LMFDB - Embedded newform 45.2.e.b.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,2,Mod(16,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("45.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	45.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:	$0.359326809096$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			31.1
Root			$0.403374 + 1.68443i$ of defining polynomial
Character	$\chi$	$=$	45.31
Dual form			45.2.e.b.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25707 - 2.17731i) q^{2} +(1.25707 - 1.19154i) q^{3} +(-2.16044 + 3.74200i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-4.17458 - 1.23917i) q^{6} +(0.257068 + 0.445256i) q^{7} +5.83502 q^{8} +(0.160442 - 2.99571i) q^{9} +O(q^{10})$	\(q+(-1.25707 - 2.17731i) q^{2} +(1.25707 - 1.19154i) q^{3} +(-2.16044 + 3.74200i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-4.17458 - 1.23917i) q^{6} +(0.257068 + 0.445256i) q^{7} +5.83502 q^{8} +(0.160442 - 2.99571i) q^{9} +2.51414 q^{10} +(1.66044 + 2.87597i) q^{11} +(1.74293 + 7.27821i) q^{12} +(0.660442 - 1.14392i) q^{13} +(0.646305 - 1.11943i) q^{14} +(0.403374 + 1.68443i) q^{15} +(-3.01414 - 5.22064i) q^{16} -3.32088 q^{17} +(-6.72426 + 3.41648i) q^{18} -1.32088 q^{19} +(-2.16044 - 3.74200i) q^{20} +(0.853695 + 0.253408i) q^{21} +(4.17458 - 7.23058i) q^{22} +(-2.06382 + 3.57463i) q^{23} +(7.33502 - 6.95269i) q^{24} +(-0.500000 - 0.866025i) q^{25} -3.32088 q^{26} +(-3.36783 - 3.95698i) q^{27} -2.22153 q^{28} +(0.693252 + 1.20075i) q^{29} +(3.16044 - 2.99571i) q^{30} +(-4.36783 + 7.56531i) q^{31} +(-1.74293 + 3.01885i) q^{32} +(5.51414 + 1.63680i) q^{33} +(4.17458 + 7.23058i) q^{34} -0.514137 q^{35} +(10.8633 + 7.07243i) q^{36} +0.292611 q^{37} +(1.66044 + 2.87597i) q^{38} +(-0.532810 - 2.22493i) q^{39} +(-2.91751 + 5.05328i) q^{40} +(5.67458 - 9.82866i) q^{41} +(-0.521405 - 2.17731i) q^{42} +(-5.17458 - 8.96263i) q^{43} -14.3492 q^{44} +(2.51414 + 1.63680i) q^{45} +10.3774 q^{46} +(2.43165 + 4.21174i) q^{47} +(-10.0096 - 2.97122i) q^{48} +(3.36783 - 5.83326i) q^{49} +(-1.25707 + 2.17731i) q^{50} +(-4.17458 + 3.95698i) q^{51} +(2.85369 + 4.94274i) q^{52} -5.02827 q^{53} +(-4.38197 + 12.3070i) q^{54} -3.32088 q^{55} +(1.50000 + 2.59808i) q^{56} +(-1.66044 + 1.57389i) q^{57} +(1.74293 - 3.01885i) q^{58} +(2.51414 - 4.35461i) q^{59} +(-7.17458 - 2.12968i) q^{60} +(-3.67458 - 6.36456i) q^{61} +21.9627 q^{62} +(1.37510 - 0.698664i) q^{63} -3.29261 q^{64} +(0.660442 + 1.14392i) q^{65} +(-3.36783 - 14.0635i) q^{66} +(-4.72426 + 8.18266i) q^{67} +(7.17458 - 12.4267i) q^{68} +(1.66498 + 6.95269i) q^{69} +(0.646305 + 1.11943i) q^{70} +8.99093 q^{71} +(0.936184 - 17.4800i) q^{72} +6.05655 q^{73} +(-0.367832 - 0.637103i) q^{74} +(-1.66044 - 0.492881i) q^{75} +(2.85369 - 4.94274i) q^{76} +(-0.853695 + 1.47864i) q^{77} +(-4.17458 + 3.95698i) q^{78} +(4.02827 + 6.97717i) q^{79} +6.02827 q^{80} +(-8.94852 - 0.961276i) q^{81} -28.5333 q^{82} +(-0.771205 - 1.33577i) q^{83} +(-2.79261 + 2.64705i) q^{84} +(1.66044 - 2.87597i) q^{85} +(-13.0096 + 22.5333i) q^{86} +(2.30221 + 0.683382i) q^{87} +(9.68872 + 16.7813i) q^{88} -3.00000 q^{89} +(0.403374 - 7.53162i) q^{90} +0.679116 q^{91} +(-8.91751 - 15.4456i) q^{92} +(3.52374 + 14.7146i) q^{93} +(6.11350 - 10.5889i) q^{94} +(0.660442 - 1.14392i) q^{95} +(1.40611 + 5.87168i) q^{96} +(6.12763 + 10.6134i) q^{97} -16.9344 q^{98} +(8.88197 - 4.51277i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} + q^{3} - 5 q^{4} - 3 q^{5} - 4 q^{6} - 5 q^{7} + 6 q^{8} - 7 q^{9}+O(q^{10}) $ 6 * q - q^2 + q^3 - 5 * q^4 - 3 * q^5 - 4 * q^6 - 5 * q^7 + 6 * q^8 - 7 * q^9	\( 6 q - q^{2} + q^{3} - 5 q^{4} - 3 q^{5} - 4 q^{6} - 5 q^{7} + 6 q^{8} - 7 q^{9} + 2 q^{10} + 2 q^{11} + 17 q^{12} - 4 q^{13} + 9 q^{14} + q^{15} - 5 q^{16} - 4 q^{17} - 23 q^{18} + 8 q^{19} - 5 q^{20} + 4 q^{22} - 3 q^{23} + 15 q^{24} - 3 q^{25} - 4 q^{26} - 2 q^{27} + 10 q^{28} + 7 q^{29} + 11 q^{30} - 8 q^{31} - 17 q^{32} + 20 q^{33} + 4 q^{34} + 10 q^{35} + 10 q^{36} + 12 q^{37} + 2 q^{38} - 14 q^{39} - 3 q^{40} + 13 q^{41} - 33 q^{42} - 10 q^{43} - 44 q^{44} + 2 q^{45} - 6 q^{46} - 13 q^{47} - 10 q^{48} + 2 q^{49} - q^{50} - 4 q^{51} + 12 q^{52} - 4 q^{53} + 5 q^{54} - 4 q^{55} + 9 q^{56} - 2 q^{57} + 17 q^{58} + 2 q^{59} - 22 q^{60} - q^{61} + 84 q^{62} + 33 q^{63} - 30 q^{64} - 4 q^{65} - 2 q^{66} - 11 q^{67} + 22 q^{68} + 39 q^{69} + 9 q^{70} - 20 q^{71} + 15 q^{72} - 16 q^{73} + 16 q^{74} - 2 q^{75} + 12 q^{76} - 4 q^{78} - 2 q^{79} + 10 q^{80} - 19 q^{81} - 58 q^{82} + 15 q^{83} - 27 q^{84} + 2 q^{85} - 28 q^{86} - 26 q^{87} + 24 q^{88} - 18 q^{89} + q^{90} + 20 q^{91} - 39 q^{92} - 42 q^{93} + 31 q^{94} - 4 q^{95} + 13 q^{96} + 18 q^{97} - 80 q^{98} + 22 q^{99}+O(q^{100}) \) 6 * q - q^2 + q^3 - 5 * q^4 - 3 * q^5 - 4 * q^6 - 5 * q^7 + 6 * q^8 - 7 * q^9 + 2 * q^10 + 2 * q^11 + 17 * q^12 - 4 * q^13 + 9 * q^14 + q^15 - 5 * q^16 - 4 * q^17 - 23 * q^18 + 8 * q^19 - 5 * q^20 + 4 * q^22 - 3 * q^23 + 15 * q^24 - 3 * q^25 - 4 * q^26 - 2 * q^27 + 10 * q^28 + 7 * q^29 + 11 * q^30 - 8 * q^31 - 17 * q^32 + 20 * q^33 + 4 * q^34 + 10 * q^35 + 10 * q^36 + 12 * q^37 + 2 * q^38 - 14 * q^39 - 3 * q^40 + 13 * q^41 - 33 * q^42 - 10 * q^43 - 44 * q^44 + 2 * q^45 - 6 * q^46 - 13 * q^47 - 10 * q^48 + 2 * q^49 - q^50 - 4 * q^51 + 12 * q^52 - 4 * q^53 + 5 * q^54 - 4 * q^55 + 9 * q^56 - 2 * q^57 + 17 * q^58 + 2 * q^59 - 22 * q^60 - q^61 + 84 * q^62 + 33 * q^63 - 30 * q^64 - 4 * q^65 - 2 * q^66 - 11 * q^67 + 22 * q^68 + 39 * q^69 + 9 * q^70 - 20 * q^71 + 15 * q^72 - 16 * q^73 + 16 * q^74 - 2 * q^75 + 12 * q^76 - 4 * q^78 - 2 * q^79 + 10 * q^80 - 19 * q^81 - 58 * q^82 + 15 * q^83 - 27 * q^84 + 2 * q^85 - 28 * q^86 - 26 * q^87 + 24 * q^88 - 18 * q^89 + q^90 + 20 * q^91 - 39 * q^92 - 42 * q^93 + 31 * q^94 - 4 * q^95 + 13 * q^96 + 18 * q^97 - 80 * q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−1.25707	−	2.17731i	−0.888882	−	1.53959i	−0.841199	−	0.540726i	$-0.818150\pi$
$2$	−1.25707	−	2.17731i	−0.888882	−	1.53959i	−0.0476826	−	0.998863i	$-0.515184\pi$
$3$	1.25707	−	1.19154i	0.725769	−	0.687939i
$3$	1.25707	−	1.19154i	0.725769	−	0.687939i
$4$	−2.16044	+	3.74200i	−1.08022	+	1.87100i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−4.17458	−	1.23917i	−1.70426	−	0.505889i
$7$	0.257068	+	0.445256i	0.0971627	+	0.168291i	0.910509	−	0.413489i	$-0.135690\pi$
$7$	0.257068	+	0.445256i	0.0971627	+	0.168291i	−0.813346	+	0.581780i	$0.802357\pi$
$8$	5.83502			2.06299
$9$	0.160442	−	2.99571i	0.0534807	−	0.998569i
$10$	2.51414			0.795040
$11$	1.66044	+	2.87597i	0.500642	+	0.867138i	1.00000		0.000741679i	$0.000236084\pi$
$11$	1.66044	+	2.87597i	0.500642	+	0.867138i	−0.499358	+	0.866396i	$0.666431\pi$
$12$	1.74293	+	7.27821i	0.503141	+	2.10104i
$13$	0.660442	−	1.14392i	0.183174	−	0.317266i	−0.759786	−	0.650173i	$-0.774696\pi$
$13$	0.660442	−	1.14392i	0.183174	−	0.317266i	0.942960	+	0.332907i	$0.108030\pi$
$14$	0.646305	−	1.11943i	0.172732	−	0.299181i
$15$	0.403374	+	1.68443i	0.104151	+	0.434917i
$16$	−3.01414	−	5.22064i	−0.753534	−	1.30516i
$17$	−3.32088			−0.805433			−0.402716	−	0.915325i	$-0.631934\pi$
$17$	−3.32088			−0.805433			−0.402716	+	0.915325i	$0.631934\pi$
$18$	−6.72426	+	3.41648i	−1.58492	+	0.805271i
$19$	−1.32088			−0.303032			−0.151516	−	0.988455i	$-0.548415\pi$
$19$	−1.32088			−0.303032			−0.151516	+	0.988455i	$0.548415\pi$
$20$	−2.16044	−	3.74200i	−0.483090	−	0.836736i
$21$	0.853695	+	0.253408i	0.186291	+	0.0552982i
$22$	4.17458	−	7.23058i	0.890023	−	1.54157i
