LMFDB - Embedded newform 690.2.m.e.211.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (of order $11$, degree $10$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{19} + 21 x^{18} - 47 x^{17} + 44 x^{16} + 232 x^{15} - 1084 x^{14} + 1484 x^{13} + \cdots + 1849 $ x^20 - 6x^19 + 21x^18 - 47x^17 + 44x^16 + 232x^15 - 1084x^14 + 1484x^13 + 2670x^12 - 12826x^11 + 18393x^10 - 2728x^9 - 12654x^8 - 6818x^7 + 39054x^6 + 33738x^5 + 67716x^4 + 45635x^3 + 32892x^2 + 9761*x + 1849
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			211.1
Root			$2.03264 + 1.30630i$ of defining polynomial
Character	$\chi$	$=$	690.211
Dual form			690.2.m.e.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 - 0.909632i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(0.841254 + 0.540641i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(-0.421385 - 2.93080i) q^{7} +(0.959493 + 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})$	\(q+(-0.415415 - 0.909632i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(0.841254 + 0.540641i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(-0.421385 - 2.93080i) q^{7} +(0.959493 + 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +(0.142315 - 0.989821i) q^{10} +(1.29850 - 2.84332i) q^{11} +(-0.415415 + 0.909632i) q^{12} +(-0.190234 + 1.32311i) q^{13} +(-2.49090 + 1.60080i) q^{14} +(0.959493 + 0.281733i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(-1.17117 - 1.35160i) q^{17} +(-0.841254 - 0.540641i) q^{18} +(0.606145 - 0.699529i) q^{19} +(-0.959493 + 0.281733i) q^{20} +(-1.23002 - 2.69336i) q^{21} -3.12579 q^{22} +(3.97003 + 2.69052i) q^{23} +1.00000 q^{24} +(0.415415 + 0.909632i) q^{25} +(1.28257 - 0.376596i) q^{26} +(0.654861 - 0.755750i) q^{27} +(2.49090 + 1.60080i) q^{28} +(-6.82896 - 7.88104i) q^{29} +(-0.142315 - 0.989821i) q^{30} +(1.95245 + 0.573290i) q^{31} +(-0.841254 + 0.540641i) q^{32} +(0.444846 - 3.09397i) q^{33} +(-0.742937 + 1.62680i) q^{34} +(1.23002 - 2.69336i) q^{35} +(-0.142315 + 0.989821i) q^{36} +(6.65243 - 4.27526i) q^{37} +(-0.888116 - 0.260774i) q^{38} +(0.190234 + 1.32311i) q^{39} +(0.654861 + 0.755750i) q^{40} +(-7.33845 - 4.71614i) q^{41} +(-1.93900 + 2.23773i) q^{42} +(6.65618 - 1.95443i) q^{43} +(1.29850 + 2.84332i) q^{44} +1.00000 q^{45} +(0.798175 - 4.72894i) q^{46} +1.85519 q^{47} +(-0.415415 - 0.909632i) q^{48} +(-1.69557 + 0.497864i) q^{49} +(0.654861 - 0.755750i) q^{50} +(-1.50452 - 0.966893i) q^{51} +(-0.875361 - 1.01022i) q^{52} +(-0.257312 - 1.78964i) q^{53} +(-0.959493 - 0.281733i) q^{54} +(2.62958 - 1.68993i) q^{55} +(0.421385 - 2.93080i) q^{56} +(0.384512 - 0.841964i) q^{57} +(-4.33200 + 9.48575i) q^{58} +(-1.26233 + 8.77972i) q^{59} +(-0.841254 + 0.540641i) q^{60} +(1.54231 + 0.452864i) q^{61} +(-0.289593 - 2.01416i) q^{62} +(-1.93900 - 2.23773i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-0.875361 + 1.01022i) q^{65} +(-2.99917 + 0.880636i) q^{66} +(4.06491 + 8.90091i) q^{67} +1.78842 q^{68} +(4.56722 + 1.46305i) q^{69} -2.96094 q^{70} +(-4.68077 - 10.2494i) q^{71} +(0.959493 - 0.281733i) q^{72} +(-1.44586 + 1.66862i) q^{73} +(-6.65243 - 4.27526i) q^{74} +(0.654861 + 0.755750i) q^{75} +(0.131728 + 0.916188i) q^{76} +(-8.88036 - 2.60751i) q^{77} +(1.12451 - 0.722682i) q^{78} +(-1.02980 + 7.16240i) q^{79} +(0.415415 - 0.909632i) q^{80} +(0.415415 - 0.909632i) q^{81} +(-1.24145 + 8.63445i) q^{82} +(-12.4077 + 7.97396i) q^{83} +(2.84100 + 0.834192i) q^{84} +(-0.254519 - 1.77022i) q^{85} +(-4.54289 - 5.24277i) q^{86} +(-8.77269 - 5.63786i) q^{87} +(2.04696 - 2.36231i) q^{88} +(-6.00345 + 1.76277i) q^{89} +(-0.415415 - 0.909632i) q^{90} +3.95792 q^{91} +(-4.63317 + 1.23843i) q^{92} +2.03487 q^{93} +(-0.770673 - 1.68754i) q^{94} +(0.888116 - 0.260774i) q^{95} +(-0.654861 + 0.755750i) q^{96} +(9.97604 + 6.41121i) q^{97} +(1.15724 + 1.33552i) q^{98} +(-0.444846 - 3.09397i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} - 4 q^{11} + 2 q^{12} - 13 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 2 q^{21} + 26 q^{22} + 24 q^{23} + 20 q^{24} - 2 q^{25} + 13 q^{26} + 2 q^{27} - 2 q^{28} + 2 q^{29} - 2 q^{30} + 6 q^{31} + 2 q^{32} + 4 q^{33} + 5 q^{34} - 2 q^{35} - 2 q^{36} - 20 q^{37} + 4 q^{38} + 13 q^{39} + 2 q^{40} - 11 q^{41} - 13 q^{42} + 4 q^{43} - 4 q^{44} + 20 q^{45} - 2 q^{46} + 18 q^{47} + 2 q^{48} - 6 q^{49} + 2 q^{50} + 27 q^{51} - 2 q^{52} - 18 q^{53} - 2 q^{54} + 18 q^{55} + 2 q^{56} - 7 q^{57} + 9 q^{58} - 52 q^{59} + 2 q^{60} - 7 q^{61} + 16 q^{62} - 13 q^{63} - 2 q^{64} - 2 q^{65} + 7 q^{66} - 10 q^{67} + 28 q^{68} + 20 q^{69} - 20 q^{70} + 7 q^{71} + 2 q^{72} - 37 q^{73} + 20 q^{74} + 2 q^{75} - 4 q^{76} - 70 q^{77} + 9 q^{78} + 20 q^{79} - 2 q^{80} - 2 q^{81} - 11 q^{82} - 19 q^{83} - 9 q^{84} + 17 q^{85} - 26 q^{86} - 2 q^{87} + 4 q^{88} + 33 q^{89} + 2 q^{90} - 42 q^{91} - 9 q^{92} + 16 q^{93} - 7 q^{94} - 4 q^{95} - 2 q^{96} + 9 q^{97} + 6 q^{98} - 4 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 + 2 * q^10 - 4 * q^11 + 2 * q^12 - 13 * q^13 + 2 * q^14 + 2 * q^15 - 2 * q^16 + 6 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 2 * q^21 + 26 * q^22 + 24 * q^23 + 20 * q^24 - 2 * q^25 + 13 * q^26 + 2 * q^27 - 2 * q^28 + 2 * q^29 - 2 * q^30 + 6 * q^31 + 2 * q^32 + 4 * q^33 + 5 * q^34 - 2 * q^35 - 2 * q^36 - 20 * q^37 + 4 * q^38 + 13 * q^39 + 2 * q^40 - 11 * q^41 - 13 * q^42 + 4 * q^43 - 4 * q^44 + 20 * q^45 - 2 * q^46 + 18 * q^47 + 2 * q^48 - 6 * q^49 + 2 * q^50 + 27 * q^51 - 2 * q^52 - 18 * q^53 - 2 * q^54 + 18 * q^55 + 2 * q^56 - 7 * q^57 + 9 * q^58 - 52 * q^59 + 2 * q^60 - 7 * q^61 + 16 * q^62 - 13 * q^63 - 2 * q^64 - 2 * q^65 + 7 * q^66 - 10 * q^67 + 28 * q^68 + 20 * q^69 - 20 * q^70 + 7 * q^71 + 2 * q^72 - 37 * q^73 + 20 * q^74 + 2 * q^75 - 4 * q^76 - 70 * q^77 + 9 * q^78 + 20 * q^79 - 2 * q^80 - 2 * q^81 - 11 * q^82 - 19 * q^83 - 9 * q^84 + 17 * q^85 - 26 * q^86 - 2 * q^87 + 4 * q^88 + 33 * q^89 + 2 * q^90 - 42 * q^91 - 9 * q^92 + 16 * q^93 - 7 * q^94 - 4 * q^95 - 2 * q^96 + 9 * q^97 + 6 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{11}\right)$

Coefficient data

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

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

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

$2$	−0.415415	−	0.909632i	−0.293743	−	0.643207i
$2$	−0.415415	−	0.909632i	−0.293743	−	0.643207i
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$4$	−0.654861	+	0.755750i	−0.327430	+	0.377875i
$5$	0.841254	+	0.540641i	0.376220	+	0.241782i
$5$	0.841254	+	0.540641i	0.376220	+	0.241782i
$6$	−0.654861	−	0.755750i	−0.267346	−	0.308533i
$7$	−0.421385	−	2.93080i	−0.159269	−	1.10774i	−0.899985	−	0.435920i	$-0.856423\pi$
$7$	−0.421385	−	2.93080i	−0.159269	−	1.10774i	0.740717	−	0.671818i	$-0.234486\pi$
$8$	0.959493	+	0.281733i	0.339232	+	0.0996075i
$9$	0.841254	−	0.540641i	0.280418	−	0.180214i
$10$	0.142315	−	0.989821i	0.0450039	−	0.313009i
$11$	1.29850	−	2.84332i	0.391512	−	0.857292i	−0.606549	−	0.795046i	$-0.707446\pi$
$11$	1.29850	−	2.84332i	0.391512	−	0.857292i	0.998061	−	0.0622458i	$-0.0198263\pi$
$12$	−0.415415	+	0.909632i	−0.119920	+	0.262588i
$13$	−0.190234	+	1.32311i	−0.0527614	+	0.366964i	0.946286	+	0.323330i	$0.104803\pi$
$13$	−0.190234	+	1.32311i	−0.0527614	+	0.366964i	−0.999048	+	0.0436336i	$0.986107\pi$
$14$	−2.49090	+	1.60080i	−0.665721	+	0.427833i
$15$	0.959493	+	0.281733i	0.247740	+	0.0727430i
$16$	−0.142315	−	0.989821i	−0.0355787	−	0.247455i
$17$	−1.17117	−	1.35160i	−0.284050	−	0.327811i	0.595737	−	0.803180i	$-0.296860\pi$
$17$	−1.17117	−	1.35160i	−0.284050	−	0.327811i	−0.879787	+	0.475369i	$0.842315\pi$
$18$	−0.841254	−	0.540641i	−0.198285	−	0.127430i
$19$	0.606145	−	0.699529i	0.139059	−	0.160483i	−0.681948	−	0.731401i	$-0.738867\pi$
$19$	0.606145	−	0.699529i	0.139059	−	0.160483i	0.821007	+	0.570918i	$0.193412\pi$
$20$	−0.959493	+	0.281733i	−0.214549	+	0.0629973i
$21$	−1.23002	−	2.69336i	−0.268412	−	0.587740i
$22$	−3.12579			−0.666420
$23$	3.97003	+	2.69052i	0.827807	+	0.561012i
$23$	3.97003	+	2.69052i	0.827807	+	0.561012i
$24$	1.00000			0.204124
$25$	0.415415	+	0.909632i	0.0830830	+	0.181926i
$26$	1.28257	−	0.376596i	0.251532	−	0.0738565i
$27$	0.654861	−	0.755750i	0.126028	−	0.145444i
$28$	2.49090	+	1.60080i	0.470736	+	0.302523i
$29$	−6.82896	−	7.88104i	−1.26811	−	1.46347i	−0.823048	−	0.567971i	$-0.807728\pi$
$29$	−6.82896	−	7.88104i	−1.26811	−	1.46347i	−0.445058	−	0.895502i	$-0.646817\pi$
$30$	−0.142315	−	0.989821i	−0.0259830	−	0.180716i
$31$	1.95245	+	0.573290i	0.350670	+	0.102966i	0.452324	−	0.891854i	$-0.350595\pi$
$31$	1.95245	+	0.573290i	0.350670	+	0.102966i	−0.101654	+	0.994820i	$0.532413\pi$
$32$	−0.841254	+	0.540641i	−0.148714	+	0.0955727i
$33$	0.444846	−	3.09397i	0.0774377	−	0.538591i
$34$	−0.742937	+	1.62680i	−0.127413	+	0.278995i
$35$	1.23002	−	2.69336i	0.207911	−	0.455262i
$36$	−0.142315	+	0.989821i	−0.0237191	+	0.164970i
$37$	6.65243	−	4.27526i	1.09365	−	0.702848i	0.135981	−	0.990711i	$-0.456581\pi$
$37$	6.65243	−	4.27526i	1.09365	−	0.702848i	0.957671	+	0.287863i	$0.0929449\pi$
$38$	−0.888116	−	0.260774i	−0.144071	−	0.0423032i
$39$	0.190234	+	1.32311i	0.0304618	+	0.211867i
$40$	0.654861	+	0.755750i	0.103543	+	0.119494i
$41$	−7.33845	−	4.71614i	−1.14607	−	0.736537i	−0.177220	−	0.984171i	$-0.556710\pi$
$41$	−7.33845	−	4.71614i	−1.14607	−	0.736537i	−0.968854	+	0.247634i	$0.920347\pi$
$42$	−1.93900	+	2.23773i	−0.299194	+	0.345289i
$43$	6.65618	−	1.95443i	1.01506	−	0.298048i	0.268436	−	0.963297i	$-0.413493\pi$
$43$	6.65618	−	1.95443i	1.01506	−	0.298048i	0.746621	+	0.665250i	$0.231675\pi$
$44$	1.29850	+	2.84332i	0.195756	+	0.428646i
$45$	1.00000			0.149071
$46$	0.798175	−	4.72894i	0.117685	−	0.697245i
$47$	1.85519			0.270607			0.135303	−	0.990804i	$-0.456799\pi$
$47$	1.85519			0.270607			0.135303	+	0.990804i	$0.456799\pi$
