LMFDB - Embedded newform 170.2.n.a.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(9,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1]))

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

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

chi := DirichletCharacter("170.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.n (of order $8$, degree $4$, 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:	$1.35745683436$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 16 x^{15} + 52 x^{14} + 992 x^{13} + 6181 x^{12} + 8952 x^{11} + 6244 x^{10} - 11448 x^{9} + \cdots + 2048 $ x^20 - 16x^15 + 52x^14 + 992x^13 + 6181x^12 + 8952x^11 + 6244x^10 - 11448x^9 - 14520x^8 + 27936x^7 + 27880x^6 - 121104x^5 + 187460x^4 - 142208x^3 + 73856x^2 - 19456*x + 2048
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			49.4
Root			$0.355063 - 0.857197i$ of defining polynomial
Character	$\chi$	$=$	170.49
Dual form			170.2.n.a.59.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(0.857197 - 0.355063i) q^{3} -1.00000i q^{4} +(2.23422 - 0.0908004i) q^{5} +(0.355063 - 0.857197i) q^{6} +(-0.939960 + 2.26926i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.51260 + 1.51260i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(0.857197 - 0.355063i) q^{3} -1.00000i q^{4} +(2.23422 - 0.0908004i) q^{5} +(0.355063 - 0.857197i) q^{6} +(-0.939960 + 2.26926i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.51260 + 1.51260i) q^{9} +(1.51563 - 1.64404i) q^{10} +(1.42570 - 3.44195i) q^{11} +(-0.355063 - 0.857197i) q^{12} -4.92512 q^{13} +(0.939960 + 2.26926i) q^{14} +(1.88293 - 0.871123i) q^{15} -1.00000 q^{16} +(-3.07691 - 2.74457i) q^{17} +2.13914i q^{18} +(2.88737 + 2.88737i) q^{19} +(-0.0908004 - 2.23422i) q^{20} +2.27895i q^{21} +(-1.42570 - 3.44195i) q^{22} +(4.93649 + 2.04476i) q^{23} +(-0.857197 - 0.355063i) q^{24} +(4.98351 - 0.405737i) q^{25} +(-3.48258 + 3.48258i) q^{26} +(-1.82472 + 4.40526i) q^{27} +(2.26926 + 0.939960i) q^{28} +(-9.69029 + 4.01385i) q^{29} +(0.715456 - 1.94741i) q^{30} +(-2.21859 - 5.35615i) q^{31} +(-0.707107 + 0.707107i) q^{32} -3.45664i q^{33} +(-4.11640 + 0.235000i) q^{34} +(-1.89403 + 5.15539i) q^{35} +(1.51260 + 1.51260i) q^{36} +(-1.79488 + 0.743464i) q^{37} +4.08336 q^{38} +(-4.22180 + 1.74873i) q^{39} +(-1.64404 - 1.51563i) q^{40} +(6.01020 + 2.48951i) q^{41} +(1.61146 + 1.61146i) q^{42} +(-1.23524 - 1.23524i) q^{43} +(-3.44195 - 1.42570i) q^{44} +(-3.24215 + 3.51684i) q^{45} +(4.93649 - 2.04476i) q^{46} +7.40275 q^{47} +(-0.857197 + 0.355063i) q^{48} +(0.683717 + 0.683717i) q^{49} +(3.23698 - 3.81077i) q^{50} +(-3.61201 - 1.26014i) q^{51} +4.92512i q^{52} +(3.36188 - 3.36188i) q^{53} +(1.82472 + 4.40526i) q^{54} +(2.87281 - 7.81953i) q^{55} +(2.26926 - 0.939960i) q^{56} +(3.50024 + 1.44985i) q^{57} +(-4.01385 + 9.69029i) q^{58} +(-3.52973 + 3.52973i) q^{59} +(-0.871123 - 1.88293i) q^{60} +(-2.70302 - 1.11963i) q^{61} +(-5.35615 - 2.21859i) q^{62} +(-2.01071 - 4.85428i) q^{63} +1.00000i q^{64} +(-11.0038 + 0.447202i) q^{65} +(-2.44421 - 2.44421i) q^{66} -10.9601i q^{67} +(-2.74457 + 3.07691i) q^{68} +4.95756 q^{69} +(2.30613 + 4.98469i) q^{70} +(4.66263 + 11.2566i) q^{71} +2.13914 q^{72} +(-2.67056 - 6.44731i) q^{73} +(-0.743464 + 1.79488i) q^{74} +(4.12779 - 2.11725i) q^{75} +(2.88737 - 2.88737i) q^{76} +(6.47058 + 6.47058i) q^{77} +(-1.74873 + 4.22180i) q^{78} +(2.57787 - 6.22353i) q^{79} +(-2.23422 + 0.0908004i) q^{80} -1.99337i q^{81} +(6.01020 - 2.48951i) q^{82} +(11.1304 - 11.1304i) q^{83} +2.27895 q^{84} +(-7.12371 - 5.85259i) q^{85} -1.74689 q^{86} +(-6.88132 + 6.88132i) q^{87} +(-3.44195 + 1.42570i) q^{88} -8.04456i q^{89} +(0.194235 + 4.77933i) q^{90} +(4.62941 - 11.1764i) q^{91} +(2.04476 - 4.93649i) q^{92} +(-3.80354 - 3.80354i) q^{93} +(5.23453 - 5.23453i) q^{94} +(6.71320 + 6.18885i) q^{95} +(-0.355063 + 0.857197i) q^{96} +(-2.77526 - 6.70007i) q^{97} +0.966921 q^{98} +(3.04978 + 7.36282i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{5}+O(q^{10}) $ 20 * q - 4 * q^5	$ 20 q - 4 q^{5} + 4 q^{10} - 8 q^{11} - 24 q^{13} + 8 q^{15} - 20 q^{16} + 8 q^{20} + 8 q^{22} + 16 q^{23} - 12 q^{25} - 12 q^{26} + 24 q^{27} - 12 q^{29} - 8 q^{30} + 8 q^{31} + 8 q^{34} - 8 q^{35} - 8 q^{37} - 8 q^{38} + 4 q^{40} + 4 q^{41} + 8 q^{42} + 16 q^{43} - 8 q^{44} - 12 q^{45} + 16 q^{46} + 40 q^{47} - 56 q^{49} + 8 q^{50} - 8 q^{51} + 44 q^{53} - 24 q^{54} - 72 q^{57} + 16 q^{59} + 16 q^{60} + 8 q^{61} - 8 q^{62} - 24 q^{63} - 8 q^{65} - 8 q^{66} + 20 q^{68} - 16 q^{69} - 16 q^{70} + 8 q^{71} - 28 q^{72} - 60 q^{73} + 28 q^{74} + 64 q^{75} + 8 q^{78} + 56 q^{79} + 4 q^{80} + 4 q^{82} + 16 q^{84} - 16 q^{85} + 48 q^{86} - 72 q^{87} - 8 q^{88} + 32 q^{90} - 24 q^{91} - 8 q^{92} + 72 q^{93} + 32 q^{94} + 8 q^{95} + 48 q^{97} - 36 q^{98} + 72 q^{99}+O(q^{100}) $ 20 * q - 4 * q^5 + 4 * q^10 - 8 * q^11 - 24 * q^13 + 8 * q^15 - 20 * q^16 + 8 * q^20 + 8 * q^22 + 16 * q^23 - 12 * q^25 - 12 * q^26 + 24 * q^27 - 12 * q^29 - 8 * q^30 + 8 * q^31 + 8 * q^34 - 8 * q^35 - 8 * q^37 - 8 * q^38 + 4 * q^40 + 4 * q^41 + 8 * q^42 + 16 * q^43 - 8 * q^44 - 12 * q^45 + 16 * q^46 + 40 * q^47 - 56 * q^49 + 8 * q^50 - 8 * q^51 + 44 * q^53 - 24 * q^54 - 72 * q^57 + 16 * q^59 + 16 * q^60 + 8 * q^61 - 8 * q^62 - 24 * q^63 - 8 * q^65 - 8 * q^66 + 20 * q^68 - 16 * q^69 - 16 * q^70 + 8 * q^71 - 28 * q^72 - 60 * q^73 + 28 * q^74 + 64 * q^75 + 8 * q^78 + 56 * q^79 + 4 * q^80 + 4 * q^82 + 16 * q^84 - 16 * q^85 + 48 * q^86 - 72 * q^87 - 8 * q^88 + 32 * q^90 - 24 * q^91 - 8 * q^92 + 72 * q^93 + 32 * q^94 + 8 * q^95 + 48 * q^97 - 36 * q^98 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$-1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	0.857197	−	0.355063i	0.494903	−	0.204996i	−0.121250	−	0.992622i	$-0.538690\pi$
$3$	0.857197	−	0.355063i	0.494903	−	0.204996i	0.616153	+	0.787626i	$0.288690\pi$
$4$		−	1.00000i		−	0.500000i
$5$	2.23422	−	0.0908004i	0.999175	−	0.0406072i
$5$	2.23422	−	0.0908004i	0.999175	−	0.0406072i
$6$	0.355063	−	0.857197i	0.144954	−	0.349949i
$7$	−0.939960	+	2.26926i	−0.355271	+	0.857701i	0.640680	+	0.767808i	$0.278652\pi$
$7$	−0.939960	+	2.26926i	−0.355271	+	0.857701i	−0.995951	+	0.0898929i	$0.971348\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−1.51260	+	1.51260i	−0.504201	+	0.504201i
$10$	1.51563	−	1.64404i	0.479284	−	0.519891i
$11$	1.42570	−	3.44195i	0.429865	−	1.03779i	−0.549465	−	0.835517i	$-0.685168\pi$
$11$	1.42570	−	3.44195i	0.429865	−	1.03779i	0.979330	−	0.202269i	$-0.0648316\pi$
$12$	−0.355063	−	0.857197i	−0.102498	−	0.247451i
$13$	−4.92512			−1.36598			−0.682991	−	0.730427i	$-0.739321\pi$
$13$	−4.92512			−1.36598			−0.682991	+	0.730427i	$0.739321\pi$
$14$	0.939960	+	2.26926i	0.251215	+	0.606486i
$15$	1.88293	−	0.871123i	0.486170	−	0.224923i
$16$	−1.00000			−0.250000
$17$	−3.07691	−	2.74457i	−0.746260	−	0.665655i
$17$	−3.07691	−	2.74457i	−0.746260	−	0.665655i
$18$			2.13914i			0.504201i
$19$	2.88737	+	2.88737i	0.662408	+	0.662408i	0.955947	−	0.293539i	$-0.0948331\pi$
$19$	2.88737	+	2.88737i	0.662408	+	0.662408i	−0.293539	+	0.955947i	$0.594833\pi$
$20$	−0.0908004	−	2.23422i	−0.0203036	−	0.499588i
$21$			2.27895i			0.497308i
$22$	−1.42570	−	3.44195i	−0.303961	−	0.733826i
$23$	4.93649	+	2.04476i	1.02933	+	0.426362i	0.832470	−	0.554070i	$-0.186926\pi$
$23$	4.93649	+	2.04476i	1.02933	+	0.426362i	0.196858	+	0.980432i	$0.436926\pi$
$24$	−0.857197	−	0.355063i	−0.174975	−	0.0724769i
$25$	4.98351	−	0.405737i	0.996702	−	0.0811473i
$26$	−3.48258	+	3.48258i	−0.682991	+	0.682991i
$27$	−1.82472	+	4.40526i	−0.351167	+	0.847792i
$28$	2.26926	+	0.939960i	0.428850	+	0.177636i
$29$	−9.69029	+	4.01385i	−1.79944	+	0.745353i	−0.812779	+	0.582573i	$0.802046\pi$
$29$	−9.69029	+	4.01385i	−1.79944	+	0.745353i	−0.986662	+	0.162780i	$0.947954\pi$
$30$	0.715456	−	1.94741i	0.130624	−	0.355547i
$31$	−2.21859	−	5.35615i	−0.398470	−	0.961993i	−0.988029	−	0.154267i	$-0.950698\pi$
$31$	−2.21859	−	5.35615i	−0.398470	−	0.961993i	0.589559	−	0.807725i	$-0.299302\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		−	3.45664i		−	0.601724i
$34$	−4.11640	+	0.235000i	−0.705957	+	0.0403022i
$35$	−1.89403	+	5.15539i	−0.320149	+	0.871420i
$36$	1.51260	+	1.51260i	0.252101	+	0.252101i
$37$	−1.79488	+	0.743464i	−0.295077	+	0.122225i	−0.525311	−	0.850911i	$-0.676051\pi$
$37$	−1.79488	+	0.743464i	−0.295077	+	0.122225i	0.230234	+	0.973135i	$0.426051\pi$
$38$	4.08336			0.662408
$39$	−4.22180	+	1.74873i	−0.676028	+	0.280020i
$40$	−1.64404	−	1.51563i	−0.259946	−	0.239642i
$41$	6.01020	+	2.48951i	0.938635	+	0.388796i	0.798948	−	0.601400i	$-0.205390\pi$
$41$	6.01020	+	2.48951i	0.938635	+	0.388796i	0.139687	+	0.990196i	$0.455390\pi$
$42$	1.61146	+	1.61146i	0.248654	+	0.248654i
$43$	−1.23524	−	1.23524i	−0.188372	−	0.188372i	0.606620	−	0.794992i	$-0.292525\pi$
$43$	−1.23524	−	1.23524i	−0.188372	−	0.188372i	−0.794992	+	0.606620i	$0.792525\pi$
$44$	−3.44195	−	1.42570i	−0.518893	−	0.214933i
$45$	−3.24215	+	3.51684i	−0.483311	+	0.524259i
$46$	4.93649	−	2.04476i	0.727845	−	0.301483i
$47$	7.40275			1.07980			0.539901	−	0.841729i	$-0.318462\pi$
$47$	7.40275			1.07980			0.539901	+	0.841729i	$0.318462\pi$
$48$	−0.857197	+	0.355063i	−0.123726	+	0.0512489i
$49$	0.683717	+	0.683717i	0.0976738	+	0.0976738i
$50$	3.23698	−	3.81077i	0.457777	−	0.538925i
