LMFDB - Embedded newform 847.2.f.p.372.1

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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 $ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			372.1
Root			$0.453245 - 1.39494i$ of defining polynomial
Character	$\chi$	$=$	847.372
Dual form			847.2.f.p.148.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453245 + 1.39494i) q^{2} +(1.30902 - 0.951057i) q^{3} +(-0.122406 - 0.0889332i) q^{4} +(0.144228 + 0.443888i) q^{5} +(0.733366 + 2.25707i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-2.19369 + 1.59381i) q^{8} +(-0.118034 + 0.363271i) q^{9} +O(q^{10})$	\(q+(-0.453245 + 1.39494i) q^{2} +(1.30902 - 0.951057i) q^{3} +(-0.122406 - 0.0889332i) q^{4} +(0.144228 + 0.443888i) q^{5} +(0.733366 + 2.25707i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-2.19369 + 1.59381i) q^{8} +(-0.118034 + 0.363271i) q^{9} -0.684570 q^{10} -0.244812 q^{12} +(-0.488963 + 1.50487i) q^{13} +(-1.18661 + 0.862123i) q^{14} +(0.610960 + 0.443888i) q^{15} +(-1.32250 - 4.07025i) q^{16} +(1.61533 + 4.97148i) q^{17} +(-0.453245 - 0.329302i) q^{18} +(-3.41560 + 2.48158i) q^{19} +(0.0218220 - 0.0671613i) q^{20} +1.61803 q^{21} -1.80505 q^{23} +(-1.35577 + 4.17264i) q^{24} +(3.86885 - 2.81088i) q^{25} +(-1.87759 - 1.36415i) q^{26} +(1.69098 + 5.20431i) q^{27} +(-0.0467549 - 0.143897i) q^{28} +(-2.20010 - 1.59846i) q^{29} +(-0.896114 + 0.651065i) q^{30} +(0.399825 - 1.23053i) q^{31} +0.854102 q^{32} -7.66708 q^{34} +(-0.144228 + 0.443888i) q^{35} +(0.0467549 - 0.0339695i) q^{36} +(1.57128 + 1.14160i) q^{37} +(-1.91356 - 5.88935i) q^{38} +(0.791158 + 2.43493i) q^{39} +(-1.02386 - 0.743880i) q^{40} +(0.842285 - 0.611956i) q^{41} +(-0.733366 + 2.25707i) q^{42} +8.70820 q^{43} -0.178276 q^{45} +(0.818132 - 2.51795i) q^{46} +(5.17390 - 3.75906i) q^{47} +(-5.60222 - 4.07025i) q^{48} +(0.309017 + 0.951057i) q^{49} +(2.16749 + 6.67085i) q^{50} +(6.84266 + 4.97148i) q^{51} +(0.193685 - 0.140720i) q^{52} +(-4.08039 + 12.5582i) q^{53} -8.02616 q^{54} -2.71154 q^{56} +(-2.11096 + 6.49687i) q^{57} +(3.22695 - 2.34452i) q^{58} +(6.96069 + 5.05724i) q^{59} +(-0.0353088 - 0.108669i) q^{60} +(-4.70947 - 14.4942i) q^{61} +(1.53531 + 1.11547i) q^{62} +(-0.309017 + 0.224514i) q^{63} +(2.25789 - 6.94907i) q^{64} -0.738517 q^{65} -4.67583 q^{67} +(0.244403 - 0.752196i) q^{68} +(-2.36285 + 1.71671i) q^{69} +(-0.553829 - 0.402380i) q^{70} +(3.01078 + 9.26624i) q^{71} +(-0.320054 - 0.985026i) q^{72} +(10.7761 + 7.82931i) q^{73} +(-2.30464 + 1.67442i) q^{74} +(2.39108 - 7.35899i) q^{75} +0.638786 q^{76} -3.75519 q^{78} +(1.10700 - 3.40699i) q^{79} +(1.61599 - 1.17409i) q^{80} +(6.23607 + 4.53077i) q^{81} +(0.471883 + 1.45231i) q^{82} +(-5.33329 - 16.4142i) q^{83} +(-0.198057 - 0.143897i) q^{84} +(-1.97381 + 1.43405i) q^{85} +(-3.94695 + 12.1475i) q^{86} -4.40020 q^{87} -8.91982 q^{89} +(0.0808026 - 0.248685i) q^{90} +(-1.28012 + 0.930062i) q^{91} +(0.220949 + 0.160529i) q^{92} +(-0.646930 - 1.99105i) q^{93} +(2.89864 + 8.92109i) q^{94} +(-1.59417 - 1.15823i) q^{95} +(1.11803 - 0.812299i) q^{96} +(-0.835464 + 2.57129i) q^{97} -1.46673 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + 6 q^{3} - 7 q^{4} + 3 q^{5} - 2 q^{6} + 2 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - q^2 + 6 * q^3 - 7 * q^4 + 3 * q^5 - 2 * q^6 + 2 * q^7 - 12 * q^8 + 8 * q^9	$ 8 q - q^{2} + 6 q^{3} - 7 q^{4} + 3 q^{5} - 2 q^{6} + 2 q^{7} - 12 q^{8} + 8 q^{9} - 28 q^{10} - 14 q^{12} - 5 q^{13} + q^{14} - 9 q^{15} + 7 q^{16} + 14 q^{17} - q^{18} + 6 q^{19} - 4 q^{20} + 4 q^{21} - 16 q^{23} - 9 q^{24} - 5 q^{25} - 9 q^{26} + 18 q^{27} - 3 q^{28} + 6 q^{29} - 26 q^{30} + 14 q^{31} - 20 q^{32} - 24 q^{34} - 3 q^{35} + 3 q^{36} + q^{37} - 15 q^{38} + 29 q^{40} + 18 q^{41} + 2 q^{42} + 16 q^{43} + 18 q^{45} - 26 q^{46} + 7 q^{47} - q^{48} - 2 q^{49} + q^{50} + 8 q^{51} - 4 q^{52} + 7 q^{53} + 4 q^{54} - 18 q^{56} - 3 q^{57} + 36 q^{58} + 17 q^{60} + 12 q^{61} - 5 q^{62} + 2 q^{63} - 4 q^{64} + 24 q^{65} - 30 q^{67} - 7 q^{68} - 22 q^{69} - 12 q^{70} + 21 q^{71} + 3 q^{72} + 8 q^{73} + q^{74} - 52 q^{76} - 18 q^{78} + q^{79} + 37 q^{80} + 32 q^{81} - 34 q^{82} - 22 q^{83} - 11 q^{84} - 5 q^{85} + 13 q^{86} + 12 q^{87} - 34 q^{89} - 18 q^{90} - 5 q^{91} + 51 q^{92} + 3 q^{93} + 50 q^{94} - 41 q^{95} - 15 q^{97} + 4 q^{98}+O(q^{100}) $ 8 * q - q^2 + 6 * q^3 - 7 * q^4 + 3 * q^5 - 2 * q^6 + 2 * q^7 - 12 * q^8 + 8 * q^9 - 28 * q^10 - 14 * q^12 - 5 * q^13 + q^14 - 9 * q^15 + 7 * q^16 + 14 * q^17 - q^18 + 6 * q^19 - 4 * q^20 + 4 * q^21 - 16 * q^23 - 9 * q^24 - 5 * q^25 - 9 * q^26 + 18 * q^27 - 3 * q^28 + 6 * q^29 - 26 * q^30 + 14 * q^31 - 20 * q^32 - 24 * q^34 - 3 * q^35 + 3 * q^36 + q^37 - 15 * q^38 + 29 * q^40 + 18 * q^41 + 2 * q^42 + 16 * q^43 + 18 * q^45 - 26 * q^46 + 7 * q^47 - q^48 - 2 * q^49 + q^50 + 8 * q^51 - 4 * q^52 + 7 * q^53 + 4 * q^54 - 18 * q^56 - 3 * q^57 + 36 * q^58 + 17 * q^60 + 12 * q^61 - 5 * q^62 + 2 * q^63 - 4 * q^64 + 24 * q^65 - 30 * q^67 - 7 * q^68 - 22 * q^69 - 12 * q^70 + 21 * q^71 + 3 * q^72 + 8 * q^73 + q^74 - 52 * q^76 - 18 * q^78 + q^79 + 37 * q^80 + 32 * q^81 - 34 * q^82 - 22 * q^83 - 11 * q^84 - 5 * q^85 + 13 * q^86 + 12 * q^87 - 34 * q^89 - 18 * q^90 - 5 * q^91 + 51 * q^92 + 3 * q^93 + 50 * q^94 - 41 * q^95 - 15 * q^97 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.453245	+	1.39494i	−0.320493	+	0.986375i	0.652942	+	0.757408i	$0.273535\pi$
$2$	−0.453245	+	1.39494i	−0.320493	+	0.986375i	−0.973434	+	0.228967i	$0.926465\pi$
$3$	1.30902	−	0.951057i	0.755761	−	0.549093i	−0.141846	−	0.989889i	$-0.545304\pi$
$3$	1.30902	−	0.951057i	0.755761	−	0.549093i	0.897607	+	0.440796i	$0.145304\pi$
$4$	−0.122406	−	0.0889332i	−0.0612030	−	0.0444666i
$5$	0.144228	+	0.443888i	0.0645007	+	0.198513i	0.978113	−	0.208073i	$-0.0667192\pi$
$5$	0.144228	+	0.443888i	0.0645007	+	0.198513i	−0.913613	+	0.406586i	$0.866719\pi$
$6$	0.733366	+	2.25707i	0.299395	+	0.921444i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$8$	−2.19369	+	1.59381i	−0.775585	+	0.563495i
$9$	−0.118034	+	0.363271i	−0.0393447	+	0.121090i
$10$	−0.684570			−0.216480
$11$		0			0
$11$		0			0
$12$	−0.244812			−0.0706712
$13$	−0.488963	+	1.50487i	−0.135614	+	0.417376i	−0.995685	−	0.0927976i	$-0.970419\pi$
$13$	−0.488963	+	1.50487i	−0.135614	+	0.417376i	0.860071	+	0.510174i	$0.170419\pi$
$14$	−1.18661	+	0.862123i	−0.317135	+	0.230412i
$15$	0.610960	+	0.443888i	0.157749	+	0.114611i
$16$	−1.32250	−	4.07025i	−0.330626	−	1.01756i
$17$	1.61533	+	4.97148i	0.391776	+	1.20576i	0.931444	+	0.363884i	$0.118549\pi$
$17$	1.61533	+	4.97148i	0.391776	+	1.20576i	−0.539669	+	0.841877i	$0.681451\pi$
$18$	−0.453245	−	0.329302i	−0.106831	−	0.0776172i
$19$	−3.41560	+	2.48158i	−0.783593	+	0.569314i	−0.906055	−	0.423159i	$-0.860921\pi$
$19$	−3.41560	+	2.48158i	−0.783593	+	0.569314i	0.122462	+	0.992473i	$0.460921\pi$
$20$	0.0218220	−	0.0671613i	0.00487955	−	0.0150177i
$21$	1.61803			0.353084
$22$		0			0
$23$	−1.80505			−0.376380			−0.188190	−	0.982133i	$-0.560262\pi$
$23$	−1.80505			−0.376380			−0.188190	+	0.982133i	$0.560262\pi$
$24$	−1.35577	+	4.17264i	−0.276746	+	0.851736i
$25$	3.86885	−	2.81088i	0.773770	−	0.562177i
$26$	−1.87759	−	1.36415i	−0.368226	−	0.267532i
$27$	1.69098	+	5.20431i	0.325430	+	1.00157i
$28$	−0.0467549	−	0.143897i	−0.00883585	−	0.0271940i
$29$	−2.20010	−	1.59846i	−0.408548	−	0.296827i	0.364466	−	0.931217i	$-0.381252\pi$
$29$	−2.20010	−	1.59846i	−0.408548	−	0.296827i	−0.773014	+	0.634389i	$0.781252\pi$
$30$	−0.896114	+	0.651065i	−0.163607	+	0.118868i
$31$	0.399825	−	1.23053i	0.0718107	−	0.221010i	−0.908709	−	0.417429i	$-0.862931\pi$
$31$	0.399825	−	1.23053i	0.0718107	−	0.221010i	0.980520	+	0.196419i	$0.0629312\pi$
$32$	0.854102			0.150985
$33$		0			0
$34$	−7.66708			−1.31489
$35$	−0.144228	+	0.443888i	−0.0243790	+	0.0750308i
$36$	0.0467549	−	0.0339695i	0.00779249	−	0.00566158i
$37$	1.57128	+	1.14160i	0.258317	+	0.187678i	0.709405	−	0.704801i	$-0.248964\pi$
$37$	1.57128	+	1.14160i	0.258317	+	0.187678i	−0.451088	+	0.892480i	$0.648964\pi$
$38$	−1.91356	−	5.88935i	−0.310421	−	0.955378i
$39$	0.791158	+	2.43493i	0.126687	+	0.389902i
$40$	−1.02386	−	0.743880i	−0.161887	−	0.117618i
$41$	0.842285	−	0.611956i	0.131543	−	0.0955715i	−0.520068	−	0.854125i	$-0.674093\pi$
$41$	0.842285	−	0.611956i	0.131543	−	0.0955715i	0.651611	+	0.758553i	$0.274093\pi$
$42$	−0.733366	+	2.25707i	−0.113161	+	0.348273i
$43$	8.70820			1.32799			0.663994	−	0.747738i	$-0.268860\pi$
$43$	8.70820			1.32799			0.663994	+	0.747738i	$0.268860\pi$
$44$		0			0
$45$	−0.178276			−0.0265758
$46$	0.818132	−	2.51795i	0.120627	−	0.371252i
$47$	5.17390	−	3.75906i	0.754691	−	0.548315i	−0.142586	−	0.989782i	$-0.545542\pi$
$47$	5.17390	−	3.75906i	0.754691	−	0.548315i	0.897277	+	0.441467i	$0.145542\pi$
$48$	−5.60222	−	4.07025i	−0.808610	−	0.587490i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	2.16749	+	6.67085i	0.306530	+	0.943401i
$51$	6.84266	+	4.97148i	0.958163	+	0.696147i
$52$	0.193685	−	0.140720i	0.0268593	−	0.0195144i
$53$	−4.08039	+	12.5582i	−0.560485	+	1.72500i	0.120514	+	0.992712i	$0.461546\pi$
$53$	−4.08039	+	12.5582i	−0.560485	+	1.72500i	−0.680999	+	0.732284i	$0.738454\pi$
