LMFDB - Embedded newform 847.2.f.y.148.5

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:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			148.5
Character	$\chi$	$=$	847.148
Dual form			847.2.f.y.372.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.651837 + 2.00615i) q^{2} +(-1.37413 - 0.998361i) q^{3} +(-1.98170 + 1.43979i) q^{4} +(0.152157 - 0.468292i) q^{5} +(1.10715 - 3.40747i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-0.767119 - 0.557345i) q^{8} +(-0.0355535 - 0.109422i) q^{9} +O(q^{10})$	\(q+(0.651837 + 2.00615i) q^{2} +(-1.37413 - 0.998361i) q^{3} +(-1.98170 + 1.43979i) q^{4} +(0.152157 - 0.468292i) q^{5} +(1.10715 - 3.40747i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-0.767119 - 0.557345i) q^{8} +(-0.0355535 - 0.109422i) q^{9} +1.03864 q^{10} +4.16054 q^{12} +(1.63788 + 5.04088i) q^{13} +(-1.70653 - 1.23987i) q^{14} +(-0.676607 + 0.491584i) q^{15} +(-0.895807 + 2.75701i) q^{16} +(0.938548 - 2.88855i) q^{17} +(0.196342 - 0.142651i) q^{18} +(3.77505 + 2.74274i) q^{19} +(0.372712 + 1.14709i) q^{20} +1.69851 q^{21} -5.63835 q^{23} +(0.497687 + 1.53172i) q^{24} +(3.84894 + 2.79642i) q^{25} +(-9.04511 + 6.57166i) q^{26} +(-1.63500 + 5.03200i) q^{27} +(0.756943 - 2.32963i) q^{28} +(-5.60079 + 4.06921i) q^{29} +(-1.42723 - 1.03694i) q^{30} +(-0.391107 - 1.20370i) q^{31} -8.01131 q^{32} +6.40665 q^{34} +(0.152157 + 0.468292i) q^{35} +(0.228002 + 0.165653i) q^{36} +(-8.79875 + 6.39267i) q^{37} +(-3.04162 + 9.36113i) q^{38} +(2.78196 - 8.56200i) q^{39} +(-0.377723 + 0.274432i) q^{40} +(1.16759 + 0.848303i) q^{41} +(1.10715 + 3.40747i) q^{42} +2.88224 q^{43} -0.0566513 q^{45} +(-3.67528 - 11.3114i) q^{46} +(7.08312 + 5.14619i) q^{47} +(3.98344 - 2.89414i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-3.10115 + 9.54435i) q^{50} +(-4.17350 + 3.03223i) q^{51} +(-10.5036 - 7.63132i) q^{52} +(2.05136 + 6.31345i) q^{53} -11.1607 q^{54} +0.948212 q^{56} +(-2.44916 - 7.53773i) q^{57} +(-11.8142 - 8.58355i) q^{58} +(6.76123 - 4.91232i) q^{59} +(0.633056 - 1.94835i) q^{60} +(-4.29388 + 13.2152i) q^{61} +(2.15987 - 1.56924i) q^{62} +(0.0930802 + 0.0676268i) q^{63} +(-3.43046 - 10.5579i) q^{64} +2.60982 q^{65} -9.70431 q^{67} +(2.29899 + 7.07557i) q^{68} +(7.74780 + 5.62911i) q^{69} +(-0.840281 + 0.610500i) q^{70} +(1.83788 - 5.65641i) q^{71} +(-0.0337122 + 0.103756i) q^{72} +(3.05340 - 2.21842i) q^{73} +(-18.5600 - 13.4846i) q^{74} +(-2.49709 - 7.68526i) q^{75} -11.4300 q^{76} +18.9900 q^{78} +(-2.72053 - 8.37294i) q^{79} +(1.15478 + 0.838998i) q^{80} +(6.99120 - 5.07941i) q^{81} +(-0.940743 + 2.89531i) q^{82} +(3.42694 - 10.5470i) q^{83} +(-3.36595 + 2.44550i) q^{84} +(-1.20988 - 0.879029i) q^{85} +(1.87875 + 5.78219i) q^{86} +11.7587 q^{87} +3.10324 q^{89} +(-0.0369274 - 0.113651i) q^{90} +(-4.28803 - 3.11543i) q^{91} +(11.1735 - 8.11805i) q^{92} +(-0.664300 + 2.04451i) q^{93} +(-5.70697 + 17.5643i) q^{94} +(1.85880 - 1.35050i) q^{95} +(11.0086 + 7.99818i) q^{96} +(-1.95199 - 6.00759i) q^{97} +2.10939 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 6 q^{6} - 6 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) $ 24 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 6 * q^6 - 6 * q^7 - 12 * q^8 - 8 * q^9	\( 24 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 6 q^{6} - 6 q^{7} - 12 q^{8} - 8 q^{9} - 32 q^{10} - 56 q^{12} - 4 q^{13} - 4 q^{14} - 2 q^{15} - 8 q^{16} - 22 q^{17} - 24 q^{18} - 6 q^{19} - 2 q^{20} - 8 q^{21} + 8 q^{23} + 20 q^{24} - 4 q^{25} - 6 q^{26} + 2 q^{27} - 4 q^{28} - 12 q^{29} - 20 q^{30} + 2 q^{31} + 32 q^{32} + 96 q^{34} + 4 q^{35} - 18 q^{36} - 14 q^{37} + 22 q^{38} - 20 q^{39} - 18 q^{40} - 26 q^{41} + 6 q^{42} - 16 q^{43} - 144 q^{45} - 12 q^{46} + 16 q^{47} + 24 q^{48} - 6 q^{49} + 4 q^{50} + 4 q^{51} - 12 q^{52} - 4 q^{53} - 128 q^{54} + 48 q^{56} - 20 q^{57} + 2 q^{58} + 4 q^{59} - 24 q^{60} + 8 q^{61} - 20 q^{62} - 8 q^{63} - 26 q^{64} + 96 q^{65} + 24 q^{67} - 12 q^{68} + 14 q^{69} + 8 q^{70} - 22 q^{71} - 16 q^{72} - 14 q^{73} - 44 q^{74} + 20 q^{75} - 120 q^{76} + 128 q^{78} + 28 q^{79} + 4 q^{80} + 6 q^{81} + 4 q^{82} - 22 q^{83} + 14 q^{84} + 24 q^{85} + 30 q^{86} + 88 q^{87} + 22 q^{90} - 4 q^{91} - 10 q^{92} + 50 q^{93} + 38 q^{94} + 24 q^{95} + 62 q^{96} + 4 q^{97} + 16 q^{98}+O(q^{100}) \) 24 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 6 * q^6 - 6 * q^7 - 12 * q^8 - 8 * q^9 - 32 * q^10 - 56 * q^12 - 4 * q^13 - 4 * q^14 - 2 * q^15 - 8 * q^16 - 22 * q^17 - 24 * q^18 - 6 * q^19 - 2 * q^20 - 8 * q^21 + 8 * q^23 + 20 * q^24 - 4 * q^25 - 6 * q^26 + 2 * q^27 - 4 * q^28 - 12 * q^29 - 20 * q^30 + 2 * q^31 + 32 * q^32 + 96 * q^34 + 4 * q^35 - 18 * q^36 - 14 * q^37 + 22 * q^38 - 20 * q^39 - 18 * q^40 - 26 * q^41 + 6 * q^42 - 16 * q^43 - 144 * q^45 - 12 * q^46 + 16 * q^47 + 24 * q^48 - 6 * q^49 + 4 * q^50 + 4 * q^51 - 12 * q^52 - 4 * q^53 - 128 * q^54 + 48 * q^56 - 20 * q^57 + 2 * q^58 + 4 * q^59 - 24 * q^60 + 8 * q^61 - 20 * q^62 - 8 * q^63 - 26 * q^64 + 96 * q^65 + 24 * q^67 - 12 * q^68 + 14 * q^69 + 8 * q^70 - 22 * q^71 - 16 * q^72 - 14 * q^73 - 44 * q^74 + 20 * q^75 - 120 * q^76 + 128 * q^78 + 28 * q^79 + 4 * q^80 + 6 * q^81 + 4 * q^82 - 22 * q^83 + 14 * q^84 + 24 * q^85 + 30 * q^86 + 88 * q^87 + 22 * q^90 - 4 * q^91 - 10 * q^92 + 50 * q^93 + 38 * q^94 + 24 * q^95 + 62 * q^96 + 4 * q^97 + 16 * 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 $

$2$	0.651837	+	2.00615i	0.460918	+	1.41856i	0.864044	+	0.503416i	$0.167924\pi$
$2$	0.651837	+	2.00615i	0.460918	+	1.41856i	−0.403126	+	0.915145i	$0.632076\pi$
$3$	−1.37413	−	0.998361i	−0.793352	−	0.576404i	0.115604	−	0.993295i	$-0.463120\pi$
$3$	−1.37413	−	0.998361i	−0.793352	−	0.576404i	−0.908956	+	0.416891i	$0.863120\pi$
$4$	−1.98170	+	1.43979i	−0.990852	+	0.719896i
$5$	0.152157	−	0.468292i	0.0680468	−	0.209426i	−0.911251	−	0.411851i	$-0.864882\pi$
$5$	0.152157	−	0.468292i	0.0680468	−	0.209426i	0.979298	+	0.202425i	$0.0648822\pi$
$6$	1.10715	−	3.40747i	0.451993	−	1.39109i
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$8$	−0.767119	−	0.557345i	−0.271218	−	0.197051i
$9$	−0.0355535	−	0.109422i	−0.0118512	−	0.0364741i
$10$	1.03864			0.328448
$11$		0			0
$11$		0			0
$12$	4.16054			1.20104
$13$	1.63788	+	5.04088i	0.454266	+	1.39809i	0.871994	+	0.489516i	$0.162826\pi$
$13$	1.63788	+	5.04088i	0.454266	+	1.39809i	−0.417728	+	0.908572i	$0.637174\pi$
$14$	−1.70653	−	1.23987i	−0.456090	−	0.331369i
$15$	−0.676607	+	0.491584i	−0.174699	+	0.126926i
$16$	−0.895807	+	2.75701i	−0.223952	+	0.689253i
$17$	0.938548	−	2.88855i	0.227631	−	0.700577i	−0.770382	−	0.637582i	$-0.779935\pi$
$17$	0.938548	−	2.88855i	0.227631	−	0.700577i	0.998014	−	0.0629954i	$-0.0200653\pi$
$18$	0.196342	−	0.142651i	0.0462783	−	0.0336232i
$19$	3.77505	+	2.74274i	0.866057	+	0.629227i	0.929526	−	0.368757i	$-0.120216\pi$
$19$	3.77505	+	2.74274i	0.866057	+	0.629227i	−0.0634692	+	0.997984i	$0.520216\pi$
$20$	0.372712	+	1.14709i	0.0833410	+	0.256497i
$21$	1.69851			0.370646
$22$		0			0
$23$	−5.63835			−1.17568			−0.587839	−	0.808978i	$-0.700021\pi$
$23$	−5.63835			−1.17568			−0.587839	+	0.808978i	$0.700021\pi$
$24$	0.497687	+	1.53172i	0.101590	+	0.312662i
$25$	3.84894	+	2.79642i	0.769788	+	0.559284i
$26$	−9.04511	+	6.57166i	−1.77389	+	1.28881i
$27$	−1.63500	+	5.03200i	−0.314655	+	0.968409i
$28$	0.756943	−	2.32963i	0.143049	−	0.440259i
$29$	−5.60079	+	4.06921i	−1.04004	+	0.755633i	−0.970293	−	0.241931i	$-0.922219\pi$
$29$	−5.60079	+	4.06921i	−1.04004	+	0.755633i	−0.0697469	+	0.997565i	$0.522219\pi$
$30$	−1.42723	−	1.03694i	−0.260575	−	0.189319i
$31$	−0.391107	−	1.20370i	−0.0702449	−	0.216192i	0.909771	−	0.415110i	$-0.136257\pi$
$31$	−0.391107	−	1.20370i	−0.0702449	−	0.216192i	−0.980016	+	0.198919i	$0.936257\pi$
$32$	−8.01131			−1.41621
$33$		0			0
$34$	6.40665			1.09873
$35$	0.152157	+	0.468292i	0.0257193	+	0.0791558i
$36$	0.228002	+	0.165653i	0.0380003	+	0.0276088i
$37$	−8.79875	+	6.39267i	−1.44651	+	1.05095i	−0.459874	+	0.887984i	$0.652105\pi$
$37$	−8.79875	+	6.39267i	−1.44651	+	1.05095i	−0.986632	+	0.162964i	$0.947895\pi$
$38$	−3.04162	+	9.36113i	−0.493415	+	1.51858i
$39$	2.78196	−	8.56200i	0.445470	−	1.37102i
$40$	−0.377723	+	0.274432i	−0.0597232	+	0.0433915i
$41$	1.16759	+	0.848303i	0.182347	+	0.132483i	0.675214	−	0.737622i	$-0.264051\pi$
$41$	1.16759	+	0.848303i	0.182347	+	0.132483i	−0.492867	+	0.870104i	$0.664051\pi$
$42$	1.10715	+	3.40747i	0.170837	+	0.525784i
$43$	2.88224			0.439537			0.219769	−	0.975552i	$-0.429470\pi$
$43$	2.88224			0.439537			0.219769	+	0.975552i	$0.429470\pi$
$44$		0			0
$45$	−0.0566513			−0.00844508
$46$	−3.67528	−	11.3114i	−0.541891	−	1.66777i
$47$	7.08312	+	5.14619i	1.03318	+	0.750649i	0.968943	−	0.247286i	$-0.0795387\pi$
$47$	7.08312	+	5.14619i	1.03318	+	0.750649i	0.0642367	+	0.997935i	$0.479539\pi$
$48$	3.98344	−	2.89414i	0.574961	−	0.417733i
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	−3.10115	+	9.54435i	−0.438568	+	1.34977i
$51$	−4.17350	+	3.03223i	−0.584407	+	0.424597i
