LMFDB - Embedded newform 273.2.bd.b.43.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(43,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("273.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bd (of order $6$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 10 x^{14} - 8 x^{13} - 3 x^{12} + 32 x^{11} - 5 x^{10} - 44 x^{9} + 214 x^{8} + \cdots + 6561 $ x^16 - 4x^15 + 10x^14 - 8x^13 - 3x^12 + 32x^11 - 5x^10 - 44x^9 + 214x^8 - 132x^7 - 45x^6 + 864x^5 - 243x^4 - 1944x^3 + 7290x^2 - 8748*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.6
Root			$-0.306536 - 1.70471i$ of defining polynomial
Character	$\chi$	$=$	273.43
Dual form			273.2.bd.b.127.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.15033 + 0.664145i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.117823 - 0.204075i) q^{4} -1.55828i q^{5} +(1.15033 - 0.664145i) q^{6} +(-0.866025 + 0.500000i) q^{7} -2.96959i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(1.15033 + 0.664145i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.117823 - 0.204075i) q^{4} -1.55828i q^{5} +(1.15033 - 0.664145i) q^{6} +(-0.866025 + 0.500000i) q^{7} -2.96959i q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.03492 - 1.79254i) q^{10} +(3.66954 + 2.11861i) q^{11} -0.235645 q^{12} +(3.29452 - 1.46497i) q^{13} -1.32829 q^{14} +(-1.34951 - 0.779138i) q^{15} +(1.73659 - 3.00786i) q^{16} +(-0.391538 - 0.678164i) q^{17} -1.32829i q^{18} +(-5.02469 + 2.90100i) q^{19} +(-0.318005 + 0.183600i) q^{20} +1.00000i q^{21} +(2.81413 + 4.87421i) q^{22} +(-2.07926 + 3.60138i) q^{23} +(-2.57174 - 1.48479i) q^{24} +2.57177 q^{25} +(4.76275 + 0.502835i) q^{26} -1.00000 q^{27} +(0.204075 + 0.117823i) q^{28} +(-5.01901 + 8.69317i) q^{29} +(-1.03492 - 1.79254i) q^{30} -6.43659i q^{31} +(-1.14816 + 0.662890i) q^{32} +(3.66954 - 2.11861i) q^{33} -1.04015i q^{34} +(0.779138 + 1.34951i) q^{35} +(-0.117823 + 0.204075i) q^{36} +(5.84044 + 3.37198i) q^{37} -7.70675 q^{38} +(0.378558 - 3.58562i) q^{39} -4.62744 q^{40} +(-0.745771 - 0.430571i) q^{41} +(-0.664145 + 1.15033i) q^{42} +(2.79587 + 4.84259i) q^{43} -0.998480i q^{44} +(-1.34951 + 0.779138i) q^{45} +(-4.78367 + 2.76185i) q^{46} +13.1993i q^{47} +(-1.73659 - 3.00786i) q^{48} +(0.500000 - 0.866025i) q^{49} +(2.95840 + 1.70803i) q^{50} -0.783076 q^{51} +(-0.687133 - 0.499722i) q^{52} -2.25508 q^{53} +(-1.15033 - 0.664145i) q^{54} +(3.30138 - 5.71815i) q^{55} +(1.48479 + 2.57174i) q^{56} +5.80201i q^{57} +(-11.5471 + 6.66670i) q^{58} +(10.2481 - 5.91673i) q^{59} +0.367201i q^{60} +(-3.69949 - 6.40770i) q^{61} +(4.27483 - 7.40422i) q^{62} +(0.866025 + 0.500000i) q^{63} -8.70738 q^{64} +(-2.28283 - 5.13377i) q^{65} +5.62825 q^{66} +(-9.30150 - 5.37022i) q^{67} +(-0.0922642 + 0.159806i) q^{68} +(2.07926 + 3.60138i) q^{69} +2.06984i q^{70} +(-3.62191 + 2.09111i) q^{71} +(-2.57174 + 1.48479i) q^{72} -13.4249i q^{73} +(4.47897 + 7.75780i) q^{74} +(1.28589 - 2.22722i) q^{75} +(1.18404 + 0.683608i) q^{76} -4.23721 q^{77} +(2.81684 - 3.87324i) q^{78} +13.8087 q^{79} +(-4.68708 - 2.70609i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.571924 - 0.990601i) q^{82} +0.989701i q^{83} +(0.204075 - 0.117823i) q^{84} +(-1.05677 + 0.610125i) q^{85} +7.42746i q^{86} +(5.01901 + 8.69317i) q^{87} +(6.29139 - 10.8970i) q^{88} +(-4.59054 - 2.65035i) q^{89} -2.06984 q^{90} +(-2.12065 + 2.91596i) q^{91} +0.979934 q^{92} +(-5.57425 - 3.21830i) q^{93} +(-8.76626 + 15.1836i) q^{94} +(4.52057 + 7.82985i) q^{95} +1.32578i q^{96} +(-0.0673109 + 0.0388620i) q^{97} +(1.15033 - 0.664145i) q^{98} -4.23721i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} + 14 q^{4} - 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 + 14 * q^4 - 8 * q^9	$ 16 q + 8 q^{3} + 14 q^{4} - 8 q^{9} - 4 q^{10} + 28 q^{12} - 12 q^{13} - 4 q^{14} - 12 q^{15} - 10 q^{16} - 2 q^{17} + 18 q^{20} - 18 q^{22} - 6 q^{23} - 20 q^{25} + 20 q^{26} - 16 q^{27} - 12 q^{29} + 4 q^{30} - 30 q^{32} + 6 q^{35} + 14 q^{36} - 6 q^{37} - 24 q^{38} - 28 q^{40} - 30 q^{41} - 2 q^{42} + 14 q^{43} - 12 q^{45} - 42 q^{46} + 10 q^{48} + 8 q^{49} + 84 q^{50} - 4 q^{51} + 30 q^{52} + 28 q^{53} + 2 q^{55} - 12 q^{56} + 66 q^{58} - 24 q^{59} + 2 q^{61} - 20 q^{62} - 48 q^{64} - 44 q^{65} - 36 q^{66} + 30 q^{67} + 36 q^{68} + 6 q^{69} - 6 q^{71} + 6 q^{74} - 10 q^{75} - 24 q^{76} + 32 q^{77} + 10 q^{78} + 92 q^{79} + 114 q^{80} - 8 q^{81} - 42 q^{82} + 48 q^{85} + 12 q^{87} + 62 q^{88} + 18 q^{89} + 8 q^{90} - 116 q^{92} - 6 q^{93} - 24 q^{94} - 24 q^{95} - 6 q^{97}+O(q^{100}) $ 16 * q + 8 * q^3 + 14 * q^4 - 8 * q^9 - 4 * q^10 + 28 * q^12 - 12 * q^13 - 4 * q^14 - 12 * q^15 - 10 * q^16 - 2 * q^17 + 18 * q^20 - 18 * q^22 - 6 * q^23 - 20 * q^25 + 20 * q^26 - 16 * q^27 - 12 * q^29 + 4 * q^30 - 30 * q^32 + 6 * q^35 + 14 * q^36 - 6 * q^37 - 24 * q^38 - 28 * q^40 - 30 * q^41 - 2 * q^42 + 14 * q^43 - 12 * q^45 - 42 * q^46 + 10 * q^48 + 8 * q^49 + 84 * q^50 - 4 * q^51 + 30 * q^52 + 28 * q^53 + 2 * q^55 - 12 * q^56 + 66 * q^58 - 24 * q^59 + 2 * q^61 - 20 * q^62 - 48 * q^64 - 44 * q^65 - 36 * q^66 + 30 * q^67 + 36 * q^68 + 6 * q^69 - 6 * q^71 + 6 * q^74 - 10 * q^75 - 24 * q^76 + 32 * q^77 + 10 * q^78 + 92 * q^79 + 114 * q^80 - 8 * q^81 - 42 * q^82 + 48 * q^85 + 12 * q^87 + 62 * q^88 + 18 * q^89 + 8 * q^90 - 116 * q^92 - 6 * q^93 - 24 * q^94 - 24 * q^95 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	1.15033	+	0.664145i	0.813408	+	0.469621i	0.848138	−	0.529775i	$-0.177724\pi$
$2$	1.15033	+	0.664145i	0.813408	+	0.469621i	−0.0347298	+	0.999397i	$0.511057\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−0.117823	−	0.204075i	−0.0589114	−	0.102037i
$5$		−	1.55828i		−	0.696882i	−0.937331	−	0.348441i	$-0.886711\pi$
$5$		−	1.55828i		−	0.696882i	0.937331	−	0.348441i	$-0.113289\pi$
$6$	1.15033	−	0.664145i	0.469621	−	0.271136i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$8$		−	2.96959i		−	1.04991i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.03492	−	1.79254i	0.327271	−	0.566850i
$11$	3.66954	+	2.11861i	1.10641	+	0.638784i	0.937896	−	0.346916i	$-0.112771\pi$
$11$	3.66954	+	2.11861i	1.10641	+	0.638784i	0.168510	+	0.985700i	$0.446104\pi$
$12$	−0.235645			−0.0680250
$13$	3.29452	−	1.46497i	0.913735	−	0.406310i
$13$	3.29452	−	1.46497i	0.913735	−	0.406310i
$14$	−1.32829			−0.355000
$15$	−1.34951	−	0.779138i	−0.348441	−	0.201173i
$16$	1.73659	−	3.00786i	0.434148	−	0.751966i
$17$	−0.391538	−	0.678164i	−0.0949619	−	0.164479i	0.814631	−	0.579980i	$-0.196940\pi$
$17$	−0.391538	−	0.678164i	−0.0949619	−	0.164479i	−0.909593	+	0.415501i	$0.863606\pi$
$18$		−	1.32829i		−	0.313081i
$19$	−5.02469	+	2.90100i	−1.15274	+	0.665536i	−0.949554	−	0.313604i	$-0.898464\pi$
$19$	−5.02469	+	2.90100i	−1.15274	+	0.665536i	−0.203188	+	0.979140i	$0.565130\pi$
$20$	−0.318005	+	0.183600i	−0.0711081	+	0.0410543i
$21$			1.00000i			0.218218i
$22$	2.81413	+	4.87421i	0.599974	+	1.03918i
$23$	−2.07926	+	3.60138i	−0.433555	+	0.750939i	−0.997176	−	0.0750941i	$-0.976074\pi$
$23$	−2.07926	+	3.60138i	−0.433555	+	0.750939i	0.563622	+	0.826033i	$0.309408\pi$
$24$	−2.57174	−	1.48479i	−0.524954	−	0.303082i
$25$	2.57177			0.514355
$26$	4.76275	+	0.502835i	0.934052	+	0.0986140i
$27$	−1.00000			−0.192450
$28$	0.204075	+	0.117823i	0.0385665	+	0.0222664i
$29$	−5.01901	+	8.69317i	−0.932006	+	1.61428i	−0.152118	+	0.988362i	$0.548609\pi$
$29$	−5.01901	+	8.69317i	−0.932006	+	1.61428i	−0.779888	+	0.625919i	$0.784724\pi$
$30$	−1.03492	−	1.79254i	−0.188950	−	0.327271i
$31$		−	6.43659i		−	1.15605i	−0.816021	−	0.578023i	$-0.803824\pi$
$31$		−	6.43659i		−	1.15605i	0.816021	−	0.578023i	$-0.196176\pi$
$32$	−1.14816	+	0.662890i	−0.202968	+	0.117184i
$33$	3.66954	−	2.11861i	0.638784	−	0.368802i
$34$		−	1.04015i		−	0.178385i
$35$	0.779138	+	1.34951i	0.131698	+	0.228108i
$36$	−0.117823	+	0.204075i	−0.0196371	+	0.0340125i
$37$	5.84044	+	3.37198i	0.960162	+	0.554350i	0.896223	−	0.443604i	$-0.146300\pi$
$37$	5.84044	+	3.37198i	0.960162	+	0.554350i	0.0639394	+	0.997954i	$0.479634\pi$
$38$	−7.70675			−1.25020
$39$	0.378558	−	3.58562i	0.0606178	−	0.574159i
$40$	−4.62744			−0.731662
$41$	−0.745771	−	0.430571i	−0.116470	−	0.0672439i	0.440633	−	0.897687i	$-0.354754\pi$
$41$	−0.745771	−	0.430571i	−0.116470	−	0.0672439i	−0.557103	+	0.830443i	$0.688087\pi$
$42$	−0.664145	+	1.15033i	−0.102480	+	0.177500i
$43$	2.79587	+	4.84259i	0.426367	+	0.738489i	0.996547	−	0.0830309i	$-0.0264600\pi$
$43$	2.79587	+	4.84259i	0.426367	+	0.738489i	−0.570180	+	0.821520i	$0.693127\pi$
$44$		−	0.998480i		−	0.150527i
$45$	−1.34951	+	0.779138i	−0.201173	+	0.116147i
$46$	−4.78367	+	2.76185i	−0.705314	+	0.407213i
$47$			13.1993i			1.92532i	0.270715	+	0.962659i	$0.412740\pi$
$47$			13.1993i			1.92532i	−0.270715	+	0.962659i	$0.587260\pi$
$48$	−1.73659	−	3.00786i	−0.250655	−	0.434148i
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	2.95840	+	1.70803i	0.418380	+	0.241552i
$51$	−0.783076			−0.109653
$52$	−0.687133	−	0.499722i	−0.0952882	−	0.0692990i
