LMFDB - Embedded newform 315.2.l.c.121.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(121,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("315.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.l (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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.16
Character	$\chi$	$=$	315.121
Dual form			315.2.l.c.151.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.08660 q^{2} +(0.878572 + 1.49269i) q^{3} +2.35391 q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.83323 + 3.11464i) q^{6} +(-0.122839 + 2.64290i) q^{7} +0.738471 q^{8} +(-1.45622 + 2.62286i) q^{9} +O(q^{10})$	\(q+2.08660 q^{2} +(0.878572 + 1.49269i) q^{3} +2.35391 q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.83323 + 3.11464i) q^{6} +(-0.122839 + 2.64290i) q^{7} +0.738471 q^{8} +(-1.45622 + 2.62286i) q^{9} +(-1.04330 - 1.80705i) q^{10} +(0.00772080 - 0.0133728i) q^{11} +(2.06808 + 3.51365i) q^{12} +(3.01043 - 5.21422i) q^{13} +(-0.256315 + 5.51468i) q^{14} +(0.853418 - 1.50721i) q^{15} -3.16693 q^{16} +(-0.453816 - 0.786032i) q^{17} +(-3.03856 + 5.47288i) q^{18} +(3.94407 - 6.83134i) q^{19} +(-1.17696 - 2.03855i) q^{20} +(-4.05294 + 2.13862i) q^{21} +(0.0161102 - 0.0279038i) q^{22} +(-1.66499 - 2.88384i) q^{23} +(0.648800 + 1.10230i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(6.28157 - 10.8800i) q^{26} +(-5.19451 + 0.130693i) q^{27} +(-0.289151 + 6.22115i) q^{28} +(1.08973 + 1.88747i) q^{29} +(1.78074 - 3.14495i) q^{30} +1.22138 q^{31} -8.08506 q^{32} +(0.0267447 - 0.000224255i) q^{33} +(-0.946933 - 1.64014i) q^{34} +(2.35024 - 1.21507i) q^{35} +(-3.42782 + 6.17399i) q^{36} +(-4.79552 + 8.30608i) q^{37} +(8.22971 - 14.2543i) q^{38} +(10.4281 - 0.0874396i) q^{39} +(-0.369235 - 0.639534i) q^{40} +(-5.46963 + 9.47367i) q^{41} +(-8.45687 + 4.46244i) q^{42} +(0.234772 + 0.406637i) q^{43} +(0.0181741 - 0.0314784i) q^{44} +(2.99958 - 0.0503066i) q^{45} +(-3.47416 - 6.01743i) q^{46} -5.06838 q^{47} +(-2.78237 - 4.72723i) q^{48} +(-6.96982 - 0.649300i) q^{49} +(-1.04330 + 1.80705i) q^{50} +(0.774589 - 1.36799i) q^{51} +(7.08629 - 12.2738i) q^{52} +(-1.39434 - 2.41507i) q^{53} +(-10.8389 + 0.272704i) q^{54} -0.0154416 q^{55} +(-0.0907127 + 1.95170i) q^{56} +(13.6622 - 0.114558i) q^{57} +(2.27384 + 3.93840i) q^{58} +5.21289 q^{59} +(2.00887 - 3.54783i) q^{60} +8.25641 q^{61} +2.54854 q^{62} +(-6.75308 - 4.17084i) q^{63} -10.5365 q^{64} -6.02086 q^{65} +(0.0558056 - 0.000467931i) q^{66} +5.32419 q^{67} +(-1.06824 - 1.85025i) q^{68} +(2.84186 - 5.01896i) q^{69} +(4.90401 - 2.53536i) q^{70} +4.77171 q^{71} +(-1.07538 + 1.93691i) q^{72} +(-0.466621 - 0.808211i) q^{73} +(-10.0063 + 17.3315i) q^{74} +(-1.73199 + 0.0145228i) q^{75} +(9.28400 - 16.0804i) q^{76} +(0.0343946 + 0.0220480i) q^{77} +(21.7592 - 0.182452i) q^{78} +7.02463 q^{79} +(1.58346 + 2.74264i) q^{80} +(-4.75883 - 7.63895i) q^{81} +(-11.4129 + 19.7678i) q^{82} +(-8.41010 - 14.5667i) q^{83} +(-9.54026 + 5.03411i) q^{84} +(-0.453816 + 0.786032i) q^{85} +(0.489876 + 0.848490i) q^{86} +(-1.85999 + 3.28491i) q^{87} +(0.00570158 - 0.00987543i) q^{88} +(-6.33695 + 10.9759i) q^{89} +(6.25893 - 0.104970i) q^{90} +(13.4109 + 8.59677i) q^{91} +(-3.91923 - 6.78830i) q^{92} +(1.07307 + 1.82314i) q^{93} -10.5757 q^{94} -7.88815 q^{95} +(-7.10331 - 12.0685i) q^{96} +(3.11544 + 5.39610i) q^{97} +(-14.5432 - 1.35483i) q^{98} +(0.0238319 + 0.0397244i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9}+O(q^{10}) $ 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9} + q^{11} + 8 q^{12} + 2 q^{13} + 9 q^{14} - q^{15} + 60 q^{16} - 5 q^{17} - 21 q^{18} - 2 q^{19} - 22 q^{20} - 23 q^{21} - 19 q^{22} - 3 q^{23} - 32 q^{24} - 18 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} + 2 q^{30} - 20 q^{32} - 35 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} - 22 q^{38} + 7 q^{39} - 4 q^{41} + 57 q^{42} - 29 q^{43} - 7 q^{44} + 6 q^{45} - 24 q^{46} + 46 q^{47} - 19 q^{48} - 7 q^{49} + 42 q^{51} - 7 q^{52} + 21 q^{54} - 2 q^{55} - 12 q^{56} + 21 q^{57} - 20 q^{58} + 10 q^{59} - 13 q^{60} + 6 q^{61} - 12 q^{62} + 2 q^{63} + 128 q^{64} - 4 q^{65} - 12 q^{66} + 70 q^{67} - 17 q^{68} - 50 q^{69} - 3 q^{70} + 24 q^{71} - 10 q^{72} - 10 q^{73} + 22 q^{74} + 2 q^{75} + 10 q^{76} + 35 q^{77} + 66 q^{78} + 56 q^{79} - 30 q^{80} - 49 q^{81} - 8 q^{82} - 22 q^{83} - 86 q^{84} - 5 q^{85} + 19 q^{86} - 42 q^{87} - 50 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - q^{93} + 4 q^{94} + 4 q^{95} - 179 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9 + q^11 + 8 * q^12 + 2 * q^13 + 9 * q^14 - q^15 + 60 * q^16 - 5 * q^17 - 21 * q^18 - 2 * q^19 - 22 * q^20 - 23 * q^21 - 19 * q^22 - 3 * q^23 - 32 * q^24 - 18 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 + 2 * q^30 - 20 * q^32 - 35 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 - 22 * q^38 + 7 * q^39 - 4 * q^41 + 57 * q^42 - 29 * q^43 - 7 * q^44 + 6 * q^45 - 24 * q^46 + 46 * q^47 - 19 * q^48 - 7 * q^49 + 42 * q^51 - 7 * q^52 + 21 * q^54 - 2 * q^55 - 12 * q^56 + 21 * q^57 - 20 * q^58 + 10 * q^59 - 13 * q^60 + 6 * q^61 - 12 * q^62 + 2 * q^63 + 128 * q^64 - 4 * q^65 - 12 * q^66 + 70 * q^67 - 17 * q^68 - 50 * q^69 - 3 * q^70 + 24 * q^71 - 10 * q^72 - 10 * q^73 + 22 * q^74 + 2 * q^75 + 10 * q^76 + 35 * q^77 + 66 * q^78 + 56 * q^79 - 30 * q^80 - 49 * q^81 - 8 * q^82 - 22 * q^83 - 86 * q^84 - 5 * q^85 + 19 * q^86 - 42 * q^87 - 50 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - q^93 + 4 * q^94 + 4 * q^95 - 179 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	2.08660			1.47545			0.737725	−	0.675101i	$-0.235900\pi$
$2$	2.08660			1.47545			0.737725	+	0.675101i	$0.235900\pi$
$3$	0.878572	+	1.49269i	0.507244	+	0.861803i
$3$	0.878572	+	1.49269i	0.507244	+	0.861803i
$4$	2.35391			1.17696
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	1.83323	+	3.11464i	0.748413	+	1.27155i
$7$	−0.122839	+	2.64290i	−0.0464286	+	0.998922i
$7$	−0.122839	+	2.64290i	−0.0464286	+	0.998922i
$8$	0.738471			0.261089
$9$	−1.45622	+	2.62286i	−0.485407	+	0.874288i
$10$	−1.04330	−	1.80705i	−0.329921	−	0.571440i
$11$	0.00772080	−	0.0133728i	0.00232791	−	0.00403206i	−0.864859	−	0.502015i	$-0.832592\pi$
$11$	0.00772080	−	0.0133728i	0.00232791	−	0.00403206i	0.867187	+	0.497983i	$0.165926\pi$
$12$	2.06808	+	3.51365i	0.597003	+	1.01430i
$13$	3.01043	−	5.21422i	0.834943	−	1.44616i	−0.0591331	−	0.998250i	$-0.518834\pi$
$13$	3.01043	−	5.21422i	0.834943	−	1.44616i	0.894077	−	0.447914i	$-0.147833\pi$
$14$	−0.256315	+	5.51468i	−0.0685032	+	1.47386i
$15$	0.853418	−	1.50721i	0.220352	−	0.389160i
$16$	−3.16693			−0.791732
$17$	−0.453816	−	0.786032i	−0.110067	−	0.190641i	0.805730	−	0.592283i	$-0.201773\pi$
$17$	−0.453816	−	0.786032i	−0.110067	−	0.190641i	−0.915797	+	0.401642i	$0.868440\pi$
$18$	−3.03856	+	5.47288i	−0.716195	+	1.28997i
$19$	3.94407	−	6.83134i	0.904833	−	1.56722i	0.0836906	−	0.996492i	$-0.473329\pi$
$19$	3.94407	−	6.83134i	0.904833	−	1.56722i	0.821142	−	0.570724i	$-0.193337\pi$
$20$	−1.17696	−	2.03855i	−0.263175	−	0.455833i
$21$	−4.05294	+	2.13862i	−0.884424	+	0.466684i
$22$	0.0161102	−	0.0279038i	0.00343472	−	0.00594910i
$23$	−1.66499	−	2.88384i	−0.347173	−	0.601322i	0.638573	−	0.769561i	$-0.279525\pi$
$23$	−1.66499	−	2.88384i	−0.347173	−	0.601322i	−0.985746	+	0.168240i	$0.946192\pi$
$24$	0.648800	+	1.10230i	0.132436	+	0.225007i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	6.28157	−	10.8800i	1.23192	−	2.13374i
$27$	−5.19451	+	0.130693i	−0.999684	+	0.0251518i
$28$	−0.289151	+	6.22115i	−0.0546444	+	1.17569i
$29$	1.08973	+	1.88747i	0.202358	+	0.350495i	0.949288	−	0.314408i	$-0.101806\pi$
$29$	1.08973	+	1.88747i	0.202358	+	0.350495i	−0.746930	+	0.664903i	$0.768473\pi$
$30$	1.78074	−	3.14495i	0.325118	−	0.574186i
$31$	1.22138			0.219367			0.109684	−	0.993967i	$-0.465016\pi$
$31$	1.22138			0.219367			0.109684	+	0.993967i	$0.465016\pi$
$32$	−8.08506			−1.42925
$33$	0.0267447		0.000224255i	0.00465565		3.90378e-5i
$34$	−0.946933	−	1.64014i	−0.162398	−	0.281281i
$35$	2.35024	−	1.21507i	0.397262	−	0.205384i
$36$	−3.42782	+	6.17399i	−0.571303	+	1.02900i
$37$	−4.79552	+	8.30608i	−0.788378	+	1.36551i	0.138581	+	0.990351i	$0.455746\pi$
$37$	−4.79552	+	8.30608i	−0.788378	+	1.36551i	−0.926960	+	0.375160i	$0.877588\pi$
$38$	8.22971	−	14.2543i	1.33504	−	2.31235i
$39$	10.4281	−	0.0874396i	1.66983	−	0.0140015i
$40$	−0.369235	−	0.639534i	−0.0583812	−	0.101119i
$41$	−5.46963	+	9.47367i	−0.854212	+	1.47954i	0.0231614	+	0.999732i	$0.492627\pi$
$41$	−5.46963	+	9.47367i	−0.854212	+	1.47954i	−0.877374	+	0.479808i	$0.840706\pi$
$42$	−8.45687	+	4.46244i	−1.30492	+	0.688570i
$43$	0.234772	+	0.406637i	0.0358024	+	0.0620116i	0.883371	−	0.468674i	$-0.155268\pi$
$43$	0.234772	+	0.406637i	0.0358024	+	0.0620116i	−0.847569	+	0.530685i	$0.821935\pi$
$44$	0.0181741	−	0.0314784i	0.00273984	−	0.00474555i
$45$	2.99958	−	0.0503066i	0.447151	−	0.00749926i
$46$	−3.47416	−	6.01743i	−0.512237	−	0.887221i
$47$	−5.06838			−0.739299			−0.369649	−	0.929171i	$-0.620522\pi$
$47$	−5.06838			−0.739299			−0.369649	+	0.929171i	$0.620522\pi$
$48$	−2.78237	−	4.72723i	−0.401601	−	0.682316i
$49$	−6.96982	−	0.649300i	−0.995689	−	0.0927571i
$50$	−1.04330	+	1.80705i	−0.147545	+	0.255556i
$51$	0.774589	−	1.36799i	0.108464	−	0.191557i
$52$	7.08629	−	12.2738i	0.982691	−	1.70207i