$52$	−10.5036	−	7.63132i	−1.45659	−	1.05827i
$53$	2.05136	+	6.31345i	0.281776	+	0.867219i	0.987346	+	0.158578i	$0.0506910\pi$
$53$	2.05136	+	6.31345i	0.281776	+	0.867219i	−0.705570	+	0.708640i	$0.749309\pi$
$54$	−11.1607			−1.51878
$55$		0			0
$56$	0.948212			0.126710
$57$	−2.44916	−	7.53773i	−0.324399	−	0.998397i
$58$	−11.8142	−	8.58355i	−1.55129	−	1.12707i
$59$	6.76123	−	4.91232i	0.880237	−	0.639529i	−0.0530775	−	0.998590i	$-0.516903\pi$
$59$	6.76123	−	4.91232i	0.880237	−	0.639529i	0.933314	+	0.359061i	$0.116903\pi$
$60$	0.633056	−	1.94835i	0.0817272	−	0.251531i
$61$	−4.29388	+	13.2152i	−0.549775	+	1.69203i	0.159583	+	0.987185i	$0.448985\pi$
$61$	−4.29388	+	13.2152i	−0.549775	+	1.69203i	−0.709358	+	0.704849i	$0.751015\pi$
$62$	2.15987	−	1.56924i	0.274304	−	0.199293i
$63$	0.0930802	+	0.0676268i	0.0117270	+	0.00852017i
$64$	−3.43046	−	10.5579i	−0.428807	−	1.31973i
$65$	2.60982			0.323708
$66$		0			0
$67$	−9.70431			−1.18557			−0.592785	−	0.805361i	$-0.701972\pi$
$67$	−9.70431			−1.18557			−0.592785	+	0.805361i	$0.701972\pi$
$68$	2.29899	+	7.07557i	0.278794	+	0.858039i
$69$	7.74780	+	5.62911i	0.932726	+	0.677665i
$70$	−0.840281	+	0.610500i	−0.100433	+	0.0729687i
$71$	1.83788	−	5.65641i	0.218116	−	0.671293i	−0.780801	−	0.624779i	$-0.785189\pi$
$71$	1.83788	−	5.65641i	0.218116	−	0.671293i	0.998918	−	0.0465136i	$-0.0148111\pi$
$72$	−0.0337122	+	0.103756i	−0.00397302	+	0.0122277i
$73$	3.05340	−	2.21842i	0.357373	−	0.259647i	−0.394582	−	0.918861i	$-0.629111\pi$
$73$	3.05340	−	2.21842i	0.357373	−	0.259647i	0.751956	+	0.659214i	$0.229111\pi$
$74$	−18.5600	−	13.4846i	−2.15755	−	1.56756i
$75$	−2.49709	−	7.68526i	−0.288339	−	0.887418i
$76$	−11.4300			−1.31111
$77$		0			0
$78$	18.9900			2.15020
$79$	−2.72053	−	8.37294i	−0.306084	−	0.942030i	−0.979271	−	0.202557i	$-0.935075\pi$
$79$	−2.72053	−	8.37294i	−0.306084	−	0.942030i	0.673187	−	0.739473i	$-0.264925\pi$
$80$	1.15478	+	0.838998i	0.129109	+	0.0938029i
$81$	6.99120	−	5.07941i	0.776800	−	0.564378i
$82$	−0.940743	+	2.89531i	−0.103888	+	0.319734i
$83$	3.42694	−	10.5470i	0.376155	−	1.15769i	−0.566541	−	0.824034i	$-0.691719\pi$
$83$	3.42694	−	10.5470i	0.376155	−	1.15769i	0.942696	−	0.333653i	$-0.108281\pi$
$84$	−3.36595	+	2.44550i	−0.367255	+	0.266826i
$85$	−1.20988	−	0.879029i	−0.131230	−	0.0953441i
$86$	1.87875	+	5.78219i	0.202591	+	0.623510i
$87$	11.7587			1.26067
$88$		0			0
$89$	3.10324			0.328943			0.164472	−	0.986382i	$-0.447408\pi$
$89$	3.10324			0.328943			0.164472	+	0.986382i	$0.447408\pi$
$90$	−0.0369274	−	0.113651i	−0.00389249	−	0.0119799i
$91$	−4.28803	−	3.11543i	−0.449507	−	0.326586i
$92$	11.1735	−	8.11805i	1.16492	−	0.846365i
$93$	−0.664300	+	2.04451i	−0.0688847	+	0.212005i
$94$	−5.70697	+	17.5643i	−0.588629	+	1.81162i
$95$	1.85880	−	1.35050i	0.190709	−	0.138558i
$96$	11.0086	+	7.99818i	1.12356	+	0.816311i
$97$	−1.95199	−	6.00759i	−0.198194	−	0.609979i	−0.999924	−	0.0122928i	$-0.996087\pi$
$97$	−1.95199	−	6.00759i	−0.198194	−	0.609979i	0.801730	−	0.597686i	$-0.203913\pi$
$98$	2.10939			0.213080
$99$		0			0
$100$	−11.6537			−1.16537
$101$	3.64591	+	11.2210i	0.362782	+	1.11653i	0.951359	+	0.308086i	$0.0996883\pi$
$101$	3.64591	+	11.2210i	0.362782	+	1.11653i	−0.588577	+	0.808441i	$0.700312\pi$
$102$	−8.80354	−	6.39615i	−0.871680	−	0.633313i
$103$	−5.66769	+	4.11782i	−0.558454	+	0.405741i	−0.830893	−	0.556433i	$-0.812170\pi$
$103$	−5.66769	+	4.11782i	−0.558454	+	0.405741i	0.272439	+	0.962173i	$0.412170\pi$
$104$	1.55306	−	4.77982i	0.152290	−	0.468700i
$105$	0.258441	−	0.795400i	0.0252213	−	0.0776231i
$106$	−11.3286	+	8.23067i	−1.10033	+	0.799434i
$107$	−9.18614	−	6.67412i	−0.888058	−	0.645212i	0.0473130	−	0.998880i	$-0.484934\pi$
$107$	−9.18614	−	6.67412i	−0.888058	−	0.645212i	−0.935371	+	0.353668i	$0.884934\pi$
$108$	−4.00496	−	12.3260i	−0.385377	−	1.18607i
$109$	18.9414			1.81426			0.907129	−	0.420853i	$-0.138269\pi$
$109$	18.9414			1.81426			0.907129	+	0.420853i	$0.138269\pi$
$110$		0			0
$111$	18.4728			1.75336
$112$	−0.895807	−	2.75701i	−0.0846458	−	0.260513i
$113$	10.9186	+	7.93282i	1.02713	+	0.746257i	0.967733	−	0.251978i	$-0.0810809\pi$
$113$	10.9186	+	7.93282i	1.02713	+	0.746257i	0.0594010	+	0.998234i	$0.481081\pi$
$114$	13.5254	−	9.82674i	1.26677	−	0.920359i
$115$	−0.857916	+	2.64039i	−0.0800011	+	0.246218i
$116$	5.24028	−	16.1279i	0.486548	−	1.49744i
$117$	0.493353	−	0.358442i	0.0456105	−	0.0331379i
$118$	14.2621	+	10.3620i	1.31293	+	0.953898i
$119$	0.938548	+	2.88855i	0.0860366	+	0.264793i
$120$	0.793021			0.0723925
$121$		0			0
$122$	−29.3106			−2.65365
$123$	−0.757501	−	2.33135i	−0.0683016	−	0.210211i
$124$	2.50814	+	1.82227i	0.225238	+	0.163645i
$125$	3.88695	−	2.82403i	0.347659	−	0.252589i
$126$	−0.0749961	+	0.230814i	−0.00668119	+	0.0205626i
$127$	−1.44022	+	4.43253i	−0.127799	+	0.393323i	−0.994401	−	0.105676i	$-0.966299\pi$
$127$	−1.44022	+	4.43253i	−0.127799	+	0.393323i	0.866602	+	0.499000i	$0.166299\pi$
$128$	5.98194	−	4.34614i	0.528734	−	0.384148i
$129$	−3.96056	−	2.87751i	−0.348708	−	0.253351i
$130$	1.70118	+	5.23568i	0.149203	+	0.459199i
$131$	9.03676			0.789545			0.394773	−	0.918779i	$-0.370823\pi$
$131$	9.03676			0.789545			0.394773	+	0.918779i	$0.370823\pi$
$132$		0			0
$133$	−4.66622			−0.404613
$134$	−6.32563	−	19.4683i	−0.546451	−	1.68180i
$135$	2.10767	+	1.53131i	0.181399	+	0.131794i
$136$	−2.32990	+	1.69277i	−0.199787	+	0.145154i
$137$	−0.506084	+	1.55757i	−0.0432377	+	0.133072i	−0.970345	−	0.241724i	$-0.922287\pi$
$137$	−0.506084	+	1.55757i	−0.0432377	+	0.133072i	0.927107	+	0.374796i	$0.122287\pi$
$138$	−6.24252	+	19.2125i	−0.531399	+	1.63548i
$139$	1.24161	−	0.902086i	0.105312	−	0.0765139i	−0.533883	−	0.845559i	$-0.679268\pi$
$139$	1.24161	−	0.902086i	0.105312	−	0.0765139i	0.639195	+	0.769045i	$0.279268\pi$
$140$	−0.975773	−	0.708941i	−0.0824679	−	0.0599164i
$141$	−4.59535	−	14.1430i	−0.386998	−	1.19106i
$142$	12.5456			1.05280
$143$		0			0
$144$	0.333528			0.0277940
$145$	1.05338	+	3.24196i	0.0874783	+	0.269230i
$146$	6.44080	+	4.67952i	0.533044	+	0.387279i
$147$	−1.37413	+	0.998361i	−0.113336	+	0.0823434i
$148$	8.23241	−	25.3367i	0.676700	−	2.08267i
$149$	4.16893	−	12.8306i	0.341532	−	1.05113i	−0.621882	−	0.783111i	$-0.713632\pi$
$149$	4.16893	−	12.8306i	0.341532	−	1.05113i	0.963414	−	0.268017i	$-0.0863682\pi$
$150$	13.7901	−	10.0191i	1.12595	−	0.818054i
$151$	9.89996	+	7.19274i	0.805647	+	0.585337i	0.912565	−	0.408931i	$-0.134098\pi$
$151$	9.89996	+	7.19274i	0.805647	+	0.585337i	−0.106918	+	0.994268i	$0.534098\pi$
$152$	−1.36727	−	4.20801i	−0.110900	−	0.341315i
$153$	−0.349441			−0.0282507
$154$		0			0
$155$	−0.623194			−0.0500562
$156$	6.81447	+	20.9728i	0.545594	+	1.67917i
$157$	−2.03906	−	1.48147i	−0.162735	−	0.118234i	0.503437	−	0.864032i	$-0.332068\pi$
$157$	−2.03906	−	1.48147i	−0.162735	−	0.118234i	−0.666172	+	0.745798i	$0.732068\pi$
$158$	15.0240	−	10.9156i	1.19525	−	0.868397i
$159$	3.48427	−	10.7235i	0.276320	−	0.850427i
$160$	−1.21898	+	3.75163i	−0.0963688	+	0.296593i
$161$	4.56152	−	3.31414i	0.359498	−	0.261191i
$162$	14.7472	+	10.7144i	1.15865	+	0.841806i
$163$	2.43476	+	7.49342i	0.190705	+	0.586930i	1.00000		0.000472827i	$-0.000150506\pi$
$163$	2.43476	+	7.49342i	0.190705	+	0.586930i	−0.809295	+	0.587403i	$0.800151\pi$
$164$	−3.53519			−0.276052
$165$		0			0
$166$	23.3927			1.81562
$167$	−0.634985	−	1.95428i	−0.0491366	−	0.151227i	0.923478	−	0.383652i	$-0.125334\pi$
$167$	−0.634985	−	1.95428i	−0.0491366	−	0.151227i	−0.972614	+	0.232425i	$0.925334\pi$
$168$	−1.30296	−	0.946657i	−0.100526	−	0.0730362i
$169$	−12.2106	+	8.87150i	−0.939275	+	0.682423i
$170$	0.974818	−	3.00018i	0.0747651	−	0.230103i
$171$	0.165901	−	0.510589i	0.0126867	−	0.0390457i
$172$	−5.71174	+	4.14982i	−0.435516	+	0.316421i
$173$	18.8264	+	13.6781i	1.43134	+	1.03993i	0.989765	+	0.142706i	$0.0455804\pi$
$173$	18.8264	+	13.6781i	1.43134	+	1.03993i	0.441576	+	0.897224i	$0.354420\pi$
$174$	7.66477	+	23.5897i	0.581065	+	1.78833i
$175$	−4.75755			−0.359637
$176$		0			0
$177$	−14.1950			−1.06696
$178$	2.02281	+	6.22557i	0.151616	+	0.466626i
$179$	−14.2869	−	10.3800i	−1.06785	−	0.775840i	−0.0923277	−	0.995729i	$-0.529431\pi$
$179$	−14.2869	−	10.3800i	−1.06785	−	0.775840i	−0.975525	+	0.219888i	$0.929431\pi$
$180$	0.112266	−	0.0815661i	0.00836782	−	0.00607958i
$181$	4.78052	−	14.7129i	0.355333	−	1.09360i	−0.600483	−	0.799638i	$-0.705025\pi$
$181$	4.78052	−	14.7129i	0.355333	−	1.09360i	0.955816	−	0.293965i	$-0.0949750\pi$
$182$	3.45493	−	10.6332i	0.256096	−	0.788183i
$183$	19.0939	−	13.8725i	1.41146	−	1.02549i
$184$	4.32529	+	3.14251i	0.318864	+	0.231669i
$185$	1.65484	+	5.09307i	0.121666	+	0.374450i
$186$	−4.53460			−0.332493
$187$		0			0
$188$	−21.4461			−1.56412
$189$	−1.63500	−	5.03200i	−0.118928	−	0.366024i
$190$	3.92094	+	2.84873i	0.284455	+	0.206668i
$191$	−12.8945	+	9.36842i	−0.933015	+	0.677875i	−0.946729	−	0.322031i	$-0.895634\pi$
$191$	−12.8945	+	9.36842i	−0.933015	+	0.677875i	0.0137145	+	0.999906i	$0.495634\pi$
$192$	−5.82667	+	17.9327i	−0.420504	+	1.29418i