$54$	−8.02616			−1.09222
$55$		0			0
$56$	−2.71154			−0.362345
$57$	−2.11096	+	6.49687i	−0.279603	+	0.860531i
$58$	3.22695	−	2.34452i	0.423720	−	0.307850i
$59$	6.96069	+	5.05724i	0.906205	+	0.658396i	0.940052	−	0.341031i	$-0.110776\pi$
$59$	6.96069	+	5.05724i	0.906205	+	0.658396i	−0.0338475	+	0.999427i	$0.510776\pi$
$60$	−0.0353088	−	0.108669i	−0.00455834	−	0.0140291i
$61$	−4.70947	−	14.4942i	−0.602985	−	1.85580i	−0.510089	−	0.860122i	$-0.670387\pi$
$61$	−4.70947	−	14.4942i	−0.602985	−	1.85580i	−0.0928967	−	0.995676i	$-0.529613\pi$
$62$	1.53531	+	1.11547i	0.194984	+	0.141664i
$63$	−0.309017	+	0.224514i	−0.0389325	+	0.0282861i
$64$	2.25789	−	6.94907i	0.282236	−	0.868634i
$65$	−0.738517			−0.0916018
$66$		0			0
$67$	−4.67583			−0.571243			−0.285622	−	0.958342i	$-0.592200\pi$
$67$	−4.67583			−0.571243			−0.285622	+	0.958342i	$0.592200\pi$
$68$	0.244403	−	0.752196i	0.0296382	−	0.0912171i
$69$	−2.36285	+	1.71671i	−0.284453	+	0.206667i
$70$	−0.553829	−	0.402380i	−0.0661952	−	0.0480937i
$71$	3.01078	+	9.26624i	0.357314	+	1.09970i	0.954655	+	0.297713i	$0.0962239\pi$
$71$	3.01078	+	9.26624i	0.357314	+	1.09970i	−0.597341	+	0.801987i	$0.703776\pi$
$72$	−0.320054	−	0.985026i	−0.0377188	−	0.116086i
$73$	10.7761	+	7.82931i	1.26125	+	0.916351i	0.998818	−	0.0485994i	$-0.0154758\pi$
$73$	10.7761	+	7.82931i	1.26125	+	0.916351i	0.262431	+	0.964951i	$0.415476\pi$
$74$	−2.30464	+	1.67442i	−0.267910	+	0.194648i
$75$	2.39108	−	7.35899i	0.276098	−	0.849743i
$76$	0.638786			0.0732737
$77$		0			0
$78$	−3.75519			−0.425191
$79$	1.10700	−	3.40699i	0.124547	−	0.383316i	−0.869271	−	0.494335i	$-0.835412\pi$
$79$	1.10700	−	3.40699i	0.124547	−	0.383316i	0.993818	+	0.111019i	$0.0354116\pi$
$80$	1.61599	−	1.17409i	0.180674	−	0.131267i
$81$	6.23607	+	4.53077i	0.692896	+	0.503419i
$82$	0.471883	+	1.45231i	0.0521108	+	0.160381i
$83$	−5.33329	−	16.4142i	−0.585404	−	1.80169i	−0.597640	−	0.801765i	$-0.703895\pi$
$83$	−5.33329	−	16.4142i	−0.585404	−	1.80169i	0.0122356	−	0.999925i	$-0.496105\pi$
$84$	−0.198057	−	0.143897i	−0.0216098	−	0.0157004i
$85$	−1.97381	+	1.43405i	−0.214089	+	0.155545i
$86$	−3.94695	+	12.1475i	−0.425611	+	1.30989i
$87$	−4.40020			−0.471750
$88$		0			0
$89$	−8.91982			−0.945499			−0.472750	−	0.881197i	$-0.656738\pi$
$89$	−8.91982			−0.945499			−0.472750	+	0.881197i	$0.656738\pi$
$90$	0.0808026	−	0.248685i	0.00851734	−	0.0262137i
$91$	−1.28012	+	0.930062i	−0.134193	+	0.0974970i
$92$	0.220949	+	0.160529i	0.0230356	+	0.0167363i
$93$	−0.646930	−	1.99105i	−0.0670835	−	0.206462i
$94$	2.89864	+	8.92109i	0.298972	+	0.920140i
$95$	−1.59417	−	1.15823i	−0.163559	−	0.118832i
$96$	1.11803	−	0.812299i	0.114109	−	0.0829049i
$97$	−0.835464	+	2.57129i	−0.0848285	+	0.261075i	−0.984470	−	0.175555i	$-0.943828\pi$
$97$	−0.835464	+	2.57129i	−0.0848285	+	0.261075i	0.899641	+	0.436630i	$0.143828\pi$
$98$	−1.46673			−0.148162
$99$		0			0
$100$	−0.723551			−0.0723551
$101$	0.0552464	−	0.170031i	0.00549722	−	0.0169187i	−0.948270	−	0.317464i	$-0.897169\pi$
$101$	0.0552464	−	0.170031i	0.00549722	−	0.0169187i	0.953768	+	0.300545i	$0.0971687\pi$
$102$	−10.0363	+	7.29183i	−0.993746	+	0.721999i
$103$	−13.6540	−	9.92019i	−1.34537	−	0.977465i	−0.999228	−	0.0392811i	$-0.987493\pi$
$103$	−13.6540	−	9.92019i	−1.34537	−	0.977465i	−0.346137	−	0.938184i	$-0.612507\pi$
$104$	−1.32584	−	4.08053i	−0.130010	−	0.400129i
$105$	0.233366	+	0.718226i	0.0227742	+	0.0700917i
$106$	−15.6685	−	11.3838i	−1.52186	−	1.10570i
$107$	12.5205	−	9.09669i	1.21040	−	0.879410i	0.215137	−	0.976584i	$-0.430980\pi$
$107$	12.5205	−	9.09669i	1.21040	−	0.879410i	0.995267	+	0.0971734i	$0.0309801\pi$
$108$	0.255849	−	0.787424i	0.0246191	−	0.0757699i
$109$	11.0349			1.05695			0.528476	−	0.848948i	$-0.322764\pi$
$109$	11.0349			1.05695			0.528476	+	0.848948i	$0.322764\pi$
$110$		0			0
$111$	3.14256			0.298278
$112$	1.32250	−	4.07025i	0.124965	−	0.384602i
$113$	−1.43202	+	1.04043i	−0.134713	+	0.0978750i	−0.653101	−	0.757271i	$-0.726532\pi$
$113$	−1.43202	+	1.04043i	−0.134713	+	0.0978750i	0.518388	+	0.855146i	$0.326532\pi$
$114$	−8.10599	−	5.88935i	−0.759195	−	0.551588i
$115$	−0.260339	−	0.801242i	−0.0242768	−	0.0747162i
$116$	0.127149	+	0.391323i	0.0118055	+	0.0363335i
$117$	−0.488963	−	0.355252i	−0.0452046	−	0.0328431i
$118$	−10.2095	+	7.41761i	−0.939857	+	0.682846i
$119$	−1.61533	+	4.97148i	−0.148077	+	0.455735i
$120$	−2.04773			−0.186931
$121$		0			0
$122$	22.3532			2.02376
$123$	0.520561	−	1.60212i	0.0469374	−	0.144458i
$124$	−0.158376	+	0.115067i	−0.0142226	+	0.0103333i
$125$	3.69369	+	2.68362i	0.330373	+	0.240030i
$126$	−0.173124	−	0.532822i	−0.0154231	−	0.0474675i
$127$	−2.63908	−	8.12224i	−0.234180	−	0.720732i	−0.997229	−	0.0743917i	$-0.976298\pi$
$127$	−2.63908	−	8.12224i	−0.234180	−	0.720732i	0.763049	−	0.646341i	$-0.223702\pi$
$128$	10.0522	+	7.30332i	0.888494	+	0.645528i
$129$	11.3992	−	8.28199i	1.00364	−	0.729189i
$130$	0.334729	−	1.03019i	0.0293577	−	0.0903537i
$131$	−9.66708			−0.844617			−0.422308	−	0.906452i	$-0.638780\pi$
$131$	−9.66708			−0.844617			−0.422308	+	0.906452i	$0.638780\pi$
$132$		0			0
$133$	−4.22192			−0.366087
$134$	2.11930	−	6.52252i	0.183079	−	0.563460i
$135$	−2.06625	+	1.50122i	−0.177834	+	0.129204i
$136$	−11.4671	−	8.33134i	−0.983296	−	0.714406i
$137$	−4.32958	−	13.3251i	−0.369901	−	1.13844i	−0.946855	−	0.321661i	$-0.895759\pi$
$137$	−4.32958	−	13.3251i	−0.369901	−	1.13844i	0.576954	−	0.816777i	$-0.304241\pi$
$138$	−1.32376	−	4.07413i	−0.112686	−	0.346813i
$139$	−7.74848	−	5.62960i	−0.657218	−	0.477497i	0.208504	−	0.978021i	$-0.433140\pi$
$139$	−7.74848	−	5.62960i	−0.657218	−	0.477497i	−0.865722	+	0.500525i	$0.833140\pi$
$140$	0.0571308	−	0.0415079i	0.00482843	−	0.00350806i
$141$	3.19765	−	9.84135i	0.269291	−	0.828791i
$142$	−14.2905			−1.19923
$143$		0			0
$144$	1.63470			0.136225
$145$	0.392224	−	1.20714i	0.0325724	−	0.100248i
$146$	−15.8057	+	11.4835i	−1.30809	+	0.950381i
$147$	1.30902	+	0.951057i	0.107966	+	0.0784418i
$148$	−0.0908078	−	0.279478i	−0.00746436	−	0.0229729i
$149$	4.62367	+	14.2302i	0.378786	+	1.16578i	0.940889	+	0.338715i	$0.109992\pi$
$149$	4.62367	+	14.2302i	0.378786	+	1.16578i	−0.562103	+	0.827067i	$0.690008\pi$
$150$	9.18164	+	6.67085i	0.749678	+	0.544673i
$151$	2.32376	−	1.68831i	0.189105	−	0.137393i	−0.489204	−	0.872169i	$-0.662713\pi$
$151$	2.32376	−	1.68831i	0.189105	−	0.137393i	0.678310	+	0.734776i	$0.262713\pi$
$152$	3.53760	−	10.8876i	0.286937	−	0.883103i
$153$	−1.99666			−0.161420
$154$		0			0
$155$	0.603886			0.0485053
$156$	0.119704	−	0.368411i	0.00958399	−	0.0294965i
$157$	15.2761	−	11.0988i	1.21917	−	0.885777i	0.223136	−	0.974787i	$-0.428370\pi$
$157$	15.2761	−	11.0988i	1.21917	−	0.885777i	0.996031	+	0.0890105i	$0.0283705\pi$
$158$	4.25082	+	3.08840i	0.338177	+	0.245700i
$159$	6.60222	+	20.3195i	0.523590	+	1.61144i
$160$	0.123185	+	0.379126i	0.00973867	+	0.0299725i
$161$	−1.46032	−	1.06098i	−0.115089	−	0.0836173i
$162$	−9.14664	+	6.64542i	−0.718628	+	0.522114i
$163$	3.58310	−	11.0276i	0.280650	−	0.863751i	−0.707019	−	0.707194i	$-0.749961\pi$
$163$	3.58310	−	11.0276i	0.280650	−	0.863751i	0.987669	−	0.156557i	$-0.0500394\pi$
$164$	−0.157524			−0.0123006
$165$		0			0
$166$	25.3142			1.96476
$167$	1.95451	−	6.01535i	0.151244	−	0.465482i	−0.846517	−	0.532362i	$-0.821305\pi$
$167$	1.95451	−	6.01535i	0.151244	−	0.465482i	0.997761	+	0.0668802i	$0.0213045\pi$
$168$	−3.54946	+	2.57883i	−0.273847	+	0.198961i
$169$	8.49166	+	6.16956i	0.653205	+	0.474581i
$170$	−1.10581	−	3.40333i	−0.0848116	−	0.261023i
$171$	−0.498330	−	1.53370i	−0.0381082	−	0.117285i
$172$	−1.06594	−	0.774448i	−0.0812769	−	0.0590511i
$173$	−1.08332	+	0.787082i	−0.0823637	+	0.0598407i	−0.628205	−	0.778048i	$-0.716210\pi$
$173$	−1.08332	+	0.787082i	−0.0823637	+	0.0598407i	0.545841	+	0.837889i	$0.316210\pi$
$174$	1.99437	−	6.13803i	0.151193	−	0.465323i
$175$	4.78216			0.361497
$176$		0			0
$177$	13.9214			1.04639
$178$	4.04286	−	12.4427i	0.303026	−	0.932617i
$179$	−14.3915	+	10.4560i	−1.07567	+	0.781518i	−0.976922	−	0.213595i	$-0.931483\pi$
$179$	−14.3915	+	10.4560i	−1.07567	+	0.781518i	−0.0987452	+	0.995113i	$0.531483\pi$
$180$	0.0218220	+	0.0158546i	0.00162652	+	0.00118173i
$181$	−0.297823	−	0.916606i	−0.0221370	−	0.0681308i	0.939378	−	0.342884i	$-0.111404\pi$
$181$	−0.297823	−	0.916606i	−0.0221370	−	0.0681308i	−0.961515	+	0.274753i	$0.911404\pi$
$182$	−0.717177	−	2.20724i	−0.0531607	−	0.163612i
$183$	−19.9496	−	14.4942i	−1.47472	−	1.07145i
$184$	3.95972	−	2.87690i	0.291914	−	0.212088i
$185$	−0.280121	+	0.862123i	−0.0205949	+	0.0633846i
$186$	3.07062			0.225149
$187$		0			0
$188$	−0.967622			−0.0705711
$189$	−1.69098	+	5.20431i	−0.123001	+	0.378558i
$190$	2.33822	−	1.69882i	0.169632	−	0.123245i
$191$	13.0162	+	9.45679i	0.941816	+	0.684269i	0.948857	−	0.315706i	$-0.102241\pi$
$191$	13.0162	+	9.45679i	0.941816	+	0.684269i	−0.00704142	+	0.999975i	$0.502241\pi$
$192$	−3.65334	−	11.2438i	−0.263657	−	0.811454i
$193$	3.75377	+	11.5529i	0.270202	+	0.831597i	0.990449	+	0.137879i	$0.0440286\pi$
$193$	3.75377	+	11.5529i	0.270202	+	0.831597i	−0.720247	+	0.693718i	$0.755971\pi$
$194$	−3.20814	−	2.33085i	−0.230331	−	0.167345i
