625	+	1.63925i	−0.0217082	+	0.0668109i
$603$	−2.34859	−	1.70635i	−0.0956420	−	0.0694880i
$604$	−4.48412	+	13.8007i	−0.182456	+	0.561543i
$605$	7.47067	−	22.9924i	0.303726	−	0.934772i
$606$	9.84117	+	7.15003i	0.399770	+	0.290450i
$607$	7.30326	−	22.4771i	0.296430	−	0.912318i	−0.686307	−	0.727312i	$-0.740769\pi$
$607$	7.30326	−	22.4771i	0.296430	−	0.912318i	0.982737	−	0.185006i	$-0.0592306\pi$
$608$	7.79062	+	23.9771i	0.315951	+	0.972398i
$609$	−5.30090	+	3.85133i	−0.214803	+	0.156064i
$610$	2.66774	+	8.21047i	0.108014	+	0.332432i
$611$	−5.23982	−	3.80695i	−0.211981	−	0.154013i
$612$	−29.4036	−	21.3630i	−1.18857	−	0.863548i
$613$	12.9748	−	9.42671i	0.524045	−	0.380741i	−0.294080	−	0.955781i	$-0.595013\pi$
$613$	12.9748	−	9.42671i	0.524045	−	0.380741i	0.818126	+	0.575039i	$0.195013\pi$
$614$	−67.1291			−2.70911
$615$	−2.11205			−0.0851661
$616$	55.2476	−	40.1398i	2.22599	−	1.61728i
$617$	11.4741	−	35.3135i	0.461929	−	1.42167i	−0.400876	−	0.916132i	$-0.631294\pi$
$617$	11.4741	−	35.3135i	0.461929	−	1.42167i	0.862805	−	0.505537i	$-0.168706\pi$
$618$	1.65048	+	5.07966i	0.0663921	+	0.204334i
$619$	9.19205			0.369460			0.184730	−	0.982789i	$-0.440859\pi$
$619$	9.19205			0.369460			0.184730	+	0.982789i	$0.440859\pi$
$620$	13.7188	−	19.7711i	0.550959	−	0.794026i
$621$	−5.59738			−0.224615
$622$	11.8774	+	36.5548i	0.476240	+	1.46571i
$623$	−3.29864	+	10.1522i	−0.132157	+	0.406738i
$624$	−5.60738	+	4.07400i	−0.224475	+	0.163091i
$625$	13.5094			0.540378
$626$	65.3429			2.61163
$627$	12.4748	−	9.06347i	0.498195	−	0.361960i
$628$	34.7055	+	25.2150i	1.38490	+	1.00619i
$629$	23.0639	+	16.7569i	0.919619	+	0.668143i
$630$	1.10091	+	3.38826i	0.0438614	+	0.134991i
$631$	−27.9512	+	20.3077i	−1.11272	+	0.808437i	−0.983090	−	0.183125i	$-0.941379\pi$
$631$	−27.9512	+	20.3077i	−1.11272	+	0.808437i	−0.129629	+	0.991563i	$0.541379\pi$
$632$	−18.5384	−	57.0553i	−0.737417	−	2.26954i
$633$	−5.85643	+	18.0242i	−0.232772	+	0.716399i
$634$	40.1108	+	29.1422i	1.59300	+	1.15739i
$635$	−4.06407	+	12.5079i	−0.161278	+	0.496362i
$636$	2.20009	−	6.77117i	0.0872391	−	0.268494i
$637$	2.78251	+	2.02161i	0.110247	+	0.0800991i
$638$	−21.4097	+	65.8922i	−0.847617	+	2.60870i
$639$	−3.97495	−	12.2336i	−0.157247	−	0.483955i
$640$	0.759469	−	0.551787i	0.0300207	−	0.0218113i
$641$	−0.508184	−	1.56403i	−0.0200720	−	0.0617754i	0.940519	−	0.339742i	$-0.110340\pi$
$641$	−0.508184	−	1.56403i	−0.0200720	−	0.0617754i	−0.960591	+	0.277966i	$0.910340\pi$
$642$	14.3039	+	10.3924i	0.564532	+	0.410156i
$643$	0.847925	+	0.616054i	0.0334389	+	0.0242948i	0.604379	−	0.796697i	$-0.293421\pi$
$643$	0.847925	+	0.616054i	0.0334389	+	0.0242948i	−0.570940	+	0.820992i	$0.693421\pi$
$644$	33.0145	−	23.9865i	1.30095	−	0.945199i
$645$	−0.391760			−0.0154255
$646$	49.4570			1.94586
$647$	5.01443	−	3.64320i	0.197138	−	0.143229i	−0.484837	−	0.874604i	$-0.661121\pi$
$647$	5.01443	−	3.64320i	0.197138	−	0.143229i	0.681975	+	0.731375i	$0.261121\pi$
$648$	2.25929	−	6.95339i	0.0887534	−	0.273155i
$649$	7.48914	+	23.0492i	0.293975	+	0.904761i
$650$	−8.00468			−0.313970
$651$	−5.11480	−	6.72778i	−0.200465	−	0.263682i
$652$	−5.72329			−0.224142
$653$	9.48236	+	29.1837i	0.371074	+	1.14205i	0.946090	+	0.323905i	$0.104996\pi$
$653$	9.48236	+	29.1837i	0.371074	+	1.14205i	−0.575016	+	0.818142i	$0.695004\pi$
$654$	9.50709	−	29.2598i	0.371757	−	1.14415i
$655$	−11.2549	+	8.17720i	−0.439767	+	0.319510i
$656$	−22.2116			−0.867218
$657$	7.33314			0.286093
$658$	−28.3244	+	20.5789i	−1.10420	+	0.802248i
$659$	19.7359	+	14.3389i	0.768800	+	0.558566i	0.901597	−	0.432577i	$-0.142396\pi$
$659$	19.7359	+	14.3389i	0.768800	+	0.558566i	−0.132797	+	0.991143i	$0.542396\pi$
$660$	21.5168	+	15.6329i	0.837541	+	0.608509i
$661$	−0.696485	−	2.14356i	−0.0270901	−	0.0833748i	0.936597	−	0.350407i	$-0.113957\pi$