$23$	−2.06382	+	3.57463i	−0.430335	+	0.745363i	−0.996902	−	0.0786532i	$-0.974938\pi$
$23$	−2.06382	+	3.57463i	−0.430335	+	0.745363i	0.566567	+	0.824016i	$0.308271\pi$
$24$	7.33502	−	6.95269i	1.49725	−	1.41921i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−3.32088			−0.651279
$27$	−3.36783	−	3.95698i	−0.648139	−	0.761522i
$28$	−2.22153			−0.419829
$29$	0.693252	+	1.20075i	0.128734	+	0.222973i	0.923186	−	0.384353i	$-0.125575\pi$
$29$	0.693252	+	1.20075i	0.128734	+	0.222973i	−0.794453	+	0.607326i	$0.792242\pi$
$30$	3.16044	−	2.99571i	0.577015	−	0.546939i
$31$	−4.36783	+	7.56531i	−0.784486	+	1.35877i	0.144820	+	0.989458i	$0.453740\pi$
$31$	−4.36783	+	7.56531i	−0.784486	+	1.35877i	−0.929306	+	0.369311i	$0.879594\pi$
$32$	−1.74293	+	3.01885i	−0.308110	+	0.533662i
$33$	5.51414	+	1.63680i	0.959888	+	0.284930i
$34$	4.17458	+	7.23058i	0.715934	+	1.24003i
$35$	−0.514137			−0.0869050
$36$	10.8633	+	7.07243i	1.81055	+	1.17874i
$37$	0.292611			0.0481049			0.0240524	−	0.999711i	$-0.492343\pi$
$37$	0.292611			0.0481049			0.0240524	+	0.999711i	$0.492343\pi$
$38$	1.66044	+	2.87597i	0.269359	+	0.466544i
$39$	−0.532810	−	2.22493i	−0.0853179	−	0.356274i
$40$	−2.91751	+	5.05328i	−0.461299	+	0.798993i
$41$	5.67458	−	9.82866i	0.886220	−	1.53498i	0.0419119	−	0.999121i	$-0.486655\pi$
$41$	5.67458	−	9.82866i	0.886220	−	1.53498i	0.844308	−	0.535857i	$-0.180012\pi$
$42$	−0.521405	−	2.17731i	−0.0804546	−	0.335966i
$43$	−5.17458	−	8.96263i	−0.789116	−	1.36679i	−0.926509	−	0.376272i	$-0.877206\pi$
$43$	−5.17458	−	8.96263i	−0.789116	−	1.36679i	0.137393	−	0.990517i	$-0.456128\pi$
$44$	−14.3492			−2.16322
$45$	2.51414	+	1.63680i	0.374785	+	0.244000i
$46$	10.3774			1.53007
$47$	2.43165	+	4.21174i	0.354692	+	0.614345i	0.987065	−	0.160319i	$-0.0512523\pi$
$47$	2.43165	+	4.21174i	0.354692	+	0.614345i	−0.632373	+	0.774664i	$0.717919\pi$
$48$	−10.0096	−	2.97122i	−1.44476	−	0.428859i
$49$	3.36783	−	5.83326i	0.481119	−	0.833322i
$50$	−1.25707	+	2.17731i	−0.177776	+	0.307918i
$51$	−4.17458	+	3.95698i	−0.584558	+	0.554088i
$52$	2.85369	+	4.94274i	0.395736	+	0.685435i
$53$	−5.02827			−0.690687			−0.345343	−	0.938476i	$-0.612238\pi$
$53$	−5.02827			−0.690687			−0.345343	+	0.938476i	$0.612238\pi$
$54$	−4.38197	+	12.3070i	−0.596310	+	1.67477i
$55$	−3.32088			−0.447788
$56$	1.50000	+	2.59808i	0.200446	+	0.347183i
$57$	−1.66044	+	1.57389i	−0.219931	+	0.208467i
$58$	1.74293	−	3.01885i	0.228858	−	0.396394i
$59$	2.51414	−	4.35461i	0.327313	−	0.566922i	−0.654665	−	0.755919i	$-0.727190\pi$
$59$	2.51414	−	4.35461i	0.327313	−	0.566922i	0.981978	+	0.188997i	$0.0605236\pi$
$60$	−7.17458	−	2.12968i	−0.926234	−	0.274941i
$61$	−3.67458	−	6.36456i	−0.470482	−	0.814898i	0.528948	−	0.848654i	$-0.322586\pi$
$61$	−3.67458	−	6.36456i	−0.470482	−	0.814898i	−0.999430	+	0.0337558i	$0.989253\pi$
$62$	21.9627			2.78926
$63$	1.37510	−	0.698664i	0.173246	−	0.0880234i
$64$	−3.29261			−0.411576
$65$	0.660442	+	1.14392i	0.0819178	+	0.141886i
$66$	−3.36783	−	14.0635i	−0.414551	−	1.73110i
$67$	−4.72426	+	8.18266i	−0.577160	+	0.999670i	0.418643	+	0.908151i	$0.362506\pi$
$67$	−4.72426	+	8.18266i	−0.577160	+	0.999670i	−0.995803	+	0.0915197i	$0.970828\pi$
$68$	7.17458	−	12.4267i	0.870046	−	1.50696i
$69$	1.66498	+	6.95269i	0.200440	+	0.837005i
$70$	0.646305	+	1.11943i	0.0772483	+	0.133798i
$71$	8.99093			1.06703			0.533513	−	0.845792i	$-0.320871\pi$
$71$	8.99093			1.06703			0.533513	+	0.845792i	$0.320871\pi$
$72$	0.936184	−	17.4800i	0.110330	−	2.06004i
$73$	6.05655			0.708865			0.354433	−	0.935082i	$-0.384674\pi$
$73$	6.05655			0.708865			0.354433	+	0.935082i	$0.384674\pi$
$74$	−0.367832	−	0.637103i	−0.0427596	−	0.0740617i
$75$	−1.66044	−	0.492881i	−0.191731	−	0.0569130i
$76$	2.85369	−	4.94274i	0.327341	−	0.566972i
$77$	−0.853695	+	1.47864i	−0.0972875	+	0.168507i
$78$	−4.17458	+	3.95698i	−0.472678	+	0.448040i
$79$	4.02827	+	6.97717i	0.453216	+	0.784994i	0.998584	−	0.0532036i	$-0.0169432\pi$
$79$	4.02827	+	6.97717i	0.453216	+	0.784994i	−0.545367	+	0.838197i	$0.683610\pi$
$80$	6.02827			0.673982
$81$	−8.94852	−	0.961276i	−0.994280	−	0.106808i
$82$	−28.5333			−3.15098
$83$	−0.771205	−	1.33577i	−0.0846508	−	0.146619i	0.820592	−	0.571515i	$-0.193644\pi$
$83$	−0.771205	−	1.33577i	−0.0846508	−	0.146619i	−0.905242	+	0.424896i	$0.860311\pi$
$84$	−2.79261	+	2.64705i	−0.304699	+	0.288817i
$85$	1.66044	−	2.87597i	0.180100	−	0.311943i
$86$	−13.0096	+	22.5333i	−1.40286	+	2.42983i
$87$	2.30221	+	0.683382i	0.246823	+	0.0732662i
$88$	9.68872	+	16.7813i	1.03282	+	1.78890i
$89$	−3.00000			−0.317999			−0.159000	−	0.987279i	$-0.550827\pi$
$89$	−3.00000			−0.317999			−0.159000	+	0.987279i	$0.550827\pi$
$90$	0.403374	−	7.53162i	0.0425193	−	0.793902i
$91$	0.679116			0.0711906
$92$	−8.91751	−	15.4456i	−0.929715	−	1.61031i
$93$	3.52374	+	14.7146i	0.365395	+	1.52583i
$94$	6.11350	−	10.5889i	0.630559	−	1.09216i
$95$	0.660442	−	1.14392i	0.0677599	−	0.117364i
$96$	1.40611	+	5.87168i	0.143510	+	0.599276i
$97$	6.12763	+	10.6134i	0.622167	+	1.07762i	0.989081	+	0.147370i	$0.0470808\pi$
$97$	6.12763	+	10.6134i	0.622167	+	1.07762i	−0.366915	+	0.930255i	$0.619586\pi$
$98$	−16.9344			−1.71063
$99$	8.88197	−	4.51277i	0.892671	−	0.453551i
$100$	4.32088			0.432088
$101$	−5.83502	−	10.1066i	−0.580606	−	1.00564i	−0.995408	−	0.0957276i	$-0.969482\pi$
$101$	−5.83502	−	10.1066i	−0.580606	−	1.00564i	0.414801	−	0.909912i	$-0.363851\pi$
$102$	13.8633	+	4.11514i	1.37267	+	0.407460i
$103$	−0.146305	+	0.253408i	−0.0144159	+	0.0249691i	−0.873143	−	0.487464i	$-0.837922\pi$
$103$	−0.146305	+	0.253408i	−0.0144159	+	0.0249691i	0.858727	+	0.512433i	$0.171256\pi$
$104$	3.85369	−	6.67479i	0.377886	−	0.654517i
$105$	−0.646305	+	0.612617i	−0.0630729	+	0.0597853i
$106$	6.32088	+	10.9481i	0.613939	+	1.06337i
$107$	1.87237			0.181009			0.0905043	−	0.995896i	$-0.471152\pi$
$107$	1.87237			0.181009			0.0905043	+	0.995896i	$0.471152\pi$
$108$	22.0830	−	4.05358i	2.12494	−	0.390056i
$109$	5.54787			0.531390			0.265695	−	0.964057i	$-0.414399\pi$
$109$	5.54787			0.531390			0.265695	+	0.964057i	$0.414399\pi$
$110$	4.17458	+	7.23058i	0.398031	+	0.689409i
$111$	0.367832	−	0.348659i	0.0349130	−	0.0330932i
$112$	1.54968	−	2.68412i	0.146431	−	0.253626i
$113$	−3.90064	+	6.75611i	−0.366942	+	0.635561i	−0.989086	−	0.147341i	$-0.952928\pi$
$113$	−3.90064	+	6.75611i	−0.366942	+	0.635561i	0.622144	+	0.782903i	$0.286262\pi$
$114$	5.51414	+	1.63680i	0.516446	+	0.153300i
$115$	−2.06382	−	3.57463i	−0.192452	−	0.333336i
$116$	−5.99093			−0.556244
$117$	−3.32088	−	2.16202i	−0.307016	−	0.199879i
$118$	−12.6418			−1.16377
$119$	−0.853695	−	1.47864i	−0.0782581	−	0.135547i
$120$	2.35369	+	9.82866i	0.214862	+	0.897230i
$121$	−0.0141369	+	0.0244859i	−0.00128518	+	0.00222599i
$122$	−9.23840	+	16.0014i	−0.836405	+	1.44870i
$123$	−4.57795	−	19.1168i	−0.412780	−	1.72370i
$124$	−18.8729	−	32.6888i	−1.69484	−	2.93554i
$125$	1.00000			0.0894427
$126$	−3.24980	−	2.11575i	−0.289515	−	0.188486i
$127$	17.8916			1.58762			0.793810	−	0.608166i	$-0.208094\pi$
$127$	17.8916			1.58762			0.793810	+	0.608166i	$0.208094\pi$
$128$	7.62490	+	13.2067i	0.673952	+	1.16732i
$129$	−17.1842	−	5.10090i	−1.51298	−	0.449109i
$130$	1.66044	−	2.87597i	0.145630	−	0.252239i
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	−0.704692	−	0.709514i	$-0.748915\pi$
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	0.966803	+	0.255524i	$0.0822479\pi$
$132$	−18.0379	+	17.0977i	−1.57000	+	1.48816i
$133$	−0.339558	−	0.588131i	−0.0294434	−	0.0509974i
