LMFDB - Embedded newform 304.2.k.b.77.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,2,Mod(77,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("304.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	304.k (of order $4$, degree $2$, 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:	$2.42745222145$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			77.10
Character	$\chi$	$=$	304.77
Dual form			304.2.k.b.229.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.869834 + 1.11507i) q^{2} +(1.14883 + 1.14883i) q^{3} +(-0.486777 - 1.93986i) q^{4} +(0.889280 - 0.889280i) q^{5} +(-2.28032 + 0.281738i) q^{6} +1.83745i q^{7} +(2.58650 + 1.14456i) q^{8} -0.360387i q^{9} +O(q^{10})$	\(q+(-0.869834 + 1.11507i) q^{2} +(1.14883 + 1.14883i) q^{3} +(-0.486777 - 1.93986i) q^{4} +(0.889280 - 0.889280i) q^{5} +(-2.28032 + 0.281738i) q^{6} +1.83745i q^{7} +(2.58650 + 1.14456i) q^{8} -0.360387i q^{9} +(0.218086 + 1.76514i) q^{10} +(-2.61705 + 2.61705i) q^{11} +(1.66934 - 2.78779i) q^{12} +(4.07506 + 4.07506i) q^{13} +(-2.04889 - 1.59828i) q^{14} +2.04326 q^{15} +(-3.52610 + 1.88856i) q^{16} +5.97037 q^{17} +(0.401858 + 0.313477i) q^{18} +(-0.707107 - 0.707107i) q^{19} +(-2.15796 - 1.29220i) q^{20} +(-2.11091 + 2.11091i) q^{21} +(-0.641804 - 5.19460i) q^{22} +2.80954i q^{23} +(1.65654 + 4.28635i) q^{24} +3.41836i q^{25} +(-8.08861 + 0.999364i) q^{26} +(3.86051 - 3.86051i) q^{27} +(3.56439 - 0.894428i) q^{28} +(-5.43272 - 5.43272i) q^{29} +(-1.77730 + 2.27839i) q^{30} -3.84790 q^{31} +(0.961239 - 5.57459i) q^{32} -6.01308 q^{33} +(-5.19323 + 6.65740i) q^{34} +(1.63401 + 1.63401i) q^{35} +(-0.699100 + 0.175428i) q^{36} +(-1.00677 + 1.00677i) q^{37} +(1.40354 - 0.173410i) q^{38} +9.36308i q^{39} +(3.31796 - 1.28229i) q^{40} -12.0024i q^{41} +(-0.517679 - 4.18997i) q^{42} +(0.380362 - 0.380362i) q^{43} +(6.35063 + 3.80279i) q^{44} +(-0.320485 - 0.320485i) q^{45} +(-3.13285 - 2.44384i) q^{46} -6.40334 q^{47} +(-6.22051 - 1.88125i) q^{48} +3.62378 q^{49} +(-3.81172 - 2.97341i) q^{50} +(6.85893 + 6.85893i) q^{51} +(5.92138 - 9.88867i) q^{52} +(-4.33394 + 4.33394i) q^{53} +(0.946748 + 7.66275i) q^{54} +4.65458i q^{55} +(-2.10307 + 4.75256i) q^{56} -1.62469i q^{57} +(10.7834 - 1.33232i) q^{58} +(6.53696 - 6.53696i) q^{59} +(-0.994613 - 3.96364i) q^{60} +(1.14953 + 1.14953i) q^{61} +(3.34704 - 4.29069i) q^{62} +0.662193 q^{63} +(5.37996 + 5.92082i) q^{64} +7.24774 q^{65} +(5.23039 - 6.70503i) q^{66} +(7.33490 + 7.33490i) q^{67} +(-2.90624 - 11.5817i) q^{68} +(-3.22768 + 3.22768i) q^{69} +(-3.24335 + 0.400723i) q^{70} -10.6431i q^{71} +(0.412486 - 0.932141i) q^{72} -15.5594i q^{73} +(-0.246900 - 1.99835i) q^{74} +(-3.92711 + 3.92711i) q^{75} +(-1.02748 + 1.71589i) q^{76} +(-4.80870 - 4.80870i) q^{77} +(-10.4405 - 8.14433i) q^{78} +5.66702 q^{79} +(-1.45623 + 4.81515i) q^{80} +7.78896 q^{81} +(13.3835 + 10.4401i) q^{82} +(-4.67992 - 4.67992i) q^{83} +(5.12242 + 3.06733i) q^{84} +(5.30933 - 5.30933i) q^{85} +(0.0932797 + 0.754983i) q^{86} -12.4825i q^{87} +(-9.76438 + 3.77362i) q^{88} -11.9814i q^{89} +(0.636134 - 0.0785956i) q^{90} +(-7.48771 + 7.48771i) q^{91} +(5.45011 - 1.36762i) q^{92} +(-4.42058 - 4.42058i) q^{93} +(5.56985 - 7.14020i) q^{94} -1.25763 q^{95} +(7.50854 - 5.29995i) q^{96} -5.83142 q^{97} +(-3.15209 + 4.04078i) q^{98} +(0.943152 + 0.943152i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6}+O(q^{10}) $ 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6	$ 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6} + 4 q^{11} - 4 q^{12} + 20 q^{14} - 16 q^{15} + 4 q^{16} + 4 q^{17} - 16 q^{18} + 16 q^{21} + 4 q^{22} - 4 q^{24} - 36 q^{26} + 28 q^{27} - 24 q^{28} + 24 q^{30} + 32 q^{31} - 20 q^{32} - 16 q^{33} - 32 q^{34} - 24 q^{35} + 52 q^{36} - 24 q^{37} - 4 q^{38} - 8 q^{40} - 40 q^{42} - 16 q^{43} - 36 q^{44} - 8 q^{46} - 24 q^{47} + 36 q^{48} - 56 q^{49} + 24 q^{50} - 52 q^{51} - 28 q^{52} + 32 q^{53} - 52 q^{54} + 12 q^{56} + 52 q^{58} + 28 q^{59} - 64 q^{60} - 12 q^{62} + 24 q^{63} - 32 q^{64} - 16 q^{65} - 44 q^{66} + 28 q^{67} - 48 q^{68} - 8 q^{69} + 4 q^{70} + 108 q^{72} + 72 q^{74} + 44 q^{75} - 12 q^{77} + 100 q^{78} + 8 q^{79} - 56 q^{80} - 76 q^{81} + 28 q^{82} + 40 q^{83} + 52 q^{84} - 8 q^{85} - 20 q^{86} - 56 q^{88} - 24 q^{90} - 4 q^{91} + 72 q^{92} - 84 q^{93} - 24 q^{94} + 32 q^{95} + 72 q^{96} - 16 q^{97} - 80 q^{98} - 24 q^{99}+O(q^{100}) $ 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6 + 4 * q^11 - 4 * q^12 + 20 * q^14 - 16 * q^15 + 4 * q^16 + 4 * q^17 - 16 * q^18 + 16 * q^21 + 4 * q^22 - 4 * q^24 - 36 * q^26 + 28 * q^27 - 24 * q^28 + 24 * q^30 + 32 * q^31 - 20 * q^32 - 16 * q^33 - 32 * q^34 - 24 * q^35 + 52 * q^36 - 24 * q^37 - 4 * q^38 - 8 * q^40 - 40 * q^42 - 16 * q^43 - 36 * q^44 - 8 * q^46 - 24 * q^47 + 36 * q^48 - 56 * q^49 + 24 * q^50 - 52 * q^51 - 28 * q^52 + 32 * q^53 - 52 * q^54 + 12 * q^56 + 52 * q^58 + 28 * q^59 - 64 * q^60 - 12 * q^62 + 24 * q^63 - 32 * q^64 - 16 * q^65 - 44 * q^66 + 28 * q^67 - 48 * q^68 - 8 * q^69 + 4 * q^70 + 108 * q^72 + 72 * q^74 + 44 * q^75 - 12 * q^77 + 100 * q^78 + 8 * q^79 - 56 * q^80 - 76 * q^81 + 28 * q^82 + 40 * q^83 + 52 * q^84 - 8 * q^85 - 20 * q^86 - 56 * q^88 - 24 * q^90 - 4 * q^91 + 72 * q^92 - 84 * q^93 - 24 * q^94 + 32 * q^95 + 72 * q^96 - 16 * q^97 - 80 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.869834	+	1.11507i	−0.615066	+	0.788476i
$2$	−0.869834	+	1.11507i	−0.615066	+	0.788476i
$3$	1.14883	+	1.14883i	0.663276	+	0.663276i	0.956151	−	0.292875i	$-0.0946118\pi$
$3$	1.14883	+	1.14883i	0.663276	+	0.663276i	−0.292875	+	0.956151i	$0.594612\pi$
$4$	−0.486777	−	1.93986i	−0.243389	−	0.969929i
$5$	0.889280	−	0.889280i	0.397698	−	0.397698i	−0.479722	−	0.877420i	$-0.659263\pi$
$5$	0.889280	−	0.889280i	0.397698	−	0.397698i	0.877420	+	0.479722i	$0.159263\pi$
$6$	−2.28032	+	0.281738i	−0.930936	+	0.115019i
$7$			1.83745i			0.694490i	0.937774	+	0.347245i	$0.112883\pi$
$7$			1.83745i			0.694490i	−0.937774	+	0.347245i	$0.887117\pi$
$8$	2.58650	+	1.14456i	0.914466	+	0.404664i
$9$		−	0.360387i		−	0.120129i
$10$	0.218086	+	1.76514i	0.0689650	+	0.558186i
$11$	−2.61705	+	2.61705i	−0.789071	+	0.789071i	−0.981342	−	0.192271i	$-0.938415\pi$
$11$	−2.61705	+	2.61705i	−0.789071	+	0.789071i	0.192271	+	0.981342i	$0.438415\pi$
$12$	1.66934	−	2.78779i	0.481897	−	0.804765i
$13$	4.07506	+	4.07506i	1.13022	+	1.13022i	0.990141	+	0.140077i	$0.0447349\pi$
$13$	4.07506	+	4.07506i	1.13022	+	1.13022i	0.140077	+	0.990141i	$0.455265\pi$
$14$	−2.04889	−	1.59828i	−0.547589	−	0.427157i
$15$	2.04326			0.527568
$16$	−3.52610	+	1.88856i	−0.881524	+	0.472139i
$17$	5.97037			1.44803			0.724014	−	0.689786i	$-0.242295\pi$
$17$	5.97037			1.44803			0.724014	+	0.689786i	$0.242295\pi$
$18$	0.401858	+	0.313477i	0.0947189	+	0.0738873i
$19$	−0.707107	−	0.707107i	−0.162221	−	0.162221i
$19$	−0.707107	−	0.707107i	−0.162221	−	0.162221i
$20$	−2.15796	−	1.29220i	−0.482534	−	0.288944i
$21$	−2.11091	+	2.11091i	−0.460639	+	0.460639i
$22$	−0.641804	−	5.19460i	−0.136833	−	1.10749i
$23$			2.80954i			0.585830i	0.956138	+	0.292915i	$0.0946253\pi$
$23$			2.80954i			0.585830i	−0.956138	+	0.292915i	$0.905375\pi$
$24$	1.65654	+	4.28635i	0.338139	+	0.874947i
$25$			3.41836i			0.683672i
$26$	−8.08861	+	0.999364i	−1.58631	+	0.195991i
$27$	3.86051	−	3.86051i	0.742955	−	0.742955i
$28$	3.56439	−	0.894428i	0.673606	−	0.169031i
$29$	−5.43272	−	5.43272i	−1.00883	−	1.00883i	−0.999961	−	0.00886973i	$-0.997177\pi$
$29$	−5.43272	−	5.43272i	−1.00883	−	1.00883i	−0.00886973	−	0.999961i	$-0.502823\pi$
$30$	−1.77730	+	2.27839i	−0.324489	+	0.415974i
$31$	−3.84790			−0.691104			−0.345552	−	0.938400i	$-0.612308\pi$
$31$	−3.84790			−0.691104			−0.345552	+	0.938400i	$0.612308\pi$
$32$	0.961239	−	5.57459i	0.169925	−	0.985457i
$33$	−6.01308			−1.04674
$34$	−5.19323	+	6.65740i	−0.890632	+	1.14173i
$35$	1.63401	+	1.63401i	0.276198	+	0.276198i
$36$	−0.699100	+	0.175428i	−0.116517	+	0.0292381i
$37$	−1.00677	+	1.00677i	−0.165512	+	0.165512i	−0.785004	−	0.619491i	$-0.787339\pi$
$37$	−1.00677	+	1.00677i	−0.165512	+	0.165512i	0.619491	+	0.785004i	$0.287339\pi$
$38$	1.40354	−	0.173410i	0.227685	−	0.0281309i
$39$			9.36308i			1.49929i
$40$	3.31796	−	1.28229i	0.524615	−	0.202747i
$41$		−	12.0024i		−	1.87446i	−0.348717	−	0.937228i	$-0.613383\pi$
$41$		−	12.0024i		−	1.87446i	0.348717	−	0.937228i	$-0.386617\pi$
$42$	−0.517679	−	4.18997i	−0.0798796	−	0.646526i
$43$	0.380362	−	0.380362i	0.0580047	−	0.0580047i	−0.677509	−	0.735514i	$-0.736941\pi$
$43$	0.380362	−	0.380362i	0.0580047	−	0.0580047i	0.735514	+	0.677509i	$0.236941\pi$
$44$	6.35063	+	3.80279i	0.957393	+	0.573291i
$45$	−0.320485	−	0.320485i	−0.0477751	−	0.0477751i
$46$	−3.13285	−	2.44384i	−0.461913	−	0.360324i
$47$	−6.40334			−0.934024			−0.467012	−	0.884251i	$-0.654669\pi$
$47$	−6.40334			−0.934024			−0.467012	+	0.884251i	$0.654669\pi$
$48$	−6.22051	−	1.88125i	−0.897853	−	0.271535i
$49$	3.62378			0.517683
$50$	−3.81172	−	2.97341i	−0.539059	−	0.420503i
$51$	6.85893	+	6.85893i	0.960442	+	0.960442i
