LMFDB - Embedded newform 847.2.f.l.323.1

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:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			323.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	847.323
Dual form			847.2.f.l.729.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.11803 + 1.53884i) q^{2} +(0.190983 - 0.587785i) q^{3} +(1.50000 + 4.61653i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(1.30902 - 0.951057i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-2.30902 + 7.10642i) q^{8} +(2.11803 + 1.53884i) q^{9} +O(q^{10})$	\(q+(2.11803 + 1.53884i) q^{2} +(0.190983 - 0.587785i) q^{3} +(1.50000 + 4.61653i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(1.30902 - 0.951057i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-2.30902 + 7.10642i) q^{8} +(2.11803 + 1.53884i) q^{9} -2.61803 q^{10} +3.00000 q^{12} +(-2.61803 - 1.90211i) q^{13} +(-0.809017 + 2.48990i) q^{14} +(0.190983 + 0.587785i) q^{15} +(-7.97214 + 5.79210i) q^{16} +(6.54508 - 4.75528i) q^{17} +(2.11803 + 6.51864i) q^{18} +(-1.92705 + 5.93085i) q^{19} +(-3.92705 - 2.85317i) q^{20} +0.618034 q^{21} -6.09017 q^{23} +(3.73607 + 2.71441i) q^{24} +(-1.23607 + 3.80423i) q^{25} +(-2.61803 - 8.05748i) q^{26} +(2.80902 - 2.04087i) q^{27} +(-3.92705 + 2.85317i) q^{28} +(-0.736068 - 2.26538i) q^{29} +(-0.500000 + 1.53884i) q^{30} +(-0.190983 - 0.138757i) q^{31} -10.8541 q^{32} +21.1803 q^{34} +(-0.809017 - 0.587785i) q^{35} +(-3.92705 + 12.0862i) q^{36} +(-0.763932 - 2.35114i) q^{37} +(-13.2082 + 9.59632i) q^{38} +(-1.61803 + 1.17557i) q^{39} +(-2.30902 - 7.10642i) q^{40} +(3.45492 - 10.6331i) q^{41} +(1.30902 + 0.951057i) q^{42} +7.56231 q^{43} -2.61803 q^{45} +(-12.8992 - 9.37181i) q^{46} +(-1.35410 + 4.16750i) q^{47} +(1.88197 + 5.79210i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-8.47214 + 6.15537i) q^{50} +(-1.54508 - 4.75528i) q^{51} +(4.85410 - 14.9394i) q^{52} +(3.73607 + 2.71441i) q^{53} +9.09017 q^{54} -7.47214 q^{56} +(3.11803 + 2.26538i) q^{57} +(1.92705 - 5.93085i) q^{58} +(-0.0278640 - 0.0857567i) q^{59} +(-2.42705 + 1.76336i) q^{60} +(4.35410 - 3.16344i) q^{61} +(-0.190983 - 0.587785i) q^{62} +(-0.809017 + 2.48990i) q^{63} +(-7.04508 - 5.11855i) q^{64} +3.23607 q^{65} +7.32624 q^{67} +(31.7705 + 23.0826i) q^{68} +(-1.16312 + 3.57971i) q^{69} +(-0.809017 - 2.48990i) q^{70} +(3.97214 - 2.88593i) q^{71} +(-15.8262 + 11.4984i) q^{72} +(-3.01722 - 9.28605i) q^{73} +(2.00000 - 6.15537i) q^{74} +(2.00000 + 1.45309i) q^{75} -30.2705 q^{76} -5.23607 q^{78} +(-6.97214 - 5.06555i) q^{79} +(3.04508 - 9.37181i) q^{80} +(1.76393 + 5.42882i) q^{81} +(23.6803 - 17.2048i) q^{82} +(8.66312 - 6.29412i) q^{83} +(0.927051 + 2.85317i) q^{84} +(-2.50000 + 7.69421i) q^{85} +(16.0172 + 11.6372i) q^{86} -1.47214 q^{87} +0.145898 q^{89} +(-5.54508 - 4.02874i) q^{90} +(1.00000 - 3.07768i) q^{91} +(-9.13525 - 28.1154i) q^{92} +(-0.118034 + 0.0857567i) q^{93} +(-9.28115 + 6.74315i) q^{94} +(-1.92705 - 5.93085i) q^{95} +(-2.07295 + 6.37988i) q^{96} +(-5.66312 - 4.11450i) q^{97} -2.61803 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 3 q^{3} + 6 q^{4} - q^{5} + 3 q^{6} - q^{7} - 7 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 3 * q^3 + 6 * q^4 - q^5 + 3 * q^6 - q^7 - 7 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} + 3 q^{3} + 6 q^{4} - q^{5} + 3 q^{6} - q^{7} - 7 q^{8} + 4 q^{9} - 6 q^{10} + 12 q^{12} - 6 q^{13} - q^{14} + 3 q^{15} - 14 q^{16} + 15 q^{17} + 4 q^{18} - q^{19} - 9 q^{20} - 2 q^{21} - 2 q^{23} + 6 q^{24} + 4 q^{25} - 6 q^{26} + 9 q^{27} - 9 q^{28} + 6 q^{29} - 2 q^{30} - 3 q^{31} - 30 q^{32} + 40 q^{34} - q^{35} - 9 q^{36} - 12 q^{37} - 26 q^{38} - 2 q^{39} - 7 q^{40} + 25 q^{41} + 3 q^{42} - 10 q^{43} - 6 q^{45} - 27 q^{46} + 8 q^{47} + 12 q^{48} - q^{49} - 16 q^{50} + 5 q^{51} + 6 q^{52} + 6 q^{53} + 14 q^{54} - 12 q^{56} + 8 q^{57} + q^{58} - 18 q^{59} - 3 q^{60} + 4 q^{61} - 3 q^{62} - q^{63} - 17 q^{64} + 4 q^{65} - 2 q^{67} + 60 q^{68} + 11 q^{69} - q^{70} - 2 q^{71} - 32 q^{72} + 17 q^{73} + 8 q^{74} + 8 q^{75} - 54 q^{76} - 12 q^{78} - 10 q^{79} + q^{80} + 16 q^{81} + 50 q^{82} + 19 q^{83} - 3 q^{84} - 10 q^{85} + 35 q^{86} + 12 q^{87} + 14 q^{89} - 11 q^{90} + 4 q^{91} - 3 q^{92} + 4 q^{93} - 17 q^{94} - q^{95} - 15 q^{96} - 7 q^{97} - 6 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 3 * q^3 + 6 * q^4 - q^5 + 3 * q^6 - q^7 - 7 * q^8 + 4 * q^9 - 6 * q^10 + 12 * q^12 - 6 * q^13 - q^14 + 3 * q^15 - 14 * q^16 + 15 * q^17 + 4 * q^18 - q^19 - 9 * q^20 - 2 * q^21 - 2 * q^23 + 6 * q^24 + 4 * q^25 - 6 * q^26 + 9 * q^27 - 9 * q^28 + 6 * q^29 - 2 * q^30 - 3 * q^31 - 30 * q^32 + 40 * q^34 - q^35 - 9 * q^36 - 12 * q^37 - 26 * q^38 - 2 * q^39 - 7 * q^40 + 25 * q^41 + 3 * q^42 - 10 * q^43 - 6 * q^45 - 27 * q^46 + 8 * q^47 + 12 * q^48 - q^49 - 16 * q^50 + 5 * q^51 + 6 * q^52 + 6 * q^53 + 14 * q^54 - 12 * q^56 + 8 * q^57 + q^58 - 18 * q^59 - 3 * q^60 + 4 * q^61 - 3 * q^62 - q^63 - 17 * q^64 + 4 * q^65 - 2 * q^67 + 60 * q^68 + 11 * q^69 - q^70 - 2 * q^71 - 32 * q^72 + 17 * q^73 + 8 * q^74 + 8 * q^75 - 54 * q^76 - 12 * q^78 - 10 * q^79 + q^80 + 16 * q^81 + 50 * q^82 + 19 * q^83 - 3 * q^84 - 10 * q^85 + 35 * q^86 + 12 * q^87 + 14 * q^89 - 11 * q^90 + 4 * q^91 - 3 * q^92 + 4 * q^93 - 17 * q^94 - q^95 - 15 * q^96 - 7 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	2.11803	+	1.53884i	1.49768	+	1.08813i	0.971295	+	0.237877i	$0.0764514\pi$
$2$	2.11803	+	1.53884i	1.49768	+	1.08813i	0.526381	+	0.850249i	$0.323549\pi$
$3$	0.190983	−	0.587785i	0.110264	−	0.339358i	−0.880666	−	0.473738i	$-0.842904\pi$
$3$	0.190983	−	0.587785i	0.110264	−	0.339358i	0.990930	+	0.134380i	$0.0429043\pi$
$4$	1.50000	+	4.61653i	0.750000	+	2.30826i
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i	−0.753804	−	0.657099i	$-0.771783\pi$
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i	0.392000	+	0.919965i	$0.371783\pi$
$6$	1.30902	−	0.951057i	0.534404	−	0.388267i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$8$	−2.30902	+	7.10642i	−0.816361	+	2.51250i
$9$	2.11803	+	1.53884i	0.706011	+	0.512947i
$10$	−2.61803			−0.827895
$11$		0			0
$11$		0			0
$12$	3.00000			0.866025
$13$	−2.61803	−	1.90211i	−0.726112	−	0.527551i	0.162219	−	0.986755i	$-0.448135\pi$
$13$	−2.61803	−	1.90211i	−0.726112	−	0.527551i	−0.888331	+	0.459204i	$0.848135\pi$
$14$	−0.809017	+	2.48990i	−0.216219	+	0.665453i
$15$	0.190983	+	0.587785i	0.0493116	+	0.151765i
$16$	−7.97214	+	5.79210i	−1.99303	+	1.44802i
$17$	6.54508	−	4.75528i	1.58742	−	1.15333i	0.679903	−	0.733302i	$-0.262022\pi$
$17$	6.54508	−	4.75528i	1.58742	−	1.15333i	0.907513	−	0.420023i	$-0.137978\pi$
$18$	2.11803	+	6.51864i	0.499225	+	1.53646i
$19$	−1.92705	+	5.93085i	−0.442096	+	1.36063i	0.443542	+	0.896254i	$0.353722\pi$
$19$	−1.92705	+	5.93085i	−0.442096	+	1.36063i	−0.885637	+	0.464377i	$0.846278\pi$
$20$	−3.92705	−	2.85317i	−0.878115	−	0.637988i
$21$	0.618034			0.134866
$22$		0			0
$23$	−6.09017			−1.26989			−0.634944	−	0.772558i	$-0.718977\pi$
$23$	−6.09017			−1.26989			−0.634944	+	0.772558i	$0.718977\pi$
$24$	3.73607	+	2.71441i	0.762622	+	0.554077i
$25$	−1.23607	+	3.80423i	−0.247214	+	0.760845i
$26$	−2.61803	−	8.05748i	−0.513439	−	1.58020i
$27$	2.80902	−	2.04087i	0.540596	−	0.392766i
$28$	−3.92705	+	2.85317i	−0.742143	+	0.539198i
$29$	−0.736068	−	2.26538i	−0.136684	−	0.420671i	0.859164	−	0.511701i	$-0.170984\pi$
$29$	−0.736068	−	2.26538i	−0.136684	−	0.420671i	−0.995848	+	0.0910293i	$0.970984\pi$
$30$	−0.500000	+	1.53884i	−0.0912871	+	0.280953i
$31$	−0.190983	−	0.138757i	−0.0343016	−	0.0249215i	0.570502	−	0.821296i	$-0.306749\pi$
$31$	−0.190983	−	0.138757i	−0.0343016	−	0.0249215i	−0.604804	+	0.796374i	$0.706749\pi$
$32$	−10.8541			−1.91875
$33$		0			0
$34$	21.1803			3.63240
$35$	−0.809017	−	0.587785i	−0.136749	−	0.0993538i
$36$	−3.92705	+	12.0862i	−0.654508	+	2.01437i
$37$	−0.763932	−	2.35114i	−0.125590	−	0.386525i	0.868418	−	0.495832i	$-0.165137\pi$
$37$	−0.763932	−	2.35114i	−0.125590	−	0.386525i	−0.994008	+	0.109307i	$0.965137\pi$
$38$	−13.2082	+	9.59632i	−2.14265	+	1.55673i
$39$	−1.61803	+	1.17557i	−0.259093	+	0.188242i
$40$	−2.30902	−	7.10642i	−0.365088	−	1.12362i
$41$	3.45492	−	10.6331i	0.539567	−	1.66062i	−0.194001	−	0.981001i	$-0.562147\pi$
$41$	3.45492	−	10.6331i	0.539567	−	1.66062i	0.733569	−	0.679615i	$-0.237853\pi$
$42$	1.30902	+	0.951057i	0.201986	+	0.146751i
$43$	7.56231			1.15324			0.576620	−	0.817012i	$-0.304371\pi$
$43$	7.56231			1.15324			0.576620	+	0.817012i	$0.304371\pi$
$44$		0			0
$45$	−2.61803			−0.390273
$46$	−12.8992	−	9.37181i	−1.90188	−	1.38180i
$47$	−1.35410	+	4.16750i	−0.197516	+	0.607892i	0.802422	+	0.596757i	$0.203544\pi$
$47$	−1.35410	+	4.16750i	−0.197516	+	0.607892i	−0.999938	+	0.0111349i	$0.996456\pi$
$48$	1.88197	+	5.79210i	0.271638	+	0.836017i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	−8.47214	+	6.15537i	−1.19814	+	0.870500i
$51$	−1.54508	−	4.75528i	−0.216355	−	0.665873i
$52$	4.85410	−	14.9394i	0.673143	−	2.07172i