$195$	−0.966732	+	0.702372i	−0.0692291	+	0.0502979i
$196$	0.0467549	−	0.143897i	0.00333964	−	0.0102784i
$197$	−2.30179			−0.163996			−0.0819978	−	0.996633i	$-0.526130\pi$
$197$	−2.30179			−0.163996			−0.0819978	+	0.996633i	$0.526130\pi$
$198$		0			0
$199$	20.2797			1.43759			0.718795	−	0.695222i	$-0.244694\pi$
$199$	20.2797			1.43759			0.718795	+	0.695222i	$0.244694\pi$
$200$	−4.00704	+	12.3324i	−0.283340	+	0.872032i
$201$	−6.12074	+	4.44698i	−0.431723	+	0.313665i
$202$	0.212144	+	0.154131i	0.0149264	+	0.0108446i
$203$	−0.840363	−	2.58637i	−0.0589819	−	0.181528i
$204$	−0.395453	−	1.21708i	−0.0276872	−	0.0852125i
$205$	0.393121	+	0.285619i	0.0274568	+	0.0199485i
$206$	20.0267	−	14.5503i	1.39533	−	1.01376i
$207$	0.213058	−	0.655724i	0.0148085	−	0.0455760i
$208$	6.77186			0.469544
$209$		0			0
$210$	−1.10766			−0.0764357
$211$	1.65797	−	5.10270i	0.114139	−	0.351284i	−0.877627	−	0.479344i	$-0.840875\pi$
$211$	1.65797	−	5.10270i	0.114139	−	0.351284i	0.991767	+	0.128059i	$0.0408748\pi$
$212$	1.61630	−	1.17431i	0.111008	−	0.0806521i
$213$	12.7539	+	9.26624i	0.873882	+	0.634912i
$214$	7.01452	+	21.5885i	0.479503	+	1.47576i
$215$	1.25597	+	3.86547i	0.0856563	+	0.263623i
$216$	−12.0041	−	8.72152i	−0.816778	−	0.593424i
$217$	1.04675	−	0.760512i	0.0710584	−	0.0516269i
$218$	−5.00151	+	15.3931i	−0.338745	+	1.04255i
$219$	21.5522			1.45637
$220$		0			0
$221$	−8.27128			−0.556387
$222$	−1.42435	+	4.38370i	−0.0955960	+	0.294214i
$223$	20.5676	−	14.9433i	1.37731	−	1.00068i	0.380186	−	0.924910i	$-0.375860\pi$
$223$	20.5676	−	14.9433i	1.37731	−	1.00068i	0.997126	−	0.0757654i	$-0.0241400\pi$
$224$	0.690983	+	0.502029i	0.0461682	+	0.0335432i
$225$	0.564458	+	1.73722i	0.0376305	+	0.115815i
$226$	−0.802279	−	2.46916i	−0.0533668	−	0.164246i
$227$	17.5636	+	12.7607i	1.16573	+	0.846956i	0.990492	−	0.137569i	$-0.0439290\pi$
$227$	17.5636	+	12.7607i	1.16573	+	0.846956i	0.175243	+	0.984525i	$0.443929\pi$
$228$	0.836181	−	0.607521i	0.0553775	−	0.0402341i
$229$	6.34433	−	19.5258i	0.419245	−	1.29030i	−0.489154	−	0.872198i	$-0.662694\pi$
$229$	6.34433	−	19.5258i	0.419245	−	1.29030i	0.908399	−	0.418105i	$-0.137306\pi$
$230$	1.23569			0.0814787
$231$		0			0
$232$	7.37396			0.484124
$233$	0.214475	−	0.660086i	0.0140507	−	0.0432437i	−0.943785	−	0.330559i	$-0.892763\pi$
$233$	0.214475	−	0.660086i	0.0140507	−	0.0432437i	0.957836	+	0.287315i	$0.0927627\pi$
$234$	0.717177	−	0.521060i	0.0468833	−	0.0340627i
$235$	2.41483	+	1.75447i	0.157526	+	0.114449i
$236$	−0.402274	−	1.23807i	−0.0261858	−	0.0805917i
$237$	−1.79116	−	5.51262i	−0.116348	−	0.358083i
$238$	−6.20280	−	4.50660i	−0.402068	−	0.292119i
$239$	−0.280374	+	0.203703i	−0.0181359	+	0.0131765i	−0.596816	−	0.802378i	$-0.703568\pi$
$239$	−0.280374	+	0.203703i	−0.0181359	+	0.0131765i	0.578680	+	0.815554i	$0.303568\pi$
$240$	0.998739	−	3.07380i	0.0644683	−	0.198413i
$241$	−10.4372			−0.672317			−0.336158	−	0.941806i	$-0.609128\pi$
$241$	−10.4372			−0.672317			−0.336158	+	0.941806i	$0.609128\pi$
$242$		0			0
$243$	−3.94427			−0.253025
$244$	−0.712552	+	2.19301i	−0.0456165	+	0.140393i
$245$	−0.377594	+	0.274338i	−0.0241236	+	0.0175268i
$246$	1.99893	+	1.45231i	0.127447	+	0.0925957i
$247$	−2.06436	−	6.35345i	−0.131352	−	0.404260i
$248$	1.08414	+	3.33665i	0.0688431	+	0.211877i
$249$	−22.5922	−	16.4142i	−1.43172	−	1.04021i
$250$	−5.41765	+	3.93615i	−0.342642	+	0.248944i
$251$	−2.16158	+	6.65266i	−0.136438	+	0.419912i	−0.995811	−	0.0914367i	$-0.970854\pi$
$251$	−2.16158	+	6.65266i	−0.136438	+	0.419912i	0.859373	+	0.511349i	$0.170854\pi$
$252$	0.0577923			0.00364057
$253$		0			0
$254$	12.5262			0.785965
$255$	−1.21988	+	3.75440i	−0.0763918	+	0.235110i
$256$	−2.92136	+	2.12249i	−0.182585	+	0.132656i
$257$	8.04845	+	5.84754i	0.502048	+	0.364760i	0.809799	−	0.586708i	$-0.199576\pi$
$257$	8.04845	+	5.84754i	0.502048	+	0.364760i	−0.307750	+	0.951467i	$0.599576\pi$
$258$	6.38630	+	19.6550i	0.397594	+	1.22367i
$259$	0.600175	+	1.84715i	0.0372931	+	0.114776i
$260$	0.0903990	+	0.0656787i	0.00560631	+	0.00407322i
$261$	0.840363	−	0.610559i	0.0520171	−	0.0377927i
$262$	4.38156	−	13.4850i	0.270694	−	0.833109i
$263$	14.1803			0.874397			0.437199	−	0.899365i	$-0.355971\pi$
$263$	14.1803			0.874397			0.437199	+	0.899365i	$0.355971\pi$
$264$		0			0
$265$	−6.16293			−0.378586
$266$	1.91356	−	5.88935i	0.117328	−	0.361099i
$267$	−11.6762	+	8.48325i	−0.714572	+	0.519167i
$268$	0.572349	+	0.415836i	0.0349618	+	0.0254012i
$269$	−5.68686	−	17.5024i	−0.346734	−	1.06714i	−0.960649	−	0.277766i	$-0.910406\pi$
$269$	−5.68686	−	17.5024i	−0.346734	−	1.06714i	0.613915	−	0.789372i	$-0.289594\pi$
$270$	−1.15760	−	3.56272i	−0.0704491	−	0.216820i
$271$	−0.591060	−	0.429431i	−0.0359044	−	0.0260861i	0.569688	−	0.821861i	$-0.307064\pi$
$271$	−0.591060	−	0.429431i	−0.0359044	−	0.0260861i	−0.605593	+	0.795775i	$0.707064\pi$
$272$	18.0989	−	13.1496i	1.09741	−	0.797312i
$273$	−0.791158	+	2.43493i	−0.0478831	+	0.147369i
$274$	20.5501			1.24148
$275$		0			0
$276$	0.441899			0.0265992
$277$	4.65515	−	14.3271i	0.279701	−	0.860832i	−0.708236	−	0.705976i	$-0.750509\pi$
$277$	4.65515	−	14.3271i	0.279701	−	0.860832i	0.987937	−	0.154856i	$-0.0494913\pi$
$278$	11.3649	−	8.25712i	0.681624	−	0.495229i
$279$	0.399825	+	0.290490i	0.0239369	+	0.0173912i
$280$	−0.391081	−	1.20362i	−0.0233715	−	0.0719302i
$281$	−3.30528	−	10.1726i	−0.197177	−	0.606847i	−0.999944	−	0.0105553i	$-0.996640\pi$
$281$	−3.30528	−	10.1726i	−0.197177	−	0.606847i	0.802768	−	0.596292i	$-0.203360\pi$
$282$	12.2788	+	8.92109i	0.731193	+	0.531243i
$283$	−7.36926	+	5.35408i	−0.438057	+	0.318267i	−0.784862	−	0.619670i	$-0.787266\pi$
$283$	−7.36926	+	5.35408i	−0.438057	+	0.318267i	0.346805	+	0.937937i	$0.387266\pi$
$284$	0.455538	−	1.40200i	0.0270312	−	0.0831936i
$285$	−3.18834			−0.188861
$286$		0			0
$287$	1.04112			0.0614555
$288$	−0.100813	+	0.310271i	−0.00594047	+	0.0182829i
$289$	−8.35303	+	6.06883i	−0.491355	+	0.356990i
$290$	1.50612	+	1.09426i	0.0884425	+	0.0642572i
$291$	1.35181	+	4.16044i	0.0792444	+	0.243889i
$292$	−0.622777	−	1.91671i	−0.0364452	−	0.112167i
$293$	−9.61840	−	6.98818i	−0.561913	−	0.408254i	0.270245	−	0.962791i	$-0.412895\pi$
$293$	−9.61840	−	6.98818i	−0.561913	−	0.408254i	−0.832159	+	0.554538i	$0.812895\pi$
$294$	−1.91998	+	1.39494i	−0.111975	+	0.0813548i
$295$	−1.24092	+	3.81916i	−0.0722493	+	0.222360i
$296$	−5.26638			−0.306102
$297$		0			0
$298$	−21.9460			−1.27130
$299$	0.882604	−	2.71638i	0.0510423	−	0.157092i
$300$	−0.947141	+	0.688138i	−0.0546832	+	0.0397297i
$301$	7.04508	+	5.11855i	0.406072	+	0.295029i
$302$	1.30187	+	4.00674i	0.0749142	+	0.230562i
$303$	−0.0893905	−	0.275116i	−0.00513535	−	0.0158050i
$304$	14.6178	+	10.6205i	0.838389	+	0.609125i
$305$	5.75459	−	4.18095i	0.329507	−	0.239401i
$306$	0.904976	−	2.78523i	0.0517341	−	0.159221i
$307$	2.22072			0.126743			0.0633716	−	0.997990i	$-0.479815\pi$
$307$	2.22072			0.126743			0.0633716	+	0.997990i	$0.479815\pi$
$308$		0			0
$309$	−27.3079			−1.55349
$310$	−0.273708	+	0.842387i	−0.0155456	+	0.0478444i
$311$	17.3231	−	12.5860i	0.982304	−	0.713686i	0.0240820	−	0.999710i	$-0.492334\pi$
$311$	17.3231	−	12.5860i	0.982304	−	0.713686i	0.958222	+	0.286024i	$0.0923337\pi$
$312$	−5.61636	−	4.08053i	−0.317964	−	0.231014i
$313$	−9.75096	−	30.0104i	−0.551157	−	1.69629i	−0.705883	−	0.708329i	$-0.749450\pi$
$313$	−9.75096	−	30.0104i	−0.551157	−	1.69629i	0.154726	−	0.987957i	$-0.450550\pi$
$314$	8.55832	+	26.3398i	0.482974	+	1.48644i
$315$	−0.144228	−	0.104788i	−0.00812633	−	0.00590412i
$316$	−0.438497	+	0.318587i	−0.0246674	+	0.0179219i
$317$	−4.07923	+	12.5546i	−0.229112	+	0.705135i	0.768736	+	0.639567i	$0.220886\pi$
$317$	−4.07923	+	12.5546i	−0.229112	+	0.705135i	−0.997848	+	0.0655687i	$0.979114\pi$
$318$	−31.3370			−1.75729
$319$		0			0
$320$	3.41026			0.190639
$321$	7.73811	−	23.8154i	0.431899	−	1.32925i
$322$	2.14190	−	1.55618i	0.119363	−	0.0867225i
$323$	−17.8545	−	12.9720i	−0.993449	−	0.721783i
$324$	−0.360397	−	1.10919i	−0.0200220	−	0.0616215i
$325$	2.33830	+	7.19654i	0.129705	+	0.399192i
$326$	13.7589	+	9.99644i	0.762036	+	0.553652i
$327$	14.4449	−	10.4948i	0.798803	−	0.580365i
$328$	−0.872370	+	2.68488i	−0.0481686	+	0.148248i
$329$	6.39530			0.352584
$330$		0			0
$331$	9.47653			0.520877			0.260439	−	0.965490i	$-0.416133\pi$
$331$	9.47653			0.520877			0.260439	+	0.965490i	$0.416133\pi$
$332$	−0.806938	+	2.48350i	−0.0442865	+	0.136300i
$333$	−0.600175	+	0.436053i	−0.0328894	+	0.0238955i
$334$	7.50521	+	5.45286i	0.410667	+	0.298367i
$335$	−0.674385	−	2.07554i	−0.0368456	−	0.113399i
$336$	−2.13986	−	6.58580i	−0.116739	−	0.359285i
$337$	15.5340	+	11.2861i	0.846191	+	0.614794i	0.924093	−	0.382167i	$-0.124822\pi$
$337$	15.5340	+	11.2861i	0.846191	+	0.614794i	−0.0779019	+	0.996961i	$0.524822\pi$
$338$	−12.4550	+	9.04908i	−0.677462	+	0.492205i
$339$	−0.885039	+	2.72387i	−0.0480687	+	0.147940i
$340$	0.369141			0.0200195
$341$		0			0
$342$	2.36530			0.127901
$343$	−0.309017	+	0.951057i	−0.0166853	+	0.0513522i
$344$	−19.1031	+	13.8792i	−1.02997	+	0.748315i
$345$	−1.10282	−	0.801242i	−0.0593736	−	0.0431374i
$346$	−0.606924	−	1.86792i	−0.0326284	−	0.100420i