$52$	5.92138	−	9.88867i	0.821148	−	1.37131i
$53$	−4.33394	+	4.33394i	−0.595313	+	0.595313i	−0.939062	−	0.343749i	$-0.888303\pi$
$53$	−4.33394	+	4.33394i	−0.595313	+	0.595313i	0.343749	+	0.939062i	$0.388303\pi$
$54$	0.946748	+	7.66275i	0.128836	+	1.04277i
$55$			4.65458i			0.627624i
$56$	−2.10307	+	4.75256i	−0.281035	+	0.635087i
$57$		−	1.62469i		−	0.215195i
$58$	10.7834	−	1.33232i	1.41594	−	0.174942i
$59$	6.53696	−	6.53696i	0.851040	−	0.851040i	−0.139222	−	0.990261i	$-0.544460\pi$
$59$	6.53696	−	6.53696i	0.851040	−	0.851040i	0.990261	+	0.139222i	$0.0444600\pi$
$60$	−0.994613	−	3.96364i	−0.128404	−	0.511703i
$61$	1.14953	+	1.14953i	0.147182	+	0.147182i	0.776858	−	0.629676i	$-0.216812\pi$
$61$	1.14953	+	1.14953i	0.147182	+	0.147182i	−0.629676	+	0.776858i	$0.716812\pi$
$62$	3.34704	−	4.29069i	0.425074	−	0.544919i
$63$	0.662193			0.0834285
$64$	5.37996	+	5.92082i	0.672494	+	0.740102i
$65$	7.24774			0.898971
$66$	5.23039	−	6.70503i	0.643816	−	0.825332i
$67$	7.33490	+	7.33490i	0.896101	+	0.896101i	0.995089	−	0.0989875i	$-0.0315604\pi$
$67$	7.33490	+	7.33490i	0.896101	+	0.896101i	−0.0989875	+	0.995089i	$0.531560\pi$
$68$	−2.90624	−	11.5817i	−0.352433	−	1.40448i
$69$	−3.22768	+	3.22768i	−0.388567	+	0.388567i
$70$	−3.24335	+	0.400723i	−0.387655	+	0.0478955i
$71$		−	10.6431i		−	1.26310i	−0.775335	−	0.631550i	$-0.782419\pi$
$71$		−	10.6431i		−	1.26310i	0.775335	−	0.631550i	$-0.217581\pi$
$72$	0.412486	−	0.932141i	0.0486119	−	0.109854i
$73$		−	15.5594i		−	1.82109i	−0.413415	−	0.910543i	$-0.635664\pi$
$73$		−	15.5594i		−	1.82109i	0.413415	−	0.910543i	$-0.364336\pi$
$74$	−0.246900	−	1.99835i	−0.0287016	−	0.232303i
$75$	−3.92711	+	3.92711i	−0.453464	+	0.453464i
$76$	−1.02748	+	1.71589i	−0.117860	+	0.196826i
$77$	−4.80870	−	4.80870i	−0.548002	−	0.548002i
$78$	−10.4405	−	8.14433i	−1.18216	−	0.922163i
$79$	5.66702			0.637590			0.318795	−	0.947824i	$-0.396722\pi$
$79$	5.66702			0.637590			0.318795	+	0.947824i	$0.396722\pi$
$80$	−1.45623	+	4.81515i	−0.162812	+	0.538350i
$81$	7.78896			0.865440
$82$	13.3835	+	10.4401i	1.47796	+	1.15291i
$83$	−4.67992	−	4.67992i	−0.513687	−	0.513687i	0.401967	−	0.915654i	$-0.368327\pi$
$83$	−4.67992	−	4.67992i	−0.513687	−	0.513687i	−0.915654	+	0.401967i	$0.868327\pi$
$84$	5.12242	+	3.06733i	0.558901	+	0.334673i
$85$	5.30933	−	5.30933i	0.575878	−	0.575878i
$86$	0.0932797	+	0.754983i	0.0100586	+	0.0814119i
$87$		−	12.4825i		−	1.33827i
$88$	−9.76438	+	3.77362i	−1.04089	+	0.402270i
$89$		−	11.9814i		−	1.27003i	−0.772501	−	0.635014i	$-0.780995\pi$
$89$		−	11.9814i		−	1.27003i	0.772501	−	0.635014i	$-0.219005\pi$
$90$	0.636134	−	0.0785956i	0.0670544	−	0.00828470i
$91$	−7.48771	+	7.48771i	−0.784925	+	0.784925i
$92$	5.45011	−	1.36762i	0.568213	−	0.142584i
$93$	−4.42058	−	4.42058i	−0.458393	−	0.458393i
$94$	5.56985	−	7.14020i	0.574486	−	0.736455i
$95$	−1.25763			−0.129030
$96$	7.50854	−	5.29995i	0.766337	−	0.540923i
$97$	−5.83142			−0.592091			−0.296046	−	0.955174i	$-0.595668\pi$
$97$	−5.83142			−0.592091			−0.296046	+	0.955174i	$0.595668\pi$
$98$	−3.15209	+	4.04078i	−0.318409	+	0.408181i
$99$	0.943152	+	0.943152i	0.0947903	+	0.0947903i
$100$	6.63113	−	1.66398i	0.663113	−	0.166398i
$101$	−8.79584	+	8.79584i	−0.875219	+	0.875219i	−0.993035	−	0.117816i	$-0.962411\pi$
$101$	−8.79584	+	8.79584i	−0.875219	+	0.875219i	0.117816	+	0.993035i	$0.462411\pi$
$102$	−13.6143	+	1.68208i	−1.34802	+	0.166551i
$103$		−	1.15666i		−	0.113969i	−0.998375	−	0.0569844i	$-0.981851\pi$
$103$		−	1.15666i		−	0.113969i	0.998375	−	0.0569844i	$-0.0181485\pi$
$104$	5.87597	+	15.2043i	0.576187	+	1.49090i
$105$			3.75439i			0.366391i
$106$	−1.06285	−	8.60247i	−0.103233	−	0.835546i
$107$	−9.01739	+	9.01739i	−0.871744	+	0.871744i	−0.992662	−	0.120918i	$-0.961416\pi$
$107$	−9.01739	+	9.01739i	−0.871744	+	0.871744i	0.120918	+	0.992662i	$0.461416\pi$
$108$	−9.36804	−	5.60963i	−0.901440	−	0.539787i
$109$	−2.21454	−	2.21454i	−0.212115	−	0.212115i	0.593050	−	0.805165i	$-0.297923\pi$
$109$	−2.21454	−	2.21454i	−0.212115	−	0.212115i	−0.805165	+	0.593050i	$0.797923\pi$
$110$	−5.19020	−	4.04872i	−0.494866	−	0.386030i
$111$	−2.31322			−0.219561
$112$	−3.47013	−	6.47902i	−0.327896	−	0.612210i
$113$	−4.54889			−0.427924			−0.213962	−	0.976842i	$-0.568637\pi$
$113$	−4.54889			−0.427924			−0.213962	+	0.976842i	$0.568637\pi$
$114$	1.81165	+	1.41321i	0.169676	+	0.132359i
$115$	2.49847	+	2.49847i	0.232984	+	0.232984i
$116$	−7.89418	+	13.1832i	−0.732956	+	1.22403i
$117$	1.46860	−	1.46860i	0.135772	−	0.135772i
$118$	1.60312	+	12.9753i	0.147579	+	1.19447i
$119$			10.9702i			1.00564i
$120$	5.28489	+	2.33864i	0.482443	+	0.213488i
$121$		−	2.69791i		−	0.245265i
$122$	−2.28171	+	0.281909i	−0.206576	+	0.0255229i
$123$	13.7887	−	13.7887i	1.24328	−	1.24328i
$124$	1.87307	+	7.46438i	0.168207	+	0.670321i
$125$	7.48628	+	7.48628i	0.669594	+	0.669594i
$126$	−0.575998	+	0.738394i	−0.0513140	+	0.0657814i
$127$	5.60421			0.497293			0.248647	−	0.968594i	$-0.420014\pi$
$127$	5.60421			0.497293			0.248647	+	0.968594i	$0.420014\pi$
$128$	−11.2818	+	0.848916i	−0.997181	+	0.0750343i
$129$	0.873941			0.0769462
$130$	−6.30433	+	8.08176i	−0.552926	+	0.708817i
$131$	3.99576	+	3.99576i	0.349111	+	0.349111i	0.859779	−	0.510667i	$-0.170602\pi$
$131$	3.99576	+	3.99576i	0.349111	+	0.349111i	−0.510667	+	0.859779i	$0.670602\pi$
$132$	2.92703	+	11.6645i	0.254765	+	1.01527i
$133$	1.29927	−	1.29927i	0.112661	−	0.112661i
$134$	−14.5591	+	1.79881i	−1.25772	+	0.155393i
$135$		−	6.86615i		−	0.590944i
$136$	15.4424	+	6.83346i	1.32417	+	0.585964i
$137$		−	6.91563i		−	0.590842i	−0.955367	−	0.295421i	$-0.904540\pi$
$137$		−	6.91563i		−	0.590842i	0.955367	−	0.295421i	$-0.0954599\pi$
$138$	−0.791554	−	6.40665i	−0.0673816	−	0.545370i
$139$	0.660054	−	0.660054i	0.0559850	−	0.0559850i	−0.678560	−	0.734545i	$-0.737396\pi$
$139$	0.660054	−	0.660054i	0.0559850	−	0.0559850i	0.734545	+	0.678560i	$0.237396\pi$
$140$	2.37434	−	3.96514i	0.200669	−	0.335115i
$141$	−7.35634	−	7.35634i	−0.619516	−	0.619516i
$142$	11.8678	+	9.25771i	0.995924	+	0.776889i
$143$	−21.3293			−1.78364
$144$	0.680612	+	1.27076i	0.0567177	+	0.105897i
$145$	−9.66242			−0.802420
$146$	17.3498	+	13.5341i	1.43588	+	1.12009i
$147$	4.16310	+	4.16310i	0.343367	+	0.343367i
$148$	2.44307	+	1.46292i	0.200819	+	0.120251i
$149$	−0.435963	+	0.435963i	−0.0357155	+	0.0357155i	−0.724739	−	0.689024i	$-0.758040\pi$
$149$	−0.435963	+	0.435963i	−0.0357155	+	0.0357155i	0.689024	+	0.724739i	$0.258040\pi$
$150$	−0.963081	−	7.79495i	−0.0786353	−	0.636455i
$151$		−	7.71210i		−	0.627602i	−0.949489	−	0.313801i	$-0.898398\pi$
$151$		−	7.71210i		−	0.627602i	0.949489	−	0.313801i	$-0.101602\pi$
$152$	−1.01960	−	2.63826i	−0.0827008	−	0.213991i
$153$		−	2.15164i		−	0.173950i
$154$	9.54482	−	1.17928i	0.769143	−	0.0950292i
$155$	−3.42186	+	3.42186i	−0.274851	+	0.274851i
$156$	18.1630	−	4.55773i	1.45421	−	0.364911i
$157$	8.34341	+	8.34341i	0.665876	+	0.665876i	0.956759	−	0.290882i	$-0.0939488\pi$
$157$	8.34341	+	8.34341i	0.665876	+	0.665876i	−0.290882	+	0.956759i	$0.593949\pi$
$158$	−4.92937	+	6.31915i	−0.392160	+	0.502724i
$159$	−9.95791			−0.789713
$160$	−4.10256	−	5.81218i	−0.324336	−	0.459493i
$161$	−5.16239			−0.406853
$162$	−6.77510	+	8.68526i	−0.532302	+	0.682379i
$163$	4.28917	+	4.28917i	0.335954	+	0.335954i	0.854842	−	0.518888i	$-0.173654\pi$
$163$	4.28917	+	4.28917i	0.335954	+	0.335954i	−0.518888	+	0.854842i	$0.673654\pi$
$164$	−23.2829	+	5.84248i	−1.81809	+	0.456221i
$165$	−5.34732	+	5.34732i	−0.416288	+	0.416288i
$166$	9.28920	−	1.14770i	0.720982	−	0.0890787i
$167$		−	9.33332i		−	0.722234i	−0.932521	−	0.361117i	$-0.882396\pi$
$167$		−	9.33332i		−	0.722234i	0.932521	−	0.361117i	$-0.117604\pi$
$168$	−7.87595	+	3.04380i	−0.607642	+	0.234835i
$169$			20.2122i			1.55478i
$170$	1.30206	+	10.5385i	0.0998632	+	0.808269i
$171$	−0.254832	+	0.254832i	−0.0194875	+	0.0194875i
$172$	−0.923000	−	0.552697i	−0.0703781	−	0.0421427i
$173$	3.71665	+	3.71665i	0.282572	+	0.282572i	0.834134	−	0.551562i	$-0.185968\pi$
$173$	3.71665	+	3.71665i	0.282572	+	0.282572i	−0.551562	+	0.834134i	$0.685968\pi$
$174$	13.9189	+	10.8577i	1.05519	+	0.823122i
$175$	−6.28106			−0.474804
$176$	4.28552	−	14.1704i	0.323033	−	1.06814i
$177$	15.0197			1.12895
$178$	13.3602	+	10.4218i	1.00139	+	0.781150i
$179$	3.76375	+	3.76375i	0.281316	+	0.281316i	0.833634	−	0.552318i	$-0.186257\pi$
$179$	3.76375	+	3.76375i	0.281316	+	0.281316i	−0.552318	+	0.833634i	$0.686257\pi$
$180$	−0.465691	+	0.777701i	−0.0347106	+	0.0579664i
$181$	−14.0843	+	14.0843i	−1.04687	+	1.04687i	−0.0480283	+	0.998846i	$0.515294\pi$
$181$	−14.0843	+	14.0843i	−1.04687	+	1.04687i	−0.998846	+	0.0480283i	$0.984706\pi$
$182$	−1.83628	−	14.8624i	−0.136114	−	1.10167i
$183$			2.64122i			0.195245i
$184$	−3.21569	+	7.26688i	−0.237064	+	0.535721i
$185$			1.79061i			0.131648i
$186$	8.77444	−	1.08410i	0.643373	−	0.0794900i
$187$	−15.6248	+	15.6248i	−1.14260	+	1.14260i
$188$	3.11700	+	12.4216i	0.227331	+	0.905937i
$189$	7.09349	+	7.09349i	0.515975	+	0.515975i
$190$	1.09393	−	1.40235i	0.0793621	−	0.101737i
