LMFDB - Embedded newform 435.2.q.d.191.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [435,2,Mod(41,435)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(435, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("435.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	435.q (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.47349248793$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			191.8
Character	$\chi$	$=$	435.191
Dual form			435.2.q.d.41.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0236294 - 0.0236294i) q^{2} +(1.03028 - 1.39231i) q^{3} -1.99888i q^{4} +1.00000 q^{5} +(-0.0572444 + 0.00855463i) q^{6} +3.42666 q^{7} +(-0.0944913 + 0.0944913i) q^{8} +(-0.877056 - 2.86893i) q^{9} +O(q^{10})$	\(q+(-0.0236294 - 0.0236294i) q^{2} +(1.03028 - 1.39231i) q^{3} -1.99888i q^{4} +1.00000 q^{5} +(-0.0572444 + 0.00855463i) q^{6} +3.42666 q^{7} +(-0.0944913 + 0.0944913i) q^{8} +(-0.877056 - 2.86893i) q^{9} +(-0.0236294 - 0.0236294i) q^{10} +(4.10386 + 4.10386i) q^{11} +(-2.78307 - 2.05940i) q^{12} +3.19797i q^{13} +(-0.0809700 - 0.0809700i) q^{14} +(1.03028 - 1.39231i) q^{15} -3.99330 q^{16} +(-4.08727 - 4.08727i) q^{17} +(-0.0470669 + 0.0885156i) q^{18} +(-1.51698 + 1.51698i) q^{19} -1.99888i q^{20} +(3.53041 - 4.77097i) q^{21} -0.193944i q^{22} +3.49892i q^{23} +(0.0342090 + 0.228913i) q^{24} +1.00000 q^{25} +(0.0755663 - 0.0755663i) q^{26} +(-4.89806 - 1.73466i) q^{27} -6.84949i q^{28} +(-4.91427 - 2.20227i) q^{29} +(-0.0572444 + 0.00855463i) q^{30} +(-0.896093 + 0.896093i) q^{31} +(0.283342 + 0.283342i) q^{32} +(9.94197 - 1.48573i) q^{33} +0.193159i q^{34} +3.42666 q^{35} +(-5.73466 + 1.75313i) q^{36} +(-1.53523 - 1.53523i) q^{37} +0.0716909 q^{38} +(4.45257 + 3.29480i) q^{39} +(-0.0944913 + 0.0944913i) q^{40} +(-4.78315 + 4.78315i) q^{41} +(-0.196157 + 0.0293138i) q^{42} +(-2.79141 + 2.79141i) q^{43} +(8.20315 - 8.20315i) q^{44} +(-0.877056 - 2.86893i) q^{45} +(0.0826775 - 0.0826775i) q^{46} +(-3.94208 + 3.94208i) q^{47} +(-4.11421 + 5.55991i) q^{48} +4.74200 q^{49} +(-0.0236294 - 0.0236294i) q^{50} +(-9.90176 + 1.47972i) q^{51} +6.39238 q^{52} +0.219714i q^{53} +(0.0747492 + 0.156727i) q^{54} +(4.10386 + 4.10386i) q^{55} +(-0.323790 + 0.323790i) q^{56} +(0.549198 + 3.67503i) q^{57} +(0.0640830 + 0.168160i) q^{58} -14.4779i q^{59} +(-2.78307 - 2.05940i) q^{60} +(7.78602 - 7.78602i) q^{61} +0.0423483 q^{62} +(-3.00537 - 9.83086i) q^{63} +7.97321i q^{64} +3.19797i q^{65} +(-0.270030 - 0.199816i) q^{66} +11.2502i q^{67} +(-8.16997 + 8.16997i) q^{68} +(4.87159 + 3.60486i) q^{69} +(-0.0809700 - 0.0809700i) q^{70} +9.21033 q^{71} +(0.353963 + 0.188215i) q^{72} +(10.7069 + 10.7069i) q^{73} +0.0725530i q^{74} +(1.03028 - 1.39231i) q^{75} +(3.03227 + 3.03227i) q^{76} +(14.0625 + 14.0625i) q^{77} +(-0.0273575 - 0.183066i) q^{78} +(1.49359 - 1.49359i) q^{79} -3.99330 q^{80} +(-7.46154 + 5.03243i) q^{81} +0.226046 q^{82} -1.76845i q^{83} +(-9.53662 - 7.05688i) q^{84} +(-4.08727 - 4.08727i) q^{85} +0.131919 q^{86} +(-8.12930 + 4.57324i) q^{87} -0.775559 q^{88} +(-6.11850 - 6.11850i) q^{89} +(-0.0470669 + 0.0885156i) q^{90} +10.9584i q^{91} +6.99394 q^{92} +(0.324415 + 2.17086i) q^{93} +0.186298 q^{94} +(-1.51698 + 1.51698i) q^{95} +(0.686421 - 0.102579i) q^{96} +(-5.10408 - 5.10408i) q^{97} +(-0.112051 - 0.112051i) q^{98} +(8.17439 - 15.3730i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{2} + 2 q^{3} + 36 q^{5} - 8 q^{6} + 8 q^{7} - 4 q^{8}+O(q^{10}) $ 36 * q + 4 * q^2 + 2 * q^3 + 36 * q^5 - 8 * q^6 + 8 * q^7 - 4 * q^8	$ 36 q + 4 q^{2} + 2 q^{3} + 36 q^{5} - 8 q^{6} + 8 q^{7} - 4 q^{8} + 4 q^{10} + 12 q^{11} + 10 q^{12} - 28 q^{14} + 2 q^{15} - 60 q^{16} + 20 q^{17} + 32 q^{18} + 16 q^{19} - 12 q^{21} + 24 q^{24} + 36 q^{25} - 4 q^{26} - 22 q^{27} + 28 q^{29} - 8 q^{30} - 8 q^{31} + 16 q^{32} + 8 q^{33} + 8 q^{35} - 28 q^{36} - 4 q^{37} - 24 q^{38} - 24 q^{39} - 4 q^{40} - 48 q^{41} + 8 q^{42} + 4 q^{43} - 16 q^{44} + 20 q^{46} + 20 q^{47} - 66 q^{48} + 28 q^{49} + 4 q^{50} - 44 q^{52} - 24 q^{54} + 12 q^{55} + 84 q^{56} - 28 q^{57} - 64 q^{58} + 10 q^{60} + 20 q^{61} - 8 q^{62} - 32 q^{63} - 8 q^{66} - 60 q^{68} - 36 q^{69} - 28 q^{70} + 16 q^{71} + 64 q^{72} + 8 q^{73} + 2 q^{75} + 16 q^{76} - 32 q^{77} + 48 q^{78} + 12 q^{79} - 60 q^{80} - 60 q^{81} + 56 q^{82} + 100 q^{84} + 20 q^{85} - 8 q^{86} - 10 q^{87} - 24 q^{88} - 20 q^{89} + 32 q^{90} + 16 q^{92} - 24 q^{93} + 52 q^{94} + 16 q^{95} + 8 q^{96} + 4 q^{97} + 8 q^{98} + 32 q^{99}+O(q^{100}) $ 36 * q + 4 * q^2 + 2 * q^3 + 36 * q^5 - 8 * q^6 + 8 * q^7 - 4 * q^8 + 4 * q^10 + 12 * q^11 + 10 * q^12 - 28 * q^14 + 2 * q^15 - 60 * q^16 + 20 * q^17 + 32 * q^18 + 16 * q^19 - 12 * q^21 + 24 * q^24 + 36 * q^25 - 4 * q^26 - 22 * q^27 + 28 * q^29 - 8 * q^30 - 8 * q^31 + 16 * q^32 + 8 * q^33 + 8 * q^35 - 28 * q^36 - 4 * q^37 - 24 * q^38 - 24 * q^39 - 4 * q^40 - 48 * q^41 + 8 * q^42 + 4 * q^43 - 16 * q^44 + 20 * q^46 + 20 * q^47 - 66 * q^48 + 28 * q^49 + 4 * q^50 - 44 * q^52 - 24 * q^54 + 12 * q^55 + 84 * q^56 - 28 * q^57 - 64 * q^58 + 10 * q^60 + 20 * q^61 - 8 * q^62 - 32 * q^63 - 8 * q^66 - 60 * q^68 - 36 * q^69 - 28 * q^70 + 16 * q^71 + 64 * q^72 + 8 * q^73 + 2 * q^75 + 16 * q^76 - 32 * q^77 + 48 * q^78 + 12 * q^79 - 60 * q^80 - 60 * q^81 + 56 * q^82 + 100 * q^84 + 20 * q^85 - 8 * q^86 - 10 * q^87 - 24 * q^88 - 20 * q^89 + 32 * q^90 + 16 * q^92 - 24 * q^93 + 52 * q^94 + 16 * q^95 + 8 * q^96 + 4 * q^97 + 8 * q^98 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/435\mathbb{Z}\right)^\times$.

$n$	$31$	$146$	$262$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.0236294	−	0.0236294i	−0.0167085	−	0.0167085i	0.698703	−	0.715412i	$-0.253761\pi$
$2$	−0.0236294	−	0.0236294i	−0.0167085	−	0.0167085i	−0.715412	+	0.698703i	$0.753761\pi$
$3$	1.03028	−	1.39231i	0.594831	−	0.803851i
$3$	1.03028	−	1.39231i	0.594831	−	0.803851i
$4$		−	1.99888i		−	0.999442i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−0.0572444	+	0.00855463i	−0.0233699	+	0.00349241i
$7$	3.42666			1.29516			0.647578	−	0.761999i	$-0.275782\pi$
$7$	3.42666			1.29516			0.647578	+	0.761999i	$0.275782\pi$
$8$	−0.0944913	+	0.0944913i	−0.0334077	+	0.0334077i
$9$	−0.877056	−	2.86893i	−0.292352	−	0.956311i
$10$	−0.0236294	−	0.0236294i	−0.00747228	−	0.00747228i
$11$	4.10386	+	4.10386i	1.23736	+	1.23736i	0.961075	+	0.276286i	$0.0891039\pi$
$11$	4.10386	+	4.10386i	1.23736	+	1.23736i	0.276286	+	0.961075i	$0.410896\pi$
$12$	−2.78307	−	2.05940i	−0.803402	−	0.594499i
$13$			3.19797i			0.886958i	0.896285	+	0.443479i	$0.146256\pi$
$13$			3.19797i			0.886958i	−0.896285	+	0.443479i	$0.853744\pi$
$14$	−0.0809700	−	0.0809700i	−0.0216401	−	0.0216401i
$15$	1.03028	−	1.39231i	0.266017	−	0.359493i
$16$	−3.99330			−0.998325
$17$	−4.08727	−	4.08727i	−0.991308	−	0.991308i	0.00865490	−	0.999963i	$-0.497245\pi$
$17$	−4.08727	−	4.08727i	−0.991308	−	0.991308i	−0.999963	+	0.00865490i	$0.997245\pi$
$18$	−0.0470669	+	0.0885156i	−0.0110938	+	0.0208633i
$19$	−1.51698	+	1.51698i	−0.348020	+	0.348020i	−0.859372	−	0.511352i	$-0.829145\pi$
$19$	−1.51698	+	1.51698i	−0.348020	+	0.348020i	0.511352	+	0.859372i	$0.329145\pi$
$20$		−	1.99888i		−	0.446964i
$21$	3.53041	−	4.77097i	0.770399	−	1.04111i
$22$		−	0.193944i		−	0.0413490i
$23$			3.49892i			0.729576i	0.931091	+	0.364788i	$0.118859\pi$
$23$			3.49892i			0.729576i	−0.931091	+	0.364788i	$0.881141\pi$
$24$	0.0342090	+	0.228913i	0.00698287	+	0.0467268i
$25$	1.00000			0.200000
$26$	0.0755663	−	0.0755663i	0.0148198	−	0.0148198i
$27$	−4.89806	−	1.73466i	−0.942631	−	0.333836i
$28$		−	6.84949i		−	1.29443i
$29$	−4.91427	−	2.20227i	−0.912556	−	0.408951i
$29$	−4.91427	−	2.20227i	−0.912556	−	0.408951i
$30$	−0.0572444	+	0.00855463i	−0.0104513	+	0.00156185i
$31$	−0.896093	+	0.896093i	−0.160943	+	0.160943i	−0.782984	−	0.622041i	$-0.786304\pi$
$31$	−0.896093	+	0.896093i	−0.160943	+	0.160943i	0.622041	+	0.782984i	$0.286304\pi$
$32$	0.283342	+	0.283342i	0.0500883	+	0.0500883i
$33$	9.94197	−	1.48573i	1.73068	−	0.258633i
$34$			0.193159i			0.0331266i
$35$	3.42666			0.579211
$36$	−5.73466	+	1.75313i	−0.955777	+	0.292189i
$37$	−1.53523	−	1.53523i	−0.252389	−	0.252389i	0.569560	−	0.821950i	$-0.307114\pi$
$37$	−1.53523	−	1.53523i	−0.252389	−	0.252389i	−0.821950	+	0.569560i	$0.807114\pi$
$38$	0.0716909			0.0116298
$39$	4.45257	+	3.29480i	0.712982	+	0.527590i
$40$	−0.0944913	+	0.0944913i	−0.0149404	+	0.0149404i
$41$	−4.78315	+	4.78315i	−0.747002	+	0.747002i	−0.973915	−	0.226913i	$-0.927137\pi$
$41$	−4.78315	+	4.78315i	−0.747002	+	0.747002i	0.226913	+	0.973915i	$0.427137\pi$
$42$	−0.196157	+	0.0293138i	−0.0302677	+	0.00452322i
$43$	−2.79141	+	2.79141i	−0.425686	+	0.425686i	−0.887156	−	0.461470i	$-0.847322\pi$
$43$	−2.79141	+	2.79141i	−0.425686	+	0.425686i	0.461470	+	0.887156i	$0.347322\pi$
$44$	8.20315	−	8.20315i	1.23667	−	1.23667i
$45$	−0.877056	−	2.86893i	−0.130744	−	0.427675i
$46$	0.0826775	−	0.0826775i	0.0121901	−	0.0121901i
$47$	−3.94208	+	3.94208i	−0.575011	+	0.575011i	−0.933524	−	0.358514i	$-0.883284\pi$
$47$	−3.94208	+	3.94208i	−0.575011	+	0.575011i	0.358514	+	0.933524i	$0.383284\pi$
