LMFDB - Embedded newform 65.2.t.a.7.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,2,Mod(7,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 11]))

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

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

chi := DirichletCharacter("65.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	65.t (of order $12$, 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:	$0.519027613138$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
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} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.5
Root			$1.51805i$ of defining polynomial
Character	$\chi$	$=$	65.7
Dual form			65.2.t.a.28.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.31467 + 0.759023i) q^{2} +(0.175069 + 0.653367i) q^{3} +(0.152233 + 0.263675i) q^{4} +(-2.15400 + 0.600231i) q^{5} +(-0.265763 + 0.991842i) q^{6} +(-1.29744 - 2.24723i) q^{7} -2.57390i q^{8} +(2.20184 - 1.27123i) q^{9} +O(q^{10})$	\(q+(1.31467 + 0.759023i) q^{2} +(0.175069 + 0.653367i) q^{3} +(0.152233 + 0.263675i) q^{4} +(-2.15400 + 0.600231i) q^{5} +(-0.265763 + 0.991842i) q^{6} +(-1.29744 - 2.24723i) q^{7} -2.57390i q^{8} +(2.20184 - 1.27123i) q^{9} +(-3.28738 - 0.845834i) q^{10} +(1.29395 + 4.82908i) q^{11} +(-0.145625 + 0.145625i) q^{12} +(-2.37567 + 2.71223i) q^{13} -3.93915i q^{14} +(-0.769270 - 1.30227i) q^{15} +(2.25812 - 3.91117i) q^{16} +(0.0790751 + 0.0211881i) q^{17} +3.85958 q^{18} +(-2.71143 - 0.726525i) q^{19} +(-0.486175 - 0.476581i) q^{20} +(1.24113 - 1.24113i) q^{21} +(-1.96427 + 7.33077i) q^{22} +(-3.91925 + 1.05016i) q^{23} +(1.68170 - 0.450611i) q^{24} +(4.27945 - 2.58580i) q^{25} +(-5.18186 + 1.76249i) q^{26} +(2.65095 + 2.65095i) q^{27} +(0.395026 - 0.684205i) q^{28} +(4.31701 + 2.49243i) q^{29} +(-0.0228795 - 2.29595i) q^{30} +(-2.32124 - 2.32124i) q^{31} +(1.47921 - 0.854024i) q^{32} +(-2.92863 + 1.69085i) q^{33} +(0.0878751 + 0.0878751i) q^{34} +(4.14355 + 4.06178i) q^{35} +(0.670383 + 0.387046i) q^{36} +(-0.285750 + 0.494934i) q^{37} +(-3.01318 - 3.01318i) q^{38} +(-2.18799 - 1.07736i) q^{39} +(1.54493 + 5.54419i) q^{40} +(10.0563 - 2.69458i) q^{41} +(2.57371 - 0.689624i) q^{42} +(0.0354017 - 0.132121i) q^{43} +(-1.07633 + 1.07633i) q^{44} +(-3.97973 + 4.05984i) q^{45} +(-5.94960 - 1.59419i) q^{46} -2.30053 q^{47} +(2.95076 + 0.790653i) q^{48} +(0.133293 - 0.230870i) q^{49} +(7.58873 - 0.151261i) q^{50} +0.0553744i q^{51} +(-1.07680 - 0.213514i) q^{52} +(6.70735 - 6.70735i) q^{53} +(1.47298 + 5.49724i) q^{54} +(-5.68573 - 9.62518i) q^{55} +(-5.78416 + 3.33948i) q^{56} -1.89875i q^{57} +(3.78362 + 6.55343i) q^{58} +(-0.694109 + 2.59045i) q^{59} +(0.226268 - 0.401085i) q^{60} +(-2.74237 - 4.74992i) q^{61} +(-1.28978 - 4.81352i) q^{62} +(-5.71351 - 3.29870i) q^{63} -6.43957 q^{64} +(3.48923 - 7.26810i) q^{65} -5.13357 q^{66} +(-13.6718 - 7.89339i) q^{67} +(0.00645104 + 0.0240756i) q^{68} +(-1.37228 - 2.37686i) q^{69} +(2.36440 + 8.48494i) q^{70} +(-1.98951 + 7.42495i) q^{71} +(-3.27202 - 5.66731i) q^{72} +6.61894i q^{73} +(-0.751333 + 0.433783i) q^{74} +(2.43867 + 2.34336i) q^{75} +(-0.221202 - 0.825536i) q^{76} +(9.17326 - 9.17326i) q^{77} +(-2.05874 - 3.07710i) q^{78} +5.71054i q^{79} +(-2.51638 + 9.78006i) q^{80} +(2.54575 - 4.40937i) q^{81} +(15.2660 + 4.09050i) q^{82} +3.70736 q^{83} +(0.516194 + 0.138314i) q^{84} +(-0.183046 + 0.00182408i) q^{85} +(0.146824 - 0.146824i) q^{86} +(-0.872695 + 3.25694i) q^{87} +(12.4296 - 3.33050i) q^{88} +(-17.2829 + 4.63094i) q^{89} +(-8.31353 + 2.31664i) q^{90} +(9.17731 + 1.81973i) q^{91} +(-0.873538 - 0.873538i) q^{92} +(1.11024 - 1.92300i) q^{93} +(-3.02443 - 1.74616i) q^{94} +(6.27651 - 0.0625465i) q^{95} +(0.816956 + 0.816956i) q^{96} +(4.65043 - 2.68493i) q^{97} +(0.350471 - 0.202345i) q^{98} +(8.98794 + 8.98794i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 8 q^{6} - 2 q^{7} + 12 q^{9}+O(q^{10}) $ 20 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 8 * q^6 - 2 * q^7 + 12 * q^9	$ 20 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 8 q^{6} - 2 q^{7} + 12 q^{9} - 2 q^{10} - 16 q^{11} - 24 q^{12} - 4 q^{13} - 20 q^{15} - 2 q^{16} + 4 q^{17} - 20 q^{19} + 4 q^{21} + 16 q^{22} - 10 q^{23} + 32 q^{24} + 18 q^{25} - 24 q^{26} + 4 q^{27} + 18 q^{28} - 26 q^{30} + 48 q^{32} + 18 q^{33} + 2 q^{34} + 40 q^{35} + 36 q^{36} - 4 q^{37} - 8 q^{38} + 4 q^{39} - 16 q^{40} + 10 q^{41} + 40 q^{42} + 10 q^{43} - 36 q^{44} + 4 q^{46} - 40 q^{47} - 56 q^{48} + 18 q^{49} + 36 q^{50} - 30 q^{52} - 10 q^{53} - 48 q^{54} - 10 q^{55} - 16 q^{59} + 28 q^{60} - 16 q^{61} - 44 q^{62} - 36 q^{63} + 20 q^{64} - 14 q^{65} - 32 q^{66} + 18 q^{67} + 22 q^{68} - 16 q^{69} - 12 q^{70} - 16 q^{71} + 4 q^{72} + 18 q^{74} - 38 q^{75} - 64 q^{76} - 28 q^{77} + 68 q^{78} - 2 q^{80} - 14 q^{81} + 56 q^{82} + 48 q^{83} - 40 q^{84} - 26 q^{85} + 60 q^{86} - 34 q^{87} + 82 q^{88} - 6 q^{89} + 46 q^{90} + 8 q^{91} - 8 q^{92} + 32 q^{93} - 48 q^{94} - 26 q^{95} + 56 q^{96} + 66 q^{97} - 30 q^{98} + 60 q^{99}+O(q^{100}) $ 20 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 8 * q^6 - 2 * q^7 + 12 * q^9 - 2 * q^10 - 16 * q^11 - 24 * q^12 - 4 * q^13 - 20 * q^15 - 2 * q^16 + 4 * q^17 - 20 * q^19 + 4 * q^21 + 16 * q^22 - 10 * q^23 + 32 * q^24 + 18 * q^25 - 24 * q^26 + 4 * q^27 + 18 * q^28 - 26 * q^30 + 48 * q^32 + 18 * q^33 + 2 * q^34 + 40 * q^35 + 36 * q^36 - 4 * q^37 - 8 * q^38 + 4 * q^39 - 16 * q^40 + 10 * q^41 + 40 * q^42 + 10 * q^43 - 36 * q^44 + 4 * q^46 - 40 * q^47 - 56 * q^48 + 18 * q^49 + 36 * q^50 - 30 * q^52 - 10 * q^53 - 48 * q^54 - 10 * q^55 - 16 * q^59 + 28 * q^60 - 16 * q^61 - 44 * q^62 - 36 * q^63 + 20 * q^64 - 14 * q^65 - 32 * q^66 + 18 * q^67 + 22 * q^68 - 16 * q^69 - 12 * q^70 - 16 * q^71 + 4 * q^72 + 18 * q^74 - 38 * q^75 - 64 * q^76 - 28 * q^77 + 68 * q^78 - 2 * q^80 - 14 * q^81 + 56 * q^82 + 48 * q^83 - 40 * q^84 - 26 * q^85 + 60 * q^86 - 34 * q^87 + 82 * q^88 - 6 * q^89 + 46 * q^90 + 8 * q^91 - 8 * q^92 + 32 * q^93 - 48 * q^94 - 26 * q^95 + 56 * q^96 + 66 * q^97 - 30 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{11}{12}\right)$

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 $

$2$	1.31467	+	0.759023i	0.929610	+	0.536710i	0.886688	−	0.462368i	$-0.153000\pi$
$2$	1.31467	+	0.759023i	0.929610	+	0.536710i	0.0429217	+	0.999078i	$0.486333\pi$
$3$	0.175069	+	0.653367i	0.101076	+	0.377222i	0.997871	−	0.0652261i	$-0.0207769\pi$
$3$	0.175069	+	0.653367i	0.101076	+	0.377222i	−0.896794	+	0.442448i	$0.854110\pi$
$4$	0.152233	+	0.263675i	0.0761163	+	0.131837i
$5$	−2.15400	+	0.600231i	−0.963299	+	0.268431i
$5$	−2.15400	+	0.600231i	−0.963299	+	0.268431i
$6$	−0.265763	+	0.991842i	−0.108497	+	0.404918i
$7$	−1.29744	−	2.24723i	−0.490387	−	0.849375i	0.509552	−	0.860440i	$-0.329811\pi$
$7$	−1.29744	−	2.24723i	−0.490387	−	0.849375i	−0.999939	+	0.0110652i	$0.996478\pi$
$8$		−	2.57390i		−	0.910011i
$9$	2.20184	−	1.27123i	0.733946	−	0.423744i
$10$	−3.28738	−	0.845834i	−1.03956	−	0.267476i
$11$	1.29395	+	4.82908i	0.390140	+	1.45602i	0.829902	+	0.557909i	$0.188396\pi$
$11$	1.29395	+	4.82908i	0.390140	+	1.45602i	−0.439762	+	0.898114i	$0.644937\pi$
$12$	−0.145625	+	0.145625i	−0.0420383	+	0.0420383i
$13$	−2.37567	+	2.71223i	−0.658892	+	0.752237i
$13$	−2.37567	+	2.71223i	−0.658892	+	0.752237i
$14$		−	3.93915i		−	1.05278i
$15$	−0.769270	−	1.30227i	−0.198625	−	0.336245i
$16$	2.25812	−	3.91117i	0.564529	−	0.977793i
$17$	0.0790751	+	0.0211881i	0.0191785	+	0.00513887i	0.268396	−	0.963309i	$-0.413507\pi$
$17$	0.0790751	+	0.0211881i	0.0191785	+	0.00513887i	−0.249217	+	0.968448i	$0.580173\pi$
$18$	3.85958			0.909711
$19$	−2.71143	−	0.726525i	−0.622045	−	0.166676i	−0.0659876	−	0.997820i	$-0.521020\pi$
$19$	−2.71143	−	0.726525i	−0.622045	−	0.166676i	−0.556057	+	0.831144i	$0.687686\pi$
$20$	−0.486175	−	0.476581i	−0.108712	−	0.106567i
$21$	1.24113	−	1.24113i	0.270836	−	0.270836i
$22$	−1.96427	+	7.33077i	−0.418785	+	1.56293i
$23$	−3.91925	+	1.05016i	−0.817220	+	0.218973i	−0.643131	−	0.765756i	$-0.722365\pi$
$23$	−3.91925	+	1.05016i	−0.817220	+	0.218973i	−0.174089	+	0.984730i	$0.555698\pi$
$24$	1.68170	−	0.450611i	0.343276	−	0.0919805i
$25$	4.27945	−	2.58580i	0.855889	−	0.517159i
$26$	−5.18186	+	1.76249i	−1.01625	+	0.345653i
$27$	2.65095	+	2.65095i	0.510175	+	0.510175i
$28$	0.395026	−	0.684205i	0.0746528	−	0.129303i
$29$	4.31701	+	2.49243i	0.801649	+	0.462833i	0.844048	−	0.536268i	$-0.180166\pi$
$29$	4.31701	+	2.49243i	0.801649	+	0.462833i	−0.0423981	+	0.999101i	$0.513500\pi$
$30$	−0.0228795	−	2.29595i	−0.00417721	−	0.419181i
$31$	−2.32124	−	2.32124i	−0.416906	−	0.416906i	0.467230	−	0.884136i	$-0.345252\pi$
$31$	−2.32124	−	2.32124i	−0.416906	−	0.416906i	−0.884136	+	0.467230i	$0.845252\pi$
$32$	1.47921	−	0.854024i	0.261490	−	0.150972i
$33$	−2.92863	+	1.69085i	−0.509809	+	0.294339i
$34$	0.0878751	+	0.0878751i	0.0150705	+	0.0150705i
$35$	4.14355	+	4.06178i	0.700388	+	0.686566i
$36$	0.670383	+	0.387046i	0.111730	+	0.0645076i
$37$	−0.285750	+	0.494934i	−0.0469771	+	0.0813667i	−0.888558	−	0.458765i	$-0.848292\pi$
$37$	−0.285750	+	0.494934i	−0.0469771	+	0.0813667i	0.841581	+	0.540131i	$0.181625\pi$
$38$	−3.01318	−	3.01318i	−0.488802	−	0.488802i
$39$	−2.18799	−	1.07736i	−0.350359	−	0.172515i
$40$	1.54493	+	5.54419i	0.244276	+	0.876613i
$41$	10.0563	−	2.69458i	1.57053	−	0.420823i	0.634554	−	0.772879i	$-0.281184\pi$
$41$	10.0563	−	2.69458i	1.57053	−	0.420823i	0.935979	+	0.352056i	$0.114517\pi$
$42$	2.57371	−	0.689624i	0.397132	−	0.106411i
$43$	0.0354017	−	0.132121i	0.00539871	−	0.0201483i	−0.963174	−	0.268879i	$-0.913347\pi$
$43$	0.0354017	−	0.132121i	0.00539871	−	0.0201483i	0.968573	+	0.248731i	$0.0800135\pi$
$44$	−1.07633	+	1.07633i	−0.162262	+	0.162262i
$45$	−3.97973	+	4.05984i	−0.593263	+	0.605206i
$46$	−5.94960	−	1.59419i	−0.877221	−	0.235051i
$47$	−2.30053			−0.335567			−0.167784	−	0.985824i	$-0.553661\pi$
$47$	−2.30053			−0.335567			−0.167784	+	0.985824i	$0.553661\pi$