$53$	−2.25508			−0.309759			−0.154880	−	0.987933i	$-0.549499\pi$
$53$	−2.25508			−0.309759			−0.154880	+	0.987933i	$0.549499\pi$
$54$	−1.15033	−	0.664145i	−0.156540	−	0.0903787i
$55$	3.30138	−	5.71815i	0.445157	−	0.771035i
$56$	1.48479	+	2.57174i	0.198414	+	0.343663i
$57$			5.80201i			0.768495i
$58$	−11.5471	+	6.66670i	−1.51620	+	0.875380i
$59$	10.2481	−	5.91673i	1.33419	−	0.770292i	0.348247	−	0.937403i	$-0.386777\pi$
$59$	10.2481	−	5.91673i	1.33419	−	0.770292i	0.985938	+	0.167111i	$0.0534437\pi$
$60$			0.367201i			0.0474054i
$61$	−3.69949	−	6.40770i	−0.473671	−	0.820422i	0.525875	−	0.850562i	$-0.323738\pi$
$61$	−3.69949	−	6.40770i	−0.473671	−	0.820422i	−0.999546	+	0.0301397i	$0.990405\pi$
$62$	4.27483	−	7.40422i	0.542904	−	0.940337i
$63$	0.866025	+	0.500000i	0.109109	+	0.0629941i
$64$	−8.70738			−1.08842
$65$	−2.28283	−	5.13377i	−0.283150	−	0.636766i
$66$	5.62825			0.692790
$67$	−9.30150	−	5.37022i	−1.13636	−	0.656077i	−0.190833	−	0.981623i	$-0.561119\pi$
$67$	−9.30150	−	5.37022i	−1.13636	−	0.656077i	−0.945526	+	0.325545i	$0.894452\pi$
$68$	−0.0922642	+	0.159806i	−0.0111887	+	0.0193794i
$69$	2.07926	+	3.60138i	0.250313	+	0.433555i
$70$			2.06984i			0.247394i
$71$	−3.62191	+	2.09111i	−0.429842	+	0.248169i	−0.699279	−	0.714849i	$-0.746496\pi$
$71$	−3.62191	+	2.09111i	−0.429842	+	0.248169i	0.269437	+	0.963018i	$0.413162\pi$
$72$	−2.57174	+	1.48479i	−0.303082	+	0.174985i
$73$		−	13.4249i		−	1.57127i	−0.618692	−	0.785634i	$-0.712337\pi$
$73$		−	13.4249i		−	1.57127i	0.618692	−	0.785634i	$-0.287663\pi$
$74$	4.47897	+	7.75780i	0.520669	+	0.901826i
$75$	1.28589	−	2.22722i	0.148481	−	0.257177i
$76$	1.18404	+	0.683608i	0.135819	+	0.0784153i
$77$	−4.23721			−0.482875
$78$	2.81684	−	3.87324i	0.318944	−	0.438558i
$79$	13.8087			1.55360			0.776799	−	0.629748i	$-0.216842\pi$
$79$	13.8087			1.55360			0.776799	+	0.629748i	$0.216842\pi$
$80$	−4.68708	−	2.70609i	−0.524032	−	0.302550i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−0.571924	−	0.990601i	−0.0631584	−	0.109394i
$83$			0.989701i			0.108634i	0.998524	+	0.0543169i	$0.0172981\pi$
$83$			0.989701i			0.108634i	−0.998524	+	0.0543169i	$0.982702\pi$
$84$	0.204075	−	0.117823i	0.0222664	−	0.0128555i
$85$	−1.05677	+	0.610125i	−0.114622	+	0.0661773i
$86$			7.42746i			0.800924i
$87$	5.01901	+	8.69317i	0.538094	+	0.932006i
$88$	6.29139	−	10.8970i	0.670664	−	1.16162i
$89$	−4.59054	−	2.65035i	−0.486597	−	0.280937i	0.236565	−	0.971616i	$-0.423978\pi$
$89$	−4.59054	−	2.65035i	−0.486597	−	0.280937i	−0.723161	+	0.690679i	$0.757312\pi$
$90$	−2.06984			−0.218181
$91$	−2.12065	+	2.91596i	−0.222305	+	0.305676i
$92$	0.979934			0.102165
$93$	−5.57425	−	3.21830i	−0.578023	−	0.333722i
$94$	−8.76626	+	15.1836i	−0.904171	+	1.56607i
$95$	4.52057	+	7.82985i	0.463800	+	0.803326i
$96$			1.32578i			0.135312i
$97$	−0.0673109	+	0.0388620i	−0.00683439	+	0.00394583i	−0.503413	−	0.864046i	$-0.667923\pi$
$97$	−0.0673109	+	0.0388620i	−0.00683439	+	0.00394583i	0.496579	+	0.867992i	$0.334589\pi$
$98$	1.15033	−	0.664145i	0.116201	−	0.0670888i
$99$		−	4.23721i		−	0.425856i
$100$	−0.303013	−	0.524835i	−0.0303013	−	0.0524835i
$101$	−1.42802	+	2.47340i	−0.142093	+	0.246113i	−0.928285	−	0.371870i	$-0.878717\pi$
$101$	−1.42802	+	2.47340i	−0.142093	+	0.246113i	0.786191	+	0.617983i	$0.212050\pi$
$102$	−0.900798	−	0.520076i	−0.0891923	−	0.0514952i
$103$	−5.72595			−0.564194			−0.282097	−	0.959386i	$-0.591030\pi$
$103$	−5.72595			−0.564194			−0.282097	+	0.959386i	$0.591030\pi$
$104$	−4.35036	−	9.78336i	−0.426588	−	0.959337i
$105$	1.55828			0.152072
$106$	−2.59410	−	1.49770i	−0.251961	−	0.145470i
$107$	−2.88588	+	4.99850i	−0.278989	+	0.483223i	−0.971134	−	0.238536i	$-0.923333\pi$
$107$	−2.88588	+	4.99850i	−0.278989	+	0.483223i	0.692145	+	0.721759i	$0.256666\pi$
$108$	0.117823	+	0.204075i	0.0113375	+	0.0196371i
$109$		−	13.4718i		−	1.29037i	−0.764028	−	0.645183i	$-0.776781\pi$
$109$		−	13.4718i		−	1.29037i	0.764028	−	0.645183i	$-0.223219\pi$
$110$	7.59536	−	4.38519i	0.724189	−	0.418111i
$111$	5.84044	−	3.37198i	0.554350	−	0.320054i
$112$			3.47318i			0.328185i
$113$	3.99812	+	6.92495i	0.376112	+	0.651445i	0.990493	−	0.137565i	$-0.0439275\pi$
$113$	3.99812	+	6.92495i	0.376112	+	0.651445i	−0.614381	+	0.789010i	$0.710594\pi$
$114$	−3.85337	+	6.67424i	−0.360902	+	0.625100i
$115$	5.61194	+	3.24006i	0.523316	+	0.302137i
$116$	2.36541			0.219623
$117$	−2.91596	−	2.12065i	−0.269581	−	0.196054i
$118$	15.7183			1.44698
$119$	0.678164	+	0.391538i	0.0621672	+	0.0358922i
$120$	−2.31372	+	4.00748i	−0.211213	+	0.365831i
$121$	3.47699	+	6.02233i	0.316090	+	0.547485i
$122$		−	9.82799i		−	0.889785i
$123$	−0.745771	+	0.430571i	−0.0672439	+	0.0388233i
$124$	−1.31355	+	0.758377i	−0.117960	+	0.0681042i
$125$		−	11.7989i		−	1.05533i
$126$	0.664145	+	1.15033i	0.0591667	+	0.102480i
$127$	−3.66963	+	6.35599i	−0.325627	+	0.564003i	−0.981639	−	0.190748i	$-0.938909\pi$
$127$	−3.66963	+	6.35599i	−0.325627	+	0.564003i	0.656012	+	0.754751i	$0.272242\pi$
$128$	−7.72007	−	4.45718i	−0.682364	−	0.393963i
$129$	5.59175			0.492326
$130$	0.783555	−	7.42168i	0.0687223	−	0.650924i
$131$	−2.13144			−0.186225			−0.0931125	−	0.995656i	$-0.529682\pi$
$131$	−2.13144			−0.186225			−0.0931125	+	0.995656i	$0.529682\pi$
$132$	−0.864709	−	0.499240i	−0.0752633	−	0.0434533i
$133$	2.90100	−	5.02469i	0.251549	−	0.435696i
$134$	−7.13321	−	12.3551i	−0.616216	−	1.06732i
$135$			1.55828i			0.134115i
$136$	−2.01387	+	1.16271i	−0.172688	+	0.0997012i
$137$	6.52853	−	3.76925i	0.557770	−	0.322029i	−0.194480	−	0.980907i	$-0.562302\pi$
$137$	6.52853	−	3.76925i	0.557770	−	0.322029i	0.752250	+	0.658878i	$0.228969\pi$
$138$			5.52371i			0.470209i
$139$	5.56775	+	9.64363i	0.472250	+	0.817962i	0.999496	−	0.0317513i	$-0.0101085\pi$
$139$	5.56775	+	9.64363i	0.472250	+	0.817962i	−0.527245	+	0.849713i	$0.676775\pi$
$140$	0.183600	−	0.318005i	0.0155171	−	0.0268763i
$141$	11.4309	+	6.59966i	0.962659	+	0.555792i
$142$	−5.55521			−0.466183
$143$	15.1931	+	1.60403i	1.27051	+	0.134136i
$144$	−3.47318			−0.289432
$145$	13.5464	+	7.82100i	1.12496	+	0.649499i
$146$	8.91609	−	15.4431i	0.737901	−	1.27808i
$147$	−0.500000	−	0.866025i	−0.0412393	−	0.0714286i
$148$		−	1.58918i		−	0.130630i
$149$	−10.3217	+	5.95922i	−0.845584	+	0.488198i	−0.859158	−	0.511710i	$-0.829012\pi$
$149$	−10.3217	+	5.95922i	−0.845584	+	0.488198i	0.0135744	+	0.999908i	$0.495679\pi$
$150$	2.95840	−	1.70803i	0.241552	−	0.139460i
$151$			10.4448i			0.849987i	0.905196	+	0.424993i	$0.139724\pi$
$151$			10.4448i			0.849987i	−0.905196	+	0.424993i	$0.860276\pi$
$152$	8.61478	+	14.9212i	0.698751	+	1.21027i
$153$	−0.391538	+	0.678164i	−0.0316540	+	0.0548263i
$154$	−4.87421	−	2.81413i	−0.392775	−	0.226769i
$155$	−10.0300			−0.805628
$156$	−0.776339	+	0.345214i	−0.0621568	+	0.0276392i
$157$	−3.31730			−0.264750			−0.132375	−	0.991200i	$-0.542260\pi$
$157$	−3.31730			−0.264750			−0.132375	+	0.991200i	$0.542260\pi$
$158$	15.8846	+	9.17097i	1.26371	+	0.729603i
$159$	−1.12754	+	1.95296i	−0.0894198	+	0.154880i
$160$	1.03297	+	1.78915i	0.0816631	+	0.141445i
$161$		−	4.15851i		−	0.327737i
$162$	−1.15033	+	0.664145i	−0.0903787	+	0.0521802i
$163$	5.80660	−	3.35244i	0.454808	−	0.262584i	−0.255050	−	0.966928i	$-0.582092\pi$
$163$	5.80660	−	3.35244i	0.454808	−	0.262584i	0.709859	+	0.704344i	$0.248759\pi$
$164$			0.202924i			0.0158457i
$165$	−3.30138	−	5.71815i	−0.257012	−	0.445157i
$166$	−0.657305	+	1.13849i	−0.0510167	+	0.0883636i
$167$	−16.0732	−	9.27985i	−1.24378	−	0.718097i	−0.273918	−	0.961753i	$-0.588320\pi$
$167$	−16.0732	−	9.27985i	−1.24378	−	0.718097i	−0.969862	+	0.243656i	$0.921653\pi$
$168$	2.96959			0.229109
$169$	8.70772	−	9.65275i	0.669825	−	0.742519i
$170$	−1.62085			−0.124313
$171$	5.02469	+	2.90100i	0.384247	+	0.221845i
$172$	0.658835	−	1.14114i	0.0502357	−	0.0870107i
$173$	−0.857721	−	1.48562i	−0.0652113	−	0.112949i	0.831576	−	0.555410i	$-0.187439\pi$
$173$	−0.857721	−	1.48562i	−0.0652113	−	0.112949i	−0.896788	+	0.442461i	$0.854105\pi$
$174$			13.3334i			1.01080i
$175$	−2.22722	+	1.28589i	−0.168362	+	0.0972039i
$176$	12.7450	−	7.35831i	0.960687	−	0.554653i
$177$		−	11.8335i		−	0.889457i
$178$	−3.52044	−	6.09757i	−0.263868	−	0.457032i
$179$	7.33903	−	12.7116i	0.548545	−	0.950108i	−0.449830	−	0.893114i	$-0.648515\pi$
$179$	7.33903	−	12.7116i	0.548545	−	0.950108i	0.998375	−	0.0569932i	$-0.0181513\pi$
$180$	0.318005	+	0.183600i	0.0237027	+	0.0136848i
$181$	−6.35871			−0.472639			−0.236320	−	0.971675i	$-0.575941\pi$
$181$	−6.35871			−0.472639			−0.236320	+	0.971675i	$0.575941\pi$
$182$	−4.37608	+	1.94591i	−0.324376	+	0.144240i
$183$	−7.39898			−0.546948
$184$	10.6946	+	6.17453i	0.788416	+	0.455192i
$185$	5.25448	−	9.10102i	0.386317	−	0.669120i
$186$	−4.27483	−	7.40422i	−0.313446	−	0.542904i
$187$		−	3.31806i		−	0.242641i
$188$	2.69365	−	1.55518i	0.196455	−	0.113423i
$189$	0.866025	−	0.500000i	0.0629941	−	0.0363696i
$190$			12.0092i			0.871242i
$191$	2.45200	+	4.24699i	0.177421	+	0.307302i	0.940996	−	0.338417i	$-0.109891\pi$