$48$	−4.11421	+	5.55991i	−0.593835	+	0.802505i
$49$	4.74200			0.677428
$50$	−0.0236294	−	0.0236294i	−0.00334171	−	0.00334171i
$51$	−9.90176	+	1.47972i	−1.38652	+	0.207203i
$52$	6.39238			0.886463
$53$			0.219714i			0.0301801i	0.999886	+	0.0150900i	$0.00480349\pi$
$53$			0.219714i			0.0301801i	−0.999886	+	0.0150900i	$0.995197\pi$
$54$	0.0747492	+	0.156727i	0.0101721	+	0.0213279i
$55$	4.10386	+	4.10386i	0.553365	+	0.553365i
$56$	−0.323790	+	0.323790i	−0.0432682	+	0.0432682i
$57$	0.549198	+	3.67503i	0.0727430	+	0.486769i
$58$	0.0640830	+	0.168160i	0.00841451	+	0.0220804i
$59$		−	14.4779i		−	1.88486i	−0.334401	−	0.942431i	$-0.608534\pi$
$59$		−	14.4779i		−	1.88486i	0.334401	−	0.942431i	$-0.391466\pi$
$60$	−2.78307	−	2.05940i	−0.359292	−	0.265868i
$61$	7.78602	−	7.78602i	0.996897	−	0.996897i	−0.00309811	−	0.999995i	$-0.500986\pi$
$61$	7.78602	−	7.78602i	0.996897	−	0.996897i	0.999995	+	0.00309811i	$0.000986162\pi$
$62$	0.0423483			0.00537824
$63$	−3.00537	−	9.83086i	−0.378642	−	1.23857i
$64$			7.97321i			0.996651i
$65$			3.19797i			0.396660i
$66$	−0.270030	−	0.199816i	−0.0332384	−	0.0245957i
$67$			11.2502i			1.37443i	0.726454	+	0.687215i	$0.241167\pi$
$67$			11.2502i			1.37443i	−0.726454	+	0.687215i	$0.758833\pi$
$68$	−8.16997	+	8.16997i	−0.990754	+	0.990754i
$69$	4.87159	+	3.60486i	0.586470	+	0.433974i
$70$	−0.0809700	−	0.0809700i	−0.00967777	−	0.00967777i
$71$	9.21033			1.09306			0.546532	−	0.837438i	$-0.315948\pi$
$71$	9.21033			1.09306			0.546532	+	0.837438i	$0.315948\pi$
$72$	0.353963	+	0.188215i	0.0417150	+	0.0221813i
$73$	10.7069	+	10.7069i	1.25314	+	1.25314i	0.954302	+	0.298842i	$0.0966005\pi$
$73$	10.7069	+	10.7069i	1.25314	+	1.25314i	0.298842	+	0.954302i	$0.403399\pi$
$74$			0.0725530i			0.00843411i
$75$	1.03028	−	1.39231i	0.118966	−	0.160770i
$76$	3.03227	+	3.03227i	0.347826	+	0.347826i
$77$	14.0625	+	14.0625i	1.60258	+	1.60258i
$78$	−0.0273575	−	0.183066i	−0.00309762	−	0.0207281i
$79$	1.49359	−	1.49359i	0.168042	−	0.168042i	−0.618076	−	0.786118i	$-0.712088\pi$
$79$	1.49359	−	1.49359i	0.168042	−	0.168042i	0.786118	+	0.618076i	$0.212088\pi$
$80$	−3.99330			−0.446465
$81$	−7.46154	+	5.03243i	−0.829060	+	0.559159i
$82$	0.226046			0.0249626
$83$		−	1.76845i		−	0.194113i	−0.995279	−	0.0970565i	$-0.969057\pi$
$83$		−	1.76845i		−	0.194113i	0.995279	−	0.0970565i	$-0.0309427\pi$
$84$	−9.53662	−	7.05688i	−1.04053	−	0.769969i
$85$	−4.08727	−	4.08727i	−0.443326	−	0.443326i
$86$	0.131919			0.0142252
$87$	−8.12930	+	4.57324i	−0.871552	+	0.490303i
$88$	−0.775559			−0.0826749
$89$	−6.11850	−	6.11850i	−0.648560	−	0.648560i	0.304085	−	0.952645i	$-0.401649\pi$
$89$	−6.11850	−	6.11850i	−0.648560	−	0.648560i	−0.952645	+	0.304085i	$0.901649\pi$
$90$	−0.0470669	+	0.0885156i	−0.00496128	+	0.00933036i
$91$			10.9584i			1.14875i
$92$	6.99394			0.729169
$93$	0.324415	+	2.17086i	0.0336403	+	0.225108i
$94$	0.186298			0.0192152
$95$	−1.51698	+	1.51698i	−0.155639	+	0.155639i
$96$	0.686421	−	0.102579i	0.0700575	−	0.0104694i
$97$	−5.10408	−	5.10408i	−0.518241	−	0.518241i	0.398798	−	0.917039i	$-0.369427\pi$
$97$	−5.10408	−	5.10408i	−0.518241	−	0.518241i	−0.917039	+	0.398798i	$0.869427\pi$
$98$	−0.112051	−	0.112051i	−0.0113188	−	0.0113188i
$99$	8.17439	−	15.3730i	0.821557	−	1.54505i
$100$		−	1.99888i		−	0.199888i
$101$	−9.67557	−	9.67557i	−0.962755	−	0.962755i	0.0365758	−	0.999331i	$-0.488355\pi$
$101$	−9.67557	−	9.67557i	−0.962755	−	0.962755i	−0.999331	+	0.0365758i	$0.988355\pi$
$102$	0.268938	+	0.199008i	0.0266288	+	0.0197047i
$103$	0.181474			0.0178811			0.00894057	−	0.999960i	$-0.497154\pi$
$103$	0.181474			0.0178811			0.00894057	+	0.999960i	$0.497154\pi$
$104$	−0.302181	−	0.302181i	−0.0296313	−	0.0296313i
$105$	3.53041	−	4.77097i	0.344533	−	0.465599i
$106$	0.00519172	−	0.00519172i	0.000504265	−	0.000504265i
$107$		−	1.42157i		−	0.137428i	−0.997636	−	0.0687142i	$-0.978110\pi$
$107$		−	1.42157i		−	0.137428i	0.997636	−	0.0687142i	$-0.0218897\pi$
$108$	−3.46739	+	9.79064i	−0.333649	+	0.942105i
$109$			1.85368i			0.177550i	0.996052	+	0.0887751i	$0.0282953\pi$
$109$			1.85368i			0.177550i	−0.996052	+	0.0887751i	$0.971705\pi$
$110$		−	0.193944i		−	0.0184918i
$111$	−3.71922	+	0.555802i	−0.353013	+	0.0527544i
$112$	−13.6837			−1.29299
$113$	−9.15667	+	9.15667i	−0.861387	+	0.861387i	−0.991499	−	0.130113i	$-0.958466\pi$
$113$	−9.15667	+	9.15667i	−0.861387	+	0.861387i	0.130113	+	0.991499i	$0.458466\pi$
$114$	0.0738615	−	0.0998160i	0.00691777	−	0.00934862i
$115$			3.49892i			0.326276i
$116$	−4.40208	+	9.82305i	−0.408722	+	0.912047i
$117$	9.17477	−	2.80480i	0.848208	−	0.259304i
$118$	−0.342104	+	0.342104i	−0.0314933	+	0.0314933i
$119$	−14.0057	−	14.0057i	−1.28390	−	1.28390i
$120$	0.0342090	+	0.228913i	0.00312284	+	0.0208968i
$121$			22.6834i			2.06213i
$122$	−0.367958			−0.0333134
$123$	1.73166	+	11.5876i	0.156138	+	1.04482i
$124$	1.79118	+	1.79118i	0.160853	+	0.160853i
$125$	1.00000			0.0894427
$126$	−0.161282	+	0.303313i	−0.0143682	+	0.0270212i
$127$	−4.83188	+	4.83188i	−0.428760	+	0.428760i	−0.888206	−	0.459446i	$-0.848048\pi$
$127$	−4.83188	+	4.83188i	−0.428760	+	0.428760i	0.459446	+	0.888206i	$0.348048\pi$
$128$	0.755086	−	0.755086i	0.0667408	−	0.0667408i
$129$	1.01058	+	6.76244i	0.0889769	+	0.595400i
$130$	0.0755663	−	0.0755663i	0.00662760	−	0.00662760i
$131$	13.6795	−	13.6795i	1.19518	−	1.19518i	0.219589	−	0.975592i	$-0.429528\pi$
$131$	13.6795	−	13.6795i	1.19518	−	1.19518i	0.975592	−	0.219589i	$-0.0704718\pi$
$132$	−2.96981	−	19.8728i	−0.258489	−	1.72971i
$133$	−5.19819	+	5.19819i	−0.450740	+	0.450740i
$134$	0.265835	−	0.265835i	0.0229647	−	0.0229647i
$135$	−4.89806	−	1.73466i	−0.421558	−	0.149296i
$136$	0.772422			0.0662347
$137$	4.96358	+	4.96358i	0.424068	+	0.424068i	0.886602	−	0.462534i	$-0.153060\pi$
$137$	4.96358	+	4.96358i	0.424068	+	0.424068i	−0.462534	+	0.886602i	$0.653060\pi$
$138$	−0.0299320	−	0.200294i	−0.00254798	−	0.0170501i
$139$	6.80276			0.577002			0.288501	−	0.957480i	$-0.406843\pi$
$139$	6.80276			0.577002			0.288501	+	0.957480i	$0.406843\pi$
$140$		−	6.84949i		−	0.578888i
$141$	1.42716	+	9.55003i	0.120189	+	0.804257i
$142$	−0.217635	−	0.217635i	−0.0182635	−	0.0182635i
$143$	−13.1241	+	13.1241i	−1.09749	+	1.09749i
$144$	3.50235	+	11.4565i	0.291863	+	0.954709i
$145$	−4.91427	−	2.20227i	−0.408108	−	0.182888i
$146$		−	0.505995i		−	0.0418764i
$147$	4.88557	−	6.60233i	0.402955	−	0.544551i
$148$	−3.06874	+	3.06874i	−0.252249	+	0.252249i
$149$	12.7788			1.04688			0.523439	−	0.852063i	$-0.324649\pi$
$149$	12.7788			1.04688			0.523439	+	0.852063i	$0.324649\pi$
$150$	−0.0572444	+	0.00855463i	−0.00467398	+	0.000698482i
$151$		−	21.8159i		−	1.77535i	−0.460469	−	0.887676i	$-0.652319\pi$
$151$		−	21.8159i		−	1.77535i	0.460469	−	0.887676i	$-0.347681\pi$
$152$		−	0.286684i		−	0.0232531i
$153$	−8.14133	+	15.3109i	−0.658187	+	1.23781i
$154$		−	0.664580i		−	0.0535534i
$155$	−0.896093	+	0.896093i	−0.0719759	+	0.0719759i
$156$	6.58592	−	8.90017i	0.527296	−	0.712584i
$157$	10.2256	+	10.2256i	0.816091	+	0.816091i	0.985539	−	0.169448i	$-0.0541985\pi$
$157$	10.2256	+	10.2256i	0.816091	+	0.816091i	−0.169448	+	0.985539i	$0.554198\pi$
$158$	−0.0705852			−0.00561545
$159$	0.305911	+	0.226367i	0.0242603	+	0.0179521i
$160$	0.283342	+	0.283342i	0.0224002	+	0.0224002i
$161$			11.9896i			0.944914i
$162$	0.295225	+	0.0573986i	0.0231951	+	0.00450966i
$163$	−15.4030	−	15.4030i	−1.20645	−	1.20645i	−0.972168	−	0.234284i	$-0.924725\pi$
$163$	−15.4030	−	15.4030i	−1.20645	−	1.20645i	−0.234284	−	0.972168i	$-0.575275\pi$
$164$	9.56096	+	9.56096i	0.746585	+	0.746585i
$165$	9.94197	−	1.48573i	0.773982	−	0.115664i
$166$	−0.0417875	+	0.0417875i	−0.00324334	+	0.00324334i
$167$	14.6643			1.13476			0.567381	−	0.823456i	$-0.307957\pi$
$167$	14.6643			1.13476			0.567381	+	0.823456i	$0.307957\pi$
$168$	0.117222	+	0.784409i	0.00904391	+	0.0605184i
$169$	2.77296			0.213305
$170$			0.193159i			0.0148147i
$171$	5.68260	+	3.02164i	0.434560	+	0.231071i
$172$	5.57971	+	5.57971i	0.425449	+	0.425449i
$173$	15.1753			1.15376			0.576879	−	0.816830i	$-0.304270\pi$
$173$	15.1753			1.15376			0.576879	+	0.816830i	$0.304270\pi$
$174$	0.300154	+	0.0840277i	0.0227546	+	0.00637012i
$175$	3.42666			0.259031
$176$	−16.3880	−	16.3880i	−1.23529	−	1.23529i
$177$	−20.1577	−	14.9163i	−1.51515	−	1.12117i
$178$			0.289153i			0.0216730i
$179$	0.0275707			0.00206073			0.00103037	−	0.999999i	$-0.499672\pi$
$179$	0.0275707			0.00206073			0.00103037	+	0.999999i	$0.499672\pi$
$180$	−5.73466	+	1.75313i	−0.427436	+	0.130671i
$181$	−15.6387			−1.16241			−0.581206	−	0.813756i	$-0.697419\pi$
$181$	−15.6387			−1.16241			−0.581206	+	0.813756i	$0.697419\pi$
$182$	0.258940	−	0.258940i	0.0191939	−	0.0191939i
$183$	−2.81879	−	18.8623i	−0.208371	−	1.39434i
$184$	−0.330618	−	0.330618i	−0.0243735	−	0.0243735i
$185$	−1.53523	−	1.53523i	−0.112872	−	0.112872i
$186$	0.0436305	−	0.0589620i	0.00319914	−	0.00432330i
$187$		−	33.5472i		−	2.45321i
$188$	7.87975	+	7.87975i	0.574690	+	0.574690i
$189$	−16.7840	−	5.94410i	−1.22085	−	0.432369i
$190$	0.0716909			0.00520100