$48$	2.95076	+	0.790653i	0.425905	+	0.114121i
$49$	0.133293	−	0.230870i	0.0190418	−	0.0329814i
$50$	7.58873	−	0.151261i	1.07321	−	0.0213915i
$51$			0.0553744i			0.00775397i
$52$	−1.07680	−	0.213514i	−0.149325	−	0.0296090i
$53$	6.70735	−	6.70735i	0.921326	−	0.921326i	−0.0757974	−	0.997123i	$-0.524150\pi$
$53$	6.70735	−	6.70735i	0.921326	−	0.921326i	0.997123	+	0.0757974i	$0.0241502\pi$
$54$	1.47298	+	5.49724i	0.200447	+	0.748080i
$55$	−5.68573	−	9.62518i	−0.766664	−	1.29786i
$56$	−5.78416	+	3.33948i	−0.772941	+	0.446257i
$57$		−	1.89875i		−	0.251496i
$58$	3.78362	+	6.55343i	0.496814	+	0.860507i
$59$	−0.694109	+	2.59045i	−0.0903653	+	0.337248i	−0.996276	−	0.0862207i	$-0.972521\pi$
$59$	−0.694109	+	2.59045i	−0.0903653	+	0.337248i	0.905911	+	0.423469i	$0.139188\pi$
$60$	0.226268	−	0.401085i	0.0292111	−	0.0517799i
$61$	−2.74237	−	4.74992i	−0.351124	−	0.608165i	0.635322	−	0.772247i	$-0.280867\pi$
$61$	−2.74237	−	4.74992i	−0.351124	−	0.608165i	−0.986447	+	0.164082i	$0.947534\pi$
$62$	−1.28978	−	4.81352i	−0.163802	−	0.611318i
$63$	−5.71351	−	3.29870i	−0.719834	−	0.415597i
$64$	−6.43957			−0.804946
$65$	3.48923	−	7.26810i	0.432786	−	0.901497i
$66$	−5.13357			−0.631899
$67$	−13.6718	−	7.89339i	−1.67027	−	0.964331i	−0.967485	−	0.252930i	$-0.918606\pi$
$67$	−13.6718	−	7.89339i	−1.67027	−	0.964331i	−0.702786	−	0.711401i	$-0.748061\pi$
$68$	0.00645104	+	0.0240756i	0.000782303	+	0.00291960i
$69$	−1.37228	−	2.37686i	−0.165203	−	0.286140i
$70$	2.36440	+	8.48494i	0.282600	+	1.01414i
$71$	−1.98951	+	7.42495i	−0.236111	+	0.881180i	0.741533	+	0.670916i	$0.234099\pi$
$71$	−1.98951	+	7.42495i	−0.236111	+	0.881180i	−0.977645	+	0.210264i	$0.932568\pi$
$72$	−3.27202	−	5.66731i	−0.385612	−	0.667899i
$73$			6.61894i			0.774688i	0.921935	+	0.387344i	$0.126607\pi$
$73$			6.61894i			0.774688i	−0.921935	+	0.387344i	$0.873393\pi$
$74$	−0.751333	+	0.433783i	−0.0873407	+	0.0504262i
$75$	2.43867	+	2.34336i	0.281594	+	0.270587i
$76$	−0.221202	−	0.825536i	−0.0253736	−	0.0946955i
$77$	9.17326	−	9.17326i	1.04539	−	1.04539i
$78$	−2.05874	−	3.07710i	−0.233106	−	0.348413i
$79$			5.71054i			0.642486i	0.946997	+	0.321243i	$0.104101\pi$
$79$			5.71054i			0.642486i	−0.946997	+	0.321243i	$0.895899\pi$
$80$	−2.51638	+	9.78006i	−0.281340	+	1.09344i
$81$	2.54575	−	4.40937i	0.282861	−	0.489930i
$82$	15.2660	+	4.09050i	1.68584	+	0.451720i
$83$	3.70736			0.406936			0.203468	−	0.979082i	$-0.434779\pi$
$83$	3.70736			0.406936			0.203468	+	0.979082i	$0.434779\pi$
$84$	0.516194	+	0.138314i	0.0563213	+	0.0150913i
$85$	−0.183046	+	0.00182408i	−0.0198541	+	0.000197849i
$86$	0.146824	−	0.146824i	0.0158325	−	0.0158325i
$87$	−0.872695	+	3.25694i	−0.0935627	+	0.349181i
$88$	12.4296	−	3.33050i	1.32500	−	0.355032i
$89$	−17.2829	+	4.63094i	−1.83198	+	0.490878i	−0.998131	−	0.0611111i	$-0.980536\pi$
$89$	−17.2829	+	4.63094i	−1.83198	+	0.490878i	−0.833851	+	0.551989i	$0.813869\pi$
$90$	−8.31353	+	2.31664i	−0.876323	+	0.244195i
$91$	9.17731	+	1.81973i	0.962043	+	0.190759i
$92$	−0.873538	−	0.873538i	−0.0910726	−	0.0910726i
$93$	1.11024	−	1.92300i	0.115127	−	0.199405i
$94$	−3.02443	−	1.74616i	−0.311946	−	0.180102i
$95$	6.27651	−	0.0625465i	0.643956	−	0.00641713i
$96$	0.816956	+	0.816956i	0.0833802	+	0.0833802i
$97$	4.65043	−	2.68493i	0.472180	−	0.272613i	−0.244972	−	0.969530i	$-0.578779\pi$
$97$	4.65043	−	2.68493i	0.472180	−	0.272613i	0.717152	+	0.696917i	$0.245445\pi$
$98$	0.350471	−	0.202345i	0.0354029	−	0.0204399i
$99$	8.98794	+	8.98794i	0.903322	+	0.903322i
$100$	1.33328	+	0.734739i	0.133328	+	0.0734739i
$101$	2.17443	+	1.25541i	0.216363	+	0.124918i	0.604265	−	0.796783i	$-0.293467\pi$
$101$	2.17443	+	1.25541i	0.216363	+	0.124918i	−0.387902	+	0.921701i	$0.626800\pi$
$102$	−0.0420305	+	0.0727989i	−0.00416164	+	0.00720817i
$103$	4.71738	+	4.71738i	0.464817	+	0.464817i	0.900230	−	0.435414i	$-0.143398\pi$
$103$	4.71738	+	4.71738i	0.464817	+	0.464817i	−0.435414	+	0.900230i	$0.643398\pi$
$104$	6.98101	+	6.11474i	0.684545	+	0.599599i
$105$	−1.92843	+	3.41835i	−0.188195	+	0.333597i
$106$	13.9090	−	3.72690i	1.35096	−	0.361988i
$107$	−3.50497	+	0.939155i	−0.338838	+	0.0907915i	−0.424226	−	0.905556i	$-0.639454\pi$
$107$	−3.50497	+	0.939155i	−0.338838	+	0.0907915i	0.0853876	+	0.996348i	$0.472787\pi$
$108$	−0.295427	+	1.10255i	−0.0284275	+	0.106093i
$109$	1.58528	−	1.58528i	0.151843	−	0.151843i	−0.627098	−	0.778941i	$-0.715757\pi$
$109$	1.58528	−	1.58528i	0.151843	−	0.151843i	0.778941	+	0.627098i	$0.215757\pi$
$110$	−0.169104	−	16.9695i	−0.0161234	−	1.61798i
$111$	−0.373400	−	0.100052i	−0.0354416	−	0.00949653i
$112$	−11.7191			−1.10735
$113$	−5.53206	−	1.48231i	−0.520412	−	0.139444i	−0.0109551	−	0.999940i	$-0.503487\pi$
$113$	−5.53206	−	1.48231i	−0.520412	−	0.139444i	−0.509457	+	0.860496i	$0.670154\pi$
$114$	1.44120	−	2.49623i	0.134980	−	0.233793i
$115$	7.81173	−	4.61450i	0.728448	−	0.430304i
$116$			1.51772i			0.140916i
$117$	−1.78297	+	8.99191i	−0.164835	+	0.831303i
$118$	−2.87873	+	2.87873i	−0.265009	+	0.265009i
$119$	−0.0549806	−	0.205190i	−0.00504007	−	0.0188098i
$120$	−3.35192	+	1.98003i	−0.305987	+	0.180751i
$121$	−12.1195	+	6.99717i	−1.10177	+	0.636106i
$122$		−	8.32609i		−	0.753809i
$123$	3.52110	+	6.09873i	0.317487	+	0.549904i
$124$	0.258683	−	0.965419i	0.0232304	−	0.0866972i
$125$	−7.66586	+	8.13846i	−0.685655	+	0.727926i
$126$	−5.00757	−	8.67337i	−0.446110	−	0.772685i
$127$	0.210801	+	0.786718i	0.0187055	+	0.0698100i	0.974648	−	0.223745i	$-0.0718283\pi$
$127$	0.210801	+	0.786718i	0.0187055	+	0.0698100i	−0.955942	+	0.293555i	$0.905162\pi$
$128$	−11.4243	−	6.59583i	−1.00978	−	0.582994i
$129$	0.0925213			0.00814605
$130$	10.1038	−	6.90672i	0.886165	−	0.605759i
$131$	−16.1062			−1.40721			−0.703604	−	0.710592i	$-0.748427\pi$
$131$	−16.1062			−1.40721			−0.703604	+	0.710592i	$0.748427\pi$
$132$	−0.891667	−	0.514804i	−0.0776096	−	0.0448079i
$133$	1.88525	+	7.03584i	0.163472	+	0.610085i
$134$	−11.9825	−	20.7544i	−1.03513	−	1.79290i
$135$	−7.30133	−	4.11897i	−0.628398	−	0.354504i
$136$	0.0545361	−	0.203531i	0.00467643	−	0.0174527i
$137$	9.61871	+	16.6601i	0.821782	+	1.42337i	0.904354	+	0.426783i	$0.140353\pi$
$137$	9.61871	+	16.6601i	0.821782	+	1.42337i	−0.0825721	+	0.996585i	$0.526313\pi$
$138$		−	4.16637i		−	0.354665i
$139$	13.7257	−	7.92451i	1.16419	−	0.672148i	0.211889	−	0.977294i	$-0.432038\pi$
$139$	13.7257	−	7.92451i	1.16419	−	0.672148i	0.952306	+	0.305146i	$0.0987052\pi$
$140$	−0.440205	+	1.71088i	−0.0372041	+	0.144596i
$141$	−0.402752	−	1.50309i	−0.0339178	−	0.126583i
$142$	−8.25125	+	8.25125i	−0.692430	+	0.692430i
$143$	−16.1716	−	7.96282i	−1.35234	−	0.665884i
$144$		−	11.4823i		−	0.956862i
$145$	−10.7949	−	2.77749i	−0.896467	−	0.230658i
$146$	−5.02393	+	8.70170i	−0.415783	+	0.720158i
$147$	0.174178	+	0.0466709i	0.0143660	+	0.00384935i
$148$	−0.174002			−0.0143029
$149$	−1.39120	−	0.372772i	−0.113972	−	0.0305387i	0.201382	−	0.979513i	$-0.435457\pi$
$149$	−1.39120	−	0.372772i	−0.113972	−	0.0305387i	−0.315354	+	0.948974i	$0.602123\pi$
$150$	1.42738	+	4.93174i	0.116545	+	0.402675i
$151$	13.9253	−	13.9253i	1.13322	−	1.13322i	0.143585	−	0.989638i	$-0.454137\pi$
$151$	13.9253	−	13.9253i	1.13322	−	1.13322i	0.989638	−	0.143585i	$-0.0458631\pi$
$152$	−1.87000	+	6.97895i	−0.151677	+	0.566068i
$153$	0.201045	−	0.0538699i	0.0162536	−	0.00435513i
$154$	19.0225	−	5.09706i	1.53288	−	0.410733i
$155$	6.39322	+	3.60667i	0.513516	+	0.289695i
$156$	−0.0490117	−	0.740926i	−0.00392408	−	0.0593215i
$157$	4.54644	+	4.54644i	0.362845	+	0.362845i	0.864859	−	0.502014i	$-0.167408\pi$
$157$	4.54644	+	4.54644i	0.362845	+	0.362845i	−0.502014	+	0.864859i	$0.667408\pi$
$158$	−4.33444	+	7.50746i	−0.344829	+	0.597262i
$159$	5.55661	+	3.20811i	0.440668	+	0.254420i
$160$	−2.67362	+	2.72744i	−0.211368	+	0.215623i
$161$	7.44495	+	7.44495i	0.586744	+	0.586744i
$162$	6.69363	−	3.86457i	0.525901	−	0.303629i
$163$	11.3759	−	6.56789i	0.891031	−	0.514437i	0.0167516	−	0.999860i	$-0.494668\pi$
$163$	11.3759	−	6.56789i	0.891031	−	0.514437i	0.874280	+	0.485423i	$0.161334\pi$
$164$	2.24139	+	2.24139i	0.175023	+	0.175023i
$165$	5.29338	−	5.39994i	0.412089	−	0.420385i
$166$	4.87395	+	2.81398i	0.378292	+	0.218407i
$167$	−1.64258	+	2.84503i	−0.127107	+	0.220155i	−0.922554	−	0.385867i	$-0.873902\pi$
$167$	−1.64258	+	2.84503i	−0.127107	+	0.220155i	0.795448	+	0.606022i	$0.207236\pi$
$168$	−3.19454	−	3.19454i	−0.246464	−	0.246464i
$169$	−1.71239	−	12.8867i	−0.131722	−	0.991287i
$170$	−0.242028	−	0.136538i	−0.0185627	−	0.0104720i
$171$	−6.89371	+	1.84716i	−0.527175	+	0.141256i
$172$	0.0402263	−	0.0107786i	0.00306722	−	0.000821860i
$173$	−1.09689	+	4.09367i	−0.0833953	+	0.311236i	−0.995005	−	0.0998202i	$-0.968173\pi$
$173$	−1.09689	+	4.09367i	−0.0833953	+	0.311236i	0.911610	+	0.411056i	$0.134840\pi$
$174$	−3.61940	+	3.61940i	−0.274386	+	0.274386i
$175$	−11.3632	−	6.26200i	−0.858979	−	0.473363i
$176$	21.8093	+	5.84377i	1.64393	+	0.440491i
$177$	−1.81403			−0.136351
$178$	−26.2362	−	7.02997i	−1.96649	−	0.526919i
$179$	−6.98083	+	12.0912i	−0.521772	+	0.903735i	0.477907	+	0.878410i	$0.341395\pi$
$179$	−6.98083	+	12.0912i	−0.521772	+	0.903735i	−0.999679	+	0.0253252i	$0.991938\pi$
$180$	−1.67632	−	0.431313i	−0.124946	−	0.0321481i
$181$			8.64775i			0.642782i	0.946947	+	0.321391i	$0.104150\pi$
$181$			8.64775i			0.642782i	−0.946947	+	0.321391i	$0.895850\pi$
$182$	10.6839	+	9.35812i	0.791942	+	0.693670i
$183$	2.62334	−	2.62334i	0.193923	−	0.193923i
$184$	2.70301	+	10.0878i	0.199268	+	0.743680i
$185$	0.318432	−	1.23761i	0.0234116	−	0.0909906i
$186$	2.91920	−	1.68540i	0.214046	−	0.123579i
$187$			0.409276i			0.0299292i
$188$	−0.350216	−	0.606592i	−0.0255421	−	0.0442402i
$189$	2.51785	−	9.39675i	0.183147	−	0.683513i
$190$	8.29899	+	4.68179i	0.602072	+	0.339653i
$191$	−8.45647	−	14.6470i	−0.611889	−	1.05982i	−0.990922	−	0.134439i	$-0.957077\pi$
$191$	−8.45647	−	14.6470i	−0.611889	−	1.05982i	0.379033	−	0.925383i	$-0.376257\pi$
$192$	−1.12737	−	4.20740i	−0.0813609	−	0.303643i
