LMFDB - Embedded newform 273.2.k.c.211.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(22,273)]

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, 4]))

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

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

chi := DirichletCharacter("273.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.k (of order $3$, 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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.1
Root			$0.222521 + 0.385418i$ of defining polynomial
Character	$\chi$	$=$	273.211
Dual form			273.2.k.c.22.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.400969 - 0.694498i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.678448 - 1.17511i) q^{4} -3.04892 q^{5} +(-0.400969 + 0.694498i) q^{6} +(-0.500000 + 0.866025i) q^{7} -2.69202 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.400969 - 0.694498i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.678448 - 1.17511i) q^{4} -3.04892 q^{5} +(-0.400969 + 0.694498i) q^{6} +(-0.500000 + 0.866025i) q^{7} -2.69202 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.22252 + 2.11747i) q^{10} +(-1.07942 - 1.86960i) q^{11} -1.35690 q^{12} +(-1.16756 + 3.41127i) q^{13} +0.801938 q^{14} +(1.52446 + 2.64044i) q^{15} +(-0.277479 - 0.480608i) q^{16} +(-0.400969 + 0.694498i) q^{17} +0.801938 q^{18} +(0.698062 - 1.20908i) q^{19} +(-2.06853 + 3.58280i) q^{20} +1.00000 q^{21} +(-0.865625 + 1.49931i) q^{22} +(-1.51357 - 2.62159i) q^{23} +(1.34601 + 2.33136i) q^{24} +4.29590 q^{25} +(2.83728 - 0.556945i) q^{26} +1.00000 q^{27} +(0.678448 + 1.17511i) q^{28} +(-1.23609 - 2.14098i) q^{29} +(1.22252 - 2.11747i) q^{30} -6.26875 q^{31} +(-2.91454 + 5.04814i) q^{32} +(-1.07942 + 1.86960i) q^{33} +0.643104 q^{34} +(1.52446 - 2.64044i) q^{35} +(0.678448 + 1.17511i) q^{36} +(-5.37531 - 9.31032i) q^{37} -1.11960 q^{38} +(3.53803 - 0.694498i) q^{39} +8.20775 q^{40} +(2.60388 + 4.51004i) q^{41} +(-0.400969 - 0.694498i) q^{42} +(4.31551 - 7.47468i) q^{43} -2.92931 q^{44} +(1.52446 - 2.64044i) q^{45} +(-1.21379 + 2.10235i) q^{46} -9.15883 q^{47} +(-0.277479 + 0.480608i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-1.72252 - 2.98349i) q^{50} +0.801938 q^{51} +(3.21648 + 3.68638i) q^{52} +1.21983 q^{53} +(-0.400969 - 0.694498i) q^{54} +(3.29105 + 5.70027i) q^{55} +(1.34601 - 2.33136i) q^{56} -1.39612 q^{57} +(-0.991271 + 1.71693i) q^{58} +(4.31551 - 7.47468i) q^{59} +4.13706 q^{60} +(5.04288 - 8.73452i) q^{61} +(2.51357 + 4.35364i) q^{62} +(-0.500000 - 0.866025i) q^{63} +3.56465 q^{64} +(3.55980 - 10.4007i) q^{65} +1.73125 q^{66} +(6.39493 + 11.0763i) q^{67} +(0.544073 + 0.942362i) q^{68} +(-1.51357 + 2.62159i) q^{69} -2.44504 q^{70} +(7.06249 - 12.2326i) q^{71} +(1.34601 - 2.33136i) q^{72} -10.1250 q^{73} +(-4.31067 + 7.46629i) q^{74} +(-2.14795 - 3.72036i) q^{75} +(-0.947198 - 1.64059i) q^{76} +2.15883 q^{77} +(-1.90097 - 2.17869i) q^{78} +1.33513 q^{79} +(0.846011 + 1.46533i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.08815 - 3.61677i) q^{82} +8.92692 q^{83} +(0.678448 - 1.17511i) q^{84} +(1.22252 - 2.11747i) q^{85} -6.92154 q^{86} +(-1.23609 + 2.14098i) q^{87} +(2.90581 + 5.03302i) q^{88} +(1.25302 + 2.17029i) q^{89} -2.44504 q^{90} +(-2.37047 - 2.71678i) q^{91} -4.10752 q^{92} +(3.13437 + 5.42890i) q^{93} +(3.67241 + 6.36080i) q^{94} +(-2.12833 + 3.68638i) q^{95} +5.82908 q^{96} +(-1.16152 + 2.01182i) q^{97} +(-0.400969 + 0.694498i) q^{98} +2.15883 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} - 3 q^{3} + 2 q^{6} - 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q + 2 * q^2 - 3 * q^3 + 2 * q^6 - 3 * q^7 - 6 * q^8 - 3 * q^9	$ 6 q + 2 q^{2} - 3 q^{3} + 2 q^{6} - 3 q^{7} - 6 q^{8} - 3 q^{9} + 7 q^{10} + 2 q^{11} - 6 q^{13} - 4 q^{14} - 2 q^{16} + 2 q^{17} - 4 q^{18} + 13 q^{19} - 7 q^{20} + 6 q^{21} - 13 q^{22} - 3 q^{23} + 3 q^{24} - 2 q^{25} - 4 q^{26} + 6 q^{27} - q^{29} + 7 q^{30} - 22 q^{31} - 7 q^{32} + 2 q^{33} + 12 q^{34} + 4 q^{37} + 36 q^{38} + 6 q^{39} + 14 q^{40} - 2 q^{41} + 2 q^{42} + 11 q^{43} - 42 q^{44} + 9 q^{46} - 38 q^{47} - 2 q^{48} - 3 q^{49} - 10 q^{50} - 4 q^{51} + 10 q^{53} + 2 q^{54} + 14 q^{55} + 3 q^{56} - 26 q^{57} + 10 q^{58} + 11 q^{59} + 14 q^{60} - 7 q^{61} + 9 q^{62} - 3 q^{63} - 22 q^{64} + 26 q^{66} + 15 q^{67} + 7 q^{68} - 3 q^{69} - 14 q^{70} + 18 q^{71} + 3 q^{72} - 12 q^{73} - 33 q^{74} + q^{75} + 14 q^{76} - 4 q^{77} - 7 q^{78} + 6 q^{79} - 3 q^{81} + 20 q^{82} - 4 q^{83} + 7 q^{85} + 10 q^{86} - q^{87} - 9 q^{88} + 17 q^{89} - 14 q^{90} + 56 q^{92} + 11 q^{93} - q^{94} + 14 q^{95} + 14 q^{96} + 13 q^{97} + 2 q^{98} - 4 q^{99}+O(q^{100}) $ 6 * q + 2 * q^2 - 3 * q^3 + 2 * q^6 - 3 * q^7 - 6 * q^8 - 3 * q^9 + 7 * q^10 + 2 * q^11 - 6 * q^13 - 4 * q^14 - 2 * q^16 + 2 * q^17 - 4 * q^18 + 13 * q^19 - 7 * q^20 + 6 * q^21 - 13 * q^22 - 3 * q^23 + 3 * q^24 - 2 * q^25 - 4 * q^26 + 6 * q^27 - q^29 + 7 * q^30 - 22 * q^31 - 7 * q^32 + 2 * q^33 + 12 * q^34 + 4 * q^37 + 36 * q^38 + 6 * q^39 + 14 * q^40 - 2 * q^41 + 2 * q^42 + 11 * q^43 - 42 * q^44 + 9 * q^46 - 38 * q^47 - 2 * q^48 - 3 * q^49 - 10 * q^50 - 4 * q^51 + 10 * q^53 + 2 * q^54 + 14 * q^55 + 3 * q^56 - 26 * q^57 + 10 * q^58 + 11 * q^59 + 14 * q^60 - 7 * q^61 + 9 * q^62 - 3 * q^63 - 22 * q^64 + 26 * q^66 + 15 * q^67 + 7 * q^68 - 3 * q^69 - 14 * q^70 + 18 * q^71 + 3 * q^72 - 12 * q^73 - 33 * q^74 + q^75 + 14 * q^76 - 4 * q^77 - 7 * q^78 + 6 * q^79 - 3 * q^81 + 20 * q^82 - 4 * q^83 + 7 * q^85 + 10 * q^86 - q^87 - 9 * q^88 + 17 * q^89 - 14 * q^90 + 56 * q^92 + 11 * q^93 - q^94 + 14 * q^95 + 14 * q^96 + 13 * q^97 + 2 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.400969	−	0.694498i	−0.283528	−	0.491085i	0.688723	−	0.725024i	$-0.258171\pi$
$2$	−0.400969	−	0.694498i	−0.283528	−	0.491085i	−0.972251	+	0.233940i	$0.924838\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.678448	−	1.17511i	0.339224	−	0.587553i
$5$	−3.04892			−1.36352			−0.681759	−	0.731577i	$-0.738785\pi$
$5$	−3.04892			−1.36352			−0.681759	+	0.731577i	$0.738785\pi$
$6$	−0.400969	+	0.694498i	−0.163695	+	0.283528i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	−2.69202			−0.951773
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.22252	+	2.11747i	0.386595	+	0.669602i
$11$	−1.07942	−	1.86960i	−0.325456	−	0.563707i	0.656148	−	0.754632i	$-0.272185\pi$
$11$	−1.07942	−	1.86960i	−0.325456	−	0.563707i	−0.981605	+	0.190925i	$0.938851\pi$
$12$	−1.35690			−0.391702
$13$	−1.16756	+	3.41127i	−0.323824	+	0.946117i
$13$	−1.16756	+	3.41127i	−0.323824	+	0.946117i
$14$	0.801938			0.214327
$15$	1.52446	+	2.64044i	0.393614	+	0.681759i
$16$	−0.277479	−	0.480608i	−0.0693698	−	0.120152i
$17$	−0.400969	+	0.694498i	−0.0972492	+	0.168441i	−0.910545	−	0.413410i	$-0.864338\pi$
$17$	−0.400969	+	0.694498i	−0.0972492	+	0.168441i	0.813296	+	0.581850i	$0.197671\pi$
$18$	0.801938			0.189019
$19$	0.698062	−	1.20908i	0.160146	−	0.277382i	−0.774775	−	0.632238i	$-0.782137\pi$
$19$	0.698062	−	1.20908i	0.160146	−	0.277382i	0.934921	+	0.354856i	$0.115470\pi$
$20$	−2.06853	+	3.58280i	−0.462538	+	0.801139i
$21$	1.00000			0.218218
$22$	−0.865625	+	1.49931i	−0.184552	+	0.319653i
$23$	−1.51357	−	2.62159i	−0.315602	−	0.546639i	0.663963	−	0.747765i	$-0.268873\pi$