$51$	−3.61201	−	1.26014i	−0.505782	−	0.176455i
$52$			4.92512i			0.682991i
$53$	3.36188	−	3.36188i	0.461790	−	0.461790i	−0.437452	−	0.899242i	$-0.644119\pi$
$53$	3.36188	−	3.36188i	0.461790	−	0.461790i	0.899242	+	0.437452i	$0.144119\pi$
$54$	1.82472	+	4.40526i	0.248313	+	0.599480i
$55$	2.87281	−	7.81953i	0.387369	−	1.05439i
$56$	2.26926	−	0.939960i	0.303243	−	0.125607i
$57$	3.50024	+	1.44985i	0.463618	+	0.192037i
$58$	−4.01385	+	9.69029i	−0.527044	+	1.27240i
$59$	−3.52973	+	3.52973i	−0.459532	+	0.459532i	−0.898502	−	0.438970i	$-0.855343\pi$
$59$	−3.52973	+	3.52973i	−0.459532	+	0.459532i	0.438970	+	0.898502i	$0.355343\pi$
$60$	−0.871123	−	1.88293i	−0.112462	−	0.243085i
$61$	−2.70302	−	1.11963i	−0.346086	−	0.143354i	0.202868	−	0.979206i	$-0.434974\pi$
$61$	−2.70302	−	1.11963i	−0.346086	−	0.143354i	−0.548954	+	0.835852i	$0.684974\pi$
$62$	−5.35615	−	2.21859i	−0.680231	−	0.281761i
$63$	−2.01071	−	4.85428i	−0.253325	−	0.611582i
$64$			1.00000i			0.125000i
$65$	−11.0038	+	0.447202i	−1.36486	+	0.0554686i
$66$	−2.44421	−	2.44421i	−0.300862	−	0.300862i
$67$		−	10.9601i		−	1.33899i	−0.742816	−	0.669495i	$-0.766510\pi$
$67$		−	10.9601i		−	1.33899i	0.742816	−	0.669495i	$-0.233490\pi$
$68$	−2.74457	+	3.07691i	−0.332828	+	0.373130i
$69$	4.95756			0.596820
$70$	2.30613	+	4.98469i	0.275635	+	0.595785i
$71$	4.66263	+	11.2566i	0.553353	+	1.33591i	0.914946	+	0.403576i	$0.132233\pi$
$71$	4.66263	+	11.2566i	0.553353	+	1.33591i	−0.361594	+	0.932336i	$0.617767\pi$
$72$	2.13914			0.252101
$73$	−2.67056	−	6.44731i	−0.312566	−	0.754601i	−0.999608	−	0.0279834i	$-0.991091\pi$
$73$	−2.67056	−	6.44731i	−0.312566	−	0.754601i	0.687043	−	0.726617i	$-0.258909\pi$
$74$	−0.743464	+	1.79488i	−0.0864259	+	0.208651i
$75$	4.12779	−	2.11725i	0.476636	−	0.244480i
$76$	2.88737	−	2.88737i	0.331204	−	0.331204i
$77$	6.47058	+	6.47058i	0.737391	+	0.737391i
$78$	−1.74873	+	4.22180i	−0.198004	+	0.478024i
$79$	2.57787	−	6.22353i	0.290033	−	0.700202i	−0.709959	−	0.704243i	$-0.751286\pi$
$79$	2.57787	−	6.22353i	0.290033	−	0.700202i	0.999992	+	0.00404145i	$0.00128644\pi$
$80$	−2.23422	+	0.0908004i	−0.249794	+	0.0101518i
$81$		−	1.99337i		−	0.221485i
$82$	6.01020	−	2.48951i	0.663715	−	0.274920i
$83$	11.1304	−	11.1304i	1.22173	−	1.22173i	0.254707	−	0.967018i	$-0.418021\pi$
$83$	11.1304	−	11.1304i	1.22173	−	1.22173i	0.967018	−	0.254707i	$-0.0819791\pi$
$84$	2.27895			0.248654
$85$	−7.12371	−	5.85259i	−0.772674	−	0.634803i
$86$	−1.74689			−0.188372
$87$	−6.88132	+	6.88132i	−0.737755	+	0.737755i
$88$	−3.44195	+	1.42570i	−0.366913	+	0.151980i
$89$		−	8.04456i		−	0.852722i	−0.904553	−	0.426361i	$-0.859795\pi$
$89$		−	8.04456i		−	0.852722i	0.904553	−	0.426361i	$-0.140205\pi$
$90$	0.194235	+	4.77933i	0.0204742	+	0.503785i
$91$	4.62941	−	11.1764i	0.485294	−	1.17160i
$92$	2.04476	−	4.93649i	0.213181	−	0.514664i
$93$	−3.80354	−	3.80354i	−0.394408	−	0.394408i
$94$	5.23453	−	5.23453i	0.539901	−	0.539901i
$95$	6.71320	+	6.18885i	0.688760	+	0.634963i
$96$	−0.355063	+	0.857197i	−0.0362384	+	0.0874873i
$97$	−2.77526	−	6.70007i	−0.281785	−	0.680289i	0.718093	−	0.695948i	$-0.245015\pi$
$97$	−2.77526	−	6.70007i	−0.281785	−	0.680289i	−0.999877	+	0.0156588i	$0.995015\pi$
$98$	0.966921			0.0976738
$99$	3.04978	+	7.36282i	0.306514	+	0.739991i
$100$	−0.405737	−	4.98351i	−0.0405737	−	0.498351i
$101$	−3.03657			−0.302150			−0.151075	−	0.988522i	$-0.548274\pi$
$101$	−3.03657			−0.302150			−0.151075	+	0.988522i	$0.548274\pi$
$102$	−3.44513	+	1.66302i	−0.341119	+	0.164664i
$103$			6.34542i			0.625232i	0.949880	+	0.312616i	$0.101205\pi$
$103$			6.34542i			0.625232i	−0.949880	+	0.312616i	$0.898795\pi$
$104$	3.48258	+	3.48258i	0.341495	+	0.341495i
$105$	0.206929	+	5.09168i	0.0201943	+	0.496897i
$106$		−	4.75442i		−	0.461790i
$107$	2.12100	+	5.12055i	0.205045	+	0.495022i	0.992630	−	0.121184i	$-0.0386690\pi$
$107$	2.12100	+	5.12055i	0.205045	+	0.495022i	−0.787585	+	0.616206i	$0.788669\pi$
$108$	4.40526	+	1.82472i	0.423896	+	0.175584i
$109$	−3.60761	−	1.49432i	−0.345547	−	0.143130i	0.203159	−	0.979146i	$-0.434879\pi$
$109$	−3.60761	−	1.49432i	−0.345547	−	0.143130i	−0.548706	+	0.836016i	$0.684879\pi$
$110$	−3.49787	−	7.56063i	−0.333508	−	0.720877i
$111$	−1.27459	+	1.27459i	−0.120979	+	0.120979i
$112$	0.939960	−	2.26926i	0.0888178	−	0.214425i
$113$	−9.06969	−	3.75679i	−0.853205	−	0.353409i	−0.0871586	−	0.996194i	$-0.527779\pi$
$113$	−9.06969	−	3.75679i	−0.853205	−	0.353409i	−0.766046	+	0.642785i	$0.777779\pi$
$114$	3.50024	−	1.44985i	0.327828	−	0.135791i
$115$	11.2149	+	4.12021i	1.04579	+	0.384212i
$116$	4.01385	+	9.69029i	0.372676	+	0.899720i
$117$	7.44975	−	7.44975i	0.688729	−	0.688729i
$118$			4.99179i			0.459532i
$119$	9.12031	−	4.40253i	0.836058	−	0.403579i
$120$	−1.94741	−	0.715456i	−0.177773	−	0.0653119i
$121$	−2.03620	−	2.03620i	−0.185109	−	0.185109i
$122$	−2.70302	+	1.11963i	−0.244720	+	0.101366i
$123$	6.03586			0.544235
$124$	−5.35615	+	2.21859i	−0.480996	+	0.199235i
$125$	11.0974	−	1.35901i	0.992585	−	0.121554i
$126$	−4.85428	−	2.01071i	−0.432454	−	0.179128i
$127$	−4.76241	−	4.76241i	−0.422596	−	0.422596i	0.463501	−	0.886096i	$-0.346593\pi$
$127$	−4.76241	−	4.76241i	−0.422596	−	0.422596i	−0.886096	+	0.463501i	$0.846593\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−1.49743	−	0.620254i	−0.131841	−	0.0546103i
$130$	−7.46465	+	8.09709i	−0.654693	+	0.710162i
$131$	−10.3104	+	4.27070i	−0.900823	+	0.373133i	−0.784536	−	0.620083i	$-0.787099\pi$
$131$	−10.3104	+	4.27070i	−0.900823	+	0.373133i	−0.116286	+	0.993216i	$0.537099\pi$
$132$	−3.45664			−0.300862
$133$	−9.26621	+	3.83819i	−0.803482	+	0.332813i
$134$	−7.74997	−	7.74997i	−0.669495	−	0.669495i
$135$	−3.67683	+	10.0080i	−0.316451	+	0.861353i
$136$	0.235000	+	4.11640i	0.0201511	+	0.352979i
$137$			12.2193i			1.04397i	0.852955	+	0.521985i	$0.174808\pi$
$137$			12.2193i			1.04397i	−0.852955	+	0.521985i	$0.825192\pi$
$138$	3.50552	−	3.50552i	0.298410	−	0.298410i
$139$	−1.83394	−	4.42752i	−0.155553	−	0.375537i	0.826821	−	0.562465i	$-0.190147\pi$
$139$	−1.83394	−	4.42752i	−0.155553	−	0.375537i	−0.982374	+	0.186928i	$0.940147\pi$
$140$	5.15539	+	1.89403i	0.435710	+	0.160075i
$141$	6.34561	−	2.62844i	0.534397	−	0.221354i
$142$	11.2566	+	4.66263i	0.944632	+	0.391279i
$143$	−7.02175	+	16.9520i	−0.587188	+	1.41760i
$144$	1.51260	−	1.51260i	0.126050	−	0.126050i
$145$	−21.2858	+	9.84772i	−1.76769	+	0.817808i
$146$	−6.44731	−	2.67056i	−0.533583	−	0.221017i
$147$	0.828842	+	0.343318i	0.0683617	+	0.0283164i
$148$	0.743464	+	1.79488i	0.0611124	+	0.147538i
$149$			7.65815i			0.627380i	0.949525	+	0.313690i	$0.101565\pi$
$149$			7.65815i			0.627380i	−0.949525	+	0.313690i	$0.898435\pi$
$150$	1.42166	−	4.41591i	0.116078	−	0.360558i
$151$	4.62832	+	4.62832i	0.376647	+	0.376647i	0.869891	−	0.493244i	$-0.164189\pi$
$151$	4.62832	+	4.62832i	0.376647	+	0.376647i	−0.493244	+	0.869891i	$0.664189\pi$
$152$		−	4.08336i		−	0.331204i
$153$	8.80558	−	0.502699i	0.711889	−	0.0406408i
$154$	9.15079			0.737391
$155$	−5.44316	−	11.7654i	−0.437205	−	0.945018i
$156$	1.74873	+	4.22180i	0.140010	+	0.338014i
$157$	14.6983			1.17306			0.586528	−	0.809929i	$-0.300494\pi$
$157$	14.6983			1.17306			0.586528	+	0.809929i	$0.300494\pi$
$158$	−2.57787	−	6.22353i	−0.205084	−	0.495117i
$159$	1.68812	−	4.07547i	0.133876	−	0.323206i
$160$	−1.51563	+	1.64404i	−0.119821	+	0.129973i
$161$	−9.28019	+	9.28019i	−0.731382	+	0.731382i
$162$	−1.40952	−	1.40952i	−0.110743	−	0.110743i
$163$	2.40573	−	5.80794i	0.188431	−	0.454913i	−0.801227	−	0.598361i	$-0.795819\pi$
$163$	2.40573	−	5.80794i	0.188431	−	0.454913i	0.989658	+	0.143448i	$0.0458190\pi$
$164$	2.48951	−	6.01020i	0.194398	−	0.469318i
$165$	−0.313864	−	7.72291i	−0.0244343	−	0.601228i
$166$		−	15.7408i		−	1.22173i
$167$	−2.36977	+	0.981591i	−0.183378	+	0.0759578i	−0.472483	−	0.881340i	$-0.656642\pi$
$167$	−2.36977	+	0.981591i	−0.183378	+	0.0759578i	0.289105	+	0.957297i	$0.406642\pi$
$168$	1.61146	−	1.61146i	0.124327	−	0.124327i
$169$	11.2568			0.865907
$170$	−9.17563	+	0.898814i	−0.703738	+	0.0689359i
$171$	−8.73489			−0.667974
$172$	−1.23524	+	1.23524i	−0.0941858	+	0.0941858i
$173$	−17.9886	+	7.45110i	−1.36764	+	0.566497i	−0.941149	−	0.337993i	$-0.890252\pi$
$173$	−17.9886	+	7.45110i	−1.36764	+	0.566497i	−0.426496	+	0.904490i	$0.640252\pi$
$174$			9.73165i			0.737755i
$175$	−3.76358	+	11.6903i	−0.284500	+	0.883702i
$176$	−1.42570	+	3.44195i	−0.107466	+	0.259447i
$177$	−1.77240	+	4.27895i	−0.133222	+	0.321626i
$178$	−5.68836	−	5.68836i	−0.426361	−	0.426361i
$179$	11.4346	−	11.4346i	0.854663	−	0.854663i	−0.136040	−	0.990703i	$-0.543438\pi$
$179$	11.4346	−	11.4346i	0.854663	−	0.854663i	0.990703	+	0.136040i	$0.0434376\pi$
$180$	3.51684	+	3.24215i	0.262130	+	0.241655i
$181$	−7.00292	+	16.9065i	−0.520523	+	1.25665i	0.417056	+	0.908881i	$0.363062\pi$
$181$	−7.00292	+	16.9065i	−0.520523	+	1.25665i	−0.937579	+	0.347773i	$0.886938\pi$
$182$	−4.62941	−	11.1764i	−0.343155	−	0.828449i
$183$	−2.71456			−0.200666
$184$	−2.04476	−	4.93649i	−0.150742	−	0.363923i
$185$	−3.94266	+	1.82404i	−0.289870	+	0.134106i
$186$	−5.37901			−0.394408
$187$	−13.8334	+	6.67762i	−1.01160	+	0.488316i
$188$		−	7.40275i		−	0.539901i
$189$	−8.28153	−	8.28153i	−0.602393	−	0.602393i
$190$	9.12313	−	0.370770i	0.661862	−	0.0268985i
$191$			8.07039i			0.583953i	0.956426	+	0.291976i	$0.0943129\pi$