$48$	−0.415415	−	0.909632i	−0.0599600	−	0.131294i
$49$	−1.69557	+	0.497864i	−0.242224	+	0.0711234i
$50$	0.654861	−	0.755750i	0.0926113	−	0.106879i
$51$	−1.50452	−	0.966893i	−0.210674	−	0.135392i
$52$	−0.875361	−	1.01022i	−0.121391	−	0.140092i
$53$	−0.257312	−	1.78964i	−0.0353445	−	0.245826i	0.964488	−	0.264127i	$-0.0850837\pi$
$53$	−0.257312	−	1.78964i	−0.0353445	−	0.245826i	−0.999833	+	0.0183001i	$0.994175\pi$
$54$	−0.959493	−	0.281733i	−0.130570	−	0.0383389i
$55$	2.62958	−	1.68993i	0.354572	−	0.227870i
$56$	0.421385	−	2.93080i	0.0563100	−	0.391645i
$57$	0.384512	−	0.841964i	0.0509299	−	0.111521i
$58$	−4.33200	+	9.48575i	−0.568819	+	1.24554i
$59$	−1.26233	+	8.77972i	−0.164342	+	1.14302i	0.725989	+	0.687707i	$0.241383\pi$
$59$	−1.26233	+	8.77972i	−0.164342	+	1.14302i	−0.890330	+	0.455315i	$0.849527\pi$
$60$	−0.841254	+	0.540641i	−0.108605	+	0.0697964i
$61$	1.54231	+	0.452864i	0.197473	+	0.0579833i	0.378973	−	0.925408i	$-0.376277\pi$
$61$	1.54231	+	0.452864i	0.197473	+	0.0579833i	−0.181500	+	0.983391i	$0.558095\pi$
$62$	−0.289593	−	2.01416i	−0.0367783	−	0.255799i
$63$	−1.93900	−	2.23773i	−0.244291	−	0.281927i
$64$	0.841254	+	0.540641i	0.105157	+	0.0675801i
$65$	−0.875361	+	1.01022i	−0.108575	+	0.125302i
$66$	−2.99917	+	0.880636i	−0.369172	+	0.108399i
$67$	4.06491	+	8.90091i	0.496608	+	1.08742i	0.977557	+	0.210671i	$0.0675647\pi$
$67$	4.06491	+	8.90091i	0.496608	+	1.08742i	−0.480950	+	0.876748i	$0.659708\pi$
$68$	1.78842			0.216878
$69$	4.56722	+	1.46305i	0.549828	+	0.176131i
$70$	−2.96094			−0.353900
$71$	−4.68077	−	10.2494i	−0.555505	−	1.21639i	−0.954163	−	0.299286i	$-0.903251\pi$
$71$	−4.68077	−	10.2494i	−0.555505	−	1.21639i	0.398659	−	0.917099i	$-0.369476\pi$
$72$	0.959493	−	0.281733i	0.113077	−	0.0332025i
$73$	−1.44586	+	1.66862i	−0.169226	+	0.195297i	−0.834027	−	0.551723i	$-0.813971\pi$
$73$	−1.44586	+	1.66862i	−0.169226	+	0.195297i	0.664802	+	0.747020i	$0.268516\pi$
$74$	−6.65243	−	4.27526i	−0.773329	−	0.496989i
$75$	0.654861	+	0.755750i	0.0756168	+	0.0872664i
$76$	0.131728	+	0.916188i	0.0151102	+	0.105094i
$77$	−8.88036	−	2.60751i	−1.01201	−	0.297153i
$78$	1.12451	−	0.722682i	0.127326	−	0.0818276i
$79$	−1.02980	+	7.16240i	−0.115861	+	0.805833i	0.846174	+	0.532907i	$0.178901\pi$
$79$	−1.02980	+	7.16240i	−0.115861	+	0.805833i	−0.962035	+	0.272926i	$0.912009\pi$
$80$	0.415415	−	0.909632i	0.0464448	−	0.101700i
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$	−1.24145	+	8.63445i	−0.137095	+	0.953515i
$83$	−12.4077	+	7.97396i	−1.36192	+	0.875256i	−0.998412	−	0.0563333i	$-0.982059\pi$
$83$	−12.4077	+	7.97396i	−1.36192	+	0.875256i	−0.363513	+	0.931589i	$0.618423\pi$
$84$	2.84100	+	0.834192i	0.309978	+	0.0910179i
$85$	−0.254519	−	1.77022i	−0.0276064	−	0.192007i
$86$	−4.54289	−	5.24277i	−0.489872	−	0.565343i
$87$	−8.77269	−	5.63786i	−0.940531	−	0.604443i
$88$	2.04696	−	2.36231i	0.218206	−	0.251823i
$89$	−6.00345	+	1.76277i	−0.636364	+	0.186853i	−0.583973	−	0.811773i	$-0.698502\pi$
$89$	−6.00345	+	1.76277i	−0.636364	+	0.186853i	−0.0523913	+	0.998627i	$0.516684\pi$
$90$	−0.415415	−	0.909632i	−0.0437886	−	0.0958836i
$91$	3.95792			0.414903
$92$	−4.63317	+	1.23843i	−0.483042	+	0.129115i
$93$	2.03487			0.211007
$94$	−0.770673	−	1.68754i	−0.0794888	−	0.174056i
$95$	0.888116	−	0.260774i	0.0911187	−	0.0267549i
$96$	−0.654861	+	0.755750i	−0.0668364	+	0.0771334i
$97$	9.97604	+	6.41121i	1.01291	+	0.650960i	0.938146	−	0.346241i	$-0.112542\pi$
$97$	9.97604	+	6.41121i	1.01291	+	0.650960i	0.0747676	+	0.997201i	$0.476178\pi$
$98$	1.15724	+	1.33552i	0.116899	+	0.134908i
$99$	−0.444846	−	3.09397i	−0.0447087	−	0.310956i
$100$	−0.959493	−	0.281733i	−0.0959493	−	0.0281733i
$101$	8.06686	−	5.18426i	0.802683	−	0.515853i	−0.0738075	−	0.997273i	$-0.523515\pi$
$101$	8.06686	−	5.18426i	0.802683	−	0.515853i	0.876490	+	0.481420i	$0.159879\pi$
$102$	−0.254519	+	1.77022i	−0.0252011	+	0.175278i
$103$	−0.416238	+	0.911434i	−0.0410132	+	0.0898063i	−0.929030	−	0.370005i	$-0.879356\pi$
$103$	−0.416238	+	0.911434i	−0.0410132	+	0.0898063i	0.888016	+	0.459812i	$0.152083\pi$
$104$	−0.555291	+	1.21592i	−0.0544507	+	0.119230i
$105$	0.421385	−	2.93080i	0.0411230	−	0.286017i
$106$	−1.52103	+	0.977504i	−0.147735	+	0.0949436i
$107$	2.34151	+	0.687529i	0.226362	+	0.0664660i	0.392947	−	0.919561i	$-0.371456\pi$
$107$	2.34151	+	0.687529i	0.226362	+	0.0664660i	−0.166584	+	0.986027i	$0.553274\pi$
$108$	0.142315	+	0.989821i	0.0136943	+	0.0952456i
$109$	−1.25026	−	1.44288i	−0.119753	−	0.138203i	0.692707	−	0.721219i	$-0.256418\pi$
$109$	−1.25026	−	1.44288i	−0.119753	−	0.138203i	−0.812460	+	0.583016i	$0.801872\pi$
$110$	−2.62958	−	1.68993i	−0.250721	−	0.161128i
$111$	5.17848	−	5.97629i	0.491520	−	0.567244i
$112$	−2.84100	+	0.834192i	−0.268449	+	0.0788238i
$113$	4.25898	+	9.32587i	0.400651	+	0.877304i	0.997204	+	0.0747299i	$0.0238095\pi$
$113$	4.25898	+	9.32587i	0.400651	+	0.877304i	−0.596553	+	0.802574i	$0.703463\pi$
$114$	−0.925609			−0.0866913
$115$	1.88519	+	4.40977i	0.175795	+	0.411213i
$116$	10.4281			0.968226
$117$	0.555291	+	1.21592i	0.0513366	+	0.112412i
$118$	8.51071	−	2.49897i	0.783474	−	0.230049i
$119$	−3.46775	+	4.00200i	−0.317888	+	0.366862i
$120$	0.841254	+	0.540641i	0.0767956	+	0.0493535i
$121$	0.805120	+	0.929158i	0.0731928	+	0.0844689i
$122$	−0.228760	−	1.59106i	−0.0207110	−	0.144048i
$123$	−8.36988	−	2.45762i	−0.754687	−	0.221596i
$124$	−1.71184	+	1.10014i	−0.153728	+	0.0987951i
$125$	−0.142315	+	0.989821i	−0.0127290	+	0.0885323i
$126$	−1.23002	+	2.69336i	−0.109579	+	0.239944i
$127$	−5.98857	+	13.1131i	−0.531400	+	1.16360i	0.433540	+	0.901134i	$0.357264\pi$
$127$	−5.98857	+	13.1131i	−0.531400	+	1.16360i	−0.964940	+	0.262469i	$0.915463\pi$
$128$	0.142315	−	0.989821i	0.0125790	−	0.0874887i
$129$	5.83593	−	3.75052i	0.513825	−	0.330215i
$130$	1.28257	+	0.376596i	0.112489	+	0.0330296i
$131$	0.100872	+	0.701580i	0.00881322	+	0.0612973i	0.993753	−	0.111598i	$-0.0355969\pi$
$131$	0.100872	+	0.701580i	0.00881322	+	0.0612973i	−0.984940	+	0.172895i	$0.944688\pi$
$132$	2.04696	+	2.36231i	0.178165	+	0.205613i
$133$	−2.30560	−	1.48172i	−0.199921	−	0.128481i
$134$	6.40793	−	7.39514i	0.553560	−	0.638843i
$135$	0.959493	−	0.281733i	0.0825800	−	0.0242477i
$136$	−0.742937	−	1.62680i	−0.0637063	−	0.139497i
$137$	17.6344			1.50660			0.753302	−	0.657675i	$-0.228460\pi$
$137$	17.6344			1.50660			0.753302	+	0.657675i	$0.228460\pi$
$138$	−0.566454	−	4.76226i	−0.0482198	−	0.405391i
$139$	0.399882			0.0339175			0.0169588	−	0.999856i	$-0.494602\pi$
$139$	0.399882			0.0339175			0.0169588	+	0.999856i	$0.494602\pi$
$140$	1.23002	+	2.69336i	0.103955	+	0.227631i
$141$	1.78004	−	0.522667i	0.149906	−	0.0440165i
$142$	−7.37876	+	8.51555i	−0.619212	+	0.714609i
$143$	3.51499	+	2.25895i	0.293939	+	0.188903i
$144$	−0.654861	−	0.755750i	−0.0545717	−	0.0629791i
$145$	−1.48408	−	10.3220i	−0.123246	−	0.857193i
$146$	2.11846	+	0.622036i	0.175325	+	0.0514801i
$147$	−1.48662	+	0.955394i	−0.122614	+	0.0787995i
$148$	−1.12539	+	7.82727i	−0.0925066	+	0.643398i
$149$	−8.03473	+	17.5936i	−0.658231	+	1.44132i	0.225931	+	0.974143i	$0.427458\pi$
$149$	−8.03473	+	17.5936i	−0.658231	+	1.44132i	−0.884162	+	0.467181i	$0.845270\pi$
$150$	0.415415	−	0.909632i	0.0339185	−	0.0742711i
$151$	0.356447	−	2.47915i	0.0290073	−	0.201750i	−0.970164	−	0.242449i	$-0.922049\pi$
$151$	0.356447	−	2.47915i	0.0290073	−	0.201750i	0.999171	+	0.0406989i	$0.0129584\pi$
$152$	0.778672	−	0.500422i	0.0631587	−	0.0405896i
$153$	−1.71598	−	0.503856i	−0.138729	−	0.0407344i
$154$	1.31716	+	9.16106i	0.106140	+	0.738219i
$155$	1.33256	+	1.53786i	0.107034	+	0.123523i
$156$	−1.12451	−	0.722682i	−0.0900332	−	0.0578608i
$157$	−12.7168	+	14.6760i	−1.01491	+	1.17127i	−0.0297676	+	0.999557i	$0.509477\pi$
$157$	−12.7168	+	14.6760i	−1.01491	+	1.17127i	−0.985146	+	0.171716i	$0.945069\pi$
$158$	6.94294	−	2.03863i	0.552351	−	0.162185i
$159$	−0.751090	−	1.64466i	−0.0595653	−	0.130430i
$160$	−1.00000			−0.0790569
$161$	6.21246	−	12.7691i	0.489611	−	1.00635i
$162$	−1.00000			−0.0785674
$163$	−0.271273	−	0.594005i	−0.0212477	−	0.0465261i	0.898711	−	0.438542i	$-0.144505\pi$
$163$	−0.271273	−	0.594005i	−0.0212477	−	0.0465261i	−0.919958	+	0.392016i	$0.871778\pi$
$164$	8.36988	−	2.45762i	0.653578	−	0.191908i
$165$	2.04696	−	2.36231i	0.159355	−	0.183906i
$166$	12.4077	+	7.97396i	0.963026	+	0.618899i
$167$	10.2352	+	11.8120i	0.792021	+	0.914040i	0.997916	−	0.0645336i	$-0.0205560\pi$
$167$	10.2352	+	11.8120i	0.792021	+	0.914040i	−0.205895	+	0.978574i	$0.566011\pi$
$168$	−0.421385	−	2.93080i	−0.0325106	−	0.226116i
$169$	10.7590	+	3.15912i	0.827614	+	0.243009i
$170$	−1.50452	+	0.966893i	−0.115391	+	0.0741573i
$171$	0.131728	−	0.916188i	0.0100735	−	0.0700626i
$172$	−2.88181	+	6.31028i	−0.219736	+	0.481154i
$173$	0.296212	−	0.648615i	0.0225206	−	0.0493133i	−0.898037	−	0.439919i	$-0.855007\pi$
$173$	0.296212	−	0.648615i	0.0225206	−	0.0493133i	0.920558	+	0.390606i	$0.127734\pi$
$174$	−1.48408	+	10.3220i	−0.112507	+	0.782507i
$175$	2.49090	−	1.60080i	0.188294	−	0.121009i
$176$	−2.99917	−	0.880636i	−0.226071	−	0.0663804i
$177$	1.26233	+	8.77972i	0.0948828	+	0.659924i
$178$	4.09739	+	4.72864i	0.307113	+	0.354427i
$179$	19.6404	+	12.6221i	1.46799	+	0.943419i	0.998158	+	0.0606624i	$0.0193213\pi$
$179$	19.6404	+	12.6221i	1.46799	+	0.943419i	0.469830	+	0.882757i	$0.344315\pi$
$180$	−0.654861	+	0.755750i	−0.0488104	+	0.0563302i
$181$	−0.871821	+	0.255990i	−0.0648019	+	0.0190276i	−0.313973	−	0.949432i	$-0.601660\pi$
$181$	−0.871821	+	0.255990i	−0.0648019	+	0.0190276i	0.249171	+	0.968460i	$0.419842\pi$
$182$	−1.64418	−	3.60025i	−0.121875	−	0.266869i
$183$	1.60742			0.118824
$184$	3.05120	+	3.70002i	0.224938	+	0.272769i
$185$	7.90776			0.581390
$186$	−0.845317	−	1.85099i	−0.0619817	−	0.135721i
$187$	−5.36378	+	1.57495i	−0.392238	+	0.115172i
