LMFDB - Embedded newform 273.2.bd.b.127.6

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} - 132 x^{7} - 45 x^{6} + 864 x^{5} - 243 x^{4} - 1944 x^{3} + 7290 x^{2} - 8748 x + 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			127.6
Root			$-0.306536 + 1.70471i$ of defining polynomial
Character	$\chi$	$=$	273.127
Dual form			273.2.bd.b.43.6

$q$-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 $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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	−0.0347298	−	0.999397i	$-0.511057\pi$
$2$	1.15033	−	0.664145i	0.813408	−	0.469621i	0.848138	+	0.529775i	$0.177724\pi$
$3$	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	$0.113289\pi$
$5$			1.55828i			0.696882i	−0.937331	+	0.348441i	$0.886711\pi$
$6$	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	0.168510	−	0.985700i	$-0.446104\pi$
$11$	3.66954	−	2.11861i	1.10641	−	0.638784i	0.937896	+	0.346916i	$0.112771\pi$
$12$	−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	−0.909593	−	0.415501i	$-0.863606\pi$
$17$	−0.391538	+	0.678164i	−0.0949619	+	0.164479i	0.814631	+	0.579980i	$0.196940\pi$
$18$			1.32829i			0.313081i
$19$	−5.02469	−	2.90100i	−1.15274	−	0.665536i	−0.203188	−	0.979140i	$-0.565130\pi$
$19$	−5.02469	−	2.90100i	−1.15274	−	0.665536i	−0.949554	+	0.313604i	$0.898464\pi$
$20$	−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	0.563622	−	0.826033i	$-0.309408\pi$
$23$	−2.07926	−	3.60138i	−0.433555	−	0.750939i	−0.997176	+	0.0750941i	$0.976074\pi$
$24$	−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	−0.779888	−	0.625919i	$-0.784724\pi$
$29$	−5.01901	−	8.69317i	−0.932006	−	1.61428i	−0.152118	−	0.988362i	$-0.548609\pi$
$30$	−1.03492	+	1.79254i	−0.188950	+	0.327271i
$31$			6.43659i			1.15605i	0.816021	+	0.578023i	$0.196176\pi$
$31$			6.43659i			1.15605i	−0.816021	+	0.578023i	$0.803824\pi$
$32$	−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	0.0639394	−	0.997954i	$-0.479634\pi$
$37$	5.84044	−	3.37198i	0.960162	−	0.554350i	0.896223	+	0.443604i	$0.146300\pi$
$38$	−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	−0.557103	−	0.830443i	$-0.688087\pi$
$41$	−0.745771	+	0.430571i	−0.116470	+	0.0672439i	0.440633	+	0.897687i	$0.354754\pi$
$42$	−0.664145	−	1.15033i	−0.102480	−	0.177500i
$43$	2.79587	−	4.84259i	0.426367	−	0.738489i	−0.570180	−	0.821520i	$-0.693127\pi$
$43$	2.79587	−	4.84259i	0.426367	−	0.738489i	0.996547	+	0.0830309i	$0.0264600\pi$
$44$			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	$-0.587260\pi$
$47$		−	13.1993i		−	1.92532i	0.270715	−	0.962659i	$-0.412740\pi$
$48$	−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	0.985938	−	0.167111i	$-0.0534437\pi$
$59$	10.2481	+	5.91673i	1.33419	+	0.770292i	0.348247	+	0.937403i	$0.386777\pi$
$60$		−	0.367201i		−	0.0474054i
$61$	−3.69949	+	6.40770i	−0.473671	+	0.820422i	−0.999546	−	0.0301397i	$-0.990405\pi$
$61$	−3.69949	+	6.40770i	−0.473671	+	0.820422i	0.525875	+	0.850562i	$0.323738\pi$
$62$	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	−0.945526	−	0.325545i	$-0.894452\pi$
$67$	−9.30150	+	5.37022i	−1.13636	+	0.656077i	−0.190833	+	0.981623i	$0.561119\pi$
$68$	−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	0.269437	−	0.963018i	$-0.413162\pi$
$71$	−3.62191	−	2.09111i	−0.429842	−	0.248169i	−0.699279	+	0.714849i	$0.746496\pi$
$72$	−2.57174	−	1.48479i	−0.303082	−	0.174985i
$73$			13.4249i			1.57127i	0.618692	+	0.785634i	$0.287663\pi$
$73$			13.4249i			1.57127i	−0.618692	+	0.785634i	$0.712337\pi$