$191$			8.07039i			0.583953i	−0.956426	+	0.291976i	$0.905687\pi$
$192$	0.355063	+	0.857197i	0.0256244	+	0.0618629i
$193$	16.1760	+	6.70033i	1.16438	+	0.482301i	0.879330	−	0.476213i	$-0.157991\pi$
$193$	16.1760	+	6.70033i	1.16438	+	0.482301i	0.285047	+	0.958514i	$0.407991\pi$
$194$	−6.70007	−	2.77526i	−0.481037	−	0.199252i
$195$	−9.27365	+	4.29038i	−0.664100	+	0.307241i
$196$	0.683717	−	0.683717i	0.0488369	−	0.0488369i
$197$	−2.33680	+	5.64153i	−0.166490	+	0.401943i	−0.985001	−	0.172548i	$-0.944800\pi$
$197$	−2.33680	+	5.64153i	−0.166490	+	0.401943i	0.818511	+	0.574491i	$0.194800\pi$
$198$	7.36282	+	3.04978i	0.523253	+	0.216738i
$199$	−11.5270	+	4.77463i	−0.817125	+	0.338464i	−0.751793	−	0.659399i	$-0.770811\pi$
$199$	−11.5270	+	4.77463i	−0.817125	+	0.338464i	−0.0653320	+	0.997864i	$0.520811\pi$
$200$	−3.81077	−	3.23698i	−0.269462	−	0.228889i
$201$	−3.89153	−	9.39498i	−0.274487	−	0.662671i
$202$	−2.14718	+	2.14718i	−0.151075	+	0.151075i
$203$		−	25.7627i		−	1.80818i
$204$	−1.26014	+	3.61201i	−0.0882274	+	0.252891i
$205$	13.6542	+	5.01639i	0.953649	+	0.350360i
$206$	4.48689	+	4.48689i	0.312616	+	0.312616i
$207$	−10.5599	+	4.37403i	−0.733960	+	0.304016i
$208$	4.92512			0.341495
$209$	14.0547	−	5.82165i	0.972184	−	0.402692i
$210$	3.74669	+	3.45404i	0.258546	+	0.238352i
$211$	9.39754	+	3.89259i	0.646954	+	0.267977i	0.681937	−	0.731411i	$-0.261138\pi$
$211$	9.39754	+	3.89259i	0.646954	+	0.267977i	−0.0349834	+	0.999388i	$0.511138\pi$
$212$	−3.36188	−	3.36188i	−0.230895	−	0.230895i
$213$	7.99359	+	7.99359i	0.547712	+	0.547712i
$214$	5.12055	+	2.12100i	0.350033	+	0.144989i
$215$	−2.87195	−	2.64763i	−0.195865	−	0.180567i
$216$	4.40526	−	1.82472i	0.299740	−	0.124156i
$217$	14.2399			0.966667
$218$	−3.60761	+	1.49432i	−0.244338	+	0.101208i
$219$	−4.57840	−	4.57840i	−0.309379	−	0.309379i
$220$	−7.81953	−	2.87281i	−0.527193	−	0.193685i
$221$	15.1541	+	13.5173i	1.01938	+	0.909273i
$222$			1.80254i			0.120979i
$223$	−13.4122	+	13.4122i	−0.898145	+	0.898145i	−0.995272	−	0.0971271i	$-0.969035\pi$
$223$	−13.4122	+	13.4122i	−0.898145	+	0.898145i	0.0971271	+	0.995272i	$0.469035\pi$
$224$	−0.939960	−	2.26926i	−0.0628037	−	0.151622i
$225$	−6.92435	+	8.15179i	−0.461624	+	0.543453i
$226$	−9.06969	+	3.75679i	−0.603307	+	0.249898i
$227$	−19.5125	−	8.08234i	−1.29509	−	0.536444i	−0.374591	−	0.927190i	$-0.622217\pi$
$227$	−19.5125	−	8.08234i	−1.29509	−	0.536444i	−0.920498	+	0.390747i	$0.872217\pi$
$228$	1.44985	−	3.50024i	0.0960185	−	0.231809i
$229$	6.64660	−	6.64660i	0.439220	−	0.439220i	−0.452530	−	0.891749i	$-0.649478\pi$
$229$	6.64660	−	6.64660i	0.439220	−	0.439220i	0.891749	+	0.452530i	$0.149478\pi$
$230$	10.8435	−	5.01668i	0.715002	−	0.330790i
$231$	7.84403	+	3.24910i	0.516099	+	0.213775i
$232$	9.69029	+	4.01385i	0.636198	+	0.263522i
$233$	8.91666	+	21.5267i	0.584150	+	1.41026i	0.889020	+	0.457868i	$0.151387\pi$
$233$	8.91666	+	21.5267i	0.584150	+	1.41026i	−0.304870	+	0.952394i	$0.598613\pi$
$234$		−	10.5355i		−	0.688729i
$235$	16.5394	−	0.672172i	1.07891	−	0.0438477i
$236$	3.52973	+	3.52973i	0.229766	+	0.229766i
$237$		−	6.25010i		−	0.405987i
$238$	3.33597	−	9.56209i	0.216239	−	0.619818i
$239$	22.7388			1.47085			0.735426	−	0.677605i	$-0.236982\pi$
$239$	22.7388			1.47085			0.735426	+	0.677605i	$0.236982\pi$
$240$	−1.88293	+	0.871123i	−0.121543	+	0.0562308i
$241$	−9.64684	−	23.2895i	−0.621408	−	1.50021i	−0.850051	−	0.526701i	$-0.823429\pi$
$241$	−9.64684	−	23.2895i	−0.621408	−	1.50021i	0.228643	−	0.973510i	$-0.426571\pi$
$242$	−2.87963			−0.185109
$243$	−6.18192	−	14.9245i	−0.396571	−	0.957406i
$244$	−1.11963	+	2.70302i	−0.0716768	+	0.173043i
$245$	1.58966	+	1.46549i	0.101559	+	0.0936270i
$246$	4.26799	−	4.26799i	0.272117	−	0.272117i
$247$	−14.2206	−	14.2206i	−0.904837	−	0.904837i
$248$	−2.21859	+	5.35615i	−0.140881	+	0.340116i
$249$	5.58898	−	13.4930i	0.354187	−	0.855084i
$250$	6.88611	−	8.80804i	0.435516	−	0.557069i
$251$		−	3.40408i		−	0.214864i	−0.994212	−	0.107432i	$-0.965737\pi$
$251$		−	3.40408i		−	0.214864i	0.994212	−	0.107432i	$-0.0342627\pi$
$252$	−4.85428	+	2.01071i	−0.305791	+	0.126663i
$253$	14.0759	−	14.0759i	0.884945	−	0.884945i
$254$	−6.73507			−0.422596
$255$	−8.18446	−	2.48746i	−0.512530	−	0.155771i
$256$	1.00000			0.0625000
$257$	9.22231	−	9.22231i	0.575272	−	0.575272i	−0.358325	−	0.933597i	$-0.616652\pi$
$257$	9.22231	−	9.22231i	0.575272	−	0.575272i	0.933597	+	0.358325i	$0.116652\pi$
$258$	−1.49743	+	0.620254i	−0.0932257	+	0.0386153i
$259$		−	4.77188i		−	0.296510i
$260$	0.447202	+	11.0038i	0.0277343	+	0.682428i
$261$	8.58620	−	20.7289i	0.531472	−	1.28309i
$262$	−4.27070	+	10.3104i	−0.263845	+	0.636978i
$263$	21.7851	+	21.7851i	1.34333	+	1.34333i	0.892724	+	0.450603i	$0.148791\pi$
$263$	21.7851	+	21.7851i	1.34333	+	1.34333i	0.450603	+	0.892724i	$0.351209\pi$
$264$	−2.44421	+	2.44421i	−0.150431	+	0.150431i
$265$	7.20594	−	7.81646i	0.442657	−	0.480161i
$266$	−3.83819	+	9.26621i	−0.235335	+	0.568148i
$267$	−2.85632	−	6.89577i	−0.174804	−	0.422015i
$268$	−10.9601			−0.669495
$269$	−2.51874	−	6.08078i	−0.153570	−	0.370752i	0.828306	−	0.560277i	$-0.189305\pi$
$269$	−2.51874	−	6.08078i	−0.153570	−	0.370752i	−0.981876	+	0.189525i	$0.939305\pi$
$270$	4.47683	+	9.67665i	0.272451	+	0.588902i
$271$	−0.844238			−0.0512838			−0.0256419	−	0.999671i	$-0.508163\pi$
$271$	−0.844238			−0.0512838			−0.0256419	+	0.999671i	$0.508163\pi$
$272$	3.07691	+	2.74457i	0.186565	+	0.166414i
$273$		−	11.2241i		−	0.679313i
$274$	8.64038	+	8.64038i	0.521985	+	0.521985i
$275$	5.70847	−	17.7314i	0.344234	−	1.06925i
$276$		−	4.95756i		−	0.298410i
$277$	−4.16817	−	10.0629i	−0.250441	−	0.604619i	0.747798	−	0.663926i	$-0.231111\pi$
$277$	−4.16817	−	10.0629i	−0.250441	−	0.604619i	−0.998240	+	0.0593070i	$0.981111\pi$
$278$	−4.42752	−	1.83394i	−0.265545	−	0.109992i
$279$	11.4576	+	4.74588i	0.685947	+	0.284128i
$280$	4.98469	−	2.30613i	0.297892	−	0.137818i
$281$	6.26217	−	6.26217i	0.373570	−	0.373570i	−0.495206	−	0.868776i	$-0.664907\pi$
$281$	6.26217	−	6.26217i	0.373570	−	0.373570i	0.868776	+	0.495206i	$0.164907\pi$
$282$	2.62844	−	6.34561i	0.156521	−	0.377876i
$283$	1.81126	+	0.750247i	0.107668	+	0.0445976i	0.435867	−	0.900011i	$-0.356442\pi$
$283$	1.81126	+	0.750247i	0.107668	+	0.0445976i	−0.328199	+	0.944609i	$0.606442\pi$
$284$	11.2566	−	4.66263i	0.667956	−	0.276676i
$285$	7.95197	+	2.92146i	0.471034	+	0.173052i
$286$	7.02175	+	16.9520i	0.415205	+	1.00239i
$287$	−11.2987	+	11.2987i	−0.666940	+	0.666940i
$288$		−	2.13914i		−	0.126050i
$289$	1.93471	+	16.8895i	0.113807	+	0.993503i
$290$	−8.08795	+	22.0147i	−0.474941	+	1.29275i
$291$	−4.75789	−	4.75789i	−0.278912	−	0.278912i
$292$	−6.44731	+	2.67056i	−0.377300	+	0.156283i
$293$	3.06041			0.178791			0.0893955	−	0.995996i	$-0.471507\pi$
$293$	3.06041			0.178791			0.0893955	+	0.995996i	$0.471507\pi$
$294$	0.828842	−	0.343318i	0.0483390	−	0.0200227i
$295$	−7.56571	+	8.20671i	−0.440492	+	0.477813i
$296$	1.79488	+	0.743464i	0.104325	+	0.0432130i
$297$	12.5612	+	12.5612i	0.728873	+	0.728873i
$298$	5.41513	+	5.41513i	0.313690	+	0.313690i
$299$	−24.3128	−	10.0707i	−1.40604	−	0.582402i
$300$	−2.11725	−	4.12779i	−0.122240	−	0.238318i
$301$	3.96414	−	1.64200i	0.228489	−	0.0946434i
$302$	6.54543			0.376647
$303$	−2.60294	+	1.07817i	−0.149535	+	0.0619395i
$304$	−2.88737	−	2.88737i	−0.165602	−	0.165602i
$305$	−6.14082	−	2.25606i	−0.351622	−	0.129182i
$306$	5.87102	−	6.58195i	0.335624	−	0.376265i
$307$			5.51955i			0.315017i	0.987518	+	0.157509i	$0.0503462\pi$
$307$			5.51955i			0.315017i	−0.987518	+	0.157509i	$0.949654\pi$
$308$	6.47058	−	6.47058i	0.368696	−	0.368696i
$309$	2.25302	+	5.43927i	0.128170	+	0.309429i
$310$	−12.1683	−	4.47048i	−0.691112	−	0.253906i
$311$	−7.02018	+	2.90785i	−0.398078	+	0.164889i	−0.572736	−	0.819740i	$-0.694118\pi$
$311$	−7.02018	+	2.90785i	−0.398078	+	0.164889i	0.174658	+	0.984629i	$0.444118\pi$
$312$	4.22180	+	1.74873i	0.239012	+	0.0990021i
$313$	−0.875684	+	2.11409i	−0.0494966	+	0.119495i	−0.946694	−	0.322135i	$-0.895600\pi$
$313$	−0.875684	+	2.11409i	−0.0494966	+	0.119495i	0.897197	+	0.441630i	$0.145600\pi$
$314$	10.3933	−	10.3933i	0.586528	−	0.586528i
$315$	−4.93314	−	10.6630i	−0.277951	−	0.600791i
$316$	−6.22353	−	2.57787i	−0.350101	−	0.145017i
$317$	5.15166	+	2.13389i	0.289346	+	0.119851i	0.522635	−	0.852556i	$-0.324949\pi$
$317$	5.15166	+	2.13389i	0.289346	+	0.119851i	−0.233289	+	0.972407i	$0.574949\pi$
$318$	−1.68812	−	4.07547i	−0.0946649	−	0.228541i
$319$			39.0760i			2.18784i
$320$	0.0908004	+	2.23422i	0.00507589	+	0.124897i
$321$	3.63623	+	3.63623i	0.202954	+	0.202954i
$322$			13.1242i			0.731382i
$323$	−0.959590	−	16.8087i	−0.0533930	−	0.935263i
$324$	−1.99337			−0.110743
$325$	−24.5444	+	1.99830i	−1.36148	+	0.110846i
$326$	−2.40573	−	5.80794i	−0.133241	−	0.321672i
$327$	−3.62301			−0.200353
$328$	−2.48951	−	6.01020i	−0.137460	−	0.331858i
$329$	−6.95828	+	16.7988i	−0.383622	+	0.926147i
$330$	−5.68286	−	5.23898i	−0.312831	−	0.288397i
$331$	−18.2648	+	18.2648i	−1.00392	+	1.00392i	−0.00393178	+	0.999992i	$0.501252\pi$
$331$	−18.2648	+	18.2648i	−1.00392	+	1.00392i	−0.999992	+	0.00393178i	$0.998748\pi$
$332$	−11.1304	−	11.1304i	−0.610863	−	0.610863i
$333$	1.59038	−	3.83951i	0.0871521	−	0.210404i
$334$	−0.981591	+	2.36977i	−0.0537102	+	0.129668i
$335$	−0.995182	−	24.4873i	−0.0543726	−	1.33789i
$336$		−	2.27895i		−	0.124327i