$53$	3.73607	+	2.71441i	0.513188	+	0.372853i	0.814032	−	0.580820i	$-0.197268\pi$
$53$	3.73607	+	2.71441i	0.513188	+	0.372853i	−0.300843	+	0.953674i	$0.597268\pi$
$54$	9.09017			1.23702
$55$		0			0
$56$	−7.47214			−0.998506
$57$	3.11803	+	2.26538i	0.412994	+	0.300057i
$58$	1.92705	−	5.93085i	0.253034	−	0.778759i
$59$	−0.0278640	−	0.0857567i	−0.00362759	−	0.0111646i	0.949226	−	0.314594i	$-0.101868\pi$
$59$	−0.0278640	−	0.0857567i	−0.00362759	−	0.0111646i	−0.952854	+	0.303429i	$0.901868\pi$
$60$	−2.42705	+	1.76336i	−0.313331	+	0.227648i
$61$	4.35410	−	3.16344i	0.557486	−	0.405037i	−0.273052	−	0.961999i	$-0.588033\pi$
$61$	4.35410	−	3.16344i	0.557486	−	0.405037i	0.830538	+	0.556962i	$0.188033\pi$
$62$	−0.190983	−	0.587785i	−0.0242549	−	0.0746488i
$63$	−0.809017	+	2.48990i	−0.101927	+	0.313698i
$64$	−7.04508	−	5.11855i	−0.880636	−	0.639819i
$65$	3.23607			0.401385
$66$		0			0
$67$	7.32624			0.895042			0.447521	−	0.894273i	$-0.352307\pi$
$67$	7.32624			0.895042			0.447521	+	0.894273i	$0.352307\pi$
$68$	31.7705	+	23.0826i	3.85274	+	2.79918i
$69$	−1.16312	+	3.57971i	−0.140023	+	0.430947i
$70$	−0.809017	−	2.48990i	−0.0966960	−	0.297600i
$71$	3.97214	−	2.88593i	0.471406	−	0.342496i	−0.326583	−	0.945168i	$-0.605897\pi$
$71$	3.97214	−	2.88593i	0.471406	−	0.342496i	0.797989	+	0.602672i	$0.205897\pi$
$72$	−15.8262	+	11.4984i	−1.86514	+	1.35510i
$73$	−3.01722	−	9.28605i	−0.353139	−	1.08685i	−0.957081	−	0.289822i	$-0.906404\pi$
$73$	−3.01722	−	9.28605i	−0.353139	−	1.08685i	0.603942	−	0.797029i	$-0.293596\pi$
$74$	2.00000	−	6.15537i	0.232495	−	0.715547i
$75$	2.00000	+	1.45309i	0.230940	+	0.167788i
$76$	−30.2705			−3.47227
$77$		0			0
$78$	−5.23607			−0.592868
$79$	−6.97214	−	5.06555i	−0.784427	−	0.569919i	0.121878	−	0.992545i	$-0.461108\pi$
$79$	−6.97214	−	5.06555i	−0.784427	−	0.569919i	−0.906304	+	0.422626i	$0.861108\pi$
$80$	3.04508	−	9.37181i	0.340451	−	1.04780i
$81$	1.76393	+	5.42882i	0.195992	+	0.603203i
$82$	23.6803	−	17.2048i	2.61506	−	1.89995i
$83$	8.66312	−	6.29412i	0.950901	−	0.690870i	−0.000118920	−	1.00000i	$-0.500038\pi$
$83$	8.66312	−	6.29412i	0.950901	−	0.690870i	0.951020	+	0.309130i	$0.100038\pi$
$84$	0.927051	+	2.85317i	0.101150	+	0.311306i
$85$	−2.50000	+	7.69421i	−0.271163	+	0.834554i
$86$	16.0172	+	11.6372i	1.72718	+	1.25487i
$87$	−1.47214			−0.157830
$88$		0			0
$89$	0.145898			0.0154652			0.00773258	−	0.999970i	$-0.497539\pi$
$89$	0.145898			0.0154652			0.00773258	+	0.999970i	$0.497539\pi$
$90$	−5.54508	−	4.02874i	−0.584503	−	0.424666i
$91$	1.00000	−	3.07768i	0.104828	−	0.322629i
$92$	−9.13525	−	28.1154i	−0.952416	−	2.93124i
$93$	−0.118034	+	0.0857567i	−0.0122396	+	0.00889256i
$94$	−9.28115	+	6.74315i	−0.957278	+	0.695503i
$95$	−1.92705	−	5.93085i	−0.197711	−	0.608493i
$96$	−2.07295	+	6.37988i	−0.211569	+	0.651144i
$97$	−5.66312	−	4.11450i	−0.575003	−	0.417764i	0.261916	−	0.965091i	$-0.415646\pi$
$97$	−5.66312	−	4.11450i	−0.575003	−	0.417764i	−0.836919	+	0.547327i	$0.815646\pi$
$98$	−2.61803			−0.264461
$99$		0			0
$100$	−19.4164			−1.94164
$101$	−7.92705	−	5.75934i	−0.788771	−	0.573076i	0.118827	−	0.992915i	$-0.462086\pi$
$101$	−7.92705	−	5.75934i	−0.788771	−	0.573076i	−0.907599	+	0.419839i	$0.862086\pi$
$102$	4.04508	−	12.4495i	0.400523	−	1.23268i
$103$	0.663119	+	2.04087i	0.0653391	+	0.201093i	0.978396	−	0.206739i	$-0.0662850\pi$
$103$	0.663119	+	2.04087i	0.0653391	+	0.201093i	−0.913057	+	0.407832i	$0.866285\pi$
$104$	19.5623	−	14.2128i	1.91824	−	1.39368i
$105$	−0.500000	+	0.363271i	−0.0487950	+	0.0354516i
$106$	3.73607	+	11.4984i	0.362879	+	1.11683i
$107$	−3.30902	+	10.1841i	−0.319895	+	0.984535i	0.653798	+	0.756669i	$0.273175\pi$
$107$	−3.30902	+	10.1841i	−0.319895	+	0.984535i	−0.973693	+	0.227866i	$0.926825\pi$
$108$	13.6353	+	9.90659i	1.31205	+	0.953262i
$109$	−10.4721			−1.00305			−0.501524	−	0.865144i	$-0.667227\pi$
$109$	−10.4721			−1.00305			−0.501524	+	0.865144i	$0.667227\pi$
$110$		0			0
$111$	−1.52786			−0.145018
$112$	−7.97214	−	5.79210i	−0.753296	−	0.547302i
$113$	2.11803	−	6.51864i	0.199248	−	0.613222i	−0.800653	−	0.599129i	$-0.795514\pi$
$113$	2.11803	−	6.51864i	0.199248	−	0.613222i	0.999901	−	0.0140933i	$-0.00448619\pi$
$114$	3.11803	+	9.59632i	0.292031	+	0.898778i
$115$	4.92705	−	3.57971i	0.459450	−	0.333810i
$116$	9.35410	−	6.79615i	0.868507	−	0.631007i
$117$	−2.61803	−	8.05748i	−0.242037	−	0.744914i
$118$	0.0729490	−	0.224514i	0.00671550	−	0.0206682i
$119$	6.54508	+	4.75528i	0.599987	+	0.435916i
$120$	−4.61803			−0.421567
$121$		0			0
$122$	14.0902			1.27566
$123$	−5.59017	−	4.06150i	−0.504049	−	0.366213i
$124$	0.354102	−	1.08981i	0.0317993	−	0.0978682i
$125$	−2.78115	−	8.55951i	−0.248754	−	0.765586i
$126$	−5.54508	+	4.02874i	−0.493995	+	0.358909i
$127$	12.0902	−	8.78402i	1.07283	−	0.779456i	0.0964105	−	0.995342i	$-0.469264\pi$
$127$	12.0902	−	8.78402i	1.07283	−	0.779456i	0.976419	+	0.215886i	$0.0692639\pi$
$128$	−0.336881	−	1.03681i	−0.0297764	−	0.0916422i
$129$	1.44427	−	4.44501i	0.127161	−	0.391361i
$130$	6.85410	+	4.97980i	0.601145	+	0.436757i
$131$	1.05573			0.0922394			0.0461197	−	0.998936i	$-0.485314\pi$
$131$	1.05573			0.0922394			0.0461197	+	0.998936i	$0.485314\pi$
$132$		0			0
$133$	−6.23607			−0.540736
$134$	15.5172	+	11.2739i	1.34048	+	0.973918i
$135$	−1.07295	+	3.30220i	−0.0923447	+	0.284208i
$136$	18.6803	+	57.4922i	1.60183	+	4.92991i
$137$	−0.263932	+	0.191758i	−0.0225492	+	0.0163830i	−0.599003	−	0.800747i	$-0.704436\pi$
$137$	−0.263932	+	0.191758i	−0.0225492	+	0.0163830i	0.576454	+	0.817130i	$0.304436\pi$
$138$	−7.97214	+	5.79210i	−0.678633	+	0.493056i
$139$	−1.83688	−	5.65334i	−0.155802	−	0.479510i	0.842439	−	0.538792i	$-0.181119\pi$
$139$	−1.83688	−	5.65334i	−0.155802	−	0.479510i	−0.998241	+	0.0592817i	$0.981119\pi$
$140$	1.50000	−	4.61653i	0.126773	−	0.390168i
$141$	2.19098	+	1.59184i	0.184514	+	0.134057i
$142$	12.8541			1.07869
$143$		0			0
$144$	−25.7984			−2.14986
$145$	1.92705	+	1.40008i	0.160033	+	0.116271i
$146$	7.89919	−	24.3112i	0.653741	−	2.01201i
$147$	0.190983	+	0.587785i	0.0157520	+	0.0484797i
$148$	9.70820	−	7.05342i	0.798009	−	0.579788i
$149$	1.73607	−	1.26133i	0.142224	−	0.103332i	−0.514398	−	0.857552i	$-0.671985\pi$
$149$	1.73607	−	1.26133i	0.142224	−	0.103332i	0.656622	+	0.754220i	$0.271985\pi$
$150$	2.00000	+	6.15537i	0.163299	+	0.502584i
$151$	5.54508	−	17.0660i	0.451253	−	1.38881i	−0.424226	−	0.905556i	$-0.639454\pi$
$151$	5.54508	−	17.0660i	0.451253	−	1.38881i	0.875479	−	0.483256i	$-0.160546\pi$
$152$	−37.6976	−	27.3889i	−3.05768	−	2.22153i
$153$	21.1803			1.71233
$154$		0			0
$155$	0.236068			0.0189614
$156$	−7.85410	−	5.70634i	−0.628831	−	0.456873i
$157$	−4.90983	+	15.1109i	−0.391847	+	1.20598i	0.539543	+	0.841958i	$0.318597\pi$
$157$	−4.90983	+	15.1109i	−0.391847	+	1.20598i	−0.931390	+	0.364023i	$0.881403\pi$
$158$	−6.97214	−	21.4580i	−0.554673	−	1.70711i
$159$	2.30902	−	1.67760i	0.183117	−	0.133042i
$160$	8.78115	−	6.37988i	0.694211	−	0.504374i
$161$	−1.88197	−	5.79210i	−0.148320	−	0.456481i
$162$	−4.61803	+	14.2128i	−0.362827	+	1.11667i
$163$	−3.80902	−	2.76741i	−0.298345	−	0.216761i	0.428534	−	0.903526i	$-0.359030\pi$
$163$	−3.80902	−	2.76741i	−0.298345	−	0.216761i	−0.726879	+	0.686765i	$0.759030\pi$
$164$	54.2705			4.23781
$165$		0			0
$166$	28.0344			2.17589
$167$	2.00000	+	1.45309i	0.154765	+	0.112443i	0.662473	−	0.749086i	$-0.269507\pi$
$167$	2.00000	+	1.45309i	0.154765	+	0.112443i	−0.507708	+	0.861529i	$0.669507\pi$
$168$	−1.42705	+	4.39201i	−0.110099	+	0.338851i
$169$	−0.781153	−	2.40414i	−0.0600887	−	0.184934i
$170$	−17.1353	+	12.4495i	−1.31421	+	0.954832i
$171$	−13.2082	+	9.59632i	−1.01006	+	0.733849i
$172$	11.3435	+	34.9116i	0.864931	+	2.66198i
$173$	−5.44427	+	16.7557i	−0.413920	+	1.27392i	0.499293	+	0.866433i	$0.333593\pi$
$173$	−5.44427	+	16.7557i	−0.413920	+	1.27392i	−0.913213	+	0.407482i	$0.866407\pi$
$174$	−3.11803	−	2.26538i	−0.236378	−	0.171738i
$175$	−4.00000			−0.302372
$176$		0			0
$177$	−0.0557281			−0.00418878
$178$	0.309017	+	0.224514i	0.0231618	+	0.0168280i
$179$	−2.54508	+	7.83297i	−0.190229	+	0.585463i	−0.999999	−	0.00128323i	$-0.999592\pi$
$179$	−2.54508	+	7.83297i	−0.190229	+	0.585463i	0.809771	+	0.586747i	$0.199592\pi$
$180$	−3.92705	−	12.0862i	−0.292705	−	0.900854i
$181$	−15.7082	+	11.4127i	−1.16758	+	0.848298i	−0.990717	−	0.135938i	$-0.956595\pi$
$181$	−15.7082	+	11.4127i	−1.16758	+	0.848298i	−0.176864	+	0.984235i	$0.556595\pi$
$182$	6.85410	−	4.97980i	0.508060	−	0.369127i
$183$	−1.02786	−	3.16344i	−0.0759819	−	0.233848i
$184$	14.0623	−	43.2793i	1.03669	−	3.19059i
$185$	2.00000	+	1.45309i	0.147043	+	0.106833i
$186$	−0.381966			−0.0280071
$187$		0			0
$188$	−21.2705			−1.55131
$189$	2.80902	+	2.04087i	0.204326	+	0.148451i
$190$	5.04508	−	15.5272i	0.366009	−	1.12646i
$191$	6.25329	+	19.2456i	0.452472	+	1.39257i	0.874077	+	0.485787i	$0.161467\pi$
$191$	6.25329	+	19.2456i	0.452472	+	1.39257i	−0.421605	+	0.906779i	$0.638533\pi$
$192$	−4.35410	+	3.16344i	−0.314230	+	0.228302i
