LMFDB - Embedded newform 435.2.q.c.41.11

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			41.11
Character	$\chi$	$=$	435.41
Dual form			435.2.q.c.191.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0236294 - 0.0236294i) q^{2} +(1.39231 + 1.03028i) q^{3} +1.99888i q^{4} -1.00000 q^{5} +(0.0572444 - 0.00855463i) q^{6} +3.42666 q^{7} +(0.0944913 + 0.0944913i) q^{8} +(0.877056 + 2.86893i) q^{9} +O(q^{10})$	\(q+(0.0236294 - 0.0236294i) q^{2} +(1.39231 + 1.03028i) 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} +(-2.05940 + 2.78307i) q^{12} -3.19797i q^{13} +(0.0809700 - 0.0809700i) q^{14} +(-1.39231 - 1.03028i) q^{15} -3.99330 q^{16} +(4.08727 - 4.08727i) q^{17} +(0.0885156 + 0.0470669i) q^{18} +(-1.51698 - 1.51698i) q^{19} -1.99888i q^{20} +(4.77097 + 3.53041i) 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} +(-1.73466 + 4.89806i) 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} +(3.29480 - 4.45257i) 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} +(-5.55991 - 4.11421i) 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} +(2.05940 - 2.78307i) 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} +(-0.199816 + 0.270030i) q^{66} -11.2502i q^{67} +(8.16997 + 8.16997i) q^{68} +(-3.60486 + 4.87159i) q^{69} +(-0.0809700 + 0.0809700i) q^{70} -9.21033 q^{71} +(-0.188215 + 0.353963i) q^{72} +(10.7069 - 10.7069i) q^{73} +0.0725530i q^{74} +(1.39231 + 1.03028i) 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} +(-7.05688 + 9.53662i) q^{84} +(-4.08727 + 4.08727i) q^{85} -0.131919 q^{86} +(9.11113 + 1.99682i) q^{87} -0.775559 q^{88} +(6.11850 - 6.11850i) q^{89} +(-0.0885156 - 0.0470669i) 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} +(-15.3730 - 8.17439i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 4 q^{2} + 6 q^{3} - 36 q^{5} + 8 q^{6} + 8 q^{7} + 4 q^{8}+O(q^{10}) $ 36 * q - 4 * q^2 + 6 * q^3 - 36 * q^5 + 8 * q^6 + 8 * q^7 + 4 * q^8	$ 36 q - 4 q^{2} + 6 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} - 6 q^{15} - 60 q^{16} - 20 q^{17} - 28 q^{18} + 16 q^{19} + 12 q^{21} + 24 q^{24} + 36 q^{25} + 4 q^{26} + 30 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} - 40 q^{39} - 4 q^{40} + 48 q^{41} - 8 q^{42} + 4 q^{43} + 16 q^{44} + 20 q^{46} - 20 q^{47} - 14 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} + 40 q^{66} + 60 q^{68} + 36 q^{69} - 28 q^{70} - 16 q^{71} - 132 q^{72} + 8 q^{73} + 6 q^{75} + 16 q^{76} + 32 q^{77} + 48 q^{78} + 12 q^{79} + 60 q^{80} - 60 q^{81} + 56 q^{82} + 44 q^{84} + 20 q^{85} + 8 q^{86} + 22 q^{87} - 24 q^{88} + 20 q^{89} + 28 q^{90} - 16 q^{92} + 24 q^{93} + 52 q^{94} - 16 q^{95} - 8 q^{96} + 4 q^{97} - 8 q^{98} - 48 q^{99}+O(q^{100}) $ 36 * q - 4 * q^2 + 6 * 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 - 6 * q^15 - 60 * q^16 - 20 * q^17 - 28 * q^18 + 16 * q^19 + 12 * q^21 + 24 * q^24 + 36 * q^25 + 4 * q^26 + 30 * 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 - 40 * q^39 - 4 * q^40 + 48 * q^41 - 8 * q^42 + 4 * q^43 + 16 * q^44 + 20 * q^46 - 20 * q^47 - 14 * 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 + 40 * q^66 + 60 * q^68 + 36 * q^69 - 28 * q^70 - 16 * q^71 - 132 * q^72 + 8 * q^73 + 6 * q^75 + 16 * q^76 + 32 * q^77 + 48 * q^78 + 12 * q^79 + 60 * q^80 - 60 * q^81 + 56 * q^82 + 44 * q^84 + 20 * q^85 + 8 * q^86 + 22 * q^87 - 24 * q^88 + 20 * q^89 + 28 * q^90 - 16 * q^92 + 24 * q^93 + 52 * q^94 - 16 * q^95 - 8 * q^96 + 4 * q^97 - 8 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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	$-0.746239\pi$
$2$	0.0236294	−	0.0236294i	0.0167085	−	0.0167085i	0.715412	+	0.698703i	$0.246239\pi$
$3$	1.39231	+	1.03028i	0.803851	+	0.594831i
$3$	1.39231	+	1.03028i	0.803851	+	0.594831i
$4$			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	−0.276286	+	0.961075i	$0.589104\pi$
$11$	−4.10386	+	4.10386i	−1.23736	+	1.23736i	−0.961075	+	0.276286i	$0.910896\pi$
$12$	−2.05940	+	2.78307i	−0.594499	+	0.803402i
$13$		−	3.19797i		−	0.886958i	−0.896285	−	0.443479i	$-0.853744\pi$
$13$		−	3.19797i		−	0.886958i	0.896285	−	0.443479i	$-0.146256\pi$
$14$	0.0809700	−	0.0809700i	0.0216401	−	0.0216401i
$15$	−1.39231	−	1.03028i	−0.359493	−	0.266017i
$16$	−3.99330			−0.998325
$17$	4.08727	−	4.08727i	0.991308	−	0.991308i	−0.00865490	−	0.999963i	$-0.502755\pi$
$17$	4.08727	−	4.08727i	0.991308	−	0.991308i	0.999963	+	0.00865490i	$0.00275497\pi$
$18$	0.0885156	+	0.0470669i	0.0208633	+	0.0110938i
$19$	−1.51698	−	1.51698i	−0.348020	−	0.348020i	0.511352	−	0.859372i	$-0.329145\pi$
$19$	−1.51698	−	1.51698i	−0.348020	−	0.348020i	−0.859372	+	0.511352i	$0.829145\pi$
$20$		−	1.99888i		−	0.446964i
$21$	4.77097	+	3.53041i	1.04111	+	0.770399i
$22$			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
$27$	−1.73466	+	4.89806i	−0.333836	+	0.942631i
$28$			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	0.622041	−	0.782984i	$-0.286304\pi$
$31$	−0.896093	−	0.896093i	−0.160943	−	0.160943i	−0.782984	+	0.622041i	$0.786304\pi$
$32$	−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	−0.821950	−	0.569560i	$-0.807114\pi$
$37$	−1.53523	+	1.53523i	−0.252389	+	0.252389i	0.569560	+	0.821950i	$0.307114\pi$
$38$	−0.0716909			−0.0116298
$39$	3.29480	−	4.45257i	0.527590	−	0.712982i
$40$	−0.0944913	−	0.0944913i	−0.0149404	−	0.0149404i
$41$	4.78315	+	4.78315i	0.747002	+	0.747002i	0.973915	−	0.226913i	$-0.0728632\pi$
$41$	4.78315	+	4.78315i	0.747002	+	0.747002i	−0.226913	+	0.973915i	$0.572863\pi$
$42$	0.196157	−	0.0293138i	0.0302677	−	0.00452322i
$43$	−2.79141	−	2.79141i	−0.425686	−	0.425686i	0.461470	−	0.887156i	$-0.347322\pi$
$43$	−2.79141	−	2.79141i	−0.425686	−	0.425686i	−0.887156	+	0.461470i	$0.847322\pi$
$44$	−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	$-0.116716\pi$
$47$	3.94208	+	3.94208i	0.575011	+	0.575011i	−0.358514	+	0.933524i	$0.616716\pi$
$48$	−5.55991	−	4.11421i	−0.802505	−	0.593835i