$53$	−1.39434	−	2.41507i	−0.191527	−	0.331735i	0.754229	−	0.656611i	$-0.228011\pi$
$53$	−1.39434	−	2.41507i	−0.191527	−	0.331735i	−0.945757	+	0.324876i	$0.894677\pi$
$54$	−10.8389	+	0.272704i	−1.47498	+	0.0371103i
$55$	−0.0154416			−0.00208215
$56$	−0.0907127	+	1.95170i	−0.0121220	+	0.260807i
$57$	13.6622	−	0.114558i	1.80960	−	0.0151735i
$58$	2.27384	+	3.93840i	0.298570	+	0.517138i
$59$	5.21289			0.678661			0.339330	−	0.940667i	$-0.389800\pi$
$59$	5.21289			0.678661			0.339330	+	0.940667i	$0.389800\pi$
$60$	2.00887	−	3.54783i	0.259344	−	0.458023i
$61$	8.25641			1.05712			0.528562	−	0.848894i	$-0.322731\pi$
$61$	8.25641			1.05712			0.528562	+	0.848894i	$0.322731\pi$
$62$	2.54854			0.323665
$63$	−6.75308	−	4.17084i	−0.850808	−	0.525476i
$64$	−10.5365			−1.31706
$65$	−6.02086			−0.746796
$66$	0.0558056		0.000467931i	0.00686919		5.75983e-5i
$67$	5.32419			0.650454			0.325227	−	0.945636i	$-0.394559\pi$
$67$	5.32419			0.650454			0.325227	+	0.945636i	$0.394559\pi$
$68$	−1.06824	−	1.85025i	−0.129543	−	0.224376i
$69$	2.84186	−	5.01896i	0.342119	−	0.604212i
$70$	4.90401	−	2.53536i	0.586141	−	0.303034i
$71$	4.77171			0.566298			0.283149	−	0.959076i	$-0.408621\pi$
$71$	4.77171			0.566298			0.283149	+	0.959076i	$0.408621\pi$
$72$	−1.07538	+	1.93691i	−0.126734	+	0.228267i
$73$	−0.466621	−	0.808211i	−0.0546138	−	0.0945939i	0.837426	−	0.546551i	$-0.184059\pi$
$73$	−0.466621	−	0.808211i	−0.0546138	−	0.0945939i	−0.892040	+	0.451957i	$0.850726\pi$
$74$	−10.0063	+	17.3315i	−1.16321	+	2.01475i
$75$	−1.73199	+	0.0145228i	−0.199993	+	0.00167695i
$76$	9.28400	−	16.0804i	1.06495	−	1.84454i
$77$	0.0343946	+	0.0220480i	0.00391963	+	0.00251260i
$78$	21.7592	−	0.182452i	2.46375	−	0.0206586i
$79$	7.02463			0.790333			0.395166	−	0.918610i	$-0.370687\pi$
$79$	7.02463			0.790333			0.395166	+	0.918610i	$0.370687\pi$
$80$	1.58346	+	2.74264i	0.177037	+	0.306636i
$81$	−4.75883	−	7.63895i	−0.528759	−	0.848772i
$82$	−11.4129	+	19.7678i	−1.26035	+	2.18299i
$83$	−8.41010	−	14.5667i	−0.923128	−	1.59890i	−0.794545	−	0.607206i	$-0.792290\pi$
$83$	−8.41010	−	14.5667i	−0.923128	−	1.59890i	−0.128583	−	0.991699i	$-0.541043\pi$
$84$	−9.54026	+	5.03411i	−1.04093	+	0.549267i
$85$	−0.453816	+	0.786032i	−0.0492232	+	0.0852571i
$86$	0.489876	+	0.848490i	0.0528247	+	0.0914950i
$87$	−1.85999	+	3.28491i	−0.199412	+	0.352179i
$88$	0.00570158	−	0.00987543i	0.000607791	−	0.00105272i
$89$	−6.33695	+	10.9759i	−0.671716	+	1.16345i	0.305701	+	0.952127i	$0.401109\pi$
$89$	−6.33695	+	10.9759i	−0.671716	+	1.16345i	−0.977417	+	0.211319i	$0.932224\pi$
$90$	6.25893	−	0.104970i	0.659749	−	0.0110648i
$91$	13.4109	+	8.59677i	1.40584	+	0.901186i
$92$	−3.91923	−	6.78830i	−0.408608	−	0.707729i
$93$	1.07307	+	1.82314i	0.111273	+	0.189051i
$94$	−10.5757			−1.09080
$95$	−7.88815			−0.809307
$96$	−7.10331	−	12.0685i	−0.724978	−	1.23173i
$97$	3.11544	+	5.39610i	0.316325	+	0.547891i	0.979718	−	0.200380i	$-0.0642177\pi$
$97$	3.11544	+	5.39610i	0.316325	+	0.547891i	−0.663393	+	0.748271i	$0.730884\pi$
$98$	−14.5432	−	1.35483i	−1.46909	−	0.136859i
$99$	0.0238319	+	0.0397244i	0.00239519	+	0.00399245i
$100$	−1.17696	+	2.03855i	−0.117696	+	0.203855i
$101$	5.92287	−	10.2587i	0.589348	−	1.02078i	−0.404970	−	0.914330i	$-0.632718\pi$
$101$	5.92287	−	10.2587i	0.589348	−	1.02078i	0.994318	−	0.106451i	$-0.0339486\pi$
$102$	1.61626	−	2.85445i	0.160034	−	0.282633i
$103$	6.87809	+	11.9132i	0.677718	+	1.17384i	0.975666	+	0.219260i	$0.0703644\pi$
$103$	6.87809	+	11.9132i	0.677718	+	1.17384i	−0.297948	+	0.954582i	$0.596302\pi$
$104$	2.22311	−	3.85055i	0.217994	−	0.377577i
$105$	3.87857	+	2.44064i	0.378509	+	0.238182i
$106$	−2.90944	−	5.03929i	−0.282589	−	0.489459i
$107$	−6.15963	+	10.6688i	−0.595474	+	1.03139i	0.398006	+	0.917383i	$0.369702\pi$
$107$	−6.15963	+	10.6688i	−0.595474	+	1.03139i	−0.993480	+	0.114009i	$0.963631\pi$
$108$	−12.2274	+	0.307639i	−1.17658	+	0.0296026i
$109$	−2.57892	−	4.46682i	−0.247015	−	0.427843i	0.715681	−	0.698427i	$-0.246117\pi$
$109$	−2.57892	−	4.46682i	−0.247015	−	0.427843i	−0.962696	+	0.270584i	$0.912783\pi$
$110$	−0.0322205			−0.00307210
$111$	−16.6116	+	0.139288i	−1.57670	+	0.0132207i
$112$	0.389021	−	8.36986i	0.0367590	−	0.790878i
$113$	−6.84910	+	11.8630i	−0.644310	+	1.11598i	0.340151	+	0.940371i	$0.389522\pi$
$113$	−6.84910	+	11.8630i	−0.644310	+	1.11598i	−0.984461	+	0.175606i	$0.943812\pi$
$114$	28.5076	−	0.239037i	2.66998	−	0.0223878i
$115$	−1.66499	+	2.88384i	−0.155261	+	0.268919i
$116$	2.56513	+	4.44294i	0.238167	+	0.412517i
$117$	9.29233	+	15.4890i	0.859077	+	1.43196i
$118$	10.8772			1.00133
$119$	2.13315	−	1.10283i	0.195545	−	0.101097i
$120$	0.630224	−	1.11303i	0.0575313	−	0.101605i
$121$	5.49988	+	9.52607i	0.499989	+	0.866007i
$122$	17.2278			1.55974
$123$	−18.9467	+	0.158868i	−1.70836	+	0.0143247i
$124$	2.87503			0.258185
$125$	1.00000			0.0894427
$126$	−14.0910	−	8.70288i	−1.25533	−	0.775314i
$127$	11.6693			1.03548			0.517742	−	0.855537i	$-0.326773\pi$
$127$	11.6693			1.03548			0.517742	+	0.855537i	$0.326773\pi$
$128$	−5.81527			−0.514002
$129$	−0.400717	+	0.707701i	−0.0352812	+	0.0623096i
$130$	−12.5631			−1.10186
$131$	−8.01997	−	13.8910i	−0.700708	−	1.21366i	−0.968218	−	0.250107i	$-0.919534\pi$
$131$	−8.01997	−	13.8910i	−0.700708	−	1.21366i	0.267510	−	0.963555i	$-0.413799\pi$
$132$	0.0629546		0.000527876i	0.00547950		4.59457e-5i
$133$	17.5700	+	11.2629i	1.52352	+	0.976620i
$134$	11.1095			0.959712
$135$	2.71044	+	4.43323i	0.233277	+	0.381552i
$136$	−0.335130	−	0.580462i	−0.0287371	−	0.0497742i
$137$	−2.87640	+	4.98207i	−0.245747	+	0.425647i	−0.962341	−	0.271843i	$-0.912367\pi$
$137$	−2.87640	+	4.98207i	−0.245747	+	0.425647i	0.716594	+	0.697490i	$0.245700\pi$
$138$	5.92982	−	10.4726i	0.504780	−	0.891485i
$139$	1.48176	−	2.56649i	0.125681	−	0.217686i	−0.796318	−	0.604879i	$-0.793222\pi$
$139$	1.48176	−	2.56649i	0.125681	−	0.217686i	0.921999	+	0.387192i	$0.126555\pi$
$140$	5.53225	−	2.86016i	0.467560	−	0.241728i
$141$	−4.45294	−	7.56550i	−0.375005	−	0.637130i
$142$	9.95667			0.835545
$143$	−0.0464859	−	0.0805159i	−0.00388734	−	0.00673308i
$144$	4.61175	−	8.30642i	0.384312	−	0.692201i
$145$	1.08973	−	1.88747i	0.0904973	−	0.156746i
$146$	−0.973652	−	1.68641i	−0.0805800	−	0.139569i
$147$	−5.15429	−	10.9742i	−0.425119	−	0.905138i
$148$	−11.2882	+	19.5518i	−0.927886	+	1.60715i
$149$	−4.04200	−	7.00095i	−0.331133	−	0.573540i	0.651601	−	0.758562i	$-0.274098\pi$
$149$	−4.04200	−	7.00095i	−0.331133	−	0.573540i	−0.982734	+	0.185022i	$0.940764\pi$
$150$	−3.61397	+	0.0303033i	−0.295080	+	0.00247425i
$151$	4.24270	−	7.34857i	0.345266	−	0.598018i	−0.640136	−	0.768262i	$-0.721122\pi$
$151$	4.24270	−	7.34857i	0.345266	−	0.598018i	0.985402	+	0.170243i	$0.0544554\pi$
$152$	2.91258	−	5.04474i	0.236242	−	0.409182i
$153$	2.72251	−	0.0456599i	0.220102	−	0.00369138i
$154$	0.0717678	+	0.0460054i	0.00578322	+	0.00370722i
$155$	−0.610692	−	1.05775i	−0.0490520	−	0.0849605i
$156$	24.5468	−	0.205825i	1.96531	−	0.0164792i
$157$	−17.2141			−1.37384			−0.686918	−	0.726735i	$-0.741037\pi$
$157$	−17.2141			−1.37384			−0.686918	+	0.726735i	$0.741037\pi$
$158$	14.6576			1.16610
$159$	2.37991	−	4.20313i	0.188739	−	0.333330i
$160$	4.04253	+	7.00187i	0.319590	+	0.553546i
$161$	7.82622	−	4.04614i	0.616792	−	0.318880i
$162$	−9.92979	−	15.9394i	−0.780158	−	1.25232i
$163$	−0.597394	+	1.03472i	−0.0467915	+	0.0810453i	−0.888473	−	0.458930i	$-0.848233\pi$
$163$	−0.597394	+	1.03472i	−0.0467915	+	0.0810453i	0.841681	+	0.539975i	$0.181566\pi$
$164$	−12.8750	+	22.3002i	−1.00537	+	1.74135i
$165$	−0.0135666	−	0.0230495i	−0.00105616	−	0.00179440i
$166$	−17.5485	−	30.3949i	−1.36203	−	2.35910i
$167$	−4.13064	+	7.15448i	−0.319638	+	0.553630i	−0.980413	−	0.196955i	$-0.936895\pi$
$167$	−4.13064	+	7.15448i	−0.319638	+	0.553630i	0.660774	+	0.750585i	$0.270228\pi$
$168$	−2.99298	+	1.57931i	−0.230913	+	0.121846i
$169$	−11.6254	−	20.1358i	−0.894261	−	1.54891i
$170$	−0.946933	+	1.64014i	−0.0726265	+	0.125793i
$171$	12.1742	+	20.2927i	0.930986	+	1.55182i
$172$	0.552632	+	0.957187i	0.0421378	+	0.0729848i
$173$	14.0390			1.06737			0.533683	−	0.845685i	$-0.320808\pi$
$173$	14.0390			1.06737			0.533683	+	0.845685i	$0.320808\pi$
$174$	−3.88107	+	6.85430i	−0.294223	+	0.519623i
$175$	−2.22740	−	1.42783i	−0.168375	−	0.107934i
$176$	−0.0244512	+	0.0423507i	−0.00184308	+	0.00319231i
$177$	4.57990	+	7.78121i	0.344247	+	0.584872i
$178$	−13.2227	+	22.9024i	−0.991084	+	1.71661i
$179$	−3.95787	−	6.85523i	−0.295825	−	0.512384i	0.679352	−	0.733813i	$-0.262261\pi$
$179$	−3.95787	−	6.85523i	−0.295825	−	0.512384i	−0.975176	+	0.221429i	$0.928928\pi$
$180$	7.06074	−	0.118417i	0.526276	−	0.00882630i
$181$	5.55480			0.412885			0.206442	−	0.978459i	$-0.433811\pi$
$181$	5.55480			0.412885			0.206442	+	0.978459i	$0.433811\pi$
$182$	27.9831	+	17.9380i	2.07425	+	1.32966i
$183$	7.25385	+	12.3242i	0.536220	+	0.911033i
$184$	−1.22954	−	2.12963i	−0.0906431	−	0.156998i
$185$	9.59104			0.705147
$186$	2.23908	+	3.80418i	0.164177	+	0.278936i
$187$	−0.0140153			−0.00102490
$188$	−11.9305			−0.870122
$189$	0.292679	−	13.7446i	0.0212892	−	0.999773i
$190$	−16.4594			−1.19409
$191$	1.34265			0.0971507			0.0485753	−	0.998820i	$-0.484532\pi$
$191$	1.34265			0.0971507			0.0485753	+	0.998820i	$0.484532\pi$
$192$	−9.25703	−	15.7276i	−0.668069	−	1.13504i
$193$	−12.4554			−0.896561			−0.448281	−	0.893893i	$-0.647964\pi$