$134$	23.7549			2.05211
$135$	5.11076	−	0.938136i	0.439864	−	0.0807419i
$136$	−19.3774			−1.66160
$137$	−2.83502	−	4.91040i	−0.242212	−	0.419524i	0.719132	−	0.694874i	$-0.244540\pi$
$137$	−2.83502	−	4.91040i	−0.242212	−	0.419524i	−0.961344	+	0.275350i	$0.911206\pi$
$138$	13.0451	−	12.3652i	1.11048	−	1.05259i
$139$	−4.00000	+	6.92820i	−0.339276	+	0.587643i	−0.984297	−	0.176522i	$-0.943515\pi$
$139$	−4.00000	+	6.92820i	−0.339276	+	0.587643i	0.645021	+	0.764165i	$0.276849\pi$
$140$	1.11076	−	1.92390i	0.0938766	−	0.162599i
$141$	8.07522	+	2.39703i	0.680056	+	0.201866i
$142$	−11.3022	−	19.5760i	−0.948460	−	1.64278i
$143$	4.38650			0.366818
$144$	−16.1231	+	8.19186i	−1.34359	+	0.682655i
$145$	−1.38650			−0.115143
$146$	−7.61350	−	13.1870i	−0.630097	−	1.09136i
$147$	−2.71699	−	11.3457i	−0.224094	−	0.935780i
$148$	−0.632168	+	1.09495i	−0.0519639	+	0.0900042i
$149$	−8.83049	+	15.2948i	−0.723422	+	1.25300i	0.236199	+	0.971705i	$0.424098\pi$
$149$	−8.83049	+	15.2948i	−0.723422	+	1.25300i	−0.959620	+	0.281298i	$0.909235\pi$
$150$	1.01414	+	4.23488i	0.0828039	+	0.345776i
$151$	−0.632168	−	1.09495i	−0.0514451	−	0.0891056i	0.839156	−	0.543891i	$-0.183049\pi$
$151$	−0.632168	−	1.09495i	−0.0514451	−	0.0891056i	−0.890601	+	0.454785i	$0.849716\pi$
$152$	−7.70739			−0.625152
$153$	−0.532810	+	9.94840i	−0.0430752	+	0.804280i
$154$	4.29261			0.345908
$155$	−4.36783	−	7.56531i	−0.350833	−	0.607660i
$156$	9.47679	+	2.81306i	0.758750	+	0.225225i
$157$	7.83502	−	13.5707i	0.625303	−	1.08306i	−0.363179	−	0.931719i	$-0.618309\pi$
$157$	7.83502	−	13.5707i	0.625303	−	1.08306i	0.988482	−	0.151337i	$-0.0483579\pi$
$158$	10.1276	−	17.5416i	0.805711	−	1.39553i
$159$	−6.32088	+	5.99141i	−0.501279	+	0.475150i
$160$	−1.74293	−	3.01885i	−0.137791	−	0.238661i
$161$	−2.12217			−0.167250
$162$	9.15591	+	20.6921i	0.719356	+	1.62572i
$163$	15.7074			1.23030			0.615149	−	0.788411i	$-0.289096\pi$
$163$	15.7074			1.23030			0.615149	+	0.788411i	$0.289096\pi$
$164$	24.5192	+	42.4685i	1.91463	+	3.31623i
$165$	−4.17458	+	3.95698i	−0.324991	+	0.308051i
$166$	−1.93892	+	3.35830i	−0.150489	+	0.260655i
$167$	−3.08249	+	5.33903i	−0.238530	+	0.413146i	−0.960293	−	0.278994i	$-0.909999\pi$
$167$	−3.08249	+	5.33903i	−0.238530	+	0.413146i	0.721763	+	0.692141i	$0.243332\pi$
$168$	4.98133	+	1.47864i	0.384318	+	0.114080i
$169$	5.62763	+	9.74734i	0.432895	+	0.749796i
$170$	−8.34916			−0.640351
$171$	−0.211926	+	3.95698i	−0.0162064	+	0.302598i
$172$	44.7175			3.40968
$173$	−4.29261	−	7.43502i	−0.326361	−	0.565274i	0.655426	−	0.755260i	$-0.272489\pi$
$173$	−4.29261	−	7.43502i	−0.326361	−	0.565274i	−0.981787	+	0.189986i	$0.939156\pi$
$174$	−1.40611	−	5.87168i	−0.106597	−	0.445131i
$175$	0.257068	−	0.445256i	0.0194325	−	0.0336582i
$176$	10.0096	−	17.3371i	0.754502	−	1.30684i
$177$	−2.02827	−	8.46975i	−0.152454	−	0.636626i
$178$	3.77121	+	6.53192i	0.282664	+	0.489588i
$179$	−1.06562			−0.0796482			−0.0398241	−	0.999207i	$-0.512680\pi$
$179$	−1.06562			−0.0796482			−0.0398241	+	0.999207i	$0.512680\pi$
$180$	−11.5565	+	5.87168i	−0.861374	+	0.437649i
$181$	−12.6700			−0.941757			−0.470878	−	0.882198i	$-0.656063\pi$
$181$	−12.6700			−0.941757			−0.470878	+	0.882198i	$0.656063\pi$
$182$	−0.853695	−	1.47864i	−0.0632801	−	0.109604i
$183$	−12.2029	−	3.62226i	−0.902061	−	0.267765i
$184$	−12.0424	+	20.8581i	−0.887778	+	1.53768i
$185$	−0.146305	+	0.253408i	−0.0107566	+	0.0186309i
$186$	27.6086	−	26.1695i	2.02436	−	1.91884i
$187$	−5.51414	−	9.55077i	−0.403234	−	0.698421i
$188$	−21.0137			−1.53258
$189$	0.896105	−	2.51676i	0.0651821	−	0.183067i
$190$	−3.32088			−0.240922
$191$	8.46719	+	14.6656i	0.612664	+	1.06117i	0.990789	+	0.135411i	$0.0432356\pi$
$191$	8.46719	+	14.6656i	0.612664	+	1.06117i	−0.378125	+	0.925754i	$0.623431\pi$
$192$	−4.13904	+	3.92329i	−0.298709	+	0.283139i
$193$	−13.3588	+	23.1380i	−0.961585	+	1.66551i	−0.243060	+	0.970011i	$0.578151\pi$
$193$	−13.3588	+	23.1380i	−0.961585	+	1.66551i	−0.718524	+	0.695502i	$0.755182\pi$
$194$	15.4057	−	26.6835i	1.10607	−	1.91576i
$195$	2.19325	+	0.651039i	0.157062	+	0.0466218i
$196$	14.5520	+	25.2048i	1.03943	+	1.80034i
$197$	−14.2553			−1.01565			−0.507823	−	0.861462i	$-0.669550\pi$
$197$	−14.2553			−1.01565			−0.507823	+	0.861462i	$0.669550\pi$
$198$	−20.9909	−	13.6659i	−1.49176	−	0.971194i
$199$	−24.6610			−1.74817			−0.874085	−	0.485773i	$-0.838538\pi$
$199$	−24.6610			−1.74817			−0.874085	+	0.485773i	$0.838538\pi$
$200$	−2.91751	−	5.05328i	−0.206299	−	0.357321i
$201$	3.81128	+	15.9153i	0.268827	+	1.12258i
$202$	−14.6700	+	25.4093i	−1.03218	+	1.78779i
$203$	−0.356427	+	0.617349i	−0.0250162	+	0.0433294i
$204$	−5.78807	−	24.1701i	−0.405246	−	1.69224i
$205$	5.67458	+	9.82866i	0.396330	+	0.686463i
$206$	0.735663			0.0512561
$207$	10.3774	+	6.75611i	0.721281	+	0.469582i
$208$	−7.96265			−0.552111
$209$	−2.19325	−	3.79882i	−0.151710	−	0.262770i
$210$	2.14631	+	0.637103i	0.148109	+	0.0439643i
$211$	2.68872	−	4.65699i	0.185099	−	0.320601i	−0.758511	−	0.651660i	$-0.774073\pi$
$211$	2.68872	−	4.65699i	0.185099	−	0.320601i	0.943610	+	0.331060i	$0.107406\pi$
$212$	10.8633	−	18.8158i	0.746094	−	1.29227i
$213$	11.3022	−	10.7131i	0.774415	−	0.734049i
$214$	−2.35369	−	4.07672i	−0.160895	−	0.278679i
$215$	10.3492			0.705807
$216$	−19.6514	−	23.0891i	−1.33711	−	1.57101i
$217$	−4.49133			−0.304891
$218$	−6.97406	−	12.0794i	−0.472343	−	0.818122i
$219$	7.61350	−	7.21665i	0.514472	−	0.487656i
$220$	7.17458	−	12.4267i	0.483710	−	0.837810i
$221$	−2.19325	+	3.79882i	−0.147534	+	0.255537i
$222$	−1.22153	−	0.362594i	−0.0819835	−	0.0243357i
$223$	−4.33229	−	7.50375i	−0.290112	−	0.502488i	0.683724	−	0.729740i	$-0.260359\pi$
$223$	−4.33229	−	7.50375i	−0.290112	−	0.502488i	−0.973836	+	0.227252i	$0.927026\pi$
$224$	−1.79221			−0.119747
$225$	−2.67458	+	1.35891i	−0.178305	+	0.0905938i
$226$	19.6135			1.30467
$227$	−1.66044	−	2.87597i	−0.110207	−	0.190885i	0.805646	−	0.592397i	$-0.201818\pi$
$227$	−1.66044	−	2.87597i	−0.110207	−	0.190885i	−0.915854	+	0.401512i	$0.868485\pi$
$228$	−2.30221	−	9.61367i	−0.152468	−	0.636681i
$229$	12.6559	−	21.9207i	0.836326	−	1.44856i	−0.0566206	−	0.998396i	$-0.518033\pi$
$229$	12.6559	−	21.9207i	0.836326	−	1.44856i	0.892946	−	0.450163i	$-0.148634\pi$
$230$	−5.18872	+	8.98712i	−0.342134	+	0.592593i
$231$	0.688716	+	2.87597i	0.0453142	+	0.189225i
$232$	4.04514	+	7.00639i	0.265577	+	0.459992i
$233$	27.6327			1.81028			0.905139	−	0.425116i	$-0.139767\pi$
$233$	27.6327			1.81028			0.905139	+	0.425116i	$0.139767\pi$
$234$	−0.532810	+	9.94840i	−0.0348309	+	0.650347i
$235$	−4.86330			−0.317246
$236$	10.8633	+	18.8158i	0.707140	+	1.22480i
$237$	13.3774	+	3.97092i	0.868958	+	0.257939i
$238$	−2.14631	+	3.71751i	−0.139124	+	0.240970i
$239$	2.09936	−	3.63620i	0.135796	−	0.235206i	−0.790105	−	0.612971i	$-0.789974\pi$
$239$	2.09936	−	3.63620i	0.135796	−	0.235206i	0.925901	+	0.377765i	$0.123307\pi$
$240$	7.57795	−	7.18296i	0.489155	−	0.463658i
$241$	−1.80221	−	3.12152i	−0.116091	−	0.201075i	0.802125	−	0.597157i	$-0.203703\pi$
$241$	−1.80221	−	3.12152i	−0.116091	−	0.201075i	−0.918215	+	0.396082i	$0.870370\pi$
$242$	0.0710844			0.00456948
$243$	−12.3943	+	9.45417i	−0.795095	+	0.606485i
$244$	31.7549			2.03290
$245$	3.36783	+	5.83326i	0.215163	+	0.372673i
$246$	−35.8684	+	33.9987i	−2.28688	+	2.16768i
$247$	−0.872368	+	1.51099i	−0.0555074	+	0.0961417i
$248$	−25.4864	+	44.1437i	−1.61839	+	2.80313i
$249$	−2.56108	−	0.760225i	−0.162302	−	0.0481773i
$250$	−1.25707	−	2.17731i	−0.0795040	−	0.137705i