$188$	−1.21489	+	1.40206i	−0.0886049	+	0.102256i
$189$	−2.49090	−	1.60080i	−0.181186	−	0.116441i
$190$	−0.606145	−	0.699529i	−0.0439744	−	0.0507492i
$191$	−3.29906	−	22.9455i	−0.238712	−	1.66028i	−0.658445	−	0.752628i	$-0.728786\pi$
$191$	−3.29906	−	22.9455i	−0.238712	−	1.66028i	0.419734	−	0.907647i	$-0.362123\pi$
$192$	0.959493	+	0.281733i	0.0692454	+	0.0203323i
$193$	10.7231	−	6.89132i	0.771865	−	0.496048i	−0.0944595	−	0.995529i	$-0.530112\pi$
$193$	10.7231	−	6.89132i	0.771865	−	0.496048i	0.866325	+	0.499481i	$0.166476\pi$
$194$	1.68765	−	11.7378i	0.121166	−	0.842728i
$195$	−0.555291	+	1.21592i	−0.0397652	+	0.0870736i
$196$	0.734101	−	1.60746i	0.0524358	−	0.114818i
$197$	0.0731107	−	0.508496i	0.00520892	−	0.0362288i	−0.987051	−	0.160405i	$-0.948720\pi$
$197$	0.0731107	−	0.508496i	0.00520892	−	0.0362288i	0.992260	+	0.124177i	$0.0396289\pi$
$198$	−2.62958	+	1.68993i	−0.186876	+	0.120098i
$199$	0.376706	+	0.110611i	0.0267040	+	0.00784100i	0.295057	−	0.955480i	$-0.404661\pi$
$199$	0.376706	+	0.110611i	0.0267040	+	0.00784100i	−0.268353	+	0.963321i	$0.586479\pi$
$200$	0.142315	+	0.989821i	0.0100632	+	0.0699909i
$201$	6.40793	+	7.39514i	0.451980	+	0.521613i
$202$	−8.06686	−	5.18426i	−0.567582	−	0.364763i
$203$	−20.2201	+	23.3353i	−1.41918	+	1.63782i
$204$	1.71598	−	0.503856i	0.120142	−	0.0352770i
$205$	−3.62376	−	7.93493i	−0.253095	−	0.554200i
$206$	1.00198			0.0698113
$207$	4.79440	+	0.117052i	0.333234	+	0.00813567i
$208$	1.33671			0.0926844
$209$	−1.20190	−	2.63180i	−0.0831374	−	0.182045i
$210$	−2.84100	+	0.834192i	−0.196048	+	0.0575647i
$211$	−1.00087	+	1.15507i	−0.0689027	+	0.0795180i	−0.789154	−	0.614195i	$-0.789481\pi$
$211$	−1.00087	+	1.15507i	−0.0689027	+	0.0795180i	0.720252	+	0.693713i	$0.244026\pi$
$212$	1.52103	+	0.977504i	0.104464	+	0.0671352i
$213$	−7.37876	−	8.51555i	−0.505585	−	0.583476i
$214$	−0.347300	−	2.41552i	−0.0237409	−	0.165122i
$215$	6.65618	+	1.95443i	0.453947	+	0.133291i
$216$	0.841254	−	0.540641i	0.0572401	−	0.0367859i
$217$	0.857466	−	5.96381i	0.0582086	−	0.404850i
$218$	−0.793110	+	1.73667i	−0.0537162	+	0.117622i
$219$	−0.917193	+	2.00837i	−0.0619782	+	0.135713i
$220$	−0.444846	+	3.09397i	−0.0299915	+	0.208596i
$221$	2.01110	−	1.29246i	0.135282	−	0.0869402i
$222$	−7.58744	−	2.22787i	−0.509236	−	0.149525i
$223$	2.36047	+	16.4174i	0.158069	+	1.09939i	0.902188	+	0.431344i	$0.141960\pi$
$223$	2.36047	+	16.4174i	0.158069	+	1.09939i	−0.744119	+	0.668047i	$0.767130\pi$
$224$	1.93900	+	2.23773i	0.129555	+	0.149514i
$225$	0.841254	+	0.540641i	0.0560836	+	0.0360427i
$226$	6.71386	−	7.74821i	0.446600	−	0.515403i
$227$	−18.9614	+	5.56758i	−1.25851	+	0.369533i	−0.841941	−	0.539569i	$-0.818587\pi$
$227$	−18.9614	+	5.56758i	−1.25851	+	0.369533i	−0.416573	+	0.909102i	$0.636769\pi$
$228$	0.384512	+	0.841964i	0.0254649	+	0.0557604i
$229$	−9.99709			−0.660626			−0.330313	−	0.943871i	$-0.607154\pi$
$229$	−9.99709			−0.660626			−0.330313	+	0.943871i	$0.607154\pi$
$230$	3.22813	−	3.54672i	0.212856	−	0.233863i
$231$	−9.25526			−0.608951
$232$	−4.33200	−	9.48575i	−0.284409	−	0.622770i
$233$	−14.0396	+	4.12241i	−0.919767	+	0.270068i	−0.707147	−	0.707067i	$-0.750018\pi$
$233$	−14.0396	+	4.12241i	−0.919767	+	0.270068i	−0.212620	+	0.977135i	$0.568200\pi$
$234$	0.875361	−	1.01022i	0.0572241	−	0.0660402i
$235$	1.56068	+	1.00299i	0.101808	+	0.0654278i
$236$	−5.80862	−	6.70350i	−0.378109	−	0.436361i
$237$	1.02980	+	7.16240i	0.0668926	+	0.465248i
$238$	5.08090	+	1.49189i	0.329346	+	0.0967047i
$239$	5.20797	−	3.34696i	0.336876	−	0.216497i	−0.361255	−	0.932467i	$-0.617652\pi$
$239$	5.20797	−	3.34696i	0.336876	−	0.216497i	0.698131	+	0.715970i	$0.254015\pi$
$240$	0.142315	−	0.989821i	0.00918638	−	0.0638927i
$241$	−9.32490	+	20.4187i	−0.600670	+	1.31528i	0.328106	+	0.944641i	$0.393590\pi$
$241$	−9.32490	+	20.4187i	−0.600670	+	1.31528i	−0.928776	+	0.370643i	$0.879137\pi$
$242$	0.510733	−	1.11835i	0.0328312	−	0.0718902i
$243$	0.142315	−	0.989821i	0.00912950	−	0.0634971i
$244$	−1.35225	+	0.869039i	−0.0865690	+	0.0556345i
$245$	−1.69557	−	0.497864i	−0.108326	−	0.0318074i
$246$	1.24145	+	8.63445i	0.0791517	+	0.550512i
$247$	0.810242	+	0.935069i	0.0515545	+	0.0594970i
$248$	1.71184	+	1.10014i	0.108702	+	0.0698587i
$249$	−9.65860	+	11.1466i	−0.612089	+	0.706388i
$250$	0.959493	−	0.281733i	0.0606837	−	0.0178183i
$251$	9.84351	+	21.5543i	0.621317	+	1.36049i	0.914558	+	0.404456i	$0.132539\pi$
$251$	9.84351	+	21.5543i	0.621317	+	1.36049i	−0.293240	+	0.956039i	$0.594734\pi$
$252$	2.96094			0.186522
$253$	12.8051	−	7.79440i	0.805048	−	0.490030i
$254$	14.4159			0.904533
$255$	−0.742937	−	1.62680i	−0.0465245	−	0.101874i
$256$	−0.959493	+	0.281733i	−0.0599683	+	0.0176083i
$257$	5.50585	−	6.35409i	0.343446	−	0.396357i	−0.557580	−	0.830123i	$-0.688270\pi$
$257$	5.50585	−	6.35409i	0.343446	−	0.396357i	0.901026	+	0.433766i	$0.142815\pi$
$258$	−5.83593	−	3.75052i	−0.363329	−	0.233497i
$259$	−15.3332	−	17.6954i	−0.952756	−	1.09954i
$260$	−0.190234	−	1.32311i	−0.0117978	−	0.0820556i
$261$	−10.0057	−	2.93794i	−0.619337	−	0.181854i
$262$	0.596276	−	0.383203i	0.0368380	−	0.0236744i
$263$	−2.09791	+	14.5913i	−0.129363	+	0.899736i	0.817002	+	0.576635i	$0.195635\pi$
$263$	−2.09791	+	14.5913i	−0.129363	+	0.899736i	−0.946364	+	0.323101i	$0.895275\pi$
$264$	1.29850	−	2.84332i	0.0799171	−	0.174994i
$265$	0.751090	−	1.64466i	0.0461391	−	0.101030i
$266$	−0.390038	+	2.71278i	−0.0239148	+	0.166331i
$267$	−5.26363	+	3.38273i	−0.322129	+	0.207020i
$268$	−9.38880	−	2.75680i	−0.573513	−	0.168398i
$269$	−2.24328	−	15.6023i	−0.136775	−	0.951291i	−0.936436	−	0.350839i	$-0.885896\pi$
$269$	−2.24328	−	15.6023i	−0.136775	−	0.951291i	0.799661	−	0.600452i	$-0.205013\pi$
$270$	−0.654861	−	0.755750i	−0.0398536	−	0.0459935i
$271$	−5.57055	−	3.57998i	−0.338387	−	0.217468i	0.360400	−	0.932798i	$-0.382640\pi$
$271$	−5.57055	−	3.57998i	−0.338387	−	0.217468i	−0.698787	+	0.715330i	$0.746277\pi$
$272$	−1.17117	+	1.35160i	−0.0710124	+	0.0819527i
$273$	3.79760	−	1.11508i	0.229841	−	0.0674875i
$274$	−7.32557	−	16.0408i	−0.442554	−	0.969058i
$275$	3.12579			0.188492
$276$	−4.09659	+	2.49358i	−0.246586	+	0.150096i
$277$	7.97573			0.479215			0.239608	−	0.970870i	$-0.422981\pi$
$277$	7.97573			0.479215			0.239608	+	0.970870i	$0.422981\pi$
$278$	−0.166117	−	0.363745i	−0.00996303	−	0.0218160i
$279$	1.95245	−	0.573290i	0.116890	−	0.0343220i
$280$	1.93900	−	2.23773i	0.115878	−	0.133730i
$281$	−20.2994	−	13.0456i	−1.21096	−	0.778236i	−0.230140	−	0.973158i	$-0.573918\pi$
$281$	−20.2994	−	13.0456i	−1.21096	−	0.778236i	−0.980819	+	0.194922i	$0.937555\pi$
$282$	−1.21489	−	1.40206i	−0.0723456	−	0.0834913i
$283$	−3.55181	−	24.7034i	−0.211133	−	1.46846i	−0.769382	−	0.638789i	$-0.779436\pi$
$283$	−3.55181	−	24.7034i	−0.211133	−	1.46846i	0.558249	−	0.829674i	$-0.311474\pi$
$284$	10.8113	+	3.17447i	0.641531	+	0.188370i
$285$	0.778672	−	0.500422i	0.0461246	−	0.0296425i
$286$	0.594631	−	4.13575i	0.0351613	−	0.244552i
$287$	−10.7297	+	23.4948i	−0.633356	+	1.38686i
$288$	−0.415415	+	0.909632i	−0.0244786	+	0.0536006i
$289$	1.96417	−	13.6611i	0.115539	−	0.803592i
$290$	−8.77269	+	5.63786i	−0.515150	+	0.331067i
$291$	11.3782	+	3.34094i	0.667001	+	0.195849i
$292$	−0.314216	−	2.18542i	−0.0183881	−	0.127892i
$293$	5.31084	+	6.12903i	0.310262	+	0.358062i	0.889369	−	0.457190i	$-0.151144\pi$
$293$	5.31084	+	6.12903i	0.310262	+	0.358062i	−0.579107	+	0.815252i	$0.696599\pi$
$294$	1.48662	+	0.955394i	0.0867015	+	0.0557197i
$295$	−5.80862	+	6.70350i	−0.338191	+	0.390293i
$296$	7.58744	−	2.22787i	0.441011	−	0.129492i
$297$	−1.29850	−	2.84332i	−0.0753466	−	0.164986i
$298$	19.3415			1.12042
$299$	−4.31508	+	4.74094i	−0.249548	+	0.274176i
$300$	−1.00000			−0.0577350
$301$	−8.53286	−	18.6843i	−0.491826	−	1.07695i
$302$	−2.40318	+	0.705638i	−0.138288	+	0.0406049i
$303$	6.27952	−	7.24696i	0.360749	−	0.416327i
$304$	−0.778672	−	0.500422i	−0.0446599	−	0.0287012i
$305$	1.05264	+	1.21481i	0.0602739	+	0.0695598i
$306$	0.254519	+	1.77022i	0.0145499	+	0.101197i
$307$	24.8979	+	7.31069i	1.42100	+	0.417243i	0.899841	−	0.436217i	$-0.143682\pi$
$307$	24.8979	+	7.31069i	1.42100	+	0.417243i	0.521158	+	0.853460i	$0.325500\pi$
$308$	7.78602	−	5.00377i	0.443650	−	0.285116i
$309$	−0.142597	+	0.991782i	−0.00811205	+	0.0564205i
$310$	0.845317	−	1.85099i	0.0480108	−	0.105129i
$311$	8.22196	−	18.0036i	0.466225	−	1.02089i	−0.519799	−	0.854288i	$-0.673993\pi$
$311$	8.22196	−	18.0036i	0.466225	−	1.02089i	0.986024	−	0.166602i	$-0.0532794\pi$
$312$	−0.190234	+	1.32311i	−0.0107699	+	0.0749062i
$313$	8.13555	−	5.22840i	0.459848	−	0.295527i	−0.290132	−	0.956987i	$-0.593699\pi$
$313$	8.13555	−	5.22840i	0.459848	−	0.295527i	0.749980	+	0.661460i	$0.230063\pi$
$314$	18.6325	+	5.47101i	1.05149	+	0.308747i
$315$	−0.421385	−	2.93080i	−0.0237424	−	0.165132i
$316$	−4.73861	−	5.46864i	−0.266568	−	0.307635i
$317$	−4.95404	−	3.18377i	−0.278247	−	0.178818i	0.394073	−	0.919079i	$-0.371066\pi$
$317$	−4.95404	−	3.18377i	−0.278247	−	0.178818i	−0.672320	+	0.740261i	$0.734702\pi$
$318$	−1.18402	+	1.36643i	−0.0663965	+	0.0766256i
$319$	−31.2757	+	9.18337i	−1.75110	+	0.514170i
$320$	0.415415	+	0.909632i	0.0232224	+	0.0508500i
$321$	2.44036			0.136208
$322$	−14.1959	−	0.346584i	−0.791108	−	0.0193143i
$323$	−1.65538			−0.0921077
$324$	0.415415	+	0.909632i	0.0230786	+	0.0505351i
$325$	−1.28257	+	0.376596i	−0.0711440	+	0.0208898i
$326$	−0.427635	+	0.493517i	−0.0236845	+	0.0273334i
$327$	−1.60612	−	1.03219i	−0.0888187	−	0.0570803i
$328$	−5.71250	−	6.59258i	−0.315420	−	0.364014i
$329$	−0.781749	−	5.43718i	−0.0430992	−	0.299761i
$330$	−2.99917	−	0.880636i	−0.165099	−	0.0484774i
$331$	11.2386	−	7.22258i	0.617727	−	0.396989i	−0.194021	−	0.980997i	$-0.562153\pi$
$331$	11.2386	−	7.22258i	0.617727	−	0.396989i	0.811747	+	0.584009i	$0.198517\pi$
$332$	2.09901	−	14.5990i	0.115198	−	0.801222i
