LMFDB - Embedded newform 462.2.ba.b.61.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(19,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 25, 9]))

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

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

chi := DirichletCharacter("462.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.ba (of order $30$, degree $8$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			61.5
Character	$\chi$	$=$	462.61
Dual form			462.2.ba.b.409.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.207912 - 0.978148i) q^{2} +(-0.994522 - 0.104528i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(-1.40387 + 1.26405i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(1.39244 - 2.24969i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.978148 + 0.207912i) q^{9} +O(q^{10})$	\(q+(0.207912 - 0.978148i) q^{2} +(-0.994522 - 0.104528i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(-1.40387 + 1.26405i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(1.39244 - 2.24969i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.978148 + 0.207912i) q^{9} +(0.944546 + 1.63600i) q^{10} +(-3.29539 + 0.374722i) q^{11} +(0.866025 + 0.500000i) q^{12} +(-0.860543 - 2.64848i) q^{13} +(-1.91102 - 1.82975i) q^{14} +(1.52831 - 1.11038i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-4.42290 + 0.940117i) q^{17} +(0.406737 - 0.913545i) q^{18} +(-7.46407 + 3.32322i) q^{19} +(1.79663 - 0.583762i) q^{20} +(-1.61997 + 2.09181i) q^{21} +(-0.318616 + 3.30129i) q^{22} +(-1.50946 + 2.61447i) q^{23} +(0.669131 - 0.743145i) q^{24} +(-0.149615 + 1.42349i) q^{25} +(-2.76952 + 0.291088i) q^{26} +(-0.951057 - 0.309017i) q^{27} +(-2.18709 + 1.48883i) q^{28} +(4.49539 + 6.18738i) q^{29} +(-0.768363 - 1.72577i) q^{30} +(-2.65536 - 2.39089i) q^{31} +(0.866025 - 0.500000i) q^{32} +(3.31650 - 0.0282076i) q^{33} +4.52171i q^{34} +(0.888908 + 4.91839i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(-0.635055 - 6.04214i) q^{37} +(1.69873 + 7.99190i) q^{38} +(0.578988 + 2.72392i) q^{39} +(-0.197464 - 1.87874i) q^{40} +(-0.583640 - 0.424039i) q^{41} +(1.70929 + 2.01949i) q^{42} -5.17151i q^{43} +(3.16290 + 0.998029i) q^{44} +(-1.63600 + 0.944546i) q^{45} +(2.24350 + 2.02006i) q^{46} +(-4.30505 - 9.66931i) q^{47} +(-0.587785 - 0.809017i) q^{48} +(-3.12220 - 6.26513i) q^{49} +(1.36128 + 0.442305i) q^{50} +(4.49694 - 0.472648i) q^{51} +(-0.291088 + 2.76952i) q^{52} +(-1.53281 + 1.70236i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(4.15263 - 4.69159i) q^{55} +(1.00158 + 2.44884i) q^{56} +(7.77055 - 2.52481i) q^{57} +(6.98681 - 3.11073i) q^{58} +(-2.19041 + 4.91974i) q^{59} +(-1.84781 + 0.392764i) q^{60} +(7.02722 + 7.80452i) q^{61} +(-2.89073 + 2.10024i) q^{62} +(1.82975 - 1.91102i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(4.55590 + 2.63035i) q^{65} +(0.661949 - 3.24990i) q^{66} +(-2.14166 - 3.70947i) q^{67} +(4.42290 + 0.940117i) q^{68} +(1.77448 - 2.44237i) q^{69} +(4.99572 + 0.153107i) q^{70} +(4.22470 - 13.0023i) q^{71} +(-0.743145 + 0.669131i) q^{72} +(-2.88873 - 1.28614i) q^{73} +(-6.04214 - 0.635055i) q^{74} +(0.297590 - 1.40005i) q^{75} +8.17044 q^{76} +(-3.74564 + 7.93538i) q^{77} +2.78478 q^{78} +(1.04715 - 4.92646i) q^{79} +(-1.87874 - 0.197464i) q^{80} +(0.913545 + 0.406737i) q^{81} +(-0.536119 + 0.482723i) q^{82} +(-3.41471 + 10.5094i) q^{83} +(2.33074 - 1.25207i) q^{84} +(5.02082 - 6.91057i) q^{85} +(-5.05850 - 1.07522i) q^{86} +(-3.82401 - 6.62338i) q^{87} +(1.63382 - 2.88628i) q^{88} +(-5.08578 - 2.93628i) q^{89} +(0.583762 + 1.79663i) q^{90} +(-7.15651 - 1.75191i) q^{91} +(2.44237 - 1.77448i) q^{92} +(2.39089 + 2.65536i) q^{93} +(-10.3531 + 2.20062i) q^{94} +(6.27787 - 14.1003i) q^{95} +(-0.913545 + 0.406737i) q^{96} +(-4.04593 + 1.31460i) q^{97} +(-6.77737 + 1.75138i) q^{98} +(-3.30129 - 0.318616i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9}+O(q^{10}) $ 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9	$ 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9} - 2 q^{10} + 4 q^{11} + 2 q^{14} - 6 q^{15} + 8 q^{16} + 30 q^{17} - 10 q^{19} - 20 q^{20} + 4 q^{21} - 2 q^{22} + 4 q^{23} + 8 q^{24} - 12 q^{26} - 20 q^{29} - 18 q^{30} + 34 q^{31} + 8 q^{33} - 2 q^{35} - 16 q^{36} - 14 q^{37} + 12 q^{38} - 18 q^{39} + 12 q^{40} + 28 q^{41} + 4 q^{42} + 6 q^{44} - 12 q^{45} + 42 q^{46} + 24 q^{47} - 44 q^{49} + 14 q^{51} - 32 q^{54} + 14 q^{55} - 4 q^{56} - 10 q^{58} - 30 q^{59} + 2 q^{60} - 28 q^{61} + 8 q^{62} + 16 q^{63} + 16 q^{64} - 12 q^{65} - 4 q^{66} + 16 q^{67} - 30 q^{68} - 30 q^{70} - 24 q^{71} - 116 q^{73} - 44 q^{74} + 12 q^{75} - 32 q^{77} - 18 q^{80} + 8 q^{81} - 28 q^{82} - 8 q^{83} - 2 q^{84} - 80 q^{85} - 18 q^{86} - 10 q^{87} - 14 q^{88} - 24 q^{89} - 4 q^{90} + 48 q^{91} + 8 q^{92} + 76 q^{93} + 6 q^{94} + 98 q^{95} - 8 q^{96} - 120 q^{97} - 40 q^{98} + 8 q^{99}+O(q^{100}) $ 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9 - 2 * q^10 + 4 * q^11 + 2 * q^14 - 6 * q^15 + 8 * q^16 + 30 * q^17 - 10 * q^19 - 20 * q^20 + 4 * q^21 - 2 * q^22 + 4 * q^23 + 8 * q^24 - 12 * q^26 - 20 * q^29 - 18 * q^30 + 34 * q^31 + 8 * q^33 - 2 * q^35 - 16 * q^36 - 14 * q^37 + 12 * q^38 - 18 * q^39 + 12 * q^40 + 28 * q^41 + 4 * q^42 + 6 * q^44 - 12 * q^45 + 42 * q^46 + 24 * q^47 - 44 * q^49 + 14 * q^51 - 32 * q^54 + 14 * q^55 - 4 * q^56 - 10 * q^58 - 30 * q^59 + 2 * q^60 - 28 * q^61 + 8 * q^62 + 16 * q^63 + 16 * q^64 - 12 * q^65 - 4 * q^66 + 16 * q^67 - 30 * q^68 - 30 * q^70 - 24 * q^71 - 116 * q^73 - 44 * q^74 + 12 * q^75 - 32 * q^77 - 18 * q^80 + 8 * q^81 - 28 * q^82 - 8 * q^83 - 2 * q^84 - 80 * q^85 - 18 * q^86 - 10 * q^87 - 14 * q^88 - 24 * q^89 - 4 * q^90 + 48 * q^91 + 8 * q^92 + 76 * q^93 + 6 * q^94 + 98 * q^95 - 8 * q^96 - 120 * q^97 - 40 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	0.207912	−	0.978148i	0.147016	−	0.691655i
$2$	0.207912	−	0.978148i	0.147016	−	0.691655i
$3$	−0.994522	−	0.104528i	−0.574187	−	0.0603495i
$3$	−0.994522	−	0.104528i	−0.574187	−	0.0603495i
$4$	−0.913545	−	0.406737i	−0.456773	−	0.203368i
$5$	−1.40387	+	1.26405i	−0.627829	+	0.565300i	−0.920417	−	0.390939i	$-0.872150\pi$
$5$	−1.40387	+	1.26405i	−0.627829	+	0.565300i	0.292587	+	0.956239i	$0.405484\pi$
$6$	−0.309017	+	0.951057i	−0.126156	+	0.388267i
$7$	1.39244	−	2.24969i	0.526295	−	0.850302i
$7$	1.39244	−	2.24969i	0.526295	−	0.850302i
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$	0.978148	+	0.207912i	0.326049	+	0.0693039i
$10$	0.944546	+	1.63600i	0.298692	+	0.517349i
$11$	−3.29539	+	0.374722i	−0.993597	+	0.112983i
$11$	−3.29539	+	0.374722i	−0.993597	+	0.112983i
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	−0.860543	−	2.64848i	−0.238672	−	0.734556i	−0.996613	−	0.0822335i	$-0.973795\pi$
$13$	−0.860543	−	2.64848i	−0.238672	−	0.734556i	0.757941	−	0.652323i	$-0.226205\pi$
$14$	−1.91102	−	1.82975i	−0.510742	−	0.489022i
$15$	1.52831	−	1.11038i	0.394607	−	0.286699i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	−4.42290	+	0.940117i	−1.07271	+	0.228012i	−0.710223	−	0.703976i	$-0.751406\pi$
$17$	−4.42290	+	0.940117i	−1.07271	+	0.228012i	−0.362488	+	0.931988i	$0.618073\pi$
$18$	0.406737	−	0.913545i	0.0958687	−	0.215325i
$19$	−7.46407	+	3.32322i	−1.71238	+	0.762399i	−0.714336	+	0.699803i	$0.753271\pi$
$19$	−7.46407	+	3.32322i	−1.71238	+	0.762399i	−0.998039	+	0.0625961i	$0.980062\pi$
$20$	1.79663	−	0.583762i	0.401740	−	0.130533i
$21$	−1.61997	+	2.09181i	−0.353507	+	0.456471i
$22$	−0.318616	+	3.30129i	−0.0679292	+	0.703836i
$23$	−1.50946	+	2.61447i	−0.314745	+	0.545155i	−0.979383	−	0.202011i	$-0.935252\pi$
$23$	−1.50946	+	2.61447i	−0.314745	+	0.545155i	0.664638	+	0.747165i	$0.268586\pi$
$24$	0.669131	−	0.743145i	0.136586	−	0.151694i
$25$	−0.149615	+	1.42349i	−0.0299229	+	0.284698i
$26$	−2.76952	+	0.291088i	−0.543148	+	0.0570871i
$27$	−0.951057	−	0.309017i	−0.183031	−	0.0594703i
$28$	−2.18709	+	1.48883i	−0.413322	+	0.281363i
$29$	4.49539	+	6.18738i	0.834773	+	1.14897i	0.987016	+	0.160624i	$0.0513505\pi$
$29$	4.49539	+	6.18738i	0.834773	+	1.14897i	−0.152243	+	0.988343i	$0.548649\pi$
$30$	−0.768363	−	1.72577i	−0.140283	−	0.315081i
$31$	−2.65536	−	2.39089i	−0.476916	−	0.429417i	0.395290	−	0.918557i	$-0.370644\pi$
$31$	−2.65536	−	2.39089i	−0.476916	−	0.429417i	−0.872206	+	0.489139i	$0.837311\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	3.31650	−	0.0282076i	0.577329	−	0.00491030i
$34$			4.52171i			0.775468i
$35$	0.888908	+	4.91839i	0.150253	+	0.831359i
$36$	−0.809017	−	0.587785i	−0.134836	−	0.0979642i
$37$	−0.635055	−	6.04214i	−0.104402	−	0.993322i	−0.913828	−	0.406100i	$-0.866888\pi$
$37$	−0.635055	−	6.04214i	−0.104402	−	0.993322i	0.809426	−	0.587222i	$-0.199778\pi$
$38$	1.69873	+	7.99190i	0.275570	+	1.29646i
$39$	0.578988	+	2.72392i	0.0927122	+	0.436177i
$40$	−0.197464	−	1.87874i	−0.0312218	−	0.297055i
$41$	−0.583640	−	0.424039i	−0.0911493	−	0.0662238i	0.541277	−	0.840844i	$-0.317941\pi$
$41$	−0.583640	−	0.424039i	−0.0911493	−	0.0662238i	−0.632426	+	0.774620i	$0.717941\pi$
$42$	1.70929	+	2.01949i	0.263749	+	0.311613i
$43$		−	5.17151i		−	0.788647i	−0.918972	−	0.394324i	$-0.870979\pi$
$43$		−	5.17151i		−	0.788647i	0.918972	−	0.394324i	$-0.129021\pi$
$44$	3.16290	+	0.998029i	0.476825	+	0.150459i
$45$	−1.63600	+	0.944546i	−0.243881	+	0.140805i
$46$	2.24350	+	2.02006i	0.330786	+	0.297841i
$47$	−4.30505	−	9.66931i	−0.627957	−	1.41041i	−0.894709	−	0.446649i	$-0.852617\pi$
$47$	−4.30505	−	9.66931i	−0.627957	−	1.41041i	0.266753	−	0.963765i	$-0.414049\pi$
$48$	−0.587785	−	0.809017i	−0.0848395	−	0.116772i
$49$	−3.12220	−	6.26513i	−0.446028	−	0.895019i
$50$	1.36128	+	0.442305i	0.192513	+	0.0625514i
$51$	4.49694	−	0.472648i	0.629698	−	0.0661839i
$52$	−0.291088	+	2.76952i	−0.0403667	+	0.384064i
$53$	−1.53281	+	1.70236i	−0.210548	+	0.233837i	−0.839164	−	0.543879i	$-0.816955\pi$
