LMFDB - Embedded newform 847.2.f.s.372.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 $ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			372.1
Root			$-0.762262 + 2.34600i$ of defining polynomial
Character	$\chi$	$=$	847.372
Dual form			847.2.f.s.148.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.762262 + 2.34600i) q^{2} +(1.30902 - 0.951057i) q^{3} +(-3.30464 - 2.40097i) q^{4} +(-1.07128 - 3.29706i) q^{5} +(1.23337 + 3.79591i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(4.16042 - 3.02272i) q^{8} +(-0.118034 + 0.363271i) q^{9} +O(q^{10})$	\(q+(-0.762262 + 2.34600i) q^{2} +(1.30902 - 0.951057i) q^{3} +(-3.30464 - 2.40097i) q^{4} +(-1.07128 - 3.29706i) q^{5} +(1.23337 + 3.79591i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(4.16042 - 3.02272i) q^{8} +(-0.118034 + 0.363271i) q^{9} +8.55150 q^{10} -6.60929 q^{12} +(0.202020 - 0.621755i) q^{13} +(1.99563 - 1.44991i) q^{14} +(-4.53801 - 3.29706i) q^{15} +(1.39545 + 4.29476i) q^{16} +(0.351400 + 1.08150i) q^{17} +(-0.762262 - 0.553816i) q^{18} +(-4.91560 + 3.57140i) q^{19} +(-4.37592 + 13.4677i) q^{20} -1.61803 q^{21} -6.66708 q^{23} +(2.57128 - 7.91358i) q^{24} +(-5.67787 + 4.12521i) q^{25} +(1.30464 + 0.947880i) q^{26} +(1.69098 + 5.20431i) q^{27} +(1.26226 + 3.88484i) q^{28} +(-3.70010 - 2.68828i) q^{29} +(11.1941 - 8.13296i) q^{30} +(0.864107 - 2.65945i) q^{31} -0.854102 q^{32} -2.80505 q^{34} +(-1.07128 + 3.29706i) q^{35} +(1.26226 - 0.917087i) q^{36} +(0.355772 + 0.258483i) q^{37} +(-4.63152 - 14.2544i) q^{38} +(-0.326876 - 1.00602i) q^{39} +(-14.4230 - 10.4790i) q^{40} +(-4.77575 + 3.46978i) q^{41} +(1.23337 - 3.79591i) q^{42} -8.70820 q^{43} +1.32417 q^{45} +(5.08206 - 15.6410i) q^{46} +(0.489215 - 0.355436i) q^{47} +(5.91123 + 4.29476i) q^{48} +(0.309017 + 0.951057i) q^{49} +(-5.34973 - 16.4648i) q^{50} +(1.48855 + 1.08150i) q^{51} +(-2.16042 + 1.56963i) q^{52} +(3.03531 - 9.34172i) q^{53} -13.4983 q^{54} -5.14256 q^{56} +(-3.03801 + 9.35004i) q^{57} +(9.12715 - 6.63126i) q^{58} +(-1.37052 - 0.995741i) q^{59} +(7.08039 + 21.7912i) q^{60} +(-2.11930 - 6.52252i) q^{61} +(5.58039 + 4.05439i) q^{62} +(0.309017 - 0.224514i) q^{63} +(-2.13986 + 6.58580i) q^{64} -2.26638 q^{65} -6.17828 q^{67} +(1.43539 - 4.41766i) q^{68} +(-8.72732 + 6.34077i) q^{69} +(-6.91831 - 5.02644i) q^{70} +(-1.67390 - 5.15175i) q^{71} +(0.606997 + 1.86814i) q^{72} +(5.42202 + 3.93933i) q^{73} +(-0.877594 + 0.637609i) q^{74} +(-3.50911 + 10.7999i) q^{75} +24.8191 q^{76} +2.60929 q^{78} +(-0.820054 + 2.52387i) q^{79} +(12.6652 - 9.20178i) q^{80} +(6.23607 + 4.53077i) q^{81} +(-4.49975 - 13.8488i) q^{82} +(-2.06936 - 6.36882i) q^{83} +(5.34703 + 3.88484i) q^{84} +(3.18931 - 2.31717i) q^{85} +(6.63793 - 20.4295i) q^{86} -7.40020 q^{87} -0.698213 q^{89} +(-1.00937 + 3.10651i) q^{90} +(-0.528896 + 0.384266i) q^{91} +(22.0323 + 16.0074i) q^{92} +(-1.39815 - 4.30308i) q^{93} +(0.460942 + 1.41863i) q^{94} +(17.0411 + 12.3811i) q^{95} +(-1.11803 + 0.812299i) q^{96} +(-4.59159 + 14.1315i) q^{97} -2.46673 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 6 q^{3} - 7 q^{4} + 3 q^{5} + 2 q^{6} - 2 q^{7} + 12 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + q^2 + 6 * q^3 - 7 * q^4 + 3 * q^5 + 2 * q^6 - 2 * q^7 + 12 * q^8 + 8 * q^9	$ 8 q + q^{2} + 6 q^{3} - 7 q^{4} + 3 q^{5} + 2 q^{6} - 2 q^{7} + 12 q^{8} + 8 q^{9} + 28 q^{10} - 14 q^{12} + 5 q^{13} + q^{14} - 9 q^{15} + 7 q^{16} - 14 q^{17} + q^{18} - 6 q^{19} - 4 q^{20} - 4 q^{21} - 16 q^{23} + 9 q^{24} - 5 q^{25} - 9 q^{26} + 18 q^{27} + 3 q^{28} - 6 q^{29} + 26 q^{30} + 14 q^{31} + 20 q^{32} - 24 q^{34} + 3 q^{35} + 3 q^{36} + q^{37} - 15 q^{38} - 29 q^{40} - 18 q^{41} + 2 q^{42} - 16 q^{43} + 18 q^{45} + 26 q^{46} + 7 q^{47} - q^{48} - 2 q^{49} - q^{50} - 8 q^{51} + 4 q^{52} + 7 q^{53} - 4 q^{54} - 18 q^{56} + 3 q^{57} + 36 q^{58} + 17 q^{60} - 12 q^{61} + 5 q^{62} - 2 q^{63} - 4 q^{64} - 24 q^{65} - 30 q^{67} + 7 q^{68} - 22 q^{69} - 12 q^{70} + 21 q^{71} - 3 q^{72} - 8 q^{73} - q^{74} + 52 q^{76} - 18 q^{78} - q^{79} + 37 q^{80} + 32 q^{81} - 34 q^{82} + 22 q^{83} + 11 q^{84} + 5 q^{85} + 13 q^{86} - 12 q^{87} - 34 q^{89} + 18 q^{90} - 5 q^{91} + 51 q^{92} + 3 q^{93} - 50 q^{94} + 41 q^{95} - 15 q^{97} - 4 q^{98}+O(q^{100}) $ 8 * q + q^2 + 6 * q^3 - 7 * q^4 + 3 * q^5 + 2 * q^6 - 2 * q^7 + 12 * q^8 + 8 * q^9 + 28 * q^10 - 14 * q^12 + 5 * q^13 + q^14 - 9 * q^15 + 7 * q^16 - 14 * q^17 + q^18 - 6 * q^19 - 4 * q^20 - 4 * q^21 - 16 * q^23 + 9 * q^24 - 5 * q^25 - 9 * q^26 + 18 * q^27 + 3 * q^28 - 6 * q^29 + 26 * q^30 + 14 * q^31 + 20 * q^32 - 24 * q^34 + 3 * q^35 + 3 * q^36 + q^37 - 15 * q^38 - 29 * q^40 - 18 * q^41 + 2 * q^42 - 16 * q^43 + 18 * q^45 + 26 * q^46 + 7 * q^47 - q^48 - 2 * q^49 - q^50 - 8 * q^51 + 4 * q^52 + 7 * q^53 - 4 * q^54 - 18 * q^56 + 3 * q^57 + 36 * q^58 + 17 * q^60 - 12 * q^61 + 5 * q^62 - 2 * q^63 - 4 * q^64 - 24 * q^65 - 30 * q^67 + 7 * q^68 - 22 * q^69 - 12 * q^70 + 21 * q^71 - 3 * q^72 - 8 * q^73 - q^74 + 52 * q^76 - 18 * q^78 - q^79 + 37 * q^80 + 32 * q^81 - 34 * q^82 + 22 * q^83 + 11 * q^84 + 5 * q^85 + 13 * q^86 - 12 * q^87 - 34 * q^89 + 18 * q^90 - 5 * q^91 + 51 * q^92 + 3 * q^93 - 50 * q^94 + 41 * q^95 - 15 * q^97 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.762262	+	2.34600i	−0.539001	+	1.65887i	0.195842	+	0.980636i	$0.437256\pi$
$2$	−0.762262	+	2.34600i	−0.539001	+	1.65887i	−0.734842	+	0.678238i	$0.762744\pi$
$3$	1.30902	−	0.951057i	0.755761	−	0.549093i	−0.141846	−	0.989889i	$-0.545304\pi$
$3$	1.30902	−	0.951057i	0.755761	−	0.549093i	0.897607	+	0.440796i	$0.145304\pi$
$4$	−3.30464	−	2.40097i	−1.65232	−	1.20048i
$5$	−1.07128	−	3.29706i	−0.479091	−	1.47449i	−0.840361	−	0.542028i	$-0.817657\pi$
$5$	−1.07128	−	3.29706i	−0.479091	−	1.47449i	0.361270	−	0.932461i	$-0.382343\pi$
$6$	1.23337	+	3.79591i	0.503520	+	1.54967i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$8$	4.16042	−	3.02272i	1.47093	−	1.06869i
$9$	−0.118034	+	0.363271i	−0.0393447	+	0.121090i
$10$	8.55150			2.70422
$11$		0			0
$11$		0			0
$12$	−6.60929			−1.90794
$13$	0.202020	−	0.621755i	0.0560304	−	0.172444i	−0.919125	−	0.393966i	$-0.871103\pi$
$13$	0.202020	−	0.621755i	0.0560304	−	0.172444i	0.975155	+	0.221523i	$0.0711027\pi$
$14$	1.99563	−	1.44991i	0.533354	−	0.387504i
$15$	−4.53801	−	3.29706i	−1.17171	−	0.851297i
$16$	1.39545	+	4.29476i	0.348863	+	1.07369i
$17$	0.351400	+	1.08150i	0.0852270	+	0.262302i	0.984584	−	0.174914i	$-0.0559647\pi$
$17$	0.351400	+	1.08150i	0.0852270	+	0.262302i	−0.899357	+	0.437216i	$0.855965\pi$
$18$	−0.762262	−	0.553816i	−0.179667	−	0.130536i
$19$	−4.91560	+	3.57140i	−1.12772	+	0.819334i	−0.985361	−	0.170481i	$-0.945468\pi$
$19$	−4.91560	+	3.57140i	−1.12772	+	0.819334i	−0.142356	+	0.989816i	$0.545468\pi$
$20$	−4.37592	+	13.4677i	−0.978486	+	3.01147i
$21$	−1.61803			−0.353084
$22$		0			0
$23$	−6.66708			−1.39018			−0.695091	−	0.718921i	$-0.744636\pi$
$23$	−6.66708			−1.39018			−0.695091	+	0.718921i	$0.744636\pi$
$24$	2.57128	−	7.91358i	0.524860	−	1.61535i
$25$	−5.67787	+	4.12521i	−1.13557	+	0.825042i
$26$	1.30464	+	0.947880i	0.255862	+	0.185895i
$27$	1.69098	+	5.20431i	0.325430	+	1.00157i
$28$	1.26226	+	3.88484i	0.238545	+	0.734166i
$29$	−3.70010	−	2.68828i	−0.687091	−	0.499201i	0.188612	−	0.982052i	$-0.439601\pi$
$29$	−3.70010	−	2.68828i	−0.687091	−	0.499201i	−0.875703	+	0.482851i	$0.839601\pi$
$30$	11.1941	−	8.13296i	2.04375	−	1.48487i
$31$	0.864107	−	2.65945i	0.155198	−	0.477651i	−0.842983	−	0.537941i	$-0.819202\pi$
$31$	0.864107	−	2.65945i	0.155198	−	0.477651i	0.998181	+	0.0602896i	$0.0192024\pi$
$32$	−0.854102			−0.150985
$33$		0			0
$34$	−2.80505			−0.481063
$35$	−1.07128	+	3.29706i	−0.181079	+	0.557304i
$36$	1.26226	−	0.917087i	0.210377	−	0.152848i
$37$	0.355772	+	0.258483i	0.0584885	+	0.0424944i	0.616645	−	0.787241i	$-0.288491\pi$
$37$	0.355772	+	0.258483i	0.0584885	+	0.0424944i	−0.558157	+	0.829735i	$0.688491\pi$
$38$	−4.63152	−	14.2544i	−0.751332	−	2.31236i
$39$	−0.326876	−	1.00602i	−0.0523420	−	0.161092i
$40$	−14.4230	−	10.4790i	−2.28048	−	1.65687i
$41$	−4.77575	+	3.46978i	−0.745847	+	0.541889i	−0.894537	−	0.446995i	$-0.852494\pi$
$41$	−4.77575	+	3.46978i	−0.745847	+	0.541889i	0.148690	+	0.988884i	$0.452494\pi$
$42$	1.23337	−	3.79591i	0.190312	−	0.585722i
$43$	−8.70820			−1.32799			−0.663994	−	0.747738i	$-0.731140\pi$
$43$	−8.70820			−1.32799			−0.663994	+	0.747738i	$0.731140\pi$
$44$		0			0
$45$	1.32417			0.197396
$46$	5.08206	−	15.6410i	0.749309	−	2.30614i
$47$	0.489215	−	0.355436i	0.0713594	−	0.0518456i	−0.551534	−	0.834153i	$-0.685957\pi$
$47$	0.489215	−	0.355436i	0.0713594	−	0.0518456i	0.622893	+	0.782307i	$0.285957\pi$
$48$	5.91123	+	4.29476i	0.853213	+	0.619895i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	−5.34973	−	16.4648i	−0.756566	−	2.32847i
$51$	1.48855	+	1.08150i	0.208439	+	0.151440i
$52$	−2.16042	+	1.56963i	−0.299596	+	0.217669i
$53$	3.03531	−	9.34172i	0.416932	−	1.28318i	−0.493580	−	0.869700i	$-0.664312\pi$
$53$	3.03531	−	9.34172i	0.416932	−	1.28318i	0.910512	−	0.413483i	$-0.135688\pi$