$191$	−23.0870			−1.67052			−0.835258	−	0.549858i	$-0.814682\pi$
$191$	−23.0870			−1.67052			−0.835258	+	0.549858i	$0.814682\pi$
$192$	−0.621357	+	12.9826i	−0.0448426	+	0.936942i
$193$	−21.9915			−1.58298			−0.791490	−	0.611182i	$-0.790695\pi$
$193$	−21.9915			−1.58298			−0.791490	+	0.611182i	$0.790695\pi$
$194$	5.07237	−	6.50246i	0.364175	−	0.466850i
$195$	8.32640	+	8.32640i	0.596266	+	0.596266i
$196$	−1.76397	−	7.02962i	−0.125998	−	0.502116i
$197$	9.39087	−	9.39087i	0.669072	−	0.669072i	−0.288429	−	0.957501i	$-0.593133\pi$
$197$	9.39087	−	9.39087i	0.669072	−	0.669072i	0.957501	+	0.288429i	$0.0931331\pi$
$198$	−1.87207	+	0.231298i	−0.133042	+	0.0164376i
$199$		−	22.4936i		−	1.59453i	−0.603632	−	0.797263i	$-0.706280\pi$
$199$		−	22.4936i		−	1.59453i	0.603632	−	0.797263i	$-0.293720\pi$
$200$	−3.91253	+	8.84159i	−0.276657	+	0.625195i
$201$			16.8531i			1.18873i
$202$	−2.15709	−	17.4589i	−0.151772	−	1.22841i
$203$	9.98234	−	9.98234i	0.700623	−	0.700623i
$204$	9.96658	−	16.6441i	0.697800	−	1.16532i
$205$	−10.6735	−	10.6735i	−0.745468	−	0.745468i
$206$	1.28976	+	1.00610i	0.0898616	+	0.0700983i
$207$	1.01252			0.0703752
$208$	−22.0650	−	6.67306i	−1.52993	−	0.462694i
$209$	3.70107			0.256008
$210$	−4.18642	−	3.26569i	−0.288890	−	0.225354i
$211$	−9.55567	−	9.55567i	−0.657839	−	0.657839i	0.297029	−	0.954868i	$-0.404004\pi$
$211$	−9.55567	−	9.55567i	−0.657839	−	0.657839i	−0.954868	+	0.297029i	$0.904004\pi$
$212$	10.5169	+	6.29756i	0.722303	+	0.432518i
$213$	12.2271	−	12.2271i	0.837784	−	0.837784i
$214$	−2.21142	−	17.8987i	−0.151169	−	1.22353i
$215$		−	0.676497i		−	0.0461367i
$216$	14.4038	−	5.56661i	0.980054	−	0.378760i
$217$		−	7.07032i		−	0.479965i
$218$	4.39566	−	0.543093i	0.297712	−	0.0367829i
$219$	17.8750	−	17.8750i	1.20788	−	1.20788i
$220$	9.02923	−	2.26575i	0.608751	−	0.152757i
$221$	24.3296	+	24.3296i	1.63659	+	1.63659i
$222$	2.01211	−	2.57941i	0.135044	−	0.173118i
$223$	−11.6663			−0.781236			−0.390618	−	0.920553i	$-0.627739\pi$
$223$	−11.6663			−0.781236			−0.390618	+	0.920553i	$0.627739\pi$
$224$	10.2430	+	1.76623i	0.684390	+	0.118011i
$225$	1.23193			0.0821289
$226$	3.95678	−	5.07235i	0.263201	−	0.337408i
$227$	−14.5685	−	14.5685i	−0.966944	−	0.966944i	0.0325271	−	0.999471i	$-0.489644\pi$
$227$	−14.5685	−	14.5685i	−0.966944	−	0.966944i	−0.999471	+	0.0325271i	$0.989644\pi$
$228$	−3.15166	+	0.790861i	−0.208724	+	0.0523761i
$229$	−11.7448	+	11.7448i	−0.776121	+	0.776121i	−0.979169	−	0.203048i	$-0.934915\pi$
$229$	−11.7448	+	11.7448i	−0.776121	+	0.776121i	0.203048	+	0.979169i	$0.434915\pi$
$230$	−4.95923	+	0.612723i	−0.327002	+	0.0404018i
$231$		−	11.0487i		−	0.726953i
$232$	−7.83364	−	20.2698i	−0.514304	−	1.33078i
$233$			8.17524i			0.535578i	0.963478	+	0.267789i	$0.0862930\pi$
$233$			8.17524i			0.535578i	−0.963478	+	0.267789i	$0.913707\pi$
$234$	0.360158	+	2.91503i	0.0235443	+	0.190562i
$235$	−5.69437	+	5.69437i	−0.371460	+	0.371460i
$236$	−15.8628	−	9.49873i	−1.03258	−	0.618315i
$237$	6.51044	+	6.51044i	0.422898	+	0.422898i
$238$	−12.2326	−	9.54230i	−0.792924	−	0.618535i
$239$	9.93904			0.642903			0.321452	−	0.946926i	$-0.395829\pi$
$239$	9.93904			0.642903			0.321452	+	0.946926i	$0.395829\pi$
$240$	−7.20473	+	3.85882i	−0.465064	+	0.249085i
$241$	15.2260			0.980792			0.490396	−	0.871500i	$-0.336852\pi$
$241$	15.2260			0.980792			0.490396	+	0.871500i	$0.336852\pi$
$242$	3.00837	+	2.34673i	0.193385	+	0.150854i
$243$	−2.63335	−	2.63335i	−0.168929	−	0.168929i
$244$	1.67036	−	2.78948i	0.106934	−	0.178578i
$245$	3.22256	−	3.22256i	0.205882	−	0.205882i
$246$	3.38152	+	27.3692i	0.215598	+	1.74500i
$247$		−	5.76300i		−	0.366691i
$248$	−9.95260	−	4.40416i	−0.631991	−	0.279665i
$249$		−	10.7528i		−	0.681433i
$250$	−14.8596	+	1.83593i	−0.939802	+	0.116114i
$251$	18.0939	−	18.0939i	1.14208	−	1.14208i	0.154009	−	0.988069i	$-0.450781\pi$
$251$	18.0939	−	18.0939i	1.14208	−	1.14208i	0.988069	−	0.154009i	$-0.0492186\pi$
$252$	−0.322341	−	1.28456i	−0.0203055	−	0.0809197i
$253$	−7.35271	−	7.35271i	−0.462261	−	0.462261i
$254$	−4.87473	+	6.24910i	−0.305868	+	0.392104i
$255$	12.1990			0.763932
$256$	8.86670	−	13.3185i	0.554169	−	0.832404i
$257$	4.79028			0.298809			0.149405	−	0.988776i	$-0.452264\pi$
$257$	4.79028			0.298809			0.149405	+	0.988776i	$0.452264\pi$
$258$	−0.760184	+	0.974508i	−0.0473270	+	0.0606702i
$259$	−1.84989	−	1.84989i	−0.114947	−	0.114947i
$260$	−3.52803	−	14.0596i	−0.218799	−	0.871938i
$261$	−1.95788	+	1.95788i	−0.121190	+	0.121190i
$262$	−7.93122	+	0.979918i	−0.489992	+	0.0605395i
$263$			3.81672i			0.235349i	0.993052	+	0.117674i	$0.0375439\pi$
$263$			3.81672i			0.235349i	−0.993052	+	0.117674i	$0.962456\pi$
$264$	−15.5528	−	6.88235i	−0.957211	−	0.423579i
$265$			7.70818i			0.473510i
$266$	0.318633	+	2.57894i	0.0195366	+	0.158125i
$267$	13.7646	−	13.7646i	0.842379	−	0.842379i
$268$	10.6582	−	17.7991i	0.651054	−	1.08726i
$269$	3.17581	+	3.17581i	0.193632	+	0.193632i	0.797264	−	0.603631i	$-0.206280\pi$
$269$	3.17581	+	3.17581i	0.193632	+	0.193632i	−0.603631	+	0.797264i	$0.706280\pi$
$270$	7.65626	+	5.97241i	0.465945	+	0.363469i
$271$	20.1526			1.22418			0.612092	−	0.790787i	$-0.290328\pi$
$271$	20.1526			1.22418			0.612092	+	0.790787i	$0.290328\pi$
$272$	−21.0521	+	11.2754i	−1.27647	+	0.683671i
$273$	−17.2042			−1.04124
$274$	7.71143	+	6.01545i	0.465865	+	0.363407i
$275$	−8.94602	−	8.94602i	−0.539466	−	0.539466i
$276$	7.83240	+	4.69008i	0.471455	+	0.282310i
$277$	2.14352	−	2.14352i	0.128792	−	0.128792i	−0.639772	−	0.768564i	$-0.720971\pi$
$277$	2.14352	−	2.14352i	0.128792	−	0.128792i	0.768564	+	0.639772i	$0.220971\pi$
$278$	0.161871	+	1.31015i	0.00970839	+	0.0785773i
$279$			1.38674i			0.0830217i
$280$	2.35614	+	6.09658i	0.140806	+	0.364340i
$281$			12.0266i			0.717446i	0.933444	+	0.358723i	$0.116788\pi$
$281$			12.0266i			0.717446i	−0.933444	+	0.358723i	$0.883212\pi$
$282$	14.6017	−	1.80406i	0.869516	−	0.107430i
$283$	−12.1219	+	12.1219i	−0.720574	+	0.720574i	−0.968722	−	0.248148i	$-0.920178\pi$
$283$	−12.1219	+	12.1219i	−0.720574	+	0.720574i	0.248148	+	0.968722i	$0.420178\pi$
$284$	−20.6460	+	5.18081i	−1.22512	+	0.307424i
$285$	−1.44480	−	1.44480i	−0.0855828	−	0.0855828i
$286$	18.5529	−	23.7837i	1.09706	−	1.40636i
$287$	22.0538			1.30179
$288$	−2.00901	−	0.346418i	−0.118382	−	0.0204129i
$289$	18.6453			1.09678
$290$	8.40470	−	10.7743i	0.493541	−	0.632689i
$291$	−6.69930	−	6.69930i	−0.392720	−	0.392720i
$292$	−30.1829	+	7.57394i	−1.76632	+	0.443231i
$293$	22.8111	−	22.8111i	1.33264	−	1.33264i	0.429633	−	0.903004i	$-0.358643\pi$
$293$	22.8111	−	22.8111i	1.33264	−	1.33264i	0.903004	−	0.429633i	$-0.141357\pi$
$294$	−8.26338	+	1.02096i	−0.481930	+	0.0595434i
$295$		−	11.6264i		−	0.676914i
$296$	−3.75633	+	1.45170i	−0.218332	+	0.0843785i
$297$			20.2063i			1.17249i
$298$	−0.106915	−	0.865346i	−0.00619343	−	0.0501281i
$299$	−11.4490	+	11.4490i	−0.662115	+	0.662115i
$300$	9.52966	+	5.70641i	0.550195	+	0.329459i
$301$	0.698896	+	0.698896i	0.0402837	+	0.0402837i
$302$	8.59955	+	6.70824i	0.494849	+	0.386016i
$303$	−20.2098			−1.16102
$304$	3.82874	+	1.15791i	0.219593	+	0.0664110i
$305$	2.04450			0.117068
$306$	2.39924	+	1.87157i	0.137156	+	0.106991i
$307$	15.1238	+	15.1238i	0.863163	+	0.863163i	0.991704	−	0.128541i	$-0.0410295\pi$
$307$	15.1238	+	15.1238i	0.863163	+	0.863163i	−0.128541	+	0.991704i	$0.541029\pi$
$308$	−6.98742	+	11.6690i	−0.398145	+	0.664900i
$309$	1.32880	−	1.32880i	0.0755928	−	0.0755928i
$310$	−0.839176	−	6.79208i	−0.0476620	−	0.385764i
$311$			30.0832i			1.70586i	0.522022	+	0.852932i	$0.325178\pi$
$311$			30.0832i			1.70586i	−0.522022	+	0.852932i	$0.674822\pi$
$312$	−10.7166	+	24.2176i	−0.606709	+	1.37105i
$313$			12.5575i			0.709792i	0.934906	+	0.354896i	$0.115484\pi$
$313$			12.5575i			0.709792i	−0.934906	+	0.354896i	$0.884516\pi$
$314$	−16.5609	+	2.04613i	−0.934585	+	0.115470i
$315$	0.588875	−	0.588875i	0.0331794	−	0.0331794i
$316$	−2.75858	−	10.9932i	−0.155182	−	0.618417i
$317$	18.4523	+	18.4523i	1.03639	+	1.03639i	0.999313	+	0.0370733i	$0.0118035\pi$
$317$	18.4523	+	18.4523i	1.03639	+	1.03639i	0.0370733	+	0.999313i	$0.488196\pi$
$318$	8.66173	−	11.1038i	0.485726	−	0.622670i
$319$	28.4354			1.59208
$320$	10.0496	+	0.480978i	0.561787	+	0.0268875i
$321$	−20.7189			−1.15641
$322$	4.49042	−	5.75644i	0.250241	−	0.320794i
$323$	−4.22169	−	4.22169i	−0.234901	−	0.234901i
$324$	−3.79149	−	15.1095i	−0.210638	−	0.839415i
$325$	−13.9300	+	13.9300i	−0.772698	+	0.772698i
$326$	−8.51361	+	1.05187i	−0.471525	+	0.0582579i
$327$		−	5.08826i		−	0.281381i
$328$	13.7375	−	31.0441i	0.758525	−	1.71413i
$329$		−	11.7658i		−	0.648670i
$330$	−1.31137	−	10.6139i	−0.0721887	−	0.584278i
$331$	−16.7338	+	16.7338i	−0.919771	+	0.919771i	−0.997012	−	0.0772413i	$-0.975389\pi$
$331$	−16.7338	+	16.7338i	−0.919771	+	0.919771i	0.0772413	+	0.997012i	$0.475389\pi$
$332$	−6.80029	+	11.3564i	−0.373215	+	0.623266i
$333$	0.362828	+	0.362828i	0.0198828	+	0.0198828i
$334$	10.4073	+	8.11844i	0.569464	+	0.444221i
$335$	13.0456			0.712756
$336$	3.45670	−	11.4299i	0.188579	−	0.623550i