$53$	−1.53281	+	1.70236i	−0.210548	+	0.233837i	0.628616	+	0.777716i	$0.283622\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	4.15263	−	4.69159i	0.559940	−	0.632615i
$56$	1.00158	+	2.44884i	0.133841	+	0.327241i
$57$	7.77055	−	2.52481i	1.02923	−	0.334419i
$58$	6.98681	−	3.11073i	0.917413	−	0.408459i
$59$	−2.19041	+	4.91974i	−0.285167	+	0.640496i	−0.998157	−	0.0606779i	$-0.980674\pi$
$59$	−2.19041	+	4.91974i	−0.285167	+	0.640496i	0.712990	+	0.701174i	$0.247340\pi$
$60$	−1.84781	+	0.392764i	−0.238551	+	0.0507057i
$61$	7.02722	+	7.80452i	0.899743	+	0.999266i	0.999991	+	0.00430379i	$0.00136994\pi$
$61$	7.02722	+	7.80452i	0.899743	+	0.999266i	−0.100247	+	0.994963i	$0.531963\pi$
$62$	−2.89073	+	2.10024i	−0.367123	+	0.266730i
$63$	1.82975	−	1.91102i	0.230527	−	0.240766i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	4.55590	+	2.63035i	0.565090	+	0.326255i
$66$	0.661949	−	3.24990i	0.0814803	−	0.400035i
$67$	−2.14166	−	3.70947i	−0.261646	−	0.453184i	0.705033	−	0.709174i	$-0.250932\pi$
$67$	−2.14166	−	3.70947i	−0.261646	−	0.453184i	−0.966679	+	0.255990i	$0.917599\pi$
$68$	4.42290	+	0.940117i	0.536356	+	0.114006i
$69$	1.77448	−	2.44237i	0.213623	−	0.294026i
$70$	4.99572	+	0.153107i	0.597103	+	0.0182998i
$71$	4.22470	−	13.0023i	0.501380	−	1.54309i	−0.305392	−	0.952227i	$-0.598787\pi$
$71$	4.22470	−	13.0023i	0.501380	−	1.54309i	0.806772	−	0.590863i	$-0.201213\pi$
$72$	−0.743145	+	0.669131i	−0.0875805	+	0.0788578i
$73$	−2.88873	−	1.28614i	−0.338100	−	0.150532i	0.230662	−	0.973034i	$-0.425911\pi$
$73$	−2.88873	−	1.28614i	−0.338100	−	0.150532i	−0.568762	+	0.822502i	$0.692578\pi$
$74$	−6.04214	−	0.635055i	−0.702385	−	0.0738236i
$75$	0.297590	−	1.40005i	0.0343628	−	0.161664i
$76$	8.17044			0.937214
$77$	−3.74564	+	7.93538i	−0.426855	+	0.904320i
$78$	2.78478			0.315314
$79$	1.04715	−	4.92646i	0.117814	−	0.554269i	−0.879160	−	0.476527i	$-0.841895\pi$
$79$	1.04715	−	4.92646i	0.117814	−	0.554269i	0.996973	−	0.0777425i	$-0.0247712\pi$
$80$	−1.87874	−	0.197464i	−0.210050	−	0.0220771i
$81$	0.913545	+	0.406737i	0.101505	+	0.0451930i
$82$	−0.536119	+	0.482723i	−0.0592044	+	0.0533079i
$83$	−3.41471	+	10.5094i	−0.374813	+	1.15356i	0.568792	+	0.822481i	$0.307411\pi$
$83$	−3.41471	+	10.5094i	−0.374813	+	1.15356i	−0.943605	+	0.331074i	$0.892589\pi$
$84$	2.33074	−	1.25207i	0.254304	−	0.136612i
$85$	5.02082	−	6.91057i	0.544585	−	0.749557i
$86$	−5.05850	−	1.07522i	−0.545472	−	0.115944i
$87$	−3.82401	−	6.62338i	−0.409977	−	0.710100i
$88$	1.63382	−	2.88628i	0.174166	−	0.307679i
$89$	−5.08578	−	2.93628i	−0.539092	−	0.311245i	0.205619	−	0.978632i	$-0.434079\pi$
$89$	−5.08578	−	2.93628i	−0.539092	−	0.311245i	−0.744711	+	0.667387i	$0.767413\pi$
$90$	0.583762	+	1.79663i	0.0615339	+	0.189382i
$91$	−7.15651	−	1.75191i	−0.750207	−	0.183650i
$92$	2.44237	−	1.77448i	0.254634	−	0.185003i
$93$	2.39089	+	2.65536i	0.247924	+	0.275348i
$94$	−10.3531	+	2.20062i	−1.06784	+	0.226976i
$95$	6.27787	−	14.1003i	0.644096	−	1.44666i
$96$	−0.913545	+	0.406737i	−0.0932383	+	0.0415124i
$97$	−4.04593	+	1.31460i	−0.410802	+	0.133478i	−0.507125	−	0.861873i	$-0.669292\pi$
$97$	−4.04593	+	1.31460i	−0.410802	+	0.133478i	0.0963232	+	0.995350i	$0.469292\pi$
$98$	−6.77737	+	1.75138i	−0.684617	+	0.176916i
$99$	−3.30129	−	0.318616i	−0.331792	−	0.0320221i
$100$	0.715665	−	1.23957i	0.0715665	−	0.123957i
$101$	−4.04745	+	4.49515i	−0.402736	+	0.447284i	−0.910063	−	0.414470i	$-0.863967\pi$
$101$	−4.04745	+	4.49515i	−0.402736	+	0.447284i	0.507327	+	0.861754i	$0.330634\pi$
$102$	0.472648	−	4.49694i	0.0467991	−	0.445264i
$103$	13.8031	−	1.45076i	1.36006	−	0.142948i	0.603754	−	0.797170i	$-0.293671\pi$
$103$	13.8031	−	1.45076i	1.36006	−	0.142948i	0.756302	+	0.654223i	$0.227004\pi$
$104$	2.64848	+	0.860543i	0.259705	+	0.0843832i
$105$	−0.369927	−	4.98436i	−0.0361012	−	0.486424i
$106$	1.34647	+	1.85325i	0.130781	+	0.180004i
$107$	−2.71529	−	6.09864i	−0.262497	−	0.589578i	0.733428	−	0.679767i	$-0.237919\pi$
$107$	−2.71529	−	6.09864i	−0.262497	−	0.589578i	−0.995925	+	0.0901898i	$0.971253\pi$
$108$	0.743145	+	0.669131i	0.0715091	+	0.0643871i
$109$	−9.17047	+	5.29457i	−0.878372	+	0.507128i	−0.870121	−	0.492838i	$-0.835960\pi$
$109$	−9.17047	+	5.29457i	−0.878372	+	0.507128i	−0.00825038	+	0.999966i	$0.502626\pi$
$110$	−3.72569	−	5.03732i	−0.355231	−	0.480290i
$111$			6.07543i			0.576654i
$112$	2.60357	−	0.470548i	0.246014	−	0.0444626i
$113$	5.41785	+	3.93630i	0.509668	+	0.370296i	0.812698	−	0.582686i	$-0.197998\pi$
$113$	5.41785	+	3.93630i	0.509668	+	0.370296i	−0.303029	+	0.952981i	$0.597998\pi$
$114$	−0.854044	−	8.12568i	−0.0799885	−	0.761040i
$115$	−1.18573	−	5.57841i	−0.110570	−	0.520190i
$116$	−1.59011	−	7.48089i	−0.147638	−	0.694583i
$117$	−0.291088	−	2.76952i	−0.0269111	−	0.256042i
$118$	4.35682	+	3.16542i	0.401078	+	0.291400i
$119$	−4.04368	+	11.2592i	−0.370683	+	1.03213i
$120$			1.88909i			0.172450i
$121$	10.7192	−	2.46971i	0.974470	−	0.224519i
$122$	9.09501	−	5.25101i	0.823424	−	0.475404i
$123$	0.536119	+	0.482723i	0.0483402	+	0.0435257i
$124$	1.45332	+	3.26422i	0.130512	+	0.293136i
$125$	−7.14122	−	9.82905i	−0.638731	−	0.879137i
$126$	−1.48883	−	2.18709i	−0.132636	−	0.194842i
$127$	19.9693	+	6.48843i	1.77199	+	0.575755i	0.998326	−	0.0578402i	$-0.0184214\pi$
$127$	19.9693	+	6.48843i	1.77199	+	0.575755i	0.773665	+	0.633595i	$0.218421\pi$
$128$	−0.994522	+	0.104528i	−0.0879041	+	0.00923910i
$129$	−0.540569	+	5.14318i	−0.0475945	+	0.452831i
$130$	3.52010	−	3.90946i	0.308733	−	0.342883i
$131$	3.26981	−	5.66348i	0.285685	−	0.494821i	−0.687090	−	0.726572i	$-0.741112\pi$
$131$	3.26981	−	5.66348i	0.285685	−	0.494821i	0.972775	+	0.231751i	$0.0744456\pi$
$132$	−3.04125	−	1.32318i	−0.264707	−	0.115168i
$133$	−2.91710	+	21.4192i	−0.252944	+	1.85728i
$134$	−4.07369	+	1.32362i	−0.351913	+	0.114343i
$135$	1.72577	−	0.768363i	0.148531	−	0.0661302i
$136$	1.83915	−	4.13079i	0.157706	−	0.354212i
$137$	11.2040	−	2.38148i	0.957221	−	0.203464i	0.297288	−	0.954788i	$-0.403918\pi$
$137$	11.2040	−	2.38148i	0.957221	−	0.203464i	0.659933	+	0.751324i	$0.270585\pi$
$138$	−2.02006	−	2.24350i	−0.171959	−	0.190980i
$139$	14.2235	−	10.3340i	1.20642	−	0.876518i	0.211522	−	0.977373i	$-0.432158\pi$
$139$	14.2235	−	10.3340i	1.20642	−	0.876518i	0.994901	+	0.100856i	$0.0321580\pi$
$140$	1.18843	−	4.85472i	0.100441	−	0.410299i
$141$	3.27075	+	10.0663i	0.275447	+	0.847739i
$142$	−11.8398	−	6.83572i	−0.993575	−	0.573641i
$143$	3.82827	+	8.40531i	0.320136	+	0.702887i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−14.1321	−	3.00387i	−1.17361	−	0.249458i
$146$	−1.85864	+	2.55820i	−0.153822	+	0.211718i
$147$	2.45021	+	6.55717i	0.202090	+	0.540826i
$148$	−1.87741	+	5.77807i	−0.154322	+	0.474955i
$149$	−15.4638	+	13.9236i	−1.26684	+	1.14067i	−0.283486	+	0.958976i	$0.591491\pi$
$149$	−15.4638	+	13.9236i	−1.26684	+	1.14067i	−0.983355	+	0.181692i	$0.941842\pi$
$150$	−1.30758	−	0.582174i	−0.106764	−	0.0475343i
$151$	−19.6533	−	2.06564i	−1.59936	−	0.168099i	−0.737536	−	0.675308i	$-0.764011\pi$
$151$	−19.6533	−	2.06564i	−1.59936	−	0.168099i	−0.861823	+	0.507208i	$0.830677\pi$
$152$	1.69873	−	7.99190i	0.137785	−	0.648229i
$153$	−4.52171			−0.365559
$154$	6.98321	+	5.31364i	0.562723	+	0.428186i
$155$	6.74998			0.542172
$156$	0.578988	−	2.72392i	0.0463561	−	0.218088i
$157$	13.8285	+	1.45344i	1.10364	+	0.115997i	0.638781	−	0.769389i	$-0.279439\pi$
$157$	13.8285	+	1.45344i	1.10364	+	0.115997i	0.464857	+	0.885386i	$0.346106\pi$
$158$	−4.60109	−	2.04854i	−0.366043	−	0.162973i
$159$	1.70236	−	1.53281i	0.135006	−	0.121560i
$160$	−0.583762	+	1.79663i	−0.0461504	+	0.142036i
$161$	3.77990	+	7.03633i	0.297898	+	0.554540i
$162$	0.587785	−	0.809017i	0.0461808	−	0.0635624i
$163$	0.119914	+	0.0254886i	0.00939242	+	0.00199642i	0.212606	−	0.977138i	$-0.431805\pi$
$163$	0.119914	+	0.0254886i	0.00939242	+	0.00199642i	−0.203213	+	0.979135i	$0.565138\pi$
$164$	0.360709	+	0.624767i	0.0281667	+	0.0487861i
$165$	−4.62028	+	4.23183i	−0.359689	+	0.329447i
$166$	9.56978	+	5.52511i	0.742759	+	0.428832i
$167$	−5.84539	−	17.9903i	−0.452330	−	1.39213i	−0.874241	−	0.485492i	$-0.838641\pi$
$167$	−5.84539	−	17.9903i	−0.452330	−	1.39213i	0.421911	−	0.906637i	$-0.361359\pi$
$168$	−0.740117	−	2.54012i	−0.0571013	−	0.195975i
$169$	4.24331	−	3.08294i	0.326408	−	0.237150i
$170$	−5.71567	−	6.34790i	−0.438372	−	0.486861i
$171$	−7.99190	+	1.69873i	−0.611156	+	0.129905i
$172$	−2.10344	+	4.72440i	−0.160386	+	0.360233i
$173$	−5.81779	+	2.59025i	−0.442318	+	0.196933i	−0.615797	−	0.787905i	$-0.711166\pi$
$173$	−5.81779	+	2.59025i	−0.442318	+	0.196933i	0.173479	+	0.984838i	$0.444499\pi$
$174$	−7.27370	+	2.36337i	−0.551417	+	0.179166i
$175$	2.99408	+	2.31872i	0.226331	+	0.175278i
$176$	−2.48352	−	2.19821i	−0.187202	−	0.165697i
$177$	2.69267	−	4.66383i	0.202393	−	0.350555i
$178$	−3.92951	+	4.36416i	−0.294529	+	0.327107i
$179$	1.50244	−	14.2947i	0.112298	−	1.06844i	−0.782709	−	0.622387i	$-0.786163\pi$
$179$	1.50244	−	14.2947i	0.112298	−	1.06844i	0.895007	−	0.446052i	$-0.147170\pi$
$180$	1.87874	−	0.197464i	0.140033	−	0.0147181i
$181$	−2.02013	−	0.656379i	−0.150155	−	0.0487883i	0.232975	−	0.972483i	$-0.425154\pi$
$181$	−2.02013	−	0.656379i	−0.150155	−	0.0487883i	−0.383130	+	0.923694i	$0.625154\pi$
$182$	−3.20155	+	6.63589i	−0.237314	+	0.491885i
$183$	−6.17293	−	8.49631i	−0.456316	−	0.628065i
$184$	−1.22791	−	2.75793i	−0.0905227	−	0.203317i
$185$	8.52910	+	7.67964i	0.627072	+	0.564618i
$186$	3.09443	−	1.78657i	0.226894	−	0.130997i
$187$	14.2229	−	4.75541i	1.04008	−	0.347750i
$188$			10.5844i			0.771945i
$189$	−2.01949	+	1.70929i	−0.146896	+	0.124333i
$190$	−12.4870	−	9.07230i	−0.905899	−	0.658174i
$191$	−0.940761	−	8.95075i	−0.0680711	−	0.647653i	−0.974360	−	0.224995i	$-0.927764\pi$
$191$	−0.940761	−	8.95075i	−0.0680711	−	0.647653i	0.906289	−	0.422659i	$-0.138903\pi$