$23$	−1.51357	−	2.62159i	−0.315602	−	0.546639i	−0.979565	+	0.201127i	$0.935540\pi$
$24$	1.34601	+	2.33136i	0.274753	+	0.475887i
$25$	4.29590			0.859179
$26$	2.83728	−	0.556945i	0.556437	−	0.109226i
$27$	1.00000			0.192450
$28$	0.678448	+	1.17511i	0.128215	+	0.222074i
$29$	−1.23609	−	2.14098i	−0.229537	−	0.397570i	0.728134	−	0.685435i	$-0.240388\pi$
$29$	−1.23609	−	2.14098i	−0.229537	−	0.397570i	−0.957671	+	0.287865i	$0.907055\pi$
$30$	1.22252	−	2.11747i	0.223201	−	0.386595i
$31$	−6.26875			−1.12590			−0.562950	−	0.826491i	$-0.690334\pi$
$31$	−6.26875			−1.12590			−0.562950	+	0.826491i	$0.690334\pi$
$32$	−2.91454	+	5.04814i	−0.515223	+	0.892393i
$33$	−1.07942	+	1.86960i	−0.187902	+	0.325456i
$34$	0.643104			0.110291
$35$	1.52446	−	2.64044i	0.257681	−	0.446316i
$36$	0.678448	+	1.17511i	0.113075	+	0.195851i
$37$	−5.37531	−	9.31032i	−0.883696	−	1.53061i	−0.847201	−	0.531273i	$-0.821714\pi$
$37$	−5.37531	−	9.31032i	−0.883696	−	1.53061i	−0.0364953	−	0.999334i	$-0.511619\pi$
$38$	−1.11960			−0.181624
$39$	3.53803	−	0.694498i	0.566539	−	0.111209i
$40$	8.20775			1.29776
$41$	2.60388	+	4.51004i	0.406657	+	0.704351i	0.994513	−	0.104615i	$-0.0333611\pi$
$41$	2.60388	+	4.51004i	0.406657	+	0.704351i	−0.587856	+	0.808966i	$0.700028\pi$
$42$	−0.400969	−	0.694498i	−0.0618708	−	0.107163i
$43$	4.31551	−	7.47468i	0.658109	−	1.13988i	−0.322995	−	0.946401i	$-0.604690\pi$
$43$	4.31551	−	7.47468i	0.658109	−	1.13988i	0.981105	−	0.193478i	$-0.0619769\pi$
$44$	−2.92931			−0.441610
$45$	1.52446	−	2.64044i	0.227253	−	0.393614i
$46$	−1.21379	+	2.10235i	−0.178964	+	0.309974i
$47$	−9.15883			−1.33595			−0.667977	−	0.744182i	$-0.732839\pi$
$47$	−9.15883			−1.33595			−0.667977	+	0.744182i	$0.732839\pi$
$48$	−0.277479	+	0.480608i	−0.0400507	+	0.0693698i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−1.72252	−	2.98349i	−0.243601	−	0.421930i
$51$	0.801938			0.112294
$52$	3.21648	+	3.68638i	0.446046	+	0.511209i
$53$	1.21983			0.167557			0.0837784	−	0.996484i	$-0.473301\pi$
$53$	1.21983			0.167557			0.0837784	+	0.996484i	$0.473301\pi$
$54$	−0.400969	−	0.694498i	−0.0545650	−	0.0945093i
$55$	3.29105	+	5.70027i	0.443765	+	0.768624i
$56$	1.34601	−	2.33136i	0.179868	−	0.311541i
$57$	−1.39612			−0.184921
$58$	−0.991271	+	1.71693i	−0.130160	+	0.225444i
$59$	4.31551	−	7.47468i	0.561832	−	0.973121i	−0.435505	−	0.900186i	$-0.643430\pi$
$59$	4.31551	−	7.47468i	0.561832	−	0.973121i	0.997337	−	0.0729348i	$-0.0232365\pi$
$60$	4.13706			0.534093
$61$	5.04288	−	8.73452i	0.645674	−	1.11834i	−0.338471	−	0.940977i	$-0.609910\pi$
$61$	5.04288	−	8.73452i	0.645674	−	1.11834i	0.984145	−	0.177364i	$-0.0567569\pi$
$62$	2.51357	+	4.35364i	0.319224	+	0.552912i
$63$	−0.500000	−	0.866025i	−0.0629941	−	0.109109i
$64$	3.56465			0.445581
$65$	3.55980	−	10.4007i	0.441539	−	1.29005i
$66$	1.73125			0.213102
$67$	6.39493	+	11.0763i	0.781265	+	1.35319i	0.931205	+	0.364495i	$0.118758\pi$
$67$	6.39493	+	11.0763i	0.781265	+	1.35319i	−0.149940	+	0.988695i	$0.547908\pi$
$68$	0.544073	+	0.942362i	0.0659785	+	0.114278i
$69$	−1.51357	+	2.62159i	−0.182213	+	0.315602i
$70$	−2.44504			−0.292238
$71$	7.06249	−	12.2326i	0.838163	−	1.45174i	−0.0532651	−	0.998580i	$-0.516963\pi$
$71$	7.06249	−	12.2326i	0.838163	−	1.45174i	0.891429	−	0.453161i	$-0.149704\pi$
$72$	1.34601	−	2.33136i	0.158629	−	0.274753i
$73$	−10.1250			−1.18504			−0.592520	−	0.805556i	$-0.701867\pi$
$73$	−10.1250			−1.18504			−0.592520	+	0.805556i	$0.701867\pi$
$74$	−4.31067	+	7.46629i	−0.501105	+	0.867939i
$75$	−2.14795	−	3.72036i	−0.248024	−	0.429590i
$76$	−0.947198	−	1.64059i	−0.108651	−	0.188189i
$77$	2.15883			0.246022
$78$	−1.90097	−	2.17869i	−0.215242	−	0.246688i
$79$	1.33513			0.150213			0.0751067	−	0.997176i	$-0.476070\pi$
$79$	1.33513			0.150213			0.0751067	+	0.997176i	$0.476070\pi$
$80$	0.846011	+	1.46533i	0.0945869	+	0.163829i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.08815	−	3.61677i	0.230597	−	0.399406i
$83$	8.92692			0.979857			0.489928	−	0.871763i	$-0.337023\pi$
$83$	8.92692			0.979857			0.489928	+	0.871763i	$0.337023\pi$
$84$	0.678448	−	1.17511i	0.0740247	−	0.128215i
$85$	1.22252	−	2.11747i	0.132601	−	0.229672i
$86$	−6.92154			−0.746369
$87$	−1.23609	+	2.14098i	−0.132523	+	0.229537i
$88$	2.90581	+	5.03302i	0.309761	+	0.536521i
$89$	1.25302	+	2.17029i	0.132820	+	0.230051i	0.924763	−	0.380545i	$-0.124263\pi$
$89$	1.25302	+	2.17029i	0.132820	+	0.230051i	−0.791943	+	0.610595i	$0.790930\pi$
$90$	−2.44504			−0.257730
$91$	−2.37047	−	2.71678i	−0.248493	−	0.284796i
$92$	−4.10752			−0.428239
$93$	3.13437	+	5.42890i	0.325020	+	0.562950i
$94$	3.67241	+	6.36080i	0.378780	+	0.656066i
$95$	−2.12833	+	3.68638i	−0.218362	+	0.378215i
$96$	5.82908			0.594928
$97$	−1.16152	+	2.01182i	−0.117935	+	0.204269i	−0.918949	−	0.394376i	$-0.870961\pi$
$97$	−1.16152	+	2.01182i	−0.117935	+	0.204269i	0.801014	+	0.598645i	$0.204294\pi$
$98$	−0.400969	+	0.694498i	−0.0405040	+	0.0701549i
$99$	2.15883			0.216971
$100$	2.91454	−	5.04814i	0.291454	−	0.504814i
$101$	−7.38620	−	12.7933i	−0.734954	−	1.27298i	−0.954743	−	0.297431i	$-0.903870\pi$
$101$	−7.38620	−	12.7933i	−0.734954	−	1.27298i	0.219789	−	0.975547i	$-0.429463\pi$
$102$	−0.321552	−	0.556945i	−0.0318384	−	0.0551457i
$103$	−10.1642			−1.00151			−0.500755	−	0.865589i	$-0.666944\pi$
$103$	−10.1642			−1.00151			−0.500755	+	0.865589i	$0.666944\pi$
$104$	3.14310	−	9.18323i	0.308207	−	0.900489i
$105$	−3.04892			−0.297544
$106$	−0.489115	−	0.847172i	−0.0475070	−	0.0822846i
$107$	8.63922	+	14.9636i	0.835185	+	1.44658i	0.893880	+	0.448307i	$0.147973\pi$
$107$	8.63922	+	14.9636i	0.835185	+	1.44658i	−0.0586950	+	0.998276i	$0.518694\pi$
$108$	0.678448	−	1.17511i	0.0652837	−	0.113075i
$109$	−14.2959			−1.36930			−0.684649	−	0.728873i	$-0.740045\pi$
$109$	−14.2959			−1.36930			−0.684649	+	0.728873i	$0.740045\pi$
$110$	2.63922	−	4.57126i	0.251640	−	0.435853i
$111$	−5.37531	+	9.31032i	−0.510202	+	0.883696i
$112$	0.554958			0.0524386
$113$	−8.13437	+	14.0892i	−0.765218	+	1.32540i	0.174914	+	0.984584i	$0.444035\pi$
$113$	−8.13437	+	14.0892i	−0.765218	+	1.32540i	−0.940131	+	0.340812i	$0.889298\pi$
$114$	0.559802	+	0.969606i	0.0524303	+	0.0908120i
$115$	4.61476	+	7.99300i	0.430329	+	0.745351i
$116$	−3.35450			−0.311458
$117$	−2.37047	−	2.71678i	−0.219150	−	0.251166i
$118$	−6.92154			−0.637180
$119$	−0.400969	−	0.694498i	−0.0367568	−	0.0636646i
$120$	−4.10388	−	7.10812i	−0.374631	−	0.648880i
$121$	3.16972	−	5.49011i	0.288156	−	0.499101i
$122$	−8.08815			−0.732266
$123$	2.60388	−	4.51004i	0.234784	−	0.406657i
$124$	−4.25302	+	7.36645i	−0.381933	+	0.661527i
$125$	2.14675			0.192011
$126$	−0.400969	+	0.694498i	−0.0357211	+	0.0618708i
$127$	2.25571	+	3.90700i	0.200162	+	0.346690i	0.948580	−	0.316536i	$-0.102520\pi$
$127$	2.25571	+	3.90700i	0.200162	+	0.346690i	−0.748419	+	0.663227i	$0.769187\pi$
$128$	4.39977	+	7.62063i	0.388889	+	0.673575i
$129$	−8.63102			−0.759919
$130$	−8.65064	+	1.69808i	−0.758711	+	0.148931i
$131$	1.04892			0.0916443			0.0458222	−	0.998950i	$-0.485409\pi$
$131$	1.04892			0.0916443			0.0458222	+	0.998950i	$0.485409\pi$
$132$	1.46466	+	2.53686i	0.127482	+	0.220805i
$133$	0.698062	+	1.20908i	0.0605297	+	0.104840i
$134$	5.12833	−	8.88254i	0.443021	−	0.767334i
$135$	−3.04892			−0.262409
$136$	1.07942	−	1.86960i	0.0925592	−	0.160317i