$191$	2.45200	+	4.24699i	0.177421	+	0.307302i	−0.763576	+	0.645718i	$0.776558\pi$
$192$	−4.35369	+	7.54081i	−0.314201	+	0.544211i
$193$	−9.33991	−	5.39240i	−0.672302	−	0.388153i	0.124647	−	0.992201i	$-0.460220\pi$
$193$	−9.33991	−	5.39240i	−0.672302	−	0.388153i	−0.796948	+	0.604048i	$0.793554\pi$
$194$	−0.103240			−0.00741219
$195$	−5.58739	−	0.589898i	−0.400121	−	0.0422434i
$196$	−0.235645			−0.0168318
$197$	−22.7973	−	13.1620i	−1.62424	−	0.937756i	−0.985768	−	0.168111i	$-0.946233\pi$
$197$	−22.7973	−	13.1620i	−1.62424	−	0.937756i	−0.638472	−	0.769645i	$-0.720433\pi$
$198$	2.81413	−	4.87421i	0.199991	−	0.346395i
$199$	13.0547	+	22.6114i	0.925422	+	1.60288i	0.790881	+	0.611970i	$0.209623\pi$
$199$	13.0547	+	22.6114i	0.925422	+	1.60288i	0.134541	+	0.990908i	$0.457044\pi$
$200$		−	7.63710i		−	0.540025i
$201$	−9.30150	+	5.37022i	−0.656077	+	0.378786i
$202$	−3.28539	+	1.89682i	−0.231160	+	0.133460i
$203$		−	10.0380i		−	0.704530i
$204$	0.0922642	+	0.159806i	0.00645978	+	0.0111887i
$205$	−0.670949	+	1.16212i	−0.0468611	+	0.0811658i
$206$	−6.58674	−	3.80286i	−0.458920	−	0.264958i
$207$	4.15851			0.289037
$208$	1.31480	−	12.4535i	0.0911649	−	0.863496i
$209$	−24.5844			−1.70054
$210$	1.79254	+	1.03492i	0.123697	+	0.0714164i
$211$	6.27361	−	10.8662i	0.431893	−	0.748060i	−0.565143	−	0.824993i	$-0.691179\pi$
$211$	6.27361	−	10.8662i	0.431893	−	0.748060i	0.997036	+	0.0769323i	$0.0245125\pi$
$212$	0.265700	+	0.460206i	0.0182484	+	0.0316071i
$213$			4.18222i			0.286561i
$214$	−6.63946	+	3.83329i	−0.453864	+	0.262038i
$215$	7.54610	−	4.35674i	0.514640	−	0.297127i
$216$			2.96959i			0.202055i
$217$	3.21830	+	5.57425i	0.218472	+	0.378405i
$218$	8.94724	−	15.4971i	0.605984	−	1.04959i
$219$	−11.6263	−	6.71246i	−0.785634	−	0.453586i
$220$	−1.55591			−0.104899
$221$	−2.28342	−	1.66063i	−0.153599	−	0.111706i
$222$	8.95793			0.601217
$223$	−14.9196	−	8.61384i	−0.999090	−	0.576825i	−0.0911113	−	0.995841i	$-0.529042\pi$
$223$	−14.9196	−	8.61384i	−0.999090	−	0.576825i	−0.907979	+	0.419016i	$0.862375\pi$
$224$	0.662890	−	1.14816i	0.0442912	−	0.0767146i
$225$	−1.28589	−	2.22722i	−0.0857258	−	0.148481i
$226$			10.6213i			0.706521i
$227$	−11.2450	+	6.49228i	−0.746354	+	0.430908i	−0.824375	−	0.566044i	$-0.808473\pi$
$227$	−11.2450	+	6.49228i	−0.746354	+	0.430908i	0.0780211	+	0.996952i	$0.475140\pi$
$228$	1.18404	−	0.683608i	0.0784153	−	0.0452731i
$229$			17.4443i			1.15275i	0.817186	+	0.576374i	$0.195533\pi$
$229$			17.4443i			1.15275i	−0.817186	+	0.576374i	$0.804467\pi$
$230$	4.30373	+	7.45428i	0.283780	+	0.491521i
$231$	−2.11861	+	3.66954i	−0.139394	+	0.241438i
$232$	25.8151	+	14.9044i	1.69485	+	0.978520i
$233$	17.7371			1.16199			0.580997	−	0.813905i	$-0.302663\pi$
$233$	17.7371			1.16199			0.580997	+	0.813905i	$0.302663\pi$
$234$	−1.94591	−	4.37608i	−0.127208	−	0.286073i
$235$	20.5682			1.34172
$236$	−2.41491	−	1.39425i	−0.157197	−	0.0907579i
$237$	6.90434	−	11.9587i	0.448485	−	0.776799i
$238$	0.520076	+	0.900798i	0.0337115	+	0.0583901i
$239$		−	10.2570i		−	0.663468i	−0.943373	−	0.331734i	$-0.892366\pi$
$239$		−	10.2570i		−	0.663468i	0.943373	−	0.331734i	$-0.107634\pi$
$240$	−4.68708	+	2.70609i	−0.302550	+	0.174677i
$241$	−11.1221	+	6.42137i	−0.716440	+	0.413637i	−0.813441	−	0.581648i	$-0.802408\pi$
$241$	−11.1221	+	6.42137i	−0.716440	+	0.413637i	0.0970010	+	0.995284i	$0.469075\pi$
$242$			9.23692i			0.593771i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−0.871768	+	1.50995i	−0.0558092	+	0.0966644i
$245$	−1.34951	−	0.779138i	−0.0862168	−	0.0497773i
$246$	−1.14385			−0.0729290
$247$	−12.3040	+	16.9184i	−0.782887	+	1.07649i
$248$	−19.1140			−1.21374
$249$	0.857106	+	0.494850i	0.0543169	+	0.0313599i
$250$	7.83619	−	13.5727i	0.495604	−	0.858412i
$251$	−1.22240	−	2.11726i	−0.0771572	−	0.133640i	0.824865	−	0.565330i	$-0.191251\pi$
$251$	−1.22240	−	2.11726i	−0.0771572	−	0.133640i	−0.902022	+	0.431689i	$0.857918\pi$
$252$		−	0.235645i		−	0.0148443i
$253$	−15.2598	+	8.81025i	−0.959376	+	0.553896i
$254$	−8.44260	+	4.87434i	−0.529736	+	0.305843i
$255$			1.22025i			0.0764150i
$256$	2.78695	+	4.82714i	0.174184	+	0.301696i
$257$	−4.56319	+	7.90367i	−0.284644	+	0.493017i	−0.972523	−	0.232808i	$-0.925209\pi$
$257$	−4.56319	+	7.90367i	−0.284644	+	0.493017i	0.687879	+	0.725825i	$0.258542\pi$
$258$	6.43237	+	3.71373i	0.400462	+	0.231207i
$259$	−6.74396			−0.419049
$260$	−0.778705	+	1.07074i	−0.0482932	+	0.0664047i
$261$	10.0380			0.621337
$262$	−2.45187	−	1.41559i	−0.151477	−	0.0874552i
$263$	−16.1356	+	27.9476i	−0.994961	+	1.72332i	−0.410650	+	0.911793i	$0.634698\pi$
$263$	−16.1356	+	27.9476i	−0.994961	+	1.72332i	−0.584311	+	0.811530i	$0.698635\pi$
$264$	−6.29139	−	10.8970i	−0.387208	−	0.670664i
$265$			3.51404i			0.215866i
$266$	6.67424	−	3.85337i	0.409224	−	0.236266i
$267$	−4.59054	+	2.65035i	−0.280937	+	0.162199i
$268$			2.53094i			0.154602i
$269$	2.75834	+	4.77758i	0.168179	+	0.291294i	0.937780	−	0.347231i	$-0.112878\pi$
$269$	2.75834	+	4.77758i	0.168179	+	0.291294i	−0.769601	+	0.638525i	$0.779545\pi$
$270$	−1.03492	+	1.79254i	−0.0629833	+	0.109090i
$271$	−25.6527	−	14.8106i	−1.55829	−	0.899680i	−0.997421	−	0.0717776i	$-0.977133\pi$
$271$	−25.6527	−	14.8106i	−1.55829	−	0.899680i	−0.560872	−	0.827903i	$-0.689534\pi$
$272$	−2.71977			−0.164910
$273$	1.46497	+	3.29452i	0.0886641	+	0.199393i
$274$	10.0133			0.604926
$275$	9.43722	+	5.44858i	0.569086	+	0.328562i
$276$	0.489967	−	0.848648i	0.0294926	−	0.0510826i
$277$	−9.82307	−	17.0141i	−0.590211	−	1.02228i	−0.994204	−	0.107513i	$-0.965711\pi$
$277$	−9.82307	−	17.0141i	−0.590211	−	1.02228i	0.403993	−	0.914762i	$-0.367622\pi$
$278$			14.7912i			0.887116i
$279$	−5.57425	+	3.21830i	−0.333722	+	0.192674i
$280$	4.00748	−	2.31372i	0.239493	−	0.138271i
$281$			0.601681i			0.0358932i	0.999839	+	0.0179466i	$0.00571289\pi$
$281$			0.601681i			0.0358932i	−0.999839	+	0.0179466i	$0.994287\pi$
$282$	8.76626	+	15.1836i	0.522023	+	0.904171i
$283$	−5.25559	+	9.10295i	−0.312412	+	0.541114i	−0.978884	−	0.204416i	$-0.934470\pi$
$283$	−5.25559	+	9.10295i	−0.312412	+	0.541114i	0.666472	+	0.745530i	$0.267804\pi$
$284$	0.853487	+	0.492761i	0.0506451	+	0.0292400i
$285$	9.04113			0.535550
$286$	16.4118	+	11.9356i	0.970448	+	0.705765i
$287$	0.861143			0.0508316
$288$	1.14816	+	0.662890i	0.0676559	+	0.0390612i
$289$	8.19340	−	14.1914i	0.481964	−	0.834787i
$290$	10.3886	+	17.9935i	0.610037	+	1.05662i
$291$			0.0777239i			0.00455626i
$292$	−2.73969	+	1.58176i	−0.160328	+	0.0925655i
$293$	7.45252	−	4.30271i	0.435381	−	0.251367i	−0.266255	−	0.963903i	$-0.585786\pi$
$293$	7.45252	−	4.30271i	0.435381	−	0.251367i	0.701636	+	0.712535i	$0.252453\pi$
$294$		−	1.32829i		−	0.0774675i
$295$	−9.21990	−	15.9693i	−0.536803	−	0.929770i
$296$	10.0134	−	17.3437i	0.582016	−	1.00808i
$297$	−3.66954	−	2.11861i	−0.212928	−	0.122934i
$298$	−15.8311			−0.917073
$299$	−1.57424	+	14.9109i	−0.0910405	+	0.862317i
$300$	−0.606027			−0.0349890
$301$	−4.84259	−	2.79587i	−0.279122	−	0.161151i
$302$	−6.93687	+	12.0150i	−0.399172	+	0.691386i
$303$	1.42802	+	2.47340i	0.0820375	+	0.142093i
$304$			20.1514i			1.15576i
$305$	−9.98497	+	5.76483i	−0.571738	+	0.330093i
$306$	−0.900798	+	0.520076i	−0.0514952	+	0.0297308i
$307$			10.8192i			0.617485i	0.951146	+	0.308742i	$0.0999081\pi$
$307$			10.8192i			0.617485i	−0.951146	+	0.308742i	$0.900092\pi$
$308$	0.499240	+	0.864709i	0.0284469	+	0.0492714i
$309$	−2.86297	+	4.95881i	−0.162869	+	0.282097i
$310$	−11.5378	−	6.66137i	−0.655304	−	0.378340i
$311$	−9.44634			−0.535653			−0.267826	−	0.963467i	$-0.586305\pi$
$311$	−9.44634			−0.535653			−0.267826	+	0.963467i	$0.586305\pi$
$312$	−10.6478	−	1.12416i	−0.602814	−	0.0636430i
$313$	7.88304			0.445576			0.222788	−	0.974867i	$-0.428484\pi$
$313$	7.88304			0.445576			0.222788	+	0.974867i	$0.428484\pi$
$314$	−3.81600	−	2.20317i	−0.215350	−	0.124332i
$315$	0.779138	−	1.34951i	0.0438995	−	0.0760361i
$316$	−1.62698	−	2.81801i	−0.0915246	−	0.158525i
$317$		−	21.7455i		−	1.22135i	−0.791882	−	0.610675i	$-0.790898\pi$
$317$		−	21.7455i		−	1.22135i	0.791882	−	0.610675i	$-0.209102\pi$
$318$	−2.59410	+	1.49770i	−0.145470	+	0.0839870i
$319$	−36.8348	+	21.2666i	−2.06236	+	1.19070i
$320$			13.5685i			0.758503i
$321$	2.88588	+	4.99850i	0.161074	+	0.278989i
$322$	2.76185	−	4.78367i	0.153912	−	0.266584i
$323$	3.93471	+	2.27171i	0.218933	+	0.126401i
$324$	0.235645			0.0130914
$325$	8.47276	−	3.76757i	0.469984	−	0.208987i
$326$	8.90604			0.493260
$327$	−11.6669	−	6.73591i	−0.645183	−	0.372497i
$328$	−1.27862	+	2.21463i	−0.0705999	+	0.122283i
$329$	−6.59966	−	11.4309i	−0.363851	−	0.630209i
$330$		−	8.77037i		−	0.482793i
$331$	22.1709	−	12.8004i	1.21862	−	0.703573i	0.254001	−	0.967204i	$-0.418253\pi$
$331$	22.1709	−	12.8004i	1.21862	−	0.703573i	0.964624	+	0.263631i	$0.0849201\pi$
$332$	0.201973	−	0.116609i	0.0110847	−	0.00639976i
$333$		−	6.74396i		−	0.369567i
$334$	−12.3263	−	21.3498i	−0.674467	−	1.16821i
$335$	−8.36829	+	14.4943i	−0.457209	+	0.791909i
$336$	3.00786	+	1.73659i	0.164092	+	0.0947388i
