LMFDB - Embedded newform 847.2.f.w.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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} + \cdots + 25 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 86x^12 - 145x^11 + 245x^10 - 245x^9 + 640x^8 - 1175x^7 + 2135x^6 - 2300x^5 + 1850x^4 - 925x^3 + 700x^2 - 200*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			323.1
Root			$-0.788594 - 2.42704i$ of defining polynomial
Character	$\chi$	$=$	847.323
Dual form			847.2.f.w.729.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.06456 - 1.49999i) q^{2} +(-0.126882 + 0.390502i) q^{3} +(1.39441 + 4.29156i) q^{4} +(-2.77410 + 2.01550i) q^{5} +(0.847707 - 0.615895i) q^{6} +(0.309017 + 0.951057i) q^{7} +(1.98127 - 6.09772i) q^{8} +(2.29066 + 1.66426i) q^{9} +O(q^{10})$	\(q+(-2.06456 - 1.49999i) q^{2} +(-0.126882 + 0.390502i) q^{3} +(1.39441 + 4.29156i) q^{4} +(-2.77410 + 2.01550i) q^{5} +(0.847707 - 0.615895i) q^{6} +(0.309017 + 0.951057i) q^{7} +(1.98127 - 6.09772i) q^{8} +(2.29066 + 1.66426i) q^{9} +8.75055 q^{10} -1.85279 q^{12} +(1.75964 + 1.27845i) q^{13} +(0.788594 - 2.42704i) q^{14} +(-0.435075 - 1.33902i) q^{15} +(-5.93578 + 4.31259i) q^{16} +(3.65445 - 2.65511i) q^{17} +(-2.23283 - 6.87195i) q^{18} +(-0.748999 + 2.30518i) q^{19} +(-12.5179 - 9.09477i) q^{20} -0.410598 q^{21} +0.648403 q^{23} +(2.12979 + 1.54738i) q^{24} +(2.08830 - 6.42713i) q^{25} +(-1.71522 - 5.27889i) q^{26} +(-1.93708 + 1.40737i) q^{27} +(-3.65062 + 2.65233i) q^{28} +(-0.387183 - 1.19163i) q^{29} +(-1.11029 + 3.41711i) q^{30} +(6.50406 + 4.72548i) q^{31} +5.90061 q^{32} -11.5275 q^{34} +(-2.77410 - 2.01550i) q^{35} +(-3.94815 + 12.1512i) q^{36} +(1.54919 + 4.76792i) q^{37} +(5.00411 - 3.63570i) q^{38} +(-0.722504 + 0.524930i) q^{39} +(6.79373 + 20.9090i) q^{40} +(-0.810151 + 2.49339i) q^{41} +(0.847707 + 0.615895i) q^{42} -1.46138 q^{43} -9.70884 q^{45} +(-1.33867 - 0.972600i) q^{46} +(-1.55757 + 4.79369i) q^{47} +(-0.930935 - 2.86512i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-13.9521 + 10.1368i) q^{50} +(0.573144 + 1.76396i) q^{51} +(-3.03289 + 9.33427i) q^{52} +(-10.8392 - 7.87516i) q^{53} +6.11028 q^{54} +6.41153 q^{56} +(-0.805144 - 0.584971i) q^{57} +(-0.988069 + 3.04096i) q^{58} +(2.37009 + 7.29440i) q^{59} +(5.13982 - 3.73430i) q^{60} +(-11.5971 + 8.42580i) q^{61} +(-6.33987 - 19.5121i) q^{62} +(-0.874954 + 2.69283i) q^{63} +(-0.310639 - 0.225693i) q^{64} -7.45814 q^{65} +6.22696 q^{67} +(16.4904 + 11.9810i) q^{68} +(-0.0822705 + 0.253203i) q^{69} +(2.70407 + 8.32227i) q^{70} +(-3.42211 + 2.48631i) q^{71} +(14.6866 - 10.6704i) q^{72} +(-1.83098 - 5.63517i) q^{73} +(3.95345 - 12.1675i) q^{74} +(2.24484 + 1.63097i) q^{75} -10.9372 q^{76} +2.27905 q^{78} +(-7.89858 - 5.73865i) q^{79} +(7.77440 - 23.9271i) q^{80} +(2.32106 + 7.14349i) q^{81} +(5.41268 - 3.93254i) q^{82} +(6.77759 - 4.92421i) q^{83} +(-0.572543 - 1.76211i) q^{84} +(-4.78643 + 14.7311i) q^{85} +(3.01711 + 2.19206i) q^{86} +0.514460 q^{87} +4.76249 q^{89} +(20.0445 + 14.5632i) q^{90} +(-0.672122 + 2.06858i) q^{91} +(0.904140 + 2.78266i) q^{92} +(-2.67056 + 1.94027i) q^{93} +(10.4062 - 7.56055i) q^{94} +(-2.56830 - 7.90441i) q^{95} +(-0.748680 + 2.30420i) q^{96} +(7.04306 + 5.11708i) q^{97} +2.55194 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} - 2 q^{6} - 4 q^{7} + 5 q^{8} - 2 q^{9}+O(q^{10}) $ 16 * q + 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 - 2 * q^6 - 4 * q^7 + 5 * q^8 - 2 * q^9	\( 16 q + 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} - 2 q^{6} - 4 q^{7} + 5 q^{8} - 2 q^{9} + 12 q^{10} + 18 q^{12} + 13 q^{13} - 3 q^{14} + 7 q^{15} - 18 q^{16} + 10 q^{17} - 19 q^{18} - 6 q^{19} - 24 q^{20} + 8 q^{21} + 32 q^{23} + 45 q^{24} - 23 q^{25} + 33 q^{26} - 20 q^{27} - 11 q^{28} - 12 q^{29} + 38 q^{30} - 2 q^{31} + 32 q^{32} - 24 q^{34} - 5 q^{35} - 38 q^{36} - 11 q^{37} + 15 q^{38} - 24 q^{39} + 5 q^{40} + 20 q^{41} - 2 q^{42} - 8 q^{43} + 70 q^{45} + 38 q^{46} + 7 q^{47} + 39 q^{48} - 4 q^{49} - 58 q^{50} + 16 q^{51} + 8 q^{52} - 41 q^{53} + 60 q^{54} + 9 q^{57} - 5 q^{58} - 18 q^{59} + 25 q^{60} - 12 q^{61} - 61 q^{62} - 12 q^{63} - 3 q^{64} - 8 q^{65} - 38 q^{67} - 7 q^{68} - 30 q^{69} + 12 q^{70} + q^{71} + 35 q^{72} + 60 q^{73} - 4 q^{74} + 4 q^{75} + 52 q^{76} - 58 q^{78} - 15 q^{79} + 83 q^{80} + 6 q^{81} - 6 q^{82} + 20 q^{83} - 17 q^{84} - 9 q^{85} + 48 q^{86} - 72 q^{87} + 74 q^{89} + 16 q^{90} - 7 q^{91} + 20 q^{92} - 53 q^{93} + 66 q^{94} - 53 q^{95} + 48 q^{96} - 35 q^{97} + 2 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 - 2 * q^6 - 4 * q^7 + 5 * q^8 - 2 * q^9 + 12 * q^10 + 18 * q^12 + 13 * q^13 - 3 * q^14 + 7 * q^15 - 18 * q^16 + 10 * q^17 - 19 * q^18 - 6 * q^19 - 24 * q^20 + 8 * q^21 + 32 * q^23 + 45 * q^24 - 23 * q^25 + 33 * q^26 - 20 * q^27 - 11 * q^28 - 12 * q^29 + 38 * q^30 - 2 * q^31 + 32 * q^32 - 24 * q^34 - 5 * q^35 - 38 * q^36 - 11 * q^37 + 15 * q^38 - 24 * q^39 + 5 * q^40 + 20 * q^41 - 2 * q^42 - 8 * q^43 + 70 * q^45 + 38 * q^46 + 7 * q^47 + 39 * q^48 - 4 * q^49 - 58 * q^50 + 16 * q^51 + 8 * q^52 - 41 * q^53 + 60 * q^54 + 9 * q^57 - 5 * q^58 - 18 * q^59 + 25 * q^60 - 12 * q^61 - 61 * q^62 - 12 * q^63 - 3 * q^64 - 8 * q^65 - 38 * q^67 - 7 * q^68 - 30 * q^69 + 12 * q^70 + q^71 + 35 * q^72 + 60 * q^73 - 4 * q^74 + 4 * q^75 + 52 * q^76 - 58 * q^78 - 15 * q^79 + 83 * q^80 + 6 * q^81 - 6 * q^82 + 20 * q^83 - 17 * q^84 - 9 * q^85 + 48 * q^86 - 72 * q^87 + 74 * q^89 + 16 * q^90 - 7 * q^91 + 20 * q^92 - 53 * q^93 + 66 * q^94 - 53 * q^95 + 48 * q^96 - 35 * q^97 + 2 * 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 $

$2$	−2.06456	−	1.49999i	−1.45987	−	1.06066i	−0.983397	−	0.181466i	$-0.941916\pi$
$2$	−2.06456	−	1.49999i	−1.45987	−	1.06066i	−0.476470	−	0.879190i	$-0.658084\pi$
$3$	−0.126882	+	0.390502i	−0.0732553	+	0.225457i	−0.980980	−	0.194110i	$-0.937818\pi$
$3$	−0.126882	+	0.390502i	−0.0732553	+	0.225457i	0.907724	+	0.419567i	$0.137818\pi$
$4$	1.39441	+	4.29156i	0.697206	+	2.14578i
$5$	−2.77410	+	2.01550i	−1.24062	+	0.901360i	−0.997639	−	0.0686724i	$-0.978124\pi$
$5$	−2.77410	+	2.01550i	−1.24062	+	0.901360i	−0.242976	+	0.970032i	$0.578124\pi$
$6$	0.847707	−	0.615895i	0.346075	−	0.251438i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$8$	1.98127	−	6.09772i	0.700485	−	2.15587i
$9$	2.29066	+	1.66426i	0.763553	+	0.554754i
$10$	8.75055			2.76717
$11$		0			0
$11$		0			0
$12$	−1.85279			−0.534854
$13$	1.75964	+	1.27845i	0.488036	+	0.354579i	0.804428	−	0.594050i	$-0.202472\pi$
$13$	1.75964	+	1.27845i	0.488036	+	0.354579i	−0.316393	+	0.948628i	$0.602472\pi$
$14$	0.788594	−	2.42704i	0.210760	−	0.648654i
$15$	−0.435075	−	1.33902i	−0.112336	−	0.345734i
$16$	−5.93578	+	4.31259i	−1.48394	+	1.07815i
$17$	3.65445	−	2.65511i	0.886334	−	0.643960i	−0.0485852	−	0.998819i	$-0.515471\pi$
$17$	3.65445	−	2.65511i	0.886334	−	0.643960i	0.934920	+	0.354859i	$0.115471\pi$
$18$	−2.23283	−	6.87195i	−0.526283	−	1.61973i
$19$	−0.748999	+	2.30518i	−0.171832	+	0.528845i	−0.999475	−	0.0324108i	$-0.989682\pi$
$19$	−0.748999	+	2.30518i	−0.171832	+	0.528845i	0.827643	+	0.561256i	$0.189682\pi$
$20$	−12.5179	−	9.09477i	−2.79908	−	2.03365i
$21$	−0.410598			−0.0895999
$22$		0			0
$23$	0.648403			0.135201			0.0676006	−	0.997712i	$-0.478466\pi$
$23$	0.648403			0.135201			0.0676006	+	0.997712i	$0.478466\pi$
$24$	2.12979	+	1.54738i	0.434741	+	0.315858i
$25$	2.08830	−	6.42713i	0.417660	−	1.28543i
$26$	−1.71522	−	5.27889i	−0.336382	−	1.03528i
$27$	−1.93708	+	1.40737i	−0.372792	+	0.270849i
$28$	−3.65062	+	2.65233i	−0.689902	+	0.501243i
$29$	−0.387183	−	1.19163i	−0.0718981	−	0.221280i	0.908650	−	0.417559i	$-0.137114\pi$
$29$	−0.387183	−	1.19163i	−0.0718981	−	0.221280i	−0.980548	+	0.196279i	$0.937114\pi$
$30$	−1.11029	+	3.41711i	−0.202710	+	0.623876i
$31$	6.50406	+	4.72548i	1.16816	+	0.848721i	0.990788	−	0.135422i	$-0.0432390\pi$
$31$	6.50406	+	4.72548i	1.16816	+	0.848721i	0.177376	+	0.984143i	$0.443239\pi$
$32$	5.90061			1.04309
$33$		0			0
$34$	−11.5275			−1.97695
$35$	−2.77410	−	2.01550i	−0.468909	−	0.340682i
$36$	−3.94815	+	12.1512i	−0.658025	+	2.02519i
$37$	1.54919	+	4.76792i	0.254686	+	0.783842i	0.993891	+	0.110362i	$0.0352011\pi$
$37$	1.54919	+	4.76792i	0.254686	+	0.783842i	−0.739206	+	0.673480i	$0.764799\pi$
$38$	5.00411	−	3.63570i	0.811775	−	0.589789i
$39$	−0.722504	+	0.524930i	−0.115693	+	0.0840561i
$40$	6.79373	+	20.9090i	1.07418	+	3.30600i
$41$	−0.810151	+	2.49339i	−0.126524	+	0.389402i	−0.994176	−	0.107771i	$-0.965629\pi$
$41$	−0.810151	+	2.49339i	−0.126524	+	0.389402i	0.867651	+	0.497173i	$0.165629\pi$
$42$	0.847707	+	0.615895i	0.130804	+	0.0950347i
$43$	−1.46138			−0.222858			−0.111429	−	0.993772i	$-0.535543\pi$
$43$	−1.46138			−0.222858			−0.111429	+	0.993772i	$0.535543\pi$
$44$		0			0
$45$	−9.70884			−1.44731
$46$	−1.33867	−	0.972600i	−0.197376	−	0.143402i
$47$	−1.55757	+	4.79369i	−0.227194	+	0.699232i	0.770867	+	0.636996i	$0.219823\pi$
$47$	−1.55757	+	4.79369i	−0.227194	+	0.699232i	−0.998061	+	0.0622362i	$0.980177\pi$
$48$	−0.930935	−	2.86512i	−0.134369	−	0.413545i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	−13.9521	+	10.1368i	−1.97312	+	1.43356i