$193$	7.40936	+	4.27780i	0.533338	+	0.307923i	0.742375	−	0.669985i	$-0.233700\pi$
$193$	7.40936	+	4.27780i	0.533338	+	0.307923i	−0.209037	+	0.977908i	$0.567033\pi$
$194$	8.15169			0.585257
$195$	5.35959	+	1.00733i	0.383808	+	0.0721364i
$196$	0.0811660			0.00579757
$197$	−6.63101	−	3.82842i	−0.472440	−	0.272764i	0.244820	−	0.969568i	$-0.421271\pi$
$197$	−6.63101	−	3.82842i	−0.472440	−	0.272764i	−0.717261	+	0.696805i	$0.754604\pi$
$198$	4.99409	+	18.6382i	0.354915	+	1.32456i
$199$	7.66380	+	13.2741i	0.543272	+	0.940975i	0.998713	+	0.0507092i	$0.0161482\pi$
$199$	7.66380	+	13.2741i	0.543272	+	0.940975i	−0.455441	+	0.890266i	$0.650519\pi$
$200$	−6.65558	−	11.0149i	−0.470621	−	0.778869i
$201$	2.76378	−	10.3146i	0.194942	−	0.727533i
$202$	1.90576	+	3.30088i	0.134089	+	0.232249i
$203$		−	12.9351i		−	0.907868i
$204$	−0.0146008	+	0.00842979i	−0.00102226	+	0.000590203i
$205$	−20.0440	+	11.8402i	−1.39993	+	0.826959i
$206$	2.62118	+	9.78238i	0.182626	+	0.681570i
$207$	−7.29455	+	7.29455i	−0.507006	+	0.507006i
$208$	5.24346	+	15.4162i	0.363569	+	1.06892i
$209$		−	14.0338i		−	0.970739i
$210$	−5.12985	+	3.03027i	−0.353993	+	0.209109i
$211$	−9.91788	+	17.1783i	−0.682775	+	1.18260i	0.291355	+	0.956615i	$0.405894\pi$
$211$	−9.91788	+	17.1783i	−0.682775	+	1.18260i	−0.974130	+	0.225986i	$0.927440\pi$
$212$	2.78964	+	0.747481i	0.191593	+	0.0513372i
$213$	−5.19952			−0.356265
$214$	−5.32071	−	1.42568i	−0.363716	−	0.0974575i
$215$	0.00304773	+	0.305838i	0.000207854	+	0.0208580i
$216$	6.82328	−	6.82328i	0.464265	−	0.464265i
$217$	−2.20469	+	8.22803i	−0.149664	+	0.558555i
$218$	3.28739	−	0.880853i	0.222650	−	0.0596589i
$219$	−4.32460	+	1.15877i	−0.292229	+	0.0783025i
$220$	1.67236	−	2.96445i	0.112751	−	0.199863i
$221$	−0.245323	+	0.164134i	−0.0165022	+	0.0110408i
$222$	−0.414955	−	0.414955i	−0.0278499	−	0.0278499i
$223$	9.48653	−	16.4311i	0.635265	−	1.10031i	−0.351194	−	0.936303i	$-0.614224\pi$
$223$	9.48653	−	16.4311i	0.635265	−	1.10031i	0.986459	−	0.164008i	$-0.0524424\pi$
$224$	−3.83838	−	2.21609i	−0.256463	−	0.148069i
$225$	6.13550	−	11.1337i	0.409033	−	0.742244i
$226$	−6.14771	−	6.14771i	−0.408939	−	0.408939i
$227$	23.3469	−	13.4794i	1.54959	−	0.894656i	0.551417	−	0.834230i	$-0.314087\pi$
$227$	23.3469	−	13.4794i	1.54959	−	0.894656i	0.998173	−	0.0604265i	$-0.0192461\pi$
$228$	0.500652	−	0.289052i	0.0331565	−	0.0191429i
$229$	−11.1801	−	11.1801i	−0.738799	−	0.738799i	0.233547	−	0.972346i	$-0.424967\pi$
$229$	−11.1801	−	11.1801i	−0.738799	−	0.738799i	−0.972346	+	0.233547i	$0.924967\pi$
$230$	13.7723	−	0.137244i	0.908121	−	0.00904959i
$231$	7.59946	+	4.38755i	0.500008	+	0.288680i
$232$	6.41527	−	11.1116i	0.421183	−	0.729510i
$233$	6.75797	+	6.75797i	0.442729	+	0.442729i	0.892928	−	0.450199i	$-0.148647\pi$
$233$	6.75797	+	6.75797i	0.442729	+	0.442729i	−0.450199	+	0.892928i	$0.648647\pi$
$234$	−9.16908	+	10.4681i	−0.599401	+	0.684318i
$235$	4.95535	−	1.38085i	0.323251	−	0.0900767i
$236$	−0.788702	+	0.211332i	−0.0513401	+	0.0137565i
$237$	−3.73108	+	0.999740i	−0.242360	+	0.0649401i
$238$	0.0834631	−	0.311489i	0.00541011	−	0.0201908i
$239$	1.98766	−	1.98766i	0.128571	−	0.128571i	−0.639893	−	0.768464i	$-0.721021\pi$
$239$	1.98766	−	1.98766i	0.128571	−	0.128571i	0.768464	+	0.639893i	$0.221021\pi$
$240$	−6.83051	+	0.0680672i	−0.440907	+	0.00439372i
$241$	−2.65141	−	0.710443i	−0.170792	−	0.0457637i	0.172409	−	0.985025i	$-0.444845\pi$
$241$	−2.65141	−	0.710443i	−0.170792	−	0.0457637i	−0.343202	+	0.939262i	$0.611511\pi$
$242$	−21.2441			−1.36562
$243$	14.1904	+	3.80231i	0.910315	+	0.243918i
$244$	0.834956	−	1.44619i	0.0534526	−	0.0925826i
$245$	−0.148538	+	0.577300i	−0.00948972	+	0.0368824i
$246$			10.6904i			0.681595i
$247$	8.41197	−	5.62804i	0.535241	−	0.358104i
$248$	−5.97463	+	5.97463i	−0.379389	+	0.379389i
$249$	0.649045	+	2.42227i	0.0411316	+	0.153505i
$250$	−16.2553	+	4.88080i	−1.02808	+	0.308689i
$251$	−2.45414	+	1.41690i	−0.154904	+	0.0894337i	−0.575448	−	0.817838i	$-0.695172\pi$
$251$	−2.45414	+	1.41690i	−0.154904	+	0.0894337i	0.420545	+	0.907272i	$0.361839\pi$
$252$		−	2.00868i		−	0.126535i
$253$	−10.1426	−	17.5675i	−0.637661	−	1.10446i
$254$	−0.320005	+	1.19428i	−0.0200789	+	0.0749355i
$255$	−0.0332374	−	0.119277i	−0.00208141	−	0.00746939i
$256$	−3.57321	−	6.18898i	−0.223325	−	0.386811i
$257$	−5.19242	−	19.3784i	−0.323894	−	1.20879i	−0.915419	−	0.402502i	$-0.868141\pi$
$257$	−5.19242	−	19.3784i	−0.323894	−	1.20879i	0.591525	−	0.806287i	$-0.298526\pi$
$258$	0.121635	+	0.0702258i	0.00757265	+	0.00437207i
$259$	1.48298			0.0921478
$260$	2.44759	−	0.186420i	0.151793	−	0.0115613i
$261$	12.6738			0.784490
$262$	−21.1743	−	12.2250i	−1.30815	−	0.755264i
$263$	2.43854	+	9.10077i	0.150367	+	0.561177i	0.999458	+	0.0329302i	$0.0104839\pi$
$263$	2.43854	+	9.10077i	0.150367	+	0.561177i	−0.849091	+	0.528247i	$0.822849\pi$
$264$	4.35207	+	7.53801i	0.267851	+	0.463932i
$265$	−10.4217	+	18.4736i	−0.640199	+	1.13482i
$266$	−2.86189	+	10.6807i	−0.175474	+	0.654878i
$267$	−6.05140	−	10.4813i	−0.370340	−	0.641447i
$268$		−	4.80653i		−	0.293605i
$269$	−2.78417	+	1.60744i	−0.169754	+	0.0980075i	−0.582470	−	0.812852i	$-0.697914\pi$
$269$	−2.78417	+	1.60744i	−0.169754	+	0.0980075i	0.412716	+	0.910860i	$0.364580\pi$
$270$	−6.47242	−	10.9569i	−0.393899	−	0.666818i
$271$	−3.93065	−	14.6694i	−0.238770	−	0.891102i	−0.976413	−	0.215911i	$-0.930728\pi$
$271$	−3.93065	−	14.6694i	−0.238770	−	0.891102i	0.737643	−	0.675191i	$-0.235939\pi$
$272$	0.261431	−	0.261431i	0.0158516	−	0.0158516i
$273$	0.417715	+	6.31473i	0.0252812	+	0.382185i
$274$			29.2033i			1.76424i
$275$	18.0244	+	17.3199i	1.08691	+	1.04443i
$276$	0.417811	−	0.723671i	0.0251493	−	0.0435598i
$277$	10.3015	+	2.76028i	0.618956	+	0.165849i	0.554653	−	0.832082i	$-0.312851\pi$
$277$	10.3015	+	2.76028i	0.618956	+	0.165849i	0.0643031	+	0.997930i	$0.479518\pi$
$278$	24.0595			1.44300
$279$	−8.06181	−	2.16016i	−0.482648	−	0.129325i
$280$	10.4546	−	10.6651i	0.624783	−	0.637361i
$281$	−12.7630	+	12.7630i	−0.761379	+	0.761379i	−0.976572	−	0.215193i	$-0.930962\pi$
$281$	−12.7630	+	12.7630i	−0.761379	+	0.761379i	0.215193	+	0.976572i	$0.430962\pi$
$282$	0.611396	−	2.28176i	0.0364081	−	0.135877i
$283$	−5.56143	+	1.49018i	−0.330592	+	0.0885820i	−0.420297	−	0.907386i	$-0.638074\pi$
$283$	−5.56143	+	1.49018i	−0.330592	+	0.0885820i	0.0897050	+	0.995968i	$0.471408\pi$
$284$	−2.26064	+	0.605736i	−0.134144	+	0.0359438i
$285$	1.13969	+	4.08991i	0.0675093	+	0.242266i
$286$	−15.2163	−	22.7431i	−0.899757	−	1.34483i
$287$	−19.1028	−	19.1028i	−1.12760	−	1.12760i
$288$	2.17132	−	3.76084i	0.127946	−	0.221610i
$289$	−14.7166	−	8.49665i	−0.865684	−	0.499803i
$290$	−12.0835	−	11.8450i	−0.709568	−	0.695565i
$291$	2.56839	+	2.56839i	0.150562	+	0.150562i
$292$	−1.74525	+	1.00762i	−0.102133	+	0.0589664i
$293$	2.76788	−	1.59804i	0.161701	−	0.0933583i	−0.416966	−	0.908922i	$-0.636906\pi$
$293$	2.76788	−	1.59804i	0.161701	−	0.0933583i	0.578667	+	0.815564i	$0.303573\pi$
$294$	0.193562	+	0.193562i	0.0112888	+	0.0112888i
$295$	−0.0597558	−	5.99646i	−0.00347912	−	0.349127i
$296$	1.27391	+	0.735493i	0.0740446	+	0.0427497i
$297$	−9.37145	+	16.2318i	−0.543787	+	0.941867i
$298$	−1.54603	−	1.54603i	−0.0895590	−	0.0895590i
$299$	6.46257	−	13.1247i	0.373740	−	0.759023i
$300$	−0.246638	+	0.999751i	−0.0142396	+	0.0577207i
$301$	−0.342839	+	0.0918633i	−0.0197609	+	0.00529491i
$302$	28.8767	−	7.73749i	1.66167	−	0.445243i
$303$	−0.439566	+	1.64048i	−0.0252524	+	0.0942432i
$304$	−8.96429	+	8.96429i	−0.514137	+	0.514137i
$305$	8.75812	+	8.58529i	0.501488	+	0.491592i
$306$	0.305196	+	0.0817771i	0.0174469	+	0.00467488i
$307$	24.2740			1.38539			0.692695	−	0.721231i	$-0.256423\pi$
$307$	24.2740			1.38539			0.692695	+	0.721231i	$0.256423\pi$
$308$	3.81522	+	1.02229i	0.217393	+	0.0582501i
$309$	−2.25631	+	3.90804i	−0.128357	+	0.222321i
$310$	5.66741	+	9.59417i	0.321887	+	0.544912i
$311$		−	16.9053i		−	0.958614i	−0.877647	−	0.479307i	$-0.840888\pi$
$311$		−	16.9053i		−	0.958614i	0.877647	−	0.479307i	$-0.159112\pi$
$312$	−2.77301	+	5.63167i	−0.156991	+	0.318830i
$313$	−8.40997	+	8.40997i	−0.475359	+	0.475359i	−0.903644	−	0.428285i	$-0.859118\pi$
$313$	−8.40997	+	8.40997i	−0.475359	+	0.475359i	0.428285	+	0.903644i	$0.359118\pi$
$314$	2.52620	+	9.42790i	0.142562	+	0.532047i
$315$	14.2869	+	3.67597i	0.804975	+	0.207118i
$316$	−1.50573	+	0.869331i	−0.0847037	+	0.0489037i
$317$			11.9484i			0.671087i	0.942025	+	0.335543i	$0.108920\pi$
$317$			11.9484i			0.671087i	−0.942025	+	0.335543i	$0.891080\pi$
$318$	4.87006	+	8.43520i	0.273100	+	0.473022i
$319$	−6.45015	+	24.0723i	−0.361139	+	1.34779i
$320$	13.8708	−	3.86523i	0.775403	−	0.216073i
$321$	−1.22723	−	2.12562i	−0.0684970	−	0.118640i
$322$	4.13674	+	15.4385i	0.230531	+	0.860355i
$323$	−0.199013	−	0.114900i	−0.0110734	−	0.00639321i
$324$	1.55018			0.0861214
$325$	−3.15328	+	17.7498i	−0.174912	+	0.984584i
$326$	19.9407			1.10442
$327$	1.31331	+	0.758238i	0.0726260	+	0.0419307i
$328$	−6.93559	−	25.8840i	−0.382954	−	1.42920i
$329$	2.98480	+	5.16983i	0.164558	+	0.285022i
$330$	11.0577	−	3.08133i	0.608707	−	0.169621i
$331$	−5.55136	+	20.7179i	−0.305130	+	1.13876i	0.627703	+	0.778453i	$0.283995\pi$
$331$	−5.55136	+	20.7179i	−0.305130	+	1.13876i	−0.932833	+	0.360308i	$0.882671\pi$
$332$	0.564382	+	0.977538i	0.0309745	+	0.0536494i
$333$			1.45302i			0.0796250i
$334$	−4.31889	+	2.49351i	−0.236319	+	0.136439i
$335$	34.1868	+	8.79617i	1.86783	+	0.480586i
$336$	−2.05165	−	7.65687i	−0.111927	−	0.417716i
$337$	14.1264	−	14.1264i	0.769514	−	0.769514i	−0.208507	−	0.978021i	$-0.566860\pi$
$337$	14.1264	−	14.1264i	0.769514	−	0.769514i	0.978021	+	0.208507i	$0.0668604\pi$
$338$	7.53011	−	18.2415i	0.409584	−	0.992206i
$339$		−	3.87397i		−	0.210405i
$340$	−0.0283465	−	0.0479868i	−0.00153730	−	0.00260245i
$341$	8.20588	−	14.2130i	0.444373	−	0.769677i
$342$	−10.4650	−	2.80408i	−0.565881	−	0.151627i
$343$	−18.8559			−1.01812
$344$	−0.340067	−	0.0911205i	−0.0183352	−	0.00491289i
$345$	4.38256	+	4.29607i	0.235949	+	0.231293i