$337$	3.85464	−	1.59664i	0.209975	−	0.0869747i	−0.275217	−	0.961382i	$-0.588750\pi$
$337$	3.85464	−	1.59664i	0.209975	−	0.0869747i	0.485192	+	0.874408i	$0.338750\pi$
$338$	7.95975	−	7.95975i	0.432953	−	0.432953i
$339$	−9.10841			−0.494701
$340$	−5.85259	+	7.12371i	−0.317401	+	0.386337i
$341$	−21.5986			−1.16963
$342$	−6.17650	+	6.17650i	−0.333987	+	0.333987i
$343$	−18.0790	+	7.48858i	−0.976176	+	0.404346i
$344$			1.74689i			0.0941858i
$345$	11.0763	−	0.450148i	0.596328	−	0.0242352i
$346$	−7.45110	+	17.9886i	−0.400574	+	0.967071i
$347$	5.54635	−	13.3901i	0.297744	−	0.718817i	−0.702233	−	0.711947i	$-0.747813\pi$
$347$	5.54635	−	13.3901i	0.297744	−	0.718817i	0.999976	−	0.00686921i	$-0.00218655\pi$
$348$	6.88132	+	6.88132i	0.368877	+	0.368877i
$349$	−3.29429	+	3.29429i	−0.176339	+	0.176339i	−0.789758	−	0.613419i	$-0.789794\pi$
$349$	−3.29429	+	3.29429i	−0.176339	+	0.176339i	0.613419	+	0.789758i	$0.289794\pi$
$350$	5.60502	+	10.9275i	0.299601	+	0.584101i
$351$	8.98695	−	21.6964i	0.479688	−	1.15807i
$352$	1.42570	+	3.44195i	0.0759901	+	0.183456i
$353$	−30.2893			−1.61214			−0.806068	−	0.591824i	$-0.798408\pi$
$353$	−30.2893			−1.61214			−0.806068	+	0.591824i	$0.798408\pi$
$354$	1.77240	+	4.27895i	0.0942019	+	0.227424i
$355$	11.4395	+	24.7264i	0.607144	+	1.31234i
$356$	−8.04456			−0.426361
$357$	6.25473	−	7.01212i	0.331035	−	0.371121i
$358$		−	16.1710i		−	0.854663i
$359$	−10.1123	−	10.1123i	−0.533709	−	0.533709i	0.387965	−	0.921674i	$-0.373178\pi$
$359$	−10.1123	−	10.1123i	−0.533709	−	0.533709i	−0.921674	+	0.387965i	$0.873178\pi$
$360$	4.77933	−	0.194235i	0.251893	−	0.0102371i
$361$		−	2.32620i		−	0.122431i
$362$	7.00292	+	16.9065i	0.368065	+	0.888588i
$363$	−2.46841	−	1.02245i	−0.129558	−	0.0536646i
$364$	−11.1764	−	4.62941i	−0.585802	−	0.242647i
$365$	−6.55205	−	14.1622i	−0.342950	−	0.741286i
$366$	−1.91948	+	1.91948i	−0.100333	+	0.100333i
$367$	1.21179	−	2.92552i	0.0632550	−	0.152711i	−0.889091	−	0.457730i	$-0.848663\pi$
$367$	1.21179	−	2.92552i	0.0632550	−	0.152711i	0.952346	+	0.305019i	$0.0986627\pi$
$368$	−4.93649	−	2.04476i	−0.257332	−	0.106590i
$369$	−12.8567	+	5.32541i	−0.669292	+	0.277230i
$370$	−1.49809	+	4.07767i	−0.0778819	+	0.211988i
$371$	4.46896	+	10.7890i	0.232017	+	0.560138i
$372$	−3.80354	+	3.80354i	−0.197204	+	0.197204i
$373$			31.8816i			1.65077i	0.564573	+	0.825383i	$0.309041\pi$
$373$			31.8816i			1.65077i	−0.564573	+	0.825383i	$0.690959\pi$
$374$	−5.05990	+	14.5035i	−0.261641	+	0.749957i
$375$	9.03016	−	5.10523i	0.466315	−	0.263633i
$376$	−5.23453	−	5.23453i	−0.269950	−	0.269950i
$377$	47.7258	−	19.7687i	2.45800	−	1.01814i
$378$	−11.7119			−0.602393
$379$	−6.76955	+	2.80404i	−0.347729	+	0.144034i	−0.549710	−	0.835355i	$-0.685262\pi$
$379$	−6.76955	+	2.80404i	−0.347729	+	0.144034i	0.201982	+	0.979389i	$0.435262\pi$
$380$	6.18885	−	6.71320i	0.317482	−	0.344380i
$381$	−5.77328	−	2.39137i	−0.295774	−	0.122514i
$382$	5.70663	+	5.70663i	0.291976	+	0.291976i
$383$	22.3480	+	22.3480i	1.14193	+	1.14193i	0.988097	+	0.153830i	$0.0491608\pi$
$383$	22.3480	+	22.3480i	1.14193	+	1.14193i	0.153830	+	0.988097i	$0.450839\pi$
$384$	0.857197	+	0.355063i	0.0437437	+	0.0181192i
$385$	15.0443	+	13.8692i	0.766726	+	0.706840i
$386$	16.1760	−	6.70033i	0.823339	−	0.341038i
$387$	3.73684			0.189954
$388$	−6.70007	+	2.77526i	−0.340144	+	0.140892i
$389$	−21.1078	−	21.1078i	−1.07021	−	1.07021i	−0.997342	−	0.0728663i	$-0.976785\pi$
$389$	−21.1078	−	21.1078i	−1.07021	−	1.07021i	−0.0728663	−	0.997342i	$-0.523215\pi$
$390$	−3.52370	+	9.59122i	−0.178430	+	0.485670i
$391$	−9.57713	−	19.8400i	−0.484336	−	1.00335i
$392$		−	0.966921i		−	0.0488369i
$393$	−7.32167	+	7.32167i	−0.369329	+	0.369329i
$394$	2.33680	+	5.64153i	0.117726	+	0.284216i
$395$	5.19444	−	14.1388i	0.261361	−	0.711402i
$396$	7.36282	−	3.04978i	0.369996	−	0.153257i
$397$	4.27759	+	1.77184i	0.214686	+	0.0889259i	0.487435	−	0.873159i	$-0.337933\pi$
$397$	4.27759	+	1.77184i	0.214686	+	0.0889259i	−0.272749	+	0.962085i	$0.587933\pi$
$398$	−4.77463	+	11.5270i	−0.239330	+	0.577795i
$399$	−6.58017	+	6.58017i	−0.329421	+	0.329421i
$400$	−4.98351	+	0.405737i	−0.249176	+	0.0202868i
$401$	22.4635	+	9.30468i	1.12177	+	0.464654i	0.864977	−	0.501812i	$-0.167333\pi$
$401$	22.4635	+	9.30468i	1.12177	+	0.464654i	0.256796	+	0.966466i	$0.417333\pi$
$402$	−9.39498	−	3.89153i	−0.468579	−	0.194092i
$403$	10.9268	+	26.3797i	0.544303	+	1.31406i
$404$			3.03657i			0.151075i
$405$	−0.180998	−	4.45363i	−0.00899389	−	0.221303i
$406$	−18.2170	−	18.2170i	−0.904092	−	0.904092i
$407$			7.23784i			0.358767i
$408$	1.66302	+	3.44513i	0.0823319	+	0.170559i
$409$	−34.8335			−1.72241			−0.861203	−	0.508261i	$-0.830288\pi$
$409$	−34.8335			−1.72241			−0.861203	+	0.508261i	$0.830288\pi$
$410$	13.2021	−	6.10784i	0.652004	−	0.301645i
$411$	4.33863	+	10.4744i	0.214009	+	0.516663i
$412$	6.34542			0.312616
$413$	−4.69208	−	11.3277i	−0.230882	−	0.557399i
$414$	−4.37403	+	10.5599i	−0.214972	+	0.518988i
$415$	23.8573	−	25.8786i	1.17111	−	1.27033i
$416$	3.48258	−	3.48258i	0.170748	−	0.170748i
$417$	−3.14409	−	3.14409i	−0.153967	−	0.153967i
$418$	5.82165	−	14.0547i	0.284746	−	0.687438i
$419$	−7.04143	+	16.9995i	−0.343996	+	0.830481i	0.653307	+	0.757093i	$0.273381\pi$
$419$	−7.04143	+	16.9995i	−0.343996	+	0.830481i	−0.997303	+	0.0733877i	$0.976619\pi$
$420$	5.09168	−	0.206929i	0.248449	−	0.0100971i
$421$			12.4559i			0.607064i	0.952821	+	0.303532i	$0.0981660\pi$
$421$			12.4559i			0.607064i	−0.952821	+	0.303532i	$0.901834\pi$
$422$	9.39754	−	3.89259i	0.457465	−	0.189488i
$423$	−11.1974	+	11.1974i	−0.544437	+	0.544437i
$424$	−4.75442			−0.230895
$425$	−16.4474	−	12.4292i	−0.797815	−	0.602903i
$426$	11.3046			0.547712
$427$	5.08146	−	5.08146i	0.245909	−	0.245909i
$428$	5.12055	−	2.12100i	0.247511	−	0.102522i
$429$			17.0244i			0.821944i
$430$	−3.90293	+	0.158618i	−0.188216	+	0.00764923i
$431$	0.639227	−	1.54323i	0.0307905	−	0.0743348i	−0.907736	−	0.419541i	$-0.862191\pi$
$431$	0.639227	−	1.54323i	0.0307905	−	0.0743348i	0.938527	+	0.345206i	$0.112191\pi$
$432$	1.82472	−	4.40526i	0.0877918	−	0.211948i
$433$	−10.7009	−	10.7009i	−0.514254	−	0.514254i	0.401573	−	0.915827i	$-0.368464\pi$
$433$	−10.7009	−	10.7009i	−0.514254	−	0.514254i	−0.915827	+	0.401573i	$0.868464\pi$
$434$	10.0691	−	10.0691i	0.483333	−	0.483333i
$435$	−14.7496	+	15.9992i	−0.707188	+	0.767104i
$436$	−1.49432	+	3.60761i	−0.0715651	+	0.172773i
$437$	8.34948	+	20.1574i	0.399410	+	0.964261i
$438$	−6.47483			−0.309379
$439$	−4.05589	−	9.79178i	−0.193577	−	0.467336i	0.797053	−	0.603909i	$-0.206391\pi$
$439$	−4.05589	−	9.79178i	−0.193577	−	0.467336i	−0.990630	+	0.136573i	$0.956391\pi$
$440$	−7.56063	+	3.49787i	−0.360439	+	0.166754i
$441$	−2.06838			−0.0984945
$442$	20.2738	−	1.15740i	0.964325	−	0.0550521i
$443$		−	24.8681i		−	1.18152i	−0.806848	−	0.590759i	$-0.798828\pi$
$443$		−	24.8681i		−	1.18152i	0.806848	−	0.590759i	$-0.201172\pi$
$444$	1.27459	+	1.27459i	0.0604894	+	0.0604894i
$445$	−0.730449	−	17.9734i	−0.0346266	−	0.852019i
$446$			18.9677i			0.898145i
$447$	2.71912	+	6.56454i	0.128610	+	0.310492i
$448$	−2.26926	−	0.939960i	−0.107213	−	0.0444089i
$449$	27.2033	+	11.2680i	1.28380	+	0.531769i	0.917133	−	0.398582i	$-0.130498\pi$
$449$	27.2033	+	11.2680i	1.28380	+	0.531769i	0.366670	+	0.930351i	$0.380498\pi$
$450$	0.867929	+	10.6604i	0.0409146	+	0.502538i
$451$	17.1375	−	17.1375i	0.806973	−	0.806973i
$452$	−3.75679	+	9.06969i	−0.176705	+	0.426602i
$453$	5.61072	+	2.32404i	0.263615	+	0.109193i
$454$	−19.5125	+	8.08234i	−0.915766	+	0.379323i
$455$	9.32832	−	25.3909i	0.437318	−	1.19034i
$456$	−1.44985	−	3.50024i	−0.0678953	−	0.163914i
$457$	−8.66979	+	8.66979i	−0.405556	+	0.405556i	−0.880186	−	0.474630i	$-0.842582\pi$
$457$	−8.66979	+	8.66979i	−0.405556	+	0.405556i	0.474630	+	0.880186i	$0.342582\pi$
$458$		−	9.39971i		−	0.439220i
$459$	17.7050	−	8.54651i	0.826399	−	0.398917i
$460$	4.12021	−	11.2149i	0.192106	−	0.522896i
$461$	6.36207	+	6.36207i	0.296311	+	0.296311i	0.839567	−	0.543256i	$-0.182809\pi$
$461$	6.36207	+	6.36207i	0.296311	+	0.296311i	−0.543256	+	0.839567i	$0.682809\pi$
$462$	7.84403	−	3.24910i	0.364937	−	0.151162i
$463$	10.1914			0.473635			0.236818	−	0.971554i	$-0.423896\pi$
$463$	10.1914			0.473635			0.236818	+	0.971554i	$0.423896\pi$
$464$	9.69029	−	4.01385i	0.449860	−	0.186338i
$465$	−8.84331	−	8.15259i	−0.410099	−	0.378067i
$466$	21.5267	+	8.91666i	0.997206	+	0.413056i
$467$	−12.8803	−	12.8803i	−0.596030	−	0.596030i	0.343223	−	0.939254i	$-0.388481\pi$
$467$	−12.8803	−	12.8803i	−0.596030	−	0.596030i	−0.939254	+	0.343223i	$0.888481\pi$
$468$	−7.44975	−	7.44975i	−0.344365	−	0.344365i
$469$	24.8714	+	10.3021i	1.14845	+	0.475705i
$470$	11.2198	−	12.1704i	0.517532	−	0.561379i
$471$	12.5994	−	5.21883i	0.580549	−	0.240471i
$472$	4.99179			0.229766
$473$	−6.01269	+	2.49054i	−0.276464	+	0.114515i
$474$	−4.41949	−	4.41949i	−0.202994	−	0.202994i
$475$	15.5607	+	13.2177i	0.713976	+	0.606471i
$476$	−4.40253	−	9.12031i	−0.201790	−	0.418029i
$477$			10.1704i			0.465670i
$478$	16.0788	−	16.0788i	0.735426	−	0.735426i
$479$	−7.11304	−	17.1724i	−0.325003	−	0.784627i	−0.998949	−	0.0458458i	$-0.985402\pi$
$479$	−7.11304	−	17.1724i	−0.325003	−	0.784627i	0.673945	−	0.738781i	$-0.264598\pi$
$480$	−0.715456	+	1.94741i	−0.0326559	+	0.0888867i
$481$	8.84000	−	3.66165i	0.403069	−	0.166957i