$193$	−12.4554			−0.896561			−0.448281	+	0.893893i	$0.647964\pi$
$194$	6.50068	+	11.2595i	0.466722	+	0.808386i
$195$	−5.28976	−	8.98726i	−0.378808	−	0.643591i
$196$	−16.4063	−	1.52839i	−1.17188	−	0.109171i
$197$	13.6680			0.973808			0.486904	−	0.873456i	$-0.338126\pi$
$197$	13.6680			0.973808			0.486904	+	0.873456i	$0.338126\pi$
$198$	0.0497277	+	0.0828891i	0.00353399	+	0.00589067i
$199$	−8.61705	−	14.9252i	−0.610846	−	1.05802i	−0.991098	−	0.133134i	$-0.957496\pi$
$199$	−8.61705	−	14.9252i	−0.610846	−	1.05802i	0.380252	−	0.924883i	$-0.375837\pi$
$200$	−0.369235	+	0.639534i	−0.0261089	+	0.0452219i
$201$	4.67769	+	7.94735i	0.329939	+	0.560563i
$202$	12.3587	−	21.4059i	0.869554	−	1.50611i
$203$	−5.12226	+	2.64820i	−0.359512	+	0.185867i
$204$	1.82331	−	3.22013i	0.127657	−	0.225454i
$205$	10.9393			0.764031
$206$	14.3518	+	24.8581i	0.999940	+	1.73195i
$207$	9.98851	−	0.167519i	0.694249	−	0.0116434i
$208$	−9.53381	+	16.5131i	−0.661051	+	1.14497i
$209$	−0.0609028	−	0.105487i	−0.00421274	−	0.00729667i
$210$	8.09303	+	5.09265i	0.558472	+	0.351426i
$211$	−4.78123	+	8.28134i	−0.329154	+	0.570111i	−0.982344	−	0.187083i	$-0.940097\pi$
$211$	−4.78123	+	8.28134i	−0.329154	+	0.570111i	0.653190	+	0.757194i	$0.273430\pi$
$212$	−3.28215	−	5.68486i	−0.225419	−	0.390438i
$213$	4.19229	+	7.12267i	0.287251	+	0.488037i
$214$	−12.8527	+	22.2615i	−0.878593	+	1.52177i
$215$	0.234772	−	0.406637i	0.0160113	−	0.0277324i
$216$	−3.83599	+	0.0965127i	−0.261006	+	0.00656686i
$217$	−0.150033	+	3.22800i	−0.0101849	+	0.219131i
$218$	−5.38118	−	9.32047i	−0.364459	−	0.631262i
$219$	0.796445	−	1.40659i	0.0538188	−	0.0950485i
$220$	−0.0363481			−0.00245059
$221$	−5.46473			−0.367597
$222$	−34.6618	+	0.290640i	−2.32635	+	0.0195065i
$223$	2.00954	+	3.48062i	0.134569	+	0.233080i	0.925433	−	0.378912i	$-0.123702\pi$
$223$	2.00954	+	3.48062i	0.134569	+	0.233080i	−0.790864	+	0.611992i	$0.790368\pi$
$224$	0.993157	−	21.3680i	0.0663581	−	1.42771i
$225$	−1.54336	−	2.57256i	−0.102890	−	0.171504i
$226$	−14.2914	+	24.7534i	−0.950647	+	1.64657i
$227$	1.39973	−	2.42441i	0.0929036	−	0.160914i	−0.815828	−	0.578294i	$-0.803719\pi$
$227$	1.39973	−	2.42441i	0.0929036	−	0.160914i	0.908732	+	0.417381i	$0.137052\pi$
$228$	32.1596	−	0.269659i	2.12982	−	0.0178586i
$229$	10.1572	+	17.5927i	0.671205	+	1.16256i	0.977563	+	0.210644i	$0.0675562\pi$
$229$	10.1572	+	17.5927i	0.671205	+	1.16256i	−0.306358	+	0.951916i	$0.599110\pi$
$230$	−3.47416	+	6.01743i	−0.229079	+	0.396777i
$231$	−0.00269260	+	0.0707111i	−0.000177160	+	0.00465245i
$232$	0.804735	+	1.39384i	0.0528335	+	0.0915102i
$233$	−3.25707	+	5.64141i	−0.213378	+	0.369581i	−0.952769	−	0.303694i	$-0.901780\pi$
$233$	−3.25707	+	5.64141i	−0.213378	+	0.369581i	0.739392	+	0.673275i	$0.235113\pi$
$234$	19.3894	+	32.3194i	1.26753	+	2.11279i
$235$	2.53419	+	4.38934i	0.165312	+	0.286329i
$236$	12.2707			0.798754
$237$	6.17164	+	10.4856i	0.400891	+	0.681111i
$238$	4.45103	−	2.30118i	0.288518	−	0.149163i
$239$	14.5402	−	25.1843i	0.940525	−	1.62904i	0.176053	−	0.984381i	$-0.443667\pi$
$239$	14.5402	−	25.1843i	0.940525	−	1.62904i	0.764472	−	0.644657i	$-0.223000\pi$
$240$	−2.70271	+	4.77322i	−0.174459	+	0.308110i
$241$	7.02246	−	12.1633i	0.452357	−	0.783504i	−0.546175	−	0.837671i	$-0.683917\pi$
$241$	7.02246	−	12.1633i	0.452357	−	0.783504i	0.998532	+	0.0541663i	$0.0172501\pi$
$242$	11.4761	+	19.8771i	0.737709	+	1.27775i
$243$	7.22157	−	13.8148i	0.463264	−	0.886220i
$244$	19.4348			1.24419
$245$	2.92260	+	6.36069i	0.186718	+	0.406370i
$246$	−39.5342	+	0.331495i	−2.52061	+	0.0211354i
$247$	−23.7467	−	41.1305i	−1.51097	−	2.61707i
$248$	0.901957			0.0572743
$249$	14.3547	−	25.3515i	0.909689	−	1.60659i
$250$	2.08660			0.131968
$251$	15.2271			0.961125			0.480562	−	0.876961i	$-0.340433\pi$
$251$	15.2271			0.961125			0.480562	+	0.876961i	$0.340433\pi$
$252$	−15.8962	−	9.81778i	−1.00136	−	0.618462i
$253$	−0.0514201			−0.00323275
$254$	24.3492			1.52781
$255$	−1.57201	+	0.0131813i	−0.0984430	+	0.000825447i
$256$	8.93874			0.558672
$257$	0.248983	+	0.431251i	0.0155311	+	0.0269007i	0.873687	−	0.486489i	$-0.161723\pi$
$257$	0.248983	+	0.431251i	0.0155311	+	0.0269007i	−0.858155	+	0.513390i	$0.828389\pi$
$258$	−0.836138	+	1.47669i	−0.0520557	+	0.0919347i
$259$	−21.3631	−	13.6944i	−1.32744	−	0.850927i
$260$	−14.1726			−0.878946
$261$	−6.53747	+	0.109641i	−0.404660	+	0.00678664i
$262$	−16.7345	−	28.9850i	−1.03386	−	1.79070i
$263$	−8.79694	+	15.2367i	−0.542443	+	0.939538i	0.456320	+	0.889816i	$0.349167\pi$
$263$	−8.79694	+	15.2367i	−0.542443	+	0.939538i	−0.998763	+	0.0497226i	$0.984166\pi$
$264$	0.0197502		0.000165606i	0.00121554		1.01923e-5i
$265$	−1.39434	+	2.41507i	−0.0856537	+	0.148357i
$266$	36.6617	+	23.5013i	2.24787	+	1.44096i
$267$	−21.9511	+	0.184060i	−1.34338	+	0.0112643i
$268$	12.5327			0.765555
$269$	7.14020	+	12.3672i	0.435346	+	0.754041i	0.997324	−	0.0731112i	$-0.0232928\pi$
$269$	7.14020	+	12.3672i	0.435346	+	0.754041i	−0.561978	+	0.827152i	$0.689959\pi$
$270$	5.65561	+	9.25039i	0.344189	+	0.562961i
$271$	−2.92303	+	5.06284i	−0.177562	+	0.307546i	−0.941045	−	0.338282i	$-0.890154\pi$
$271$	−2.92303	+	5.06284i	−0.177562	+	0.307546i	0.763483	+	0.645828i	$0.223488\pi$
$272$	1.43720	+	2.48931i	0.0871431	+	0.150936i
$273$	−1.04988	+	27.5711i	−0.0635414	+	1.66868i
$274$	−6.00190	+	10.3956i	−0.362588	+	0.628021i
$275$	0.00772080	+	0.0133728i	0.000465582	+	0.000806411i
$276$	6.68947	−	11.8142i	0.402659	−	0.711130i
$277$	−5.80940	+	10.0622i	−0.349053	+	0.604577i	−0.986081	−	0.166263i	$-0.946830\pi$
$277$	−5.80940	+	10.0622i	−0.349053	+	0.604577i	0.637029	+	0.770840i	$0.280163\pi$
$278$	3.09185	−	5.35524i	0.185437	−	0.321186i
$279$	−1.77861	+	3.20353i	−0.106482	+	0.191790i
$280$	1.73558	−	0.897292i	0.103721	−	0.0536234i
$281$	2.00648	+	3.47533i	0.119697	+	0.207321i	0.919647	−	0.392745i	$-0.128474\pi$
$281$	2.00648	+	3.47533i	0.119697	+	0.207321i	−0.799951	+	0.600066i	$0.795141\pi$
$282$	−9.29151	−	15.7862i	−0.553301	−	0.940054i
$283$	−12.3717			−0.735424			−0.367712	−	0.929940i	$-0.619859\pi$
$283$	−12.3717			−0.735424			−0.367712	+	0.929940i	$0.619859\pi$
$284$	11.2322			0.666508
$285$	−6.93031	−	11.7745i	−0.410516	−	0.697463i
$286$	−0.0969976	−	0.168005i	−0.00573559	−	0.00993433i
$287$	−24.3661	−	15.6194i	−1.43828	−	0.921984i
$288$	11.7736	−	21.2060i	0.693768	−	1.24958i
$289$	8.08810	−	14.0090i	0.475771	−	0.824059i
$290$	2.27384	−	3.93840i	0.133524	−	0.231271i
$291$	−5.31754	+	9.39123i	−0.311720	+	0.550524i
$292$	−1.09838	−	1.90246i	−0.0642780	−	0.111333i
$293$	12.9308	−	22.3968i	0.755426	−	1.30844i	−0.189736	−	0.981835i	$-0.560763\pi$
$293$	12.9308	−	22.3968i	0.755426	−	1.30844i	0.945162	−	0.326601i	$-0.105903\pi$
$294$	−10.7550	−	22.8988i	−0.627242	−	1.33549i
$295$	−2.60645	−	4.51450i	−0.151753	−	0.262844i
$296$	−3.54135	+	6.13380i	−0.205837	+	0.356520i
$297$	−0.0383580	+	0.0704743i	−0.00222576	+	0.00408933i
$298$	−8.43404	−	14.6082i	−0.488571	−	0.846230i
$299$	−20.0493			−1.15948
$300$	−4.07695	+	0.0341853i	−0.235383	+	0.00197369i
$301$	−1.10354	+	0.570528i	−0.0636069	+	0.0328847i
$302$	8.85283	−	15.3335i	0.509423	−	0.882346i
$303$	20.5167	−	0.172033i	1.17865	−	0.00988304i
$304$	−12.4906	+	21.6343i	−0.716384	+	1.24081i
$305$	−4.12820	−	7.15026i	−0.236380	−	0.409423i
$306$	5.68080	−	0.0952740i	0.324750	−	0.00544645i
$307$	7.24147			0.413293			0.206646	−	0.978416i	$-0.433745\pi$
$307$	7.24147			0.413293			0.206646	+	0.978416i	$0.433745\pi$
$308$	0.0809618	+	0.0518990i	0.00461323	+	0.00295722i
$309$	−11.7398	+	20.7334i	−0.667852	+	1.17948i
$310$	−1.27427	−	2.20710i	−0.0723738	−	0.125355i
$311$	−33.4342			−1.89588			−0.947938	−	0.318454i	$-0.896836\pi$
$311$	−33.4342			−1.89588			−0.947938	+	0.318454i	$0.896836\pi$
$312$	7.70083	−	0.0645716i	0.435973	−	0.00365565i
$313$	−20.9121			−1.18202			−0.591010	−	0.806664i	$-0.701271\pi$
$313$	−20.9121			−1.18202			−0.591010	+	0.806664i	$0.701271\pi$
$314$	−35.9190			−2.02703
$315$	−0.235509	+	7.93376i	−0.0132694	+	0.447017i
$316$	16.5354			0.930186
$317$	9.67604			0.543461			0.271730	−	0.962373i	$-0.412404\pi$
$317$	9.67604			0.543461			0.271730	+	0.962373i	$0.412404\pi$
$318$	4.96593	−	8.77025i	0.278475	−	0.491811i
$319$	0.0336544			0.00188429
$320$	5.26823	+	9.12483i	0.294503	+	0.510094i
$321$	−21.3368	+	0.178910i	−1.19091	+	0.00998578i
$322$	16.3302	−	8.44268i	0.910047	−	0.470492i
$323$	−7.15953			−0.398367
$324$	−11.2019	−	17.9814i	−0.622326	−	0.998966i
$325$	3.01043	+	5.21422i	0.166989	+	0.289233i
$326$	−1.24652	+	2.15904i	−0.0690386	+	0.119578i
$327$	4.40179	−	7.77393i	0.243419	−	0.429899i
$328$	−4.03916	+	6.99603i	−0.223025	+	0.386291i
$329$	0.622593	−	13.3952i	0.0343246	−	0.738502i
$330$	−0.0283080	−	0.0480951i	−0.00155831	−	0.00264755i
$331$	−16.8177			−0.924386			−0.462193	−	0.886779i	$-0.652937\pi$
$331$	−16.8177			−0.924386			−0.462193	+	0.886779i	$0.652937\pi$
$332$	−19.7966	−	34.2887i	−1.08648	−	1.88184i
$333$	−14.8024	−	24.6735i	−0.811166	−	1.35210i
$334$	−8.61900	+	14.9285i	−0.471611	+	0.816854i
$335$	−2.66210	−	4.61089i	−0.145446	−	0.251920i
$336$	12.8354	−	6.77284i	0.700226	−	0.369489i
$337$	−0.286076	+	0.495498i	−0.0155836	+	0.0269915i	−0.873712	−	0.486444i	$-0.838294\pi$
$337$	−0.286076	+	0.495498i	−0.0155836	+	0.0269915i	0.858128	+	0.513435i	$0.171627\pi$
$338$	−24.2576	−	42.0154i	−1.31944	−	2.28533i
$339$	−23.7252	+	0.198936i	−1.28857	+	0.0108047i