$337$	27.8560			1.51741			0.758707	−	0.651432i	$-0.225832\pi$
$337$	27.8560			1.51741			0.758707	+	0.651432i	$0.225832\pi$
$338$	−22.5381	−	17.5812i	−1.22591	−	0.956293i
$339$	−5.22590	−	5.22590i	−0.283832	−	0.283832i
$340$	−12.8838	−	7.71489i	−0.698723	−	0.418399i
$341$	10.0702	−	10.0702i	0.545330	−	0.545330i
$342$	−0.0624949	−	0.505818i	−0.00337934	−	0.0273515i
$343$			19.5207i			1.05402i
$344$	1.41915	−	0.548458i	0.0765156	−	0.0295709i
$345$			5.74063i			0.309065i
$346$	−7.37720	+	0.911468i	−0.396601	+	0.0490008i
$347$	−4.91382	+	4.91382i	−0.263788	+	0.263788i	−0.826591	−	0.562803i	$-0.809723\pi$
$347$	−4.91382	+	4.91382i	−0.263788	+	0.263788i	0.562803	+	0.826591i	$0.309723\pi$
$348$	−24.2143	+	6.07621i	−1.29802	+	0.325719i
$349$	−16.7590	−	16.7590i	−0.897090	−	0.897090i	0.0980874	−	0.995178i	$-0.468728\pi$
$349$	−16.7590	−	16.7590i	−0.897090	−	0.897090i	−0.995178	+	0.0980874i	$0.968728\pi$
$350$	5.46348	−	7.00385i	0.292035	−	0.374371i
$351$	31.4636			1.67940
$352$	12.0734	+	17.1046i	0.643513	+	0.911678i
$353$	7.50139			0.399259			0.199629	−	0.979871i	$-0.436026\pi$
$353$	7.50139			0.399259			0.199629	+	0.979871i	$0.436026\pi$
$354$	−13.0646	+	16.7481i	−0.694378	+	0.890149i
$355$	−9.46468	−	9.46468i	−0.502333	−	0.502333i
$356$	−23.2422	+	5.83228i	−1.23184	+	0.309110i
$357$	−12.6029	+	12.6029i	−0.667018	+	0.667018i
$358$	−7.47069	+	0.923019i	−0.394838	+	0.0487830i
$359$			7.90936i			0.417440i	0.977975	+	0.208720i	$0.0669298\pi$
$359$			7.90936i			0.417440i	−0.977975	+	0.208720i	$0.933070\pi$
$360$	−0.462120	−	1.19575i	−0.0243558	−	0.0630216i
$361$			1.00000i			0.0526316i
$362$	−3.45401	−	27.9559i	−0.181539	−	1.46933i
$363$	3.09944	−	3.09944i	0.162678	−	0.162678i
$364$	18.1699	+	10.8802i	0.952363	+	0.570280i
$365$	−13.8366	−	13.8366i	−0.724243	−	0.724243i
$366$	−2.94515	−	2.29742i	−0.153946	−	0.120088i
$367$	−14.5659			−0.760336			−0.380168	−	0.924918i	$-0.624134\pi$
$367$	−14.5659			−0.760336			−0.380168	+	0.924918i	$0.624134\pi$
$368$	−5.30598	−	9.90671i	−0.276593	−	0.516423i
$369$	−4.32550			−0.225177
$370$	−1.99666	−	1.55753i	−0.103801	−	0.0809721i
$371$	−7.96339	−	7.96339i	−0.413439	−	0.413439i
$372$	−6.42346	+	10.7271i	−0.333041	+	0.556176i
$373$	−17.7684	+	17.7684i	−0.920014	+	0.920014i	−0.997030	−	0.0770156i	$-0.975461\pi$
$373$	−17.7684	+	17.7684i	−0.920014	+	0.920014i	0.0770156	+	0.997030i	$0.475461\pi$
$374$	−3.83180	−	31.0137i	−0.198138	−	1.60368i
$375$			17.2009i			0.888251i
$376$	−16.5622	−	7.32902i	−0.854132	−	0.377966i
$377$		−	44.2773i		−	2.28040i
$378$	−14.0799	+	1.73960i	−0.724193	+	0.0894754i
$379$	14.0751	−	14.0751i	0.722990	−	0.722990i	−0.246224	−	0.969213i	$-0.579190\pi$
$379$	14.0751	−	14.0751i	0.722990	−	0.722990i	0.969213	+	0.246224i	$0.0791897\pi$
$380$	0.612187	+	2.43963i	0.0314045	+	0.125150i
$381$	6.43827	+	6.43827i	0.329843	+	0.329843i
$382$	20.0819	−	25.7437i	1.02748	−	1.31716i
$383$	−3.42765			−0.175145			−0.0875724	−	0.996158i	$-0.527911\pi$
$383$	−3.42765			−0.175145			−0.0875724	+	0.996158i	$0.527911\pi$
$384$	−13.9361	−	11.9856i	−0.711175	−	0.611638i
$385$	−8.55256			−0.435879
$386$	19.1289	−	24.5221i	0.973637	−	1.24814i
$387$	−0.137078	−	0.137078i	−0.00696805	−	0.00696805i
$388$	2.83860	+	11.3121i	0.144108	+	0.574286i
$389$	−14.9368	+	14.9368i	−0.757326	+	0.757326i	−0.975835	−	0.218509i	$-0.929881\pi$
$389$	−14.9368	+	14.9368i	−0.757326	+	0.757326i	0.218509	+	0.975835i	$0.429881\pi$
$390$	−16.5271	+	2.04196i	−0.836884	+	0.103399i
$391$			16.7740i			0.848298i
$392$	9.37291	+	4.14764i	0.473403	+	0.209488i
$393$			9.18089i			0.463115i
$394$	2.30301	+	18.6400i	0.116024	+	0.939070i
$395$	5.03957	−	5.03957i	0.253568	−	0.253568i
$396$	1.37048	−	2.28869i	0.0688690	−	0.115011i
$397$	9.90506	+	9.90506i	0.497121	+	0.497121i	0.910541	−	0.413420i	$-0.135666\pi$
$397$	9.90506	+	9.90506i	0.497121	+	0.497121i	−0.413420	+	0.910541i	$0.635666\pi$
$398$	25.0820	+	19.5657i	1.25725	+	0.980738i
$399$	2.98528			0.149451
$400$	−6.45577	−	12.0535i	−0.322788	−	0.602673i
$401$	3.80802			0.190163			0.0950816	−	0.995469i	$-0.469689\pi$
$401$	3.80802			0.190163			0.0950816	+	0.995469i	$0.469689\pi$
$402$	−18.7924	−	14.6594i	−0.937281	−	0.731144i
$403$	−15.6804	−	15.6804i	−0.781097	−	0.781097i
$404$	21.3443	+	12.7811i	1.06192	+	0.635882i
$405$	6.92657	−	6.92657i	0.344184	−	0.344184i
$406$	2.44806	+	19.8140i	0.121495	+	0.983353i
$407$		−	5.26955i		−	0.261202i
$408$	9.89014	+	25.5911i	0.489635	+	1.26695i
$409$		−	2.54878i		−	0.126029i	−0.998013	−	0.0630146i	$-0.979929\pi$
$409$		−	2.54878i		−	0.126029i	0.998013	−	0.0630146i	$-0.0200715\pi$
$410$	21.1859	−	2.61756i	1.04630	−	0.129272i
$411$	7.94487	−	7.94487i	0.391891	−	0.391891i
$412$	−2.24375	+	0.563034i	−0.110542	+	0.0277387i
$413$	12.0113	+	12.0113i	0.591039	+	0.591039i
$414$	−0.880727	+	1.12904i	−0.0432854	+	0.0554892i
$415$	−8.32351			−0.408585
$416$	26.6339	−	18.7997i	1.30583	−	0.921729i
$417$	1.51658			0.0742671
$418$	−3.21932	+	4.12696i	−0.157462	+	0.201856i
$419$	21.2347	+	21.2347i	1.03738	+	1.03738i	0.999274	+	0.0381075i	$0.0121329\pi$
$419$	21.2347	+	21.2347i	1.03738	+	1.03738i	0.0381075	+	0.999274i	$0.487867\pi$
$420$	7.28298	−	1.82755i	0.355373	−	0.0891753i
$421$	8.18291	−	8.18291i	0.398811	−	0.398811i	−0.479003	−	0.877813i	$-0.659002\pi$
$421$	8.18291	−	8.18291i	0.398811	−	0.398811i	0.877813	+	0.479003i	$0.159002\pi$
$422$	18.9671	−	2.34342i	0.923305	−	0.114076i
$423$			2.30768i			0.112203i
$424$	−16.1702	+	6.24927i	−0.785294	+	0.303491i
$425$			20.4089i			0.989976i
$426$	2.99856	+	24.2696i	0.145280	+	1.17587i
$427$	−2.11220	+	2.11220i	−0.102216	+	0.102216i
$428$	21.8819	+	13.1030i	1.05770	+	0.633357i
$429$	−24.5037	−	24.5037i	−1.18305	−	1.18305i
$430$	0.754344	+	0.588440i	0.0363777	+	0.0283771i
$431$	−38.9142			−1.87443			−0.937216	−	0.348750i	$-0.886606\pi$
$431$	−38.9142			−1.87443			−0.937216	+	0.348750i	$0.886606\pi$
$432$	−6.32173	+	20.9033i	−0.304154	+	1.00571i
$433$	−1.91787			−0.0921670			−0.0460835	−	0.998938i	$-0.514674\pi$
$433$	−1.91787			−0.0921670			−0.0460835	+	0.998938i	$0.514674\pi$
$434$	7.88393	+	6.15001i	0.378441	+	0.295210i
$435$	−11.1005	−	11.1005i	−0.532226	−	0.532226i
$436$	−3.21791	+	5.37389i	−0.154110	+	0.257363i
$437$	1.98665	−	1.98665i	0.0950342	−	0.0950342i
$438$	4.38366	+	35.4803i	0.209459	+	1.69531i
$439$		−	40.6764i		−	1.94138i	−0.240342	−	0.970688i	$-0.577260\pi$
$439$		−	40.6764i		−	1.94138i	0.240342	−	0.970688i	$-0.422740\pi$
$440$	−5.32746	+	12.0391i	−0.253977	+	0.573941i
$441$		−	1.30596i		−	0.0621888i
$442$	−48.2920	+	5.96657i	−2.29702	+	0.283801i
$443$	−11.7761	+	11.7761i	−0.559498	+	0.559498i	−0.929165	−	0.369666i	$-0.879472\pi$
$443$	−11.7761	+	11.7761i	−0.559498	+	0.559498i	0.369666	+	0.929165i	$0.379472\pi$
$444$	1.12602	+	4.48731i	0.0534386	+	0.212958i
$445$	−10.6548	−	10.6548i	−0.505088	−	0.505088i
$446$	10.1478	−	13.0088i	0.480512	−	0.615986i
$447$	−1.00169			−0.0473784
$448$	−10.8792	+	9.88539i	−0.513994	+	0.467041i
$449$	−14.9288			−0.704533			−0.352266	−	0.935900i	$-0.614589\pi$
$449$	−14.9288			−0.704533			−0.352266	+	0.935900i	$0.614589\pi$
$450$	−1.07158	+	1.37370i	−0.0505147	+	0.0647567i
$451$	31.4108	+	31.4108i	1.47908	+	1.47908i
$452$	2.21430	+	8.82421i	0.104152	+	0.415056i
$453$	8.85987	−	8.85987i	0.416273	−	0.416273i
$454$	28.9171	−	3.57276i	1.35715	−	0.167678i
$455$			13.3173i			0.624327i
$456$	1.85956	−	4.20226i	0.0870817	−	0.196789i
$457$			16.6871i			0.780591i	0.920690	+	0.390295i	$0.127627\pi$
$457$			16.6871i			0.780591i	−0.920690	+	0.390295i	$0.872373\pi$
$458$	−2.88030	−	23.3124i	−0.134587	−	1.08932i
$459$	23.0487	−	23.0487i	1.07582	−	1.07582i
$460$	3.63048	−	6.06288i	0.169272	−	0.282683i
$461$	−4.55203	−	4.55203i	−0.212009	−	0.212009i	0.593111	−	0.805120i	$-0.297899\pi$
$461$	−4.55203	−	4.55203i	−0.212009	−	0.212009i	−0.805120	+	0.593111i	$0.797899\pi$
$462$	12.3201	+	9.61057i	0.573185	+	0.447124i
$463$	21.7494			1.01078			0.505390	−	0.862891i	$-0.331349\pi$
$463$	21.7494			1.01078			0.505390	+	0.862891i	$0.331349\pi$
$464$	29.4163	+	8.89629i	1.36562	+	0.413000i
$465$	−7.86227			−0.364604
$466$	−9.11599	−	7.11110i	−0.422290	−	0.329415i
$467$	2.26332	+	2.26332i	0.104734	+	0.104734i	0.757532	−	0.652798i	$-0.226405\pi$
$467$	2.26332	+	2.26332i	0.104734	+	0.104734i	−0.652798	+	0.757532i	$0.726405\pi$
$468$	−3.56375	−	2.13399i	−0.164735	−	0.0986438i
$469$	−13.4775	+	13.4775i	−0.622334	+	0.622334i
$470$	−1.39648	−	11.3028i	−0.0644149	−	0.521359i
$471$			19.1703i			0.883320i
$472$	24.3898	−	9.42588i	1.12263	−	0.433861i
$473$			1.99085i			0.0915395i
$474$	−12.9226	+	1.59662i	−0.593555	+	0.0733350i
$475$	2.41715	−	2.41715i	0.110906	−	0.110906i
$476$	21.2807	−	5.34007i	0.975400	−	0.244762i
$477$	1.56190	+	1.56190i	0.0715143	+	0.0715143i
$478$	−8.64532	+	11.0828i	−0.395428	+	0.506914i
$479$	34.5195			1.57723			0.788617	−	0.614885i	$-0.210797\pi$
$479$	34.5195			1.57723			0.788617	+	0.614885i	$0.210797\pi$
$480$	1.96406	−	11.3903i	0.0896467	−	0.519895i
$481$	−8.20531			−0.374130
$482$	−13.2441	+	16.9781i	−0.603252	+	0.773331i