$191$	9.92163	+	9.92163i	0.717904	+	0.717904i	0.968176	−	0.250272i	$-0.0805200\pi$
$191$	9.92163	+	9.92163i	0.717904	+	0.717904i	−0.250272	+	0.968176i	$0.580520\pi$
$192$	11.1012	+	8.21462i	0.801159	+	0.592839i
$193$	13.0779	−	13.0779i	0.941365	−	0.941365i	−0.0570086	−	0.998374i	$-0.518156\pi$
$193$	13.0779	−	13.0779i	0.941365	−	0.941365i	0.998374	+	0.0570086i	$0.0181562\pi$
$194$			0.241213i			0.0173181i
$195$	4.45257	+	3.29480i	0.318855	+	0.235946i
$196$		−	9.47870i		−	0.677050i
$197$		−	6.69199i		−	0.476785i	−0.971169	−	0.238392i	$-0.923380\pi$
$197$		−	6.69199i		−	0.476785i	0.971169	−	0.238392i	$-0.0766204\pi$
$198$	−0.556412	+	0.170100i	−0.0395425	+	0.0120885i
$199$	4.43567			0.314436			0.157218	−	0.987564i	$-0.449747\pi$
$199$	4.43567			0.314436			0.157218	+	0.987564i	$0.449747\pi$
$200$	−0.0944913	+	0.0944913i	−0.00668154	+	0.00668154i
$201$	15.6638	+	11.5908i	1.10484	+	0.817553i
$202$			0.457256i			0.0321724i
$203$	−16.8395	−	7.54642i	−1.18190	−	0.529655i
$204$	2.95780	+	19.7925i	0.207087	+	1.38575i
$205$	−4.78315	+	4.78315i	−0.334070	+	0.334070i
$206$	−0.00428812	−	0.00428812i	−0.000298768	−	0.000298768i
$207$	10.0382	−	3.06875i	0.697701	−	0.213293i
$208$		−	12.7705i		−	0.885473i
$209$	−12.4510			−0.861253
$210$	−0.196157	+	0.0293138i	−0.0135361	+	0.00202284i
$211$	−12.8624	−	12.8624i	−0.885487	−	0.885487i	0.108599	−	0.994086i	$-0.465364\pi$
$211$	−12.8624	−	12.8624i	−0.885487	−	0.885487i	−0.994086	+	0.108599i	$0.965364\pi$
$212$	0.439183			0.0301632
$213$	9.48919	−	12.8236i	0.650189	−	0.878661i
$214$	−0.0335909	+	0.0335909i	−0.00229623	+	0.00229623i
$215$	−2.79141	+	2.79141i	−0.190373	+	0.190373i
$216$	0.626734	−	0.298913i	0.0426439	−	0.0203385i
$217$	−3.07061	+	3.07061i	−0.208446	+	0.208446i
$218$	0.0438014	−	0.0438014i	0.00296660	−	0.00296660i
$219$	25.9383	−	3.87624i	1.75275	−	0.261932i
$220$	8.20315	−	8.20315i	0.553056	−	0.553056i
$221$	13.0710	−	13.0710i	0.879249	−	0.879249i
$222$	0.101016	+	0.0747497i	0.00677977	+	0.00501687i
$223$	−1.47430			−0.0987265			−0.0493633	−	0.998781i	$-0.515719\pi$
$223$	−1.47430			−0.0987265			−0.0493633	+	0.998781i	$0.515719\pi$
$224$	0.970917	+	0.970917i	0.0648721	+	0.0648721i
$225$	−0.877056	−	2.86893i	−0.0584704	−	0.191262i
$226$	0.432733			0.0287850
$227$			21.1275i			1.40228i	0.713023	+	0.701140i	$0.247325\pi$
$227$			21.1275i			1.40228i	−0.713023	+	0.701140i	$0.752675\pi$
$228$	7.34595	−	1.09778i	0.486497	−	0.0727024i
$229$	−4.56792	−	4.56792i	−0.301857	−	0.301857i	0.539883	−	0.841740i	$-0.318468\pi$
$229$	−4.56792	−	4.56792i	−0.301857	−	0.301857i	−0.841740	+	0.539883i	$0.818468\pi$
$230$	0.0826775	−	0.0826775i	0.00545160	−	0.00545160i
$231$	34.0678	−	5.09110i	2.24149	−	0.334970i
$232$	0.672451	−	0.256260i	0.0441485	−	0.0168243i
$233$		−	0.0136176i		−	0.000892116i	−1.00000		0.000446058i	$-0.999858\pi$
$233$		−	0.0136176i		−	0.000892116i	1.00000		0.000446058i	$-0.000141985\pi$
$234$	−0.283070	−	0.150519i	−0.0185049	−	0.00983971i
$235$	−3.94208	+	3.94208i	−0.257153	+	0.257153i
$236$	−28.9396			−1.88381
$237$	−0.540727	−	3.61834i	−0.0351240	−	0.235037i
$238$			0.661892i			0.0429041i
$239$		−	17.0951i		−	1.10579i	−0.833251	−	0.552896i	$-0.813523\pi$
$239$		−	17.0951i		−	1.10579i	0.833251	−	0.552896i	$-0.186477\pi$
$240$	−4.11421	+	5.55991i	−0.265571	+	0.358891i
$241$		−	11.1853i		−	0.720506i	−0.932855	−	0.360253i	$-0.882690\pi$
$241$		−	11.1853i		−	0.720506i	0.932855	−	0.360253i	$-0.117310\pi$
$242$	0.535996	−	0.535996i	0.0344551	−	0.0344551i
$243$	−0.680756	+	15.5736i	−0.0436705	+	0.999046i
$244$	−15.5633	−	15.5633i	−0.996340	−	0.996340i
$245$	4.74200			0.302955
$246$	0.232890	−	0.314726i	0.0148485	−	0.0200662i
$247$	−4.85127	−	4.85127i	−0.308679	−	0.308679i
$248$		−	0.169346i		−	0.0107535i
$249$	−2.46224	−	1.82200i	−0.156038	−	0.115464i
$250$	−0.0236294	−	0.0236294i	−0.00149446	−	0.00149446i
$251$	3.76151	+	3.76151i	0.237424	+	0.237424i	0.815783	−	0.578358i	$-0.196306\pi$
$251$	3.76151	+	3.76151i	0.237424	+	0.237424i	−0.578358	+	0.815783i	$0.696306\pi$
$252$	−19.6507	+	6.00739i	−1.23788	+	0.378430i
$253$	−14.3591	+	14.3591i	−0.902749	+	0.902749i
$254$	0.228349			0.0143279
$255$	−9.90176	+	1.47972i	−0.620072	+	0.0926639i
$256$	15.9107			0.994421
$257$			5.39473i			0.336514i	0.985743	+	0.168257i	$0.0538139\pi$
$257$			5.39473i			0.336514i	−0.985743	+	0.168257i	$0.946186\pi$
$258$	0.135913	−	0.183672i	0.00846158	−	0.0114349i
$259$	−5.26069	−	5.26069i	−0.326884	−	0.326884i
$260$	6.39238			0.396438
$261$	−2.00807	+	16.0302i	−0.124296	+	0.992245i
$262$	−0.646476			−0.0399395
$263$	−14.6301	−	14.6301i	−0.902133	−	0.902133i	0.0934873	−	0.995620i	$-0.470199\pi$
$263$	−14.6301	−	14.6301i	−0.902133	−	0.902133i	−0.995620	+	0.0934873i	$0.970199\pi$
$264$	−0.799041	+	1.07982i	−0.0491776	+	0.0664583i
$265$			0.219714i			0.0134969i
$266$	0.245660			0.0150624
$267$	−14.8226	+	2.21510i	−0.907129	+	0.135562i
$268$	22.4878			1.37366
$269$	4.29151	−	4.29151i	0.261658	−	0.261658i	−0.564069	−	0.825727i	$-0.690765\pi$
$269$	4.29151	−	4.29151i	0.261658	−	0.261658i	0.825727	+	0.564069i	$0.190765\pi$
$270$	0.0747492	+	0.156727i	0.00454909	+	0.00953812i
$271$	7.12704	+	7.12704i	0.432937	+	0.432937i	0.889626	−	0.456689i	$-0.150965\pi$
$271$	7.12704	+	7.12704i	0.432937	+	0.432937i	−0.456689	+	0.889626i	$0.650965\pi$
$272$	16.3217	+	16.3217i	0.989647	+	0.989647i
$273$	15.2575	+	11.2902i	0.923423	+	0.683312i
$274$		−	0.234573i		−	0.0141711i
$275$	4.10386	+	4.10386i	0.247472	+	0.247472i
$276$	7.20570	−	9.73773i	0.433732	−	0.586143i
$277$	1.52133			0.0914079			0.0457040	−	0.998955i	$-0.485447\pi$
$277$	1.52133			0.0914079			0.0457040	+	0.998955i	$0.485447\pi$
$278$	−0.160745	−	0.160745i	−0.00964086	−	0.00964086i
$279$	3.35675	+	1.78491i	0.200964	+	0.106860i
$280$	−0.323790	+	0.323790i	−0.0193501	+	0.0193501i
$281$		−	11.2725i		−	0.672462i	−0.941780	−	0.336231i	$-0.890848\pi$
$281$		−	11.2725i		−	0.672462i	0.941780	−	0.336231i	$-0.109152\pi$
$282$	0.191939	−	0.259385i	0.0114298	−	0.0154461i
$283$		−	7.34630i		−	0.436692i	−0.975871	−	0.218346i	$-0.929934\pi$
$283$		−	7.34630i		−	0.436692i	0.975871	−	0.218346i	$-0.0700661\pi$
$284$		−	18.4104i		−	1.09245i
$285$	0.549198	+	3.67503i	0.0325317	+	0.217690i
$286$	0.620228			0.0366748
$287$	−16.3902	+	16.3902i	−0.967484	+	0.967484i
$288$	0.564382	−	1.06140i	0.0332565	−	0.0625434i
$289$			16.4115i			0.965382i
$290$	0.0640830	+	0.168160i	0.00376308	+	0.00987467i
$291$	−12.3651	+	1.84784i	−0.724854	+	0.108323i
$292$	21.4018	−	21.4018i	1.25245	−	1.25245i
$293$	−12.7319	−	12.7319i	−0.743806	−	0.743806i	0.229502	−	0.973308i	$-0.426290\pi$
$293$	−12.7319	−	12.7319i	−0.743806	−	0.743806i	−0.973308	+	0.229502i	$0.926290\pi$
$294$	−0.271453	+	0.0405660i	−0.0158314	+	0.00236586i
$295$		−	14.4779i		−	0.842936i
$296$	0.290131			0.0168635
$297$	−12.9821	−	27.2198i	−0.753300	−	1.57945i
$298$	−0.301955	−	0.301955i	−0.0174918	−	0.0174918i
$299$	−11.1895			−0.647103
$300$	−2.78307	−	2.05940i	−0.160680	−	0.118900i
$301$	−9.56522	+	9.56522i	−0.551330	+	0.551330i
$302$	−0.515497	+	0.515497i	−0.0296635	+	0.0296635i
$303$	−23.4399	+	3.50287i	−1.34659	+	0.201235i
$304$	6.05777	−	6.05777i	0.347437	−	0.347437i
$305$	7.78602	−	7.78602i	0.445826	−	0.445826i
$306$	0.554161	−	0.169412i	0.0316793	−	0.00968463i
$307$	−6.21116	+	6.21116i	−0.354490	+	0.354490i	−0.861777	−	0.507287i	$-0.830648\pi$
$307$	−6.21116	+	6.21116i	−0.354490	+	0.354490i	0.507287	+	0.861777i	$0.330648\pi$
$308$	28.1094	−	28.1094i	1.60168	−	1.60168i
$309$	0.186968	−	0.252668i	0.0106363	−	0.0143738i
$310$	0.0423483			0.00240522
$311$	15.0524	+	15.0524i	0.853544	+	0.853544i	0.990568	−	0.137024i	$-0.0437536\pi$
$311$	15.0524	+	15.0524i	0.853544	+	0.853544i	−0.137024	+	0.990568i	$0.543754\pi$
$312$	−0.732059	+	0.109399i	−0.0414447	+	0.00619352i
$313$	0.262042			0.0148115			0.00740573	−	0.999973i	$-0.497643\pi$
$313$	0.262042			0.0148115			0.00740573	+	0.999973i	$0.497643\pi$
$314$		−	0.483250i		−	0.0272714i
$315$	−3.00537	−	9.83086i	−0.169334	−	0.553906i
$316$	−2.98550	−	2.98550i	−0.167948	−	0.167948i
$317$	−14.0287	+	14.0287i	−0.787932	+	0.787932i	−0.981155	−	0.193223i	$-0.938106\pi$
$317$	−14.0287	+	14.0287i	−0.787932	+	0.787932i	0.193223	+	0.981155i	$0.438106\pi$
$318$	−0.00187957	−	0.0125774i	−0.000105401	−	0.000705306i
$319$	−11.1297	−	29.2053i	−0.623142	−	1.63518i
$320$			7.97321i			0.445716i
$321$	−1.97927	−	1.46461i	−0.110472	−	0.0817466i
$322$	0.283308	−	0.283308i	0.0157881	−	0.0157881i
$323$	12.4006			0.689990
$324$	10.0592	+	14.9148i	0.558847	+	0.828598i
$325$			3.19797i			0.177392i
$326$			0.727926i			0.0403161i
$327$	2.58090	+	1.90980i	0.142724	+	0.105612i
$328$		−	0.903932i		−	0.0499113i
$329$	−13.5082	+	13.5082i	−0.744729	+	0.744729i
$330$	−0.270030	−	0.199816i	−0.0148647	−	0.0109995i
$331$	8.00083	+	8.00083i	0.439765	+	0.439765i	0.891933	−	0.452168i	$-0.149349\pi$
$331$	8.00083	+	8.00083i	0.439765	+	0.439765i	−0.452168	+	0.891933i	$0.649349\pi$
$332$	−3.53493			−0.194005
$333$	−3.05798	+	5.75094i	−0.167576	+	0.315149i
$334$	−0.346510	−	0.346510i	−0.0189602	−	0.0189602i