$192$	0.207912	+	0.978148i	0.0150047	+	0.0705917i
$193$	−1.08354	−	5.09764i	−0.0779947	−	0.366936i	0.921790	−	0.387690i	$-0.126727\pi$
$193$	−1.08354	−	5.09764i	−0.0779947	−	0.366936i	−0.999785	+	0.0207535i	$0.993393\pi$
$194$	0.444679	+	4.23084i	0.0319261	+	0.303756i
$195$	−4.25600	−	3.09216i	−0.304778	−	0.221434i
$196$	0.304010	+	6.99340i	0.0217150	+	0.499528i
$197$			13.2975i			0.947410i	0.880684	+	0.473705i	$0.157084\pi$
$197$			13.2975i			0.947410i	−0.880684	+	0.473705i	$0.842916\pi$
$198$	−0.998029	+	3.16290i	−0.0709269	+	0.224778i
$199$	−18.6246	+	10.7529i	−1.32026	+	0.762254i	−0.983770	−	0.179432i	$-0.942574\pi$
$199$	−18.6246	+	10.7529i	−1.32026	+	0.762254i	−0.336493	+	0.941686i	$0.609241\pi$
$200$	−1.06369	−	0.957747i	−0.0752139	−	0.0677229i
$201$	1.74219	+	3.91302i	0.122884	+	0.276003i
$202$	3.55541	+	4.89360i	0.250158	+	0.344312i
$203$	20.1792	−	1.49765i	1.41631	−	0.105115i
$204$	−4.30041	−	1.39729i	−0.301089	−	0.0978296i
$205$	1.35536	−	0.142454i	0.0946625	−	0.00994943i
$206$	1.45076	−	13.8031i	0.101079	−	0.961705i
$207$	−2.02006	+	2.24350i	−0.140404	+	0.155934i
$208$	1.39239	−	2.41169i	0.0965448	−	0.167220i
$209$	23.3517	−	13.7482i	1.61527	−	0.950986i
$210$	−4.95235	−	0.674464i	−0.341745	−	0.0465424i
$211$	−23.9569	+	7.78407i	−1.64926	+	0.535877i	−0.978580	−	0.205868i	$-0.933998\pi$
$211$	−23.9569	+	7.78407i	−1.64926	+	0.535877i	−0.670682	+	0.741745i	$0.733998\pi$
$212$	2.09270	−	0.931731i	0.143727	−	0.0639915i
$213$	−5.56067	+	12.4895i	−0.381011	+	0.855765i
$214$	−6.52991	+	1.38797i	−0.446375	+	0.0948800i
$215$	6.53704	+	7.26012i	0.445822	+	0.495136i
$216$	0.809017	−	0.587785i	0.0550466	−	0.0399937i
$217$	−9.07620	+	2.64454i	−0.616133	+	0.179523i
$218$	3.27223	+	10.0709i	0.221623	+	0.682086i
$219$	2.73847	+	1.58105i	0.185048	+	0.106838i
$220$	−5.70186	+	2.59696i	−0.384419	+	0.175087i
$221$	6.29598	+	10.9050i	0.423514	+	0.733547i
$222$	5.94266	+	1.26315i	0.398845	+	0.0847772i
$223$	−6.77373	+	9.32324i	−0.453602	+	0.624330i	−0.973167	−	0.230101i	$-0.926094\pi$
$223$	−6.77373	+	9.32324i	−0.453602	+	0.624330i	0.519564	+	0.854431i	$0.326094\pi$
$224$	0.0810480	−	2.64451i	0.00541524	−	0.176694i
$225$	−0.442305	+	1.36128i	−0.0294870	+	0.0907517i
$226$	4.97671	−	4.48105i	0.331046	−	0.298075i
$227$	−1.54828	−	0.689339i	−0.102763	−	0.0457530i	0.354711	−	0.934976i	$-0.384579\pi$
$227$	−1.54828	−	0.689339i	−0.102763	−	0.0457530i	−0.457474	+	0.889223i	$0.651246\pi$
$228$	−8.12568	−	0.854044i	−0.538137	−	0.0565604i
$229$	−0.727651	+	3.42333i	−0.0480845	+	0.226220i	−0.995628	−	0.0934070i	$-0.970224\pi$
$229$	−0.727651	+	3.42333i	−0.0480845	+	0.226220i	0.947543	+	0.319627i	$0.103558\pi$
$230$	−5.70304			−0.376047
$231$	4.55459	−	7.50038i	0.299670	−	0.493489i
$232$	−7.64802			−0.502117
$233$	−5.47111	+	25.7396i	−0.358425	+	1.68625i	0.316680	+	0.948532i	$0.397432\pi$
$233$	−5.47111	+	25.7396i	−0.358425	+	1.68625i	−0.675104	+	0.737722i	$0.735901\pi$
$234$	−2.76952	−	0.291088i	−0.181049	−	0.0190290i
$235$	18.2662	+	8.13264i	1.19156	+	0.530515i
$236$	4.00208	−	3.60349i	0.260513	−	0.234567i
$237$	−1.55637	+	4.79001i	−0.101097	+	0.311145i
$238$	10.1724	+	6.29624i	0.659382	+	0.408124i
$239$	−1.86014	+	2.56027i	−0.120323	+	0.165610i	−0.864929	−	0.501893i	$-0.832637\pi$
$239$	−1.86014	+	2.56027i	−0.120323	+	0.165610i	0.744607	+	0.667503i	$0.232637\pi$
$240$	1.84781	+	0.392764i	0.119276	+	0.0253528i
$241$	0.919616	+	1.59282i	0.0592377	+	0.102603i	0.894123	−	0.447821i	$-0.147800\pi$
$241$	0.919616	+	1.59282i	0.0592377	+	0.102603i	−0.834886	+	0.550423i	$0.814466\pi$
$242$	−0.187101	−	10.9984i	−0.0120273	−	0.707004i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−3.24530	−	9.98801i	−0.207759	−	0.639417i
$245$	12.3026	+	4.84882i	0.785984	+	0.309779i
$246$	0.583640	−	0.424039i	0.0372115	−	0.0270358i
$247$	15.2246	+	16.9087i	0.968720	+	1.07587i
$248$	3.49505	−	0.742896i	0.221936	−	0.0471740i
$249$	4.49453	−	10.0949i	0.284829	−	0.639737i
$250$	−11.0990	+	4.94160i	−0.701963	+	0.312534i
$251$	−24.8863	+	8.08607i	−1.57081	+	0.510388i	−0.959669	−	0.281132i	$-0.909290\pi$
$251$	−24.8863	+	8.08607i	−1.57081	+	0.510388i	−0.611143	+	0.791520i	$0.709290\pi$
$252$	−2.44884	+	1.00158i	−0.154263	+	0.0630935i
$253$	3.99457	−	9.18132i	0.251137	−	0.577225i
$254$	10.4985	−	18.1839i	0.658734	−	1.14096i
$255$	−5.71567	+	6.34790i	−0.357929	+	0.397521i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	−11.4633	+	1.20484i	−0.715061	+	0.0751560i	−0.455071	−	0.890455i	$-0.650386\pi$
$257$	−11.4633	+	1.20484i	−0.715061	+	0.0751560i	−0.259990	+	0.965611i	$0.583719\pi$
$258$	4.91839	+	1.59808i	0.306206	+	0.0994923i
$259$	−14.4772	−	6.98467i	−0.899571	−	0.434006i
$260$	−3.09216	−	4.25600i	−0.191768	−	0.263946i
$261$	3.11073	+	6.98681i	0.192549	+	0.432473i
$262$	−4.85989	−	4.37587i	−0.300245	−	0.270342i
$263$	0.308534	−	0.178132i	0.0190250	−	0.0109841i	−0.490457	−	0.871465i	$-0.663170\pi$
$263$	0.308534	−	0.178132i	0.0190250	−	0.0109841i	0.509482	+	0.860481i	$0.329837\pi$
$264$	−1.92657	+	2.69969i	−0.118572	+	0.166154i
$265$		−	4.32743i		−	0.265832i
$266$	20.3447	+	7.30666i	1.24741	+	0.448000i
$267$	4.75100	+	3.45180i	0.290756	+	0.211247i
$268$	0.447730	+	4.25987i	0.0273495	+	0.260213i
$269$	−2.48535	−	11.6926i	−0.151534	−	0.712913i	−0.986652	−	0.162842i	$-0.947934\pi$
$269$	−2.48535	−	11.6926i	−0.151534	−	0.712913i	0.835118	−	0.550071i	$-0.185399\pi$
$270$	−0.392764	−	1.84781i	−0.0239029	−	0.112454i
$271$	2.63118	+	25.0340i	0.159833	+	1.52071i	0.720959	+	0.692978i	$0.243702\pi$
$271$	2.63118	+	25.0340i	0.159833	+	1.52071i	−0.561126	+	0.827731i	$0.689632\pi$
$272$	−3.65814	−	2.65780i	−0.221808	−	0.161153i
$273$	6.93419	+	2.49037i	0.419676	+	0.150724i
$274$		−	11.4543i		−	0.691979i
$275$	−0.0403743	−	4.74701i	−0.00243466	−	0.286256i
$276$	−2.61447	+	1.50946i	−0.157373	+	0.0908591i
$277$	−8.83550	−	7.95552i	−0.530874	−	0.478001i	0.359555	−	0.933124i	$-0.382929\pi$
$277$	−8.83550	−	7.95552i	−0.530874	−	0.478001i	−0.890429	+	0.455123i	$0.849595\pi$
$278$	−7.15093	−	16.0613i	−0.428884	−	0.963290i
$279$	−2.10024	−	2.89073i	−0.125738	−	0.173063i
$280$	−4.50155	−	2.17181i	−0.269019	−	0.129791i
$281$	16.7826	+	5.45299i	1.00116	+	0.325298i	0.763331	−	0.646008i	$-0.223563\pi$
$281$	16.7826	+	5.45299i	1.00116	+	0.325298i	0.237834	+	0.971306i	$0.423563\pi$
$282$	10.5264	−	1.10637i	0.626838	−	0.0658833i
$283$	−1.62836	+	15.4928i	−0.0967957	+	0.920950i	0.833099	+	0.553124i	$0.186564\pi$
$283$	−1.62836	+	15.4928i	−0.0967957	+	0.920950i	−0.929895	+	0.367826i	$0.880102\pi$
$284$	−9.14797	+	10.1599i	−0.542832	+	0.602876i
$285$	−7.71736	+	13.3669i	−0.457137	+	0.791785i
$286$	9.01757	−	1.99705i	0.533220	−	0.118088i
$287$	−1.76664	+	0.722557i	−0.104282	+	0.0426512i
$288$	0.951057	−	0.309017i	0.0560415	−	0.0182090i
$289$	3.14799	−	1.40157i	0.185176	−	0.0824455i
$290$	−5.87645	+	13.1987i	−0.345077	+	0.775056i
$291$	4.16118	−	0.884486i	0.243933	−	0.0518495i
$292$	2.11586	+	2.34990i	0.123822	+	0.137518i
$293$	8.57346	−	6.22899i	0.500867	−	0.363901i	−0.308481	−	0.951230i	$-0.599821\pi$
$293$	8.57346	−	6.22899i	0.500867	−	0.363901i	0.809348	+	0.587329i	$0.199821\pi$
$294$	6.92331	−	1.03335i	0.403775	−	0.0602664i
$295$	−3.14375	−	9.67547i	−0.183036	−	0.563327i
$296$	5.26147	+	3.03771i	0.305817	+	0.176563i
$297$	3.24990	+	0.661949i	0.188578	+	0.0384102i
$298$	10.4043	+	18.0207i	0.602704	+	1.04391i
$299$	8.22333	+	1.74792i	0.475568	+	0.101085i
$300$	−0.841315	+	1.15797i	−0.0485733	+	0.0668554i
$301$	−11.6343	−	7.20103i	−0.670589	−	0.415061i
$302$	−6.10664	+	18.7943i	−0.351398	+	1.08149i
$303$	4.49515	−	4.04745i	0.258240	−	0.232520i
$304$	−7.46407	−	3.32322i	−0.428094	−	0.190600i
$305$	−19.7306	−	2.07377i	−1.12977	−	0.118744i
$306$	−0.940117	+	4.42290i	−0.0537429	+	0.252841i
$307$	−20.9921			−1.19808			−0.599042	−	0.800718i	$-0.704452\pi$
$307$	−20.9921			−1.19808			−0.599042	+	0.800718i	$0.704452\pi$
$308$	6.64942	−	5.72584i	0.378886	−	0.326260i
$309$	−13.8791			−0.789554
$310$	1.40340	−	6.60248i	0.0797078	−	0.374996i
$311$	−9.13264	−	0.959879i	−0.517864	−	0.0544297i	−0.158009	−	0.987438i	$-0.550507\pi$
$311$	−9.13264	−	0.959879i	−0.517864	−	0.0544297i	−0.359856	+	0.933008i	$0.617174\pi$
$312$	−2.54402	−	1.13267i	−0.144027	−	0.0641249i
$313$	2.73040	−	2.45846i	0.154331	−	0.138961i	−0.588348	−	0.808608i	$-0.700221\pi$
$313$	2.73040	−	2.45846i	0.154331	−	0.138961i	0.742679	+	0.669647i	$0.233555\pi$
$314$	4.29679	−	13.2242i	0.242482	−	0.746283i
$315$	−0.153107	+	4.99572i	−0.00862661	+	0.281477i
$316$	−2.96039	+	4.07463i	−0.166535	+	0.229216i
$317$	−20.1852	−	4.29051i	−1.13372	−	0.240979i	−0.397419	−	0.917637i	$-0.630094\pi$
$317$	−20.1852	−	4.29051i	−1.13372	−	0.240979i	−0.736297	+	0.676658i	$0.763427\pi$
$318$	−1.14537	−	1.98385i	−0.0642294	−	0.111249i
$319$	−17.1326	−	18.7053i	−0.959242	−	1.04729i
$320$	1.63600	+	0.944546i	0.0914553	+	0.0528017i
$321$	2.06293	+	6.34905i	0.115142	+	0.354370i
$322$	7.66845	−	2.23436i	0.427346	−	0.124516i
$323$	29.8887	−	21.7154i	1.66305	−	1.20828i
$324$	−0.669131	−	0.743145i	−0.0371739	−	0.0412858i
$325$	3.89883	−	0.828722i	0.216268	−	0.0459692i
$326$	0.0498632	−	0.111995i	0.00276167	−	0.00620281i
$327$	9.67366	−	4.30699i	0.534955	−	0.238177i
$328$	0.686110	−	0.222931i	0.0378841	−	0.0123093i
$329$	−27.7475	−	3.77894i	−1.52977	−	0.208340i
$330$	3.17874	+	5.39917i	0.174984	+	0.297214i
$331$	−3.30821	+	5.72998i	−0.181836	+	0.314948i	−0.942506	−	0.334190i	$-0.891537\pi$
$331$	−3.30821	+	5.72998i	−0.181836	+	0.314948i	0.760670	+	0.649139i	$0.224871\pi$
$332$	7.39404	−	8.21192i	0.405801	−	0.450688i
$333$	0.635055	−	6.04214i	0.0348008	−	0.331107i
$334$	−18.8125	+	1.97727i	−1.02937	+	0.108191i
$335$	7.69557	+	2.50044i	0.420454	+	0.136614i
$336$	−2.63849	+	0.195823i	−0.143942	+	0.0106830i
$337$	−12.4912	−	17.1926i	−0.680437	−	0.936541i	0.319502	−	0.947586i	$-0.396484\pi$