$49$	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	$-0.391466\pi$
$60$	2.05940	−	2.78307i	0.265868	−	0.359292i
$61$	7.78602	+	7.78602i	0.996897	+	0.996897i	0.999995	−	0.00309811i	$-0.000986162\pi$
$61$	7.78602	+	7.78602i	0.996897	+	0.996897i	−0.00309811	+	0.999995i	$0.500986\pi$
$62$	−0.0423483			−0.00537824
$63$	3.00537	+	9.83086i	0.378642	+	1.23857i
$64$		−	7.97321i		−	0.996651i
$65$			3.19797i			0.396660i
$66$	−0.199816	+	0.270030i	−0.0245957	+	0.0332384i
$67$		−	11.2502i		−	1.37443i	−0.726454	−	0.687215i	$-0.758833\pi$
$67$		−	11.2502i		−	1.37443i	0.726454	−	0.687215i	$-0.241167\pi$
$68$	8.16997	+	8.16997i	0.990754	+	0.990754i
$69$	−3.60486	+	4.87159i	−0.433974	+	0.586470i
$70$	−0.0809700	+	0.0809700i	−0.00967777	+	0.00967777i
$71$	−9.21033			−1.09306			−0.546532	−	0.837438i	$-0.684052\pi$
$71$	−9.21033			−1.09306			−0.546532	+	0.837438i	$0.684052\pi$
$72$	−0.188215	+	0.353963i	−0.0221813	+	0.0417150i
$73$	10.7069	−	10.7069i	1.25314	−	1.25314i	0.298842	−	0.954302i	$-0.403399\pi$
$73$	10.7069	−	10.7069i	1.25314	−	1.25314i	0.954302	−	0.298842i	$-0.0966005\pi$
$74$			0.0725530i			0.00843411i
$75$	1.39231	+	1.03028i	0.160770	+	0.118966i
$76$	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	0.786118	−	0.618076i	$-0.212088\pi$
$79$	1.49359	+	1.49359i	0.168042	+	0.168042i	−0.618076	+	0.786118i	$0.712088\pi$
$80$	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	$-0.0309427\pi$
$84$	−7.05688	+	9.53662i	−0.769969	+	1.04053i
$85$	−4.08727	+	4.08727i	−0.443326	+	0.443326i
$86$	−0.131919			−0.0142252
$87$	9.11113	+	1.99682i	0.976816	+	0.214081i
$88$	−0.775559			−0.0826749
$89$	6.11850	−	6.11850i	0.648560	−	0.648560i	−0.304085	−	0.952645i	$-0.598351\pi$
$89$	6.11850	−	6.11850i	0.648560	−	0.648560i	0.952645	+	0.304085i	$0.0983507\pi$
$90$	−0.0885156	−	0.0470669i	−0.00933036	−	0.00496128i
$91$		−	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	−0.917039	−	0.398798i	$-0.869427\pi$
$97$	−5.10408	+	5.10408i	−0.518241	+	0.518241i	0.398798	+	0.917039i	$0.369427\pi$
$98$	0.112051	−	0.112051i	0.0113188	−	0.0113188i
$99$	−15.3730	−	8.17439i	−1.54505	−	0.821557i
$100$			1.99888i			0.199888i
$101$	9.67557	−	9.67557i	0.962755	−	0.962755i	−0.0365758	−	0.999331i	$-0.511645\pi$
$101$	9.67557	−	9.67557i	0.962755	−	0.962755i	0.999331	+	0.0365758i	$0.0116450\pi$
$102$	0.199008	−	0.268938i	0.0197047	−	0.0266288i
$103$	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
$105$	−4.77097	−	3.53041i	−0.465599	−	0.344533i
$106$	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	$-0.0218897\pi$
$108$	−9.79064	−	3.46739i	−0.942105	−	0.333649i
$109$		−	1.85368i		−	0.177550i	−0.996052	−	0.0887751i	$-0.971705\pi$
$109$		−	1.85368i		−	0.177550i	0.996052	−	0.0887751i	$-0.0282953\pi$
$110$		−	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	$-0.0415339\pi$
$113$	9.15667	+	9.15667i	0.861387	+	0.861387i	−0.130113	+	0.991499i	$0.541534\pi$
$114$	−0.0998160	−	0.0738615i	−0.00934862	−	0.00691777i
$115$		−	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
$126$	0.303313	+	0.161282i	0.0270212	+	0.0143682i
$127$	−4.83188	−	4.83188i	−0.428760	−	0.428760i	0.459446	−	0.888206i	$-0.348048\pi$
$127$	−4.83188	−	4.83188i	−0.428760	−	0.428760i	−0.888206	+	0.459446i	$0.848048\pi$
$128$	−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	−0.975592	−	0.219589i	$-0.929528\pi$
$131$	−13.6795	−	13.6795i	−1.19518	−	1.19518i	−0.219589	−	0.975592i	$-0.570472\pi$
$132$	−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
$135$	1.73466	−	4.89806i	0.149296	−	0.421558i
$136$	0.772422			0.0662347
$137$	−4.96358	+	4.96358i	−0.424068	+	0.424068i	−0.886602	−	0.462534i	$-0.846940\pi$
$137$	−4.96358	+	4.96358i	−0.424068	+	0.424068i	0.462534	+	0.886602i	$0.346940\pi$
$138$	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
$147$	6.60233	+	4.88557i	0.544551	+	0.402955i
$148$	−3.06874	−	3.06874i	−0.252249	−	0.252249i
$149$	−12.7788			−1.04688			−0.523439	−	0.852063i	$-0.675351\pi$
$149$	−12.7788			−1.04688			−0.523439	+	0.852063i	$0.675351\pi$
$150$	0.0572444	−	0.00855463i	0.00467398	−	0.000698482i
$151$			21.8159i			1.77535i	0.460469	+	0.887676i	$0.347681\pi$
$151$			21.8159i			1.77535i	−0.460469	+	0.887676i	$0.652319\pi$
$152$		−	0.286684i		−	0.0232531i
$153$	15.3109	+	8.14133i	1.23781	+	0.658187i
$154$			0.664580i			0.0535534i
$155$	0.896093	+	0.896093i	0.0719759	+	0.0719759i
$156$	8.90017	+	6.58592i	0.712584	+	0.527296i
$157$	10.2256	−	10.2256i	0.816091	−	0.816091i	−0.169448	−	0.985539i	$-0.554198\pi$
$157$	10.2256	−	10.2256i	0.816091	−	0.816091i	0.985539	+	0.169448i	$0.0541985\pi$
$158$	0.0705852			0.00561545
$159$	−0.226367	+	0.305911i	−0.0179521	+	0.0242603i
$160$	0.283342	−	0.283342i	0.0224002	−	0.0224002i
$161$			11.9896i			0.944914i
$162$	−0.0573986	+	0.295225i	−0.00450966	+	0.0231951i
$163$	−15.4030	+	15.4030i	−1.20645	+	1.20645i	−0.234284	+	0.972168i	$0.575275\pi$
$163$	−15.4030	+	15.4030i	−1.20645	+	1.20645i	−0.972168	+	0.234284i	$0.924725\pi$
$164$	−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	$-0.692043\pi$
$167$	−14.6643			−1.13476			−0.567381	+	0.823456i	$0.692043\pi$
$168$	0.117222	+	0.784409i	0.00904391	+	0.0605184i
$169$	2.77296			0.213305
$170$			0.193159i			0.0148147i
$171$	3.02164	−	5.68260i	0.231071	−	0.434560i
$172$	5.57971	−	5.57971i	0.425449	−	0.425449i
$173$	−15.1753			−1.15376			−0.576879	−	0.816830i	$-0.695730\pi$
$173$	−15.1753			−1.15376			−0.576879	+	0.816830i	$0.695730\pi$
$174$	0.262474	−	0.168107i	0.0198981	−	0.0127442i
$175$	3.42666			0.259031
$176$	16.3880	−	16.3880i	1.23529	−	1.23529i
$177$	14.9163	−	20.1577i	1.12117	−	1.51515i
$178$		−	0.289153i		−	0.0216730i
$179$	−0.0275707			−0.00206073			−0.00103037	−	0.999999i	$-0.500328\pi$
$179$	−0.0275707			−0.00206073			−0.00103037	+	0.999999i	$0.500328\pi$
$180$	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