$337$	−14.4361			−0.786384			−0.393192	−	0.919456i	$-0.628629\pi$
$337$	−14.4361			−0.786384			−0.393192	+	0.919456i	$0.628629\pi$
$338$	16.4276	−	5.32069i	0.893544	−	0.289407i
$339$	7.99625			0.434297
$340$	0.249022	+	0.143773i	0.0135051	+	0.00779719i
$341$	13.6366	−	23.6193i	0.738464	−	1.27906i
$342$	3.85337	+	6.67424i	0.208367	+	0.360902i
$343$			1.00000i			0.0539949i
$344$	14.3805	−	8.30258i	0.775344	−	0.447645i
$345$	5.61194	−	3.24006i	0.302137	−	0.174439i
$346$		−	2.27860i		−	0.122499i
$347$	7.05457	+	12.2189i	0.378709	+	0.655943i	0.990875	−	0.134786i	$-0.0430348\pi$
$347$	7.05457	+	12.2189i	0.378709	+	0.655943i	−0.612166	+	0.790730i	$0.709701\pi$
$348$	1.18271	−	2.04851i	0.0633997	−	0.109811i
$349$	11.8136	+	6.82060i	0.632369	+	0.365098i	0.781669	−	0.623694i	$-0.214369\pi$
$349$	11.8136	+	6.82060i	0.632369	+	0.365098i	−0.149300	+	0.988792i	$0.547702\pi$
$350$	−3.41606			−0.182596
$351$	−3.29452	+	1.46497i	−0.175848	+	0.0781944i
$352$	−5.61762			−0.299420
$353$	−8.54783	−	4.93509i	−0.454955	−	0.262668i	0.254966	−	0.966950i	$-0.417936\pi$
$353$	−8.54783	−	4.93509i	−0.454955	−	0.262668i	−0.709921	+	0.704282i	$0.751269\pi$
$354$	7.85913	−	13.6124i	0.417708	−	0.723492i
$355$	3.25853	+	5.64394i	0.172945	+	0.299549i
$356$			1.24909i			0.0662015i
$357$	0.678164	−	0.391538i	0.0358922	−	0.0207224i
$358$	16.8847	−	9.74836i	0.892382	−	0.515217i
$359$			14.4485i			0.762564i	0.924459	+	0.381282i	$0.124517\pi$
$359$			14.4485i			0.762564i	−0.924459	+	0.381282i	$0.875483\pi$
$360$	2.31372	+	4.00748i	0.121944	+	0.211213i
$361$	7.33164	−	12.6988i	0.385876	−	0.668357i
$362$	−7.31464	−	4.22311i	−0.384449	−	0.221962i
$363$	6.95399			0.364990
$364$	0.844936	+	0.0892054i	0.0442867	+	0.00467563i
$365$	−20.9197			−1.09499
$366$	−8.51129	−	4.91400i	−0.444892	−	0.256859i
$367$	12.2325	−	21.1874i	0.638533	−	1.10597i	−0.347222	−	0.937783i	$-0.612875\pi$
$367$	12.2325	−	21.1874i	0.638533	−	1.10597i	0.985755	−	0.168188i	$-0.0537916\pi$
$368$	7.22163	+	12.5082i	0.376453	+	0.652037i
$369$			0.861143i			0.0448293i
$370$	12.0888	−	6.97947i	0.628466	−	0.362845i
$371$	1.95296	−	1.12754i	0.101393	−	0.0585390i
$372$			1.51675i			0.0786400i
$373$	−12.2403	−	21.2008i	−0.633777	−	1.09773i	−0.986773	−	0.162110i	$-0.948170\pi$
$373$	−12.2403	−	21.2008i	−0.633777	−	1.09773i	0.352995	−	0.935625i	$-0.385163\pi$
$374$	2.20367	−	3.81688i	0.113949	−	0.197366i
$375$	−10.2182	−	5.89946i	−0.527664	−	0.304647i
$376$	39.1965			2.02141
$377$	−3.79997	+	35.9925i	−0.195708	+	1.85371i
$378$	1.32829			0.0683199
$379$	16.3588	+	9.44475i	0.840294	+	0.485144i	0.857364	−	0.514710i	$-0.172100\pi$
$379$	16.3588	+	9.44475i	0.840294	+	0.485144i	−0.0170699	+	0.999854i	$0.505434\pi$
$380$	1.06525	−	1.84507i	0.0546462	−	0.0946500i
$381$	3.66963	+	6.35599i	0.188001	+	0.325627i
$382$			6.51394i			0.333282i
$383$	9.76071	−	5.63535i	0.498749	−	0.287953i	−0.229448	−	0.973321i	$-0.573692\pi$
$383$	9.76071	−	5.63535i	0.498749	−	0.287953i	0.728197	+	0.685368i	$0.240359\pi$
$384$	−7.72007	+	4.45718i	−0.393963	+	0.227455i
$385$			6.60275i			0.336507i
$386$	−7.16267	−	12.4061i	−0.364570	−	0.631454i
$387$	2.79587	−	4.84259i	0.142122	−	0.246163i
$388$	0.0158615	+	0.00915764i	0.000805246	+	0.000464909i
$389$	24.9797			1.26652			0.633261	−	0.773938i	$-0.281716\pi$
$389$	24.9797			1.26652			0.633261	+	0.773938i	$0.281716\pi$
$390$	−6.03558	−	4.38942i	−0.305624	−	0.222267i
$391$	3.25643			0.164685
$392$	−2.57174	−	1.48479i	−0.129892	−	0.0749934i
$393$	−1.06572	+	1.84588i	−0.0537585	+	0.0931125i
$394$	−17.4830	−	30.2814i	−0.880780	−	1.52556i
$395$		−	21.5178i		−	1.08268i
$396$	−0.864709	+	0.499240i	−0.0434533	+	0.0250878i
$397$	−2.94325	+	1.69928i	−0.147717	+	0.0852846i	−0.572037	−	0.820228i	$-0.693847\pi$
$397$	−2.94325	+	1.69928i	−0.147717	+	0.0852846i	0.424320	+	0.905512i	$0.360513\pi$
$398$			34.6808i			1.73839i
$399$	−2.90100	−	5.02469i	−0.145232	−	0.251549i
$400$	4.46612	−	7.73554i	0.223306	−	0.386777i
$401$	−12.0360	−	6.94897i	−0.601047	−	0.347015i	0.168406	−	0.985718i	$-0.446138\pi$
$401$	−12.0360	−	6.94897i	−0.601047	−	0.347015i	−0.769454	+	0.638703i	$0.779471\pi$
$402$	−14.2664			−0.711545
$403$	−9.42942	−	21.2055i	−0.469713	−	1.05632i
$404$	0.673012			0.0334836
$405$	1.34951	+	0.779138i	0.0670575	+	0.0387157i
$406$	6.66670	−	11.5471i	0.330863	−	0.573071i
$407$	14.2878	+	24.7472i	0.708220	+	1.22667i
$408$			2.32541i			0.115125i
$409$	14.9695	−	8.64262i	0.740192	−	0.427350i	−0.0819473	−	0.996637i	$-0.526114\pi$
$409$	14.9695	−	8.64262i	0.740192	−	0.427350i	0.822139	+	0.569287i	$0.192781\pi$
$410$	−1.54363	+	0.891215i	−0.0762344	+	0.0440140i
$411$		−	7.53850i		−	0.371847i
$412$	0.674647	+	1.16852i	0.0332375	+	0.0575690i
$413$	−5.91673	+	10.2481i	−0.291143	+	0.504275i
$414$	4.78367	+	2.76185i	0.235105	+	0.135738i
$415$	1.54223			0.0757049
$416$	−2.81152	+	3.86593i	−0.137846	+	0.189543i
$417$	11.1355			0.545308
$418$	−28.2802	−	16.3276i	−1.38323	−	0.798608i
$419$	3.73240	−	6.46471i	0.182340	−	0.315822i	−0.760337	−	0.649529i	$-0.774966\pi$
$419$	3.73240	−	6.46471i	0.182340	−	0.315822i	0.942677	+	0.333707i	$0.108300\pi$
$420$	−0.183600	−	0.318005i	−0.00895878	−	0.0155171i
$421$		−	17.2523i		−	0.840826i	−0.907333	−	0.420413i	$-0.861885\pi$
$421$		−	17.2523i		−	0.840826i	0.907333	−	0.420413i	$-0.138115\pi$
$422$	14.4335	−	8.33317i	0.702610	−	0.405652i
$423$	11.4309	−	6.59966i	0.555792	−	0.320886i
$424$			6.69666i			0.325219i
$425$	−1.00695	−	1.74408i	−0.0488441	−	0.0846005i
$426$	−2.77760	+	4.81095i	−0.134575	+	0.233091i
$427$	6.40770	+	3.69949i	0.310091	+	0.179031i
$428$	1.36009			0.0657425
$429$	8.98566	−	12.3556i	0.433832	−	0.596532i
$430$	11.5740			0.558150
$431$	25.4090	+	14.6699i	1.22391	+	0.706625i	0.965749	−	0.259477i	$-0.0835501\pi$
$431$	25.4090	+	14.6699i	1.22391	+	0.706625i	0.258161	+	0.966102i	$0.416883\pi$
$432$	−1.73659	+	3.00786i	−0.0835517	+	0.144716i
$433$	−3.69938	−	6.40751i	−0.177781	−	0.307925i	0.763339	−	0.645998i	$-0.223558\pi$
$433$	−3.69938	−	6.40751i	−0.177781	−	0.307925i	−0.941120	+	0.338072i	$0.890225\pi$
$434$			8.54966i			0.410397i
$435$	13.5464	−	7.82100i	0.649499	−	0.374988i
$436$	−2.74926	+	1.58729i	−0.131666	+	0.0760172i
$437$		−	24.1277i		−	1.15419i
$438$	−8.91609	−	15.4431i	−0.426027	−	0.737901i
$439$	−14.2042	+	24.6024i	−0.677930	+	1.17421i	0.297673	+	0.954668i	$0.403790\pi$
$439$	−14.2042	+	24.6024i	−0.677930	+	1.17421i	−0.975603	+	0.219542i	$0.929544\pi$
$440$	−16.9805	−	9.80372i	−0.809515	−	0.467374i
$441$	−1.00000			−0.0476190
$442$	−1.52379	−	3.42680i	−0.0724794	−	0.162996i
$443$	7.87863			0.374325			0.187162	−	0.982329i	$-0.440071\pi$
$443$	7.87863			0.374325			0.187162	+	0.982329i	$0.440071\pi$
$444$	−1.37627	−	0.794592i	−0.0653150	−	0.0377096i
$445$	−4.12998	+	7.15334i	−0.195780	+	0.339101i
$446$	−11.4417	−	19.8176i	−0.541779	−	0.938389i
$447$			11.9184i			0.563723i
$448$	7.54081	−	4.35369i	0.356270	−	0.205693i
$449$	16.1294	−	9.31229i	0.761192	−	0.439474i	−0.0685319	−	0.997649i	$-0.521831\pi$
$449$	16.1294	−	9.31229i	0.761192	−	0.439474i	0.829723	+	0.558175i	$0.188498\pi$
$450$		−	3.41606i		−	0.161035i
$451$	−1.82442	−	3.15999i	−0.0859087	−	0.148798i
$452$	0.942140	−	1.63183i	0.0443145	−	0.0767550i
$453$	9.04547	+	5.22241i	0.424993	+	0.245370i
$454$	−17.2473			−0.809454
$455$	4.54387	+	3.30456i	0.213020	+	0.154920i
$456$	17.2296			0.806848
$457$	10.0858	+	5.82301i	0.471792	+	0.272389i	0.716989	−	0.697084i	$-0.245520\pi$
$457$	10.0858	+	5.82301i	0.471792	+	0.272389i	−0.245198	+	0.969473i	$0.578853\pi$
$458$	−11.5855	+	20.0667i	−0.541355	+	0.937655i
$459$	0.391538	+	0.678164i	0.0182754	+	0.0316540i
$460$		−	1.52701i		−	0.0711971i
$461$	22.1591	−	12.7935i	1.03205	−	0.595854i	0.114479	−	0.993426i	$-0.463480\pi$
$461$	22.1591	−	12.7935i	1.03205	−	0.595854i	0.917571	+	0.397571i	$0.130147\pi$
$462$	−4.87421	+	2.81413i	−0.226769	+	0.130925i
$463$		−	25.8560i		−	1.20163i	−0.799389	−	0.600814i	$-0.794843\pi$
$463$		−	25.8560i		−	1.20163i	0.799389	−	0.600814i	$-0.205157\pi$
$464$	17.4319	+	30.1930i	0.809256	+	1.40167i
$465$	−5.01499	+	8.68622i	−0.232565	+	0.402814i
$466$	20.4035	+	11.7800i	0.945176	+	0.545698i
$467$	19.6800			0.910681			0.455341	−	0.890317i	$-0.349517\pi$
$467$	19.6800			0.910681			0.455341	+	0.890317i	$0.349517\pi$
$468$	−0.0892054	+	0.844936i	−0.00412352	+	0.0390572i
$469$	10.7404			0.495948
$470$	23.6603	+	13.6603i	1.09137	+	0.630101i
$471$	−1.65865	+	2.87287i	−0.0764266	+	0.132375i
$472$	−17.5702	−	30.4325i	−0.808735	−	1.40077i
$473$			23.6934i			1.08943i
$474$	15.8846	−	9.17097i	0.729603	−	0.421237i
$475$	−12.9224	+	7.46073i	−0.592918	+	0.342322i
$476$		−	0.184528i		−	0.00845784i
$477$	1.12754	+	1.95296i	0.0516266	+	0.0894198i
$478$	6.81211	−	11.7989i	0.311579	−	0.539670i
$479$	0.962929	+	0.555947i	0.0439974	+	0.0254019i	0.521837	−	0.853045i	$-0.325247\pi$
$479$	0.962929	+	0.555947i	0.0439974	+	0.0254019i	−0.477840	+	0.878447i	$0.658580\pi$
$480$	2.06593			0.0942965
$481$	24.1813	+	2.55298i	1.10257	+	0.116406i
$482$	−17.0589			−0.777011