$337$	−12.4912	−	17.1926i	−0.680437	−	0.936541i	−0.999939	+	0.0110446i	$0.996484\pi$
$338$	−2.13334	−	4.79156i	−0.116038	−	0.260627i
$339$	−4.97671	−	4.48105i	−0.270298	−	0.243377i
$340$	−7.39753	+	4.27097i	−0.401188	+	0.231626i
$341$	9.64635	+	6.88390i	0.522379	+	0.372784i
$342$			8.17044i			0.441807i
$343$	−18.4421	−	1.69988i	−0.995779	−	0.0917848i
$344$	4.18384	+	3.03973i	0.225577	+	0.163891i
$345$	0.596130	+	5.67180i	0.0320945	+	0.305359i
$346$	1.32406	+	6.22920i	0.0711817	+	0.334884i
$347$	−1.81638	−	8.54541i	−0.0975086	−	0.458742i	−0.999628	−	0.0272563i	$-0.991323\pi$
$347$	−1.81638	−	8.54541i	−0.0975086	−	0.458742i	0.902120	−	0.431485i	$-0.142010\pi$
$348$	0.799435	+	7.60612i	0.0428542	+	0.407731i
$349$	−17.2815	−	12.5557i	−0.925055	−	0.672092i	0.0197222	−	0.999805i	$-0.493722\pi$
$349$	−17.2815	−	12.5557i	−0.925055	−	0.672092i	−0.944777	+	0.327714i	$0.893722\pi$
$350$	2.89055	−	2.44656i	0.154506	−	0.130774i
$351$			2.78478i			0.148640i
$352$	−2.66653	+	1.97221i	−0.142126	+	0.105119i
$353$	25.0099	−	14.4395i	1.33114	−	0.768535i	0.345668	−	0.938357i	$-0.387652\pi$
$353$	25.0099	−	14.4395i	1.33114	−	0.768535i	0.985475	+	0.169821i	$0.0543191\pi$
$354$	−4.00208	−	3.60349i	−0.212708	−	0.191523i
$355$	10.5046	+	23.5938i	0.557528	+	1.25223i
$356$	3.45180	+	4.75100i	0.182945	+	0.251802i
$357$	5.19843	−	10.7749i	0.275130	−	0.570266i
$358$	−13.6700	−	4.44165i	−0.722482	−	0.234749i
$359$	−28.9410	+	3.04182i	−1.52745	+	0.160541i	−0.830677	−	0.556755i	$-0.812046\pi$
$359$	−28.9410	+	3.04182i	−1.52745	+	0.160541i	−0.696768	+	0.717296i	$0.745379\pi$
$360$	0.197464	−	1.87874i	0.0104073	−	0.0990185i
$361$	31.9551	−	35.4897i	1.68185	−	1.86788i
$362$	−1.06204	+	1.83951i	−0.0558198	+	0.0966827i
$363$	−10.9186	+	1.33572i	−0.573078	+	0.0701073i
$364$	5.82524	+	4.51126i	0.305325	+	0.236454i
$365$	5.68115	−	1.84592i	0.297365	−	0.0966197i
$366$	−9.59407	+	4.27156i	−0.501490	+	0.223278i
$367$	−11.4885	+	25.8036i	−0.599695	+	1.34694i	0.317410	+	0.948288i	$0.397187\pi$
$367$	−11.4885	+	25.8036i	−0.599695	+	1.34694i	−0.917104	+	0.398647i	$0.869480\pi$
$368$	−2.95296	+	0.627671i	−0.153934	+	0.0327196i
$369$	−0.482723	−	0.536119i	−0.0251296	−	0.0279092i
$370$	9.28512	−	6.74604i	0.482710	−	0.350710i
$371$	1.69542	+	5.81878i	0.0880219	+	0.302096i
$372$	−1.10416	−	3.39825i	−0.0572480	−	0.176191i
$373$	8.28769	+	4.78490i	0.429120	+	0.247753i	0.698972	−	0.715149i	$-0.253641\pi$
$373$	8.28769	+	4.78490i	0.429120	+	0.247753i	−0.269852	+	0.962902i	$0.586975\pi$
$374$	−1.69439	−	14.9008i	−0.0876146	−	0.770502i
$375$	6.07469	+	10.5217i	0.313696	+	0.543337i
$376$	10.3531	+	2.20062i	0.533919	+	0.113488i
$377$	12.5187	−	17.2305i	0.644744	−	0.887414i
$378$	1.25207	+	2.33074i	0.0643993	+	0.119880i
$379$	−5.89404	+	18.1400i	−0.302757	+	0.931789i	0.677748	+	0.735294i	$0.262956\pi$
$379$	−5.89404	+	18.1400i	−0.302757	+	0.931789i	−0.980505	+	0.196495i	$0.937044\pi$
$380$	−11.4702	+	10.3278i	−0.588411	+	0.529807i
$381$	−19.1817	−	8.54024i	−0.982708	−	0.437530i
$382$	−8.95075	−	0.940761i	−0.457960	−	0.0481335i
$383$	4.98553	−	23.4551i	0.254748	−	1.19850i	−0.645719	−	0.763575i	$-0.723442\pi$
$383$	4.98553	−	23.4551i	0.254748	−	1.19850i	0.900468	−	0.434922i	$-0.143224\pi$
$384$	1.00000			0.0510310
$385$	−4.77233	−	15.8749i	−0.243220	−	0.809060i
$386$	−5.21153			−0.265260
$387$	1.07522	−	5.05850i	0.0546563	−	0.257138i
$388$	4.23084	+	0.444679i	0.214788	+	0.0225751i
$389$	16.9768	+	7.55857i	0.860759	+	0.383235i	0.789152	−	0.614198i	$-0.210520\pi$
$389$	16.9768	+	7.55857i	0.860759	+	0.383235i	0.0716075	+	0.997433i	$0.477187\pi$
$390$	−3.90946	+	3.52010i	−0.197963	+	0.178247i
$391$	4.21831	−	12.9826i	0.213329	−	0.656559i
$392$	6.90378	+	1.15664i	0.348694	+	0.0584192i
$393$	−3.84390	+	5.29067i	−0.193899	+	0.266879i
$394$	13.0069	+	2.76471i	0.655281	+	0.139284i
$395$	4.75722	+	8.23975i	0.239362	+	0.414587i
$396$	2.88628	+	1.63382i	0.145041	+	0.0821027i
$397$	18.4527	+	10.6536i	0.926112	+	0.534691i	0.885580	−	0.464487i	$-0.153761\pi$
$397$	18.4527	+	10.6536i	0.926112	+	0.534691i	0.0405324	+	0.999178i	$0.487095\pi$
$398$	6.64567	+	20.4533i	0.333117	+	1.02523i
$399$	5.14004	−	20.9970i	0.257324	−	1.05116i
$400$	−1.15797	+	0.841315i	−0.0578985	+	0.0420657i
$401$	4.86843	+	5.40693i	0.243118	+	0.270009i	0.852338	−	0.522992i	$-0.175184\pi$
$401$	4.86843	+	5.40693i	0.243118	+	0.270009i	−0.609220	+	0.793001i	$0.708517\pi$
$402$	4.18973	−	0.890554i	0.208965	−	0.0444168i
$403$	−4.04719	+	9.09013i	−0.201605	+	0.452811i
$404$	5.52587	−	2.46028i	0.274922	−	0.122403i
$405$	−1.79663	+	0.583762i	−0.0892754	+	0.0290074i
$406$	2.73058	−	20.0497i	0.135516	−	0.995048i
$407$	4.35688	+	19.6732i	0.215962	+	0.975166i
$408$	−2.26086	+	3.91592i	−0.111929	+	0.193867i
$409$	23.4302	−	26.0219i	1.15855	−	1.28670i	0.207301	−	0.978277i	$-0.433532\pi$
$409$	23.4302	−	26.0219i	1.15855	−	1.28670i	0.951249	−	0.308423i	$-0.0998013\pi$
$410$	0.142454	−	1.35536i	0.00703531	−	0.0669365i
$411$	−11.3915	+	1.19730i	−0.561903	+	0.0590584i
$412$	−13.1998	−	4.28888i	−0.650308	−	0.211298i
$413$	8.01787	+	11.7782i	0.394533	+	0.579568i
$414$	1.77448	+	2.44237i	0.0872110	+	0.120036i
$415$	−8.49059	−	19.0702i	−0.416787	−	0.936118i
$416$	−2.06949	−	1.86338i	−0.101465	−	0.0913597i
$417$	−15.2258	+	8.79062i	−0.745610	+	0.430478i
$418$	−8.59272	−	25.6999i	−0.420284	−	1.25702i
$419$		−	14.5321i		−	0.709940i	−0.934878	−	0.354970i	$-0.884491\pi$
$419$		−	14.5321i		−	0.709940i	0.934878	−	0.354970i	$-0.115509\pi$
$420$	−1.68938	+	4.70390i	−0.0824331	+	0.229527i
$421$	−2.20107	−	1.59917i	−0.107274	−	0.0779389i	0.532855	−	0.846206i	$-0.321119\pi$
$421$	−2.20107	−	1.59917i	−0.107274	−	0.0779389i	−0.640129	+	0.768268i	$0.721119\pi$
$422$	2.63305	+	25.0518i	0.128175	+	1.21950i
$423$	−2.20062	−	10.3531i	−0.106998	−	0.503384i
$424$	−0.476273	−	2.24069i	−0.0231299	−	0.108817i
$425$	−0.676515	−	6.43661i	−0.0328158	−	0.312221i
$426$	11.0604	+	8.03587i	0.535879	+	0.389339i
$427$	27.3428	−	4.94170i	1.32321	−	0.239146i
$428$			6.67579i			0.322687i
$429$	−2.92870	−	8.75942i	−0.141399	−	0.422909i
$430$	8.46059	−	4.88473i	0.408006	−	0.235562i
$431$	9.30690	+	8.37997i	0.448297	+	0.403649i	0.862116	−	0.506710i	$-0.169139\pi$
$431$	9.30690	+	8.37997i	0.448297	+	0.403649i	−0.413819	+	0.910359i	$0.635805\pi$
$432$	−0.406737	−	0.913545i	−0.0195691	−	0.0439530i
$433$	15.1412	+	20.8400i	0.727638	+	1.00151i	0.999235	+	0.0390972i	$0.0124482\pi$
$433$	15.1412	+	20.8400i	0.727638	+	1.00151i	−0.271597	+	0.962411i	$0.587552\pi$
$434$	0.699700	+	9.42770i	0.0335867	+	0.452544i
$435$	13.7407	+	4.46462i	0.658815	+	0.214062i
$436$	10.5311	−	1.10687i	0.504350	−	0.0530093i
$437$	2.57830	−	24.5309i	0.123337	−	1.17347i
$438$	2.11586	−	2.34990i	0.101100	−	0.112283i
$439$	8.85368	−	15.3350i	0.422563	−	0.731900i	−0.573626	−	0.819117i	$-0.694464\pi$
$439$	8.85368	−	15.3350i	0.422563	−	0.731900i	0.996189	+	0.0872166i	$0.0277972\pi$
$440$	1.35473	+	6.11720i	0.0645841	+	0.291626i
$441$	−1.75138	−	6.77737i	−0.0833988	−	0.322732i
$442$	11.9757	−	3.89113i	0.569625	−	0.185082i
$443$	−4.05463	+	1.80524i	−0.192641	+	0.0857693i	−0.500790	−	0.865569i	$-0.666957\pi$
$443$	−4.05463	+	1.80524i	−0.192641	+	0.0857693i	0.308149	+	0.951338i	$0.400290\pi$
$444$	2.47110	−	5.55018i	0.117273	−	0.263400i
$445$	10.8514	−	2.30653i	0.514404	−	0.109340i
$446$	7.71117	+	8.56412i	0.365134	+	0.405523i
$447$	16.8345	−	12.2310i	0.796243	−	0.578505i
$448$	−2.56987	−	0.629101i	−0.121415	−	0.0297222i
$449$	−4.81349	−	14.8144i	−0.227163	−	0.699135i	−0.998065	−	0.0621811i	$-0.980194\pi$
$449$	−4.81349	−	14.8144i	−0.227163	−	0.699135i	0.770902	−	0.636953i	$-0.219806\pi$
$450$	1.23957	+	0.715665i	0.0584338	+	0.0337368i
$451$	2.08222	+	1.17867i	0.0980478	+	0.0555015i
$452$	−3.34841	−	5.79962i	−0.157496	−	0.272791i
$453$	19.3297	+	4.10865i	0.908187	+	0.193041i
$454$	−0.996181	+	1.37112i	−0.0467531	+	0.0643501i
$455$	12.2613	−	6.58674i	0.574819	−	0.308791i
$456$	−2.52481	+	7.77055i	−0.118235	+	0.363889i
$457$	−25.1633	+	22.6571i	−1.17709	+	1.05986i	−0.179996	+	0.983667i	$0.557608\pi$
$457$	−25.1633	+	22.6571i	−1.17709	+	1.05986i	−0.997093	+	0.0761885i	$0.975725\pi$
$458$	3.19723	+	1.42350i	0.149397	+	0.0665158i
$459$	4.49694	+	0.472648i	0.209899	+	0.0220613i
$460$	−1.18573	+	5.57841i	−0.0552849	+	0.260095i
$461$	−3.87045			−0.180265			−0.0901324	−	0.995930i	$-0.528729\pi$
$461$	−3.87045			−0.180265			−0.0901324	+	0.995930i	$0.528729\pi$
$462$	−6.38953	−	6.01448i	−0.297268	−	0.279819i
$463$	18.6532			0.866886			0.433443	−	0.901181i	$-0.357299\pi$
$463$	18.6532			0.866886			0.433443	+	0.901181i	$0.357299\pi$
$464$	−1.59011	+	7.48089i	−0.0738191	+	0.347292i
$465$	−6.71300	−	0.705565i	−0.311308	−	0.0327198i
$466$	24.0396	+	10.7031i	1.11361	+	0.495812i
$467$	22.9177	−	20.6352i	1.06050	−	0.954882i	0.0614387	−	0.998111i	$-0.480431\pi$
$467$	22.9177	−	20.6352i	1.06050	−	0.954882i	0.999065	+	0.0432289i	$0.0137645\pi$
$468$	−0.860543	+	2.64848i	−0.0397786	+	0.122426i
$469$	−11.3273	−	0.347155i	−0.523046	−	0.0160301i
$470$	11.7527	−	16.1762i	0.542111	−	0.746152i
$471$	−13.6009	−	2.89095i	−0.626695	−	0.133208i
$472$	−2.69267	−	4.66383i	−0.123940	−	0.214670i
$473$	1.93788	+	17.0421i	0.0891037	+	0.783597i
$474$	4.36175	+	2.51826i	0.200342	+	0.115667i
$475$	−3.61383	−	11.1222i	−0.165814	−	0.510323i
$476$	8.27362	−	8.64110i	0.379221	−	0.396064i
$477$	−1.85325	+	1.34647i	−0.0848547	+	0.0616505i
$478$	2.11757	+	2.35180i	0.0968555	+	0.107569i
$479$	13.8040	−	2.93413i	0.630721	−	0.134064i	0.118551	−	0.992948i	$-0.462175\pi$
$479$	13.8040	−	2.93413i	0.630721	−	0.134064i	0.512170	+	0.858884i	$0.328842\pi$
$480$	0.768363	−	1.72577i	0.0350708	−	0.0787703i
$481$	−15.4560	+	6.88146i	−0.704733	+	0.313767i
$482$	1.74921	−	0.568354i	0.0796745	−	0.0258878i
$483$	−3.02369	−	7.39289i	−0.137583	−	0.336388i
$484$	−10.7970	−	2.10369i	−0.490771	−	0.0956221i
