LMFDB - Embedded newform 847.2.f.u.148.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, degree $4$, not 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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7 x^{10} - 15 x^{9} + 59 x^{8} + 118 x^{7} + 266 x^{6} + 324 x^{5} + 1036 x^{4} + \cdots + 16 $ x^12 - x^11 + 7x^10 - 15x^9 + 59x^8 + 118x^7 + 266x^6 + 324x^5 + 1036x^4 + 376x^3 + 136x^2 + 48x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			148.2
Root			$-0.293939 + 0.213559i$ of defining polynomial
Character	$\chi$	$=$	847.148
Dual form			847.2.f.u.372.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.421292 - 1.29660i) q^{2} +(-0.293939 - 0.213559i) q^{3} +(0.114343 - 0.0830753i) q^{4} +(0.970726 - 2.98759i) q^{5} +(-0.153067 + 0.471092i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-2.36180 - 1.71595i) q^{8} +(-0.886258 - 2.72762i) q^{9} +O(q^{10})$	\(q+(-0.421292 - 1.29660i) q^{2} +(-0.293939 - 0.213559i) q^{3} +(0.114343 - 0.0830753i) q^{4} +(0.970726 - 2.98759i) q^{5} +(-0.153067 + 0.471092i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-2.36180 - 1.71595i) q^{8} +(-0.886258 - 2.72762i) q^{9} -4.28267 q^{10} -0.0513514 q^{12} +(-1.47649 - 4.54416i) q^{13} +(-1.10296 - 0.801344i) q^{14} +(-0.923360 + 0.670861i) q^{15} +(-1.14254 + 3.51639i) q^{16} +(-1.47649 + 4.54416i) q^{17} +(-3.16327 + 2.29825i) q^{18} +(5.67067 + 4.11998i) q^{19} +(-0.137199 - 0.422254i) q^{20} -0.363328 q^{21} +5.14134 q^{23} +(0.327768 + 1.00877i) q^{24} +(-3.93829 - 2.86133i) q^{25} +(-5.26993 + 3.82883i) q^{26} +(-0.658827 + 2.02766i) q^{27} +(0.0436753 - 0.134419i) q^{28} +(-5.67067 + 4.11998i) q^{29} +(1.25884 + 0.914603i) q^{30} +(-1.12379 - 3.45868i) q^{31} -0.797984 q^{32} +6.51399 q^{34} +(-0.970726 - 2.98759i) q^{35} +(-0.327936 - 0.238259i) q^{36} +(7.98337 - 5.80026i) q^{37} +(2.95297 - 9.08831i) q^{38} +(-0.536449 + 1.65102i) q^{39} +(-7.41920 + 5.39037i) q^{40} +(2.60665 + 1.89384i) q^{41} +(0.153067 + 0.471092i) q^{42} +4.28267 q^{43} -9.00933 q^{45} +(-2.16600 - 6.66627i) q^{46} +(0.629422 + 0.457302i) q^{47} +(1.08679 - 0.789603i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-2.05084 + 6.31185i) q^{50} +(1.40444 - 1.02039i) q^{51} +(-0.546333 - 0.396934i) q^{52} +(0.705385 + 2.17095i) q^{53} +2.90663 q^{54} -2.91934 q^{56} +(-0.786970 - 2.42204i) q^{57} +(7.73098 + 5.61689i) q^{58} +(0.293939 - 0.213559i) q^{59} +(-0.0498482 + 0.153417i) q^{60} +(0.995650 - 3.06430i) q^{61} +(-4.01109 + 2.91423i) q^{62} +(-2.32025 - 1.68576i) q^{63} +(2.62127 + 8.06745i) q^{64} -15.0093 q^{65} -6.59465 q^{67} +(0.208681 + 0.642253i) q^{68} +(-1.51124 - 1.09798i) q^{69} +(-3.46475 + 2.51729i) q^{70} +(-4.68470 + 14.4180i) q^{71} +(-2.58729 + 7.96287i) q^{72} +(2.60665 - 1.89384i) q^{73} +(-10.8840 - 7.90766i) q^{74} +(0.546552 + 1.68211i) q^{75} +0.990671 q^{76} +2.36672 q^{78} +(-1.14872 - 3.53539i) q^{79} +(9.39643 + 6.82691i) q^{80} +(-6.33408 + 4.60198i) q^{81} +(1.35740 - 4.17764i) q^{82} +(0.480835 - 1.47986i) q^{83} +(-0.0415442 + 0.0301836i) q^{84} +(12.1428 + 8.82226i) q^{85} +(-1.80425 - 5.55292i) q^{86} +2.54669 q^{87} -5.58532 q^{89} +(3.79555 + 11.6815i) q^{90} +(-3.86549 - 2.80844i) q^{91} +(0.587877 - 0.427118i) q^{92} +(-0.408306 + 1.25664i) q^{93} +(0.327768 - 1.00877i) q^{94} +(17.8135 - 12.9422i) q^{95} +(0.234558 + 0.170417i) q^{96} +(1.90066 + 5.84963i) q^{97} -1.36333 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + q^{3} - 8 q^{4} - q^{5} + 12 q^{6} + 3 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) $ 12 * q + 2 * q^2 + q^3 - 8 * q^4 - q^5 + 12 * q^6 + 3 * q^7 + 6 * q^8 - 4 * q^9	$ 12 q + 2 q^{2} + q^{3} - 8 q^{4} - q^{5} + 12 q^{6} + 3 q^{7} + 6 q^{8} - 4 q^{9} + 16 q^{10} + 8 q^{12} + 8 q^{13} - 2 q^{14} + 5 q^{15} - 10 q^{16} + 8 q^{17} - 18 q^{18} + 14 q^{20} + 4 q^{21} + 28 q^{23} + 20 q^{24} - 2 q^{25} + 12 q^{26} + 19 q^{27} + 8 q^{28} - 8 q^{30} + 13 q^{31} - 136 q^{32} - 48 q^{34} + q^{35} - 18 q^{36} + 17 q^{37} - 16 q^{38} - 20 q^{39} - 36 q^{40} + 16 q^{41} - 12 q^{42} - 16 q^{43} - 24 q^{45} - 4 q^{47} - 36 q^{48} - 3 q^{49} + 22 q^{50} - 20 q^{51} + 10 q^{53} - 32 q^{54} + 24 q^{56} + 16 q^{57} + 16 q^{58} - q^{59} + 30 q^{60} - 16 q^{61} + 4 q^{62} + 4 q^{63} - 34 q^{64} - 96 q^{65} - 12 q^{67} + 7 q^{69} + 4 q^{70} - 5 q^{71} + 2 q^{72} + 16 q^{73} - 32 q^{74} - 20 q^{75} + 96 q^{76} + 112 q^{78} + 28 q^{79} + 56 q^{80} - 15 q^{81} - 28 q^{82} + 8 q^{83} + 2 q^{84} + 24 q^{85} - 12 q^{86} + 64 q^{87} - 84 q^{89} - 20 q^{90} - 8 q^{91} - 2 q^{92} - 17 q^{93} + 20 q^{94} + 24 q^{95} + 20 q^{96} + 11 q^{97} - 8 q^{98}+O(q^{100}) $ 12 * q + 2 * q^2 + q^3 - 8 * q^4 - q^5 + 12 * q^6 + 3 * q^7 + 6 * q^8 - 4 * q^9 + 16 * q^10 + 8 * q^12 + 8 * q^13 - 2 * q^14 + 5 * q^15 - 10 * q^16 + 8 * q^17 - 18 * q^18 + 14 * q^20 + 4 * q^21 + 28 * q^23 + 20 * q^24 - 2 * q^25 + 12 * q^26 + 19 * q^27 + 8 * q^28 - 8 * q^30 + 13 * q^31 - 136 * q^32 - 48 * q^34 + q^35 - 18 * q^36 + 17 * q^37 - 16 * q^38 - 20 * q^39 - 36 * q^40 + 16 * q^41 - 12 * q^42 - 16 * q^43 - 24 * q^45 - 4 * q^47 - 36 * q^48 - 3 * q^49 + 22 * q^50 - 20 * q^51 + 10 * q^53 - 32 * q^54 + 24 * q^56 + 16 * q^57 + 16 * q^58 - q^59 + 30 * q^60 - 16 * q^61 + 4 * q^62 + 4 * q^63 - 34 * q^64 - 96 * q^65 - 12 * q^67 + 7 * q^69 + 4 * q^70 - 5 * q^71 + 2 * q^72 + 16 * q^73 - 32 * q^74 - 20 * q^75 + 96 * q^76 + 112 * q^78 + 28 * q^79 + 56 * q^80 - 15 * q^81 - 28 * q^82 + 8 * q^83 + 2 * q^84 + 24 * q^85 - 12 * q^86 + 64 * q^87 - 84 * q^89 - 20 * q^90 - 8 * q^91 - 2 * q^92 - 17 * q^93 + 20 * q^94 + 24 * q^95 + 20 * q^96 + 11 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−0.421292	−	1.29660i	−0.297898	−	0.916836i	−0.982233	−	0.187668i	$-0.939907\pi$
$2$	−0.421292	−	1.29660i	−0.297898	−	0.916836i	0.684334	−	0.729168i	$-0.260093\pi$
$3$	−0.293939	−	0.213559i	−0.169706	−	0.123298i	0.499691	−	0.866204i	$-0.333447\pi$
$3$	−0.293939	−	0.213559i	−0.169706	−	0.123298i	−0.669396	+	0.742906i	$0.733447\pi$
$4$	0.114343	−	0.0830753i	0.0571717	−	0.0415376i
$5$	0.970726	−	2.98759i	0.434122	−	1.33609i	−0.459862	−	0.887991i	$-0.652101\pi$
$5$	0.970726	−	2.98759i	0.434122	−	1.33609i	0.893984	−	0.448100i	$-0.147899\pi$
$6$	−0.153067	+	0.471092i	−0.0624894	+	0.192323i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$8$	−2.36180	−	1.71595i	−0.835022	−	0.606679i
$9$	−0.886258	−	2.72762i	−0.295419	−	0.909208i
$10$	−4.28267			−1.35430
$11$		0			0
$11$		0			0
$12$	−0.0513514			−0.0148239
$13$	−1.47649	−	4.54416i	−0.409503	−	1.26032i	−0.917076	−	0.398713i	$-0.869457\pi$
$13$	−1.47649	−	4.54416i	−0.409503	−	1.26032i	0.507572	−	0.861609i	$-0.330543\pi$
$14$	−1.10296	−	0.801344i	−0.294777	−	0.214168i
$15$	−0.923360	+	0.670861i	−0.238411	+	0.173215i
$16$	−1.14254	+	3.51639i	−0.285636	+	0.879098i
$17$	−1.47649	+	4.54416i	−0.358100	+	1.10212i	0.596090	+	0.802918i	$0.296720\pi$
$17$	−1.47649	+	4.54416i	−0.358100	+	1.10212i	−0.954190	+	0.299202i	$0.903280\pi$
$18$	−3.16327	+	2.29825i	−0.745590	+	0.541703i
$19$	5.67067	+	4.11998i	1.30094	+	0.945188i	0.999964	−	0.00844358i	$-0.00268771\pi$
$19$	5.67067	+	4.11998i	1.30094	+	0.945188i	0.300976	+	0.953632i	$0.402688\pi$
$20$	−0.137199	−	0.422254i	−0.0306786	−	0.0944189i
$21$	−0.363328			−0.0792847
$22$		0			0
$23$	5.14134			1.07204			0.536021	−	0.844204i	$-0.319927\pi$
$23$	5.14134			1.07204			0.536021	+	0.844204i	$0.319927\pi$
$24$	0.327768	+	1.00877i	0.0669054	+	0.205914i
$25$	−3.93829	−	2.86133i	−0.787658	−	0.572267i
$26$	−5.26993	+	3.82883i	−1.03352	+	0.750895i
$27$	−0.658827	+	2.02766i	−0.126791	+	0.390223i
$28$	0.0436753	−	0.134419i	0.00825385	−	0.0254027i
$29$	−5.67067	+	4.11998i	−1.05302	+	0.765061i	−0.972784	−	0.231715i	$-0.925566\pi$
$29$	−5.67067	+	4.11998i	−1.05302	+	0.765061i	−0.0802326	+	0.996776i	$0.525566\pi$
$30$	1.25884	+	0.914603i	0.229832	+	0.166983i
$31$	−1.12379	−	3.45868i	−0.201839	−	0.621197i	−0.999828	−	0.0185255i	$-0.994103\pi$
$31$	−1.12379	−	3.45868i	−0.201839	−	0.621197i	0.797989	−	0.602672i	$-0.205897\pi$
$32$	−0.797984			−0.141065
$33$		0			0
$34$	6.51399			1.11714
$35$	−0.970726	−	2.98759i	−0.164083	−	0.504995i
$36$	−0.327936	−	0.238259i	−0.0546560	−	0.0397099i
$37$	7.98337	−	5.80026i	1.31246	−	0.953557i	0.312465	−	0.949929i	$-0.398845\pi$
$37$	7.98337	−	5.80026i	1.31246	−	0.953557i	0.999993	−	0.00362773i	$-0.00115474\pi$
$38$	2.95297	−	9.08831i	0.479035	−	1.47432i
$39$	−0.536449	+	1.65102i	−0.0859006	+	0.264375i
$40$	−7.41920	+	5.39037i	−1.17308	+	0.852292i
$41$	2.60665	+	1.89384i	0.407090	+	0.295768i	0.772423	−	0.635109i	$-0.219045\pi$
$41$	2.60665	+	1.89384i	0.407090	+	0.295768i	−0.365333	+	0.930877i	$0.619045\pi$
$42$	0.153067	+	0.471092i	0.0236188	+	0.0726911i
$43$	4.28267			0.653101			0.326551	−	0.945180i	$-0.394114\pi$
$43$	4.28267			0.653101			0.326551	+	0.945180i	$0.394114\pi$
$44$		0			0
$45$	−9.00933			−1.34303
$46$	−2.16600	−	6.66627i	−0.319360	−	0.982888i
$47$	0.629422	+	0.457302i	0.0918106	+	0.0667043i	0.632744	−	0.774361i	$-0.281929\pi$
$47$	0.629422	+	0.457302i	0.0918106	+	0.0667043i	−0.540933	+	0.841066i	$0.681929\pi$