$137$	−6.17994	+	10.7040i	−0.527988	+	0.914502i	0.471480	+	0.881877i	$0.343720\pi$
$137$	−6.17994	+	10.7040i	−0.527988	+	0.914502i	−0.999468	+	0.0326250i	$0.989613\pi$
$138$	2.42758			0.206650
$139$	−6.80074	+	11.7792i	−0.576831	+	0.999101i	0.419009	+	0.907982i	$0.362378\pi$
$139$	−6.80074	+	11.7792i	−0.576831	+	0.999101i	−0.995840	+	0.0911190i	$0.970956\pi$
$140$	−2.06853	−	3.58280i	−0.174823	−	0.302802i
$141$	4.57942	+	7.93178i	0.385656	+	0.667977i
$142$	−11.3274			−0.950571
$143$	7.63802	−	1.49931i	0.638724	−	0.125378i
$144$	0.554958			0.0462465
$145$	3.76875	+	6.52767i	0.312978	+	0.542093i
$146$	4.05980	+	7.03178i	0.335992	+	0.581955i
$147$	−0.500000	+	0.866025i	−0.0412393	+	0.0714286i
$148$	−14.5875			−1.19908
$149$	−4.16756	+	7.21843i	−0.341420	+	0.591357i	−0.984697	−	0.174277i	$-0.944241\pi$
$149$	−4.16756	+	7.21843i	−0.341420	+	0.591357i	0.643277	+	0.765634i	$0.277575\pi$
$150$	−1.72252	+	2.98349i	−0.140643	+	0.243601i
$151$	11.4819			0.934382			0.467191	−	0.884156i	$-0.345266\pi$
$151$	11.4819			0.934382			0.467191	+	0.884156i	$0.345266\pi$
$152$	−1.87920	+	3.25487i	−0.152423	+	0.264005i
$153$	−0.400969	−	0.694498i	−0.0324164	−	0.0561469i
$154$	−0.865625	−	1.49931i	−0.0697541	−	0.120818i
$155$	19.1129			1.53519
$156$	1.58426	−	4.62874i	0.126842	−	0.370596i
$157$	−2.99330			−0.238891			−0.119445	−	0.992841i	$-0.538112\pi$
$157$	−2.99330			−0.238891			−0.119445	+	0.992841i	$0.538112\pi$
$158$	−0.535344	−	0.927243i	−0.0425897	−	0.0737675i
$159$	−0.609916	−	1.05641i	−0.0483695	−	0.0837784i
$160$	8.88620	−	15.3913i	0.702516	−	1.21679i
$161$	3.02715			0.238573
$162$	−0.400969	+	0.694498i	−0.0315031	+	0.0545650i
$163$	7.81767	−	13.5406i	0.612327	−	1.06058i	−0.378520	−	0.925593i	$-0.623567\pi$
$163$	7.81767	−	13.5406i	0.612327	−	1.06058i	0.990847	−	0.134988i	$-0.0430997\pi$
$164$	7.06638			0.551791
$165$	3.29105	−	5.70027i	0.256208	−	0.443765i
$166$	−3.57942	−	6.19973i	−0.277817	−	0.481193i
$167$	3.35086	+	5.80385i	0.259297	+	0.449115i	0.966054	−	0.258341i	$-0.0831758\pi$
$167$	3.35086	+	5.80385i	0.259297	+	0.449115i	−0.706757	+	0.707457i	$0.749843\pi$
$168$	−2.69202			−0.207694
$169$	−10.2736	−	7.96576i	−0.790276	−	0.612750i
$170$	−1.96077			−0.150384
$171$	0.698062	+	1.20908i	0.0533822	+	0.0924606i
$172$	−5.85570	−	10.1424i	−0.446493	−	0.773348i
$173$	3.52566	−	6.10661i	0.268051	−	0.464277i	−0.700308	−	0.713841i	$-0.746954\pi$
$173$	3.52566	−	6.10661i	0.268051	−	0.464277i	0.968358	+	0.249564i	$0.0802872\pi$
$174$	1.98254			0.150296
$175$	−2.14795	+	3.72036i	−0.162370	+	0.281232i
$176$	−0.599031	+	1.03755i	−0.0451537	+	0.0782085i
$177$	−8.63102			−0.648747
$178$	1.00484	−	1.74044i	0.0753163	−	0.130452i
$179$	−3.23072	−	5.59577i	−0.241475	−	0.418247i	0.719660	−	0.694327i	$-0.244298\pi$
$179$	−3.23072	−	5.59577i	−0.241475	−	0.418247i	−0.961135	+	0.276080i	$0.910965\pi$
$180$	−2.06853	−	3.58280i	−0.154179	−	0.267046i
$181$	−0.576728			−0.0428679			−0.0214339	−	0.999770i	$-0.506823\pi$
$181$	−0.576728			−0.0428679			−0.0214339	+	0.999770i	$0.506823\pi$
$182$	−0.936313	+	2.73563i	−0.0694041	+	0.202778i
$183$	−10.0858			−0.745560
$184$	4.07457	+	7.05737i	0.300381	+	0.520276i
$185$	16.3889	+	28.3864i	1.20493	+	2.08701i
$186$	2.51357	−	4.35364i	0.184304	−	0.319224i
$187$	1.73125			0.126602
$188$	−6.21379	+	10.7626i	−0.453187	+	0.784943i
$189$	−0.500000	+	0.866025i	−0.0363696	+	0.0629941i
$190$	3.41358			0.247647
$191$	4.56249	−	7.90247i	0.330130	−	0.571802i	−0.652407	−	0.757869i	$-0.726241\pi$
$191$	4.56249	−	7.90247i	0.330130	−	0.571802i	0.982537	+	0.186067i	$0.0595740\pi$
$192$	−1.78232	−	3.08707i	−0.128628	−	0.222790i
$193$	−3.63318	−	6.29285i	−0.261522	−	0.452969i	0.705125	−	0.709083i	$-0.250891\pi$
$193$	−3.63318	−	6.29285i	−0.261522	−	0.452969i	−0.966647	+	0.256114i	$0.917558\pi$
$194$	1.86294			0.133751
$195$	−10.7872	+	2.11747i	−0.772485	+	0.151635i
$196$	−1.35690			−0.0969211
$197$	−2.82759	−	4.89753i	−0.201458	−	0.348935i	0.747541	−	0.664216i	$-0.231235\pi$
$197$	−2.82759	−	4.89753i	−0.201458	−	0.348935i	−0.948998	+	0.315281i	$0.897901\pi$
$198$	−0.865625	−	1.49931i	−0.0615173	−	0.106551i
$199$	−8.64460	+	14.9729i	−0.612799	+	1.06140i	0.377967	+	0.925819i	$0.376623\pi$
$199$	−8.64460	+	14.9729i	−0.612799	+	1.06140i	−0.990766	+	0.135580i	$0.956710\pi$
$200$	−11.5646			−0.817744
$201$	6.39493	−	11.0763i	0.451063	−	0.781265i
$202$	−5.92327	+	10.2594i	−0.416760	+	0.721849i
$203$	2.47219			0.173514
$204$	0.544073	−	0.942362i	0.0380927	−	0.0659785i
$205$	−7.93900	−	13.7508i	−0.554484	−	0.960394i
$206$	4.07553	+	7.05903i	0.283956	+	0.491826i
$207$	3.02715			0.210401
$208$	1.96346	−	0.385418i	0.136141	−	0.0267239i
$209$	−3.01400			−0.208483
$210$	1.22252	+	2.11747i	0.0843620	+	0.146119i
$211$	−4.58426	−	7.94017i	−0.315594	−	0.546624i	0.663970	−	0.747759i	$-0.268870\pi$
$211$	−4.58426	−	7.94017i	−0.315594	−	0.546624i	−0.979563	+	0.201135i	$0.935537\pi$
$212$	0.827593	−	1.43343i	0.0568393	−	0.0984486i
$213$	−14.1250			−0.967828
$214$	6.92812	−	11.9998i	0.473596	−	0.820293i
$215$	−13.1576	+	22.7897i	−0.897343	+	1.55424i
$216$	−2.69202			−0.183169
$217$	3.13437	−	5.42890i	0.212775	−	0.368538i
$218$	5.73221	+	9.92848i	0.388234	+	0.672441i
$219$	5.06249	+	8.76849i	0.342091	+	0.592520i
$220$	8.93123			0.602143
$221$	−1.90097	−	2.17869i	−0.127873	−	0.146554i
$222$	8.62133			0.578626
$223$	9.54892	+	16.5392i	0.639443	+	1.10755i	0.985555	+	0.169354i	$0.0541682\pi$
$223$	9.54892	+	16.5392i	0.639443	+	1.10755i	−0.346112	+	0.938193i	$0.612498\pi$
$224$	−2.91454	−	5.04814i	−0.194736	−	0.337293i
$225$	−2.14795	+	3.72036i	−0.143197	+	0.248024i
$226$	13.0465			0.867842
$227$	13.9731	−	24.2022i	0.927430	−	1.60636i	0.139825	−	0.990176i	$-0.455346\pi$
$227$	13.9731	−	24.2022i	0.927430	−	1.60636i	0.787605	−	0.616180i	$-0.211321\pi$
$228$	−0.947198	+	1.64059i	−0.0627297	+	0.108651i
$229$	−19.8388			−1.31098			−0.655492	−	0.755203i	$-0.727539\pi$
$229$	−19.8388			−1.31098			−0.655492	+	0.755203i	$0.727539\pi$
$230$	3.70075	−	6.40989i	0.244020	−	0.422656i
$231$	−1.07942	−	1.86960i	−0.0710204	−	0.123011i
$232$	3.32759	+	5.76356i	0.218467	+	0.378396i
$233$	−5.71379			−0.374323			−0.187161	−	0.982329i	$-0.559929\pi$
$233$	−5.71379			−0.374323			−0.187161	+	0.982329i	$0.559929\pi$
$234$	−0.936313	+	2.73563i	−0.0612087	+	0.178834i
$235$	27.9245			1.82160
$236$	−5.85570	−	10.1424i	−0.381174	−	0.660212i
$237$	−0.667563	−	1.15625i	−0.0433629	−	0.0751067i
$238$	−0.321552	+	0.556945i	−0.0208431	+	0.0361014i
$239$	11.3840			0.736373			0.368186	−	0.929752i	$-0.379979\pi$
$239$	11.3840			0.736373			0.368186	+	0.929752i	$0.379979\pi$
$240$	0.846011	−	1.46533i	0.0546098	−	0.0945869i
$241$	13.2201	−	22.8979i	0.851583	−	1.47499i	−0.0281956	−	0.999602i	$-0.508976\pi$
$241$	13.2201	−	22.8979i	0.851583	−	1.47499i	0.879779	−	0.475383i	$-0.157691\pi$
$242$	−5.08383			−0.326801
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−6.84266	−	11.8518i	−0.438056	−	0.758736i
$245$	1.52446	+	2.64044i	0.0973941	+	0.168692i
$246$	−4.17629			−0.266271
$247$	3.30947	+	3.79296i	0.210577	+	0.241340i
$248$	16.8756			1.07160
$249$	−4.46346	−	7.73094i	−0.282860	−	0.489928i
$250$	−0.860781	−	1.49092i	−0.0544406	−	0.0942938i
$251$	11.2986	−	19.5697i	0.713160	−	1.23523i	−0.250504	−	0.968115i	$-0.580596\pi$