$335$			11.2502i			0.614664i
$336$	−14.0980	+	19.0519i	−0.769109	+	1.03937i
$337$	11.7821	+	11.7821i	0.641810	+	0.641810i	0.951000	−	0.309190i	$-0.100058\pi$
$337$	11.7821	+	11.7821i	0.641810	+	0.641810i	−0.309190	+	0.951000i	$0.600058\pi$
$338$	−0.0655235	−	0.0655235i	−0.00356401	−	0.00356401i
$339$	3.31501	+	22.1828i	0.180047	+	1.20481i
$340$	−8.16997	+	8.16997i	−0.443079	+	0.443079i
$341$	−7.35489			−0.398289
$342$	−0.0628770	−	0.205676i	−0.00340000	−	0.0111217i
$343$	−7.73740			−0.417781
$344$		−	0.527528i		−	0.0284424i
$345$	4.87159	+	3.60486i	0.262277	+	0.194079i
$346$	−0.358584	−	0.358584i	−0.0192776	−	0.0192776i
$347$	−7.19432			−0.386211			−0.193106	−	0.981178i	$-0.561856\pi$
$347$	−7.19432			−0.386211			−0.193106	+	0.981178i	$0.561856\pi$
$348$	9.14137	+	16.2495i	0.490029	+	0.871066i
$349$	−19.0937			−1.02206			−0.511030	−	0.859563i	$-0.670736\pi$
$349$	−19.0937			−1.02206			−0.511030	+	0.859563i	$0.670736\pi$
$350$	−0.0809700	−	0.0809700i	−0.00432803	−	0.00432803i
$351$	5.54740	−	15.6639i	0.296098	−	0.836075i
$352$			2.32559i			0.123955i
$353$	22.6944			1.20790			0.603951	−	0.797021i	$-0.293592\pi$
$353$	22.6944			1.20790			0.603951	+	0.797021i	$0.293592\pi$
$354$	0.123853	+	0.828778i	0.00658271	+	0.0440491i
$355$	9.21033			0.488833
$356$	−12.2302	+	12.2302i	−0.648198	+	0.648198i
$357$	−33.9300	+	5.07051i	−1.79576	+	0.268360i
$358$	−0.000651480	0	0.000651480i	−3.44318e−5	0	3.44318e-5i
$359$	1.27514	+	1.27514i	0.0672991	+	0.0672991i	0.739955	−	0.672656i	$-0.234847\pi$
$359$	1.27514	+	1.27514i	0.0672991	+	0.0672991i	−0.672656	+	0.739955i	$0.734847\pi$
$360$	0.353963	+	0.188215i	0.0186555	+	0.00991980i
$361$			14.3975i			0.757764i
$362$	0.369532	+	0.369532i	0.0194222	+	0.0194222i
$363$	31.5824	+	23.3702i	1.65764	+	1.22662i
$364$	21.9045			1.14811
$365$	10.7069	+	10.7069i	0.560423	+	0.560423i
$366$	−0.379099	+	0.512312i	−0.0198158	+	0.0267790i
$367$	−11.1733	+	11.1733i	−0.583242	+	0.583242i	−0.935793	−	0.352551i	$-0.885314\pi$
$367$	−11.1733	+	11.1733i	−0.583242	+	0.583242i	0.352551	+	0.935793i	$0.385314\pi$
$368$		−	13.9723i		−	0.728354i
$369$	17.9176	+	9.52744i	0.932754	+	0.495979i
$370$			0.0725530i			0.00377185i
$371$			0.752887i			0.0390879i
$372$	4.33930	−	0.648468i	0.224982	−	0.0336215i
$373$	−3.65153			−0.189069			−0.0945344	−	0.995522i	$-0.530136\pi$
$373$	−3.65153			−0.189069			−0.0945344	+	0.995522i	$0.530136\pi$
$374$	−0.792700	+	0.792700i	−0.0409896	+	0.0409896i
$375$	1.03028	−	1.39231i	0.0532033	−	0.0718986i
$376$		−	0.744984i		−	0.0384196i
$377$	7.04279	−	15.7157i	0.362722	−	0.809400i
$378$	0.256140	+	0.537051i	0.0131744	+	0.0276229i
$379$	−23.6343	+	23.6343i	−1.21401	+	1.21401i	−0.244316	+	0.969696i	$0.578563\pi$
$379$	−23.6343	+	23.6343i	−1.21401	+	1.21401i	−0.969696	+	0.244316i	$0.921437\pi$
$380$	3.03227	+	3.03227i	0.155552	+	0.155552i
$381$	1.74930	+	11.7056i	0.0896192	+	0.599698i
$382$		−	0.468885i		−	0.0239902i
$383$	24.0070			1.22670			0.613349	−	0.789812i	$-0.289822\pi$
$383$	24.0070			1.22670			0.613349	+	0.789812i	$0.289822\pi$
$384$	−0.273366	−	1.82926i	−0.0139502	−	0.0933492i
$385$	14.0625	+	14.0625i	0.716694	+	0.716694i
$386$	−0.618045			−0.0314576
$387$	10.4566	+	5.56015i	0.531539	+	0.282638i
$388$	−10.2025	+	10.2025i	−0.517951	+	0.517951i
$389$	−24.7490	+	24.7490i	−1.25482	+	1.25482i	−0.301290	+	0.953533i	$0.597417\pi$
$389$	−24.7490	+	24.7490i	−1.25482	+	1.25482i	−0.953533	+	0.301290i	$0.902583\pi$
$390$	−0.0273575	−	0.183066i	−0.00138530	−	0.00926990i
$391$	14.3010	−	14.3010i	0.723234	−	0.723234i
$392$	−0.448078	+	0.448078i	−0.0226313	+	0.0226313i
$393$	−4.95242	−	33.1397i	−0.249817	−	1.67168i
$394$	−0.158128	+	0.158128i	−0.00796637	+	0.00796637i
$395$	1.49359	−	1.49359i	0.0751505	−	0.0751505i
$396$	−30.7289	−	16.3397i	−1.54419	−	0.821098i
$397$	−32.7634			−1.64435			−0.822173	−	0.569238i	$-0.807238\pi$
$397$	−32.7634			−1.64435			−0.822173	+	0.569238i	$0.807238\pi$
$398$	−0.104812	−	0.104812i	−0.00525377	−	0.00525377i
$399$	1.88191	+	12.5931i	0.0942136	+	0.630442i
$400$	−3.99330			−0.199665
$401$			8.99536i			0.449207i	0.974450	+	0.224603i	$0.0721087\pi$
$401$			8.99536i			0.449207i	−0.974450	+	0.224603i	$0.927891\pi$
$402$	−0.0962412	−	0.644010i	−0.00480007	−	0.0321203i
$403$	−2.86568	−	2.86568i	−0.142750	−	0.142750i
$404$	−19.3403	+	19.3403i	−0.962218	+	0.962218i
$405$	−7.46154	+	5.03243i	−0.370767	+	0.250063i
$406$	0.219591	+	0.576226i	0.0108981	+	0.0285976i
$407$		−	12.6007i		−	0.624594i
$408$	0.795809	−	1.07545i	0.0393984	−	0.0532428i
$409$	−9.91083	+	9.91083i	−0.490059	+	0.490059i	−0.908325	−	0.418266i	$-0.862638\pi$
$409$	−9.91083	+	9.91083i	−0.490059	+	0.490059i	0.418266	+	0.908325i	$0.362638\pi$
$410$	0.226046			0.0111636
$411$	12.0247	−	1.79698i	0.593136	−	0.0886385i
$412$		−	0.362745i		−	0.0178712i
$413$		−	49.6108i		−	2.44119i
$414$	−0.309709	−	0.164683i	−0.0152214	−	0.00809375i
$415$		−	1.76845i		−	0.0868099i
$416$	−0.906120	+	0.906120i	−0.0444262	+	0.0444262i
$417$	7.00873	−	9.47155i	0.343219	−	0.463824i
$418$	0.294210	+	0.294210i	0.0143903	+	0.0143903i
$419$	−20.7079			−1.01165			−0.505823	−	0.862637i	$-0.668811\pi$
$419$	−20.7079			−1.01165			−0.505823	+	0.862637i	$0.668811\pi$
$420$	−9.53662	−	7.05688i	−0.465339	−	0.344340i
$421$	−14.7489	−	14.7489i	−0.718817	−	0.718817i	0.249546	−	0.968363i	$-0.419719\pi$
$421$	−14.7489	−	14.7489i	−0.718817	−	0.718817i	−0.968363	+	0.249546i	$0.919719\pi$
$422$			0.607864i			0.0295904i
$423$	14.7670	+	7.85213i	0.717995	+	0.381783i
$424$	−0.0207611	−	0.0207611i	−0.00100825	−	0.00100825i
$425$	−4.08727	−	4.08727i	−0.198262	−	0.198262i
$426$	−0.527239	+	0.0787909i	−0.0255448	+	0.00381743i
$427$	26.6800	−	26.6800i	1.29114	−	1.29114i
$428$	−2.84155			−0.137352
$429$	4.75134	+	31.7942i	0.229397	+	1.53504i
$430$	0.131919			0.00636170
$431$		−	29.7104i		−	1.43110i	−0.698561	−	0.715550i	$-0.746176\pi$
$431$		−	29.7104i		−	1.43110i	0.698561	−	0.715550i	$-0.253824\pi$
$432$	19.5594	+	6.92703i	0.941053	+	0.333277i
$433$	−2.06412	−	2.06412i	−0.0991953	−	0.0991953i	0.655768	−	0.754963i	$-0.272345\pi$
$433$	−2.06412	−	2.06412i	−0.0991953	−	0.0991953i	−0.754963	+	0.655768i	$0.772345\pi$
$434$	0.145113			0.00696566
$435$	−8.12930	+	4.57324i	−0.389770	+	0.219270i
$436$	3.70529			0.177451
$437$	−5.30781	−	5.30781i	−0.253907	−	0.253907i
$438$	−0.704501	−	0.521315i	−0.0336624	−	0.0249094i
$439$		−	29.2516i		−	1.39610i	−0.716047	−	0.698052i	$-0.754050\pi$
$439$		−	29.2516i		−	1.39610i	0.716047	−	0.698052i	$-0.245950\pi$
$440$	−0.775559			−0.0369733
$441$	−4.15900	−	13.6045i	−0.198048	−	0.647832i
$442$	−0.617719			−0.0293819
$443$	15.4059	−	15.4059i	0.731956	−	0.731956i	−0.239051	−	0.971007i	$-0.576836\pi$
$443$	15.4059	−	15.4059i	0.731956	−	0.731956i	0.971007	+	0.239051i	$0.0768364\pi$
$444$	1.11098	+	7.43428i	0.0527249	+	0.352815i
$445$	−6.11850	−	6.11850i	−0.290045	−	0.290045i
$446$	0.0348369	+	0.0348369i	0.00164957	+	0.00164957i
$447$	13.1657	−	17.7920i	0.622716	−	0.841534i
$448$			27.3215i			1.29082i
$449$	23.7030	+	23.7030i	1.11861	+	1.11861i	0.991945	+	0.126670i	$0.0404289\pi$
$449$	23.7030	+	23.7030i	1.11861	+	1.11861i	0.126670	+	0.991945i	$0.459571\pi$
$450$	−0.0470669	+	0.0885156i	−0.00221875	+	0.00417266i
$451$	−39.2588			−1.84862
$452$	18.3031	+	18.3031i	0.860906	+	0.860906i
$453$	−30.3745	−	22.4764i	−1.42712	−	1.05603i
$454$	0.499230	−	0.499230i	0.0234300	−	0.0234300i
$455$			10.9584i			0.513736i
$456$	−0.399152	−	0.295364i	−0.0186920	−	0.0138317i
$457$			24.8531i			1.16258i	0.813697	+	0.581289i	$0.197451\pi$
$457$			24.8531i			1.16258i	−0.813697	+	0.581289i	$0.802549\pi$
$458$			0.215875i			0.0100872i
$459$	12.9296	+	27.1097i	0.603504	+	1.26537i
$460$	6.99394			0.326094
$461$	13.4808	−	13.4808i	0.627863	−	0.627863i	−0.319667	−	0.947530i	$-0.603571\pi$
$461$	13.4808	−	13.4808i	0.627863	−	0.627863i	0.947530	+	0.319667i	$0.103571\pi$
$462$	−0.925301	−	0.684702i	−0.0430489	−	0.0318552i
$463$		−	29.3869i		−	1.36572i	−0.730548	−	0.682862i	$-0.760735\pi$
$463$		−	29.3869i		−	1.36572i	0.730548	−	0.682862i	$-0.239265\pi$
$464$	19.6241	+	8.79432i	0.911028	+	0.408266i
$465$	0.324415	+	2.17086i	0.0150444	+	0.100671i
$466$	−0.000321775	0	0.000321775i	−1.49059e−5	0	1.49059e-5i
$467$	−10.8604	−	10.8604i	−0.502559	−	0.502559i	0.409673	−	0.912232i	$-0.365643\pi$
$467$	−10.8604	−	10.8604i	−0.502559	−	0.502559i	−0.912232	+	0.409673i	$0.865643\pi$
$468$	−5.60647	−	18.3393i	−0.259159	−	0.847734i
$469$			38.5506i			1.78010i
$470$	0.186298			0.00859328
$471$	24.7724	−	3.70200i	1.14145	−	0.170579i
$472$	1.36804	+	1.36804i	0.0629689	+	0.0629689i
$473$	−22.9112			−1.05346
$474$	−0.0727223	+	0.0982764i	−0.00334025	+	0.00451399i
$475$	−1.51698	+	1.51698i	−0.0696040	+	0.0696040i
$476$	−27.9957	+	27.9957i	−1.28318	+	1.28318i
$477$	0.630346	−	0.192702i	0.0288615	−	0.00882322i
$478$	−0.403948	+	0.403948i	−0.0184761	+	0.0184761i
$479$	−4.61610	+	4.61610i	−0.210915	+	0.210915i	−0.804656	−	0.593741i	$-0.797650\pi$
$479$	−4.61610	+	4.61610i	−0.210915	+	0.210915i	0.593741	+	0.804656i	$0.297650\pi$
$480$	0.686421	−	0.102579i	0.0313307	−	0.00468207i