$51$	0.573144	+	1.76396i	0.0802562	+	0.247003i
$52$	−3.03289	+	9.33427i	−0.420586	+	1.29443i
$53$	−10.8392	−	7.87516i	−1.48888	−	1.08174i	−0.974556	−	0.224143i	$-0.928042\pi$
$53$	−10.8392	−	7.87516i	−1.48888	−	1.08174i	−0.514327	−	0.857594i	$-0.671958\pi$
$54$	6.11028			0.831504
$55$		0			0
$56$	6.41153			0.856776
$57$	−0.805144	−	0.584971i	−0.106644	−	0.0774813i
$58$	−0.988069	+	3.04096i	−0.129740	+	0.399298i
$59$	2.37009	+	7.29440i	0.308560	+	0.949649i	0.978325	+	0.207076i	$0.0663948\pi$
$59$	2.37009	+	7.29440i	0.308560	+	0.949649i	−0.669765	+	0.742573i	$0.733605\pi$
$60$	5.13982	−	3.73430i	0.663548	−	0.482096i
$61$	−11.5971	+	8.42580i	−1.48486	+	1.07881i	−0.508908	+	0.860821i	$0.669951\pi$
$61$	−11.5971	+	8.42580i	−1.48486	+	1.07881i	−0.975950	+	0.217992i	$0.930049\pi$
$62$	−6.33987	−	19.5121i	−0.805164	−	2.47804i
$63$	−0.874954	+	2.69283i	−0.110234	+	0.339265i
$64$	−0.310639	−	0.225693i	−0.0388299	−	0.0282116i
$65$	−7.45814			−0.925068
$66$		0			0
$67$	6.22696			0.760744			0.380372	−	0.924834i	$-0.375796\pi$
$67$	6.22696			0.760744			0.380372	+	0.924834i	$0.375796\pi$
$68$	16.4904	+	11.9810i	1.99975	+	1.45291i
$69$	−0.0822705	+	0.253203i	−0.00990421	+	0.0304820i
$70$	2.70407	+	8.32227i	0.323198	+	0.994701i
$71$	−3.42211	+	2.48631i	−0.406130	+	0.295071i	−0.772033	−	0.635582i	$-0.780760\pi$
$71$	−3.42211	+	2.48631i	−0.406130	+	0.295071i	0.365903	+	0.930653i	$0.380760\pi$
$72$	14.6866	−	10.6704i	1.73083	−	1.25752i
$73$	−1.83098	−	5.63517i	−0.214300	−	0.659547i	−0.999203	−	0.0399280i	$-0.987287\pi$
$73$	−1.83098	−	5.63517i	−0.214300	−	0.659547i	0.784903	−	0.619619i	$-0.212713\pi$
$74$	3.95345	−	12.1675i	0.459579	−	1.41444i
$75$	2.24484	+	1.63097i	0.259212	+	0.188328i
$76$	−10.9372			−1.25459
$77$		0			0
$78$	2.27905			0.258051
$79$	−7.89858	−	5.73865i	−0.888660	−	0.645649i	0.0468685	−	0.998901i	$-0.485076\pi$
$79$	−7.89858	−	5.73865i	−0.888660	−	0.645649i	−0.935528	+	0.353252i	$0.885076\pi$
$80$	7.77440	−	23.9271i	0.869204	−	2.67514i
$81$	2.32106	+	7.14349i	0.257895	+	0.793721i
$82$	5.41268	−	3.93254i	0.597730	−	0.434277i
$83$	6.77759	−	4.92421i	0.743937	−	0.540502i	−0.150004	−	0.988685i	$-0.547929\pi$
$83$	6.77759	−	4.92421i	0.743937	−	0.540502i	0.893942	+	0.448183i	$0.147929\pi$
$84$	−0.572543	−	1.76211i	−0.0624695	−	0.192261i
$85$	−4.78643	+	14.7311i	−0.519161	+	1.59781i
$86$	3.01711	+	2.19206i	0.325344	+	0.236376i
$87$	0.514460			0.0551559
$88$		0			0
$89$	4.76249			0.504823			0.252412	−	0.967620i	$-0.418776\pi$
$89$	4.76249			0.504823			0.252412	+	0.967620i	$0.418776\pi$
$90$	20.0445	+	14.5632i	2.11288	+	1.53510i
$91$	−0.672122	+	2.06858i	−0.0704575	+	0.216846i
$92$	0.904140	+	2.78266i	0.0942631	+	0.290112i
$93$	−2.67056	+	1.94027i	−0.276924	+	0.201197i
$94$	10.4062	−	7.56055i	1.07332	−	0.779812i
$95$	−2.56830	−	7.90441i	−0.263502	−	0.810976i
$96$	−0.748680	+	2.30420i	−0.0764119	+	0.235172i
$97$	7.04306	+	5.11708i	0.715115	+	0.519561i	0.884820	−	0.465934i	$-0.154281\pi$
$97$	7.04306	+	5.11708i	0.715115	+	0.519561i	−0.169705	+	0.985495i	$0.554281\pi$
$98$	2.55194			0.257785
$99$		0			0
$100$	30.4943			3.04943
$101$	4.67177	+	3.39424i	0.464858	+	0.337739i	0.795434	−	0.606040i	$-0.207243\pi$
$101$	4.67177	+	3.39424i	0.464858	+	0.337739i	−0.330576	+	0.943779i	$0.607243\pi$
$102$	1.46263	−	4.50152i	0.144822	−	0.445716i
$103$	−1.43414	−	4.41383i	−0.141310	−	0.434908i	0.855208	−	0.518285i	$-0.173429\pi$
$103$	−1.43414	−	4.41383i	−0.141310	−	0.434908i	−0.996518	+	0.0833771i	$0.973429\pi$
$104$	11.2820	−	8.19683i	1.10629	−	0.803765i
$105$	1.13904	−	0.827562i	0.111159	−	0.0807617i
$106$	10.5656	+	32.5176i	1.02622	+	3.15839i
$107$	−1.24287	+	3.82517i	−0.120153	+	0.369793i	−0.992987	−	0.118224i	$-0.962280\pi$
$107$	−1.24287	+	3.82517i	−0.120153	+	0.369793i	0.872834	+	0.488018i	$0.162280\pi$
$108$	−8.74091	−	6.35064i	−0.841095	−	0.611091i
$109$	−6.14762			−0.588835			−0.294418	−	0.955677i	$-0.595126\pi$
$109$	−6.14762			−0.588835			−0.294418	+	0.955677i	$0.595126\pi$
$110$		0			0
$111$	−2.05845			−0.195379
$112$	−5.93578	−	4.31259i	−0.560878	−	0.407502i
$113$	−0.765858	+	2.35707i	−0.0720458	+	0.221734i	−0.980595	−	0.196043i	$-0.937191\pi$
$113$	−0.765858	+	2.35707i	−0.0720458	+	0.221734i	0.908549	+	0.417777i	$0.137191\pi$
$114$	0.784818	+	2.41542i	0.0735050	+	0.226225i
$115$	−1.79873	+	1.30686i	−0.167733	+	0.121865i
$116$	4.57404	−	3.32324i	0.424689	−	0.308555i
$117$	1.90305	+	5.85699i	0.175937	+	0.541479i
$118$	6.04834	−	18.6149i	0.556795	−	1.71364i
$119$	3.65445	+	2.65511i	0.335003	+	0.243394i
$120$	−9.02699			−0.824048
$121$		0			0
$122$	36.5817			3.31195
$123$	−0.870880	−	0.632732i	−0.0785246	−	0.0570515i
$124$	−11.2103	+	34.5018i	−1.00672	+	3.09835i
$125$	1.86267	+	5.73272i	0.166602	+	0.512750i
$126$	5.84563	−	4.24710i	0.520770	−	0.378361i
$127$	5.62588	−	4.08744i	0.499216	−	0.362702i	−0.309501	−	0.950899i	$-0.600162\pi$
$127$	5.62588	−	4.08744i	0.499216	−	0.362702i	0.808718	+	0.588197i	$0.200162\pi$
$128$	−3.34398	−	10.2917i	−0.295569	−	0.909668i
$129$	0.185423	−	0.570672i	0.0163255	−	0.0502449i
$130$	15.3978	+	11.1872i	1.35048	+	0.981179i
$131$	−20.9388			−1.82943			−0.914715	−	0.404101i	$-0.867585\pi$
$131$	−20.9388			−1.82943			−0.914715	+	0.404101i	$0.867585\pi$
$132$		0			0
$133$	−2.42381			−0.210171
$134$	−12.8560	−	9.34040i	−1.11059	−	0.806888i
$135$	2.53710	−	7.80839i	0.218359	−	0.672039i
$136$	−8.94969	−	27.5443i	−0.767430	−	2.36191i
$137$	−7.39154	+	5.37027i	−0.631502	+	0.458813i	−0.856920	−	0.515449i	$-0.827625\pi$
$137$	−7.39154	+	5.37027i	−0.631502	+	0.458813i	0.225419	+	0.974262i	$0.427625\pi$
$138$	0.549655	−	0.399348i	0.0467898	−	0.0339947i
$139$	3.32251	+	10.2256i	0.281811	+	0.867326i	0.987336	+	0.158641i	$0.0507113\pi$
$139$	3.32251	+	10.2256i	0.281811	+	0.867326i	−0.705525	+	0.708685i	$0.749289\pi$
$140$	4.78140	−	14.7156i	0.404102	−	1.24370i
$141$	−1.67432	−	1.21647i	−0.141003	−	0.102445i
$142$	10.7946			0.905865
$143$		0			0
$144$	−20.7741			−1.73118
$145$	3.47581	+	2.52533i	0.288651	+	0.209717i
$146$	−4.67255	+	14.3806i	−0.386703	+	1.19015i
$147$	−0.126882	−	0.390502i	−0.0104650	−	0.0322081i
$148$	−18.3016	+	13.2969i	−1.50438	+	1.09300i
$149$	−8.70132	+	6.32188i	−0.712840	+	0.517908i	−0.884089	−	0.467319i	$-0.845220\pi$
$149$	−8.70132	+	6.32188i	−0.712840	+	0.517908i	0.171249	+	0.985228i	$0.445220\pi$
$150$	−2.18817	−	6.73449i	−0.178663	−	0.549869i
$151$	−2.36838	+	7.28911i	−0.192736	+	0.593179i	0.807260	+	0.590196i	$0.200950\pi$
$151$	−2.36838	+	7.28911i	−0.192736	+	0.593179i	−0.999996	+	0.00298318i	$0.999050\pi$
$152$	12.5724	+	9.13437i	1.01976	+	0.740896i
$153$	12.7899			1.03400
$154$		0			0
$155$	−27.5671			−2.21425
$156$	−3.26024	−	2.36870i	−0.261028	−	0.189648i
$157$	5.67016	−	17.4510i	0.452528	−	1.39274i	−0.421485	−	0.906835i	$-0.638491\pi$
$157$	5.67016	−	17.4510i	0.452528	−	1.39274i	0.874013	−	0.485903i	$-0.161509\pi$
$158$	7.69918	+	23.6956i	0.612514	+	1.88512i
$159$	4.45057	−	3.23353i	0.352953	−	0.256435i
$160$	−16.3689	+	11.8927i	−1.29407	+	0.940200i
$161$	0.200367	+	0.616668i	0.0157912	+	0.0486002i
$162$	5.92321	−	18.2298i	0.465371	−	1.43227i
$163$	−0.305473	−	0.221939i	−0.0239265	−	0.0173836i	0.575758	−	0.817620i	$-0.304707\pi$
$163$	−0.305473	−	0.221939i	−0.0239265	−	0.0173836i	−0.599684	+	0.800237i	$0.704707\pi$
$164$	−11.8302			−0.923784
$165$		0			0
$166$	−21.3791			−1.65934
$167$	0.0923401	+	0.0670890i	0.00714549	+	0.00519150i	0.591352	−	0.806413i	$-0.298594\pi$
$167$	0.0923401	+	0.0670890i	0.00714549	+	0.00519150i	−0.584207	+	0.811605i	$0.698594\pi$
$168$	−0.813506	+	2.50371i	−0.0627634	+	0.193166i
$169$	−2.55533	−	7.86451i	−0.196564	−	0.604962i
$170$	31.9785	−	23.2337i	2.45264	−	1.78194i
$171$	−5.55212	+	4.03385i	−0.424581	+	0.308476i
$172$	−2.03777	−	6.27160i	−0.155378	−	0.478205i
$173$	−4.11024	+	12.6500i	−0.312496	+	0.961763i	0.664277	+	0.747486i	$0.268740\pi$
$173$	−4.11024	+	12.6500i	−0.312496	+	0.961763i	−0.976773	+	0.214277i	$0.931260\pi$
$174$	−1.06214	−	0.771686i	−0.0805203	−	0.0585014i
$175$	6.75788			0.510848
$176$		0			0
$177$	−3.14920			−0.236708
$178$	−9.83248	−	7.14371i	−0.736975	−	0.535444i
$179$	3.50456	−	10.7859i	0.261943	−	0.806177i	−0.730439	−	0.682978i	$-0.760685\pi$
$179$	3.50456	−	10.7859i	0.261943	−	0.806177i	0.992382	−	0.123199i	$-0.0393154\pi$
$180$	−13.5381	−	41.6660i	−1.00907	−	3.10560i
$181$	−9.51149	+	6.91050i	−0.706984	+	0.513654i	−0.882199	−	0.470876i	$-0.843938\pi$
$181$	−9.51149	+	6.91050i	−0.706984	+	0.513654i	0.175216	+	0.984530i	$0.443938\pi$
$182$	4.49050	−	3.26254i	0.332858	−	0.241835i
$183$	−1.81883	−	5.59778i	−0.134452	−	0.413800i
$184$	1.28466	−	3.95378i	0.0947065	−	0.291476i
$185$	−13.9074	−	10.1043i	−1.02249	−	0.742883i
$186$	8.42394			0.617673
$187$		0			0
$188$	−22.7443			−1.65880
$189$	−1.93708	−	1.40737i	−0.140902	−	0.102371i
$190$	−6.55415	+	20.1716i	−0.475488	+	1.46340i
$191$	−6.96351	−	21.4315i	−0.503862	−	1.55073i	−0.802676	−	0.596416i	$-0.796591\pi$
$191$	−6.96351	−	21.4315i	−0.503862	−	1.55073i	0.298814	−	0.954311i	$-0.403409\pi$