$346$	−4.54924	+	4.54924i	−0.244569	+	0.244569i
$347$	−6.37467	+	23.7906i	−0.342210	+	1.27715i	0.553627	+	0.832765i	$0.313243\pi$
$347$	−6.37467	+	23.7906i	−0.342210	+	1.27715i	−0.895837	+	0.444382i	$0.853423\pi$
$348$	−0.991626	+	0.265705i	−0.0531567	+	0.0142433i
$349$	26.3190	−	7.05214i	1.40882	−	0.377493i	0.527317	−	0.849669i	$-0.323198\pi$
$349$	26.3190	−	7.05214i	1.40882	−	0.377493i	0.881504	+	0.472176i	$0.156531\pi$
$350$	−10.1858	−	16.8574i	−0.544456	−	0.901065i
$351$	−13.4878	+	0.892205i	−0.719923	+	0.0476224i
$352$	6.03818	+	6.03818i	0.321836	+	0.321836i
$353$	4.39963	−	7.62038i	0.234169	−	0.405592i	−0.724862	−	0.688894i	$-0.758097\pi$
$353$	4.39963	−	7.62038i	0.234169	−	0.405592i	0.959031	+	0.283302i	$0.0914299\pi$
$354$	−2.38485	−	1.37689i	−0.126753	−	0.0731810i
$355$	−0.171277	−	17.1875i	−0.00909042	−	0.912219i
$356$	−3.85208	−	3.85208i	−0.204160	−	0.204160i
$357$	0.124439	−	0.0718451i	0.00658603	−	0.00380244i
$358$	−18.3549	+	10.5972i	−0.970089	+	0.560081i
$359$	11.1256	+	11.1256i	0.587186	+	0.587186i	0.936868	−	0.349683i	$-0.113711\pi$
$359$	11.1256	+	11.1256i	0.587186	+	0.587186i	−0.349683	+	0.936868i	$0.613711\pi$
$360$	10.4496	+	10.2434i	0.550744	+	0.539876i
$361$	−9.63047	−	5.56015i	−0.506867	−	0.292640i
$362$	−6.56385	+	11.3689i	−0.344988	+	0.597537i
$363$	−6.69346	−	6.69346i	−0.351316	−	0.351316i
$364$	0.917270	+	2.69684i	0.0480780	+	0.141353i
$365$	−3.97289	−	14.2572i	−0.207951	−	0.746256i
$366$	5.43999	−	1.45764i	0.284353	−	0.0761921i
$367$	−10.6044	+	2.84144i	−0.553545	+	0.148322i	−0.524739	−	0.851263i	$-0.675837\pi$
$367$	−10.6044	+	2.84144i	−0.553545	+	0.148322i	−0.0288057	+	0.999585i	$0.509170\pi$
$368$	−4.74276	+	17.7002i	−0.247234	+	0.922689i
$369$	18.7169	−	18.7169i	0.974365	−	0.974365i
$370$	1.35800	−	1.38534i	0.0705993	−	0.0720205i
$371$	−23.7754	−	6.37060i	−1.23436	−	0.330745i
$372$	0.676060			0.0350521
$373$	−10.2193	−	2.73825i	−0.529135	−	0.141781i	−0.0156462	−	0.999878i	$-0.504981\pi$
$373$	−10.2193	−	2.73825i	−0.529135	−	0.141781i	−0.513489	+	0.858096i	$0.671647\pi$
$374$	−0.310650	+	0.538062i	−0.0160633	+	0.0278225i
$375$	−6.65946	−	3.58383i	−0.343893	−	0.185068i
$376$			5.92134i			0.305370i
$377$	−17.0158	+	5.78755i	−0.876361	+	0.298074i
$378$	10.4425	−	10.4425i	0.537104	−	0.537104i
$379$	−2.53694	−	9.46800i	−0.130314	−	0.486338i	0.869659	−	0.493652i	$-0.164338\pi$
$379$	−2.53694	−	9.46800i	−0.130314	−	0.486338i	−0.999973	+	0.00731411i	$0.997672\pi$
$380$	0.971981	+	1.64543i	0.0498616	+	0.0844090i
$381$	−0.477111	+	0.275460i	−0.0244431	+	0.0141123i
$382$		−	25.6746i		−	1.31363i
$383$	13.0283	+	22.5658i	0.665718	+	1.15306i	0.979090	+	0.203426i	$0.0652078\pi$
$383$	13.0283	+	22.5658i	0.665718	+	1.15306i	−0.313373	+	0.949630i	$0.601459\pi$
$384$	2.30945	−	8.61899i	0.117854	−	0.439836i
$385$	−14.2531	+	25.2653i	−0.726407	+	1.28764i
$386$	6.49390	+	11.2478i	0.330531	+	0.572496i
$387$	−0.0900076	−	0.335913i	−0.00457534	−	0.0170754i
$388$	1.41589	+	0.817467i	0.0718812	+	0.0415006i
$389$	−32.4888			−1.64725			−0.823623	−	0.567138i	$-0.808050\pi$
$389$	−32.4888			−1.64725			−0.823623	+	0.567138i	$0.808050\pi$
$390$	6.28149	+	5.39236i	0.318076	+	0.273053i
$391$	−0.332166			−0.0167983
$392$	−0.594236	−	0.343082i	−0.0300134	−	0.0173283i
$393$	−2.81971	−	10.5233i	−0.142235	−	0.530830i
$394$	−5.81172	−	10.0662i	−0.292790	−	0.507127i
$395$	−3.42764	−	12.3005i	−0.172463	−	0.618906i
$396$	−1.00163	+	3.73815i	−0.0503340	+	0.187849i
$397$	−12.0927	−	20.9451i	−0.606914	−	1.05121i	−0.991746	−	0.128219i	$-0.959074\pi$
$397$	−12.0927	−	20.9451i	−0.606914	−	1.05121i	0.384832	−	0.922987i	$-0.374259\pi$
$398$			23.2680i			1.16632i
$399$	−4.26694	+	2.46352i	−0.213614	+	0.123330i
$400$	−0.450006	−	22.5767i	−0.0225003	−	1.12883i
$401$	−8.49918	−	31.7194i	−0.424429	−	1.58399i	−0.765167	−	0.643832i	$-0.777343\pi$
$401$	−8.49918	−	31.7194i	−0.424429	−	1.58399i	0.340738	−	0.940158i	$-0.389323\pi$
$402$	11.4624	−	11.4624i	0.571695	−	0.571695i
$403$	11.8102	−	0.781237i	0.588309	−	0.0389162i
$404$			0.764454i			0.0380330i
$405$	−2.83691	+	11.0258i	−0.140967	+	0.547878i
$406$	9.81806	−	17.0054i	0.487262	−	0.843963i
$407$	−2.75983	−	0.739493i	−0.136799	−	0.0366553i
$408$	0.142528			0.00705620
$409$	13.4843	+	3.61312i	0.666758	+	0.178657i	0.576294	−	0.817243i	$-0.304498\pi$
$409$	13.4843	+	3.61312i	0.666758	+	0.178657i	0.0904639	+	0.995900i	$0.471165\pi$
$410$	−35.3381	+	0.352151i	−1.74523	+	0.0173915i
$411$	−9.20122	+	9.20122i	−0.453863	+	0.453863i
$412$	−0.525714	+	1.96199i	−0.0259001	+	0.0966603i
$413$	6.72192	−	1.80113i	0.330764	−	0.0886279i
$414$	−15.1266	+	4.05317i	−0.743434	+	0.199203i
$415$	−7.98567	+	2.22527i	−0.392001	+	0.109234i
$416$	−1.19781	+	6.04084i	−0.0587275	+	0.296177i
$417$	7.58055	+	7.58055i	0.371221	+	0.371221i
$418$	10.6520	−	18.4498i	0.521006	−	0.902408i
$419$	−1.92240	−	1.10990i	−0.0939155	−	0.0542221i	0.452307	−	0.891862i	$-0.350601\pi$
$419$	−1.92240	−	1.10990i	−0.0939155	−	0.0542221i	−0.546222	+	0.837640i	$0.683935\pi$
$420$	−1.19490	+	0.0119074i	−0.0583052	+	0.000581022i
$421$	24.4795	+	24.4795i	1.19306	+	1.19306i	0.976204	+	0.216853i	$0.0695792\pi$
$421$	24.4795	+	24.4795i	1.19306	+	1.19306i	0.216853	+	0.976204i	$0.430421\pi$
$422$	−26.0774	+	15.0558i	−1.26943	+	0.732905i
$423$	−5.06540	+	2.92451i	−0.246288	+	0.142194i
$424$	−17.2641	−	17.2641i	−0.838417	−	0.838417i
$425$	0.393186	−	0.113799i	0.0190723	−	0.00552004i
$426$	−6.83564	−	3.94656i	−0.331188	−	0.191211i
$427$	−7.11613	+	12.3255i	−0.344374	+	0.596472i
$428$	−0.781202	−	0.781202i	−0.0377608	−	0.0377608i
$429$	2.37150	−	11.9600i	0.114497	−	0.577435i
$430$	−0.228132	+	0.404389i	−0.0110015	+	0.0195014i
$431$	1.59621	−	0.427704i	0.0768868	−	0.0206018i	−0.220171	−	0.975461i	$-0.570661\pi$
$431$	1.59621	−	0.427704i	0.0768868	−	0.0206018i	0.297057	+	0.954860i	$0.403995\pi$
$432$	16.3545	−	4.38216i	0.786854	−	0.210837i
$433$	−3.83465	+	14.3111i	−0.184281	+	0.687748i	0.810502	+	0.585736i	$0.199195\pi$
$433$	−3.83465	+	14.3111i	−0.184281	+	0.687748i	−0.994783	+	0.102012i	$0.967472\pi$
$434$	−9.14370	+	9.14370i	−0.438912	+	0.438912i
$435$	−0.0751302	−	7.53928i	−0.00360222	−	0.361481i
$436$	0.659331	+	0.176667i	0.0315762	+	0.00846083i
$437$	11.3897			0.544845
$438$	−6.56494	−	1.75907i	−0.313685	−	0.0840516i
$439$	10.9363	−	18.9422i	0.521959	−	0.904060i	−0.477714	−	0.878515i	$-0.658535\pi$
$439$	10.9363	−	18.9422i	0.521959	−	0.904060i	0.999674	−	0.0255448i	$-0.00813206\pi$
$440$	−24.7743	+	14.6345i	−1.18107	+	0.697673i
$441$		−	0.677783i		−	0.0322754i
$442$	−0.447100	+	0.0295753i	−0.0212664	+	0.00140675i
$443$	−6.14972	+	6.14972i	−0.292182	+	0.292182i	−0.837942	−	0.545760i	$-0.816241\pi$
$443$	−6.14972	+	6.14972i	−0.292182	+	0.292182i	0.545760	+	0.837942i	$0.316241\pi$
$444$	−0.0304624	−	0.113687i	−0.00144568	−	0.00539536i
$445$	34.4477	−	20.3488i	1.63298	−	0.964624i
$446$	24.9432	−	14.4010i	1.18110	−	0.681907i
$447$		−	0.974228i		−	0.0460794i
$448$	8.35496	+	14.4712i	0.394735	+	0.683701i
$449$	1.20994	−	4.51557i	0.0571008	−	0.213103i	−0.931481	−	0.363791i	$-0.881482\pi$
$449$	1.20994	−	4.51557i	0.0571008	−	0.213103i	0.988581	+	0.150688i	$0.0481489\pi$
$450$	16.5168	−	9.98008i	0.778612	−	0.470465i
$451$	26.0247	+	45.0761i	1.22546	+	2.12255i
$452$	−0.451312	−	1.68432i	−0.0212279	−	0.0792237i
$453$	11.5362	+	6.66043i	0.542018	+	0.312934i
$454$	40.9246			1.92069
$455$	−20.8602	+	1.58881i	−0.977941	+	0.0744845i
$456$	−4.88720			−0.228864
$457$	26.0120	+	15.0180i	1.21679	+	0.702514i	0.964230	−	0.265067i	$-0.0853941\pi$
$457$	26.0120	+	15.0180i	1.21679	+	0.702514i	0.252560	+	0.967581i	$0.418727\pi$
$458$	−6.21213	−	23.1840i	−0.290274	−	1.08332i
$459$	0.153455	+	0.265792i	0.00716268	+	0.0124061i
$460$	2.40593	+	1.35728i	0.112177	+	0.0632834i
$461$	0.680045	−	2.53796i	0.0316729	−	0.118205i	−0.948280	−	0.317436i	$-0.897178\pi$
$461$	0.680045	−	2.53796i	0.0316729	−	0.118205i	0.979952	+	0.199232i	$0.0638447\pi$
$462$	6.66050	+	11.5363i	0.309875	+	0.536719i
$463$		−	25.1475i		−	1.16870i	−0.811500	−	0.584352i	$-0.801349\pi$
$463$		−	25.1475i		−	1.16870i	0.811500	−	0.584352i	$-0.198651\pi$
$464$	19.4966	−	11.2564i	0.905109	−	0.522565i
$465$	−1.23722	+	4.80854i	−0.0573748	+	0.222991i
$466$	3.75502	+	14.0139i	0.173948	+	0.649183i
$467$	−14.9907	+	14.9907i	−0.693688	+	0.693688i	−0.963041	−	0.269354i	$-0.913190\pi$
$467$	−14.9907	+	14.9907i	−0.693688	+	0.693688i	0.269354	+	0.963041i	$0.413190\pi$
$468$	−2.64236	+	0.898740i	−0.122143	+	0.0415443i
$469$			40.9648i			1.89158i
$470$	7.56273	+	1.94587i	0.348843	+	0.0897562i
$471$	−2.17455	+	3.76643i	−0.100198	+	0.173548i
$472$	6.66756	+	1.78657i	0.306899	+	0.0822335i
$473$	0.683832			0.0314426
$474$	−5.66395	−	1.51765i	−0.260154	−	0.0697081i
$475$	−13.4821	+	3.90208i	−0.618600	+	0.179040i
$476$	0.0457337	−	0.0457337i	0.00209620	−	0.00209620i
$477$	6.24190	−	23.2951i	0.285797	−	1.06661i
$478$	4.12178	−	1.10443i	0.188526	−	0.0505154i
$479$	2.21157	−	0.592587i	0.101049	−	0.0270760i	−0.207940	−	0.978142i	$-0.566676\pi$
$479$	2.21157	−	0.592587i	0.101049	−	0.0270760i	0.308989	+	0.951066i	$0.400009\pi$
$480$	−2.25009	−	1.26936i	−0.102702	−	0.0579382i
$481$	−0.663527	−	1.95082i	−0.0302542	−	0.0889498i
$482$	−2.94648	−	2.94648i	−0.134208	−	0.134208i
$483$	−3.56090	+	6.16767i	−0.162027	+	0.280639i
$484$	−3.68995	−	2.13039i	−0.167725	−	0.0968361i
$485$	−8.40546	+	8.57467i	−0.381672	+	0.389356i
$486$	15.7696	+	15.7696i	0.715324	+	0.715324i
$487$	−4.82067	+	2.78321i	−0.218445	+	0.126119i	−0.605230	−	0.796050i	$-0.706919\pi$
$487$	−4.82067	+	2.78321i	−0.218445	+	0.126119i	0.386785	+	0.922170i	$0.373586\pi$
$488$	−12.2258	+	7.05859i	−0.553437	+	0.319527i
$489$	6.28282	+	6.28282i	0.284119	+	0.284119i
$490$	−0.633462	+	0.646214i	−0.0286169	+	0.0291930i
$491$	5.29139	+	3.05498i	0.238797	+	0.137869i	0.614624	−	0.788820i	$-0.289308\pi$
$491$	5.29139	+	3.05498i	0.238797	+	0.137869i	−0.375827	+	0.926690i	$0.622641\pi$
$492$	−1.07205	+	1.85685i	−0.0483319	+	0.0837133i