$482$	−23.2895	−	9.64684i	−1.06081	−	0.439402i
$483$	−4.65990	+	11.2500i	−0.212033	+	0.511893i
$484$	−2.03620	+	2.03620i	−0.0925547	+	0.0925547i
$485$	−6.80892	−	14.7175i	−0.309177	−	0.668285i
$486$	−14.9245	−	6.18192i	−0.676988	−	0.280418i
$487$	−34.5909	−	14.3280i	−1.56746	−	0.649264i	−0.581096	−	0.813835i	$-0.697376\pi$
$487$	−34.5909	−	14.3280i	−1.56746	−	0.649264i	−0.986365	+	0.164571i	$0.947376\pi$
$488$	1.11963	+	2.70302i	0.0506832	+	0.122360i
$489$		−	5.83273i		−	0.263765i
$490$	2.16032	−	0.0877968i	0.0975932	−	0.00396626i
$491$	21.7956	+	21.7956i	0.983622	+	0.983622i	0.999868	−	0.0162456i	$-0.00517137\pi$
$491$	21.7956	+	21.7956i	0.983622	+	0.983622i	−0.0162456	+	0.999868i	$0.505171\pi$
$492$		−	6.03586i		−	0.272117i
$493$	40.8324	+	14.2454i	1.83900	+	0.641580i
$494$	−20.1110			−0.904837
$495$	7.48244	+	16.1733i	0.336311	+	0.726934i
$496$	2.21859	+	5.35615i	0.0996176	+	0.240498i
$497$	−29.9269			−1.34240
$498$	−5.58898	−	13.4930i	−0.250448	−	0.604635i
$499$	−9.87864	+	23.8491i	−0.442228	+	1.06763i	0.532937	+	0.846155i	$0.321088\pi$
$499$	−9.87864	+	23.8491i	−0.442228	+	1.06763i	−0.975165	+	0.221479i	$0.928912\pi$
$500$	−1.35901	−	11.0974i	−0.0607768	−	0.496292i
$501$	−1.68283	+	1.68283i	−0.0751834	+	0.0751834i
$502$	−2.40705	−	2.40705i	−0.107432	−	0.107432i
$503$	2.36773	−	5.71621i	0.105572	−	0.254873i	−0.862262	−	0.506462i	$-0.830953\pi$
$503$	2.36773	−	5.71621i	0.105572	−	0.254873i	0.967834	+	0.251589i	$0.0809531\pi$
$504$	−2.01071	+	4.85428i	−0.0895641	+	0.216227i
$505$	−6.78439	+	0.275722i	−0.301901	+	0.0122695i
$506$		−	19.9063i		−	0.884945i
$507$	9.64928	−	3.99686i	0.428540	−	0.177507i
$508$	−4.76241	+	4.76241i	−0.211298	+	0.211298i
$509$	19.8162			0.878336			0.439168	−	0.898405i	$-0.355273\pi$
$509$	19.8162			0.878336			0.439168	+	0.898405i	$0.355273\pi$
$510$	−7.54619	+	4.02838i	−0.334151	+	0.178380i
$511$	17.1409			0.758267
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−17.9882	+	7.45097i	−0.794200	+	0.328969i
$514$		−	13.0423i		−	0.575272i
$515$	0.576166	+	14.1771i	0.0253889	+	0.624717i
$516$	−0.620254	+	1.49743i	−0.0273052	+	0.0659205i
$517$	10.5541	−	25.4799i	0.464169	−	1.12060i
$518$	−3.37423	−	3.37423i	−0.148255	−	0.148255i
$519$	−12.7741	+	12.7741i	−0.560722	+	0.560722i
$520$	8.09709	+	7.46465i	0.355081	+	0.327347i
$521$	1.27510	−	3.07836i	0.0558631	−	0.134865i	−0.893484	−	0.449095i	$-0.851746\pi$
$521$	1.27510	−	3.07836i	0.0558631	−	0.134865i	0.949347	+	0.314230i	$0.101746\pi$
$522$	−8.58620	−	20.7289i	−0.375808	−	0.907280i
$523$	−30.7640			−1.34521			−0.672607	−	0.740000i	$-0.734826\pi$
$523$	−30.7640			−1.34521			−0.672607	+	0.740000i	$0.734826\pi$
$524$	4.27070	+	10.3104i	0.186566	+	0.450411i
$525$	0.924654	+	11.3572i	0.0403552	+	0.495668i
$526$	30.8088			1.34333
$527$	−7.87391	+	22.5694i	−0.342993	+	0.983140i
$528$			3.45664i			0.150431i
$529$	3.92439	+	3.92439i	0.170626	+	0.170626i
$530$	−0.431703	−	10.6224i	−0.0187520	−	0.461409i
$531$		−	10.6782i		−	0.463393i
$532$	3.83819	+	9.26621i	0.166407	+	0.401741i
$533$	−29.6009	−	12.2611i	−1.28216	−	0.531088i
$534$	−6.89577	−	2.85632i	−0.298409	−	0.123605i
$535$	5.20373	+	11.2479i	0.224977	+	0.486287i
$536$	−7.74997	+	7.74997i	−0.334748	+	0.334748i
$537$	5.74171	−	13.8617i	0.247773	−	0.598177i
$538$	−6.08078	−	2.51874i	−0.262161	−	0.108591i
$539$	3.32809	−	1.37854i	0.143351	−	0.0593780i
$540$	10.0080	+	3.67683i	0.430677	+	0.158226i
$541$	−17.0007	−	41.0433i	−0.730917	−	1.76459i	−0.639518	−	0.768776i	$-0.720866\pi$
$541$	−17.0007	−	41.0433i	−0.730917	−	1.76459i	−0.0913987	−	0.995814i	$-0.529134\pi$
$542$	−0.596966	+	0.596966i	−0.0256419	+	0.0256419i
$543$			16.9787i			0.728626i
$544$	4.11640	−	0.235000i	0.176489	−	0.0100756i
$545$	−8.19590	−	3.01108i	−0.351074	−	0.128980i
$546$	−7.93664	−	7.93664i	−0.339657	−	0.339657i
$547$	−7.44827	+	3.08518i	−0.318465	+	0.131913i	−0.536189	−	0.844098i	$-0.680137\pi$
$547$	−7.44827	+	3.08518i	−0.318465	+	0.131913i	0.217724	+	0.976010i	$0.430137\pi$
$548$	12.2193			0.521985
$549$	5.78215	−	2.39504i	0.246776	−	0.102218i
$550$	−8.50152	−	16.5745i	−0.362506	−	0.706740i
$551$	−39.5689	−	16.3900i	−1.68569	−	0.698236i
$552$	−3.50552	−	3.50552i	−0.149205	−	0.149205i
$553$	11.6997	+	11.6997i	0.497523	+	0.497523i
$554$	−10.0629	−	4.16817i	−0.427530	−	0.177089i
$555$	−2.73199	+	2.96345i	−0.115966	+	0.125792i
$556$	−4.42752	+	1.83394i	−0.187769	+	0.0777763i
$557$	−12.0303			−0.509740			−0.254870	−	0.966975i	$-0.582033\pi$
$557$	−12.0303			−0.509740			−0.254870	+	0.966975i	$0.582033\pi$
$558$	11.4576	−	4.74588i	0.485038	−	0.200909i
$559$	6.08368	+	6.08368i	0.257312	+	0.257312i
$560$	1.89403	−	5.15539i	0.0800374	−	0.217855i
$561$	−9.48698	+	10.6358i	−0.400541	+	0.449042i
$562$		−	8.85604i		−	0.373570i
$563$	29.4427	−	29.4427i	1.24086	−	1.24086i	0.281221	−	0.959643i	$-0.409261\pi$
$563$	29.4427	−	29.4427i	1.24086	−	1.24086i	0.959643	−	0.281221i	$-0.0907393\pi$
$564$	−2.62844	−	6.34561i	−0.110677	−	0.267198i
$565$	−20.6048	−	7.56998i	−0.866852	−	0.318471i
$566$	1.81126	−	0.750247i	0.0761328	−	0.0315352i
$567$	4.52347	+	1.87368i	0.189968	+	0.0786874i
$568$	4.66263	−	11.2566i	0.195640	−	0.472316i
$569$	−2.14498	+	2.14498i	−0.0899223	+	0.0899223i	−0.750637	−	0.660715i	$-0.770253\pi$
$569$	−2.14498	+	2.14498i	−0.0899223	+	0.0899223i	0.660715	+	0.750637i	$0.270253\pi$
$570$	7.68868	−	3.55711i	0.322043	−	0.148991i
$571$	7.26497	+	3.00925i	0.304029	+	0.125933i	0.529482	−	0.848321i	$-0.322386\pi$
$571$	7.26497	+	3.00925i	0.304029	+	0.125933i	−0.225453	+	0.974254i	$0.572386\pi$
$572$	16.9520	+	7.02175i	0.708799	+	0.293594i
$573$	2.86549	+	6.91791i	0.119708	+	0.289000i
$574$			15.9788i			0.666940i
$575$	25.4307	+	8.18717i	1.06053	+	0.341428i
$576$	−1.51260	−	1.51260i	−0.0630251	−	0.0630251i
$577$			25.5182i			1.06234i	0.847266	+	0.531169i	$0.178247\pi$
$577$			25.5182i			1.06234i	−0.847266	+	0.531169i	$0.821753\pi$
$578$	13.3108	+	10.5747i	0.553655	+	0.439848i
$579$	16.2451			0.675123
$580$	9.84772	+	21.2858i	0.408904	+	0.883845i
$581$	14.7957	+	35.7201i	0.613831	+	1.48192i
$582$	−6.72867			−0.278912
$583$	−6.77838	−	16.3645i	−0.280732	−	0.677747i
$584$	−2.67056	+	6.44731i	−0.110509	+	0.266792i
$585$	15.9680	−	17.3208i	0.660194	−	0.716129i
$586$	2.16403	−	2.16403i	0.0893955	−	0.0893955i
$587$	23.3528	+	23.3528i	0.963873	+	0.963873i	0.999370	−	0.0354969i	$-0.0113014\pi$
$587$	23.3528	+	23.3528i	0.963873	+	0.963873i	−0.0354969	+	0.999370i	$0.511301\pi$
$588$	0.343318	−	0.828842i	0.0141582	−	0.0341809i
$589$	9.05929	−	21.8711i	0.373282	−	0.901181i
$590$	0.453257	+	11.1528i	0.0186603	+	0.459153i
$591$			5.66562i			0.233052i
$592$	1.79488	−	0.743464i	0.0737692	−	0.0305562i
$593$	−11.6550	+	11.6550i	−0.478612	+	0.478612i	−0.904687	−	0.426076i	$-0.859896\pi$
$593$	−11.6550	+	11.6550i	−0.478612	+	0.478612i	0.426076	+	0.904687i	$0.359896\pi$
$594$	17.7642			0.728873
$595$	19.9771	−	10.6644i	0.818980	−	0.437196i
$596$	7.65815			0.313690
$597$	−8.18559	+	8.18559i	−0.335014	+	0.335014i
$598$	−24.3128	+	10.0707i	−0.994223	+	0.411821i
$599$			12.3399i			0.504197i	0.967702	+	0.252098i	$0.0811206\pi$
$599$			12.3399i			0.504197i	−0.967702	+	0.252098i	$0.918879\pi$
$600$	−4.41591	−	1.42166i	−0.180279	−	0.0580391i
$601$	−2.79356	+	6.74424i	−0.113952	+	0.275103i	−0.970558	−	0.240867i	$-0.922568\pi$
$601$	−2.79356	+	6.74424i	−0.113952	+	0.275103i	0.856607	+	0.515970i	$0.172568\pi$
$602$	1.64200	−	3.96414i	0.0669230	−	0.161566i
$603$	16.5783	+	16.5783i	0.675121	+	0.675121i
$604$	4.62832	−	4.62832i	0.188324	−	0.188324i
$605$	−4.73422	−	4.36445i	−0.192473	−	0.177440i
$606$	−1.07817	+	2.60294i	−0.0437978	+	0.105737i
$607$	5.14628	+	12.4242i	0.208881	+	0.504283i	0.993248	−	0.116014i	$-0.0370118\pi$
$607$	5.14628	+	12.4242i	0.208881	+	0.504283i	−0.784367	+	0.620298i	$0.787012\pi$
$608$	−4.08336			−0.165602
$609$	−9.14736	−	22.0837i	−0.370670	−	0.894876i
$610$	−5.93749	+	2.74693i	−0.240402	+	0.111220i
$611$	−36.4594			−1.47499
$612$	−0.502699	−	8.80558i	−0.0203204	−	0.355944i
$613$		−	44.9852i		−	1.81694i	−0.417955	−	0.908468i	$-0.637253\pi$
$613$		−	44.9852i		−	1.81694i	0.417955	−	0.908468i	$-0.362747\pi$
$614$	3.90291	+	3.90291i	0.157509	+	0.157509i
$615$	13.4855	−	0.548058i	0.543786	−	0.0220998i
$616$		−	9.15079i		−	0.368696i
$617$	7.34507	+	17.7326i	0.295701	+	0.713886i	0.999992	+	0.00397450i	$0.00126513\pi$
$617$	7.34507	+	17.7326i	0.295701	+	0.713886i	−0.704291	+	0.709912i	$0.748735\pi$
$618$	5.43927	+	2.25302i	0.218800	+	0.0906298i
$619$	−44.6634	−	18.5002i	−1.79517	−	0.743585i	−0.988234	−	0.152949i	$-0.951123\pi$
$619$	−44.6634	−	18.5002i	−1.79517	−	0.743585i	−0.806939	−	0.590635i	$-0.798877\pi$
$620$	−11.7654	+	5.44316i	−0.472509	+	0.218603i
$621$	−18.0154	+	18.0154i	−0.722933	+	0.722933i
$622$	−2.90785	+	7.02018i	−0.116594	+	0.281483i
$623$	18.2552	+	7.56156i	0.731380	+	0.302948i
$624$	4.22180	−	1.74873i	0.169007	−	0.0700050i
$625$	24.6708	−	4.04399i	0.986830	−	0.161759i
$626$	0.875684	+	2.11409i	0.0349994	+	0.0844960i
$627$	9.98060	−	9.98060i	0.398587	−	0.398587i
$628$		−	14.6983i		−	0.586528i
$629$	7.56317	+	2.63860i	0.301563	+	0.105208i
$630$	−11.0281	−	4.05160i	−0.439371	−	0.161420i
$631$	8.25985	+	8.25985i	0.328820	+	0.328820i	0.852138	−	0.523318i	$-0.175306\pi$
$631$	8.25985	+	8.25985i	0.328820	+	0.328820i	−0.523318	+	0.852138i	$0.675306\pi$