$333$	3.28500	−	7.19315i	0.180017	−	0.394182i
$334$	6.49274	−	14.2171i	0.355267	−	0.777926i
$335$	−1.39258	+	9.68557i	−0.0760845	+	0.529179i
$336$	−2.49090	+	1.60080i	−0.135890	+	0.0873310i
$337$	10.9154	+	3.20504i	0.594598	+	0.174590i	0.565166	−	0.824977i	$-0.308812\pi$
$337$	10.9154	+	3.20504i	0.594598	+	0.174590i	0.0294316	+	0.999567i	$0.490630\pi$
$338$	−1.59580	−	11.0991i	−0.0868003	−	0.603709i
$339$	6.71386	+	7.74821i	0.364647	+	0.420825i
$340$	1.50452	+	0.966893i	0.0815938	+	0.0524371i
$341$	4.16530	−	4.80701i	0.225563	−	0.260314i
$342$	−0.888116	+	0.260774i	−0.0480238	+	0.0141011i
$343$	−6.43650	−	14.0940i	−0.347538	−	0.761003i
$344$	6.93718			0.374028
$345$	3.05120	+	3.70002i	0.164271	+	0.199202i
$346$	−0.713052			−0.0383339
$347$	−5.74685	−	12.5838i	−0.308507	−	0.675536i	0.690343	−	0.723482i	$-0.257460\pi$
$347$	−5.74685	−	12.5838i	−0.308507	−	0.675536i	−0.998850	+	0.0479463i	$0.984732\pi$
$348$	10.0057	−	2.93794i	0.536362	−	0.157490i
$349$	0.679975	−	0.784733i	0.0363982	−	0.0420058i	−0.737259	−	0.675611i	$-0.763880\pi$
$349$	0.679975	−	0.784733i	0.0363982	−	0.0420058i	0.773657	+	0.633605i	$0.218426\pi$
$350$	−2.49090	−	1.60080i	−0.133144	−	0.0855666i
$351$	0.875361	+	1.01022i	0.0467233	+	0.0539216i
$352$	0.444846	+	3.09397i	0.0237104	+	0.164909i
$353$	−29.9321	−	8.78885i	−1.59312	−	0.467784i	−0.639502	−	0.768789i	$-0.720859\pi$
$353$	−29.9321	−	8.78885i	−1.59312	−	0.467784i	−0.953622	+	0.301006i	$0.902678\pi$
$354$	7.46192	−	4.79549i	0.396597	−	0.254877i
$355$	1.60356	−	11.1530i	0.0851081	−	0.591940i
$356$	2.59921	−	5.69147i	0.137758	−	0.301647i
$357$	−2.19979	+	4.81687i	−0.116425	+	0.254936i
$358$	3.32256	−	23.1089i	0.175603	−	1.22134i
$359$	−14.1481	+	9.09245i	−0.746710	+	0.479881i	−0.857835	−	0.513925i	$-0.828191\pi$
$359$	−14.1481	+	9.09245i	−0.746710	+	0.479881i	0.111125	+	0.993806i	$0.464555\pi$
$360$	0.959493	+	0.281733i	0.0505697	+	0.0148486i
$361$	2.58205	+	17.9586i	0.135898	+	0.945188i
$362$	0.595024	+	0.686694i	0.0312738	+	0.0360918i
$363$	1.03428	+	0.664692i	0.0542857	+	0.0348873i
$364$	−2.59189	+	2.99120i	−0.135852	+	0.156781i
$365$	−2.11846	+	0.622036i	−0.110885	+	0.0325589i
$366$	−0.667748	−	1.46216i	−0.0349038	−	0.0764286i
$367$	18.1919			0.949610			0.474805	−	0.880091i	$-0.342519\pi$
$367$	18.1919			0.949610			0.474805	+	0.880091i	$0.342519\pi$
$368$	2.09814	−	4.31252i	0.109373	−	0.224805i
$369$	−8.72324			−0.454113
$370$	−3.28500	−	7.19315i	−0.170779	−	0.373954i
$371$	−5.13666	+	1.50826i	−0.266682	+	0.0783049i
$372$	−1.33256	+	1.53786i	−0.0690900	+	0.0797341i
$373$	−20.8931	−	13.4272i	−1.08180	−	0.695234i	−0.126831	−	0.991924i	$-0.540481\pi$
$373$	−20.8931	−	13.4272i	−1.08180	−	0.695234i	−0.954974	+	0.296691i	$0.904117\pi$
$374$	3.66082	+	4.22481i	0.189296	+	0.218460i
$375$	0.142315	+	0.989821i	0.00734911	+	0.0511142i
$376$	1.78004	+	0.522667i	0.0917985	+	0.0269545i
$377$	11.7266	−	7.53621i	0.603949	−	0.388134i
$378$	−0.421385	+	2.93080i	−0.0216737	+	0.150744i
$379$	−10.5396	+	23.0785i	−0.541383	+	1.18546i	0.419309	+	0.907844i	$0.362273\pi$
$379$	−10.5396	+	23.0785i	−0.541383	+	1.18546i	−0.960691	+	0.277619i	$0.910455\pi$
$380$	−0.384512	+	0.841964i	−0.0197251	+	0.0431918i
$381$	−2.05159	+	14.2691i	−0.105106	+	0.731031i
$382$	−19.5015	+	12.5328i	−0.997781	+	0.641235i
$383$	−28.2900	−	8.30671i	−1.44555	−	0.424453i	−0.537485	−	0.843274i	$-0.680625\pi$
$383$	−28.2900	−	8.30671i	−1.44555	−	0.424453i	−0.908069	+	0.418821i	$0.862444\pi$
$384$	−0.142315	−	0.989821i	−0.00726247	−	0.0505116i
$385$	−6.06091	−	6.99466i	−0.308892	−	0.356481i
$386$	−10.7231	−	6.89132i	−0.545791	−	0.350759i
$387$	4.54289	−	5.24277i	0.230928	−	0.266505i
$388$	−11.3782	+	3.34094i	−0.577640	+	0.169610i
$389$	−11.5208	−	25.2271i	−0.584130	−	1.27907i	−0.938925	−	0.344122i	$-0.888177\pi$
$389$	−11.5208	−	25.2271i	−0.584130	−	1.27907i	0.354795	−	0.934944i	$-0.384551\pi$
$390$	1.33671			0.0676871
$391$	−1.01306	−	8.51693i	−0.0512326	−	0.430719i
$392$	−1.76715			−0.0892546
$393$	0.294444	+	0.644742i	0.0148527	+	0.0325229i
$394$	−0.492916	+	0.144733i	−0.0248327	+	0.00729155i
$395$	−4.73861	+	5.46864i	−0.238425	+	0.275157i
$396$	2.62958	+	1.68993i	0.132141	+	0.0849221i
$397$	−19.1258	−	22.0724i	−0.959898	−	1.10778i	−0.994111	−	0.108366i	$-0.965438\pi$
$397$	−19.1258	−	22.0724i	−0.959898	−	1.10778i	0.0342135	−	0.999415i	$-0.489107\pi$
$398$	−0.0558742	−	0.388613i	−0.00280072	−	0.0194794i
$399$	−2.62966	−	0.772136i	−0.131647	−	0.0386552i
$400$	0.841254	−	0.540641i	0.0420627	−	0.0270320i
$401$	0.320984	−	2.23249i	0.0160292	−	0.111485i	−0.980236	−	0.197832i	$-0.936610\pi$
$401$	0.320984	−	2.23249i	0.0160292	−	0.111485i	0.996265	+	0.0863463i	$0.0275192\pi$
$402$	4.06491	−	8.90091i	0.202739	−	0.443937i
$403$	−1.12995	+	2.47424i	−0.0562866	+	0.123251i
$404$	−1.36467	+	9.49149i	−0.0678949	+	0.472219i
$405$	0.841254	−	0.540641i	0.0418022	−	0.0268647i
$406$	29.6263	+	8.69906i	1.47033	+	0.431727i
$407$	−3.51773	−	24.4664i	−0.174368	−	1.21275i
$408$	−1.17117	−	1.35160i	−0.0579814	−	0.0669141i
$409$	−27.3201	−	17.5576i	−1.35089	−	0.868167i	−0.353167	−	0.935560i	$-0.614895\pi$
$409$	−27.3201	−	17.5576i	−1.35089	−	0.868167i	−0.997726	+	0.0673934i	$0.978532\pi$
$410$	−5.71250	+	6.59258i	−0.282120	+	0.325584i
$411$	16.9200	−	4.96817i	0.834604	−	0.245062i
$412$	−0.416238	−	0.911434i	−0.0205066	−	0.0449031i
$413$	26.2635			1.29234
$414$	−1.88519	−	4.40977i	−0.0926522	−	0.216728i
$415$	−14.7491			−0.724004
$416$	−0.555291	−	1.21592i	−0.0272254	−	0.0596152i
$417$	0.383684	−	0.112660i	0.0187891	−	0.00551697i
$418$	−1.89468	+	2.18658i	−0.0926719	+	0.106949i
$419$	20.8003	+	13.3675i	1.01616	+	0.653047i	0.938981	−	0.343970i	$-0.111772\pi$
$419$	20.8003	+	13.3675i	1.01616	+	0.653047i	0.0771809	+	0.997017i	$0.475408\pi$
$420$	1.93900	+	2.23773i	0.0946136	+	0.109190i
$421$	−0.411418	−	2.86148i	−0.0200513	−	0.139460i	0.977337	−	0.211691i	$-0.0678971\pi$
$421$	−0.411418	−	2.86148i	−0.0200513	−	0.139460i	−0.997388	+	0.0722313i	$0.976988\pi$
$422$	1.46646	+	0.430592i	0.0713862	+	0.0209609i
$423$	1.56068	−	1.00299i	0.0758830	−	0.0487670i
$424$	0.257312	−	1.78964i	0.0124962	−	0.0869128i
$425$	0.742937	−	1.62680i	0.0360377	−	0.0789116i
$426$	−4.68077	+	10.2494i	−0.226784	+	0.496587i
$427$	0.677345	−	4.71104i	0.0327790	−	0.227983i
$428$	−2.05296	+	1.31936i	−0.0992337	+	0.0637736i
$429$	4.00903	+	1.17716i	0.193558	+	0.0568337i
$430$	−0.987264	−	6.86657i	−0.0476101	−	0.331135i
$431$	16.2097	+	18.7070i	0.780794	+	0.901085i	0.997167	−	0.0752261i	$-0.0239679\pi$
$431$	16.2097	+	18.7070i	0.780794	+	0.901085i	−0.216372	+	0.976311i	$0.569422\pi$
$432$	−0.841254	−	0.540641i	−0.0404748	−	0.0260116i
$433$	12.3236	−	14.2222i	0.592235	−	0.683476i	−0.377954	−	0.925824i	$-0.623372\pi$
$433$	12.3236	−	14.2222i	0.592235	−	0.683476i	0.970189	+	0.242349i	$0.0779178\pi$
$434$	−5.78107	+	1.69748i	−0.277500	+	0.0814815i
$435$	−4.33200	−	9.48575i	−0.207703	−	0.454807i
$436$	1.90920			0.0914341
$437$	4.28851	−	1.14630i	0.205147	−	0.0548350i
$438$	2.20790			0.105497
$439$	−12.3240	−	26.9857i	−0.588191	−	1.28796i	−0.936529	−	0.350589i	$-0.885981\pi$
$439$	−12.3240	−	26.9857i	−0.588191	−	1.28796i	0.348339	−	0.937369i	$-0.386746\pi$
$440$	2.99917	−	0.880636i	0.142980	−	0.0419827i
$441$	−1.15724	+	1.33552i	−0.0551065	+	0.0635963i
$442$	−2.01110	−	1.29246i	−0.0956585	−	0.0614760i
$443$	13.3146	+	15.3659i	0.632597	+	0.730056i	0.978048	−	0.208381i	$-0.0668194\pi$
$443$	13.3146	+	15.3659i	0.632597	+	0.730056i	−0.345451	+	0.938437i	$0.612274\pi$
$444$	1.12539	+	7.82727i	0.0534087	+	0.371466i
$445$	−6.00345	−	1.76277i	−0.284591	−	0.0835633i
$446$	13.9532	−	8.96720i	0.660705	−	0.424609i
$447$	−2.75258	+	19.1446i	−0.130192	+	0.905508i
$448$	1.23002	−	2.69336i	0.0581129	−	0.127249i
$449$	6.71425	−	14.7021i	0.316865	−	0.693837i	−0.682447	−	0.730935i	$-0.739084\pi$
$449$	6.71425	−	14.7021i	0.316865	−	0.693837i	0.999312	+	0.0370981i	$0.0118114\pi$
$450$	0.142315	−	0.989821i	0.00670879	−	0.0466606i
$451$	−22.9384	+	14.7416i	−1.08013	+	0.694157i
$452$	−9.83706	−	2.88842i	−0.462696	−	0.135860i
$453$	−0.356447	−	2.47915i	−0.0167474	−	0.116480i
$454$	12.9413	+	14.9351i	0.607366	+	0.700938i
$455$	3.32962	+	2.13982i	0.156095	+	0.100316i
$456$	0.606145	−	0.699529i	0.0283854	−	0.0327584i
$457$	13.4589	−	3.95190i	0.629583	−	0.184862i	0.0486529	−	0.998816i	$-0.484507\pi$
$457$	13.4589	−	3.95190i	0.629583	−	0.184862i	0.580930	+	0.813954i	$0.302689\pi$
$458$	4.15294	+	9.09367i	0.194054	+	0.424919i
$459$	−1.78842			−0.0834763
$460$	−4.56722	−	1.46305i	−0.212948	−	0.0682151i
$461$	10.3441			0.481773			0.240887	−	0.970553i	$-0.422562\pi$
$461$	10.3441			0.481773			0.240887	+	0.970553i	$0.422562\pi$
$462$	3.84477	+	8.41888i	0.178875	+	0.391682i
$463$	−34.2095	+	10.0448i	−1.58985	+	0.466823i	−0.952699	−	0.303915i	$-0.901706\pi$
$463$	−34.2095	+	10.0448i	−1.58985	+	0.466823i	−0.637153	+	0.770737i	$0.719888\pi$
$464$	−6.82896	+	7.88104i	−0.317027	+	0.365868i
$465$	1.71184	+	1.10014i	0.0793849	+	0.0510176i
$466$	9.58215	+	11.0584i	0.443884	+	0.512270i
$467$	2.66562	+	18.5398i	0.123350	+	0.857920i	0.953718	+	0.300703i	$0.0972215\pi$
$467$	2.66562	+	18.5398i	0.123350	+	0.857920i	−0.830367	+	0.557216i	$0.811869\pi$
$468$	−1.28257	−	0.376596i	−0.0592867	−	0.0174081i
$469$	24.3739	−	15.6641i	1.12548	−	0.723303i
$470$	0.264021	−	1.83630i	0.0121784	−	0.0847024i
$471$	−8.06700	+	17.6643i	−0.371708	+	0.813927i
$472$	−3.68473	+	8.06844i	−0.169604	+	0.371380i
$473$	3.08598	−	21.4634i	0.141893	−	0.986890i
$474$	6.08736	−	3.91211i	0.279602	−	0.179689i
$475$	0.888116	+	0.260774i	0.0407495	+	0.0119651i
$476$	−0.753614	−	5.24150i	−0.0345418	−	0.240244i
$477$	−1.18402	−	1.36643i	−0.0542125	−	0.0625645i
$478$	−5.20797	−	3.34696i	−0.238207	−	0.153086i
$479$	0.126595	−	0.146098i	0.00578428	−	0.00667541i	−0.752850	−	0.658192i	$-0.771321\pi$
