LMFDB - Embedded newform 189.2.w.a.25.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(25,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([10, 12]))

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

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

chi := DirichletCharacter("189.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.w (of order $9$, degree $6$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.5
Character	$\chi$	$=$	189.25
Dual form			189.2.w.a.121.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.47150 + 0.535583i) q^{2} +(0.0586596 + 1.73106i) q^{3} +(0.346382 - 0.290649i) q^{4} +(3.26769 + 1.18934i) q^{5} +(-1.01344 - 2.51584i) q^{6} +(-0.172863 + 2.64010i) q^{7} +(1.21191 - 2.09908i) q^{8} +(-2.99312 + 0.203086i) q^{9} +O(q^{10})$	\(q+(-1.47150 + 0.535583i) q^{2} +(0.0586596 + 1.73106i) q^{3} +(0.346382 - 0.290649i) q^{4} +(3.26769 + 1.18934i) q^{5} +(-1.01344 - 2.51584i) q^{6} +(-0.172863 + 2.64010i) q^{7} +(1.21191 - 2.09908i) q^{8} +(-2.99312 + 0.203086i) q^{9} -5.44540 q^{10} +(3.82352 - 1.39165i) q^{11} +(0.523448 + 0.582557i) q^{12} +(-0.0193280 - 0.109614i) q^{13} +(-1.15962 - 3.97749i) q^{14} +(-1.86714 + 5.72632i) q^{15} +(-0.816126 + 4.62848i) q^{16} -3.19244 q^{17} +(4.29561 - 1.90191i) q^{18} -6.67057 q^{19} +(1.47755 - 0.537783i) q^{20} +(-4.58030 - 0.144369i) q^{21} +(-4.88098 + 4.09563i) q^{22} +(0.749091 + 4.24830i) q^{23} +(3.70472 + 1.97475i) q^{24} +(5.43302 + 4.55885i) q^{25} +(0.0871487 + 0.150946i) q^{26} +(-0.527129 - 5.16935i) q^{27} +(0.707465 + 0.964724i) q^{28} +(1.65539 - 9.38817i) q^{29} +(-0.319425 - 9.42630i) q^{30} +(3.19029 - 2.67697i) q^{31} +(-0.436224 - 2.47395i) q^{32} +(2.63331 + 6.53710i) q^{33} +(4.69768 - 1.70982i) q^{34} +(-3.70484 + 8.42142i) q^{35} +(-0.977734 + 0.940291i) q^{36} +(1.65756 - 2.87098i) q^{37} +(9.81577 - 3.57265i) q^{38} +(0.188615 - 0.0398877i) q^{39} +(6.45665 - 5.41777i) q^{40} +(-0.169276 - 0.960010i) q^{41} +(6.81725 - 2.24069i) q^{42} +(5.64237 + 4.73451i) q^{43} +(0.919917 - 1.59334i) q^{44} +(-10.0221 - 2.89622i) q^{45} +(-3.37761 - 5.85019i) q^{46} +(4.36301 + 3.66100i) q^{47} +(-8.06004 - 1.14126i) q^{48} +(-6.94024 - 0.912751i) q^{49} +(-10.4363 - 3.79852i) q^{50} +(-0.187267 - 5.52630i) q^{51} +(-0.0385541 - 0.0323507i) q^{52} +(4.61341 - 7.99066i) q^{53} +(3.54429 + 7.32438i) q^{54} +14.1492 q^{55} +(5.33229 + 3.56240i) q^{56} +(-0.391293 - 11.5471i) q^{57} +(2.59224 + 14.7013i) q^{58} +(1.10471 + 6.26513i) q^{59} +(1.01761 + 2.52617i) q^{60} +(-2.96003 - 2.48376i) q^{61} +(-3.26078 + 5.64783i) q^{62} +(-0.0187681 - 7.93723i) q^{63} +(-2.73297 - 4.73365i) q^{64} +(0.0672110 - 0.381173i) q^{65} +(-7.37609 - 8.20901i) q^{66} +(2.63767 + 0.960035i) q^{67} +(-1.10580 + 0.927878i) q^{68} +(-7.31012 + 1.54592i) q^{69} +(0.941308 - 14.3764i) q^{70} +(0.320883 + 0.555786i) q^{71} +(-3.20108 + 6.52892i) q^{72} +(0.416497 + 0.721395i) q^{73} +(-0.901458 + 5.11242i) q^{74} +(-7.57293 + 9.67229i) q^{75} +(-2.31056 + 1.93879i) q^{76} +(3.01314 + 10.3350i) q^{77} +(-0.256184 + 0.159714i) q^{78} +(-2.03880 + 0.742063i) q^{79} +(-8.17168 + 14.1538i) q^{80} +(8.91751 - 1.21572i) q^{81} +(0.763254 + 1.32200i) q^{82} +(-1.66349 + 9.43414i) q^{83} +(-1.62849 + 1.28125i) q^{84} +(-10.4319 - 3.79690i) q^{85} +(-10.8385 - 3.94489i) q^{86} +(16.3486 + 2.31486i) q^{87} +(1.71256 - 9.71243i) q^{88} +0.420642 q^{89} +(16.2987 - 1.10589i) q^{90} +(0.292734 - 0.0320794i) q^{91} +(1.49424 + 1.25381i) q^{92} +(4.82113 + 5.36554i) q^{93} +(-8.38096 - 3.05042i) q^{94} +(-21.7973 - 7.93359i) q^{95} +(4.25696 - 0.900249i) q^{96} +(8.06794 + 6.76980i) q^{97} +(10.7014 - 2.37396i) q^{98} +(-11.1616 + 4.94187i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} + 3 q^{11} - 3 q^{12} - 12 q^{13} + 15 q^{14} - 9 q^{16} - 54 q^{17} - 3 q^{18} - 6 q^{19} - 18 q^{20} - 21 q^{21} - 12 q^{22} + 45 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 57 q^{30} - 3 q^{31} + 51 q^{32} + 15 q^{33} - 18 q^{34} - 12 q^{35} - 60 q^{36} + 3 q^{37} - 57 q^{38} - 66 q^{39} - 66 q^{40} + 33 q^{42} - 12 q^{43} + 3 q^{44} + 33 q^{45} + 3 q^{46} - 21 q^{47} + 90 q^{48} + 12 q^{49} - 39 q^{50} - 48 q^{51} + 9 q^{52} + 9 q^{53} - 63 q^{54} - 24 q^{55} + 57 q^{56} - 18 q^{57} - 3 q^{58} - 18 q^{59} + 81 q^{60} + 33 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} + 81 q^{65} + 69 q^{66} - 3 q^{67} + 6 q^{68} - 6 q^{69} - 42 q^{70} - 18 q^{71} - 105 q^{72} + 21 q^{73} - 93 q^{74} + 18 q^{75} - 24 q^{76} + 87 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} + 39 q^{81} - 6 q^{82} - 42 q^{83} - 36 q^{84} - 63 q^{85} + 159 q^{86} + 30 q^{87} + 57 q^{88} - 150 q^{89} - 39 q^{90} + 6 q^{91} - 66 q^{92} - 27 q^{93} + 33 q^{94} - 147 q^{95} + 81 q^{96} - 12 q^{97} + 99 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^10 + 3 * q^11 - 3 * q^12 - 12 * q^13 + 15 * q^14 - 9 * q^16 - 54 * q^17 - 3 * q^18 - 6 * q^19 - 18 * q^20 - 21 * q^21 - 12 * q^22 + 45 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 57 * q^30 - 3 * q^31 + 51 * q^32 + 15 * q^33 - 18 * q^34 - 12 * q^35 - 60 * q^36 + 3 * q^37 - 57 * q^38 - 66 * q^39 - 66 * q^40 + 33 * q^42 - 12 * q^43 + 3 * q^44 + 33 * q^45 + 3 * q^46 - 21 * q^47 + 90 * q^48 + 12 * q^49 - 39 * q^50 - 48 * q^51 + 9 * q^52 + 9 * q^53 - 63 * q^54 - 24 * q^55 + 57 * q^56 - 18 * q^57 - 3 * q^58 - 18 * q^59 + 81 * q^60 + 33 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 + 81 * q^65 + 69 * q^66 - 3 * q^67 + 6 * q^68 - 6 * q^69 - 42 * q^70 - 18 * q^71 - 105 * q^72 + 21 * q^73 - 93 * q^74 + 18 * q^75 - 24 * q^76 + 87 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 + 39 * q^81 - 6 * q^82 - 42 * q^83 - 36 * q^84 - 63 * q^85 + 159 * q^86 + 30 * q^87 + 57 * q^88 - 150 * q^89 - 39 * q^90 + 6 * q^91 - 66 * q^92 - 27 * q^93 + 33 * q^94 - 147 * q^95 + 81 * q^96 - 12 * q^97 + 99 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.47150	+	0.535583i	−1.04051	+	0.378714i	−0.805073	−	0.593175i	$-0.797874\pi$
$2$	−1.47150	+	0.535583i	−1.04051	+	0.378714i	−0.235436	+	0.971890i	$0.575652\pi$
$3$	0.0586596	+	1.73106i	0.0338671	+	0.999426i
$3$	0.0586596	+	1.73106i	0.0338671	+	0.999426i
$4$	0.346382	−	0.290649i	0.173191	−	0.145324i
$5$	3.26769	+	1.18934i	1.46135	+	0.531889i	0.945738	−	0.324930i	$-0.105341\pi$
$5$	3.26769	+	1.18934i	1.46135	+	0.531889i	0.515616	+	0.856820i	$0.327563\pi$
$6$	−1.01344	−	2.51584i	−0.413736	−	1.02709i
$7$	−0.172863	+	2.64010i	−0.0653361	+	0.997863i
$7$	−0.172863	+	2.64010i	−0.0653361	+	0.997863i
$8$	1.21191	−	2.09908i	0.428473	−	0.742137i
$9$	−2.99312	+	0.203086i	−0.997706	+	0.0676954i
$10$	−5.44540			−1.72199
$11$	3.82352	−	1.39165i	1.15284	−	0.419598i	0.306303	−	0.951934i	$-0.400908\pi$
$11$	3.82352	−	1.39165i	1.15284	−	0.419598i	0.846533	+	0.532336i	$0.178686\pi$
$12$	0.523448	+	0.582557i	0.151106	+	0.168170i
$13$	−0.0193280	−	0.109614i	−0.00536061	−	0.0304015i	0.982010	−	0.188828i	$-0.0604689\pi$
$13$	−0.0193280	−	0.109614i	−0.00536061	−	0.0304015i	−0.987371	+	0.158427i	$0.949358\pi$
$14$	−1.15962	−	3.97749i	−0.309922	−	1.06303i
$15$	−1.86714	+	5.72632i	−0.482092	+	1.47853i
$16$	−0.816126	+	4.62848i	−0.204031	+	1.15712i
$17$	−3.19244			−0.774280			−0.387140	−	0.922021i	$-0.626537\pi$
$17$	−3.19244			−0.774280			−0.387140	+	0.922021i	$0.626537\pi$
$18$	4.29561	−	1.90191i	1.01249	−	0.448283i
$19$	−6.67057			−1.53033			−0.765167	−	0.643831i	$-0.777344\pi$
$19$	−6.67057			−1.53033			−0.765167	+	0.643831i	$0.777344\pi$
$20$	1.47755	−	0.537783i	0.330390	−	0.120252i
$21$	−4.58030	−	0.144369i	−0.999504	−	0.0315038i
$22$	−4.88098	+	4.09563i	−1.04063	+	0.873191i
$23$	0.749091	+	4.24830i	0.156196	+	0.885833i	0.957684	+	0.287822i	$0.0929310\pi$
$23$	0.749091	+	4.24830i	0.156196	+	0.885833i	−0.801488	+	0.598011i	$0.795958\pi$
$24$	3.70472	+	1.97475i	0.756223	+	0.403093i
$25$	5.43302	+	4.55885i	1.08660	+	0.911770i
$26$	0.0871487	+	0.150946i	0.0170913	+	0.0296029i
$27$	−0.527129	−	5.16935i	−0.101446	−	0.994841i
$28$	0.707465	+	0.964724i	0.133698	+	0.182316i
$29$	1.65539	−	9.38817i	0.307398	−	1.74334i	−0.304601	−	0.952480i	$-0.598523\pi$
$29$	1.65539	−	9.38817i	0.307398	−	1.74334i	0.611998	−	0.790859i	$-0.290366\pi$
$30$	−0.319425	−	9.42630i	−0.0583188	−	1.72100i
$31$	3.19029	−	2.67697i	0.572992	−	0.480798i	−0.309645	−	0.950852i	$-0.600210\pi$
$31$	3.19029	−	2.67697i	0.572992	−	0.480798i	0.882637	+	0.470055i	$0.155766\pi$
$32$	−0.436224	−	2.47395i	−0.0771142	−	0.437336i
$33$	2.63331	+	6.53710i	0.458400	+	1.13796i
$34$	4.69768	−	1.70982i	0.805646	−	0.293231i
$35$	−3.70484	+	8.42142i	−0.626232	+	1.42348i
$36$	−0.977734	+	0.940291i	−0.162956	+	0.156715i
$37$	1.65756	−	2.87098i	0.272502	−	0.471987i	−0.697000	−	0.717071i	$-0.745482\pi$
$37$	1.65756	−	2.87098i	0.272502	−	0.471987i	0.969502	+	0.245084i	$0.0788157\pi$
$38$	9.81577	−	3.57265i	1.59233	−	0.579560i
$39$	0.188615	−	0.0398877i	0.0302025	−	0.00638715i
$40$	6.45665	−	5.41777i	1.02089	−	0.856625i
$41$	−0.169276	−	0.960010i	−0.0264364	−	0.149928i	0.968732	−	0.248109i	$-0.0798090\pi$
$41$	−0.169276	−	0.960010i	−0.0264364	−	0.149928i	−0.995169	+	0.0981802i	$0.968698\pi$
$42$	6.81725	−	2.24069i	1.05192	−	0.345746i
$43$	5.64237	+	4.73451i	0.860454	+	0.722007i	0.962066	−	0.272818i	$-0.0879556\pi$
$43$	5.64237	+	4.73451i	0.860454	+	0.722007i	−0.101612	+	0.994824i	$0.532400\pi$
$44$	0.919917	−	1.59334i	0.138683	−	0.240206i
$45$	−10.0221	−	2.89622i	−1.49401	−	0.431742i
$46$	−3.37761	−	5.85019i	−0.498001	−	0.862563i
$47$	4.36301	+	3.66100i	0.636411	+	0.534012i	0.902914	−	0.429822i	$-0.141424\pi$
$47$	4.36301	+	3.66100i	0.636411	+	0.534012i	−0.266503	+	0.963834i	$0.585868\pi$
$48$	−8.06004	−	1.14126i	−1.16337	−	0.164726i
$49$	−6.94024	−	0.912751i	−0.991462	−	0.130393i
$50$	−10.4363	−	3.79852i	−1.47592	−	0.537192i
$51$	−0.187267	−	5.52630i	−0.0262227	−	0.773836i