$347$	0.941979	+	2.89911i	0.0505681	+	0.155632i	0.973152	−	0.230165i	$-0.0739265\pi$
$347$	0.941979	+	2.89911i	0.0505681	+	0.155632i	−0.922584	+	0.385797i	$0.873926\pi$
$348$	0.538610	+	0.391323i	0.0288726	+	0.0209771i
$349$	−15.6918	+	11.4007i	−0.839962	+	0.610268i	−0.922360	−	0.386331i	$-0.873742\pi$
$349$	−15.6918	+	11.4007i	−0.839962	+	0.610268i	0.0823980	+	0.996600i	$0.473742\pi$
$350$	−2.16749	+	6.67085i	−0.115857	+	0.356572i
$351$	−8.65865			−0.462165
$352$		0			0
$353$	−10.7585			−0.572619			−0.286309	−	0.958137i	$-0.592428\pi$
$353$	−10.7585			−0.572619			−0.286309	+	0.958137i	$0.592428\pi$
$354$	−6.30980	+	19.4196i	−0.335362	+	1.03214i
$355$	−3.67894	+	2.67290i	−0.195258	+	0.141863i
$356$	1.09184	+	0.793268i	0.0578674	+	0.0420431i
$357$	2.61366	+	8.04402i	0.138330	+	0.425735i
$358$	−8.06269	−	24.8144i	−0.426126	−	1.31148i
$359$	−0.491256	−	0.356918i	−0.0259275	−	0.0188374i	0.574746	−	0.818332i	$-0.305101\pi$
$359$	−0.491256	−	0.356918i	−0.0259275	−	0.0188374i	−0.600674	+	0.799494i	$0.705101\pi$
$360$	0.391081	−	0.284137i	0.0206118	−	0.0149753i
$361$	−0.363217	+	1.11787i	−0.0191167	+	0.0588351i
$362$	1.41360			0.0742973
$363$		0			0
$364$	0.239408			0.0125484
$365$	−1.92112	+	5.91260i	−0.100556	+	0.309480i
$366$	29.2607	−	21.2592i	1.52948	−	1.11123i
$367$	−22.3797	−	16.2598i	−1.16821	−	0.848755i	−0.177418	−	0.984136i	$-0.556774\pi$
$367$	−22.3797	−	16.2598i	−1.16821	−	0.848755i	−0.990794	+	0.135380i	$0.956774\pi$
$368$	2.38719	+	7.34702i	0.124441	+	0.382990i
$369$	0.122888	+	0.378210i	0.00639728	+	0.0196888i
$370$	−1.07565	−	0.781506i	−0.0559204	−	0.0406286i
$371$	−10.6826	+	7.76137i	−0.554613	+	0.402950i
$372$	−0.0978819	+	0.301250i	−0.00507494	+	0.0156191i
$373$	−29.4513			−1.52493			−0.762465	−	0.647029i	$-0.776011\pi$
$373$	−29.4513			−1.52493			−0.762465	+	0.647029i	$0.776011\pi$
$374$		0			0
$375$	7.38737			0.381482
$376$	−5.35870	+	16.4924i	−0.276354	+	0.850530i
$377$	3.48125	−	2.52928i	0.179294	−	0.130264i
$378$	−6.49330	−	4.71766i	−0.333979	−	0.242650i
$379$	7.83162	+	24.1032i	0.402283	+	1.23810i	0.923143	+	0.384458i	$0.125612\pi$
$379$	7.83162	+	24.1032i	0.402283	+	1.23810i	−0.520859	+	0.853643i	$0.674388\pi$
$380$	0.0921308	+	0.283550i	0.00472621	+	0.0145458i
$381$	−11.1793	−	8.12224i	−0.572733	−	0.416115i
$382$	−19.0912	+	13.8706i	−0.976791	+	0.709680i
$383$	−9.86759	+	30.3693i	−0.504210	+	1.55180i	0.297884	+	0.954602i	$0.403719\pi$
$383$	−9.86759	+	30.3693i	−0.504210	+	1.55180i	−0.802094	+	0.597197i	$0.796281\pi$
$384$	20.1043			1.02594
$385$		0			0
$386$	−17.8171			−0.906865
$387$	−1.02786	+	3.16344i	−0.0522493	+	0.160807i
$388$	0.330939	−	0.240441i	0.0168009	−	0.0122066i
$389$	−14.3614	−	10.4342i	−0.728153	−	0.529034i	0.160825	−	0.986983i	$-0.448584\pi$
$389$	−14.3614	−	10.4342i	−0.728153	−	0.529034i	−0.888979	+	0.457949i	$0.848584\pi$
$390$	−0.541603	−	1.66688i	−0.0274252	−	0.0844060i
$391$	−2.91576	−	8.97379i	−0.147456	−	0.453824i
$392$	−2.19369	−	1.59381i	−0.110798	−	0.0804993i
$393$	−12.6544	+	9.19394i	−0.638329	+	0.463773i
$394$	1.04327	−	3.21087i	0.0525594	−	0.161761i
$395$	1.67198			0.0841265
$396$		0			0
$397$	−13.3047			−0.667742			−0.333871	−	0.942619i	$-0.608355\pi$
$397$	−13.3047			−0.667742			−0.333871	+	0.942619i	$0.608355\pi$
$398$	−9.19168	+	28.2891i	−0.460737	+	1.41800i
$399$	−5.52656	+	4.01528i	−0.276674	+	0.201016i
$400$	−16.5576	−	12.0298i	−0.827878	−	0.601489i
$401$	−1.07835	−	3.31883i	−0.0538504	−	0.165734i	0.920514	−	0.390709i	$-0.127770\pi$
$401$	−1.07835	−	3.31883i	−0.0538504	−	0.165734i	−0.974365	+	0.224975i	$0.927770\pi$
$402$	−3.42909	−	10.5537i	−0.171028	−	0.526369i
$403$	1.65630	+	1.20337i	0.0825061	+	0.0599442i
$404$	−0.0218839	+	0.0158996i	−0.00108876	+	0.000791033i
$405$	−1.11174	+	3.42158i	−0.0552428	+	0.170020i
$406$	3.98873			0.197958
$407$		0			0
$408$	−22.9342			−1.13541
$409$	−9.15478	+	28.1755i	−0.452675	+	1.39319i	0.421168	+	0.906982i	$0.361620\pi$
$409$	−9.15478	+	28.1755i	−0.452675	+	1.39319i	−0.873843	+	0.486208i	$0.838380\pi$
$410$	−0.576603	+	0.418927i	−0.0284764	+	0.0206893i
$411$	−18.3404	−	13.3251i	−0.904665	−	0.657277i
$412$	0.789094	+	2.42858i	0.0388759	+	0.119648i
$413$	2.65875	+	8.18278i	0.130828	+	0.402648i
$414$	0.818132	+	0.594407i	0.0402090	+	0.0292135i
$415$	6.51685	−	4.73477i	0.319900	−	0.232421i
$416$	−0.417624	+	1.28531i	−0.0204757	+	0.0630177i
$417$	−15.4970			−0.758890
$418$		0			0
$419$	−11.6452			−0.568907			−0.284454	−	0.958690i	$-0.591812\pi$
$419$	−11.6452			−0.568907			−0.284454	+	0.958690i	$0.591812\pi$
$420$	0.0353088	−	0.108669i	0.00172289	−	0.00530252i
$421$	−16.0872	+	11.6880i	−0.784041	+	0.569639i	−0.906189	−	0.422873i	$-0.861022\pi$
$421$	−16.0872	+	11.6880i	−0.784041	+	0.569639i	0.122148	+	0.992512i	$0.461022\pi$
$422$	6.36652	+	4.62555i	0.309917	+	0.225168i
$423$	0.754862	+	2.32323i	0.0367027	+	0.112959i
$424$	−11.0642	−	34.0520i	−0.537323	−	1.65371i
$425$	20.2237	+	14.6934i	0.980995	+	0.712735i
$426$	−18.7065	+	13.5911i	−0.906335	+	0.658491i
$427$	4.70947	−	14.4942i	0.227907	−	0.701426i
$428$	−2.34159			−0.113185
$429$		0			0
$430$	−5.96138			−0.287483
$431$	9.34664	−	28.7660i	0.450212	−	1.38561i	−0.426454	−	0.904509i	$-0.640237\pi$
$431$	9.34664	−	28.7660i	0.450212	−	1.38561i	0.876666	−	0.481100i	$-0.159763\pi$
$432$	18.9465	−	13.7654i	0.911564	−	0.662290i
$433$	4.61722	+	3.35460i	0.221889	+	0.161212i	0.693177	−	0.720768i	$-0.256211\pi$
$433$	4.61722	+	3.35460i	0.221889	+	0.161212i	−0.471287	+	0.881980i	$0.656211\pi$
$434$	0.586436	+	1.80486i	0.0281498	+	0.0866362i
$435$	−0.634632	−	1.95320i	−0.0304283	−	0.0936485i
$436$	−1.35074	−	0.981369i	−0.0646886	−	0.0469990i
$437$	6.16535	−	4.47939i	0.294929	−	0.214278i
$438$	−9.76845	+	30.0642i	−0.466754	+	1.43652i
$439$	6.84875			0.326873			0.163436	−	0.986554i	$-0.447742\pi$
$439$	6.84875			0.326873			0.163436	+	0.986554i	$0.447742\pi$
$440$		0			0
$441$	−0.381966			−0.0181889
$442$	3.74892	−	11.5380i	0.178318	−	0.548806i
$443$	−0.0814641	+	0.0591871i	−0.00387047	+	0.00281206i	−0.589719	−	0.807609i	$-0.700761\pi$
$443$	−0.0814641	+	0.0591871i	−0.00387047	+	0.00281206i	0.585848	+	0.810421i	$0.300761\pi$
$444$	−0.384668	−	0.279478i	−0.0182555	−	0.0132634i
$445$	−1.28649	−	3.95940i	−0.0609854	−	0.187694i
$446$	11.5229	+	35.4637i	0.545623	+	1.67925i
$447$	19.5862	+	14.2302i	0.926394	+	0.673065i
$448$	5.91123	−	4.29476i	0.279279	−	0.202908i
$449$	−9.51919	+	29.2971i	−0.449238	+	1.38261i	0.428530	+	0.903528i	$0.359032\pi$
$449$	−9.51919	+	29.2971i	−0.449238	+	1.38261i	−0.877768	+	0.479086i	$0.840968\pi$
$450$	−2.67917			−0.126297
$451$		0			0
$452$	0.267817			0.0125970
$453$	1.43617	−	4.42006i	0.0674770	−	0.207673i
$454$	−25.7610	+	18.7165i	−1.20903	+	0.878409i
$455$	−0.597473	−	0.434090i	−0.0280100	−	0.0203504i
$456$	−5.72396	−	17.6165i	−0.268049	−	0.824970i
$457$	7.14928	+	22.0032i	0.334429	+	1.02927i	0.967002	+	0.254767i	$0.0819988\pi$
$457$	7.14928	+	22.0032i	0.334429	+	1.02927i	−0.632573	+	0.774501i	$0.718001\pi$
$458$	24.3619	+	17.7000i	1.13836	+	0.827065i
$459$	−23.1416	+	16.8134i	−1.08016	+	0.784781i
$460$	−0.0393899	+	0.121230i	−0.00183656	+	0.00565236i
$461$	−2.77839			−0.129403			−0.0647013	−	0.997905i	$-0.520609\pi$
$461$	−2.77839			−0.129403			−0.0647013	+	0.997905i	$0.520609\pi$
$462$		0			0
$463$	−26.0950			−1.21274			−0.606369	−	0.795184i	$-0.707374\pi$
$463$	−26.0950			−1.21274			−0.606369	+	0.795184i	$0.707374\pi$
$464$	−3.59651	+	11.0689i	−0.166964	+	0.513862i
$465$	0.790497	−	0.574329i	0.0366584	−	0.0266339i
$466$	0.823574	+	0.598362i	0.0381513	+	0.0277186i
$467$	−0.821457	−	2.52818i	−0.0380125	−	0.116990i	0.930250	−	0.366927i	$-0.119590\pi$
$467$	−0.821457	−	2.52818i	−0.0380125	−	0.116990i	−0.968262	+	0.249937i	$0.919590\pi$
$468$	0.0282583	+	0.0869700i	0.00130624	+	0.00402019i
$469$	−3.78282	−	2.74838i	−0.174675	−	0.126908i
$470$	−3.54190	+	2.57334i	−0.163376	+	0.118699i
$471$	9.44116	−	29.0569i	0.435026	−	1.33887i
$472$	−23.3298			−1.07384
$473$		0			0
$474$	8.50163			0.390493
$475$	−6.23902	+	19.2017i	−0.286266	+	0.881036i
$476$	0.639856	−	0.464883i	0.0293278	−	0.0213079i
$477$	−4.08039	−	2.96458i	−0.186828	−	0.135739i
$478$	−0.157077	−	0.483433i	−0.00718453	−	0.0221117i
$479$	−2.55935	−	7.87687i	−0.116940	−	0.359904i	0.875407	−	0.483387i	$-0.160593\pi$
$479$	−2.55935	−	7.87687i	−0.116940	−	0.359904i	−0.992347	+	0.123483i	$0.960593\pi$
$480$	0.521822	+	0.379126i	0.0238178	+	0.0173047i
$481$	−2.48626	+	1.80637i	−0.113364	+	0.0823636i
$482$	4.73059	−	14.5593i	0.215473	−	0.663156i
$483$	−2.92064			−0.132894
$484$		0			0
$485$	−1.26186			−0.0572983
$486$	1.78772	−	5.50204i	0.0810927	−	0.249578i
$487$	15.8531	−	11.5180i	0.718375	−	0.521930i	−0.167490	−	0.985874i	$-0.553566\pi$
$487$	15.8531	−	11.5180i	0.718375	−	0.521930i	0.885865	+	0.463944i	$0.153566\pi$
$488$	33.4321	+	24.2898i	1.51340	+	1.09955i
$489$	−5.79757	−	17.8431i	−0.262175	−	0.806892i
$490$	−0.211544	−	0.651065i	−0.00955658	−	0.0294121i
$491$	23.2039	+	16.8587i	1.04718	+	0.760821i	0.971674	−	0.236325i	$-0.0759430\pi$
$491$	23.2039	+	16.8587i	1.04718	+	0.760821i	0.0755055	+	0.997145i	$0.475943\pi$
$492$	−0.206202	+	0.149814i	−0.00929629	+	0.00675415i