$479$	0.126595	−	0.146098i	0.00578428	−	0.00667541i	0.758634	+	0.651517i	$0.225867\pi$
$480$	−0.959493	+	0.281733i	−0.0437947	+	0.0128593i
$481$	4.39110	+	9.61518i	0.200217	+	0.438414i
$482$	22.4472			1.02244
$483$	2.36335	−	14.0021i	0.107536	−	0.637118i
$484$	−1.22945			−0.0558842
$485$	4.92622	+	10.7869i	0.223688	+	0.489808i
$486$	−0.959493	+	0.281733i	−0.0435235	+	0.0127796i
$487$	19.8322	−	22.8875i	0.898681	−	1.03713i	−0.100429	−	0.994944i	$-0.532021\pi$
$487$	19.8322	−	22.8875i	0.898681	−	1.03713i	0.999110	−	0.0421889i	$-0.0134331\pi$
$488$	1.35225	+	0.869039i	0.0612135	+	0.0393395i
$489$	−0.427635	−	0.493517i	−0.0193383	−	0.0223176i
$490$	0.251492	+	1.74916i	0.0113612	+	0.0790191i
$491$	29.7897	+	8.74706i	1.34439	+	0.394749i	0.873235	−	0.487300i	$-0.162018\pi$
$491$	29.7897	+	8.74706i	1.34439	+	0.394749i	0.471158	+	0.882049i	$0.343836\pi$
$492$	7.33845	−	4.71614i	0.330843	−	0.212620i
$493$	−2.65415	+	18.4600i	−0.119537	+	0.831398i
$494$	0.513982	−	1.12546i	0.0231252	−	0.0506370i
$495$	1.29850	−	2.84332i	0.0583632	−	0.127798i
$496$	0.289593	−	2.01416i	0.0130031	−	0.0904385i
$497$	−28.0667	+	18.0374i	−1.25896	+	0.809086i
$498$	14.1516	+	4.15530i	0.634151	+	0.186203i
$499$	3.31283	+	23.0413i	0.148303	+	1.03147i	0.918997	+	0.394264i	$0.129000\pi$
$499$	3.31283	+	23.0413i	0.148303	+	1.03147i	−0.770695	+	0.637205i	$0.780091\pi$
$500$	−0.654861	−	0.755750i	−0.0292863	−	0.0337981i
$501$	13.1484	+	8.44996i	0.587427	+	0.377516i
$502$	15.5173	−	17.9079i	0.692572	−	0.799271i
$503$	−12.7175	+	3.73419i	−0.567045	+	0.166499i	−0.552674	−	0.833397i	$-0.686393\pi$
$503$	−12.7175	+	3.73419i	−0.567045	+	0.166499i	−0.0143706	+	0.999897i	$0.504574\pi$
$504$	−1.23002	−	2.69336i	−0.0547894	−	0.119972i
$505$	9.58910			0.426709
$506$	−12.4095	−	8.40999i	−0.551668	−	0.373870i
$507$	11.2132			0.497996
$508$	−5.98857	−	13.1131i	−0.265700	−	0.581802i
$509$	−19.3458	+	5.68044i	−0.857488	+	0.251781i	−0.680785	−	0.732483i	$-0.738361\pi$
$509$	−19.3458	+	5.68044i	−0.857488	+	0.251781i	−0.176703	+	0.984264i	$0.556543\pi$
$510$	−1.17117	+	1.35160i	−0.0518601	+	0.0598498i
$511$	5.49965	+	3.53441i	0.243290	+	0.156353i
$512$	0.654861	+	0.755750i	0.0289410	+	0.0333997i
$513$	−0.131728	−	0.916188i	−0.00581593	−	0.0404507i
$514$	−8.06710	−	2.36871i	−0.355825	−	0.104480i
$515$	−0.842920	+	0.541712i	−0.0371435	+	0.0238707i
$516$	−0.987264	+	6.86657i	−0.0434619	+	0.302284i
$517$	2.40896	−	5.27488i	0.105946	−	0.231989i
$518$	−9.72668	+	21.2985i	−0.427366	+	0.935801i
$519$	0.101478	−	0.705794i	0.00445438	−	0.0309809i
$520$	−1.12451	+	0.722682i	−0.0493132	+	0.0316917i
$521$	−16.8641	−	4.95173i	−0.738828	−	0.216939i	−0.109399	−	0.993998i	$-0.534893\pi$
$521$	−16.8641	−	4.95173i	−0.738828	−	0.216939i	−0.629428	+	0.777059i	$0.716711\pi$
$522$	1.48408	+	10.3220i	0.0649562	+	0.451780i
$523$	8.18886	+	9.45045i	0.358074	+	0.413239i	0.905993	−	0.423292i	$-0.139125\pi$
$523$	8.18886	+	9.45045i	0.358074	+	0.413239i	−0.547920	+	0.836531i	$0.684580\pi$
$524$	−0.596276	−	0.383203i	−0.0260484	−	0.0167403i
$525$	1.93900	−	2.23773i	0.0846250	−	0.0976624i
$526$	14.1442	−	4.15311i	0.616716	−	0.181084i
$527$	−1.51178	−	3.31034i	−0.0658543	−	0.144201i
$528$	−3.12579			−0.136032
$529$	8.52220	+	21.3629i	0.370530	+	0.928820i
$530$	−1.80805			−0.0785365
$531$	3.68473	+	8.06844i	0.159904	+	0.350140i
$532$	2.62966	−	0.772136i	0.114010	−	0.0334764i
$533$	7.63598	−	8.81239i	0.330751	−	0.381707i
$534$	5.26363	+	3.38273i	0.227780	+	0.146385i
$535$	1.59810	+	1.84430i	0.0690918	+	0.0797361i
$536$	1.39258	+	9.68557i	0.0601501	+	0.418353i
$537$	22.4008	+	6.57748i	0.966667	+	0.283839i
$538$	−13.2605	+	8.52200i	−0.571700	+	0.367409i
$539$	−0.786110	+	5.46751i	−0.0338601	+	0.235502i
$540$	−0.415415	+	0.909632i	−0.0178766	+	0.0391443i
$541$	−18.3248	+	40.1257i	−0.787844	+	1.72514i	−0.105121	+	0.994459i	$0.533523\pi$
$541$	−18.3248	+	40.1257i	−0.787844	+	1.72514i	−0.682723	+	0.730677i	$0.739204\pi$
$542$	−0.942370	+	6.55433i	−0.0404783	+	0.281533i
$543$	−0.764385	+	0.491241i	−0.0328029	+	0.0210812i
$544$	1.71598	+	0.503856i	0.0735719	+	0.0216027i
$545$	−0.271707	−	1.88977i	−0.0116387	−	0.0809487i
$546$	−2.59189	−	2.99120i	−0.110923	−	0.128012i
$547$	20.9874	+	13.4878i	0.897354	+	0.576695i	0.906005	−	0.423268i	$-0.139117\pi$
$547$	20.9874	+	13.4878i	0.897354	+	0.576695i	−0.00865023	+	0.999963i	$0.502753\pi$
$548$	−11.5480	+	13.3272i	−0.493308	+	0.569308i
$549$	1.54231	−	0.452864i	0.0658243	−	0.0193278i
$550$	−1.29850	−	2.84332i	−0.0553682	−	0.121239i
$551$	−9.65236			−0.411204
$552$	3.97003	+	2.69052i	0.168975	+	0.114516i
$553$	21.4255			0.911105
$554$	−3.31324	−	7.25498i	−0.140766	−	0.308235i
$555$	7.58744	−	2.22787i	0.322069	−	0.0945679i
$556$	−0.261867	+	0.302210i	−0.0111056	+	0.0128166i
$557$	9.63729	+	6.19351i	0.408345	+	0.262427i	0.728649	−	0.684887i	$-0.240149\pi$
$557$	9.63729	+	6.19351i	0.408345	+	0.262427i	−0.320304	+	0.947315i	$0.603785\pi$
$558$	−1.33256	−	1.53786i	−0.0564117	−	0.0651026i
$559$	1.31969	+	9.17863i	0.0558169	+	0.388215i
$560$	−2.84100	−	0.834192i	−0.120054	−	0.0352511i
$561$	−4.70279	+	3.02230i	−0.198552	+	0.127602i
$562$	−3.43404	+	23.8843i	−0.144856	+	1.00750i
$563$	−15.7813	+	34.5561i	−0.665101	+	1.45637i	0.212591	+	0.977141i	$0.431810\pi$
$563$	−15.7813	+	34.5561i	−0.665101	+	1.45637i	−0.877692	+	0.479226i	$0.840918\pi$
$564$	−0.770673	+	1.68754i	−0.0324512	+	0.0710581i
$565$	−1.45906	+	10.1480i	−0.0613832	+	0.426930i
$566$	−20.9955	+	13.4930i	−0.882507	+	0.567153i
$567$	−2.84100	−	0.834192i	−0.119311	−	0.0350328i
$568$	−1.60356	−	11.1530i	−0.0672838	−	0.467969i
$569$	8.85465	+	10.2188i	0.371206	+	0.428395i	0.910363	−	0.413810i	$-0.135802\pi$
$569$	8.85465	+	10.2188i	0.371206	+	0.428395i	−0.539157	+	0.842205i	$0.681257\pi$
$570$	−0.778672	−	0.500422i	−0.0326150	−	0.0209604i
$571$	18.0410	−	20.8204i	0.754992	−	0.871308i	−0.240050	−	0.970761i	$-0.577164\pi$
$571$	18.0410	−	20.8204i	0.754992	−	0.871308i	0.995042	+	0.0994530i	$0.0317093\pi$
$572$	−4.00903	+	1.17716i	−0.167626	+	0.0492194i
$573$	−9.62991	−	21.0866i	−0.402295	−	0.880904i
$574$	25.8290			1.07808
$575$	−0.798175	+	4.72894i	−0.0332862	+	0.197211i
$576$	1.00000			0.0416667
$577$	−12.1488	−	26.6023i	−0.505763	−	1.10747i	−0.974553	−	0.224157i	$-0.928037\pi$
$577$	−12.1488	−	26.6023i	−0.505763	−	1.10747i	0.468790	−	0.883310i	$-0.344690\pi$
$578$	−13.2425	+	3.88835i	−0.550815	+	0.161734i
$579$	8.34723	−	9.63321i	0.346899	−	0.400343i
$580$	8.77269	+	5.63786i	0.364266	+	0.234100i
$581$	28.5985	+	33.0044i	1.18647	+	1.36925i
$582$	−1.68765	−	11.7378i	−0.0699552	−	0.486549i
$583$	−5.42264	−	1.59223i	−0.224583	−	0.0659435i
$584$	−1.85740	+	1.19368i	−0.0768598	+	0.0493948i
$585$	−0.190234	+	1.32311i	−0.00786521	+	0.0547038i
$586$	3.36896	−	7.37700i	0.139171	−	0.304741i
$587$	7.74712	−	16.9638i	0.319758	−	0.700172i	−0.679687	−	0.733503i	$-0.737884\pi$
$587$	7.74712	−	16.9638i	0.319758	−	0.700172i	0.999444	+	0.0333308i	$0.0106115\pi$
$588$	0.251492	−	1.74916i	0.0103713	−	0.0721343i
$589$	1.58450	−	1.01830i	0.0652882	−	0.0419582i
$590$	8.51071	+	2.49897i	0.350380	+	0.102881i
$591$	−0.0731107	−	0.508496i	−0.00300737	−	0.0209167i
$592$	−5.17848	−	5.97629i	−0.212834	−	0.245624i
$593$	18.3720	+	11.8070i	0.754447	+	0.484854i	0.860465	−	0.509510i	$-0.170173\pi$
$593$	18.3720	+	11.8070i	0.754447	+	0.484854i	−0.106017	+	0.994364i	$0.533810\pi$
$594$	−2.04696	+	2.36231i	−0.0839876	+	0.0969269i
$595$	−5.08090	+	1.49189i	−0.208297	+	0.0611614i
$596$	−8.03473	−	17.5936i	−0.329115	−	0.720662i
$597$	0.392610			0.0160684
$598$	6.10506	+	1.95568i	0.249654	+	0.0799736i
$599$	−3.34616			−0.136720			−0.0683601	−	0.997661i	$-0.521777\pi$
$599$	−3.34616			−0.136720			−0.0683601	+	0.997661i	$0.521777\pi$
$600$	0.415415	+	0.909632i	0.0169592	+	0.0371356i
$601$	−40.9727	+	12.0307i	−1.67131	+	0.490741i	−0.974098	−	0.226125i	$-0.927394\pi$
$601$	−40.9727	+	12.0307i	−1.67131	+	0.490741i	−0.697211	+	0.716866i	$0.745576\pi$
$602$	−13.4512	+	15.5235i	−0.548230	+	0.632691i
$603$	8.23181	+	5.29026i	0.335225	+	0.215436i
$604$	1.64019	+	1.89288i	0.0667384	+	0.0770202i
$605$	0.174969	+	1.21694i	0.00711352	+	0.0494756i
$606$	−9.20067	−	2.70156i	−0.373752	−	0.109743i
$607$	13.9924	−	8.99238i	0.567935	−	0.364990i	−0.224941	−	0.974372i	$-0.572219\pi$
$607$	13.9924	−	8.99238i	0.567935	−	0.364990i	0.792876	+	0.609383i	$0.208583\pi$
$608$	−0.131728	+	0.916188i	−0.00534227	+	0.0371563i
$609$	−12.8268	+	28.0867i	−0.519767	+	1.13813i
$610$	0.667748	−	1.46216i	0.0270363	−	0.0592013i
$611$	−0.352920	+	2.45461i	−0.0142776	+	0.0993029i
$612$	1.50452	−	0.966893i	0.0608164	−	0.0390843i
$613$	−20.5555	−	6.03564i	−0.830229	−	0.243777i	−0.161114	−	0.986936i	$-0.551509\pi$
$613$	−20.5555	−	6.03564i	−0.830229	−	0.243777i	−0.669115	+	0.743159i	$0.733327\pi$
$614$	−3.69293	−	25.6849i	−0.149035	−	1.03656i
$615$	−5.71250	−	6.59258i	−0.230350	−	0.265839i
$616$	−7.78602	−	5.00377i	−0.313708	−	0.201608i
$617$	28.6813	−	33.0999i	1.15466	−	1.33255i	0.220635	−	0.975356i	$-0.429187\pi$
$617$	28.6813	−	33.0999i	1.15466	−	1.33255i	0.934029	−	0.357197i	$-0.116268\pi$
$618$	0.961394	−	0.282291i	0.0386729	−	0.0113554i
$619$	−5.79306	−	12.6850i	−0.232843	−	0.509855i	0.756758	−	0.653695i	$-0.226782\pi$
$619$	−5.79306	−	12.6850i	−0.232843	−	0.509855i	−0.989601	+	0.143840i	$0.954055\pi$
$620$	−2.03487			−0.0817225
$621$	4.63317	−	1.23843i	0.185923	−	0.0496964i
$622$	−19.7922			−0.793594
$623$	7.69609	+	16.8521i	0.308337	+	0.675165i
$624$	1.28257	−	0.376596i	0.0513438	−	0.0150759i
$625$	−0.654861	+	0.755750i	−0.0261944	+	0.0302300i
$626$	−8.13555	−	5.22840i	−0.325162	−	0.208969i
$627$	−1.89468	−	2.18658i	−0.0756663	−	0.0873235i
$628$	−2.76363	−	19.2215i	−0.110281	−	0.767021i
$629$	−13.5695	−	3.98437i	−0.541053	−	0.158867i