$251$	11.2986	−	19.5697i	0.713160	−	1.23523i	0.963665	−	0.267115i	$-0.0860702\pi$
$252$	−1.35690			−0.0854764
$253$	−3.26755	+	5.65957i	−0.205429	+	0.355814i
$254$	1.80894	−	3.13317i	0.113503	−	0.196593i
$255$	−2.44504			−0.153114
$256$	7.09299	−	12.2854i	0.443312	−	0.767839i
$257$	−5.51961	−	9.56025i	−0.344304	−	0.596352i	0.640923	−	0.767605i	$-0.278552\pi$
$257$	−5.51961	−	9.56025i	−0.344304	−	0.596352i	−0.985227	+	0.171253i	$0.945218\pi$
$258$	3.46077	+	5.99423i	0.215458	+	0.373185i
$259$	10.7506			0.668011
$260$	−9.80678	−	11.2395i	−0.608191	−	0.697043i
$261$	2.47219			0.153025
$262$	−0.420583	−	0.728471i	−0.0259837	−	0.0450051i
$263$	7.12349	+	12.3382i	0.439253	+	0.760809i	0.997632	−	0.0687772i	$-0.0219098\pi$
$263$	7.12349	+	12.3382i	0.439253	+	0.760809i	−0.558379	+	0.829586i	$0.688576\pi$
$264$	2.90581	−	5.03302i	0.178840	−	0.309761i
$265$	−3.71917			−0.228467
$266$	0.559802	−	0.969606i	0.0343237	−	0.0594504i
$267$	1.25302	−	2.17029i	0.0766836	−	0.132820i
$268$	17.3545			1.06009
$269$	−10.1833	+	17.6380i	−0.620886	+	1.07541i	0.368435	+	0.929654i	$0.379894\pi$
$269$	−10.1833	+	17.6380i	−0.620886	+	1.07541i	−0.989321	+	0.145753i	$0.953440\pi$
$270$	1.22252	+	2.11747i	0.0744003	+	0.128865i
$271$	8.49880	+	14.7204i	0.516266	+	0.894198i	0.999822	+	0.0188848i	$0.00601158\pi$
$271$	8.49880	+	14.7204i	0.516266	+	0.894198i	−0.483556	+	0.875313i	$0.660655\pi$
$272$	0.445042			0.0269846
$273$	−1.16756	+	3.41127i	−0.0706641	+	0.206460i
$274$	9.91185			0.598797
$275$	−4.63706	−	8.03163i	−0.279625	−	0.484325i
$276$	2.05376	+	3.55722i	0.123622	+	0.214119i
$277$	7.63102	−	13.2173i	0.458504	−	0.794152i	−0.540378	−	0.841422i	$-0.681719\pi$
$277$	7.63102	−	13.2173i	0.458504	−	0.794152i	0.998882	+	0.0472704i	$0.0150522\pi$
$278$	10.9075			0.654191
$279$	3.13437	−	5.42890i	0.187650	−	0.325020i
$280$	−4.10388	+	7.10812i	−0.245253	+	0.424791i
$281$	9.80492			0.584913			0.292456	−	0.956279i	$-0.405527\pi$
$281$	9.80492			0.584913			0.292456	+	0.956279i	$0.405527\pi$
$282$	3.67241	−	6.36080i	0.218689	−	0.378780i
$283$	−2.34601	−	4.06341i	−0.139456	−	0.241545i	0.787835	−	0.615886i	$-0.211202\pi$
$283$	−2.34601	−	4.06341i	−0.139456	−	0.241545i	−0.927291	+	0.374342i	$0.877869\pi$
$284$	−9.58306	−	16.5984i	−0.568650	−	0.984931i
$285$	4.25667			0.252143
$286$	−4.10388	−	4.70342i	−0.242667	−	0.278119i
$287$	−5.20775			−0.307404
$288$	−2.91454	−	5.04814i	−0.171741	−	0.297464i
$289$	8.17845	+	14.1655i	0.481085	+	0.833264i
$290$	3.02230	−	5.23478i	0.177476	−	0.307397i
$291$	2.32304			0.136179
$292$	−6.86927	+	11.8979i	−0.401994	+	0.696274i
$293$	10.5221	−	18.2248i	0.614706	−	1.06470i	−0.375730	−	0.926729i	$-0.622608\pi$
$293$	10.5221	−	18.2248i	0.614706	−	1.06470i	0.990436	−	0.137972i	$-0.0440585\pi$
$294$	0.801938			0.0467700
$295$	−13.1576	+	22.7897i	−0.766067	+	1.32687i
$296$	14.4705	+	25.0636i	0.841078	+	1.45679i
$297$	−1.07942	−	1.86960i	−0.0626341	−	0.108485i
$298$	6.68425			0.387208
$299$	10.7101	−	2.10235i	0.619384	−	0.121582i
$300$	−5.82908			−0.336542
$301$	4.31551	+	7.47468i	0.248742	+	0.430834i
$302$	−4.60388	−	7.97415i	−0.264923	−	0.458861i
$303$	−7.38620	+	12.7933i	−0.424326	+	0.734954i
$304$	−0.774791			−0.0444373
$305$	−15.3753	+	26.6308i	−0.880388	+	1.52488i
$306$	−0.321552	+	0.556945i	−0.0183819	+	0.0318384i
$307$	−12.8140			−0.731335			−0.365667	−	0.930746i	$-0.619159\pi$
$307$	−12.8140			−0.731335			−0.365667	+	0.930746i	$0.619159\pi$
$308$	1.46466	−	2.53686i	0.0834565	−	0.144551i
$309$	5.08211	+	8.80246i	0.289111	+	0.500755i
$310$	−7.66368	−	13.2739i	−0.435268	−	0.753906i
$311$	9.16315			0.519594			0.259797	−	0.965663i	$-0.416344\pi$
$311$	9.16315			0.519594			0.259797	+	0.965663i	$0.416344\pi$
$312$	−9.52446	+	1.86960i	−0.539216	+	0.105846i
$313$	11.0683			0.625617			0.312809	−	0.949816i	$-0.398730\pi$
$313$	11.0683			0.625617			0.312809	+	0.949816i	$0.398730\pi$
$314$	1.20022	+	2.07884i	0.0677322	+	0.117316i
$315$	1.52446	+	2.64044i	0.0858935	+	0.148772i
$316$	0.905813	−	1.56891i	0.0509560	−	0.0882583i
$317$	−15.9420			−0.895391			−0.447696	−	0.894186i	$-0.647755\pi$
$317$	−15.9420			−0.895391			−0.447696	+	0.894186i	$0.647755\pi$
$318$	−0.489115	+	0.847172i	−0.0274282	+	0.0475070i
$319$	−2.66852	+	4.62202i	−0.149409	+	0.258783i
$320$	−10.8683			−0.607557
$321$	8.63922	−	14.9636i	0.482194	−	0.835185i
$322$	−1.21379	−	2.10235i	−0.0676420	−	0.117159i
$323$	0.559802	+	0.969606i	0.0311482	+	0.0539503i
$324$	−1.35690			−0.0753831
$325$	−5.01573	+	14.6545i	−0.278223	+	0.812885i
$326$	−12.5386			−0.694447
$327$	7.14795	+	12.3806i	0.395282	+	0.684649i
$328$	−7.00969	−	12.1411i	−0.387045	−	0.670382i
$329$	4.57942	−	7.93178i	0.252471	−	0.437293i
$330$	−5.27844			−0.290568
$331$	−2.66368	+	4.61363i	−0.146409	+	0.253588i	−0.929898	−	0.367818i	$-0.880105\pi$
$331$	−2.66368	+	4.61363i	−0.146409	+	0.253588i	0.783489	+	0.621406i	$0.213438\pi$
$332$	6.05645	−	10.4901i	0.332391	−	0.575718i
$333$	10.7506			0.589131
$334$	2.68718	−	4.65433i	0.147036	−	0.254673i
$335$	−19.4976	−	33.7708i	−1.06527	−	1.84510i
$336$	−0.277479	−	0.480608i	−0.0151377	−	0.0262193i
$337$	−29.5937			−1.61207			−0.806036	−	0.591866i	$-0.798391\pi$
$337$	−29.5937			−1.61207			−0.806036	+	0.591866i	$0.798391\pi$
$338$	−1.41281	+	10.3290i	−0.0768469	+	0.561824i
$339$	16.2687			0.883597
$340$	−1.65883	−	2.87318i	−0.0899629	−	0.155820i
$341$	6.76659	+	11.7201i	0.366432	+	0.634678i
$342$	0.559802	−	0.969606i	0.0302707	−	0.0524303i
$343$	1.00000			0.0539949
$344$	−11.6174	+	20.1220i	−0.626371	+	1.08491i
$345$	4.61476	−	7.99300i	0.248450	−	0.430329i
$346$	−5.65471			−0.303999
$347$	−10.1359	+	17.5558i	−0.544122	+	0.942447i	0.454540	+	0.890726i	$0.349804\pi$
$347$	−10.1359	+	17.5558i	−0.544122	+	0.942447i	−0.998662	+	0.0517202i	$0.983530\pi$
$348$	1.67725	+	2.90508i	0.0899101	+	0.155729i
$349$	−6.01626	−	10.4205i	−0.322043	−	0.557795i	0.658866	−	0.752260i	$-0.271036\pi$
$349$	−6.01626	−	10.4205i	−0.322043	−	0.557795i	−0.980909	+	0.194465i	$0.937703\pi$
$350$	3.44504			0.184145
$351$	−1.16756	+	3.41127i	−0.0623199	+	0.182080i
$352$	12.5840			0.670731
$353$	−17.3421	−	30.0374i	−0.923028	−	1.59873i	−0.794702	−	0.607000i	$-0.792373\pi$
$353$	−17.3421	−	30.0374i	−0.923028	−	1.59873i	−0.128326	−	0.991732i	$-0.540960\pi$
$354$	3.46077	+	5.99423i	0.183938	+	0.318590i
$355$	−21.5330	+	37.2962i	−1.14285	+	1.97947i
$356$	3.40044			0.180223
$357$	−0.400969	+	0.694498i	−0.0212215	+	0.0367568i
$358$	−2.59083	+	4.48746i	−0.136930	+	0.237169i
$359$	−29.5991			−1.56218			−0.781090	−	0.624418i	$-0.785336\pi$
$359$	−29.5991			−1.56218			−0.781090	+	0.624418i	$0.785336\pi$
$360$	−4.10388	+	7.10812i	−0.216293	+	0.374631i
$361$	8.52542	+	14.7665i	0.448706	+	0.777182i
$362$	0.231250	+	0.400537i	0.0121542	+	0.0210518i
$363$	−6.33944			−0.332734
$364$	−4.80074	+	0.942362i	−0.251627	+	0.0493932i
$365$	30.8702			1.61582
$366$	4.04407	+	7.00454i	0.211387	+	0.366133i
$367$	−16.8681	−	29.2164i	−0.880506	−	1.52508i	−0.850779	−	0.525524i	$-0.823869\pi$
$367$	−16.8681	−	29.2164i	−0.880506	−	1.52508i	−0.0297275	−	0.999558i	$-0.509464\pi$
$368$	−0.839970	+	1.45487i	−0.0437865	+	0.0758404i
$369$	−5.20775			−0.271105
$370$	13.1429	−	22.7641i	0.683265	−	1.18345i
$371$	−0.609916	+	1.05641i	−0.0316653	+	0.0548459i