$340$	−1.06824	+	1.85025i	−0.0579335	+	0.100344i
$341$	0.00943007	−	0.0163334i	0.000510667	−	0.000884501i
$342$	25.4028	+	42.3428i	1.37362	+	2.28964i
$343$	2.57220	−	18.3408i	0.138886	−	0.990308i
$344$	0.173372	+	0.300289i	0.00934760	+	0.0161905i
$345$	−5.76747	+	0.0483604i	−0.310510	+	0.00260364i
$346$	29.2938			1.57485
$347$	7.05109			0.378523			0.189261	−	0.981927i	$-0.439391\pi$
$347$	7.05109			0.378523			0.189261	+	0.981927i	$0.439391\pi$
$348$	−4.37826	+	7.73238i	−0.234699	+	0.414499i
$349$	−2.29666	−	3.97793i	−0.122937	−	0.212934i	0.797988	−	0.602674i	$-0.205898\pi$
$349$	−2.29666	−	3.97793i	−0.122937	−	0.212934i	−0.920925	+	0.389740i	$0.872565\pi$
$350$	−4.64769	−	2.97931i	−0.248430	−	0.159251i
$351$	−14.9563	+	27.4788i	−0.798306	+	1.46671i
$352$	−0.0624231	+	0.108120i	−0.00332716	+	0.00576282i
$353$	12.0803	−	20.9238i	0.642972	−	1.11366i	−0.341794	−	0.939775i	$-0.611034\pi$
$353$	12.0803	−	20.9238i	0.642972	−	1.11366i	0.984766	−	0.173885i	$-0.0556322\pi$
$354$	9.55644	+	16.2363i	0.507919	+	0.862949i
$355$	−2.38586	−	4.13243i	−0.126628	−	0.219326i
$356$	−14.9166	+	25.8363i	−0.790579	+	1.36932i
$357$	3.52031	+	2.21520i	0.186315	+	0.117241i
$358$	−8.25849	−	14.3041i	−0.436475	−	0.755997i
$359$	−5.16729	+	8.95001i	−0.272719	+	0.472364i	−0.969557	−	0.244865i	$-0.921256\pi$
$359$	−5.16729	+	8.95001i	−0.272719	+	0.472364i	0.696838	+	0.717229i	$0.254590\pi$
$360$	2.21510	−	0.0371499i	0.116746	−	0.00195797i
$361$	−21.6114	−	37.4321i	−1.13744	−	1.97011i
$362$	11.5907			0.609191
$363$	−9.38739	+	16.5789i	−0.492710	+	0.870168i
$364$	31.5680	+	20.2360i	1.65461	+	1.06066i
$365$	−0.466621	+	0.808211i	−0.0244240	+	0.0423037i
$366$	15.1359	+	25.7158i	0.791166	+	1.34418i
$367$	14.5176	−	25.1452i	0.757812	−	1.31257i	−0.186152	−	0.982521i	$-0.559602\pi$
$367$	14.5176	−	25.1452i	0.757812	−	1.31257i	0.943964	−	0.330048i	$-0.107065\pi$
$368$	5.27289	+	9.13291i	0.274868	+	0.476086i
$369$	−16.8832	−	28.1419i	−0.878902	−	1.46501i
$370$	20.0127			1.04041
$371$	6.55406	−	3.38844i	0.340270	−	0.175919i
$372$	2.52592	+	4.29152i	0.130963	+	0.222505i
$373$	6.69761	+	11.6006i	0.346789	+	0.600656i	0.985677	−	0.168644i	$-0.0539387\pi$
$373$	6.69761	+	11.6006i	0.346789	+	0.600656i	−0.638888	+	0.769300i	$0.720605\pi$
$374$	−0.0292443			−0.00151219
$375$	0.878572	+	1.49269i	0.0453693	+	0.0770820i
$376$	−3.74285			−0.193023
$377$	13.1223			0.675831
$378$	0.610704	−	28.6795i	0.0314112	−	1.47512i
$379$	33.0340			1.69684			0.848420	−	0.529323i	$-0.177554\pi$
$379$	33.0340			1.69684			0.848420	+	0.529323i	$0.177554\pi$
$380$	−18.5680			−0.952518
$381$	10.2523	+	17.4186i	0.525243	+	0.892383i
$382$	2.80157			0.143341
$383$	6.41329	+	11.1082i	0.327704	+	0.567600i	0.982056	−	0.188590i	$-0.0603918\pi$
$383$	6.41329	+	11.1082i	0.327704	+	0.567600i	−0.654352	+	0.756190i	$0.727058\pi$
$384$	−5.10913	−	8.68037i	−0.260724	−	0.442968i
$385$	0.00189682	−	0.0408106i	9.66711e−5	−	0.00207990i
$386$	−25.9895			−1.32283
$387$	−1.40843	+	0.0236212i	−0.0715947	+	0.00120073i
$388$	7.33347	+	12.7019i	0.372300	+	0.644843i
$389$	−3.73359	+	6.46678i	−0.189301	+	0.327879i	−0.945017	−	0.327020i	$-0.893955\pi$
$389$	−3.73359	+	6.46678i	−0.189301	+	0.327879i	0.755717	+	0.654899i	$0.227289\pi$
$390$	−11.0376	−	18.7528i	−0.558912	−	0.949587i
$391$	−1.51119	+	2.61746i	−0.0764243	+	0.132371i
$392$	−5.14701	−	0.479489i	−0.259963	−	0.0242178i
$393$	13.6888	−	24.1755i	0.690507	−	1.21949i
$394$	28.5198			1.43681
$395$	−3.51232	−	6.08351i	−0.176724	−	0.306095i
$396$	0.0560981	+	0.0935077i	0.00281904	+	0.00469894i
$397$	−5.56382	+	9.63681i	−0.279240	+	0.483658i	−0.971196	−	0.238282i	$-0.923416\pi$
$397$	−5.56382	+	9.63681i	−0.279240	+	0.483658i	0.691956	+	0.721940i	$0.256749\pi$
$398$	−17.9804	−	31.1429i	−0.901274	−	1.56105i
$399$	−1.37548	+	36.1219i	−0.0688601	+	1.80835i
$400$	1.58346	−	2.74264i	0.0791732	−	0.137132i
$401$	−8.99095	−	15.5728i	−0.448987	−	0.777668i	0.549334	−	0.835603i	$-0.314882\pi$
$401$	−8.99095	−	15.5728i	−0.448987	−	0.777668i	−0.998320	+	0.0579353i	$0.981548\pi$
$402$	9.76047	+	16.5830i	0.486808	+	0.827083i
$403$	3.67689	−	6.36857i	0.183159	−	0.317241i
$404$	13.9419	−	24.1481i	0.693636	−	1.20141i
$405$	−4.23611	+	7.94074i	−0.210494	+	0.394579i
$406$	−10.6881	+	5.52574i	−0.530442	+	0.274238i
$407$	0.0740505	+	0.128259i	0.00367055	+	0.00635757i
$408$	0.572011	−	1.01022i	0.0283188	−	0.0500134i
$409$	34.1802			1.69010			0.845051	−	0.534686i	$-0.179570\pi$
$409$	34.1802			1.69010			0.845051	+	0.534686i	$0.179570\pi$
$410$	22.8259			1.12729
$411$	−9.96379	+	0.0835466i	−0.491478	+	0.00412105i
$412$	16.1904	+	28.0426i	0.797644	+	1.38156i
$413$	−0.640345	+	13.7771i	−0.0315093	+	0.677929i
$414$	20.8420	−	0.349547i	1.02433	−	0.0171793i
$415$	−8.41010	+	14.5667i	−0.412835	+	0.715052i
$416$	−24.3395	+	42.1573i	−1.19334	+	2.06693i
$417$	5.13279	−	0.0430386i	0.251354	−	0.00210761i
$418$	−0.127080	−	0.220109i	−0.00621568	−	0.0107659i
$419$	−10.7526	+	18.6241i	−0.525299	+	0.909845i	0.474266	+	0.880381i	$0.342713\pi$
$419$	−10.7526	+	18.6241i	−0.525299	+	0.909845i	−0.999566	+	0.0294638i	$0.990620\pi$
$420$	9.12980	+	5.74505i	0.445489	+	0.280330i
$421$	11.1492	+	19.3110i	0.543379	+	0.941160i	0.998707	+	0.0508365i	$0.0161887\pi$
$421$	11.1492	+	19.3110i	0.543379	+	0.941160i	−0.455328	+	0.890324i	$0.650478\pi$
$422$	−9.97654	+	17.2799i	−0.485650	+	0.841171i
$423$	7.38068	−	13.2937i	0.358861	−	0.646360i
$424$	−1.02968	−	1.78346i	−0.0500057	−	0.0866124i
$425$	0.907632			0.0440266
$426$	8.74765	+	14.8622i	0.423825	+	0.720075i
$427$	−1.01421	+	21.8208i	−0.0490809	+	1.05598i
$428$	−14.4992	+	25.1134i	−0.700846	+	1.21390i
$429$	0.0793438	−	0.140128i	0.00383075	−	0.00676544i
$430$	0.489876	−	0.848490i	0.0236239	−	0.0409178i
$431$	7.82668	+	13.5562i	0.376998	+	0.652980i	0.990624	−	0.136617i	$-0.0436230\pi$
$431$	7.82668	+	13.5562i	0.376998	+	0.652980i	−0.613626	+	0.789597i	$0.710290\pi$
$432$	16.4506	−	0.413894i	0.791481	−	0.0199135i
$433$	−31.0383			−1.49160			−0.745802	−	0.666167i	$-0.767934\pi$
$433$	−31.0383			−1.49160			−0.745802	+	0.666167i	$0.767934\pi$
$434$	−0.313060	+	6.73554i	−0.0150273	+	0.323316i
$435$	3.77481	−	0.0316519i	0.180988	−	0.00151759i
$436$	−6.07054	−	10.5145i	−0.290726	−	0.503552i
$437$	−26.2673			−1.25654
$438$	1.66186	−	2.93499i	0.0794069	−	0.140239i
$439$	−1.83060			−0.0873697			−0.0436849	−	0.999045i	$-0.513910\pi$
$439$	−1.83060			−0.0873697			−0.0436849	+	0.999045i	$0.513910\pi$
$440$	−0.0114032			−0.000543625
$441$	11.8526	−	17.3354i	0.564411	−	0.825494i
$442$	−11.4027			−0.542372
$443$	−17.8148			−0.846405			−0.423202	−	0.906035i	$-0.639094\pi$
$443$	−17.8148			−0.846405			−0.423202	+	0.906035i	$0.639094\pi$
$444$	−39.1022	+	0.327873i	−1.85571	+	0.0155601i
$445$	12.6739			0.600801
$446$	4.19311	+	7.26268i	0.198550	+	0.343898i
$447$	6.89903	−	12.1843i	0.326313	−	0.576296i
$448$	1.29428	−	27.8468i	0.0611491	−	1.31564i
$449$	13.1843			0.622204			0.311102	−	0.950377i	$-0.399302\pi$
$449$	13.1843			0.622204			0.311102	+	0.950377i	$0.399302\pi$
$450$	−3.22037	−	5.36791i	−0.151810	−	0.253045i
$451$	0.0844598	+	0.146289i	0.00397706	+	0.00688847i
$452$	−16.1222	+	27.9244i	−0.758323	+	1.31345i
$453$	14.6966	−	0.123232i	0.690508	−	0.00578992i
$454$	2.92069	−	5.05878i	0.137075	−	0.237420i
$455$	0.739594	−	15.9125i	0.0346727	−	0.745991i
$456$	10.0891	−	0.0845975i	0.472467	−	0.00396164i
$457$	−24.3010			−1.13675			−0.568376	−	0.822769i	$-0.692428\pi$
$457$	−24.3010			−1.13675			−0.568376	+	0.822769i	$0.692428\pi$
$458$	21.1940	+	36.7090i	0.990330	+	1.71530i
$459$	2.46008	+	4.02374i	0.114827	+	0.187812i
$460$	−3.91923	+	6.78830i	−0.182735	+	0.316506i
$461$	3.59092	+	6.21965i	0.167246	+	0.289678i	0.937450	−	0.348119i	$-0.113179\pi$
$461$	3.59092	+	6.21965i	0.167246	+	0.289678i	−0.770205	+	0.637797i	$0.779846\pi$
$462$	−0.00561838	+	0.147546i	−0.000261391	+	0.00686446i
$463$	6.29354	−	10.9007i	0.292486	−	0.506600i	−0.681911	−	0.731435i	$-0.738851\pi$
$463$	6.29354	−	10.9007i	0.292486	−	0.506600i	0.974397	+	0.224835i	$0.0721843\pi$
$464$	−3.45110	−	5.97748i	−0.160213	−	0.277498i
$465$	1.04235	−	1.84088i	0.0483379	−	0.0853688i
$466$	−6.79621	+	11.7714i	−0.314828	+	0.545299i
$467$	−7.03434	+	12.1838i	−0.325511	+	0.563801i	−0.981616	−	0.190869i	$-0.938870\pi$
$467$	−7.03434	+	12.1838i	−0.325511	+	0.563801i	0.656105	+	0.754670i	$0.272203\pi$
$468$	21.8733	+	36.4598i	1.01109	+	1.68535i
$469$	−0.654016	+	14.0713i	−0.0301997	+	0.649752i
$470$	5.28785	+	9.15882i	0.243910	+	0.422465i
$471$	−15.1238	−	25.6953i	−0.696869	−	1.18397i
$472$	3.84957			0.177191
$473$	0.00725051			0.000333379
$474$	12.8778	+	21.8792i	0.591495	+	1.00495i
$475$	3.94407	+	6.83134i	0.180967	+	0.313443i
$476$	5.02124	−	2.59597i	0.230148	−	0.118986i
$477$	8.36487	−	0.140289i	0.383001	−	0.00642340i
$478$	30.3395	−	52.5496i	1.38770	−	2.40356i
$479$	13.8241	−	23.9440i	0.631639	−	1.09403i	−0.355578	−	0.934647i	$-0.615716\pi$
$479$	13.8241	−	23.9440i	0.631639	−	1.09403i	0.987217	−	0.159384i	$-0.0509508\pi$
$480$	−6.89993	+	12.1859i	−0.314937	+	0.556206i
$481$	28.8732	+	50.0098i	1.31650	+	2.28025i
$482$	14.6531	−	25.3799i	0.667430	−	1.15602i
$483$	12.9155	+	8.12726i	0.587676	+	0.369803i
$484$	12.9462	+	22.4235i	0.588465	+	1.01925i
$485$	3.11544	−	5.39610i	0.141465	−	0.245024i
$486$	15.0685	−	28.8260i	0.683523	−	1.30757i