$193$	−0.263932	+	0.191758i	−0.0189982	+	0.0138030i	−0.597244	−	0.802060i	$-0.703738\pi$
$193$	−0.263932	+	0.191758i	−0.0189982	+	0.0138030i	0.578246	+	0.815863i	$0.303738\pi$
$194$	−5.66312	−	17.4293i	−0.406588	−	1.25135i
$195$	0.618034	−	1.90211i	0.0442583	−	0.136213i
$196$	−3.92705	−	2.85317i	−0.280504	−	0.203798i
$197$	−17.7082			−1.26166			−0.630829	−	0.775922i	$-0.717285\pi$
$197$	−17.7082			−1.26166			−0.630829	+	0.775922i	$0.717285\pi$
$198$		0			0
$199$	−3.76393			−0.266818			−0.133409	−	0.991061i	$-0.542592\pi$
$199$	−3.76393			−0.266818			−0.133409	+	0.991061i	$0.542592\pi$
$200$	−24.1803	−	17.5680i	−1.70981	−	1.24225i
$201$	1.39919	−	4.30625i	0.0986910	−	0.303740i
$202$	−7.92705	−	24.3970i	−0.557745	−	1.71656i
$203$	1.92705	−	1.40008i	0.135252	−	0.0982667i
$204$	19.6353	−	14.2658i	1.37474	−	0.998809i
$205$	3.45492	+	10.6331i	0.241302	+	0.742650i
$206$	−1.73607	+	5.34307i	−0.120958	+	0.372269i
$207$	−12.8992	−	9.37181i	−0.896555	−	0.651386i
$208$	31.8885			2.21107
$209$		0			0
$210$	−1.61803			−0.111655
$211$	−10.8262	−	7.86572i	−0.745309	−	0.541499i	0.149060	−	0.988828i	$-0.452375\pi$
$211$	−10.8262	−	7.86572i	−0.745309	−	0.541499i	−0.894369	+	0.447329i	$0.852375\pi$
$212$	−6.92705	+	21.3193i	−0.475752	+	1.46421i
$213$	−0.937694	−	2.88593i	−0.0642497	−	0.197740i
$214$	−22.6803	+	16.4782i	−1.55040	+	1.12643i
$215$	−6.11803	+	4.44501i	−0.417246	+	0.303147i
$216$	8.01722	+	24.6745i	0.545503	+	1.67888i
$217$	0.0729490	−	0.224514i	0.00495210	−	0.0152410i
$218$	−22.1803	−	16.1150i	−1.50224	−	1.09144i
$219$	−6.03444			−0.407770
$220$		0			0
$221$	−26.1803			−1.76108
$222$	−3.23607	−	2.35114i	−0.217191	−	0.157798i
$223$	−8.35410	+	25.7113i	−0.559432	+	1.72175i	0.124510	+	0.992218i	$0.460264\pi$
$223$	−8.35410	+	25.7113i	−0.559432	+	1.72175i	−0.683942	+	0.729536i	$0.739736\pi$
$224$	−3.35410	−	10.3229i	−0.224105	−	0.689725i
$225$	−8.47214	+	6.15537i	−0.564809	+	0.410358i
$226$	14.5172	−	10.5474i	0.965671	−	0.701601i
$227$	4.02786	+	12.3965i	0.267339	+	0.822784i	0.991145	+	0.132781i	$0.0423907\pi$
$227$	4.02786	+	12.3965i	0.267339	+	0.822784i	−0.723807	+	0.690003i	$0.757609\pi$
$228$	−5.78115	+	17.7926i	−0.382866	+	1.17834i
$229$	−9.09017	−	6.60440i	−0.600695	−	0.436431i	0.245430	−	0.969414i	$-0.421071\pi$
$229$	−9.09017	−	6.60440i	−0.600695	−	0.436431i	−0.846126	+	0.532984i	$0.821071\pi$
$230$	15.9443			1.05133
$231$		0			0
$232$	17.7984			1.16852
$233$	2.09017	+	1.51860i	0.136932	+	0.0994866i	0.654142	−	0.756371i	$-0.273030\pi$
$233$	2.09017	+	1.51860i	0.136932	+	0.0994866i	−0.517211	+	0.855858i	$0.673030\pi$
$234$	6.85410	−	21.0948i	0.448067	−	1.37901i
$235$	−1.35410	−	4.16750i	−0.0883319	−	0.271858i
$236$	0.354102	−	0.257270i	0.0230501	−	0.0167469i
$237$	−4.30902	+	3.13068i	−0.279901	+	0.203360i
$238$	6.54508	+	20.1437i	0.424255	+	1.30572i
$239$	−1.82624	+	5.62058i	−0.118130	+	0.363565i	−0.992587	−	0.121537i	$-0.961218\pi$
$239$	−1.82624	+	5.62058i	−0.118130	+	0.363565i	0.874457	+	0.485102i	$0.161218\pi$
$240$	−4.92705	−	3.57971i	−0.318040	−	0.231069i
$241$	−17.2705			−1.11249			−0.556246	−	0.831018i	$-0.687759\pi$
$241$	−17.2705			−1.11249			−0.556246	+	0.831018i	$0.687759\pi$
$242$		0			0
$243$	13.9443			0.894525
$244$	21.1353	+	15.3557i	1.35305	+	0.983045i
$245$	0.309017	−	0.951057i	0.0197424	−	0.0607608i
$246$	−5.59017	−	17.2048i	−0.356416	−	1.09694i
$247$	16.3262	−	11.8617i	1.03881	−	0.754742i
$248$	1.42705	−	1.03681i	0.0906178	−	0.0658377i
$249$	−2.04508	−	6.29412i	−0.129602	−	0.398874i
$250$	7.28115	−	22.4091i	0.460501	−	1.41727i
$251$	−18.6074	−	13.5191i	−1.17449	−	0.853316i	−0.182949	−	0.983122i	$-0.558564\pi$
$251$	−18.6074	−	13.5191i	−1.17449	−	0.853316i	−0.991539	+	0.129807i	$0.958564\pi$
$252$	−12.7082			−0.800542
$253$		0			0
$254$	39.1246			2.45490
$255$	4.04508	+	2.93893i	0.253313	+	0.184043i
$256$	−4.50000	+	13.8496i	−0.281250	+	0.865598i
$257$	3.57295	+	10.9964i	0.222874	+	0.685937i	0.998500	+	0.0547442i	$0.0174343\pi$
$257$	3.57295	+	10.9964i	0.222874	+	0.685937i	−0.775626	+	0.631193i	$0.782566\pi$
$258$	9.89919	−	7.19218i	0.616296	−	0.447766i
$259$	2.00000	−	1.45309i	0.124274	−	0.0902903i
$260$	4.85410	+	14.9394i	0.301039	+	0.926502i
$261$	1.92705	−	5.93085i	0.119281	−	0.367111i
$262$	2.23607	+	1.62460i	0.138145	+	0.100368i
$263$	23.1246			1.42592			0.712962	−	0.701202i	$-0.247353\pi$
$263$	23.1246			1.42592			0.712962	+	0.701202i	$0.247353\pi$
$264$		0			0
$265$	−4.61803			−0.283684
$266$	−13.2082	−	9.59632i	−0.809847	−	0.588388i
$267$	0.0278640	−	0.0857567i	0.00170525	−	0.00524823i
$268$	10.9894	+	33.8218i	0.671282	+	2.06599i
$269$	−8.20820	+	5.96361i	−0.500463	+	0.363608i	−0.809194	−	0.587542i	$-0.800096\pi$
$269$	−8.20820	+	5.96361i	−0.500463	+	0.363608i	0.308731	+	0.951149i	$0.400096\pi$
$270$	−7.35410	+	5.34307i	−0.447556	+	0.325169i
$271$	6.11803	+	18.8294i	0.371644	+	1.14380i	0.945715	+	0.324997i	$0.105363\pi$
$271$	6.11803	+	18.8294i	0.371644	+	1.14380i	−0.574071	+	0.818806i	$0.694637\pi$
$272$	−24.6353	+	75.8195i	−1.49373	+	4.59723i
$273$	−1.61803	−	1.17557i	−0.0979279	−	0.0711488i
$274$	−0.854102			−0.0515982
$275$		0			0
$276$	−18.2705			−1.09976
$277$	4.88197	+	3.54696i	0.293329	+	0.213116i	0.724710	−	0.689054i	$-0.241974\pi$
$277$	4.88197	+	3.54696i	0.293329	+	0.213116i	−0.431381	+	0.902170i	$0.641974\pi$
$278$	4.80902	−	14.8006i	0.288426	−	0.887683i
$279$	−0.190983	−	0.587785i	−0.0114339	−	0.0351898i
$280$	6.04508	−	4.39201i	0.361263	−	0.262473i
$281$	2.28115	−	1.65735i	0.136082	−	0.0988695i	−0.517662	−	0.855585i	$-0.673197\pi$
$281$	2.28115	−	1.65735i	0.136082	−	0.0988695i	0.653744	+	0.756716i	$0.273197\pi$
$282$	2.19098	+	6.74315i	0.130471	+	0.401549i
$283$	−1.83688	+	5.65334i	−0.109191	+	0.336056i	−0.990691	−	0.136128i	$-0.956534\pi$
$283$	−1.83688	+	5.65334i	−0.109191	+	0.336056i	0.881500	+	0.472184i	$0.156534\pi$
$284$	19.2812	+	14.0086i	1.14413	+	0.831256i
$285$	−3.85410			−0.228297
$286$		0			0
$287$	11.1803			0.659955
$288$	−22.9894	−	16.7027i	−1.35466	−	0.984219i
$289$	14.9721	−	46.0795i	0.880714	−	2.71056i
$290$	1.92705	+	5.93085i	0.113160	+	0.348272i
$291$	−3.50000	+	2.54290i	−0.205174	+	0.149067i
$292$	38.3435	−	27.8582i	2.24388	−	1.63028i
$293$	−3.39919	−	10.4616i	−0.198583	−	0.611174i	−0.999916	−	0.0129565i	$-0.995876\pi$
$293$	−3.39919	−	10.4616i	−0.198583	−	0.611174i	0.801333	−	0.598218i	$-0.204124\pi$
$294$	−0.500000	+	1.53884i	−0.0291606	+	0.0897471i
$295$	0.0729490	+	0.0530006i	0.00424726	+	0.00308581i
$296$	18.4721			1.07367
$297$		0			0
$298$	5.61803			0.325444
$299$	15.9443	+	11.5842i	0.922081	+	0.669931i
$300$	−3.70820	+	11.4127i	−0.214093	+	0.658911i
$301$	2.33688	+	7.19218i	0.134696	+	0.414550i
$302$	38.0066	−	27.6134i	2.18703	−	1.58897i
$303$	−4.89919	+	3.55947i	−0.281451	+	0.204486i
$304$	−18.9894	−	58.4432i	−1.08911	−	3.35195i
$305$	−1.66312	+	5.11855i	−0.0952299	+	0.293088i
$306$	44.8607	+	32.5932i	2.56451	+	1.86323i
$307$	−0.819660			−0.0467805			−0.0233902	−	0.999726i	$-0.507446\pi$
$307$	−0.819660			−0.0467805			−0.0233902	+	0.999726i	$0.507446\pi$
$308$		0			0
$309$	1.32624			0.0754470
$310$	0.500000	+	0.363271i	0.0283981	+	0.0206324i
$311$	2.78115	−	8.55951i	0.157705	−	0.485365i	−0.840720	−	0.541470i	$-0.817868\pi$
$311$	2.78115	−	8.55951i	0.157705	−	0.485365i	0.998425	+	0.0561046i	$0.0178680\pi$
$312$	−4.61803	−	14.2128i	−0.261445	−	0.804644i
$313$	−2.16312	+	1.57160i	−0.122267	+	0.0888320i	−0.647238	−	0.762288i	$-0.724076\pi$
$313$	−2.16312	+	1.57160i	−0.122267	+	0.0888320i	0.524971	+	0.851120i	$0.324076\pi$
$314$	−33.6525	+	24.4500i	−1.89912	+	1.37979i
$315$	−0.809017	−	2.48990i	−0.0455829	−	0.140290i
$316$	12.9271	−	39.7854i	0.727203	−	2.23810i
$317$	19.8713	+	14.4374i	1.11608	+	0.810883i	0.983611	−	0.180304i	$-0.0577080\pi$
$317$	19.8713	+	14.4374i	1.11608	+	0.810883i	0.132474	+	0.991187i	$0.457708\pi$
$318$	7.47214			0.419017
$319$		0			0
$320$	8.70820			0.486803
$321$	5.35410	+	3.88998i	0.298837	+	0.217118i
$322$	4.92705	−	15.1639i	0.274574	−	0.845051i
$323$	15.5902	+	47.9816i	0.867460	+	2.66977i
$324$	−22.4164	+	16.2865i	−1.24536	+	0.904804i
$325$	10.4721	−	7.60845i	0.580890	−	0.422041i
$326$	−3.80902	−	11.7229i	−0.210962	−	0.649274i
$327$	−2.00000	+	6.15537i	−0.110600	+	0.340393i
$328$	67.5861	+	49.1042i	3.73182	+	2.71132i
$329$	−4.38197			−0.241586
$330$		0			0
$331$	−16.1803			−0.889352			−0.444676	−	0.895692i	$-0.646681\pi$
$331$	−16.1803			−0.889352			−0.444676	+	0.895692i	$0.646681\pi$
$332$	42.0517	+	30.5523i	2.30788	+	1.67678i
$333$	2.00000	−	6.15537i	0.109599	−	0.337312i
$334$	2.00000	+	6.15537i	0.109435	+	0.336807i
$335$	−5.92705	+	4.30625i	−0.323829	+	0.235276i
$336$	−4.92705	+	3.57971i	−0.268793	+	0.195289i
$337$	2.48936	+	7.66145i	0.135604	+	0.417346i	0.995683	−	0.0928140i	$-0.0295862\pi$
$337$	2.48936	+	7.66145i	0.135604	+	0.417346i	−0.860080	+	0.510160i	$0.829586\pi$
$338$	2.04508	−	6.29412i	0.111238	−	0.342355i
$339$	−3.42705	−	2.48990i	−0.186132	−	0.135233i