$372$	8.50604			0.441018
$373$	−12.2913	+	21.2892i	−0.636422	+	1.10232i	0.349790	+	0.936828i	$0.386253\pi$
$373$	−12.2913	+	21.2892i	−0.636422	+	1.10232i	−0.986212	+	0.165487i	$0.947080\pi$
$374$	−0.694177	−	1.20235i	−0.0358951	−	0.0621721i
$375$	−1.07338	−	1.85914i	−0.0554289	−	0.0960057i
$376$	24.6558			1.27152
$377$	8.74668	−	1.71693i	0.450477	−	0.0884265i
$378$	0.801938			0.0412472
$379$	0.966148	+	1.67342i	0.0496277	+	0.0859577i	0.889772	−	0.456405i	$-0.150863\pi$
$379$	0.966148	+	1.67342i	0.0496277	+	0.0859577i	−0.840144	+	0.542363i	$0.817530\pi$
$380$	2.88793	+	5.00204i	0.148148	+	0.256599i
$381$	2.25571	−	3.90700i	0.115563	−	0.200162i
$382$	−7.31767			−0.374404
$383$	−9.48188	+	16.4231i	−0.484501	+	0.839181i	−0.999841	−	0.0178048i	$-0.994332\pi$
$383$	−9.48188	+	16.4231i	−0.484501	+	0.839181i	0.515340	+	0.856986i	$0.327666\pi$
$384$	4.39977	−	7.62063i	0.224525	−	0.388889i
$385$	−6.58211			−0.335455
$386$	−2.91358	+	5.04647i	−0.148297	+	0.256859i
$387$	4.31551	+	7.47468i	0.219370	+	0.379960i
$388$	1.57606	+	2.72982i	0.0800125	+	0.138586i
$389$	17.4711			0.885821			0.442911	−	0.896566i	$-0.353946\pi$
$389$	17.4711			0.885821			0.442911	+	0.896566i	$0.353946\pi$
$390$	5.79590	+	6.64263i	0.293487	+	0.336363i
$391$	2.42758			0.122768
$392$	1.34601	+	2.33136i	0.0679838	+	0.117751i
$393$	−0.524459	−	0.908389i	−0.0264554	−	0.0458222i
$394$	−2.26755	+	3.92752i	−0.114238	+	0.197865i
$395$	−4.07069			−0.204819
$396$	1.46466	−	2.53686i	0.0736017	−	0.127482i
$397$	13.6102	−	23.5736i	0.683077	−	1.18312i	−0.290960	−	0.956735i	$-0.593975\pi$
$397$	13.6102	−	23.5736i	0.683077	−	1.18312i	0.974037	−	0.226389i	$-0.0726920\pi$
$398$	13.8649			0.694982
$399$	0.698062	−	1.20908i	0.0349468	−	0.0605297i
$400$	−1.19202	−	2.06464i	−0.0596011	−	0.103232i
$401$	−10.6637	−	18.4700i	−0.532519	−	0.922349i	−0.999279	−	0.0379656i	$-0.987912\pi$
$401$	−10.6637	−	18.4700i	−0.532519	−	0.922349i	0.466760	−	0.884384i	$-0.345421\pi$
$402$	−10.2567			−0.511556
$403$	7.31916	−	21.3844i	0.364593	−	1.06523i
$404$	−20.0446			−0.997256
$405$	1.52446	+	2.64044i	0.0757510	+	0.131205i
$406$	−0.991271	−	1.71693i	−0.0491959	−	0.0852099i
$407$	−11.6044	+	20.0994i	−0.575209	+	0.996291i
$408$	−2.15883			−0.106878
$409$	−13.6298	+	23.6076i	−0.673952	+	1.16732i	0.302823	+	0.953047i	$0.402071\pi$
$409$	−13.6298	+	23.6076i	−0.673952	+	1.16732i	−0.976774	+	0.214271i	$0.931262\pi$
$410$	−6.36658	+	11.0272i	−0.314423	+	0.544597i
$411$	12.3599			0.609668
$412$	−6.89589	+	11.9440i	−0.339736	+	0.588440i
$413$	4.31551	+	7.47468i	0.212352	+	0.367805i
$414$	−1.21379	−	2.10235i	−0.0596546	−	0.103325i
$415$	−27.2174			−1.33605
$416$	−13.8177	−	15.8363i	−0.677467	−	0.776440i
$417$	13.6015			0.666067
$418$	1.20852	+	2.09322i	0.0591107	+	0.102383i
$419$	−13.6494	−	23.6415i	−0.666819	−	1.15496i	−0.978789	−	0.204872i	$-0.934322\pi$
$419$	−13.6494	−	23.6415i	−0.666819	−	1.15496i	0.311970	−	0.950092i	$-0.399011\pi$
$420$	−2.06853	+	3.58280i	−0.100934	+	0.174823i
$421$	0.817003			0.0398183			0.0199092	−	0.999802i	$-0.493662\pi$
$421$	0.817003			0.0398183			0.0199092	+	0.999802i	$0.493662\pi$
$422$	−3.67629	+	6.36752i	−0.178959	+	0.309966i
$423$	4.57942	−	7.93178i	0.222659	−	0.385656i
$424$	−3.28382			−0.159476
$425$	−1.72252	+	2.98349i	−0.0835545	+	0.144721i
$426$	5.66368	+	9.80978i	0.274406	+	0.475285i
$427$	5.04288	+	8.73452i	0.244042	+	0.422693i
$428$	23.4450			1.13326
$429$	−5.11745	−	5.86507i	−0.247073	−	0.283168i
$430$	21.1032			1.01769
$431$	−14.2811	−	24.7356i	−0.687898	−	1.19147i	−0.972517	−	0.232833i	$-0.925200\pi$
$431$	−14.2811	−	24.7356i	−0.687898	−	1.19147i	0.284619	−	0.958641i	$-0.408133\pi$
$432$	−0.277479	−	0.480608i	−0.0133502	−	0.0231233i
$433$	6.25063	−	10.8264i	0.300386	−	0.520284i	−0.675837	−	0.737051i	$-0.736218\pi$
$433$	6.25063	−	10.8264i	0.300386	−	0.520284i	0.976223	+	0.216767i	$0.0695512\pi$
$434$	−5.02715			−0.241311
$435$	3.76875	−	6.52767i	0.180698	−	0.312978i
$436$	−9.69902	+	16.7992i	−0.464499	+	0.804536i
$437$	−4.22627			−0.202170
$438$	4.05980	−	7.03178i	0.193985	−	0.335992i
$439$	−2.14257	−	3.71104i	−0.102259	−	0.177118i	0.810356	−	0.585938i	$-0.199274\pi$
$439$	−2.14257	−	3.71104i	−0.102259	−	0.177118i	−0.912615	+	0.408820i	$0.865940\pi$
$440$	−8.85958	−	15.3453i	−0.422364	−	0.731556i
$441$	1.00000			0.0476190
$442$	−0.750864	+	2.19381i	−0.0357150	+	0.104349i
$443$	−17.5724			−0.834891			−0.417445	−	0.908702i	$-0.637074\pi$
$443$	−17.5724			−0.834891			−0.417445	+	0.908702i	$0.637074\pi$
$444$	7.29374	+	12.6331i	0.346146	+	0.599542i
$445$	−3.82036	−	6.61705i	−0.181102	−	0.313678i
$446$	7.65764	−	13.2634i	0.362600	−	0.628041i
$447$	8.33513			0.394238
$448$	−1.78232	+	3.08707i	−0.0842069	+	0.145851i
$449$	11.2775	−	19.5332i	0.532217	−	0.921827i	−0.467075	−	0.884218i	$-0.654692\pi$
$449$	11.2775	−	19.5332i	0.532217	−	0.921827i	0.999293	−	0.0376096i	$-0.0119743\pi$
$450$	3.44504			0.162401
$451$	5.62133	−	9.73644i	0.264698	−	0.458471i
$452$	11.0375	+	19.1175i	0.519160	+	0.899212i
$453$	−5.74094	−	9.94360i	−0.269733	−	0.467191i
$454$	−22.4112			−1.05181
$455$	7.22737	+	8.28323i	0.338824	+	0.388324i
$456$	3.75840			0.176003
$457$	11.8748	+	20.5677i	0.555479	+	0.962118i	0.997866	+	0.0652934i	$0.0207983\pi$
$457$	11.8748	+	20.5677i	0.555479	+	0.962118i	−0.442387	+	0.896824i	$0.645868\pi$
$458$	7.95473	+	13.7780i	0.371700	+	0.643804i
$459$	−0.400969	+	0.694498i	−0.0187156	+	0.0324164i
$460$	12.5235			0.583911
$461$	−6.73287	+	11.6617i	−0.313581	+	0.543139i	−0.979135	−	0.203211i	$-0.934862\pi$
$461$	−6.73287	+	11.6617i	−0.313581	+	0.543139i	0.665554	+	0.746350i	$0.268195\pi$
$462$	−0.865625	+	1.49931i	−0.0402725	+	0.0697541i
$463$	25.2556			1.17373			0.586864	−	0.809686i	$-0.300362\pi$
$463$	25.2556			1.17373			0.586864	+	0.809686i	$0.300362\pi$
$464$	−0.685981	+	1.18815i	−0.0318459	+	0.0551586i
$465$	−9.55645	−	16.5523i	−0.443170	−	0.767593i
$466$	2.29105	+	3.96822i	0.106131	+	0.183824i
$467$	−33.9734			−1.57210			−0.786052	−	0.618161i	$-0.787878\pi$
$467$	−33.9734			−1.57210			−0.786052	+	0.618161i	$0.787878\pi$
$468$	−4.80074	+	0.942362i	−0.221914	+	0.0435607i
$469$	−12.7899			−0.590581
$470$	−11.1969	−	19.3935i	−0.516473	−	0.894557i
$471$	1.49665	+	2.59227i	0.0689619	+	0.119445i
$472$	−11.6174	+	20.1220i	−0.534736	+	0.926191i
$473$	−18.6329			−0.856744
$474$	−0.535344	+	0.927243i	−0.0245892	+	0.0425897i
$475$	2.99880	−	5.19408i	0.137595	−	0.238321i
$476$	−1.08815			−0.0498751
$477$	−0.609916	+	1.05641i	−0.0279261	+	0.0483695i
$478$	−4.56465	−	7.90620i	−0.208782	−	0.361621i
$479$	0.162718	+	0.281837i	0.00743480	+	0.0128774i	0.869719	−	0.493547i	$-0.164300\pi$
$479$	0.162718	+	0.281837i	0.00743480	+	0.0128774i	−0.862284	+	0.506425i	$0.830967\pi$
$480$	−17.7724			−0.811195
$481$	38.0361	−	7.46629i	1.73430	−	0.340434i
$482$	−21.2034			−0.965790
$483$	−1.51357	−	2.62159i	−0.0688700	−	0.119286i
$484$	−4.30098	−	7.44951i	−0.195499	−	0.338614i
$485$	3.54138	−	6.13386i	0.160806	−	0.278524i
$486$	0.801938			0.0363766
$487$	−5.18478	+	8.98031i	−0.234945	+	0.406937i	−0.959257	−	0.282536i	$-0.908824\pi$
$487$	−5.18478	+	8.98031i	−0.234945	+	0.406937i	0.724312	+	0.689473i	$0.242158\pi$
$488$	−13.5755	+	23.5135i	−0.614535	+	1.06441i
$489$	−15.6353			−0.707054
$490$	1.22252	−	2.11747i	0.0552279	−	0.0956575i