$251$	−6.87783			−0.434125			−0.217062	−	0.976158i	$-0.569648\pi$
$251$	−6.87783			−0.434125			−0.217062	+	0.976158i	$0.569648\pi$
$252$	−0.356427	+	6.65504i	−0.0224528	+	0.419228i
$253$	−13.7074			−0.861776
$254$	−22.4909	−	38.9554i	−1.41121	−	2.44428i
$255$	−1.33956	−	5.59378i	−0.0838864	−	0.350296i
$256$	15.8774	−	27.5005i	0.992340	−	1.71878i
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	−0.435970	−	0.899961i	$-0.643595\pi$
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	0.997374	−	0.0724199i	$-0.0230722\pi$
$258$	10.4955	+	43.8274i	0.653419	+	2.72858i
$259$	0.0752210	+	0.130287i	0.00467400	+	0.00809561i
$260$	−5.70739			−0.353957
$261$	3.70832	−	1.88413i	0.229539	−	0.116625i
$262$	−15.0848			−0.931943
$263$	−3.11803	−	5.40059i	−0.192266	−	0.333015i	0.753735	−	0.657179i	$-0.228250\pi$
$263$	−3.11803	−	5.40059i	−0.192266	−	0.333015i	−0.946001	+	0.324164i	$0.894917\pi$
$264$	32.1751	+	9.55077i	1.98024	+	0.587809i
$265$	2.51414	−	4.35461i	0.154442	−	0.267502i
$266$	−0.853695	+	1.47864i	−0.0523434	+	0.0906614i
$267$	−3.77121	+	3.57463i	−0.230794	+	0.218764i
$268$	−20.4130	−	35.3563i	−1.24692	−	2.15973i
$269$	9.92345			0.605044			0.302522	−	0.953142i	$-0.402172\pi$
$269$	9.92345			0.605044			0.302522	+	0.953142i	$0.402172\pi$
$270$	−8.46719	−	9.94840i	−0.515297	−	0.605440i
$271$	6.60442			0.401190			0.200595	−	0.979674i	$-0.435712\pi$
$271$	6.60442			0.401190			0.200595	+	0.979674i	$0.435712\pi$
$272$	10.0096	+	17.3371i	0.606921	+	1.05122i
$273$	0.853695	−	0.809197i	0.0516680	−	0.0489748i
$274$	−7.12763	+	12.3454i	−0.430596	+	0.745814i
$275$	1.66044	−	2.87597i	0.100128	−	0.173428i
$276$	−29.6140	−	8.79054i	−1.78255	−	0.529128i
$277$	−11.3305	−	19.6250i	−0.680783	−	1.17915i	−0.974742	−	0.223333i	$-0.928306\pi$
$277$	−11.3305	−	19.6250i	−0.680783	−	1.17915i	0.293959	−	0.955818i	$-0.405027\pi$
$278$	20.1131			1.20630
$279$	21.9627	+	14.2985i	1.31487	+	0.856031i
$280$	−3.00000			−0.179284
$281$	7.77394	+	13.4649i	0.463754	+	0.803246i	0.999144	−	0.0413590i	$-0.0131687\pi$
$281$	7.77394	+	13.4649i	0.463754	+	0.803246i	−0.535390	+	0.844605i	$0.679835\pi$
$282$	−4.93205	−	20.5955i	−0.293699	−	1.22644i
$283$	−0.322689	+	0.558913i	−0.0191819	+	0.0332240i	−0.875457	−	0.483296i	$-0.839439\pi$
$283$	−0.322689	+	0.558913i	−0.0191819	+	0.0332240i	0.856275	+	0.516520i	$0.172773\pi$
$284$	−19.4244	+	33.6440i	−1.15262	+	1.99640i
$285$	−0.532810	−	2.22493i	−0.0315610	−	0.131794i
$286$	−5.51414	−	9.55077i	−0.326058	−	0.564749i
$287$	5.83502			0.344430
$288$	8.76394	+	5.70566i	0.516420	+	0.336209i
$289$	−5.97173			−0.351278
$290$	1.74293	+	3.01885i	0.102348	+	0.177273i
$291$	20.3492	+	6.04039i	1.19289	+	0.354094i
$292$	−13.0848	+	22.6636i	−0.765731	+	1.32629i
$293$	0.688716	−	1.19289i	0.0402352	−	0.0696895i	−0.845207	−	0.534440i	$-0.820523\pi$
$293$	0.688716	−	1.19289i	0.0402352	−	0.0696895i	0.885442	+	0.464750i	$0.153856\pi$
$294$	−21.2877	+	20.1781i	−1.24152	+	1.17681i
$295$	2.51414	+	4.35461i	0.146379	+	0.253535i
$296$	1.70739			0.0992400
$297$	5.78807	−	16.2561i	0.335858	−	0.943276i
$298$	44.4021			2.57214
$299$	2.72606	+	4.72168i	0.157652	+	0.273062i
$300$	5.43165	−	5.14853i	0.313596	−	0.297250i
$301$	2.66044	−	4.60802i	0.153345	−	0.265602i
$302$	−1.58936	+	2.75285i	−0.0914573	+	0.158409i
$303$	−19.3774	−	5.75194i	−1.11320	−	0.330440i
$304$	3.98133	+	6.89586i	0.228345	+	0.395505i
$305$	7.34916			0.420812
$306$	22.3305	−	11.3457i	1.27655	−	0.648592i
$307$	−7.98546			−0.455754			−0.227877	−	0.973690i	$-0.573178\pi$
$307$	−7.98546			−0.455754			−0.227877	+	0.973690i	$0.573178\pi$
$308$	−3.68872	−	6.38904i	−0.210184	−	0.364050i
$309$	0.118031	+	0.492881i	0.00671458	+	0.0280390i
$310$	−10.9813	+	19.0202i	−0.623697	+	1.08028i
$311$	−4.81635	+	8.34216i	−0.273110	+	0.473040i	−0.969657	−	0.244471i	$-0.921386\pi$
$311$	−4.81635	+	8.34216i	−0.273110	+	0.473040i	0.696547	+	0.717512i	$0.254719\pi$
$312$	−3.10896	−	12.9825i	−0.176010	−	0.734991i
$313$	12.2685	+	21.2496i	0.693455	+	1.20110i	0.970699	+	0.240300i	$0.0772458\pi$
$313$	12.2685	+	21.2496i	0.693455	+	1.20110i	−0.277244	+	0.960800i	$0.589421\pi$
$314$	−39.3966			−2.22328
$315$	−0.0824893	+	1.54020i	−0.00464774	+	0.0867806i
$316$	−34.8114			−1.95829
$317$	10.1746	+	17.6229i	0.571461	+	0.989800i	0.996416	+	0.0845855i	$0.0269566\pi$
$317$	10.1746	+	17.6229i	0.571461	+	0.989800i	−0.424955	+	0.905215i	$0.639710\pi$
$318$	20.9909	+	6.23089i	1.17711	+	0.349411i
$319$	−2.30221	+	3.98755i	−0.128899	+	0.223260i
$320$	1.64631	−	2.85148i	0.0920313	−	0.159403i
$321$	2.35369	−	2.23101i	0.131370	−	0.124523i
$322$	2.66771	+	4.62061i	0.148666	+	0.257497i
$323$	4.38650			0.244072
$324$	22.9298	−	31.4085i	1.27388	−	1.74492i
$325$	−1.32088			−0.0732695
$326$	−19.7453	−	34.1998i	−1.09359	−	1.89415i
$327$	6.97406	−	6.61054i	0.385666	−	0.365564i
$328$	33.1113	−	57.3504i	1.82827	−	3.16665i
$329$	−1.25020	+	2.16541i	−0.0689257	+	0.119383i
$330$	13.8633	+	4.11514i	0.763149	+	0.226531i
$331$	−8.22153	−	14.2401i	−0.451896	−	0.782707i	0.546608	−	0.837389i	$-0.315919\pi$
$331$	−8.22153	−	14.2401i	−0.451896	−	0.782707i	−0.998504	+	0.0546819i	$0.982586\pi$
$332$	6.66458			0.365766
$333$	0.0469471	−	0.876576i	0.00257269	−	0.0480360i
$334$	15.4996			0.848100
$335$	−4.72426	−	8.18266i	−0.258114	−	0.447066i
$336$	−1.25020	−	5.22064i	−0.0682040	−	0.284809i
$337$	−2.44852	+	4.24096i	−0.133379	+	0.231020i	−0.924977	−	0.380023i	$-0.875916\pi$
$337$	−2.44852	+	4.24096i	−0.133379	+	0.231020i	0.791598	+	0.611042i	$0.209249\pi$
$338$	14.1486	−	24.5062i	0.769584	−	1.33296i
$339$	3.14683	+	13.1407i	0.170913	+	0.713704i
$340$	7.17458	+	12.4267i	0.389096	+	0.673934i
$341$	−29.0101			−1.57099
$342$	8.88197	−	4.51277i	0.480282	−	0.244023i
$343$	7.06201			0.381313
$344$	−30.1938	−	52.2972i	−1.62794	−	2.81967i
$345$	−6.85369	−	2.03443i	−0.368991	−	0.109530i
$346$	−10.7922	+	18.6927i	−0.580193	+	1.00492i
$347$	−11.1372	+	19.2903i	−0.597878	+	1.03556i	0.395256	+	0.918571i	$0.370656\pi$
$347$	−11.1372	+	19.2903i	−0.597878	+	1.03556i	−0.993134	+	0.116984i	$0.962677\pi$
$348$	−7.53101	+	7.13846i	−0.403704	+	0.382662i
$349$	1.47173	+	2.54910i	0.0787797	+	0.136450i	0.902724	−	0.430221i	$-0.141564\pi$
$349$	1.47173	+	2.54910i	0.0787797	+	0.136450i	−0.823944	+	0.566671i	$0.808231\pi$
$350$	−1.29261			−0.0690929
$351$	−6.75073	+	1.23917i	−0.360327	+	0.0661420i
$352$	−11.5761			−0.617011
$353$	−9.41478	−	16.3069i	−0.501098	−	0.867927i	−0.999999	−	0.00126845i	$-0.999596\pi$
$353$	−9.41478	−	16.3069i	−0.501098	−	0.867927i	0.498901	−	0.866659i	$-0.333737\pi$
$354$	−15.8916	+	15.0632i	−0.844627	+	0.800602i
$355$	−4.49546	+	7.78637i	−0.238594	+	0.413258i
$356$	6.48133	−	11.2260i	0.343510	−	0.594976i
$357$	−2.83502	−	0.841540i	−0.150045	−	0.0445390i
$358$	1.33956	+	2.32018i	0.0707978	+	0.122625i
$359$	−31.8770			−1.68241			−0.841203	−	0.540720i	$-0.818152\pi$
$359$	−31.8770			−1.68241			−0.841203	+	0.540720i	$0.818152\pi$
$360$	14.6700	+	9.55077i	0.773179	+	0.503370i
$361$	−17.2553			−0.908172
$362$	15.9271	+	27.5866i	0.837110	+	1.44992i
$363$	0.0114049	+	0.0476252i	0.000598604	+	0.00249968i
$364$	−1.46719	+	2.54125i	−0.0769016	+	0.133198i
$365$	−3.02827	+	5.24512i	−0.158507	+	0.274542i
$366$	7.45305	+	31.1228i	0.389577	+	1.62681i
$367$	9.17458	+	15.8908i	0.478909	+	0.829495i	0.999708	−	0.0241848i	$-0.00769900\pi$
$367$	9.17458	+	15.8908i	0.478909	+	0.829495i	−0.520798	+	0.853680i	$0.674366\pi$
$368$	24.8825			1.29709
$369$	−28.5333	−	18.5763i	−1.48539	−	0.967044i