$630$	−2.49090	+	1.60080i	−0.0992398	+	0.0637775i
$631$	−1.03818	+	7.22068i	−0.0413292	+	0.287451i	0.958667	+	0.284532i	$0.0918382\pi$
$631$	−1.03818	+	7.22068i	−0.0413292	+	0.287451i	−0.999996	+	0.00291886i	$0.999071\pi$
$632$	−3.00597	+	6.58215i	−0.119571	+	0.261824i
$633$	−0.634908	+	1.39025i	−0.0252353	+	0.0552577i
$634$	−0.838075	+	5.82894i	−0.0332842	+	0.231497i
$635$	−12.1274	+	7.79381i	−0.481262	+	0.309288i
$636$	1.73481	+	0.509386i	0.0687896	+	0.0201985i
$637$	−0.336172	−	2.33813i	−0.0133196	−	0.0926401i
$638$	21.3459	+	24.6345i	0.845092	+	0.975288i
$639$	−9.47898	−	6.09177i	−0.374983	−	0.240987i
$640$	0.654861	−	0.755750i	0.0258856	−	0.0298736i
$641$	−41.5325	+	12.1950i	−1.64043	+	0.481675i	−0.966404	−	0.257028i	$-0.917257\pi$
$641$	−41.5325	+	12.1950i	−1.64043	+	0.481675i	−0.674031	+	0.738703i	$0.735439\pi$
$642$	−1.01376	−	2.21983i	−0.0400100	−	0.0876097i
$643$	32.1228			1.26680			0.633400	−	0.773824i	$-0.281659\pi$
$643$	32.1228			1.26680			0.633400	+	0.773824i	$0.281659\pi$
$644$	5.58194	+	13.0570i	0.219959	+	0.514520i
$645$	6.93718			0.273151
$646$	0.687669	+	1.50579i	0.0270560	+	0.0592443i
$647$	30.4777	−	8.94906i	1.19820	−	0.351824i	0.379037	−	0.925382i	$-0.376255\pi$
$647$	30.4777	−	8.94906i	1.19820	−	0.351824i	0.819165	+	0.573558i	$0.194437\pi$
$648$	0.654861	−	0.755750i	0.0257254	−	0.0296886i
$649$	23.3244	+	14.9897i	0.915562	+	0.588396i
$650$	0.875361	+	1.01022i	0.0343345	+	0.0396241i
$651$	−0.857466	−	5.96381i	−0.0336067	−	0.233740i
$652$	0.626565	+	0.183976i	0.0245382	+	0.00720506i
$653$	39.2369	−	25.2161i	1.53546	−	0.986780i	0.546690	−	0.837335i	$-0.315887\pi$
$653$	39.2369	−	25.2161i	1.53546	−	0.986780i	0.988770	−	0.149446i	$-0.0477489\pi$
$654$	−0.271707	+	1.88977i	−0.0106246	+	0.0738957i
$655$	−0.294444	+	0.644742i	−0.0115049	+	0.0251922i
$656$	−3.62376	+	7.93493i	−0.141484	+	0.309807i
$657$	−0.314216	+	2.18542i	−0.0122588	+	0.0852615i
$658$	−4.62108	+	2.96979i	−0.180149	+	0.115774i
$659$	15.1395	+	4.44536i	0.589752	+	0.173167i	0.562974	−	0.826475i	$-0.309657\pi$
$659$	15.1395	+	4.44536i	0.589752	+	0.173167i	0.0267777	+	0.999641i	$0.491475\pi$
$660$	0.444846	+	3.09397i	0.0173156	+	0.120433i
$661$	4.66404	+	5.38259i	0.181410	+	0.209358i	0.839170	−	0.543869i	$-0.183041\pi$
$661$	4.66404	+	5.38259i	0.181410	+	0.209358i	−0.657760	+	0.753228i	$0.728496\pi$
$662$	−11.2386	−	7.22258i	−0.436799	−	0.280713i
$663$	1.56551	−	1.80670i	0.0607995	−	0.0701664i
$664$	−14.1516	+	4.15530i	−0.549191	+	0.161257i
$665$	−1.13852	−	2.49300i	−0.0441498	−	0.0966745i
$666$	−7.90776			−0.306419
$667$	−5.90705	−	49.6614i	−0.228722	−	1.92290i
$668$	−15.6295			−0.604724
$669$	6.89017	+	15.0874i	0.266389	+	0.583311i
$670$	9.38880	−	2.75680i	0.362721	−	0.106505i
$671$	3.29033	−	3.79724i	0.127022	−	0.146591i
$672$	2.49090	+	1.60080i	0.0960885	+	0.0617523i
$673$	−4.00576	−	4.62289i	−0.154411	−	0.178199i	0.673274	−	0.739393i	$-0.264888\pi$
$673$	−4.00576	−	4.62289i	−0.154411	−	0.178199i	−0.827684	+	0.561194i	$0.810342\pi$
$674$	−1.61900	−	11.2604i	−0.0623615	−	0.433734i
$675$	0.959493	+	0.281733i	0.0369309	+	0.0108439i
$676$	−9.43314	+	6.06231i	−0.362813	+	0.233166i
$677$	1.29003	−	8.97236i	0.0495799	−	0.344836i	−0.949899	−	0.312557i	$-0.898814\pi$
$677$	1.29003	−	8.97236i	0.0495799	−	0.344836i	0.999479	−	0.0322787i	$-0.0102764\pi$
$678$	4.25898	−	9.32587i	0.163565	−	0.358158i
$679$	14.5862	−	31.9394i	0.559768	−	1.22572i
$680$	0.254519	−	1.77022i	0.00976035	−	0.0678847i
$681$	−16.6248	+	10.6841i	−0.637064	+	0.409416i
$682$	−6.10294	−	1.79198i	−0.233693	−	0.0686186i
$683$	5.92466	+	41.2069i	0.226701	+	1.57674i	0.711865	+	0.702316i	$0.247851\pi$
$683$	5.92466	+	41.2069i	0.226701	+	1.57674i	−0.485164	+	0.874423i	$0.661240\pi$
$684$	0.606145	+	0.699529i	0.0231765	+	0.0267472i
$685$	14.8350	+	9.53385i	0.566815	+	0.364270i
$686$	−10.1465	+	11.7097i	−0.387395	+	0.447078i
$687$	−9.59213	+	2.81650i	−0.365963	+	0.107456i
$688$	−2.88181	−	6.31028i	−0.109868	−	0.240577i
$689$	2.41684			0.0920742
$690$	2.09814	−	4.31252i	0.0798749	−	0.164175i
$691$	−23.1642			−0.881207			−0.440604	−	0.897702i	$-0.645236\pi$
$691$	−23.1642			−0.881207			−0.440604	+	0.897702i	$0.645236\pi$
$692$	0.296212	+	0.648615i	0.0112603	+	0.0246566i
$693$	−8.88036	+	2.60751i	−0.337337	+	0.0990511i
$694$	−9.05934	+	10.4550i	−0.343888	+	0.396868i
$695$	0.336402	+	0.216192i	0.0127605	+	0.00820064i
$696$	−6.82896	−	7.88104i	−0.258851	−	0.298730i
$697$	2.22023	+	15.4420i	0.0840971	+	0.584908i
$698$	−0.996290	−	0.292537i	−0.0377101	−	0.0110727i
$699$	−12.3095	+	7.91084i	−0.465589	+	0.299216i
$700$	−0.421385	+	2.93080i	−0.0159269	+	0.110774i
$701$	8.26668	−	18.1015i	0.312228	−	0.683685i	−0.686841	−	0.726807i	$-0.741003\pi$
$701$	8.26668	−	18.1015i	0.312228	−	0.683685i	0.999070	+	0.0431226i	$0.0137306\pi$
$702$	0.555291	−	1.21592i	0.0209581	−	0.0458918i
$703$	1.04167	−	7.24499i	0.0392874	−	0.273250i
$704$	2.62958	−	1.68993i	0.0991060	−	0.0636916i
$705$	1.78004	+	0.522667i	0.0670401	+	0.0196848i
$706$	4.43962	+	30.8782i	0.167087	+	1.16212i
$707$	−18.5933	−	21.4578i	−0.699272	−	0.807003i
$708$	−7.46192	−	4.79549i	−0.280436	−	0.180225i
$709$	−0.560927	+	0.647344i	−0.0210661	+	0.0243115i	−0.766185	−	0.642620i	$-0.777847\pi$
$709$	−0.560927	+	0.647344i	−0.0210661	+	0.0243115i	0.745119	+	0.666932i	$0.232393\pi$
$710$	−10.8113	+	3.17447i	−0.405740	+	0.119136i
$711$	3.00597	+	6.58215i	0.112733	+	0.246850i
$712$	−6.25689			−0.234487
$713$	6.20882	+	7.52908i	0.232522	+	0.281966i
$714$	5.29540			0.198175
$715$	1.73572	+	3.80070i	0.0649123	+	0.142138i
$716$	−22.4008	+	6.57748i	−0.837158	+	0.245812i
$717$	4.05407	−	4.67864i	0.151402	−	0.174727i
$718$	14.1481	+	9.09245i	0.528004	+	0.339327i
$719$	−22.5302	−	26.0013i	−0.840236	−	0.969684i	0.159611	−	0.987180i	$-0.448976\pi$
$719$	−22.5302	−	26.0013i	−0.840236	−	0.969684i	−0.999847	+	0.0174959i	$0.994431\pi$
$720$	−0.142315	−	0.989821i	−0.00530376	−	0.0368885i
$721$	2.84663	+	0.835845i	0.106014	+	0.0311285i
$722$	15.2631	−	9.80898i	0.568033	−	0.365052i
$723$	−3.19457	+	22.2187i	−0.118807	+	0.826323i
$724$	0.377457	−	0.826516i	0.0140281	−	0.0307172i
$725$	4.33200	−	9.48575i	0.160886	−	0.352292i
$726$	0.174969	−	1.21694i	0.00649372	−	0.0451648i
$727$	17.1929	−	11.0492i	0.637648	−	0.409792i	−0.181486	−	0.983394i	$-0.558091\pi$
$727$	17.1929	−	11.0492i	0.637648	−	0.409792i	0.819134	+	0.573602i	$0.194454\pi$
$728$	3.79760	+	1.11508i	0.140748	+	0.0413275i
$729$	−0.142315	−	0.989821i	−0.00527092	−	0.0366601i
$730$	1.44586	+	1.66862i	0.0535139	+	0.0617583i
$731$	−10.4371	−	6.70751i	−0.386030	−	0.248086i
$732$	−1.05264	+	1.21481i	−0.0389067	+	0.0449007i
$733$	19.8704	−	5.83447i	0.733929	−	0.215501i	0.106651	−	0.994297i	$-0.465987\pi$
$733$	19.8704	−	5.83447i	0.733929	−	0.215501i	0.627278	+	0.778796i	$0.284169\pi$
$734$	−7.55719	−	16.5479i	−0.278941	−	0.610796i
$735$	−1.76715			−0.0651823
$736$	−4.79440	−	0.117052i	−0.176724	−	0.00431459i
$737$	30.5864			1.12666
$738$	3.62376	+	7.93493i	0.133393	+	0.292089i
$739$	10.9661	−	3.21994i	0.403395	−	0.118447i	−0.0737402	−	0.997277i	$-0.523494\pi$
$739$	10.9661	−	3.21994i	0.403395	−	0.118447i	0.477135	+	0.878830i	$0.341675\pi$
$740$	−5.17848	+	5.97629i	−0.190365	+	0.219693i
$741$	1.04086	+	0.668921i	0.0382370	+	0.0245734i
$742$	3.50581	+	4.04591i	0.128702	+	0.148530i
$743$	0.648284	+	4.50892i	0.0237832	+	0.165416i	0.998252	−	0.0591091i	$-0.0188260\pi$
$743$	0.648284	+	4.50892i	0.0237832	+	0.165416i	−0.974468	+	0.224525i	$0.927917\pi$
$744$	1.95245	+	0.573290i	0.0715802	+	0.0210178i
$745$	−16.2711	+	10.4568i	−0.596126	+	0.383107i
$746$	−3.53449	+	24.5829i	−0.129407	+	0.900044i
$747$	−6.12699	+	13.4162i	−0.224175	+	0.490875i
$748$	2.32226	−	5.08505i	0.0849103	−	0.185928i
$749$	1.02833	−	7.15221i	0.0375745	−	0.261336i
$750$	0.841254	−	0.540641i	0.0307182	−	0.0197414i
$751$	16.9606	+	4.98009i	0.618903	+	0.181726i	0.576129	−	0.817359i	$-0.304562\pi$
$751$	16.9606	+	4.98009i	0.618903	+	0.181726i	0.0427733	+	0.999085i	$0.486381\pi$
$752$	−0.264021	−	1.83630i	−0.00962784	−	0.0669631i
$753$	15.5173	+	17.9079i	0.565483	+	0.652602i
$754$	−11.7266	−	7.53621i	−0.427056	−	0.274452i
$755$	1.64019	−	1.89288i	0.0596926	−	0.0688889i
$756$	2.84100	−	0.834192i	0.103326	−	0.0303393i
$757$	1.20973	+	2.64895i	0.0439685	+	0.0962776i	0.930342	−	0.366694i	$-0.119510\pi$
$757$	1.20973	+	2.64895i	0.0439685	+	0.0962776i	−0.886373	+	0.462972i	$0.846783\pi$
$758$	25.3712			0.921525
$759$	10.0904	−	11.0863i	0.366260	−	0.402406i
$760$	0.925609			0.0335754
$761$	−10.5934	−	23.1963i	−0.384011	−	0.840867i	−0.998644	−	0.0520539i	$-0.983423\pi$
$761$	−10.5934	−	23.1963i	−0.384011	−	0.840867i	0.614633	−	0.788813i	$-0.289304\pi$
$762$	13.8319	−	4.06142i	0.501078	−	0.147130i
$763$	−3.70194	+	4.27227i	−0.134019	+	0.154666i
$764$	19.5015	+	12.5328i	0.705538	+	0.453422i
$765$	−1.17117	−	1.35160i	−0.0423436	−	0.0488671i
$766$	4.19606	+	29.1843i	0.151610	+	1.05447i
$767$	−11.3764	−	3.34040i	−0.410777	−	0.120615i
$768$	−0.841254	+	0.540641i	−0.0303561	+	0.0195087i
$769$	2.71148	−	18.8588i	0.0977786	−	0.680065i	−0.880694	−	0.473686i	$-0.842923\pi$
$769$	2.71148	−	18.8588i	0.0977786	−	0.680065i	0.978472	−	0.206379i	$-0.0661679\pi$
$770$	−3.84477	+	8.41888i	−0.138556	+	0.303395i
$771$	3.49267	−	7.64789i	0.125786	−	0.275432i
$772$	−1.81403	+	12.6168i	−0.0652882	+	0.454090i
$773$	15.2078	−	9.77349i	0.546988	−	0.351528i	−0.237778	−	0.971319i	$-0.576419\pi$
$773$	15.2078	−	9.77349i	0.546988	−	0.351528i	0.784767	+	0.619791i	$0.212783\pi$
$774$	−6.65618	−	1.95443i	−0.239251	−	0.0702505i
$775$	0.289593	+	2.01416i	0.0104025	+	0.0723508i
$776$	7.76569	+	8.96209i	0.278772	+	0.321720i
$777$	−19.6974	−	12.6588i	−0.706641	−	0.454131i
$778$	−18.1615	+	20.9595i	−0.651120	+	0.751433i
$779$	−7.74724	+	2.27480i	−0.277574	+	0.0815030i
$780$	−0.555291	−	1.21592i	−0.0198826	−	0.0435368i