$48$	1.08679	−	0.789603i	0.156865	−	0.113969i
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	−2.05084	+	6.31185i	−0.290033	+	0.892630i
$51$	1.40444	−	1.02039i	0.196661	−	0.142883i
$52$	−0.546333	−	0.396934i	−0.0757628	−	0.0550449i
$53$	0.705385	+	2.17095i	0.0968920	+	0.298203i	0.987742	−	0.156094i	$-0.0498904\pi$
$53$	0.705385	+	2.17095i	0.0968920	+	0.298203i	−0.890850	+	0.454297i	$0.849890\pi$
$54$	2.90663			0.395542
$55$		0			0
$56$	−2.91934			−0.390114
$57$	−0.786970	−	2.42204i	−0.104237	−	0.320807i
$58$	7.73098	+	5.61689i	1.01513	+	0.737533i
$59$	0.293939	−	0.213559i	0.0382676	−	0.0278030i	−0.568487	−	0.822692i	$-0.692471\pi$
$59$	0.293939	−	0.213559i	0.0382676	−	0.0278030i	0.606755	+	0.794889i	$0.292471\pi$
$60$	−0.0498482	+	0.153417i	−0.00643537	+	0.0198060i
$61$	0.995650	−	3.06430i	0.127480	−	0.392343i	−0.866865	−	0.498543i	$-0.833868\pi$
$61$	0.995650	−	3.06430i	0.127480	−	0.392343i	0.994345	+	0.106200i	$0.0338685\pi$
$62$	−4.01109	+	2.91423i	−0.509409	+	0.370107i
$63$	−2.32025	−	1.68576i	−0.292325	−	0.212386i
$64$	2.62127	+	8.06745i	0.327659	+	1.00843i
$65$	−15.0093			−1.86168
$66$		0			0
$67$	−6.59465			−0.805665			−0.402832	−	0.915274i	$-0.631974\pi$
$67$	−6.59465			−0.805665			−0.402832	+	0.915274i	$0.631974\pi$
$68$	0.208681	+	0.642253i	0.0253063	+	0.0778847i
$69$	−1.51124	−	1.09798i	−0.181932	−	0.132181i
$70$	−3.46475	+	2.51729i	−0.414117	+	0.300874i
$71$	−4.68470	+	14.4180i	−0.555971	+	1.71110i	0.137394	+	0.990516i	$0.456127\pi$
$71$	−4.68470	+	14.4180i	−0.555971	+	1.71110i	−0.693365	+	0.720587i	$0.743873\pi$
$72$	−2.58729	+	7.96287i	−0.304915	+	0.938433i
$73$	2.60665	−	1.89384i	0.305085	−	0.221657i	−0.424700	−	0.905334i	$-0.639620\pi$
$73$	2.60665	−	1.89384i	0.305085	−	0.221657i	0.729785	+	0.683677i	$0.239620\pi$
$74$	−10.8840	−	7.90766i	−1.26523	−	0.919247i
$75$	0.546552	+	1.68211i	0.0631104	+	0.194234i
$76$	0.990671			0.113638
$77$		0			0
$78$	2.36672			0.267978
$79$	−1.14872	−	3.53539i	−0.129241	−	0.397762i	0.865409	−	0.501066i	$-0.167059\pi$
$79$	−1.14872	−	3.53539i	−0.129241	−	0.397762i	−0.994650	+	0.103304i	$0.967059\pi$
$80$	9.39643	+	6.82691i	1.05055	+	0.763271i
$81$	−6.33408	+	4.60198i	−0.703787	+	0.511331i
$82$	1.35740	−	4.17764i	0.149900	−	0.461343i
$83$	0.480835	−	1.47986i	0.0527785	−	0.162436i	−0.921193	−	0.389106i	$-0.872784\pi$
$83$	0.480835	−	1.47986i	0.0527785	−	0.162436i	0.973972	+	0.226670i	$0.0727840\pi$
$84$	−0.0415442	+	0.0301836i	−0.00453284	+	0.00329330i
$85$	12.1428	+	8.82226i	1.31707	+	0.956909i
$86$	−1.80425	−	5.55292i	−0.194558	−	0.598787i
$87$	2.54669			0.273034
$88$		0			0
$89$	−5.58532			−0.592043			−0.296021	−	0.955181i	$-0.595660\pi$
$89$	−5.58532			−0.592043			−0.296021	+	0.955181i	$0.595660\pi$
$90$	3.79555	+	11.6815i	0.400087	+	1.23134i
$91$	−3.86549	−	2.80844i	−0.405213	−	0.294405i
$92$	0.587877	−	0.427118i	0.0612905	−	0.0445301i
$93$	−0.408306	+	1.25664i	−0.0423393	+	0.130307i
$94$	0.327768	−	1.00877i	0.0338067	−	0.104046i
$95$	17.8135	−	12.9422i	1.82762	−	1.32785i
$96$	0.234558	+	0.170417i	0.0239395	+	0.0173931i
$97$	1.90066	+	5.84963i	0.192983	+	0.593940i	0.999994	+	0.00340410i	$0.00108356\pi$
$97$	1.90066	+	5.84963i	0.192983	+	0.593940i	−0.807011	+	0.590536i	$0.798916\pi$
$98$	−1.36333			−0.137717
$99$		0			0
$100$	−0.688023			−0.0688023
$101$	−3.33635	−	10.2682i	−0.331980	−	1.02173i	−0.968191	−	0.250213i	$-0.919499\pi$
$101$	−3.33635	−	10.2682i	−0.331980	−	1.02173i	0.636211	−	0.771515i	$-0.280501\pi$
$102$	−1.91471	−	1.39112i	−0.189585	−	0.137742i
$103$	10.7119	−	7.78266i	1.05548	−	0.766848i	0.0822298	−	0.996613i	$-0.473796\pi$
$103$	10.7119	−	7.78266i	1.05548	−	0.766848i	0.973246	+	0.229765i	$0.0737958\pi$
$104$	−4.31037	+	13.2660i	−0.422667	+	1.30083i
$105$	−0.352692	+	1.08548i	−0.0344192	+	0.105932i
$106$	2.51769	−	1.82921i	0.244539	−	0.177668i
$107$	−11.3413	−	8.23996i	−1.09641	−	0.796587i	−0.115938	−	0.993256i	$-0.536987\pi$
$107$	−11.3413	−	8.23996i	−1.09641	−	0.796587i	−0.980470	+	0.196669i	$0.936987\pi$
$108$	0.0931160	+	0.286582i	0.00896009	+	0.0275763i
$109$	−15.5747			−1.49178			−0.745892	−	0.666067i	$-0.767976\pi$
$109$	−15.5747			−1.49178			−0.745892	+	0.666067i	$0.767976\pi$
$110$		0			0
$111$	−3.58532			−0.340304
$112$	1.14254	+	3.51639i	0.107960	+	0.332268i
$113$	−3.34286	−	2.42873i	−0.314470	−	0.228476i	0.419342	−	0.907828i	$-0.362261\pi$
$113$	−3.34286	−	2.42873i	−0.314470	−	0.228476i	−0.733812	+	0.679352i	$0.762261\pi$
$114$	−2.80888	+	2.04077i	−0.263076	+	0.191136i
$115$	4.99083	−	15.3602i	0.465397	−	1.43235i
$116$	−0.306134	+	0.942184i	−0.0284239	+	0.0874796i
$117$	−11.0862	+	8.05459i	−1.02492	+	0.744647i
$118$	−0.400735	−	0.291151i	−0.0368906	−	0.0268026i
$119$	1.47649	+	4.54416i	0.135349	+	0.416562i
$120$	3.33195			0.304164
$121$		0			0
$122$	−4.39263			−0.397690
$123$	−0.361748	−	1.11335i	−0.0326177	−	0.100387i
$124$	−0.415829	−	0.302118i	−0.0373426	−	0.0271310i
$125$	0.335483	−	0.243743i	0.0300065	−	0.0218010i
$126$	−1.20826	+	3.71865i	−0.107640	+	0.331283i
$127$	6.80414	−	20.9410i	0.603770	−	1.85821i	0.0987337	−	0.995114i	$-0.468521\pi$
$127$	6.80414	−	20.9410i	0.603770	−	1.85821i	0.505036	−	0.863098i	$-0.331479\pi$
$128$	8.06479	−	5.85941i	0.712833	−	0.517904i
$129$	−1.25884	−	0.914603i	−0.110835	−	0.0805263i
$130$	6.32330	+	19.4611i	0.554590	+	1.70685i
$131$	15.0093			1.31137			0.655686	−	0.755034i	$-0.272380\pi$
$131$	15.0093			1.31137			0.655686	+	0.755034i	$0.272380\pi$
$132$		0			0
$133$	7.00933			0.607786
$134$	2.77827	+	8.55064i	0.240006	+	0.738662i
$135$	5.41827	+	3.93660i	0.466331	+	0.338809i
$136$	11.2847	−	8.19881i	0.967655	−	0.703042i
$137$	−3.30566	+	10.1738i	−0.282422	+	0.869205i	0.704738	+	0.709468i	$0.251065\pi$
$137$	−3.30566	+	10.1738i	−0.282422	+	0.869205i	−0.987160	+	0.159737i	$0.948935\pi$
$138$	−0.786970	+	2.42204i	−0.0669913	+	0.206178i
$139$	−3.31916	+	2.41151i	−0.281527	+	0.204541i	−0.719583	−	0.694406i	$-0.755667\pi$
$139$	−3.31916	+	2.41151i	−0.281527	+	0.204541i	0.438056	+	0.898948i	$0.355667\pi$
$140$	−0.359191	−	0.260967i	−0.0303572	−	0.0220558i
$141$	−0.0873505	−	0.268837i	−0.00735624	−	0.0226402i
$142$	20.6680			1.73442
$143$		0			0
$144$	10.6040			0.883665
$145$	6.80414	+	20.9410i	0.565053	+	1.73905i
$146$	−3.55371	−	2.58192i	−0.294108	−	0.213682i
$147$	−0.293939	+	0.213559i	−0.0242437	+	0.0176140i
$148$	0.430987	−	1.32644i	0.0354269	−	0.109033i
$149$	4.33200	−	13.3325i	0.354892	−	1.09224i	−0.601181	−	0.799113i	$-0.705303\pi$
$149$	4.33200	−	13.3325i	0.354892	−	1.09224i	0.956072	−	0.293131i	$-0.0946972\pi$
$150$	1.95077	−	1.41732i	0.159280	−	0.115724i
$151$	5.52507	+	4.01420i	0.449624	+	0.326671i	0.789447	−	0.613819i	$-0.210367\pi$
$151$	5.52507	+	4.01420i	0.449624	+	0.326671i	−0.339824	+	0.940489i	$0.610367\pi$
$152$	−6.32330	−	19.4611i	−0.512888	−	1.57851i
$153$	13.7033			1.10785
$154$		0			0
$155$	−11.4240			−0.917598
$156$	0.0758196	+	0.233349i	0.00607043	+	0.0186829i
$157$	18.9655	+	13.7793i	1.51361	+	1.09970i	0.964542	+	0.263928i	$0.0850182\pi$
$157$	18.9655	+	13.7793i	1.51361	+	1.09970i	0.549071	+	0.835776i	$0.314982\pi$
$158$	−4.10005	+	2.97886i	−0.326182	+	0.236985i
$159$	0.256286	−	0.788768i	0.0203248	−	0.0625533i
$160$	−0.774624	+	2.38405i	−0.0612394	+	0.188475i
$161$	4.15943	−	3.02200i	0.327809	−	0.238167i
$162$	8.63544	+	6.27401i	0.678464	+	0.492933i
$163$	−0.306134	−	0.942184i	−0.0239783	−	0.0737976i	0.938351	−	0.345683i	$-0.112353\pi$
$163$	−0.306134	−	0.942184i	−0.0239783	−	0.0737976i	−0.962330	+	0.271886i	$0.912353\pi$
$164$	0.455384			0.0355595
$165$		0			0
$166$	−2.12136			−0.164649
$167$	0.174701	+	0.537675i	0.0135188	+	0.0416065i	0.957588	−	0.288140i	$-0.0930368\pi$
$167$	0.174701	+	0.537675i	0.0135188	+	0.0416065i	−0.944070	+	0.329746i	$0.893037\pi$
$168$	0.858108	+	0.623452i	0.0662045	+	0.0481004i
$169$	−7.95212	+	5.77755i	−0.611701	+	0.444427i
$170$	6.32330	−	19.4611i	0.484975	−	1.49260i
$171$	6.21208	−	19.1188i	0.475049	−	1.46205i
$172$	0.489695	−	0.355784i	0.0373389	−	0.0271283i
$173$	13.9480	+	10.1338i	1.06045	+	0.770459i	0.974171	−	0.225813i	$-0.0725038\pi$
$173$	13.9480	+	10.1338i	1.06045	+	0.770459i	0.0862745	+	0.996271i	$0.472504\pi$
$174$	−1.07290	−	3.30204i	−0.0813362	−	0.250327i
$175$	−4.86799			−0.367986
$176$		0			0
$177$	−0.132007			−0.00992228
$178$	2.35305	+	7.24194i	0.176368	+	0.542806i
$179$	−9.15913	−	6.65450i	−0.684585	−	0.497380i	0.190290	−	0.981728i	$-0.439057\pi$
$179$	−9.15913	−	6.65450i	−0.684585	−	0.497380i	−0.874876	+	0.484347i	$0.839057\pi$
$180$	−1.03016	+	0.748453i	−0.0767833	+	0.0557864i
$181$	4.59735	−	14.1492i	0.341718	−	1.05170i	−0.621599	−	0.783335i	$-0.713517\pi$
$181$	4.59735	−	14.1492i	0.341718	−	1.05170i	0.963317	−	0.268365i	$-0.0864832\pi$
$182$	−2.01293	+	6.19518i	−0.149209	+	0.459217i
$183$	−0.947068	+	0.688085i	−0.0700093	+	0.0508647i
$184$	−12.1428	−	8.82226i	−0.895179	−	0.650386i
$185$	−9.57912	−	29.4815i	−0.704271	−	2.16752i
$186$	1.80137			0.132083
$187$		0			0
$188$	0.109961			0.00801970
$189$	0.658827	+	2.02766i	0.0479226	+	0.147491i
$190$	−24.2856	−	17.6445i	−1.76186	−	1.28007i