$186$	−0.0589620	−	0.0436305i	−0.00432330	−	0.00319914i
$187$			33.5472i			2.45321i
$188$	−7.87975	+	7.87975i	−0.574690	+	0.574690i
$189$	−5.94410	+	16.7840i	−0.432369	+	1.22085i
$190$	0.0716909			0.00520100
$191$	−9.92163	+	9.92163i	−0.717904	+	0.717904i	−0.968176	−	0.250272i	$-0.919480\pi$
$191$	−9.92163	+	9.92163i	−0.717904	+	0.717904i	0.250272	+	0.968176i	$0.419480\pi$
$192$	8.21462	−	11.1012i	0.592839	−	0.801159i
$193$	13.0779	+	13.0779i	0.941365	+	0.941365i	0.998374	−	0.0570086i	$-0.0181562\pi$
$193$	13.0779	+	13.0779i	0.941365	+	0.941365i	−0.0570086	+	0.998374i	$0.518156\pi$
$194$			0.241213i			0.0173181i
$195$	−3.29480	+	4.45257i	−0.235946	+	0.318855i
$196$			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
$201$	11.5908	−	15.6638i	0.817553	−	1.10484i
$202$		−	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	−0.994086	−	0.108599i	$-0.965364\pi$
$211$	−12.8624	+	12.8624i	−0.885487	+	0.885487i	0.108599	+	0.994086i	$0.465364\pi$
$212$	−0.439183			−0.0301632
$213$	−12.8236	−	9.48919i	−0.878661	−	0.650189i
$214$	−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
$222$	−0.0747497	+	0.101016i	−0.00501687	+	0.00677977i
$223$	−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	−0.841740	−	0.539883i	$-0.818468\pi$
$229$	−4.56792	+	4.56792i	−0.301857	+	0.301857i	0.539883	+	0.841740i	$0.318468\pi$
$230$	−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	$-0.000141985\pi$
$234$	0.150519	−	0.283070i	0.00983971	−	0.0185049i
$235$	−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	$-0.186477\pi$
$240$	5.55991	+	4.11421i	0.358891	+	0.265571i
$241$			11.1853i			0.720506i	0.932855	+	0.360253i	$0.117310\pi$
$241$			11.1853i			0.720506i	−0.932855	+	0.360253i	$0.882690\pi$
$242$	−0.535996	−	0.535996i	−0.0344551	−	0.0344551i
$243$	−15.5736	−	0.680756i	−0.999046	−	0.0436705i
$244$	−15.5633	+	15.5633i	−0.996340	+	0.996340i
$245$	−4.74200			−0.302955
$246$	0.314726	+	0.232890i	0.0200662	+	0.0148485i
$247$	−4.85127	+	4.85127i	−0.308679	+	0.308679i
$248$		−	0.169346i		−	0.0107535i
$249$	1.82200	−	2.46224i	0.115464	−	0.156038i
$250$	−0.0236294	+	0.0236294i	−0.00149446	+	0.00149446i
$251$	−3.76151	+	3.76151i	−0.237424	+	0.237424i	−0.815783	−	0.578358i	$-0.803694\pi$
$251$	−3.76151	+	3.76151i	−0.237424	+	0.237424i	0.578358	+	0.815783i	$0.303694\pi$
$252$	−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	$0.946186\pi$
$258$	−0.183672	−	0.135913i	−0.0114349	−	0.00846158i
$259$	−5.26069	+	5.26069i	−0.326884	+	0.326884i
$260$	−6.39238			−0.396438
$261$	10.6282	+	12.1672i	0.657872	+	0.753130i
$262$	−0.646476			−0.0399395
$263$	14.6301	−	14.6301i	0.902133	−	0.902133i	−0.0934873	−	0.995620i	$-0.529801\pi$
$263$	14.6301	−	14.6301i	0.902133	−	0.902133i	0.995620	+	0.0934873i	$0.0298015\pi$
$264$	−1.07982	−	0.799041i	−0.0664583	−	0.0491776i
$265$		−	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	$-0.309235\pi$
$269$	−4.29151	−	4.29151i	−0.261658	−	0.261658i	−0.825727	+	0.564069i	$0.809235\pi$
$270$	−0.0747492	−	0.156727i	−0.00454909	−	0.00953812i
$271$	7.12704	−	7.12704i	0.432937	−	0.432937i	−0.456689	−	0.889626i	$-0.650965\pi$
$271$	7.12704	−	7.12704i	0.432937	−	0.432937i	0.889626	+	0.456689i	$0.150965\pi$
$272$	−16.3217	+	16.3217i	−0.989647	+	0.989647i
$273$	11.2902	−	15.2575i	0.683312	−	0.923423i
$274$			0.234573i			0.0141711i
$275$	−4.10386	+	4.10386i	−0.247472	+	0.247472i
$276$	−9.73773	−	7.20570i	−0.586143	−	0.433732i
$277$	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
$279$	1.78491	−	3.35675i	0.106860	−	0.200964i
$280$	−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	$-0.109152\pi$
$282$	0.259385	+	0.191939i	0.0154461	+	0.0114298i
$283$			7.34630i			0.436692i	0.975871	+	0.218346i	$0.0700661\pi$
$283$			7.34630i			0.436692i	−0.975871	+	0.218346i	$0.929934\pi$
$284$		−	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
$288$	−1.06140	−	0.564382i	−0.0625434	−	0.0332565i
$289$		−	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	$-0.573710\pi$
$293$	12.7319	−	12.7319i	0.743806	−	0.743806i	0.973308	+	0.229502i	$0.0737097\pi$
$294$	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
$300$	−2.05940	+	2.78307i	−0.118900	+	0.160680i
$301$	−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	0.507287	−	0.861777i	$-0.330648\pi$
$307$	−6.21116	−	6.21116i	−0.354490	−	0.354490i	−0.861777	+	0.507287i	$0.830648\pi$
$308$	−28.1094	−	28.1094i	−1.60168	−	1.60168i
$309$	0.252668	+	0.186968i	0.0143738	+	0.0106363i
$310$	0.0423483			0.00240522
$311$	−15.0524	+	15.0524i	−0.853544	+	0.853544i	−0.990568	−	0.137024i	$-0.956246\pi$
$311$	−15.0524	+	15.0524i	−0.853544	+	0.853544i	0.137024	+	0.990568i	$0.456246\pi$
$312$	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	$-0.0618940\pi$
$317$	14.0287	+	14.0287i	0.787932	+	0.787932i	−0.193223	+	0.981155i	$0.561894\pi$
$318$	0.00187957	+	0.0125774i	0.000105401	+	0.000705306i
$319$	−11.1297	+	29.2053i	−0.623142	+	1.63518i
$320$			7.97321i			0.445716i
$321$	1.46461	−	1.97927i	0.0817466	−	0.110472i
$322$	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
$327$	1.90980	−	2.58090i	0.105612	−	0.142724i
$328$			0.903932i			0.0499113i
$329$	13.5082	+	13.5082i	0.744729	+	0.744729i
$330$	0.199816	−	0.270030i	0.0109995	−	0.0148647i
$331$	8.00083	−	8.00083i	0.439765	−	0.439765i	−0.452168	−	0.891933i	$-0.649349\pi$
$331$	8.00083	−	8.00083i	0.439765	−	0.439765i	0.891933	+	0.452168i	$0.149349\pi$
$332$	3.53493			0.194005
$333$	−5.75094	−	3.05798i	−0.315149	−	0.167576i
$334$	−0.346510	+	0.346510i	−0.0189602	+	0.0189602i
$335$			11.2502i			0.614664i
$336$	−19.0519	−	14.0980i	−1.03937	−	0.769109i
$337$	11.7821	−	11.7821i	0.641810	−	0.641810i	−0.309190	−	0.951000i	$-0.600058\pi$
$337$	11.7821	−	11.7821i	0.641810	−	0.641810i	0.951000	+	0.309190i	$0.100058\pi$
$338$	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
$345$	3.60486	−	4.87159i	0.194079	−	0.262277i