$54$	−13.4983			−1.83688
$55$		0			0
$56$	−5.14256			−0.687203
$57$	−3.03801	+	9.35004i	−0.402394	+	1.23844i
$58$	9.12715	−	6.63126i	1.19845	−	0.870727i
$59$	−1.37052	−	0.995741i	−0.178426	−	0.129634i	0.494987	−	0.868900i	$-0.335173\pi$
$59$	−1.37052	−	0.995741i	−0.178426	−	0.129634i	−0.673414	+	0.739266i	$0.735173\pi$
$60$	7.08039	+	21.7912i	0.914075	+	2.81323i
$61$	−2.11930	−	6.52252i	−0.271348	−	0.835123i	−0.990163	−	0.139921i	$-0.955315\pi$
$61$	−2.11930	−	6.52252i	−0.271348	−	0.835123i	0.718815	−	0.695202i	$-0.244685\pi$
$62$	5.58039	+	4.05439i	0.708711	+	0.514908i
$63$	0.309017	−	0.224514i	0.0389325	−	0.0282861i
$64$	−2.13986	+	6.58580i	−0.267482	+	0.823225i
$65$	−2.26638			−0.281110
$66$		0			0
$67$	−6.17828			−0.754797			−0.377398	−	0.926051i	$-0.623181\pi$
$67$	−6.17828			−0.754797			−0.377398	+	0.926051i	$0.623181\pi$
$68$	1.43539	−	4.41766i	0.174066	−	0.535721i
$69$	−8.72732	+	6.34077i	−1.05065	+	0.763339i
$70$	−6.91831	−	5.02644i	−0.826896	−	0.600775i
$71$	−1.67390	−	5.15175i	−0.198656	−	0.611400i	−0.999914	−	0.0130816i	$-0.995836\pi$
$71$	−1.67390	−	5.15175i	−0.198656	−	0.611400i	0.801259	−	0.598318i	$-0.204164\pi$
$72$	0.606997	+	1.86814i	0.0715352	+	0.220163i
$73$	5.42202	+	3.93933i	0.634599	+	0.461063i	0.857990	−	0.513666i	$-0.171713\pi$
$73$	5.42202	+	3.93933i	0.634599	+	0.461063i	−0.223391	+	0.974729i	$0.571713\pi$
$74$	−0.877594	+	0.637609i	−0.102018	+	0.0741206i
$75$	−3.50911	+	10.7999i	−0.405198	+	1.24707i
$76$	24.8191			2.84695
$77$		0			0
$78$	2.60929			0.295444
$79$	−0.820054	+	2.52387i	−0.0922633	+	0.283957i	−0.986531	−	0.163576i	$-0.947697\pi$
$79$	−0.820054	+	2.52387i	−0.0922633	+	0.283957i	0.894267	+	0.447533i	$0.147697\pi$
$80$	12.6652	−	9.20178i	1.41601	−	1.02879i
$81$	6.23607	+	4.53077i	0.692896	+	0.503419i
$82$	−4.49975	−	13.8488i	−0.496914	−	1.52934i
$83$	−2.06936	−	6.36882i	−0.227141	−	0.699069i	−0.998067	−	0.0621443i	$-0.980206\pi$
$83$	−2.06936	−	6.36882i	−0.227141	−	0.699069i	0.770926	−	0.636925i	$-0.219794\pi$
$84$	5.34703	+	3.88484i	0.583409	+	0.423871i
$85$	3.18931	−	2.31717i	0.345930	−	0.251333i
$86$	6.63793	−	20.4295i	0.715787	−	2.20297i
$87$	−7.40020			−0.793384
$88$		0			0
$89$	−0.698213			−0.0740105			−0.0370052	−	0.999315i	$-0.511782\pi$
$89$	−0.698213			−0.0740105			−0.0370052	+	0.999315i	$0.511782\pi$
$90$	−1.00937	+	3.10651i	−0.106397	+	0.327455i
$91$	−0.528896	+	0.384266i	−0.0554434	+	0.0402820i
$92$	22.0323	+	16.0074i	2.29703	+	1.66889i
$93$	−1.39815	−	4.30308i	−0.144982	−	0.446208i
$94$	0.460942	+	1.41863i	0.0475426	+	0.146321i
$95$	17.0411	+	12.3811i	1.74838	+	1.27027i
$96$	−1.11803	+	0.812299i	−0.114109	+	0.0829049i
$97$	−4.59159	+	14.1315i	−0.466205	+	1.43483i	0.391256	+	0.920282i	$0.372041\pi$
$97$	−4.59159	+	14.1315i	−0.466205	+	1.43483i	−0.857461	+	0.514550i	$0.827959\pi$
$98$	−2.46673			−0.249178
$99$		0			0
$100$	28.6678			2.86678
$101$	−2.66360	+	8.19772i	−0.265038	+	0.815704i	0.726646	+	0.687012i	$0.241078\pi$
$101$	−2.66360	+	8.19772i	−0.265038	+	0.815704i	−0.991685	+	0.128692i	$0.958922\pi$
$102$	−3.67186	+	2.66776i	−0.363569	+	0.264148i
$103$	0.754779	+	0.548379i	0.0743706	+	0.0540334i	0.624349	−	0.781145i	$-0.285364\pi$
$103$	0.754779	+	0.548379i	0.0743706	+	0.0540334i	−0.549979	+	0.835179i	$0.685364\pi$
$104$	−1.03890	−	3.19741i	−0.101873	−	0.313532i
$105$	1.73337	+	5.33475i	0.169159	+	0.520618i
$106$	19.6020	+	14.2417i	1.90391	+	1.38327i
$107$	5.35740	−	3.89238i	0.517920	−	0.376291i	−0.297900	−	0.954597i	$-0.596286\pi$
$107$	5.35740	−	3.89238i	0.517920	−	0.376291i	0.815820	+	0.578306i	$0.196286\pi$
$108$	6.90727	−	21.2584i	0.664652	−	2.04559i
$109$	4.12507			0.395110			0.197555	−	0.980292i	$-0.436700\pi$
$109$	4.12507			0.395110			0.197555	+	0.980292i	$0.436700\pi$
$110$		0			0
$111$	0.711544			0.0675368
$112$	1.39545	−	4.29476i	0.131858	−	0.405817i
$113$	15.2304	−	11.0655i	1.43276	−	1.04096i	0.443260	−	0.896393i	$-0.353822\pi$
$113$	15.2304	−	11.0655i	1.43276	−	1.04096i	0.989495	−	0.144564i	$-0.0461781\pi$
$114$	−19.6194	−	14.2544i	−1.83753	−	1.33504i
$115$	7.14231	+	21.9818i	0.666023	+	2.04981i
$116$	5.77305	+	17.7676i	0.536014	+	1.64968i
$117$	0.202020	+	0.146776i	0.0186768	+	0.0135695i
$118$	3.38070	−	2.45623i	0.311219	−	0.226114i
$119$	0.351400	−	1.08150i	0.0322128	−	0.0991407i
$120$	−28.8461			−2.63328
$121$		0			0
$122$	16.9173			1.53162
$123$	−2.95158	+	9.08401i	−0.266135	+	0.819078i
$124$	−9.24081	+	6.71384i	−0.829849	+	0.602921i
$125$	5.66042	+	4.11253i	0.506283	+	0.367836i
$126$	0.291158	+	0.896093i	0.0259384	+	0.0798303i
$127$	2.46174	+	7.57645i	0.218444	+	0.672301i	0.998891	+	0.0470794i	$0.0149914\pi$
$127$	2.46174	+	7.57645i	0.218444	+	0.672301i	−0.780447	+	0.625221i	$0.785009\pi$
$128$	−15.2011	−	11.0443i	−1.34360	−	0.976185i
$129$	−11.3992	+	8.28199i	−1.00364	+	0.729189i
$130$	1.72758	−	5.31693i	0.151518	−	0.466326i
$131$	4.80505			0.419819			0.209910	−	0.977721i	$-0.432683\pi$
$131$	4.80505			0.419819			0.209910	+	0.977721i	$0.432683\pi$
$132$		0			0
$133$	6.07602			0.526858
$134$	4.70947	−	14.4942i	0.406836	−	1.25211i
$135$	15.3474	−	11.1505i	1.32089	−	0.959685i
$136$	4.73103	+	3.43730i	0.405683	+	0.294746i
$137$	−6.76059	−	20.8070i	−0.577596	−	1.77766i	−0.627163	−	0.778888i	$-0.715784\pi$
$137$	−6.76059	−	20.8070i	−0.577596	−	1.77766i	0.0495667	−	0.998771i	$-0.484216\pi$
$138$	−8.22295	−	25.3076i	−0.699984	−	2.15433i
$139$	−16.0296	−	11.6462i	−1.35962	−	0.987819i	−0.998469	−	0.0553100i	$-0.982385\pi$
$139$	−16.0296	−	11.6462i	−1.35962	−	0.987819i	−0.361147	−	0.932509i	$-0.617615\pi$
$140$	11.4563	−	8.32350i	0.968236	−	0.703464i
$141$	0.302352	−	0.930543i	0.0254626	−	0.0783658i
$142$	13.3620			1.12131
$143$		0			0
$144$	−1.72487			−0.143740
$145$	−4.89957	+	15.0793i	−0.406887	+	1.25227i
$146$	−13.3747	+	9.71726i	−1.10689	+	0.804206i
$147$	1.30902	+	0.951057i	0.107966	+	0.0784418i
$148$	−0.555090	−	1.70839i	−0.0456281	−	0.140429i
$149$	−0.977146	−	3.00735i	−0.0800509	−	0.246371i	0.903019	−	0.429600i	$-0.141345\pi$
$149$	−0.977146	−	3.00735i	−0.0800509	−	0.246371i	−0.983070	+	0.183228i	$0.941345\pi$
$150$	−22.6618	−	16.4648i	−1.85033	−	1.34434i
$151$	7.22295	−	5.24778i	0.587795	−	0.427058i	−0.253731	−	0.967275i	$-0.581658\pi$
$151$	7.22295	−	5.24778i	0.587795	−	0.427058i	0.841526	+	0.540217i	$0.181658\pi$
$152$	−9.65564	+	29.7170i	−0.783175	+	2.41037i
$153$	−0.434354			−0.0351155
$154$		0			0
$155$	−9.69406			−0.778645
$156$	−1.33521	+	4.10936i	−0.106902	+	0.329012i
$157$	−0.922017	+	0.669885i	−0.0735850	+	0.0534626i	−0.623970	−	0.781449i	$-0.714481\pi$
$157$	−0.922017	+	0.669885i	−0.0735850	+	0.0534626i	0.550385	+	0.834911i	$0.314481\pi$
$158$	−5.29590	−	3.84770i	−0.421319	−	0.306106i
$159$	−4.91123	−	15.1152i	−0.389486	−	1.19871i
$160$	0.914982	+	2.81602i	0.0723356	+	0.222626i
$161$	5.39378	+	3.91881i	0.425090	+	0.308846i
$162$	−15.3827	+	11.1762i	−1.20858	+	0.878084i
$163$	−1.56587	+	4.81927i	−0.122649	+	0.377474i	−0.993465	−	0.114134i	$-0.963591\pi$
$163$	−1.56587	+	4.81927i	−0.122649	+	0.377474i	0.870817	+	0.491608i	$0.163591\pi$
$164$	24.1130			1.88291
$165$		0			0
$166$	16.5187			1.28210
$167$	6.08976	−	18.7424i	0.471240	−	1.45033i	−0.379722	−	0.925100i	$-0.623981\pi$
$167$	6.08976	−	18.7424i	0.471240	−	1.45033i	0.850962	−	0.525227i	$-0.176019\pi$
$168$	−6.73170	+	4.89086i	−0.519362	+	0.377338i
$169$	10.1715	+	7.38999i	0.782420	+	0.568461i
$170$	3.00500	+	9.24842i	0.230473	+	0.709322i
$171$	−0.717177	−	2.20724i	−0.0548439	−	0.168792i
$172$	28.7775	+	20.9081i	2.19427	+	1.59423i
$173$	−11.6456	+	8.46105i	−0.885401	+	0.643281i	−0.934675	−	0.355504i	$-0.884309\pi$
$173$	−11.6456	+	8.46105i	−0.885401	+	0.643281i	0.0492739	+	0.998785i	$0.484309\pi$
$174$	5.64089	−	17.3609i	0.427635	−	1.31612i
$175$	7.01823			0.530528
$176$		0			0
$177$	−2.74104			−0.206029
$178$	0.532221	−	1.63801i	0.0398917	−	0.122774i
$179$	3.77342	−	2.74155i	0.282038	−	0.204913i	−0.437768	−	0.899088i	$-0.644231\pi$
$179$	3.77342	−	2.74155i	0.282038	−	0.204913i	0.719806	+	0.694175i	$0.244231\pi$
$180$	−4.37592	−	3.17929i	−0.326162	−	0.236971i
$181$	3.06176	+	9.42311i	0.227578	+	0.700415i	0.998020	+	0.0629034i	$0.0200360\pi$
$181$	3.06176	+	9.42311i	0.227578	+	0.700415i	−0.770441	+	0.637511i	$0.779964\pi$
$182$	−0.498330	−	1.53370i	−0.0369387	−	0.113686i
$183$	−8.97748	−	6.52252i	−0.663634	−	0.482159i
$184$	−27.7378	+	20.1527i	−2.04486	+	1.48568i
$185$	0.471104	−	1.44991i	0.0346362	−	0.106599i
$186$	11.1608			0.818349
$187$		0			0
$188$	−2.47007			−0.180148
$189$	1.69098	−	5.20431i	0.123001	−	0.378558i
$190$	−42.0358	+	30.5408i	−3.04960	+	2.21566i
$191$	−8.04401	−	5.84432i	−0.582044	−	0.422880i	0.257416	−	0.966301i	$-0.417129\pi$
$191$	−8.04401	−	5.84432i	−0.582044	−	0.422880i	−0.839461	+	0.543421i	$0.817129\pi$
$192$	3.46236	+	10.6560i	0.249874	+	0.769034i
$193$	−1.14542	−	3.52523i	−0.0824489	−	0.253752i	0.901331	−	0.433131i	$-0.142591\pi$
$193$	−1.14542	−	3.52523i	−0.0824489	−	0.253752i	−0.983780	+	0.179379i	$0.942591\pi$
$194$	−29.6524	−	21.5437i	−2.12892	−	1.54675i