$370$	0.735663			0.0382453
$371$	−1.29261	−	2.23887i	−0.0671090	−	0.116236i
$372$	−62.6747	−	18.6042i	−3.24953	−	0.964582i
$373$	1.09936	−	1.90414i	0.0569226	−	0.0985929i	−0.836160	−	0.548486i	$-0.815205\pi$
$373$	1.09936	−	1.90414i	0.0569226	−	0.0985929i	0.893083	+	0.449893i	$0.148538\pi$
$374$	−13.8633	+	24.0119i	−0.716854	+	1.24163i
$375$	1.25707	−	1.19154i	0.0649147	−	0.0615311i
$376$	14.1887	+	24.5756i	0.731727	+	1.26739i
$377$	1.83141			0.0943226
$378$	−6.60623	+	1.21265i	−0.339788	+	0.0623717i
$379$	15.4713			0.794709			0.397354	−	0.917665i	$-0.369928\pi$
$379$	15.4713			0.794709			0.397354	+	0.917665i	$0.369928\pi$
$380$	2.85369	+	4.94274i	0.146391	+	0.253557i
$381$	22.4909	−	21.3186i	1.15225	−	1.09219i
$382$	21.2877	−	36.8713i	1.08917	−	1.88650i
$383$	−3.85369	+	6.67479i	−0.196915	+	0.341066i	−0.947526	−	0.319677i	$-0.896426\pi$
$383$	−3.85369	+	6.67479i	−0.196915	+	0.341066i	0.750612	+	0.660743i	$0.229759\pi$
$384$	25.3214	+	7.51633i	1.29218	+	0.383566i
$385$	−0.853695	−	1.47864i	−0.0435083	−	0.0753586i
$386$	67.1715			3.41894
$387$	−27.6796	+	14.0635i	−1.40704	+	0.714890i
$388$	−52.9536			−2.68831
$389$	12.3163	+	21.3325i	0.624464	+	1.08160i	0.988644	+	0.150274i	$0.0480157\pi$
$389$	12.3163	+	21.3325i	0.624464	+	1.08160i	−0.364181	+	0.931328i	$0.618651\pi$
$390$	−1.33956	−	5.59378i	−0.0678311	−	0.283252i
$391$	6.85369	−	11.8709i	0.346606	−	0.600340i
$392$	19.6514	−	34.0372i	0.992544	−	1.71914i
$393$	−2.42024	−	10.1066i	−0.122085	−	0.509808i
$394$	17.9198	+	31.0381i	0.902789	+	1.56368i
$395$	−8.05655			−0.405369
$396$	−2.30221	+	42.9859i	−0.115690	+	2.16012i
$397$	−6.77301			−0.339928			−0.169964	−	0.985450i	$-0.554365\pi$
$397$	−6.77301			−0.339928			−0.169964	+	0.985450i	$0.554365\pi$
$398$	31.0005	+	53.6945i	1.55392	+	2.69146i
$399$	−1.12763	−	0.334723i	−0.0564522	−	0.0167571i
$400$	−3.01414	+	5.22064i	−0.150707	+	0.261032i
$401$	9.24980	−	16.0211i	0.461913	−	0.800057i	−0.537143	−	0.843491i	$-0.680497\pi$
$401$	9.24980	−	16.0211i	0.461913	−	0.800057i	0.999056	+	0.0434343i	$0.0138299\pi$
$402$	29.8615	−	28.3050i	1.48936	−	1.41172i
$403$	5.76940	+	9.99290i	0.287394	+	0.497782i
$404$	50.4249			2.50873
$405$	5.30675	−	7.26900i	0.263694	−	0.361200i
$406$	1.79221			0.0889459
$407$	0.485863	+	0.841540i	0.0240833	+	0.0417136i
$408$	−24.3588	+	23.0891i	−1.20594	+	1.14308i
$409$	6.70739	−	11.6175i	0.331659	−	0.574450i	−0.651178	−	0.758925i	$-0.725725\pi$
$409$	6.70739	−	11.6175i	0.331659	−	0.574450i	0.982837	+	0.184474i	$0.0590583\pi$
$410$	14.2667	−	24.7106i	0.704581	−	1.22037i
$411$	−9.41478	−	2.79466i	−0.464397	−	0.137850i
$412$	−0.632168	−	1.09495i	−0.0311447	−	0.0539442i
$413$	2.58522			0.127210
$414$	1.66498	−	31.0877i	0.0818292	−	1.52788i
$415$	1.54241			0.0757140
$416$	2.30221	+	3.98755i	0.112875	+	0.195506i
$417$	3.22699	+	13.4754i	0.158026	+	0.659893i
$418$	−5.51414	+	9.55077i	−0.269705	+	0.467143i
$419$	16.5575	−	28.6784i	0.808886	−	1.40103i	−0.104751	−	0.994499i	$-0.533404\pi$
$419$	16.5575	−	28.6784i	0.808886	−	1.40103i	0.913636	−	0.406532i	$-0.133262\pi$
$420$	−0.896105	−	3.74200i	−0.0437255	−	0.182591i
$421$	7.34916	+	12.7291i	0.358176	+	0.620379i	0.987656	−	0.156637i	$-0.0500654\pi$
$421$	7.34916	+	12.7291i	0.358176	+	0.620379i	−0.629480	+	0.777017i	$0.716732\pi$
$422$	−13.5196			−0.658124
$423$	13.0073	−	6.60876i	0.632435	−	0.321329i
$424$	−29.3401			−1.42488
$425$	1.66044	+	2.87597i	0.0805433	+	0.139505i
$426$	−37.5333	−	11.1413i	−1.81850	−	0.539797i
$427$	1.88924	−	3.27225i	0.0914266	−	0.158355i
$428$	−4.04514	+	7.00639i	−0.195529	+	0.338667i
$429$	5.51414	−	5.22672i	0.266225	−	0.252348i
$430$	−13.0096	−	22.5333i	−0.627379	−	1.08665i
$431$	−32.7549			−1.57775			−0.788873	−	0.614556i	$-0.789335\pi$
$431$	−32.7549			−1.57775			−0.788873	+	0.614556i	$0.789335\pi$
$432$	−10.5069	+	29.5091i	−0.505512	+	1.41976i
$433$	−11.8314			−0.568581			−0.284291	−	0.958738i	$-0.591758\pi$
$433$	−11.8314			−0.568581			−0.284291	+	0.958738i	$0.591758\pi$
$434$	5.64591	+	9.77900i	0.271012	+	0.469407i
$435$	−1.74293	+	1.65208i	−0.0835672	+	0.0792113i
$436$	−11.9859	+	20.7601i	−0.574019	+	0.994230i
$437$	2.72606	−	4.72168i	0.130405	−	0.225869i
$438$	−25.2835	−	7.50509i	−1.20809	−	0.358607i
$439$	−4.15591	−	7.19824i	−0.198351	−	0.343553i	0.749643	−	0.661842i	$-0.230225\pi$
$439$	−4.15591	−	7.19824i	−0.198351	−	0.343553i	−0.947994	+	0.318289i	$0.896892\pi$
$440$	−19.3774			−0.923783
$441$	−16.9344	−	11.0249i	−0.806399	−	0.524997i
$442$	11.0283			0.524561
$443$	14.5876	+	25.2664i	0.693076	+	1.20044i	0.970825	+	0.239789i	$0.0770781\pi$
$443$	14.5876	+	25.2664i	0.693076	+	1.20044i	−0.277750	+	0.960654i	$0.589589\pi$
$444$	0.510000	+	2.12968i	0.0242035	+	0.101070i
$445$	1.50000	−	2.59808i	0.0711068	−	0.123161i
$446$	−10.8920	+	18.8654i	−0.515750	+	0.893305i
$447$	7.12397	+	29.7486i	0.336952	+	1.40706i
$448$	−0.846426	−	1.46605i	−0.0399899	−	0.0692645i
$449$	18.9717			0.895331			0.447666	−	0.894201i	$-0.352256\pi$
$449$	18.9717			0.895331			0.447666	+	0.894201i	$0.352256\pi$
$450$	6.32088	+	4.11514i	0.297969	+	0.193990i
$451$	37.6892			1.77472
$452$	−16.8542	−	29.1924i	−0.792756	−	1.37309i
$453$	−2.09936	−	0.623167i	−0.0986365	−	0.0292790i
$454$	−4.17458	+	7.23058i	−0.195923	+	0.339348i
$455$	−0.339558	+	0.588131i	−0.0159187	+	0.0275720i
$456$	−9.68872	+	9.18370i	−0.453716	+	0.430066i
$457$	11.6176	+	20.1223i	0.543450	+	0.941283i	0.998703	+	0.0509206i	$0.0162155\pi$
$457$	11.6176	+	20.1223i	0.543450	+	0.941283i	−0.455253	+	0.890362i	$0.650451\pi$
$458$	−63.6374			−2.97358
$459$	11.1842	+	13.1407i	0.522033	+	0.613354i
$460$	17.8350			0.831562
$461$	−2.21285	−	3.83277i	−0.103063	−	0.178510i	0.809882	−	0.586592i	$-0.199531\pi$
$461$	−2.21285	−	3.83277i	−0.103063	−	0.178510i	−0.912945	+	0.408082i	$0.866198\pi$
$462$	5.39611	−	5.11484i	0.251050	−	0.237964i
$463$	9.75434	−	16.8950i	0.453322	−	0.785178i	−0.545268	−	0.838262i	$-0.683572\pi$
$463$	9.75434	−	16.8950i	0.453322	−	0.785178i	0.998590	+	0.0530845i	$0.0169053\pi$
$464$	4.17912	−	7.23844i	0.194011	−	0.336036i
$465$	−14.5051	−	4.30564i	−0.672656	−	0.199669i
$466$	−34.7362	−	60.1648i	−1.60912	−	2.78708i
$467$	−24.5935			−1.13805			−0.569026	−	0.822320i	$-0.692679\pi$
$467$	−24.5935			−1.13805			−0.569026	+	0.822320i	$0.692679\pi$
$468$	15.2649	−	7.75581i	0.705619	−	0.358512i
$469$	−4.85783			−0.224314
$470$	6.11350	+	10.5889i	0.281995	+	0.488429i
$471$	−6.32088	−	26.3950i	−0.291251	−	1.21622i
$472$	14.6700	−	25.4093i	0.675243	−	1.16956i
$473$	17.1842	−	29.7639i	0.790129	−	1.36854i
$474$	−8.17044	−	34.1185i	−0.375281	−	1.56711i
$475$	0.660442	+	1.14392i	0.0303032	+	0.0524866i
$476$	7.37743			0.338144
$477$	−0.806748	+	15.0632i	−0.0369384	+	0.689698i
$478$	−10.5561			−0.482827
$479$	−16.3774	−	28.3665i	−0.748304	−	1.29610i	−0.948635	−	0.316372i	$-0.897535\pi$
$479$	−16.3774	−	28.3665i	−0.748304	−	1.29610i	0.200331	−	0.979728i	$-0.435798\pi$
$480$	−5.78807	−	1.71812i	−0.264188	−	0.0784209i
$481$	0.193252	−	0.334723i	0.00881155	−	0.0152621i
$482$	−4.53101	+	7.84793i	−0.206382	+	0.357464i
$483$	−2.66771	+	2.52866i	−0.121385	+	0.115058i
$484$	−0.0610840	−	0.105801i	−0.00277655	−	0.00480912i
$485$	−12.2553			−0.556483
$486$	36.1651	+	15.1017i	1.64048	+	0.685025i
$487$	−6.03735			−0.273578			−0.136789	−	0.990600i	$-0.543678\pi$
$487$	−6.03735			−0.273578			−0.136789	+	0.990600i	$0.543678\pi$
$488$	−21.4412	−	37.1373i	−0.970600	−	1.68113i
$489$	19.7453	−	18.7161i	0.892912	−	0.846369i
$490$	8.46719	−	14.6656i	0.382509	−	0.662524i