$487$	11.3473	+	19.6541i	0.514196	+	0.890613i	0.999864	+	0.0164702i	$0.00524286\pi$
$487$	11.3473	+	19.6541i	0.514196	+	0.890613i	−0.485669	+	0.874143i	$0.661424\pi$
$488$	6.09712			0.276003
$489$	−2.06936	+	0.0173516i	−0.0935798	+	0.000784669i
$490$	6.09831	+	13.2722i	0.275493	+	0.599579i
$491$	9.71567	−	16.8280i	0.438462	−	0.759439i	−0.559109	−	0.829094i	$-0.688857\pi$
$491$	9.71567	−	16.8280i	0.438462	−	0.759439i	0.997571	+	0.0696555i	$0.0221900\pi$
$492$	−44.5988	+	0.373962i	−2.01067	+	0.0168595i
$493$	0.989076	−	1.71313i	0.0445457	−	0.0771555i
$494$	−49.5500	−	85.8231i	−2.22936	−	3.86136i
$495$	0.0224864	−	0.0405012i	0.00101069	−	0.00182039i
$496$	−3.86804			−0.173680
$497$	−0.586151	+	12.6112i	−0.0262925	+	0.565688i
$498$	29.9525	−	52.8986i	1.34220	−	2.37044i
$499$	−9.32000	−	16.1427i	−0.417220	−	0.722647i	0.578438	−	0.815726i	$-0.303662\pi$
$499$	−9.32000	−	16.1427i	−0.417220	−	0.722647i	−0.995659	+	0.0930791i	$0.970329\pi$
$500$	2.35391			0.105270
$501$	−14.3084	+	0.119977i	−0.639254	+	0.00536016i
$502$	31.7729			1.41809
$503$	23.0793			1.02905			0.514527	−	0.857474i	$-0.327967\pi$
$503$	23.0793			1.02905			0.514527	+	0.857474i	$0.327967\pi$
$504$	−4.98695	−	3.08004i	−0.222137	−	0.137196i
$505$	−11.8457			−0.527129
$506$	−0.107293			−0.00476977
$507$	19.8426	−	35.0438i	0.881242	−	1.55635i
$508$	27.4685			1.21872
$509$	18.2993	+	31.6953i	0.811101	+	1.40487i	0.912094	+	0.409982i	$0.134465\pi$
$509$	18.2993	+	31.6953i	0.811101	+	1.40487i	−0.100992	+	0.994887i	$0.532202\pi$
$510$	−3.28016	+	0.0275042i	−0.145248	+	0.00121791i
$511$	2.19334	−	1.13395i	0.0970275	−	0.0501631i
$512$	30.2821			1.33829
$513$	−19.5947	+	36.0009i	−0.865128	+	1.58948i
$514$	0.519528	+	0.899849i	0.0229154	+	0.0396906i
$515$	6.87809	−	11.9132i	0.303085	−	0.524958i
$516$	−0.943252	+	1.66586i	−0.0415244	+	0.0733356i
$517$	−0.0391319	+	0.0677785i	−0.00172102	+	0.00298089i
$518$	−44.5762	−	28.5747i	−1.95857	−	1.25550i
$519$	12.3343	+	20.9558i	0.541415	+	0.919859i
$520$	−4.44623			−0.194980
$521$	−5.46507	−	9.46578i	−0.239429	−	0.414703i	0.721122	−	0.692809i	$-0.243627\pi$
$521$	−5.46507	−	9.46578i	−0.239429	−	0.414703i	−0.960551	+	0.278105i	$0.910294\pi$
$522$	−13.6411	+	0.228778i	−0.597055	+	0.0100133i
$523$	3.42296	−	5.92875i	0.149676	−	0.259246i	−0.781432	−	0.623991i	$-0.785510\pi$
$523$	3.42296	−	5.92875i	0.149676	−	0.259246i	0.931108	+	0.364745i	$0.118844\pi$
$524$	−18.8783	−	32.6982i	−0.824702	−	1.42843i
$525$	0.174373	−	4.57926i	0.00761026	−	0.199855i
$526$	−18.3557	+	31.7930i	−0.800347	+	1.38624i
$527$	−0.554284	−	0.960048i	−0.0241450	−	0.0418203i
$528$	−0.0846985		0.000710199i	−0.00368603		3.09074e-5i
$529$	5.95565	−	10.3155i	0.258941	−	0.448499i
$530$	−2.90944	+	5.03929i	−0.126378	+	0.218893i
$531$	−7.59113	+	13.6727i	−0.329427	+	0.593345i
$532$	41.3583	+	26.5119i	1.79311	+	1.14944i
$533$	32.9319	+	57.0397i	1.42644	+	2.47066i
$534$	−45.8032	+	0.384061i	−1.98210	+	0.0166199i
$535$	12.3193			0.532608
$536$	3.93176			0.169826
$537$	6.75543	−	11.9307i	0.291518	−	0.514846i
$538$	14.8988	+	25.8054i	0.642331	+	1.11255i
$539$	−0.0624956	+	0.0881930i	−0.00269187	+	0.00379874i
$540$	6.38013	+	10.4354i	0.274557	+	0.449069i
$541$	−3.96333	+	6.86468i	−0.170397	+	0.295136i	−0.938559	−	0.345120i	$-0.887838\pi$
$541$	−3.96333	+	6.86468i	−0.170397	+	0.295136i	0.768162	+	0.640256i	$0.221172\pi$
$542$	−6.09921	+	10.5641i	−0.261983	+	0.453769i
$543$	4.88029	+	8.29157i	0.209433	+	0.355825i
$544$	3.66913	+	6.35511i	0.157313	+	0.272473i
$545$	−2.57892	+	4.46682i	−0.110469	+	0.191337i
$546$	−2.19067	+	57.5299i	−0.0937522	+	2.46205i
$547$	−11.0438	−	19.1285i	−0.472201	−	0.817876i	0.527293	−	0.849683i	$-0.323207\pi$
$547$	−11.0438	−	19.1285i	−0.472201	−	0.817876i	−0.999494	+	0.0318076i	$0.989874\pi$
$548$	−6.77079	+	11.7273i	−0.289234	+	0.500968i
$549$	−12.0232	+	21.6554i	−0.513136	+	0.924232i
$550$	0.0161102	+	0.0279038i	0.000686943	+	0.00118982i
$551$	17.1919			0.732401
$552$	2.09863	−	3.70635i	0.0893235	−	0.157753i
$553$	−0.862896	+	18.5654i	−0.0366941	+	0.789480i
$554$	−12.1219	+	20.9958i	−0.515010	+	0.892024i
$555$	8.42642	+	14.3164i	0.357682	+	0.607698i
$556$	3.48793	−	6.04128i	0.147921	−	0.256207i
$557$	4.88781	+	8.46594i	0.207103	+	0.358713i	0.950801	−	0.309803i	$-0.100263\pi$
$557$	4.88781	+	8.46594i	0.207103	+	0.358713i	−0.743698	+	0.668516i	$0.766930\pi$
$558$	−3.71125	+	6.68449i	−0.157110	+	0.282977i
$559$	2.82706			0.119572
$560$	−7.44303	+	3.84803i	−0.314525	+	0.162609i
$561$	−0.0123134	−	0.0209204i	−0.000519874	−	0.000883261i
$562$	4.18673	+	7.25163i	0.176606	+	0.305891i
$563$	−8.28298			−0.349086			−0.174543	−	0.984650i	$-0.555845\pi$
$563$	−8.28298			−0.349086			−0.174543	+	0.984650i	$0.555845\pi$
$564$	−10.4818	−	17.8085i	−0.441364	−	0.749873i
$565$	13.6982			0.576288
$566$	−25.8149			−1.08508
$567$	20.7735	−	11.6388i	0.872406	−	0.488782i
$568$	3.52377			0.147854
$569$	21.4483			0.899160			0.449580	−	0.893240i	$-0.351574\pi$
$569$	21.4483			0.899160			0.449580	+	0.893240i	$0.351574\pi$
$570$	−14.4608	−	24.5688i	−0.605696	−	1.02907i
$571$	−7.68133			−0.321453			−0.160727	−	0.986999i	$-0.551384\pi$
$571$	−7.68133			−0.321453			−0.160727	+	0.986999i	$0.551384\pi$
$572$	−0.109424	−	0.189527i	−0.00457523	−	0.00792453i
$573$	1.17961	+	2.00415i	0.0492791	+	0.0837247i
$574$	−50.8423	−	32.5915i	−2.12212	−	1.36034i
$575$	3.32997			0.138869
$576$	15.3434	−	27.6357i	0.639309	−	1.15149i
$577$	2.67530	+	4.63376i	0.111374	+	0.192906i	0.916325	−	0.400436i	$-0.131141\pi$
$577$	2.67530	+	4.63376i	0.111374	+	0.192906i	−0.804950	+	0.593342i	$0.797808\pi$
$578$	16.8767	−	29.2312i	0.701976	−	1.21586i
$579$	−10.9430	−	18.5920i	−0.454775	−	0.772659i
$580$	2.56513	−	4.44294i	0.106511	−	0.184483i
$581$	39.5314	−	20.4377i	1.64004	−	0.847897i
$582$	−11.0956	+	19.5958i	−0.459927	+	0.812271i
$583$	−0.0430617			−0.00178343
$584$	−0.344586	−	0.596840i	−0.0142591	−	0.0246974i
$585$	8.76771	−	15.7919i	0.362500	−	0.652915i
$586$	26.9815	−	46.7333i	1.11459	−	1.93053i
$587$	−16.6897	−	28.9075i	−0.688859	−	1.19314i	−0.972207	−	0.234122i	$-0.924778\pi$
$587$	−16.6897	−	28.9075i	−0.688859	−	1.19314i	0.283348	−	0.959017i	$-0.408555\pi$
$588$	−12.1327	−	25.8323i	−0.500346	−	1.06531i
$589$	4.81723	−	8.34369i	0.198491	−	0.343796i
$590$	−5.43862	−	9.41996i	−0.223904	−	0.387814i
$591$	12.0084	+	20.4021i	0.493958	+	0.839230i
$592$	15.1871	−	26.3048i	0.624184	−	1.08112i
$593$	1.54029	−	2.66786i	0.0632521	−	0.109556i	−0.832665	−	0.553777i	$-0.813186\pi$
$593$	1.54029	−	2.66786i	0.0632521	−	0.109556i	0.895917	+	0.444221i	$0.146519\pi$
$594$	−0.0800380	+	0.147052i	−0.00328400	+	0.00603361i
$595$	−2.02166	−	1.29594i	−0.0828798	−	0.0531285i
$596$	−9.51450	−	16.4796i	−0.389729	−	0.675031i
$597$	14.7079	−	25.9754i	0.601954	−	1.06310i
$598$	−41.8349			−1.71076
$599$	26.5658			1.08545			0.542725	−	0.839911i	$-0.317393\pi$
$599$	26.5658			1.08545			0.542725	+	0.839911i	$0.317393\pi$
$600$	−1.27902	+	0.0107246i	−0.0522159	+	0.000437832i
$601$	−20.2237	−	35.0284i	−0.824941	−	1.42884i	−0.901965	−	0.431810i	$-0.857875\pi$
$601$	−20.2237	−	35.0284i	−0.824941	−	1.42884i	0.0770237	−	0.997029i	$-0.475458\pi$
$602$	−2.30265	+	1.19046i	−0.0938489	+	0.0485197i
$603$	−7.75321	+	13.9646i	−0.315735	+	0.568684i
$604$	9.98693	−	17.2979i	0.406363	−	0.703841i
$605$	5.49988	−	9.52607i	0.223602	−	0.387290i
$606$	42.8102	−	0.358965i	1.73905	−	0.0145819i
$607$	−2.87994	−	4.98821i	−0.116893	−	0.202465i	0.801642	−	0.597805i	$-0.203960\pi$
$607$	−2.87994	−	4.98821i	−0.116893	−	0.202465i	−0.918535	+	0.395340i	$0.870627\pi$
$608$	−31.8881	+	55.2317i	−1.29323	+	2.23994i
$609$	−8.45320	−	5.31929i	−0.342541	−	0.215548i
$610$	−8.61392	−	14.9198i	−0.348768	−	0.604083i
$611$	−15.2580	+	26.4276i	−0.617273	+	1.06915i
$612$	6.40855	−	0.107479i	0.259050	−	0.00434459i
$613$	−17.6856	−	30.6324i	−0.714315	−	1.23723i	−0.963223	−	0.268702i	$-0.913405\pi$
$613$	−17.6856	−	30.6324i	−0.714315	−	1.23723i	0.248909	−	0.968527i	$-0.419928\pi$
$614$	15.1101			0.609793
$615$	9.61092	+	16.3289i	0.387550	+	0.658444i
$616$	0.0253994	+	0.0162818i	0.00102337	+	0.000656012i
$617$	−15.8253	+	27.4103i	−0.637104	+	1.10350i	0.348961	+	0.937137i	$0.386534\pi$
$617$	−15.8253	+	27.4103i	−0.637104	+	1.10350i	−0.986065	+	0.166359i	$0.946799\pi$
$618$	−24.4962	+	43.2624i	−0.985383	+	1.74027i
$619$	1.55309	−	2.69003i	0.0624240	−	0.108122i	−0.833124	−	0.553086i	$-0.813450\pi$
$619$	1.55309	−	2.69003i	0.0624240	−	0.108122i	0.895548	+	0.444964i	$0.146784\pi$
$620$	−1.43752	−	2.48985i	−0.0577320	−	0.0999948i
$621$	9.02568	+	14.7625i	0.362188	+	0.592400i
$622$	−69.7638			−2.79727
$623$	−28.2298	−	18.0962i	−1.13100	−	0.725009i
$624$	−33.0249	+	0.276915i	−1.32206	+	0.0110855i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−43.6352			−1.74401
$627$	0.103951	−	0.183586i	0.00415141	−	0.00733174i
$628$	−40.5205			−1.61694
$629$	8.70513			0.347096
$630$	−0.491413	+	16.5546i	−0.0195784	+	0.659551i
$631$	48.2486			1.92075			0.960374	−	0.278715i	$-0.0899085\pi$
$631$	48.2486			1.92075			0.960374	+	0.278715i	$0.0899085\pi$
$632$	5.18748			0.206347
$633$	−16.5621	+	0.138874i	−0.658284	+	0.00551973i
$634$	20.1901			0.801850
$635$	−5.83466	−	10.1059i	−0.231541	−	0.401041i
$636$	5.60210	−	9.89378i	0.222138	−	0.392314i
$637$	−24.3678	+	34.3875i	−0.965486	+	1.36248i
$638$	0.0702234			0.00278017
$639$	−6.94868	+	12.5156i	−0.274885	+	0.495108i