$195$	−2.96673	+	2.15546i	−0.212452	+	0.154355i
$196$	1.26226	−	3.88484i	0.0901616	−	0.277489i
$197$	−5.91982			−0.421770			−0.210885	−	0.977511i	$-0.567635\pi$
$197$	−5.91982			−0.421770			−0.210885	+	0.977511i	$0.567635\pi$
$198$		0			0
$199$	11.4842			0.814095			0.407047	−	0.913407i	$-0.366558\pi$
$199$	11.4842			0.814095			0.407047	+	0.913407i	$0.366558\pi$
$200$	−11.1529	+	34.3252i	−0.788632	+	2.42716i
$201$	−8.08747	+	5.87589i	−0.570446	+	0.414453i
$202$	−17.2015	−	12.4976i	−1.21029	−	0.879330i
$203$	1.41331	+	4.34973i	0.0991950	+	0.305291i
$204$	−2.32250	−	7.14793i	−0.162608	−	0.500455i
$205$	16.5562	+	12.0288i	1.15634	+	0.840129i
$206$	−1.86184	+	1.35270i	−0.129720	+	0.0942474i
$207$	0.786942	−	2.42196i	0.0546963	−	0.168338i
$208$	2.95220			0.204698
$209$		0			0
$210$	−13.8366			−0.954817
$211$	−2.69613	+	8.29785i	−0.185610	+	0.571247i	−0.999958	−	0.00912833i	$-0.997094\pi$
$211$	−2.69613	+	8.29785i	−0.185610	+	0.571247i	0.814349	+	0.580376i	$0.197094\pi$
$212$	−32.4598	+	23.5834i	−2.22935	+	1.61971i
$213$	−7.09077	−	5.15175i	−0.485852	−	0.352992i
$214$	5.04779	+	15.5355i	0.345060	+	1.06198i
$215$	9.32892	+	28.7115i	0.636227	+	1.95810i
$216$	22.7664	+	16.5407i	1.54906	+	1.12545i
$217$	−2.26226	+	1.64363i	−0.153572	+	0.111577i
$218$	−3.14438	+	9.67742i	−0.212965	+	0.655438i
$219$	10.8440			0.732772
$220$		0			0
$221$	0.743416			0.0500076
$222$	−0.542383	+	1.66928i	−0.0364024	+	0.112035i
$223$	−8.35944	+	6.07349i	−0.559790	+	0.406711i	−0.831382	−	0.555701i	$-0.812450\pi$
$223$	−8.35944	+	6.07349i	−0.559790	+	0.406711i	0.271592	+	0.962412i	$0.412450\pi$
$224$	0.690983	+	0.502029i	0.0461682	+	0.0335432i
$225$	−0.828390	−	2.54952i	−0.0552260	−	0.169968i
$226$	14.3502	+	44.1654i	0.954561	+	2.93784i
$227$	−10.7348	−	7.79929i	−0.712494	−	0.517657i	0.171483	−	0.985187i	$-0.445144\pi$
$227$	−10.7348	−	7.79929i	−0.712494	−	0.517657i	−0.883977	+	0.467530i	$0.845144\pi$
$228$	32.4887	−	23.6044i	2.15161	−	1.56324i
$229$	−0.771377	+	2.37405i	−0.0509740	+	0.156882i	−0.973303	−	0.229523i	$-0.926283\pi$
$229$	−0.771377	+	2.37405i	−0.0509740	+	0.156882i	0.922329	+	0.386405i	$0.126283\pi$
$230$	−57.0135			−3.75936
$231$		0			0
$232$	−23.5199			−1.54415
$233$	2.96776	−	9.13384i	0.194425	−	0.598378i	−0.805558	−	0.592517i	$-0.798134\pi$
$233$	2.96776	−	9.13384i	0.194425	−	0.598378i	0.999983	−	0.00586090i	$-0.00186559\pi$
$234$	−0.498330	+	0.362058i	−0.0325769	+	0.0236685i
$235$	−1.69598	−	1.23220i	−0.110633	−	0.0803799i
$236$	2.13834	+	6.58114i	0.139194	+	0.428396i
$237$	1.32688	+	4.08370i	0.0861898	+	0.265265i
$238$	2.26934	+	1.64877i	0.147099	+	0.106874i
$239$	4.50078	−	3.27001i	0.291131	−	0.211519i	−0.432627	−	0.901573i	$-0.642413\pi$
$239$	4.50078	−	3.27001i	0.291131	−	0.211519i	0.723758	+	0.690054i	$0.242413\pi$
$240$	7.82750	−	24.0906i	0.505263	−	1.55504i
$241$	−15.0208			−0.967572			−0.483786	−	0.875186i	$-0.660739\pi$
$241$	−15.0208			−0.967572			−0.483786	+	0.875186i	$0.660739\pi$
$242$		0			0
$243$	−3.94427			−0.253025
$244$	−8.65682	+	26.6430i	−0.554196	+	1.70564i
$245$	2.80464	−	2.03769i	0.179182	−	0.130183i
$246$	−19.0612	−	13.8488i	−1.21530	−	0.882967i
$247$	1.22748	+	3.77780i	0.0781027	+	0.240375i
$248$	−4.44372	−	13.6764i	−0.282177	−	0.868450i
$249$	−8.76593	−	6.36882i	−0.555519	−	0.403608i
$250$	−13.9627	+	10.1445i	−0.883081	+	0.641596i
$251$	8.53290	−	26.2616i	0.538592	−	1.65762i	−0.197165	−	0.980370i	$-0.563173\pi$
$251$	8.53290	−	26.2616i	0.538592	−	1.65762i	0.735757	−	0.677246i	$-0.236827\pi$
$252$	−1.56024			−0.0982860
$253$		0			0
$254$	−19.6508			−1.23300
$255$	1.97110	−	6.06643i	0.123435	−	0.379895i
$256$	26.2927	−	19.1027i	1.64329	−	1.19392i
$257$	23.0311	+	16.7331i	1.43664	+	1.04378i	0.988732	+	0.149700i	$0.0478307\pi$
$257$	23.0311	+	16.7331i	1.43664	+	1.04378i	0.447908	+	0.894080i	$0.352169\pi$
$258$	−10.7404	−	33.0556i	−0.668668	−	2.05795i
$259$	−0.135893	−	0.418235i	−0.00844397	−	0.0259879i
$260$	7.48959	+	5.44150i	0.464484	+	0.337468i
$261$	1.41331	−	1.02683i	0.0874818	−	0.0635592i
$262$	−3.66271	+	11.2727i	−0.226283	+	0.696427i
$263$	−14.1803			−0.874397			−0.437199	−	0.899365i	$-0.644029\pi$
$263$	−14.1803			−0.874397			−0.437199	+	0.899365i	$0.644029\pi$
$264$		0			0
$265$	−34.0519			−2.09179
$266$	−4.63152	+	14.2544i	−0.283977	+	0.873991i
$267$	−0.913973	+	0.664040i	−0.0559342	+	0.0406386i
$268$	20.4170	+	14.8338i	1.24717	+	0.906120i
$269$	−7.47626	−	23.0095i	−0.455835	−	1.40292i	−0.870152	−	0.492784i	$-0.835979\pi$
$269$	−7.47626	−	23.0095i	−0.455835	−	1.40292i	0.414316	−	0.910133i	$-0.364021\pi$
$270$	14.4604	+	44.5046i	0.880034	+	2.70847i
$271$	6.02697	+	4.37885i	0.366113	+	0.265996i	0.755597	−	0.655037i	$-0.227347\pi$
$271$	6.02697	+	4.37885i	0.366113	+	0.265996i	−0.389485	+	0.921033i	$0.627347\pi$
$272$	−4.15441	+	3.01836i	−0.251898	+	0.183015i
$273$	−0.326876	+	1.00602i	−0.0197834	+	0.0608871i
$274$	53.9665			3.26024
$275$		0			0
$276$	44.0647			2.65238
$277$	5.92973	−	18.2498i	0.356283	−	1.09653i	−0.598979	−	0.800765i	$-0.704427\pi$
$277$	5.92973	−	18.2498i	0.356283	−	1.09653i	0.955262	−	0.295761i	$-0.0955733\pi$
$278$	39.5408	−	28.7281i	2.37150	−	1.72300i
$279$	0.864107	+	0.627811i	0.0517327	+	0.0375860i
$280$	5.50911	+	16.9553i	0.329233	+	1.01327i
$281$	0.587326	+	1.80760i	0.0350370	+	0.107833i	0.967045	−	0.254604i	$-0.0819450\pi$
$281$	0.587326	+	1.80760i	0.0350370	+	0.107833i	−0.932009	+	0.362436i	$0.881945\pi$
$282$	1.95258	+	1.41863i	0.116275	+	0.0844785i
$283$	5.86681	−	4.26249i	0.348746	−	0.253379i	−0.399597	−	0.916691i	$-0.630850\pi$
$283$	5.86681	−	4.26249i	0.348746	−	0.253379i	0.748343	+	0.663312i	$0.230850\pi$
$284$	−6.83750	+	21.0437i	−0.405731	+	1.24871i
$285$	34.0822			2.01885
$286$		0			0
$287$	5.90315			0.348452
$288$	0.100813	−	0.310271i	0.00594047	−	0.0182829i
$289$	12.7071	−	9.23227i	0.747478	−	0.543075i
$290$	−31.6414	−	22.9888i	−1.85805	−	1.34995i
$291$	7.42934	+	22.8652i	0.435516	+	1.34038i
$292$	−8.45966	−	26.0361i	−0.495064	−	1.52365i
$293$	−2.64627	−	1.92263i	−0.154597	−	0.112321i	0.507798	−	0.861476i	$-0.330460\pi$
$293$	−2.64627	−	1.92263i	−0.154597	−	0.112321i	−0.662394	+	0.749155i	$0.730460\pi$
$294$	−3.22899	+	2.34600i	−0.188319	+	0.136822i
$295$	−1.81481	+	5.58540i	−0.105662	+	0.325195i
$296$	2.26148			0.131446
$297$		0			0
$298$	7.80008			0.451846
$299$	−1.34689	+	4.14529i	−0.0778924	+	0.239728i
$300$	37.5267	−	27.2647i	2.16660	−	1.57413i
$301$	7.04508	+	5.11855i	0.406072	+	0.295029i
$302$	6.80552	+	20.9452i	0.391614	+	1.20526i
$303$	4.30980	+	13.2642i	0.247591	+	0.762008i
$304$	−22.1978	−	16.1276i	−1.27313	−	0.924983i
$305$	−19.2348	+	13.9749i	−1.10138	+	0.800199i
$306$	0.331092	−	1.01900i	0.0189273	−	0.0582521i
$307$	−31.6121			−1.80420			−0.902099	−	0.431530i	$-0.857974\pi$
$307$	−31.6121			−1.80420			−0.902099	+	0.431530i	$0.857974\pi$
$308$		0			0
$309$	1.50956			0.0858758
$310$	7.38941	−	22.7423i	0.419690	−	1.29167i
$311$	7.31213	−	5.31257i	0.414633	−	0.301248i	−0.360842	−	0.932627i	$-0.617511\pi$
$311$	7.31213	−	5.31257i	0.414633	−	0.301248i	0.775475	+	0.631379i	$0.217511\pi$
$312$	−4.40086	−	3.19741i	−0.249149	−	0.181018i
$313$	4.48045	+	13.7894i	0.253250	+	0.779423i	0.994169	+	0.107829i	$0.0343900\pi$
$313$	4.48045	+	13.7894i	0.253250	+	0.779423i	−0.740920	+	0.671594i	$0.765610\pi$
$314$	−0.868732	−	2.67368i	−0.0490254	−	0.150885i
$315$	−1.07128	−	0.778330i	−0.0603597	−	0.0438539i
$316$	8.76971	−	6.37156i	0.493335	−	0.358429i
$317$	−5.69128	+	17.5160i	−0.319654	+	0.983794i	0.654142	+	0.756372i	$0.273030\pi$
$317$	−5.69128	+	17.5160i	−0.319654	+	0.983794i	−0.973796	+	0.227423i	$0.926970\pi$
$318$	39.2040			2.19845
$319$		0			0
$320$	24.0061			1.34198
$321$	3.31106	−	10.1904i	0.184805	−	0.568772i
$322$	−13.3050	+	9.66666i	−0.741460	+	0.538702i
$323$	−5.58980	−	4.06123i	−0.311025	−	0.225973i
$324$	−9.72977	−	29.9452i	−0.540543	−	1.66362i
$325$	1.41783	+	4.36362i	0.0786468	+	0.242050i
$326$	−10.1124	−	7.34709i	−0.560074	−	0.406918i
$327$	5.39979	−	3.92317i	0.298609	−	0.216952i
$328$	−9.38092	+	28.8715i	−0.517975	+	1.59416i
$329$	−0.604703			−0.0333384
$330$		0			0
$331$	−6.47653			−0.355982			−0.177991	−	0.984032i	$-0.556960\pi$
$331$	−6.47653			−0.355982			−0.177991	+	0.984032i	$0.556960\pi$
$332$	−8.45284	+	26.0152i	−0.463910	+	1.42777i
$333$	−0.135893	+	0.0987319i	−0.00744688	+	0.00541047i
$334$	39.3276	+	28.5732i	2.15191	+	1.56345i
$335$	6.61866	+	20.3701i	0.361616	+	1.11294i
$336$	−2.25789	−	6.94907i	−0.123178	−	0.379103i
$337$	5.06187	+	3.67767i	0.275738	+	0.200335i	0.717056	−	0.697015i	$-0.245489\pi$
$337$	5.06187	+	3.67767i	0.275738	+	0.200335i	−0.441318	+	0.897351i	$0.645489\pi$
$338$	−25.0902	+	18.2291i	−1.36473	+	0.991534i
$339$	9.41290	−	28.9699i	0.511239	−	1.57343i
$340$	−16.1030			−0.873308
$341$		0			0
$342$	5.72487			0.309566
$343$	0.309017	−	0.951057i	0.0166853	−	0.0513522i
$344$	−36.2298	+	26.3225i	−1.95338	+	1.41921i
$345$	30.2553	+	21.9818i	1.62889	+	1.18346i
$346$	−10.9726	−	33.7702i	−0.589891	−	1.81550i