$491$	−7.22153	+	12.5081i	−0.325903	+	0.564480i	−0.981695	−	0.190461i	$-0.939002\pi$
$491$	−7.22153	+	12.5081i	−0.325903	+	0.564480i	0.655792	+	0.754942i	$0.272335\pi$
$492$	81.4254	+	24.1701i	3.67094	+	1.08967i
$493$	−2.30221	−	3.98755i	−0.103686	−	0.179590i
$494$	4.38650			0.197358
$495$	−0.532810	+	9.94840i	−0.0239480	+	0.447147i
$496$	52.6610			2.36455
$497$	2.31128	+	4.00326i	0.103675	+	0.179571i
$498$	1.56422	+	6.53192i	0.0700942	+	0.292702i
$499$	−10.4859	+	18.1620i	−0.469412	+	0.813045i	−0.999388	−	0.0349673i	$-0.988867\pi$
$499$	−10.4859	+	18.1620i	−0.469412	+	0.813045i	0.529977	+	0.848012i	$0.322201\pi$
$500$	−2.16044	+	3.74200i	−0.0966179	+	0.167347i
$501$	2.48679	+	10.3844i	0.111102	+	0.463943i
$502$	8.64591	+	14.9751i	0.385886	+	0.668374i
$503$	−5.31728			−0.237086			−0.118543	−	0.992949i	$-0.537822\pi$
$503$	−5.31728			−0.237086			−0.118543	+	0.992949i	$0.537822\pi$
$504$	8.02374	−	4.07672i	0.357406	−	0.181591i
$505$	11.6700			0.519310
$506$	17.2311	+	29.8452i	0.766017	+	1.32678i
$507$	18.6887	+	5.54750i	0.829995	+	0.246373i
$508$	−38.6537	+	66.9502i	−1.71498	+	2.97043i
$509$	−9.11350	+	15.7850i	−0.403949	+	0.699659i	−0.994198	−	0.107561i	$-0.965696\pi$
$509$	−9.11350	+	15.7850i	−0.403949	+	0.699659i	0.590250	+	0.807221i	$0.299029\pi$
$510$	−10.4955	+	9.94840i	−0.464747	+	0.440522i
$511$	1.55695	+	2.69671i	0.0688753	+	0.119296i
$512$	−49.3365			−2.18038
$513$	4.44852	+	5.22672i	0.196407	+	0.230765i
$514$	−45.2545			−1.99609
$515$	−0.146305	−	0.253408i	−0.00644698	−	0.0111665i
$516$	56.2130	−	53.2829i	2.47464	−	2.34565i
$517$	−8.07522	+	13.9867i	−0.355148	+	0.615134i
$518$	0.189116	−	0.327558i	0.00830927	−	0.0143921i
$519$	−14.2553	−	4.23149i	−0.625737	−	0.185742i
$520$	3.85369	+	6.67479i	0.168996	+	0.292709i
$521$	40.1232			1.75783			0.878915	−	0.476978i	$-0.158268\pi$
$521$	40.1232			1.75783			0.878915	+	0.476978i	$0.158268\pi$
$522$	−8.76394	−	5.70566i	−0.383587	−	0.249730i
$523$	18.9873			0.830257			0.415129	−	0.909763i	$-0.363737\pi$
$523$	18.9873			0.830257			0.415129	+	0.909763i	$0.363737\pi$
$524$	12.9627	+	22.4520i	0.566276	+	0.980819i
$525$	−0.207389	−	0.866025i	−0.00905121	−	0.0377964i
$526$	−7.83916	+	13.5778i	−0.341804	+	0.592021i
$527$	14.5051	−	25.1235i	0.631851	−	1.09440i
$528$	−8.07522	−	33.7209i	−0.351429	−	1.46751i
$529$	2.98133	+	5.16381i	0.129623	+	0.224513i
$530$	−12.6418			−0.549123
$531$	−12.6418	−	8.23028i	−0.548606	−	0.357164i
$532$	2.93438			0.127221
$533$	−7.49546	−	12.9825i	−0.324665	−	0.562336i
$534$	12.5237	+	3.71751i	0.541955	+	0.160872i
$535$	−0.936184	+	1.62152i	−0.0404748	+	0.0701043i
$536$	−27.5661	+	47.7460i	−1.19068	+	2.06231i
$537$	−1.33956	+	1.26973i	−0.0578062	+	0.0547931i
$538$	−12.4745	−	21.6064i	−0.537812	−	0.931518i
$539$	22.3684			0.963473
$540$	−7.53101	+	21.1512i	−0.324083	+	0.910205i
$541$	16.5279			0.710589			0.355294	−	0.934754i	$-0.384381\pi$
$541$	16.5279			0.710589			0.355294	+	0.934754i	$0.384381\pi$
$542$	−8.30221	−	14.3799i	−0.356611	−	0.617668i
$543$	−15.9271	+	15.0969i	−0.683498	+	0.647871i
$544$	5.78807	−	10.0252i	0.248162	−	0.429829i
$545$	−2.77394	+	4.80460i	−0.118822	+	0.205806i
$546$	−2.83502	−	0.841540i	−0.121328	−	0.0360146i
$547$	−8.83683	−	15.3058i	−0.377835	−	0.654430i	0.612912	−	0.790151i	$-0.289998\pi$
$547$	−8.83683	−	15.3058i	−0.377835	−	0.654430i	−0.990747	+	0.135721i	$0.956665\pi$
$548$	24.4996			1.04657
$549$	−19.6559	+	9.98682i	−0.838894	+	0.426227i
$550$	−8.34916			−0.356009
$551$	−0.915706	−	1.58605i	−0.0390104	−	0.0675680i
$552$	9.71519	+	40.5691i	0.413506	+	1.72674i
$553$	−2.07108	+	3.58722i	−0.0880715	+	0.152544i
$554$	−28.4864	+	49.3399i	−1.21027	+	2.09625i
$555$	0.118031	+	0.492881i	0.00501016	+	0.0209216i
$556$	−17.2835	−	29.9360i	−0.732985	−	1.26957i
$557$	17.3401			0.734723			0.367362	−	0.930078i	$-0.380261\pi$
$557$	17.3401			0.734723			0.367362	+	0.930078i	$0.380261\pi$
$558$	3.52374	−	65.7937i	0.149172	−	2.78527i
$559$	−13.6700			−0.578181
$560$	1.54968	+	2.68412i	0.0654859	+	0.113425i
$561$	−18.3118	−	5.43563i	−0.773125	−	0.229492i
$562$	19.5447	−	33.8525i	0.824445	−	1.42798i
$563$	−6.49727	+	11.2536i	−0.273827	+	0.474283i	−0.969839	−	0.243748i	$-0.921623\pi$
$563$	−6.49727	+	11.2536i	−0.273827	+	0.474283i	0.696011	+	0.718031i	$0.254956\pi$
$564$	−26.4157	+	25.0388i	−1.11230	+	1.05432i
$565$	−3.90064	−	6.75611i	−0.164101	−	0.284232i
$566$	1.62257			0.0682016
$567$	−1.87237	−	4.23149i	−0.0786321	−	0.177706i
$568$	52.4623			2.20127
$569$	8.34009	+	14.4455i	0.349635	+	0.605585i	0.986184	−	0.165651i	$-0.0529724\pi$
$569$	8.34009	+	14.4455i	0.349635	+	0.605585i	−0.636550	+	0.771236i	$0.719639\pi$
$570$	−4.17458	+	3.95698i	−0.174854	+	0.165740i
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	−0.995788	−	0.0916910i	$-0.970773\pi$
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	0.577301	+	0.816532i	$0.304106\pi$
$572$	−9.47679	+	16.4143i	−0.396245	+	0.686316i
$573$	28.1186	+	8.34663i	1.17467	+	0.348686i
$574$	−7.33502	−	12.7046i	−0.306158	−	0.530281i
$575$	4.12763			0.172134
$576$	−0.528274	+	9.86370i	−0.0220114	+	0.410987i
$577$	−23.5953			−0.982287			−0.491144	−	0.871079i	$-0.663421\pi$
$577$	−23.5953			−0.982287			−0.491144	+	0.871079i	$0.663421\pi$
$578$	7.50687	+	13.0023i	0.312245	+	0.540823i
$579$	10.7771	+	45.0037i	0.447883	+	1.87029i
$580$	2.99546	−	5.18830i	0.124380	−	0.215432i
$581$	0.396505	−	0.686767i	0.0164498	−	0.0284919i
$582$	−12.4285	−	51.8995i	−0.515179	−	2.15130i
$583$	−8.34916	−	14.4612i	−0.345787	−	0.598920i
$584$	35.3401			1.46238
$585$	3.53281	−	1.79496i	0.146064	−	0.0742124i
$586$	−3.46305			−0.143057
$587$	−14.0638	−	24.3592i	−0.580476	−	1.00541i	−0.995423	−	0.0955681i	$-0.969533\pi$
$587$	−14.0638	−	24.3592i	−0.580476	−	1.00541i	0.414947	−	0.909846i	$-0.363800\pi$
$588$	48.3255	+	14.3448i	1.99291	+	0.591570i
$589$	5.76940	−	9.99290i	0.237724	−	0.411750i
$590$	6.32088	−	10.9481i	0.260227	−	0.450726i
$591$	−17.9198	+	16.9858i	−0.737124	+	0.698702i
$592$	−0.881969	−	1.52761i	−0.0362487	−	0.0627846i
$593$	−9.17872			−0.376925			−0.188462	−	0.982080i	$-0.560350\pi$
$593$	−9.17872			−0.376925			−0.188462	+	0.982080i	$0.560350\pi$
$594$	−42.6706	+	7.83265i	−1.75079	+	0.321378i
$595$	1.70739			0.0699961
$596$	−38.1555	−	66.0873i	−1.56291	−	2.70704i
$597$	−31.0005	+	29.3846i	−1.26877	+	1.20263i
$598$	6.85369	−	11.8709i	0.280268	−	0.485439i
$599$	15.7357	−	27.2550i	0.642942	−	1.11361i	−0.341831	−	0.939761i	$-0.611047\pi$
$599$	15.7357	−	27.2550i	0.642942	−	1.11361i	0.984773	−	0.173846i	$-0.0556196\pi$
$600$	−9.68872	−	2.87597i	−0.395540	−	0.117411i
$601$	14.6327	+	25.3446i	0.596880	+	1.03383i	0.993279	+	0.115748i	$0.0369265\pi$
$601$	14.6327	+	25.3446i	0.596880	+	1.03383i	−0.396398	+	0.918079i	$0.629740\pi$
$602$	−13.3774			−0.545223
$603$	23.7549	+	15.4653i	0.967373	+	0.629797i
$604$	5.46305			0.222288
$605$	−0.0141369	−	0.0244859i	−0.000574748	−	0.000995493i
$606$	11.8350	+	49.4212i	0.480765	+	2.00760i
$607$	22.1017	−	38.2813i	0.897080	−	1.55379i	0.0658708	−	0.997828i	$-0.479017\pi$
$607$	22.1017	−	38.2813i	0.897080	−	1.55379i	0.831209	−	0.555960i	$-0.187649\pi$
$608$	2.30221	−	3.98755i	0.0933670	−	0.161716i
$609$	0.287546	+	1.20075i	0.0116520	+	0.0486568i
$610$	−9.23840	−	16.0014i	−0.374052	−	0.647877i
$611$	6.42385			0.259881
$612$	−36.0757	−	23.4867i	−1.45828	−	0.949394i
$613$	−35.1715			−1.42056			−0.710282	−	0.703918i	$-0.751432\pi$
$613$	−35.1715			−1.42056			−0.710282	+	0.703918i	$0.751432\pi$