$193$	2.61239	−	8.04010i	0.188044	−	0.578739i	−0.811944	−	0.583736i	$-0.801590\pi$
$193$	2.61239	−	8.04010i	0.188044	−	0.578739i	0.999988	+	0.00499653i	$0.00159045\pi$
$194$	10.7797	−	7.83194i	0.773941	−	0.562301i
$195$	−3.58622	−	2.60554i	−0.256814	−	0.186587i
$196$	0.756943	+	2.32963i	0.0540674	+	0.166402i
$197$	−14.3384			−1.02157			−0.510785	−	0.859708i	$-0.670645\pi$
$197$	−14.3384			−1.02157			−0.510785	+	0.859708i	$0.670645\pi$
$198$		0			0
$199$	−22.1343			−1.56906			−0.784528	−	0.620094i	$-0.787095\pi$
$199$	−22.1343			−1.56906			−0.784528	+	0.620094i	$0.787095\pi$
$200$	−1.39403	−	4.29037i	−0.0985726	−	0.303375i
$201$	13.3349	+	9.68840i	0.940574	+	0.683367i
$202$	−20.1344	+	14.6285i	−1.41665	+	1.02926i
$203$	2.13931	−	6.58412i	0.150150	−	0.462115i
$204$	3.90487	−	12.0180i	0.273396	−	0.841425i
$205$	0.574910	−	0.417697i	0.0401535	−	0.0291732i
$206$	−11.9554	−	8.68608i	−0.832969	−	0.605188i
$207$	0.200463	+	0.616962i	0.0139331	+	0.0428818i
$208$	−15.3650			−1.06537
$209$		0			0
$210$	1.76415			0.121738
$211$	0.674591	+	2.07618i	0.0464408	+	0.142930i	0.971588	−	0.236678i	$-0.0760587\pi$
$211$	0.674591	+	2.07618i	0.0464408	+	0.142930i	−0.925147	+	0.379608i	$0.876059\pi$
$212$	−13.1552	−	9.55784i	−0.903506	−	0.656435i
$213$	−8.17262	+	5.93776i	−0.559979	+	0.406848i
$214$	7.40141	−	22.7792i	0.505950	−	1.55715i
$215$	0.438553	−	1.34973i	0.0299091	−	0.0920507i
$216$	4.05880	−	2.94889i	0.276166	−	0.200646i
$217$	1.02393	+	0.743930i	0.0695090	+	0.0505012i
$218$	12.3467	+	37.9993i	0.836225	+	2.57363i
$219$	−6.41054			−0.433184
$220$		0			0
$221$	16.0981			1.08287
$222$	12.0412	+	37.0591i	0.808155	+	2.48725i
$223$	−22.0541	−	16.0232i	−1.47685	−	1.07299i	−0.978555	−	0.205987i	$-0.933960\pi$
$223$	−22.0541	−	16.0232i	−1.47685	−	1.07299i	−0.498295	−	0.867007i	$-0.666040\pi$
$224$	6.48129	−	4.70893i	0.433049	−	0.314629i
$225$	0.169148	−	0.520583i	0.0112765	−	0.0347055i
$226$	−8.79726	+	27.0752i	−0.585185	+	1.80102i
$227$	10.9939	−	7.98752i	0.729689	−	0.530150i	−0.159776	−	0.987153i	$-0.551077\pi$
$227$	10.9939	−	7.98752i	0.729689	−	0.530150i	0.889465	+	0.457003i	$0.151077\pi$
$228$	15.7063	+	11.4113i	1.04017	+	0.755730i
$229$	−2.56528	−	7.89511i	−0.169518	−	0.521724i	0.829822	−	0.558028i	$-0.188442\pi$
$229$	−2.56528	−	7.89511i	−0.169518	−	0.521724i	−0.999341	+	0.0363037i	$0.988442\pi$
$230$	−5.85624			−0.386149
$231$		0			0
$232$	6.56443			0.430976
$233$	4.00104	+	12.3139i	0.262117	+	0.806713i	0.992344	+	0.123508i	$0.0394145\pi$
$233$	4.00104	+	12.3139i	0.262117	+	0.806713i	−0.730226	+	0.683205i	$0.760585\pi$
$234$	1.04067	+	0.756093i	0.0680309	+	0.0494273i
$235$	3.48767	−	2.53394i	0.227510	−	0.165296i
$236$	−6.32603	+	19.4695i	−0.411789	+	1.26736i
$237$	−4.62086	+	14.2215i	−0.300157	+	0.923789i
$238$	−5.18309	+	3.76573i	−0.335970	+	0.244096i
$239$	−1.53181	−	1.11292i	−0.0990844	−	0.0719890i	0.537140	−	0.843493i	$-0.319505\pi$
$239$	−1.53181	−	1.11292i	−0.0990844	−	0.0719890i	−0.636224	+	0.771504i	$0.719505\pi$
$240$	−0.749193	−	2.30578i	−0.0483602	−	0.148837i
$241$	−11.6983			−0.753557			−0.376778	−	0.926303i	$-0.622968\pi$
$241$	−11.6983			−0.753557			−0.376778	+	0.926303i	$0.622968\pi$
$242$		0			0
$243$	1.19500			0.0766595
$244$	−10.5179	−	32.3709i	−0.673342	−	2.07233i
$245$	−0.398353	−	0.289420i	−0.0254498	−	0.0184904i
$246$	4.18326	−	3.03932i	0.266715	−	0.193780i
$247$	−7.64272	+	23.5219i	−0.486294	+	1.49666i
$248$	−0.370852	+	1.14137i	−0.0235491	+	0.0724768i
$249$	−15.2388	+	11.0716i	−0.965718	+	0.701635i
$250$	8.19908	+	5.95698i	0.518556	+	0.376753i
$251$	−4.07469	−	12.5406i	−0.257192	−	0.791556i	−0.993390	−	0.114789i	$-0.963381\pi$
$251$	−4.07469	−	12.5406i	−0.257192	−	0.791556i	0.736198	−	0.676766i	$-0.236619\pi$
$252$	−0.281826			−0.0177534
$253$		0			0
$254$	−9.83110			−0.616858
$255$	0.784939	+	2.41579i	0.0491548	+	0.151283i
$256$	−5.34386	−	3.88254i	−0.333991	−	0.242659i
$257$	12.4140	−	9.01928i	0.774363	−	0.562607i	−0.128919	−	0.991655i	$-0.541151\pi$
$257$	12.4140	−	9.01928i	0.774363	−	0.562607i	0.903282	+	0.429048i	$0.141151\pi$
$258$	3.19108	−	9.82113i	0.198668	−	0.611437i
$259$	3.36082	−	10.3436i	0.208831	−	0.642717i
$260$	−5.17188	+	3.75759i	−0.320747	+	0.233036i
$261$	0.644390	+	0.468177i	0.0398868	+	0.0289794i
$262$	5.89049	+	18.1291i	0.363916	+	1.12002i
$263$	10.4197			0.642507			0.321254	−	0.946993i	$-0.395896\pi$
$263$	10.4197			0.642507			0.321254	+	0.946993i	$0.395896\pi$
$264$		0			0
$265$	3.26867			0.200792
$266$	−3.04162	−	9.36113i	−0.186493	−	0.573968i
$267$	−4.26425	−	3.09816i	−0.260968	−	0.189604i
$268$	19.2311	−	13.9722i	1.17472	−	0.853487i
$269$	5.02809	−	15.4749i	0.306568	−	0.943519i	−0.672520	−	0.740079i	$-0.734788\pi$
$269$	5.02809	−	15.4749i	0.306568	−	0.943519i	0.979088	−	0.203439i	$-0.0652120\pi$
$270$	−1.69818	+	5.22646i	−0.103348	+	0.318072i
$271$	4.72403	−	3.43221i	0.286964	−	0.208492i	−0.434985	−	0.900438i	$-0.643246\pi$
$271$	4.72403	−	3.43221i	0.286964	−	0.208492i	0.721949	+	0.691946i	$0.243246\pi$
$272$	7.12302	+	5.17518i	0.431896	+	0.313791i
$273$	2.78196	+	8.56200i	0.168372	+	0.518196i
$274$	−3.45459			−0.208700
$275$		0			0
$276$	−23.4586			−1.41204
$277$	4.92124	+	15.1460i	0.295689	+	0.910036i	0.982989	+	0.183663i	$0.0587955\pi$
$277$	4.92124	+	15.1460i	0.295689	+	0.910036i	−0.687301	+	0.726373i	$0.741205\pi$
$278$	2.61905	+	1.90285i	0.157080	+	0.114125i
$279$	−0.117807	+	0.0855917i	−0.00705291	+	0.00512424i
$280$	0.144277	−	0.444040i	0.00862222	−	0.0265365i
$281$	3.15209	−	9.70114i	0.188038	−	0.578721i	−0.811950	−	0.583728i	$-0.801594\pi$
$281$	3.15209	−	9.70114i	0.188038	−	0.578721i	0.999987	+	0.00500633i	$0.00159357\pi$
$282$	25.3776	−	18.4379i	1.51121	−	1.09796i
$283$	13.0764	+	9.50058i	0.777313	+	0.564751i	0.904171	−	0.427170i	$-0.140489\pi$
$283$	13.0764	+	9.50058i	0.777313	+	0.564751i	−0.126858	+	0.991921i	$0.540489\pi$
$284$	4.50192	+	13.8555i	0.267140	+	0.822173i
$285$	−3.90252			−0.231165
$286$		0			0
$287$	−1.44322			−0.0851905
$288$	0.284830	+	0.876617i	0.0167838	+	0.0516552i
$289$	6.29041	+	4.57025i	0.370024	+	0.268838i
$290$	−5.81723	+	4.22646i	−0.341599	+	0.248186i
$291$	−3.31547	+	10.2040i	−0.194356	+	0.598168i
$292$	−2.85686	+	8.79251i	−0.167185	+	0.514543i
$293$	−21.8853	+	15.9006i	−1.27855	+	0.928922i	−0.999508	−	0.0313567i	$-0.990017\pi$
$293$	−21.8853	+	15.9006i	−1.27855	+	0.928922i	−0.279043	+	0.960279i	$0.590017\pi$
$294$	−2.89857	−	2.10593i	−0.169048	−	0.122820i
$295$	−1.27163	−	3.91367i	−0.0740371	−	0.227863i
$296$	10.3126			0.599408
$297$		0			0
$298$	28.4576			1.64851
$299$	−9.23494	−	28.4222i	−0.534071	−	1.64370i
$300$	16.0137	+	11.6346i	0.924550	+	0.671725i
$301$	−2.33178	+	1.69414i	−0.134402	+	0.0976484i
$302$	−7.97654	+	24.5493i	−0.458998	+	1.41265i
$303$	6.19262	−	19.0589i	0.355757	−	1.09491i
$304$	−10.9435	+	7.95090i	−0.627651	+	0.456015i
$305$	5.53523	+	4.02158i	0.316946	+	0.230275i
$306$	−0.227779	−	0.701031i	−0.0130212	−	0.0400753i
$307$	29.7251			1.69650			0.848250	−	0.529596i	$-0.177657\pi$
$307$	29.7251			1.69650			0.848250	+	0.529596i	$0.177657\pi$
$308$		0			0
$309$	11.8992			0.676921
$310$	−0.406221	−	1.25022i	−0.0230718	−	0.0710077i
$311$	−18.1243	−	13.1681i	−1.02774	−	0.746694i	−0.0598820	−	0.998205i	$-0.519072\pi$
$311$	−18.1243	−	13.1681i	−1.02774	−	0.746694i	−0.967854	+	0.251511i	$0.919072\pi$
$312$	−6.90608	+	5.01756i	−0.390980	+	0.284063i
$313$	3.07420	−	9.46143i	0.173764	−	0.534792i	−0.825811	−	0.563948i	$-0.809282\pi$
$313$	3.07420	−	9.46143i	0.173764	−	0.534792i	0.999575	+	0.0291561i	$0.00928198\pi$
$314$	1.64290	−	5.05634i	0.0927144	−	0.285346i
$315$	0.0458319	−	0.0332988i	0.00258233	−	0.00187618i
$316$	17.4466	+	12.6757i	0.981447	+	0.713063i
$317$	−3.44306	−	10.5967i	−0.193382	−	0.595167i	−0.999992	−	0.00408350i	$-0.998700\pi$
$317$	−3.44306	−	10.5967i	−0.193382	−	0.595167i	0.806610	−	0.591084i	$-0.201300\pi$
$318$	23.7840			1.33374
$319$		0			0
$320$	−5.46613			−0.305566
$321$	5.95973	+	18.3422i	0.332640	+	1.02376i
$322$	9.62202	+	6.99081i	0.536214	+	0.389582i
$323$	11.4656	−	8.33026i	0.637964	−	0.463508i
$324$	−6.54120	+	20.1317i	−0.363400	+	1.11843i
$325$	−7.79230	+	23.9822i	−0.432239	+	1.33029i
$326$	−13.4458	+	9.76897i	−0.744696	+	0.541053i
$327$	−26.0279	−	18.9104i	−1.43934	−	1.04575i
$328$	−0.422883	−	1.30150i	−0.0233498	−	0.0718633i
$329$	−8.75522			−0.482691
$330$		0			0
$331$	14.5950			0.802214			0.401107	−	0.916031i	$-0.368626\pi$
$331$	14.5950			0.802214			0.401107	+	0.916031i	$0.368626\pi$
$332$	8.39435	+	25.8351i	0.460700	+	1.41789i
$333$	1.01233	+	0.735499i	0.0554752	+	0.0403051i
$334$	3.50667	−	2.54775i	0.191877	−	0.139406i
$335$	−1.47658	+	4.54445i	−0.0806742	+	0.248290i
$336$	−1.52154	+	4.68282i	−0.0830068	+	0.255469i
$337$	−10.1984	+	7.40957i	−0.555542	+	0.403625i	−0.829825	−	0.558024i	$-0.811560\pi$
$337$	−10.1984	+	7.40957i	−0.555542	+	0.403625i	0.274282	+	0.961649i	$0.411560\pi$
$338$	−25.7568	−	18.7134i	−1.40099	−	1.01788i
$339$	−7.08370	−	21.8014i	−0.384734	−	1.18409i
$340$	3.66324			0.198667
$341$		0			0