$340$	−39.2705			−2.12974
$341$		0			0
$342$	−42.7426			−2.31126
$343$	−0.809017	−	0.587785i	−0.0436828	−	0.0317374i
$344$	−17.4615	+	53.7409i	−0.941461	+	2.89752i
$345$	−1.16312	−	3.57971i	−0.0626202	−	0.192725i
$346$	−37.3156	+	27.1114i	−2.00610	+	1.45752i
$347$	−27.2254	+	19.7804i	−1.46154	+	1.06187i	−0.478578	+	0.878045i	$0.658848\pi$
$347$	−27.2254	+	19.7804i	−1.46154	+	1.06187i	−0.982959	+	0.183824i	$0.941152\pi$
$348$	−2.20820	−	6.79615i	−0.118372	−	0.364312i
$349$	2.53444	−	7.80021i	0.135666	−	0.417536i	−0.860027	−	0.510248i	$-0.829554\pi$
$349$	2.53444	−	7.80021i	0.135666	−	0.417536i	0.995693	+	0.0927122i	$0.0295537\pi$
$350$	−8.47214	−	6.15537i	−0.452855	−	0.329018i
$351$	−11.2361			−0.599737
$352$		0			0
$353$	12.9098			0.687121			0.343560	−	0.939131i	$-0.388367\pi$
$353$	12.9098			0.687121			0.343560	+	0.939131i	$0.388367\pi$
$354$	−0.118034	−	0.0857567i	−0.00627344	−	0.00455792i
$355$	−1.51722	+	4.66953i	−0.0805257	+	0.247833i
$356$	0.218847	+	0.673542i	0.0115989	+	0.0356977i
$357$	4.04508	−	2.93893i	0.214089	−	0.155544i
$358$	−17.4443	+	12.6740i	−0.921958	+	0.669842i
$359$	−4.13525	−	12.7270i	−0.218250	−	0.671706i	−0.998907	−	0.0467453i	$-0.985115\pi$
$359$	−4.13525	−	12.7270i	−0.218250	−	0.671706i	0.780656	−	0.624960i	$-0.214885\pi$
$360$	6.04508	−	18.6049i	0.318604	−	0.980562i
$361$	−16.0902	−	11.6902i	−0.846851	−	0.615273i
$362$	−50.8328			−2.67171
$363$		0			0
$364$	15.7082			0.823334
$365$	7.89919	+	5.73910i	0.413462	+	0.300398i
$366$	2.69098	−	8.28199i	0.140660	−	0.432907i
$367$	−6.43769	−	19.8132i	−0.336045	−	1.03424i	−0.966205	−	0.257775i	$-0.917011\pi$
$367$	−6.43769	−	19.8132i	−0.336045	−	1.03424i	0.630160	−	0.776465i	$-0.282989\pi$
$368$	48.5517	−	35.2748i	2.53093	−	1.83883i
$369$	23.6803	−	17.2048i	1.23275	−	0.895645i
$370$	2.00000	+	6.15537i	0.103975	+	0.320002i
$371$	−1.42705	+	4.39201i	−0.0740888	+	0.228022i
$372$	−0.572949	−	0.416272i	−0.0297060	−	0.0215827i
$373$	−35.5623			−1.84135			−0.920673	−	0.390334i	$-0.872359\pi$
$373$	−35.5623			−1.84135			−0.920673	+	0.390334i	$0.872359\pi$
$374$		0			0
$375$	−5.56231			−0.287236
$376$	−26.4894	−	19.2456i	−1.36608	−	0.992518i
$377$	−2.38197	+	7.33094i	−0.122677	+	0.377562i
$378$	2.80902	+	8.64527i	0.144480	+	0.444664i
$379$	21.0902	−	15.3229i	1.08333	−	0.787085i	0.105069	−	0.994465i	$-0.466494\pi$
$379$	21.0902	−	15.3229i	1.08333	−	0.787085i	0.978260	+	0.207380i	$0.0664937\pi$
$380$	24.4894	−	17.7926i	1.25628	−	0.912739i
$381$	−2.85410	−	8.78402i	−0.146220	−	0.450019i
$382$	−16.3713	+	50.3858i	−0.837630	+	2.57796i
$383$	−11.8090	−	8.57975i	−0.603413	−	0.438405i	0.243676	−	0.969857i	$-0.421647\pi$
$383$	−11.8090	−	8.57975i	−0.603413	−	0.438405i	−0.847089	+	0.531452i	$0.821647\pi$
$384$	−0.673762			−0.0343828
$385$		0			0
$386$	−0.854102			−0.0434726
$387$	16.0172	+	11.6372i	0.814201	+	0.591552i
$388$	10.5000	−	32.3157i	0.533057	−	1.64058i
$389$	−3.65248	−	11.2412i	−0.185188	−	0.569950i	0.814764	−	0.579793i	$-0.196867\pi$
$389$	−3.65248	−	11.2412i	−0.185188	−	0.569950i	−0.999952	+	0.00984352i	$0.996867\pi$
$390$	4.23607	−	3.07768i	0.214502	−	0.155845i
$391$	−39.8607	+	28.9605i	−2.01584	+	1.46459i
$392$	−2.30902	−	7.10642i	−0.116623	−	0.358929i
$393$	0.201626	−	0.620541i	0.0101707	−	0.0313022i
$394$	−37.5066	−	27.2501i	−1.88955	−	1.37284i
$395$	8.61803			0.433620
$396$		0			0
$397$	−23.1803			−1.16339			−0.581694	−	0.813408i	$-0.697610\pi$
$397$	−23.1803			−1.16339			−0.581694	+	0.813408i	$0.697610\pi$
$398$	−7.97214	−	5.79210i	−0.399607	−	0.290332i
$399$	−1.19098	+	3.66547i	−0.0596237	+	0.183503i
$400$	−12.1803	−	37.4872i	−0.609017	−	1.87436i
$401$	21.4164	−	15.5599i	1.06948	−	0.777026i	0.0936649	−	0.995604i	$-0.470142\pi$
$401$	21.4164	−	15.5599i	1.06948	−	0.777026i	0.975820	+	0.218578i	$0.0701418\pi$
$402$	9.59017	−	6.96767i	0.478314	−	0.347516i
$403$	0.236068	+	0.726543i	0.0117594	+	0.0361917i
$404$	14.6976	−	45.2344i	0.731231	−	2.25050i
$405$	−4.61803	−	3.35520i	−0.229472	−	0.166721i
$406$	6.23607			0.309491
$407$		0			0
$408$	37.3607			1.84963
$409$	3.47214	+	2.52265i	0.171686	+	0.124737i	0.670310	−	0.742081i	$-0.266161\pi$
$409$	3.47214	+	2.52265i	0.171686	+	0.124737i	−0.498624	+	0.866818i	$0.666161\pi$
$410$	−9.04508	+	27.8379i	−0.446705	+	1.37482i
$411$	0.0623059	+	0.191758i	0.00307332	+	0.00945872i
$412$	−8.42705	+	6.12261i	−0.415171	+	0.301639i
$413$	0.0729490	−	0.0530006i	0.00358959	−	0.00260799i
$414$	−12.8992	−	39.6996i	−0.633960	−	1.95113i
$415$	−3.30902	+	10.1841i	−0.162433	+	0.499918i
$416$	28.4164	+	20.6457i	1.39323	+	1.01224i
$417$	−3.67376			−0.179905
$418$		0			0
$419$	−5.88854			−0.287674			−0.143837	−	0.989601i	$-0.545944\pi$
$419$	−5.88854			−0.287674			−0.143837	+	0.989601i	$0.545944\pi$
$420$	−2.42705	−	1.76336i	−0.118428	−	0.0860430i
$421$	1.61803	−	4.97980i	0.0788582	−	0.242700i	−0.903854	−	0.427841i	$-0.859274\pi$
$421$	1.61803	−	4.97980i	0.0788582	−	0.242700i	0.982712	+	0.185141i	$0.0592742\pi$
$422$	−10.8262	−	33.3197i	−0.527013	−	1.62198i
$423$	−9.28115	+	6.74315i	−0.451265	+	0.327863i
$424$	−27.9164	+	20.2825i	−1.35574	+	0.985003i
$425$	10.0000	+	30.7768i	0.485071	+	1.49290i
$426$	2.45492	−	7.55545i	0.118941	−	0.366063i
$427$	4.35410	+	3.16344i	0.210710	+	0.153090i
$428$	−51.9787			−2.51249
$429$		0			0
$430$	−19.7984			−0.954762
$431$	5.78115	+	4.20025i	0.278468	+	0.202319i	0.718249	−	0.695786i	$-0.244944\pi$
$431$	5.78115	+	4.20025i	0.278468	+	0.202319i	−0.439781	+	0.898105i	$0.644944\pi$
$432$	−10.5729	+	32.5402i	−0.508691	+	1.56559i
$433$	−11.7533	−	36.1729i	−0.564827	−	1.73836i	−0.668465	−	0.743744i	$-0.733048\pi$
$433$	−11.7533	−	36.1729i	−0.564827	−	1.73836i	0.103638	−	0.994615i	$-0.466952\pi$
$434$	0.500000	−	0.363271i	0.0240008	−	0.0174376i
$435$	1.19098	−	0.865300i	0.0571033	−	0.0414880i
$436$	−15.7082	−	48.3449i	−0.752287	−	2.31530i
$437$	11.7361	−	36.1199i	0.561412	−	1.72785i
$438$	−12.7812	−	9.28605i	−0.610707	−	0.443705i
$439$	5.61803			0.268134			0.134067	−	0.990972i	$-0.457196\pi$
$439$	5.61803			0.268134			0.134067	+	0.990972i	$0.457196\pi$
$440$		0			0
$441$	−2.61803			−0.124668
$442$	−55.4508	−	40.2874i	−2.63753	−	1.91628i
$443$	−2.50000	+	7.69421i	−0.118779	+	0.365563i	−0.992716	−	0.120475i	$-0.961558\pi$
$443$	−2.50000	+	7.69421i	−0.118779	+	0.365563i	0.873938	+	0.486038i	$0.161558\pi$
$444$	−2.29180	−	7.05342i	−0.108764	−	0.334741i
$445$	−0.118034	+	0.0857567i	−0.00559535	+	0.00406526i
$446$	−57.2599	+	41.6017i	−2.71133	+	1.96990i
$447$	−0.409830	−	1.26133i	−0.0193843	−	0.0596587i
$448$	2.69098	−	8.28199i	0.127137	−	0.391287i
$449$	2.69098	+	1.95511i	0.126995	+	0.0922675i	0.649470	−	0.760388i	$-0.274991\pi$
$449$	2.69098	+	1.95511i	0.126995	+	0.0922675i	−0.522474	+	0.852655i	$0.674991\pi$
$450$	−27.4164			−1.29242
$451$		0			0
$452$	33.2705			1.56491
$453$	−8.97214	−	6.51864i	−0.421548	−	0.306272i
$454$	−10.5451	+	32.4544i	−0.494905	+	1.52316i
$455$	1.00000	+	3.07768i	0.0468807	+	0.144284i
$456$	−23.2984	+	16.9273i	−1.09105	+	0.792692i
$457$	5.54508	−	4.02874i	0.259388	−	0.188457i	−0.450489	−	0.892782i	$-0.648750\pi$
$457$	5.54508	−	4.02874i	0.259388	−	0.188457i	0.709877	+	0.704325i	$0.248750\pi$
$458$	−9.09017	−	27.9767i	−0.424756	−	1.30726i
$459$	8.68034	−	26.7153i	0.405164	−	1.24697i
$460$	23.9164	+	17.3763i	1.11511	+	0.810174i
$461$	19.5066			0.908512			0.454256	−	0.890871i	$-0.349905\pi$
$461$	19.5066			0.908512			0.454256	+	0.890871i	$0.349905\pi$
$462$		0			0
$463$	17.7639			0.825560			0.412780	−	0.910831i	$-0.364558\pi$
$463$	17.7639			0.825560			0.412780	+	0.910831i	$0.364558\pi$
$464$	18.9894	+	13.7966i	0.881559	+	0.640490i
$465$	0.0450850	−	0.138757i	0.00209077	−	0.00643471i
$466$	2.09017	+	6.43288i	0.0968253	+	0.297997i
$467$	−27.1074	+	19.6947i	−1.25438	+	0.911361i	−0.998468	−	0.0553391i	$-0.982376\pi$
$467$	−27.1074	+	19.6947i	−1.25438	+	0.911361i	−0.255913	+	0.966700i	$0.582376\pi$
$468$	33.2705	−	24.1724i	1.53793	−	1.11737i
$469$	2.26393	+	6.96767i	0.104539	+	0.321737i
$470$	3.54508	−	10.9106i	0.163523	−	0.503271i
$471$	7.94427	+	5.77185i	0.366053	+	0.265953i
$472$	0.673762			0.0310124
$473$		0			0
$474$	−13.9443			−0.640482
$475$	−20.1803	−	14.6619i	−0.925937	−	0.672733i
$476$	−12.1353	+	37.3485i	−0.556218	+	1.71186i
$477$	3.73607	+	11.4984i	0.171063	+	0.526477i
$478$	−12.5172	+	9.09429i	−0.572524	+	0.415963i
$479$	−21.2254	+	15.4212i	−0.969814	+	0.704611i	−0.955409	−	0.295285i	$-0.904585\pi$
$479$	−21.2254	+	15.4212i	−0.969814	+	0.704611i	−0.0144051	+	0.999896i	$0.504585\pi$
$480$	−2.07295	−	6.37988i	−0.0946167	−	0.291200i
$481$	−2.47214	+	7.60845i	−0.112720	+	0.346916i
$482$	−36.5795	−	26.5766i	−1.66615	−	1.21053i
$483$	−3.76393			−0.171265
$484$		0			0
$485$	7.00000			0.317854
$486$	29.5344	+	21.4580i	1.33971	+	0.973356i
$487$	5.12868	−	15.7844i	0.232403	−	0.715261i	−0.765053	−	0.643968i	$-0.777287\pi$
$487$	5.12868	−	15.7844i	0.232403	−	0.715261i	0.997455	−	0.0712939i	$-0.0227128\pi$
$488$	12.4271	+	38.2465i	0.562546	+	1.73134i