$483$	−3.60138	−	2.07926i	−0.163868	−	0.0946094i
$484$	0.819338	−	1.41914i	0.0372426	−	0.0645061i
$485$	0.0605577	+	0.104889i	0.00274978	+	0.00476276i
$486$			1.32829i			0.0602525i
$487$	−23.0343	+	13.2988i	−1.04378	+	0.602628i	−0.920902	−	0.389794i	$-0.872546\pi$
$487$	−23.0343	+	13.2988i	−1.04378	+	0.602628i	−0.122879	+	0.992422i	$0.539213\pi$
$488$	−19.0282	+	10.9860i	−0.861367	+	0.497311i
$489$		−	6.70489i		−	0.303206i
$490$	−1.03492	−	1.79254i	−0.0467530	−	0.0809786i
$491$	5.97054	−	10.3413i	0.269447	−	0.466695i	−0.699272	−	0.714855i	$-0.746493\pi$
$491$	5.97054	−	10.3413i	0.269447	−	0.466695i	0.968719	+	0.248160i	$0.0798259\pi$
$492$	0.175738	+	0.101462i	0.00792286	+	0.00457427i
$493$	7.86053			0.354020
$494$	−25.3900	+	11.2902i	−1.14235	+	0.507968i
$495$	−6.60275			−0.296772
$496$	−19.3604	−	11.1777i	−0.869307	−	0.501894i
$497$	2.09111	−	3.62191i	0.0937992	−	0.162465i
$498$	0.657305	+	1.13849i	0.0294545	+	0.0510167i
$499$		−	17.7894i		−	0.796364i	−0.917306	−	0.398182i	$-0.869641\pi$
$499$		−	17.7894i		−	0.796364i	0.917306	−	0.398182i	$-0.130359\pi$
$500$	−2.40786	+	1.39018i	−0.107683	+	0.0621708i
$501$	−16.0732	+	9.27985i	−0.718097	+	0.414593i
$502$		−	3.24740i		−	0.144939i
$503$	8.54622	+	14.8025i	0.381057	+	0.660010i	0.991214	−	0.132271i	$-0.0422268\pi$
$503$	8.54622	+	14.8025i	0.381057	+	0.660010i	−0.610157	+	0.792281i	$0.708893\pi$
$504$	1.48479	−	2.57174i	0.0661379	−	0.114554i
$505$	3.85424	+	2.22525i	0.171512	+	0.0990223i
$506$	−23.4051			−1.04049
$507$	−4.00567	−	12.3675i	−0.177898	−	0.549259i
$508$	1.72947			0.0767326
$509$	11.5350	+	6.65972i	0.511279	+	0.295187i	0.733359	−	0.679841i	$-0.237951\pi$
$509$	11.5350	+	6.65972i	0.511279	+	0.295187i	−0.222080	+	0.975028i	$0.571285\pi$
$510$	−0.810423	+	1.40369i	−0.0358861	+	0.0621566i
$511$	6.71246	+	11.6263i	0.296942	+	0.514318i
$512$			25.2325i			1.11513i
$513$	5.02469	−	2.90100i	0.221845	−	0.128082i
$514$	−10.4984	+	6.06123i	−0.463063	+	0.267350i
$515$			8.92261i			0.393177i
$516$	−0.658835	−	1.14114i	−0.0290036	−	0.0502357i
$517$	−27.9642	+	48.4354i	−1.22986	+	2.13019i
$518$	−7.75780	−	4.47897i	−0.340858	−	0.196795i
$519$	−1.71544			−0.0752995
$520$	−15.2452	+	6.77906i	−0.668545	+	0.297281i
$521$	25.4363			1.11438			0.557192	−	0.830384i	$-0.311879\pi$
$521$	25.4363			1.11438			0.557192	+	0.830384i	$0.311879\pi$
$522$	11.5471	+	6.66670i	0.505401	+	0.291793i
$523$	1.05293	−	1.82372i	0.0460413	−	0.0797459i	−0.842086	−	0.539343i	$-0.818673\pi$
$523$	1.05293	−	1.82372i	0.0460413	−	0.0797459i	0.888128	+	0.459597i	$0.152006\pi$
$524$	0.251132	+	0.434974i	0.0109708	+	0.0190019i
$525$			2.57177i			0.112241i
$526$	−37.1225	+	21.4327i	−1.61862	+	0.934510i
$527$	−4.36506	+	2.52017i	−0.190145	+	0.109780i
$528$		−	14.7166i		−	0.640458i
$529$	2.85339	+	4.94222i	0.124060	+	0.214879i
$530$	−2.33383	+	4.04232i	−0.101375	+	0.175587i
$531$	−10.2481	−	5.91673i	−0.444728	−	0.256764i
$532$	−1.36722			−0.0592764
$533$	−3.08773	−	0.325992i	−0.133745	−	0.0141203i
$534$	−7.04087			−0.304688
$535$	7.78904	+	4.49701i	0.336750	+	0.194423i
$536$	−15.9473	+	27.6216i	−0.688820	+	1.19307i
$537$	−7.33903	−	12.7116i	−0.316703	−	0.548545i
$538$			7.32774i			0.315921i
$539$	3.66954	−	2.11861i	0.158058	−	0.0912549i
$540$	0.318005	−	0.183600i	0.0136848	−	0.00790090i
$541$			4.66916i			0.200743i	0.994950	+	0.100371i	$0.0320031\pi$
$541$			4.66916i			0.200743i	−0.994950	+	0.100371i	$0.967997\pi$
$542$	−19.6728	−	34.0743i	−0.845018	−	1.46361i
$543$	−3.17936	+	5.50681i	−0.136439	+	0.236320i
$544$	0.899096	+	0.519094i	0.0385484	+	0.0222560i
$545$	−20.9928			−0.899234
$546$	−0.502835	+	4.76275i	−0.0215193	+	0.203827i
$547$	−42.9518			−1.83648			−0.918242	−	0.396019i	$-0.870391\pi$
$547$	−42.9518			−1.83648			−0.918242	+	0.396019i	$0.870391\pi$
$548$	−1.53842	−	0.888207i	−0.0657180	−	0.0379423i
$549$	−3.69949	+	6.40770i	−0.157890	+	0.273474i
$550$	7.23730	+	12.5354i	0.308599	+	0.534510i
$551$		−	58.2406i		−	2.48113i
$552$	10.6946	−	6.17453i	0.455192	−	0.262805i
$553$	−11.9587	+	6.90434i	−0.508535	+	0.293603i
$554$		−	26.0958i		−	1.10870i
$555$	−5.25448	−	9.10102i	−0.223040	−	0.386317i
$556$	1.31202	−	2.27248i	0.0556418	−	0.0963745i
$557$	−30.7295	−	17.7417i	−1.30205	−	0.751740i	−0.321297	−	0.946979i	$-0.604119\pi$
$557$	−30.7295	−	17.7417i	−1.30205	−	0.751740i	−0.980756	+	0.195238i	$0.937452\pi$
$558$	−8.54966			−0.361936
$559$	16.3053	+	11.8581i	0.689641	+	0.501546i
$560$	5.41218			0.228706
$561$	−2.87353	−	1.65903i	−0.121320	−	0.0700444i
$562$	−0.399603	+	0.692133i	−0.0168562	+	0.0291959i
$563$	7.59798	+	13.1601i	0.320217	+	0.554631i	0.980533	−	0.196357i	$-0.0629110\pi$
$563$	7.59798	+	13.1601i	0.320217	+	0.554631i	−0.660316	+	0.750988i	$0.729578\pi$
$564$		−	3.11036i		−	0.130970i
$565$	10.7910	−	6.23018i	0.453980	−	0.262106i
$566$	−12.0914	+	6.98095i	−0.508238	+	0.293431i
$567$		−	1.00000i		−	0.0419961i
$568$	6.20974	+	10.7556i	0.260555	+	0.451294i
$569$	−5.99318	+	10.3805i	−0.251247	+	0.435173i	−0.963869	−	0.266375i	$-0.914174\pi$
$569$	−5.99318	+	10.3805i	−0.251247	+	0.435173i	0.712622	+	0.701548i	$0.247507\pi$
$570$	10.4003	+	6.00462i	0.435621	+	0.251506i
$571$	35.9171			1.50308			0.751542	−	0.659685i	$-0.229310\pi$
$571$	35.9171			1.50308			0.751542	+	0.659685i	$0.229310\pi$
$572$	−1.46274	−	3.28951i	−0.0611604	−	0.137541i
$573$	4.90400			0.204868
$574$	0.990601	+	0.571924i	0.0413469	+	0.0238716i
$575$	−5.34738	+	9.26193i	−0.223001	+	0.386249i
$576$	4.35369	+	7.54081i	0.181404	+	0.314201i
$577$			38.6603i			1.60945i	0.593648	+	0.804725i	$0.297687\pi$
$577$			38.6603i			1.60945i	−0.593648	+	0.804725i	$0.702313\pi$
$578$	18.8503	−	10.8832i	0.784068	−	0.452682i
$579$	−9.33991	+	5.39240i	−0.388153	+	0.224101i
$580$		−	3.68597i		−	0.153051i
$581$	−0.494850	−	0.857106i	−0.0205298	−	0.0355587i
$582$	−0.0516200	+	0.0894084i	−0.00213972	+	0.00370610i
$583$	−8.27511	−	4.77763i	−0.342720	−	0.197869i
$584$	−39.8664			−1.64969
$585$	−3.30456	+	4.54387i	−0.136627	+	0.187866i
$586$	11.4305			0.472190
$587$	1.80169	+	1.04021i	0.0743639	+	0.0429340i	0.536721	−	0.843760i	$-0.319663\pi$
$587$	1.80169	+	1.04021i	0.0743639	+	0.0429340i	−0.462357	+	0.886694i	$0.652996\pi$
$588$	−0.117823	+	0.204075i	−0.00485893	+	0.00841591i
$589$	18.6726	+	32.3418i	0.769390	+	1.33262i
$590$		−	24.4934i		−	1.00838i
$591$	−22.7973	+	13.1620i	−0.937756	+	0.541413i
$592$	20.2849	−	11.7115i	0.833704	−	0.481339i
$593$			41.6938i			1.71216i	0.516844	+	0.856080i	$0.327107\pi$
$593$			41.6938i			1.71216i	−0.516844	+	0.856080i	$0.672893\pi$
$594$	−2.81413	−	4.87421i	−0.115465	−	0.199991i
$595$	0.610125	−	1.05677i	0.0250127	−	0.0433232i
$596$	2.43225	+	1.40426i	0.0996290	+	0.0575208i
$597$	26.1094			1.06859
$598$	−11.7139	+	16.1069i	−0.479016	+	0.658661i
$599$	−14.2359			−0.581663			−0.290831	−	0.956774i	$-0.593932\pi$
$599$	−14.2359			−0.581663			−0.290831	+	0.956774i	$0.593932\pi$
$600$	−6.61393	−	3.81855i	−0.270012	−	0.155892i
$601$	−3.38144	+	5.85683i	−0.137932	+	0.238905i	−0.926714	−	0.375768i	$-0.877379\pi$
$601$	−3.38144	+	5.85683i	−0.137932	+	0.238905i	0.788782	+	0.614673i	$0.210712\pi$
$602$	−3.71373	−	6.43237i	−0.151360	−	0.262164i
$603$			10.7404i			0.437385i
$604$	2.13152	−	1.23064i	0.0867305	−	0.0500739i
$605$	9.38446	−	5.41812i	0.381532	−	0.220278i
$606$			3.79365i			0.154106i
$607$	2.41439	+	4.18184i	0.0979969	+	0.169736i	0.910855	−	0.412726i	$-0.135423\pi$
$607$	2.41439	+	4.18184i	0.0979969	+	0.169736i	−0.812859	+	0.582461i	$0.802090\pi$
$608$	3.84609	−	6.66163i	0.155980	−	0.270165i
$609$	−8.69317	−	5.01901i	−0.352265	−	0.203380i
$610$	−15.3147			−0.620075
$611$	19.3366	+	43.4854i	0.782276	+	1.75923i
$612$	0.184528			0.00745912
$613$	15.0293	+	8.67719i	0.607029	+	0.350468i	0.771802	−	0.635863i	$-0.219356\pi$
$613$	15.0293	+	8.67719i	0.607029	+	0.350468i	−0.164773	+	0.986332i	$0.552689\pi$
$614$	−7.18553	+	12.4457i	−0.289984	+	0.502267i
$615$	0.670949	+	1.16212i	0.0270553	+	0.0468611i
$616$			12.5828i			0.506974i
$617$	0.135605	−	0.0782913i	0.00545923	−	0.00315189i	−0.497268	−	0.867597i	$-0.665663\pi$
$617$	0.135605	−	0.0782913i	0.00545923	−	0.00315189i	0.502727	+	0.864445i	$0.332330\pi$
$618$	−6.58674	+	3.80286i	−0.264958	+	0.152973i
$619$		−	37.4947i		−	1.50704i	−0.657426	−	0.753519i	$-0.728355\pi$
$619$		−	37.4947i		−	1.50704i	0.657426	−	0.753519i	$-0.271645\pi$
$620$	1.18176	+	2.04687i	0.0474606	+	0.0822042i
$621$	2.07926	−	3.60138i	0.0834377	−	0.144518i
$622$	−10.8664	−	6.27374i	−0.435704	−	0.251554i
$623$	5.30070			0.212368
$624$	−10.1277	−	7.36541i	−0.405431	−	0.294852i
$625$	−5.52710			−0.221084
$626$	9.06813	+	5.23548i	0.362435	+	0.209252i
$627$	−12.2922	+	21.2907i	−0.490902	+	0.850268i
$628$	0.390854	+	0.676979i	0.0155968	+	0.0270144i
$629$		−	5.28103i		−	0.210569i
$630$	1.79254	−	1.03492i	0.0714164	−	0.0412323i
$631$	18.0447	−	10.4181i	0.718346	−	0.414737i	−0.0957974	−	0.995401i	$-0.530540\pi$
$631$	18.0447	−	10.4181i	0.718346	−	0.414737i	0.814144	+	0.580663i	$0.197207\pi$