$342$	1.13246			0.0612363
$343$	0.309017	+	0.951057i	0.0166853	+	0.0513522i
$344$	−2.21102	−	1.60640i	−0.119210	−	0.0866113i
$345$	3.81495	−	2.77172i	0.205390	−	0.149225i
$346$	−15.1687	+	46.6844i	−0.815473	+	2.50977i
$347$	0.126924	−	0.390631i	0.00681363	−	0.0209702i	−0.947592	−	0.319483i	$-0.896491\pi$
$347$	0.126924	−	0.390631i	0.00681363	−	0.0209702i	0.954406	+	0.298513i	$0.0964907\pi$
$348$	−23.3023	+	16.9301i	−1.24913	+	0.907550i
$349$	−10.8429	−	7.87782i	−0.580407	−	0.421690i	0.258464	−	0.966021i	$-0.416784\pi$
$349$	−10.8429	−	7.87782i	−0.580407	−	0.421690i	−0.838871	+	0.544331i	$0.816784\pi$
$350$	−3.10115	−	9.54435i	−0.165763	−	0.510167i
$351$	−28.0436			−1.49686
$352$		0			0
$353$	12.3419			0.656892			0.328446	−	0.944523i	$-0.393475\pi$
$353$	12.3419			0.656892			0.328446	+	0.944523i	$0.393475\pi$
$354$	−9.25285	−	28.4773i	−0.491783	−	1.51355i
$355$	−2.36921	−	1.72133i	−0.125744	−	0.0913587i
$356$	−6.14971	+	4.46803i	−0.325934	+	0.236805i
$357$	1.59414	−	4.90625i	0.0843707	−	0.259666i
$358$	11.5112	−	35.4277i	0.608384	−	1.87241i
$359$	20.2333	−	14.7003i	1.06787	−	0.775854i	0.0923426	−	0.995727i	$-0.470565\pi$
$359$	20.2333	−	14.7003i	1.06787	−	0.775854i	0.975528	+	0.219874i	$0.0705645\pi$
$360$	0.0434583	+	0.0315743i	0.00229046	+	0.00166411i
$361$	0.857101	+	2.63789i	0.0451106	+	0.138836i
$362$	32.6324			1.71512
$363$		0			0
$364$	12.9832			0.680503
$365$	−0.574273	−	1.76743i	−0.0300588	−	0.0925115i
$366$	40.2764	+	29.2625i	2.10528	+	1.52958i
$367$	1.67398	−	1.21622i	0.0873809	−	0.0634859i	−0.543237	−	0.839579i	$-0.682802\pi$
$367$	1.67398	−	1.21622i	0.0873809	−	0.0634859i	0.630618	+	0.776093i	$0.282802\pi$
$368$	5.05087	−	15.5450i	0.263295	−	0.810339i
$369$	0.0513115	−	0.157920i	0.00267117	−	0.00822101i
$370$	−9.13877	+	6.63971i	−0.475102	+	0.345182i
$371$	−5.37054	−	3.90192i	−0.278824	−	0.202578i
$372$	−1.62722	−	5.00806i	−0.0843673	−	0.259656i
$373$	−14.7623			−0.764365			−0.382183	−	0.924087i	$-0.624828\pi$
$373$	−14.7623			−0.764365			−0.382183	+	0.924087i	$0.624828\pi$
$374$		0			0
$375$	−8.16056			−0.421410
$376$	−2.56540	−	7.89548i	−0.132300	−	0.407178i
$377$	−29.6858	−	21.5680i	−1.52890	−	1.11081i
$378$	9.02919	−	6.56009i	0.464411	−	0.337415i
$379$	8.57546	−	26.3925i	0.440492	−	1.35569i	−0.446862	−	0.894603i	$-0.647458\pi$
$379$	8.57546	−	26.3925i	0.440492	−	1.35569i	0.887353	−	0.461090i	$-0.152542\pi$
$380$	−1.73916	+	5.35258i	−0.0892169	+	0.274581i
$381$	6.40430	−	4.65300i	0.328102	−	0.238380i
$382$	−27.1995	−	19.7616i	−1.39165	−	1.01109i
$383$	−5.57263	−	17.1508i	−0.284748	−	0.876365i	−0.986474	−	0.163918i	$-0.947587\pi$
$383$	−5.57263	−	17.1508i	−0.284748	−	0.876365i	0.701726	−	0.712447i	$-0.252413\pi$
$384$	−12.5590			−0.640897
$385$		0			0
$386$	17.8325			0.907649
$387$	−0.102474	−	0.315381i	−0.00520903	−	0.0160317i
$388$	12.5179	+	9.09481i	0.635502	+	0.461719i
$389$	−10.9550	+	7.95929i	−0.555442	+	0.403552i	−0.829788	−	0.558079i	$-0.811539\pi$
$389$	−10.9550	+	7.95929i	−0.555442	+	0.403552i	0.274346	+	0.961631i	$0.411539\pi$
$390$	2.88947	−	8.89287i	0.146314	−	0.450308i
$391$	−5.29186	+	16.2867i	−0.267621	+	0.823653i
$392$	−0.767119	+	0.557345i	−0.0387454	+	0.0281502i
$393$	−12.4176	−	9.02195i	−0.626387	−	0.455097i
$394$	−9.34632	−	28.7650i	−0.470861	−	1.44916i
$395$	−4.33493			−0.218114
$396$		0			0
$397$	−24.6525			−1.23727			−0.618637	−	0.785677i	$-0.712315\pi$
$397$	−24.6525			−1.23727			−0.618637	+	0.785677i	$0.712315\pi$
$398$	−14.4279	−	44.4046i	−0.723206	−	2.22580i
$399$	6.41198	+	4.65857i	0.321000	+	0.233220i
$400$	−11.1577	+	8.10652i	−0.557883	+	0.405326i
$401$	5.79065	−	17.8218i	0.289171	−	0.889978i	−0.695946	−	0.718094i	$-0.745015\pi$
$401$	5.79065	−	17.8218i	0.289171	−	0.889978i	0.985117	−	0.171884i	$-0.0549853\pi$
$402$	−10.7442	+	33.0671i	−0.535870	+	1.64924i
$403$	5.42714	−	3.94305i	0.270345	−	0.196417i
$404$	−23.3809	−	16.9873i	−1.16325	−	0.845147i
$405$	−1.31488	−	4.04679i	−0.0653370	−	0.201087i
$406$	14.6032			0.724745
$407$		0			0
$408$	4.89157			0.242169
$409$	4.85461	+	14.9409i	0.240045	+	0.738782i	0.996412	+	0.0846347i	$0.0269723\pi$
$409$	4.85461	+	14.9409i	0.240045	+	0.738782i	−0.756367	+	0.654147i	$0.773028\pi$
$410$	1.21271	+	0.881085i	0.0598914	+	0.0435137i
$411$	2.25044	−	1.63504i	0.111006	−	0.0806505i
$412$	5.30288	−	16.3206i	0.261254	−	0.804057i
$413$	−2.58256	+	7.94830i	−0.127079	+	0.391110i
$414$	−1.10705	+	0.804317i	−0.0544084	+	0.0395300i
$415$	−4.41765	−	3.20961i	−0.216854	−	0.157554i
$416$	−13.1216	−	40.3841i	−0.643338	−	1.97999i
$417$	−2.60674			−0.127653
$418$		0			0
$419$	22.6034			1.10425			0.552125	−	0.833761i	$-0.313817\pi$
$419$	22.6034			1.10425			0.552125	+	0.833761i	$0.313817\pi$
$420$	0.633056	+	1.94835i	0.0308900	+	0.0950696i
$421$	18.8752	+	13.7137i	0.919923	+	0.668363i	0.943505	−	0.331359i	$-0.107507\pi$
$421$	18.8752	+	13.7137i	0.919923	+	0.668363i	−0.0235816	+	0.999722i	$0.507507\pi$
$422$	−3.72540	+	2.70666i	−0.181350	+	0.131758i
$423$	0.311279	−	0.958017i	0.0151349	−	0.0465804i
$424$	1.94513	−	5.98648i	0.0944637	−	0.290729i
$425$	11.6900	−	8.49330i	0.567049	−	0.411986i
$426$	−17.2392	−	12.5250i	−0.835244	−	0.606840i
$427$	−4.29388	−	13.2152i	−0.207795	−	0.639528i
$428$	27.8136			1.34442
$429$		0			0
$430$	2.99362			0.144365
$431$	−2.94771	−	9.07211i	−0.141986	−	0.436988i	0.854625	−	0.519246i	$-0.173787\pi$
$431$	−2.94771	−	9.07211i	−0.141986	−	0.436988i	−0.996611	+	0.0822576i	$0.973787\pi$
$432$	−12.4086	−	9.01540i	−0.597011	−	0.433754i
$433$	18.6159	−	13.5252i	0.894623	−	0.649982i	−0.0424564	−	0.999098i	$-0.513518\pi$
$433$	18.6159	−	13.5252i	0.894623	−	0.649982i	0.937079	+	0.349117i	$0.113518\pi$
$434$	−0.824997	+	2.53908i	−0.0396011	+	0.121880i
$435$	1.78918	−	5.50652i	0.0857844	−	0.264017i
$436$	−37.5362	+	27.2717i	−1.79766	+	1.30608i
$437$	−21.2851	−	15.4645i	−1.01820	−	0.739768i
$438$	−4.17863	−	12.8605i	−0.199662	−	0.614498i
$439$	−27.6434			−1.31935			−0.659673	−	0.751553i	$-0.729305\pi$
$439$	−27.6434			−1.31935			−0.659673	+	0.751553i	$0.729305\pi$
$440$		0			0
$441$	−0.115054			−0.00547874
$442$	10.4933	+	32.2951i	0.499117	+	1.53612i
$443$	−11.9503	−	8.68237i	−0.567774	−	0.412512i	0.266522	−	0.963829i	$-0.414125\pi$
$443$	−11.9503	−	8.68237i	−0.567774	−	0.412512i	−0.834296	+	0.551317i	$0.814125\pi$
$444$	−36.6076	+	26.5970i	−1.73732	+	1.26224i
$445$	0.472181	−	1.45322i	0.0223835	−	0.0688894i
$446$	17.7693	−	54.6883i	0.841400	−	2.58956i
$447$	−18.5382	+	13.4688i	−0.876829	+	0.637054i
$448$	8.98105	+	6.52511i	0.424315	+	0.308283i
$449$	9.35299	+	28.7855i	0.441395	+	1.35847i	0.886390	+	0.462940i	$0.153205\pi$
$449$	9.35299	+	28.7855i	0.441395	+	1.35847i	−0.444995	+	0.895533i	$0.646795\pi$
$450$	1.15462			0.0544294
$451$		0			0
$452$	−33.0590			−1.55496
$453$	−6.42284	−	19.7675i	−0.301771	−	0.928756i
$454$	23.1903	+	16.8488i	1.08838	+	0.790752i
$455$	−2.11139	+	1.53401i	−0.0989833	+	0.0719156i
$456$	−2.32232	+	7.14737i	−0.108753	+	0.334706i
$457$	−6.25960	+	19.2651i	−0.292812	+	0.901182i	0.691136	+	0.722725i	$0.257111\pi$
$457$	−6.25960	+	19.2651i	−0.292812	+	0.901182i	−0.983948	+	0.178457i	$0.942889\pi$
$458$	14.1666	−	10.2927i	0.661963	−	0.480944i
$459$	13.0007	+	9.44555i	0.606820	+	0.440881i
$460$	−2.10148	−	6.46770i	−0.0979821	−	0.301558i
$461$	8.51184			0.396436			0.198218	−	0.980158i	$-0.436485\pi$
$461$	8.51184			0.396436			0.198218	+	0.980158i	$0.436485\pi$
$462$		0			0
$463$	−0.591469			−0.0274879			−0.0137440	−	0.999906i	$-0.504375\pi$
$463$	−0.591469			−0.0274879			−0.0137440	+	0.999906i	$0.504375\pi$
$464$	−6.20163	−	19.0867i	−0.287904	−	0.886076i
$465$	0.856347	+	0.622173i	0.0397122	+	0.0288526i
$466$	−22.0956	+	16.0534i	−1.02356	+	0.743658i
$467$	−12.6804	+	39.0263i	−0.586780	+	1.80592i	0.00522191	+	0.999986i	$0.498338\pi$
$467$	−12.6804	+	39.0263i	−0.586780	+	1.80592i	−0.592002	+	0.805937i	$0.701662\pi$
$468$	−0.461597	+	1.42065i	−0.0213373	+	0.0656696i
$469$	7.85095	−	5.70405i	0.362523	−	0.263389i
$470$	7.35684	+	5.34506i	0.339346	+	0.246549i
$471$	1.32289	+	4.07144i	0.0609556	+	0.187602i
$472$	−7.92452			−0.364756
$473$		0			0
$474$	−31.5426			−1.44880
$475$	6.86011	+	21.1133i	0.314764	+	0.968743i
$476$	−6.01884	−	4.37294i	−0.275873	−	0.200434i
$477$	0.617899	−	0.448930i	0.0282917	−	0.0205551i
$478$	1.23420	−	3.79848i	0.0564510	−	0.173738i
$479$	6.28654	−	19.3480i	0.287240	−	0.884032i	−0.698479	−	0.715631i	$-0.746139\pi$
$479$	6.28654	−	19.3480i	0.287240	−	0.884032i	0.985718	−	0.168402i	$-0.0538606\pi$
$480$	5.42051	−	3.93823i	0.247412	−	0.179755i
$481$	−46.6360	−	33.8830i	−2.12642	−	1.54493i
$482$	−7.62541	−	23.4686i	−0.347328	−	1.06897i
$483$	−9.57681			−0.435760
$484$		0			0
$485$	−3.11032			−0.141232
$486$	0.778947	+	2.39735i	0.0353338	+	0.108746i
$487$	23.3130	+	16.9379i	1.05641	+	0.767530i	0.973422	−	0.229020i	$-0.0735523\pi$
$487$	23.3130	+	16.9379i	1.05641	+	0.767530i	0.0829924	+	0.996550i	$0.473552\pi$
$488$	10.6593	−	7.74447i	0.482526	−	0.350575i
$489$	4.13547	−	12.7277i	0.187012	−	0.575565i