$52$	−0.0385541	−	0.0323507i	−0.00534649	−	0.00448624i
$53$	4.61341	−	7.99066i	0.633700	−	1.09760i	−0.353089	−	0.935590i	$-0.614869\pi$
$53$	4.61341	−	7.99066i	0.633700	−	1.09760i	0.986789	−	0.162011i	$-0.0517981\pi$
$54$	3.54429	+	7.32438i	0.482316	+	0.996722i
$55$	14.1492			1.90788
$56$	5.33229	+	3.56240i	0.712557	+	0.476046i
$57$	−0.391293	−	11.5471i	−0.0518280	−	1.52946i
$58$	2.59224	+	14.7013i	0.340377	+	1.93038i
$59$	1.10471	+	6.26513i	0.143821	+	0.815651i	0.968306	+	0.249767i	$0.0803540\pi$
$59$	1.10471	+	6.26513i	0.143821	+	0.815651i	−0.824485	+	0.565884i	$0.808535\pi$
$60$	1.01761	+	2.52617i	0.131372	+	0.326127i
$61$	−2.96003	−	2.48376i	−0.378993	−	0.318013i	0.433314	−	0.901243i	$-0.357344\pi$
$61$	−2.96003	−	2.48376i	−0.378993	−	0.318013i	−0.812307	+	0.583230i	$0.801789\pi$
$62$	−3.26078	+	5.64783i	−0.414119	+	0.717275i
$63$	−0.0187681	−	7.93723i	−0.00236455	−	0.999997i
$64$	−2.73297	−	4.73365i	−0.341622	−	0.591706i
$65$	0.0672110	−	0.381173i	0.00833650	−	0.0472787i
$66$	−7.37609	−	8.20901i	−0.907933	−	1.01046i
$67$	2.63767	+	0.960035i	0.322243	+	0.117287i	0.498077	−	0.867133i	$-0.334040\pi$
$67$	2.63767	+	0.960035i	0.322243	+	0.117287i	−0.175833	+	0.984420i	$0.556262\pi$
$68$	−1.10580	+	0.927878i	−0.134098	+	0.112522i
$69$	−7.31012	+	1.54592i	−0.880035	+	0.186107i
$70$	0.941308	−	14.3764i	0.112508	−	1.71831i
$71$	0.320883	+	0.555786i	0.0380818	+	0.0659596i	0.884438	−	0.466657i	$-0.154542\pi$
$71$	0.320883	+	0.555786i	0.0380818	+	0.0659596i	−0.846356	+	0.532617i	$0.821209\pi$
$72$	−3.20108	+	6.52892i	−0.377251	+	0.769441i
$73$	0.416497	+	0.721395i	0.0487473	+	0.0844328i	0.889369	−	0.457189i	$-0.151144\pi$
$73$	0.416497	+	0.721395i	0.0487473	+	0.0844328i	−0.840622	+	0.541622i	$0.817810\pi$
$74$	−0.901458	+	5.11242i	−0.104792	+	0.594307i
$75$	−7.57293	+	9.67229i	−0.874446	+	1.11686i
$76$	−2.31056	+	1.93879i	−0.265040	+	0.222395i
$77$	3.01314	+	10.3350i	0.343380	+	1.17779i
$78$	−0.256184	+	0.159714i	−0.0290071	+	0.0180840i
$79$	−2.03880	+	0.742063i	−0.229383	+	0.0834886i	−0.454155	−	0.890923i	$-0.650059\pi$
$79$	−2.03880	+	0.742063i	−0.229383	+	0.0834886i	0.224772	+	0.974411i	$0.427836\pi$
$80$	−8.17168	+	14.1538i	−0.913622	+	1.58244i
$81$	8.91751	−	1.21572i	0.990835	−	0.135080i
$82$	0.763254	+	1.32200i	0.0842874	+	0.145990i
$83$	−1.66349	+	9.43414i	−0.182592	+	1.03553i	0.746418	+	0.665477i	$0.231772\pi$
$83$	−1.66349	+	9.43414i	−0.182592	+	1.03553i	−0.929010	+	0.370054i	$0.879339\pi$
$84$	−1.62849	+	1.28125i	−0.177683	+	0.139796i
$85$	−10.4319	−	3.79690i	−1.13150	−	0.411831i
$86$	−10.8385	−	3.94489i	−1.16874	−	0.425388i
$87$	16.3486	+	2.31486i	1.75275	+	0.248179i
$88$	1.71256	−	9.71243i	0.182560	−	1.03535i
$89$	0.420642			0.0445879			0.0222940	−	0.999751i	$-0.492903\pi$
$89$	0.420642			0.0445879			0.0222940	+	0.999751i	$0.492903\pi$
$90$	16.2987	−	1.10589i	1.71804	−	0.116571i
$91$	0.292734	−	0.0320794i	0.0306868	−	0.00336284i
$92$	1.49424	+	1.25381i	0.155785	+	0.130719i
$93$	4.82113	+	5.36554i	0.499927	+	0.556380i
$94$	−8.38096	−	3.05042i	−0.864430	−	0.314627i
$95$	−21.7973	−	7.93359i	−2.23636	−	0.813969i
$96$	4.25696	−	0.900249i	0.434474	−	0.0918813i
$97$	8.06794	+	6.76980i	0.819175	+	0.687370i	0.952779	−	0.303665i	$-0.0982105\pi$
$97$	8.06794	+	6.76980i	0.819175	+	0.687370i	−0.133604	+	0.991035i	$0.542655\pi$
$98$	10.7014	−	2.37396i	1.08101	−	0.239806i
$99$	−11.1616	+	4.94187i	−1.12179	+	0.496677i
$100$	3.20692			0.320692
$101$	1.46461	−	8.30622i	0.145734	−	0.826500i	−0.821040	−	0.570870i	$-0.806606\pi$
$101$	1.46461	−	8.30622i	0.145734	−	0.826500i	0.966775	−	0.255630i	$-0.0822829\pi$
$102$	3.23535	+	8.03166i	0.320348	+	0.795253i
$103$	4.99736	+	1.81889i	0.492405	+	0.179221i	0.576275	−	0.817256i	$-0.304506\pi$
$103$	4.99736	+	1.81889i	0.492405	+	0.179221i	−0.0838700	+	0.996477i	$0.526728\pi$
$104$	−0.253513	−	0.0922712i	−0.0248590	−	0.00904793i
$105$	−14.7953	−	5.91929i	−1.44387	−	0.577664i
$106$	−2.50898	+	14.2291i	−0.243694	+	1.38206i
$107$	−3.55714	−	6.16115i	−0.343882	−	0.595621i	0.641268	−	0.767317i	$-0.278409\pi$
$107$	−3.55714	−	6.16115i	−0.343882	−	0.595621i	−0.985150	+	0.171696i	$0.945075\pi$
$108$	−1.68505	−	1.63736i	−0.162144	−	0.157555i
$109$	−6.74684	+	11.6859i	−0.646230	+	1.11930i	0.337786	+	0.941223i	$0.390322\pi$
$109$	−6.74684	+	11.6859i	−0.646230	+	1.11930i	−0.984016	+	0.178080i	$0.943011\pi$
$110$	−20.8206	+	7.57808i	−1.98517	+	0.722542i
$111$	5.06707	+	2.70093i	0.480945	+	0.256360i
$112$	−12.0786	−	2.95475i	−1.14132	−	0.279197i
$113$	8.07931	−	6.77935i	0.760037	−	0.637747i	−0.178099	−	0.984013i	$-0.556995\pi$
$113$	8.07931	−	6.77935i	0.760037	−	0.637747i	0.938137	+	0.346265i	$0.112550\pi$
$114$	6.76025	+	16.7821i	0.633155	+	1.57179i
$115$	−2.60489	+	14.7731i	−0.242907	+	1.37759i
$116$	−2.15526	−	3.73303i	−0.200111	−	0.346603i
$117$	0.0801120	+	0.324163i	0.00740636	+	0.0299689i
$118$	−4.98109	−	8.62750i	−0.458546	−	0.794225i
$119$	0.551855	−	8.42835i	0.0505884	−	0.772626i
$120$	9.75722	+	10.8590i	0.890708	+	0.991289i
$121$	4.25616	−	3.57134i	0.386923	−	0.324667i
$122$	5.68595	+	2.06952i	0.514782	+	0.187365i
$123$	1.65190	−	0.349340i	0.148947	−	0.0314989i
$124$	0.326999	−	1.85451i	0.0293654	−	0.166539i
$125$	3.63790	+	6.30102i	0.325383	+	0.563580i
$126$	4.27866	+	11.6696i	0.381174	+	1.03961i
$127$	1.80508	−	3.12650i	0.160175	−	0.277432i	−0.774756	−	0.632260i	$-0.782127\pi$
$127$	1.80508	−	3.12650i	0.160175	−	0.277432i	0.934931	+	0.354828i	$0.115461\pi$
$128$	10.4056	+	8.73135i	0.919735	+	0.771750i
$129$	−7.86473	+	10.0450i	−0.692451	+	0.884413i
$130$	0.105248	+	0.596894i	0.00923090	+	0.0523510i
$131$	−2.68876	−	15.2487i	−0.234918	−	1.33229i	−0.842786	−	0.538249i	$-0.819086\pi$
$131$	−2.68876	−	15.2487i	−0.234918	−	1.33229i	0.607868	−	0.794038i	$-0.292025\pi$
$132$	2.81213	+	1.49896i	0.244765	+	0.130468i
$133$	1.15310	−	17.6110i	0.0999861	−	1.52706i
$134$	−4.39552			−0.379715
$135$	4.42562	−	17.5187i	0.380897	−	1.50777i
$136$	−3.86893	+	6.70119i	−0.331758	+	0.574622i
$137$	−11.6673	−	9.79006i	−0.996808	−	0.836421i	−0.0102688	−	0.999947i	$-0.503269\pi$
$137$	−11.6673	−	9.79006i	−0.996808	−	0.836421i	−0.986539	+	0.163526i	$0.947713\pi$
$138$	9.92888	−	6.19000i	0.845203	−	0.526928i
$139$	1.37493	+	0.500432i	0.116620	+	0.0424461i	0.399671	−	0.916659i	$-0.369124\pi$
$139$	1.37493	+	0.500432i	0.116620	+	0.0424461i	−0.283051	+	0.959105i	$0.591347\pi$
$140$	1.16439	+	3.99383i	0.0984087	+	0.337540i
$141$	−6.08147	+	7.76738i	−0.512152	+	0.654131i
$142$	−0.769850	−	0.645981i	−0.0646044	−	0.0542095i
$143$	−0.226445	−	0.392215i	−0.0189363	−	0.0327987i
$144$	1.50278	−	14.0193i	0.125232	−	1.16828i
$145$	16.5750	−	28.7088i	1.37648	−	2.38413i
$146$	−0.999244	−	0.838465i	−0.0826980	−	0.0693919i
$147$	1.17291	−	12.0675i	0.0967402	−	0.995310i
$148$	−0.260298	−	1.47622i	−0.0213964	−	0.121345i
$149$	9.53636	−	8.00195i	0.781249	−	0.655546i	−0.162314	−	0.986739i	$-0.551896\pi$
$149$	9.53636	−	8.00195i	0.781249	−	0.655546i	0.943563	+	0.331194i	$0.107451\pi$
$150$	5.96326	−	18.2887i	0.486899	−	1.49327i
$151$	1.41378	−	0.514576i	0.115052	−	0.0418756i	−0.283853	−	0.958868i	$-0.591613\pi$
$151$	1.41378	−	0.514576i	0.115052	−	0.0418756i	0.398905	+	0.916992i	$0.369390\pi$
$152$	−8.08411	+	14.0021i	−0.655708	+	1.13572i
$153$	9.55535	−	0.648340i	0.772504	−	0.0524152i
$154$	−9.96912	−	13.5943i	−0.803335	−	1.09546i
$155$	13.6087	−	4.95316i	1.09308	−	0.397847i
$156$	0.0537394	−	0.0686370i	0.00430260	−	0.00549536i
$157$	1.21859	+	6.91100i	0.0972545	+	0.551557i	0.994033	+	0.109078i	$0.0347899\pi$
$157$	1.21859	+	6.91100i	0.0972545	+	0.551557i	−0.896779	+	0.442479i	$0.854099\pi$
$158$	2.60266	−	2.18390i	0.207057	−	0.173741i
$159$	14.1029	+	7.51734i	1.11843	+	0.596164i
$160$	1.51692	−	8.60290i	0.119923	−	0.680119i
$161$	−11.3454	+	1.24330i	−0.894145	+	0.0979856i
$162$	−12.4710	+	6.56501i	−0.979816	+	0.515796i
$163$	−11.2418	−	19.4713i	−0.880524	−	1.52511i	−0.850760	−	0.525555i	$-0.823858\pi$
$163$	−11.2418	−	19.4713i	−0.880524	−	1.52511i	−0.0297644	−	0.999557i	$-0.509476\pi$
$164$	−0.337660	−	0.283330i	−0.0263668	−	0.0221244i
$165$	0.829988	+	24.4931i	0.0646144	+	1.90679i
$166$	−2.60493	−	14.7733i	−0.202182	−	1.14663i
$167$	0.698941	−	0.586481i	0.0540857	−	0.0453833i	−0.615344	−	0.788259i	$-0.710983\pi$
$167$	0.698941	−	0.586481i	0.0540857	−	0.0453833i	0.669430	+	0.742875i	$0.266538\pi$
$168$	−5.85393	+	9.43946i	−0.451641	+	0.728271i
$169$	12.2044	−	4.44202i	0.938797	−	0.341694i
$170$	17.3841			1.33330
$171$	19.9658	−	1.35470i	1.52682	−	0.103597i
$172$	3.33049			0.253948
$173$	0.474745	−	2.69242i	0.0360942	−	0.204701i	−0.961428	−	0.275058i	$-0.911303\pi$
$173$	0.474745	−	2.69242i	0.0360942	−	0.204701i	0.997522	+	0.0703575i	$0.0224140\pi$
$174$	−25.2968	+	5.34968i	−1.91774	+	0.405559i
$175$	−12.9750	+	13.5557i	−0.980816	+	1.02471i
$176$	3.32074	+	18.8329i	0.250310	+	1.41958i
$177$	−10.7805	+	2.27983i	−0.810312	+	0.171363i
$178$	−0.618975	+	0.225289i	−0.0463941	+	0.0168861i
$179$	2.46922			0.184558			0.0922789	−	0.995733i	$-0.470585\pi$
$179$	2.46922			0.184558			0.0922789	+	0.995733i	$0.470585\pi$
$180$	−4.31326	+	1.90972i	−0.321491	+	0.142342i
$181$	−11.6476	+	20.1742i	−0.865757	+	1.49954i	0.000536603		1.00000i	$0.499829\pi$
$181$	−11.6476	+	20.1742i	−0.865757	+	1.49954i	−0.866294	+	0.499535i	$0.833504\pi$
$182$	−0.413577	+	0.203988i	−0.0306564	+	0.0151206i
$183$	4.12590	−	5.26968i	0.304995	−	0.389546i
$184$	9.82536	+	3.57614i	0.724335	+	0.263637i
$185$	8.83097	−	7.41007i	0.649266	−	0.544799i
$186$	−9.96799	−	5.31329i	−0.730888	−	0.389589i
$187$	−12.2064	+	4.44275i	−0.892618	+	0.324886i
$188$	2.57533			0.187825
$189$	13.7387	−	0.498083i	0.999343	−	0.0362302i
$190$	36.3239			2.63522
$191$	−17.7560	+	6.46266i	−1.28478	+	0.467622i	−0.892010	−	0.452015i	$-0.850705\pi$