$192$	0.127548	−	0.0926690i	0.00920498	−	0.00668781i
$193$	−2.78563	+	2.02388i	−0.200514	+	0.145682i	−0.683511	−	0.729940i	$-0.739548\pi$
$193$	−2.78563	+	2.02388i	−0.200514	+	0.145682i	0.482997	+	0.875622i	$0.339548\pi$
$194$	−6.86526	−	21.1291i	−0.492897	−	1.51698i
$195$	0.946302	−	2.91242i	0.0677661	−	0.208563i
$196$	−3.65062	−	2.65233i	−0.260758	−	0.189452i
$197$	−2.18213			−0.155470			−0.0777352	−	0.996974i	$-0.524769\pi$
$197$	−2.18213			−0.155470			−0.0777352	+	0.996974i	$0.524769\pi$
$198$		0			0
$199$	2.33434			0.165477			0.0827386	−	0.996571i	$-0.473633\pi$
$199$	2.33434			0.165477			0.0827386	+	0.996571i	$0.473633\pi$
$200$	−35.0534	−	25.4678i	−2.47865	−	1.80084i
$201$	−0.790088	+	2.43164i	−0.0557285	+	0.171515i
$202$	−4.55383	−	14.0152i	−0.320406	−	0.986109i
$203$	1.01366	−	0.736466i	0.0711449	−	0.0516898i
$204$	−6.77092	+	4.91936i	−0.474059	+	0.344424i
$205$	−2.77799	−	8.54977i	−0.194023	−	0.597142i
$206$	−3.65985	+	11.2639i	−0.254994	+	0.784790i
$207$	1.48527	+	1.07911i	0.103233	+	0.0750034i
$208$	−15.9583			−1.10651
$209$		0			0
$210$	−3.59296			−0.247938
$211$	11.0575	+	8.03377i	0.761233	+	0.553068i	0.899288	−	0.437357i	$-0.144085\pi$
$211$	11.0575	+	8.03377i	0.761233	+	0.553068i	−0.138056	+	0.990424i	$0.544085\pi$
$212$	18.6824	−	57.4984i	1.28311	−	3.94901i
$213$	−0.536706	−	1.65181i	−0.0367745	−	0.113180i
$214$	8.30373	−	6.03301i	0.567631	−	0.412408i
$215$	4.05402	−	2.94541i	0.276482	−	0.200876i
$216$	4.74389	+	14.6002i	0.322781	+	0.993417i
$217$	−2.48433	+	7.64599i	−0.168647	+	0.519043i
$218$	12.6922	+	9.22140i	0.859622	+	0.624552i
$219$	2.43286			0.164398
$220$		0			0
$221$	9.82495			0.660897
$222$	4.24980	+	3.08766i	0.285228	+	0.207230i
$223$	−1.65900	+	5.10589i	−0.111095	+	0.341916i	−0.991113	−	0.133026i	$-0.957531\pi$
$223$	−1.65900	+	5.10589i	−0.111095	+	0.341916i	0.880017	+	0.474941i	$0.157531\pi$
$224$	1.82339	+	5.61181i	0.121830	+	0.374955i
$225$	15.4800	−	11.2469i	1.03200	−	0.749792i
$226$	5.11675	−	3.71754i	0.340361	−	0.247287i
$227$	3.27959	+	10.0935i	0.217674	+	0.669932i	0.998953	+	0.0457497i	$0.0145677\pi$
$227$	3.27959	+	10.0935i	0.217674	+	0.669932i	−0.781279	+	0.624182i	$0.785432\pi$
$228$	1.38774	−	4.27101i	0.0919050	−	0.282855i
$229$	−18.3169	−	13.3080i	−1.21042	−	0.879419i	−0.215148	−	0.976581i	$-0.569023\pi$
$229$	−18.3169	−	13.3080i	−1.21042	−	0.879419i	−0.995269	+	0.0971622i	$0.969023\pi$
$230$	5.67388			0.374125
$231$		0			0
$232$	−8.03333			−0.527414
$233$	−11.9926	−	8.71311i	−0.785659	−	0.570815i	0.121013	−	0.992651i	$-0.461386\pi$
$233$	−11.9926	−	8.71311i	−0.785659	−	0.570815i	−0.906672	+	0.421836i	$0.861386\pi$
$234$	4.85648	−	14.9467i	0.317478	−	0.977097i
$235$	−5.34086	−	16.4375i	−0.348399	−	1.07226i
$236$	−27.9994	+	20.3428i	−1.82261	+	1.32420i
$237$	3.24314	−	2.35628i	0.210665	−	0.153057i
$238$	−3.56219	−	10.9633i	−0.230903	−	0.710646i
$239$	0.605456	−	1.86340i	0.0391637	−	0.120534i	−0.929563	−	0.368663i	$-0.879816\pi$
$239$	0.605456	−	1.86340i	0.0391637	−	0.120534i	0.968727	+	0.248129i	$0.0798157\pi$
$240$	8.35717	+	6.07184i	0.539453	+	0.391935i
$241$	0.790252			0.0509046			0.0254523	−	0.999676i	$-0.491897\pi$
$241$	0.790252			0.0509046			0.0254523	+	0.999676i	$0.491897\pi$
$242$		0			0
$243$	−10.2671			−0.658638
$244$	−52.3309	−	38.0207i	−3.35015	−	2.43402i
$245$	1.05961	−	3.26115i	0.0676961	−	0.208347i
$246$	0.848895	+	2.61263i	0.0541236	+	0.166575i
$247$	−4.26503	+	3.09873i	−0.271377	+	0.197167i
$248$	41.7010	−	30.2975i	2.64801	−	1.92389i
$249$	1.06296	+	3.27146i	0.0673624	+	0.207320i
$250$	4.75343	−	14.6296i	0.300633	−	0.925255i
$251$	16.6782	+	12.1174i	1.05272	+	0.764845i	0.972728	−	0.231950i	$-0.0745107\pi$
$251$	16.6782	+	12.1174i	1.05272	+	0.764845i	0.0799915	+	0.996796i	$0.474511\pi$
$252$	−12.7765			−0.804842
$253$		0			0
$254$	−17.7461			−1.11349
$255$	−5.14522	−	3.73822i	−0.322206	−	0.234096i
$256$	−8.77095	+	26.9942i	−0.548185	+	1.68714i
$257$	1.60059	+	4.92610i	0.0998419	+	0.307282i	0.988485	−	0.151317i	$-0.0483515\pi$
$257$	1.60059	+	4.92610i	0.0998419	+	0.307282i	−0.888643	+	0.458599i	$0.848351\pi$
$258$	−1.23882	+	0.900057i	−0.0771257	+	0.0560351i
$259$	−4.05584	+	2.94674i	−0.252018	+	0.183101i
$260$	−10.3997	−	32.0070i	−0.644963	−	1.98499i
$261$	1.09627	−	3.37398i	0.0678577	−	0.208844i
$262$	43.2295	+	31.4080i	2.67072	+	1.94039i
$263$	23.1920			1.43008			0.715041	−	0.699083i	$-0.246408\pi$
$263$	23.1920			1.43008			0.715041	+	0.699083i	$0.246408\pi$
$264$		0			0
$265$	45.9415			2.82217
$266$	5.00411	+	3.63570i	0.306822	+	0.222919i
$267$	−0.604274	+	1.85976i	−0.0369810	+	0.113816i
$268$	8.68294	+	26.7234i	0.530395	+	1.63239i
$269$	−15.0962	+	10.9681i	−0.920434	+	0.668735i	−0.943632	−	0.330996i	$-0.892615\pi$
$269$	−15.0962	+	10.9681i	−0.920434	+	0.668735i	0.0231978	+	0.999731i	$0.492615\pi$
$270$	−16.9505	+	12.3153i	−1.03158	+	0.749485i
$271$	9.34120	+	28.7493i	0.567437	+	1.74639i	0.660596	+	0.750742i	$0.270304\pi$
$271$	9.34120	+	28.7493i	0.567437	+	1.74639i	−0.0931585	+	0.995651i	$0.529696\pi$
$272$	−10.2416	+	31.5203i	−0.620987	+	1.91120i
$273$	−0.722504	−	0.524930i	−0.0437279	−	0.0317702i
$274$	23.3157			1.40855
$275$		0			0
$276$	−1.20135			−0.0723129
$277$	−10.9153	−	7.93044i	−0.655838	−	0.476494i	0.209417	−	0.977826i	$-0.432843\pi$
$277$	−10.9153	−	7.93044i	−0.655838	−	0.476494i	−0.865255	+	0.501332i	$0.832843\pi$
$278$	8.47885	−	26.0952i	0.508528	−	1.56509i
$279$	7.03416	+	21.6489i	0.421124	+	1.29609i
$280$	−17.7862	+	12.9224i	−1.06293	+	0.772264i
$281$	−6.55523	+	4.76266i	−0.391052	+	0.284116i	−0.765887	−	0.642976i	$-0.777700\pi$
$281$	−6.55523	+	4.76266i	−0.391052	+	0.284116i	0.374834	+	0.927092i	$0.377700\pi$
$282$	1.63205	+	5.02294i	0.0971874	+	0.299112i
$283$	3.08744	−	9.50217i	0.183529	−	0.564845i	−0.816391	−	0.577500i	$-0.804028\pi$
$283$	3.08744	−	9.50217i	0.183529	−	0.564845i	0.999920	+	0.0126548i	$0.00402826\pi$
$284$	−15.4420	−	11.2193i	−0.916313	−	0.665740i
$285$	3.41256			0.202143
$286$		0			0
$287$	−2.62170			−0.154754
$288$	13.5163	+	9.82015i	0.796455	+	0.578658i
$289$	1.05209	−	3.23800i	0.0618877	−	0.190471i
$290$	−3.38807	−	10.4274i	−0.198954	−	0.612318i
$291$	−2.89187	+	2.10107i	−0.169524	+	0.123167i
$292$	21.6305	−	15.7155i	1.26583	−	0.919680i
$293$	9.49598	+	29.2256i	0.554761	+	1.70738i	0.696574	+	0.717485i	$0.254707\pi$
$293$	9.49598	+	29.2256i	0.554761	+	1.70738i	−0.141813	+	0.989894i	$0.545293\pi$
$294$	−0.323795	+	0.996539i	−0.0188841	+	0.0581193i
$295$	−21.2767	−	15.4585i	−1.23878	−	0.900026i
$296$	32.1429			1.86827
$297$		0			0
$298$	27.4472			1.58997
$299$	1.14095	+	0.828952i	0.0659831	+	0.0479395i
$300$	−3.86918	+	11.9081i	−0.223387	+	0.687515i
$301$	−0.451591	−	1.38986i	−0.0260293	−	0.0801099i
$302$	15.8233	−	11.4963i	0.910528	−	0.661537i
$303$	−1.91822	+	1.39367i	−0.110199	+	0.0800641i
$304$	−5.49542	−	16.9132i	−0.315184	−	0.970037i
$305$	15.1894	−	46.7480i	0.869740	−	2.67678i
$306$	−26.4056	−	19.1848i	−1.50951	−	1.09672i
$307$	−20.0677			−1.14532			−0.572661	−	0.819792i	$-0.694089\pi$
$307$	−20.0677			−1.14532			−0.572661	+	0.819792i	$0.694089\pi$
$308$		0			0
$309$	1.90558			0.108405
$310$	56.9141	+	41.3505i	3.23251	+	2.34855i
$311$	−7.25146	+	22.3177i	−0.411193	+	1.26552i	0.504420	+	0.863458i	$0.331706\pi$
$311$	−7.25146	+	22.3177i	−0.411193	+	1.26552i	−0.915612	+	0.402062i	$0.868294\pi$
$312$	1.76940	+	5.44566i	0.100173	+	0.308300i
$313$	11.8707	−	8.62457i	0.670971	−	0.487489i	−0.199379	−	0.979922i	$-0.563892\pi$
$313$	11.8707	−	8.62457i	0.670971	−	0.487489i	0.870350	+	0.492433i	$0.163892\pi$
$314$	−37.8828	+	27.5234i	−2.13785	+	1.55324i
$315$	−3.00020	−	9.23365i	−0.169042	−	0.520257i
$316$	13.6139	−	41.8993i	0.765841	−	2.35702i
$317$	−14.6035	−	10.6101i	−0.820215	−	0.595921i	0.0965592	−	0.995327i	$-0.469216\pi$
$317$	−14.6035	−	10.6101i	−0.820215	−	0.595921i	−0.916774	+	0.399406i	$0.869216\pi$
$318$	−14.0388			−0.787255
$319$		0			0
$320$	1.31663			0.0736018
$321$	−1.33604	−	0.970689i	−0.0745704	−	0.0541786i
$322$	0.511326	−	1.57370i	0.0284951	−	0.0876989i
$323$	3.38334	+	10.4128i	0.188254	+	0.579386i
$324$	−27.4202	+	19.9219i	−1.52334	+	1.10677i
$325$	11.8914	−	8.63963i	0.659618	−	0.479240i
$326$	0.297761	+	0.916414i	0.0164915	+	0.0507555i
$327$	0.780022	−	2.40066i	0.0431353	−	0.132757i
$328$	13.5989	+	9.88016i	0.750872	+	0.545540i
$329$	−5.04039			−0.277886
$330$		0			0
$331$	−19.8300			−1.08996			−0.544979	−	0.838450i	$-0.683462\pi$
$331$	−19.8300			−1.08996			−0.544979	+	0.838450i	$0.683462\pi$
$332$	30.5833	+	22.2200i	1.67847	+	1.21948i
$333$	−4.38640	+	13.4999i	−0.240373	+	0.739792i
$334$	−0.0900090	−	0.277019i	−0.00492507	−	0.0151578i
$335$	−17.2742	+	12.5505i	−0.943791	+	0.685704i
$336$	2.43722	−	1.77074i	0.132961	−	0.0966020i
$337$	−6.02842	−	18.5536i	−0.328389	−	1.01068i	−0.969888	−	0.243553i	$-0.921687\pi$
$337$	−6.02842	−	18.5536i	−0.328389	−	1.01068i	0.641499	−	0.767124i	$-0.278313\pi$
$338$	−6.52107	+	20.0698i	−0.354699	+	1.09165i
$339$	−0.823267	−	0.598138i	−0.0447137	−	0.0324864i
$340$	−69.8936			−3.79051
$341$		0			0
$342$	17.5135			0.947020