$781$	−35.2204			−1.26028
$782$	−7.32643	+	4.45957i	−0.261993	+	0.159474i
$783$	−10.4281			−0.372670
$784$	0.734101	+	1.60746i	0.0262179	+	0.0574092i
$785$	−18.6325	+	5.47101i	−0.665024	+	0.195269i
$786$	0.464162	−	0.535671i	0.0165561	−	0.0191068i
$787$	10.4086	+	6.68922i	0.371028	+	0.238445i	0.712845	−	0.701321i	$-0.247406\pi$
$787$	10.4086	+	6.68922i	0.371028	+	0.238445i	−0.341818	+	0.939766i	$0.611042\pi$
$788$	0.336418	+	0.388248i	0.0119844	+	0.0138307i
$789$	2.09791	+	14.5913i	0.0746875	+	0.519463i
$790$	6.94294	+	2.03863i	0.247019	+	0.0725313i
$791$	25.5376	−	16.4120i	0.908012	−	0.583544i
$792$	0.444846	−	3.09397i	0.0158069	−	0.109939i
$793$	−0.892588	+	1.95449i	−0.0316967	+	0.0694061i
$794$	−12.1326	+	26.5667i	−0.430569	+	0.942815i
$795$	0.257312	−	1.78964i	0.00912591	−	0.0634721i
$796$	−0.330284	+	0.212261i	−0.0117066	+	0.00752338i
$797$	−29.5131	−	8.66583i	−1.04541	−	0.306960i	−0.286448	−	0.958096i	$-0.592474\pi$
$797$	−29.5131	−	8.66583i	−1.04541	−	0.306960i	−0.758961	+	0.651136i	$0.774293\pi$
$798$	0.390038	+	2.71278i	0.0138072	+	0.0960312i
$799$	−2.17273	−	2.50747i	−0.0768658	−	0.0887078i
$800$	−0.841254	−	0.540641i	−0.0297428	−	0.0191145i
$801$	−4.09739	+	4.72864i	−0.144774	+	0.167078i
$802$	−2.16409	+	0.635433i	−0.0764166	+	0.0224379i
$803$	2.86695	+	6.27775i	0.101173	+	0.221537i
$804$	−9.78517			−0.345096
$805$	12.1298	−	7.38333i	0.427518	−	0.260228i
$806$	2.72004			0.0958094
$807$	−6.54809	−	14.3383i	−0.230504	−	0.504733i
$808$	9.20067	−	2.70156i	0.323678	−	0.0950406i
$809$	−19.6843	+	22.7169i	−0.692065	+	0.798685i	−0.987658	−	0.156629i	$-0.949937\pi$
$809$	−19.6843	+	22.7169i	−0.692065	+	0.798685i	0.295593	+	0.955314i	$0.404483\pi$
$810$	−0.841254	−	0.540641i	−0.0295586	−	0.0189962i
$811$	−13.0500	−	15.0605i	−0.458248	−	0.528846i	0.478858	−	0.877892i	$-0.341051\pi$
$811$	−13.0500	−	15.0605i	−0.458248	−	0.528846i	−0.937105	+	0.349047i	$0.886505\pi$
$812$	−4.39425	−	30.5627i	−0.154208	−	1.07254i
$813$	−6.35350	−	1.86556i	−0.222827	−	0.0654279i
$814$	−20.7941	+	13.3635i	−0.728832	+	0.468392i
$815$	0.0929340	−	0.646370i	0.00325534	−	0.0226414i
$816$	−0.742937	+	1.62680i	−0.0260080	+	0.0569496i
$817$	2.66743	−	5.84086i	0.0933215	−	0.204346i
$818$	−4.62175	+	32.1450i	−0.161596	+	1.12392i
$819$	3.32962	−	2.13982i	0.116346	−	0.0747712i
$820$	8.36988	+	2.45762i	0.292289	+	0.0858238i
$821$	−5.43300	−	37.7874i	−0.189613	−	1.31879i	−0.833011	−	0.553256i	$-0.813385\pi$
$821$	−5.43300	−	37.7874i	−0.189613	−	1.31879i	0.643398	−	0.765532i	$-0.277524\pi$
$822$	−11.5480	−	13.3272i	−0.402784	−	0.464838i
$823$	−31.1823	−	20.0397i	−1.08695	−	0.698539i	−0.130796	−	0.991409i	$-0.541753\pi$
$823$	−31.1823	−	20.0397i	−1.08695	−	0.698539i	−0.956152	+	0.292870i	$0.905390\pi$
$824$	−0.656158	+	0.757247i	−0.0228584	+	0.0263799i
$825$	2.99917	−	0.880636i	0.104418	−	0.0306598i
$826$	−10.9103	−	23.8901i	−0.379617	−	0.831244i
$827$	12.9044			0.448730			0.224365	−	0.974505i	$-0.427969\pi$
$827$	12.9044			0.448730			0.224365	+	0.974505i	$0.427969\pi$
$828$	−3.22813	+	3.54672i	−0.112185	+	0.123257i
$829$	36.1008			1.25383			0.626916	−	0.779087i	$-0.284317\pi$
$829$	36.1008			1.25383			0.626916	+	0.779087i	$0.284317\pi$
$830$	6.12699	+	13.4162i	0.212671	+	0.465685i
$831$	7.65266	−	2.24702i	0.265468	−	0.0779484i
$832$	−0.875361	+	1.01022i	−0.0303477	+	0.0350231i
$833$	2.65870	+	1.70865i	0.0921187	+	0.0592011i
$834$	−0.261867	−	0.302210i	−0.00906771	−	0.0104647i
$835$	2.22431	+	15.4704i	0.0769755	+	0.535377i
$836$	2.77606	+	0.815125i	0.0960121	+	0.0281917i
$837$	1.71184	−	1.10014i	0.0591700	−	0.0380263i
$838$	3.51879	−	24.4737i	0.121555	−	0.845430i
$839$	15.3520	−	33.6162i	0.530010	−	1.16056i	−0.435499	−	0.900189i	$-0.643428\pi$
$839$	15.3520	−	33.6162i	0.530010	−	1.16056i	0.965509	−	0.260370i	$-0.0838447\pi$
$840$	1.23002	−	2.69336i	0.0424396	−	0.0929299i
$841$	−11.3490	+	78.9339i	−0.391344	+	2.72186i
$842$	−2.43198	+	1.56294i	−0.0838116	+	0.0538625i
$843$	−23.1525	−	6.79818i	−0.797414	−	0.234142i
$844$	−0.217510	−	1.51281i	−0.00748700	−	0.0520732i
$845$	7.34308	+	8.47437i	0.252610	+	0.291527i
$846$	−1.56068	−	1.00299i	−0.0536574	−	0.0344835i
$847$	2.38391	−	2.75118i	0.0819121	−	0.0945317i
$848$	−1.73481	+	0.509386i	−0.0595735	+	0.0174924i
$849$	−10.3677	−	22.7020i	−0.355818	−	0.779132i
$850$	−1.78842			−0.0613423
$851$	37.9130	+	0.925619i	1.29964	+	0.0317298i
$852$	11.2677			0.386025
$853$	7.60590	+	16.6546i	0.260421	+	0.570242i	0.994002	−	0.109359i	$-0.0348799\pi$
$853$	7.60590	+	16.6546i	0.260421	+	0.570242i	−0.733581	+	0.679602i	$0.762153\pi$
$854$	−4.56669	+	1.34090i	−0.156269	+	0.0458847i
$855$	0.606145	−	0.699529i	0.0207297	−	0.0239234i
$856$	2.05296	+	1.31936i	0.0701688	+	0.0450948i
$857$	−25.4437	−	29.3636i	−0.869142	−	1.00304i	−0.999932	−	0.0116329i	$-0.996297\pi$
$857$	−25.4437	−	29.3636i	−0.869142	−	1.00304i	0.130791	−	0.991410i	$-0.458248\pi$
$858$	−0.594631	−	4.13575i	−0.0203004	−	0.141192i
$859$	−9.37384	−	2.75241i	−0.319831	−	0.0939110i	0.117876	−	0.993028i	$-0.462391\pi$
$859$	−9.37384	−	2.75241i	−0.319831	−	0.0939110i	−0.437708	+	0.899117i	$0.644210\pi$
$860$	−5.83593	+	3.75052i	−0.199003	+	0.127892i
$861$	−3.67584	+	25.5661i	−0.125272	+	0.871289i
$862$	10.2827	−	22.5160i	0.350231	−	0.766900i
$863$	2.05965	−	4.51001i	0.0701115	−	0.153523i	−0.871332	−	0.490695i	$-0.836743\pi$
$863$	2.05965	−	4.51001i	0.0701115	−	0.153523i	0.941443	+	0.337172i	$0.109470\pi$
$864$	−0.142315	+	0.989821i	−0.00484165	+	0.0336744i
$865$	0.599857	−	0.385505i	0.0203958	−	0.0131076i
$866$	−18.0564	−	5.30183i	−0.613581	−	0.180164i
$867$	−1.96417	−	13.6611i	−0.0667066	−	0.463954i
$868$	3.94562	+	4.55349i	0.133923	+	0.154556i
$869$	19.0278	+	12.2284i	0.645473	+	0.414820i
$870$	−6.82896	+	7.88104i	−0.231524	+	0.267192i
$871$	−12.5501	+	3.68505i	−0.425245	+	0.124863i
$872$	−0.793110	−	1.73667i	−0.0268581	−	0.0588110i
$873$	11.8585			0.401351
$874$	−2.82422	−	3.42477i	−0.0955308	−	0.115845i
$875$	2.96094			0.100098
$876$	−0.917193	−	2.00837i	−0.0309891	−	0.0678566i
$877$	−43.1608	+	12.6732i	−1.45744	+	0.427942i	−0.911993	−	0.410205i	$-0.865457\pi$
$877$	−43.1608	+	12.6732i	−1.45744	+	0.427942i	−0.545444	+	0.838147i	$0.683639\pi$
$878$	−19.4275	+	22.4205i	−0.655647	+	0.756656i
$879$	6.82246	+	4.38453i	0.230116	+	0.147886i
$880$	−2.04696	−	2.36231i	−0.0690029	−	0.0796335i
$881$	4.86638	+	33.8464i	0.163953	+	1.14032i	0.891091	+	0.453825i	$0.149941\pi$
$881$	4.86638	+	33.8464i	0.163953	+	1.14032i	−0.727138	+	0.686491i	$0.759150\pi$
$882$	1.69557	+	0.497864i	0.0570928	+	0.0167639i
$883$	0.555968	−	0.357299i	0.0187098	−	0.0120241i	−0.531252	−	0.847214i	$-0.678278\pi$
$883$	0.555968	−	0.357299i	0.0187098	−	0.0120241i	0.549962	+	0.835189i	$0.314642\pi$
$884$	−0.340219	+	2.36627i	−0.0114428	+	0.0795863i
$885$	−3.68473	+	8.06844i	−0.123861	+	0.271218i
$886$	8.44622	−	18.4946i	0.283756	−	0.621339i
$887$	−3.67081	+	25.5310i	−0.123254	+	0.857248i	0.830577	+	0.556904i	$0.188011\pi$
$887$	−3.67081	+	25.5310i	−0.123254	+	0.857248i	−0.953831	+	0.300345i	$0.902898\pi$
$888$	6.65243	−	4.27526i	0.223241	−	0.143468i
$889$	40.9555	+	12.0256i	1.37360	+	0.403326i
$890$	0.890449	+	6.19321i	0.0298479	+	0.207597i
$891$	−2.04696	−	2.36231i	−0.0685756	−	0.0791404i
$892$	−13.9532	−	8.96720i	−0.467189	−	0.300244i
$893$	1.12451	−	1.29776i	0.0376304	−	0.0434278i
$894$	18.5580	−	5.44912i	0.620672	−	0.182246i
$895$	9.69850	+	21.2368i	0.324185	+	0.709866i
$896$	−2.96094			−0.0989180
$897$	−2.80461	+	5.76460i	−0.0936433	+	0.192474i
$898$	−16.1627			−0.539358
$899$	−8.81507	−	19.3023i	−0.293999	−	0.643768i
$900$	−0.959493	+	0.281733i	−0.0319831	+	0.00939109i
$901$	−2.11752	+	2.44375i	−0.0705449	+	0.0814132i
$902$	22.9384	+	14.7416i	0.763767	+	0.490843i
$903$	−13.4512	−	15.5235i	−0.447628	−	0.516590i
$904$	1.45906	+	10.1480i	0.0485277	+	0.337517i
$905$	−0.871821	−	0.255990i	−0.0289803	−	0.00850939i
$906$	−2.10704	+	1.35411i	−0.0700016	+	0.0449873i
$907$	−3.41797	+	23.7725i	−0.113492	+	0.789352i	0.850986	+	0.525188i	$0.176005\pi$
$907$	−3.41797	+	23.7725i	−0.113492	+	0.789352i	−0.964478	+	0.264164i	$0.914904\pi$
$908$	8.20940	−	17.9761i	0.272439	−	0.596557i
$909$	3.98345	−	8.72255i	0.132123	−	0.289309i
$910$	0.563271	−	3.91764i	0.0186723	−	0.129868i
$911$	−13.7421	+	8.83150i	−0.455296	+	0.292601i	−0.748117	−	0.663566i	$-0.769042\pi$
$911$	−13.7421	+	8.83150i	−0.455296	+	0.292601i	0.292822	+	0.956167i	$0.405406\pi$
$912$	−0.888116	−	0.260774i	−0.0294084	−	0.00863510i
$913$	6.56107	+	45.6333i	0.217140	+	1.51024i
$914$	−9.18582	−	10.6010i	−0.303840	−	0.350650i
$915$	1.35225	+	0.869039i	0.0447040	+	0.0287295i
$916$	6.54670	−	7.55529i	0.216309	−	0.249634i
$917$	2.01368	−	0.591271i	0.0664977	−	0.0195255i
$918$	0.742937	+	1.62680i	0.0245206	+	0.0536926i
$919$	−6.75528			−0.222836			−0.111418	−	0.993774i	$-0.535539\pi$
$919$	−6.75528			−0.222836			−0.111418	+	0.993774i	$0.535539\pi$
$920$	0.566454	+	4.76226i	0.0186754	+	0.157007i
$921$	25.9490			0.855050
$922$	−4.29710	−	9.40933i	−0.141517	−	0.309880i
$923$	14.4516	−	4.24336i	0.475679	−	0.139672i
$924$	6.06091	−	6.99466i	0.199389	−	0.230107i
$925$	6.65243	+	4.27526i	0.218731	+	0.140570i
$926$	23.3483	+	26.9453i	0.767271	+	0.885478i
$927$	0.142597	+	0.991782i	0.00468349	+	0.0325744i
$928$	10.0057	+	2.93794i	0.328453	+	0.0964426i
$929$	4.64635	−	2.98603i	0.152442	−	0.0979684i	−0.462196	−	0.886778i	$-0.652938\pi$
$929$	4.64635	−	2.98603i	0.152442	−	0.0979684i	0.614638	+	0.788809i	$0.289302\pi$
$930$	0.289593	−	2.01416i	0.00949612	−	0.0660470i
$931$	−0.679491	+	1.48788i	−0.0222694	+	0.0487632i
$932$	6.07850	−	13.3100i	0.199108	−	0.435985i
$933$	2.81672	−	19.5907i	0.0922153	−	0.641371i
$934$	15.7571	−	10.1264i	0.515587	−	0.331347i
$935$	−5.36378	−	1.57495i	−0.175414	−	0.0515063i
$936$	0.190234	+	1.32311i	0.00621800	+	0.0432471i