$661$	−0.696485	−	2.14356i	−0.0270901	−	0.0833748i	−0.963687	+	0.267033i	$0.913957\pi$
$662$	−5.57828	+	4.05286i	−0.216806	+	0.157519i
$663$	1.71260	+	5.27085i	0.0665119	+	0.204703i
$664$	−9.33469	+	28.7292i	−0.362256	+	1.11491i
$665$	−2.76902	−	2.01181i	−0.107378	−	0.0780148i
$666$	−3.03661	+	9.34571i	−0.117666	+	0.362139i
$667$	−7.46651	+	22.9796i	−0.289105	+	0.889772i
$668$	51.5096	+	37.4239i	1.99297	+	1.44797i
$669$	3.55898	−	10.9534i	0.137598	−	0.423483i
$670$	2.10553	+	6.48014i	0.0813436	+	0.250350i
$671$	18.3111	−	13.3038i	0.706893	−	0.513588i
$672$	4.71913	+	14.5240i	0.182044	+	0.560275i
$673$	−9.21797	−	6.69725i	−0.355327	−	0.258160i	0.395773	−	0.918348i	$-0.370477\pi$
$673$	−9.21797	−	6.69725i	−0.355327	−	0.258160i	−0.751100	+	0.660188i	$0.770477\pi$
$674$	−40.4636	−	29.3985i	−1.55860	−	1.13239i
$675$	3.38998	−	2.46297i	0.130481	−	0.0947996i
$676$	−59.8637			−2.30245
$677$	−45.5880			−1.75209			−0.876044	−	0.482230i	$-0.839827\pi$
$677$	−45.5880			−1.75209			−0.876044	+	0.482230i	$0.839827\pi$
$678$	−1.80197	+	1.30921i	−0.0692041	+	0.0502797i
$679$	−1.78553	+	5.49530i	−0.0685224	+	0.210890i
$680$	15.3841	+	47.3473i	0.589952	+	1.81568i
$681$	−17.4011			−0.666812
$682$	−85.5688	−	25.7631i	−3.27660	−	0.986520i
$683$	5.74959			0.220002			0.110001	−	0.993931i	$-0.464915\pi$
$683$	5.74959			0.220002			0.110001	+	0.993931i	$0.464915\pi$
$684$	3.71924	+	11.4467i	0.142209	+	0.437674i
$685$	−1.16233	+	3.57730i	−0.0444105	+	0.136682i
$686$	37.4619	−	27.2177i	1.43030	−	1.03917i
$687$	23.6933			0.903956
$688$	−4.11998			−0.157073
$689$	−0.878306	+	0.638126i	−0.0334608	+	0.0243107i
$690$	10.6285	+	7.72205i	0.404619	+	0.293973i
$691$	−26.4244	−	19.1985i	−1.00523	−	0.730344i	−0.0420288	−	0.999116i	$-0.513382\pi$
$691$	−26.4244	−	19.1985i	−1.00523	−	0.730344i	−0.963204	+	0.268772i	$0.913382\pi$
$692$	−2.81159	−	8.65319i	−0.106881	−	0.328945i
$693$	7.55655	−	5.49016i	0.287050	−	0.208554i
$694$	−14.1533	−	43.5595i	−0.537253	−	1.65350i
$695$	2.96572	−	9.12754i	0.112496	−	0.346228i
$696$	−25.5328	−	18.5507i	−0.967818	−	0.703161i
$697$	−5.48825	+	16.8911i	−0.207882	+	0.639796i
$698$	20.6753	−	63.6321i	0.782572	−	2.40851i
$699$	−4.31817	−	3.13733i	−0.163328	−	0.118665i
$700$	−9.44028	+	29.0542i	−0.356809	+	1.09815i
$701$	12.8956	+	39.6887i	0.487061	+	1.49902i	0.828973	+	0.559288i	$0.188926\pi$
$701$	12.8956	+	39.6887i	0.487061	+	1.49902i	−0.341912	+	0.939732i	$0.611074\pi$
$702$	−1.54547	+	1.12285i	−0.0583302	+	0.0423794i
$703$	−2.91734	−	8.97865i	−0.110030	−	0.338636i
$704$	36.4146	+	26.4568i	1.37243	+	0.997127i
$705$	−6.43785	−	4.67737i	−0.242463	−	0.176160i
$706$	16.3888	−	11.9071i	0.616799	−	0.448131i
$707$	−7.07909			−0.266237
$708$	−18.9167			−0.710934
$709$	−32.8560	+	23.8713i	−1.23393	+	0.896504i	−0.997179	−	0.0750655i	$-0.976083\pi$
$709$	−32.8560	+	23.8713i	−1.23393	+	0.896504i	−0.236754	+	0.971570i	$0.576083\pi$
$710$	−9.32954	+	28.7134i	−0.350131	+	1.07759i
$711$	−2.53560	−	7.80379i	−0.0950926	−	0.292665i
$712$	−51.4163			−1.92691
$713$	−29.8417	−	8.98475i	−1.11758	−	0.336481i
$714$	29.9583			1.12116
$715$	−1.25324	−	3.85707i	−0.0468684	−	0.144246i
$716$	−33.9557	+	104.505i	−1.26899	+	3.90554i
$717$	−2.46672	+	1.79218i	−0.0921213	+	0.0669300i
$718$	−47.9620			−1.78993
$719$	−42.4623			−1.58357			−0.791787	−	0.610797i	$-0.790849\pi$
$719$	−42.4623			−1.58357			−0.791787	+	0.610797i	$0.790849\pi$
$720$	−6.88945	+	5.00548i	−0.256755	+	0.186543i
$721$	−2.51463	−	1.82699i	−0.0936499	−	0.0680406i
$722$	26.8427	+	19.5023i	0.998981	+	0.725802i
$723$	−0.535552	−	1.64826i	−0.0199174	−	0.0612994i
$724$	−51.7183	+	37.5755i	−1.92209	+	1.39648i
$725$	−5.58950	−	17.2027i	−0.207589	−	0.638892i
$726$	21.6539	−	66.6440i	0.803653	−	2.47339i