$191$	−3.11418	+	2.26258i	−0.225334	+	0.163715i	−0.694724	−	0.719276i	$-0.744474\pi$
$191$	−3.11418	+	2.26258i	−0.225334	+	0.163715i	0.469390	+	0.882991i	$0.344474\pi$
$192$	0.952382	−	2.93113i	0.0687323	−	0.211536i
$193$	−0.786970	+	2.42204i	−0.0566473	+	0.174342i	−0.975377	−	0.220545i	$-0.929216\pi$
$193$	−0.786970	+	2.42204i	−0.0566473	+	0.174342i	0.918729	+	0.394887i	$0.129216\pi$
$194$	6.78391	−	4.92880i	0.487056	−	0.353867i
$195$	4.41182	+	3.20538i	0.315937	+	0.229542i
$196$	−0.0436753	−	0.134419i	−0.00311966	−	0.00960133i
$197$	−10.5467			−0.751420			−0.375710	−	0.926737i	$-0.622601\pi$
$197$	−10.5467			−0.751420			−0.375710	+	0.926737i	$0.622601\pi$
$198$		0			0
$199$	11.6846			0.828302			0.414151	−	0.910208i	$-0.364079\pi$
$199$	11.6846			0.828302			0.414151	+	0.910208i	$0.364079\pi$
$200$	4.39155	+	13.5158i	0.310529	+	0.955711i
$201$	1.93842	+	1.40835i	0.136726	+	0.0993371i
$202$	−11.9082	+	8.65185i	−0.837861	+	0.608742i
$203$	−2.16600	+	6.66627i	−0.152024	+	0.467880i
$204$	0.0758196	−	0.233349i	0.00530843	−	0.0163377i
$205$	8.18835	−	5.94919i	0.571899	−	0.415509i
$206$	−14.6039	−	10.6103i	−1.01750	−	0.739256i
$207$	−4.55655	−	14.0236i	−0.316702	−	0.974709i
$208$	17.6660			1.22492
$209$		0			0
$210$	1.55602			0.107375
$211$	3.43381	+	10.5682i	0.236393	+	0.727543i	0.996934	+	0.0782524i	$0.0249340\pi$
$211$	3.43381	+	10.5682i	0.236393	+	0.727543i	−0.760541	+	0.649290i	$0.775066\pi$
$212$	0.261008	+	0.189634i	0.0179261	+	0.0130241i
$213$	4.45611	−	3.23755i	0.305328	−	0.221833i
$214$	−5.90594	+	18.1766i	−0.403722	+	1.24253i
$215$	4.15730	−	12.7949i	0.283526	−	0.872602i
$216$	5.03537	−	3.65841i	0.342614	−	0.248923i
$217$	−2.94213	−	2.13758i	−0.199725	−	0.145109i
$218$	6.56148	+	20.1942i	0.444399	+	1.36772i
$219$	−1.17064			−0.0791046
$220$		0			0
$221$	22.8294			1.53567
$222$	1.51047	+	4.64873i	0.101376	+	0.312003i
$223$	−22.6854	−	16.4819i	−1.51913	−	1.10371i	−0.961918	−	0.273338i	$-0.911872\pi$
$223$	−22.6854	−	16.4819i	−1.51913	−	1.10371i	−0.557209	−	0.830372i	$-0.688128\pi$
$224$	−0.645582	+	0.469043i	−0.0431348	+	0.0313393i
$225$	−4.31430	+	13.2780i	−0.287620	+	0.885203i
$226$	−1.74078	+	5.35757i	−0.115795	+	0.356380i
$227$	18.6149	−	13.5245i	1.23552	−	0.897656i	0.238226	−	0.971210i	$-0.423434\pi$
$227$	18.6149	−	13.5245i	1.23552	−	0.897656i	0.997291	+	0.0735543i	$0.0234342\pi$
$228$	−0.291197	−	0.211567i	−0.0192850	−	0.0140114i
$229$	4.14825	+	12.7670i	0.274124	+	0.843666i	0.989450	+	0.144876i	$0.0462782\pi$
$229$	4.14825	+	12.7670i	0.274124	+	0.843666i	−0.715326	+	0.698791i	$0.753722\pi$
$230$	−22.0187			−1.45187
$231$		0			0
$232$	20.4626			1.34344
$233$	−1.09310	−	3.36423i	−0.0716116	−	0.220398i	0.908845	−	0.417135i	$-0.136966\pi$
$233$	−1.09310	−	3.36423i	−0.0716116	−	0.220398i	−0.980456	+	0.196737i	$0.936966\pi$
$234$	15.1141	+	10.9811i	0.988041	+	0.717854i
$235$	1.97722	−	1.43654i	0.128980	−	0.0937094i
$236$	0.0158685	−	0.0488381i	0.00103295	−	0.00317909i
$237$	−0.417361	+	1.28451i	−0.0271105	+	0.0834377i
$238$	5.26993	−	3.82883i	0.341599	−	0.248186i
$239$	−17.8135	−	12.9422i	−1.15226	−	0.837164i	−0.163478	−	0.986547i	$-0.552271\pi$
$239$	−17.8135	−	12.9422i	−1.15226	−	0.837164i	−0.988779	+	0.149383i	$0.952271\pi$
$240$	−1.30403	−	4.01338i	−0.0841746	−	0.259063i
$241$	−0.315366			−0.0203145			−0.0101573	−	0.999948i	$-0.503233\pi$
$241$	−0.315366			−0.0203145			−0.0101573	+	0.999948i	$0.503233\pi$
$242$		0			0
$243$	9.24065			0.592788
$244$	−0.140721	−	0.433096i	−0.00900876	−	0.0277261i
$245$	−2.54139	−	1.84643i	−0.162364	−	0.117964i
$246$	−1.29116	+	0.938086i	−0.0823217	+	0.0598102i
$247$	10.3492	−	31.8515i	0.658502	−	2.02666i
$248$	−3.28074	+	10.0971i	−0.208327	+	0.641165i
$249$	−0.457373	+	0.332301i	−0.0289849	+	0.0210587i
$250$	−0.457373	−	0.332301i	−0.0289268	−	0.0210166i
$251$	5.76193	+	17.7334i	0.363690	+	1.11932i	0.950797	+	0.309813i	$0.100267\pi$
$251$	5.76193	+	17.7334i	0.363690	+	1.11932i	−0.587108	+	0.809509i	$0.699733\pi$
$252$	−0.405351			−0.0255347
$253$		0			0
$254$	−30.0187			−1.88354
$255$	−1.68517	−	5.18641i	−0.105529	−	0.324786i
$256$	2.73021	+	1.98362i	0.170638	+	0.123976i
$257$	6.91442	−	5.02362i	0.431309	−	0.313365i	−0.350863	−	0.936427i	$-0.614112\pi$
$257$	6.91442	−	5.02362i	0.431309	−	0.313365i	0.782172	+	0.623062i	$0.214112\pi$
$258$	−0.655536	+	2.01753i	−0.0408119	+	0.125606i
$259$	3.04938	−	9.38502i	0.189479	−	0.583157i
$260$	−1.71622	+	1.24690i	−0.106435	+	0.0773297i
$261$	16.2634	+	11.8161i	1.00668	+	0.731397i
$262$	−6.32330	−	19.4611i	−0.390655	−	1.20231i
$263$	16.0000			0.986602			0.493301	−	0.869859i	$-0.335790\pi$
$263$	16.0000			0.986602			0.493301	+	0.869859i	$0.335790\pi$
$264$		0			0
$265$	7.17064			0.440489
$266$	−2.95297	−	9.08831i	−0.181058	−	0.557240i
$267$	1.64174	+	1.19280i	0.100473	+	0.0729979i
$268$	−0.754054	+	0.547852i	−0.0460612	+	0.0334654i
$269$	2.33494	−	7.18620i	0.142364	−	0.438150i	−0.854299	−	0.519782i	$-0.826013\pi$
$269$	2.33494	−	7.18620i	0.142364	−	0.438150i	0.996663	+	0.0816318i	$0.0260132\pi$
$270$	2.82154	−	8.68380i	0.171713	−	0.528479i
$271$	−11.3413	+	8.23996i	−0.688937	+	0.500542i	−0.876310	−	0.481747i	$-0.840002\pi$
$271$	−11.3413	+	8.23996i	−0.688937	+	0.500542i	0.187374	+	0.982289i	$0.440002\pi$
$272$	−14.2921	−	10.3838i	−0.866584	−	0.629610i
$273$	0.536449	+	1.65102i	0.0324674	+	0.0999243i
$274$	14.5840			0.881052
$275$		0			0
$276$	−0.264015			−0.0158918
$277$	−1.85987	−	5.72408i	−0.111749	−	0.343927i	0.879506	−	0.475887i	$-0.157873\pi$
$277$	−1.85987	−	5.72408i	−0.111749	−	0.343927i	−0.991255	+	0.131960i	$0.957873\pi$
$278$	4.52510	+	3.28768i	0.271397	+	0.197182i
$279$	−8.43800	+	6.13057i	−0.505170	+	0.367028i
$280$	−2.83388	+	8.72180i	−0.169357	+	0.521227i
$281$	−6.38678	+	19.6565i	−0.381003	+	1.17261i	0.558335	+	0.829615i	$0.311440\pi$
$281$	−6.38678	+	19.6565i	−0.381003	+	1.17261i	−0.939338	+	0.342992i	$0.888560\pi$
$282$	−0.311775	+	0.226518i	−0.0185659	+	0.0134889i
$283$	−8.02218	−	5.82845i	−0.476869	−	0.346466i	0.323243	−	0.946316i	$-0.395227\pi$
$283$	−8.02218	−	5.82845i	−0.476869	−	0.346466i	−0.800112	+	0.599850i	$0.795227\pi$
$284$	0.662117	+	2.03779i	0.0392894	+	0.120920i
$285$	−8.00000			−0.473879
$286$		0			0
$287$	3.22199			0.190188
$288$	0.707220	+	2.17660i	0.0416733	+	0.128257i
$289$	−4.71605	−	3.42641i	−0.277415	−	0.201554i
$290$	24.2856	−	17.6445i	1.42610	−	1.03612i
$291$	0.690563	−	2.12534i	0.0404815	−	0.124589i
$292$	0.140721	−	0.433096i	0.00823509	−	0.0253450i
$293$	21.6790	−	15.7507i	1.26650	−	0.920165i	0.267441	−	0.963574i	$-0.413822\pi$
$293$	21.6790	−	15.7507i	1.26650	−	0.920165i	0.999057	+	0.0434095i	$0.0138220\pi$
$294$	0.400735	+	0.291151i	0.0233713	+	0.0169803i
$295$	−0.352692	−	1.08548i	−0.0205345	−	0.0631988i
$296$	−28.8081			−1.67443
$297$		0			0
$298$	−19.1120			−1.10713
$299$	−7.59111	−	23.3630i	−0.439005	−	1.35112i
$300$	0.202237	+	0.146934i	0.0116761	+	0.00848321i
$301$	3.46475	−	2.51729i	0.199705	−	0.145094i
$302$	2.87715	−	8.85496i	0.165561	−	0.509546i
$303$	−1.21219	+	3.73074i	−0.0696386	+	0.214325i
$304$	−20.9664	+	15.2330i	−1.20251	+	0.873673i
$305$	−8.18835	−	5.94919i	−0.468864	−	0.340649i
$306$	−5.77308	−	17.7677i	−0.330025	−	1.01571i
$307$	11.8973			0.679015			0.339507	−	0.940603i	$-0.389740\pi$
$307$	11.8973			0.679015			0.339507	+	0.940603i	$0.389740\pi$
$308$		0			0
$309$	−4.81070			−0.273671
$310$	4.81284	+	14.8124i	0.273351	+	0.841287i
$311$	17.1840	+	12.4849i	0.974418	+	0.707956i	0.956454	−	0.291883i	$-0.0942817\pi$
$311$	17.1840	+	12.4849i	0.974418	+	0.707956i	0.0179637	+	0.999839i	$0.494282\pi$
$312$	4.10005	−	2.97886i	0.232120	−	0.168645i
$313$	−3.92370	+	12.0759i	−0.221780	+	0.682570i	0.776822	+	0.629720i	$0.216830\pi$
$313$	−3.92370	+	12.0759i	−0.221780	+	0.682570i	−0.998602	+	0.0528499i	$0.983170\pi$
$314$	9.87620	−	30.3958i	0.557346	−	1.71533i
$315$	−7.28870	+	5.29555i	−0.410672	+	0.298370i
$316$	−0.425052	−	0.308818i	−0.0239110	−	0.0173724i
$317$	−3.66741	−	11.2871i	−0.205982	−	0.633948i	−0.999672	−	0.0256251i	$-0.991842\pi$
$317$	−3.66741	−	11.2871i	−0.205982	−	0.633948i	0.793689	−	0.608323i	$-0.208158\pi$
$318$	−1.13069			−0.0634059
$319$		0			0
$320$	26.6468			1.48960
$321$	1.57394	+	4.84409i	0.0878487	+	0.270371i
$322$	−5.67067	−	4.11998i	−0.316014	−	0.229598i
$323$	−27.0945	+	19.6853i	−1.50758	+	1.09532i
$324$	−0.341949	+	1.05241i	−0.0189972	+	0.0584673i
$325$	−7.18752	+	22.1209i	−0.398692	+	1.22705i
$326$	−1.09267	+	0.793869i	−0.0605172	+	0.0439683i
$327$	4.57800	+	3.32611i	0.253164	+	0.183934i
$328$	−2.90665	−	8.94574i	−0.160493	−	0.493946i
$329$	0.778008			0.0428930
$330$		0			0
$331$	−11.8867			−0.653349			−0.326675	−	0.945137i	$-0.605928\pi$
$331$	−11.8867			−0.653349			−0.326675	+	0.945137i	$0.605928\pi$
$332$	−0.0679594	−	0.209158i	−0.00372976	−	0.0114790i
$333$	−22.8963	−	16.6351i	−1.25471	−	0.911598i
$334$	0.623550	−	0.453036i	0.0341191	−	0.0247890i
$335$	−6.40160	+	19.7021i	−0.349757	+	1.07644i
$336$	0.415119	−	1.27760i	0.0226466	−	0.0696990i
$337$	−0.801470	+	0.582302i	−0.0436588	+	0.0317200i	−0.609401	−	0.792862i	$-0.708590\pi$