$640$	2.90763	+	5.03617i	0.114934	+	0.199072i
$641$	−1.04770	+	1.81468i	−0.0413818	+	0.0716754i	−0.885974	−	0.463734i	$-0.846509\pi$
$641$	−1.04770	+	1.81468i	−0.0413818	+	0.0716754i	0.844593	+	0.535409i	$0.179843\pi$
$642$	−44.5215	+	0.373314i	−1.75712	+	0.0147335i
$643$	−1.93014	+	3.34309i	−0.0761171	+	0.131839i	−0.901572	−	0.432630i	$-0.857586\pi$
$643$	−1.93014	+	3.34309i	−0.0761171	+	0.131839i	0.825454	+	0.564469i	$0.190919\pi$
$644$	18.4222	−	9.52425i	0.725937	−	0.375308i
$645$	0.813245	−	0.00681908i	0.0320215	−	0.000268501i
$646$	−14.9391			−0.587771
$647$	−20.6094	−	35.6965i	−0.810238	−	1.40337i	−0.912698	−	0.408636i	$-0.866005\pi$
$647$	−20.6094	−	35.6965i	−0.810238	−	1.40337i	0.102460	−	0.994737i	$-0.467329\pi$
$648$	−3.51426	−	5.64114i	−0.138053	−	0.221605i
$649$	0.0402477	−	0.0697111i	0.00157986	−	0.00273640i
$650$	6.28157	+	10.8800i	0.246384	+	0.426749i
$651$	−4.95020	+	2.61207i	−0.194014	+	0.102375i
$652$	−1.40621	+	2.43563i	−0.0550716	+	0.0953867i
$653$	9.87379	+	17.1019i	0.386391	+	0.669249i	0.991961	−	0.126543i	$-0.0403881\pi$
$653$	9.87379	+	17.1019i	0.386391	+	0.669249i	−0.605570	+	0.795792i	$0.707055\pi$
$654$	9.18478	−	16.2211i	0.359153	−	0.634296i
$655$	−8.01997	+	13.8910i	−0.313366	+	0.542766i
$656$	17.3219	−	30.0024i	0.676307	−	1.17140i
$657$	2.79933	−	0.0469482i	0.109212	−	0.00183162i
$658$	1.29910	−	27.9505i	0.0506443	−	1.08962i
$659$	6.81311	+	11.8007i	0.265401	+	0.459688i	0.967669	−	0.252225i	$-0.0811623\pi$
$659$	6.81311	+	11.8007i	0.265401	+	0.459688i	−0.702268	+	0.711913i	$0.747829\pi$
$660$	−0.0319345	−	0.0542564i	−0.00124305	−	0.00211193i
$661$	−29.5025			−1.14751			−0.573757	−	0.819025i	$-0.694515\pi$
$661$	−29.5025			−1.14751			−0.573757	+	0.819025i	$0.694515\pi$
$662$	−35.0919			−1.36389
$663$	−4.80115	−	8.15712i	−0.186461	−	0.316796i
$664$	−6.21061	−	10.7571i	−0.241018	−	0.417456i
$665$	0.968969	−	20.8476i	0.0375750	−	0.808434i
$666$	−30.8867	−	51.4838i	−1.19684	−	1.99496i
$667$	3.62878	−	6.28522i	0.140507	−	0.243365i
$668$	−9.72315	+	16.8410i	−0.376200	+	0.651598i
$669$	−3.42995	+	6.05759i	−0.132610	+	0.234200i
$670$	−5.55474	−	9.62109i	−0.214598	−	0.371695i
$671$	0.0637461	−	0.110411i	0.00246089	−	0.00426239i
$672$	32.7682	−	17.2908i	1.26406	−	0.667009i
$673$	−12.4123	−	21.4987i	−0.478458	−	0.828714i	0.521237	−	0.853412i	$-0.325471\pi$
$673$	−12.4123	−	21.4987i	−0.478458	−	0.828714i	−0.999695	+	0.0246979i	$0.992138\pi$
$674$	−0.596927	+	1.03391i	−0.0229928	+	0.0398246i
$675$	2.48407	−	4.56392i	0.0956119	−	0.175665i
$676$	−27.3651	−	47.3978i	−1.05251	−	1.82299i
$677$	−25.4960			−0.979890			−0.489945	−	0.871753i	$-0.662983\pi$
$677$	−25.4960			−0.979890			−0.489945	+	0.871753i	$0.662983\pi$
$678$	−49.5050	+	0.415100i	−1.90123	+	0.0159418i
$679$	−14.6440	+	7.57094i	−0.561987	+	0.290546i
$680$	−0.335130	+	0.580462i	−0.0128516	+	0.0222597i
$681$	4.84865	−	0.0406560i	0.185801	−	0.00155794i
$682$	0.0196768	−	0.0340812i	0.000753464	−	0.00130504i
$683$	19.1745	+	33.2112i	0.733692	+	1.27079i	0.955295	+	0.295655i	$0.0955377\pi$
$683$	19.1745	+	33.2112i	0.733692	+	1.27079i	−0.221603	+	0.975137i	$0.571129\pi$
$684$	28.6570	+	47.7672i	1.09573	+	1.82643i
$685$	5.75280			0.219803
$686$	5.36715	−	38.2699i	0.204919	−	1.46115i
$687$	−17.3366	+	30.6180i	−0.661433	+	1.16815i
$688$	−0.743506	−	1.28779i	−0.0283459	−	0.0490965i
$689$	−16.7903			−0.639658
$690$	−12.0344	+	0.100909i	−0.458143	+	0.00384154i
$691$	6.65345			0.253109			0.126555	−	0.991960i	$-0.459608\pi$
$691$	6.65345			0.253109			0.126555	+	0.991960i	$0.459608\pi$
$692$	33.0466			1.25624
$693$	−0.107915	+	0.0581056i	−0.00409935	+	0.00220725i
$694$	14.7128			0.558492
$695$	−2.96352			−0.112413
$696$	−1.37355	+	2.42581i	−0.0520643	+	0.0919500i
$697$	9.92881			0.376081
$698$	−4.79221	−	8.30035i	−0.181388	−	0.314173i
$699$	−11.2824	+	0.0946033i	−0.426740	+	0.00357823i
$700$	−5.24309	−	3.36099i	−0.198170	−	0.127033i
$701$	15.9966			0.604183			0.302091	−	0.953279i	$-0.402315\pi$
$701$	15.9966			0.604183			0.302091	+	0.953279i	$0.402315\pi$
$702$	−31.2078	+	57.3372i	−1.17786	+	2.16405i
$703$	37.8278	+	65.5196i	1.42670	+	2.47112i
$704$	−0.0813498	+	0.140902i	−0.00306599	+	0.00531045i
$705$	−4.32544	+	7.63910i	−0.162906	+	0.287705i
$706$	25.2069	−	43.6596i	0.948674	−	1.64315i
$707$	26.3852	+	16.9137i	0.992317	+	0.636106i
$708$	10.7807	+	18.3163i	0.405163	+	0.688368i
$709$	−39.0083			−1.46499			−0.732494	−	0.680773i	$-0.761644\pi$
$709$	−39.0083			−1.46499			−0.732494	+	0.680773i	$0.761644\pi$
$710$	−4.97834	−	8.62273i	−0.186834	−	0.323605i
$711$	−10.2294	+	18.4247i	−0.383633	+	0.690978i
$712$	−4.67965	+	8.10540i	−0.175377	+	0.303763i
$713$	−2.03359	−	3.52228i	−0.0761584	−	0.131910i
$714$	7.34549	+	4.62225i	0.274898	+	0.172983i
$715$	−0.0464859	+	0.0805159i	−0.00173847	+	0.00301112i
$716$	−9.31646	−	16.1366i	−0.348173	−	0.603053i
$717$	50.3668	−	0.422327i	1.88098	−	0.0157721i
$718$	−10.7821	+	18.6751i	−0.402384	+	0.696949i
$719$	22.0049	−	38.1135i	0.820643	−	1.42140i	−0.0845611	−	0.996418i	$-0.526949\pi$
$719$	22.0049	−	38.1135i	0.820643	−	1.42140i	0.905204	−	0.424977i	$-0.139718\pi$
$720$	−9.49944	+	0.159317i	−0.354023	+	0.00593740i
$721$	−32.3303	+	16.7147i	−1.20404	+	0.622487i
$722$	−45.0945	−	78.1059i	−1.67824	−	2.90680i
$723$	24.3257	−	0.203971i	0.904681	−	0.00758577i
$724$	13.0755			0.485947
$725$	−2.17946			−0.0809433
$726$	−19.5878	+	34.5937i	−0.726970	+	1.28389i
$727$	−9.74378	−	16.8767i	−0.361377	−	0.625923i	0.626811	−	0.779171i	$-0.284360\pi$
$727$	−9.74378	−	16.8767i	−0.361377	−	0.625923i	−0.988188	+	0.153248i	$0.951027\pi$
$728$	9.90352	+	6.34846i	0.367049	+	0.235290i
$729$	26.9658	−	1.35777i	0.998735	−	0.0502877i
$730$	−0.973652	+	1.68641i	−0.0360365	+	0.0624170i
$731$	0.213086	−	0.369077i	0.00788129	−	0.0136508i
$732$	17.0749	+	29.0101i	0.631107	+	1.07225i
$733$	−20.6630	−	35.7893i	−0.763204	−	1.32191i	−0.941191	−	0.337875i	$-0.890292\pi$
$733$	−20.6630	−	35.7893i	−0.763204	−	1.32191i	0.177987	−	0.984033i	$-0.443042\pi$
$734$	30.2925	−	52.4681i	1.11811	−	1.93663i
$735$	−6.92680	+	9.95085i	−0.255499	+	0.367043i
$736$	13.4615	+	23.3160i	0.496198	+	0.859439i
$737$	0.0411070	−	0.0711995i	0.00151420	−	0.00262267i
$738$	−35.2285	−	58.7209i	−1.29678	−	2.16155i
$739$	19.1130	+	33.1047i	0.703084	+	1.21778i	0.967379	+	0.253335i	$0.0815276\pi$
$739$	19.1130	+	33.1047i	0.703084	+	1.21778i	−0.264294	+	0.964442i	$0.585139\pi$
$740$	22.5764			0.829927
$741$	40.5318	−	71.5825i	1.48897	−	2.62965i
$742$	13.6757	−	7.07032i	0.502052	−	0.259560i
$743$	−23.1922	+	40.1701i	−0.850839	+	1.47370i	0.0296124	+	0.999561i	$0.490573\pi$
$743$	−23.1922	+	40.1701i	−0.850839	+	1.47370i	−0.880452	+	0.474136i	$0.842761\pi$
$744$	0.792434	+	1.34634i	0.0290520	+	0.0493591i
$745$	−4.04200	+	7.00095i	−0.148087	+	0.256495i
$746$	13.9752	+	24.2058i	0.511670	+	0.886238i
$747$	50.4535	−	0.846167i	1.84600	−	0.0309596i
$748$	−0.0329907			−0.00120626
$749$	−27.4399	−	17.5898i	−1.00263	−	0.642718i
$750$	1.83323	+	3.11464i	0.0669401	+	0.113731i
$751$	−6.26516	−	10.8516i	−0.228619	−	0.395980i	0.728780	−	0.684748i	$-0.240088\pi$
$751$	−6.26516	−	10.8516i	−0.228619	−	0.395980i	−0.957399	+	0.288768i	$0.906754\pi$
$752$	16.0512			0.585326
$753$	13.3781	+	22.7292i	0.487525	+	0.828300i
$754$	27.3809			0.997155
$755$	−8.48540			−0.308815
$756$	0.688940	−	32.3536i	0.0250565	−	1.17669i
$757$	14.1254			0.513397			0.256698	−	0.966492i	$-0.417365\pi$
$757$	14.1254			0.513397			0.256698	+	0.966492i	$0.417365\pi$
$758$	68.9288			2.50361
$759$	−0.0451762	−	0.0767540i	−0.00163979	−	0.00278599i
$760$	−5.82516			−0.211301
$761$	−4.97487	−	8.61673i	−0.180339	−	0.312356i	0.761657	−	0.647980i	$-0.224386\pi$
$761$	−4.97487	−	8.61673i	−0.180339	−	0.312356i	−0.941996	+	0.335624i	$0.891053\pi$
$762$	21.3925	+	36.3457i	0.774970	+	1.31667i
$763$	12.1221	−	6.26712i	0.438851	−	0.226885i
$764$	3.16048			0.114342
$765$	−1.40080	−	2.33493i	−0.0506460	−	0.0844197i
$766$	13.3820	+	23.1783i	0.483511	+	0.837466i
$767$	15.6931	−	27.1812i	0.566643	−	0.981455i
$768$	7.85333	+	13.3427i	0.283383	+	0.481465i
$769$	−24.1352	+	41.8033i	−0.870336	+	1.50747i	−0.00868735	+	0.999962i	$0.502765\pi$
$769$	−24.1352	+	41.8033i	−0.870336	+	1.50747i	−0.861649	+	0.507505i	$0.830568\pi$
$770$	0.00395792	−	0.0851555i	0.000142634	−	0.00306879i
$771$	−0.424972	+	0.750538i	−0.0153050	+	0.0270299i
$772$	−29.3190			−1.05521
$773$	7.45682	+	12.9156i	0.268203	+	0.464542i	0.968398	−	0.249410i	$-0.0802368\pi$
$773$	7.45682	+	12.9156i	0.268203	+	0.464542i	−0.700195	+	0.713952i	$0.746903\pi$
$774$	−2.93884	+	0.0492880i	−0.105634	+	0.00177162i
$775$	−0.610692	+	1.05775i	−0.0219367	+	0.0379955i
$776$	2.30066	+	3.98486i	0.0825889	+	0.143048i
$777$	1.67242	−	43.9198i	0.0599977	−	1.57561i
$778$	−7.79053	+	13.4936i	−0.279304	+	0.483769i
$779$	43.1452	+	74.7297i	1.54584	+	2.67747i
$780$	−12.4516	−	21.1552i	−0.445840	−	0.757478i
$781$	0.0368415	−	0.0638113i	0.00131829	−	0.00228335i
$782$	−3.15326	+	5.46161i	−0.112760	+	0.195307i
$783$	−5.90730	−	9.66207i	−0.211110	−	0.345294i
$784$	22.0729	+	2.05629i	0.788318	+	0.0734388i
$785$	8.60705	+	14.9079i	0.307199	+	0.532084i
$786$	28.5630	−	50.4447i	1.01881	−	1.79930i
$787$	−6.10920			−0.217769			−0.108885	−	0.994054i	$-0.534728\pi$
$787$	−6.10920			−0.217769			−0.108885	+	0.994054i	$0.534728\pi$
$788$	32.1733			1.14613
$789$	−30.4724	+	0.255512i	−1.08485	+	0.00909647i