$727$	1.79822	+	1.30648i	0.0666924	+	0.0484548i	0.620632	−	0.784102i	$-0.286876\pi$
$727$	1.79822	+	1.30648i	0.0666924	+	0.0484548i	−0.553940	+	0.832557i	$0.686876\pi$
$728$	2.51169	−	7.73018i	0.0930893	−	0.286499i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−13.9244	−	10.1167i	−0.515365	−	0.374434i
$731$	−1.01800	+	3.13309i	−0.0376522	+	0.115882i
$732$	5.45929	+	16.8020i	0.201781	+	0.621019i
$733$	−39.0363	+	28.3615i	−1.44184	+	1.04756i	−0.454183	+	0.890908i	$0.650069\pi$
$733$	−39.0363	+	28.3615i	−1.44184	+	1.04756i	−0.987655	+	0.156648i	$0.949931\pi$
$734$	22.2102	+	68.3560i	0.819794	+	2.52307i
$735$	3.41870	+	2.48383i	0.126101	+	0.0916174i
$736$	45.5597	+	33.1010i	1.67935	+	1.22012i
$737$	14.4521	−	10.5001i	0.532351	−	0.386775i
$738$	−6.12184			−0.225348
$739$	31.9274			1.17447			0.587234	−	0.809417i	$-0.300217\pi$
$739$	31.9274			1.17447			0.587234	+	0.809417i	$0.300217\pi$
$740$	13.1737	−	9.57123i	0.484274	−	0.351845i
$741$	0.567133	−	1.74546i	0.0208342	−	0.0641210i
$742$	1.81349	+	5.58133i	0.0665752	+	0.204897i
$743$	37.5875			1.37895			0.689477	−	0.724308i	$-0.257841\pi$
$743$	37.5875			1.37895			0.689477	+	0.724308i	$0.257841\pi$
$744$	23.2065	−	33.4445i	0.850790	−	1.22613i
$745$	−14.1571			−0.518677
$746$	−8.16059	−	25.1157i	−0.298781	−	0.919552i
$747$	−1.27676	+	3.92947i	−0.0467143	+	0.143772i
$748$	180.936	−	131.458i	6.61568	−	4.80657i
$749$	−10.2893			−0.375964
$750$	−21.5703			−0.787636
$751$	4.63513	−	3.36762i	0.169138	−	0.122886i	−0.499996	−	0.866028i	$-0.666665\pi$
$751$	4.63513	−	3.36762i	0.169138	−	0.122886i	0.669134	+	0.743142i	$0.266665\pi$
$752$	−67.7044	−	49.1901i	−2.46893	−	1.79378i
$753$	−6.01715	−	4.37172i	−0.219277	−	0.159314i
$754$	2.54822	+	7.84262i	0.0928007	+	0.285611i
$755$	2.19942	−	1.59797i	0.0800450	−	0.0581561i
$756$	2.25292	+	6.93376i	0.0819377	+	0.252178i
$757$	−0.674487	+	2.07586i	−0.0245146	+	0.0754483i	−0.962565	−	0.271050i	$-0.912629\pi$
$757$	−0.674487	+	2.07586i	−0.0245146	+	0.0754483i	0.938051	+	0.346498i	$0.112629\pi$
$758$	−52.0970	−	37.8507i	−1.89225	−	1.37480i
$759$	10.6437	−	32.7579i	0.386341	−	1.18904i
$760$	5.09448	−	15.6792i	0.184796	−	0.568744i
$761$	−15.8479	−	11.5142i	−0.574485	−	0.417388i	0.262246	−	0.965001i	$-0.415537\pi$
$761$	−15.8479	−	11.5142i	−0.574485	−	0.417388i	−0.836732	+	0.547613i	$0.815537\pi$
$762$	−11.7798	+	36.2546i	−0.426738	+	1.31336i
$763$	5.53269	+	17.0279i	0.200297	+	0.616450i
$764$	−11.4342	+	8.30742i	−0.413674	+	0.300552i
$765$	2.10417	+	6.47597i	0.0760764	+	0.234139i
$766$	10.7685	+	7.82380i	0.389083	+	0.282685i
$767$	2.33364	+	1.69549i	0.0842629	+	0.0612206i
$768$	14.0367	−	10.1983i	0.506506	−	0.367998i
$769$	−40.1037			−1.44618			−0.723089	−	0.690755i	$-0.757278\pi$
$769$	−40.1037			−1.44618			−0.723089	+	0.690755i	$0.757278\pi$
$770$	−21.9227			−0.790040
$771$	−19.2571	+	13.9911i	−0.693528	+	0.503878i
$772$	32.0646	−	98.6847i	1.15403	−	3.55174i
$773$	−3.25264	−	10.0106i	−0.116989	−	0.360056i	0.875367	−	0.483458i	$-0.160619\pi$
$773$	−3.25264	−	10.0106i	−0.116989	−	0.360056i	−0.992357	+	0.123402i	$0.960619\pi$
$774$	−1.13553			−0.0408157
$775$	22.0267	−	7.68948i	0.791223	−	0.276214i
$776$	−27.8313			−0.999086
$777$	−1.76716	−	5.43877i	−0.0633967	−	0.195115i
$778$	8.50886	−	26.1876i	0.305057	−	0.938870i
$779$	4.75815	−	3.45700i	0.170478	−	0.123860i
$780$	3.16554			0.113344
$781$	79.1541			2.83236
$782$	89.3755	−	64.9351i	3.19606	−	2.32208i
$783$	−3.49227	−	2.53728i	−0.124804	−	0.0906751i
$784$	35.9531	+	26.1215i	1.28404	+	0.932910i
$785$	−2.48358	−	7.64367i	−0.0886428	−	0.272814i
$786$	−32.6228	+	23.7018i	−1.16362	+	0.845417i
$787$	10.6281	+	32.7100i	0.378852	+	1.16599i	0.940843	+	0.338843i	$0.110035\pi$
$787$	10.6281	+	32.7100i	0.378852	+	1.16599i	−0.561991	+	0.827143i	$0.689965\pi$
$788$	23.1711	−	71.3133i	0.825436	−	2.54043i