$346$	−0.358584	+	0.358584i	−0.0192776	+	0.0192776i
$347$	7.19432			0.386211			0.193106	−	0.981178i	$-0.438144\pi$
$347$	7.19432			0.386211			0.193106	+	0.981178i	$0.438144\pi$
$348$	−3.99141	+	18.2121i	−0.213962	+	0.976270i
$349$	−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
$351$	15.6639	+	5.54740i	0.836075	+	0.296098i
$352$		−	2.32559i		−	0.123955i
$353$	−22.6944			−1.20790			−0.603951	−	0.797021i	$-0.706408\pi$
$353$	−22.6944			−1.20790			−0.603951	+	0.797021i	$0.706408\pi$
$354$	−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	$-0.765153\pi$
$359$	−1.27514	+	1.27514i	−0.0672991	+	0.0672991i	0.672656	+	0.739955i	$0.265153\pi$
$360$	0.188215	−	0.353963i	0.00991980	−	0.0186555i
$361$		−	14.3975i		−	0.757764i
$362$	−0.369532	+	0.369532i	−0.0194222	+	0.0194222i
$363$	23.3702	−	31.5824i	1.22662	−	1.65764i
$364$	21.9045			1.14811
$365$	−10.7069	+	10.7069i	−0.560423	+	0.560423i
$366$	0.512312	+	0.379099i	0.0267790	+	0.0198158i
$367$	−11.1733	−	11.1733i	−0.583242	−	0.583242i	0.352551	−	0.935793i	$-0.385314\pi$
$367$	−11.1733	−	11.1733i	−0.583242	−	0.583242i	−0.935793	+	0.352551i	$0.885314\pi$
$368$		−	13.9723i		−	0.728354i
$369$	−9.52744	+	17.9176i	−0.495979	+	0.932754i
$370$		−	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
$375$	−1.39231	−	1.03028i	−0.0718986	−	0.0532033i
$376$			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	−0.969696	−	0.244316i	$-0.921437\pi$
$379$	−23.6343	−	23.6343i	−1.21401	−	1.21401i	−0.244316	−	0.969696i	$-0.578563\pi$
$380$	−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	$-0.710178\pi$
$383$	−24.0070			−1.22670			−0.613349	+	0.789812i	$0.710178\pi$
$384$	−0.273366	−	1.82926i	−0.0139502	−	0.0933492i
$385$	14.0625	−	14.0625i	0.716694	−	0.716694i
$386$	0.618045			0.0314576
$387$	5.56015	−	10.4566i	0.282638	−	0.531539i
$388$	−10.2025	−	10.2025i	−0.517951	−	0.517951i
$389$	24.7490	+	24.7490i	1.25482	+	1.25482i	0.953533	+	0.301290i	$0.0974172\pi$
$389$	24.7490	+	24.7490i	1.25482	+	1.25482i	0.301290	+	0.953533i	$0.402583\pi$
$390$	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
$396$	16.3397	−	30.7289i	0.821098	−	1.54419i
$397$	−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
$408$	1.07545	+	0.795809i	0.0532428	+	0.0393984i
$409$	−9.91083	−	9.91083i	−0.490059	−	0.490059i	0.418266	−	0.908325i	$-0.362638\pi$
$409$	−9.91083	−	9.91083i	−0.490059	−	0.490059i	−0.908325	+	0.418266i	$0.862638\pi$
$410$	−0.226046			−0.0111636
$411$	−12.0247	+	1.79698i	−0.593136	+	0.0886385i
$412$			0.362745i			0.0178712i
$413$		−	49.6108i		−	2.44119i
$414$	−0.164683	+	0.309709i	−0.00809375	+	0.0152214i
$415$			1.76845i			0.0868099i
$416$	0.906120	+	0.906120i	0.0444262	+	0.0444262i
$417$	9.47155	+	7.00873i	0.463824	+	0.343219i
$418$	0.294210	−	0.294210i	0.0143903	−	0.0143903i
$419$	20.7079			1.01165			0.505823	−	0.862637i	$-0.331189\pi$
$419$	20.7079			1.01165			0.505823	+	0.862637i	$0.331189\pi$
$420$	7.05688	−	9.53662i	0.344340	−	0.465339i
$421$	−14.7489	+	14.7489i	−0.718817	+	0.718817i	−0.968363	−	0.249546i	$-0.919719\pi$
$421$	−14.7489	+	14.7489i	−0.718817	+	0.718817i	0.249546	+	0.968363i	$0.419719\pi$
$422$			0.607864i			0.0295904i
$423$	−7.85213	+	14.7670i	−0.381783	+	0.717995i
$424$	−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	$-0.253824\pi$
$432$	6.92703	−	19.5594i	0.333277	−	0.941053i
$433$	−2.06412	+	2.06412i	−0.0991953	+	0.0991953i	−0.754963	−	0.655768i	$-0.772345\pi$
$433$	−2.06412	+	2.06412i	−0.0991953	+	0.0991953i	0.655768	+	0.754963i	$0.272345\pi$
$434$	−0.145113			−0.00696566
$435$	−9.11113	−	1.99682i	−0.436845	−	0.0957401i
$436$	3.70529			0.177451
$437$	5.30781	−	5.30781i	0.253907	−	0.253907i
$438$	0.521315	−	0.704501i	0.0249094	−	0.0336624i
$439$			29.2516i			1.39610i	0.716047	+	0.698052i	$0.245950\pi$
$439$			29.2516i			1.39610i	−0.716047	+	0.698052i	$0.754050\pi$
$440$	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	$-0.423164\pi$
$443$	−15.4059	−	15.4059i	−0.731956	−	0.731956i	−0.971007	+	0.239051i	$0.923164\pi$
$444$	−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
$447$	−17.7920	−	13.1657i	−0.841534	−	0.622716i
$448$		−	27.3215i		−	1.29082i
$449$	−23.7030	+	23.7030i	−1.11861	+	1.11861i	−0.126670	+	0.991945i	$0.540429\pi$
$449$	−23.7030	+	23.7030i	−1.11861	+	1.11861i	−0.991945	+	0.126670i	$0.959571\pi$
$450$	0.0885156	+	0.0470669i	0.00417266	+	0.00221875i
$451$	−39.2588			−1.84862
$452$	−18.3031	+	18.3031i	−0.860906	+	0.860906i
$453$	−22.4764	+	30.3745i	−1.05603	+	1.42712i
$454$	0.499230	+	0.499230i	0.0234300	+	0.0234300i
$455$			10.9584i			0.513736i
$456$	0.295364	−	0.399152i	0.0138317	−	0.0186920i
$457$		−	24.8531i		−	1.16258i	−0.813697	−	0.581289i	$-0.802549\pi$
$457$		−	24.8531i		−	1.16258i	0.813697	−	0.581289i	$-0.197451\pi$
$458$			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	$-0.396429\pi$
$461$	−13.4808	−	13.4808i	−0.627863	−	0.627863i	−0.947530	+	0.319667i	$0.896429\pi$
$462$	−0.684702	+	0.925301i	−0.0318552	+	0.0430489i
$463$			29.3869i			1.36572i	0.730548	+	0.682862i	$0.239265\pi$
$463$			29.3869i			1.36572i	−0.730548	+	0.682862i	$0.760735\pi$
$464$	−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	$-0.634357\pi$
$467$	10.8604	−	10.8604i	0.502559	−	0.502559i	0.912232	+	0.409673i	$0.134357\pi$
$468$	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
$474$	0.0982764	+	0.0727223i	0.00451399	+	0.00334025i
$475$	−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	$-0.202350\pi$
$479$	4.61610	+	4.61610i	0.210915	+	0.210915i	−0.593741	+	0.804656i	$0.702350\pi$
$480$	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
$483$	−12.3526	+	16.6933i	−0.562064	+	0.759570i
$484$	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	$-0.0560936\pi$
$491$	17.9307	+	17.9307i	0.809200	+	0.809200i	−0.175313	+	0.984513i	$0.556094\pi$
$492$	−23.1623	+	3.46138i	−1.04424	+	0.156051i
$493$	11.0847	−	29.0872i	0.499228	−	1.31002i