$74$	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	$-0.982702\pi$
$83$		−	0.989701i		−	0.108634i	0.998524	−	0.0543169i	$-0.0172981\pi$
$84$	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	−0.723161	−	0.690679i	$-0.757312\pi$
$89$	−4.59054	+	2.65035i	−0.486597	+	0.280937i	0.236565	+	0.971616i	$0.423978\pi$
$90$	−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	0.496579	−	0.867992i	$-0.334589\pi$
$97$	−0.0673109	−	0.0388620i	−0.00683439	−	0.00394583i	−0.503413	+	0.864046i	$0.667923\pi$
$98$	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	0.786191	−	0.617983i	$-0.212050\pi$
$101$	−1.42802	−	2.47340i	−0.142093	−	0.246113i	−0.928285	+	0.371870i	$0.878717\pi$
$102$	−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	0.692145	−	0.721759i	$-0.256666\pi$
$107$	−2.88588	−	4.99850i	−0.278989	−	0.483223i	−0.971134	+	0.238536i	$0.923333\pi$
$108$	0.117823	−	0.204075i	0.0113375	−	0.0196371i
$109$			13.4718i			1.29037i	0.764028	+	0.645183i	$0.223219\pi$
$109$			13.4718i			1.29037i	−0.764028	+	0.645183i	$0.776781\pi$
$110$	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	−0.614381	−	0.789010i	$-0.710594\pi$
$113$	3.99812	−	6.92495i	0.376112	−	0.651445i	0.990493	+	0.137565i	$0.0439275\pi$
$114$	−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	0.656012	−	0.754751i	$-0.272242\pi$
$127$	−3.66963	−	6.35599i	−0.325627	−	0.564003i	−0.981639	+	0.190748i	$0.938909\pi$
$128$	−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	0.752250	−	0.658878i	$-0.228969\pi$
$137$	6.52853	+	3.76925i	0.557770	+	0.322029i	−0.194480	+	0.980907i	$0.562302\pi$
$138$		−	5.52371i		−	0.470209i
$139$	5.56775	−	9.64363i	0.472250	−	0.817962i	−0.527245	−	0.849713i	$-0.676775\pi$
$139$	5.56775	−	9.64363i	0.472250	−	0.817962i	0.999496	+	0.0317513i	$0.0101085\pi$
$140$	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	0.0135744	−	0.999908i	$-0.495679\pi$
$149$	−10.3217	−	5.95922i	−0.845584	−	0.488198i	−0.859158	+	0.511710i	$0.829012\pi$
$150$	2.95840	+	1.70803i	0.241552	+	0.139460i
$151$		−	10.4448i		−	0.849987i	−0.905196	−	0.424993i	$-0.860276\pi$
$151$		−	10.4448i		−	0.849987i	0.905196	−	0.424993i	$-0.139724\pi$
$152$	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	0.709859	−	0.704344i	$-0.248759\pi$
$163$	5.80660	+	3.35244i	0.454808	+	0.262584i	−0.255050	+	0.966928i	$0.582092\pi$
$164$		−	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	−0.969862	−	0.243656i	$-0.921653\pi$
$167$	−16.0732	+	9.27985i	−1.24378	+	0.718097i	−0.273918	+	0.961753i	$0.588320\pi$
$168$	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	−0.896788	−	0.442461i	$-0.854105\pi$
$173$	−0.857721	+	1.48562i	−0.0652113	+	0.112949i	0.831576	+	0.555410i	$0.187439\pi$
$174$		−	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	0.998375	+	0.0569932i	$0.0181513\pi$
$179$	7.33903	+	12.7116i	0.548545	+	0.950108i	−0.449830	+	0.893114i	$0.648515\pi$
$180$	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	−0.763576	−	0.645718i	$-0.776558\pi$
$191$	2.45200	−	4.24699i	0.177421	−	0.307302i	0.940996	+	0.338417i	$0.109891\pi$
$192$	−4.35369	−	7.54081i	−0.314201	−	0.544211i
$193$	−9.33991	+	5.39240i	−0.672302	+	0.388153i	−0.796948	−	0.604048i	$-0.793554\pi$
$193$	−9.33991	+	5.39240i	−0.672302	+	0.388153i	0.124647	+	0.992201i	$0.460220\pi$
$194$	−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	−0.638472	+	0.769645i	$0.720433\pi$
$197$	−22.7973	+	13.1620i	−1.62424	+	0.937756i	−0.985768	+	0.168111i	$0.946233\pi$