$789$	−10.2848	−	7.47232i	−0.366147	−	0.266022i
$790$	−5.95128	+	18.3161i	−0.211737	+	0.651659i
$791$	0.400553	−	1.23278i	0.0142420	−	0.0438325i
$792$	36.3975	+	26.4444i	1.29333	+	0.939659i
$793$	0.832466	−	2.56207i	0.0295618	−	0.0909817i
$794$	6.81968	+	20.9888i	0.242022	+	0.744866i
$795$	−1.07912	+	0.784027i	−0.0382725	+	0.0278066i
$796$	15.7912	+	48.6004i	0.559705	+	1.72259i
$797$	−21.4309	−	15.5704i	−0.759121	−	0.551533i	0.139520	−	0.990219i	$-0.455444\pi$
$797$	−21.4309	−	15.5704i	−0.759121	−	0.551533i	−0.898640	+	0.438686i	$0.855444\pi$
$798$	−8.02609	−	5.83130i	−0.284121	−	0.206426i
$799$	−54.1363	+	39.3323i	−1.91520	+	1.39148i
$800$	−42.1578			−1.49050
$801$	−7.03252			−0.248482
$802$	−31.1943	+	22.6640i	−1.10151	+	0.800293i
$803$	−13.9443	+	42.9161i	−0.492083	+	1.51448i
$804$	4.30877	+	13.2610i	0.151958	+	0.467680i
$805$	−7.64544			−0.269466
$806$	−10.0419	+	3.50559i	−0.353709	+	0.123479i
$807$	8.02797			0.282598
$808$	−10.5368	−	32.4289i	−0.370683	−	1.14084i
$809$	7.46263	−	22.9676i	0.262372	−	0.807498i	−0.729915	−	0.683538i	$-0.760440\pi$
$809$	7.46263	−	22.9676i	0.262372	−	0.807498i	0.992287	−	0.123960i	$-0.0395595\pi$
$810$	−1.89883	+	1.37958i	−0.0667181	+	0.0484735i
$811$	44.3609			1.55772			0.778861	−	0.627197i	$-0.215798\pi$
$811$	44.3609			1.55772			0.778861	+	0.627197i	$0.215798\pi$
$812$	31.4712			1.10442
$813$	−1.52793	+	1.11011i	−0.0535869	+	0.0389332i
$814$	−48.9202	−	35.5426i	−1.71465	−	1.24577i
$815$	0.867478	+	0.630260i	0.0303864	+	0.0220770i
$816$	22.1287	+	68.1053i	0.774661	+	2.38416i
$817$	0.882579	−	0.641231i	0.0308775	−	0.0224338i
$818$	0.306008	+	0.941795i	0.0106993	+	0.0329291i
$819$	0.343538	−	1.05730i	0.0120042	−	0.0369451i
$820$	8.20696	+	5.96271i	0.286600	+	0.208227i
$821$	−15.7587	+	48.5001i	−0.549981	+	1.69267i	0.158863	+	0.987301i	$0.449217\pi$
$821$	−15.7587	+	48.5001i	−0.549981	+	1.69267i	−0.708843	+	0.705366i	$0.750783\pi$
$822$	−3.36906	+	10.3689i	−0.117509	+	0.361657i
$823$	28.4722	+	20.6862i	0.992477	+	0.721077i	0.960462	−	0.278410i	$-0.0898076\pi$
$823$	28.4722	+	20.6862i	0.992477	+	0.721077i	0.0320150	+	0.999487i	$0.489808\pi$
$824$	4.62645	−	14.2388i	0.161170	−	0.496030i
$825$	7.96795	+	24.5228i	0.277408	+	0.853775i
$826$	12.6147	−	9.16514i	0.438923	−	0.318896i
$827$	3.32228	+	10.2249i	0.115527	+	0.355556i	0.992057	−	0.125792i	$-0.0401473\pi$
$827$	3.32228	+	10.2249i	0.115527	+	0.355556i	−0.876529	+	0.481348i	$0.840147\pi$
$828$	21.7502	+	15.8025i	0.755872	+	0.549173i
$829$	−39.0138	−	28.3452i	−1.35500	−	0.984468i	−0.998745	−	0.0500811i	$-0.984052\pi$
$829$	−39.0138	−	28.3452i	−1.35500	−	0.984468i	−0.356259	−	0.934387i	$-0.615948\pi$
$830$	7.84538	−	5.70000i	0.272317	−	0.197850i
$831$	4.61831			0.160208
$832$	5.35729			0.185731
$833$	28.7480	−	20.8867i	0.996060	−	0.723680i
$834$	8.59622	−	26.4565i	0.297663	−	0.916112i
$835$	−3.68611	−	11.3447i	−0.127563	−	0.392598i
$836$	−74.0622			−2.56149
$837$	3.17409	−	4.57440i	0.109713	−	0.158115i
$838$	16.7709			0.579340
$839$	9.27096	+	28.5331i	0.320069	+	0.985071i	0.973617	+	0.228186i	$0.0732796\pi$
$839$	9.27096	+	28.5331i	0.320069	+	0.985071i	−0.653548	+	0.756885i	$0.726720\pi$
$840$	3.08596	−	9.49760i	0.106476	−	0.327698i
$841$	8.38645	−	6.09311i	0.289188	−	0.210107i
$842$	−23.0556			−0.794550
$843$	−9.66072			−0.332733
$844$	73.6425	−	53.5044i	2.53488	−	1.84170i
$845$	9.07353	+	6.59230i	0.312139	+	0.226782i
$846$	−18.6603	−	13.5575i	−0.641554	−	0.466116i
$847$	12.6016	+	38.7837i	0.432996	+	1.33263i
$848$	−11.3487	+	8.24531i	−0.389716	+	0.283145i
$849$	5.54717	+	17.0724i	0.190378	+	0.585924i
$850$	−25.5563	+	78.6543i	−0.876574	+	2.69782i
$851$	−17.0607	−	12.3953i	−0.584832	−	0.424905i
$852$	−19.0920	+	58.7592i	−0.654082	+	2.01306i