$337$	−0.801470	+	0.582302i	−0.0436588	+	0.0317200i	0.565742	+	0.824582i	$0.308590\pi$
$338$	10.8413	+	7.87670i	0.589692	+	0.428436i
$339$	0.463919	+	1.42780i	0.0251966	+	0.0775473i
$340$	2.12136			0.115047
$341$		0			0
$342$	−27.4066			−1.48198
$343$	−0.309017	−	0.951057i	−0.0166853	−	0.0513522i
$344$	−10.1148	−	7.34884i	−0.545354	−	0.396223i
$345$	−4.74731	+	3.44912i	−0.255586	+	0.185694i
$346$	7.26334	−	22.3543i	0.390480	−	1.20177i
$347$	−4.69375	+	14.4459i	−0.251974	+	0.775496i	0.742437	+	0.669916i	$0.233670\pi$
$347$	−4.69375	+	14.4459i	−0.251974	+	0.775496i	−0.994411	+	0.105580i	$0.966330\pi$
$348$	0.291197	−	0.211567i	0.0156098	−	0.0113412i
$349$	24.0305	+	17.4592i	1.28632	+	0.934567i	0.999724	−	0.0234839i	$-0.00747586\pi$
$349$	24.0305	+	17.4592i	1.28632	+	0.934567i	0.286597	+	0.958051i	$0.407476\pi$
$350$	2.05084	+	6.31185i	0.109622	+	0.337383i
$351$	10.1867			0.543728
$352$		0			0
$353$	−6.71601			−0.357457			−0.178729	−	0.983898i	$-0.557198\pi$
$353$	−6.71601			−0.357457			−0.178729	+	0.983898i	$0.557198\pi$
$354$	0.0556136	+	0.171161i	0.00295583	+	0.00909711i
$355$	38.5275	+	27.9919i	2.04483	+	1.48565i
$356$	−0.638644	+	0.464002i	−0.0338481	+	0.0245921i
$357$	0.536449	−	1.65102i	0.0283919	−	0.0873812i
$358$	−4.76957	+	14.6792i	−0.252080	+	0.775821i
$359$	−14.3487	+	10.4250i	−0.757296	+	0.550208i	−0.898080	−	0.439833i	$-0.855038\pi$
$359$	−14.3487	+	10.4250i	−0.757296	+	0.550208i	0.140784	+	0.990040i	$0.455038\pi$
$360$	21.2782	+	15.4595i	1.12146	+	0.814789i
$361$	9.31089	+	28.6560i	0.490047	+	1.50821i
$362$	−20.2827			−1.06603
$363$		0			0
$364$	−0.675305			−0.0353956
$365$	−3.12767	−	9.62599i	−0.163710	−	0.503847i
$366$	1.29116	+	0.938086i	0.0674903	+	0.0490346i
$367$	6.55248	−	4.76066i	0.342037	−	0.248504i	−0.403484	−	0.914987i	$-0.632201\pi$
$367$	6.55248	−	4.76066i	0.342037	−	0.248504i	0.745521	+	0.666482i	$0.232201\pi$
$368$	−5.87421	+	18.0789i	−0.306214	+	0.942430i
$369$	2.85552	−	8.78838i	0.148652	−	0.457505i
$370$	−34.1902	+	24.8406i	−1.77746	+	1.29140i
$371$	1.84672	+	1.34172i	0.0958770	+	0.0696587i
$372$	0.0577084	+	0.177608i	0.00299204	+	0.00920855i
$373$	0.565344			0.0292724			0.0146362	−	0.999893i	$-0.495341\pi$
$373$	0.565344			0.0292724			0.0146362	+	0.999893i	$0.495341\pi$
$374$		0			0
$375$	−0.150665			−0.00778030
$376$	−0.701862	−	2.16011i	−0.0361958	−	0.111399i
$377$	27.0945	+	19.6853i	1.39544	+	1.01384i
$378$	2.35151	−	1.70847i	0.120949	−	0.0878743i
$379$	−6.96402	+	21.4330i	−0.357718	+	1.10094i	0.596699	+	0.802465i	$0.296479\pi$
$379$	−6.96402	+	21.4330i	−0.357718	+	1.10094i	−0.954417	+	0.298477i	$0.903521\pi$
$380$	0.961671	−	2.95972i	0.0493327	−	0.151830i
$381$	−6.47214	+	4.70228i	−0.331578	+	0.240905i
$382$	4.24565	+	3.08464i	0.217226	+	0.157824i
$383$	6.61028	+	20.3443i	0.337770	+	1.03955i	0.965342	+	0.260989i	$0.0840487\pi$
$383$	6.61028	+	20.3443i	0.337770	+	1.03955i	−0.627572	+	0.778558i	$0.715951\pi$
$384$	−3.62188			−0.184828
$385$		0			0
$386$	3.47197			0.176719
$387$	−3.79555	−	11.6815i	−0.192939	−	0.593805i
$388$	0.703287	+	0.510968i	0.0357040	+	0.0259405i
$389$	−8.63925	+	6.27678i	−0.438027	+	0.318245i	−0.784851	−	0.619685i	$-0.787260\pi$
$389$	−8.63925	+	6.27678i	−0.438027	+	0.318245i	0.346823	+	0.937930i	$0.387260\pi$
$390$	2.29743	−	7.07078i	0.116335	−	0.358043i
$391$	−7.59111	+	23.3630i	−0.383899	+	1.18152i
$392$	−2.36180	+	1.71595i	−0.119289	+	0.0866684i
$393$	−4.41182	−	3.20538i	−0.222547	−	0.161690i
$394$	4.44323	+	13.6749i	0.223847	+	0.688929i
$395$	−11.6774			−0.587553
$396$		0			0
$397$	−23.9160			−1.20031			−0.600154	−	0.799885i	$-0.704894\pi$
$397$	−23.9160			−1.20031			−0.600154	+	0.799885i	$0.704894\pi$
$398$	−4.92264	−	15.1503i	−0.246750	−	0.759417i
$399$	−2.06031	−	1.49691i	−0.103145	−	0.0749390i
$400$	14.5612	−	10.5794i	0.728062	−	0.528968i
$401$	3.60274	−	11.0881i	0.179912	−	0.553713i	−0.819911	−	0.572491i	$-0.805977\pi$
$401$	3.60274	−	11.0881i	0.179912	−	0.553713i	0.999824	+	0.0187772i	$0.00597733\pi$
$402$	1.00942	−	3.10669i	0.0503455	−	0.154947i
$403$	−14.0575	+	10.2134i	−0.700255	+	0.508765i
$404$	−1.23453	−	0.896936i	−0.0614200	−	0.0446242i
$405$	7.60016	+	23.3909i	0.377655	+	1.16230i
$406$	9.55602			0.474257
$407$		0			0
$408$	−5.06794			−0.250900
$409$	10.1405	+	31.2092i	0.501415	+	1.54320i	0.806715	+	0.590941i	$0.201243\pi$
$409$	10.1405	+	31.2092i	0.501415	+	1.54320i	−0.305300	+	0.952256i	$0.598757\pi$
$410$	−11.1634	−	8.11069i	−0.551322	−	0.400559i
$411$	3.14437	−	2.28452i	0.155100	−	0.112687i
$412$	0.578289	−	1.77979i	0.0284902	−	0.0876840i
$413$	0.112275	−	0.345546i	0.00552467	−	0.0170032i
$414$	−16.2634	+	11.8161i	−0.799304	+	0.580728i
$415$	−3.95445	−	2.87308i	−0.194116	−	0.141034i
$416$	1.17821	+	3.62616i	0.0577666	+	0.177787i
$417$	1.49063			0.0729964
$418$		0			0
$419$	10.7967			0.527452			0.263726	−	0.964598i	$-0.415049\pi$
$419$	10.7967			0.527452			0.263726	+	0.964598i	$0.415049\pi$
$420$	0.0498482	+	0.153417i	0.00243234	+	0.00748598i
$421$	0.931974	+	0.677119i	0.0454216	+	0.0330008i	0.610264	−	0.792198i	$-0.291063\pi$
$421$	0.931974	+	0.677119i	0.0454216	+	0.0330008i	−0.564843	+	0.825199i	$0.691063\pi$
$422$	12.2561	−	8.90456i	0.596617	−	0.433467i
$423$	0.689516	−	2.12211i	0.0335254	−	0.103181i
$424$	2.05926	−	6.33775i	0.100007	−	0.307788i
$425$	18.8172	−	13.6715i	0.912767	−	0.663164i
$426$	−6.07514	−	4.41385i	−0.294341	−	0.213852i
$427$	−0.995650	−	3.06430i	−0.0481829	−	0.148292i
$428$	−1.98134			−0.0957718
$429$		0			0
$430$	−18.3413			−0.884495
$431$	−9.87620	−	30.3958i	−0.475720	−	1.46411i	−0.844985	−	0.534791i	$-0.820391\pi$
$431$	−9.87620	−	30.3958i	−0.475720	−	1.46411i	0.369265	−	0.929324i	$-0.379609\pi$
$432$	−6.37730	−	4.63338i	−0.306828	−	0.222924i
$433$	3.58665	−	2.60585i	0.172363	−	0.125229i	−0.498259	−	0.867028i	$-0.666027\pi$
$433$	3.58665	−	2.60585i	0.172363	−	0.125229i	0.670622	+	0.741799i	$0.266027\pi$
$434$	−1.53210	+	4.71532i	−0.0735431	+	0.226342i
$435$	2.47214	−	7.60845i	0.118530	−	0.364797i
$436$	−1.78086	+	1.29387i	−0.0852877	+	0.0619652i
$437$	29.1548	+	21.1822i	1.39466	+	1.01328i
$438$	0.493181	+	1.51786i	0.0235651	+	0.0725259i
$439$	−27.4720			−1.31117			−0.655583	−	0.755123i	$-0.727577\pi$
$439$	−27.4720			−1.31117			−0.655583	+	0.755123i	$0.727577\pi$
$440$		0			0
$441$	−2.86799			−0.136571
$442$	−9.61782	−	29.6006i	−0.457473	−	1.40796i
$443$	6.30283	+	4.57927i	0.299456	+	0.217568i	0.727359	−	0.686257i	$-0.240747\pi$
$443$	6.30283	+	4.57927i	0.299456	+	0.217568i	−0.427903	+	0.903825i	$0.640747\pi$
$444$	−0.409957	+	0.297852i	−0.0194557	+	0.0141354i
$445$	−5.42182	+	16.6866i	−0.257019	+	0.791022i
$446$	−11.8133	+	36.3576i	−0.559377	+	1.72158i
$447$	−4.12063	+	2.99381i	−0.194899	+	0.141602i
$448$	6.86258	+	4.98596i	0.324227	+	0.235564i
$449$	6.33813	+	19.5067i	0.299115	+	0.920580i	0.981808	+	0.189875i	$0.0608084\pi$
$449$	6.33813	+	19.5067i	0.299115	+	0.920580i	−0.682694	+	0.730705i	$0.739192\pi$
$450$	19.0339			0.897268
$451$		0			0
$452$	−0.584002			−0.0274691
$453$	−0.766764	−	2.35986i	−0.0360257	−	0.110876i
$454$	−25.3783	−	18.4384i	−1.19106	−	0.865357i
$455$	−12.1428	+	8.82226i	−0.569263	+	0.413594i
$456$	−2.29743	+	7.07078i	−0.107587	+	0.331119i
$457$	−2.64684	+	8.14613i	−0.123814	+	0.381060i	−0.993683	−	0.112223i	$-0.964203\pi$
$457$	−2.64684	+	8.14613i	−0.123814	+	0.381060i	0.869869	+	0.493282i	$0.164203\pi$
$458$	14.8061	−	10.7573i	0.691843	−	0.502653i
$459$	−8.24125	−	5.98762i	−0.384669	−	0.279478i
$460$	−0.705385	−	2.17095i	−0.0328887	−	0.101221i
$461$	9.66598			0.450189			0.225095	−	0.974337i	$-0.427731\pi$
$461$	9.66598			0.450189			0.225095	+	0.974337i	$0.427731\pi$
$462$		0			0
$463$	11.4240			0.530919			0.265459	−	0.964122i	$-0.414476\pi$
$463$	11.4240			0.530919			0.265459	+	0.964122i	$0.414476\pi$
$464$	−8.00847	−	24.6475i	−0.371784	−	1.14423i
$465$	3.35796	+	2.43970i	0.155722	+	0.113138i
$466$	−3.90155	+	2.83464i	−0.180736	+	0.131312i
$467$	5.63050	−	17.3289i	0.260548	−	0.801885i	−0.732137	−	0.681157i	$-0.761477\pi$
$467$	5.63050	−	17.3289i	0.260548	−	0.801885i	0.992686	−	0.120728i	$-0.0385230\pi$
$468$	−0.598495	+	1.84198i	−0.0276654	+	0.0851454i
$469$	−5.33518	+	3.87624i	−0.246356	+	0.178988i
$470$	−2.69561	−	1.95847i	−0.124339	−	0.0903376i
$471$	−2.63202	−	8.10051i	−0.121277	−	0.373252i
$472$	−1.06068			−0.0488218
$473$		0			0
$474$	1.84132			0.0845749
$475$	−10.5441	−	32.4513i	−0.483796	−	1.48897i
$476$	0.546333	+	0.396934i	0.0250411	+	0.0181935i
$477$	5.29638	−	3.84805i	0.242505	−	0.176190i
$478$	−9.27628	+	28.5494i	−0.424287	+	1.30582i
$479$	1.07290	−	3.30204i	0.0490220	−	0.150874i	−0.923549	−	0.383480i	$-0.874725\pi$
$479$	1.07290	−	3.30204i	0.0490220	−	0.150874i	0.972571	+	0.232606i	$0.0747254\pi$
$480$	0.736827	−	0.535336i	0.0336314	−	0.0244346i
$481$	−38.1446	−	27.7137i	−1.73925	−	1.26364i
$482$	0.132861	+	0.408905i	0.00605166	+	0.0186251i
$483$	−1.86799			−0.0849966
$484$		0			0
$485$	19.3213			0.877335
$486$	−3.89301	−	11.9814i	−0.176590	−	0.543489i
$487$	22.2167	+	16.1414i	1.00673	+	0.731435i	0.963521	−	0.267631i	$-0.0862408\pi$