$343$	−0.809017	−	0.587785i	−0.0436828	−	0.0317374i
$344$	−2.89539	+	8.91109i	−0.156109	+	0.480454i
$345$	−0.282104	−	0.868226i	−0.0151880	−	0.0467437i
$346$	27.4608	−	19.9515i	1.47630	−	1.07260i
$347$	23.0126	−	16.7196i	1.23538	−	0.897556i	0.238099	−	0.971241i	$-0.423476\pi$
$347$	23.0126	−	16.7196i	1.23538	−	0.897556i	0.997282	+	0.0736845i	$0.0234758\pi$
$348$	0.717368	+	2.20783i	0.0384550	+	0.118352i
$349$	6.20717	−	19.1037i	0.332262	−	1.02260i	−0.635793	−	0.771860i	$-0.719327\pi$
$349$	6.20717	−	19.1037i	0.332262	−	1.02260i	0.968055	−	0.250738i	$-0.0806731\pi$
$350$	−13.9521	−	10.1368i	−0.745770	−	0.541834i
$351$	−5.20782			−0.277973
$352$		0			0
$353$	8.99700			0.478862			0.239431	−	0.970913i	$-0.423039\pi$
$353$	8.99700			0.478862			0.239431	+	0.970913i	$0.423039\pi$
$354$	6.50172	+	4.72378i	0.345563	+	0.251066i
$355$	4.48212	−	13.7946i	0.237886	−	0.732139i
$356$	6.64088	+	20.4385i	0.351966	+	1.08324i
$357$	−1.50051	+	1.09019i	−0.0794155	+	0.0576987i
$358$	−23.4142	+	17.0114i	−1.23748	+	0.899081i
$359$	2.92516	+	9.00271i	0.154384	+	0.475145i	0.998098	−	0.0616480i	$-0.0196356\pi$
$359$	2.92516	+	9.00271i	0.154384	+	0.475145i	−0.843714	+	0.536793i	$0.819636\pi$
$360$	−19.2358	+	59.2018i	−1.01382	+	3.12021i
$361$	10.6185	+	7.71476i	0.558866	+	0.406040i
$362$	30.0028			1.57691
$363$		0			0
$364$	−9.81464			−0.514427
$365$	16.4370	+	11.9422i	0.860353	+	0.625083i
$366$	−4.64155	+	14.2852i	−0.242618	+	0.746700i
$367$	0.424939	+	1.30783i	0.0221817	+	0.0682681i	0.961535	−	0.274684i	$-0.0885732\pi$
$367$	0.424939	+	1.30783i	0.0221817	+	0.0682681i	−0.939353	+	0.342952i	$0.888573\pi$
$368$	−3.84877	+	2.79630i	−0.200631	+	0.145767i
$369$	−6.00543	+	4.36320i	−0.312630	+	0.227139i
$370$	13.5563	+	41.7220i	0.704758	+	2.16902i
$371$	4.14022	−	12.7423i	0.214949	−	0.661546i
$372$	−12.0506	−	8.75531i	−0.624797	−	0.453942i
$373$	5.07180			0.262608			0.131304	−	0.991342i	$-0.458084\pi$
$373$	5.07180			0.262608			0.131304	+	0.991342i	$0.458084\pi$
$374$		0			0
$375$	−2.47498			−0.127807
$376$	26.1447	+	18.9952i	1.34831	+	0.979603i
$377$	0.842136	−	2.59183i	0.0433722	−	0.133486i
$378$	1.88818	+	5.81123i	0.0971176	+	0.298897i
$379$	22.6381	−	16.4475i	1.16284	−	0.844853i	0.172706	−	0.984973i	$-0.444749\pi$
$379$	22.6381	−	16.4475i	1.16284	−	0.844853i	0.990135	+	0.140120i	$0.0447489\pi$
$380$	30.3410	−	22.0440i	1.55646	−	1.13083i
$381$	0.882333	+	2.71554i	0.0452033	+	0.139121i
$382$	−17.7705	+	54.6919i	−0.909216	+	2.79828i
$383$	25.3065	+	18.3862i	1.29310	+	0.939493i	0.999863	−	0.0165464i	$-0.00526712\pi$
$383$	25.3065	+	18.3862i	1.29310	+	0.939493i	0.293238	+	0.956039i	$0.405267\pi$
$384$	4.44323			0.226742
$385$		0			0
$386$	8.78692			0.447243
$387$	−3.34752	−	2.43212i	−0.170164	−	0.123631i
$388$	−12.1393	+	37.3610i	−0.616281	+	1.89672i
$389$	3.29214	+	10.1322i	0.166918	+	0.513721i	0.999173	−	0.0406730i	$-0.0129502\pi$
$389$	3.29214	+	10.1322i	0.166918	+	0.513721i	−0.832255	+	0.554394i	$0.812950\pi$
$390$	−6.32231	+	4.59343i	−0.320143	+	0.232597i
$391$	2.36956	−	1.72158i	0.119834	−	0.0870642i
$392$	1.98127	+	6.09772i	0.100069	+	0.307982i
$393$	2.65675	−	8.17664i	0.134015	−	0.412457i
$394$	4.50515	+	3.27319i	0.226966	+	0.164901i
$395$	33.4777			1.68445
$396$		0			0
$397$	21.1755			1.06277			0.531385	−	0.847131i	$-0.321672\pi$
$397$	21.1755			1.06277			0.531385	+	0.847131i	$0.321672\pi$
$398$	−4.81940	−	3.50150i	−0.241575	−	0.175514i
$399$	0.307538	−	0.946503i	0.0153961	−	0.0473844i
$400$	15.3219	+	47.1560i	0.766095	+	2.35780i
$401$	27.2727	−	19.8148i	1.36194	−	0.989504i	0.363616	−	0.931549i	$-0.381542\pi$
$401$	27.2727	−	19.8148i	1.36194	−	0.989504i	0.998319	−	0.0579548i	$-0.0184579\pi$
$402$	5.27864	−	3.83515i	0.263274	−	0.191280i
$403$	5.40350	+	16.6303i	0.269168	+	0.828413i
$404$	−8.05220	+	24.7821i	−0.400612	+	1.23296i
$405$	−20.8366	−	15.1386i	−1.03538	−	0.752245i
$406$	−3.19746			−0.158687
$407$		0			0
$408$	11.8917			0.588725
$409$	2.13907	+	1.55413i	0.105770	+	0.0768466i	0.639413	−	0.768863i	$-0.279177\pi$
$409$	2.13907	+	1.55413i	0.105770	+	0.0768466i	−0.533643	+	0.845710i	$0.679177\pi$
$410$	−7.08927	+	21.8185i	−0.350114	+	1.07754i
$411$	−1.15925	−	3.56780i	−0.0571815	−	0.175987i
$412$	16.9424	−	12.3094i	0.834694	−	0.606441i
$413$	−6.20498	+	4.50818i	−0.305327	+	0.221833i
$414$	−1.44777	−	4.45579i	−0.0711542	−	0.218990i
$415$	−8.87697	+	27.3205i	−0.435753	+	1.34111i
$416$	10.3829	+	7.54365i	0.509065	+	0.369858i
$417$	−4.41470			−0.216189
$418$		0			0
$419$	33.0757			1.61585			0.807926	−	0.589284i	$-0.200590\pi$
$419$	33.0757			1.61585			0.807926	+	0.589284i	$0.200590\pi$
$420$	5.13982	+	3.73430i	0.250797	+	0.182215i
$421$	10.4083	−	32.0334i	0.507268	−	1.56121i	−0.289656	−	0.957131i	$-0.593541\pi$
$421$	10.4083	−	32.0334i	0.507268	−	1.56121i	0.796924	−	0.604079i	$-0.206459\pi$
$422$	−10.7784	−	33.1725i	−0.524684	−	1.61481i
$423$	−11.5458	+	8.38852i	−0.561376	+	0.407864i
$424$	−69.4960	+	50.4918i	−3.37503	+	2.45210i
$425$	−9.43316	−	29.0323i	−0.457576	−	1.40827i
$426$	−1.36964	+	4.21533i	−0.0663594	+	0.204233i
$427$	−11.5971	−	8.42580i	−0.561224	−	0.407753i
$428$	−18.1490			−0.877266
$429$		0			0
$430$	−12.7879			−0.616686
$431$	24.0703	+	17.4881i	1.15943	+	0.842374i	0.989706	−	0.143118i	$-0.0457130\pi$
$431$	24.0703	+	17.4881i	1.15943	+	0.842374i	0.169722	+	0.985492i	$0.445713\pi$
$432$	5.42866	−	16.7077i	0.261187	−	0.803850i
$433$	−7.15404	−	22.0179i	−0.343801	−	1.05811i	−0.962222	−	0.272265i	$-0.912227\pi$
$433$	−7.15404	−	22.0179i	−0.343801	−	1.05811i	0.618421	−	0.785847i	$-0.287773\pi$
$434$	16.5980	−	12.0591i	0.796729	−	0.578858i
$435$	−1.42716	+	1.03689i	−0.0684272	+	0.0497153i
$436$	−8.57231	−	26.3829i	−0.410539	−	1.26351i
$437$	−0.485653	+	1.49469i	−0.0232319	+	0.0715005i
$438$	−5.02281	−	3.64928i	−0.239999	−	0.174369i
$439$	15.8166			0.754884			0.377442	−	0.926033i	$-0.376804\pi$
$439$	15.8166			0.754884			0.377442	+	0.926033i	$0.376804\pi$
$440$		0			0
$441$	−2.83141			−0.134829
$442$	−20.2842	−	14.7374i	−0.964823	−	0.700985i
$443$	−3.09841	+	9.53592i	−0.147210	+	0.453065i	−0.997289	−	0.0735904i	$-0.976554\pi$
$443$	−3.09841	+	9.53592i	−0.147210	+	0.453065i	0.850079	+	0.526656i	$0.176554\pi$
$444$	−2.87032	−	8.83395i	−0.136220	−	0.419241i
$445$	−13.2116	+	9.59882i	−0.626292	+	0.455027i
$446$	11.0839	−	8.05294i	0.524839	−	0.381318i
$447$	−1.36467	−	4.20001i	−0.0645466	−	0.198654i
$448$	0.118654	−	0.365178i	0.00560586	−	0.0172531i
$449$	−1.29950	−	0.944139i	−0.0613270	−	0.0445567i	0.556699	−	0.830714i	$-0.312068\pi$
$449$	−1.29950	−	0.944139i	−0.0613270	−	0.0445567i	−0.618026	+	0.786157i	$0.712068\pi$
$450$	−48.8297			−2.30185
$451$		0			0
$452$	−11.1834			−0.526023
$453$	−2.54591	−	1.84971i	−0.119617	−	0.0869070i
$454$	8.36932	−	25.7581i	0.392792	−	1.20889i
$455$	−2.30469	−	7.09311i	−0.108046	−	0.332530i
$456$	−5.16220	+	3.75056i	−0.241742	+	0.175636i
$457$	−3.03944	+	2.20828i	−0.142179	+	0.103299i	−0.656601	−	0.754238i	$-0.728006\pi$
$457$	−3.03944	+	2.20828i	−0.142179	+	0.103299i	0.514422	+	0.857537i	$0.328006\pi$
$458$	17.8545	+	54.9506i	0.834287	+	2.56767i
$459$	−3.34224	+	10.2864i	−0.156002	+	0.480126i
$460$	−8.11662	−	5.89707i	−0.378440	−	0.274952i
$461$	−14.1849			−0.660657			−0.330329	−	0.943866i	$-0.607160\pi$
$461$	−14.1849			−0.660657			−0.330329	+	0.943866i	$0.607160\pi$
$462$		0			0
$463$	−5.34265			−0.248294			−0.124147	−	0.992264i	$-0.539619\pi$
$463$	−5.34265			−0.248294			−0.124147	+	0.992264i	$0.539619\pi$
$464$	7.43724	+	5.40347i	0.345265	+	0.250850i
$465$	3.49777	−	10.7650i	0.162205	−	0.499216i
$466$	11.6898	+	35.9776i	0.541520	+	1.66663i
$467$	19.3109	−	14.0302i	0.893601	−	0.649239i	−0.0432136	−	0.999066i	$-0.513760\pi$
$467$	19.3109	−	14.0302i	0.893601	−	0.649239i	0.936814	+	0.349827i	$0.113760\pi$
$468$	−22.4820	+	16.3341i	−1.03923	+	0.755045i
$469$	1.92424	+	5.92219i	0.0888530	+	0.273461i
$470$	−13.6296	+	41.9475i	−0.628685	+	1.93489i
$471$	6.09520	+	4.42842i	0.280852	+	0.204051i
$472$	49.1750			2.26346
$473$		0			0
$474$	−10.2301			−0.469883
$475$	13.2516	+	9.62782i	0.608023	+	0.441755i
$476$	−6.29876	+	19.3856i	−0.288703	+	0.888538i
$477$	−11.7227	−	36.0786i	−0.536743	−	1.65193i
$478$	−4.04510	+	2.93893i	−0.185018	+	0.134424i
$479$	0.353149	−	0.256578i	0.0161358	−	0.0117233i	−0.579688	−	0.814838i	$-0.696826\pi$
$479$	0.353149	−	0.256578i	0.0161358	−	0.0117233i	0.595824	+	0.803115i	$0.296826\pi$
$480$	−2.56721	−	7.90105i	−0.117176	−	0.360632i
$481$	−3.36954	+	10.3704i	−0.153638	+	0.472849i
$482$	−1.63153	−	1.18537i	−0.0743140	−	0.0539923i
$483$	−0.266233			−0.0121140
$484$		0			0
$485$	−29.8517			−1.35549
$486$	21.1972	+	15.4007i	0.961524	+	0.698588i
$487$	0.226720	−	0.697771i	0.0102736	−	0.0316190i	−0.945788	−	0.324784i	$-0.894708\pi$
$487$	0.226720	−	0.697771i	0.0102736	−	0.0316190i	0.956062	+	0.293165i	$0.0947085\pi$
$488$	28.4012	+	87.4098i	1.28566	+	3.95686i
$489$	0.125426	−	0.0911277i	0.00567198	−	0.00412094i
$490$	−7.07934	+	5.14344i	−0.319812	+	0.232357i
$491$	0.805765	+	2.47989i	0.0363637	+	0.111916i	0.967591	−	0.252524i	$-0.0812606\pi$