$198$	2.81413	+	4.87421i	0.199991	+	0.346395i
$199$	13.0547	−	22.6114i	0.925422	−	1.60288i	0.134541	−	0.990908i	$-0.457044\pi$
$199$	13.0547	−	22.6114i	0.925422	−	1.60288i	0.790881	−	0.611970i	$-0.209623\pi$
$200$			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	0.997036	−	0.0769323i	$-0.0245125\pi$
$211$	6.27361	+	10.8662i	0.431893	+	0.748060i	−0.565143	+	0.824993i	$0.691179\pi$
$212$	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	−0.907979	−	0.419016i	$-0.862375\pi$
$223$	−14.9196	+	8.61384i	−0.999090	+	0.576825i	−0.0911113	+	0.995841i	$0.529042\pi$
$224$	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	0.0780211	−	0.996952i	$-0.475140\pi$
$227$	−11.2450	−	6.49228i	−0.746354	−	0.430908i	−0.824375	+	0.566044i	$0.808473\pi$
$228$	1.18404	+	0.683608i	0.0784153	+	0.0452731i
$229$		−	17.4443i		−	1.15275i	−0.817186	−	0.576374i	$-0.804467\pi$
$229$		−	17.4443i		−	1.15275i	0.817186	−	0.576374i	$-0.195533\pi$
$230$	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	$0.107634\pi$
$239$			10.2570i			0.663468i	−0.943373	+	0.331734i	$0.892366\pi$
$240$	−4.68708	−	2.70609i	−0.302550	−	0.174677i
$241$	−11.1221	−	6.42137i	−0.716440	−	0.413637i	0.0970010	−	0.995284i	$-0.469075\pi$
$241$	−11.1221	−	6.42137i	−0.716440	−	0.413637i	−0.813441	+	0.581648i	$0.802408\pi$
$242$		−	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	−0.902022	−	0.431689i	$-0.857918\pi$
$251$	−1.22240	+	2.11726i	−0.0771572	+	0.133640i	0.824865	+	0.565330i	$0.191251\pi$
$252$			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	0.687879	−	0.725825i	$-0.258542\pi$
$257$	−4.56319	−	7.90367i	−0.284644	−	0.493017i	−0.972523	+	0.232808i	$0.925209\pi$
$258$	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	−0.584311	−	0.811530i	$-0.698635\pi$
$263$	−16.1356	−	27.9476i	−0.994961	−	1.72332i	−0.410650	−	0.911793i	$-0.634698\pi$
$264$	−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	−0.769601	−	0.638525i	$-0.779545\pi$
$269$	2.75834	−	4.77758i	0.168179	−	0.291294i	0.937780	+	0.347231i	$0.112878\pi$
$270$	−1.03492	−	1.79254i	−0.0629833	−	0.109090i
$271$	−25.6527	+	14.8106i	−1.55829	+	0.899680i	−0.560872	+	0.827903i	$0.689534\pi$
$271$	−25.6527	+	14.8106i	−1.55829	+	0.899680i	−0.997421	+	0.0717776i	$0.977133\pi$
$272$	−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	0.403993	+	0.914762i	$0.367622\pi$
$277$	−9.82307	+	17.0141i	−0.590211	+	1.02228i	−0.994204	+	0.107513i	$0.965711\pi$
$278$		−	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	$-0.994287\pi$
$281$		−	0.601681i		−	0.0358932i	0.999839	−	0.0179466i	$-0.00571289\pi$
$282$	8.76626	−	15.1836i	0.522023	−	0.904171i
$283$	−5.25559	−	9.10295i	−0.312412	−	0.541114i	0.666472	−	0.745530i	$-0.267804\pi$
$283$	−5.25559	−	9.10295i	−0.312412	−	0.541114i	−0.978884	+	0.204416i	$0.934470\pi$
$284$	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	0.701636	−	0.712535i	$-0.252453\pi$
$293$	7.45252	+	4.30271i	0.435381	+	0.251367i	−0.266255	+	0.963903i	$0.585786\pi$
$294$			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	$-0.900092\pi$
$307$		−	10.8192i		−	0.617485i	0.951146	−	0.308742i	$-0.0999081\pi$
$308$	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	$0.209102\pi$
$317$			21.7455i			1.22135i	−0.791882	+	0.610675i	$0.790898\pi$
$318$	−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	0.964624	−	0.263631i	$-0.0849201\pi$
$331$	22.1709	+	12.8004i	1.21862	+	0.703573i	0.254001	+	0.967204i	$0.418253\pi$
$332$	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	−0.612166	−	0.790730i	$-0.709701\pi$