$487$	22.2167	+	16.1414i	1.00673	+	0.731435i	0.0432123	+	0.999066i	$0.486241\pi$
$488$	−7.60970	+	5.52877i	−0.344475	+	0.250276i
$489$	−0.111227	+	0.342322i	−0.00502987	+	0.0154803i
$490$	−1.32342	+	4.07306i	−0.0597860	+	0.184002i
$491$	5.06769	−	3.68190i	0.228702	−	0.166162i	−0.467533	−	0.883976i	$-0.654857\pi$
$491$	5.06769	−	3.68190i	0.228702	−	0.166162i	0.696235	+	0.717814i	$0.254857\pi$
$492$	−0.133855	−	0.0972513i	−0.00603465	−	0.00438443i
$493$	−10.3492	−	31.8515i	−0.466103	−	1.43452i
$494$	−45.6587			−2.05428
$495$		0			0
$496$	13.4461			0.603746
$497$	4.68470	+	14.4180i	0.210137	+	0.646736i
$498$	0.623550	+	0.453036i	0.0279419	+	0.0203010i
$499$	16.7208	−	12.1484i	0.748526	−	0.543836i	−0.146844	−	0.989160i	$-0.546911\pi$
$499$	16.7208	−	12.1484i	0.748526	−	0.543836i	0.895370	+	0.445324i	$0.146911\pi$
$500$	0.0181112	−	0.0557407i	0.000809959	−	0.00249280i
$501$	0.0634738	−	0.195352i	0.00283580	−	0.00872770i
$502$	20.5657	−	14.9419i	0.917893	−	0.666888i
$503$	−17.8135	−	12.9422i	−0.794263	−	0.577066i	0.114962	−	0.993370i	$-0.463325\pi$
$503$	−17.8135	−	12.9422i	−0.794263	−	0.577066i	−0.909226	+	0.416304i	$0.863325\pi$
$504$	2.58729	+	7.96287i	0.115247	+	0.354694i
$505$	−33.9160			−1.50924
$506$		0			0
$507$	3.57128			0.158606
$508$	−0.961671	−	2.95972i	−0.0426672	−	0.131316i
$509$	−17.3324	−	12.5927i	−0.768245	−	0.558162i	0.133183	−	0.991091i	$-0.457480\pi$
$509$	−17.3324	−	12.5927i	−0.768245	−	0.558162i	−0.901428	+	0.432929i	$0.857480\pi$
$510$	−6.01476	+	4.36998i	−0.266338	+	0.193506i
$511$	0.995650	−	3.06430i	0.0440450	−	0.135557i
$512$	7.58269	−	23.3371i	0.335111	−	1.03137i
$513$	−12.0899	+	8.78383i	−0.533782	+	0.387815i
$514$	−9.42662	−	6.84884i	−0.415790	−	0.302089i
$515$	−12.8530	−	39.5576i	−0.566373	−	1.74312i
$516$	−0.219921			−0.00968149
$517$		0			0
$518$	−13.4533			−0.591105
$519$	−1.93569	−	5.95743i	−0.0849672	−	0.261502i
$520$	35.4490	+	25.7552i	1.55454	+	1.12944i
$521$	−11.2820	+	8.19682i	−0.494271	+	0.359109i	−0.806825	−	0.590791i	$-0.798816\pi$
$521$	−11.2820	+	8.19682i	−0.494271	+	0.359109i	0.312553	+	0.949900i	$0.398816\pi$
$522$	8.46910	−	26.0652i	0.370682	−	1.14084i
$523$	−5.71104	+	17.5768i	−0.249726	+	0.768578i	0.745097	+	0.666956i	$0.232403\pi$
$523$	−5.71104	+	17.5768i	−0.249726	+	0.768578i	−0.994823	+	0.101622i	$0.967597\pi$
$524$	1.71622	−	1.24690i	0.0749733	−	0.0544713i
$525$	1.43089	+	1.03960i	0.0624492	+	0.0453720i
$526$	−6.74067	−	20.7456i	−0.293907	−	0.904553i
$527$	17.3760			0.756912
$528$		0			0
$529$	3.43334			0.149276
$530$	−3.02093	−	9.29747i	−0.131221	−	0.403856i
$531$	−0.843014	−	0.612486i	−0.0365837	−	0.0265796i
$532$	0.801470	−	0.582302i	0.0347481	−	0.0252460i
$533$	4.75723	−	14.6412i	0.206058	−	0.634182i
$534$	0.854929	−	2.63120i	0.0369964	−	0.113863i
$535$	−35.6269	+	25.8845i	−1.54029	+	1.11908i
$536$	15.5752	+	11.3161i	0.672748	+	0.488780i
$537$	1.27110	+	3.91203i	0.0548518	+	0.168816i
$538$	−10.3013			−0.444122
$539$		0			0
$540$	0.946578			0.0407342
$541$	11.5737	+	35.6202i	0.497593	+	1.53143i	0.812877	+	0.582435i	$0.197900\pi$
$541$	11.5737	+	35.6202i	0.497593	+	1.53143i	−0.315284	+	0.948997i	$0.602100\pi$
$542$	15.4620	+	11.2338i	0.664148	+	0.482532i
$543$	−4.37302	+	3.17719i	−0.187664	+	0.136346i
$544$	1.17821	−	3.62616i	0.0505154	−	0.155470i
$545$	−15.1187	+	46.5307i	−0.647616	+	1.99316i
$546$	1.91471	−	1.39112i	0.0819422	−	0.0595345i
$547$	13.8590	+	10.0692i	0.592569	+	0.430526i	0.843233	−	0.537548i	$-0.180649\pi$
$547$	13.8590	+	10.0692i	0.592569	+	0.430526i	−0.250665	+	0.968074i	$0.580649\pi$
$548$	0.467210	+	1.43792i	0.0199582	+	0.0614250i
$549$	−9.24065			−0.394381
$550$		0			0
$551$	−49.1307			−2.09304
$552$	1.68517	+	5.18641i	0.0717254	+	0.220748i
$553$	−3.00738	−	2.18499i	−0.127887	−	0.0929152i
$554$	−6.63831	+	4.82302i	−0.282035	+	0.204910i
$555$	−3.48036	+	10.7115i	−0.147733	+	0.454676i
$556$	−0.179187	+	0.551480i	−0.00759921	+	0.0233879i
$557$	−19.8738	+	14.4391i	−0.842079	+	0.611806i	−0.922951	−	0.384918i	$-0.874230\pi$
$557$	−19.8738	+	14.4391i	−0.842079	+	0.611806i	0.0808715	+	0.996725i	$0.474230\pi$
$558$	11.5038	+	8.35798i	0.486993	+	0.353821i
$559$	−6.32330	−	19.4611i	−0.267447	−	0.823118i
$560$	11.6146			0.490807
$561$		0			0
$562$	28.1773			1.18859
$563$	−4.63814	−	14.2747i	−0.195474	−	0.601608i	−0.999971	−	0.00765038i	$-0.997565\pi$
$563$	−4.63814	−	14.2747i	−0.195474	−	0.601608i	0.804497	−	0.593957i	$-0.202435\pi$
$564$	−0.0323217	−	0.0234831i	−0.00136099	−	0.000988816i
$565$	−10.5011	+	7.62947i	−0.441783	+	0.320974i
$566$	−4.17751	+	12.8570i	−0.175594	+	0.540422i
$567$	−2.41941	+	7.44616i	−0.101605	+	0.312709i
$568$	35.8049	−	26.0138i	1.50234	−	1.09151i
$569$	−9.79129	−	7.11379i	−0.410472	−	0.298226i	0.363321	−	0.931664i	$-0.381643\pi$
$569$	−9.79129	−	7.11379i	−0.410472	−	0.298226i	−0.773793	+	0.633439i	$0.781643\pi$
$570$	3.37033	+	10.3728i	0.141168	+	0.434470i
$571$	38.9439			1.62975			0.814877	−	0.579634i	$-0.196805\pi$
$571$	38.9439			1.62975			0.814877	+	0.579634i	$0.196805\pi$
$572$		0			0
$573$	1.39857			0.0584262
$574$	−1.35740	−	4.17764i	−0.0566567	−	0.174371i
$575$	−20.2481	−	14.7111i	−0.844403	−	0.613494i
$576$	19.6818	−	14.2997i	0.820076	−	0.595820i
$577$	11.7892	−	36.2834i	0.490791	−	1.51050i	−0.332624	−	0.943060i	$-0.607934\pi$
$577$	11.7892	−	36.2834i	0.490791	−	1.51050i	0.823415	−	0.567440i	$-0.192066\pi$
$578$	−2.45586	+	7.55836i	−0.102150	+	0.314386i
$579$	0.748570	−	0.543868i	0.0311095	−	0.0226024i
$580$	2.51769	+	1.82921i	0.104541	+	0.0759537i
$581$	−0.480835	−	1.47986i	−0.0199484	−	0.0613949i
$582$	−3.04664			−0.126287
$583$		0			0
$584$	−9.40610			−0.389227
$585$	13.3021	+	40.9398i	0.549976	+	1.69265i
$586$	−29.5555	−	21.4734i	−1.22093	−	0.887056i
$587$	28.1511	−	20.4530i	1.16192	−	0.844184i	0.171900	−	0.985114i	$-0.445009\pi$
$587$	28.1511	−	20.4530i	1.16192	−	0.844184i	0.990020	+	0.140930i	$0.0450093\pi$
$588$	−0.0158685	+	0.0488381i	−0.000654404	+	0.00201405i
$589$	7.87704	−	24.2430i	0.324568	−	0.998917i
$590$	−1.25884	+	0.914603i	−0.0518258	+	0.0376536i
$591$	3.10008	+	2.25234i	0.127520	+	0.0926489i
$592$	11.2746	+	34.6997i	0.463384	+	1.42615i
$593$	−18.5913			−0.763452			−0.381726	−	0.924276i	$-0.624670\pi$
$593$	−18.5913			−0.763452			−0.381726	+	0.924276i	$0.624670\pi$
$594$		0			0
$595$	15.0093			0.615322
$596$	−0.612269	−	1.88437i	−0.0250795	−	0.0771868i
$597$	−3.43457	−	2.49536i	−0.140567	−	0.102128i
$598$	−27.0945	+	19.6853i	−1.10798	+	0.804992i
$599$	7.62285	−	23.4607i	0.311461	−	0.958579i	−0.665726	−	0.746197i	$-0.731878\pi$
$599$	7.62285	−	23.4607i	0.311461	−	0.958579i	0.977187	−	0.212382i	$-0.0681221\pi$
$600$	1.59557	−	4.91067i	0.0651390	−	0.200477i
$601$	24.3746	−	17.7092i	0.994259	−	0.722372i	0.0334095	−	0.999442i	$-0.489363\pi$
$601$	24.3746	−	17.7092i	0.994259	−	0.722372i	0.960850	+	0.277070i	$0.0893634\pi$
$602$	−4.72360	−	3.43189i	−0.192519	−	0.139874i
$603$	5.84456	+	17.9877i	0.238009	+	0.732516i
$604$	0.965235			0.0392749
$605$		0			0
$606$	5.34797			0.217247
$607$	−4.22078	−	12.9902i	−0.171316	−	0.527256i	0.828130	−	0.560536i	$-0.189405\pi$
$607$	−4.22078	−	12.9902i	−0.171316	−	0.527256i	−0.999446	+	0.0332795i	$0.989405\pi$
$608$	−4.52510	−	3.28768i	−0.183517	−	0.133333i
$609$	2.06031	−	1.49691i	0.0834881	−	0.0606577i
$610$	−4.26404	+	13.1234i	−0.172646	+	0.531350i
$611$	1.14872	−	3.53539i	0.0464721	−	0.143027i
$612$	1.56688	−	1.13840i	0.0633374	−	0.0460173i
$613$	36.4284	+	26.4668i	1.47133	+	1.06898i	0.980226	+	0.197882i	$0.0634064\pi$
$613$	36.4284	+	26.4668i	1.47133	+	1.06898i	0.491104	+	0.871101i	$0.336594\pi$
$614$	−5.01223	−	15.4261i	−0.202277	−	0.622545i
$615$	−3.67738			−0.148286
$616$		0			0
$617$	−8.26401			−0.332697			−0.166348	−	0.986067i	$-0.553198\pi$
$617$	−8.26401			−0.332697			−0.166348	+	0.986067i	$0.553198\pi$
$618$	2.02671	+	6.23757i	0.0815262	+	0.250912i
$619$	−34.8282	−	25.3042i	−1.39986	−	1.01706i	−0.994700	−	0.102816i	$-0.967215\pi$
$619$	−34.8282	−	25.3042i	−1.39986	−	1.01706i	−0.405164	−	0.914244i	$-0.632785\pi$
$620$	−1.30626	+	0.949053i	−0.0524606	+	0.0381149i
$621$	−3.38725	+	10.4249i	−0.135926	+	0.418336i
$622$	8.94851	−	27.5407i	0.358802	−	1.10428i
$623$	−4.51862	+	3.28297i	−0.181035	+	0.131529i
$624$	−5.19271	−	3.77273i	−0.207875	−	0.151030i
$625$	−7.92400	−	24.3876i	−0.316960	−	0.975503i
$626$	17.3107			0.691873
$627$		0			0
$628$	3.31330			0.132215
$629$	14.5699	+	44.8417i	0.580942	+	1.78796i
$630$	9.93689	+	7.21957i	0.395895	+	0.287635i
$631$	−0.840272	+	0.610493i	−0.0334507	+	0.0243034i	−0.604385	−	0.796692i	$-0.706581\pi$
$631$	−0.840272	+	0.610493i	−0.0334507	+	0.0243034i	0.570934	+	0.820996i	$0.306581\pi$
$632$	−3.35350	+	10.3210i	−0.133395	+	0.410548i
$633$	1.24760	−	3.83971i	0.0495876	−	0.152615i
$634$	−13.0899	+	9.51035i	−0.519865	+	0.377704i
$635$	−55.9581	−	40.6559i	−2.22063	−	1.61338i
$636$	−0.0362225	−	0.111481i	−0.00143631	−	0.00442052i
$637$	−4.77801			−0.189312
$638$		0			0
$639$	43.4787			1.71999
$640$	−9.67681	−	29.7821i	−0.382509	−	1.17724i