$493$	0.288558	+	0.288558i	0.0129960	+	0.0129960i
$494$	15.3307	−	1.01412i	0.689763	−	0.0456273i
$495$	−24.7549	−	13.9652i	−1.11265	−	0.627689i
$496$	−14.3204	+	3.83713i	−0.643004	+	0.172292i
$497$	19.2669	−	5.16254i	0.864237	−	0.231572i
$498$	−0.985281	+	3.67712i	−0.0441515	+	0.164776i
$499$	−6.22738	+	6.22738i	−0.278776	+	0.278776i	−0.832620	−	0.553844i	$-0.813160\pi$
$499$	−6.22738	+	6.22738i	−0.278776	+	0.278776i	0.553844	+	0.832620i	$0.313160\pi$
$500$	−3.31290	−	0.782353i	−0.148157	−	0.0349879i
$501$	−2.14642	−	0.575130i	−0.0958948	−	0.0256949i
$502$	−4.30183			−0.192000
$503$	−3.55090	−	0.951461i	−0.158327	−	0.0424236i	0.178785	−	0.983888i	$-0.442783\pi$
$503$	−3.55090	−	0.951461i	−0.158327	−	0.0424236i	−0.337112	+	0.941465i	$0.609450\pi$
$504$	−8.49051	+	14.7060i	−0.378198	+	0.655057i
$505$	−5.43725	−	1.39899i	−0.241954	−	0.0622542i
$506$		−	30.7939i		−	1.36896i
$507$	8.11998	−	3.37489i	0.360621	−	0.149884i
$508$	−0.175347	+	0.175347i	−0.00777976	+	0.00777976i
$509$	−2.90050	−	10.8248i	−0.128563	−	0.479802i	0.871379	−	0.490610i	$-0.163226\pi$
$509$	−2.90050	−	10.8248i	−0.128563	−	0.479802i	−0.999942	+	0.0108085i	$0.996559\pi$
$510$	0.0468376	−	0.182037i	0.00207400	−	0.00806073i
$511$	14.8743	−	8.58768i	0.658000	−	0.379897i
$512$			15.5347i			0.686544i
$513$	−5.26188	−	9.11384i	−0.232318	−	0.402386i
$514$	7.88233	−	29.4173i	0.347675	−	1.29754i
$515$	−12.9927	−	7.32972i	−0.572529	−	0.322986i
$516$	0.0140848	+	0.0243955i	0.000620047	+	0.00107395i
$517$	−2.97677	−	11.1095i	−0.130918	−	0.488593i
$518$	1.94962	+	1.12561i	0.0856615	+	0.0494567i
$519$	−2.86670			−0.125834
$520$	−18.7074	−	8.98094i	−0.820372	−	0.393840i
$521$	35.9604			1.57545			0.787726	−	0.616026i	$-0.211258\pi$
$521$	35.9604			1.57545			0.787726	+	0.616026i	$0.211258\pi$
$522$	16.6618	+	9.61972i	0.729269	+	0.421044i
$523$	−2.17209	−	8.10636i	−0.0949790	−	0.354467i	0.902037	−	0.431658i	$-0.142071\pi$
$523$	−2.17209	−	8.10636i	−0.0949790	−	0.354467i	−0.997016	+	0.0771917i	$0.975405\pi$
$524$	−2.45189	−	4.24681i	−0.107112	−	0.185523i
$525$	2.10203	−	8.52064i	0.0917403	−	0.371871i
$526$	−3.70182	+	13.8154i	−0.161407	+	0.602380i
$527$	−0.134369	−	0.232734i	−0.00585322	−	0.0101381i
$528$			15.2725i			0.664651i
$529$	−5.66090	+	3.26832i	−0.246126	+	0.142101i
$530$	−27.7230	+	16.3763i	−1.20421	+	0.711343i
$531$	1.76475	+	6.58612i	0.0765835	+	0.285813i
$532$	−1.56818	+	1.56818i	−0.0679891	+	0.0679891i
$533$	−16.5822	+	33.6765i	−0.718253	+	1.45869i
$534$		−	18.3726i		−	0.795061i
$535$	6.98601	−	4.12673i	0.302031	−	0.178414i
$536$	−20.3168	+	35.1897i	−0.877552	+	1.51997i
$537$	−9.12209	−	2.44426i	−0.393647	−	0.105477i
$538$	−4.88034			−0.210407
$539$	1.28736	+	0.344948i	0.0554506	+	0.0148580i
$540$	−0.0254333	−	2.55222i	−0.00109447	−	0.109830i
$541$	4.13066	−	4.13066i	0.177591	−	0.177591i	−0.612714	−	0.790305i	$-0.709922\pi$
$541$	4.13066	−	4.13066i	0.177591	−	0.177591i	0.790305	+	0.612714i	$0.209922\pi$
$542$	5.96691	−	22.2688i	0.256301	−	0.956528i
$543$	−5.65016	+	1.51396i	−0.242471	+	0.0649700i
$544$	0.135064	−	0.0361903i	0.00579082	−	0.00155165i
$545$	−2.46317	+	4.36624i	−0.105511	+	0.187029i
$546$	−4.24387	+	8.61882i	−0.181621	+	0.368851i
$547$	−7.90229	−	7.90229i	−0.337877	−	0.337877i	0.517691	−	0.855568i	$-0.326792\pi$
$547$	−7.90229	−	7.90229i	−0.337877	−	0.337877i	−0.855568	+	0.517691i	$0.826792\pi$
$548$	−2.92856	+	5.07242i	−0.125102	+	0.216683i
$549$	−12.0765	−	6.97237i	−0.515413	−	0.297574i
$550$	10.5499	+	36.4509i	0.449848	+	1.55427i
$551$	−9.89447	−	9.89447i	−0.421519	−	0.421519i
$552$	−6.11780	+	3.53211i	−0.260391	+	0.150337i
$553$	12.8329	−	7.40909i	0.545712	−	0.315067i
$554$	11.4479	+	11.4479i	0.486375	+	0.486375i
$555$	0.864358	−	0.00861348i	0.0366900	−	0.000365622i
$556$	4.17898	+	2.41274i	0.177228	+	0.102323i
$557$	5.89341	−	10.2077i	0.249712	−	0.432513i	−0.713734	−	0.700417i	$-0.752997\pi$
$557$	5.89341	−	10.2077i	0.249712	−	0.432513i	0.963446	+	0.267903i	$0.0863308\pi$
$558$	−8.95899	−	8.95899i	−0.379264	−	0.379264i
$559$	0.274240	+	0.409894i	0.0115991	+	0.0173367i
$560$	25.2429	−	7.03416i	1.06671	−	0.297247i
$561$	−0.267408	+	0.0716517i	−0.0112900	+	0.00302514i
$562$	−26.4666	+	7.09170i	−1.11643	+	0.299145i
$563$	8.32255	−	31.0602i	0.350754	−	1.30903i	−0.534991	−	0.844858i	$-0.679685\pi$
$563$	8.32255	−	31.0602i	0.350754	−	1.30903i	0.885745	−	0.464172i	$-0.153648\pi$
$564$	0.335015	−	0.335015i	0.0141067	−	0.0141067i
$565$	12.8058	−	0.127612i	0.538744	−	0.00536868i
$566$	−8.44250	−	2.26216i	−0.354865	−	0.0950858i
$567$	−13.2118			−0.554845
$568$	19.1111	+	5.12080i	0.801883	+	0.214864i
$569$	4.64237	−	8.04082i	0.194618	−	0.337089i	−0.752157	−	0.658984i	$-0.770987\pi$
$569$	4.64237	−	8.04082i	0.194618	−	0.337089i	0.946775	+	0.321895i	$0.104320\pi$
$570$	−1.60603	+	6.24192i	−0.0672691	+	0.261445i
$571$		−	31.1596i		−	1.30399i	−0.758223	−	0.651995i	$-0.773932\pi$
$571$		−	31.1596i		−	1.30399i	0.758223	−	0.651995i	$-0.226068\pi$
$572$	−0.362249	−	5.47623i	−0.0151464	−	0.228973i
$573$	8.08942	−	8.08942i	0.337940	−	0.337940i
$574$	−10.6144	−	39.6134i	−0.443035	−	1.65343i
$575$	−14.0567	+	14.6285i	−0.586206	+	0.610050i
$576$	−14.1789	+	8.18618i	−0.590786	+	0.341091i
$577$			4.57285i			0.190370i	0.995460	+	0.0951852i	$0.0303443\pi$
$577$			4.57285i			0.190370i	−0.995460	+	0.0951852i	$0.969656\pi$
$578$	−12.8983	−	22.3405i	−0.536499	−	0.929243i
$579$	−1.49782	+	5.58994i	−0.0622473	+	0.232310i
$580$	−0.910980	−	3.26916i	−0.0378264	−	0.135745i
$581$	−4.81009	−	8.33132i	−0.199556	−	0.345641i
$582$	1.42711	+	5.32605i	0.0591556	+	0.220772i
$583$	41.0693	+	23.7114i	1.70092	+	0.982025i
$584$	17.0365			0.704975
$585$	−1.55671	−	20.4388i	−0.0643622	−	0.845040i
$586$	4.85179			0.200425
$587$	6.22829	+	3.59590i	0.257069	+	0.148419i	0.622997	−	0.782224i	$-0.285915\pi$
$587$	6.22829	+	3.59590i	0.257069	+	0.148419i	−0.365928	+	0.930643i	$0.619248\pi$
$588$	0.0142097	+	0.0530312i	0.000585997	+	0.00218697i
$589$	4.60743	+	7.98031i	0.189846	+	0.328823i
$590$	4.47289	−	7.92870i	0.184146	−	0.326420i
$591$	1.34048	−	5.00272i	0.0551398	−	0.205785i
$592$	1.29052	+	2.23524i	0.0530399	+	0.0918677i
$593$		−	28.0561i		−	1.15212i	−0.817406	−	0.576062i	$-0.804589\pi$
$593$		−	28.0561i		−	1.15212i	0.817406	−	0.576062i	$-0.195411\pi$
$594$	−24.6407	+	14.2263i	−1.01102	+	0.583712i
$595$	0.241590	+	0.408980i	0.00990422	+	0.0167665i
$596$	−0.113496	−	0.423573i	−0.00464898	−	0.0173502i
$597$	−7.33116	+	7.33116i	−0.300044	+	0.300044i
$598$	18.4581	−	12.3494i	0.754808	−	0.505005i
$599$			0.912959i			0.0373025i	0.999826	+	0.0186513i	$0.00593722\pi$
$599$			0.912959i			0.0373025i	−0.999826	+	0.0186513i	$0.994063\pi$
$600$	6.03157	−	6.27690i	0.246238	−	0.256253i
$601$	−6.22691	+	10.7853i	−0.254001	+	0.439943i	−0.964624	−	0.263631i	$-0.915080\pi$
$601$	−6.22691	+	10.7853i	−0.254001	+	0.439943i	0.710623	+	0.703573i	$0.248413\pi$
$602$	−0.520445	−	0.139453i	−0.0212118	−	0.00568367i
$603$	−40.1373			−1.63452
$604$	5.79162	+	1.55186i	0.235658	+	0.0631443i
$605$	21.9054	−	22.3464i	0.890581	−	0.908509i
$606$	−1.82305	+	1.82305i	−0.0740562	+	0.0740562i
$607$	−10.0350	+	37.4512i	−0.407309	+	1.52010i	0.392448	+	0.919774i	$0.371628\pi$
$607$	−10.0350	+	37.4512i	−0.407309	+	1.52010i	−0.799757	+	0.600324i	$0.795038\pi$
$608$	−4.63125	+	1.24094i	−0.187822	+	0.0503268i
$609$	8.45138	−	2.26454i	0.342467	−	0.0917638i
$610$	4.99757	+	17.9344i	0.202346	+	0.726143i
$611$	5.46530	−	6.23957i	0.221102	−	0.252426i
$612$	0.0448098	+	0.0448098i	0.00181133	+	0.00181133i
$613$	−12.3057	+	21.3140i	−0.497021	+	0.860865i	−0.999994	−	0.00343656i	$-0.998906\pi$
$613$	−12.3057	+	21.3140i	−0.497021	+	0.860865i	0.502973	+	0.864302i	$0.332239\pi$
$614$	31.9122	+	18.4245i	1.28787	+	0.743553i
$615$	−11.2451	−	11.0232i	−0.453446	−	0.444498i
$616$	−23.6110	−	23.6110i	−0.951316	−	0.951316i
$617$	−13.3501	+	7.70769i	−0.537455	+	0.310300i	−0.744047	−	0.668127i	$-0.767096\pi$
$617$	−13.3501	+	7.70769i	−0.537455	+	0.310300i	0.206592	+	0.978427i	$0.433763\pi$
$618$	−5.93259	+	3.42518i	−0.238644	+	0.137781i
$619$	−20.7915	−	20.7915i	−0.835683	−	0.835683i	0.152604	−	0.988287i	$-0.451234\pi$
$619$	−20.7915	−	20.7915i	−0.835683	−	0.835683i	−0.988287	+	0.152604i	$0.951234\pi$
$620$	0.0222700	+	2.23478i	0.000894385	+	0.0897510i
$621$	−13.1736	−	7.60581i	−0.528640	−	0.305211i
$622$	12.8316	−	22.2249i	0.514498	−	0.891137i
$623$	32.8303	+	32.8303i	1.31532	+	1.31532i
$624$	−9.15446	+	6.12480i	−0.366472	+	0.245188i
$625$	11.6273	−	22.1315i	0.465093	−	0.885262i
$626$	−17.4397	+	4.67294i	−0.697029	+	0.186768i
$627$	9.16923	−	2.45689i	0.366184	−	0.0981186i
$628$	−0.506664	+	1.89090i	−0.0202181	+	0.0754549i
$629$	−0.0330825	+	0.0330825i	−0.00131908	+	0.00131908i
$630$	15.9923	+	15.6768i	0.637150	+	0.624577i
$631$	12.1738	+	3.26195i	0.484631	+	0.129856i	0.492858	−	0.870110i	$-0.335952\pi$
$631$	12.1738	+	3.26195i	0.484631	+	0.129856i	−0.00822739	+	0.999966i	$0.502619\pi$
$632$	14.6984			0.584670
$633$	−12.9600	−	3.47263i	−0.515115	−	0.138025i
$634$	−9.06908	+	15.7081i	−0.360179	+	0.623849i
$635$	−0.926277	−	1.56806i	−0.0367582	−	0.0622267i
$636$			1.95352i			0.0774620i
$637$	0.309512	+	0.909991i	0.0122633	+	0.0360551i
$638$	−26.7512	+	26.7512i	−1.05909	+	1.05909i
$639$	5.05825	+	18.8777i	0.200101	+	0.746789i
$640$	28.5670	+	7.35020i	1.12921	+	0.290542i
$641$	−8.45341	+	4.88058i	−0.333890	+	0.192771i	−0.657567	−	0.753396i	$-0.728414\pi$
$641$	−8.45341	+	4.88058i	−0.333890	+	0.192771i	0.323677	+	0.946168i	$0.395081\pi$
$642$		−	3.72597i		−	0.147052i
$643$	−13.9057	−	24.0854i	−0.548387	−	0.949834i	−0.998385	−	0.0568044i	$-0.981909\pi$
$643$	−13.9057	−	24.0854i	−0.548387	−	0.949834i	0.449999	−	0.893029i	$-0.351424\pi$
$644$	−0.829680	+	3.09641i	−0.0326940	+	0.122016i
$645$	−0.199291	+	0.0555341i	−0.00784708	+	0.00218665i
$646$	−0.174424	−	0.302111i	−0.00686261	−	0.0118864i
$647$	−4.76862	−	17.7967i	−0.187474	−	0.699662i	−0.994087	−	0.108583i	$-0.965369\pi$