$614$	10.0383	+	17.3868i	0.405112	+	0.701674i
$615$	18.8446	+	5.59378i	0.759889	+	0.225563i
$616$	−4.98133	+	8.62791i	−0.200703	+	0.347628i
$617$	3.71285	−	6.43085i	0.149474	−	0.258896i	−0.781559	−	0.623831i	$-0.785575\pi$
$617$	3.71285	−	6.43085i	0.149474	−	0.258896i	0.931033	+	0.364935i	$0.118909\pi$
$618$	0.924779	−	0.876576i	0.0372001	−	0.0352610i
$619$	−4.27394	−	7.40268i	−0.171784	−	0.297539i	0.767260	−	0.641337i	$-0.221620\pi$
$619$	−4.27394	−	7.40268i	−0.171784	−	0.297539i	−0.939044	+	0.343798i	$0.888286\pi$
$620$	37.7458			1.51591
$621$	21.0953	−	3.87228i	0.846527	−	0.155389i
$622$	24.2179			0.971050
$623$	−0.771205	−	1.33577i	−0.0308977	−	0.0535164i
$624$	−10.0096	+	9.48786i	−0.400705	+	0.379818i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	30.8446	−	53.4245i	1.23280	−	2.13527i
$627$	−7.28354	−	2.16202i	−0.290876	−	0.0863429i
$628$	33.8542	+	58.6372i	1.35093	+	2.33988i
$629$	−0.971726			−0.0387453
$630$	3.45719	−	1.75654i	0.137738	−	0.0699821i
$631$	−2.36836			−0.0942829			−0.0471415	−	0.998888i	$-0.515011\pi$
$631$	−2.36836			−0.0942829			−0.0471415	+	0.998888i	$0.515011\pi$
$632$	23.5051	+	40.7120i	0.934981	+	1.61944i
$633$	−2.16912	−	9.05788i	−0.0862146	−	0.360019i
$634$	25.5803	−	44.3064i	1.01592	−	1.75963i
$635$	−8.94578	+	15.4946i	−0.355003	+	0.614883i
$636$	−8.76394	−	36.5968i	−0.347513	−	1.45116i
$637$	−4.44852	−	7.70506i	−0.176257	−	0.305285i
$638$	11.5761			0.458304
$639$	1.44252	−	26.9342i	0.0570654	−	1.06550i
$640$	−15.2498			−0.602801
$641$	0.0665480	+	0.115265i	0.00262849	+	0.00455268i	0.867337	−	0.497722i	$-0.165830\pi$
$641$	0.0665480	+	0.115265i	0.00262849	+	0.00455268i	−0.864708	+	0.502275i	$0.832497\pi$
$642$	−7.81635	−	2.32018i	−0.308487	−	0.0915703i
$643$	11.3232	−	19.6124i	0.446544	−	0.773437i	−0.551614	−	0.834099i	$-0.685988\pi$
$643$	11.3232	−	19.6124i	0.446544	−	0.773437i	0.998158	+	0.0606623i	$0.0193213\pi$
$644$	4.58482	−	7.94114i	0.180667	−	0.312925i
$645$	13.0096	−	12.3315i	0.512253	−	0.485552i
$646$	−5.51414	−	9.55077i	−0.216951	−	0.375770i
$647$	46.3912			1.82383			0.911913	−	0.410385i	$-0.134606\pi$
$647$	46.3912			1.82383			0.911913	+	0.410385i	$0.134606\pi$
$648$	−52.2148	−	5.60907i	−2.05119	−	0.220345i
$649$	16.6983			0.655466
$650$	1.66044	+	2.87597i	0.0651279	+	0.112805i
$651$	−5.64591	+	5.35162i	−0.221280	+	0.209746i
$652$	−33.9349	+	58.7770i	−1.32899	+	2.30188i
$653$	−18.2029	+	31.5283i	−0.712333	+	1.23380i	0.251647	+	0.967819i	$0.419028\pi$
$653$	−18.2029	+	31.5283i	−0.712333	+	1.23380i	−0.963979	+	0.265977i	$0.914305\pi$
$654$	−23.1600	−	6.87476i	−0.905629	−	0.268824i
$655$	3.00000	+	5.19615i	0.117220	+	0.203030i
$656$	−68.4158			−2.67119
$657$	0.971726	−	18.1436i	0.0379106	−	0.707851i
$658$	6.28635			0.245067
$659$	−9.57068	−	16.5769i	−0.372821	−	0.645745i	0.617177	−	0.786824i	$-0.288276\pi$
$659$	−9.57068	−	16.5769i	−0.372821	−	0.645745i	−0.989998	+	0.141079i	$0.954943\pi$
$660$	−5.78807	−	24.1701i	−0.225300	−	0.940819i
$661$	−19.9536	+	34.5606i	−0.776104	+	1.34425i	0.158067	+	0.987428i	$0.449474\pi$
$661$	−19.9536	+	34.5606i	−0.776104	+	1.34425i	−0.934172	+	0.356824i	$0.883860\pi$
$662$	−20.6700	+	35.8016i	−0.803364	+	1.39147i
$663$	1.76940	+	7.38874i	0.0687178	+	0.286955i
$664$	−4.50000	−	7.79423i	−0.174634	−	0.302475i
$665$	0.679116			0.0263350
$666$	−1.96759	+	0.999697i	−0.0762425	+	0.0387375i
$667$	−5.72298			−0.221595
$668$	−13.3191	−	23.0693i	−0.515331	−	0.892579i
$669$	−14.3870	−	4.27061i	−0.556235	−	0.165111i
$670$	−11.8774	+	20.5723i	−0.458865	+	0.794778i
$671$	12.2029	−	21.1360i	0.471086	−	0.815945i
$672$	−2.25293	+	2.13550i	−0.0869087	+	0.0823787i
$673$	−11.8254	−	20.4822i	−0.455836	−	0.789532i	0.542899	−	0.839798i	$-0.317326\pi$
$673$	−11.8254	−	20.4822i	−0.455836	−	0.789532i	−0.998736	+	0.0502658i	$0.983993\pi$
$674$	12.3118			0.474233
$675$	−1.74293	+	4.89512i	−0.0670855	+	0.188413i
$676$	−48.6327			−1.87049
$677$	7.40157	+	12.8199i	0.284465	+	0.492709i	0.972479	−	0.232989i	$-0.0748506\pi$
$677$	7.40157	+	12.8199i	0.284465	+	0.492709i	−0.688014	+	0.725697i	$0.741517\pi$
$678$	24.6555	−	23.3704i	0.946889	−	0.897533i
$679$	−3.15044	+	5.45673i	−0.120903	+	0.209410i
$680$	9.68872	−	16.7813i	0.371545	−	0.643535i
$681$	−5.51414	−	1.63680i	−0.211302	−	0.0627223i
$682$	36.4677	+	63.1639i	1.39642	+	2.41867i
$683$	−4.95252			−0.189503			−0.0947515	−	0.995501i	$-0.530206\pi$
$683$	−4.95252			−0.189503			−0.0947515	+	0.995501i	$0.530206\pi$
$684$	−14.3492	−	9.34186i	−0.548654	−	0.357195i
$685$	5.67004			0.216641
$686$	−8.87743	−	15.3762i	−0.338942	−	0.587065i
$687$	−10.2101	−	42.6359i	−0.389540	−	1.62666i
$688$	−31.1938	+	54.0292i	−1.18925	+	2.05984i
$689$	−3.32088	+	5.75194i	−0.126516	+	0.219131i
$690$	4.18598	+	17.4800i	0.159358	+	0.665453i
$691$	9.60442	+	16.6353i	0.365369	+	0.632838i	0.988835	−	0.149012i	$-0.0476093\pi$
$691$	9.60442	+	16.6353i	0.365369	+	0.632838i	−0.623466	+	0.781851i	$0.714276\pi$
$692$	37.0957			1.41017
$693$	4.29261	+	2.79466i	0.163063	+	0.106160i
$694$	56.0011			2.12577
$695$	−4.00000	−	6.92820i	−0.151729	−	0.262802i
$696$	13.4335	+	3.98755i	0.509194	+	0.151148i
$697$	−18.8446	+	32.6398i	−0.713791	+	1.23632i
$698$	3.70012	−	6.40880i	0.140052	−	0.242577i
$699$	34.7362	−	32.9256i	1.31384	−	1.24536i
$700$	1.11076	+	1.92390i	0.0419829	+	0.0727165i
$701$	−29.3492			−1.10850			−0.554251	−	0.832349i	$-0.686995\pi$
$701$	−29.3492			−1.10850			−0.554251	+	0.832349i	$0.686995\pi$
$702$	11.1842	+	13.1407i	0.422120	+	0.495963i
$703$	−0.386505			−0.0145773
$704$	−5.46719	−	9.46945i	−0.206052	−	0.356893i
$705$	−6.11350	+	5.79483i	−0.230248	+	0.218246i
$706$	−23.6700	+	40.9977i	−0.890834	+	1.54297i
$707$	3.00000	−	5.19615i	0.112827	−	0.195421i
$708$	36.0757	+	10.7086i	1.35581	+	0.402455i
$709$	−19.3633	−	33.5382i	−0.727204	−	1.25955i	−0.958060	−	0.286566i	$-0.907486\pi$
$709$	−19.3633	−	33.5382i	−0.727204	−	1.25955i	0.230857	−	0.972988i	$-0.425847\pi$
$710$	22.6044			0.848329
$711$	21.5479	−	10.9481i	0.808108	−	0.410586i
$712$	−17.5051			−0.656030
$713$	−18.0288	−	31.2268i	−0.675184	−	1.16945i
$714$	1.73153	+	7.23058i	0.0648008	+	0.270598i
$715$	−2.19325	+	3.79882i	−0.0820230	+	0.142068i
$716$	2.30221	−	3.98755i	0.0860377	−	0.149022i
$717$	−1.69365	−	7.07243i	−0.0632506	−	0.264125i
$718$	40.0716	+	69.4061i	1.49546	+	2.59021i
$719$	−15.0848			−0.562569			−0.281284	−	0.959624i	$-0.590760\pi$
$719$	−15.0848			−0.562569			−0.281284	+	0.959624i	$0.590760\pi$
$720$	0.967190	−	18.0589i	0.0360450	−	0.673017i
$721$	−0.150442			−0.00560275
$722$	21.6910	+	37.5700i	0.807257	+	1.39821i
$723$	−5.98494	−	1.77655i	−0.222582	−	0.0660706i
$724$	27.3729	−	47.4112i	1.01731	−	1.76203i
$725$	0.693252	−	1.20075i	0.0257467	−	0.0445947i
$726$	0.0893579	−	0.0847002i	0.00331638	−	0.00314352i
$727$	−6.17277	−	10.6916i	−0.228936	−	0.396528i	0.728557	−	0.684985i	$-0.240191\pi$
$727$	−6.17277	−	10.6916i	−0.228936	−	0.396528i	−0.957493	+	0.288457i	$0.906858\pi$
$728$	3.96265			0.146866
$729$	−4.31542	+	26.6529i	−0.159830	+	0.987144i
$730$	15.2270			0.563576
$731$	17.1842	+	29.7639i	0.635580	+	1.10086i
$732$	39.9180	−	37.8373i	1.47541	−	1.39851i
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	−0.588177	−	0.808732i	$-0.700154\pi$
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	0.994471	+	0.105010i	$0.0334875\pi$
$734$	23.0661	−	39.9517i	0.851387	−	1.47465i
$735$	11.1842	+	3.31988i	0.412535	+	0.122456i
$736$	−7.19418	−	12.4607i	−0.265181	−	0.459307i
$737$	−31.3774			−1.15580