$191$	−17.7560	+	6.46266i	−1.28478	+	0.467622i	−0.392770	+	0.919637i	$0.628483\pi$
$192$	8.03390	−	5.00861i	0.579797	−	0.361465i
$193$	−3.00338	+	2.52014i	−0.216188	+	0.181404i	−0.744450	−	0.667678i	$-0.767288\pi$
$193$	−3.00338	+	2.52014i	−0.216188	+	0.181404i	0.528262	+	0.849081i	$0.322844\pi$
$194$	−15.4978	−	5.64073i	−1.11268	−	0.404981i
$195$	0.663774	+	0.0939867i	0.0475339	+	0.00673053i
$196$	−2.66926	+	1.70101i	−0.190661	+	0.121501i
$197$	−5.25085	+	9.09475i	−0.374108	+	0.647974i	−0.990193	−	0.139706i	$-0.955384\pi$
$197$	−5.25085	+	9.09475i	−0.374108	+	0.647974i	0.616085	+	0.787680i	$0.288718\pi$
$198$	13.7776	−	13.2500i	0.979130	−	0.941634i
$199$	−10.9582			−0.776805			−0.388402	−	0.921490i	$-0.626973\pi$
$199$	−10.9582			−0.776805			−0.388402	+	0.921490i	$0.626973\pi$
$200$	16.1537	−	5.87947i	1.14224	−	0.415741i
$201$	−1.50715	+	4.62228i	−0.106306	+	0.326031i
$202$	2.29349	+	13.0071i	0.161370	+	0.915173i
$203$	24.4995	+	5.99325i	1.71953	+	0.420644i
$204$	−1.67108	−	1.85978i	−0.116999	−	0.130211i
$205$	0.588639	−	3.33834i	0.0411123	−	0.233160i
$206$	−8.32780			−0.580225
$207$	−3.10489	−	12.5635i	−0.215805	−	0.873227i
$208$	0.523122			0.0362720
$209$	−25.5051	+	9.28310i	−1.76422	+	0.642125i
$210$	24.9416	+	0.786145i	1.72113	+	0.0542492i
$211$	7.42531	−	6.23057i	0.511179	−	0.428930i	−0.350365	−	0.936613i	$-0.613942\pi$
$211$	7.42531	−	6.23057i	0.511179	−	0.428930i	0.861544	+	0.507683i	$0.169498\pi$
$212$	−0.724474	−	4.10870i	−0.0497571	−	0.282187i
$213$	−0.943274	+	0.588069i	−0.0646321	+	0.0402938i
$214$	8.53416	+	7.16101i	0.583383	+	0.489516i
$215$	12.8066	+	22.1816i	0.873400	+	1.51277i
$216$	−11.4897	−	5.15827i	−0.781776	−	0.350976i
$217$	6.51598	+	8.88542i	0.442333	+	0.603181i
$218$	3.66924	−	20.8093i	0.248512	−	1.40938i
$219$	−1.22434	+	0.763297i	−0.0827335	+	0.0515789i
$220$	4.90103	−	4.11245i	0.330427	−	0.277262i
$221$	0.0617033	+	0.349937i	0.00415062	+	0.0235393i
$222$	−8.90277	−	1.26058i	−0.597515	−	0.0846048i
$223$	−15.4852	+	5.63617i	−1.03697	+	0.377426i	−0.803730	−	0.594994i	$-0.797154\pi$
$223$	−15.4852	+	5.63617i	−1.03697	+	0.377426i	−0.233238	+	0.972420i	$0.574932\pi$
$224$	6.60687	−	0.724019i	0.441440	−	0.0483756i
$225$	−17.1875	−	12.5418i	−1.14583	−	0.836120i
$226$	−8.25782	+	14.3030i	−0.549302	+	0.951419i
$227$	2.42341	−	0.882050i	0.160848	−	0.0585437i	−0.260341	−	0.965517i	$-0.583835\pi$
$227$	2.42341	−	0.882050i	0.160848	−	0.0585437i	0.421189	+	0.906973i	$0.361613\pi$
$228$	−3.49170	−	3.88599i	−0.231243	−	0.257356i
$229$	−0.904076	+	0.758610i	−0.0597431	+	0.0501304i	−0.672170	−	0.740397i	$-0.734638\pi$
$229$	−0.904076	+	0.758610i	−0.0597431	+	0.0501304i	0.612427	+	0.790527i	$0.290193\pi$
$230$	−4.07910	−	23.1337i	−0.268968	−	1.52539i
$231$	−17.7138	+	5.82217i	−1.16548	+	0.383071i
$232$	−17.7004	−	14.8524i	−1.16209	−	0.975106i
$233$	10.2228	−	17.7065i	0.669721	−	1.15999i	−0.308262	−	0.951302i	$-0.599747\pi$
$233$	10.2228	−	17.7065i	0.669721	−	1.15999i	0.977982	−	0.208688i	$-0.0669194\pi$
$234$	−0.291501	−	0.434100i	−0.0190560	−	0.0283780i
$235$	9.90278	+	17.1521i	0.645986	+	1.11888i
$236$	2.20361	+	1.84904i	0.143442	+	0.120363i
$237$	−1.40415	−	3.48575i	−0.0912093	−	0.226424i
$238$	3.70203	+	12.6979i	0.239967	+	0.823083i
$239$	−7.54157	−	2.74491i	−0.487824	−	0.177553i	0.0863857	−	0.996262i	$-0.472468\pi$
$239$	−7.54157	−	2.74491i	−0.487824	−	0.177553i	−0.574209	+	0.818708i	$0.694690\pi$
$240$	−24.9803	−	13.3154i	−1.61247	−	0.859505i
$241$	−14.5101	−	12.1754i	−0.934677	−	0.784287i	0.0419744	−	0.999119i	$-0.486635\pi$
$241$	−14.5101	−	12.1754i	−0.934677	−	0.784287i	−0.976651	+	0.214832i	$0.931080\pi$
$242$	−4.35020	+	7.53476i	−0.279641	+	0.484353i
$243$	2.62758	+	15.3654i	0.168559	+	0.985691i
$244$	−1.74720			−0.111853
$245$	−21.5929	−	11.2369i	−1.37952	−	0.717899i
$246$	−2.24368	+	1.39878i	−0.143052	+	0.0891833i
$247$	0.128929	+	0.731190i	0.00820353	+	0.0465245i
$248$	−1.75285	−	9.94090i	−0.111306	−	0.631248i
$249$	−16.4286	−	2.32620i	−1.04112	−	0.147417i
$250$	−8.72789	−	7.32357i	−0.552000	−	0.463183i
$251$	9.52282	−	16.4940i	0.601075	−	1.04109i	−0.391583	−	0.920143i	$-0.628073\pi$
$251$	9.52282	−	16.4940i	0.601075	−	1.04109i	0.992659	−	0.120950i	$-0.0385942\pi$
$252$	−2.31345	−	2.74386i	−0.145733	−	0.172847i
$253$	8.77631	+	15.2010i	0.551762	+	0.955680i
$254$	−0.981687	+	5.56742i	−0.0615965	+	0.349331i
$255$	5.96072	−	18.2809i	0.373275	−	1.14480i
$256$	−9.71564	−	3.53620i	−0.607227	−	0.221013i
$257$	−13.6046	+	11.4156i	−0.848633	+	0.712088i	−0.959488	−	0.281749i	$-0.909086\pi$
$257$	−13.6046	+	11.4156i	−0.848633	+	0.712088i	0.110855	+	0.993837i	$0.464641\pi$
$258$	6.19305	−	18.9935i	0.385562	−	1.18248i
$259$	7.29315	+	4.87242i	0.453174	+	0.302757i
$260$	−0.0875067	−	0.151566i	−0.00542693	−	0.00939973i
$261$	−3.04816	+	28.4361i	−0.188677	+	1.76015i
$262$	12.1235	+	20.9985i	0.748991	+	1.29729i
$263$	−4.79189	+	27.1762i	−0.295481	+	1.67575i	0.369761	+	0.929127i	$0.379440\pi$
$263$	−4.79189	+	27.1762i	−0.295481	+	1.67575i	−0.665242	+	0.746628i	$0.731672\pi$
$264$	16.9132	+	2.39482i	1.04094	+	0.147391i
$265$	24.5788	−	20.6241i	1.50986	−	1.26693i
$266$	7.73536	+	26.5322i	0.474285	+	1.62679i
$267$	0.0246747	+	0.728155i	0.00151006	+	0.0445623i
$268$	1.19267	−	0.434098i	0.0728542	−	0.0265168i
$269$	8.35177	−	14.4657i	0.509216	−	0.881989i	−0.490727	−	0.871314i	$-0.663269\pi$
$269$	8.35177	−	14.4657i	0.509216	−	0.881989i	0.999943	−	0.0106750i	$-0.00339802\pi$
$270$	2.87043	+	28.1492i	0.174689	+	1.71310i
$271$	−6.25503	−	10.8340i	−0.379966	−	0.658120i	0.611091	−	0.791560i	$-0.290731\pi$
$271$	−6.25503	−	10.8340i	−0.379966	−	0.658120i	−0.991057	+	0.133440i	$0.957398\pi$
$272$	2.60543	−	14.7761i	0.157978	−	0.895935i
$273$	0.0727030	+	0.504857i	0.00440018	+	0.0305553i
$274$	22.4119	+	8.15727i	1.35395	+	0.492798i
$275$	27.1176	+	9.87000i	1.63525	+	0.595183i
$276$	−2.08277	+	2.66016i	−0.125368	+	0.160123i
$277$	1.85461	−	10.5180i	0.111433	−	0.631967i	−0.877022	−	0.480450i	$-0.840473\pi$
$277$	1.85461	−	10.5180i	0.111433	−	0.631967i	0.988455	−	0.151516i	$-0.0484156\pi$
$278$	−2.29123			−0.137419
$279$	−9.00525	+	8.66038i	−0.539130	+	0.518484i
$280$	13.1873	+	17.9827i	0.788094	+	1.07467i
$281$	−8.60406	−	7.21966i	−0.513275	−	0.430689i	0.349005	−	0.937121i	$-0.386520\pi$
$281$	−8.60406	−	7.21966i	−0.513275	−	0.430689i	−0.862280	+	0.506432i	$0.830964\pi$
$282$	4.78883	−	14.6868i	0.285170	−	0.874589i
$283$	8.30507	+	3.02280i	0.493685	+	0.179687i	0.576852	−	0.816849i	$-0.304281\pi$
$283$	8.30507	+	3.02280i	0.493685	+	0.179687i	−0.0831665	+	0.996536i	$0.526503\pi$
$284$	0.272686	+	0.0992497i	0.0161810	+	0.00588939i
$285$	12.4549	−	38.1978i	0.737763	−	2.26264i
$286$	0.543279	+	0.455865i	0.0321248	+	0.0269559i
$287$	2.56378	−	0.280954i	0.151335	−	0.0165842i
$288$	1.80809	+	7.31623i	0.106543	+	0.431113i
$289$	−6.80833			−0.400490
$290$	−9.01425	+	51.1223i	−0.529335	+	3.00201i
$291$	−11.2457	+	14.3632i	−0.659232	+	0.841984i
$292$	0.353939	+	0.128823i	0.0207127	+	0.00753882i
$293$	12.1570	+	4.42479i	0.710220	+	0.258499i	0.671768	−	0.740761i	$-0.265535\pi$
$293$	12.1570	+	4.42479i	0.710220	+	0.258499i	0.0384521	+	0.999260i	$0.487757\pi$
$294$	4.73720	+	18.3855i	0.276279	+	1.07227i
$295$	−3.84153	+	21.7864i	−0.223662	+	1.26845i
$296$	−4.01762	−	6.95872i	−0.233519	−	0.404467i
$297$	−9.20940	−	19.0315i	−0.534384	−	1.10432i
$298$	−9.74706	+	16.8824i	−0.564632	+	0.977972i
$299$	0.451196	−	0.164222i	0.0260934	−	0.00949721i
$300$	0.188117	+	5.55137i	0.0108609	+	0.320508i
$301$	−13.4749	+	14.0780i	−0.776682	+	0.811442i
$302$	−1.80479	+	1.51440i	−0.103854	+	0.0871438i
$303$	14.4645	+	2.04809i	0.830962	+	0.117659i
$304$	5.44403	−	30.8746i	0.312236	−	1.77078i
$305$	−6.71842	−	11.6366i	−0.384695	−	0.666312i
$306$	−13.7135	+	6.07172i	−0.783947	+	0.347097i
$307$	−9.05717	−	15.6875i	−0.516920	−	0.895331i	−0.999807	−	0.0196488i	$-0.993745\pi$
$307$	−9.05717	−	15.6875i	−0.516920	−	0.895331i	0.482887	−	0.875683i	$-0.339588\pi$
$308$	4.04756	+	2.70410i	0.230631	+	0.154081i
$309$	−2.85546	+	8.75742i	−0.162442	+	0.498192i
$310$	−17.3724	+	14.5772i	−0.986685	+	0.827927i
$311$	17.0951	+	6.22212i	0.969375	+	0.352824i	0.777701	−	0.628635i	$-0.216386\pi$
$311$	17.0951	+	6.22212i	0.969375	+	0.352824i	0.191675	+	0.981459i	$0.438608\pi$
$312$	0.144856	−	0.444258i	0.00820084	−	0.0251512i
$313$	−5.75976	+	32.6652i	−0.325561	+	1.84635i	0.180143	+	0.983640i	$0.442344\pi$
$313$	−5.75976	+	32.6652i	−0.325561	+	1.84635i	−0.505704	+	0.862707i	$0.668767\pi$
$314$	−5.49458	−	9.51689i	−0.310077	−	0.537069i
$315$	9.37874	−	25.9587i	0.528432	−	1.46261i
$316$	−0.490524	+	0.849612i	−0.0275941	+	0.0477944i
$317$	−6.90477	−	5.79379i	−0.387810	−	0.325412i	0.427949	−	0.903803i	$-0.359236\pi$
$317$	−6.90477	−	5.79379i	−0.387810	−	0.325412i	−0.815760	+	0.578391i	$0.803681\pi$
$318$	−24.7786	−	3.50851i	−1.38952	−	0.196748i
$319$	−6.73562	−	38.1996i	−0.377122	−	2.13877i
$320$	−3.30058	−	18.7185i	−0.184508	−	1.04640i
$321$	10.4566	−	6.51903i	0.583633	−	0.363857i
$322$	16.0289	−	7.90594i	0.893258	−	0.440581i
$323$	21.2954			1.18491
$324$	2.73551	−	3.01297i	0.151973	−	0.167387i
$325$	0.394706	−	0.683650i	0.0218943	−	0.0379221i
$326$	26.9708	+	22.6312i	1.49378	+	1.25343i
$327$	−20.6247	−	10.9937i	−1.14055	−	0.607951i
$328$	−2.22028	−	0.808118i	−0.122595	−	0.0446208i
$329$	−10.4196	+	10.8859i	−0.574452	+	0.600161i
$330$	−14.3394	−	35.5971i	−0.789359	−	1.95956i
$331$	18.2578	+	15.3201i	1.00354	+	0.842071i	0.987471	−	0.157800i	$-0.0504402\pi$
$331$	18.2578	+	15.3201i	1.00354	+	0.842071i	0.0160695	+	0.999871i	$0.494885\pi$
$332$	2.16582	+	3.75131i	0.118865	+	0.205880i
$333$	−4.37822	+	8.92982i	−0.239925	+	0.489351i
$334$	−0.714384	+	1.23735i	−0.0390894	+	0.0677048i
$335$	7.47728	+	6.27419i	0.408528	+	0.342795i
$336$	4.40631	−	21.0820i	0.240384	−	1.15012i