$641$	−27.2164	−	19.7739i	−1.07498	−	0.781020i	−0.0981811	−	0.995169i	$-0.531302\pi$
$641$	−27.2164	−	19.7739i	−1.07498	−	0.781020i	−0.976801	+	0.214148i	$0.931302\pi$
$642$	5.61777	−	4.08155i	0.221716	−	0.161086i
$643$	−6.49905	+	20.0020i	−0.256298	+	0.788803i	0.737274	+	0.675594i	$0.236113\pi$
$643$	−6.49905	+	20.0020i	−0.256298	+	0.788803i	−0.993571	+	0.113209i	$0.963887\pi$
$644$	0.224549	−	0.691091i	0.00884848	−	0.0272328i
$645$	−3.95445	+	2.87308i	−0.155706	+	0.113127i
$646$	36.9387	+	26.8375i	1.45333	+	1.05591i
$647$	7.79650	+	23.9952i	0.306512	+	0.943347i	0.979109	+	0.203338i	$0.0651789\pi$
$647$	7.79650	+	23.9952i	0.306512	+	0.943347i	−0.672597	+	0.740009i	$0.734821\pi$
$648$	22.8566			0.897892
$649$		0			0
$650$	31.7101			1.24377
$651$	0.408306	+	1.25664i	0.0160028	+	0.0492515i
$652$	−0.113277	−	0.0823003i	−0.00443626	−	0.00322313i
$653$	−16.6971	+	12.1311i	−0.653408	+	0.474729i	−0.864430	−	0.502753i	$-0.832321\pi$
$653$	−16.6971	+	12.1311i	−0.653408	+	0.474729i	0.211023	+	0.977481i	$0.432321\pi$
$654$	2.38397	−	7.33711i	0.0932206	−	0.286904i
$655$	14.5699	−	44.8417i	0.569295	−	1.75211i
$656$	−9.63769	+	7.00219i	−0.376289	+	0.273390i
$657$	−7.47584	−	5.43152i	−0.291660	−	0.211904i
$658$	−0.327768	−	1.00877i	−0.0127777	−	0.0393258i
$659$	−18.5067			−0.720920			−0.360460	−	0.932775i	$-0.617380\pi$
$659$	−18.5067			−0.720920			−0.360460	+	0.932775i	$0.617380\pi$
$660$		0			0
$661$	16.8001			0.653446			0.326723	−	0.945120i	$-0.394056\pi$
$661$	16.8001			0.653446			0.326723	+	0.945120i	$0.394056\pi$
$662$	5.00775	+	15.4123i	0.194632	+	0.599014i
$663$	−6.71043	−	4.87541i	−0.260612	−	0.189345i
$664$	−3.67500	+	2.67004i	−0.142618	+	0.103618i
$665$	6.80414	−	20.9410i	0.263853	−	0.812057i
$666$	−11.9231	+	36.6956i	−0.462011	+	1.42192i
$667$	−29.1548	+	21.1822i	−1.12888	+	0.820178i
$668$	0.0646434	+	0.0469662i	0.00250113	+	0.00181717i
$669$	3.14826	+	9.68934i	0.121719	+	0.374612i
$670$	28.2427			1.09111
$671$		0			0
$672$	0.289930			0.0111843
$673$	5.42511	+	16.6968i	0.209123	+	0.643613i	0.999519	+	0.0310171i	$0.00987464\pi$
$673$	5.42511	+	16.6968i	0.209123	+	0.643613i	−0.790396	+	0.612596i	$0.790125\pi$
$674$	1.09267	+	0.793869i	0.0420879	+	0.0305787i
$675$	8.39646	−	6.10039i	0.323180	−	0.234804i
$676$	−0.429300	+	1.32125i	−0.0165115	+	0.0508173i
$677$	−1.12708	+	3.46881i	−0.0433173	+	0.133317i	−0.970376	−	0.241599i	$-0.922328\pi$
$677$	−1.12708	+	3.46881i	−0.0433173	+	0.133317i	0.927059	+	0.374916i	$0.122328\pi$
$678$	1.65584	−	1.20304i	0.0635921	−	0.0462024i
$679$	4.97599	+	3.61527i	0.190961	+	0.138741i
$680$	−13.5403	−	41.6728i	−0.519248	−	1.59808i
$681$	−8.35994			−0.320354
$682$		0			0
$683$	27.4720			1.05119			0.525593	−	0.850736i	$-0.323844\pi$
$683$	27.4720			1.05119			0.525593	+	0.850736i	$0.323844\pi$
$684$	−0.877991	−	2.70218i	−0.0335708	−	0.103320i
$685$	27.1862	+	19.7519i	1.03873	+	0.754682i
$686$	−1.10296	+	0.801344i	−0.0421110	+	0.0305955i
$687$	1.50718	−	4.63861i	0.0575023	−	0.176974i
$688$	−4.89314	+	15.0595i	−0.186549	+	0.574140i
$689$	8.82365	−	6.41075i	0.336154	−	0.244230i
$690$	6.47214	+	4.70228i	0.246390	+	0.179013i
$691$	−1.84071	−	5.66512i	−0.0700239	−	0.215511i	0.909920	−	0.414783i	$-0.136142\pi$
$691$	−1.84071	−	5.66512i	−0.0700239	−	0.215511i	−0.979944	+	0.199271i	$0.936142\pi$
$692$	2.43673			0.0926304
$693$		0			0
$694$	20.7080			0.786065
$695$	3.98260	+	12.2572i	0.151069	+	0.464942i
$696$	−6.01476	−	4.36998i	−0.227989	−	0.165644i
$697$	−12.4546	+	9.04878i	−0.471751	+	0.342747i
$698$	12.5137	−	38.5134i	0.473652	−	1.45775i
$699$	−0.397155	+	1.22232i	−0.0150218	+	0.0462323i
$700$	−0.556622	+	0.404410i	−0.0210384	+	0.0152853i
$701$	−5.96186	−	4.33155i	−0.225176	−	0.163600i	0.469477	−	0.882945i	$-0.344442\pi$
$701$	−5.96186	−	4.33155i	−0.225176	−	0.163600i	−0.694654	+	0.719344i	$0.744442\pi$
$702$	−4.29159	−	13.2082i	−0.161976	−	0.498510i
$703$	69.1680			2.60872
$704$		0			0
$705$	−0.887968			−0.0334428
$706$	2.82940	+	8.70799i	0.106486	+	0.327730i
$707$	−8.73469	−	6.34612i	−0.328502	−	0.238670i
$708$	−0.0150942	+	0.0109666i	−0.000567273	+	0.000412148i
$709$	−10.7278	+	33.0169i	−0.402892	+	1.23998i	0.519750	+	0.854318i	$0.326025\pi$
$709$	−10.7278	+	33.0169i	−0.402892	+	1.23998i	−0.922642	+	0.385657i	$0.873975\pi$
$710$	20.0630	−	61.7476i	0.752952	−	2.31735i
$711$	−8.62515	+	6.26654i	−0.323468	+	0.235013i
$712$	13.1914	+	9.58412i	0.494369	+	0.359180i
$713$	−5.77780	−	17.7822i	−0.216380	−	0.665950i
$714$	−2.36672			−0.0885722
$715$		0			0
$716$	−1.60011			−0.0597989
$717$	2.47214	+	7.60845i	0.0923236	+	0.284143i
$718$	19.5620	+	14.2126i	0.730048	+	0.530411i
$719$	3.28623	−	2.38758i	0.122556	−	0.0890418i	−0.524819	−	0.851214i	$-0.675867\pi$
$719$	3.28623	−	2.38758i	0.122556	−	0.0890418i	0.647375	+	0.762172i	$0.275867\pi$
$720$	10.2936	−	31.6803i	0.383618	−	1.18066i
$721$	4.09159	−	12.5926i	0.152379	−	0.468973i
$722$	33.2328	−	24.1451i	1.23680	−	0.898586i
$723$	0.0926983	+	0.0673493i	0.00344749	+	0.00250475i
$724$	−0.649771	−	1.99979i	−0.0241485	−	0.0743216i
$725$	34.1214			1.26724
$726$		0			0
$727$	−30.5433			−1.13279			−0.566394	−	0.824135i	$-0.691662\pi$
$727$	−30.5433			−1.13279			−0.566394	+	0.824135i	$0.691662\pi$
$728$	4.31037	+	13.2660i	0.159753	+	0.491669i
$729$	16.2861	+	11.8325i	0.603188	+	0.438242i
$730$	−11.1634	+	8.11069i	−0.413176	+	0.300190i
$731$	−6.32330	+	19.4611i	−0.233876	+	0.719796i
$732$	−0.0511280	+	0.157356i	−0.00188975	+	0.00581604i
$733$	24.9452	−	18.1238i	0.921372	−	0.669416i	−0.0224928	−	0.999747i	$-0.507160\pi$
$733$	24.9452	−	18.1238i	0.921372	−	0.669416i	0.943865	+	0.330331i	$0.107160\pi$
$734$	−8.93318	−	6.49034i	−0.329730	−	0.239563i
$735$	0.352692	+	1.08548i	0.0130092	+	0.0400384i
$736$	−4.10270			−0.151228
$737$		0			0
$738$	−12.5980			−0.463740
$739$	6.86761	+	21.1363i	0.252629	+	0.777513i	0.994288	+	0.106735i	$0.0340396\pi$
$739$	6.86761	+	21.1363i	0.252629	+	0.777513i	−0.741658	+	0.670778i	$0.765960\pi$
$740$	−3.54449	−	2.57522i	−0.130298	−	0.0946671i
$741$	−9.84419	+	7.15222i	−0.361635	+	0.262744i
$742$	0.961671	−	2.95972i	0.0353040	−	0.108655i
$743$	−9.62568	+	29.6248i	−0.353132	+	1.08683i	0.603953	+	0.797020i	$0.293591\pi$
$743$	−9.62568	+	29.6248i	−0.353132	+	1.08683i	−0.957085	+	0.289808i	$0.906409\pi$
$744$	3.12066	−	2.26729i	0.114409	−	0.0831229i
$745$	−35.6269	−	25.8845i	−1.30527	−	0.948334i
$746$	−0.238175	−	0.733027i	−0.00872020	−	0.0268380i
$747$	−4.46264			−0.163280
$748$		0			0
$749$	−14.0187			−0.512231
$750$	0.0634738	+	0.195352i	0.00231774	+	0.00713326i
$751$	−9.69959	−	7.04716i	−0.353943	−	0.257155i	0.396578	−	0.918001i	$-0.370198\pi$
$751$	−9.69959	−	7.04716i	−0.353943	−	0.257155i	−0.750521	+	0.660846i	$0.770198\pi$
$752$	−2.32719	+	1.69080i	−0.0848640	+	0.0616573i
$753$	2.09347	−	6.44305i	0.0762904	−	0.234798i
$754$	14.1093	−	43.4240i	0.513831	−	1.58141i
$755$	17.3561	−	12.6099i	0.631653	−	0.458923i
$756$	0.243781	+	0.177117i	0.00886622	+	0.00644169i
$757$	−3.53927	−	10.8927i	−0.128637	−	0.395904i	0.865909	−	0.500201i	$-0.166741\pi$
$757$	−3.53927	−	10.8927i	−0.128637	−	0.395904i	−0.994546	+	0.104297i	$0.966741\pi$
$758$	30.7240			1.11595
$759$		0			0
$760$	−64.2800			−2.33168
$761$	2.43816	+	7.50387i	0.0883831	+	0.272015i	0.985473	−	0.169833i	$-0.0543229\pi$
$761$	2.43816	+	7.50387i	0.0883831	+	0.272015i	−0.897090	+	0.441848i	$0.854323\pi$
$762$	8.82365	+	6.41075i	0.319647	+	0.232237i
$763$	−12.6002	+	9.15456i	−0.456157	+	0.331417i
$764$	−0.168121	+	0.517422i	−0.00608239	+	0.0187197i
$765$	13.3021	−	40.9398i	0.480940	−	1.48018i
$766$	23.5937	−	17.1418i	0.852474	−	0.619359i
$767$	−1.40444	−	1.02039i	−0.0507114	−	0.0368440i
$768$	−0.378896	−	1.16612i	−0.0136722	−	0.0420788i
$769$	−48.8153			−1.76033			−0.880163	−	0.474672i	$-0.842567\pi$
$769$	−48.8153			−1.76033			−0.880163	+	0.474672i	$0.842567\pi$
$770$		0			0
$771$	−3.10525			−0.111833
$772$	0.111227	+	0.342322i	0.00400316	+	0.0123204i
$773$	2.58568	+	1.87861i	0.0930005	+	0.0675688i	0.633314	−	0.773895i	$-0.281694\pi$
$773$	2.58568	+	1.87861i	0.0930005	+	0.0675688i	−0.540313	+	0.841464i	$0.681694\pi$
$774$	−13.5472	+	9.84265i	−0.486946	+	0.353787i
$775$	−5.47062	+	16.8368i	−0.196510	+	0.604797i
$776$	5.54868	−	17.0771i	0.199186	−	0.613032i
$777$	−2.90059	+	2.10740i	−0.104058	+	0.0756025i
$778$	11.7781	+	8.55731i	0.422266	+	0.306794i
$779$	6.97884	+	21.4787i	0.250043	+	0.769553i
$780$	0.770750			0.0275973
$781$		0			0
$782$	33.4906			1.19762
$783$	−4.61793	−	14.2125i	−0.165031	−	0.507914i
$784$	2.99122	+	2.17325i	0.106829	+	0.0776160i
$785$	59.5771	−	43.2853i	2.12640	−	1.54492i
$786$	−2.29743	+	7.07078i	−0.0819468	+	0.252206i
$787$	−13.1274	+	40.4021i	−0.467943	+	1.44018i	0.387301	+	0.921953i	$0.373408\pi$
$787$	−13.1274	+	40.4021i	−0.467943	+	1.44018i	−0.855243	+	0.518226i	$0.826592\pi$
$788$	−1.20594	+	0.876169i	−0.0429599	+	0.0312122i
$789$	−4.70302	−	3.41694i	−0.167432	−	0.121646i
$790$	4.91958	+	15.1409i	0.175031	+	0.538689i
$791$	−4.13201			−0.146917
$792$		0			0
$793$	−15.3947			−0.546682
$794$	10.0756	+	31.0095i	0.357569	+	1.10049i