$481$	4.90961	−	4.90961i	0.223859	−	0.223859i
$482$	−0.264301	+	0.264301i	−0.0120386	+	0.0120386i
$483$	16.6933	+	12.3526i	0.759570	+	0.562064i
$484$	45.3415			2.06098
$485$	−5.10408	−	5.10408i	−0.231764	−	0.231764i
$486$	0.384081	−	0.351909i	0.0174223	−	0.0159629i
$487$	−26.4492			−1.19853			−0.599263	−	0.800552i	$-0.704540\pi$
$487$	−26.4492			−1.19853			−0.599263	+	0.800552i	$0.704540\pi$
$488$			1.47142i			0.0666081i
$489$	−37.3150	+	5.57637i	−1.68744	+	0.252172i
$490$	−0.112051	−	0.112051i	−0.00506193	−	0.00506193i
$491$	−17.9307	+	17.9307i	−0.809200	+	0.809200i	−0.984513	−	0.175313i	$-0.943906\pi$
$491$	−17.9307	+	17.9307i	−0.809200	+	0.809200i	0.175313	+	0.984513i	$0.443906\pi$
$492$	23.1623	−	3.46138i	1.04424	−	0.156051i
$493$	11.0847	+	29.0872i	0.499228	+	1.31002i
$494$			0.229266i			0.0103151i
$495$	8.17439	−	15.3730i	0.367411	−	0.690966i
$496$	3.57837	−	3.57837i	0.160673	−	0.160673i
$497$	31.5607			1.41569
$498$	0.0151285	+	0.101234i	0.000677922	+	0.00453640i
$499$			23.5610i			1.05473i	0.849637	+	0.527367i	$0.176821\pi$
$499$			23.5610i			1.05473i	−0.849637	+	0.527367i	$0.823179\pi$
$500$		−	1.99888i		−	0.0893928i
$501$	15.1083	−	20.4173i	0.674991	−	0.912179i
$502$		−	0.177765i		−	0.00793402i
$503$	−11.5174	+	11.5174i	−0.513536	+	0.513536i	−0.915608	−	0.402072i	$-0.868290\pi$
$503$	−11.5174	+	11.5174i	−0.513536	+	0.513536i	0.402072	+	0.915608i	$0.368290\pi$
$504$	1.21291	+	0.644949i	0.0540274	+	0.0287283i
$505$	−9.67557	−	9.67557i	−0.430557	−	0.430557i
$506$	0.678595			0.0301672
$507$	2.85692	−	3.86083i	0.126880	−	0.171465i
$508$	9.65836	+	9.65836i	0.428520	+	0.428520i
$509$		−	7.20202i		−	0.319224i	−0.987180	−	0.159612i	$-0.948976\pi$
$509$		−	7.20202i		−	0.319224i	0.987180	−	0.159612i	$-0.0510243\pi$
$510$	0.268938	+	0.199008i	0.0119088	+	0.00881222i
$511$	36.6888	+	36.6888i	1.62302	+	1.62302i
$512$	−1.88613	−	1.88613i	−0.0833562	−	0.0833562i
$513$	10.0617	−	4.79882i	0.444236	−	0.211873i
$514$	0.127474	−	0.127474i	0.00562265	−	0.00562265i
$515$	0.181474			0.00799669
$516$	13.5173	−	2.02004i	0.595067	−	0.0889272i
$517$	−32.3555			−1.42299
$518$			0.248614i			0.0109235i
$519$	15.6348	−	21.1287i	0.686291	−	0.927449i
$520$	−0.302181	−	0.302181i	−0.0132515	−	0.0132515i
$521$	−6.61725			−0.289907			−0.144954	−	0.989438i	$-0.546303\pi$
$521$	−6.61725			−0.289907			−0.144954	+	0.989438i	$0.546303\pi$
$522$	0.426234	−	0.331335i	0.0186558	−	0.0145021i
$523$	18.3471			0.802262			0.401131	−	0.916021i	$-0.368617\pi$
$523$	18.3471			0.802262			0.401131	+	0.916021i	$0.368617\pi$
$524$	−27.3437	−	27.3437i	−1.19451	−	1.19451i
$525$	3.53041	−	4.77097i	0.154080	−	0.208222i
$526$			0.691404i			0.0301466i
$527$	7.32514			0.319088
$528$	−39.7013	+	5.93298i	−1.72778	+	0.258200i
$529$	10.7575			0.467719
$530$	0.00519172	−	0.00519172i	0.000225514	−	0.000225514i
$531$	−41.5361	+	12.6979i	−1.80251	+	0.551043i
$532$	10.3906	+	10.3906i	0.450488	+	0.450488i
$533$	−15.2964	−	15.2964i	−0.662560	−	0.662560i
$534$	0.402591	+	0.297908i	0.0174218	+	0.0128917i
$535$		−	1.42157i		−	0.0614598i
$536$	−1.06305	−	1.06305i	−0.0459166	−	0.0459166i
$537$	0.0284055	−	0.0383870i	0.00122579	−	0.00165652i
$538$	−0.202812			−0.00874384
$539$	19.4605	+	19.4605i	0.838224	+	0.838224i
$540$	−3.46739	+	9.79064i	−0.149213	+	0.421322i
$541$	−11.2647	+	11.2647i	−0.484308	+	0.484308i	−0.906504	−	0.422196i	$-0.861259\pi$
$541$	−11.2647	+	11.2647i	−0.484308	+	0.484308i	0.422196	+	0.906504i	$0.361259\pi$
$542$		−	0.336816i		−	0.0144675i
$543$	−16.1122	+	21.7739i	−0.691439	+	0.934406i
$544$		−	2.31619i		−	0.0993058i
$545$			1.85368i			0.0794029i
$546$	−0.0937448	−	0.627305i	−0.00401191	−	0.0268462i
$547$	39.9388			1.70766			0.853830	−	0.520551i	$-0.174273\pi$
$547$	39.9388			1.70766			0.853830	+	0.520551i	$0.174273\pi$
$548$	9.92162	−	9.92162i	0.423831	−	0.423831i
$549$	−29.1663	−	15.5088i	−1.24479	−	0.661898i
$550$		−	0.193944i		−	0.00826980i
$551$	10.7957	−	4.11406i	0.459911	−	0.175265i
$552$	−0.800951	+	0.119695i	−0.0340907	+	0.00509454i
$553$	5.11801	−	5.11801i	0.217640	−	0.217640i
$554$	−0.0359482	−	0.0359482i	−0.00152729	−	0.00152729i
$555$	−3.71922	+	0.555802i	−0.157872	+	0.0235925i
$556$		−	13.5979i		−	0.576680i
$557$	1.74034			0.0737404			0.0368702	−	0.999320i	$-0.488261\pi$
$557$	1.74034			0.0737404			0.0368702	+	0.999320i	$0.488261\pi$
$558$	−0.0371419	−	0.121494i	−0.00157234	−	0.00514327i
$559$	−8.92687	−	8.92687i	−0.377566	−	0.377566i
$560$	−13.6837			−0.578241
$561$	−46.7081	−	34.5629i	−1.97202	−	1.45925i
$562$	−0.266363	+	0.266363i	−0.0112358	+	0.0112358i
$563$	−7.23563	+	7.23563i	−0.304945	+	0.304945i	−0.842945	−	0.538000i	$-0.819180\pi$
$563$	−7.23563	+	7.23563i	−0.304945	+	0.304945i	0.538000	+	0.842945i	$0.319180\pi$
$564$	19.0894	−	2.85273i	0.803808	−	0.120122i
$565$	−9.15667	+	9.15667i	−0.385224	+	0.385224i
$566$	−0.173589	+	0.173589i	−0.00729648	+	0.00729648i
$567$	−25.5682	+	17.2444i	−1.07376	+	0.724198i
$568$	−0.870296	+	0.870296i	−0.0365168	+	0.0365168i
$569$	1.08100	−	1.08100i	0.0453178	−	0.0453178i	−0.684085	−	0.729403i	$-0.739798\pi$
$569$	1.08100	−	1.08100i	0.0453178	−	0.0453178i	0.729403	+	0.684085i	$0.239798\pi$
$570$	0.0738615	−	0.0998160i	0.00309372	−	0.00418083i
$571$	−3.81623			−0.159704			−0.0798522	−	0.996807i	$-0.525445\pi$
$571$	−3.81623			−0.159704			−0.0798522	+	0.996807i	$0.525445\pi$
$572$	26.2334	+	26.2334i	1.09688	+	1.09688i
$573$	24.0360	−	3.59195i	1.00412	−	0.150056i
$574$	0.774583			0.0323305
$575$			3.49892i			0.145915i
$576$	22.8746	−	6.99296i	0.953108	−	0.291373i
$577$	7.65123	+	7.65123i	0.318525	+	0.318525i	0.848200	−	0.529676i	$-0.177686\pi$
$577$	7.65123	+	7.65123i	0.318525	+	0.318525i	−0.529676	+	0.848200i	$0.677686\pi$
$578$	0.387794	−	0.387794i	0.0161301	−	0.0161301i
$579$	−4.73462	−	31.6823i	−0.196764	−	1.31667i
$580$	−4.40208	+	9.82305i	−0.182786	+	0.407880i
$581$		−	6.05989i		−	0.251406i
$582$	0.335843	+	0.248516i	0.0139211	+	0.0103013i
$583$	−0.901678	+	0.901678i	−0.0373437	+	0.0373437i
$584$	−2.02341			−0.0837294
$585$	9.17477	−	2.80480i	0.379330	−	0.115964i
$586$			0.601696i			0.0248558i
$587$		−	43.9332i		−	1.81332i	−0.421865	−	0.906659i	$-0.638624\pi$
$587$		−	43.9332i		−	1.81332i	0.421865	−	0.906659i	$-0.361376\pi$
$588$	−13.1973	−	9.76569i	−0.544247	−	0.402730i
$589$		−	2.71872i		−	0.112023i
$590$	−0.342104	+	0.342104i	−0.0140842	+	0.0140842i
$591$	−9.31733	−	6.89461i	−0.383264	−	0.283606i
$592$	6.13062	+	6.13062i	0.251967	+	0.251967i
$593$	41.9930			1.72445			0.862224	−	0.506528i	$-0.169071\pi$
$593$	41.9930			1.72445			0.862224	+	0.506528i	$0.169071\pi$
$594$	−0.336427	+	0.949948i	−0.0138038	+	0.0389768i
$595$	−14.0057	−	14.0057i	−0.574177	−	0.574177i
$596$		−	25.5433i		−	1.04629i
$597$	4.56997	−	6.17583i	0.187037	−	0.252760i
$598$	0.264401	+	0.264401i	0.0108121	+	0.0108121i
$599$	−1.12622	−	1.12622i	−0.0460162	−	0.0460162i	0.683724	−	0.729740i	$-0.260359\pi$
$599$	−1.12622	−	1.12622i	−0.0460162	−	0.0460162i	−0.729740	+	0.683724i	$0.760359\pi$
$600$	0.0342090	+	0.228913i	0.00139657	+	0.00934535i
$601$	−2.00982	+	2.00982i	−0.0819821	+	0.0819821i	−0.746909	−	0.664927i	$-0.768463\pi$
$601$	−2.00982	+	2.00982i	−0.0819821	+	0.0819821i	0.664927	+	0.746909i	$0.268463\pi$
$602$	0.452041			0.0184238
$603$	32.2760	−	9.86705i	1.31438	−	0.401817i
$604$	−43.6074			−1.77436
$605$			22.6834i			0.922212i
$606$	0.636643	+	0.471101i	0.0258618	+	0.0191372i
$607$	−20.6809	−	20.6809i	−0.839413	−	0.839413i	0.149369	−	0.988782i	$-0.452276\pi$
$607$	−20.6809	−	20.6809i	−0.839413	−	0.839413i	−0.988782	+	0.149369i	$0.952276\pi$
$608$	−0.859650			−0.0348634
$609$	−27.8563	+	15.6709i	−1.12880	+	0.635018i
$610$	−0.367958			−0.0148982
$611$	−12.6067	−	12.6067i	−0.510011	−	0.510011i
$612$	30.6046	+	16.2736i	1.23712	+	0.657820i
$613$			33.7976i			1.36507i	0.730853	+	0.682535i	$0.239123\pi$
$613$			33.7976i			1.36507i	−0.730853	+	0.682535i	$0.760877\pi$
$614$	0.293532			0.0118460
$615$	1.73166	+	11.5876i	0.0698272	+	0.467257i
$616$	−2.65758			−0.107077
$617$	−11.4148	+	11.4148i	−0.459543	+	0.459543i	−0.898505	−	0.438963i	$-0.855346\pi$
$617$	−11.4148	+	11.4148i	−0.459543	+	0.459543i	0.438963	+	0.898505i	$0.355346\pi$
$618$	−0.0103884	+	0.00155244i	−0.000417881	+	6.24483e-5i
$619$	3.33662	+	3.33662i	0.134110	+	0.134110i	0.770975	−	0.636865i	$-0.219769\pi$
$619$	3.33662	+	3.33662i	0.134110	+	0.134110i	−0.636865	+	0.770975i	$0.719769\pi$
$620$	1.79118	+	1.79118i	0.0719357	+	0.0719357i
$621$	6.06945	−	17.1379i	0.243559	−	0.687721i
$622$		−	0.711360i		−	0.0285229i
$623$	−20.9660	−	20.9660i	−0.839986	−	0.839986i
$624$	−17.7805	−	13.1571i	−0.711788	−	0.526707i
$625$	1.00000			0.0400000
$626$	−0.00619189	−	0.00619189i	−0.000247478	−	0.000247478i
$627$	−12.8280	+	17.3356i	−0.512300	+	0.692319i
$628$	20.4398	−	20.4398i	0.815636	−	0.815636i
$629$			12.5497i			0.500391i
$630$	−0.161282	+	0.303313i	−0.00642564	+	0.0120843i
$631$		−	3.73546i		−	0.148706i	−0.997232	−	0.0743532i	$-0.976311\pi$
$631$		−	3.73546i		−	0.148706i	0.997232	−	0.0743532i	$-0.0236892\pi$
$632$			0.282262i			0.0112278i