$493$	4.39285	−	13.5198i	0.197844	−	0.608901i
$494$	9.79837			0.440850
$495$		0			0
$496$	−5.53735			−0.248634
$497$	−3.01078	+	9.26624i	−0.135052	+	0.415648i
$498$	33.1367	−	24.0752i	1.48489	−	1.07884i
$499$	−22.6120	−	16.4285i	−1.01225	−	0.735443i	−0.0475702	−	0.998868i	$-0.515148\pi$
$499$	−22.6120	−	16.4285i	−1.01225	−	0.735443i	−0.964680	+	0.263425i	$0.915148\pi$
$500$	−0.213467	−	0.656982i	−0.00954651	−	0.0293811i
$501$	−3.16246	−	9.73304i	−0.141288	−	0.434840i
$502$	−8.30037	−	6.03057i	−0.370464	−	0.269158i
$503$	6.55090	−	4.75951i	0.292090	−	0.212216i	−0.432083	−	0.901834i	$-0.642221\pi$
$503$	6.55090	−	4.75951i	0.292090	−	0.212216i	0.724174	+	0.689618i	$0.242221\pi$
$504$	0.320054	−	0.985026i	0.0142564	−	0.0438765i
$505$	0.0834428			0.00371316
$506$		0			0
$507$	16.9833			0.754256
$508$	−0.399298	+	1.22891i	−0.0177160	+	0.0545242i
$509$	−13.1871	+	9.58099i	−0.584508	+	0.424670i	−0.840346	−	0.542050i	$-0.817648\pi$
$509$	−13.1871	+	9.58099i	−0.584508	+	0.424670i	0.255839	+	0.966720i	$0.417648\pi$
$510$	−4.68428	−	3.40333i	−0.207423	−	0.150702i
$511$	4.11611	+	12.6681i	0.182086	+	0.560403i
$512$	6.04250	+	18.5969i	0.267043	+	0.821875i
$513$	−18.6907	−	13.5796i	−0.825213	−	0.599552i
$514$	−11.8049	+	8.57677i	−0.520692	+	0.378305i
$515$	2.43417	−	7.49161i	0.107262	−	0.330120i
$516$	−2.13187			−0.0938505
$517$		0			0
$518$	−2.84870			−0.125165
$519$	−0.669532	+	2.06061i	−0.0293892	+	0.0904506i
$520$	1.62007	−	1.17705i	0.0710450	−	0.0516172i
$521$	−6.21815	−	4.51775i	−0.272422	−	0.197926i	0.443183	−	0.896431i	$-0.353849\pi$
$521$	−6.21815	−	4.51775i	−0.272422	−	0.197926i	−0.715605	+	0.698505i	$0.753849\pi$
$522$	0.470806	+	1.44899i	0.0206066	+	0.0634207i
$523$	8.07243	+	24.8444i	0.352983	+	1.08637i	0.957170	+	0.289527i	$0.0934979\pi$
$523$	8.07243	+	24.8444i	0.352983	+	1.08637i	−0.604187	+	0.796842i	$0.706502\pi$
$524$	1.18331	+	0.859724i	0.0516931	+	0.0375572i
$525$	6.25993	−	4.54811i	0.273206	−	0.198496i
$526$	−6.42717	+	19.7808i	−0.280238	+	0.862484i
$527$	6.76343			0.294619
$528$		0			0
$529$	−19.7418			−0.858338
$530$	2.79332	−	8.59694i	0.121334	−	0.373427i
$531$	−2.65875	+	1.93169i	−0.115380	+	0.0838283i
$532$	0.516788	+	0.375469i	0.0224056	+	0.0162786i
$533$	0.509070	+	1.56676i	0.0220503	+	0.0678637i
$534$	−6.54149	−	20.1326i	−0.283078	−	0.871225i
$535$	5.84373	+	4.24572i	0.252646	+	0.183558i
$536$	10.2573	−	7.45236i	0.443047	−	0.321893i
$537$	−8.89441	+	27.3742i	−0.383822	+	1.18128i
$538$	26.9924			1.16372
$539$		0			0
$540$	0.386429			0.0166292
$541$	−7.99664	+	24.6111i	−0.343802	+	1.05811i	0.618420	+	0.785848i	$0.287773\pi$
$541$	−7.99664	+	24.6111i	−0.343802	+	1.05811i	−0.962222	+	0.272266i	$0.912227\pi$
$542$	0.866927	−	0.629859i	0.0372377	−	0.0270548i
$543$	−1.26160	−	0.916606i	−0.0541405	−	0.0393353i
$544$	1.37966	+	4.24615i	0.0591524	+	0.182052i
$545$	1.59154	+	4.89826i	0.0681742	+	0.209819i
$546$	−3.03801	−	2.20724i	−0.130015	−	0.0944613i
$547$	30.8210	−	22.3927i	1.31781	−	0.957445i	0.317853	−	0.948140i	$-0.397038\pi$
$547$	30.8210	−	22.3927i	1.31781	−	0.957445i	0.999957	−	0.00930483i	$-0.00296186\pi$
$548$	−0.655075	+	2.01611i	−0.0279834	+	0.0861240i
$549$	5.82122			0.248444
$550$		0			0
$551$	11.4814			0.489123
$552$	2.44724	−	7.53183i	0.104162	−	0.320576i
$553$	2.89815	−	2.10563i	0.123242	−	0.0895406i
$554$	17.8756	+	12.9874i	0.759460	+	0.551780i
$555$	0.453245	+	1.39494i	0.0192392	+	0.0592121i
$556$	0.447803	+	1.37819i	0.0189911	+	0.0584485i
$557$	−27.9452	−	20.3034i	−1.18408	−	0.860282i	−0.191451	−	0.981502i	$-0.561319\pi$
$557$	−27.9452	−	20.3034i	−1.18408	−	0.860282i	−0.992626	+	0.121220i	$0.961319\pi$
$558$	−0.586436	+	0.426071i	−0.0248258	+	0.0180370i
$559$	−4.25799	+	13.1047i	−0.180094	+	0.554271i
$560$	1.99748			0.0844088
$561$		0			0
$562$	15.6883			0.661773
$563$	6.02025	−	18.5284i	0.253723	−	0.780880i	−0.740355	−	0.672216i	$-0.765343\pi$
$563$	6.02025	−	18.5284i	0.253723	−	0.780880i	0.994079	−	0.108664i	$-0.0346573\pi$
$564$	−1.26663	+	0.920264i	−0.0533349	+	0.0387501i
$565$	−0.668371	−	0.485600i	−0.0281186	−	0.0204293i
$566$	−4.12857	−	12.7064i	−0.173537	−	0.534091i
$567$	2.38197	+	7.33094i	0.100033	+	0.307870i
$568$	−21.3733	−	15.5286i	−0.896804	−	0.651566i
$569$	−13.8575	+	10.0680i	−0.580935	+	0.422074i	−0.839061	−	0.544037i	$-0.816895\pi$
$569$	−13.8575	+	10.0680i	−0.580935	+	0.422074i	0.258126	+	0.966111i	$0.416895\pi$
$570$	1.44510	−	4.44756i	0.0605286	−	0.186288i
$571$	−3.85581			−0.161360			−0.0806802	−	0.996740i	$-0.525709\pi$
$571$	−3.85581			−0.161360			−0.0806802	+	0.996740i	$0.525709\pi$
$572$		0			0
$573$	26.0323			1.08751
$574$	−0.471883	+	1.45231i	−0.0196960	+	0.0606181i
$575$	−6.98348	+	5.07380i	−0.291231	+	0.211592i
$576$	2.25789	+	1.64045i	0.0940787	+	0.0683522i
$577$	−3.02276	−	9.30309i	−0.125839	−	0.387293i	0.868214	−	0.496190i	$-0.165268\pi$
$577$	−3.02276	−	9.30309i	−0.125839	−	0.387293i	−0.994053	+	0.108897i	$0.965268\pi$
$578$	−4.67972	−	14.4027i	−0.194651	−	0.599073i
$579$	15.9012	+	11.5529i	0.660832	+	0.480123i
$580$	−0.155365	+	0.112880i	−0.00645120	+	0.00468707i
$581$	5.33329	−	16.4142i	0.221262	−	0.680975i
$582$	−6.41628			−0.265964
$583$		0			0
$584$	−36.1178			−1.49457
$585$	0.0871702	−	0.268282i	0.00360404	−	0.0110921i
$586$	14.1076	−	10.2498i	0.582780	−	0.423415i
$587$	4.93413	+	3.58485i	0.203653	+	0.147963i	0.684937	−	0.728602i	$-0.259830\pi$
$587$	4.93413	+	3.58485i	0.203653	+	0.147963i	−0.481284	+	0.876565i	$0.659830\pi$
$588$	−0.0756511	−	0.232830i	−0.00311980	−	0.00960175i
$589$	1.68803	+	5.19522i	0.0695540	+	0.214065i
$590$	−4.76508	−	3.46203i	−0.196175	−	0.142530i
$591$	−3.01308	+	2.18913i	−0.123941	+	0.0900487i
$592$	2.56858	−	7.90527i	0.105568	−	0.324904i
$593$	13.2330			0.543413			0.271706	−	0.962380i	$-0.412412\pi$
$593$	13.2330			0.543413			0.271706	+	0.962380i	$0.412412\pi$
$594$		0			0
$595$	−2.43976			−0.100020
$596$	0.699571	−	2.15306i	0.0286555	−	0.0881927i
$597$	26.5465	−	19.2872i	1.08648	−	0.789371i
$598$	3.38916	+	2.46237i	0.138593	+	0.100694i
$599$	−1.83097	−	5.63515i	−0.0748115	−	0.230246i	0.906657	−	0.421868i	$-0.138625\pi$
$599$	−1.83097	−	5.63515i	−0.0748115	−	0.230246i	−0.981469	+	0.191622i	$0.938625\pi$
$600$	6.48352	+	19.9542i	0.264689	+	0.814628i
$601$	−10.3075	−	7.48886i	−0.420453	−	0.305477i	0.357367	−	0.933964i	$-0.383674\pi$
$601$	−10.3075	−	7.48886i	−0.420453	−	0.305477i	−0.777820	+	0.628487i	$0.783674\pi$
$602$	−10.3333	+	7.50755i	−0.421152	+	0.305985i
$603$	0.551906	−	1.69859i	0.0224754	−	0.0691721i
$604$	−0.434590			−0.0176832
$605$		0			0
$606$	0.424287			0.0172355
$607$	2.58382	−	7.95217i	0.104874	−	0.322769i	−0.884827	−	0.465920i	$-0.845724\pi$
$607$	2.58382	−	7.95217i	0.104874	−	0.322769i	0.989701	+	0.143151i	$0.0457235\pi$
$608$	−2.91727	+	2.11952i	−0.118311	+	0.0859581i
$609$	−3.55983	−	2.58637i	−0.144252	−	0.104805i
$610$	3.22396	+	9.92233i	0.130534	+	0.401743i
$611$	3.12706	+	9.62410i	0.126507	+	0.389350i
$612$	0.244403	+	0.177569i	0.00987942	+	0.00717782i
$613$	5.40661	−	3.92813i	0.218371	−	0.158656i	−0.473222	−	0.880943i	$-0.656909\pi$
$613$	5.40661	−	3.92813i	0.218371	−	0.158656i	0.691593	+	0.722287i	$0.256909\pi$
$614$	−1.00653	+	3.09778i	−0.0406203	+	0.125016i
$615$	0.786243			0.0317044
$616$		0			0
$617$	11.8669			0.477741			0.238871	−	0.971051i	$-0.423223\pi$
$617$	11.8669			0.477741			0.238871	+	0.971051i	$0.423223\pi$
$618$	12.3772	−	38.0931i	0.497883	−	1.53233i
$619$	−16.6825	+	12.1205i	−0.670524	+	0.487165i	−0.870201	−	0.492697i	$-0.836011\pi$
$619$	−16.6825	+	12.1205i	−0.670524	+	0.487165i	0.199676	+	0.979862i	$0.436011\pi$
$620$	−0.0739193	−	0.0537055i	−0.00296867	−	0.00215686i
$621$	−3.05232	−	9.39406i	−0.122485	−	0.376971i
$622$	9.70514	+	29.8693i	0.389141	+	1.19765i
$623$	−7.21629	−	5.24294i	−0.289114	−	0.210054i
$624$	8.86448	−	6.44042i	0.354863	−	0.257823i
$625$	6.73035	−	20.7139i	0.269214	−	0.828556i
$626$	46.2824			1.84982
$627$		0			0
$628$	−2.85694			−0.114004
$629$	−3.13731	+	9.65565i	−0.125093	+	0.384996i
$630$	0.211544	−	0.153696i	0.00842811	−	0.00612338i
$631$	12.5232	+	9.09861i	0.498539	+	0.362210i	0.808459	−	0.588553i	$-0.200302\pi$
$631$	12.5232	+	9.09861i	0.498539	+	0.362210i	−0.309920	+	0.950763i	$0.600302\pi$
$632$	3.00167	+	9.23819i	0.119400	+	0.367475i
$633$	−2.68265	−	8.25634i	−0.106626	−	0.328160i
$634$	−15.6641	−	11.3806i	−0.622099	−	0.451981i
$635$	3.22474	−	2.34291i	0.127970	−	0.0929756i
$636$	0.998930	−	3.07439i	0.0396101	−	0.121907i
$637$	−1.58232			−0.0626937
$638$		0			0
$639$	−3.72153			−0.147222
$640$	−1.79206	+	5.51538i	−0.0708372	+	0.218015i
$641$	19.0754	−	13.8591i	0.753432	−	0.547401i	−0.143457	−	0.989657i	$-0.545822\pi$
$641$	19.0754	−	13.8591i	0.753432	−	0.547401i	0.896889	+	0.442256i	$0.145822\pi$
$642$	29.7140	+	21.5885i	1.17272	+	0.852029i
$643$	8.86281	+	27.2769i	0.349515	+	1.07570i	0.959122	+	0.282993i	$0.0913273\pi$
$643$	8.86281	+	27.2769i	0.349515	+	1.07570i	−0.609607	+	0.792704i	$0.708673\pi$
$644$	0.0843952	+	0.259742i	0.00332564	+	0.0102353i
$645$	5.32036	+	3.86547i	0.209489	+	0.152203i
$646$	26.1877	−	19.0265i	1.03034	−	0.748587i
$647$	1.67723	−	5.16198i	0.0659387	−	0.202938i	−0.912659	−	0.408722i	$-0.865974\pi$