$853$	−10.9932	+	33.8335i	−0.376399	+	1.15844i	0.566132	+	0.824315i	$0.308439\pi$
$853$	−10.9932	+	33.8335i	−0.376399	+	1.15844i	−0.942530	+	0.334121i	$0.891561\pi$
$854$	−11.7811	−	8.55947i	−0.403141	−	0.292899i
$855$	0.696802	−	2.14454i	0.0238301	−	0.0733416i
$856$	−15.3150	−	47.1348i	−0.523457	−	1.61103i
$857$	26.5542	−	19.2927i	0.907073	−	0.659027i	−0.0331999	−	0.999449i	$-0.510570\pi$
$857$	26.5542	−	19.2927i	0.907073	−	0.659027i	0.940273	+	0.340422i	$0.110570\pi$
$858$	−3.63254	−	11.1798i	−0.124013	−	0.381673i
$859$	8.89793	+	6.46472i	0.303593	+	0.220573i	0.729143	−	0.684362i	$-0.239919\pi$
$859$	8.89793	+	6.46472i	0.303593	+	0.220573i	−0.425549	+	0.904935i	$0.639919\pi$
$860$	1.52229	+	1.10601i	0.0519097	+	0.0377146i
$861$	2.88223	−	2.09406i	0.0982260	−	0.0713654i
$862$	86.3533			2.94121
$863$	−39.8291			−1.35580			−0.677899	−	0.735155i	$-0.737109\pi$
$863$	−39.8291			−1.35580			−0.677899	+	0.735155i	$0.737109\pi$
$864$	−8.13946	+	5.91366i	−0.276910	+	0.201187i
$865$	−0.526753	+	1.62118i	−0.0179101	+	0.0551218i
$866$	−22.5557	−	69.4194i	−0.766475	−	2.35897i
$867$	40.2593			1.36728
$868$	0.881253	+	40.5827i	0.0299117	+	1.37747i
$869$	50.4921			1.71283
$870$	3.13084	+	9.63575i	0.106146	+	0.326682i
$871$	0.657027	−	2.02212i	0.0222625	−	0.0685170i
$872$	−69.7686	+	50.6898i	−2.36266	+	1.71657i
$873$	−3.80665			−0.128836
$874$	−36.5839			−1.23747
$875$	10.1555	−	7.37842i	0.343319	−	0.249436i
$876$	−28.4950	−	20.7028i	−0.962755	−	0.699483i
$877$	−7.66096	−	5.56601i	−0.258692	−	0.187951i	0.450878	−	0.892586i	$-0.351111\pi$
$877$	−7.66096	−	5.56601i	−0.258692	−	0.187951i	−0.709570	+	0.704635i	$0.751111\pi$
$878$	−28.4552	−	87.5760i	−0.960316	−	2.95555i
$879$	17.7613	−	12.9044i	0.599075	−	0.435254i
$880$	−16.1932	−	49.8376i	−0.545874	−	1.68003i
$881$	−7.55568	+	23.2540i	−0.254557	+	0.783447i	0.739359	+	0.673311i	$0.235129\pi$
$881$	−7.55568	+	23.2540i	−0.254557	+	0.783447i	−0.993917	+	0.110136i	$0.964871\pi$
$882$	9.90919	+	7.19945i	0.333660	+	0.242418i
$883$	10.3715	−	31.9202i	0.349029	−	1.07420i	−0.610363	−	0.792122i	$-0.708976\pi$
$883$	10.3715	−	31.9202i	0.349029	−	1.07420i	0.959391	−	0.282078i	$-0.0910237\pi$
$884$	8.22578	−	25.3163i	0.276663	−	0.851481i
$885$	2.86720	+	2.08315i	0.0963800	+	0.0700242i
$886$	26.1443	−	80.4640i	0.878337	−	2.70324i
$887$	3.53504	+	10.8797i	0.118695	+	0.365306i	0.992700	−	0.120612i	$-0.0384856\pi$
$887$	3.53504	+	10.8797i	0.118695	+	0.365306i	−0.874005	+	0.485917i	$0.838486\pi$
$888$	22.2844	−	16.1906i	0.747815	−	0.543319i
$889$	−6.85532	−	21.0985i	−0.229920	−	0.707621i
$890$	13.3536	+	9.70193i	0.447613	+	0.325210i
$891$	4.97831	+	3.61695i	0.166780	+	0.121172i
$892$	−44.7529	+	32.5149i	−1.49844	+	1.08868i
$893$	22.1595			0.741539
$894$	−41.0348			−1.37241
$895$	16.6549	−	12.1005i	0.556714	−	0.404476i
$896$	−0.489329	+	1.50600i	−0.0163473	+	0.0503120i
$897$	−1.26683	−	3.89890i	−0.0422982	−	0.130181i
$898$	87.1520			2.90830
$899$	−14.5458	−	19.1329i	−0.485130	−	0.638117i
$900$	−20.1261			−0.670872
$901$	3.46611	+	10.6676i	0.115473	+	0.355389i
$902$	11.6409	−	35.8271i	0.387601	−	1.19291i
$903$	0.534618	−	0.388423i	0.0177910	−	0.0129259i
$904$	6.24347			0.207655
$905$	11.9768			0.398123
$906$	6.37507	−	4.63176i	0.211798	−	0.153880i
$907$	38.2848	+	27.8155i	1.27122	+	0.923599i	0.999251	−	0.0387057i	$-0.0123235\pi$
$907$	38.2848	+	27.8155i	1.27122	+	0.923599i	0.271974	+	0.962305i	$0.412323\pi$
$908$	67.6169	+	49.1265i	2.24394	+	1.63032i
$909$	−1.44118	−	4.43550i	−0.0478009	−	0.147116i
$910$	−2.11096	+	1.53370i	−0.0699775	+	0.0508416i
$911$	0.570035	+	1.75439i	0.0188861	+	0.0581254i	0.960055	−	0.279810i	$-0.0902715\pi$
$911$	0.570035	+	1.75439i	0.0188861	+	0.0581254i	−0.941169	+	0.337935i	$0.890271\pi$
$912$	7.32800	−	22.5533i	0.242654	−	0.746813i
$913$	−20.5688	−	14.9441i	−0.680729	−	0.494578i