$490$	0.320959	−	0.987809i	0.0144994	−	0.0446247i
$491$	−2.16853	+	1.57553i	−0.0978643	+	0.0711025i	−0.635641	−	0.771985i	$-0.719264\pi$
$491$	−2.16853	+	1.57553i	−0.0978643	+	0.0711025i	0.537777	+	0.843087i	$0.319264\pi$
$492$	4.85780	+	3.52940i	0.219007	+	0.159118i
$493$	6.49753	+	19.9973i	0.292634	+	0.900635i
$494$	−52.1701			−2.34725
$495$		0			0
$496$	3.66898			0.164742
$497$	1.83788	+	5.65641i	0.0824402	+	0.253725i
$498$	−32.1445	−	23.3543i	−1.44043	−	1.04653i
$499$	−18.0755	+	13.1326i	−0.809171	+	0.587897i	−0.913590	−	0.406637i	$-0.866702\pi$
$499$	−18.0755	+	13.1326i	−0.809171	+	0.587897i	0.104419	+	0.994533i	$0.466702\pi$
$500$	−3.63676	+	11.1928i	−0.162641	+	0.500557i
$501$	−1.07853	+	3.31937i	−0.0481852	+	0.148299i
$502$	22.5023	−	16.3489i	1.00433	−	0.729685i
$503$	3.62115	+	2.63092i	0.161459	+	0.117307i	0.665581	−	0.746326i	$-0.268184\pi$
$503$	3.62115	+	2.63092i	0.161459	+	0.117307i	−0.504122	+	0.863633i	$0.668184\pi$
$504$	−0.0337122	−	0.103756i	−0.00150166	−	0.00462164i
$505$	5.80943			0.258516
$506$		0			0
$507$	25.6358			1.13853
$508$	−3.52784	−	10.8576i	−0.156523	−	0.481727i
$509$	13.8784	+	10.0833i	0.615150	+	0.446933i	0.851224	−	0.524802i	$-0.175861\pi$
$509$	13.8784	+	10.0833i	0.615150	+	0.446933i	−0.236074	+	0.971735i	$0.575861\pi$
$510$	−4.33479	+	3.14941i	−0.191948	+	0.139458i
$511$	−1.16629	+	3.58948i	−0.0515938	+	0.158789i
$512$	8.87542	−	27.3157i	0.392242	−	1.20720i
$513$	−19.9737	+	14.5117i	−0.881858	+	0.640708i
$514$	26.1859	+	19.0252i	1.15501	+	0.839164i
$515$	1.06596	+	3.28069i	0.0469718	+	0.144564i
$516$	11.9917			0.527904
$517$		0			0
$518$	22.9414			1.00799
$519$	−12.2141	−	37.5910i	−0.536137	−	1.65006i
$520$	−2.00204	−	1.45457i	−0.0877953	−	0.0637870i
$521$	−0.816758	+	0.593409i	−0.0357828	+	0.0259977i	−0.605533	−	0.795820i	$-0.707040\pi$
$521$	−0.816758	+	0.593409i	−0.0357828	+	0.0259977i	0.569750	+	0.821818i	$0.307040\pi$
$522$	−0.519195	+	1.59792i	−0.0227245	+	0.0699389i
$523$	−4.21600	+	12.9755i	−0.184353	+	0.567380i	−0.999937	−	0.0112594i	$-0.996416\pi$
$523$	−4.21600	+	12.9755i	−0.184353	+	0.567380i	0.815584	+	0.578639i	$0.196416\pi$
$524$	−17.9082	+	13.0111i	−0.782322	+	0.568390i
$525$	6.53747	+	4.74975i	0.285319	+	0.207296i
$526$	6.79196	+	20.9035i	0.296143	+	0.911436i
$527$	−3.84404			−0.167449
$528$		0			0
$529$	8.79099			0.382217
$530$	2.13064	+	6.55742i	0.0925489	+	0.284836i
$531$	−0.777903	−	0.565179i	−0.0337581	−	0.0245267i
$532$	9.24707	−	6.71839i	0.400911	−	0.291279i
$533$	−2.36382	+	7.27509i	−0.102388	+	0.315119i
$534$	3.43577	−	10.5742i	0.148680	−	0.457591i
$535$	−4.52318	+	3.28628i	−0.195554	+	0.142078i
$536$	7.44436	+	5.40865i	0.321547	+	0.233618i
$537$	9.26897	+	28.5270i	0.399986	+	1.23103i
$538$	34.3223			1.47974
$539$		0			0
$540$	−6.38154			−0.274618
$541$	−0.853921	−	2.62810i	−0.0367129	−	0.112991i	0.931021	−	0.364967i	$-0.118920\pi$
$541$	−0.853921	−	2.62810i	−0.0367129	−	0.112991i	−0.967734	+	0.251976i	$0.918920\pi$
$542$	9.96481	+	7.23986i	0.428025	+	0.310979i
$543$	−21.2578	+	15.4447i	−0.912261	+	0.662797i
$544$	−7.51901	+	23.1411i	−0.322375	+	0.992167i
$545$	2.88207	−	8.87011i	0.123454	−	0.379954i
$546$	−15.3632	+	11.1621i	−0.657486	+	0.477692i
$547$	−12.3308	−	8.95883i	−0.527226	−	0.383052i	0.292093	−	0.956390i	$-0.405648\pi$
$547$	−12.3308	−	8.95883i	−0.527226	−	0.383052i	−0.819319	+	0.573338i	$0.805648\pi$
$548$	−1.23966	−	3.81529i	−0.0529558	−	0.162981i
$549$	1.59870			0.0682309
$550$		0			0
$551$	−32.3041			−1.37620
$552$	−2.80614	−	8.63640i	−0.119437	−	0.367589i
$553$	7.12245	+	5.17476i	0.302877	+	0.220053i
$554$	−27.1773	+	19.7455i	−1.15465	+	0.838904i
$555$	2.81077	−	8.65065i	0.119310	−	0.367200i
$556$	−1.16170	+	3.57533i	−0.0492669	+	0.151628i
$557$	−2.88601	+	2.09681i	−0.122284	+	0.0888446i	−0.647246	−	0.762281i	$-0.724079\pi$
$557$	−2.88601	+	2.09681i	−0.122284	+	0.0888446i	0.524962	+	0.851126i	$0.324079\pi$
$558$	−0.248501	−	0.180546i	−0.0105199	−	0.00764313i
$559$	4.72076	+	14.5290i	0.199667	+	0.614511i
$560$	−1.42739			−0.0603182
$561$		0			0
$562$	21.5166			0.907621
$563$	11.3564	+	34.9513i	0.478614	+	1.47302i	0.841021	+	0.541003i	$0.181955\pi$
$563$	11.3564	+	34.9513i	0.478614	+	1.47302i	−0.362406	+	0.932020i	$0.618045\pi$
$564$	29.4696	+	21.4109i	1.24089	+	0.901563i
$565$	5.37621	−	3.90605i	0.226179	−	0.164329i
$566$	−10.5359	+	32.4261i	−0.442856	+	1.36297i
$567$	−2.67040	+	8.21865i	−0.112146	+	0.345151i
$568$	−4.56245	+	3.31481i	−0.191436	+	0.139086i
$569$	27.5715	+	20.0319i	1.15586	+	0.839779i	0.989249	−	0.146244i	$-0.0467184\pi$
$569$	27.5715	+	20.0319i	1.15586	+	0.839779i	0.166609	+	0.986023i	$0.446718\pi$
$570$	−2.54380	−	7.82902i	−0.106548	−	0.327922i
$571$	−5.79312			−0.242434			−0.121217	−	0.992626i	$-0.538680\pi$
$571$	−5.79312			−0.242434			−0.121217	+	0.992626i	$0.538680\pi$
$572$		0			0
$573$	27.0718			1.13094
$574$	−0.940743	−	2.89531i	−0.0392659	−	0.120848i
$575$	−21.7017	−	15.7672i	−0.905022	−	0.657537i
$576$	−1.03330	+	0.750737i	−0.0430542	+	0.0312807i
$577$	−9.61758	+	29.5999i	−0.400385	+	1.23226i	0.524303	+	0.851532i	$0.324326\pi$
$577$	−9.61758	+	29.5999i	−0.400385	+	1.23226i	−0.924688	+	0.380726i	$0.875674\pi$
$578$	−5.06828	+	15.5986i	−0.210813	+	0.648814i
$579$	−11.6167	+	8.44001i	−0.482772	+	0.350755i
$580$	−6.75523	−	4.90796i	−0.280496	−	0.203792i
$581$	3.42694	+	10.5470i	0.142173	+	0.437564i
$582$	−22.6318			−0.938120
$583$		0			0
$584$	−3.57875			−0.148090
$585$	−0.0927881	−	0.285572i	−0.00383632	−	0.0118070i
$586$	−46.1645	−	33.5405i	−1.90704	−	1.38555i
$587$	38.5857	−	28.0342i	1.59260	−	1.15709i	0.692498	−	0.721420i	$-0.256510\pi$
$587$	38.5857	−	28.0342i	1.59260	−	1.15709i	0.900105	−	0.435673i	$-0.143490\pi$
$588$	1.28568	−	3.95691i	0.0530205	−	0.163180i
$589$	1.82499	−	5.61675i	0.0751975	−	0.231434i
$590$	7.02251	−	5.10215i	0.289112	−	0.210052i
$591$	19.7028	+	14.3149i	0.810465	+	0.588838i
$592$	−9.74267	−	29.9849i	−0.400421	−	1.23237i
$593$	44.5859			1.83092			0.915462	−	0.402404i	$-0.131825\pi$
$593$	44.5859			1.83092			0.915462	+	0.402404i	$0.131825\pi$
$594$		0			0
$595$	1.49549			0.0613093
$596$	10.2119	+	31.4289i	0.418295	+	1.28738i
$597$	30.4153	+	22.0980i	1.24481	+	0.904410i
$598$	50.9995	−	37.0533i	2.08553	−	1.51522i
$599$	−2.49357	+	7.67443i	−0.101885	+	0.313569i	−0.988987	−	0.148005i	$-0.952715\pi$
$599$	−2.49357	+	7.67443i	−0.101885	+	0.313569i	0.887102	+	0.461573i	$0.152715\pi$
$600$	−2.36777	+	7.28725i	−0.0966639	+	0.297501i
$601$	23.3875	−	16.9920i	0.953997	−	0.693119i	0.00224823	−	0.999997i	$-0.499284\pi$
$601$	23.3875	−	16.9920i	0.953997	−	0.693119i	0.951749	+	0.306878i	$0.0992844\pi$
$602$	−4.91863	−	3.57359i	−0.200468	−	0.145649i
$603$	0.345022	+	1.06187i	0.0140504	+	0.0432426i
$604$	−29.9748			−1.21966
$605$		0			0
$606$	42.2716			1.71717
$607$	−3.04477	−	9.37085i	−0.123584	−	0.380351i	0.870057	−	0.492952i	$-0.164082\pi$
$607$	−3.04477	−	9.37085i	−0.123584	−	0.380351i	−0.993640	+	0.112600i	$0.964082\pi$
$608$	−30.2431	−	21.9729i	−1.22652	−	0.891120i
$609$	−9.51301	+	6.91161i	−0.385487	+	0.280072i
$610$	−4.45981	+	13.7259i	−0.180573	+	0.555745i
$611$	−14.3400	+	44.1340i	−0.580134	+	1.78547i
$612$	0.692489	−	0.503123i	0.0279922	−	0.0203375i
$613$	28.9894	+	21.0620i	1.17087	+	0.850687i	0.991113	−	0.133024i	$-0.0424686\pi$
$613$	28.9894	+	21.0620i	1.17087	+	0.850687i	0.179758	+	0.983711i	$0.442469\pi$
$614$	19.3759	+	59.6329i	0.781948	+	2.40659i
$615$	−1.20701			−0.0486714
$616$		0			0
$617$	−38.4398			−1.54753			−0.773764	−	0.633474i	$-0.781628\pi$
$617$	−38.4398			−1.54753			−0.773764	+	0.633474i	$0.781628\pi$
$618$	7.75633	+	23.8715i	0.312005	+	0.960254i
$619$	−3.39425	−	2.46607i	−0.136426	−	0.0991196i	0.517479	−	0.855696i	$-0.326871\pi$
$619$	−3.39425	−	2.46607i	−0.136426	−	0.0991196i	−0.653905	+	0.756576i	$0.726871\pi$
$620$	1.23499	−	0.897270i	0.0495982	−	0.0360352i
$621$	9.21868	−	28.3722i	0.369933	−	1.13854i
$622$	14.6030	−	44.9435i	0.585528	−	1.80207i
$623$	−2.51058	+	1.82404i	−0.100584	+	0.0730787i
$624$	21.1134	+	15.3398i	0.845213	+	0.614083i
$625$	6.61978	+	20.3736i	0.264791	+	0.814943i
$626$	20.9849			0.838725
$627$		0			0
$628$	6.17382			0.246362
$629$	10.2075	+	31.4155i	0.407000	+	1.25262i
$630$	0.0966773	+	0.0702401i	0.00385171	+	0.00279843i
$631$	2.84611	−	2.06782i	0.113302	−	0.0823185i	−0.529692	−	0.848190i	$-0.677692\pi$
$631$	2.84611	−	2.06782i	0.113302	−	0.0823185i	0.642993	+	0.765872i	$0.277692\pi$
$632$	−2.57964	+	7.93932i	−0.102613	+	0.315809i
$633$	1.14580	−	3.52642i	0.0455416	−	0.140162i
$634$	19.0141	−	13.8146i	0.755148	−	0.548647i
$635$	1.85658	+	1.34888i	0.0736761	+	0.0535288i
$636$	8.53478	+	26.2674i	0.338426	+	1.04157i
$637$	5.30029			0.210005
$638$		0			0
$639$	−0.684281			−0.0270698
$640$	−1.12506	−	3.46259i	−0.0444721	−	0.136871i
$641$	−13.0213	−	9.46054i	−0.514311	−	0.373669i	0.300146	−	0.953893i	$-0.402965\pi$
$641$	−13.0213	−	9.46054i	−0.514311	−	0.373669i	−0.814456	+	0.580225i	$0.802965\pi$
$642$	−32.9123	+	23.9122i	−1.29895	+	0.943740i