$491$	7.83459	+	13.5699i	0.353570	+	0.612402i	0.986872	−	0.161503i	$-0.0516342\pi$
$491$	7.83459	+	13.5699i	0.353570	+	0.612402i	−0.633302	+	0.773905i	$0.718301\pi$
$492$	−3.53319	−	6.11966i	−0.159288	−	0.275896i
$493$	1.98254			0.0892892
$494$	1.30721	−	3.81928i	0.0588141	−	0.171838i
$495$	−6.58211			−0.295844
$496$	1.73945	+	3.01281i	0.0781035	+	0.135279i
$497$	7.06249	+	12.2326i	0.316796	+	0.548707i
$498$	−3.57942	+	6.19973i	−0.160398	+	0.277817i
$499$	21.5700			0.965607			0.482803	−	0.875729i	$-0.339619\pi$
$499$	21.5700			0.965607			0.482803	+	0.875729i	$0.339619\pi$
$500$	1.45646	−	2.52266i	0.0651348	−	0.112817i
$501$	3.35086	−	5.80385i	0.149705	−	0.259297i
$502$	−18.1215			−0.808803
$503$	4.73490	−	8.20108i	0.211119	−	0.365668i	−0.740946	−	0.671564i	$-0.765623\pi$
$503$	4.73490	−	8.20108i	0.211119	−	0.365668i	0.952065	+	0.305896i	$0.0989560\pi$
$504$	1.34601	+	2.33136i	0.0599561	+	0.103847i
$505$	22.5199	+	39.0056i	1.00212	+	1.73573i
$506$	5.24075			0.232980
$507$	−1.76175	+	12.8801i	−0.0782420	+	0.572024i
$508$	6.12152			0.271599
$509$	2.71917	+	4.70974i	0.120525	+	0.208755i	0.919975	−	0.391977i	$-0.128209\pi$
$509$	2.71917	+	4.70974i	0.120525	+	0.208755i	−0.799450	+	0.600733i	$0.794876\pi$
$510$	0.980386	+	1.69808i	0.0434122	+	0.0751921i
$511$	5.06249	−	8.76849i	0.223951	−	0.387895i
$512$	6.22282			0.275012
$513$	0.698062	−	1.20908i	0.0308202	−	0.0533822i
$514$	−4.42639	+	7.66673i	−0.195240	+	0.338165i
$515$	30.9898			1.36558
$516$	−5.85570	+	10.1424i	−0.257783	+	0.446493i
$517$	9.88620	+	17.1234i	0.434795	+	0.753086i
$518$	−4.31067	−	7.46629i	−0.189400	−	0.328050i
$519$	−7.05131			−0.309518
$520$	−9.58306	+	27.9989i	−0.420245	+	1.22783i
$521$	−37.5424			−1.64476			−0.822381	−	0.568937i	$-0.807355\pi$
$521$	−37.5424			−1.64476			−0.822381	+	0.568937i	$0.807355\pi$
$522$	−0.991271	−	1.71693i	−0.0433867	−	0.0751480i
$523$	−15.9242	−	27.5816i	−0.696318	−	1.20606i	−0.969734	−	0.244162i	$-0.921487\pi$
$523$	−15.9242	−	27.5816i	−0.696318	−	1.20606i	0.273416	−	0.961896i	$-0.411846\pi$
$524$	0.711636	−	1.23259i	0.0310880	−	0.0538459i
$525$	4.29590			0.187488
$526$	5.71260	−	9.89451i	0.249081	−	0.431421i
$527$	2.51357	−	4.35364i	0.109493	−	0.189647i
$528$	1.19806			0.0521390
$529$	6.91819	−	11.9827i	0.300791	−	0.520985i
$530$	1.49127	+	2.58296i	0.0647767	+	0.112196i
$531$	4.31551	+	7.47468i	0.187277	+	0.324374i
$532$	1.89440			0.0821325
$533$	−18.4252	+	3.61677i	−0.798084	+	0.156660i
$534$	−2.00969			−0.0869677
$535$	−26.3403	−	45.6227i	−1.13879	−	1.97244i
$536$	−17.2153	−	29.8177i	−0.743587	−	1.28793i
$537$	−3.23072	+	5.59577i	−0.139416	+	0.241475i
$538$	16.3327			0.704154
$539$	−1.07942	+	1.86960i	−0.0464938	+	0.0805296i
$540$	−2.06853	+	3.58280i	−0.0890154	+	0.154179i
$541$	22.5652			0.970155			0.485078	−	0.874471i	$-0.338791\pi$
$541$	22.5652			0.970155			0.485078	+	0.874471i	$0.338791\pi$
$542$	6.81551	−	11.8048i	0.292751	−	0.507060i
$543$	0.288364	+	0.499461i	0.0123749	+	0.0214339i
$544$	−2.33728	−	4.04829i	−0.100210	−	0.173569i
$545$	43.5870			1.86706
$546$	2.83728	−	0.556945i	0.121424	−	0.0238350i
$547$	33.1739			1.41841			0.709207	−	0.705001i	$-0.249053\pi$
$547$	33.1739			1.41841			0.709207	+	0.705001i	$0.249053\pi$
$548$	8.38553	+	14.5242i	0.358212	+	0.620442i
$549$	5.04288	+	8.73452i	0.215225	+	0.372780i
$550$	−3.71864	+	6.44087i	−0.158563	+	0.274639i
$551$	−3.45148			−0.147038
$552$	4.07457	−	7.05737i	0.173425	−	0.300381i
$553$	−0.667563	+	1.15625i	−0.0283877	+	0.0491689i
$554$	−12.2392			−0.519994
$555$	16.3889	−	28.3864i	0.695670	−	1.20493i
$556$	9.22790	+	15.9832i	0.391350	+	0.677838i
$557$	−11.6419	−	20.1644i	−0.493283	−	0.854392i	0.506687	−	0.862130i	$-0.330870\pi$
$557$	−11.6419	−	20.1644i	−0.493283	−	0.854392i	−0.999970	+	0.00773831i	$0.997537\pi$
$558$	−5.02715			−0.212816
$559$	20.4596	+	23.4486i	0.865348	+	0.991768i
$560$	−1.69202			−0.0715010
$561$	−0.865625	−	1.49931i	−0.0365467	−	0.0633008i
$562$	−3.93147	−	6.80950i	−0.165839	−	0.287242i
$563$	−1.63288	+	2.82824i	−0.0688178	+	0.119196i	−0.898381	−	0.439217i	$-0.855256\pi$
$563$	−1.63288	+	2.82824i	−0.0688178	+	0.119196i	0.829563	+	0.558413i	$0.188589\pi$
$564$	12.4276			0.523296
$565$	24.8010	−	42.9567i	1.04339	−	1.80720i
$566$	−1.88135	+	3.25860i	−0.0790792	+	0.136969i
$567$	1.00000			0.0419961
$568$	−19.0124	+	32.9304i	−0.797742	+	1.38173i
$569$	11.0390	+	19.1201i	0.462779	+	0.801556i	0.999098	−	0.0424589i	$-0.0135192\pi$
$569$	11.0390	+	19.1201i	0.462779	+	0.801556i	−0.536320	+	0.844015i	$0.680186\pi$
$570$	−1.70679	−	2.95625i	−0.0714896	−	0.123824i
$571$	−10.8649			−0.454680			−0.227340	−	0.973815i	$-0.573003\pi$
$571$	−10.8649			−0.454680			−0.227340	+	0.973815i	$0.573003\pi$
$572$	3.42016	−	9.99269i	0.143004	−	0.417815i
$573$	−9.12498			−0.381202
$574$	2.08815	+	3.61677i	0.0871575	+	0.150961i
$575$	−6.50216	−	11.2621i	−0.271159	−	0.469661i
$576$	−1.78232	+	3.08707i	−0.0742635	+	0.128628i
$577$	10.5526			0.439309			0.219655	−	0.975578i	$-0.429507\pi$
$577$	10.5526			0.439309			0.219655	+	0.975578i	$0.429507\pi$
$578$	6.55861	−	11.3598i	0.272802	−	0.472507i
$579$	−3.63318	+	6.29285i	−0.150990	+	0.261522i
$580$	10.2276			0.424678
$581$	−4.46346	+	7.73094i	−0.185176	+	0.320733i
$582$	−0.931468	−	1.61335i	−0.0386106	−	0.0668755i
$583$	−1.31671	−	2.28060i	−0.0545325	−	0.0944530i
$584$	27.2567			1.12789
$585$	7.22737	+	8.28323i	0.298815	+	0.342469i
$586$	−16.8761			−0.697145
$587$	0.979853	+	1.69716i	0.0404429	+	0.0700491i	0.885538	−	0.464566i	$-0.153790\pi$
$587$	0.979853	+	1.69716i	0.0404429	+	0.0700491i	−0.845095	+	0.534615i	$0.820456\pi$
$588$	0.678448	+	1.17511i	0.0279787	+	0.0484606i
$589$	−4.37598	+	7.57942i	−0.180309	+	0.312304i
$590$	21.1032			0.868805
$591$	−2.82759	+	4.89753i	−0.116312	+	0.201458i
$592$	−2.98307	+	5.16684i	−0.122604	+	0.212356i
$593$	40.9178			1.68029			0.840147	−	0.542359i	$-0.182469\pi$
$593$	40.9178			1.68029			0.840147	+	0.542359i	$0.182469\pi$
$594$	−0.865625	+	1.49931i	−0.0355170	+	0.0615173i
$595$	1.22252	+	2.11747i	0.0501185	+	0.0868077i
$596$	5.65495	+	9.79466i	0.231636	+	0.401205i
$597$	17.2892			0.707600
$598$	−5.75451	−	6.59520i	−0.235320	−	0.269698i
$599$	15.7875			0.645058			0.322529	−	0.946560i	$-0.395467\pi$
$599$	15.7875			0.645058			0.322529	+	0.946560i	$0.395467\pi$
$600$	5.78232	+	10.0153i	0.236062	+	0.408872i
$601$	7.08911	+	12.2787i	0.289171	+	0.500858i	0.973612	−	0.228210i	$-0.0732872\pi$
$601$	7.08911	+	12.2787i	0.289171	+	0.500858i	−0.684441	+	0.729068i	$0.739954\pi$
$602$	3.46077	−	5.99423i	0.141051	−	0.244307i
$603$	−12.7899			−0.520843
$604$	7.78986	−	13.4924i	0.316965	−	0.548999i
$605$	−9.66421	+	16.7389i	−0.392906	+	0.680533i
$606$	11.8465			0.481233
$607$	16.8111	−	29.1177i	0.682341	−	1.18185i	−0.291923	−	0.956442i	$-0.594295\pi$
$607$	16.8111	−	29.1177i	0.682341	−	1.18185i	0.974264	−	0.225408i	$-0.0723715\pi$
$608$	4.06906	+	7.04783i	0.165022	+	0.285827i
$609$	−1.23609	−	2.14098i	−0.0500891	−	0.0867568i
$610$	24.6601			0.998458
$611$	10.6935	−	31.2433i	0.432613	−	1.26397i
$612$	−1.08815			−0.0439857
$613$	−19.3579	−	33.5288i	−0.781856	−	1.35422i	−0.930859	−	0.365378i	$-0.880940\pi$
$613$	−19.3579	−	33.5288i	−0.781856	−	1.35422i	0.149003	−	0.988837i	$-0.452394\pi$
$614$	5.13802	+	8.89932i	0.207354	+	0.359147i