$337$	2.31533	+	13.1309i	0.126124	+	0.715285i	0.980634	+	0.195850i	$0.0627465\pi$
$337$	2.31533	+	13.1309i	0.126124	+	0.715285i	−0.854510	+	0.519435i	$0.826142\pi$
$338$	−15.5797	+	13.0729i	−0.847423	+	0.711072i
$339$	12.2094	+	13.5881i	0.663122	+	0.738003i
$340$	−4.71698	+	1.71684i	−0.255814	+	0.0931087i
$341$	8.47273	−	14.6752i	0.458824	−	0.794707i
$342$	−28.6542	+	12.6868i	−1.54944	+	0.686024i
$343$	3.60946	−	18.1651i	0.194893	−	0.980825i
$344$	16.7762	−	6.10602i	0.904510	−	0.329215i
$345$	−25.7258	−	3.64263i	−1.38503	−	0.196113i
$346$	0.743423	+	4.21616i	0.0399667	+	0.226662i
$347$	−19.5705	+	16.4216i	−1.05060	+	0.881557i	−0.993156	−	0.116792i	$-0.962739\pi$
$347$	−19.5705	+	16.4216i	−1.05060	+	0.881557i	−0.0574424	+	0.998349i	$0.518295\pi$
$348$	6.33565	−	3.94986i	0.339627	−	0.211735i
$349$	−0.310889	+	1.76314i	−0.0166415	+	0.0943787i	−0.991997	−	0.126259i	$-0.959703\pi$
$349$	−0.310889	+	1.76314i	−0.0166415	+	0.0943787i	0.975356	+	0.220638i	$0.0708140\pi$
$350$	11.8325	−	26.8964i	0.632475	−	1.43767i
$351$	−0.556446	+	0.157694i	−0.0297009	+	0.00841707i
$352$	−5.11078	−	8.85213i	−0.272405	−	0.471820i
$353$	1.38987	+	1.16624i	0.0739751	+	0.0620725i	0.679025	−	0.734115i	$-0.262403\pi$
$353$	1.38987	+	1.16624i	0.0739751	+	0.0620725i	−0.605050	+	0.796187i	$0.706847\pi$
$354$	14.6425	−	9.12863i	0.778240	−	0.485181i
$355$	0.387527	+	2.19777i	0.0205678	+	0.116646i
$356$	0.145703	−	0.122259i	0.00772222	−	0.00647971i
$357$	14.6223	+	0.460888i	0.773896	+	0.0243928i
$358$	−3.63346	+	1.32247i	−0.192034	+	0.0698947i
$359$	−15.5581			−0.821126			−0.410563	−	0.911832i	$-0.634668\pi$
$359$	−15.5581			−0.821126			−0.410563	+	0.911832i	$0.634668\pi$
$360$	−18.2252	+	17.5273i	−0.960555	+	0.923769i
$361$	25.4966			1.34192
$362$	6.33448	−	35.9246i	0.332933	−	1.88816i
$363$	6.43186	+	7.15816i	0.337585	+	0.375706i
$364$	0.0920737	−	0.0961944i	0.00482597	−	0.00504195i
$365$	0.502999	+	2.85265i	0.0263282	+	0.149314i
$366$	−3.24892	+	9.96411i	−0.169824	+	0.520832i
$367$	−22.3160	+	8.12237i	−1.16489	+	0.423984i	−0.850841	−	0.525424i	$-0.823907\pi$
$367$	−22.3160	+	8.12237i	−1.16489	+	0.423984i	−0.314046	+	0.949408i	$0.601685\pi$
$368$	−20.2745			−1.05688
$369$	0.701627	+	2.83904i	0.0365252	+	0.147795i
$370$	−9.02609	+	15.6337i	−0.469244	+	0.812755i
$371$	20.2986	+	13.5611i	1.05385	+	0.704059i
$372$	3.22944	+	0.457270i	0.167438	+	0.0237083i
$373$	−19.0201	−	6.92277i	−0.984826	−	0.358447i	−0.201111	−	0.979568i	$-0.564455\pi$
$373$	−19.0201	−	6.92277i	−0.984826	−	0.358447i	−0.783715	+	0.621121i	$0.786677\pi$
$374$	15.5822	−	13.0750i	0.805738	−	0.676095i
$375$	−10.6940	+	6.66702i	−0.552237	+	0.344283i
$376$	12.9723	−	4.72153i	0.668995	−	0.243494i
$377$	−1.06107			−0.0546480
$378$	−19.9498	+	8.09115i	−1.02611	+	0.416164i
$379$	8.77618			0.450802			0.225401	−	0.974266i	$-0.427631\pi$
$379$	8.77618			0.450802			0.225401	+	0.974266i	$0.427631\pi$
$380$	−9.85609	+	3.58732i	−0.505607	+	0.184026i
$381$	5.51803	+	2.94131i	0.282697	+	0.150688i
$382$	22.6667	−	19.0196i	1.15973	−	0.973130i
$383$	2.21936	+	0.807781i	0.113404	+	0.0412757i	0.398099	−	0.917342i	$-0.369670\pi$
$383$	2.21936	+	0.807781i	0.113404	+	0.0412757i	−0.284695	+	0.958618i	$0.591892\pi$
$384$	−14.5041	+	18.5249i	−0.740158	+	0.945345i
$385$	−2.44588	+	37.3553i	−0.124653	+	1.90380i
$386$	3.06974	−	5.31695i	0.156246	−	0.270626i
$387$	−17.8498	−	13.0251i	−0.907357	−	0.662101i
$388$	4.76222			0.241765
$389$	−14.2059	+	5.17053i	−0.720269	+	0.262156i	−0.676040	−	0.736865i	$-0.736305\pi$
$389$	−14.2059	+	5.17053i	−0.720269	+	0.262156i	−0.0442287	+	0.999021i	$0.514083\pi$
$390$	−1.02708	+	0.217205i	−0.0520084	+	0.0109986i
$391$	−2.39143	−	13.5625i	−0.120940	−	0.685883i
$392$	−10.3268	+	13.4620i	−0.521585	+	0.679931i
$393$	26.2387	−	5.54888i	1.32357	−	0.279904i
$394$	2.85565	−	16.1952i	0.143866	−	0.815903i
$395$	−7.54473			−0.379617
$396$	−2.42984	+	4.95589i	−0.122104	+	0.249043i
$397$	19.6734			0.987379			0.493690	−	0.869638i	$-0.335648\pi$
$397$	19.6734			0.987379			0.493690	+	0.869638i	$0.335648\pi$
$398$	16.1250	−	5.86902i	0.808273	−	0.294187i
$399$	30.5532	+	0.963022i	1.52958	+	0.0482114i
$400$	−25.5346	+	21.4260i	−1.27673	+	1.07130i
$401$	0.783010	+	4.44067i	0.0391017	+	0.221757i	0.998097	−	0.0616658i	$-0.0196413\pi$
$401$	0.783010	+	4.44067i	0.0391017	+	0.221757i	−0.958995	+	0.283422i	$0.908530\pi$
$402$	−0.257840	−	7.60890i	−0.0128599	−	0.379498i
$403$	−0.355096	−	0.297961i	−0.0176886	−	0.0148425i
$404$	−1.90688	−	3.30281i	−0.0948708	−	0.164321i
$405$	30.5855	+	6.63336i	1.51981	+	0.329614i
$406$	−39.2610	+	4.30245i	−1.94849	+	0.213527i
$407$	2.34233	−	13.2840i	0.116105	−	0.658464i
$408$	−11.8271	−	6.30426i	−0.585528	−	0.312107i
$409$	14.6704	−	12.3100i	0.725407	−	0.608688i	−0.203468	−	0.979082i	$-0.565221\pi$
$409$	14.6704	−	12.3100i	0.725407	−	0.608688i	0.928875	+	0.370393i	$0.120777\pi$
$410$	0.921773	+	5.22764i	0.0455231	+	0.258175i
$411$	16.2627	−	20.7711i	0.802182	−	1.02456i
$412$	2.25965	−	0.822446i	0.111325	−	0.0405190i
$413$	−16.7315	+	1.83354i	−0.823305	+	0.0902225i
$414$	11.2977	+	16.8244i	0.555250	+	0.826872i
$415$	−16.6562	+	28.8494i	−0.817620	+	1.41616i
$416$	−0.262749	+	0.0956327i	−0.0128823	+	0.00468878i
$417$	−0.785624	+	2.40943i	−0.0384722	+	0.117990i
$418$	32.5589	−	27.3202i	1.59251	−	1.33627i
$419$	−1.39020	−	7.88419i	−0.0679155	−	0.385168i	−0.999752	−	0.0222884i	$-0.992905\pi$
$419$	−1.39020	−	7.88419i	−0.0679155	−	0.385168i	0.931836	−	0.362879i	$-0.118206\pi$
$420$	−6.84525	+	2.24990i	−0.334014	+	0.109784i
$421$	−5.29363	−	4.44188i	−0.257996	−	0.216484i	0.504611	−	0.863347i	$-0.331636\pi$
$421$	−5.29363	−	4.44188i	−0.257996	−	0.216484i	−0.762606	+	0.646863i	$0.776081\pi$
$422$	−7.58937	+	13.1452i	−0.369445	+	0.639897i
$423$	−13.8025	−	10.0717i	−0.671101	−	0.489705i
$424$	−11.1820	−	19.3678i	−0.543047	−	0.940586i
$425$	−17.3446	−	14.5538i	−0.841337	−	0.705965i
$426$	1.07307	−	1.37055i	0.0519904	−	0.0664032i
$427$	7.06905	−	7.38542i	0.342095	−	0.357406i
$428$	−3.02286	−	1.10023i	−0.146115	−	0.0531817i
$429$	0.665664	−	0.414997i	0.0321385	−	0.0200363i
$430$	−30.7250	−	25.7813i	−1.48169	−	1.24329i
$431$	14.2371	−	24.6593i	0.685775	−	1.18780i	−0.287417	−	0.957805i	$-0.592797\pi$
$431$	14.2371	−	24.6593i	0.685775	−	1.18780i	0.973193	−	0.229992i	$-0.0738700\pi$
$432$	24.3564	+	1.77903i	1.17185	+	0.0855937i
$433$	−24.5920			−1.18182			−0.590909	−	0.806738i	$-0.701231\pi$
$433$	−24.5920			−1.18182			−0.590909	+	0.806738i	$0.701231\pi$
$434$	−14.3472	−	9.58507i	−0.688685	−	0.460098i
$435$	50.6688	+	27.0083i	2.42938	+	1.29495i
$436$	1.05950	+	6.00873i	0.0507409	+	0.287766i
$437$	−4.99686	−	28.3386i	−0.239032	−	1.35562i
$438$	1.39282	−	1.77893i	0.0665513	−	0.0850007i
$439$	−20.2261	−	16.9717i	−0.965340	−	0.810016i	0.0164739	−	0.999864i	$-0.494756\pi$
$439$	−20.2261	−	16.9717i	−0.965340	−	0.810016i	−0.981813	+	0.189848i	$0.939200\pi$
$440$	17.1475	−	29.7004i	0.817476	−	1.41591i
$441$	20.9583	+	1.32250i	0.998015	+	0.0629764i
$442$	−0.278217	−	0.481886i	−0.0132334	−	0.0229210i
$443$	5.56324	−	31.5507i	0.264318	−	1.49902i	−0.506654	−	0.862150i	$-0.669118\pi$
$443$	5.56324	−	31.5507i	0.264318	−	1.49902i	0.770971	−	0.636870i	$-0.219771\pi$
$444$	2.54016	−	0.537186i	0.120551	−	0.0254937i
$445$	1.37452	+	0.500286i	0.0651587	+	0.0237158i
$446$	19.7679	−	16.5873i	0.936039	−	0.785430i
$447$	14.4112	+	16.0386i	0.681628	+	0.758599i
$448$	12.9697	−	6.39704i	0.612762	−	0.302232i
$449$	0.717585	+	1.24289i	0.0338649	+	0.0586558i	0.882461	−	0.470385i	$-0.155885\pi$
$449$	0.717585	+	1.24289i	0.0338649	+	0.0586558i	−0.848596	+	0.529041i	$0.822552\pi$
$450$	32.0087	+	9.24994i	1.50890	+	0.436046i
$451$	−1.98323	−	3.43505i	−0.0933864	−	0.161750i
$452$	0.828116	−	4.69648i	0.0389513	−	0.220904i
$453$	0.973692	+	2.41716i	0.0457480	+	0.113568i
$454$	−3.09365	+	2.59588i	−0.145192	+	0.121831i
$455$	0.994715	+	0.243334i	0.0466330	+	0.0114077i
$456$	−24.7126	−	13.1727i	−1.15727	−	0.616868i
$457$	27.2688	−	9.92502i	1.27558	−	0.464273i	0.386611	−	0.922243i	$-0.373646\pi$
$457$	27.2688	−	9.92502i	1.27558	−	0.464273i	0.888968	+	0.457970i	$0.151423\pi$
$458$	0.924052	−	1.60051i	0.0431781	−	0.0747867i
$459$	1.68283	+	16.5028i	0.0785477	+	0.770286i
$460$	3.39148	+	5.87422i	0.158129	+	0.273887i
$461$	−5.23302	+	29.6779i	−0.243726	+	1.38224i	0.579707	+	0.814825i	$0.303167\pi$
$461$	−5.23302	+	29.6779i	−0.243726	+	1.38224i	−0.823433	+	0.567414i	$0.807944\pi$
$462$	22.9476	−	18.0546i	1.06762	−	0.839974i
$463$	−35.8106	−	13.0340i	−1.66426	−	0.605740i	−0.673235	−	0.739429i	$-0.735096\pi$
$463$	−35.8106	−	13.0340i	−1.66426	−	0.605740i	−0.991023	+	0.133688i	$0.957318\pi$
$464$	42.1019	+	15.3239i	1.95453	+	0.711392i
$465$	9.37247	+	23.2669i	0.434638	+	1.07897i
$466$	−5.55964	+	31.5303i	−0.257546	+	1.46061i
$467$	−15.8593			−0.733883			−0.366941	−	0.930244i	$-0.619595\pi$
$467$	−15.8593			−0.733883			−0.366941	+	0.930244i	$0.619595\pi$
$468$	0.121967	+	0.0889998i	0.00563792	+	0.00411402i
$469$	−2.99054	+	6.79776i	−0.138090	+	0.313892i
$470$	−23.7584	−	19.9356i	−1.09589	−	0.919562i
$471$	−11.8918	+	2.51485i	−0.547947	+	0.115878i
$472$	14.4898	+	5.27387i	0.666949	+	0.242750i
$473$	28.1625	+	10.2503i	1.29491	+	0.471310i
$474$	3.93312	+	4.37726i	0.180654	+	0.201054i
$475$	−36.2414	−	30.4101i	−1.66287	−	1.39531i
$476$	−2.25854	−	3.07982i	−0.103520	−	0.141163i
$477$	−12.1857	+	24.8539i	−0.557944	+	1.13798i
$478$	12.5676			0.574827
$479$	−0.130226	+	0.738549i	−0.00595019	+	0.0337452i	−0.987638	−	0.156750i	$-0.949898\pi$
$479$	−0.130226	+	0.738549i	−0.00595019	+	0.0337452i	0.981688	+	0.190495i	$0.0610094\pi$
$480$	14.9811	+	2.12124i	0.683791	+	0.0968209i
$481$	−0.346738	−	0.126202i	−0.0158099	−	0.00575433i
$482$	27.8726	+	10.1448i	1.26956	+	0.462082i
$483$	−2.81774	−	19.5667i	−0.128212	−	0.890314i
$484$	0.436249	−	2.47409i	0.0198295	−	0.112459i