$347$	7.05457	−	12.2189i	0.378709	−	0.655943i	0.990875	+	0.134786i	$0.0430348\pi$
$348$	1.18271	+	2.04851i	0.0633997	+	0.109811i
$349$	11.8136	−	6.82060i	0.632369	−	0.365098i	−0.149300	−	0.988792i	$-0.547702\pi$
$349$	11.8136	−	6.82060i	0.632369	−	0.365098i	0.781669	+	0.623694i	$0.214369\pi$
$350$	−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	−0.709921	−	0.704282i	$-0.751269\pi$
$353$	−8.54783	+	4.93509i	−0.454955	+	0.262668i	0.254966	+	0.966950i	$0.417936\pi$
$354$	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	$-0.875483\pi$
$359$		−	14.4485i		−	0.762564i	0.924459	−	0.381282i	$-0.124517\pi$
$360$	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	0.985755	+	0.168188i	$0.0537916\pi$
$367$	12.2325	+	21.1874i	0.638533	+	1.10597i	−0.347222	+	0.937783i	$0.612875\pi$
$368$	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	0.352995	+	0.935625i	$0.385163\pi$
$373$	−12.2403	+	21.2008i	−0.633777	+	1.09773i	−0.986773	+	0.162110i	$0.948170\pi$
$374$	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	−0.0170699	−	0.999854i	$-0.505434\pi$
$379$	16.3588	−	9.44475i	0.840294	−	0.485144i	0.857364	+	0.514710i	$0.172100\pi$
$380$	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	0.728197	−	0.685368i	$-0.240359\pi$
$383$	9.76071	+	5.63535i	0.498749	+	0.287953i	−0.229448	+	0.973321i	$0.573692\pi$
$384$	−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	0.424320	−	0.905512i	$-0.360513\pi$
$397$	−2.94325	−	1.69928i	−0.147717	−	0.0852846i	−0.572037	+	0.820228i	$0.693847\pi$
$398$		−	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	−0.769454	−	0.638703i	$-0.779471\pi$
$401$	−12.0360	+	6.94897i	−0.601047	+	0.347015i	0.168406	+	0.985718i	$0.446138\pi$
$402$	−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	0.822139	−	0.569287i	$-0.192781\pi$
$409$	14.9695	+	8.64262i	0.740192	+	0.427350i	−0.0819473	+	0.996637i	$0.526114\pi$
$410$	−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	0.942677	−	0.333707i	$-0.108300\pi$
$419$	3.73240	+	6.46471i	0.182340	+	0.315822i	−0.760337	+	0.649529i	$0.774966\pi$
$420$	−0.183600	+	0.318005i	−0.00895878	+	0.0155171i
$421$			17.2523i			0.840826i	0.907333	+	0.420413i	$0.138115\pi$
$421$			17.2523i			0.840826i	−0.907333	+	0.420413i	$0.861885\pi$
$422$	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	0.258161	−	0.966102i	$-0.416883\pi$
$431$	25.4090	−	14.6699i	1.22391	−	0.706625i	0.965749	+	0.259477i	$0.0835501\pi$
$432$	−1.73659	−	3.00786i	−0.0835517	−	0.144716i
$433$	−3.69938	+	6.40751i	−0.177781	+	0.307925i	−0.941120	−	0.338072i	$-0.890225\pi$
$433$	−3.69938	+	6.40751i	−0.177781	+	0.307925i	0.763339	+	0.645998i	$0.223558\pi$
$434$		−	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	−0.975603	−	0.219542i	$-0.929544\pi$
$439$	−14.2042	−	24.6024i	−0.677930	−	1.17421i	0.297673	−	0.954668i	$-0.403790\pi$
$440$	−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	0.829723	−	0.558175i	$-0.188498\pi$
$449$	16.1294	+	9.31229i	0.761192	+	0.439474i	−0.0685319	+	0.997649i	$0.521831\pi$
$450$			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	−0.245198	−	0.969473i	$-0.578853\pi$
$457$	10.0858	−	5.82301i	0.471792	−	0.272389i	0.716989	+	0.697084i	$0.245520\pi$
$458$	−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	0.917571	−	0.397571i	$-0.130147\pi$
$461$	22.1591	+	12.7935i	1.03205	+	0.595854i	0.114479	+	0.993426i	$0.463480\pi$
$462$	−4.87421	−	2.81413i	−0.226769	−	0.130925i