$615$	−7.93900	+	13.7508i	−0.320131	+	0.554484i
$616$	−5.81163			−0.234157
$617$	−14.0848	+	24.3956i	−0.567032	+	0.982129i	0.429825	+	0.902912i	$0.358575\pi$
$617$	−14.0848	+	24.3956i	−0.567032	+	0.982129i	−0.996857	+	0.0792168i	$0.974758\pi$
$618$	4.07553	−	7.05903i	0.163942	−	0.283956i
$619$	−13.0556			−0.524750			−0.262375	−	0.964966i	$-0.584506\pi$
$619$	−13.0556			−0.524750			−0.262375	+	0.964966i	$0.584506\pi$
$620$	12.9671	−	22.4597i	0.520772	−	0.902003i
$621$	−1.51357	−	2.62159i	−0.0607376	−	0.105201i
$622$	−3.67414	−	6.36379i	−0.147319	−	0.255165i
$623$	−2.50604			−0.100402
$624$	−1.31551	−	1.50770i	−0.0526626	−	0.0603562i
$625$	−28.0248			−1.12099
$626$	−4.43804	−	7.68691i	−0.177380	−	0.307231i
$627$	1.50700	+	2.61020i	0.0601838	+	0.104241i
$628$	−2.03079	+	3.51744i	−0.0810375	+	0.140361i
$629$	8.62133			0.343755
$630$	1.22252	−	2.11747i	0.0487064	−	0.0843620i
$631$	13.4934	−	23.3713i	0.537165	−	0.930397i	−0.461890	−	0.886937i	$-0.652829\pi$
$631$	13.4934	−	23.3713i	0.537165	−	0.930397i	0.999055	−	0.0434597i	$-0.0138380\pi$
$632$	−3.59419			−0.142969
$633$	−4.58426	+	7.94017i	−0.182208	+	0.315594i
$634$	6.39224	+	11.0717i	0.253868	+	0.439713i
$635$	−6.87747	−	11.9121i	−0.272924	−	0.472718i
$636$	−1.65519			−0.0656324
$637$	3.53803	−	0.694498i	0.140182	−	0.0275170i
$638$	4.27998			0.169446
$639$	7.06249	+	12.2326i	0.279388	+	0.483914i
$640$	−13.4145	−	23.2347i	−0.530256	−	0.918431i
$641$	−20.0661	+	34.7556i	−0.792565	+	1.37276i	0.131809	+	0.991275i	$0.457921\pi$
$641$	−20.0661	+	34.7556i	−0.792565	+	1.37276i	−0.924374	+	0.381487i	$0.875412\pi$
$642$	−13.8562			−0.546862
$643$	17.3780	−	30.0996i	0.685322	−	1.18701i	−0.288014	−	0.957626i	$-0.592995\pi$
$643$	17.3780	−	30.0996i	0.685322	−	1.18701i	0.973336	−	0.229386i	$-0.0736716\pi$
$644$	2.05376	−	3.55722i	0.0809295	−	0.140174i
$645$	26.3153			1.03616
$646$	0.448927	−	0.777564i	0.0176628	−	0.0305928i
$647$	2.04474	+	3.54159i	0.0803869	+	0.139234i	0.903416	−	0.428765i	$-0.141051\pi$
$647$	2.04474	+	3.54159i	0.0803869	+	0.139234i	−0.823029	+	0.567999i	$0.807718\pi$
$648$	1.34601	+	2.33136i	0.0528763	+	0.0915844i
$649$	−18.6329			−0.731407
$650$	12.1887	−	2.39258i	0.478079	−	0.0938446i
$651$	−6.26875			−0.245692
$652$	−10.6078	−	18.3732i	−0.415432	−	0.719549i
$653$	7.11596	+	12.3252i	0.278469	+	0.482322i	0.971004	−	0.239061i	$-0.0768397\pi$
$653$	7.11596	+	12.3252i	0.278469	+	0.482322i	−0.692536	+	0.721384i	$0.743506\pi$
$654$	5.73221	−	9.92848i	0.224147	−	0.388234i
$655$	−3.19806			−0.124959
$656$	1.44504	−	2.50289i	0.0564194	−	0.0977213i
$657$	5.06249	−	8.76849i	0.197507	−	0.342091i
$658$	−7.34481			−0.286331
$659$	−11.5348	+	19.9789i	−0.449332	+	0.778267i	−0.998343	−	0.0575490i	$-0.981671\pi$
$659$	−11.5348	+	19.9789i	−0.449332	+	0.778267i	0.549010	+	0.835816i	$0.315005\pi$
$660$	−4.46562	−	7.73467i	−0.173824	−	0.301072i
$661$	5.67725	+	9.83329i	0.220819	+	0.382471i	0.955057	−	0.296422i	$-0.0957935\pi$
$661$	5.67725	+	9.83329i	0.220819	+	0.382471i	−0.734238	+	0.678893i	$0.762460\pi$
$662$	4.27221			0.166044
$663$	−0.936313	+	2.73563i	−0.0363634	+	0.106243i
$664$	−24.0315			−0.932601
$665$	−2.12833	−	3.68638i	−0.0825333	−	0.142952i
$666$	−4.31067	−	7.46629i	−0.167035	−	0.289313i
$667$	−3.74184	+	6.48106i	−0.144885	+	0.250948i
$668$	9.09352			0.351839
$669$	9.54892	−	16.5392i	0.369182	−	0.639443i
$670$	−15.6359	+	27.0821i	−0.604066	+	1.04627i
$671$	−21.7735			−0.840555
$672$	−2.91454	+	5.04814i	−0.112431	+	0.194736i
$673$	−23.5480	−	40.7864i	−0.907709	−	1.57220i	−0.817239	−	0.576300i	$-0.804496\pi$
$673$	−23.5480	−	40.7864i	−0.907709	−	1.57220i	−0.0904708	−	0.995899i	$-0.528837\pi$
$674$	11.8662	+	20.5528i	0.457067	+	0.791664i
$675$	4.29590			0.165349
$676$	−16.3307	+	6.66821i	−0.628104	+	0.256470i
$677$	−20.0653			−0.771173			−0.385586	−	0.922672i	$-0.626001\pi$
$677$	−20.0653			−0.771173			−0.385586	+	0.922672i	$0.626001\pi$
$678$	−6.52326	−	11.2986i	−0.250524	−	0.433921i
$679$	−1.16152	−	2.01182i	−0.0445751	−	0.0772064i
$680$	−3.29105	+	5.70027i	−0.126206	+	0.218595i
$681$	−27.9463			−1.07090
$682$	5.42639	−	9.39878i	0.207787	−	0.359898i
$683$	16.9858	−	29.4202i	0.649942	−	1.12573i	−0.333194	−	0.942858i	$-0.608126\pi$
$683$	16.9858	−	29.4202i	0.649942	−	1.12573i	0.983136	−	0.182875i	$-0.0585402\pi$
$684$	1.89440			0.0724340
$685$	18.8421	−	32.6355i	0.719921	−	1.24694i
$686$	−0.400969	−	0.694498i	−0.0153091	−	0.0265161i
$687$	9.91939	+	17.1809i	0.378448	+	0.655492i
$688$	−4.78986			−0.182612
$689$	−1.42423	+	4.16118i	−0.0542589	+	0.158528i
$690$	−7.40150			−0.281770
$691$	16.8922	+	29.2582i	0.642611	+	1.11304i	0.984848	+	0.173421i	$0.0554822\pi$
$691$	16.8922	+	29.2582i	0.642611	+	1.11304i	−0.342237	+	0.939614i	$0.611184\pi$
$692$	−4.78395	−	8.28604i	−0.181858	−	0.314988i
$693$	−1.07942	+	1.86960i	−0.0410037	+	0.0710204i
$694$	16.2567			0.617095
$695$	20.7349	−	35.9139i	0.786520	−	1.36229i
$696$	3.32759	−	5.76356i	0.126132	−	0.218467i
$697$	−4.17629			−0.158188
$698$	−4.82467	+	8.35657i	−0.182616	+	0.316301i
$699$	2.85690	+	4.94829i	0.108058	+	0.187161i
$700$	2.91454	+	5.04814i	0.110159	+	0.190802i
$701$	−2.13036			−0.0804625			−0.0402313	−	0.999190i	$-0.512809\pi$
$701$	−2.13036			−0.0804625			−0.0402313	+	0.999190i	$0.512809\pi$
$702$	2.83728	−	0.556945i	0.107086	−	0.0210205i
$703$	−15.0092			−0.566083
$704$	−3.84774	−	6.66448i	−0.145017	−	0.251177i
$705$	−13.9623	−	24.1833i	−0.525849	−	0.910798i
$706$	−13.9073	+	24.0882i	−0.523408	+	0.906570i
$707$	14.7724			0.555573
$708$	−5.85570	+	10.1424i	−0.220071	+	0.381174i
$709$	−15.1090	+	26.1696i	−0.567431	+	0.982819i	0.429388	+	0.903120i	$0.358729\pi$
$709$	−15.1090	+	26.1696i	−0.567431	+	0.982819i	−0.996819	+	0.0796992i	$0.974604\pi$
$710$	34.5362			1.29612
$711$	−0.667563	+	1.15625i	−0.0250356	+	0.0433629i
$712$	−3.37316	−	5.84248i	−0.126414	−	0.218956i
$713$	9.48821	+	16.4341i	0.355336	+	0.615461i
$714$	0.643104			0.0240676
$715$	−23.2877	+	4.57126i	−0.870911	+	0.170956i
$716$	−8.76749			−0.327657
$717$	−5.69202	−	9.85887i	−0.212572	−	0.368186i
$718$	11.8683	+	20.5565i	0.442922	+	0.767163i
$719$	−4.94289	+	8.56133i	−0.184339	+	0.319284i	−0.943353	−	0.331790i	$-0.892348\pi$
$719$	−4.94289	+	8.56133i	−0.184339	+	0.319284i	0.759015	+	0.651073i	$0.225681\pi$
$720$	−1.69202			−0.0630579
$721$	5.08211	−	8.80246i	0.189267	−	0.327821i
$722$	6.83685	−	11.8418i	0.254441	−	0.440705i
$723$	−26.4403			−0.983324
$724$	−0.391280	+	0.677717i	−0.0145418	+	0.0251872i
$725$	−5.31013	−	9.19742i	−0.197213	−	0.341584i
$726$	2.54192	+	4.40273i	0.0943394	+	0.163401i
$727$	−23.5579			−0.873716			−0.436858	−	0.899531i	$-0.643909\pi$
$727$	−23.5579			−0.873716			−0.436858	+	0.899531i	$0.643909\pi$
$728$	6.38135	+	7.31362i	0.236509	+	0.271061i
$729$	1.00000			0.0370370
$730$	−12.3780	−	21.4393i	−0.458130	−	0.793505i
$731$	3.46077	+	5.99423i	0.128001	+	0.221705i
$732$	−6.84266	+	11.8518i	−0.252912	+	0.438056i
$733$	0.958852			0.0354160			0.0177080	−	0.999843i	$-0.494363\pi$
$733$	0.958852			0.0354160			0.0177080	+	0.999843i	$0.494363\pi$
$734$	−13.5271	+	23.4297i	−0.499296	+	0.864806i
$735$	1.52446	−	2.64044i	0.0562305	−	0.0973941i
$736$	17.6455			0.650422
$737$	13.8056	−	23.9120i	0.508535	−	0.880809i
$738$	2.08815	+	3.61677i	0.0768657	+	0.133135i