$647$	1.67723	−	5.16198i	0.0659387	−	0.202938i	0.978597	+	0.205784i	$0.0659744\pi$
$648$	−20.9011			−0.821074
$649$		0			0
$650$	−11.0986			−0.435323
$651$	0.646930	−	1.99105i	0.0253552	−	0.0780353i
$652$	−1.41932	+	1.03119i	−0.0555847	+	0.0403846i
$653$	9.98496	+	7.25450i	0.390742	+	0.283890i	0.765759	−	0.643127i	$-0.222363\pi$
$653$	9.98496	+	7.25450i	0.390742	+	0.283890i	−0.375018	+	0.927018i	$0.622363\pi$
$654$	8.09262	+	24.9065i	0.316446	+	0.973922i
$655$	−1.39426	−	4.29110i	−0.0544784	−	0.167667i
$656$	−3.60474	−	2.61900i	−0.140741	−	0.102255i
$657$	−4.11611	+	2.99053i	−0.160585	+	0.116672i
$658$	−2.89864	+	8.92109i	−0.113001	+	0.347780i
$659$	16.2115			0.631512			0.315756	−	0.948840i	$-0.397742\pi$
$659$	16.2115			0.631512			0.315756	+	0.948840i	$0.397742\pi$
$660$		0			0
$661$	43.7050			1.69993			0.849964	−	0.526840i	$-0.176623\pi$
$661$	43.7050			1.69993			0.849964	+	0.526840i	$0.176623\pi$
$662$	−4.29519	+	13.2192i	−0.166937	+	0.513780i
$663$	−10.8272	+	7.86645i	−0.420495	+	0.305508i
$664$	37.8606	+	27.5073i	1.46927	+	1.06749i
$665$	−0.608919	−	1.87406i	−0.0236129	−	0.0726730i
$666$	−0.336243	−	1.03485i	−0.0130292	−	0.0400996i
$667$	3.97129	+	2.88531i	0.153769	+	0.111720i
$668$	−0.774208	+	0.562495i	−0.0299550	+	0.0217636i
$669$	12.7115	−	39.1220i	0.491455	−	1.51254i
$670$	3.20093			0.123663
$671$		0			0
$672$	1.38197			0.0533105
$673$	−1.81115	+	5.57416i	−0.0698149	+	0.214868i	−0.979876	−	0.199605i	$-0.936034\pi$
$673$	−1.81115	+	5.57416i	−0.0698149	+	0.214868i	0.910062	+	0.414473i	$0.136034\pi$
$674$	−22.7842	+	16.5537i	−0.877616	+	0.637625i
$675$	21.1709	+	15.3815i	0.814867	+	0.592036i
$676$	−0.490753	−	1.51038i	−0.0188751	−	0.0580916i
$677$	−6.34347	−	19.5232i	−0.243799	−	0.750338i	−0.995832	−	0.0912112i	$-0.970926\pi$
$677$	−6.34347	−	19.5232i	−0.243799	−	0.750338i	0.752032	−	0.659127i	$-0.229074\pi$
$678$	−3.39851	−	2.46916i	−0.130519	−	0.0948275i
$679$	−2.18727	+	1.58915i	−0.0839398	+	0.0609858i
$680$	2.04431	−	6.29173i	0.0783955	−	0.241277i
$681$	35.1271			1.34607
$682$		0			0
$683$	38.7055			1.48103			0.740513	−	0.672042i	$-0.234583\pi$
$683$	38.7055			1.48103			0.740513	+	0.672042i	$0.234583\pi$
$684$	−0.0753984	+	0.232052i	−0.00288293	+	0.00887275i
$685$	5.29040	−	3.84370i	0.202136	−	0.146860i
$686$	−1.18661	−	0.862123i	−0.0453050	−	0.0329160i
$687$	−10.2653	−	31.5935i	−0.391647	−	1.20537i
$688$	−11.5166	−	35.4445i	−0.439067	−	1.35131i
$689$	−16.9033	−	12.2809i	−0.643963	−	0.467867i
$690$	1.61753	−	1.17521i	0.0615785	−	0.0447394i
$691$	−7.14757	+	21.9980i	−0.271906	+	0.836842i	0.718115	+	0.695924i	$0.245005\pi$
$691$	−7.14757	+	21.9980i	−0.271906	+	0.836842i	−0.990021	+	0.140917i	$0.954995\pi$
$692$	0.202603			0.00770182
$693$		0			0
$694$	−4.47105			−0.169719
$695$	1.38137	−	4.25141i	0.0523982	−	0.161265i
$696$	9.65264	−	7.01306i	0.365882	−	0.265829i
$697$	4.40290	+	3.19889i	0.166772	+	0.121167i
$698$	−8.79119	−	27.0565i	−0.332752	−	1.02410i
$699$	−0.347028	−	1.06804i	−0.0131258	−	0.0403971i
$700$	−0.585365	−	0.425293i	−0.0221247	−	0.0160746i
$701$	−28.7288	+	20.8727i	−1.08507	+	0.788350i	−0.978560	−	0.205962i	$-0.933968\pi$
$701$	−28.7288	+	20.8727i	−1.08507	+	0.788350i	−0.106510	+	0.994312i	$0.533968\pi$
$702$	3.92449	−	12.0783i	0.148120	−	0.455868i
$703$	−8.19985			−0.309263
$704$		0			0
$705$	4.82965			0.181895
$706$	4.87625	−	15.0076i	0.183520	−	0.564817i
$707$	0.144637	−	0.105085i	0.00543963	−	0.00395212i
$708$	−1.70406	−	1.23807i	−0.0640425	−	0.0465296i
$709$	13.5363	+	41.6605i	0.508367	+	1.56459i	0.795035	+	0.606564i	$0.207453\pi$
$709$	13.5363	+	41.6605i	0.508367	+	1.56459i	−0.286667	+	0.958030i	$0.592547\pi$
$710$	−2.06109	−	6.34340i	−0.0773515	−	0.238063i
$711$	1.10700	+	0.804280i	0.0415156	+	0.0301629i
$712$	19.5673	−	14.2165i	0.733315	−	0.532784i
$713$	−0.721705	+	2.22118i	−0.0270281	+	0.0831839i
$714$	−12.4056			−0.464268
$715$		0			0
$716$	2.69149			0.100586
$717$	−0.173280	+	0.533302i	−0.00647127	+	0.0199165i
$718$	0.720541	−	0.523503i	0.0268903	−	0.0195370i
$719$	−12.8314	−	9.32255i	−0.478530	−	0.347672i	0.322226	−	0.946663i	$-0.395569\pi$
$719$	−12.8314	−	9.32255i	−0.478530	−	0.347672i	−0.800756	+	0.598990i	$0.795569\pi$
$720$	0.235770	+	0.725626i	0.00878664	+	0.0270425i
$721$	−5.21535	−	16.0512i	−0.194230	−	0.597778i
$722$	−1.39474	−	1.01333i	−0.0519067	−	0.0377124i
$723$	−13.6624	+	9.92633i	−0.508111	+	0.369164i
$724$	−0.0450613	+	0.138685i	−0.00167469	+	0.00515417i
$725$	−13.0049			−0.482992
$726$		0			0
$727$	13.7719			0.510770			0.255385	−	0.966839i	$-0.417798\pi$
$727$	13.7719			0.510770			0.255385	+	0.966839i	$0.417798\pi$
$728$	1.32584	−	4.08053i	0.0491390	−	0.151234i
$729$	−23.8713	+	17.3435i	−0.884123	+	0.642353i
$730$	−7.37701	−	5.35971i	−0.273035	−	0.198372i
$731$	14.0666	+	43.2927i	0.520273	+	1.60124i
$732$	1.15293	+	3.54837i	0.0426137	+	0.131151i
$733$	15.8306	+	11.5016i	0.584717	+	0.424822i	0.840422	−	0.541933i	$-0.182307\pi$
$733$	15.8306	+	11.5016i	0.584717	+	0.424822i	−0.255705	+	0.966755i	$0.582307\pi$
$734$	32.8250	−	23.8488i	1.21159	−	0.880275i
$735$	−0.233366	+	0.718226i	−0.00860783	+	0.0264922i
$736$	−1.54170			−0.0568278
$737$		0			0
$738$	−0.583280			−0.0214708
$739$	−3.44683	+	10.6083i	−0.126794	+	0.390231i	−0.994224	−	0.107328i	$-0.965770\pi$
$739$	−3.44683	+	10.6083i	−0.126794	+	0.390231i	0.867430	+	0.497560i	$0.165770\pi$
$740$	0.110960	−	0.0806171i	0.00407897	−	0.00296354i
$741$	−8.74477	−	6.35345i	−0.321247	−	0.233400i
$742$	−5.98484	−	18.4195i	−0.219711	−	0.676199i
$743$	6.38273	+	19.6440i	0.234160	+	0.720669i	0.997232	+	0.0743560i	$0.0236901\pi$
$743$	6.38273	+	19.6440i	0.234160	+	0.720669i	−0.763072	+	0.646313i	$0.776310\pi$
$744$	4.59250	+	3.33665i	0.168369	+	0.122327i
$745$	−5.64975	+	4.10478i	−0.206991	+	0.150388i
$746$	13.3487	−	41.0829i	0.488729	−	1.50415i
$747$	6.59231			0.241200
$748$		0			0
$749$	15.4762			0.565489
$750$	−3.34829	+	10.3050i	−0.122262	+	0.376284i
$751$	−21.5191	+	15.6345i	−0.785243	+	0.570513i	−0.906548	−	0.422103i	$-0.861292\pi$
$751$	−21.5191	+	15.6345i	−0.785243	+	0.570513i	0.121305	+	0.992615i	$0.461292\pi$
$752$	−22.1428	−	16.0877i	−0.807465	−	0.586658i
$753$	3.49751	+	10.7642i	0.127456	+	0.392271i
$754$	1.95034	+	6.00253i	0.0710273	+	0.218599i
$755$	1.08457	+	0.787990i	0.0394717	+	0.0286779i
$756$	0.669822	−	0.486655i	0.0243612	−	0.0176995i
$757$	6.52024	−	20.0672i	0.236982	−	0.729356i	−0.759870	−	0.650075i	$-0.774738\pi$
$757$	6.52024	−	20.0672i	0.236982	−	0.729356i	0.996852	−	0.0792809i	$-0.0252624\pi$
$758$	−37.1723			−1.35016
$759$		0			0
$760$	5.34311			0.193815
$761$	−2.47134	+	7.60601i	−0.0895861	+	0.275718i	−0.985805	−	0.167895i	$-0.946303\pi$
$761$	−2.47134	+	7.60601i	−0.0895861	+	0.275718i	0.896219	+	0.443612i	$0.146303\pi$
$762$	16.3970	−	11.9132i	0.594002	−	0.431568i
$763$	8.92742	+	6.48615i	0.323194	+	0.234814i
$764$	−0.752233	−	2.31514i	−0.0272148	−	0.0837587i
$765$	−0.287974	−	0.886294i	−0.0104117	−	0.0320440i
$766$	−37.8911	−	27.5295i	−1.36906	−	0.994681i
$767$	−11.0140	+	8.00215i	−0.397693	+	0.288941i
$768$	−1.80550	+	5.55675i	−0.0651503	+	0.200512i
$769$	−52.0476			−1.87689			−0.938443	−	0.345435i	$-0.887731\pi$
$769$	−52.0476			−1.87689			−0.938443	+	0.345435i	$0.887731\pi$
$770$		0			0
$771$	16.0969			0.579716
$772$	0.567954	−	1.74798i	0.0204411	−	0.0629112i
$773$	1.27905	−	0.929285i	0.0460042	−	0.0334240i	−0.564545	−	0.825402i	$-0.690949\pi$
$773$	1.27905	−	0.929285i	0.0460042	−	0.0334240i	0.610550	+	0.791978i	$0.290949\pi$
$774$	−3.94695	−	2.86763i	−0.141870	−	0.103075i
$775$	−1.91203	−	5.88461i	−0.0686820	−	0.211382i
$776$	−2.26540	−	6.97217i	−0.0813230	−	0.250286i
$777$	2.54238	+	1.84715i	0.0912075	+	0.0662661i
$778$	21.0644	−	15.3042i	0.755194	−	0.548681i
$779$	−1.35829	+	4.18040i	−0.0486659	+	0.149778i
$780$	0.180798			0.00647361
$781$		0			0
$782$	13.8395			0.494899
$783$	4.59858	−	14.1530i	0.164340	−	0.505786i
$784$	3.46236	−	2.51555i	0.123656	−	0.0898411i
$785$	7.12985	+	5.18014i	0.254475	+	0.184887i
$786$	−7.08951	−	21.8193i	−0.252874	−	0.778267i
$787$	7.22813	+	22.2459i	0.257655	+	0.792980i	0.993295	+	0.115608i	$0.0368815\pi$
$787$	7.22813	+	22.2459i	0.257655	+	0.792980i	−0.735640	+	0.677373i	$0.763118\pi$
$788$	0.281753	+	0.204705i	0.0100370	+	0.00729232i
$789$	18.5623	−	13.4863i	0.660836	−	0.480125i
$790$	−0.757817	+	2.33232i	−0.0269619	+	0.0829803i
$791$	−1.77008			−0.0629367
$792$		0			0
$793$	24.1147			0.856339
$794$	6.03028	−	18.5593i	0.214006	−	0.658644i
$795$	−8.06738	+	5.86129i	−0.286120	+	0.207879i
$796$	−2.48236	−	1.80354i	−0.0879849	−	0.0639248i
$797$	−14.2617	−	43.8930i	−0.505175	−	1.55477i	−0.800476	−	0.599365i	$-0.795420\pi$
$797$	−14.2617	−	43.8930i	−0.505175	−	1.55477i	0.295301	−	0.955404i	$-0.404580\pi$
$798$	−3.09621	−	9.52916i	−0.109605	−	0.337329i
$799$	27.0457	+	19.6498i	0.956807	+	0.695161i
$800$	3.30439	−	2.40078i	0.116828	−	0.0848804i
$801$	1.05284	−	3.24031i	0.0372003	−	0.114491i
$802$	5.11834			0.180735
$803$		0			0
$804$	1.14470			0.0403704
$805$	0.260339	−	0.801242i	0.00917576	−	0.0282401i
$806$	−2.42934	+	1.76502i	−0.0855700	+	0.0621702i
$807$	−24.0899	−	17.5024i	−0.848006	−	0.616112i