$347$	−7.01951	−	21.6038i	−0.376827	−	1.15976i	−0.942238	−	0.334945i	$-0.891282\pi$
$347$	−7.01951	−	21.6038i	−0.376827	−	1.15976i	0.565410	−	0.824810i	$-0.308718\pi$
$348$	24.4550	+	17.7676i	1.31093	+	0.952444i
$349$	24.0230	−	17.4537i	1.28592	−	0.934277i	0.286207	−	0.958168i	$-0.407606\pi$
$349$	24.0230	−	17.4537i	1.28592	−	0.934277i	0.999715	+	0.0238912i	$0.00760553\pi$
$350$	−5.34973	+	16.4648i	−0.285955	+	0.880079i
$351$	3.57742			0.190948
$352$		0			0
$353$	−6.82506			−0.363262			−0.181631	−	0.983367i	$-0.558138\pi$
$353$	−6.82506			−0.363262			−0.181631	+	0.983367i	$0.558138\pi$
$354$	2.08939	−	6.43048i	0.111050	−	0.341776i
$355$	−15.1924	+	11.0379i	−0.806328	+	0.585832i
$356$	2.30735	+	1.67639i	0.122289	+	0.0888483i
$357$	−0.568577	−	1.74990i	−0.0300923	−	0.0926145i
$358$	3.55534	+	10.9422i	0.187906	+	0.578314i
$359$	−5.87322	−	4.26715i	−0.309977	−	0.225211i	0.421910	−	0.906638i	$-0.361360\pi$
$359$	−5.87322	−	4.26715i	−0.309977	−	0.225211i	−0.731887	+	0.681427i	$0.761360\pi$
$360$	5.50911	−	4.00261i	0.290356	−	0.210956i
$361$	5.53698	−	17.0411i	0.291420	−	0.896898i
$362$	−24.4405			−1.28456
$363$		0			0
$364$	2.67042			0.139968
$365$	7.17969	−	22.0968i	0.375802	−	1.15660i
$366$	22.1450	−	16.0893i	1.15754	−	0.841002i
$367$	29.3969	+	21.3581i	1.53451	+	1.11488i	0.953666	+	0.300869i	$0.0972766\pi$
$367$	29.3969	+	21.3581i	1.53451	+	1.11488i	0.580842	+	0.814016i	$0.302723\pi$
$368$	−9.30360	−	28.6335i	−0.484984	−	1.49263i
$369$	−0.696772	−	2.14444i	−0.0362725	−	0.111635i
$370$	3.04238	+	2.21042i	0.158166	+	0.114914i
$371$	−7.94654	+	5.77350i	−0.412564	+	0.299745i
$372$	−5.71114	+	17.5771i	−0.296109	+	0.911328i
$373$	14.2913			0.739977			0.369989	−	0.929036i	$-0.379362\pi$
$373$	14.2913			0.739977			0.369989	+	0.929036i	$0.379362\pi$
$374$		0			0
$375$	11.3208			0.584605
$376$	0.960957	−	2.95752i	0.0495576	−	0.152523i
$377$	−2.41894	+	1.75747i	−0.124582	+	0.0905141i
$378$	10.9203	+	7.93410i	0.561682	+	0.408086i
$379$	−0.786533	−	2.42070i	−0.0404015	−	0.124343i	0.928821	−	0.370528i	$-0.120823\pi$
$379$	−0.786533	−	2.42070i	−0.0404015	−	0.124343i	−0.969223	+	0.246184i	$0.920823\pi$
$380$	−26.5882	−	81.8301i	−1.36395	−	4.19780i
$381$	10.4281	+	7.57645i	0.534247	+	0.388153i
$382$	19.8424	−	14.4164i	1.01523	−	0.737605i
$383$	−7.14963	+	22.0043i	−0.365329	+	1.12437i	0.584446	+	0.811433i	$0.301312\pi$
$383$	−7.14963	+	22.0043i	−0.365329	+	1.12437i	−0.949775	+	0.312935i	$0.898688\pi$
$384$	−30.4023			−1.55146
$385$		0			0
$386$	9.14330			0.465382
$387$	1.02786	−	3.16344i	0.0522493	−	0.160807i
$388$	49.1027	−	35.6752i	2.49281	−	1.81113i
$389$	−24.4820	−	17.7872i	−1.24129	−	0.901849i	−0.243605	−	0.969875i	$-0.578330\pi$
$389$	−24.4820	−	17.7872i	−1.24129	−	0.901849i	−0.997684	+	0.0680260i	$0.978330\pi$
$390$	−2.79528	−	8.60298i	−0.141544	−	0.435629i
$391$	−2.34281	−	7.21043i	−0.118481	−	0.364647i
$392$	4.16042	+	3.02272i	0.210133	+	0.152670i
$393$	6.28990	−	4.56988i	0.317283	−	0.230520i
$394$	4.51245	−	13.8879i	0.227334	−	0.699663i
$395$	9.19985			0.462894
$396$		0			0
$397$	−22.6740			−1.13798			−0.568989	−	0.822345i	$-0.692665\pi$
$397$	−22.6740			−1.13798			−0.568989	+	0.822345i	$0.692665\pi$
$398$	−8.75399	+	26.9420i	−0.438798	+	1.35048i
$399$	7.95362	−	5.77864i	0.398179	−	0.289294i
$400$	−25.6400	−	18.6285i	−1.28200	−	0.931427i
$401$	−5.01182	−	15.4248i	−0.250278	−	0.770277i	−0.994723	−	0.102593i	$-0.967286\pi$
$401$	−5.01182	−	15.4248i	−0.250278	−	0.770277i	0.744445	−	0.667684i	$-0.232714\pi$
$402$	−7.62007	−	23.4522i	−0.380055	−	1.16969i
$403$	−1.47896	−	1.07453i	−0.0736721	−	0.0535259i
$404$	28.4847	−	20.6953i	1.41717	−	1.02963i
$405$	8.25764	−	25.4144i	0.410325	−	1.26285i
$406$	−11.2818			−0.559905
$407$		0			0
$408$	9.46207			0.468442
$409$	10.8346	−	33.3454i	0.535735	−	1.64882i	−0.206320	−	0.978485i	$-0.566149\pi$
$409$	10.8346	−	33.3454i	0.535735	−	1.64882i	0.742055	−	0.670339i	$-0.233851\pi$
$410$	−40.8398	+	29.6719i	−2.01693	+	1.46539i
$411$	−28.6383	−	20.8070i	−1.41262	−	1.02633i
$412$	−1.17764	−	3.62440i	−0.0580181	−	0.178561i
$413$	0.523492	+	1.61114i	0.0257594	+	0.0792791i
$414$	5.08206	+	3.69234i	0.249770	+	0.181468i
$415$	−18.7815	+	13.6456i	−0.921949	+	0.669835i
$416$	−0.172546	+	0.531042i	−0.00845976	+	0.0260365i
$417$	−32.0593			−1.56995
$418$		0			0
$419$	28.2633			1.38075			0.690376	−	0.723451i	$-0.257445\pi$
$419$	28.2633			1.38075			0.690376	+	0.723451i	$0.257445\pi$
$420$	7.08039	−	21.7912i	0.345488	−	1.06330i
$421$	11.1601	−	8.10831i	0.543911	−	0.395175i	−0.281624	−	0.959525i	$-0.590873\pi$
$421$	11.1601	−	8.10831i	0.543911	−	0.395175i	0.825536	+	0.564350i	$0.190873\pi$
$422$	−17.4116	−	12.6503i	−0.847584	−	0.615806i
$423$	0.0713756	+	0.219671i	0.00347040	+	0.0106808i
$424$	−15.6093	−	48.0403i	−0.758052	−	2.33305i
$425$	−6.45661	−	4.69100i	−0.313192	−	0.227547i
$426$	17.4910	−	12.7080i	0.847443	−	0.615703i
$427$	−2.11930	+	6.52252i	−0.102560	+	0.315647i
$428$	−27.0498			−1.30750
$429$		0			0
$430$	−74.4682			−3.59117
$431$	−8.70502	+	26.7913i	−0.419306	+	1.29049i	0.489036	+	0.872264i	$0.337349\pi$
$431$	−8.70502	+	26.7913i	−0.419306	+	1.29049i	−0.908342	+	0.418228i	$0.862651\pi$
$432$	−19.9916	+	14.5247i	−0.961846	+	0.698822i
$433$	−11.4713	−	8.33440i	−0.551276	−	0.400526i	0.276979	−	0.960876i	$-0.410667\pi$
$433$	−11.4713	−	8.33440i	−0.551276	−	0.400526i	−0.828256	+	0.560350i	$0.810667\pi$
$434$	−2.13152	−	6.56015i	−0.102316	−	0.314897i
$435$	7.92767	+	24.3989i	0.380103	+	1.16984i
$436$	−13.6319	−	9.90415i	−0.652849	−	0.474323i
$437$	32.7727	−	23.8108i	1.56773	−	1.13902i
$438$	−8.26600	+	25.4401i	−0.394965	+	1.21558i
$439$	−28.0185			−1.33725			−0.668625	−	0.743599i	$-0.733117\pi$
$439$	−28.0185			−1.33725			−0.668625	+	0.743599i	$0.733117\pi$
$440$		0			0
$441$	−0.381966			−0.0181889
$442$	−0.566678	+	1.74406i	−0.0269541	+	0.0829563i
$443$	−14.0259	+	10.1904i	−0.666392	+	0.484162i	−0.868815	−	0.495136i	$-0.835118\pi$
$443$	−14.0259	+	10.1904i	−0.666392	+	0.484162i	0.202424	+	0.979298i	$0.435118\pi$
$444$	−2.35140	−	1.70839i	−0.111593	−	0.0810767i
$445$	0.747981	+	2.30205i	0.0354577	+	0.109128i
$446$	−7.87633	−	24.2409i	−0.372955	−	1.14784i
$447$	−4.13926	−	3.00735i	−0.195780	−	0.142243i
$448$	5.60222	−	4.07025i	0.264680	−	0.192301i
$449$	−9.12264	+	28.0766i	−0.430524	+	1.32502i	0.467080	+	0.884215i	$0.345306\pi$
$449$	−9.12264	+	28.0766i	−0.430524	+	1.32502i	−0.897604	+	0.440802i	$0.854694\pi$
$450$	6.61263			0.311722
$451$		0			0
$452$	−76.8990			−3.61702
$453$	4.46403	−	13.7389i	0.209738	−	0.645508i
$454$	26.4799	−	19.2388i	1.24276	−	0.902920i
$455$	1.83354	+	1.33215i	0.0859577	+	0.0624519i
$456$	15.6231	+	48.0831i	0.731621	+	2.25170i
$457$	−2.99662	−	9.22263i	−0.140176	−	0.431417i	0.856183	−	0.516672i	$-0.172829\pi$
$457$	−2.99662	−	9.22263i	−0.140176	−	0.431417i	−0.996359	+	0.0852555i	$0.972829\pi$
$458$	−4.98154	−	3.61930i	−0.232772	−	0.169119i
$459$	−5.03424	+	3.65759i	−0.234978	+	0.170722i
$460$	29.1746	−	89.7903i	1.36027	−	4.18650i
$461$	19.2216			0.895240			0.447620	−	0.894224i	$-0.352272\pi$
$461$	19.2216			0.895240			0.447620	+	0.894224i	$0.352272\pi$
$462$		0			0
$463$	20.5327			0.954235			0.477117	−	0.878840i	$-0.341682\pi$
$463$	20.5327			0.954235			0.477117	+	0.878840i	$0.341682\pi$
$464$	6.38220	−	19.6424i	0.296286	−	0.911876i
$465$	−12.6897	+	9.21959i	−0.588470	+	0.427548i
$466$	19.1658	+	13.9248i	0.887838	+	0.645052i
$467$	10.4050	+	32.0234i	0.481488	+	1.48187i	0.837003	+	0.547198i	$0.184305\pi$
$467$	10.4050	+	32.0234i	0.481488	+	1.48187i	−0.355515	+	0.934671i	$0.615695\pi$
$468$	−0.315201	−	0.970088i	−0.0145702	−	0.0448423i
$469$	4.99833	+	3.63150i	0.230801	+	0.167687i
$470$	4.18352	−	3.03951i	0.192972	−	0.140202i
$471$	−0.569838	+	1.75378i	−0.0262568	+	0.0808100i
$472$	−8.71178			−0.400992
$473$		0			0
$474$	−10.5918			−0.486498
$475$	13.1774	−	40.5558i	0.604620	−	1.86083i
$476$	−3.75789	+	2.73027i	−0.172243	+	0.125142i
$477$	3.03531	+	2.20528i	0.138977	+	0.100973i
$478$	4.24067	+	13.0514i	0.193964	+	0.596959i
$479$	−4.37901	−	13.4772i	−0.200082	−	0.615789i	−0.999880	−	0.0155195i	$-0.995060\pi$
$479$	−4.37901	−	13.4772i	−0.200082	−	0.615789i	0.799797	−	0.600270i	$-0.204940\pi$
$480$	3.87592	+	2.81602i	0.176911	+	0.128533i
$481$	0.232586	−	0.168984i	0.0106050	−	0.00770501i
$482$	11.4497	−	35.2387i	0.521522	−	1.60508i
$483$	10.7876			0.490851
$484$		0			0
$485$	51.5111			2.33900
$486$	3.00657	−	9.25327i	0.136381	−	0.419737i
$487$	−22.4433	+	16.3060i	−1.01700	+	0.738897i	−0.965667	−	0.259785i	$-0.916348\pi$
$487$	−22.4433	+	16.3060i	−1.01700	+	0.738897i	−0.0513373	+	0.998681i	$0.516348\pi$
$488$	−28.5329	−	20.7304i	−1.29162	−	0.938420i
$489$	2.53364	+	7.79774i	0.114575	+	0.352626i
$490$	2.64256	+	8.13296i	0.119379	+	0.367410i
$491$	−2.78541	−	2.02372i	−0.125704	−	0.0913291i	0.523157	−	0.852236i	$-0.324754\pi$
$491$	−2.78541	−	2.02372i	−0.125704	−	0.0913291i	−0.648861	+	0.760907i	$0.724754\pi$
$492$	31.5643	−	22.9328i	1.42303	−	1.03389i
$493$	1.60715	−	4.94631i	0.0723825	−	0.222770i
$494$	−9.79837			−0.440850
$495$		0			0