$485$	4.01823	−	6.95978i	0.182459	−	0.316027i
$486$	−0.669131	+	0.743145i	−0.0303524	+	0.0337097i
$487$	−2.69673	+	25.6576i	−0.122200	+	1.16266i	0.745826	+	0.666140i	$0.232055\pi$
$487$	−2.69673	+	25.6576i	−0.122200	+	1.16266i	−0.868027	+	0.496518i	$0.834612\pi$
$488$	−10.4445	+	1.09776i	−0.472800	+	0.0496932i
$489$	−0.116593	−	0.0378834i	−0.00527253	−	0.00171315i
$490$	7.30071	−	11.0256i	0.329812	−	0.498087i
$491$	−19.7190	−	27.1408i	−0.889905	−	1.22485i	−0.973578	−	0.228356i	$-0.926665\pi$
$491$	−19.7190	−	27.1408i	−0.889905	−	1.22485i	0.0836728	−	0.996493i	$-0.473335\pi$
$492$	−0.293427	−	0.659049i	−0.0132287	−	0.0297122i
$493$	−25.6995	−	23.1400i	−1.15745	−	1.04217i
$494$	19.7046	−	11.3764i	0.886550	−	0.511850i
$495$	5.03732	−	3.72569i	0.226411	−	0.167457i
$496$		−	3.57313i		−	0.160438i
$497$	−23.3685	−	27.6093i	−1.04822	−	1.23844i
$498$	−8.93982	−	6.49516i	−0.400603	−	0.291055i
$499$	0.376448	+	3.58166i	0.0168521	+	0.160337i	0.999711	−	0.0240197i	$-0.00764644\pi$
$499$	0.376448	+	3.58166i	0.0168521	+	0.160337i	−0.982859	+	0.184357i	$0.940980\pi$
$500$	2.52600	+	11.8839i	0.112966	+	0.531463i
$501$	3.93288	+	18.5027i	0.175708	+	0.826641i
$502$	2.73520	+	26.0237i	0.122078	+	1.16150i
$503$	15.2498	+	11.0797i	0.679957	+	0.494018i	0.873343	−	0.487105i	$-0.161947\pi$
$503$	15.2498	+	11.0797i	0.679957	+	0.494018i	−0.193386	+	0.981123i	$0.561947\pi$
$504$	0.470548	+	2.60357i	0.0209599	+	0.115972i
$505$		−	11.4268i		−	0.508485i
$506$	−8.15017	−	5.81619i	−0.362319	−	0.258561i
$507$	−4.54232	+	2.62251i	−0.201731	+	0.116470i
$508$	−15.6038	−	14.0497i	−0.692307	−	0.623356i
$509$	−8.02734	−	18.0297i	−0.355806	−	0.799152i	−0.999428	−	0.0338095i	$-0.989236\pi$
$509$	−8.02734	−	18.0297i	−0.355806	−	0.799152i	0.643623	−	0.765343i	$-0.277431\pi$
$510$	5.02082	+	6.91057i	0.222326	+	0.306005i
$511$	−6.91582	+	4.70785i	−0.305938	+	0.208263i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$	8.12568	−	0.854044i	0.358758	−	0.0377070i
$514$	−1.20484	+	11.4633i	−0.0531433	+	0.505625i
$515$	−17.5439	+	19.4844i	−0.773075	+	0.858587i
$516$	2.58575	−	4.47865i	0.113831	−	0.197162i
$517$	17.8101	+	30.2509i	0.783288	+	1.33043i
$518$	−9.84202	+	12.7087i	−0.432434	+	0.558387i
$519$	6.05667	−	1.96793i	0.265858	−	0.0863826i
$520$	−4.80589	+	2.13972i	−0.210752	+	0.0938329i
$521$	−7.61505	+	17.1037i	−0.333621	+	0.749326i	0.666372	+	0.745620i	$0.267846\pi$
$521$	−7.61505	+	17.1037i	−0.333621	+	0.749326i	−0.999993	+	0.00370631i	$0.998820\pi$
$522$	7.48089	−	1.59011i	0.327430	−	0.0695973i
$523$	13.8355	+	15.3659i	0.604985	+	0.671904i	0.965365	−	0.260902i	$-0.0840198\pi$
$523$	13.8355	+	15.3659i	0.604985	+	0.671904i	−0.360381	+	0.932805i	$0.617353\pi$
$524$	−5.29067	+	3.84390i	−0.231124	+	0.167921i
$525$	−2.73530	−	2.61898i	−0.119378	−	0.114302i
$526$	−0.110092	−	0.338827i	−0.00480022	−	0.0147736i
$527$	13.9921	+	8.07835i	0.609506	+	0.351898i
$528$	2.24014	+	2.44577i	0.0974895	+	0.106438i
$529$	6.94303	+	12.0257i	0.301871	+	0.522856i
$530$	−4.23287	−	0.899724i	−0.183864	−	0.0390815i
$531$	−3.16542	+	4.35682i	−0.137367	+	0.189070i
$532$	11.3769	−	18.3810i	0.493251	−	0.796915i
$533$	−0.620812	+	1.91066i	−0.0268904	+	0.0827600i
$534$	4.36416	−	3.92951i	0.188856	−	0.170046i
$535$	11.5209	+	5.12943i	0.498092	+	0.221765i
$536$	4.25987	+	0.447730i	0.183998	+	0.0193390i
$537$	−2.98842	+	14.0594i	−0.128960	+	0.606708i
$538$	−11.9539			−0.515368
$539$	12.6365	+	19.4761i	0.544294	+	0.838894i
$540$	−1.88909			−0.0812936
$541$	−6.43989	+	30.2973i	−0.276872	+	1.30258i	0.591353	+	0.806413i	$0.298594\pi$
$541$	−6.43989	+	30.2973i	−0.276872	+	1.30258i	−0.868226	+	0.496170i	$0.834739\pi$
$542$	25.0340	+	2.63118i	1.07530	+	0.113019i
$543$	1.94045	+	0.863945i	0.0832727	+	0.0370754i
$544$	−3.36029	+	3.02562i	−0.144071	+	0.129722i
$545$	6.18154	−	19.0248i	0.264788	−	0.814933i
$546$	3.87765	−	6.26488i	0.165948	−	0.268112i
$547$	10.0534	−	13.8374i	0.429853	−	0.591643i	−0.538066	−	0.842903i	$-0.680845\pi$
$547$	10.0534	−	13.8374i	0.429853	−	0.591643i	0.967920	+	0.251260i	$0.0808449\pi$
$548$	−11.2040	−	2.38148i	−0.478611	−	0.101732i
$549$	5.25101	+	9.09501i	0.224108	+	0.388166i
$550$	−4.65167	−	0.947467i	−0.198348	−	0.0404001i
$551$	−54.1159	−	31.2438i	−2.30542	−	1.33103i
$552$	0.932901	+	2.87117i	0.0397069	+	0.122205i
$553$	−9.62489	−	9.21558i	−0.409292	−	0.391886i
$554$	−9.61868	+	6.98838i	−0.408658	+	0.296908i
$555$	−7.67964	−	8.52910i	−0.325983	−	0.362040i
$556$	−17.1970	+	3.65534i	−0.729317	+	0.155021i
$557$	−2.38836	+	5.36435i	−0.101198	+	0.227295i	−0.957048	−	0.289930i	$-0.906368\pi$
$557$	−2.38836	+	5.36435i	−0.101198	+	0.227295i	0.855850	+	0.517224i	$0.173035\pi$
$558$	−3.26422	+	1.45332i	−0.138185	+	0.0615241i
$559$	−13.6966	+	4.45030i	−0.579306	+	0.188228i
$560$	−3.06028	+	3.95163i	−0.129320	+	0.166987i
$561$	−14.6421	+	3.24266i	−0.618188	+	0.136905i
$562$	8.82312	−	15.2821i	0.372181	−	0.644636i
$563$	12.5827	−	13.9746i	0.530299	−	0.588957i	−0.417160	−	0.908833i	$-0.636975\pi$
$563$	12.5827	−	13.9746i	0.530299	−	0.588957i	0.947459	+	0.319876i	$0.103641\pi$
$564$	1.10637	−	10.5264i	0.0465865	−	0.443241i
$565$	−12.5816	+	1.32238i	−0.529313	+	0.0556330i
$566$	14.8157	+	4.81390i	0.622749	+	0.202343i
$567$	2.18709	−	1.48883i	0.0918492	−	0.0625252i
$568$	8.03587	+	11.0604i	0.337177	+	0.464085i
$569$	−5.24149	−	11.7726i	−0.219735	−	0.493533i	0.769719	−	0.638383i	$-0.220397\pi$
$569$	−5.24149	−	11.7726i	−0.219735	−	0.493533i	−0.989454	+	0.144851i	$0.953730\pi$
$570$	11.4702	+	10.3278i	0.480435	+	0.432586i
$571$	28.7484	−	16.5979i	1.20308	−	0.694600i	0.241844	−	0.970315i	$-0.422248\pi$
$571$	28.7484	−	16.5979i	1.20308	−	0.694600i	0.961240	+	0.275715i	$0.0889145\pi$
$572$	−0.0785517	−	9.23573i	−0.00328441	−	0.386165i
$573$			9.00005i			0.375982i
$574$	0.339462	+	1.87827i	0.0141689	+	0.0783973i
$575$	−3.49583	−	2.53987i	−0.145786	−	0.105920i
$576$	−0.104528	−	0.994522i	−0.00435535	−	0.0414384i
$577$	−1.19028	−	5.59981i	−0.0495518	−	0.233123i	0.946402	−	0.322992i	$-0.104689\pi$
$577$	−1.19028	−	5.59981i	−0.0495518	−	0.233123i	−0.995954	+	0.0898686i	$0.971355\pi$
$578$	−0.716443	−	3.37060i	−0.0298001	−	0.140198i
$579$	0.544753	+	5.18298i	0.0226392	+	0.215397i
$580$	11.6885	+	8.49221i	0.485340	+	0.352620i
$581$	18.8881	+	22.3158i	0.783609	+	0.925814i
$582$		−	4.25414i		−	0.176340i
$583$	4.41329	−	6.18431i	0.182780	−	0.256128i
$584$	2.73847	−	1.58105i	0.113319	−	0.0654245i
$585$	3.90946	+	3.52010i	0.161636	+	0.145538i
$586$	−4.31034	−	9.68119i	−0.178059	−	0.399926i
$587$	−5.69262	−	7.83521i	−0.234959	−	0.323394i	0.675214	−	0.737622i	$-0.264051\pi$
$587$	−5.69262	−	7.83521i	−0.234959	−	0.323394i	−0.910173	+	0.414228i	$0.864051\pi$
$588$	0.428664	−	6.98686i	0.0176778	−	0.288133i
$589$	27.7652	+	9.02147i	1.14405	+	0.371723i
$590$	−10.1177	+	1.06341i	−0.416537	+	0.0437798i
$591$	1.38997	−	13.2247i	0.0571757	−	0.543991i
$592$	4.06525	−	4.51492i	0.167081	−	0.185562i
$593$	7.28313	−	12.6148i	0.299082	−	0.518026i	−0.676844	−	0.736127i	$-0.736653\pi$
$593$	7.28313	−	12.6148i	0.299082	−	0.518026i	0.975926	+	0.218101i	$0.0699861\pi$
$594$	1.32318	−	3.04125i	0.0542905	−	0.124784i
$595$	−8.55542	−	20.9179i	−0.350738	−	0.857549i
$596$	19.7901	−	6.43020i	0.810634	−	0.263391i
$597$	19.6466	−	8.74721i	0.804080	−	0.358000i
$598$	3.41945	−	7.68022i	0.139832	−	0.314067i
$599$	−36.9878	+	7.86201i	−1.51128	+	0.321233i	−0.887662	−	0.460495i	$-0.847672\pi$
$599$	−36.9878	+	7.86201i	−1.51128	+	0.321233i	−0.623620	+	0.781728i	$0.714339\pi$
$600$	0.957747	+	1.06369i	0.0390998	+	0.0434248i
$601$	−10.9546	+	7.95895i	−0.446845	+	0.324652i	−0.788349	−	0.615228i	$-0.789064\pi$
$601$	−10.9546	+	7.95895i	−0.446845	+	0.324652i	0.341504	+	0.939880i	$0.389064\pi$
$602$	−9.46258	+	9.88286i	−0.385666	+	0.402795i
$603$	−1.32362	−	4.07369i	−0.0539020	−	0.165893i
$604$	17.1140	+	9.88076i	0.696358	+	0.402042i
$605$	−11.9265	+	17.0167i	−0.484880	+	0.691828i
$606$	−3.02441	−	5.23843i	−0.122858	−	0.212797i
$607$	−0.768343	−	0.163316i	−0.0311861	−	0.00662880i	0.192292	−	0.981338i	$-0.438408\pi$
$607$	−0.768343	−	0.163316i	−0.0311861	−	0.00662880i	−0.223478	+	0.974709i	$0.571741\pi$
$608$	−4.80247	+	6.61003i	−0.194766	+	0.268072i
$609$	−20.2253	−	0.619856i	−0.819569	−	0.0251178i
$610$	−6.13068	+	18.8683i	−0.248224	+	0.763954i
$611$	−21.9043	+	19.7227i	−0.886152	+	0.797895i
$612$	4.13079	+	1.83915i	0.166977	+	0.0743431i
$613$	27.2888	+	2.86817i	1.10219	+	0.115844i	0.638105	−	0.769949i	$-0.279718\pi$
$613$	27.2888	+	2.86817i	1.10219	+	0.115844i	0.464080	+	0.885793i	$0.346385\pi$
$614$	−4.36451	+	20.5334i	−0.176137	+	0.828660i
$615$	−1.36283			−0.0549545
$616$	−4.21822	−	7.69458i	−0.169957	−	0.310024i
$617$	−33.1892			−1.33614			−0.668072	−	0.744096i	$-0.732880\pi$
$617$	−33.1892			−1.33614			−0.668072	+	0.744096i	$0.732880\pi$
$618$	−2.88563	+	13.5758i	−0.116077	+	0.546099i
$619$	20.9652	+	2.20353i	0.842661	+	0.0885672i	0.516015	−	0.856580i	$-0.327415\pi$
$619$	20.9652	+	2.20353i	0.842661	+	0.0885672i	0.326646	+	0.945147i	$0.394082\pi$
$620$	−6.16642	−	2.74546i	−0.247649	−	0.110261i
$621$	2.24350	−	2.02006i	0.0900286	−	0.0810621i
$622$	−2.83768	+	8.73350i	−0.113781	+	0.350181i
$623$	−13.6874	+	7.35282i	−0.548373	+	0.294585i
$624$	−1.63685	+	2.25293i	−0.0655265	+	0.0901894i
$625$	15.4495	+	3.28389i	0.617980	+	0.131356i
$626$	−1.83706	−	3.18188i	−0.0734236	−	0.127173i
$627$	−24.6609	+	11.2320i	−0.984861	+	0.448563i
$628$	−12.0418	−	6.95236i	−0.480522	−	0.277429i
$629$	8.48911	+	26.1268i	0.338483	+	1.04174i
$630$	4.85472	+	1.18843i	0.193417	+	0.0473482i
$631$	3.13559	−	2.27814i	0.124826	−	0.0906913i	−0.523621	−	0.851952i	$-0.675419\pi$
$631$	3.13559	−	2.27814i	0.124826	−	0.0906913i	0.648446	+	0.761260i	$0.275419\pi$
$632$	3.37009	+	3.74286i	0.134055	+	0.148883i
$633$	24.6393	−	5.23725i	0.979325	−	0.208162i