$485$	18.3119	+	31.7171i	0.831500	+	1.44020i
$486$	−12.0959	−	21.2030i	−0.548683	−	0.961785i
$487$	−6.90405	+	11.9582i	−0.312852	+	0.541876i	−0.978979	−	0.203963i	$-0.934618\pi$
$487$	−6.90405	+	11.9582i	−0.312852	+	0.541876i	0.666126	+	0.745839i	$0.267951\pi$
$488$	−8.80090	+	3.20326i	−0.398398	+	0.145005i
$489$	33.0465	−	20.6023i	1.49442	−	0.931670i
$490$	37.7924	+	4.97029i	1.70729	+	0.224535i
$491$	−18.7898	+	15.7665i	−0.847974	+	0.711534i	−0.959342	−	0.282245i	$-0.908921\pi$
$491$	−18.7898	+	15.7665i	−0.847974	+	0.711534i	0.111369	+	0.993779i	$0.464477\pi$
$492$	0.470653	−	0.601128i	0.0212187	−	0.0271009i
$493$	−5.28472	+	29.9712i	−0.238012	+	1.34983i
$494$	−0.581332	−	1.00690i	−0.0261554	−	0.0453024i
$495$	−42.3503	+	2.87351i	−1.90350	+	0.129155i
$496$	9.78662	+	16.9509i	0.439432	+	0.761119i
$497$	−1.52280	+	0.751088i	−0.0683068	+	0.0336909i
$498$	25.4206	−	5.37588i	1.13913	−	0.240899i
$499$	25.2424	−	21.1809i	1.13001	−	0.948188i	0.130940	−	0.991390i	$-0.458201\pi$
$499$	25.2424	−	21.1809i	1.13001	−	0.948188i	0.999066	+	0.0432027i	$0.0137561\pi$
$500$	3.09148	+	1.12521i	0.138255	+	0.0503208i
$501$	1.05623	+	1.17550i	0.0471890	+	0.0525177i
$502$	−5.17894	+	29.3712i	−0.231148	+	1.31090i
$503$	−6.42750	−	11.1328i	−0.286588	−	0.496385i	0.686405	−	0.727219i	$-0.259188\pi$
$503$	−6.42750	−	11.1328i	−0.286588	−	0.496385i	−0.972993	+	0.230834i	$0.925854\pi$
$504$	−16.6836	−	9.57978i	−0.743149	−	0.426717i
$505$	14.6648	−	25.4002i	0.652576	−	1.13029i
$506$	−21.0558	−	17.6679i	−0.936043	−	0.785434i
$507$	8.40530	+	20.8659i	0.373293	+	0.926686i
$508$	−0.283465	−	1.60761i	−0.0125767	−	0.0713260i
$509$	3.01173	+	17.0804i	0.133493	+	0.757074i	0.975898	+	0.218229i	$0.0700280\pi$
$509$	3.01173	+	17.0804i	0.133493	+	0.757074i	−0.842405	+	0.538845i	$0.818861\pi$
$510$	1.01974	+	30.0929i	0.0451551	+	1.33254i
$511$	−1.97655	+	0.974891i	−0.0874374	+	0.0431267i
$512$	−10.9766			−0.485103
$513$	3.51625	+	34.4825i	0.155246	+	1.52244i
$514$	13.9052	−	24.0846i	0.613333	−	1.06232i
$515$	14.1665	+	11.8871i	0.624252	+	0.523810i
$516$	0.195365	+	5.76528i	0.00860048	+	0.253802i
$517$	21.7769	+	7.92615i	0.957747	+	0.348592i
$518$	−13.3415	−	3.26369i	−0.586190	−	0.143398i
$519$	4.68857	+	0.663876i	0.205806	+	0.0291409i
$520$	−0.718659	−	0.603027i	−0.0315153	−	0.0264445i
$521$	3.73429	+	6.46798i	0.163602	+	0.283367i	0.936158	−	0.351580i	$-0.114355\pi$
$521$	3.73429	+	6.46798i	0.163602	+	0.283367i	−0.772556	+	0.634947i	$0.781022\pi$
$522$	−10.7445	−	43.4763i	−0.470274	−	1.90291i
$523$	−21.2770	+	36.8528i	−0.930378	+	1.61146i	−0.147702	+	0.989032i	$0.547188\pi$
$523$	−21.2770	+	36.8528i	−0.930378	+	1.61146i	−0.782676	+	0.622430i	$0.786146\pi$
$524$	−5.36336	−	4.50039i	−0.234299	−	0.196601i
$525$	−24.2267	−	21.6653i	−1.05734	−	0.945549i
$526$	−7.50382	−	42.5563i	−0.327182	−	1.85554i
$527$	−10.1848	+	8.54606i	−0.443657	+	0.372272i
$528$	−32.4060	+	6.85312i	−1.41029	+	0.298244i
$529$	4.12598	−	1.50173i	0.179390	−	0.0652928i
$530$	−25.1219	+	43.5123i	−1.09122	+	1.89005i
$531$	−4.57890	−	18.5279i	−0.198707	−	0.804044i
$532$	−4.71920	−	6.43526i	−0.204603	−	0.279004i
$533$	−0.101959	+	0.0371101i	−0.00441634	+	0.00160741i
$534$	−0.426296	−	1.05827i	−0.0184476	−	0.0457957i
$535$	−4.29592	−	24.3634i	−0.185729	−	1.05332i
$536$	5.21180	−	4.37322i	0.225116	−	0.188894i
$537$	0.144843	+	4.27435i	0.00625044	+	0.184452i
$538$	−4.54207	+	25.7594i	−0.195823	+	1.11056i
$539$	−27.8064	+	6.16845i	−1.19771	+	0.265694i
$540$	−3.55884	−	7.35447i	−0.153148	−	0.316486i
$541$	−17.6681	−	30.6020i	−0.759611	−	1.31568i	−0.943049	−	0.332653i	$-0.892056\pi$
$541$	−17.6681	−	30.6020i	−0.759611	−	1.31568i	0.183438	−	0.983031i	$-0.441277\pi$
$542$	15.0068	+	12.5922i	0.644598	+	0.540882i
$543$	−35.6059	−	18.9792i	−1.52800	−	0.814475i
$544$	1.39262	+	7.89793i	0.0597080	+	0.338621i
$545$	−35.9450	+	30.1614i	−1.53972	+	1.29197i
$546$	−0.377375	−	0.703960i	−0.0161502	−	0.0301267i
$547$	6.10255	−	2.22115i	0.260926	−	0.0949694i	−0.208245	−	0.978077i	$-0.566775\pi$
$547$	6.10255	−	2.22115i	0.260926	−	0.0949694i	0.469171	+	0.883107i	$0.344553\pi$
$548$	−6.88682			−0.294190
$549$	9.36414	+	6.83305i	0.399652	+	0.291627i
$550$	−45.1898			−1.92690
$551$	−11.0424	+	62.6245i	−0.470421	+	2.66789i
$552$	−5.61415	+	17.2180i	−0.238954	+	0.732849i
$553$	−1.60669	−	5.51091i	−0.0683232	−	0.234348i
$554$	2.90421	+	16.4706i	0.123388	+	0.699768i
$555$	13.3453	+	14.8522i	0.566475	+	0.630443i
$556$	0.621699	−	0.226280i	0.0263659	−	0.00959641i
$557$	7.80661			0.330777			0.165388	−	0.986229i	$-0.447112\pi$
$557$	7.80661			0.330777			0.165388	+	0.986229i	$0.447112\pi$
$558$	8.61289	−	17.5668i	0.364613	−	0.743663i
$559$	0.409915	−	0.709993i	0.0173375	−	0.0300295i
$560$	−35.9548	−	24.0207i	−1.51937	−	1.01506i
$561$	−8.40668	−	20.8693i	−0.354930	−	0.881103i
$562$	16.5276	+	6.01556i	0.697176	+	0.253751i
$563$	−29.0794	+	24.4005i	−1.22555	+	1.02836i	−0.227034	+	0.973887i	$0.572903\pi$
$563$	−29.0794	+	24.4005i	−1.22555	+	1.02836i	−0.998515	+	0.0544708i	$0.982653\pi$
$564$	0.151068	+	4.45805i	0.00636111	+	0.187718i
$565$	34.4636	−	12.5437i	1.44989	−	0.527718i
$566$	−13.8399			−0.581734
$567$	1.66812	+	23.7533i	0.0700543	+	0.997543i
$568$	1.55552			0.0652682
$569$	−1.14497	+	0.416735i	−0.0479996	+	0.0174704i	−0.365908	−	0.930651i	$-0.619242\pi$
$569$	−1.14497	+	0.416735i	−0.0479996	+	0.0174704i	0.317909	+	0.948121i	$0.397019\pi$
$570$	2.13075	+	62.8788i	0.0892472	+	2.63370i
$571$	14.5897	−	12.2422i	0.610558	−	0.512319i	−0.284261	−	0.958747i	$-0.591748\pi$
$571$	14.5897	−	12.2422i	0.610558	−	0.512319i	0.894820	+	0.446427i	$0.147304\pi$
$572$	−0.192433	−	0.0700400i	−0.00804604	−	0.00292852i
$573$	−12.2288	−	30.3576i	−0.510865	−	1.26821i
$574$	−3.62214	+	1.78654i	−0.151185	+	0.0745688i
$575$	−15.2975	+	26.4961i	−0.637952	+	1.10496i
$576$	9.14145	+	13.6133i	0.380894	+	0.567222i
$577$	40.9761			1.70586			0.852928	−	0.522029i	$-0.174825\pi$
$577$	40.9761			1.70586			0.852928	+	0.522029i	$0.174825\pi$
$578$	10.0185	−	3.64643i	0.416714	−	0.151671i
$579$	−4.53868	−	5.05120i	−0.188621	−	0.209921i
$580$	−2.60289	−	14.7617i	−0.108079	−	0.612946i
$581$	−24.6195	−	6.02260i	−1.02139	−	0.249860i
$582$	8.85534	−	27.1584i	0.367066	−	1.12575i
$583$	6.51929	−	36.9727i	0.270001	−	1.53125i
$584$	2.01902			0.0835477
$585$	−0.123760	+	1.15454i	−0.00511683	+	0.0477345i
$586$	−20.2589			−0.836888
$587$	9.19965	−	3.34840i	0.379710	−	0.138203i	−0.145112	−	0.989415i	$-0.546354\pi$
$587$	9.19965	−	3.34840i	0.379710	−	0.138203i	0.524822	+	0.851212i	$0.324132\pi$
$588$	−3.10112	−	4.52086i	−0.127888	−	0.186437i
$589$	−21.2810	+	17.8569i	−0.876870	+	0.735781i
$590$	−6.01560	−	34.1162i	−0.247658	−	1.40454i
$591$	−16.0515	−	8.55603i	−0.660272	−	0.351948i
$592$	11.9355	+	10.0151i	0.490546	+	0.411617i
$593$	−7.91173	−	13.7035i	−0.324896	−	0.562736i	0.656595	−	0.754243i	$-0.271996\pi$
$593$	−7.91173	−	13.7035i	−0.324896	−	0.562736i	−0.981491	+	0.191507i	$0.938663\pi$
$594$	23.7446	+	23.0726i	0.974254	+	0.946678i
$595$	11.8275	−	26.8849i	0.484879	−	1.10217i
$596$	0.977462	−	5.54346i	0.0400384	−	0.227069i
$597$	−0.642802	−	18.9692i	−0.0263081	−	0.776359i
$598$	−0.575982	+	0.483306i	−0.0235537	+	0.0197639i
$599$	2.97735	+	16.8854i	0.121651	+	0.689918i	0.983241	+	0.182312i	$0.0583582\pi$
$599$	2.97735	+	16.8854i	0.121651	+	0.689918i	−0.861589	+	0.507606i	$0.830531\pi$
$600$	11.1253	+	27.6181i	0.454187	+	1.12750i
$601$	37.5176	−	13.6553i	1.53037	−	0.557010i	0.566660	−	0.823952i	$-0.308235\pi$
$601$	37.5176	−	13.6553i	1.53037	−	0.557010i	0.963713	+	0.266941i	$0.0860130\pi$
$602$	12.2885	−	27.9328i	0.500841	−	1.13845i
$603$	−8.08984	−	2.33782i	−0.329444	−	0.0952035i
$604$	0.340148	−	0.589154i	0.0138404	−	0.0239723i
$605$	18.1553	−	6.60800i	0.738119	−	0.268653i
$606$	−22.3814	+	4.73316i	−0.909183	+	0.192271i
$607$	−27.7291	+	23.2675i	−1.12549	+	0.944398i	−0.998869	−	0.0475534i	$-0.984858\pi$
$607$	−27.7291	+	23.2675i	−1.12549	+	0.944398i	−0.126621	+	0.991951i	$0.540413\pi$
$608$	2.90986	+	16.5027i	0.118011	+	0.669271i
$609$	−8.93753	+	42.7617i	−0.362167	+	1.73279i
$610$	16.1186	+	13.5251i	0.652621	+	0.547614i
$611$	0.316970	−	0.549008i	0.0128232	−	0.0222105i
$612$	3.12136	−	3.00182i	0.126173	−	0.121342i
$613$	−2.84968	−	4.93580i	−0.115098	−	0.199355i	0.802721	−	0.596355i	$-0.203385\pi$
$613$	−2.84968	−	4.93580i	−0.115098	−	0.199355i	−0.917819	+	0.397000i	$0.870051\pi$
$614$	21.7296	+	18.2333i	0.876935	+	0.735836i
$615$	5.81338	+	0.823142i	0.234418	+	0.0331923i
$616$	25.3457	+	6.20026i	1.02121	+	0.249816i
$617$	−9.77727	−	3.55864i	−0.393618	−	0.143265i	0.137626	−	0.990484i	$-0.456053\pi$
$617$	−9.77727	−	3.55864i	−0.393618	−	0.143265i	−0.531244	+	0.847219i	$0.678275\pi$
$618$	−0.488505	−	14.4159i	−0.0196506	−	0.579892i
$619$	−28.4956	−	23.9107i	−1.14534	−	0.961051i	−0.145735	−	0.989324i	$-0.546555\pi$
$619$	−28.4956	−	23.9107i	−1.14534	−	0.961051i	−0.999600	+	0.0282731i	$0.990999\pi$
$620$	3.27417	−	5.67103i	0.131494	−	0.227754i
$621$	21.5661	−	6.11171i	0.865417	−	0.245255i
$622$	−28.4880			−1.14226
$623$	−0.0727134	+	1.11054i	−0.00291320	+	0.0444926i
$624$	0.0306861	+	0.905553i	0.00122843	+	0.0362511i
$625$	−1.76439	−	10.0063i	−0.0705755	−	0.400254i
$626$	−9.01944	−	51.1518i	−0.360489	−	2.04444i
$627$	−17.5657	−	43.6062i	−0.701506	−	1.74147i
$628$	2.43077	+	2.03966i	0.0969983	+	0.0813912i
$629$	−5.29167	+	9.16544i	−0.210993	+	0.365450i
$630$	0.102200	+	43.2214i	0.00407173	+	1.72198i
$631$	2.45359	+	4.24974i	0.0976759	+	0.169180i	0.910722	−	0.413019i	$-0.135526\pi$
$631$	2.45359	+	4.24974i	0.0976759	+	0.169180i	−0.813046	+	0.582199i	$0.802192\pi$
$632$	−0.913183	+	5.17892i	−0.0363245	+	0.206006i
$633$	11.2210	+	12.4881i	0.445996	+	0.496359i
$634$	13.2634	+	4.82750i	0.526759	+	0.191724i
$635$	9.61692	−	8.06956i	0.381636	−	0.320231i