$643$	−10.7619	+	33.1216i	−0.424406	+	1.30619i	0.479156	+	0.877730i	$0.340943\pi$
$643$	−10.7619	+	33.1216i	−0.424406	+	1.30619i	−0.903562	+	0.428458i	$0.859057\pi$
$644$	−4.26791	+	13.1353i	−0.168179	+	0.517603i
$645$	−1.95014	+	1.41686i	−0.0767868	+	0.0557889i
$646$	24.1854	+	17.5718i	0.951563	+	0.691351i
$647$	5.22396	+	16.0777i	0.205375	+	0.632079i	0.999698	+	0.0245833i	$0.00782590\pi$
$647$	5.22396	+	16.0777i	0.205375	+	0.632079i	−0.794323	+	0.607496i	$0.792174\pi$
$648$	−8.19407			−0.321893
$649$		0			0
$650$	−53.1912			−2.08633
$651$	−0.664300	−	2.04451i	−0.0260360	−	0.0801305i
$652$	−15.6139	−	11.3442i	−0.611489	−	0.444273i
$653$	−2.85420	+	2.07370i	−0.111694	+	0.0811501i	−0.642230	−	0.766512i	$-0.721991\pi$
$653$	−2.85420	+	2.07370i	−0.111694	+	0.0811501i	0.530536	+	0.847662i	$0.321991\pi$
$654$	20.9710	−	64.5422i	0.820033	−	2.52380i
$655$	1.37501	−	4.23184i	0.0537260	−	0.165352i
$656$	−3.38471	+	2.45914i	−0.132151	+	0.0960132i
$657$	−0.351304	−	0.255237i	−0.0137057	−	0.00995776i
$658$	−5.70697	−	17.5643i	−0.222481	−	0.684726i
$659$	29.4409			1.14686			0.573428	−	0.819256i	$-0.305613\pi$
$659$	29.4409			1.14686			0.573428	+	0.819256i	$0.305613\pi$
$660$		0			0
$661$	15.2989			0.595059			0.297529	−	0.954713i	$-0.403837\pi$
$661$	15.2989			0.595059			0.297529	+	0.954713i	$0.403837\pi$
$662$	9.51356	+	29.2797i	0.369755	+	1.13799i
$663$	−22.1208	−	16.0717i	−0.859100	−	0.624173i
$664$	−8.50720	+	6.18084i	−0.330143	+	0.239863i
$665$	−0.710000	+	2.18515i	−0.0275326	+	0.0847366i
$666$	−0.815647	+	2.51030i	−0.0316057	+	0.0972723i
$667$	31.5792	−	22.9436i	1.22275	−	0.888381i
$668$	4.07211	+	2.95856i	0.157555	+	0.114470i
$669$	14.3081	+	44.0358i	0.553184	+	1.70252i
$670$	−10.0793			−0.389398
$671$		0			0
$672$	−13.6073			−0.524914
$673$	3.75927	+	11.5698i	0.144909	+	0.445985i	0.996999	−	0.0774105i	$-0.0246652\pi$
$673$	3.75927	+	11.5698i	0.144909	+	0.445985i	−0.852090	+	0.523395i	$0.824665\pi$
$674$	−21.5124	−	15.6297i	−0.828626	−	0.602032i
$675$	−20.3646	+	14.7957i	−0.783833	+	0.569488i
$676$	11.4246	−	35.1614i	0.439409	−	1.35236i
$677$	−0.0969135	+	0.298269i	−0.00372469	+	0.0114634i	−0.952902	−	0.303280i	$-0.901918\pi$
$677$	−0.0969135	+	0.298269i	−0.00372469	+	0.0114634i	0.949177	+	0.314743i	$0.101918\pi$
$678$	39.1194	−	28.4219i	1.50237	−	1.09154i
$679$	5.11036	+	3.71290i	0.196118	+	0.142488i
$680$	0.438200	+	1.34864i	0.0168042	+	0.0517180i
$681$	−23.0814			−0.884481
$682$		0			0
$683$	38.2419			1.46328			0.731642	−	0.681689i	$-0.238754\pi$
$683$	38.2419			1.46328			0.731642	+	0.681689i	$0.238754\pi$
$684$	0.406377	+	1.25070i	0.0155382	+	0.0478217i
$685$	0.652391	+	0.473990i	0.0249266	+	0.0181102i
$686$	−1.70653	+	1.23987i	−0.0651557	+	0.0473384i
$687$	−4.35716	+	13.4100i	−0.166236	+	0.511622i
$688$	−2.58193	+	7.94636i	−0.0984351	+	0.302952i
$689$	−28.4654	+	20.6813i	−1.08445	+	0.787896i
$690$	8.04721	+	5.84664i	0.306352	+	0.222578i
$691$	−3.17528	−	9.77251i	−0.120793	−	0.371764i	0.872318	−	0.488939i	$-0.162616\pi$
$691$	−3.17528	−	9.77251i	−0.120793	−	0.371764i	−0.993111	+	0.117175i	$0.962616\pi$
$692$	−57.0019			−2.16689
$693$		0			0
$694$	0.866398			0.0328880
$695$	−0.233519	−	0.718697i	−0.00885787	−	0.0272617i
$696$	−9.02035	−	6.55367i	−0.341915	−	0.248416i
$697$	3.54621	−	2.57647i	0.134322	−	0.0975908i
$698$	8.73628	−	26.8875i	0.330673	−	1.01771i
$699$	6.79582	−	20.9154i	0.257042	−	0.791093i
$700$	9.42805	−	6.84988i	0.356347	−	0.258901i
$701$	−15.3056	−	11.1202i	−0.578084	−	0.420003i	0.259949	−	0.965622i	$-0.416294\pi$
$701$	−15.3056	−	11.1202i	−0.578084	−	0.420003i	−0.838033	+	0.545620i	$0.816294\pi$
$702$	−18.2799	−	56.2597i	−0.689929	−	2.12338i
$703$	−50.7492			−1.91404
$704$		0			0
$705$	−7.32228			−0.275773
$706$	8.04489	+	24.7596i	0.302773	+	0.931841i
$707$	−9.54511	−	6.93493i	−0.358981	−	0.260815i
$708$	28.1304	−	20.4379i	1.05720	−	0.768103i
$709$	−4.37254	+	13.4573i	−0.164214	+	0.505400i	−0.998978	−	0.0452094i	$-0.985605\pi$
$709$	−4.37254	+	13.4573i	−0.164214	+	0.505400i	0.834763	+	0.550609i	$0.185605\pi$
$710$	1.90890	−	5.87500i	0.0716399	−	0.220485i
$711$	−0.819463	+	0.595375i	−0.0307323	+	0.0223283i
$712$	−2.38056	−	1.72958i	−0.0892152	−	0.0648187i
$713$	2.20520	+	6.78690i	0.0825853	+	0.254171i
$714$	10.8818			0.407240
$715$		0			0
$716$	43.2575			1.61661
$717$	0.993797	+	3.05859i	0.0371140	+	0.114225i
$718$	42.6798	+	31.0087i	1.59280	+	1.15723i
$719$	12.8901	−	9.36519i	0.480719	−	0.349263i	−0.320885	−	0.947118i	$-0.603980\pi$
$719$	12.8901	−	9.36519i	0.480719	−	0.349263i	0.801604	+	0.597855i	$0.203980\pi$
$720$	0.0507487	−	0.156188i	0.00189129	−	0.00582080i
$721$	2.16486	−	6.66277i	0.0806238	−	0.248134i
$722$	−4.73330	+	3.43894i	−0.176155	+	0.127984i
$723$	16.0750	+	11.6792i	0.597836	+	0.434353i
$724$	11.7100	+	36.0396i	0.435198	+	1.33940i
$725$	−32.9363			−1.22322
$726$		0			0
$727$	−4.20455			−0.155938			−0.0779691	−	0.996956i	$-0.524844\pi$
$727$	−4.20455			−0.155938			−0.0779691	+	0.996956i	$0.524844\pi$
$728$	1.55306	+	4.77982i	0.0575601	+	0.177152i
$729$	−22.6157	−	16.4313i	−0.837618	−	0.608565i
$730$	3.17139	−	2.30415i	0.117379	−	0.0852805i
$731$	2.70512	−	8.32550i	0.100052	−	0.307930i
$732$	−17.8649	+	54.9824i	−0.660304	+	2.03221i
$733$	−27.5695	+	20.0304i	−1.01830	+	0.739839i	−0.965934	−	0.258789i	$-0.916677\pi$
$733$	−27.5695	+	20.0304i	−1.01830	+	0.739839i	−0.0523671	+	0.998628i	$0.516677\pi$
$734$	3.53107	+	2.56547i	0.130334	+	0.0946932i
$735$	0.258441	+	0.795400i	0.00953274	+	0.0293388i
$736$	45.1706			1.66501
$737$		0			0
$738$	0.350258			0.0128932
$739$	8.07481	+	24.8517i	0.297037	+	0.914185i	0.982530	+	0.186105i	$0.0595866\pi$
$739$	8.07481	+	24.8517i	0.297037	+	0.914185i	−0.685493	+	0.728079i	$0.740413\pi$
$740$	−10.6124	−	7.71034i	−0.390118	−	0.283438i
$741$	33.9854	−	24.6918i	1.24848	−	0.907076i
$742$	4.32712	−	13.3175i	0.158854	−	0.488901i
$743$	−7.30093	+	22.4700i	−0.267845	+	0.824343i	0.723179	+	0.690661i	$0.242680\pi$
$743$	−7.30093	+	22.4700i	−0.267845	+	0.824343i	−0.991024	+	0.133682i	$0.957320\pi$
$744$	1.64909	−	1.19814i	0.0604587	−	0.0439258i
$745$	−5.37415	−	3.90455i	−0.196894	−	0.143052i
$746$	−9.62264	−	29.6155i	−0.352310	−	1.08430i
$747$	−1.27592			−0.0466835
$748$		0			0
$749$	11.3547			0.414892
$750$	−5.31935	−	16.3713i	−0.194235	−	0.597795i
$751$	1.87982	+	1.36577i	0.0685957	+	0.0498377i	0.621555	−	0.783371i	$-0.286501\pi$
$751$	1.87982	+	1.36577i	0.0685957	+	0.0498377i	−0.552959	+	0.833208i	$0.686501\pi$
$752$	−20.5332	+	14.9182i	−0.748769	+	0.544012i
$753$	−6.92091	+	21.3004i	−0.252212	+	0.776229i
$754$	23.9183	−	73.6130i	0.871053	−	2.68083i
$755$	4.87465	−	3.54164i	0.177407	−	0.128894i
$756$	10.4851	+	7.61788i	0.381340	+	0.277060i
$757$	−4.56267	−	14.0425i	−0.165833	−	0.510382i	0.833264	−	0.552876i	$-0.186470\pi$
$757$	−4.56267	−	14.0425i	−0.165833	−	0.510382i	−0.999097	+	0.0424940i	$0.986470\pi$
$758$	58.5371			2.12616
$759$		0			0
$760$	−2.17862			−0.0790268
$761$	−14.5818	−	44.8781i	−0.528589	−	1.62683i	−0.757108	−	0.653289i	$-0.773389\pi$
$761$	−14.5818	−	44.8781i	−0.528589	−	1.62683i	0.228520	−	0.973539i	$-0.426611\pi$
$762$	13.5092	+	9.81498i	0.489385	+	0.355559i
$763$	−15.3239	+	11.1335i	−0.554763	+	0.403059i
$764$	12.0645	−	37.1308i	0.436480	−	1.34335i
$765$	−0.0531700	+	0.163640i	−0.00192237	+	0.00591643i
$766$	30.7746	−	22.3590i	1.11193	−	0.807865i
$767$	35.8365	+	26.0367i	1.29398	+	0.940132i
$768$	3.46696	+	10.6702i	0.125103	+	0.385027i
$769$	−12.4418			−0.448662			−0.224331	−	0.974513i	$-0.572020\pi$
$769$	−12.4418			−0.448662			−0.224331	+	0.974513i	$0.572020\pi$
$770$		0			0
$771$	−26.0629			−0.938631
$772$	6.39909	+	19.6944i	0.230308	+	0.708816i
$773$	28.5339	+	20.7311i	1.02629	+	0.745645i	0.967563	−	0.252629i	$-0.0812952\pi$
$773$	28.5339	+	20.7311i	1.02629	+	0.745645i	0.0587290	+	0.998274i	$0.481295\pi$
$774$	0.565905	−	0.411154i	0.0203410	−	0.0147786i
$775$	1.86071	−	5.72668i	0.0668387	−	0.205708i
$776$	−1.85090	+	5.69647i	−0.0664433	+	0.204491i
$777$	−14.9448	+	10.8580i	−0.536142	+	0.389530i
$778$	−23.1084	−	16.7892i	−0.828477	−	0.601924i
$779$	2.08104	+	6.40478i	0.0745609	+	0.229475i
$780$	10.8583			0.388788
$781$		0			0
$782$	−36.1229			−1.29175
$783$	−11.3190	−	34.8363i	−0.404508	−	1.24495i
$784$	2.34525	+	1.70393i	0.0837591	+	0.0608545i
$785$	−1.00402	+	0.729461i	−0.0358349	+	0.0260356i
$786$	10.0051	−	30.7925i	0.356869	−	1.09833i
$787$	−5.04881	+	15.5386i	−0.179970	+	0.553892i	−0.999826	−	0.0186789i	$-0.994054\pi$
$787$	−5.04881	+	15.5386i	−0.179970	+	0.553892i	0.819855	+	0.572571i	$0.194054\pi$
$788$	28.4145	−	20.6444i	1.01223	−	0.735425i
$789$	−14.3180	−	10.4026i	−0.509735	−	0.370344i
$790$	−2.82567	−	8.69651i	−0.100533	−	0.309408i
$791$	−13.4961			−0.479867
$792$		0			0
$793$	−73.6491			−2.61536
$794$	−16.0694	−	49.4566i	−0.570282	−	1.75515i
$795$	−4.49156	−	3.26331i	−0.159299	−	0.115738i
$796$	43.8635	−	31.8687i	1.55470	−	1.12956i
$797$	−0.0905116	+	0.278566i	−0.00320609	+	0.00986732i	−0.952647	−	0.304079i	$-0.901651\pi$