$647$	−4.76862	−	17.7967i	−0.187474	−	0.699662i	0.806613	−	0.591079i	$-0.201298\pi$
$648$	−11.3493	−	6.55251i	−0.445842	−	0.257407i
$649$	−13.4076			−0.526296
$650$	−17.6180	+	20.9417i	−0.691037	+	0.821402i
$651$	−5.76190			−0.225826
$652$	3.46357	+	1.99970i	0.135644	+	0.0783141i
$653$	1.90911	+	7.12491i	0.0747094	+	0.278819i	0.993167	−	0.116700i	$-0.0372315\pi$
$653$	1.90911	+	7.12491i	0.0747094	+	0.278819i	−0.918458	+	0.395519i	$0.870565\pi$
$654$	1.15104	+	1.99366i	0.0450093	+	0.0779583i
$655$	34.6929	−	9.66746i	1.35556	−	0.377739i
$656$	12.1694	−	45.4167i	0.475134	−	1.77322i
$657$	8.41420	+	14.5738i	0.328269	+	0.568579i
$658$			9.06214i			0.353279i
$659$	−12.0786	+	6.97358i	−0.470515	+	0.271652i	−0.716455	−	0.697633i	$-0.754237\pi$
$659$	−12.0786	+	6.97358i	−0.470515	+	0.271652i	0.245940	+	0.969285i	$0.420903\pi$
$660$	2.22965	+	0.573683i	0.0867891	+	0.0223306i
$661$	0.0586648	+	0.218940i	0.00228180	+	0.00851578i	0.967057	−	0.254559i	$-0.0819302\pi$
$661$	0.0586648	+	0.218940i	0.00228180	+	0.00851578i	−0.964776	+	0.263074i	$0.915264\pi$
$662$	−23.0236	+	23.0236i	−0.894837	+	0.894837i
$663$	−0.150188	−	0.131551i	−0.00583283	−	0.00510903i
$664$		−	9.54239i		−	0.370317i
$665$	−8.28396	−	14.0236i	−0.321238	−	0.543813i
$666$	−1.10288	+	1.91024i	−0.0427356	+	0.0740202i
$667$	−19.5369	−	5.23490i	−0.756472	−	0.202696i
$668$	−1.00022			−0.0386996
$669$	12.3964	+	3.32160i	0.479271	+	0.128420i
$670$	38.2678	+	37.5126i	1.47841	+	1.44924i
$671$	19.3893	−	19.3893i	0.748515	−	0.748515i
$672$	0.775939	−	2.89584i	0.0299325	−	0.111710i
$673$	−32.4730	+	8.70112i	−1.25174	+	0.335404i	−0.823010	−	0.568027i	$-0.807707\pi$
$673$	−32.4730	+	8.70112i	−1.25174	+	0.335404i	−0.428734	+	0.903431i	$0.641040\pi$
$674$	29.2938	−	7.84924i	1.12835	−	0.302341i
$675$	18.1994	+	4.48978i	0.700495	+	0.172812i
$676$	3.13722	−	2.41329i	0.120662	−	0.0928190i
$677$	25.1691	+	25.1691i	0.967326	+	0.967326i	0.999483	−	0.0321566i	$-0.0102375\pi$
$677$	25.1691	+	25.1691i	0.967326	+	0.967326i	−0.0321566	+	0.999483i	$0.510238\pi$
$678$	2.94044	−	5.09298i	0.112927	−	0.195595i
$679$	−12.0673	−	6.96707i	−0.463101	−	0.267372i
$680$	0.00469500	+	0.471141i	0.000180045	+	0.0180674i
$681$	12.8943	+	12.8943i	0.494110	+	0.494110i
$682$	21.5760	−	12.4569i	0.826187	−	0.477000i
$683$	26.6361	−	15.3784i	1.01920	−	0.588437i	0.105329	−	0.994437i	$-0.466410\pi$
$683$	26.6361	−	15.3784i	1.01920	−	0.588437i	0.913873	+	0.406001i	$0.133077\pi$
$684$	−1.53650	−	1.53650i	−0.0587494	−	0.0587494i
$685$	−30.7186	−	30.1124i	−1.17370	−	1.15054i
$686$	−24.7893	−	14.3121i	−0.946459	−	0.546438i
$687$	5.34740	−	9.26197i	0.204016	−	0.353366i
$688$	−0.436807	−	0.436807i	−0.0166531	−	0.0166531i
$689$	2.25743	+	34.1263i	0.0860013	+	1.30011i
$690$	2.50078	+	8.97436i	0.0952032	+	0.341648i
$691$	−37.4215	+	10.0271i	−1.42358	+	0.381447i	−0.886753	−	0.462244i	$-0.847044\pi$
$691$	−37.4215	+	10.0271i	−1.42358	+	0.381447i	−0.536828	+	0.843692i	$0.680378\pi$
$692$	−1.24638	+	0.333966i	−0.0473802	+	0.0126955i
$693$	8.53668	−	31.8593i	0.324282	−	1.21024i
$694$	−26.4382	+	26.4382i	−1.00358	+	1.00358i
$695$	−24.8085	+	25.3080i	−0.941042	+	0.959986i
$696$	8.38305	+	2.24623i	0.317759	+	0.0851432i
$697$	0.852297			0.0322831
$698$	39.9534	+	10.7055i	1.51226	+	0.405208i
$699$	−3.23232	+	5.59854i	−0.122258	+	0.211756i
$700$	−0.0787222	−	3.94947i	−0.00297542	−	0.149276i
$701$			19.8876i			0.751143i	0.926793	+	0.375571i	$0.122553\pi$
$701$			19.8876i			0.751143i	−0.926793	+	0.375571i	$0.877447\pi$
$702$	−18.4091	−	9.06457i	−0.694807	−	0.342120i
$703$	1.13437	−	1.13437i	0.0427838	−	0.0427838i
$704$	−8.33247	−	31.0972i	−0.314042	−	1.17202i
$705$	1.76973	+	2.99592i	0.0666519	+	0.112833i
$706$	11.5681	−	6.67884i	0.435371	−	0.251361i
$707$		−	6.51526i		−	0.245032i
$708$	−0.276155	−	0.478314i	−0.0103785	−	0.0179761i
$709$	−8.24828	+	30.7830i	−0.309771	+	1.15608i	0.618990	+	0.785399i	$0.287542\pi$
$709$	−8.24828	+	30.7830i	−0.309771	+	1.15608i	−0.928760	+	0.370680i	$0.879125\pi$
$710$	12.8206	−	22.7259i	0.481147	−	0.852887i
$711$	7.25942	+	12.5737i	0.272250	+	0.471550i
$712$	11.9196	+	44.4844i	0.446705	+	1.66712i
$713$	11.5352	+	6.65983i	0.431996	+	0.249413i
$714$	0.218128			0.00816325
$715$	39.6131	+	7.44524i	1.48145	+	0.278436i
$716$	−4.25084			−0.158861
$717$	1.64665	+	0.950692i	0.0614951	+	0.0355042i
$718$	6.18186	+	23.0710i	0.230705	+	0.861002i
$719$	15.4818	+	26.8152i	0.577372	+	1.00004i	0.995779	+	0.0917785i	$0.0292552\pi$
$719$	15.4818	+	26.8152i	0.577372	+	1.00004i	−0.418407	+	0.908260i	$0.637411\pi$
$720$	6.89206	+	24.7330i	0.256852	+	0.921744i
$721$	4.48053	−	16.7216i	0.166864	−	0.622744i
$722$	−8.44057	−	14.6195i	−0.314126	−	0.544081i
$723$		−	1.85672i		−	0.0690522i
$724$	−2.28019	+	1.31647i	−0.0847427	+	0.0489262i
$725$	24.9193	−	0.496701i	0.925481	−	0.0184470i
$726$	−3.71918	−	13.8802i	−0.138032	−	0.515141i
$727$	16.2588	−	16.2588i	0.603007	−	0.603007i	−0.338103	−	0.941109i	$-0.609785\pi$
$727$	16.2588	−	16.2588i	0.603007	−	0.603007i	0.941109	+	0.338103i	$0.109785\pi$
$728$	4.68379	−	23.6215i	0.173593	−	0.875470i
$729$		−	5.33729i		−	0.197678i
$730$	5.59852	−	21.7590i	0.207211	−	0.805336i
$731$	0.00559879	−	0.00969739i	0.000207079	−	0.000358671i
$732$	1.09107	+	0.292350i	0.0403269	+	0.0108056i
$733$	31.2515			1.15430			0.577150	−	0.816638i	$-0.304165\pi$
$733$	31.2515			1.15430			0.577150	+	0.816638i	$0.304165\pi$
$734$	−16.0980	−	4.31344i	−0.594187	−	0.159212i
$735$	−0.403193	+	0.00401789i	−0.0148720	+	0.000148202i
$736$	−4.90054	+	4.90054i	−0.180636	+	0.180636i
$737$	20.4273	−	76.2357i	0.752449	−	2.80818i
$738$	38.8131	−	10.3999i	1.42873	−	0.382827i
$739$	−26.3668	+	7.06496i	−0.969918	+	0.259889i	−0.708793	−	0.705416i	$-0.750760\pi$
$739$	−26.3668	+	7.06496i	−0.969918	+	0.259889i	−0.261125	+	0.965305i	$0.584093\pi$
$740$	0.374801	−	0.104441i	0.0137780	−	0.00383934i
$741$	5.14985	+	4.51081i	0.189184	+	0.165709i
$742$	−26.4213	−	26.4213i	−0.969956	−	0.969956i
$743$	−16.4830	+	28.5494i	−0.604703	+	1.04738i	0.387395	+	0.921914i	$0.373375\pi$
$743$	−16.4830	+	28.5494i	−0.604703	+	1.04738i	−0.992098	+	0.125463i	$0.959958\pi$
$744$	−4.94960	−	2.85765i	−0.181461	−	0.104767i
$745$	3.22041	−	0.0320919i	0.117987	−	0.00117576i
$746$	−11.3566	−	11.3566i	−0.415794	−	0.415794i
$747$	8.16301	−	4.71292i	0.298669	−	0.172437i
$748$	−0.107916	+	0.0623052i	−0.00394579	+	0.00227810i
$749$	6.65800	+	6.65800i	0.243278	+	0.243278i
$750$	−6.03476	−	9.76622i	−0.220358	−	0.356612i
$751$	26.8241	+	15.4869i	0.978826	+	0.565125i	0.901915	−	0.431913i	$-0.142161\pi$
$751$	26.8241	+	15.4869i	0.978826	+	0.565125i	0.0769103	+	0.997038i	$0.475494\pi$
$752$	−5.19487	+	8.99777i	−0.189437	+	0.328115i
$753$	−1.35540	−	1.35540i	−0.0493934	−	0.0493934i
$754$	−26.7630	−	5.30672i	−0.974653	−	0.193259i
$755$	−21.6367	+	38.3535i	−0.787440	+	1.39583i
$756$	2.86098	−	0.766598i	0.104053	−	0.0278809i
$757$	−49.3561	+	13.2249i	−1.79388	+	0.480668i	−0.992995	−	0.118154i	$-0.962302\pi$
$757$	−49.3561	+	13.2249i	−1.79388	+	0.480668i	−0.800882	+	0.598822i	$0.795636\pi$
$758$	3.85120	−	14.3729i	0.139882	−	0.522046i
$759$	9.70238	−	9.70238i	0.352174	−	0.352174i
$760$	−0.160988	−	16.1551i	−0.00583967	−	0.586007i
$761$	1.11809	+	0.299592i	0.0405308	+	0.0108602i	0.279027	−	0.960283i	$-0.409988\pi$
$761$	1.11809	+	0.299592i	0.0405308	+	0.0108602i	−0.238497	+	0.971143i	$0.576655\pi$
$762$	−0.836323			−0.0302968
$763$	−5.61932	−	1.50569i	−0.203433	−	0.0545097i
$764$	2.57470	−	4.45951i	0.0931494	−	0.161339i
$765$	−0.400718	+	0.236710i	−0.0144880	+	0.00855825i
$766$			39.5553i			1.42919i
$767$	−5.37693	−	8.03664i	−0.194150	−	0.290186i
$768$	3.41812	−	3.41812i	0.123341	−	0.123341i
$769$	7.82422	+	29.2004i	0.282148	+	1.05299i	0.950898	+	0.309505i	$0.100163\pi$
$769$	7.82422	+	29.2004i	0.282148	+	1.05299i	−0.668750	+	0.743488i	$0.733170\pi$
$770$	−37.9151	+	22.3970i	−1.36636	+	0.807130i
$771$	11.7522	−	6.78511i	0.423243	−	0.244360i
$772$			2.60488i			0.0937517i
$773$	−3.59641	−	6.22916i	−0.129354	−	0.224047i	0.794073	−	0.607823i	$-0.207957\pi$
$773$	−3.59641	−	6.22916i	−0.129354	−	0.224047i	−0.923426	+	0.383776i	$0.874624\pi$
$774$	0.136636	−	0.509931i	0.00491127	−	0.0183291i
$775$	−15.9358	−	3.93136i	−0.572432	−	0.141219i
$776$	−6.91074	−	11.9698i	−0.248081	−	0.429689i
$777$	0.259624	+	0.968929i	0.00931395	+	0.0347601i
$778$	−42.7119	−	24.6597i	−1.53130	−	0.884094i
$779$	−29.2247			−1.04708
$780$	0.550298	+	1.56654i	0.0197038	+	0.0560910i
$781$	−38.4300			−1.37513
$782$	−0.436687	−	0.252122i	−0.0156159	−	0.00901585i
$783$	4.83688	+	18.0515i	0.172856	+	0.645107i
$784$	−0.601981	−	1.04266i	−0.0214993	−	0.0372379i
$785$	−12.5219	−	7.06412i	−0.446927	−	0.252129i
$786$	4.28044	−	15.9748i	0.152678	−	0.569804i
$787$	−3.58943	−	6.21708i	−0.127949	−	0.221615i	0.794933	−	0.606698i	$-0.207506\pi$
$787$	−3.58943	−	6.21708i	−0.127949	−	0.221615i	−0.922882	+	0.385083i	$0.874173\pi$
$788$		−	2.33124i		−	0.0830470i
$789$	−5.51923	+	3.18653i	−0.196490	+	0.113443i
$790$	4.83017	−	18.7727i	0.171850	−	0.667904i
$791$	3.84642	+	14.3550i	0.136763	+	0.510407i
$792$	23.1341	−	23.1341i	0.822034	−	0.822034i
$793$	19.3979	+	3.84631i	0.688838	+	0.136586i
$794$		−	36.7145i		−	1.30295i
$795$	−13.8946	−	3.57503i	−0.492789	−	0.126793i
$796$	−2.33336	+	4.04150i	−0.0827037	+	0.143247i
$797$	−38.0553	−	10.1969i	−1.34799	−	0.361192i	−0.488596	−	0.872510i	$-0.662491\pi$
$797$	−38.0553	−	10.1969i	−1.34799	−	0.361192i	−0.859391	+	0.511318i	$0.829157\pi$
$798$	−7.47947			−0.264770
$799$	−0.181915	−	0.0487439i	−0.00643568	−	0.00172443i
$800$	4.12188	−	7.47969i	0.145730	−	0.264447i
$801$	−32.1671	+	32.1671i	−1.13657	+	1.13657i
$802$	12.9022	−	48.1515i	0.455591	−	1.70029i
$803$	−31.9634	+	8.56456i	−1.12796	+	0.302237i
$804$	3.14043	−	0.841474i	0.110754	−	0.0296765i
$805$	−20.5051	−	11.5677i	−0.722711	−	0.407710i
$806$	16.1195	+	7.93716i	0.567784	+	0.279575i
$807$	−1.53767	−	1.53767i	−0.0541286	−	0.0541286i
$808$	3.23129	−	5.59676i	0.113676	−	0.196893i