$632$	−6.22353	+	2.57787i	−0.247559	+	0.102542i
$633$	9.43766			0.375113
$634$	5.15166	−	2.13389i	0.204599	−	0.0847475i
$635$	−11.0727	−	10.2079i	−0.439408	−	0.405087i
$636$	−4.07547	−	1.68812i	−0.161603	−	0.0669382i
$637$	−3.36738	−	3.36738i	−0.133421	−	0.133421i
$638$	27.6309	+	27.6309i	1.09392	+	1.09392i
$639$	−24.0795	−	9.97404i	−0.952569	−	0.394567i
$640$	1.64404	+	1.51563i	0.0649864	+	0.0599105i
$641$	5.20543	−	2.15616i	0.205602	−	0.0851632i	−0.277506	−	0.960724i	$-0.589508\pi$
$641$	5.20543	−	2.15616i	0.205602	−	0.0851632i	0.483108	+	0.875561i	$0.339508\pi$
$642$	5.14240			0.202954
$643$	13.8696	−	5.74499i	0.546965	−	0.226560i	−0.0920505	−	0.995754i	$-0.529342\pi$
$643$	13.8696	−	5.74499i	0.546965	−	0.226560i	0.639015	+	0.769194i	$0.279342\pi$
$644$	9.28019	+	9.28019i	0.365691	+	0.365691i
$645$	−3.40190	−	1.24982i	−0.133950	−	0.0492116i
$646$	−12.5641	−	11.2070i	−0.494328	−	0.440935i
$647$		−	35.2433i		−	1.38556i	−0.721151	−	0.692778i	$-0.756386\pi$
$647$		−	35.2433i		−	1.38556i	0.721151	−	0.692778i	$-0.243614\pi$
$648$	−1.40952	+	1.40952i	−0.0553713	+	0.0553713i
$649$	7.11680	+	17.1815i	0.279359	+	0.674432i
$650$	−15.9425	+	18.7685i	−0.625316	+	0.736161i
$651$	12.2064	−	5.05605i	0.478406	−	0.198162i
$652$	−5.80794	−	2.40573i	−0.227456	−	0.0942155i
$653$	−8.25928	+	19.9397i	−0.323211	+	0.780300i	0.675853	+	0.737036i	$0.263775\pi$
$653$	−8.25928	+	19.9397i	−0.323211	+	0.780300i	−0.999064	+	0.0432632i	$0.986225\pi$
$654$	−2.56186	+	2.56186i	−0.100177	+	0.100177i
$655$	−22.6479	+	10.4779i	−0.884928	+	0.409405i
$656$	−6.01020	−	2.48951i	−0.234659	−	0.0971989i
$657$	13.7917	+	5.71272i	0.538066	+	0.222874i
$658$	6.95828	+	16.7988i	0.271262	+	0.654885i
$659$		−	29.7250i		−	1.15792i	−0.815356	−	0.578961i	$-0.803459\pi$
$659$		−	29.7250i		−	1.15792i	0.815356	−	0.578961i	$-0.196541\pi$
$660$	−7.72291	+	0.313864i	−0.300614	+	0.0122171i
$661$	4.13044	+	4.13044i	0.160656	+	0.160656i	0.782857	−	0.622201i	$-0.213762\pi$
$661$	4.13044	+	4.13044i	0.160656	+	0.160656i	−0.622201	+	0.782857i	$0.713762\pi$
$662$			25.8303i			1.00392i
$663$	17.7896	+	6.20634i	0.690890	+	0.241034i
$664$	−15.7408			−0.610863
$665$	−20.3543	+	9.41675i	−0.789305	+	0.365166i
$666$	−1.59038	−	3.83951i	−0.0616258	−	0.148778i
$667$	−56.0433			−2.17001
$668$	0.981591	+	2.36977i	0.0379789	+	0.0916891i
$669$	−6.73471	+	16.2590i	−0.260379	+	0.628610i
$670$	−18.0189	−	16.6115i	−0.696130	−	0.641757i
$671$	−7.70740	+	7.70740i	−0.297541	+	0.297541i
$672$	−1.61146	−	1.61146i	−0.0621635	−	0.0621635i
$673$	2.11864	−	5.11485i	0.0816675	−	0.197163i	−0.877771	−	0.479080i	$-0.840970\pi$
$673$	2.11864	−	5.11485i	0.0816675	−	0.197163i	0.959439	+	0.281917i	$0.0909704\pi$
$674$	1.59664	−	3.85464i	0.0615004	−	0.148475i
$675$	−7.30613	+	22.6940i	−0.281213	+	0.873493i
$676$		−	11.2568i		−	0.432953i
$677$	−23.3326	+	9.66468i	−0.896744	+	0.371444i	−0.782967	−	0.622063i	$-0.786295\pi$
$677$	−23.3326	+	9.66468i	−0.896744	+	0.371444i	−0.113777	+	0.993506i	$0.536295\pi$
$678$	−6.44062	+	6.44062i	−0.247350	+	0.247350i
$679$	17.8128			0.683594
$680$	0.898814	+	9.17563i	0.0344679	+	0.351869i
$681$	−19.5958			−0.750912
$682$	−15.2725	+	15.2725i	−0.584816	+	0.584816i
$683$	7.09300	−	2.93802i	0.271406	−	0.112420i	−0.242830	−	0.970069i	$-0.578076\pi$
$683$	7.09300	−	2.93802i	0.271406	−	0.112420i	0.514236	+	0.857649i	$0.328076\pi$
$684$			8.73489i			0.333987i
$685$	1.10952	+	27.3008i	0.0423926	+	1.04311i
$686$	−7.48858	+	18.0790i	−0.285915	+	0.690261i
$687$	3.33749	−	8.05741i	0.127333	−	0.307409i
$688$	1.23524	+	1.23524i	0.0470929	+	0.0470929i
$689$	−16.5577	+	16.5577i	−0.630797	+	0.630797i
$690$	7.51382	−	8.15042i	0.286046	−	0.310281i
$691$	8.03502	−	19.3982i	0.305666	−	0.737944i	−0.694169	−	0.719812i	$-0.744228\pi$
$691$	8.03502	−	19.3982i	0.305666	−	0.737944i	0.999836	−	0.0181321i	$-0.00577193\pi$
$692$	7.45110	+	17.9886i	0.283248	+	0.683822i
$693$	−19.5748			−0.743587
$694$	−5.54635	−	13.3901i	−0.210536	−	0.508280i
$695$	−4.49945	−	9.72554i	−0.170674	−	0.368911i
$696$	9.73165			0.368877
$697$	−11.6602	−	24.1554i	−0.441662	−	0.914950i
$698$			4.65883i			0.176339i
$699$	15.2867	+	15.2867i	0.578195	+	0.578195i
$700$	11.6903	+	3.76358i	0.441851	+	0.142250i
$701$		−	5.78625i		−	0.218544i	−0.994012	−	0.109272i	$-0.965148\pi$
$701$		−	5.78625i		−	0.218544i	0.994012	−	0.109272i	$-0.0348519\pi$
$702$	−8.98695	−	21.6964i	−0.339191	−	0.818879i
$703$	−7.32914	−	3.03583i	−0.276424	−	0.114498i
$704$	3.44195	+	1.42570i	0.129723	+	0.0537331i
$705$	13.9389	−	6.44870i	0.524968	−	0.242872i
$706$	−21.4177	+	21.4177i	−0.806068	+	0.806068i
$707$	2.85426	−	6.89079i	0.107345	−	0.259155i
$708$	4.27895	+	1.77240i	0.160813	+	0.0666108i
$709$	15.4263	−	6.38980i	0.579348	−	0.239974i	−0.0737122	−	0.997280i	$-0.523485\pi$
$709$	15.4263	−	6.38980i	0.579348	−	0.239974i	0.653061	+	0.757306i	$0.273485\pi$
$710$	25.5731	+	9.39526i	0.959742	+	0.352598i
$711$	5.51444	+	13.3130i	0.206807	+	0.499277i
$712$	−5.68836	+	5.68836i	−0.213180	+	0.213180i
$713$		−	30.9770i		−	1.16010i
$714$	−0.535554	−	9.38108i	−0.0200426	−	0.351078i
$715$	−14.1489	+	38.5121i	−0.529139	+	1.44027i
$716$	−11.4346	−	11.4346i	−0.427332	−	0.427332i
$717$	19.4916	−	8.07370i	0.727929	−	0.301518i
$718$	−14.3010			−0.533709
$719$	0.958450	−	0.397003i	0.0357442	−	0.0148057i	−0.364740	−	0.931110i	$-0.618842\pi$
$719$	0.958450	−	0.397003i	0.0357442	−	0.0148057i	0.400484	+	0.916304i	$0.368842\pi$
$720$	3.24215	−	3.51684i	0.120828	−	0.131065i
$721$	−14.3994	−	5.96443i	−0.536262	−	0.222127i
$722$	−1.64487	−	1.64487i	−0.0612157	−	0.0612157i
$723$	−16.5385	−	16.5385i	−0.615073	−	0.615073i
$724$	16.9065	+	7.00292i	0.628327	+	0.260262i
$725$	−46.6631	+	23.9348i	−1.73302	+	0.888915i
$726$	−2.46841	+	1.02245i	−0.0916112	+	0.0379466i
$727$	28.2391			1.04733			0.523666	−	0.851924i	$-0.324564\pi$
$727$	28.2391			1.04733			0.523666	+	0.851924i	$0.324564\pi$
$728$	−11.1764	+	4.62941i	−0.414224	+	0.171577i
$729$	−6.36968	−	6.36968i	−0.235914	−	0.235914i
$730$	−14.6472	−	5.38122i	−0.542118	−	0.199168i
$731$	0.410519	+	7.19089i	0.0151836	+	0.265965i
$732$			2.71456i			0.100333i
$733$	29.6708	−	29.6708i	1.09592	−	1.09592i	0.101033	−	0.994883i	$-0.467785\pi$
$733$	29.6708	−	29.6708i	1.09592	−	1.09592i	0.994883	−	0.101033i	$-0.0322148\pi$
$734$	−1.21179	−	2.92552i	−0.0447281	−	0.107983i
$735$	1.88299	+	0.691789i	0.0694552	+	0.0255170i
$736$	−4.93649	+	2.04476i	−0.181961	+	0.0753708i
$737$	−37.7241	−	15.6258i	−1.38959	−	0.575585i
$738$	−5.32541	+	12.8567i	−0.196031	+	0.473261i
$739$	34.1067	−	34.1067i	1.25464	−	1.25464i	0.301018	−	0.953618i	$-0.402674\pi$
$739$	34.1067	−	34.1067i	1.25464	−	1.25464i	0.953618	−	0.301018i	$-0.0973264\pi$
$740$	1.82404	+	3.94266i	0.0670531	+	0.144935i
$741$	−17.2391	−	7.14067i	−0.633294	−	0.262319i
$742$	10.7890	+	4.46896i	0.396078	+	0.164061i
$743$	16.2373	+	39.2003i	0.595688	+	1.43812i	0.877936	+	0.478778i	$0.158920\pi$
$743$	16.2373	+	39.2003i	0.595688	+	1.43812i	−0.282248	+	0.959342i	$0.591080\pi$
$744$			5.37901i			0.197204i
$745$	0.695363	+	17.1100i	0.0254761	+	0.626863i
$746$	22.5437	+	22.5437i	0.825383	+	0.825383i
$747$			33.6719i			1.23199i
$748$	6.67762	+	13.8334i	0.244158	+	0.505799i
$749$	−13.6135			−0.497427
$750$	2.77534	−	9.99522i	0.101341	−	0.364974i
$751$	−12.7996	−	30.9009i	−0.467062	−	1.12759i	−0.965439	−	0.260628i	$-0.916070\pi$
$751$	−12.7996	−	30.9009i	−0.467062	−	1.12759i	0.498377	−	0.866961i	$-0.333930\pi$
$752$	−7.40275			−0.269950
$753$	−1.20866	−	2.91797i	−0.0440461	−	0.106337i
$754$	19.7687	−	47.7258i	0.719933	−	1.73807i
$755$	10.7609	+	9.92044i	0.391631	+	0.361042i
$756$	−8.28153	+	8.28153i	−0.301196	+	0.301196i
$757$	−14.7370	−	14.7370i	−0.535627	−	0.535627i	0.386614	−	0.922241i	$-0.373644\pi$
$757$	−14.7370	−	14.7370i	−0.535627	−	0.535627i	−0.922241	+	0.386614i	$0.873644\pi$
$758$	−2.80404	+	6.76955i	−0.101847	+	0.245881i
$759$	7.06800	−	17.0637i	0.256552	−	0.619371i
$760$	−0.370770	−	9.12313i	−0.0134493	−	0.330931i
$761$			38.9832i			1.41314i	0.707644	+	0.706569i	$0.249758\pi$
$761$			38.9832i			1.41314i	−0.707644	+	0.706569i	$0.750242\pi$
$762$	−5.77328	+	2.39137i	−0.209144	+	0.0866302i
$763$	6.78202	−	6.78202i	0.245526	−	0.245526i
$764$	8.07039			0.291976
$765$	19.6280	−	1.92269i	0.709651	−	0.0695151i
$766$	31.6048			1.14193
$767$	17.3843	−	17.3843i	0.627712	−	0.627712i
$768$	0.857197	−	0.355063i	0.0309314	−	0.0128122i
$769$		−	9.43564i		−	0.340258i	−0.985422	−	0.170129i	$-0.945582\pi$
$769$		−	9.43564i		−	0.340258i	0.985422	−	0.170129i	$-0.0544184\pi$
$770$	20.4449	−	0.830895i	0.736783	−	0.0299434i
$771$	4.63084	−	11.1798i	0.166776	−	0.402632i
$772$	6.70033	−	16.1760i	0.241150	−	0.582188i
$773$	−27.3826	−	27.3826i	−0.984884	−	0.984884i	0.0150031	−	0.999887i	$-0.495224\pi$
$773$	−27.3826	−	27.3826i	−0.984884	−	0.984884i	−0.999887	+	0.0150031i	$0.995224\pi$
$774$	2.64235	−	2.64235i	0.0949771	−	0.0949771i
$775$	−13.2295	−	25.7923i	−0.475219	−	0.926485i
$776$	−2.77526	+	6.70007i	−0.0996260	+	0.240518i
$777$	−1.69432	−	4.09044i	−0.0607833	−	0.146744i
$778$	−29.8509			−1.07021
$779$	10.1655	+	24.5418i	0.364218	+	0.879301i
$780$	4.29038	+	9.27365i	0.153620	+	0.332050i
$781$	45.3921			1.62426
$782$	−20.8011	−	7.25698i	−0.743845	−	0.259509i
$783$		−	50.0124i		−	1.78730i
$784$	−0.683717	−	0.683717i	−0.0244184	−	0.0244184i
$785$	32.8394	−	1.33461i	1.17209	−	0.0476344i