$496$	12.6275			0.566992
$497$	−1.67390	+	5.15175i	−0.0750848	+	0.231087i
$498$	21.6232	−	15.7102i	0.968959	−	0.703990i
$499$	2.09473	+	1.52191i	0.0937731	+	0.0681302i	0.633684	−	0.773592i	$-0.281542\pi$
$499$	2.09473	+	1.52191i	0.0937731	+	0.0681302i	−0.539911	+	0.841722i	$0.681542\pi$
$500$	−8.83162	−	27.1809i	−0.394962	−	1.21557i
$501$	−9.85344	−	30.3258i	−0.440219	−	1.35486i
$502$	55.1054	+	40.0364i	2.45947	+	1.78691i
$503$	−18.5286	+	13.4618i	−0.826151	+	0.600234i	−0.918468	−	0.395496i	$-0.870573\pi$
$503$	−18.5286	+	13.4618i	−0.826151	+	0.600234i	0.0923170	+	0.995730i	$0.470573\pi$
$504$	0.606997	−	1.86814i	0.0270378	−	0.0832137i
$505$	29.8818			1.32972
$506$		0			0
$507$	20.3429			0.903460
$508$	10.0556	−	30.9480i	0.446146	−	1.37310i
$509$	19.4961	−	14.1648i	0.864150	−	0.627842i	−0.0648607	−	0.997894i	$-0.520660\pi$
$509$	19.4961	−	14.1648i	0.864150	−	0.627842i	0.929011	+	0.370052i	$0.120660\pi$
$510$	12.7294	+	9.24842i	0.563666	+	0.409527i
$511$	−2.07103	−	6.37396i	−0.0916168	−	0.281968i
$512$	13.1605	+	40.5040i	0.581619	+	1.79004i
$513$	−26.8989	−	19.5432i	−1.18761	−	0.862852i
$514$	−56.8115	+	41.2760i	−2.50585	+	1.82060i
$515$	0.999459	−	3.07602i	0.0440414	−	0.135546i
$516$	57.5550			2.53372
$517$		0			0
$518$	1.08477			0.0476619
$519$	−7.19740	+	22.1513i	−0.315931	+	0.972334i
$520$	−9.42909	+	6.85064i	−0.413493	+	0.300420i
$521$	27.1067	+	19.6942i	1.18757	+	0.862817i	0.993005	−	0.118073i	$-0.0376718\pi$
$521$	27.1067	+	19.6942i	1.18757	+	0.862817i	0.194561	+	0.980890i	$0.437672\pi$
$522$	1.33163	+	4.09835i	0.0582840	+	0.179380i
$523$	9.62816	+	29.6324i	0.421010	+	1.29574i	0.906764	+	0.421640i	$0.138545\pi$
$523$	9.62816	+	29.6324i	0.421010	+	1.29574i	−0.485754	+	0.874096i	$0.661455\pi$
$524$	−15.8790	−	11.5368i	−0.693677	−	0.503986i
$525$	9.18698	−	6.67473i	0.400953	−	0.291309i
$526$	10.8091	−	33.2671i	0.471301	−	1.45051i
$527$	3.17983			0.138516
$528$		0			0
$529$	21.4500			0.932608
$530$	25.9564	−	79.8857i	1.12748	−	3.47001i
$531$	0.523492	−	0.380339i	0.0227176	−	0.0165053i
$532$	−20.0791	−	14.5883i	−0.870539	−	0.632484i
$533$	1.19256	+	3.67031i	0.0516554	+	0.158979i
$534$	−0.861152	−	2.65035i	−0.0372657	−	0.114692i
$535$	−18.5727	−	13.4938i	−0.802967	−	0.583390i
$536$	−25.7042	+	18.6752i	−1.11025	+	0.806646i
$537$	2.33210	−	7.17747i	0.100638	−	0.309731i
$538$	59.6793			2.57296
$539$		0			0
$540$	−77.4898			−3.33463
$541$	−6.98599	+	21.5007i	−0.300351	+	0.924386i	0.681020	+	0.732265i	$0.261537\pi$
$541$	−6.98599	+	21.5007i	−0.300351	+	0.924386i	−0.981371	+	0.192121i	$0.938463\pi$
$542$	−14.8669	+	10.8015i	−0.638589	+	0.463962i
$543$	12.9698	+	9.42311i	0.556588	+	0.404385i
$544$	−0.300131	−	0.923709i	−0.0128680	−	0.0396037i
$545$	−4.41910	−	13.6006i	−0.189293	−	0.582585i
$546$	−2.11096	−	1.53370i	−0.0903407	−	0.0656364i
$547$	−22.2028	+	16.1313i	−0.949324	+	0.689724i	−0.950647	−	0.310275i	$-0.899579\pi$
$547$	−22.2028	+	16.1313i	−0.949324	+	0.689724i	0.00132275	+	0.999999i	$0.499579\pi$
$548$	−27.6154	+	84.9916i	−1.17967	+	3.63066i
$549$	2.61959			0.111801
$550$		0			0
$551$	27.7891			1.18386
$552$	−17.1429	+	52.7605i	−0.729651	+	2.24564i
$553$	2.14693	−	1.55984i	0.0912968	−	0.0663310i
$554$	38.2941	+	27.8223i	1.62696	+	1.18206i
$555$	−0.762262	−	2.34600i	−0.0323562	−	0.0995822i
$556$	25.0101	+	76.9732i	1.06066	+	3.26439i
$557$	−24.4731	−	17.7807i	−1.03696	−	0.753393i	−0.0672679	−	0.997735i	$-0.521428\pi$
$557$	−24.4731	−	17.7807i	−1.03696	−	0.753393i	−0.969689	+	0.244341i	$0.921428\pi$
$558$	−2.13152	+	1.54864i	−0.0902345	+	0.0655592i
$559$	−1.75923	+	5.41437i	−0.0744077	+	0.229003i
$560$	−15.6550			−0.661544
$561$		0			0
$562$	−4.68834			−0.197766
$563$	−2.30599	+	7.09711i	−0.0971859	+	0.299107i	−0.987817	−	0.155619i	$-0.950263\pi$
$563$	−2.30599	+	7.09711i	−0.0971859	+	0.299107i	0.890631	+	0.454726i	$0.150263\pi$
$564$	−3.23337	+	2.34918i	−0.136149	+	0.0989182i
$565$	−52.7997	−	38.3612i	−2.22130	−	1.61387i
$566$	5.52775	+	17.0127i	0.232349	+	0.715096i
$567$	−2.38197	−	7.33094i	−0.100033	−	0.307870i
$568$	−22.5364	−	16.3737i	−0.945607	−	0.687024i
$569$	28.8401	−	20.9536i	1.20904	−	0.878419i	0.213896	−	0.976856i	$-0.431384\pi$
$569$	28.8401	−	20.9536i	1.20904	−	0.878419i	0.995143	+	0.0984376i	$0.0313845\pi$
$570$	−25.9795	+	79.9568i	−1.08816	+	3.34902i
$571$	−25.8902			−1.08347			−0.541737	−	0.840548i	$-0.682233\pi$
$571$	−25.8902			−1.08347			−0.541737	+	0.840548i	$0.682233\pi$
$572$		0			0
$573$	−16.0880			−0.672087
$574$	−4.49975	+	13.8488i	−0.187816	+	0.578038i
$575$	37.8548	−	27.5031i	1.57865	−	1.14696i
$576$	−2.13986	−	1.55470i	−0.0891607	−	0.0647790i
$577$	2.52276	+	7.76425i	0.105024	+	0.323230i	0.989736	−	0.142908i	$-0.0456452\pi$
$577$	2.52276	+	7.76425i	0.105024	+	0.323230i	−0.884712	+	0.466138i	$0.845645\pi$
$578$	11.9728	+	36.8484i	0.498001	+	1.53269i
$579$	−4.85206	−	3.52523i	−0.201645	−	0.146504i
$580$	52.3963	−	38.0681i	2.17564	−	1.58069i
$581$	−2.06936	+	6.36882i	−0.0858514	+	0.264223i
$582$	−59.3048			−2.45826
$583$		0			0
$584$	34.4653			1.42619
$585$	0.267510	−	0.823311i	0.0110602	−	0.0340397i
$586$	6.52764	−	4.74260i	0.269654	−	0.195915i
$587$	10.0831	+	7.32580i	0.416174	+	0.302368i	0.776097	−	0.630614i	$-0.217197\pi$
$587$	10.0831	+	7.32580i	0.416174	+	0.302368i	−0.359923	+	0.932982i	$0.617197\pi$
$588$	−2.04238	−	6.28581i	−0.0842265	−	0.259222i
$589$	5.25033	+	16.1589i	0.216336	+	0.665815i
$590$	−11.7200	−	8.51508i	−0.482505	−	0.350560i
$591$	−7.74915	+	5.63008i	−0.318757	+	0.231591i
$592$	−0.613662	+	1.88866i	−0.0252214	+	0.0776233i
$593$	23.6707			0.972037			0.486019	−	0.873948i	$-0.338449\pi$
$593$	23.6707			0.972037			0.486019	+	0.873948i	$0.338449\pi$
$594$		0			0
$595$	−3.94221			−0.161615
$596$	−3.99141	+	12.2843i	−0.163495	+	0.503185i
$597$	15.0330	−	10.9221i	0.615261	−	0.447014i
$598$	−8.69818	−	6.31959i	−0.355695	−	0.258427i
$599$	12.0458	+	37.0730i	0.492176	+	1.51476i	0.821312	+	0.570480i	$0.193243\pi$
$599$	12.0458	+	37.0730i	0.492176	+	1.51476i	−0.329136	+	0.944283i	$0.606757\pi$
$600$	18.0458	+	55.5393i	0.736718	+	2.26738i
$601$	24.7163	+	17.9574i	1.00820	+	0.732499i	0.963830	−	0.266517i	$-0.0858728\pi$
$601$	24.7163	+	17.9574i	1.00820	+	0.732499i	0.0443675	+	0.999015i	$0.485873\pi$
$602$	−17.3783	+	12.6261i	−0.708288	+	0.514601i
$603$	0.729247	−	2.24439i	0.0296972	−	0.0913986i
$604$	−36.4690			−1.48390
$605$		0			0
$606$	−34.4030			−1.39753
$607$	−11.6244	+	35.7762i	−0.471819	+	1.45211i	0.378380	+	0.925650i	$0.376481\pi$
$607$	−11.6244	+	35.7762i	−0.471819	+	1.45211i	−0.850200	+	0.526460i	$0.823519\pi$
$608$	4.19843	−	3.05034i	0.170269	−	0.123707i
$609$	5.98688	+	4.34973i	0.242601	+	0.176260i
$610$	−18.1231	−	55.7773i	−0.733785	−	2.25836i
$611$	−0.122162	−	0.375977i	−0.00494216	−	0.0152104i
$612$	1.43539	+	1.04287i	0.0580221	+	0.0421555i
$613$	14.2607	−	10.3610i	0.575985	−	0.418477i	−0.261290	−	0.965260i	$-0.584148\pi$
$613$	14.2607	−	10.3610i	0.575985	−	0.418477i	0.837274	+	0.546783i	$0.184148\pi$
$614$	24.0967	−	74.1620i	0.972464	−	2.99294i
$615$	33.1125			1.33522
$616$		0			0
$617$	−44.4849			−1.79089			−0.895447	−	0.445168i	$-0.853144\pi$
$617$	−44.4849			−1.79089			−0.895447	+	0.445168i	$0.853144\pi$
$618$	−1.15068	+	3.54143i	−0.0462871	+	0.142457i
$619$	5.01933	−	3.64676i	0.201744	−	0.146576i	−0.482326	−	0.875992i	$-0.660208\pi$
$619$	5.01933	−	3.64676i	0.201744	−	0.146576i	0.684070	+	0.729416i	$0.260208\pi$
$620$	32.0354	+	23.2751i	1.28657	+	0.934750i
$621$	−11.2739	−	34.6976i	−0.452407	−	1.39237i
$622$	6.88954	+	21.2038i	0.276246	+	0.850196i
$623$	0.564866	+	0.410399i	0.0226309	+	0.0164423i
$624$	3.86448	−	2.80771i	0.154703	−	0.112398i
$625$	−3.34839	+	10.3053i	−0.133935	+	0.412211i
$626$	−35.7652			−1.42947
$627$		0			0
$628$	4.65531			0.185767
$629$	−0.154531	+	0.475598i	−0.00616156	+	0.0189633i
$630$	2.64256	−	1.91993i	0.105282	−	0.0764919i
$631$	−36.2486	−	26.3361i	−1.44303	−	1.04843i	−0.987398	−	0.158259i	$-0.949412\pi$
$631$	−36.2486	−	26.3361i	−1.44303	−	1.04843i	−0.455636	−	0.890166i	$-0.650588\pi$
$632$	4.21718	+	12.9791i	0.167750	+	0.516282i
$633$	4.36244	+	13.4262i	0.173391	+	0.533644i
$634$	−36.7542	−	26.7035i	−1.45970	−	1.06053i
$635$	22.3428	−	16.2330i	0.886646	−	0.644186i
$636$	−20.0612	+	61.7421i	−0.795480	+	2.44823i
$637$	0.653752			0.0259026
$638$		0			0
$639$	2.06906			0.0818507
$640$	−20.1289	+	61.9505i	−0.795666	+	2.44881i
$641$	8.31316	−	6.03986i	0.328350	−	0.238560i	−0.411380	−	0.911464i	$-0.634953\pi$
$641$	8.31316	−	6.03986i	0.328350	−	0.238560i	0.739730	+	0.672904i	$0.234953\pi$
$642$	21.3828	+	15.5355i	0.843911	+	0.613137i
$643$	−5.08165	−	15.6397i	−0.200401	−	0.616771i	−0.999871	−	0.0160646i	$-0.994886\pi$
$643$	−5.08165	−	15.6397i	−0.200401	−	0.616771i	0.799470	−	0.600706i	$-0.205114\pi$
$644$	−8.41560	−	25.9006i	−0.331621	−	1.02063i
$645$	39.5179	+	28.7115i	1.55602	+	1.13051i
$646$	13.7885	−	10.0180i	0.542503	−	0.394151i
$647$	−8.33377	+	25.6487i	−0.327634	+	1.00835i	0.642603	+	0.766199i	$0.277854\pi$
$647$	−8.33377	+	25.6487i	−0.327634	+	1.00835i	−0.970237	+	0.242156i	$0.922146\pi$