$491$	0.805765	+	2.47989i	0.0363637	+	0.111916i	−0.931227	+	0.364440i	$0.881261\pi$
$492$	1.50104	−	4.61972i	0.0676720	−	0.208273i
$493$	−4.57885	−	3.32673i	−0.206221	−	0.149828i
$494$	13.4535			0.605302
$495$		0			0
$496$	−58.9857			−2.64854
$497$	−3.42211	−	2.48631i	−0.153503	−	0.111526i
$498$	2.71261	−	8.34857i	0.121555	−	0.374108i
$499$	−2.55186	−	7.85383i	−0.114237	−	0.351586i	0.877550	−	0.479485i	$-0.159177\pi$
$499$	−2.55186	−	7.85383i	−0.114237	−	0.351586i	−0.991787	+	0.127899i	$0.959177\pi$
$500$	−22.0049	+	15.9875i	−0.984091	+	0.714984i
$501$	−0.0379147	+	0.0275466i	−0.00169390	+	0.00123069i
$502$	−16.2572	−	50.0344i	−0.725593	−	2.23315i
$503$	10.4793	−	32.2519i	0.467248	−	1.43804i	−0.388884	−	0.921287i	$-0.627139\pi$
$503$	10.4793	−	32.2519i	0.467248	−	1.43804i	0.856133	−	0.516756i	$-0.172861\pi$
$504$	14.6866	+	10.6704i	0.654194	+	0.475300i
$505$	−19.8010			−0.881135
$506$		0			0
$507$	3.39533			0.150792
$508$	25.3863	+	18.4442i	1.12633	+	0.818330i
$509$	−9.03680	+	27.8124i	−0.400549	+	1.23276i	0.524006	+	0.851714i	$0.324437\pi$
$509$	−9.03680	+	27.8124i	−0.400549	+	1.23276i	−0.924555	+	0.381048i	$0.875563\pi$
$510$	5.01533	+	15.4356i	0.222082	+	0.683499i
$511$	4.79356	−	3.48273i	0.212055	−	0.154067i
$512$	41.0901	−	29.8537i	1.81594	−	1.31936i
$513$	−1.79338	−	5.51945i	−0.0791795	−	0.243690i
$514$	4.08461	−	12.5711i	0.180164	−	0.554488i
$515$	12.8745	+	9.35391i	0.567320	+	0.412182i
$516$	2.70763			0.119197
$517$		0			0
$518$	12.7936			0.562120
$519$	−4.41835	−	3.21012i	−0.193944	−	0.140908i
$520$	−14.7766	+	45.4776i	−0.647996	+	1.99433i
$521$	−3.00226	−	9.23999i	−0.131531	−	0.404811i	0.863503	−	0.504343i	$-0.168265\pi$
$521$	−3.00226	−	9.23999i	−0.131531	−	0.404811i	−0.995034	+	0.0995320i	$0.968265\pi$
$522$	−7.32429	+	5.32141i	−0.320575	+	0.232912i
$523$	10.3762	−	7.53879i	0.453722	−	0.329648i	−0.337342	−	0.941382i	$-0.609528\pi$
$523$	10.3762	−	7.53879i	0.453722	−	0.329648i	0.791063	+	0.611734i	$0.209528\pi$
$524$	−29.1973	−	89.8599i	−1.27549	−	3.92555i
$525$	−0.857452	+	2.63897i	−0.0374223	+	0.115174i
$526$	−47.8814	−	34.7879i	−2.08773	−	1.51682i
$527$	36.3155			1.58193
$528$		0			0
$529$	−22.5796			−0.981721
$530$	−94.8493	−	68.9120i	−4.11999	−	2.99335i
$531$	−6.71070	+	20.6534i	−0.291220	+	0.896282i
$532$	−3.37979	−	10.4019i	−0.146532	−	0.450981i
$533$	−4.61325	+	3.35172i	−0.199822	+	0.145179i
$534$	4.03720	−	2.93320i	0.174707	−	0.126932i
$535$	−4.26178	−	13.1164i	−0.184253	−	0.567072i
$536$	12.3373	−	37.9703i	0.532890	−	1.64007i
$537$	3.76726	+	2.73707i	0.162569	+	0.118113i
$538$	47.6192			2.05301
$539$		0			0
$540$	37.0479			1.59429
$541$	5.58323	+	4.05646i	0.240042	+	0.174401i	0.701302	−	0.712864i	$-0.252602\pi$
$541$	5.58323	+	4.05646i	0.240042	+	0.174401i	−0.461260	+	0.887265i	$0.652602\pi$
$542$	23.8382	−	73.3664i	1.02394	−	3.15136i
$543$	−1.49173	−	4.59108i	−0.0640163	−	0.197022i
$544$	21.5635	−	15.6668i	0.924527	−	0.671708i
$545$	17.0541	−	12.3905i	0.730518	−	0.530753i
$546$	0.704265	+	2.16750i	0.0301398	+	0.0927606i
$547$	−5.47634	+	16.8544i	−0.234151	+	0.720643i	0.763082	+	0.646302i	$0.223685\pi$
$547$	−5.47634	+	16.8544i	−0.234151	+	0.720643i	−0.997233	+	0.0743412i	$0.976315\pi$
$548$	−33.3536	−	24.2328i	−1.42480	−	1.03518i
$549$	−40.5878			−1.73224
$550$		0			0
$551$	3.03692			0.129377
$552$	1.38096	+	1.00333i	0.0587775	+	0.0427044i
$553$	3.01699	−	9.28534i	0.128295	−	0.394853i
$554$	10.6398	+	32.7458i	0.452040	+	1.39124i
$555$	5.71034	−	4.14881i	0.242391	−	0.176107i
$556$	−39.2509	+	28.5175i	−1.66461	+	1.20941i
$557$	13.4198	+	41.3018i	0.568614	+	1.75001i	0.656962	+	0.753924i	$0.271841\pi$
$557$	13.4198	+	41.3018i	0.568614	+	1.75001i	−0.0883477	+	0.996090i	$0.528159\pi$
$558$	17.9508	−	55.2468i	0.759917	−	2.33878i
$559$	−2.57150	−	1.86830i	−0.108763	−	0.0790208i
$560$	25.1585			1.06314
$561$		0			0
$562$	20.6777			0.872234
$563$	−18.0522	−	13.1157i	−0.760809	−	0.552760i	0.138349	−	0.990384i	$-0.455820\pi$
$563$	−18.0522	−	13.1157i	−0.760809	−	0.552760i	−0.899158	+	0.437623i	$0.855820\pi$
$564$	2.88584	−	8.88170i	0.121516	−	0.373987i
$565$	−2.62611	−	8.08233i	−0.110481	−	0.340026i
$566$	−20.6274	+	14.9867i	−0.867035	+	0.629938i
$567$	−6.07661	+	4.41492i	−0.255194	+	0.185409i
$568$	8.38071	+	25.7932i	0.351647	+	1.08226i
$569$	7.00513	−	21.5596i	0.293670	−	0.903824i	−0.689994	−	0.723815i	$-0.742387\pi$
$569$	7.00513	−	21.5596i	0.293670	−	0.903824i	0.983665	−	0.180010i	$-0.0576129\pi$
$570$	−7.04545	−	5.11882i	−0.295102	−	0.214404i
$571$	35.0994			1.46886			0.734432	−	0.678683i	$-0.237449\pi$
$571$	35.0994			1.46886			0.734432	+	0.678683i	$0.237449\pi$
$572$		0			0
$573$	9.25258			0.386532
$574$	5.41268	+	3.93254i	0.225921	+	0.164141i
$575$	1.35406	−	4.16737i	0.0564682	−	0.173791i
$576$	−0.335957	−	1.03397i	−0.0139982	−	0.0430820i
$577$	26.4029	−	19.1828i	1.09917	−	0.798591i	0.118243	−	0.992985i	$-0.462274\pi$
$577$	26.4029	−	19.1828i	1.09917	−	0.798591i	0.980924	+	0.194393i	$0.0622739\pi$
$578$	−7.02910	+	5.10694i	−0.292372	+	0.212421i
$579$	−0.436883	−	1.34459i	−0.0181562	−	0.0558792i
$580$	−5.99087	+	18.4380i	−0.248757	+	0.765596i
$581$	6.77759	+	4.92421i	0.281182	+	0.204291i
$582$	9.12204			0.378121
$583$		0			0
$584$	−37.9894			−1.57201
$585$	−17.0840	−	12.4123i	−0.706338	−	0.513185i
$586$	24.2332	−	74.5821i	1.00106	−	3.08096i
$587$	11.4390	+	35.2057i	0.472139	+	1.45309i	0.849778	+	0.527140i	$0.176736\pi$
$587$	11.4390	+	35.2057i	0.472139	+	1.45309i	−0.377640	+	0.925953i	$0.623264\pi$
$588$	1.49894	−	1.08904i	0.0618151	−	0.0449113i
$589$	−15.7646	+	11.4537i	−0.649570	+	0.471940i
$590$	20.7396	+	63.8300i	0.853837	+	2.62784i
$591$	0.276873	−	0.852127i	0.0113890	−	0.0350518i
$592$	−29.7578	−	21.6203i	−1.22304	−	0.888589i
$593$	−16.2161			−0.665915			−0.332958	−	0.942942i	$-0.608047\pi$
$593$	−16.2161			−0.665915			−0.332958	+	0.942942i	$0.608047\pi$
$594$		0			0
$595$	−15.4892			−0.634995
$596$	−39.2639	−	28.5269i	−1.60831	−	1.16851i
$597$	−0.296186	+	0.911565i	−0.0121221	+	0.0373079i
$598$	−1.11215	−	3.42285i	−0.0454792	−	0.139971i
$599$	−8.53313	+	6.19968i	−0.348654	+	0.253312i	−0.748304	−	0.663356i	$-0.769132\pi$
$599$	−8.53313	+	6.19968i	−0.348654	+	0.253312i	0.399650	+	0.916668i	$0.369132\pi$
$600$	14.3928	−	10.4570i	0.587585	−	0.426906i
$601$	−11.2764	−	34.7051i	−0.459973	−	1.41565i	−0.865196	−	0.501434i	$-0.832806\pi$
$601$	−11.2764	−	34.7051i	−0.459973	−	1.41565i	0.405222	−	0.914218i	$-0.367194\pi$
$602$	−1.15243	+	3.54683i	−0.0469697	+	0.144558i
$603$	14.2638	+	10.3633i	0.580868	+	0.422026i
$604$	−34.5841			−1.40721
$605$		0			0
$606$	6.05078			0.245796
$607$	27.2731	+	19.8151i	1.10698	+	0.804269i	0.982186	−	0.187914i	$-0.0601725\pi$
$607$	27.2731	+	19.8151i	1.10698	+	0.804269i	0.124796	+	0.992182i	$0.460173\pi$
$608$	−4.41955	+	13.6020i	−0.179236	+	0.551633i
$609$	0.158977	+	0.489280i	0.00644206	+	0.0198266i
$610$	−101.481	+	73.7304i	−4.10885	+	2.98526i
$611$	−8.86926	+	6.44389i	−0.358812	+	0.260692i
$612$	17.8344	+	54.8886i	0.720912	+	2.21874i
$613$	7.48027	−	23.0219i	0.302125	−	0.929845i	−0.678609	−	0.734499i	$-0.737417\pi$
$613$	7.48027	−	23.0219i	0.302125	−	0.929845i	0.980734	−	0.195346i	$-0.0625830\pi$
$614$	41.4310	+	30.1014i	1.67202	+	1.21479i
$615$	3.69118			0.148843
$616$		0			0
$617$	17.6040			0.708710			0.354355	−	0.935111i	$-0.384700\pi$
$617$	17.6040			0.708710			0.354355	+	0.935111i	$0.384700\pi$
$618$	−3.93419	−	2.85836i	−0.158256	−	0.114980i
$619$	−7.51455	+	23.1274i	−0.302035	+	0.929569i	0.678732	+	0.734386i	$0.262530\pi$
$619$	−7.51455	+	23.1274i	−0.302035	+	0.929569i	−0.980767	+	0.195183i	$0.937470\pi$
$620$	−38.4399	−	118.306i	−1.54378	−	4.75128i
$621$	−1.25601	+	0.912544i	−0.0504019	+	0.0366191i
$622$	48.4475	−	35.1992i	1.94257	−	1.41136i
$623$	1.47169	+	4.52940i	0.0589621	+	0.181467i
$624$	2.02481	−	6.23174i	0.0810574	−	0.249469i
$625$	10.6147	+	7.71201i	0.424587	+	0.308480i
$626$	−37.4446			−1.49659
$627$		0			0
$628$	82.7983			3.30401
$629$	18.3208	+	13.3109i	0.730499	+	0.530739i
$630$	−7.65633	+	23.5637i	−0.305035	+	0.938802i
$631$	1.24857	+	3.84271i	0.0497049	+	0.152976i	0.972828	−	0.231528i	$-0.0743725\pi$
$631$	1.24857	+	3.84271i	0.0497049	+	0.152976i	−0.923123	+	0.384504i	$0.874372\pi$
$632$	−50.6420	+	36.7935i	−2.01443	+	1.46357i
$633$	−4.54021	+	3.29865i	−0.180457	+	0.131110i
$634$	14.2348	+	43.8104i	0.565338	+	1.73993i
$635$	−7.36851	+	22.6779i	−0.292410	+	0.899947i
$636$	20.0828	+	14.5910i	0.796335	+	0.578571i
$637$	−2.17503			−0.0861779
$638$		0			0
$639$	−11.9768			−0.473793
$640$	30.0195	+	21.8104i	1.18663	+	0.862134i
$641$	−6.60314	+	20.3224i	−0.260808	+	0.802686i	0.731821	+	0.681497i	$0.238671\pi$
$641$	−6.60314	+	20.3224i	−0.260808	+	0.802686i	−0.992629	+	0.121189i	$0.961329\pi$
$642$	1.30231	+	4.00810i	0.0513981	+	0.158187i
$643$	−18.2636	+	13.2693i	−0.720246	+	0.523289i	−0.886463	−	0.462800i	$-0.846845\pi$
$643$	−18.2636	+	13.2693i	−0.720246	+	0.523289i	0.166217	+	0.986089i	$0.446845\pi$
$644$	−2.36707	+	1.71978i	−0.0932756	+	0.0677687i
$645$	0.635810	+	1.95682i	0.0250350	+	0.0770498i
$646$	8.63409	−	26.5730i	0.339704	−	1.04550i