$786$			10.3544i			0.369329i
$787$	11.1223	+	26.8517i	0.396468	+	0.957159i	0.988497	+	0.151242i	$0.0483273\pi$
$787$	11.1223	+	26.8517i	0.396468	+	0.957159i	−0.592028	+	0.805917i	$0.701673\pi$
$788$	5.64153	+	2.33680i	0.200971	+	0.0832450i
$789$	26.4092	+	10.9391i	0.940193	+	0.389441i
$790$	−6.32464	−	13.6707i	−0.225021	−	0.486381i
$791$	17.0503	−	17.0503i	0.606238	−	0.606238i
$792$	3.04978	−	7.36282i	0.108369	−	0.261626i
$793$	13.3127	+	5.51430i	0.472748	+	0.195818i
$794$	4.27759	−	1.77184i	0.151806	−	0.0628801i
$795$	3.40158	−	9.25880i	0.120641	−	0.328376i
$796$	4.77463	+	11.5270i	0.169232	+	0.408562i
$797$	−10.4843	+	10.4843i	−0.371374	+	0.371374i	−0.867978	−	0.496603i	$-0.834580\pi$
$797$	−10.4843	+	10.4843i	−0.371374	+	0.371374i	0.496603	+	0.867978i	$0.334580\pi$
$798$			9.30577i			0.329421i
$799$	−22.7776	−	20.3173i	−0.805812	−	0.718775i
$800$	−3.23698	+	3.81077i	−0.114444	+	0.134731i
$801$	12.1682	+	12.1682i	0.429943	+	0.429943i
$802$	22.4635	−	9.30468i	0.793214	−	0.328560i
$803$	−25.9987			−0.917475
$804$	−9.39498	+	3.89153i	−0.331335	+	0.137244i
$805$	−19.8914	+	21.5767i	−0.701079	+	0.760478i
$806$	26.3797	+	10.9268i	0.929184	+	0.384881i
$807$	−4.31811	−	4.31811i	−0.152005	−	0.152005i
$808$	2.14718	+	2.14718i	0.0755376	+	0.0755376i
$809$	−20.7434	−	8.59221i	−0.729300	−	0.302086i	−0.0130357	−	0.999915i	$-0.504149\pi$
$809$	−20.7434	−	8.59221i	−0.729300	−	0.302086i	−0.716264	+	0.697829i	$0.754149\pi$
$810$	−3.27718	−	3.02121i	−0.115148	−	0.106154i
$811$	−33.0087	+	13.6726i	−1.15909	+	0.480111i	−0.877572	−	0.479445i	$-0.840838\pi$
$811$	−33.0087	+	13.6726i	−1.15909	+	0.480111i	−0.281519	+	0.959556i	$0.590838\pi$
$812$	−25.7627			−0.904092
$813$	−0.723678	+	0.299757i	−0.0253805	+	0.0105129i
$814$	5.11793	+	5.11793i	0.179383	+	0.179383i
$815$	4.84757	−	13.1947i	0.169803	−	0.462189i
$816$	3.61201	+	1.26014i	0.126446	+	0.0441137i
$817$		−	7.13316i		−	0.249558i
$818$	−24.6310	+	24.6310i	−0.861203	+	0.861203i
$819$	9.90298	+	23.9079i	0.346038	+	0.835410i
$820$	5.01639	−	13.6542i	0.175180	−	0.476825i
$821$	−23.3477	+	9.67095i	−0.814842	+	0.337519i	−0.750884	−	0.660434i	$-0.770372\pi$
$821$	−23.3477	+	9.67095i	−0.814842	+	0.337519i	−0.0639578	+	0.997953i	$0.520372\pi$
$822$	10.4744	+	4.33863i	0.365336	+	0.151327i
$823$	−5.68231	+	13.7183i	−0.198073	+	0.478190i	−0.991442	−	0.130551i	$-0.958325\pi$
$823$	−5.68231	+	13.7183i	−0.198073	+	0.478190i	0.793369	+	0.608741i	$0.208325\pi$
$824$	4.48689	−	4.48689i	0.156308	−	0.156308i
$825$	−1.40249	−	17.2262i	−0.0488283	−	0.599739i
$826$	−11.3277	−	4.69208i	−0.394141	−	0.163258i
$827$	37.2852	+	15.4441i	1.29653	+	0.537042i	0.920927	−	0.389736i	$-0.127434\pi$
$827$	37.2852	+	15.4441i	1.29653	+	0.537042i	0.375608	+	0.926779i	$0.377434\pi$
$828$	4.37403	+	10.5599i	0.152008	+	0.366980i
$829$		−	24.2428i		−	0.841986i	−0.907064	−	0.420993i	$-0.861682\pi$
$829$		−	24.2428i		−	0.841986i	0.907064	−	0.420993i	$-0.138318\pi$
$830$	−1.42927	−	35.1685i	−0.0496108	−	1.22072i
$831$	−7.14589	−	7.14589i	−0.247888	−	0.247888i
$832$		−	4.92512i		−	0.170748i
$833$	−0.227227	−	3.98024i	−0.00787294	−	0.137907i
$834$	−4.44642			−0.153967
$835$	−5.20547	+	2.40827i	−0.180143	+	0.0833416i
$836$	−5.82165	−	14.0547i	−0.201346	−	0.486092i
$837$	27.6435			0.955500
$838$	7.04143	+	16.9995i	0.243242	+	0.587238i
$839$	19.2518	−	46.4779i	0.664644	−	1.60459i	−0.125797	−	0.992056i	$-0.540149\pi$
$839$	19.2518	−	46.4779i	0.664644	−	1.60459i	0.790441	−	0.612538i	$-0.209851\pi$
$840$	3.45404	−	3.74669i	0.119176	−	0.129273i
$841$	57.2846	−	57.2846i	1.97533	−	1.97533i
$842$	8.80767	+	8.80767i	0.303532	+	0.303532i
$843$	3.14445	−	7.59137i	0.108301	−	0.261461i
$844$	3.89259	−	9.39754i	0.133988	−	0.323477i
$845$	25.1502	−	1.02212i	0.865192	−	0.0351620i
$846$			15.8355i			0.544437i
$847$	6.53463	−	2.70673i	0.224533	−	0.0930044i
$848$	−3.36188	+	3.36188i	−0.115447	+	0.115447i
$849$	1.81899			0.0624275
$850$	−20.4188	+	2.84130i	−0.700359	+	0.0974559i
$851$	−10.3806			−0.355843
$852$	7.99359	−	7.99359i	0.273856	−	0.273856i
$853$	−22.4366	+	9.29353i	−0.768214	+	0.318204i	−0.732149	−	0.681145i	$-0.761482\pi$
$853$	−22.4366	+	9.29353i	−0.768214	+	0.318204i	−0.0360650	+	0.999349i	$0.511482\pi$
$854$		−	7.18627i		−	0.245909i
$855$	−19.5157	+	0.793131i	−0.667423	+	0.0271245i
$856$	2.12100	−	5.12055i	0.0724943	−	0.175017i
$857$	9.08562	−	21.9346i	0.310359	−	0.749272i	−0.689333	−	0.724445i	$-0.742096\pi$
$857$	9.08562	−	21.9346i	0.310359	−	0.749272i	0.999692	−	0.0248277i	$-0.00790372\pi$
$858$	12.0380	+	12.0380i	0.410972	+	0.410972i
$859$	31.3939	−	31.3939i	1.07115	−	1.07115i	0.0738798	−	0.997267i	$-0.476462\pi$
$859$	31.3939	−	31.3939i	1.07115	−	1.07115i	0.997267	−	0.0738798i	$-0.0235381\pi$
$860$	−2.64763	+	2.87195i	−0.0902835	+	0.0979327i
$861$	−5.67346	+	13.6969i	−0.193351	+	0.466791i
$862$	−0.639227	−	1.54323i	−0.0217722	−	0.0525627i
$863$	−30.1419			−1.02604			−0.513021	−	0.858376i	$-0.671474\pi$
$863$	−30.1419			−1.02604			−0.513021	+	0.858376i	$0.671474\pi$
$864$	−1.82472	−	4.40526i	−0.0620782	−	0.149870i
$865$	−39.5139	+	18.2808i	−1.34351	+	0.621566i
$866$	−15.1334			−0.514254
$867$	7.65528	+	13.7907i	0.259987	+	0.468358i
$868$		−	14.2399i		−	0.483333i
$869$	−17.7458	−	17.7458i	−0.601985	−	0.601985i
$870$	0.883638	+	21.7427i	0.0299581	+	0.737146i
$871$			53.9798i			1.82904i
$872$	1.49432	+	3.60761i	0.0506042	+	0.122169i
$873$	14.3324	+	5.93668i	0.485078	+	0.200926i
$874$	20.1574	+	8.34948i	0.681835	+	0.282425i
$875$	−7.34719	+	26.4604i	−0.248380	+	0.894525i
$876$	−4.57840	+	4.57840i	−0.154690	+	0.154690i
$877$	−11.8269	+	28.5526i	−0.399364	+	0.964151i	0.588453	+	0.808532i	$0.299737\pi$
$877$	−11.8269	+	28.5526i	−0.399364	+	0.964151i	−0.987817	+	0.155619i	$0.950263\pi$
$878$	−9.79178	−	4.05589i	−0.330457	−	0.136880i
$879$	2.62337	−	1.08664i	0.0884842	−	0.0366513i
$880$	−2.87281	+	7.81953i	−0.0968423	+	0.263596i
$881$	−12.6259	−	30.4817i	−0.425378	−	1.02695i	−0.980735	−	0.195341i	$-0.937418\pi$
$881$	−12.6259	−	30.4817i	−0.425378	−	1.02695i	0.555357	−	0.831612i	$-0.312582\pi$
$882$	−1.46257	+	1.46257i	−0.0492472	+	0.0492472i
$883$		−	1.34248i		−	0.0451781i	−0.999745	−	0.0225891i	$-0.992809\pi$
$883$		−	1.34248i		−	0.0451781i	0.999745	−	0.0225891i	$-0.00719094\pi$
$884$	13.5173	−	15.1541i	0.454636	−	0.509689i
$885$	−3.57141	+	9.72106i	−0.120051	+	0.326770i
$886$	−17.5844	−	17.5844i	−0.590759	−	0.590759i
$887$	40.1104	−	16.6143i	1.34677	−	0.557852i	0.411381	−	0.911463i	$-0.365046\pi$
$887$	40.1104	−	16.6143i	1.34677	−	0.557852i	0.935392	+	0.353611i	$0.115046\pi$
$888$	1.80254			0.0604894
$889$	15.2836	−	6.33069i	0.512597	−	0.212325i
$890$	−13.2256	−	12.1926i	−0.443323	−	0.408696i
$891$	−6.86107	−	2.84195i	−0.229854	−	0.0952088i
$892$	13.4122	+	13.4122i	0.449072	+	0.449072i
$893$	21.3745	+	21.3745i	0.715269	+	0.715269i
$894$	6.56454	+	2.71912i	0.219551	+	0.0909411i
$895$	24.5092	−	26.5857i	0.819253	−	0.888664i
$896$	−2.26926	+	0.939960i	−0.0758108	+	0.0314018i
$897$	−24.4166			−0.815245
$898$	27.2033	−	11.2680i	0.907786	−	0.376017i
$899$	42.9975	+	42.9975i	1.43405	+	1.43405i
$900$	8.15179	+	6.92435i	0.271726	+	0.230812i
$901$	−19.5711	+	1.11729i	−0.652008	+	0.0372223i
$902$		−	24.2361i		−	0.806973i
$903$	2.81504	−	2.81504i	0.0936786	−	0.0936786i
$904$	3.75679	+	9.06969i	0.124949	+	0.301653i
$905$	−14.1110	+	38.4089i	−0.469065	+	1.27675i
$906$	5.61072	−	2.32404i	0.186404	−	0.0772110i
$907$	34.5791	+	14.3232i	1.14818	+	0.475592i	0.873923	−	0.486064i	$-0.161568\pi$
$907$	34.5791	+	14.3232i	1.14818	+	0.475592i	0.274258	+	0.961656i	$0.411568\pi$
$908$	−8.08234	+	19.5125i	−0.268222	+	0.647545i
$909$	4.59313	−	4.59313i	0.152345	−	0.152345i
$910$	−11.3580	−	24.5502i	−0.376513	−	0.813831i
$911$	47.7163	+	19.7648i	1.58091	+	0.654836i	0.988558	−	0.150841i	$-0.0481982\pi$
$911$	47.7163	+	19.7648i	1.58091	+	0.654836i	0.592355	+	0.805677i	$0.298198\pi$
$912$	−3.50024	−	1.44985i	−0.115905	−	0.0480092i
$913$	−22.4417	−	54.1791i	−0.742713	−	1.79307i
$914$			12.2609i			0.405556i
$915$	−6.06493	+	0.246483i	−0.200500	+	0.00814848i
$916$	−6.64660	−	6.64660i	−0.219610	−	0.219610i
$917$		−	27.4113i		−	0.905200i
$918$	6.47604	−	18.5626i	0.213741	−	0.612658i
$919$	55.8488			1.84228			0.921142	−	0.389228i	$-0.127258\pi$
$919$	55.8488			1.84228			0.921142	+	0.389228i	$0.127258\pi$
$920$	−5.01668	−	10.8435i	−0.165395	−	0.357501i
$921$	1.95979	+	4.73134i	0.0645771	+	0.155903i
$922$	8.99733			0.296311
$923$	−22.9640	−	55.4400i	−0.755870	−	1.82483i
$924$	3.24910	−	7.84403i	0.106888	−	0.258050i
$925$	−8.64316	+	4.43331i	−0.284185	+	0.145766i
$926$	7.20642	−	7.20642i	0.236818	−	0.236818i
$927$	−9.59810	−	9.59810i	−0.315243	−	0.315243i
$928$	4.01385	−	9.69029i	0.131761	−	0.318099i
$929$	−6.70613	+	16.1900i	−0.220021	+	0.531178i	−0.994892	−	0.100941i	$-0.967815\pi$
$929$	−6.70613	+	16.1900i	−0.220021	+	0.531178i	0.774871	+	0.632119i	$0.217815\pi$
$930$	−12.0179	+	0.488416i	−0.394083	+	0.0160158i
$931$			3.94828i			0.129400i
$932$	21.5267	−	8.91666i	0.705131	−	0.292075i
$933$	−4.98520	+	4.98520i	−0.163208	+	0.163208i
$934$	−18.2155			−0.596030
$935$	−30.3006	+	16.1754i	−0.990935	+	0.528991i
$936$	−10.5355			−0.344365
$937$	−23.0077	+	23.0077i	−0.751628	+	0.751628i	−0.974783	−	0.223155i	$-0.928364\pi$
$937$	−23.0077	+	23.0077i	−0.751628	+	0.751628i	0.223155	+	0.974783i	$0.428364\pi$