$648$	39.6399			1.55720
$649$		0			0
$650$	−11.3178			−0.443921
$651$	−1.39815	+	4.30308i	−0.0547980	+	0.168651i
$652$	16.7456	−	12.1664i	0.655806	−	0.476471i
$653$	−5.74889	−	4.17682i	−0.224972	−	0.163451i	0.469590	−	0.882885i	$-0.344402\pi$
$653$	−5.74889	−	4.17682i	−0.224972	−	0.163451i	−0.694562	+	0.719433i	$0.744402\pi$
$654$	5.08772	+	15.6584i	0.198946	+	0.612292i
$655$	−5.14755	−	15.8425i	−0.201132	−	0.619019i
$656$	−21.5662	−	15.6688i	−0.842020	−	0.611763i
$657$	−2.07103	+	1.50469i	−0.0807984	+	0.0587035i
$658$	0.460942	−	1.41863i	0.0179694	−	0.0553041i
$659$	32.6279			1.27100			0.635502	−	0.772099i	$-0.280793\pi$
$659$	32.6279			1.27100			0.635502	+	0.772099i	$0.280793\pi$
$660$		0			0
$661$	−33.8165			−1.31531			−0.657654	−	0.753320i	$-0.728451\pi$
$661$	−33.8165			−1.31531			−0.657654	+	0.753320i	$0.728451\pi$
$662$	4.93681	−	15.1939i	0.191875	−	0.590530i
$663$	0.973144	−	0.707031i	0.0377938	−	0.0274588i
$664$	−27.8606	−	20.2419i	−1.08120	−	0.785537i
$665$	−6.50911	−	20.0330i	−0.252413	−	0.776846i
$666$	−0.128039	−	0.394064i	−0.00496142	−	0.0152697i
$667$	24.6689	+	17.9230i	0.955182	+	0.693980i
$668$	−65.1242	+	47.3155i	−2.51973	+	1.83069i
$669$	−5.16642	+	15.9006i	−0.199745	+	0.614753i
$670$	−52.8335			−2.04114
$671$		0			0
$672$	1.38197			0.0533105
$673$	−7.33902	+	22.5872i	−0.282898	+	0.870672i	0.704122	+	0.710079i	$0.251341\pi$
$673$	−7.33902	+	22.5872i	−0.282898	+	0.870672i	−0.987021	+	0.160593i	$0.948659\pi$
$674$	−12.4863	+	9.07182i	−0.480954	+	0.349433i
$675$	−31.0701	−	22.5737i	−1.19589	−	0.868863i
$676$	−15.8699	−	48.8426i	−0.610382	−	1.87856i
$677$	14.1008	+	43.3978i	0.541938	+	1.66791i	0.728162	+	0.685405i	$0.240375\pi$
$677$	14.1008	+	43.3978i	0.541938	+	1.66791i	−0.186224	+	0.982507i	$0.559625\pi$
$678$	60.7884	+	44.1654i	2.33456	+	1.69616i
$679$	12.0209	−	8.73372i	0.461321	−	0.335169i
$680$	6.26471	−	19.2808i	0.240241	−	0.739385i
$681$	−21.4696			−0.822717
$682$		0			0
$683$	−28.8727			−1.10478			−0.552392	−	0.833585i	$-0.686285\pi$
$683$	−28.8727			−1.10478			−0.552392	+	0.833585i	$0.686285\pi$
$684$	−2.92950	+	9.01608i	−0.112012	+	0.344738i
$685$	−61.3593	+	44.5801i	−2.34442	+	1.70332i
$686$	1.99563	+	1.44991i	0.0761934	+	0.0553578i
$687$	1.24811	+	3.84130i	0.0476185	+	0.146555i
$688$	−12.1519	−	37.3997i	−0.463286	−	1.42585i
$689$	−5.19506	−	3.77444i	−0.197916	−	0.143795i
$690$	−74.6317	+	54.2231i	−2.84118	+	2.06424i
$691$	−8.36308	+	25.7389i	−0.318146	+	0.979154i	0.656294	+	0.754506i	$0.272123\pi$
$691$	−8.36308	+	25.7389i	−0.318146	+	0.979154i	−0.974440	+	0.224648i	$0.927877\pi$
$692$	58.7994			2.23522
$693$		0			0
$694$	56.0334			2.12700
$695$	−21.2260	+	65.3270i	−0.805149	+	2.47799i
$696$	−30.7879	+	22.3687i	−1.16701	+	0.847884i
$697$	−5.43076	−	3.94568i	−0.205705	−	0.149453i
$698$	22.6347	+	69.6623i	0.856734	+	2.63676i
$699$	−4.80194	−	14.7789i	−0.181626	−	0.558988i
$700$	−23.1928	−	16.8505i	−0.876604	−	0.636890i
$701$	31.1598	−	22.6389i	1.17689	−	0.855060i	0.185071	−	0.982725i	$-0.440748\pi$
$701$	31.1598	−	22.6389i	1.17689	−	0.855060i	0.991817	+	0.127665i	$0.0407484\pi$
$702$	−2.72693	+	8.39263i	−0.102921	+	0.316759i
$703$	−2.67198			−0.100776
$704$		0			0
$705$	−3.39196			−0.127748
$706$	5.20249	−	16.0116i	0.195798	−	0.602605i
$707$	6.97340	−	5.06647i	0.262262	−	0.190544i
$708$	9.05816	+	6.58114i	0.340427	+	0.247334i
$709$	−0.585477	−	1.80191i	−0.0219880	−	0.0676722i	0.939460	−	0.342657i	$-0.111327\pi$
$709$	−0.585477	−	1.80191i	−0.0219880	−	0.0676722i	−0.961448	+	0.274985i	$0.911327\pi$
$710$	−14.3144	−	44.0551i	−0.537209	−	1.65336i
$711$	−0.820054	−	0.595804i	−0.0307544	−	0.0223444i
$712$	−2.90486	+	2.11050i	−0.108864	+	0.0790944i
$713$	−5.76107	+	17.7308i	−0.215754	+	0.664022i
$714$	4.53867			0.169856
$715$		0			0
$716$	−19.0522			−0.712013
$717$	2.78163	−	8.56099i	0.103882	−	0.319716i
$718$	14.4877	−	10.5259i	0.540675	−	0.392823i
$719$	−11.7932	−	8.56828i	−0.439813	−	0.319543i	0.345748	−	0.938328i	$-0.387625\pi$
$719$	−11.7932	−	8.56828i	−0.439813	−	0.319543i	−0.785561	+	0.618785i	$0.787625\pi$
$720$	1.84782	+	5.68701i	0.0688643	+	0.211942i
$721$	−0.288300	−	0.887296i	−0.0107369	−	0.0330446i
$722$	35.7577	+	25.9795i	1.33077	+	0.966858i
$723$	−19.6624	+	14.2856i	−0.731253	+	0.531287i
$724$	12.5066	−	38.4912i	0.464802	−	1.43051i
$725$	32.0984			1.19210
$726$		0			0
$727$	4.04780			0.150125			0.0750623	−	0.997179i	$-0.476084\pi$
$727$	4.04780			0.150125			0.0750623	+	0.997179i	$0.476084\pi$
$728$	−1.03890	+	3.19741i	−0.0385042	+	0.118504i
$729$	−23.8713	+	17.3435i	−0.884123	+	0.642353i
$730$	46.3664	+	33.6871i	1.71610	+	1.24682i
$731$	−3.06006	−	9.41790i	−0.113180	−	0.348334i
$732$	14.0070	+	43.1092i	0.517715	+	1.59336i
$733$	−19.0128	−	13.8136i	−0.702256	−	0.510219i	0.178410	−	0.983956i	$-0.442905\pi$
$733$	−19.0128	−	13.8136i	−0.702256	−	0.510219i	−0.880666	+	0.473738i	$0.842905\pi$
$734$	−72.5144	+	52.6848i	−2.67655	+	1.94463i
$735$	1.73337	−	5.33475i	0.0639362	−	0.196775i
$736$	5.69437			0.209897
$737$		0			0
$738$	5.56199			0.204740
$739$	10.0983	−	31.0792i	0.371470	−	1.14327i	−0.574359	−	0.818603i	$-0.694749\pi$
$739$	10.0983	−	31.0792i	0.371470	−	1.14327i	0.945829	−	0.324664i	$-0.105251\pi$
$740$	−5.03801	+	3.66033i	−0.185201	+	0.134556i
$741$	5.19969	+	3.77780i	0.191015	+	0.138781i
$742$	−7.48729	−	23.0435i	−0.274867	−	0.845954i
$743$	5.59500	+	17.2196i	0.205261	+	0.631727i	0.999703	+	0.0243872i	$0.00776346\pi$
$743$	5.59500	+	17.2196i	0.205261	+	0.631727i	−0.794442	+	0.607340i	$0.792237\pi$
$744$	−18.8239	−	13.6764i	−0.690118	−	0.501400i
$745$	−8.86860	+	6.44341i	−0.324920	+	0.236068i
$746$	−10.8937	+	33.5275i	−0.398848	+	1.22753i
$747$	2.55787			0.0935874
$748$		0			0
$749$	−6.62212			−0.241967
$750$	−8.62944	+	26.5587i	−0.315103	+	0.969786i
$751$	−7.39730	+	5.37445i	−0.269931	+	0.196117i	−0.714514	−	0.699621i	$-0.753352\pi$
$751$	−7.39730	+	5.37445i	−0.269931	+	0.196117i	0.444582	+	0.895738i	$0.353352\pi$
$752$	2.20919	+	1.60507i	0.0805608	+	0.0585309i
$753$	−13.8065	−	42.4921i	−0.503138	−	1.54850i
$754$	−2.27915	−	7.01450i	−0.0830017	−	0.255453i
$755$	−25.0400	−	18.1927i	−0.911300	−	0.662098i
$756$	−18.0835	+	13.1384i	−0.657689	+	0.477839i
$757$	14.6322	−	45.0334i	0.531818	−	1.63677i	−0.218608	−	0.975813i	$-0.570152\pi$
$757$	14.6322	−	45.0334i	0.531818	−	1.63677i	0.750426	−	0.660954i	$-0.229848\pi$
$758$	6.27851			0.228046
$759$		0			0
$760$	108.323			3.92927
$761$	−1.06558	+	3.27951i	−0.0386271	+	0.118882i	−0.968511	−	0.248972i	$-0.919907\pi$
$761$	−1.06558	+	3.27951i	−0.0386271	+	0.118882i	0.929884	+	0.367854i	$0.119907\pi$
$762$	−25.7233	+	18.6891i	−0.931856	+	0.677033i
$763$	−3.33725	−	2.42466i	−0.120817	−	0.0877784i
$764$	12.5506	+	38.6268i	0.454065	+	1.39747i
$765$	0.465315	+	1.43209i	0.0168235	+	0.0517774i
$766$	−46.1722	−	33.5461i	−1.66827	−	1.21207i
$767$	−0.895980	+	0.650967i	−0.0323519	+	0.0235051i
$768$	16.2498	−	50.0116i	0.586363	−	1.80464i
$769$	−34.9787			−1.26137			−0.630683	−	0.776041i	$-0.717225\pi$
$769$	−34.9787			−1.26137			−0.630683	+	0.776041i	$0.717225\pi$
$770$		0			0
$771$	46.0622			1.65889
$772$	−4.67876	+	14.3997i	−0.168392	+	0.518258i
$773$	−20.5323	+	14.9176i	−0.738497	+	0.536549i	−0.892240	−	0.451561i	$-0.850867\pi$
$773$	−20.5323	+	14.9176i	−0.738497	+	0.536549i	0.153743	+	0.988111i	$0.450867\pi$
$774$	6.63793	+	4.82274i	0.238596	+	0.173350i
$775$	6.06450	+	18.6646i	0.217843	+	0.670453i
$776$	23.6125	+	72.6718i	0.847639	+	2.60877i
$777$	−0.575651	−	0.418235i	−0.0206514	−	0.0150041i
$778$	60.3906	−	43.8763i	2.16511	−	1.57304i
$779$	11.0837	−	34.1122i	0.397115	−	1.22220i
$780$	14.9792			0.536340
$781$		0			0
$782$	18.7015			0.668765
$783$	7.73383	−	23.8023i	0.276385	−	0.850624i
$784$	−3.65334	+	2.65431i	−0.130477	+	0.0947967i
$785$	3.19639	+	2.32231i	0.114084	+	0.0828868i
$786$	5.92639	+	18.2396i	0.211387	+	0.650583i
$787$	−9.19486	−	28.2989i	−0.327761	−	1.00875i	−0.970179	−	0.242391i	$-0.922068\pi$
$787$	−9.19486	−	28.2989i	−0.327761	−	1.00875i	0.642417	−	0.766355i	$-0.277932\pi$
$788$	19.5629	+	14.2133i	0.696900	+	0.506327i
$789$	−18.5623	+	13.4863i	−0.660836	+	0.480125i
$790$	−7.01269	+	21.5828i	−0.249500	+	0.767883i
$791$	−18.8258			−0.669369
$792$		0			0
$793$	−4.48355			−0.159215
$794$	17.2836	−	53.1933i	0.613371	−	1.88776i
$795$	−44.5745	+	32.3852i	−1.58089	+	1.14859i
$796$	−37.9513	−	27.5732i	−1.34515	−	0.977307i
$797$	−1.92929	−	5.93773i	−0.0683388	−	0.210325i	0.911055	−	0.412285i	$-0.135269\pi$
$797$	−1.92929	−	5.93773i	−0.0683388	−	0.210325i	−0.979394	+	0.201959i	$0.935269\pi$
$798$	7.49396	+	23.0640i	0.265283	+	0.816458i
$799$	0.556313	+	0.404185i	0.0196809	+	0.0142990i
$800$	4.84948	−	3.52335i	0.171455	−	0.124569i
$801$	0.0824129	−	0.253641i	0.00291192	−	0.00896196i
$802$	40.0069			1.41269
$803$		0			0
$804$	40.8340			1.44010
$805$	7.14231	−	21.9818i	0.251733	−	0.774755i
$806$	3.64819	−	2.65057i	0.128502	−	0.0933622i
$807$	−31.6699	−	23.0095i	−1.11483	−	0.809974i
$808$	13.6977	+	42.1573i	0.481884	+	1.48309i