$634$	−8.39350	+	18.8521i	−0.333348	+	0.748713i
$635$	−36.2360	+	16.1333i	−1.43798	+	0.640231i
$636$	−2.17863	+	0.707880i	−0.0863883	+	0.0280693i
$637$	−13.9063	+	13.6605i	−0.550987	+	0.541249i
$638$	−21.8586	+	12.8692i	−0.865390	+	0.509495i
$639$	6.83572	−	11.8398i	0.270417	−	0.468376i
$640$	1.26405	−	1.40387i	0.0499659	−	0.0554928i
$641$	0.825276	−	7.85198i	0.0325965	−	0.310135i	−0.966060	−	0.258317i	$-0.916832\pi$
$641$	0.825276	−	7.85198i	0.0325965	−	0.310135i	0.998657	−	0.0518172i	$-0.0165013\pi$
$642$	6.63922	−	0.697810i	0.262029	−	0.0275404i
$643$	−0.359457	−	0.116795i	−0.0141756	−	0.00460593i	0.301921	−	0.953333i	$-0.402372\pi$
$643$	−0.359457	−	0.116795i	−0.0141756	−	0.00460593i	−0.316096	+	0.948727i	$0.602372\pi$
$644$	−0.591175	−	7.96543i	−0.0232955	−	0.313882i
$645$	−5.74234	−	7.90365i	−0.226104	−	0.311206i
$646$	−15.0266	−	33.7504i	−0.591215	−	1.32789i
$647$	9.10792	+	8.20081i	0.358069	+	0.322407i	0.828457	−	0.560053i	$-0.189219\pi$
$647$	9.10792	+	8.20081i	0.358069	+	0.322407i	−0.470388	+	0.882460i	$0.655886\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	5.37472	−	17.0333i	0.210976	−	0.668614i
$650$		−	3.98593i		−	0.156341i
$651$	9.30291	−	1.68133i	0.364610	−	0.0658965i
$652$	−0.0991801	−	0.0720586i	−0.00388419	−	0.00282203i
$653$	−1.44127	−	13.7127i	−0.0564012	−	0.536621i	−0.985845	−	0.167658i	$-0.946380\pi$
$653$	−1.44127	−	13.7127i	−0.0564012	−	0.536621i	0.929444	−	0.368963i	$-0.120287\pi$
$654$	−2.20161	−	10.3577i	−0.0860896	−	0.405020i
$655$	2.56853	+	12.0840i	0.100361	+	0.472161i
$656$	−0.0754088	−	0.717467i	−0.00294422	−	0.0280124i
$657$	−2.55820	−	1.85864i	−0.0998048	−	0.0725125i
$658$	−9.46539	+	26.3554i	−0.368999	+	1.02744i
$659$			25.8349i			1.00639i	0.864174	+	0.503193i	$0.167841\pi$
$659$			25.8349i			1.00639i	−0.864174	+	0.503193i	$0.832159\pi$
$660$	5.94208	−	1.98673i	0.231295	−	0.0773332i
$661$	13.7688	−	7.94939i	0.535542	−	0.309196i	−0.207728	−	0.978187i	$-0.566607\pi$
$661$	13.7688	−	7.94939i	0.535542	−	0.309196i	0.743270	+	0.668991i	$0.233274\pi$
$662$	4.91696	+	4.42725i	0.191103	+	0.172070i
$663$	−5.12161	−	11.5033i	−0.198907	−	0.446752i
$664$	−6.49516	−	8.93982i	−0.252061	−	0.346932i
$665$	−22.9797	−	33.7572i	−0.891116	−	1.30905i
$666$	−5.77807	−	1.87741i	−0.223896	−	0.0727481i
$667$	−22.9623	+	2.41344i	−0.889105	+	0.0934487i
$668$	−1.97727	+	18.8125i	−0.0765029	+	0.727876i
$669$	7.71117	−	8.56412i	0.298131	−	0.331108i
$670$	4.04580	−	7.00754i	0.156303	−	0.270725i
$671$	−26.0819	−	23.0857i	−1.00688	−	0.891212i
$672$	−0.357030	+	2.62155i	−0.0137728	+	0.101129i
$673$	−35.0260	+	11.3807i	−1.35015	+	0.438692i	−0.892744	−	0.450564i	$-0.851223\pi$
$673$	−35.0260	+	11.3807i	−1.35015	+	0.438692i	−0.457411	+	0.889256i	$0.651223\pi$
$674$	−19.4140	+	8.64365i	−0.747798	+	0.332941i
$675$	0.582174	−	1.30758i	0.0224079	−	0.0503290i
$676$	−5.13040	+	1.09050i	−0.197323	+	0.0419423i
$677$	−17.5577	−	19.4998i	−0.674798	−	0.749439i	0.304356	−	0.952558i	$-0.401559\pi$
$677$	−17.5577	−	19.4998i	−0.674798	−	0.749439i	−0.979154	+	0.203120i	$0.934892\pi$
$678$	−5.41785	+	3.93630i	−0.208071	+	0.151173i
$679$	−2.67629	+	10.9326i	−0.102706	+	0.419554i
$680$	2.63960	+	8.12386i	0.101224	+	0.311536i
$681$	1.46774	+	0.847402i	0.0562440	+	0.0324725i
$682$	8.73906	−	8.00431i	0.334636	−	0.306501i
$683$	9.86589	+	17.0882i	0.377508	+	0.653863i	0.990699	−	0.136072i	$-0.0434477\pi$
$683$	9.86589	+	17.0882i	0.377508	+	0.653863i	−0.613191	+	0.789935i	$0.710114\pi$
$684$	7.99190	+	1.69873i	0.305578	+	0.0649526i
$685$	−12.7186	+	17.5057i	−0.485954	+	0.668858i
$686$	−5.49706	+	17.6857i	−0.209879	+	0.675241i
$687$	1.08150	−	3.32851i	0.0412618	−	0.126991i
$688$	3.84318	−	3.46041i	0.146520	−	0.131927i
$689$	5.82771	+	2.59466i	0.222018	+	0.0988488i
$690$	5.67180	+	0.596130i	0.215922	+	0.0226943i
$691$	−1.52268	+	7.16365i	−0.0579255	+	0.272518i	−0.997573	−	0.0696254i	$-0.977820\pi$
$691$	−1.52268	+	7.16365i	−0.0579255	+	0.272518i	0.939648	+	0.342144i	$0.111153\pi$
$692$	6.36836			0.242089
$693$	−5.31364	+	6.98321i	−0.201849	+	0.265270i
$694$	−8.73632			−0.331626
$695$	−6.90528	+	32.4868i	−0.261932	+	1.23229i
$696$	7.60612	+	0.799435i	0.288309	+	0.0303025i
$697$	2.98003	+	1.32679i	0.112877	+	0.0502559i
$698$	−15.8744	+	14.2933i	−0.600853	+	0.541011i
$699$	8.13166	−	25.0267i	0.307568	−	0.946596i
$700$	−1.79212	−	3.33605i	−0.0677357	−	0.126091i
$701$	−15.0486	+	20.7126i	−0.568377	+	0.782303i	−0.992361	−	0.123366i	$-0.960631\pi$
$701$	−15.0486	+	20.7126i	−0.568377	+	0.782303i	0.423985	+	0.905669i	$0.360631\pi$
$702$	2.72392	+	0.578988i	0.102808	+	0.0218525i
$703$	24.8195	+	42.9886i	0.936084	+	1.62134i
$704$	1.37471	+	3.01830i	0.0518114	+	0.113757i
$705$	−17.3161	−	9.99743i	−0.652161	−	0.376525i
$706$	−8.92408	−	27.4655i	−0.335862	−	1.03368i
$707$	4.47684	+	15.3647i	0.168369	+	0.577851i
$708$	−4.35682	+	3.16542i	−0.163739	+	0.118964i
$709$	−8.55258	−	9.49860i	−0.321199	−	0.356727i	0.560823	−	0.827936i	$-0.310485\pi$
$709$	−8.55258	−	9.49860i	−0.321199	−	0.356727i	−0.882022	+	0.471208i	$0.843818\pi$
$710$	25.2622	−	5.36965i	0.948074	−	0.201519i
$711$	2.04854	−	4.60109i	0.0768261	−	0.172554i
$712$	5.36485	−	2.38858i	0.201056	−	0.0895159i
$713$	10.2591	−	3.33338i	0.384206	−	0.124836i
$714$	−9.45859	−	7.32505i	−0.353979	−	0.274133i
$715$	−15.9991	−	6.96083i	−0.598333	−	0.260320i
$716$	−7.18674	+	12.4478i	−0.268581	+	0.465196i
$717$	2.11757	−	2.35180i	0.0790822	−	0.0878297i
$718$	−3.04182	+	28.9410i	−0.113520	+	1.08007i
$719$	−16.5601	+	1.74053i	−0.617586	+	0.0649109i	−0.408155	−	0.912913i	$-0.633828\pi$
$719$	−16.5601	+	1.74053i	−0.617586	+	0.0649109i	−0.209431	+	0.977824i	$0.567161\pi$
$720$	−1.79663	−	0.583762i	−0.0669566	−	0.0217555i
$721$	15.9562	−	33.0727i	0.594241	−	1.23169i
$722$	−28.0704	−	38.6355i	−1.04467	−	1.43787i
$723$	−0.748083	−	1.68022i	−0.0278215	−	0.0624881i
$724$	1.57851	+	1.42129i	0.0586647	+	0.0528219i
$725$	−9.48024	+	5.47342i	−0.352087	+	0.203278i
$726$	−0.963571	+	10.9577i	−0.0357615	+	0.406679i
$727$			47.6448i			1.76705i	0.468385	+	0.883524i	$0.344836\pi$
$727$			47.6448i			1.76705i	−0.468385	+	0.883524i	$0.655164\pi$
$728$	5.62382	−	4.76000i	0.208432	−	0.176417i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$	−0.624402	−	5.94079i	−0.0231102	−	0.219878i
$731$	4.86182	+	22.8731i	0.179821	+	0.845991i
$732$	2.18349	+	10.2725i	0.0807042	+	0.379683i
$733$	−2.06596	−	19.6563i	−0.0763079	−	0.726021i	−0.964057	−	0.265694i	$-0.914399\pi$
$733$	−2.06596	−	19.6563i	−0.0763079	−	0.726021i	0.887749	−	0.460327i	$-0.152268\pi$
$734$	22.8511	+	16.6023i	0.843450	+	0.612802i
$735$	−11.7284	−	6.10822i	−0.432607	−	0.225305i
$736$			3.01893i			0.111279i
$737$	8.44764	+	11.4216i	0.311173	+	0.420721i
$738$	−0.624767	+	0.360709i	−0.0229980	+	0.0132779i
$739$	−31.4377	−	28.3066i	−1.15645	−	1.04128i	−0.998551	−	0.0538220i	$-0.982860\pi$
$739$	−31.4377	−	28.3066i	−1.15645	−	1.04128i	−0.157904	−	0.987454i	$-0.550474\pi$
$740$	−4.66813	−	10.4848i	−0.171604	−	0.385429i
$741$	−13.3738	−	18.4074i	−0.491299	−	0.676215i
$742$	6.04413	−	0.448580i	0.221887	−	0.0164679i
$743$	0.505730	+	0.164322i	0.0185534	+	0.00602838i	0.318279	−	0.947997i	$-0.396895\pi$
$743$	0.505730	+	0.164322i	0.0185534	+	0.00602838i	−0.299726	+	0.954025i	$0.596895\pi$
$744$	−3.55356	+	0.373494i	−0.130280	+	0.0136930i
$745$	4.10894	−	39.0939i	0.150540	−	1.43229i
$746$	6.40345	−	7.11175i	0.234447	−	0.260380i
$747$	−5.52511	+	9.56978i	−0.202153	+	0.350140i
$748$	−14.9275	−	1.44069i	−0.545802	−	0.0526769i
$749$	−17.5009	−	2.38346i	−0.639470	−	0.0870898i
$750$	11.5547	−	3.75436i	0.421920	−	0.137090i
$751$	29.3370	−	13.0617i	1.07052	−	0.476627i	0.205654	−	0.978625i	$-0.434068\pi$
$751$	29.3370	−	13.0617i	1.07052	−	0.476627i	0.864869	+	0.501997i	$0.167401\pi$
$752$	4.30505	−	9.66931i	0.156989	−	0.352603i
$753$	25.5952	−	5.44044i	0.932743	−	0.198261i
$754$	−14.2512	−	15.8275i	−0.518996	−	0.576404i
$755$	30.2017	−	21.9428i	1.09915	−	0.798580i
$756$	2.54012	−	0.740117i	0.0923834	−	0.0269178i
$757$	−12.2800	−	37.7940i	−0.446324	−	1.37364i	−0.881025	−	0.473070i	$-0.843146\pi$
$757$	−12.2800	−	37.7940i	−0.446324	−	1.37364i	0.434701	−	0.900575i	$-0.356854\pi$
$758$	16.5182	+	9.53676i	0.599966	+	0.346391i
$759$	−4.93240	+	8.71348i	−0.179035	+	0.316279i
$760$	7.71736	+	13.3669i	0.279938	+	0.484867i
$761$	1.95034	+	0.414558i	0.0706999	+	0.0150277i	0.243126	−	0.969995i	$-0.421827\pi$
$761$	1.95034	+	0.414558i	0.0706999	+	0.0150277i	−0.172426	+	0.985022i	$0.555161\pi$
$762$	−12.3417	+	16.9869i	−0.447093	+	0.615371i
$763$	−0.858228	+	28.0031i	−0.0310700	+	1.01378i
$764$	−2.78117	+	8.55956i	−0.100619	+	0.309674i
$765$	6.34790	−	5.71567i	0.229509	−	0.206651i
$766$	−21.9060	−	9.75316i	−0.791494	−	0.352396i
$767$	14.9148	+	1.56761i	0.538542	+	0.0566030i
$768$	0.207912	−	0.978148i	0.00750237	−	0.0352959i
$769$	−9.87384			−0.356060			−0.178030	−	0.984025i	$-0.556972\pi$
$769$	−9.87384			−0.356060			−0.178030	+	0.984025i	$0.556972\pi$
$770$	−16.5202	+	1.36746i	−0.595347	+	0.0492799i
$771$	11.5264			0.415115
$772$	−1.08354	+	5.09764i	−0.0389974	+	0.183468i
$773$	0.787875	+	0.0828090i	0.0283379	+	0.00297843i	0.118687	−	0.992932i	$-0.462132\pi$
$773$	0.787875	+	0.0828090i	0.0283379	+	0.00297843i	−0.0903489	+	0.995910i	$0.528798\pi$
$774$	−4.72440	−	2.10344i	−0.169815	−	0.0756066i
$775$	3.80069	−	3.42216i	0.136525	−	0.122928i
$776$	1.31460	−	4.04593i	0.0471915	−	0.145240i
$777$	13.6678	+	8.45969i	0.490330	+	0.303490i
$778$	10.9231	−	15.0343i	0.391611	−	0.539007i
$779$	5.76551	+	1.22550i	0.206571	+	0.0439080i
$780$	2.63035	+	4.55590i	0.0941817	+	0.163127i
$781$	−9.04979	+	44.4307i	−0.323827	+	1.58986i
$782$	−11.8219	−	6.82537i	−0.422750	−	0.244075i
$783$	−2.36337	−	7.27370i	−0.0844598	−	0.259941i
$784$	2.56674	−	6.51244i	0.0916694	−	0.232587i
$785$	−21.2507	+	15.4395i	−0.758470	+	0.551060i