$790$	−7.32881	−	12.6939i	−0.260747	−	0.451627i
$791$	−30.5114	−	19.5587i	−1.08486	−	0.695428i
$792$	0.0175991	+	0.0293353i	0.000625358	+	0.00104238i
$793$	24.8554	−	43.0507i	0.882639	−	1.52878i
$794$	−11.6095	+	20.1082i	−0.412005	+	0.713613i
$795$	−4.82997	+	0.0404994i	−0.171301	+	0.00143637i
$796$	−20.2838	−	35.1325i	−0.718939	−	1.24524i
$797$	−10.2256	+	17.7112i	−0.362209	+	0.627364i	−0.988324	−	0.152367i	$-0.951311\pi$
$797$	−10.2256	+	17.7112i	−0.362209	+	0.627364i	0.626115	+	0.779730i	$0.284644\pi$
$798$	−2.87008	+	75.3720i	−0.101600	+	2.66814i
$799$	2.30011	+	3.98391i	0.0813720	+	0.140941i
$800$	4.04253	−	7.00187i	0.142925	−	0.247553i
$801$	−19.5604	−	32.6044i	−0.691131	−	1.15202i
$802$	−18.7605	−	32.4942i	−0.662458	−	1.14741i
$803$	−0.0144107			−0.000508544
$804$	11.0109	+	18.7073i	0.388323	+	0.659757i
$805$	−7.41717	−	4.75463i	−0.261421	−	0.167579i
$806$	7.67222	−	13.2887i	0.270242	−	0.468073i
$807$	−12.1871	+	21.5235i	−0.429008	+	0.757665i
$808$	4.37387	−	7.57576i	0.153872	−	0.266514i
$809$	25.4615	+	44.1006i	0.895178	+	1.55049i	0.833584	+	0.552392i	$0.186285\pi$
$809$	25.4615	+	44.1006i	0.895178	+	1.55049i	0.0615935	+	0.998101i	$0.480382\pi$
$810$	−8.83907	+	16.5692i	−0.310573	+	0.582182i
$811$	28.5592			1.00285			0.501424	−	0.865202i	$-0.332810\pi$
$811$	28.5592			1.00285			0.501424	+	0.865202i	$0.332810\pi$
$812$	−12.0573	+	6.23362i	−0.423129	+	0.218757i
$813$	−10.1253	+	0.0849011i	−0.355111	+	0.00297761i
$814$	0.154514	+	0.267626i	0.00541571	+	0.00938029i
$815$	1.19479			0.0418516
$816$	−2.45307	+	4.33232i	−0.0858745	+	0.151662i
$817$	3.70383			0.129581
$818$	71.3205			2.49366
$819$	−42.0773	+	22.6560i	−1.47030	+	0.791666i
$820$	25.7500			0.899230
$821$	34.1178			1.19072			0.595359	−	0.803460i	$-0.297010\pi$
$821$	34.1178			1.19072			0.595359	+	0.803460i	$0.297010\pi$
$822$	−20.7905	+	0.174329i	−0.725151	+	0.00608041i
$823$	40.1262			1.39871			0.699356	−	0.714774i	$-0.253470\pi$
$823$	40.1262			1.39871			0.699356	+	0.714774i	$0.253470\pi$
$824$	5.07927	+	8.79755i	0.176945	+	0.306477i
$825$	−0.0131781	+	0.0232737i	−0.000458804	+	0.000810287i
$826$	−1.33614	+	28.7474i	−0.0464904	+	1.00025i
$827$	−3.36758			−0.117102			−0.0585511	−	0.998284i	$-0.518648\pi$
$827$	−3.36758			−0.117102			−0.0585511	+	0.998284i	$0.518648\pi$
$828$	23.5120	−	0.394326i	0.817100	−	0.0137038i
$829$	−8.14761	−	14.1121i	−0.282978	−	0.490133i	0.689139	−	0.724630i	$-0.257989\pi$
$829$	−8.14761	−	14.1121i	−0.282978	−	0.490133i	−0.972117	+	0.234497i	$0.924656\pi$
$830$	−17.5485	+	30.3949i	−0.609118	+	1.05502i
$831$	−20.1236	+	0.168737i	−0.698081	+	0.00585343i
$832$	−31.7193	+	54.9394i	−1.09967	+	1.90468i
$833$	2.65264	+	5.77317i	0.0919087	+	0.200028i
$834$	10.7101	−	0.0898044i	0.370860	−	0.00310967i
$835$	8.26128			0.285893
$836$	−0.143360	−	0.248306i	−0.00495820	−	0.00858786i
$837$	−6.34449	+	0.159626i	−0.219298	+	0.00551748i
$838$	−22.4364	+	38.8610i	−0.775053	+	1.34243i
$839$	−2.95539	−	5.11888i	−0.102031	−	0.176723i	0.810490	−	0.585752i	$-0.199201\pi$
$839$	−2.95539	−	5.11888i	−0.102031	−	0.176723i	−0.912521	+	0.409029i	$0.865868\pi$
$840$	2.86421	+	1.80234i	0.0988245	+	0.0621867i
$841$	12.1250	−	21.0011i	0.418102	−	0.724174i
$842$	23.2640	+	40.2944i	0.801729	+	1.38864i
$843$	−3.42473	+	6.04837i	−0.117954	+	0.208317i
$844$	−11.2546	+	19.4935i	−0.387399	+	0.670995i
$845$	−11.6254	+	20.1358i	−0.399926	+	0.692692i
$846$	15.4006	−	27.7386i	0.529482	−	0.953673i
$847$	−25.8520	+	13.3655i	−0.888287	+	0.459242i
$848$	4.41578	+	7.64835i	0.151638	+	0.262645i
$849$	−10.8695	−	18.4671i	−0.373039	−	0.633790i
$850$	1.89387			0.0649591
$851$	31.9379			1.09482
$852$	9.86829	+	16.7661i	0.338082	+	0.574398i
$853$	3.68713	+	6.38630i	0.126245	+	0.218663i	0.922219	−	0.386668i	$-0.126374\pi$
$853$	3.68713	+	6.38630i	0.126245	+	0.218663i	−0.795974	+	0.605331i	$0.793041\pi$
$854$	−2.11624	+	45.5314i	−0.0724164	+	1.55805i
$855$	11.4869	−	20.6895i	0.392844	−	0.707567i
$856$	−4.54871	+	7.87859i	−0.155472	+	0.269285i
$857$	7.25314	−	12.5628i	0.247762	−	0.429137i	−0.715142	−	0.698979i	$-0.753638\pi$
$857$	7.25314	−	12.5628i	0.247762	−	0.429137i	0.962905	+	0.269842i	$0.0869714\pi$
$858$	0.165559	−	0.292391i	0.00565209	−	0.00998207i
$859$	−16.4260	−	28.4506i	−0.560447	−	0.970722i	−0.997457	−	0.0712660i	$-0.977296\pi$
$859$	−16.4260	−	28.4506i	−0.560447	−	0.970722i	0.437010	−	0.899456i	$-0.356037\pi$
$860$	0.552632	−	0.957187i	0.0188446	−	0.0326398i
$861$	1.90751	−	50.0937i	0.0650078	−	1.70719i
$862$	16.3312	+	28.2864i	0.556242	+	0.963440i
$863$	7.99037	−	13.8397i	0.271995	−	0.471109i	−0.697377	−	0.716704i	$-0.745650\pi$
$863$	7.99037	−	13.8397i	0.271995	−	0.471109i	0.969373	+	0.245595i	$0.0789832\pi$
$864$	41.9979	−	1.05666i	1.42880	−	0.0359482i
$865$	−7.01950	−	12.1581i	−0.238670	−	0.413389i
$866$	−64.7646			−2.20079
$867$	28.0170	−	0.234923i	0.951508	−	0.00797842i
$868$	−0.353165	+	7.59841i	−0.0119872	+	0.257907i
$869$	0.0542358	−	0.0939391i	0.00183982	−	0.00318667i
$870$	7.87653	−	0.0660449i	0.267039	−	0.00223913i
$871$	16.0281	−	27.7615i	0.543092	−	0.940663i
$872$	−1.90445	−	3.29861i	−0.0644930	−	0.111705i
$873$	−18.6900	+	0.313454i	−0.632561	+	0.0106088i
$874$	−54.8094			−1.85396
$875$	−0.122839	+	2.64290i	−0.00415270	+	0.0893463i
$876$	1.87476	−	3.31099i	0.0633423	−	0.111868i
$877$	1.61029	+	2.78910i	0.0543755	+	0.0941812i	0.891932	−	0.452170i	$-0.149350\pi$
$877$	1.61029	+	2.78910i	0.0543755	+	0.0941812i	−0.837556	+	0.546351i	$0.816017\pi$
$878$	−3.81973			−0.128910
$879$	44.7921	−	0.375582i	1.51080	−	0.0126681i
$880$	0.0489024			0.00164850
$881$	8.42574			0.283871			0.141935	−	0.989876i	$-0.454668\pi$
$881$	8.42574			0.283871			0.141935	+	0.989876i	$0.454668\pi$
$882$	24.7317	−	36.1720i	0.832761	−	1.21798i
$883$	−54.8523			−1.84593			−0.922964	−	0.384886i	$-0.874241\pi$
$883$	−54.8523			−1.84593			−0.922964	+	0.384886i	$0.874241\pi$
$884$	−12.8635			−0.432645
$885$	4.44878	−	7.85692i	0.149544	−	0.264107i
$886$	−37.1723			−1.24883
$887$	−11.2361	−	19.4614i	−0.377270	−	0.653451i	0.613394	−	0.789777i	$-0.289804\pi$
$887$	−11.2361	−	19.4614i	−0.377270	−	0.653451i	−0.990664	+	0.136326i	$0.956470\pi$
$888$	−12.2672	+	0.102860i	−0.411659	+	0.00345177i
$889$	−1.43344	+	30.8408i	−0.0480761	+	1.03437i
$890$	26.4454			0.886452
$891$	−0.138896	+	0.00466023i	−0.00465320	+	0.000156124i
$892$	4.73028	+	8.19308i	0.158381	+	0.274325i
$893$	−19.9901	+	34.6238i	−0.668942	+	1.15864i
$894$	14.3955	−	25.4237i	0.481458	−	0.850297i
$895$	−3.95787	+	6.85523i	−0.132297	+	0.229145i
$896$	0.714340	−	15.3692i	0.0238644	−	0.513448i
$897$	−17.6147	−	29.9273i	−0.588139	−	0.999243i
$898$	27.5103			0.918031
$899$	1.33098	+	2.30533i	0.0443907	+	0.0768870i
$900$	−3.63292	−	6.05557i	−0.121097	−	0.201852i
$901$	−1.26555	+	2.19199i	−0.0421615	+	0.0730259i
$902$	0.176234	+	0.305246i	0.00586795	+	0.0101636i
$903$	−1.82116	−	1.14599i	−0.0606043	−	0.0381361i
$904$	−5.05786	+	8.76047i	−0.168222	+	0.291369i
$905$	−2.77740	−	4.81059i	−0.0923238	−	0.159910i
$906$	30.6660	−	0.257135i	1.01881	−	0.00854275i
$907$	−18.9856	+	32.8840i	−0.630407	+	1.09190i	0.357062	+	0.934081i	$0.383779\pi$
$907$	−18.9856	+	32.8840i	−0.630407	+	1.09190i	−0.987469	+	0.157816i	$0.949555\pi$
$908$	3.29485	−	5.70684i	0.109343	−	0.189388i
$909$	18.2822	+	30.4739i	0.606382	+	1.01075i
$910$	1.54324	−	33.2031i	0.0511579	−	1.10067i
$911$	1.75368	+	3.03747i	0.0581021	+	0.100636i	0.893613	−	0.448837i	$-0.148162\pi$
$911$	1.75368	+	3.03747i	0.0581021	+	0.100636i	−0.835511	+	0.549473i	$0.814828\pi$
$912$	−43.2672	+	0.362796i	−1.43272	+	0.0120134i
$913$	−0.259731			−0.00859583
$914$	−50.7065			−1.67722
$915$	7.04617	−	12.4441i	0.232939	−	0.411390i
$916$	23.9091	+	41.4117i	0.789978	+	1.36828i
$917$	37.6976	−	19.4896i	1.24489	−	0.643604i
$918$	5.13321	+	8.39595i	0.169421	+	0.277108i
$919$	−6.42021	+	11.1201i	−0.211783	+	0.366819i	−0.952273	−	0.305249i	$-0.901260\pi$
$919$	−6.42021	+	11.1201i	−0.211783	+	0.366819i	0.740490	+	0.672068i	$0.234594\pi$
$920$	−1.22954	+	2.12963i	−0.0405368	+	0.0702118i
$921$	6.36216	+	10.8092i	0.209640	+	0.356177i
$922$	7.49282	+	12.9779i	0.246763	+	0.427406i
$923$	14.3649	−	24.8808i	0.472827	−	0.818960i
$924$	−0.00633814	+	0.166448i	−0.000208509	+	0.00547572i
$925$	−4.79552	−	8.30608i	−0.157676	−	0.273102i
$926$	13.1321	−	22.7455i	0.431548	−	0.747464i
$927$	−41.2627	+	0.692026i	−1.35525	+	0.0227291i
$928$	−8.81055	−	15.2603i	−0.289220	−	0.500945i
$929$	−51.2183			−1.68042			−0.840208	−	0.542264i	$-0.817567\pi$
$929$	−51.2183			−1.68042			−0.840208	+	0.542264i	$0.817567\pi$
$930$	2.17497	−	3.84119i	0.0713202	−	0.125958i
$931$	−31.9251	+	45.0523i	−1.04630	+	1.47653i
$932$	−7.66685	+	13.2794i	−0.251136	+	0.434980i
$933$	−29.3743	−	49.9067i	−0.961672	−	1.63387i
$934$	−14.6779	+	25.4228i	−0.480275	+	0.831861i
$935$	0.00700764	+	0.0121376i	0.000229174	+	0.000396942i
$936$	6.86211	+	11.4382i	0.224295	+	0.373869i
$937$	32.2456			1.05342			0.526708	−	0.850046i	$-0.323426\pi$
$937$	32.2456			1.05342			0.526708	+	0.850046i	$0.323426\pi$
$938$	−1.36467	+	29.3612i	−0.0445581	+	0.958677i
$939$	−18.3728	−	31.2151i	−0.599572	−	1.01867i
$940$	5.96525	+	10.3321i	0.194565	+	0.336997i
$941$	−47.8128			−1.55865			−0.779326	−	0.626619i	$-0.784438\pi$
$941$	−47.8128			−1.55865			−0.779326	+	0.626619i	$0.784438\pi$
$942$	−31.5574	−	53.6158i	−1.02820	−	1.74690i