$809$	−12.1091	−	37.2681i	−0.425735	−	1.31028i	−0.902289	−	0.431132i	$-0.858114\pi$
$809$	−12.1091	−	37.2681i	−0.425735	−	1.31028i	0.476554	−	0.879145i	$-0.341886\pi$
$810$	53.3277	+	38.7449i	1.87375	+	1.36136i
$811$	−10.0164	+	7.27732i	−0.351722	+	0.255541i	−0.749591	−	0.661901i	$-0.769750\pi$
$811$	−10.0164	+	7.27732i	−0.351722	+	0.255541i	0.397869	+	0.917442i	$0.369750\pi$
$812$	5.77305	−	17.7676i	0.202594	−	0.623521i
$813$	12.0539			0.422750
$814$		0			0
$815$	17.5669			0.615341
$816$	−2.56757	+	7.90216i	−0.0898829	+	0.276631i
$817$	42.8061	−	31.1004i	1.49760	−	1.08807i
$818$	69.9695	+	50.8358i	2.44643	+	1.77743i
$819$	−0.0771649	−	0.237489i	−0.00269636	−	0.00829854i
$820$	−25.8317	−	79.5019i	−0.902083	−	2.77633i
$821$	38.5891	+	28.0366i	1.34677	+	0.978484i	0.999166	+	0.0408426i	$0.0130042\pi$
$821$	38.5891	+	28.0366i	1.34677	+	0.978484i	0.347603	+	0.937642i	$0.386996\pi$
$822$	70.6431	−	51.3252i	2.46396	−	1.79017i
$823$	−4.48715	+	13.8100i	−0.156412	+	0.481387i	−0.998301	−	0.0582633i	$-0.981444\pi$
$823$	−4.48715	+	13.8100i	−0.156412	+	0.481387i	0.841889	+	0.539651i	$0.181444\pi$
$824$	4.79779			0.167139
$825$		0			0
$826$	−4.17878			−0.145398
$827$	9.56013	−	29.4231i	0.332438	−	1.02314i	−0.635532	−	0.772075i	$-0.719219\pi$
$827$	9.56013	−	29.4231i	0.332438	−	1.02314i	0.967970	−	0.251065i	$-0.0807809\pi$
$828$	−8.41560	+	6.11429i	−0.292462	+	0.212486i
$829$	−0.0694183	−	0.0504353i	−0.00241100	−	0.00175169i	0.586579	−	0.809892i	$-0.300474\pi$
$829$	−0.0694183	−	0.0504353i	−0.00241100	−	0.00175169i	−0.588990	+	0.808140i	$0.700474\pi$
$830$	−17.6961	−	54.4630i	−0.614240	−	1.89044i
$831$	−9.59450	−	29.5288i	−0.332830	−	1.02434i
$832$	3.66246	+	2.66093i	0.126973	+	0.0922512i
$833$	−0.919977	+	0.668402i	−0.0318753	+	0.0231588i
$834$	24.4376	−	75.2111i	0.846204	−	2.60435i
$835$	−68.3185			−2.36426
$836$		0			0
$837$	15.3018			0.528907
$838$	−21.5440	+	66.3057i	−0.744226	+	2.29049i
$839$	−8.64881	+	6.28373i	−0.298590	+	0.216939i	−0.726985	−	0.686653i	$-0.759079\pi$
$839$	−8.64881	+	6.28373i	−0.298590	+	0.216939i	0.428395	+	0.903592i	$0.359079\pi$
$840$	23.3370	+	16.9553i	0.805202	+	0.585014i
$841$	−2.49761	−	7.68685i	−0.0861245	−	0.265064i
$842$	10.5152	+	32.3623i	0.362376	+	1.11528i
$843$	2.48795	+	1.80760i	0.0856897	+	0.0622572i
$844$	28.8326	−	20.9481i	0.992459	−	0.721064i
$845$	13.4688	−	41.4526i	0.463340	−	1.42601i
$846$	−0.569756			−0.0195886
$847$		0			0
$848$	44.3561			1.52319
$849$	3.62589	−	11.1593i	0.124440	−	0.382987i
$850$	15.9267	−	11.5714i	0.546282	−	0.396897i
$851$	−2.37196	−	1.72333i	−0.0813098	−	0.0590750i
$852$	11.0633	+	34.0494i	0.379023	+	1.16651i
$853$	−6.55124	−	20.1627i	−0.224310	−	0.690356i	−0.998361	−	0.0572325i	$-0.981772\pi$
$853$	−6.55124	−	20.1627i	−0.224310	−	0.690356i	0.774051	−	0.633124i	$-0.218228\pi$
$854$	−13.6864	−	9.94374i	−0.468338	−	0.340268i
$855$	−6.50911	+	4.72915i	−0.222607	+	0.161733i
$856$	10.5235	−	32.3879i	0.359684	−	1.10699i
$857$	9.45359			0.322929			0.161464	−	0.986879i	$-0.448378\pi$
$857$	9.45359			0.322929			0.161464	+	0.986879i	$0.448378\pi$
$858$		0			0
$859$	−38.8261			−1.32473			−0.662365	−	0.749181i	$-0.730447\pi$
$859$	−38.8261			−1.32473			−0.662365	+	0.749181i	$0.730447\pi$
$860$	38.1064	−	117.280i	1.29942	−	3.99920i
$861$	7.72732	−	5.61423i	0.263346	−	0.191332i
$862$	−56.2169	−	40.8440i	−1.91476	−	1.39115i
$863$	−11.6205	−	35.7641i	−0.395565	−	1.21742i	−0.928520	−	0.371281i	$-0.878919\pi$
$863$	−11.6205	−	35.7641i	−0.395565	−	1.21742i	0.532955	−	0.846144i	$-0.321081\pi$
$864$	−1.44427	−	4.44501i	−0.0491351	−	0.151222i
$865$	40.3723	+	29.3322i	1.37270	+	0.997324i
$866$	28.2967	−	20.5587i	0.961560	−	0.698614i
$867$	7.85344	−	24.1704i	0.266717	−	0.820870i
$868$	11.4223			0.387697
$869$		0			0
$870$	−63.2828			−2.14549
$871$	−1.24814	+	3.84137i	−0.0422915	+	0.130160i
$872$	17.1620	−	12.4689i	0.581179	−	0.422251i
$873$	−4.59159	−	3.33598i	−0.155402	−	0.112906i
$874$	30.8787	+	95.0350i	1.04449	+	3.21461i
$875$	−2.16209	−	6.65422i	−0.0730919	−	0.224954i
$876$	−35.8357	−	26.0361i	−1.21078	−	0.879680i
$877$	17.8053	−	12.9363i	0.601243	−	0.436829i	−0.245077	−	0.969504i	$-0.578813\pi$
$877$	17.8053	−	12.9363i	0.601243	−	0.436829i	0.846320	+	0.532675i	$0.178813\pi$
$878$	21.3574	−	65.7315i	0.720779	−	2.21833i
$879$	−5.29254			−0.178513
$880$		0			0
$881$	−6.92969			−0.233467			−0.116734	−	0.993163i	$-0.537242\pi$
$881$	−6.92969			−0.233467			−0.116734	+	0.993163i	$0.537242\pi$
$882$	0.291158	−	0.896093i	0.00980381	−	0.0301730i
$883$	−34.2528	+	24.8861i	−1.15270	+	0.837485i	−0.988837	−	0.148999i	$-0.952395\pi$
$883$	−34.2528	+	24.8861i	−1.15270	+	0.837485i	−0.163861	+	0.986483i	$0.552395\pi$
$884$	−2.45673	−	1.78492i	−0.0826287	−	0.0600332i
$885$	2.93642	+	9.03737i	0.0987066	+	0.303788i
$886$	−13.2153	−	40.6726i	−0.443978	−	1.36642i
$887$	6.51782	+	4.73547i	0.218847	+	0.159002i	0.691807	−	0.722082i	$-0.256815\pi$
$887$	6.51782	+	4.73547i	0.218847	+	0.159002i	−0.472961	+	0.881084i	$0.656815\pi$
$888$	2.96032	−	2.15080i	0.0993418	−	0.0721760i
$889$	2.46174	−	7.57645i	0.0825640	−	0.254106i
$890$	−5.97077			−0.200141
$891$		0			0
$892$	42.2072			1.41320
$893$	−1.13539	+	3.49436i	−0.0379943	+	0.116934i
$894$	10.2104	−	7.41832i	0.341488	−	0.248106i
$895$	−13.0814	−	9.50421i	−0.437264	−	0.317691i
$896$	5.80631	+	17.8700i	0.193975	+	0.596995i
$897$	2.17931	+	6.70722i	0.0727650	+	0.223948i
$898$	−58.9139	−	42.8035i	−1.96598	−	1.42837i
$899$	−10.3466	+	7.51726i	−0.345079	+	0.250715i
$900$	−3.38378	+	10.4142i	−0.112793	+	0.347140i
$901$	11.1697			0.372115
$902$		0			0
$903$	14.0902			0.468891
$904$	29.9168	−	92.0744i	0.995018	−	3.06235i
$905$	27.7886	−	20.1896i	0.923723	−	0.671124i
$906$	28.8286	+	20.9452i	0.957768	+	0.695859i
$907$	0.894385	+	2.75263i	0.0296976	+	0.0913997i	0.964807	−	0.262960i	$-0.0846988\pi$
$907$	0.894385	+	2.75263i	0.0296976	+	0.0913997i	−0.935109	+	0.354360i	$0.884699\pi$
$908$	16.7489	+	51.5478i	0.555832	+	1.71067i
$909$	−2.66360	−	1.93522i	−0.0883461	−	0.0641872i
$910$	−4.52285	+	3.28605i	−0.149931	+	0.108931i
$911$	−6.25759	+	19.2589i	−0.207323	+	0.638075i	0.792287	+	0.610149i	$0.208890\pi$
$911$	−6.25759	+	19.2589i	−0.207323	+	0.638075i	−0.999610	+	0.0279265i	$0.991110\pi$
$912$	−44.3956			−1.47008
$913$		0			0
$914$	23.9205			0.791220
$915$	−11.8877	+	36.5867i	−0.392997	+	1.20952i
$916$	8.24915	−	5.99336i	0.272559	−	0.198026i
$917$	−3.88737	−	2.82434i	−0.128372	−	0.0932679i
$918$	−4.74330	−	14.5984i	−0.156552	−	0.481818i
$919$	−5.78669	−	17.8096i	−0.190885	−	0.587484i	0.809115	−	0.587651i	$-0.199947\pi$
$919$	−5.78669	−	17.8096i	−0.190885	−	0.587484i	−1.00000		0.000166260i	$0.999947\pi$
$920$	96.1597	+	69.8641i	3.17029	+	2.30335i
$921$	−41.3808	+	30.0649i	−1.36354	+	0.990672i
$922$	−14.6519	+	45.0939i	−0.482535	+	1.48509i
$923$	−3.54128			−0.116563
$924$		0			0
$925$	−3.08632			−0.101478
$926$	−15.6513	+	48.1697i	−0.514333	+	1.58295i
$927$	−0.288300	+	0.209462i	−0.00946901	+	0.00687964i
$928$	3.16026	+	2.29606i	0.103741	+	0.0753720i
$929$	−13.9892	−	43.0544i	−0.458971	−	1.41257i	−0.866409	−	0.499336i	$-0.833577\pi$
$929$	−13.9892	−	43.0544i	−0.458971	−	1.41257i	0.407437	−	0.913233i	$-0.366423\pi$
$930$	−11.9563	−	36.7978i	−0.392063	−	1.20665i
$931$	−4.91560	−	3.57140i	−0.161102	−	0.117048i
$932$	−31.7374	+	23.0586i	−1.03959	+	0.755309i
$933$	4.51914	−	13.9085i	0.147950	−	0.455344i
$934$	−83.0584			−2.71775
$935$		0			0
$936$	1.28415			0.0419738
$937$	−9.10361	+	28.0180i	−0.297402	+	0.915309i	0.685002	+	0.728541i	$0.259801\pi$
$937$	−9.10361	+	28.0180i	−0.297402	+	0.915309i	−0.982404	+	0.186768i	$0.940199\pi$
$938$	−12.3295	+	8.95793i	−0.402574	+	0.292487i
$939$	18.9795	+	13.7894i	0.619372	+	0.450000i
$940$	2.64614	+	8.14397i	0.0863074	+	0.265627i
$941$	−17.9955	−	55.3844i	−0.586636	−	1.80548i	−0.592600	−	0.805497i	$-0.701898\pi$
$941$	−17.9955	−	55.3844i	−0.586636	−	1.80548i	0.00596369	−	0.999982i	$-0.498102\pi$
$942$	−3.68001	−	2.67368i	−0.119901	−	0.0871133i
$943$	31.8403	−	23.1333i	1.03686	−	0.753325i
$944$	2.36397	−	7.27557i	0.0769408	−	0.236800i
$945$	−18.9704			−0.617108
$946$		0			0
$947$	45.3642			1.47414			0.737069	−	0.675818i	$-0.236209\pi$
$947$	45.3642			1.47414			0.737069	+	0.675818i	$0.236209\pi$
$948$	5.41998	−	16.6810i	0.176033	−	0.541773i
$949$	3.54465	−	2.57534i	0.115064	−	0.0835991i
$950$	85.0994	+	61.8283i	2.76099	+	2.00598i
$951$	9.20869	+	28.3414i	0.298612	+	0.919034i
$952$	−1.80709	−	5.56166i	−0.0585683	−	0.180255i
$953$	−33.4428	−	24.2976i	−1.08332	−	0.787076i	−0.105059	−	0.994466i	$-0.533503\pi$
$953$	−33.4428	−	24.2976i	−1.08332	−	0.787076i	−0.978258	+	0.207390i	$0.933503\pi$
$954$	−7.48729	+	5.43984i	−0.242410	+	0.176121i
$955$	−10.6517	+	32.7825i	−0.344680	+	1.06082i
$956$	−22.7247			−0.734968
$957$		0			0
$958$	34.9555			1.12936
$959$	−6.76059	+	20.8070i	−0.218311	+	0.671892i
$960$	31.4245	−	22.8312i	1.01422	−	0.736874i
$961$	18.7535	+	13.6252i	0.604953	+	0.439524i
$962$	0.219145	+	0.674458i	0.00706551	+	0.0217454i
$963$	0.781635	+	2.40562i	0.0251878	+	0.0775202i