$937$	26.7841	+	30.9105i	0.874997	+	1.00980i	0.999845	+	0.0176245i	$0.00561033\pi$
$937$	26.7841	+	30.9105i	0.874997	+	1.00980i	−0.124848	+	0.992176i	$0.539844\pi$
$938$	−24.3739	−	15.6641i	−0.795835	−	0.511452i
$939$	6.33299	−	7.30866i	0.206669	−	0.238509i
$940$	−1.78004	+	0.522667i	−0.0580585	+	0.0170475i
$941$	−3.73449	−	8.17739i	−0.121741	−	0.266575i	0.838943	−	0.544219i	$-0.183174\pi$
$941$	−3.73449	−	8.17739i	−0.121741	−	0.266575i	−0.960684	+	0.277644i	$0.910447\pi$
$942$	19.4191			0.632710
$943$	−16.4450	−	38.4674i	−0.535522	−	1.25267i
$944$	8.87000			0.288694
$945$	−1.23002	−	2.69336i	−0.0400125	−	0.0876151i
$946$	−20.8058	+	6.10913i	−0.676455	+	0.198625i
$947$	6.05918	−	6.99266i	0.196897	−	0.227231i	−0.648712	−	0.761034i	$-0.724692\pi$
$947$	6.05918	−	6.99266i	0.196897	−	0.227231i	0.845609	+	0.533803i	$0.179238\pi$
$948$	−6.08736	−	3.91211i	−0.197708	−	0.127059i
$949$	−1.93271	−	2.23046i	−0.0627383	−	0.0724039i
$950$	−0.131728	−	0.916188i	−0.00427382	−	0.0297251i
$951$	−5.65034	−	1.65909i	−0.183225	−	0.0537997i
$952$	−4.45478	+	2.86291i	−0.144380	+	0.0927875i
$953$	5.71477	−	39.7471i	0.185120	−	1.28754i	−0.659311	−	0.751871i	$-0.729152\pi$
$953$	5.71477	−	39.7471i	0.185120	−	1.28754i	0.844430	−	0.535665i	$-0.179939\pi$
$954$	−0.751090	+	1.64466i	−0.0243174	+	0.0532477i
$955$	9.62991	−	21.0866i	0.311617	−	0.682345i
$956$	−0.881033	+	6.12772i	−0.0284946	+	0.198185i
$957$	−27.4216	+	17.6228i	−0.886413	+	0.569663i
$958$	−0.185485	−	0.0544634i	−0.00599276	−	0.00175963i
$959$	−7.43086	−	51.6827i	−0.239955	−	1.66892i
$960$	0.654861	+	0.755750i	0.0211355	+	0.0243917i
$961$	−22.5955	−	14.5212i	−0.728886	−	0.468427i
$962$	6.92214	−	7.98858i	0.223179	−	0.257562i
$963$	2.34151	−	0.687529i	0.0754541	−	0.0221553i
$964$	−9.32490	−	20.4187i	−0.300335	−	0.657642i
$965$	12.7466			0.410327
$966$	−13.7185	+	3.66691i	−0.441387	+	0.117981i
$967$	−25.2373			−0.811577			−0.405788	−	0.913967i	$-0.633003\pi$
$967$	−25.2373			−0.811577			−0.405788	+	0.913967i	$0.633003\pi$
$968$	0.510733	+	1.11835i	0.0164156	+	0.0359451i
$969$	−1.58832	+	0.466374i	−0.0510243	+	0.0149821i
$970$	7.76569	−	8.96209i	0.249341	−	0.287755i
$971$	−26.6691	−	17.1392i	−0.855853	−	0.550024i	0.0375419	−	0.999295i	$-0.488047\pi$
$971$	−26.6691	−	17.1392i	−0.855853	−	0.550024i	−0.893395	+	0.449271i	$0.851684\pi$
$972$	0.654861	+	0.755750i	0.0210047	+	0.0242407i
$973$	−0.168504	−	1.17197i	−0.00540200	−	0.0375717i
$974$	−29.0578	−	8.53214i	−0.931072	−	0.273388i
$975$	−1.12451	+	0.722682i	−0.0360133	+	0.0231443i
$976$	0.228760	−	1.59106i	0.00732244	−	0.0509287i
$977$	−16.3810	+	35.8693i	−0.524074	+	1.14756i	0.443800	+	0.896126i	$0.353630\pi$
$977$	−16.3810	+	35.8693i	−0.524074	+	1.14756i	−0.967874	+	0.251436i	$0.919097\pi$
$978$	−0.271273	+	0.594005i	−0.00867436	+	0.0189942i
$979$	−2.78335	+	19.3586i	−0.0889564	+	0.618705i
$980$	1.48662	−	0.955394i	0.0474884	−	0.0305189i
$981$	−1.83186	−	0.537884i	−0.0584869	−	0.0171733i
$982$	−4.41850	−	30.7314i	−0.141000	−	0.980677i
$983$	7.90554	+	9.12348i	0.252148	+	0.290994i	0.867686	−	0.497113i	$-0.165607\pi$
$983$	7.90554	+	9.12348i	0.252148	+	0.290994i	−0.615538	+	0.788107i	$0.711061\pi$
$984$	−7.33845	−	4.71614i	−0.233941	−	0.150345i
$985$	0.336418	−	0.388248i	0.0107192	−	0.0123706i
$986$	17.8944	−	5.25427i	0.569874	−	0.167330i
$987$	−2.28191	−	4.99669i	−0.0726341	−	0.159046i
$988$	−1.23727			−0.0393629
$989$	31.6836	+	10.1494i	1.00748	+	0.322733i
$990$	−3.12579			−0.0993440
$991$	−9.97898	−	21.8509i	−0.316993	−	0.694117i	0.682325	−	0.731049i	$-0.260969\pi$
$991$	−9.97898	−	21.8509i	−0.316993	−	0.694117i	−0.999318	+	0.0369316i	$0.988242\pi$
$992$	−1.95245	+	0.573290i	−0.0619903	+	0.0182020i
$993$	8.74848	−	10.0963i	0.277624	−	0.320396i
$994$	28.0667	+	18.0374i	0.890221	+	0.572110i
$995$	0.257105	+	0.296715i	0.00815077	+	0.00940648i
$996$	−2.09901	−	14.5990i	−0.0665098	−	0.462586i
$997$	18.2312	+	5.35317i	0.577388	+	0.169536i	0.557372	−	0.830263i	$-0.311810\pi$
$997$	18.2312	+	5.35317i	0.577388	+	0.169536i	0.0200166	+	0.999800i	$0.493628\pi$
$998$	19.5829	−	12.5851i	0.619885	−	0.398376i
$999$	1.12539	−	7.82727i	0.0356058	−	0.247644i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.e.211.1	yes	20
23.6	even	11	inner	690.2.m.e.121.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.e.121.1	✓	20	23.6	even	11	inner
690.2.m.e.211.1	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 - 0.909632i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(0.841254 + 0.540641i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(-0.421385 - 2.93080i) q^{7} +(0.959493 + 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})\)	\(q+(-0.415415 - 0.909632i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(0.841254 + 0.540641i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(-0.421385 - 2.93080i) q^{7} +(0.959493 + 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +(0.142315 - 0.989821i) q^{10} +(1.29850 - 2.84332i) q^{11} +(-0.415415 + 0.909632i) q^{12} +(-0.190234 + 1.32311i) q^{13} +(-2.49090 + 1.60080i) q^{14} +(0.959493 + 0.281733i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(-1.17117 - 1.35160i) q^{17} +(-0.841254 - 0.540641i) q^{18} +(0.606145 - 0.699529i) q^{19} +(-0.959493 + 0.281733i) q^{20} +(-1.23002 - 2.69336i) q^{21} -3.12579 q^{22} +(3.97003 + 2.69052i) q^{23} +1.00000 q^{24} +(0.415415 + 0.909632i) q^{25} +(1.28257 - 0.376596i) q^{26} +(0.654861 - 0.755750i) q^{27} +(2.49090 + 1.60080i) q^{28} +(-6.82896 - 7.88104i) q^{29} +(-0.142315 - 0.989821i) q^{30} +(1.95245 + 0.573290i) q^{31} +(-0.841254 + 0.540641i) q^{32} +(0.444846 - 3.09397i) q^{33} +(-0.742937 + 1.62680i) q^{34} +(1.23002 - 2.69336i) q^{35} +(-0.142315 + 0.989821i) q^{36} +(6.65243 - 4.27526i) q^{37} +(-0.888116 - 0.260774i) q^{38} +(0.190234 + 1.32311i) q^{39} +(0.654861 + 0.755750i) q^{40} +(-7.33845 - 4.71614i) q^{41} +(-1.93900 + 2.23773i) q^{42} +(6.65618 - 1.95443i) q^{43} +(1.29850 + 2.84332i) q^{44} +1.00000 q^{45} +(0.798175 - 4.72894i) q^{46} +1.85519 q^{47} +(-0.415415 - 0.909632i) q^{48} +(-1.69557 + 0.497864i) q^{49} +(0.654861 - 0.755750i) q^{50} +(-1.50452 - 0.966893i) q^{51} +(-0.875361 - 1.01022i) q^{52} +(-0.257312 - 1.78964i) q^{53} +(-0.959493 - 0.281733i) q^{54} +(2.62958 - 1.68993i) q^{55} +(0.421385 - 2.93080i) q^{56} +(0.384512 - 0.841964i) q^{57} +(-4.33200 + 9.48575i) q^{58} +(-1.26233 + 8.77972i) q^{59} +(-0.841254 + 0.540641i) q^{60} +(1.54231 + 0.452864i) q^{61} +(-0.289593 - 2.01416i) q^{62} +(-1.93900 - 2.23773i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-0.875361 + 1.01022i) q^{65} +(-2.99917 + 0.880636i) q^{66} +(4.06491 + 8.90091i) q^{67} +1.78842 q^{68} +(4.56722 + 1.46305i) q^{69} -2.96094 q^{70} +(-4.68077 - 10.2494i) q^{71} +(0.959493 - 0.281733i) q^{72} +(-1.44586 + 1.66862i) q^{73} +(-6.65243 - 4.27526i) q^{74} +(0.654861 + 0.755750i) q^{75} +(0.131728 + 0.916188i) q^{76} +(-8.88036 - 2.60751i) q^{77} +(1.12451 - 0.722682i) q^{78} +(-1.02980 + 7.16240i) q^{79} +(0.415415 - 0.909632i) q^{80} +(0.415415 - 0.909632i) q^{81} +(-1.24145 + 8.63445i) q^{82} +(-12.4077 + 7.97396i) q^{83} +(2.84100 + 0.834192i) q^{84} +(-0.254519 - 1.77022i) q^{85} +(-4.54289 - 5.24277i) q^{86} +(-8.77269 - 5.63786i) q^{87} +(2.04696 - 2.36231i) q^{88} +(-6.00345 + 1.76277i) q^{89} +(-0.415415 - 0.909632i) q^{90} +3.95792 q^{91} +(-4.63317 + 1.23843i) q^{92} +2.03487 q^{93} +(-0.770673 - 1.68754i) q^{94} +(0.888116 - 0.260774i) q^{95} +(-0.654861 + 0.755750i) q^{96} +(9.97604 + 6.41121i) q^{97} +(1.15724 + 1.33552i) q^{98} +(-0.444846 - 3.09397i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} - 4 q^{11} + 2 q^{12} - 13 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 2 q^{21} + 26 q^{22} + 24 q^{23} + 20 q^{24} - 2 q^{25} + 13 q^{26} + 2 q^{27} - 2 q^{28} + 2 q^{29} - 2 q^{30} + 6 q^{31} + 2 q^{32} + 4 q^{33} + 5 q^{34} - 2 q^{35} - 2 q^{36} - 20 q^{37} + 4 q^{38} + 13 q^{39} + 2 q^{40} - 11 q^{41} - 13 q^{42} + 4 q^{43} - 4 q^{44} + 20 q^{45} - 2 q^{46} + 18 q^{47} + 2 q^{48} - 6 q^{49} + 2 q^{50} + 27 q^{51} - 2 q^{52} - 18 q^{53} - 2 q^{54} + 18 q^{55} + 2 q^{56} - 7 q^{57} + 9 q^{58} - 52 q^{59} + 2 q^{60} - 7 q^{61} + 16 q^{62} - 13 q^{63} - 2 q^{64} - 2 q^{65} + 7 q^{66} - 10 q^{67} + 28 q^{68} + 20 q^{69} - 20 q^{70} + 7 q^{71} + 2 q^{72} - 37 q^{73} + 20 q^{74} + 2 q^{75} - 4 q^{76} - 70 q^{77} + 9 q^{78} + 20 q^{79} - 2 q^{80} - 2 q^{81} - 11 q^{82} - 19 q^{83} - 9 q^{84} + 17 q^{85} - 26 q^{86} - 2 q^{87} + 4 q^{88} + 33 q^{89} + 2 q^{90} - 42 q^{91} - 9 q^{92} + 16 q^{93} - 7 q^{94} - 4 q^{95} - 2 q^{96} + 9 q^{97} + 6 q^{98} - 4 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 + 2 * q^10 - 4 * q^11 + 2 * q^12 - 13 * q^13 + 2 * q^14 + 2 * q^15 - 2 * q^16 + 6 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 2 * q^21 + 26 * q^22 + 24 * q^23 + 20 * q^24 - 2 * q^25 + 13 * q^26 + 2 * q^27 - 2 * q^28 + 2 * q^29 - 2 * q^30 + 6 * q^31 + 2 * q^32 + 4 * q^33 + 5 * q^34 - 2 * q^35 - 2 * q^36 - 20 * q^37 + 4 * q^38 + 13 * q^39 + 2 * q^40 - 11 * q^41 - 13 * q^42 + 4 * q^43 - 4 * q^44 + 20 * q^45 - 2 * q^46 + 18 * q^47 + 2 * q^48 - 6 * q^49 + 2 * q^50 + 27 * q^51 - 2 * q^52 - 18 * q^53 - 2 * q^54 + 18 * q^55 + 2 * q^56 - 7 * q^57 + 9 * q^58 - 52 * q^59 + 2 * q^60 - 7 * q^61 + 16 * q^62 - 13 * q^63 - 2 * q^64 - 2 * q^65 + 7 * q^66 - 10 * q^67 + 28 * q^68 + 20 * q^69 - 20 * q^70 + 7 * q^71 + 2 * q^72 - 37 * q^73 + 20 * q^74 + 2 * q^75 - 4 * q^76 - 70 * q^77 + 9 * q^78 + 20 * q^79 - 2 * q^80 - 2 * q^81 - 11 * q^82 - 19 * q^83 - 9 * q^84 + 17 * q^85 - 26 * q^86 - 2 * q^87 + 4 * q^88 + 33 * q^89 + 2 * q^90 - 42 * q^91 - 9 * q^92 + 16 * q^93 - 7 * q^94 - 4 * q^95 - 2 * q^96 + 9 * q^97 + 6 * q^98 - 4 * q^99

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