$938$	24.8714	−	10.3021i	0.812079	−	0.336374i
$939$			2.12311i			0.0692852i
$940$	−0.672172	−	16.5394i	−0.0219238	−	0.539455i
$941$	6.44004	−	15.5476i	0.209939	−	0.506839i	−0.783474	−	0.621425i	$-0.786554\pi$
$941$	6.44004	−	15.5476i	0.209939	−	0.506839i	0.993413	+	0.114586i	$0.0365542\pi$
$942$	5.21883	−	12.5994i	0.170039	−	0.410510i
$943$	24.5788	+	24.5788i	0.800396	+	0.800396i
$944$	3.52973	−	3.52973i	0.114883	−	0.114883i
$945$	−19.2548	−	17.7508i	−0.626357	−	0.577434i
$946$	−2.49054	+	6.01269i	−0.0809744	+	0.195489i
$947$	2.68223	+	6.47548i	0.0871608	+	0.210425i	0.961450	−	0.274981i	$-0.0886717\pi$
$947$	2.68223	+	6.47548i	0.0871608	+	0.210425i	−0.874289	+	0.485406i	$0.838672\pi$
$948$	−6.25010			−0.202994
$949$	13.1528	+	31.7538i	0.426959	+	1.03077i
$950$	20.3495	−	1.65677i	0.660223	−	0.0537526i
$951$	5.17365			0.167767
$952$	−9.56209	−	3.33597i	−0.309909	−	0.108120i
$953$			38.4477i			1.24544i	0.782443	+	0.622722i	$0.213973\pi$
$953$			38.4477i			1.24544i	−0.782443	+	0.622722i	$0.786027\pi$
$954$	7.19155	+	7.19155i	0.232835	+	0.232835i
$955$	0.732794	+	18.0311i	0.0237127	+	0.583471i
$956$		−	22.7388i		−	0.735426i
$957$	13.8744	+	33.4958i	0.448497	+	1.08277i
$958$	−17.1724	−	7.11304i	−0.554815	−	0.229812i
$959$	−27.7289	−	11.4857i	−0.895413	−	0.370892i
$960$	0.871123	+	1.88293i	0.0281154	+	0.0607713i
$961$	−1.84587	+	1.84587i	−0.0595442	+	0.0595442i
$962$	3.66165	−	8.84000i	0.118056	−	0.285013i
$963$	−10.9536	−	4.53712i	−0.352974	−	0.146207i
$964$	−23.2895	+	9.64684i	−0.750106	+	0.310704i
$965$	36.7493	+	13.5013i	1.18300	+	0.434621i
$966$	4.65990	+	11.2500i	0.149930	+	0.361963i
$967$	−13.1021	+	13.1021i	−0.421335	+	0.421335i	−0.885663	−	0.464328i	$-0.846296\pi$
$967$	−13.1021	+	13.1021i	−0.421335	+	0.421335i	0.464328	+	0.885663i	$0.346296\pi$
$968$			2.87963i			0.0925547i
$969$	−6.79071	−	14.0677i	−0.218149	−	0.451919i
$970$	−15.2214	−	5.59218i	−0.488731	−	0.179554i
$971$	25.8676	+	25.8676i	0.830132	+	0.830132i	0.987534	−	0.157403i	$-0.0503121\pi$
$971$	25.8676	+	25.8676i	0.830132	+	0.830132i	−0.157403	+	0.987534i	$0.550312\pi$
$972$	−14.9245	+	6.18192i	−0.478703	+	0.198285i
$973$	11.7710			0.377362
$974$	−34.5909	+	14.3280i	−1.10836	+	0.459099i
$975$	−20.3298	+	10.4277i	−0.651076	+	0.333955i
$976$	2.70302	+	1.11963i	0.0865216	+	0.0358384i
$977$	−7.86298	−	7.86298i	−0.251559	−	0.251559i	0.570051	−	0.821610i	$-0.306924\pi$
$977$	−7.86298	−	7.86298i	−0.251559	−	0.251559i	−0.821610	+	0.570051i	$0.806924\pi$
$978$	−4.12436	−	4.12436i	−0.131883	−	0.131883i
$979$	−27.6890	−	11.4691i	−0.884943	−	0.366555i
$980$	1.46549	−	1.58966i	0.0468135	−	0.0507797i
$981$	7.71721	−	3.19657i	0.246391	−	0.102059i
$982$	30.8237			0.983622
$983$	−33.0610	+	13.6943i	−1.05448	+	0.436780i	−0.841489	−	0.540273i	$-0.818321\pi$
$983$	−33.0610	+	13.6943i	−1.05448	+	0.436780i	−0.212992	+	0.977054i	$0.568321\pi$
$984$	−4.26799	−	4.26799i	−0.136059	−	0.136059i
$985$	−4.70868	+	12.8166i	−0.150031	+	0.408372i
$986$	38.9459	−	18.7998i	1.24029	−	0.598709i
$987$			16.8705i			0.536994i
$988$	−14.2206	+	14.2206i	−0.452419	+	0.452419i
$989$	−3.57196	−	8.62348i	−0.113582	−	0.274211i
$990$	16.7271	+	6.14534i	0.531622	+	0.195312i
$991$	−46.3224	+	19.1874i	−1.47148	+	0.609506i	−0.967196	−	0.254032i	$-0.918243\pi$
$991$	−46.3224	+	19.1874i	−1.47148	+	0.609506i	−0.504283	+	0.863539i	$0.668243\pi$
$992$	5.35615	+	2.21859i	0.170058	+	0.0704403i
$993$	−9.17138	+	22.1417i	−0.291045	+	0.702645i
$994$	−21.1615	+	21.1615i	−0.671201	+	0.671201i
$995$	−25.3203	+	11.7142i	−0.802707	+	0.371366i
$996$	−13.4930	−	5.58898i	−0.427542	−	0.177094i
$997$	−11.4434	−	4.74002i	−0.362417	−	0.150118i	0.194042	−	0.980993i	$-0.437840\pi$
$997$	−11.4434	−	4.74002i	−0.362417	−	0.150118i	−0.556459	+	0.830875i	$0.687840\pi$
$998$	9.87864	+	23.8491i	0.312703	+	0.754931i
$999$		−	9.26353i		−	0.293085i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.n.a.49.4	✓	20
5.2	odd	4		850.2.l.h.151.2		20
5.3	odd	4		850.2.l.i.151.4		20
5.4	even	2		170.2.n.b.49.2	yes	20
17.8	even	8		170.2.n.b.59.2	yes	20
85.8	odd	8		850.2.l.i.501.4		20
85.42	odd	8		850.2.l.h.501.2		20
85.59	even	8	inner	170.2.n.a.59.4	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.n.a.49.4	✓	20	1.1	even	1	trivial
170.2.n.a.59.4	yes	20	85.59	even	8	inner
170.2.n.b.49.2	yes	20	5.4	even	2
170.2.n.b.59.2	yes	20	17.8	even	8
850.2.l.h.151.2		20	5.2	odd	4
850.2.l.h.501.2		20	85.42	odd	8
850.2.l.i.151.4		20	5.3	odd	4
850.2.l.i.501.4		20	85.8	odd	8

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:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.n (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.857197 - 0.355063i) q^{3} -1.00000i q^{4} +(2.23422 - 0.0908004i) q^{5} +(0.355063 - 0.857197i) q^{6} +(-0.939960 + 2.26926i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.51260 + 1.51260i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.857197 - 0.355063i) q^{3} -1.00000i q^{4} +(2.23422 - 0.0908004i) q^{5} +(0.355063 - 0.857197i) q^{6} +(-0.939960 + 2.26926i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.51260 + 1.51260i) q^{9} +(1.51563 - 1.64404i) q^{10} +(1.42570 - 3.44195i) q^{11} +(-0.355063 - 0.857197i) q^{12} -4.92512 q^{13} +(0.939960 + 2.26926i) q^{14} +(1.88293 - 0.871123i) q^{15} -1.00000 q^{16} +(-3.07691 - 2.74457i) q^{17} +2.13914i q^{18} +(2.88737 + 2.88737i) q^{19} +(-0.0908004 - 2.23422i) q^{20} +2.27895i q^{21} +(-1.42570 - 3.44195i) q^{22} +(4.93649 + 2.04476i) q^{23} +(-0.857197 - 0.355063i) q^{24} +(4.98351 - 0.405737i) q^{25} +(-3.48258 + 3.48258i) q^{26} +(-1.82472 + 4.40526i) q^{27} +(2.26926 + 0.939960i) q^{28} +(-9.69029 + 4.01385i) q^{29} +(0.715456 - 1.94741i) q^{30} +(-2.21859 - 5.35615i) q^{31} +(-0.707107 + 0.707107i) q^{32} -3.45664i q^{33} +(-4.11640 + 0.235000i) q^{34} +(-1.89403 + 5.15539i) q^{35} +(1.51260 + 1.51260i) q^{36} +(-1.79488 + 0.743464i) q^{37} +4.08336 q^{38} +(-4.22180 + 1.74873i) q^{39} +(-1.64404 - 1.51563i) q^{40} +(6.01020 + 2.48951i) q^{41} +(1.61146 + 1.61146i) q^{42} +(-1.23524 - 1.23524i) q^{43} +(-3.44195 - 1.42570i) q^{44} +(-3.24215 + 3.51684i) q^{45} +(4.93649 - 2.04476i) q^{46} +7.40275 q^{47} +(-0.857197 + 0.355063i) q^{48} +(0.683717 + 0.683717i) q^{49} +(3.23698 - 3.81077i) q^{50} +(-3.61201 - 1.26014i) q^{51} +4.92512i q^{52} +(3.36188 - 3.36188i) q^{53} +(1.82472 + 4.40526i) q^{54} +(2.87281 - 7.81953i) q^{55} +(2.26926 - 0.939960i) q^{56} +(3.50024 + 1.44985i) q^{57} +(-4.01385 + 9.69029i) q^{58} +(-3.52973 + 3.52973i) q^{59} +(-0.871123 - 1.88293i) q^{60} +(-2.70302 - 1.11963i) q^{61} +(-5.35615 - 2.21859i) q^{62} +(-2.01071 - 4.85428i) q^{63} +1.00000i q^{64} +(-11.0038 + 0.447202i) q^{65} +(-2.44421 - 2.44421i) q^{66} -10.9601i q^{67} +(-2.74457 + 3.07691i) q^{68} +4.95756 q^{69} +(2.30613 + 4.98469i) q^{70} +(4.66263 + 11.2566i) q^{71} +2.13914 q^{72} +(-2.67056 - 6.44731i) q^{73} +(-0.743464 + 1.79488i) q^{74} +(4.12779 - 2.11725i) q^{75} +(2.88737 - 2.88737i) q^{76} +(6.47058 + 6.47058i) q^{77} +(-1.74873 + 4.22180i) q^{78} +(2.57787 - 6.22353i) q^{79} +(-2.23422 + 0.0908004i) q^{80} -1.99337i q^{81} +(6.01020 - 2.48951i) q^{82} +(11.1304 - 11.1304i) q^{83} +2.27895 q^{84} +(-7.12371 - 5.85259i) q^{85} -1.74689 q^{86} +(-6.88132 + 6.88132i) q^{87} +(-3.44195 + 1.42570i) q^{88} -8.04456i q^{89} +(0.194235 + 4.77933i) q^{90} +(4.62941 - 11.1764i) q^{91} +(2.04476 - 4.93649i) q^{92} +(-3.80354 - 3.80354i) q^{93} +(5.23453 - 5.23453i) q^{94} +(6.71320 + 6.18885i) q^{95} +(-0.355063 + 0.857197i) q^{96} +(-2.77526 - 6.70007i) q^{97} +0.966921 q^{98} +(3.04978 + 7.36282i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{5}+O(q^{10}) \) 20 * q - 4 * q^5	\( 20 q - 4 q^{5} + 4 q^{10} - 8 q^{11} - 24 q^{13} + 8 q^{15} - 20 q^{16} + 8 q^{20} + 8 q^{22} + 16 q^{23} - 12 q^{25} - 12 q^{26} + 24 q^{27} - 12 q^{29} - 8 q^{30} + 8 q^{31} + 8 q^{34} - 8 q^{35} - 8 q^{37} - 8 q^{38} + 4 q^{40} + 4 q^{41} + 8 q^{42} + 16 q^{43} - 8 q^{44} - 12 q^{45} + 16 q^{46} + 40 q^{47} - 56 q^{49} + 8 q^{50} - 8 q^{51} + 44 q^{53} - 24 q^{54} - 72 q^{57} + 16 q^{59} + 16 q^{60} + 8 q^{61} - 8 q^{62} - 24 q^{63} - 8 q^{65} - 8 q^{66} + 20 q^{68} - 16 q^{69} - 16 q^{70} + 8 q^{71} - 28 q^{72} - 60 q^{73} + 28 q^{74} + 64 q^{75} + 8 q^{78} + 56 q^{79} + 4 q^{80} + 4 q^{82} + 16 q^{84} - 16 q^{85} + 48 q^{86} - 72 q^{87} - 8 q^{88} + 32 q^{90} - 24 q^{91} - 8 q^{92} + 72 q^{93} + 32 q^{94} + 8 q^{95} + 48 q^{97} - 36 q^{98} + 72 q^{99}+O(q^{100}) \) 20 * q - 4 * q^5 + 4 * q^10 - 8 * q^11 - 24 * q^13 + 8 * q^15 - 20 * q^16 + 8 * q^20 + 8 * q^22 + 16 * q^23 - 12 * q^25 - 12 * q^26 + 24 * q^27 - 12 * q^29 - 8 * q^30 + 8 * q^31 + 8 * q^34 - 8 * q^35 - 8 * q^37 - 8 * q^38 + 4 * q^40 + 4 * q^41 + 8 * q^42 + 16 * q^43 - 8 * q^44 - 12 * q^45 + 16 * q^46 + 40 * q^47 - 56 * q^49 + 8 * q^50 - 8 * q^51 + 44 * q^53 - 24 * q^54 - 72 * q^57 + 16 * q^59 + 16 * q^60 + 8 * q^61 - 8 * q^62 - 24 * q^63 - 8 * q^65 - 8 * q^66 + 20 * q^68 - 16 * q^69 - 16 * q^70 + 8 * q^71 - 28 * q^72 - 60 * q^73 + 28 * q^74 + 64 * q^75 + 8 * q^78 + 56 * q^79 + 4 * q^80 + 4 * q^82 + 16 * q^84 - 16 * q^85 + 48 * q^86 - 72 * q^87 - 8 * q^88 + 32 * q^90 - 24 * q^91 - 8 * q^92 + 72 * q^93 + 32 * q^94 + 8 * q^95 + 48 * q^97 - 36 * q^98 + 72 * q^99

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