$647$	−13.8480	−	10.0612i	−0.544422	−	0.395546i	0.281303	−	0.959619i	$-0.409233\pi$
$647$	−13.8480	−	10.0612i	−0.544422	−	0.395546i	−0.825725	+	0.564073i	$0.809233\pi$
$648$	48.1576			1.89181
$649$		0			0
$650$	−37.5100			−1.47126
$651$	−2.67056	−	1.94027i	−0.104667	−	0.0760453i
$652$	0.526509	−	1.62043i	0.0206197	−	0.0634608i
$653$	−4.09173	−	12.5930i	−0.160122	−	0.492804i	0.838522	−	0.544868i	$-0.183420\pi$
$653$	−4.09173	−	12.5930i	−0.160122	−	0.492804i	−0.998644	+	0.0520637i	$0.983420\pi$
$654$	−5.21138	+	3.78629i	−0.203781	+	0.148056i
$655$	58.0863	−	42.2021i	2.26962	−	1.64897i
$656$	−5.94410	−	18.2941i	−0.232078	−	0.714263i
$657$	5.18425	−	15.9555i	0.202257	−	0.622482i
$658$	10.4062	+	7.56055i	0.405676	+	0.294741i
$659$	28.3747			1.10532			0.552660	−	0.833407i	$-0.313613\pi$
$659$	28.3747			1.10532			0.552660	+	0.833407i	$0.313613\pi$
$660$		0			0
$661$	18.9657			0.737679			0.368840	−	0.929493i	$-0.379755\pi$
$661$	18.9657			0.737679			0.368840	+	0.929493i	$0.379755\pi$
$662$	40.9404	+	29.7449i	1.59119	+	1.15607i
$663$	−1.24661	+	3.83666i	−0.0484142	+	0.149004i
$664$	−16.5982	−	51.0841i	−0.644136	−	1.98245i
$665$	6.72389	−	4.88520i	0.260741	−	0.189440i
$666$	29.3058	−	21.2919i	1.13558	−	0.825046i
$667$	−0.251051	−	0.772654i	−0.00972072	−	0.0299173i
$668$	−0.159156	+	0.489833i	−0.00615794	+	0.0189522i
$669$	−1.78336	−	1.29569i	−0.0689488	−	0.0500942i
$670$	54.4893			2.10511
$671$		0			0
$672$	−2.42278			−0.0934608
$673$	−37.6551	−	27.3580i	−1.45150	−	1.05458i	−0.985478	−	0.169801i	$-0.945688\pi$
$673$	−37.6551	−	27.3580i	−1.45150	−	1.05458i	−0.466020	−	0.884774i	$-0.654312\pi$
$674$	−15.3842	+	47.3476i	−0.592577	+	1.82376i
$675$	5.00016	+	15.3889i	0.192456	+	0.592319i
$676$	30.1878	−	21.9327i	1.16107	−	0.843566i
$677$	−23.1132	+	16.7927i	−0.888312	+	0.645396i	−0.935437	−	0.353493i	$-0.884994\pi$
$677$	−23.1132	+	16.7927i	−0.888312	+	0.645396i	0.0471255	+	0.998889i	$0.484994\pi$
$678$	0.802483	+	2.46979i	0.0308192	+	0.0948517i
$679$	−2.69021	+	8.27962i	−0.103241	+	0.317743i
$680$	80.3430	+	58.3726i	3.08101	+	2.23849i
$681$	−4.35767			−0.166986
$682$		0			0
$683$	−21.9450			−0.839704			−0.419852	−	0.907593i	$-0.637918\pi$
$683$	−21.9450			−0.839704			−0.419852	+	0.907593i	$0.637918\pi$
$684$	−25.0535	−	18.2024i	−0.957943	−	0.695986i
$685$	9.68108	−	29.7953i	0.369895	−	1.13842i
$686$	0.788594	+	2.42704i	0.0301086	+	0.0926649i
$687$	7.52090	−	5.46425i	0.286940	−	0.208474i
$688$	8.67443	−	6.30234i	0.330709	−	0.240274i
$689$	−9.00511	−	27.7149i	−0.343067	−	1.05585i
$690$	−0.719912	+	2.21566i	−0.0274066	+	0.0843488i
$691$	−9.00403	−	6.54181i	−0.342529	−	0.248862i	0.403199	−	0.915112i	$-0.367898\pi$
$691$	−9.00403	−	6.54181i	−0.342529	−	0.248862i	−0.745728	+	0.666250i	$0.767898\pi$
$692$	−60.0197			−2.28161
$693$		0			0
$694$	−72.5903			−2.75549
$695$	−29.8267	−	21.6704i	−1.13139	−	0.822005i
$696$	1.01928	−	3.13703i	0.0386358	−	0.118909i
$697$	3.65957	+	11.2630i	0.138616	+	0.426617i
$698$	−41.4705	+	30.1301i	−1.56968	+	1.14044i
$699$	4.92413	−	3.57759i	0.186248	−	0.135317i
$700$	9.42327	+	29.0018i	0.356166	+	1.09617i
$701$	−11.8651	+	36.5170i	−0.448139	+	1.37923i	0.430865	+	0.902416i	$0.358208\pi$
$701$	−11.8651	+	36.5170i	−0.448139	+	1.37923i	−0.879004	+	0.476814i	$0.841792\pi$
$702$	10.7519	+	7.81171i	0.405804	+	0.294834i
$703$	−12.1513			−0.458294
$704$		0			0
$705$	7.09652			0.267271
$706$	−18.5749	−	13.4954i	−0.699075	−	0.507908i
$707$	−1.78446	+	5.49199i	−0.0671114	+	0.206548i
$708$	−4.39128	−	13.5150i	−0.165034	−	0.507923i
$709$	0.388734	−	0.282432i	0.0145992	−	0.0106070i	−0.580462	−	0.814288i	$-0.697128\pi$
$709$	0.388734	−	0.282432i	0.0145992	−	0.0106070i	0.595061	+	0.803681i	$0.297128\pi$
$710$	−29.9454	+	21.7566i	−1.12383	+	0.816511i
$711$	−8.54233	−	26.2906i	−0.320362	−	0.985974i
$712$	9.43579	−	29.0404i	0.353621	−	1.08833i
$713$	4.21725	+	3.06401i	0.157937	+	0.114748i
$714$	4.73317			0.177135
$715$		0			0
$716$	51.1752			1.91251
$717$	0.650841	+	0.472864i	0.0243061	+	0.0176594i
$718$	7.46483	−	22.9744i	0.278585	−	0.857397i
$719$	11.2698	+	34.6848i	0.420292	+	1.29352i	0.907431	+	0.420200i	$0.138040\pi$
$719$	11.2698	+	34.6848i	0.420292	+	1.29352i	−0.487140	+	0.873324i	$0.661960\pi$
$720$	57.6295	−	41.8703i	2.14772	−	1.56041i
$721$	3.75463	−	2.72790i	0.139830	−	0.101592i
$722$	−10.3504	−	31.8553i	−0.385202	−	1.18553i
$723$	−0.100269	+	0.308595i	−0.00372903	+	0.0114768i
$724$	−42.9198	−	31.1830i	−1.59510	−	1.15891i
$725$	−8.46730			−0.314467
$726$		0			0
$727$	−33.6867			−1.24937			−0.624686	−	0.780876i	$-0.714773\pi$
$727$	−33.6867			−1.24937			−0.624686	+	0.780876i	$0.714773\pi$
$728$	11.2820	+	8.19683i	0.418137	+	0.303795i
$729$	−5.66046	+	17.4211i	−0.209647	+	0.645226i
$730$	−16.0221	−	49.3109i	−0.593003	−	1.82508i
$731$	−5.34054	+	3.88013i	−0.197527	+	0.143512i
$732$	21.4870	−	15.6112i	0.794182	−	0.577007i
$733$	−8.36313	−	25.7391i	−0.308899	−	0.950694i	−0.978193	−	0.207697i	$-0.933403\pi$
$733$	−8.36313	−	25.7391i	−0.308899	−	0.950694i	0.669294	−	0.742998i	$-0.266597\pi$
$734$	1.08442	−	3.33750i	0.0400267	−	0.123190i
$735$	1.13904	+	0.827562i	0.0420142	+	0.0305251i
$736$	3.82597			0.141027
$737$		0			0
$738$	18.9434			0.697315
$739$	8.42399	+	6.12039i	0.309882	+	0.225142i	0.731846	−	0.681470i	$-0.238659\pi$
$739$	8.42399	+	6.12039i	0.309882	+	0.225142i	−0.421964	+	0.906613i	$0.638659\pi$
$740$	23.9706	−	73.7739i	0.881176	−	2.71198i
$741$	−0.668904	−	2.05868i	−0.0245728	−	0.0756273i
$742$	−27.6611	+	20.0970i	−1.01547	+	0.737783i
$743$	−38.4705	+	27.9505i	−1.41135	+	1.02540i	−0.418220	+	0.908346i	$0.637346\pi$
$743$	−38.4705	+	27.9505i	−1.41135	+	1.02540i	−0.993125	+	0.117057i	$0.962654\pi$
$744$	6.54015	+	20.1285i	0.239774	+	0.737947i
$745$	11.3966	−	35.0750i	0.417538	−	1.28505i
$746$	−10.4710	−	7.60766i	−0.383372	−	0.278536i
$747$	23.7203			0.867881
$748$		0			0
$749$	−4.02202			−0.146961
$750$	5.10975	+	3.71245i	0.186582	+	0.135560i
$751$	−9.17002	+	28.2224i	−0.334619	+	1.02985i	0.632291	+	0.774731i	$0.282115\pi$
$751$	−9.17002	+	28.2224i	−0.334619	+	1.02985i	−0.966910	+	0.255119i	$0.917885\pi$
$752$	−11.4279	−	35.1715i	−0.416733	−	1.28257i
$753$	−6.84804	+	4.97539i	−0.249557	+	0.181313i
$754$	−5.62637	+	4.08780i	−0.204900	+	0.148869i
$755$	−8.12110	−	24.9942i	−0.295557	−	0.909632i
$756$	3.33873	−	10.2756i	0.121428	−	0.373718i
$757$	25.0626	+	18.2090i	0.910915	+	0.661818i	0.941246	−	0.337722i	$-0.109656\pi$
$757$	25.0626	+	18.2090i	0.910915	+	0.661818i	−0.0303313	+	0.999540i	$0.509656\pi$
$758$	−71.4090			−2.59369
$759$		0			0
$760$	−53.2874			−1.93294
$761$	−9.51993	−	6.91663i	−0.345097	−	0.250728i	0.401712	−	0.915766i	$-0.368415\pi$
$761$	−9.51993	−	6.91663i	−0.345097	−	0.250728i	−0.746809	+	0.665038i	$0.768415\pi$
$762$	2.25166	−	6.92990i	0.0815691	−	0.251044i
$763$	−1.89972	−	5.84674i	−0.0687745	−	0.211666i
$764$	82.2644	−	59.7686i	2.97622	−	2.16235i
$765$	−35.4805	+	25.7781i	−1.28280	+	0.932008i
$766$	−24.6676	−	75.9192i	−0.891278	−	2.74307i
$767$	−5.15503	+	15.8655i	−0.186137	+	0.572872i
$768$	−9.42843	−	6.85015i	−0.340219	−	0.247184i
$769$	4.17897			0.150697			0.0753487	−	0.997157i	$-0.475993\pi$
$769$	4.17897			0.150697			0.0753487	+	0.997157i	$0.475993\pi$
$770$		0			0
$771$	−2.12674			−0.0765926
$772$	−12.5699	−	9.13257i	−0.452401	−	0.328689i
$773$	0.0258938	−	0.0796928i	0.000931334	−	0.00286635i	−0.950590	−	0.310450i	$-0.899520\pi$
$773$	0.0258938	−	0.0796928i	0.000931334	−	0.00286635i	0.951521	+	0.307583i	$0.0995203\pi$
$774$	3.26301	+	10.0425i	0.117287	+	0.360971i
$775$	43.9537	−	31.9342i	1.57886	−	1.14711i
$776$	45.1568	−	32.8083i	1.62103	−	1.17775i
$777$	−0.636096	−	1.95770i	−0.0228198	−	0.0702322i
$778$	8.40135	−	25.8567i	0.301203	−	0.927007i
$779$	−5.14091	−	3.73509i	−0.184192	−	0.133824i
$780$	13.8183			0.494776
$781$		0			0
$782$	−7.47446			−0.267286
$783$	2.42707	+	1.76337i	0.0867364	+	0.0630177i
$784$	2.26726	−	6.97792i	0.0809737	−	0.249212i
$785$	19.4428	+	59.8389i	0.693945	+	2.13574i
$786$	−17.7499	+	12.8961i	−0.633119	+	0.459988i
$787$	−10.8728	+	7.89952i	−0.387572	+	0.281588i	−0.764460	−	0.644671i	$-0.776994\pi$
$787$	−10.8728	+	7.89952i	−0.387572	+	0.281588i	0.376888	+	0.926259i	$0.376994\pi$
$788$	−3.04279	−	9.36474i	−0.108395	−	0.333605i
$789$	−2.94265	+	9.05653i	−0.104761	+	0.322421i
$790$	−69.1169	−	50.2164i	−2.45907	−	1.78662i
$791$	−2.47837			−0.0881206
$792$		0			0
$793$	−31.1787			−1.10719
$794$	−43.7183	−	31.7632i	−1.55150	−	1.12723i
$795$	−5.82915	+	17.9403i	−0.206738	+	0.636276i
$796$	3.25503	+	10.0180i	0.115372	+	0.355077i
$797$	11.0009	−	7.99263i	0.389672	−	0.283113i	−0.375649	−	0.926762i	$-0.622580\pi$
$797$	11.0009	−	7.99263i	0.389672	−	0.283113i	0.765321	+	0.643649i	$0.222580\pi$
$798$	−2.05468	+	1.49281i	−0.0727349	+	0.0528450i
$799$	7.03576	+	21.6538i	0.248907	+	0.766058i
$800$	12.3222	−	37.9240i	0.435657	−	1.34081i
$801$	10.9092	+	7.92603i	0.385459	+	0.280053i
$802$	−86.0284			−3.03777
$803$		0			0
$804$	−11.5372			−0.406887
$805$	−1.79873	−	1.30686i	−0.0633970	−	0.0460606i
$806$	13.7894	−	42.4395i	0.485712	−	1.49487i