$914$	−26.6117	+	81.9023i	−0.880236	+	2.70909i
$915$	1.02280	−	3.14786i	0.0338128	−	0.104065i
$916$	−92.0670	−	66.8906i	−3.04198	−	2.21013i
$917$	7.25161	−	22.3182i	0.239469	−	0.737010i
$918$	6.09900	+	18.7708i	0.201297	+	0.619528i
$919$	−19.8718	+	14.4377i	−0.655511	+	0.476257i	−0.865144	−	0.501523i	$-0.832773\pi$
$919$	−19.8718	+	14.4377i	−0.655511	+	0.476257i	0.209633	+	0.977780i	$0.432773\pi$
$920$	−11.3798	−	35.0233i	−0.375180	−	1.15468i
$921$	20.8217	+	15.1278i	0.686097	+	0.498478i
$922$	49.9655	+	36.3020i	1.64553	+	1.19554i
$923$	7.62181	−	5.53757i	0.250875	−	0.182271i
$924$	−44.8628			−1.47588
$925$	15.7868			0.519065
$926$	−22.3344	+	16.2269i	−0.733954	+	0.533249i
$927$	0.632787	−	1.94752i	0.0207835	−	0.0639649i
$928$	13.4206	+	41.3042i	0.440551	+	1.35588i
$929$	−34.2997			−1.12534			−0.562668	−	0.826683i	$-0.690225\pi$
$929$	−34.2997			−1.12534			−0.562668	+	0.826683i	$0.690225\pi$
$930$	−12.3378	+	4.30710i	−0.404573	+	0.141236i
$931$	−11.7674			−0.385660
$932$	7.92219	+	24.3820i	0.259500	+	0.798659i
$933$	4.55373	−	14.0149i	0.149083	−	0.458829i
$934$	−39.2642	+	28.5271i	−1.28476	+	0.933435i
$935$	−41.9008			−1.37030
$936$	5.35478			0.175026
$937$	−25.2853	+	18.3709i	−0.826035	+	0.600150i	−0.918435	−	0.395572i	$-0.870546\pi$
$937$	−25.2853	+	18.3709i	−0.826035	+	0.600150i	0.0923996	+	0.995722i	$0.470546\pi$
$938$	−9.29827	−	6.75559i	−0.303599	−	0.220578i
$939$	−20.2676	−	14.7253i	−0.661409	−	0.480542i
$940$	11.8110	+	36.3505i	0.385232	+	1.18562i
$941$	27.6024	−	20.0543i	0.899812	−	0.653752i	−0.0386054	−	0.999255i	$-0.512292\pi$
$941$	27.6024	−	20.0543i	0.899812	−	0.653752i	0.938418	+	0.345503i	$0.112292\pi$
$942$	−7.19873	−	22.1554i	−0.234547	−	0.721862i
$943$	4.05972	−	12.4945i	0.132203	−	0.406878i
$944$	30.1533	+	21.9076i	0.981406	+	0.713033i
$945$	0.422085	−	1.29904i	0.0137304	−	0.0422579i
$946$	2.15925	−	6.64550i	0.0702034	−	0.216064i
$947$	25.6936	+	18.6675i	0.834928	+	0.606611i	0.920949	−	0.389682i	$-0.127415\pi$
$947$	25.6936	+	18.6675i	0.834928	+	0.606611i	−0.0860209	+	0.996293i	$0.527415\pi$
$948$	−12.1787	+	37.4823i	−0.395547	+	1.21737i
$949$	1.65968	+	5.10796i	0.0538754	+	0.165811i
$950$	22.1566	−	16.0977i	0.718854	−	0.522278i
$951$	−5.87399	−	18.0783i	−0.190477	−	0.586229i
$952$	−67.9379	−	49.3598i	−2.20188	−	1.59976i
$953$	−14.2248	−	10.3349i	−0.460787	−	0.334782i	0.333053	−	0.942908i	$-0.391921\pi$
$953$	−14.2248	−	10.3349i	−0.460787	−	0.334782i	−0.793840	+	0.608127i	$0.791921\pi$
$954$	−3.12786	+	2.27253i	−0.101268	+	0.0735757i
$955$	2.64790			0.0856842
$956$	14.6448			0.473646
$957$	21.4898	−	15.6132i	0.694666	−	0.504705i
$958$	−22.7275	+	69.9481i	−0.734293	+	2.25992i
$959$	−1.96064	−	6.03422i	−0.0633123	−	0.194855i
$960$	6.58218			0.212439
$961$	24.2649	−	19.2929i	0.782739	−	0.622350i
$962$	−7.19709			−0.232044
$963$	−2.09473	−	6.44691i	−0.0675016	−	0.207749i
$964$	−2.57230	+	7.91673i	−0.0828483	+	0.254981i
$965$	−15.7274	+	11.4266i	−0.506282	+	0.367835i
$966$	−22.1605			−0.713003
$967$	8.59038			0.276248			0.138124	−	0.990415i	$-0.455893\pi$
$967$	8.59038			0.276248			0.138124	+	0.990415i	$0.455893\pi$
$968$	−158.909	+	115.454i	−5.10754	+	3.71084i
$969$	−15.3402	−	11.1453i	−0.492800	−	0.358040i
$970$	7.22819	+	5.25159i	0.232083	+	0.168618i
$971$	10.9058	+	33.5645i	0.349982	+	1.07713i	0.958862	+	0.283872i	$0.0916192\pi$
$971$	10.9058	+	33.5645i	0.349982	+	1.07713i	−0.608880	+	0.793263i	$0.708381\pi$
$972$	−3.88578	+	2.82319i	−0.124636	+	0.0905537i
$973$	5.00261	+	15.3964i	0.160376	+	0.493587i
$974$	−29.4036	+	90.4951i	−0.942154	+	2.89965i
$975$	2.48284	+	1.80389i	0.0795145	+	0.0577707i
$976$	10.7564	−	33.1048i	0.344304	−	1.05966i
$977$	−0.405674	+	1.24854i	−0.0129786	+	0.0399442i	−0.957336	−	0.288977i	$-0.906685\pi$