$632$		−	41.0061i		−	1.63113i
$633$	−6.27361	−	10.8662i	−0.249353	−	0.431893i
$634$	14.4422	−	25.0146i	0.573572	−	0.993456i
$635$	9.90439	+	5.71830i	0.393044	+	0.226924i
$636$	0.531400			0.0210714
$637$	0.378558	−	3.58562i	0.0149990	−	0.142068i
$638$	−56.4964			−2.23672
$639$	3.62191	+	2.09111i	0.143281	+	0.0827231i
$640$	−6.94552	+	12.0300i	−0.274546	+	0.475528i
$641$	−23.5836	−	40.8479i	−0.931494	−	1.61340i	−0.780769	−	0.624820i	$-0.785172\pi$
$641$	−23.5836	−	40.8479i	−0.931494	−	1.61340i	−0.150726	−	0.988576i	$-0.548161\pi$
$642$			7.66658i			0.302576i
$643$	−16.2935	+	9.40707i	−0.642554	+	0.370979i	−0.785598	−	0.618738i	$-0.787644\pi$
$643$	−16.2935	+	9.40707i	−0.642554	+	0.370979i	0.143044	+	0.989716i	$0.454311\pi$
$644$	−0.848648	+	0.489967i	−0.0334414	+	0.0193074i
$645$		−	8.71349i		−	0.343093i
$646$	3.01749	+	5.22644i	0.118721	+	0.205631i
$647$	12.0645	−	20.8964i	0.474306	−	0.821522i	−0.525261	−	0.850941i	$-0.676032\pi$
$647$	12.0645	−	20.8964i	0.474306	−	0.821522i	0.999567	+	0.0294191i	$0.00936573\pi$
$648$	2.57174	+	1.48479i	0.101027	+	0.0583282i
$649$	50.1409			1.96820
$650$	12.2487	+	1.29318i	0.480434	+	0.0507226i
$651$	6.43659			0.252270
$652$	−1.36830	−	0.789988i	−0.0535868	−	0.0309383i
$653$	−12.3404	+	21.3743i	−0.482919	+	0.836439i	−0.999808	−	0.0196129i	$-0.993757\pi$
$653$	−12.3404	+	21.3743i	−0.482919	+	0.836439i	0.516889	+	0.856052i	$0.327090\pi$
$654$	−8.94724	−	15.4971i	−0.349865	−	0.605984i
$655$			3.32138i			0.129777i
$656$	−2.59020	+	1.49545i	−0.101130	+	0.0583876i
$657$	−11.6263	+	6.71246i	−0.453586	+	0.261878i
$658$		−	17.5325i		−	0.683489i
$659$	0.910300	+	1.57669i	0.0354603	+	0.0614190i	0.883211	−	0.468976i	$-0.155377\pi$
$659$	0.910300	+	1.57669i	0.0354603	+	0.0614190i	−0.847751	+	0.530395i	$0.822044\pi$
$660$	−0.777954	+	1.34746i	−0.0302818	+	0.0524497i
$661$	36.4761	+	21.0595i	1.41876	+	0.819120i	0.996190	−	0.0872120i	$-0.0277957\pi$
$661$	36.4761	+	21.0595i	1.41876	+	0.819120i	0.422567	+	0.906332i	$0.361129\pi$
$662$	34.0053			1.32165
$663$	−2.57986	+	1.14718i	−0.100193	+	0.0445529i
$664$	2.93900			0.114055
$665$	−7.82985	−	4.52057i	−0.303629	−	0.175300i
$666$	4.47897	−	7.75780i	0.173556	−	0.300609i
$667$	−20.8716	−	36.1507i	−0.808151	−	1.39976i
$668$			4.37351i			0.169216i
$669$	−14.9196	+	8.61384i	−0.576825	+	0.333030i
$670$	−19.2526	+	11.1155i	−0.743795	+	0.429430i
$671$		−	31.3511i		−	1.21029i
$672$	−0.662890	−	1.14816i	−0.0255715	−	0.0442912i
$673$	0.957403	−	1.65827i	0.0369052	−	0.0639216i	−0.846983	−	0.531620i	$-0.821583\pi$
$673$	0.957403	−	1.65827i	0.0369052	−	0.0639216i	0.883888	+	0.467699i	$0.154917\pi$
$674$	−16.6063	−	9.58766i	−0.639651	−	0.369303i
$675$	−2.57177			−0.0989876
$676$	−2.99585	−	0.639714i	−0.115225	−	0.0246044i
$677$	−3.78799			−0.145584			−0.0727922	−	0.997347i	$-0.523191\pi$
$677$	−3.78799			−0.145584			−0.0727922	+	0.997347i	$0.523191\pi$
$678$	9.19835	+	5.31067i	0.353260	+	0.203955i
$679$	0.0388620	−	0.0673109i	0.00149139	−	0.00258316i
$680$	1.81182	+	3.13816i	0.0694800	+	0.120343i
$681$			12.9846i			0.497569i
$682$	31.3733	−	18.1134i	1.20135	−	0.693597i
$683$	15.0087	−	8.66527i	0.574291	−	0.331567i	−0.184570	−	0.982819i	$-0.559089\pi$
$683$	15.0087	−	8.66527i	0.574291	−	0.331567i	0.758861	+	0.651252i	$0.225756\pi$
$684$		−	1.36722i		−	0.0522768i
$685$	−5.87353	−	10.1733i	−0.224416	−	0.388700i
$686$	−0.664145	+	1.15033i	−0.0253572	+	0.0439199i
$687$	15.1072	+	8.72213i	0.576374	+	0.332770i
$688$	19.4211			0.740424
$689$	−7.42941	+	3.30363i	−0.283038	+	0.125858i
$690$	8.60747			0.327681
$691$	0.816299	+	0.471291i	0.0310535	+	0.0179287i	0.515446	−	0.856922i	$-0.327626\pi$
$691$	0.816299	+	0.471291i	0.0310535	+	0.0179287i	−0.484393	+	0.874851i	$0.660959\pi$
$692$	−0.202118	+	0.350079i	−0.00768337	+	0.0133080i
$693$	2.11861	+	3.66954i	0.0804792	+	0.139394i
$694$			18.7410i			0.711400i
$695$	15.0274	−	8.67609i	0.570023	−	0.329103i
$696$	25.8151	−	14.9044i	0.978520	−	0.564949i
$697$			0.674340i			0.0255425i
$698$	9.05973	+	15.6919i	0.342916	+	0.593948i
$699$	8.86854	−	15.3608i	0.335439	−	0.580997i
$700$	0.524835	+	0.303013i	0.0198369	+	0.0114528i
$701$	18.9241			0.714753			0.357376	−	0.933960i	$-0.383671\pi$
$701$	18.9241			0.714753			0.357376	+	0.933960i	$0.383671\pi$
$702$	−4.76275	−	0.502835i	−0.179758	−	0.0189783i
$703$	−39.1285			−1.47576
$704$	−31.9520	−	18.4475i	−1.20424	−	0.695267i
$705$	10.2841	−	17.8126i	0.387321	−	0.670860i
$706$	−6.55523	−	11.3540i	−0.246709	−	0.427313i
$707$		−	2.85604i		−	0.107412i
$708$	−2.41491	+	1.39425i	−0.0907579	+	0.0523991i
$709$	−21.0949	+	12.1792i	−0.792236	+	0.457398i	−0.840749	−	0.541425i	$-0.817885\pi$
$709$	−21.0949	+	12.1792i	−0.792236	+	0.457398i	0.0485130	+	0.998823i	$0.484552\pi$
$710$			8.65655i			0.324874i
$711$	−6.90434	−	11.9587i	−0.258933	−	0.448485i
$712$	−7.87045	+	13.6320i	−0.294957	+	0.510881i
$713$	23.1806	+	13.3833i	0.868120	+	0.501209i
$714$	1.04015			0.0389267
$715$	2.49952	−	23.6750i	0.0934769	−	0.885394i
$716$	−3.45882			−0.129262
$717$	−8.88279	−	5.12848i	−0.331734	−	0.191527i
$718$	−9.59592	+	16.6206i	−0.358117	+	0.620276i
$719$	−22.9232	−	39.7042i	−0.854891	−	1.48072i	−0.876746	−	0.480954i	$-0.840290\pi$
$719$	−22.9232	−	39.7042i	−0.854891	−	1.48072i	0.0218547	−	0.999761i	$-0.493043\pi$
$720$			5.41218i			0.201700i
$721$	4.95881	−	2.86297i	0.184676	−	0.106623i
$722$	16.8677	−	9.73855i	0.627749	−	0.362431i
$723$			12.8427i			0.477627i
$724$	0.749201	+	1.29765i	0.0278438	+	0.0482269i
$725$	−12.9078	+	22.3569i	−0.479382	+	0.830314i
$726$	7.99940	+	4.61846i	0.296886	+	0.171407i
$727$	22.8355			0.846922			0.423461	−	0.905914i	$-0.360815\pi$
$727$	22.8355			0.846922			0.423461	+	0.905914i	$0.360815\pi$
$728$	8.65920	+	6.29746i	0.320931	+	0.233399i
$729$	1.00000			0.0370370
$730$	−24.0647	−	13.8937i	−0.890673	−	0.514230i
$731$	2.18938	−	3.79212i	0.0809772	−	0.140257i
$732$	0.871768	+	1.50995i	0.0322215	+	0.0558092i
$733$			23.9682i			0.885287i	0.896698	+	0.442643i	$0.145959\pi$
$733$			23.9682i			0.885287i	−0.896698	+	0.442643i	$0.854041\pi$
$734$	28.1430	−	16.2483i	1.03878	−	0.599737i
$735$	−1.34951	+	0.779138i	−0.0497773	+	0.0287389i
$736$		−	5.51327i		−	0.203222i
$737$	−22.7548	−	39.4124i	−0.838183	−	1.45178i
$738$	−0.571924	+	0.990601i	−0.0210528	+	0.0364645i
$739$	20.5591	+	11.8698i	0.756280	+	0.436638i	0.827958	−	0.560790i	$-0.189502\pi$
$739$	20.5591	+	11.8698i	0.756280	+	0.436638i	−0.0716788	+	0.997428i	$0.522836\pi$
$740$	−2.47639			−0.0910338
$741$	8.49977	+	19.1148i	0.312247	+	0.702201i
$742$	2.99540			0.109965
$743$	−17.2529	−	9.96099i	−0.632949	−	0.365433i	0.148944	−	0.988846i	$-0.452412\pi$
$743$	−17.2529	−	9.96099i	−0.632949	−	0.365433i	−0.781893	+	0.623412i	$0.785746\pi$
$744$	−9.55700	+	16.5532i	−0.350377	+	0.606870i
$745$	9.28611	+	16.0840i	0.340217	+	0.589273i
$746$		−	32.5173i		−	1.19054i
$747$	0.857106	−	0.494850i	0.0313599	−	0.0181056i
$748$	−0.677133	+	0.390943i	−0.0247584	+	0.0142943i
$749$		−	5.77177i		−	0.210896i
$750$	−7.83619	−	13.5727i	−0.286137	−	0.495604i
$751$	−7.31735	+	12.6740i	−0.267014	+	0.462482i	−0.968089	−	0.250606i	$-0.919370\pi$
$751$	−7.31735	+	12.6740i	−0.267014	+	0.462482i	0.701075	+	0.713087i	$0.252704\pi$
$752$	39.7017	+	22.9218i	1.44777	+	0.835872i
$753$	−2.44480			−0.0890934
$754$	−28.2755	+	38.8797i	−1.02973	+	1.41591i
$755$	16.2759			0.592341
$756$	−0.204075	−	0.117823i	−0.00742213	−	0.00428517i
$757$	−19.5456	+	33.8539i	−0.710395	+	1.23044i	0.254314	+	0.967122i	$0.418150\pi$
$757$	−19.5456	+	33.8539i	−0.710395	+	1.23044i	−0.964709	+	0.263319i	$0.915183\pi$
$758$	12.5454	+	21.7292i	0.455668	+	0.789241i
$759$			17.6205i			0.639584i
$760$	23.2514	−	13.4242i	0.843417	−	0.486947i
$761$	−3.26731	+	1.88638i	−0.118440	+	0.0683813i	−0.558050	−	0.829808i	$-0.688450\pi$
$761$	−3.26731	+	1.88638i	−0.118440	+	0.0683813i	0.439610	+	0.898189i	$0.355117\pi$
$762$			9.74868i			0.353157i
$763$	6.73591	+	11.6669i	0.243856	+	0.422371i
$764$	0.577803	−	1.00078i	0.0209042	−	0.0362071i
$765$	1.05677	+	0.610125i	0.0382075	+	0.0220591i
$766$	14.9707			0.540915
$767$	25.0946	−	34.5059i	0.906115	−	1.24594i
$768$	5.57390			0.201131
$769$	−0.0823798	−	0.0475620i	−0.00297069	−	0.00171513i	0.498514	−	0.866882i	$-0.333879\pi$
$769$	−0.0823798	−	0.0475620i	−0.00297069	−	0.00171513i	−0.501485	+	0.865167i	$0.667213\pi$
$770$	−4.38519	+	7.59536i	−0.158031	+	0.273718i
$771$	4.56319	+	7.90367i	0.164339	+	0.284644i
$772$			2.54139i			0.0914666i
$773$	−19.1419	+	11.0516i	−0.688487	+	0.397498i	−0.803045	−	0.595918i	$-0.796788\pi$
$773$	−19.1419	+	11.0516i	−0.688487	+	0.397498i	0.114558	+	0.993417i	$0.463455\pi$
$774$	6.43237	−	3.71373i	0.231207	−	0.133487i
$775$		−	16.5535i		−	0.594618i
$776$	0.115404	+	0.199885i	0.00414276	+	0.00717547i
$777$	−3.37198	+	5.84044i	−0.120969	+	0.209525i
$778$	28.7350	+	16.5902i	1.03020	+	0.594786i
$779$	4.99636			0.179013
$780$	0.537938	+	1.20975i	0.0192613	+	0.0433160i
$781$	−17.7210			−0.634107
$782$	3.74598	+	2.16274i	0.133956	+	0.0773395i