$797$	−0.0905116	+	0.278566i	−0.00320609	+	0.00986732i	0.949441	+	0.313946i	$0.101651\pi$
$798$	−5.16622	+	15.9000i	−0.182882	+	0.562854i
$799$	21.5129	−	15.6300i	0.761072	−	0.552951i
$800$	−30.8351	−	22.4030i	−1.09018	−	0.792065i
$801$	−0.110331	−	0.339564i	−0.00389836	−	0.0119979i
$802$	39.5277			1.39577
$803$		0			0
$804$	−40.3752			−1.42392
$805$	−0.857916	−	2.64039i	−0.0302376	−	0.0930616i
$806$	11.4479	+	8.31741i	0.403236	+	0.292968i
$807$	−22.3587	+	16.2446i	−0.787064	+	0.571836i
$808$	3.45709	−	10.6398i	0.121620	−	0.374308i
$809$	−3.41071	+	10.4971i	−0.119914	+	0.369058i	−0.992940	−	0.118616i	$-0.962154\pi$
$809$	−3.41071	+	10.4971i	−0.119914	+	0.369058i	0.873026	+	0.487673i	$0.162154\pi$
$810$	7.26137	−	5.27570i	0.255139	−	0.185369i
$811$	4.22115	+	3.06684i	0.148225	+	0.107691i	0.659426	−	0.751769i	$-0.270799\pi$
$811$	4.22115	+	3.06684i	0.148225	+	0.107691i	−0.511201	+	0.859461i	$0.670799\pi$
$812$	5.24028	+	16.1279i	0.183898	+	0.565980i
$813$	−9.91799			−0.347839
$814$		0			0
$815$	3.87957			0.135896
$816$	−4.62123	−	14.2227i	−0.161775	−	0.497894i
$817$	10.8806	+	7.90522i	0.380664	+	0.276569i
$818$	−26.8093	+	19.4781i	−0.937366	+	0.681036i
$819$	−0.188444	+	0.579971i	−0.00658476	+	0.0202658i
$820$	−0.537905	+	1.65550i	−0.0187845	+	0.0578126i
$821$	−21.3959	+	15.5450i	−0.746723	+	0.542526i	−0.894809	−	0.446448i	$-0.852689\pi$
$821$	−21.3959	+	15.5450i	−0.746723	+	0.542526i	0.148086	+	0.988974i	$0.452689\pi$
$822$	4.74704	+	3.44893i	0.165572	+	0.120295i
$823$	−15.2004	−	46.7820i	−0.529852	−	1.63072i	−0.754517	−	0.656281i	$-0.772129\pi$
$823$	−15.2004	−	46.7820i	−0.529852	−	1.63072i	0.224665	−	0.974436i	$-0.427871\pi$
$824$	6.64284			0.231414
$825$		0			0
$826$	−17.6289			−0.613387
$827$	−12.9171	−	39.7547i	−0.449171	−	1.38241i	−0.877844	−	0.478947i	$-0.841019\pi$
$827$	−12.9171	−	39.7547i	−0.449171	−	1.38241i	0.428672	−	0.903460i	$-0.358981\pi$
$828$	−1.28555	−	0.934010i	−0.0446761	−	0.0324591i
$829$	20.1435	−	14.6351i	0.699614	−	0.508300i	−0.180192	−	0.983631i	$-0.557672\pi$
$829$	20.1435	−	14.6351i	0.699614	−	0.508300i	0.879807	+	0.475332i	$0.157672\pi$
$830$	3.55937	−	10.9546i	0.123547	−	0.380240i
$831$	8.35879	−	25.7257i	0.289963	−	0.892415i
$832$	47.6022	−	34.5850i	1.65031	−	1.19902i
$833$	−2.45715	−	1.78523i	−0.0851353	−	0.0618544i
$834$	−1.69917	−	5.22951i	−0.0588375	−	0.181083i
$835$	−1.01179			−0.0350145
$836$		0			0
$837$	6.69650			0.231465
$838$	14.7337	+	45.3458i	0.508969	+	1.56645i
$839$	43.1135	+	31.3238i	1.48844	+	1.08142i	0.974712	+	0.223465i	$0.0717367\pi$
$839$	43.1135	+	31.3238i	1.48844	+	1.08142i	0.513730	+	0.857952i	$0.328263\pi$
$840$	−0.641567	+	0.466126i	−0.0221362	+	0.0160829i
$841$	5.84886	−	18.0009i	0.201685	−	0.620722i
$842$	−15.2081	+	46.8056i	−0.524105	+	1.61303i
$843$	−14.0166	+	10.1837i	−0.482758	+	0.350744i
$844$	−4.32610	−	3.14310i	−0.148911	−	0.108190i
$845$	2.29652	+	7.06798i	0.0790029	+	0.243146i
$846$	2.12483			0.0730530
$847$		0			0
$848$	−19.2439			−0.660837
$849$	−8.48365	−	26.1100i	−0.291158	−	0.896092i
$850$	24.6588	+	17.9157i	0.845790	+	0.614502i
$851$	49.6104	−	36.0441i	1.70062	−	1.23558i
$852$	7.64658	−	23.5337i	0.261967	−	0.806253i
$853$	4.13173	−	12.7162i	0.141468	−	0.435393i	−0.855072	−	0.518509i	$-0.826487\pi$
$853$	4.13173	−	12.7162i	0.141468	−	0.435393i	0.996540	+	0.0831159i	$0.0264872\pi$
$854$	23.7127	−	17.2283i	0.811433	−	0.589541i
$855$	−0.213862	−	0.155380i	−0.00731392	−	0.00531387i
$856$	3.32708	+	10.2397i	0.113717	+	0.349986i
$857$	43.4419			1.48395			0.741974	−	0.670429i	$-0.233890\pi$
$857$	43.4419			1.48395			0.741974	+	0.670429i	$0.233890\pi$
$858$		0			0
$859$	−7.96898			−0.271898			−0.135949	−	0.990716i	$-0.543408\pi$
$859$	−7.96898			−0.271898			−0.135949	+	0.990716i	$0.543408\pi$
$860$	1.07424	+	3.30619i	0.0366314	+	0.112740i
$861$	1.98316	+	1.44085i	0.0675861	+	0.0491042i
$862$	16.2786	−	11.8271i	0.554450	−	0.402832i
$863$	15.5581	−	47.8830i	0.529605	−	1.62996i	−0.225422	−	0.974261i	$-0.572376\pi$
$863$	15.5581	−	47.8830i	0.529605	−	1.62996i	0.755027	−	0.655694i	$-0.227624\pi$
$864$	13.0985	−	40.3129i	0.445619	−	1.37147i
$865$	9.26993	−	6.73500i	0.315187	−	0.228997i
$866$	39.2682	+	28.5300i	1.33439	+	0.969488i
$867$	−4.08106	−	12.5602i	−0.138600	−	0.426567i
$868$	−3.10023			−0.105229
$869$		0			0
$870$	12.2131			0.414064
$871$	−15.8945	−	48.9182i	−0.538565	−	1.65753i
$872$	−14.5303	−	10.5569i	−0.492059	−	0.357502i
$873$	−0.587965	+	0.427182i	−0.0198996	+	0.0144579i
$874$	17.1497	−	52.7813i	0.580097	−	1.78536i
$875$	−1.48468	+	4.56938i	−0.0501914	+	0.154473i
$876$	12.7038	−	9.22984i	0.429221	−	0.311847i
$877$	44.6416	+	32.4340i	1.50744	+	1.09522i	0.967297	+	0.253646i	$0.0816298\pi$
$877$	44.6416	+	32.4340i	1.50744	+	1.09522i	0.540143	+	0.841573i	$0.318370\pi$
$878$	−18.0190	−	55.4567i	−0.608111	−	1.87157i
$879$	45.9476			1.54978
$880$		0			0
$881$	−22.6475			−0.763014			−0.381507	−	0.924366i	$-0.624595\pi$
$881$	−22.6475			−0.763014			−0.381507	+	0.924366i	$0.624595\pi$
$882$	−0.0749961	−	0.230814i	−0.00252525	−	0.00777192i
$883$	10.2786	+	7.46781i	0.345901	+	0.251312i	0.747147	−	0.664658i	$-0.231423\pi$
$883$	10.2786	+	7.46781i	0.345901	+	0.251312i	−0.401246	+	0.915970i	$0.631423\pi$
$884$	−31.9016	+	23.1779i	−1.07297	+	0.779557i
$885$	−2.15988	+	6.64742i	−0.0726035	+	0.223451i
$886$	9.62850	−	29.6335i	0.323476	−	0.995556i
$887$	−5.42044	+	3.93818i	−0.182001	+	0.132231i	−0.675055	−	0.737767i	$-0.735880\pi$
$887$	−5.42044	+	3.93818i	−0.182001	+	0.132231i	0.493055	+	0.869998i	$0.335880\pi$
$888$	−14.1708	−	10.2957i	−0.475542	−	0.345501i
$889$	−1.44022	−	4.43253i	−0.0483033	−	0.148662i
$890$	3.22317			0.108041
$891$		0			0
$892$	66.7747			2.23578
$893$	12.6245	+	38.8543i	0.422463	+	1.30021i
$894$	−39.1044	−	28.4110i	−1.30785	−	0.950205i
$895$	−7.03474	+	5.11104i	−0.235145	+	0.170843i
$896$	−2.28490	+	7.03220i	−0.0763331	+	0.234929i
$897$	−15.6857	+	48.2755i	−0.523729	+	1.61187i
$898$	−51.6514	+	37.5269i	−1.72363	+	1.25229i
$899$	7.08863	+	5.15019i	0.236419	+	0.171769i
$900$	0.414330	+	1.27518i	0.0138110	+	0.0425059i
$901$	20.1620			0.671695
$902$		0			0
$903$	4.89552			0.162913
$904$	−3.95454	−	12.1708i	−0.131526	−	0.404796i
$905$	−6.16255	−	4.47736i	−0.204850	−	0.148832i
$906$	35.4698	−	25.7703i	1.17841	−	0.856162i
$907$	−17.8360	+	54.8935i	−0.592234	+	1.82271i	−0.0241923	+	0.999707i	$0.507701\pi$
$907$	−17.8360	+	54.8935i	−0.592234	+	1.82271i	−0.568041	+	0.823000i	$0.692299\pi$
$908$	−10.2862	+	31.6578i	−0.341361	+	1.05060i
$909$	1.09820	−	0.797888i	0.0364250	−	0.0264643i
$910$	−4.45373	−	3.23583i	−0.147640	−	0.107267i
$911$	−0.878728	−	2.70445i	−0.0291135	−	0.0896023i	0.935444	−	0.353475i	$-0.115000\pi$
$911$	−0.878728	−	2.70445i	−0.0291135	−	0.0896023i	−0.964557	+	0.263873i	$0.915000\pi$
$912$	22.9756			0.760798
$913$		0			0
$914$	−42.7288			−1.41334
$915$	−3.59111	−	11.0523i	−0.118719	−	0.365378i
$916$	16.4509	+	11.9523i	0.543554	+	0.394915i
$917$	−7.31089	+	5.31167i	−0.241427	+	0.175407i
$918$	−10.4748	+	32.2383i	−0.345721	+	1.06402i
$919$	−2.89495	+	8.90973i	−0.0954954	+	0.293905i	−0.987382	−	0.158353i	$-0.949381\pi$
$919$	−2.89495	+	8.90973i	−0.0954954	+	0.293905i	0.891887	+	0.452258i	$0.149381\pi$
$920$	2.12973	−	1.54734i	0.0702152	−	0.0510144i
$921$	−40.8460	−	29.6763i	−1.34592	−	0.977869i
$922$	5.54833	+	17.0760i	0.182724	+	0.562368i
$923$	31.5235			1.03761
$924$		0			0
$925$	−51.7424			−1.70128
$926$	−0.385542	−	1.18657i	−0.0126697	−	0.0389933i
$927$	0.652088	+	0.473769i	0.0214174	+	0.0155606i
$928$	44.8697	−	32.5997i	1.47292	−	1.07014i
$929$	−13.5484	+	41.6978i	−0.444510	+	1.36806i	0.438510	+	0.898726i	$0.355506\pi$
$929$	−13.5484	+	41.6978i	−0.444510	+	1.36806i	−0.883020	+	0.469335i	$0.844494\pi$
$930$	−0.689972	+	2.12351i	−0.0226251	+	0.0696328i
$931$	3.77505	−	2.74274i	0.123722	−	0.0898896i
$932$	−25.6584	−	18.6419i	−0.840469	−	0.610636i
$933$	11.7586	+	36.1892i	0.384959	+	1.18478i
$934$	−86.5581			−2.83227
$935$		0			0
$936$	−0.578236			−0.0189002
$937$	0.991712	+	3.05218i	0.0323978	+	0.0997103i	0.965948	−	0.258737i	$-0.0833063\pi$
$937$	0.991712	+	3.05218i	0.0323978	+	0.0997103i	−0.933550	+	0.358447i	$0.883306\pi$
$938$	16.5607	+	12.0321i	0.540726	+	0.392861i
$939$	−13.6703	+	9.93203i	−0.446112	+	0.324119i
$940$	−3.26318	+	10.0430i	−0.106433	+	0.327567i
$941$	3.43998	−	10.5872i	0.112140	−	0.345131i	−0.879200	−	0.476453i	$-0.841922\pi$
$941$	3.43998	−	10.5872i	0.112140	−	0.345131i	0.991340	+	0.131322i	$0.0419221\pi$
$942$	−7.30561	+	5.30783i	−0.238029	+	0.172939i
$943$	−6.58327	−	4.78303i	−0.214381	−	0.155757i
$944$	7.48656	+	23.0413i	0.243667	+	0.749929i
$945$	−2.60522			−0.0847479
$946$		0			0
$947$	51.6934			1.67981			0.839905	−	0.542733i	$-0.182610\pi$
$947$	51.6934			1.67981			0.839905	+	0.542733i	$0.182610\pi$
$948$	−11.3189	−	34.8360i	−0.367621	−	1.13142i
$949$	16.1839	+	11.7583i	0.525352	+	0.381690i
$950$	−37.8846	+	27.5248i	−1.22914	+	0.893022i
$951$	−5.84809	+	17.9986i	−0.189637	+	0.583643i
$952$	0.889943	−	2.73896i	0.0288432	−	0.0887703i