$483$	−5.93070	−	5.93070i	−0.269856	−	0.269856i
$484$	−5.23356	+	1.31328i	−0.237889	+	0.0596946i
$485$	−5.18577	+	5.18577i	−0.235474	+	0.235474i
$486$	5.22695	−	0.645800i	0.237099	−	0.0292941i
$487$			29.7644i			1.34876i	0.738386	+	0.674378i	$0.235588\pi$
$487$			29.7644i			1.34876i	−0.738386	+	0.674378i	$0.764412\pi$
$488$	1.65755	+	4.28896i	0.0750336	+	0.194152i
$489$			9.85505i			0.445661i
$490$	0.790298	+	6.39648i	0.0357020	+	0.288964i
$491$	−10.8611	+	10.8611i	−0.490155	+	0.490155i	−0.908355	−	0.418200i	$-0.862661\pi$
$491$	−10.8611	+	10.8611i	−0.490155	+	0.490155i	0.418200	+	0.908355i	$0.362661\pi$
$492$	−33.4601	−	20.0360i	−1.50850	−	0.903295i
$493$	−32.4353	−	32.4353i	−1.46081	−	1.46081i
$494$	6.42617	+	5.01285i	0.289127	+	0.225539i
$495$	1.67745			0.0753959
$496$	13.5681	−	7.26698i	0.609224	−	0.326297i
$497$	19.5561			0.877211
$498$	11.9902	+	9.35318i	0.537294	+	0.419126i
$499$	−17.3334	−	17.3334i	−0.775948	−	0.775948i	0.203191	−	0.979139i	$-0.434869\pi$
$499$	−17.3334	−	17.3334i	−0.775948	−	0.775948i	−0.979139	+	0.203191i	$0.934869\pi$
$500$	10.8782	−	18.1665i	0.486487	−	0.812430i
$501$	10.7224	−	10.7224i	0.479041	−	0.479041i
$502$	4.43734	+	35.9148i	0.198048	+	1.60296i
$503$		−	6.07230i		−	0.270750i	−0.990794	−	0.135375i	$-0.956776\pi$
$503$		−	6.07230i		−	0.270750i	0.990794	−	0.135375i	$-0.0432240\pi$
$504$	1.71276	+	0.757921i	0.0762925	+	0.0337605i
$505$			15.6439i			0.696146i
$506$	14.5945	−	1.80317i	0.648803	−	0.0801609i
$507$	−23.2203	+	23.2203i	−1.03125	+	1.03125i
$508$	−2.72800	−	10.8714i	−0.121035	−	0.482339i
$509$	21.8745	+	21.8745i	0.969570	+	0.969570i	0.999550	−	0.0299809i	$-0.00954465\pi$
$509$	21.8745	+	21.8745i	0.969570	+	0.969570i	−0.0299809	+	0.999550i	$0.509545\pi$
$510$	−10.6111	+	13.6028i	−0.469869	+	0.602342i
$511$	28.5895			1.26473
$512$	7.13851	+	21.4719i	0.315480	+	0.948932i
$513$	−5.45958			−0.241046
$514$	−4.16675	+	5.34151i	−0.183787	+	0.235604i
$515$	−1.02859	−	1.02859i	−0.0453252	−	0.0453252i
$516$	−0.425415	−	1.69532i	−0.0187278	−	0.0746324i
$517$	16.7579	−	16.7579i	0.737011	−	0.737011i
$518$	3.67187	−	0.453666i	0.161333	−	0.0199330i
$519$			8.53958i			0.374846i
$520$	18.7463	+	8.29548i	0.822078	+	0.363781i
$521$		−	30.0851i		−	1.31805i	−0.752120	−	0.659026i	$-0.770969\pi$
$521$		−	30.0851i		−	1.31805i	0.752120	−	0.659026i	$-0.229031\pi$
$522$	−0.480150	−	3.88622i	−0.0210156	−	0.170095i
$523$	2.68366	−	2.68366i	0.117348	−	0.117348i	−0.645994	−	0.763342i	$-0.723557\pi$
$523$	2.68366	−	2.68366i	0.117348	−	0.117348i	0.763342	+	0.645994i	$0.223557\pi$
$524$	5.80617	−	9.69626i	0.253644	−	0.423583i
$525$	−7.21586	−	7.21586i	−0.314926	−	0.314926i
$526$	−4.25592	−	3.31991i	−0.185567	−	0.144755i
$527$	−22.9734			−1.00074
$528$	21.2027	−	11.3561i	0.922730	−	0.494209i
$529$	15.1065			0.656803
$530$	−8.59518	−	6.70484i	−0.373351	−	0.291239i
$531$	−2.35584	−	2.35584i	−0.102235	−	0.102235i
$532$	−3.15286	−	1.88795i	−0.136694	−	0.0818529i
$533$	48.9104	−	48.9104i	2.11854	−	2.11854i
$534$	3.37562	+	27.3214i	0.146077	+	1.18231i
$535$			16.0380i			0.693382i
$536$	10.5765	+	27.3670i	0.456834	+	1.18207i
$537$			8.64780i			0.373180i
$538$	−6.30369	+	0.778833i	−0.271771	+	0.0335779i
$539$	−9.48362	+	9.48362i	−0.408489	+	0.408489i
$540$	−13.3194	+	3.34228i	−0.573174	+	0.143829i
$541$	−10.1312	−	10.1312i	−0.435575	−	0.435575i	0.454944	−	0.890520i	$-0.349659\pi$
$541$	−10.1312	−	10.1312i	−0.435575	−	0.435575i	−0.890520	+	0.454944i	$0.849659\pi$
$542$	−17.5294	+	22.4716i	−0.752954	+	0.965240i
$543$	−32.3608			−1.38873
$544$	5.73895	−	33.2823i	0.246055	−	1.42697i
$545$	−3.93870			−0.168715
$546$	14.9648	−	19.1839i	0.640434	−	0.820996i
$547$	−21.1554	−	21.1554i	−0.904541	−	0.904541i	0.0912842	−	0.995825i	$-0.470903\pi$
$547$	−21.1554	−	21.1554i	−0.904541	−	0.904541i	−0.995825	+	0.0912842i	$0.970903\pi$
$548$	−13.4153	+	3.36637i	−0.573075	+	0.143804i
$549$	0.414275	−	0.414275i	0.0176808	−	0.0176808i
$550$	17.7570	−	2.19392i	0.757162	−	0.0935489i
$551$			7.68302i			0.327308i
$552$	−12.0427	+	4.65411i	−0.512570	+	0.198092i
$553$			10.4129i			0.442800i
$554$	0.525676	+	4.25470i	0.0223338	+	0.180765i
$555$	−2.05710	+	2.05710i	−0.0873190	+	0.0873190i
$556$	−1.60171	−	0.959111i	−0.0679276	−	0.0406754i
$557$	−5.83794	−	5.83794i	−0.247361	−	0.247361i	0.572525	−	0.819887i	$-0.305964\pi$
$557$	−5.83794	−	5.83794i	−0.247361	−	0.247361i	−0.819887	+	0.572525i	$0.805964\pi$
$558$	−1.54631	−	1.20623i	−0.0654606	−	0.0510638i
$559$	3.09999			0.131116
$560$	−8.84758	−	2.67575i	−0.373879	−	0.113071i
$561$	−35.9003			−1.51571
$562$	−13.4105	−	10.4611i	−0.565689	−	0.441276i
$563$	−17.0590	−	17.0590i	−0.718950	−	0.718950i	0.249440	−	0.968390i	$-0.419754\pi$
$563$	−17.0590	−	17.0590i	−0.718950	−	0.718950i	−0.968390	+	0.249440i	$0.919754\pi$
$564$	−10.6894	+	17.8512i	−0.450103	+	0.751669i
$565$	−4.04524	+	4.04524i	−0.170185	+	0.170185i
$566$	−2.97277	−	24.0609i	−0.124955	−	1.01136i
$567$			14.3118i			0.601040i
$568$	12.1817	−	27.5283i	0.511131	−	1.15506i
$569$			37.8084i			1.58501i	0.609865	+	0.792505i	$0.291224\pi$
$569$			37.8084i			1.58501i	−0.609865	+	0.792505i	$0.708776\pi$
$570$	2.86780	−	0.354323i	0.120119	−	0.0148409i
$571$	−24.4405	+	24.4405i	−1.02280	+	1.02280i	−0.0230698	+	0.999734i	$0.507344\pi$
$571$	−24.4405	+	24.4405i	−1.02280	+	1.02280i	−0.999734	+	0.0230698i	$0.992656\pi$
$572$	10.3826	+	41.3757i	0.434118	+	1.73001i
$573$	−26.5230	−	26.5230i	−1.10801	−	1.10801i
$574$	−19.1831	+	24.5916i	−0.800687	+	1.02643i
$575$	−9.60403			−0.400516
$576$	2.13379	−	1.93887i	0.0889078	−	0.0807861i
$577$	−12.2125			−0.508414			−0.254207	−	0.967150i	$-0.581814\pi$
$577$	−12.2125			−0.508414			−0.254207	+	0.967150i	$0.581814\pi$
$578$	−16.2183	+	20.7909i	−0.674593	+	0.864787i
$579$	−25.2644	−	25.2644i	−1.04995	−	1.04995i
$580$	4.70345	+	18.7437i	0.195300	+	0.778291i
$581$	8.59910	−	8.59910i	0.356751	−	0.356751i
$582$	13.2975	−	1.64293i	0.551199	−	0.0681017i
$583$		−	22.6843i		−	0.939487i
$584$	17.8087	−	40.2443i	0.736927	−	1.66532i
$585$		−	2.61199i		−	0.107993i
$586$	5.59417	+	45.2779i	0.231093	+	1.87041i
$587$	−23.4814	+	23.4814i	−0.969179	+	0.969179i	−0.999539	−	0.0303599i	$-0.990335\pi$
$587$	−23.4814	+	23.4814i	−0.969179	+	0.969179i	0.0303599	+	0.999539i	$0.490335\pi$
$588$	6.04932	−	10.1023i	0.249470	−	0.416613i
$589$	2.72088	+	2.72088i	0.112112	+	0.112112i
$590$	12.9643	+	10.1130i	0.533730	+	0.416347i
$591$	21.5770			0.887559
$592$	1.64863	−	5.45132i	0.0677582	−	0.224048i
$593$	5.79824			0.238105			0.119053	−	0.992888i	$-0.462014\pi$
$593$	5.79824			0.238105			0.119053	+	0.992888i	$0.462014\pi$
$594$	−22.5315	−	17.5761i	−0.924479	−	0.721157i
$595$	9.75563	+	9.75563i	0.399942	+	0.399942i
$596$	1.05792	+	0.633489i	0.0433342	+	0.0259487i
$597$	25.8412	−	25.8412i	1.05761	−	1.05761i
$598$	−2.80775	−	22.7253i	−0.114818	−	0.929306i
$599$		−	39.0424i		−	1.59523i	−0.603168	−	0.797614i	$-0.706095\pi$
$599$		−	39.0424i		−	1.59523i	0.603168	−	0.797614i	$-0.293905\pi$
$600$	−14.6523	+	5.66264i	−0.598177	+	0.231176i
$601$		−	15.4986i		−	0.632200i	−0.948726	−	0.316100i	$-0.897627\pi$
$601$		−	15.4986i		−	0.632200i	0.948726	−	0.316100i	$-0.102373\pi$
$602$	−1.38724	+	0.171397i	−0.0565398	+	0.00698561i
$603$	2.64341	−	2.64341i	0.107648	−	0.107648i
$604$	−14.9604	+	3.75407i	−0.608729	+	0.152751i
$605$	−2.39920	−	2.39920i	−0.0975413	−	0.0975413i
$606$	17.5792	−	22.5354i	0.714106	−	0.915440i
$607$	13.5738			0.550942			0.275471	−	0.961309i	$-0.411166\pi$
$607$	13.5738			0.550942			0.275471	+	0.961309i	$0.411166\pi$
$608$	−4.62153	+	3.26213i	−0.187428	+	0.132297i
$609$	22.9360			0.929413
$610$	−1.77838	+	2.27977i	−0.0720045	+	0.0923053i
$611$	−26.0940	−	26.0940i	−1.05565	−	1.05565i
$612$	−4.17389	+	1.04737i	−0.168719	+	0.0423375i
$613$	−21.2191	+	21.2191i	−0.857031	+	0.857031i	−0.990987	−	0.133956i	$-0.957232\pi$
$613$	−21.2191	+	21.2191i	−0.857031	+	0.857031i	0.133956	+	0.990987i	$0.457232\pi$
$614$	−30.0194	+	3.70896i	−1.21148	+	0.149681i
$615$		−	24.5240i		−	0.988903i
$616$	−6.93384	−	17.9415i	−0.279372	−	0.722885i
$617$		−	6.67989i		−	0.268922i	−0.990919	−	0.134461i	$-0.957070\pi$
$617$		−	6.67989i		−	0.268922i	0.990919	−	0.134461i	$-0.0429304\pi$
$618$	0.325874	+	2.63754i	0.0131086	+	0.106098i
$619$	20.7743	−	20.7743i	0.834990	−	0.834990i	−0.153205	−	0.988195i	$-0.548959\pi$
$619$	20.7743	−	20.7743i	0.834990	−	0.834990i	0.988195	+	0.153205i	$0.0489593\pi$
$620$	8.30362	+	4.97224i	0.333481	+	0.199690i
$621$	10.8463	+	10.8463i	0.435245	+	0.435245i
$622$	−33.5450	−	26.1674i	−1.34503	−	1.04922i
$623$	22.0152			0.882022
$624$	−17.6827	−	33.0151i	−0.707875	−	1.32166i
$625$	−3.77699			−0.151080
$626$	−14.0025	−	10.9229i	−0.559654	−	0.436569i
$627$	4.25189	+	4.25189i	0.169804	+	0.169804i
$628$	12.1236	−	20.2464i	0.483786	−	0.807919i
$629$	−6.01080	+	6.01080i	−0.239666	+	0.239666i
$630$	0.144415	+	1.16886i	0.00575365	+	0.0465686i
$631$		−	11.3198i		−	0.450634i	−0.974286	−	0.225317i	$-0.927658\pi$
$631$		−	11.3198i		−	0.450634i	0.974286	−	0.225317i	$-0.0723417\pi$
$632$	14.6578	+	6.48626i	0.583054	+	0.258010i