$633$	−31.1604	+	4.65663i	−1.23851	+	0.185084i
$634$	0.662982			0.0263304
$635$	−4.83188	+	4.83188i	−0.191747	+	0.191747i
$636$	0.452481	−	0.611480i	0.0179420	−	0.0242467i
$637$			15.1648i			0.600851i
$638$	−0.427116	+	0.953092i	−0.0169097	+	0.0377333i
$639$	−8.07797	−	26.4238i	−0.319560	−	1.04531i
$640$	0.755086	−	0.755086i	0.0298474	−	0.0298474i
$641$	8.17031	+	8.17031i	0.322708	+	0.322708i	0.849805	−	0.527097i	$-0.176720\pi$
$641$	8.17031	+	8.17031i	0.322708	+	0.322708i	−0.527097	+	0.849805i	$0.676720\pi$
$642$	0.0121610	+	0.0813769i	0.000479956	+	0.00321169i
$643$		−	18.9978i		−	0.749199i	−0.927187	−	0.374600i	$-0.877780\pi$
$643$		−	18.9978i		−	0.749199i	0.927187	−	0.374600i	$-0.122220\pi$
$644$	23.9659			0.944387
$645$	1.01058	+	6.76244i	0.0397917	+	0.266271i
$646$	−0.293020	−	0.293020i	−0.0115287	−	0.0115287i
$647$	2.61653			0.102866			0.0514331	−	0.998676i	$-0.483621\pi$
$647$	2.61653			0.102866			0.0514331	+	0.998676i	$0.483621\pi$
$648$	0.229530	−	1.18057i	0.00901679	−	0.0463772i
$649$	59.4153	−	59.4153i	2.33226	−	2.33226i
$650$	0.0755663	−	0.0755663i	0.00296395	−	0.00296395i
$651$	1.11166	+	7.43881i	0.0435694	+	0.291550i
$652$	−30.7887	+	30.7887i	−1.20578	+	1.20578i
$653$	−24.3495	+	24.3495i	−0.952871	+	0.952871i	−0.998938	−	0.0460674i	$-0.985331\pi$
$653$	−24.3495	+	24.3495i	−0.952871	+	0.952871i	0.0460674	+	0.998938i	$0.485331\pi$
$654$	−0.0158575	−	0.106113i	−0.000620079	−	0.00414933i
$655$	13.6795	−	13.6795i	0.534502	−	0.534502i
$656$	19.1006	−	19.1006i	0.745751	−	0.745751i
$657$	21.3268	−	40.1078i	0.832036	−	1.56476i
$658$	0.638380			0.0248866
$659$	11.1710	+	11.1710i	0.435159	+	0.435159i	0.890379	−	0.455220i	$-0.150439\pi$
$659$	11.1710	+	11.1710i	0.435159	+	0.435159i	−0.455220	+	0.890379i	$0.650439\pi$
$660$	−2.96981	−	19.8728i	−0.115600	−	0.773549i
$661$	28.5984			1.11235			0.556175	−	0.831065i	$-0.312268\pi$
$661$	28.5984			1.11235			0.556175	+	0.831065i	$0.312268\pi$
$662$		−	0.378110i		−	0.0146957i
$663$	−4.73212	−	31.6656i	−0.183780	−	1.22979i
$664$	0.167103	+	0.167103i	0.00648487	+	0.00648487i
$665$	−5.19819	+	5.19819i	−0.201577	+	0.201577i
$666$	0.208150	−	0.0636330i	0.00806563	−	0.00246573i
$667$	7.70557	−	17.1946i	0.298361	−	0.665779i
$668$		−	29.3123i		−	1.13413i
$669$	−1.51894	+	2.05269i	−0.0587256	+	0.0793614i
$670$	0.265835	−	0.265835i	0.0102701	−	0.0102701i
$671$	63.9055			2.46704
$672$	2.35213	−	0.351504i	0.0907354	−	0.0135596i
$673$		−	48.2530i		−	1.86002i	−0.367540	−	0.930008i	$-0.619800\pi$
$673$		−	48.2530i		−	1.86002i	0.367540	−	0.930008i	$-0.380200\pi$
$674$		−	0.556807i		−	0.0214474i
$675$	−4.89806	−	1.73466i	−0.188526	−	0.0667672i
$676$		−	5.54283i		−	0.213186i
$677$	−21.8349	+	21.8349i	−0.839182	+	0.839182i	−0.988751	−	0.149569i	$-0.952211\pi$
$677$	−21.8349	+	21.8349i	−0.839182	+	0.839182i	0.149569	+	0.988751i	$0.452211\pi$
$678$	0.445836	−	0.602499i	0.0171222	−	0.0231388i
$679$	−17.4899	−	17.4899i	−0.671202	−	0.671202i
$680$	0.772422			0.0296210
$681$	29.4160	+	21.7672i	1.12722	+	0.834120i
$682$	0.173792	+	0.173792i	0.00665483	+	0.00665483i
$683$			49.8359i			1.90692i	0.301522	+	0.953459i	$0.402505\pi$
$683$			49.8359i			1.90692i	−0.301522	+	0.953459i	$0.597495\pi$
$684$	6.03991	−	11.3589i	0.230942	−	0.434317i
$685$	4.96358	+	4.96358i	0.189649	+	0.189649i
$686$	0.182830	+	0.182830i	0.00698050	+	0.00698050i
$687$	−11.0662	+	1.65374i	−0.422201	+	0.0630940i
$688$	11.1470	−	11.1470i	0.424974	−	0.424974i
$689$	−0.702641			−0.0267685
$690$	−0.0299320	−	0.200294i	−0.00113949	−	0.00762505i
$691$	24.6015			0.935885			0.467943	−	0.883759i	$-0.344995\pi$
$691$	24.6015			0.935885			0.467943	+	0.883759i	$0.344995\pi$
$692$		−	30.3337i		−	1.15311i
$693$	28.0109	−	52.6781i	1.06404	−	2.00108i
$694$	0.169998	+	0.169998i	0.00645302	+	0.00645302i
$695$	6.80276			0.258043
$696$	0.336017	−	1.20028i	0.0127367	−	0.0454965i
$697$	39.1000			1.48102
$698$	0.451172	+	0.451172i	0.0170771	+	0.0170771i
$699$	−0.0189599	−	0.0140299i	−0.000717128	−	0.000530658i
$700$		−	6.84949i		−	0.258887i
$701$	7.28948			0.275320			0.137660	−	0.990480i	$-0.456042\pi$
$701$	7.28948			0.275320			0.137660	+	0.990480i	$0.456042\pi$
$702$	−0.501210	+	0.239046i	−0.0189169	+	0.00902221i
$703$	4.65782			0.175673
$704$	−32.7210	+	32.7210i	−1.23322	+	1.23322i
$705$	1.42716	+	9.55003i	0.0537500	+	0.359675i
$706$	−0.536256	−	0.536256i	−0.0201823	−	0.0201823i
$707$	−33.1549	−	33.1549i	−1.24692	−	1.24692i
$708$	−29.8159	+	40.2929i	−1.12055	+	1.51430i
$709$			19.8675i			0.746140i	0.927803	+	0.373070i	$0.121695\pi$
$709$			19.8675i			0.746140i	−0.927803	+	0.373070i	$0.878305\pi$
$710$	−0.217635	−	0.217635i	−0.00816768	−	0.00816768i
$711$	−5.59496	−	2.97504i	−0.209827	−	0.111573i
$712$	1.15629			0.0433338
$713$	−3.13536	−	3.13536i	−0.117420	−	0.117420i
$714$	0.921559	+	0.681932i	0.0344885	+	0.0255207i
$715$	−13.1241	+	13.1241i	−0.490812	+	0.490812i
$716$		−	0.0551107i		−	0.00205958i
$717$	−23.8017	−	17.6127i	−0.888891	−	0.657759i
$718$		−	0.0602614i		−	0.00224894i
$719$		−	22.6164i		−	0.843449i	−0.906724	−	0.421724i	$-0.861425\pi$
$719$		−	22.6164i		−	0.843449i	0.906724	−	0.421724i	$-0.138575\pi$
$720$	3.50235	+	11.4565i	0.130525	+	0.426959i
$721$	0.621849			0.0231589
$722$	0.340205	−	0.340205i	0.0126611	−	0.0126611i
$723$	−15.5734	−	11.5239i	−0.579180	−	0.428580i
$724$			31.2599i			1.16176i
$725$	−4.91427	−	2.20227i	−0.182511	−	0.0817902i
$726$	−0.194048	−	1.29850i	−0.00720180	−	0.0481918i
$727$	26.7292	−	26.7292i	0.991331	−	0.991331i	−0.00863198	−	0.999963i	$-0.502748\pi$
$727$	26.7292	−	26.7292i	0.991331	−	0.991331i	0.999963	+	0.00863198i	$0.00274768\pi$
$728$	−1.03547	−	1.03547i	−0.0383771	−	0.0383771i
$729$	20.9819	+	16.9929i	0.777107	+	0.629368i
$730$		−	0.505995i		−	0.0187277i
$731$	22.8185			0.843973
$732$	−37.7035	+	5.63444i	−1.39356	+	0.208255i
$733$	5.46553	+	5.46553i	0.201874	+	0.201874i	0.800802	−	0.598929i	$-0.204407\pi$
$733$	5.46553	+	5.46553i	0.201874	+	0.201874i	−0.598929	+	0.800802i	$0.704407\pi$
$734$	0.528038			0.0194902
$735$	4.88557	−	6.60233i	0.180207	−	0.243531i
$736$	−0.991392	+	0.991392i	−0.0365432	+	0.0365432i
$737$	−46.1693	+	46.1693i	−1.70067	+	1.70067i
$738$	−0.198255	−	0.648511i	−0.00729787	−	0.0238720i
$739$	0.977655	−	0.977655i	0.0359636	−	0.0359636i	−0.688896	−	0.724860i	$-0.741904\pi$
$739$	0.977655	−	0.977655i	0.0359636	−	0.0359636i	0.724860	+	0.688896i	$0.241904\pi$
$740$	−3.06874	+	3.06874i	−0.112809	+	0.112809i
$741$	−11.7526	+	1.75632i	−0.431744	+	0.0645200i
$742$	0.0177903	−	0.0177903i	0.000653102	−	0.000653102i
$743$	−25.7217	+	25.7217i	−0.943638	+	0.943638i	−0.998494	−	0.0548559i	$-0.982530\pi$
$743$	−25.7217	+	25.7217i	−0.943638	+	0.943638i	0.0548559	+	0.998494i	$0.482530\pi$
$744$	−0.235782	−	0.174473i	−0.00864419	−	0.00639650i
$745$	12.7788			0.468178
$746$	0.0862835	+	0.0862835i	0.00315906	+	0.00315906i
$747$	−5.07357	+	1.55103i	−0.185632	+	0.0567493i
$748$	−67.0569			−2.45184
$749$		−	4.87124i		−	0.177991i
$750$	−0.0572444	+	0.00855463i	−0.00209027	+	0.000312371i
$751$	−28.8386	−	28.8386i	−1.05234	−	1.05234i	−0.998553	−	0.0537846i	$-0.982872\pi$
$751$	−28.8386	−	28.8386i	−1.05234	−	1.05234i	−0.0537846	−	0.998553i	$-0.517128\pi$
$752$	15.7419	−	15.7419i	0.574048	−	0.574048i
$753$	9.11259	−	1.36179i	0.332081	−	0.0496264i
$754$	−0.537770	+	0.204936i	−0.0195844	+	0.00746332i
$755$		−	21.8159i		−	0.793961i
$756$	−11.8816	+	33.5492i	−0.432128	+	1.22017i
$757$	31.4138	−	31.4138i	1.14176	−	1.14176i	0.153626	−	0.988129i	$-0.450905\pi$
$757$	31.4138	−	31.4138i	1.14176	−	1.14176i	0.988129	−	0.153626i	$-0.0490952\pi$
$758$	1.11693			0.0405687
$759$	5.19847	+	34.7862i	0.188692	+	1.26266i
$760$		−	0.286684i		−	0.0103991i
$761$		−	50.4832i		−	1.83002i	−0.403436	−	0.915008i	$-0.632184\pi$
$761$		−	50.4832i		−	1.83002i	0.403436	−	0.915008i	$-0.367816\pi$
$762$	0.235263	−	0.317933i	0.00852267	−	0.0115175i
$763$			6.35193i			0.229955i
$764$	19.8322	−	19.8322i	0.717503	−	0.717503i
$765$	−8.14133	+	15.3109i	−0.294350	+	0.553565i
$766$	−0.567271	−	0.567271i	−0.0204963	−	0.0204963i
$767$	46.2999			1.67179
$768$	16.3925	−	22.1527i	0.591513	−	0.799366i
$769$	38.7242	+	38.7242i	1.39643	+	1.39643i	0.809999	+	0.586431i	$0.199467\pi$
$769$	38.7242	+	38.7242i	1.39643	+	1.39643i	0.586431	+	0.809999i	$0.300533\pi$
$770$		−	0.664580i		−	0.0239498i
$771$	7.51114	+	5.55807i	0.270507	+	0.200169i
$772$	−26.1411	−	26.1411i	−0.940840	−	0.940840i
$773$	−11.1637	−	11.1637i	−0.401531	−	0.401531i	0.477241	−	0.878772i	$-0.341637\pi$
$773$	−11.1637	−	11.1637i	−0.401531	−	0.401531i	−0.878772	+	0.477241i	$0.841637\pi$
$774$	−0.115700	−	0.378467i	−0.00415876	−	0.0136037i
$775$	−0.896093	+	0.896093i	−0.0321886	+	0.0321886i
$776$	0.964582			0.0346265
$777$	−12.7445	+	1.90454i	−0.457206	+	0.0683251i
$778$	1.16961			0.0419325
$779$		−	14.5119i		−	0.519943i
$780$	6.58592	−	8.90017i	0.235814	−	0.318677i
$781$	37.7979	+	37.7979i	1.35252	+	1.35252i
$782$	−0.675850			−0.0241684
$783$	20.2502	+	19.3114i	0.723682	+	0.690134i
$784$	−18.9362			−0.676294
$785$	10.2256	+	10.2256i	0.364967	+	0.364967i