$786$	4.37587	+	4.85989i	0.156082	+	0.173347i
$787$	24.6876	−	5.24750i	0.880017	−	0.187053i	0.254320	−	0.967120i	$-0.418148\pi$
$787$	24.6876	−	5.24750i	0.880017	−	0.187053i	0.625696	+	0.780067i	$0.284815\pi$
$788$	5.40859	−	12.1479i	0.192673	−	0.432751i
$789$	−0.325463	+	0.144906i	−0.0115868	+	0.00515878i
$790$	9.04877	−	2.94012i	0.321941	−	0.104605i
$791$	16.3995	−	6.70740i	0.583099	−	0.238488i
$792$	2.19821	−	2.48352i	0.0781101	−	0.0882480i
$793$	14.6229	−	25.3276i	0.519274	−	0.899409i
$794$	14.2574	−	15.8344i	0.505975	−	0.561942i
$795$	−0.452340	+	4.30373i	−0.0160428	+	0.152638i
$796$	21.3880	−	2.24797i	0.758078	−	0.0796773i
$797$	27.2394	+	8.85063i	0.964871	+	0.313505i	0.748744	−	0.662860i	$-0.230657\pi$
$797$	27.2394	+	8.85063i	0.964871	+	0.313505i	0.216127	+	0.976365i	$0.430657\pi$
$798$	−19.4695	−	9.39323i	−0.689212	−	0.332517i
$799$	28.1311	+	38.7192i	0.995207	+	1.36979i
$800$	0.582174	+	1.30758i	0.0205830	+	0.0462301i
$801$	−4.36416	−	3.92951i	−0.154200	−	0.138842i
$802$	6.30098	−	3.63787i	0.222495	−	0.128458i
$803$	10.0014	+	3.15588i	0.352943	+	0.111368i
$804$		−	4.28333i		−	0.151061i
$805$	−14.2008	−	5.10011i	−0.500511	−	0.179755i
$806$	8.05003	+	5.84869i	0.283550	+	0.206011i
$807$	1.24952	+	11.8884i	0.0439852	+	0.418491i
$808$	−1.25762	−	5.91664i	−0.0442429	−	0.208147i
$809$	−4.88930	−	23.0023i	−0.171899	−	0.808719i	−0.976604	−	0.215045i	$-0.931010\pi$
$809$	−4.88930	−	23.0023i	−0.171899	−	0.808719i	0.804706	−	0.593674i	$-0.202323\pi$
$810$	0.197464	+	1.87874i	0.00693818	+	0.0660123i
$811$	36.0602	+	26.1993i	1.26624	+	0.919981i	0.999046	−	0.0436608i	$-0.0139021\pi$
$811$	36.0602	+	26.1993i	1.26624	+	0.919981i	0.267198	+	0.963642i	$0.413902\pi$
$812$	−19.0438	−	6.83947i	−0.668307	−	0.240018i
$813$		−	25.1719i		−	0.882818i
$814$	20.1492	−	0.171373i	0.706228	−	0.00600662i
$815$	−0.200563	+	0.115795i	−0.00702541	+	0.00405612i
$816$	3.36029	+	3.02562i	0.117634	+	0.105918i
$817$	17.1860	+	38.6005i	0.601263	+	1.35046i
$818$	−20.5818	−	28.3285i	−0.719627	−	0.990482i
$819$	−6.63589	−	3.20155i	−0.231877	−	0.111871i
$820$	−1.29613	−	0.421137i	−0.0452627	−	0.0147067i
$821$	−22.4550	+	2.36011i	−0.783684	+	0.0823685i	−0.487915	−	0.872891i	$-0.662243\pi$
$821$	−22.4550	+	2.36011i	−0.783684	+	0.0823685i	−0.295769	+	0.955260i	$0.595576\pi$
$822$	−1.19730	+	11.3915i	−0.0417606	+	0.397326i
$823$	−27.3007	+	30.3205i	−0.951642	+	1.05691i	0.0466745	+	0.998910i	$0.485138\pi$
$823$	−27.3007	+	30.3205i	−0.951642	+	1.05691i	−0.998317	+	0.0579957i	$0.981529\pi$
$824$	−6.93955	+	12.0196i	−0.241751	+	0.418724i
$825$	−0.456045	+	4.72523i	−0.0158774	+	0.164511i
$826$	13.1878	−	5.39383i	0.458864	−	0.187675i
$827$	−30.6014	+	9.94299i	−1.06411	+	0.345752i	−0.788193	−	0.615428i	$-0.788983\pi$
$827$	−30.6014	+	9.94299i	−1.06411	+	0.345752i	−0.275922	+	0.961180i	$0.588983\pi$
$828$	2.75793	−	1.22791i	0.0958447	−	0.0426728i
$829$	3.94670	−	8.86444i	0.137075	−	0.307875i	−0.831945	−	0.554858i	$-0.812773\pi$
$829$	3.94670	−	8.86444i	0.137075	−	0.307875i	0.969020	+	0.246983i	$0.0794393\pi$
$830$	−20.4187	+	4.34014i	−0.708745	+	0.150648i
$831$	7.95552	+	8.83550i	0.275974	+	0.306500i
$832$	−2.25293	+	1.63685i	−0.0781064	+	0.0567476i
$833$	19.6991	+	24.7748i	0.682535	+	0.858398i
$834$	5.43290	+	16.7207i	0.188126	+	0.578992i
$835$	30.9468	+	17.8671i	1.07096	+	0.618317i
$836$	−26.9248	+	3.06165i	−0.931213	+	0.105889i
$837$	1.78657	+	3.09443i	0.0617528	+	0.106959i
$838$	−14.2145	−	3.02140i	−0.491033	−	0.104372i
$839$	−23.6405	+	32.5383i	−0.816160	+	1.12335i	0.174183	+	0.984713i	$0.444271\pi$
$839$	−23.6405	+	32.5383i	−0.816160	+	1.12335i	−0.990344	+	0.138635i	$0.955729\pi$
$840$	4.24987	+	2.63046i	0.146634	+	0.0907594i
$841$	−9.11358	+	28.0487i	−0.314261	+	0.967197i
$842$	−2.02185	+	1.82049i	−0.0696777	+	0.0627381i
$843$	−16.1207	−	7.17738i	−0.555225	−	0.247202i
$844$	25.0518	+	2.63305i	0.862318	+	0.0906333i
$845$	−2.06006	+	9.69180i	−0.0708681	+	0.333408i
$846$	−10.5844			−0.363898
$847$	9.36977	−	27.5537i	0.321949	−	0.946757i
$848$	−2.29075			−0.0786646
$849$	3.23887	−	15.2377i	0.111158	−	0.522956i
$850$	−6.43661	−	0.676515i	−0.220774	−	0.0232043i
$851$	16.7556	+	7.46007i	0.574374	+	0.255728i
$852$	10.1599	−	9.14797i	0.348071	−	0.313404i
$853$	−2.96388	+	9.12189i	−0.101481	+	0.312328i	−0.988889	−	0.148659i	$-0.952504\pi$
$853$	−2.96388	+	9.12189i	−0.101481	+	0.312328i	0.887407	+	0.460986i	$0.152504\pi$
$854$	0.851167	−	27.7727i	0.0291263	−	0.950362i
$855$	9.07230	−	12.4870i	0.310266	−	0.427045i
$856$	6.52991	+	1.38797i	0.223188	+	0.0474400i
$857$	−2.67442	−	4.63224i	−0.0913566	−	0.158234i	0.816726	−	0.577026i	$-0.195787\pi$
$857$	−2.67442	−	4.63224i	−0.0913566	−	0.158234i	−0.908082	+	0.418792i	$0.862454\pi$
$858$	−9.17692	+	1.04352i	−0.313295	+	0.0356251i
$859$	−46.7340	−	26.9819i	−1.59454	−	0.920610i	−0.992513	−	0.122137i	$-0.961025\pi$
$859$	−46.7340	−	26.9819i	−1.59454	−	0.920610i	−0.602030	−	0.798473i	$-0.705641\pi$
$860$	−3.01893	−	9.29130i	−0.102945	−	0.316831i
$861$	1.83249	−	0.533934i	0.0624512	−	0.0181964i
$862$	10.1319	−	7.36122i	0.345092	−	0.250724i
$863$	1.70601	+	1.89471i	0.0580732	+	0.0644968i	0.771481	−	0.636252i	$-0.219516\pi$
$863$	1.70601	+	1.89471i	0.0580732	+	0.0644968i	−0.713408	+	0.700749i	$0.752849\pi$
$864$	−0.978148	+	0.207912i	−0.0332773	+	0.00707330i
$865$	4.89321	−	10.9903i	0.166374	−	0.373683i
$866$	23.5327	−	10.4774i	0.799672	−	0.356037i
$867$	−3.27725	+	1.06484i	−0.111301	+	0.0361639i
$868$	9.36715	+	1.27572i	0.317942	+	0.0433007i
$869$	−1.60471	+	16.6270i	−0.0544362	+	0.564031i
$870$	7.22391	−	12.5122i	0.244913	−	0.424202i
$871$	−7.98147	+	8.86432i	−0.270442	+	0.300356i
$872$	1.10687	−	10.5311i	0.0374832	−	0.356629i
$873$	−4.23084	+	0.444679i	−0.143192	+	0.0150501i
$874$	−23.4588	−	7.62221i	−0.793504	−	0.257825i
$875$	−32.0561	+	2.37912i	−1.08369	+	0.0804290i
$876$	−1.85864	−	2.55820i	−0.0627976	−	0.0864335i
$877$	5.67822	+	12.7535i	0.191740	+	0.430655i	0.983676	−	0.179949i	$-0.0575934\pi$
$877$	5.67822	+	12.7535i	0.191740	+	0.430655i	−0.791936	+	0.610604i	$0.790927\pi$
$878$	−13.1591	−	11.8485i	−0.444099	−	0.399869i
$879$	−9.17760	+	5.29869i	−0.309553	+	0.178720i
$880$	6.26518	−	0.0532867i	0.211199	−	0.00179629i
$881$			22.2220i			0.748677i	0.927292	+	0.374338i	$0.122130\pi$
$881$			22.2220i			0.748677i	−0.927292	+	0.374338i	$0.877870\pi$
$882$	−6.99340	+	0.304010i	−0.235480	+	0.0102366i
$883$	−11.6319	−	8.45109i	−0.391445	−	0.284402i	0.374602	−	0.927186i	$-0.377779\pi$
$883$	−11.6319	−	8.45109i	−0.391445	−	0.284402i	−0.766048	+	0.642784i	$0.777779\pi$
$884$	−1.31622	−	12.5230i	−0.0442692	−	0.421194i
$885$	2.11517	+	9.95107i	0.0711005	+	0.334502i
$886$	0.922783	+	4.34135i	0.0310015	+	0.145851i
$887$	−1.09496	−	10.4179i	−0.0367653	−	0.349798i	−0.997405	−	0.0719996i	$-0.977062\pi$
$887$	−1.09496	−	10.4179i	−0.0367653	−	0.349798i	0.960639	−	0.277798i	$-0.0896047\pi$
$888$	−4.91512	−	3.57105i	−0.164941	−	0.119836i
$889$	42.4031	−	35.8900i	1.42215	−	1.20371i
$890$		−	11.0938i		−	0.371865i
$891$	−3.16290	−	0.998029i	−0.105961	−	0.0334352i
$892$	9.98021	−	5.76208i	0.334162	−	0.192929i
$893$	64.2664	+	57.8658i	2.15059	+	1.93640i
$894$	−8.46360	−	19.0096i	−0.283065	−	0.635775i
$895$	15.9600	+	21.9671i	0.533485	+	0.734280i
$896$	−1.14966	+	2.38291i	−0.0384074	+	0.0796076i
$897$	−7.99557	−	2.59792i	−0.266964	−	0.0867420i
$898$	−15.4914	+	1.62822i	−0.516956	+	0.0543343i
$899$	2.85649	−	27.1777i	0.0952693	−	0.906427i
$900$	0.957747	−	1.06369i	0.0319249	−	0.0354562i
$901$	5.17905	−	8.97038i	0.172539	−	0.298847i
$902$	1.58583	−	1.79166i	0.0528024	−	0.0596556i
$903$	10.8178	+	8.37770i	0.359995	+	0.278792i
$904$	−6.36906	+	2.06943i	−0.211832	+	0.0688283i
$905$	3.66569	−	1.63207i	0.121852	−	0.0542519i
$906$	8.03773	−	18.0530i	0.267036	−	0.599772i
$907$	10.1223	−	2.15156i	0.336105	−	0.0714414i	−0.0367676	−	0.999324i	$-0.511706\pi$
$907$	10.1223	−	2.15156i	0.336105	−	0.0714414i	0.372873	+	0.927882i	$0.378373\pi$
$908$	1.13405	+	1.25948i	0.0376346	+	0.0417975i
$909$	−4.89360	+	3.55541i	−0.162310	+	0.117925i
$910$	−3.89354	−	13.3628i	−0.129069	−	0.442973i
$911$	−5.94482	−	18.2963i	−0.196961	−	0.606183i	−0.999948	−	0.0101868i	$-0.996757\pi$
$911$	−5.94482	−	18.2963i	−0.196961	−	0.606183i	0.802987	−	0.595996i	$-0.203243\pi$
$912$	7.07581	+	4.08522i	0.234304	+	0.135275i
$913$	7.31469	−	35.9121i	0.242081	−	1.18852i
$914$	16.9303	+	29.3241i	0.560004	+	0.969955i
$915$	19.4057	+	4.12482i	0.641534	+	0.136362i
$916$	2.05714	−	2.83140i	0.0679697	−	0.0935522i
$917$	−8.18804	−	15.2422i	−0.270393	−	0.503340i
$918$	1.39729	−	4.30041i	0.0461173	−	0.141935i
$919$	−3.58474	+	3.22772i	−0.118250	+	0.106473i	−0.726134	−	0.687553i	$-0.758685\pi$
$919$	−3.58474	+	3.22772i	−0.118250	+	0.106473i	0.607885	+	0.794025i	$0.292018\pi$
$920$	5.20998	+	2.31963i	0.171768	+	0.0764761i
$921$	20.8771	+	2.19427i	0.687924	+	0.0723038i
$922$	−0.804711	+	3.78587i	−0.0265018	+	0.124681i
$923$	−38.0719			−1.25315
$924$	−7.21150	+	4.99942i	−0.237241	+	0.164469i
$925$	8.69594			0.285921
$926$	3.87821	−	18.2455i	0.127446	−	0.599586i
$927$	13.8031	+	1.45076i	0.453352	+	0.0476492i
$928$	6.98681	+	3.11073i	0.229353	+	0.102115i
$929$	3.88628	−	3.49922i	0.127505	−	0.114806i	−0.602911	−	0.797808i	$-0.705993\pi$
$929$	3.88628	−	3.49922i	0.127505	−	0.114806i	0.730416	+	0.683002i	$0.239326\pi$
$930$	−2.08586	+	6.41961i	−0.0683980	+	0.210507i
$931$	44.1247	+	36.3876i	1.44613	+	1.19256i
$932$	15.4673	−	21.2890i	0.506649	−	0.697343i
$933$	8.98227	+	1.90924i	0.294066	+	0.0625057i
$934$	−15.4194	−	26.7072i	−0.504538	−	0.873885i
$935$	−13.9560	+	24.6544i	−0.456411	+	0.806286i
$936$	2.41169	+	1.39239i	0.0788285	+	0.0455116i
$937$	−13.0876	−	40.2795i	−0.427553	−	1.31587i	−0.900528	−	0.434798i	$-0.856820\pi$
$937$	−13.0876	−	40.2795i	−0.427553	−	1.31587i	0.472975	−	0.881076i	$-0.343180\pi$