$489$	−2.35410	+	1.71036i	−0.106456	+	0.0773449i
$490$	2.11803	−	1.53884i	0.0956830	−	0.0695178i
$491$	8.91641	+	27.4419i	0.402392	+	1.23843i	0.923053	+	0.384672i	$0.125685\pi$
$491$	8.91641	+	27.4419i	0.402392	+	1.23843i	−0.520662	+	0.853763i	$0.674315\pi$
$492$	10.3647	−	31.8994i	0.467279	−	1.43814i
$493$	−15.5902	−	11.3269i	−0.702146	−	0.510139i
$494$	52.8328			2.37706
$495$		0			0
$496$	2.32624			0.104451
$497$	3.97214	+	2.88593i	0.178175	+	0.129451i
$498$	5.35410	−	16.4782i	0.239923	−	0.738407i
$499$	0.336881	+	1.03681i	0.0150809	+	0.0464141i	0.958314	−	0.285718i	$-0.0922320\pi$
$499$	0.336881	+	1.03681i	0.0150809	+	0.0464141i	−0.943233	+	0.332132i	$0.892232\pi$
$500$	35.3435	−	25.6785i	1.58061	−	1.14838i
$501$	1.23607	−	0.898056i	0.0552234	−	0.0401222i
$502$	−18.6074	−	57.2677i	−0.830488	−	2.55598i
$503$	5.81966	−	17.9111i	0.259486	−	0.798615i	−0.733427	−	0.679768i	$-0.762080\pi$
$503$	5.81966	−	17.9111i	0.259486	−	0.798615i	0.992913	−	0.118847i	$-0.0379197\pi$
$504$	−15.8262	−	11.4984i	−0.704957	−	0.512181i
$505$	9.79837			0.436022
$506$		0			0
$507$	−1.56231			−0.0693844
$508$	58.6869	+	42.6385i	2.60381	+	1.89178i
$509$	9.80902	−	30.1891i	0.434777	−	1.33811i	−0.458538	−	0.888675i	$-0.651627\pi$
$509$	9.80902	−	30.1891i	0.434777	−	1.33811i	0.893315	−	0.449431i	$-0.148373\pi$
$510$	4.04508	+	12.4495i	0.179119	+	0.551273i
$511$	7.89919	−	5.73910i	0.349439	−	0.253883i
$512$	−32.6074	+	23.6907i	−1.44106	+	1.04699i
$513$	6.69098	+	20.5927i	0.295414	+	0.909191i
$514$	−9.35410	+	28.7890i	−0.412592	+	1.26983i
$515$	−1.73607	−	1.26133i	−0.0765003	−	0.0555807i
$516$	22.6869			0.998736
$517$		0			0
$518$	6.47214			0.284369
$519$	8.80902	+	6.40013i	0.386673	+	0.280934i
$520$	−7.47214	+	22.9969i	−0.327675	+	1.00848i
$521$	−2.39919	−	7.38394i	−0.105110	−	0.323496i	0.884646	−	0.466263i	$-0.154400\pi$
$521$	−2.39919	−	7.38394i	−0.105110	−	0.323496i	−0.989756	+	0.142767i	$0.954400\pi$
$522$	13.2082	−	9.59632i	0.578107	−	0.420020i
$523$	2.88197	−	2.09387i	0.126020	−	0.0915586i	−0.522990	−	0.852339i	$-0.675183\pi$
$523$	2.88197	−	2.09387i	0.126020	−	0.0915586i	0.649010	+	0.760780i	$0.275183\pi$
$524$	1.58359	+	4.87380i	0.0691795	+	0.212913i
$525$	−0.763932	+	2.35114i	−0.0333407	+	0.102612i
$526$	48.9787	+	35.5851i	2.13557	+	1.55158i
$527$	−1.90983			−0.0831935
$528$		0			0
$529$	14.0902			0.612616
$530$	−9.78115	−	7.10642i	−0.424866	−	0.308683i
$531$	0.0729490	−	0.224514i	0.00316572	−	0.00974308i
$532$	−9.35410	−	28.7890i	−0.405552	−	1.24816i
$533$	−29.2705	+	21.2663i	−1.26785	+	0.921144i
$534$	0.190983	−	0.138757i	0.00826464	−	0.00600461i
$535$	−3.30902	−	10.1841i	−0.143061	−	0.440297i
$536$	−16.9164	+	52.0633i	−0.730678	+	2.24879i
$537$	4.11803	+	2.99193i	0.177706	+	0.129111i
$538$	−26.5623			−1.14518
$539$		0			0
$540$	−16.8541			−0.725285
$541$	10.2812	+	7.46969i	0.442021	+	0.321147i	0.786438	−	0.617670i	$-0.211923\pi$
$541$	10.2812	+	7.46969i	0.442021	+	0.321147i	−0.344416	+	0.938817i	$0.611923\pi$
$542$	−16.0172	+	49.2959i	−0.687999	+	2.11744i
$543$	3.70820	+	11.4127i	0.159134	+	0.489765i
$544$	−71.0410	+	51.6143i	−3.04586	+	2.21295i
$545$	8.47214	−	6.15537i	0.362906	−	0.263667i
$546$	−1.61803	−	4.97980i	−0.0692455	−	0.213116i
$547$	−10.8992	+	33.5442i	−0.466016	+	1.43425i	0.391685	+	0.920099i	$0.371892\pi$
$547$	−10.8992	+	33.5442i	−0.466016	+	1.43425i	−0.857701	+	0.514149i	$0.828108\pi$
$548$	−1.28115	−	0.930812i	−0.0547281	−	0.0397623i
$549$	14.0902			0.601354
$550$		0			0
$551$	14.8541			0.632806
$552$	−22.7533	−	16.5312i	−0.968444	−	0.703616i
$553$	2.66312	−	8.19624i	0.113247	−	0.348539i
$554$	4.88197	+	15.0251i	0.207415	+	0.638357i
$555$	1.23607	−	0.898056i	0.0524682	−	0.0381204i
$556$	23.3435	−	16.9600i	0.989983	−	0.719265i
$557$	−4.39919	−	13.5393i	−0.186400	−	0.573679i	0.813570	−	0.581467i	$-0.197521\pi$
$557$	−4.39919	−	13.5393i	−0.186400	−	0.573679i	−0.999970	+	0.00778802i	$0.997521\pi$
$558$	0.500000	−	1.53884i	0.0211667	−	0.0651444i
$559$	−19.7984	−	14.3844i	−0.837382	−	0.608394i
$560$	9.85410			0.416412
$561$		0			0
$562$	7.38197			0.311389
$563$	−12.1180	−	8.80427i	−0.510714	−	0.371056i	0.302380	−	0.953187i	$-0.402219\pi$
$563$	−12.1180	−	8.80427i	−0.510714	−	0.371056i	−0.813094	+	0.582132i	$0.802219\pi$
$564$	−4.06231	+	12.5025i	−0.171054	+	0.526450i
$565$	2.11803	+	6.51864i	0.0891064	+	0.274241i
$566$	−12.5902	+	9.14729i	−0.529204	+	0.384489i
$567$	−4.61803	+	3.35520i	−0.193939	+	0.140905i
$568$	11.3369	+	34.8913i	0.475685	+	1.46401i
$569$	−7.81966	+	24.0664i	−0.327817	+	1.00892i	0.642336	+	0.766423i	$0.277966\pi$
$569$	−7.81966	+	24.0664i	−0.327817	+	1.00892i	−0.970153	+	0.242494i	$0.922034\pi$
$570$	−8.16312	−	5.93085i	−0.341915	−	0.248416i
$571$	−28.3050			−1.18453			−0.592263	−	0.805745i	$-0.701765\pi$
$571$	−28.3050			−1.18453			−0.592263	+	0.805745i	$0.701765\pi$
$572$		0			0
$573$	12.5066			0.522470
$574$	23.6803	+	17.2048i	0.988398	+	0.718113i
$575$	7.52786	−	23.1684i	0.313934	−	0.966188i
$576$	−7.04508	−	21.6825i	−0.293545	−	0.903439i
$577$	17.5172	−	12.7270i	0.729251	−	0.529832i	−0.160075	−	0.987105i	$-0.551174\pi$
$577$	17.5172	−	12.7270i	0.729251	−	0.529832i	0.889327	+	0.457273i	$0.151174\pi$
$578$	102.621	−	74.5582i	4.26845	−	3.10121i
$579$	0.0623059	+	0.191758i	0.00258934	+	0.00796918i
$580$	−3.57295	+	10.9964i	−0.148359	+	0.456601i
$581$	8.66312	+	6.29412i	0.359407	+	0.261124i
$582$	−11.3262			−0.469488
$583$		0			0
$584$	72.9574			3.01900
$585$	6.85410	+	4.97980i	0.283382	+	0.205889i
$586$	8.89919	−	27.3889i	0.367622	−	1.13142i
$587$	0.309017	+	0.951057i	0.0127545	+	0.0392543i	0.957231	−	0.289324i	$-0.0934305\pi$
$587$	0.309017	+	0.951057i	0.0127545	+	0.0392543i	−0.944477	+	0.328578i	$0.893431\pi$
$588$	−2.42705	+	1.76336i	−0.100090	+	0.0727196i
$589$	1.19098	−	0.865300i	0.0490736	−	0.0356541i
$590$	0.0729490	+	0.224514i	0.00300326	+	0.00924309i
$591$	−3.38197	+	10.4086i	−0.139115	+	0.428153i
$592$	19.7082	+	14.3188i	0.810002	+	0.588501i
$593$	−29.1246			−1.19600			−0.598002	−	0.801494i	$-0.704039\pi$
$593$	−29.1246			−1.19600			−0.598002	+	0.801494i	$0.704039\pi$
$594$		0			0
$595$	−8.09017			−0.331665
$596$	8.42705	+	6.12261i	0.345185	+	0.250792i
$597$	−0.718847	+	2.21238i	−0.0294205	+	0.0905468i
$598$	15.9443	+	49.0714i	0.652010	+	2.00668i
$599$	12.9443	−	9.40456i	0.528889	−	0.384260i	−0.291053	−	0.956707i	$-0.594006\pi$
$599$	12.9443	−	9.40456i	0.528889	−	0.384260i	0.819942	+	0.572447i	$0.194006\pi$
$600$	−14.9443	+	10.8576i	−0.610097	+	0.443262i
$601$	0.0901699	+	0.277515i	0.00367811	+	0.0113201i	0.952879	−	0.303351i	$-0.0981056\pi$
$601$	0.0901699	+	0.277515i	0.00367811	+	0.0113201i	−0.949201	+	0.314672i	$0.898106\pi$
$602$	−6.11803	+	18.8294i	−0.249352	+	0.767428i
$603$	15.5172	+	11.2739i	0.631910	+	0.459110i
$604$	87.1033			3.54418
$605$		0			0
$606$	−15.8541			−0.644029
$607$	−36.2426	−	26.3318i	−1.47104	−	1.06878i	−0.980310	−	0.197466i	$-0.936729\pi$
$607$	−36.2426	−	26.3318i	−1.47104	−	1.06878i	−0.490734	−	0.871309i	$-0.663271\pi$
$608$	20.9164	−	64.3741i	0.848272	−	2.61071i
$609$	−0.454915	−	1.40008i	−0.0184341	−	0.0567343i
$610$	−11.3992	+	8.28199i	−0.461540	+	0.335328i
$611$	11.4721	−	8.33499i	0.464113	−	0.337198i
$612$	31.7705	+	97.7796i	1.28425	+	3.95251i
$613$	10.7812	−	33.1810i	0.435447	−	1.34017i	−0.457182	−	0.889373i	$-0.651141\pi$
$613$	10.7812	−	33.1810i	0.435447	−	1.34017i	0.892628	−	0.450794i	$-0.148859\pi$
$614$	−1.73607	−	1.26133i	−0.0700620	−	0.0509030i
$615$	6.90983			0.278631
$616$		0			0
$617$	−17.4164			−0.701158			−0.350579	−	0.936533i	$-0.614015\pi$
$617$	−17.4164			−0.701158			−0.350579	+	0.936533i	$0.614015\pi$
$618$	2.80902	+	2.04087i	0.112995	+	0.0820958i
$619$	−8.12461	+	25.0050i	−0.326556	+	1.00504i	0.644178	+	0.764876i	$0.277200\pi$
$619$	−8.12461	+	25.0050i	−0.326556	+	1.00504i	−0.970733	+	0.240159i	$0.922800\pi$
$620$	0.354102	+	1.08981i	0.0142211	+	0.0437680i
$621$	−17.1074	+	12.4292i	−0.686496	+	0.498769i
$622$	19.0623	−	13.8496i	0.764329	−	0.555317i
$623$	0.0450850	+	0.138757i	0.00180629	+	0.00555919i
$624$	6.09017	−	18.7436i	0.243802	−	0.750345i
$625$	−8.89919	−	6.46564i	−0.355967	−	0.258626i
$626$	−7.00000			−0.279776
$627$		0			0
$628$	−77.1246			−3.07761
$629$	−16.1803	−	11.7557i	−0.645152	−	0.468731i
$630$	2.11803	−	6.51864i	0.0843845	−	0.259709i
$631$	−11.0729	−	34.0790i	−0.440807	−	1.35666i	−0.887017	−	0.461737i	$-0.847227\pi$
$631$	−11.0729	−	34.0790i	−0.440807	−	1.35666i	0.446210	−	0.894928i	$-0.352773\pi$
$632$	52.0967	−	37.8505i	2.07230	−	1.50561i
$633$	−6.69098	+	4.86128i	−0.265943	+	0.193219i
$634$	19.8713	+	61.1576i	0.789191	+	2.42888i
$635$	−4.61803	+	14.2128i	−0.183261	+	0.564020i
$636$	11.2082	+	8.14324i	0.444434	+	0.322900i
$637$	3.23607			0.128218
$638$		0			0
$639$	12.8541			0.508500
$640$	0.881966	+	0.640786i	0.0348628	+	0.0253293i
$641$	0.107391	−	0.330515i	0.00424168	−	0.0130546i	−0.948913	−	0.315537i	$-0.897815\pi$
$641$	0.107391	−	0.330515i	0.00424168	−	0.0130546i	0.953155	+	0.302482i	$0.0978154\pi$