$786$	−0.666050	+	0.900096i	−0.0237572	+	0.0321054i
$787$		−	7.58685i		−	0.270442i	−0.990815	−	0.135221i	$-0.956826\pi$
$787$		−	7.58685i		−	0.270442i	0.990815	−	0.135221i	$-0.0431744\pi$
$788$	−13.3765			−0.476519
$789$	−35.4428	+	5.29659i	−1.26180	+	0.188564i
$790$	−0.0705852			−0.00251131
$791$	−31.3768	+	31.3768i	−1.11563	+	1.11563i
$792$	0.680209	+	2.22503i	0.0241702	+	0.0790629i
$793$	24.8995	+	24.8995i	0.884206	+	0.884206i
$794$	0.774179	+	0.774179i	0.0274746	+	0.0274746i
$795$	0.305911	+	0.226367i	0.0108495	+	0.00802840i
$796$		−	8.86639i		−	0.314261i
$797$	16.9872	+	16.9872i	0.601718	+	0.601718i	0.940768	−	0.339050i	$-0.110106\pi$
$797$	16.9872	+	16.9872i	0.601718	+	0.601718i	−0.339050	+	0.940768i	$0.610106\pi$
$798$	0.253098	−	0.342035i	0.00895958	−	0.0121079i
$799$	32.2246			1.14003
$800$	0.283342	+	0.283342i	0.0100177	+	0.0100177i
$801$	−12.1873	+	22.9198i	−0.430617	+	0.809832i
$802$	0.212555	−	0.212555i	0.00750559	−	0.00750559i
$803$			87.8791i			3.10119i
$804$	23.1687	−	31.3100i	0.817097	−	1.10422i
$805$			11.9896i			0.422579i
$806$			0.135429i			0.00477028i
$807$	−1.55367	−	10.3966i	−0.0546917	−	0.365976i
$808$	1.82851			0.0643269
$809$	−7.37587	+	7.37587i	−0.259322	+	0.259322i	−0.824778	−	0.565456i	$-0.808700\pi$
$809$	−7.37587	+	7.37587i	−0.259322	+	0.259322i	0.565456	+	0.824778i	$0.308700\pi$
$810$	0.295225	+	0.0573986i	0.0103732	+	0.00201678i
$811$			5.31063i			0.186481i	0.995644	+	0.0932406i	$0.0297226\pi$
$811$			5.31063i			0.186481i	−0.995644	+	0.0932406i	$0.970277\pi$
$812$	−15.0844	+	33.6602i	−0.529359	+	1.18124i
$813$	17.2659	−	2.58022i	0.605541	−	0.0904924i
$814$	−0.297748	+	0.297748i	−0.0104360	+	0.0104360i
$815$	−15.4030	−	15.4030i	−0.539542	−	0.539542i
$816$	39.5407	−	5.90899i	1.38420	−	0.206856i
$817$		−	8.46906i		−	0.296295i
$818$	0.468375			0.0163763
$819$	31.4388	−	9.61111i	1.09856	−	0.335839i
$820$	9.56096	+	9.56096i	0.333883	+	0.333883i
$821$	42.9816			1.50007			0.750034	−	0.661400i	$-0.230037\pi$
$821$	42.9816			1.50007			0.750034	+	0.661400i	$0.230037\pi$
$822$	−0.326599	−	0.241676i	−0.0113914	−	0.00842940i
$823$	−11.5876	+	11.5876i	−0.403919	+	0.403919i	−0.879612	−	0.475693i	$-0.842197\pi$
$823$	−11.5876	+	11.5876i	−0.403919	+	0.403919i	0.475693	+	0.879612i	$0.342197\pi$
$824$	−0.0171477	+	0.0171477i	−0.000597368	+	0.000597368i
$825$	9.94197	−	1.48573i	0.346135	−	0.0517266i
$826$	−1.17228	+	1.17228i	−0.0407887	+	0.0407887i
$827$	2.24369	−	2.24369i	0.0780209	−	0.0780209i	−0.667019	−	0.745040i	$-0.732430\pi$
$827$	2.24369	−	2.24369i	0.0780209	−	0.0780209i	0.745040	+	0.667019i	$0.232430\pi$
$828$	−6.13408	−	20.0651i	−0.213174	−	0.697312i
$829$	15.8863	−	15.8863i	0.551754	−	0.551754i	−0.375193	−	0.926947i	$-0.622424\pi$
$829$	15.8863	−	15.8863i	0.551754	−	0.551754i	0.926947	+	0.375193i	$0.122424\pi$
$830$	−0.0417875	+	0.0417875i	−0.00145047	+	0.00145047i
$831$	1.56739	−	2.11816i	0.0543723	−	0.0734783i
$832$	−25.4981			−0.883988
$833$	−19.3818	−	19.3818i	−0.671540	−	0.671540i
$834$	−0.389419	+	0.0581950i	−0.0134845	+	0.00201513i
$835$	14.6643			0.507481
$836$			24.8881i			0.860772i
$837$	5.94353	−	2.83469i	0.205438	−	0.0979814i
$838$	0.489315	+	0.489315i	0.0169031	+	0.0169031i
$839$	31.6909	−	31.6909i	1.09409	−	1.09409i	0.0990061	−	0.995087i	$-0.468434\pi$
$839$	31.6909	−	31.6909i	1.09409	−	1.09409i	0.995087	−	0.0990061i	$-0.0315663\pi$
$840$	0.117222	+	0.784409i	0.00404456	+	0.0270647i
$841$	19.3000	+	21.6451i	0.665518	+	0.746381i
$842$			0.697015i			0.0240207i
$843$	−15.6948	−	11.6138i	−0.540559	−	0.400001i
$844$	−25.7105	+	25.7105i	−0.884992	+	0.884992i
$845$	2.77296			0.0953928
$846$	−0.163394	−	0.534476i	−0.00561759	−	0.0183757i
$847$			77.7283i			2.67078i
$848$		−	0.877386i		−	0.0301296i
$849$	−10.2283	−	7.56872i	−0.351035	−	0.259758i
$850$			0.193159i			0.00662532i
$851$	5.37163	−	5.37163i	0.184137	−	0.184137i
$852$	−25.6329	−	18.9678i	−0.878170	−	0.649826i
$853$	−14.9819	−	14.9819i	−0.512969	−	0.512969i	0.402466	−	0.915435i	$-0.368153\pi$
$853$	−14.9819	−	14.9819i	−0.512969	−	0.512969i	−0.915435	+	0.402466i	$0.868153\pi$
$854$	−1.26087			−0.0431460
$855$	5.68260	+	3.02164i	0.194341	+	0.103338i
$856$	0.134326	+	0.134326i	0.00459117	+	0.00459117i
$857$		−	28.7776i		−	0.983023i	−0.870871	−	0.491512i	$-0.836445\pi$
$857$		−	28.7776i		−	0.983023i	0.870871	−	0.491512i	$-0.163555\pi$
$858$	0.639007	−	0.863549i	0.0218153	−	0.0294811i
$859$	−25.0210	−	25.0210i	−0.853704	−	0.853704i	0.136883	−	0.990587i	$-0.456292\pi$
$859$	−25.0210	−	25.0210i	−0.853704	−	0.853704i	−0.990587	+	0.136883i	$0.956292\pi$
$860$	5.57971	+	5.57971i	0.190266	+	0.190266i
$861$	5.93380	+	39.7068i	0.202223	+	1.35320i
$862$	−0.702040	+	0.702040i	−0.0239116	+	0.0239116i
$863$	−34.0768			−1.15999			−0.579994	−	0.814621i	$-0.696945\pi$
$863$	−34.0768			−1.15999			−0.579994	+	0.814621i	$0.696945\pi$
$864$	−0.896322	−	1.87933i	−0.0304935	−	0.0639360i
$865$	15.1753			0.515976
$866$			0.0975480i			0.00331482i
$867$	22.8499	+	16.9084i	0.776023	+	0.574239i
$868$	6.13778	+	6.13778i	0.208330	+	0.208330i
$869$	12.2590			0.415856
$870$	0.300154	+	0.0840277i	0.0101762	+	0.00284880i
$871$	−35.9778			−1.21906
$872$	−0.175157	−	0.175157i	−0.00593155	−	0.00593155i
$873$	−10.1667	+	19.1198i	−0.344090	+	0.647108i
$874$			0.250841i			0.00848482i
$875$	3.42666			0.115842
$876$	−7.74815	−	51.8477i	−0.261786	−	1.75177i
$877$	−24.9769			−0.843411			−0.421705	−	0.906733i	$-0.638568\pi$
$877$	−24.9769			−0.843411			−0.421705	+	0.906733i	$0.638568\pi$
$878$	−0.691199	+	0.691199i	−0.0233269	+	0.0233269i
$879$	−30.8442	+	4.60937i	−1.04035	+	0.155470i
$880$	−16.3880	−	16.3880i	−0.552438	−	0.552438i
$881$	−18.7725	−	18.7725i	−0.632462	−	0.632462i	0.316223	−	0.948685i	$-0.397585\pi$
$881$	−18.7725	−	18.7725i	−0.632462	−	0.632462i	−0.948685	+	0.316223i	$0.897585\pi$
$882$	−0.223191	+	0.419741i	−0.00751523	+	0.0141334i
$883$			33.2647i			1.11945i	0.828679	+	0.559724i	$0.189093\pi$
$883$			33.2647i			1.11945i	−0.828679	+	0.559724i	$0.810907\pi$
$884$	−26.1273	−	26.1273i	−0.878758	−	0.878758i
$885$	−20.1577	−	14.9163i	−0.677595	−	0.501404i
$886$	−0.728064			−0.0244598
$887$	1.00769	+	1.00769i	0.0338348	+	0.0338348i	0.723822	−	0.689987i	$-0.242384\pi$
$887$	1.00769	+	1.00769i	0.0338348	+	0.0338348i	−0.689987	+	0.723822i	$0.742384\pi$
$888$	0.298915	−	0.403952i	0.0100309	−	0.0135557i
$889$	−16.5572	+	16.5572i	−0.555311	+	0.555311i
$890$			0.289153i			0.00969244i
$891$	−51.2736	−	9.96875i	−1.71773	−	0.333966i
$892$			2.94696i			0.0986714i
$893$		−	11.9601i		−	0.400230i
$894$	−0.731513	+	0.109318i	−0.0244654	+	0.00365613i
$895$	0.0275707			0.000921588
$896$	2.58742	−	2.58742i	0.0864398	−	0.0864398i
$897$	−11.5283	+	15.5792i	−0.384917	+	0.520175i
$898$		−	1.12018i		−	0.0373808i
$899$	6.37707	−	2.43020i	0.212687	−	0.0810518i
$900$	−5.73466	+	1.75313i	−0.191155	+	0.0584378i
$901$	0.898031	−	0.898031i	0.0299178	−	0.0299178i
$902$	0.927663	+	0.927663i	0.0308878	+	0.0308878i
$903$	3.46292	+	23.1726i	0.115239	+	0.771136i
$904$		−	1.73045i		−	0.0575539i
$905$	−15.6387			−0.519847
$906$	0.186627	+	1.24884i	0.00620026	+	0.0414898i
$907$	23.2499	+	23.2499i	0.772002	+	0.772002i	0.978456	−	0.206454i	$-0.0661925\pi$
$907$	23.2499	+	23.2499i	0.772002	+	0.772002i	−0.206454	+	0.978456i	$0.566192\pi$
$908$	42.2314			1.40150
$909$	−19.2725	+	36.2446i	−0.639230	+	1.20216i
$910$	0.258940	−	0.258940i	0.00858378	−	0.00858378i
$911$	4.75503	−	4.75503i	0.157541	−	0.157541i	−0.623935	−	0.781476i	$-0.714467\pi$
$911$	4.75503	−	4.75503i	0.157541	−	0.157541i	0.781476	+	0.623935i	$0.214467\pi$
$912$	−2.19311	−	14.6755i	−0.0726212	−	0.485954i
$913$	7.25749	−	7.25749i	0.240188	−	0.240188i
$914$	0.587264	−	0.587264i	0.0194250	−	0.0194250i
$915$	−2.81879	−	18.8623i	−0.0931864	−	0.623569i
$916$	−9.13074	+	9.13074i	−0.301688	+	0.301688i
$917$	46.8749	−	46.8749i	1.54795	−	1.54795i
$918$	0.335066	−	0.946106i	0.0110588	−	0.0312261i
$919$	−33.7289			−1.11261			−0.556307	−	0.830977i	$-0.687782\pi$
$919$	−33.7289			−1.11261			−0.556307	+	0.830977i	$0.687782\pi$
$920$	−0.330618	−	0.330618i	−0.0109001	−	0.0109001i
$921$	2.24865	+	15.0471i	0.0740954	+	0.495818i
$922$	−0.637087			−0.0209813
$923$			29.4544i			0.969503i
$924$	−10.1765	−	68.0975i	−0.334783	−	2.24024i
$925$	−1.53523	−	1.53523i	−0.0504779	−	0.0504779i
$926$	−0.694394	+	0.694394i	−0.0228192	+	0.0228192i
$927$	−0.159163	−	0.520636i	−0.00522759	−	0.0170999i
$928$	−0.768423	−	2.01641i	−0.0252247	−	0.0661920i
$929$		−	12.0759i		−	0.396199i	−0.980182	−	0.198099i	$-0.936523\pi$
$929$		−	12.0759i		−	0.396199i	0.980182	−	0.198099i	$-0.0634769\pi$
$930$	0.0436305	−	0.0589620i	0.00143070	−	0.00193344i
$931$	−7.19353	+	7.19353i	−0.235759	+	0.235759i
$932$	−0.0272199			−0.000891618
$933$	36.4658	−	5.44947i	1.19384	−	0.178408i
$934$			0.513249i			0.0167940i
$935$		−	33.5472i		−	1.09711i
$936$	−0.601906	+	1.13197i	−0.0196739	+	0.0369995i
$937$			39.5873i			1.29326i	0.762804	+	0.646630i	$0.223822\pi$
$937$			39.5873i			1.29326i	−0.762804	+	0.646630i	$0.776178\pi$
$938$	0.910928	−	0.910928i	0.0297428	−	0.0297428i