$938$	−2.69465	+	11.0076i	−0.0879834	+	0.359411i
$939$	−2.97242	+	2.15959i	−0.0970013	+	0.0704756i
$940$	−13.3792	−	14.8591i	−0.436381	−	0.484650i
$941$	−34.8826	+	7.41452i	−1.13714	+	0.241706i	−0.737749	−	0.675075i	$-0.764111\pi$
$941$	−34.8826	+	7.41452i	−1.13714	+	0.241706i	−0.399390	+	0.916781i	$0.630778\pi$
$942$	−5.65556	+	12.7026i	−0.184268	+	0.413873i
$943$	1.98962	−	0.885837i	0.0647910	−	0.0288468i
$944$	−5.12175	+	1.66416i	−0.166699	+	0.0541638i
$945$	0.674464	−	4.95235i	0.0219403	−	0.161100i
$946$	17.0726	+	1.64772i	0.555079	+	0.0535722i
$947$	27.5004	−	47.6321i	0.893643	−	1.54783i	0.0581669	−	0.998307i	$-0.481474\pi$
$947$	27.5004	−	47.6321i	0.893643	−	1.54783i	0.835476	−	0.549527i	$-0.185192\pi$
$948$	3.37009	−	3.74286i	0.109455	−	0.121562i
$949$	−0.920453	+	8.75752i	−0.0298792	+	0.284281i
$950$	−11.6305	+	1.22242i	−0.377344	+	0.0396605i
$951$	19.6262	+	6.37694i	0.636423	+	0.206786i
$952$	−6.73208	−	9.88941i	−0.218188	−	0.320517i
$953$	35.7281	+	49.1756i	1.15735	+	1.59295i	0.720568	+	0.693384i	$0.243881\pi$
$953$	35.7281	+	49.1756i	1.15735	+	1.59295i	0.436779	+	0.899569i	$0.356119\pi$
$954$	0.931731	+	2.09270i	0.0301659	+	0.0677537i
$955$	12.6349	+	11.3765i	0.408856	+	0.368135i
$956$	2.74068	−	1.58233i	0.0886398	−	0.0511762i
$957$	15.0835	+	20.3937i	0.487581	+	0.659233i
$958$		−	14.1124i		−	0.455950i
$959$	10.2433	−	28.5216i	0.330775	−	0.921009i
$960$	−1.52831	−	1.11038i	−0.0493259	−	0.0358374i
$961$	−1.90584	−	18.1328i	−0.0614786	−	0.584930i
$962$	3.51760	+	16.5490i	0.113412	+	0.533561i
$963$	−1.38797	−	6.52991i	−0.0447269	−	0.210423i
$964$	−0.192252	−	1.82916i	−0.00619202	−	0.0589132i
$965$	7.96482	+	5.78678i	0.256397	+	0.186283i
$966$	−7.86000	+	1.42055i	−0.252891	+	0.0457054i
$967$			36.7683i			1.18239i	0.806530	+	0.591194i	$0.201343\pi$
$967$			36.7683i			1.18239i	−0.806530	+	0.591194i	$0.798657\pi$
$968$	−4.30253	+	10.1236i	−0.138289	+	0.325386i
$969$	−31.9948	+	18.4722i	−1.02782	+	0.593413i
$970$	−5.97226	−	5.37744i	−0.191758	−	0.172659i
$971$	18.3533	+	41.2222i	0.588986	+	1.32288i	0.924620	+	0.380892i	$0.124383\pi$
$971$	18.3533	+	41.2222i	0.588986	+	1.32288i	−0.335633	+	0.941993i	$0.608950\pi$
$972$	0.587785	+	0.809017i	0.0188532	+	0.0259492i
$973$	−3.44280	−	46.3880i	−0.110371	−	1.48713i
$974$	24.5363	+	7.97232i	0.786193	+	0.255449i
$975$	−3.96410	+	0.416644i	−0.126953	+	0.0133433i
$976$	−1.09776	+	10.4445i	−0.0351384	+	0.334320i
$977$	32.3071	−	35.8807i	1.03360	−	1.14792i	0.0447478	−	0.998998i	$-0.485752\pi$
$977$	32.3071	−	35.8807i	1.03360	−	1.14792i	0.988848	−	0.148926i	$-0.0475817\pi$
$978$	−0.0612967	+	0.106169i	−0.00196005	+	0.00339491i
$979$	17.8599	+	7.77042i	0.570805	+	0.248344i
$980$	−9.26679	−	9.43353i	−0.296017	−	0.301343i
$981$	−10.0709	+	3.27223i	−0.321538	+	0.104474i
$982$	−30.6476	+	13.6452i	−0.978003	+	0.435435i
$983$	14.8328	−	33.3151i	0.473093	−	1.06259i	−0.506618	−	0.862171i	$-0.669104\pi$
$983$	14.8328	−	33.3151i	0.473093	−	1.06259i	0.979711	−	0.200415i	$-0.0642289\pi$
$984$	−0.705654	+	0.149991i	−0.0224954	+	0.00478155i
$985$	−16.8087	−	18.6680i	−0.535571	−	0.594812i
$986$	−27.9775	+	20.3269i	−0.890986	+	0.647340i
$987$	27.2005	+	6.65864i	0.865800	+	0.211947i
$988$	−7.03102	−	21.6393i	−0.223687	−	0.688436i
$989$	13.5207	+	7.80620i	0.429935	+	0.248223i
$990$	−2.59696	−	5.70186i	−0.0825368	−	0.181217i
$991$	1.78658	+	3.09445i	0.0567525	+	0.0982983i	0.893006	−	0.450045i	$-0.148592\pi$
$991$	1.78658	+	3.09445i	0.0567525	+	0.0982983i	−0.836253	+	0.548343i	$0.815259\pi$
$992$	−3.49505	−	0.742896i	−0.110968	−	0.0235870i
$993$	3.88903	−	5.35279i	0.123415	−	0.169866i
$994$	−31.8645	+	17.1175i	−1.01068	+	0.542935i
$995$	12.5543	−	38.6381i	0.397998	−	1.22491i
$996$	−8.21192	+	7.39404i	−0.260205	+	0.234289i
$997$	−27.0048	−	12.0233i	−0.855249	−	0.380781i	−0.0682000	−	0.997672i	$-0.521726\pi$
$997$	−27.0048	−	12.0233i	−0.855249	−	0.380781i	−0.787049	+	0.616890i	$0.788392\pi$
$998$	3.58166	+	0.376448i	0.113376	+	0.0119163i
$999$	−1.26315	+	5.94266i	−0.0399644	+	0.188018i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.ba.b.61.5	yes	64
7.3	odd	6		462.2.ba.a.325.8	yes	64
11.2	odd	10		462.2.ba.a.145.8	✓	64
77.24	even	30	inner	462.2.ba.b.409.5	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.ba.a.145.8	✓	64	11.2	odd	10
462.2.ba.a.325.8	yes	64	7.3	odd	6
462.2.ba.b.61.5	yes	64	1.1	even	1	trivial
462.2.ba.b.409.5	yes	64	77.24	even	30	inner

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.ba (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.207912 - 0.978148i) q^{2} +(-0.994522 - 0.104528i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(-1.40387 + 1.26405i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(1.39244 - 2.24969i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.978148 + 0.207912i) q^{9} +O(q^{10})\)	\(q+(0.207912 - 0.978148i) q^{2} +(-0.994522 - 0.104528i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(-1.40387 + 1.26405i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(1.39244 - 2.24969i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.978148 + 0.207912i) q^{9} +(0.944546 + 1.63600i) q^{10} +(-3.29539 + 0.374722i) q^{11} +(0.866025 + 0.500000i) q^{12} +(-0.860543 - 2.64848i) q^{13} +(-1.91102 - 1.82975i) q^{14} +(1.52831 - 1.11038i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-4.42290 + 0.940117i) q^{17} +(0.406737 - 0.913545i) q^{18} +(-7.46407 + 3.32322i) q^{19} +(1.79663 - 0.583762i) q^{20} +(-1.61997 + 2.09181i) q^{21} +(-0.318616 + 3.30129i) q^{22} +(-1.50946 + 2.61447i) q^{23} +(0.669131 - 0.743145i) q^{24} +(-0.149615 + 1.42349i) q^{25} +(-2.76952 + 0.291088i) q^{26} +(-0.951057 - 0.309017i) q^{27} +(-2.18709 + 1.48883i) q^{28} +(4.49539 + 6.18738i) q^{29} +(-0.768363 - 1.72577i) q^{30} +(-2.65536 - 2.39089i) q^{31} +(0.866025 - 0.500000i) q^{32} +(3.31650 - 0.0282076i) q^{33} +4.52171i q^{34} +(0.888908 + 4.91839i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(-0.635055 - 6.04214i) q^{37} +(1.69873 + 7.99190i) q^{38} +(0.578988 + 2.72392i) q^{39} +(-0.197464 - 1.87874i) q^{40} +(-0.583640 - 0.424039i) q^{41} +(1.70929 + 2.01949i) q^{42} -5.17151i q^{43} +(3.16290 + 0.998029i) q^{44} +(-1.63600 + 0.944546i) q^{45} +(2.24350 + 2.02006i) q^{46} +(-4.30505 - 9.66931i) q^{47} +(-0.587785 - 0.809017i) q^{48} +(-3.12220 - 6.26513i) q^{49} +(1.36128 + 0.442305i) q^{50} +(4.49694 - 0.472648i) q^{51} +(-0.291088 + 2.76952i) q^{52} +(-1.53281 + 1.70236i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(4.15263 - 4.69159i) q^{55} +(1.00158 + 2.44884i) q^{56} +(7.77055 - 2.52481i) q^{57} +(6.98681 - 3.11073i) q^{58} +(-2.19041 + 4.91974i) q^{59} +(-1.84781 + 0.392764i) q^{60} +(7.02722 + 7.80452i) q^{61} +(-2.89073 + 2.10024i) q^{62} +(1.82975 - 1.91102i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(4.55590 + 2.63035i) q^{65} +(0.661949 - 3.24990i) q^{66} +(-2.14166 - 3.70947i) q^{67} +(4.42290 + 0.940117i) q^{68} +(1.77448 - 2.44237i) q^{69} +(4.99572 + 0.153107i) q^{70} +(4.22470 - 13.0023i) q^{71} +(-0.743145 + 0.669131i) q^{72} +(-2.88873 - 1.28614i) q^{73} +(-6.04214 - 0.635055i) q^{74} +(0.297590 - 1.40005i) q^{75} +8.17044 q^{76} +(-3.74564 + 7.93538i) q^{77} +2.78478 q^{78} +(1.04715 - 4.92646i) q^{79} +(-1.87874 - 0.197464i) q^{80} +(0.913545 + 0.406737i) q^{81} +(-0.536119 + 0.482723i) q^{82} +(-3.41471 + 10.5094i) q^{83} +(2.33074 - 1.25207i) q^{84} +(5.02082 - 6.91057i) q^{85} +(-5.05850 - 1.07522i) q^{86} +(-3.82401 - 6.62338i) q^{87} +(1.63382 - 2.88628i) q^{88} +(-5.08578 - 2.93628i) q^{89} +(0.583762 + 1.79663i) q^{90} +(-7.15651 - 1.75191i) q^{91} +(2.44237 - 1.77448i) q^{92} +(2.39089 + 2.65536i) q^{93} +(-10.3531 + 2.20062i) q^{94} +(6.27787 - 14.1003i) q^{95} +(-0.913545 + 0.406737i) q^{96} +(-4.04593 + 1.31460i) q^{97} +(-6.77737 + 1.75138i) q^{98} +(-3.30129 - 0.318616i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9}+O(q^{10}) \) 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9	\( 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9} - 2 q^{10} + 4 q^{11} + 2 q^{14} - 6 q^{15} + 8 q^{16} + 30 q^{17} - 10 q^{19} - 20 q^{20} + 4 q^{21} - 2 q^{22} + 4 q^{23} + 8 q^{24} - 12 q^{26} - 20 q^{29} - 18 q^{30} + 34 q^{31} + 8 q^{33} - 2 q^{35} - 16 q^{36} - 14 q^{37} + 12 q^{38} - 18 q^{39} + 12 q^{40} + 28 q^{41} + 4 q^{42} + 6 q^{44} - 12 q^{45} + 42 q^{46} + 24 q^{47} - 44 q^{49} + 14 q^{51} - 32 q^{54} + 14 q^{55} - 4 q^{56} - 10 q^{58} - 30 q^{59} + 2 q^{60} - 28 q^{61} + 8 q^{62} + 16 q^{63} + 16 q^{64} - 12 q^{65} - 4 q^{66} + 16 q^{67} - 30 q^{68} - 30 q^{70} - 24 q^{71} - 116 q^{73} - 44 q^{74} + 12 q^{75} - 32 q^{77} - 18 q^{80} + 8 q^{81} - 28 q^{82} - 8 q^{83} - 2 q^{84} - 80 q^{85} - 18 q^{86} - 10 q^{87} - 14 q^{88} - 24 q^{89} - 4 q^{90} + 48 q^{91} + 8 q^{92} + 76 q^{93} + 6 q^{94} + 98 q^{95} - 8 q^{96} - 120 q^{97} - 40 q^{98} + 8 q^{99}+O(q^{100}) \) 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9 - 2 * q^10 + 4 * q^11 + 2 * q^14 - 6 * q^15 + 8 * q^16 + 30 * q^17 - 10 * q^19 - 20 * q^20 + 4 * q^21 - 2 * q^22 + 4 * q^23 + 8 * q^24 - 12 * q^26 - 20 * q^29 - 18 * q^30 + 34 * q^31 + 8 * q^33 - 2 * q^35 - 16 * q^36 - 14 * q^37 + 12 * q^38 - 18 * q^39 + 12 * q^40 + 28 * q^41 + 4 * q^42 + 6 * q^44 - 12 * q^45 + 42 * q^46 + 24 * q^47 - 44 * q^49 + 14 * q^51 - 32 * q^54 + 14 * q^55 - 4 * q^56 - 10 * q^58 - 30 * q^59 + 2 * q^60 - 28 * q^61 + 8 * q^62 + 16 * q^63 + 16 * q^64 - 12 * q^65 - 4 * q^66 + 16 * q^67 - 30 * q^68 - 30 * q^70 - 24 * q^71 - 116 * q^73 - 44 * q^74 + 12 * q^75 - 32 * q^77 - 18 * q^80 + 8 * q^81 - 28 * q^82 - 8 * q^83 - 2 * q^84 - 80 * q^85 - 18 * q^86 - 10 * q^87 - 14 * q^88 - 24 * q^89 - 4 * q^90 + 48 * q^91 + 8 * q^92 + 76 * q^93 + 6 * q^94 + 98 * q^95 - 8 * q^96 - 120 * q^97 - 40 * q^98 + 8 * q^99

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