$494$			0.229266i			0.0103151i
$495$	15.3730	+	8.17439i	0.690966	+	0.367411i
$496$	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	$-0.823179\pi$
$499$		−	23.5610i		−	1.05473i	0.849637	−	0.527367i	$-0.176821\pi$
$500$		−	1.99888i		−	0.0893928i
$501$	−20.4173	−	15.1083i	−0.912179	−	0.674991i
$502$			0.177765i			0.00793402i
$503$	11.5174	+	11.5174i	0.513536	+	0.513536i	0.915608	−	0.402072i	$-0.131710\pi$
$503$	11.5174	+	11.5174i	0.513536	+	0.513536i	−0.402072	+	0.915608i	$0.631710\pi$
$504$	−0.644949	+	1.21291i	−0.0287283	+	0.0540274i
$505$	−9.67557	+	9.67557i	−0.430557	+	0.430557i
$506$	−0.678595			−0.0301672
$507$	3.86083	+	2.85692i	0.171465	+	0.126880i
$508$	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	$-0.0510243\pi$
$510$	−0.199008	+	0.268938i	−0.00881222	+	0.0119088i
$511$	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
$519$	−21.1287	−	15.6348i	−0.927449	−	0.686291i
$520$	−0.302181	+	0.302181i	−0.0132515	+	0.0132515i
$521$	6.61725			0.289907			0.144954	−	0.989438i	$-0.453697\pi$
$521$	6.61725			0.289907			0.144954	+	0.989438i	$0.453697\pi$
$522$	0.538643	+	0.0363643i	0.0235758	+	0.00159162i
$523$	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
$525$	4.77097	+	3.53041i	0.208222	+	0.154080i
$526$		−	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
$534$	0.297908	−	0.402591i	0.0128917	−	0.0174218i
$535$			1.42157i			0.0614598i
$536$	1.06305	−	1.06305i	0.0459166	−	0.0459166i
$537$	−0.0383870	−	0.0284055i	−0.00165652	−	0.00122579i
$538$	−0.202812			−0.00874384
$539$	−19.4605	+	19.4605i	−0.838224	+	0.838224i
$540$	9.79064	+	3.46739i	0.421322	+	0.149213i
$541$	−11.2647	−	11.2647i	−0.484308	−	0.484308i	0.422196	−	0.906504i	$-0.361259\pi$
$541$	−11.2647	−	11.2647i	−0.484308	−	0.484308i	−0.906504	+	0.422196i	$0.861259\pi$
$542$		−	0.336816i		−	0.0144675i
$543$	−21.7739	−	16.1122i	−0.934406	−	0.691439i
$544$			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
$549$	−15.5088	+	29.1663i	−0.661898	+	1.24479i
$550$			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	$-0.511739\pi$
$557$	−1.74034			−0.0737404			−0.0368702	+	0.999320i	$0.511739\pi$
$558$	−0.0371419	−	0.121494i	−0.00157234	−	0.00514327i
$559$	−8.92687	+	8.92687i	−0.377566	+	0.377566i
$560$	13.6837			0.578241
$561$	−34.5629	+	46.7081i	−1.45925	+	1.97202i
$562$	−0.266363	−	0.266363i	−0.0112358	−	0.0112358i
$563$	7.23563	+	7.23563i	0.304945	+	0.304945i	0.842945	−	0.538000i	$-0.180820\pi$
$563$	7.23563	+	7.23563i	0.304945	+	0.304945i	−0.538000	+	0.842945i	$0.680820\pi$
$564$	−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	$-0.260202\pi$
$569$	−1.08100	−	1.08100i	−0.0453178	−	0.0453178i	−0.729403	+	0.684085i	$0.760202\pi$
$570$	0.0998160	+	0.0738615i	0.00418083	+	0.00309372i
$571$	−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	−0.529676	−	0.848200i	$-0.677686\pi$
$577$	7.65123	−	7.65123i	0.318525	−	0.318525i	0.848200	+	0.529676i	$0.177686\pi$
$578$	−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
$582$	−0.248516	+	0.335843i	−0.0103013	+	0.0139211i
$583$	−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	$-0.361376\pi$
$588$	−9.76569	+	13.1973i	−0.402730	+	0.544247i
$589$			2.71872i			0.112023i
$590$	0.342104	+	0.342104i	0.0140842	+	0.0140842i
$591$	6.89461	−	9.31733i	0.283606	−	0.383264i
$592$	6.13062	−	6.13062i	0.251967	−	0.251967i
$593$	−41.9930			−1.72445			−0.862224	−	0.506528i	$-0.830929\pi$
$593$	−41.9930			−1.72445			−0.862224	+	0.506528i	$0.830929\pi$
$594$	−0.949948	−	0.336427i	−0.0389768	−	0.0138038i
$595$	−14.0057	+	14.0057i	−0.574177	+	0.574177i
$596$		−	25.5433i		−	1.04629i
$597$	6.17583	+	4.56997i	0.252760	+	0.187037i
$598$	0.264401	−	0.264401i	0.0108121	−	0.0108121i
$599$	1.12622	−	1.12622i	0.0460162	−	0.0460162i	−0.683724	−	0.729740i	$-0.739641\pi$
$599$	1.12622	−	1.12622i	0.0460162	−	0.0460162i	0.729740	+	0.683724i	$0.239641\pi$
$600$	0.0342090	+	0.228913i	0.00139657	+	0.00934535i
$601$	−2.00982	−	2.00982i	−0.0819821	−	0.0819821i	0.664927	−	0.746909i	$-0.268463\pi$
$601$	−2.00982	−	2.00982i	−0.0819821	−	0.0819821i	−0.746909	+	0.664927i	$0.768463\pi$
$602$	−0.452041			−0.0184238
$603$	32.2760	−	9.86705i	1.31438	−	0.401817i
$604$	−43.6074			−1.77436
$605$			22.6834i			0.922212i
$606$	0.471101	−	0.636643i	0.0191372	−	0.0258618i
$607$	−20.6809	+	20.6809i	−0.839413	+	0.839413i	−0.988782	−	0.149369i	$-0.952276\pi$
$607$	−20.6809	+	20.6809i	−0.839413	+	0.839413i	0.149369	+	0.988782i	$0.452276\pi$
$608$	0.859650			0.0348634
$609$	31.2207	+	6.84242i	1.26513	+	0.277269i
$610$	−0.367958			−0.0148982
$611$	12.6067	−	12.6067i	0.510011	−	0.510011i
$612$	−16.2736	+	30.6046i	−0.657820	+	1.23712i
$613$		−	33.7976i		−	1.36507i	−0.730853	−	0.682535i	$-0.760877\pi$
$613$		−	33.7976i		−	1.36507i	0.730853	−	0.682535i	$-0.239123\pi$
$614$	−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	$-0.144654\pi$
$617$	11.4148	+	11.4148i	0.459543	+	0.459543i	−0.438963	+	0.898505i	$0.644654\pi$
$618$	0.0103884	−	0.00155244i	0.000417881	−	6.24483e-5i
$619$	3.33662	−	3.33662i	0.134110	−	0.134110i	−0.636865	−	0.770975i	$-0.719769\pi$
$619$	3.33662	−	3.33662i	0.134110	−	0.134110i	0.770975	+	0.636865i	$0.219769\pi$
$620$	−1.79118	+	1.79118i	−0.0719357	+	0.0719357i
$621$	−17.1379	−	6.06945i	−0.687721	−	0.243559i
$622$			0.711360i			0.0285229i
$623$	20.9660	−	20.9660i	0.839986	−	0.839986i
$624$	−13.1571	+	17.7805i	−0.526707	+	0.711788i
$625$	1.00000			0.0400000
$626$	0.00619189	−	0.00619189i	0.000247478	−	0.000247478i
$627$	17.3356	+	12.8280i	0.692319	+	0.512300i
$628$	20.4398	+	20.4398i	0.815636	+	0.815636i
$629$			12.5497i			0.500391i
$630$	−0.303313	−	0.161282i	−0.0120843	−	0.00642564i
$631$			3.73546i			0.148706i	0.997232	+	0.0743532i	$0.0236892\pi$
$631$			3.73546i			0.148706i	−0.997232	+	0.0743532i	$0.976311\pi$
$632$			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