$783$	5.01901	−	8.69317i	0.179365	−	0.310669i
$784$	−1.73659	−	3.00786i	−0.0620211	−	0.107424i
$785$			5.16928i			0.184499i
$786$	−2.45187	+	1.41559i	−0.0874552	+	0.0504923i
$787$	40.6828	−	23.4882i	1.45018	−	0.837264i	0.451693	−	0.892174i	$-0.350820\pi$
$787$	40.6828	−	23.4882i	1.45018	−	0.837264i	0.998491	+	0.0549096i	$0.0174871\pi$
$788$			6.20314i			0.220978i
$789$	16.1356	+	27.9476i	0.574441	+	0.994961i
$790$	14.2909	−	24.7526i	0.508448	−	0.880657i
$791$	−6.92495	−	3.99812i	−0.246223	−	0.142157i
$792$	−12.5828			−0.447109
$793$	−21.5751	−	15.6907i	−0.766156	−	0.557192i
$794$	−4.51428			−0.160206
$795$	3.04325	+	1.75702i	0.107933	+	0.0623151i
$796$	3.07628	−	5.32827i	0.109036	−	0.188855i
$797$	−6.15030	−	10.6526i	−0.217855	−	0.377336i	0.736297	−	0.676658i	$-0.236573\pi$
$797$	−6.15030	−	10.6526i	−0.217855	−	0.377336i	−0.954152	+	0.299323i	$0.903239\pi$
$798$		−	7.70675i		−	0.272816i
$799$	8.95130	−	5.16804i	0.316674	−	0.182832i
$800$	−2.95281	+	1.70480i	−0.104397	+	0.0602739i
$801$			5.30070i			0.187291i
$802$	−9.23025	−	15.9873i	−0.325931	−	0.564530i
$803$	28.4421	−	49.2632i	1.00370	−	1.73846i
$804$	2.19186	+	1.26547i	0.0773008	+	0.0446296i
$805$	−6.48011			−0.228394
$806$	3.23654	−	30.6559i	0.114002	−	1.07981i
$807$	5.51667			0.194196
$808$	7.34498	+	4.24062i	0.258395	+	0.149185i
$809$	11.6038	−	20.0983i	0.407966	−	0.706618i	−0.586695	−	0.809808i	$-0.699571\pi$
$809$	11.6038	−	20.0983i	0.407966	−	0.706618i	0.994662	+	0.103189i	$0.0329048\pi$
$810$	1.03492	+	1.79254i	0.0363634	+	0.0629833i
$811$		−	35.0940i		−	1.23232i	−0.787622	−	0.616159i	$-0.788688\pi$
$811$		−	35.0940i		−	1.23232i	0.787622	−	0.616159i	$-0.211312\pi$
$812$	−2.04851	+	1.18271i	−0.0718885	+	0.0415048i
$813$	−25.6527	+	14.8106i	−0.899680	+	0.519431i
$814$			37.9567i			1.33038i
$815$	−5.22404	−	9.04830i	−0.182990	−	0.316948i
$816$	−1.35988	+	2.35539i	−0.0476054	+	0.0824550i
$817$	−28.0968	−	16.2217i	−0.982981	−	0.567525i
$818$	22.9598			0.802771
$819$	3.58562	+	0.378558i	0.125292	+	0.0132279i
$820$	0.316212			0.0110426
$821$	30.5121	+	17.6162i	1.06488	+	0.614808i	0.926778	−	0.375610i	$-0.122567\pi$
$821$	30.5121	+	17.6162i	1.06488	+	0.614808i	0.138102	+	0.990418i	$0.455900\pi$
$822$	5.00666	−	8.67178i	0.174627	−	0.302463i
$823$	3.68891	+	6.38939i	0.128587	+	0.222720i	0.923130	−	0.384489i	$-0.125622\pi$
$823$	3.68891	+	6.38939i	0.128587	+	0.222720i	−0.794542	+	0.607209i	$0.792289\pi$
$824$			17.0037i			0.592352i
$825$	9.43722	−	5.44858i	0.328562	−	0.189695i
$826$	−13.6124	+	7.85913i	−0.473636	+	0.273454i
$827$		−	17.4344i		−	0.606252i	−0.952950	−	0.303126i	$-0.901970\pi$
$827$		−	17.4344i		−	0.606252i	0.952950	−	0.303126i	$-0.0980303\pi$
$828$	−0.489967	−	0.848648i	−0.0170275	−	0.0294926i
$829$	−14.5694	+	25.2350i	−0.506017	+	0.876447i	0.493959	+	0.869485i	$0.335549\pi$
$829$	−14.5694	+	25.2350i	−0.506017	+	0.876447i	−0.999976	+	0.00696168i	$0.997784\pi$
$830$	1.77407	+	1.02426i	0.0615790	+	0.0355527i
$831$	−19.6461			−0.681517
$832$	−28.6866	+	12.7561i	−0.994530	+	0.442237i
$833$	−0.783076			−0.0271320
$834$	12.8095	+	7.39559i	0.443558	+	0.256088i
$835$	−14.4606	+	25.0465i	−0.500429	+	0.866768i
$836$	2.89660	+	5.01705i	0.100181	+	0.173518i
$837$			6.43659i			0.222481i
$838$	8.58701	−	4.95772i	0.296633	−	0.171261i
$839$	18.2808	−	10.5544i	0.631123	−	0.364379i	−0.150064	−	0.988676i	$-0.547948\pi$
$839$	18.2808	−	10.5544i	0.631123	−	0.364379i	0.781187	+	0.624297i	$0.214615\pi$
$840$		−	4.62744i		−	0.159662i
$841$	−35.8808	−	62.1474i	−1.23727	−	2.14302i
$842$	11.4580	−	19.8459i	0.394870	−	0.683934i
$843$	0.521071	+	0.300840i	0.0179466	+	0.0103615i
$844$	−2.95669			−0.101774
$845$	−15.0417	−	13.5690i	−0.517449	−	0.466789i
$846$	17.5325			0.602781
$847$	−6.02233	−	3.47699i	−0.206930	−	0.119471i
$848$	−3.91615	+	6.78298i	−0.134481	+	0.232928i
$849$	5.25559	+	9.10295i	0.180371	+	0.312412i
$850$		−	2.67504i		−	0.0917530i
$851$	−24.2875	+	14.0224i	−0.832566	+	0.480682i
$852$	0.853487	−	0.492761i	0.0292400	−	0.0168817i
$853$		−	45.0396i		−	1.54213i	−0.636759	−	0.771063i	$-0.719725\pi$
$853$		−	45.0396i		−	1.54213i	0.636759	−	0.771063i	$-0.280275\pi$
$854$	4.91400	+	8.51129i	0.168153	+	0.291250i
$855$	4.52057	−	7.82985i	0.154600	−	0.267775i
$856$	14.8435	+	8.56988i	0.507339	+	0.292913i
$857$	−34.7636			−1.18750			−0.593751	−	0.804649i	$-0.702353\pi$
$857$	−34.7636			−1.18750			−0.593751	+	0.804649i	$0.702353\pi$
$858$	18.5424	−	8.24522i	0.633026	−	0.281487i
$859$	−2.09890			−0.0716137			−0.0358069	−	0.999359i	$-0.511400\pi$
$859$	−2.09890			−0.0716137			−0.0358069	+	0.999359i	$0.511400\pi$
$860$	−1.77820	−	1.02665i	−0.0606363	−	0.0350084i
$861$	0.430571	−	0.745771i	0.0146738	−	0.0254158i
$862$	19.4859	+	33.7506i	0.663693	+	1.14955i
$863$			49.8251i			1.69607i	0.529944	+	0.848033i	$0.322213\pi$
$863$			49.8251i			1.69607i	−0.529944	+	0.848033i	$0.677787\pi$
$864$	1.14816	−	0.662890i	0.0390612	−	0.0225520i
$865$	−2.31500	+	1.33657i	−0.0787124	+	0.0454446i
$866$		−	9.82769i		−	0.333959i
$867$	−8.19340	−	14.1914i	−0.278262	−	0.481964i
$868$	0.758377	−	1.31355i	0.0257410	−	0.0445847i
$869$	50.6715	+	29.2552i	1.71891	+	0.992414i
$870$	20.7771			0.704410
$871$	−38.5112	−	4.06588i	−1.30490	−	0.137767i
$872$	−40.0057			−1.35476
$873$	0.0673109	+	0.0388620i	0.00227813	+	0.00131528i
$874$	16.0243	−	27.7549i	0.542030	−	0.938824i
$875$	5.89946	+	10.2182i	0.199438	+	0.345437i
$876$			3.16352i			0.106885i
$877$	−2.61198	+	1.50803i	−0.0882004	+	0.0509225i	−0.543452	−	0.839441i	$-0.682883\pi$
$877$	−2.61198	+	1.50803i	−0.0882004	+	0.0509225i	0.455251	+	0.890363i	$0.349549\pi$
$878$	−32.6792	+	18.8673i	−1.10287	+	0.636741i
$879$		−	8.60543i		−	0.290254i
$880$	−11.4663	−	19.8602i	−0.386528	−	0.669486i
$881$	−13.8207	+	23.9381i	−0.465630	+	0.806494i	−0.999230	−	0.0392426i	$-0.987505\pi$
$881$	−13.8207	+	23.9381i	−0.465630	+	0.806494i	0.533600	+	0.845737i	$0.320839\pi$
$882$	−1.15033	−	0.664145i	−0.0387337	−	0.0223629i
$883$	−11.3425			−0.381705			−0.190852	−	0.981619i	$-0.561125\pi$
$883$	−11.3425			−0.381705			−0.190852	+	0.981619i	$0.561125\pi$
$884$	−0.0698546	+	0.661649i	−0.00234947	+	0.0222537i
$885$	−18.4398			−0.619847
$886$	9.06304	+	5.23255i	0.304479	+	0.175791i
$887$	−22.6735	+	39.2717i	−0.761302	+	1.31861i	0.180878	+	0.983506i	$0.442106\pi$
$887$	−22.6735	+	39.2717i	−0.761302	+	1.31861i	−0.942180	+	0.335108i	$0.891227\pi$
$888$	−10.0134	−	17.3437i	−0.336027	−	0.582016i
$889$		−	7.33927i		−	0.246151i
$890$	−9.50171	+	5.48581i	−0.318498	+	0.183885i
$891$	−3.66954	+	2.11861i	−0.122934	+	0.0709760i
$892$			4.05962i			0.135926i
$893$	−38.2913	−	66.3224i	−1.28137	−	2.21940i
$894$	−7.91557	+	13.7102i	−0.264736	+	0.458537i
$895$	−19.8081	−	11.4362i	−0.662113	−	0.382271i
$896$	8.91437			0.297808
$897$	12.1261	+	8.81876i	0.404877	+	0.294450i
$898$	24.7388			0.825546
$899$	55.9544	+	32.3053i	1.86618	+	1.07744i
$900$	−0.303013	+	0.524835i	−0.0101004	+	0.0174945i
$901$	0.882951	+	1.52932i	0.0294154	+	0.0509489i
$902$		−	4.84673i		−	0.161378i
$903$	−4.84259	+	2.79587i	−0.161151	+	0.0930408i
$904$	20.5642	−	11.8728i	0.683957	−	0.394883i
$905$			9.90863i			0.329374i
$906$	6.93687	+	12.0150i	0.230462	+	0.399172i
$907$	2.43950	−	4.22534i	0.0810023	−	0.140300i	−0.822678	−	0.568507i	$-0.807521\pi$
$907$	2.43950	−	4.22534i	0.0810023	−	0.140300i	0.903681	+	0.428207i	$0.140855\pi$
$908$	2.64982	+	1.52988i	0.0879374	+	0.0507707i
$909$	2.85604			0.0947288
$910$	3.03226	+	6.81914i	0.100518	+	0.226052i
$911$	−33.8772			−1.12240			−0.561201	−	0.827679i	$-0.689661\pi$
$911$	−33.8772			−1.12240			−0.561201	+	0.827679i	$0.689661\pi$
$912$	17.4516	+	10.0757i	0.577882	+	0.333640i
$913$	−2.09679	+	3.63174i	−0.0693935	+	0.120193i
$914$	7.73465	+	13.3968i	0.255840	+	0.443127i
$915$			11.5297i			0.381159i
$916$	3.55993	−	2.05533i	0.117624	−	0.0679100i
$917$	1.84588	−	1.06572i	0.0609564	−	0.0351932i
$918$			1.04015i			0.0343301i
$919$	21.3063	+	36.9037i	0.702831	+	1.21734i	0.967469	+	0.252991i	$0.0814144\pi$
$919$	21.3063	+	36.9037i	0.702831	+	1.21734i	−0.264638	+	0.964348i	$0.585252\pi$
$920$	9.62162	−	16.6651i	0.317215	−	0.549433i
$921$	9.36971	+	5.40961i	0.308742	+	0.178253i
$922$	33.9871			1.11930
$923$	−8.86904	+	12.1952i	−0.291928	+	0.401410i
$924$	0.998480			0.0328476
$925$	15.0203	+	8.67197i	0.493864	+	0.285133i
$926$	17.1721	−	29.7430i	0.564310	−	0.977414i
$927$	2.86297	+	4.95881i	0.0940324	+	0.162869i
$928$		−	13.3082i		−	0.436863i
$929$	24.6676	−	14.2419i	0.809318	−	0.467260i	−0.0374010	−	0.999300i	$-0.511908\pi$
$929$	24.6676	−	14.2419i	0.809318	−	0.467260i	0.846719	+	0.532040i	$0.178575\pi$
$930$	−11.5378	+	6.66137i	−0.378340	+	0.218435i
$931$			5.80201i			0.190153i
$932$	−2.08983	−	3.61969i	−0.0684547	−	0.118567i
$933$	−4.72317	+	8.18077i	−0.154630	+	0.267826i
$934$	22.6385	+	13.0704i	0.740756	+	0.427676i
$935$	−5.17046			−0.169092
$936$	−6.29746	+	8.65920i	−0.205839	+	0.283035i
$937$	38.0480			1.24297			0.621486	−	0.783425i	$-0.286529\pi$
$937$	38.0480			1.24297			0.621486	+	0.783425i	$0.286529\pi$