$964$	49.6383	+	36.0643i	1.59874	+	1.16155i
$965$	−10.3958	+	7.55301i	−0.334653	+	0.243140i
$966$	−8.22295	+	25.3076i	−0.264569	+	0.814260i
$967$	6.52818			0.209932			0.104966	−	0.994476i	$-0.466527\pi$
$967$	6.52818			0.209932			0.104966	+	0.994476i	$0.466527\pi$
$968$		0			0
$969$	−11.1796			−0.359140
$970$	−39.2649	+	120.845i	−1.26072	+	3.88010i
$971$	−23.3472	+	16.9627i	−0.749246	+	0.544359i	−0.895593	−	0.444874i	$-0.853248\pi$
$971$	−23.3472	+	16.9627i	−0.749246	+	0.544359i	0.146347	+	0.989233i	$0.453248\pi$
$972$	13.0344	+	9.47006i	0.418079	+	0.303752i
$973$	6.12278	+	18.8440i	0.196287	+	0.604110i
$974$	−21.1463	−	65.0815i	−0.677570	−	2.08535i
$975$	6.00600	+	4.36362i	0.192346	+	0.139748i
$976$	25.0553	−	18.2037i	0.802000	−	0.582687i
$977$	−2.77637	+	8.54479i	−0.0888240	+	0.273372i	−0.985595	−	0.169123i	$-0.945907\pi$
$977$	−2.77637	+	8.54479i	−0.0888240	+	0.273372i	0.896771	+	0.442495i	$0.145907\pi$
$978$	−20.2248			−0.646718
$979$		0			0
$980$	−14.1608			−0.452350
$981$	−0.486898	+	1.49852i	−0.0155455	+	0.0478440i
$982$	6.87085	−	4.99197i	0.219258	−	0.159300i
$983$	−29.8381	−	21.6786i	−0.951687	−	0.691441i	−0.000481513	−	1.00000i	$-0.500153\pi$
$983$	−29.8381	−	21.6786i	−0.951687	−	0.691441i	−0.951205	+	0.308559i	$0.900153\pi$
$984$	15.1786	+	46.7151i	0.483878	+	1.48922i
$985$	6.34178	+	19.5180i	0.202066	+	0.621895i
$986$	10.3790	+	7.54077i	0.330534	+	0.240147i
$987$	−0.791567	+	0.575107i	−0.0251959	+	0.0183059i
$988$	5.01397	−	15.4314i	0.159516	−	0.490938i
$989$	58.0583			1.84615
$990$		0			0
$991$	−2.98352			−0.0947746			−0.0473873	−	0.998877i	$-0.515089\pi$
$991$	−2.98352			−0.0947746			−0.0473873	+	0.998877i	$0.515089\pi$
$992$	−0.738036	+	2.27144i	−0.0234327	+	0.0721183i
$993$	−8.47789	+	6.15955i	−0.269038	+	0.195467i
$994$	−10.8100	−	7.85396i	−0.342874	−	0.249112i
$995$	−12.3028	−	37.8641i	−0.390025	−	1.20037i
$996$	13.6770	+	42.0934i	0.433372	+	1.33378i
$997$	50.8510	+	36.9454i	1.61047	+	1.17007i	0.862010	+	0.506891i	$0.169205\pi$
$997$	50.8510	+	36.9454i	1.61047	+	1.17007i	0.748458	+	0.663182i	$0.230795\pi$
$998$	−5.16714	+	3.75415i	−0.163563	+	0.118836i
$999$	−0.743624	+	2.28864i	−0.0235272	+	0.0724093i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.s.372.1		8
11.2	odd	10		77.2.f.a.36.1	yes	8
11.3	even	5		847.2.f.q.323.2		8
11.4	even	5		847.2.a.k.1.1		4
11.5	even	5	inner	847.2.f.s.148.1		8
11.6	odd	10		847.2.f.p.148.2		8
11.7	odd	10		847.2.a.l.1.4		4
11.8	odd	10		77.2.f.a.15.1	✓	8
11.9	even	5		847.2.f.q.729.2		8
11.10	odd	2		847.2.f.p.372.2		8
33.2	even	10		693.2.m.g.190.2		8
33.8	even	10		693.2.m.g.631.2		8
33.26	odd	10		7623.2.a.co.1.4		4
33.29	even	10		7623.2.a.ch.1.1		4
77.2	odd	30		539.2.q.c.410.2		16
77.13	even	10		539.2.f.d.344.1		8
77.19	even	30		539.2.q.b.312.1		16
77.24	even	30		539.2.q.b.520.1		16
77.30	odd	30		539.2.q.c.312.1		16
77.41	even	10		539.2.f.d.246.1		8
77.46	odd	30		539.2.q.c.520.1		16
77.48	odd	10		5929.2.a.bb.1.1		4
77.52	even	30		539.2.q.b.422.2		16
77.62	even	10		5929.2.a.bi.1.4		4
77.68	even	30		539.2.q.b.410.2		16
77.74	odd	30		539.2.q.c.422.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.a.15.1	✓	8	11.8	odd	10
77.2.f.a.36.1	yes	8	11.2	odd	10
539.2.f.d.246.1		8	77.41	even	10
539.2.f.d.344.1		8	77.13	even	10
539.2.q.b.312.1		16	77.19	even	30
539.2.q.b.410.2		16	77.68	even	30
539.2.q.b.422.2		16	77.52	even	30
539.2.q.b.520.1		16	77.24	even	30
539.2.q.c.312.1		16	77.30	odd	30
539.2.q.c.410.2		16	77.2	odd	30
539.2.q.c.422.2		16	77.74	odd	30
539.2.q.c.520.1		16	77.46	odd	30
693.2.m.g.190.2		8	33.2	even	10
693.2.m.g.631.2		8	33.8	even	10
847.2.a.k.1.1		4	11.4	even	5
847.2.a.l.1.4		4	11.7	odd	10
847.2.f.p.148.2		8	11.6	odd	10
847.2.f.p.372.2		8	11.10	odd	2
847.2.f.q.323.2		8	11.3	even	5
847.2.f.q.729.2		8	11.9	even	5
847.2.f.s.148.1		8	11.5	even	5	inner
847.2.f.s.372.1		8	1.1	even	1	trivial
5929.2.a.bb.1.1		4	77.48	odd	10
5929.2.a.bi.1.4		4	77.62	even	10
7623.2.a.ch.1.1		4	33.29	even	10
7623.2.a.co.1.4		4	33.26	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.762262 + 2.34600i) q^{2} +(1.30902 - 0.951057i) q^{3} +(-3.30464 - 2.40097i) q^{4} +(-1.07128 - 3.29706i) q^{5} +(1.23337 + 3.79591i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(4.16042 - 3.02272i) q^{8} +(-0.118034 + 0.363271i) q^{9} +O(q^{10})\)	\(q+(-0.762262 + 2.34600i) q^{2} +(1.30902 - 0.951057i) q^{3} +(-3.30464 - 2.40097i) q^{4} +(-1.07128 - 3.29706i) q^{5} +(1.23337 + 3.79591i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(4.16042 - 3.02272i) q^{8} +(-0.118034 + 0.363271i) q^{9} +8.55150 q^{10} -6.60929 q^{12} +(0.202020 - 0.621755i) q^{13} +(1.99563 - 1.44991i) q^{14} +(-4.53801 - 3.29706i) q^{15} +(1.39545 + 4.29476i) q^{16} +(0.351400 + 1.08150i) q^{17} +(-0.762262 - 0.553816i) q^{18} +(-4.91560 + 3.57140i) q^{19} +(-4.37592 + 13.4677i) q^{20} -1.61803 q^{21} -6.66708 q^{23} +(2.57128 - 7.91358i) q^{24} +(-5.67787 + 4.12521i) q^{25} +(1.30464 + 0.947880i) q^{26} +(1.69098 + 5.20431i) q^{27} +(1.26226 + 3.88484i) q^{28} +(-3.70010 - 2.68828i) q^{29} +(11.1941 - 8.13296i) q^{30} +(0.864107 - 2.65945i) q^{31} -0.854102 q^{32} -2.80505 q^{34} +(-1.07128 + 3.29706i) q^{35} +(1.26226 - 0.917087i) q^{36} +(0.355772 + 0.258483i) q^{37} +(-4.63152 - 14.2544i) q^{38} +(-0.326876 - 1.00602i) q^{39} +(-14.4230 - 10.4790i) q^{40} +(-4.77575 + 3.46978i) q^{41} +(1.23337 - 3.79591i) q^{42} -8.70820 q^{43} +1.32417 q^{45} +(5.08206 - 15.6410i) q^{46} +(0.489215 - 0.355436i) q^{47} +(5.91123 + 4.29476i) q^{48} +(0.309017 + 0.951057i) q^{49} +(-5.34973 - 16.4648i) q^{50} +(1.48855 + 1.08150i) q^{51} +(-2.16042 + 1.56963i) q^{52} +(3.03531 - 9.34172i) q^{53} -13.4983 q^{54} -5.14256 q^{56} +(-3.03801 + 9.35004i) q^{57} +(9.12715 - 6.63126i) q^{58} +(-1.37052 - 0.995741i) q^{59} +(7.08039 + 21.7912i) q^{60} +(-2.11930 - 6.52252i) q^{61} +(5.58039 + 4.05439i) q^{62} +(0.309017 - 0.224514i) q^{63} +(-2.13986 + 6.58580i) q^{64} -2.26638 q^{65} -6.17828 q^{67} +(1.43539 - 4.41766i) q^{68} +(-8.72732 + 6.34077i) q^{69} +(-6.91831 - 5.02644i) q^{70} +(-1.67390 - 5.15175i) q^{71} +(0.606997 + 1.86814i) q^{72} +(5.42202 + 3.93933i) q^{73} +(-0.877594 + 0.637609i) q^{74} +(-3.50911 + 10.7999i) q^{75} +24.8191 q^{76} +2.60929 q^{78} +(-0.820054 + 2.52387i) q^{79} +(12.6652 - 9.20178i) q^{80} +(6.23607 + 4.53077i) q^{81} +(-4.49975 - 13.8488i) q^{82} +(-2.06936 - 6.36882i) q^{83} +(5.34703 + 3.88484i) q^{84} +(3.18931 - 2.31717i) q^{85} +(6.63793 - 20.4295i) q^{86} -7.40020 q^{87} -0.698213 q^{89} +(-1.00937 + 3.10651i) q^{90} +(-0.528896 + 0.384266i) q^{91} +(22.0323 + 16.0074i) q^{92} +(-1.39815 - 4.30308i) q^{93} +(0.460942 + 1.41863i) q^{94} +(17.0411 + 12.3811i) q^{95} +(-1.11803 + 0.812299i) q^{96} +(-4.59159 + 14.1315i) q^{97} -2.46673 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 6 q^{3} - 7 q^{4} + 3 q^{5} + 2 q^{6} - 2 q^{7} + 12 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + q^2 + 6 * q^3 - 7 * q^4 + 3 * q^5 + 2 * q^6 - 2 * q^7 + 12 * q^8 + 8 * q^9	\( 8 q + q^{2} + 6 q^{3} - 7 q^{4} + 3 q^{5} + 2 q^{6} - 2 q^{7} + 12 q^{8} + 8 q^{9} + 28 q^{10} - 14 q^{12} + 5 q^{13} + q^{14} - 9 q^{15} + 7 q^{16} - 14 q^{17} + q^{18} - 6 q^{19} - 4 q^{20} - 4 q^{21} - 16 q^{23} + 9 q^{24} - 5 q^{25} - 9 q^{26} + 18 q^{27} + 3 q^{28} - 6 q^{29} + 26 q^{30} + 14 q^{31} + 20 q^{32} - 24 q^{34} + 3 q^{35} + 3 q^{36} + q^{37} - 15 q^{38} - 29 q^{40} - 18 q^{41} + 2 q^{42} - 16 q^{43} + 18 q^{45} + 26 q^{46} + 7 q^{47} - q^{48} - 2 q^{49} - q^{50} - 8 q^{51} + 4 q^{52} + 7 q^{53} - 4 q^{54} - 18 q^{56} + 3 q^{57} + 36 q^{58} + 17 q^{60} - 12 q^{61} + 5 q^{62} - 2 q^{63} - 4 q^{64} - 24 q^{65} - 30 q^{67} + 7 q^{68} - 22 q^{69} - 12 q^{70} + 21 q^{71} - 3 q^{72} - 8 q^{73} - q^{74} + 52 q^{76} - 18 q^{78} - q^{79} + 37 q^{80} + 32 q^{81} - 34 q^{82} + 22 q^{83} + 11 q^{84} + 5 q^{85} + 13 q^{86} - 12 q^{87} - 34 q^{89} + 18 q^{90} - 5 q^{91} + 51 q^{92} + 3 q^{93} - 50 q^{94} + 41 q^{95} - 15 q^{97} - 4 q^{98}+O(q^{100}) \) 8 * q + q^2 + 6 * q^3 - 7 * q^4 + 3 * q^5 + 2 * q^6 - 2 * q^7 + 12 * q^8 + 8 * q^9 + 28 * q^10 - 14 * q^12 + 5 * q^13 + q^14 - 9 * q^15 + 7 * q^16 - 14 * q^17 + q^18 - 6 * q^19 - 4 * q^20 - 4 * q^21 - 16 * q^23 + 9 * q^24 - 5 * q^25 - 9 * q^26 + 18 * q^27 + 3 * q^28 - 6 * q^29 + 26 * q^30 + 14 * q^31 + 20 * q^32 - 24 * q^34 + 3 * q^35 + 3 * q^36 + q^37 - 15 * q^38 - 29 * q^40 - 18 * q^41 + 2 * q^42 - 16 * q^43 + 18 * q^45 + 26 * q^46 + 7 * q^47 - q^48 - 2 * q^49 - q^50 - 8 * q^51 + 4 * q^52 + 7 * q^53 - 4 * q^54 - 18 * q^56 + 3 * q^57 + 36 * q^58 + 17 * q^60 - 12 * q^61 + 5 * q^62 - 2 * q^63 - 4 * q^64 - 24 * q^65 - 30 * q^67 + 7 * q^68 - 22 * q^69 - 12 * q^70 + 21 * q^71 - 3 * q^72 - 8 * q^73 - q^74 + 52 * q^76 - 18 * q^78 - q^79 + 37 * q^80 + 32 * q^81 - 34 * q^82 + 22 * q^83 + 11 * q^84 + 5 * q^85 + 13 * q^86 - 12 * q^87 - 34 * q^89 + 18 * q^90 - 5 * q^91 + 51 * q^92 + 3 * q^93 - 50 * q^94 + 41 * q^95 - 15 * q^97 - 4 * q^98

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