$642$	5.35410	+	16.4782i	0.211310	+	0.650344i
$643$	−22.9894	+	16.7027i	−0.906612	+	0.658692i	−0.940156	−	0.340745i	$-0.889321\pi$
$643$	−22.9894	+	16.7027i	−0.906612	+	0.658692i	0.0335439	+	0.999437i	$0.489321\pi$
$644$	23.9164	−	17.3763i	0.942438	−	0.684722i
$645$	1.44427	+	4.44501i	0.0568682	+	0.175022i
$646$	−40.8156	+	125.617i	−1.60587	+	4.94235i
$647$	13.0902	+	9.51057i	0.514628	+	0.373899i	0.814576	−	0.580056i	$-0.196970\pi$
$647$	13.0902	+	9.51057i	0.514628	+	0.373899i	−0.299949	+	0.953955i	$0.596970\pi$
$648$	−42.6525			−1.67555
$649$		0			0
$650$	33.8885			1.32922
$651$	−0.118034	−	0.0857567i	−0.00462612	−	0.00336107i
$652$	7.06231	−	21.7355i	0.276581	−	0.851230i
$653$	4.25329	+	13.0903i	0.166444	+	0.512262i	0.999140	−	0.0414687i	$-0.0132037\pi$
$653$	4.25329	+	13.0903i	0.166444	+	0.512262i	−0.832696	+	0.553731i	$0.813204\pi$
$654$	−13.7082	+	9.95959i	−0.536033	+	0.389451i
$655$	−0.854102	+	0.620541i	−0.0333725	+	0.0242466i
$656$	34.0451	+	104.780i	1.32924	+	4.09097i
$657$	7.89919	−	24.3112i	0.308177	−	0.948470i
$658$	−9.28115	−	6.74315i	−0.361817	−	0.262875i
$659$	22.5279			0.877561			0.438780	−	0.898594i	$-0.355411\pi$
$659$	22.5279			0.877561			0.438780	+	0.898594i	$0.355411\pi$
$660$		0			0
$661$	−14.4377			−0.561561			−0.280781	−	0.959772i	$-0.590593\pi$
$661$	−14.4377			−0.561561			−0.280781	+	0.959772i	$0.590593\pi$
$662$	−34.2705	−	24.8990i	−1.33196	−	0.967726i
$663$	−5.00000	+	15.3884i	−0.194184	+	0.597637i
$664$	24.7254	+	76.0970i	0.959533	+	2.95314i
$665$	5.04508	−	3.66547i	0.195640	−	0.142141i
$666$	13.7082	−	9.95959i	0.531182	−	0.385926i
$667$	4.48278	+	13.7966i	0.173574	+	0.534206i
$668$	−3.70820	+	11.4127i	−0.143475	+	0.441570i
$669$	13.5172	+	9.82084i	0.522606	+	0.379695i
$670$	−19.1803			−0.741001
$671$		0			0
$672$	−6.70820			−0.258775
$673$	27.0344	+	19.6417i	1.04210	+	0.757131i	0.970695	−	0.240316i	$-0.0772512\pi$
$673$	27.0344	+	19.6417i	1.04210	+	0.757131i	0.0714066	+	0.997447i	$0.477251\pi$
$674$	−6.51722	+	20.0579i	−0.251034	+	0.772603i
$675$	4.29180	+	13.2088i	0.165191	+	0.508407i
$676$	9.92705	−	7.21242i	0.381810	−	0.277401i
$677$	2.20820	−	1.60435i	0.0848682	−	0.0616603i	−0.544542	−	0.838734i	$-0.683297\pi$
$677$	2.20820	−	1.60435i	0.0848682	−	0.0616603i	0.629410	+	0.777073i	$0.283297\pi$
$678$	−3.42705	−	10.5474i	−0.131615	−	0.405070i
$679$	2.16312	−	6.65740i	0.0830129	−	0.255487i
$680$	−48.9058	−	35.5321i	−1.87545	−	1.36259i
$681$	8.05573			0.308696
$682$		0			0
$683$	38.5066			1.47341			0.736707	−	0.676213i	$-0.236380\pi$
$683$	38.5066			1.47341			0.736707	+	0.676213i	$0.236380\pi$
$684$	−64.1140	−	46.5815i	−2.45146	−	1.78109i
$685$	0.100813	−	0.310271i	0.00385187	−	0.0118548i
$686$	−0.809017	−	2.48990i	−0.0308884	−	0.0950648i
$687$	−5.61803	+	4.08174i	−0.214341	+	0.155728i
$688$	−60.2877	+	43.8016i	−2.29845	+	1.66992i
$689$	−4.61803	−	14.2128i	−0.175933	−	0.541466i
$690$	3.04508	−	9.37181i	0.115924	−	0.356779i
$691$	39.2705	+	28.5317i	1.49392	+	1.08540i	0.972725	+	0.231959i	$0.0745136\pi$
$691$	39.2705	+	28.5317i	1.49392	+	1.08540i	0.521195	+	0.853438i	$0.325486\pi$
$692$	−85.5197			−3.25097
$693$		0			0
$694$	−88.1033			−3.34436
$695$	4.80902	+	3.49396i	0.182416	+	0.132533i
$696$	3.39919	−	10.4616i	0.128846	−	0.396547i
$697$	−27.9508	−	86.0239i	−1.05871	−	3.25839i
$698$	17.3713	−	12.6210i	0.657514	−	0.477712i
$699$	1.29180	−	0.938545i	0.0488602	−	0.0354990i
$700$	−6.00000	−	18.4661i	−0.226779	−	0.697953i
$701$	−6.02786	+	18.5519i	−0.227669	+	0.700694i	0.770340	+	0.637633i	$0.220086\pi$
$701$	−6.02786	+	18.5519i	−0.227669	+	0.700694i	−0.998010	+	0.0630611i	$0.979914\pi$
$702$	−23.7984	−	17.2905i	−0.898212	−	0.652589i
$703$	15.4164			0.581441
$704$		0			0
$705$	−2.70820			−0.101997
$706$	27.3435	+	19.8662i	1.02908	+	0.747674i
$707$	3.02786	−	9.31881i	0.113875	−	0.350470i
$708$	−0.0835921	−	0.257270i	−0.00314158	−	0.00966880i
$709$	−17.8262	+	12.9515i	−0.669478	+	0.486405i	−0.869851	−	0.493315i	$-0.835785\pi$
$709$	−17.8262	+	12.9515i	−0.669478	+	0.486405i	0.200372	+	0.979720i	$0.435785\pi$
$710$	−10.3992	+	7.55545i	−0.390275	+	0.283551i
$711$	−6.97214	−	21.4580i	−0.261476	−	0.804739i
$712$	−0.336881	+	1.03681i	−0.0126252	+	0.0388562i
$713$	1.16312	+	0.845055i	0.0435591	+	0.0316476i
$714$	13.0902			0.489887
$715$		0			0
$716$	−39.9787			−1.49407
$717$	2.95492	+	2.14687i	0.110353	+	0.0801764i
$718$	10.8262	−	33.3197i	0.404032	−	1.24348i
$719$	10.1631	+	31.2789i	0.379020	+	1.16650i	0.940726	+	0.339168i	$0.110145\pi$
$719$	10.1631	+	31.2789i	0.379020	+	1.16650i	−0.561706	+	0.827337i	$0.689855\pi$
$720$	20.8713	−	15.1639i	0.777828	−	0.565125i
$721$	−1.73607	+	1.26133i	−0.0646546	+	0.0469743i
$722$	−16.0902	−	49.5205i	−0.598814	−	1.84296i
$723$	−3.29837	+	10.1514i	−0.122668	+	0.377533i
$724$	−76.2492	−	55.3983i	−2.83378	−	2.05886i
$725$	9.52786			0.353856
$726$		0			0
$727$	43.4508			1.61150			0.805751	−	0.592254i	$-0.201762\pi$
$727$	43.4508			1.61150			0.805751	+	0.592254i	$0.201762\pi$
$728$	19.5623	+	14.2128i	0.725027	+	0.526763i
$729$	−2.62868	+	8.09024i	−0.0973584	+	0.299638i
$730$	7.89919	+	24.3112i	0.292362	+	0.899798i
$731$	49.4959	−	35.9609i	1.83067	−	1.33006i
$732$	13.0623	−	9.49032i	0.482797	−	0.350772i
$733$	10.8328	+	33.3400i	0.400119	+	1.23144i	0.924903	+	0.380204i	$0.124146\pi$
$733$	10.8328	+	33.3400i	0.400119	+	1.23144i	−0.524783	+	0.851236i	$0.675854\pi$
$734$	16.8541	−	51.8716i	0.622096	−	1.91462i
$735$	−0.500000	−	0.363271i	−0.0184428	−	0.0133995i
$736$	66.1033			2.43660
$737$		0			0
$738$	76.6312			2.82083
$739$	11.0172	+	8.00448i	0.405275	+	0.294450i	0.771686	−	0.636004i	$-0.219414\pi$
$739$	11.0172	+	8.00448i	0.405275	+	0.294450i	−0.366411	+	0.930453i	$0.619414\pi$
$740$	−3.70820	+	11.4127i	−0.136316	+	0.419538i
$741$	−3.85410	−	11.8617i	−0.141584	−	0.435751i
$742$	−9.78115	+	7.10642i	−0.359077	+	0.260885i
$743$	21.1074	−	15.3354i	0.774355	−	0.562602i	−0.128924	−	0.991654i	$-0.541152\pi$
$743$	21.1074	−	15.3354i	0.774355	−	0.562602i	0.903280	+	0.429053i	$0.141152\pi$
$744$	−0.336881	−	1.03681i	−0.0123507	−	0.0380114i
$745$	−0.663119	+	2.04087i	−0.0242948	+	0.0747717i
$746$	−75.3222	−	54.7248i	−2.75774	−	2.00362i
$747$	28.0344			1.02573
$748$		0			0
$749$	−10.7082			−0.391269
$750$	−11.7812	−	8.55951i	−0.430187	−	0.312549i
$751$	−6.58359	+	20.2622i	−0.240239	+	0.739379i	0.756144	+	0.654405i	$0.227081\pi$
$751$	−6.58359	+	20.2622i	−0.240239	+	0.739379i	−0.996383	+	0.0849740i	$0.972919\pi$
$752$	−13.3435	−	41.0669i	−0.486586	−	1.49756i
$753$	−11.5000	+	8.35524i	−0.419083	+	0.304482i
$754$	−16.3262	+	11.8617i	−0.594567	+	0.431978i
$755$	5.54508	+	17.0660i	0.201806	+	0.621096i
$756$	−5.20820	+	16.0292i	−0.189421	+	0.582976i
$757$	15.5623	+	11.3067i	0.565622	+	0.410948i	0.833512	−	0.552501i	$-0.186327\pi$
$757$	15.5623	+	11.3067i	0.565622	+	0.410948i	−0.267890	+	0.963449i	$0.586327\pi$
$758$	68.2492			2.47892
$759$		0			0
$760$	46.5967			1.69024
$761$	38.2705	+	27.8052i	1.38730	+	1.00794i	0.996155	+	0.0876091i	$0.0279226\pi$
$761$	38.2705	+	27.8052i	1.38730	+	1.00794i	0.391150	+	0.920327i	$0.372077\pi$
$762$	7.47214	−	22.9969i	0.270687	−	0.833089i
$763$	−3.23607	−	9.95959i	−0.117154	−	0.360561i
$764$	−79.4681	+	57.7369i	−2.87505	+	2.08885i
$765$	−17.1353	+	12.4495i	−0.619526	+	0.450112i
$766$	−11.8090	−	36.3444i	−0.426677	−	1.31318i
$767$	−0.0901699	+	0.277515i	−0.00325585	+	0.0100205i
$768$	7.28115	+	5.29007i	0.262736	+	0.190889i
$769$	28.4377			1.02549			0.512745	−	0.858541i	$-0.328629\pi$
$769$	28.4377			1.02549			0.512745	+	0.858541i	$0.328629\pi$
$770$		0			0
$771$	7.14590			0.257353
$772$	−1.28115	−	0.930812i	−0.0461097	−	0.0335007i
$773$	11.0517	−	34.0135i	0.397501	−	1.22338i	−0.529496	−	0.848312i	$-0.677619\pi$
$773$	11.0517	−	34.0135i	0.397501	−	1.22338i	0.926997	−	0.375069i	$-0.122381\pi$
$774$	16.0172	+	49.2959i	0.575727	+	1.77191i
$775$	0.763932	−	0.555029i	0.0274412	−	0.0199372i
$776$	42.3156	−	30.7441i	1.51904	−	1.10365i
$777$	−0.472136	−	1.45309i	−0.0169378	−	0.0521291i
$778$	9.56231	−	29.4298i	0.342825	−	1.05511i
$779$	56.4058	+	40.9812i	2.02095	+	1.46830i
$780$	9.70820			0.347609
$781$		0			0
$782$	−128.992			−4.61274
$783$	−6.69098	−	4.86128i	−0.239116	−	0.173728i
$784$	3.04508	−	9.37181i	0.108753	−	0.334707i
$785$	−4.90983	−	15.1109i	−0.175239	−	0.539331i
$786$	1.38197	−	1.00406i	0.0492931	−	0.0358135i
$787$	−0.354102	+	0.257270i	−0.0126224	+	0.00917069i	−0.594079	−	0.804407i	$-0.702483\pi$
$787$	−0.354102	+	0.257270i	−0.0126224	+	0.00917069i	0.581456	+	0.813578i	$0.302483\pi$
$788$	−26.5623	−	81.7504i	−0.946243	−	2.91224i
$789$	4.41641	−	13.5923i	0.157228	−	0.483899i
$790$	18.2533	+	13.2618i	0.649423	+	0.471833i
$791$	6.85410			0.243704
$792$		0			0
$793$	−17.4164			−0.618475
$794$	−49.0967	−	35.6709i	−1.74238	−	1.26591i
$795$	−0.881966	+	2.71441i	−0.0312801	+	0.0962703i
$796$	−5.64590	−	17.3763i	−0.200114	−	0.615886i
$797$	−22.4615	+	16.3192i	−0.795627	+	0.578057i	−0.909628	−	0.415424i	$-0.863633\pi$