$807$	−2.36761	−	7.28676i	−0.0833439	−	0.256506i
$808$	29.9532	−	21.7622i	1.05375	−	0.765593i
$809$	−36.0013	+	26.1565i	−1.26574	+	0.919612i	−0.999024	−	0.0441638i	$-0.985938\pi$
$809$	−36.0013	+	26.1565i	−1.26574	+	0.919612i	−0.266713	+	0.963776i	$0.585938\pi$
$810$	20.3105	+	62.5094i	0.713640	+	2.19636i
$811$	−7.47960	+	23.0199i	−0.262644	+	0.808336i	0.729582	+	0.683893i	$0.239715\pi$
$811$	−7.47960	+	23.0199i	−0.262644	+	0.808336i	−0.992227	+	0.124443i	$0.960285\pi$
$812$	4.57404	+	3.32324i	0.160517	+	0.116623i
$813$	−12.4119			−0.435303
$814$		0			0
$815$	1.29473			0.0453524
$816$	−11.0093	−	7.99871i	−0.385402	−	0.280011i
$817$	1.09457	−	3.36875i	0.0382942	−	0.117857i
$818$	−2.08507	−	6.41719i	−0.0729028	−	0.224372i
$819$	−4.98226	+	3.61982i	−0.174094	+	0.126487i
$820$	32.8182	−	23.8438i	1.14606	−	0.832662i
$821$	−2.86779	−	8.82615i	−0.100087	−	0.308035i	0.888459	−	0.458955i	$-0.151776\pi$
$821$	−2.86779	−	8.82615i	−0.100087	−	0.308035i	−0.988546	+	0.150921i	$0.951776\pi$
$822$	−2.95834	+	9.10482i	−0.103184	+	0.317567i
$823$	18.9984	+	13.8031i	0.662242	+	0.481147i	0.867419	−	0.497578i	$-0.165777\pi$
$823$	18.9984	+	13.8031i	0.662242	+	0.481147i	−0.205177	+	0.978725i	$0.565777\pi$
$824$	−29.7558			−1.03659
$825$		0			0
$826$	19.5728			0.681026
$827$	15.9690	+	11.6022i	0.555297	+	0.403447i	0.829735	−	0.558158i	$-0.188492\pi$
$827$	15.9690	+	11.6022i	0.555297	+	0.403447i	−0.274438	+	0.961605i	$0.588492\pi$
$828$	−2.55999	+	7.87884i	−0.0889658	+	0.273809i
$829$	−12.3588	−	38.0364i	−0.429238	−	1.32106i	−0.898878	−	0.438200i	$-0.855616\pi$
$829$	−12.3588	−	38.0364i	−0.429238	−	1.32106i	0.469640	−	0.882858i	$-0.344384\pi$
$830$	59.3077	−	43.0895i	2.05860	−	1.49566i
$831$	4.48181	−	3.25622i	0.155472	−	0.112957i
$832$	−0.258075	−	0.794275i	−0.00894716	−	0.0275365i
$833$	−1.39588	+	4.29606i	−0.0483642	+	0.148850i
$834$	9.11442	+	6.62202i	0.315607	+	0.229302i
$835$	−0.391379			−0.0135442
$836$		0			0
$837$	−19.2494			−0.665357
$838$	−68.2869	−	49.6133i	−2.35893	−	1.71386i
$839$	−2.42521	+	7.46403i	−0.0837276	+	0.257687i	−0.984152	−	0.177325i	$-0.943256\pi$
$839$	−2.42521	+	7.46403i	−0.0837276	+	0.257687i	0.900425	+	0.435012i	$0.143256\pi$
$840$	−2.78949	−	8.58518i	−0.0962467	−	0.296217i
$841$	22.1914	−	16.1230i	0.765222	−	0.555966i
$842$	−69.5384	+	50.5226i	−2.39645	+	1.74112i
$843$	−1.02809	−	3.16413i	−0.0354092	−	0.108978i
$844$	−19.0586	+	58.6565i	−0.656025	+	2.01904i
$845$	22.9397	+	16.6667i	0.789149	+	0.573350i
$846$	36.4198			1.25214
$847$		0			0
$848$	98.3017			3.37569
$849$	3.31888	+	2.41131i	0.113904	+	0.0827558i
$850$	−24.0729	+	74.0887i	−0.825693	+	2.54122i
$851$	1.00450	+	3.09153i	0.0344338	+	0.105976i
$852$	6.34045	−	4.60661i	0.217220	−	0.157820i
$853$	33.1689	−	24.0986i	1.13568	−	0.825121i	0.149170	−	0.988812i	$-0.452340\pi$
$853$	33.1689	−	24.0986i	1.13568	−	0.825121i	0.986512	+	0.163691i	$0.0523399\pi$
$854$	11.3044	+	34.7912i	0.386827	+	1.19053i
$855$	7.27191	−	22.3806i	0.248694	−	0.765401i
$856$	20.8624	+	15.1574i	0.713061	+	0.518069i
$857$	31.1892			1.06540			0.532702	−	0.846303i	$-0.321177\pi$
$857$	31.1892			1.06540			0.532702	+	0.846303i	$0.321177\pi$
$858$		0			0
$859$	7.95825			0.271532			0.135766	−	0.990741i	$-0.456650\pi$
$859$	7.95825			0.271532			0.135766	+	0.990741i	$0.456650\pi$
$860$	18.2934	+	13.2909i	0.623799	+	0.453217i
$861$	0.332647	−	1.02378i	0.0113366	−	0.0348904i
$862$	−23.4627	−	72.2107i	−0.799143	−	2.45951i
$863$	−25.1639	+	18.2826i	−0.856588	+	0.622347i	−0.926954	−	0.375174i	$-0.877583\pi$
$863$	−25.1639	+	18.2826i	−0.856588	+	0.622347i	0.0703669	+	0.997521i	$0.477583\pi$
$864$	−11.4300	+	8.30436i	−0.388856	+	0.282520i
$865$	−14.0939	−	43.3766i	−0.479208	−	1.47485i
$866$	−18.2567	+	56.1883i	−0.620388	+	1.90936i
$867$	1.13096	+	0.821688i	0.0384093	+	0.0279060i
$868$	−36.2774			−1.23133
$869$		0			0
$870$	4.50180			0.152625
$871$	10.9572	+	7.96087i	0.371270	+	0.269744i
$872$	−12.1801	+	37.4865i	−0.412470	+	1.26945i
$873$	7.61709	+	23.4430i	0.257799	+	0.793425i
$874$	3.24468	−	2.35740i	0.109753	−	0.0797402i
$875$	−4.87654	+	3.54301i	−0.164857	+	0.119776i
$876$	3.39241	+	10.4408i	0.114619	+	0.352761i
$877$	−16.0371	+	49.3571i	−0.541534	+	1.66667i	0.187556	+	0.982254i	$0.439943\pi$
$877$	−16.0371	+	49.3571i	−0.541534	+	1.66667i	−0.729090	+	0.684417i	$0.760057\pi$
$878$	−32.6544	−	23.7248i	−1.10203	−	0.800672i
$879$	−12.6175			−0.425579
$880$		0			0
$881$	42.1448			1.41989			0.709947	−	0.704256i	$-0.248719\pi$
$881$	42.1448			1.41989			0.709947	+	0.704256i	$0.248719\pi$
$882$	5.84563	+	4.24710i	0.196833	+	0.143007i
$883$	−5.45656	+	16.7936i	−0.183628	+	0.565149i	−0.999922	−	0.0124878i	$-0.996025\pi$
$883$	−5.45656	+	16.7936i	−0.183628	+	0.565149i	0.816294	+	0.577637i	$0.196025\pi$
$884$	13.7000	+	42.1643i	0.460781	+	1.41814i
$885$	8.73619	−	6.34722i	0.293664	−	0.213359i
$886$	20.7007	−	15.0399i	0.695453	−	0.505276i
$887$	−3.29195	−	10.1316i	−0.110533	−	0.340185i	0.880456	−	0.474127i	$-0.157236\pi$
$887$	−3.29195	−	10.1316i	−0.110533	−	0.340185i	−0.990989	+	0.133942i	$0.957236\pi$
$888$	−4.07834	+	12.5519i	−0.136860	+	0.421213i
$889$	5.62588	+	4.08744i	0.188686	+	0.137088i
$890$	41.6744			1.39693
$891$		0			0
$892$	−24.2255			−0.811131
$893$	−9.88372	−	7.18094i	−0.330746	−	0.240301i
$894$	−3.48255	+	10.7182i	−0.116474	+	0.358470i
$895$	12.0170	+	36.9846i	0.401685	+	1.23626i
$896$	8.75466	−	6.36063i	0.292473	−	0.212494i
$897$	−0.468474	+	0.340366i	−0.0156419	+	0.0113645i
$898$	1.26669	+	3.89847i	0.0422700	+	0.130094i
$899$	3.11275	−	9.58005i	0.103816	−	0.319512i
$900$	69.8521	+	50.7505i	2.32840	+	1.69168i
$901$	−60.5209			−2.01624
$902$		0			0
$903$	0.600040			0.0199681
$904$	12.8554	+	9.33998i	0.427563	+	0.310643i
$905$	12.4577	−	38.3409i	0.414108	−	1.27449i
$906$	2.48164	+	7.63770i	0.0824469	+	0.253745i
$907$	−40.6939	+	29.5659i	−1.35122	+	0.981719i	−0.352270	+	0.935898i	$0.614590\pi$
$907$	−40.6939	+	29.5659i	−1.35122	+	0.981719i	−0.998950	+	0.0458205i	$0.985410\pi$
$908$	−38.7439	+	28.1491i	−1.28576	+	0.934160i
$909$	5.05253	+	15.5501i	0.167582	+	0.515763i
$910$	−5.88144	+	18.1012i	−0.194968	+	0.600049i
$911$	18.6375	+	13.5410i	0.617489	+	0.448632i	0.852044	−	0.523471i	$-0.175363\pi$
$911$	18.6375	+	13.5410i	0.617489	+	0.448632i	−0.234554	+	0.972103i	$0.575363\pi$
$912$	7.30190			0.241790
$913$		0			0
$914$	9.58753			0.317127
$915$	16.3280	+	11.8630i	0.539785	+	0.392177i
$916$	31.5708	−	97.1650i	1.04313	−	3.21042i
$917$	−6.47044	−	19.9140i	−0.213673	−	0.657617i
$918$	22.3297	−	16.2235i	0.736991	−	0.535455i
$919$	30.7956	−	22.3743i	1.01585	−	0.738061i	0.0504252	−	0.998728i	$-0.483942\pi$
$919$	30.7956	−	22.3743i	1.01585	−	0.738061i	0.965429	+	0.260667i	$0.0839423\pi$
$920$	4.40507	+	13.5574i	0.145231	+	0.446975i
$921$	2.54622	−	7.83647i	0.0839009	−	0.258220i
$922$	29.2857	+	21.2773i	0.964472	+	0.700730i
$923$	−9.20031			−0.302832
$924$		0			0
$925$	33.8792			1.11394
$926$	11.0302	+	8.01394i	0.362476	+	0.263354i
$927$	4.06064	−	12.4974i	0.133369	−	0.410468i
$928$	−2.28462	−	7.03133i	−0.0749962	−	0.230815i
$929$	14.1887	−	10.3087i	0.465516	−	0.338217i	−0.330175	−	0.943920i	$-0.607108\pi$
$929$	14.1887	−	10.3087i	0.465516	−	0.338217i	0.795691	+	0.605703i	$0.207108\pi$
$930$	−23.3688	+	16.9785i	−0.766295	+	0.556746i
$931$	−0.748999	−	2.30518i	−0.0245474	−	0.0755493i
$932$	20.6702	−	63.6164i	0.677076	−	2.08383i
$933$	−7.79503	−	5.66342i	−0.255198	−	0.185412i
$934$	−60.9137			−1.99316
$935$		0			0
$936$	39.4848			1.29060
$937$	45.9190	+	33.3621i	1.50011	+	1.08989i	0.970339	+	0.241749i	$0.0777211\pi$
$937$	45.9190	+	33.3621i	1.50011	+	1.08989i	0.529768	+	0.848142i	$0.322279\pi$
$938$	4.91054	−	15.1131i	0.160335	−	0.493460i
$939$	1.86174	+	5.72983i	0.0607554	+	0.186986i
$940$	63.0950	−	45.8412i	2.05793	−	1.49517i
$941$	18.0399	−	13.1068i	0.588084	−	0.427268i	−0.253545	−	0.967324i	$-0.581597\pi$
$941$	18.0399	−	13.1068i	0.588084	−	0.427268i	0.841630	+	0.540055i	$0.181597\pi$
$942$	−5.94133	−	18.2855i	−0.193579	−	0.595774i
$943$	−0.525304	+	1.61672i	−0.0171063	+	0.0526477i
$944$	−45.5261	−	33.0767i	−1.48175	−	1.07655i
$945$	8.21023			0.267079
$946$		0			0
$947$	44.7782			1.45510			0.727548	−	0.686057i	$-0.240660\pi$
$947$	44.7782			1.45510			0.727548	+	0.686057i	$0.240660\pi$
$948$	14.6344	+	10.6325i	0.475303	+	0.345328i
$949$	3.98244	−	12.2567i	0.129275	−	0.397869i
$950$	−12.9170	−	39.7545i	−0.419084	−	1.28981i
$951$	5.99617	−	4.35648i	0.194439	−	0.141268i
$952$	23.4306	−	17.0233i	0.759390	−	0.551729i
$953$	0.572242	+	1.76118i	0.0185367	+	0.0570502i	0.959897	−	0.280353i	$-0.0904515\pi$
$953$	0.572242	+	1.76118i	0.0185367	+	0.0570502i	−0.941360	+	0.337403i	$0.890451\pi$
$954$	−29.9155	+	92.0706i	−0.968551	+	2.98089i
$955$	62.5126	+	45.4181i	2.02286	+	1.46970i
$956$	8.84115			0.285943
$957$		0			0
$958$	−1.11396			−0.0359906
$959$	−7.39154	−	5.37027i	−0.238685	−	0.173415i
$960$	−0.167056	+	0.514146i	−0.00539172	+	0.0165940i
$961$	10.3932	+	31.9869i	0.335263	+	1.03183i
$962$	22.5122	−	16.3560i	0.725821	−	0.527340i
$963$	−9.21308	+	6.69369i	−0.296887	+	0.215701i