$809$	24.2062	+	13.9754i	0.851043	+	0.491350i	0.861003	−	0.508600i	$-0.169837\pi$
$809$	24.2062	+	13.9754i	0.851043	+	0.491350i	−0.00995956	+	0.999950i	$0.503170\pi$
$810$	−12.0985	+	12.3420i	−0.425096	+	0.433654i
$811$	−23.2784	−	23.2784i	−0.817415	−	0.817415i	0.168317	−	0.985733i	$-0.446167\pi$
$811$	−23.2784	−	23.2784i	−0.817415	−	0.817415i	−0.985733	+	0.168317i	$0.946167\pi$
$812$	3.41066	−	1.96915i	0.119691	−	0.0691035i
$813$	8.89636	−	5.13632i	0.312009	−	0.180138i
$814$	−3.06696	−	3.06696i	−0.107497	−	0.107497i
$815$	−20.5615	+	20.9754i	−0.720238	+	0.734737i
$816$	0.216579	+	0.125042i	0.00758178	+	0.00437734i
$817$	−0.191979	+	0.332517i	−0.00671648	+	0.0116333i
$818$	14.9850	+	14.9850i	0.523937	+	0.523937i
$819$	22.5202	−	7.65974i	0.786920	−	0.267653i
$820$	−6.17331	−	3.48261i	−0.215582	−	0.121618i
$821$	18.8872	−	5.06082i	0.659169	−	0.176624i	0.0862981	−	0.996269i	$-0.472496\pi$
$821$	18.8872	−	5.06082i	0.659169	−	0.176624i	0.572871	+	0.819646i	$0.305830\pi$
$822$	−19.0805	+	5.11260i	−0.665508	+	0.178322i
$823$	−10.5653	+	39.4302i	−0.368283	+	1.37445i	0.494633	+	0.869102i	$0.335303\pi$
$823$	−10.5653	+	39.4302i	−0.368283	+	1.37445i	−0.862915	+	0.505348i	$0.831364\pi$
$824$	12.1421	−	12.1421i	0.422989	−	0.422989i
$825$	−8.16074	+	14.8087i	−0.284121	+	0.515574i
$826$	10.2042	+	2.73420i	0.355049	+	0.0951350i
$827$	31.8649			1.10805			0.554026	−	0.832499i	$-0.313091\pi$
$827$	31.8649			1.10805			0.554026	+	0.832499i	$0.313091\pi$
$828$	−3.03386	−	0.812920i	−0.105434	−	0.0282509i
$829$	27.6391	−	47.8724i	0.959946	−	1.66268i	0.237326	−	0.971430i	$-0.423729\pi$
$829$	27.6391	−	47.8724i	0.959946	−	1.66268i	0.722620	−	0.691246i	$-0.242938\pi$
$830$	−12.1875	−	3.13582i	−0.423035	−	0.108846i
$831$			7.21389i			0.250247i
$832$	15.2983	−	17.4656i	0.530373	−	0.605510i
$833$	0.0154318	−	0.0154318i	0.000534681	−	0.000534681i
$834$	4.21208	+	15.7197i	0.145853	+	0.544329i
$835$	1.83044	−	7.11413i	0.0633452	−	0.246195i
$836$	3.70036	−	2.13640i	0.127980	−	0.0738890i
$837$		−	12.3070i		−	0.425390i
$838$	−1.68488	−	2.91830i	−0.0582032	−	0.100811i
$839$	1.00953	−	3.76762i	0.0348528	−	0.130073i	−0.946307	−	0.323268i	$-0.895218\pi$
$839$	1.00953	−	3.76762i	0.0348528	−	0.130073i	0.981160	+	0.193195i	$0.0618851\pi$
$840$	8.79850	+	4.96358i	0.303577	+	0.171260i
$841$	−2.07559	−	3.59503i	−0.0715721	−	0.123966i
$842$	13.6019	+	50.7629i	0.468751	+	1.74940i
$843$	−10.5734	−	6.10453i	−0.364166	−	0.210251i
$844$	−6.03930			−0.207881
$845$	11.4235	+	26.7302i	0.392980	+	0.919547i
$846$	−8.87908			−0.305269
$847$	31.4485	+	18.1568i	1.08058	+	0.623876i
$848$	−11.0876	−	41.3796i	−0.380751	−	1.42098i
$849$	−1.94727	−	3.37277i	−0.0668301	−	0.115753i
$850$	0.603284	+	0.148830i	0.0206925	+	0.00510482i
$851$	0.600167	−	2.23986i	0.0205735	−	0.0767812i
$852$	−0.791536	−	1.37098i	−0.0271176	−	0.0469690i
$853$			53.5726i			1.83429i	0.398554	+	0.917145i	$0.369512\pi$
$853$			53.5726i			1.83429i	−0.398554	+	0.917145i	$0.630488\pi$
$854$	−18.7107	+	10.8026i	−0.640266	+	0.369658i
$855$	13.7403	−	8.11661i	0.469910	−	0.277582i
$856$	2.41729	+	9.02145i	0.0826213	+	0.308347i
$857$	−18.9164	+	18.9164i	−0.646171	+	0.646171i	−0.952066	−	0.305894i	$-0.901045\pi$
$857$	−18.9164	+	18.9164i	−0.646171	+	0.646171i	0.305894	+	0.952066i	$0.401045\pi$
$858$	12.1957	−	13.9234i	0.416353	−	0.475338i
$859$			18.1203i			0.618258i	0.951020	+	0.309129i	$0.100037\pi$
$859$			18.1203i			0.618258i	−0.951020	+	0.309129i	$0.899963\pi$
$860$	−0.0801778	+	0.0473622i	−0.00273404	+	0.00161504i
$861$	9.13685	−	15.8255i	0.311383	−	0.539331i
$862$	2.42312	+	0.649274i	0.0825320	+	0.0221144i
$863$	21.4967			0.731757			0.365879	−	0.930663i	$-0.380768\pi$
$863$	21.4967			0.731757			0.365879	+	0.930663i	$0.380768\pi$
$864$	6.18529	+	1.65734i	0.210428	+	0.0563840i
$865$	−0.0944315	−	9.47615i	−0.00321077	−	0.322199i
$866$	−15.9037	+	15.9037i	−0.540431	+	0.540431i
$867$	2.97500	−	11.1029i	0.101036	−	0.377073i
$868$	−2.50515	+	0.671252i	−0.0850303	+	0.0227838i
$869$	−27.5767	+	7.38915i	−0.935475	+	0.250660i
$870$	5.62372	−	9.96866i	0.190662	−	0.337969i
$871$	53.8883	−	18.3289i	1.82593	−	0.621050i
$872$	−4.08036	−	4.08036i	−0.138179	−	0.138179i
$873$	6.82633	−	11.8235i	0.231036	−	0.400167i
$874$	14.9737	+	8.64508i	0.506493	+	0.292424i
$875$	28.2350	+	6.66780i	0.954518	+	0.225413i
$876$	−0.963883	−	0.963883i	−0.0325666	−	0.0325666i
$877$	−18.4889	+	10.6745i	−0.624324	+	0.360454i	−0.778551	−	0.627582i	$-0.784045\pi$
$877$	−18.4889	+	10.6745i	−0.624324	+	0.360454i	0.154226	+	0.988036i	$0.450711\pi$
$878$	28.7551	−	16.6018i	0.970437	−	0.560282i
$879$	1.52867	+	1.52867i	0.0515609	+	0.0515609i
$880$	−50.4848	+	0.503090i	−1.70184	+	0.0169591i
$881$	11.4703	+	6.62238i	0.386444	+	0.223114i	0.680618	−	0.732638i	$-0.261711\pi$
$881$	11.4703	+	6.62238i	0.386444	+	0.223114i	−0.294174	+	0.955752i	$0.595045\pi$
$882$	0.514453	−	0.891059i	0.0173225	−	0.0300035i
$883$	−32.5668	−	32.5668i	−1.09596	−	1.09596i	−0.994878	−	0.101082i	$-0.967770\pi$
$883$	−32.5668	−	32.5668i	−1.09596	−	1.09596i	−0.101082	−	0.994878i	$-0.532230\pi$
$884$	−0.0806241	−	0.0396990i	−0.00271168	−	0.00133522i
$885$	3.90743	−	1.08884i	0.131347	−	0.0366009i
$886$	−12.7526	+	3.41705i	−0.428432	+	0.114798i
$887$	−15.4358	+	4.13600i	−0.518282	+	0.138873i	−0.508472	−	0.861079i	$-0.669789\pi$
$887$	−15.4358	+	4.13600i	−0.518282	+	0.138873i	−0.00981024	+	0.999952i	$0.503123\pi$
$888$	−0.257524	+	0.961094i	−0.00864195	+	0.0322522i
$889$	1.49444	−	1.49444i	0.0501219	−	0.0501219i
$890$	60.7325	−	0.605210i	2.03576	−	0.0202867i
$891$	24.5873	+	6.58814i	0.823705	+	0.220711i
$892$	5.77663			0.193416
$893$	6.23773	+	1.67139i	0.208738	+	0.0559311i
$894$	0.739462	−	1.28079i	0.0247313	−	0.0428359i
$895$	7.77924	−	30.2345i	0.260031	−	1.01063i
$896$			34.2308i			1.14357i
$897$	9.70667	+	1.92469i	0.324096	+	0.0642636i
$898$	5.01810	−	5.01810i	0.167456	−	0.167456i
$899$	−4.23529	−	15.8063i	−0.141255	−	0.527170i
$900$	3.86969	−	0.0771319i	0.128990	−	0.00257106i
$901$	0.672500	−	0.388268i	0.0224042	−	0.0129351i
$902$			79.0135i			2.63086i
$903$	−0.120041	−	0.207917i	−0.00399471	−	0.00691905i
$904$	−3.81532	+	14.2390i	−0.126896	+	0.473581i
$905$	−5.19065	−	18.6273i	−0.172543	−	0.619192i
$906$	10.1108	+	17.5125i	0.335910	+	0.581814i
$907$	1.35973	+	5.07458i	0.0451491	+	0.168499i	0.984819	−	0.173583i	$-0.0555346\pi$
$907$	1.35973	+	5.07458i	0.0451491	+	0.168499i	−0.939670	+	0.342082i	$0.888868\pi$
$908$	7.10833	+	4.10399i	0.235898	+	0.136196i
$909$	6.38364			0.211732
$910$	−28.6301	−	13.7446i	−0.949080	−	0.455630i
$911$	9.49722			0.314657			0.157328	−	0.987546i	$-0.449712\pi$
$911$	9.49722			0.314657			0.157328	+	0.987546i	$0.449712\pi$
$912$	−7.42634	−	4.28760i	−0.245911	−	0.141977i
$913$	4.79714	+	17.9032i	0.158762	+	0.592508i
$914$	22.7981	+	39.4874i	0.754093	+	1.30613i
$915$	−4.07607	+	7.22529i	−0.134751	+	0.238861i
$916$	1.24593	−	4.64987i	0.0411666	−	0.153636i
$917$	20.8969	+	36.1945i	0.690076	+	1.19525i
$918$			0.465905i			0.0153771i
$919$	45.6207	−	26.3391i	1.50489	−	0.868847i	0.504903	−	0.863176i	$-0.331528\pi$
$919$	45.6207	−	26.3391i	1.50489	−	0.868847i	0.999984	−	0.00567026i	$-0.00180491\pi$
$920$	−11.8773	−	20.1066i	−0.391582	−	0.662896i
$921$	4.24963	+	15.8598i	0.140030	+	0.522599i
$922$	2.82041	−	2.82041i	0.0928851	−	0.0928851i
$923$	−15.4118	−	23.0352i	−0.507284	−	0.758214i
$924$			2.67171i			0.0878929i
$925$	0.0569454	+	2.85694i	0.00187235	+	0.0939355i
$926$	19.0876	−	33.0606i	0.627256	−	1.08644i
$927$	16.3838	+	4.39002i	0.538114	+	0.144187i
$928$	8.51438			0.279498
$929$	−8.04841	−	2.15657i	−0.264060	−	0.0707546i	0.124360	−	0.992237i	$-0.460312\pi$
$929$	−8.04841	−	2.15657i	−0.264060	−	0.0707546i	−0.388420	+	0.921483i	$0.626979\pi$
$930$	−5.27633	+	5.38254i	−0.173018	+	0.176501i
$931$	−0.529147	+	0.529147i	−0.0173421	+	0.0173421i
$932$	−0.753121	+	2.81069i	−0.0246693	+	0.0920671i
$933$	11.0454	−	2.95960i	0.361610	−	0.0968931i
$934$	−31.0861	+	8.32950i	−1.01717	+	0.272549i
$935$	−0.245660	−	0.881582i	−0.00803395	−	0.0288308i
$936$	23.1443	+	4.58918i	0.756495	+	0.150002i
$937$	16.3814	+	16.3814i	0.535156	+	0.535156i	0.922102	−	0.386947i	$-0.126470\pi$
$937$	16.3814	+	16.3814i	0.535156	+	0.535156i	−0.386947	+	0.922102i	$0.626470\pi$
$938$	−31.0933	+	53.8551i	−1.01523	+	1.75843i
$939$	−6.96712	−	4.02247i	−0.227363	−	0.131268i
$940$	1.11846	+	1.09639i	0.0364802	+	0.0357603i
$941$	−24.2325	−	24.2325i	−0.789956	−	0.789956i	0.191530	−	0.981487i	$-0.438655\pi$
$941$	−24.2325	−	24.2325i	−0.789956	−	0.789956i	−0.981487	+	0.191530i	$0.938655\pi$
$942$	−5.71762	+	3.30107i	−0.186290	+	0.107555i
$943$	−36.5835	+	21.1215i	−1.19132	+	0.687810i
$944$	8.56432	+	8.56432i	0.278745	+	0.278745i
$945$	0.216762	+	21.7519i	0.00705125	+	0.707590i
$946$	0.899011	+	0.519044i	0.0292294	+	0.0168756i
$947$	16.7208	−	28.9613i	0.543353	−	0.941114i	−0.455356	−	0.890309i	$-0.650488\pi$
$947$	16.7208	−	28.9613i	0.543353	−	0.941114i	0.998709	−	0.0508048i	$-0.0161786\pi$
$948$	−0.831598	−	0.831598i	−0.0270091	−	0.0270091i
$949$	−17.9521	−	15.7244i	−0.582749	−	0.510436i
$950$	−20.6862	−	5.10327i	−0.671149	−	0.165572i
$951$	−7.80666	+	2.09179i	−0.253148	+	0.0678309i
$952$	−0.528140	+	0.141515i	−0.0171171	+	0.00458652i
$953$	3.88895	−	14.5138i	0.125975	−	0.470147i	−0.873897	−	0.486111i	$-0.838415\pi$
$953$	3.88895	−	14.5138i	0.125975	−	0.470147i	0.999873	+	0.0159642i	$0.00508177\pi$
$954$	25.8875	−	25.8875i	0.838140	−	0.838140i
$955$	27.0068	+	26.4739i	0.873921	+	0.856675i
$956$	0.826681	+	0.221508i	0.0267368	+	0.00716409i
$957$	−16.8573			−0.544918
$958$	3.35726	+	0.899575i	0.108468	+	0.0290640i
$959$	24.9594	−	43.2310i	0.805982	−	1.39600i
$960$	4.95377	+	8.38607i	0.159882	+	0.270659i
$961$		−	20.2237i		−	0.652378i
$962$	0.608402	−	3.06831i	0.0196157	−	0.0989264i
$963$	−6.52350	+	6.52350i	−0.210217	+	0.210217i
$964$	−0.216305	−	0.807262i	−0.00696672	−	0.0260002i
$965$	−18.5274	−	4.76706i	−0.596420	−	0.153457i
$966$	−9.36281	+	5.40562i	−0.301243	+	0.173923i