$795$	−2.10773	−	1.53135i	−0.0747534	−	0.0543116i
$796$	1.33606	−	0.970704i	0.0473554	−	0.0344057i
$797$	−8.91782	+	27.4462i	−0.315885	+	0.972195i	0.659503	+	0.751702i	$0.270767\pi$
$797$	−8.91782	+	27.4462i	−0.315885	+	0.972195i	−0.975389	+	0.220493i	$0.929233\pi$
$798$	−1.07290	+	3.30204i	−0.0379802	+	0.116891i
$799$	−3.00738	+	2.18499i	−0.106394	+	0.0772994i
$800$	3.14269	+	2.28330i	0.111111	+	0.0807268i
$801$	4.95004	+	15.2346i	0.174901	+	0.538290i
$802$	−15.8947			−0.561260
$803$		0			0
$804$	0.338644			0.0119431
$805$	−4.99083	−	15.3602i	−0.175904	−	0.541376i
$806$	19.1650	+	13.9242i	0.675059	+	0.490459i
$807$	−2.22101	+	1.61366i	−0.0781831	+	0.0568033i
$808$	−9.73996	+	29.9765i	−0.342651	+	1.05457i
$809$	−9.10157	+	28.0118i	−0.319994	+	0.984841i	0.653655	+	0.756792i	$0.273235\pi$
$809$	−9.10157	+	28.0118i	−0.319994	+	0.984841i	−0.973650	+	0.228049i	$0.926765\pi$
$810$	27.1268	−	19.7088i	0.953139	−	0.692496i
$811$	2.00741	+	1.45847i	0.0704898	+	0.0512138i	0.622472	−	0.782642i	$-0.286128\pi$
$811$	2.00741	+	1.45847i	0.0704898	+	0.0512138i	−0.551982	+	0.833856i	$0.686128\pi$
$812$	0.306134	+	0.942184i	0.0107432	+	0.0330642i
$813$	5.09337			0.178632
$814$		0			0
$815$	−3.11203			−0.109010
$816$	1.98344	+	6.10440i	0.0694343	+	0.213697i
$817$	24.2856	+	17.6445i	0.849646	+	0.617304i
$818$	36.1938	−	26.2964i	1.26549	−	0.919431i
$819$	−4.23455	+	13.0326i	−0.147967	+	0.455396i
$820$	0.442053	−	1.36050i	0.0154372	−	0.0475107i
$821$	11.3413	−	8.23996i	0.395815	−	0.287577i	−0.372019	−	0.928225i	$-0.621334\pi$
$821$	11.3413	−	8.23996i	0.395815	−	0.287577i	0.767834	+	0.640648i	$0.221334\pi$
$822$	−4.28680	−	3.11454i	−0.149519	−	0.108632i
$823$	−13.2238	−	40.6988i	−0.460954	−	1.41867i	−0.864000	−	0.503492i	$-0.832048\pi$
$823$	−13.2238	−	40.6988i	−0.460954	−	1.41867i	0.403046	−	0.915180i	$-0.367952\pi$
$824$	−38.6540			−1.34658
$825$		0			0
$826$	−0.495336			−0.0172349
$827$	2.83388	+	8.72180i	0.0985438	+	0.303287i	0.988161	−	0.153420i	$-0.0490288\pi$
$827$	2.83388	+	8.72180i	0.0985438	+	0.303287i	−0.889617	+	0.456707i	$0.849029\pi$
$828$	−1.68603	−	1.22497i	−0.0585935	−	0.0425707i
$829$	−23.6211	+	17.1617i	−0.820395	+	0.596052i	−0.916826	−	0.399288i	$-0.869257\pi$
$829$	−23.6211	+	17.1617i	−0.820395	+	0.596052i	0.0964304	+	0.995340i	$0.469257\pi$
$830$	−2.05926	+	6.33775i	−0.0714780	+	0.219987i
$831$	−0.675742	+	2.07972i	−0.0234412	+	0.0721447i
$832$	32.7895	−	23.8229i	1.13677	−	0.825912i
$833$	3.86549	+	2.80844i	0.133931	+	0.0973068i
$834$	−0.627989	−	1.93275i	−0.0217455	−	0.0669257i
$835$	1.77594			0.0614588
$836$		0			0
$837$	7.75341			0.267997
$838$	−4.54854	−	13.9990i	−0.157127	−	0.483587i
$839$	−15.9640	−	11.5985i	−0.551139	−	0.400426i	0.277066	−	0.960851i	$-0.410638\pi$
$839$	−15.9640	−	11.5985i	−0.551139	−	0.400426i	−0.828205	+	0.560425i	$0.810638\pi$
$840$	2.69561	−	1.95847i	0.0930073	−	0.0675737i
$841$	6.22072	−	19.1454i	0.214508	−	0.660187i
$842$	0.485321	−	1.49366i	0.0167253	−	0.0514751i
$843$	6.07514	−	4.41385i	0.209239	−	0.152021i
$844$	1.27059	+	0.923135i	0.0437354	+	0.0317756i
$845$	9.54162	+	29.3661i	0.328242	+	1.01022i
$846$	−3.04202			−0.104587
$847$		0			0
$848$	−8.43984			−0.289825
$849$	1.11331	+	3.42642i	0.0382087	+	0.117594i
$850$	−25.6540	−	18.6387i	−0.879924	−	0.639303i
$851$	41.0452	−	29.8211i	1.40701	−	1.02225i
$852$	0.240566	−	0.740385i	0.00824164	−	0.0253652i
$853$	8.76146	−	26.9650i	0.299987	−	0.923264i	−0.681514	−	0.731805i	$-0.738678\pi$
$853$	8.76146	−	26.9650i	0.299987	−	0.923264i	0.981501	−	0.191459i	$-0.0613219\pi$
$854$	−3.55371	+	2.58192i	−0.121606	+	0.0883516i
$855$	−51.0889	−	37.1183i	−1.74720	−	1.26942i
$856$	12.6466	+	38.9223i	0.432252	+	1.33034i
$857$	−13.2033			−0.451017			−0.225509	−	0.974241i	$-0.572404\pi$
$857$	−13.2033			−0.451017			−0.225509	+	0.974241i	$0.572404\pi$
$858$		0			0
$859$	−20.8260			−0.710573			−0.355286	−	0.934757i	$-0.615617\pi$
$859$	−20.8260			−0.710573			−0.355286	+	0.934757i	$0.615617\pi$
$860$	−0.587577	−	1.80838i	−0.0200362	−	0.0616651i
$861$	−0.947068	−	0.688085i	−0.0322760	−	0.0234499i
$862$	−35.2505	+	25.6110i	−1.20064	+	0.872314i
$863$	10.7983	−	33.2337i	0.367577	−	1.13129i	−0.580774	−	0.814065i	$-0.697250\pi$
$863$	10.7983	−	33.2337i	0.367577	−	1.13129i	0.948351	−	0.317222i	$-0.102750\pi$
$864$	0.525733	−	1.61804i	0.0178858	−	0.0550468i
$865$	43.8153	−	31.8337i	1.48976	−	1.08238i
$866$	−4.88977	−	3.55263i	−0.166161	−	0.120723i
$867$	0.654489	+	2.01431i	0.0222276	+	0.0684096i
$868$	−0.513993			−0.0174461
$869$		0			0
$870$	−10.9066			−0.369769
$871$	9.73690	+	29.9671i	0.329922	+	1.01540i
$872$	36.7842	+	26.7253i	1.24567	+	0.905034i
$873$	14.2711	−	10.3686i	0.483004	−	0.350923i
$874$	15.1822	−	46.7261i	0.513546	−	1.58053i
$875$	0.128143	−	0.394384i	0.00433203	−	0.0133326i
$876$	−0.133855	+	0.0972513i	−0.00452254	+	0.00328582i
$877$	−21.4238	−	15.5653i	−0.723431	−	0.525603i	0.164048	−	0.986452i	$-0.447545\pi$
$877$	−21.4238	−	15.5653i	−0.723431	−	0.525603i	−0.887479	+	0.460849i	$0.847545\pi$
$878$	11.5737	+	35.6202i	0.390594	+	1.20212i
$879$	−9.73599			−0.328387
$880$		0			0
$881$	17.2627			0.581595			0.290798	−	0.956785i	$-0.406079\pi$
$881$	17.2627			0.581595			0.290798	+	0.956785i	$0.406079\pi$
$882$	1.20826	+	3.71865i	0.0406843	+	0.125213i
$883$	36.0843	+	26.2168i	1.21433	+	0.882265i	0.995617	−	0.0935234i	$-0.0298130\pi$
$883$	36.0843	+	26.2168i	1.21433	+	0.882265i	0.218717	+	0.975788i	$0.429813\pi$
$884$	2.61038	−	1.89656i	0.0877967	−	0.0637881i
$885$	−0.128143	+	0.394384i	−0.00430748	+	0.0132571i
$886$	3.28217	−	10.1015i	0.110267	−	0.339366i
$887$	24.9092	−	18.0976i	0.836368	−	0.607657i	−0.0849861	−	0.996382i	$-0.527085\pi$
$887$	24.9092	−	18.0976i	0.836368	−	0.607657i	0.921354	+	0.388726i	$0.127085\pi$
$888$	8.46781	+	6.15222i	0.284161	+	0.206455i
$889$	−6.80414	−	20.9410i	−0.228204	−	0.702338i
$890$	23.9201			0.801803
$891$		0			0
$892$	−3.96316			−0.132697
$893$	1.68517	+	5.18641i	0.0563919	+	0.173557i
$894$	5.61777	+	4.08155i	0.187886	+	0.136507i
$895$	−28.7719	+	20.9040i	−0.961739	+	0.698744i
$896$	3.08047	−	9.48073i	0.102911	−	0.316729i
$897$	−2.75806	+	8.48845i	−0.0920891	+	0.283421i
$898$	22.6223	−	16.4361i	0.754916	−	0.548478i
$899$	20.6224	+	14.9830i	0.687794	+	0.499712i
$900$	0.609766	+	1.87667i	0.0203255	+	0.0625556i
$901$	−10.9066			−0.363352
$902$		0			0
$903$	−1.55602			−0.0517810
$904$	3.72760	+	11.4724i	0.123978	+	0.381565i
$905$	−37.8091	−	27.4699i	−1.25682	−	0.913132i
$906$	−2.73676	+	1.98837i	−0.0909229	+	0.0660593i
$907$	7.34845	−	22.6162i	0.244001	−	0.750959i	−0.751798	−	0.659394i	$-0.770813\pi$
$907$	7.34845	−	22.6162i	0.244001	−	0.750959i	0.995799	−	0.0915649i	$-0.0291869\pi$
$908$	1.00494	−	3.09288i	0.0333501	−	0.102641i
$909$	−25.0510	+	18.2006i	−0.830890	+	0.603677i
$910$	16.5546	+	12.0276i	0.548780	+	0.398712i
$911$	15.1505	+	46.6284i	0.501958	+	1.54487i	0.805825	+	0.592153i	$0.201722\pi$
$911$	15.1505	+	46.6284i	0.501958	+	1.54487i	−0.303868	+	0.952714i	$0.598278\pi$
$912$	9.41600			0.311795
$913$		0			0
$914$	11.6774			0.386253
$915$	1.13637	+	3.49739i	0.0375673	+	0.115620i
$916$	1.53495	+	1.11520i	0.0507160	+	0.0368474i
$917$	12.1428	−	8.82226i	0.400991	−	0.291337i
$918$	−4.29159	+	13.2082i	−0.141644	+	0.435934i
$919$	12.3607	−	38.0423i	0.407741	−	1.25490i	−0.510843	−	0.859674i	$-0.670667\pi$
$919$	12.3607	−	38.0423i	0.407741	−	1.25490i	0.918585	−	0.395225i	$-0.129333\pi$
$920$	−38.1446	+	27.7137i	−1.25759	+	0.913693i
$921$	−3.49708	−	2.54077i	−0.115233	−	0.0837214i
$922$	−4.07219	−	12.5329i	−0.134111	−	0.412750i
$923$	72.4346			2.38421
$924$		0			0
$925$	−48.0373			−1.57946
$926$	−4.81284	−	14.8124i	−0.158160	−	0.486765i
$927$	−30.7217	−	22.3206i	−1.00903	−	0.733105i
$928$	4.52510	−	3.28768i	0.148544	−	0.107923i
$929$	−17.4854	+	53.8146i	−0.573678	+	1.76560i	0.0669595	+	0.997756i	$0.478670\pi$
$929$	−17.4854	+	53.8146i	−0.573678	+	1.76560i	−0.640637	+	0.767844i	$0.721330\pi$
$930$	1.74864	−	5.38176i	0.0573402	−	0.176475i
$931$	5.67067	−	4.11998i	0.185849	−	0.135027i
$932$	−0.404473	−	0.293867i	−0.0132490	−	0.00962594i
$933$	−2.38479	−	7.33961i	−0.0780744	−	0.240288i
$934$	−24.8408			−0.812814
$935$		0			0
$936$	40.0046			1.30759
$937$	−5.19622	−	15.9923i	−0.169753	−	0.522446i	0.829602	−	0.558355i	$-0.188567\pi$
$937$	−5.19622	−	15.9923i	−0.169753	−	0.522446i	−0.999355	+	0.0359089i	$0.988567\pi$
$938$	7.27361	+	5.28458i	0.237492	+	0.172548i
$939$	3.73224	−	2.71163i	0.121797	−	0.0884908i
$940$	0.106742	−	0.328517i	0.00348153	−	0.0107150i
$941$	2.24325	−	6.90401i	0.0731278	−	0.225064i	−0.907812	−	0.419378i	$-0.862248\pi$
$941$	2.24325	−	6.90401i	0.0731278	−	0.225064i	0.980939	+	0.194314i	$0.0622481\pi$
$942$	−9.39430	+	6.82536i	−0.306083	+	0.222382i
$943$	13.4016	+	9.73687i	0.436418	+	0.317076i
$944$	0.415119	+	1.27760i	0.0135110	+	0.0415825i
$945$	6.69735			0.217865
$946$		0			0
$947$	−25.6040			−0.832017			−0.416009	−	0.909361i	$-0.636571\pi$
$947$	−25.6040			−0.832017			−0.416009	+	0.909361i	$0.636571\pi$
$948$	0.0589883	+	0.181547i	0.00191585	+	0.00589638i
$949$	−12.4546	−	9.04878i	−0.404293	−	0.293736i