$636$	−0.611480	−	0.452481i	−0.0242467	−	0.0179420i
$637$		−	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	$-0.823280\pi$
$641$	−8.17031	+	8.17031i	−0.322708	+	0.322708i	0.527097	+	0.849805i	$0.323280\pi$
$642$	−0.0121610	−	0.0813769i	−0.000479956	−	0.00321169i
$643$			18.9978i			0.749199i	0.927187	+	0.374600i	$0.122220\pi$
$643$			18.9978i			0.749199i	−0.927187	+	0.374600i	$0.877780\pi$
$644$	−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	$-0.516379\pi$
$647$	−2.61653			−0.102866			−0.0514331	+	0.998676i	$0.516379\pi$
$648$	−1.18057	−	0.229530i	−0.0463772	−	0.00901679i
$649$	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	$-0.0146689\pi$
$653$	24.3495	+	24.3495i	0.952871	+	0.952871i	−0.0460674	+	0.998938i	$0.514669\pi$
$654$	−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
$657$	40.1078	+	21.3268i	1.56476	+	0.832036i
$658$	0.638380			0.0248866
$659$	−11.1710	+	11.1710i	−0.435159	+	0.435159i	−0.890379	−	0.455220i	$-0.849561\pi$
$659$	−11.1710	+	11.1710i	−0.435159	+	0.435159i	0.455220	+	0.890379i	$0.349561\pi$
$660$	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
$669$	−2.05269	−	1.51894i	−0.0793614	−	0.0587256i
$670$	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	$0.380200\pi$
$673$			48.2530i			1.86002i	−0.367540	+	0.930008i	$0.619800\pi$
$674$		−	0.556807i		−	0.0214474i
$675$	−1.73466	+	4.89806i	−0.0667672	+	0.188526i
$676$			5.54283i			0.213186i
$677$	21.8349	+	21.8349i	0.839182	+	0.839182i	0.988751	−	0.149569i	$-0.0477888\pi$
$677$	21.8349	+	21.8349i	0.839182	+	0.839182i	−0.149569	+	0.988751i	$0.547789\pi$
$678$	0.602499	+	0.445836i	0.0231388	+	0.0171222i
$679$	−17.4899	+	17.4899i	−0.671202	+	0.671202i
$680$	−0.772422			−0.0296210
$681$	−21.7672	+	29.4160i	−0.834120	+	1.12722i
$682$	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	$0.597495\pi$
$684$	11.3589	+	6.03991i	0.434317	+	0.230942i
$685$	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
$693$	−52.6781	−	28.0109i	−2.00108	−	1.06404i
$694$	0.169998	−	0.169998i	0.00645302	−	0.00645302i
$695$	−6.80276			−0.258043
$696$	0.672241	+	1.04960i	0.0254812	+	0.0397852i
$697$	39.1000			1.48102
$698$	−0.451172	+	0.451172i	−0.0170771	+	0.0170771i
$699$	0.0140299	−	0.0189599i	0.000530658	−	0.000717128i
$700$			6.84949i			0.258887i
$701$	−7.28948			−0.275320			−0.137660	−	0.990480i	$-0.543958\pi$
$701$	−7.28948			−0.275320			−0.137660	+	0.990480i	$0.543958\pi$
$702$	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
$708$	40.2929	+	29.8159i	1.51430	+	1.12055i
$709$		−	19.8675i		−	0.746140i	−0.927803	−	0.373070i	$-0.878305\pi$
$709$		−	19.8675i		−	0.746140i	0.927803	−	0.373070i	$-0.121695\pi$
$710$	0.217635	−	0.217635i	0.00816768	−	0.00816768i
$711$	−2.97504	+	5.59496i	−0.111573	+	0.209827i
$712$	1.15629			0.0433338
$713$	3.13536	−	3.13536i	0.117420	−	0.117420i
$714$	0.681932	−	0.921559i	0.0255207	−	0.0344885i
$715$	−13.1241	−	13.1241i	−0.490812	−	0.490812i
$716$		−	0.0551107i		−	0.00205958i
$717$	17.6127	−	23.8017i	0.657759	−	0.888891i
$718$			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
$723$	−11.5239	+	15.5734i	−0.428580	+	0.579180i
$724$		−	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	0.999963	−	0.00863198i	$-0.00274768\pi$
$727$	26.7292	+	26.7292i	0.991331	+	0.991331i	−0.00863198	+	0.999963i	$0.502748\pi$
$728$	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	−0.598929	−	0.800802i	$-0.704407\pi$
$733$	5.46553	−	5.46553i	0.201874	−	0.201874i	0.800802	+	0.598929i	$0.204407\pi$
$734$	−0.528038			−0.0194902
$735$	−6.60233	−	4.88557i	−0.243531	−	0.180207i
$736$	−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	0.724860	−	0.688896i	$-0.241904\pi$
$739$	0.977655	+	0.977655i	0.0359636	+	0.0359636i	−0.688896	+	0.724860i	$0.741904\pi$
$740$	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	$-0.0174699\pi$
$743$	25.7217	+	25.7217i	0.943638	+	0.943638i	−0.0548559	+	0.998494i	$0.517470\pi$
$744$	0.174473	−	0.235782i	0.00639650	−	0.00864419i
$745$	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	−0.0537846	+	0.998553i	$0.517128\pi$
$751$	−28.8386	+	28.8386i	−1.05234	+	1.05234i	−0.998553	+	0.0537846i	$0.982872\pi$
$752$	−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
$756$	−33.5492	−	11.8816i	−1.22017	−	0.432128i
$757$	31.4138	+	31.4138i	1.14176	+	1.14176i	0.988129	+	0.153626i	$0.0490952\pi$
$757$	31.4138	+	31.4138i	1.14176	+	1.14176i	0.153626	+	0.988129i	$0.450905\pi$
$758$	−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	$-0.367816\pi$
$762$	−0.317933	−	0.235263i	−0.0115175	−	0.00852267i
$763$		−	6.35193i		−	0.229955i
$764$	−19.8322	−	19.8322i	−0.717503	−	0.717503i
$765$	−15.3109	−	8.14133i	−0.553565	−	0.294350i
$766$	−0.567271	+	0.567271i	−0.0204963	+	0.0204963i
$767$	−46.2999			−1.67179
$768$	22.1527	+	16.3925i	0.799366	+	0.591513i
$769$	38.7242	−	38.7242i	1.39643	−	1.39643i	0.586431	−	0.809999i	$-0.300533\pi$
$769$	38.7242	−	38.7242i	1.39643	−	1.39643i	0.809999	−	0.586431i	$-0.199467\pi$
$770$		−	0.664580i		−	0.0239498i
$771$	−5.55807	+	7.51114i	−0.200169	+	0.270507i
$772$	−26.1411	+	26.1411i	−0.940840	+	0.940840i
$773$	11.1637	−	11.1637i	0.401531	−	0.401531i	−0.477241	−	0.878772i	$-0.658363\pi$
$773$	11.1637	−	11.1637i	0.401531	−	0.401531i	0.878772	+	0.477241i	$0.158363\pi$
$774$	−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
$780$	−8.90017	−	6.58592i	−0.318677	−	0.235814i
$781$	37.7979	−	37.7979i	1.35252	−	1.35252i
$782$	0.675850			0.0241684
$783$	2.26224	+	27.8905i	0.0808458	+	0.996727i
$784$	−18.9362			−0.676294
$785$	−10.2256	+	10.2256i	−0.364967	+	0.364967i
$786$	−0.900096	−	0.666050i	−0.0321054	−	0.0237572i
$787$			7.58685i			0.270442i	0.990815	+	0.135221i	$0.0431744\pi$
$787$			7.58685i			0.270442i	−0.990815	+	0.135221i	$0.956826\pi$
$788$	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
$795$	0.226367	−	0.305911i	0.00802840	−	0.0108495i