$977$	−0.405674	+	1.24854i	−0.0129786	+	0.0399442i	0.944357	+	0.328921i	$0.106685\pi$
$978$	2.51441	+	1.82683i	0.0804020	+	0.0584155i
$979$	13.3727	−	41.1568i	0.427392	−	1.31538i
$980$	−6.27200	−	19.3032i	−0.200352	−	0.616619i
$981$	−9.54267	+	6.93315i	−0.304674	+	0.221359i
$982$	−12.5087	−	38.4977i	−0.399167	−	1.22851i
$983$	27.8090	+	20.2044i	0.886969	+	0.644421i	0.935086	−	0.354421i	$-0.115322\pi$
$983$	27.8090	+	20.2044i	0.886969	+	0.644421i	−0.0481168	+	0.998842i	$0.515322\pi$
$984$	13.8828	+	10.0864i	0.442567	+	0.321544i
$985$	−11.3652	+	8.25729i	−0.362125	+	0.263099i
$986$	85.1974			2.71324
$987$	13.4230			0.427259
$988$	−7.13150	+	5.18134i	−0.226883	+	0.164840i
$989$	0.753029	−	2.31758i	0.0239449	−	0.0736949i
$990$	−4.46309	−	13.7360i	−0.141846	−	0.436558i
$991$	−35.4436			−1.12590			−0.562952	−	0.826490i	$-0.690334\pi$
$991$	−35.4436			−1.12590			−0.562952	+	0.826490i	$0.690334\pi$
$992$	−52.8868	+	18.4627i	−1.67916	+	0.586191i
$993$	2.64356			0.0838909
$994$	−15.7372	−	48.4340i	−0.499152	−	1.53623i
$995$	2.95849	−	9.10530i	0.0937905	−	0.288657i
$996$	16.0548	−	11.6645i	0.508717	−	0.369605i
$997$	16.4838			0.522048			0.261024	−	0.965332i	$-0.415940\pi$
$997$	16.4838			0.522048			0.261024	+	0.965332i	$0.415940\pi$
$998$	51.9594			1.64474
$999$	3.04797	−	2.21448i	0.0964335	−	0.0700630i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	93.2.f.b.4.4	✓	16
3.2	odd	2		279.2.i.c.190.1		16
31.8	even	5	inner	93.2.f.b.70.4	yes	16
31.15	odd	10		2883.2.a.o.1.7		8
31.16	even	5		2883.2.a.p.1.7		8
93.8	odd	10		279.2.i.c.163.1		16
93.47	odd	10		8649.2.a.bh.1.2		8
93.77	even	10		8649.2.a.bg.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.f.b.4.4	✓	16	1.1	even	1	trivial
93.2.f.b.70.4	yes	16	31.8	even	5	inner
279.2.i.c.163.1		16	93.8	odd	10
279.2.i.c.190.1		16	3.2	odd	2
2883.2.a.o.1.7		8	31.15	odd	10
2883.2.a.p.1.7		8	31.16	even	5
8649.2.a.bg.1.2		8	93.77	even	10
8649.2.a.bh.1.2		8	93.47	odd	10

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:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	93.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.806001 + 2.48062i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-3.88578 + 2.82319i) q^{4} +0.899861 q^{5} +2.60827 q^{6} +(-1.22800 + 0.892196i) q^{7} +(-5.91490 - 4.29743i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.806001 + 2.48062i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-3.88578 + 2.82319i) q^{4} +0.899861 q^{5} +2.60827 q^{6} +(-1.22800 + 0.892196i) q^{7} +(-5.91490 - 4.29743i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(0.725289 + 2.23221i) q^{10} +(4.97831 - 3.61695i) q^{11} +(1.48424 + 4.56801i) q^{12} +(0.226326 - 0.696558i) q^{13} +(-3.20297 - 2.32709i) q^{14} +(0.278072 - 0.855819i) q^{15} +(2.92438 - 9.00032i) q^{16} +(-6.12182 - 4.44776i) q^{17} +(0.806001 - 2.48062i) q^{18} +(0.774344 + 2.38319i) q^{19} +(-3.49666 + 2.54047i) q^{20} +(0.469055 + 1.44360i) q^{21} +(12.9848 + 9.43400i) q^{22} +(4.52838 + 3.29006i) q^{23} +(-5.91490 + 4.29743i) q^{24} -4.19025 q^{25} +1.91031 q^{26} +(-0.809017 + 0.587785i) q^{27} +(2.25292 - 6.93376i) q^{28} +(1.33393 + 4.10541i) q^{29} +2.34708 q^{30} +(-5.25666 + 1.83509i) q^{31} +10.0609 q^{32} +(-1.90154 - 5.85235i) q^{33} +(6.09900 - 18.7708i) q^{34} +(-1.10503 + 0.802853i) q^{35} +4.80309 q^{36} -3.76750 q^{37} +(-5.28765 + 3.84170i) q^{38} +(-0.592528 - 0.430497i) q^{39} +(-5.32259 - 3.86709i) q^{40} +(-0.725289 - 2.23221i) q^{41} +(-3.20297 + 2.32709i) q^{42} +(-0.134532 - 0.414048i) q^{43} +(-9.13329 + 28.1094i) q^{44} +(-0.728003 - 0.528925i) q^{45} +(-4.51150 + 13.8850i) q^{46} +(2.73269 - 8.41035i) q^{47} +(-7.65613 - 5.56250i) q^{48} +(-1.45114 + 4.46616i) q^{49} +(-3.37734 - 10.3944i) q^{50} +(-6.12182 + 4.44776i) q^{51} +(1.08706 + 