$633$		−	21.9556i		−	0.872658i
$634$	−36.6262	+	4.52523i	−1.45461	+	0.179720i
$635$	4.98371	−	4.98371i	0.197773	−	0.197773i
$636$	4.84728	+	19.3169i	0.192207	+	0.765966i
$637$	14.7671	+	14.7671i	0.585094	+	0.585094i
$638$	−24.7341	+	31.7076i	−0.979232	+	1.25531i
$639$	−3.83563			−0.151735
$640$	−9.27777	+	10.7876i	−0.366736	+	0.426418i
$641$	−6.57068			−0.259526			−0.129763	−	0.991545i	$-0.541422\pi$
$641$	−6.57068			−0.259526			−0.129763	+	0.991545i	$0.541422\pi$
$642$	18.0220	−	23.1031i	0.711271	−	0.911805i
$643$	24.1325	+	24.1325i	0.951692	+	0.951692i	0.998886	−	0.0471940i	$-0.0150279\pi$
$643$	24.1325	+	24.1325i	0.951692	+	0.951692i	−0.0471940	+	0.998886i	$0.515028\pi$
$644$	2.51293	+	10.0143i	0.0990235	+	0.394619i
$645$	0.777179	−	0.777179i	0.0306014	−	0.0306014i
$646$	8.37966	−	1.03532i	0.329693	−	0.0407343i
$647$			5.97038i			0.234720i	0.993089	+	0.117360i	$0.0374431\pi$
$647$			5.97038i			0.234720i	−0.993089	+	0.117360i	$0.962557\pi$
$648$	20.1461	+	8.91495i	0.791415	+	0.350212i
$649$			34.2151i			1.34306i
$650$	−3.41619	−	27.6498i	−0.133994	−	1.08451i
$651$	8.12259	−	8.12259i	0.318349	−	0.318349i
$652$	6.23251	−	10.4083i	0.244084	−	0.407619i
$653$	3.74090	+	3.74090i	0.146393	+	0.146393i	0.776505	−	0.630112i	$-0.216991\pi$
$653$	3.74090	+	3.74090i	0.146393	+	0.146393i	−0.630112	+	0.776505i	$0.716991\pi$
$654$	5.67378	+	4.42594i	0.221862	+	0.173068i
$655$	7.10671			0.277682
$656$	22.6672	+	42.3215i	0.885004	+	1.65238i
$657$	−5.60739			−0.218765
$658$	13.1197	+	10.2343i	0.511461	+	0.398975i
$659$	12.1075	+	12.1075i	0.471642	+	0.471642i	0.902446	−	0.430803i	$-0.141770\pi$
$659$	12.1075	+	12.1075i	0.471642	+	0.471642i	−0.430803	+	0.902446i	$0.641770\pi$
$660$	12.9760	+	7.77008i	0.505090	+	0.302450i
$661$	0.970211	−	0.970211i	0.0377368	−	0.0377368i	−0.687987	−	0.725723i	$-0.741505\pi$
$661$	0.970211	−	0.970211i	0.0377368	−	0.0377368i	0.725723	+	0.687987i	$0.241505\pi$
$662$	−4.10378	−	33.2150i	−0.159498	−	1.29094i
$663$			55.9010i			2.17102i
$664$	−6.74814	−	17.4610i	−0.261879	−	0.677620i
$665$		−	2.31084i		−	0.0896103i
$666$	−0.720180	+	0.0889796i	−0.0279064	+	0.00344789i
$667$	15.2634	−	15.2634i	0.591003	−	0.591003i
$668$	−18.1053	+	4.54325i	−0.700515	+	0.175783i
$669$	−13.4026	−	13.4026i	−0.518176	−	0.518176i
$670$	−11.3475	+	14.5468i	−0.438392	+	0.561991i
$671$	−6.01674			−0.232274
$672$	9.73838	+	13.7966i	0.375666	+	0.532214i
$673$	−9.08670			−0.350267			−0.175133	−	0.984545i	$-0.556036\pi$
$673$	−9.08670			−0.350267			−0.175133	+	0.984545i	$0.556036\pi$
$674$	−24.2301	+	31.0615i	−0.933309	+	1.19644i
$675$	13.1966	+	13.1966i	0.507938	+	0.507938i
$676$	39.2087	−	9.83882i	1.50803	−	0.378416i
$677$	17.6088	−	17.6088i	0.676763	−	0.676763i	−0.282504	−	0.959266i	$-0.591165\pi$
$677$	17.6088	−	17.6088i	0.676763	−	0.676763i	0.959266	+	0.282504i	$0.0911649\pi$
$678$	10.3729	−	1.28160i	0.398370	−	0.0492194i
$679$		−	10.7149i		−	0.411202i
$680$	19.8094	−	7.65572i	0.759658	−	0.293584i
$681$		−	33.4734i		−	1.28270i
$682$	2.46960	+	19.9883i	0.0945658	+	0.765393i
$683$	10.8657	−	10.8657i	0.415766	−	0.415766i	−0.467975	−	0.883741i	$-0.655016\pi$
$683$	10.8657	−	10.8657i	0.415766	−	0.415766i	0.883741	+	0.467975i	$0.155016\pi$
$684$	0.618385	+	0.370292i	0.0236445	+	0.0141585i
$685$	−6.14993	−	6.14993i	−0.234977	−	0.234977i
$686$	−21.7670	−	16.9797i	−0.831066	−	0.648289i
$687$	−26.9856			−1.02957
$688$	−0.622857	+	2.05953i	−0.0237462	+	0.0785188i
$689$	−35.3221			−1.34566
$690$	−6.40122	−	4.99339i	−0.243690	−	0.190095i
$691$	5.09443	+	5.09443i	0.193801	+	0.193801i	0.797336	−	0.603535i	$-0.206242\pi$
$691$	5.09443	+	5.09443i	0.193801	+	0.193801i	−0.603535	+	0.797336i	$0.706242\pi$
$692$	5.40059	−	9.01895i	0.205300	−	0.342849i
$693$	−1.73299	+	1.73299i	−0.0658310	+	0.0658310i
$694$	−1.20506	−	9.75348i	−0.0457435	−	0.370237i
$695$		−	1.17395i		−	0.0445303i
$696$	14.2870	−	32.2860i	0.541548	−	1.22380i
$697$		−	71.6586i		−	2.71426i
$698$	33.2651	−	4.10997i	1.25910	−	0.155565i
$699$	−9.39195	+	9.39195i	−0.355236	+	0.355236i
$700$	3.05748	+	12.1844i	0.115562	+	0.460526i
$701$	17.8852	+	17.8852i	0.675516	+	0.675516i	0.958982	−	0.283466i	$-0.0914845\pi$
$701$	17.8852	+	17.8852i	0.675516	+	0.675516i	−0.283466	+	0.958982i	$0.591484\pi$
$702$	−27.3681	+	35.0842i	−1.03294	+	1.32417i
$703$	1.42379			0.0536993
$704$	−29.5747	−	1.41546i	−1.11464	−	0.0533473i
$705$	−13.0837			−0.492761
$706$	−6.52497	+	8.36460i	−0.245570	+	0.314806i
$707$	−16.1619	−	16.1619i	−0.607831	−	0.607831i
$708$	−7.31124	−	29.1361i	−0.274773	−	1.09500i
$709$	5.87695	−	5.87695i	0.220714	−	0.220714i	−0.588085	−	0.808799i	$-0.700118\pi$
$709$	5.87695	−	5.87695i	0.220714	−	0.220714i	0.808799	+	0.588085i	$0.200118\pi$
$710$	18.7865	−	2.32111i	0.705045	−	0.0871097i
$711$		−	2.04232i		−	0.0765931i
$712$	13.7135	−	30.9899i	0.513934	−	1.16140i
$713$		−	10.8108i		−	0.404869i
$714$	−3.09073	−	25.0157i	−0.115668	−	0.936187i
$715$	−18.9677	+	18.9677i	−0.709352	+	0.709352i
$716$	5.46903	−	9.13324i	0.204387	−	0.341325i
$717$	11.4183	+	11.4183i	0.426422	+	0.426422i
$718$	−8.81952	−	6.87983i	−0.329142	−	0.256753i
$719$	5.56041			0.207368			0.103684	−	0.994610i	$-0.466937\pi$
$719$	5.56041			0.207368			0.103684	+	0.994610i	$0.466937\pi$
$720$	1.73532	+	0.524807i	0.0646714	+	0.0195584i
$721$	2.12530			0.0791502
$722$	−1.11507	−	0.869834i	−0.0414987	−	0.0323719i
$723$	17.4920	+	17.4920i	0.650536	+	0.650536i
$724$	34.1773	+	20.4656i	1.27019	+	0.760596i
$725$	18.5710	−	18.5710i	0.689709	−	0.689709i
$726$	0.760104	+	6.15209i	0.0282101	+	0.228326i
$727$			36.9085i			1.36886i	0.729079	+	0.684430i	$0.239949\pi$
$727$			36.9085i			1.36886i	−0.729079	+	0.684430i	$0.760051\pi$
$728$	−27.9371	+	10.7968i	−1.03542	+	0.400156i
$729$		−	29.4174i		−	1.08953i
$730$	27.4644	−	3.39329i	1.01650	−	0.125591i
$731$	2.27090	−	2.27090i	0.0839923	−	0.0839923i
$732$	5.12359	−	1.28569i	0.189373	−	0.0475203i
$733$	−12.9609	−	12.9609i	−0.478723	−	0.478723i	0.426000	−	0.904723i	$-0.359922\pi$
$733$	−12.9609	−	12.9609i	−0.478723	−	0.478723i	−0.904723	+	0.426000i	$0.859922\pi$
$734$	12.6699	−	16.2421i	0.467656	−	0.599506i
$735$	7.40433			0.273113
$736$	15.6620	+	2.70064i	0.577310	+	0.0995469i
$737$	−38.3916			−1.41417
$738$	3.76247	−	4.82325i	0.138498	−	0.177546i
$739$	−16.2818	−	16.2818i	−0.598936	−	0.598936i	0.341094	−	0.940029i	$-0.389203\pi$
$739$	−16.2818	−	16.2818i	−0.598936	−	0.598936i	−0.940029	+	0.341094i	$0.889203\pi$
$740$	3.47352	−	0.871626i	0.127689	−	0.0320416i
$741$	6.62070	−	6.62070i	0.243217	−	0.243217i
$742$	15.8066	−	1.95294i	0.580279	−	0.0716946i
$743$			24.0773i			0.883309i	0.897185	+	0.441654i	$0.145608\pi$
$743$			24.0773i			0.883309i	−0.897185	+	0.441654i	$0.854392\pi$
$744$	−6.37420	−	16.4935i	−0.233689	−	0.604679i
$745$			0.775386i			0.0284080i
$746$	−4.35752	−	35.2687i	−0.159540	−	1.29128i
$747$	−1.68658	+	1.68658i	−0.0617088	+	0.0617088i
$748$	37.9156	+	22.7040i	1.38633	+	0.830142i
$749$	−16.5690	−	16.5690i	−0.605418	−	0.605418i
$750$	−19.1803	−	14.9619i	−0.700365	−	0.546333i
$751$	18.9950			0.693136			0.346568	−	0.938025i	$-0.387347\pi$
$751$	18.9950			0.693136			0.346568	+	0.938025i	$0.387347\pi$
$752$	22.5788	−	12.0931i	0.823364	−	0.440989i
$753$	41.5736			1.51503
$754$	49.3724	+	38.5139i	1.79804	+	1.40259i
$755$	−6.85822	−	6.85822i	−0.249596	−	0.249596i
$756$	10.3074	−	17.2133i	0.374877	−	0.626042i
$757$	21.0647	−	21.0647i	0.765608	−	0.765608i	−0.211722	−	0.977330i	$-0.567907\pi$
$757$	21.0647	−	21.0647i	0.765608	−	0.765608i	0.977330	+	0.211722i	$0.0679070\pi$
$758$	3.45177	+	27.9378i	0.125374	+	1.01475i
$759$		−	16.8940i		−	0.613214i
$760$	−3.25287	−	1.43944i	−0.117994	−	0.0522139i
$761$			35.7587i			1.29625i	0.761533	+	0.648126i	$0.224447\pi$
$761$			35.7587i			1.29625i	−0.761533	+	0.648126i	$0.775553\pi$
$762$	−12.7794	+	1.57892i	−0.462948	+	0.0571981i
$763$	4.06911	−	4.06911i	0.147312	−	0.147312i
$764$	11.2382	+	44.7855i	0.406585	+	1.62028i
$765$	−1.91342	−	1.91342i	−0.0691797	−	0.0691797i
$766$	2.98149	−	3.82208i	0.107725	−	0.138097i
$767$	53.2770			1.92372
$768$	25.4870	−	5.11431i	0.919681	−	0.184547i
$769$	−22.1800			−0.799833			−0.399917	−	0.916552i	$-0.630961\pi$
$769$	−22.1800			−0.799833			−0.399917	+	0.916552i	$0.630961\pi$
$770$	7.43931	−	9.53673i	0.268094	−	0.343680i
$771$	5.50321	+	5.50321i	0.198193	+	0.198193i
$772$	10.7049	+	42.6603i	0.385280	+	1.53538i
$773$	−10.5550	+	10.5550i	−0.379638	+	0.379638i	−0.870971	−	0.491334i	$-0.836510\pi$
$773$	−10.5550	+	10.5550i	−0.379638	+	0.379638i	0.491334	+	0.870971i	$0.336510\pi$
$774$	0.272086	−	0.0336168i	0.00977994	−	0.00120833i
$775$		−	13.1535i		−	0.472488i
$776$	−15.0830	−	6.67443i	−0.541447	−	0.239598i
$777$		−	4.25042i		−	0.152483i
$778$	−3.66309	−	29.6482i	−0.131328	−	1.06294i
$779$	−8.48696	+	8.48696i	−0.304077	+	0.304077i
$780$	12.0989	−	20.2051i	0.433211	−	0.723460i
$781$	27.8535	+	27.8535i	0.996675	+	0.996675i
$782$	−18.7042	−	14.5906i	−0.668862	−	0.521759i
$783$	−41.9461			−1.49903
$784$	−12.7778	+	6.84372i	−0.456350	+	0.244419i
$785$	14.8393			0.529636