$964$	1.10194	+	3.39141i	0.0354910	+	0.109230i
$965$	3.64849	−	11.2289i	0.117449	−	0.361471i
$966$	0.549655	+	0.399348i	0.0176849	+	0.0128488i
$967$	−33.5800			−1.07986			−0.539930	−	0.841710i	$-0.681549\pi$
$967$	−33.5800			−1.07986			−0.539930	+	0.841710i	$0.681549\pi$
$968$		0			0
$969$	−4.49552			−0.144417
$970$	61.6307	+	44.7773i	1.97884	+	1.43771i
$971$	13.1253	−	40.3955i	0.421210	−	1.29635i	−0.485366	−	0.874311i	$-0.661314\pi$
$971$	13.1253	−	40.3955i	0.421210	−	1.29635i	0.906577	−	0.422041i	$-0.138686\pi$
$972$	−14.3166	−	44.0620i	−0.459206	−	1.41329i
$973$	−8.69844	+	6.31979i	−0.278859	+	0.202603i
$974$	−1.51473	+	1.10052i	−0.0485351	+	0.0352628i
$975$	1.86499	+	5.73984i	0.0597274	+	0.183822i
$976$	32.5008	−	100.027i	1.04033	−	3.20180i
$977$	−37.4839	−	27.2337i	−1.19922	−	0.871282i	−0.205009	−	0.978760i	$-0.565722\pi$
$977$	−37.4839	−	27.2337i	−1.19922	−	0.871282i	−0.994207	+	0.107478i	$0.965722\pi$
$978$	−0.395642			−0.0126512
$979$		0			0
$980$	15.4729			0.494265
$981$	−14.0821	−	10.2312i	−0.449607	−	0.326659i
$982$	2.05627	−	6.32854i	0.0656181	−	0.201952i
$983$	7.75344	+	23.8626i	0.247296	+	0.761100i	0.995250	+	0.0973492i	$0.0310364\pi$
$983$	7.75344	+	23.8626i	0.247296	+	0.761100i	−0.747954	+	0.663751i	$0.768964\pi$
$984$	−5.58367	+	4.05677i	−0.178001	+	0.129325i
$985$	6.05345	−	4.39809i	0.192879	−	0.140135i
$986$	4.46326	+	13.7365i	0.142139	+	0.437459i
$987$	0.639534	−	1.96828i	0.0203566	−	0.0626511i
$988$	−19.2456	−	13.9827i	−0.612283	−	0.444850i
$989$	−0.947563			−0.0301307
$990$		0			0
$991$	37.5645			1.19328			0.596638	−	0.802510i	$-0.296503\pi$
$991$	37.5645			1.19328			0.596638	+	0.802510i	$0.296503\pi$
$992$	38.3779	+	27.8832i	1.21850	+	0.885293i
$993$	2.51607	−	7.74367i	0.0798451	−	0.245738i
$994$	3.33572	+	10.2663i	0.105803	+	0.325627i
$995$	−6.47570	+	4.70487i	−0.205293	+	0.149154i
$996$	−12.5574	+	9.12351i	−0.397898	+	0.289090i
$997$	11.0749	+	34.0849i	0.350745	+	1.07948i	0.958436	+	0.285308i	$0.0920957\pi$
$997$	11.0749	+	34.0849i	0.350745	+	1.07948i	−0.607691	+	0.794173i	$0.707904\pi$
$998$	−6.51221	+	20.0425i	−0.206140	+	0.634435i
$999$	−9.71116	−	7.05557i	−0.307248	−	0.223228i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.w.323.1		16
11.2	odd	10		847.2.f.x.148.1		16
11.3	even	5	inner	847.2.f.w.729.1		16
11.4	even	5		77.2.f.b.64.4	✓	16
11.5	even	5		847.2.a.p.1.8		8
11.6	odd	10		847.2.a.o.1.1		8
11.7	odd	10		847.2.f.x.372.1		16
11.8	odd	10		847.2.f.v.729.4		16
11.9	even	5		77.2.f.b.71.4	yes	16
11.10	odd	2		847.2.f.v.323.4		16
33.5	odd	10		7623.2.a.ct.1.1		8
33.17	even	10		7623.2.a.cw.1.8		8
33.20	odd	10		693.2.m.i.379.1		16
33.26	odd	10		693.2.m.i.64.1		16
77.4	even	15		539.2.q.g.471.4		32
77.6	even	10		5929.2.a.bs.1.1		8
77.9	even	15		539.2.q.g.214.4		32
77.20	odd	10		539.2.f.e.148.4		16
77.26	odd	30		539.2.q.f.361.1		32
77.27	odd	10		5929.2.a.bt.1.8		8
77.31	odd	30		539.2.q.f.324.1		32
77.37	even	15		539.2.q.g.361.1		32
77.48	odd	10		539.2.f.e.295.4		16
77.53	even	15		539.2.q.g.324.1		32
77.59	odd	30		539.2.q.f.471.4		32
77.75	odd	30		539.2.q.f.214.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.64.4	✓	16	11.4	even	5
77.2.f.b.71.4	yes	16	11.9	even	5
539.2.f.e.148.4		16	77.20	odd	10
539.2.f.e.295.4		16	77.48	odd	10
539.2.q.f.214.4		32	77.75	odd	30
539.2.q.f.324.1		32	77.31	odd	30
539.2.q.f.361.1		32	77.26	odd	30
539.2.q.f.471.4		32	77.59	odd	30
539.2.q.g.214.4		32	77.9	even	15
539.2.q.g.324.1		32	77.53	even	15
539.2.q.g.361.1		32	77.37	even	15
539.2.q.g.471.4		32	77.4	even	15
693.2.m.i.64.1		16	33.26	odd	10
693.2.m.i.379.1		16	33.20	odd	10
847.2.a.o.1.1		8	11.6	odd	10
847.2.a.p.1.8		8	11.5	even	5
847.2.f.v.323.4		16	11.10	odd	2
847.2.f.v.729.4		16	11.8	odd	10
847.2.f.w.323.1		16	1.1	even	1	trivial
847.2.f.w.729.1		16	11.3	even	5	inner
847.2.f.x.148.1		16	11.2	odd	10
847.2.f.x.372.1		16	11.7	odd	10
5929.2.a.bs.1.1		8	77.6	even	10
5929.2.a.bt.1.8		8	77.27	odd	10
7623.2.a.ct.1.1		8	33.5	odd	10
7623.2.a.cw.1.8		8	33.17	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.06456 - 1.49999i) q^{2} +(-0.126882 + 0.390502i) q^{3} +(1.39441 + 4.29156i) q^{4} +(-2.77410 + 2.01550i) q^{5} +(0.847707 - 0.615895i) q^{6} +(0.309017 + 0.951057i) q^{7} +(1.98127 - 6.09772i) q^{8} +(2.29066 + 1.66426i) q^{9} +O(q^{10})\)	\(q+(-2.06456 - 1.49999i) q^{2} +(-0.126882 + 0.390502i) q^{3} +(1.39441 + 4.29156i) q^{4} +(-2.77410 + 2.01550i) q^{5} +(0.847707 - 0.615895i) q^{6} +(0.309017 + 0.951057i) q^{7} +(1.98127 - 6.09772i) q^{8} +(2.29066 + 1.66426i) q^{9} +8.75055 q^{10} -1.85279 q^{12} +(1.75964 + 1.27845i) q^{13} +(0.788594 - 2.42704i) q^{14} +(-0.435075 - 1.33902i) q^{15} +(-5.93578 + 4.31259i) q^{16} +(3.65445 - 2.65511i) q^{17} +(-2.23283 - 6.87195i) q^{18} +(-0.748999 + 2.30518i) q^{19} +(-12.5179 - 9.09477i) q^{20} -0.410598 q^{21} +0.648403 q^{23} +(2.12979 + 1.54738i) q^{24} +(2.08830 - 6.42713i) q^{25} +(-1.71522 - 5.27889i) q^{26} +(-1.93708 + 1.40737i) q^{27} +(-3.65062 + 2.65233i) q^{28} +(-0.387183 - 1.19163i) q^{29} +(-1.11029 + 3.41711i) q^{30} +(6.50406 + 4.72548i) q^{31} +5.90061 q^{32} -11.5275 q^{34} +(-2.77410 - 2.01550i) q^{35} +(-3.94815 + 12.1512i) q^{36} +(1.54919 + 4.76792i) q^{37} +(5.00411 - 3.63570i) q^{38} +(-0.722504 + 0.524930i) q^{39} +(6.79373 + 20.9090i) q^{40} +(-0.810151 + 2.49339i) q^{41} +(0.847707 + 0.615895i) q^{42} -1.46138 q^{43} -9.70884 q^{45} +(-1.33867 - 0.972600i) q^{46} +(-1.55757 + 4.79369i) q^{47} +(-0.930935 - 2.86512i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-13.9521 + 10.1368i) q^{50} +(0.573144 + 1.76396i) q^{51} +(-3.03289 + 9.33427i) q^{52} +(-10.8392 - 7.87516i) q^{53} +6.11028 q^{54} +6.41153 q^{56} +(-0.805144 - 0.584971i) q^{57} +(-0.988069 + 3.04096i) q^{58} +(2.37009 + 7.29440i) q^{59} +(5.13982 - 3.73430i) q^{60} +(-11.5971 + 8.42580i) q^{61} +(-6.33987 - 19.5121i) q^{62} +(-0.874954 + 2.69283i) q^{63} +(-0.310639 - 0.225693i) q^{64} -7.45814 q^{65} +6.22696 q^{67} +(16.4904 + 11.9810i) q^{68} +(-0.0822705 + 0.253203i) q^{69} +(2.70407 + 8.32227i) q^{70} +(-3.42211 + 2.48631i) q^{71} +(14.6866 - 10.6704i) q^{72} +(-1.83098 - 5.63517i) q^{73} +(3.95345 - 12.1675i) q^{74} +(2.24484 + 1.63097i) q^{75} -10.9372 q^{76} +2.27905 q^{78} +(-7.89858 - 5.73865i) q^{79} +(7.77440 - 23.9271i) q^{80} +(2.32106 + 7.14349i) q^{81} +(5.41268 - 3.93254i) q^{82} +(6.77759 - 4.92421i) q^{83} +(-0.572543 - 1.76211i) q^{84} +(-4.78643 + 14.7311i) q^{85} +(3.01711 + 2.19206i) q^{86} +0.514460 q^{87} +4.76249 q^{89} +(20.0445 + 14.5632i) q^{90} +(-0.672122 + 2.06858i) q^{91} +(0.904140 + 2.78266i) q^{92} +(-2.67056 + 1.94027i) q^{93} +(10.4062 - 7.56055i) q^{94} +(-2.56830 - 7.90441i) q^{95} +(-0.748680 + 2.30420i) q^{96} +(7.04306 + 5.11708i) q^{97} +2.55194 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} - 2 q^{6} - 4 q^{7} + 5 q^{8} - 2 q^{9}+O(q^{10}) \) 16 * q + 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 - 2 * q^6 - 4 * q^7 + 5 * q^8 - 2 * q^9	\( 16 q + 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} - 2 q^{6} - 4 q^{7} + 5 q^{8} - 2 q^{9} + 12 q^{10} + 18 q^{12} + 13 q^{13} - 3 q^{14} + 7 q^{15} - 18 q^{16} + 10 q^{17} - 19 q^{18} - 6 q^{19} - 24 q^{20} + 8 q^{21} + 32 q^{23} + 45 q^{24} - 23 q^{25} + 33 q^{26} - 20 q^{27} - 11 q^{28} - 12 q^{29} + 38 q^{30} - 2 q^{31} + 32 q^{32} - 24 q^{34} - 5 q^{35} - 38 q^{36} - 11 q^{37} + 15 q^{38} - 24 q^{39} + 5 q^{40} + 20 q^{41} - 2 q^{42} - 8 q^{43} + 70 q^{45} + 38 q^{46} + 7 q^{47} + 39 q^{48} - 4 q^{49} - 58 q^{50} + 16 q^{51} + 8 q^{52} - 41 q^{53} + 60 q^{54} + 9 q^{57} - 5 q^{58} - 18 q^{59} + 25 q^{60} - 12 q^{61} - 61 q^{62} - 12 q^{63} - 3 q^{64} - 8 q^{65} - 38 q^{67} - 7 q^{68} - 30 q^{69} + 12 q^{70} + q^{71} + 35 q^{72} + 60 q^{73} - 4 q^{74} + 4 q^{75} + 52 q^{76} - 58 q^{78} - 15 q^{79} + 83 q^{80} + 6 q^{81} - 6 q^{82} + 20 q^{83} - 17 q^{84} - 9 q^{85} + 48 q^{86} - 72 q^{87} + 74 q^{89} + 16 q^{90} - 7 q^{91} + 20 q^{92} - 53 q^{93} + 66 q^{94} - 53 q^{95} + 48 q^{96} - 35 q^{97} + 2 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 - 2 * q^6 - 4 * q^7 + 5 * q^8 - 2 * q^9 + 12 * q^10 + 18 * q^12 + 13 * q^13 - 3 * q^14 + 7 * q^15 - 18 * q^16 + 10 * q^17 - 19 * q^18 - 6 * q^19 - 24 * q^20 + 8 * q^21 + 32 * q^23 + 45 * q^24 - 23 * q^25 + 33 * q^26 - 20 * q^27 - 11 * q^28 - 12 * q^29 + 38 * q^30 - 2 * q^31 + 32 * q^32 - 24 * q^34 - 5 * q^35 - 38 * q^36 - 11 * q^37 + 15 * q^38 - 24 * q^39 + 5 * q^40 + 20 * q^41 - 2 * q^42 - 8 * q^43 + 70 * q^45 + 38 * q^46 + 7 * q^47 + 39 * q^48 - 4 * q^49 - 58 * q^50 + 16 * q^51 + 8 * q^52 - 41 * q^53 + 60 * q^54 + 9 * q^57 - 5 * q^58 - 18 * q^59 + 25 * q^60 - 12 * q^61 - 61 * q^62 - 12 * q^63 - 3 * q^64 - 8 * q^65 - 38 * q^67 - 7 * q^68 - 30 * q^69 + 12 * q^70 + q^71 + 35 * q^72 + 60 * q^73 - 4 * q^74 + 4 * q^75 + 52 * q^76 - 58 * q^78 - 15 * q^79 + 83 * q^80 + 6 * q^81 - 6 * q^82 + 20 * q^83 - 17 * q^84 - 9 * q^85 + 48 * q^86 - 72 * q^87 + 74 * q^89 + 16 * q^90 - 7 * q^91 + 20 * q^92 - 53 * q^93 + 66 * q^94 - 53 * q^95 + 48 * q^96 - 35 * q^97 + 2 * q^98

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