$796$			8.86639i			0.314261i
$797$	−16.9872	+	16.9872i	−0.601718	+	0.601718i	−0.940768	−	0.339050i	$-0.889894\pi$
$797$	−16.9872	+	16.9872i	−0.601718	+	0.601718i	0.339050	+	0.940768i	$0.389894\pi$
$798$	−0.342035	−	0.253098i	−0.0121079	−	0.00895958i
$799$	32.2246			1.14003
$800$	−0.283342	+	0.283342i	−0.0100177	+	0.0100177i
$801$	22.9198	+	12.1873i	0.809832	+	0.430617i
$802$	0.212555	+	0.212555i	0.00750559	+	0.00750559i
$803$			87.8791i			3.10119i
$804$	31.3100	+	23.1687i	1.10422	+	0.817097i
$805$		−	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	$-0.191300\pi$
$809$	7.37587	+	7.37587i	0.259322	+	0.259322i	−0.565456	+	0.824778i	$0.691300\pi$
$810$	0.0573986	−	0.295225i	0.00201678	−	0.0103732i
$811$		−	5.31063i		−	0.186481i	−0.995644	−	0.0932406i	$-0.970277\pi$
$811$		−	5.31063i		−	0.186481i	0.995644	−	0.0932406i	$-0.0297226\pi$
$812$	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	$-0.769963\pi$
$821$	−42.9816			−1.50007			−0.750034	+	0.661400i	$0.769963\pi$
$822$	−0.241676	+	0.326599i	−0.00842940	+	0.0113914i
$823$	−11.5876	−	11.5876i	−0.403919	−	0.403919i	0.475693	−	0.879612i	$-0.342197\pi$
$823$	−11.5876	−	11.5876i	−0.403919	−	0.403919i	−0.879612	+	0.475693i	$0.842197\pi$
$824$	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	$-0.267570\pi$
$827$	−2.24369	−	2.24369i	−0.0780209	−	0.0780209i	−0.745040	+	0.667019i	$0.767570\pi$
$828$	−6.13408	−	20.0651i	−0.213174	−	0.697312i
$829$	15.8863	+	15.8863i	0.551754	+	0.551754i	0.926947	−	0.375193i	$-0.122424\pi$
$829$	15.8863	+	15.8863i	0.551754	+	0.551754i	−0.375193	+	0.926947i	$0.622424\pi$
$830$	0.0417875	+	0.0417875i	0.00145047	+	0.00145047i
$831$	2.11816	+	1.56739i	0.0734783	+	0.0543723i
$832$	−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	−0.995087	−	0.0990061i	$-0.968434\pi$
$839$	−31.6909	−	31.6909i	−1.09409	−	1.09409i	−0.0990061	−	0.995087i	$-0.531566\pi$
$840$	−0.117222	−	0.784409i	−0.00404456	−	0.0270647i
$841$	19.3000	−	21.6451i	0.665518	−	0.746381i
$842$			0.697015i			0.0240207i
$843$	11.6138	−	15.6948i	0.400001	−	0.540559i
$844$	−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
$849$	−7.56872	+	10.2283i	−0.259758	+	0.351035i
$850$		−	0.193159i		−	0.00662532i
$851$	−5.37163	−	5.37163i	−0.184137	−	0.184137i
$852$	18.9678	−	25.6329i	0.649826	−	0.878170i
$853$	−14.9819	+	14.9819i	−0.512969	+	0.512969i	−0.915435	−	0.402466i	$-0.868153\pi$
$853$	−14.9819	+	14.9819i	−0.512969	+	0.512969i	0.402466	+	0.915435i	$0.368153\pi$
$854$	1.26087			0.0431460
$855$	−3.02164	+	5.68260i	−0.103338	+	0.194341i
$856$	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	$-0.163555\pi$
$858$	0.863549	+	0.639007i	0.0294811	+	0.0218153i
$859$	−25.0210	+	25.0210i	−0.853704	+	0.853704i	−0.990587	−	0.136883i	$-0.956292\pi$
$859$	−25.0210	+	25.0210i	−0.853704	+	0.853704i	0.136883	+	0.990587i	$0.456292\pi$
$860$	−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	$-0.303055\pi$
$863$	34.0768			1.15999			0.579994	+	0.814621i	$0.303055\pi$
$864$	−0.896322	−	1.87933i	−0.0304935	−	0.0639360i
$865$	15.1753			0.515976
$866$			0.0975480i			0.00331482i
$867$	16.9084	−	22.8499i	0.574239	−	0.776023i
$868$	6.13778	−	6.13778i	0.208330	−	0.208330i
$869$	−12.2590			−0.415856
$870$	−0.262474	+	0.168107i	−0.00889872	+	0.00569936i
$871$	−35.9778			−1.21906
$872$	0.175157	−	0.175157i	0.00593155	−	0.00593155i
$873$	−19.1198	−	10.1667i	−0.647108	−	0.344090i
$874$		−	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	$-0.602415\pi$
$881$	18.7725	−	18.7725i	0.632462	−	0.632462i	0.948685	+	0.316223i	$0.102415\pi$
$882$	0.419741	+	0.223191i	0.0141334	+	0.00751523i
$883$		−	33.2647i		−	1.11945i	−0.828679	−	0.559724i	$-0.810907\pi$
$883$		−	33.2647i		−	1.11945i	0.828679	−	0.559724i	$-0.189093\pi$
$884$	26.1273	−	26.1273i	0.878758	−	0.878758i
$885$	−14.9163	+	20.1577i	−0.501404	+	0.677595i
$886$	−0.728064			−0.0244598
$887$	−1.00769	+	1.00769i	−0.0338348	+	0.0338348i	−0.723822	−	0.689987i	$-0.757616\pi$
$887$	−1.00769	+	1.00769i	−0.0338348	+	0.0338348i	0.689987	+	0.723822i	$0.257616\pi$
$888$	−0.403952	−	0.298915i	−0.0135557	−	0.0100309i
$889$	−16.5572	−	16.5572i	−0.555311	−	0.555311i
$890$			0.289153i			0.00969244i
$891$	9.96875	−	51.2736i	0.333966	−	1.71773i
$892$		−	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
$897$	15.5792	+	11.5283i	0.520175	+	0.384917i
$898$			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	−0.206454	−	0.978456i	$-0.566192\pi$
$907$	23.2499	−	23.2499i	0.772002	−	0.772002i	0.978456	+	0.206454i	$0.0661925\pi$
$908$	−42.2314			−1.40150
$909$	36.2446	+	19.2725i	1.20216	+	0.639230i
$910$	0.258940	+	0.258940i	0.00858378	+	0.00858378i
$911$	−4.75503	−	4.75503i	−0.157541	−	0.157541i	0.623935	−	0.781476i	$-0.285533\pi$
$911$	−4.75503	−	4.75503i	−0.157541	−	0.157541i	−0.781476	+	0.623935i	$0.785533\pi$
$912$	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
$918$	0.946106	+	0.335066i	0.0312261	+	0.0110588i
$919$	−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	$-0.0634769\pi$
$930$	0.0589620	+	0.0436305i	0.00193344	+	0.00143070i
$931$	−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
$936$	1.13197	+	0.601906i	0.0369995	+	0.0196739i
$937$		−	39.5873i		−	1.29326i	−0.762804	−	0.646630i	$-0.776178\pi$
$937$		−	39.5873i		−	1.29326i	0.762804	−	0.646630i	$-0.223822\pi$
$938$	−0.910928	−	0.910928i	−0.0297428	−	0.0297428i
$939$	0.364843	+	0.269976i	0.0119062	+	0.00881032i
$940$	7.87975	−	7.87975i	0.257009	−	0.257009i
$941$	14.9928			0.488751			0.244375	−	0.969681i	$-0.421417\pi$
$941$	14.9928			0.488751			0.244375	+	0.969681i	$0.421417\pi$
$942$	0.497881	−	0.672834i	0.0162219	−	0.0219221i
$943$	−16.7359	+	16.7359i	−0.544995	+	0.544995i
$944$			57.8146i			1.88171i
$945$	5.94410	−	16.7840i	0.193361	−	0.545983i
$946$	0.541378	−	0.541378i	0.0176017	−	0.0176017i
$947$	9.17141	−	9.17141i	0.298031	−	0.298031i	−0.542211	−	0.840242i	$-0.682413\pi$