$797$	−22.4615	+	16.3192i	−0.795627	+	0.578057i	0.114001	+	0.993481i	$0.463633\pi$
$798$	−8.16312	+	5.93085i	−0.288971	+	0.209950i
$799$	10.9549	+	33.7158i	0.387557	+	1.19278i
$800$	13.4164	−	41.2915i	0.474342	−	1.45987i
$801$	0.309017	+	0.224514i	0.0109186	+	0.00793281i
$802$	69.3050			2.44724
$803$		0			0
$804$	21.9787			0.775129
$805$	4.92705	+	3.57971i	0.173656	+	0.126168i
$806$	−0.618034	+	1.90211i	−0.0217693	+	0.0669991i
$807$	1.93769	+	5.96361i	0.0682101	+	0.209929i
$808$	59.2320	−	43.0346i	2.08377	−	1.51395i
$809$	4.45492	−	3.23669i	0.156626	−	0.113796i	−0.506712	−	0.862116i	$-0.669139\pi$
$809$	4.45492	−	3.23669i	0.156626	−	0.113796i	0.663338	+	0.748320i	$0.269139\pi$
$810$	−4.61803	−	14.2128i	−0.162261	−	0.499389i
$811$	16.9443	−	52.1491i	0.594994	−	1.83120i	0.0402372	−	0.999190i	$-0.487189\pi$
$811$	16.9443	−	52.1491i	0.594994	−	1.83120i	0.554757	−	0.832013i	$-0.312811\pi$
$812$	9.35410	+	6.79615i	0.328265	+	0.238498i
$813$	12.2361			0.429138
$814$		0			0
$815$	4.70820			0.164921
$816$	39.8607	+	28.9605i	1.39540	+	1.01382i
$817$	−14.5729	+	44.8509i	−0.509843	+	1.56914i
$818$	3.47214	+	10.6861i	0.121400	+	0.373632i
$819$	6.85410	−	4.97980i	0.239502	−	0.174008i
$820$	−43.9058	+	31.8994i	−1.53326	+	1.11398i
$821$	−15.6565	−	48.1859i	−0.546417	−	1.68170i	−0.717597	−	0.696459i	$-0.754758\pi$
$821$	−15.6565	−	48.1859i	−0.546417	−	1.68170i	0.171180	−	0.985240i	$-0.445242\pi$
$822$	−0.163119	+	0.502029i	−0.00568943	+	0.0175103i
$823$	−3.14590	−	2.28563i	−0.109659	−	0.0796720i	0.531604	−	0.846993i	$-0.321589\pi$
$823$	−3.14590	−	2.28563i	−0.109659	−	0.0796720i	−0.641263	+	0.767321i	$0.721589\pi$
$824$	−16.0344			−0.558586
$825$		0			0
$826$	0.236068			0.00821386
$827$	−23.9443	−	17.3965i	−0.832624	−	0.604937i	0.0876765	−	0.996149i	$-0.472056\pi$
$827$	−23.9443	−	17.3965i	−0.832624	−	0.604937i	−0.920300	+	0.391212i	$0.872056\pi$
$828$	23.9164	−	73.6071i	0.831153	−	2.55802i
$829$	−0.315595	−	0.971301i	−0.0109611	−	0.0337347i	0.945426	−	0.325836i	$-0.105646\pi$
$829$	−0.315595	−	0.971301i	−0.0109611	−	0.0337347i	−0.956387	+	0.292101i	$0.905646\pi$
$830$	−22.6803	+	16.4782i	−0.787246	+	0.571968i
$831$	3.01722	−	2.19214i	0.104666	−	0.0760445i
$832$	8.70820	+	26.8011i	0.301903	+	0.929161i
$833$	−2.50000	+	7.69421i	−0.0866199	+	0.266589i
$834$	−7.78115	−	5.65334i	−0.269439	−	0.195759i
$835$	−2.47214			−0.0855518
$836$		0			0
$837$	−0.819660			−0.0283316
$838$	−12.4721	−	9.06154i	−0.430843	−	0.313026i
$839$	−5.74671	+	17.6866i	−0.198398	+	0.610608i	0.801522	+	0.597966i	$0.204024\pi$
$839$	−5.74671	+	17.6866i	−0.198398	+	0.610608i	−0.999920	+	0.0126420i	$0.995976\pi$
$840$	−1.42705	−	4.39201i	−0.0492379	−	0.151539i
$841$	18.8713	−	13.7108i	0.650735	−	0.472787i
$842$	11.0902	−	8.05748i	0.382192	−	0.277679i
$843$	−0.538507	−	1.65735i	−0.0185472	−	0.0570823i
$844$	20.0729	−	61.7782i	0.690939	−	2.12649i
$845$	2.04508	+	1.48584i	0.0703531	+	0.0511145i
$846$	−30.0344			−1.03261
$847$		0			0
$848$	−45.5066			−1.56270
$849$	2.97214	+	2.15938i	0.102003	+	0.0741098i
$850$	−26.1803	+	80.5748i	−0.897978	+	2.76369i
$851$	4.65248	+	14.3188i	0.159485	+	0.490844i
$852$	11.9164	−	8.65778i	0.408249	−	0.296611i
$853$	37.2877	−	27.0911i	1.27671	−	0.927582i	0.277259	−	0.960795i	$-0.410574\pi$
$853$	37.2877	−	27.0911i	1.27671	−	0.927582i	0.999448	+	0.0332128i	$0.0105739\pi$
$854$	4.35410	+	13.4005i	0.148994	+	0.458557i
$855$	5.04508	−	15.5272i	0.172538	−	0.531018i
$856$	−64.7320	−	47.0306i	−2.21249	−	1.60747i
$857$	−3.90983			−0.133557			−0.0667786	−	0.997768i	$-0.521272\pi$
$857$	−3.90983			−0.133557			−0.0667786	+	0.997768i	$0.521272\pi$
$858$		0			0
$859$	1.43769			0.0490535			0.0245267	−	0.999699i	$-0.492192\pi$
$859$	1.43769			0.0490535			0.0245267	+	0.999699i	$0.492192\pi$
$860$	−29.6976	−	21.5765i	−1.01268	−	0.735754i
$861$	2.13525	−	6.57164i	0.0727693	−	0.223961i
$862$	5.78115	+	17.7926i	0.196907	+	0.606017i
$863$	24.3156	−	17.6663i	0.827712	−	0.601368i	−0.0911988	−	0.995833i	$-0.529070\pi$
$863$	24.3156	−	17.6663i	0.827712	−	0.601368i	0.918911	+	0.394464i	$0.129070\pi$
$864$	−30.4894	+	22.1518i	−1.03727	+	0.753620i
$865$	−5.44427	−	16.7557i	−0.185111	−	0.569712i
$866$	30.7705	−	94.7019i	1.04562	−	3.21810i
$867$	−24.2254	−	17.6008i	−0.822739	−	0.597755i
$868$	1.14590			0.0388943
$869$		0			0
$870$	3.85410			0.130666
$871$	−19.1803	−	13.9353i	−0.649901	−	0.472181i
$872$	24.1803	−	74.4194i	0.818850	−	2.52016i
$873$	−5.66312	−	17.4293i	−0.191668	−	0.589892i
$874$	80.4402	−	58.4432i	2.72093	−	1.97687i
$875$	7.28115	−	5.29007i	0.246148	−	0.178837i
$876$	−9.05166	−	27.8582i	−0.305827	−	0.941240i
$877$	4.01722	−	12.3637i	0.135652	−	0.417494i	−0.860039	−	0.510228i	$-0.829561\pi$
$877$	4.01722	−	12.3637i	0.135652	−	0.417494i	0.995691	+	0.0927348i	$0.0295609\pi$
$878$	11.8992	+	8.64527i	0.401578	+	0.291764i
$879$	−6.79837			−0.229303
$880$		0			0
$881$	20.8541			0.702593			0.351296	−	0.936264i	$-0.385741\pi$
$881$	20.8541			0.702593			0.351296	+	0.936264i	$0.385741\pi$
$882$	−5.54508	−	4.02874i	−0.186713	−	0.135655i
$883$	−14.4098	+	44.3489i	−0.484929	+	1.49246i	0.347154	+	0.937808i	$0.387148\pi$
$883$	−14.4098	+	44.3489i	−0.484929	+	1.49246i	−0.832083	+	0.554651i	$0.812852\pi$
$884$	−39.2705	−	120.862i	−1.32081	−	4.06504i
$885$	0.0450850	−	0.0327561i	0.00151551	−	0.00110109i
$886$	−17.1353	+	12.4495i	−0.575670	+	0.418249i
$887$	1.78773	+	5.50207i	0.0600261	+	0.184741i	0.976573	−	0.215185i	$-0.0690356\pi$
$887$	1.78773	+	5.50207i	0.0600261	+	0.184741i	−0.916547	+	0.399927i	$0.869036\pi$
$888$	3.52786	−	10.8576i	0.118387	−	0.364359i
$889$	12.0902	+	8.78402i	0.405491	+	0.294607i
$890$	−0.381966			−0.0128035
$891$		0			0
$892$	−131.228			−4.39384
$893$	−22.1074	−	16.0620i	−0.739796	−	0.537493i
$894$	1.07295	−	3.30220i	0.0358848	−	0.110442i
$895$	−2.54508	−	7.83297i	−0.0850728	−	0.261827i
$896$	0.881966	−	0.640786i	0.0294644	−	0.0214072i
$897$	9.85410	−	7.15942i	0.329019	−	0.239046i
$898$	2.69098	+	8.28199i	0.0897993	+	0.276374i
$899$	−0.173762	+	0.534785i	−0.00579529	+	0.0178361i
$900$	−41.1246	−	29.8788i	−1.37082	−	0.995959i
$901$	37.3607			1.24466
$902$		0			0
$903$	4.67376			0.155533
$904$	41.4336	+	30.1033i	1.37806	+	1.00122i
$905$	6.00000	−	18.4661i	0.199447	−	0.613834i
$906$	−8.97214	−	27.6134i	−0.298079	−	0.917394i
$907$	16.3713	−	11.8945i	0.543601	−	0.394949i	−0.281820	−	0.959467i	$-0.590938\pi$
$907$	16.3713	−	11.8945i	0.543601	−	0.394949i	0.825421	+	0.564518i	$0.190938\pi$
$908$	−51.1869	+	37.1895i	−1.69870	+	1.23418i
$909$	−7.92705	−	24.3970i	−0.262924	−	0.809196i
$910$	−2.61803	+	8.05748i	−0.0867870	+	0.267103i
$911$	18.4615	+	13.4131i	0.611657	+	0.444394i	0.849997	−	0.526787i	$-0.176603\pi$
$911$	18.4615	+	13.4131i	0.611657	+	0.444394i	−0.238341	+	0.971182i	$0.576603\pi$
$912$	−37.9787			−1.25760
$913$		0			0
$914$	17.9443			0.593544
$915$	2.69098	+	1.95511i	0.0889612	+	0.0646341i
$916$	16.8541	−	51.8716i	0.556875	−	1.71389i
$917$	0.326238	+	1.00406i	0.0107733	+	0.0331569i
$918$	59.4959	−	43.2263i	1.96366	−	1.42668i
$919$	−16.8992	+	12.2780i	−0.557453	+	0.405013i	−0.830526	−	0.556980i	$-0.811960\pi$
$919$	−16.8992	+	12.2780i	−0.557453	+	0.405013i	0.273073	+	0.961993i	$0.411960\pi$
$920$	14.0623	+	43.2793i	0.463620	+	1.42688i
$921$	−0.156541	+	0.481784i	−0.00515821	+	0.0158753i
$922$	41.3156	+	30.0175i	1.36066	+	0.988575i
$923$	−15.8885			−0.522978
$924$		0			0
$925$	9.88854			0.325133
$926$	37.6246	+	27.3359i	1.23642	+	0.898313i
$927$	−1.73607	+	5.34307i	−0.0570200	+	0.175489i
$928$	7.98936	+	24.5887i	0.262263	+	0.807164i
$929$	−19.4164	+	14.1068i	−0.637032	+	0.462831i	−0.858829	−	0.512262i	$-0.828808\pi$
$929$	−19.4164	+	14.1068i	−0.637032	+	0.462831i	0.221797	+	0.975093i	$0.428808\pi$
$930$	0.309017	−	0.224514i	0.0101331	−	0.00736210i
$931$	−1.92705	−	5.93085i	−0.0631565	−	0.194376i
$932$	−3.87539	+	11.9272i	−0.126943	+	0.390689i
$933$	−4.50000	−	3.26944i	−0.147323	−	0.107037i
$934$	−87.7214			−2.87033
$935$		0			0
$936$	63.3050			2.06919
$937$	−30.5172	−	22.1721i	−0.996954	−	0.724330i	−0.0355212	−	0.999369i	$-0.511309\pi$
$937$	−30.5172	−	22.1721i	−0.996954	−	0.724330i	−0.961433	+	0.275039i	$0.911309\pi$
$938$	−5.92705	+	18.2416i	−0.193525	+	0.595609i
$939$	0.510643	+	1.57160i	0.0166642	+	0.0512872i
$940$	17.2082	−	12.5025i	0.561270	−	0.407786i
$941$	25.1353	−	18.2618i	0.819386	−	0.595319i	−0.0971506	−	0.995270i	$-0.530973\pi$
$941$	25.1353	−	18.2618i	0.819386	−	0.595319i	0.916537	+	0.399951i	$0.130973\pi$
$942$	7.94427	+	24.4500i	0.258838	+	0.796623i
$943$	−21.0410	+	64.7576i	−0.685190	+	2.10880i
$944$	0.718847	+	0.522273i	0.0233965	+	0.0169985i
$945$	−3.47214			−0.112949
$946$		0			0
$947$	19.7082			0.640431			0.320215	−	0.947345i	$-0.396245\pi$
$947$	19.7082			0.640431			0.320215	+	0.947345i	$0.396245\pi$
$948$	−20.9164	−	15.1967i	−0.679333	−	0.493565i
$949$	−9.76393	+	30.0503i	−0.316951	+	0.975474i
$950$	−20.1803	−	62.1087i	−0.654737	−	2.01507i