$786$	−10.2374	−	7.98585i	−0.365155	−	0.284846i
$787$	−12.9665	−	12.9665i	−0.462204	−	0.462204i	0.437173	−	0.899377i	$-0.355980\pi$
$787$	−12.9665	−	12.9665i	−0.462204	−	0.462204i	−0.899377	+	0.437173i	$0.855980\pi$
$788$	−22.7882	−	13.6457i	−0.811796	−	0.486107i
$789$	−4.38475	+	4.38475i	−0.156101	+	0.156101i
$790$	1.23590	+	10.0031i	0.0439714	+	0.355894i
$791$		−	8.35836i		−	0.297189i
$792$	1.35997	+	3.51896i	0.0483243	+	0.125041i
$793$			9.36878i			0.332695i
$794$	−19.6606	+	2.42911i	−0.697730	+	0.0862059i
$795$	−8.85537	+	8.85537i	−0.314068	+	0.314068i
$796$	−43.6343	+	10.9494i	−1.54658	+	0.388090i
$797$	−0.991568	−	0.991568i	−0.0351231	−	0.0351231i	0.689327	−	0.724450i	$-0.257906\pi$
$797$	−0.991568	−	0.991568i	−0.0351231	−	0.0351231i	−0.724450	+	0.689327i	$0.757906\pi$
$798$	−2.59670	+	3.32881i	−0.0919222	+	0.117839i
$799$	−38.2303			−1.35249
$800$	19.0559	+	3.28586i	0.673730	+	0.116173i
$801$	−4.31795			−0.152567
$802$	−3.31234	+	4.24622i	−0.116963	+	0.149939i
$803$	40.7196	+	40.7196i	1.43696	+	1.43696i
$804$	32.6926	−	8.20370i	1.15298	−	0.289322i
$805$	−4.59081	+	4.59081i	−0.161805	+	0.161805i
$806$	31.1242	−	3.84545i	1.09630	−	0.135450i
$807$			7.29692i			0.256864i
$808$	−32.8178	+	12.6831i	−1.15453	+	0.446188i
$809$			44.2686i			1.55640i	0.628015	+	0.778201i	$0.283868\pi$
$809$			44.2686i			1.55640i	−0.628015	+	0.778201i	$0.716132\pi$
$810$	1.69867	+	13.7486i	0.0596851	+	0.483077i
$811$	−28.8169	+	28.8169i	−1.01190	+	1.01190i	−0.0119707	+	0.999928i	$0.503810\pi$
$811$	−28.8169	+	28.8169i	−1.01190	+	1.01190i	−0.999928	+	0.0119707i	$0.996190\pi$
$812$	−24.2235	−	14.5051i	−0.850078	−	0.509031i
$813$	23.1519	+	23.1519i	0.811972	+	0.811972i
$814$	5.87593	+	4.58363i	0.205951	+	0.160656i
$815$	7.62856			0.267217
$816$	−37.1387	−	11.2318i	−1.30012	−	0.393190i
$817$	−0.537913			−0.0188192
$818$	2.84208	+	2.21702i	0.0993710	+	0.0775162i
$819$	2.69847	+	2.69847i	0.0942923	+	0.0942923i
$820$	−15.5094	+	25.9006i	−0.541613	+	0.904489i
$821$	−4.51193	+	4.51193i	−0.157467	+	0.157467i	−0.781443	−	0.623976i	$-0.785516\pi$
$821$	−4.51193	+	4.51193i	−0.157467	+	0.157467i	0.623976	+	0.781443i	$0.285516\pi$
$822$	1.94839	+	15.7698i	0.0679580	+	0.550036i
$823$		−	23.2433i		−	0.810211i	−0.914270	−	0.405105i	$-0.867235\pi$
$823$		−	23.2433i		−	0.810211i	0.914270	−	0.405105i	$-0.132765\pi$
$824$	1.32387	−	2.99169i	0.0461190	−	0.104221i
$825$		−	20.5549i		−	0.715629i
$826$	−23.8414	+	2.94565i	−0.829548	+	0.102492i
$827$	29.5976	−	29.5976i	1.02921	−	1.02921i	0.0296475	−	0.999560i	$-0.490562\pi$
$827$	29.5976	−	29.5976i	1.02921	−	1.02921i	0.999560	−	0.0296475i	$-0.00943848\pi$
$828$	−0.492873	−	1.96415i	−0.0171285	−	0.0682590i
$829$	−34.2303	−	34.2303i	−1.18887	−	1.18887i	−0.977381	−	0.211487i	$-0.932169\pi$
$829$	−34.2303	−	34.2303i	−1.18887	−	1.18887i	−0.211487	−	0.977381i	$-0.567831\pi$
$830$	7.24008	−	9.28133i	0.251307	−	0.322160i
$831$	4.92508			0.170849
$832$	−2.20404	+	46.0513i	−0.0764114	+	1.59654i
$833$	21.6353			0.749619
$834$	−1.31917	+	1.69109i	−0.0456791	+	0.0585578i
$835$	−8.29994	−	8.29994i	−0.287231	−	0.287231i
$836$	−1.80160	−	7.17955i	−0.0623095	−	0.248310i
$837$	−14.8549	+	14.8549i	−0.513459	+	0.513459i
$838$	−42.1488	+	5.20757i	−1.45601	+	0.179893i
$839$			12.6385i			0.436331i	0.975912	+	0.218165i	$0.0700073\pi$
$839$			12.6385i			0.436331i	−0.975912	+	0.218165i	$0.929993\pi$
$840$	−4.29713	+	9.71072i	−0.148265	+	0.335052i
$841$			30.0288i			1.03548i
$842$	2.00677	+	16.2423i	0.0691579	+	0.559747i
$843$	−13.8165	+	13.8165i	−0.475865	+	0.475865i
$844$	−13.8852	+	23.1881i	−0.477947	+	0.798168i
$845$	17.9743	+	17.9743i	0.618334	+	0.618334i
$846$	−2.57324	−	2.00730i	−0.0884697	−	0.0690125i
$847$	4.95727			0.170334
$848$	7.09699	−	23.4668i	0.243712	−	0.805853i
$849$	−27.8520			−0.955879
$850$	−22.7574	−	17.7523i	−0.780572	−	0.608900i
$851$	−2.82857	−	2.82857i	−0.0969621	−	0.0969621i
$852$	−29.6706	−	17.7669i	−1.01650	−	0.608684i
$853$	23.9625	−	23.9625i	0.820462	−	0.820462i	−0.165713	−	0.986174i	$-0.552992\pi$
$853$	23.9625	−	23.9625i	0.820462	−	0.820462i	0.986174	+	0.165713i	$0.0529924\pi$
$854$	−0.517994	−	4.19252i	−0.0177254	−	0.143465i
$855$			0.453235i			0.0155003i
$856$	−33.6444	+	13.0025i	−1.14994	+	0.444417i
$857$		−	0.206291i		−	0.00704678i	−0.999994	−	0.00352339i	$-0.998878\pi$
$857$		−	0.206291i		−	0.00704678i	0.999994	−	0.00352339i	$-0.00112153\pi$
$858$	48.6375	−	6.00926i	1.66046	−	0.205153i
$859$	−6.86742	+	6.86742i	−0.234313	+	0.234313i	−0.814490	−	0.580177i	$-0.802983\pi$
$859$	−6.86742	+	6.86742i	−0.234313	+	0.234313i	0.580177	+	0.814490i	$0.302983\pi$
$860$	−1.31231	+	0.329303i	−0.0447493	+	0.0112291i
$861$	25.3360	+	25.3360i	0.863448	+	0.863448i
$862$	33.8489	−	43.3922i	1.15290	−	1.47794i
$863$	−47.3026			−1.61020			−0.805100	−	0.593140i	$-0.797888\pi$
$863$	−47.3026			−1.61020			−0.805100	+	0.593140i	$0.797888\pi$
$864$	−17.8099	−	25.2316i	−0.605904	−	0.858397i
$865$	6.61029			0.224756
$866$	1.66823	−	2.13857i	0.0566888	−	0.0726715i
$867$	21.4203	+	21.4203i	0.727470	+	0.727470i
$868$	−13.7154	+	3.44167i	−0.465532	+	0.116818i
$869$	−14.8309	+	14.8309i	−0.503104	+	0.503104i
$870$	22.0334	−	2.72227i	0.747002	−	0.0922936i
$871$			59.7803i			2.02558i
$872$	−3.19323	−	8.26260i	−0.108136	−	0.279807i
$873$			2.10157i			0.0711274i
$874$	0.487204	+	3.94331i	0.0164799	+	0.133384i
$875$	−13.7557	+	13.7557i	−0.465026	+	0.465026i
$876$	−43.3762	−	25.9739i	−1.46555	−	0.877575i
$877$	−32.0798	−	32.0798i	−1.08326	−	1.08326i	−0.996204	−	0.0870541i	$-0.972255\pi$
$877$	−32.0798	−	32.0798i	−1.08326	−	1.08326i	−0.0870541	−	0.996204i	$-0.527745\pi$
$878$	45.3571	+	35.3817i	1.53073	+	1.19407i
$879$	52.4120			1.76781
$880$	−8.79045	−	16.4125i	−0.296326	−	0.553266i
$881$	18.9570			0.638679			0.319339	−	0.947640i	$-0.396539\pi$
$881$	18.9570			0.638679			0.319339	+	0.947640i	$0.396539\pi$
$882$	1.45625	+	1.13597i	0.0490344	+	0.0382502i
$883$	26.1961	+	26.1961i	0.881569	+	0.881569i	0.993694	−	0.112125i	$-0.0357657\pi$
$883$	26.1961	+	26.1961i	0.881569	+	0.881569i	−0.112125	+	0.993694i	$0.535766\pi$
$884$	35.3529	−	59.0390i	1.18905	−	1.98570i
$885$	13.3567	−	13.3567i	0.448981	−	0.448981i
$886$	−2.88796	−	23.3744i	−0.0970228	−	0.785279i
$887$		−	38.4041i		−	1.28948i	−0.764401	−	0.644741i	$-0.776965\pi$
$887$		−	38.4041i		−	1.28948i	0.764401	−	0.644741i	$-0.223035\pi$
$888$	−5.98313	−	2.64762i	−0.200781	−	0.0888483i
$889$			10.2974i			0.345365i
$890$	21.1489	−	2.61298i	0.708911	−	0.0875874i
$891$	−20.3841	+	20.3841i	−0.682893	+	0.682893i
$892$	5.67891	+	22.6311i	0.190144	+	0.757744i
$893$	4.52785	+	4.52785i	0.151519	+	0.151519i
$894$	0.871306	−	1.11696i	0.0291408	−	0.0373568i
$895$	6.69405			0.223758
$896$	−1.55984	−	20.7298i	−0.0521106	−	0.692533i
$897$	−26.3060			−0.878331
$898$	12.9856	−	16.6467i	0.433334	−	0.555507i
$899$	20.9046	+	20.9046i	0.697206	+	0.697206i
$900$	−0.599677	−	2.38978i	−0.0199892	−	0.0796592i
$901$	−25.8752	+	25.8752i	−0.862029	+	0.862029i
$902$	−62.3476	+	7.70317i	−2.07595	+	0.256487i
$903$			1.60582i			0.0534384i
$904$	−11.7657	−	5.20649i	−0.391322	−	0.173165i
$905$			25.0497i			0.832680i
$906$	2.17279	+	17.5860i	0.0721861	+	0.584257i
$907$	33.1319	−	33.1319i	1.10013	−	1.10013i	0.105730	−	0.994395i	$-0.466282\pi$
$907$	33.1319	−	33.1319i	1.10013	−	1.10013i	0.994395	−	0.105730i	$-0.0337180\pi$
$908$	−21.1692	+	35.3524i	−0.702524	+	1.17321i
$909$	3.16991	+	3.16991i	0.105139	+	0.105139i
$910$	−14.8498	−	11.5839i	−0.492267	−	0.384002i
$911$	−25.6957			−0.851337			−0.425669	−	0.904879i	$-0.639961\pi$
$911$	−25.6957			−0.851337			−0.425669	+	0.904879i	$0.639961\pi$
$912$	3.06832	+	5.72881i	0.101602	+	0.189700i
$913$	24.4952			0.810671
$914$	−18.6074	−	14.5150i	−0.615477	−	0.480114i
$915$	2.34878	+	2.34878i	0.0776484	+	0.0776484i
$916$	28.5005	+	17.0662i	0.941682	+	0.563883i
$917$	−7.34201	+	7.34201i	−0.242455	+	0.242455i
$918$	5.65244	+	45.7495i	0.186558	+	1.50996i
$919$		−	50.7942i		−	1.67555i	−0.546019	−	0.837773i	$-0.683857\pi$
$919$		−	50.7942i		−	1.67555i	0.546019	−	0.837773i	$-0.316143\pi$
$920$	3.60264	+	9.32195i	0.118775	+	0.307335i
$921$			34.7494i			1.14503i
$922$	9.03535	−	1.11634i	0.297563	−	0.0367645i
$923$	43.3711	−	43.3711i	1.42758	−	1.42758i
$924$	−21.4330	+	5.37827i	−0.705093	+	0.176932i
$925$	−3.44151	−	3.44151i	−0.113156	−	0.113156i
$926$	−18.9184	+	24.2522i	−0.621696	+	0.796976i
$927$	−0.416844			−0.0136910
$928$	−35.5073	+	25.0630i	−1.16558	+	0.822734i
$929$	13.5368			0.444126			0.222063	−	0.975032i	$-0.428721\pi$
$929$	13.5368			0.444126			0.222063	+	0.975032i	$0.428721\pi$
$930$	6.83887	−	8.76701i	0.224255	−	0.287481i
$931$	−2.56240	−	2.56240i	−0.0839793	−	0.0839793i
$932$	15.8588	−	3.97952i	0.519472	−	0.130354i
$933$	−34.5605	+	34.5605i	−1.13146	+	1.13146i
$934$	−4.49249	+	0.555056i	−0.146999	+	0.0181620i
$935$			27.7896i			0.908817i
$936$	5.47943	−	2.11763i	0.179101	−	0.0692168i
$937$			41.5930i			1.35878i	0.733776	+	0.679392i	$0.237756\pi$
$937$			41.5930i			1.35878i	−0.733776	+	0.679392i	$0.762244\pi$