$636$	7.06989	−	1.49512i	0.280340	−	0.0592854i
$637$	0.0340901	+	0.778391i	0.00135070	+	0.0308410i
$638$	30.3705	+	52.6033i	1.20238	+	2.08259i
$639$	−1.07331	−	1.59837i	−0.0424596	−	0.0632304i
$640$	23.6177	+	40.9071i	0.933573	+	1.61700i
$641$	−1.54675	+	8.77204i	−0.0610929	+	0.346475i	0.938905	+	0.344178i	$0.111842\pi$
$641$	−1.54675	+	8.77204i	−0.0610929	+	0.346475i	−0.999997	+	0.00229706i	$0.999269\pi$
$642$	−11.8955	+	15.1932i	−0.469478	+	0.599627i
$643$	−20.7057	+	17.3741i	−0.816553	+	0.685169i	−0.952162	−	0.305593i	$-0.901145\pi$
$643$	−20.7057	+	17.3741i	−0.816553	+	0.685169i	0.135609	+	0.990762i	$0.456701\pi$
$644$	−3.56849	+	3.72819i	−0.140618	+	0.146911i
$645$	−37.6464	+	23.4701i	−1.48233	+	0.924132i
$646$	−31.3362	+	11.4055i	−1.23291	+	0.448742i
$647$	−22.8442	+	39.5674i	−0.898100	+	1.55555i	−0.0681793	+	0.997673i	$0.521719\pi$
$647$	−22.8442	+	39.5674i	−0.898100	+	1.55555i	−0.829921	+	0.557882i	$0.811614\pi$
$648$	8.25528	−	20.1919i	0.324298	−	0.793214i
$649$	12.9428	+	22.4175i	0.508048	+	0.879965i
$650$	−0.214659	+	1.21739i	−0.00841961	+	0.0477500i
$651$	−14.9989	+	11.8007i	−0.587855	+	0.462508i
$652$	−9.55326	−	3.47710i	−0.374135	−	0.136174i
$653$	28.1735	+	10.2543i	1.10251	+	0.401282i	0.828242	−	0.560371i	$-0.189341\pi$
$653$	28.1735	+	10.2543i	1.10251	+	0.401282i	0.274271	+	0.961653i	$0.411564\pi$
$654$	36.2373	+	5.13099i	1.41699	+	0.200638i
$655$	9.34990	−	53.0259i	0.365331	−	2.07189i
$656$	4.58154			0.178879
$657$	−1.39313	−	2.07463i	−0.0543512	−	0.0809392i
$658$	9.50216	−	21.5992i	0.370433	−	0.842026i
$659$	−4.49499	−	3.77174i	−0.175100	−	0.146926i	0.551026	−	0.834488i	$-0.314237\pi$
$659$	−4.49499	−	3.77174i	−0.175100	−	0.146926i	−0.726126	+	0.687562i	$0.758681\pi$
$660$	7.40638	+	8.24273i	0.288293	+	0.320848i
$661$	21.4794	+	7.81787i	0.835453	+	0.304080i	0.724095	−	0.689700i	$-0.242258\pi$
$661$	21.4794	+	7.81787i	0.835453	+	0.304080i	0.111358	+	0.993780i	$0.464480\pi$
$662$	−35.0716	−	12.7650i	−1.36310	−	0.496127i
$663$	−0.602141	+	0.127339i	−0.0233852	+	0.00494544i
$664$	17.7870	+	14.9251i	0.690271	+	0.579206i
$665$	24.7134	−	56.1757i	0.958345	−	2.17840i
$666$	1.65991	−	15.4852i	0.0643201	−	0.600038i
$667$	41.1238			1.59232
$668$	0.0716404	−	0.406293i	0.00277185	−	0.0157199i
$669$	−10.6649	−	26.4752i	−0.412328	−	1.02359i
$670$	−14.3632	−	5.22777i	−0.554899	−	0.201967i
$671$	−14.7743	−	5.37740i	−0.570354	−	0.207592i
$672$	1.64088	+	11.3944i	0.0632981	+	0.439549i
$673$	−1.92608	+	10.9233i	−0.0742449	+	0.421064i	0.924918	+	0.380166i	$0.124133\pi$
$673$	−1.92608	+	10.9233i	−0.0742449	+	0.421064i	−0.999163	+	0.0408981i	$0.986978\pi$
$674$	−10.4397	−	18.0821i	−0.402122	−	0.696496i
$675$	20.7024	−	30.4883i	0.796834	−	1.17349i
$676$	2.93630	−	5.08582i	0.112935	−	0.195608i
$677$	42.8729	−	15.6045i	1.64774	−	0.599728i	0.659372	−	0.751816i	$-0.270822\pi$
$677$	42.8729	−	15.6045i	1.64774	−	0.599728i	0.988367	+	0.152088i	$0.0485998\pi$
$678$	−25.2437	−	13.4558i	−0.969477	−	0.516765i
$679$	−19.2676	+	20.1299i	−0.739423	+	0.772515i
$680$	−20.6125	+	17.2959i	−0.790452	+	0.663268i
$681$	1.66904	+	4.14332i	0.0639576	+	0.158773i
$682$	−4.60786	+	26.1325i	−0.176444	+	1.00066i
$683$	4.41005	+	7.63842i	0.168746	+	0.292276i	0.937979	−	0.346692i	$-0.112695\pi$
$683$	4.41005	+	7.63842i	0.168746	+	0.292276i	−0.769233	+	0.638968i	$0.779362\pi$
$684$	6.52205	−	6.27228i	0.249377	−	0.239827i
$685$	−26.4815	−	45.8673i	−1.01181	−	1.75250i
$686$	4.41760	+	28.6632i	0.168665	+	1.09437i
$687$	−1.36623	−	1.52051i	−0.0521249	−	0.0580110i
$688$	−26.5185	+	22.2517i	−1.01101	+	0.848336i
$689$	−0.965058	−	0.351252i	−0.0367658	−	0.0133816i
$690$	39.8065	−	8.41817i	1.51541	−	0.320474i
$691$	−2.04360	+	11.5898i	−0.0777423	+	0.440898i	0.920946	+	0.389691i	$0.127418\pi$
$691$	−2.04360	+	11.5898i	−0.0777423	+	0.440898i	−0.998688	+	0.0512076i	$0.983693\pi$
$692$	−0.618104	−	1.07059i	−0.0234968	−	0.0406976i
$693$	−11.1176	−	30.3221i	−0.422323	−	1.15184i
$694$	20.0029	−	34.6460i	0.759300	−	1.31515i
$695$	3.89764	+	3.27051i	0.147846	+	0.124058i
$696$	24.6720	−	31.5116i	0.935190	−	1.19444i
$697$	0.540402	+	3.06477i	0.0204692	+	0.116087i
$698$	−0.486834	−	2.76097i	−0.0184269	−	0.104504i
$699$	31.2506	+	16.6577i	1.18201	+	0.630051i
$700$	−0.554358	+	8.46659i	−0.0209528	+	0.320007i
$701$	26.9258			1.01698			0.508488	−	0.861069i	$-0.330205\pi$
$701$	26.9258			1.01698			0.508488	+	0.861069i	$0.330205\pi$
$702$	0.734353	−	0.530070i	0.0277164	−	0.0200062i
$703$	−11.0569	+	19.1511i	−0.417019	+	0.722298i
$704$	−17.0372	−	14.2959i	−0.642112	−	0.538796i
$705$	−29.1104	+	18.1484i	−1.09636	+	0.683509i
$706$	−2.66981	−	0.971731i	−0.100480	−	0.0365716i
$707$	21.6761	+	5.30256i	0.815212	+	0.199423i
$708$	−3.07154	+	3.92303i	−0.115436	+	0.147437i
$709$	−0.959978	−	0.805517i	−0.0360527	−	0.0302518i	0.624583	−	0.780958i	$-0.285269\pi$
$709$	−0.959978	−	0.805517i	−0.0360527	−	0.0302518i	−0.660636	+	0.750706i	$0.729713\pi$
$710$	−1.74734	−	3.02648i	−0.0655764	−	0.113582i
$711$	5.95167	−	2.63513i	0.223205	−	0.0988253i
$712$	0.509778	−	0.882961i	0.0191047	−	0.0330904i
$713$	13.7624	+	11.5480i	0.515405	+	0.432477i
$714$	−21.7636	+	7.15328i	−0.814484	+	0.267705i
$715$	−0.273476	−	1.55096i	−0.0102274	−	0.0580025i
$716$	0.855291	−	0.717674i	0.0319637	−	0.0268207i
$717$	4.30921	−	13.2159i	0.160930	−	0.493557i
$718$	22.8938	−	8.33266i	0.854389	−	0.310972i
$719$	21.1406	−	36.6166i	0.788411	−	1.36557i	−0.138528	−	0.990358i	$-0.544237\pi$
$719$	21.1406	−	36.6166i	0.788411	−	1.36557i	0.926940	−	0.375210i	$-0.122429\pi$
$720$	21.5844	−	44.0235i	0.804402	−	1.64066i
$721$	−5.66591	+	12.8791i	−0.211010	+	0.479643i
$722$	−37.5183	+	13.6555i	−1.39629	+	0.508206i
$723$	20.2252	−	25.8320i	0.752182	−	0.960702i
$724$	1.82910	+	10.3733i	0.0679778	+	0.385521i
$725$	51.7930	−	43.4595i	1.92354	−	1.61404i
$726$	−13.2983	−	7.08845i	−0.493546	−	0.263077i
$727$	−0.858198	+	4.86709i	−0.0318288	+	0.180510i	−0.996578	−	0.0826623i	$-0.973658\pi$
$727$	−0.858198	+	4.86709i	−0.0318288	+	0.180510i	0.964749	+	0.263172i	$0.0847688\pi$
$728$	0.287428	−	0.653349i	0.0106528	−	0.0242147i
$729$	−26.4443	+	5.44982i	−0.979417	+	0.201845i
$730$	−2.26799	−	3.92828i	−0.0839422	−	0.145392i
$731$	−18.0129	−	15.1146i	−0.666232	−	0.559035i
$732$	−0.102490	−	3.02451i	−0.00378815	−	0.111789i
$733$	5.75297	+	32.6267i	0.212491	+	1.20510i	0.885208	+	0.465196i	$0.154016\pi$
$733$	5.75297	+	32.6267i	0.212491	+	1.20510i	−0.672717	+	0.739900i	$0.734873\pi$
$734$	28.4879	−	23.9042i	1.05151	−	0.882319i
$735$	18.1851	−	38.0378i	0.670766	−	1.40304i
$736$	10.1833	−	3.70642i	0.375362	−	0.136621i
$737$	11.4212			0.420707
$738$	−2.55299	−	3.80188i	−0.0939769	−	0.139949i
$739$	32.2809			1.18747			0.593736	−	0.804660i	$-0.297652\pi$
$739$	32.2809			1.18747			0.593736	+	0.804660i	$0.297652\pi$
$740$	0.905161	−	5.13342i	0.0332744	−	0.188708i
$741$	−1.25817	+	0.266074i	−0.0462200	+	0.00977447i
$742$	−37.1326	−	9.08365i	−1.36318	−	0.333471i
$743$	−5.25887	−	29.8245i	−0.192929	−	1.09416i	−0.915337	−	0.402689i	$-0.868076\pi$
$743$	−5.25887	−	29.8245i	−0.192929	−	1.09416i	0.722408	−	0.691467i	$-0.243035\pi$
$744$	17.1055	−	3.61741i	0.627116	−	0.132621i
$745$	40.6789	−	14.8059i	1.49036	−	0.542446i
$746$	31.6959			1.16047
$747$	3.06309	−	28.5753i	0.112073	−	1.04552i
$748$	−2.93678	+	5.08665i	−0.107379	+	0.185986i
$749$	16.8809	−	8.32617i	0.616816	−	0.304232i
$750$	12.1655	−	15.5381i	0.444223	−	0.567370i
$751$	−11.5075	−	4.18837i	−0.419913	−	0.152836i	0.123417	−	0.992355i	$-0.460615\pi$
$751$	−11.5075	−	4.18837i	−0.419913	−	0.152836i	−0.543330	+	0.839519i	$0.682837\pi$
$752$	−20.5056	+	17.2063i	−0.747764	+	0.627448i
$753$	29.1107	+	15.5170i	1.06085	+	0.565472i
$754$	1.56137	−	0.568293i	0.0568618	−	0.0206960i
$755$	5.23181			0.190405
$756$	4.61407	−	4.16566i	0.167812	−	0.151504i
$757$	−1.90478			−0.0692306			−0.0346153	−	0.999401i	$-0.511021\pi$
$757$	−1.90478			−0.0692306			−0.0346153	+	0.999401i	$0.511021\pi$
$758$	−12.9142	+	4.70038i	−0.469064	+	0.170725i
$759$	−25.7990	+	16.0840i	−0.936445	+	0.583812i
$760$	−43.0696	+	36.1397i	−1.56230	+	1.31092i
$761$	−18.4040	−	6.69851i	−0.667145	−	0.242821i	−0.0138268	−	0.999904i	$-0.504401\pi$
$761$	−18.4040	−	6.69851i	−0.667145	−	0.242821i	−0.653318	+	0.757084i	$0.726624\pi$
$762$	−9.69511	−	1.37277i	−0.351217	−	0.0497303i
$763$	−29.6855	−	19.8324i	−1.07469	−	0.717980i
$764$	−4.27199	+	7.39931i	−0.154555	+	0.267698i
$765$	31.9950	+	9.24599i	1.15678	+	0.334290i
$766$	−3.69843			−0.133630
$767$	0.665396	−	0.242185i	0.0240261	−	0.00874478i
$768$	5.55145	−	17.0258i	0.200321	−	0.614364i
$769$	6.33650	+	35.9361i	0.228500	+	1.29589i	0.855880	+	0.517175i	$0.173016\pi$
$769$	6.33650	+	35.9361i	0.228500	+	1.29589i	−0.627380	+	0.778713i	$0.715873\pi$
$770$	−16.4078	−	56.2784i	−0.591295	−	2.02813i
$771$	−20.5592	−	22.8808i	−0.740420	−	0.824030i
$772$	−0.307842	+	1.74586i	−0.0110795	+	0.0628349i
$773$	−29.6405			−1.06610			−0.533048	−	0.846085i	$-0.678954\pi$
$773$	−29.6405			−1.06610			−0.533048	+	0.846085i	$0.678954\pi$
$774$	33.2420	+	9.60637i	1.19486	+	0.345294i
$775$	29.5368			1.06099
$776$	23.9880	−	8.73090i	0.861117	−	0.313421i
$777$	−8.00662	+	12.9107i	−0.287236	+	0.463168i
$778$	18.1348	−	15.2169i	0.650164	−	0.545552i
$779$	1.12917	+	6.40382i	0.0404566	+	0.229441i
$780$	0.257236	−	0.160370i	0.00921054	−	0.00574216i
$781$	2.00036	+	1.67850i	0.0715786	+	0.0600616i
$782$	10.7828	+	18.6764i	0.385593	+	0.667866i
$783$	−49.4033	−	3.60849i	−1.76553	−	0.128957i
$784$	9.88875	−	31.3778i	0.353170	−	1.12064i
$785$	−4.23754	+	24.0323i	−0.151244	+	0.857749i
$786$	−35.6384	+	22.2182i	−1.27118	+	0.792497i
$787$	−17.2312	+	14.4587i	−0.614224	+	0.515395i	−0.895982	−	0.444090i	$-0.853527\pi$
$787$	−17.2312	+	14.4587i	−0.614224	+	0.515395i	0.281758	+	0.959486i	$0.409083\pi$
$788$	0.824577	+	4.67641i	0.0293743	+	0.166590i