$951$	12.2812	−	8.92278i	0.398244	−	0.289341i
$952$	−48.9058	+	35.5321i	−1.58504	+	1.15160i
$953$	−0.545085	−	1.67760i	−0.0176570	−	0.0543428i	0.941840	−	0.336062i	$-0.109095\pi$
$953$	−0.545085	−	1.67760i	−0.0176570	−	0.0543428i	−0.959497	+	0.281719i	$0.909095\pi$
$954$	−9.78115	+	30.1033i	−0.316677	+	0.974630i
$955$	−16.3713	−	11.8945i	−0.529764	−	0.384896i
$956$	−28.6869			−0.927801
$957$		0			0
$958$	−68.6869			−2.21917
$959$	−0.263932	−	0.191758i	−0.00852281	−	0.00619218i
$960$	1.66312	−	5.11855i	0.0536769	−	0.165201i
$961$	−9.56231	−	29.4298i	−0.308461	−	0.949347i
$962$	−16.9443	+	12.3107i	−0.546305	+	0.396914i
$963$	−22.6803	+	16.4782i	−0.730864	+	0.531004i
$964$	−25.9058	−	79.7297i	−0.834369	−	2.56792i
$965$	0.100813	−	0.310271i	0.00324529	−	0.00998797i
$966$	−7.97214	−	5.79210i	−0.256499	−	0.186358i
$967$	−28.4508			−0.914918			−0.457459	−	0.889231i	$-0.651240\pi$
$967$	−28.4508			−0.914918			−0.457459	+	0.889231i	$0.651240\pi$
$968$		0			0
$969$	31.1803			1.00166
$970$	14.8262	+	10.7719i	0.476042	+	0.345865i
$971$	16.1459	−	49.6920i	0.518147	−	1.59469i	−0.259336	−	0.965787i	$-0.583504\pi$
$971$	16.1459	−	49.6920i	0.518147	−	1.59469i	0.777483	−	0.628904i	$-0.216496\pi$
$972$	20.9164	+	64.3741i	0.670894	+	2.06480i
$973$	4.80902	−	3.49396i	0.154170	−	0.112011i
$974$	35.1525	−	25.5398i	1.12636	−	0.818347i
$975$	−2.47214	−	7.60845i	−0.0791717	−	0.243665i
$976$	−16.3885	+	50.4388i	−0.524585	+	1.61451i
$977$	26.8435	+	19.5029i	0.858798	+	0.623954i	0.927558	−	0.373680i	$-0.121904\pi$
$977$	26.8435	+	19.5029i	0.858798	+	0.623954i	−0.0687594	+	0.997633i	$0.521904\pi$
$978$	−7.61803			−0.243598
$979$		0			0
$980$	4.85410			0.155059
$981$	−22.1803	−	16.1150i	−0.708164	−	0.514511i
$982$	−23.3435	+	71.8438i	−0.744920	+	2.29263i
$983$	−4.51722	−	13.9026i	−0.144077	−	0.443423i	0.852814	−	0.522215i	$-0.174894\pi$
$983$	−4.51722	−	13.9026i	−0.144077	−	0.443423i	−0.996891	+	0.0787912i	$0.974894\pi$
$984$	41.7705	−	30.3481i	1.33160	−	0.967461i
$985$	14.3262	−	10.4086i	0.456472	−	0.331646i
$986$	−15.5902	−	47.9816i	−0.496492	−	1.52805i
$987$	−0.836881	+	2.57565i	−0.0266382	+	0.0819840i
$988$	79.2492	+	57.5779i	2.52125	+	1.83180i
$989$	−46.0557			−1.46449
$990$		0			0
$991$	−34.2705			−1.08864			−0.544319	−	0.838878i	$-0.683212\pi$
$991$	−34.2705			−1.08864			−0.544319	+	0.838878i	$0.683212\pi$
$992$	2.07295	+	1.50609i	0.0658162	+	0.0478183i
$993$	−3.09017	+	9.51057i	−0.0980636	+	0.301809i
$994$	3.97214	+	12.2250i	0.125989	+	0.387753i
$995$	3.04508	−	2.21238i	0.0965357	−	0.0701373i
$996$	25.9894	−	18.8824i	0.823504	−	0.598311i
$997$	8.30244	+	25.5523i	0.262941	+	0.809249i	0.992161	+	0.124969i	$0.0398832\pi$
$997$	8.30244	+	25.5523i	0.262941	+	0.809249i	−0.729220	+	0.684280i	$0.760117\pi$
$998$	−0.881966	+	2.71441i	−0.0279181	+	0.0859232i
$999$	−6.94427	−	5.04531i	−0.219707	−	0.159627i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.l.323.1		4
11.2	odd	10		847.2.f.j.148.1		4
11.3	even	5	inner	847.2.f.l.729.1		4
11.4	even	5		847.2.f.d.372.1		4
11.5	even	5		847.2.a.d.1.1	✓	2
11.6	odd	10		847.2.a.h.1.2	yes	2
11.7	odd	10		847.2.f.j.372.1		4
11.8	odd	10		847.2.f.c.729.1		4
11.9	even	5		847.2.f.d.148.1		4
11.10	odd	2		847.2.f.c.323.1		4
33.5	odd	10		7623.2.a.bx.1.2		2
33.17	even	10		7623.2.a.t.1.1		2
77.6	even	10		5929.2.a.s.1.2		2
77.27	odd	10		5929.2.a.i.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.d.1.1	✓	2	11.5	even	5
847.2.a.h.1.2	yes	2	11.6	odd	10
847.2.f.c.323.1		4	11.10	odd	2
847.2.f.c.729.1		4	11.8	odd	10
847.2.f.d.148.1		4	11.9	even	5
847.2.f.d.372.1		4	11.4	even	5
847.2.f.j.148.1		4	11.2	odd	10
847.2.f.j.372.1		4	11.7	odd	10
847.2.f.l.323.1		4	1.1	even	1	trivial
847.2.f.l.729.1		4	11.3	even	5	inner
5929.2.a.i.1.1		2	77.27	odd	10
5929.2.a.s.1.2		2	77.6	even	10
7623.2.a.t.1.1		2	33.17	even	10
7623.2.a.bx.1.2		2	33.5	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.11803 + 1.53884i) q^{2} +(0.190983 - 0.587785i) q^{3} +(1.50000 + 4.61653i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(1.30902 - 0.951057i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-2.30902 + 7.10642i) q^{8} +(2.11803 + 1.53884i) q^{9} +O(q^{10})\)	\(q+(2.11803 + 1.53884i) q^{2} +(0.190983 - 0.587785i) q^{3} +(1.50000 + 4.61653i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(1.30902 - 0.951057i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-2.30902 + 7.10642i) q^{8} +(2.11803 + 1.53884i) q^{9} -2.61803 q^{10} +3.00000 q^{12} +(-2.61803 - 1.90211i) q^{13} +(-0.809017 + 2.48990i) q^{14} +(0.190983 + 0.587785i) q^{15} +(-7.97214 + 5.79210i) q^{16} +(6.54508 - 4.75528i) q^{17} +(2.11803 + 6.51864i) q^{18} +(-1.92705 + 5.93085i) q^{19} +(-3.92705 - 2.85317i) q^{20} +0.618034 q^{21} -6.09017 q^{23} +(3.73607 + 2.71441i) q^{24} +(-1.23607 + 3.80423i) q^{25} +(-2.61803 - 8.05748i) q^{26} +(2.80902 - 2.04087i) q^{27} +(-3.92705 + 2.85317i) q^{28} +(-0.736068 - 2.26538i) q^{29} +(-0.500000 + 1.53884i) q^{30} +(-0.190983 - 0.138757i) q^{31} -10.8541 q^{32} +21.1803 q^{34} +(-0.809017 - 0.587785i) q^{35} +(-3.92705 + 12.0862i) q^{36} +(-0.763932 - 2.35114i) q^{37} +(-13.2082 + 9.59632i) q^{38} +(-1.61803 + 1.17557i) q^{39} +(-2.30902 - 7.10642i) q^{40} +(3.45492 - 10.6331i) q^{41} +(1.30902 + 0.951057i) q^{42} +7.56231 q^{43} -2.61803 q^{45} +(-12.8992 - 9.37181i) q^{46} +(-1.35410 + 4.16750i) q^{47} +(1.88197 + 5.79210i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-8.47214 + 6.15537i) q^{50} +(-1.54508 - 4.75528i) q^{51} +(4.85410 - 14.9394i) q^{52} +(3.73607 + 2.71441i) q^{53} +9.09017 q^{54} -7.47214 q^{56} +(3.11803 + 2.26538i) q^{57} +(1.92705 - 5.93085i) q^{58} +(-0.0278640 - 0.0857567i) q^{59} +(-2.42705 + 1.76336i) q^{60} +(4.35410 - 3.16344i) q^{61} +(-0.190983 - 0.587785i) q^{62} +(-0.809017 + 2.48990i) q^{63} +(-7.04508 - 5.11855i) q^{64} +3.23607 q^{65} +7.32624 q^{67} +(31.7705 + 23.0826i) q^{68} +(-1.16312 + 3.57971i) q^{69} +(-0.809017 - 2.48990i) q^{70} +(3.97214 - 2.88593i) q^{71} +(-15.8262 + 11.4984i) q^{72} +(-3.01722 - 9.28605i) q^{73} +(2.00000 - 6.15537i) q^{74} +(2.00000 + 1.45309i) q^{75} -30.2705 q^{76} -5.23607 q^{78} +(-6.97214 - 5.06555i) q^{79} +(3.04508 - 9.37181i) q^{80} +(1.76393 + 5.42882i) q^{81} +(23.6803 - 17.2048i) q^{82} +(8.66312 - 6.29412i) q^{83} +(0.927051 + 2.85317i) q^{84} +(-2.50000 + 7.69421i) q^{85} +(16.0172 + 11.6372i) q^{86} -1.47214 q^{87} +0.145898 q^{89} +(-5.54508 - 4.02874i) q^{90} +(1.00000 - 3.07768i) q^{91} +(-9.13525 - 28.1154i) q^{92} +(-0.118034 + 0.0857567i) q^{93} +(-9.28115 + 6.74315i) q^{94} +(-1.92705 - 5.93085i) q^{95} +(-2.07295 + 6.37988i) q^{96} +(-5.66312 - 4.11450i) q^{97} -2.61803 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 3 q^{3} + 6 q^{4} - q^{5} + 3 q^{6} - q^{7} - 7 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 3 * q^3 + 6 * q^4 - q^5 + 3 * q^6 - q^7 - 7 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 3 q^{3} + 6 q^{4} - q^{5} + 3 q^{6} - q^{7} - 7 q^{8} + 4 q^{9} - 6 q^{10} + 12 q^{12} - 6 q^{13} - q^{14} + 3 q^{15} - 14 q^{16} + 15 q^{17} + 4 q^{18} - q^{19} - 9 q^{20} - 2 q^{21} - 2 q^{23} + 6 q^{24} + 4 q^{25} - 6 q^{26} + 9 q^{27} - 9 q^{28} + 6 q^{29} - 2 q^{30} - 3 q^{31} - 30 q^{32} + 40 q^{34} - q^{35} - 9 q^{36} - 12 q^{37} - 26 q^{38} - 2 q^{39} - 7 q^{40} + 25 q^{41} + 3 q^{42} - 10 q^{43} - 6 q^{45} - 27 q^{46} + 8 q^{47} + 12 q^{48} - q^{49} - 16 q^{50} + 5 q^{51} + 6 q^{52} + 6 q^{53} + 14 q^{54} - 12 q^{56} + 8 q^{57} + q^{58} - 18 q^{59} - 3 q^{60} + 4 q^{61} - 3 q^{62} - q^{63} - 17 q^{64} + 4 q^{65} - 2 q^{67} + 60 q^{68} + 11 q^{69} - q^{70} - 2 q^{71} - 32 q^{72} + 17 q^{73} + 8 q^{74} + 8 q^{75} - 54 q^{76} - 12 q^{78} - 10 q^{79} + q^{80} + 16 q^{81} + 50 q^{82} + 19 q^{83} - 3 q^{84} - 10 q^{85} + 35 q^{86} + 12 q^{87} + 14 q^{89} - 11 q^{90} + 4 q^{91} - 3 q^{92} + 4 q^{93} - 17 q^{94} - q^{95} - 15 q^{96} - 7 q^{97} - 6 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 3 * q^3 + 6 * q^4 - q^5 + 3 * q^6 - q^7 - 7 * q^8 + 4 * q^9 - 6 * q^10 + 12 * q^12 - 6 * q^13 - q^14 + 3 * q^15 - 14 * q^16 + 15 * q^17 + 4 * q^18 - q^19 - 9 * q^20 - 2 * q^21 - 2 * q^23 + 6 * q^24 + 4 * q^25 - 6 * q^26 + 9 * q^27 - 9 * q^28 + 6 * q^29 - 2 * q^30 - 3 * q^31 - 30 * q^32 + 40 * q^34 - q^35 - 9 * q^36 - 12 * q^37 - 26 * q^38 - 2 * q^39 - 7 * q^40 + 25 * q^41 + 3 * q^42 - 10 * q^43 - 6 * q^45 - 27 * q^46 + 8 * q^47 + 12 * q^48 - q^49 - 16 * q^50 + 5 * q^51 + 6 * q^52 + 6 * q^53 + 14 * q^54 - 12 * q^56 + 8 * q^57 + q^58 - 18 * q^59 - 3 * q^60 + 4 * q^61 - 3 * q^62 - q^63 - 17 * q^64 + 4 * q^65 - 2 * q^67 + 60 * q^68 + 11 * q^69 - q^70 - 2 * q^71 - 32 * q^72 + 17 * q^73 + 8 * q^74 + 8 * q^75 - 54 * q^76 - 12 * q^78 - 10 * q^79 + q^80 + 16 * q^81 + 50 * q^82 + 19 * q^83 - 3 * q^84 - 10 * q^85 + 35 * q^86 + 12 * q^87 + 14 * q^89 - 11 * q^90 + 4 * q^91 - 3 * q^92 + 4 * q^93 - 17 * q^94 - q^95 - 15 * q^96 - 7 * q^97 - 6 * q^98

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