$967$			7.49252i			0.240943i	0.992717	+	0.120472i	$0.0384407\pi$
$967$			7.49252i			0.240943i	−0.992717	+	0.120472i	$0.961559\pi$
$968$	18.0100	+	31.1943i	0.578864	+	1.00262i
$969$	0.0402309	−	0.150144i	0.00129240	−	0.00482332i
$970$	−17.5588	+	4.89290i	−0.563778	+	0.157101i
$971$	−13.9303	−	24.1280i	−0.447045	−	0.774304i	0.551147	−	0.834408i	$-0.314190\pi$
$971$	−13.9303	−	24.1280i	−0.447045	−	0.774304i	−0.998192	+	0.0601036i	$0.980857\pi$
$972$	1.15767	+	4.32048i	0.0371323	+	0.138580i
$973$	−35.6165	−	20.5632i	−1.14181	−	0.659225i
$974$	−8.45010			−0.270759
$975$	−12.1492	+	1.04720i	−0.389086	+	0.0335373i
$976$	−24.7704			−0.792880
$977$	−33.6679	−	19.4382i	−1.07713	−	0.621883i	−0.147011	−	0.989135i	$-0.546965\pi$
$977$	−33.6679	−	19.4382i	−1.07713	−	0.621883i	−0.930122	+	0.367252i	$0.880299\pi$
$978$	3.49101	+	13.0286i	0.111630	+	0.416609i
$979$	−44.7263	−	77.4683i	−1.42946	−	2.47590i
$980$	−0.174832	+	0.0487183i	−0.00558479	+	0.00155625i
$981$	1.47527	−	5.50580i	0.0471019	−	0.175787i
$982$	4.63761	+	8.03257i	0.147992	+	0.256330i
$983$		−	0.207440i		−	0.00661630i	−0.999995	−	0.00330815i	$-0.998947\pi$
$983$		−	0.207440i		−	0.00661630i	0.999995	−	0.00330815i	$-0.00105302\pi$
$984$	15.6975	−	9.06297i	0.500419	−	0.288917i
$985$	16.5812	+	4.26628i	0.528319	+	0.135935i
$986$	0.160336	+	0.598381i	0.00510613	+	0.0190563i
$987$	−2.85525	+	2.85525i	−0.0908836	+	0.0908836i
$988$	2.76455	+	1.36125i	0.0879519	+	0.0433072i
$989$			0.554993i			0.0176477i
$990$	−21.9445	−	37.1491i	−0.697442	−	1.18068i
$991$	12.7480	−	22.0803i	0.404955	−	0.701402i	−0.589361	−	0.807869i	$-0.700621\pi$
$991$	12.7480	−	22.0803i	0.404955	−	0.701402i	0.994316	+	0.106467i	$0.0339539\pi$
$992$	−5.41599	−	1.45121i	−0.171958	−	0.0460760i
$993$	−14.5083			−0.460407
$994$	29.2480	+	7.83698i	0.927691	+	0.248574i
$995$	−24.4753	−	23.9924i	−0.775921	−	0.760609i
$996$	−0.539885	+	0.539885i	−0.0171069	+	0.0171069i
$997$	−8.96942	+	33.4743i	−0.284064	+	1.06014i	0.665456	+	0.746437i	$0.268237\pi$
$997$	−8.96942	+	33.4743i	−0.284064	+	1.06014i	−0.949520	+	0.313706i	$0.898429\pi$
$998$	−12.9137	+	3.46020i	−0.408774	+	0.109531i
$999$	−2.06955	+	0.554536i	−0.0654778	+	0.0175447i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.2.t.a.7.5	yes	20
3.2	odd	2		585.2.dp.a.397.1		20
5.2	odd	4		325.2.s.b.293.1		20
5.3	odd	4		65.2.o.a.33.5	yes	20
5.4	even	2		325.2.x.b.7.1		20
13.2	odd	12		65.2.o.a.2.5	✓	20
13.3	even	3		845.2.t.f.427.1		20
13.4	even	6		845.2.f.d.437.9		20
13.5	odd	4		845.2.o.e.357.5		20
13.6	odd	12		845.2.k.e.577.2		20
13.7	odd	12		845.2.k.d.577.9		20
13.8	odd	4		845.2.o.f.357.1		20
13.9	even	3		845.2.f.e.437.2		20
13.10	even	6		845.2.t.e.427.5		20
13.11	odd	12		845.2.o.g.587.1		20
13.12	even	2		845.2.t.g.657.1		20
15.8	even	4		585.2.cf.a.163.1		20
39.2	even	12		585.2.cf.a.262.1		20
65.2	even	12		325.2.x.b.93.1		20
65.3	odd	12		845.2.o.e.258.5		20
65.8	even	4		845.2.t.e.188.5		20
65.18	even	4		845.2.t.f.188.1		20
65.23	odd	12		845.2.o.f.258.1		20
65.28	even	12	inner	65.2.t.a.28.5	yes	20
65.33	even	12		845.2.f.d.408.2		20
65.38	odd	4		845.2.o.g.488.1		20
65.43	odd	12		845.2.k.d.268.9		20
65.48	odd	12		845.2.k.e.268.2		20
65.54	odd	12		325.2.s.b.132.1		20
65.58	even	12		845.2.f.e.408.9		20
65.63	even	12		845.2.t.g.418.1		20
195.158	odd	12		585.2.dp.a.28.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.5	✓	20	13.2	odd	12
65.2.o.a.33.5	yes	20	5.3	odd	4
65.2.t.a.7.5	yes	20	1.1	even	1	trivial
65.2.t.a.28.5	yes	20	65.28	even	12	inner
325.2.s.b.132.1		20	65.54	odd	12
325.2.s.b.293.1		20	5.2	odd	4
325.2.x.b.7.1		20	5.4	even	2
325.2.x.b.93.1		20	65.2	even	12
585.2.cf.a.163.1		20	15.8	even	4
585.2.cf.a.262.1		20	39.2	even	12
585.2.dp.a.28.1		20	195.158	odd	12
585.2.dp.a.397.1		20	3.2	odd	2
845.2.f.d.408.2		20	65.33	even	12
845.2.f.d.437.9		20	13.4	even	6
845.2.f.e.408.9		20	65.58	even	12
845.2.f.e.437.2		20	13.9	even	3
845.2.k.d.268.9		20	65.43	odd	12
845.2.k.d.577.9		20	13.7	odd	12
845.2.k.e.268.2		20	65.48	odd	12
845.2.k.e.577.2		20	13.6	odd	12
845.2.o.e.258.5		20	65.3	odd	12
845.2.o.e.357.5		20	13.5	odd	4
845.2.o.f.258.1		20	65.23	odd	12
845.2.o.f.357.1		20	13.8	odd	4
845.2.o.g.488.1		20	65.38	odd	4
845.2.o.g.587.1		20	13.11	odd	12
845.2.t.e.188.5		20	65.8	even	4
845.2.t.e.427.5		20	13.10	even	6
845.2.t.f.188.1		20	65.18	even	4
845.2.t.f.427.1		20	13.3	even	3
845.2.t.g.418.1		20	65.63	even	12
845.2.t.g.657.1		20	13.12	even	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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	65.t (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.31467 + 0.759023i) q^{2} +(0.175069 + 0.653367i) q^{3} +(0.152233 + 0.263675i) q^{4} +(-2.15400 + 0.600231i) q^{5} +(-0.265763 + 0.991842i) q^{6} +(-1.29744 - 2.24723i) q^{7} -2.57390i q^{8} +(2.20184 - 1.27123i) q^{9} +O(q^{10})\)	\(q+(1.31467 + 0.759023i) q^{2} +(0.175069 + 0.653367i) q^{3} +(0.152233 + 0.263675i) q^{4} +(-2.15400 + 0.600231i) q^{5} +(-0.265763 + 0.991842i) q^{6} +(-1.29744 - 2.24723i) q^{7} -2.57390i q^{8} +(2.20184 - 1.27123i) q^{9} +(-3.28738 - 0.845834i) q^{10} +(1.29395 + 4.82908i) q^{11} +(-0.145625 + 0.145625i) q^{12} +(-2.37567 + 2.71223i) q^{13} -3.93915i q^{14} +(-0.769270 - 1.30227i) q^{15} +(2.25812 - 3.91117i) q^{16} +(0.0790751 + 0.0211881i) q^{17} +3.85958 q^{18} +(-2.71143 - 0.726525i) q^{19} +(-0.486175 - 0.476581i) q^{20} +(1.24113 - 1.24113i) q^{21} +(-1.96427 + 7.33077i) q^{22} +(-3.91925 + 1.05016i) q^{23} +(1.68170 - 0.450611i) q^{24} +(4.27945 - 2.58580i) q^{25} +(-5.18186 + 1.76249i) q^{26} +(2.65095 + 2.65095i) q^{27} +(0.395026 - 0.684205i) q^{28} +(4.31701 + 2.49243i) q^{29} +(-0.0228795 - 2.29595i) q^{30} +(-2.32124 - 2.32124i) q^{31} +(1.47921 - 0.854024i) q^{32} +(-2.92863 + 1.69085i) q^{33} +(0.0878751 + 0.0878751i) q^{34} +(4.14355 + 4.06178i) q^{35} +(0.670383 + 0.387046i) q^{36} +(-0.285750 + 0.494934i) q^{37} +(-3.01318 - 3.01318i) q^{38} +(-2.18799 - 1.07736i) q^{39} +(1.54493 + 5.54419i) q^{40} +(10.0563 - 2.69458i) q^{41} +(2.57371 - 0.689624i) q^{42} +(0.0354017 - 0.132121i) q^{43} +(-1.07633 + 1.07633i) q^{44} +(-3.97973 + 4.05984i) q^{45} +(-5.94960 - 1.59419i) q^{46} -2.30053 q^{47} +(2.95076 + 0.790653i) q^{48} +(0.133293 - 0.230870i) q^{49} +(7.58873 - 0.151261i) q^{50} +0.0553744i q^{51} +(-1.07680 - 0.213514i) q^{52} +(6.70735 - 6.70735i) q^{53} +(1.47298 + 5.49724i) q^{54} +(-5.68573 - 9.62518i) q^{55} +(-5.78416 + 3.33948i) q^{56} -1.89875i q^{57} +(3.78362 + 6.55343i) q^{58} +(-0.694109 + 2.59045i) q^{59} +(0.226268 - 0.401085i) q^{60} +(-2.74237 - 4.74992i) q^{61} +(-1.28978 - 4.81352i) q^{62} +(-5.71351 - 3.29870i) q^{63} -6.43957 q^{64} +(3.48923 - 7.26810i) q^{65} -5.13357 q^{66} +(-13.6718 - 7.89339i) q^{67} +(0.00645104 + 0.0240756i) q^{68} +(-1.37228 - 2.37686i) q^{69} +(2.36440 + 8.48494i) q^{70} +(-1.98951 + 7.42495i) q^{71} +(-3.27202 - 5.66731i) q^{72} +6.61894i q^{73} +(-0.751333 + 0.433783i) q^{74} +(2.43867 + 2.34336i) q^{75} +(-0.221202 - 0.825536i) q^{76} +(9.17326 - 9.17326i) q^{77} +(-2.05874 - 3.07710i) q^{78} +5.71054i q^{79} +(-2.51638 + 9.78006i) q^{80} +(2.54575 - 4.40937i) q^{81} +(15.2660 + 4.09050i) q^{82} +3.70736 q^{83} +(0.516194 + 0.138314i) q^{84} +(-0.183046 + 0.00182408i) q^{85} +(0.146824 - 0.146824i) q^{86} +(-0.872695 + 3.25694i) q^{87} +(12.4296 - 3.33050i) q^{88} +(-17.2829 + 4.63094i) q^{89} +(-8.31353 + 2.31664i) q^{90} +(9.17731 + 1.81973i) q^{91} +(-0.873538 - 0.873538i) q^{92} +(1.11024 - 1.92300i) q^{93} +(-3.02443 - 1.74616i) q^{94} +(6.27651 - 0.0625465i) q^{95} +(0.816956 + 0.816956i) q^{96} +(4.65043 - 2.68493i) q^{97} +(0.350471 - 0.202345i) q^{98} +(8.98794 + 8.98794i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 8 q^{6} - 2 q^{7} + 12 q^{9}+O(q^{10}) \) 20 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 8 * q^6 - 2 * q^7 + 12 * q^9	\( 20 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 8 q^{6} - 2 q^{7} + 12 q^{9} - 2 q^{10} - 16 q^{11} - 24 q^{12} - 4 q^{13} - 20 q^{15} - 2 q^{16} + 4 q^{17} - 20 q^{19} + 4 q^{21} + 16 q^{22} - 10 q^{23} + 32 q^{24} + 18 q^{25} - 24 q^{26} + 4 q^{27} + 18 q^{28} - 26 q^{30} + 48 q^{32} + 18 q^{33} + 2 q^{34} + 40 q^{35} + 36 q^{36} - 4 q^{37} - 8 q^{38} + 4 q^{39} - 16 q^{40} + 10 q^{41} + 40 q^{42} + 10 q^{43} - 36 q^{44} + 4 q^{46} - 40 q^{47} - 56 q^{48} + 18 q^{49} + 36 q^{50} - 30 q^{52} - 10 q^{53} - 48 q^{54} - 10 q^{55} - 16 q^{59} + 28 q^{60} - 16 q^{61} - 44 q^{62} - 36 q^{63} + 20 q^{64} - 14 q^{65} - 32 q^{66} + 18 q^{67} + 22 q^{68} - 16 q^{69} - 12 q^{70} - 16 q^{71} + 4 q^{72} + 18 q^{74} - 38 q^{75} - 64 q^{76} - 28 q^{77} + 68 q^{78} - 2 q^{80} - 14 q^{81} + 56 q^{82} + 48 q^{83} - 40 q^{84} - 26 q^{85} + 60 q^{86} - 34 q^{87} + 82 q^{88} - 6 q^{89} + 46 q^{90} + 8 q^{91} - 8 q^{92} + 32 q^{93} - 48 q^{94} - 26 q^{95} + 56 q^{96} + 66 q^{97} - 30 q^{98} + 60 q^{99}+O(q^{100}) \) 20 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 8 * q^6 - 2 * q^7 + 12 * q^9 - 2 * q^10 - 16 * q^11 - 24 * q^12 - 4 * q^13 - 20 * q^15 - 2 * q^16 + 4 * q^17 - 20 * q^19 + 4 * q^21 + 16 * q^22 - 10 * q^23 + 32 * q^24 + 18 * q^25 - 24 * q^26 + 4 * q^27 + 18 * q^28 - 26 * q^30 + 48 * q^32 + 18 * q^33 + 2 * q^34 + 40 * q^35 + 36 * q^36 - 4 * q^37 - 8 * q^38 + 4 * q^39 - 16 * q^40 + 10 * q^41 + 40 * q^42 + 10 * q^43 - 36 * q^44 + 4 * q^46 - 40 * q^47 - 56 * q^48 + 18 * q^49 + 36 * q^50 - 30 * q^52 - 10 * q^53 - 48 * q^54 - 10 * q^55 - 16 * q^59 + 28 * q^60 - 16 * q^61 - 44 * q^62 - 36 * q^63 + 20 * q^64 - 14 * q^65 - 32 * q^66 + 18 * q^67 + 22 * q^68 - 16 * q^69 - 12 * q^70 - 16 * q^71 + 4 * q^72 + 18 * q^74 - 38 * q^75 - 64 * q^76 - 28 * q^77 + 68 * q^78 - 2 * q^80 - 14 * q^81 + 56 * q^82 + 48 * q^83 - 40 * q^84 - 26 * q^85 + 60 * q^86 - 34 * q^87 + 82 * q^88 - 6 * q^89 + 46 * q^90 + 8 * q^91 - 8 * q^92 + 32 * q^93 - 48 * q^94 - 26 * q^95 + 56 * q^96 + 66 * q^97 - 30 * q^98 + 60 * q^99

Introduction

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