$738$	−4.57795	+	85.4775i	−0.168517	+	3.14647i
$739$	29.7266			1.09351			0.546755	−	0.837293i	$-0.315863\pi$
$739$	29.7266			1.09351			0.546755	+	0.837293i	$0.315863\pi$
$740$	−0.632168	−	1.09495i	−0.0232390	−	0.0402511i
$741$	0.703781	+	2.93888i	0.0258540	+	0.107962i
$742$	−3.24980	+	5.62882i	−0.119304	+	0.206640i
$743$	−24.1824	+	41.8851i	−0.887165	+	1.53662i	−0.0439537	+	0.999034i	$0.513995\pi$
$743$	−24.1824	+	41.8851i	−0.887165	+	1.53662i	−0.843212	+	0.537582i	$0.819338\pi$
$744$	20.5611	+	85.8599i	0.753806	+	3.14778i
$745$	−8.83049	−	15.2948i	−0.323524	−	0.560360i
$746$	−5.52787			−0.202390
$747$	−4.12530	+	2.09599i	−0.150937	+	0.0766883i
$748$	47.6519			1.74233
$749$	0.481327	+	0.833682i	0.0175873	+	0.0304621i
$750$	−4.17458	−	1.23917i	−0.152434	−	0.0452481i
$751$	15.9102	−	27.5573i	0.580573	−	1.00558i	−0.414838	−	0.909895i	$-0.636162\pi$
$751$	15.9102	−	27.5573i	0.580573	−	1.00558i	0.995411	−	0.0956869i	$-0.0305047\pi$
$752$	14.6586	−	25.3895i	0.534546	−	0.925860i
$753$	−8.64591	+	8.19524i	−0.315074	+	0.298651i
$754$	−2.30221	−	3.98755i	−0.0838416	−	0.145218i
$755$	1.26434			0.0460139
$756$	7.48173	+	8.79054i	0.272108	+	0.319709i
$757$	4.94531			0.179740			0.0898701	−	0.995953i	$-0.471355\pi$
$757$	4.94531			0.179740			0.0898701	+	0.995953i	$0.471355\pi$
$758$	−19.4485	−	33.6858i	−0.706402	−	1.22352i
$759$	−17.2311	+	16.3330i	−0.625450	+	0.592849i
$760$	3.85369	−	6.67479i	0.139788	−	0.242120i
$761$	−17.7125	+	30.6789i	−0.642076	+	1.11211i	0.342893	+	0.939375i	$0.388593\pi$
$761$	−17.7125	+	30.6789i	−0.642076	+	1.11211i	−0.984969	+	0.172734i	$0.944740\pi$
$762$	−74.6898	−	22.1707i	−2.70572	−	0.803160i
$763$	1.42618	+	2.47022i	0.0516313	+	0.0894281i
$764$	−73.1715			−2.64725
$765$	−8.34916	−	5.43563i	−0.301864	−	0.196525i
$766$	19.3774			0.700135
$767$	−3.32088	−	5.75194i	−0.119910	−	0.207691i
$768$	−12.8091	−	53.4887i	−0.462208

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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	45.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25707 - 2.17731i) q^{2} +(1.25707 - 1.19154i) q^{3} +(-2.16044 + 3.74200i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-4.17458 - 1.23917i) q^{6} +(0.257068 + 0.445256i) q^{7} +5.83502 q^{8} +(0.160442 - 2.99571i) q^{9} +O(q^{10})\)	\(q+(-1.25707 - 2.17731i) q^{2} +(1.25707 - 1.19154i) q^{3} +(-2.16044 + 3.74200i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-4.17458 - 1.23917i) q^{6} +(0.257068 + 0.445256i) q^{7} +5.83502 q^{8} +(0.160442 - 2.99571i) q^{9} +2.51414 q^{10} +(1.66044 + 2.87597i) q^{11} +(1.74293 + 7.27821i) q^{12} +(0.660442 - 1.14392i) q^{13} +(0.646305 - 1.11943i) q^{14} +(0.403374 + 1.68443i) q^{15} +(-3.01414 - 5.22064i) q^{16} -3.32088 q^{17} +(-6.72426 + 3.41648i) q^{18} -1.32088 q^{19} +(-2.16044 - 3.74200i) q^{20} +(0.853695 + 0.253408i) q^{21} +(4.17458 - 7.23058i) q^{22} +(-2.06382 + 3.57463i) q^{23} +(7.33502 - 6.95269i) q^{24} +(-0.500000 - 0.866025i) q^{25} -3.32088 q^{26} +(-3.36783 - 3.95698i) q^{27} -2.22153 q^{28} +(0.693252 + 1.20075i) q^{29} +(3.16044 - 2.99571i) q^{30} +(-4.36783 + 7.56531i) q^{31} +(-1.74293 + 3.01885i) q^{32} +(5.51414 + 1.63680i) q^{33} +(4.17458 + 7.23058i) q^{34} -0.514137 q^{35} +(10.8633 + 7.07243i) q^{36} +0.292611 q^{37} +(1.66044 + 2.87597i) q^{38} +(-0.532810 - 2.22493i) q^{39} +(-2.91751 + 5.05328i) q^{40} +(5.67458 - 9.82866i) q^{41} +(-0.521405 - 2.17731i) q^{42} +(-5.17458 - 8.96263i) q^{43} -14.3492 q^{44} +(2.51414 + 1.63680i) q^{45} +10.3774 q^{46} +(2.43165 + 4.21174i) q^{47} +(-10.0096 - 2.97122i) q^{48} +(3.36783 - 5.83326i) q^{49} +(-1.25707 + 2.17731i) q^{50} +(-4.17458 + 3.95698i) q^{51} +(2.85369 + 4.94274i) q^{52} -5.02827 q^{53} +(-4.38197 + 12.3070i) q^{54} -3.32088 q^{55} +(1.50000 + 2.59808i) q^{56} +(-1.66044 + 1.57389i) q^{57} +(1.74293 - 3.01885i) q^{58} +(2.51414 - 4.35461i) q^{59} +(-7.17458 - 2.12968i) q^{60} +(-3.67458 - 6.36456i) q^{61} +21.9627 q^{62} +(1.37510 - 0.698664i) q^{63} -3.29261 q^{64} +(0.660442 + 1.14392i) q^{65} +(-3.36783 - 14.0635i) q^{66} +(-4.72426 + 8.18266i) q^{67} +(7.17458 - 12.4267i) q^{68} +(1.66498 + 6.95269i) q^{69} +(0.646305 + 1.11943i) q^{70} +8.99093 q^{71} +(0.936184 - 17.4800i) q^{72} +6.05655 q^{73} +(-0.367832 - 0.637103i) q^{74} +(-1.66044 - 0.492881i) q^{75} +(2.85369 - 4.94274i) q^{76} +(-0.853695 + 1.47864i) q^{77} +(-4.17458 + 3.95698i) q^{78} +(4.02827 + 6.97717i) q^{79} +6.02827 q^{80} +(-8.94852 - 0.961276i) q^{81} -28.5333 q^{82} +(-0.771205 - 1.33577i) q^{83} +(-2.79261 + 2.64705i) q^{84} +(1.66044 - 2.87597i) q^{85} +(-13.0096 + 22.5333i) q^{86} +(2.30221 + 0.683382i) q^{87} +(9.68872 + 16.7813i) q^{88} -3.00000 q^{89} +(0.403374 - 7.53162i) q^{90} +0.679116 q^{91} +(-8.91751 - 15.4456i) q^{92} +(3.52374 + 14.7146i) q^{93} +(6.11350 - 10.5889i) q^{94} +(0.660442 - 1.14392i) q^{95} +(1.40611 + 5.87168i) q^{96} +(6.12763 + 10.6134i) q^{97} -16.9344 q^{98} +(8.88197 - 4.51277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} + q^{3} - 5 q^{4} - 3 q^{5} - 4 q^{6} - 5 q^{7} + 6 q^{8} - 7 q^{9}+O(q^{10}) \) 6 * q - q^2 + q^3 - 5 * q^4 - 3 * q^5 - 4 * q^6 - 5 * q^7 + 6 * q^8 - 7 * q^9	\( 6 q - q^{2} + q^{3} - 5 q^{4} - 3 q^{5} - 4 q^{6} - 5 q^{7} + 6 q^{8} - 7 q^{9} + 2 q^{10} + 2 q^{11} + 17 q^{12} - 4 q^{13} + 9 q^{14} + q^{15} - 5 q^{16} - 4 q^{17} - 23 q^{18} + 8 q^{19} - 5 q^{20} + 4 q^{22} - 3 q^{23} + 15 q^{24} - 3 q^{25} - 4 q^{26} - 2 q^{27} + 10 q^{28} + 7 q^{29} + 11 q^{30} - 8 q^{31} - 17 q^{32} + 20 q^{33} + 4 q^{34} + 10 q^{35} + 10 q^{36} + 12 q^{37} + 2 q^{38} - 14 q^{39} - 3 q^{40} + 13 q^{41} - 33 q^{42} - 10 q^{43} - 44 q^{44} + 2 q^{45} - 6 q^{46} - 13 q^{47} - 10 q^{48} + 2 q^{49} - q^{50} - 4 q^{51} + 12 q^{52} - 4 q^{53} + 5 q^{54} - 4 q^{55} + 9 q^{56} - 2 q^{57} + 17 q^{58} + 2 q^{59} - 22 q^{60} - q^{61} + 84 q^{62} + 33 q^{63} - 30 q^{64} - 4 q^{65} - 2 q^{66} - 11 q^{67} + 22 q^{68} + 39 q^{69} + 9 q^{70} - 20 q^{71} + 15 q^{72} - 16 q^{73} + 16 q^{74} - 2 q^{75} + 12 q^{76} - 4 q^{78} - 2 q^{79} + 10 q^{80} - 19 q^{81} - 58 q^{82} + 15 q^{83} - 27 q^{84} + 2 q^{85} - 28 q^{86} - 26 q^{87} + 24 q^{88} - 18 q^{89} + q^{90} + 20 q^{91} - 39 q^{92} - 42 q^{93} + 31 q^{94} - 4 q^{95} + 13 q^{96} + 18 q^{97} - 80 q^{98} + 22 q^{99}+O(q^{100}) \) 6 * q - q^2 + q^3 - 5 * q^4 - 3 * q^5 - 4 * q^6 - 5 * q^7 + 6 * q^8 - 7 * q^9 + 2 * q^10 + 2 * q^11 + 17 * q^12 - 4 * q^13 + 9 * q^14 + q^15 - 5 * q^16 - 4 * q^17 - 23 * q^18 + 8 * q^19 - 5 * q^20 + 4 * q^22 - 3 * q^23 + 15 * q^24 - 3 * q^25 - 4 * q^26 - 2 * q^27 + 10 * q^28 + 7 * q^29 + 11 * q^30 - 8 * q^31 - 17 * q^32 + 20 * q^33 + 4 * q^34 + 10 * q^35 + 10 * q^36 + 12 * q^37 + 2 * q^38 - 14 * q^39 - 3 * q^40 + 13 * q^41 - 33 * q^42 - 10 * q^43 - 44 * q^44 + 2 * q^45 - 6 * q^46 - 13 * q^47 - 10 * q^48 + 2 * q^49 - q^50 - 4 * q^51 + 12 * q^52 - 4 * q^53 + 5 * q^54 - 4 * q^55 + 9 * q^56 - 2 * q^57 + 17 * q^58 + 2 * q^59 - 22 * q^60 - q^61 + 84 * q^62 + 33 * q^63 - 30 * q^64 - 4 * q^65 - 2 * q^66 - 11 * q^67 + 22 * q^68 + 39 * q^69 + 9 * q^70 - 20 * q^71 + 15 * q^72 - 16 * q^73 + 16 * q^74 - 2 * q^75 + 12 * q^76 - 4 * q^78 - 2 * q^79 + 10 * q^80 - 19 * q^81 - 58 * q^82 + 15 * q^83 - 27 * q^84 + 2 * q^85 - 28 * q^86 - 26 * q^87 + 24 * q^88 - 18 * q^89 + q^90 + 20 * q^91 - 39 * q^92 - 42 * q^93 + 31 * q^94 - 4 * q^95 + 13 * q^96 + 18 * q^97 - 80 * q^98 + 22 * q^99

Introduction

L-functions

Modular forms

Varieties

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