$939$	0.269976	−	0.364843i	0.00881032	−	0.0119062i
$940$	7.87975	+	7.87975i	0.257009	+	0.257009i
$941$	−14.9928			−0.488751			−0.244375	−	0.969681i	$-0.578583\pi$
$941$	−14.9928			−0.488751			−0.244375	+	0.969681i	$0.578583\pi$
$942$	−0.672834	−	0.497881i	−0.0219221	−	0.0162219i
$943$	−16.7359	−	16.7359i	−0.544995	−	0.544995i
$944$			57.8146i			1.88171i
$945$	−16.7840	−	5.94410i	−0.545983	−	0.193361i
$946$	0.541378	+	0.541378i	0.0176017	+	0.0176017i
$947$	−9.17141	−	9.17141i	−0.298031	−	0.298031i	0.542211	−	0.840242i	$-0.317587\pi$
$947$	−9.17141	−	9.17141i	−0.298031	−	0.298031i	−0.840242	+	0.542211i	$0.817587\pi$
$948$	−7.23265	+	1.08085i	−0.234905	+	0.0351044i
$949$	−34.2403	+	34.2403i	−1.11149	+	1.11149i
$950$	0.0716909			0.00232596
$951$	5.07886	+	33.9858i	0.164693	+	1.10207i
$952$	2.64683			0.0857842
$953$			17.9115i			0.580210i	0.956995	+	0.290105i	$0.0936903\pi$
$953$			17.9115i			0.580210i	−0.956995	+	0.290105i	$0.906310\pi$
$954$	−0.0194481	−	0.0103413i	−0.000629657	−	0.000334811i
$955$	9.92163	+	9.92163i	0.321056	+	0.321056i
$956$	−34.1711			−1.10517
$957$	−52.1295	−	14.5936i	−1.68511	−	0.471744i
$958$	0.218152			0.00704816
$959$	17.0085	+	17.0085i	0.549234	+	0.549234i
$960$	11.1012	+	8.21462i	0.358289	+	0.265126i
$961$			29.3940i			0.948195i
$962$	−0.232022			−0.00748071
$963$	−4.07839	+	1.24680i	−0.131424	+	0.0401775i
$964$	−22.3580			−0.720104
$965$	13.0779	−	13.0779i	0.420991	−	0.420991i
$966$	−0.102567	−	0.686338i	−0.00330003	−	0.0220826i
$967$	14.7034	+	14.7034i	0.472830	+	0.472830i	0.902829	−	0.429999i	$-0.141486\pi$
$967$	14.7034	+	14.7034i	0.472830	+	0.472830i	−0.429999	+	0.902829i	$0.641486\pi$
$968$	−2.14339	−	2.14339i	−0.0688910	−	0.0688910i
$969$	12.7761	−	17.2655i	0.410427	−	0.554649i
$970$			0.241213i			0.00774488i
$971$	15.4558	+	15.4558i	0.495999	+	0.495999i	0.910190	−	0.414191i	$-0.135936\pi$
$971$	15.4558	+	15.4558i	0.495999	+	0.495999i	−0.414191	+	0.910190i	$0.635936\pi$
$972$	31.1298	+	1.36075i	0.998488	+	0.0436461i
$973$	23.3107			0.747308
$974$	0.624979	+	0.624979i	0.0200256	+	0.0200256i
$975$	4.45257	+	3.29480i	0.142596	+	0.105518i
$976$	−31.0919	+	31.0919i	−0.995228	+	0.995228i
$977$			11.3655i			0.363614i	0.983334	+	0.181807i	$0.0581946\pi$
$977$			11.3655i			0.363614i	−0.983334	+	0.181807i	$0.941805\pi$
$978$	1.01350	+	0.749966i	0.0324081	+	0.0239813i
$979$		−	50.2190i		−	1.60501i
$980$		−	9.47870i		−	0.302786i
$981$	5.31808	−	1.62578i	0.169793	−	0.0519072i
$982$	0.847383			0.0270411
$983$	−32.4423	+	32.4423i	−1.03475	+	1.03475i	−0.0353761	+	0.999374i	$0.511263\pi$
$983$	−32.4423	+	32.4423i	−1.03475	+	1.03475i	−0.999374	+	0.0353761i	$0.988737\pi$
$984$	−1.25855	−	0.931301i	−0.0401212	−	0.0296888i
$985$		−	6.69199i		−	0.213225i
$986$	0.425389	−	0.949237i	0.0135471	−	0.0302299i
$987$	4.89040	+	32.7247i	0.155663	+	1.04164i
$988$	−9.69713	+	9.69713i	−0.308507	+	0.308507i
$989$	−9.76694	−	9.76694i	−0.310571	−	0.310571i
$990$	−0.556412	+	0.170100i	−0.0176839	+	0.00540612i
$991$		−	8.59647i		−	0.273076i	−0.990635	−	0.136538i	$-0.956402\pi$
$991$		−	8.59647i		−	0.273076i	0.990635	−	0.136538i	$-0.0435976\pi$
$992$	−0.507801			−0.0161227
$993$	19.3827	−	2.89656i	0.615092	−	0.0919197i
$994$	−0.745760	−	0.745760i	−0.0236541	−	0.0236541i
$995$	4.43567			0.140620
$996$	−3.64196	+	4.92172i	−0.115400	+	0.155951i
$997$	−17.1664	+	17.1664i	−0.543666	+	0.543666i	−0.924602	−	0.380935i	$-0.875602\pi$
$997$	−17.1664	+	17.1664i	−0.543666	+	0.543666i	0.380935	+	0.924602i	$0.375602\pi$
$998$	0.556732	−	0.556732i	0.0176231	−	0.0176231i
$999$	4.85652	+	10.1827i	0.153654	+	0.322167i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.2.q.d.191.8	yes	36
3.2	odd	2		435.2.q.c.191.11	yes	36
29.12	odd	4		435.2.q.c.41.11	✓	36
87.41	even	4	inner	435.2.q.d.41.8	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.2.q.c.41.11	✓	36	29.12	odd	4
435.2.q.c.191.11	yes	36	3.2	odd	2
435.2.q.d.41.8	yes	36	87.41	even	4	inner
435.2.q.d.191.8	yes	36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	435.q (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0236294 - 0.0236294i) q^{2} +(1.03028 - 1.39231i) q^{3} -1.99888i q^{4} +1.00000 q^{5} +(-0.0572444 + 0.00855463i) q^{6} +3.42666 q^{7} +(-0.0944913 + 0.0944913i) q^{8} +(-0.877056 - 2.86893i) q^{9} +O(q^{10})\)	\(q+(-0.0236294 - 0.0236294i) q^{2} +(1.03028 - 1.39231i) q^{3} -1.99888i q^{4} +1.00000 q^{5} +(-0.0572444 + 0.00855463i) q^{6} +3.42666 q^{7} +(-0.0944913 + 0.0944913i) q^{8} +(-0.877056 - 2.86893i) q^{9} +(-0.0236294 - 0.0236294i) q^{10} +(4.10386 + 4.10386i) q^{11} +(-2.78307 - 2.05940i) q^{12} +3.19797i q^{13} +(-0.0809700 - 0.0809700i) q^{14} +(1.03028 - 1.39231i) q^{15} -3.99330 q^{16} +(-4.08727 - 4.08727i) q^{17} +(-0.0470669 + 0.0885156i) q^{18} +(-1.51698 + 1.51698i) q^{19} -1.99888i q^{20} +(3.53041 - 4.77097i) q^{21} -0.193944i q^{22} +3.49892i q^{23} +(0.0342090 + 0.228913i) q^{24} +1.00000 q^{25} +(0.0755663 - 0.0755663i) q^{26} +(-4.89806 - 1.73466i) q^{27} -6.84949i q^{28} +(-4.91427 - 2.20227i) q^{29} +(-0.0572444 + 0.00855463i) q^{30} +(-0.896093 + 0.896093i) q^{31} +(0.283342 + 0.283342i) q^{32} +(9.94197 - 1.48573i) q^{33} +0.193159i q^{34} +3.42666 q^{35} +(-5.73466 + 1.75313i) q^{36} +(-1.53523 - 1.53523i) q^{37} +0.0716909 q^{38} +(4.45257 + 3.29480i) q^{39} +(-0.0944913 + 0.0944913i) q^{40} +(-4.78315 + 4.78315i) q^{41} +(-0.196157 + 0.0293138i) q^{42} +(-2.79141 + 2.79141i) q^{43} +(8.20315 - 8.20315i) q^{44} +(-0.877056 - 2.86893i) q^{45} +(0.0826775 - 0.0826775i) q^{46} +(-3.94208 + 3.94208i) q^{47} +(-4.11421 + 5.55991i) q^{48} +4.74200 q^{49} +(-0.0236294 - 0.0236294i) q^{50} +(-9.90176 + 1.47972i) q^{51} +6.39238 q^{52} +0.219714i q^{53} +(0.0747492 + 0.156727i) q^{54} +(4.10386 + 4.10386i) q^{55} +(-0.323790 + 0.323790i) q^{56} +(0.549198 + 3.67503i) q^{57} +(0.0640830 + 0.168160i) q^{58} -14.4779i q^{59} +(-2.78307 - 2.05940i) q^{60} +(7.78602 - 7.78602i) q^{61} +0.0423483 q^{62} +(-3.00537 - 9.83086i) q^{63} +7.97321i q^{64} +3.19797i q^{65} +(-0.270030 - 0.199816i) q^{66} +11.2502i q^{67} +(-8.16997 + 8.16997i) q^{68} +(4.87159 + 3.60486i) q^{69} +(-0.0809700 - 0.0809700i) q^{70} +9.21033 q^{71} +(0.353963 + 0.188215i) q^{72} +(10.7069 + 10.7069i) q^{73} +0.0725530i q^{74} +(1.03028 - 1.39231i) q^{75} +(3.03227 + 3.03227i) q^{76} +(14.0625 + 14.0625i) q^{77} +(-0.0273575 - 0.183066i) q^{78} +(1.49359 - 1.49359i) q^{79} -3.99330 q^{80} +(-7.46154 + 5.03243i) q^{81} +0.226046 q^{82} -1.76845i q^{83} +(-9.53662 - 7.05688i) q^{84} +(-4.08727 - 4.08727i) q^{85} +0.131919 q^{86} +(-8.12930 + 4.57324i) q^{87} -0.775559 q^{88} +(-6.11850 - 6.11850i) q^{89} +(-0.0470669 + 0.0885156i) q^{90} +10.9584i q^{91} +6.99394 q^{92} +(0.324415 + 2.17086i) q^{93} +0.186298 q^{94} +(-1.51698 + 1.51698i) q^{95} +(0.686421 - 0.102579i) q^{96} +(-5.10408 - 5.10408i) q^{97} +(-0.112051 - 0.112051i) q^{98} +(8.17439 - 15.3730i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{2} + 2 q^{3} + 36 q^{5} - 8 q^{6} + 8 q^{7} - 4 q^{8}+O(q^{10}) \) 36 * q + 4 * q^2 + 2 * q^3 + 36 * q^5 - 8 * q^6 + 8 * q^7 - 4 * q^8	\( 36 q + 4 q^{2} + 2 q^{3} + 36 q^{5} - 8 q^{6} + 8 q^{7} - 4 q^{8} + 4 q^{10} + 12 q^{11} + 10 q^{12} - 28 q^{14} + 2 q^{15} - 60 q^{16} + 20 q^{17} + 32 q^{18} + 16 q^{19} - 12 q^{21} + 24 q^{24} + 36 q^{25} - 4 q^{26} - 22 q^{27} + 28 q^{29} - 8 q^{30} - 8 q^{31} + 16 q^{32} + 8 q^{33} + 8 q^{35} - 28 q^{36} - 4 q^{37} - 24 q^{38} - 24 q^{39} - 4 q^{40} - 48 q^{41} + 8 q^{42} + 4 q^{43} - 16 q^{44} + 20 q^{46} + 20 q^{47} - 66 q^{48} + 28 q^{49} + 4 q^{50} - 44 q^{52} - 24 q^{54} + 12 q^{55} + 84 q^{56} - 28 q^{57} - 64 q^{58} + 10 q^{60} + 20 q^{61} - 8 q^{62} - 32 q^{63} - 8 q^{66} - 60 q^{68} - 36 q^{69} - 28 q^{70} + 16 q^{71} + 64 q^{72} + 8 q^{73} + 2 q^{75} + 16 q^{76} - 32 q^{77} + 48 q^{78} + 12 q^{79} - 60 q^{80} - 60 q^{81} + 56 q^{82} + 100 q^{84} + 20 q^{85} - 8 q^{86} - 10 q^{87} - 24 q^{88} - 20 q^{89} + 32 q^{90} + 16 q^{92} - 24 q^{93} + 52 q^{94} + 16 q^{95} + 8 q^{96} + 4 q^{97} + 8 q^{98} + 32 q^{99}+O(q^{100}) \) 36 * q + 4 * q^2 + 2 * q^3 + 36 * q^5 - 8 * q^6 + 8 * q^7 - 4 * q^8 + 4 * q^10 + 12 * q^11 + 10 * q^12 - 28 * q^14 + 2 * q^15 - 60 * q^16 + 20 * q^17 + 32 * q^18 + 16 * q^19 - 12 * q^21 + 24 * q^24 + 36 * q^25 - 4 * q^26 - 22 * q^27 + 28 * q^29 - 8 * q^30 - 8 * q^31 + 16 * q^32 + 8 * q^33 + 8 * q^35 - 28 * q^36 - 4 * q^37 - 24 * q^38 - 24 * q^39 - 4 * q^40 - 48 * q^41 + 8 * q^42 + 4 * q^43 - 16 * q^44 + 20 * q^46 + 20 * q^47 - 66 * q^48 + 28 * q^49 + 4 * q^50 - 44 * q^52 - 24 * q^54 + 12 * q^55 + 84 * q^56 - 28 * q^57 - 64 * q^58 + 10 * q^60 + 20 * q^61 - 8 * q^62 - 32 * q^63 - 8 * q^66 - 60 * q^68 - 36 * q^69 - 28 * q^70 + 16 * q^71 + 64 * q^72 + 8 * q^73 + 2 * q^75 + 16 * q^76 - 32 * q^77 + 48 * q^78 + 12 * q^79 - 60 * q^80 - 60 * q^81 + 56 * q^82 + 100 * q^84 + 20 * q^85 - 8 * q^86 - 10 * q^87 - 24 * q^88 - 20 * q^89 + 32 * q^90 + 16 * q^92 - 24 * q^93 + 52 * q^94 + 16 * q^95 + 8 * q^96 + 4 * q^97 + 8 * q^98 + 32 * q^99

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