$808$	0.149803	+	0.461046i	0.00527005	+	0.0162195i
$809$	10.4294	+	32.0983i	0.366677	+	1.12851i	0.948924	+	0.315503i	$0.102173\pi$
$809$	10.4294	+	32.0983i	0.366677	+	1.12851i	−0.582248	+	0.813011i	$0.697827\pi$
$810$	−4.26903	−	3.10163i	−0.149998	−	0.108980i
$811$	24.8894	−	18.0832i	0.873985	−	0.634987i	−0.0576684	−	0.998336i	$-0.518367\pi$
$811$	24.8894	−	18.0832i	0.873985	−	0.634987i	0.931653	+	0.363349i	$0.118367\pi$
$812$	−0.127149	+	0.391323i	−0.00446204	+	0.0137328i
$813$	−1.18212			−0.0414588
$814$		0			0
$815$	5.41182			0.189568
$816$	11.1857	−	34.4261i	0.391579	−	1.20515i
$817$	−29.7438	+	21.6101i	−1.04060	+	0.756043i
$818$	−35.1539	−	25.5408i	−1.22913	−	0.893014i
$819$	−0.186767	−	0.574810i	−0.00652617	−	0.0200855i
$820$	−0.0227194	−	0.0699231i	−0.000793395	−	0.00244182i
$821$	−9.77159	−	7.09948i	−0.341031	−	0.247774i	0.404066	−	0.914730i	$-0.367597\pi$
$821$	−9.77159	−	7.09948i	−0.341031	−	0.247774i	−0.745097	+	0.666956i	$0.767597\pi$
$822$	26.9004	−	19.5443i	0.938260	−	0.681686i
$823$	−7.66939	+	23.6040i	−0.267338	+	0.822782i	0.723807	+	0.690002i	$0.242390\pi$
$823$	−7.66939	+	23.6040i	−0.267338	+	0.822782i	−0.991146	+	0.132780i	$0.957610\pi$
$824$	45.7634			1.59424
$825$		0			0
$826$	−12.6196			−0.439092
$827$	1.59864	−	4.92010i	0.0555901	−	0.171089i	−0.919406	−	0.393309i	$-0.871330\pi$
$827$	1.59864	−	4.92010i	0.0555901	−	0.171089i	0.974997	+	0.222220i	$0.0713303\pi$
$828$	−0.0843952	+	0.0613167i	−0.00293294	+	0.00213090i
$829$	−25.5273	−	18.5467i	−0.886601	−	0.644153i	0.0483887	−	0.998829i	$-0.484591\pi$
$829$	−25.5273	−	18.5467i	−0.886601	−	0.644153i	−0.934989	+	0.354675i	$0.884591\pi$
$830$	3.65101	+	11.2367i	0.126728	+	0.390030i
$831$	−7.53220	−	23.1817i	−0.261289	−	0.804165i
$832$	9.35344	+	6.79567i	0.324272	+	0.235598i
$833$	−4.22899	+	3.07254i	−0.146526	+	0.106457i
$834$	7.02392	−	21.6174i	0.243219	−	0.748550i
$835$	2.95204			0.102160
$836$		0			0
$837$	7.08018			0.244727
$838$	5.27815	−	16.2445i	0.182331	−	0.561156i
$839$	4.72176	−	3.43056i	0.163013	−	0.118436i	−0.503288	−	0.864119i	$-0.667876\pi$
$839$	4.72176	−	3.43056i	0.163013	−	0.118436i	0.666301	+	0.745683i	$0.267876\pi$
$840$	−1.65664	−	1.20362i	−0.0571597	−	0.0415289i
$841$	−6.67615	−	20.5471i	−0.230212	−	0.708520i
$842$	−9.01271	−	27.7383i	−0.310598	−	0.955924i
$843$	−14.0014	−	10.1726i	−0.482234	−	0.350363i
$844$	−0.656745	+	0.477153i	−0.0226061	+	0.0164243i
$845$	−1.51386	+	4.65917i	−0.0520783	+	0.160280i
$846$	−3.58291			−0.123183
$847$		0			0
$848$	56.5112			1.94060
$849$	−4.55445	+	14.0172i	−0.156308	+	0.481068i
$850$	−29.6628	+	21.5513i	−1.01743	+	0.739203i
$851$	−2.83624	−	2.06065i	−0.0972252	−	0.0706382i
$852$	−0.737076	−	2.26849i	−0.0252518	−	0.0777171i
$853$	−6.28731	−	19.3504i	−0.215273	−	0.662544i	−0.999134	−	0.0416068i	$-0.986752\pi$
$853$	−6.28731	−	19.3504i	−0.215273	−	0.662544i	0.783861	−	0.620937i	$-0.213248\pi$
$854$	18.0841	+	13.1389i	0.618826	+	0.449603i
$855$	0.608919	−	0.442406i	0.0208246	−	0.0151300i
$856$	−12.9677	+	39.9106i	−0.443228	+	1.36411i
$857$	−15.1087			−0.516104			−0.258052	−	0.966131i	$-0.583081\pi$
$857$	−15.1087			−0.516104			−0.258052	+	0.966131i	$0.583081\pi$
$858$		0			0
$859$	−33.9641			−1.15884			−0.579420	−	0.815029i	$-0.696721\pi$
$859$	−33.9641			−1.15884			−0.579420	+	0.815029i	$0.696721\pi$
$860$	0.190031	−	0.584854i	0.00647999	−	0.0199434i
$861$	1.36285	−	0.990166i	0.0464457	−	0.0337448i
$862$	35.8907	+	26.0761i	1.22244	+	0.888156i
$863$	−0.858245	−	2.64141i	−0.0292150	−	0.0899145i	0.935386	−	0.353629i	$-0.115052\pi$
$863$	−0.858245	−	2.64141i	−0.0292150	−	0.0899145i	−0.964601	+	0.263714i	$0.915052\pi$
$864$	1.44427	+	4.44501i	0.0491351	+	0.151222i
$865$	−0.505622	−	0.367356i	−0.0171917	−	0.0124905i
$866$	−6.77222	+	4.92030i	−0.230129	+	0.167199i
$867$	−5.16246	+	15.8884i	−0.175326	+	0.539599i
$868$	−0.195764			−0.00664466
$869$		0			0
$870$	3.01224			0.102125
$871$	2.28630	−	7.03652i	0.0774685	−	0.238423i
$872$	−24.2071	+	17.5875i	−0.819756	+	0.595587i
$873$	−0.835464	−	0.607000i	−0.0282762	−	0.0205438i
$874$	3.45409	+	10.6306i	0.116836	+	0.359585i
$875$	1.41086	+	4.34219i	0.0476958	+	0.146793i
$876$	−2.63812	−	1.91671i	−0.0891340	−	0.0647596i
$877$	−40.1906	+	29.2002i	−1.35714	+	0.986020i	−0.358519	+	0.933522i	$0.616718\pi$
$877$	−40.1906	+	29.2002i	−1.35714	+	0.986020i	−0.998621	+	0.0524978i	$0.983282\pi$
$878$	−3.10416	+	9.55362i	−0.104760	+	0.322419i
$879$	−19.2368			−0.648841
$880$		0			0
$881$	−27.3064			−0.919975			−0.459988	−	0.887925i	$-0.652146\pi$
$881$	−27.3064			−0.919975			−0.459988	+	0.887925i	$0.652146\pi$
$882$	0.173124	−	0.532822i	0.00582940	−	0.0179410i
$883$	14.4093	−	10.4690i	0.484913	−	0.352310i	−0.318312	−	0.947986i	$-0.603116\pi$
$883$	14.4093	−	10.4690i	0.484913	−	0.352310i	0.803225	+	0.595676i	$0.203116\pi$
$884$	1.01245	+	0.735591i	0.0340525	+	0.0247406i
$885$	2.00785	+	6.17954i	0.0674933	+	0.207723i
$886$	−0.0456396	−	0.140464i	−0.00153329	−	0.00471899i
$887$	13.3268	+	9.68251i	0.447471	+	0.325107i	0.788597	−	0.614911i	$-0.210808\pi$
$887$	13.3268	+	9.68251i	0.447471	+	0.325107i	−0.341125	+	0.940018i	$0.610808\pi$
$888$	−6.89378	+	5.00863i	−0.231340	+	0.168078i
$889$	2.63908	−	8.12224i	0.0885118	−	0.272411i
$890$	6.10625			0.204682
$891$		0			0
$892$	−3.84656			−0.128792
$893$	−8.34359	+	25.6789i	−0.279208	+	0.859313i
$894$	−28.7277	+	20.8719i	−0.960797	+	0.698060i
$895$	−6.71695	−	4.88015i	−0.224523	−	0.163125i
$896$	3.83958	+	11.8170i	0.128271	+	0.394779i
$897$	−1.42808	−	4.39519i	−0.0476823	−	0.146751i
$898$	−36.5532	−	26.5575i	−1.21980	−	0.886235i
$899$	−2.84662	+	2.06819i	−0.0949401	+	0.0689780i
$900$	0.0854037	−	0.262845i	0.00284679	−	0.00876152i
$901$	−69.0238			−2.29952
$902$		0			0
$903$	14.0902			0.468891
$904$	1.48317	−	4.56473i	0.0493295	−	0.151821i
$905$	0.363916	−	0.264401i	0.0120970	−	0.00878898i
$906$	5.51481	+	4.00674i	0.183217	+	0.133115i
$907$	8.80318	+	27.0934i	0.292305	+	0.899621i	0.984113	+	0.177541i	$0.0568141\pi$
$907$	8.80318	+	27.0934i	0.292305	+	0.899621i	−0.691809	+	0.722081i	$0.743186\pi$
$908$	−1.01504	−	3.12397i	−0.0336852	−	0.103673i
$909$	0.0552464	+	0.0401388i	0.00183241	+	0.00133132i
$910$	0.876333	−	0.636693i	0.0290501	−	0.0211062i
$911$	−3.47190	+	10.6854i	−0.115029	+	0.354023i	−0.991953	−	0.126606i	$-0.959592\pi$
$911$	−3.47190	+	10.6854i	−0.115029	+	0.354023i	0.876924	+	0.480629i	$0.159592\pi$
$912$	29.2356			0.968088
$913$		0			0
$914$	−33.9337			−1.12243
$915$	3.55653	−	10.9459i	0.117575	−	0.361860i
$916$	−2.51308	+	1.82586i	−0.0830344	+	0.0603280i
$917$	−7.82083	−	5.68217i	−0.258267	−	0.187642i
$918$	−12.9649	−	39.9019i	−0.427906	−	1.31696i
$919$	0.241174	+	0.742259i	0.00795561	+	0.0244848i	0.954956	−	0.296749i	$-0.0959025\pi$
$919$	0.241174	+	0.742259i	0.00795561	+	0.0244848i	−0.947000	+	0.321234i	$0.895902\pi$
$920$	1.84813	+	1.34274i	0.0609309	+	0.0442689i
$921$	2.90696	−	2.11203i	0.0957876	−	0.0695938i
$922$	1.25929	−	3.87570i	0.0414726	−	0.127640i
$923$	−15.4167			−0.507446
$924$		0			0
$925$	9.28795			0.305386
$926$	11.8274	−	36.4011i	0.388673	−	1.19621i
$927$	5.21535	−	3.78917i	0.171295	−	0.124453i
$928$	−1.87911	−	1.36525i	−0.0616847	−	0.0448166i
$929$	8.21871	+	25.2946i	0.269647	+	0.829889i	0.990586	+	0.136890i	$0.0437108\pi$
$929$	8.21871	+	25.2946i	0.269647	+	0.829889i	−0.720939	+	0.692999i	$0.756289\pi$
$930$	0.442869	+	1.36301i	0.0145223	+	0.0446949i
$931$	−3.41560	−	2.48158i	−0.111942	−	0.0813306i
$932$	−0.0849566	+	0.0617246i	−0.00278285	+	0.00202186i
$933$	10.7063	−	32.9505i	0.350508	−	1.07875i
$934$	3.89900			0.127579
$935$		0			0
$936$	1.63883			0.0535669
$937$	12.9693	−	39.9155i	0.423690	−	1.30398i	−0.480554	−	0.876965i	$-0.659564\pi$
$937$	12.9693	−	39.9155i	0.423690	−	1.30398i	0.904243	−	0.427018i	$-0.140436\pi$
$938$	5.54839	−	4.03114i	0.181161	−	0.131621i
$939$	−41.3057	−	30.0104i	−1.34796	−	0.979351i
$940$	−0.139558	−	0.429516i	−0.00455189	−	0.0140093i
$941$	−15.1520	−	46.6331i	−0.493942	−	1.52020i	−0.818599	−	0.574365i	$-0.805249\pi$
$941$	−15.1520	−	46.6331i	−0.493942	−	1.52020i	0.324658	−	0.945832i	$-0.394751\pi$
$942$	36.2536	+	26.3398i	1.18121	+	0.858197i
$943$	−1.52037	+	1.10461i	−0.0495101	+	0.0359712i
$944$	11.3787	−	35.0199i	0.370344	−	1.13980i
$945$	−2.55402			−0.0830823
$946$		0			0
$947$	−27.2953			−0.886978			−0.443489	−	0.896280i	$-0.646259\pi$
$947$	−27.2953			−0.886978			−0.443489	+	0.896280i	$0.646259\pi$
$948$	−0.271006	+	0.834071i	−0.00880187	+	0.0270894i
$949$	−17.0512	+	12.3884i	−0.553506	+	0.402146i
$950$	−23.9576	−	17.4062i	−0.777286	−	0.564731i
$951$	6.60033	+	20.3137i	0.214030	+	0.658718i
$952$	−4.38004	−	13.4804i	−0.141958	−	0.436902i
$953$	−15.9706	−	11.6033i	−0.517339	−	0.375869i	0.298261	−	0.954484i	$-0.403593\pi$
$953$	−15.9706	−	11.6033i	−0.517339	−	0.375869i	−0.815601	+	0.578615i	$0.803593\pi$
$954$	5.98484	−	4.34824i	0.193766	−	0.140780i
$955$	−2.32046	+	7.14165i	−0.0750884	+	0.231098i
$956$	0.0524354			0.00169588
$957$		0			0
$958$	12.1478			0.392478
$959$	4.32958	−	13.3251i	0.139809	−	0.430289i
$960$	4.46409	−	3.24335i	0.144078	−	0.104679i
$961$	23.7252	+	17.2373i	0.765328	+	0.556043i