$947$	9.17141	−	9.17141i	0.298031	−	0.298031i	0.840242	+	0.542211i	$0.182413\pi$
$948$	−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	$0.906310\pi$
$954$	−0.0103413	+	0.0194481i	−0.000334811	+	0.000629657i
$955$	9.92163	−	9.92163i	0.321056	−	0.321056i
$956$	34.1711			1.10517
$957$	−45.5855	+	29.1962i	−1.47357	+	0.943778i
$958$	0.218152			0.00704816
$959$	−17.0085	+	17.0085i	−0.549234	+	0.549234i
$960$	−8.21462	+	11.1012i	−0.265126	+	0.358289i
$961$		−	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	−0.429999	−	0.902829i	$-0.641486\pi$
$967$	14.7034	−	14.7034i	0.472830	−	0.472830i	0.902829	+	0.429999i	$0.141486\pi$
$968$	2.14339	−	2.14339i	0.0688910	−	0.0688910i
$969$	−17.2655	−	12.7761i	−0.554649	−	0.410427i
$970$		−	0.241213i		−	0.00774488i
$971$	−15.4558	+	15.4558i	−0.495999	+	0.495999i	−0.910190	−	0.414191i	$-0.864064\pi$
$971$	−15.4558	+	15.4558i	−0.495999	+	0.495999i	0.414191	+	0.910190i	$0.364064\pi$
$972$	1.36075	−	31.1298i	0.0436461	−	0.998488i
$973$	23.3107			0.747308
$974$	−0.624979	+	0.624979i	−0.0200256	+	0.0200256i
$975$	3.29480	−	4.45257i	0.105518	−	0.142596i
$976$	−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	$0.941805\pi$
$978$	−0.749966	+	1.01350i	−0.0239813	+	0.0324081i
$979$			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	0.999374	+	0.0353761i	$0.0112629\pi$
$983$	32.4423	+	32.4423i	1.03475	+	1.03475i	0.0353761	+	0.999374i	$0.488737\pi$
$984$	−0.931301	+	1.25855i	−0.0296888	+	0.0401212i
$985$			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	$0.0435976\pi$
$991$			8.59647i			0.273076i	−0.990635	+	0.136538i	$0.956402\pi$
$992$	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
$996$	4.92172	+	3.64196i	0.155951	+	0.115400i
$997$	−17.1664	−	17.1664i	−0.543666	−	0.543666i	0.380935	−	0.924602i	$-0.375602\pi$
$997$	−17.1664	−	17.1664i	−0.543666	−	0.543666i	−0.924602	+	0.380935i	$0.875602\pi$
$998$	−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.c.41.11	✓	36
3.2	odd	2		435.2.q.d.41.8	yes	36
29.17	odd	4		435.2.q.d.191.8	yes	36
87.17	even	4	inner	435.2.q.c.191.11	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.2.q.c.41.11	✓	36	1.1	even	1	trivial
435.2.q.c.191.11	yes	36	87.17	even	4	inner
435.2.q.d.41.8	yes	36	3.2	odd	2
435.2.q.d.191.8	yes	36	29.17	odd	4

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)

\(f(q)\)	\(=\)	\(q+(0.0236294 - 0.0236294i) q^{2} +(1.39231 + 1.03028i) q^{3} +1.99888i q^{4} -1.00000 q^{5} +(0.0572444 - 0.00855463i) q^{6} +3.42666 q^{7} +(0.0944913 + 0.0944913i) q^{8} +(0.877056 + 2.86893i) q^{9} +O(q^{10})\)	\(q+(0.0236294 - 0.0236294i) q^{2} +(1.39231 + 1.03028i) 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} +(-2.05940 + 2.78307i) q^{12} -3.19797i q^{13} +(0.0809700 - 0.0809700i) q^{14} +(-1.39231 - 1.03028i) q^{15} -3.99330 q^{16} +(4.08727 - 4.08727i) q^{17} +(0.0885156 + 0.0470669i) q^{18} +(-1.51698 - 1.51698i) q^{19} -1.99888i q^{20} +(4.77097 + 3.53041i) 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} +(-1.73466 + 4.89806i) 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} +(3.29480 - 4.45257i) 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} +(-5.55991 - 4.11421i) 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} +(2.05940 - 2.78307i) 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} +(-0.199816 + 0.270030i) q^{66} -11.2502i q^{67} +(8.16997 + 8.16997i) q^{68} +(-3.60486 + 4.87159i) q^{69} +(-0.0809700 + 0.0809700i) q^{70} -9.21033 q^{71} +(-0.188215 + 0.353963i) q^{72} +(10.7069 - 10.7069i) q^{73} +0.0725530i q^{74} +(1.39231 + 1.03028i) 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} +(-7.05688 + 9.53662i) q^{84} +(-4.08727 + 4.08727i) q^{85} -0.131919 q^{86} +(9.11113 + 1.99682i) q^{87} -0.775559 q^{88} +(6.11850 - 6.11850i) q^{89} +(-0.0885156 - 0.0470669i) 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} +(-15.3730 - 8.17439i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 4 q^{2} + 6 q^{3} - 36 q^{5} + 8 q^{6} + 8 q^{7} + 4 q^{8}+O(q^{10}) \) 36 * q - 4 * q^2 + 6 * q^3 - 36 * q^5 + 8 * q^6 + 8 * q^7 + 4 * q^8	\( 36 q - 4 q^{2} + 6 q^{3} - 36 q^{5} + 8 q^{6} + 8 q^{7} + 4 q^{8} + 4 q^{10} - 12 q^{11} + 10 q^{12} + 28 q^{14} - 6 q^{15} - 60 q^{16} - 20 q^{17} - 28 q^{18} + 16 q^{19} + 12 q^{21} + 24 q^{24} + 36 q^{25} + 4 q^{26} + 30 q^{27} - 28 q^{29} - 8 q^{30} - 8 q^{31} - 16 q^{32} - 8 q^{33} - 8 q^{35} - 28 q^{36} - 4 q^{37} + 24 q^{38} - 40 q^{39} - 4 q^{40} + 48 q^{41} - 8 q^{42} + 4 q^{43} + 16 q^{44} + 20 q^{46} - 20 q^{47} - 14 q^{48} + 28 q^{49} - 4 q^{50} - 44 q^{52} - 24 q^{54} + 12 q^{55} - 84 q^{56} + 28 q^{57} - 64 q^{58} - 10 q^{60} + 20 q^{61} + 8 q^{62} + 32 q^{63} + 40 q^{66} + 60 q^{68} + 36 q^{69} - 28 q^{70} - 16 q^{71} - 132 q^{72} + 8 q^{73} + 6 q^{75} + 16 q^{76} + 32 q^{77} + 48 q^{78} + 12 q^{79} + 60 q^{80} - 60 q^{81} + 56 q^{82} + 44 q^{84} + 20 q^{85} + 8 q^{86} + 22 q^{87} - 24 q^{88} + 20 q^{89} + 28 q^{90} - 16 q^{92} + 24 q^{93} + 52 q^{94} - 16 q^{95} - 8 q^{96} + 4 q^{97} - 8 q^{98} - 48 q^{99}+O(q^{100}) \) 36 * q - 4 * q^2 + 6 * 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 - 6 * q^15 - 60 * q^16 - 20 * q^17 - 28 * q^18 + 16 * q^19 + 12 * q^21 + 24 * q^24 + 36 * q^25 + 4 * q^26 + 30 * 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 - 40 * q^39 - 4 * q^40 + 48 * q^41 - 8 * q^42 + 4 * q^43 + 16 * q^44 + 20 * q^46 - 20 * q^47 - 14 * 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 + 40 * q^66 + 60 * q^68 + 36 * q^69 - 28 * q^70 - 16 * q^71 - 132 * q^72 + 8 * q^73 + 6 * q^75 + 16 * q^76 + 32 * q^77 + 48 * q^78 + 12 * q^79 + 60 * q^80 - 60 * q^81 + 56 * q^82 + 44 * q^84 + 20 * q^85 + 8 * q^86 + 22 * q^87 - 24 * q^88 + 20 * q^89 + 28 * q^90 - 16 * q^92 + 24 * q^93 + 52 * q^94 - 16 * q^95 - 8 * q^96 + 4 * q^97 - 8 * q^98 - 48 * q^99

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