$938$	12.3551	+	7.13321i	0.403408	+	0.232908i
$939$	3.94152	−	6.82692i	0.128627	−	0.222788i
$940$	−2.42340	−	4.19745i	−0.0790426	−	0.136906i
$941$		−	48.2486i		−	1.57286i	−0.617679	−	0.786430i	$-0.711927\pi$
$941$		−	48.2486i		−	1.57286i	0.617679	−	0.786430i	$-0.288073\pi$
$942$	−3.81600	+	2.20317i	−0.124332	+	0.0717832i
$943$	3.10130	−	1.79054i	0.100992	−	0.0583079i
$944$		−	41.0997i		−	1.33768i
$945$	−0.779138	−	1.34951i	−0.0253454	−	0.0438995i
$946$	−15.7359	+	27.2553i	−0.511617	+	0.886147i
$947$	−0.345431	−	0.199434i	−0.0112250	−	0.00648075i	0.494377	−	0.869248i	$-0.335396\pi$
$947$	−0.345431	−	0.199434i	−0.0112250	−	0.00648075i	−0.505602	+	0.862767i	$0.668730\pi$
$948$	−3.25395			−0.105684
$949$	−19.6671	−	44.2287i	−0.638422	−	1.43572i
$950$	−19.8200			−0.643046
$951$	−18.8322	−	10.8728i	−0.610675	−	0.352573i
$952$	1.16271	−	2.01387i	0.0376835	−	0.0652698i
$953$	17.6699	+	30.6052i	0.572385	+	0.991399i	0.996320	+	0.0857071i	$0.0273149\pi$
$953$	17.6699	+	30.6052i	0.572385	+	0.991399i	−0.423936	+	0.905692i	$0.639352\pi$
$954$			2.99540i			0.0969798i
$955$	6.61799	−	3.82090i	0.214153	−	0.123641i
$956$	−2.09319	+	1.20850i	−0.0676986	+	0.0390858i
$957$			42.5332i			1.37490i
$958$	0.738459	+	1.27905i	0.0238585	+	0.0413242i
$959$	−3.76925	+	6.52853i	−0.121715	+	0.210817i
$960$	11.7507	+	6.78425i	0.379251	+	0.218961i
$961$	−10.4297			−0.336442
$962$	26.1210	+	18.9967i	0.842175	+	0.612477i
$963$	5.77177			0.185993
$964$	2.62088	+	1.51317i	0.0844129	+	0.0487358i
$965$	−8.40285	+	14.5542i	−0.270497	+	0.468515i
$966$	−2.76185	−	4.78367i	−0.0888612	−	0.153912i
$967$		−	40.5799i		−	1.30496i	−0.757805	−	0.652482i	$-0.773728\pi$
$967$		−	40.5799i		−	1.30496i	0.757805	−	0.652482i	$-0.226272\pi$
$968$	17.8838	−	10.3252i	0.574808	−	0.331866i
$969$	3.93471	−	2.27171i	0.126401	−	0.0729777i
$970$			0.160876i			0.00516543i
$971$	−14.2769	−	24.7283i	−0.458167	−	0.793569i	0.540697	−	0.841217i	$-0.318161\pi$
$971$	−14.2769	−	24.7283i	−0.458167	−	0.793569i	−0.998864	+	0.0476485i	$0.984827\pi$
$972$	0.117823	−	0.204075i	0.00377917	−	0.00654571i
$973$	−9.64363	−	5.56775i	−0.309160	−	0.178494i
$974$	−35.3294			−1.13203
$975$	0.973565	−	9.22141i	0.0311790	−	0.295322i
$976$	−25.6980			−0.822573
$977$	38.4832	+	22.2183i	1.23119	+	0.710827i	0.967278	−	0.253721i	$-0.0816544\pi$
$977$	38.4832	+	22.2183i	1.23119	+	0.710827i	0.263910	+	0.964547i	$0.414988\pi$
$978$	4.45302	−	7.71286i	0.142392	−	0.246630i
$979$	−11.2301	−	19.4511i	−0.358916	−	0.621660i
$980$			0.367201i			0.0117298i
$981$	−11.6669	+	6.73591i	−0.372497	+	0.215061i
$982$	13.7362	−	7.93061i	0.438340	−	0.253076i
$983$			32.8766i			1.04860i	0.851533	+	0.524301i	$0.175673\pi$
$983$			32.8766i			1.04860i	−0.851533	+	0.524301i	$0.824327\pi$
$984$	1.27862	+	2.21463i	0.0407609	+	0.0705999i
$985$	−20.5101	+	35.5245i	−0.653505	+	1.13190i
$986$	9.04223	+	5.22053i	0.287963	+	0.166256i
$987$	−13.1993			−0.420139
$988$	4.90232	+	0.517570i	0.155964	+	0.0164661i
$989$	−23.2533			−0.739413
$990$	−7.59536	−	4.38519i	−0.241396	−	0.139370i
$991$	−14.2326	+	24.6517i	−0.452115	+	0.783086i	−0.998517	−	0.0544368i	$-0.982664\pi$
$991$	−14.2326	+	24.6517i	−0.452115	+	0.783086i	0.546402	+	0.837523i	$0.315997\pi$
$992$	4.26675	+	7.39023i	0.135470	+	0.234640i
$993$		−	25.6008i		−	0.812416i
$994$	4.81095	−	2.77760i	0.152594	−	0.0881002i
$995$	35.2348	−	20.3428i	1.11702	−	0.644910i
$996$		−	0.233218i		−	0.00738981i
$997$	7.09601	+	12.2907i	0.224733	+	0.389249i	0.956239	−	0.292586i	$-0.0945157\pi$
$997$	7.09601	+	12.2907i	0.224733	+	0.389249i	−0.731506	+	0.681835i	$0.761182\pi$
$998$	11.8148	−	20.4638i	0.373989	−	0.647769i
$999$	−5.84044	−	3.37198i	−0.184783	−	0.106685i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bd.b.43.6	✓	16
3.2	odd	2		819.2.ct.c.316.3		16
13.6	odd	12		3549.2.a.ba.1.4		8
13.7	odd	12		3549.2.a.bc.1.5		8
13.10	even	6	inner	273.2.bd.b.127.6	yes	16
39.23	odd	6		819.2.ct.c.127.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bd.b.43.6	✓	16	1.1	even	1	trivial
273.2.bd.b.127.6	yes	16	13.10	even	6	inner
819.2.ct.c.127.3		16	39.23	odd	6
819.2.ct.c.316.3		16	3.2	odd	2
3549.2.a.ba.1.4		8	13.6	odd	12
3549.2.a.bc.1.5		8	13.7	odd	12

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bd (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.15033 + 0.664145i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.117823 - 0.204075i) q^{4} -1.55828i q^{5} +(1.15033 - 0.664145i) q^{6} +(-0.866025 + 0.500000i) q^{7} -2.96959i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.15033 + 0.664145i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.117823 - 0.204075i) q^{4} -1.55828i q^{5} +(1.15033 - 0.664145i) q^{6} +(-0.866025 + 0.500000i) q^{7} -2.96959i q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.03492 - 1.79254i) q^{10} +(3.66954 + 2.11861i) q^{11} -0.235645 q^{12} +(3.29452 - 1.46497i) q^{13} -1.32829 q^{14} +(-1.34951 - 0.779138i) q^{15} +(1.73659 - 3.00786i) q^{16} +(-0.391538 - 0.678164i) q^{17} -1.32829i q^{18} +(-5.02469 + 2.90100i) q^{19} +(-0.318005 + 0.183600i) q^{20} +1.00000i q^{21} +(2.81413 + 4.87421i) q^{22} +(-2.07926 + 3.60138i) q^{23} +(-2.57174 - 1.48479i) q^{24} +2.57177 q^{25} +(4.76275 + 0.502835i) q^{26} -1.00000 q^{27} +(0.204075 + 0.117823i) q^{28} +(-5.01901 + 8.69317i) q^{29} +(-1.03492 - 1.79254i) q^{30} -6.43659i q^{31} +(-1.14816 + 0.662890i) q^{32} +(3.66954 - 2.11861i) q^{33} -1.04015i q^{34} +(0.779138 + 1.34951i) q^{35} +(-0.117823 + 0.204075i) q^{36} +(5.84044 + 3.37198i) q^{37} -7.70675 q^{38} +(0.378558 - 3.58562i) q^{39} -4.62744 q^{40} +(-0.745771 - 0.430571i) q^{41} +(-0.664145 + 1.15033i) q^{42} +(2.79587 + 4.84259i) q^{43} -0.998480i q^{44} +(-1.34951 + 0.779138i) q^{45} +(-4.78367 + 2.76185i) q^{46} +13.1993i q^{47} +(-1.73659 - 3.00786i) q^{48} +(0.500000 - 0.866025i) q^{49} +(2.95840 + 1.70803i) q^{50} -0.783076 q^{51} +(-0.687133 - 0.499722i) q^{52} -2.25508 q^{53} +(-1.15033 - 0.664145i) q^{54} +(3.30138 - 5.71815i) q^{55} +(1.48479 + 2.57174i) q^{56} +5.80201i q^{57} +(-11.5471 + 6.66670i) q^{58} +(10.2481 - 5.91673i) q^{59} +0.367201i q^{60} +(-3.69949 - 6.40770i) q^{61} +(4.27483 - 7.40422i) q^{62} +(0.866025 + 0.500000i) q^{63} -8.70738 q^{64} +(-2.28283 - 5.13377i) q^{65} +5.62825 q^{66} +(-9.30150 - 5.37022i) q^{67} +(-0.0922642 + 0.159806i) q^{68} +(2.07926 + 3.60138i) q^{69} +2.06984i q^{70} +(-3.62191 + 2.09111i) q^{71} +(-2.57174 + 1.48479i) q^{72} -13.4249i q^{73} +(4.47897 + 7.75780i) q^{74} +(1.28589 - 2.22722i) q^{75} +(1.18404 + 0.683608i) q^{76} -4.23721 q^{77} +(2.81684 - 3.87324i) q^{78} +13.8087 q^{79} +(-4.68708 - 2.70609i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.571924 - 0.990601i) q^{82} +0.989701i q^{83} +(0.204075 - 0.117823i) q^{84} +(-1.05677 + 0.610125i) q^{85} +7.42746i q^{86} +(5.01901 + 8.69317i) q^{87} +(6.29139 - 10.8970i) q^{88} +(-4.59054 - 2.65035i) q^{89} -2.06984 q^{90} +(-2.12065 + 2.91596i) q^{91} +0.979934 q^{92} +(-5.57425 - 3.21830i) q^{93} +(-8.76626 + 15.1836i) q^{94} +(4.52057 + 7.82985i) q^{95} +1.32578i q^{96} +(-0.0673109 + 0.0388620i) q^{97} +(1.15033 - 0.664145i) q^{98} -4.23721i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} + 14 q^{4} - 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 + 14 * q^4 - 8 * q^9	\( 16 q + 8 q^{3} + 14 q^{4} - 8 q^{9} - 4 q^{10} + 28 q^{12} - 12 q^{13} - 4 q^{14} - 12 q^{15} - 10 q^{16} - 2 q^{17} + 18 q^{20} - 18 q^{22} - 6 q^{23} - 20 q^{25} + 20 q^{26} - 16 q^{27} - 12 q^{29} + 4 q^{30} - 30 q^{32} + 6 q^{35} + 14 q^{36} - 6 q^{37} - 24 q^{38} - 28 q^{40} - 30 q^{41} - 2 q^{42} + 14 q^{43} - 12 q^{45} - 42 q^{46} + 10 q^{48} + 8 q^{49} + 84 q^{50} - 4 q^{51} + 30 q^{52} + 28 q^{53} + 2 q^{55} - 12 q^{56} + 66 q^{58} - 24 q^{59} + 2 q^{61} - 20 q^{62} - 48 q^{64} - 44 q^{65} - 36 q^{66} + 30 q^{67} + 36 q^{68} + 6 q^{69} - 6 q^{71} + 6 q^{74} - 10 q^{75} - 24 q^{76} + 32 q^{77} + 10 q^{78} + 92 q^{79} + 114 q^{80} - 8 q^{81} - 42 q^{82} + 48 q^{85} + 12 q^{87} + 62 q^{88} + 18 q^{89} + 8 q^{90} - 116 q^{92} - 6 q^{93} - 24 q^{94} - 24 q^{95} - 6 q^{97}+O(q^{100}) \) 16 * q + 8 * q^3 + 14 * q^4 - 8 * q^9 - 4 * q^10 + 28 * q^12 - 12 * q^13 - 4 * q^14 - 12 * q^15 - 10 * q^16 - 2 * q^17 + 18 * q^20 - 18 * q^22 - 6 * q^23 - 20 * q^25 + 20 * q^26 - 16 * q^27 - 12 * q^29 + 4 * q^30 - 30 * q^32 + 6 * q^35 + 14 * q^36 - 6 * q^37 - 24 * q^38 - 28 * q^40 - 30 * q^41 - 2 * q^42 + 14 * q^43 - 12 * q^45 - 42 * q^46 + 10 * q^48 + 8 * q^49 + 84 * q^50 - 4 * q^51 + 30 * q^52 + 28 * q^53 + 2 * q^55 - 12 * q^56 + 66 * q^58 - 24 * q^59 + 2 * q^61 - 20 * q^62 - 48 * q^64 - 44 * q^65 - 36 * q^66 + 30 * q^67 + 36 * q^68 + 6 * q^69 - 6 * q^71 + 6 * q^74 - 10 * q^75 - 24 * q^76 + 32 * q^77 + 10 * q^78 + 92 * q^79 + 114 * q^80 - 8 * q^81 - 42 * q^82 + 48 * q^85 + 12 * q^87 + 62 * q^88 + 18 * q^89 + 8 * q^90 - 116 * q^92 - 6 * q^93 - 24 * q^94 - 24 * q^95 - 6 * q^97

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