3.34563i) q^{52} +(-1.19921 - 0.871276i) q^{53} +(-2.11014 - 1.53310i) q^{54} +(4.47979 - 3.25476i) q^{55} +11.0977 q^{56} +2.50583 q^{57} +(-9.10880 + 6.61793i) q^{58} +(-1.21705 + 3.74569i) q^{59} +(1.33561 + 4.11057i) q^{60} +3.67818 q^{61} +(-8.78902 - 11.5607i) q^{62} +1.51790 q^{63} +(2.26035 + 6.95665i) q^{64} +(0.203662 - 0.626806i) q^{65} +(12.9848 - 9.43400i) q^{66} +2.90302 q^{67} +36.3449 q^{68} +(4.52838 - 3.29006i) q^{69} +(-2.88223 - 2.09406i) q^{70} +(10.4065 + 7.56080i) q^{71} +(2.25929 + 6.95339i) q^{72} +(-5.93263 + 4.31031i) q^{73} +(-3.03661 - 9.34571i) q^{74} +(-1.29486 + 3.98516i) q^{75} +(-9.73711 - 7.07442i) q^{76} +(-2.88635 + 8.88326i) q^{77} +(0.590319 - 1.81681i) q^{78} +(6.63830 + 4.82301i) q^{79} +(2.63154 - 8.09903i) q^{80} +(0.309017 + 0.951057i) q^{81} +(4.95267 - 3.59833i) q^{82} +(-1.27676 - 3.92947i) q^{83} +(-5.89821 - 4.28530i) q^{84} +(-5.50879 - 4.00237i) q^{85} +(0.918660 - 0.667446i) q^{86} +4.31669 q^{87} -44.9898 q^{88} +(5.68943 - 4.13361i) q^{89} +(0.725289 - 2.23221i) q^{90} +(0.343538 + 1.05730i) q^{91} -26.8847 q^{92} +(0.120875 + 5.56645i) q^{93} +23.0654 q^{94} +(0.696802 + 2.14454i) q^{95} +(3.10900 - 9.56851i) q^{96} +(3.07965 - 2.23750i) q^{97} -12.2484 q^{98} -6.15353 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} - 4 q^{3} - 9 q^{4} + 6 q^{5} + 2 q^{6} - 7 q^{7} - 2 q^{8} - 4 q^{9}+O(q^{10}) \) 16 * q - 3 * q^2 - 4 * q^3 - 9 * q^4 + 6 * q^5 + 2 * q^6 - 7 * q^7 - 2 * q^8 - 4 * q^9	\( 16 q - 3 q^{2} - 4 q^{3} - 9 q^{4} + 6 q^{5} + 2 q^{6} - 7 q^{7} - 2 q^{8} - 4 q^{9} - 3 q^{10} + 10 q^{11} - 4 q^{12} - 3 q^{13} - 4 q^{14} - 4 q^{15} - 17 q^{16} - q^{17} - 3 q^{18} - 4 q^{19} + 7 q^{20} + 8 q^{21} + 10 q^{22} + 7 q^{23} - 2 q^{24} + 30 q^{25} - 16 q^{26} - 4 q^{27} + 9 q^{28} - 2 q^{29} + 12 q^{30} - 13 q^{31} + 108 q^{32} - 5 q^{33} - 4 q^{34} - 33 q^{35} + 26 q^{36} - 28 q^{37} - 62 q^{38} + 7 q^{39} - 27 q^{40} + 3 q^{41} - 4 q^{42} - 13 q^{43} - 64 q^{44} + q^{45} - q^{46} - 20 q^{47} - 2 q^{48} + q^{49} - 44 q^{50} - q^{51} + 88 q^{52} - 4 q^{53} + 2 q^{54} - 8 q^{55} + 104 q^{56} - 14 q^{57} - 31 q^{58} + 49 q^{59} - 8 q^{60} - 13 q^{62} - 2 q^{63} - 26 q^{64} - q^{65} + 10 q^{66} + 60 q^{67} - 30 q^{68} + 7 q^{69} + 85 q^{70} + 23 q^{71} - 7 q^{72} - 17 q^{73} + 70 q^{74} - 5 q^{75} + 7 q^{76} + 2 q^{77} + 19 q^{78} - 13 q^{79} - 94 q^{80} - 4 q^{81} - 9 q^{82} - 49 q^{83} - 6 q^{84} - 4 q^{85} + 24 q^{86} - 2 q^{87} - 32 q^{88} + 3 q^{89} - 3 q^{90} - 2 q^{91} - 70 q^{92} + 17 q^{93} + 74 q^{94} - 10 q^{95} - 32 q^{96} + 3 q^{97} - 82 q^{98} - 10 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 - 4 * q^3 - 9 * q^4 + 6 * q^5 + 2 * q^6 - 7 * q^7 - 2 * q^8 - 4 * q^9 - 3 * q^10 + 10 * q^11 - 4 * q^12 - 3 * q^13 - 4 * q^14 - 4 * q^15 - 17 * q^16 - q^17 - 3 * q^18 - 4 * q^19 + 7 * q^20 + 8 * q^21 + 10 * q^22 + 7 * q^23 - 2 * q^24 + 30 * q^25 - 16 * q^26 - 4 * q^27 + 9 * q^28 - 2 * q^29 + 12 * q^30 - 13 * q^31 + 108 * q^32 - 5 * q^33 - 4 * q^34 - 33 * q^35 + 26 * q^36 - 28 * q^37 - 62 * q^38 + 7 * q^39 - 27 * q^40 + 3 * q^41 - 4 * q^42 - 13 * q^43 - 64 * q^44 + q^45 - q^46 - 20 * q^47 - 2 * q^48 + q^49 - 44 * q^50 - q^51 + 88 * q^52 - 4 * q^53 + 2 * q^54 - 8 * q^55 + 104 * q^56 - 14 * q^57 - 31 * q^58 + 49 * q^59 - 8 * q^60 - 13 * q^62 - 2 * q^63 - 26 * q^64 - q^65 + 10 * q^66 + 60 * q^67 - 30 * q^68 + 7 * q^69 + 85 * q^70 + 23 * q^71 - 7 * q^72 - 17 * q^73 + 70 * q^74 - 5 * q^75 + 7 * q^76 + 2 * q^77 + 19 * q^78 - 13 * q^79 - 94 * q^80 - 4 * q^81 - 9 * q^82 - 49 * q^83 - 6 * q^84 - 4 * q^85 + 24 * q^86 - 2 * q^87 - 32 * q^88 + 3 * q^89 - 3 * q^90 - 2 * q^91 - 70 * q^92 + 17 * q^93 + 74 * q^94 - 10 * q^95 - 32 * q^96 + 3 * q^97 - 82 * q^98 - 10 * q^99

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