$962$	−1.39291	−	4.28693i	−0.0449091	−	0.138216i
$963$	1.82672	+	5.62206i	0.0588652	+	0.181169i
$964$	1.27757	+	0.928210i	0.0411478	+	0.0298956i
$965$	−4.58681	+	3.33251i	−0.147655	+	0.107277i
$966$	1.32376	−	4.07413i	0.0425914	−	0.131083i
$967$	−12.6734			−0.407551			−0.203775	−	0.979018i	$-0.565321\pi$
$967$	−12.6734			−0.407551			−0.203775	+	0.979018i	$0.565321\pi$
$968$		0			0
$969$	−35.7089			−1.14714
$970$	0.571934	−	1.76023i	0.0183637	−	0.0565176i
$971$	−13.5135	+	9.81814i	−0.433669	+	0.315079i	−0.783114	−	0.621878i	$-0.786370\pi$
$971$	−13.5135	+	9.81814i	−0.433669	+	0.315079i	0.349445	+	0.936957i	$0.386370\pi$
$972$	0.482803	+	0.350777i	0.0154859	+	0.0112512i
$973$	−2.95966	−	9.10889i	−0.0948823	−	0.292018i
$974$	8.88160	+	27.3347i	0.284585	+	0.875862i
$975$	9.90519	+	7.19654i	0.317220	+	0.230474i
$976$	−52.7669	+	38.3374i	−1.68903	+	1.22715i
$977$	8.45013	−	26.0068i	0.270344	−	0.832032i	−0.720070	−	0.693901i	$-0.755890\pi$
$977$	8.45013	−	26.0068i	0.270344	−	0.832032i	0.990414	−	0.138131i	$-0.0441096\pi$
$978$	27.5178			0.879924
$979$		0			0
$980$	0.0706175			0.00225579
$981$	−1.30249	+	4.00866i	−0.0415854	+	0.127987i
$982$	−34.0340	+	24.7271i	−1.08607	+	0.789074i
$983$	44.5012	+	32.3320i	1.41937	+	1.03123i	0.991876	+	0.127212i	$0.0406028\pi$
$983$	44.5012	+	32.3320i	1.41937	+	1.03123i	0.427492	+	0.904019i	$0.359397\pi$
$984$	1.41152	+	4.34422i	0.0449977	+	0.138489i
$985$	−0.331982	−	1.02174i	−0.0105778	−	0.0325552i
$986$	16.8683	+	12.2556i	0.537197	+	0.390297i
$987$	8.37155	−	6.08229i	0.266469	−	0.193601i
$988$	−0.312342	+	0.961291i	−0.00993693	+	0.0305827i
$989$	−15.7188			−0.499828
$990$		0			0
$991$	53.2327			1.69099			0.845497	−	0.533980i	$-0.179304\pi$
$991$	53.2327			1.69099			0.845497	+	0.533980i	$0.179304\pi$
$992$	0.341491	−	1.05100i	0.0108424	−	0.0333693i
$993$	12.4049	−	9.01272i	0.393659	−	0.286010i
$994$	−11.5613	−	8.39976i	−0.366701	−	0.266424i
$995$	2.92490	+	9.00193i	0.0927257	+	0.285380i
$996$	1.30565	+	4.01839i	0.0413712	+	0.127327i
$997$	−26.4990	−	19.2527i	−0.839232	−	0.609738i	0.0829239	−	0.996556i	$-0.473574\pi$
$997$	−26.4990	−	19.2527i	−0.839232	−	0.609738i	−0.922156	+	0.386818i	$0.873574\pi$
$998$	33.1657	−	24.0963i	1.04984	−	0.762754i
$999$	−3.28424	+	10.1079i	−0.103909	+	0.319798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.p.372.1		8
11.2	odd	10		847.2.f.q.729.1		8
11.3	even	5		77.2.f.a.15.2	✓	8
11.4	even	5		847.2.a.l.1.1		4
11.5	even	5	inner	847.2.f.p.148.1		8
11.6	odd	10		847.2.f.s.148.2		8
11.7	odd	10		847.2.a.k.1.4		4
11.8	odd	10		847.2.f.q.323.1		8
11.9	even	5		77.2.f.a.36.2	yes	8
11.10	odd	2		847.2.f.s.372.2		8
33.14	odd	10		693.2.m.g.631.1		8
33.20	odd	10		693.2.m.g.190.1		8
33.26	odd	10		7623.2.a.ch.1.4		4
33.29	even	10		7623.2.a.co.1.1		4
77.3	odd	30		539.2.q.b.422.1		16
77.9	even	15		539.2.q.c.410.1		16
77.20	odd	10		539.2.f.d.344.2		8
77.25	even	15		539.2.q.c.422.1		16
77.31	odd	30		539.2.q.b.520.2		16
77.47	odd	30		539.2.q.b.312.2		16
77.48	odd	10		5929.2.a.bi.1.1		4
77.53	even	15		539.2.q.c.520.2		16
77.58	even	15		539.2.q.c.312.2		16
77.62	even	10		5929.2.a.bb.1.4		4
77.69	odd	10		539.2.f.d.246.2		8
77.75	odd	30		539.2.q.b.410.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.a.15.2	✓	8	11.3	even	5
77.2.f.a.36.2	yes	8	11.9	even	5
539.2.f.d.246.2		8	77.69	odd	10
539.2.f.d.344.2		8	77.20	odd	10
539.2.q.b.312.2		16	77.47	odd	30
539.2.q.b.410.1		16	77.75	odd	30
539.2.q.b.422.1		16	77.3	odd	30
539.2.q.b.520.2		16	77.31	odd	30
539.2.q.c.312.2		16	77.58	even	15
539.2.q.c.410.1		16	77.9	even	15
539.2.q.c.422.1		16	77.25	even	15
539.2.q.c.520.2		16	77.53	even	15
693.2.m.g.190.1		8	33.20	odd	10
693.2.m.g.631.1		8	33.14	odd	10
847.2.a.k.1.4		4	11.7	odd	10
847.2.a.l.1.1		4	11.4	even	5
847.2.f.p.148.1		8	11.5	even	5	inner
847.2.f.p.372.1		8	1.1	even	1	trivial
847.2.f.q.323.1		8	11.8	odd	10
847.2.f.q.729.1		8	11.2	odd	10
847.2.f.s.148.2		8	11.6	odd	10
847.2.f.s.372.2		8	11.10	odd	2
5929.2.a.bb.1.4		4	77.62	even	10
5929.2.a.bi.1.1		4	77.48	odd	10
7623.2.a.ch.1.4		4	33.26	odd	10
7623.2.a.co.1.1		4	33.29	even	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)

\(f(q)\)	\(=\)	\(q+(-0.453245 + 1.39494i) q^{2} +(1.30902 - 0.951057i) q^{3} +(-0.122406 - 0.0889332i) q^{4} +(0.144228 + 0.443888i) q^{5} +(0.733366 + 2.25707i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-2.19369 + 1.59381i) q^{8} +(-0.118034 + 0.363271i) q^{9} +O(q^{10})\)	\(q+(-0.453245 + 1.39494i) q^{2} +(1.30902 - 0.951057i) q^{3} +(-0.122406 - 0.0889332i) q^{4} +(0.144228 + 0.443888i) q^{5} +(0.733366 + 2.25707i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-2.19369 + 1.59381i) q^{8} +(-0.118034 + 0.363271i) q^{9} -0.684570 q^{10} -0.244812 q^{12} +(-0.488963 + 1.50487i) q^{13} +(-1.18661 + 0.862123i) q^{14} +(0.610960 + 0.443888i) q^{15} +(-1.32250 - 4.07025i) q^{16} +(1.61533 + 4.97148i) q^{17} +(-0.453245 - 0.329302i) q^{18} +(-3.41560 + 2.48158i) q^{19} +(0.0218220 - 0.0671613i) q^{20} +1.61803 q^{21} -1.80505 q^{23} +(-1.35577 + 4.17264i) q^{24} +(3.86885 - 2.81088i) q^{25} +(-1.87759 - 1.36415i) q^{26} +(1.69098 + 5.20431i) q^{27} +(-0.0467549 - 0.143897i) q^{28} +(-2.20010 - 1.59846i) q^{29} +(-0.896114 + 0.651065i) q^{30} +(0.399825 - 1.23053i) q^{31} +0.854102 q^{32} -7.66708 q^{34} +(-0.144228 + 0.443888i) q^{35} +(0.0467549 - 0.0339695i) q^{36} +(1.57128 + 1.14160i) q^{37} +(-1.91356 - 5.88935i) q^{38} +(0.791158 + 2.43493i) q^{39} +(-1.02386 - 0.743880i) q^{40} +(0.842285 - 0.611956i) q^{41} +(-0.733366 + 2.25707i) q^{42} +8.70820 q^{43} -0.178276 q^{45} +(0.818132 - 2.51795i) q^{46} +(5.17390 - 3.75906i) q^{47} +(-5.60222 - 4.07025i) q^{48} +(0.309017 + 0.951057i) q^{49} +(2.16749 + 6.67085i) q^{50} +(6.84266 + 4.97148i) q^{51} +(0.193685 - 0.140720i) q^{52} +(-4.08039 + 12.5582i) q^{53} -8.02616 q^{54} -2.71154 q^{56} +(-2.11096 + 6.49687i) q^{57} +(3.22695 - 2.34452i) q^{58} +(6.96069 + 5.05724i) q^{59} +(-0.0353088 - 0.108669i) q^{60} +(-4.70947 - 14.4942i) q^{61} +(1.53531 + 1.11547i) q^{62} +(-0.309017 + 0.224514i) q^{63} +(2.25789 - 6.94907i) q^{64} -0.738517 q^{65} -4.67583 q^{67} +(0.244403 - 0.752196i) q^{68} +(-2.36285 + 1.71671i) q^{69} +(-0.553829 - 0.402380i) q^{70} +(3.01078 + 9.26624i) q^{71} +(-0.320054 - 0.985026i) q^{72} +(10.7761 + 7.82931i) q^{73} +(-2.30464 + 1.67442i) q^{74} +(2.39108 - 7.35899i) q^{75} +0.638786 q^{76} -3.75519 q^{78} +(1.10700 - 3.40699i) q^{79} +(1.61599 - 1.17409i) q^{80} +(6.23607 + 4.53077i) q^{81} +(0.471883 + 1.45231i) q^{82} +(-5.33329 - 16.4142i) q^{83} +(-0.198057 - 0.143897i) q^{84} +(-1.97381 + 1.43405i) q^{85} +(-3.94695 + 12.1475i) q^{86} -4.40020 q^{87} -8.91982 q^{89} +(0.0808026 - 0.248685i) q^{90} +(-1.28012 + 0.930062i) q^{91} +(0.220949 + 0.160529i) q^{92} +(-0.646930 - 1.99105i) q^{93} +(2.89864 + 8.92109i) q^{94} +(-1.59417 - 1.15823i) q^{95} +(1.11803 - 0.812299i) q^{96} +(-0.835464 + 2.57129i) q^{97} -1.46673 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + 6 q^{3} - 7 q^{4} + 3 q^{5} - 2 q^{6} + 2 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - q^2 + 6 * q^3 - 7 * q^4 + 3 * q^5 - 2 * q^6 + 2 * q^7 - 12 * q^8 + 8 * q^9	\( 8 q - q^{2} + 6 q^{3} - 7 q^{4} + 3 q^{5} - 2 q^{6} + 2 q^{7} - 12 q^{8} + 8 q^{9} - 28 q^{10} - 14 q^{12} - 5 q^{13} + q^{14} - 9 q^{15} + 7 q^{16} + 14 q^{17} - q^{18} + 6 q^{19} - 4 q^{20} + 4 q^{21} - 16 q^{23} - 9 q^{24} - 5 q^{25} - 9 q^{26} + 18 q^{27} - 3 q^{28} + 6 q^{29} - 26 q^{30} + 14 q^{31} - 20 q^{32} - 24 q^{34} - 3 q^{35} + 3 q^{36} + q^{37} - 15 q^{38} + 29 q^{40} + 18 q^{41} + 2 q^{42} + 16 q^{43} + 18 q^{45} - 26 q^{46} + 7 q^{47} - q^{48} - 2 q^{49} + q^{50} + 8 q^{51} - 4 q^{52} + 7 q^{53} + 4 q^{54} - 18 q^{56} - 3 q^{57} + 36 q^{58} + 17 q^{60} + 12 q^{61} - 5 q^{62} + 2 q^{63} - 4 q^{64} + 24 q^{65} - 30 q^{67} - 7 q^{68} - 22 q^{69} - 12 q^{70} + 21 q^{71} + 3 q^{72} + 8 q^{73} + q^{74} - 52 q^{76} - 18 q^{78} + q^{79} + 37 q^{80} + 32 q^{81} - 34 q^{82} - 22 q^{83} - 11 q^{84} - 5 q^{85} + 13 q^{86} + 12 q^{87} - 34 q^{89} - 18 q^{90} - 5 q^{91} + 51 q^{92} + 3 q^{93} + 50 q^{94} - 41 q^{95} - 15 q^{97} + 4 q^{98}+O(q^{100}) \) 8 * q - q^2 + 6 * q^3 - 7 * q^4 + 3 * q^5 - 2 * q^6 + 2 * q^7 - 12 * q^8 + 8 * q^9 - 28 * q^10 - 14 * q^12 - 5 * q^13 + q^14 - 9 * q^15 + 7 * q^16 + 14 * q^17 - q^18 + 6 * q^19 - 4 * q^20 + 4 * q^21 - 16 * q^23 - 9 * q^24 - 5 * q^25 - 9 * q^26 + 18 * q^27 - 3 * q^28 + 6 * q^29 - 26 * q^30 + 14 * q^31 - 20 * q^32 - 24 * q^34 - 3 * q^35 + 3 * q^36 + q^37 - 15 * q^38 + 29 * q^40 + 18 * q^41 + 2 * q^42 + 16 * q^43 + 18 * q^45 - 26 * q^46 + 7 * q^47 - q^48 - 2 * q^49 + q^50 + 8 * q^51 - 4 * q^52 + 7 * q^53 + 4 * q^54 - 18 * q^56 - 3 * q^57 + 36 * q^58 + 17 * q^60 + 12 * q^61 - 5 * q^62 + 2 * q^63 - 4 * q^64 + 24 * q^65 - 30 * q^67 - 7 * q^68 - 22 * q^69 - 12 * q^70 + 21 * q^71 + 3 * q^72 + 8 * q^73 + q^74 - 52 * q^76 - 18 * q^78 + q^79 + 37 * q^80 + 32 * q^81 - 34 * q^82 - 22 * q^83 - 11 * q^84 - 5 * q^85 + 13 * q^86 + 12 * q^87 - 34 * q^89 - 18 * q^90 - 5 * q^91 + 51 * q^92 + 3 * q^93 + 50 * q^94 - 41 * q^95 - 15 * q^97 + 4 * q^98

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