$463$			25.8560i			1.20163i	0.799389	+	0.600814i	$0.205157\pi$
$463$			25.8560i			1.20163i	−0.799389	+	0.600814i	$0.794843\pi$
$464$	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	−0.477840	−	0.878447i	$-0.658580\pi$
$479$	0.962929	−	0.555947i	0.0439974	−	0.0254019i	0.521837	+	0.853045i	$0.325247\pi$
$480$	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	−0.122879	−	0.992422i	$-0.539213\pi$
$487$	−23.0343	−	13.2988i	−1.04378	−	0.602628i	−0.920902	+	0.389794i	$0.872546\pi$
$488$	−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	0.968719	−	0.248160i	$-0.0798259\pi$
$491$	5.97054	+	10.3413i	0.269447	+	0.466695i	−0.699272	+	0.714855i	$0.746493\pi$
$492$	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	$0.130359\pi$
$499$			17.7894i			0.796364i	−0.917306	+	0.398182i	$0.869641\pi$
$500$	−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	−0.610157	−	0.792281i	$-0.708893\pi$
$503$	8.54622	−	14.8025i	0.381057	−	0.660010i	0.991214	+	0.132271i	$0.0422268\pi$
$504$	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	−0.222080	−	0.975028i	$-0.571285\pi$
$509$	11.5350	−	6.65972i	0.511279	−	0.295187i	0.733359	+	0.679841i	$0.237951\pi$
$510$	−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	0.888128	−	0.459597i	$-0.152006\pi$
$523$	1.05293	+	1.82372i	0.0460413	+	0.0797459i	−0.842086	+	0.539343i	$0.818673\pi$
$524$	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	$-0.967997\pi$
$541$		−	4.66916i		−	0.200743i	0.994950	−	0.100371i	$-0.0320031\pi$
$542$	−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	−0.980756	−	0.195238i	$-0.937452\pi$
$557$	−30.7295	+	17.7417i	−1.30205	+	0.751740i	−0.321297	+	0.946979i	$0.604119\pi$
$558$	−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	−0.660316	−	0.750988i	$-0.729578\pi$
$563$	7.59798	−	13.1601i	0.320217	−	0.554631i	0.980533	+	0.196357i	$0.0629110\pi$
$564$			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	0.712622	−	0.701548i	$-0.247507\pi$
$569$	−5.99318	−	10.3805i	−0.251247	−	0.435173i	−0.963869	+	0.266375i	$0.914174\pi$
$570$	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	$-0.702313\pi$
$577$		−	38.6603i		−	1.60945i	0.593648	−	0.804725i	$-0.297687\pi$
$578$	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	−0.462357	−	0.886694i	$-0.652996\pi$
$587$	1.80169	−	1.04021i	0.0743639	−	0.0429340i	0.536721	+	0.843760i	$0.319663\pi$
$588$	−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	$-0.672893\pi$
$593$		−	41.6938i		−	1.71216i	0.516844	−	0.856080i	$-0.327107\pi$
$594$	−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	0.788782	−	0.614673i	$-0.210712\pi$
$601$	−3.38144	−	5.85683i	−0.137932	−	0.238905i	−0.926714	+	0.375768i	$0.877379\pi$
$602$	−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	−0.812859	−	0.582461i	$-0.802090\pi$
$607$	2.41439	−	4.18184i	0.0979969	−	0.169736i	0.910855	+	0.412726i	$0.135423\pi$
$608$	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	−0.164773	−	0.986332i	$-0.552689\pi$
$613$	15.0293	−	8.67719i	0.607029	−	0.350468i	0.771802	+	0.635863i	$0.219356\pi$
$614$	−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	0.502727	−	0.864445i	$-0.332330\pi$
$617$	0.135605	+	0.0782913i	0.00545923	+	0.00315189i	−0.497268	+	0.867597i	$0.665663\pi$
$618$	−6.58674	−	3.80286i	−0.264958	−	0.152973i
$619$			37.4947i			1.50704i	0.657426	+	0.753519i	$0.271645\pi$
$619$			37.4947i			1.50704i	−0.657426	+	0.753519i	$0.728355\pi$
$620$	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	0.814144	−	0.580663i	$-0.197207\pi$