$789$	−47.3246	−	6.70090i	−1.68480	−	0.238558i
$790$	11.1021	−	4.04083i	0.394995	−	0.143766i
$791$	16.5015	+	22.5021i	0.586727	+	0.800081i
$792$	−3.15345	+	29.4183i	−0.112053	+	1.04533i
$793$	−0.215044	+	0.372468i	−0.00763645	+	0.0132267i
$794$	−28.9494	+	10.5367i	−1.02738	+	0.373935i
$795$	37.1432	+	41.3375i	1.31733	+	1.46609i
$796$	−3.79571	+	3.18498i	−0.134535	+	0.112889i
$797$	−0.242917	−	1.37765i	−0.00860457	−	0.0487989i	0.980203	−	0.197994i	$-0.0634428\pi$
$797$	−0.242917	−	1.37765i	−0.00860457	−	0.0487989i	−0.988808	+	0.149195i	$0.952332\pi$
$798$	−45.4749	+	14.9467i	−1.60980	+	0.529108i
$799$	−13.9287	−	11.6875i	−0.492760	−	0.413475i
$800$	8.90834	−	15.4297i	0.314957	−	0.545522i
$801$	−1.25903	+	0.0854265i	−0.0444856	+	0.00301840i
$802$	−3.53055	−	6.11509i	−0.124668	−	0.215931i
$803$	2.59642	+	2.17865i	0.0916255	+	0.0768829i
$804$	0.821411	+	2.03912i	0.0289689	+	0.0719144i
$805$	−38.5520	−	9.43087i	−1.35878	−	0.332395i
$806$	0.682107	+	0.248267i	0.0240262	+	0.00874482i
$807$	25.5308	+	13.6088i	0.898728	+	0.479054i
$808$	−15.6605	−	13.1407i	−0.550933	−	0.462288i
$809$	−16.1359	+	27.9481i	−0.567306	+	0.982604i	0.429525	+	0.903055i	$0.358681\pi$
$809$	−16.1359	+	27.9481i	−0.567306	+	0.982604i	−0.996831	+	0.0795484i	$0.974652\pi$
$810$	−48.5594	+	6.62009i	−1.70620	+	0.232606i
$811$	36.0094			1.26446			0.632230	−	0.774781i	$-0.282140\pi$
$811$	36.0094			1.26446			0.632230	+	0.774781i	$0.282140\pi$
$812$	10.2281	−	5.04480i	0.358937	−	0.177038i
$813$	18.3874	−	11.4633i	0.644875	−	0.402037i
$814$	3.66795	+	20.8020i	0.128562	+	0.729109i
$815$	−13.5766	−	76.9965i	−0.475566	−	2.69707i
$816$	25.7312	+	3.64339i	0.900771	+	0.127544i
$817$	−37.6379	−	31.5819i	−1.31678	−	1.10491i
$818$	−14.9946	+	25.9714i	−0.524273	+	0.908068i
$819$	−0.869671	+	0.155468i	−0.0303888	+	0.00543248i
$820$	−0.766390	−	1.32743i	−0.0267635	−	0.0463557i
$821$	−2.75247	+	15.6100i	−0.0960619	+	0.544794i	0.898355	+	0.439270i	$0.144763\pi$
$821$	−2.75247	+	15.6100i	−0.0960619	+	0.544794i	−0.994417	+	0.105524i	$0.966348\pi$
$822$	−12.8060	+	39.2748i	−0.446661	+	1.36987i
$823$	−23.2857	−	8.47532i	−0.811690	−	0.295431i	−0.0973682	−	0.995248i	$-0.531042\pi$
$823$	−23.2857	−	8.47532i	−0.811690	−	0.295431i	−0.714322	+	0.699817i	$0.753265\pi$
$824$	9.87433	−	8.28555i	0.343989	−	0.288641i
$825$	−15.4948	+	47.5211i	−0.539461	+	1.65447i
$826$	23.6385	−	11.6592i	0.822488	−	0.405675i
$827$	15.1716	+	26.2780i	0.527568	+	0.913774i	0.999484	+	0.0321307i	$0.0102293\pi$
$827$	15.1716	+	26.2780i	0.527568	+	0.913774i	−0.471916	+	0.881644i	$0.656437\pi$
$828$	−4.72705	−	3.44935i	−0.164277	−	0.119873i
$829$	−9.83979	−	17.0430i	−0.341750	−	0.591928i	0.643008	−	0.765860i	$-0.277686\pi$
$829$	−9.83979	−	17.0430i	−0.341750	−	0.591928i	−0.984758	+	0.173931i	$0.944353\pi$
$830$	9.05839	−	51.3727i	0.314421	−	1.78317i
$831$	18.3161	+	2.59345i	0.635378	+	0.0899660i
$832$	−0.466053	+	0.391065i	−0.0161575	+	0.0135577i
$833$	22.1563	+	2.91390i	0.767670	+	0.100961i
$834$	−0.134403	−	3.96625i	−0.00465398	−	0.137340i
$835$	2.98145	−	1.08516i	0.103177	−	0.0375534i
$836$	−6.13638	+	10.6285i	−0.212231	+	0.367595i
$837$	−15.5199	−	15.0806i	−0.536445	−	0.521261i
$838$	6.26832	+	10.8570i	0.216535	+	0.375050i
$839$	2.53595	−	14.3821i	0.0875507	−	0.496525i	−0.909226	−	0.416302i	$-0.863326\pi$
$839$	2.53595	−	14.3821i	0.0875507	−	0.496525i	0.996777	−	0.0802225i	$-0.0255631\pi$
$840$	−30.3556	+	23.8829i	−1.04737	+	0.824038i
$841$	−58.1463	−	21.1635i	−2.00505	−	0.729777i
$842$	10.1686	+	3.70106i	0.350432	+	0.127547i
$843$	11.9929	−	15.3176i	0.413059	−	0.527567i
$844$	0.761082	−	4.31631i	0.0261975	−	0.148574i
$845$	45.1631			1.55366
$846$	25.7047	+	7.42821i	0.883745	+	0.255387i
$847$	8.69295	+	11.8540i	0.298693	+	0.407309i
$848$	33.2195	+	27.8744i	1.14076	+	0.957212i
$849$	−4.74546	+	14.5539i	−0.162864	+	0.499487i
$850$	33.3174	+	12.1265i	1.14278	+	0.415937i
$851$	13.4385	+	4.89120i	0.460665	+	0.167668i
$852$	−0.155811	+	0.477858i	−0.00533801	+	0.0163711i
$853$	−10.0537	−	8.43605i	−0.344232	−	0.288845i	0.454237	−	0.890881i	$-0.349912\pi$
$853$	−10.0537	−	8.43605i	−0.344232	−	0.288845i	−0.798469	+	0.602036i	$0.794356\pi$
$854$	−6.44662	+	14.6537i	−0.220599	+	0.501440i
$855$	66.8532	+	19.3194i	2.28633	+	0.660710i
$856$	−17.2437			−0.589377
$857$	4.06916	−	23.0773i	0.139000	−	0.788307i	−0.832991	−	0.553287i	$-0.813373\pi$
$857$	4.06916	−	23.0773i	0.139000	−	0.788307i	0.971991	−	0.235020i	$-0.0755156\pi$
$858$	−0.757260	+	0.967188i	−0.0258524	+	0.0330192i
$859$	45.4200	+	16.5315i	1.54971	+	0.564049i	0.968350	−	0.249597i	$-0.0802980\pi$
$859$	45.4200	+	16.5315i	1.54971	+	0.564049i	0.581361	+	0.813645i	$0.302520\pi$
$860$	10.8830	+	3.96109i	0.371108	+	0.135072i
$861$	0.636738	+	4.42157i	0.0217000	+	0.150687i
$862$	−7.74276	+	43.9114i	−0.263719	+	1.49563i
$863$	−29.0398	−	50.2984i	−0.988527	−	1.71218i	−0.625074	−	0.780565i	$-0.714931\pi$
$863$	−29.0398	−	50.2984i	−0.988527	−	1.71218i	−0.363452	−	0.931613i	$-0.618402\pi$
$864$	−12.5587	+	3.55908i	−0.427257	+	0.121082i
$865$	4.75352	−	8.23334i	0.161624	−	0.279942i
$866$	36.1872	−	13.1711i	1.22969	−	0.447571i
$867$	−0.399374	−	11.7856i	−0.0135634	−	0.400260i
$868$	4.83955	+	1.18389i	0.164265	+	0.0401837i
$869$	−6.76271	+	5.67459i	−0.229409	+	0.192497i
$870$	−89.0245	−	12.6054i	−3.01821	−	0.427362i
$871$	0.0542527	−	0.307682i	0.00183828	−	0.0104254i
$872$	16.3531	+	28.3243i	0.553784	+	0.959182i
$873$	−25.5231	−	18.6243i	−0.863828	−	0.630338i
$874$	22.5306	+	39.0241i	0.762109	+	1.32001i
$875$	−17.2642	+	8.51519i	−0.583635	+	0.287866i
$876$	−0.202239	+	0.620246i	−0.00683301	+	0.0209562i
$877$	−29.0495	+	24.3754i	−0.980932	+	0.823100i	−0.984230	−	0.176895i	$-0.943395\pi$
$877$	−29.0495	+	24.3754i	−0.980932	+	0.823100i	0.00329784	+	0.999995i	$0.498950\pi$
$878$	38.8525	+	14.1412i	1.31121	+	0.477241i
$879$	−6.94644	+	21.3040i	−0.234298	+	0.718568i
$880$	−11.5475	+	65.4894i	−0.389268	+	2.20765i
$881$	−6.22587	−	10.7835i	−0.209755	−	0.363306i	0.741882	−	0.670530i	$-0.233933\pi$
$881$	−6.22587	−	10.7835i	−0.209755	−	0.363306i	−0.951637	+	0.307224i	$0.900600\pi$
$882$	−31.5485	+	9.27885i	−1.06229	+	0.312435i
$883$	−5.13403	+	8.89240i	−0.172774	+	0.299253i	−0.939389	−	0.342854i	$-0.888606\pi$
$883$	−5.13403	+	8.89240i	−0.172774	+	0.299253i	0.766615	+	0.642107i	$0.221940\pi$
$884$	0.123082	+	0.103278i	0.00413968	+	0.00347361i
$885$	−37.9388	−	5.37192i	−1.27530	−	0.180575i
$886$	8.71170	+	49.4065i	0.292675	+	1.65984i
$887$	−3.50383	−	19.8712i	−0.117647	−	0.667210i	−0.985405	−	0.170224i	$-0.945551\pi$
$887$	−3.50383	−	19.8712i	−0.117647	−	0.667210i	0.867758	−	0.496986i	$-0.165560\pi$
$888$	11.8103	−	7.36292i	0.396327	−	0.247084i
$889$	7.94223	+	5.30606i	0.266374	+	0.177959i
$890$	−2.29056			−0.0767798
$891$	32.4045	−	17.0584i	1.08559	−	0.571477i
$892$	−3.72566	+	6.45303i	−0.124744	+	0.216063i
$893$	−29.1038	−	24.4210i	−0.973922	−	0.817217i
$894$	−29.7962	−	15.8824i	−0.996533	−	0.531187i
$895$	8.06862	+	2.93674i	0.269704	+	0.0981643i
$896$	−24.8504	+	25.9625i	−0.830192	+	0.867347i
$897$	0.310745	+	0.771414i	0.0103755	+	0.0257568i
$898$	−1.72160	−	1.44459i	−0.0574506	−	0.0482068i
$899$	−19.8507	−	34.3824i	−0.662057	−	1.14672i
$900$	−9.59870	+	0.651282i	−0.319957	+	0.0217094i
$901$	−14.7280	+	25.5097i	−0.490662	+	0.849851i
$902$	4.75807	+	3.99250i	0.158427	+	0.132936i
$903$	−25.1603	−	22.5001i	−0.837281	−	0.748756i
$904$	−4.43904	−	25.1751i	−0.147640	−	0.837310i
$905$	−62.0546	+	52.0700i	−2.06276	+	1.73086i
$906$	−2.72738	−	3.03536i	−0.0906111	−	0.100843i
$907$	−46.9861	+	17.1016i	−1.56015	+	0.567848i	−0.970771	−	0.240009i	$-0.922850\pi$
$907$	−46.9861	+	17.1016i	−1.56015	+	0.567848i	−0.589379	+	0.807857i	$0.700627\pi$
$908$	0.583059	−	1.00989i	0.0193495	−	0.0335143i
$909$	−2.69688	+	25.1590i	−0.0894497	+	0.834470i
$910$	−1.59405	+	0.174685i	−0.0528423	+	0.00579077i
$911$	36.7726	−	13.3841i	1.21833	−	0.443436i	0.348745	−	0.937218i	$-0.386608\pi$
$911$	36.7726	−	13.3841i	1.21833	−	0.443436i	0.869586	+	0.493782i	$0.164386\pi$
$912$	53.7651	+	7.61283i	1.78034	+	0.252086i
$913$	6.76860	+	38.3867i	0.224008	+	1.27041i
$914$	−34.8104	+	29.2094i	−1.15142	+	0.966160i
$915$	19.7496	−	12.3126i	0.652901	−	0.407041i
$916$	−0.0926664	+	0.525537i	−0.00306178	+	0.0173642i
$917$	40.7229	−	4.46265i	1.34479	−	0.147370i
$918$	−11.3149	−	23.3827i	−0.373448	−	0.771743i
$919$	18.4964	+	32.0368i	0.610141	+	1.05680i	0.991216	+	0.132252i	$0.0422207\pi$
$919$	18.4964	+	32.0368i	0.610141	+	1.05680i	−0.381075	+	0.924544i	$0.624446\pi$
$920$	27.8530	+	23.3714i	0.918285	+	0.770533i
$921$	26.6246	−	16.5987i	0.877311	−	0.546946i
$922$	−8.19460	−	46.4739i	−0.269875	−	1.53054i
$923$	0.0547200	−	0.0459156i	0.00180113	−	0.00151133i
$924$	−4.44353	+	7.16519i	−0.146181	+	0.235717i
$925$	22.0939	−	8.04154i	0.726445	−	0.264404i
$926$	59.6761			1.96108
$927$	−15.3271	−	4.42926i	−0.503408	−	0.145476i
$928$	−23.9480			−0.786130
$929$	4.35478	−	24.6972i	0.142876	−	0.810287i	−0.826173	−	0.563417i	$-0.809487\pi$
$929$	4.35478	−	24.6972i	0.142876	−	0.810287i	0.969048	−	0.246871i	$-0.0794023\pi$
$930$	−26.2530	−	29.2175i	−0.860868	−	0.958080i
$931$	46.2954	+	6.08857i	1.51727	+	0.199545i
$932$	−1.60536	−	9.10445i	−0.0525853	−	0.298226i
$933$	−9.76805	+	29.9576i	−0.319791	+	0.980769i
$934$	23.3371	−	8.49400i	0.763612	−	0.277932i
$935$	−45.1705			−1.47723
$936$	0.777533	+	0.224694i	0.0254145	+	0.00734434i
$937$	26.6354	−	46.1338i	0.870140	−	1.50713i	0.00828920	−	0.999966i	$-0.497361\pi$
$937$	26.6354	−	46.1338i	0.870140	−	1.50713i	0.861851	−	0.507161i	$-0.169305\pi$
$938$	0.759823	−	11.6046i	0.0248091	−	0.378904i
$939$	−56.8832	−	8.05435i	−1.85631	−	0.262844i
$940$	8.41538	+	3.06295i	0.274479	+	0.0999024i
$941$	−15.0784	+	12.6523i	−0.491542	+	0.412452i	−0.854578	−	0.519322i	$-0.826184\pi$