$943$	36.4274			1.18624
$944$	−16.5088			−0.537317
$945$	−12.0495	+	6.61884i	−0.391971	+	0.215311i
$946$	0.0151289			0.000491884
$947$	20.0771			0.652418			0.326209	−	0.945298i	$-0.394229\pi$
$947$	20.0771			0.652418			0.326209	+	0.945298i	$0.394229\pi$
$948$	14.5275	+	24.6821i	0.471831	+	0.801637i
$949$	−5.61892			−0.182398
$950$	8.22971	+	14.2543i	0.267007	+	0.462470i
$951$	8.50110	+	14.4433i	0.275667	+	0.468356i
$952$	1.57527	−	0.814410i	0.0510547	−	0.0263952i
$953$	−34.9184			−1.13112			−0.565560	−	0.824707i	$-0.691340\pi$
$953$	−34.9184			−1.13112			−0.565560	+	0.824707i	$0.691340\pi$
$954$	17.4542	−	0.292728i	0.565099	−	0.00947741i
$955$	−0.671325	−	1.16277i	−0.0217236	−	0.0376263i
$956$	34.2262	−	59.2816i	1.10696	−	1.91730i
$957$	0.0295678	+	0.0502355i	0.000955792	+	0.00162388i
$958$	28.8454	−	49.9617i	0.931952	−	1.61419i
$959$	−12.8138	−	8.21402i	−0.413778	−	0.265245i
$960$	−8.99200	+	15.8806i	−0.290215	+	0.512545i
$961$	−29.5082			−0.951878
$962$	60.2468	+	104.351i	1.94244	+	3.36440i
$963$	−19.0130	−	31.6920i	−0.612686	−	1.02126i
$964$	16.5302	−	28.6312i	0.532403	−	0.922150i
$965$	6.22771	+	10.7867i	0.200477	+	0.347237i
$966$	26.9495	+	16.9584i	0.867087	+	0.545626i
$967$	−13.1123	+	22.7112i	−0.421664	+	0.730343i	−0.996102	−	0.0882047i	$-0.971887\pi$
$967$	−13.1123	+	22.7112i	−0.421664	+	0.730343i	0.574439	+	0.818548i	$0.305220\pi$
$968$	4.06150	+	7.03472i	0.130542	+	0.226105i
$969$	−6.29016	−	10.6869i	−0.202069	−	0.343314i
$970$	6.50068	−	11.2595i	0.208724	−	0.361521i
$971$	−28.3045	+	49.0249i	−0.908336	+	1.57328i	−0.0919602	+	0.995763i	$0.529313\pi$
$971$	−28.3045	+	49.0249i	−0.908336	+	1.57328i	−0.816376	+	0.577521i	$0.804020\pi$
$972$	16.9989	−	32.5188i	0.545241	−	1.04304i
$973$	6.60094	+	4.23141i	0.211617	+	0.135653i
$974$	23.6773	+	41.0103i	0.758671	+	1.31406i
$975$	−5.13831	+	9.07470i	−0.164558	+	0.290623i
$976$	−26.1474			−0.836959
$977$	−23.3541			−0.747163			−0.373582	−	0.927597i	$-0.621870\pi$
$977$	−23.3541			−0.747163			−0.373582	+	0.927597i	$0.621870\pi$
$978$	−4.31794	+	0.0362060i	−0.138072	+	0.00115774i
$979$	0.0978527	+	0.169486i	0.00312739	+	0.00541679i
$980$	6.87954	+	14.9725i	0.219759	+	0.478279i
$981$	15.4713	−	0.259473i	0.493961	−	0.00828434i
$982$	20.2727	−	35.1134i	0.646929	−	1.12051i
$983$	20.0839	−	34.7863i	0.640576	−	1.10951i	−0.344728	−	0.938703i	$-0.612029\pi$
$983$	20.0839	−	34.7863i	0.640576	−	1.10951i	0.985304	−	0.170808i	$-0.0546379\pi$
$984$	−13.9916	+	0.117320i	−0.446035	+	0.00374001i
$985$	−6.83402	−	11.8369i	−0.217750	−	0.377154i
$986$	2.06381	−	3.57462i	0.0657250	−	0.113839i
$987$	20.5418	−	10.8393i	0.653854	−	0.345019i
$988$	−55.8977	−	96.8176i	−1.77834	−	3.08018i
$989$	0.781784	−	1.35409i	0.0248593	−	0.0430575i
$990$	0.0469202	−	0.0845100i	0.00149122	−	0.00268590i
$991$	16.5599	+	28.6826i	0.526042	+	0.911131i	0.999540	+	0.0303363i	$0.00965783\pi$
$991$	16.5599	+	28.6826i	0.526042	+	0.911131i	−0.473498	+	0.880795i	$0.657009\pi$
$992$	−9.87497			−0.313530
$993$	−14.7756	−	25.1036i	−0.468889	−	0.796638i
$994$	−1.22306	+	26.3145i	−0.0387932	+	0.834644i
$995$	−8.61705	+	14.9252i	−0.273179	+	0.473160i
$996$	33.7896	−	59.6752i	1.07066	−	1.89088i
$997$	−8.11279	+	14.0518i	−0.256935	+	0.445024i	−0.965419	−	0.260702i	$-0.916046\pi$
$997$	−8.11279	+	14.0518i	−0.256935	+	0.445024i	0.708485	+	0.705726i	$0.249379\pi$
$998$	−19.4471	−	33.6834i	−0.615588	−	1.06623i
$999$	23.8248	−	43.7728i	0.753784	−	1.38491i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.l.c.121.16	yes	36
3.2	odd	2		945.2.l.c.226.3		36
7.4	even	3		315.2.k.c.256.3	yes	36
9.2	odd	6		945.2.k.c.856.16		36
9.7	even	3		315.2.k.c.16.3	✓	36
21.11	odd	6		945.2.k.c.361.16		36
63.11	odd	6		945.2.l.c.46.3		36
63.25	even	3	inner	315.2.l.c.151.16	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.c.16.3	✓	36	9.7	even	3
315.2.k.c.256.3	yes	36	7.4	even	3
315.2.l.c.121.16	yes	36	1.1	even	1	trivial
315.2.l.c.151.16	yes	36	63.25	even	3	inner
945.2.k.c.361.16		36	21.11	odd	6
945.2.k.c.856.16		36	9.2	odd	6
945.2.l.c.46.3		36	63.11	odd	6
945.2.l.c.226.3		36	3.2	odd	2

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.08660 q^{2} +(0.878572 + 1.49269i) q^{3} +2.35391 q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.83323 + 3.11464i) q^{6} +(-0.122839 + 2.64290i) q^{7} +0.738471 q^{8} +(-1.45622 + 2.62286i) q^{9} +O(q^{10})\)	\(q+2.08660 q^{2} +(0.878572 + 1.49269i) q^{3} +2.35391 q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.83323 + 3.11464i) q^{6} +(-0.122839 + 2.64290i) q^{7} +0.738471 q^{8} +(-1.45622 + 2.62286i) q^{9} +(-1.04330 - 1.80705i) q^{10} +(0.00772080 - 0.0133728i) q^{11} +(2.06808 + 3.51365i) q^{12} +(3.01043 - 5.21422i) q^{13} +(-0.256315 + 5.51468i) q^{14} +(0.853418 - 1.50721i) q^{15} -3.16693 q^{16} +(-0.453816 - 0.786032i) q^{17} +(-3.03856 + 5.47288i) q^{18} +(3.94407 - 6.83134i) q^{19} +(-1.17696 - 2.03855i) q^{20} +(-4.05294 + 2.13862i) q^{21} +(0.0161102 - 0.0279038i) q^{22} +(-1.66499 - 2.88384i) q^{23} +(0.648800 + 1.10230i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(6.28157 - 10.8800i) q^{26} +(-5.19451 + 0.130693i) q^{27} +(-0.289151 + 6.22115i) q^{28} +(1.08973 + 1.88747i) q^{29} +(1.78074 - 3.14495i) q^{30} +1.22138 q^{31} -8.08506 q^{32} +(0.0267447 - 0.000224255i) q^{33} +(-0.946933 - 1.64014i) q^{34} +(2.35024 - 1.21507i) q^{35} +(-3.42782 + 6.17399i) q^{36} +(-4.79552 + 8.30608i) q^{37} +(8.22971 - 14.2543i) q^{38} +(10.4281 - 0.0874396i) q^{39} +(-0.369235 - 0.639534i) q^{40} +(-5.46963 + 9.47367i) q^{41} +(-8.45687 + 4.46244i) q^{42} +(0.234772 + 0.406637i) q^{43} +(0.0181741 - 0.0314784i) q^{44} +(2.99958 - 0.0503066i) q^{45} +(-3.47416 - 6.01743i) q^{46} -5.06838 q^{47} +(-2.78237 - 4.72723i) q^{48} +(-6.96982 - 0.649300i) q^{49} +(-1.04330 + 1.80705i) q^{50} +(0.774589 - 1.36799i) q^{51} +(7.08629 - 12.2738i) q^{52} +(-1.39434 - 2.41507i) q^{53} +(-10.8389 + 0.272704i) q^{54} -0.0154416 q^{55} +(-0.0907127 + 1.95170i) q^{56} +(13.6622 - 0.114558i) q^{57} +(2.27384 + 3.93840i) q^{58} +5.21289 q^{59} +(2.00887 - 3.54783i) q^{60} +8.25641 q^{61} +2.54854 q^{62} +(-6.75308 - 4.17084i) q^{63} -10.5365 q^{64} -6.02086 q^{65} +(0.0558056 - 0.000467931i) q^{66} +5.32419 q^{67} +(-1.06824 - 1.85025i) q^{68} +(2.84186 - 5.01896i) q^{69} +(4.90401 - 2.53536i) q^{70} +4.77171 q^{71} +(-1.07538 + 1.93691i) q^{72} +(-0.466621 - 0.808211i) q^{73} +(-10.0063 + 17.3315i) q^{74} +(-1.73199 + 0.0145228i) q^{75} +(9.28400 - 16.0804i) q^{76} +(0.0343946 + 0.0220480i) q^{77} +(21.7592 - 0.182452i) q^{78} +7.02463 q^{79} +(1.58346 + 2.74264i) q^{80} +(-4.75883 - 7.63895i) q^{81} +(-11.4129 + 19.7678i) q^{82} +(-8.41010 - 14.5667i) q^{83} +(-9.54026 + 5.03411i) q^{84} +(-0.453816 + 0.786032i) q^{85} +(0.489876 + 0.848490i) q^{86} +(-1.85999 + 3.28491i) q^{87} +(0.00570158 - 0.00987543i) q^{88} +(-6.33695 + 10.9759i) q^{89} +(6.25893 - 0.104970i) q^{90} +(13.4109 + 8.59677i) q^{91} +(-3.91923 - 6.78830i) q^{92} +(1.07307 + 1.82314i) q^{93} -10.5757 q^{94} -7.88815 q^{95} +(-7.10331 - 12.0685i) q^{96} +(3.11544 + 5.39610i) q^{97} +(-14.5432 - 1.35483i) q^{98} +(0.0238319 + 0.0397244i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9}+O(q^{10}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9} + q^{11} + 8 q^{12} + 2 q^{13} + 9 q^{14} - q^{15} + 60 q^{16} - 5 q^{17} - 21 q^{18} - 2 q^{19} - 22 q^{20} - 23 q^{21} - 19 q^{22} - 3 q^{23} - 32 q^{24} - 18 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} + 2 q^{30} - 20 q^{32} - 35 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} - 22 q^{38} + 7 q^{39} - 4 q^{41} + 57 q^{42} - 29 q^{43} - 7 q^{44} + 6 q^{45} - 24 q^{46} + 46 q^{47} - 19 q^{48} - 7 q^{49} + 42 q^{51} - 7 q^{52} + 21 q^{54} - 2 q^{55} - 12 q^{56} + 21 q^{57} - 20 q^{58} + 10 q^{59} - 13 q^{60} + 6 q^{61} - 12 q^{62} + 2 q^{63} + 128 q^{64} - 4 q^{65} - 12 q^{66} + 70 q^{67} - 17 q^{68} - 50 q^{69} - 3 q^{70} + 24 q^{71} - 10 q^{72} - 10 q^{73} + 22 q^{74} + 2 q^{75} + 10 q^{76} + 35 q^{77} + 66 q^{78} + 56 q^{79} - 30 q^{80} - 49 q^{81} - 8 q^{82} - 22 q^{83} - 86 q^{84} - 5 q^{85} + 19 q^{86} - 42 q^{87} - 50 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - q^{93} + 4 q^{94} + 4 q^{95} - 179 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9 + q^11 + 8 * q^12 + 2 * q^13 + 9 * q^14 - q^15 + 60 * q^16 - 5 * q^17 - 21 * q^18 - 2 * q^19 - 22 * q^20 - 23 * q^21 - 19 * q^22 - 3 * q^23 - 32 * q^24 - 18 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 + 2 * q^30 - 20 * q^32 - 35 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 - 22 * q^38 + 7 * q^39 - 4 * q^41 + 57 * q^42 - 29 * q^43 - 7 * q^44 + 6 * q^45 - 24 * q^46 + 46 * q^47 - 19 * q^48 - 7 * q^49 + 42 * q^51 - 7 * q^52 + 21 * q^54 - 2 * q^55 - 12 * q^56 + 21 * q^57 - 20 * q^58 + 10 * q^59 - 13 * q^60 + 6 * q^61 - 12 * q^62 + 2 * q^63 + 128 * q^64 - 4 * q^65 - 12 * q^66 + 70 * q^67 - 17 * q^68 - 50 * q^69 - 3 * q^70 + 24 * q^71 - 10 * q^72 - 10 * q^73 + 22 * q^74 + 2 * q^75 + 10 * q^76 + 35 * q^77 + 66 * q^78 + 56 * q^79 - 30 * q^80 - 49 * q^81 - 8 * q^82 - 22 * q^83 - 86 * q^84 - 5 * q^85 + 19 * q^86 - 42 * q^87 - 50 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - q^93 + 4 * q^94 + 4 * q^95 - 179 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

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