$739$	1.03170	+	1.78695i	0.0379515	+	0.0657340i	0.884377	−	0.466773i	$-0.154583\pi$
$739$	1.03170	+	1.78695i	0.0379515	+	0.0657340i	−0.846426	+	0.532507i	$0.821250\pi$
$740$	44.4760			1.63497
$741$	1.63006	−	4.76256i	0.0598819	−	0.174957i
$742$	0.978230			0.0359119
$743$	−21.7247	−	37.6282i	−0.797001	−	1.38045i	−0.921561	−	0.388234i	$-0.873085\pi$
$743$	−21.7247	−	37.6282i	−0.797001	−	1.38045i	0.124560	−	0.992212i	$-0.460248\pi$
$744$	−8.43780	−	14.6147i	−0.309345	−	0.535801i
$745$	12.7066	−	22.0084i	0.465532	−	0.806325i
$746$	19.7138			0.721773
$747$	−4.46346	+	7.73094i	−0.163309	+	0.282860i
$748$	1.17456	−	2.03440i	0.0429463	−	0.0743851i
$749$	−17.2784			−0.631340
$750$	−0.860781	+	1.49092i	−0.0314313	+	0.0544406i
$751$	16.8889	+	29.2524i	0.616284	+	1.06744i	0.990158	+	0.139956i	$0.0446961\pi$
$751$	16.8889	+	29.2524i	0.616284	+	1.06744i	−0.373873	+	0.927480i	$0.621971\pi$
$752$	2.54138	+	4.40181i	0.0926748	+	0.160517i
$753$	−22.5972			−0.823487
$754$	−4.69955	−	5.38612i	−0.171148	−	0.196151i
$755$	−35.0073			−1.27405
$756$	0.678448	+	1.17511i	0.0246749	+	0.0427382i
$757$	22.5262	+	39.0166i	0.818730	+	1.41808i	0.906618	+	0.421952i	$0.138655\pi$
$757$	22.5262	+	39.0166i	0.818730	+	1.41808i	−0.0878878	+	0.996130i	$0.528012\pi$
$758$	0.774791	−	1.34198i	0.0281417	−	0.0487428i
$759$	6.53511			0.237209
$760$	5.72952	−	9.92382i	0.207832	−	0.359975i
$761$	−9.43027	+	16.3337i	−0.341847	+	0.592097i	−0.984776	−	0.173830i	$-0.944386\pi$
$761$	−9.43027	+	16.3337i	−0.341847	+	0.592097i	0.642929	+	0.765926i	$0.277719\pi$
$762$	−3.61788			−0.131062
$763$	7.14795	−	12.3806i	0.258773	−	0.448208i
$764$	−6.19083	−	10.7228i	−0.223976	−	0.387938i
$765$	1.22252	+	2.11747i	0.0442003	+	0.0765572i
$766$	15.2078			0.549478
$767$	20.4596	+	23.4486i	0.738752	+	0.846678i
$768$	−14.1860			−0.511892
$769$	3.10321	+	5.37492i	0.111905	+	0.193825i	0.916538	−	0.399947i	$-0.130972\pi$
$769$	3.10321	+	5.37492i	0.111905	+	0.193825i	−0.804634	+	0.593772i	$0.797638\pi$
$770$	2.63922	+	4.57126i	0.0951109	+	0.164737i
$771$	−5.51961	+	9.56025i	−0.198784	+	0.344304i
$772$

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.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.400969 - 0.694498i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.678448 - 1.17511i) q^{4} -3.04892 q^{5} +(-0.400969 + 0.694498i) q^{6} +(-0.500000 + 0.866025i) q^{7} -2.69202 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.400969 - 0.694498i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.678448 - 1.17511i) q^{4} -3.04892 q^{5} +(-0.400969 + 0.694498i) q^{6} +(-0.500000 + 0.866025i) q^{7} -2.69202 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.22252 + 2.11747i) q^{10} +(-1.07942 - 1.86960i) q^{11} -1.35690 q^{12} +(-1.16756 + 3.41127i) q^{13} +0.801938 q^{14} +(1.52446 + 2.64044i) q^{15} +(-0.277479 - 0.480608i) q^{16} +(-0.400969 + 0.694498i) q^{17} +0.801938 q^{18} +(0.698062 - 1.20908i) q^{19} +(-2.06853 + 3.58280i) q^{20} +1.00000 q^{21} +(-0.865625 + 1.49931i) q^{22} +(-1.51357 - 2.62159i) q^{23} +(1.34601 + 2.33136i) q^{24} +4.29590 q^{25} +(2.83728 - 0.556945i) q^{26} +1.00000 q^{27} +(0.678448 + 1.17511i) q^{28} +(-1.23609 - 2.14098i) q^{29} +(1.22252 - 2.11747i) q^{30} -6.26875 q^{31} +(-2.91454 + 5.04814i) q^{32} +(-1.07942 + 1.86960i) q^{33} +0.643104 q^{34} +(1.52446 - 2.64044i) q^{35} +(0.678448 + 1.17511i) q^{36} +(-5.37531 - 9.31032i) q^{37} -1.11960 q^{38} +(3.53803 - 0.694498i) q^{39} +8.20775 q^{40} +(2.60388 + 4.51004i) q^{41} +(-0.400969 - 0.694498i) q^{42} +(4.31551 - 7.47468i) q^{43} -2.92931 q^{44} +(1.52446 - 2.64044i) q^{45} +(-1.21379 + 2.10235i) q^{46} -9.15883 q^{47} +(-0.277479 + 0.480608i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-1.72252 - 2.98349i) q^{50} +0.801938 q^{51} +(3.21648 + 3.68638i) q^{52} +1.21983 q^{53} +(-0.400969 - 0.694498i) q^{54} +(3.29105 + 5.70027i) q^{55} +(1.34601 - 2.33136i) q^{56} -1.39612 q^{57} +(-0.991271 + 1.71693i) q^{58} +(4.31551 - 7.47468i) q^{59} +4.13706 q^{60} +(5.04288 - 8.73452i) q^{61} +(2.51357 + 4.35364i) q^{62} +(-0.500000 - 0.866025i) q^{63} +3.56465 q^{64} +(3.55980 - 10.4007i) q^{65} +1.73125 q^{66} +(6.39493 + 11.0763i) q^{67} +(0.544073 + 0.942362i) q^{68} +(-1.51357 + 2.62159i) q^{69} -2.44504 q^{70} +(7.06249 - 12.2326i) q^{71} +(1.34601 - 2.33136i) q^{72} -10.1250 q^{73} +(-4.31067 + 7.46629i) q^{74} +(-2.14795 - 3.72036i) q^{75} +(-0.947198 - 1.64059i) q^{76} +2.15883 q^{77} +(-1.90097 - 2.17869i) q^{78} +1.33513 q^{79} +(0.846011 + 1.46533i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.08815 - 3.61677i) q^{82} +8.92692 q^{83} +(0.678448 - 1.17511i) q^{84} +(1.22252 - 2.11747i) q^{85} -6.92154 q^{86} +(-1.23609 + 2.14098i) q^{87} +(2.90581 + 5.03302i) q^{88} +(1.25302 + 2.17029i) q^{89} -2.44504 q^{90} +(-2.37047 - 2.71678i) q^{91} -4.10752 q^{92} +(3.13437 + 5.42890i) q^{93} +(3.67241 + 6.36080i) q^{94} +(-2.12833 + 3.68638i) q^{95} +5.82908 q^{96} +(-1.16152 + 2.01182i) q^{97} +(-0.400969 + 0.694498i) q^{98} +2.15883 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} - 3 q^{3} + 2 q^{6} - 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + 2 * q^2 - 3 * q^3 + 2 * q^6 - 3 * q^7 - 6 * q^8 - 3 * q^9	\( 6 q + 2 q^{2} - 3 q^{3} + 2 q^{6} - 3 q^{7} - 6 q^{8} - 3 q^{9} + 7 q^{10} + 2 q^{11} - 6 q^{13} - 4 q^{14} - 2 q^{16} + 2 q^{17} - 4 q^{18} + 13 q^{19} - 7 q^{20} + 6 q^{21} - 13 q^{22} - 3 q^{23} + 3 q^{24} - 2 q^{25} - 4 q^{26} + 6 q^{27} - q^{29} + 7 q^{30} - 22 q^{31} - 7 q^{32} + 2 q^{33} + 12 q^{34} + 4 q^{37} + 36 q^{38} + 6 q^{39} + 14 q^{40} - 2 q^{41} + 2 q^{42} + 11 q^{43} - 42 q^{44} + 9 q^{46} - 38 q^{47} - 2 q^{48} - 3 q^{49} - 10 q^{50} - 4 q^{51} + 10 q^{53} + 2 q^{54} + 14 q^{55} + 3 q^{56} - 26 q^{57} + 10 q^{58} + 11 q^{59} + 14 q^{60} - 7 q^{61} + 9 q^{62} - 3 q^{63} - 22 q^{64} + 26 q^{66} + 15 q^{67} + 7 q^{68} - 3 q^{69} - 14 q^{70} + 18 q^{71} + 3 q^{72} - 12 q^{73} - 33 q^{74} + q^{75} + 14 q^{76} - 4 q^{77} - 7 q^{78} + 6 q^{79} - 3 q^{81} + 20 q^{82} - 4 q^{83} + 7 q^{85} + 10 q^{86} - q^{87} - 9 q^{88} + 17 q^{89} - 14 q^{90} + 56 q^{92} + 11 q^{93} - q^{94} + 14 q^{95} + 14 q^{96} + 13 q^{97} + 2 q^{98} - 4 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 - 3 * q^3 + 2 * q^6 - 3 * q^7 - 6 * q^8 - 3 * q^9 + 7 * q^10 + 2 * q^11 - 6 * q^13 - 4 * q^14 - 2 * q^16 + 2 * q^17 - 4 * q^18 + 13 * q^19 - 7 * q^20 + 6 * q^21 - 13 * q^22 - 3 * q^23 + 3 * q^24 - 2 * q^25 - 4 * q^26 + 6 * q^27 - q^29 + 7 * q^30 - 22 * q^31 - 7 * q^32 + 2 * q^33 + 12 * q^34 + 4 * q^37 + 36 * q^38 + 6 * q^39 + 14 * q^40 - 2 * q^41 + 2 * q^42 + 11 * q^43 - 42 * q^44 + 9 * q^46 - 38 * q^47 - 2 * q^48 - 3 * q^49 - 10 * q^50 - 4 * q^51 + 10 * q^53 + 2 * q^54 + 14 * q^55 + 3 * q^56 - 26 * q^57 + 10 * q^58 + 11 * q^59 + 14 * q^60 - 7 * q^61 + 9 * q^62 - 3 * q^63 - 22 * q^64 + 26 * q^66 + 15 * q^67 + 7 * q^68 - 3 * q^69 - 14 * q^70 + 18 * q^71 + 3 * q^72 - 12 * q^73 - 33 * q^74 + q^75 + 14 * q^76 - 4 * q^77 - 7 * q^78 + 6 * q^79 - 3 * q^81 + 20 * q^82 - 4 * q^83 + 7 * q^85 + 10 * q^86 - q^87 - 9 * q^88 + 17 * q^89 - 14 * q^90 + 56 * q^92 + 11 * q^93 - q^94 + 14 * q^95 + 14 * q^96 + 13 * q^97 + 2 * q^98 - 4 * q^99

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