$938$	−3.30521	−	26.7516i	−0.107919	−	0.873471i
$939$	−14.4264	+	14.4264i	−0.470788	+	0.470788i
$940$	13.8182	+	8.27438i	0.450698	+	0.269880i
$941$	−27.8897	−	27.8897i	−0.909178	−	0.909178i	0.0870282	−	0.996206i	$-0.472263\pi$
$941$	−27.8897	−	27.8897i	−0.909178	−	0.909178i	−0.996206	+	0.0870282i	$0.972263\pi$
$942$	−21.3763	−	16.6750i	−0.696477	−	0.543300i
$943$	33.7212			1.09811
$944$	−10.7045	+	35.3954i	−0.348403	+	1.15202i
$945$	12.6162			0.410405
$946$	−2.21995	−	1.73171i	−0.0721767	−	0.0563028i
$947$	−27.9853	−	27.9853i	−0.909400	−	0.909400i	0.0868238	−	0.996224i	$-0.472328\pi$
$947$	−27.9853	−	27.9853i	−0.909400	−	0.909400i	−0.996224	+	0.0868238i	$0.972328\pi$
$948$	9.46019	−	15.7985i	0.307253	−	0.513110i
$949$	63.4053	−	63.4053i	2.05822	−	2.05822i
$950$	0.592779	+	4.79781i	0.0192323	+	0.155662i
$951$			42.3971i			1.37482i
$952$	−12.5561	+	28.3745i	−0.406946	+	0.919624i
$953$		−	14.4602i		−	0.468413i	−0.972187	−	0.234207i	$-0.924751\pi$
$953$		−	14.4602i		−	0.468413i	0.972187	−	0.234207i	$-0.0752492\pi$
$954$	−3.10022	+	0.383038i	−0.100373	+	0.0124013i
$955$	−20.5308	+	20.5308i	−0.664362	+	0.664362i
$956$	−4.83810	−	19.2803i	−0.156475	−	0.623570i
$957$	32.6674	+	32.6674i	1.05599	+	1.05599i
$958$	−30.0262	+	38.4917i	−0.970102	+	1.24361i
$959$	12.7071			0.410334
$960$	10.9927	+	12.0978i	0.354786	+	0.390454i
$961$	−16.1936			−0.522376
$962$	7.13726	−	9.14952i	0.230114	−	0.294992i
$963$	3.24975	+	3.24975i	0.104722	+	0.104722i
$964$	−7.41167	−	29.5363i	−0.238714	−	0.951299i
$965$	−19.5566	+	19.5566i	−0.629549	+	0.629549i
$966$	11.7719	−	1.45444i	0.378754	−	0.0467958i
$967$		−	40.4968i		−	1.30229i	−0.758954	−	0.651144i	$-0.774289\pi$
$967$		−	40.4968i		−	1.30229i	0.758954	−	0.651144i	$-0.225711\pi$
$968$	3.08793	−	6.97814i	0.0992497	−	0.224286i
$969$		−	9.69999i		−	0.311609i
$970$	−1.27175	−	10.2933i	−0.0408336	−	0.330497i
$971$	−9.33690	+	9.33690i	−0.299635	+	0.299635i	−0.840871	−	0.541236i	$-0.817957\pi$
$971$	−9.33690	+	9.33690i	−0.299635	+	0.299635i	0.541236	+	0.840871i	$0.317957\pi$
$972$	−3.82647	+	6.39017i	−0.122734	+	0.204965i
$973$	1.21282	+	1.21282i	0.0388811	+	0.0388811i
$974$	−33.1895	−	25.8901i	−1.06346	−	0.829573i
$975$	−32.0064			−1.02502
$976$	−6.22429	−	1.88240i	−0.199235	−	0.0602540i
$977$	12.1768			0.389570			0.194785	−	0.980846i	$-0.437599\pi$
$977$	12.1768			0.389570			0.194785	+	0.980846i	$0.437599\pi$
$978$	−10.9891	−	8.57226i	−0.351393	−	0.274111i
$979$	31.3560	+	31.3560i	1.00214	+	1.00214i
$980$	−7.81997	−	4.68264i	−0.249800	−	0.149581i
$981$	−0.798093	+	0.798093i	−0.0254812	+	0.0254812i
$982$	−2.66357	−	21.5583i	−0.0849980	−	0.687954i
$983$			34.4304i			1.09816i	0.835770	+	0.549080i	$0.185022\pi$
$983$			34.4304i			1.09816i	−0.835770	+	0.549080i	$0.814978\pi$
$984$	51.4464	−	19.8824i	1.64005	−	0.633828i
$985$		−	16.7022i		−	0.532177i
$986$	64.3811	−	7.95442i	2.05031	−	0.253320i
$987$	13.5169	−	13.5169i	0.430248	−	0.430248i
$988$	−11.1794	+	2.80530i	−0.355664	+	0.0892484i
$989$	1.06864	+	1.06864i	0.0339809	+	0.0339809i
$990$	−1.45911	+	1.87048i	−0.0463734	+	0.0594479i
$991$	−9.53519			−0.302895			−0.151448	−	0.988465i	$-0.548394\pi$
$991$	−9.53519			−0.302895			−0.151448	+	0.988465i	$0.548394\pi$
$992$	−3.69875	+	21.4505i	−0.117436	+	0.681053i
$993$	−38.4485			−1.22012
$994$	−17.0106	+	21.8065i	−0.539542	+	0.691660i
$995$	−20.0031	−	20.0031i	−0.634141	−	0.634141i
$996$	−20.8590	+	5.23424i	−0.660942	+	0.165853i
$997$	−1.95727	+	1.95727i	−0.0619873	+	0.0619873i	−0.737421	−	0.675434i	$-0.763957\pi$
$997$	−1.95727	+	1.95727i	−0.0619873	+	0.0619873i	0.675434	+	0.737421i	$0.263957\pi$
$998$	34.4051	−	4.25082i	1.08908	−	0.134557i
$999$			7.77330i			0.245936i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.2.k.b.77.10	✓	68
4.3	odd	2		1216.2.k.b.913.10		68
16.5	even	4	inner	304.2.k.b.229.10	yes	68
16.11	odd	4		1216.2.k.b.305.10		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
304.2.k.b.77.10	✓	68	1.1	even	1	trivial
304.2.k.b.229.10	yes	68	16.5	even	4	inner
1216.2.k.b.305.10		68	16.11	odd	4
1216.2.k.b.913.10		68	4.3	odd	2

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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.869834 + 1.11507i) q^{2} +(1.14883 + 1.14883i) q^{3} +(-0.486777 - 1.93986i) q^{4} +(0.889280 - 0.889280i) q^{5} +(-2.28032 + 0.281738i) q^{6} +1.83745i q^{7} +(2.58650 + 1.14456i) q^{8} -0.360387i q^{9} +O(q^{10})\)	\(q+(-0.869834 + 1.11507i) q^{2} +(1.14883 + 1.14883i) q^{3} +(-0.486777 - 1.93986i) q^{4} +(0.889280 - 0.889280i) q^{5} +(-2.28032 + 0.281738i) q^{6} +1.83745i q^{7} +(2.58650 + 1.14456i) q^{8} -0.360387i q^{9} +(0.218086 + 1.76514i) q^{10} +(-2.61705 + 2.61705i) q^{11} +(1.66934 - 2.78779i) q^{12} +(4.07506 + 4.07506i) q^{13} +(-2.04889 - 1.59828i) q^{14} +2.04326 q^{15} +(-3.52610 + 1.88856i) q^{16} +5.97037 q^{17} +(0.401858 + 0.313477i) q^{18} +(-0.707107 - 0.707107i) q^{19} +(-2.15796 - 1.29220i) q^{20} +(-2.11091 + 2.11091i) q^{21} +(-0.641804 - 5.19460i) q^{22} +2.80954i q^{23} +(1.65654 + 4.28635i) q^{24} +3.41836i q^{25} +(-8.08861 + 0.999364i) q^{26} +(3.86051 - 3.86051i) q^{27} +(3.56439 - 0.894428i) q^{28} +(-5.43272 - 5.43272i) q^{29} +(-1.77730 + 2.27839i) q^{30} -3.84790 q^{31} +(0.961239 - 5.57459i) q^{32} -6.01308 q^{33} +(-5.19323 + 6.65740i) q^{34} +(1.63401 + 1.63401i) q^{35} +(-0.699100 + 0.175428i) q^{36} +(-1.00677 + 1.00677i) q^{37} +(1.40354 - 0.173410i) q^{38} +9.36308i q^{39} +(3.31796 - 1.28229i) q^{40} -12.0024i q^{41} +(-0.517679 - 4.18997i) q^{42} +(0.380362 - 0.380362i) q^{43} +(6.35063 + 3.80279i) q^{44} +(-0.320485 - 0.320485i) q^{45} +(-3.13285 - 2.44384i) q^{46} -6.40334 q^{47} +(-6.22051 - 1.88125i) q^{48} +3.62378 q^{49} +(-3.81172 - 2.97341i) q^{50} +(6.85893 + 6.85893i) q^{51} +(5.92138 - 9.88867i) q^{52} +(-4.33394 + 4.33394i) q^{53} +(0.946748 + 7.66275i) q^{54} +4.65458i q^{55} +(-2.10307 + 4.75256i) q^{56} -1.62469i q^{57} +(10.7834 - 1.33232i) q^{58} +(6.53696 - 6.53696i) q^{59} +(-0.994613 - 3.96364i) q^{60} +(1.14953 + 1.14953i) q^{61} +(3.34704 - 4.29069i) q^{62} +0.662193 q^{63} +(5.37996 + 5.92082i) q^{64} +7.24774 q^{65} +(5.23039 - 6.70503i) q^{66} +(7.33490 + 7.33490i) q^{67} +(-2.90624 - 11.5817i) q^{68} +(-3.22768 + 3.22768i) q^{69} +(-3.24335 + 0.400723i) q^{70} -10.6431i q^{71} +(0.412486 - 0.932141i) q^{72} -15.5594i q^{73} +(-0.246900 - 1.99835i) q^{74} +(-3.92711 + 3.92711i) q^{75} +(-1.02748 + 1.71589i) q^{76} +(-4.80870 - 4.80870i) q^{77} +(-10.4405 - 8.14433i) q^{78} +5.66702 q^{79} +(-1.45623 + 4.81515i) q^{80} +7.78896 q^{81} +(13.3835 + 10.4401i) q^{82} +(-4.67992 - 4.67992i) q^{83} +(5.12242 + 3.06733i) q^{84} +(5.30933 - 5.30933i) q^{85} +(0.0932797 + 0.754983i) q^{86} -12.4825i q^{87} +(-9.76438 + 3.77362i) q^{88} -11.9814i q^{89} +(0.636134 - 0.0785956i) q^{90} +(-7.48771 + 7.48771i) q^{91} +(5.45011 - 1.36762i) q^{92} +(-4.42058 - 4.42058i) q^{93} +(5.56985 - 7.14020i) q^{94} -1.25763 q^{95} +(7.50854 - 5.29995i) q^{96} -5.83142 q^{97} +(-3.15209 + 4.04078i) q^{98} +(0.943152 + 0.943152i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6}+O(q^{10}) \) 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6	\( 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6} + 4 q^{11} - 4 q^{12} + 20 q^{14} - 16 q^{15} + 4 q^{16} + 4 q^{17} - 16 q^{18} + 16 q^{21} + 4 q^{22} - 4 q^{24} - 36 q^{26} + 28 q^{27} - 24 q^{28} + 24 q^{30} + 32 q^{31} - 20 q^{32} - 16 q^{33} - 32 q^{34} - 24 q^{35} + 52 q^{36} - 24 q^{37} - 4 q^{38} - 8 q^{40} - 40 q^{42} - 16 q^{43} - 36 q^{44} - 8 q^{46} - 24 q^{47} + 36 q^{48} - 56 q^{49} + 24 q^{50} - 52 q^{51} - 28 q^{52} + 32 q^{53} - 52 q^{54} + 12 q^{56} + 52 q^{58} + 28 q^{59} - 64 q^{60} - 12 q^{62} + 24 q^{63} - 32 q^{64} - 16 q^{65} - 44 q^{66} + 28 q^{67} - 48 q^{68} - 8 q^{69} + 4 q^{70} + 108 q^{72} + 72 q^{74} + 44 q^{75} - 12 q^{77} + 100 q^{78} + 8 q^{79} - 56 q^{80} - 76 q^{81} + 28 q^{82} + 40 q^{83} + 52 q^{84} - 8 q^{85} - 20 q^{86} - 56 q^{88} - 24 q^{90} - 4 q^{91} + 72 q^{92} - 84 q^{93} - 24 q^{94} + 32 q^{95} + 72 q^{96} - 16 q^{97} - 80 q^{98} - 24 q^{99}+O(q^{100}) \) 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6 + 4 * q^11 - 4 * q^12 + 20 * q^14 - 16 * q^15 + 4 * q^16 + 4 * q^17 - 16 * q^18 + 16 * q^21 + 4 * q^22 - 4 * q^24 - 36 * q^26 + 28 * q^27 - 24 * q^28 + 24 * q^30 + 32 * q^31 - 20 * q^32 - 16 * q^33 - 32 * q^34 - 24 * q^35 + 52 * q^36 - 24 * q^37 - 4 * q^38 - 8 * q^40 - 40 * q^42 - 16 * q^43 - 36 * q^44 - 8 * q^46 - 24 * q^47 + 36 * q^48 - 56 * q^49 + 24 * q^50 - 52 * q^51 - 28 * q^52 + 32 * q^53 - 52 * q^54 + 12 * q^56 + 52 * q^58 + 28 * q^59 - 64 * q^60 - 12 * q^62 + 24 * q^63 - 32 * q^64 - 16 * q^65 - 44 * q^66 + 28 * q^67 - 48 * q^68 - 8 * q^69 + 4 * q^70 + 108 * q^72 + 72 * q^74 + 44 * q^75 - 12 * q^77 + 100 * q^78 + 8 * q^79 - 56 * q^80 - 76 * q^81 + 28 * q^82 + 40 * q^83 + 52 * q^84 - 8 * q^85 - 20 * q^86 - 56 * q^88 - 24 * q^90 - 4 * q^91 + 72 * q^92 - 84 * q^93 - 24 * q^94 + 32 * q^95 + 72 * q^96 - 16 * q^97 - 80 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more