$950$	−37.6343	+	27.3430i	−1.22102	+	0.887123i
$951$	−1.33247	+	4.10093i	−0.0432084	+	0.132982i
$952$	4.31037	−	13.2660i	0.139700	−	0.429952i
$953$	−5.78394	+	4.20228i	−0.187360	+	0.136125i	−0.677511	−	0.735512i	$-0.736942\pi$
$953$	−5.78394	+	4.20228i	−0.187360	+	0.136125i	0.490151	+	0.871637i	$0.336942\pi$
$954$	−7.22071	−	5.24615i	−0.233779	−	0.169850i
$955$	3.73665	+	11.5002i	0.120915	+	0.372139i
$956$	−3.11203			−0.100650
$957$		0			0
$958$	−4.73344			−0.152930
$959$	3.30566	+	10.1738i	0.106745	+	0.328529i
$960$	−7.83251	−	5.69065i	−0.252793	−	0.183665i
$961$	14.3800	−	10.4477i	0.463870	−	0.337021i
$962$	−19.8636	+	61.1339i	−0.640429	+	1.97104i
$963$	−12.4242	+	38.2376i	−0.400363	+	1.23219i
$964$	−0.0360600	+	0.0261991i	−0.00116142	+	0.000843817i
$965$	6.47214	+	4.70228i	0.208345	+	0.151372i
$966$	0.786970	+	2.42204i	0.0253203	+	0.0779280i
$967$	15.9600			0.513241			0.256620	−	0.966512i	$-0.417391\pi$
$967$	15.9600			0.513241			0.256620	+	0.966512i	$0.417391\pi$
$968$		0			0
$969$	12.1681			0.390895
$970$	−8.13990	−	25.0520i	−0.261357	−	0.804373i
$971$	24.6571	+	17.9145i	0.791285	+	0.574903i	0.908345	−	0.418222i	$-0.137347\pi$
$971$	24.6571	+	17.9145i	0.791285	+	0.574903i	−0.117059	+	0.993125i	$0.537347\pi$
$972$	1.05661	−	0.767670i	0.0338907	−	0.0246230i
$973$	−1.26780	+	3.90190i	−0.0406440	+	0.125089i
$974$	11.5692	−	35.6064i	0.370702	−	1.14090i
$975$	6.83681	−	4.96723i	0.218953	−	0.159079i
$976$	9.63769	+	7.00219i	0.308495	+	0.224135i
$977$	1.27686	+	3.92977i	0.0408504	+	0.125725i	0.969402	−	0.245479i	$-0.0789452\pi$
$977$	1.27686	+	3.92977i	0.0408504	+	0.125725i	−0.928552	+	0.371204i	$0.878945\pi$
$978$	0.490715			0.0156913
$979$		0			0
$980$	−0.443984			−0.0141826
$981$	13.8032	+	42.4818i	0.440702	+	1.35634i
$982$	−6.90893	−	5.01963i	−0.220473	−	0.160183i
$983$	20.2453	−	14.7091i	0.645726	−	0.469147i	−0.216087	−	0.976374i	$-0.569329\pi$
$983$	20.2453	−	14.7091i	0.645726	−	0.469147i	0.861812	+	0.507227i	$0.169329\pi$
$984$	−1.05607	+	3.25024i	−0.0336662	+	0.103614i
$985$	−10.2379	+	31.5092i	−0.326208	+	1.00397i
$986$	−36.9387	+	26.8375i	−1.17637	+	0.854681i
$987$	−0.228687	−	0.166151i	−0.00727918	−	0.00528863i
$988$	−1.46271	−	4.50176i	−0.0465351	−	0.143220i
$989$	22.0187			0.700153
$990$		0			0
$991$	−27.5747			−0.875938			−0.437969	−	0.898990i	$-0.644302\pi$
$991$	−27.5747			−0.875938			−0.437969	+	0.898990i	$0.644302\pi$
$992$	0.896769	+	2.75997i	0.0284724	+	0.0876292i
$993$	3.49395	+	2.53850i	0.110877	+	0.0805569i
$994$	16.7208	−	12.1484i	0.530352	−	0.385323i
$995$	11.3426	−	34.9089i	0.359584	−	1.10669i
$996$	−0.0246916	+	0.0759928i	−0.000782382	+	0.00240792i
$997$	−19.1613	+	13.9215i	−0.606844	+	0.440898i	−0.848301	−	0.529514i	$-0.822374\pi$
$997$	−19.1613	+	13.9215i	−0.606844	+	0.440898i	0.241458	+	0.970411i	$0.422374\pi$
$998$	−22.7959	−	16.5622i	−0.721593	−	0.524268i
$999$	6.50130	+	20.0089i	0.205692	+	0.633055i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.u.148.2		12
11.2	odd	10		847.2.f.t.372.2		12
11.3	even	5		847.2.a.i.1.2	✓	3
11.4	even	5	inner	847.2.f.u.729.2		12
11.5	even	5	inner	847.2.f.u.323.2		12
11.6	odd	10		847.2.f.t.323.2		12
11.7	odd	10		847.2.f.t.729.2		12
11.8	odd	10		847.2.a.j.1.2	yes	3
11.9	even	5	inner	847.2.f.u.372.2		12
11.10	odd	2		847.2.f.t.148.2		12
33.8	even	10		7623.2.a.bz.1.2		3
33.14	odd	10		7623.2.a.ce.1.2		3
77.41	even	10		5929.2.a.y.1.2		3
77.69	odd	10		5929.2.a.t.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.i.1.2	✓	3	11.3	even	5
847.2.a.j.1.2	yes	3	11.8	odd	10
847.2.f.t.148.2		12	11.10	odd	2
847.2.f.t.323.2		12	11.6	odd	10
847.2.f.t.372.2		12	11.2	odd	10
847.2.f.t.729.2		12	11.7	odd	10
847.2.f.u.148.2		12	1.1	even	1	trivial
847.2.f.u.323.2		12	11.5	even	5	inner
847.2.f.u.372.2		12	11.9	even	5	inner
847.2.f.u.729.2		12	11.4	even	5	inner
5929.2.a.t.1.2		3	77.69	odd	10
5929.2.a.y.1.2		3	77.41	even	10
7623.2.a.bz.1.2		3	33.8	even	10
7623.2.a.ce.1.2		3	33.14	odd	10

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.421292 - 1.29660i) q^{2} +(-0.293939 - 0.213559i) q^{3} +(0.114343 - 0.0830753i) q^{4} +(0.970726 - 2.98759i) q^{5} +(-0.153067 + 0.471092i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-2.36180 - 1.71595i) q^{8} +(-0.886258 - 2.72762i) q^{9} +O(q^{10})\)	\(q+(-0.421292 - 1.29660i) q^{2} +(-0.293939 - 0.213559i) q^{3} +(0.114343 - 0.0830753i) q^{4} +(0.970726 - 2.98759i) q^{5} +(-0.153067 + 0.471092i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-2.36180 - 1.71595i) q^{8} +(-0.886258 - 2.72762i) q^{9} -4.28267 q^{10} -0.0513514 q^{12} +(-1.47649 - 4.54416i) q^{13} +(-1.10296 - 0.801344i) q^{14} +(-0.923360 + 0.670861i) q^{15} +(-1.14254 + 3.51639i) q^{16} +(-1.47649 + 4.54416i) q^{17} +(-3.16327 + 2.29825i) q^{18} +(5.67067 + 4.11998i) q^{19} +(-0.137199 - 0.422254i) q^{20} -0.363328 q^{21} +5.14134 q^{23} +(0.327768 + 1.00877i) q^{24} +(-3.93829 - 2.86133i) q^{25} +(-5.26993 + 3.82883i) q^{26} +(-0.658827 + 2.02766i) q^{27} +(0.0436753 - 0.134419i) q^{28} +(-5.67067 + 4.11998i) q^{29} +(1.25884 + 0.914603i) q^{30} +(-1.12379 - 3.45868i) q^{31} -0.797984 q^{32} +6.51399 q^{34} +(-0.970726 - 2.98759i) q^{35} +(-0.327936 - 0.238259i) q^{36} +(7.98337 - 5.80026i) q^{37} +(2.95297 - 9.08831i) q^{38} +(-0.536449 + 1.65102i) q^{39} +(-7.41920 + 5.39037i) q^{40} +(2.60665 + 1.89384i) q^{41} +(0.153067 + 0.471092i) q^{42} +4.28267 q^{43} -9.00933 q^{45} +(-2.16600 - 6.66627i) q^{46} +(0.629422 + 0.457302i) q^{47} +(1.08679 - 0.789603i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-2.05084 + 6.31185i) q^{50} +(1.40444 - 1.02039i) q^{51} +(-0.546333 - 0.396934i) q^{52} +(0.705385 + 2.17095i) q^{53} +2.90663 q^{54} -2.91934 q^{56} +(-0.786970 - 2.42204i) q^{57} +(7.73098 + 5.61689i) q^{58} +(0.293939 - 0.213559i) q^{59} +(-0.0498482 + 0.153417i) q^{60} +(0.995650 - 3.06430i) q^{61} +(-4.01109 + 2.91423i) q^{62} +(-2.32025 - 1.68576i) q^{63} +(2.62127 + 8.06745i) q^{64} -15.0093 q^{65} -6.59465 q^{67} +(0.208681 + 0.642253i) q^{68} +(-1.51124 - 1.09798i) q^{69} +(-3.46475 + 2.51729i) q^{70} +(-4.68470 + 14.4180i) q^{71} +(-2.58729 + 7.96287i) q^{72} +(2.60665 - 1.89384i) q^{73} +(-10.8840 - 7.90766i) q^{74} +(0.546552 + 1.68211i) q^{75} +0.990671 q^{76} +2.36672 q^{78} +(-1.14872 - 3.53539i) q^{79} +(9.39643 + 6.82691i) q^{80} +(-6.33408 + 4.60198i) q^{81} +(1.35740 - 4.17764i) q^{82} +(0.480835 - 1.47986i) q^{83} +(-0.0415442 + 0.0301836i) q^{84} +(12.1428 + 8.82226i) q^{85} +(-1.80425 - 5.55292i) q^{86} +2.54669 q^{87} -5.58532 q^{89} +(3.79555 + 11.6815i) q^{90} +(-3.86549 - 2.80844i) q^{91} +(0.587877 - 0.427118i) q^{92} +(-0.408306 + 1.25664i) q^{93} +(0.327768 - 1.00877i) q^{94} +(17.8135 - 12.9422i) q^{95} +(0.234558 + 0.170417i) q^{96} +(1.90066 + 5.84963i) q^{97} -1.36333 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + q^{3} - 8 q^{4} - q^{5} + 12 q^{6} + 3 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) \) 12 * q + 2 * q^2 + q^3 - 8 * q^4 - q^5 + 12 * q^6 + 3 * q^7 + 6 * q^8 - 4 * q^9	\( 12 q + 2 q^{2} + q^{3} - 8 q^{4} - q^{5} + 12 q^{6} + 3 q^{7} + 6 q^{8} - 4 q^{9} + 16 q^{10} + 8 q^{12} + 8 q^{13} - 2 q^{14} + 5 q^{15} - 10 q^{16} + 8 q^{17} - 18 q^{18} + 14 q^{20} + 4 q^{21} + 28 q^{23} + 20 q^{24} - 2 q^{25} + 12 q^{26} + 19 q^{27} + 8 q^{28} - 8 q^{30} + 13 q^{31} - 136 q^{32} - 48 q^{34} + q^{35} - 18 q^{36} + 17 q^{37} - 16 q^{38} - 20 q^{39} - 36 q^{40} + 16 q^{41} - 12 q^{42} - 16 q^{43} - 24 q^{45} - 4 q^{47} - 36 q^{48} - 3 q^{49} + 22 q^{50} - 20 q^{51} + 10 q^{53} - 32 q^{54} + 24 q^{56} + 16 q^{57} + 16 q^{58} - q^{59} + 30 q^{60} - 16 q^{61} + 4 q^{62} + 4 q^{63} - 34 q^{64} - 96 q^{65} - 12 q^{67} + 7 q^{69} + 4 q^{70} - 5 q^{71} + 2 q^{72} + 16 q^{73} - 32 q^{74} - 20 q^{75} + 96 q^{76} + 112 q^{78} + 28 q^{79} + 56 q^{80} - 15 q^{81} - 28 q^{82} + 8 q^{83} + 2 q^{84} + 24 q^{85} - 12 q^{86} + 64 q^{87} - 84 q^{89} - 20 q^{90} - 8 q^{91} - 2 q^{92} - 17 q^{93} + 20 q^{94} + 24 q^{95} + 20 q^{96} + 11 q^{97} - 8 q^{98}+O(q^{100}) \) 12 * q + 2 * q^2 + q^3 - 8 * q^4 - q^5 + 12 * q^6 + 3 * q^7 + 6 * q^8 - 4 * q^9 + 16 * q^10 + 8 * q^12 + 8 * q^13 - 2 * q^14 + 5 * q^15 - 10 * q^16 + 8 * q^17 - 18 * q^18 + 14 * q^20 + 4 * q^21 + 28 * q^23 + 20 * q^24 - 2 * q^25 + 12 * q^26 + 19 * q^27 + 8 * q^28 - 8 * q^30 + 13 * q^31 - 136 * q^32 - 48 * q^34 + q^35 - 18 * q^36 + 17 * q^37 - 16 * q^38 - 20 * q^39 - 36 * q^40 + 16 * q^41 - 12 * q^42 - 16 * q^43 - 24 * q^45 - 4 * q^47 - 36 * q^48 - 3 * q^49 + 22 * q^50 - 20 * q^51 + 10 * q^53 - 32 * q^54 + 24 * q^56 + 16 * q^57 + 16 * q^58 - q^59 + 30 * q^60 - 16 * q^61 + 4 * q^62 + 4 * q^63 - 34 * q^64 - 96 * q^65 - 12 * q^67 + 7 * q^69 + 4 * q^70 - 5 * q^71 + 2 * q^72 + 16 * q^73 - 32 * q^74 - 20 * q^75 + 96 * q^76 + 112 * q^78 + 28 * q^79 + 56 * q^80 - 15 * q^81 - 28 * q^82 + 8 * q^83 + 2 * q^84 + 24 * q^85 - 12 * q^86 + 64 * q^87 - 84 * q^89 - 20 * q^90 - 8 * q^91 - 2 * q^92 - 17 * q^93 + 20 * q^94 + 24 * q^95 + 20 * q^96 + 11 * q^97 - 8 * q^98

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