$631$	18.0447	+	10.4181i	0.718346	+	0.414737i	−0.0957974	+	0.995401i	$0.530540\pi$
$632$			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	−0.150726	+	0.988576i	$0.548161\pi$
$641$	−23.5836	+	40.8479i	−0.931494	+	1.61340i	−0.780769	+	0.624820i	$0.785172\pi$
$642$		−	7.66658i		−	0.302576i
$643$	−16.2935	−	9.40707i	−0.642554	−	0.370979i	0.143044	−	0.989716i	$-0.454311\pi$
$643$	−16.2935	−	9.40707i	−0.642554	−	0.370979i	−0.785598	+	0.618738i	$0.787644\pi$
$644$	−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	0.999567	−	0.0294191i	$-0.00936573\pi$
$647$	12.0645	+	20.8964i	0.474306	+	0.821522i	−0.525261	+	0.850941i	$0.676032\pi$
$648$	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	0.516889	−	0.856052i	$-0.327090\pi$
$653$	−12.3404	−	21.3743i	−0.482919	−	0.836439i	−0.999808	+	0.0196129i	$0.993757\pi$
$654$	−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	−0.847751	−	0.530395i	$-0.822044\pi$
$659$	0.910300	−	1.57669i	0.0354603	−	0.0614190i	0.883211	+	0.468976i	$0.155377\pi$
$660$	−0.777954	−	1.34746i	−0.0302818	−	0.0524497i
$661$	36.4761	−	21.0595i	1.41876	−	0.819120i	0.422567	−	0.906332i	$-0.361129\pi$
$661$	36.4761	−	21.0595i	1.41876	−	0.819120i	0.996190	+	0.0872120i	$0.0277957\pi$
$662$	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	0.883888	−	0.467699i	$-0.154917\pi$
$673$	0.957403	+	1.65827i	0.0369052	+	0.0639216i	−0.846983	+	0.531620i	$0.821583\pi$
$674$	−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	0.758861	−	0.651252i	$-0.225756\pi$
$683$	15.0087	+	8.66527i	0.574291	+	0.331567i	−0.184570	+	0.982819i	$0.559089\pi$
$684$			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	−0.484393	−	0.874851i	$-0.660959\pi$
$691$	0.816299	−	0.471291i	0.0310535	−	0.0179287i	0.515446	+	0.856922i	$0.327626\pi$
$692$	−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	0.0485130	−	0.998823i	$-0.484552\pi$
$709$	−21.0949	−	12.1792i	−0.792236	−	0.457398i	−0.840749	+	0.541425i	$0.817885\pi$
$710$		−	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	0.0218547	+	0.999761i	$0.493043\pi$
$719$	−22.9232	+	39.7042i	−0.854891	+	1.48072i	−0.876746	+	0.480954i	$0.840290\pi$
$720$		−	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	$-0.854041\pi$
$733$		−	23.9682i		−	0.885287i	0.896698	−	0.442643i	$-0.145959\pi$
$734$	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	−0.0716788	−	0.997428i	$-0.522836\pi$
$739$	20.5591	−	11.8698i	0.756280	−	0.436638i	0.827958	+	0.560790i	$0.189502\pi$
$740$	−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	−0.781893	−	0.623412i	$-0.785746\pi$
$743$	−17.2529	+	9.96099i	−0.632949	+	0.365433i	0.148944	+	0.988846i	$0.452412\pi$
$744$	−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	0.701075	−	0.713087i	$-0.252704\pi$
$751$	−7.31735	−	12.6740i	−0.267014	−	0.462482i	−0.968089	+	0.250606i	$0.919370\pi$
$752$	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	−0.964709	−	0.263319i	$-0.915183\pi$
$757$	−19.5456	−	33.8539i	−0.710395	−	1.23044i	0.254314	−	0.967122i	$-0.418150\pi$
$758$	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	0.439610	−	0.898189i	$-0.355117\pi$
$761$	−3.26731	−	1.88638i	−0.118440	−	0.0683813i	−0.558050	+	0.829808i	$0.688450\pi$
$762$		−	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	−0.501485	−	0.865167i	$-0.667213\pi$
$769$	−0.0823798	+	0.0475620i	−0.00297069	+	0.00171513i	0.498514	+

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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