$953$	−22.6771	+	16.4759i	−0.734584	+	0.533707i	−0.891010	−	0.453983i	$-0.850003\pi$
$953$	−22.6771	+	16.4759i	−0.734584	+	0.533707i	0.156426	+	0.987690i	$0.450003\pi$
$954$	1.30339	+	0.946968i	0.0421988	+	0.0306592i
$955$	2.42516	+	7.46387i	0.0784763	+	0.241525i
$956$	4.63796			0.150002
$957$		0			0
$958$	42.9127			1.38645
$959$	−0.506084	−	1.55757i	−0.0163423	−	0.0502964i
$960$	7.51115	+	5.45717i	0.242421	+	0.176129i
$961$	23.7836	−	17.2798i	0.767213	−	0.557413i
$962$	37.5753	−	115.645i	1.21148	−	3.72854i
$963$	−0.403699	+	1.24246i	−0.0130090	+	0.0400377i
$964$	23.1826	−	16.8432i	0.746663	−	0.542482i
$965$	−3.36762	−	2.44672i	−0.108408	−	0.0787627i
$966$	−6.24252	−	19.2125i	−0.200850	−	0.618152i
$967$	−25.5912			−0.822957			−0.411479	−	0.911419i	$-0.634988\pi$
$967$	−25.5912			−0.822957			−0.411479	+	0.911419i	$0.634988\pi$
$968$		0			0
$969$	−24.0718			−0.773298
$970$	−2.02742	−	6.23975i	−0.0650965	−	0.200346i
$971$	−10.1723	−	7.39061i	−0.326445	−	0.237176i	0.412476	−	0.910969i	$-0.364664\pi$
$971$	−10.1723	−	7.39061i	−0.326445	−	0.237176i	−0.738921	+	0.673793i	$0.764664\pi$
$972$	−2.36814	+	1.72056i	−0.0759582	+	0.0551868i
$973$	−0.474255	+	1.45961i	−0.0152039	+	0.0467928i
$974$	−18.7836	+	57.8101i	−0.601867	+	1.85236i
$975$	34.6505	−	25.1751i	1.10970	−	0.806248i
$976$	−32.5880	−	23.6765i	−1.04312	−	0.757868i
$977$	−4.48581	−	13.8059i	−0.143514	−	0.441690i	0.853303	−	0.521415i	$-0.174596\pi$
$977$	−4.48581	−	13.8059i	−0.143514	−	0.441690i	−0.996817	+	0.0797254i	$0.974596\pi$
$978$	28.2292			0.902671
$979$		0			0
$980$	1.20612			0.0385281
$981$	−0.673433	−	2.07261i	−0.0215011	−	0.0661735i
$982$	−4.57427	−	3.32340i	−0.145971	−	0.106054i
$983$	10.5078	−	7.63435i	0.335146	−	0.243498i	−0.407465	−	0.913221i	$-0.633587\pi$
$983$	10.5078	−	7.63435i	0.335146	−	0.243498i	0.742611	+	0.669723i	$0.233587\pi$
$984$	−0.718272	+	2.21061i	−0.0228977	+	0.0704718i
$985$	−2.18170	+	6.71457i	−0.0695146	+	0.213944i
$986$	−35.8823	+	26.0700i	−1.14272	+	0.830238i
$987$	12.0308	+	8.74087i	0.382944	+	0.278225i
$988$	−18.7210	−	57.6173i	−0.595594	−	1.83305i
$989$	−16.2511			−0.516754
$990$		0			0
$991$	7.01006			0.222682			0.111341	−	0.993782i	$-0.464485\pi$
$991$	7.01006			0.222682			0.111341	+	0.993782i	$0.464485\pi$
$992$	3.13328	+	9.64325i	0.0994818	+	0.306173i
$993$	−20.0554	−	14.5711i	−0.636438	−	0.462399i
$994$	−10.1496	+	7.37412i	−0.321926	+	0.233893i
$995$	−3.36789	+	10.3653i	−0.106769	+	0.328602i
$996$	14.2579	−	43.8813i	0.451779	−	1.39043i
$997$	25.7906	−	18.7379i	0.816795	−	0.593436i	−0.0989975	−	0.995088i	$-0.531564\pi$
$997$	25.7906	−	18.7379i	0.816795	−	0.593436i	0.915793	+	0.401651i	$0.131564\pi$
$998$	−38.1283	−	27.7018i	−1.20693	−	0.876885i
$999$	−17.7820	−	54.7273i	−0.562597	−	1.73150i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.y.148.5		24
11.2	odd	10		847.2.f.z.372.2		24
11.3	even	5		847.2.a.n.1.5	yes	6
11.4	even	5	inner	847.2.f.y.729.2		24
11.5	even	5	inner	847.2.f.y.323.2		24
11.6	odd	10		847.2.f.z.323.5		24
11.7	odd	10		847.2.f.z.729.5		24
11.8	odd	10		847.2.a.m.1.2	✓	6
11.9	even	5	inner	847.2.f.y.372.5		24
11.10	odd	2		847.2.f.z.148.2		24
33.8	even	10		7623.2.a.cs.1.5		6
33.14	odd	10		7623.2.a.cp.1.2		6
77.41	even	10		5929.2.a.bj.1.2		6
77.69	odd	10		5929.2.a.bm.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.m.1.2	✓	6	11.8	odd	10
847.2.a.n.1.5	yes	6	11.3	even	5
847.2.f.y.148.5		24	1.1	even	1	trivial
847.2.f.y.323.2		24	11.5	even	5	inner
847.2.f.y.372.5		24	11.9	even	5	inner
847.2.f.y.729.2		24	11.4	even	5	inner
847.2.f.z.148.2		24	11.10	odd	2
847.2.f.z.323.5		24	11.6	odd	10
847.2.f.z.372.2		24	11.2	odd	10
847.2.f.z.729.5		24	11.7	odd	10
5929.2.a.bj.1.2		6	77.41	even	10
5929.2.a.bm.1.5		6	77.69	odd	10
7623.2.a.cp.1.2		6	33.14	odd	10
7623.2.a.cs.1.5		6	33.8	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)

\(f(q)\)	\(=\)	\(q+(0.651837 + 2.00615i) q^{2} +(-1.37413 - 0.998361i) q^{3} +(-1.98170 + 1.43979i) q^{4} +(0.152157 - 0.468292i) q^{5} +(1.10715 - 3.40747i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-0.767119 - 0.557345i) q^{8} +(-0.0355535 - 0.109422i) q^{9} +O(q^{10})\)	\(q+(0.651837 + 2.00615i) q^{2} +(-1.37413 - 0.998361i) q^{3} +(-1.98170 + 1.43979i) q^{4} +(0.152157 - 0.468292i) q^{5} +(1.10715 - 3.40747i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-0.767119 - 0.557345i) q^{8} +(-0.0355535 - 0.109422i) q^{9} +1.03864 q^{10} +4.16054 q^{12} +(1.63788 + 5.04088i) q^{13} +(-1.70653 - 1.23987i) q^{14} +(-0.676607 + 0.491584i) q^{15} +(-0.895807 + 2.75701i) q^{16} +(0.938548 - 2.88855i) q^{17} +(0.196342 - 0.142651i) q^{18} +(3.77505 + 2.74274i) q^{19} +(0.372712 + 1.14709i) q^{20} +1.69851 q^{21} -5.63835 q^{23} +(0.497687 + 1.53172i) q^{24} +(3.84894 + 2.79642i) q^{25} +(-9.04511 + 6.57166i) q^{26} +(-1.63500 + 5.03200i) q^{27} +(0.756943 - 2.32963i) q^{28} +(-5.60079 + 4.06921i) q^{29} +(-1.42723 - 1.03694i) q^{30} +(-0.391107 - 1.20370i) q^{31} -8.01131 q^{32} +6.40665 q^{34} +(0.152157 + 0.468292i) q^{35} +(0.228002 + 0.165653i) q^{36} +(-8.79875 + 6.39267i) q^{37} +(-3.04162 + 9.36113i) q^{38} +(2.78196 - 8.56200i) q^{39} +(-0.377723 + 0.274432i) q^{40} +(1.16759 + 0.848303i) q^{41} +(1.10715 + 3.40747i) q^{42} +2.88224 q^{43} -0.0566513 q^{45} +(-3.67528 - 11.3114i) q^{46} +(7.08312 + 5.14619i) q^{47} +(3.98344 - 2.89414i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-3.10115 + 9.54435i) q^{50} +(-4.17350 + 3.03223i) q^{51} +(-10.5036 - 7.63132i) q^{52} +(2.05136 + 6.31345i) q^{53} -11.1607 q^{54} +0.948212 q^{56} +(-2.44916 - 7.53773i) q^{57} +(-11.8142 - 8.58355i) q^{58} +(6.76123 - 4.91232i) q^{59} +(0.633056 - 1.94835i) q^{60} +(-4.29388 + 13.2152i) q^{61} +(2.15987 - 1.56924i) q^{62} +(0.0930802 + 0.0676268i) q^{63} +(-3.43046 - 10.5579i) q^{64} +2.60982 q^{65} -9.70431 q^{67} +(2.29899 + 7.07557i) q^{68} +(7.74780 + 5.62911i) q^{69} +(-0.840281 + 0.610500i) q^{70} +(1.83788 - 5.65641i) q^{71} +(-0.0337122 + 0.103756i) q^{72} +(3.05340 - 2.21842i) q^{73} +(-18.5600 - 13.4846i) q^{74} +(-2.49709 - 7.68526i) q^{75} -11.4300 q^{76} +18.9900 q^{78} +(-2.72053 - 8.37294i) q^{79} +(1.15478 + 0.838998i) q^{80} +(6.99120 - 5.07941i) q^{81} +(-0.940743 + 2.89531i) q^{82} +(3.42694 - 10.5470i) q^{83} +(-3.36595 + 2.44550i) q^{84} +(-1.20988 - 0.879029i) q^{85} +(1.87875 + 5.78219i) q^{86} +11.7587 q^{87} +3.10324 q^{89} +(-0.0369274 - 0.113651i) q^{90} +(-4.28803 - 3.11543i) q^{91} +(11.1735 - 8.11805i) q^{92} +(-0.664300 + 2.04451i) q^{93} +(-5.70697 + 17.5643i) q^{94} +(1.85880 - 1.35050i) q^{95} +(11.0086 + 7.99818i) q^{96} +(-1.95199 - 6.00759i) q^{97} +2.10939 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 6 q^{6} - 6 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) \) 24 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 6 * q^6 - 6 * q^7 - 12 * q^8 - 8 * q^9	\( 24 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 6 q^{6} - 6 q^{7} - 12 q^{8} - 8 q^{9} - 32 q^{10} - 56 q^{12} - 4 q^{13} - 4 q^{14} - 2 q^{15} - 8 q^{16} - 22 q^{17} - 24 q^{18} - 6 q^{19} - 2 q^{20} - 8 q^{21} + 8 q^{23} + 20 q^{24} - 4 q^{25} - 6 q^{26} + 2 q^{27} - 4 q^{28} - 12 q^{29} - 20 q^{30} + 2 q^{31} + 32 q^{32} + 96 q^{34} + 4 q^{35} - 18 q^{36} - 14 q^{37} + 22 q^{38} - 20 q^{39} - 18 q^{40} - 26 q^{41} + 6 q^{42} - 16 q^{43} - 144 q^{45} - 12 q^{46} + 16 q^{47} + 24 q^{48} - 6 q^{49} + 4 q^{50} + 4 q^{51} - 12 q^{52} - 4 q^{53} - 128 q^{54} + 48 q^{56} - 20 q^{57} + 2 q^{58} + 4 q^{59} - 24 q^{60} + 8 q^{61} - 20 q^{62} - 8 q^{63} - 26 q^{64} + 96 q^{65} + 24 q^{67} - 12 q^{68} + 14 q^{69} + 8 q^{70} - 22 q^{71} - 16 q^{72} - 14 q^{73} - 44 q^{74} + 20 q^{75} - 120 q^{76} + 128 q^{78} + 28 q^{79} + 4 q^{80} + 6 q^{81} + 4 q^{82} - 22 q^{83} + 14 q^{84} + 24 q^{85} + 30 q^{86} + 88 q^{87} + 22 q^{90} - 4 q^{91} - 10 q^{92} + 50 q^{93} + 38 q^{94} + 24 q^{95} + 62 q^{96} + 4 q^{97} + 16 q^{98}+O(q^{100}) \) 24 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 6 * q^6 - 6 * q^7 - 12 * q^8 - 8 * q^9 - 32 * q^10 - 56 * q^12 - 4 * q^13 - 4 * q^14 - 2 * q^15 - 8 * q^16 - 22 * q^17 - 24 * q^18 - 6 * q^19 - 2 * q^20 - 8 * q^21 + 8 * q^23 + 20 * q^24 - 4 * q^25 - 6 * q^26 + 2 * q^27 - 4 * q^28 - 12 * q^29 - 20 * q^30 + 2 * q^31 + 32 * q^32 + 96 * q^34 + 4 * q^35 - 18 * q^36 - 14 * q^37 + 22 * q^38 - 20 * q^39 - 18 * q^40 - 26 * q^41 + 6 * q^42 - 16 * q^43 - 144 * q^45 - 12 * q^46 + 16 * q^47 + 24 * q^48 - 6 * q^49 + 4 * q^50 + 4 * q^51 - 12 * q^52 - 4 * q^53 - 128 * q^54 + 48 * q^56 - 20 * q^57 + 2 * q^58 + 4 * q^59 - 24 * q^60 + 8 * q^61 - 20 * q^62 - 8 * q^63 - 26 * q^64 + 96 * q^65 + 24 * q^67 - 12 * q^68 + 14 * q^69 + 8 * q^70 - 22 * q^71 - 16 * q^72 - 14 * q^73 - 44 * q^74 + 20 * q^75 - 120 * q^76 + 128 * q^78 + 28 * q^79 + 4 * q^80 + 6 * q^81 + 4 * q^82 - 22 * q^83 + 14 * q^84 + 24 * q^85 + 30 * q^86 + 88 * q^87 + 22 * q^90 - 4 * q^91 - 10 * q^92 + 50 * q^93 + 38 * q^94 + 24 * q^95 + 62 * q^96 + 4 * q^97 + 16 * q^98

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