$941$	−15.0784	+	12.6523i	−0.491542	+	0.412452i	0.363037	+	0.931775i	$0.381740\pi$
$942$	16.1520	−	10.0697i	0.526260	−	0.328088i
$943$	3.95161	−	1.43827i	0.128682	−	0.0468365i
$944$	−29.8996			−0.973150
$945$	45.4862	+	14.7124i	1.47966	+	0.478595i
$946$	−46.9311			−1.52586
$947$	15.0921	−	5.49306i	0.490426	−	0.178501i	−0.0849568	−	0.996385i	$-0.527075\pi$
$947$	15.0921	−	5.49306i	0.490426	−	0.178501i	0.575383	+	0.817884i	$0.304853\pi$
$948$	−1.49950	−	0.799287i	−0.0487015	−	0.0259596i
$949$	0.0710251	−	0.0595971i	0.00230557	−	0.00193461i
$950$	69.6164	+	25.3383i	2.25866	+	0.822083i
$951$	9.62435	−	12.2924i	0.312091	−	0.398609i
$952$	−17.0230	−	11.3728i	−0.551719	−	0.368593i
$953$	13.2295	−	22.9142i	0.428546	−	0.742264i	−0.568198	−	0.822892i	$-0.692359\pi$
$953$	13.2295	−	22.9142i	0.428546	−	0.742264i	0.996744	+	0.0806280i	$0.0256926\pi$
$954$	4.61993	−	43.0990i	0.149576	−	1.39538i
$955$	−65.7074			−2.12624
$956$	−3.41007	+	1.24116i	−0.110289	+	0.0401421i
$957$	65.7306	−	13.9005i	2.12477	−	0.449340i
$958$	−0.203926	−	1.15652i	−0.00658856	−	0.0373656i
$959$	27.8636	−	29.1106i	0.899761	−	0.940029i
$960$	32.2092	−	6.81151i	1.03955	−	0.219841i
$961$	−2.37133	+	13.4485i	−0.0764944	+	0.433821i
$962$	0.577818			0.0186296
$963$	11.8982	+	17.7187i	0.383414	+	0.570976i
$964$	−8.56479			−0.275853
$965$	−12.8114	+	4.66298i	−0.412414	+	0.150107i
$966$	14.6259	+	27.2833i	0.470580	+	0.877824i
$967$	23.9460	−	20.0931i	0.770053	−	0.646151i	−0.170670	−	0.985328i	$-0.554593\pi$
$967$	23.9460	−	20.0931i	0.770053	−	0.646151i	0.940722	+	0.339177i	$0.110149\pi$
$968$	−2.33847	−	13.2621i	−0.0751614	−	0.426261i
$969$	1.24918	+	36.8636i	0.0401294	+	1.18423i
$970$	−43.9332	−	36.8643i	−1.41061	−	1.18364i
$971$	22.7633	+	39.4271i	0.730508	+	1.26528i	0.956666	+	0.291186i	$0.0940499\pi$
$971$	22.7633	+	39.4271i	0.730508	+	1.26528i	−0.226159	+	0.974090i	$0.572617\pi$
$972$	5.37608	+	4.55859i	0.172438	+	0.146217i
$973$	−1.55886	+	3.54343i	−0.0499749	+	0.113597i
$974$	3.75474	−	21.2942i	0.120309	−	0.682309i
$975$	1.20659	+	0.643155i	0.0386418	+	0.0205975i
$976$	13.9118	−	11.6734i	0.445306	−	0.373656i
$977$	−6.00010	−	34.0282i	−0.191960	−	1.08866i	−0.916682	−	0.399618i	$-0.869143\pi$
$977$	−6.00010	−	34.0282i	−0.191960	−	1.08866i	0.724722	−	0.689042i	$-0.241968\pi$
$978$	−37.5938	+	48.0156i	−1.20212	+	1.53537i
$979$	1.60833	−	0.585385i	0.0514025	−	0.0187090i
$980$	−10.7454	+	2.38371i	−0.343249	+	0.0761448i
$981$	17.8208	−	36.3474i	0.568976	−	1.16048i
$982$	19.2050	−	33.2640i	0.612856	−	1.06150i
$983$	−22.1194	+	8.05082i	−0.705500	+	0.256781i	−0.669757	−	0.742580i	$-0.733602\pi$
$983$	−22.1194	+	8.05082i	−0.705500	+	0.256781i	−0.0357428	+	0.999361i	$0.511380\pi$
$984$	1.26866	−	3.89084i	0.0404433	−	0.124036i
$985$	−27.9749	+	23.4737i	−0.891354	+	0.747935i
$986$	−8.27556	−	46.9330i	−0.263548	−	1.49465i
$987$	−19.4554	−	17.3984i	−0.619271	−	0.553796i
$988$	0.257178	+	0.215798i	0.00818192	+	0.00686545i
$989$	−15.8870	+	27.5171i	−0.505177	+	0.874993i
$990$	60.7796	−	26.9105i	1.93170	−	0.855271i
$991$	8.78720	+	15.2199i	0.279134	+	0.483475i	0.971170	−	0.238388i	$-0.0766191\pi$
$991$	8.78720	+	15.2199i	0.279134	+	0.483475i	−0.692035	+	0.721864i	$0.743286\pi$
$992$	−8.01436	−	6.72484i	−0.254456	−	0.213514i
$993$	−25.4490	+	32.5040i	−0.807600	+	1.03148i
$994$	1.83853	−	1.92081i	0.0583147	−	0.0609245i
$995$	−35.8079	−	13.0330i	−1.13519	−	0.413174i
$996$	−6.36668	+	3.96920i	−0.201736	+	0.125769i
$997$	38.0025	+	31.8879i	1.20355	+	1.00990i	0.999521	+	0.0309340i	$0.00984816\pi$
$997$	38.0025	+	31.8879i	1.20355	+	1.00990i	0.204029	+	0.978965i	$0.434596\pi$
$998$	−25.8002	+	44.6872i	−0.816690	+	1.41455i
$999$	−15.7149	−	7.05514i	−0.497196	−	0.223215i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.w.a.25.5	yes	132
3.2	odd	2		567.2.w.a.235.18		132
7.2	even	3		189.2.u.a.79.18	yes	132
21.2	odd	6		567.2.u.a.478.5		132
27.13	even	9		189.2.u.a.67.18	✓	132
27.14	odd	18		567.2.u.a.172.5		132
189.121	even	9	inner	189.2.w.a.121.5	yes	132
189.149	odd	18		567.2.w.a.415.18		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.67.18	✓	132	27.13	even	9
189.2.u.a.79.18	yes	132	7.2	even	3
189.2.w.a.25.5	yes	132	1.1	even	1	trivial
189.2.w.a.121.5	yes	132	189.121	even	9	inner
567.2.u.a.172.5		132	27.14	odd	18
567.2.u.a.478.5		132	21.2	odd	6
567.2.w.a.235.18		132	3.2	odd	2
567.2.w.a.415.18		132	189.149	odd	18

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.47150 + 0.535583i) q^{2} +(0.0586596 + 1.73106i) q^{3} +(0.346382 - 0.290649i) q^{4} +(3.26769 + 1.18934i) q^{5} +(-1.01344 - 2.51584i) q^{6} +(-0.172863 + 2.64010i) q^{7} +(1.21191 - 2.09908i) q^{8} +(-2.99312 + 0.203086i) q^{9} +O(q^{10})\)	\(q+(-1.47150 + 0.535583i) q^{2} +(0.0586596 + 1.73106i) q^{3} +(0.346382 - 0.290649i) q^{4} +(3.26769 + 1.18934i) q^{5} +(-1.01344 - 2.51584i) q^{6} +(-0.172863 + 2.64010i) q^{7} +(1.21191 - 2.09908i) q^{8} +(-2.99312 + 0.203086i) q^{9} -5.44540 q^{10} +(3.82352 - 1.39165i) q^{11} +(0.523448 + 0.582557i) q^{12} +(-0.0193280 - 0.109614i) q^{13} +(-1.15962 - 3.97749i) q^{14} +(-1.86714 + 5.72632i) q^{15} +(-0.816126 + 4.62848i) q^{16} -3.19244 q^{17} +(4.29561 - 1.90191i) q^{18} -6.67057 q^{19} +(1.47755 - 0.537783i) q^{20} +(-4.58030 - 0.144369i) q^{21} +(-4.88098 + 4.09563i) q^{22} +(0.749091 + 4.24830i) q^{23} +(3.70472 + 1.97475i) q^{24} +(5.43302 + 4.55885i) q^{25} +(0.0871487 + 0.150946i) q^{26} +(-0.527129 - 5.16935i) q^{27} +(0.707465 + 0.964724i) q^{28} +(1.65539 - 9.38817i) q^{29} +(-0.319425 - 9.42630i) q^{30} +(3.19029 - 2.67697i) q^{31} +(-0.436224 - 2.47395i) q^{32} +(2.63331 + 6.53710i) q^{33} +(4.69768 - 1.70982i) q^{34} +(-3.70484 + 8.42142i) q^{35} +(-0.977734 + 0.940291i) q^{36} +(1.65756 - 2.87098i) q^{37} +(9.81577 - 3.57265i) q^{38} +(0.188615 - 0.0398877i) q^{39} +(6.45665 - 5.41777i) q^{40} +(-0.169276 - 0.960010i) q^{41} +(6.81725 - 2.24069i) q^{42} +(5.64237 + 4.73451i) q^{43} +(0.919917 - 1.59334i) q^{44} +(-10.0221 - 2.89622i) q^{45} +(-3.37761 - 5.85019i) q^{46} +(4.36301 + 3.66100i) q^{47} +(-8.06004 - 1.14126i) q^{48} +(-6.94024 - 0.912751i) q^{49} +(-10.4363 - 3.79852i) q^{50} +(-0.187267 - 5.52630i) q^{51} +(-0.0385541 - 0.0323507i) q^{52} +(4.61341 - 7.99066i) q^{53} +(3.54429 + 7.32438i) q^{54} +14.1492 q^{55} +(5.33229 + 3.56240i) q^{56} +(-0.391293 - 11.5471i) q^{57} +(2.59224 + 14.7013i) q^{58} +(1.10471 + 6.26513i) q^{59} +(1.01761 + 2.52617i) q^{60} +(-2.96003 - 2.48376i) q^{61} +(-3.26078 + 5.64783i) q^{62} +(-0.0187681 - 7.93723i) q^{63} +(-2.73297 - 4.73365i) q^{64} +(0.0672110 - 0.381173i) q^{65} +(-7.37609 - 8.20901i) q^{66} +(2.63767 + 0.960035i) q^{67} +(-1.10580 + 0.927878i) q^{68} +(-7.31012 + 1.54592i) q^{69} +(0.941308 - 14.3764i) q^{70} +(0.320883 + 0.555786i) q^{71} +(-3.20108 + 6.52892i) q^{72} +(0.416497 + 0.721395i) q^{73} +(-0.901458 + 5.11242i) q^{74} +(-7.57293 + 9.67229i) q^{75} +(-2.31056 + 1.93879i) q^{76} +(3.01314 + 10.3350i) q^{77} +(-0.256184 + 0.159714i) q^{78} +(-2.03880 + 0.742063i) q^{79} +(-8.17168 + 14.1538i) q^{80} +(8.91751 - 1.21572i) q^{81} +(0.763254 + 1.32200i) q^{82} +(-1.66349 + 9.43414i) q^{83} +(-1.62849 + 1.28125i) q^{84} +(-10.4319 - 3.79690i) q^{85} +(-10.8385 - 3.94489i) q^{86} +(16.3486 + 2.31486i) q^{87} +(1.71256 - 9.71243i) q^{88} +0.420642 q^{89} +(16.2987 - 1.10589i) q^{90} +(0.292734 - 0.0320794i) q^{91} +(1.49424 + 1.25381i) q^{92} +(4.82113 + 5.36554i) q^{93} +(-8.38096 - 3.05042i) q^{94} +(-21.7973 - 7.93359i) q^{95} +(4.25696 - 0.900249i) q^{96} +(8.06794 + 6.76980i) q^{97} +(10.7014 - 2.37396i) q^{98} +(-11.1616 + 4.94187i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} + 3 q^{11} - 3 q^{12} - 12 q^{13} + 15 q^{14} - 9 q^{16} - 54 q^{17} - 3 q^{18} - 6 q^{19} - 18 q^{20} - 21 q^{21} - 12 q^{22} + 45 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 57 q^{30} - 3 q^{31} + 51 q^{32} + 15 q^{33} - 18 q^{34} - 12 q^{35} - 60 q^{36} + 3 q^{37} - 57 q^{38} - 66 q^{39} - 66 q^{40} + 33 q^{42} - 12 q^{43} + 3 q^{44} + 33 q^{45} + 3 q^{46} - 21 q^{47} + 90 q^{48} + 12 q^{49} - 39 q^{50} - 48 q^{51} + 9 q^{52} + 9 q^{53} - 63 q^{54} - 24 q^{55} + 57 q^{56} - 18 q^{57} - 3 q^{58} - 18 q^{59} + 81 q^{60} + 33 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} + 81 q^{65} + 69 q^{66} - 3 q^{67} + 6 q^{68} - 6 q^{69} - 42 q^{70} - 18 q^{71} - 105 q^{72} + 21 q^{73} - 93 q^{74} + 18 q^{75} - 24 q^{76} + 87 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} + 39 q^{81} - 6 q^{82} - 42 q^{83} - 36 q^{84} - 63 q^{85} + 159 q^{86} + 30 q^{87} + 57 q^{88} - 150 q^{89} - 39 q^{90} + 6 q^{91} - 66 q^{92} - 27 q^{93} + 33 q^{94} - 147 q^{95} + 81 q^{96} - 12 q^{97} + 99 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^10 + 3 * q^11 - 3 * q^12 - 12 * q^13 + 15 * q^14 - 9 * q^16 - 54 * q^17 - 3 * q^18 - 6 * q^19 - 18 * q^20 - 21 * q^21 - 12 * q^22 + 45 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 57 * q^30 - 3 * q^31 + 51 * q^32 + 15 * q^33 - 18 * q^34 - 12 * q^35 - 60 * q^36 + 3 * q^37 - 57 * q^38 - 66 * q^39 - 66 * q^40 + 33 * q^42 - 12 * q^43 + 3 * q^44 + 33 * q^45 + 3 * q^46 - 21 * q^47 + 90 * q^48 + 12 * q^49 - 39 * q^50 - 48 * q^51 + 9 * q^52 + 9 * q^53 - 63 * q^54 - 24 * q^55 + 57 * q^56 - 18 * q^57 - 3 * q^58 - 18 * q^59 + 81 * q^60 + 33 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 + 81 * q^65 + 69 * q^66 - 3 * q^67 + 6 * q^68 - 6 * q^69 - 42 * q^70 - 18 * q^71 - 105 * q^72 + 21 * q^73 - 93 * q^74 + 18 * q^75 - 24 * q^76 + 87 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 + 39 * q^81 - 6 * q^82 - 42 * q^83 - 36 * q^84 - 63 * q^85 + 159 * q^86 + 30 * q^87 + 57 * q^88 - 150 * q^89 - 39 * q^90 + 6 * q^91 - 66 * q^92 - 27 * q^93 + 33 * q^94 - 147 * q^95 + 81 * q^96 - 12 * q^97 + 99 * q^98 + 24 * q^99

Introduction

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